id	sid	tid	token	lemma	pos
ejpam-4275	1	1	european	european	PROPN
ejpam-4275	1	2	journal	journal	PROPN
ejpam-4275	1	3	of	of	ADP
ejpam-4275	1	4	pure	pure	ADJ
ejpam-4275	1	5	and	and	CCONJ
ejpam-4275	1	6	applied	apply	VERB
ejpam-4275	1	7	mathematics	mathematic	NOUN
ejpam-4275	1	8	vol	vol	NOUN
ejpam-4275	1	9	.	.	PROPN
ejpam-4275	2	1	15	15	NUM
ejpam-4275	2	2	,	,	PUNCT
ejpam-4275	2	3	no	no	INTJ
ejpam-4275	2	4	.	.	NOUN
ejpam-4275	2	5	1	1	NUM
ejpam-4275	2	6	,	,	PUNCT
ejpam-4275	2	7	2022	2022	NUM
ejpam-4275	2	8	,	,	PUNCT
ejpam-4275	2	9	261	261	NUM
ejpam-4275	2	10	-	-	SYM
ejpam-4275	2	11	280	280	NUM
ejpam-4275	2	12	issn	issn	PROPN
ejpam-4275	2	13	1307	1307	NUM
ejpam-4275	2	14	-	-	SYM
ejpam-4275	2	15	5543	5543	NUM
ejpam-4275	2	16	–	–	PUNCT
ejpam-4275	2	17	ejpam.com	ejpam.com	X
ejpam-4275	2	18	published	publish	VERB
ejpam-4275	2	19	by	by	ADP
ejpam-4275	2	20	new	new	PROPN
ejpam-4275	2	21	york	york	PROPN
ejpam-4275	2	22	business	business	PROPN
ejpam-4275	2	23	global	global	ADJ
ejpam-4275	2	24	infra	infra	NOUN
ejpam-4275	2	25	pre	pre	ADJ
ejpam-4275	2	26	-	-	ADJ
ejpam-4275	2	27	open	open	ADJ
ejpam-4275	2	28	sets	set	NOUN
ejpam-4275	2	29	and	and	CCONJ
ejpam-4275	2	30	their	their	PRON
ejpam-4275	2	31	applications	application	NOUN
ejpam-4275	2	32	to	to	PART
ejpam-4275	2	33	generate	generate	VERB
ejpam-4275	2	34	new	new	ADJ
ejpam-4275	2	35	types	type	NOUN
ejpam-4275	2	36	of	of	ADP
ejpam-4275	2	37	operators	operator	NOUN
ejpam-4275	2	38	and	and	CCONJ
ejpam-4275	3	1	maps	map	NOUN
ejpam-4275	3	2	tareq	tareq	PROPN
ejpam-4275	3	3	m.	m.	PROPN
ejpam-4275	3	4	al	al	PROPN
ejpam-4275	3	5	-	-	PUNCT
ejpam-4275	3	6	shami1∗	shami1∗	PROPN
ejpam-4275	3	7	,	,	PUNCT
ejpam-4275	3	8	hakeem	hakeem	VERB
ejpam-4275	3	9	a.	a.	NOUN
ejpam-4275	3	10	othman2,3	othman2,3	PROPN
ejpam-4275	3	11	1	1	NUM
ejpam-4275	3	12	department	department	NOUN
ejpam-4275	3	13	of	of	ADP
ejpam-4275	3	14	mathematics	mathematic	NOUN
ejpam-4275	3	15	,	,	PUNCT
ejpam-4275	3	16	sana’a	sana’a	NOUN
ejpam-4275	3	17	university	university	NOUN
ejpam-4275	3	18	,	,	PUNCT
ejpam-4275	3	19	sana’a	sana’a	NOUN
ejpam-4275	3	20	,	,	PUNCT
ejpam-4275	3	21	yemen	yemen	PROPN
ejpam-4275	3	22	2	2	NUM
ejpam-4275	3	23	department	department	NOUN
ejpam-4275	3	24	of	of	ADP
ejpam-4275	3	25	mathematics	mathematics	PROPN
ejpam-4275	3	26	,	,	PUNCT
ejpam-4275	3	27	al	al	PROPN
ejpam-4275	3	28	-	-	PUNCT
ejpam-4275	3	29	qunfudhah	qunfudhah	PROPN
ejpam-4275	3	30	university	university	NOUN
ejpam-4275	3	31	college	college	NOUN
ejpam-4275	3	32	,	,	PUNCT
ejpam-4275	3	33	umm	umm	INTJ
ejpam-4275	3	34	al	al	PROPN
ejpam-4275	3	35	-	-	PUNCT
ejpam-4275	3	36	qura	qura	PROPN
ejpam-4275	3	37	university	university	PROPN
ejpam-4275	3	38	,	,	PUNCT
ejpam-4275	3	39	saudi	saudi	PROPN
ejpam-4275	3	40	arabia	arabia	PROPN
ejpam-4275	3	41	3	3	NUM
ejpam-4275	3	42	department	department	NOUN
ejpam-4275	3	43	of	of	ADP
ejpam-4275	3	44	mathematics	mathematic	NOUN
ejpam-4275	3	45	,	,	PUNCT
ejpam-4275	3	46	rada’a	rada’a	NOUN
ejpam-4275	3	47	college	college	PROPN
ejpam-4275	3	48	of	of	ADP
ejpam-4275	3	49	education	education	NOUN
ejpam-4275	3	50	and	and	CCONJ
ejpam-4275	3	51	science	science	NOUN
ejpam-4275	3	52	,	,	PUNCT
ejpam-4275	3	53	albaydha	albaydha	PROPN
ejpam-4275	3	54	university	university	NOUN
ejpam-4275	3	55	,	,	PUNCT
ejpam-4275	3	56	albaydha	albaydha	PROPN
ejpam-4275	3	57	,	,	PUNCT
ejpam-4275	3	58	yemen	yemen	PROPN
ejpam-4275	3	59	abstract	abstract	NOUN
ejpam-4275	3	60	.	.	PUNCT
ejpam-4275	4	1	herein	herein	NOUN
ejpam-4275	4	2	,	,	PUNCT
ejpam-4275	4	3	we	we	PRON
ejpam-4275	4	4	introduce	introduce	VERB
ejpam-4275	4	5	the	the	DET
ejpam-4275	4	6	concepts	concept	NOUN
ejpam-4275	4	7	of	of	ADP
ejpam-4275	4	8	infra	infra	NOUN
ejpam-4275	4	9	soft	soft	ADJ
ejpam-4275	4	10	pre	pre	ADJ
ejpam-4275	4	11	-	-	ADJ
ejpam-4275	4	12	open	open	ADJ
ejpam-4275	4	13	infra	infra	NOUN
ejpam-4275	4	14	soft	soft	ADJ
ejpam-4275	4	15	pre	pre	ADJ
ejpam-4275	4	16	-	-	ADJ
ejpam-4275	4	17	closed	closed	ADJ
ejpam-4275	4	18	sets	set	NOUN
ejpam-4275	4	19	which	which	PRON
ejpam-4275	4	20	are	be	AUX
ejpam-4275	4	21	respectively	respectively	ADV
ejpam-4275	4	22	generalizations	generalization	NOUN
ejpam-4275	4	23	of	of	ADP
ejpam-4275	4	24	infra	infra	NOUN
ejpam-4275	4	25	soft	soft	ADJ
ejpam-4275	4	26	open	open	ADJ
ejpam-4275	4	27	and	and	CCONJ
ejpam-4275	4	28	infra	infra	NOUN
ejpam-4275	4	29	soft	soft	ADJ
ejpam-4275	4	30	closed	closed	ADJ
ejpam-4275	4	31	sets	set	NOUN
ejpam-4275	4	32	.	.	PUNCT
ejpam-4275	5	1	we	we	PRON
ejpam-4275	5	2	characterize	characterize	VERB
ejpam-4275	5	3	them	they	PRON
ejpam-4275	5	4	and	and	CCONJ
ejpam-4275	5	5	investigate	investigate	VERB
ejpam-4275	5	6	their	their	PRON
ejpam-4275	5	7	behaviours	behaviour	NOUN
ejpam-4275	5	8	under	under	ADP
ejpam-4275	5	9	infra	infra	NOUN
ejpam-4275	5	10	soft	soft	ADJ
ejpam-4275	5	11	homeomorphism	homeomorphism	NOUN
ejpam-4275	5	12	maps	map	NOUN
ejpam-4275	5	13	and	and	CCONJ
ejpam-4275	5	14	finite	finite	ADJ
ejpam-4275	5	15	product	product	NOUN
ejpam-4275	5	16	of	of	ADP
ejpam-4275	5	17	soft	soft	ADJ
ejpam-4275	5	18	spaces	space	NOUN
ejpam-4275	5	19	.	.	PUNCT
ejpam-4275	6	1	then	then	ADV
ejpam-4275	6	2	,	,	PUNCT
ejpam-4275	6	3	we	we	PRON
ejpam-4275	6	4	apply	apply	VERB
ejpam-4275	6	5	infra	infra	NOUN
ejpam-4275	6	6	soft	soft	ADJ
ejpam-4275	6	7	pre	pre	ADJ
ejpam-4275	6	8	-	-	ADJ
ejpam-4275	6	9	open	open	ADJ
ejpam-4275	6	10	infra	infra	NOUN
ejpam-4275	6	11	soft	soft	ADJ
ejpam-4275	6	12	pre	pre	ADJ
ejpam-4275	6	13	-	-	ADJ
ejpam-4275	6	14	closed	closed	ADJ
ejpam-4275	6	15	sets	set	NOUN
ejpam-4275	6	16	to	to	PART
ejpam-4275	6	17	define	define	VERB
ejpam-4275	6	18	the	the	DET
ejpam-4275	6	19	operators	operator	NOUN
ejpam-4275	6	20	of	of	ADP
ejpam-4275	6	21	infra	infra	NOUN
ejpam-4275	6	22	pre	pre	ADJ
ejpam-4275	6	23	-	-	ADJ
ejpam-4275	6	24	interior	interior	ADJ
ejpam-4275	6	25	,	,	PUNCT
ejpam-4275	6	26	infra	infra	NOUN
ejpam-4275	6	27	pre	pre	NOUN
ejpam-4275	6	28	-	-	ADJ
ejpam-4275	6	29	closure	closure	ADJ
ejpam-4275	6	30	,	,	PUNCT
ejpam-4275	6	31	infra	infra	NOUN
ejpam-4275	6	32	pre	pre	ADJ
ejpam-4275	6	33	-	-	NOUN
ejpam-4275	6	34	limit	limit	NOUN
ejpam-4275	6	35	and	and	CCONJ
ejpam-4275	6	36	infra	infra	NOUN
ejpam-4275	6	37	pre	pre	ADJ
ejpam-4275	6	38	-	-	NOUN
ejpam-4275	6	39	boundary	boundary	ADJ
ejpam-4275	6	40	.	.	PUNCT
ejpam-4275	7	1	we	we	PRON
ejpam-4275	7	2	discuss	discuss	VERB
ejpam-4275	7	3	their	their	PRON
ejpam-4275	7	4	main	main	ADJ
ejpam-4275	7	5	properties	property	NOUN
ejpam-4275	7	6	and	and	CCONJ
ejpam-4275	7	7	show	show	VERB
ejpam-4275	7	8	the	the	DET
ejpam-4275	7	9	interrelations	interrelation	NOUN
ejpam-4275	7	10	between	between	ADP
ejpam-4275	7	11	them	they	PRON
ejpam-4275	7	12	.	.	PUNCT
ejpam-4275	8	1	in	in	ADP
ejpam-4275	8	2	the	the	DET
ejpam-4275	8	3	end	end	NOUN
ejpam-4275	8	4	,	,	PUNCT
ejpam-4275	8	5	we	we	PRON
ejpam-4275	8	6	introduce	introduce	VERB
ejpam-4275	8	7	new	new	ADJ
ejpam-4275	8	8	types	type	NOUN
ejpam-4275	8	9	of	of	ADP
ejpam-4275	8	10	soft	soft	ADJ
ejpam-4275	8	11	maps	map	NOUN
ejpam-4275	8	12	using	use	VERB
ejpam-4275	8	13	infra	infra	NOUN
ejpam-4275	8	14	soft	soft	ADJ
ejpam-4275	8	15	pre	pre	ADJ
ejpam-4275	8	16	-	-	ADJ
ejpam-4275	8	17	open	open	ADJ
ejpam-4275	8	18	and	and	CCONJ
ejpam-4275	8	19	infra	infra	VERB
ejpam-4275	8	20	soft	soft	ADJ
ejpam-4275	8	21	pre	pre	ADJ
ejpam-4275	8	22	-	-	ADJ
ejpam-4275	8	23	closed	closed	ADJ
ejpam-4275	8	24	sets	set	NOUN
ejpam-4275	8	25	and	and	CCONJ
ejpam-4275	8	26	explore	explore	VERB
ejpam-4275	8	27	their	their	PRON
ejpam-4275	8	28	essential	essential	ADJ
ejpam-4275	8	29	properties	property	NOUN
ejpam-4275	8	30	.	.	PUNCT
ejpam-4275	9	1	2020	2020	NUM
ejpam-4275	9	2	mathematics	mathematic	NOUN
ejpam-4275	9	3	subject	subject	NOUN
ejpam-4275	9	4	classifications	classification	NOUN
ejpam-4275	9	5	:	:	PUNCT
ejpam-4275	9	6	54a40	54a40	NUM
ejpam-4275	9	7	,	,	PUNCT
ejpam-4275	9	8	54c08	54c08	NUM
ejpam-4275	9	9	,	,	PUNCT
ejpam-4275	9	10	54c99	54c99	DET
ejpam-4275	9	11	key	key	ADJ
ejpam-4275	9	12	words	word	NOUN
ejpam-4275	9	13	and	and	CCONJ
ejpam-4275	9	14	phrases	phrase	NOUN
ejpam-4275	9	15	:	:	PUNCT
ejpam-4275	9	16	infra	infra	NOUN
ejpam-4275	9	17	soft	soft	ADJ
ejpam-4275	9	18	pre	pre	ADJ
ejpam-4275	9	19	-	-	ADJ
ejpam-4275	9	20	open	open	ADJ
ejpam-4275	9	21	set	set	NOUN
ejpam-4275	9	22	,	,	PUNCT
ejpam-4275	9	23	infra	infra	NOUN
ejpam-4275	9	24	soft	soft	ADJ
ejpam-4275	9	25	pre	pre	ADJ
ejpam-4275	9	26	-	-	ADJ
ejpam-4275	9	27	interior	interior	ADJ
ejpam-4275	9	28	points	point	NOUN
ejpam-4275	9	29	,	,	PUNCT
ejpam-4275	9	30	infra	infra	NOUN
ejpam-4275	9	31	soft	soft	ADJ
ejpam-4275	9	32	preclosure	preclosure	ADJ
ejpam-4275	9	33	points	point	NOUN
ejpam-4275	9	34	,	,	PUNCT
ejpam-4275	9	35	infra	infra	NOUN
ejpam-4275	9	36	soft	soft	ADJ
ejpam-4275	9	37	pre	pre	NOUN
ejpam-4275	9	38	-	-	NOUN
ejpam-4275	9	39	continuity	continuity	ADJ
ejpam-4275	9	40	1	1	NUM
ejpam-4275	9	41	.	.	PUNCT
ejpam-4275	10	1	introduction	introduction	NOUN
ejpam-4275	10	2	soft	soft	ADJ
ejpam-4275	10	3	set	set	NOUN
ejpam-4275	10	4	is	be	AUX
ejpam-4275	10	5	a	a	DET
ejpam-4275	10	6	new	new	ADJ
ejpam-4275	10	7	mathematical	mathematical	ADJ
ejpam-4275	10	8	tool	tool	NOUN
ejpam-4275	10	9	to	to	PART
ejpam-4275	10	10	address	address	VERB
ejpam-4275	10	11	uncertainity	uncertainity	NOUN
ejpam-4275	10	12	/	/	SYM
ejpam-4275	10	13	vagueness	vagueness	NOUN
ejpam-4275	10	14	;	;	PUNCT
ejpam-4275	10	15	it	it	PRON
ejpam-4275	10	16	was	be	AUX
ejpam-4275	10	17	introduced	introduce	VERB
ejpam-4275	10	18	in	in	ADP
ejpam-4275	10	19	1999	1999	NUM
ejpam-4275	10	20	by	by	ADP
ejpam-4275	10	21	molodtsov	molodtsov	NOUN
ejpam-4275	10	22	[	[	X
ejpam-4275	10	23	34	34	NUM
ejpam-4275	10	24	]	]	PUNCT
ejpam-4275	10	25	.	.	PUNCT
ejpam-4275	11	1	he	he	PRON
ejpam-4275	11	2	proved	prove	VERB
ejpam-4275	11	3	its	its	PRON
ejpam-4275	11	4	efficiency	efficiency	NOUN
ejpam-4275	11	5	by	by	ADP
ejpam-4275	11	6	applying	apply	VERB
ejpam-4275	11	7	successfully	successfully	ADV
ejpam-4275	11	8	in	in	ADP
ejpam-4275	11	9	many	many	ADJ
ejpam-4275	11	10	areas	area	NOUN
ejpam-4275	11	11	.	.	PUNCT
ejpam-4275	12	1	aktaş	aktaş	ADV
ejpam-4275	12	2	and	and	CCONJ
ejpam-4275	12	3	çağman	çağman	NOUN
ejpam-4275	13	1	[	[	X
ejpam-4275	13	2	1	1	X
ejpam-4275	13	3	]	]	PUNCT
ejpam-4275	13	4	showed	show	VERB
ejpam-4275	13	5	that	that	SCONJ
ejpam-4275	13	6	rough	rough	ADJ
ejpam-4275	13	7	set	set	NOUN
ejpam-4275	13	8	and	and	CCONJ
ejpam-4275	13	9	fuzzy	fuzzy	ADJ
ejpam-4275	13	10	set	set	NOUN
ejpam-4275	13	11	,	,	PUNCT
ejpam-4275	13	12	which	which	PRON
ejpam-4275	13	13	are	be	AUX
ejpam-4275	13	14	two	two	NUM
ejpam-4275	13	15	approaches	approach	NOUN
ejpam-4275	13	16	to	to	PART
ejpam-4275	13	17	handle	handle	VERB
ejpam-4275	13	18	uncertainty	uncertainty	NOUN
ejpam-4275	13	19	,	,	PUNCT
ejpam-4275	13	20	may	may	AUX
ejpam-4275	13	21	be	be	AUX
ejpam-4275	13	22	considered	consider	VERB
ejpam-4275	13	23	soft	soft	ADJ
ejpam-4275	13	24	sets	set	NOUN
ejpam-4275	13	25	.	.	PUNCT
ejpam-4275	14	1	in	in	ADP
ejpam-4275	14	2	the	the	DET
ejpam-4275	14	3	literature	literature	NOUN
ejpam-4275	14	4	,	,	PUNCT
ejpam-4275	14	5	one	one	PRON
ejpam-4275	14	6	can	can	AUX
ejpam-4275	14	7	note	note	VERB
ejpam-4275	14	8	many	many	ADJ
ejpam-4275	14	9	authors	author	NOUN
ejpam-4275	14	10	have	have	AUX
ejpam-4275	14	11	been	be	AUX
ejpam-4275	14	12	applied	apply	VERB
ejpam-4275	14	13	soft	soft	ADJ
ejpam-4275	14	14	sets	set	NOUN
ejpam-4275	14	15	to	to	PART
ejpam-4275	14	16	model	model	VERB
ejpam-4275	14	17	some	some	DET
ejpam-4275	14	18	phenomena	phenomenon	NOUN
ejpam-4275	14	19	and	and	CCONJ
ejpam-4275	14	20	problems	problem	NOUN
ejpam-4275	14	21	in	in	ADP
ejpam-4275	14	22	different	different	ADJ
ejpam-4275	14	23	disciplines	discipline	NOUN
ejpam-4275	14	24	such	such	ADJ
ejpam-4275	14	25	as	as	ADP
ejpam-4275	14	26	decision	decision	NOUN
ejpam-4275	14	27	-	-	PUNCT
ejpam-4275	14	28	making	make	VERB
ejpam-4275	14	29	problems	problem	NOUN
ejpam-4275	14	30	[	[	X
ejpam-4275	14	31	28	28	NUM
ejpam-4275	14	32	,	,	PUNCT
ejpam-4275	14	33	38	38	NUM
ejpam-4275	14	34	]	]	PUNCT
ejpam-4275	14	35	and	and	CCONJ
ejpam-4275	14	36	computer	computer	NOUN
ejpam-4275	14	37	science	science	NOUN
ejpam-4275	15	1	[	[	X
ejpam-4275	15	2	22	22	NUM
ejpam-4275	15	3	]	]	PUNCT
ejpam-4275	15	4	.	.	PUNCT
ejpam-4275	16	1	maji	maji	PROPN
ejpam-4275	16	2	et	et	PROPN
ejpam-4275	16	3	al	al	PROPN
ejpam-4275	16	4	.	.	PUNCT
ejpam-4275	17	1	[	[	X
ejpam-4275	17	2	33	33	NUM
ejpam-4275	17	3	]	]	PUNCT
ejpam-4275	17	4	,	,	PUNCT
ejpam-4275	17	5	in	in	ADP
ejpam-4275	17	6	2003	2003	NUM
ejpam-4275	17	7	,	,	PUNCT
ejpam-4275	17	8	formulated	formulate	VERB
ejpam-4275	17	9	the	the	DET
ejpam-4275	17	10	basic	basic	ADJ
ejpam-4275	17	11	operations	operation	NOUN
ejpam-4275	17	12	and	and	CCONJ
ejpam-4275	17	13	operators	operator	NOUN
ejpam-4275	17	14	between	between	ADP
ejpam-4275	17	15	soft	soft	ADJ
ejpam-4275	17	16	sets	set	NOUN
ejpam-4275	17	17	like	like	ADP
ejpam-4275	17	18	the	the	DET
ejpam-4275	17	19	difference	difference	NOUN
ejpam-4275	17	20	between	between	ADP
ejpam-4275	17	21	two	two	NUM
ejpam-4275	17	22	soft	soft	ADJ
ejpam-4275	17	23	sets	set	NOUN
ejpam-4275	17	24	,	,	PUNCT
ejpam-4275	17	25	a	a	DET
ejpam-4275	17	26	complement	complement	NOUN
ejpam-4275	17	27	of	of	ADP
ejpam-4275	17	28	a	a	DET
ejpam-4275	17	29	soft	soft	ADJ
ejpam-4275	17	30	set	set	NOUN
ejpam-4275	17	31	,	,	PUNCT
ejpam-4275	17	32	and	and	CCONJ
ejpam-4275	17	33	intersection	intersection	NOUN
ejpam-4275	17	34	and	and	CCONJ
ejpam-4275	17	35	union	union	NOUN
ejpam-4275	17	36	operators	operator	NOUN
ejpam-4275	17	37	.	.	PUNCT
ejpam-4275	18	1	to	to	PART
ejpam-4275	18	2	remove	remove	VERB
ejpam-4275	18	3	anomaly	anomaly	NOUN
ejpam-4275	18	4	appeared	appear	VERB
ejpam-4275	18	5	in	in	ADP
ejpam-4275	18	6	their	their	PRON
ejpam-4275	18	7	definitions	definition	NOUN
ejpam-4275	18	8	and	and	CCONJ
ejpam-4275	18	9	keep	keep	VERB
ejpam-4275	18	10	some	some	DET
ejpam-4275	18	11	∗corresponding	∗corresponde	VERB
ejpam-4275	18	12	author	author	NOUN
ejpam-4275	18	13	.	.	PUNCT
ejpam-4275	19	1	doi	doi	NOUN
ejpam-4275	19	2	:	:	PUNCT
ejpam-4275	19	3	https://doi.org/10.29020/nybg.ejpam.v15i1.4275	https://doi.org/10.29020/nybg.ejpam.v15i1.4275	PROPN
ejpam-4275	19	4	email	email	NOUN
ejpam-4275	19	5	addresses	address	NOUN
ejpam-4275	19	6	:	:	PUNCT
ejpam-4275	19	7	tareqalshami83@gmail.com	tareqalshami83@gmail.com	X
ejpam-4275	19	8	(	(	PUNCT
ejpam-4275	19	9	t.m	t.m	PROPN
ejpam-4275	19	10	.	.	PROPN
ejpam-4275	19	11	al	al	PROPN
ejpam-4275	19	12	-	-	PUNCT
ejpam-4275	19	13	shami	shami	PROPN
ejpam-4275	19	14	)	)	PUNCT
ejpam-4275	19	15	,	,	PUNCT
ejpam-4275	19	16	haoali@uqu.edu.sa;hakim−albdoie@yahoo.com	haoali@uqu.edu.sa;hakim−albdoie@yahoo.com	X
ejpam-4275	19	17	(	(	PUNCT
ejpam-4275	19	18	h.a	h.a	PROPN
ejpam-4275	19	19	.	.	PROPN
ejpam-4275	19	20	othman	othman	PROPN
ejpam-4275	19	21	)	)	PUNCT
ejpam-4275	19	22	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4275	20	1	261	261	NUM
ejpam-4275	20	2	©	©	PROPN
ejpam-4275	20	3	2022	2022	NUM
ejpam-4275	20	4	ejpam	ejpam	VERB
ejpam-4275	20	5	all	all	DET
ejpam-4275	20	6	rights	right	NOUN
ejpam-4275	20	7	reserved	reserve	VERB
ejpam-4275	20	8	.	.	PUNCT
ejpam-4275	21	1	t.m	t.m	X
ejpam-4275	21	2	.	.	PUNCT
ejpam-4275	21	3	al	al	PROPN
ejpam-4275	21	4	-	-	PUNCT
ejpam-4275	21	5	shami	shami	PROPN
ejpam-4275	21	6	,	,	PUNCT
ejpam-4275	21	7	h.a	h.a	PROPN
ejpam-4275	21	8	.	.	PROPN
ejpam-4275	21	9	othman	othman	PROPN
ejpam-4275	21	10	/	/	SYM
ejpam-4275	21	11	eur	eur	PROPN
ejpam-4275	21	12	.	.	PUNCT
ejpam-4275	22	1	j.	j.	PROPN
ejpam-4275	22	2	pure	pure	PROPN
ejpam-4275	22	3	appl	appl	PROPN
ejpam-4275	22	4	.	.	PROPN
ejpam-4275	22	5	math	math	PROPN
ejpam-4275	22	6	,	,	PUNCT
ejpam-4275	22	7	15	15	NUM
ejpam-4275	22	8	(	(	PUNCT
ejpam-4275	22	9	1	1	NUM
ejpam-4275	22	10	)	)	PUNCT
ejpam-4275	22	11	(	(	PUNCT
ejpam-4275	22	12	2022	2022	NUM
ejpam-4275	22	13	)	)	PUNCT
ejpam-4275	22	14	,	,	PUNCT
ejpam-4275	22	15	261	261	NUM
ejpam-4275	22	16	-	-	SYM
ejpam-4275	22	17	280	280	NUM
ejpam-4275	22	18	262	262	NUM
ejpam-4275	22	19	crisp	crisp	ADJ
ejpam-4275	22	20	properties	property	NOUN
ejpam-4275	22	21	in	in	ADP
ejpam-4275	22	22	the	the	DET
ejpam-4275	22	23	soft	soft	ADJ
ejpam-4275	22	24	set	set	NOUN
ejpam-4275	22	25	theory	theory	NOUN
ejpam-4275	22	26	,	,	PUNCT
ejpam-4275	22	27	ali	ali	PROPN
ejpam-4275	22	28	et	et	PROPN
ejpam-4275	22	29	al	al	PROPN
ejpam-4275	22	30	.	.	PUNCT
ejpam-4275	23	1	[	[	X
ejpam-4275	23	2	19	19	NUM
ejpam-4275	23	3	]	]	PUNCT
ejpam-4275	23	4	initiated	initiate	VERB
ejpam-4275	23	5	new	new	ADJ
ejpam-4275	23	6	operations	operation	NOUN
ejpam-4275	23	7	and	and	CCONJ
ejpam-4275	23	8	operators	operator	NOUN
ejpam-4275	23	9	between	between	ADP
ejpam-4275	23	10	soft	soft	ADJ
ejpam-4275	23	11	sets	set	NOUN
ejpam-4275	23	12	.	.	PUNCT
ejpam-4275	24	1	attempts	attempt	NOUN
ejpam-4275	24	2	were	be	AUX
ejpam-4275	24	3	still	still	ADV
ejpam-4275	24	4	in	in	ADP
ejpam-4275	24	5	this	this	DET
ejpam-4275	24	6	path	path	NOUN
ejpam-4275	24	7	to	to	PART
ejpam-4275	24	8	produce	produce	VERB
ejpam-4275	24	9	new	new	ADJ
ejpam-4275	24	10	operators	operator	NOUN
ejpam-4275	24	11	and	and	CCONJ
ejpam-4275	24	12	relations	relation	NOUN
ejpam-4275	24	13	like	like	ADP
ejpam-4275	24	14	those	those	PRON
ejpam-4275	24	15	introduced	introduce	VERB
ejpam-4275	24	16	in	in	ADP
ejpam-4275	24	17	[	[	X
ejpam-4275	24	18	15	15	NUM
ejpam-4275	24	19	,	,	PUNCT
ejpam-4275	24	20	36	36	NUM
ejpam-4275	24	21	]	]	PUNCT
ejpam-4275	24	22	.	.	PUNCT
ejpam-4275	25	1	in	in	ADP
ejpam-4275	25	2	2011	2011	NUM
ejpam-4275	25	3	,	,	PUNCT
ejpam-4275	25	4	çaǧman	çaǧman	PROPN
ejpam-4275	25	5	et	et	PROPN
ejpam-4275	25	6	al	al	PROPN
ejpam-4275	25	7	.	.	PUNCT
ejpam-4275	26	1	[	[	X
ejpam-4275	26	2	23	23	NUM
ejpam-4275	26	3	]	]	PUNCT
ejpam-4275	26	4	and	and	CCONJ
ejpam-4275	26	5	shabir	shabir	PROPN
ejpam-4275	26	6	and	and	CCONJ
ejpam-4275	26	7	naz	naz	PROPN
ejpam-4275	26	8	[	[	X
ejpam-4275	26	9	37	37	NUM
ejpam-4275	26	10	]	]	PUNCT
ejpam-4275	26	11	applied	apply	VERB
ejpam-4275	26	12	soft	soft	ADJ
ejpam-4275	26	13	sets	set	NOUN
ejpam-4275	26	14	to	to	PART
ejpam-4275	26	15	define	define	VERB
ejpam-4275	26	16	a	a	DET
ejpam-4275	26	17	soft	soft	ADJ
ejpam-4275	26	18	topology	topology	NOUN
ejpam-4275	26	19	.	.	PUNCT
ejpam-4275	27	1	whereas	whereas	SCONJ
ejpam-4275	27	2	,	,	PUNCT
ejpam-4275	27	3	çaǧman	çaǧman	PROPN
ejpam-4275	27	4	et	et	PROPN
ejpam-4275	27	5	al	al	PROPN
ejpam-4275	27	6	.	.	PROPN
ejpam-4275	27	7	defined	define	VERB
ejpam-4275	27	8	a	a	DET
ejpam-4275	27	9	soft	soft	ADJ
ejpam-4275	27	10	topology	topology	NOUN
ejpam-4275	27	11	over	over	ADP
ejpam-4275	27	12	an	an	DET
ejpam-4275	27	13	absolute	absolute	ADJ
ejpam-4275	27	14	soft	soft	ADJ
ejpam-4275	27	15	set	set	NOUN
ejpam-4275	27	16	and	and	CCONJ
ejpam-4275	27	17	different	different	ADJ
ejpam-4275	27	18	sets	set	NOUN
ejpam-4275	27	19	of	of	ADP
ejpam-4275	27	20	parameters	parameter	NOUN
ejpam-4275	27	21	,	,	PUNCT
ejpam-4275	27	22	shabir	shabir	PROPN
ejpam-4275	27	23	and	and	CCONJ
ejpam-4275	27	24	naz	naz	PROPN
ejpam-4275	27	25	defined	define	VERB
ejpam-4275	27	26	a	a	DET
ejpam-4275	27	27	soft	soft	ADJ
ejpam-4275	27	28	topology	topology	NOUN
ejpam-4275	27	29	over	over	ADP
ejpam-4275	27	30	a	a	DET
ejpam-4275	27	31	fixed	fix	VERB
ejpam-4275	27	32	set	set	NOUN
ejpam-4275	27	33	of	of	ADP
ejpam-4275	27	34	universe	universe	NOUN
ejpam-4275	27	35	and	and	CCONJ
ejpam-4275	27	36	a	a	DET
ejpam-4275	27	37	fixed	fix	VERB
ejpam-4275	27	38	set	set	NOUN
ejpam-4275	27	39	of	of	ADP
ejpam-4275	27	40	parameters	parameter	NOUN
ejpam-4275	27	41	.	.	PUNCT
ejpam-4275	28	1	this	this	DET
ejpam-4275	28	2	article	article	NOUN
ejpam-4275	28	3	follows	follow	VERB
ejpam-4275	28	4	shabir	shabir	PROPN
ejpam-4275	28	5	and	and	CCONJ
ejpam-4275	28	6	naz	naz	PROPN
ejpam-4275	28	7	’	'	PUNCT
ejpam-4275	28	8	definition	definition	NOUN
ejpam-4275	28	9	.	.	PUNCT
ejpam-4275	29	1	the	the	DET
ejpam-4275	29	2	main	main	ADJ
ejpam-4275	29	3	concepts	concept	NOUN
ejpam-4275	29	4	and	and	CCONJ
ejpam-4275	29	5	notions	notion	NOUN
ejpam-4275	29	6	of	of	ADP
ejpam-4275	29	7	general	general	ADJ
ejpam-4275	29	8	topology	topology	NOUN
ejpam-4275	29	9	were	be	AUX
ejpam-4275	29	10	studied	study	VERB
ejpam-4275	29	11	in	in	ADP
ejpam-4275	29	12	soft	soft	ADJ
ejpam-4275	29	13	topology	topology	NOUN
ejpam-4275	29	14	such	such	ADJ
ejpam-4275	29	15	as	as	ADP
ejpam-4275	29	16	basis	basis	NOUN
ejpam-4275	29	17	[	[	X
ejpam-4275	29	18	18	18	NUM
ejpam-4275	29	19	]	]	PUNCT
ejpam-4275	29	20	,	,	PUNCT
ejpam-4275	29	21	separation	separation	NOUN
ejpam-4275	29	22	axioms	axiom	VERB
ejpam-4275	29	23	[	[	X
ejpam-4275	29	24	27	27	NUM
ejpam-4275	29	25	]	]	PUNCT
ejpam-4275	29	26	,	,	PUNCT
ejpam-4275	29	27	compactness	compactness	NOUN
ejpam-4275	29	28	[	[	X
ejpam-4275	29	29	6	6	NUM
ejpam-4275	29	30	,	,	PUNCT
ejpam-4275	29	31	21	21	NUM
ejpam-4275	29	32	]	]	PUNCT
ejpam-4275	29	33	,	,	PUNCT
ejpam-4275	29	34	connectedness	connectedness	NOUN
ejpam-4275	29	35	[	[	X
ejpam-4275	29	36	32	32	NUM
ejpam-4275	29	37	]	]	PUNCT
ejpam-4275	29	38	,	,	PUNCT
ejpam-4275	29	39	bioperators	bioperator	NOUN
ejpam-4275	30	1	[	[	X
ejpam-4275	30	2	20	20	NUM
ejpam-4275	30	3	]	]	PUNCT
ejpam-4275	30	4	,	,	PUNCT
ejpam-4275	30	5	covering	cover	VERB
ejpam-4275	30	6	properties	property	NOUN
ejpam-4275	30	7	[	[	X
ejpam-4275	30	8	13	13	NUM
ejpam-4275	30	9	,	,	PUNCT
ejpam-4275	30	10	14	14	NUM
ejpam-4275	30	11	,	,	PUNCT
ejpam-4275	30	12	25	25	NUM
ejpam-4275	30	13	]	]	PUNCT
ejpam-4275	30	14	,	,	PUNCT
ejpam-4275	30	15	generalized	generalize	VERB
ejpam-4275	30	16	open	open	ADJ
ejpam-4275	30	17	sets	set	NOUN
ejpam-4275	30	18	[	[	X
ejpam-4275	30	19	2–4	2–4	X
ejpam-4275	30	20	]	]	X
ejpam-4275	30	21	and	and	CCONJ
ejpam-4275	30	22	bipolarity	bipolarity	NOUN
ejpam-4275	31	1	[	[	X
ejpam-4275	31	2	5	5	NUM
ejpam-4275	31	3	]	]	PUNCT
ejpam-4275	31	4	.	.	PUNCT
ejpam-4275	32	1	soft	soft	ADJ
ejpam-4275	32	2	topologies	topology	NOUN
ejpam-4275	32	3	were	be	AUX
ejpam-4275	32	4	generalized	generalize	VERB
ejpam-4275	32	5	to	to	ADP
ejpam-4275	32	6	various	various	ADJ
ejpam-4275	32	7	structures	structure	NOUN
ejpam-4275	32	8	such	such	ADJ
ejpam-4275	32	9	as	as	ADP
ejpam-4275	32	10	infra	infra	NOUN
ejpam-4275	32	11	soft	soft	ADJ
ejpam-4275	32	12	topologies	topology	NOUN
ejpam-4275	32	13	[	[	X
ejpam-4275	32	14	10	10	NUM
ejpam-4275	32	15	]	]	PUNCT
ejpam-4275	32	16	which	which	PRON
ejpam-4275	32	17	is	be	AUX
ejpam-4275	32	18	the	the	DET
ejpam-4275	32	19	frame	frame	NOUN
ejpam-4275	32	20	of	of	ADP
ejpam-4275	32	21	this	this	DET
ejpam-4275	32	22	study	study	NOUN
ejpam-4275	32	23	.	.	PUNCT
ejpam-4275	33	1	the	the	DET
ejpam-4275	33	2	inducements	inducement	NOUN
ejpam-4275	33	3	of	of	ADP
ejpam-4275	33	4	continuous	continuous	ADJ
ejpam-4275	33	5	investigation	investigation	NOUN
ejpam-4275	33	6	of	of	ADP
ejpam-4275	33	7	infra	infra	NOUN
ejpam-4275	33	8	soft	soft	ADJ
ejpam-4275	33	9	topologies	topology	NOUN
ejpam-4275	33	10	are	be	AUX
ejpam-4275	33	11	that	that	SCONJ
ejpam-4275	33	12	several	several	ADJ
ejpam-4275	33	13	topological	topological	ADJ
ejpam-4275	33	14	features	feature	NOUN
ejpam-4275	33	15	are	be	AUX
ejpam-4275	33	16	still	still	ADV
ejpam-4275	33	17	valid	valid	ADJ
ejpam-4275	33	18	via	via	ADP
ejpam-4275	33	19	the	the	DET
ejpam-4275	33	20	frame	frame	NOUN
ejpam-4275	33	21	of	of	ADP
ejpam-4275	33	22	infra	infra	NOUN
ejpam-4275	33	23	soft	soft	ADJ
ejpam-4275	33	24	topologies	topology	NOUN
ejpam-4275	33	25	,	,	PUNCT
ejpam-4275	33	26	also	also	ADV
ejpam-4275	33	27	,	,	PUNCT
ejpam-4275	33	28	easily	easily	ADV
ejpam-4275	33	29	building	build	VERB
ejpam-4275	33	30	the	the	DET
ejpam-4275	33	31	examples	example	NOUN
ejpam-4275	33	32	that	that	PRON
ejpam-4275	33	33	elucidate	elucidate	VERB
ejpam-4275	33	34	the	the	DET
ejpam-4275	33	35	interrelationships	interrelationship	NOUN
ejpam-4275	33	36	among	among	ADP
ejpam-4275	33	37	the	the	DET
ejpam-4275	33	38	topological	topological	ADJ
ejpam-4275	33	39	notions	notion	NOUN
ejpam-4275	33	40	and	and	CCONJ
ejpam-4275	33	41	concepts	concept	NOUN
ejpam-4275	33	42	.	.	PUNCT
ejpam-4275	34	1	in	in	ADP
ejpam-4275	34	2	[	[	X
ejpam-4275	34	3	9	9	NUM
ejpam-4275	34	4	,	,	PUNCT
ejpam-4275	34	5	11	11	NUM
ejpam-4275	34	6	]	]	PUNCT
ejpam-4275	34	7	,	,	PUNCT
ejpam-4275	34	8	the	the	DET
ejpam-4275	34	9	authors	author	NOUN
ejpam-4275	34	10	discussed	discuss	VERB
ejpam-4275	34	11	these	these	DET
ejpam-4275	34	12	advantages	advantage	NOUN
ejpam-4275	34	13	for	for	ADP
ejpam-4275	34	14	compact	compact	ADJ
ejpam-4275	34	15	and	and	CCONJ
ejpam-4275	34	16	connected	connected	ADJ
ejpam-4275	34	17	spaces	space	NOUN
ejpam-4275	34	18	.	.	PUNCT
ejpam-4275	35	1	some	some	DET
ejpam-4275	35	2	studies	study	NOUN
ejpam-4275	35	3	have	have	AUX
ejpam-4275	35	4	en	en	ADV
ejpam-4275	35	5	recently	recently	ADV
ejpam-4275	35	6	conducted	conduct	VERB
ejpam-4275	35	7	in	in	ADP
ejpam-4275	35	8	frame	frame	NOUN
ejpam-4275	35	9	of	of	ADP
ejpam-4275	35	10	infra	infra	NOUN
ejpam-4275	35	11	soft	soft	ADJ
ejpam-4275	35	12	topologies	topology	NOUN
ejpam-4275	35	13	such	such	ADJ
ejpam-4275	35	14	as	as	ADP
ejpam-4275	35	15	[	[	X
ejpam-4275	35	16	7	7	NUM
ejpam-4275	35	17	,	,	PUNCT
ejpam-4275	35	18	12	12	NUM
ejpam-4275	35	19	,	,	PUNCT
ejpam-4275	35	20	16	16	NUM
ejpam-4275	35	21	,	,	PUNCT
ejpam-4275	35	22	17	17	NUM
ejpam-4275	35	23	]	]	PUNCT
ejpam-4275	35	24	extension	extension	NOUN
ejpam-4275	35	25	of	of	ADP
ejpam-4275	35	26	soft	soft	ADJ
ejpam-4275	35	27	open	open	ADJ
ejpam-4275	35	28	sets	set	NOUN
ejpam-4275	35	29	was	be	AUX
ejpam-4275	35	30	a	a	DET
ejpam-4275	35	31	goal	goal	NOUN
ejpam-4275	35	32	of	of	ADP
ejpam-4275	35	33	some	some	DET
ejpam-4275	35	34	papers	paper	NOUN
ejpam-4275	35	35	.	.	PUNCT
ejpam-4275	36	1	some	some	DET
ejpam-4275	36	2	types	type	NOUN
ejpam-4275	36	3	of	of	ADP
ejpam-4275	36	4	these	these	DET
ejpam-4275	36	5	extensions	extension	NOUN
ejpam-4275	36	6	were	be	AUX
ejpam-4275	36	7	investigated	investigate	VERB
ejpam-4275	36	8	such	such	ADJ
ejpam-4275	36	9	as	as	ADP
ejpam-4275	36	10	soft	soft	ADJ
ejpam-4275	36	11	semi	semi	ADJ
ejpam-4275	36	12	-	-	ADJ
ejpam-4275	36	13	open	open	ADJ
ejpam-4275	36	14	and	and	CCONJ
ejpam-4275	36	15	soft	soft	ADJ
ejpam-4275	36	16	pre	pre	ADJ
ejpam-4275	36	17	-	-	ADJ
ejpam-4275	36	18	open	open	ADJ
ejpam-4275	36	19	sets	set	NOUN
ejpam-4275	36	20	which	which	PRON
ejpam-4275	36	21	were	be	AUX
ejpam-4275	36	22	presented	present	VERB
ejpam-4275	36	23	in	in	ADP
ejpam-4275	36	24	[	[	X
ejpam-4275	36	25	24	24	NUM
ejpam-4275	36	26	]	]	PUNCT
ejpam-4275	36	27	and	and	CCONJ
ejpam-4275	36	28	[	[	X
ejpam-4275	36	29	30	30	NUM
ejpam-4275	36	30	]	]	PUNCT
ejpam-4275	36	31	,	,	PUNCT
ejpam-4275	36	32	respectively	respectively	ADV
ejpam-4275	36	33	.	.	PUNCT
ejpam-4275	37	1	the	the	DET
ejpam-4275	37	2	target	target	NOUN
ejpam-4275	37	3	of	of	ADP
ejpam-4275	37	4	this	this	DET
ejpam-4275	37	5	work	work	NOUN
ejpam-4275	37	6	is	be	AUX
ejpam-4275	37	7	to	to	PART
ejpam-4275	37	8	scrutinize	scrutinize	VERB
ejpam-4275	37	9	the	the	DET
ejpam-4275	37	10	behaviours	behaviour	NOUN
ejpam-4275	37	11	of	of	ADP
ejpam-4275	37	12	soft	soft	ADJ
ejpam-4275	37	13	pre	pre	ADJ
ejpam-4275	37	14	-	-	ADJ
ejpam-4275	37	15	open	open	ADJ
ejpam-4275	37	16	sets	set	NOUN
ejpam-4275	37	17	via	via	ADP
ejpam-4275	37	18	infra	infra	NOUN
ejpam-4275	37	19	soft	soft	ADJ
ejpam-4275	37	20	topological	topological	ADJ
ejpam-4275	37	21	spaces	space	NOUN
ejpam-4275	37	22	.	.	PUNCT
ejpam-4275	38	1	as	as	SCONJ
ejpam-4275	38	2	we	we	PRON
ejpam-4275	38	3	shall	shall	AUX
ejpam-4275	38	4	show	show	VERB
ejpam-4275	38	5	many	many	ADJ
ejpam-4275	38	6	properties	property	NOUN
ejpam-4275	38	7	of	of	ADP
ejpam-4275	38	8	soft	soft	ADJ
ejpam-4275	38	9	pre	pre	ADJ
ejpam-4275	38	10	-	-	ADJ
ejpam-4275	38	11	open	open	ADJ
ejpam-4275	38	12	sets	set	NOUN
ejpam-4275	38	13	are	be	AUX
ejpam-4275	38	14	still	still	ADV
ejpam-4275	38	15	valid	valid	ADJ
ejpam-4275	38	16	for	for	ADP
ejpam-4275	38	17	infra	infra	NOUN
ejpam-4275	38	18	soft	soft	ADJ
ejpam-4275	38	19	pre	pre	ADJ
ejpam-4275	38	20	-	-	ADJ
ejpam-4275	38	21	open	open	ADJ
ejpam-4275	38	22	sets	set	NOUN
ejpam-4275	38	23	which	which	PRON
ejpam-4275	38	24	offers	offer	VERB
ejpam-4275	38	25	a	a	DET
ejpam-4275	38	26	flexible	flexible	ADJ
ejpam-4275	38	27	frame	frame	NOUN
ejpam-4275	38	28	(	(	PUNCT
ejpam-4275	38	29	in	in	ADP
ejpam-4275	38	30	lieu	lieu	NOUN
ejpam-4275	38	31	of	of	ADP
ejpam-4275	38	32	soft	soft	ADJ
ejpam-4275	38	33	topologies	topology	NOUN
ejpam-4275	38	34	)	)	PUNCT
ejpam-4275	38	35	to	to	PART
ejpam-4275	38	36	study	study	VERB
ejpam-4275	38	37	the	the	DET
ejpam-4275	38	38	topological	topological	ADJ
ejpam-4275	38	39	notions	notion	NOUN
ejpam-4275	38	40	and	and	CCONJ
ejpam-4275	38	41	the	the	DET
ejpam-4275	38	42	interrelationships	interrelationship	NOUN
ejpam-4275	38	43	between	between	ADP
ejpam-4275	38	44	them	they	PRON
ejpam-4275	38	45	.	.	PUNCT
ejpam-4275	39	1	we	we	PRON
ejpam-4275	39	2	layout	layout	VERB
ejpam-4275	39	3	the	the	DET
ejpam-4275	39	4	remainder	remainder	NOUN
ejpam-4275	39	5	of	of	ADP
ejpam-4275	39	6	this	this	DET
ejpam-4275	39	7	article	article	NOUN
ejpam-4275	39	8	as	as	ADP
ejpam-4275	39	9	following	follow	VERB
ejpam-4275	39	10	.	.	PUNCT
ejpam-4275	40	1	in	in	ADP
ejpam-4275	40	2	sect	sect	NOUN
ejpam-4275	40	3	.	.	PUNCT
ejpam-4275	41	1	2	2	NUM
ejpam-4275	41	2	,	,	PUNCT
ejpam-4275	41	3	we	we	PRON
ejpam-4275	41	4	survey	survey	VERB
ejpam-4275	41	5	the	the	DET
ejpam-4275	41	6	related	related	ADJ
ejpam-4275	41	7	literature	literature	NOUN
ejpam-4275	41	8	and	and	CCONJ
ejpam-4275	41	9	locate	locate	VERB
ejpam-4275	41	10	the	the	DET
ejpam-4275	41	11	current	current	ADJ
ejpam-4275	41	12	study	study	NOUN
ejpam-4275	41	13	in	in	ADP
ejpam-4275	41	14	its	its	PRON
ejpam-4275	41	15	context	context	NOUN
ejpam-4275	41	16	.	.	PUNCT
ejpam-4275	42	1	sect	sect	NOUN
ejpam-4275	42	2	.	.	PUNCT
ejpam-4275	43	1	3	3	NUM
ejpam-4275	43	2	is	be	AUX
ejpam-4275	43	3	first	first	ADV
ejpam-4275	43	4	of	of	ADP
ejpam-4275	43	5	the	the	DET
ejpam-4275	43	6	three	three	NUM
ejpam-4275	43	7	main	main	ADJ
ejpam-4275	43	8	sections	section	NOUN
ejpam-4275	43	9	of	of	ADP
ejpam-4275	43	10	this	this	DET
ejpam-4275	43	11	study	study	NOUN
ejpam-4275	43	12	.	.	PUNCT
ejpam-4275	44	1	it	it	PRON
ejpam-4275	44	2	introduces	introduce	VERB
ejpam-4275	44	3	the	the	DET
ejpam-4275	44	4	concept	concept	NOUN
ejpam-4275	44	5	of	of	ADP
ejpam-4275	44	6	infra	infra	NOUN
ejpam-4275	44	7	soft	soft	ADJ
ejpam-4275	44	8	pre	pre	ADJ
ejpam-4275	44	9	-	-	ADJ
ejpam-4275	44	10	open	open	ADJ
ejpam-4275	44	11	sets	set	NOUN
ejpam-4275	44	12	and	and	CCONJ
ejpam-4275	44	13	establishes	establish	VERB
ejpam-4275	44	14	its	its	PRON
ejpam-4275	44	15	characterization	characterization	NOUN
ejpam-4275	44	16	.	.	PUNCT
ejpam-4275	45	1	sect	sect	NOUN
ejpam-4275	45	2	.	.	PUNCT
ejpam-4275	46	1	4	4	NUM
ejpam-4275	46	2	is	be	AUX
ejpam-4275	46	3	the	the	DET
ejpam-4275	46	4	second	second	ADJ
ejpam-4275	46	5	main	main	ADJ
ejpam-4275	46	6	section	section	NOUN
ejpam-4275	46	7	which	which	PRON
ejpam-4275	46	8	defines	define	VERB
ejpam-4275	46	9	and	and	CCONJ
ejpam-4275	46	10	discusses	discuss	VERB
ejpam-4275	46	11	the	the	DET
ejpam-4275	46	12	concepts	concept	NOUN
ejpam-4275	46	13	of	of	ADP
ejpam-4275	46	14	infra	infra	NOUN
ejpam-4275	46	15	pre	pre	ADJ
ejpam-4275	46	16	-	-	ADJ
ejpam-4275	46	17	interior	interior	ADJ
ejpam-4275	46	18	,	,	PUNCT
ejpam-4275	46	19	infra	infra	NOUN
ejpam-4275	46	20	pre	pre	NOUN
ejpam-4275	46	21	-	-	ADJ
ejpam-4275	46	22	closure	closure	ADJ
ejpam-4275	46	23	,	,	PUNCT
ejpam-4275	46	24	infra	infra	NOUN
ejpam-4275	46	25	pre	pre	ADJ
ejpam-4275	46	26	-	-	NOUN
ejpam-4275	46	27	limit	limit	NOUN
ejpam-4275	46	28	and	and	CCONJ
ejpam-4275	46	29	infra	infra	NOUN
ejpam-4275	46	30	pre	pre	ADJ
ejpam-4275	46	31	-	-	ADJ
ejpam-4275	46	32	boundary	boundary	ADJ
ejpam-4275	46	33	soft	soft	ADJ
ejpam-4275	46	34	points	point	NOUN
ejpam-4275	46	35	of	of	ADP
ejpam-4275	46	36	a	a	DET
ejpam-4275	46	37	soft	soft	ADJ
ejpam-4275	46	38	set	set	NOUN
ejpam-4275	46	39	.	.	PUNCT
ejpam-4275	47	1	sect	sect	NOUN
ejpam-4275	47	2	.	.	PUNCT
ejpam-4275	48	1	5	5	NUM
ejpam-4275	48	2	is	be	AUX
ejpam-4275	48	3	the	the	DET
ejpam-4275	48	4	last	last	ADJ
ejpam-4275	48	5	main	main	ADJ
ejpam-4275	48	6	section	section	NOUN
ejpam-4275	48	7	which	which	PRON
ejpam-4275	48	8	initiates	initiate	VERB
ejpam-4275	48	9	and	and	CCONJ
ejpam-4275	48	10	explores	explore	VERB
ejpam-4275	48	11	new	new	ADJ
ejpam-4275	48	12	types	type	NOUN
ejpam-4275	48	13	of	of	ADP
ejpam-4275	48	14	soft	soft	ADJ
ejpam-4275	48	15	maps	map	NOUN
ejpam-4275	48	16	namely	namely	ADV
ejpam-4275	48	17	infra	infra	VERB
ejpam-4275	48	18	soft	soft	ADJ
ejpam-4275	48	19	pre	pre	ADJ
ejpam-4275	48	20	-	-	ADJ
ejpam-4275	48	21	continuous	continuous	ADJ
ejpam-4275	48	22	,	,	PUNCT
ejpam-4275	48	23	infra	infra	NOUN
ejpam-4275	48	24	soft	soft	ADJ
ejpam-4275	48	25	pre	pre	ADJ
ejpam-4275	48	26	-	-	ADJ
ejpam-4275	48	27	open	open	ADJ
ejpam-4275	48	28	,	,	PUNCT
ejpam-4275	48	29	infra	infra	NOUN
ejpam-4275	48	30	soft	soft	ADJ
ejpam-4275	48	31	pre	pre	ADJ
ejpam-4275	48	32	-	-	ADJ
ejpam-4275	48	33	closed	closed	ADJ
ejpam-4275	48	34	and	and	CCONJ
ejpam-4275	48	35	infra	infra	VERB
ejpam-4275	48	36	soft	soft	ADJ
ejpam-4275	48	37	pre	pre	ADJ
ejpam-4275	48	38	-	-	ADJ
ejpam-4275	48	39	homeomorphism	homeomorphism	ADJ
ejpam-4275	48	40	maps	map	NOUN
ejpam-4275	48	41	.	.	PUNCT
ejpam-4275	49	1	finally	finally	ADV
ejpam-4275	49	2	,	,	PUNCT
ejpam-4275	49	3	sect	sect	NOUN
ejpam-4275	49	4	.	.	PUNCT
ejpam-4275	50	1	6	6	NUM
ejpam-4275	50	2	gives	give	VERB
ejpam-4275	50	3	some	some	DET
ejpam-4275	50	4	conclusions	conclusion	NOUN
ejpam-4275	50	5	and	and	CCONJ
ejpam-4275	50	6	proposes	propose	VERB
ejpam-4275	50	7	some	some	DET
ejpam-4275	50	8	future	future	ADJ
ejpam-4275	50	9	works	work	NOUN
ejpam-4275	50	10	.	.	PUNCT
ejpam-4275	51	1	2	2	X
ejpam-4275	51	2	.	.	X
ejpam-4275	51	3	preliminaries	preliminary	NOUN
ejpam-4275	51	4	in	in	ADP
ejpam-4275	51	5	this	this	DET
ejpam-4275	51	6	part	part	NOUN
ejpam-4275	51	7	,	,	PUNCT
ejpam-4275	51	8	we	we	PRON
ejpam-4275	51	9	recall	recall	VERB
ejpam-4275	51	10	the	the	DET
ejpam-4275	51	11	concepts	concept	NOUN
ejpam-4275	51	12	and	and	CCONJ
ejpam-4275	51	13	findings	finding	NOUN
ejpam-4275	51	14	that	that	PRON
ejpam-4275	51	15	help	help	VERB
ejpam-4275	51	16	us	we	PRON
ejpam-4275	51	17	to	to	PART
ejpam-4275	51	18	understand	understand	VERB
ejpam-4275	51	19	this	this	DET
ejpam-4275	51	20	article	article	NOUN
ejpam-4275	51	21	.	.	PUNCT
ejpam-4275	52	1	2.1	2.1	NUM
ejpam-4275	52	2	.	.	PUNCT
ejpam-4275	52	3	soft	soft	ADJ
ejpam-4275	52	4	set	set	ADJ
ejpam-4275	52	5	theory	theory	NOUN
ejpam-4275	52	6	definition	definition	NOUN
ejpam-4275	52	7	1	1	NUM
ejpam-4275	52	8	.	.	PUNCT
ejpam-4275	53	1	[	[	X
ejpam-4275	53	2	34	34	NUM
ejpam-4275	53	3	]	]	PUNCT
ejpam-4275	53	4	consider	consider	VERB
ejpam-4275	53	5	σ	σ	NOUN
ejpam-4275	53	6	as	as	ADP
ejpam-4275	53	7	a	a	DET
ejpam-4275	53	8	parameters	parameter	NOUN
ejpam-4275	53	9	set	set	VERB
ejpam-4275	53	10	and	and	CCONJ
ejpam-4275	53	11	2x	2x	NUM
ejpam-4275	53	12	the	the	DET
ejpam-4275	53	13	power	power	NOUN
ejpam-4275	53	14	set	set	NOUN
ejpam-4275	53	15	of	of	ADP
ejpam-4275	53	16	x	x	PRON
ejpam-4275	53	17	which	which	PRON
ejpam-4275	53	18	is	be	AUX
ejpam-4275	53	19	the	the	DET
ejpam-4275	53	20	universe	universe	NOUN
ejpam-4275	53	21	.	.	PUNCT
ejpam-4275	54	1	we	we	PRON
ejpam-4275	54	2	call	call	VERB
ejpam-4275	54	3	(	(	PUNCT
ejpam-4275	54	4	ω	ω	PROPN
ejpam-4275	54	5	,	,	PUNCT
ejpam-4275	54	6	σ	σ	PROPN
ejpam-4275	54	7	)	)	PUNCT
ejpam-4275	54	8	a	a	DET
ejpam-4275	54	9	soft	soft	ADJ
ejpam-4275	54	10	set	set	NOUN
ejpam-4275	54	11	over	over	ADP
ejpam-4275	54	12	x	x	PUNCT
ejpam-4275	54	13	if	if	SCONJ
ejpam-4275	54	14	ω	ω	PROPN
ejpam-4275	54	15	:	:	PUNCT
ejpam-4275	54	16	σ	σ	NOUN
ejpam-4275	54	17	→	→	SYM
ejpam-4275	54	18	2x	2x	NUM
ejpam-4275	54	19	is	be	AUX
ejpam-4275	54	20	a	a	DET
ejpam-4275	54	21	crisp	crisp	ADJ
ejpam-4275	54	22	map	map	NOUN
ejpam-4275	54	23	.	.	PUNCT
ejpam-4275	55	1	a	a	DET
ejpam-4275	55	2	soft	soft	ADJ
ejpam-4275	55	3	set	set	NOUN
ejpam-4275	55	4	is	be	AUX
ejpam-4275	55	5	t.m	t.m	PROPN
ejpam-4275	55	6	.	.	PUNCT
ejpam-4275	55	7	al	al	PROPN
ejpam-4275	55	8	-	-	PUNCT
ejpam-4275	55	9	shami	shami	PROPN
ejpam-4275	55	10	,	,	PUNCT
ejpam-4275	55	11	h.a	h.a	PROPN
ejpam-4275	55	12	.	.	PROPN
ejpam-4275	55	13	othman	othman	PROPN
ejpam-4275	55	14	/	/	SYM
ejpam-4275	55	15	eur	eur	PROPN
ejpam-4275	55	16	.	.	PUNCT
ejpam-4275	56	1	j.	j.	PROPN
ejpam-4275	56	2	pure	pure	PROPN
ejpam-4275	56	3	appl	appl	PROPN
ejpam-4275	56	4	.	.	PROPN
ejpam-4275	56	5	math	math	PROPN
ejpam-4275	56	6	,	,	PUNCT
ejpam-4275	56	7	15	15	NUM
ejpam-4275	56	8	(	(	PUNCT
ejpam-4275	56	9	1	1	NUM
ejpam-4275	56	10	)	)	PUNCT
ejpam-4275	56	11	(	(	PUNCT
ejpam-4275	56	12	2022	2022	NUM
ejpam-4275	56	13	)	)	PUNCT
ejpam-4275	56	14	,	,	PUNCT
ejpam-4275	56	15	261	261	NUM
ejpam-4275	56	16	-	-	SYM
ejpam-4275	56	17	280	280	NUM
ejpam-4275	56	18	263	263	NUM
ejpam-4275	56	19	expressed	express	VERB
ejpam-4275	56	20	as	as	ADP
ejpam-4275	56	21	(	(	PUNCT
ejpam-4275	56	22	ω	ω	PROPN
ejpam-4275	56	23	,	,	PUNCT
ejpam-4275	56	24	σ	σ	PROPN
ejpam-4275	56	25	)	)	PUNCT
ejpam-4275	56	26	=	=	PRON
ejpam-4275	56	27	{	{	PUNCT
ejpam-4275	56	28	(	(	PUNCT
ejpam-4275	56	29	η	η	NOUN
ejpam-4275	56	30	,	,	PUNCT
ejpam-4275	56	31	ω(η	ω(η	NUM
ejpam-4275	56	32	)	)	PUNCT
ejpam-4275	56	33	)	)	PUNCT
ejpam-4275	56	34	:	:	PUNCT
ejpam-4275	57	1	η	η	PROPN
ejpam-4275	57	2	∈	∈	PROPN
ejpam-4275	57	3	σ	σ	PROPN
ejpam-4275	57	4	and	and	CCONJ
ejpam-4275	57	5	ω(η	ω(η	PROPN
ejpam-4275	57	6	)	)	PUNCT
ejpam-4275	57	7	∈	∈	NOUN
ejpam-4275	57	8	2x	2x	NUM
ejpam-4275	57	9	}	}	PUNCT
ejpam-4275	57	10	.	.	PUNCT
ejpam-4275	58	1	a	a	DET
ejpam-4275	58	2	class	class	NOUN
ejpam-4275	58	3	of	of	ADP
ejpam-4275	58	4	all	all	DET
ejpam-4275	58	5	soft	soft	ADJ
ejpam-4275	58	6	sets	set	NOUN
ejpam-4275	58	7	over	over	ADP
ejpam-4275	58	8	x	x	PUNCT
ejpam-4275	58	9	under	under	ADP
ejpam-4275	58	10	a	a	DET
ejpam-4275	58	11	set	set	NOUN
ejpam-4275	58	12	of	of	ADP
ejpam-4275	58	13	parameters	parameter	NOUN
ejpam-4275	58	14	σ	σ	PROPN
ejpam-4275	58	15	is	be	AUX
ejpam-4275	58	16	symbolized	symbolize	VERB
ejpam-4275	58	17	by	by	ADP
ejpam-4275	58	18	c(xς	c(xς	PROPN
ejpam-4275	58	19	)	)	PUNCT
ejpam-4275	58	20	.	.	PUNCT
ejpam-4275	59	1	definition	definition	NOUN
ejpam-4275	59	2	2	2	NUM
ejpam-4275	59	3	.	.	PUNCT
ejpam-4275	60	1	[	[	X
ejpam-4275	60	2	19	19	NUM
ejpam-4275	60	3	]	]	PUNCT
ejpam-4275	60	4	a	a	DET
ejpam-4275	60	5	complement	complement	NOUN
ejpam-4275	60	6	of	of	ADP
ejpam-4275	60	7	a	a	DET
ejpam-4275	60	8	soft	soft	ADJ
ejpam-4275	60	9	set	set	NOUN
ejpam-4275	60	10	(	(	PUNCT
ejpam-4275	60	11	ω	ω	PROPN
ejpam-4275	60	12	,	,	PUNCT
ejpam-4275	60	13	σ	σ	PROPN
ejpam-4275	60	14	)	)	PUNCT
ejpam-4275	60	15	,	,	PUNCT
ejpam-4275	60	16	denoted	denote	VERB
ejpam-4275	60	17	by	by	ADP
ejpam-4275	60	18	(	(	PUNCT
ejpam-4275	60	19	ωc	ωc	PROPN
ejpam-4275	60	20	,	,	PUNCT
ejpam-4275	60	21	σ	σ	PROPN
ejpam-4275	60	22	)	)	PUNCT
ejpam-4275	60	23	,	,	PUNCT
ejpam-4275	60	24	provided	provide	VERB
ejpam-4275	60	25	that	that	SCONJ
ejpam-4275	60	26	a	a	DET
ejpam-4275	60	27	map	map	NOUN
ejpam-4275	60	28	ωc	ωc	ADP
ejpam-4275	60	29	:	:	PUNCT
ejpam-4275	60	30	σ	σ	NOUN
ejpam-4275	60	31	→	→	SYM
ejpam-4275	60	32	2x	2x	NUM
ejpam-4275	60	33	is	be	AUX
ejpam-4275	60	34	given	give	VERB
ejpam-4275	60	35	by	by	ADP
ejpam-4275	60	36	ωc(η	ωc(η	NOUN
ejpam-4275	60	37	)	)	PUNCT
ejpam-4275	60	38	=	=	PUNCT
ejpam-4275	60	39	x	x	SYM
ejpam-4275	60	40	\	\	PROPN
ejpam-4275	60	41	ω(η	ω(η	PROPN
ejpam-4275	60	42	)	)	PUNCT
ejpam-4275	60	43	for	for	ADP
ejpam-4275	60	44	each	each	DET
ejpam-4275	60	45	η	η	PROPN
ejpam-4275	60	46	∈	∈	PROPN
ejpam-4275	60	47	σ	σ	PROPN
ejpam-4275	60	48	.	.	PUNCT
ejpam-4275	60	49	definition	definition	NOUN
ejpam-4275	60	50	3	3	NUM
ejpam-4275	60	51	.	.	PUNCT
ejpam-4275	61	1	[	[	X
ejpam-4275	61	2	33	33	NUM
ejpam-4275	61	3	]	]	PUNCT
ejpam-4275	61	4	let	let	AUX
ejpam-4275	61	5	(	(	PUNCT
ejpam-4275	61	6	ω	ω	PROPN
ejpam-4275	61	7	,	,	PUNCT
ejpam-4275	61	8	σ	σ	PROPN
ejpam-4275	61	9	)	)	PUNCT
ejpam-4275	61	10	be	be	VERB
ejpam-4275	61	11	a	a	DET
ejpam-4275	61	12	soft	soft	ADJ
ejpam-4275	61	13	set	set	NOUN
ejpam-4275	61	14	on	on	ADP
ejpam-4275	61	15	x	x	PUNCT
ejpam-4275	61	16	such	such	ADJ
ejpam-4275	61	17	that	that	SCONJ
ejpam-4275	61	18	ω(η	ω(η	NOUN
ejpam-4275	61	19	)	)	PUNCT
ejpam-4275	61	20	=	=	NOUN
ejpam-4275	61	21	∅	∅	NOUN
ejpam-4275	61	22	(	(	PUNCT
ejpam-4275	61	23	resp	resp	NOUN
ejpam-4275	61	24	.	.	PUNCT
ejpam-4275	61	25	,	,	PUNCT
ejpam-4275	61	26	ω(η	ω(η	X
ejpam-4275	61	27	)	)	PUNCT
ejpam-4275	61	28	=	=	SYM
ejpam-4275	61	29	x	x	X
ejpam-4275	61	30	)	)	PUNCT
ejpam-4275	61	31	for	for	ADP
ejpam-4275	61	32	each	each	DET
ejpam-4275	61	33	η	η	PROPN
ejpam-4275	61	34	∈	∈	PROPN
ejpam-4275	61	35	σ	σ	PROPN
ejpam-4275	61	36	.	.	PUNCT
ejpam-4275	62	1	then	then	ADV
ejpam-4275	62	2	we	we	PRON
ejpam-4275	62	3	say	say	VERB
ejpam-4275	62	4	that	that	SCONJ
ejpam-4275	62	5	(	(	PUNCT
ejpam-4275	62	6	ω	ω	PROPN
ejpam-4275	62	7	,	,	PUNCT
ejpam-4275	62	8	σ	σ	PROPN
ejpam-4275	62	9	)	)	PUNCT
ejpam-4275	62	10	is	be	AUX
ejpam-4275	62	11	a	a	DET
ejpam-4275	62	12	null	null	ADJ
ejpam-4275	62	13	(	(	PUNCT
ejpam-4275	62	14	resp	resp	NOUN
ejpam-4275	62	15	.	.	PROPN
ejpam-4275	62	16	,	,	PUNCT
ejpam-4275	62	17	an	an	DET
ejpam-4275	62	18	absolute	absolute	ADJ
ejpam-4275	62	19	)	)	PUNCT
ejpam-4275	62	20	soft	soft	ADJ
ejpam-4275	62	21	set	set	NOUN
ejpam-4275	62	22	over	over	ADP
ejpam-4275	62	23	x.	x.	NOUN
ejpam-4275	62	24	the	the	DET
ejpam-4275	62	25	null	null	ADJ
ejpam-4275	62	26	and	and	CCONJ
ejpam-4275	62	27	absolute	absolute	ADJ
ejpam-4275	62	28	soft	soft	ADJ
ejpam-4275	62	29	sets	set	NOUN
ejpam-4275	62	30	are	be	AUX
ejpam-4275	62	31	respectively	respectively	ADV
ejpam-4275	62	32	symbolized	symbolize	VERB
ejpam-4275	62	33	by	by	ADP
ejpam-4275	62	34	φ	φ	PROPN
ejpam-4275	62	35	and	and	CCONJ
ejpam-4275	62	36	x̃.	x̃.	ADJ
ejpam-4275	62	37	definition	definition	NOUN
ejpam-4275	62	38	4	4	NUM
ejpam-4275	62	39	.	.	PUNCT
ejpam-4275	63	1	[	[	X
ejpam-4275	63	2	26	26	NUM
ejpam-4275	63	3	,	,	PUNCT
ejpam-4275	63	4	27	27	NUM
ejpam-4275	63	5	]	]	PUNCT
ejpam-4275	63	6	we	we	PRON
ejpam-4275	63	7	call	call	VERB
ejpam-4275	63	8	a	a	DET
ejpam-4275	63	9	soft	soft	ADJ
ejpam-4275	63	10	set	set	NOUN
ejpam-4275	63	11	(	(	PUNCT
ejpam-4275	63	12	ω	ω	PROPN
ejpam-4275	63	13	,	,	PUNCT
ejpam-4275	63	14	σ	σ	PROPN
ejpam-4275	63	15	)	)	PUNCT
ejpam-4275	63	16	stable	stable	ADJ
ejpam-4275	63	17	(	(	PUNCT
ejpam-4275	63	18	resp	resp	NOUN
ejpam-4275	63	19	.	.	PUNCT
ejpam-4275	63	20	,	,	PUNCT
ejpam-4275	63	21	finite	finite	PROPN
ejpam-4275	63	22	,	,	PUNCT
ejpam-4275	63	23	countable	countable	ADJ
ejpam-4275	63	24	)	)	PUNCT
ejpam-4275	63	25	if	if	SCONJ
ejpam-4275	63	26	all	all	DET
ejpam-4275	63	27	components	component	NOUN
ejpam-4275	63	28	are	be	AUX
ejpam-4275	63	29	equal	equal	ADJ
ejpam-4275	63	30	(	(	PUNCT
ejpam-4275	63	31	resp	resp	NOUN
ejpam-4275	63	32	.	.	PUNCT
ejpam-4275	63	33	,	,	PUNCT
ejpam-4275	63	34	finite	finite	PROPN
ejpam-4275	63	35	,	,	PUNCT
ejpam-4275	63	36	countable	countable	ADJ
ejpam-4275	63	37	)	)	PUNCT
ejpam-4275	63	38	.	.	PUNCT
ejpam-4275	64	1	otherwise	otherwise	ADV
ejpam-4275	64	2	,	,	PUNCT
ejpam-4275	64	3	we	we	PRON
ejpam-4275	64	4	call	call	VERB
ejpam-4275	64	5	(	(	PUNCT
ejpam-4275	64	6	ω	ω	PROPN
ejpam-4275	64	7	,	,	PUNCT
ejpam-4275	64	8	σ	σ	NOUN
ejpam-4275	64	9	)	)	PUNCT
ejpam-4275	64	10	unstable	unstable	ADJ
ejpam-4275	64	11	(	(	PUNCT
ejpam-4275	64	12	resp	resp	NOUN
ejpam-4275	64	13	.	.	PUNCT
ejpam-4275	64	14	,	,	PUNCT
ejpam-4275	64	15	infinite	infinite	ADJ
ejpam-4275	64	16	,	,	PUNCT
ejpam-4275	64	17	uncountable	uncountable	ADJ
ejpam-4275	64	18	)	)	PUNCT
ejpam-4275	64	19	.	.	PUNCT
ejpam-4275	65	1	definition	definition	NOUN
ejpam-4275	65	2	5	5	NUM
ejpam-4275	65	3	.	.	PUNCT
ejpam-4275	66	1	[	[	X
ejpam-4275	66	2	35	35	NUM
ejpam-4275	66	3	]	]	PUNCT
ejpam-4275	66	4	we	we	PRON
ejpam-4275	66	5	call	call	VERB
ejpam-4275	66	6	a	a	DET
ejpam-4275	66	7	soft	soft	ADJ
ejpam-4275	66	8	set	set	NOUN
ejpam-4275	66	9	(	(	PUNCT
ejpam-4275	66	10	ω	ω	PROPN
ejpam-4275	66	11	,	,	PUNCT
ejpam-4275	66	12	σ	σ	PROPN
ejpam-4275	66	13	)	)	PUNCT
ejpam-4275	66	14	a	a	DET
ejpam-4275	66	15	soft	soft	ADJ
ejpam-4275	66	16	point	point	NOUN
ejpam-4275	66	17	on	on	ADP
ejpam-4275	66	18	x	x	PUNCT
ejpam-4275	66	19	if	if	SCONJ
ejpam-4275	66	20	there	there	PRON
ejpam-4275	66	21	is	be	VERB
ejpam-4275	66	22	η	η	PROPN
ejpam-4275	66	23	∈	∈	PROPN
ejpam-4275	66	24	σ	σ	NOUN
ejpam-4275	66	25	such	such	ADJ
ejpam-4275	66	26	that	that	SCONJ
ejpam-4275	66	27	ω(η	ω(η	NOUN
ejpam-4275	66	28	)	)	PUNCT
ejpam-4275	67	1	=	=	PUNCT
ejpam-4275	67	2	x	x	SYM
ejpam-4275	67	3	∈	∈	PROPN
ejpam-4275	67	4	x	x	X
ejpam-4275	67	5	and	and	CCONJ
ejpam-4275	67	6	ω(η′	ω(η′	NUM
ejpam-4275	67	7	)	)	PUNCT
ejpam-4275	67	8	=	=	NOUN
ejpam-4275	67	9	∅	∅	NOUN
ejpam-4275	67	10	for	for	ADP
ejpam-4275	67	11	each	each	DET
ejpam-4275	67	12	η′	η′	NUM
ejpam-4275	67	13	̸=	̸=	PROPN
ejpam-4275	67	14	η	η	PROPN
ejpam-4275	67	15	.	.	PROPN
ejpam-4275	67	16	henceforth	henceforth	ADV
ejpam-4275	67	17	,	,	PUNCT
ejpam-4275	67	18	δxη	δxη	NOUN
ejpam-4275	67	19	denotes	denote	VERB
ejpam-4275	67	20	a	a	DET
ejpam-4275	67	21	soft	soft	ADJ
ejpam-4275	67	22	point	point	NOUN
ejpam-4275	67	23	.	.	PUNCT
ejpam-4275	68	1	definition	definition	NOUN
ejpam-4275	68	2	6	6	NUM
ejpam-4275	68	3	.	.	PUNCT
ejpam-4275	69	1	[	[	X
ejpam-4275	69	2	19	19	NUM
ejpam-4275	69	3	]	]	PUNCT
ejpam-4275	69	4	the	the	DET
ejpam-4275	69	5	intersection	intersection	NOUN
ejpam-4275	69	6	of	of	ADP
ejpam-4275	69	7	soft	soft	ADJ
ejpam-4275	69	8	sets	set	NOUN
ejpam-4275	69	9	(	(	PUNCT
ejpam-4275	69	10	ω	ω	PROPN
ejpam-4275	69	11	,	,	PUNCT
ejpam-4275	69	12	σ	σ	PROPN
ejpam-4275	69	13	)	)	PUNCT
ejpam-4275	69	14	and	and	CCONJ
ejpam-4275	69	15	(	(	PUNCT
ejpam-4275	69	16	ψ,∆	ψ,∆	PUNCT
ejpam-4275	69	17	)	)	PUNCT
ejpam-4275	69	18	on	on	ADP
ejpam-4275	69	19	x	x	SYM
ejpam-4275	69	20	,	,	PUNCT
ejpam-4275	69	21	symbolized	symbolize	VERB
ejpam-4275	69	22	by	by	ADP
ejpam-4275	69	23	(	(	PUNCT
ejpam-4275	69	24	ω	ω	PROPN
ejpam-4275	69	25	,	,	PUNCT
ejpam-4275	69	26	σ	σ	PROPN
ejpam-4275	69	27	)	)	PUNCT
ejpam-4275	69	28	⋂̃	⋂̃	NOUN
ejpam-4275	69	29	(	(	PUNCT
ejpam-4275	69	30	ψ,∆	ψ,∆	NUM
ejpam-4275	69	31	)	)	PUNCT
ejpam-4275	69	32	,	,	PUNCT
ejpam-4275	69	33	is	be	AUX
ejpam-4275	69	34	a	a	DET
ejpam-4275	69	35	soft	soft	ADJ
ejpam-4275	69	36	set	set	NOUN
ejpam-4275	69	37	(	(	PUNCT
ejpam-4275	69	38	υ	υ	NOUN
ejpam-4275	69	39	,	,	PUNCT
ejpam-4275	69	40	t	t	PROPN
ejpam-4275	69	41	)	)	PUNCT
ejpam-4275	69	42	,	,	PUNCT
ejpam-4275	69	43	where	where	SCONJ
ejpam-4275	69	44	t	t	NOUN
ejpam-4275	69	45	=	=	SYM
ejpam-4275	69	46	σ∩∆	σ∩∆	PROPN
ejpam-4275	69	47	̸=	̸=	PROPN
ejpam-4275	69	48	∅	∅	NOUN
ejpam-4275	69	49	,	,	PUNCT
ejpam-4275	69	50	and	and	CCONJ
ejpam-4275	69	51	a	a	DET
ejpam-4275	69	52	map	map	NOUN
ejpam-4275	69	53	υ	υ	INTJ
ejpam-4275	69	54	:	:	PUNCT
ejpam-4275	69	55	t	t	PROPN
ejpam-4275	69	56	→	→	SYM
ejpam-4275	69	57	2x	2x	NUM
ejpam-4275	69	58	is	be	AUX
ejpam-4275	69	59	given	give	VERB
ejpam-4275	69	60	by	by	ADP
ejpam-4275	69	61	υ(η	υ(η	PROPN
ejpam-4275	69	62	)	)	PUNCT
ejpam-4275	69	63	=	=	SYM
ejpam-4275	69	64	ω(η	ω(η	NOUN
ejpam-4275	69	65	)	)	PUNCT
ejpam-4275	69	66	∩ψ(η	∩ψ(η	NOUN
ejpam-4275	69	67	)	)	PUNCT
ejpam-4275	69	68	for	for	ADP
ejpam-4275	69	69	each	each	DET
ejpam-4275	69	70	η	η	PROPN
ejpam-4275	69	71	∈	∈	PROPN
ejpam-4275	69	72	t	t	PROPN
ejpam-4275	69	73	.	.	PUNCT
ejpam-4275	70	1	definition	definition	NOUN
ejpam-4275	70	2	7	7	NUM
