id	sid	tid	token	lemma	pos
ejpam-3442	1	1	european	european	PROPN
ejpam-3442	1	2	journal	journal	PROPN
ejpam-3442	1	3	of	of	ADP
ejpam-3442	1	4	pure	pure	ADJ
ejpam-3442	1	5	and	and	CCONJ
ejpam-3442	1	6	applied	apply	VERB
ejpam-3442	1	7	mathematics	mathematic	NOUN
ejpam-3442	1	8	vol	vol	NOUN
ejpam-3442	1	9	.	.	PROPN
ejpam-3442	2	1	12	12	NUM
ejpam-3442	2	2	,	,	PUNCT
ejpam-3442	2	3	no	no	INTJ
ejpam-3442	2	4	.	.	NOUN
ejpam-3442	2	5	3	3	NUM
ejpam-3442	2	6	,	,	PUNCT
ejpam-3442	2	7	2019	2019	NUM
ejpam-3442	2	8	,	,	PUNCT
ejpam-3442	2	9	857	857	NUM
ejpam-3442	2	10	-	-	SYM
ejpam-3442	2	11	869	869	NUM
ejpam-3442	2	12	issn	issn	PROPN
ejpam-3442	2	13	1307	1307	NUM
ejpam-3442	2	14	-	-	SYM
ejpam-3442	2	15	5543	5543	NUM
ejpam-3442	2	16	–	–	PUNCT
ejpam-3442	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3442	2	18	published	publish	VERB
ejpam-3442	2	19	by	by	ADP
ejpam-3442	2	20	new	new	PROPN
ejpam-3442	2	21	york	york	PROPN
ejpam-3442	2	22	business	business	PROPN
ejpam-3442	2	23	global	global	ADJ
ejpam-3442	2	24	soft	soft	ADJ
ejpam-3442	2	25	semi	semi	ADJ
ejpam-3442	2	26	local	local	ADJ
ejpam-3442	2	27	functions	function	NOUN
ejpam-3442	2	28	in	in	ADP
ejpam-3442	2	29	soft	soft	ADJ
ejpam-3442	2	30	ideal	ideal	ADJ
ejpam-3442	2	31	topological	topological	ADJ
ejpam-3442	2	32	spaces	space	NOUN
ejpam-3442	2	33	f.	f.	PROPN
ejpam-3442	2	34	a.	a.	PROPN
ejpam-3442	2	35	gharib1,∗	gharib1,∗	PROPN
ejpam-3442	2	36	,	,	PUNCT
ejpam-3442	2	37	a.	a.	NOUN
ejpam-3442	2	38	m.	m.	NOUN
ejpam-3442	2	39	abd	abd	PROPN
ejpam-3442	2	40	el	el	PROPN
ejpam-3442	2	41	-	-	PROPN
ejpam-3442	2	42	latif1,2	latif1,2	ADJ
ejpam-3442	2	43	1	1	NUM
ejpam-3442	2	44	faculty	faculty	NOUN
ejpam-3442	2	45	of	of	ADP
ejpam-3442	2	46	arts	art	NOUN
ejpam-3442	2	47	and	and	CCONJ
ejpam-3442	2	48	science	science	NOUN
ejpam-3442	2	49	,	,	PUNCT
ejpam-3442	2	50	northern	northern	ADJ
ejpam-3442	2	51	border	border	NOUN
ejpam-3442	2	52	university	university	PROPN
ejpam-3442	2	53	,	,	PUNCT
ejpam-3442	2	54	rafha	rafha	NOUN
ejpam-3442	2	55	,	,	PUNCT
ejpam-3442	2	56	p.	p.	PROPN
ejpam-3442	2	57	o.	o.	PROPN
ejpam-3442	2	58	box	box	PROPN
ejpam-3442	2	59	,	,	PUNCT
ejpam-3442	2	60	840	840	NUM
ejpam-3442	2	61	,	,	PUNCT
ejpam-3442	2	62	k.	k.	PROPN
ejpam-3442	2	63	s.	s.	PROPN
ejpam-3442	2	64	a.	a.	PROPN
ejpam-3442	2	65	2	2	NUM
ejpam-3442	2	66	mathematics	mathematics	PROPN
ejpam-3442	2	67	department	department	NOUN
ejpam-3442	2	68	,	,	PUNCT
ejpam-3442	2	69	faculty	faculty	NOUN
ejpam-3442	2	70	of	of	ADP
ejpam-3442	2	71	education	education	NOUN
ejpam-3442	2	72	,	,	PUNCT
ejpam-3442	2	73	ain	ain	PROPN
ejpam-3442	2	74	shams	shams	PROPN
ejpam-3442	2	75	university	university	PROPN
ejpam-3442	2	76	,	,	PUNCT
ejpam-3442	2	77	roxy	roxy	PROPN
ejpam-3442	2	78	,	,	PUNCT
ejpam-3442	2	79	11341	11341	NUM
ejpam-3442	2	80	,	,	PUNCT
ejpam-3442	2	81	cairo	cairo	PROPN
ejpam-3442	2	82	,	,	PUNCT
ejpam-3442	2	83	egypt	egypt	PROPN
ejpam-3442	2	84	abstract	abstract	PROPN
ejpam-3442	2	85	.	.	PUNCT
ejpam-3442	3	1	in	in	ADP
ejpam-3442	3	2	this	this	DET
ejpam-3442	3	3	paper	paper	NOUN
ejpam-3442	3	4	,	,	PUNCT
ejpam-3442	3	5	we	we	PRON
ejpam-3442	3	6	define	define	VERB
ejpam-3442	3	7	a	a	DET
ejpam-3442	3	8	soft	soft	ADJ
ejpam-3442	3	9	semi	semi	ADJ
ejpam-3442	3	10	local	local	ADJ
ejpam-3442	3	11	function	function	NOUN
ejpam-3442	3	12	(	(	PUNCT
ejpam-3442	3	13	f	f	X
ejpam-3442	3	14	,	,	PUNCT
ejpam-3442	3	15	e)∗s(ĩ	e)∗s(ĩ	PROPN
ejpam-3442	3	16	,	,	PUNCT
ejpam-3442	3	17	τ	τ	X
ejpam-3442	3	18	)	)	PUNCT
ejpam-3442	3	19	by	by	ADP
ejpam-3442	3	20	using	use	VERB
ejpam-3442	3	21	semi	semi	ADV
ejpam-3442	3	22	open	open	ADJ
ejpam-3442	3	23	soft	soft	ADJ
ejpam-3442	3	24	sets	set	NOUN
ejpam-3442	3	25	in	in	ADP
ejpam-3442	3	26	a	a	DET
ejpam-3442	3	27	soft	soft	ADJ
ejpam-3442	3	28	ideal	ideal	ADJ
ejpam-3442	3	29	topological	topological	ADJ
ejpam-3442	3	30	space	space	NOUN
ejpam-3442	3	31	(	(	PUNCT
ejpam-3442	3	32	x	x	X
ejpam-3442	3	33	,	,	PUNCT
ejpam-3442	3	34	τ	τ	PROPN
ejpam-3442	3	35	,	,	PUNCT
ejpam-3442	3	36	e	e	PROPN
ejpam-3442	3	37	,	,	PUNCT
ejpam-3442	3	38	ĩ	ĩ	PROPN
ejpam-3442	3	39	)	)	PUNCT
ejpam-3442	3	40	.	.	PUNCT
ejpam-3442	4	1	this	this	DET
ejpam-3442	4	2	concept	concept	NOUN
ejpam-3442	4	3	is	be	AUX
ejpam-3442	4	4	discussed	discuss	VERB
ejpam-3442	4	5	with	with	ADP
ejpam-3442	4	6	a	a	DET
ejpam-3442	4	7	view	view	NOUN
ejpam-3442	4	8	to	to	PART
ejpam-3442	4	9	find	find	VERB
ejpam-3442	4	10	new	new	ADJ
ejpam-3442	4	11	soft	soft	ADJ
ejpam-3442	4	12	topologies	topology	NOUN
ejpam-3442	4	13	from	from	ADP
ejpam-3442	4	14	the	the	DET
ejpam-3442	4	15	original	original	ADJ
ejpam-3442	4	16	one	one	NOUN
ejpam-3442	4	17	,	,	PUNCT
ejpam-3442	4	18	called	call	VERB
ejpam-3442	4	19	∗s	∗s	NOUN
ejpam-3442	4	20	-	-	PUNCT
ejpam-3442	4	21	soft	soft	ADJ
ejpam-3442	4	22	topology	topology	NOUN
ejpam-3442	4	23	.	.	PUNCT
ejpam-3442	5	1	some	some	DET
ejpam-3442	5	2	properties	property	NOUN
ejpam-3442	5	3	and	and	CCONJ
ejpam-3442	5	4	characterizations	characterization	NOUN
ejpam-3442	5	5	of	of	ADP
ejpam-3442	5	6	soft	soft	ADJ
ejpam-3442	5	7	semi	semi	ADJ
ejpam-3442	5	8	local	local	ADJ
ejpam-3442	5	9	function	function	NOUN
ejpam-3442	5	10	are	be	AUX
ejpam-3442	5	11	explored	explore	VERB
ejpam-3442	5	12	.	.	PUNCT
ejpam-3442	6	1	finally	finally	ADV
ejpam-3442	6	2	,	,	PUNCT
ejpam-3442	6	3	the	the	DET
ejpam-3442	6	4	notion	notion	NOUN
ejpam-3442	6	5	of	of	ADP
ejpam-3442	6	6	soft	soft	ADJ
ejpam-3442	6	7	semi	semi	ADJ
ejpam-3442	6	8	compatibility	compatibility	NOUN
ejpam-3442	6	9	of	of	ADP
ejpam-3442	6	10	soft	soft	ADJ
ejpam-3442	6	11	ideals	ideal	NOUN
ejpam-3442	6	12	with	with	ADP
ejpam-3442	6	13	soft	soft	ADJ
ejpam-3442	6	14	topologies	topology	NOUN
ejpam-3442	6	15	is	be	AUX
ejpam-3442	6	16	introduced	introduce	VERB
ejpam-3442	6	17	and	and	CCONJ
ejpam-3442	6	18	some	some	DET
ejpam-3442	6	19	equivalent	equivalent	ADJ
ejpam-3442	6	20	conditions	condition	NOUN
ejpam-3442	6	21	concerning	concern	VERB
ejpam-3442	6	22	this	this	DET
ejpam-3442	6	23	topic	topic	NOUN
ejpam-3442	6	24	are	be	AUX
ejpam-3442	6	25	established	establish	VERB
ejpam-3442	6	26	here	here	ADV
ejpam-3442	6	27	.	.	PUNCT
ejpam-3442	7	1	2010	2010	NUM
ejpam-3442	7	2	mathematics	mathematic	NOUN
ejpam-3442	7	3	subject	subject	NOUN
ejpam-3442	7	4	classifications	classification	NOUN
ejpam-3442	7	5	:	:	PUNCT
ejpam-3442	7	6	54a05	54a05	NUM
ejpam-3442	7	7	,	,	PUNCT
ejpam-3442	7	8	54a40	54a40	NUM
ejpam-3442	7	9	,	,	PUNCT
ejpam-3442	7	10	06d72	06d72	VERB
ejpam-3442	7	11	key	key	ADJ
ejpam-3442	7	12	words	word	NOUN
ejpam-3442	7	13	and	and	CCONJ
ejpam-3442	7	14	phrases	phrase	NOUN
ejpam-3442	7	15	:	:	PUNCT
ejpam-3442	7	16	soft	soft	ADJ
ejpam-3442	7	17	ideal	ideal	ADJ
ejpam-3442	7	18	,	,	PUNCT
ejpam-3442	7	19	soft	soft	ADJ
ejpam-3442	7	20	semi	semi	ADJ
ejpam-3442	7	21	local	local	ADJ
ejpam-3442	7	22	function	function	NOUN
ejpam-3442	7	23	,	,	PUNCT
ejpam-3442	7	24	∗s	∗s	NOUN
ejpam-3442	7	25	-	-	PUNCT
ejpam-3442	7	26	soft	soft	ADJ
ejpam-3442	7	27	topology	topology	NOUN
ejpam-3442	7	28	,	,	PUNCT
ejpam-3442	7	29	soft	soft	ADJ
ejpam-3442	7	30	semi	semi	ADJ
ejpam-3442	7	31	compatibility	compatibility	NOUN
ejpam-3442	7	32	1	1	NUM
ejpam-3442	7	33	.	.	PUNCT
ejpam-3442	8	1	introduction	introduction	NOUN
ejpam-3442	8	2	the	the	DET
ejpam-3442	8	3	notion	notion	NOUN
ejpam-3442	8	4	of	of	ADP
ejpam-3442	8	5	ideal	ideal	ADJ
ejpam-3442	8	6	topological	topological	ADJ
ejpam-3442	8	7	spaces	space	NOUN
ejpam-3442	8	8	can	can	AUX
ejpam-3442	8	9	be	be	AUX
ejpam-3442	8	10	found	find	VERB
ejpam-3442	8	11	in	in	ADP
ejpam-3442	8	12	some	some	DET
ejpam-3442	8	13	classical	classical	ADJ
ejpam-3442	8	14	texts	text	NOUN
ejpam-3442	8	15	of	of	ADP
ejpam-3442	8	16	kuratowski	kuratowski	NOUN
ejpam-3442	9	1	[	[	X
ejpam-3442	9	2	16	16	NUM
ejpam-3442	9	3	,	,	PUNCT
ejpam-3442	9	4	17	17	NUM
ejpam-3442	9	5	]	]	PUNCT
ejpam-3442	9	6	and	and	CCONJ
ejpam-3442	9	7	vaidyanathaswamy	vaidyanathaswamy	NOUN
ejpam-3442	10	1	[	[	X
ejpam-3442	10	2	29	29	NUM
ejpam-3442	10	3	]	]	PUNCT
ejpam-3442	10	4	.	.	PUNCT
ejpam-3442	11	1	some	some	DET
ejpam-3442	11	2	early	early	ADJ
ejpam-3442	11	3	applications	application	NOUN
ejpam-3442	11	4	of	of	ADP
ejpam-3442	11	5	ideal	ideal	ADJ
ejpam-3442	11	6	topological	topological	ADJ
ejpam-3442	11	7	spaces	space	NOUN
ejpam-3442	11	8	can	can	AUX
ejpam-3442	11	9	be	be	AUX
ejpam-3442	11	10	found	find	VERB
ejpam-3442	11	11	in	in	ADP
ejpam-3442	11	12	various	various	ADJ
ejpam-3442	11	13	branches	branch	NOUN
ejpam-3442	11	14	of	of	ADP
ejpam-3442	11	15	mathematics	mathematic	NOUN
ejpam-3442	11	16	,	,	PUNCT
ejpam-3442	11	17	like	like	ADP
ejpam-3442	11	18	measure	measure	NOUN
ejpam-3442	11	19	theory	theory	NOUN
ejpam-3442	11	20	by	by	ADP
ejpam-3442	11	21	scheinberg	scheinberg	PROPN
ejpam-3442	11	22	[	[	X
ejpam-3442	11	23	27	27	NUM
ejpam-3442	11	24	]	]	PUNCT
ejpam-3442	11	25	.	.	PUNCT
ejpam-3442	12	1	in	in	ADP
ejpam-3442	12	2	1990	1990	NUM
ejpam-3442	12	3	jankovic	jankovic	PROPN
ejpam-3442	12	4	and	and	CCONJ
ejpam-3442	12	5	hamlett	hamlett	PROPN
ejpam-3442	12	6	[	[	X
ejpam-3442	12	7	6	6	NUM
ejpam-3442	12	8	]	]	PUNCT
ejpam-3442	12	9	wrote	write	VERB
ejpam-3442	12	10	a	a	DET
ejpam-3442	12	11	paper	paper	NOUN
ejpam-3442	12	12	in	in	ADP
ejpam-3442	12	13	which	which	PRON
ejpam-3442	12	14	they	they	PRON
ejpam-3442	12	15	,	,	PUNCT
ejpam-3442	12	16	among	among	ADP
ejpam-3442	12	17	their	their	PRON
ejpam-3442	12	18	results	result	NOUN
ejpam-3442	12	19	,	,	PUNCT
ejpam-3442	12	20	included	include	VERB
ejpam-3442	12	21	many	many	ADJ
ejpam-3442	12	22	other	other	ADJ
ejpam-3442	12	23	results	result	NOUN
ejpam-3442	12	24	in	in	ADP
ejpam-3442	12	25	this	this	DET
ejpam-3442	12	26	area	area	NOUN
ejpam-3442	12	27	using	use	VERB
ejpam-3442	12	28	modern	modern	ADJ
ejpam-3442	12	29	notation	notation	NOUN
ejpam-3442	12	30	,	,	PUNCT
ejpam-3442	12	31	and	and	CCONJ
ejpam-3442	12	32	logically	logically	ADV
ejpam-3442	12	33	and	and	CCONJ
ejpam-3442	12	34	systematically	systematically	ADV
ejpam-3442	12	35	arranging	arrange	VERB
ejpam-3442	12	36	them	they	PRON
ejpam-3442	12	37	.	.	PUNCT
ejpam-3442	13	1	this	this	DET
ejpam-3442	13	2	paper	paper	NOUN
ejpam-3442	13	3	rekindled	rekindle	VERB
ejpam-3442	13	4	the	the	DET
ejpam-3442	13	5	interest	interest	NOUN
ejpam-3442	13	6	in	in	ADP
ejpam-3442	13	7	this	this	DET
ejpam-3442	13	8	topic	topic	NOUN
ejpam-3442	13	9	,	,	PUNCT
ejpam-3442	13	10	resulting	result	VERB
ejpam-3442	13	11	in	in	ADP
ejpam-3442	13	12	many	many	ADJ
ejpam-3442	13	13	generalizations	generalization	NOUN
ejpam-3442	13	14	of	of	ADP
ejpam-3442	13	15	the	the	DET
ejpam-3442	13	16	ideal	ideal	ADJ
ejpam-3442	13	17	topological	topological	ADJ
ejpam-3442	13	18	space	space	NOUN
ejpam-3442	13	19	and	and	CCONJ
ejpam-3442	13	20	many	many	ADJ
ejpam-3442	13	21	generalizations	generalization	NOUN
ejpam-3442	13	22	of	of	ADP
ejpam-3442	13	23	the	the	DET
ejpam-3442	13	24	notion	notion	NOUN
ejpam-3442	13	25	of	of	ADP
ejpam-3442	13	26	open	open	ADJ
ejpam-3442	13	27	sets	set	NOUN
ejpam-3442	13	28	,	,	PUNCT
ejpam-3442	13	29	like	like	ADP
ejpam-3442	13	30	in	in	ADP
ejpam-3442	13	31	papers	paper	NOUN
ejpam-3442	13	32	of	of	ADP
ejpam-3442	13	33	jafari	jafari	PROPN
ejpam-3442	13	34	and	and	CCONJ
ejpam-3442	13	35	rajesh	rajesh	PROPN
ejpam-3442	13	36	[	[	X
ejpam-3442	13	37	5	5	NUM
ejpam-3442	13	38	]	]	PUNCT
ejpam-3442	13	39	and	and	CCONJ
ejpam-3442	13	40	manoharan	manoharan	NOUN
ejpam-3442	13	41	and	and	CCONJ
ejpam-3442	13	42	thangavelu	thangavelu	NOUN
ejpam-3442	13	43	[	[	X
ejpam-3442	13	44	22	22	NUM
ejpam-3442	13	45	]	]	PUNCT
ejpam-3442	13	46	.	.	PUNCT
ejpam-3442	14	1	in	in	ADP
ejpam-3442	14	2	1966	1966	NUM
ejpam-3442	14	3	,	,	PUNCT
ejpam-3442	14	4	velicko	velicko	NOUN
ejpam-3442	15	1	[	[	X
ejpam-3442	15	2	30	30	NUM
ejpam-3442	15	3	]	]	PUNCT
ejpam-3442	15	4	introduced	introduce	VERB
ejpam-3442	15	5	the	the	DET
ejpam-3442	15	6	notions	notion	NOUN
ejpam-3442	15	7	of	of	ADP
ejpam-3442	15	8	θ	θ	NOUN
ejpam-3442	15	9	-	-	ADJ
ejpam-3442	15	10	open	open	ADJ
ejpam-3442	15	11	and	and	CCONJ
ejpam-3442	15	12	θ	θ	ADJ
ejpam-3442	15	13	-	-	PUNCT
ejpam-3442	15	14	closed	closed	ADJ
ejpam-3442	15	15	sets	set	NOUN
ejpam-3442	15	16	,	,	PUNCT
ejpam-3442	15	17	and	and	CCONJ
ejpam-3442	15	18	also	also	ADV
ejpam-3442	15	19	a	a	DET
ejpam-3442	15	20	θ	θ	NOUN
ejpam-3442	15	21	-	-	NOUN
ejpam-3442	15	22	closure	closure	NOUN
ejpam-3442	15	23	,	,	PUNCT
ejpam-3442	15	24	examining	examine	VERB
ejpam-3442	15	25	h	h	NOUN
ejpam-3442	15	26	-	-	PUNCT
ejpam-3442	15	27	closed	closed	ADJ
ejpam-3442	15	28	spaces	space	NOUN
ejpam-3442	15	29	in	in	ADP
ejpam-3442	15	30	terms	term	NOUN
ejpam-3442	15	31	of	of	ADP
ejpam-3442	15	32	an	an	DET
ejpam-3442	15	33	arbitrary	arbitrary	ADJ
ejpam-3442	15	34	filter	filter	NOUN
ejpam-3442	15	35	base	base	NOUN
ejpam-3442	15	36	.	.	PUNCT
ejpam-3442	16	1	∗corresponding	∗corresponde	VERB
ejpam-3442	16	2	author	author	NOUN
ejpam-3442	16	3	.	.	PUNCT
ejpam-3442	17	1	doi	doi	NOUN
ejpam-3442	17	2	:	:	PUNCT
ejpam-3442	17	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3442	https://doi.org/10.29020/nybg.ejpam.v12i3.3442	PROPN
ejpam-3442	17	4	email	email	NOUN
ejpam-3442	17	5	addresses	address	NOUN
ejpam-3442	17	6	:	:	PUNCT
ejpam-3442	17	7	fatouhalmg@yahoo.com	fatouhalmg@yahoo.com	X
ejpam-3442	17	8	(	(	PUNCT
ejpam-3442	17	9	f.	f.	PROPN
ejpam-3442	17	10	a.	a.	PROPN
ejpam-3442	17	11	gharib	gharib	PROPN
ejpam-3442	17	12	)	)	PUNCT
ejpam-3442	17	13	,	,	PUNCT
ejpam-3442	17	14	alaa	alaa	PROPN
ejpam-3442	17	15	8560@yahoo.com	8560@yahoo.com	PROPN
ejpam-3442	17	16	,	,	PUNCT
ejpam-3442	17	17	alaa.ali@nbu.edu.sa	alaa.ali@nbu.edu.sa	PROPN
ejpam-3442	17	18	(	(	PUNCT
ejpam-3442	17	19	a.	a.	NOUN
ejpam-3442	17	20	m.	m.	PROPN
ejpam-3442	17	21	abd	abd	PROPN
ejpam-3442	17	22	el	el	PROPN
ejpam-3442	17	23	-	-	PROPN
ejpam-3442	17	24	latif	latif	PROPN
ejpam-3442	17	25	)	)	PUNCT
ejpam-3442	17	26	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3442	18	1	857	857	NUM
ejpam-3442	18	2	c	c	NOUN
ejpam-3442	18	3	©	©	PROPN
ejpam-3442	18	4	2019	2019	NUM
ejpam-3442	18	5	ejpam	ejpam	NOUN
ejpam-3442	18	6	all	all	DET
ejpam-3442	18	7	rights	right	NOUN
ejpam-3442	18	8	reserved	reserve	VERB
ejpam-3442	18	9	.	.	PUNCT
ejpam-3442	19	1	f.	f.	PROPN
ejpam-3442	19	2	a.	a.	PROPN
ejpam-3442	19	3	gharib	gharib	PROPN
ejpam-3442	19	4	,	,	PUNCT
ejpam-3442	19	5	a.	a.	PROPN
ejpam-3442	19	6	m.	m.	PROPN
ejpam-3442	19	7	abd	abd	PROPN
ejpam-3442	19	8	el	el	PROPN
ejpam-3442	19	9	-	-	PROPN
ejpam-3442	19	10	latif	latif	PROPN
ejpam-3442	19	11	/	/	SYM
ejpam-3442	19	12	eur	eur	PROPN
ejpam-3442	19	13	.	.	PUNCT
ejpam-3442	20	1	j.	j.	PROPN
ejpam-3442	20	2	pure	pure	PROPN
ejpam-3442	20	3	appl	appl	PROPN
ejpam-3442	20	4	.	.	PROPN
ejpam-3442	20	5	math	math	PROPN
ejpam-3442	20	6	,	,	PUNCT
ejpam-3442	20	7	12	12	NUM
ejpam-3442	20	8	(	(	PUNCT
ejpam-3442	20	9	3	3	NUM
ejpam-3442	20	10	)	)	PUNCT
ejpam-3442	20	11	(	(	PUNCT
ejpam-3442	20	12	2019	2019	NUM
ejpam-3442	20	13	)	)	PUNCT
ejpam-3442	20	14	,	,	PUNCT
ejpam-3442	20	15	857	857	NUM
ejpam-3442	20	16	-	-	SYM
ejpam-3442	20	17	869	869	NUM
ejpam-3442	20	18	858	858	NUM
ejpam-3442	20	19	in	in	ADP
ejpam-3442	20	20	[	[	X
ejpam-3442	20	21	2	2	NUM
ejpam-3442	20	22	]	]	PUNCT
ejpam-3442	20	23	,	,	PUNCT
ejpam-3442	20	24	al	al	PROPN
ejpam-3442	20	25	-	-	PUNCT
ejpam-3442	20	26	omari	omari	PROPN
ejpam-3442	20	27	and	and	CCONJ
ejpam-3442	20	28	noiri	noiri	PROPN
ejpam-3442	20	29	introduced	introduce	VERB
ejpam-3442	20	30	the	the	DET
ejpam-3442	20	31	local	local	ADJ
ejpam-3442	20	32	closure	closure	NOUN
ejpam-3442	20	33	function	function	NOUN
ejpam-3442	20	34	as	as	ADP
ejpam-3442	20	35	a	a	DET
ejpam-3442	20	36	generalization	generalization	NOUN
ejpam-3442	20	37	of	of	ADP
ejpam-3442	20	38	the	the	DET
ejpam-3442	20	39	θ	θ	NOUN
ejpam-3442	20	40	-	-	NOUN
ejpam-3442	20	41	closure	closure	NOUN
ejpam-3442	20	42	and	and	CCONJ
ejpam-3442	20	43	the	the	DET
ejpam-3442	20	44	local	local	ADJ
ejpam-3442	20	45	function	function	NOUN
ejpam-3442	20	46	in	in	ADP
ejpam-3442	20	47	an	an	DET
ejpam-3442	20	48	ideal	ideal	ADJ
ejpam-3442	20	49	topological	topological	ADJ
ejpam-3442	20	50	space	space	NOUN
ejpam-3442	20	51	.	.	PUNCT
ejpam-3442	21	1	they	they	PRON
ejpam-3442	21	2	proved	prove	VERB
ejpam-3442	21	3	some	some	DET
ejpam-3442	21	4	basic	basic	ADJ
ejpam-3442	21	5	properties	property	NOUN
ejpam-3442	21	6	for	for	ADP
ejpam-3442	21	7	the	the	DET
ejpam-3442	21	8	local	local	ADJ
ejpam-3442	21	9	closure	closure	NOUN
ejpam-3442	21	10	function	function	NOUN
ejpam-3442	21	11	,	,	PUNCT
ejpam-3442	21	12	and	and	CCONJ
ejpam-3442	21	13	also	also	ADV
ejpam-3442	21	14	introduced	introduce	VERB
ejpam-3442	21	15	two	two	NUM
ejpam-3442	21	16	new	new	ADJ
ejpam-3442	21	17	topologies	topology	NOUN
ejpam-3442	21	18	obtained	obtain	VERB
ejpam-3442	21	19	from	from	ADP
ejpam-3442	21	20	the	the	DET
ejpam-3442	21	21	original	original	ADJ
ejpam-3442	21	22	one	one	NOUN
ejpam-3442	21	23	using	use	VERB
ejpam-3442	21	24	the	the	DET
ejpam-3442	21	25	local	local	ADJ
ejpam-3442	21	26	closure	closure	NOUN
ejpam-3442	21	27	function	function	NOUN
ejpam-3442	21	28	.	.	PUNCT
ejpam-3442	22	1	abd	abd	PROPN
ejpam-3442	22	2	el	el	PROPN
ejpam-3442	22	3	monsef	monsef	PROPN
ejpam-3442	22	4	et	et	PROPN
ejpam-3442	22	5	al	al	PROPN
ejpam-3442	22	6	.	.	PUNCT
ejpam-3442	23	1	[	[	X
ejpam-3442	23	2	1	1	X
ejpam-3442	23	3	]	]	PUNCT
ejpam-3442	23	4	introduced	introduce	VERB
ejpam-3442	23	5	semi	semi	ADV
ejpam-3442	23	6	local	local	ADJ
ejpam-3442	23	7	function	function	NOUN
ejpam-3442	23	8	in	in	ADP
ejpam-3442	23	9	1992	1992	NUM
ejpam-3442	23	10	and	and	CCONJ
ejpam-3442	23	11	defined	define	VERB
ejpam-3442	23	12	a	a	DET
ejpam-3442	23	13	topologyτ∗s	topologyτ∗s	NOUN
ejpam-3442	23	14	,	,	PUNCT
ejpam-3442	23	15	which	which	PRON
ejpam-3442	23	16	investigated	investigate	VERB
ejpam-3442	23	17	recently	recently	ADV
ejpam-3442	23	18	in	in	ADP
ejpam-3442	23	19	2010	2010	NUM
ejpam-3442	23	20	in	in	ADP
ejpam-3442	23	21	[	[	X
ejpam-3442	23	22	15	15	NUM
ejpam-3442	23	23	]	]	PUNCT
ejpam-3442	23	24	.	.	PUNCT
ejpam-3442	24	1	in	in	ADP
ejpam-3442	24	2	2012	2012	NUM
ejpam-3442	24	3	,	,	PUNCT
ejpam-3442	24	4	s.	s.	PROPN
ejpam-3442	24	5	mistry	mistry	PROPN
ejpam-3442	24	6	and	and	CCONJ
ejpam-3442	24	7	s.	s.	PROPN
ejpam-3442	24	8	modak	modak	PROPN
ejpam-3442	24	9	[	[	X
ejpam-3442	24	10	20	20	NUM
ejpam-3442	24	11	]	]	SYM
ejpam-3442	24	12	defined	define	VERB
ejpam-3442	24	13	pre	pre	ADJ
ejpam-3442	24	14	local	local	ADJ
ejpam-3442	24	15	function	function	NOUN
ejpam-3442	24	16	.	.	PUNCT
ejpam-3442	25	1	the	the	DET
ejpam-3442	25	2	concept	concept	NOUN
ejpam-3442	25	3	of	of	ADP
ejpam-3442	25	4	soft	soft	ADJ
ejpam-3442	25	5	sets	set	NOUN
ejpam-3442	25	6	was	be	AUX
ejpam-3442	25	7	first	first	ADV
ejpam-3442	25	8	introduced	introduce	VERB
ejpam-3442	25	9	by	by	ADP
ejpam-3442	25	10	molodtsov	molodtsov	NOUN
ejpam-3442	25	11	[	[	X
ejpam-3442	25	12	24	24	NUM
ejpam-3442	25	13	]	]	PUNCT
ejpam-3442	25	14	in	in	ADP
ejpam-3442	25	15	1999	1999	NUM
ejpam-3442	25	16	as	as	ADP
ejpam-3442	25	17	a	a	DET
ejpam-3442	25	18	general	general	ADJ
ejpam-3442	25	19	mathematical	mathematical	ADJ
ejpam-3442	25	20	tool	tool	NOUN
ejpam-3442	25	21	for	for	ADP
ejpam-3442	25	22	dealing	deal	VERB
ejpam-3442	25	23	with	with	ADP
ejpam-3442	25	24	uncertain	uncertain	ADJ
ejpam-3442	25	25	objects	object	NOUN
ejpam-3442	25	26	.	.	PUNCT
ejpam-3442	26	1	after	after	ADP
ejpam-3442	26	2	presentation	presentation	NOUN
ejpam-3442	26	3	of	of	ADP
ejpam-3442	26	4	the	the	DET
ejpam-3442	26	5	operations	operation	NOUN
ejpam-3442	26	6	of	of	ADP
ejpam-3442	26	7	soft	soft	ADJ
ejpam-3442	26	8	sets	set	NOUN
ejpam-3442	26	9	[	[	X
ejpam-3442	26	10	21	21	NUM
ejpam-3442	26	11	]	]	PUNCT
ejpam-3442	26	12	,	,	PUNCT
ejpam-3442	26	13	the	the	DET
ejpam-3442	26	14	properties	property	NOUN
ejpam-3442	26	15	and	and	CCONJ
ejpam-3442	26	16	applications	application	NOUN
ejpam-3442	26	17	of	of	ADP
ejpam-3442	26	18	soft	soft	ADJ
ejpam-3442	26	19	set	set	NOUN
ejpam-3442	26	20	theory	theory	NOUN
ejpam-3442	26	21	have	have	AUX
ejpam-3442	26	22	been	be	AUX
ejpam-3442	26	23	studied	study	VERB
ejpam-3442	26	24	increasingly	increasingly	ADV
ejpam-3442	26	25	[	[	X
ejpam-3442	26	26	3	3	NUM
ejpam-3442	26	27	,	,	PUNCT
ejpam-3442	26	28	18	18	NUM
ejpam-3442	26	29	,	,	PUNCT
ejpam-3442	26	30	23	23	NUM
ejpam-3442	26	31	,	,	PUNCT
ejpam-3442	26	32	26	26	NUM
ejpam-3442	26	33	]	]	PUNCT
ejpam-3442	26	34	.	.	PUNCT
ejpam-3442	27	1	recently	recently	ADV
ejpam-3442	27	2	,	,	PUNCT
ejpam-3442	27	3	in	in	ADP
ejpam-3442	27	4	2011	2011	NUM
ejpam-3442	27	5	,	,	PUNCT
ejpam-3442	27	6	shabir	shabir	NOUN
ejpam-3442	27	7	and	and	CCONJ
ejpam-3442	27	8	naz	naz	PROPN
ejpam-3442	28	1	[	[	X
ejpam-3442	28	2	28	28	NUM
ejpam-3442	28	3	]	]	PUNCT
ejpam-3442	28	4	initiated	initiate	VERB
ejpam-3442	28	5	the	the	DET
ejpam-3442	28	6	study	study	NOUN
ejpam-3442	28	7	of	of	ADP
ejpam-3442	28	8	soft	soft	ADJ
ejpam-3442	28	9	topological	topological	ADJ
ejpam-3442	28	10	spaces	space	NOUN
ejpam-3442	28	11	.	.	PUNCT
ejpam-3442	29	1	the	the	DET
ejpam-3442	29	2	notion	notion	NOUN
ejpam-3442	29	3	of	of	ADP
ejpam-3442	29	4	soft	soft	ADJ
ejpam-3442	29	5	ideal	ideal	NOUN
ejpam-3442	29	6	was	be	AUX
ejpam-3442	29	7	initiated	initiate	VERB
ejpam-3442	29	8	for	for	ADP
ejpam-3442	29	9	the	the	DET
ejpam-3442	29	10	first	first	ADJ
ejpam-3442	29	11	time	time	NOUN
ejpam-3442	29	12	by	by	ADP
ejpam-3442	29	13	kandil	kandil	PROPN
ejpam-3442	29	14	et	et	PROPN
ejpam-3442	29	15	al	al	PROPN
ejpam-3442	29	16	.	.	PUNCT
ejpam-3442	30	1	[	[	X
ejpam-3442	30	2	10	10	NUM
ejpam-3442	30	3	]	]	PUNCT
ejpam-3442	30	4	.	.	PUNCT
ejpam-3442	31	1	they	they	PRON
ejpam-3442	31	2	also	also	ADV
ejpam-3442	31	3	introduced	introduce	VERB
ejpam-3442	31	4	the	the	DET
ejpam-3442	31	5	concept	concept	NOUN
ejpam-3442	31	6	of	of	ADP
ejpam-3442	31	7	soft	soft	ADJ
ejpam-3442	31	8	local	local	ADJ
ejpam-3442	31	9	function	function	NOUN
ejpam-3442	31	10	.	.	PUNCT
ejpam-3442	32	1	these	these	DET
ejpam-3442	32	2	concepts	concept	NOUN
ejpam-3442	32	3	are	be	AUX
ejpam-3442	32	4	discussed	discuss	VERB
ejpam-3442	32	5	with	with	ADP
ejpam-3442	32	6	a	a	DET
ejpam-3442	32	7	view	view	NOUN
ejpam-3442	32	8	to	to	PART
ejpam-3442	32	9	find	find	VERB
ejpam-3442	32	10	new	new	ADJ
ejpam-3442	32	11	soft	soft	ADJ
ejpam-3442	32	12	topologies	topology	NOUN
ejpam-3442	32	13	from	from	ADP
ejpam-3442	32	14	the	the	DET
ejpam-3442	32	15	original	original	ADJ
ejpam-3442	32	16	one	one	NOUN
ejpam-3442	32	17	,	,	PUNCT
ejpam-3442	32	18	called	call	VERB
ejpam-3442	32	19	soft	soft	ADJ
ejpam-3442	32	20	ideal	ideal	ADJ
ejpam-3442	32	21	topological	topological	ADJ
ejpam-3442	32	22	spaces	space	NOUN
ejpam-3442	32	23	(	(	PUNCT
ejpam-3442	32	24	x	x	X
ejpam-3442	32	25	,	,	PUNCT
ejpam-3442	32	26	τ	τ	PROPN
ejpam-3442	32	27	,	,	PUNCT
ejpam-3442	32	28	e	e	PROPN
ejpam-3442	32	29	,	,	PUNCT
ejpam-3442	32	30	ĩ	ĩ	PROPN
ejpam-3442	32	31	)	)	PUNCT
ejpam-3442	32	32	.	.	PUNCT
ejpam-3442	33	1	applications	application	NOUN
ejpam-3442	33	2	to	to	ADP
ejpam-3442	33	3	various	various	ADJ
ejpam-3442	33	4	fields	field	NOUN
ejpam-3442	33	5	were	be	AUX
ejpam-3442	33	6	further	far	ADV
ejpam-3442	33	7	investigated	investigate	VERB
ejpam-3442	33	8	by	by	ADP
ejpam-3442	33	9	kandil	kandil	PROPN
ejpam-3442	33	10	et	et	PROPN
ejpam-3442	33	11	al.[8	al.[8	PROPN
ejpam-3442	33	12	,	,	PUNCT
ejpam-3442	33	13	9	9	NUM
ejpam-3442	33	14	,	,	PUNCT
ejpam-3442	33	15	11–14	11–14	NUM
ejpam-3442	33	16	]	]	PUNCT
ejpam-3442	33	17	.	.	PUNCT
ejpam-3442	34	1	in	in	ADP
ejpam-3442	34	2	this	this	DET
ejpam-3442	34	3	paper	paper	NOUN
ejpam-3442	34	4	,	,	PUNCT
ejpam-3442	34	5	we	we	PRON
ejpam-3442	34	6	will	will	AUX
ejpam-3442	34	7	introduce	introduce	VERB
ejpam-3442	34	8	and	and	CCONJ
ejpam-3442	34	9	study	study	VERB
ejpam-3442	34	10	two	two	NUM
ejpam-3442	34	11	different	different	ADJ
ejpam-3442	34	12	notions	notion	NOUN
ejpam-3442	34	13	via	via	ADP
ejpam-3442	34	14	soft	soft	ADJ
ejpam-3442	34	15	ideals	ideal	NOUN
ejpam-3442	34	16	namely	namely	ADV
ejpam-3442	34	17	,	,	PUNCT
ejpam-3442	34	18	soft	soft	ADJ
ejpam-3442	34	19	semi	semi	ADJ
ejpam-3442	34	20	local	local	ADJ
ejpam-3442	34	21	function	function	NOUN
ejpam-3442	34	22	and	and	CCONJ
ejpam-3442	34	23	soft	soft	ADJ
ejpam-3442	34	24	semi	semi	ADJ
ejpam-3442	34	25	compatibility	compatibility	NOUN
ejpam-3442	34	26	of	of	ADP
ejpam-3442	34	27	τ	τ	PROPN
ejpam-3442	34	28	with	with	ADP
ejpam-3442	34	29	ĩ	ĩ	PROPN
ejpam-3442	34	30	and	and	CCONJ
ejpam-3442	34	31	investigate	investigate	VERB
ejpam-3442	34	32	their	their	PRON
ejpam-3442	34	33	relationships	relationship	NOUN
ejpam-3442	34	34	with	with	ADP
ejpam-3442	34	35	other	other	ADJ
ejpam-3442	34	36	types	type	NOUN
ejpam-3442	34	37	of	of	ADP
ejpam-3442	34	38	similar	similar	ADJ
ejpam-3442	34	39	operators	operator	NOUN
ejpam-3442	34	40	.	.	PUNCT
ejpam-3442	35	1	2	2	X
ejpam-3442	35	2	.	.	X
ejpam-3442	35	3	preliminaries	preliminary	NOUN
ejpam-3442	35	4	in	in	ADP
ejpam-3442	35	5	this	this	DET
ejpam-3442	35	6	section	section	NOUN
ejpam-3442	35	7	,	,	PUNCT
ejpam-3442	35	8	we	we	PRON
ejpam-3442	35	9	will	will	AUX
ejpam-3442	35	10	present	present	VERB
ejpam-3442	35	11	the	the	DET
ejpam-3442	35	12	basic	basic	ADJ
ejpam-3442	35	13	definitions	definition	NOUN
ejpam-3442	35	14	and	and	CCONJ
ejpam-3442	35	15	results	result	NOUN
ejpam-3442	35	16	of	of	ADP
ejpam-3442	35	17	soft	soft	ADJ
ejpam-3442	35	18	set	set	NOUN
ejpam-3442	35	19	theory	theory	NOUN
ejpam-3442	35	20	which	which	PRON
ejpam-3442	35	21	will	will	AUX
ejpam-3442	35	22	be	be	AUX
ejpam-3442	35	23	needed	need	VERB
ejpam-3442	35	24	in	in	ADP
ejpam-3442	35	25	the	the	DET
ejpam-3442	35	26	sequel	sequel	NOUN
ejpam-3442	35	27	.	.	PUNCT
ejpam-3442	36	1	definition	definition	NOUN
ejpam-3442	36	2	1	1	NUM
ejpam-3442	36	3	.	.	PUNCT
ejpam-3442	37	1	[	[	X
ejpam-3442	37	2	24	24	NUM
ejpam-3442	37	3	]	]	PUNCT
ejpam-3442	37	4	let	let	VERB
ejpam-3442	37	5	x	x	PRON
ejpam-3442	37	6	be	be	AUX
ejpam-3442	37	7	an	an	DET
ejpam-3442	37	8	initial	initial	ADJ
ejpam-3442	37	9	universe	universe	NOUN
ejpam-3442	37	10	and	and	CCONJ
ejpam-3442	37	11	e	e	NOUN
ejpam-3442	37	12	be	be	AUX
ejpam-3442	37	13	a	a	DET
ejpam-3442	37	14	set	set	NOUN
ejpam-3442	37	15	of	of	ADP
ejpam-3442	37	16	parameters	parameter	NOUN
ejpam-3442	37	17	.	.	PUNCT
ejpam-3442	38	1	let	let	VERB
ejpam-3442	38	2	p	p	NOUN
ejpam-3442	38	3	(	(	PUNCT
ejpam-3442	38	4	x	x	NOUN
ejpam-3442	38	5	)	)	PUNCT
ejpam-3442	38	6	denote	denote	VERB
ejpam-3442	38	7	the	the	DET
ejpam-3442	38	8	power	power	NOUN
ejpam-3442	38	9	set	set	NOUN
ejpam-3442	38	10	of	of	ADP
ejpam-3442	38	11	x	x	PROPN
ejpam-3442	38	12	and	and	CCONJ
ejpam-3442	38	13	a	a	DET
ejpam-3442	38	14	be	be	AUX
ejpam-3442	38	15	a	a	DET
ejpam-3442	38	16	non	non	ADJ
ejpam-3442	38	17	-	-	ADJ
ejpam-3442	38	18	empty	empty	ADJ
ejpam-3442	38	19	subset	subset	NOUN
ejpam-3442	38	20	of	of	ADP
ejpam-3442	38	21	e.	e.	PROPN
ejpam-3442	38	22	a	a	DET
ejpam-3442	38	23	pair	pair	NOUN
ejpam-3442	38	24	(	(	PUNCT
ejpam-3442	38	25	f	f	X
ejpam-3442	38	26	,	,	PUNCT
ejpam-3442	38	27	a	a	PRON
ejpam-3442	38	28	)	)	PUNCT
ejpam-3442	38	29	denoted	denote	VERB
ejpam-3442	38	30	by	by	ADP
ejpam-3442	38	31	fa	fa	PROPN
ejpam-3442	38	32	is	be	AUX
ejpam-3442	38	33	called	call	VERB
ejpam-3442	38	34	a	a	DET
ejpam-3442	38	35	soft	soft	ADJ
ejpam-3442	38	36	set	set	NOUN
ejpam-3442	38	37	over	over	ADP
ejpam-3442	38	38	x	x	PUNCT
ejpam-3442	38	39	,	,	PUNCT
ejpam-3442	38	40	where	where	SCONJ
ejpam-3442	38	41	f	f	PROPN
ejpam-3442	38	42	is	be	AUX
ejpam-3442	38	43	a	a	DET
ejpam-3442	38	44	mapping	mapping	NOUN
ejpam-3442	38	45	given	give	VERB
ejpam-3442	38	46	by	by	ADP
ejpam-3442	38	47	f	f	PROPN
ejpam-3442	38	48	:	:	PUNCT
ejpam-3442	38	49	a→	a→	PUNCT
ejpam-3442	38	50	p	p	X