ejpam-4275	70	3	.	.	PUNCT
ejpam-4275	71	1	[	[	X
ejpam-4275	71	2	33	33	NUM
ejpam-4275	71	3	]	]	PUNCT
ejpam-4275	71	4	the	the	DET
ejpam-4275	71	5	union	union	NOUN
ejpam-4275	71	6	of	of	ADP
ejpam-4275	71	7	soft	soft	ADJ
ejpam-4275	71	8	sets	set	NOUN
ejpam-4275	71	9	(	(	PUNCT
ejpam-4275	71	10	ω	ω	PROPN
ejpam-4275	71	11	,	,	PUNCT
ejpam-4275	71	12	σ	σ	PROPN
ejpam-4275	71	13	)	)	PUNCT
ejpam-4275	71	14	and	and	CCONJ
ejpam-4275	71	15	(	(	PUNCT
ejpam-4275	71	16	ψ,∆	ψ,∆	PUNCT
ejpam-4275	71	17	)	)	PUNCT
ejpam-4275	71	18	on	on	ADP
ejpam-4275	71	19	x	x	SYM
ejpam-4275	71	20	,	,	PUNCT
ejpam-4275	71	21	symbolized	symbolize	VERB
ejpam-4275	71	22	by	by	ADP
ejpam-4275	71	23	(	(	PUNCT
ejpam-4275	71	24	ω	ω	PROPN
ejpam-4275	71	25	,	,	PUNCT
ejpam-4275	71	26	σ	σ	PROPN
ejpam-4275	71	27	)	)	PUNCT
ejpam-4275	71	28	⋃̃	⋃̃	PROPN
ejpam-4275	71	29	(	(	PUNCT
ejpam-4275	71	30	ψ,∆	ψ,∆	NUM
ejpam-4275	71	31	)	)	PUNCT
ejpam-4275	71	32	,	,	PUNCT
ejpam-4275	71	33	is	be	AUX
ejpam-4275	71	34	a	a	DET
ejpam-4275	71	35	soft	soft	ADJ
ejpam-4275	71	36	set	set	NOUN
ejpam-4275	71	37	(	(	PUNCT
ejpam-4275	71	38	υ	υ	NOUN
ejpam-4275	71	39	,	,	PUNCT
ejpam-4275	71	40	t	t	PROPN
ejpam-4275	71	41	)	)	PUNCT
ejpam-4275	71	42	,	,	PUNCT
ejpam-4275	71	43	where	where	SCONJ
ejpam-4275	71	44	t	t	NOUN
ejpam-4275	71	45	=	=	SYM
ejpam-4275	71	46	σ	σ	PROPN
ejpam-4275	71	47	∪∆	∪∆	NOUN
ejpam-4275	71	48	and	and	CCONJ
ejpam-4275	71	49	a	a	DET
ejpam-4275	71	50	map	map	NOUN
ejpam-4275	71	51	t	t	NOUN
ejpam-4275	71	52	:	:	PUNCT
ejpam-4275	71	53	σ	σ	PROPN
ejpam-4275	71	54	→	→	SYM
ejpam-4275	71	55	2x	2x	NUM
ejpam-4275	71	56	is	be	AUX
ejpam-4275	71	57	given	give	VERB
ejpam-4275	71	58	as	as	SCONJ
ejpam-4275	71	59	follows	follow	VERB
ejpam-4275	71	60	:	:	PUNCT
ejpam-4275	71	61	υ(η	υ(η	PROPN
ejpam-4275	71	62	)	)	PUNCT
ejpam-4275	71	63	=	=	SYM
ejpam-4275	71	64			PUNCT
ejpam-4275	71	65	ω(η	ω(η	PROPN
ejpam-4275	71	66	)	)	PUNCT
ejpam-4275	71	67	:	:	PUNCT
ejpam-4275	71	68	η	η	PROPN
ejpam-4275	71	69	∈	∈	PROPN
ejpam-4275	71	70	σ	σ	PROPN
ejpam-4275	71	71	\∆	\∆	X
ejpam-4275	71	72	ψ(η	ψ(η	PROPN
ejpam-4275	71	73	)	)	PUNCT
ejpam-4275	71	74	:	:	PUNCT
ejpam-4275	71	75	η	η	PROPN
ejpam-4275	71	76	∈	∈	PROPN
ejpam-4275	71	77	∆	∆	X
ejpam-4275	71	78	\	\	PROPN
ejpam-4275	71	79	σ	σ	PROPN
ejpam-4275	71	80	ω(η	ω(η	PROPN
ejpam-4275	71	81	)	)	PUNCT
ejpam-4275	71	82	∪ψ(η	∪ψ(η	PROPN
ejpam-4275	71	83	)	)	PUNCT
ejpam-4275	71	84	:	:	PUNCT
ejpam-4275	71	85	η	η	PROPN
ejpam-4275	71	86	∈	∈	PROPN
ejpam-4275	71	87	σ	σ	NOUN
ejpam-4275	71	88	∩∆	∩∆	PROPN
ejpam-4275	71	89	definition	definition	NOUN
ejpam-4275	71	90	8	8	NUM
ejpam-4275	71	91	.	.	PUNCT
ejpam-4275	72	1	[	[	X
ejpam-4275	72	2	29	29	NUM
ejpam-4275	72	3	]	]	PUNCT
ejpam-4275	72	4	a	a	DET
ejpam-4275	72	5	soft	soft	ADJ
ejpam-4275	72	6	set	set	NOUN
ejpam-4275	72	7	(	(	PUNCT
ejpam-4275	72	8	ω	ω	PROPN
ejpam-4275	72	9	,	,	PUNCT
ejpam-4275	72	10	σ	σ	PROPN
ejpam-4275	72	11	)	)	PUNCT
ejpam-4275	72	12	is	be	AUX
ejpam-4275	72	13	a	a	DET
ejpam-4275	72	14	subset	subset	NOUN
ejpam-4275	72	15	of	of	ADP
ejpam-4275	72	16	a	a	DET
ejpam-4275	72	17	soft	soft	ADJ
ejpam-4275	72	18	set	set	NOUN
ejpam-4275	72	19	(	(	PUNCT
ejpam-4275	72	20	ψ,∆	ψ,∆	NOUN
ejpam-4275	72	21	)	)	PUNCT
ejpam-4275	72	22	,	,	PUNCT
ejpam-4275	72	23	symbolized	symbolize	VERB
ejpam-4275	72	24	by	by	ADP
ejpam-4275	72	25	(	(	PUNCT
ejpam-4275	72	26	ω	ω	PROPN
ejpam-4275	72	27	,	,	PUNCT
ejpam-4275	72	28	σ)⊆̃(ψ,∆	σ)⊆̃(ψ,∆	NOUN
ejpam-4275	72	29	)	)	PUNCT
ejpam-4275	72	30	,	,	PUNCT
ejpam-4275	72	31	if	if	SCONJ
ejpam-4275	72	32	σ	σ	NOUN
ejpam-4275	72	33	⊆	⊆	NUM
ejpam-4275	72	34	∆	∆	PROPN
ejpam-4275	72	35	and	and	CCONJ
ejpam-4275	72	36	ω(η	ω(η	NUM
ejpam-4275	72	37	)	)	PUNCT
ejpam-4275	72	38	⊆	⊆	NUM
ejpam-4275	72	39	ψ(η	ψ(η	NOUN
ejpam-4275	72	40	)	)	PUNCT
ejpam-4275	72	41	for	for	ADP
ejpam-4275	72	42	all	all	DET
ejpam-4275	72	43	η	η	PROPN
ejpam-4275	72	44	∈	∈	PROPN
ejpam-4275	72	45	σ	σ	PROPN
ejpam-4275	72	46	.	.	PUNCT
ejpam-4275	73	1	if	if	SCONJ
ejpam-4275	73	2	(	(	PUNCT
ejpam-4275	73	3	ω	ω	NOUN
ejpam-4275	73	4	,	,	PUNCT
ejpam-4275	73	5	σ)⊆̃(ψ,∆	σ)⊆̃(ψ,∆	NOUN
ejpam-4275	73	6	)	)	PUNCT
ejpam-4275	73	7	and	and	CCONJ
ejpam-4275	73	8	(	(	PUNCT
ejpam-4275	73	9	ψ,∆)⊆̃(ω	ψ,∆)⊆̃(ω	NOUN
ejpam-4275	73	10	,	,	PUNCT
ejpam-4275	73	11	σ	σ	PROPN
ejpam-4275	73	12	)	)	PUNCT
ejpam-4275	73	13	,	,	PUNCT
ejpam-4275	73	14	then	then	ADV
ejpam-4275	73	15	(	(	PUNCT
ejpam-4275	73	16	ω	ω	PROPN
ejpam-4275	73	17	,	,	PUNCT
ejpam-4275	73	18	σ	σ	PROPN
ejpam-4275	73	19	)	)	PUNCT
ejpam-4275	73	20	and	and	CCONJ
ejpam-4275	73	21	(	(	PUNCT
ejpam-4275	73	22	ψ,∆	ψ,∆	PUNCT
ejpam-4275	73	23	)	)	PUNCT
ejpam-4275	73	24	are	be	AUX
ejpam-4275	73	25	called	call	VERB
ejpam-4275	73	26	soft	soft	ADJ
ejpam-4275	73	27	equal	equal	ADJ
ejpam-4275	73	28	.	.	PUNCT
ejpam-4275	74	1	definition	definition	NOUN
ejpam-4275	74	2	9	9	NUM
ejpam-4275	74	3	.	.	PUNCT
ejpam-4275	75	1	[	[	X
ejpam-4275	75	2	21	21	NUM
ejpam-4275	75	3	]	]	PUNCT
ejpam-4275	75	4	the	the	DET
ejpam-4275	75	5	cartesian	cartesian	ADJ
ejpam-4275	75	6	product	product	NOUN
ejpam-4275	75	7	of	of	ADP
ejpam-4275	75	8	(	(	PUNCT
ejpam-4275	75	9	ω	ω	PROPN
ejpam-4275	75	10	,	,	PUNCT
ejpam-4275	75	11	σ	σ	PROPN
ejpam-4275	75	12	)	)	PUNCT
ejpam-4275	75	13	and	and	CCONJ
ejpam-4275	75	14	(	(	PUNCT
ejpam-4275	75	15	ψ,∆	ψ,∆	PROPN
ejpam-4275	75	16	)	)	PUNCT
ejpam-4275	75	17	,	,	PUNCT
ejpam-4275	75	18	symbolized	symbolize	VERB
ejpam-4275	75	19	by	by	ADP
ejpam-4275	75	20	(	(	PUNCT
ejpam-4275	75	21	ω×ψ	ω×ψ	PROPN
ejpam-4275	75	22	,	,	PUNCT
ejpam-4275	75	23	σ×	σ×	NOUN
ejpam-4275	75	24	∆	∆	PROPN
ejpam-4275	75	25	)	)	PUNCT
ejpam-4275	75	26	,	,	PUNCT
ejpam-4275	75	27	is	be	AUX
ejpam-4275	75	28	defined	define	VERB
ejpam-4275	75	29	as	as	ADP
ejpam-4275	75	30	(	(	PUNCT
ejpam-4275	75	31	ω×ψ)(η	ω×ψ)(η	ADV
ejpam-4275	75	32	,	,	PUNCT
ejpam-4275	75	33	η′	η′	NUM
ejpam-4275	75	34	)	)	PUNCT
ejpam-4275	76	1	=	=	PUNCT
ejpam-4275	76	2	ω(η)×ψ(η′	ω(η)×ψ(η′	X
ejpam-4275	76	3	)	)	PUNCT
ejpam-4275	76	4	for	for	ADP
ejpam-4275	76	5	each	each	DET
ejpam-4275	76	6	(	(	PUNCT
ejpam-4275	76	7	η	η	PROPN
ejpam-4275	76	8	,	,	PUNCT
ejpam-4275	76	9	η′	η′	X
ejpam-4275	76	10	)	)	PUNCT
ejpam-4275	76	11	∈	∈	NOUN
ejpam-4275	76	12	σ×∆.	σ×∆.	X
ejpam-4275	76	13	definition	definition	NOUN
ejpam-4275	76	14	10	10	NUM
ejpam-4275	76	15	.	.	PUNCT
ejpam-4275	77	1	[	[	X
ejpam-4275	77	2	31	31	NUM
ejpam-4275	77	3	]	]	PUNCT
ejpam-4275	77	4	a	a	DET
ejpam-4275	77	5	soft	soft	ADJ
ejpam-4275	77	6	map	map	NOUN
ejpam-4275	77	7	fτ	fτ	ADP
ejpam-4275	77	8	from	from	ADP
ejpam-4275	77	9	c(xς	c(xς	PROPN
ejpam-4275	77	10	)	)	PUNCT
ejpam-4275	77	11	to	to	ADP
ejpam-4275	77	12	c(s∆	c(s∆	PROPN
ejpam-4275	77	13	)	)	PUNCT
ejpam-4275	77	14	is	be	AUX
ejpam-4275	77	15	a	a	DET
ejpam-4275	77	16	pair	pair	NOUN
ejpam-4275	77	17	of	of	ADP
ejpam-4275	77	18	crisp	crisp	ADJ
ejpam-4275	77	19	maps	map	NOUN
ejpam-4275	77	20	f	f	PROPN
ejpam-4275	77	21	and	and	CCONJ
ejpam-4275	77	22	τ	τ	PROPN
ejpam-4275	77	23	,	,	PUNCT
ejpam-4275	77	24	where	where	SCONJ
ejpam-4275	77	25	f	f	X
ejpam-4275	77	26	:	:	PUNCT
ejpam-4275	77	27	x	x	X
ejpam-4275	77	28	→	→	SYM
ejpam-4275	77	29	s	s	PROPN
ejpam-4275	77	30	,	,	PUNCT
ejpam-4275	77	31	τ	τ	PROPN
ejpam-4275	77	32	:	:	PUNCT
ejpam-4275	77	33	σ	σ	PROPN
ejpam-4275	77	34	→	→	PUNCT
ejpam-4275	77	35	∆.	∆.	NOUN
ejpam-4275	77	36	let	let	VERB
ejpam-4275	77	37	(	(	PUNCT
ejpam-4275	77	38	ω	ω	NOUN
ejpam-4275	77	39	,	,	PUNCT
ejpam-4275	77	40	m	m	PROPN
ejpam-4275	77	41	)	)	PUNCT
ejpam-4275	77	42	and	and	CCONJ
ejpam-4275	77	43	(	(	PUNCT
ejpam-4275	77	44	ψ	ψ	X
ejpam-4275	77	45	,	,	PUNCT
ejpam-4275	77	46	n	n	NUM
ejpam-4275	77	47	)	)	PUNCT
ejpam-4275	77	48	be	be	AUX
ejpam-4275	77	49	respectively	respectively	ADV
ejpam-4275	77	50	subsets	subset	NOUN
ejpam-4275	77	51	of	of	ADP
ejpam-4275	77	52	c(xς	c(xς	PROPN
ejpam-4275	77	53	)	)	PUNCT
ejpam-4275	77	54	and	and	CCONJ
ejpam-4275	77	55	c(s∆	c(s∆	PROPN
ejpam-4275	77	56	)	)	PUNCT
ejpam-4275	77	57	.	.	PUNCT
ejpam-4275	78	1	then	then	ADV
ejpam-4275	78	2	the	the	DET
ejpam-4275	78	3	image	image	NOUN
ejpam-4275	78	4	of	of	ADP
ejpam-4275	78	5	(	(	PUNCT
ejpam-4275	78	6	ω	ω	PROPN
ejpam-4275	78	7	,	,	PUNCT
ejpam-4275	78	8	m	m	NOUN
ejpam-4275	78	9	)	)	PUNCT
ejpam-4275	78	10	and	and	CCONJ
ejpam-4275	78	11	pre	pre	ADJ
ejpam-4275	78	12	-	-	NOUN
ejpam-4275	78	13	image	image	NOUN
ejpam-4275	78	14	of	of	ADP
ejpam-4275	78	15	(	(	PUNCT
ejpam-4275	78	16	ψ	ψ	X
ejpam-4275	78	17	,	,	PUNCT
ejpam-4275	78	18	n	n	NUM
ejpam-4275	78	19	)	)	PUNCT
ejpam-4275	78	20	are	be	AUX
ejpam-4275	78	21	given	give	VERB
ejpam-4275	78	22	by	by	ADP
ejpam-4275	78	23	the	the	DET
ejpam-4275	78	24	following	following	NOUN
ejpam-4275	78	25	.	.	PUNCT
ejpam-4275	79	1	(	(	PUNCT
ejpam-4275	79	2	i	i	NOUN
ejpam-4275	79	3	)	)	PUNCT
ejpam-4275	79	4	fτ	fτ	X
ejpam-4275	79	5	(	(	PUNCT
ejpam-4275	79	6	ω	ω	PROPN
ejpam-4275	79	7	,	,	PUNCT
ejpam-4275	79	8	m	m	NOUN
ejpam-4275	79	9	)	)	PUNCT
ejpam-4275	79	10	=	=	SYM
ejpam-4275	79	11	(	(	PUNCT
ejpam-4275	79	12	f(ω),∆	f(ω),∆	NOUN
ejpam-4275	79	13	)	)	PUNCT
ejpam-4275	79	14	is	be	AUX
ejpam-4275	79	15	a	a	DET
ejpam-4275	79	16	soft	soft	ADJ
ejpam-4275	79	17	set	set	NOUN
ejpam-4275	79	18	in	in	ADP
ejpam-4275	79	19	c(v∆	c(v∆	PROPN
ejpam-4275	79	20	)	)	PUNCT
ejpam-4275	79	21	such	such	ADJ
ejpam-4275	79	22	that	that	SCONJ
ejpam-4275	79	23	f(ω)(ω	f(ω)(ω	NOUN
ejpam-4275	79	24	)	)	PUNCT
ejpam-4275	79	25	=	=	PRON
ejpam-4275	79	26	{	{	PUNCT
ejpam-4275	79	27	⋃̃	⋃̃	PROPN
ejpam-4275	79	28	η∈τ−1(ω	η∈τ−1(ω	SYM
ejpam-4275	79	29	)	)	PUNCT
ejpam-4275	79	30	⋂	⋂	PROPN
ejpam-4275	79	31	mf(ω(η	mf(ω(η	NOUN
ejpam-4275	79	32	)	)	PUNCT
ejpam-4275	79	33	)	)	PUNCT
ejpam-4275	79	34	:	:	PUNCT
ejpam-4275	79	35	τ−1(ω	τ−1(ω	X
ejpam-4275	79	36	)	)	PUNCT
ejpam-4275	79	37	̸=	̸=	NOUN
ejpam-4275	79	38	∅	∅	NOUN
ejpam-4275	79	39	∅	∅	NOUN
ejpam-4275	79	40	:	:	PUNCT
ejpam-4275	79	41	τ−1(ω	τ−1(ω	X
ejpam-4275	79	42	)	)	PUNCT
ejpam-4275	80	1	=	=	NOUN
ejpam-4275	80	2	∅	∅	NOUN
ejpam-4275	80	3	for	for	ADP
ejpam-4275	80	4	each	each	DET
ejpam-4275	80	5	ω	ω	NUM
ejpam-4275	80	6	∈	∈	PROPN
ejpam-4275	80	7	∆.	∆.	PROPN
ejpam-4275	80	8	t.m	t.m	PROPN
ejpam-4275	80	9	.	.	PROPN
ejpam-4275	80	10	al	al	PROPN
ejpam-4275	80	11	-	-	PUNCT
ejpam-4275	80	12	shami	shami	PROPN
ejpam-4275	80	13	,	,	PUNCT
ejpam-4275	80	14	h.a	h.a	PROPN
ejpam-4275	80	15	.	.	PROPN
ejpam-4275	80	16	othman	othman	PROPN
ejpam-4275	80	17	/	/	SYM
ejpam-4275	80	18	eur	eur	PROPN
ejpam-4275	80	19	.	.	PUNCT
ejpam-4275	81	1	j.	j.	PROPN
ejpam-4275	81	2	pure	pure	PROPN
ejpam-4275	81	3	appl	appl	PROPN
ejpam-4275	81	4	.	.	PROPN
ejpam-4275	81	5	math	math	PROPN
ejpam-4275	81	6	,	,	PUNCT
ejpam-4275	81	7	15	15	NUM
ejpam-4275	81	8	(	(	PUNCT
ejpam-4275	81	9	1	1	NUM
ejpam-4275	81	10	)	)	PUNCT
ejpam-4275	81	11	(	(	PUNCT
ejpam-4275	81	12	2022	2022	NUM
ejpam-4275	81	13	)	)	PUNCT
ejpam-4275	81	14	,	,	PUNCT
ejpam-4275	81	15	261	261	NUM
ejpam-4275	81	16	-	-	SYM
ejpam-4275	81	17	280	280	NUM
ejpam-4275	81	18	264	264	NUM
ejpam-4275	81	19	(	(	PUNCT
ejpam-4275	81	20	ii	ii	NOUN
ejpam-4275	81	21	)	)	PUNCT
ejpam-4275	81	22	f−1	f−1	PROPN
ejpam-4275	81	23	τ	τ	X
ejpam-4275	81	24	(	(	PUNCT
ejpam-4275	81	25	ψ	ψ	X
ejpam-4275	81	26	,	,	PUNCT
ejpam-4275	81	27	n	n	NOUN
ejpam-4275	81	28	)	)	PUNCT
ejpam-4275	81	29	=	=	SYM
ejpam-4275	81	30	(	(	PUNCT
ejpam-4275	81	31	f−1(ψ),σ	f−1(ψ),σ	NOUN
ejpam-4275	81	32	)	)	PUNCT
ejpam-4275	81	33	is	be	AUX
ejpam-4275	81	34	a	a	DET
ejpam-4275	81	35	soft	soft	ADJ
ejpam-4275	81	36	set	set	NOUN
ejpam-4275	81	37	in	in	ADP
ejpam-4275	81	38	c(xς	c(xς	NOUN
ejpam-4275	81	39	)	)	PUNCT
ejpam-4275	81	40	such	such	ADJ
ejpam-4275	81	41	that	that	DET
ejpam-4275	81	42	f−1(ψ)(η	f−1(ψ)(η	NOUN
ejpam-4275	81	43	)	)	PUNCT
ejpam-4275	82	1	=	=	PRON
ejpam-4275	82	2	{	{	PUNCT
ejpam-4275	82	3	f−1(ψ(τ(η	f−1(ψ(τ(η	VERB
ejpam-4275	82	4	)	)	PUNCT
ejpam-4275	82	5	)	)	PUNCT
ejpam-4275	82	6	)	)	PUNCT
ejpam-4275	82	7	:	:	PUNCT
ejpam-4275	83	1	τ(η	τ(η	X
ejpam-4275	83	2	)	)	PUNCT
ejpam-4275	83	3	∈	∈	NOUN
ejpam-4275	83	4	n	n	NOUN
ejpam-4275	83	5	∅	∅	NOUN
ejpam-4275	83	6	:	:	PUNCT
ejpam-4275	83	7	τ(η	τ(η	PROPN
ejpam-4275	83	8	)	)	PUNCT
ejpam-4275	83	9	̸∈	̸∈	PROPN
ejpam-4275	83	10	n	n	PROPN
ejpam-4275	83	11	for	for	ADP
ejpam-4275	83	12	each	each	DET
ejpam-4275	83	13	η	η	PROPN
ejpam-4275	83	14	∈	∈	PROPN
ejpam-4275	83	15	σ	σ	PROPN
ejpam-4275	83	16	.	.	PUNCT
ejpam-4275	83	17	definition	definition	NOUN
ejpam-4275	83	18	11	11	NUM
ejpam-4275	83	19	.	.	PUNCT
ejpam-4275	84	1	[	[	X
ejpam-4275	84	2	31	31	NUM
ejpam-4275	84	3	]	]	PUNCT
ejpam-4275	84	4	we	we	PRON
ejpam-4275	84	5	call	call	VERB
ejpam-4275	84	6	a	a	DET
ejpam-4275	84	7	soft	soft	ADJ
ejpam-4275	84	8	map	map	NOUN
ejpam-4275	84	9	fτ	fτ	ADP
ejpam-4275	84	10	:	:	PUNCT
ejpam-4275	84	11	c(xς	c(xς	X
ejpam-4275	84	12	)	)	PUNCT
ejpam-4275	84	13	→	→	SYM
ejpam-4275	84	14	c(s∆	c(s∆	PROPN
ejpam-4275	84	15	)	)	PUNCT
ejpam-4275	84	16	injective	injective	ADJ
ejpam-4275	84	17	(	(	PUNCT
ejpam-4275	84	18	resp	resp	NOUN
ejpam-4275	84	19	.	.	PUNCT
ejpam-4275	84	20	,	,	PUNCT
ejpam-4275	84	21	surjective	surjective	ADJ
ejpam-4275	84	22	,	,	PUNCT
ejpam-4275	84	23	bijective	bijective	ADJ
ejpam-4275	84	24	)	)	PUNCT
ejpam-4275	84	25	if	if	SCONJ
ejpam-4275	84	26	f	f	PROPN
ejpam-4275	84	27	and	and	CCONJ
ejpam-4275	84	28	τ	τ	PROPN
ejpam-4275	84	29	are	be	AUX
ejpam-4275	84	30	injective	injective	ADJ
ejpam-4275	84	31	(	(	PUNCT
ejpam-4275	84	32	resp	resp	NOUN
ejpam-4275	84	33	.	.	PUNCT
ejpam-4275	84	34	,	,	PUNCT
ejpam-4275	84	35	surjective	surjective	ADJ
ejpam-4275	84	36	,	,	PUNCT
ejpam-4275	84	37	bijective	bijective	ADJ
ejpam-4275	84	38	)	)	PUNCT
ejpam-4275	84	39	.	.	PUNCT
ejpam-4275	85	1	2.2	2.2	NUM
ejpam-4275	85	2	.	.	PUNCT
ejpam-4275	86	1	infra	infra	NOUN
ejpam-4275	86	2	soft	soft	ADJ
ejpam-4275	86	3	topological	topological	ADJ
ejpam-4275	86	4	spaces	space	NOUN
ejpam-4275	86	5	definition	definition	NOUN
ejpam-4275	86	6	12	12	NUM
ejpam-4275	86	7	.	.	PUNCT
ejpam-4275	87	1	[	[	X
ejpam-4275	87	2	10	10	NUM
ejpam-4275	87	3	]	]	X
ejpam-4275	87	4	a	a	DET
ejpam-4275	87	5	family	family	NOUN
ejpam-4275	87	6	ξ	ξ	X
ejpam-4275	87	7	of	of	ADP
ejpam-4275	87	8	soft	soft	ADJ
ejpam-4275	87	9	sets	set	NOUN
ejpam-4275	87	10	over	over	ADP
ejpam-4275	87	11	x	x	PUNCT
ejpam-4275	87	12	with	with	ADP
ejpam-4275	87	13	σ	σ	NOUN
ejpam-4275	87	14	as	as	SCONJ
ejpam-4275	87	15	a	a	DET
ejpam-4275	87	16	parameters	parameter	NOUN
ejpam-4275	87	17	set	set	VERB
ejpam-4275	87	18	is	be	AUX
ejpam-4275	87	19	said	say	VERB
ejpam-4275	87	20	to	to	PART
ejpam-4275	87	21	be	be	AUX
ejpam-4275	87	22	an	an	DET
ejpam-4275	87	23	infra	infra	NOUN
ejpam-4275	87	24	soft	soft	ADJ
ejpam-4275	87	25	topology	topology	NOUN
ejpam-4275	87	26	on	on	ADP
ejpam-4275	87	27	x	x	PUNCT
ejpam-4275	87	28	if	if	SCONJ
ejpam-4275	87	29	it	it	PRON
ejpam-4275	87	30	is	be	AUX
ejpam-4275	87	31	closed	close	VERB
ejpam-4275	87	32	under	under	ADP
ejpam-4275	87	33	finite	finite	ADJ
ejpam-4275	87	34	intersection	intersection	NOUN
ejpam-4275	87	35	and	and	CCONJ
ejpam-4275	87	36	φ	φ	PROPN
ejpam-4275	87	37	is	be	AUX
ejpam-4275	87	38	a	a	DET
ejpam-4275	87	39	member	member	NOUN
ejpam-4275	87	40	of	of	ADP
ejpam-4275	87	41	ξ	ξ	PROPN
ejpam-4275	87	42	.	.	PUNCT
ejpam-4275	88	1	the	the	PRON
ejpam-4275	88	2	triple	triple	ADJ
ejpam-4275	88	3	(	(	PUNCT
ejpam-4275	88	4	x	x	NOUN
ejpam-4275	88	5	,	,	PUNCT
ejpam-4275	88	6	ξ	ξ	PROPN
ejpam-4275	88	7	,	,	PUNCT
ejpam-4275	88	8	σ	σ	NOUN
ejpam-4275	88	9	)	)	PUNCT
ejpam-4275	88	10	is	be	AUX
ejpam-4275	88	11	called	call	VERB
ejpam-4275	88	12	an	an	DET
ejpam-4275	88	13	infra	infra	NOUN
ejpam-4275	88	14	soft	soft	ADJ
ejpam-4275	88	15	topological	topological	ADJ
ejpam-4275	88	16	space	space	NOUN
ejpam-4275	88	17	(	(	PUNCT
ejpam-4275	88	18	briefly	briefly	ADV
ejpam-4275	88	19	,	,	PUNCT
ejpam-4275	88	20	ists	ist	NOUN
ejpam-4275	88	21	)	)	PUNCT
ejpam-4275	88	22	.	.	PUNCT
ejpam-4275	89	1	we	we	PRON
ejpam-4275	89	2	call	call	VERB
ejpam-4275	89	3	a	a	DET
ejpam-4275	89	4	member	member	NOUN
ejpam-4275	89	5	of	of	ADP
ejpam-4275	89	6	ξ	ξ	PROPN
ejpam-4275	89	7	an	an	DET
ejpam-4275	89	8	infra	infra	NOUN
ejpam-4275	89	9	soft	soft	ADJ
ejpam-4275	89	10	open	open	ADJ
ejpam-4275	89	11	set	set	NOUN
ejpam-4275	89	12	and	and	CCONJ
ejpam-4275	89	13	called	call	VERB
ejpam-4275	89	14	its	its	PRON
ejpam-4275	89	15	complement	complement	NOUN
ejpam-4275	89	16	an	an	DET
ejpam-4275	89	17	infra	infra	NOUN
ejpam-4275	89	18	soft	soft	ADJ
ejpam-4275	89	19	closed	closed	ADJ
ejpam-4275	89	20	set	set	NOUN
ejpam-4275	89	21	.	.	PUNCT
ejpam-4275	90	1	we	we	PRON
ejpam-4275	90	2	call	call	VERB
ejpam-4275	90	3	(	(	PUNCT
ejpam-4275	90	4	x	x	NOUN
ejpam-4275	90	5	,	,	PUNCT
ejpam-4275	90	6	ξ	ξ	PROPN
ejpam-4275	90	7	,	,	PUNCT
ejpam-4275	90	8	σ	σ	NOUN
ejpam-4275	90	9	)	)	PUNCT
ejpam-4275	90	10	stable	stable	ADJ
ejpam-4275	90	11	if	if	SCONJ
ejpam-4275	90	12	all	all	DET
ejpam-4275	90	13	its	its	PRON
ejpam-4275	90	14	infra	infra	NOUN
ejpam-4275	90	15	soft	soft	ADJ
ejpam-4275	90	16	open	open	ADJ
ejpam-4275	90	17	sets	set	NOUN
ejpam-4275	90	18	are	be	AUX
ejpam-4275	90	19	stable	stable	ADJ
ejpam-4275	90	20	.	.	PUNCT
ejpam-4275	91	1	definition	definition	NOUN
ejpam-4275	91	2	13	13	NUM
ejpam-4275	91	3	.	.	PUNCT
ejpam-4275	92	1	[	[	X
ejpam-4275	92	2	10	10	NUM
ejpam-4275	92	3	]	]	X
ejpam-4275	92	4	let	let	VERB
ejpam-4275	92	5	(	(	PUNCT
ejpam-4275	92	6	ω	ω	PROPN
ejpam-4275	92	7	,	,	PUNCT
ejpam-4275	92	8	σ	σ	PROPN
ejpam-4275	92	9	)	)	PUNCT
ejpam-4275	92	10	be	be	VERB
ejpam-4275	92	11	a	a	DET
ejpam-4275	92	12	subset	subset	NOUN
ejpam-4275	92	13	of	of	ADP
ejpam-4275	92	14	(	(	PUNCT
ejpam-4275	92	15	x	x	NOUN
ejpam-4275	92	16	,	,	PUNCT
ejpam-4275	92	17	ξ	ξ	PROPN
ejpam-4275	92	18	,	,	PUNCT
ejpam-4275	92	19	σ	σ	NOUN
ejpam-4275	92	20	)	)	PUNCT
ejpam-4275	92	21	.	.	PUNCT
ejpam-4275	93	1	(	(	PUNCT
ejpam-4275	93	2	i	i	NOUN
ejpam-4275	93	3	)	)	PUNCT
ejpam-4275	93	4	the	the	DET
ejpam-4275	93	5	intersection	intersection	NOUN
ejpam-4275	93	6	of	of	ADP
ejpam-4275	93	7	all	all	DET
ejpam-4275	93	8	infra	infra	NOUN
ejpam-4275	93	9	soft	soft	ADJ
ejpam-4275	93	10	closed	closed	ADJ
ejpam-4275	93	11	subsets	subset	NOUN
ejpam-4275	93	12	of	of	ADP
ejpam-4275	93	13	(	(	PUNCT
ejpam-4275	93	14	x	x	NOUN
ejpam-4275	93	15	,	,	PUNCT
ejpam-4275	93	16	ξ	ξ	PROPN
ejpam-4275	93	17	,	,	PUNCT
ejpam-4275	93	18	σ	σ	PROPN
ejpam-4275	93	19	)	)	PUNCT
ejpam-4275	93	20	which	which	PRON
ejpam-4275	93	21	contains	contain	VERB
ejpam-4275	93	22	a	a	DET
ejpam-4275	93	23	soft	soft	ADJ
ejpam-4275	93	24	set	set	NOUN
ejpam-4275	93	25	(	(	PUNCT
ejpam-4275	93	26	ω	ω	PROPN
ejpam-4275	93	27	,	,	PUNCT
ejpam-4275	93	28	σ	σ	PROPN
ejpam-4275	93	29	)	)	PUNCT
ejpam-4275	93	30	is	be	AUX
ejpam-4275	93	31	called	call	VERB
ejpam-4275	93	32	the	the	DET
ejpam-4275	93	33	infra	infra	NOUN
ejpam-4275	93	34	soft	soft	ADJ
ejpam-4275	93	35	closure	closure	NOUN
ejpam-4275	93	36	points	point	NOUN
ejpam-4275	93	37	of	of	ADP
ejpam-4275	93	38	(	(	PUNCT
ejpam-4275	93	39	ω	ω	PROPN
ejpam-4275	93	40	,	,	PUNCT
ejpam-4275	93	41	σ	σ	PROPN
ejpam-4275	93	42	)	)	PUNCT
ejpam-4275	93	43	.	.	PUNCT
ejpam-4275	94	1	it	it	PRON
ejpam-4275	94	2	is	be	AUX
ejpam-4275	94	3	denoted	denote	VERB
ejpam-4275	94	4	by	by	ADP
ejpam-4275	94	5	cl(ω	cl(ω	X
ejpam-4275	94	6	,	,	PUNCT
ejpam-4275	94	7	σ	σ	PROPN
ejpam-4275	94	8	)	)	PUNCT
ejpam-4275	94	9	.	.	PUNCT
ejpam-4275	95	1	(	(	PUNCT
ejpam-4275	95	2	ii	ii	X
ejpam-4275	95	3	)	)	PUNCT
ejpam-4275	95	4	the	the	DET
ejpam-4275	95	5	union	union	NOUN
ejpam-4275	95	6	of	of	ADP
ejpam-4275	95	7	all	all	DET
ejpam-4275	95	8	infra	infra	NOUN
ejpam-4275	95	9	soft	soft	ADJ
ejpam-4275	95	10	open	open	ADJ
ejpam-4275	95	11	subsets	subset	NOUN
ejpam-4275	95	12	of	of	ADP
ejpam-4275	95	13	(	(	PUNCT
ejpam-4275	95	14	x	x	NOUN
ejpam-4275	95	15	,	,	PUNCT
ejpam-4275	95	16	ξ	ξ	PROPN
ejpam-4275	95	17	,	,	PUNCT
ejpam-4275	95	18	σ	σ	PROPN
ejpam-4275	95	19	)	)	PUNCT
ejpam-4275	95	20	which	which	PRON
ejpam-4275	95	21	are	be	AUX
ejpam-4275	95	22	contained	contain	VERB
ejpam-4275	95	23	in	in	ADP
ejpam-4275	95	24	a	a	DET
ejpam-4275	95	25	soft	soft	ADJ
ejpam-4275	95	26	set	set	NOUN
ejpam-4275	95	27	(	(	PUNCT
ejpam-4275	95	28	ω	ω	PROPN
ejpam-4275	95	29	,	,	PUNCT
ejpam-4275	95	30	σ	σ	PROPN
ejpam-4275	95	31	)	)	PUNCT
ejpam-4275	95	32	is	be	AUX
ejpam-4275	95	33	called	call	VERB
ejpam-4275	95	34	the	the	DET
ejpam-4275	95	35	infra	infra	NOUN
ejpam-4275	95	36	soft	soft	ADJ
ejpam-4275	95	37	interior	interior	ADJ
ejpam-4275	95	38	points	point	NOUN
ejpam-4275	95	39	of	of	ADP
ejpam-4275	95	40	(	(	PUNCT
ejpam-4275	95	41	ω	ω	PROPN
ejpam-4275	95	42	,	,	PUNCT
ejpam-4275	95	43	σ	σ	PROPN
ejpam-4275	95	44	)	)	PUNCT
ejpam-4275	95	45	.	.	PUNCT
ejpam-4275	96	1	it	it	PRON
ejpam-4275	96	2	is	be	AUX
ejpam-4275	96	3	denoted	denote	VERB
ejpam-4275	96	4	by	by	ADP
ejpam-4275	96	5	int(ω	int(ω	NOUN
ejpam-4275	96	6	,	,	PUNCT
ejpam-4275	96	7	σ	σ	NOUN
ejpam-4275	96	8	)	)	PUNCT
ejpam-4275	96	9	.	.	PUNCT
ejpam-4275	97	1	it	it	PRON
ejpam-4275	97	2	was	be	AUX
ejpam-4275	97	3	showed	show	VERB
ejpam-4275	97	4	in	in	ADP
ejpam-4275	97	5	[	[	X
ejpam-4275	97	6	10	10	NUM
ejpam-4275	97	7	]	]	PUNCT
ejpam-4275	97	8	that	that	SCONJ
ejpam-4275	97	9	cl(ω	cl(ω	X
ejpam-4275	97	10	,	,	PUNCT
ejpam-4275	97	11	σ	σ	NOUN
ejpam-4275	97	12	)	)	PUNCT
ejpam-4275	97	13	and	and	CCONJ
ejpam-4275	97	14	int(ω	int(ω	PROPN
ejpam-4275	97	15	,	,	PUNCT
ejpam-4275	97	16	σ	σ	NOUN
ejpam-4275	97	17	)	)	PUNCT
ejpam-4275	97	18	need	need	AUX
ejpam-4275	97	19	not	not	PART
ejpam-4275	97	20	be	be	AUX
ejpam-4275	97	21	infra	infra	NOUN
ejpam-4275	97	22	soft	soft	ADJ
ejpam-4275	97	23	closed	closed	ADJ
ejpam-4275	97	24	and	and	CCONJ
ejpam-4275	97	25	infra	infra	VERB
ejpam-4275	97	26	soft	soft	ADJ
ejpam-4275	97	27	open	open	ADJ
ejpam-4275	97	28	,	,	PUNCT
ejpam-4275	97	29	respectively	respectively	ADV
ejpam-4275	97	30	.	.	PUNCT
ejpam-4275	98	1	through	through	ADP
ejpam-4275	98	2	this	this	DET
ejpam-4275	98	3	paper	paper	NOUN
ejpam-4275	98	4	,	,	PUNCT
ejpam-4275	98	5	(	(	PUNCT
ejpam-4275	98	6	ω	ω	PROPN
ejpam-4275	98	7	,	,	PUNCT
ejpam-4275	98	8	σ	σ	PROPN
ejpam-4275	98	9	)	)	PUNCT
ejpam-4275	98	10	is	be	AUX
ejpam-4275	98	11	called	call	VERB
ejpam-4275	98	12	ξ	ξ	NOUN
ejpam-4275	98	13	-	-	ADJ
ejpam-4275	98	14	infra	infra	ADJ
ejpam-4275	98	15	soft	soft	ADJ
ejpam-4275	98	16	open	open	ADJ
ejpam-4275	98	17	(	(	PUNCT
ejpam-4275	98	18	resp	resp	NOUN
ejpam-4275	98	19	.	.	PUNCT
ejpam-4275	98	20	,	,	PUNCT
ejpam-4275	98	21	ξ	ξ	X
ejpam-4275	98	22	-	-	ADJ
ejpam-4275	98	23	infra	infra	ADJ
ejpam-4275	98	24	soft	soft	ADJ
ejpam-4275	98	25	closed	closed	ADJ
ejpam-4275	98	26	)	)	PUNCT
ejpam-4275	99	1	if	if	SCONJ
ejpam-4275	99	2	int(ω	int(ω	NOUN
ejpam-4275	99	3	,	,	PUNCT
ejpam-4275	99	4	σ	σ	NOUN
ejpam-4275	99	5	)	)	PUNCT
ejpam-4275	99	6	=	=	SYM
ejpam-4275	99	7	(	(	PUNCT
ejpam-4275	99	8	ω	ω	PROPN
ejpam-4275	99	9	,	,	PUNCT
ejpam-4275	99	10	σ	σ	PROPN
ejpam-4275	99	11	)	)	PUNCT
ejpam-4275	99	12	(	(	PUNCT
ejpam-4275	99	13	resp	resp	NOUN
ejpam-4275	99	14	.	.	PUNCT
ejpam-4275	99	15	,	,	PUNCT
ejpam-4275	99	16	cl(ω	cl(ω	X
ejpam-4275	99	17	,	,	PUNCT
ejpam-4275	99	18	σ	σ	NOUN
ejpam-4275	99	19	)	)	PUNCT
ejpam-4275	99	20	)	)	PUNCT
ejpam-4275	99	21	=	=	SYM
ejpam-4275	99	22	(	(	PUNCT
ejpam-4275	99	23	ω	ω	PROPN
ejpam-4275	99	24	,	,	PUNCT
ejpam-4275	99	25	σ	σ	PROPN
ejpam-4275	99	26	)	)	PUNCT
ejpam-4275	99	27	.	.	PUNCT
ejpam-4275	100	1	proposition	proposition	NOUN
ejpam-4275	100	2	1	1	NUM
ejpam-4275	100	3	.	.	PUNCT
ejpam-4275	101	1	[	[	X
ejpam-4275	101	2	10	10	NUM
ejpam-4275	101	3	]	]	X
ejpam-4275	101	4	let	let	VERB
ejpam-4275	101	5	(	(	PUNCT
ejpam-4275	101	6	ω	ω	PROPN
ejpam-4275	101	7	,	,	PUNCT
ejpam-4275	101	8	σ	σ	PROPN
ejpam-4275	101	9	)	)	PUNCT
ejpam-4275	101	10	and	and	CCONJ
ejpam-4275	101	11	(	(	PUNCT
ejpam-4275	101	12	ψ	ψ	X
ejpam-4275	101	13	,	,	PUNCT
ejpam-4275	101	14	σ	σ	NOUN
ejpam-4275	101	15	)	)	PUNCT
ejpam-4275	101	16	subsets	subset	NOUN
ejpam-4275	101	17	of	of	ADP
ejpam-4275	101	18	an	an	DET
ejpam-4275	101	19	ists	ist	NOUN
ejpam-4275	101	20	(	(	PUNCT
ejpam-4275	101	21	x	x	X
ejpam-4275	101	22	,	,	PUNCT
ejpam-4275	101	23	ξ	ξ	PROPN
ejpam-4275	101	24	,	,	PUNCT
ejpam-4275	101	25	σ	σ	NOUN
ejpam-4275	101	26	)	)	PUNCT
ejpam-4275	101	27	.	.	PUNCT
ejpam-4275	102	1	then	then	ADV
ejpam-4275	102	2	(	(	PUNCT
ejpam-4275	102	3	i	i	NOUN
ejpam-4275	102	4	)	)	PUNCT
ejpam-4275	102	5	cl[(ω	cl[(ω	PROPN
ejpam-4275	102	6	,	,	PUNCT
ejpam-4275	102	7	σ	σ	PROPN
ejpam-4275	102	8	)	)	PUNCT
ejpam-4275	102	9	⋃̃	⋃̃	PROPN
ejpam-4275	102	10	(	(	PUNCT
ejpam-4275	102	11	ψ	ψ	X
ejpam-4275	102	12	,	,	PUNCT
ejpam-4275	102	13	σ	σ	PROPN
ejpam-4275	102	14	)	)	PUNCT
ejpam-4275	102	15	]	]	PUNCT
ejpam-4275	103	1	=	=	X
ejpam-4275	103	2	cl(ω	cl(ω	X
ejpam-4275	103	3	,	,	PUNCT
ejpam-4275	103	4	σ	σ	PROPN
ejpam-4275	103	5	)	)	PUNCT
ejpam-4275	103	6	⋃̃	⋃̃	PROPN
ejpam-4275	103	7	cl(ψ	cl(ψ	NUM
ejpam-4275	103	8	,	,	PUNCT
ejpam-4275	103	9	σ	σ	PROPN
ejpam-4275	103	10	)	)	PUNCT
ejpam-4275	103	11	,	,	PUNCT
ejpam-4275	103	12	and	and	CCONJ
ejpam-4275	103	13	(	(	PUNCT
ejpam-4275	103	14	ii	ii	NOUN
ejpam-4275	103	15	)	)	PUNCT
ejpam-4275	103	16	int[(ω	int[(ω	PROPN
ejpam-4275	103	17	,	,	PUNCT
ejpam-4275	103	18	σ	σ	PROPN
ejpam-4275	103	19	)	)	PUNCT
ejpam-4275	103	20	⋂̃	⋂̃	NOUN
ejpam-4275	103	21	(	(	PUNCT
ejpam-4275	103	22	ψ	ψ	X
ejpam-4275	103	23	,	,	PUNCT
ejpam-4275	103	24	σ	σ	PROPN
ejpam-4275	103	25	)	)	PUNCT
ejpam-4275	103	26	]	]	PUNCT
ejpam-4275	103	27	=	=	SYM
ejpam-4275	103	28	int(ω	int(ω	PROPN
ejpam-4275	103	29	,	,	PUNCT
ejpam-4275	103	30	σ	σ	NOUN
ejpam-4275	103	31	)	)	PUNCT
ejpam-4275	103	32	⋂̃	⋂̃	NOUN
ejpam-4275	103	33	int(ψ	int(ψ	NOUN
ejpam-4275	103	34	,	,	PUNCT
ejpam-4275	103	35	σ	σ	PROPN
ejpam-4275	103	36	)	)	PUNCT
ejpam-4275	103	37	.	.	PUNCT
ejpam-4275	104	1	proposition	proposition	NOUN
ejpam-4275	104	2	2	2	NUM
ejpam-4275	104	3	.	.	PUNCT
ejpam-4275	105	1	[	[	X
ejpam-4275	105	2	10	10	NUM
ejpam-4275	105	3	]	]	X
ejpam-4275	105	4	let	let	VERB
ejpam-4275	105	5	(	(	PUNCT
ejpam-4275	105	6	ω	ω	PROPN
ejpam-4275	105	7	,	,	PUNCT
ejpam-4275	105	8	σ	σ	PROPN
ejpam-4275	105	9	)	)	PUNCT
ejpam-4275	105	10	be	be	VERB
ejpam-4275	105	11	an	an	DET
ejpam-4275	105	12	infra	infra	NOUN
ejpam-4275	105	13	soft	soft	ADJ
ejpam-4275	105	14	open	open	ADJ
ejpam-4275	105	15	set	set	NOUN
ejpam-4275	105	16	.	.	PUNCT
ejpam-4275	106	1	then	then	ADV
ejpam-4275	106	2	(	(	PUNCT
ejpam-4275	106	3	ω	ω	PROPN
ejpam-4275	106	4	,	,	PUNCT
ejpam-4275	106	5	σ	σ	PROPN
ejpam-4275	106	6	)	)	PUNCT
ejpam-4275	106	7	⋂̃	⋂̃	NOUN
ejpam-4275	106	8	cl(ψ	cl(ψ	NOUN
ejpam-4275	106	9	,	,	PUNCT
ejpam-4275	106	10	σ)⊆̃cl[(ω	σ)⊆̃cl[(ω	PROPN
ejpam-4275	106	11	,	,	PUNCT
ejpam-4275	106	12	σ	σ	PROPN
ejpam-4275	106	13	)	)	PUNCT
ejpam-4275	106	14	⋃̃	⋃̃	PROPN
ejpam-4275	106	15	(	(	PUNCT
ejpam-4275	106	16	ψ	ψ	X
ejpam-4275	106	17	,	,	PUNCT
ejpam-4275	106	18	σ	σ	PROPN
ejpam-4275	106	19	)	)	PUNCT
ejpam-4275	106	20	]	]	PUNCT
ejpam-4275	106	21	for	for	ADP
ejpam-4275	106	22	any	any	DET
ejpam-4275	106	23	subset	subset	NOUN
ejpam-4275	106	24	(	(	PUNCT
ejpam-4275	106	25	ψ	ψ	X
ejpam-4275	106	26	,	,	PUNCT
ejpam-4275	106	27	σ	σ	NOUN
ejpam-4275	106	28	)	)	PUNCT
ejpam-4275	106	29	of	of	ADP
ejpam-4275	106	30	(	(	PUNCT
ejpam-4275	106	31	x	x	NOUN
ejpam-4275	106	32	,	,	PUNCT
ejpam-4275	106	33	ξ	ξ	PROPN
ejpam-4275	106	34	,	,	PUNCT
ejpam-4275	106	35	σ	σ	NOUN
ejpam-4275	106	36	)	)	PUNCT
ejpam-4275	106	37	.	.	PUNCT
ejpam-4275	107	1	proposition	proposition	NOUN
ejpam-4275	107	2	3	3	NUM
ejpam-4275	107	3	.	.	PUNCT
ejpam-4275	108	1	[	[	X
ejpam-4275	108	2	10	10	NUM
ejpam-4275	108	3	]	]	X
ejpam-4275	108	4	let	let	VERB
ejpam-4275	108	5	(	(	PUNCT
ejpam-4275	108	6	ω	ω	PROPN
ejpam-4275	108	7	,	,	PUNCT
ejpam-4275	108	8	σ	σ	PROPN
ejpam-4275	108	9	)	)	PUNCT
ejpam-4275	108	10	be	be	VERB
ejpam-4275	108	11	an	an	DET
ejpam-4275	108	12	infra	infra	NOUN
ejpam-4275	108	13	soft	soft	ADJ
ejpam-4275	108	14	closed	closed	ADJ
ejpam-4275	108	15	set	set	NOUN
ejpam-4275	108	16	.	.	PUNCT
ejpam-4275	109	1	then	then	ADV
ejpam-4275	109	2	int[(ω	int[(ω	PROPN
ejpam-4275	109	3	,	,	PUNCT
ejpam-4275	109	4	σ	σ	PROPN
ejpam-4275	109	5	)	)	PUNCT
ejpam-4275	109	6	⋃̃	⋃̃	PROPN
ejpam-4275	109	7	(	(	PUNCT
ejpam-4275	109	8	ψ	ψ	NOUN
ejpam-4275	109	9	,	,	PUNCT
ejpam-4275	109	10	σ)]⊆̃(ω	σ)]⊆̃(ω	NOUN
ejpam-4275	109	11	,	,	PUNCT
ejpam-4275	109	12	σ	σ	PROPN
ejpam-4275	109	13	)	)	PUNCT
ejpam-4275	109	14	⋃̃	⋃̃	PROPN
ejpam-4275	109	15	int(ψ	int(ψ	PROPN
ejpam-4275	109	16	,	,	PUNCT
ejpam-4275	109	17	σ	σ	PROPN
ejpam-4275	109	18	)	)	PUNCT
ejpam-4275	109	19	for	for	ADP
ejpam-4275	109	20	any	any	DET
ejpam-4275	109	21	subset	subset	NOUN
ejpam-4275	109	22	(	(	PUNCT
ejpam-4275	109	23	ω	ω	PROPN
ejpam-4275	109	24	,	,	PUNCT
ejpam-4275	109	25	σ	σ	PROPN
ejpam-4275	109	26	)	)	PUNCT
ejpam-4275	109	27	of	of	ADP
ejpam-4275	109	28	(	(	PUNCT
ejpam-4275	109	29	x	x	NOUN
ejpam-4275	109	30	,	,	PUNCT
ejpam-4275	109	31	ξ	ξ	PROPN
ejpam-4275	109	32	,	,	PUNCT
ejpam-4275	109	33	σ	σ	NOUN
ejpam-4275	109	34	)	)	PUNCT
ejpam-4275	109	35	.	.	PUNCT
ejpam-4275	110	1	definition	definition	NOUN
ejpam-4275	110	2	14	14	NUM
ejpam-4275	110	3	.	.	PUNCT
ejpam-4275	111	1	a	a	DET
ejpam-4275	111	2	soft	soft	ADJ
ejpam-4275	111	3	map	map	NOUN
ejpam-4275	111	4	fτ	fτ	ADP
ejpam-4275	111	5	:	:	PUNCT
ejpam-4275	111	6	(	(	PUNCT
ejpam-4275	111	7	x	x	X
ejpam-4275	111	8	,	,	PUNCT
ejpam-4275	111	9	ξ	ξ	PROPN
ejpam-4275	111	10	,	,	PUNCT
ejpam-4275	111	11	σ	σ	NOUN
ejpam-4275	111	12	)	)	PUNCT
ejpam-4275	111	13	→	→	SYM
ejpam-4275	111	14	(	(	PUNCT
ejpam-4275	111	15	s	s	PROPN
ejpam-4275	111	16	,	,	PUNCT
ejpam-4275	111	17	π,∆	π,∆	NUM
ejpam-4275	111	18	)	)	PUNCT
ejpam-4275	111	19	is	be	AUX
ejpam-4275	111	20	said	say	VERB
ejpam-4275	111	21	to	to	PART
ejpam-4275	111	22	be	be	AUX
ejpam-4275	111	23	an	an	DET
ejpam-4275	111	24	infra	infra	NOUN
ejpam-4275	111	25	soft	soft	ADJ
ejpam-4275	111	26	homeomorphism	homeomorphism	NOUN
ejpam-4275	111	27	if	if	SCONJ
ejpam-4275	111	28	it	it	PRON
ejpam-4275	111	29	is	be	AUX
ejpam-4275	111	30	bijective	bijective	ADJ
ejpam-4275	111	31	,	,	PUNCT
ejpam-4275	111	32	infra	infra	NOUN
ejpam-4275	111	33	soft	soft	ADJ
ejpam-4275	111	34	continuous	continuous	ADJ
ejpam-4275	111	35	(	(	PUNCT
ejpam-4275	111	36	i.e	i.e	PROPN
ejpam-4275	111	37	,	,	PUNCT
ejpam-4275	111	38	the	the	DET
ejpam-4275	111	39	image	image	NOUN
ejpam-4275	111	40	of	of	ADP
ejpam-4275	111	41	every	every	DET
ejpam-4275	111	42	infra	infra	NOUN
ejpam-4275	111	43	soft	soft	ADJ
ejpam-4275	111	44	open	open	ADJ
ejpam-4275	111	45	set	set	NOUN
ejpam-4275	111	46	is	be	AUX
ejpam-4275	111	47	infra	infra	NOUN
ejpam-4275	111	48	soft	soft	ADJ
ejpam-4275	111	49	open	open	NOUN
ejpam-4275	111	50	)	)	PUNCT
ejpam-4275	111	51	,	,	PUNCT
ejpam-4275	111	52	and	and	CCONJ
ejpam-4275	111	53	infra	infra	VERB
ejpam-4275	111	54	soft	soft	ADJ
ejpam-4275	111	55	open	open	ADJ
ejpam-4275	111	56	(	(	PUNCT
ejpam-4275	111	57	i.e	i.e	NOUN
ejpam-4275	111	58	,	,	PUNCT
ejpam-4275	111	59	the	the	DET
ejpam-4275	111	60	image	image	NOUN
ejpam-4275	111	61	of	of	ADP
ejpam-4275	111	62	every	every	DET
ejpam-4275	111	63	infra	infra	NOUN
ejpam-4275	111	64	soft	soft	ADJ
ejpam-4275	111	65	open	open	ADJ
ejpam-4275	111	66	set	set	NOUN
ejpam-4275	111	67	is	be	AUX
ejpam-4275	111	68	infra	infra	NOUN
ejpam-4275	111	69	soft	soft	ADJ
ejpam-4275	111	70	open	open	NOUN
ejpam-4275	111	71	)	)	PUNCT
ejpam-4275	111	72	.	.	PUNCT
ejpam-4275	112	1	t.m	t.m	PROPN
ejpam-4275	112	2	.	.	PUNCT
ejpam-4275	112	3	al	al	PROPN
ejpam-4275	112	4	-	-	PUNCT
ejpam-4275	112	5	shami	shami	PROPN
ejpam-4275	112	6	,	,	PUNCT
ejpam-4275	112	7	h.a	h.a	PROPN
ejpam-4275	112	8	.	.	PROPN
ejpam-4275	112	9	othman	othman	PROPN
ejpam-4275	112	10	/	/	SYM
ejpam-4275	112	11	eur	eur	PROPN
ejpam-4275	112	12	.	.	PUNCT
ejpam-4275	113	1	j.	j.	PROPN
ejpam-4275	113	2	pure	pure	PROPN
ejpam-4275	113	3	appl	appl	PROPN
ejpam-4275	113	4	.	.	PROPN
ejpam-4275	113	5	math	math	PROPN
ejpam-4275	113	6	,	,	PUNCT
ejpam-4275	113	7	15	15	NUM
ejpam-4275	113	8	(	(	PUNCT
ejpam-4275	113	9	1	1	NUM
ejpam-4275	113	10	)	)	PUNCT
ejpam-4275	113	11	(	(	PUNCT
ejpam-4275	113	12	2022	2022	NUM
ejpam-4275	113	13	)	)	PUNCT
ejpam-4275	113	14	,	,	PUNCT
ejpam-4275	113	15	261	261	NUM
ejpam-4275	113	16	-	-	SYM
ejpam-4275	113	17	280	280	NUM
ejpam-4275	113	18	265	265	NUM
ejpam-4275	113	19	we	we	PRON
ejpam-4275	113	20	call	call	VERB
ejpam-4275	113	21	a	a	DET
ejpam-4275	113	22	property	property	NOUN
ejpam-4275	113	23	which	which	PRON
ejpam-4275	113	24	is	be	AUX
ejpam-4275	113	25	kept	keep	VERB
ejpam-4275	113	26	by	by	ADP
ejpam-4275	113	27	any	any	DET
ejpam-4275	113	28	infra	infra	NOUN
ejpam-4275	113	29	soft	soft	ADJ
ejpam-4275	113	30	homeomorphism	homeomorphism	NOUN
ejpam-4275	113	31	an	an	DET
ejpam-4275	113	32	infra	infra	NOUN
ejpam-4275	113	33	soft	soft	ADJ
ejpam-4275	113	34	topological	topological	ADJ
ejpam-4275	113	35	property	property	NOUN
ejpam-4275	113	36	(	(	PUNCT
ejpam-4275	113	37	in	in	ADP
ejpam-4275	113	38	short	short	ADJ
ejpam-4275	113	39	,	,	PUNCT
ejpam-4275	113	40	ist	ist	NOUN
ejpam-4275	113	41	property	property	NOUN
ejpam-4275	113	42	)	)	PUNCT
ejpam-4275	113	43	.	.	PUNCT
ejpam-4275	114	1	definition	definition	NOUN
ejpam-4275	114	2	15	15	NUM
ejpam-4275	114	3	.	.	PUNCT
ejpam-4275	115	1	[	[	X
ejpam-4275	115	2	10	10	NUM
ejpam-4275	115	3	]	]	PUNCT
ejpam-4275	115	4	let	let	VERB
ejpam-4275	115	5	eτ	eτ	NOUN
ejpam-4275	115	6	:	:	PUNCT
ejpam-4275	115	7	(	(	PUNCT
ejpam-4275	115	8	x	x	X
ejpam-4275	115	9	,	,	PUNCT
ejpam-4275	115	10	ξ	ξ	PROPN
ejpam-4275	115	11	,	,	PUNCT
ejpam-4275	115	12	σ	σ	NOUN
ejpam-4275	115	13	)	)	PUNCT
ejpam-4275	115	14	→	→	SYM
ejpam-4275	115	15	(	(	PUNCT
ejpam-4275	115	16	s	s	PROPN
ejpam-4275	115	17	,	,	PUNCT
ejpam-4275	115	18	π,∆	π,∆	NUM
ejpam-4275	115	19	)	)	PUNCT
ejpam-4275	115	20	be	be	AUX
ejpam-4275	115	21	a	a	DET
ejpam-4275	115	22	soft	soft	ADJ
ejpam-4275	115	23	map	map	NOUN
ejpam-4275	115	24	and	and	CCONJ
ejpam-4275	115	25	m	m	PROPN
ejpam-4275	115	26	̸=	̸=	PROPN
ejpam-4275	115	27	∅	∅	NOUN
ejpam-4275	115	28	be	be	AUX
ejpam-4275	115	29	a	a	DET
ejpam-4275	115	30	subset	subset	NOUN
ejpam-4275	115	31	of	of	ADP
ejpam-4275	115	32	x.	x.	NOUN
ejpam-4275	115	33	a	a	DET
ejpam-4275	115	34	soft	soft	ADJ
ejpam-4275	115	35	map	map	NOUN
ejpam-4275	115	36	eτ|m	eτ|m	PROPN
ejpam-4275	115	37	:	:	PUNCT
ejpam-4275	115	38	(	(	PUNCT
ejpam-4275	115	39	m	m	PROPN
ejpam-4275	115	40	,	,	PUNCT
ejpam-4275	115	41	ξm	ξm	PROPN
ejpam-4275	115	42	,	,	PUNCT
ejpam-4275	115	43	σ	σ	PROPN
ejpam-4275	115	44	)	)	PUNCT
ejpam-4275	115	45	→	→	SYM
ejpam-4275	115	46	(	(	PUNCT
ejpam-4275	115	47	s	s	PROPN
ejpam-4275	115	48	,	,	PUNCT
ejpam-4275	115	49	π,∆	π,∆	NUM
ejpam-4275	115	50	)	)	PUNCT
ejpam-4275	115	51	which	which	PRON
ejpam-4275	115	52	given	give	VERB
ejpam-4275	115	53	by	by	ADP
ejpam-4275	115	54	eτ|m(δmη	eτ|m(δmη	PROPN
ejpam-4275	115	55	)	)	PUNCT
ejpam-4275	116	1	=	=	SYM
ejpam-4275	116	2	eτ	eτ	PROPN
ejpam-4275	116	3	(	(	PUNCT
ejpam-4275	116	4	δ	δ	PROPN
ejpam-4275	116	5	m	m	PROPN
ejpam-4275	116	6	η	η	PROPN
ejpam-4275	116	7	)	)	PUNCT
ejpam-4275	116	8	for	for	ADP
ejpam-4275	116	9	every	every	DET
ejpam-4275	116	10	δmη	δmη	PROPN
ejpam-4275	116	11	∈	∈	PROPN
ejpam-4275	116	12	m̃	m̃	PROPN
ejpam-4275	116	13	is	be	AUX
ejpam-4275	116	14	called	call	VERB
ejpam-4275	116	15	a	a	DET
ejpam-4275	116	16	restriction	restriction	NOUN
ejpam-4275	116	17	soft	soft	ADJ
ejpam-4275	116	18	map	map	NOUN
ejpam-4275	116	19	of	of	ADP
ejpam-4275	116	20	eτ	eτ	NOUN
ejpam-4275	116	21	on	on	ADP
ejpam-4275	116	22	m.	m.	NOUN
ejpam-4275	116	23	proposition	proposition	NOUN
ejpam-4275	116	24	4	4	NUM
ejpam-4275	116	25	.	.	PUNCT
ejpam-4275	117	1	let	let	VERB
ejpam-4275	117	2	{	{	PUNCT
ejpam-4275	117	3	(	(	PUNCT
ejpam-4275	117	4	xk	xk	INTJ
ejpam-4275	117	5	,	,	PUNCT
ejpam-4275	117	6	ξk	ξk	ADV
ejpam-4275	117	7	,	,	PUNCT
ejpam-4275	117	8	σk	σk	PROPN
ejpam-4275	117	9	)	)	PUNCT
ejpam-4275	117	10	:	:	PUNCT
ejpam-4275	118	1	k	k	PROPN
ejpam-4275	118	2	∈	∈	PROPN
ejpam-4275	118	3	k	k	AUX
ejpam-4275	118	4	}	}	PUNCT
ejpam-4275	118	5	be	be	VERB
ejpam-4275	118	6	a	a	DET
ejpam-4275	118	7	family	family	NOUN
ejpam-4275	118	8	of	of	ADP
ejpam-4275	118	9	istss	istss	NOUN
ejpam-4275	118	10	.	.	PUNCT
ejpam-4275	119	1	then	then	ADV
ejpam-4275	119	2	ξ	ξ	X
ejpam-4275	119	3	=	=	SYM
ejpam-4275	119	4	{	{	PUNCT
ejpam-4275	119	5	∏	∏	PROPN
ejpam-4275	119	6	k∈k(ηk	k∈k(ηk	PROPN
ejpam-4275	119	7	,	,	PUNCT
ejpam-4275	119	8	σk	σk	NOUN
ejpam-4275	119	9	)	)	PUNCT
ejpam-4275	119	10	:	:	PUNCT
ejpam-4275	119	11	(	(	PUNCT
ejpam-4275	119	12	ηk	ηk	X
ejpam-4275	119	13	,	,	PUNCT
ejpam-4275	119	14	σk	σk	NOUN
ejpam-4275	119	15	)	)	PUNCT
ejpam-4275	119	16	∈	∈	PROPN
ejpam-4275	119	17	τk	τk	AUX
ejpam-4275	119	18	}	}	PUNCT
ejpam-4275	119	19	is	be	AUX
ejpam-4275	119	20	an	an	DET
ejpam-4275	119	21	infra	infra	NOUN
ejpam-4275	119	22	soft	soft	ADJ
ejpam-4275	119	23	topology	topology	NOUN
ejpam-4275	119	24	on	on	ADP
ejpam-4275	119	25	t	t	PROPN
ejpam-4275	119	26	=	=	SYM
ejpam-4275	119	27	∏	∏	PROPN
ejpam-4275	119	28	k∈k	k∈k	X
ejpam-4275	119	29	xk	xk	PROPN
ejpam-4275	119	30	under	under	ADP
ejpam-4275	119	31	a	a	DET
ejpam-4275	119	32	set	set	NOUN
ejpam-4275	119	33	of	of	ADP
ejpam-4275	119	34	parameters	parameter	NOUN
ejpam-4275	120	1	b	b	NOUN
ejpam-4275	120	2	=	=	SYM
ejpam-4275	120	3	∏	∏	PROPN
ejpam-4275	120	4	k∈k	k∈k	NOUN
ejpam-4275	120	5	σk	σk	NOUN
ejpam-4275	120	6	.	.	PUNCT
ejpam-4275	121	1	we	we	PRON
ejpam-4275	121	2	call	call	VERB
ejpam-4275	121	3	ξ	ξ	ADV
ejpam-4275	121	4	given	give	VERB
ejpam-4275	121	5	in	in	ADP
ejpam-4275	121	6	proposition	proposition	NOUN
ejpam-4275	121	7	above	above	ADV
ejpam-4275	121	8	,	,	PUNCT
ejpam-4275	121	9	a	a	DET
ejpam-4275	121	10	product	product	NOUN
ejpam-4275	121	11	of	of	ADP
ejpam-4275	121	12	infra	infra	NOUN
ejpam-4275	121	13	soft	soft	ADJ
ejpam-4275	121	14	topologies	topology	NOUN
ejpam-4275	121	15	,	,	PUNCT
ejpam-4275	121	16	and	and	CCONJ
ejpam-4275	121	17	(	(	PUNCT
ejpam-4275	121	18	t	t	PROPN
ejpam-4275	121	19	,	,	PUNCT
ejpam-4275	121	20	ξ	ξ	PROPN
ejpam-4275	121	21	,	,	PUNCT
ejpam-4275	121	22	b	b	NOUN
ejpam-4275	121	23	)	)	PUNCT
ejpam-4275	121	24	a	a	DET
ejpam-4275	121	25	product	product	NOUN
ejpam-4275	121	26	of	of	ADP
ejpam-4275	121	27	infra	infra	NOUN
ejpam-4275	121	28	soft	soft	ADJ
ejpam-4275	121	29	spaces	space	NOUN
ejpam-4275	121	30	.	.	PUNCT
ejpam-4275	122	1	3	3	X
ejpam-4275	122	2	.	.	X
ejpam-4275	122	3	main	main	ADJ
ejpam-4275	122	4	properties	property	NOUN
ejpam-4275	122	5	of	of	ADP
ejpam-4275	122	6	infra	infra	NOUN
ejpam-4275	122	7	soft	soft	ADJ
ejpam-4275	122	8	pre	pre	ADJ
ejpam-4275	122	9	-	-	ADJ
ejpam-4275	122	10	open	open	ADJ
ejpam-4275	122	11	sets	set	NOUN
ejpam-4275	122	12	in	in	ADP
ejpam-4275	122	13	this	this	DET
ejpam-4275	122	14	section	section	NOUN
ejpam-4275	122	15	,	,	PUNCT
ejpam-4275	122	16	we	we	PRON
ejpam-4275	122	17	define	define	VERB
ejpam-4275	122	18	infra	infra	NOUN
ejpam-4275	122	19	soft	soft	ADJ
ejpam-4275	122	20	pre	pre	ADJ
ejpam-4275	122	21	-	-	ADJ
ejpam-4275	122	22	open	open	ADJ
ejpam-4275	122	23	and	and	CCONJ
ejpam-4275	122	24	infra	infra	VERB
ejpam-4275	122	25	soft	soft	ADJ
ejpam-4275	122	26	pre	pre	ADJ
ejpam-4275	122	27	-	-	ADJ
ejpam-4275	122	28	closed	closed	ADJ
ejpam-4275	122	29	sets	set	NOUN
ejpam-4275	122	30	which	which	PRON
ejpam-4275	122	31	are	be	AUX
ejpam-4275	122	32	the	the	DET
ejpam-4275	122	33	core	core	ADJ
ejpam-4275	122	34	concepts	concept	NOUN
ejpam-4275	122	35	of	of	ADP
ejpam-4275	122	36	this	this	DET
ejpam-4275	122	37	article	article	NOUN
ejpam-4275	122	38	.	.	PUNCT
ejpam-4275	123	1	we	we	PRON
ejpam-4275	123	2	characterize	characterize	VERB
ejpam-4275	123	3	them	they	PRON
ejpam-4275	123	4	and	and	CCONJ
ejpam-4275	123	5	investigate	investigate	VERB
ejpam-4275	123	6	some	some	PRON
ejpam-4275	123	7	of	of	ADP
ejpam-4275	123	8	their	their	PRON
ejpam-4275	123	9	properties	property	NOUN
ejpam-4275	123	10	.	.	PUNCT
ejpam-4275	124	1	we	we	PRON
ejpam-4275	124	2	show	show	VERB
ejpam-4275	124	3	that	that	SCONJ
ejpam-4275	124	4	the	the	DET
ejpam-4275	124	5	class	class	NOUN
ejpam-4275	124	6	of	of	ADP
ejpam-4275	124	7	infra	infra	NOUN
ejpam-4275	124	8	soft	soft	ADJ
ejpam-4275	124	9	pre	pre	ADJ
ejpam-4275	124	10	-	-	ADJ
ejpam-4275	124	11	open	open	ADJ
ejpam-4275	124	12	sets	set	NOUN
ejpam-4275	124	13	forms	form	VERB
ejpam-4275	124	14	a	a	DET
ejpam-4275	124	15	supra	supra	ADJ
ejpam-4275	124	16	soft	soft	ADJ
ejpam-4275	124	17	topology	topology	NOUN
ejpam-4275	124	18	and	and	CCONJ
ejpam-4275	124	19	discuss	discuss	VERB
ejpam-4275	124	20	under	under	ADP
ejpam-4275	124	21	what	what	DET
ejpam-4275	124	22	conditions	condition	NOUN
ejpam-4275	124	23	this	this	DET
ejpam-4275	124	24	class	class	NOUN
ejpam-4275	124	25	forms	form	VERB
ejpam-4275	124	26	a	a	DET
ejpam-4275	124	27	soft	soft	ADJ
ejpam-4275	124	28	topology	topology	NOUN
ejpam-4275	124	29	.	.	PUNCT
ejpam-4275	125	1	we	we	PRON
ejpam-4275	125	2	complete	complete	VERB
ejpam-4275	125	3	this	this	DET
ejpam-4275	125	4	section	section	NOUN
ejpam-4275	125	5	by	by	ADP
ejpam-4275	125	6	proving	prove	VERB
ejpam-4275	125	7	that	that	SCONJ
ejpam-4275	125	8	this	this	DET
ejpam-4275	125	9	class	class	NOUN
ejpam-4275	125	10	is	be	AUX
ejpam-4275	125	11	kept	keep	VERB
ejpam-4275	125	12	under	under	ADP
ejpam-4275	125	13	infra	infra	NOUN
ejpam-4275	125	14	soft	soft	ADJ
ejpam-4275	125	15	homeomorphism	homeomorphism	NOUN
ejpam-4275	125	16	maps	map	NOUN
ejpam-4275	125	17	and	and	CCONJ
ejpam-4275	125	18	finite	finite	ADJ
ejpam-4275	125	19	product	product	NOUN
ejpam-4275	125	20	of	of	ADP
ejpam-4275	125	21	soft	soft	ADJ
ejpam-4275	125	22	spaces	space	NOUN
ejpam-4275	125	23	.	.	PUNCT
ejpam-4275	126	1	definition	definition	NOUN
ejpam-4275	126	2	16	16	NUM
ejpam-4275	126	3	.	.	PUNCT
ejpam-4275	127	1	a	a	DET
ejpam-4275	127	2	subset	subset	NOUN
ejpam-4275	127	3	(	(	PUNCT
ejpam-4275	127	4	ω	ω	PROPN
ejpam-4275	127	5	,	,	PUNCT
ejpam-4275	127	6	σ	σ	PROPN
ejpam-4275	127	7	)	)	PUNCT
ejpam-4275	127	8	of	of	ADP
ejpam-4275	127	9	an	an	DET
ejpam-4275	127	10	ists	ist	NOUN
ejpam-4275	127	11	(	(	PUNCT
ejpam-4275	127	12	x	x	X
ejpam-4275	127	13	,	,	PUNCT
ejpam-4275	127	14	ξ	ξ	PROPN
ejpam-4275	127	15	,	,	PUNCT
ejpam-4275	127	16	σ	σ	NOUN
ejpam-4275	127	17	)	)	PUNCT
ejpam-4275	127	18	is	be	AUX
ejpam-4275	127	19	said	say	VERB
ejpam-4275	127	20	to	to	PART
ejpam-4275	127	21	be	be	AUX
ejpam-4275	127	22	infra	infra	NOUN
ejpam-4275	127	23	soft	soft	ADJ
ejpam-4275	127	24	pre	pre	ADJ
ejpam-4275	127	25	-	-	ADJ
ejpam-4275	127	26	open	open	ADJ
ejpam-4275	127	27	if	if	SCONJ
ejpam-4275	127	28	(	(	PUNCT
ejpam-4275	127	29	ω	ω	NOUN
ejpam-4275	127	30	,	,	PUNCT
ejpam-4275	127	31	σ)⊆̃int(cl(ω	σ)⊆̃int(cl(ω	X
ejpam-4275	127	32	,	,	PUNCT
ejpam-4275	127	33	σ	σ	NOUN
ejpam-4275	127	34	)	)	PUNCT
ejpam-4275	127	35	)	)	PUNCT
ejpam-4275	127	36	.	.	PUNCT
ejpam-4275	128	1	its	its	PRON
ejpam-4275	128	2	complement	complement	NOUN
ejpam-4275	128	3	is	be	AUX
ejpam-4275	128	4	said	say	VERB
ejpam-4275	128	5	to	to	PART
ejpam-4275	128	6	be	be	AUX
ejpam-4275	128	7	an	an	DET
ejpam-4275	128	8	infra	infra	NOUN
ejpam-4275	128	9	soft	soft	ADJ
ejpam-4275	128	10	pre	pre	ADJ
ejpam-4275	128	11	-	-	ADJ
ejpam-4275	128	12	closed	closed	ADJ
ejpam-4275	128	13	set	set	NOUN
ejpam-4275	128	14	.	.	PUNCT
ejpam-4275	129	1	proposition	proposition	NOUN
ejpam-4275	129	2	5	5	NUM
ejpam-4275	129	3	.	.	PUNCT
ejpam-4275	130	1	if	if	SCONJ
ejpam-4275	130	2	(	(	PUNCT
ejpam-4275	130	3	ω	ω	PROPN
ejpam-4275	130	4	,	,	PUNCT
ejpam-4275	130	5	σ	σ	PROPN
ejpam-4275	130	6	)	)	PUNCT
ejpam-4275	130	7	is	be	AUX
ejpam-4275	130	8	an	an	DET
ejpam-4275	130	9	infra	infra	NOUN
ejpam-4275	130	10	soft	soft	ADJ
ejpam-4275	130	11	pre	pre	ADJ
ejpam-4275	130	12	-	-	ADJ
ejpam-4275	130	13	open	open	ADJ
ejpam-4275	130	14	subset	subset	NOUN
ejpam-4275	130	15	of	of	ADP
ejpam-4275	130	16	an	an	DET
ejpam-4275	130	17	ists	ist	NOUN
ejpam-4275	130	18	(	(	PUNCT
ejpam-4275	130	19	x	x	X
ejpam-4275	130	20	,	,	PUNCT
ejpam-4275	130	21	ξ	ξ	PROPN
ejpam-4275	130	22	,	,	PUNCT
ejpam-4275	130	23	σ	σ	PROPN
ejpam-4275	130	24	)	)	PUNCT
ejpam-4275	130	25	,	,	PUNCT
ejpam-4275	130	26	then	then	ADV
ejpam-4275	130	27	cl(ω	cl(ω	X
ejpam-4275	130	28	,	,	PUNCT
ejpam-4275	130	29	σ	σ	NOUN
ejpam-4275	130	30	)	)	PUNCT
ejpam-4275	130	31	is	be	AUX
ejpam-4275	130	32	infra	infra	NOUN
ejpam-4275	130	33	soft	soft	ADJ
ejpam-4275	130	34	semi	semi	ADJ
ejpam-4275	130	35	-	-	ADJ
ejpam-4275	130	36	open	open	ADJ
ejpam-4275	130	37	.	.	PUNCT
ejpam-4275	131	1	proof	proof	NOUN
ejpam-4275	131	2	.	.	PUNCT
ejpam-4275	132	1	since	since	SCONJ
ejpam-4275	132	2	(	(	PUNCT
ejpam-4275	132	3	ω	ω	PROPN
ejpam-4275	132	4	,	,	PUNCT
ejpam-4275	132	5	σ	σ	PROPN
ejpam-4275	132	6	)	)	PUNCT
ejpam-4275	132	7	is	be	AUX
ejpam-4275	132	8	an	an	DET
ejpam-4275	132	9	infra	infra	NOUN
ejpam-4275	132	10	soft	soft	ADJ
ejpam-4275	132	11	pre	pre	ADJ
ejpam-4275	132	12	-	-	ADJ
ejpam-4275	132	13	open	open	ADJ
ejpam-4275	132	14	set	set	NOUN
ejpam-4275	132	15	,	,	PUNCT
ejpam-4275	132	16	(	(	PUNCT
ejpam-4275	132	17	ω	ω	NOUN
ejpam-4275	132	18	,	,	PUNCT
ejpam-4275	132	19	σ)⊆̃int(cl(ω	σ)⊆̃int(cl(ω	X
ejpam-4275	132	20	,	,	PUNCT
ejpam-4275	132	21	σ	σ	NOUN
ejpam-4275	132	22	)	)	PUNCT
ejpam-4275	132	23	)	)	PUNCT
ejpam-4275	132	24	.	.	PUNCT
ejpam-4275	133	1	therefore	therefore	ADV
ejpam-4275	133	2	,	,	PUNCT
ejpam-4275	133	3	cl(ω	cl(ω	X
ejpam-4275	133	4	,	,	PUNCT
ejpam-4275	133	5	σ	σ	PROPN
ejpam-4275	133	6	)	)	PUNCT
ejpam-4275	133	7	⊆̃cl(int(cl(ω	⊆̃cl(int(cl(ω	PROPN
ejpam-4275	133	8	,	,	PUNCT
ejpam-4275	133	9	σ)))⊆̃cl(ω	σ)))⊆̃cl(ω	ADV
ejpam-4275	133	10	,	,	PUNCT
ejpam-4275	133	11	σ	σ	PROPN
ejpam-4275	133	12	)	)	PUNCT
ejpam-4275	133	13	.	.	PUNCT
ejpam-4275	134	1	thus	thus	ADV
ejpam-4275	134	2	,	,	PUNCT
ejpam-4275	134	3	cl(ω	cl(ω	X
ejpam-4275	134	4	,	,	PUNCT
ejpam-4275	134	5	σ	σ	NOUN
ejpam-4275	134	6	)	)	PUNCT
ejpam-4275	134	7	=	=	SYM
ejpam-4275	134	8	cl(int(cl(ω	cl(int(cl(ω	PROPN
ejpam-4275	134	9	,	,	PUNCT
ejpam-4275	134	10	σ	σ	PROPN
ejpam-4275	134	11	)	)	PUNCT
ejpam-4275	134	12	)	)	PUNCT
ejpam-4275	134	13	)	)	PUNCT
ejpam-4275	134	14	.	.	PUNCT
ejpam-4275	135	1	hence	hence	ADV
ejpam-4275	135	2	,	,	PUNCT
ejpam-4275	135	3	cl(ω	cl(ω	X
ejpam-4275	135	4	,	,	PUNCT
ejpam-4275	135	5	σ	σ	NOUN
ejpam-4275	135	6	)	)	PUNCT
ejpam-4275	135	7	is	be	AUX
ejpam-4275	135	8	infra	infra	NOUN
ejpam-4275	135	9	soft	soft	ADJ
ejpam-4275	135	10	semi	semi	ADJ
ejpam-4275	135	11	-	-	ADJ
ejpam-4275	135	12	open	open	ADJ
ejpam-4275	135	13	.	.	PUNCT
ejpam-4275	136	1	in	in	ADP
ejpam-4275	136	2	the	the	DET
ejpam-4275	136	3	next	next	ADJ
ejpam-4275	136	4	two	two	NUM
ejpam-4275	136	5	results	result	NOUN
ejpam-4275	136	6	,	,	PUNCT
ejpam-4275	136	7	we	we	PRON
ejpam-4275	136	8	present	present	VERB
ejpam-4275	136	9	some	some	DET
ejpam-4275	136	10	characterizations	characterization	NOUN
ejpam-4275	136	11	for	for	ADP
ejpam-4275	136	12	infra	infra	NOUN
ejpam-4275	136	13	soft	soft	ADJ
ejpam-4275	136	14	pre	pre	ADJ
ejpam-4275	136	15	-	-	ADJ
ejpam-4275	136	16	open	open	ADJ
ejpam-4275	136	17	and	and	CCONJ
ejpam-4275	136	18	infra	infra	VERB
ejpam-4275	136	19	soft	soft	ADJ
ejpam-4275	136	20	pre	pre	ADJ
ejpam-4275	136	21	-	-	ADJ
ejpam-4275	136	22	closed	closed	ADJ
ejpam-4275	136	23	sets	set	NOUN
ejpam-4275	136	24	.	.	PUNCT
ejpam-4275	137	1	proposition	proposition	NOUN
ejpam-4275	137	2	6	6	NUM
ejpam-4275	137	3	.	.	PUNCT
ejpam-4275	138	1	a	a	DET
ejpam-4275	138	2	subset	subset	NOUN
ejpam-4275	138	3	(	(	PUNCT
ejpam-4275	138	4	ω	ω	PROPN
ejpam-4275	138	5	,	,	PUNCT
ejpam-4275	138	6	σ	σ	PROPN
ejpam-4275	138	7	)	)	PUNCT
ejpam-4275	138	8	of	of	ADP
ejpam-4275	138	9	an	an	DET
ejpam-4275	138	10	ists	ist	NOUN
ejpam-4275	138	11	(	(	PUNCT
ejpam-4275	138	12	x	x	X
ejpam-4275	138	13	,	,	PUNCT
ejpam-4275	138	14	ξ	ξ	PROPN
ejpam-4275	138	15	,	,	PUNCT
ejpam-4275	138	16	σ	σ	NOUN
ejpam-4275	138	17	)	)	PUNCT
ejpam-4275	138	18	is	be	AUX
ejpam-4275	138	19	infra	infra	NOUN
ejpam-4275	138	20	soft	soft	ADJ
ejpam-4275	138	21	pre	pre	ADJ
ejpam-4275	138	22	-	-	ADJ
ejpam-4275	138	23	open	open	ADJ