ejpam-3442	38	51	(	(	PUNCT
ejpam-3442	38	52	x	x	X
ejpam-3442	38	53	)	)	PUNCT
ejpam-3442	39	1	i.e	i.e	PRON
ejpam-3442	39	2	fa	fa	NOUN
ejpam-3442	39	3	=	=	SYM
ejpam-3442	39	4	{	{	PUNCT
ejpam-3442	39	5	(	(	PUNCT
ejpam-3442	39	6	e	e	NOUN
ejpam-3442	39	7	,	,	PUNCT
ejpam-3442	39	8	f	f	PROPN
ejpam-3442	39	9	(	(	PUNCT
ejpam-3442	39	10	e	e	NOUN
ejpam-3442	39	11	)	)	PUNCT
ejpam-3442	39	12	)	)	PUNCT
ejpam-3442	39	13	:	:	PUNCT
ejpam-3442	40	1	e	e	X
ejpam-3442	40	2	∈	∈	PROPN
ejpam-3442	40	3	a	a	DET
ejpam-3442	40	4	⊆	⊆	NUM
ejpam-3442	40	5	e	e	NOUN
ejpam-3442	40	6	,	,	PUNCT
ejpam-3442	40	7	f	f	X
ejpam-3442	40	8	:	:	PUNCT
ejpam-3442	40	9	a	a	DET
ejpam-3442	40	10	→	→	X
ejpam-3442	40	11	p	p	X
ejpam-3442	40	12	(	(	PUNCT
ejpam-3442	40	13	x	x	NOUN
ejpam-3442	40	14	)	)	PUNCT
ejpam-3442	40	15	}	}	PUNCT
ejpam-3442	40	16	.	.	PUNCT
ejpam-3442	41	1	the	the	DET
ejpam-3442	41	2	family	family	NOUN
ejpam-3442	41	3	of	of	ADP
ejpam-3442	41	4	all	all	DET
ejpam-3442	41	5	these	these	DET
ejpam-3442	41	6	soft	soft	ADJ
ejpam-3442	41	7	sets	set	NOUN
ejpam-3442	41	8	denoted	denote	VERB
ejpam-3442	41	9	by	by	ADP
ejpam-3442	41	10	ss(x)a	ss(x)a	PROPN
ejpam-3442	41	11	.	.	PUNCT
ejpam-3442	41	12	definition	definition	NOUN
ejpam-3442	41	13	2	2	NUM
ejpam-3442	41	14	.	.	PUNCT
ejpam-3442	42	1	[	[	X
ejpam-3442	42	2	28	28	NUM
ejpam-3442	42	3	]	]	X
ejpam-3442	42	4	let	let	VERB
ejpam-3442	42	5	τ	τ	PROPN
ejpam-3442	42	6	be	be	AUX
ejpam-3442	42	7	a	a	DET
ejpam-3442	42	8	collection	collection	NOUN
ejpam-3442	42	9	of	of	ADP
ejpam-3442	42	10	soft	soft	ADJ
ejpam-3442	42	11	sets	set	NOUN
ejpam-3442	42	12	over	over	ADP
ejpam-3442	42	13	a	a	DET
ejpam-3442	42	14	universe	universe	NOUN
ejpam-3442	42	15	x	x	PUNCT
ejpam-3442	42	16	with	with	ADP
ejpam-3442	42	17	a	a	DET
ejpam-3442	42	18	fixed	fix	VERB
ejpam-3442	42	19	set	set	NOUN
ejpam-3442	42	20	of	of	ADP
ejpam-3442	42	21	parameters	parameter	NOUN
ejpam-3442	42	22	e	e	NOUN
ejpam-3442	42	23	,	,	PUNCT
ejpam-3442	42	24	then	then	ADV
ejpam-3442	42	25	it	it	PRON
ejpam-3442	42	26	is	be	AUX
ejpam-3442	42	27	called	call	VERB
ejpam-3442	42	28	a	a	DET
ejpam-3442	42	29	soft	soft	ADJ
ejpam-3442	42	30	topology	topology	NOUN
ejpam-3442	42	31	on	on	ADP
ejpam-3442	42	32	x	x	SYM
ejpam-3442	42	33	if	if	SCONJ
ejpam-3442	42	34	:	:	PUNCT
ejpam-3442	42	35	(	(	PUNCT
ejpam-3442	42	36	1	1	X
ejpam-3442	42	37	)	)	PUNCT
ejpam-3442	42	38	x̃	x̃	PROPN
ejpam-3442	42	39	,	,	PUNCT
ejpam-3442	42	40	φ̃	φ̃	PROPN
ejpam-3442	42	41	∈	∈	PROPN
ejpam-3442	42	42	τ	τ	X
ejpam-3442	42	43	,	,	PUNCT
ejpam-3442	42	44	where	where	SCONJ
ejpam-3442	42	45	φ̃(e	φ̃(e	PROPN
ejpam-3442	42	46	)	)	PUNCT
ejpam-3442	42	47	=	=	PUNCT
ejpam-3442	42	48	φ	φ	PROPN
ejpam-3442	42	49	and	and	CCONJ
ejpam-3442	42	50	x̃(e	x̃(e	PROPN
ejpam-3442	42	51	)	)	PUNCT
ejpam-3442	43	1	=	=	SYM
ejpam-3442	43	2	x	x	X
ejpam-3442	43	3	,	,	PUNCT
ejpam-3442	43	4	∀e	∀e	PROPN
ejpam-3442	43	5	∈	∈	PROPN
ejpam-3442	43	6	e	e	NOUN
ejpam-3442	43	7	,	,	PUNCT
ejpam-3442	43	8	(	(	PUNCT
ejpam-3442	43	9	2	2	X
ejpam-3442	43	10	)	)	PUNCT
ejpam-3442	43	11	the	the	DET
ejpam-3442	43	12	union	union	NOUN
ejpam-3442	43	13	of	of	ADP
ejpam-3442	43	14	any	any	DET
ejpam-3442	43	15	number	number	NOUN
ejpam-3442	43	16	of	of	ADP
ejpam-3442	43	17	soft	soft	ADJ
ejpam-3442	43	18	sets	set	NOUN
ejpam-3442	43	19	in	in	ADP
ejpam-3442	43	20	τ	τ	PROPN
ejpam-3442	43	21	belongs	belong	VERB
ejpam-3442	43	22	to	to	ADP
ejpam-3442	43	23	τ	τ	PROPN
ejpam-3442	43	24	,	,	PUNCT
ejpam-3442	43	25	(	(	PUNCT
ejpam-3442	43	26	3	3	X
ejpam-3442	43	27	)	)	PUNCT
ejpam-3442	43	28	the	the	DET
ejpam-3442	43	29	intersection	intersection	NOUN
ejpam-3442	43	30	of	of	ADP
ejpam-3442	43	31	any	any	DET
ejpam-3442	43	32	two	two	NUM
ejpam-3442	43	33	soft	soft	ADJ
ejpam-3442	43	34	sets	set	NOUN
ejpam-3442	43	35	in	in	ADP
ejpam-3442	43	36	τ	τ	PROPN
ejpam-3442	43	37	belongs	belong	VERB
ejpam-3442	43	38	to	to	ADP
ejpam-3442	43	39	τ	τ	PROPN
ejpam-3442	43	40	.	.	PUNCT
ejpam-3442	44	1	the	the	DET
ejpam-3442	44	2	triplet	triplet	NOUN
ejpam-3442	44	3	(	(	PUNCT
ejpam-3442	44	4	x	x	NOUN
ejpam-3442	44	5	,	,	PUNCT
ejpam-3442	44	6	τ	τ	PROPN
ejpam-3442	44	7	,	,	PUNCT
ejpam-3442	44	8	e	e	NOUN
ejpam-3442	44	9	)	)	PUNCT
ejpam-3442	44	10	is	be	AUX
ejpam-3442	44	11	called	call	VERB
ejpam-3442	44	12	a	a	DET
ejpam-3442	44	13	soft	soft	ADJ
ejpam-3442	44	14	topological	topological	ADJ
ejpam-3442	44	15	space	space	NOUN
ejpam-3442	44	16	over	over	ADP
ejpam-3442	44	17	x.	x.	NOUN
ejpam-3442	44	18	a	a	DET
ejpam-3442	44	19	soft	soft	ADJ
ejpam-3442	44	20	set	set	NOUN
ejpam-3442	44	21	(	(	PUNCT
ejpam-3442	44	22	f	f	X
ejpam-3442	44	23	,	,	PUNCT
ejpam-3442	44	24	a	a	PRON
ejpam-3442	44	25	)	)	PUNCT
ejpam-3442	44	26	over	over	ADP
ejpam-3442	44	27	x	x	VERB
ejpam-3442	44	28	is	be	AUX
ejpam-3442	44	29	said	say	VERB
ejpam-3442	44	30	to	to	PART
ejpam-3442	44	31	be	be	AUX
ejpam-3442	44	32	closed	close	VERB
ejpam-3442	44	33	soft	soft	ADJ
ejpam-3442	44	34	set	set	NOUN
ejpam-3442	44	35	in	in	ADP
ejpam-3442	44	36	x	x	NOUN
ejpam-3442	44	37	,	,	PUNCT
ejpam-3442	44	38	if	if	SCONJ
ejpam-3442	44	39	its	its	PRON
ejpam-3442	44	40	relative	relative	ADJ
ejpam-3442	44	41	complement	complement	NOUN
ejpam-3442	44	42	(	(	PUNCT
ejpam-3442	44	43	f	f	X
ejpam-3442	44	44	,	,	PUNCT
ejpam-3442	44	45	a)′	a)′	PROPN
ejpam-3442	44	46	is	be	AUX
ejpam-3442	44	47	an	an	DET
ejpam-3442	44	48	open	open	ADJ
ejpam-3442	44	49	soft	soft	ADJ
ejpam-3442	44	50	set	set	NOUN
ejpam-3442	44	51	.	.	PUNCT
ejpam-3442	45	1	we	we	PRON
ejpam-3442	45	2	denote	denote	VERB
ejpam-3442	45	3	the	the	DET
ejpam-3442	45	4	set	set	NOUN
ejpam-3442	45	5	of	of	ADP
ejpam-3442	45	6	all	all	DET
ejpam-3442	45	7	open	open	ADJ
ejpam-3442	45	8	soft	soft	ADJ
ejpam-3442	45	9	sets	set	NOUN
ejpam-3442	45	10	over	over	ADP
ejpam-3442	45	11	x	x	PUNCT
ejpam-3442	45	12	by	by	ADP
ejpam-3442	45	13	os(x	os(x	NOUN
ejpam-3442	45	14	,	,	PUNCT
ejpam-3442	45	15	τ	τ	X
ejpam-3442	45	16	,	,	PUNCT
ejpam-3442	45	17	e	e	NOUN
ejpam-3442	45	18	)	)	PUNCT
ejpam-3442	45	19	,	,	PUNCT
ejpam-3442	45	20	or	or	CCONJ
ejpam-3442	45	21	os(x	os(x	NOUN
ejpam-3442	45	22	)	)	PUNCT
ejpam-3442	45	23	and	and	CCONJ
ejpam-3442	45	24	the	the	DET
ejpam-3442	45	25	set	set	NOUN
ejpam-3442	45	26	of	of	ADP
ejpam-3442	45	27	all	all	DET
ejpam-3442	45	28	closed	closed	ADJ
ejpam-3442	45	29	soft	soft	ADJ
ejpam-3442	45	30	sets	set	NOUN
ejpam-3442	45	31	by	by	ADP
ejpam-3442	45	32	cs(x	cs(x	NOUN
ejpam-3442	45	33	,	,	PUNCT
ejpam-3442	45	34	τ	τ	PROPN
ejpam-3442	45	35	,	,	PUNCT
ejpam-3442	45	36	e	e	NOUN
ejpam-3442	45	37	)	)	PUNCT
ejpam-3442	45	38	,	,	PUNCT
ejpam-3442	45	39	or	or	CCONJ
ejpam-3442	45	40	cs(x	cs(x	NOUN
ejpam-3442	45	41	)	)	PUNCT
ejpam-3442	45	42	.	.	PUNCT
ejpam-3442	46	1	definition	definition	NOUN
ejpam-3442	46	2	3	3	NUM
ejpam-3442	46	3	.	.	PUNCT
ejpam-3442	47	1	[	[	X
ejpam-3442	47	2	28	28	NUM
ejpam-3442	47	3	]	]	X
ejpam-3442	47	4	let	let	AUX
ejpam-3442	47	5	(	(	PUNCT
ejpam-3442	47	6	x	x	NOUN
ejpam-3442	47	7	,	,	PUNCT
ejpam-3442	47	8	τ	τ	PROPN
ejpam-3442	47	9	,	,	PUNCT
ejpam-3442	47	10	e	e	NOUN
ejpam-3442	47	11	)	)	PUNCT
ejpam-3442	47	12	be	be	AUX
ejpam-3442	47	13	a	a	DET
ejpam-3442	47	14	soft	soft	ADJ
ejpam-3442	47	15	topological	topological	ADJ
ejpam-3442	47	16	space	space	NOUN
ejpam-3442	47	17	and	and	CCONJ
ejpam-3442	47	18	(	(	PUNCT
ejpam-3442	47	19	f	f	X
ejpam-3442	47	20	,	,	PUNCT
ejpam-3442	47	21	e	e	NOUN
ejpam-3442	47	22	)	)	PUNCT
ejpam-3442	47	23	∈	∈	PROPN
ejpam-3442	47	24	ss(x)e	ss(x)e	PROPN
ejpam-3442	47	25	.	.	PUNCT
ejpam-3442	48	1	the	the	DET
ejpam-3442	48	2	soft	soft	ADJ
ejpam-3442	48	3	closure	closure	NOUN
ejpam-3442	48	4	of	of	ADP
ejpam-3442	48	5	(	(	PUNCT
ejpam-3442	48	6	f	f	X
ejpam-3442	48	7	,	,	PUNCT
ejpam-3442	48	8	e	e	NOUN
ejpam-3442	48	9	)	)	PUNCT
ejpam-3442	48	10	,	,	PUNCT
ejpam-3442	48	11	denoted	denote	VERB
ejpam-3442	48	12	by	by	ADP
ejpam-3442	48	13	cl(f	cl(f	PROPN
ejpam-3442	48	14	,	,	PUNCT
ejpam-3442	48	15	e	e	NOUN
ejpam-3442	48	16	)	)	PUNCT
ejpam-3442	48	17	is	be	AUX
ejpam-3442	48	18	the	the	DET
ejpam-3442	48	19	intersection	intersection	NOUN
ejpam-3442	48	20	of	of	ADP
ejpam-3442	48	21	all	all	DET
ejpam-3442	48	22	closed	closed	ADJ
ejpam-3442	48	23	soft	soft	ADJ
ejpam-3442	48	24	super	super	ADJ
ejpam-3442	48	25	sets	set	NOUN
ejpam-3442	48	26	of	of	ADP
ejpam-3442	48	27	(	(	PUNCT
ejpam-3442	48	28	f	f	X
ejpam-3442	48	29	,	,	PUNCT
ejpam-3442	48	30	e	e	NOUN
ejpam-3442	48	31	)	)	PUNCT
ejpam-3442	48	32	.	.	PUNCT
ejpam-3442	49	1	f.	f.	PROPN
ejpam-3442	49	2	a.	a.	PROPN
ejpam-3442	49	3	gharib	gharib	PROPN
ejpam-3442	49	4	,	,	PUNCT
ejpam-3442	49	5	a.	a.	PROPN
ejpam-3442	49	6	m.	m.	PROPN
ejpam-3442	49	7	abd	abd	PROPN
ejpam-3442	49	8	el	el	PROPN
ejpam-3442	49	9	-	-	PROPN
ejpam-3442	49	10	latif	latif	PROPN
ejpam-3442	49	11	/	/	SYM
ejpam-3442	49	12	eur	eur	PROPN
ejpam-3442	49	13	.	.	PUNCT
ejpam-3442	50	1	j.	j.	PROPN
ejpam-3442	50	2	pure	pure	PROPN
ejpam-3442	50	3	appl	appl	PROPN
ejpam-3442	50	4	.	.	PROPN
ejpam-3442	50	5	math	math	PROPN
ejpam-3442	50	6	,	,	PUNCT
ejpam-3442	50	7	12	12	NUM
ejpam-3442	50	8	(	(	PUNCT
ejpam-3442	50	9	3	3	NUM
ejpam-3442	50	10	)	)	PUNCT
ejpam-3442	50	11	(	(	PUNCT
ejpam-3442	50	12	2019	2019	NUM
ejpam-3442	50	13	)	)	PUNCT
ejpam-3442	50	14	,	,	PUNCT
ejpam-3442	50	15	857	857	NUM
ejpam-3442	50	16	-	-	SYM
ejpam-3442	50	17	869	869	NUM
ejpam-3442	50	18	859	859	NUM
ejpam-3442	50	19	definition	definition	NOUN
ejpam-3442	50	20	4	4	NUM
ejpam-3442	50	21	.	.	PUNCT
ejpam-3442	51	1	[	[	X
ejpam-3442	51	2	31	31	NUM
ejpam-3442	51	3	]	]	X
ejpam-3442	51	4	let	let	VERB
ejpam-3442	51	5	(	(	PUNCT
ejpam-3442	51	6	x	x	NOUN
ejpam-3442	51	7	,	,	PUNCT
ejpam-3442	51	8	τ	τ	PROPN
ejpam-3442	51	9	,	,	PUNCT
ejpam-3442	51	10	e	e	NOUN
ejpam-3442	51	11	)	)	PUNCT
ejpam-3442	51	12	be	be	AUX
ejpam-3442	51	13	a	a	DET
ejpam-3442	51	14	soft	soft	ADJ
ejpam-3442	51	15	topological	topological	ADJ
ejpam-3442	51	16	space	space	NOUN
ejpam-3442	51	17	and	and	CCONJ
ejpam-3442	51	18	(	(	PUNCT
ejpam-3442	51	19	f	f	X
ejpam-3442	51	20	,	,	PUNCT
ejpam-3442	51	21	e	e	NOUN
ejpam-3442	51	22	)	)	PUNCT
ejpam-3442	51	23	∈	∈	PROPN
ejpam-3442	51	24	ss(x)e	ss(x)e	PROPN
ejpam-3442	51	25	.	.	PUNCT
ejpam-3442	52	1	the	the	DET
ejpam-3442	52	2	soft	soft	ADJ
ejpam-3442	52	3	interior	interior	NOUN
ejpam-3442	52	4	of	of	ADP
ejpam-3442	52	5	(	(	PUNCT
ejpam-3442	52	6	g	g	PROPN
ejpam-3442	52	7	,	,	PUNCT
ejpam-3442	52	8	e	e	NOUN
ejpam-3442	52	9	)	)	PUNCT
ejpam-3442	52	10	,	,	PUNCT
ejpam-3442	52	11	denoted	denote	VERB
ejpam-3442	52	12	by	by	ADP
ejpam-3442	52	13	int(g	int(g	PROPN
ejpam-3442	52	14	,	,	PUNCT
ejpam-3442	52	15	e	e	NOUN
ejpam-3442	52	16	)	)	PUNCT
ejpam-3442	52	17	is	be	AUX
ejpam-3442	52	18	the	the	DET
ejpam-3442	52	19	union	union	NOUN
ejpam-3442	52	20	of	of	ADP
ejpam-3442	52	21	all	all	DET
ejpam-3442	52	22	open	open	ADJ
ejpam-3442	52	23	soft	soft	ADJ
ejpam-3442	52	24	subsets	subset	NOUN
ejpam-3442	52	25	of	of	ADP
ejpam-3442	52	26	(	(	PUNCT
ejpam-3442	52	27	g	g	PROPN
ejpam-3442	52	28	,	,	PUNCT
ejpam-3442	52	29	e	e	NOUN
ejpam-3442	52	30	)	)	PUNCT
ejpam-3442	52	31	.	.	PUNCT
ejpam-3442	53	1	definition	definition	NOUN
ejpam-3442	53	2	5	5	NUM
ejpam-3442	53	3	.	.	PUNCT
ejpam-3442	54	1	[	[	X
ejpam-3442	54	2	31	31	NUM
ejpam-3442	54	3	]	]	PUNCT
ejpam-3442	54	4	the	the	DET
ejpam-3442	54	5	soft	soft	ADJ
ejpam-3442	54	6	set	set	NOUN
ejpam-3442	54	7	(	(	PUNCT
ejpam-3442	54	8	f	f	X
ejpam-3442	54	9	,	,	PUNCT
ejpam-3442	54	10	e	e	NOUN
ejpam-3442	54	11	)	)	PUNCT
ejpam-3442	54	12	∈	∈	PROPN
ejpam-3442	55	1	ss(x)e	ss(x)e	PROPN
ejpam-3442	55	2	is	be	AUX
ejpam-3442	55	3	called	call	VERB
ejpam-3442	55	4	a	a	DET
ejpam-3442	55	5	soft	soft	ADJ
ejpam-3442	55	6	point	point	NOUN
ejpam-3442	55	7	in	in	ADP
ejpam-3442	55	8	x̃	x̃	PROPN
ejpam-3442	55	9	if	if	SCONJ
ejpam-3442	55	10	there	there	PRON
ejpam-3442	55	11	exist	exist	VERB
ejpam-3442	55	12	x	x	X
ejpam-3442	55	13	∈	∈	PROPN
ejpam-3442	55	14	x	x	X
ejpam-3442	55	15	and	and	CCONJ
ejpam-3442	55	16	e	e	PROPN
ejpam-3442	55	17	∈	∈	PROPN
ejpam-3442	55	18	e	e	NOUN
ejpam-3442	55	19	such	such	ADJ
ejpam-3442	55	20	that	that	SCONJ
ejpam-3442	55	21	f	f	PROPN
ejpam-3442	55	22	(	(	PUNCT
ejpam-3442	55	23	e	e	NOUN
ejpam-3442	55	24	)	)	PUNCT
ejpam-3442	55	25	=	=	SYM
ejpam-3442	55	26	{	{	PUNCT
ejpam-3442	55	27	x	x	NOUN
ejpam-3442	55	28	}	}	PUNCT
ejpam-3442	55	29	and	and	CCONJ
ejpam-3442	55	30	f	f	PROPN
ejpam-3442	55	31	(	(	PUNCT
ejpam-3442	55	32	e′	e′	PROPN
ejpam-3442	55	33	)	)	PUNCT
ejpam-3442	55	34	=	=	SYM
ejpam-3442	56	1	φ	φ	PROPN
ejpam-3442	56	2	for	for	ADP
ejpam-3442	56	3	each	each	DET
ejpam-3442	56	4	e′	e′	PROPN
ejpam-3442	56	5	∈	∈	PROPN
ejpam-3442	56	6	e	e	X
ejpam-3442	56	7	−	−	PROPN
ejpam-3442	56	8	{	{	PUNCT
ejpam-3442	56	9	e	e	NOUN
ejpam-3442	56	10	}	}	PUNCT
ejpam-3442	56	11	,	,	PUNCT
ejpam-3442	56	12	and	and	CCONJ
ejpam-3442	56	13	the	the	DET
ejpam-3442	56	14	soft	soft	ADJ
ejpam-3442	56	15	point	point	NOUN
ejpam-3442	56	16	(	(	PUNCT
ejpam-3442	56	17	f	f	X
ejpam-3442	56	18	,	,	PUNCT
ejpam-3442	56	19	e	e	NOUN
ejpam-3442	56	20	)	)	PUNCT
ejpam-3442	56	21	is	be	AUX
ejpam-3442	56	22	denoted	denote	VERB
ejpam-3442	56	23	by	by	ADP
ejpam-3442	56	24	xe	xe	PROPN
ejpam-3442	56	25	.	.	PUNCT
ejpam-3442	57	1	we	we	PRON
ejpam-3442	57	2	denote	denote	VERB
ejpam-3442	57	3	the	the	DET
ejpam-3442	57	4	set	set	NOUN
ejpam-3442	57	5	of	of	ADP
ejpam-3442	57	6	all	all	DET
ejpam-3442	57	7	soft	soft	ADJ
ejpam-3442	57	8	point	point	NOUN
ejpam-3442	57	9	of	of	ADP
ejpam-3442	57	10	the	the	DET
ejpam-3442	57	11	universal	universal	ADJ
ejpam-3442	57	12	set	set	NOUN
ejpam-3442	57	13	x	x	PUNCT
ejpam-3442	57	14	by	by	ADP
ejpam-3442	57	15	ε	ε	PROPN
ejpam-3442	57	16	.	.	PUNCT
ejpam-3442	57	17	definition	definition	NOUN
ejpam-3442	57	18	6	6	NUM
ejpam-3442	57	19	.	.	PUNCT
ejpam-3442	58	1	[	[	X
ejpam-3442	58	2	31	31	NUM
ejpam-3442	58	3	]	]	PUNCT
ejpam-3442	58	4	the	the	DET
ejpam-3442	58	5	soft	soft	ADJ
ejpam-3442	58	6	point	point	NOUN
ejpam-3442	58	7	xe	xe	PROPN
ejpam-3442	58	8	is	be	AUX
ejpam-3442	58	9	said	say	VERB
ejpam-3442	58	10	to	to	PART
ejpam-3442	58	11	be	be	AUX
ejpam-3442	58	12	belonging	belong	VERB
ejpam-3442	58	13	to	to	ADP
ejpam-3442	58	14	the	the	DET
ejpam-3442	58	15	soft	soft	ADJ
ejpam-3442	58	16	set	set	NOUN
ejpam-3442	58	17	(	(	PUNCT
ejpam-3442	58	18	g	g	NOUN
ejpam-3442	58	19	,	,	PUNCT
ejpam-3442	58	20	a	a	PRON
ejpam-3442	58	21	)	)	PUNCT
ejpam-3442	58	22	,	,	PUNCT
ejpam-3442	58	23	denoted	denote	VERB
ejpam-3442	58	24	by	by	ADP
ejpam-3442	58	25	xe∈̃(g	xe∈̃(g	NOUN
ejpam-3442	58	26	,	,	PUNCT
ejpam-3442	58	27	a	a	PRON
ejpam-3442	58	28	)	)	PUNCT
ejpam-3442	58	29	,	,	PUNCT
ejpam-3442	58	30	if	if	SCONJ
ejpam-3442	58	31	for	for	ADP
ejpam-3442	58	32	the	the	DET
ejpam-3442	58	33	element	element	NOUN
ejpam-3442	58	34	e	e	PROPN
ejpam-3442	58	35	∈	∈	PROPN
ejpam-3442	58	36	a	a	PROPN
ejpam-3442	58	37	,	,	PUNCT
ejpam-3442	58	38	f	f	PROPN
ejpam-3442	58	39	(	(	PUNCT
ejpam-3442	58	40	e	e	NOUN
ejpam-3442	58	41	)	)	PUNCT
ejpam-3442	58	42	⊆	⊆	NUM
ejpam-3442	58	43	g(e	g(e	PROPN
ejpam-3442	58	44	)	)	PUNCT
ejpam-3442	58	45	.	.	PUNCT
ejpam-3442	59	1	definition	definition	NOUN
ejpam-3442	59	2	7	7	NUM
ejpam-3442	59	3	.	.	PUNCT
ejpam-3442	60	1	[	[	X
ejpam-3442	60	2	25	25	NUM
ejpam-3442	60	3	]	]	X
ejpam-3442	60	4	let	let	VERB
ejpam-3442	60	5	(	(	PUNCT
ejpam-3442	60	6	x	x	NOUN
ejpam-3442	60	7	,	,	PUNCT
ejpam-3442	60	8	τ	τ	PROPN
ejpam-3442	60	9	,	,	PUNCT
ejpam-3442	60	10	e	e	NOUN
ejpam-3442	60	11	)	)	PUNCT
ejpam-3442	60	12	be	be	AUX
ejpam-3442	60	13	a	a	DET
ejpam-3442	60	14	soft	soft	ADJ
ejpam-3442	60	15	topological	topological	ADJ
ejpam-3442	60	16	space	space	NOUN
ejpam-3442	60	17	and	and	CCONJ
ejpam-3442	60	18	(	(	PUNCT
ejpam-3442	60	19	f	f	X
ejpam-3442	60	20	,	,	PUNCT
ejpam-3442	60	21	e	e	NOUN
ejpam-3442	60	22	)	)	PUNCT
ejpam-3442	60	23	∈	∈	PROPN
ejpam-3442	60	24	ss(x)e	ss(x)e	PROPN
ejpam-3442	60	25	.	.	PUNCT
ejpam-3442	61	1	define	define	VERB
ejpam-3442	61	2	τ(f	τ(f	NOUN
ejpam-3442	61	3	,	,	PUNCT
ejpam-3442	61	4	e	e	NOUN
ejpam-3442	61	5	)	)	PUNCT
ejpam-3442	61	6	=	=	SYM
ejpam-3442	61	7	{	{	PUNCT
ejpam-3442	61	8	(	(	PUNCT
ejpam-3442	61	9	g	g	NOUN
ejpam-3442	61	10	,	,	PUNCT
ejpam-3442	61	11	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	61	12	,	,	PUNCT
ejpam-3442	61	13	e	e	NOUN
ejpam-3442	61	14	)	)	PUNCT
ejpam-3442	61	15	:	:	PUNCT
ejpam-3442	61	16	(	(	PUNCT
ejpam-3442	61	17	g	g	NOUN
ejpam-3442	61	18	,	,	PUNCT
ejpam-3442	61	19	e	e	NOUN
ejpam-3442	61	20	)	)	PUNCT
ejpam-3442	61	21	∈	∈	PROPN
ejpam-3442	61	22	τ	τ	PROPN
ejpam-3442	61	23	}	}	PUNCT
ejpam-3442	61	24	,	,	PUNCT
ejpam-3442	61	25	which	which	PRON
ejpam-3442	61	26	is	be	AUX
ejpam-3442	61	27	a	a	DET
ejpam-3442	61	28	soft	soft	ADJ
ejpam-3442	61	29	topology	topology	NOUN
ejpam-3442	61	30	on	on	ADP
ejpam-3442	61	31	(	(	PUNCT
ejpam-3442	61	32	f	f	X
ejpam-3442	61	33	,	,	PUNCT
ejpam-3442	61	34	e	e	NOUN
ejpam-3442	61	35	)	)	PUNCT
ejpam-3442	61	36	.	.	PUNCT
ejpam-3442	62	1	this	this	DET
ejpam-3442	62	2	soft	soft	ADJ
ejpam-3442	62	3	topology	topology	NOUN
ejpam-3442	62	4	is	be	AUX
ejpam-3442	62	5	called	call	VERB
ejpam-3442	62	6	a	a	DET
ejpam-3442	62	7	soft	soft	ADJ
ejpam-3442	62	8	relative	relative	ADJ
ejpam-3442	62	9	topology	topology	NOUN
ejpam-3442	62	10	of	of	ADP
ejpam-3442	62	11	τ	τ	PROPN
ejpam-3442	62	12	on	on	ADP
ejpam-3442	62	13	(	(	PUNCT
ejpam-3442	62	14	f	f	X
ejpam-3442	62	15	,	,	PUNCT
ejpam-3442	62	16	e	e	NOUN
ejpam-3442	62	17	)	)	PUNCT
ejpam-3442	62	18	,	,	PUNCT
ejpam-3442	62	19	and	and	CCONJ
ejpam-3442	62	20	[	[	X
ejpam-3442	62	21	(	(	PUNCT
ejpam-3442	62	22	f	f	X
ejpam-3442	62	23	,	,	PUNCT
ejpam-3442	62	24	e	e	NOUN
ejpam-3442	62	25	)	)	PUNCT
ejpam-3442	62	26	,	,	PUNCT
ejpam-3442	62	27	τ(f	τ(f	PROPN
ejpam-3442	62	28	,	,	PUNCT
ejpam-3442	62	29	e	e	NOUN
ejpam-3442	62	30	)	)	PUNCT
ejpam-3442	62	31	]	]	PUNCT
ejpam-3442	62	32	is	be	AUX
ejpam-3442	62	33	called	call	VERB
ejpam-3442	62	34	a	a	DET
ejpam-3442	62	35	soft	soft	ADJ
ejpam-3442	62	36	subspace	subspace	NOUN
ejpam-3442	62	37	of	of	ADP
ejpam-3442	62	38	(	(	PUNCT
ejpam-3442	62	39	x	x	PROPN
ejpam-3442	62	40	,	,	PUNCT
ejpam-3442	62	41	τ	τ	PROPN
ejpam-3442	62	42	,	,	PUNCT
ejpam-3442	62	43	e	e	NOUN
ejpam-3442	62	44	)	)	PUNCT
ejpam-3442	62	45	.	.	PUNCT
ejpam-3442	63	1	definition	definition	NOUN
ejpam-3442	63	2	8	8	NUM
ejpam-3442	63	3	.	.	PUNCT
ejpam-3442	64	1	[	[	X
ejpam-3442	64	2	4	4	NUM
ejpam-3442	64	3	,	,	PUNCT
ejpam-3442	64	4	7	7	NUM
ejpam-3442	64	5	]	]	PUNCT
ejpam-3442	64	6	a	a	DET
ejpam-3442	64	7	soft	soft	ADJ
ejpam-3442	64	8	set	set	NOUN
ejpam-3442	64	9	(	(	PUNCT
ejpam-3442	64	10	f	f	X
ejpam-3442	64	11	,	,	PUNCT
ejpam-3442	64	12	e	e	NOUN
ejpam-3442	64	13	)	)	PUNCT
ejpam-3442	64	14	of	of	ADP
ejpam-3442	64	15	a	a	DET
ejpam-3442	64	16	soft	soft	ADJ
ejpam-3442	64	17	topological	topological	ADJ
ejpam-3442	64	18	space	space	NOUN
ejpam-3442	64	19	(	(	PUNCT
ejpam-3442	64	20	x	x	X
ejpam-3442	64	21	,	,	PUNCT
ejpam-3442	64	22	τ	τ	PROPN
ejpam-3442	64	23	,	,	PUNCT
ejpam-3442	64	24	e	e	NOUN
ejpam-3442	64	25	)	)	PUNCT
ejpam-3442	64	26	is	be	AUX
ejpam-3442	64	27	called	call	VERB
ejpam-3442	64	28	semi	semi	ADV
ejpam-3442	64	29	open	open	ADJ
ejpam-3442	64	30	soft	soft	ADJ
ejpam-3442	64	31	,	,	PUNCT
ejpam-3442	64	32	if	if	SCONJ
ejpam-3442	64	33	fe⊆̃cl(int(fe	fe⊆̃cl(int(fe	NOUN
ejpam-3442	64	34	)	)	PUNCT
ejpam-3442	64	35	)	)	PUNCT
ejpam-3442	65	1	(	(	PUNCT
ejpam-3442	65	2	resp	resp	NOUN
ejpam-3442	65	3	.	.	PUNCT
ejpam-3442	65	4	,	,	PUNCT
ejpam-3442	65	5	semi	semi	ADV
ejpam-3442	65	6	closed	close	VERB
ejpam-3442	65	7	soft	soft	ADJ
ejpam-3442	65	8	,	,	PUNCT
ejpam-3442	65	9	if	if	SCONJ
ejpam-3442	65	10	int(cl(fe))⊆̃fe	int(cl(fe))⊆̃fe	NOUN
ejpam-3442	65	11	)	)	PUNCT
ejpam-3442	65	12	.	.	PUNCT
ejpam-3442	66	1	the	the	DET
ejpam-3442	66	2	set	set	NOUN
ejpam-3442	66	3	of	of	ADP
ejpam-3442	66	4	all	all	DET
ejpam-3442	66	5	semi	semi	ADV
ejpam-3442	66	6	open	open	ADJ
ejpam-3442	66	7	soft	soft	ADJ
ejpam-3442	66	8	sets	set	NOUN
ejpam-3442	66	9	is	be	AUX
ejpam-3442	66	10	denoted	denote	VERB
ejpam-3442	66	11	by	by	ADP
ejpam-3442	66	12	sos(x	sos(x	PROPN
ejpam-3442	66	13	)	)	PUNCT
ejpam-3442	66	14	and	and	CCONJ
ejpam-3442	66	15	the	the	DET
ejpam-3442	66	16	set	set	NOUN
ejpam-3442	66	17	of	of	ADP
ejpam-3442	66	18	all	all	DET
ejpam-3442	66	19	semi	semi	ADV
ejpam-3442	66	20	closed	closed	ADJ
ejpam-3442	66	21	soft	soft	ADJ
ejpam-3442	66	22	sets	set	NOUN
ejpam-3442	66	23	is	be	AUX
ejpam-3442	66	24	denoted	denote	VERB
ejpam-3442	66	25	by	by	ADP
ejpam-3442	66	26	scs(x	scs(x	PROPN
ejpam-3442	66	27	)	)	PUNCT
ejpam-3442	66	28	.	.	PUNCT
ejpam-3442	67	1	also	also	ADV
ejpam-3442	67	2	,	,	PUNCT
ejpam-3442	67	3	the	the	DET
ejpam-3442	67	4	semi	semi	ADJ
ejpam-3442	67	5	soft	soft	ADJ
ejpam-3442	67	6	closure	closure	NOUN
ejpam-3442	67	7	of	of	ADP
ejpam-3442	67	8	(	(	PUNCT
ejpam-3442	67	9	f	f	X
ejpam-3442	67	10	,	,	PUNCT
ejpam-3442	67	11	e	e	NOUN
ejpam-3442	67	12	)	)	PUNCT
ejpam-3442	67	13	,	,	PUNCT
ejpam-3442	67	14	denoted	denote	VERB
ejpam-3442	67	15	by	by	ADP
ejpam-3442	67	16	scl(f	scl(f	PROPN
ejpam-3442	67	17	,	,	PUNCT
ejpam-3442	67	18	e	e	NOUN
ejpam-3442	67	19	)	)	PUNCT
ejpam-3442	67	20	,	,	PUNCT
ejpam-3442	67	21	is	be	AUX
ejpam-3442	67	22	defined	define	VERB
ejpam-3442	67	23	by	by	ADP
ejpam-3442	67	24	the	the	DET
ejpam-3442	67	25	intersection	intersection	NOUN
ejpam-3442	67	26	of	of	ADP
ejpam-3442	67	27	all	all	DET
ejpam-3442	67	28	semi	semi	ADV
ejpam-3442	67	29	closed	closed	ADJ
ejpam-3442	67	30	soft	soft	ADJ
ejpam-3442	67	31	sets	set	NOUN
ejpam-3442	67	32	containing	contain	VERB
ejpam-3442	67	33	(	(	PUNCT
ejpam-3442	67	34	f	f	X
ejpam-3442	67	35	,	,	PUNCT
ejpam-3442	67	36	e	e	NOUN
ejpam-3442	67	37	)	)	PUNCT
ejpam-3442	67	38	.	.	PUNCT
ejpam-3442	68	1	definition	definition	NOUN
ejpam-3442	68	2	9	9	NUM
ejpam-3442	68	3	.	.	PUNCT
ejpam-3442	69	1	[	[	X
ejpam-3442	69	2	6	6	NUM
ejpam-3442	69	3	]	]	PUNCT
ejpam-3442	69	4	.	.	PUNCT
ejpam-3442	70	1	a	a	DET
ejpam-3442	70	2	non	non	ADJ
ejpam-3442	70	3	-	-	ADJ
ejpam-3442	70	4	empty	empty	ADJ
ejpam-3442	70	5	collection	collection	NOUN
ejpam-3442	70	6	i	i	PROPN
ejpam-3442	70	7	of	of	ADP
ejpam-3442	70	8	subsets	subset	NOUN
ejpam-3442	70	9	of	of	ADP
ejpam-3442	70	10	a	a	DET
ejpam-3442	70	11	set	set	NOUN
ejpam-3442	70	12	x	x	PUNCT
ejpam-3442	70	13	is	be	AUX
ejpam-3442	70	14	called	call	VERB
ejpam-3442	70	15	an	an	DET
ejpam-3442	70	16	ideal	ideal	NOUN
ejpam-3442	70	17	on	on	ADP
ejpam-3442	70	18	x	x	NOUN
ejpam-3442	70	19	,	,	PUNCT
ejpam-3442	70	20	if	if	SCONJ
ejpam-3442	70	21	it	it	PRON
ejpam-3442	70	22	is	be	AUX
ejpam-3442	70	23	closed	close	VERB
ejpam-3442	70	24	under	under	ADP
ejpam-3442	70	25	finite	finite	ADJ
ejpam-3442	70	26	unions	union	NOUN
ejpam-3442	70	27	and	and	CCONJ
ejpam-3442	70	28	subsets	subset	NOUN
ejpam-3442	70	29	.	.	PUNCT
ejpam-3442	71	1	3	3	X
ejpam-3442	71	2	.	.	X
ejpam-3442	71	3	soft	soft	ADJ
ejpam-3442	71	4	semi	semi	ADJ
ejpam-3442	71	5	local	local	ADJ
ejpam-3442	71	6	functions	function	NOUN
ejpam-3442	71	7	and	and	CCONJ
ejpam-3442	71	8	generated	generate	VERB
ejpam-3442	71	9	a	a	DET
ejpam-3442	71	10	new	new	ADJ
ejpam-3442	71	11	soft	soft	ADJ
ejpam-3442	71	12	topology	topology	NOUN
ejpam-3442	71	13	in	in	ADP
ejpam-3442	71	14	this	this	DET
ejpam-3442	71	15	section	section	NOUN
ejpam-3442	71	16	,	,	PUNCT
ejpam-3442	71	17	we	we	PRON
ejpam-3442	71	18	will	will	AUX
ejpam-3442	71	19	introduce	introduce	VERB
ejpam-3442	71	20	a	a	DET
ejpam-3442	71	21	soft	soft	ADJ
ejpam-3442	71	22	semi	semi	ADJ
ejpam-3442	71	23	local	local	ADJ
ejpam-3442	71	24	function	function	NOUN
ejpam-3442	71	25	(	(	PUNCT
ejpam-3442	71	26	f	f	X
ejpam-3442	71	27	,	,	PUNCT
ejpam-3442	71	28	e)∗s(ĩ	e)∗s(ĩ	PROPN
ejpam-3442	71	29	,	,	PUNCT
ejpam-3442	71	30	τ	τ	X
ejpam-3442	71	31	)	)	PUNCT
ejpam-3442	71	32	by	by	ADP
ejpam-3442	71	33	using	use	VERB
ejpam-3442	71	34	semi	semi	ADV
ejpam-3442	71	35	open	open	ADJ
ejpam-3442	71	36	soft	soft	ADJ
ejpam-3442	71	37	sets	set	NOUN
ejpam-3442	71	38	in	in	ADP
ejpam-3442	71	39	a	a	DET
ejpam-3442	71	40	soft	soft	ADJ
ejpam-3442	71	41	ideal	ideal	ADJ
ejpam-3442	71	42	topological	topological	ADJ
ejpam-3442	71	43	space	space	NOUN
ejpam-3442	71	44	(	(	PUNCT
ejpam-3442	71	45	x	x	X
ejpam-3442	71	46	,	,	PUNCT
ejpam-3442	71	47	τ	τ	PROPN
ejpam-3442	71	48	,	,	PUNCT
ejpam-3442	71	49	e	e	PROPN
ejpam-3442	71	50	,	,	PUNCT
ejpam-3442	71	51	ĩ	ĩ	PROPN
ejpam-3442	71	52	)	)	PUNCT
ejpam-3442	71	53	.	.	PUNCT
ejpam-3442	72	1	this	this	DET
ejpam-3442	72	2	concept	concept	NOUN
ejpam-3442	72	3	is	be	AUX
ejpam-3442	72	4	discussed	discuss	VERB
ejpam-3442	72	5	with	with	ADP
ejpam-3442	72	6	a	a	DET
ejpam-3442	72	7	view	view	NOUN
ejpam-3442	72	8	to	to	PART
ejpam-3442	72	9	find	find	VERB
ejpam-3442	72	10	new	new	ADJ
ejpam-3442	72	11	soft	soft	ADJ
ejpam-3442	72	12	topologies	topology	NOUN
ejpam-3442	72	13	from	from	ADP
ejpam-3442	72	14	the	the	DET
ejpam-3442	72	15	original	original	ADJ
ejpam-3442	72	16	one	one	NOUN
ejpam-3442	72	17	,	,	PUNCT
ejpam-3442	72	18	called	call	VERB
ejpam-3442	72	19	∗s	∗s	NOUN
ejpam-3442	72	20	-	-	PUNCT
ejpam-3442	72	21	soft	soft	ADJ
ejpam-3442	72	22	topology	topology	NOUN
ejpam-3442	72	23	.	.	PUNCT
ejpam-3442	73	1	some	some	DET
ejpam-3442	73	2	properties	property	NOUN
ejpam-3442	73	3	and	and	CCONJ
ejpam-3442	73	4	characterizations	characterization	NOUN
ejpam-3442	73	5	of	of	ADP
ejpam-3442	73	6	soft	soft	ADJ
ejpam-3442	73	7	semi	semi	ADJ
ejpam-3442	73	8	local	local	ADJ
ejpam-3442	73	9	function	function	NOUN
ejpam-3442	73	10	will	will	AUX
ejpam-3442	73	11	be	be	AUX
ejpam-3442	73	12	studied	study	VERB
ejpam-3442	73	13	.	.	PUNCT
ejpam-3442	74	1	definition	definition	NOUN
ejpam-3442	74	2	10	10	NUM
ejpam-3442	74	3	.	.	PUNCT
ejpam-3442	75	1	[	[	X
ejpam-3442	75	2	10	10	NUM
ejpam-3442	75	3	]	]	PUNCT
ejpam-3442	75	4	let	let	VERB
ejpam-3442	75	5	ĩ	ĩ	PROPN
ejpam-3442	75	6	be	be	AUX
ejpam-3442	75	7	a	a	DET
ejpam-3442	75	8	non	non	ADJ
ejpam-3442	75	9	-	-	ADJ
ejpam-3442	75	10	null	null	ADJ
ejpam-3442	75	11	collection	collection	NOUN
ejpam-3442	75	12	of	of	ADP
ejpam-3442	75	13	soft	soft	ADJ
ejpam-3442	75	14	sets	set	NOUN
ejpam-3442	75	15	over	over	ADP
ejpam-3442	75	16	a	a	DET
ejpam-3442	75	17	universe	universe	NOUN
ejpam-3442	75	18	x	x	PUNCT
ejpam-3442	75	19	with	with	ADP
ejpam-3442	75	20	the	the	DET
ejpam-3442	75	21	same	same	ADJ
ejpam-3442	75	22	set	set	NOUN
ejpam-3442	75	23	of	of	ADP
ejpam-3442	75	24	parameters	parameter	NOUN
ejpam-3442	75	25	e.	e.	PROPN
ejpam-3442	75	26	then	then	ADV
ejpam-3442	75	27	,	,	PUNCT
ejpam-3442	75	28	ĩ	ĩ	PROPN
ejpam-3442	75	29	⊆	⊆	PRON
ejpam-3442	75	30	ss(x)e	ss(x)e	PROPN
ejpam-3442	75	31	is	be	AUX
ejpam-3442	75	32	called	call	VERB
ejpam-3442	75	33	a	a	DET
ejpam-3442	75	34	soft	soft	ADJ
ejpam-3442	75	35	ideal	ideal	NOUN
ejpam-3442	75	36	on	on	ADP
ejpam-3442	75	37	x	x	PUNCT
ejpam-3442	75	38	if	if	SCONJ
ejpam-3442	75	39	it	it	PRON
ejpam-3442	75	40	is	be	AUX
ejpam-3442	75	41	closed	close	VERB
ejpam-3442	75	42	under	under	ADP
ejpam-3442	75	43	finite	finite	ADJ
ejpam-3442	75	44	soft	soft	ADJ
ejpam-3442	75	45	unions	union	NOUN
ejpam-3442	75	46	and	and	CCONJ
ejpam-3442	75	47	soft	soft	ADJ
ejpam-3442	75	48	subsets	subset	NOUN
ejpam-3442	75	49	.	.	PUNCT
ejpam-3442	76	1	definition	definition	NOUN
ejpam-3442	76	2	11	11	NUM
ejpam-3442	76	3	.	.	PUNCT
ejpam-3442	77	1	[	[	X
ejpam-3442	77	2	10	10	NUM
ejpam-3442	77	3	]	]	X
ejpam-3442	77	4	let	let	VERB
ejpam-3442	77	5	(	(	PUNCT
ejpam-3442	77	6	x	x	NOUN
ejpam-3442	77	7	,	,	PUNCT
ejpam-3442	77	8	τ	τ	PROPN
ejpam-3442	77	9	,	,	PUNCT
ejpam-3442	77	10	e	e	NOUN
ejpam-3442	77	11	)	)	PUNCT
ejpam-3442	77	12	be	be	AUX
ejpam-3442	77	13	a	a	DET
ejpam-3442	77	14	soft	soft	ADJ
ejpam-3442	77	15	topological	topological	ADJ
ejpam-3442	77	16	space	space	NOUN
ejpam-3442	77	17	and	and	CCONJ
ejpam-3442	77	18	ĩ	ĩ	PROPN
ejpam-3442	77	19	be	be	VERB
ejpam-3442	77	20	a	a	DET
ejpam-3442	77	21	soft	soft	ADJ