ejpam-4275	138	24	iff	iff	NOUN
ejpam-4275	138	25	there	there	PRON
ejpam-4275	138	26	exists	exist	VERB
ejpam-4275	138	27	an	an	DET
ejpam-4275	138	28	ξ	ξ	NOUN
ejpam-4275	138	29	-	-	ADJ
ejpam-4275	138	30	infra	infra	ADJ
ejpam-4275	138	31	soft	soft	ADJ
ejpam-4275	138	32	open	open	ADJ
ejpam-4275	138	33	set	set	NOUN
ejpam-4275	138	34	(	(	PUNCT
ejpam-4275	138	35	ψ	ψ	X
ejpam-4275	138	36	,	,	PUNCT
ejpam-4275	138	37	σ	σ	NOUN
ejpam-4275	138	38	)	)	PUNCT
ejpam-4275	138	39	such	such	ADJ
ejpam-4275	138	40	that	that	SCONJ
ejpam-4275	138	41	(	(	PUNCT
ejpam-4275	138	42	ω	ω	NOUN
ejpam-4275	138	43	,	,	PUNCT
ejpam-4275	138	44	σ)⊆̃(ψ	σ)⊆̃(ψ	PROPN
ejpam-4275	138	45	,	,	PUNCT
ejpam-4275	138	46	σ)⊆̃cl(ω	σ)⊆̃cl(ω	PROPN
ejpam-4275	138	47	,	,	PUNCT
ejpam-4275	138	48	σ	σ	PROPN
ejpam-4275	138	49	)	)	PUNCT
ejpam-4275	138	50	.	.	PUNCT
ejpam-4275	139	1	proof	proof	NOUN
ejpam-4275	139	2	.	.	PUNCT
ejpam-4275	140	1	necessity	necessity	NOUN
ejpam-4275	140	2	:	:	PUNCT
ejpam-4275	140	3	let	let	VERB
ejpam-4275	140	4	(	(	PUNCT
ejpam-4275	140	5	ω	ω	PROPN
ejpam-4275	140	6	,	,	PUNCT
ejpam-4275	140	7	σ	σ	PROPN
ejpam-4275	140	8	)	)	PUNCT
ejpam-4275	140	9	be	be	VERB
ejpam-4275	140	10	an	an	DET
ejpam-4275	140	11	infra	infra	NOUN
ejpam-4275	140	12	soft	soft	ADJ
ejpam-4275	140	13	pre	pre	ADJ
ejpam-4275	140	14	-	-	ADJ
ejpam-4275	140	15	open	open	ADJ
ejpam-4275	140	16	set	set	NOUN
ejpam-4275	140	17	.	.	PUNCT
ejpam-4275	141	1	then	then	ADV
ejpam-4275	141	2	(	(	PUNCT
ejpam-4275	141	3	ω	ω	NOUN
ejpam-4275	141	4	,	,	PUNCT
ejpam-4275	141	5	σ)⊆̃int(cl(ω	σ)⊆̃int(cl(ω	X
ejpam-4275	141	6	,	,	PUNCT
ejpam-4275	141	7	σ	σ	NOUN
ejpam-4275	141	8	)	)	PUNCT
ejpam-4275	141	9	)	)	PUNCT
ejpam-4275	141	10	⊆̃cl(ω	⊆̃cl(ω	NUM
ejpam-4275	141	11	,	,	PUNCT
ejpam-4275	141	12	σ	σ	NOUN
ejpam-4275	141	13	)	)	PUNCT
ejpam-4275	141	14	.	.	PUNCT
ejpam-4275	142	1	putting	put	VERB
ejpam-4275	142	2	(	(	PUNCT
ejpam-4275	142	3	ψ	ψ	X
ejpam-4275	142	4	,	,	PUNCT
ejpam-4275	142	5	σ	σ	NOUN
ejpam-4275	142	6	)	)	PUNCT
ejpam-4275	142	7	=	=	SYM
ejpam-4275	142	8	int(cl(ω	int(cl(ω	PROPN
ejpam-4275	142	9	,	,	PUNCT
ejpam-4275	142	10	σ	σ	NOUN
ejpam-4275	142	11	)	)	PUNCT
ejpam-4275	142	12	)	)	PUNCT
ejpam-4275	142	13	.	.	PUNCT
ejpam-4275	143	1	then	then	ADV
ejpam-4275	143	2	int(ψ	int(ψ	PROPN
ejpam-4275	143	3	,	,	PUNCT
ejpam-4275	143	4	σ	σ	NOUN
ejpam-4275	143	5	)	)	PUNCT
ejpam-4275	143	6	=	=	SYM
ejpam-4275	143	7	int(int(cl(ω	int(int(cl(ω	X
ejpam-4275	143	8	,	,	PUNCT
ejpam-4275	143	9	σ	σ	NOUN
ejpam-4275	143	10	)	)	PUNCT
ejpam-4275	143	11	)	)	PUNCT
ejpam-4275	143	12	)	)	PUNCT
ejpam-4275	144	1	=	=	PUNCT
ejpam-4275	144	2	(	(	PUNCT
ejpam-4275	144	3	ψ	ψ	X
ejpam-4275	144	4	,	,	PUNCT
ejpam-4275	144	5	σ	σ	PROPN
ejpam-4275	144	6	)	)	PUNCT
ejpam-4275	144	7	.	.	PUNCT
ejpam-4275	145	1	therefore	therefore	ADV
ejpam-4275	145	2	,	,	PUNCT
ejpam-4275	145	3	(	(	PUNCT
ejpam-4275	145	4	ψ	ψ	X
ejpam-4275	145	5	,	,	PUNCT
ejpam-4275	145	6	σ	σ	PROPN
ejpam-4275	145	7	)	)	PUNCT
ejpam-4275	145	8	is	be	AUX
ejpam-4275	145	9	an	an	DET
ejpam-4275	145	10	ξ	ξ	NOUN
ejpam-4275	145	11	-	-	ADJ
ejpam-4275	145	12	infra	infra	ADJ
ejpam-4275	145	13	soft	soft	ADJ
ejpam-4275	145	14	open	open	ADJ
ejpam-4275	145	15	set	set	NOUN
ejpam-4275	145	16	.	.	PUNCT
ejpam-4275	146	1	sufficiency	sufficiency	NOUN
ejpam-4275	146	2	:	:	PUNCT
ejpam-4275	147	1	let	let	VERB
ejpam-4275	147	2	(	(	PUNCT
ejpam-4275	147	3	ψ	ψ	X
ejpam-4275	147	4	,	,	PUNCT
ejpam-4275	147	5	σ	σ	PROPN
ejpam-4275	147	6	)	)	PUNCT
ejpam-4275	147	7	is	be	AUX
ejpam-4275	147	8	an	an	DET
ejpam-4275	147	9	ξ	ξ	NOUN
ejpam-4275	147	10	-	-	ADJ
ejpam-4275	147	11	infra	infra	ADJ
ejpam-4275	147	12	soft	soft	ADJ
ejpam-4275	147	13	open	open	ADJ
ejpam-4275	147	14	set	set	NOUN
ejpam-4275	147	15	such	such	ADJ
ejpam-4275	147	16	that	that	SCONJ
ejpam-4275	147	17	(	(	PUNCT
ejpam-4275	147	18	ω	ω	NOUN
ejpam-4275	147	19	,	,	PUNCT
ejpam-4275	147	20	σ)⊆̃(ψ	σ)⊆̃(ψ	PROPN
ejpam-4275	147	21	,	,	PUNCT
ejpam-4275	147	22	σ)⊆̃cl(ω	σ)⊆̃cl(ω	PROPN
ejpam-4275	147	23	,	,	PUNCT
ejpam-4275	147	24	σ	σ	PROPN
ejpam-4275	147	25	)	)	PUNCT
ejpam-4275	147	26	.	.	PUNCT
ejpam-4275	148	1	then	then	ADV
ejpam-4275	148	2	int(ω	int(ω	NOUN
ejpam-4275	148	3	,	,	PUNCT
ejpam-4275	148	4	σ)⊆̃(ψ	σ)⊆̃(ψ	NOUN
ejpam-4275	148	5	,	,	PUNCT
ejpam-4275	148	6	σ)⊆̃int(cl(ω	σ)⊆̃int(cl(ω	X
ejpam-4275	148	7	,	,	PUNCT
ejpam-4275	148	8	σ	σ	NOUN
ejpam-4275	148	9	)	)	PUNCT
ejpam-4275	148	10	)	)	PUNCT
ejpam-4275	148	11	.	.	PUNCT
ejpam-4275	149	1	therefore	therefore	ADV
ejpam-4275	149	2	,	,	PUNCT
ejpam-4275	149	3	(	(	PUNCT
ejpam-4275	149	4	ω	ω	NOUN
ejpam-4275	149	5	,	,	PUNCT
ejpam-4275	149	6	σ)⊆̃int(cl(ω	σ)⊆̃int(cl(ω	X
ejpam-4275	149	7	,	,	PUNCT
ejpam-4275	149	8	σ	σ	PROPN
ejpam-4275	149	9	)	)	PUNCT
ejpam-4275	149	10	)	)	PUNCT
ejpam-4275	149	11	which	which	PRON
ejpam-4275	149	12	means	mean	VERB
ejpam-4275	149	13	that	that	SCONJ
ejpam-4275	149	14	(	(	PUNCT
ejpam-4275	149	15	ω	ω	PROPN
ejpam-4275	149	16	,	,	PUNCT
ejpam-4275	149	17	σ	σ	PROPN
ejpam-4275	149	18	)	)	PUNCT
ejpam-4275	149	19	is	be	AUX
ejpam-4275	149	20	an	an	DET
ejpam-4275	149	21	infra	infra	NOUN
ejpam-4275	149	22	soft	soft	ADJ
ejpam-4275	149	23	pre	pre	ADJ
ejpam-4275	149	24	-	-	ADJ
ejpam-4275	149	25	open	open	ADJ
ejpam-4275	149	26	set	set	NOUN
ejpam-4275	149	27	.	.	PUNCT
ejpam-4275	150	1	t.m	t.m	PROPN
ejpam-4275	150	2	.	.	PUNCT
ejpam-4275	150	3	al	al	PROPN
ejpam-4275	150	4	-	-	PUNCT
ejpam-4275	150	5	shami	shami	PROPN
ejpam-4275	150	6	,	,	PUNCT
ejpam-4275	150	7	h.a	h.a	PROPN
ejpam-4275	150	8	.	.	PROPN
ejpam-4275	150	9	othman	othman	PROPN
ejpam-4275	150	10	/	/	SYM
ejpam-4275	150	11	eur	eur	PROPN
ejpam-4275	150	12	.	.	PUNCT
ejpam-4275	151	1	j.	j.	PROPN
ejpam-4275	151	2	pure	pure	PROPN
ejpam-4275	151	3	appl	appl	PROPN
ejpam-4275	151	4	.	.	PROPN
ejpam-4275	151	5	math	math	PROPN
ejpam-4275	151	6	,	,	PUNCT
ejpam-4275	151	7	15	15	NUM
ejpam-4275	151	8	(	(	PUNCT
ejpam-4275	151	9	1	1	NUM
ejpam-4275	151	10	)	)	PUNCT
ejpam-4275	151	11	(	(	PUNCT
ejpam-4275	151	12	2022	2022	NUM
ejpam-4275	151	13	)	)	PUNCT
ejpam-4275	151	14	,	,	PUNCT
ejpam-4275	151	15	261	261	NUM
ejpam-4275	151	16	-	-	SYM
ejpam-4275	151	17	280	280	NUM
ejpam-4275	151	18	266	266	NUM
ejpam-4275	151	19	proposition	proposition	NOUN
ejpam-4275	151	20	7	7	NUM
ejpam-4275	151	21	.	.	PUNCT
ejpam-4275	151	22	a	a	DET
ejpam-4275	151	23	subset	subset	NOUN
ejpam-4275	151	24	(	(	PUNCT
ejpam-4275	151	25	ω	ω	PROPN
ejpam-4275	151	26	,	,	PUNCT
ejpam-4275	151	27	σ	σ	PROPN
ejpam-4275	151	28	)	)	PUNCT
ejpam-4275	151	29	of	of	ADP
ejpam-4275	151	30	an	an	DET
ejpam-4275	151	31	ists	ist	NOUN
ejpam-4275	151	32	(	(	PUNCT
ejpam-4275	151	33	x	x	X
ejpam-4275	151	34	,	,	PUNCT
ejpam-4275	151	35	ξ	ξ	PROPN
ejpam-4275	151	36	,	,	PUNCT
ejpam-4275	151	37	σ	σ	NOUN
ejpam-4275	151	38	)	)	PUNCT
ejpam-4275	151	39	is	be	AUX
ejpam-4275	151	40	infra	infra	NOUN
ejpam-4275	151	41	soft	soft	ADJ
ejpam-4275	151	42	pre	pre	ADJ
ejpam-4275	151	43	-	-	ADJ
ejpam-4275	151	44	closed	closed	ADJ
ejpam-4275	151	45	iff	iff	NOUN
ejpam-4275	151	46	there	there	PRON
ejpam-4275	151	47	exists	exist	VERB
ejpam-4275	151	48	an	an	DET
ejpam-4275	151	49	ξ	ξ	ADJ
ejpam-4275	151	50	-	-	ADJ
ejpam-4275	151	51	infra	infra	ADJ
ejpam-4275	151	52	soft	soft	ADJ
ejpam-4275	151	53	closed	closed	ADJ
ejpam-4275	151	54	set	set	NOUN
ejpam-4275	151	55	(	(	PUNCT
ejpam-4275	151	56	ψ	ψ	X
ejpam-4275	151	57	,	,	PUNCT
ejpam-4275	151	58	σ	σ	NOUN
ejpam-4275	151	59	)	)	PUNCT
ejpam-4275	151	60	such	such	ADJ
ejpam-4275	151	61	that	that	SCONJ
ejpam-4275	151	62	int(ω	int(ω	NOUN
ejpam-4275	151	63	,	,	PUNCT
ejpam-4275	151	64	σ)⊆̃(ψ	σ)⊆̃(ψ	NOUN
ejpam-4275	151	65	,	,	PUNCT
ejpam-4275	151	66	σ)⊆̃(ω	σ)⊆̃(ω	PROPN
ejpam-4275	151	67	,	,	PUNCT
ejpam-4275	151	68	σ	σ	PROPN
ejpam-4275	151	69	)	)	PUNCT
ejpam-4275	151	70	.	.	PUNCT
ejpam-4275	152	1	proof	proof	NOUN
ejpam-4275	152	2	.	.	PUNCT
ejpam-4275	153	1	similar	similar	ADJ
ejpam-4275	153	2	to	to	ADP
ejpam-4275	153	3	the	the	DET
ejpam-4275	153	4	proof	proof	NOUN
ejpam-4275	153	5	of	of	ADP
ejpam-4275	153	6	proposition	proposition	NOUN
ejpam-4275	153	7	6	6	NUM
ejpam-4275	153	8	.	.	PUNCT
ejpam-4275	153	9	proposition	proposition	NOUN
ejpam-4275	153	10	8	8	NUM
ejpam-4275	153	11	.	.	PUNCT
ejpam-4275	154	1	the	the	DET
ejpam-4275	154	2	class	class	NOUN
ejpam-4275	154	3	of	of	ADP
ejpam-4275	154	4	infra	infra	NOUN
ejpam-4275	154	5	soft	soft	ADJ
ejpam-4275	154	6	pre	pre	ADJ
ejpam-4275	154	7	-	-	ADJ
ejpam-4275	154	8	open	open	ADJ
ejpam-4275	154	9	sets	set	NOUN
ejpam-4275	154	10	is	be	AUX
ejpam-4275	154	11	closed	close	VERB
ejpam-4275	154	12	under	under	ADP
ejpam-4275	154	13	arbitrary	arbitrary	ADJ
ejpam-4275	154	14	unions	union	NOUN
ejpam-4275	154	15	.	.	PUNCT
ejpam-4275	155	1	proof	proof	NOUN
ejpam-4275	155	2	.	.	PUNCT
ejpam-4275	156	1	consider	consider	VERB
ejpam-4275	156	2	{	{	PUNCT
ejpam-4275	156	3	(	(	PUNCT
ejpam-4275	156	4	ωj	ωj	INTJ
ejpam-4275	156	5	,	,	PUNCT
ejpam-4275	156	6	σ	σ	PROPN
ejpam-4275	156	7	)	)	PUNCT
ejpam-4275	156	8	:	:	PUNCT
ejpam-4275	157	1	j	j	PROPN
ejpam-4275	157	2	∈	∈	PROPN
ejpam-4275	157	3	j	j	PROPN
ejpam-4275	157	4	}	}	PUNCT
ejpam-4275	157	5	as	as	ADP
ejpam-4275	157	6	a	a	DET
ejpam-4275	157	7	family	family	NOUN
ejpam-4275	157	8	of	of	ADP
ejpam-4275	157	9	infra	infra	NOUN
ejpam-4275	157	10	soft	soft	ADJ
ejpam-4275	157	11	pre	pre	ADJ
ejpam-4275	157	12	-	-	ADJ
ejpam-4275	157	13	open	open	ADJ
ejpam-4275	157	14	sets	set	NOUN
ejpam-4275	157	15	.	.	PUNCT
ejpam-4275	157	16	suppose	suppose	VERB
ejpam-4275	157	17	that	that	SCONJ
ejpam-4275	157	18	j	j	PROPN
ejpam-4275	157	19	̸=	̸=	PROPN
ejpam-4275	157	20	∅.	∅.	VERB
ejpam-4275	157	21	then	then	ADV
ejpam-4275	157	22	(	(	PUNCT
ejpam-4275	157	23	ωj	ωj	INTJ
ejpam-4275	157	24	,	,	PUNCT
ejpam-4275	157	25	σ)⊆̃int(cl(ωj	σ)⊆̃int(cl(ωj	PROPN
ejpam-4275	157	26	,	,	PUNCT
ejpam-4275	157	27	σ	σ	PROPN
ejpam-4275	157	28	)	)	PUNCT
ejpam-4275	157	29	)	)	PUNCT
ejpam-4275	157	30	for	for	ADP
ejpam-4275	157	31	each	each	DET
ejpam-4275	157	32	j	j	PROPN
ejpam-4275	157	33	∈	∈	PROPN
ejpam-4275	157	34	j	j	PROPN
ejpam-4275	157	35	.	.	PUNCT
ejpam-4275	158	1	consequentially	consequentially	ADV
ejpam-4275	158	2	,	,	PUNCT
ejpam-4275	158	3	⋃̃	⋃̃	PROPN
ejpam-4275	158	4	j∈j	j∈j	NOUN
ejpam-4275	158	5	(	(	PUNCT
ejpam-4275	158	6	ωj	ωj	INTJ
ejpam-4275	158	7	,	,	PUNCT
ejpam-4275	158	8	σ)⊆̃	σ)⊆̃	ADJ
ejpam-4275	158	9	⋃̃	⋃̃	NUM
ejpam-4275	158	10	j∈jint(cl(ωj	j∈jint(cl(ωj	NOUN
ejpam-4275	158	11	,	,	PUNCT
ejpam-4275	158	12	σ	σ	NOUN
ejpam-4275	158	13	)	)	PUNCT
ejpam-4275	158	14	)	)	PUNCT
ejpam-4275	158	15	⊆̃int(cl	⊆̃int(cl	NOUN
ejpam-4275	158	16	(	(	PUNCT
ejpam-4275	158	17	⋃̃	⋃̃	PROPN
ejpam-4275	158	18	j∈j(ωj	j∈j(ωj	PROPN
ejpam-4275	158	19	,	,	PUNCT
ejpam-4275	158	20	σ	σ	PROPN
ejpam-4275	158	21	)	)	PUNCT
ejpam-4275	158	22	)	)	PUNCT
ejpam-4275	158	23	)	)	PUNCT
ejpam-4275	158	24	.	.	PUNCT
ejpam-4275	159	1	hence	hence	ADV
ejpam-4275	159	2	,	,	PUNCT
ejpam-4275	159	3	⋃̃	⋃̃	PROPN
ejpam-4275	159	4	j∈j(ωj	j∈j(ωj	PROPN
ejpam-4275	159	5	,	,	PUNCT
ejpam-4275	159	6	σ	σ	PROPN
ejpam-4275	159	7	)	)	PUNCT
ejpam-4275	159	8	is	be	AUX
ejpam-4275	159	9	infra	infra	NOUN
ejpam-4275	159	10	soft	soft	ADJ
ejpam-4275	159	11	pre	pre	ADJ
ejpam-4275	159	12	-	-	ADJ
ejpam-4275	159	13	open	open	ADJ
ejpam-4275	159	14	.	.	PUNCT
ejpam-4275	160	1	corollary	corollary	ADJ
ejpam-4275	160	2	1	1	NUM
ejpam-4275	160	3	.	.	PUNCT
ejpam-4275	161	1	the	the	DET
ejpam-4275	161	2	class	class	NOUN
ejpam-4275	161	3	of	of	ADP
ejpam-4275	161	4	infra	infra	NOUN
ejpam-4275	161	5	soft	soft	ADJ
ejpam-4275	161	6	pre	pre	ADJ
ejpam-4275	161	7	-	-	ADJ
ejpam-4275	161	8	closed	closed	ADJ
ejpam-4275	161	9	sets	set	NOUN
ejpam-4275	161	10	is	be	AUX
ejpam-4275	161	11	closed	close	VERB
ejpam-4275	161	12	under	under	ADP
ejpam-4275	161	13	arbitrary	arbitrary	ADJ
ejpam-4275	161	14	intersections	intersection	NOUN
ejpam-4275	161	15	.	.	PUNCT
ejpam-4275	162	1	corollary	corollary	ADJ
ejpam-4275	162	2	2	2	NUM
ejpam-4275	162	3	.	.	PUNCT
ejpam-4275	163	1	the	the	DET
ejpam-4275	163	2	class	class	NOUN
ejpam-4275	163	3	of	of	ADP
ejpam-4275	163	4	infra	infra	NOUN
ejpam-4275	163	5	soft	soft	ADJ
ejpam-4275	163	6	pre	pre	ADJ
ejpam-4275	163	7	-	-	ADJ
ejpam-4275	163	8	open	open	ADJ
ejpam-4275	163	9	subsets	subset	NOUN
ejpam-4275	163	10	of	of	ADP
ejpam-4275	163	11	an	an	DET
ejpam-4275	163	12	ists	ist	NOUN
ejpam-4275	163	13	(	(	PUNCT
ejpam-4275	163	14	x	x	X
ejpam-4275	163	15	,	,	PUNCT
ejpam-4275	163	16	ξ	ξ	PROPN
ejpam-4275	163	17	,	,	PUNCT
ejpam-4275	163	18	σ	σ	NOUN
ejpam-4275	163	19	)	)	PUNCT
ejpam-4275	163	20	forms	form	VERB
ejpam-4275	163	21	a	a	DET
ejpam-4275	163	22	supra	supra	ADJ
ejpam-4275	163	23	soft	soft	ADJ
ejpam-4275	163	24	topology	topology	NOUN
ejpam-4275	163	25	over	over	ADP
ejpam-4275	163	26	x.	x.	NOUN
ejpam-4275	163	27	to	to	PART
ejpam-4275	163	28	illustrate	illustrate	VERB
ejpam-4275	163	29	that	that	SCONJ
ejpam-4275	163	30	the	the	DET
ejpam-4275	163	31	class	class	NOUN
ejpam-4275	163	32	of	of	ADP
ejpam-4275	163	33	infra	infra	NOUN
ejpam-4275	163	34	soft	soft	ADJ
ejpam-4275	163	35	pre	pre	ADJ
ejpam-4275	163	36	-	-	ADJ
ejpam-4275	163	37	open	open	ADJ
ejpam-4275	163	38	sets	set	NOUN
ejpam-4275	163	39	does	do	AUX
ejpam-4275	163	40	not	not	PART
ejpam-4275	163	41	form	form	VERB
ejpam-4275	163	42	an	an	DET
ejpam-4275	163	43	infra	infra	NOUN
ejpam-4275	163	44	soft	soft	ADJ
ejpam-4275	163	45	topology	topology	NOUN
ejpam-4275	163	46	,	,	PUNCT
ejpam-4275	163	47	we	we	PRON
ejpam-4275	163	48	present	present	VERB
ejpam-4275	163	49	the	the	DET
ejpam-4275	163	50	following	follow	VERB
ejpam-4275	163	51	example	example	NOUN
ejpam-4275	163	52	.	.	PUNCT
ejpam-4275	164	1	example	example	NOUN
ejpam-4275	165	1	1	1	NUM
ejpam-4275	165	2	.	.	PUNCT
ejpam-4275	165	3	let	let	VERB
ejpam-4275	165	4	x	x	PUNCT
ejpam-4275	165	5	=	=	PRON
ejpam-4275	165	6	{	{	PUNCT
ejpam-4275	165	7	x1	x1	PROPN
ejpam-4275	165	8	,	,	PUNCT
ejpam-4275	165	9	x2	x2	PROPN
ejpam-4275	165	10	,	,	PUNCT
ejpam-4275	165	11	x3	x3	ADJ
ejpam-4275	165	12	,	,	PUNCT
ejpam-4275	165	13	x4	x4	PROPN
ejpam-4275	165	14	}	}	PUNCT
ejpam-4275	165	15	and	and	CCONJ
ejpam-4275	165	16	σ	σ	NOUN
ejpam-4275	165	17	=	=	SYM
ejpam-4275	165	18	{	{	PUNCT
ejpam-4275	165	19	η1	η1	NOUN
ejpam-4275	165	20	,	,	PUNCT
ejpam-4275	165	21	η2	η2	PROPN
ejpam-4275	165	22	}	}	PUNCT
ejpam-4275	165	23	.	.	PUNCT
ejpam-4275	166	1	then	then	ADV
ejpam-4275	166	2	ξ	ξ	X
ejpam-4275	166	3	=	=	SYM
ejpam-4275	166	4	{	{	PUNCT
ejpam-4275	166	5	φ	φ	PROPN
ejpam-4275	166	6	,	,	PUNCT
ejpam-4275	166	7	x̃	x̃	PROPN
ejpam-4275	166	8	,	,	PUNCT
ejpam-4275	166	9	(	(	PUNCT
ejpam-4275	166	10	ω1,σ	ω1,σ	PROPN
ejpam-4275	166	11	)	)	PUNCT
ejpam-4275	166	12	,	,	PUNCT
ejpam-4275	166	13	(	(	PUNCT
ejpam-4275	166	14	ω2,σ	ω2,σ	PROPN
ejpam-4275	166	15	)	)	PUNCT
ejpam-4275	166	16	}	}	PUNCT
ejpam-4275	166	17	is	be	AUX
ejpam-4275	166	18	an	an	DET
ejpam-4275	166	19	infra	infra	NOUN
ejpam-4275	166	20	soft	soft	ADJ
ejpam-4275	166	21	topology	topology	NOUN
ejpam-4275	166	22	on	on	ADP
ejpam-4275	166	23	x	x	PUNCT
ejpam-4275	166	24	with	with	ADP
ejpam-4275	166	25	σ	σ	NOUN
ejpam-4275	166	26	as	as	ADP
ejpam-4275	166	27	a	a	DET
ejpam-4275	166	28	set	set	NOUN
ejpam-4275	166	29	of	of	ADP
ejpam-4275	166	30	parameters	parameter	NOUN
ejpam-4275	166	31	,	,	PUNCT
ejpam-4275	166	32	where	where	SCONJ
ejpam-4275	166	33	(	(	PUNCT
ejpam-4275	166	34	ω1,σ	ω1,σ	NOUN
ejpam-4275	166	35	)	)	PUNCT
ejpam-4275	166	36	=	=	SYM
ejpam-4275	166	37	{	{	PUNCT
ejpam-4275	166	38	(	(	PUNCT
ejpam-4275	166	39	η1	η1	NOUN
ejpam-4275	166	40	,	,	PUNCT
ejpam-4275	166	41	{	{	PUNCT
ejpam-4275	166	42	x1	x1	NOUN
ejpam-4275	166	43	}	}	PUNCT
ejpam-4275	166	44	)	)	PUNCT
ejpam-4275	166	45	,	,	PUNCT
ejpam-4275	166	46	(	(	PUNCT
ejpam-4275	166	47	η2	η2	X
ejpam-4275	166	48	,	,	PUNCT
ejpam-4275	166	49	{	{	PUNCT
ejpam-4275	166	50	x1	x1	ADJ
ejpam-4275	166	51	}	}	PUNCT
ejpam-4275	166	52	)	)	PUNCT
ejpam-4275	166	53	}	}	PUNCT
ejpam-4275	166	54	and	and	CCONJ
ejpam-4275	166	55	(	(	PUNCT
ejpam-4275	166	56	ω2,σ	ω2,σ	PROPN
ejpam-4275	166	57	)	)	PUNCT
ejpam-4275	166	58	=	=	PRON
ejpam-4275	166	59	{	{	PUNCT
ejpam-4275	166	60	(	(	PUNCT
ejpam-4275	166	61	η1	η1	NOUN
ejpam-4275	166	62	,	,	PUNCT
ejpam-4275	166	63	{	{	PUNCT
ejpam-4275	166	64	x2	x2	ADJ
ejpam-4275	166	65	}	}	PUNCT
ejpam-4275	166	66	)	)	PUNCT
ejpam-4275	166	67	,	,	PUNCT
ejpam-4275	166	68	(	(	PUNCT
ejpam-4275	166	69	η2	η2	X
ejpam-4275	166	70	,	,	PUNCT
ejpam-4275	166	71	{	{	PUNCT
ejpam-4275	166	72	x2	x2	ADJ
ejpam-4275	166	73	}	}	PUNCT
ejpam-4275	166	74	)	)	PUNCT
ejpam-4275	166	75	}	}	PUNCT
ejpam-4275	166	76	.	.	PUNCT
ejpam-4275	167	1	let	let	VERB
ejpam-4275	167	2	(	(	PUNCT
ejpam-4275	167	3	ω5,σ	ω5,σ	PROPN
ejpam-4275	167	4	)	)	PUNCT
ejpam-4275	167	5	=	=	PRON
ejpam-4275	167	6	{	{	PUNCT
ejpam-4275	167	7	(	(	PUNCT
ejpam-4275	167	8	η1	η1	NOUN
ejpam-4275	167	9	,	,	PUNCT
ejpam-4275	167	10	x	x	NOUN
ejpam-4275	167	11	)	)	PUNCT
ejpam-4275	167	12	,	,	PUNCT
ejpam-4275	167	13	(	(	PUNCT
ejpam-4275	167	14	η2	η2	X
ejpam-4275	167	15	,	,	PUNCT
ejpam-4275	167	16	{	{	PUNCT
ejpam-4275	167	17	x1	x1	ADJ
ejpam-4275	167	18	,	,	PUNCT
ejpam-4275	167	19	x3	x3	ADJ
ejpam-4275	167	20	}	}	PUNCT
ejpam-4275	167	21	)	)	PUNCT
ejpam-4275	167	22	}	}	PUNCT
ejpam-4275	167	23	and	and	CCONJ
ejpam-4275	167	24	(	(	PUNCT
ejpam-4275	167	25	ω6,σ	ω6,σ	PROPN
ejpam-4275	167	26	)	)	PUNCT
ejpam-4275	167	27	=	=	PRON
ejpam-4275	167	28	{	{	PUNCT
ejpam-4275	167	29	(	(	PUNCT
ejpam-4275	167	30	η1	η1	NOUN
ejpam-4275	167	31	,	,	PUNCT
ejpam-4275	167	32	{	{	PUNCT
ejpam-4275	167	33	x1	x1	ADJ
ejpam-4275	167	34	,	,	PUNCT
ejpam-4275	167	35	x3	x3	ADJ
ejpam-4275	167	36	}	}	PUNCT
ejpam-4275	167	37	)	)	PUNCT
ejpam-4275	167	38	,	,	PUNCT
ejpam-4275	167	39	(	(	PUNCT
ejpam-4275	167	40	η2	η2	X
ejpam-4275	167	41	,	,	PUNCT
ejpam-4275	167	42	x	x	NOUN
ejpam-4275	167	43	)	)	PUNCT
ejpam-4275	167	44	}	}	PUNCT
ejpam-4275	167	45	.	.	PUNCT
ejpam-4275	168	1	then	then	ADV
ejpam-4275	168	2	(	(	PUNCT
ejpam-4275	168	3	ω5,σ	ω5,σ	PROPN
ejpam-4275	168	4	)	)	PUNCT
ejpam-4275	168	5	and	and	CCONJ
ejpam-4275	168	6	(	(	PUNCT
ejpam-4275	168	7	ω6,σ	ω6,σ	PROPN
ejpam-4275	168	8	)	)	PUNCT
ejpam-4275	168	9	are	be	AUX
ejpam-4275	168	10	infra	infra	NOUN
ejpam-4275	168	11	soft	soft	ADJ
ejpam-4275	168	12	pre	pre	ADJ
ejpam-4275	168	13	-	-	ADJ
ejpam-4275	168	14	open	open	ADJ
ejpam-4275	168	15	sets	set	NOUN
ejpam-4275	168	16	because	because	SCONJ
ejpam-4275	168	17	int(cl(ω5,σ	int(cl(ω5,σ	VERB
ejpam-4275	168	18	)	)	PUNCT
ejpam-4275	168	19	)	)	PUNCT
ejpam-4275	169	1	=	=	PUNCT
ejpam-4275	169	2	x̃	x̃	PROPN
ejpam-4275	169	3	and	and	CCONJ
ejpam-4275	169	4	int(cl(ω6,σ	int(cl(ω6,σ	PROPN
ejpam-4275	169	5	)	)	PUNCT
ejpam-4275	169	6	)	)	PUNCT
ejpam-4275	170	1	=	=	PUNCT
ejpam-4275	171	1	x̃.	x̃.	ADJ
ejpam-4275	171	2	but	but	CCONJ
ejpam-4275	171	3	(	(	PUNCT
ejpam-4275	171	4	ω5,σ	ω5,σ	PROPN
ejpam-4275	171	5	)	)	PUNCT
ejpam-4275	171	6	⋂̃	⋂̃	NOUN
ejpam-4275	171	7	(	(	PUNCT
ejpam-4275	171	8	ω6,σ	ω6,σ	PROPN
ejpam-4275	171	9	)	)	PUNCT
ejpam-4275	171	10	is	be	AUX
ejpam-4275	171	11	not	not	PART
ejpam-4275	171	12	infra	infra	NOUN
ejpam-4275	171	13	soft	soft	ADJ
ejpam-4275	171	14	pre	pre	ADJ
ejpam-4275	171	15	-	-	ADJ
ejpam-4275	171	16	open	open	ADJ
ejpam-4275	171	17	because	because	SCONJ
ejpam-4275	171	18	int(cl[(ω5,σ	int(cl[(ω5,σ	NOUN
ejpam-4275	171	19	)	)	PUNCT
ejpam-4275	171	20	⋂̃	⋂̃	NOUN
ejpam-4275	171	21	(	(	PUNCT
ejpam-4275	171	22	ω6,σ	ω6,σ	PROPN
ejpam-4275	171	23	)	)	PUNCT
ejpam-4275	171	24	]	]	PUNCT
ejpam-4275	171	25	)	)	PUNCT
ejpam-4275	172	1	=	=	PRON
ejpam-4275	172	2	{	{	PUNCT
ejpam-4275	172	3	(	(	PUNCT
ejpam-4275	172	4	η1	η1	NOUN
ejpam-4275	172	5	,	,	PUNCT
ejpam-4275	172	6	{	{	PUNCT
ejpam-4275	172	7	x1	x1	NOUN
ejpam-4275	172	8	}	}	PUNCT
ejpam-4275	172	9	)	)	PUNCT
ejpam-4275	172	10	,	,	PUNCT
ejpam-4275	172	11	(	(	PUNCT
ejpam-4275	172	12	η2	η2	X
ejpam-4275	172	13	,	,	PUNCT
ejpam-4275	172	14	{	{	PUNCT
ejpam-4275	172	15	x1})}˜̸⊇[(ω5,σ	x1})}˜̸⊇[(ω5,σ	NOUN
ejpam-4275	172	16	)	)	PUNCT
ejpam-4275	172	17	⋂̃	⋂̃	NOUN
ejpam-4275	172	18	(	(	PUNCT
ejpam-4275	172	19	ω6,σ	ω6,σ	PROPN
ejpam-4275	172	20	)	)	PUNCT
ejpam-4275	172	21	]	]	PUNCT
ejpam-4275	172	22	.	.	PUNCT
ejpam-4275	173	1	proposition	proposition	NOUN
ejpam-4275	173	2	9	9	NUM
ejpam-4275	173	3	.	.	PUNCT
ejpam-4275	174	1	the	the	DET
ejpam-4275	174	2	intersection	intersection	NOUN
ejpam-4275	174	3	of	of	ADP
ejpam-4275	174	4	infra	infra	NOUN
ejpam-4275	174	5	soft	soft	ADJ
ejpam-4275	174	6	open	open	ADJ
ejpam-4275	174	7	and	and	CCONJ
ejpam-4275	174	8	infra	infra	NOUN
ejpam-4275	174	9	soft	soft	ADJ
ejpam-4275	174	10	pre	pre	ADJ
ejpam-4275	174	11	-	-	ADJ
ejpam-4275	174	12	open	open	ADJ
ejpam-4275	174	13	sets	set	NOUN
ejpam-4275	174	14	is	be	AUX
ejpam-4275	174	15	an	an	DET
ejpam-4275	174	16	infra	infra	NOUN
ejpam-4275	174	17	soft	soft	ADJ
ejpam-4275	174	18	pre	pre	ADJ
ejpam-4275	174	19	-	-	ADJ
ejpam-4275	174	20	open	open	ADJ
ejpam-4275	174	21	set	set	NOUN
ejpam-4275	174	22	.	.	PUNCT
ejpam-4275	175	1	proof	proof	NOUN
ejpam-4275	175	2	.	.	PUNCT
ejpam-4275	176	1	let	let	VERB
ejpam-4275	176	2	(	(	PUNCT
ejpam-4275	176	3	ω1,σ	ω1,σ	PROPN
ejpam-4275	176	4	)	)	PUNCT
ejpam-4275	176	5	be	be	AUX
ejpam-4275	176	6	an	an	DET
ejpam-4275	176	7	infra	infra	NOUN
ejpam-4275	176	8	soft	soft	ADJ
ejpam-4275	176	9	open	open	ADJ
ejpam-4275	176	10	set	set	VERB
ejpam-4275	176	11	and	and	CCONJ
ejpam-4275	176	12	(	(	PUNCT
ejpam-4275	176	13	ω2,σ	ω2,σ	PROPN
ejpam-4275	176	14	)	)	PUNCT
ejpam-4275	176	15	be	be	AUX
ejpam-4275	176	16	an	an	DET
ejpam-4275	176	17	infra	infra	NOUN
ejpam-4275	176	18	soft	soft	ADJ
ejpam-4275	176	19	pre	pre	ADJ
ejpam-4275	176	20	-	-	ADJ
ejpam-4275	176	21	open	open	ADJ
ejpam-4275	176	22	set	set	NOUN
ejpam-4275	176	23	.	.	PUNCT
ejpam-4275	177	1	then	then	ADV
ejpam-4275	177	2	(	(	PUNCT
ejpam-4275	177	3	ω1,σ	ω1,σ	PROPN
ejpam-4275	177	4	)	)	PUNCT
ejpam-4275	177	5	⋂̃	⋂̃	NOUN
ejpam-4275	177	6	(	(	PUNCT
ejpam-4275	177	7	ω2,σ)⊆̃(ω1,σ	ω2,σ)⊆̃(ω1,σ	PROPN
ejpam-4275	177	8	)	)	PUNCT
ejpam-4275	177	9	⋂̃	⋂̃	NOUN
ejpam-4275	177	10	int(cl(ω2,σ	int(cl(ω2,σ	NOUN
ejpam-4275	177	11	)	)	PUNCT
ejpam-4275	177	12	)	)	PUNCT
ejpam-4275	178	1	=	=	SYM
ejpam-4275	178	2	int[(ω1,σ	int[(ω1,σ	PROPN
ejpam-4275	178	3	)	)	PUNCT
ejpam-4275	178	4	⋂̃	⋂̃	ADJ
ejpam-4275	178	5	cl(ω2,σ	cl(ω2,σ	NOUN
ejpam-4275	178	6	)	)	PUNCT
ejpam-4275	178	7	]	]	PUNCT
ejpam-4275	178	8	;	;	PUNCT
ejpam-4275	178	9	by	by	ADP
ejpam-4275	178	10	proposition	proposition	NOUN
ejpam-4275	178	11	2	2	NUM
ejpam-4275	178	12	we	we	PRON
ejpam-4275	178	13	obtain	obtain	VERB
ejpam-4275	178	14	int[(ω1,σ	int[(ω1,σ	PROPN
ejpam-4275	178	15	)	)	PUNCT
ejpam-4275	178	16	⋂̃	⋂̃	ADJ
ejpam-4275	178	17	cl(ω2,σ)]⊆̃int(cl[(ω1,σ	cl(ω2,σ)]⊆̃int(cl[(ω1,σ	NOUN
ejpam-4275	178	18	)	)	PUNCT
ejpam-4275	178	19	⋂̃	⋂̃	NOUN
ejpam-4275	178	20	(	(	PUNCT
ejpam-4275	178	21	ω2,σ	ω2,σ	PROPN
ejpam-4275	178	22	)	)	PUNCT
ejpam-4275	178	23	]	]	PUNCT
ejpam-4275	178	24	.	.	PUNCT
ejpam-4275	179	1	hence	hence	ADV
ejpam-4275	179	2	,	,	PUNCT
ejpam-4275	179	3	(	(	PUNCT
ejpam-4275	179	4	ω1,σ	ω1,σ	NOUN
ejpam-4275	179	5	)	)	PUNCT
ejpam-4275	179	6	⋂̃	⋂̃	NOUN
ejpam-4275	179	7	(	(	PUNCT
ejpam-4275	179	8	ω2,σ	ω2,σ	PROPN
ejpam-4275	179	9	)	)	PUNCT
ejpam-4275	179	10	is	be	AUX
ejpam-4275	179	11	an	an	DET
ejpam-4275	179	12	infra	infra	NOUN
ejpam-4275	179	13	soft	soft	ADJ
ejpam-4275	179	14	pre	pre	ADJ
ejpam-4275	179	15	-	-	ADJ
ejpam-4275	179	16	open	open	ADJ
ejpam-4275	179	17	set	set	NOUN
ejpam-4275	179	18	,	,	PUNCT
ejpam-4275	179	19	as	as	SCONJ
ejpam-4275	179	20	required	require	VERB
ejpam-4275	179	21	.	.	PUNCT
ejpam-4275	180	1	corollary	corollary	ADJ
ejpam-4275	180	2	3	3	NUM
ejpam-4275	180	3	.	.	PUNCT
ejpam-4275	181	1	the	the	DET
ejpam-4275	181	2	union	union	NOUN
ejpam-4275	181	3	of	of	ADP
ejpam-4275	181	4	infra	infra	NOUN
ejpam-4275	181	5	soft	soft	ADJ
ejpam-4275	181	6	closed	closed	ADJ
ejpam-4275	181	7	and	and	CCONJ
ejpam-4275	181	8	infra	infra	VERB
ejpam-4275	181	9	soft	soft	ADJ
ejpam-4275	181	10	pre	pre	ADJ
ejpam-4275	181	11	-	-	ADJ
ejpam-4275	181	12	closed	closed	ADJ
ejpam-4275	181	13	sets	set	NOUN
ejpam-4275	181	14	is	be	AUX
ejpam-4275	181	15	an	an	DET
ejpam-4275	181	16	infra	infra	NOUN
ejpam-4275	181	17	soft	soft	ADJ
ejpam-4275	181	18	pre	pre	ADJ
ejpam-4275	181	19	-	-	ADJ
ejpam-4275	181	20	closed	closed	ADJ
ejpam-4275	181	21	set	set	NOUN
ejpam-4275	181	22	.	.	PUNCT
ejpam-4275	182	1	definition	definition	NOUN
ejpam-4275	182	2	17	17	NUM
ejpam-4275	182	3	.	.	PUNCT
ejpam-4275	183	1	an	an	DET
ejpam-4275	183	2	ists	ist	NOUN
ejpam-4275	183	3	(	(	PUNCT
ejpam-4275	183	4	x	x	X
ejpam-4275	183	5	,	,	PUNCT
ejpam-4275	183	6	ξ	ξ	PROPN
ejpam-4275	183	7	,	,	PUNCT
ejpam-4275	183	8	σ	σ	NOUN
ejpam-4275	183	9	)	)	PUNCT
ejpam-4275	183	10	is	be	AUX
ejpam-4275	183	11	said	say	VERB
ejpam-4275	183	12	to	to	PART
ejpam-4275	183	13	be	be	AUX
ejpam-4275	183	14	infra	infra	NOUN
ejpam-4275	183	15	soft	soft	ADJ
ejpam-4275	183	16	hyperconnected	hyperconnecte	VERB
ejpam-4275	183	17	if	if	SCONJ
ejpam-4275	183	18	the	the	DET
ejpam-4275	183	19	intersection	intersection	NOUN
ejpam-4275	183	20	of	of	ADP
ejpam-4275	183	21	any	any	DET
ejpam-4275	183	22	two	two	NUM
ejpam-4275	183	23	non	non	ADJ
ejpam-4275	183	24	-	-	ADJ
ejpam-4275	183	25	null	null	ADJ
ejpam-4275	183	26	ξ	ξ	NOUN
ejpam-4275	183	27	-	-	ADJ
ejpam-4275	183	28	infra	infra	ADJ
ejpam-4275	183	29	soft	soft	ADJ
ejpam-4275	183	30	open	open	ADJ
ejpam-4275	183	31	sets	set	NOUN
ejpam-4275	183	32	is	be	AUX
ejpam-4275	183	33	non	non	ADJ
ejpam-4275	183	34	-	-	ADJ
ejpam-4275	183	35	null	null	ADJ
ejpam-4275	183	36	.	.	PUNCT
ejpam-4275	184	1	otherwise	otherwise	ADV
ejpam-4275	184	2	,	,	PUNCT
ejpam-4275	184	3	(	(	PUNCT
ejpam-4275	184	4	x	x	X
ejpam-4275	184	5	,	,	PUNCT
ejpam-4275	184	6	ξ	ξ	PROPN
ejpam-4275	184	7	,	,	PUNCT
ejpam-4275	184	8	σ	σ	NOUN
ejpam-4275	184	9	)	)	PUNCT
ejpam-4275	184	10	is	be	AUX
ejpam-4275	184	11	said	say	VERB
ejpam-4275	184	12	to	to	PART
ejpam-4275	184	13	be	be	AUX
ejpam-4275	184	14	infra	infra	NOUN
ejpam-4275	184	15	soft	soft	ADJ
ejpam-4275	184	16	dishyperconnected	dishyperconnecte	VERB
ejpam-4275	184	17	.	.	PUNCT
ejpam-4275	185	1	proposition	proposition	NOUN
ejpam-4275	185	2	10	10	NUM
ejpam-4275	185	3	.	.	PUNCT
ejpam-4275	186	1	the	the	DET
ejpam-4275	186	2	intersection	intersection	NOUN
ejpam-4275	186	3	of	of	ADP
ejpam-4275	186	4	two	two	NUM
ejpam-4275	186	5	infra	infra	NOUN
ejpam-4275	186	6	soft	soft	ADJ
ejpam-4275	186	7	pre	pre	ADJ
ejpam-4275	186	8	-	-	ADJ
ejpam-4275	186	9	open	open	ADJ
ejpam-4275	186	10	subsets	subset	NOUN
ejpam-4275	186	11	of	of	ADP
ejpam-4275	186	12	an	an	DET
ejpam-4275	186	13	infra	infra	NOUN
ejpam-4275	186	14	soft	soft	ADJ
ejpam-4275	186	15	hyperconnected	hyperconnecte	VERB
ejpam-4275	186	16	space	space	NOUN
ejpam-4275	186	17	is	be	AUX
ejpam-4275	186	18	an	an	DET
ejpam-4275	186	19	infra	infra	NOUN
ejpam-4275	186	20	soft	soft	ADJ
ejpam-4275	186	21	pre	pre	ADJ
ejpam-4275	186	22	-	-	ADJ
ejpam-4275	186	23	open	open	ADJ
ejpam-4275	186	24	set	set	NOUN
ejpam-4275	186	25	.	.	PUNCT
ejpam-4275	187	1	t.m	t.m	PROPN
ejpam-4275	187	2	.	.	PUNCT
ejpam-4275	187	3	al	al	PROPN
ejpam-4275	187	4	-	-	PUNCT
ejpam-4275	187	5	shami	shami	PROPN
ejpam-4275	187	6	,	,	PUNCT
ejpam-4275	187	7	h.a	h.a	PROPN
ejpam-4275	187	8	.	.	PROPN
ejpam-4275	187	9	othman	othman	PROPN
ejpam-4275	187	10	/	/	SYM
ejpam-4275	187	11	eur	eur	PROPN
ejpam-4275	187	12	.	.	PUNCT
ejpam-4275	188	1	j.	j.	PROPN
ejpam-4275	188	2	pure	pure	PROPN
ejpam-4275	188	3	appl	appl	PROPN
ejpam-4275	188	4	.	.	PROPN
ejpam-4275	188	5	math	math	PROPN
ejpam-4275	188	6	,	,	PUNCT
ejpam-4275	188	7	15	15	NUM
ejpam-4275	188	8	(	(	PUNCT
ejpam-4275	188	9	1	1	NUM
ejpam-4275	188	10	)	)	PUNCT
ejpam-4275	188	11	(	(	PUNCT
ejpam-4275	188	12	2022	2022	NUM
ejpam-4275	188	13	)	)	PUNCT
ejpam-4275	188	14	,	,	PUNCT
ejpam-4275	188	15	261	261	NUM
ejpam-4275	188	16	-	-	SYM
ejpam-4275	188	17	280	280	NUM
ejpam-4275	188	18	267	267	NUM
ejpam-4275	188	19	proof	proof	NOUN
ejpam-4275	188	20	.	.	PUNCT
ejpam-4275	189	1	let	let	VERB
ejpam-4275	189	2	(	(	PUNCT
ejpam-4275	189	3	ω1,σ	ω1,σ	PROPN
ejpam-4275	189	4	)	)	PUNCT
ejpam-4275	189	5	and	and	CCONJ
ejpam-4275	189	6	(	(	PUNCT
ejpam-4275	189	7	ω2,σ	ω2,σ	PROPN
ejpam-4275	189	8	)	)	PUNCT
ejpam-4275	189	9	be	be	VERB
ejpam-4275	189	10	infra	infra	NOUN
ejpam-4275	189	11	soft	soft	ADJ
ejpam-4275	189	12	pre	pre	ADJ
ejpam-4275	189	13	-	-	ADJ
ejpam-4275	189	14	open	open	ADJ
ejpam-4275	189	15	sets	set	NOUN
ejpam-4275	189	16	.	.	PUNCT
ejpam-4275	190	1	if	if	SCONJ
ejpam-4275	190	2	one	one	NUM
ejpam-4275	190	3	of	of	ADP
ejpam-4275	190	4	them	they	PRON
ejpam-4275	190	5	is	be	AUX
ejpam-4275	190	6	the	the	DET
ejpam-4275	190	7	null	null	ADJ
ejpam-4275	190	8	soft	soft	ADJ
ejpam-4275	190	9	set	set	NOUN
ejpam-4275	190	10	,	,	PUNCT
ejpam-4275	190	11	then	then	ADV
ejpam-4275	190	12	we	we	PRON
ejpam-4275	190	13	obtain	obtain	VERB
ejpam-4275	190	14	the	the	DET
ejpam-4275	190	15	desired	desire	VERB
ejpam-4275	190	16	result	result	NOUN
ejpam-4275	190	17	.	.	PUNCT
ejpam-4275	191	1	suppose	suppose	VERB
ejpam-4275	191	2	that	that	SCONJ
ejpam-4275	191	3	(	(	PUNCT
ejpam-4275	191	4	ω1,σ	ω1,σ	PROPN
ejpam-4275	191	5	)	)	PUNCT
ejpam-4275	191	6	and	and	CCONJ
ejpam-4275	191	7	(	(	PUNCT
ejpam-4275	191	8	ω2,σ	ω2,σ	PROPN
ejpam-4275	191	9	)	)	PUNCT
ejpam-4275	191	10	are	be	AUX
ejpam-4275	191	11	non	non	ADJ
ejpam-4275	191	12	-	-	ADJ
ejpam-4275	191	13	null	null	ADJ
ejpam-4275	191	14	.	.	PUNCT
ejpam-4275	192	1	according	accord	VERB
ejpam-4275	192	2	to	to	ADP
ejpam-4275	192	3	proposition	proposition	NOUN
ejpam-4275	192	4	6	6	NUM
ejpam-4275	192	5	there	there	PRON
ejpam-4275	192	6	are	be	VERB
ejpam-4275	192	7	two	two	NUM
ejpam-4275	192	8	ξ	ξ	NOUN
ejpam-4275	192	9	-	-	ADJ
ejpam-4275	192	10	infra	infra	ADJ
ejpam-4275	192	11	soft	soft	ADJ
ejpam-4275	192	12	open	open	ADJ
ejpam-4275	192	13	sets	set	NOUN
ejpam-4275	192	14	(	(	PUNCT
ejpam-4275	192	15	ψ1,σ	ψ1,σ	PROPN
ejpam-4275	192	16	)	)	PUNCT
ejpam-4275	192	17	̸=	̸=	PROPN
ejpam-4275	192	18	φ	φ	PROPN
ejpam-4275	192	19	and	and	CCONJ
ejpam-4275	192	20	(	(	PUNCT
ejpam-4275	192	21	ψ2,σ	ψ2,σ	NOUN
ejpam-4275	192	22	)	)	PUNCT
ejpam-4275	192	23	̸=	̸=	PROPN
ejpam-4275	192	24	φ	φ	NUM
ejpam-4275	192	25	such	such	ADJ
ejpam-4275	192	26	that	that	SCONJ
ejpam-4275	192	27	(	(	PUNCT
ejpam-4275	192	28	ω1,σ)⊆̃(ψ1,σ)⊆̃cl(ω1,σ	ω1,σ)⊆̃(ψ1,σ)⊆̃cl(ω1,σ	PROPN
ejpam-4275	192	29	)	)	PUNCT
ejpam-4275	192	30	and	and	CCONJ
ejpam-4275	192	31	(	(	PUNCT
ejpam-4275	192	32	ω2,σ)⊆̃(ψ2,σ)⊆̃cl(ω2,σ	ω2,σ)⊆̃(ψ2,σ)⊆̃cl(ω2,σ	NOUN
ejpam-4275	192	33	)	)	PUNCT
ejpam-4275	192	34	.	.	PUNCT
ejpam-4275	193	1	by	by	ADP
ejpam-4275	193	2	hypothesis	hypothesis	NOUN
ejpam-4275	193	3	of	of	ADP
ejpam-4275	193	4	infra	infra	NOUN
ejpam-4275	193	5	soft	soft	ADJ
ejpam-4275	193	6	hyperconnectedness	hyperconnectedness	NOUN
ejpam-4275	193	7	,	,	PUNCT
ejpam-4275	193	8	(	(	PUNCT
ejpam-4275	193	9	ψ1,σ	ψ1,σ	PROPN
ejpam-4275	193	10	)	)	PUNCT
ejpam-4275	193	11	⋂̃	⋂̃	NOUN
ejpam-4275	193	12	(	(	PUNCT
ejpam-4275	193	13	ψ2,σ	ψ2,σ	NOUN
ejpam-4275	193	14	)	)	PUNCT
ejpam-4275	193	15	is	be	AUX
ejpam-4275	193	16	a	a	DET
ejpam-4275	193	17	non	non	ADJ
ejpam-4275	193	18	-	-	ADJ
ejpam-4275	193	19	null	null	ADJ
ejpam-4275	193	20	ξ	ξ	NOUN
ejpam-4275	193	21	-	-	ADJ
ejpam-4275	193	22	infra	infra	ADJ
ejpam-4275	193	23	soft	soft	ADJ
ejpam-4275	193	24	open	open	ADJ
ejpam-4275	193	25	set	set	NOUN
ejpam-4275	193	26	.	.	PUNCT
ejpam-4275	194	1	now	now	ADV
ejpam-4275	194	2	,	,	PUNCT
ejpam-4275	194	3	(	(	PUNCT
ejpam-4275	194	4	ω1,σ	ω1,σ	NOUN
ejpam-4275	194	5	)	)	PUNCT
ejpam-4275	194	6	⋂̃	⋂̃	NOUN
ejpam-4275	194	7	(	(	PUNCT
ejpam-4275	194	8	ω2,σ)⊆̃(ψ1,σ	ω2,σ)⊆̃(ψ1,σ	NOUN
ejpam-4275	194	9	)	)	PUNCT
ejpam-4275	194	10	⋂̃	⋂̃	NOUN
ejpam-4275	194	11	(	(	PUNCT
ejpam-4275	194	12	ψ2,σ)⊆̃cl[(ω1,σ	ψ2,σ)⊆̃cl[(ω1,σ	X
ejpam-4275	194	13	)	)	PUNCT
ejpam-4275	194	14	⋂̃	⋂̃	NOUN
ejpam-4275	194	15	(	(	PUNCT
ejpam-4275	194	16	ω2,σ	ω2,σ	PROPN
ejpam-4275	194	17	)	)	PUNCT
ejpam-4275	194	18	]	]	PUNCT
ejpam-4275	194	19	.	.	PUNCT
ejpam-4275	195	1	hence	hence	ADV
ejpam-4275	195	2	,	,	PUNCT
ejpam-4275	195	3	(	(	PUNCT
ejpam-4275	195	4	ω1,σ	ω1,σ	NOUN
ejpam-4275	195	5	)	)	PUNCT
ejpam-4275	195	6	⋂̃	⋂̃	NOUN
ejpam-4275	195	7	(	(	PUNCT
ejpam-4275	195	8	ω2,σ	ω2,σ	PROPN
ejpam-4275	195	9	)	)	PUNCT
ejpam-4275	195	10	is	be	AUX
ejpam-4275	195	11	an	an	DET
ejpam-4275	195	12	infra	infra	NOUN
ejpam-4275	195	13	soft	soft	ADJ
ejpam-4275	195	14	pre	pre	ADJ
ejpam-4275	195	15	-	-	ADJ
ejpam-4275	195	16	open	open	ADJ
ejpam-4275	195	17	set	set	NOUN
ejpam-4275	195	18	.	.	PUNCT
ejpam-4275	196	1	lemma	lemma	PROPN
ejpam-4275	196	2	1	1	X
ejpam-4275	196	3	.	.	PUNCT
ejpam-4275	197	1	let	let	VERB
ejpam-4275	197	2	eτ	eτ	VERB
ejpam-4275	197	3	:	:	PUNCT
ejpam-4275	197	4	(	(	PUNCT
ejpam-4275	197	5	x1	x1	PROPN
ejpam-4275	197	6	,	,	PUNCT
ejpam-4275	197	7	ξ1,σ1	ξ1,σ1	PROPN
ejpam-4275	197	8	)	)	PUNCT
ejpam-4275	197	9	→	→	SYM
ejpam-4275	197	10	(	(	PUNCT
ejpam-4275	197	11	x2	x2	PROPN
ejpam-4275	197	12	,	,	PUNCT
ejpam-4275	197	13	ξ2,σ2	ξ2,σ2	PROPN
ejpam-4275	197	14	)	)	PUNCT
ejpam-4275	197	15	be	be	VERB
ejpam-4275	197	16	an	an	DET
ejpam-4275	197	17	infra	infra	NOUN
ejpam-4275	197	18	soft	soft	ADJ
ejpam-4275	197	19	homeomorphism	homeomorphism	NOUN
ejpam-4275	197	20	map	map	NOUN
ejpam-4275	197	21	.	.	PUNCT
ejpam-4275	198	1	then	then	ADV
ejpam-4275	198	2	for	for	ADP
ejpam-4275	198	3	any	any	DET
ejpam-4275	198	4	subset	subset	NOUN
ejpam-4275	198	5	(	(	PUNCT
ejpam-4275	198	6	ω	ω	PROPN
ejpam-4275	198	7	,	,	PUNCT
ejpam-4275	198	8	σ1	σ1	PROPN
ejpam-4275	198	9	)	)	PUNCT
ejpam-4275	198	10	we	we	PRON
ejpam-4275	198	11	have	have	VERB
ejpam-4275	198	12	the	the	DET
ejpam-4275	198	13	next	next	ADJ
ejpam-4275	198	14	two	two	NUM
ejpam-4275	198	15	results	result	NOUN
ejpam-4275	198	16	.	.	PUNCT
ejpam-4275	199	1	(	(	PUNCT
ejpam-4275	199	2	i	i	NOUN
ejpam-4275	199	3	)	)	PUNCT
ejpam-4275	199	4	eτ	eτ	PROPN
ejpam-4275	199	5	(	(	PUNCT
ejpam-4275	199	6	int(ω	int(ω	PROPN
ejpam-4275	199	7	,	,	PUNCT
ejpam-4275	199	8	σ1	σ1	NOUN
ejpam-4275	199	9	)	)	PUNCT
ejpam-4275	199	10	)	)	PUNCT
ejpam-4275	200	1	=	=	PRON
ejpam-4275	200	2	int(eτ	int(eτ	PROPN
ejpam-4275	200	3	(	(	PUNCT
ejpam-4275	200	4	ω	ω	PROPN
ejpam-4275	200	5	,	,	PUNCT
ejpam-4275	200	6	σ1	σ1	PROPN
ejpam-4275	200	7	)	)	PUNCT
ejpam-4275	200	8	)	)	PUNCT
ejpam-4275	200	9	.	.	PUNCT
ejpam-4275	201	1	(	(	PUNCT
ejpam-4275	201	2	ii	ii	NOUN
ejpam-4275	201	3	)	)	PUNCT
ejpam-4275	201	4	eτ	eτ	PROPN
ejpam-4275	201	5	(	(	PUNCT
ejpam-4275	201	6	cl(ω	cl(ω	X
ejpam-4275	201	7	,	,	PUNCT
ejpam-4275	201	8	σ1	σ1	NOUN
ejpam-4275	201	9	)	)	PUNCT
ejpam-4275	201	10	)	)	PUNCT
ejpam-4275	202	1	=	=	PUNCT
ejpam-4275	202	2	cl(eτ	cl(eτ	NOUN
ejpam-4275	202	3	(	(	PUNCT
ejpam-4275	202	4	ω	ω	PROPN
ejpam-4275	202	5	,	,	PUNCT
ejpam-4275	202	6	σ1	σ1	PROPN
ejpam-4275	202	7	)	)	PUNCT
ejpam-4275	202	8	)	)	PUNCT
ejpam-4275	202	9	.	.	PUNCT
ejpam-4275	203	1	proof	proof	NOUN
ejpam-4275	203	2	.	.	PUNCT
ejpam-4275	204	1	to	to	PART
ejpam-4275	204	2	prove	prove	VERB
ejpam-4275	204	3	(	(	PUNCT
ejpam-4275	204	4	i	i	NOUN
ejpam-4275	204	5	)	)	PUNCT
ejpam-4275	204	6	,	,	PUNCT
ejpam-4275	204	7	let	let	VERB
ejpam-4275	204	8	δsη′	δsη′	NUM
ejpam-4275	204	9	∈	∈	NOUN
ejpam-4275	204	10	eτ	eτ	X
ejpam-4275	204	11	(	(	PUNCT
ejpam-4275	204	12	int(ω	int(ω	PROPN
ejpam-4275	204	13	,	,	PUNCT
ejpam-4275	204	14	σ1	σ1	NOUN
ejpam-4275	204	15	)	)	PUNCT
ejpam-4275	204	16	)	)	PUNCT
ejpam-4275	204	17	.	.	PUNCT
ejpam-4275	205	1	then	then	ADV
ejpam-4275	205	2	there	there	PRON
ejpam-4275	205	3	is	be	VERB
ejpam-4275	205	4	δxη	δxη	NOUN
ejpam-4275	205	5	∈	∈	PROPN
ejpam-4275	205	6	int(ω	int(ω	NOUN
ejpam-4275	205	7	,	,	PUNCT
ejpam-4275	205	8	σ1	σ1	PROPN
ejpam-4275	205	9	)	)	PUNCT
ejpam-4275	205	10	such	such	ADJ
ejpam-4275	205	11	that	that	SCONJ
ejpam-4275	205	12	eτ	eτ	PROPN
ejpam-4275	205	13	(	(	PUNCT
ejpam-4275	205	14	δ	δ	PROPN
ejpam-4275	205	15	x	x	SYM
ejpam-4275	205	16	η	η	PROPN
ejpam-4275	205	17	)	)	PUNCT
ejpam-4275	205	18	=	=	SYM
ejpam-4275	205	19	δsη′	δsη′	PROPN
ejpam-4275	205	20	.	.	PUNCT
ejpam-4275	206	1	this	this	PRON
ejpam-4275	206	2	means	mean	VERB
ejpam-4275	206	3	there	there	PRON
ejpam-4275	206	4	exists	exist	VERB
ejpam-4275	206	5	an	an	DET
ejpam-4275	206	6	infra	infra	NOUN
ejpam-4275	206	7	soft	soft	ADJ
ejpam-4275	206	8	open	open	ADJ
ejpam-4275	206	9	set	set	NOUN
ejpam-4275	206	10	(	(	PUNCT
ejpam-4275	206	11	ψ	ψ	NOUN
ejpam-4275	206	12	,	,	PUNCT
ejpam-4275	206	13	σ1	σ1	NOUN
ejpam-4275	206	14	)	)	PUNCT
ejpam-4275	206	15	such	such	ADJ
ejpam-4275	206	16	that	that	DET
ejpam-4275	206	17	δxη	δxη	NOUN
ejpam-4275	206	18	∈	∈	PROPN
ejpam-4275	206	19	(	(	PUNCT
ejpam-4275	206	20	ψ	ψ	NOUN
ejpam-4275	206	21	,	,	PUNCT
ejpam-4275	206	22	σ1)⊆̃(ω	σ1)⊆̃(ω	PROPN
ejpam-4275	206	23	,	,	PUNCT
ejpam-4275	206	24	σ1	σ1	PROPN
ejpam-4275	206	25	)	)	PUNCT
ejpam-4275	206	26	.	.	PUNCT
ejpam-4275	207	1	therefore	therefore	ADV
ejpam-4275	207	2	,	,	PUNCT
ejpam-4275	207	3	δsη′	δsη′	PROPN
ejpam-4275	207	4	=	=	SYM
ejpam-4275	207	5	eτ	eτ	X
ejpam-4275	207	6	(	(	PUNCT
ejpam-4275	207	7	δ	δ	PROPN
ejpam-4275	207	8	x	x	PROPN
ejpam-4275	207	9	η	η	PROPN
ejpam-4275	207	10	)	)	PUNCT
ejpam-4275	207	11	∈	∈	PROPN
ejpam-4275	207	12	eτ	eτ	ADP
ejpam-4275	207	13	(	(	PUNCT
ejpam-4275	207	14	ψ	ψ	NOUN
ejpam-4275	207	15	,	,	PUNCT
ejpam-4275	207	16	σ1)⊆̃eτ	σ1)⊆̃eτ	NOUN
ejpam-4275	207	17	(	(	PUNCT
ejpam-4275	207	18	ω	ω	PROPN
ejpam-4275	207	19	,	,	PUNCT
ejpam-4275	207	20	σ1	σ1	PROPN
ejpam-4275	207	21	)	)	PUNCT
ejpam-4275	207	22	.	.	PUNCT
ejpam-4275	208	1	this	this	PRON
ejpam-4275	208	2	implies	imply	VERB
ejpam-4275	208	3	that	that	SCONJ
ejpam-4275	208	4	δsη′	δsη′	PROPN
ejpam-4275	208	5	∈	∈	PROPN
ejpam-4275	208	6	int(eτ	int(eτ	NOUN
ejpam-4275	208	7	(	(	PUNCT
ejpam-4275	208	8	ω	ω	PROPN
ejpam-4275	208	9	,	,	PUNCT
ejpam-4275	208	10	σ1	σ1	PROPN
ejpam-4275	208	11	)	)	PUNCT
ejpam-4275	208	12	)	)	PUNCT
ejpam-4275	208	13	.	.	PUNCT
ejpam-4275	209	1	thus	thus	ADV
ejpam-4275	209	2	,	,	PUNCT
ejpam-4275	209	3	eτ	eτ	X
ejpam-4275	209	4	(	(	PUNCT
ejpam-4275	209	5	int(ω	int(ω	PROPN
ejpam-4275	209	6	,	,	PUNCT
ejpam-4275	209	7	σ1))⊆̃int(eτ	σ1))⊆̃int(eτ	X
ejpam-4275	209	8	(	(	PUNCT
ejpam-4275	209	9	ω	ω	PROPN
ejpam-4275	209	10	,	,	PUNCT
ejpam-4275	209	11	σ1	σ1	PROPN
ejpam-4275	209	12	)	)	PUNCT
ejpam-4275	209	13	)	)	PUNCT
ejpam-4275	209	14	.	.	PUNCT
ejpam-4275	210	1	conversely	conversely	ADV
ejpam-4275	210	2	,	,	PUNCT
ejpam-4275	210	3	let	let	VERB
ejpam-4275	210	4	δsη′	δsη′	PROPN
ejpam-4275	210	5	∈	∈	PROPN
ejpam-4275	210	6	int(eτ	int(eτ	NOUN
ejpam-4275	210	7	(	(	PUNCT
ejpam-4275	210	8	ω	ω	PROPN
ejpam-4275	210	9	,	,	PUNCT
ejpam-4275	210	10	σ1	σ1	PROPN
ejpam-4275	210	11	)	)	PUNCT
ejpam-4275	210	12	)	)	PUNCT
ejpam-4275	210	13	.	.	PUNCT
ejpam-4275	211	1	then	then	ADV
ejpam-4275	211	2	there	there	PRON
ejpam-4275	211	3	exists	exist	VERB
ejpam-4275	211	4	an	an	DET
ejpam-4275	211	5	infra	infra	NOUN
ejpam-4275	211	6	soft	soft	ADJ
ejpam-4275	211	7	open	open	ADJ
ejpam-4275	211	8	set	set	NOUN
ejpam-4275	211	9	(	(	PUNCT
ejpam-4275	211	10	ψ	ψ	NOUN
ejpam-4275	211	11	,	,	PUNCT
ejpam-4275	211	12	σ2	σ2	NOUN
ejpam-4275	211	13	)	)	PUNCT
ejpam-4275	211	14	such	such	ADJ
ejpam-4275	211	15	that	that	DET
ejpam-4275	211	16	δsη′	δsη′	PROPN
ejpam-4275	211	17	∈	∈	PROPN
ejpam-4275	211	18	(	(	PUNCT
ejpam-4275	211	19	ψ	ψ	NOUN
ejpam-4275	211	20	,	,	PUNCT
ejpam-4275	211	21	σ2)⊆̃eτ	σ2)⊆̃eτ	NOUN
ejpam-4275	211	22	(	(	PUNCT
ejpam-4275	211	23	ω	ω	PROPN
ejpam-4275	211	24	,	,	PUNCT
ejpam-4275	211	25	σ1	σ1	PROPN
ejpam-4275	211	26	)	)	PUNCT
ejpam-4275	211	27	.	.	PUNCT
ejpam-4275	212	1	therefore	therefore	ADV
ejpam-4275	212	2	,	,	PUNCT
ejpam-4275	212	3	e−1	e−1	PROPN
ejpam-4275	212	4	τ	τ	X
ejpam-4275	212	5	(	(	PUNCT
ejpam-4275	212	6	δsη′	δsη′	PROPN
ejpam-4275	212	7	)	)	PUNCT
ejpam-4275	212	8	∈	∈	PROPN
ejpam-4275	212	9	e−1	e−1	PROPN
ejpam-4275	212	10	τ	τ	X
ejpam-4275	212	11	(	(	PUNCT
ejpam-4275	212	12	ψ	ψ	NOUN
ejpam-4275	212	13	,	,	PUNCT
ejpam-4275	212	14	σ2)⊆̃(ω	σ2)⊆̃(ω	NOUN
ejpam-4275	212	15	,	,	PUNCT
ejpam-4275	212	16	σ1	σ1	PROPN
ejpam-4275	212	17	)	)	PUNCT
ejpam-4275	212	18	.	.	PUNCT
ejpam-4275	213	1	automatically	automatically	ADV
ejpam-4275	213	2	,	,	PUNCT
ejpam-4275	213	3	we	we	PRON
ejpam-4275	213	4	obtain	obtain	VERB
ejpam-4275	213	5	e−1	e−1	PROPN
ejpam-4275	213	6	τ	τ	PROPN
ejpam-4275	213	7	(	(	PUNCT
ejpam-4275	213	8	δsη′	δsη′	PROPN
ejpam-4275	213	9	)	)	PUNCT
ejpam-4275	213	10	∈	∈	PROPN
ejpam-4275	213	11	int(ω	int(ω	NOUN
ejpam-4275	213	12	,	,	PUNCT
ejpam-4275	213	13	σ1	σ1	PROPN
ejpam-4275	213	14	)	)	PUNCT
ejpam-4275	213	15	.	.	PUNCT
ejpam-4275	214	1	so	so	ADV
ejpam-4275	214	2	that	that	SCONJ
ejpam-4275	214	3	,	,	PUNCT
ejpam-4275	214	4	δ	δ	PROPN
ejpam-4275	214	5	s	s	PART
ejpam-4275	214	6	η′	η′	NOUN
ejpam-4275	214	7	∈	∈	NOUN
ejpam-4275	214	8	eτ	eτ	X
ejpam-4275	214	9	(	(	PUNCT
ejpam-4275	214	10	int(ω	int(ω	PROPN
ejpam-4275	214	11	,	,	PUNCT
ejpam-4275	214	12	σ1	σ1	NOUN
ejpam-4275	214	13	)	)	PUNCT
ejpam-4275	214	14	)	)	PUNCT
ejpam-4275	214	15	.	.	PUNCT
ejpam-4275	215	1	thus	thus	ADV
ejpam-4275	215	2	,	,	PUNCT
ejpam-4275	215	3	int(eτ	int(eτ	PROPN
ejpam-4275	215	4	(	(	PUNCT
ejpam-4275	215	5	ω	ω	PROPN
ejpam-4275	215	6	,	,	PUNCT
ejpam-4275	215	7	σ1))⊆̃eτ	σ1))⊆̃eτ	ADJ
ejpam-4275	215	8	(	(	PUNCT
ejpam-4275	215	9	int(ω	int(ω	PROPN
ejpam-4275	215	10	,	,	PUNCT
ejpam-4275	215	11	σ1	σ1	NOUN
ejpam-4275	215	12	)	)	PUNCT
ejpam-4275	215	13	)	)	PUNCT
ejpam-4275	215	14	.	.	PUNCT
ejpam-4275	216	1	hence	hence	ADV
ejpam-4275	216	2	,	,	PUNCT
ejpam-4275	216	3	the	the	DET
ejpam-4275	216	4	proof	proof	NOUN
ejpam-4275	216	5	is	be	AUX
ejpam-4275	216	6	complete	complete	ADJ
ejpam-4275	216	7	.	.	PUNCT
ejpam-4275	217	1	following	follow	VERB
ejpam-4275	217	2	similar	similar	ADJ
ejpam-4275	217	3	arguments	argument	NOUN
ejpam-4275	217	4	,	,	PUNCT
ejpam-4275	217	5	one	one	PRON
ejpam-4275	217	6	can	can	AUX
ejpam-4275	217	7	prove	prove	VERB
ejpam-4275	217	8	(	(	PUNCT
ejpam-4275	217	9	ii	ii	NOUN
ejpam-4275	217	10	)	)	PUNCT
ejpam-4275	217	11	.	.	PUNCT
ejpam-4275	218	1	proposition	proposition	NOUN
ejpam-4275	218	2	11	11	NUM
ejpam-4275	218	3	.	.	PUNCT
ejpam-4275	219	1	the	the	DET
ejpam-4275	219	2	infra	infra	NOUN
ejpam-4275	219	3	soft	soft	ADJ
ejpam-4275	219	4	homeomorphism	homeomorphism	NOUN
ejpam-4275	219	5	image	image	NOUN
ejpam-4275	219	6	of	of	ADP
ejpam-4275	219	7	an	an	DET
ejpam-4275	219	8	infra	infra	NOUN
ejpam-4275	219	9	soft	soft	ADJ
ejpam-4275	219	10	pre	pre	ADJ
ejpam-4275	219	11	-	-	ADJ
ejpam-4275	219	12	open	open	ADJ
ejpam-4275	219	13	set	set	NOUN
ejpam-4275	219	14	is	be	AUX
ejpam-4275	219	15	an	an	DET
ejpam-4275	219	16	infra	infra	NOUN
ejpam-4275	219	17	soft	soft	ADJ
ejpam-4275	219	18	pre	pre	ADJ
ejpam-4275	219	19	-	-	ADJ
ejpam-4275	219	20	open	open	ADJ
ejpam-4275	219	21	set	set	NOUN
ejpam-4275	219	22	.	.	PUNCT
ejpam-4275	220	1	proof	proof	NOUN
ejpam-4275	220	2	.	.	PUNCT
ejpam-4275	221	1	consider	consider	VERB
ejpam-4275	221	2	eτ	eτ	NOUN
ejpam-4275	221	3	:	:	PUNCT
ejpam-4275	221	4	(	(	PUNCT
ejpam-4275	221	5	x1	x1	PROPN
ejpam-4275	221	6	,	,	PUNCT
ejpam-4275	221	7	ξ1,σ1	ξ1,σ1	PROPN
ejpam-4275	221	8	)	)	PUNCT
ejpam-4275	221	9	→	→	SYM
ejpam-4275	221	10	(	(	PUNCT
ejpam-4275	221	11	x2	x2	PROPN
ejpam-4275	221	12	,	,	PUNCT
ejpam-4275	221	13	ξ2,σ2	ξ2,σ2	PROPN
ejpam-4275	221	14	)	)	PUNCT
ejpam-4275	221	15	as	as	ADP
ejpam-4275	221	16	an	an	DET
ejpam-4275	221	17	infra	infra	NOUN
ejpam-4275	221	18	soft	soft	ADJ
ejpam-4275	221	19	continuous	continuous	ADJ
ejpam-4275	221	20	map	map	NOUN
ejpam-4275	221	21	and	and	CCONJ
ejpam-4275	221	22	let	let	VERB
ejpam-4275	221	23	(	(	PUNCT
ejpam-4275	221	24	ω	ω	NOUN
ejpam-4275	221	25	,	,	PUNCT
ejpam-4275	221	26	σ1	σ1	PROPN
ejpam-4275	221	27	)	)	PUNCT
ejpam-4275	221	28	be	be	VERB
ejpam-4275	221	29	an	an	DET
ejpam-4275	221	30	infra	infra	NOUN
ejpam-4275	221	31	soft	soft	ADJ
ejpam-4275	221	32	pre	pre	ADJ
ejpam-4275	221	33	-	-	ADJ
ejpam-4275	221	34	open	open	ADJ
ejpam-4275	221	35	subset	subset	NOUN
ejpam-4275	221	36	of	of	ADP
ejpam-4275	221	37	(	(	PUNCT
ejpam-4275	221	38	x1	x1	PROPN
ejpam-4275	221	39	,	,	PUNCT
ejpam-4275	221	40	ξ1,σ1	ξ1,σ1	PROPN
ejpam-4275	221	41	)	)	PUNCT
ejpam-4275	221	42	.	.	PUNCT
ejpam-4275	222	1	then	then	ADV
ejpam-4275	222	2	eτ	eτ	PROPN
ejpam-4275	222	3	(	(	PUNCT
ejpam-4275	222	4	ω	ω	PROPN
ejpam-4275	222	5	,	,	PUNCT
ejpam-4275	222	6	σ1)⊆̃eτ	σ1)⊆̃eτ	NOUN
ejpam-4275	222	7	(	(	PUNCT
ejpam-4275	222	8	int(cl(ω	int(cl(ω	NOUN
ejpam-4275	222	9	,	,	PUNCT
ejpam-4275	222	10	σ1	σ1	NOUN
ejpam-4275	222	11	)	)	PUNCT
ejpam-4275	222	12	)	)	PUNCT
ejpam-4275	222	13	)	)	PUNCT
ejpam-4275	222	14	.	.	PUNCT
ejpam-4275	223	1	it	it	PRON
ejpam-4275	223	2	follows	follow	VERB
ejpam-4275	223	3	from	from	ADP
ejpam-4275	223	4	the	the	DET
ejpam-4275	223	5	above	above	ADJ
ejpam-4275	223	6	lemma	lemma	PROPN
ejpam-4275	223	7	that	that	PRON
ejpam-4275	223	8	eτ	eτ	PROPN
ejpam-4275	223	9	(	(	PUNCT
ejpam-4275	223	10	ω	ω	PROPN
ejpam-4275	223	11	,	,	PUNCT
ejpam-4275	223	12	σ1)⊆̃int(cl(eτ	σ1)⊆̃int(cl(eτ	PROPN
ejpam-4275	223	13	(	(	PUNCT
ejpam-4275	223	14	ω	ω	PROPN
ejpam-4275	223	15	,	,	PUNCT
ejpam-4275	223	16	σ1	σ1	PROPN
ejpam-4275	223	17	)	)	PUNCT
ejpam-4275	223	18	)	)	PUNCT
ejpam-4275	223	19	)	)	PUNCT
ejpam-4275	223	20	.	.	PUNCT
ejpam-4275	224	1	hence	hence	ADV
ejpam-4275	224	2	,	,	PUNCT
ejpam-4275	224	3	eτ	eτ	PROPN
ejpam-4275	224	4	(	(	PUNCT
ejpam-4275	224	5	ω	ω	PROPN
ejpam-4275	224	6	,	,	PUNCT
ejpam-4275	224	7	σ1	σ1	PROPN
ejpam-4275	224	8	)	)	PUNCT
ejpam-4275	224	9	is	be	AUX
ejpam-4275	224	10	an	an	DET
ejpam-4275	224	11	infra	infra	NOUN
ejpam-4275	224	12	soft	soft	ADJ
ejpam-4275	224	13	pre	pre	ADJ
ejpam-4275	224	14	-	-	ADJ
ejpam-4275	224	15	open	open	ADJ
ejpam-4275	224	16	subset	subset	NOUN
ejpam-4275	224	17	of	of	ADP
ejpam-4275	224	18	(	(	PUNCT
ejpam-4275	224	19	x2	x2	PROPN
ejpam-4275	224	20	,	,	PUNCT
ejpam-4275	224	21	ξ2,σ2	ξ2,σ2	PROPN
ejpam-4275	224	22	)	)	PUNCT
ejpam-4275	224	23	,	,	PUNCT
ejpam-4275	224	24	as	as	SCONJ
ejpam-4275	224	25	required	require	VERB
ejpam-4275	224	26	.	.	PUNCT
ejpam-4275	225	1	lemma	lemma	PROPN
ejpam-4275	225	2	2	2	X
ejpam-4275	225	3	.	.	X
ejpam-4275	226	1	consider	consider	VERB
ejpam-4275	226	2	(	(	PUNCT
ejpam-4275	226	3	ω1,σ1	ω1,σ1	PROPN
ejpam-4275	226	4	)	)	PUNCT
ejpam-4275	226	5	and	and	CCONJ
ejpam-4275	226	6	(	(	PUNCT
ejpam-4275	226	7	ω2,σ2	ω2,σ2	PROPN
ejpam-4275	226	8	)	)	PUNCT
ejpam-4275	226	9	as	as	ADP
ejpam-4275	226	10	subsets	subset	NOUN
ejpam-4275	226	11	of	of	ADP
ejpam-4275	226	12	(	(	PUNCT
ejpam-4275	226	13	x1	x1	PROPN
ejpam-4275	226	14	,	,	PUNCT
ejpam-4275	226	15	ξ1,σ1	ξ1,σ1	PROPN
ejpam-4275	226	16	)	)	PUNCT
ejpam-4275	226	17	and	and	CCONJ
ejpam-4275	226	18	(	(	PUNCT
ejpam-4275	226	19	x2	x2	PROPN
ejpam-4275	226	20	,	,	PUNCT
ejpam-4275	226	21	ξ2,σ2	ξ2,σ2	PROPN
ejpam-4275	226	22	)	)	PUNCT
ejpam-4275	226	23	,	,	PUNCT
ejpam-4275	226	24	respectively	respectively	ADV
ejpam-4275	226	25	.	.	PUNCT
ejpam-4275	227	1	then	then	ADV
ejpam-4275	227	2	(	(	PUNCT
ejpam-4275	227	3	i	i	NOUN
ejpam-4275	227	4	)	)	PUNCT
ejpam-4275	227	5	cl[(ω1,σ1)×	cl[(ω1,σ1)×	PROPN
ejpam-4275	227	6	(	(	PUNCT
ejpam-4275	227	7	ω2,σ2	ω2,σ2	PROPN
ejpam-4275	227	8	)	)	PUNCT
ejpam-4275	227	9	]	]	PUNCT
ejpam-4275	228	1	=	=	PUNCT
ejpam-4275	228	2	cl(ω1,σ1)×	cl(ω1,σ1)×	NOUN
ejpam-4275	228	3	cl(ω2,σ2	cl(ω2,σ2	NOUN
ejpam-4275	228	4	)	)	PUNCT
ejpam-4275	228	5	.	.	PUNCT
ejpam-4275	229	1	(	(	PUNCT
ejpam-4275	229	2	ii	ii	NOUN
ejpam-4275	229	3	)	)	PUNCT
ejpam-4275	229	4	int[(ω1,σ1)×	int[(ω1,σ1)×	PROPN
ejpam-4275	229	5	(	(	PUNCT
ejpam-4275	229	6	ω2,σ2	ω2,σ2	PROPN
ejpam-4275	229	7	)	)	PUNCT
ejpam-4275	229	8	]	]	PUNCT
ejpam-4275	230	1	=	=	PUNCT
ejpam-4275	230	2	int(ω1,σ1)×	int(ω1,σ1)×	PROPN
ejpam-4275	231	1	int(ω2,σ2	int(ω2,σ2	PROPN
ejpam-4275	231	2	)	)	PUNCT
ejpam-4275	231	3	.	.	PUNCT
ejpam-4275	232	1	proof	proof	NOUN
ejpam-4275	232	2	.	.	PUNCT
ejpam-4275	233	1	(	(	PUNCT
ejpam-4275	233	2	i	i	NOUN
ejpam-4275	233	3	):	):	PUNCT
ejpam-4275	233	4	let	let	VERB
ejpam-4275	233	5	δ	δ	PROPN
ejpam-4275	233	6	(	(	PUNCT
ejpam-4275	233	7	t	t	PROPN
ejpam-4275	233	8	,	,	PUNCT