ejpam-3442	77	22	ideal	ideal	NOUN
ejpam-3442	77	23	over	over	ADP
ejpam-3442	77	24	x	x	PUNCT
ejpam-3442	77	25	with	with	ADP
ejpam-3442	77	26	the	the	DET
ejpam-3442	77	27	same	same	ADJ
ejpam-3442	77	28	set	set	NOUN
ejpam-3442	77	29	of	of	ADP
ejpam-3442	77	30	parameters	parameter	NOUN
ejpam-3442	78	1	e.	e.	PROPN
ejpam-3442	78	2	then	then	ADV
ejpam-3442	78	3	,	,	PUNCT
ejpam-3442	78	4	(	(	PUNCT
ejpam-3442	78	5	f	f	X
ejpam-3442	78	6	,	,	PUNCT
ejpam-3442	78	7	e)∗(ĩ	e)∗(ĩ	NOUN
ejpam-3442	78	8	,	,	PUNCT
ejpam-3442	78	9	τ	τ	X
ejpam-3442	78	10	)	)	PUNCT
ejpam-3442	78	11	(	(	PUNCT
ejpam-3442	78	12	(	(	PUNCT
ejpam-3442	78	13	f	f	X
ejpam-3442	78	14	,	,	PUNCT
ejpam-3442	78	15	e)∗(ĩ	e)∗(ĩ	NOUN
ejpam-3442	78	16	)	)	PUNCT
ejpam-3442	78	17	or	or	CCONJ
ejpam-3442	78	18	(	(	PUNCT
ejpam-3442	78	19	f	f	X
ejpam-3442	78	20	,	,	PUNCT
ejpam-3442	78	21	e)∗	e)∗	PROPN
ejpam-3442	78	22	)	)	PUNCT
ejpam-3442	78	23	=	=	SYM
ejpam-3442	78	24	∪̃{xe	∪̃{xe	PROPN
ejpam-3442	78	25	∈	∈	PROPN
ejpam-3442	78	26	ε	ε	PROPN
ejpam-3442	78	27	:	:	PUNCT
ejpam-3442	78	28	oxe∩̃(f	oxe∩̃(f	X
ejpam-3442	78	29	,	,	PUNCT
ejpam-3442	78	30	e)˜6∈ĩ	e)˜6∈ĩ	X
ejpam-3442	78	31	∀	∀	X
ejpam-3442	78	32	oxe	oxe	PRON
ejpam-3442	78	33	∈	∈	PROPN
ejpam-3442	78	34	τ	τ	X
ejpam-3442	78	35	}	}	PUNCT
ejpam-3442	78	36	is	be	AUX
ejpam-3442	78	37	called	call	VERB
ejpam-3442	78	38	the	the	DET
ejpam-3442	78	39	soft	soft	ADJ
ejpam-3442	78	40	local	local	ADJ
ejpam-3442	78	41	function	function	NOUN
ejpam-3442	78	42	of	of	ADP
ejpam-3442	78	43	(	(	PUNCT
ejpam-3442	78	44	f	f	X
ejpam-3442	78	45	,	,	PUNCT
ejpam-3442	78	46	e	e	NOUN
ejpam-3442	78	47	)	)	PUNCT
ejpam-3442	78	48	with	with	ADP
ejpam-3442	78	49	respect	respect	NOUN
ejpam-3442	78	50	to	to	ADP
ejpam-3442	78	51	ĩ	ĩ	PROPN
ejpam-3442	78	52	and	and	CCONJ
ejpam-3442	78	53	τ	τ	PROPN
ejpam-3442	78	54	,	,	PUNCT
ejpam-3442	78	55	where	where	SCONJ
ejpam-3442	78	56	oxe	oxe	PROPN
ejpam-3442	78	57	is	be	AUX
ejpam-3442	78	58	an	an	DET
ejpam-3442	78	59	open	open	ADJ
ejpam-3442	78	60	soft	soft	ADJ
ejpam-3442	78	61	set	set	NOUN
ejpam-3442	78	62	containing	contain	VERB
ejpam-3442	78	63	xe	xe	PROPN
ejpam-3442	78	64	.	.	PUNCT
ejpam-3442	79	1	definition	definition	NOUN
ejpam-3442	79	2	12	12	NUM
ejpam-3442	79	3	.	.	PUNCT
ejpam-3442	80	1	let	let	VERB
ejpam-3442	80	2	(	(	PUNCT
ejpam-3442	80	3	x	x	X
ejpam-3442	80	4	,	,	PUNCT
ejpam-3442	80	5	τ	τ	PROPN
ejpam-3442	80	6	,	,	PUNCT
ejpam-3442	80	7	e	e	NOUN
ejpam-3442	80	8	)	)	PUNCT
ejpam-3442	80	9	be	be	AUX
ejpam-3442	80	10	a	a	DET
ejpam-3442	80	11	soft	soft	ADJ
ejpam-3442	80	12	topological	topological	ADJ
ejpam-3442	80	13	space	space	NOUN
ejpam-3442	80	14	and	and	CCONJ
ejpam-3442	80	15	ĩ	ĩ	PROPN
ejpam-3442	80	16	be	be	VERB
ejpam-3442	80	17	a	a	DET
ejpam-3442	80	18	soft	soft	ADJ
ejpam-3442	80	19	ideal	ideal	NOUN
ejpam-3442	80	20	over	over	ADP
ejpam-3442	80	21	x	x	PUNCT
ejpam-3442	80	22	with	with	ADP
ejpam-3442	80	23	the	the	DET
ejpam-3442	80	24	same	same	ADJ
ejpam-3442	80	25	set	set	NOUN
ejpam-3442	80	26	of	of	ADP
ejpam-3442	80	27	parameters	parameter	NOUN
ejpam-3442	81	1	e.	e.	PROPN
ejpam-3442	81	2	then	then	ADV
ejpam-3442	81	3	,	,	PUNCT
ejpam-3442	81	4	f.	f.	PROPN
ejpam-3442	81	5	a.	a.	PROPN
ejpam-3442	81	6	gharib	gharib	PROPN
ejpam-3442	81	7	,	,	PUNCT
ejpam-3442	81	8	a.	a.	PROPN
ejpam-3442	81	9	m.	m.	PROPN
ejpam-3442	81	10	abd	abd	PROPN
ejpam-3442	81	11	el	el	PROPN
ejpam-3442	81	12	-	-	PROPN
ejpam-3442	81	13	latif	latif	PROPN
ejpam-3442	81	14	/	/	SYM
ejpam-3442	81	15	eur	eur	PROPN
ejpam-3442	81	16	.	.	PUNCT
ejpam-3442	82	1	j.	j.	PROPN
ejpam-3442	82	2	pure	pure	PROPN
ejpam-3442	82	3	appl	appl	PROPN
ejpam-3442	82	4	.	.	PROPN
ejpam-3442	82	5	math	math	PROPN
ejpam-3442	82	6	,	,	PUNCT
ejpam-3442	82	7	12	12	NUM
ejpam-3442	82	8	(	(	PUNCT
ejpam-3442	82	9	3	3	NUM
ejpam-3442	82	10	)	)	PUNCT
ejpam-3442	82	11	(	(	PUNCT
ejpam-3442	82	12	2019	2019	NUM
ejpam-3442	82	13	)	)	PUNCT
ejpam-3442	82	14	,	,	PUNCT
ejpam-3442	82	15	857	857	NUM
ejpam-3442	82	16	-	-	SYM
ejpam-3442	82	17	869	869	NUM
ejpam-3442	82	18	860	860	NUM
ejpam-3442	82	19	(	(	PUNCT
ejpam-3442	82	20	f	f	X
ejpam-3442	82	21	,	,	PUNCT
ejpam-3442	82	22	e)∗s(ĩ	e)∗s(ĩ	PROPN
ejpam-3442	82	23	,	,	PUNCT
ejpam-3442	82	24	τ	τ	PROPN
ejpam-3442	82	25	)	)	PUNCT
ejpam-3442	82	26	(	(	PUNCT
ejpam-3442	82	27	(	(	PUNCT
ejpam-3442	82	28	f	f	X
ejpam-3442	82	29	,	,	PUNCT
ejpam-3442	82	30	e)∗s(ĩ	e)∗s(ĩ	NOUN
ejpam-3442	82	31	)	)	PUNCT
ejpam-3442	82	32	or	or	CCONJ
ejpam-3442	82	33	(	(	PUNCT
ejpam-3442	82	34	f	f	X
ejpam-3442	82	35	,	,	PUNCT
ejpam-3442	82	36	e)∗s	e)∗s	PROPN
ejpam-3442	82	37	)	)	PUNCT
ejpam-3442	82	38	=	=	SYM
ejpam-3442	82	39	∪̃{xe	∪̃{xe	PROPN
ejpam-3442	82	40	∈	∈	PROPN
ejpam-3442	82	41	ε	ε	PROPN
ejpam-3442	82	42	:	:	PUNCT
ejpam-3442	82	43	oxe∩̃(f	oxe∩̃(f	X
ejpam-3442	82	44	,	,	PUNCT
ejpam-3442	82	45	e)˜6∈ĩ	e)˜6∈ĩ	X
ejpam-3442	82	46	∀	∀	X
ejpam-3442	82	47	oxe	oxe	VERB
ejpam-3442	82	48	∈	∈	PROPN
ejpam-3442	82	49	sos(x	sos(x	PROPN
ejpam-3442	82	50	)	)	PUNCT
ejpam-3442	82	51	}	}	PUNCT
ejpam-3442	82	52	is	be	AUX
ejpam-3442	82	53	called	call	VERB
ejpam-3442	82	54	the	the	DET
ejpam-3442	82	55	soft	soft	ADJ
ejpam-3442	82	56	semi	semi	ADJ
ejpam-3442	82	57	local	local	ADJ
ejpam-3442	82	58	function	function	NOUN
ejpam-3442	82	59	of	of	ADP
ejpam-3442	82	60	(	(	PUNCT
ejpam-3442	82	61	f	f	X
ejpam-3442	82	62	,	,	PUNCT
ejpam-3442	82	63	e	e	NOUN
ejpam-3442	82	64	)	)	PUNCT
ejpam-3442	82	65	with	with	ADP
ejpam-3442	82	66	respect	respect	NOUN
ejpam-3442	82	67	to	to	ADP
ejpam-3442	82	68	ĩ	ĩ	PROPN
ejpam-3442	82	69	and	and	CCONJ
ejpam-3442	82	70	τ	τ	PROPN
ejpam-3442	82	71	,	,	PUNCT
ejpam-3442	82	72	where	where	SCONJ
ejpam-3442	82	73	oxe	oxe	PROPN
ejpam-3442	82	74	is	be	AUX
ejpam-3442	82	75	a	a	DET
ejpam-3442	82	76	semi	semi	ADJ
ejpam-3442	82	77	open	open	ADJ
ejpam-3442	82	78	soft	soft	ADJ
ejpam-3442	82	79	set	set	NOUN
ejpam-3442	82	80	containing	contain	VERB
ejpam-3442	82	81	xe	xe	PROPN
ejpam-3442	82	82	.	.	PUNCT
ejpam-3442	82	83	theorem	theorem	PROPN
ejpam-3442	82	84	1	1	NUM
ejpam-3442	82	85	.	.	PUNCT
ejpam-3442	83	1	let	let	VERB
ejpam-3442	83	2	ĩ	ĩ	PROPN
ejpam-3442	83	3	be	be	AUX
ejpam-3442	83	4	a	a	DET
ejpam-3442	83	5	soft	soft	ADJ
ejpam-3442	83	6	ideal	ideal	NOUN
ejpam-3442	83	7	with	with	ADP
ejpam-3442	83	8	the	the	DET
ejpam-3442	83	9	same	same	ADJ
ejpam-3442	83	10	set	set	NOUN
ejpam-3442	83	11	of	of	ADP
ejpam-3442	83	12	parameters	parameter	NOUN
ejpam-3442	83	13	e	e	X
ejpam-3442	83	14	on	on	ADP
ejpam-3442	83	15	a	a	DET
ejpam-3442	83	16	soft	soft	ADJ
ejpam-3442	83	17	topological	topological	ADJ
ejpam-3442	83	18	space	space	NOUN
ejpam-3442	83	19	(	(	PUNCT
ejpam-3442	83	20	x	x	X
ejpam-3442	83	21	,	,	PUNCT
ejpam-3442	83	22	τ	τ	PROPN
ejpam-3442	83	23	,	,	PUNCT
ejpam-3442	83	24	e	e	NOUN
ejpam-3442	83	25	)	)	PUNCT
ejpam-3442	83	26	and	and	CCONJ
ejpam-3442	84	1	(	(	PUNCT
ejpam-3442	84	2	f	f	X
ejpam-3442	84	3	,	,	PUNCT
ejpam-3442	84	4	e	e	NOUN
ejpam-3442	84	5	)	)	PUNCT
ejpam-3442	84	6	∈	∈	PROPN
ejpam-3442	84	7	ss(x)e	ss(x)e	PROPN
ejpam-3442	84	8	.	.	PUNCT
ejpam-3442	85	1	then	then	ADV
ejpam-3442	85	2	,	,	PUNCT
ejpam-3442	85	3	(	(	PUNCT
ejpam-3442	85	4	f	f	X
ejpam-3442	85	5	,	,	PUNCT
ejpam-3442	85	6	e)∗s⊆̃(f	e)∗s⊆̃(f	PROPN
ejpam-3442	85	7	,	,	PUNCT
ejpam-3442	85	8	e)∗.	e)∗.	NOUN
ejpam-3442	85	9	proof	proof	NOUN
ejpam-3442	85	10	.	.	PUNCT
ejpam-3442	86	1	let	let	VERB
ejpam-3442	86	2	xe∈̃(f	xe∈̃(f	PRON
ejpam-3442	86	3	,	,	PUNCT
ejpam-3442	86	4	e)∗s	e)∗s	PROPN
ejpam-3442	86	5	.	.	PUNCT
ejpam-3442	87	1	then	then	ADV
ejpam-3442	87	2	,	,	PUNCT
ejpam-3442	87	3	oxe∩̃(f	oxe∩̃(f	ADV
ejpam-3442	87	4	,	,	PUNCT
ejpam-3442	87	5	e	e	NOUN
ejpam-3442	87	6	)	)	PUNCT
ejpam-3442	87	7	6∈	6∈	NOUN
ejpam-3442	87	8	ĩ	ĩ	PROPN
ejpam-3442	87	9	∀	∀	NOUN
ejpam-3442	87	10	oxe	oxe	PRON
ejpam-3442	87	11	∈	∈	PROPN
ejpam-3442	87	12	sos(x	sos(x	PROPN
ejpam-3442	87	13	)	)	PUNCT
ejpam-3442	87	14	.	.	PUNCT
ejpam-3442	88	1	since	since	SCONJ
ejpam-3442	88	2	τ	τ	PROPN
ejpam-3442	88	3	⊆	⊆	NUM
ejpam-3442	88	4	sos(x	sos(x	PROPN
ejpam-3442	88	5	)	)	PUNCT
ejpam-3442	88	6	and	and	CCONJ
ejpam-3442	88	7	oxe∩̃(f	oxe∩̃(f	ADV
ejpam-3442	88	8	,	,	PUNCT
ejpam-3442	88	9	e	e	NOUN
ejpam-3442	88	10	)	)	PUNCT
ejpam-3442	88	11	6∈	6∈	PROPN
ejpam-3442	88	12	ĩ	ĩ	PROPN
ejpam-3442	88	13	,	,	PUNCT
ejpam-3442	88	14	oxe∩̃(f	oxe∩̃(f	ADV
ejpam-3442	88	15	,	,	PUNCT
ejpam-3442	88	16	e	e	NOUN
ejpam-3442	88	17	)	)	PUNCT
ejpam-3442	88	18	6∈	6∈	NOUN
ejpam-3442	88	19	ĩ	ĩ	PROPN
ejpam-3442	88	20	∀	∀	NOUN
ejpam-3442	88	21	oxe	oxe	PRON
ejpam-3442	88	22	∈	∈	PROPN
ejpam-3442	88	23	τ	τ	X
ejpam-3442	88	24	from	from	ADP
ejpam-3442	88	25	definition	definition	NOUN
ejpam-3442	88	26	10	10	NUM
ejpam-3442	88	27	.	.	PUNCT
ejpam-3442	89	1	hence	hence	ADV
ejpam-3442	89	2	,	,	PUNCT
ejpam-3442	89	3	xe∈̃(f	xe∈̃(f	PRON
ejpam-3442	89	4	,	,	PUNCT
ejpam-3442	89	5	e)∗.	e)∗.	NOUN
ejpam-3442	89	6	remarks	remark	VERB
ejpam-3442	89	7	1	1	NUM
ejpam-3442	89	8	.	.	PUNCT
ejpam-3442	90	1	the	the	DET
ejpam-3442	90	2	converse	converse	NOUN
ejpam-3442	90	3	of	of	ADP
ejpam-3442	90	4	the	the	DET
ejpam-3442	90	5	above	above	ADJ
ejpam-3442	90	6	theorem	theorem	NOUN
ejpam-3442	90	7	is	be	AUX
ejpam-3442	90	8	not	not	PART
ejpam-3442	90	9	true	true	ADJ
ejpam-3442	90	10	in	in	ADP
ejpam-3442	90	11	general	general	ADJ
ejpam-3442	90	12	as	as	SCONJ
ejpam-3442	90	13	will	will	AUX
ejpam-3442	90	14	shown	show	VERB
ejpam-3442	90	15	in	in	ADP
ejpam-3442	90	16	the	the	DET
ejpam-3442	90	17	following	follow	VERB
ejpam-3442	90	18	example	example	NOUN
ejpam-3442	90	19	.	.	PUNCT
ejpam-3442	91	1	example	example	NOUN
ejpam-3442	92	1	1	1	NUM
ejpam-3442	92	2	.	.	PUNCT
ejpam-3442	92	3	suppose	suppose	VERB
ejpam-3442	92	4	that	that	SCONJ
ejpam-3442	92	5	there	there	PRON
ejpam-3442	92	6	are	be	VERB
ejpam-3442	92	7	three	three	NUM
ejpam-3442	92	8	cars	car	NOUN
ejpam-3442	92	9	in	in	ADP
ejpam-3442	92	10	the	the	DET
ejpam-3442	92	11	universe	universe	NOUN
ejpam-3442	92	12	x	x	PUNCT
ejpam-3442	92	13	given	give	VERB
ejpam-3442	92	14	by	by	ADP
ejpam-3442	92	15	x	x	X
ejpam-3442	92	16	=	=	SYM
ejpam-3442	92	17	{	{	PUNCT
ejpam-3442	92	18	c1	c1	PROPN
ejpam-3442	92	19	,	,	PUNCT
ejpam-3442	92	20	c2	c2	PROPN
ejpam-3442	92	21	,	,	PUNCT
ejpam-3442	92	22	c3	c3	PROPN
ejpam-3442	92	23	}	}	PUNCT
ejpam-3442	92	24	.	.	PUNCT
ejpam-3442	93	1	let	let	AUX
ejpam-3442	93	2	e	e	NOUN
ejpam-3442	93	3	=	=	PRON
ejpam-3442	93	4	{	{	PUNCT
ejpam-3442	93	5	e1	e1	PROPN
ejpam-3442	93	6	,	,	PUNCT
ejpam-3442	93	7	e2	e2	PROPN
ejpam-3442	93	8	}	}	PUNCT
ejpam-3442	93	9	be	be	VERB
ejpam-3442	93	10	the	the	DET
ejpam-3442	93	11	set	set	NOUN
ejpam-3442	93	12	of	of	ADP
ejpam-3442	93	13	decision	decision	NOUN
ejpam-3442	93	14	parameters	parameter	NOUN
ejpam-3442	93	15	which	which	PRON
ejpam-3442	93	16	are	be	AUX
ejpam-3442	93	17	stands	stand	VERB
ejpam-3442	93	18	for	for	ADP
ejpam-3442	93	19	”	"	PUNCT
ejpam-3442	93	20	expensive	expensive	ADJ
ejpam-3442	93	21	”	"	PUNCT
ejpam-3442	93	22	and	and	CCONJ
ejpam-3442	93	23	”	"	PUNCT
ejpam-3442	93	24	color	color	NOUN
ejpam-3442	93	25	”	"	PUNCT
ejpam-3442	93	26	respectively	respectively	ADV
ejpam-3442	93	27	.	.	PUNCT
ejpam-3442	94	1	let	let	AUX
ejpam-3442	94	2	(	(	PUNCT
ejpam-3442	94	3	f1	f1	NOUN
ejpam-3442	94	4	,	,	PUNCT
ejpam-3442	94	5	e	e	NOUN
ejpam-3442	94	6	)	)	PUNCT
ejpam-3442	94	7	,	,	PUNCT
ejpam-3442	94	8	(	(	PUNCT
ejpam-3442	94	9	f2	f2	PROPN
ejpam-3442	94	10	,	,	PUNCT
ejpam-3442	94	11	e	e	NOUN
ejpam-3442	94	12	)	)	PUNCT
ejpam-3442	94	13	,	,	PUNCT
ejpam-3442	94	14	(	(	PUNCT
ejpam-3442	94	15	f3	f3	ADJ
ejpam-3442	94	16	,	,	PUNCT
ejpam-3442	94	17	e	e	NOUN
ejpam-3442	94	18	)	)	PUNCT
ejpam-3442	94	19	be	be	AUX
ejpam-3442	94	20	soft	soft	ADJ
ejpam-3442	94	21	sets	set	NOUN
ejpam-3442	94	22	over	over	ADP
ejpam-3442	94	23	the	the	DET
ejpam-3442	94	24	common	common	ADJ
ejpam-3442	94	25	universe	universe	NOUN
ejpam-3442	94	26	x	x	NOUN
ejpam-3442	94	27	,	,	PUNCT
ejpam-3442	94	28	which	which	PRON
ejpam-3442	94	29	describe	describe	VERB
ejpam-3442	94	30	the	the	DET
ejpam-3442	94	31	composition	composition	NOUN
ejpam-3442	94	32	of	of	ADP
ejpam-3442	94	33	the	the	DET
ejpam-3442	94	34	cars	car	NOUN
ejpam-3442	94	35	,	,	PUNCT
ejpam-3442	94	36	where	where	SCONJ
ejpam-3442	94	37	f1(e1	f1(e1	ADV
ejpam-3442	94	38	)	)	PUNCT
ejpam-3442	95	1	=	=	PRON
ejpam-3442	95	2	{	{	PUNCT
ejpam-3442	95	3	c1	c1	NOUN
ejpam-3442	95	4	}	}	PUNCT
ejpam-3442	95	5	,	,	PUNCT
ejpam-3442	95	6	f1(e2	f1(e2	NOUN
ejpam-3442	95	7	)	)	PUNCT
ejpam-3442	95	8	=	=	PRON
ejpam-3442	95	9	{	{	PUNCT
ejpam-3442	95	10	c1	c1	NOUN
ejpam-3442	95	11	}	}	PUNCT
ejpam-3442	95	12	.	.	PUNCT
ejpam-3442	96	1	f2(e1	f2(e1	NOUN
ejpam-3442	96	2	)	)	PUNCT
ejpam-3442	97	1	=	=	PRON
ejpam-3442	97	2	{	{	PUNCT
ejpam-3442	97	3	c2	c2	PROPN
ejpam-3442	97	4	}	}	PUNCT
ejpam-3442	97	5	,	,	PUNCT
ejpam-3442	97	6	f2(e2	f2(e2	NOUN
ejpam-3442	97	7	)	)	PUNCT
ejpam-3442	97	8	=	=	SYM
ejpam-3442	97	9	{	{	PUNCT
ejpam-3442	97	10	c2	c2	PROPN
ejpam-3442	97	11	}	}	PUNCT
ejpam-3442	97	12	.	.	PUNCT
ejpam-3442	98	1	f3(e1	f3(e1	NOUN
ejpam-3442	98	2	)	)	PUNCT
ejpam-3442	99	1	=	=	PRON
ejpam-3442	99	2	{	{	PUNCT
ejpam-3442	99	3	c1	c1	PROPN
ejpam-3442	99	4	,	,	PUNCT
ejpam-3442	99	5	c2	c2	PROPN
ejpam-3442	99	6	}	}	PUNCT
ejpam-3442	99	7	,	,	PUNCT
ejpam-3442	99	8	f3(e2	f3(e2	PROPN
ejpam-3442	99	9	)	)	PUNCT
ejpam-3442	99	10	=	=	PRON
ejpam-3442	99	11	{	{	PUNCT
ejpam-3442	99	12	c1	c1	PROPN
ejpam-3442	99	13	,	,	PUNCT
ejpam-3442	99	14	c2	c2	PROPN
ejpam-3442	99	15	}	}	PUNCT
ejpam-3442	99	16	.	.	PUNCT
ejpam-3442	100	1	then	then	ADV
ejpam-3442	100	2	,	,	PUNCT
ejpam-3442	100	3	τ	τ	PROPN
ejpam-3442	100	4	=	=	SYM
ejpam-3442	100	5	{	{	PUNCT
ejpam-3442	100	6	x̃	x̃	PROPN
ejpam-3442	100	7	,	,	PUNCT
ejpam-3442	100	8	φ̃	φ̃	PROPN
ejpam-3442	100	9	,	,	PUNCT
ejpam-3442	100	10	(	(	PUNCT
ejpam-3442	100	11	f1	f1	NOUN
ejpam-3442	100	12	,	,	PUNCT
ejpam-3442	100	13	e	e	NOUN
ejpam-3442	100	14	)	)	PUNCT
ejpam-3442	100	15	,	,	PUNCT
ejpam-3442	100	16	(	(	PUNCT
ejpam-3442	100	17	f2	f2	PROPN
ejpam-3442	100	18	,	,	PUNCT
ejpam-3442	100	19	e	e	NOUN
ejpam-3442	100	20	)	)	PUNCT
ejpam-3442	100	21	,	,	PUNCT
ejpam-3442	100	22	(	(	PUNCT
ejpam-3442	100	23	f3	f3	ADJ
ejpam-3442	100	24	,	,	PUNCT
ejpam-3442	100	25	e	e	NOUN
ejpam-3442	100	26	)	)	PUNCT
ejpam-3442	100	27	}	}	PUNCT
ejpam-3442	100	28	defines	define	VERB
ejpam-3442	100	29	a	a	DET
ejpam-3442	100	30	soft	soft	ADJ
ejpam-3442	100	31	topology	topology	NOUN
ejpam-3442	100	32	on	on	ADP
ejpam-3442	100	33	x.	x.	NOUN
ejpam-3442	100	34	let	let	VERB
ejpam-3442	100	35	ĩ	ĩ	PROPN
ejpam-3442	100	36	=	=	SYM
ejpam-3442	100	37	{	{	PUNCT
ejpam-3442	100	38	φ̃	φ̃	PROPN
ejpam-3442	100	39	}	}	PUNCT
ejpam-3442	100	40	and	and	CCONJ
ejpam-3442	100	41	(	(	PUNCT
ejpam-3442	100	42	g	g	NOUN
ejpam-3442	100	43	,	,	PUNCT
ejpam-3442	100	44	e	e	NOUN
ejpam-3442	100	45	)	)	PUNCT
ejpam-3442	100	46	be	be	AUX
ejpam-3442	100	47	a	a	DET
ejpam-3442	100	48	soft	soft	ADJ
ejpam-3442	100	49	set	set	NOUN
ejpam-3442	100	50	defined	define	VERB
ejpam-3442	100	51	by	by	ADP
ejpam-3442	100	52	g(e1	g(e1	NOUN
ejpam-3442	100	53	)	)	PUNCT
ejpam-3442	101	1	=	=	PRON
ejpam-3442	101	2	{	{	PUNCT
ejpam-3442	101	3	c2	c2	PROPN
ejpam-3442	101	4	,	,	PUNCT
ejpam-3442	101	5	c3	c3	PROPN
ejpam-3442	101	6	}	}	PUNCT
ejpam-3442	101	7	,	,	PUNCT
ejpam-3442	101	8	g(e2	g(e2	NOUN
ejpam-3442	101	9	)	)	PUNCT
ejpam-3442	101	10	=	=	SYM
ejpam-3442	101	11	{	{	PUNCT
ejpam-3442	101	12	c2	c2	PROPN
ejpam-3442	101	13	}	}	PUNCT
ejpam-3442	101	14	.	.	PUNCT
ejpam-3442	102	1	hence	hence	ADV
ejpam-3442	102	2	,	,	PUNCT
ejpam-3442	102	3	(	(	PUNCT
ejpam-3442	102	4	g	g	NOUN
ejpam-3442	102	5	,	,	PUNCT
ejpam-3442	102	6	e)∗s	e)∗s	NOUN
ejpam-3442	102	7	=	=	SYM
ejpam-3442	102	8	scl(g	scl(g	NOUN
ejpam-3442	102	9	,	,	PUNCT
ejpam-3442	102	10	e	e	NOUN
ejpam-3442	102	11	)	)	PUNCT
ejpam-3442	102	12	=	=	SYM
ejpam-3442	102	13	scl(g	scl(g	NOUN
ejpam-3442	102	14	,	,	PUNCT
ejpam-3442	102	15	e)∗s	e)∗s	NUM
ejpam-3442	102	16	=	=	SYM
ejpam-3442	102	17	(	(	PUNCT
ejpam-3442	102	18	g	g	NOUN
ejpam-3442	102	19	,	,	PUNCT
ejpam-3442	102	20	e	e	NOUN
ejpam-3442	102	21	)	)	PUNCT
ejpam-3442	102	22	and	and	CCONJ
ejpam-3442	102	23	(	(	PUNCT
ejpam-3442	102	24	g	g	NOUN
ejpam-3442	102	25	,	,	PUNCT
ejpam-3442	102	26	e)∗	e)∗	PROPN
ejpam-3442	102	27	=	=	SYM
ejpam-3442	102	28	cl(g	cl(g	PROPN
ejpam-3442	102	29	,	,	PUNCT
ejpam-3442	102	30	e	e	NOUN
ejpam-3442	102	31	)	)	PUNCT
ejpam-3442	102	32	=	=	SYM
ejpam-3442	102	33	cl(g	cl(g	PROPN
ejpam-3442	102	34	,	,	PUNCT
ejpam-3442	102	35	e)∗	e)∗	PROPN
ejpam-3442	102	36	=	=	PUNCT
ejpam-3442	102	37	(	(	PUNCT
ejpam-3442	102	38	h	h	NOUN
ejpam-3442	102	39	,	,	PUNCT
ejpam-3442	102	40	e	e	NOUN
ejpam-3442	102	41	)	)	PUNCT
ejpam-3442	102	42	,	,	PUNCT
ejpam-3442	102	43	where	where	SCONJ
ejpam-3442	102	44	h(e1	h(e1	NOUN
ejpam-3442	102	45	)	)	PUNCT
ejpam-3442	102	46	=	=	SYM
ejpam-3442	102	47	{	{	PUNCT
ejpam-3442	102	48	c2	c2	PROPN
ejpam-3442	102	49	,	,	PUNCT
ejpam-3442	102	50	c3	c3	PROPN
ejpam-3442	102	51	}	}	PUNCT
ejpam-3442	102	52	,	,	PUNCT
ejpam-3442	102	53	h(e2	h(e2	PROPN
ejpam-3442	102	54	)	)	PUNCT
ejpam-3442	102	55	=	=	PRON
ejpam-3442	102	56	{	{	PUNCT
ejpam-3442	102	57	c2	c2	PROPN
ejpam-3442	102	58	,	,	PUNCT
ejpam-3442	102	59	c3	c3	PROPN
ejpam-3442	102	60	}	}	PUNCT
ejpam-3442	102	61	.	.	PUNCT
ejpam-3442	103	1	remarks	remark	VERB
ejpam-3442	103	2	2	2	NUM
ejpam-3442	103	3	.	.	PUNCT
ejpam-3442	104	1	the	the	DET
ejpam-3442	104	2	collection	collection	NOUN
ejpam-3442	104	3	of	of	ADP
ejpam-3442	104	4	all	all	DET
ejpam-3442	104	5	semi	semi	ADV
ejpam-3442	104	6	open	open	ADJ
ejpam-3442	104	7	soft	soft	ADJ
ejpam-3442	104	8	sets	set	NOUN
ejpam-3442	104	9	of	of	ADP
ejpam-3442	104	10	a	a	DET
ejpam-3442	104	11	soft	soft	ADJ
ejpam-3442	104	12	topological	topological	ADJ
ejpam-3442	104	13	space	space	NOUN
ejpam-3442	104	14	(	(	PUNCT
ejpam-3442	104	15	x	x	X
ejpam-3442	104	16	,	,	PUNCT
ejpam-3442	104	17	τ	τ	PROPN
ejpam-3442	104	18	,	,	PUNCT
ejpam-3442	104	19	e	e	NOUN
ejpam-3442	104	20	)	)	PUNCT
ejpam-3442	104	21	fails	fail	VERB
ejpam-3442	104	22	to	to	PART
ejpam-3442	104	23	form	form	VERB
ejpam-3442	104	24	a	a	DET
ejpam-3442	104	25	soft	soft	ADJ
ejpam-3442	104	26	ideal	ideal	NOUN
ejpam-3442	104	27	on	on	ADP
ejpam-3442	104	28	x	x	PUNCT
ejpam-3442	104	29	as	as	SCONJ
ejpam-3442	104	30	will	will	AUX
ejpam-3442	104	31	shown	show	VERB
ejpam-3442	104	32	in	in	ADP
ejpam-3442	104	33	the	the	DET
ejpam-3442	104	34	following	follow	VERB
ejpam-3442	104	35	example	example	NOUN
ejpam-3442	104	36	.	.	PUNCT
ejpam-3442	105	1	example	example	NOUN
ejpam-3442	106	1	2	2	NUM
ejpam-3442	106	2	.	.	PUNCT
ejpam-3442	106	3	suppose	suppose	VERB
ejpam-3442	106	4	that	that	SCONJ
ejpam-3442	106	5	there	there	PRON
ejpam-3442	106	6	are	be	VERB
ejpam-3442	106	7	two	two	NUM
ejpam-3442	106	8	houses	house	NOUN
ejpam-3442	106	9	in	in	ADP
ejpam-3442	106	10	the	the	DET
ejpam-3442	106	11	universe	universe	NOUN
ejpam-3442	106	12	x	x	PUNCT
ejpam-3442	106	13	given	give	VERB
ejpam-3442	106	14	by	by	ADP
ejpam-3442	106	15	x	x	X
ejpam-3442	106	16	=	=	X
ejpam-3442	106	17	{	{	PUNCT
ejpam-3442	106	18	h1	h1	PROPN
ejpam-3442	106	19	,	,	PUNCT
ejpam-3442	106	20	h2	h2	PROPN
ejpam-3442	106	21	}	}	PUNCT
ejpam-3442	106	22	.	.	PUNCT
ejpam-3442	107	1	let	let	VERB
ejpam-3442	107	2	e	e	NOUN
ejpam-3442	107	3	=	=	PRON
ejpam-3442	107	4	{	{	PUNCT
ejpam-3442	107	5	e1	e1	PROPN
ejpam-3442	107	6	,	,	PUNCT
ejpam-3442	107	7	e2	e2	PROPN
ejpam-3442	107	8	}	}	PUNCT
ejpam-3442	107	9	be	be	VERB
ejpam-3442	107	10	the	the	DET
ejpam-3442	107	11	set	set	NOUN
ejpam-3442	107	12	of	of	ADP
ejpam-3442	107	13	decision	decision	NOUN
ejpam-3442	107	14	parameters	parameter	NOUN
ejpam-3442	107	15	which	which	PRON
ejpam-3442	107	16	are	be	AUX
ejpam-3442	107	17	stands	stand	VERB
ejpam-3442	107	18	for	for	ADP
ejpam-3442	107	19	”	"	PUNCT
ejpam-3442	107	20	wooden	wooden	ADJ
ejpam-3442	107	21	”	"	PUNCT
ejpam-3442	107	22	and	and	CCONJ
ejpam-3442	107	23	”	"	PUNCT
ejpam-3442	107	24	position	position	NOUN
ejpam-3442	107	25	”	"	PUNCT
ejpam-3442	107	26	respectively	respectively	ADV
ejpam-3442	107	27	.	.	PUNCT
ejpam-3442	108	1	let	let	AUX
ejpam-3442	108	2	(	(	PUNCT
ejpam-3442	108	3	f1	f1	NOUN
ejpam-3442	108	4	,	,	PUNCT
ejpam-3442	108	5	e	e	NOUN
ejpam-3442	108	6	)	)	PUNCT
ejpam-3442	108	7	,	,	PUNCT
ejpam-3442	108	8	(	(	PUNCT
ejpam-3442	108	9	f2	f2	X
ejpam-3442	108	10	,	,	PUNCT
ejpam-3442	108	11	e	e	NOUN
ejpam-3442	108	12	)	)	PUNCT
ejpam-3442	108	13	be	be	AUX
ejpam-3442	108	14	soft	soft	ADJ
ejpam-3442	108	15	sets	set	NOUN
ejpam-3442	108	16	over	over	ADP
ejpam-3442	108	17	the	the	DET
ejpam-3442	108	18	common	common	ADJ
ejpam-3442	108	19	universe	universe	NOUN
ejpam-3442	108	20	x	x	NOUN
ejpam-3442	108	21	,	,	PUNCT
ejpam-3442	108	22	which	which	PRON
ejpam-3442	108	23	describe	describe	VERB
ejpam-3442	108	24	the	the	DET
ejpam-3442	108	25	composition	composition	NOUN
ejpam-3442	108	26	of	of	ADP
ejpam-3442	108	27	the	the	DET
ejpam-3442	108	28	houses	house	NOUN
ejpam-3442	108	29	,	,	PUNCT
ejpam-3442	108	30	where	where	SCONJ
ejpam-3442	108	31	f1(e1	f1(e1	ADV
ejpam-3442	108	32	)	)	PUNCT
ejpam-3442	109	1	=	=	PRON
ejpam-3442	109	2	{	{	PUNCT
ejpam-3442	109	3	h1	h1	PROPN
ejpam-3442	109	4	}	}	PUNCT
ejpam-3442	109	5	,	,	PUNCT
ejpam-3442	109	6	f1(e2	f1(e2	NOUN
ejpam-3442	109	7	)	)	PUNCT
ejpam-3442	109	8	=	=	PRON
ejpam-3442	109	9	{	{	PUNCT
ejpam-3442	109	10	h2	h2	NOUN
ejpam-3442	109	11	}	}	PUNCT
ejpam-3442	109	12	.	.	PUNCT
ejpam-3442	110	1	f2(e1	f2(e1	NOUN
ejpam-3442	110	2	)	)	PUNCT
ejpam-3442	110	3	=	=	PRON
ejpam-3442	110	4	{	{	PUNCT
ejpam-3442	110	5	h2	h2	NOUN
ejpam-3442	110	6	}	}	PUNCT
ejpam-3442	110	7	,	,	PUNCT
ejpam-3442	110	8	f2(e2	f2(e2	NOUN
ejpam-3442	110	9	)	)	PUNCT
ejpam-3442	110	10	=	=	PUNCT
ejpam-3442	110	11	{	{	PUNCT
ejpam-3442	110	12	h1	h1	PROPN
ejpam-3442	110	13	}	}	PUNCT
ejpam-3442	110	14	.	.	PUNCT
ejpam-3442	111	1	then	then	ADV
ejpam-3442	111	2	,	,	PUNCT
ejpam-3442	111	3	τ	τ	PROPN
ejpam-3442	111	4	=	=	SYM
ejpam-3442	111	5	{	{	PUNCT
ejpam-3442	111	6	x̃	x̃	PROPN
ejpam-3442	111	7	,	,	PUNCT
ejpam-3442	111	8	φ̃	φ̃	PROPN
ejpam-3442	111	9	,	,	PUNCT
ejpam-3442	111	10	(	(	PUNCT
ejpam-3442	111	11	f1	f1	NOUN
ejpam-3442	111	12	,	,	PUNCT
ejpam-3442	111	13	e	e	NOUN
ejpam-3442	111	14	)	)	PUNCT
ejpam-3442	111	15	,	,	PUNCT
ejpam-3442	111	16	(	(	PUNCT
ejpam-3442	111	17	f2	f2	X
ejpam-3442	111	18	,	,	PUNCT
ejpam-3442	111	19	e	e	NOUN
ejpam-3442	111	20	)	)	PUNCT
ejpam-3442	111	21	}	}	PUNCT
ejpam-3442	111	22	defines	define	VERB
ejpam-3442	111	23	a	a	DET
ejpam-3442	111	24	soft	soft	ADJ
ejpam-3442	111	25	topology	topology	NOUN
ejpam-3442	111	26	on	on	ADP
ejpam-3442	111	27	x.	x.	NOUN
ejpam-3442	111	28	also	also	ADV
ejpam-3442	111	29	,	,	PUNCT
ejpam-3442	111	30	sos(x	sos(x	PROPN
ejpam-3442	111	31	)	)	PUNCT
ejpam-3442	111	32	=	=	PRON
ejpam-3442	111	33	{	{	PUNCT
ejpam-3442	111	34	φ̃	φ̃	PROPN
ejpam-3442	111	35	,	,	PUNCT
ejpam-3442	111	36	(	(	PUNCT
ejpam-3442	111	37	f1	f1	NOUN
ejpam-3442	111	38	,	,	PUNCT
ejpam-3442	111	39	e	e	NOUN
ejpam-3442	111	40	)	)	PUNCT
ejpam-3442	111	41	,	,	PUNCT
ejpam-3442	111	42	(	(	PUNCT
ejpam-3442	111	43	f2	f2	PROPN
ejpam-3442	111	44	,	,	PUNCT
ejpam-3442	111	45	e	e	NOUN
ejpam-3442	111	46	)	)	PUNCT
ejpam-3442	111	47	,	,	PUNCT
ejpam-3442	111	48	x̃	x̃	PROPN
ejpam-3442	111	49	}	}	PUNCT
ejpam-3442	111	50	is	be	AUX
ejpam-3442	111	51	not	not	PART
ejpam-3442	111	52	soft	soft	ADJ
ejpam-3442	111	53	ideal	ideal	NOUN
ejpam-3442	111	54	,	,	PUNCT
ejpam-3442	111	55	because	because	SCONJ
ejpam-3442	111	56	it	it	PRON
ejpam-3442	111	57	is	be	AUX
ejpam-3442	111	58	not	not	PART
ejpam-3442	111	59	closed	close	VERB
ejpam-3442	111	60	under	under	ADP
ejpam-3442	111	61	soft	soft	ADJ
ejpam-3442	111	62	subset	subset	NOUN
ejpam-3442	111	63	.	.	PUNCT
ejpam-3442	112	1	remarks	remark	VERB
ejpam-3442	112	2	3	3	NUM
ejpam-3442	112	3	.	.	PUNCT
ejpam-3442	113	1	(	(	PUNCT
ejpam-3442	113	2	1	1	X
ejpam-3442	113	3	)	)	PUNCT
ejpam-3442	113	4	if	if	SCONJ
ejpam-3442	113	5	(	(	PUNCT
ejpam-3442	113	6	f	f	X
ejpam-3442	113	7	,	,	PUNCT
ejpam-3442	113	8	e	e	NOUN
ejpam-3442	113	9	)	)	PUNCT
ejpam-3442	113	10	∈	∈	PROPN
ejpam-3442	113	11	ĩ	ĩ	PROPN
ejpam-3442	113	12	,	,	PUNCT
ejpam-3442	113	13	then	then	ADV
ejpam-3442	113	14	(	(	PUNCT
ejpam-3442	113	15	f	f	X
ejpam-3442	113	16	,	,	PUNCT
ejpam-3442	113	17	e)∗s	e)∗s	PROPN
ejpam-3442	113	18	=	=	SYM
ejpam-3442	113	19	φ̃.	φ̃.	PROPN
ejpam-3442	113	20	(	(	PUNCT
ejpam-3442	113	21	2	2	NUM
ejpam-3442	113	22	)	)	PUNCT
ejpam-3442	113	23	if	if	SCONJ
ejpam-3442	113	24	ĩ	ĩ	PROPN
ejpam-3442	113	25	=	=	SYM
ejpam-3442	113	26	ss(x)e	ss(x)e	NOUN
ejpam-3442	113	27	,	,	PUNCT
ejpam-3442	113	28	then	then	ADV
ejpam-3442	113	29	(	(	PUNCT
ejpam-3442	113	30	f	f	X
ejpam-3442	113	31	,	,	PUNCT
ejpam-3442	113	32	e)∗s	e)∗s	PROPN
ejpam-3442	113	33	=	=	SYM
ejpam-3442	113	34	φ̃	φ̃	PROPN
ejpam-3442	113	35	=	=	SYM
ejpam-3442	113	36	(	(	PUNCT
ejpam-3442	113	37	f	f	X
ejpam-3442	113	38	,	,	PUNCT
ejpam-3442	113	39	e)∗.	e)∗.	PROPN
ejpam-3442	113	40	(	(	PUNCT
ejpam-3442	113	41	3	3	NUM
ejpam-3442	113	42	)	)	PUNCT
ejpam-3442	113	43	if	if	SCONJ
ejpam-3442	113	44	ĩ	ĩ	PROPN
ejpam-3442	113	45	=	=	SYM
ejpam-3442	113	46	{	{	PUNCT
ejpam-3442	113	47	φ̃	φ̃	PROPN
ejpam-3442	113	48	}	}	PUNCT
ejpam-3442	113	49	,	,	PUNCT
ejpam-3442	113	50	then	then	ADV
ejpam-3442	113	51	(	(	PUNCT
ejpam-3442	113	52	f	f	X
ejpam-3442	113	53	,	,	PUNCT
ejpam-3442	113	54	e)∗s	e)∗s	PROPN
ejpam-3442	113	55	=	=	SYM
ejpam-3442	113	56	scl(f	scl(f	PROPN
ejpam-3442	113	57	,	,	PUNCT
ejpam-3442	113	58	e	e	NOUN
ejpam-3442	113	59	)	)	PUNCT
ejpam-3442	113	60	6=	6=	ADP
ejpam-3442	113	61	cl(f	cl(f	PROPN
ejpam-3442	113	62	,	,	PUNCT
ejpam-3442	113	63	e	e	NOUN
ejpam-3442	113	64	)	)	PUNCT
ejpam-3442	113	65	.	.	PUNCT
ejpam-3442	114	1	f.	f.	PROPN
ejpam-3442	114	2	a.	a.	PROPN
ejpam-3442	114	3	gharib	gharib	PROPN
ejpam-3442	114	4	,	,	PUNCT
ejpam-3442	114	5	a.	a.	PROPN
ejpam-3442	114	6	m.	m.	PROPN
ejpam-3442	114	7	abd	abd	PROPN
ejpam-3442	114	8	el	el	PROPN
ejpam-3442	114	9	-	-	PROPN
ejpam-3442	114	10	latif	latif	PROPN
ejpam-3442	114	11	/	/	SYM
ejpam-3442	114	12	eur	eur	PROPN
ejpam-3442	114	13	.	.	PUNCT
ejpam-3442	115	1	j.	j.	PROPN
ejpam-3442	115	2	pure	pure	PROPN
ejpam-3442	115	3	appl	appl	PROPN
ejpam-3442	115	4	.	.	PROPN
ejpam-3442	115	5	math	math	PROPN
ejpam-3442	115	6	,	,	PUNCT
ejpam-3442	115	7	12	12	NUM
ejpam-3442	115	8	(	(	PUNCT
ejpam-3442	115	9	3	3	NUM
ejpam-3442	115	10	)	)	PUNCT
ejpam-3442	115	11	(	(	PUNCT
ejpam-3442	115	12	2019	2019	NUM
ejpam-3442	115	13	)	)	PUNCT
ejpam-3442	115	14	,	,	PUNCT
ejpam-3442	115	15	857	857	NUM
ejpam-3442	115	16	-	-	SYM
ejpam-3442	115	17	869	869	NUM
ejpam-3442	115	18	861	861	NUM
ejpam-3442	115	19	(	(	PUNCT
ejpam-3442	115	20	4	4	NUM
ejpam-3442	115	21	)	)	PUNCT
ejpam-3442	115	22	neither	neither	CCONJ
ejpam-3442	115	23	(	(	PUNCT
ejpam-3442	115	24	f	f	X
ejpam-3442	115	25	,	,	PUNCT
ejpam-3442	115	26	e)∗s⊆̃(f	e)∗s⊆̃(f	PROPN
ejpam-3442	115	27	,	,	PUNCT
ejpam-3442	115	28	e	e	NOUN
ejpam-3442	115	29	)	)	PUNCT
ejpam-3442	115	30	nor	nor	CCONJ
ejpam-3442	115	31	(	(	PUNCT
ejpam-3442	115	32	f	f	X
ejpam-3442	115	33	,	,	PUNCT
ejpam-3442	115	34	e)⊆̃(f	e)⊆̃(f	PROPN
ejpam-3442	115	35	,	,	PUNCT
ejpam-3442	115	36	e)∗s	e)∗s	PROPN
ejpam-3442	115	37	in	in	ADP
ejpam-3442	115	38	general	general	ADJ
ejpam-3442	115	39	.	.	PUNCT
ejpam-3442	116	1	(	(	PUNCT
ejpam-3442	116	2	5	5	NUM
ejpam-3442	116	3	)	)	PUNCT
ejpam-3442	116	4	if	if	SCONJ
ejpam-3442	116	5	τ	τ	PROPN
ejpam-3442	116	6	=	=	SYM
ejpam-3442	116	7	sos(x	sos(x	PROPN
ejpam-3442	116	8	)	)	PUNCT
ejpam-3442	116	9	,	,	PUNCT
ejpam-3442	116	10	then	then	ADV
ejpam-3442	116	11	(	(	PUNCT
ejpam-3442	116	12	f	f	X
ejpam-3442	116	13	,	,	PUNCT
ejpam-3442	116	14	e)∗s	e)∗s	PROPN
ejpam-3442	116	15	=	=	SYM
ejpam-3442	116	16	(	(	PUNCT
ejpam-3442	116	17	f	f	X
ejpam-3442	116	18	,	,	PUNCT
ejpam-3442	116	19	e)∗.	e)∗.	NOUN
ejpam-3442	116	20	theorem	theorem	NOUN
ejpam-3442	116	21	2	2	NUM