ejpam-4275	233	9	s	s	PART
ejpam-4275	233	10	)	)	PUNCT
ejpam-4275	233	11	(	(	PUNCT
ejpam-4275	233	12	η,ϑ	η,ϑ	PROPN
ejpam-4275	233	13	)	)	PUNCT
ejpam-4275	233	14	̸∈	̸∈	PROPN
ejpam-4275	233	15	cl[(ω1,σ1)×	cl[(ω1,σ1)×	PROPN
ejpam-4275	233	16	(	(	PUNCT
ejpam-4275	233	17	ω2,σ2	ω2,σ2	PROPN
ejpam-4275	233	18	)	)	PUNCT
ejpam-4275	233	19	]	]	PUNCT
ejpam-4275	233	20	.	.	PUNCT
ejpam-4275	234	1	then	then	ADV
ejpam-4275	234	2	there	there	PRON
ejpam-4275	234	3	is	be	VERB
ejpam-4275	234	4	an	an	DET
ejpam-4275	234	5	infra	infra	NOUN
ejpam-4275	234	6	soft	soft	ADJ
ejpam-4275	234	7	open	open	ADJ
ejpam-4275	234	8	subset	subset	NOUN
ejpam-4275	234	9	(	(	PUNCT
ejpam-4275	234	10	ψ1,σ1)×(ψ2,σ2	ψ1,σ1)×(ψ2,σ2	VERB
ejpam-4275	234	11	)	)	PUNCT
ejpam-4275	234	12	of	of	ADP
ejpam-4275	234	13	x̃1×x̃2	x̃1×x̃2	PROPN
ejpam-4275	234	14	containing	contain	VERB
ejpam-4275	234	15	δ	δ	PROPN
ejpam-4275	234	16	(	(	PUNCT
ejpam-4275	234	17	t	t	PROPN
ejpam-4275	234	18	,	,	PUNCT
ejpam-4275	234	19	s	s	PART
ejpam-4275	234	20	)	)	PUNCT
ejpam-4275	234	21	(	(	PUNCT
ejpam-4275	234	22	η,ϑ	η,ϑ	PROPN
ejpam-4275	234	23	)	)	PUNCT
ejpam-4275	234	24	such	such	ADJ
ejpam-4275	234	25	that	that	SCONJ
ejpam-4275	234	26	[	[	X
ejpam-4275	234	27	(	(	PUNCT
ejpam-4275	234	28	ω1,σ1)×(ω2,σ2	ω1,σ1)×(ω2,σ2	NOUN
ejpam-4275	234	29	)	)	PUNCT
ejpam-4275	234	30	]	]	PUNCT
ejpam-4275	235	1	⋂̃	⋂̃	X
ejpam-4275	235	2	[	[	X
ejpam-4275	235	3	(	(	PUNCT
ejpam-4275	235	4	ψ1,σ1)×	ψ1,σ1)×	X
ejpam-4275	235	5	(	(	PUNCT
ejpam-4275	235	6	ψ2,σ2	ψ2,σ2	PROPN
ejpam-4275	235	7	)	)	PUNCT
ejpam-4275	235	8	]	]	PUNCT
ejpam-4275	236	1	=	=	PUNCT
ejpam-4275	236	2	φς1×σ2	φς1×σ2	PROPN
ejpam-4275	236	3	.	.	PUNCT
ejpam-4275	237	1	this	this	PRON
ejpam-4275	237	2	implies	imply	VERB
ejpam-4275	237	3	that	that	SCONJ
ejpam-4275	237	4	(	(	PUNCT
ejpam-4275	237	5	ω1,σ1	ω1,σ1	PROPN
ejpam-4275	237	6	)	)	PUNCT
ejpam-4275	237	7	⋂̃	⋂̃	NOUN
ejpam-4275	237	8	(	(	PUNCT
ejpam-4275	237	9	ψ1,σ1	ψ1,σ1	PROPN
ejpam-4275	237	10	)	)	PUNCT
ejpam-4275	237	11	=	=	SYM
ejpam-4275	237	12	φς1	φς1	NOUN
ejpam-4275	237	13	or	or	CCONJ
ejpam-4275	237	14	(	(	PUNCT
ejpam-4275	237	15	ω2,σ2	ω2,σ2	PROPN
ejpam-4275	237	16	)	)	PUNCT
ejpam-4275	237	17	⋂̃	⋂̃	NOUN
ejpam-4275	237	18	(	(	PUNCT
ejpam-4275	237	19	ψ2,σ2	ψ2,σ2	PROPN
ejpam-4275	237	20	)	)	PUNCT
ejpam-4275	237	21	=	=	PUNCT
ejpam-4275	237	22	t.m	t.m	PROPN
ejpam-4275	237	23	.	.	PUNCT
ejpam-4275	237	24	al	al	PROPN
ejpam-4275	237	25	-	-	PUNCT
ejpam-4275	237	26	shami	shami	PROPN
ejpam-4275	237	27	,	,	PUNCT
ejpam-4275	237	28	h.a	h.a	PROPN
ejpam-4275	237	29	.	.	PROPN
ejpam-4275	237	30	othman	othman	PROPN
ejpam-4275	237	31	/	/	SYM
ejpam-4275	237	32	eur	eur	PROPN
ejpam-4275	237	33	.	.	PUNCT
ejpam-4275	238	1	j.	j.	PROPN
ejpam-4275	238	2	pure	pure	PROPN
ejpam-4275	238	3	appl	appl	PROPN
ejpam-4275	238	4	.	.	PROPN
ejpam-4275	238	5	math	math	PROPN
ejpam-4275	238	6	,	,	PUNCT
ejpam-4275	238	7	15	15	NUM
ejpam-4275	238	8	(	(	PUNCT
ejpam-4275	238	9	1	1	NUM
ejpam-4275	238	10	)	)	PUNCT
ejpam-4275	238	11	(	(	PUNCT
ejpam-4275	238	12	2022	2022	NUM
ejpam-4275	238	13	)	)	PUNCT
ejpam-4275	238	14	,	,	PUNCT
ejpam-4275	238	15	261	261	NUM
ejpam-4275	238	16	-	-	SYM
ejpam-4275	238	17	280	280	NUM
ejpam-4275	238	18	268	268	NUM
ejpam-4275	238	19	φς2	φς2	NOUN
ejpam-4275	238	20	.	.	PUNCT
ejpam-4275	239	1	therefore	therefore	ADV
ejpam-4275	239	2	,	,	PUNCT
ejpam-4275	239	3	δtη	δtη	PROPN
ejpam-4275	239	4	̸∈	̸∈	PROPN
ejpam-4275	239	5	cl(ω1,σ1	cl(ω1,σ1	ADV
ejpam-4275	239	6	)	)	PUNCT
ejpam-4275	239	7	or	or	CCONJ
ejpam-4275	239	8	δsϑ	δsϑ	NOUN
ejpam-4275	239	9	̸∈	̸∈	PROPN
ejpam-4275	239	10	cl(ω2,σ2	cl(ω2,σ2	NUM
ejpam-4275	239	11	)	)	PUNCT
ejpam-4275	239	12	.	.	PUNCT
ejpam-4275	240	1	thus	thus	ADV
ejpam-4275	240	2	,	,	PUNCT
ejpam-4275	240	3	δ	δ	PROPN
ejpam-4275	240	4	(	(	PUNCT
ejpam-4275	240	5	t	t	PROPN
ejpam-4275	240	6	,	,	PUNCT
ejpam-4275	240	7	s	s	PART
ejpam-4275	240	8	)	)	PUNCT
ejpam-4275	240	9	(	(	PUNCT
ejpam-4275	240	10	η,ϑ	η,ϑ	PROPN
ejpam-4275	240	11	)	)	PUNCT
ejpam-4275	240	12	̸∈	̸∈	PROPN
ejpam-4275	240	13	[	[	X
ejpam-4275	240	14	cl(ω1,σ1	cl(ω1,σ1	PROPN
ejpam-4275	240	15	)	)	PUNCT
ejpam-4275	240	16	×	×	NOUN
ejpam-4275	240	17	cl(ω2,σ2	cl(ω2,σ2	NUM
ejpam-4275	240	18	)	)	PUNCT
ejpam-4275	240	19	]	]	PUNCT
ejpam-4275	240	20	.	.	PUNCT
ejpam-4275	241	1	hence	hence	ADV
ejpam-4275	241	2	,	,	PUNCT
ejpam-4275	241	3	cl(ω1,σ1	cl(ω1,σ1	ADV
ejpam-4275	241	4	)	)	PUNCT
ejpam-4275	241	5	×	×	NOUN
ejpam-4275	241	6	cl(ω2,σ2)⊆̃cl[(ω1,σ1	cl(ω2,σ2)⊆̃cl[(ω1,σ1	NOUN
ejpam-4275	241	7	)	)	PUNCT
ejpam-4275	241	8	×	×	NOUN
ejpam-4275	241	9	(	(	PUNCT
ejpam-4275	241	10	ω2,σ2	ω2,σ2	PROPN
ejpam-4275	241	11	)	)	PUNCT
ejpam-4275	241	12	]	]	PUNCT
ejpam-4275	241	13	.	.	PUNCT
ejpam-4275	242	1	conversely	conversely	ADV
ejpam-4275	242	2	,	,	PUNCT
ejpam-4275	242	3	let	let	VERB
ejpam-4275	242	4	δ	δ	PROPN
ejpam-4275	242	5	(	(	PUNCT
ejpam-4275	242	6	t	t	PROPN
ejpam-4275	242	7	,	,	PUNCT
ejpam-4275	242	8	s	s	PART
ejpam-4275	242	9	)	)	PUNCT
ejpam-4275	242	10	(	(	PUNCT
ejpam-4275	242	11	η,ϑ	η,ϑ	PROPN
ejpam-4275	242	12	)	)	PUNCT
ejpam-4275	242	13	̸∈	̸∈	PROPN
ejpam-4275	242	14	cl(ω1,σ1	cl(ω1,σ1	ADV
ejpam-4275	242	15	)	)	PUNCT
ejpam-4275	242	16	×	×	NOUN
ejpam-4275	242	17	cl(ω2,σ2	cl(ω2,σ2	NUM
ejpam-4275	242	18	)	)	PUNCT
ejpam-4275	242	19	.	.	PUNCT
ejpam-4275	243	1	then	then	ADV
ejpam-4275	243	2	δxη	δxη	VERB
ejpam-4275	243	3	̸∈	̸∈	PROPN
ejpam-4275	243	4	cl(ω1,σ1	cl(ω1,σ1	X
ejpam-4275	243	5	)	)	PUNCT
ejpam-4275	243	6	or	or	CCONJ
ejpam-4275	243	7	δsϑ	δsϑ	NOUN
ejpam-4275	243	8	̸∈	̸∈	PROPN
ejpam-4275	243	9	cl(ω2,σ2	cl(ω2,σ2	NUM
ejpam-4275	243	10	)	)	PUNCT
ejpam-4275	243	11	.	.	PUNCT
ejpam-4275	244	1	suppose	suppose	VERB
ejpam-4275	244	2	,	,	PUNCT
ejpam-4275	244	3	without	without	ADP
ejpam-4275	244	4	loss	loss	NOUN
ejpam-4275	244	5	of	of	ADP
ejpam-4275	244	6	generality	generality	NOUN
ejpam-4275	244	7	,	,	PUNCT
ejpam-4275	244	8	that	that	PRON
ejpam-4275	244	9	δxη	δxη	NOUN
ejpam-4275	244	10	̸∈	̸∈	PROPN
ejpam-4275	244	11	cl(ω1,σ1	cl(ω1,σ1	NUM
ejpam-4275	244	12	)	)	PUNCT
ejpam-4275	244	13	.	.	PUNCT
ejpam-4275	245	1	then	then	ADV
ejpam-4275	245	2	there	there	PRON
ejpam-4275	245	3	is	be	VERB
ejpam-4275	245	4	an	an	DET
ejpam-4275	245	5	infra	infra	NOUN
ejpam-4275	245	6	soft	soft	ADJ
ejpam-4275	245	7	open	open	ADJ
ejpam-4275	245	8	subset	subset	NOUN
ejpam-4275	245	9	(	(	PUNCT
ejpam-4275	245	10	ψ1,σ1	ψ1,σ1	PROPN
ejpam-4275	245	11	)	)	PUNCT
ejpam-4275	245	12	of	of	ADP
ejpam-4275	245	13	(	(	PUNCT
ejpam-4275	245	14	x1	x1	PROPN
ejpam-4275	245	15	,	,	PUNCT
ejpam-4275	245	16	ξ1,σ1	ξ1,σ1	PROPN
ejpam-4275	245	17	)	)	PUNCT
ejpam-4275	245	18	containing	contain	VERB
ejpam-4275	245	19	δxη	δxη	NOUN
ejpam-4275	245	20	such	such	ADJ
ejpam-4275	245	21	that	that	SCONJ
ejpam-4275	245	22	(	(	PUNCT
ejpam-4275	245	23	ω1,σ1	ω1,σ1	PROPN
ejpam-4275	245	24	)	)	PUNCT
ejpam-4275	245	25	⋂̃	⋂̃	NOUN
ejpam-4275	245	26	(	(	PUNCT
ejpam-4275	245	27	ψ1,σ1	ψ1,σ1	PROPN
ejpam-4275	245	28	)	)	PUNCT
ejpam-4275	245	29	=	=	SYM
ejpam-4275	245	30	φς1	φς1	NOUN
ejpam-4275	245	31	.	.	PUNCT
ejpam-4275	246	1	obviously	obviously	ADV
ejpam-4275	246	2	,	,	PUNCT
ejpam-4275	246	3	(	(	PUNCT
ejpam-4275	246	4	ψ1,σ1	ψ1,σ1	PROPN
ejpam-4275	246	5	)	)	PUNCT
ejpam-4275	246	6	×	×	PROPN
ejpam-4275	246	7	x̃2	x̃2	PROPN
ejpam-4275	246	8	is	be	AUX
ejpam-4275	246	9	an	an	DET
ejpam-4275	246	10	infra	infra	NOUN
ejpam-4275	246	11	soft	soft	ADJ
ejpam-4275	246	12	open	open	ADJ
ejpam-4275	246	13	subset	subset	NOUN
ejpam-4275	246	14	of	of	ADP
ejpam-4275	246	15	x̃1	x̃1	PROPN
ejpam-4275	246	16	×	×	PROPN
ejpam-4275	246	17	x̃2	x̃2	PROPN
ejpam-4275	246	18	containing	contain	VERB
ejpam-4275	246	19	δ	δ	PROPN
ejpam-4275	246	20	(	(	PUNCT
ejpam-4275	246	21	t	t	PROPN
ejpam-4275	246	22	,	,	PUNCT
ejpam-4275	246	23	s	s	PART
ejpam-4275	246	24	)	)	PUNCT
ejpam-4275	246	25	(	(	PUNCT
ejpam-4275	246	26	η,ϑ	η,ϑ	PROPN
ejpam-4275	246	27	)	)	PUNCT
ejpam-4275	246	28	such	such	ADJ
ejpam-4275	246	29	that	that	SCONJ
ejpam-4275	246	30	[	[	X
ejpam-4275	247	1	(	(	PUNCT
ejpam-4275	247	2	ψ1,σ1)×x̃2	ψ1,σ1)×x̃2	X
ejpam-4275	247	3	]	]	X
ejpam-4275	247	4	⋂̃	⋂̃	X
ejpam-4275	248	1	[	[	X
ejpam-4275	248	2	(	(	PUNCT
ejpam-4275	248	3	ω1,σ1)×(ω2,σ2	ω1,σ1)×(ω2,σ2	NOUN
ejpam-4275	248	4	)	)	PUNCT
ejpam-4275	248	5	]	]	PUNCT
ejpam-4275	249	1	=	=	SYM
ejpam-4275	249	2	φς1×σ2	φς1×σ2	PROPN
ejpam-4275	249	3	.	.	PUNCT
ejpam-4275	250	1	therefore	therefore	ADV
ejpam-4275	250	2	,	,	PUNCT
ejpam-4275	250	3	δ	δ	PROPN
ejpam-4275	250	4	(	(	PUNCT
ejpam-4275	250	5	t	t	PROPN
ejpam-4275	250	6	,	,	PUNCT
ejpam-4275	250	7	s	s	PART
ejpam-4275	250	8	)	)	PUNCT
ejpam-4275	250	9	(	(	PUNCT
ejpam-4275	250	10	η,ϑ	η,ϑ	PROPN
ejpam-4275	250	11	)	)	PUNCT
ejpam-4275	250	12	̸∈	̸∈	PROPN
ejpam-4275	250	13	cl[(ω1,σ1)×(ω2,σ2	cl[(ω1,σ1)×(ω2,σ2	PROPN
ejpam-4275	250	14	)	)	PUNCT
ejpam-4275	250	15	]	]	PUNCT
ejpam-4275	250	16	.	.	PUNCT
ejpam-4275	251	1	thus	thus	ADV
ejpam-4275	251	2	,	,	PUNCT
ejpam-4275	251	3	cl[(ω1,σ1)×	cl[(ω1,σ1)×	PROPN
ejpam-4275	251	4	(	(	PUNCT
ejpam-4275	251	5	ω2,σ2)]⊆̃cl(ω1,σ1)×	ω2,σ2)]⊆̃cl(ω1,σ1)×	NOUN
ejpam-4275	251	6	cl(ω2,σ2	cl(ω2,σ2	NUM
ejpam-4275	251	7	)	)	PUNCT
ejpam-4275	251	8	.	.	PUNCT
ejpam-4275	252	1	hence	hence	ADV
ejpam-4275	252	2	,	,	PUNCT
ejpam-4275	252	3	the	the	DET
ejpam-4275	252	4	proof	proof	NOUN
ejpam-4275	252	5	is	be	AUX
ejpam-4275	252	6	complete	complete	ADJ
ejpam-4275	252	7	.	.	PUNCT
ejpam-4275	253	1	following	follow	VERB
ejpam-4275	253	2	similar	similar	ADJ
ejpam-4275	253	3	arguments	argument	NOUN
ejpam-4275	253	4	,	,	PUNCT
ejpam-4275	253	5	one	one	PRON
ejpam-4275	253	6	can	can	AUX
ejpam-4275	253	7	prove	prove	VERB
ejpam-4275	253	8	(	(	PUNCT
ejpam-4275	253	9	ii	ii	NOUN
ejpam-4275	253	10	)	)	PUNCT
ejpam-4275	253	11	.	.	PUNCT
ejpam-4275	254	1	proposition	proposition	NOUN
ejpam-4275	254	2	12	12	NUM
ejpam-4275	254	3	.	.	PUNCT
ejpam-4275	255	1	the	the	DET
ejpam-4275	255	2	product	product	NOUN
ejpam-4275	255	3	of	of	ADP
ejpam-4275	255	4	infra	infra	NOUN
ejpam-4275	255	5	soft	soft	ADJ
ejpam-4275	255	6	pre	pre	ADJ
ejpam-4275	255	7	-	-	ADJ
ejpam-4275	255	8	open	open	ADJ
ejpam-4275	255	9	sets	set	NOUN
ejpam-4275	255	10	is	be	AUX
ejpam-4275	255	11	an	an	DET
ejpam-4275	255	12	infra	infra	NOUN
ejpam-4275	255	13	soft	soft	ADJ
ejpam-4275	255	14	pre	pre	ADJ
ejpam-4275	255	15	-	-	ADJ
ejpam-4275	255	16	open	open	ADJ
ejpam-4275	255	17	set	set	NOUN
ejpam-4275	255	18	.	.	PUNCT
ejpam-4275	256	1	proof	proof	NOUN
ejpam-4275	256	2	.	.	PUNCT
ejpam-4275	257	1	let	let	AUX
ejpam-4275	257	2	(	(	PUNCT
ejpam-4275	257	3	ω1,σ1	ω1,σ1	PROPN
ejpam-4275	257	4	)	)	PUNCT
ejpam-4275	257	5	and	and	CCONJ
ejpam-4275	257	6	(	(	PUNCT
ejpam-4275	257	7	ω2,σ2	ω2,σ2	PROPN
ejpam-4275	257	8	)	)	PUNCT
ejpam-4275	257	9	be	be	AUX
ejpam-4275	257	10	infra	infra	NOUN
ejpam-4275	257	11	soft	soft	ADJ
ejpam-4275	257	12	pre	pre	ADJ
ejpam-4275	257	13	-	-	ADJ
ejpam-4275	257	14	open	open	ADJ
ejpam-4275	257	15	subsets	subset	NOUN
ejpam-4275	257	16	of	of	ADP
ejpam-4275	257	17	(	(	PUNCT
ejpam-4275	257	18	x1	x1	PROPN
ejpam-4275	257	19	,	,	PUNCT
ejpam-4275	257	20	ξ1,σ1	ξ1,σ1	PROPN
ejpam-4275	257	21	)	)	PUNCT
ejpam-4275	257	22	and	and	CCONJ
ejpam-4275	257	23	(	(	PUNCT
ejpam-4275	257	24	x2	x2	PROPN
ejpam-4275	257	25	,	,	PUNCT
ejpam-4275	257	26	ξ2,σ2	ξ2,σ2	PROPN
ejpam-4275	257	27	)	)	PUNCT
ejpam-4275	257	28	,	,	PUNCT
ejpam-4275	257	29	respectively	respectively	ADV
ejpam-4275	257	30	.	.	PUNCT
ejpam-4275	258	1	then	then	ADV
ejpam-4275	258	2	(	(	PUNCT
ejpam-4275	258	3	ω1,σ1	ω1,σ1	PROPN
ejpam-4275	258	4	)	)	PUNCT
ejpam-4275	258	5	×	×	NOUN
ejpam-4275	258	6	(	(	PUNCT
ejpam-4275	258	7	ω2,σ2)⊆̃int(cl(ω1,σ1	ω2,σ2)⊆̃int(cl(ω1,σ1	NUM
ejpam-4275	258	8	)	)	PUNCT
ejpam-4275	258	9	)	)	PUNCT
ejpam-4275	258	10	×	×	PROPN
ejpam-4275	258	11	int(cl(ω2,σ2	int(cl(ω2,σ2	PROPN
ejpam-4275	258	12	)	)	PUNCT
ejpam-4275	258	13	)	)	PUNCT
ejpam-4275	258	14	.	.	PUNCT
ejpam-4275	259	1	according	accord	VERB
ejpam-4275	259	2	to	to	ADP
ejpam-4275	259	3	the	the	DET
ejpam-4275	259	4	above	above	ADJ
ejpam-4275	259	5	lemma	lemma	PROPN
ejpam-4275	259	6	,	,	PUNCT
ejpam-4275	259	7	we	we	PRON
ejpam-4275	259	8	obtain	obtain	VERB
ejpam-4275	259	9	(	(	PUNCT
ejpam-4275	259	10	ω1,σ1)×(ω2,σ2)⊆̃int(cl[(ω1,σ1)×(ω2,σ2	ω1,σ1)×(ω2,σ2)⊆̃int(cl[(ω1,σ1)×(ω2,σ2	ADV
ejpam-4275	259	11	)	)	PUNCT
ejpam-4275	259	12	]	]	PUNCT
ejpam-4275	259	13	)	)	PUNCT
ejpam-4275	259	14	which	which	PRON
ejpam-4275	259	15	means	mean	VERB
ejpam-4275	259	16	that	that	SCONJ
ejpam-4275	259	17	(	(	PUNCT
ejpam-4275	259	18	ω1,σ1)×	ω1,σ1)×	NUM
ejpam-4275	259	19	(	(	PUNCT
ejpam-4275	259	20	ω2,σ2	ω2,σ2	PROPN
ejpam-4275	259	21	)	)	PUNCT
ejpam-4275	259	22	is	be	AUX
ejpam-4275	259	23	an	an	DET
ejpam-4275	259	24	infra	infra	NOUN
ejpam-4275	259	25	soft	soft	ADJ
ejpam-4275	259	26	pre	pre	ADJ
ejpam-4275	259	27	-	-	ADJ
ejpam-4275	259	28	open	open	ADJ
ejpam-4275	259	29	subset	subset	NOUN
ejpam-4275	259	30	of	of	ADP
ejpam-4275	259	31	x̃1	x̃1	PROPN
ejpam-4275	259	32	×	×	PROPN
ejpam-4275	259	33	x̃2	x̃2	PROPN
ejpam-4275	259	34	.	.	PUNCT
ejpam-4275	260	1	4	4	X
ejpam-4275	260	2	.	.	X
ejpam-4275	260	3	infra	infra	NOUN
ejpam-4275	260	4	pre	pre	ADJ
ejpam-4275	260	5	-	-	ADJ
ejpam-4275	260	6	interior	interior	ADJ
ejpam-4275	260	7	,	,	PUNCT
ejpam-4275	260	8	infra	infra	NOUN
ejpam-4275	260	9	pre	pre	NOUN
ejpam-4275	260	10	-	-	ADJ
ejpam-4275	260	11	closure	closure	ADJ
ejpam-4275	260	12	,	,	PUNCT
ejpam-4275	260	13	infra	infra	NOUN
ejpam-4275	260	14	pre	pre	ADJ
ejpam-4275	260	15	-	-	NOUN
ejpam-4275	260	16	limit	limit	NOUN
ejpam-4275	260	17	and	and	CCONJ
ejpam-4275	260	18	infra	infra	NOUN
ejpam-4275	260	19	pre	pre	ADJ
ejpam-4275	260	20	-	-	ADJ
ejpam-4275	260	21	boundary	boundary	ADJ
ejpam-4275	260	22	soft	soft	ADJ
ejpam-4275	260	23	points	point	NOUN
ejpam-4275	260	24	of	of	ADP
ejpam-4275	260	25	a	a	DET
ejpam-4275	260	26	soft	soft	ADJ
ejpam-4275	260	27	set	set	NOUN
ejpam-4275	260	28	the	the	DET
ejpam-4275	260	29	goal	goal	NOUN
ejpam-4275	260	30	of	of	ADP
ejpam-4275	260	31	this	this	DET
ejpam-4275	260	32	part	part	NOUN
ejpam-4275	260	33	is	be	AUX
ejpam-4275	260	34	to	to	PART
ejpam-4275	260	35	introduce	introduce	VERB
ejpam-4275	260	36	the	the	DET
ejpam-4275	260	37	concepts	concept	NOUN
ejpam-4275	260	38	of	of	ADP
ejpam-4275	260	39	infra	infra	NOUN
ejpam-4275	260	40	soft	soft	ADJ
ejpam-4275	260	41	pre	pre	ADJ
ejpam-4275	260	42	-	-	ADJ
ejpam-4275	260	43	interior	interior	ADJ
ejpam-4275	260	44	and	and	CCONJ
ejpam-4275	260	45	infra	infra	NOUN
ejpam-4275	260	46	soft	soft	ADJ
ejpam-4275	260	47	pre	pre	NOUN
ejpam-4275	260	48	-	-	ADJ
ejpam-4275	260	49	closure	closure	ADJ
ejpam-4275	260	50	,	,	PUNCT
ejpam-4275	260	51	infra	infra	NOUN
ejpam-4275	260	52	soft	soft	ADJ
ejpam-4275	260	53	pre	pre	NOUN
ejpam-4275	260	54	-	-	NOUN
ejpam-4275	260	55	limit	limit	ADJ
ejpam-4275	260	56	and	and	CCONJ
ejpam-4275	260	57	infra	infra	VERB
ejpam-4275	260	58	soft	soft	ADJ
ejpam-4275	260	59	pre	pre	ADJ
ejpam-4275	260	60	-	-	ADJ
ejpam-4275	260	61	boundary	boundary	ADJ
ejpam-4275	260	62	soft	soft	ADJ
ejpam-4275	260	63	points	point	NOUN
ejpam-4275	260	64	of	of	ADP
ejpam-4275	260	65	a	a	DET
ejpam-4275	260	66	soft	soft	ADJ
ejpam-4275	260	67	set	set	NOUN
ejpam-4275	260	68	.	.	PUNCT
ejpam-4275	261	1	we	we	PRON
ejpam-4275	261	2	explore	explore	VERB
ejpam-4275	261	3	their	their	PRON
ejpam-4275	261	4	essential	essential	ADJ
ejpam-4275	261	5	properties	property	NOUN
ejpam-4275	261	6	and	and	CCONJ
ejpam-4275	261	7	explain	explain	VERB
ejpam-4275	261	8	the	the	DET
ejpam-4275	261	9	interrelationships	interrelationship	NOUN
ejpam-4275	261	10	between	between	ADP
ejpam-4275	261	11	them	they	PRON
ejpam-4275	261	12	with	with	ADP
ejpam-4275	261	13	the	the	DET
ejpam-4275	261	14	aid	aid	NOUN
ejpam-4275	261	15	of	of	ADP
ejpam-4275	261	16	illustrative	illustrative	ADJ
ejpam-4275	261	17	examples	example	NOUN
ejpam-4275	261	18	.	.	PUNCT
ejpam-4275	262	1	definition	definition	NOUN
ejpam-4275	262	2	18	18	NUM
ejpam-4275	262	3	.	.	PUNCT
ejpam-4275	263	1	let	let	AUX
ejpam-4275	263	2	(	(	PUNCT
ejpam-4275	263	3	ω	ω	PROPN
ejpam-4275	263	4	,	,	PUNCT
ejpam-4275	263	5	σ	σ	PROPN
ejpam-4275	263	6	)	)	PUNCT
ejpam-4275	263	7	be	be	VERB
ejpam-4275	263	8	a	a	DET
ejpam-4275	263	9	subset	subset	NOUN
ejpam-4275	263	10	of	of	ADP
ejpam-4275	263	11	(	(	PUNCT
ejpam-4275	263	12	x	x	NOUN
ejpam-4275	263	13	,	,	PUNCT
ejpam-4275	263	14	ξ	ξ	PROPN
ejpam-4275	263	15	,	,	PUNCT
ejpam-4275	263	16	σ	σ	NOUN
ejpam-4275	263	17	)	)	PUNCT
ejpam-4275	263	18	.	.	PUNCT
ejpam-4275	264	1	then	then	ADV
ejpam-4275	264	2	:	:	PUNCT
ejpam-4275	264	3	(	(	PUNCT
ejpam-4275	264	4	i	i	NOUN
ejpam-4275	264	5	)	)	PUNCT
ejpam-4275	264	6	the	the	DET
ejpam-4275	264	7	infra	infra	NOUN
ejpam-4275	264	8	soft	soft	ADJ
ejpam-4275	264	9	pre	pre	ADJ
ejpam-4275	264	10	-	-	ADJ
ejpam-4275	264	11	interior	interior	ADJ
ejpam-4275	264	12	of	of	ADP
ejpam-4275	264	13	(	(	PUNCT
ejpam-4275	264	14	ω	ω	PROPN
ejpam-4275	264	15	,	,	PUNCT
ejpam-4275	264	16	σ	σ	PROPN
ejpam-4275	264	17	)	)	PUNCT
ejpam-4275	264	18	,	,	PUNCT
ejpam-4275	264	19	denoted	denote	VERB
ejpam-4275	264	20	by	by	ADP
ejpam-4275	264	21	pint(ω	pint(ω	NOUN
ejpam-4275	264	22	,	,	PUNCT
ejpam-4275	264	23	σ	σ	PROPN
ejpam-4275	264	24	)	)	PUNCT
ejpam-4275	264	25	,	,	PUNCT
ejpam-4275	264	26	is	be	AUX
ejpam-4275	264	27	the	the	DET
ejpam-4275	264	28	union	union	NOUN
ejpam-4275	264	29	of	of	ADP
ejpam-4275	264	30	all	all	DET
ejpam-4275	264	31	infra	infra	NOUN
ejpam-4275	264	32	soft	soft	ADJ
ejpam-4275	264	33	pre	pre	ADJ
ejpam-4275	264	34	-	-	ADJ
ejpam-4275	264	35	open	open	ADJ
ejpam-4275	264	36	sets	set	NOUN
ejpam-4275	264	37	that	that	PRON
ejpam-4275	264	38	are	be	AUX
ejpam-4275	264	39	contained	contain	VERB
ejpam-4275	264	40	in	in	ADP
ejpam-4275	264	41	(	(	PUNCT
ejpam-4275	264	42	ω	ω	PROPN
ejpam-4275	264	43	,	,	PUNCT
ejpam-4275	264	44	σ	σ	PROPN
ejpam-4275	264	45	)	)	PUNCT
ejpam-4275	264	46	.	.	PUNCT
ejpam-4275	265	1	(	(	PUNCT
ejpam-4275	265	2	ii	ii	X
ejpam-4275	265	3	)	)	PUNCT
ejpam-4275	265	4	the	the	DET
ejpam-4275	265	5	infra	infra	NOUN
ejpam-4275	265	6	soft	soft	ADJ
ejpam-4275	265	7	pre	pre	NOUN
ejpam-4275	265	8	-	-	NOUN
ejpam-4275	265	9	closure	closure	NOUN
ejpam-4275	265	10	of	of	ADP
ejpam-4275	265	11	(	(	PUNCT
ejpam-4275	265	12	ω	ω	PROPN
ejpam-4275	265	13	,	,	PUNCT
ejpam-4275	265	14	σ	σ	PROPN
ejpam-4275	265	15	)	)	PUNCT
ejpam-4275	265	16	,	,	PUNCT
ejpam-4275	265	17	denoted	denote	VERB
ejpam-4275	265	18	by	by	ADP
ejpam-4275	265	19	pcl(ω	pcl(ω	PROPN
ejpam-4275	265	20	,	,	PUNCT
ejpam-4275	265	21	σ	σ	PROPN
ejpam-4275	265	22	)	)	PUNCT
ejpam-4275	265	23	,	,	PUNCT
ejpam-4275	265	24	is	be	AUX
ejpam-4275	265	25	the	the	DET
ejpam-4275	265	26	intersection	intersection	NOUN
ejpam-4275	265	27	of	of	ADP
ejpam-4275	265	28	all	all	DET
ejpam-4275	265	29	infra	infra	NOUN
ejpam-4275	265	30	soft	soft	ADJ
ejpam-4275	265	31	pre	pre	ADJ
ejpam-4275	265	32	-	-	ADJ
ejpam-4275	265	33	closed	closed	ADJ
ejpam-4275	265	34	sets	set	NOUN
ejpam-4275	265	35	containing	contain	VERB
ejpam-4275	265	36	(	(	PUNCT
ejpam-4275	265	37	ω	ω	PROPN
ejpam-4275	265	38	,	,	PUNCT
ejpam-4275	265	39	σ	σ	PROPN
ejpam-4275	265	40	)	)	PUNCT
ejpam-4275	265	41	.	.	PUNCT
ejpam-4275	266	1	proposition	proposition	NOUN
ejpam-4275	266	2	13	13	NUM
ejpam-4275	266	3	.	.	PUNCT
ejpam-4275	267	1	we	we	PRON
ejpam-4275	267	2	have	have	VERB
ejpam-4275	267	3	the	the	DET
ejpam-4275	267	4	following	follow	VERB
ejpam-4275	267	5	properties	property	NOUN
ejpam-4275	267	6	.	.	PUNCT
ejpam-4275	268	1	(	(	PUNCT
ejpam-4275	268	2	i	i	NOUN
ejpam-4275	268	3	)	)	PUNCT
ejpam-4275	268	4	(	(	PUNCT
ejpam-4275	268	5	ω	ω	PROPN
ejpam-4275	268	6	,	,	PUNCT
ejpam-4275	268	7	σ	σ	PROPN
ejpam-4275	268	8	)	)	PUNCT
ejpam-4275	268	9	is	be	AUX
ejpam-4275	268	10	an	an	DET
ejpam-4275	268	11	infra	infra	NOUN
ejpam-4275	268	12	soft	soft	ADJ
ejpam-4275	268	13	pre	pre	ADJ
ejpam-4275	268	14	-	-	ADJ
ejpam-4275	268	15	open	open	ADJ
ejpam-4275	268	16	subset	subset	NOUN
ejpam-4275	268	17	of	of	ADP
ejpam-4275	268	18	(	(	PUNCT
ejpam-4275	268	19	x	x	NOUN
ejpam-4275	268	20	,	,	PUNCT
ejpam-4275	268	21	ξ	ξ	PROPN
ejpam-4275	268	22	,	,	PUNCT
ejpam-4275	268	23	σ	σ	PROPN
ejpam-4275	268	24	)	)	PUNCT
ejpam-4275	268	25	iff	iff	PROPN
ejpam-4275	268	26	pint(ω	pint(ω	PROPN
ejpam-4275	268	27	,	,	PUNCT
ejpam-4275	268	28	σ	σ	PROPN
ejpam-4275	268	29	)	)	PUNCT
ejpam-4275	268	30	=	=	SYM
ejpam-4275	268	31	(	(	PUNCT
ejpam-4275	268	32	ω	ω	PROPN
ejpam-4275	268	33	,	,	PUNCT
ejpam-4275	268	34	σ	σ	PROPN
ejpam-4275	268	35	)	)	PUNCT
ejpam-4275	268	36	.	.	PUNCT
ejpam-4275	269	1	(	(	PUNCT
ejpam-4275	269	2	ii	ii	NOUN
ejpam-4275	269	3	)	)	PUNCT
ejpam-4275	269	4	(	(	PUNCT
ejpam-4275	269	5	ω	ω	PROPN
ejpam-4275	269	6	,	,	PUNCT
ejpam-4275	269	7	σ	σ	PROPN
ejpam-4275	269	8	)	)	PUNCT
ejpam-4275	269	9	is	be	AUX
ejpam-4275	269	10	an	an	DET
ejpam-4275	269	11	infra	infra	NOUN
ejpam-4275	269	12	soft	soft	ADJ
ejpam-4275	269	13	pre	pre	ADJ
ejpam-4275	269	14	-	-	ADJ
ejpam-4275	269	15	closed	closed	ADJ
ejpam-4275	269	16	subset	subset	NOUN
ejpam-4275	269	17	of	of	ADP
ejpam-4275	269	18	(	(	PUNCT
ejpam-4275	269	19	x	x	NOUN
ejpam-4275	269	20	,	,	PUNCT
ejpam-4275	269	21	ξ	ξ	PROPN
ejpam-4275	269	22	,	,	PUNCT
ejpam-4275	269	23	σ	σ	PROPN
ejpam-4275	269	24	)	)	PUNCT
ejpam-4275	269	25	iff	iff	PROPN
ejpam-4275	269	26	pcl(ω	pcl(ω	PROPN
ejpam-4275	269	27	,	,	PUNCT
ejpam-4275	269	28	σ	σ	PROPN
ejpam-4275	269	29	)	)	PUNCT
ejpam-4275	269	30	=	=	SYM
ejpam-4275	269	31	(	(	PUNCT
ejpam-4275	269	32	ω	ω	PROPN
ejpam-4275	269	33	,	,	PUNCT
ejpam-4275	269	34	σ	σ	PROPN
ejpam-4275	269	35	)	)	PUNCT
ejpam-4275	269	36	.	.	PUNCT
ejpam-4275	270	1	proof	proof	NOUN
ejpam-4275	270	2	.	.	PUNCT
ejpam-4275	271	1	it	it	PRON
ejpam-4275	271	2	comes	come	VERB
ejpam-4275	271	3	from	from	ADP
ejpam-4275	271	4	proposition	proposition	NOUN
ejpam-4275	271	5	8	8	NUM
ejpam-4275	271	6	and	and	CCONJ
ejpam-4275	271	7	corollary	corollary	ADJ
ejpam-4275	271	8	1	1	NUM
ejpam-4275	271	9	.	.	PUNCT
ejpam-4275	272	1	note	note	VERB
ejpam-4275	272	2	that	that	SCONJ
ejpam-4275	272	3	the	the	DET
ejpam-4275	272	4	the	the	DET
ejpam-4275	272	5	above	above	ADJ
ejpam-4275	272	6	two	two	NUM
ejpam-4275	272	7	properties	property	NOUN
ejpam-4275	272	8	are	be	AUX
ejpam-4275	272	9	not	not	PART
ejpam-4275	272	10	valid	valid	ADJ
ejpam-4275	272	11	for	for	ADP
ejpam-4275	272	12	infra	infra	NOUN
ejpam-4275	272	13	soft	soft	ADJ
ejpam-4275	272	14	open	open	ADJ
ejpam-4275	272	15	and	and	CCONJ
ejpam-4275	272	16	infra	infra	NOUN
ejpam-4275	272	17	soft	soft	ADJ
ejpam-4275	272	18	closed	closed	ADJ
ejpam-4275	272	19	sets	set	NOUN
ejpam-4275	272	20	.	.	PUNCT
ejpam-4275	273	1	t.m	t.m	X
ejpam-4275	273	2	.	.	PUNCT
ejpam-4275	273	3	al	al	PROPN
ejpam-4275	273	4	-	-	PUNCT
ejpam-4275	273	5	shami	shami	PROPN
ejpam-4275	273	6	,	,	PUNCT
ejpam-4275	273	7	h.a	h.a	PROPN
ejpam-4275	273	8	.	.	PROPN
ejpam-4275	273	9	othman	othman	PROPN
ejpam-4275	273	10	/	/	SYM
ejpam-4275	273	11	eur	eur	PROPN
ejpam-4275	273	12	.	.	PUNCT
ejpam-4275	274	1	j.	j.	PROPN
ejpam-4275	274	2	pure	pure	PROPN
ejpam-4275	274	3	appl	appl	PROPN
ejpam-4275	274	4	.	.	PROPN
ejpam-4275	274	5	math	math	PROPN
ejpam-4275	274	6	,	,	PUNCT
ejpam-4275	274	7	15	15	NUM
ejpam-4275	274	8	(	(	PUNCT
ejpam-4275	274	9	1	1	NUM
ejpam-4275	274	10	)	)	PUNCT
ejpam-4275	274	11	(	(	PUNCT
ejpam-4275	274	12	2022	2022	NUM
ejpam-4275	274	13	)	)	PUNCT
ejpam-4275	274	14	,	,	PUNCT
ejpam-4275	274	15	261	261	NUM
ejpam-4275	274	16	-	-	SYM
ejpam-4275	274	17	280	280	NUM
ejpam-4275	274	18	269	269	NUM
ejpam-4275	274	19	proposition	proposition	NOUN
ejpam-4275	274	20	14	14	NUM
ejpam-4275	274	21	.	.	PUNCT
ejpam-4275	275	1	let	let	AUX
ejpam-4275	275	2	(	(	PUNCT
ejpam-4275	275	3	ω	ω	PROPN
ejpam-4275	275	4	,	,	PUNCT
ejpam-4275	275	5	σ	σ	PROPN
ejpam-4275	275	6	)	)	PUNCT
ejpam-4275	275	7	be	be	VERB
ejpam-4275	275	8	a	a	DET
ejpam-4275	275	9	subset	subset	NOUN
ejpam-4275	275	10	of	of	ADP
ejpam-4275	275	11	(	(	PUNCT
ejpam-4275	275	12	x	x	NOUN
ejpam-4275	275	13	,	,	PUNCT
ejpam-4275	275	14	ξ	ξ	PROPN
ejpam-4275	275	15	,	,	PUNCT
ejpam-4275	275	16	σ	σ	NOUN
ejpam-4275	275	17	)	)	PUNCT
ejpam-4275	275	18	.	.	PUNCT
ejpam-4275	276	1	(	(	PUNCT
ejpam-4275	276	2	i	i	NOUN
ejpam-4275	276	3	)	)	PUNCT
ejpam-4275	276	4	δxη	δxη	NOUN
ejpam-4275	276	5	∈	∈	PROPN
ejpam-4275	276	6	pint(ω	pint(ω	NOUN
ejpam-4275	276	7	,	,	PUNCT
ejpam-4275	276	8	σ	σ	PROPN
ejpam-4275	276	9	)	)	PUNCT
ejpam-4275	276	10	iff	iff	PROPN
ejpam-4275	276	11	there	there	PRON
ejpam-4275	276	12	is	be	VERB
ejpam-4275	276	13	an	an	DET
ejpam-4275	276	14	infra	infra	NOUN
ejpam-4275	276	15	soft	soft	ADJ
ejpam-4275	276	16	pre	pre	ADJ
ejpam-4275	276	17	-	-	ADJ
ejpam-4275	276	18	open	open	ADJ
ejpam-4275	276	19	set	set	NOUN
ejpam-4275	276	20	(	(	PUNCT
ejpam-4275	276	21	ψ	ψ	X
ejpam-4275	276	22	,	,	PUNCT
ejpam-4275	276	23	σ	σ	NOUN
ejpam-4275	276	24	)	)	PUNCT
ejpam-4275	276	25	such	such	ADJ
ejpam-4275	276	26	that	that	DET
ejpam-4275	276	27	δxη	δxη	NOUN
ejpam-4275	276	28	∈	∈	PROPN
ejpam-4275	276	29	(	(	PUNCT
ejpam-4275	276	30	ψ	ψ	X
ejpam-4275	276	31	,	,	PUNCT
ejpam-4275	276	32	σ)⊆̃(ω	σ)⊆̃(ω	PROPN
ejpam-4275	276	33	,	,	PUNCT
ejpam-4275	276	34	σ	σ	PROPN
ejpam-4275	276	35	)	)	PUNCT
ejpam-4275	276	36	.	.	PUNCT
ejpam-4275	277	1	(	(	PUNCT
ejpam-4275	277	2	ii	ii	NOUN
ejpam-4275	277	3	)	)	PUNCT
ejpam-4275	277	4	δxη	δxη	NOUN
ejpam-4275	277	5	∈	∈	PROPN
ejpam-4275	277	6	pcl(ω	pcl(ω	PROPN
ejpam-4275	277	7	,	,	PUNCT
ejpam-4275	277	8	σ	σ	PROPN
ejpam-4275	277	9	)	)	PUNCT
ejpam-4275	277	10	iff	iff	VERB
ejpam-4275	277	11	the	the	DET
ejpam-4275	277	12	intersection	intersection	NOUN
ejpam-4275	277	13	of	of	ADP
ejpam-4275	277	14	any	any	DET
ejpam-4275	277	15	infra	infra	NOUN
ejpam-4275	277	16	soft	soft	ADJ
ejpam-4275	277	17	pre	pre	ADJ
ejpam-4275	277	18	-	-	ADJ
ejpam-4275	277	19	open	open	ADJ
ejpam-4275	277	20	set	set	NOUN
ejpam-4275	277	21	(	(	PUNCT
ejpam-4275	277	22	ψ	ψ	X
ejpam-4275	277	23	,	,	PUNCT
ejpam-4275	277	24	σ	σ	NOUN
ejpam-4275	277	25	)	)	PUNCT
ejpam-4275	277	26	containing	contain	VERB
ejpam-4275	277	27	δxη	δxη	NOUN
ejpam-4275	277	28	and	and	CCONJ
ejpam-4275	277	29	(	(	PUNCT
ejpam-4275	277	30	ω	ω	PROPN
ejpam-4275	277	31	,	,	PUNCT
ejpam-4275	277	32	σ	σ	PROPN
ejpam-4275	277	33	)	)	PUNCT
ejpam-4275	277	34	is	be	AUX
ejpam-4275	277	35	non	non	ADJ
ejpam-4275	277	36	-	-	ADJ
ejpam-4275	277	37	null	null	ADJ
ejpam-4275	277	38	.	.	PUNCT
ejpam-4275	278	1	proof	proof	NOUN
ejpam-4275	278	2	.	.	PUNCT
ejpam-4275	279	1	the	the	DET
ejpam-4275	279	2	proof	proof	NOUN
ejpam-4275	279	3	of	of	ADP
ejpam-4275	279	4	(	(	PUNCT
ejpam-4275	279	5	i	i	NOUN
ejpam-4275	279	6	)	)	PUNCT
ejpam-4275	279	7	is	be	AUX
ejpam-4275	279	8	obvious	obvious	ADJ
ejpam-4275	279	9	,	,	PUNCT
ejpam-4275	279	10	so	so	ADV
ejpam-4275	279	11	we	we	PRON
ejpam-4275	279	12	prove	prove	VERB
ejpam-4275	279	13	(	(	PUNCT
ejpam-4275	279	14	ii	ii	NOUN
ejpam-4275	279	15	)	)	PUNCT
ejpam-4275	279	16	.	.	PUNCT
ejpam-4275	280	1	let	let	VERB
ejpam-4275	280	2	δxη	δxη	PROPN
ejpam-4275	280	3	∈	∈	PROPN
ejpam-4275	280	4	pcl(ω	pcl(ω	PROPN
ejpam-4275	280	5	,	,	PUNCT
ejpam-4275	280	6	σ	σ	PROPN
ejpam-4275	280	7	)	)	PUNCT
ejpam-4275	280	8	.	.	PUNCT
ejpam-4275	281	1	then	then	ADV
ejpam-4275	281	2	every	every	DET
ejpam-4275	281	3	infra	infra	NOUN
ejpam-4275	281	4	soft	soft	ADJ
ejpam-4275	281	5	pre	pre	ADJ
ejpam-4275	281	6	-	-	ADJ
ejpam-4275	281	7	closed	closed	ADJ
ejpam-4275	281	8	set	set	NOUN
ejpam-4275	281	9	contains	contain	VERB
ejpam-4275	281	10	(	(	PUNCT
ejpam-4275	281	11	ω	ω	PROPN
ejpam-4275	281	12	,	,	PUNCT
ejpam-4275	281	13	σ	σ	PROPN
ejpam-4275	281	14	)	)	PUNCT
ejpam-4275	281	15	contains	contain	VERB
ejpam-4275	281	16	δxη	δxη	NOUN
ejpam-4275	281	17	as	as	ADV
ejpam-4275	281	18	well	well	ADV
ejpam-4275	281	19	.	.	PUNCT
ejpam-4275	282	1	suppose	suppose	VERB
ejpam-4275	282	2	that	that	SCONJ
ejpam-4275	282	3	there	there	PRON
ejpam-4275	282	4	exists	exist	VERB
ejpam-4275	282	5	an	an	DET
ejpam-4275	282	6	infra	infra	NOUN
ejpam-4275	282	7	soft	soft	ADJ
ejpam-4275	282	8	pre	pre	ADJ
ejpam-4275	282	9	-	-	ADJ
ejpam-4275	282	10	open	open	ADJ
ejpam-4275	282	11	set	set	NOUN
ejpam-4275	282	12	(	(	PUNCT
ejpam-4275	282	13	ψ	ψ	X
ejpam-4275	282	14	,	,	PUNCT
ejpam-4275	282	15	σ	σ	NOUN
ejpam-4275	282	16	)	)	PUNCT
ejpam-4275	282	17	containing	contain	VERB
ejpam-4275	282	18	δxη	δxη	NOUN
ejpam-4275	283	1	such	such	ADJ
ejpam-4275	283	2	that	that	SCONJ
ejpam-4275	283	3	(	(	PUNCT
ejpam-4275	283	4	ω	ω	PROPN
ejpam-4275	283	5	,	,	PUNCT
ejpam-4275	283	6	σ	σ	PROPN
ejpam-4275	283	7	)	)	PUNCT
ejpam-4275	283	8	⋂̃	⋂̃	NOUN
ejpam-4275	283	9	(	(	PUNCT
ejpam-4275	283	10	ψ	ψ	X
ejpam-4275	283	11	,	,	PUNCT
ejpam-4275	283	12	σ	σ	NOUN
ejpam-4275	283	13	)	)	PUNCT
ejpam-4275	283	14	=	=	SYM
ejpam-4275	283	15	φ	φ	PROPN
ejpam-4275	283	16	.	.	PUNCT
ejpam-4275	284	1	therefore	therefore	ADV
ejpam-4275	284	2	,	,	PUNCT
ejpam-4275	284	3	(	(	PUNCT
ejpam-4275	284	4	ω	ω	NOUN
ejpam-4275	284	5	,	,	PUNCT
ejpam-4275	284	6	σ)⊆̃(ψc	σ)⊆̃(ψc	PROPN
ejpam-4275	284	7	,	,	PUNCT
ejpam-4275	284	8	σ	σ	PROPN
ejpam-4275	284	9	)	)	PUNCT
ejpam-4275	284	10	which	which	PRON
ejpam-4275	284	11	means	mean	VERB
ejpam-4275	284	12	that	that	SCONJ
ejpam-4275	284	13	δxη	δxη	PROPN
ejpam-4275	284	14	̸∈	̸∈	PROPN
ejpam-4275	284	15	pcl(ω	pcl(ω	PROPN
ejpam-4275	284	16	,	,	PUNCT
ejpam-4275	284	17	σ	σ	PROPN
ejpam-4275	284	18	)	)	PUNCT
ejpam-4275	284	19	.	.	PUNCT
ejpam-4275	285	1	this	this	PRON
ejpam-4275	285	2	is	be	AUX
ejpam-4275	285	3	a	a	DET
ejpam-4275	285	4	contradiction	contradiction	NOUN
ejpam-4275	285	5	.	.	PUNCT
ejpam-4275	286	1	conversely	conversely	ADV
ejpam-4275	286	2	,	,	PUNCT
ejpam-4275	286	3	suppose	suppose	VERB
ejpam-4275	286	4	that	that	SCONJ
ejpam-4275	286	5	there	there	PRON
ejpam-4275	286	6	exists	exist	VERB
ejpam-4275	286	7	an	an	DET
ejpam-4275	286	8	infra	infra	NOUN
ejpam-4275	286	9	soft	soft	ADJ
ejpam-4275	286	10	pre	pre	ADJ
ejpam-4275	286	11	-	-	ADJ
ejpam-4275	286	12	open	open	ADJ
ejpam-4275	286	13	set	set	NOUN
ejpam-4275	286	14	(	(	PUNCT
ejpam-4275	286	15	ψ	ψ	X
ejpam-4275	286	16	,	,	PUNCT
ejpam-4275	286	17	σ	σ	NOUN
ejpam-4275	286	18	)	)	PUNCT
ejpam-4275	286	19	containing	contain	VERB
ejpam-4275	286	20	δxη	δxη	NOUN
ejpam-4275	287	1	such	such	ADJ
ejpam-4275	287	2	that	that	SCONJ
ejpam-4275	287	3	(	(	PUNCT
ejpam-4275	287	4	ω	ω	PROPN
ejpam-4275	287	5	,	,	PUNCT
ejpam-4275	287	6	σ	σ	PROPN
ejpam-4275	287	7	)	)	PUNCT
ejpam-4275	287	8	⋂̃	⋂̃	NOUN
ejpam-4275	287	9	(	(	PUNCT
ejpam-4275	287	10	ψ	ψ	X
ejpam-4275	287	11	,	,	PUNCT
ejpam-4275	287	12	σ	σ	NOUN
ejpam-4275	287	13	)	)	PUNCT
ejpam-4275	287	14	=	=	SYM
ejpam-4275	287	15	φ	φ	PROPN
ejpam-4275	287	16	.	.	PUNCT
ejpam-4275	287	17	therefore	therefore	ADV
ejpam-4275	287	18	,	,	PUNCT
ejpam-4275	287	19	pcl(ω	pcl(ω	PROPN
ejpam-4275	287	20	,	,	PUNCT
ejpam-4275	287	21	σ)⊆̃(ψc	σ)⊆̃(ψc	ADJ
ejpam-4275	287	22	,	,	PUNCT
ejpam-4275	287	23	σ	σ	PROPN
ejpam-4275	287	24	)	)	PUNCT
ejpam-4275	287	25	which	which	PRON
ejpam-4275	287	26	means	mean	VERB
ejpam-4275	287	27	that	that	SCONJ
ejpam-4275	287	28	δxη	δxη	PROPN
ejpam-4275	287	29	̸∈	̸∈	PROPN
ejpam-4275	287	30	pcl(ω	pcl(ω	PROPN
ejpam-4275	287	31	,	,	PUNCT
ejpam-4275	287	32	σ	σ	PROPN
ejpam-4275	287	33	)	)	PUNCT
ejpam-4275	287	34	.	.	PUNCT
ejpam-4275	288	1	hence	hence	ADV
ejpam-4275	288	2	,	,	PUNCT
ejpam-4275	288	3	we	we	PRON
ejpam-4275	288	4	obtain	obtain	VERB
ejpam-4275	288	5	the	the	DET
ejpam-4275	288	6	desired	desire	VERB
ejpam-4275	288	7	result	result	NOUN
ejpam-4275	288	8	.	.	PUNCT
ejpam-4275	289	1	proposition	proposition	NOUN
ejpam-4275	289	2	15	15	NUM
ejpam-4275	289	3	.	.	PUNCT
ejpam-4275	290	1	let	let	AUX
ejpam-4275	290	2	(	(	PUNCT
ejpam-4275	290	3	ω	ω	PROPN
ejpam-4275	290	4	,	,	PUNCT
ejpam-4275	290	5	σ	σ	PROPN
ejpam-4275	290	6	)	)	PUNCT
ejpam-4275	290	7	be	be	VERB
ejpam-4275	290	8	a	a	DET
ejpam-4275	290	9	subset	subset	NOUN
ejpam-4275	290	10	of	of	ADP
ejpam-4275	290	11	(	(	PUNCT
ejpam-4275	290	12	x	x	NOUN
ejpam-4275	290	13	,	,	PUNCT
ejpam-4275	290	14	ξ	ξ	PROPN
ejpam-4275	290	15	,	,	PUNCT
ejpam-4275	290	16	σ	σ	NOUN
ejpam-4275	290	17	)	)	PUNCT
ejpam-4275	290	18	.	.	PUNCT
ejpam-4275	291	1	then	then	ADV
ejpam-4275	291	2	:	:	PUNCT
ejpam-4275	291	3	(	(	PUNCT
ejpam-4275	291	4	i	i	NOUN
ejpam-4275	291	5	)	)	PUNCT
ejpam-4275	291	6	(	(	PUNCT
ejpam-4275	291	7	pint(ω	pint(ω	NOUN
ejpam-4275	291	8	,	,	PUNCT
ejpam-4275	291	9	σ))c	σ))c	ADJ
ejpam-4275	291	10	=	=	SYM
ejpam-4275	291	11	pcl(ωc	pcl(ωc	NOUN
ejpam-4275	291	12	,	,	PUNCT
ejpam-4275	291	13	σ	σ	PROPN
ejpam-4275	291	14	)	)	PUNCT
ejpam-4275	291	15	.	.	PUNCT
ejpam-4275	292	1	(	(	PUNCT
ejpam-4275	292	2	ii	ii	NOUN
ejpam-4275	292	3	)	)	PUNCT
ejpam-4275	292	4	(	(	PUNCT
ejpam-4275	292	5	pcl(ω	pcl(ω	PROPN
ejpam-4275	292	6	,	,	PUNCT
ejpam-4275	292	7	σ))c	σ))c	ADJ
ejpam-4275	292	8	=	=	SYM
ejpam-4275	292	9	pint(ωc	pint(ωc	PROPN
ejpam-4275	292	10	,	,	PUNCT
ejpam-4275	292	11	σ	σ	PROPN
ejpam-4275	292	12	)	)	PUNCT
ejpam-4275	292	13	.	.	PUNCT
ejpam-4275	293	1	proof	proof	NOUN
ejpam-4275	293	2	.	.	PUNCT
ejpam-4275	294	1	(	(	PUNCT
ejpam-4275	294	2	i	i	NOUN
ejpam-4275	294	3	):	):	PUNCT
ejpam-4275	294	4	(	(	PUNCT
ejpam-4275	294	5	pint(ω	pint(ω	NOUN
ejpam-4275	294	6	,	,	PUNCT
ejpam-4275	294	7	σ))c	σ))c	NOUN
ejpam-4275	294	8	=	=	SYM
ejpam-4275	294	9	{	{	PUNCT
ejpam-4275	294	10	⋃̃	⋃̃	PROPN
ejpam-4275	294	11	j∈j	j∈j	NOUN
ejpam-4275	294	12	(	(	PUNCT
ejpam-4275	294	13	ψj	ψj	ADV
ejpam-4275	294	14	,	,	PUNCT
ejpam-4275	294	15	σ	σ	PROPN
ejpam-4275	294	16	)	)	PUNCT
ejpam-4275	294	17	:	:	PUNCT
ejpam-4275	294	18	(	(	PUNCT
ejpam-4275	294	19	ψj	ψj	ADV
ejpam-4275	294	20	,	,	PUNCT
ejpam-4275	294	21	σ	σ	PROPN
ejpam-4275	294	22	)	)	PUNCT
ejpam-4275	294	23	is	be	AUX
ejpam-4275	294	24	an	an	DET
ejpam-4275	294	25	infra	infra	NOUN
ejpam-4275	294	26	soft	soft	ADJ
ejpam-4275	294	27	pre	pre	ADJ
ejpam-4275	294	28	-	-	ADJ
ejpam-4275	294	29	open	open	ADJ
ejpam-4275	294	30	set	set	NOUN
ejpam-4275	294	31	contained	contain	VERB
ejpam-4275	294	32	in	in	ADP
ejpam-4275	294	33	(	(	PUNCT
ejpam-4275	294	34	ω	ω	PROPN
ejpam-4275	294	35	,	,	PUNCT
ejpam-4275	294	36	σ)}c	σ)}c	PROPN
ejpam-4275	294	37	=	=	SYM
ejpam-4275	294	38	⋂̃	⋂̃	SYM
ejpam-4275	294	39	j∈j	j∈j	NOUN
ejpam-4275	294	40	{	{	PUNCT
ejpam-4275	294	41	(	(	PUNCT
ejpam-4275	294	42	ψc	ψc	PROPN
ejpam-4275	294	43	j	j	PROPN
ejpam-4275	294	44	,	,	PUNCT
ejpam-4275	294	45	σ	σ	PROPN
ejpam-4275	294	46	)	)	PUNCT
ejpam-4275	294	47	:	:	PUNCT
ejpam-4275	294	48	(	(	PUNCT
ejpam-4275	294	49	ψc	ψc	PROPN
ejpam-4275	294	50	j	j	PROPN
ejpam-4275	294	51	,	,	PUNCT
ejpam-4275	294	52	σ	σ	PROPN
ejpam-4275	294	53	)	)	PUNCT
ejpam-4275	294	54	is	be	AUX
ejpam-4275	294	55	an	an	DET
ejpam-4275	294	56	infra	infra	NOUN
ejpam-4275	294	57	soft	soft	ADJ
ejpam-4275	294	58	pre	pre	ADJ
ejpam-4275	294	59	-	-	ADJ
ejpam-4275	294	60	closed	closed	ADJ
ejpam-4275	294	61	set	set	NOUN
ejpam-4275	294	62	containing	contain	VERB
ejpam-4275	294	63	(	(	PUNCT
ejpam-4275	294	64	ωc	ωc	PROPN
ejpam-4275	294	65	,	,	PUNCT
ejpam-4275	294	66	σ	σ	NOUN
ejpam-4275	294	67	)	)	PUNCT
ejpam-4275	294	68	}	}	PUNCT
ejpam-4275	294	69	=	=	SYM
ejpam-4275	294	70	pcl(ωc	pcl(ωc	X
ejpam-4275	294	71	,	,	PUNCT
ejpam-4275	294	72	σ	σ	PROPN
ejpam-4275	294	73	)	)	PUNCT
ejpam-4275	294	74	.	.	PUNCT
ejpam-4275	295	1	the	the	DET
ejpam-4275	295	2	proof	proof	NOUN
ejpam-4275	295	3	of	of	ADP
ejpam-4275	295	4	(	(	PUNCT
ejpam-4275	295	5	ii	ii	NOUN
ejpam-4275	295	6	)	)	PUNCT
ejpam-4275	295	7	is	be	AUX
ejpam-4275	295	8	similar	similar	ADJ
ejpam-4275	295	9	to	to	ADP
ejpam-4275	295	10	(	(	PUNCT
ejpam-4275	295	11	i	i	NOUN
ejpam-4275	295	12	)	)	PUNCT
ejpam-4275	295	13	.	.	PUNCT
ejpam-4275	296	1	proposition	proposition	NOUN
ejpam-4275	296	2	16	16	NUM
ejpam-4275	296	3	.	.	PUNCT
ejpam-4275	297	1	let	let	AUX
ejpam-4275	297	2	(	(	PUNCT
ejpam-4275	297	3	ψ	ψ	X
ejpam-4275	297	4	,	,	PUNCT
ejpam-4275	297	5	σ	σ	PROPN
ejpam-4275	297	6	)	)	PUNCT
ejpam-4275	297	7	be	be	VERB
ejpam-4275	297	8	an	an	DET
ejpam-4275	297	9	infra	infra	NOUN
ejpam-4275	297	10	soft	soft	ADJ
ejpam-4275	297	11	open	open	ADJ
ejpam-4275	297	12	set	set	NOUN
ejpam-4275	297	13	and	and	CCONJ
ejpam-4275	297	14	(	(	PUNCT
ejpam-4275	297	15	λ	λ	PROPN
ejpam-4275	297	16	,	,	PUNCT
ejpam-4275	297	17	σ	σ	PROPN
ejpam-4275	297	18	)	)	PUNCT
ejpam-4275	297	19	be	be	VERB
ejpam-4275	297	20	an	an	DET
ejpam-4275	297	21	infra	infra	NOUN
ejpam-4275	297	22	soft	soft	ADJ
ejpam-4275	297	23	closed	closed	ADJ
ejpam-4275	297	24	set	set	VERB
ejpam-4275	297	25	in	in	ADP
ejpam-4275	297	26	(	(	PUNCT
ejpam-4275	297	27	x	x	NOUN
ejpam-4275	297	28	,	,	PUNCT
ejpam-4275	297	29	ξ	ξ	PROPN
ejpam-4275	297	30	,	,	PUNCT
ejpam-4275	297	31	σ	σ	NOUN
ejpam-4275	297	32	)	)	PUNCT
ejpam-4275	297	33	.	.	PUNCT
ejpam-4275	298	1	then	then	ADV
ejpam-4275	298	2	:	:	PUNCT
ejpam-4275	298	3	(	(	PUNCT
ejpam-4275	298	4	i	i	NOUN
ejpam-4275	298	5	)	)	PUNCT
ejpam-4275	298	6	(	(	PUNCT
ejpam-4275	298	7	ψ	ψ	X
ejpam-4275	298	8	,	,	PUNCT
ejpam-4275	298	9	σ	σ	NOUN
ejpam-4275	298	10	)	)	PUNCT
ejpam-4275	298	11	⋂̃	⋂̃	X
ejpam-4275	298	12	pcl(ω	pcl(ω	PROPN
ejpam-4275	298	13	,	,	PUNCT
ejpam-4275	298	14	σ)⊆̃pcl((ψ	σ)⊆̃pcl((ψ	PROPN
ejpam-4275	298	15	,	,	PUNCT
ejpam-4275	298	16	σ	σ	PROPN
ejpam-4275	298	17	)	)	PUNCT
ejpam-4275	298	18	⋂̃	⋂̃	NOUN
ejpam-4275	298	19	(	(	PUNCT
ejpam-4275	298	20	ω	ω	PROPN
ejpam-4275	298	21	,	,	PUNCT
ejpam-4275	298	22	σ	σ	PROPN
ejpam-4275	298	23	)	)	PUNCT
ejpam-4275	298	24	)	)	PUNCT
ejpam-4275	298	25	.	.	PUNCT
ejpam-4275	299	1	(	(	PUNCT
ejpam-4275	299	2	ii	ii	X
ejpam-4275	299	3	)	)	PUNCT
ejpam-4275	299	4	pint((λ	pint((λ	PROPN
ejpam-4275	299	5	,	,	PUNCT
ejpam-4275	299	6	σ	σ	PROPN
ejpam-4275	299	7	)	)	PUNCT
ejpam-4275	299	8	⋃̃	⋃̃	PROPN
ejpam-4275	299	9	(	(	PUNCT
ejpam-4275	299	10	ω	ω	PROPN
ejpam-4275	299	11	,	,	PUNCT
ejpam-4275	299	12	σ))⊆̃(λ	σ))⊆̃(λ	PROPN
ejpam-4275	299	13	,	,	PUNCT
ejpam-4275	299	14	σ	σ	PROPN
ejpam-4275	299	15	)	)	PUNCT
ejpam-4275	299	16	⋃̃	⋃̃	PROPN
ejpam-4275	299	17	pint(ω	pint(ω	PROPN
ejpam-4275	299	18	,	,	PUNCT
ejpam-4275	299	19	σ	σ	PROPN
ejpam-4275	299	20	)	)	PUNCT
ejpam-4275	299	21	.	.	PUNCT
ejpam-4275	300	1	proof	proof	NOUN
ejpam-4275	300	2	.	.	PUNCT
ejpam-4275	301	1	(	(	PUNCT
ejpam-4275	301	2	i	i	NOUN
ejpam-4275	301	3	):	):	PUNCT
ejpam-4275	301	4	let	let	VERB
ejpam-4275	301	5	δxη	δxη	NOUN
ejpam-4275	301	6	∈	∈	PROPN
ejpam-4275	301	7	(	(	PUNCT
ejpam-4275	301	8	ψ	ψ	X
ejpam-4275	301	9	,	,	PUNCT
ejpam-4275	301	10	σ	σ	NOUN
ejpam-4275	301	11	)	)	PUNCT
ejpam-4275	301	12	⋂̃	⋂̃	X
ejpam-4275	301	13	pcl(ω	pcl(ω	PROPN
ejpam-4275	301	14	,	,	PUNCT
ejpam-4275	301	15	σ	σ	PROPN
ejpam-4275	301	16	)	)	PUNCT
ejpam-4275	301	17	.	.	PUNCT
ejpam-4275	302	1	then	then	ADV
ejpam-4275	302	2	δxη	δxη	NOUN
ejpam-4275	302	3	∈	∈	PROPN
ejpam-4275	302	4	(	(	PUNCT
ejpam-4275	302	5	ψ	ψ	X
ejpam-4275	302	6	,	,	PUNCT
ejpam-4275	302	7	σ	σ	NOUN
ejpam-4275	302	8	)	)	PUNCT
ejpam-4275	302	9	and	and	CCONJ
ejpam-4275	302	10	δxη	δxη	PROPN
ejpam-4275	302	11	∈	∈	PROPN
ejpam-4275	302	12	pcl(ω	pcl(ω	PROPN
ejpam-4275	302	13	,	,	PUNCT
ejpam-4275	302	14	σ	σ	PROPN
ejpam-4275	302	15	)	)	PUNCT
ejpam-4275	302	16	.	.	PUNCT
ejpam-4275	303	1	this	this	PRON
ejpam-4275	303	2	implies	imply	VERB
ejpam-4275	303	3	that	that	SCONJ
ejpam-4275	303	4	(	(	PUNCT
ejpam-4275	303	5	γ	γ	X
ejpam-4275	303	6	,	,	PUNCT
ejpam-4275	303	7	σ	σ	PROPN
ejpam-4275	303	8	)	)	PUNCT
ejpam-4275	303	9	⋂̃	⋂̃	NOUN
ejpam-4275	303	10	(	(	PUNCT
ejpam-4275	303	11	ω	ω	PROPN
ejpam-4275	303	12	,	,	PUNCT
ejpam-4275	303	13	σ	σ	PROPN
ejpam-4275	303	14	)	)	PUNCT
ejpam-4275	303	15	̸=	̸=	PROPN
ejpam-4275	303	16	φ	φ	NUM
ejpam-4275	303	17	for	for	ADP
ejpam-4275	303	18	every	every	DET
ejpam-4275	303	19	infra	infra	NOUN
ejpam-4275	303	20	soft	soft	ADJ
ejpam-4275	303	21	pre	pre	ADJ
ejpam-4275	303	22	-	-	ADJ
ejpam-4275	303	23	open	open	ADJ
ejpam-4275	303	24	set	set	NOUN
ejpam-4275	303	25	(	(	PUNCT
ejpam-4275	303	26	γ	γ	X
ejpam-4275	303	27	,	,	PUNCT
ejpam-4275	303	28	σ	σ	PROPN
ejpam-4275	303	29	)	)	PUNCT
ejpam-4275	303	30	containing	contain	VERB
ejpam-4275	303	31	δxη	δxη	NOUN
ejpam-4275	303	32	.	.	PUNCT
ejpam-4275	304	1	it	it	PRON
ejpam-4275	304	2	follows	follow	VERB
ejpam-4275	304	3	from	from	ADP
ejpam-4275	304	4	proposition	proposition	NOUN
ejpam-4275	304	5	9	9	NUM
ejpam-4275	304	6	that	that	SCONJ
ejpam-4275	304	7	(	(	PUNCT
ejpam-4275	304	8	ψ	ψ	X
ejpam-4275	304	9	,	,	PUNCT
ejpam-4275	304	10	σ	σ	NOUN
ejpam-4275	304	11	)	)	PUNCT
ejpam-4275	304	12	⋂̃	⋂̃	NOUN
ejpam-4275	304	13	(	(	PUNCT
ejpam-4275	304	14	γ	γ	X
ejpam-4275	304	15	,	,	PUNCT
ejpam-4275	304	16	σ	σ	PROPN
ejpam-4275	304	17	)	)	PUNCT
ejpam-4275	304	18	is	be	AUX
ejpam-4275	304	19	an	an	DET
ejpam-4275	304	20	infra	infra	NOUN
ejpam-4275	304	21	soft	soft	ADJ
ejpam-4275	304	22	pre	pre	ADJ
ejpam-4275	304	23	-	-	ADJ
ejpam-4275	304	24	open	open	ADJ
ejpam-4275	304	25	set	set	NOUN
ejpam-4275	304	26	containing	contain	VERB
ejpam-4275	304	27	δxη	δxη	NOUN
ejpam-4275	304	28	.	.	PUNCT
ejpam-4275	305	1	therefore	therefore	ADV
ejpam-4275	305	2	,	,	PUNCT
ejpam-4275	305	3	[	[	X
ejpam-4275	305	4	(	(	PUNCT
ejpam-4275	305	5	ψ	ψ	X
ejpam-4275	305	6	,	,	PUNCT
ejpam-4275	305	7	σ	σ	NOUN
ejpam-4275	305	8	)	)	PUNCT
ejpam-4275	305	9	⋂̃	⋂̃	NOUN
ejpam-4275	305	10	(	(	PUNCT
ejpam-4275	305	11	γ	γ	X
ejpam-4275	305	12	,	,	PUNCT
ejpam-4275	305	13	σ	σ	PROPN
ejpam-4275	305	14	)	)	PUNCT
ejpam-4275	305	15	]	]	PUNCT
ejpam-4275	306	1	⋂̃	⋂̃	X
ejpam-4275	306	2	(	(	PUNCT
ejpam-4275	306	3	ω	ω	PROPN
ejpam-4275	306	4	,	,	PUNCT
ejpam-4275	306	5	σ	σ	PROPN
ejpam-4275	306	6	)	)	PUNCT
ejpam-4275	306	7	̸=	̸=	PROPN
ejpam-4275	306	8	φ	φ	NUM
ejpam-4275	306	9	.	.	PUNCT
ejpam-4275	307	1	now	now	ADV
ejpam-4275	307	2	,	,	PUNCT
ejpam-4275	307	3	(	(	PUNCT
ejpam-4275	307	4	γ	γ	X
ejpam-4275	307	5	,	,	PUNCT
ejpam-4275	307	6	σ	σ	NOUN
ejpam-4275	307	7	)	)	PUNCT
ejpam-4275	307	8	⋂̃	⋂̃	NOUN
ejpam-4275	307	9	[	[	X
ejpam-4275	307	10	(	(	PUNCT
ejpam-4275	307	11	ψ	ψ	X
ejpam-4275	307	12	,	,	PUNCT
ejpam-4275	307	13	σ	σ	NOUN
ejpam-4275	307	14	)	)	PUNCT
ejpam-4275	307	15	⋂̃	⋂̃	NOUN
ejpam-4275	307	16	(	(	PUNCT
ejpam-4275	307	17	ω	ω	PROPN
ejpam-4275	307	18	,	,	PUNCT
ejpam-4275	307	19	σ	σ	PROPN
ejpam-4275	307	20	)	)	PUNCT
ejpam-4275	307	21	]	]	PUNCT
ejpam-4275	308	1	̸=	̸=	PROPN
ejpam-4275	308	2	φ	φ	NUM
ejpam-4275	308	3	which	which	PRON
ejpam-4275	308	4	means	mean	VERB
ejpam-4275	308	5	that	that	SCONJ
ejpam-4275	308	6	δxη	δxη	PROPN
ejpam-4275	308	7	∈	∈	PROPN
ejpam-4275	308	8	pcl((ψ	pcl((ψ	PROPN
ejpam-4275	308	9	,	,	PUNCT
ejpam-4275	308	10	σ	σ	PROPN
ejpam-4275	308	11	)	)	PUNCT
ejpam-4275	308	12	⋂̃	⋂̃	PROPN
ejpam-4275	308	13	(	(	PUNCT
ejpam-4275	308	14	ω	ω	PROPN
ejpam-4275	308	15	,	,	PUNCT
ejpam-4275	308	16	σ	σ	PROPN
ejpam-4275	308	17	)	)	PUNCT
ejpam-4275	308	18	)	)	PUNCT
ejpam-4275	308	19	.	.	PUNCT
ejpam-4275	309	1	hence	hence	ADV
ejpam-4275	309	2	,	,	PUNCT
ejpam-4275	309	3	(	(	PUNCT
ejpam-4275	309	4	ψ	ψ	X
ejpam-4275	309	5	,	,	PUNCT
ejpam-4275	309	6	σ	σ	NOUN
ejpam-4275	309	7	)	)	PUNCT
ejpam-4275	309	8	⋂̃	⋂̃	X
ejpam-4275	309	9	pcl(ω	pcl(ω	PROPN
ejpam-4275	309	10	,	,	PUNCT
ejpam-4275	309	11	σ)⊆̃pcl((ψ	σ)⊆̃pcl((ψ	PROPN
ejpam-4275	309	12	,	,	PUNCT
ejpam-4275	309	13	σ	σ	PROPN
ejpam-4275	309	14	)	)	PUNCT
ejpam-4275	309	15	⋂̃	⋂̃	NOUN
ejpam-4275	309	16	(	(	PUNCT
ejpam-4275	309	17	ω	ω	PROPN
ejpam-4275	309	18	,	,	PUNCT
ejpam-4275	309	19	σ	σ	PROPN
ejpam-4275	309	20	)	)	PUNCT
ejpam-4275	309	21	)	)	PUNCT
ejpam-4275	309	22	.	.	PUNCT
ejpam-4275	310	1	one	one	PRON
ejpam-4275	310	2	can	can	AUX
ejpam-4275	310	3	prove	prove	VERB
ejpam-4275	310	4	(	(	PUNCT
ejpam-4275	310	5	ii	ii	NOUN
ejpam-4275	310	6	)	)	PUNCT
ejpam-4275	310	7	following	follow	VERB
ejpam-4275	310	8	similar	similar	ADJ
ejpam-4275	310	9	arguments	argument	NOUN
ejpam-4275	310	10	.	.	PUNCT
ejpam-4275	311	1	theorem	theorem	NOUN
ejpam-4275	311	2	1	1	NUM
ejpam-4275	311	3	.	.	PUNCT
ejpam-4275	312	1	let	let	VERB
ejpam-4275	312	2	(	(	PUNCT
ejpam-4275	312	3	ω	ω	PROPN
ejpam-4275	312	4	,	,	PUNCT
ejpam-4275	312	5	σ	σ	PROPN
ejpam-4275	312	6	)	)	PUNCT
ejpam-4275	312	7	and	and	CCONJ
ejpam-4275	312	8	(	(	PUNCT
ejpam-4275	312	9	ψ	ψ	X
ejpam-4275	312	10	,	,	PUNCT
ejpam-4275	312	11	σ	σ	PROPN
ejpam-4275	312	12	)	)	PUNCT
ejpam-4275	312	13	be	be	VERB
ejpam-4275	312	14	subsets	subset	NOUN
ejpam-4275	312	15	of	of	ADP
ejpam-4275	312	16	(	(	PUNCT
ejpam-4275	312	17	x	x	NOUN
ejpam-4275	312	18	,	,	PUNCT
ejpam-4275	312	19	ξ	ξ	PROPN
ejpam-4275	312	20	,	,	PUNCT
ejpam-4275	312	21	σ	σ	NOUN
ejpam-4275	312	22	)	)	PUNCT
ejpam-4275	312	23	.	.	PUNCT
ejpam-4275	313	1	then	then	ADV
ejpam-4275	313	2	we	we	PRON
ejpam-4275	313	3	have	have	VERB
ejpam-4275	313	4	the	the	DET
ejpam-4275	313	5	following	follow	VERB
ejpam-4275	313	6	properties	property	NOUN
ejpam-4275	313	7	.	.	PUNCT
ejpam-4275	314	1	(	(	PUNCT
ejpam-4275	314	2	i	i	NOUN
ejpam-4275	314	3	)	)	PUNCT
ejpam-4275	314	4	pint(x̃	pint(x̃	PROPN
ejpam-4275	314	5	)	)	PUNCT
ejpam-4275	314	6	=	=	SYM
ejpam-4275	315	1	x̃.	x̃.	PROPN
ejpam-4275	315	2	t.m	t.m	PROPN
ejpam-4275	315	3	.	.	PROPN
ejpam-4275	315	4	al	al	PROPN
ejpam-4275	315	5	-	-	PUNCT
ejpam-4275	315	6	shami	shami	PROPN
ejpam-4275	315	7	,	,	PUNCT
ejpam-4275	315	8	h.a	h.a	PROPN
ejpam-4275	315	9	.	.	PROPN
ejpam-4275	315	10	othman	othman	PROPN
ejpam-4275	315	11	/	/	SYM
ejpam-4275	315	12	eur	eur	PROPN
ejpam-4275	315	13	.	.	PUNCT
ejpam-4275	316	1	j.	j.	PROPN
ejpam-4275	316	2	pure	pure	PROPN
ejpam-4275	316	3	appl	appl	PROPN
ejpam-4275	316	4	.	.	PROPN
ejpam-4275	316	5	math	math	PROPN
ejpam-4275	316	6	,	,	PUNCT
ejpam-4275	316	7	15	15	NUM
ejpam-4275	316	8	(	(	PUNCT
ejpam-4275	316	9	1	1	NUM
ejpam-4275	316	10	)	)	PUNCT
ejpam-4275	316	11	(	(	PUNCT
ejpam-4275	316	12	2022	2022	NUM
ejpam-4275	316	13	)	)	PUNCT
ejpam-4275	316	14	,	,	PUNCT
ejpam-4275	316	15	261	261	NUM
ejpam-4275	316	16	-	-	SYM
ejpam-4275	316	17	280	280	NUM
ejpam-4275	316	18	270	270	NUM
ejpam-4275	316	19	(	(	PUNCT
ejpam-4275	316	20	ii	ii	NOUN
ejpam-4275	316	21	)	)	PUNCT
ejpam-4275	316	22	pint(ω	pint(ω	PROPN
ejpam-4275	316	23	,	,	PUNCT
ejpam-4275	316	24	σ)⊆̃(ω	σ)⊆̃(ω	PROPN
ejpam-4275	316	25	,	,	PUNCT
ejpam-4275	316	26	σ	σ	PROPN
ejpam-4275	316	27	)	)	PUNCT
ejpam-4275	316	28	.	.	PUNCT
ejpam-4275	317	1	(	(	PUNCT
ejpam-4275	317	2	iii	iii	X
ejpam-4275	317	3	)	)	PUNCT
ejpam-4275	317	4	if	if	SCONJ
ejpam-4275	317	5	(	(	PUNCT
ejpam-4275	317	6	ψ	ψ	X
ejpam-4275	317	7	,	,	PUNCT
ejpam-4275	317	8	σ)⊆̃(ω	σ)⊆̃(ω	PROPN
ejpam-4275	317	9	,	,	PUNCT
ejpam-4275	317	10	σ	σ	PROPN
ejpam-4275	317	11	)	)	PUNCT
ejpam-4275	317	12	,	,	PUNCT
ejpam-4275	317	13	then	then	ADV
ejpam-4275	317	14	pint(ψ	pint(ψ	NOUN
ejpam-4275	317	15	,	,	PUNCT
ejpam-4275	317	16	σ)⊆̃pint(ω	σ)⊆̃pint(ω	NOUN
ejpam-4275	317	17	,	,	PUNCT
ejpam-4275	317	18	σ	σ	NOUN
ejpam-4275	317	19	)	)	PUNCT
ejpam-4275	317	20	.	.	PUNCT
ejpam-4275	318	1	(	(	PUNCT
ejpam-4275	318	2	iv	iv	X
ejpam-4275	318	3	)	)	PUNCT
ejpam-4275	318	4	pint(pint(ω	pint(pint(ω	NOUN
ejpam-4275	318	5	,	,	PUNCT
ejpam-4275	318	6	σ	σ	NOUN
ejpam-4275	318	7	)	)	PUNCT
ejpam-4275	318	8	)	)	PUNCT
ejpam-4275	319	1	=	=	SYM
ejpam-4275	319	2	pint(ω	pint(ω	PROPN
ejpam-4275	319	3	,	,	PUNCT
ejpam-4275	319	4	σ	σ	PROPN
ejpam-4275	319	5	)	)	PUNCT
ejpam-4275	319	6	.	.	PUNCT
ejpam-4275	320	1	(	(	PUNCT
ejpam-4275	320	2	v	v	NOUN
ejpam-4275	320	3	)	)	PUNCT
ejpam-4275	320	4	pint(ψ	pint(ψ	NOUN
ejpam-4275	320	5	,	,	PUNCT
ejpam-4275	320	6	σ	σ	NOUN
ejpam-4275	320	7	)	)	PUNCT
ejpam-4275	320	8	⋂̃	⋂̃	NOUN
ejpam-4275	320	9	pint(ω	pint(ω	NOUN
ejpam-4275	320	10	,	,	PUNCT
ejpam-4275	320	11	σ)⊆̃pint((ψ	σ)⊆̃pint((ψ	PROPN
ejpam-4275	320	12	,	,	PUNCT
ejpam-4275	320	13	σ	σ	PROPN
ejpam-4275	320	14	)	)	PUNCT
ejpam-4275	320	15	⋂̃	⋂̃	PROPN
ejpam-4275	320	16	(	(	PUNCT
ejpam-4275	320	17	ω	ω	PROPN
ejpam-4275	320	18	,	,	PUNCT
ejpam-4275	320	19	σ	σ	PROPN
ejpam-4275	320	20	)	)	PUNCT
ejpam-4275	320	21	)	)	PUNCT
ejpam-4275	320	22	.	.	PUNCT
ejpam-4275	321	1	proof	proof	NOUN
ejpam-4275	321	2	.	.	PUNCT
ejpam-4275	322	1	(	(	PUNCT
ejpam-4275	322	2	i	i	NOUN
ejpam-4275	322	3	):	):	PUNCT
ejpam-4275	322	4	since	since	SCONJ
ejpam-4275	322	5	x̃	x̃	PROPN
ejpam-4275	322	6	is	be	AUX
ejpam-4275	322	7	infra	infra	NOUN
ejpam-4275	322	8	soft	soft	ADJ