ejpam-3442	116	22	.	.	PUNCT
ejpam-3442	116	23	let	let	VERB
ejpam-3442	116	24	ĩ	ĩ	PROPN
ejpam-3442	116	25	and	and	CCONJ
ejpam-3442	116	26	j̃	j̃	PROPN
ejpam-3442	116	27	be	be	VERB
ejpam-3442	116	28	any	any	DET
ejpam-3442	116	29	two	two	NUM
ejpam-3442	116	30	soft	soft	ADJ
ejpam-3442	116	31	ideals	ideal	NOUN
ejpam-3442	116	32	with	with	ADP
ejpam-3442	116	33	the	the	DET
ejpam-3442	116	34	same	same	ADJ
ejpam-3442	116	35	set	set	NOUN
ejpam-3442	116	36	of	of	ADP
ejpam-3442	116	37	parameters	parameter	NOUN
ejpam-3442	116	38	e	e	X
ejpam-3442	116	39	on	on	ADP
ejpam-3442	116	40	a	a	DET
ejpam-3442	116	41	soft	soft	ADJ
ejpam-3442	116	42	topological	topological	ADJ
ejpam-3442	116	43	space	space	NOUN
ejpam-3442	116	44	(	(	PUNCT
ejpam-3442	116	45	x	x	X
ejpam-3442	116	46	,	,	PUNCT
ejpam-3442	116	47	τ	τ	PROPN
ejpam-3442	116	48	,	,	PUNCT
ejpam-3442	116	49	e	e	NOUN
ejpam-3442	116	50	)	)	PUNCT
ejpam-3442	116	51	.	.	PUNCT
ejpam-3442	117	1	let	let	VERB
ejpam-3442	117	2	(	(	PUNCT
ejpam-3442	117	3	f	f	X
ejpam-3442	117	4	,	,	PUNCT
ejpam-3442	117	5	e	e	NOUN
ejpam-3442	117	6	)	)	PUNCT
ejpam-3442	117	7	,	,	PUNCT
ejpam-3442	117	8	(	(	PUNCT
ejpam-3442	117	9	g	g	NOUN
ejpam-3442	117	10	,	,	PUNCT
ejpam-3442	117	11	e	e	NOUN
ejpam-3442	117	12	)	)	PUNCT
ejpam-3442	117	13	∈	∈	PROPN
ejpam-3442	118	1	ss(x)e	ss(x)e	PROPN
ejpam-3442	118	2	.	.	PUNCT
ejpam-3442	119	1	then	then	ADV
ejpam-3442	119	2	,	,	PUNCT
ejpam-3442	119	3	(	(	PUNCT
ejpam-3442	119	4	1	1	X
ejpam-3442	119	5	)	)	PUNCT
ejpam-3442	119	6	(	(	PUNCT
ejpam-3442	119	7	φ̃)∗s	φ̃)∗s	NOUN
ejpam-3442	119	8	=	=	SYM
ejpam-3442	119	9	φ̃	φ̃	PROPN
ejpam-3442	119	10	,	,	PUNCT
ejpam-3442	119	11	(	(	PUNCT
ejpam-3442	119	12	2	2	X
ejpam-3442	119	13	)	)	PUNCT
ejpam-3442	119	14	if	if	SCONJ
ejpam-3442	119	15	(	(	PUNCT
ejpam-3442	119	16	f	f	X
ejpam-3442	119	17	,	,	PUNCT
ejpam-3442	119	18	e)⊆̃(g	e)⊆̃(g	PROPN
ejpam-3442	119	19	,	,	PUNCT
ejpam-3442	119	20	e	e	NOUN
ejpam-3442	119	21	)	)	PUNCT
ejpam-3442	119	22	,	,	PUNCT
ejpam-3442	119	23	then	then	ADV
ejpam-3442	119	24	(	(	PUNCT
ejpam-3442	119	25	f	f	X
ejpam-3442	119	26	,	,	PUNCT
ejpam-3442	119	27	e)∗s⊆̃(g	e)∗s⊆̃(g	NOUN
ejpam-3442	119	28	,	,	PUNCT
ejpam-3442	119	29	e)∗s	e)∗	NOUN
ejpam-3442	119	30	,	,	PUNCT
ejpam-3442	119	31	(	(	PUNCT
ejpam-3442	119	32	3	3	X
ejpam-3442	119	33	)	)	PUNCT
ejpam-3442	119	34	if	if	SCONJ
ejpam-3442	119	35	ĩ	ĩ	PROPN
ejpam-3442	119	36	⊆	⊆	NUM
ejpam-3442	119	37	j̃	j̃	PROPN
ejpam-3442	119	38	,	,	PUNCT
ejpam-3442	119	39	then	then	ADV
ejpam-3442	119	40	(	(	PUNCT
ejpam-3442	119	41	f	f	X
ejpam-3442	119	42	,	,	PUNCT
ejpam-3442	119	43	e)∗s(j̃)⊆̃(f	e)∗s(j̃)⊆̃(f	PROPN
ejpam-3442	119	44	,	,	PUNCT
ejpam-3442	119	45	e)∗s(ĩ	e)∗s(ĩ	NOUN
ejpam-3442	119	46	)	)	PUNCT
ejpam-3442	119	47	,	,	PUNCT
ejpam-3442	119	48	(	(	PUNCT
ejpam-3442	119	49	4	4	X
ejpam-3442	119	50	)	)	PUNCT
ejpam-3442	119	51	(	(	PUNCT
ejpam-3442	119	52	f	f	X
ejpam-3442	119	53	,	,	PUNCT
ejpam-3442	119	54	e)∗s	e)∗s	PROPN
ejpam-3442	119	55	=	=	SYM
ejpam-3442	119	56	scl(f	scl(f	PROPN
ejpam-3442	119	57	,	,	PUNCT
ejpam-3442	119	58	e)∗s⊆̃scl(f	e)∗s⊆̃scl(f	PROPN
ejpam-3442	119	59	,	,	PUNCT
ejpam-3442	119	60	e	e	NOUN
ejpam-3442	119	61	)	)	PUNCT
ejpam-3442	119	62	,	,	PUNCT
ejpam-3442	119	63	where	where	SCONJ
ejpam-3442	119	64	scl	scl	PROPN
ejpam-3442	119	65	is	be	AUX
ejpam-3442	119	66	the	the	DET
ejpam-3442	119	67	semi	semi	ADJ
ejpam-3442	119	68	soft	soft	ADJ
ejpam-3442	119	69	closure	closure	NOUN
ejpam-3442	119	70	w.r.t	w.r.t	NOUN
ejpam-3442	119	71	.	.	PUNCT
ejpam-3442	120	1	τ	τ	PROPN
ejpam-3442	120	2	,	,	PUNCT
ejpam-3442	120	3	(	(	PUNCT
ejpam-3442	120	4	f	f	X
ejpam-3442	120	5	,	,	PUNCT
ejpam-3442	120	6	e)∗s	e)∗s	PROPN
ejpam-3442	120	7	is	be	AUX
ejpam-3442	120	8	semi	semi	ADV
ejpam-3442	120	9	closed	closed	ADJ
ejpam-3442	120	10	soft	soft	ADJ
ejpam-3442	120	11	set	set	NOUN
ejpam-3442	120	12	.	.	PUNCT
ejpam-3442	121	1	(	(	PUNCT
ejpam-3442	121	2	5	5	NUM
ejpam-3442	121	3	)	)	PUNCT
ejpam-3442	121	4	(	(	PUNCT
ejpam-3442	121	5	(	(	PUNCT
ejpam-3442	121	6	f	f	X
ejpam-3442	121	7	,	,	PUNCT
ejpam-3442	121	8	e)∗s)∗s⊆̃(f	e)∗s)∗s⊆̃(f	PROPN
ejpam-3442	121	9	,	,	PUNCT
ejpam-3442	121	10	e)∗s	e)∗	NOUN
ejpam-3442	121	11	,	,	PUNCT
ejpam-3442	121	12	(	(	PUNCT
ejpam-3442	121	13	6	6	NUM
ejpam-3442	121	14	)	)	PUNCT
ejpam-3442	121	15	(	(	PUNCT
ejpam-3442	121	16	(	(	PUNCT
ejpam-3442	121	17	f	f	X
ejpam-3442	121	18	,	,	PUNCT
ejpam-3442	121	19	e)∪̃(g	e)∪̃(g	NOUN
ejpam-3442	121	20	,	,	PUNCT
ejpam-3442	121	21	e))∗s	e))∗s	NOUN
ejpam-3442	121	22	=	=	SYM
ejpam-3442	121	23	(	(	PUNCT
ejpam-3442	121	24	f	f	X
ejpam-3442	121	25	,	,	PUNCT
ejpam-3442	121	26	e)∗s∪̃(g	e)∗s∪̃(g	PROPN
ejpam-3442	121	27	,	,	PUNCT
ejpam-3442	121	28	e)∗s	e)∗	NOUN
ejpam-3442	121	29	,	,	PUNCT
ejpam-3442	121	30	(	(	PUNCT
ejpam-3442	121	31	7	7	X
ejpam-3442	121	32	)	)	PUNCT
ejpam-3442	121	33	∪̃j(f	∪̃j(f	PROPN
ejpam-3442	121	34	,	,	PUNCT
ejpam-3442	121	35	e)∗s	e)∗s	NOUN
ejpam-3442	121	36	=	=	SYM
ejpam-3442	121	37	(	(	PUNCT
ejpam-3442	121	38	∪̃j(f	∪̃j(f	PROPN
ejpam-3442	121	39	,	,	PUNCT
ejpam-3442	121	40	e))∗s	e))∗s	NOUN
ejpam-3442	121	41	,	,	PUNCT
ejpam-3442	121	42	(	(	PUNCT
ejpam-3442	121	43	8)	8)	NUM
ejpam-3442	121	44	(	(	PUNCT
ejpam-3442	121	45	(	(	PUNCT
ejpam-3442	121	46	f	f	X
ejpam-3442	121	47	,	,	PUNCT
ejpam-3442	121	48	e)∩̃(g	e)∩̃(g	PROPN
ejpam-3442	121	49	,	,	PUNCT
ejpam-3442	121	50	e))∗s	e))∗s	NOUN
ejpam-3442	121	51	⊆	⊆	NUM
ejpam-3442	121	52	(	(	PUNCT
ejpam-3442	121	53	f	f	NUM
ejpam-3442	121	54	,	,	PUNCT
ejpam-3442	121	55	e)∗s∩̃(g	e)∗s∩̃(g	NOUN
ejpam-3442	121	56	,	,	PUNCT
ejpam-3442	121	57	e)∗s	e)∗	NOUN
ejpam-3442	121	58	,	,	PUNCT
ejpam-3442	121	59	(	(	PUNCT
ejpam-3442	121	60	9	9	NUM
ejpam-3442	121	61	)	)	PUNCT
ejpam-3442	121	62	(	(	PUNCT
ejpam-3442	121	63	f	f	X
ejpam-3442	121	64	,	,	PUNCT
ejpam-3442	121	65	e)∗s	e)∗s	PROPN
ejpam-3442	121	66	−	−	PROPN
ejpam-3442	121	67	(	(	PUNCT
ejpam-3442	121	68	g	g	NOUN
ejpam-3442	121	69	,	,	PUNCT
ejpam-3442	121	70	e)∗s	e)∗s	PROPN
ejpam-3442	121	71	=	=	SYM
ejpam-3442	121	72	(	(	PUNCT
ejpam-3442	121	73	(	(	PUNCT
ejpam-3442	121	74	f	f	X
ejpam-3442	121	75	,	,	PUNCT
ejpam-3442	121	76	e)−	e)−	PROPN
ejpam-3442	121	77	(	(	PUNCT
ejpam-3442	121	78	g	g	NOUN
ejpam-3442	121	79	,	,	PUNCT
ejpam-3442	121	80	e))∗s	e))∗s	NOUN
ejpam-3442	121	81	−	−	NOUN
ejpam-3442	121	82	(	(	PUNCT
ejpam-3442	121	83	g	g	NOUN
ejpam-3442	121	84	,	,	PUNCT
ejpam-3442	121	85	e)∗s⊆̃((f	e)∗s⊆̃((f	NUM
ejpam-3442	121	86	,	,	PUNCT
ejpam-3442	121	87	e)−	e)−	PROPN
ejpam-3442	121	88	(	(	PUNCT
ejpam-3442	121	89	g	g	NOUN
ejpam-3442	121	90	,	,	PUNCT
ejpam-3442	121	91	e))∗s	e))∗s	NOUN
ejpam-3442	121	92	,	,	PUNCT
ejpam-3442	121	93	(	(	PUNCT
ejpam-3442	121	94	10	10	NUM
ejpam-3442	121	95	)	)	PUNCT
ejpam-3442	122	1	if	if	SCONJ
ejpam-3442	122	2	(	(	PUNCT
ejpam-3442	122	3	i	i	NOUN
ejpam-3442	122	4	,	,	PUNCT
ejpam-3442	122	5	e	e	NOUN
ejpam-3442	122	6	)	)	PUNCT
ejpam-3442	122	7	∈	∈	PROPN
ejpam-3442	122	8	ĩ	ĩ	PROPN
ejpam-3442	122	9	,	,	PUNCT
ejpam-3442	122	10	then	then	ADV
ejpam-3442	122	11	(	(	PUNCT
ejpam-3442	122	12	(	(	PUNCT
ejpam-3442	122	13	f	f	X
ejpam-3442	122	14	,	,	PUNCT
ejpam-3442	122	15	e)−	e)−	PROPN
ejpam-3442	122	16	(	(	PUNCT
ejpam-3442	122	17	i	i	NOUN
ejpam-3442	122	18	,	,	PUNCT
ejpam-3442	122	19	e))∗s	e))∗s	NOUN
ejpam-3442	122	20	=	=	SYM
ejpam-3442	122	21	(	(	PUNCT
ejpam-3442	122	22	f	f	NOUN
ejpam-3442	122	23	,	,	PUNCT
ejpam-3442	122	24	e)∗s	e)∗s	PROPN
ejpam-3442	122	25	=	=	SYM
ejpam-3442	122	26	(	(	PUNCT
ejpam-3442	122	27	(	(	PUNCT
ejpam-3442	122	28	f	f	X
ejpam-3442	122	29	,	,	PUNCT
ejpam-3442	122	30	e)∪̃(i	e)∪̃(i	NOUN
ejpam-3442	122	31	,	,	PUNCT
ejpam-3442	122	32	e))∗s	e))∗s	NOUN
ejpam-3442	122	33	.	.	PUNCT
ejpam-3442	123	1	proof	proof	NOUN
ejpam-3442	123	2	.	.	PUNCT
ejpam-3442	124	1	(	(	PUNCT
ejpam-3442	124	2	1	1	X
ejpam-3442	124	3	)	)	PUNCT
ejpam-3442	124	4	obvious	obvious	ADJ
ejpam-3442	124	5	from	from	ADP
ejpam-3442	124	6	definition	definition	NOUN
ejpam-3442	124	7	12	12	NUM
ejpam-3442	124	8	.	.	PUNCT
ejpam-3442	125	1	(	(	PUNCT
ejpam-3442	125	2	2	2	X
ejpam-3442	125	3	)	)	PUNCT
ejpam-3442	125	4	assume	assume	VERB
ejpam-3442	125	5	that	that	SCONJ
ejpam-3442	125	6	xe∈̃(f	xe∈̃(f	PROPN
ejpam-3442	125	7	,	,	PUNCT
ejpam-3442	125	8	e)∗s	e)∗s	PROPN
ejpam-3442	125	9	and	and	CCONJ
ejpam-3442	125	10	xe˜6∈(g	xe˜6∈(g	PROPN
ejpam-3442	125	11	,	,	PUNCT
ejpam-3442	125	12	e)∗s	e)∗s	PROPN
ejpam-3442	125	13	.	.	PUNCT
ejpam-3442	126	1	then	then	ADV
ejpam-3442	126	2	,	,	PUNCT
ejpam-3442	126	3	there	there	PRON
ejpam-3442	126	4	exist	exist	VERB
ejpam-3442	126	5	oxe	oxe	PRON
ejpam-3442	126	6	∈	∈	PROPN
ejpam-3442	126	7	sos(x	sos(x	PROPN
ejpam-3442	126	8	)	)	PUNCT
ejpam-3442	126	9	such	such	ADJ
ejpam-3442	126	10	thatoxe∩̃(g	thatoxe∩̃(g	NOUN
ejpam-3442	126	11	,	,	PUNCT
ejpam-3442	126	12	e	e	NOUN
ejpam-3442	126	13	)	)	PUNCT
ejpam-3442	126	14	∈	∈	PROPN
ejpam-3442	126	15	ĩ.	ĩ.	PROPN
ejpam-3442	126	16	since	since	SCONJ
ejpam-3442	126	17	(	(	PUNCT
ejpam-3442	126	18	f	f	X
ejpam-3442	126	19	,	,	PUNCT
ejpam-3442	126	20	e)⊆̃(g	e)⊆̃(g	PROPN
ejpam-3442	126	21	,	,	PUNCT
ejpam-3442	126	22	e	e	NOUN
ejpam-3442	126	23	)	)	PUNCT
ejpam-3442	126	24	,	,	PUNCT
ejpam-3442	126	25	oxe∩̃(f	oxe∩̃(f	ADV
ejpam-3442	126	26	,	,	PUNCT
ejpam-3442	126	27	e)⊆̃oxe∩̃(g	e)⊆̃oxe∩̃(g	X
ejpam-3442	126	28	,	,	PUNCT
ejpam-3442	126	29	e	e	NOUN
ejpam-3442	126	30	)	)	PUNCT
ejpam-3442	126	31	andoxe∩̃(f	andoxe∩̃(f	PROPN
ejpam-3442	126	32	,	,	PUNCT
ejpam-3442	126	33	e	e	NOUN
ejpam-3442	126	34	)	)	PUNCT
ejpam-3442	126	35	∈	∈	PROPN
ejpam-3442	126	36	ĩ.	ĩ.	PROPN
ejpam-3442	126	37	hence	hence	ADV
ejpam-3442	126	38	,	,	PUNCT
ejpam-3442	126	39	xe˜6∈(f	xe˜6∈(f	PROPN
ejpam-3442	126	40	,	,	PUNCT
ejpam-3442	126	41	e)∗s	e)∗s	PROPN
ejpam-3442	126	42	,	,	PUNCT
ejpam-3442	126	43	which	which	PRON
ejpam-3442	126	44	is	be	AUX
ejpam-3442	126	45	a	a	DET
ejpam-3442	126	46	contradiction	contradiction	NOUN
ejpam-3442	126	47	.	.	PUNCT
ejpam-3442	127	1	thus	thus	ADV
ejpam-3442	127	2	,	,	PUNCT
ejpam-3442	127	3	xe∈̃(g	xe∈̃(g	NOUN
ejpam-3442	127	4	,	,	PUNCT
ejpam-3442	127	5	e)∗s	e)∗s	PROPN
ejpam-3442	127	6	and	and	CCONJ
ejpam-3442	127	7	so	so	ADV
ejpam-3442	127	8	(	(	PUNCT
ejpam-3442	127	9	f	f	X
ejpam-3442	127	10	,	,	PUNCT
ejpam-3442	127	11	e)∗s⊆̃(g	e)∗s⊆̃(g	NOUN
ejpam-3442	127	12	,	,	PUNCT
ejpam-3442	127	13	e)∗s	e)∗s	PROPN
ejpam-3442	127	14	.	.	PUNCT
ejpam-3442	128	1	(	(	PUNCT
ejpam-3442	128	2	3	3	X
ejpam-3442	128	3	)	)	PUNCT
ejpam-3442	128	4	let	let	VERB
ejpam-3442	128	5	xe∈̃(f	xe∈̃(f	PRON
ejpam-3442	128	6	,	,	PUNCT
ejpam-3442	128	7	e)∗s(j̃	e)∗s(j̃	PRON
ejpam-3442	128	8	)	)	PUNCT
ejpam-3442	128	9	.	.	PUNCT
ejpam-3442	129	1	then	then	ADV
ejpam-3442	129	2	,	,	PUNCT
ejpam-3442	129	3	oxe∩̃(f	oxe∩̃(f	ADV
ejpam-3442	129	4	,	,	PUNCT
ejpam-3442	129	5	e	e	NOUN
ejpam-3442	129	6	)	)	PUNCT
ejpam-3442	129	7	6∈	6∈	NOUN
ejpam-3442	129	8	j̃	j̃	PROPN
ejpam-3442	129	9	∀	∀	X
ejpam-3442	129	10	oxe	oxe	PRON
ejpam-3442	129	11	∈	∈	PROPN
ejpam-3442	129	12	sos(x	sos(x	PROPN
ejpam-3442	129	13	)	)	PUNCT
ejpam-3442	129	14	.	.	PUNCT
ejpam-3442	130	1	since	since	SCONJ
ejpam-3442	130	2	ĩ	ĩ	PROPN
ejpam-3442	130	3	⊆	⊆	NUM
ejpam-3442	130	4	j̃	j̃	PROPN
ejpam-3442	130	5	.	.	PUNCT
ejpam-3442	131	1	then	then	ADV
ejpam-3442	131	2	,	,	PUNCT
ejpam-3442	131	3	oxe∩̃(f	oxe∩̃(f	ADV
ejpam-3442	131	4	,	,	PUNCT
ejpam-3442	131	5	e	e	NOUN
ejpam-3442	131	6	)	)	PUNCT
ejpam-3442	131	7	6∈	6∈	NOUN
ejpam-3442	131	8	ĩ	ĩ	PROPN
ejpam-3442	131	9	∀	∀	NOUN
ejpam-3442	131	10	oxe	oxe	PRON
ejpam-3442	131	11	∈	∈	PROPN
ejpam-3442	131	12	sos(x	sos(x	PROPN
ejpam-3442	131	13	)	)	PUNCT
ejpam-3442	131	14	.	.	PUNCT
ejpam-3442	132	1	hence	hence	ADV
ejpam-3442	132	2	,	,	PUNCT
ejpam-3442	132	3	xe∈̃(f	xe∈̃(f	PROPN
ejpam-3442	132	4	,	,	PUNCT
ejpam-3442	132	5	e)∗s(ĩ	e)∗s(ĩ	NOUN
ejpam-3442	132	6	)	)	PUNCT
ejpam-3442	132	7	.	.	PUNCT
ejpam-3442	133	1	thus	thus	ADV
ejpam-3442	133	2	,	,	PUNCT
ejpam-3442	133	3	(	(	PUNCT
ejpam-3442	133	4	f	f	X
ejpam-3442	133	5	,	,	PUNCT
ejpam-3442	133	6	e)∗s(j̃)⊆̃(f	e)∗s(j̃)⊆̃(f	PROPN
ejpam-3442	133	7	,	,	PUNCT
ejpam-3442	133	8	e)∗s(ĩ	e)∗s(ĩ	NOUN
ejpam-3442	133	9	)	)	PUNCT
ejpam-3442	133	10	.	.	PUNCT
ejpam-3442	134	1	(	(	PUNCT
ejpam-3442	134	2	4	4	X
ejpam-3442	134	3	)	)	PUNCT
ejpam-3442	134	4	we	we	PRON
ejpam-3442	134	5	first	first	ADV
ejpam-3442	134	6	prove	prove	VERB
ejpam-3442	134	7	that	that	SCONJ
ejpam-3442	134	8	(	(	PUNCT
ejpam-3442	134	9	f	f	X
ejpam-3442	134	10	,	,	PUNCT
ejpam-3442	134	11	e)∗s	e)∗s	PROPN
ejpam-3442	134	12	=	=	SYM
ejpam-3442	134	13	scl(f	scl(f	PROPN
ejpam-3442	134	14	,	,	PUNCT
ejpam-3442	134	15	e)∗s	e)∗s	PROPN
ejpam-3442	134	16	.	.	PUNCT
ejpam-3442	135	1	let	let	VERB
ejpam-3442	135	2	xe∈̃scl(f	xe∈̃scl(f	PROPN
ejpam-3442	135	3	,	,	PUNCT
ejpam-3442	135	4	e)∗s	e)∗s	PROPN
ejpam-3442	135	5	.	.	PUNCT
ejpam-3442	136	1	then	then	ADV
ejpam-3442	136	2	,	,	PUNCT
ejpam-3442	136	3	oxe∩̃(f	oxe∩̃(f	ADV
ejpam-3442	136	4	,	,	PUNCT
ejpam-3442	136	5	e)∗s	e)∗s	PROPN
ejpam-3442	136	6	6=	6=	ADP
ejpam-3442	136	7	φ̃	φ̃	PROPN
ejpam-3442	136	8	for	for	ADP
ejpam-3442	136	9	every	every	DET
ejpam-3442	136	10	oxe	oxe	PROPN
ejpam-3442	136	11	∈	∈	PROPN
ejpam-3442	136	12	sos(x	sos(x	PROPN
ejpam-3442	136	13	)	)	PUNCT
ejpam-3442	136	14	.	.	PUNCT
ejpam-3442	137	1	therefore	therefore	ADV
ejpam-3442	137	2	,	,	PUNCT
ejpam-3442	137	3	there	there	PRON
ejpam-3442	137	4	exists	exist	VERB
ejpam-3442	137	5	a	a	DET
ejpam-3442	137	6	soft	soft	ADJ
ejpam-3442	137	7	point	point	NOUN
ejpam-3442	137	8	ye′	ye′	NOUN
ejpam-3442	137	9	such	such	ADJ
ejpam-3442	137	10	that	that	SCONJ
ejpam-3442	137	11	ye′∈̃oxe∩̃(f	ye′∈̃oxe∩̃(f	NOUN
ejpam-3442	137	12	,	,	PUNCT
ejpam-3442	137	13	e)∗s	e)∗s	PROPN
ejpam-3442	137	14	and	and	CCONJ
ejpam-3442	137	15	so	so	ADV
ejpam-3442	137	16	ye′∈̃(f	ye′∈̃(f	NOUN
ejpam-3442	137	17	,	,	PUNCT
ejpam-3442	137	18	e)∗s	e)∗s	PROPN
ejpam-3442	137	19	.	.	PUNCT
ejpam-3442	138	1	hence	hence	ADV
ejpam-3442	138	2	,	,	PUNCT
ejpam-3442	138	3	oy′e∩̃(f	oy′e∩̃(f	PRON
ejpam-3442	138	4	,	,	PUNCT
ejpam-3442	138	5	e	e	NOUN