ejpam-4275	322	9	pre	pre	ADJ
ejpam-4275	322	10	-	-	ADJ
ejpam-4275	322	11	open	open	ADJ
ejpam-4275	322	12	,	,	PUNCT
ejpam-4275	322	13	pint(x̃	pint(x̃	PROPN
ejpam-4275	322	14	)	)	PUNCT
ejpam-4275	322	15	=	=	SYM
ejpam-4275	323	1	x̃.	x̃.	ADJ
ejpam-4275	323	2	(	(	PUNCT
ejpam-4275	323	3	ii	ii	NOUN
ejpam-4275	323	4	)	)	PUNCT
ejpam-4275	323	5	and	and	CCONJ
ejpam-4275	323	6	(	(	PUNCT
ejpam-4275	323	7	iii	iii	X
ejpam-4275	323	8	)	)	PUNCT
ejpam-4275	323	9	are	be	AUX
ejpam-4275	323	10	obvious	obvious	ADJ
ejpam-4275	323	11	.	.	PUNCT
ejpam-4275	324	1	(	(	PUNCT
ejpam-4275	324	2	iv	iv	X
ejpam-4275	324	3	):	):	PUNCT
ejpam-4275	324	4	it	it	PRON
ejpam-4275	324	5	is	be	AUX
ejpam-4275	324	6	clear	clear	ADJ
ejpam-4275	324	7	that	that	SCONJ
ejpam-4275	324	8	pint(pint(ω	pint(pint(ω	NOUN
ejpam-4275	324	9	,	,	PUNCT
ejpam-4275	324	10	σ	σ	NOUN
ejpam-4275	324	11	)	)	PUNCT
ejpam-4275	324	12	)	)	PUNCT
ejpam-4275	324	13	is	be	AUX
ejpam-4275	324	14	the	the	DET
ejpam-4275	324	15	largest	large	ADJ
ejpam-4275	324	16	infra	infra	NOUN
ejpam-4275	324	17	soft	soft	ADJ
ejpam-4275	324	18	pre	pre	ADJ
ejpam-4275	324	19	-	-	ADJ
ejpam-4275	324	20	open	open	ADJ
ejpam-4275	324	21	set	set	NOUN
ejpam-4275	324	22	contained	contain	VERB
ejpam-4275	324	23	in	in	ADP
ejpam-4275	324	24	pint(ω	pint(ω	PROPN
ejpam-4275	324	25	,	,	PUNCT
ejpam-4275	324	26	σ	σ	PROPN
ejpam-4275	324	27	)	)	PUNCT
ejpam-4275	324	28	;	;	PUNCT
ejpam-4275	324	29	however	however	ADV
ejpam-4275	324	30	,	,	PUNCT
ejpam-4275	324	31	pint(ω	pint(ω	PROPN
ejpam-4275	324	32	,	,	PUNCT
ejpam-4275	324	33	σ	σ	PROPN
ejpam-4275	324	34	)	)	PUNCT
ejpam-4275	324	35	is	be	AUX
ejpam-4275	324	36	an	an	DET
ejpam-4275	324	37	infra	infra	NOUN
ejpam-4275	324	38	soft	soft	ADJ
ejpam-4275	324	39	pre	pre	ADJ
ejpam-4275	324	40	-	-	ADJ
ejpam-4275	324	41	open	open	ADJ
ejpam-4275	324	42	set	set	NOUN
ejpam-4275	324	43	;	;	PUNCT
ejpam-4275	324	44	hence	hence	ADV
ejpam-4275	324	45	,	,	PUNCT
ejpam-4275	324	46	pint(pint(ω	pint(pint(ω	PROPN
ejpam-4275	324	47	,	,	PUNCT
ejpam-4275	324	48	σ	σ	NOUN
ejpam-4275	324	49	)	)	PUNCT
ejpam-4275	324	50	)	)	PUNCT
ejpam-4275	325	1	=	=	SYM
ejpam-4275	325	2	pint(ω	pint(ω	PROPN
ejpam-4275	325	3	,	,	PUNCT
ejpam-4275	325	4	σ	σ	PROPN
ejpam-4275	325	5	)	)	PUNCT
ejpam-4275	325	6	.	.	PUNCT
ejpam-4275	326	1	(	(	PUNCT
ejpam-4275	326	2	v	v	NOUN
ejpam-4275	326	3	):	):	PUNCT
ejpam-4275	326	4	it	it	PRON
ejpam-4275	326	5	comes	come	VERB
ejpam-4275	326	6	from	from	ADP
ejpam-4275	326	7	(	(	PUNCT
ejpam-4275	326	8	iii	iii	NOUN
ejpam-4275	326	9	)	)	PUNCT
ejpam-4275	326	10	.	.	PUNCT
ejpam-4275	327	1	theorem	theorem	NOUN
ejpam-4275	327	2	2	2	NUM
ejpam-4275	327	3	.	.	X
ejpam-4275	328	1	let	let	VERB
ejpam-4275	328	2	(	(	PUNCT
ejpam-4275	328	3	ω	ω	PROPN
ejpam-4275	328	4	,	,	PUNCT
ejpam-4275	328	5	σ	σ	PROPN
ejpam-4275	328	6	)	)	PUNCT
ejpam-4275	328	7	and	and	CCONJ
ejpam-4275	328	8	(	(	PUNCT
ejpam-4275	328	9	ψ	ψ	X
ejpam-4275	328	10	,	,	PUNCT
ejpam-4275	328	11	σ	σ	PROPN
ejpam-4275	328	12	)	)	PUNCT
ejpam-4275	328	13	be	be	VERB
ejpam-4275	328	14	subsets	subset	NOUN
ejpam-4275	328	15	of	of	ADP
ejpam-4275	328	16	(	(	PUNCT
ejpam-4275	328	17	x	x	NOUN
ejpam-4275	328	18	,	,	PUNCT
ejpam-4275	328	19	ξ	ξ	PROPN
ejpam-4275	328	20	,	,	PUNCT
ejpam-4275	328	21	σ	σ	NOUN
ejpam-4275	328	22	)	)	PUNCT
ejpam-4275	328	23	.	.	PUNCT
ejpam-4275	329	1	then	then	ADV
ejpam-4275	329	2	we	we	PRON
ejpam-4275	329	3	have	have	VERB
ejpam-4275	329	4	the	the	DET
ejpam-4275	329	5	following	follow	VERB
ejpam-4275	329	6	properties	property	NOUN
ejpam-4275	329	7	.	.	PUNCT
ejpam-4275	330	1	(	(	PUNCT
ejpam-4275	330	2	i	i	NOUN
ejpam-4275	330	3	)	)	PUNCT
ejpam-4275	330	4	pcl(φ	pcl(φ	PROPN
ejpam-4275	330	5	)	)	PUNCT
ejpam-4275	330	6	=	=	SYM
ejpam-4275	331	1	φ	φ	PROPN
ejpam-4275	331	2	.	.	PUNCT
ejpam-4275	331	3	(	(	PUNCT
ejpam-4275	331	4	ii	ii	NOUN
ejpam-4275	331	5	)	)	PUNCT
ejpam-4275	331	6	(	(	PUNCT
ejpam-4275	331	7	ω	ω	NOUN
ejpam-4275	331	8	,	,	PUNCT
ejpam-4275	331	9	σ)⊆̃pcl(ω	σ)⊆̃pcl(ω	NOUN
ejpam-4275	331	10	,	,	PUNCT
ejpam-4275	331	11	σ	σ	NOUN
ejpam-4275	331	12	)	)	PUNCT
ejpam-4275	331	13	.	.	PUNCT
ejpam-4275	332	1	(	(	PUNCT
ejpam-4275	332	2	iii	iii	X
ejpam-4275	332	3	)	)	PUNCT
ejpam-4275	332	4	if	if	SCONJ
ejpam-4275	332	5	(	(	PUNCT
ejpam-4275	332	6	ψ	ψ	X
ejpam-4275	332	7	,	,	PUNCT
ejpam-4275	332	8	σ)⊆̃(ω	σ)⊆̃(ω	PROPN
ejpam-4275	332	9	,	,	PUNCT
ejpam-4275	332	10	σ	σ	PROPN
ejpam-4275	332	11	)	)	PUNCT
ejpam-4275	332	12	,	,	PUNCT
ejpam-4275	332	13	then	then	ADV
ejpam-4275	332	14	pcl(ψ	pcl(ψ	PROPN
ejpam-4275	332	15	,	,	PUNCT
ejpam-4275	332	16	σ)⊆̃pcl(ω	σ)⊆̃pcl(ω	NOUN
ejpam-4275	332	17	,	,	PUNCT
ejpam-4275	332	18	σ	σ	NOUN
ejpam-4275	332	19	)	)	PUNCT
ejpam-4275	332	20	.	.	PUNCT
ejpam-4275	333	1	(	(	PUNCT
ejpam-4275	333	2	iv	iv	X
ejpam-4275	333	3	)	)	PUNCT
ejpam-4275	333	4	pcl(pcl(ω	pcl(pcl(ω	PROPN
ejpam-4275	333	5	,	,	PUNCT
ejpam-4275	333	6	σ))⊆̃pcl(ω	σ))⊆̃pcl(ω	NOUN
ejpam-4275	333	7	,	,	PUNCT
ejpam-4275	333	8	σ	σ	PROPN
ejpam-4275	333	9	)	)	PUNCT
ejpam-4275	333	10	.	.	PUNCT
ejpam-4275	334	1	(	(	PUNCT
ejpam-4275	334	2	v	v	X
ejpam-4275	334	3	)	)	PUNCT
ejpam-4275	334	4	pcl((ψ	pcl((ψ	PROPN
ejpam-4275	334	5	,	,	PUNCT
ejpam-4275	334	6	σ	σ	PROPN
ejpam-4275	334	7	)	)	PUNCT
ejpam-4275	334	8	⋃̃	⋃̃	PROPN
ejpam-4275	334	9	(	(	PUNCT
ejpam-4275	334	10	ω	ω	PROPN
ejpam-4275	334	11	,	,	PUNCT
ejpam-4275	334	12	σ	σ	PROPN
ejpam-4275	334	13	)	)	PUNCT
ejpam-4275	334	14	)	)	PUNCT
ejpam-4275	335	1	=	=	SYM
ejpam-4275	335	2	pcl(ψ	pcl(ψ	PROPN
ejpam-4275	335	3	,	,	PUNCT
ejpam-4275	335	4	σ	σ	PROPN
ejpam-4275	335	5	)	)	PUNCT
ejpam-4275	335	6	⋃̃	⋃̃	PROPN
ejpam-4275	335	7	pcl(ω	pcl(ω	PROPN
ejpam-4275	335	8	,	,	PUNCT
ejpam-4275	335	9	σ	σ	PROPN
ejpam-4275	335	10	)	)	PUNCT
ejpam-4275	335	11	.	.	PUNCT
ejpam-4275	336	1	proof	proof	NOUN
ejpam-4275	336	2	.	.	PUNCT
ejpam-4275	337	1	it	it	PRON
ejpam-4275	337	2	can	can	AUX
ejpam-4275	337	3	be	be	AUX
ejpam-4275	337	4	proved	prove	VERB
ejpam-4275	337	5	following	follow	VERB
ejpam-4275	337	6	similar	similar	ADJ
ejpam-4275	337	7	arguments	argument	NOUN
ejpam-4275	337	8	given	give	VERB
ejpam-4275	337	9	in	in	ADP
ejpam-4275	337	10	the	the	DET
ejpam-4275	337	11	proof	proof	NOUN
ejpam-4275	337	12	of	of	ADP
ejpam-4275	337	13	theorem	theorem	NOUN
ejpam-4275	337	14	1	1	NUM
ejpam-4275	337	15	.	.	PUNCT
ejpam-4275	338	1	the	the	DET
ejpam-4275	338	2	next	next	ADJ
ejpam-4275	338	3	example	example	NOUN
ejpam-4275	338	4	shows	show	VERB
ejpam-4275	338	5	that	that	SCONJ
ejpam-4275	338	6	the	the	DET
ejpam-4275	338	7	inclusion	inclusion	NOUN
ejpam-4275	338	8	relations	relation	NOUN
ejpam-4275	338	9	given	give	VERB
ejpam-4275	338	10	in	in	ADP
ejpam-4275	338	11	the	the	DET
ejpam-4275	338	12	above	above	ADJ
ejpam-4275	338	13	two	two	NUM
ejpam-4275	338	14	theorems	theorem	NOUN
ejpam-4275	338	15	are	be	AUX
ejpam-4275	338	16	proper	proper	ADJ
ejpam-4275	338	17	.	.	PUNCT
ejpam-4275	339	1	example	example	NOUN
ejpam-4275	339	2	2	2	NUM
ejpam-4275	339	3	.	.	PUNCT
ejpam-4275	340	1	let	let	VERB
ejpam-4275	340	2	x	x	PUNCT
ejpam-4275	340	3	=	=	PRON
ejpam-4275	340	4	{	{	PUNCT
ejpam-4275	340	5	x1	x1	PROPN
ejpam-4275	340	6	,	,	PUNCT
ejpam-4275	340	7	x2	x2	PROPN
ejpam-4275	340	8	}	}	PUNCT
ejpam-4275	340	9	and	and	CCONJ
ejpam-4275	340	10	σ	σ	NOUN
ejpam-4275	340	11	=	=	SYM
ejpam-4275	340	12	{	{	PUNCT
ejpam-4275	340	13	η1	η1	NOUN
ejpam-4275	340	14	,	,	PUNCT
ejpam-4275	340	15	η2	η2	PROPN
ejpam-4275	340	16	}	}	PUNCT
ejpam-4275	340	17	.	.	PUNCT
ejpam-4275	341	1	then	then	ADV
ejpam-4275	341	2	ξ	ξ	X
ejpam-4275	341	3	=	=	SYM
ejpam-4275	341	4	{	{	PUNCT
ejpam-4275	341	5	φ	φ	PROPN
ejpam-4275	341	6	,	,	PUNCT
ejpam-4275	341	7	x̃	x̃	PROPN
ejpam-4275	341	8	,	,	PUNCT
ejpam-4275	341	9	(	(	PUNCT
ejpam-4275	341	10	ωj	ωj	INTJ
ejpam-4275	341	11	,	,	PUNCT
ejpam-4275	341	12	σ	σ	PROPN
ejpam-4275	341	13	)	)	PUNCT
ejpam-4275	341	14	:	:	PUNCT
ejpam-4275	342	1	j	j	X
ejpam-4275	342	2	=	=	SYM
ejpam-4275	342	3	1	1	NUM
ejpam-4275	342	4	,	,	PUNCT
ejpam-4275	342	5	2	2	NUM
ejpam-4275	342	6	,	,	PUNCT
ejpam-4275	342	7	3	3	NUM
ejpam-4275	342	8	}	}	PUNCT
ejpam-4275	342	9	is	be	AUX
ejpam-4275	342	10	an	an	DET
ejpam-4275	342	11	infra	infra	NOUN
ejpam-4275	342	12	soft	soft	ADJ
ejpam-4275	342	13	topology	topology	NOUN
ejpam-4275	342	14	on	on	ADP
ejpam-4275	342	15	x	x	PUNCT
ejpam-4275	342	16	over	over	ADP
ejpam-4275	342	17	x	x	PUNCT
ejpam-4275	342	18	with	with	ADP
ejpam-4275	342	19	σ	σ	NOUN
ejpam-4275	342	20	as	as	ADP
ejpam-4275	342	21	a	a	DET
ejpam-4275	342	22	set	set	NOUN
ejpam-4275	342	23	of	of	ADP
ejpam-4275	342	24	parameters	parameter	NOUN
ejpam-4275	342	25	,	,	PUNCT
ejpam-4275	342	26	where	where	SCONJ
ejpam-4275	342	27	(	(	PUNCT
ejpam-4275	342	28	ω1,σ	ω1,σ	NOUN
ejpam-4275	342	29	)	)	PUNCT
ejpam-4275	342	30	=	=	SYM
ejpam-4275	342	31	{	{	PUNCT
ejpam-4275	342	32	(	(	PUNCT
ejpam-4275	342	33	η1	η1	NOUN
ejpam-4275	342	34	,	,	PUNCT
ejpam-4275	342	35	{	{	PUNCT
ejpam-4275	342	36	x1	x1	NOUN
ejpam-4275	342	37	}	}	PUNCT
ejpam-4275	342	38	)	)	PUNCT
ejpam-4275	342	39	,	,	PUNCT
ejpam-4275	342	40	(	(	PUNCT
ejpam-4275	342	41	η2	η2	X
ejpam-4275	342	42	,	,	PUNCT
ejpam-4275	342	43	∅	∅	NOUN
ejpam-4275	342	44	)	)	PUNCT
ejpam-4275	342	45	}	}	PUNCT
ejpam-4275	342	46	;	;	PUNCT
ejpam-4275	342	47	(	(	PUNCT
ejpam-4275	342	48	ω2,σ	ω2,σ	PROPN
ejpam-4275	342	49	)	)	PUNCT
ejpam-4275	342	50	=	=	PRON
ejpam-4275	342	51	{	{	PUNCT
ejpam-4275	342	52	(	(	PUNCT
ejpam-4275	342	53	η1	η1	NOUN
ejpam-4275	342	54	,	,	PUNCT
ejpam-4275	342	55	∅	∅	NOUN
ejpam-4275	342	56	)	)	PUNCT
ejpam-4275	342	57	,	,	PUNCT
ejpam-4275	342	58	(	(	PUNCT
ejpam-4275	342	59	η2	η2	X
ejpam-4275	342	60	,	,	PUNCT
ejpam-4275	342	61	{	{	PUNCT
ejpam-4275	342	62	x1	x1	ADJ
ejpam-4275	342	63	}	}	PUNCT
ejpam-4275	342	64	)	)	PUNCT
ejpam-4275	342	65	}	}	PUNCT
ejpam-4275	342	66	and	and	CCONJ
ejpam-4275	342	67	(	(	PUNCT
ejpam-4275	342	68	ω3,σ	ω3,σ	PROPN
ejpam-4275	342	69	)	)	PUNCT
ejpam-4275	342	70	=	=	SYM
ejpam-4275	342	71	{	{	PUNCT
ejpam-4275	342	72	(	(	PUNCT
ejpam-4275	342	73	η1	η1	NOUN
ejpam-4275	342	74	,	,	PUNCT
ejpam-4275	342	75	x	x	NOUN
ejpam-4275	342	76	)	)	PUNCT
ejpam-4275	342	77	,	,	PUNCT
ejpam-4275	342	78	(	(	PUNCT
ejpam-4275	342	79	η2	η2	X
ejpam-4275	342	80	,	,	PUNCT
ejpam-4275	342	81	{	{	PUNCT
ejpam-4275	342	82	x2	x2	ADJ
ejpam-4275	342	83	}	}	PUNCT
ejpam-4275	342	84	)	)	PUNCT
ejpam-4275	342	85	}	}	PUNCT
ejpam-4275	342	86	.	.	PUNCT
ejpam-4275	343	1	let	let	VERB
ejpam-4275	343	2	(	(	PUNCT
ejpam-4275	343	3	ψ1,σ	ψ1,σ	PROPN
ejpam-4275	343	4	)	)	PUNCT
ejpam-4275	343	5	=	=	PRON
ejpam-4275	343	6	{	{	PUNCT
ejpam-4275	343	7	(	(	PUNCT
ejpam-4275	343	8	η1	η1	NOUN
ejpam-4275	343	9	,	,	PUNCT
ejpam-4275	343	10	{	{	PUNCT
ejpam-4275	343	11	x2	x2	ADJ
ejpam-4275	343	12	}	}	PUNCT
ejpam-4275	343	13	)	)	PUNCT
ejpam-4275	343	14	,	,	PUNCT
ejpam-4275	343	15	(	(	PUNCT
ejpam-4275	343	16	η2	η2	X
ejpam-4275	343	17	,	,	PUNCT
ejpam-4275	343	18	{	{	PUNCT
ejpam-4275	343	19	x1	x1	NOUN
ejpam-4275	343	20	}	}	PUNCT
ejpam-4275	343	21	)	)	PUNCT
ejpam-4275	343	22	}	}	PUNCT
ejpam-4275	343	23	.	.	PUNCT
ejpam-4275	344	1	then	then	ADV
ejpam-4275	344	2	pint(ψ1,σ	pint(ψ1,σ	NUM
ejpam-4275	344	3	)	)	PUNCT
ejpam-4275	345	1	=	=	PRON
ejpam-4275	345	2	{	{	PUNCT
ejpam-4275	345	3	(	(	PUNCT
ejpam-4275	345	4	η1	η1	NOUN
ejpam-4275	345	5	,	,	PUNCT
ejpam-4275	345	6	∅	∅	NOUN
ejpam-4275	345	7	)	)	PUNCT
ejpam-4275	345	8	,	,	PUNCT
ejpam-4275	345	9	(	(	PUNCT
ejpam-4275	345	10	η2	η2	X
ejpam-4275	345	11	,	,	PUNCT
ejpam-4275	345	12	{	{	PUNCT
ejpam-4275	345	13	x1})}⊂̃(ψ1,σ	x1})}⊂̃(ψ1,σ	PROPN
ejpam-4275	345	14	)	)	PUNCT
ejpam-4275	345	15	and	and	CCONJ
ejpam-4275	345	16	pcl(ψ1,σ	pcl(ψ1,σ	PROPN
ejpam-4275	345	17	)	)	PUNCT
ejpam-4275	346	1	=	=	PRON
ejpam-4275	346	2	{	{	PUNCT
ejpam-4275	346	3	(	(	PUNCT
ejpam-4275	346	4	η1	η1	NOUN
ejpam-4275	346	5	,	,	PUNCT
ejpam-4275	346	6	{	{	PUNCT
ejpam-4275	346	7	x2	x2	ADJ
ejpam-4275	346	8	}	}	PUNCT
ejpam-4275	346	9	)	)	PUNCT
ejpam-4275	346	10	,	,	PUNCT
ejpam-4275	346	11	(	(	PUNCT
ejpam-4275	346	12	η2	η2	X
ejpam-4275	346	13	,	,	PUNCT
ejpam-4275	346	14	x)}⊃̃(ψ1,σ	x)}⊃̃(ψ1,σ	PROPN
ejpam-4275	346	15	)	)	PUNCT
ejpam-4275	346	16	.	.	PUNCT
ejpam-4275	347	1	also	also	ADV
ejpam-4275	347	2	,	,	PUNCT
ejpam-4275	347	3	consider	consider	VERB
ejpam-4275	347	4	(	(	PUNCT
ejpam-4275	347	5	ψ2,σ	ψ2,σ	NOUN
ejpam-4275	347	6	)	)	PUNCT
ejpam-4275	347	7	=	=	PRON
ejpam-4275	347	8	{	{	PUNCT
ejpam-4275	347	9	(	(	PUNCT
ejpam-4275	347	10	η1	η1	NOUN
ejpam-4275	347	11	,	,	PUNCT
ejpam-4275	347	12	{	{	PUNCT
ejpam-4275	347	13	x2	x2	ADJ
ejpam-4275	347	14	}	}	PUNCT
ejpam-4275	347	15	)	)	PUNCT
ejpam-4275	347	16	,	,	PUNCT
ejpam-4275	347	17	(	(	PUNCT
ejpam-4275	347	18	η2	η2	X
ejpam-4275	347	19	,	,	PUNCT
ejpam-4275	347	20	∅	∅	NOUN
ejpam-4275	347	21	)	)	PUNCT
ejpam-4275	347	22	}	}	PUNCT
ejpam-4275	347	23	.	.	PUNCT
ejpam-4275	348	1	then	then	ADV
ejpam-4275	348	2	pcl((ψ1,σ	pcl((ψ1,σ	PROPN
ejpam-4275	348	3	)	)	PUNCT
ejpam-4275	348	4	⋃̃	⋃̃	PROPN
ejpam-4275	348	5	(	(	PUNCT
ejpam-4275	348	6	ψ2,σ	ψ2,σ	NOUN
ejpam-4275	348	7	)	)	PUNCT
ejpam-4275	348	8	)	)	PUNCT
ejpam-4275	349	1	=	=	PRON
ejpam-4275	349	2	{	{	PUNCT
ejpam-4275	349	3	(	(	PUNCT
ejpam-4275	349	4	η1	η1	NOUN
ejpam-4275	349	5	,	,	PUNCT
ejpam-4275	349	6	{	{	PUNCT
ejpam-4275	349	7	x2	x2	ADJ
ejpam-4275	349	8	}	}	PUNCT
ejpam-4275	349	9	)	)	PUNCT
ejpam-4275	349	10	,	,	PUNCT
ejpam-4275	349	11	(	(	PUNCT
ejpam-4275	349	12	η2	η2	X
ejpam-4275	349	13	,	,	PUNCT
ejpam-4275	349	14	x)}⊇̃pcl(ψ1,σ	x)}⊇̃pcl(ψ1,σ	PROPN
ejpam-4275	349	15	)	)	PUNCT
ejpam-4275	349	16	⋂̃	⋂̃	ADJ
ejpam-4275	350	1	pcl(ψ2,σ	pcl(ψ2,σ	ADJ
ejpam-4275	350	2	)	)	PUNCT
ejpam-4275	350	3	=	=	PRON
ejpam-4275	350	4	{	{	PUNCT
ejpam-4275	350	5	(	(	PUNCT
ejpam-4275	350	6	η1	η1	NOUN
ejpam-4275	350	7	,	,	PUNCT
ejpam-4275	350	8	{	{	PUNCT
ejpam-4275	350	9	x2	x2	ADJ
ejpam-4275	350	10	}	}	PUNCT
ejpam-4275	350	11	)	)	PUNCT
ejpam-4275	350	12	,	,	PUNCT
ejpam-4275	350	13	(	(	PUNCT
ejpam-4275	350	14	η2	η2	X
ejpam-4275	350	15	,	,	PUNCT
ejpam-4275	350	16	{	{	PUNCT
ejpam-4275	350	17	x2	x2	ADJ
ejpam-4275	350	18	}	}	PUNCT
ejpam-4275	350	19	)	)	PUNCT
ejpam-4275	350	20	}	}	PUNCT
ejpam-4275	350	21	.	.	PUNCT
ejpam-4275	351	1	definition	definition	NOUN
ejpam-4275	351	2	19	19	NUM
ejpam-4275	351	3	.	.	PUNCT
ejpam-4275	352	1	a	a	DET
ejpam-4275	352	2	soft	soft	ADJ
ejpam-4275	352	3	point	point	NOUN
ejpam-4275	352	4	δxη	δxη	NOUN
ejpam-4275	352	5	is	be	AUX
ejpam-4275	352	6	said	say	VERB
ejpam-4275	352	7	to	to	PART
ejpam-4275	352	8	be	be	AUX
ejpam-4275	352	9	an	an	DET
ejpam-4275	352	10	infra	infra	NOUN
ejpam-4275	352	11	soft	soft	ADJ
ejpam-4275	352	12	pre	pre	ADJ
ejpam-4275	352	13	-	-	ADJ
ejpam-4275	352	14	limit	limit	ADJ
ejpam-4275	352	15	point	point	NOUN
ejpam-4275	352	16	of	of	ADP
ejpam-4275	352	17	a	a	DET
ejpam-4275	352	18	subset	subset	NOUN
ejpam-4275	352	19	(	(	PUNCT
ejpam-4275	352	20	ω	ω	PROPN
ejpam-4275	352	21	,	,	PUNCT
ejpam-4275	352	22	σ	σ	PROPN
ejpam-4275	352	23	)	)	PUNCT
ejpam-4275	352	24	of	of	ADP
ejpam-4275	352	25	(	(	PUNCT
ejpam-4275	352	26	x	x	NOUN
ejpam-4275	352	27	,	,	PUNCT
ejpam-4275	352	28	ξ	ξ	PROPN
ejpam-4275	352	29	,	,	PUNCT
ejpam-4275	352	30	σ	σ	NOUN
ejpam-4275	352	31	)	)	PUNCT
ejpam-4275	352	32	provided	provide	VERB
ejpam-4275	352	33	that	that	SCONJ
ejpam-4275	352	34	[	[	X
ejpam-4275	352	35	(	(	PUNCT
ejpam-4275	352	36	ψ	ψ	NOUN
ejpam-4275	352	37	,	,	PUNCT
ejpam-4275	352	38	σ)\δxη	σ)\δxη	PROPN
ejpam-4275	352	39	]	]	PUNCT
ejpam-4275	352	40	⋂̃	⋂̃	PROPN
ejpam-4275	352	41	(	(	PUNCT
ejpam-4275	352	42	ω	ω	PROPN
ejpam-4275	352	43	,	,	PUNCT
ejpam-4275	352	44	σ	σ	PROPN
ejpam-4275	352	45	)	)	PUNCT
ejpam-4275	352	46	̸=	̸=	PROPN
ejpam-4275	352	47	φ	φ	NUM
ejpam-4275	352	48	for	for	ADP
ejpam-4275	352	49	every	every	DET
ejpam-4275	352	50	infra	infra	NOUN
ejpam-4275	352	51	soft	soft	ADJ
ejpam-4275	352	52	pre	pre	ADJ
ejpam-4275	352	53	-	-	ADJ
ejpam-4275	352	54	open	open	ADJ
ejpam-4275	352	55	set	set	NOUN
ejpam-4275	352	56	(	(	PUNCT
ejpam-4275	352	57	ψ	ψ	X
ejpam-4275	352	58	,	,	PUNCT
ejpam-4275	352	59	σ	σ	NOUN
ejpam-4275	352	60	)	)	PUNCT
ejpam-4275	352	61	containing	contain	VERB
ejpam-4275	352	62	δxη	δxη	NOUN
ejpam-4275	352	63	.	.	PUNCT
ejpam-4275	353	1	the	the	DET
ejpam-4275	353	2	soft	soft	ADJ
ejpam-4275	353	3	set	set	NOUN
ejpam-4275	353	4	of	of	ADP
ejpam-4275	353	5	all	all	DET
ejpam-4275	353	6	infra	infra	NOUN
ejpam-4275	353	7	soft	soft	ADJ
ejpam-4275	353	8	pre	pre	ADJ
ejpam-4275	353	9	-	-	ADJ
ejpam-4275	353	10	limit	limit	ADJ
ejpam-4275	353	11	points	point	NOUN
ejpam-4275	353	12	of	of	ADP
ejpam-4275	353	13	(	(	PUNCT
ejpam-4275	353	14	ω	ω	PROPN
ejpam-4275	353	15	,	,	PUNCT
ejpam-4275	353	16	σ	σ	PROPN
ejpam-4275	353	17	)	)	PUNCT
ejpam-4275	353	18	is	be	AUX
ejpam-4275	353	19	said	say	VERB
ejpam-4275	353	20	to	to	PART
ejpam-4275	353	21	be	be	AUX
ejpam-4275	353	22	an	an	DET
ejpam-4275	353	23	infra	infra	NOUN
ejpam-4275	353	24	pre	pre	ADJ
ejpam-4275	353	25	-	-	ADJ
ejpam-4275	353	26	derived	derived	ADJ
ejpam-4275	353	27	soft	soft	ADJ
ejpam-4275	353	28	set	set	NOUN
ejpam-4275	353	29	.	.	PUNCT
ejpam-4275	354	1	it	it	PRON
ejpam-4275	354	2	is	be	AUX
ejpam-4275	354	3	denoted	denote	VERB
ejpam-4275	354	4	by	by	ADP
ejpam-4275	354	5	(	(	PUNCT
ejpam-4275	354	6	ω	ω	PROPN
ejpam-4275	354	7	,	,	PUNCT
ejpam-4275	354	8	σ)ps′.	σ)ps′.	PROPN
ejpam-4275	355	1	t.m	t.m	PROPN
ejpam-4275	355	2	.	.	PROPN
ejpam-4275	355	3	al	al	PROPN
ejpam-4275	355	4	-	-	PUNCT
ejpam-4275	355	5	shami	shami	PROPN
ejpam-4275	355	6	,	,	PUNCT
ejpam-4275	355	7	h.a	h.a	PROPN
ejpam-4275	355	8	.	.	PROPN
ejpam-4275	355	9	othman	othman	PROPN
ejpam-4275	355	10	/	/	SYM
ejpam-4275	355	11	eur	eur	PROPN
ejpam-4275	355	12	.	.	PUNCT
ejpam-4275	356	1	j.	j.	PROPN
ejpam-4275	356	2	pure	pure	PROPN
ejpam-4275	356	3	appl	appl	PROPN
ejpam-4275	356	4	.	.	PROPN
ejpam-4275	356	5	math	math	PROPN
ejpam-4275	356	6	,	,	PUNCT
ejpam-4275	356	7	15	15	NUM
ejpam-4275	356	8	(	(	PUNCT
ejpam-4275	356	9	1	1	NUM
ejpam-4275	356	10	)	)	PUNCT
ejpam-4275	356	11	(	(	PUNCT
ejpam-4275	356	12	2022	2022	NUM
ejpam-4275	356	13	)	)	PUNCT
ejpam-4275	356	14	,	,	PUNCT
ejpam-4275	356	15	261	261	NUM
ejpam-4275	356	16	-	-	SYM
ejpam-4275	356	17	280	280	NUM
ejpam-4275	356	18	271	271	NUM
ejpam-4275	356	19	proposition	proposition	NOUN
ejpam-4275	356	20	17	17	NUM
ejpam-4275	356	21	.	.	PUNCT
ejpam-4275	357	1	consider	consider	VERB
ejpam-4275	357	2	(	(	PUNCT
ejpam-4275	357	3	ψ	ψ	X
ejpam-4275	357	4	,	,	PUNCT
ejpam-4275	357	5	σ	σ	NOUN
ejpam-4275	357	6	)	)	PUNCT
ejpam-4275	357	7	and	and	CCONJ
ejpam-4275	357	8	(	(	PUNCT
ejpam-4275	357	9	ω	ω	PROPN
ejpam-4275	357	10	,	,	PUNCT
ejpam-4275	357	11	σ	σ	PROPN
ejpam-4275	357	12	)	)	PUNCT
ejpam-4275	357	13	as	as	ADP
ejpam-4275	357	14	subsets	subset	NOUN
ejpam-4275	357	15	of	of	ADP
ejpam-4275	357	16	(	(	PUNCT
ejpam-4275	357	17	x	x	NOUN
ejpam-4275	357	18	,	,	PUNCT
ejpam-4275	357	19	ξ	ξ	PROPN
ejpam-4275	357	20	,	,	PUNCT
ejpam-4275	357	21	σ	σ	NOUN
ejpam-4275	357	22	)	)	PUNCT
ejpam-4275	357	23	.	.	PUNCT
ejpam-4275	358	1	then	then	ADV
ejpam-4275	358	2	(	(	PUNCT
ejpam-4275	358	3	i	i	NOUN
ejpam-4275	358	4	)	)	PUNCT
ejpam-4275	358	5	φps′	φps′	PROPN
ejpam-4275	358	6	=	=	SYM
ejpam-4275	358	7	φ	φ	PROPN
ejpam-4275	358	8	and	and	CCONJ
ejpam-4275	358	9	x̃ps′⊆̃x̃.	x̃ps′⊆̃x̃.	PROPN
ejpam-4275	358	10	(	(	PUNCT
ejpam-4275	358	11	ii	ii	NOUN
ejpam-4275	358	12	)	)	PUNCT
ejpam-4275	358	13	if	if	SCONJ
ejpam-4275	358	14	(	(	PUNCT
ejpam-4275	358	15	ψ	ψ	X
ejpam-4275	358	16	,	,	PUNCT
ejpam-4275	358	17	σ)⊆̃(ω	σ)⊆̃(ω	PROPN
ejpam-4275	358	18	,	,	PUNCT
ejpam-4275	358	19	σ	σ	PROPN
ejpam-4275	358	20	)	)	PUNCT
ejpam-4275	358	21	,	,	PUNCT
ejpam-4275	358	22	then	then	ADV
ejpam-4275	358	23	(	(	PUNCT
ejpam-4275	358	24	ψ	ψ	X
ejpam-4275	358	25	,	,	PUNCT
ejpam-4275	358	26	σ)ps′⊆̃(ω	σ)ps′⊆̃(ω	NOUN
ejpam-4275	358	27	,	,	PUNCT
ejpam-4275	358	28	σ)ps′.	σ)ps′.	PROPN
ejpam-4275	358	29	(	(	PUNCT
ejpam-4275	358	30	iii	iii	NOUN
ejpam-4275	358	31	)	)	PUNCT
ejpam-4275	358	32	if	if	SCONJ
ejpam-4275	358	33	δxη	δxη	NOUN
ejpam-4275	358	34	∈	∈	PROPN
ejpam-4275	358	35	(	(	PUNCT
ejpam-4275	358	36	ω	ω	PROPN
ejpam-4275	358	37	,	,	PUNCT
ejpam-4275	358	38	σ)ps′	σ)ps′	NUM
ejpam-4275	358	39	,	,	PUNCT
ejpam-4275	358	40	then	then	ADV
ejpam-4275	358	41	δxη	δxη	NOUN
ejpam-4275	358	42	∈	∈	PROPN
ejpam-4275	358	43	(	(	PUNCT
ejpam-4275	358	44	(	(	PUNCT
ejpam-4275	358	45	ω	ω	PROPN
ejpam-4275	358	46	,	,	PUNCT
ejpam-4275	358	47	σ	σ	NOUN
ejpam-4275	358	48	)	)	PUNCT
ejpam-4275	358	49	\	\	PROPN
ejpam-4275	358	50	δxη	δxη	NOUN
ejpam-4275	358	51	)	)	PUNCT
ejpam-4275	358	52	ps′.	ps′.	PROPN
ejpam-4275	358	53	(	(	PUNCT
ejpam-4275	358	54	iv	iv	NUM
ejpam-4275	358	55	)	)	PUNCT
ejpam-4275	358	56	(	(	PUNCT
ejpam-4275	358	57	ψ	ψ	X
ejpam-4275	358	58	,	,	PUNCT
ejpam-4275	358	59	σ)ps′	σ)ps′	PROPN
ejpam-4275	358	60	⋃̃	⋃̃	PROPN
ejpam-4275	358	61	(	(	PUNCT
ejpam-4275	358	62	ω	ω	PROPN
ejpam-4275	358	63	,	,	PUNCT
ejpam-4275	358	64	σ)ps′⊆̃((ψ	σ)ps′⊆̃((ψ	PROPN
ejpam-4275	358	65	,	,	PUNCT
ejpam-4275	358	66	σ	σ	PROPN
ejpam-4275	358	67	)	)	PUNCT
ejpam-4275	358	68	⋃̃	⋃̃	PROPN
ejpam-4275	358	69	(	(	PUNCT
ejpam-4275	358	70	ω	ω	NOUN
ejpam-4275	358	71	,	,	PUNCT
ejpam-4275	358	72	σ))ps′.	σ))ps′.	PROPN
ejpam-4275	358	73	proof	proof	NOUN
ejpam-4275	358	74	.	.	PUNCT
ejpam-4275	359	1	straightforward	straightforward	ADJ
ejpam-4275	359	2	.	.	PUNCT
ejpam-4275	360	1	theorem	theorem	NOUN
ejpam-4275	360	2	3	3	X
ejpam-4275	360	3	.	.	PUNCT
ejpam-4275	361	1	let	let	AUX
ejpam-4275	361	2	(	(	PUNCT
ejpam-4275	361	3	ω	ω	PROPN
ejpam-4275	361	4	,	,	PUNCT
ejpam-4275	361	5	σ	σ	PROPN
ejpam-4275	361	6	)	)	PUNCT
ejpam-4275	361	7	be	be	VERB
ejpam-4275	361	8	a	a	DET
ejpam-4275	361	9	subset	subset	NOUN
ejpam-4275	361	10	of	of	ADP
ejpam-4275	361	11	(	(	PUNCT
ejpam-4275	361	12	x	x	NOUN
ejpam-4275	361	13	,	,	PUNCT
ejpam-4275	361	14	ξ	ξ	PROPN
ejpam-4275	361	15	,	,	PUNCT
ejpam-4275	361	16	σ	σ	NOUN
ejpam-4275	361	17	)	)	PUNCT
ejpam-4275	361	18	.	.	PUNCT
ejpam-4275	362	1	then	then	ADV
ejpam-4275	362	2	(	(	PUNCT
ejpam-4275	362	3	i	i	NOUN
ejpam-4275	362	4	)	)	PUNCT
ejpam-4275	362	5	if	if	SCONJ
ejpam-4275	362	6	(	(	PUNCT
ejpam-4275	362	7	ω	ω	PROPN
ejpam-4275	362	8	,	,	PUNCT
ejpam-4275	362	9	σ	σ	PROPN
ejpam-4275	362	10	)	)	PUNCT
ejpam-4275	362	11	is	be	AUX
ejpam-4275	362	12	an	an	DET
ejpam-4275	362	13	infra	infra	NOUN
ejpam-4275	362	14	soft	soft	ADJ
ejpam-4275	362	15	pre	pre	ADJ
ejpam-4275	362	16	-	-	ADJ
ejpam-4275	362	17	closed	closed	ADJ
ejpam-4275	362	18	set	set	NOUN
ejpam-4275	362	19	,	,	PUNCT
ejpam-4275	362	20	then	then	ADV
ejpam-4275	362	21	(	(	PUNCT
ejpam-4275	362	22	ω	ω	PROPN
ejpam-4275	362	23	,	,	PUNCT
ejpam-4275	362	24	σ)ps′	σ)ps′	NUM
ejpam-4275	362	25	⊆	⊆	NUM
ejpam-4275	362	26	(	(	PUNCT
ejpam-4275	362	27	ω	ω	PROPN
ejpam-4275	362	28	,	,	PUNCT
ejpam-4275	362	29	σ	σ	PROPN
ejpam-4275	362	30	)	)	PUNCT
ejpam-4275	362	31	.	.	PUNCT
ejpam-4275	363	1	(	(	PUNCT
ejpam-4275	363	2	ii	ii	NOUN
ejpam-4275	363	3	)	)	PUNCT
ejpam-4275	363	4	(	(	PUNCT
ejpam-4275	363	5	(	(	PUNCT
ejpam-4275	363	6	ω	ω	PROPN
ejpam-4275	363	7	,	,	PUNCT
ejpam-4275	363	8	σ	σ	PROPN
ejpam-4275	363	9	)	)	PUNCT
ejpam-4275	363	10	⋃̃	⋃̃	PROPN
ejpam-4275	363	11	(	(	PUNCT
ejpam-4275	363	12	ω	ω	NOUN
ejpam-4275	363	13	,	,	PUNCT
ejpam-4275	363	14	σ)ps′)ps′⊆̃(ω	σ)ps′)ps′⊆̃(ω	NUM
ejpam-4275	363	15	,	,	PUNCT
ejpam-4275	363	16	σ	σ	PROPN
ejpam-4275	363	17	)	)	PUNCT
ejpam-4275	363	18	⋃̃	⋃̃	PROPN
ejpam-4275	363	19	(	(	PUNCT
ejpam-4275	363	20	ω	ω	PROPN
ejpam-4275	363	21	,	,	PUNCT
ejpam-4275	363	22	σ)ps′.	σ)ps′.	PROPN
ejpam-4275	363	23	(	(	PUNCT
ejpam-4275	363	24	iii	iii	NOUN
ejpam-4275	363	25	)	)	PUNCT
ejpam-4275	363	26	pcl(ω	pcl(ω	PROPN
ejpam-4275	363	27	,	,	PUNCT
ejpam-4275	363	28	σ	σ	NOUN
ejpam-4275	363	29	)	)	PUNCT
ejpam-4275	363	30	=	=	SYM
ejpam-4275	363	31	(	(	PUNCT
ejpam-4275	363	32	ω	ω	PROPN
ejpam-4275	363	33	,	,	PUNCT
ejpam-4275	363	34	σ	σ	PROPN
ejpam-4275	363	35	)	)	PUNCT
ejpam-4275	363	36	⋃̃	⋃̃	PROPN
ejpam-4275	363	37	(	(	PUNCT
ejpam-4275	363	38	ω	ω	PROPN
ejpam-4275	363	39	,	,	PUNCT
ejpam-4275	363	40	σ)ps′.	σ)ps′.	X
ejpam-4275	363	41	proof	proof	NOUN
ejpam-4275	363	42	.	.	PUNCT
ejpam-4275	364	1	(	(	PUNCT
ejpam-4275	364	2	i	i	NOUN
ejpam-4275	364	3	)	)	PUNCT
ejpam-4275	364	4	consider	consider	VERB
ejpam-4275	364	5	(	(	PUNCT
ejpam-4275	364	6	ω	ω	PROPN
ejpam-4275	364	7	,	,	PUNCT
ejpam-4275	364	8	σ	σ	PROPN
ejpam-4275	364	9	)	)	PUNCT
ejpam-4275	364	10	as	as	ADP
ejpam-4275	364	11	an	an	DET
ejpam-4275	364	12	infra	infra	NOUN
ejpam-4275	364	13	soft	soft	ADJ
ejpam-4275	364	14	pre	pre	ADJ
ejpam-4275	364	15	-	-	ADJ
ejpam-4275	364	16	closed	closed	ADJ
ejpam-4275	364	17	set	set	NOUN
ejpam-4275	364	18	such	such	DET
ejpam-4275	364	19	that	that	DET
ejpam-4275	364	20	δxη	δxη	NOUN
ejpam-4275	364	21	̸∈	̸∈	PROPN
ejpam-4275	364	22	(	(	PUNCT
ejpam-4275	364	23	ω	ω	PROPN
ejpam-4275	364	24	,	,	PUNCT
ejpam-4275	364	25	σ	σ	PROPN
ejpam-4275	364	26	)	)	PUNCT
ejpam-4275	364	27	.	.	PUNCT
ejpam-4275	365	1	then	then	ADV
ejpam-4275	365	2	δxη	δxη	NOUN
ejpam-4275	365	3	∈	∈	PROPN
ejpam-4275	365	4	(	(	PUNCT
ejpam-4275	365	5	ωc	ωc	PROPN
ejpam-4275	365	6	,	,	PUNCT
ejpam-4275	365	7	σ	σ	PROPN
ejpam-4275	365	8	)	)	PUNCT
ejpam-4275	365	9	.	.	PUNCT
ejpam-4275	366	1	now	now	ADV
ejpam-4275	366	2	,	,	PUNCT
ejpam-4275	366	3	(	(	PUNCT
ejpam-4275	366	4	ωc	ωc	PROPN
ejpam-4275	366	5	,	,	PUNCT
ejpam-4275	366	6	σ	σ	PROPN
ejpam-4275	366	7	)	)	PUNCT
ejpam-4275	366	8	is	be	AUX
ejpam-4275	366	9	an	an	DET
ejpam-4275	366	10	infra	infra	NOUN
ejpam-4275	366	11	soft	soft	ADJ
ejpam-4275	366	12	pre	pre	ADJ
ejpam-4275	366	13	-	-	ADJ
ejpam-4275	366	14	open	open	ADJ
ejpam-4275	366	15	set	set	NOUN
ejpam-4275	366	16	such	such	ADJ
ejpam-4275	366	17	that	that	SCONJ
ejpam-4275	366	18	(	(	PUNCT
ejpam-4275	366	19	ωc	ωc	PROPN
ejpam-4275	366	20	,	,	PUNCT
ejpam-4275	366	21	σ	σ	NOUN
ejpam-4275	366	22	)	)	PUNCT
ejpam-4275	366	23	⋂̃	⋂̃	NOUN
ejpam-4275	366	24	(	(	PUNCT
ejpam-4275	366	25	ω	ω	PROPN
ejpam-4275	366	26	,	,	PUNCT
ejpam-4275	366	27	σ	σ	PROPN
ejpam-4275	366	28	)	)	PUNCT
ejpam-4275	366	29	=	=	PUNCT
ejpam-4275	366	30	φ	φ	PROPN
ejpam-4275	366	31	which	which	PRON
ejpam-4275	366	32	means	mean	VERB
ejpam-4275	366	33	that	that	SCONJ
ejpam-4275	366	34	δxη	δxη	NOUN
ejpam-4275	366	35	̸∈	̸∈	PROPN
ejpam-4275	366	36	(	(	PUNCT
ejpam-4275	366	37	ω	ω	PROPN
ejpam-4275	366	38	,	,	PUNCT
ejpam-4275	366	39	σ)ps′.	σ)ps′.	PUNCT
ejpam-4275	366	40	thus	thus	ADV
ejpam-4275	366	41	,	,	PUNCT
ejpam-4275	366	42	(	(	PUNCT
ejpam-4275	366	43	ω	ω	NOUN
ejpam-4275	366	44	,	,	PUNCT
ejpam-4275	366	45	σ)ps′⊆̃(ω	σ)ps′⊆̃(ω	NOUN
ejpam-4275	366	46	,	,	PUNCT
ejpam-4275	366	47	σ	σ	PROPN
ejpam-4275	366	48	)	)	PUNCT
ejpam-4275	366	49	.	.	PUNCT
ejpam-4275	367	1	(	(	PUNCT
ejpam-4275	367	2	ii	ii	NOUN
ejpam-4275	367	3	)	)	PUNCT
ejpam-4275	367	4	consider	consider	VERB
ejpam-4275	367	5	δxη	δxη	ADJ
ejpam-4275	367	6	̸∈	̸∈	PROPN
ejpam-4275	367	7	(	(	PUNCT
ejpam-4275	367	8	ω	ω	PROPN
ejpam-4275	367	9	,	,	PUNCT
ejpam-4275	367	10	σ	σ	PROPN
ejpam-4275	367	11	)	)	PUNCT
ejpam-4275	367	12	⋃̃	⋃̃	PROPN
ejpam-4275	367	13	(	(	PUNCT
ejpam-4275	367	14	ω	ω	PROPN
ejpam-4275	367	15	,	,	PUNCT
ejpam-4275	367	16	σ)ps′.	σ)ps′.	X
ejpam-4275	368	1	then	then	ADV
ejpam-4275	368	2	δxη	δxη	VERB
ejpam-4275	368	3	̸∈	̸∈	PROPN
ejpam-4275	368	4	(	(	PUNCT
ejpam-4275	368	5	ω	ω	PROPN
ejpam-4275	368	6	,	,	PUNCT
ejpam-4275	368	7	σ	σ	NOUN
ejpam-4275	368	8	)	)	PUNCT
ejpam-4275	368	9	and	and	CCONJ
ejpam-4275	368	10	δxη	δxη	NOUN
ejpam-4275	368	11	̸∈	̸∈	PROPN
ejpam-4275	368	12	(	(	PUNCT
ejpam-4275	368	13	ω	ω	PROPN
ejpam-4275	368	14	,	,	PUNCT
ejpam-4275	368	15	σ)ps′.	σ)ps′.	X
ejpam-4275	369	1	therefore	therefore	ADV
ejpam-4275	369	2	,	,	PUNCT
ejpam-4275	369	3	there	there	PRON
ejpam-4275	369	4	exists	exist	VERB
ejpam-4275	369	5	an	an	DET
ejpam-4275	369	6	infra	infra	NOUN
ejpam-4275	369	7	soft	soft	ADJ
ejpam-4275	369	8	pre	pre	ADJ
ejpam-4275	369	9	-	-	ADJ
ejpam-4275	369	10	open	open	ADJ
ejpam-4275	369	11	set	set	NOUN
ejpam-4275	369	12	(	(	PUNCT
ejpam-4275	369	13	ψ	ψ	X
ejpam-4275	369	14	,	,	PUNCT
ejpam-4275	369	15	σ	σ	NOUN
ejpam-4275	369	16	)	)	PUNCT
ejpam-4275	369	17	such	such	ADJ
ejpam-4275	369	18	that	that	SCONJ
ejpam-4275	369	19	(	(	PUNCT
ejpam-4275	369	20	ψ	ψ	X
ejpam-4275	369	21	,	,	PUNCT
ejpam-4275	369	22	σ	σ	NOUN
ejpam-4275	369	23	)	)	PUNCT
ejpam-4275	369	24	⋂̃	⋂̃	NOUN
ejpam-4275	369	25	(	(	PUNCT
ejpam-4275	369	26	ω	ω	PROPN
ejpam-4275	369	27	,	,	PUNCT
ejpam-4275	369	28	σ	σ	PROPN
ejpam-4275	369	29	)	)	PUNCT
ejpam-4275	369	30	=	=	SYM
ejpam-4275	369	31	φ	φ	PROPN
ejpam-4275	369	32	(	(	PUNCT
ejpam-4275	369	33	1	1	NUM
ejpam-4275	369	34	)	)	PUNCT
ejpam-4275	369	35	this	this	PRON
ejpam-4275	369	36	implies	imply	VERB
ejpam-4275	369	37	that	that	SCONJ
ejpam-4275	369	38	(	(	PUNCT
ejpam-4275	369	39	ψ	ψ	X
ejpam-4275	369	40	,	,	PUNCT
ejpam-4275	369	41	σ	σ	NOUN
ejpam-4275	369	42	)	)	PUNCT
ejpam-4275	369	43	⋂̃	⋂̃	NOUN
ejpam-4275	369	44	(	(	PUNCT
ejpam-4275	369	45	ω	ω	PROPN
ejpam-4275	369	46	,	,	PUNCT
ejpam-4275	369	47	σ)ps′	σ)ps′	PROPN
ejpam-4275	369	48	=	=	SYM
ejpam-4275	369	49	φ	φ	X
ejpam-4275	369	50	(	(	PUNCT
ejpam-4275	369	51	2	2	NUM
ejpam-4275	369	52	)	)	PUNCT
ejpam-4275	369	53	it	it	PRON
ejpam-4275	369	54	follows	follow	VERB
ejpam-4275	369	55	from	from	ADP
ejpam-4275	369	56	(	(	PUNCT
ejpam-4275	369	57	1	1	NUM
ejpam-4275	369	58	)	)	PUNCT
ejpam-4275	369	59	and	and	CCONJ
ejpam-4275	369	60	(	(	PUNCT
ejpam-4275	369	61	2	2	X
ejpam-4275	369	62	)	)	PUNCT
ejpam-4275	369	63	that	that	SCONJ
ejpam-4275	369	64	(	(	PUNCT
ejpam-4275	369	65	ψ	ψ	X
ejpam-4275	369	66	,	,	PUNCT
ejpam-4275	369	67	σ	σ	NOUN
ejpam-4275	369	68	)	)	PUNCT
ejpam-4275	369	69	⋂̃	⋂̃	NOUN
ejpam-4275	369	70	(	(	PUNCT
ejpam-4275	369	71	(	(	PUNCT
ejpam-4275	369	72	ω	ω	PROPN
ejpam-4275	369	73	,	,	PUNCT
ejpam-4275	369	74	σ	σ	PROPN
ejpam-4275	369	75	)	)	PUNCT
ejpam-4275	369	76	⋃̃	⋃̃	PROPN
ejpam-4275	369	77	(	(	PUNCT
ejpam-4275	369	78	ω	ω	PROPN
ejpam-4275	369	79	,	,	PUNCT
ejpam-4275	369	80	σ)ps′	σ)ps′	NUM
ejpam-4275	369	81	)	)	PUNCT
ejpam-4275	369	82	=	=	SYM
ejpam-4275	370	1	φ	φ	PROPN
ejpam-4275	370	2	.	.	PUNCT
ejpam-4275	371	1	thus	thus	ADV
ejpam-4275	371	2	,	,	PUNCT
ejpam-4275	371	3	δxη	δxη	PROPN
ejpam-4275	371	4	̸∈	̸∈	PROPN
ejpam-4275	371	5	(	(	PUNCT
ejpam-4275	371	6	(	(	PUNCT
ejpam-4275	371	7	ω	ω	PROPN
ejpam-4275	371	8	,	,	PUNCT
ejpam-4275	371	9	σ	σ	PROPN
ejpam-4275	371	10	)	)	PUNCT
ejpam-4275	371	11	⋃̃	⋃̃	PROPN
ejpam-4275	371	12	(	(	PUNCT
ejpam-4275	371	13	ω	ω	PROPN
ejpam-4275	371	14	,	,	PUNCT
ejpam-4275	371	15	σ)ps′)ps′.	σ)ps′)ps′.	VERB
ejpam-4275	371	16	hence	hence	ADV
ejpam-4275	371	17	,	,	PUNCT
ejpam-4275	371	18	(	(	PUNCT
ejpam-4275	371	19	(	(	PUNCT
ejpam-4275	371	20	ω	ω	PROPN
ejpam-4275	371	21	,	,	PUNCT
ejpam-4275	371	22	σ	σ	PROPN
ejpam-4275	371	23	)	)	PUNCT
ejpam-4275	371	24	⋃̃	⋃̃	PROPN
ejpam-4275	371	25	(	(	PUNCT
ejpam-4275	371	26	ω	ω	PROPN
ejpam-4275	371	27	,	,	PUNCT
ejpam-4275	371	28	σ)ps′)ps′⊆̃((ω	σ)ps′)ps′⊆̃((ω	PROPN
ejpam-4275	371	29	,	,	PUNCT
ejpam-4275	371	30	σ	σ	PROPN
ejpam-4275	371	31	)	)	PUNCT
ejpam-4275	371	32	⋃̃	⋃̃	PROPN
ejpam-4275	371	33	(	(	PUNCT
ejpam-4275	371	34	ω	ω	PROPN
ejpam-4275	371	35	,	,	PUNCT
ejpam-4275	371	36	σ)ps′	σ)ps′	NUM
ejpam-4275	371	37	)	)	PUNCT
ejpam-4275	371	38	,	,	PUNCT
ejpam-4275	371	39	as	as	SCONJ
ejpam-4275	371	40	required	require	VERB
ejpam-4275	371	41	.	.	PUNCT
ejpam-4275	372	1	(	(	PUNCT
ejpam-4275	372	2	iii	iii	X
ejpam-4275	372	3	)	)	PUNCT
ejpam-4275	372	4	it	it	PRON
ejpam-4275	372	5	is	be	AUX
ejpam-4275	372	6	clear	clear	ADJ
ejpam-4275	372	7	that	that	SCONJ
ejpam-4275	372	8	(	(	PUNCT
ejpam-4275	372	9	ω	ω	PROPN
ejpam-4275	372	10	,	,	PUNCT
ejpam-4275	372	11	σ	σ	PROPN
ejpam-4275	372	12	)	)	PUNCT
ejpam-4275	372	13	⋃̃	⋃̃	PROPN
ejpam-4275	372	14	(	(	PUNCT
ejpam-4275	372	15	ω	ω	NOUN
ejpam-4275	372	16	,	,	PUNCT
ejpam-4275	372	17	σ)ps′⊆̃pcl(ω	σ)ps′⊆̃pcl(ω	PRON
ejpam-4275	372	18	,	,	PUNCT
ejpam-4275	372	19	σ	σ	NOUN
ejpam-4275	372	20	)	)	PUNCT
ejpam-4275	372	21	.	.	PUNCT
ejpam-4275	373	1	conversely	conversely	ADV
ejpam-4275	373	2	,	,	PUNCT
ejpam-4275	373	3	let	let	VERB
ejpam-4275	373	4	δxη	δxη	NOUN
ejpam-4275	373	5	∈	∈	PROPN
ejpam-4275	373	6	pcl(ω	pcl(ω	PROPN
ejpam-4275	373	7	,	,	PUNCT
ejpam-4275	373	8	σ	σ	PROPN
ejpam-4275	373	9	)	)	PUNCT
ejpam-4275	373	10	.	.	PUNCT
ejpam-4275	374	1	then	then	ADV
ejpam-4275	374	2	for	for	ADP
ejpam-4275	374	3	every	every	DET
ejpam-4275	374	4	infra	infra	NOUN
ejpam-4275	374	5	soft	soft	ADJ
ejpam-4275	374	6	pre	pre	ADJ
ejpam-4275	374	7	-	-	ADJ
ejpam-4275	374	8	open	open	ADJ
ejpam-4275	374	9	set	set	NOUN
ejpam-4275	374	10	containing	contain	VERB
ejpam-4275	374	11	δxη	δxη	NOUN
ejpam-4275	374	12	we	we	PRON
ejpam-4275	374	13	have	have	VERB
ejpam-4275	374	14	(	(	PUNCT
ejpam-4275	374	15	ω	ω	PROPN
ejpam-4275	374	16	,	,	PUNCT
ejpam-4275	374	17	σ	σ	PROPN
ejpam-4275	374	18	)	)	PUNCT
ejpam-4275	374	19	⋂̃	⋂̃	NOUN
ejpam-4275	374	20	(	(	PUNCT
ejpam-4275	374	21	ψ	ψ	X
ejpam-4275	374	22	,	,	PUNCT
ejpam-4275	374	23	σ	σ	NOUN
ejpam-4275	374	24	)	)	PUNCT
ejpam-4275	374	25	̸=	̸=	PROPN
ejpam-4275	374	26	φ	φ	NUM
ejpam-4275	374	27	.	.	PUNCT
ejpam-4275	375	1	without	without	ADP
ejpam-4275	375	2	loss	loss	NOUN
ejpam-4275	375	3	of	of	ADP
ejpam-4275	375	4	generality	generality	NOUN
ejpam-4275	375	5	,	,	PUNCT
ejpam-4275	375	6	let	let	VERB
ejpam-4275	375	7	δxη	δxη	PROPN
ejpam-4275	375	8	̸∈	̸∈	PROPN
ejpam-4275	375	9	(	(	PUNCT
ejpam-4275	375	10	ω	ω	PROPN
ejpam-4275	375	11	,	,	PUNCT
ejpam-4275	375	12	σ	σ	PROPN
ejpam-4275	375	13	)	)	PUNCT
ejpam-4275	375	14	.	.	PUNCT
ejpam-4275	376	1	then	then	ADV
ejpam-4275	377	1	[	[	X
ejpam-4275	377	2	(	(	PUNCT
ejpam-4275	377	3	ω	ω	NOUN
ejpam-4275	377	4	,	,	PUNCT
ejpam-4275	377	5	σ)\δxη	σ)\δxη	PROPN
ejpam-4275	377	6	]	]	PUNCT
ejpam-4275	377	7	⋂̃	⋂̃	X
ejpam-4275	377	8	(	(	PUNCT
ejpam-4275	377	9	ψ	ψ	X
ejpam-4275	377	10	,	,	PUNCT
ejpam-4275	377	11	σ	σ	NOUN
ejpam-4275	377	12	)	)	PUNCT
ejpam-4275	377	13	̸=	̸=	PROPN
ejpam-4275	377	14	φ	φ	NUM
ejpam-4275	377	15	.	.	PUNCT
ejpam-4275	378	1	consequentially	consequentially	ADV
ejpam-4275	378	2	,	,	PUNCT
ejpam-4275	378	3	δxη	δxη	NOUN
ejpam-4275	378	4	∈	∈	PROPN
ejpam-4275	378	5	(	(	PUNCT
ejpam-4275	378	6	ω	ω	PROPN
ejpam-4275	378	7	,	,	PUNCT
ejpam-4275	378	8	σ)ps′.	σ)ps′.	X
ejpam-4275	378	9	hence	hence	ADV
ejpam-4275	378	10	,	,	PUNCT
ejpam-4275	378	11	the	the	DET
ejpam-4275	378	12	proof	proof	NOUN
ejpam-4275	378	13	is	be	AUX
ejpam-4275	378	14	complete	complete	ADJ
ejpam-4275	378	15	.	.	PUNCT
ejpam-4275	379	1	definition	definition	NOUN
ejpam-4275	379	2	20	20	NUM
ejpam-4275	379	3	.	.	PUNCT
ejpam-4275	380	1	the	the	DET
ejpam-4275	380	2	infra	infra	NOUN
ejpam-4275	380	3	soft	soft	ADJ
ejpam-4275	380	4	pre	pre	ADJ
ejpam-4275	380	5	-	-	ADJ
ejpam-4275	380	6	boundary	boundary	ADJ
ejpam-4275	380	7	points	point	NOUN
ejpam-4275	380	8	of	of	ADP
ejpam-4275	380	9	a	a	DET
ejpam-4275	380	10	subset	subset	NOUN
ejpam-4275	380	11	(	(	PUNCT
ejpam-4275	380	12	ω	ω	PROPN
ejpam-4275	380	13	,	,	PUNCT
ejpam-4275	380	14	σ	σ	PROPN
ejpam-4275	380	15	)	)	PUNCT
ejpam-4275	380	16	of	of	ADP
ejpam-4275	380	17	(	(	PUNCT
ejpam-4275	380	18	x	x	NOUN
ejpam-4275	380	19	,	,	PUNCT
ejpam-4275	380	20	ξ	ξ	PROPN
ejpam-4275	380	21	,	,	PUNCT
ejpam-4275	380	22	σ	σ	PROPN
ejpam-4275	380	23	)	)	PUNCT
ejpam-4275	380	24	,	,	PUNCT
ejpam-4275	380	25	denoted	denote	VERB
ejpam-4275	380	26	by	by	ADP
ejpam-4275	380	27	pb(ω	pb(ω	NOUN
ejpam-4275	380	28	,	,	PUNCT
ejpam-4275	380	29	σ	σ	PROPN
ejpam-4275	380	30	)	)	PUNCT
ejpam-4275	380	31	,	,	PUNCT
ejpam-4275	380	32	are	be	AUX
ejpam-4275	380	33	all	all	DET
ejpam-4275	380	34	the	the	DET
ejpam-4275	380	35	soft	soft	ADJ
ejpam-4275	380	36	points	point	NOUN
ejpam-4275	380	37	which	which	PRON
ejpam-4275	380	38	belong	belong	VERB
ejpam-4275	380	39	to	to	ADP
ejpam-4275	380	40	the	the	DET
ejpam-4275	380	41	complement	complement	NOUN
ejpam-4275	380	42	of	of	ADP
ejpam-4275	380	43	pint(ω	pint(ω	PROPN
ejpam-4275	380	44	,	,	PUNCT
ejpam-4275	380	45	σ	σ	PROPN
ejpam-4275	380	46	)	)	PUNCT
ejpam-4275	380	47	⋃̃	⋃̃	PROPN
ejpam-4275	380	48	pint(ωc	pint(ωc	PROPN
ejpam-4275	380	49	,	,	PUNCT
ejpam-4275	380	50	σ	σ	PROPN
ejpam-4275	380	51	)	)	PUNCT
ejpam-4275	380	52	.	.	PUNCT
ejpam-4275	381	1	t.m	t.m	PROPN
ejpam-4275	381	2	.	.	PUNCT
ejpam-4275	381	3	al	al	PROPN
ejpam-4275	381	4	-	-	PUNCT
ejpam-4275	381	5	shami	shami	PROPN
ejpam-4275	381	6	,	,	PUNCT
ejpam-4275	381	7	h.a	h.a	PROPN
ejpam-4275	381	8	.	.	PROPN
ejpam-4275	381	9	othman	othman	PROPN
ejpam-4275	381	10	/	/	SYM
ejpam-4275	381	11	eur	eur	PROPN
ejpam-4275	381	12	.	.	PUNCT
ejpam-4275	382	1	j.	j.	PROPN
ejpam-4275	382	2	pure	pure	PROPN
ejpam-4275	382	3	appl	appl	PROPN
ejpam-4275	382	4	.	.	PROPN
ejpam-4275	382	5	math	math	PROPN
ejpam-4275	382	6	,	,	PUNCT
ejpam-4275	382	7	15	15	NUM
ejpam-4275	382	8	(	(	PUNCT
ejpam-4275	382	9	1	1	NUM
ejpam-4275	382	10	)	)	PUNCT
ejpam-4275	382	11	(	(	PUNCT
ejpam-4275	382	12	2022	2022	NUM
ejpam-4275	382	13	)	)	PUNCT
ejpam-4275	382	14	,	,	PUNCT
ejpam-4275	382	15	261	261	NUM
ejpam-4275	382	16	-	-	SYM
ejpam-4275	382	17	280	280	NUM
ejpam-4275	382	18	272	272	NUM
ejpam-4275	382	19	proposition	proposition	NOUN
ejpam-4275	382	20	18	18	NUM
ejpam-4275	382	21	.	.	PUNCT
ejpam-4275	383	1	let	let	AUX
ejpam-4275	383	2	(	(	PUNCT
ejpam-4275	383	3	ω	ω	PROPN
ejpam-4275	383	4	,	,	PUNCT
ejpam-4275	383	5	σ	σ	PROPN
ejpam-4275	383	6	)	)	PUNCT
ejpam-4275	383	7	be	be	VERB
ejpam-4275	383	8	a	a	DET
ejpam-4275	383	9	subset	subset	NOUN
ejpam-4275	383	10	of	of	ADP
ejpam-4275	383	11	(	(	PUNCT
ejpam-4275	383	12	x	x	NOUN
ejpam-4275	383	13	,	,	PUNCT
ejpam-4275	383	14	ξ	ξ	PROPN
ejpam-4275	383	15	,	,	PUNCT
ejpam-4275	383	16	σ	σ	NOUN
ejpam-4275	383	17	)	)	PUNCT
ejpam-4275	383	18	.	.	PUNCT
ejpam-4275	384	1	then	then	ADV
ejpam-4275	384	2	:	:	PUNCT
ejpam-4275	384	3	(	(	PUNCT
ejpam-4275	384	4	i	i	NOUN
ejpam-4275	384	5	)	)	PUNCT
ejpam-4275	384	6	pb(ω	pb(ω	ADV
ejpam-4275	384	7	,	,	PUNCT
ejpam-4275	384	8	σ	σ	X
ejpam-4275	384	9	)	)	PUNCT
ejpam-4275	384	10	=	=	SYM
ejpam-4275	384	11	pcl(ω	pcl(ω	PROPN
ejpam-4275	384	12	,	,	PUNCT
ejpam-4275	384	13	σ	σ	NOUN
ejpam-4275	384	14	)	)	PUNCT
ejpam-4275	384	15	⋂̃	⋂̃	NOUN
ejpam-4275	384	16	pcl((ωc	pcl((ωc	PROPN
ejpam-4275	384	17	,	,	PUNCT
ejpam-4275	384	18	σ	σ	PROPN
ejpam-4275	384	19	)	)	PUNCT
ejpam-4275	384	20	)	)	PUNCT
ejpam-4275	384	21	.	.	PUNCT
ejpam-4275	385	1	(	(	PUNCT
ejpam-4275	385	2	ii	ii	NOUN
ejpam-4275	385	3	)	)	PUNCT
ejpam-4275	385	4	pb(ω	pb(ω	ADV
ejpam-4275	385	5	,	,	PUNCT
ejpam-4275	385	6	σ	σ	X
ejpam-4275	385	7	)	)	PUNCT
ejpam-4275	385	8	=	=	SYM
ejpam-4275	385	9	pcl(ω	pcl(ω	PROPN
ejpam-4275	385	10	,	,	PUNCT
ejpam-4275	385	11	σ	σ	NOUN
ejpam-4275	385	12	)	)	PUNCT
ejpam-4275	385	13	\	\	PROPN
ejpam-4275	385	14	pint(ω	pint(ω	PROPN
ejpam-4275	385	15	,	,	PUNCT
ejpam-4275	385	16	σ	σ	PROPN
ejpam-4275	385	17	)	)	PUNCT
ejpam-4275	385	18	.	.	PUNCT
ejpam-4275	386	1	proof	proof	NOUN
ejpam-4275	386	2	.	.	PUNCT
ejpam-4275	387	1	(	(	PUNCT
ejpam-4275	387	2	i	i	NOUN
ejpam-4275	387	3	)	)	PUNCT
ejpam-4275	387	4	pb(ω	pb(ω	ADV
ejpam-4275	387	5	,	,	PUNCT
ejpam-4275	387	6	σ	σ	X
ejpam-4275	387	7	)	)	PUNCT
ejpam-4275	387	8	=	=	PRON
ejpam-4275	387	9	{	{	PUNCT
ejpam-4275	387	10	δxη	δxη	NOUN
ejpam-4275	387	11	∈	∈	PROPN
ejpam-4275	387	12	x̃	x̃	PROPN
ejpam-4275	387	13	:	:	PUNCT
ejpam-4275	387	14	δxη	δxη	NOUN
ejpam-4275	387	15	̸∈	̸∈	PROPN
ejpam-4275	387	16	pint(ω	pint(ω	PROPN
ejpam-4275	387	17	,	,	PUNCT
ejpam-4275	387	18	σ	σ	PROPN
ejpam-4275	387	19	)	)	PUNCT
ejpam-4275	387	20	and	and	CCONJ
ejpam-4275	387	21	δxη	δxη	PROPN
ejpam-4275	387	22	̸∈	̸∈	PROPN
ejpam-4275	387	23	pint((ωc	pint((ωc	PROPN
ejpam-4275	387	24	,	,	PUNCT
ejpam-4275	387	25	σ	σ	PROPN
ejpam-4275	387	26	)	)	PUNCT
ejpam-4275	387	27	)	)	PUNCT
ejpam-4275	387	28	}	}	PUNCT
ejpam-4275	388	1	=	=	PRON
ejpam-4275	388	2	{	{	PUNCT
ejpam-4275	388	3	δxη	δxη	NOUN
ejpam-4275	388	4	∈	∈	PROPN
ejpam-4275	388	5	x̃	x̃	PROPN
ejpam-4275	388	6	:	:	PUNCT
ejpam-4275	388	7	δxη	δxη	PROPN
ejpam-4275	388	8	̸∈	̸∈	PROPN
ejpam-4275	388	9	(	(	PUNCT
ejpam-4275	388	10	pcl(ωc	pcl(ωc	PROPN
ejpam-4275	388	11	,	,	PUNCT
ejpam-4275	388	12	σ))c	σ))c	ADJ
ejpam-4275	388	13	and	and	CCONJ
ejpam-4275	388	14	δxη	δxη	NOUN
ejpam-4275	388	15	̸∈	̸∈	PROPN
ejpam-4275	388	16	(	(	PUNCT
ejpam-4275	388	17	pcl(ω	pcl(ω	PROPN
ejpam-4275	388	18	,	,	PUNCT
ejpam-4275	388	19	σ))c	σ))c	ADJ
ejpam-4275	388	20	}	}	PUNCT
ejpam-4275	388	21	=	=	SYM
ejpam-4275	388	22	{	{	PUNCT
ejpam-4275	388	23	δxη	δxη	NOUN
ejpam-4275	388	24	∈	∈	PROPN
ejpam-4275	388	25	x̃	x̃	PROPN
ejpam-4275	388	26	:	:	PUNCT
ejpam-4275	388	27	δxη	δxη	PROPN
ejpam-4275	388	28	∈	∈	PROPN
ejpam-4275	388	29	pcl(ωc	pcl(ωc	NOUN
ejpam-4275	388	30	,	,	PUNCT
ejpam-4275	388	31	σ	σ	NOUN
ejpam-4275	388	32	)	)	PUNCT
ejpam-4275	388	33	and	and	CCONJ
ejpam-4275	388	34	δxη	δxη	PROPN
ejpam-4275	388	35	∈	∈	PROPN
ejpam-4275	388	36	pcl(ω	pcl(ω	PROPN
ejpam-4275	388	37	,	,	PUNCT
ejpam-4275	388	38	σ	σ	PROPN
ejpam-4275	388	39	)	)	PUNCT
ejpam-4275	388	40	}	}	PUNCT
ejpam-4275	388	41	=	=	SYM
ejpam-4275	388	42	pcl(ω	pcl(ω	PROPN
ejpam-4275	388	43	,	,	PUNCT
ejpam-4275	388	44	σ	σ	NOUN
ejpam-4275	388	45	)	)	PUNCT
ejpam-4275	388	46	⋂̃	⋂̃	NOUN
ejpam-4275	388	47	pcl(ωc	pcl(ωc	NOUN
ejpam-4275	388	48	,	,	PUNCT
ejpam-4275	388	49	σ	σ	PROPN
ejpam-4275	388	50	)	)	PUNCT
ejpam-4275	388	51	(	(	PUNCT
ejpam-4275	388	52	ii	ii	NOUN
ejpam-4275	388	53	)	)	PUNCT
ejpam-4275	388	54	pb(ω	pb(ω	ADV
ejpam-4275	388	55	,	,	PUNCT
ejpam-4275	388	56	σ	σ	X
ejpam-4275	388	57	)	)	PUNCT
ejpam-4275	388	58	=	=	SYM
ejpam-4275	388	59	pcl(ω	pcl(ω	PROPN
ejpam-4275	388	60	,	,	PUNCT
ejpam-4275	388	61	σ	σ	NOUN
ejpam-4275	388	62	)	)	PUNCT
ejpam-4275	388	63	⋂̃	⋂̃	NOUN
ejpam-4275	388	64	pcl(ωc	pcl(ωc	NOUN
ejpam-4275	388	65	,	,	PUNCT
ejpam-4275	388	66	σ	σ	NOUN
ejpam-4275	388	67	)	)	PUNCT
ejpam-4275	388	68	=	=	SYM
ejpam-4275	388	69	pcl(ω	pcl(ω	PROPN
ejpam-4275	388	70	,	,	PUNCT
ejpam-4275	388	71	σ	σ	NOUN
ejpam-4275	388	72	)	)	PUNCT
ejpam-4275	388	73	⋂̃	⋂̃	NOUN
ejpam-4275	388	74	(	(	PUNCT
ejpam-4275	388	75	pint(ω	pint(ω	NOUN
ejpam-4275	388	76	,	,	PUNCT
ejpam-4275	388	77	σ))c	σ))c	ADJ
ejpam-4275	388	78	=	=	SYM
ejpam-4275	388	79	pcl(ω	pcl(ω	PROPN
ejpam-4275	388	80	,	,	PUNCT
ejpam-4275	388	81	σ	σ	NOUN
ejpam-4275	388	82	)	)	PUNCT
ejpam-4275	388	83	\	\	PROPN
ejpam-4275	388	84	pint(ω	pint(ω	PROPN
ejpam-4275	388	85	,	,	PUNCT
ejpam-4275	388	86	σ	σ	PROPN
ejpam-4275	388	87	)	)	PUNCT
ejpam-4275	388	88	corollary	corollary	NOUN
ejpam-4275	388	89	4	4	NUM
ejpam-4275	388	90	.	.	PUNCT
ejpam-4275	389	1	let	let	AUX
ejpam-4275	389	2	(	(	PUNCT
ejpam-4275	389	3	ω	ω	PROPN
ejpam-4275	389	4	,	,	PUNCT
ejpam-4275	389	5	σ	σ	PROPN
ejpam-4275	389	6	)	)	PUNCT
ejpam-4275	389	7	be	be	VERB
ejpam-4275	389	8	a	a	DET
ejpam-4275	389	9	subset	subset	NOUN
ejpam-4275	389	10	of	of	ADP
ejpam-4275	389	11	(	(	PUNCT
ejpam-4275	389	12	x	x	NOUN
ejpam-4275	389	13	,	,	PUNCT
ejpam-4275	389	14	ξ	ξ	PROPN
ejpam-4275	389	15	,	,	PUNCT
ejpam-4275	389	16	σ	σ	NOUN
ejpam-4275	389	17	)	)	PUNCT
ejpam-4275	389	18	.	.	PUNCT
ejpam-4275	390	1	then	then	ADV
ejpam-4275	390	2	(	(	PUNCT
ejpam-4275	390	3	i	i	NOUN
ejpam-4275	390	4	)	)	PUNCT
ejpam-4275	390	5	pb(ω	pb(ω	ADV
ejpam-4275	390	6	,	,	PUNCT
ejpam-4275	390	7	σ	σ	X
ejpam-4275	390	8	)	)	PUNCT
ejpam-4275	390	9	=	=	SYM
ejpam-4275	390	10	pb(ωc	pb(ωc	PROPN
ejpam-4275	390	11	,	,	PUNCT
ejpam-4275	390	12	σ	σ	PROPN
ejpam-4275	390	13	)	)	PUNCT
ejpam-4275	390	14	(	(	PUNCT
ejpam-4275	390	15	ii	ii	NOUN
ejpam-4275	390	16	)	)	PUNCT
ejpam-4275	390	17	pcl(ω	pcl(ω	PROPN
ejpam-4275	390	18	,	,	PUNCT
ejpam-4275	390	19	σ	σ	NOUN
ejpam-4275	390	20	)	)	PUNCT
ejpam-4275	390	21	=	=	SYM
ejpam-4275	390	22	pint(ω	pint(ω	PROPN
ejpam-4275	390	23	,	,	PUNCT
ejpam-4275	390	24	σ	σ	PROPN
ejpam-4275	390	25	)	)	PUNCT
ejpam-4275	390	26	⋃̃	⋃̃	PROPN
ejpam-4275	390	27	pb(ω	pb(ω	NUM
ejpam-4275	390	28	,	,	PUNCT
ejpam-4275	390	29	σ	σ	NUM
ejpam-4275	390	30	)	)	PUNCT
ejpam-4275	390	31	proposition	proposition	NOUN
ejpam-4275	390	32	19	19	NUM
ejpam-4275	390	33	.	.	PUNCT
ejpam-4275	391	1	let	let	AUX
ejpam-4275	391	2	(	(	PUNCT
ejpam-4275	391	3	ω	ω	PROPN
ejpam-4275	391	4	,	,	PUNCT
ejpam-4275	391	5	σ	σ	PROPN
ejpam-4275	391	6	)	)	PUNCT
ejpam-4275	391	7	be	be	VERB
ejpam-4275	391	8	a	a	DET
ejpam-4275	391	9	subset	subset	NOUN
ejpam-4275	391	10	of	of	ADP
ejpam-4275	391	11	(	(	PUNCT
ejpam-4275	391	12	x	x	NOUN
ejpam-4275	391	13	,	,	PUNCT
ejpam-4275	391	14	ξ	ξ	PROPN
ejpam-4275	391	15	,	,	PUNCT
ejpam-4275	391	16	σ	σ	NOUN
ejpam-4275	391	17	)	)	PUNCT
ejpam-4275	391	18	.	.	PUNCT
ejpam-4275	392	1	then	then	ADV
ejpam-4275	392	2	(	(	PUNCT
ejpam-4275	392	3	i	i	NOUN
ejpam-4275	392	4	)	)	PUNCT
ejpam-4275	392	5	(	(	PUNCT
ejpam-4275	392	6	ω	ω	PROPN
ejpam-4275	392	7	,	,	PUNCT
ejpam-4275	392	8	σ	σ	PROPN
ejpam-4275	392	9	)	)	PUNCT
ejpam-4275	392	10	is	be	AUX
ejpam-4275	392	11	infra	infra	NOUN
ejpam-4275	392	12	soft	soft	ADJ
ejpam-4275	392	13	pre	pre	ADJ
ejpam-4275	392	14	-	-	ADJ
ejpam-4275	392	15	open	open	ADJ
ejpam-4275	392	16	iff	iff	PROPN
ejpam-4275	392	17	pb(ω	pb(ω	SYM
ejpam-4275	392	18	,	,	PUNCT
ejpam-4275	392	19	σ	σ	NOUN
ejpam-4275	392	20	)	)	PUNCT
ejpam-4275	392	21	⋂̃	⋂̃	NOUN
ejpam-4275	392	22	(	(	PUNCT
ejpam-4275	392	23	ω	ω	PROPN
ejpam-4275	392	24	,	,	PUNCT
ejpam-4275	392	25	σ	σ	PROPN
ejpam-4275	392	26	)	)	PUNCT
ejpam-4275	392	27	=	=	SYM
ejpam-4275	393	1	φ	φ	PROPN
ejpam-4275	393	2	.	.	PUNCT
ejpam-4275	393	3	(	(	PUNCT
ejpam-4275	393	4	ii	ii	NOUN
ejpam-4275	393	5	)	)	PUNCT
ejpam-4275	393	6	(	(	PUNCT
ejpam-4275	393	7	ω	ω	PROPN
ejpam-4275	393	8	,	,	PUNCT
ejpam-4275	393	9	σ	σ	PROPN
ejpam-4275	393	10	)	)	PUNCT
ejpam-4275	393	11	is	be	AUX
ejpam-4275	393	12	infra	infra	NOUN
ejpam-4275	393	13	soft	soft	ADJ
ejpam-4275	393	14	pre	pre	ADJ
ejpam-4275	393	15	-	-	ADJ
ejpam-4275	393	16	closed	closed	ADJ
ejpam-4275	393	17	iff	iff	PROPN
ejpam-4275	393	18	pb(ω	pb(ω	SYM
ejpam-4275	393	19	,	,	PUNCT
ejpam-4275	393	20	σ)⊆̃(ω	σ)⊆̃(ω	PROPN
ejpam-4275	393	21	,	,	PUNCT
ejpam-4275	393	22	σ	σ	PROPN
ejpam-4275	393	23	)	)	PUNCT
ejpam-4275	393	24	.	.	PUNCT
ejpam-4275	394	1	proof	proof	NOUN
ejpam-4275	394	2	.	.	PUNCT
ejpam-4275	395	1	(	(	PUNCT
ejpam-4275	395	2	i	i	NOUN
ejpam-4275	395	3	)	)	PUNCT
ejpam-4275	395	4	pb(ω	pb(ω	ADV
ejpam-4275	395	5	,	,	PUNCT
ejpam-4275	395	6	σ	σ	PROPN
ejpam-4275	395	7	)	)	PUNCT
ejpam-4275	395	8	⋂	⋂	PROPN
ejpam-4275	395	9	(	(	PUNCT
ejpam-4275	395	10	ω	ω	PROPN
ejpam-4275	395	11	,	,	PUNCT
ejpam-4275	395	12	σ	σ	NOUN
ejpam-4275	395	13	)	)	PUNCT
ejpam-4275	395	14	=	=	PUNCT
ejpam-4275	396	1	pb(ω	pb(ω	X
ejpam-4275	396	2	,	,	PUNCT
ejpam-4275	396	3	σ	σ	PROPN
ejpam-4275	396	4	)	)	PUNCT
ejpam-4275	396	5	⋂	⋂	PROPN
ejpam-4275	396	6	pint(ω	pint(ω	PROPN
ejpam-4275	396	7	,	,	PUNCT
ejpam-4275	396	8	σ	σ	PROPN
ejpam-4275	396	9	)	)	PUNCT
ejpam-4275	396	10	=	=	SYM
ejpam-4275	396	11	φ	φ	PROPN
ejpam-4275	396	12	.	.	PUNCT
ejpam-4275	397	1	conversely	conversely	ADV
ejpam-4275	397	2	,	,	PUNCT
ejpam-4275	397	3	let	let	VERB
ejpam-4275	397	4	δxη	δxη	NOUN
ejpam-4275	397	5	∈	∈	PROPN
ejpam-4275	397	6	(	(	PUNCT
ejpam-4275	397	7	ω	ω	PROPN
ejpam-4275	397	8	,	,	PUNCT
ejpam-4275	397	9	σ	σ	PROPN
ejpam-4275	397	10	)	)	PUNCT
ejpam-4275	397	11	.	.	PUNCT
ejpam-4275	398	1	then	then	ADV
ejpam-4275	398	2	δxη	δxη	NOUN
ejpam-4275	398	3	∈	∈	PROPN
ejpam-4275	398	4	pint(ω	pint(ω	PROPN
ejpam-4275	398	5	,	,	PUNCT
ejpam-4275	398	6	σ	σ	NOUN
ejpam-4275	398	7	)	)	PUNCT
ejpam-4275	398	8	or	or	CCONJ
ejpam-4275	398	9	δxη	δxη	NOUN
ejpam-4275	398	10	∈	∈	PROPN
ejpam-4275	398	11	pb(ω	pb(ω	X
ejpam-4275	398	12	,	,	PUNCT
ejpam-4275	398	13	σ	σ	NOUN
ejpam-4275	398	14	)	)	PUNCT
ejpam-4275	398	15	.	.	PUNCT
ejpam-4275	399	1	since	since	SCONJ
ejpam-4275	399	2	pb(ω	pb(ω	ADV
ejpam-4275	399	3	,	,	PUNCT
ejpam-4275	399	4	σ	σ	PROPN
ejpam-4275	399	5	)	)	PUNCT
ejpam-4275	399	6	⋂	⋂	PROPN
ejpam-4275	399	7	(	(	PUNCT
ejpam-4275	399	8	ω	ω	PROPN
ejpam-4275	399	9	,	,	PUNCT
ejpam-4275	399	10	σ	σ	PROPN
ejpam-4275	399	11	)	)	PUNCT
ejpam-4275	399	12	=	=	SYM
ejpam-4275	399	13	φ	φ	PROPN
ejpam-4275	399	14	,	,	PUNCT
ejpam-4275	399	15	δxη	δxη	NOUN
ejpam-4275	399	16	∈	∈	PROPN
ejpam-4275	399	17	pint(ω	pint(ω	NOUN
ejpam-4275	399	18	,	,	PUNCT
ejpam-4275	399	19	σ	σ	PROPN
ejpam-4275	399	20	)	)	PUNCT
ejpam-4275	399	21	.	.	PUNCT
ejpam-4275	400	1	thus	thus	ADV
ejpam-4275	400	2	,	,	PUNCT
ejpam-4275	400	3	(	(	PUNCT
ejpam-4275	400	4	ω	ω	PROPN
ejpam-4275	400	5	,	,	PUNCT
ejpam-4275	400	6	σ	σ	PROPN
ejpam-4275	400	7	)	)	PUNCT
ejpam-4275	400	8	⊆	⊆	NUM
ejpam-4275	400	9	pint(ω	pint(ω	NOUN
ejpam-4275	400	10	,	,	PUNCT
ejpam-4275	400	11	σ	σ	PROPN
ejpam-4275	400	12	)	)	PUNCT
ejpam-4275	400	13	which	which	PRON
ejpam-4275	400	14	means	mean	VERB
ejpam-4275	400	15	that	that	SCONJ
ejpam-4275	400	16	(	(	PUNCT
ejpam-4275	400	17	ω	ω	PROPN
ejpam-4275	400	18	,	,	PUNCT
ejpam-4275	400	19	σ	σ	NOUN
ejpam-4275	400	20	)	)	PUNCT
ejpam-4275	400	21	=	=	SYM
ejpam-4275	400	22	pint(ω	pint(ω	PROPN
ejpam-4275	400	23	,	,	PUNCT
ejpam-4275	400	24	σ	σ	PROPN
ejpam-4275	400	25	)	)	PUNCT
ejpam-4275	400	26	.	.	PUNCT
ejpam-4275	401	1	hence	hence	ADV
ejpam-4275	401	2	,	,	PUNCT
ejpam-4275	401	3	(	(	PUNCT
ejpam-4275	401	4	ω	ω	PROPN
ejpam-4275	401	5	,	,	PUNCT
ejpam-4275	401	6	σ	σ	PROPN
ejpam-4275	401	7	)	)	PUNCT
ejpam-4275	401	8	is	be	AUX
ejpam-4275	401	9	infra	infra	NOUN
ejpam-4275	401	10	soft	soft	ADJ
ejpam-4275	401	11	pre	pre	ADJ
ejpam-4275	401	12	-	-	ADJ
ejpam-4275	401	13	open	open	ADJ
ejpam-4275	401	14	.	.	PUNCT
ejpam-4275	402	1	(	(	PUNCT
ejpam-4275	402	2	ii	ii	NOUN
ejpam-4275	402	3	)	)	PUNCT
ejpam-4275	402	4	(	(	PUNCT
ejpam-4275	402	5	ω	ω	PROPN
ejpam-4275	402	6	,	,	PUNCT
ejpam-4275	402	7	σ	σ	PROPN
ejpam-4275	402	8	)	)	PUNCT
ejpam-4275	402	9	is	be	AUX
ejpam-4275	402	10	infra	infra	NOUN
ejpam-4275	402	11	soft	soft	ADJ
ejpam-4275	402	12	pre	pre	ADJ
ejpam-4275	402	13	-	-	ADJ
ejpam-4275	402	14	closed	closed	ADJ
ejpam-4275	402	15	⇔	⇔	X
ejpam-4275	402	16	(	(	PUNCT
ejpam-4275	402	17	ωc	ωc	PROPN
ejpam-4275	402	18	,	,	PUNCT
ejpam-4275	402	19	σ	σ	NOUN
ejpam-4275	402	20	)	)	PUNCT
ejpam-4275	402	21	is	be	AUX
ejpam-4275	402	22	infra	infra	NOUN
ejpam-4275	402	23	soft	soft	ADJ
ejpam-4275	402	24	pre	pre	ADJ
ejpam-4275	402	25	-	-	ADJ
ejpam-4275	402	26	open	open	ADJ
ejpam-4275	402	27	⇔	⇔	PROPN
ejpam-4275	402	28	pb(ωc	pb(ωc	PROPN
ejpam-4275	402	29	,	,	PUNCT
ejpam-4275	402	30	σ	σ	PROPN
ejpam-4275	402	31	)	)	PUNCT
ejpam-4275	402	32	⋂	⋂	PROPN
ejpam-4275	402	33	(	(	PUNCT
ejpam-4275	402	34	ωc	ωc	PROPN
ejpam-4275	402	35	,	,	PUNCT
ejpam-4275	402	36	σ	σ	NOUN
ejpam-4275	402	37	)	)	PUNCT
ejpam-4275	403	1	=	=	PROPN
ejpam-4275	403	2	φ	φ	PROPN
ejpam-4275	403	3	⇔	⇔	PROPN
ejpam-4275	403	4	pb(ω	pb(ω	NUM
ejpam-4275	403	5	,	,	PUNCT
ejpam-4275	403	6	σ	σ	PROPN
ejpam-4275	403	7	)	)	PUNCT
ejpam-4275	403	8	⋂	⋂	PROPN
ejpam-4275	403	9	(	(	PUNCT
ejpam-4275	403	10	ωc	ωc	PROPN
ejpam-4275	403	11	,	,	PUNCT
ejpam-4275	403	12	σ	σ	NOUN
ejpam-4275	403	13	)	)	PUNCT
ejpam-4275	403	14	=	=	PROPN
ejpam-4275	403	15	φ	φ	PROPN
ejpam-4275	403	16	⇔	⇔	PROPN
ejpam-4275	403	17	pb(ω	pb(ω	NUM
ejpam-4275	403	18	,	,	PUNCT
ejpam-4275	403	19	σ	σ	PROPN
ejpam-4275	403	20	)	)	PUNCT
ejpam-4275	403	21	⊆	⊆	NUM
ejpam-4275	403	22	(	(	PUNCT
ejpam-4275	403	23	ω	ω	PROPN
ejpam-4275	403	24	,	,	PUNCT
ejpam-4275	403	25	σ	σ	PROPN
ejpam-4275	403	26	)	)	PUNCT
ejpam-4275	403	27	.	.	PUNCT
ejpam-4275	404	1	corollary	corollary	ADJ
ejpam-4275	404	2	5	5	NUM
ejpam-4275	404	3	.	.	PUNCT
ejpam-4275	404	4	a	a	DET
ejpam-4275	404	5	subset	subset	NOUN
ejpam-4275	404	6	(	(	PUNCT
ejpam-4275	404	7	ω	ω	PROPN
ejpam-4275	404	8	,	,	PUNCT
ejpam-4275	404	9	σ	σ	PROPN
ejpam-4275	404	10	)	)	PUNCT
ejpam-4275	404	11	of	of	ADP
ejpam-4275	404	12	(	(	PUNCT
ejpam-4275	404	13	x	x	NOUN
ejpam-4275	404	14	,	,	PUNCT
ejpam-4275	404	15	ξ	ξ	PROPN
ejpam-4275	404	16	,	,	PUNCT
ejpam-4275	404	17	σ	σ	NOUN
ejpam-4275	404	18	)	)	PUNCT
ejpam-4275	404	19	is	be	AUX
ejpam-4275	404	20	infra	infra	NOUN
ejpam-4275	404	21	soft	soft	ADJ
ejpam-4275	404	22	pre	pre	ADJ
ejpam-4275	404	23	-	-	ADJ
ejpam-4275	404	24	open	open	ADJ
ejpam-4275	404	25	and	and	CCONJ
ejpam-4275	404	26	infra	infra	VERB
ejpam-4275	404	27	soft	soft	ADJ
ejpam-4275	404	28	pre	pre	ADJ
ejpam-4275	404	29	-	-	ADJ
ejpam-4275	404	30	closed	closed	ADJ
ejpam-4275	404	31	iff	iff	NOUN
ejpam-4275	404	32	pb(ω	pb(ω	SYM
ejpam-4275	404	33	,	,	PUNCT
ejpam-4275	404	34	σ	σ	X
ejpam-4275	404	35	)	)	PUNCT
ejpam-4275	404	36	=	=	SYM
ejpam-4275	405	1	φ	φ	PROPN
ejpam-4275	405	2	.	.	PUNCT
ejpam-4275	406	1	t.m	t.m	PROPN
ejpam-4275	406	2	.	.	PUNCT
ejpam-4275	406	3	al	al	PROPN
ejpam-4275	406	4	-	-	PUNCT
ejpam-4275	406	5	shami	shami	PROPN
ejpam-4275	406	6	,	,	PUNCT
ejpam-4275	406	7	h.a	h.a	PROPN
ejpam-4275	406	8	.	.	PROPN
ejpam-4275	406	9	othman	othman	PROPN
ejpam-4275	406	10	/	/	SYM
ejpam-4275	406	11	eur	eur	PROPN
ejpam-4275	406	12	.	.	PUNCT
ejpam-4275	407	1	j.	j.	PROPN
ejpam-4275	407	2	pure	pure	PROPN
ejpam-4275	407	3	appl	appl	PROPN
ejpam-4275	407	4	.	.	PROPN
ejpam-4275	407	5	math	math	PROPN
ejpam-4275	407	6	,	,	PUNCT
ejpam-4275	407	7	15	15	NUM
ejpam-4275	407	8	(	(	PUNCT
ejpam-4275	407	9	1	1	NUM
ejpam-4275	407	10	)	)	PUNCT
ejpam-4275	407	11	(	(	PUNCT
ejpam-4275	407	12	2022	2022	NUM
ejpam-4275	407	13	)	)	PUNCT
ejpam-4275	407	14	,	,	PUNCT
ejpam-4275	407	15	261	261	NUM
ejpam-4275	407	16	-	-	SYM
ejpam-4275	407	17	280	280	NUM
ejpam-4275	407	18	273	273	NUM
ejpam-4275	407	19	5	5	NUM
ejpam-4275	407	20	.	.	PUNCT
ejpam-4275	408	1	infra	infra	NOUN
ejpam-4275	408	2	soft	soft	ADJ
ejpam-4275	408	3	pre	pre	ADJ
ejpam-4275	408	4	-	-	ADJ
ejpam-4275	408	5	homeomorphism	homeomorphism	ADJ
ejpam-4275	408	6	maps	map	NOUN
ejpam-4275	408	7	we	we	PRON
ejpam-4275	408	8	devote	devote	VERB
ejpam-4275	408	9	this	this	DET
ejpam-4275	408	10	section	section	NOUN
ejpam-4275	408	11	to	to	ADP
ejpam-4275	408	12	introducing	introduce	VERB
ejpam-4275	408	13	new	new	ADJ
ejpam-4275	408	14	types	type	NOUN
ejpam-4275	408	15	of	of	ADP
ejpam-4275	408	16	soft	soft	ADJ
ejpam-4275	408	17	maps	map	NOUN
ejpam-4275	408	18	called	call	VERB
ejpam-4275	408	19	infra	infra	NOUN
ejpam-4275	408	20	soft	soft	ADJ
ejpam-4275	408	21	precontinuous	precontinuous	NOUN
ejpam-4275	408	22	,	,	PUNCT
ejpam-4275	408	23	infra	infra	NOUN
ejpam-4275	408	24	soft	soft	ADJ
ejpam-4275	408	25	pre	pre	ADJ
ejpam-4275	408	26	-	-	ADJ
ejpam-4275	408	27	open	open	ADJ
ejpam-4275	408	28	,	,	PUNCT
ejpam-4275	408	29	infra	infra	NOUN
ejpam-4275	408	30	soft	soft	ADJ
ejpam-4275	408	31	pre	pre	ADJ
ejpam-4275	408	32	-	-	ADJ
ejpam-4275	408	33	closed	closed	ADJ
ejpam-4275	408	34	and	and	CCONJ
ejpam-4275	408	35	infra	infra	VERB
ejpam-4275	408	36	soft	soft	ADJ
ejpam-4275	408	37	pre	pre	ADJ
ejpam-4275	408	38	-	-	ADJ
ejpam-4275	408	39	homeomorphism	homeomorphism	ADJ
ejpam-4275	408	40	maps	map	NOUN
ejpam-4275	408	41	.	.	PUNCT
ejpam-4275	409	1	we	we	PRON
ejpam-4275	409	2	study	study	VERB
ejpam-4275	409	3	their	their	PRON
ejpam-4275	409	4	characterizations	characterization	NOUN
ejpam-4275	409	5	and	and	CCONJ
ejpam-4275	409	6	establish	establish	VERB
ejpam-4275	409	7	main	main	ADJ
ejpam-4275	409	8	properties	property	NOUN
ejpam-4275	409	9	.	.	PUNCT
ejpam-4275	410	1	definition	definition	NOUN
ejpam-4275	410	2	21	21	NUM
ejpam-4275	410	3	.	.	PUNCT
ejpam-4275	411	1	a	a	DET
ejpam-4275	411	2	soft	soft	ADJ
ejpam-4275	411	3	map	map	NOUN
ejpam-4275	411	4	eτ	eτ	ADP
ejpam-4275	411	5	:	:	PUNCT
ejpam-4275	411	6	(	(	PUNCT
ejpam-4275	411	7	x	x	X
ejpam-4275	411	8	,	,	PUNCT
ejpam-4275	411	9	ξ	ξ	PROPN
ejpam-4275	411	10	,	,	PUNCT
ejpam-4275	411	11	σ	σ	NOUN
ejpam-4275	411	12	)	)	PUNCT
ejpam-4275	411	13	→	→	SYM
ejpam-4275	411	14	(	(	PUNCT
ejpam-4275	411	15	s	s	PROPN
ejpam-4275	411	16	,	,	PUNCT
ejpam-4275	411	17	π,∆	π,∆	NUM
ejpam-4275	411	18	)	)	PUNCT
ejpam-4275	411	19	is	be	AUX
ejpam-4275	411	20	said	say	VERB
ejpam-4275	411	21	to	to	PART
ejpam-4275	411	22	be	be	AUX
ejpam-4275	411	23	infra	infra	NOUN
ejpam-4275	411	24	soft	soft	ADJ
ejpam-4275	411	25	precontinuous	precontinuous	NOUN
ejpam-4275	411	26	at	at	ADP
ejpam-4275	411	27	δxη	δxη	NOUN
ejpam-4275	411	28	∈	∈	PROPN
ejpam-4275	411	29	x̃	x̃	PROPN
ejpam-4275	412	1	if	if	SCONJ
ejpam-4275	412	2	for	for	ADP
ejpam-4275	412	3	any	any	DET
ejpam-4275	412	4	infra	infra	NOUN
ejpam-4275	412	5	soft	soft	ADJ
ejpam-4275	412	6	pre	pre	ADJ
ejpam-4275	412	7	-	-	ADJ
ejpam-4275	412	8	open	open	ADJ
ejpam-4275	412	9	set	set	NOUN
ejpam-4275	412	10	(	(	PUNCT
ejpam-4275	412	11	ψ,∆	ψ,∆	NOUN
ejpam-4275	412	12	)	)	PUNCT
ejpam-4275	412	13	containing	contain	VERB
ejpam-4275	412	14	eτ	eτ	PROPN
ejpam-4275	412	15	(	(	PUNCT
ejpam-4275	412	16	δ	δ	PROPN
ejpam-4275	412	17	x	x	SYM
ejpam-4275	412	18	η	η	PROPN
ejpam-4275	412	19	)	)	PUNCT
ejpam-4275	412	20	,	,	PUNCT
ejpam-4275	412	21	there	there	PRON
ejpam-4275	412	22	is	be	VERB
ejpam-4275	412	23	an	an	DET
ejpam-4275	412	24	infra	infra	NOUN
ejpam-4275	412	25	soft	soft	ADJ
ejpam-4275	412	26	pre	pre	ADJ
ejpam-4275	412	27	-	-	ADJ
ejpam-4275	412	28	open	open	ADJ
ejpam-4275	412	29	set	set	NOUN
ejpam-4275	412	30	(	(	PUNCT
ejpam-4275	412	31	ω	ω	PROPN
ejpam-4275	412	32	,	,	PUNCT
ejpam-4275	412	33	σ	σ	PROPN
ejpam-4275	412	34	)	)	PUNCT
ejpam-4275	412	35	containing	contain	VERB
ejpam-4275	412	36	δxη	δxη	NOUN
ejpam-4275	412	37	suchthat	suchthat	PROPN
ejpam-4275	412	38	eτ	eτ	PROPN
ejpam-4275	412	39	(	(	PUNCT
ejpam-4275	412	40	ω	ω	PROPN
ejpam-4275	412	41	,	,	PUNCT
ejpam-4275	412	42	σ)⊆̃(ψ,∆	σ)⊆̃(ψ,∆	NOUN
ejpam-4275	412	43	)	)	PUNCT
ejpam-4275	412	44	.	.	PUNCT
ejpam-4275	413	1	if	if	SCONJ
ejpam-4275	413	2	eτ	eτ	PROPN
ejpam-4275	413	3	is	be	AUX
ejpam-4275	413	4	infra	infra	NOUN
ejpam-4275	413	5	soft	soft	ADJ
ejpam-4275	413	6	pre	pre	ADJ
ejpam-4275	413	7	-	-	ADJ
ejpam-4275	413	8	continuous	continuous	ADJ
ejpam-4275	413	9	at	at	ADP
ejpam-4275	413	10	all	all	DET
ejpam-4275	413	11	soft	soft	ADJ
ejpam-4275	413	12	points	point	NOUN
ejpam-4275	413	13	of	of	ADP
ejpam-4275	413	14	the	the	DET
ejpam-4275	413	15	domain	domain	NOUN
ejpam-4275	413	16	,	,	PUNCT
ejpam-4275	413	17	then	then	ADV
ejpam-4275	413	18	it	it	PRON
ejpam-4275	413	19	is	be	AUX
ejpam-4275	413	20	called	call	VERB
ejpam-4275	413	21	infra	infra	NOUN
ejpam-4275	413	22	soft	soft	ADJ
ejpam-4275	413	23	pre	pre	ADJ
ejpam-4275	413	24	-	-	ADJ
ejpam-4275	413	25	continuous	continuous	ADJ
ejpam-4275	413	26	.	.	PUNCT
ejpam-4275	414	1	theorem	theorem	NOUN
ejpam-4275	414	2	4	4	NUM
ejpam-4275	414	3	.	.	PUNCT
ejpam-4275	415	1	let	let	VERB
ejpam-4275	415	2	eτ	eτ	VERB
ejpam-4275	415	3	:	:	PUNCT
ejpam-4275	415	4	(	(	PUNCT
ejpam-4275	415	5	x	x	X
ejpam-4275	415	6	,	,	PUNCT
ejpam-4275	415	7	ξ	ξ	PROPN
ejpam-4275	415	8	,	,	PUNCT
ejpam-4275	415	9	σ	σ	NOUN
ejpam-4275	415	10	)	)	PUNCT
ejpam-4275	415	11	→	→	SYM
ejpam-4275	415	12	(	(	PUNCT
ejpam-4275	415	13	s	s	PROPN
ejpam-4275	415	14	,	,	PUNCT
ejpam-4275	415	15	π,∆	π,∆	NUM
ejpam-4275	415	16	)	)	PUNCT
ejpam-4275	415	17	be	be	VERB
ejpam-4275	415	18	an	an	DET
ejpam-4275	415	19	infra	infra	NOUN
ejpam-4275	415	20	soft	soft	ADJ
ejpam-4275	415	21	pre	pre	ADJ
ejpam-4275	415	22	-	-	ADJ
ejpam-4275	415	23	continuous	continuous	ADJ
ejpam-4275	415	24	map	map	NOUN
ejpam-4275	415	25	.	.	PUNCT
ejpam-4275	416	1	then	then	ADV
ejpam-4275	416	2	we	we	PRON
ejpam-4275	416	3	have	have	VERB
ejpam-4275	416	4	the	the	DET
ejpam-4275	416	5	following	follow	VERB
ejpam-4275	416	6	five	five	NUM
ejpam-4275	416	7	equivalent	equivalent	ADJ
ejpam-4275	416	8	statements	statement	NOUN
ejpam-4275	416	9	:	:	PUNCT
ejpam-4275	416	10	(	(	PUNCT
ejpam-4275	416	11	i	i	NOUN
ejpam-4275	416	12	)	)	PUNCT
ejpam-4275	416	13	eτ	eτ	ADP
ejpam-4275	416	14	is	be	AUX
ejpam-4275	416	15	an	an	DET
ejpam-4275	416	16	infra	infra	NOUN
ejpam-4275	416	17	soft	soft	ADJ
ejpam-4275	416	18	pre	pre	ADJ
ejpam-4275	416	19	-	-	ADJ
ejpam-4275	416	20	continuous	continuous	ADJ
ejpam-4275	416	21	map	map	NOUN
ejpam-4275	416	22	;	;	PUNCT
ejpam-4275	416	23	(	(	PUNCT
ejpam-4275	416	24	ii	ii	NOUN
ejpam-4275	416	25	)	)	PUNCT
ejpam-4275	416	26	the	the	DET
ejpam-4275	416	27	pre	pre	NOUN
ejpam-4275	416	28	-	-	NOUN
ejpam-4275	416	29	image	image	NOUN
ejpam-4275	416	30	of	of	ADP
ejpam-4275	416	31	each	each	DET
ejpam-4275	416	32	infra	infra	NOUN
ejpam-4275	416	33	soft	soft	ADJ
ejpam-4275	416	34	pre	pre	ADJ
ejpam-4275	416	35	-	-	ADJ
ejpam-4275	416	36	closed	closed	ADJ
ejpam-4275	416	37	set	set	NOUN
ejpam-4275	416	38	is	be	AUX
ejpam-4275	416	39	infra	infra	NOUN
ejpam-4275	416	40	soft	soft	ADJ
ejpam-4275	416	41	pre	pre	ADJ
ejpam-4275	416	42	-	-	ADJ
ejpam-4275	416	43	closed	closed	ADJ
ejpam-4275	416	44	;	;	PUNCT
ejpam-4275	416	45	(	(	PUNCT
ejpam-4275	416	46	iii	iii	X
ejpam-4275	416	47	)	)	PUNCT
ejpam-4275	416	48	pcl(e−1	pcl(e−1	NOUN
ejpam-4275	416	49	τ	τ	PROPN
ejpam-4275	416	50	(	(	PUNCT
ejpam-4275	416	51	ω,∆))⊆̃e−1	ω,∆))⊆̃e−1	PROPN
ejpam-4275	416	52	τ	τ	PROPN
ejpam-4275	416	53	(	(	PUNCT
ejpam-4275	416	54	pcl(ω,∆	pcl(ω,∆	NOUN
ejpam-4275	416	55	)	)	PUNCT
ejpam-4275	416	56	)	)	PUNCT
ejpam-4275	416	57	for	for	ADP
ejpam-4275	416	58	each	each	PRON
ejpam-4275	416	59	(	(	PUNCT
ejpam-4275	416	60	ω,∆)⊆̃s̃	ω,∆)⊆̃s̃	PROPN
ejpam-4275	416	61	;	;	PUNCT
ejpam-4275	416	62	(	(	PUNCT
ejpam-4275	416	63	iv	iv	X
ejpam-4275	416	64	)	)	PUNCT
ejpam-4275	416	65	eτ	eτ	PROPN
ejpam-4275	416	66	(	(	PUNCT
ejpam-4275	416	67	pcl(ψ	pcl(ψ	PROPN
ejpam-4275	416	68	,	,	PUNCT
ejpam-4275	416	69	σ))⊆̃pcl(eτ	σ))⊆̃pcl(eτ	X
ejpam-4275	416	70	(	(	PUNCT
ejpam-4275	416	71	ψ	ψ	X
ejpam-4275	416	72	,	,	PUNCT
ejpam-4275	416	73	σ	σ	NOUN
ejpam-4275	416	74	)	)	PUNCT
ejpam-4275	416	75	)	)	PUNCT
ejpam-4275	416	76	for	for	ADP
ejpam-4275	416	77	each	each	DET
ejpam-4275	416	78	(	(	PUNCT
ejpam-4275	416	79	ψ	ψ	X
ejpam-4275	416	80	,	,	PUNCT
ejpam-4275	416	81	σ)⊆̃x̃	σ)⊆̃x̃	PROPN
ejpam-4275	416	82	;	;	PUNCT
ejpam-4275	416	83	(	(	PUNCT
ejpam-4275	416	84	v	v	NOUN
ejpam-4275	416	85	)	)	PUNCT
ejpam-4275	416	86	e−1	e−1	PROPN
ejpam-4275	416	87	τ	τ	X
ejpam-4275	416	88	(	(	PUNCT
ejpam-4275	416	89	pint(ω,∆))⊆̃pint(e−1	pint(ω,∆))⊆̃pint(e−1	PROPN
ejpam-4275	416	90	τ	τ	X
ejpam-4275	416	91	(	(	PUNCT
ejpam-4275	416	92	ω,∆	ω,∆	PROPN
ejpam-4275	416	93	)	)	PUNCT
ejpam-4275	416	94	)	)	PUNCT
ejpam-4275	416	95	for	for	ADP
ejpam-4275	416	96	each	each	DET
ejpam-4275	416	97	(	(	PUNCT
ejpam-4275	416	98	ω,∆)⊆̃s̃.	ω,∆)⊆̃s̃.	ADJ
ejpam-4275	416	99	proof	proof	NOUN
ejpam-4275	416	100	.	.	PUNCT
ejpam-4275	417	1	(	(	PUNCT
ejpam-4275	417	2	i	i	NOUN
ejpam-4275	417	3	)	)	PUNCT
ejpam-4275	417	4	⇒	⇒	PROPN
ejpam-4275	417	5	(	(	PUNCT
ejpam-4275	417	6	ii	ii	PROPN
ejpam-4275	417	7	):	):	PUNCT
ejpam-4275	417	8	let	let	VERB
ejpam-4275	417	9	(	(	PUNCT
ejpam-4275	417	10	ω,∆	ω,∆	PROPN
ejpam-4275	417	11	)	)	PUNCT
ejpam-4275	417	12	be	be	AUX
ejpam-4275	417	13	an	an	DET
ejpam-4275	417	14	infra	infra	NOUN
ejpam-4275	417	15	soft	soft	ADJ
ejpam-4275	417	16	pre	pre	ADJ
ejpam-4275	417	17	-	-	ADJ
ejpam-4275	417	18	closed	closed	ADJ
ejpam-4275	417	19	set	set	NOUN
ejpam-4275	417	20	in	in	ADP
ejpam-4275	417	21	(	(	PUNCT
ejpam-4275	417	22	s	s	PROPN
ejpam-4275	417	23	,	,	PUNCT
ejpam-4275	417	24	π,∆	π,∆	NUM
ejpam-4275	417	25	)	)	PUNCT
ejpam-4275	417	26	.	.	PUNCT
ejpam-4275	418	1	then	then	ADV
ejpam-4275	418	2	e−1	e−1	PROPN
ejpam-4275	418	3	τ	τ	X
ejpam-4275	418	4	(	(	PUNCT
ejpam-4275	418	5	ωc,∆	ωc,∆	PROPN
ejpam-4275	418	6	)	)	PUNCT
ejpam-4275	418	7	is	be	AUX
ejpam-4275	418	8	an	an	DET
ejpam-4275	418	9	infrasoft	infrasoft	ADJ
ejpam-4275	418	10	pre	pre	ADJ
ejpam-4275	418	11	-	-	ADJ
ejpam-4275	418	12	open	open	ADJ
ejpam-4275	418	13	subset	subset	NOUN
ejpam-4275	418	14	of	of	ADP
ejpam-4275	418	15	x̃.	x̃.	ADJ
ejpam-4275	418	16	obviously	obviously	ADV
ejpam-4275	418	17	,	,	PUNCT
ejpam-4275	418	18	e−1	e−1	PROPN
ejpam-4275	418	19	τ	τ	X
ejpam-4275	418	20	(	(	PUNCT
ejpam-4275	418	21	ωc,∆	ωc,∆	PROPN
ejpam-4275	418	22	)	)	PUNCT
ejpam-4275	418	23	=	=	SYM
ejpam-4275	418	24	x̃−e−1	x̃−e−1	PROPN
ejpam-4275	418	25	τ	τ	PROPN
ejpam-4275	418	26	(	(	PUNCT
ejpam-4275	418	27	ω,∆	ω,∆	PROPN
ejpam-4275	418	28	)	)	PUNCT
ejpam-4275	418	29	;	;	PUNCT
ejpam-4275	418	30	hence	hence	ADV
ejpam-4275	418	31	,	,	PUNCT
ejpam-4275	418	32	e−1	e−1	PROPN
ejpam-4275	418	33	τ	τ	X
ejpam-4275	418	34	(	(	PUNCT
ejpam-4275	418	35	ω,∆	ω,∆	PROPN
ejpam-4275	418	36	)	)	PUNCT
ejpam-4275	418	37	is	be	AUX
ejpam-4275	418	38	an	an	DET
ejpam-4275	418	39	infra	infra	NOUN
ejpam-4275	418	40	soft	soft	ADJ
ejpam-4275	418	41	pre	pre	ADJ
ejpam-4275	418	42	-	-	ADJ
ejpam-4275	418	43	closed	closed	ADJ
ejpam-4275	418	44	subset	subset	NOUN
ejpam-4275	418	45	of	of	ADP
ejpam-4275	418	46	x̃.	x̃.	PROPN
ejpam-4275	418	47	(	(	PUNCT
ejpam-4275	418	48	ii	ii	NOUN
ejpam-4275	418	49	)	)	PUNCT
ejpam-4275	418	50	⇒	⇒	NOUN
ejpam-4275	418	51	(	(	PUNCT
ejpam-4275	418	52	iii	iii	NOUN
ejpam-4275	418	53	):	):	PUNCT
ejpam-4275	418	54	according	accord	VERB
ejpam-4275	418	55	to	to	ADP
ejpam-4275	418	56	(	(	PUNCT
ejpam-4275	418	57	ii	ii	NOUN
ejpam-4275	418	58	)	)	PUNCT
ejpam-4275	418	59	,	,	PUNCT
ejpam-4275	418	60	e−1	e−1	PROPN
ejpam-4275	418	61	τ	τ	X
ejpam-4275	418	62	(	(	PUNCT
ejpam-4275	418	63	pcl(ω,∆	pcl(ω,∆	NOUN
ejpam-4275	418	64	)	)	PUNCT
ejpam-4275	418	65	)	)	PUNCT
ejpam-4275	418	66	is	be	AUX
ejpam-4275	418	67	an	an	DET
ejpam-4275	418	68	infra	infra	NOUN
ejpam-4275	418	69	soft	soft	ADJ
ejpam-4275	418	70	pre	pre	ADJ
ejpam-4275	418	71	-	-	ADJ
ejpam-4275	418	72	closed	closed	ADJ
ejpam-4275	418	73	subset	subset	NOUN
ejpam-4275	418	74	of	of	ADP
ejpam-4275	418	75	x̃.	x̃.	PROPN
ejpam-4275	418	76	then	then	ADV
ejpam-4275	418	77	pcl(e−1	pcl(e−1	NOUN
ejpam-4275	418	78	τ	τ	PROPN
ejpam-4275	418	79	(	(	PUNCT
ejpam-4275	418	80	ω,∆))⊆̃pcl(e−1	ω,∆))⊆̃pcl(e−1	PROPN
ejpam-4275	418	81	τ	τ	PROPN
ejpam-4275	418	82	(	(	PUNCT
ejpam-4275	418	83	pcl(ω,∆	pcl(ω,∆	NOUN
ejpam-4275	418	84	)	)	PUNCT
ejpam-4275	418	85	)	)	PUNCT
ejpam-4275	418	86	)	)	PUNCT
ejpam-4275	419	1	=	=	SYM
ejpam-4275	420	1	e−1	e−1	PROPN
ejpam-4275	420	2	τ	τ	X
ejpam-4275	420	3	(	(	PUNCT
ejpam-4275	420	4	pcl(ω,∆	pcl(ω,∆	NOUN
ejpam-4275	420	5	)	)	PUNCT
ejpam-4275	420	6	)	)	PUNCT
ejpam-4275	420	7	.	.	PUNCT
ejpam-4275	421	1	(	(	PUNCT
ejpam-4275	421	2	iii	iii	X
ejpam-4275	421	3	)	)	PUNCT
ejpam-4275	421	4	⇒	⇒	NOUN
ejpam-4275	421	5	(	(	PUNCT
ejpam-4275	421	6	vi	vi	ADJ
ejpam-4275	421	7	):	):	PUNCT
ejpam-4275	421	8	according	accord	VERB
ejpam-4275	421	9	to	to	ADP
ejpam-4275	421	10	(	(	PUNCT
ejpam-4275	421	11	iii	iii	NOUN
ejpam-4275	421	12	)	)	PUNCT
ejpam-4275	421	13	,	,	PUNCT
ejpam-4275	421	14	pcl(e−1	pcl(e−1	NOUN
ejpam-4275	421	15	τ	τ	X
ejpam-4275	421	16	(	(	PUNCT
ejpam-4275	421	17	eτ	eτ	X
ejpam-4275	421	18	(	(	PUNCT
ejpam-4275	421	19	ψ	ψ	NOUN
ejpam-4275	421	20	,	,	PUNCT
ejpam-4275	421	21	σ)))⊆̃e−1	σ)))⊆̃e−1	NOUN
ejpam-4275	421	22	τ	τ	X
ejpam-4275	421	23	(	(	PUNCT
ejpam-4275	421	24	pcl(eτ	pcl(eτ	X
ejpam-4275	421	25	(	(	PUNCT
ejpam-4275	421	26	ψ	ψ	X
ejpam-4275	421	27	,	,	PUNCT
ejpam-4275	421	28	σ	σ	NOUN
ejpam-4275	421	29	)	)	PUNCT
ejpam-4275	421	30	)	)	PUNCT
ejpam-4275	421	31	)	)	PUNCT
ejpam-4275	421	32	.	.	PUNCT
ejpam-4275	422	1	then	then	ADV
ejpam-4275	422	2	eτ	eτ	X
ejpam-4275	422	3	(	(	PUNCT
ejpam-4275	422	4	pcl(ψ	pcl(ψ	PROPN
ejpam-4275	422	5	,	,	PUNCT
ejpam-4275	422	6	σ))⊆̃eτ	σ))⊆̃eτ	X
ejpam-4275	422	7	(	(	PUNCT
ejpam-4275	422	8	e	e	NOUN
ejpam-4275	422	9	−1	−1	NOUN
ejpam-4275	422	10	τ	τ	X
ejpam-4275	422	11	(	(	PUNCT
ejpam-4275	422	12	pcl(eτ	pcl(eτ	X
ejpam-4275	422	13	(	(	PUNCT
ejpam-4275	422	14	ψ	ψ	NOUN
ejpam-4275	422	15	,	,	PUNCT
ejpam-4275	422	16	σ))))⊆̃pcl(eτ	σ))))⊆̃pcl(eτ	X
ejpam-4275	422	17	(	(	PUNCT
ejpam-4275	422	18	ψ	ψ	X
ejpam-4275	422	19	,	,	PUNCT
ejpam-4275	422	20	σ	σ	NOUN
ejpam-4275	422	21	)	)	PUNCT
ejpam-4275	422	22	)	)	PUNCT
ejpam-4275	422	23	.	.	PUNCT
ejpam-4275	423	1	(	(	PUNCT
ejpam-4275	423	2	iv	iv	X
ejpam-4275	423	3	)	)	PUNCT
ejpam-4275	423	4	⇒	⇒	NOUN
ejpam-4275	423	5	(	(	PUNCT
ejpam-4275	423	6	v	v	NOUN
ejpam-4275	423	7	):	):	PUNCT
ejpam-4275	423	8	according	accord	VERB
ejpam-4275	423	9	to	to	ADP
ejpam-4275	423	10	(	(	PUNCT
ejpam-4275	423	11	iv	iv	NUM
ejpam-4275	423	12	)	)	PUNCT
ejpam-4275	423	13	,	,	PUNCT
ejpam-4275	423	14	eτ	eτ	PROPN
ejpam-4275	423	15	(	(	PUNCT
ejpam-4275	423	16	pcl(x̃−e−1	pcl(x̃−e−1	PROPN
ejpam-4275	423	17	τ	τ	X
ejpam-4275	423	18	(	(	PUNCT
ejpam-4275	423	19	ω,∆)))⊆̃pcl(eτ	ω,∆)))⊆̃pcl(eτ	NUM
ejpam-4275	423	20	(	(	PUNCT
ejpam-4275	423	21	x̃−e−1	x̃−e−1	PROPN
ejpam-4275	423	22	τ	τ	PROPN
ejpam-4275	423	23	(	(	PUNCT
ejpam-4275	423	24	ω,∆	ω,∆	PROPN
ejpam-4275	423	25	)	)	PUNCT
ejpam-4275	423	26	)	)	PUNCT
ejpam-4275	423	27	)	)	PUNCT
ejpam-4275	423	28	.	.	PUNCT
ejpam-4275	424	1	therefore	therefore	ADV
ejpam-4275	424	2	,	,	PUNCT
ejpam-4275	424	3	eτ	eτ	PROPN
ejpam-4275	424	4	(	(	PUNCT
ejpam-4275	424	5	x̃	x̃	PROPN
ejpam-4275	424	6	−	−	PROPN
ejpam-4275	424	7	pint(e−1	pint(e−1	NOUN
ejpam-4275	424	8	τ	τ	X
ejpam-4275	424	9	(	(	PUNCT
ejpam-4275	424	10	ω,∆	ω,∆	PROPN
ejpam-4275	424	11	)	)	PUNCT
ejpam-4275	424	12	)	)	PUNCT
ejpam-4275	424	13	)	)	PUNCT
ejpam-4275	425	1	=	=	SYM
ejpam-4275	425	2	eτ	eτ	X
ejpam-4275	425	3	(	(	PUNCT
ejpam-4275	425	4	pcl(x̃	pcl(x̃	PROPN
ejpam-4275	425	5	−	−	PROPN
ejpam-4275	426	1	e−1	e−1	PROPN
ejpam-4275	426	2	τ	τ	X
ejpam-4275	426	3	(	(	PUNCT
ejpam-4275	426	4	ω,∆	ω,∆	PROPN
ejpam-4275	426	5	)	)	PUNCT
ejpam-4275	426	6	)	)	PUNCT
ejpam-4275	426	7	)	)	PUNCT
ejpam-4275	427	1	⊆	⊆	NUM
ejpam-4275	427	2	pcl(s̃	pcl(s̃	NOUN
ejpam-4275	427	3	−	−	PROPN
ejpam-4275	427	4	(	(	PUNCT
ejpam-4275	427	5	ω,∆	ω,∆	PROPN
ejpam-4275	427	6	)	)	PUNCT
ejpam-4275	427	7	)	)	PUNCT
ejpam-4275	428	1	=	=	SYM
ejpam-4275	429	1	s̃	s̃	NOUN
ejpam-4275	429	2	−	−	PROPN
ejpam-4275	429	3	pint(ω,∆	pint(ω,∆	NOUN
ejpam-4275	429	4	)	)	PUNCT
ejpam-4275	429	5	.	.	PUNCT
ejpam-4275	430	1	thus	thus	ADV
ejpam-4275	430	2	x̃−pint(e−1	x̃−pint(e−1	PROPN
ejpam-4275	430	3	τ	τ	PROPN
ejpam-4275	430	4	(	(	PUNCT
ejpam-4275	430	5	ω,∆))⊆̃e−1	ω,∆))⊆̃e−1	PROPN
ejpam-4275	430	6	τ	τ	X
ejpam-4275	430	7	(	(	PUNCT
ejpam-4275	430	8	s̃−pint(ω,∆	s̃−pint(ω,∆	NOUN
ejpam-4275	430	9	)	)	PUNCT
ejpam-4275	430	10	)	)	PUNCT
ejpam-4275	431	1	=	=	SYM
ejpam-4275	432	1	e−1	e−1	PROPN
ejpam-4275	432	2	τ	τ	X
ejpam-4275	432	3	(	(	PUNCT
ejpam-4275	432	4	s̃)−e−1	s̃)−e−1	PROPN
ejpam-4275	432	5	τ	τ	PROPN
ejpam-4275	432	6	(	(	PUNCT
ejpam-4275	432	7	pint(ω,∆	pint(ω,∆	NOUN
ejpam-4275	432	8	)	)	PUNCT
ejpam-4275	432	9	)	)	PUNCT
ejpam-4275	432	10	.	.	PUNCT
ejpam-4275	433	1	hence	hence	ADV
ejpam-4275	433	2	e−1	e−1	PROPN
ejpam-4275	433	3	τ	τ	X
ejpam-4275	433	4	(	(	PUNCT
ejpam-4275	433	5	pint(ω,∆))⊆̃pint(e−1	pint(ω,∆))⊆̃pint(e−1	PROPN
ejpam-4275	433	6	τ	τ	X
ejpam-4275	433	7	(	(	PUNCT
ejpam-4275	433	8	ω,∆	ω,∆	PROPN
ejpam-4275	433	9	)	)	PUNCT
ejpam-4275	433	10	)	)	PUNCT
ejpam-4275	433	11	.	.	PUNCT
ejpam-4275	434	1	(	(	PUNCT
ejpam-4275	434	2	v	v	NOUN
ejpam-4275	434	3	)	)	PUNCT
ejpam-4275	434	4	⇒	⇒	NOUN
ejpam-4275	434	5	(	(	PUNCT
ejpam-4275	434	6	i	i	NOUN
ejpam-4275	434	7	):	):	PUNCT
ejpam-4275	434	8	let	let	VERB
ejpam-4275	434	9	(	(	PUNCT
ejpam-4275	434	10	ω,∆	ω,∆	NUM
ejpam-4275	434	11	)	)	PUNCT
ejpam-4275	434	12	be	be	AUX
ejpam-4275	434	13	an	an	DET
ejpam-4275	434	14	infra	infra	NOUN
ejpam-4275	434	15	soft	soft	ADJ
ejpam-4275	434	16	open	open	ADJ
ejpam-4275	434	17	subset	subset	NOUN
ejpam-4275	434	18	of	of	ADP
ejpam-4275	434	19	s̃.	s̃.	PROPN
ejpam-4275	434	20	according	accord	VERB
ejpam-4275	434	21	to	to	ADP
ejpam-4275	434	22	(	(	PUNCT
ejpam-4275	434	23	v	v	NOUN
ejpam-4275	434	24	)	)	PUNCT
ejpam-4275	434	25	,	,	PUNCT
ejpam-4275	434	26	e−1	e−1	PROPN
ejpam-4275	434	27	τ	τ	X
ejpam-4275	434	28	(	(	PUNCT
ejpam-4275	434	29	ω,∆)⊆̃pint(e−1	ω,∆)⊆̃pint(e−1	PROPN
ejpam-4275	434	30	τ	τ	PROPN
ejpam-4275	434	31	(	(	PUNCT
ejpam-4275	434	32	ω,∆	ω,∆	PROPN
ejpam-4275	434	33	)	)	PUNCT
ejpam-4275	434	34	)	)	PUNCT
ejpam-4275	434	35	.	.	PUNCT
ejpam-4275	435	1	this	this	PRON
ejpam-4275	435	2	implies	imply	VERB
ejpam-4275	435	3	that	that	SCONJ
ejpam-4275	435	4	e−1	e−1	PROPN
ejpam-4275	435	5	τ	τ	X
ejpam-4275	435	6	(	(	PUNCT
ejpam-4275	435	7	ω,∆	ω,∆	PROPN
ejpam-4275	435	8	)	)	PUNCT
ejpam-4275	435	9	=	=	SYM
ejpam-4275	435	10	pint(e−1	pint(e−1	NOUN
ejpam-4275	435	11	τ	τ	X
ejpam-4275	435	12	(	(	PUNCT
ejpam-4275	435	13	ω,∆	ω,∆	PROPN
ejpam-4275	435	14	)	)	PUNCT
ejpam-4275	435	15	)	)	PUNCT
ejpam-4275	435	16	.	.	PUNCT
ejpam-4275	436	1	hence	hence	ADV
ejpam-4275	436	2	,	,	PUNCT
ejpam-4275	436	3	eτ	eτ	ADV
ejpam-4275	436	4	is	be	AUX
ejpam-4275	436	5	infra	infra	NOUN
ejpam-4275	436	6	soft	soft	ADJ
ejpam-4275	436	7	pre	pre	ADJ
ejpam-4275	436	8	-	-	ADJ
ejpam-4275	436	9	continuous	continuous	ADJ
ejpam-4275	436	10	.	.	PUNCT
ejpam-4275	437	1	theorem	theorem	NOUN
ejpam-4275	437	2	5	5	NUM
ejpam-4275	437	3	.	.	PUNCT
ejpam-4275	438	1	if	if	SCONJ
ejpam-4275	438	2	eτ	eτ	X
ejpam-4275	438	3	:	:	PUNCT
ejpam-4275	438	4	(	(	PUNCT
ejpam-4275	438	5	x	x	X
ejpam-4275	438	6	,	,	PUNCT
ejpam-4275	438	7	ξ	ξ	PROPN
ejpam-4275	438	8	,	,	PUNCT
ejpam-4275	438	9	σ	σ	NOUN
ejpam-4275	438	10	)	)	PUNCT
ejpam-4275	438	11	→	→	SYM
ejpam-4275	438	12	(	(	PUNCT
ejpam-4275	438	13	s	s	PROPN
ejpam-4275	438	14	,	,	PUNCT
ejpam-4275	438	15	π,∆	π,∆	NUM
ejpam-4275	438	16	)	)	PUNCT
ejpam-4275	438	17	is	be	AUX
ejpam-4275	438	18	infra	infra	NOUN
ejpam-4275	438	19	soft	soft	ADJ
ejpam-4275	438	20	pre	pre	ADJ
ejpam-4275	438	21	-	-	ADJ
ejpam-4275	438	22	continuous	continuous	ADJ
ejpam-4275	438	23	,	,	PUNCT
ejpam-4275	438	24	then	then	ADV
ejpam-4275	438	25	the	the	DET
ejpam-4275	438	26	restriction	restriction	NOUN
ejpam-4275	438	27	soft	soft	ADJ
ejpam-4275	438	28	map	map	NOUN
ejpam-4275	439	1	eτ|m	eτ|m	PROPN
ejpam-4275	439	2	:	:	PUNCT
ejpam-4275	439	3	(	(	PUNCT
ejpam-4275	439	4	m	m	PROPN
ejpam-4275	439	5	,	,	PUNCT
ejpam-4275	439	6	ξm	ξm	PROPN
ejpam-4275	439	7	,	,	PUNCT
ejpam-4275	439	8	σ	σ	PROPN
ejpam-4275	439	9	)	)	PUNCT
ejpam-4275	439	10	→	→	SYM
ejpam-4275	439	11	(	(	PUNCT
ejpam-4275	439	12	s	s	PROPN
ejpam-4275	439	13	,	,	PUNCT
ejpam-4275	439	14	π,∆	π,∆	NUM
ejpam-4275	439	15	)	)	PUNCT
ejpam-4275	439	16	is	be	AUX
ejpam-4275	439	17	infra	infra	NOUN
ejpam-4275	439	18	soft	soft	ADJ
ejpam-4275	439	19	pre	pre	ADJ
ejpam-4275	439	20	-	-	ADJ
ejpam-4275	439	21	continuous	continuous	ADJ
ejpam-4275	439	22	provided	provide	VERB
ejpam-4275	439	23	that	that	SCONJ
ejpam-4275	439	24	m̃	m̃	PROPN
ejpam-4275	439	25	is	be	AUX
ejpam-4275	439	26	an	an	DET
ejpam-4275	439	27	infra	infra	NOUN
ejpam-4275	439	28	soft	soft	ADJ
ejpam-4275	439	29	open	open	ADJ
ejpam-4275	439	30	set	set	NOUN
ejpam-4275	439	31	.	.	PUNCT
ejpam-4275	440	1	proof	proof	NOUN
ejpam-4275	440	2	.	.	PUNCT
ejpam-4275	441	1	consider	consider	VERB
ejpam-4275	441	2	(	(	PUNCT
ejpam-4275	441	3	ω,∆	ω,∆	PROPN
ejpam-4275	441	4	)	)	PUNCT
ejpam-4275	441	5	is	be	AUX
ejpam-4275	441	6	an	an	DET
ejpam-4275	441	7	infra	infra	NOUN
ejpam-4275	441	8	soft	soft	ADJ
ejpam-4275	441	9	pre	pre	ADJ
ejpam-4275	441	10	-	-	ADJ
ejpam-4275	441	11	open	open	ADJ
ejpam-4275	441	12	set	set	NOUN
ejpam-4275	441	13	in	in	ADP
ejpam-4275	441	14	(	(	PUNCT
ejpam-4275	441	15	s	s	PROPN
ejpam-4275	441	16	,	,	PUNCT
ejpam-4275	441	17	π,∆	π,∆	NUM
ejpam-4275	441	18	)	)	PUNCT
ejpam-4275	441	19	.	.	PUNCT
ejpam-4275	442	1	by	by	ADP
ejpam-4275	442	2	hypothesis	hypothesis	NOUN
ejpam-4275	442	3	,	,	PUNCT
ejpam-4275	442	4	e−1	e−1	PROPN
ejpam-4275	442	5	τ	τ	X
ejpam-4275	442	6	(	(	PUNCT
ejpam-4275	442	7	ω,∆	ω,∆	PROPN
ejpam-4275	442	8	)	)	PUNCT
ejpam-4275	442	9	is	be	AUX
ejpam-4275	442	10	infra	infra	NOUN
ejpam-4275	442	11	soft	soft	ADJ
ejpam-4275	442	12	pre	pre	ADJ
ejpam-4275	442	13	-	-	ADJ
ejpam-4275	442	14	open	open	ADJ
ejpam-4275	442	15	.	.	PUNCT
ejpam-4275	443	1	now	now	ADV
ejpam-4275	443	2	,	,	PUNCT
ejpam-4275	443	3	e−1	e−1	PROPN
ejpam-4275	443	4	τ|m	τ|m	X
ejpam-4275	443	5	(	(	PUNCT
ejpam-4275	443	6	ω,∆	ω,∆	NUM
ejpam-4275	443	7	)	)	PUNCT
ejpam-4275	444	1	=	=	SYM
ejpam-4275	445	1	e−1	e−1	PROPN
ejpam-4275	445	2	τ	τ	X
ejpam-4275	445	3	(	(	PUNCT
ejpam-4275	445	4	ω,∆	ω,∆	PROPN
ejpam-4275	445	5	)	)	PUNCT
ejpam-4275	445	6	⋂̃	⋂̃	NOUN
ejpam-4275	445	7	m̃.	m̃.	NOUN
ejpam-4275	445	8	since	since	SCONJ
ejpam-4275	445	9	m̃	m̃	PROPN
ejpam-4275	445	10	is	be	AUX
ejpam-4275	445	11	an	an	DET
ejpam-4275	445	12	t.m	t.m	PROPN
ejpam-4275	445	13	.	.	PUNCT
ejpam-4275	445	14	al	al	PROPN
ejpam-4275	445	15	-	-	PUNCT
ejpam-4275	445	16	shami	shami	PROPN
ejpam-4275	445	17	,	,	PUNCT
ejpam-4275	445	18	h.a	h.a	PROPN
ejpam-4275	445	19	.	.	PROPN
ejpam-4275	445	20	othman	othman	PROPN
ejpam-4275	445	21	/	/	SYM
ejpam-4275	445	22	eur	eur	PROPN
ejpam-4275	445	23	.	.	PUNCT
ejpam-4275	446	1	j.	j.	PROPN
ejpam-4275	446	2	pure	pure	PROPN
ejpam-4275	446	3	appl	appl	PROPN
ejpam-4275	446	4	.	.	PROPN
ejpam-4275	446	5	math	math	PROPN
ejpam-4275	446	6	,	,	PUNCT
ejpam-4275	446	7	15	15	NUM
ejpam-4275	446	8	(	(	PUNCT
ejpam-4275	446	9	1	1	NUM
ejpam-4275	446	10	)	)	PUNCT
ejpam-4275	446	11	(	(	PUNCT
ejpam-4275	446	12	2022	2022	NUM
ejpam-4275	446	13	)	)	PUNCT
ejpam-4275	446	14	,	,	PUNCT
ejpam-4275	446	15	261	261	NUM
ejpam-4275	446	16	-	-	SYM
ejpam-4275	446	17	280	280	NUM
ejpam-4275	446	18	274	274	NUM
ejpam-4275	446	19	infra	infra	NOUN
ejpam-4275	446	20	soft	soft	ADJ
ejpam-4275	446	21	open	open	ADJ
ejpam-4275	446	22	set	set	NOUN
ejpam-4275	446	23	,	,	PUNCT
ejpam-4275	446	24	it	it	PRON
ejpam-4275	446	25	follows	follow	VERB
ejpam-4275	446	26	from	from	ADP
ejpam-4275	446	27	proposition	proposition	NOUN
ejpam-4275	446	28	9	9	NUM
ejpam-4275	446	29	that	that	PRON
ejpam-4275	446	30	e−1	e−1	PROPN
ejpam-4275	446	31	τ|m	τ|m	X
ejpam-4275	446	32	(	(	PUNCT
ejpam-4275	446	33	ω,∆	ω,∆	PROPN
ejpam-4275	446	34	)	)	PUNCT
ejpam-4275	446	35	is	be	AUX
ejpam-4275	446	36	infra	infra	NOUN
ejpam-4275	446	37	soft	soft	ADJ
ejpam-4275	446	38	pre	pre	ADJ
ejpam-4275	446	39	-	-	ADJ
ejpam-4275	446	40	open	open	ADJ
ejpam-4275	446	41	.	.	PUNCT
ejpam-4275	447	1	hence	hence	ADV
ejpam-4275	447	2	,	,	PUNCT
ejpam-4275	447	3	eτ|m	eτ|m	PROPN
ejpam-4275	447	4	is	be	AUX
ejpam-4275	447	5	an	an	DET
ejpam-4275	447	6	infra	infra	NOUN
ejpam-4275	447	7	soft	soft	ADJ
ejpam-4275	447	8	pre	pre	ADJ
ejpam-4275	447	9	-	-	ADJ
ejpam-4275	447	10	continuous	continuous	ADJ
ejpam-4275	447	11	map	map	NOUN
ejpam-4275	447	12	.	.	PUNCT
ejpam-4275	448	1	proposition	proposition	NOUN
ejpam-4275	448	2	20	20	NUM
ejpam-4275	448	3	.	.	PUNCT
ejpam-4275	449	1	let	let	VERB
ejpam-4275	449	2	eτ	eτ	VERB
ejpam-4275	449	3	:	:	PUNCT
ejpam-4275	449	4	(	(	PUNCT
ejpam-4275	449	5	x	x	X
ejpam-4275	449	6	,	,	PUNCT
ejpam-4275	449	7	ξ	ξ	PROPN
ejpam-4275	449	8	,	,	PUNCT
ejpam-4275	449	9	σ	σ	NOUN
ejpam-4275	449	10	)	)	PUNCT
ejpam-4275	449	11	→	→	SYM
ejpam-4275	449	12	(	(	PUNCT
ejpam-4275	449	13	s	s	PROPN
ejpam-4275	449	14	,	,	PUNCT
ejpam-4275	449	15	π,∆	π,∆	NUM
ejpam-4275	449	16	)	)	PUNCT
ejpam-4275	449	17	and	and	CCONJ
ejpam-4275	449	18	fν	fν	INTJ
ejpam-4275	449	19	:	:	PUNCT
ejpam-4275	449	20	(	(	PUNCT
ejpam-4275	449	21	s	s	X
ejpam-4275	449	22	,	,	PUNCT
ejpam-4275	449	23	π,∆	π,∆	NUM
ejpam-4275	449	24	)	)	PUNCT
ejpam-4275	449	25	→	→	SYM
ejpam-4275	449	26	(	(	PUNCT
ejpam-4275	449	27	v	v	NOUN
ejpam-4275	449	28	,	,	PUNCT
ejpam-4275	449	29	σ	σ	PROPN
ejpam-4275	449	30	,	,	PUNCT
ejpam-4275	449	31	γ	γ	NOUN
ejpam-4275	449	32	)	)	PUNCT
ejpam-4275	449	33	be	be	VERB
ejpam-4275	449	34	infra	infra	NOUN
ejpam-4275	449	35	soft	soft	ADJ
ejpam-4275	449	36	pre	pre	ADJ
ejpam-4275	449	37	-	-	ADJ
ejpam-4275	449	38	continuous	continuous	ADJ
ejpam-4275	449	39	.	.	PUNCT
ejpam-4275	450	1	then	then	ADV
ejpam-4275	450	2	fν	fν	VERB
ejpam-4275	450	3	◦	◦	NOUN
ejpam-4275	450	4	eτ	eτ	ADP
ejpam-4275	450	5	is	be	AUX
ejpam-4275	450	6	infra	infra	NOUN
ejpam-4275	450	7	soft	soft	ADJ
ejpam-4275	450	8	pre	pre	ADJ
ejpam-4275	450	9	-	-	ADJ
ejpam-4275	450	10	continuous	continuous	ADJ
ejpam-4275	450	11	.	.	PUNCT
ejpam-4275	451	1	proof	proof	NOUN
ejpam-4275	451	2	.	.	PUNCT
ejpam-4275	452	1	straightforward	straightforward	ADJ
ejpam-4275	452	2	.	.	PUNCT
ejpam-4275	453	1	definition	definition	NOUN
ejpam-4275	453	2	22	22	NUM
ejpam-4275	453	3	.	.	PUNCT
ejpam-4275	454	1	a	a	DET
ejpam-4275	454	2	soft	soft	ADJ
ejpam-4275	454	3	map	map	NOUN
ejpam-4275	454	4	eτ	eτ	ADP
ejpam-4275	454	5	:	:	PUNCT
ejpam-4275	454	6	(	(	PUNCT
ejpam-4275	454	7	x	x	X
ejpam-4275	454	8	,	,	PUNCT
ejpam-4275	454	9	ξ	ξ	PROPN
ejpam-4275	454	10	,	,	PUNCT
ejpam-4275	454	11	σ	σ	NOUN
ejpam-4275	454	12	)	)	PUNCT
ejpam-4275	454	13	→	→	SYM
ejpam-4275	454	14	(	(	PUNCT
ejpam-4275	454	15	s	s	PROPN
ejpam-4275	454	16	,	,	PUNCT
ejpam-4275	454	17	π,∆	π,∆	NUM
ejpam-4275	454	18	)	)	PUNCT
ejpam-4275	454	19	is	be	AUX
ejpam-4275	454	20	said	say	VERB
ejpam-4275	454	21	to	to	PART
ejpam-4275	454	22	be	be	AUX
ejpam-4275	454	23	infra	infra	NOUN
ejpam-4275	454	24	soft	soft	ADJ
ejpam-4275	454	25	pre	pre	ADJ
ejpam-4275	454	26	-	-	ADJ
ejpam-4275	454	27	open	open	ADJ
ejpam-4275	454	28	(	(	PUNCT
ejpam-4275	454	29	resp	resp	NOUN
ejpam-4275	454	30	.	.	PUNCT
ejpam-4275	454	31	,	,	PUNCT
ejpam-4275	454	32	infra	infra	NOUN
ejpam-4275	454	33	soft	soft	ADJ
ejpam-4275	454	34	pre	pre	ADJ
ejpam-4275	454	35	-	-	ADJ
ejpam-4275	454	36	closed	closed	ADJ
ejpam-4275	454	37	)	)	PUNCT
ejpam-4275	454	38	if	if	SCONJ
ejpam-4275	454	39	the	the	DET
ejpam-4275	454	40	image	image	NOUN
ejpam-4275	454	41	of	of	ADP
ejpam-4275	454	42	each	each	DET
ejpam-4275	454	43	infra	infra	NOUN
ejpam-4275	454	44	soft	soft	ADJ
ejpam-4275	454	45	pre	pre	ADJ
ejpam-4275	454	46	-	-	ADJ
ejpam-4275	454	47	open	open	ADJ
ejpam-4275	454	48	(	(	PUNCT
ejpam-4275	454	49	resp	resp	NOUN
ejpam-4275	454	50	.	.	PUNCT
ejpam-4275	454	51	,	,	PUNCT
ejpam-4275	454	52	infra	infra	NOUN
ejpam-4275	454	53	soft	soft	ADJ
ejpam-4275	454	54	pre	pre	ADJ
ejpam-4275	454	55	-	-	ADJ
ejpam-4275	454	56	closed	closed	ADJ
ejpam-4275	454	57	)	)	PUNCT
ejpam-4275	454	58	set	set	NOUN
ejpam-4275	454	59	is	be	AUX
ejpam-4275	454	60	infra	infra	NOUN
ejpam-4275	454	61	soft	soft	ADJ
ejpam-4275	454	62	pre	pre	ADJ
ejpam-4275	454	63	-	-	ADJ
ejpam-4275	454	64	open	open	ADJ
ejpam-4275	454	65	(	(	PUNCT
ejpam-4275	454	66	resp	resp	NOUN
ejpam-4275	454	67	.	.	PUNCT
ejpam-4275	454	68	,	,	PUNCT
ejpam-4275	454	69	infra	infra	NOUN
ejpam-4275	454	70	soft	soft	ADJ
ejpam-4275	454	71	pre	pre	ADJ
ejpam-4275	454	72	-	-	ADJ
ejpam-4275	454	73	closed	closed	ADJ
ejpam-4275	454	74	)	)	PUNCT
ejpam-4275	454	75	.	.	PUNCT
ejpam-4275	455	1	proposition	proposition	NOUN
ejpam-4275	455	2	21	21	NUM
ejpam-4275	455	3	.	.	PUNCT
ejpam-4275	456	1	eτ	eτ	PROPN
ejpam-4275	456	2	:	:	PUNCT
ejpam-4275	456	3	(	(	PUNCT
ejpam-4275	456	4	x	x	X
ejpam-4275	456	5	,	,	PUNCT
ejpam-4275	456	6	ξ	ξ	PROPN
ejpam-4275	456	7	,	,	PUNCT
ejpam-4275	456	8	σ	σ	NOUN
ejpam-4275	456	9	)	)	PUNCT
ejpam-4275	456	10	→	→	SYM
ejpam-4275	456	11	(	(	PUNCT
ejpam-4275	456	12	s	s	PROPN
ejpam-4275	456	13	,	,	PUNCT
ejpam-4275	456	14	π,∆	π,∆	NUM
ejpam-4275	456	15	)	)	PUNCT
ejpam-4275	456	16	is	be	AUX
ejpam-4275	456	17	an	an	DET
ejpam-4275	456	18	infra	infra	NOUN
ejpam-4275	456	19	soft	soft	ADJ
ejpam-4275	456	20	pre	pre	ADJ
ejpam-4275	456	21	-	-	ADJ
ejpam-4275	456	22	open	open	ADJ
ejpam-4275	456	23	map	map	NOUN
ejpam-4275	456	24	iff	iff	PROPN
ejpam-4275	456	25	eτ	eτ	ADP
ejpam-4275	456	26	(	(	PUNCT
ejpam-4275	456	27	pint(ω	pint(ω	PROPN
ejpam-4275	456	28	,	,	PUNCT
ejpam-4275	456	29	σ	σ	PROPN
ejpam-4275	456	30	)	)	PUNCT
ejpam-4275	456	31	)	)	PUNCT
ejpam-4275	457	1	⊆̃pint(eτ	⊆̃pint(eτ	PROPN
ejpam-4275	457	2	(	(	PUNCT
ejpam-4275	457	3	ω	ω	PROPN
ejpam-4275	457	4	,	,	PUNCT
ejpam-4275	457	5	σ	σ	PROPN
ejpam-4275	457	6	)	)	PUNCT
ejpam-4275	457	7	)	)	PUNCT
ejpam-4275	457	8	for	for	ADP
ejpam-4275	457	9	each	each	DET
ejpam-4275	457	10	subset	subset	NOUN
ejpam-4275	457	11	of	of	ADP
ejpam-4275	457	12	(	(	PUNCT
ejpam-4275	457	13	ω	ω	PROPN
ejpam-4275	457	14	,	,	PUNCT
ejpam-4275	457	15	σ	σ	PROPN
ejpam-4275	457	16	)	)	PUNCT
ejpam-4275	457	17	of	of	ADP
ejpam-4275	457	18	x̃.	x̃.	ADJ
ejpam-4275	457	19	proof	proof	NOUN
ejpam-4275	457	20	.	.	PUNCT
ejpam-4275	458	1	⇒	⇒	NOUN
ejpam-4275	458	2	:	:	PUNCT
ejpam-4275	458	3	let	let	VERB
ejpam-4275	458	4	(	(	PUNCT
ejpam-4275	458	5	ω	ω	PROPN
ejpam-4275	458	6	,	,	PUNCT
ejpam-4275	458	7	σ	σ	PROPN
ejpam-4275	458	8	)	)	PUNCT
ejpam-4275	458	9	be	be	VERB
ejpam-4275	458	10	a	a	DET
ejpam-4275	458	11	subset	subset	NOUN
ejpam-4275	458	12	of	of	ADP
ejpam-4275	458	13	x̃.	x̃.	ADJ
ejpam-4275	458	14	now	now	ADV
ejpam-4275	458	15	,	,	PUNCT
ejpam-4275	458	16	eτ	eτ	PROPN
ejpam-4275	458	17	(	(	PUNCT
ejpam-4275	458	18	pint(ω	pint(ω	PROPN
ejpam-4275	458	19	,	,	PUNCT
ejpam-4275	458	20	σ))⊆̃eτ	σ))⊆̃eτ	PROPN
ejpam-4275	458	21	(	(	PUNCT
ejpam-4275	458	22	ω	ω	PROPN
ejpam-4275	458	23	,	,	PUNCT
ejpam-4275	458	24	σ	σ	NOUN
ejpam-4275	458	25	)	)	PUNCT
ejpam-4275	458	26	and	and	CCONJ
ejpam-4275	458	27	pint(ω	pint(ω	PROPN
ejpam-4275	458	28	,	,	PUNCT
ejpam-4275	458	29	σ	σ	PROPN
ejpam-4275	458	30	)	)	PUNCT
ejpam-4275	458	31	is	be	AUX
ejpam-4275	458	32	an	an	DET
ejpam-4275	458	33	infra	infra	NOUN
ejpam-4275	458	34	soft	soft	ADJ
ejpam-4275	458	35	pre	pre	ADJ
ejpam-4275	458	36	-	-	ADJ
ejpam-4275	458	37	open	open	ADJ
ejpam-4275	458	38	set	set	NOUN
ejpam-4275	458	39	.	.	PUNCT
ejpam-4275	459	1	by	by	ADP
ejpam-4275	459	2	hypothesis	hypothesis	NOUN
ejpam-4275	459	3	,	,	PUNCT
ejpam-4275	459	4	eτ	eτ	PROPN
ejpam-4275	459	5	(	(	PUNCT
ejpam-4275	459	6	pint(ω	pint(ω	PROPN
ejpam-4275	459	7	,	,	PUNCT
ejpam-4275	459	8	σ	σ	PROPN
ejpam-4275	459	9	)	)	PUNCT
ejpam-4275	459	10	)	)	PUNCT
ejpam-4275	459	11	is	be	AUX
ejpam-4275	459	12	infra	infra	NOUN
ejpam-4275	459	13	soft	soft	ADJ
ejpam-4275	459	14	pre	pre	ADJ
ejpam-4275	459	15	-	-	ADJ
ejpam-4275	459	16	open	open	ADJ
ejpam-4275	459	17	.	.	PUNCT
ejpam-4275	460	1	therefore	therefore	ADV
ejpam-4275	460	2	,	,	PUNCT
ejpam-4275	460	3	eτ	eτ	PROPN
ejpam-4275	460	4	(	(	PUNCT
ejpam-4275	460	5	pint(ω	pint(ω	PROPN
ejpam-4275	460	6	,	,	PUNCT
ejpam-4275	460	7	σ))⊆̃pint(eτ	σ))⊆̃pint(eτ	PROPN
ejpam-4275	460	8	(	(	PUNCT
ejpam-4275	460	9	ω	ω	PROPN
ejpam-4275	460	10	,	,	PUNCT
ejpam-4275	460	11	σ	σ	PROPN
ejpam-4275	460	12	)	)	PUNCT
ejpam-4275	460	13	)	)	PUNCT
ejpam-4275	460	14	.	.	PUNCT
ejpam-4275	461	1	⇐	⇐	ADJ
ejpam-4275	461	2	:	:	PUNCT
ejpam-4275	461	3	let	let	VERB
ejpam-4275	461	4	(	(	PUNCT
ejpam-4275	461	5	λ	λ	NOUN
ejpam-4275	461	6	,	,	PUNCT
ejpam-4275	461	7	σ	σ	PROPN
ejpam-4275	461	8	)	)	PUNCT
ejpam-4275	461	9	be	be	VERB
ejpam-4275	461	10	an	an	DET
ejpam-4275	461	11	infra	infra	NOUN
ejpam-4275	461	12	soft	soft	ADJ
ejpam-4275	461	13	open	open	ADJ
ejpam-4275	461	14	subset	subset	NOUN
ejpam-4275	461	15	of	of	ADP
ejpam-4275	461	16	x̃.	x̃.	PROPN
ejpam-4275	461	17	then	then	ADV
ejpam-4275	461	18	eτ	eτ	X
ejpam-4275	461	19	(	(	PUNCT
ejpam-4275	461	20	ω	ω	PROPN
ejpam-4275	461	21	,	,	PUNCT
ejpam-4275	461	22	σ)⊆̃pint(eτ	σ)⊆̃pint(eτ	PRON
ejpam-4275	461	23	(	(	PUNCT
ejpam-4275	461	24	ω	ω	PROPN
ejpam-4275	461	25	,	,	PUNCT
ejpam-4275	461	26	σ	σ	PROPN
ejpam-4275	461	27	)	)	PUNCT
ejpam-4275	461	28	)	)	PUNCT
ejpam-4275	461	29	.	.	PUNCT
ejpam-4275	462	1	therefore	therefore	ADV
ejpam-4275	462	2	,	,	PUNCT
ejpam-4275	462	3	eτ	eτ	PROPN
ejpam-4275	462	4	(	(	PUNCT
ejpam-4275	462	5	ω	ω	PROPN
ejpam-4275	462	6	,	,	PUNCT
ejpam-4275	462	7	σ	σ	NOUN
ejpam-4275	462	8	)	)	PUNCT
ejpam-4275	462	9	=	=	SYM
ejpam-4275	462	10	pint(eτ	pint(eτ	PROPN
ejpam-4275	462	11	(	(	PUNCT
ejpam-4275	462	12	ω	ω	PROPN
ejpam-4275	462	13	,	,	PUNCT
ejpam-4275	462	14	σ	σ	PROPN
ejpam-4275	462	15	)	)	PUNCT
ejpam-4275	462	16	)	)	PUNCT
ejpam-4275	462	17	which	which	PRON
ejpam-4275	462	18	means	mean	VERB
ejpam-4275	462	19	that	that	SCONJ
ejpam-4275	462	20	eτ	eτ	PROPN
ejpam-4275	462	21	is	be	AUX
ejpam-4275	462	22	an	an	DET
ejpam-4275	462	23	infra	infra	NOUN
ejpam-4275	462	24	soft	soft	ADJ
ejpam-4275	462	25	pre	pre	ADJ
ejpam-4275	462	26	-	-	ADJ
ejpam-4275	462	27	open	open	ADJ
ejpam-4275	462	28	map	map	NOUN
ejpam-4275	462	29	.	.	PUNCT
ejpam-4275	463	1	proposition	proposition	NOUN
ejpam-4275	463	2	22	22	NUM
ejpam-4275	463	3	.	.	PUNCT
ejpam-4275	464	1	eτ	eτ	PUNCT
ejpam-4275	464	2	:	:	PUNCT
ejpam-4275	464	3	(	(	PUNCT
ejpam-4275	464	4	x	x	X
ejpam-4275	464	5	,	,	PUNCT
ejpam-4275	464	6	ξ	ξ	PROPN
ejpam-4275	464	7	,	,	PUNCT
ejpam-4275	464	8	σ	σ	NOUN
ejpam-4275	464	9	)	)	PUNCT
ejpam-4275	464	10	→	→	SYM
ejpam-4275	464	11	(	(	PUNCT
ejpam-4275	464	12	s	s	PROPN
ejpam-4275	464	13	,	,	PUNCT
ejpam-4275	464	14	π,∆	π,∆	NUM
ejpam-4275	464	15	)	)	PUNCT
ejpam-4275	464	16	is	be	AUX
ejpam-4275	464	17	an	an	DET
ejpam-4275	464	18	infra	infra	NOUN
ejpam-4275	464	19	soft	soft	ADJ
ejpam-4275	464	20	pre	pre	ADJ
ejpam-4275	464	21	-	-	ADJ
ejpam-4275	464	22	closed	closed	ADJ
ejpam-4275	464	23	map	map	NOUN
ejpam-4275	464	24	iff	iff	PROPN
ejpam-4275	464	25	pcl(eτ	pcl(eτ	ADJ
ejpam-4275	464	26	(	(	PUNCT
ejpam-4275	464	27	ω	ω	PROPN
ejpam-4275	464	28	,	,	PUNCT
ejpam-4275	464	29	σ	σ	PROPN
ejpam-4275	464	30	)	)	PUNCT
ejpam-4275	464	31	)	)	PUNCT
ejpam-4275	465	1	⊆̃eτ	⊆̃eτ	NOUN
ejpam-4275	465	2	(	(	PUNCT
ejpam-4275	465	3	pcl(ω	pcl(ω	PROPN
ejpam-4275	465	4	,	,	PUNCT
ejpam-4275	465	5	σ	σ	PROPN
ejpam-4275	465	6	)	)	PUNCT
ejpam-4275	465	7	)	)	PUNCT
ejpam-4275	465	8	for	for	ADP
ejpam-4275	465	9	each	each	DET
ejpam-4275	465	10	subset	subset	NOUN
ejpam-4275	465	11	(	(	PUNCT
ejpam-4275	465	12	ω	ω	PROPN
ejpam-4275	465	13	,	,	PUNCT
ejpam-4275	465	14	σ	σ	PROPN
ejpam-4275	465	15	)	)	PUNCT
ejpam-4275	465	16	of	of	ADP
ejpam-4275	465	17	x̃.	x̃.	ADJ
ejpam-4275	465	18	proof	proof	NOUN
ejpam-4275	465	19	.	.	PUNCT
ejpam-4275	466	1	⇒	⇒	NOUN
ejpam-4275	466	2	:	:	PUNCT
ejpam-4275	466	3	let	let	VERB
ejpam-4275	466	4	eτ	eτ	PART
ejpam-4275	466	5	be	be	AUX
ejpam-4275	466	6	an	an	DET
ejpam-4275	466	7	infra	infra	NOUN
ejpam-4275	466	8	soft	soft	ADJ
ejpam-4275	466	9	pre	pre	ADJ
ejpam-4275	466	10	-	-	ADJ
ejpam-4275	466	11	closed	closed	ADJ
ejpam-4275	466	12	map	map	NOUN
ejpam-4275	466	13	and	and	CCONJ
ejpam-4275	466	14	(	(	PUNCT
ejpam-4275	466	15	ω	ω	PROPN
ejpam-4275	466	16	,	,	PUNCT
ejpam-4275	466	17	σ	σ	PROPN
ejpam-4275	466	18	)	)	PUNCT
ejpam-4275	466	19	be	be	VERB
ejpam-4275	466	20	a	a	DET
ejpam-4275	466	21	subset	subset	NOUN
ejpam-4275	466	22	of	of	ADP
ejpam-4275	466	23	x̃.	x̃.	ADJ
ejpam-4275	466	24	by	by	ADP
ejpam-4275	466	25	hypothesis	hypothesis	NOUN
ejpam-4275	466	26	,	,	PUNCT
ejpam-4275	466	27	eτ	eτ	PROPN
ejpam-4275	466	28	(	(	PUNCT
ejpam-4275	466	29	pcl(ω	pcl(ω	PROPN
ejpam-4275	466	30	,	,	PUNCT
ejpam-4275	466	31	σ	σ	PROPN
ejpam-4275	466	32	)	)	PUNCT
ejpam-4275	466	33	)	)	PUNCT
ejpam-4275	466	34	is	be	AUX
ejpam-4275	466	35	infra	infra	NOUN
ejpam-4275	466	36	soft	soft	ADJ
ejpam-4275	466	37	pre	pre	ADJ
ejpam-4275	466	38	-	-	ADJ
ejpam-4275	466	39	closed	closed	ADJ
ejpam-4275	466	40	.	.	PUNCT
ejpam-4275	467	1	since	since	SCONJ
ejpam-4275	467	2	eτ	eτ	PROPN
ejpam-4275	467	3	(	(	PUNCT
ejpam-4275	467	4	ω	ω	PROPN
ejpam-4275	467	5	,	,	PUNCT
ejpam-4275	467	6	σ)⊆̃eτ	σ)⊆̃eτ	PROPN
ejpam-4275	467	7	(	(	PUNCT
ejpam-4275	467	8	pcl(ω	pcl(ω	PROPN
ejpam-4275	467	9	,	,	PUNCT
ejpam-4275	467	10	σ	σ	PROPN
ejpam-4275	467	11	)	)	PUNCT
ejpam-4275	467	12	)	)	PUNCT
ejpam-4275	467	13	,	,	PUNCT
ejpam-4275	467	14	pcl(eτ	pcl(eτ	X
ejpam-4275	467	15	(	(	PUNCT
ejpam-4275	467	16	ω	ω	PROPN
ejpam-4275	467	17	,	,	PUNCT
ejpam-4275	467	18	σ	σ	PROPN
ejpam-4275	467	19	)	)	PUNCT
ejpam-4275	467	20	)	)	PUNCT
ejpam-4275	467	21	⊆̃eτ	⊆̃eτ	NOUN
ejpam-4275	467	22	(	(	PUNCT
ejpam-4275	467	23	pcl(ω	pcl(ω	PROPN
ejpam-4275	467	24	,	,	PUNCT
ejpam-4275	467	25	σ	σ	PROPN
ejpam-4275	467	26	)	)	PUNCT
ejpam-4275	467	27	)	)	PUNCT
ejpam-4275	467	28	.	.	PUNCT
ejpam-4275	468	1	⇐	⇐	ADJ
ejpam-4275	468	2	:	:	PUNCT
ejpam-4275	468	3	suppose	suppose	VERB
ejpam-4275	468	4	that	that	SCONJ
ejpam-4275	468	5	(	(	PUNCT
ejpam-4275	468	6	ω	ω	PROPN
ejpam-4275	468	7	,	,	PUNCT
ejpam-4275	468	8	σ	σ	PROPN
ejpam-4275	468	9	)	)	PUNCT
ejpam-4275	468	10	is	be	AUX
ejpam-4275	468	11	an	an	DET
ejpam-4275	468	12	infra	infra	NOUN
ejpam-4275	468	13	soft	soft	ADJ
ejpam-4275	468	14	pre	pre	ADJ
ejpam-4275	468	15	-	-	ADJ
ejpam-4275	468	16	closed	closed	ADJ
ejpam-4275	468	17	subset	subset	NOUN
ejpam-4275	468	18	of	of	ADP
ejpam-4275	468	19	x̃.	x̃.	ADJ
ejpam-4275	468	20	by	by	ADP
ejpam-4275	468	21	hypothesis	hypothesis	NOUN
ejpam-4275	468	22	,	,	PUNCT
ejpam-4275	468	23	eτ	eτ	PROPN
ejpam-4275	468	24	(	(	PUNCT
ejpam-4275	468	25	ω	ω	PROPN
ejpam-4275	468	26	,	,	PUNCT
ejpam-4275	468	27	σ)⊆̃	σ)⊆̃	X
ejpam-4275	468	28	pcl(eτ	pcl(eτ	ADJ
ejpam-4275	468	29	(	(	PUNCT
ejpam-4275	468	30	ω	ω	NOUN
ejpam-4275	468	31	,	,	PUNCT
ejpam-4275	468	32	σ))⊆̃eτ	σ))⊆̃eτ	PROPN
ejpam-4275	468	33	(	(	PUNCT
ejpam-4275	468	34	pcl(ω	pcl(ω	PROPN
ejpam-4275	468	35	,	,	PUNCT
ejpam-4275	468	36	σ	σ	NOUN
ejpam-4275	468	37	)	)	PUNCT
ejpam-4275	468	38	)	)	PUNCT
ejpam-4275	469	1	=	=	SYM
ejpam-4275	469	2	eτ	eτ	PROPN
ejpam-4275	469	3	(	(	PUNCT
ejpam-4275	469	4	ω	ω	PROPN
ejpam-4275	469	5	,	,	PUNCT
ejpam-4275	469	6	σ	σ	PROPN
ejpam-4275	469	7	)	)	PUNCT
ejpam-4275	469	8	.	.	PUNCT
ejpam-4275	470	1	therefore	therefore	ADV
ejpam-4275	470	2	,	,	PUNCT
ejpam-4275	470	3	eτ	eτ	PROPN
ejpam-4275	470	4	(	(	PUNCT
ejpam-4275	470	5	ω	ω	PROPN
ejpam-4275	470	6	,	,	PUNCT
ejpam-4275	470	7	σ	σ	PROPN
ejpam-4275	470	8	)	)	PUNCT
ejpam-4275	470	9	is	be	AUX
ejpam-4275	470	10	infra	infra	NOUN
ejpam-4275	470	11	soft	soft	ADJ
ejpam-4275	470	12	pre	pre	ADJ
ejpam-4275	470	13	-	-	ADJ
ejpam-4275	470	14	closed	closed	ADJ
ejpam-4275	470	15	.	.	PUNCT
ejpam-4275	471	1	hence	hence	ADV
ejpam-4275	471	2	,	,	PUNCT
ejpam-4275	471	3	eτ	eτ	ADV
ejpam-4275	471	4	is	be	AUX
ejpam-4275	471	5	an	an	DET
ejpam-4275	471	6	infra	infra	NOUN
ejpam-4275	471	7	soft	soft	ADJ
ejpam-4275	471	8	pre	pre	ADJ
ejpam-4275	471	9	-	-	ADJ
ejpam-4275	471	10	closed	closed	ADJ
ejpam-4275	471	11	map	map	NOUN
ejpam-4275	471	12	.	.	PUNCT
ejpam-4275	472	1	proposition	proposition	NOUN
ejpam-4275	472	2	23	23	NUM
ejpam-4275	472	3	.	.	PUNCT
ejpam-4275	473	1	the	the	DET
ejpam-4275	473	2	concepts	concept	NOUN
ejpam-4275	473	3	of	of	ADP
ejpam-4275	473	4	infra	infra	NOUN
ejpam-4275	473	5	soft	soft	ADJ
ejpam-4275	473	6	pre	pre	ADJ
ejpam-4275	473	7	-	-	ADJ
ejpam-4275	473	8	open	open	ADJ
ejpam-4275	473	9	and	and	CCONJ
ejpam-4275	473	10	infra	infra	VERB
ejpam-4275	473	11	soft	soft	ADJ
ejpam-4275	473	12	pre	pre	ADJ
ejpam-4275	473	13	-	-	ADJ
ejpam-4275	473	14	closed	closed	ADJ
ejpam-4275	473	15	maps	map	NOUN
ejpam-4275	473	16	are	be	AUX
ejpam-4275	473	17	equivalent	equivalent	ADJ
ejpam-4275	473	18	under	under	ADP
ejpam-4275	473	19	bijectiveness	bijectiveness	ADV
ejpam-4275	473	20	.	.	PUNCT
ejpam-4275	474	1	proof	proof	NOUN
ejpam-4275	474	2	.	.	PUNCT
ejpam-4275	475	1	it	it	PRON
ejpam-4275	475	2	comes	come	VERB
ejpam-4275	475	3	from	from	ADP
ejpam-4275	475	4	the	the	DET
ejpam-4275	475	5	fact	fact	NOUN
ejpam-4275	475	6	that	that	SCONJ
ejpam-4275	475	7	a	a	DET
ejpam-4275	475	8	bijective	bijective	ADJ
ejpam-4275	475	9	soft	soft	ADJ
ejpam-4275	475	10	map	map	NOUN
ejpam-4275	475	11	eτ	eτ	ADP
ejpam-4275	475	12	:	:	PUNCT
ejpam-4275	475	13	(	(	PUNCT
ejpam-4275	475	14	x	x	X
ejpam-4275	475	15	,	,	PUNCT
ejpam-4275	475	16	ξ	ξ	PROPN
ejpam-4275	475	17	,	,	PUNCT
ejpam-4275	475	18	σ	σ	NOUN
ejpam-4275	475	19	)	)	PUNCT
ejpam-4275	475	20	→	→	SYM
ejpam-4275	475	21	(	(	PUNCT
ejpam-4275	475	22	s	s	PROPN
ejpam-4275	475	23	,	,	PUNCT
ejpam-4275	475	24	π,∆	π,∆	NUM
ejpam-4275	475	25	)	)	PUNCT
ejpam-4275	475	26	implies	imply	VERB
ejpam-4275	475	27	that	that	SCONJ
ejpam-4275	475	28	eτ	eτ	PROPN
ejpam-4275	475	29	(	(	PUNCT
ejpam-4275	475	30	ω	ω	PROPN
ejpam-4275	475	31	c	c	PROPN
ejpam-4275	475	32	,	,	PUNCT
ejpam-4275	475	33	σ	σ	PROPN
ejpam-4275	475	34	)	)	PUNCT
ejpam-4275	475	35	=	=	SYM
ejpam-4275	475	36	(	(	PUNCT
ejpam-4275	475	37	eτ	eτ	X
ejpam-4275	475	38	(	(	PUNCT
ejpam-4275	475	39	ω	ω	PROPN
ejpam-4275	475	40	,	,	PUNCT
ejpam-4275	475	41	σ	σ	PROPN
ejpam-4275	475	42	)	)	PUNCT
ejpam-4275	475	43	)	)	PUNCT
ejpam-4275	475	44	c.	c.	NOUN
ejpam-4275	475	45	proposition	proposition	NOUN
ejpam-4275	475	46	24	24	NUM
ejpam-4275	475	47	.	.	PUNCT
ejpam-4275	476	1	let	let	VERB
ejpam-4275	476	2	eτ	eτ	VERB
ejpam-4275	476	3	:	:	PUNCT
ejpam-4275	476	4	(	(	PUNCT
ejpam-4275	476	5	x	x	X
ejpam-4275	476	6	,	,	PUNCT
ejpam-4275	476	7	ξ	ξ	PROPN
ejpam-4275	476	8	,	,	PUNCT
ejpam-4275	476	9	σ	σ	NOUN
ejpam-4275	476	10	)	)	PUNCT
ejpam-4275	476	11	→	→	SYM
ejpam-4275	476	12	(	(	PUNCT
ejpam-4275	476	13	s	s	PROPN
ejpam-4275	476	14	,	,	PUNCT
ejpam-4275	476	15	π,∆	π,∆	NUM
ejpam-4275	476	16	)	)	PUNCT
ejpam-4275	476	17	and	and	CCONJ
ejpam-4275	476	18	fν	fν	INTJ
ejpam-4275	476	19	:	:	PUNCT
ejpam-4275	476	20	(	(	PUNCT
ejpam-4275	476	21	s	s	X
ejpam-4275	476	22	,	,	PUNCT
ejpam-4275	476	23	π,∆	π,∆	NUM
ejpam-4275	476	24	)	)	PUNCT
ejpam-4275	476	25	→	→	SYM
ejpam-4275	476	26	(	(	PUNCT
ejpam-4275	476	27	v	v	NOUN
ejpam-4275	476	28	,	,	PUNCT
ejpam-4275	476	29	σ	σ	PROPN
ejpam-4275	476	30	,	,	PUNCT
ejpam-4275	476	31	γ	γ	PROPN
ejpam-4275	476	32	)	)	PUNCT
ejpam-4275	476	33	be	be	VERB
ejpam-4275	476	34	two	two	NUM
ejpam-4275	476	35	soft	soft	ADJ
ejpam-4275	476	36	maps	map	NOUN
ejpam-4275	476	37	.	.	PUNCT
ejpam-4275	477	1	then	then	ADV
ejpam-4275	477	2	:	:	PUNCT
ejpam-4275	477	3	(	(	PUNCT
ejpam-4275	477	4	i	i	NOUN
ejpam-4275	477	5	)	)	PUNCT
ejpam-4275	477	6	if	if	SCONJ
ejpam-4275	477	7	eτ	eτ	PROPN
ejpam-4275	477	8	and	and	CCONJ
ejpam-4275	477	9	fν	fν	NOUN
ejpam-4275	477	10	are	be	AUX
ejpam-4275	477	11	infra	infra	NOUN
ejpam-4275	477	12	soft	soft	ADJ
ejpam-4275	477	13	pre	pre	ADJ
ejpam-4275	477	14	-	-	ADJ
ejpam-4275	477	15	open	open	ADJ
ejpam-4275	477	16	maps	map	NOUN
ejpam-4275	477	17	,	,	PUNCT
ejpam-4275	477	18	then	then	ADV
ejpam-4275	477	19	fν	fν	VERB
ejpam-4275	477	20	◦	◦	NOUN
ejpam-4275	477	21	eτ	eτ	NOUN
ejpam-4275	477	22	is	be	AUX
ejpam-4275	477	23	an	an	DET
ejpam-4275	477	24	infra	infra	NOUN
ejpam-4275	477	25	soft	soft	ADJ
ejpam-4275	477	26	pre	pre	ADJ
ejpam-4275	477	27	-	-	ADJ
ejpam-4275	477	28	open	open	ADJ
ejpam-4275	477	29	map	map	NOUN
ejpam-4275	477	30	.	.	PUNCT
ejpam-4275	478	1	(	(	PUNCT
ejpam-4275	478	2	ii	ii	NOUN
ejpam-4275	478	3	)	)	PUNCT
ejpam-4275	478	4	if	if	SCONJ
ejpam-4275	478	5	fν	fν	NOUN
ejpam-4275	478	6	◦	◦	NOUN
ejpam-4275	478	7	eτ	eτ	NOUN
ejpam-4275	478	8	is	be	AUX
ejpam-4275	478	9	an	an	DET
ejpam-4275	478	10	infra	infra	NOUN
ejpam-4275	478	11	soft	soft	ADJ
ejpam-4275	478	12	pre	pre	ADJ
ejpam-4275	478	13	-	-	ADJ
ejpam-4275	478	14	open	open	ADJ
ejpam-4275	478	15	map	map	NOUN
ejpam-4275	478	16	and	and	CCONJ
ejpam-4275	478	17	eτ	eτ	NOUN
ejpam-4275	478	18	is	be	AUX
ejpam-4275	478	19	a	a	DET
ejpam-4275	478	20	surjective	surjective	ADJ
ejpam-4275	478	21	infra	infra	NOUN
ejpam-4275	478	22	soft	soft	ADJ
ejpam-4275	478	23	pre	pre	ADJ
ejpam-4275	478	24	-	-	ADJ
ejpam-4275	478	25	continuous	continuous	ADJ
ejpam-4275	478	26	map	map	NOUN
ejpam-4275	478	27	,	,	PUNCT
ejpam-4275	478	28	then	then	ADV
ejpam-4275	478	29	fν	fν	NOUN
ejpam-4275	478	30	is	be	AUX
ejpam-4275	478	31	an	an	DET
ejpam-4275	478	32	infra	infra	NOUN
ejpam-4275	478	33	soft	soft	ADJ
ejpam-4275	478	34	pre	pre	ADJ
ejpam-4275	478	35	-	-	ADJ
ejpam-4275	478	36	open	open	ADJ
ejpam-4275	478	37	map	map	NOUN
ejpam-4275	478	38	.	.	PUNCT
ejpam-4275	479	1	t.m	t.m	PROPN
ejpam-4275	479	2	.	.	PUNCT
ejpam-4275	479	3	al	al	PROPN
ejpam-4275	479	4	-	-	PUNCT
ejpam-4275	479	5	shami	shami	PROPN
ejpam-4275	479	6	,	,	PUNCT
ejpam-4275	479	7	h.a	h.a	PROPN
ejpam-4275	479	8	.	.	PROPN
ejpam-4275	479	9	othman	othman	PROPN
ejpam-4275	479	10	/	/	SYM
ejpam-4275	479	11	eur	eur	PROPN
ejpam-4275	479	12	.	.	PUNCT
ejpam-4275	480	1	j.	j.	PROPN
ejpam-4275	480	2	pure	pure	PROPN
ejpam-4275	480	3	appl	appl	PROPN
ejpam-4275	480	4	.	.	PROPN
ejpam-4275	480	5	math	math	PROPN
ejpam-4275	480	6	,	,	PUNCT
ejpam-4275	480	7	15	15	NUM
ejpam-4275	480	8	(	(	PUNCT
ejpam-4275	480	9	1	1	NUM
ejpam-4275	480	10	)	)	PUNCT
ejpam-4275	480	11	(	(	PUNCT
ejpam-4275	480	12	2022	2022	NUM
ejpam-4275	480	13	)	)	PUNCT
ejpam-4275	480	14	,	,	PUNCT
ejpam-4275	480	15	261	261	NUM
ejpam-4275	480	16	-	-	SYM
ejpam-4275	480	17	280	280	NUM
ejpam-4275	480	18	275	275	NUM
ejpam-4275	480	19	(	(	PUNCT
ejpam-4275	480	20	iii	iii	NOUN
ejpam-4275	480	21	)	)	PUNCT
ejpam-4275	480	22	if	if	SCONJ
ejpam-4275	480	23	fν	fν	NOUN
ejpam-4275	480	24	◦	◦	NOUN
ejpam-4275	480	25	eτ	eτ	NOUN
ejpam-4275	480	26	is	be	AUX
ejpam-4275	480	27	an	an	DET
ejpam-4275	480	28	infra	infra	NOUN
ejpam-4275	480	29	soft	soft	ADJ
ejpam-4275	480	30	pre	pre	ADJ
ejpam-4275	480	31	-	-	ADJ
ejpam-4275	480	32	open	open	ADJ
ejpam-4275	480	33	map	map	NOUN
ejpam-4275	480	34	and	and	CCONJ
ejpam-4275	480	35	fν	fν	NOUN
ejpam-4275	480	36	is	be	AUX
ejpam-4275	480	37	an	an	DET
ejpam-4275	480	38	injective	injective	ADJ
ejpam-4275	480	39	infra	infra	NOUN
ejpam-4275	480	40	soft	soft	ADJ
ejpam-4275	480	41	pre	pre	ADJ
ejpam-4275	480	42	-	-	ADJ
ejpam-4275	480	43	continuous	continuous	ADJ
ejpam-4275	480	44	map	map	NOUN
ejpam-4275	480	45	,	,	PUNCT
ejpam-4275	480	46	then	then	ADV
ejpam-4275	480	47	eτ	eτ	PROPN
ejpam-4275	480	48	is	be	AUX
ejpam-4275	480	49	an	an	DET
ejpam-4275	480	50	infra	infra	NOUN
ejpam-4275	480	51	soft	soft	ADJ
ejpam-4275	480	52	pre	pre	ADJ
ejpam-4275	480	53	-	-	ADJ
ejpam-4275	480	54	open	open	ADJ
ejpam-4275	480	55	map	map	NOUN
ejpam-4275	480	56	.	.	PUNCT
ejpam-4275	481	1	proof	proof	NOUN
ejpam-4275	481	2	.	.	PUNCT
ejpam-4275	482	1	(	(	PUNCT
ejpam-4275	482	2	i	i	NOUN
ejpam-4275	482	3	)	)	PUNCT
ejpam-4275	482	4	straightforward	straightforward	VERB
ejpam-4275	482	5	.	.	PUNCT
ejpam-4275	483	1	(	(	PUNCT
ejpam-4275	483	2	ii	ii	NOUN
ejpam-4275	483	3	)	)	PUNCT
ejpam-4275	483	4	consider	consider	VERB
ejpam-4275	483	5	(	(	PUNCT
ejpam-4275	483	6	ω,∆	ω,∆	PROPN
ejpam-4275	483	7	)	)	PUNCT
ejpam-4275	483	8	as	as	ADP
ejpam-4275	483	9	an	an	DET
ejpam-4275	483	10	infra	infra	NOUN
ejpam-4275	483	11	soft	soft	ADJ
ejpam-4275	483	12	pre	pre	ADJ
ejpam-4275	483	13	-	-	ADJ
ejpam-4275	483	14	open	open	ADJ
ejpam-4275	483	15	subset	subset	NOUN
ejpam-4275	483	16	of	of	ADP
ejpam-4275	483	17	(	(	PUNCT
ejpam-4275	483	18	s	s	PROPN
ejpam-4275	483	19	,	,	PUNCT
ejpam-4275	483	20	π,∆	π,∆	NUM
ejpam-4275	483	21	)	)	PUNCT
ejpam-4275	483	22	.	.	PUNCT
ejpam-4275	484	1	by	by	ADP
ejpam-4275	484	2	hypothesis	hypothesis	NOUN
ejpam-4275	484	3	,	,	PUNCT
ejpam-4275	484	4	e−1	e−1	PROPN
ejpam-4275	484	5	τ	τ	X
ejpam-4275	484	6	(	(	PUNCT
ejpam-4275	484	7	ω,∆	ω,∆	PROPN
ejpam-4275	484	8	)	)	PUNCT
ejpam-4275	484	9	is	be	AUX
ejpam-4275	484	10	an	an	DET
ejpam-4275	484	11	infra	infra	NOUN
ejpam-4275	484	12	soft	soft	ADJ
ejpam-4275	484	13	pre	pre	ADJ
ejpam-4275	484	14	-	-	ADJ
ejpam-4275	484	15	open	open	ADJ
ejpam-4275	484	16	subset	subset	NOUN
ejpam-4275	484	17	of	of	ADP
ejpam-4275	484	18	(	(	PUNCT
ejpam-4275	484	19	x	x	NOUN
ejpam-4275	484	20	,	,	PUNCT
ejpam-4275	484	21	ξ	ξ	PROPN
ejpam-4275	484	22	,	,	PUNCT
ejpam-4275	484	23	σ	σ	NOUN
ejpam-4275	484	24	)	)	PUNCT
ejpam-4275	484	25	.	.	PUNCT
ejpam-4275	485	1	again	again	ADV
ejpam-4275	485	2	,	,	PUNCT
ejpam-4275	485	3	by	by	ADP
ejpam-4275	485	4	hypothesis	hypothesis	NOUN
ejpam-4275	485	5	,	,	PUNCT
ejpam-4275	485	6	(	(	PUNCT
ejpam-4275	485	7	fν	fν	NOUN
ejpam-4275	485	8	◦	◦	NOUN
ejpam-4275	485	9	eτ	eτ	NOUN
ejpam-4275	485	10	)	)	PUNCT
ejpam-4275	485	11	(	(	PUNCT
ejpam-4275	485	12	e	e	X
ejpam-4275	485	13	−1	−1	PRON
ejpam-4275	485	14	τ	τ	X
ejpam-4275	485	15	(	(	PUNCT
ejpam-4275	485	16	ω,∆	ω,∆	PROPN
ejpam-4275	485	17	)	)	PUNCT
ejpam-4275	485	18	)	)	PUNCT
ejpam-4275	485	19	is	be	AUX
ejpam-4275	485	20	an	an	DET
ejpam-4275	485	21	infra	infra	NOUN
ejpam-4275	485	22	soft	soft	ADJ
ejpam-4275	485	23	pre	pre	ADJ
ejpam-4275	485	24	-	-	ADJ
ejpam-4275	485	25	open	open	ADJ
ejpam-4275	485	26	subset	subset	NOUN
ejpam-4275	485	27	of	of	ADP
ejpam-4275	485	28	(	(	PUNCT
ejpam-4275	485	29	v	v	PROPN
ejpam-4275	485	30	,	,	PUNCT
ejpam-4275	485	31	σ	σ	PROPN
ejpam-4275	485	32	,	,	PUNCT
ejpam-4275	485	33	γ	γ	NOUN
ejpam-4275	485	34	)	)	PUNCT
ejpam-4275	485	35	.	.	PUNCT
ejpam-4275	486	1	since	since	SCONJ
ejpam-4275	486	2	eτ	eτ	PROPN
ejpam-4275	486	3	is	be	AUX
ejpam-4275	486	4	surjective	surjective	ADJ
ejpam-4275	486	5	,	,	PUNCT
ejpam-4275	486	6	then	then	ADV
ejpam-4275	486	7	(	(	PUNCT
ejpam-4275	486	8	fν	fν	NOUN
ejpam-4275	486	9	◦	◦	NOUN
ejpam-4275	486	10	eτ	eτ	PROPN
ejpam-4275	486	11	)	)	PUNCT
ejpam-4275	486	12	(	(	PUNCT
ejpam-4275	486	13	e	e	X
ejpam-4275	486	14	−1	−1	PRON
ejpam-4275	486	15	τ	τ	X
ejpam-4275	486	16	(	(	PUNCT
ejpam-4275	486	17	ω,∆	ω,∆	PROPN
ejpam-4275	486	18	)	)	PUNCT
ejpam-4275	486	19	)	)	PUNCT
ejpam-4275	487	1	=	=	PRON
ejpam-4275	487	2	fν(eτ	fν(eτ	PROPN
ejpam-4275	487	3	(	(	PUNCT
ejpam-4275	487	4	e	e	NOUN
ejpam-4275	487	5	−1	−1	PRON
ejpam-4275	487	6	τ	τ	X
ejpam-4275	487	7	(	(	PUNCT
ejpam-4275	487	8	ω,∆	ω,∆	PROPN
ejpam-4275	487	9	)	)	PUNCT
ejpam-4275	487	10	)	)	PUNCT
ejpam-4275	487	11	)	)	PUNCT
ejpam-4275	488	1	=	=	PUNCT
ejpam-4275	488	2	fν(ω,∆	fν(ω,∆	NOUN
ejpam-4275	488	3	)	)	PUNCT
ejpam-4275	488	4	.	.	PUNCT
ejpam-4275	489	1	hence	hence	ADV
ejpam-4275	489	2	,	,	PUNCT
ejpam-4275	489	3	fν	fν	NOUN
ejpam-4275	489	4	is	be	AUX
ejpam-4275	489	5	an	an	DET
ejpam-4275	489	6	infra	infra	NOUN
ejpam-4275	489	7	soft	soft	ADJ
ejpam-4275	489	8	preopen	preopen	ADJ
ejpam-4275	489	9	map	map	NOUN
ejpam-4275	489	10	.	.	PUNCT
ejpam-4275	490	1	(	(	PUNCT
ejpam-4275	490	2	iii	iii	NOUN
ejpam-4275	490	3	)	)	PUNCT
ejpam-4275	490	4	consider	consider	VERB
ejpam-4275	490	5	(	(	PUNCT
ejpam-4275	490	6	ω	ω	PROPN
ejpam-4275	490	7	,	,	PUNCT
ejpam-4275	490	8	σ	σ	PROPN
ejpam-4275	490	9	)	)	PUNCT
ejpam-4275	490	10	as	as	ADP
ejpam-4275	490	11	an	an	DET
ejpam-4275	490	12	infra	infra	NOUN
ejpam-4275	490	13	soft	soft	ADJ
ejpam-4275	490	14	pre	pre	ADJ
ejpam-4275	490	15	-	-	ADJ
ejpam-4275	490	16	open	open	ADJ
ejpam-4275	490	17	subset	subset	NOUN
ejpam-4275	490	18	of	of	ADP
ejpam-4275	490	19	(	(	PUNCT
ejpam-4275	490	20	x	x	NOUN
ejpam-4275	490	21	,	,	PUNCT
ejpam-4275	490	22	ξ	ξ	PROPN
ejpam-4275	490	23	,	,	PUNCT
ejpam-4275	490	24	σ	σ	NOUN
ejpam-4275	490	25	)	)	PUNCT
ejpam-4275	490	26	.	.	PUNCT
ejpam-4275	491	1	by	by	ADP
ejpam-4275	491	2	hypothesis	hypothesis	NOUN
ejpam-4275	491	3	,	,	PUNCT
ejpam-4275	491	4	(	(	PUNCT
ejpam-4275	491	5	fν	fν	NOUN
ejpam-4275	491	6	◦	◦	NOUN
ejpam-4275	491	7	eτ	eτ	PROPN
ejpam-4275	491	8	)	)	PUNCT
ejpam-4275	491	9	(	(	PUNCT
ejpam-4275	491	10	ω	ω	PROPN
ejpam-4275	491	11	,	,	PUNCT
ejpam-4275	491	12	σ	σ	PROPN
ejpam-4275	491	13	)	)	PUNCT
ejpam-4275	491	14	is	be	AUX
ejpam-4275	491	15	an	an	DET
ejpam-4275	491	16	infra	infra	NOUN
ejpam-4275	491	17	soft	soft	ADJ
ejpam-4275	491	18	pre	pre	ADJ
ejpam-4275	491	19	-	-	ADJ
ejpam-4275	491	20	open	open	ADJ
ejpam-4275	491	21	subset	subset	NOUN
ejpam-4275	491	22	of	of	ADP
ejpam-4275	491	23	(	(	PUNCT
ejpam-4275	491	24	v	v	PROPN
ejpam-4275	491	25	,	,	PUNCT
ejpam-4275	491	26	σ	σ	PROPN
ejpam-4275	491	27	,	,	PUNCT
ejpam-4275	491	28	γ	γ	NOUN
ejpam-4275	491	29	)	)	PUNCT
ejpam-4275	491	30	.	.	PUNCT
ejpam-4275	492	1	again	again	ADV
ejpam-4275	492	2	,	,	PUNCT
ejpam-4275	492	3	by	by	ADP
ejpam-4275	492	4	hypothesis	hypothesis	NOUN
ejpam-4275	492	5	,	,	PUNCT
ejpam-4275	492	6	f−1	f−1	PROPN
ejpam-4275	492	7	ν	ν	X
ejpam-4275	492	8	(	(	PUNCT
ejpam-4275	492	9	fν	fν	NOUN
ejpam-4275	492	10	◦	◦	NOUN
ejpam-4275	492	11	eτ	eτ	PROPN
ejpam-4275	492	12	(	(	PUNCT
ejpam-4275	492	13	ω	ω	PROPN
ejpam-4275	492	14	,	,	PUNCT
ejpam-4275	492	15	σ	σ	PROPN
ejpam-4275	492	16	)	)	PUNCT
ejpam-4275	492	17	)	)	PUNCT
ejpam-4275	492	18	is	be	AUX
ejpam-4275	492	19	an	an	DET
ejpam-4275	492	20	infra	infra	NOUN
ejpam-4275	492	21	soft	soft	ADJ
ejpam-4275	492	22	pre	pre	ADJ
ejpam-4275	492	23	-	-	ADJ
ejpam-4275	492	24	open	open	ADJ
ejpam-4275	492	25	subset	subset	NOUN
ejpam-4275	492	26	of	of	ADP
ejpam-4275	492	27	(	(	PUNCT
ejpam-4275	492	28	s	s	PROPN
ejpam-4275	492	29	,	,	PUNCT
ejpam-4275	492	30	π,∆	π,∆	NUM
ejpam-4275	492	31	)	)	PUNCT
ejpam-4275	492	32	.	.	PUNCT
ejpam-4275	493	1	since	since	SCONJ
ejpam-4275	493	2	fν	fν	NOUN
ejpam-4275	493	3	is	be	AUX
ejpam-4275	493	4	injective	injective	ADJ
ejpam-4275	493	5	,	,	PUNCT
ejpam-4275	493	6	then	then	ADV
ejpam-4275	493	7	f−1	f−1	PROPN
ejpam-4275	493	8	ν	ν	X
ejpam-4275	493	9	(	(	PUNCT
ejpam-4275	493	10	fν	fν	NOUN
ejpam-4275	493	11	◦	◦	NOUN
ejpam-4275	493	12	eτ	eτ	PROPN
ejpam-4275	493	13	(	(	PUNCT
ejpam-4275	493	14	ω	ω	PROPN
ejpam-4275	493	15	,	,	PUNCT
ejpam-4275	493	16	σ	σ	PROPN
ejpam-4275	493	17	)	)	PUNCT
ejpam-4275	493	18	)	)	PUNCT
ejpam-4275	494	1	=	=	SYM
ejpam-4275	494	2	(	(	PUNCT
ejpam-4275	494	3	f−1	f−1	PROPN
ejpam-4275	494	4	ν	ν	PROPN
ejpam-4275	494	5	fν)(eτ	fν)(eτ	PUNCT
ejpam-4275	494	6	(	(	PUNCT
ejpam-4275	494	7	ω	ω	PROPN
ejpam-4275	494	8	,	,	PUNCT
ejpam-4275	494	9	σ	σ	PROPN
ejpam-4275	494	10	)	)	PUNCT
ejpam-4275	494	11	)	)	PUNCT
ejpam-4275	495	1	=	=	SYM
ejpam-4275	495	2	eτ	eτ	PROPN
ejpam-4275	495	3	(	(	PUNCT
ejpam-4275	495	4	ω	ω	PROPN
ejpam-4275	495	5	,	,	PUNCT
ejpam-4275	495	6	σ	σ	PROPN
ejpam-4275	495	7	)	)	PUNCT
ejpam-4275	495	8	.	.	PUNCT
ejpam-4275	496	1	hence	hence	ADV
ejpam-4275	496	2	,	,	PUNCT
ejpam-4275	496	3	eτ	eτ	ADV
ejpam-4275	496	4	is	be	AUX
ejpam-4275	496	5	an	an	DET
ejpam-4275	496	6	infra	infra	NOUN
ejpam-4275	496	7	soft	soft	ADJ
ejpam-4275	496	8	pre	pre	ADJ
ejpam-4275	496	9	-	-	ADJ
ejpam-4275	496	10	open	open	ADJ
ejpam-4275	496	11	map	map	NOUN
ejpam-4275	496	12	.	.	PUNCT
ejpam-4275	497	1	in	in	ADP
ejpam-4275	497	2	a	a	DET
ejpam-4275	497	3	similar	similar	ADJ
ejpam-4275	497	4	way	way	NOUN
ejpam-4275	497	5	,	,	PUNCT
ejpam-4275	497	6	one	one	PRON
ejpam-4275	497	7	can	can	AUX
ejpam-4275	497	8	prove	prove	VERB
ejpam-4275	497	9	the	the	DET
ejpam-4275	497	10	next	next	ADJ
ejpam-4275	497	11	proposition	proposition	NOUN
ejpam-4275	497	12	.	.	PUNCT
ejpam-4275	498	1	proposition	proposition	NOUN
ejpam-4275	498	2	25	25	NUM
ejpam-4275	498	3	.	.	PUNCT
ejpam-4275	499	1	let	let	VERB
ejpam-4275	499	2	eτ	eτ	VERB
ejpam-4275	499	3	:	:	PUNCT
ejpam-4275	499	4	(	(	PUNCT
ejpam-4275	499	5	x	x	X
ejpam-4275	499	6	,	,	PUNCT
ejpam-4275	499	7	ξ	ξ	PROPN
ejpam-4275	499	8	,	,	PUNCT
ejpam-4275	499	9	σ	σ	NOUN
ejpam-4275	499	10	)	)	PUNCT
ejpam-4275	499	11	→	→	SYM
ejpam-4275	499	12	(	(	PUNCT
ejpam-4275	499	13	s	s	PROPN
ejpam-4275	499	14	,	,	PUNCT
ejpam-4275	499	15	π,∆	π,∆	NUM
ejpam-4275	499	16	)	)	PUNCT
ejpam-4275	499	17	and	and	CCONJ
ejpam-4275	499	18	fν	fν	INTJ
ejpam-4275	499	19	:	:	PUNCT
ejpam-4275	499	20	(	(	PUNCT
ejpam-4275	499	21	s	s	X
ejpam-4275	499	22	,	,	PUNCT
ejpam-4275	499	23	π,∆	π,∆	NUM
ejpam-4275	499	24	)	)	PUNCT
ejpam-4275	499	25	→	→	SYM
ejpam-4275	499	26	(	(	PUNCT
ejpam-4275	499	27	v	v	NOUN
ejpam-4275	499	28	,	,	PUNCT
ejpam-4275	499	29	σ	σ	PROPN
ejpam-4275	499	30	,	,	PUNCT
ejpam-4275	499	31	γ	γ	PROPN
ejpam-4275	499	32	)	)	PUNCT
ejpam-4275	499	33	be	be	VERB
ejpam-4275	499	34	two	two	NUM
ejpam-4275	499	35	infra	infra	NOUN
ejpam-4275	499	36	soft	soft	ADJ
ejpam-4275	499	37	maps	map	NOUN
ejpam-4275	499	38	.	.	PUNCT
ejpam-4275	500	1	then	then	ADV
ejpam-4275	500	2	the	the	DET
ejpam-4275	500	3	following	follow	VERB
ejpam-4275	500	4	statements	statement	NOUN
ejpam-4275	500	5	hold	hold	VERB
ejpam-4275	500	6	.	.	PUNCT
ejpam-4275	501	1	(	(	PUNCT
ejpam-4275	501	2	i	i	NOUN
ejpam-4275	501	3	)	)	PUNCT
ejpam-4275	501	4	if	if	SCONJ
ejpam-4275	501	5	eτ	eτ	PROPN
ejpam-4275	501	6	and	and	CCONJ
ejpam-4275	501	7	fν	fν	NOUN
ejpam-4275	501	8	are	be	AUX
ejpam-4275	501	9	infra	infra	NOUN
ejpam-4275	501	10	soft	soft	ADJ
ejpam-4275	501	11	pre	pre	ADJ
ejpam-4275	501	12	-	-	ADJ
ejpam-4275	501	13	closed	closed	ADJ
ejpam-4275	501	14	maps	map	NOUN
ejpam-4275	501	15	,	,	PUNCT
ejpam-4275	501	16	then	then	ADV
ejpam-4275	501	17	fν	fν	VERB
ejpam-4275	501	18	◦	◦	NOUN
ejpam-4275	501	19	eτ	eτ	PROPN
ejpam-4275	501	20	is	be	AUX
ejpam-4275	501	21	an	an	DET
ejpam-4275	501	22	infra	infra	NOUN
ejpam-4275	501	23	soft	soft	ADJ
ejpam-4275	501	24	pre	pre	ADJ
ejpam-4275	501	25	-	-	ADJ
ejpam-4275	501	26	closed	closed	ADJ
ejpam-4275	501	27	map	map	NOUN
ejpam-4275	501	28	.	.	PUNCT
ejpam-4275	502	1	(	(	PUNCT
ejpam-4275	502	2	ii	ii	NOUN
ejpam-4275	502	3	)	)	PUNCT
ejpam-4275	502	4	if	if	SCONJ
ejpam-4275	502	5	fν	fν	NOUN
ejpam-4275	502	6	◦	◦	NOUN
ejpam-4275	502	7	eτ	eτ	ADV
ejpam-4275	502	8	is	be	AUX
ejpam-4275	502	9	an	an	DET
ejpam-4275	502	10	infra	infra	NOUN
ejpam-4275	502	11	soft	soft	ADJ
ejpam-4275	502	12	pre	pre	ADJ
ejpam-4275	502	13	-	-	ADJ
ejpam-4275	502	14	closed	closed	ADJ
ejpam-4275	502	15	map	map	NOUN
ejpam-4275	502	16	and	and	CCONJ
ejpam-4275	502	17	eτ	eτ	NOUN
ejpam-4275	502	18	is	be	AUX
ejpam-4275	502	19	a	a	DET
ejpam-4275	502	20	surjective	surjective	ADJ
ejpam-4275	502	21	infra	infra	NOUN
ejpam-4275	502	22	soft	soft	ADJ
ejpam-4275	502	23	precontinuous	precontinuous	ADJ
ejpam-4275	502	24	map	map	NOUN
ejpam-4275	502	25	,	,	PUNCT
ejpam-4275	502	26	then	then	ADV
ejpam-4275	502	27	fν	fν	NOUN
ejpam-4275	502	28	is	be	AUX
ejpam-4275	502	29	an	an	DET
ejpam-4275	502	30	infra	infra	NOUN
ejpam-4275	502	31	soft	soft	ADJ
ejpam-4275	502	32	pre	pre	ADJ
ejpam-4275	502	33	-	-	ADJ
ejpam-4275	502	34	closed	closed	ADJ
ejpam-4275	502	35	map	map	NOUN
ejpam-4275	502	36	.	.	PUNCT
ejpam-4275	503	1	(	(	PUNCT
ejpam-4275	503	2	iii	iii	X
ejpam-4275	503	3	)	)	PUNCT
ejpam-4275	503	4	if	if	SCONJ
ejpam-4275	503	5	fν	fν	NOUN
ejpam-4275	503	6	◦	◦	NOUN
ejpam-4275	503	7	eτ	eτ	ADV
ejpam-4275	503	8	is	be	AUX
ejpam-4275	503	9	an	an	DET
ejpam-4275	503	10	infra	infra	NOUN
ejpam-4275	503	11	soft	soft	ADJ
ejpam-4275	503	12	pre	pre	ADJ
ejpam-4275	503	13	-	-	ADJ
ejpam-4275	503	14	closed	closed	ADJ
ejpam-4275	503	15	map	map	NOUN
ejpam-4275	503	16	and	and	CCONJ
ejpam-4275	503	17	fν	fν	NOUN
ejpam-4275	503	18	is	be	AUX
ejpam-4275	503	19	an	an	DET
ejpam-4275	503	20	injective	injective	ADJ
ejpam-4275	503	21	infra	infra	NOUN
ejpam-4275	503	22	soft	soft	ADJ
ejpam-4275	503	23	precontinuous	precontinuous	ADJ
ejpam-4275	503	24	map	map	NOUN
ejpam-4275	503	25	,	,	PUNCT
ejpam-4275	503	26	then	then	ADV
ejpam-4275	503	27	eτ	eτ	PROPN
ejpam-4275	503	28	is	be	AUX
ejpam-4275	503	29	an	an	DET
ejpam-4275	503	30	infra	infra	NOUN
ejpam-4275	503	31	soft	soft	ADJ
ejpam-4275	503	32	pre	pre	ADJ
ejpam-4275	503	33	-	-	ADJ
ejpam-4275	503	34	closed	closed	ADJ
ejpam-4275	503	35	map	map	NOUN
ejpam-4275	503	36	.	.	PUNCT
ejpam-4275	504	1	definition	definition	NOUN
ejpam-4275	504	2	23	23	NUM
ejpam-4275	504	3	.	.	PUNCT
ejpam-4275	505	1	a	a	DET
ejpam-4275	505	2	bijective	bijective	ADJ
ejpam-4275	505	3	soft	soft	ADJ
ejpam-4275	505	4	map	map	NOUN
ejpam-4275	505	5	eτ	eτ	ADP
ejpam-4275	505	6	:	:	PUNCT
ejpam-4275	505	7	(	(	PUNCT
ejpam-4275	505	8	x	x	X
ejpam-4275	505	9	,	,	PUNCT
ejpam-4275	505	10	ξ	ξ	PROPN
ejpam-4275	505	11	,	,	PUNCT
ejpam-4275	505	12	σ	σ	NOUN
ejpam-4275	505	13	)	)	PUNCT
ejpam-4275	505	14	→	→	SYM
ejpam-4275	505	15	(	(	PUNCT
ejpam-4275	505	16	s	s	PROPN
ejpam-4275	505	17	,	,	PUNCT
ejpam-4275	505	18	π,∆	π,∆	NUM
ejpam-4275	505	19	)	)	PUNCT
ejpam-4275	505	20	is	be	AUX
ejpam-4275	505	21	said	say	VERB
ejpam-4275	505	22	to	to	PART
ejpam-4275	505	23	be	be	AUX
ejpam-4275	505	24	an	an	DET
ejpam-4275	505	25	infra	infra	NOUN
ejpam-4275	505	26	soft	soft	ADJ
ejpam-4275	505	27	pre	pre	NOUN
ejpam-4275	505	28	-	-	NOUN
ejpam-4275	505	29	homeomorphism	homeomorphism	ADJ
ejpam-4275	505	30	if	if	SCONJ
ejpam-4275	505	31	it	it	PRON
ejpam-4275	505	32	is	be	AUX
ejpam-4275	505	33	infra	infra	NOUN
ejpam-4275	505	34	soft	soft	ADJ
ejpam-4275	505	35	pre	pre	ADJ
ejpam-4275	505	36	-	-	ADJ
ejpam-4275	505	37	continuous	continuous	ADJ
ejpam-4275	505	38	and	and	CCONJ
ejpam-4275	505	39	infra	infra	NOUN
ejpam-4275	505	40	soft	soft	ADJ
ejpam-4275	505	41	pre	pre	ADJ
ejpam-4275	505	42	-	-	ADJ
ejpam-4275	505	43	open	open	ADJ
ejpam-4275	505	44	.	.	PUNCT
ejpam-4275	506	1	we	we	PRON
ejpam-4275	506	2	cancel	cancel	VERB
ejpam-4275	506	3	the	the	DET
ejpam-4275	506	4	proofs	proof	NOUN
ejpam-4275	506	5	of	of	ADP
ejpam-4275	506	6	the	the	DET
ejpam-4275	506	7	next	next	ADJ
ejpam-4275	506	8	two	two	NUM
ejpam-4275	506	9	results	result	NOUN
ejpam-4275	506	10	because	because	SCONJ
ejpam-4275	506	11	they	they	PRON
ejpam-4275	506	12	are	be	AUX
ejpam-4275	506	13	easy	easy	ADJ
ejpam-4275	506	14	.	.	PUNCT
ejpam-4275	507	1	proposition	proposition	NOUN
ejpam-4275	507	2	26	26	NUM
ejpam-4275	507	3	.	.	PUNCT
ejpam-4275	508	1	let	let	VERB
ejpam-4275	508	2	eτ	eτ	VERB
ejpam-4275	508	3	:	:	PUNCT
ejpam-4275	508	4	(	(	PUNCT
ejpam-4275	508	5	x	x	X
ejpam-4275	508	6	,	,	PUNCT
ejpam-4275	508	7	ξ	ξ	PROPN
ejpam-4275	508	8	,	,	PUNCT
ejpam-4275	508	9	σ	σ	NOUN
ejpam-4275	508	10	)	)	PUNCT
ejpam-4275	508	11	→	→	SYM
ejpam-4275	508	12	(	(	PUNCT
ejpam-4275	508	13	s	s	PROPN
ejpam-4275	508	14	,	,	PUNCT
ejpam-4275	508	15	π,∆	π,∆	NUM
ejpam-4275	508	16	)	)	PUNCT
ejpam-4275	508	17	and	and	CCONJ
ejpam-4275	508	18	fν	fν	INTJ
ejpam-4275	508	19	:	:	PUNCT
ejpam-4275	508	20	(	(	PUNCT
ejpam-4275	508	21	s	s	X
ejpam-4275	508	22	,	,	PUNCT
ejpam-4275	508	23	π,∆	π,∆	NUM
ejpam-4275	508	24	)	)	PUNCT
ejpam-4275	508	25	→	→	SYM
ejpam-4275	508	26	(	(	PUNCT
ejpam-4275	508	27	v	v	NOUN
ejpam-4275	508	28	,	,	PUNCT
ejpam-4275	508	29	σ	σ	PROPN
ejpam-4275	508	30	,	,	PUNCT
ejpam-4275	508	31	γ	γ	NOUN
ejpam-4275	508	32	)	)	PUNCT
ejpam-4275	508	33	be	be	VERB
ejpam-4275	508	34	infra	infra	NOUN
ejpam-4275	508	35	soft	soft	ADJ
ejpam-4275	508	36	pre	pre	ADJ
ejpam-4275	508	37	-	-	ADJ
ejpam-4275	508	38	homeomorphism	homeomorphism	ADJ
ejpam-4275	508	39	maps	map	NOUN
ejpam-4275	508	40	.	.	PUNCT
ejpam-4275	509	1	then	then	ADV
ejpam-4275	509	2	fν	fν	VERB
ejpam-4275	509	3	◦	◦	NOUN
ejpam-4275	509	4	eτ	eτ	PROPN
ejpam-4275	509	5	is	be	AUX
ejpam-4275	509	6	an	an	DET
ejpam-4275	509	7	infra	infra	NOUN
ejpam-4275	509	8	soft	soft	ADJ
ejpam-4275	509	9	pre	pre	ADJ
ejpam-4275	509	10	-	-	ADJ
ejpam-4275	509	11	homeomorphism	homeomorphism	ADJ
ejpam-4275	509	12	map	map	NOUN
ejpam-4275	509	13	.	.	PUNCT
ejpam-4275	510	1	proposition	proposition	NOUN
ejpam-4275	510	2	27	27	NUM
ejpam-4275	510	3	.	.	PUNCT
ejpam-4275	511	1	if	if	SCONJ
ejpam-4275	511	2	eτ	eτ	X
ejpam-4275	511	3	:	:	PUNCT
ejpam-4275	511	4	(	(	PUNCT
ejpam-4275	511	5	x	x	X
ejpam-4275	511	6	,	,	PUNCT
ejpam-4275	511	7	ξ	ξ	PROPN
ejpam-4275	511	8	,	,	PUNCT
ejpam-4275	511	9	σ	σ	NOUN
ejpam-4275	511	10	)	)	PUNCT
ejpam-4275	511	11	→	→	SYM
ejpam-4275	511	12	(	(	PUNCT
ejpam-4275	511	13	s	s	PROPN
ejpam-4275	511	14	,	,	PUNCT
ejpam-4275	511	15	π,∆	π,∆	NUM
ejpam-4275	511	16	)	)	PUNCT
ejpam-4275	511	17	is	be	AUX
ejpam-4275	511	18	a	a	DET
ejpam-4275	511	19	bijective	bijective	ADJ
ejpam-4275	511	20	soft	soft	ADJ
ejpam-4275	511	21	map	map	NOUN
ejpam-4275	511	22	,	,	PUNCT
ejpam-4275	511	23	then	then	ADV
ejpam-4275	511	24	the	the	DET
ejpam-4275	511	25	following	following	ADJ
ejpam-4275	511	26	statements	statement	NOUN
ejpam-4275	511	27	are	be	AUX
ejpam-4275	511	28	equivalent	equivalent	ADJ
ejpam-4275	511	29	.	.	PUNCT
ejpam-4275	512	1	(	(	PUNCT
ejpam-4275	512	2	i	i	NOUN
ejpam-4275	512	3	)	)	PUNCT
ejpam-4275	512	4	eτ	eτ	ADP
ejpam-4275	512	5	is	be	AUX
ejpam-4275	512	6	an	an	DET
ejpam-4275	512	7	infra	infra	NOUN
ejpam-4275	512	8	soft	soft	ADJ
ejpam-4275	512	9	pre	pre	NOUN
ejpam-4275	512	10	-	-	NOUN
ejpam-4275	512	11	homeomorphism	homeomorphism	ADJ
ejpam-4275	512	12	.	.	PUNCT
ejpam-4275	513	1	(	(	PUNCT
ejpam-4275	513	2	ii	ii	NOUN
ejpam-4275	513	3	)	)	PUNCT
ejpam-4275	513	4	eτ	eτ	PROPN
ejpam-4275	513	5	and	and	CCONJ
ejpam-4275	513	6	e−1	e−1	PROPN
ejpam-4275	513	7	τ	τ	PROPN
ejpam-4275	513	8	is	be	AUX
ejpam-4275	513	9	infra	infra	NOUN
ejpam-4275	513	10	soft	soft	ADJ
ejpam-4275	513	11	pre	pre	ADJ
ejpam-4275	513	12	-	-	ADJ
ejpam-4275	513	13	continuous	continuous	ADJ
ejpam-4275	513	14	.	.	PUNCT
ejpam-4275	514	1	(	(	PUNCT
ejpam-4275	514	2	iii	iii	X
ejpam-4275	514	3	)	)	PUNCT
ejpam-4275	514	4	eτ	eτ	ADP
ejpam-4275	514	5	is	be	AUX
ejpam-4275	514	6	infra	infra	NOUN
ejpam-4275	514	7	soft	soft	ADJ
ejpam-4275	514	8	pre	pre	ADJ
ejpam-4275	514	9	-	-	ADJ
ejpam-4275	514	10	closed	closed	ADJ
ejpam-4275	514	11	and	and	CCONJ
ejpam-4275	514	12	infra	infra	VERB
ejpam-4275	514	13	soft	soft	ADJ
ejpam-4275	514	14	pre	pre	ADJ
ejpam-4275	514	15	-	-	ADJ
ejpam-4275	514	16	continuous	continuous	ADJ
ejpam-4275	514	17	.	.	PUNCT
ejpam-4275	515	1	t.m	t.m	PROPN
ejpam-4275	515	2	.	.	PUNCT
ejpam-4275	515	3	al	al	PROPN
ejpam-4275	515	4	-	-	PUNCT
ejpam-4275	515	5	shami	shami	PROPN
ejpam-4275	515	6	,	,	PUNCT
ejpam-4275	515	7	h.a	h.a	PROPN
ejpam-4275	515	8	.	.	PROPN
ejpam-4275	515	9	othman	othman	PROPN
ejpam-4275	515	10	/	/	SYM
ejpam-4275	515	11	eur	eur	PROPN
ejpam-4275	515	12	.	.	PUNCT
ejpam-4275	516	1	j.	j.	PROPN
ejpam-4275	516	2	pure	pure	PROPN
ejpam-4275	516	3	appl	appl	PROPN
ejpam-4275	516	4	.	.	PROPN
ejpam-4275	516	5	math	math	PROPN
ejpam-4275	516	6	,	,	PUNCT
ejpam-4275	516	7	15	15	NUM
ejpam-4275	516	8	(	(	PUNCT
ejpam-4275	516	9	1	1	NUM
ejpam-4275	516	10	)	)	PUNCT
ejpam-4275	516	11	(	(	PUNCT
ejpam-4275	516	12	2022	2022	NUM
ejpam-4275	516	13	)	)	PUNCT
ejpam-4275	516	14	,	,	PUNCT
ejpam-4275	516	15	261	261	NUM
ejpam-4275	516	16	-	-	SYM
ejpam-4275	516	17	280	280	NUM
ejpam-4275	516	18	276	276	NUM
ejpam-4275	516	19	proposition	proposition	NOUN
ejpam-4275	516	20	28	28	NUM
ejpam-4275	516	21	.	.	PUNCT
ejpam-4275	517	1	if	if	SCONJ
ejpam-4275	517	2	eτ	eτ	X
ejpam-4275	517	3	:	:	PUNCT
ejpam-4275	517	4	(	(	PUNCT
ejpam-4275	517	5	x	x	X
ejpam-4275	517	6	,	,	PUNCT
ejpam-4275	517	7	ξ	ξ	PROPN
ejpam-4275	517	8	,	,	PUNCT
ejpam-4275	517	9	σ	σ	NOUN
ejpam-4275	517	10	)	)	PUNCT
ejpam-4275	517	11	→	→	SYM
ejpam-4275	517	12	(	(	PUNCT
ejpam-4275	517	13	s	s	PROPN
ejpam-4275	517	14	,	,	PUNCT
ejpam-4275	517	15	π,∆	π,∆	NUM
ejpam-4275	517	16	)	)	PUNCT
ejpam-4275	517	17	is	be	AUX
ejpam-4275	517	18	an	an	DET
ejpam-4275	517	19	infra	infra	NOUN
ejpam-4275	517	20	soft	soft	ADJ
ejpam-4275	517	21	pre	pre	ADJ
ejpam-4275	517	22	-	-	ADJ
ejpam-4275	517	23	homeomorphism	homeomorphism	ADJ
ejpam-4275	517	24	map	map	NOUN
ejpam-4275	517	25	,	,	PUNCT
ejpam-4275	517	26	then	then	ADV
ejpam-4275	517	27	the	the	DET
ejpam-4275	517	28	following	follow	VERB
ejpam-4275	517	29	statements	statement	NOUN
ejpam-4275	517	30	hold	hold	VERB
ejpam-4275	517	31	for	for	ADP
ejpam-4275	517	32	each	each	DET
ejpam-4275	517	33	(	(	PUNCT
ejpam-4275	517	34	ω	ω	PROPN
ejpam-4275	517	35	,	,	PUNCT
ejpam-4275	517	36	σ	σ	PROPN
ejpam-4275	517	37	)	)	PUNCT
ejpam-4275	517	38	∈	∈	PROPN
ejpam-4275	517	39	s(x)a	s(x)a	PROPN
ejpam-4275	517	40	.	.	PUNCT
ejpam-4275	518	1	(	(	PUNCT
ejpam-4275	518	2	i	i	NOUN
ejpam-4275	518	3	)	)	PUNCT
ejpam-4275	518	4	eτ	eτ	PROPN
ejpam-4275	518	5	(	(	PUNCT
ejpam-4275	518	6	pint(ω	pint(ω	PROPN
ejpam-4275	518	7	,	,	PUNCT
ejpam-4275	518	8	σ	σ	NOUN
ejpam-4275	518	9	)	)	PUNCT
ejpam-4275	518	10	)	)	PUNCT
ejpam-4275	519	1	=	=	PRON
ejpam-4275	519	2	pint(eτ	pint(eτ	PROPN
ejpam-4275	519	3	(	(	PUNCT
ejpam-4275	519	4	ω	ω	PROPN
ejpam-4275	519	5	,	,	PUNCT
ejpam-4275	519	6	σ	σ	PROPN
ejpam-4275	519	7	)	)	PUNCT
ejpam-4275	519	8	)	)	PUNCT
ejpam-4275	519	9	.	.	PUNCT
ejpam-4275	520	1	(	(	PUNCT
ejpam-4275	520	2	ii	ii	NOUN
ejpam-4275	520	3	)	)	PUNCT
ejpam-4275	520	4	eτ	eτ	PROPN
ejpam-4275	520	5	(	(	PUNCT
ejpam-4275	520	6	pcl(ω	pcl(ω	PROPN
ejpam-4275	520	7	,	,	PUNCT
ejpam-4275	520	8	σ	σ	NOUN
ejpam-4275	520	9	)	)	PUNCT
ejpam-4275	520	10	)	)	PUNCT
ejpam-4275	521	1	=	=	PRON
ejpam-4275	521	2	pcl(eτ	pcl(eτ	X
ejpam-4275	521	3	(	(	PUNCT
ejpam-4275	521	4	ω	ω	PROPN
ejpam-4275	521	5	,	,	PUNCT
ejpam-4275	521	6	σ	σ	PROPN
ejpam-4275	521	7	)	)	PUNCT
ejpam-4275	521	8	)	)	PUNCT
ejpam-4275	521	9	.	.	PUNCT
ejpam-4275	522	1	proof	proof	NOUN
ejpam-4275	522	2	.	.	PUNCT
ejpam-4275	523	1	(	(	PUNCT
ejpam-4275	523	2	i	i	NOUN
ejpam-4275	523	3	):	):	PUNCT
ejpam-4275	523	4	according	accord	VERB
ejpam-4275	523	5	to	to	ADP
ejpam-4275	523	6	proposition	proposition	NOUN
ejpam-4275	523	7	21	21	NUM
ejpam-4275	523	8	(	(	PUNCT
ejpam-4275	523	9	i	i	NOUN
ejpam-4275	523	10	)	)	PUNCT
ejpam-4275	523	11	,	,	PUNCT
ejpam-4275	523	12	we	we	PRON
ejpam-4275	523	13	obtain	obtain	VERB
ejpam-4275	523	14	eτ	eτ	PROPN
ejpam-4275	523	15	(	(	PUNCT
ejpam-4275	523	16	pint(ω	pint(ω	PROPN
ejpam-4275	523	17	,	,	PUNCT
ejpam-4275	523	18	σ))⊆̃pint(eτ	σ))⊆̃pint(eτ	PROPN
ejpam-4275	523	19	(	(	PUNCT
ejpam-4275	523	20	ω	ω	PROPN
ejpam-4275	523	21	,	,	PUNCT
ejpam-4275	523	22	σ	σ	PROPN
ejpam-4275	523	23	)	)	PUNCT
ejpam-4275	523	24	)	)	PUNCT
ejpam-4275	523	25	.	.	PUNCT
ejpam-4275	524	1	conversely	conversely	ADV
ejpam-4275	524	2	,	,	PUNCT
ejpam-4275	524	3	let	let	VERB
ejpam-4275	524	4	δsκ	δsκ	PROPN
ejpam-4275	524	5	∈	∈	PROPN
ejpam-4275	524	6	pint(eτ	pint(eτ	PROPN
ejpam-4275	524	7	(	(	PUNCT
ejpam-4275	524	8	ω	ω	PROPN
ejpam-4275	524	9	,	,	PUNCT
ejpam-4275	524	10	σ	σ	PROPN
ejpam-4275	524	11	)	)	PUNCT
ejpam-4275	524	12	.	.	PUNCT
ejpam-4275	525	1	then	then	ADV
ejpam-4275	525	2	there	there	PRON
ejpam-4275	525	3	is	be	VERB
ejpam-4275	525	4	an	an	DET
ejpam-4275	525	5	infra	infra	NOUN
ejpam-4275	525	6	soft	soft	ADJ
ejpam-4275	525	7	pre	pre	ADJ
ejpam-4275	525	8	-	-	ADJ
ejpam-4275	525	9	open	open	ADJ
ejpam-4275	525	10	set	set	NOUN
ejpam-4275	525	11	(	(	PUNCT
ejpam-4275	525	12	ψ,∆	ψ,∆	SYM
ejpam-4275	525	13	)	)	PUNCT
ejpam-4275	525	14	such	such	ADJ
ejpam-4275	525	15	that	that	SCONJ
ejpam-4275	525	16	δsκ	δsκ	PROPN
ejpam-4275	525	17	∈	∈	PROPN
ejpam-4275	525	18	(	(	PUNCT
ejpam-4275	525	19	ψ,∆)⊆̃eτ	ψ,∆)⊆̃eτ	PROPN
ejpam-4275	525	20	(	(	PUNCT
ejpam-4275	525	21	ω	ω	PROPN
ejpam-4275	525	22	,	,	PUNCT
ejpam-4275	525	23	σ	σ	PROPN
ejpam-4275	525	24	)	)	PUNCT
ejpam-4275	525	25	.	.	PUNCT
ejpam-4275	526	1	by	by	ADP
ejpam-4275	526	2	hypothesis	hypothesis	NOUN
ejpam-4275	526	3	,	,	PUNCT
ejpam-4275	526	4	δxη	δxη	NOUN
ejpam-4275	526	5	=	=	SYM
ejpam-4275	526	6	e−1	e−1	PROPN
ejpam-4275	526	7	τ	τ	X
ejpam-4275	526	8	(	(	PUNCT
ejpam-4275	526	9	δsκ	δsκ	NOUN
ejpam-4275	526	10	)	)	PUNCT
ejpam-4275	526	11	∈	∈	PROPN
ejpam-4275	526	12	e−1	e−1	PROPN
ejpam-4275	526	13	τ	τ	X
ejpam-4275	526	14	(	(	PUNCT
ejpam-4275	526	15	ψ,∆)⊆̃(ω	ψ,∆)⊆̃(ω	PROPN
ejpam-4275	526	16	,	,	PUNCT
ejpam-4275	526	17	σ	σ	NOUN
ejpam-4275	526	18	)	)	PUNCT
ejpam-4275	526	19	such	such	ADJ
ejpam-4275	526	20	that	that	SCONJ
ejpam-4275	526	21	e−1	e−1	PROPN
ejpam-4275	526	22	τ	τ	X
ejpam-4275	526	23	(	(	PUNCT
ejpam-4275	526	24	ψ,∆	ψ,∆	PROPN
ejpam-4275	526	25	)	)	PUNCT
ejpam-4275	526	26	is	be	AUX
ejpam-4275	526	27	an	an	DET
ejpam-4275	526	28	infra	infra	NOUN
ejpam-4275	526	29	soft	soft	ADJ
ejpam-4275	526	30	pre	pre	ADJ
ejpam-4275	526	31	-	-	ADJ
ejpam-4275	526	32	open	open	ADJ
ejpam-4275	526	33	set	set	NOUN
ejpam-4275	526	34	.	.	PUNCT
ejpam-4275	527	1	so	so	ADV
ejpam-4275	527	2	that	that	SCONJ
ejpam-4275	527	3	,	,	PUNCT
ejpam-4275	527	4	δxη	δxη	NOUN
ejpam-4275	527	5	∈	∈	PROPN
ejpam-4275	527	6	pint(ω	pint(ω	NOUN
ejpam-4275	527	7	,	,	PUNCT
ejpam-4275	527	8	σ	σ	PROPN
ejpam-4275	527	9	)	)	PUNCT
ejpam-4275	527	10	which	which	PRON
ejpam-4275	527	11	means	mean	VERB
ejpam-4275	527	12	that	that	SCONJ
ejpam-4275	527	13	δsκ	δsκ	VERB
ejpam-4275	527	14	∈	∈	PRON
ejpam-4275	527	15	eτ	eτ	ADP
ejpam-4275	527	16	(	(	PUNCT
ejpam-4275	527	17	pint(ω	pint(ω	PROPN
ejpam-4275	527	18	,	,	PUNCT
ejpam-4275	527	19	σ	σ	PROPN
ejpam-4275	527	20	)	)	PUNCT
ejpam-4275	527	21	)	)	PUNCT
ejpam-4275	527	22	.	.	PUNCT
ejpam-4275	528	1	one	one	PRON
ejpam-4275	528	2	can	can	AUX
ejpam-4275	528	3	achieve	achieve	VERB
ejpam-4275	528	4	item	item	NOUN
ejpam-4275	528	5	(	(	PUNCT
ejpam-4275	528	6	ii	ii	NOUN
ejpam-4275	528	7	)	)	PUNCT
ejpam-4275	528	8	following	follow	VERB
ejpam-4275	528	9	similar	similar	ADJ
ejpam-4275	528	10	arguments	argument	NOUN
ejpam-4275	528	11	.	.	PUNCT
ejpam-4275	529	1	theorem	theorem	NOUN
ejpam-4275	529	2	6	6	NUM
ejpam-4275	529	3	.	.	PUNCT
ejpam-4275	530	1	the	the	DET
ejpam-4275	530	2	property	property	NOUN
ejpam-4275	530	3	of	of	ADP
ejpam-4275	530	4	an	an	DET
ejpam-4275	530	5	infra	infra	NOUN
ejpam-4275	530	6	soft	soft	ADJ
ejpam-4275	530	7	pre	pre	ADJ
ejpam-4275	530	8	-	-	ADJ
ejpam-4275	530	9	dense	dense	ADJ
ejpam-4275	530	10	set	set	NOUN
ejpam-4275	530	11	is	be	AUX
ejpam-4275	530	12	an	an	DET
ejpam-4275	530	13	infra	infra	NOUN
ejpam-4275	530	14	soft	soft	ADJ
ejpam-4275	530	15	topological	topological	ADJ
ejpam-4275	530	16	invariant	invariant	ADJ
ejpam-4275	530	17	.	.	PUNCT
ejpam-4275	531	1	proof	proof	NOUN
ejpam-4275	531	2	.	.	PUNCT
ejpam-4275	532	1	let	let	VERB
ejpam-4275	532	2	eτ	eτ	VERB
ejpam-4275	532	3	:	:	PUNCT
ejpam-4275	532	4	(	(	PUNCT
ejpam-4275	532	5	x	x	X
ejpam-4275	532	6	,	,	PUNCT
ejpam-4275	532	7	ξ	ξ	PROPN
ejpam-4275	532	8	,	,	PUNCT
ejpam-4275	532	9	σ	σ	NOUN
ejpam-4275	532	10	)	)	PUNCT
ejpam-4275	532	11	→	→	SYM
ejpam-4275	532	12	(	(	PUNCT
ejpam-4275	532	13	s	s	PROPN
ejpam-4275	532	14	,	,	PUNCT
ejpam-4275	532	15	π,∆	π,∆	NUM
ejpam-4275	532	16	)	)	PUNCT
ejpam-4275	532	17	be	be	VERB
ejpam-4275	532	18	an	an	DET
ejpam-4275	532	19	infra	infra	NOUN
ejpam-4275	532	20	soft	soft	ADJ
ejpam-4275	532	21	pre	pre	ADJ
ejpam-4275	532	22	-	-	ADJ
ejpam-4275	532	23	homeomorphism	homeomorphism	ADJ
ejpam-4275	532	24	map	map	NOUN
ejpam-4275	532	25	and	and	CCONJ
ejpam-4275	532	26	consider	consider	VERB
ejpam-4275	532	27	(	(	PUNCT
ejpam-4275	532	28	ω	ω	PROPN
ejpam-4275	532	29	,	,	PUNCT
ejpam-4275	532	30	σ	σ	PROPN
ejpam-4275	532	31	)	)	PUNCT
ejpam-4275	532	32	as	as	ADP
ejpam-4275	532	33	an	an	DET
ejpam-4275	532	34	infra	infra	NOUN
ejpam-4275	532	35	soft	soft	ADJ
ejpam-4275	532	36	pre	pre	ADJ
ejpam-4275	532	37	-	-	ADJ
ejpam-4275	532	38	dense	dense	ADJ
ejpam-4275	532	39	subset	subset	NOUN
ejpam-4275	532	40	of	of	ADP
ejpam-4275	532	41	(	(	PUNCT
ejpam-4275	532	42	x	x	NOUN
ejpam-4275	532	43	,	,	PUNCT
ejpam-4275	532	44	ξ	ξ	PROPN
ejpam-4275	532	45	,	,	PUNCT
ejpam-4275	532	46	σ	σ	PROPN
ejpam-4275	532	47	)	)	PUNCT
ejpam-4275	532	48	,	,	PUNCT
ejpam-4275	532	49	i.e.	i.e.	X
ejpam-4275	532	50	pcl(ω	pcl(ω	PROPN
ejpam-4275	532	51	,	,	PUNCT
ejpam-4275	532	52	σ	σ	NOUN
ejpam-4275	532	53	)	)	PUNCT
ejpam-4275	532	54	=	=	PUNCT
ejpam-4275	533	1	x̃.	x̃.	ADV
ejpam-4275	533	2	it	it	PRON
ejpam-4275	533	3	comes	come	VERB
ejpam-4275	533	4	from	from	ADP
ejpam-4275	533	5	proposition	proposition	NOUN
ejpam-4275	533	6	28	28	NUM
ejpam-4275	533	7	(	(	PUNCT
ejpam-4275	533	8	ii	ii	NOUN
ejpam-4275	533	9	)	)	PUNCT
ejpam-4275	533	10	that	that	PRON
ejpam-4275	533	11	pcl(eτ	pcl(eτ	ADJ
ejpam-4275	533	12	(	(	PUNCT
ejpam-4275	533	13	ω	ω	PROPN
ejpam-4275	533	14	,	,	PUNCT
ejpam-4275	533	15	σ	σ	PROPN
ejpam-4275	533	16	)	)	PUNCT
ejpam-4275	533	17	)	)	PUNCT
ejpam-4275	534	1	=	=	SYM
ejpam-4275	534	2	eτ	eτ	X
ejpam-4275	534	3	(	(	PUNCT
ejpam-4275	534	4	pcl(ω	pcl(ω	PROPN
ejpam-4275	534	5	,	,	PUNCT
ejpam-4275	534	6	σ	σ	NOUN
ejpam-4275	534	7	)	)	PUNCT
ejpam-4275	534	8	)	)	PUNCT
ejpam-4275	535	1	=	=	SYM
ejpam-4275	535	2	eτ	eτ	PROPN
ejpam-4275	535	3	(	(	PUNCT
ejpam-4275	535	4	x̃	x̃	PROPN
ejpam-4275	535	5	)	)	PUNCT
ejpam-4275	535	6	=	=	SYM
ejpam-4275	535	7	pcl(s̃	pcl(s̃	NOUN
ejpam-4275	535	8	)	)	PUNCT
ejpam-4275	535	9	=	=	PUNCT
ejpam-4275	535	10	s̃.	s̃.	PROPN
ejpam-4275	535	11	thus	thus	ADV
ejpam-4275	535	12	,	,	PUNCT
ejpam-4275	535	13	eτ	eτ	PROPN
ejpam-4275	535	14	(	(	PUNCT
ejpam-4275	535	15	ω	ω	PROPN
ejpam-4275	535	16	,	,	PUNCT
ejpam-4275	535	17	σ	σ	PROPN
ejpam-4275	535	18	)	)	PUNCT
ejpam-4275	535	19	is	be	AUX
ejpam-4275	535	20	an	an	DET
ejpam-4275	535	21	infra	infra	NOUN
ejpam-4275	535	22	soft	soft	ADJ
ejpam-4275	535	23	pre	pre	ADJ
ejpam-4275	535	24	-	-	ADJ
ejpam-4275	535	25	dense	dense	ADJ
ejpam-4275	535	26	set	set	NOUN
ejpam-4275	535	27	in	in	ADP
ejpam-4275	535	28	(	(	PUNCT
ejpam-4275	535	29	s	s	PROPN
ejpam-4275	535	30	,	,	PUNCT
ejpam-4275	535	31	π,∆	π,∆	NUM
ejpam-4275	535	32	)	)	PUNCT
ejpam-4275	535	33	,	,	PUNCT
ejpam-4275	535	34	as	as	SCONJ
ejpam-4275	535	35	required	require	VERB
ejpam-4275	535	36	.	.	PUNCT
ejpam-4275	536	1	we	we	PRON
ejpam-4275	536	2	complete	complete	VERB
ejpam-4275	536	3	this	this	DET
ejpam-4275	536	4	section	section	NOUN
ejpam-4275	536	5	by	by	ADP
ejpam-4275	536	6	studying	study	VERB
ejpam-4275	536	7	the	the	DET
ejpam-4275	536	8	concept	concept	NOUN
ejpam-4275	536	9	of	of	ADP
ejpam-4275	536	10	fixed	fix	VERB
ejpam-4275	536	11	soft	soft	ADJ
ejpam-4275	536	12	points	point	NOUN
ejpam-4275	536	13	with	with	ADP
ejpam-4275	536	14	respect	respect	NOUN
ejpam-4275	536	15	to	to	ADP
ejpam-4275	536	16	infra	infra	NOUN
ejpam-4275	536	17	soft	soft	ADJ
ejpam-4275	536	18	pre	pre	ADJ
ejpam-4275	536	19	-	-	ADJ
ejpam-4275	536	20	open	open	ADJ
ejpam-4275	536	21	sets	set	NOUN
ejpam-4275	536	22	.	.	PUNCT
ejpam-4275	537	1	definition	definition	NOUN
ejpam-4275	537	2	24	24	NUM
ejpam-4275	537	3	.	.	PUNCT
ejpam-4275	538	1	we	we	PRON
ejpam-4275	538	2	say	say	VERB
ejpam-4275	538	3	that	that	SCONJ
ejpam-4275	538	4	(	(	PUNCT
ejpam-4275	538	5	x	x	X
ejpam-4275	538	6	,	,	PUNCT
ejpam-4275	538	7	ξ	ξ	PROPN
ejpam-4275	538	8	,	,	PUNCT
ejpam-4275	538	9	σ	σ	NOUN
ejpam-4275	538	10	)	)	PUNCT
ejpam-4275	538	11	has	have	VERB
ejpam-4275	538	12	a	a	DET
ejpam-4275	538	13	pre	pre	ADJ
ejpam-4275	538	14	-	-	ADJ
ejpam-4275	538	15	fixed	fixed	ADJ
ejpam-4275	538	16	soft	soft	ADJ
ejpam-4275	538	17	point	point	NOUN
ejpam-4275	538	18	property	property	NOUN
ejpam-4275	538	19	provided	provide	VERB
ejpam-4275	538	20	that	that	SCONJ
ejpam-4275	538	21	for	for	ADP
ejpam-4275	538	22	every	every	DET
ejpam-4275	538	23	infra	infra	NOUN
ejpam-4275	538	24	soft	soft	ADJ
ejpam-4275	538	25	pre	pre	ADJ
ejpam-4275	538	26	-	-	ADJ
ejpam-4275	538	27	continuous	continuous	ADJ
ejpam-4275	538	28	map	map	NOUN
ejpam-4275	538	29	eτ	eτ	AUX
ejpam-4275	538	30	:	:	PUNCT
ejpam-4275	538	31	(	(	PUNCT
ejpam-4275	538	32	x	x	X
ejpam-4275	538	33	,	,	PUNCT
ejpam-4275	538	34	ξ	ξ	PROPN
ejpam-4275	538	35	,	,	PUNCT
ejpam-4275	538	36	σ	σ	NOUN
ejpam-4275	538	37	)	)	PUNCT
ejpam-4275	538	38	→	→	SYM
ejpam-4275	538	39	(	(	PUNCT
ejpam-4275	538	40	x	x	X
ejpam-4275	538	41	,	,	PUNCT
ejpam-4275	538	42	ξ	ξ	PROPN
ejpam-4275	538	43	,	,	PUNCT
ejpam-4275	538	44	σ	σ	NOUN
ejpam-4275	538	45	)	)	PUNCT
ejpam-4275	538	46	there	there	PRON
ejpam-4275	538	47	exists	exist	VERB
ejpam-4275	538	48	δsη	δsη	PROPN
ejpam-4275	538	49	∈	∈	PROPN
ejpam-4275	538	50	x	x	PUNCT
ejpam-4275	538	51	such	such	ADJ
ejpam-4275	538	52	that	that	SCONJ
ejpam-4275	538	53	eτ	eτ	PROPN
ejpam-4275	538	54	(	(	PUNCT
ejpam-4275	538	55	δ	δ	PROPN
ejpam-4275	538	56	s	s	PROPN
ejpam-4275	538	57	η	η	PROPN
ejpam-4275	538	58	)	)	PUNCT
ejpam-4275	538	59	=	=	SYM
ejpam-4275	538	60	δsη	δsη	PROPN
ejpam-4275	538	61	.	.	PUNCT
ejpam-4275	538	62	proposition	proposition	NOUN
ejpam-4275	538	63	29	29	NUM
ejpam-4275	538	64	.	.	PUNCT
ejpam-4275	539	1	the	the	DET
ejpam-4275	539	2	property	property	NOUN
ejpam-4275	539	3	of	of	ADP
ejpam-4275	539	4	being	be	AUX
ejpam-4275	539	5	a	a	DET
ejpam-4275	539	6	pre	pre	ADJ
ejpam-4275	539	7	-	-	ADJ
ejpam-4275	539	8	fixed	fixed	ADJ
ejpam-4275	539	9	soft	soft	ADJ
ejpam-4275	539	10	point	point	NOUN
ejpam-4275	539	11	is	be	AUX
ejpam-4275	539	12	preserved	preserve	VERB
ejpam-4275	539	13	under	under	ADP
ejpam-4275	539	14	an	an	DET
ejpam-4275	539	15	infra	infra	NOUN
ejpam-4275	539	16	soft	soft	ADJ
ejpam-4275	539	17	pre	pre	NOUN
ejpam-4275	539	18	-	-	ADJ
ejpam-4275	539	19	homeomorphism	homeomorphism	ADJ
ejpam-4275	539	20	.	.	PUNCT
ejpam-4275	540	1	proof	proof	NOUN
ejpam-4275	540	2	.	.	PUNCT
ejpam-4275	541	1	consider	consider	VERB
ejpam-4275	541	2	(	(	PUNCT
ejpam-4275	541	3	x1	x1	PROPN
ejpam-4275	541	4	,	,	PUNCT
ejpam-4275	541	5	ξ1,σ1	ξ1,σ1	PROPN
ejpam-4275	541	6	)	)	PUNCT
ejpam-4275	541	7	and	and	CCONJ
ejpam-4275	541	8	(	(	PUNCT
ejpam-4275	541	9	x2	x2	PROPN
ejpam-4275	541	10	,	,	PUNCT
ejpam-4275	541	11	ξ2,σ2	ξ2,σ2	PROPN
ejpam-4275	541	12	)	)	PUNCT
ejpam-4275	541	13	as	as	ADP
ejpam-4275	541	14	two	two	NUM
ejpam-4275	541	15	infra	infra	NOUN
ejpam-4275	541	16	soft	soft	ADJ
ejpam-4275	541	17	pre	pre	NOUN
ejpam-4275	541	18	-	-	NOUN
ejpam-4275	541	19	homeomorphism	homeomorphism	ADJ
ejpam-4275	541	20	.	.	PUNCT
ejpam-4275	542	1	this	this	PRON
ejpam-4275	542	2	means	mean	VERB
ejpam-4275	542	3	that	that	SCONJ
ejpam-4275	542	4	there	there	PRON
ejpam-4275	542	5	exists	exist	VERB
ejpam-4275	542	6	a	a	DET
ejpam-4275	542	7	bijective	bijective	ADJ
ejpam-4275	542	8	soft	soft	ADJ
ejpam-4275	542	9	map	map	NOUN
ejpam-4275	542	10	eτ	eτ	ADP
ejpam-4275	542	11	:	:	PUNCT
ejpam-4275	542	12	(	(	PUNCT
ejpam-4275	542	13	x1	x1	PROPN
ejpam-4275	542	14	,	,	PUNCT
ejpam-4275	542	15	ξ1,σ1	ξ1,σ1	PROPN
ejpam-4275	542	16	)	)	PUNCT
ejpam-4275	542	17	→	→	SYM
ejpam-4275	542	18	(	(	PUNCT
ejpam-4275	542	19	x2	x2	PROPN
ejpam-4275	542	20	,	,	PUNCT
ejpam-4275	542	21	ξ2,σ2	ξ2,σ2	PROPN
ejpam-4275	542	22	)	)	PUNCT
ejpam-4275	542	23	suchthat	suchthat	VERB
ejpam-4275	542	24	eτ	eτ	NOUN
ejpam-4275	542	25	and	and	CCONJ
ejpam-4275	542	26	e−1	e−1	PROPN
ejpam-4275	542	27	τ	τ	PROPN
ejpam-4275	542	28	are	be	AUX
ejpam-4275	542	29	infra	infra	NOUN
ejpam-4275	542	30	soft	soft	ADJ
ejpam-4275	542	31	pre	pre	ADJ
ejpam-4275	542	32	-	-	ADJ
ejpam-4275	542	33	continuous	continuous	ADJ
ejpam-4275	542	34	.	.	PUNCT
ejpam-4275	543	1	suppose	suppose	VERB
ejpam-4275	543	2	that	that	SCONJ
ejpam-4275	543	3	(	(	PUNCT
ejpam-4275	543	4	x1	x1	PROPN
ejpam-4275	543	5	,	,	PUNCT
ejpam-4275	543	6	ξ1,σ1	ξ1,σ1	PROPN
ejpam-4275	543	7	)	)	PUNCT
ejpam-4275	543	8	has	have	VERB
ejpam-4275	543	9	the	the	DET
ejpam-4275	543	10	property	property	NOUN
ejpam-4275	543	11	of	of	ADP
ejpam-4275	543	12	pre	pre	ADJ
ejpam-4275	543	13	-	-	ADJ
ejpam-4275	543	14	fixed	fixed	ADJ
ejpam-4275	543	15	soft	soft	ADJ
ejpam-4275	543	16	point	point	NOUN
ejpam-4275	543	17	.	.	PUNCT
ejpam-4275	544	1	that	that	PRON
ejpam-4275	544	2	is	be	AUX
ejpam-4275	544	3	any	any	DET
ejpam-4275	544	4	infra	infra	NOUN
ejpam-4275	544	5	soft	soft	ADJ
ejpam-4275	544	6	pre	pre	ADJ
ejpam-4275	544	7	-	-	ADJ
ejpam-4275	544	8	continuous	continuous	ADJ
ejpam-4275	544	9	map	map	NOUN
ejpam-4275	544	10	eτ	eτ	ADP
ejpam-4275	544	11	:	:	PUNCT
ejpam-4275	544	12	(	(	PUNCT
ejpam-4275	544	13	x1	x1	PROPN
ejpam-4275	544	14	,	,	PUNCT
ejpam-4275	544	15	ξ1,σ1	ξ1,σ1	PROPN
ejpam-4275	544	16	)	)	PUNCT
ejpam-4275	544	17	→	→	SYM
ejpam-4275	544	18	(	(	PUNCT
ejpam-4275	544	19	x1	x1	PROPN
ejpam-4275	544	20	,	,	PUNCT
ejpam-4275	544	21	ξ1,σ1	ξ1,σ1	PROPN
ejpam-4275	544	22	)	)	PUNCT
ejpam-4275	544	23	has	have	VERB
ejpam-4275	544	24	a	a	DET
ejpam-4275	544	25	pre	pre	ADJ
ejpam-4275	544	26	-	-	ADJ
ejpam-4275	544	27	fixed	fixed	ADJ
ejpam-4275	544	28	soft	soft	ADJ
ejpam-4275	544	29	point	point	NOUN
ejpam-4275	544	30	.	.	PUNCT
ejpam-4275	545	1	now	now	ADV
ejpam-4275	545	2	,	,	PUNCT
ejpam-4275	545	3	consider	consider	VERB
ejpam-4275	545	4	cτ	cτ	VERB
ejpam-4275	545	5	:	:	PUNCT
ejpam-4275	545	6	(	(	PUNCT
ejpam-4275	545	7	x2	x2	INTJ
ejpam-4275	545	8	,	,	PUNCT
ejpam-4275	545	9	ξ2,σ2	ξ2,σ2	PROPN
ejpam-4275	545	10	)	)	PUNCT
ejpam-4275	545	11	→	→	SYM
ejpam-4275	545	12	(	(	PUNCT
ejpam-4275	545	13	x2	x2	PROPN
ejpam-4275	545	14	,	,	PUNCT
ejpam-4275	545	15	ξ2,σ2	ξ2,σ2	PROPN
ejpam-4275	545	16	)	)	PUNCT
ejpam-4275	545	17	is	be	AUX
ejpam-4275	545	18	infra	infra	NOUN
ejpam-4275	545	19	soft	soft	ADJ
ejpam-4275	545	20	pre	pre	ADJ
ejpam-4275	545	21	-	-	ADJ
ejpam-4275	545	22	continuous	continuous	ADJ
ejpam-4275	545	23	.	.	PUNCT
ejpam-4275	546	1	it	it	PRON
ejpam-4275	546	2	is	be	AUX
ejpam-4275	546	3	clear	clear	ADJ
ejpam-4275	546	4	that	that	SCONJ
ejpam-4275	546	5	cτ	cτ	AUX
ejpam-4275	546	6	◦	◦	NOUN
ejpam-4275	546	7	eτ	eτ	NOUN
ejpam-4275	546	8	:	:	PUNCT
ejpam-4275	546	9	(	(	PUNCT
ejpam-4275	546	10	x1	x1	PROPN
ejpam-4275	546	11	,	,	PUNCT
ejpam-4275	546	12	ξ1,σ1	ξ1,σ1	PROPN
ejpam-4275	546	13	)	)	PUNCT
ejpam-4275	546	14	→	→	SYM
ejpam-4275	546	15	(	(	PUNCT
ejpam-4275	546	16	x2	x2	PROPN
ejpam-4275	546	17	,	,	PUNCT
ejpam-4275	546	18	ξ2,σ2	ξ2,σ2	PROPN
ejpam-4275	546	19	)	)	PUNCT
ejpam-4275	546	20	is	be	AUX
ejpam-4275	546	21	infra	infra	NOUN
ejpam-4275	546	22	soft	soft	ADJ
ejpam-4275	546	23	pre	pre	ADJ
ejpam-4275	546	24	-	-	ADJ
ejpam-4275	546	25	continuous	continuous	ADJ
ejpam-4275	546	26	.	.	PUNCT
ejpam-4275	547	1	therefore	therefore	ADV
ejpam-4275	547	2	,	,	PUNCT
ejpam-4275	547	3	e−1	e−1	PROPN
ejpam-4275	547	4	τ	τ	PROPN
ejpam-4275	547	5	◦	◦	NOUN
ejpam-4275	547	6	cτ	cτ	ADP
ejpam-4275	547	7	◦	◦	NOUN
ejpam-4275	547	8	eτ	eτ	NOUN
ejpam-4275	547	9	:	:	PUNCT
ejpam-4275	547	10	(	(	PUNCT
ejpam-4275	547	11	x1	x1	PROPN
ejpam-4275	547	12	,	,	PUNCT
ejpam-4275	547	13	ξ1,σ1	ξ1,σ1	PROPN
ejpam-4275	547	14	)	)	PUNCT
ejpam-4275	547	15	→	→	SYM
ejpam-4275	547	16	(	(	PUNCT
ejpam-4275	547	17	x1	x1	PROPN
ejpam-4275	547	18	,	,	PUNCT
ejpam-4275	547	19	ξ1,σ1	ξ1,σ1	PROPN
ejpam-4275	547	20	)	)	PUNCT
ejpam-4275	547	21	is	be	AUX
ejpam-4275	547	22	infra	infra	NOUN
ejpam-4275	547	23	soft	soft	ADJ
ejpam-4275	547	24	precontinuous	precontinuous	NOUN
ejpam-4275	547	25	.	.	PUNCT
ejpam-4275	548	1	since	since	SCONJ
ejpam-4275	548	2	(	(	PUNCT
ejpam-4275	548	3	x1	x1	PROPN
ejpam-4275	548	4	,	,	PUNCT
ejpam-4275	548	5	ξ1,σ1	ξ1,σ1	PROPN
ejpam-4275	548	6	)	)	PUNCT
ejpam-4275	548	7	has	have	VERB
ejpam-4275	548	8	a	a	DET
ejpam-4275	548	9	pre	pre	ADJ
ejpam-4275	548	10	-	-	ADJ
ejpam-4275	548	11	fixed	fixed	ADJ
ejpam-4275	548	12	soft	soft	ADJ
ejpam-4275	548	13	point	point	NOUN
ejpam-4275	548	14	property	property	NOUN
ejpam-4275	548	15	,	,	PUNCT
ejpam-4275	548	16	e−1	e−1	PROPN
ejpam-4275	548	17	τ	τ	X
ejpam-4275	548	18	(	(	PUNCT
ejpam-4275	548	19	hτ	hτ	INTJ
ejpam-4275	548	20	(	(	PUNCT
ejpam-4275	548	21	eτ	eτ	PROPN
ejpam-4275	548	22	(	(	PUNCT
ejpam-4275	548	23	δ	δ	PROPN
ejpam-4275	548	24	s	s	PROPN
ejpam-4275	548	25	η	η	PROPN
ejpam-4275	548	26	)	)	PUNCT
ejpam-4275	548	27	)	)	PUNCT
ejpam-4275	548	28	)	)	PUNCT
ejpam-4275	549	1	=	=	PUNCT
ejpam-4275	549	2	δsη	δsη	NOUN
ejpam-4275	549	3	for	for	ADP
ejpam-4275	549	4	some	some	DET
ejpam-4275	549	5	δsη	δsη	NOUN
ejpam-4275	549	6	∈	∈	PROPN
ejpam-4275	549	7	x̃.	x̃.	ADV
ejpam-4275	550	1	thus	thus	ADV
ejpam-4275	550	2	,	,	PUNCT
ejpam-4275	550	3	eτ	eτ	X
ejpam-4275	550	4	(	(	PUNCT
ejpam-4275	550	5	e	e	NOUN
ejpam-4275	550	6	−1	−1	PRON
ejpam-4275	550	7	τ	τ	PROPN
ejpam-4275	550	8	(	(	PUNCT
ejpam-4275	550	9	hτ	hτ	INTJ
ejpam-4275	550	10	(	(	PUNCT
ejpam-4275	550	11	eτ	eτ	PROPN
ejpam-4275	550	12	(	(	PUNCT
ejpam-4275	550	13	δ	δ	PROPN
ejpam-4275	550	14	s	s	PROPN
ejpam-4275	550	15	η	η	PROPN
ejpam-4275	550	16	)	)	PUNCT
ejpam-4275	550	17	)	)	PUNCT
ejpam-4275	550	18	)	)	PUNCT
ejpam-4275	550	19	)	)	PUNCT
ejpam-4275	551	1	=	=	SYM
ejpam-4275	551	2	eτ	eτ	X
ejpam-4275	551	3	(	(	PUNCT
ejpam-4275	551	4	δ	δ	PROPN
ejpam-4275	551	5	s	s	PROPN
ejpam-4275	551	6	η	η	PROPN
ejpam-4275	551	7	)	)	PUNCT
ejpam-4275	551	8	.	.	PUNCT
ejpam-4275	552	1	this	this	PRON
ejpam-4275	552	2	implies	imply	VERB
ejpam-4275	552	3	that	that	SCONJ
ejpam-4275	552	4	hτ	hτ	INTJ
ejpam-4275	552	5	(	(	PUNCT
ejpam-4275	552	6	eτ	eτ	PROPN
ejpam-4275	552	7	(	(	PUNCT
ejpam-4275	552	8	δ	δ	PROPN
ejpam-4275	552	9	s	s	PROPN
ejpam-4275	552	10	η	η	PROPN
ejpam-4275	552	11	)	)	PUNCT
ejpam-4275	552	12	)	)	PUNCT
ejpam-4275	553	1	=	=	SYM
ejpam-4275	553	2	eτ	eτ	PROPN
ejpam-4275	553	3	(	(	PUNCT
ejpam-4275	553	4	δ	δ	PROPN
ejpam-4275	553	5	s	s	PROPN
ejpam-4275	553	6	η	η	PROPN
ejpam-4275	553	7	)	)	PUNCT
ejpam-4275	553	8	.	.	PUNCT
ejpam-4275	554	1	hence	hence	ADV
ejpam-4275	554	2	,	,	PUNCT
ejpam-4275	554	3	eτ	eτ	PROPN
ejpam-4275	554	4	(	(	PUNCT
ejpam-4275	554	5	δ	δ	PROPN
ejpam-4275	554	6	s	s	PROPN
ejpam-4275	554	7	η	η	PROPN
ejpam-4275	554	8	)	)	PUNCT
ejpam-4275	554	9	is	be	AUX
ejpam-4275	554	10	a	a	DET
ejpam-4275	554	11	pre	pre	ADJ
ejpam-4275	554	12	-	-	ADJ
ejpam-4275	554	13	fixed	fixed	ADJ
ejpam-4275	554	14	soft	soft	ADJ
ejpam-4275	554	15	point	point	NOUN
ejpam-4275	554	16	of	of	ADP
ejpam-4275	554	17	cτ	cτ	ADP
ejpam-4275	554	18	which	which	PRON
ejpam-4275	554	19	means	mean	VERB
ejpam-4275	554	20	that	that	SCONJ
ejpam-4275	554	21	(	(	PUNCT
ejpam-4275	554	22	x2	x2	INTJ
ejpam-4275	554	23	,	,	PUNCT
ejpam-4275	554	24	ξ2,σ2	ξ2,σ2	PROPN
ejpam-4275	554	25	)	)	PUNCT
ejpam-4275	554	26	has	have	VERB
ejpam-4275	554	27	a	a	DET
ejpam-4275	554	28	pre	pre	ADJ
ejpam-4275	554	29	-	-	ADJ
ejpam-4275	554	30	fixed	fixed	ADJ
ejpam-4275	554	31	soft	soft	ADJ
ejpam-4275	554	32	point	point	NOUN
ejpam-4275	554	33	property	property	NOUN
ejpam-4275	554	34	.	.	PUNCT
ejpam-4275	555	1	references	reference	NOUN
ejpam-4275	555	2	277	277	NUM
ejpam-4275	555	3	6	6	NUM
ejpam-4275	555	4	.	.	PUNCT
ejpam-4275	555	5	concluding	conclude	VERB
ejpam-4275	555	6	remark	remark	NOUN
ejpam-4275	555	7	and	and	CCONJ
ejpam-4275	555	8	further	further	ADJ
ejpam-4275	555	9	work	work	NOUN
ejpam-4275	555	10	in	in	ADP
ejpam-4275	555	11	this	this	DET
ejpam-4275	555	12	paper	paper	NOUN
ejpam-4275	555	13	,	,	PUNCT
ejpam-4275	555	14	we	we	PRON
ejpam-4275	555	15	contribute	contribute	VERB
ejpam-4275	555	16	to	to	ADP
ejpam-4275	555	17	the	the	DET
ejpam-4275	555	18	area	area	NOUN
ejpam-4275	555	19	of	of	ADP
ejpam-4275	555	20	infra	infra	NOUN
ejpam-4275	555	21	soft	soft	ADJ
ejpam-4275	555	22	topologies	topology	NOUN
ejpam-4275	555	23	.	.	PUNCT
ejpam-4275	556	1	we	we	PRON
ejpam-4275	556	2	have	have	VERB
ejpam-4275	556	3	generalized	generalized	ADJ
ejpam-4275	556	4	infra	infra	NOUN
ejpam-4275	556	5	soft	soft	ADJ
ejpam-4275	556	6	open	open	ADJ
ejpam-4275	556	7	and	and	CCONJ
ejpam-4275	556	8	infra	infra	NOUN
ejpam-4275	556	9	soft	soft	ADJ
ejpam-4275	556	10	closed	closed	ADJ
ejpam-4275	556	11	sets	set	NOUN
ejpam-4275	556	12	by	by	ADP
ejpam-4275	556	13	introducing	introduce	VERB
ejpam-4275	556	14	the	the	DET
ejpam-4275	556	15	concepts	concept	NOUN
ejpam-4275	556	16	of	of	ADP
ejpam-4275	556	17	infra	infra	NOUN
ejpam-4275	556	18	soft	soft	ADJ
ejpam-4275	556	19	preopen	preopen	NOUN
ejpam-4275	556	20	and	and	CCONJ
ejpam-4275	556	21	infra	infra	NOUN
ejpam-4275	556	22	soft	soft	ADJ
ejpam-4275	556	23	pre	pre	ADJ
ejpam-4275	556	24	-	-	ADJ
ejpam-4275	556	25	closed	closed	ADJ
ejpam-4275	556	26	sets	set	NOUN
ejpam-4275	556	27	.	.	PUNCT
ejpam-4275	557	1	then	then	ADV
ejpam-4275	557	2	,	,	PUNCT
ejpam-4275	557	3	we	we	PRON
ejpam-4275	557	4	have	have	AUX
ejpam-4275	557	5	applied	apply	VERB
ejpam-4275	557	6	them	they	PRON
ejpam-4275	557	7	to	to	PART
ejpam-4275	557	8	define	define	VERB
ejpam-4275	557	9	new	new	ADJ
ejpam-4275	557	10	kinds	kind	NOUN
ejpam-4275	557	11	of	of	ADP
ejpam-4275	557	12	soft	soft	ADJ
ejpam-4275	557	13	operators	operator	NOUN
ejpam-4275	557	14	and	and	CCONJ
ejpam-4275	557	15	soft	soft	ADJ
ejpam-4275	557	16	maps	map	NOUN
ejpam-4275	557	17	.	.	PUNCT
ejpam-4275	558	1	to	to	PART
ejpam-4275	558	2	validate	validate	VERB
ejpam-4275	558	3	and	and	CCONJ
ejpam-4275	558	4	illustrate	illustrate	VERB
ejpam-4275	558	5	the	the	DET
ejpam-4275	558	6	obtained	obtain	VERB
ejpam-4275	558	7	findings	finding	NOUN
ejpam-4275	558	8	and	and	CCONJ
ejpam-4275	558	9	relationships	relationship	NOUN
ejpam-4275	558	10	,	,	PUNCT
ejpam-4275	558	11	we	we	PRON
ejpam-4275	558	12	have	have	AUX
ejpam-4275	558	13	constructed	construct	VERB
ejpam-4275	558	14	some	some	DET
ejpam-4275	558	15	examples	example	NOUN
ejpam-4275	558	16	.	.	PUNCT
ejpam-4275	559	1	as	as	SCONJ
ejpam-4275	559	2	we	we	PRON
ejpam-4275	559	3	have	have	AUX
ejpam-4275	559	4	noted	note	VERB
ejpam-4275	559	5	,	,	PUNCT
ejpam-4275	559	6	most	most	ADJ
ejpam-4275	559	7	of	of	ADP
ejpam-4275	559	8	soft	soft	ADJ
ejpam-4275	559	9	topological	topological	ADJ
ejpam-4275	559	10	properties	property	NOUN
ejpam-4275	559	11	of	of	ADP
ejpam-4275	559	12	initiated	initiate	VERB
ejpam-4275	559	13	concepts	concept	NOUN
ejpam-4275	559	14	are	be	AUX
ejpam-4275	559	15	kept	keep	VERB
ejpam-4275	559	16	via	via	ADP
ejpam-4275	559	17	infra	infra	NOUN
ejpam-4275	559	18	soft	soft	ADJ
ejpam-4275	559	19	topologies	topology	NOUN
ejpam-4275	559	20	.	.	PUNCT
ejpam-4275	560	1	this	this	PRON
ejpam-4275	560	2	means	mean	VERB
ejpam-4275	560	3	the	the	DET
ejpam-4275	560	4	absence	absence	NOUN
ejpam-4275	560	5	of	of	ADP
ejpam-4275	560	6	some	some	DET
ejpam-4275	560	7	topology	topology	NOUN
ejpam-4275	560	8	’s	’s	PART
ejpam-4275	560	9	stipulations	stipulation	NOUN
ejpam-4275	560	10	does	do	AUX
ejpam-4275	560	11	not	not	PART
ejpam-4275	560	12	effected	effect	VERB
ejpam-4275	560	13	in	in	ADP
ejpam-4275	560	14	the	the	DET
ejpam-4275	560	15	behaviours	behaviour	NOUN
ejpam-4275	560	16	and	and	CCONJ
ejpam-4275	560	17	properties	property	NOUN
ejpam-4275	560	18	of	of	ADP
ejpam-4275	560	19	topological	topological	ADJ
ejpam-4275	560	20	concepts	concept	NOUN
ejpam-4275	560	21	which	which	PRON
ejpam-4275	560	22	considers	consider	VERB
ejpam-4275	560	23	an	an	DET
ejpam-4275	560	24	advantage	advantage	NOUN
ejpam-4275	560	25	of	of	ADP
ejpam-4275	560	26	studying	study	VERB
ejpam-4275	560	27	infra	infra	NOUN
ejpam-4275	560	28	soft	soft	ADJ
ejpam-4275	560	29	topological	topological	ADJ
ejpam-4275	560	30	spaces	space	NOUN
ejpam-4275	560	31	.	.	PUNCT
ejpam-4275	561	1	however	however	ADV
ejpam-4275	561	2	,	,	PUNCT
ejpam-4275	561	3	there	there	PRON
ejpam-4275	561	4	is	be	VERB
ejpam-4275	561	5	a	a	DET
ejpam-4275	561	6	few	few	ADJ
ejpam-4275	561	7	properties	property	NOUN
ejpam-4275	561	8	of	of	ADP
ejpam-4275	561	9	some	some	DET
ejpam-4275	561	10	topological	topological	ADJ
ejpam-4275	561	11	concept	concept	NOUN
ejpam-4275	561	12	are	be	AUX
ejpam-4275	561	13	partially	partially	ADV
ejpam-4275	561	14	losing	lose	VERB
ejpam-4275	561	15	such	such	ADJ
ejpam-4275	561	16	as	as	ADP
ejpam-4275	561	17	the	the	DET
ejpam-4275	561	18	those	those	PRON
ejpam-4275	561	19	given	give	VERB
ejpam-4275	561	20	in	in	ADP
ejpam-4275	561	21	proposition	proposition	NOUN
ejpam-4275	561	22	6	6	NUM
ejpam-4275	561	23	and	and	CCONJ
ejpam-4275	561	24	proposition	proposition	NOUN
ejpam-4275	561	25	21	21	NUM
ejpam-4275	561	26	.	.	PUNCT
ejpam-4275	562	1	in	in	ADP
ejpam-4275	562	2	the	the	DET
ejpam-4275	562	3	upcoming	upcoming	ADJ
ejpam-4275	562	4	works	work	NOUN
ejpam-4275	562	5	,	,	PUNCT
ejpam-4275	562	6	we	we	PRON
ejpam-4275	562	7	will	will	AUX
ejpam-4275	562	8	apply	apply	VERB
ejpam-4275	562	9	infra	infra	NOUN
ejpam-4275	562	10	soft	soft	ADJ
ejpam-4275	562	11	pre	pre	ADJ
ejpam-4275	562	12	-	-	ADJ
ejpam-4275	562	13	open	open	ADJ
ejpam-4275	562	14	sets	set	NOUN
ejpam-4275	562	15	to	to	PART
ejpam-4275	562	16	introduce	introduce	VERB
ejpam-4275	562	17	the	the	DET
ejpam-4275	562	18	some	some	DET
ejpam-4275	562	19	topological	topological	ADJ
ejpam-4275	562	20	concepts	concept	NOUN
ejpam-4275	562	21	like	like	ADP
ejpam-4275	562	22	separation	separation	NOUN
ejpam-4275	562	23	axioms	axiom	NOUN
ejpam-4275	562	24	,	,	PUNCT
ejpam-4275	562	25	compactness	compactness	NOUN
ejpam-4275	562	26	and	and	CCONJ
ejpam-4275	562	27	connectedness	connectedness	NOUN
ejpam-4275	562	28	.	.	PUNCT
ejpam-4275	563	1	also	also	ADV
ejpam-4275	563	2	,	,	PUNCT
ejpam-4275	563	3	we	we	PRON
ejpam-4275	563	4	will	will	AUX
ejpam-4275	563	5	present	present	VERB
ejpam-4275	563	6	the	the	DET
ejpam-4275	563	7	concepts	concept	NOUN
ejpam-4275	563	8	and	and	CCONJ
ejpam-4275	563	9	results	result	NOUN
ejpam-4275	563	10	given	give	VERB
ejpam-4275	563	11	in	in	ADP
ejpam-4275	563	12	this	this	DET
ejpam-4275	563	13	paper	paper	NOUN
ejpam-4275	563	14	using	use	VERB
ejpam-4275	563	15	new	new	ADJ
ejpam-4275	563	16	generalizations	generalization	NOUN
ejpam-4275	563	17	of	of	ADP
ejpam-4275	563	18	infra	infra	NOUN
ejpam-4275	563	19	soft	soft	ADJ
ejpam-4275	563	20	open	open	ADJ
ejpam-4275	563	21	sets	set	NOUN
ejpam-4275	563	22	such	such	ADJ
ejpam-4275	563	23	as	as	ADP
ejpam-4275	563	24	infra	infra	NOUN
ejpam-4275	563	25	soft	soft	ADJ
ejpam-4275	563	26	α	α	NOUN
ejpam-4275	563	27	-	-	ADJ
ejpam-4275	563	28	open	open	ADJ
ejpam-4275	563	29	and	and	CCONJ
ejpam-4275	563	30	infra	infra	VERB
ejpam-4275	563	31	soft	soft	ADJ
ejpam-4275	563	32	b	b	NOUN
ejpam-4275	563	33	-	-	PUNCT
ejpam-4275	563	34	open	open	ADJ
ejpam-4275	563	35	sets	set	NOUN
ejpam-4275	563	36	.	.	PUNCT
ejpam-4275	564	1	furthermore	furthermore	ADV
ejpam-4275	564	2	,	,	PUNCT
ejpam-4275	564	3	we	we	PRON
ejpam-4275	564	4	shall	shall	AUX
ejpam-4275	564	5	define	define	VERB
ejpam-4275	564	6	new	new	ADJ
ejpam-4275	564	7	rough	rough	ADJ
ejpam-4275	564	8	set	set	NOUN
ejpam-4275	564	9	models	model	NOUN
ejpam-4275	564	10	using	use	VERB
ejpam-4275	564	11	infra	infra	NOUN
ejpam-4275	564	12	soft	soft	ADJ
ejpam-4275	564	13	pre	pre	ADJ
ejpam-4275	564	14	-	-	ADJ
ejpam-4275	564	15	open	open	ADJ
ejpam-4275	564	16	sets	set	NOUN
ejpam-4275	564	17	to	to	PART
ejpam-4275	564	18	improve	improve	VERB
ejpam-4275	564	19	the	the	DET
ejpam-4275	564	20	accuracy	accuracy	NOUN
ejpam-4275	564	21	measures	measure	NOUN
ejpam-4275	564	22	of	of	ADP
ejpam-4275	564	23	sets	set	NOUN
ejpam-4275	564	24	following	follow	VERB
ejpam-4275	564	25	a	a	DET
ejpam-4275	564	26	similar	similar	ADJ
ejpam-4275	564	27	technique	technique	NOUN
ejpam-4275	564	28	what	what	PRON
ejpam-4275	564	29	was	be	AUX
ejpam-4275	564	30	given	give	VERB
ejpam-4275	564	31	in	in	ADP
ejpam-4275	564	32	[	[	NOUN
ejpam-4275	564	33	8	8	NUM
ejpam-4275	564	34	]	]	PUNCT
ejpam-4275	564	35	.	.	PUNCT
ejpam-4275	565	1	conflict	conflict	NOUN
ejpam-4275	565	2	of	of	ADP
ejpam-4275	565	3	interest	interest	NOUN
ejpam-4275	565	4	the	the	DET
ejpam-4275	565	5	authors	author	NOUN
ejpam-4275	565	6	declare	declare	VERB
ejpam-4275	565	7	that	that	SCONJ
ejpam-4275	565	8	there	there	PRON
ejpam-4275	565	9	is	be	VERB
ejpam-4275	565	10	no	no	DET
ejpam-4275	565	11	conflict	conflict	NOUN
ejpam-4275	565	12	of	of	ADP
ejpam-4275	565	13	interest	interest	NOUN
ejpam-4275	565	14	regarding	regard	VERB
ejpam-4275	565	15	the	the	DET
ejpam-4275	565	16	publication	publication	NOUN
ejpam-4275	565	17	of	of	ADP
ejpam-4275	565	18	this	this	DET
ejpam-4275	565	19	paper	paper	NOUN
ejpam-4275	565	20	.	.	PUNCT
ejpam-4275	566	1	acknowledgements	acknowledgement	NOUN
ejpam-4275	566	2	the	the	DET
ejpam-4275	566	3	authors	author	NOUN
ejpam-4275	566	4	would	would	AUX
ejpam-4275	566	5	like	like	VERB
ejpam-4275	566	6	to	to	PART
ejpam-4275	566	7	thank	thank	VERB
ejpam-4275	566	8	the	the	DET
ejpam-4275	566	9	deanship	deanship	NOUN
ejpam-4275	566	10	of	of	ADP
ejpam-4275	566	11	scientific	scientific	ADJ
ejpam-4275	566	12	research	research	NOUN
ejpam-4275	566	13	at	at	ADP
ejpam-4275	566	14	umm	umm	INTJ
ejpam-4275	566	15	al	al	PROPN
ejpam-4275	566	16	-	-	PUNCT
ejpam-4275	566	17	qura	qura	PROPN
ejpam-4275	566	18	university	university	NOUN
ejpam-4275	566	19	for	for	ADP
ejpam-4275	566	20	supporting	support	VERB
ejpam-4275	566	21	this	this	DET
ejpam-4275	566	22	work	work	NOUN
ejpam-4275	566	23	by	by	ADP
ejpam-4275	566	24	grant	grant	PROPN
ejpam-4275	566	25	code	code	PROPN
ejpam-4275	566	26	22uqu4330052dsr01	22uqu4330052dsr01	PROPN
ejpam-4275	566	27	.	.	PUNCT
ejpam-4275	567	1	references	reference	NOUN
ejpam-4275	567	2	[	[	X
ejpam-4275	567	3	1	1	NUM
ejpam-4275	567	4	]	]	PUNCT
ejpam-4275	567	5	h	h	NOUN
ejpam-4275	567	6	aktaş	aktaş	PROPN
ejpam-4275	567	7	and	and	CCONJ
ejpam-4275	567	8	n	n	PRON
ejpam-4275	567	9	çağman	çağman	NOUN
ejpam-4275	567	10	.	.	PUNCT
ejpam-4275	567	11	soft	soft	ADJ
ejpam-4275	567	12	sets	set	NOUN
ejpam-4275	567	13	and	and	CCONJ
ejpam-4275	567	14	soft	soft	ADJ
ejpam-4275	567	15	groups	group	NOUN
ejpam-4275	567	16	.	.	PUNCT
ejpam-4275	568	1	information	information	NOUN
ejpam-4275	568	2	sciences	sciences	PROPN
ejpam-4275	568	3	,	,	PUNCT
ejpam-4275	568	4	177	177	NUM
ejpam-4275	568	5	,	,	PUNCT
ejpam-4275	568	6	2007	2007	NUM
ejpam-4275	568	7	.	.	PUNCT
ejpam-4275	569	1	[	[	X
ejpam-4275	569	2	2	2	NUM
ejpam-4275	569	3	]	]	X
ejpam-4275	569	4	s	s	PART
ejpam-4275	569	5	al	al	PROPN
ejpam-4275	569	6	-	-	PUNCT
ejpam-4275	569	7	ghour	ghour	PROPN
ejpam-4275	569	8	.	.	PUNCT
ejpam-4275	570	1	strong	strong	ADJ
ejpam-4275	570	2	form	form	NOUN
ejpam-4275	570	3	of	of	ADP
ejpam-4275	570	4	soft	soft	ADJ
ejpam-4275	570	5	pre	pre	ADJ
ejpam-4275	570	6	-	-	ADJ
ejpam-4275	570	7	open	open	ADJ
ejpam-4275	570	8	sets	set	NOUN
ejpam-4275	570	9	in	in	ADP
ejpam-4275	570	10	soft	soft	ADJ
ejpam-4275	570	11	topological	topological	ADJ
ejpam-4275	570	12	spaces	space	NOUN
ejpam-4275	570	13	.	.	PUNCT
ejpam-4275	571	1	international	international	ADJ
ejpam-4275	571	2	journal	journal	NOUN
ejpam-4275	571	3	of	of	ADP
ejpam-4275	571	4	fuzzy	fuzzy	ADJ
ejpam-4275	571	5	logic	logic	NOUN
ejpam-4275	571	6	and	and	CCONJ
ejpam-4275	571	7	intelligent	intelligent	ADJ
ejpam-4275	571	8	systems	system	NOUN
ejpam-4275	571	9	,	,	PUNCT
ejpam-4275	571	10	21(2):159–168	21(2):159–168	NOUN
ejpam-4275	571	11	,	,	PUNCT
ejpam-4275	571	12	2021	2021	NUM
ejpam-4275	571	13	.	.	PUNCT
ejpam-4275	572	1	[	[	X
ejpam-4275	572	2	3	3	NUM
ejpam-4275	572	3	]	]	X
ejpam-4275	572	4	s	s	PART
ejpam-4275	572	5	al	al	PROPN
ejpam-4275	572	6	-	-	PUNCT
ejpam-4275	572	7	ghour	ghour	PROPN
ejpam-4275	572	8	and	and	CCONJ
ejpam-4275	572	9	w	w	PROPN
ejpam-4275	572	10	hamed	hamed	PROPN
ejpam-4275	572	11	.	.	PUNCT
ejpam-4275	573	1	on	on	ADP
ejpam-4275	573	2	two	two	NUM
ejpam-4275	573	3	classes	class	NOUN
ejpam-4275	573	4	of	of	ADP
ejpam-4275	573	5	soft	soft	ADJ
ejpam-4275	573	6	sets	set	NOUN
ejpam-4275	573	7	in	in	ADP
ejpam-4275	573	8	soft	soft	ADJ
ejpam-4275	573	9	topological	topological	ADJ
ejpam-4275	573	10	spaces	space	NOUN
ejpam-4275	573	11	.	.	PUNCT
ejpam-4275	574	1	symmetry	symmetry	NOUN
ejpam-4275	574	2	,	,	PUNCT
ejpam-4275	574	3	12(2):265	12(2):265	NUM
ejpam-4275	574	4	,	,	PUNCT
ejpam-4275	574	5	2020	2020	NUM
ejpam-4275	574	6	.	.	PUNCT
ejpam-4275	575	1	[	[	X
ejpam-4275	575	2	4	4	NUM
ejpam-4275	575	3	]	]	X
ejpam-4275	575	4	t	t	PROPN
ejpam-4275	575	5	m	m	PROPN
ejpam-4275	575	6	al	al	PROPN
ejpam-4275	575	7	-	-	PUNCT
ejpam-4275	575	8	shami	shami	PROPN
ejpam-4275	575	9	.	.	PUNCT
ejpam-4275	576	1	soft	soft	ADJ
ejpam-4275	576	2	somewhere	somewhere	ADV
ejpam-4275	576	3	dense	dense	ADJ
ejpam-4275	576	4	sets	set	NOUN
ejpam-4275	576	5	on	on	ADP
ejpam-4275	576	6	soft	soft	ADJ
ejpam-4275	576	7	topological	topological	ADJ
ejpam-4275	576	8	spaces	space	NOUN
ejpam-4275	576	9	.	.	PUNCT
ejpam-4275	577	1	communications	communication	NOUN
ejpam-4275	577	2	of	of	ADP
ejpam-4275	577	3	the	the	DET
ejpam-4275	577	4	korean	korean	ADJ
ejpam-4275	577	5	mathematical	mathematical	ADJ
ejpam-4275	577	6	society	society	NOUN
ejpam-4275	577	7	,	,	PUNCT
ejpam-4275	577	8	33(4):1341–1356	33(4):1341–1356	NUM
ejpam-4275	577	9	,	,	PUNCT
ejpam-4275	577	10	2018	2018	NUM
ejpam-4275	577	11	.	.	PUNCT
ejpam-4275	578	1	references	reference	NOUN
ejpam-4275	578	2	278	278	NUM
ejpam-4275	579	1	[	[	X
ejpam-4275	579	2	5	5	NUM
ejpam-4275	579	3	]	]	PUNCT
ejpam-4275	580	1	t	t	PROPN
ejpam-4275	580	2	m	m	PROPN
ejpam-4275	580	3	al	al	PROPN
ejpam-4275	580	4	-	-	PUNCT
ejpam-4275	580	5	shami	shami	PROPN
ejpam-4275	580	6	.	.	PUNCT
ejpam-4275	581	1	bipolar	bipolar	ADJ
ejpam-4275	581	2	soft	soft	ADJ
ejpam-4275	581	3	sets	set	NOUN
ejpam-4275	581	4	:	:	PUNCT
ejpam-4275	581	5	relations	relation	NOUN
ejpam-4275	581	6	between	between	ADP
ejpam-4275	581	7	them	they	PRON
ejpam-4275	581	8	and	and	CCONJ
ejpam-4275	581	9	ordinary	ordinary	ADJ
ejpam-4275	581	10	points	point	NOUN
ejpam-4275	581	11	and	and	CCONJ
ejpam-4275	581	12	their	their	PRON
ejpam-4275	581	13	applications	application	NOUN
ejpam-4275	581	14	.	.	PUNCT
ejpam-4275	582	1	complexity	complexity	NOUN
ejpam-4275	582	2	,	,	PUNCT
ejpam-4275	582	3	volume	volume	NOUN
ejpam-4275	582	4	2021	2021	NUM
ejpam-4275	582	5	,	,	PUNCT
ejpam-4275	582	6	article	article	NOUN
ejpam-4275	582	7	i	i	PROPN
ejpam-4275	582	8	d	d	PROPN
ejpam-4275	582	9	6621854	6621854	NUM
ejpam-4275	582	10	,	,	PUNCT
ejpam-4275	582	11	2021	2021	NUM
ejpam-4275	582	12	.	.	PUNCT
ejpam-4275	583	1	[	[	X
ejpam-4275	583	2	6	6	NUM
ejpam-4275	583	3	]	]	PUNCT
ejpam-4275	583	4	t	t	PROPN
ejpam-4275	583	5	m	m	PROPN
ejpam-4275	583	6	al	al	PROPN
ejpam-4275	583	7	-	-	PUNCT
ejpam-4275	583	8	shami	shami	PROPN
ejpam-4275	583	9	.	.	PUNCT
ejpam-4275	584	1	compactness	compactness	NOUN
ejpam-4275	584	2	on	on	ADP
ejpam-4275	584	3	soft	soft	ADJ
ejpam-4275	584	4	topological	topological	ADJ
ejpam-4275	584	5	ordered	order	VERB
ejpam-4275	584	6	spaces	space	NOUN
ejpam-4275	584	7	and	and	CCONJ
ejpam-4275	584	8	its	its	PRON
ejpam-4275	584	9	application	application	NOUN
ejpam-4275	584	10	on	on	ADP
ejpam-4275	584	11	the	the	DET
ejpam-4275	584	12	information	information	NOUN
ejpam-4275	584	13	system	system	NOUN
ejpam-4275	584	14	.	.	PUNCT
ejpam-4275	585	1	journal	journal	NOUN
ejpam-4275	585	2	of	of	ADP
ejpam-4275	585	3	mathematics	mathematic	NOUN
ejpam-4275	585	4	,	,	PUNCT
ejpam-4275	585	5	volume	volume	NOUN
ejpam-4275	585	6	2021	2021	NUM
ejpam-4275	585	7	,	,	PUNCT
ejpam-4275	585	8	article	article	NOUN
ejpam-4275	585	9	i	i	PROPN
ejpam-4275	585	10	d	d	PROPN
ejpam-4275	585	11	6699092	6699092	NUM
ejpam-4275	585	12	,	,	PUNCT
ejpam-4275	585	13	2021	2021	NUM
ejpam-4275	585	14	.	.	PUNCT
ejpam-4275	586	1	[	[	X
ejpam-4275	586	2	7	7	X
ejpam-4275	586	3	]	]	X
ejpam-4275	586	4	t	t	PROPN
ejpam-4275	586	5	m	m	PROPN
ejpam-4275	586	6	al	al	PROPN
ejpam-4275	586	7	-	-	PUNCT
ejpam-4275	586	8	shami	shami	PROPN
ejpam-4275	586	9	.	.	PUNCT
ejpam-4275	587	1	homeomorphism	homeomorphism	PROPN
ejpam-4275	587	2	and	and	CCONJ
ejpam-4275	587	3	quotient	quotient	NOUN
ejpam-4275	587	4	mappings	mapping	NOUN
ejpam-4275	587	5	in	in	ADP
ejpam-4275	587	6	infra	infra	NOUN
ejpam-4275	587	7	soft	soft	ADJ
ejpam-4275	587	8	topological	topological	ADJ
ejpam-4275	587	9	spaces	space	NOUN
ejpam-4275	587	10	.	.	PUNCT
ejpam-4275	588	1	journal	journal	NOUN
ejpam-4275	588	2	of	of	ADP
ejpam-4275	588	3	mathematics	mathematic	NOUN
ejpam-4275	588	4	,	,	PUNCT
ejpam-4275	588	5	volume	volume	NOUN
ejpam-4275	588	6	2021	2021	NUM
ejpam-4275	588	7	,	,	PUNCT
ejpam-4275	588	8	article	article	NOUN
ejpam-4275	588	9	i	i	PROPN
ejpam-4275	588	10	d	d	PROPN
ejpam-4275	588	11	3388288	3388288	NUM
ejpam-4275	588	12	,	,	PUNCT
ejpam-4275	588	13	2021	2021	NUM
ejpam-4275	588	14	.	.	PUNCT
ejpam-4275	589	1	[	[	X
ejpam-4275	589	2	8	8	NUM
ejpam-4275	589	3	]	]	X
ejpam-4275	589	4	t	t	PROPN
ejpam-4275	589	5	m	m	PROPN
ejpam-4275	589	6	al	al	PROPN
ejpam-4275	589	7	-	-	PUNCT
ejpam-4275	589	8	shami	shami	PROPN
ejpam-4275	589	9	.	.	PUNCT
ejpam-4275	590	1	improvement	improvement	NOUN
ejpam-4275	590	2	of	of	ADP
ejpam-4275	590	3	the	the	DET
ejpam-4275	590	4	approximations	approximation	NOUN
ejpam-4275	590	5	and	and	CCONJ
ejpam-4275	590	6	accuracy	accuracy	NOUN
ejpam-4275	590	7	measure	measure	NOUN
ejpam-4275	590	8	of	of	ADP
ejpam-4275	590	9	a	a	DET
ejpam-4275	590	10	rough	rough	ADJ
ejpam-4275	590	11	set	set	NOUN
ejpam-4275	590	12	using	use	VERB
ejpam-4275	590	13	somewhere	somewhere	ADV
ejpam-4275	590	14	dense	dense	ADJ
ejpam-4275	590	15	sets	set	NOUN
ejpam-4275	590	16	.	.	PUNCT
ejpam-4275	591	1	soft	soft	ADJ
ejpam-4275	591	2	computing	computing	NOUN
ejpam-4275	591	3	,	,	PUNCT
ejpam-4275	591	4	25(23):14449–14460	25(23):14449–14460	NUM
ejpam-4275	591	5	,	,	PUNCT
ejpam-4275	591	6	2021	2021	NUM
ejpam-4275	591	7	.	.	PUNCT
ejpam-4275	592	1	[	[	X
ejpam-4275	592	2	9	9	NUM
ejpam-4275	592	3	]	]	X
ejpam-4275	592	4	t	t	PROPN
ejpam-4275	592	5	m	m	PROPN
ejpam-4275	592	6	al	al	PROPN
ejpam-4275	592	7	-	-	PUNCT
ejpam-4275	592	8	shami	shami	PROPN
ejpam-4275	592	9	.	.	PUNCT
ejpam-4275	593	1	infra	infra	NOUN
ejpam-4275	593	2	soft	soft	ADJ
ejpam-4275	593	3	compact	compact	ADJ
ejpam-4275	593	4	spaces	space	NOUN
ejpam-4275	593	5	and	and	CCONJ
ejpam-4275	593	6	application	application	NOUN
ejpam-4275	593	7	to	to	ADP
ejpam-4275	593	8	fixed	fix	VERB
ejpam-4275	593	9	point	point	NOUN
ejpam-4275	593	10	theorem	theorem	VERB
ejpam-4275	593	11	.	.	PROPN
ejpam-4275	593	12	journal	journal	PROPN
ejpam-4275	593	13	of	of	ADP
ejpam-4275	593	14	function	function	NOUN
ejpam-4275	593	15	spaces	space	NOUN
ejpam-4275	593	16	,	,	PUNCT
ejpam-4275	593	17	volume	volume	NOUN
ejpam-4275	593	18	2021	2021	NUM
ejpam-4275	593	19	,	,	PUNCT
ejpam-4275	593	20	article	article	NOUN
ejpam-4275	593	21	i	i	PROPN
ejpam-4275	593	22	d	d	PROPN
ejpam-4275	593	23	3417096	3417096	NUM
ejpam-4275	593	24	,	,	PUNCT
ejpam-4275	593	25	2021	2021	NUM
ejpam-4275	593	26	.	.	PUNCT
ejpam-4275	594	1	[	[	X
ejpam-4275	594	2	10	10	NUM
ejpam-4275	594	3	]	]	X
ejpam-4275	594	4	t	t	PROPN
ejpam-4275	594	5	m	m	PROPN
ejpam-4275	594	6	al	al	PROPN
ejpam-4275	594	7	-	-	PUNCT
ejpam-4275	594	8	shami	shami	PROPN
ejpam-4275	594	9	.	.	PUNCT
ejpam-4275	595	1	new	new	ADJ
ejpam-4275	595	2	soft	soft	ADJ
ejpam-4275	595	3	structure	structure	NOUN
ejpam-4275	595	4	:	:	PUNCT
ejpam-4275	595	5	infra	infra	NOUN
ejpam-4275	595	6	soft	soft	ADJ
ejpam-4275	595	7	topological	topological	ADJ
ejpam-4275	595	8	spaces	space	NOUN
ejpam-4275	595	9	.	.	PUNCT
ejpam-4275	596	1	mathematical	mathematical	ADJ
ejpam-4275	596	2	problems	problem	NOUN
ejpam-4275	596	3	in	in	ADP
ejpam-4275	596	4	engineering	engineering	NOUN
ejpam-4275	596	5	,	,	PUNCT
ejpam-4275	596	6	volume	volume	NOUN
ejpam-4275	596	7	2021	2021	NUM
ejpam-4275	596	8	,	,	PUNCT
ejpam-4275	596	9	article	article	NOUN
ejpam-4275	596	10	i	i	PROPN
ejpam-4275	596	11	d	d	PROPN
ejpam-4275	596	12	3361604	3361604	NUM
ejpam-4275	596	13	,	,	PUNCT
ejpam-4275	596	14	2021	2021	NUM
ejpam-4275	596	15	.	.	PUNCT
ejpam-4275	597	1	[	[	X
ejpam-4275	597	2	11	11	NUM
ejpam-4275	597	3	]	]	X
ejpam-4275	597	4	t	t	PROPN
ejpam-4275	597	5	m	m	PROPN
ejpam-4275	597	6	al	al	PROPN
ejpam-4275	597	7	-	-	PUNCT
ejpam-4275	597	8	shami	shami	PROPN
ejpam-4275	597	9	and	and	CCONJ
ejpam-4275	597	10	e	e	X
ejpam-4275	597	11	a	a	DET
ejpam-4275	597	12	abo	abo	NOUN
ejpam-4275	597	13	-	-	PUNCT
ejpam-4275	597	14	tabl	tabl	NOUN
ejpam-4275	597	15	.	.	PUNCT
ejpam-4275	598	1	connectedness	connectedness	NOUN
ejpam-4275	598	2	and	and	CCONJ
ejpam-4275	598	3	local	local	ADJ
ejpam-4275	598	4	connectedness	connectedness	NOUN
ejpam-4275	598	5	on	on	ADP
ejpam-4275	598	6	infra	infra	NOUN
ejpam-4275	598	7	soft	soft	ADJ
ejpam-4275	598	8	topological	topological	ADJ
ejpam-4275	598	9	spaces	space	NOUN
ejpam-4275	598	10	.	.	PUNCT
ejpam-4275	599	1	mathematics	mathematic	NOUN
ejpam-4275	599	2	,	,	PUNCT
ejpam-4275	599	3	9(15):1759	9(15):1759	NUM
ejpam-4275	599	4	,	,	PUNCT
ejpam-4275	599	5	2021	2021	NUM
ejpam-4275	599	6	.	.	PUNCT
ejpam-4275	600	1	[	[	X
ejpam-4275	600	2	12	12	NUM
ejpam-4275	600	3	]	]	X
ejpam-4275	600	4	t	t	PROPN
ejpam-4275	600	5	m	m	PROPN
ejpam-4275	600	6	al	al	PROPN
ejpam-4275	600	7	-	-	PUNCT
ejpam-4275	600	8	shami	shami	PROPN
ejpam-4275	600	9	and	and	CCONJ
ejpam-4275	600	10	a	a	DET
ejpam-4275	600	11	a	a	DET
ejpam-4275	600	12	azzam	azzam	PROPN
ejpam-4275	600	13	.	.	PUNCT
ejpam-4275	601	1	infra	infra	NOUN
ejpam-4275	601	2	soft	soft	ADJ
ejpam-4275	601	3	semiopen	semiopen	ADJ
ejpam-4275	601	4	sets	set	NOUN
ejpam-4275	601	5	and	and	CCONJ
ejpam-4275	601	6	infra	infra	VERB
ejpam-4275	601	7	soft	soft	ADJ
ejpam-4275	601	8	semicontinuity	semicontinuity	NOUN
ejpam-4275	601	9	.	.	PUNCT
ejpam-4275	602	1	journal	journal	PROPN
ejpam-4275	602	2	of	of	ADP
ejpam-4275	602	3	function	function	NOUN
ejpam-4275	602	4	spaces	space	NOUN
ejpam-4275	602	5	,	,	PUNCT
ejpam-4275	602	6	volume	volume	NOUN
ejpam-4275	602	7	2021	2021	NUM
ejpam-4275	602	8	,	,	PUNCT
ejpam-4275	602	9	article	article	NOUN
ejpam-4275	602	10	i	i	PROPN
ejpam-4275	602	11	d	d	PROPN
ejpam-4275	602	12	5716876	5716876	NUM
ejpam-4275	602	13	,	,	PUNCT
ejpam-4275	602	14	2021	2021	NUM
ejpam-4275	602	15	.	.	PUNCT
ejpam-4275	603	1	[	[	X
ejpam-4275	603	2	13	13	NUM
ejpam-4275	603	3	]	]	X
ejpam-4275	603	4	t	t	PROPN
ejpam-4275	603	5	m	m	PROPN
ejpam-4275	603	6	al	al	PROPN
ejpam-4275	603	7	-	-	PUNCT
ejpam-4275	603	8	shami	shami	PROPN
ejpam-4275	603	9	and	and	CCONJ
ejpam-4275	603	10	l	l	NOUN
ejpam-4275	603	11	d	d	NOUN
ejpam-4275	603	12	r	r	NOUN
ejpam-4275	603	13	kočinac	kočinac	PROPN
ejpam-4275	603	14	.	.	PUNCT
ejpam-4275	604	1	nearly	nearly	ADV
ejpam-4275	604	2	soft	soft	ADJ
ejpam-4275	604	3	menger	menger	NOUN
ejpam-4275	604	4	spaces	space	NOUN
ejpam-4275	604	5	.	.	PUNCT
ejpam-4275	605	1	journal	journal	NOUN
ejpam-4275	605	2	of	of	ADP
ejpam-4275	605	3	mathematics	mathematic	NOUN
ejpam-4275	605	4	,	,	PUNCT
ejpam-4275	605	5	volume	volume	NOUN
ejpam-4275	605	6	2020	2020	NUM
ejpam-4275	605	7	,	,	PUNCT
ejpam-4275	605	8	article	article	NOUN
ejpam-4275	605	9	i	i	PROPN
ejpam-4275	605	10	d	d	PROPN
ejpam-4275	605	11	3807418	3807418	NUM
ejpam-4275	605	12	,	,	PUNCT
ejpam-4275	605	13	2020	2020	NUM
ejpam-4275	605	14	.	.	PUNCT
ejpam-4275	606	1	[	[	X
ejpam-4275	606	2	14	14	NUM
ejpam-4275	606	3	]	]	X
ejpam-4275	606	4	t	t	PROPN
ejpam-4275	606	5	m	m	PROPN
ejpam-4275	606	6	al	al	PROPN
ejpam-4275	606	7	-	-	PUNCT
ejpam-4275	606	8	shami	shami	PROPN
ejpam-4275	606	9	and	and	CCONJ
ejpam-4275	606	10	l	l	NOUN
ejpam-4275	606	11	d	d	NOUN
ejpam-4275	606	12	r	r	NOUN
ejpam-4275	606	13	kočinac	kočinac	PROPN
ejpam-4275	606	14	.	.	PUNCT
ejpam-4275	607	1	almost	almost	ADV
ejpam-4275	607	2	soft	soft	ADJ
ejpam-4275	607	3	menger	menger	NOUN
ejpam-4275	607	4	and	and	CCONJ
ejpam-4275	607	5	weakly	weakly	ADJ
ejpam-4275	607	6	soft	soft	ADJ
ejpam-4275	607	7	menger	menger	NOUN
ejpam-4275	607	8	spaces	space	NOUN
ejpam-4275	607	9	.	.	PUNCT
ejpam-4275	608	1	applied	apply	VERB
ejpam-4275	608	2	and	and	CCONJ
ejpam-4275	608	3	computational	computational	ADJ
ejpam-4275	608	4	mathematics	mathematic	NOUN
ejpam-4275	608	5	,	,	PUNCT
ejpam-4275	608	6	21(1	21(1	NUM
ejpam-4275	608	7	)	)	PUNCT
ejpam-4275	608	8	,	,	PUNCT
ejpam-4275	608	9	2022	2022	NUM
ejpam-4275	608	10	.	.	PUNCT
ejpam-4275	609	1	[	[	X
ejpam-4275	609	2	15	15	NUM
ejpam-4275	609	3	]	]	X
ejpam-4275	610	1	t	t	PROPN
ejpam-4275	610	2	m	m	PROPN
ejpam-4275	610	3	al	al	PROPN
ejpam-4275	610	4	-	-	PUNCT
ejpam-4275	610	5	shami	shami	PROPN
ejpam-4275	610	6	and	and	CCONJ
ejpam-4275	610	7	m	m	PROPN
ejpam-4275	610	8	e	e	PROPN
ejpam-4275	610	9	el	el	PROPN
ejpam-4275	610	10	-	-	PUNCT
ejpam-4275	610	11	shafei	shafei	PROPN
ejpam-4275	610	12	.	.	PUNCT
ejpam-4275	611	1	t	t	PROPN
ejpam-4275	611	2	-soft	-soft	PROPN
ejpam-4275	611	3	equality	equality	NOUN
ejpam-4275	611	4	relation	relation	NOUN
ejpam-4275	611	5	.	.	PUNCT
ejpam-4275	612	1	turkish	turkish	ADJ
ejpam-4275	612	2	journal	journal	NOUN
ejpam-4275	612	3	of	of	ADP
ejpam-4275	612	4	mathematics	mathematic	NOUN
ejpam-4275	612	5	,	,	PUNCT
ejpam-4275	612	6	44(8):1427–1441	44(8):1427–1441	NUM
ejpam-4275	612	7	,	,	PUNCT
ejpam-4275	612	8	2020	2020	NUM
ejpam-4275	612	9	.	.	PUNCT
ejpam-4275	613	1	[	[	X
ejpam-4275	613	2	16	16	NUM
ejpam-4275	613	3	]	]	X
ejpam-4275	613	4	t	t	PROPN
ejpam-4275	613	5	m	m	PROPN
ejpam-4275	613	6	al	al	PROPN
ejpam-4275	613	7	-	-	PUNCT
ejpam-4275	613	8	shami	shami	PROPN
ejpam-4275	613	9	and	and	CCONJ
ejpam-4275	613	10	j	j	PROPN
ejpam-4275	613	11	b	b	PROPN
ejpam-4275	613	12	liu	liu	PROPN
ejpam-4275	613	13	.	.	PUNCT
ejpam-4275	614	1	two	two	NUM
ejpam-4275	614	2	classes	class	NOUN
ejpam-4275	614	3	of	of	ADP
ejpam-4275	614	4	infrasoft	infrasoft	ADJ
ejpam-4275	614	5	separation	separation	NOUN
ejpam-4275	614	6	axioms	axiom	NOUN
ejpam-4275	614	7	.	.	PUNCT
ejpam-4275	615	1	journal	journal	NOUN
ejpam-4275	615	2	of	of	ADP
ejpam-4275	615	3	mathematics	mathematic	NOUN
ejpam-4275	615	4	,	,	PUNCT
ejpam-4275	615	5	volume	volume	NOUN
ejpam-4275	615	6	2021	2021	NUM
ejpam-4275	615	7	,	,	PUNCT
ejpam-4275	615	8	article	article	NOUN
ejpam-4275	615	9	i	i	PROPN
ejpam-4275	615	10	d	d	PROPN
ejpam-4275	615	11	4816893	4816893	NUM
ejpam-4275	615	12	,	,	PUNCT
ejpam-4275	615	13	2021	2021	NUM
ejpam-4275	615	14	.	.	PUNCT
ejpam-4275	616	1	[	[	X
ejpam-4275	616	2	17	17	NUM
ejpam-4275	616	3	]	]	X
ejpam-4275	616	4	t	t	PROPN
ejpam-4275	616	5	m	m	PROPN
ejpam-4275	616	6	al	al	PROPN
ejpam-4275	616	7	-	-	PUNCT
ejpam-4275	616	8	shami	shami	PROPN
ejpam-4275	616	9	and	and	CCONJ
ejpam-4275	616	10	a	a	DET
ejpam-4275	616	11	mhemdi	mhemdi	NOUN
ejpam-4275	616	12	.	.	PUNCT
ejpam-4275	617	1	two	two	NUM
ejpam-4275	617	2	families	family	NOUN
ejpam-4275	617	3	of	of	ADP
ejpam-4275	617	4	separation	separation	NOUN
ejpam-4275	617	5	axioms	axiom	NOUN
ejpam-4275	617	6	on	on	ADP
ejpam-4275	617	7	infra	infra	NOUN
ejpam-4275	617	8	soft	soft	ADJ
ejpam-4275	617	9	topological	topological	ADJ
ejpam-4275	617	10	spaces	space	NOUN
ejpam-4275	617	11	.	.	PUNCT
ejpam-4275	618	1	filomat	filomat	NOUN
ejpam-4275	618	2	,	,	PUNCT
ejpam-4275	618	3	2022	2022	NUM
ejpam-4275	618	4	.	.	PUNCT
ejpam-4275	619	1	[	[	X
ejpam-4275	619	2	18	18	NUM
ejpam-4275	619	3	]	]	X
ejpam-4275	619	4	j	j	PROPN
ejpam-4275	619	5	c	c	NOUN
ejpam-4275	619	6	r	r	NOUN
ejpam-4275	619	7	alcantud	alcantud	PROPN
ejpam-4275	619	8	.	.	PUNCT
ejpam-4275	620	1	soft	soft	ADJ
ejpam-4275	620	2	open	open	ADJ
ejpam-4275	620	3	bases	basis	NOUN
ejpam-4275	620	4	and	and	CCONJ
ejpam-4275	620	5	a	a	DET
ejpam-4275	620	6	novel	novel	ADJ
ejpam-4275	620	7	construction	construction	NOUN
ejpam-4275	620	8	of	of	ADP
ejpam-4275	620	9	soft	soft	ADJ
ejpam-4275	620	10	topologies	topology	NOUN
ejpam-4275	620	11	from	from	ADP
ejpam-4275	620	12	bases	basis	NOUN
ejpam-4275	620	13	for	for	ADP
ejpam-4275	620	14	topologies	topology	NOUN
ejpam-4275	620	15	.	.	PUNCT
ejpam-4275	621	1	mathematics	mathematic	NOUN
ejpam-4275	621	2	,	,	PUNCT
ejpam-4275	621	3	8(5):672	8(5):672	NUM
ejpam-4275	621	4	,	,	PUNCT
ejpam-4275	621	5	2020	2020	NUM
ejpam-4275	621	6	.	.	PUNCT
ejpam-4275	622	1	[	[	X
ejpam-4275	622	2	19	19	NUM
ejpam-4275	622	3	]	]	X
ejpam-4275	622	4	m	m	VERB
ejpam-4275	622	5	i	i	NOUN
ejpam-4275	622	6	ali	ali	PROPN
ejpam-4275	622	7	,	,	PUNCT
ejpam-4275	622	8	f	f	PROPN
ejpam-4275	622	9	feng	feng	PROPN
ejpam-4275	622	10	,	,	PUNCT
ejpam-4275	622	11	x	x	PROPN
ejpam-4275	622	12	liu	liu	PROPN
ejpam-4275	622	13	,	,	PUNCT
ejpam-4275	622	14	w	w	PROPN
ejpam-4275	622	15	k	k	PROPN
ejpam-4275	622	16	min	min	PROPN
ejpam-4275	622	17	,	,	PUNCT
ejpam-4275	622	18	and	and	CCONJ
ejpam-4275	622	19	m	m	PROPN
ejpam-4275	622	20	shabir	shabir	PROPN
ejpam-4275	622	21	.	.	PUNCT
ejpam-4275	623	1	on	on	ADP
ejpam-4275	623	2	some	some	DET
ejpam-4275	623	3	new	new	ADJ
ejpam-4275	623	4	operations	operation	NOUN
ejpam-4275	623	5	in	in	ADP
ejpam-4275	623	6	soft	soft	ADJ
ejpam-4275	623	7	set	set	NOUN
ejpam-4275	623	8	theory	theory	NOUN
ejpam-4275	623	9	.	.	PUNCT
ejpam-4275	624	1	computers	computer	NOUN
ejpam-4275	624	2	and	and	CCONJ
ejpam-4275	624	3	mathematics	mathematic	NOUN
ejpam-4275	624	4	with	with	ADP
ejpam-4275	624	5	applications	application	NOUN
ejpam-4275	624	6	,	,	PUNCT
ejpam-4275	624	7	57	57	NUM
ejpam-4275	624	8	,	,	PUNCT
ejpam-4275	624	9	2009	2009	NUM
ejpam-4275	624	10	.	.	PUNCT
ejpam-4275	625	1	[	[	X
ejpam-4275	625	2	20	20	NUM
ejpam-4275	625	3	]	]	SYM
ejpam-4275	625	4	b	b	NOUN
ejpam-4275	625	5	a	a	DET
ejpam-4275	625	6	asaad	asaad	NOUN
ejpam-4275	625	7	,	,	PUNCT
ejpam-4275	625	8	t	t	PROPN
ejpam-4275	625	9	m	m	PROPN
ejpam-4275	625	10	al	al	PROPN
ejpam-4275	625	11	-	-	PUNCT
ejpam-4275	625	12	shami	shami	PROPN
ejpam-4275	625	13	,	,	PUNCT
ejpam-4275	625	14	and	and	CCONJ
ejpam-4275	625	15	a	a	DET
ejpam-4275	625	16	mhemdi	mhemdi	NOUN
ejpam-4275	625	17	.	.	PUNCT
ejpam-4275	626	1	bioperators	bioperator	NOUN
ejpam-4275	626	2	on	on	ADP
ejpam-4275	626	3	soft	soft	ADJ
ejpam-4275	626	4	topological	topological	ADJ
ejpam-4275	626	5	spaces	space	NOUN
ejpam-4275	626	6	.	.	PUNCT
ejpam-4275	627	1	aims	aim	VERB
ejpam-4275	627	2	mathematics	mathematic	NOUN
ejpam-4275	627	3	,	,	PUNCT
ejpam-4275	627	4	6(11):12471–12490	6(11):12471–12490	NUM
ejpam-4275	627	5	,	,	PUNCT
ejpam-4275	627	6	2021	2021	NUM
ejpam-4275	627	7	.	.	PUNCT
ejpam-4275	628	1	references	reference	NOUN
ejpam-4275	628	2	279	279	NUM
ejpam-4275	628	3	[	[	X
ejpam-4275	628	4	21	21	NUM
ejpam-4275	628	5	]	]	PUNCT
ejpam-4275	628	6	a	a	DET
ejpam-4275	628	7	aygünoǧlu	aygünoǧlu	PROPN
ejpam-4275	628	8	and	and	CCONJ
ejpam-4275	628	9	h	h	NOUN
ejpam-4275	628	10	aygün	aygün	NOUN
ejpam-4275	628	11	.	.	PUNCT
ejpam-4275	629	1	some	some	DET
ejpam-4275	629	2	notes	note	NOUN
ejpam-4275	629	3	on	on	ADP
ejpam-4275	629	4	soft	soft	ADJ
ejpam-4275	629	5	topological	topological	ADJ
ejpam-4275	629	6	spaces	space	NOUN
ejpam-4275	629	7	.	.	PUNCT
ejpam-4275	630	1	neural	neural	ADJ
ejpam-4275	630	2	computing	computing	NOUN
ejpam-4275	630	3	and	and	CCONJ
ejpam-4275	630	4	applications	application	NOUN
ejpam-4275	630	5	,	,	PUNCT
ejpam-4275	630	6	21	21	NUM
ejpam-4275	630	7	,	,	PUNCT
ejpam-4275	630	8	2012	2012	NUM
ejpam-4275	630	9	.	.	PUNCT
ejpam-4275	631	1	[	[	X
ejpam-4275	631	2	22	22	NUM
ejpam-4275	631	3	]	]	PUNCT
ejpam-4275	631	4	n	n	PRON
ejpam-4275	631	5	çağman	çağman	NOUN
ejpam-4275	631	6	and	and	CCONJ
ejpam-4275	631	7	s	s	NOUN
ejpam-4275	631	8	enginoğlu	enginoğlu	PROPN
ejpam-4275	631	9	.	.	PUNCT
ejpam-4275	631	10	soft	soft	ADJ
ejpam-4275	631	11	matrix	matrix	NOUN
ejpam-4275	631	12	theory	theory	NOUN
ejpam-4275	631	13	and	and	CCONJ
ejpam-4275	631	14	its	its	PRON
ejpam-4275	631	15	decision	decision	NOUN
ejpam-4275	631	16	making	making	NOUN
ejpam-4275	631	17	.	.	PUNCT
ejpam-4275	632	1	computers	computer	NOUN
ejpam-4275	632	2	and	and	CCONJ
ejpam-4275	632	3	mathematics	mathematic	NOUN
ejpam-4275	632	4	with	with	ADP
ejpam-4275	632	5	applications	application	NOUN
ejpam-4275	632	6	,	,	PUNCT
ejpam-4275	632	7	59:3308–3314	59:3308–3314	NUM
ejpam-4275	632	8	,	,	PUNCT
ejpam-4275	632	9	2010	2010	NUM
ejpam-4275	632	10	.	.	PUNCT
ejpam-4275	633	1	[	[	X
ejpam-4275	633	2	23	23	NUM
ejpam-4275	633	3	]	]	PUNCT
ejpam-4275	633	4	n	n	DET
ejpam-4275	633	5	çağman	çağman	NOUN
ejpam-4275	633	6	,	,	PUNCT
ejpam-4275	633	7	s	s	VERB
ejpam-4275	633	8	karataş	karataş	PROPN
ejpam-4275	633	9	,	,	PUNCT
ejpam-4275	633	10	and	and	CCONJ
ejpam-4275	633	11	s	s	VERB
ejpam-4275	633	12	enginoglu	enginoglu	NOUN
ejpam-4275	633	13	.	.	PUNCT
ejpam-4275	633	14	soft	soft	ADJ
ejpam-4275	633	15	topology	topology	NOUN
ejpam-4275	633	16	.	.	PUNCT
ejpam-4275	634	1	computers	computer	NOUN
ejpam-4275	634	2	and	and	CCONJ
ejpam-4275	634	3	mathematics	mathematic	NOUN
ejpam-4275	634	4	with	with	ADP
ejpam-4275	634	5	applications	application	NOUN
ejpam-4275	634	6	,	,	PUNCT
ejpam-4275	634	7	62	62	NUM
ejpam-4275	634	8	,	,	PUNCT
ejpam-4275	634	9	2011	2011	NUM
ejpam-4275	634	10	.	.	PUNCT
ejpam-4275	635	1	[	[	X
ejpam-4275	635	2	24	24	NUM
ejpam-4275	635	3	]	]	X
ejpam-4275	635	4	b	b	X
ejpam-4275	635	5	chen	chen	PROPN
ejpam-4275	635	6	.	.	PUNCT
ejpam-4275	636	1	soft	soft	ADJ
ejpam-4275	636	2	semi	semi	ADJ
ejpam-4275	636	3	-	-	ADJ
ejpam-4275	636	4	open	open	ADJ
ejpam-4275	636	5	sets	set	NOUN
ejpam-4275	636	6	and	and	CCONJ
ejpam-4275	636	7	related	related	ADJ
ejpam-4275	636	8	properties	property	NOUN
ejpam-4275	636	9	in	in	ADP
ejpam-4275	636	10	soft	soft	ADJ
ejpam-4275	636	11	topological	topological	ADJ
ejpam-4275	636	12	spaces	space	NOUN
ejpam-4275	636	13	.	.	PUNCT
ejpam-4275	637	1	appl	appl	PROPN
ejpam-4275	637	2	.	.	PROPN
ejpam-4275	638	1	math	math	PROPN
ejpam-4275	638	2	.	.	PUNCT
ejpam-4275	639	1	inf	inf	PROPN
ejpam-4275	639	2	.	.	PUNCT
ejpam-4275	640	1	sci	sci	PROPN
ejpam-4275	640	2	.	.	PROPN
ejpam-4275	640	3	,	,	PUNCT
ejpam-4275	640	4	7(1):287–294	7(1):287–294	PROPN
ejpam-4275	640	5	,	,	PUNCT
ejpam-4275	640	6	2013	2013	NUM
ejpam-4275	640	7	.	.	PUNCT
ejpam-4275	641	1	[	[	X
ejpam-4275	641	2	25	25	NUM
ejpam-4275	641	3	]	]	PUNCT
ejpam-4275	641	4	l	l	PUNCT
ejpam-4275	641	5	d	d	X
ejpam-4275	641	6	r.	r.	PROPN
ejpam-4275	641	7	kočinac	kočinac	PROPN
ejpam-4275	641	8	,	,	PUNCT
ejpam-4275	641	9	t	t	PROPN
ejpam-4275	641	10	m	m	PROPN
ejpam-4275	641	11	al	al	PROPN
ejpam-4275	641	12	-	-	PUNCT
ejpam-4275	641	13	shami	shami	PROPN
ejpam-4275	641	14	,	,	PUNCT
ejpam-4275	641	15	and	and	CCONJ
ejpam-4275	641	16	v	v	ADP
ejpam-4275	641	17	çetkin	çetkin	PROPN
ejpam-4275	641	18	.	.	PUNCT
ejpam-4275	642	1	selection	selection	NOUN
ejpam-4275	642	2	principles	principle	NOUN
ejpam-4275	642	3	in	in	ADP
ejpam-4275	642	4	the	the	DET
ejpam-4275	642	5	context	context	NOUN
ejpam-4275	642	6	of	of	ADP
ejpam-4275	642	7	soft	soft	ADJ
ejpam-4275	642	8	sets	set	NOUN
ejpam-4275	642	9	:	:	PUNCT
ejpam-4275	642	10	menger	menger	PROPN
ejpam-4275	642	11	spaces	space	VERB
ejpam-4275	642	12	.	.	PUNCT
ejpam-4275	643	1	soft	soft	ADJ
ejpam-4275	643	2	computing	computing	NOUN
ejpam-4275	643	3	,	,	PUNCT
ejpam-4275	643	4	25:12693–12702	25:12693–12702	NUM
ejpam-4275	643	5	,	,	PUNCT
ejpam-4275	643	6	2021	2021	NUM
ejpam-4275	643	7	.	.	PUNCT
ejpam-4275	644	1	[	[	X
ejpam-4275	644	2	26	26	NUM
ejpam-4275	644	3	]	]	X
ejpam-4275	644	4	s	s	VERB
ejpam-4275	644	5	das	das	PROPN
ejpam-4275	644	6	and	and	CCONJ
ejpam-4275	644	7	s	s	PROPN
ejpam-4275	644	8	k	k	PROPN
ejpam-4275	644	9	samanta	samanta	PROPN
ejpam-4275	644	10	.	.	PUNCT
ejpam-4275	645	1	soft	soft	ADJ
ejpam-4275	645	2	metric	metric	NOUN
ejpam-4275	645	3	.	.	PUNCT
ejpam-4275	646	1	annals	annal	NOUN
ejpam-4275	646	2	of	of	ADP
ejpam-4275	646	3	fuzzy	fuzzy	ADJ
ejpam-4275	646	4	mathematics	mathematic	NOUN
ejpam-4275	646	5	and	and	CCONJ
ejpam-4275	646	6	informatics	informatic	NOUN
ejpam-4275	646	7	,	,	PUNCT
ejpam-4275	646	8	6(1):77–94	6(1):77–94	NUM
ejpam-4275	646	9	,	,	PUNCT
ejpam-4275	646	10	2013	2013	NUM
ejpam-4275	646	11	.	.	PUNCT
ejpam-4275	647	1	[	[	X
ejpam-4275	647	2	27	27	NUM
ejpam-4275	647	3	]	]	X
ejpam-4275	647	4	m	m	PROPN
ejpam-4275	647	5	e	e	NOUN
ejpam-4275	647	6	el	el	PROPN
ejpam-4275	647	7	-	-	PUNCT
ejpam-4275	647	8	shafei	shafei	PROPN
ejpam-4275	647	9	,	,	PUNCT
ejpam-4275	647	10	m	m	NOUN
ejpam-4275	647	11	abo	abo	NOUN
ejpam-4275	647	12	-	-	PUNCT
ejpam-4275	647	13	elhamayel	elhamayel	NOUN
ejpam-4275	647	14	,	,	PUNCT
ejpam-4275	647	15	and	and	CCONJ
ejpam-4275	647	16	t	t	PROPN
ejpam-4275	647	17	m	m	PROPN
ejpam-4275	647	18	al	al	PROPN
ejpam-4275	647	19	-	-	PUNCT
ejpam-4275	647	20	shami	shami	PROPN
ejpam-4275	647	21	.	.	PUNCT
ejpam-4275	648	1	partial	partial	ADJ
ejpam-4275	648	2	soft	soft	ADJ
ejpam-4275	648	3	separation	separation	NOUN
ejpam-4275	648	4	axioms	axiom	NOUN
ejpam-4275	648	5	and	and	CCONJ
ejpam-4275	648	6	soft	soft	ADJ
ejpam-4275	648	7	compact	compact	ADJ
ejpam-4275	648	8	spaces	space	NOUN
ejpam-4275	648	9	.	.	PUNCT
ejpam-4275	649	1	filomat	filomat	NOUN
ejpam-4275	649	2	,	,	PUNCT
ejpam-4275	649	3	32(13):4755–4771	32(13):4755–4771	NUM
ejpam-4275	649	4	,	,	PUNCT
ejpam-4275	649	5	2018	2018	NUM
ejpam-4275	649	6	.	.	PUNCT
ejpam-4275	650	1	[	[	X
ejpam-4275	650	2	28	28	NUM
ejpam-4275	650	3	]	]	X
ejpam-4275	650	4	m	m	PROPN
ejpam-4275	650	5	e	e	NOUN
ejpam-4275	650	6	el	el	PROPN
ejpam-4275	650	7	-	-	PROPN
ejpam-4275	650	8	shafei	shafei	PROPN
ejpam-4275	650	9	and	and	CCONJ
ejpam-4275	650	10	t	t	PROPN
ejpam-4275	650	11	m	m	PROPN
ejpam-4275	650	12	al	al	PROPN
ejpam-4275	650	13	-	-	PUNCT
ejpam-4275	650	14	shami	shami	PROPN
ejpam-4275	650	15	.	.	PUNCT
ejpam-4275	651	1	applications	application	NOUN
ejpam-4275	651	2	of	of	ADP
ejpam-4275	651	3	partial	partial	ADJ
ejpam-4275	651	4	belong	belong	NOUN
ejpam-4275	651	5	and	and	CCONJ
ejpam-4275	651	6	total	total	ADJ
ejpam-4275	651	7	non	non	ADJ
ejpam-4275	651	8	-	-	ADJ
ejpam-4275	651	9	belong	belong	ADJ
ejpam-4275	651	10	relations	relation	NOUN
ejpam-4275	651	11	on	on	ADP
ejpam-4275	651	12	soft	soft	ADJ
ejpam-4275	651	13	separation	separation	NOUN
ejpam-4275	651	14	axioms	axiom	NOUN
ejpam-4275	651	15	and	and	CCONJ
ejpam-4275	651	16	decision	decision	NOUN
ejpam-4275	651	17	-	-	PUNCT
ejpam-4275	651	18	making	make	VERB
ejpam-4275	651	19	problem	problem	NOUN
ejpam-4275	651	20	.	.	PUNCT
ejpam-4275	652	1	computational	computational	ADJ
ejpam-4275	652	2	and	and	CCONJ
ejpam-4275	652	3	applied	applied	ADJ
ejpam-4275	652	4	mathematics	mathematic	NOUN
ejpam-4275	652	5	,	,	PUNCT
ejpam-4275	652	6	39(3):138	39(3):138	NUM
ejpam-4275	652	7	,	,	PUNCT
ejpam-4275	652	8	2020	2020	NUM
ejpam-4275	652	9	.	.	PUNCT
ejpam-4275	653	1	[	[	X
ejpam-4275	653	2	29	29	NUM
ejpam-4275	653	3	]	]	X
ejpam-4275	653	4	f	f	PROPN
ejpam-4275	653	5	feng	feng	PROPN
ejpam-4275	653	6	,	,	PUNCT
ejpam-4275	653	7	y	y	PROPN
ejpam-4275	653	8	m	m	PROPN
ejpam-4275	653	9	li	li	PROPN
ejpam-4275	653	10	,	,	PUNCT
ejpam-4275	653	11	b	b	PROPN
ejpam-4275	653	12	davvaz	davvaz	NOUN
ejpam-4275	653	13	,	,	PUNCT
ejpam-4275	653	14	and	and	CCONJ
ejpam-4275	653	15	m	m	VERB
ejpam-4275	653	16	i	i	PROPN
ejpam-4275	653	17	ali	ali	PROPN
ejpam-4275	653	18	.	.	PROPN
ejpam-4275	654	1	soft	soft	ADJ
ejpam-4275	654	2	sets	set	NOUN
ejpam-4275	654	3	combined	combine	VERB
ejpam-4275	654	4	with	with	ADP
ejpam-4275	654	5	fuzzy	fuzzy	ADJ
ejpam-4275	654	6	sets	set	NOUN
ejpam-4275	654	7	and	and	CCONJ
ejpam-4275	654	8	rough	rough	ADJ
ejpam-4275	654	9	sets	set	NOUN
ejpam-4275	654	10	:	:	PUNCT
ejpam-4275	654	11	a	a	DET
ejpam-4275	654	12	tentative	tentative	ADJ
ejpam-4275	654	13	approach	approach	NOUN
ejpam-4275	654	14	.	.	PUNCT
ejpam-4275	655	1	soft	soft	ADJ
ejpam-4275	655	2	computing	computing	NOUN
ejpam-4275	655	3	,	,	PUNCT
ejpam-4275	655	4	14	14	NUM
ejpam-4275	655	5	,	,	PUNCT
ejpam-4275	655	6	2010	2010	NUM
ejpam-4275	655	7	.	.	PUNCT
ejpam-4275	656	1	[	[	X
ejpam-4275	656	2	30	30	NUM
ejpam-4275	656	3	]	]	X
ejpam-4275	656	4	g	g	NOUN
ejpam-4275	656	5	ilango	ilango	NOUN
ejpam-4275	656	6	and	and	CCONJ
ejpam-4275	656	7	m	m	PROPN
ejpam-4275	656	8	ravindran	ravindran	NOUN
ejpam-4275	656	9	.	.	PUNCT
ejpam-4275	657	1	on	on	ADP
ejpam-4275	657	2	soft	soft	ADJ
ejpam-4275	657	3	preopen	preopen	ADJ
ejpam-4275	657	4	sets	set	NOUN
ejpam-4275	657	5	in	in	ADP
ejpam-4275	657	6	soft	soft	ADJ
ejpam-4275	657	7	topological	topological	ADJ
ejpam-4275	657	8	spaces	space	NOUN
ejpam-4275	657	9	.	.	PUNCT
ejpam-4275	658	1	international	international	ADJ
ejpam-4275	658	2	journal	journal	PROPN
ejpam-4275	658	3	of	of	ADP
ejpam-4275	658	4	mathematics	mathematics	PROPN
ejpam-4275	658	5	research	research	NOUN
ejpam-4275	658	6	,	,	PUNCT
ejpam-4275	658	7	5(4):399–409	5(4):399–409	NUM
ejpam-4275	658	8	,	,	PUNCT
ejpam-4275	658	9	2013	2013	NUM
ejpam-4275	658	10	.	.	PUNCT
ejpam-4275	659	1	[	[	X
ejpam-4275	659	2	31	31	NUM
ejpam-4275	659	3	]	]	PUNCT
ejpam-4275	659	4	a	a	DET
ejpam-4275	659	5	kharal	kharal	ADJ
ejpam-4275	659	6	and	and	CCONJ
ejpam-4275	659	7	b	b	NOUN
ejpam-4275	659	8	ahmed	ahme	VERB
ejpam-4275	659	9	.	.	PUNCT
ejpam-4275	659	10	mappings	mapping	NOUN
ejpam-4275	659	11	on	on	ADP
ejpam-4275	659	12	soft	soft	ADJ
ejpam-4275	659	13	classes	class	NOUN
ejpam-4275	659	14	.	.	PUNCT
ejpam-4275	660	1	new	new	ADJ
ejpam-4275	660	2	mathematic	mathematic	ADJ
ejpam-4275	660	3	natural	natural	ADJ
ejpam-4275	660	4	computing	computing	NOUN
ejpam-4275	660	5	,	,	PUNCT
ejpam-4275	660	6	7(3):471–481	7(3):471–481	NUM
ejpam-4275	660	7	,	,	PUNCT
ejpam-4275	660	8	2011	2011	NUM
ejpam-4275	660	9	.	.	PUNCT
ejpam-4275	661	1	[	[	X
ejpam-4275	661	2	32	32	NUM
ejpam-4275	661	3	]	]	X
ejpam-4275	661	4	f	f	PROPN
ejpam-4275	661	5	lin	lin	PROPN
ejpam-4275	661	6	.	.	PUNCT
ejpam-4275	661	7	soft	soft	ADJ
ejpam-4275	661	8	connected	connect	VERB
ejpam-4275	661	9	spaces	space	NOUN
ejpam-4275	661	10	and	and	CCONJ
ejpam-4275	661	11	soft	soft	ADJ
ejpam-4275	661	12	paracompact	paracompact	ADJ
ejpam-4275	661	13	spaces	space	NOUN
ejpam-4275	661	14	.	.	PUNCT
ejpam-4275	662	1	international	international	ADJ
ejpam-4275	662	2	journal	journal	PROPN
ejpam-4275	662	3	of	of	ADP
ejpam-4275	662	4	mathematical	mathematical	ADJ
ejpam-4275	662	5	science	science	NOUN
ejpam-4275	662	6	and	and	CCONJ
ejpam-4275	662	7	engineering	engineering	NOUN
ejpam-4275	662	8	,	,	PUNCT
ejpam-4275	662	9	7(2):1–7	7(2):1–7	NUM
ejpam-4275	662	10	,	,	PUNCT
ejpam-4275	662	11	2013	2013	NUM
ejpam-4275	662	12	.	.	PUNCT
ejpam-4275	663	1	[	[	X
ejpam-4275	663	2	33	33	NUM
ejpam-4275	663	3	]	]	X
ejpam-4275	663	4	p	p	X
ejpam-4275	663	5	k	k	PROPN
ejpam-4275	663	6	maji	maji	PROPN
ejpam-4275	663	7	,	,	PUNCT
ejpam-4275	663	8	r	r	NOUN
ejpam-4275	663	9	biswas	biswas	PROPN
ejpam-4275	663	10	,	,	PUNCT
ejpam-4275	663	11	and	and	CCONJ
ejpam-4275	663	12	r	r	PROPN
ejpam-4275	663	13	roy	roy	PROPN
ejpam-4275	663	14	.	.	PROPN
ejpam-4275	663	15	soft	soft	ADJ
ejpam-4275	663	16	set	set	NOUN
ejpam-4275	663	17	theory	theory	NOUN
ejpam-4275	663	18	.	.	PUNCT
ejpam-4275	664	1	computers	computer	NOUN
ejpam-4275	664	2	&	&	CCONJ
ejpam-4275	664	3	mathematics	mathematics	PROPN
ejpam-4275	664	4	with	with	ADP
ejpam-4275	664	5	applications	application	NOUN
ejpam-4275	664	6	,	,	PUNCT
ejpam-4275	664	7	45	45	NUM
ejpam-4275	664	8	,	,	PUNCT
ejpam-4275	664	9	2003	2003	NUM
ejpam-4275	664	10	.	.	PUNCT
ejpam-4275	665	1	[	[	X
ejpam-4275	665	2	34	34	NUM
ejpam-4275	665	3	]	]	X
ejpam-4275	665	4	d	d	X
ejpam-4275	665	5	molodtsov	molodtsov	PROPN
ejpam-4275	665	6	.	.	PUNCT
ejpam-4275	666	1	soft	soft	ADJ
ejpam-4275	666	2	set	set	NOUN
ejpam-4275	666	3	theory	theory	NOUN
ejpam-4275	666	4	-	-	PUNCT
ejpam-4275	666	5	first	first	ADJ
ejpam-4275	666	6	results	result	NOUN
ejpam-4275	666	7	.	.	PUNCT
ejpam-4275	667	1	computers	computer	NOUN
ejpam-4275	667	2	&	&	CCONJ
ejpam-4275	667	3	mathematics	mathematics	PROPN
ejpam-4275	667	4	with	with	ADP
ejpam-4275	667	5	applications	application	NOUN
ejpam-4275	667	6	,	,	PUNCT
ejpam-4275	667	7	37:19–31	37:19–31	NUM
ejpam-4275	667	8	,	,	PUNCT
ejpam-4275	667	9	1999	1999	NUM
ejpam-4275	667	10	.	.	PUNCT
ejpam-4275	668	1	[	[	X
ejpam-4275	668	2	35	35	NUM
ejpam-4275	668	3	]	]	SYM
ejpam-4275	668	4	s	s	VERB
ejpam-4275	668	5	nazmul	nazmul	ADJ
ejpam-4275	668	6	and	and	CCONJ
ejpam-4275	668	7	s	s	PROPN
ejpam-4275	669	1	k	k	PROPN
ejpam-4275	669	2	samanta	samanta	PROPN
ejpam-4275	669	3	.	.	PUNCT
ejpam-4275	670	1	neighbourhood	neighbourhood	NOUN
ejpam-4275	670	2	properties	property	NOUN
ejpam-4275	670	3	of	of	ADP
ejpam-4275	670	4	soft	soft	ADJ
ejpam-4275	670	5	topological	topological	ADJ
ejpam-4275	670	6	spaces	space	NOUN
ejpam-4275	670	7	.	.	PUNCT
ejpam-4275	671	1	annals	annal	NOUN
ejpam-4275	671	2	of	of	ADP
ejpam-4275	671	3	fuzzy	fuzzy	ADJ
ejpam-4275	671	4	mathematics	mathematic	NOUN
ejpam-4275	671	5	and	and	CCONJ
ejpam-4275	671	6	informatics	informatic	NOUN
ejpam-4275	671	7	,	,	PUNCT
ejpam-4275	671	8	6(1):1–15	6(1):1–15	NUM
ejpam-4275	671	9	,	,	PUNCT
ejpam-4275	671	10	2013	2013	NUM
ejpam-4275	671	11	.	.	PUNCT
ejpam-4275	672	1	[	[	X
ejpam-4275	672	2	36	36	NUM
ejpam-4275	672	3	]	]	X
ejpam-4275	672	4	k	k	X
ejpam-4275	672	5	qin	qin	PROPN
ejpam-4275	672	6	and	and	CCONJ
ejpam-4275	672	7	z	z	PROPN
ejpam-4275	672	8	hong	hong	PROPN
ejpam-4275	672	9	.	.	PUNCT
ejpam-4275	673	1	on	on	ADP
ejpam-4275	673	2	soft	soft	ADJ
ejpam-4275	673	3	equality	equality	NOUN
ejpam-4275	673	4	.	.	PUNCT
ejpam-4275	674	1	journal	journal	NOUN
ejpam-4275	674	2	of	of	ADP
ejpam-4275	674	3	computational	computational	ADJ
ejpam-4275	674	4	and	and	CCONJ
ejpam-4275	674	5	applied	applied	ADJ
ejpam-4275	674	6	mathematics	mathematic	NOUN
ejpam-4275	674	7	,	,	PUNCT
ejpam-4275	674	8	234	234	NUM
ejpam-4275	674	9	,	,	PUNCT
ejpam-4275	674	10	2010	2010	NUM
ejpam-4275	674	11	.	.	PUNCT
ejpam-4275	675	1	references	reference	NOUN
ejpam-4275	675	2	280	280	NUM
ejpam-4275	675	3	[	[	X
ejpam-4275	675	4	37	37	NUM
ejpam-4275	675	5	]	]	X
ejpam-4275	675	6	m	m	VERB
ejpam-4275	675	7	shabir	shabir	NOUN
ejpam-4275	675	8	and	and	CCONJ
ejpam-4275	675	9	m	m	PROPN
ejpam-4275	675	10	naz	naz	PROPN
ejpam-4275	675	11	.	.	PUNCT
ejpam-4275	676	1	on	on	ADP
ejpam-4275	676	2	soft	soft	ADJ
ejpam-4275	676	3	topological	topological	ADJ
ejpam-4275	676	4	spaces	space	NOUN
ejpam-4275	676	5	.	.	PUNCT
ejpam-4275	677	1	computers	computer	NOUN
ejpam-4275	677	2	&	&	CCONJ
ejpam-4275	677	3	mathematics	mathematics	PROPN
ejpam-4275	677	4	with	with	ADP
ejpam-4275	677	5	applications	application	NOUN
ejpam-4275	677	6	,	,	PUNCT
ejpam-4275	677	7	61	61	NUM
ejpam-4275	677	8	,	,	PUNCT
ejpam-4275	677	9	2011	2011	NUM
ejpam-4275	677	10	.	.	PUNCT
ejpam-4275	678	1	[	[	X
ejpam-4275	678	2	38	38	NUM
ejpam-4275	678	3	]	]	X
ejpam-4275	678	4	j	j	PROPN
ejpam-4275	678	5	yang	yang	PROPN
ejpam-4275	678	6	and	and	CCONJ
ejpam-4275	678	7	y	y	PROPN
ejpam-4275	678	8	yao	yao	PROPN
ejpam-4275	678	9	.	.	PUNCT
ejpam-4275	679	1	semantics	semantic	NOUN
ejpam-4275	679	2	of	of	ADP
ejpam-4275	679	3	soft	soft	ADJ
ejpam-4275	679	4	sets	set	NOUN
ejpam-4275	679	5	and	and	CCONJ
ejpam-4275	679	6	three	three	NUM
ejpam-4275	679	7	-	-	PUNCT
ejpam-4275	679	8	way	way	NOUN
ejpam-4275	679	9	decision	decision	NOUN
ejpam-4275	679	10	with	with	ADP
ejpam-4275	679	11	soft	soft	ADJ
ejpam-4275	679	12	sets	set	NOUN
ejpam-4275	679	13	.	.	PUNCT
ejpam-4275	680	1	knowledge	knowledge	NOUN
ejpam-4275	680	2	-	-	PUNCT
ejpam-4275	680	3	based	base	VERB
ejpam-4275	680	4	systems	system	NOUN
ejpam-4275	680	5	,	,	PUNCT
ejpam-4275	680	6	article	article	NOUN
ejpam-4275	680	7	i	i	PROPN
ejpam-4275	680	8	d	d	PROPN
ejpam-4275	680	9	105538	105538	NUM
ejpam-4275	680	10	,	,	PUNCT
ejpam-4275	680	11	2020	2020	NUM
ejpam-4275	680	12	.	.	PUNCT