ejpam-3442	138	6	)	)	PUNCT
ejpam-3442	138	7	6∈	6∈	PROPN
ejpam-3442	138	8	ĩ.	ĩ.	PROPN
ejpam-3442	138	9	thus	thus	ADV
ejpam-3442	138	10	,	,	PUNCT
ejpam-3442	138	11	xe∈̃(f	xe∈̃(f	PROPN
ejpam-3442	138	12	,	,	PUNCT
ejpam-3442	138	13	e)∗s	e)∗s	PROPN
ejpam-3442	138	14	.	.	PUNCT
ejpam-3442	139	1	this	this	PRON
ejpam-3442	139	2	shows	show	VERB
ejpam-3442	139	3	that	that	SCONJ
ejpam-3442	139	4	,	,	PUNCT
ejpam-3442	139	5	scl(f	scl(f	PROPN
ejpam-3442	139	6	,	,	PUNCT
ejpam-3442	139	7	e)∗s⊆̃(f	e)∗s⊆̃(f	PROPN
ejpam-3442	139	8	,	,	PUNCT
ejpam-3442	139	9	e)∗s	e)∗s	PROPN
ejpam-3442	139	10	but	but	CCONJ
ejpam-3442	139	11	we	we	PRON
ejpam-3442	139	12	have	have	VERB
ejpam-3442	139	13	(	(	PUNCT
ejpam-3442	139	14	f	f	X
ejpam-3442	139	15	,	,	PUNCT
ejpam-3442	139	16	e)∗s⊆̃scl(f	e)∗s⊆̃scl(f	PROPN
ejpam-3442	139	17	,	,	PUNCT
ejpam-3442	139	18	e)∗s	e)∗s	PROPN
ejpam-3442	139	19	.	.	PUNCT
ejpam-3442	140	1	now	now	ADV
ejpam-3442	140	2	,	,	PUNCT
ejpam-3442	140	3	we	we	PRON
ejpam-3442	140	4	prove	prove	VERB
ejpam-3442	140	5	that	that	SCONJ
ejpam-3442	140	6	scl(f	scl(f	NOUN
ejpam-3442	140	7	,	,	PUNCT
ejpam-3442	140	8	e)∗s	e)∗s	PROPN
ejpam-3442	140	9	=	=	SYM
ejpam-3442	140	10	(	(	PUNCT
ejpam-3442	140	11	f	f	X
ejpam-3442	140	12	,	,	PUNCT
ejpam-3442	140	13	e)∗s⊆̃scl(f	e)∗s⊆̃scl(f	PROPN
ejpam-3442	140	14	,	,	PUNCT
ejpam-3442	140	15	e	e	NOUN
ejpam-3442	140	16	)	)	PUNCT
ejpam-3442	140	17	.	.	PUNCT
ejpam-3442	141	1	assume	assume	VERB
ejpam-3442	141	2	that	that	SCONJ
ejpam-3442	141	3	,	,	PUNCT
ejpam-3442	141	4	xe˜6∈scl(f	xe˜6∈scl(f	PROPN
ejpam-3442	141	5	,	,	PUNCT
ejpam-3442	141	6	e	e	NOUN
ejpam-3442	141	7	)	)	PUNCT
ejpam-3442	141	8	.	.	PUNCT
ejpam-3442	142	1	then	then	ADV
ejpam-3442	142	2	,	,	PUNCT
ejpam-3442	142	3	there	there	PRON
ejpam-3442	142	4	existsoxe	existsoxe	VERB
ejpam-3442	142	5	∈	∈	PROPN
ejpam-3442	142	6	sos(x	sos(x	PROPN
ejpam-3442	142	7	)	)	PUNCT
ejpam-3442	142	8	such	such	ADJ
ejpam-3442	142	9	thatoxe∩̃(f	thatoxe∩̃(f	NOUN
ejpam-3442	142	10	,	,	PUNCT
ejpam-3442	142	11	e	e	NOUN
ejpam-3442	142	12	)	)	PUNCT
ejpam-3442	142	13	=	=	PUNCT
ejpam-3442	142	14	φ̃	φ̃	PROPN
ejpam-3442	142	15	∈	∈	PROPN
ejpam-3442	142	16	ĩ.	ĩ.	PROPN
ejpam-3442	142	17	hence	hence	ADV
ejpam-3442	142	18	,	,	PUNCT
ejpam-3442	142	19	xe˜6∈(f	xe˜6∈(f	PROPN
ejpam-3442	142	20	,	,	PUNCT
ejpam-3442	142	21	e)∗s	e)∗s	PROPN
ejpam-3442	142	22	.	.	PUNCT
ejpam-3442	143	1	thus	thus	ADV
ejpam-3442	143	2	,	,	PUNCT
ejpam-3442	143	3	(	(	PUNCT
ejpam-3442	143	4	f	f	X
ejpam-3442	143	5	,	,	PUNCT
ejpam-3442	143	6	e)∗s⊆̃scl(f	e)∗s⊆̃scl(f	PROPN
ejpam-3442	143	7	,	,	PUNCT
ejpam-3442	143	8	e	e	NOUN
ejpam-3442	143	9	)	)	PUNCT
ejpam-3442	143	10	.	.	PUNCT
ejpam-3442	144	1	(	(	PUNCT
ejpam-3442	144	2	5	5	NUM
ejpam-3442	144	3	)	)	PUNCT
ejpam-3442	144	4	since	since	SCONJ
ejpam-3442	144	5	(	(	PUNCT
ejpam-3442	144	6	f	f	X
ejpam-3442	144	7	,	,	PUNCT
ejpam-3442	144	8	e)∗s⊆̃scl(f	e)∗s⊆̃scl(f	PROPN
ejpam-3442	144	9	,	,	PUNCT
ejpam-3442	144	10	e	e	NOUN
ejpam-3442	144	11	)	)	PUNCT
ejpam-3442	144	12	from	from	ADP
ejpam-3442	144	13	(	(	PUNCT
ejpam-3442	144	14	4	4	NUM
ejpam-3442	144	15	)	)	PUNCT
ejpam-3442	144	16	.	.	PUNCT
ejpam-3442	145	1	replace	replace	NOUN
ejpam-3442	145	2	(	(	PUNCT
ejpam-3442	145	3	f	f	X
ejpam-3442	145	4	,	,	PUNCT
ejpam-3442	145	5	e	e	NOUN
ejpam-3442	145	6	)	)	PUNCT
ejpam-3442	145	7	with	with	ADP
ejpam-3442	145	8	(	(	PUNCT
ejpam-3442	145	9	f	f	X
ejpam-3442	145	10	,	,	PUNCT
ejpam-3442	145	11	e)∗s	e)∗s	PROPN
ejpam-3442	145	12	,	,	PUNCT
ejpam-3442	145	13	we	we	PRON
ejpam-3442	145	14	get	get	VERB
ejpam-3442	145	15	(	(	PUNCT
ejpam-3442	145	16	(	(	PUNCT
ejpam-3442	145	17	f	f	X
ejpam-3442	145	18	,	,	PUNCT
ejpam-3442	145	19	e)∗s)∗s⊆̃scl	e)∗s)∗s⊆̃scl	PROPN
ejpam-3442	145	20	(	(	PUNCT
ejpam-3442	145	21	f	f	X
ejpam-3442	145	22	,	,	PUNCT
ejpam-3442	145	23	e)∗s	e)∗s	PROPN
ejpam-3442	145	24	=	=	SYM
ejpam-3442	145	25	(	(	PUNCT
ejpam-3442	145	26	f	f	X
ejpam-3442	145	27	,	,	PUNCT
ejpam-3442	145	28	e)∗s	e)∗s	PROPN
ejpam-3442	145	29	from	from	ADP
ejpam-3442	145	30	(	(	PUNCT
ejpam-3442	145	31	4	4	NUM
ejpam-3442	145	32	)	)	PUNCT
ejpam-3442	145	33	.	.	PUNCT
ejpam-3442	146	1	f.	f.	PROPN
ejpam-3442	146	2	a.	a.	PROPN
ejpam-3442	146	3	gharib	gharib	PROPN
ejpam-3442	146	4	,	,	PUNCT
ejpam-3442	146	5	a.	a.	PROPN
ejpam-3442	146	6	m.	m.	PROPN
ejpam-3442	146	7	abd	abd	PROPN
ejpam-3442	146	8	el	el	PROPN
ejpam-3442	146	9	-	-	PROPN
ejpam-3442	146	10	latif	latif	PROPN
ejpam-3442	146	11	/	/	SYM
ejpam-3442	146	12	eur	eur	PROPN
ejpam-3442	146	13	.	.	PUNCT
ejpam-3442	147	1	j.	j.	PROPN
ejpam-3442	147	2	pure	pure	PROPN
ejpam-3442	147	3	appl	appl	PROPN
ejpam-3442	147	4	.	.	PROPN
ejpam-3442	147	5	math	math	PROPN
ejpam-3442	147	6	,	,	PUNCT
ejpam-3442	147	7	12	12	NUM
ejpam-3442	147	8	(	(	PUNCT
ejpam-3442	147	9	3	3	NUM
ejpam-3442	147	10	)	)	PUNCT
ejpam-3442	147	11	(	(	PUNCT
ejpam-3442	147	12	2019	2019	NUM
ejpam-3442	147	13	)	)	PUNCT
ejpam-3442	147	14	,	,	PUNCT
ejpam-3442	147	15	857	857	NUM
ejpam-3442	147	16	-	-	SYM
ejpam-3442	147	17	869	869	NUM
ejpam-3442	147	18	862	862	NUM
ejpam-3442	147	19	(	(	PUNCT
ejpam-3442	147	20	6	6	NUM
ejpam-3442	147	21	)	)	PUNCT
ejpam-3442	147	22	let	let	VERB
ejpam-3442	147	23	xe∈̃((f	xe∈̃((f	NOUN
ejpam-3442	147	24	,	,	PUNCT
ejpam-3442	147	25	e)∪̃(g	e)∪̃(g	NOUN
ejpam-3442	147	26	,	,	PUNCT
ejpam-3442	147	27	e))∗s	e))∗s	NOUN
ejpam-3442	147	28	.	.	PUNCT
ejpam-3442	148	1	then	then	ADV
ejpam-3442	148	2	,	,	PUNCT
ejpam-3442	148	3	oxe∩̃((f	oxe∩̃((f	PROPN
ejpam-3442	148	4	,	,	PUNCT
ejpam-3442	148	5	e)∪̃(g	e)∪̃(g	NOUN
ejpam-3442	148	6	,	,	PUNCT
ejpam-3442	148	7	e	e	NOUN
ejpam-3442	148	8	)	)	PUNCT
ejpam-3442	148	9	)	)	PUNCT
ejpam-3442	149	1	=	=	PUNCT
ejpam-3442	149	2	(	(	PUNCT
ejpam-3442	149	3	oxe∩̃(f	oxe∩̃(f	X
ejpam-3442	149	4	,	,	PUNCT
ejpam-3442	149	5	e	e	NOUN
ejpam-3442	149	6	)	)	PUNCT
ejpam-3442	149	7	)	)	PUNCT
ejpam-3442	149	8	∪̃(oxe∩̃(g	∪̃(oxe∩̃(g	NOUN
ejpam-3442	149	9	,	,	PUNCT
ejpam-3442	149	10	e	e	NOUN
ejpam-3442	149	11	)	)	PUNCT
ejpam-3442	149	12	)	)	PUNCT
ejpam-3442	150	1	6∈	6∈	PROPN
ejpam-3442	150	2	ĩ	ĩ	PROPN
ejpam-3442	150	3	∀	∀	NOUN
ejpam-3442	150	4	oxe	oxe	PRON
ejpam-3442	150	5	∈	∈	PROPN
ejpam-3442	150	6	sos(x	sos(x	PROPN
ejpam-3442	150	7	)	)	PUNCT
ejpam-3442	150	8	.	.	PUNCT
ejpam-3442	151	1	hence	hence	ADV
ejpam-3442	151	2	,	,	PUNCT
ejpam-3442	151	3	eitheroxe∩̃(f	eitheroxe∩̃(f	PROPN
ejpam-3442	151	4	,	,	PUNCT
ejpam-3442	151	5	e	e	NOUN
ejpam-3442	151	6	)	)	PUNCT
ejpam-3442	151	7	6∈	6∈	NOUN
ejpam-3442	151	8	ĩ	ĩ	PROPN
ejpam-3442	151	9	oroxe∩̃(g	oroxe∩̃(g	NOUN
ejpam-3442	151	10	,	,	PUNCT
ejpam-3442	151	11	e	e	NOUN
ejpam-3442	151	12	)	)	PUNCT
ejpam-3442	151	13	6∈	6∈	NOUN
ejpam-3442	151	14	ĩ	ĩ	PROPN
ejpam-3442	151	15	from	from	ADP
ejpam-3442	151	16	definition	definition	NOUN
ejpam-3442	151	17	10	10	NUM
ejpam-3442	151	18	∀	∀	NOUN
ejpam-3442	151	19	oxe	oxe	PRON
ejpam-3442	151	20	∈	∈	PROPN
ejpam-3442	151	21	sos(x	sos(x	PROPN
ejpam-3442	151	22	)	)	PUNCT
ejpam-3442	151	23	.	.	PUNCT
ejpam-3442	152	1	this	this	PRON
ejpam-3442	152	2	means	mean	VERB
ejpam-3442	152	3	that	that	SCONJ
ejpam-3442	152	4	,	,	PUNCT
ejpam-3442	152	5	either	either	CCONJ
ejpam-3442	152	6	xe∈̃(f	xe∈̃(f	PROPN
ejpam-3442	152	7	,	,	PUNCT
ejpam-3442	152	8	e)∗s	e)∗s	PROPN
ejpam-3442	152	9	or	or	CCONJ
ejpam-3442	152	10	xe∈̃(g	xe∈̃(g	NOUN
ejpam-3442	152	11	,	,	PUNCT
ejpam-3442	152	12	e)∗s	e)∗s	PROPN
ejpam-3442	152	13	.	.	PUNCT
ejpam-3442	153	1	thus	thus	ADV
ejpam-3442	153	2	,	,	PUNCT
ejpam-3442	153	3	xe∈̃(f	xe∈̃(f	PROPN
ejpam-3442	153	4	,	,	PUNCT
ejpam-3442	153	5	e)∗s∪̃(g	e)∗s∪̃(g	PROPN
ejpam-3442	153	6	,	,	PUNCT
ejpam-3442	153	7	e)∗s	e)∗s	PROPN
ejpam-3442	153	8	.	.	PUNCT
ejpam-3442	154	1	it	it	PRON
ejpam-3442	154	2	follows	follow	VERB
ejpam-3442	154	3	that	that	SCONJ
ejpam-3442	154	4	,	,	PUNCT
ejpam-3442	154	5	(	(	PUNCT
ejpam-3442	154	6	(	(	PUNCT
ejpam-3442	154	7	f	f	X
ejpam-3442	154	8	,	,	PUNCT
ejpam-3442	154	9	e)∪̃(g	e)∪̃(g	NOUN
ejpam-3442	154	10	,	,	PUNCT
ejpam-3442	154	11	e))∗s⊆̃(f	e))∗s⊆̃(f	PROPN
ejpam-3442	154	12	,	,	PUNCT
ejpam-3442	154	13	e)∗s∪̃	e)∗s∪̃	PROPN
ejpam-3442	154	14	(	(	PUNCT
ejpam-3442	154	15	g	g	NOUN
ejpam-3442	154	16	,	,	PUNCT
ejpam-3442	154	17	e)∗s	e)∗s	PROPN
ejpam-3442	154	18	.	.	PUNCT
ejpam-3442	155	1	for	for	ADP
ejpam-3442	155	2	the	the	DET
ejpam-3442	155	3	reverse	reverse	ADJ
ejpam-3442	155	4	inclusion	inclusion	NOUN
ejpam-3442	155	5	,	,	PUNCT
ejpam-3442	155	6	since	since	SCONJ
ejpam-3442	155	7	(	(	PUNCT
ejpam-3442	155	8	f	f	X
ejpam-3442	155	9	,	,	PUNCT
ejpam-3442	155	10	e	e	NOUN
ejpam-3442	155	11	)	)	PUNCT
ejpam-3442	155	12	,	,	PUNCT
ejpam-3442	155	13	(	(	PUNCT
ejpam-3442	155	14	g	g	NOUN
ejpam-3442	155	15	,	,	PUNCT
ejpam-3442	155	16	e)⊆̃((f	e)⊆̃((f	NOUN
ejpam-3442	155	17	,	,	PUNCT
ejpam-3442	155	18	e)∪̃(g	e)∪̃(g	NOUN
ejpam-3442	155	19	,	,	PUNCT
ejpam-3442	155	20	e	e	NOUN
ejpam-3442	155	21	)	)	PUNCT
ejpam-3442	155	22	)	)	PUNCT
ejpam-3442	155	23	.	.	PUNCT
ejpam-3442	156	1	then	then	ADV
ejpam-3442	156	2	,	,	PUNCT
ejpam-3442	156	3	(	(	PUNCT
ejpam-3442	156	4	f	f	X
ejpam-3442	156	5	,	,	PUNCT
ejpam-3442	156	6	e)∗s⊆̃((f	e)∗s⊆̃((f	NUM
ejpam-3442	156	7	,	,	PUNCT
ejpam-3442	156	8	e)∪̃(g	e)∪̃(g	NOUN
ejpam-3442	156	9	,	,	PUNCT
ejpam-3442	156	10	e))∗s	e))∗s	NOUN
ejpam-3442	156	11	and	and	CCONJ
ejpam-3442	156	12	(	(	PUNCT
ejpam-3442	156	13	g	g	NOUN
ejpam-3442	156	14	,	,	PUNCT
ejpam-3442	156	15	e)∗s⊆̃((f	e)∗s⊆̃((f	NUM
ejpam-3442	156	16	,	,	PUNCT
ejpam-3442	156	17	e)∪̃(g	e)∪̃(g	NOUN
ejpam-3442	156	18	,	,	PUNCT
ejpam-3442	156	19	e))∗s	e))∗s	NOUN
ejpam-3442	156	20	from	from	ADP
ejpam-3442	156	21	(	(	PUNCT
ejpam-3442	156	22	2	2	NUM
ejpam-3442	156	23	)	)	PUNCT
ejpam-3442	156	24	.	.	PUNCT
ejpam-3442	157	1	hence	hence	ADV
ejpam-3442	157	2	,	,	PUNCT
ejpam-3442	157	3	(	(	PUNCT
ejpam-3442	157	4	f	f	X
ejpam-3442	157	5	,	,	PUNCT
ejpam-3442	157	6	e)∗s∪̃(g	e)∗s∪̃(g	PROPN
ejpam-3442	157	7	,	,	PUNCT
ejpam-3442	157	8	e)∗s	e)∗	NOUN
ejpam-3442	157	9	⊆̃((f	⊆̃((f	ADJ
ejpam-3442	157	10	,	,	PUNCT
ejpam-3442	157	11	e)∪̃(g	e)∪̃(g	NOUN
ejpam-3442	157	12	,	,	PUNCT
ejpam-3442	157	13	e))∗s	e))∗s	NOUN
ejpam-3442	157	14	and	and	CCONJ
ejpam-3442	157	15	it	it	PRON
ejpam-3442	157	16	is	be	AUX
ejpam-3442	157	17	implies	imply	VERB
ejpam-3442	157	18	that	that	SCONJ
ejpam-3442	157	19	(	(	PUNCT
ejpam-3442	157	20	(	(	PUNCT
ejpam-3442	157	21	f	f	X
ejpam-3442	157	22	,	,	PUNCT
ejpam-3442	157	23	e)∪̃(g	e)∪̃(g	NOUN
ejpam-3442	157	24	,	,	PUNCT
ejpam-3442	157	25	e))∗s	e))∗s	NOUN
ejpam-3442	157	26	=	=	SYM
ejpam-3442	157	27	(	(	PUNCT
ejpam-3442	157	28	f	f	X
ejpam-3442	157	29	,	,	PUNCT
ejpam-3442	157	30	e)∗s∪̃(g	e)∗s∪̃(g	PROPN
ejpam-3442	157	31	,	,	PUNCT
ejpam-3442	157	32	e)∗s	e)∗s	PROPN
ejpam-3442	157	33	.	.	PUNCT
ejpam-3442	158	1	(	(	PUNCT
ejpam-3442	158	2	7	7	X
ejpam-3442	158	3	)	)	PUNCT
ejpam-3442	158	4	obvious	obvious	ADJ
ejpam-3442	158	5	from	from	ADP
ejpam-3442	158	6	(	(	PUNCT
ejpam-3442	158	7	6	6	NUM
ejpam-3442	158	8	)	)	PUNCT
ejpam-3442	158	9	.	.	PUNCT
ejpam-3442	159	1	(	(	PUNCT
ejpam-3442	159	2	8)	8)	NUM
ejpam-3442	159	3	since	since	SCONJ
ejpam-3442	159	4	(	(	PUNCT
ejpam-3442	159	5	(	(	PUNCT
ejpam-3442	159	6	f	f	X
ejpam-3442	159	7	,	,	PUNCT
ejpam-3442	159	8	e)∩̃(g	e)∩̃(g	PROPN
ejpam-3442	159	9	,	,	PUNCT
ejpam-3442	159	10	e))⊆̃(f	e))⊆̃(f	PROPN
ejpam-3442	159	11	,	,	PUNCT
ejpam-3442	159	12	e	e	NOUN
ejpam-3442	159	13	)	)	PUNCT
ejpam-3442	159	14	,	,	PUNCT
ejpam-3442	159	15	(	(	PUNCT
ejpam-3442	159	16	g	g	NOUN
ejpam-3442	159	17	,	,	PUNCT
ejpam-3442	159	18	e	e	NOUN
ejpam-3442	159	19	)	)	PUNCT
ejpam-3442	159	20	.	.	PUNCT
ejpam-3442	160	1	then	then	ADV
ejpam-3442	160	2	,	,	PUNCT
ejpam-3442	160	3	(	(	PUNCT
ejpam-3442	160	4	(	(	PUNCT
ejpam-3442	160	5	f	f	X
ejpam-3442	160	6	,	,	PUNCT
ejpam-3442	160	7	e)∩̃(g	e)∩̃(g	PROPN
ejpam-3442	160	8	,	,	PUNCT
ejpam-3442	160	9	e))∗s⊆̃(f	e))∗s⊆̃(f	PROPN
ejpam-3442	160	10	,	,	PUNCT
ejpam-3442	160	11	e)∗s	e)∗s	PROPN
ejpam-3442	160	12	and	and	CCONJ
ejpam-3442	160	13	(	(	PUNCT
ejpam-3442	160	14	(	(	PUNCT
ejpam-3442	160	15	f	f	X
ejpam-3442	160	16	,	,	PUNCT
ejpam-3442	160	17	e)∩̃(g	e)∩̃(g	PROPN
ejpam-3442	160	18	,	,	PUNCT
ejpam-3442	160	19	e	e	NOUN
ejpam-3442	160	20	)	)	PUNCT
ejpam-3442	160	21	)	)	PUNCT
ejpam-3442	160	22	⊆̃(g	⊆̃(g	NOUN
ejpam-3442	160	23	,	,	PUNCT
ejpam-3442	160	24	e)∗s	e)∗s	NOUN
ejpam-3442	160	25	from	from	ADP
ejpam-3442	160	26	(	(	PUNCT
ejpam-3442	160	27	2	2	NUM
ejpam-3442	160	28	)	)	PUNCT
ejpam-3442	160	29	.	.	PUNCT
ejpam-3442	161	1	hence	hence	ADV
ejpam-3442	161	2	,	,	PUNCT
ejpam-3442	161	3	(	(	PUNCT
ejpam-3442	161	4	(	(	PUNCT
ejpam-3442	161	5	f	f	X
ejpam-3442	161	6	,	,	PUNCT
ejpam-3442	161	7	e)∩̃(g	e)∩̃(g	PROPN
ejpam-3442	161	8	,	,	PUNCT
ejpam-3442	161	9	e))∗s⊆̃(f	e))∗s⊆̃(f	PROPN
ejpam-3442	161	10	,	,	PUNCT
ejpam-3442	161	11	e)∗s∩̃(g	e)∗s∩̃(g	NOUN
ejpam-3442	161	12	,	,	PUNCT
ejpam-3442	161	13	e)∗s	e)∗s	NUM
ejpam-3442	161	14	.	.	PUNCT
ejpam-3442	162	1	(	(	PUNCT
ejpam-3442	162	2	9	9	X
ejpam-3442	162	3	)	)	PUNCT
ejpam-3442	162	4	we	we	PRON
ejpam-3442	162	5	first	first	ADV
ejpam-3442	162	6	prove	prove	VERB
ejpam-3442	162	7	that	that	SCONJ
ejpam-3442	162	8	(	(	PUNCT
ejpam-3442	162	9	f	f	X
ejpam-3442	162	10	,	,	PUNCT
ejpam-3442	162	11	e)∗s−(g	e)∗s−(g	NOUN
ejpam-3442	162	12	,	,	PUNCT
ejpam-3442	162	13	e)∗s	e)∗s	NOUN
ejpam-3442	162	14	=	=	SYM
ejpam-3442	162	15	(	(	PUNCT
ejpam-3442	162	16	(	(	PUNCT
ejpam-3442	162	17	f	f	X
ejpam-3442	162	18	,	,	PUNCT
ejpam-3442	162	19	e)−(g	e)−(g	NOUN
ejpam-3442	162	20	,	,	PUNCT
ejpam-3442	162	21	e))∗s−(g	e))∗s−(g	NOUN
ejpam-3442	162	22	,	,	PUNCT
ejpam-3442	162	23	e)∗s	e)∗s	PROPN
ejpam-3442	162	24	.	.	PUNCT
ejpam-3442	163	1	since	since	SCONJ
ejpam-3442	163	2	(	(	PUNCT
ejpam-3442	163	3	f	f	X
ejpam-3442	163	4	,	,	PUNCT
ejpam-3442	163	5	e)−	e)−	PROPN
ejpam-3442	163	6	(	(	PUNCT
ejpam-3442	163	7	g	g	NOUN
ejpam-3442	163	8	,	,	PUNCT
ejpam-3442	163	9	e)⊆̃(f	e)⊆̃(f	PROPN
ejpam-3442	163	10	,	,	PUNCT
ejpam-3442	163	11	e	e	NOUN
ejpam-3442	163	12	)	)	PUNCT
ejpam-3442	163	13	.	.	PUNCT
ejpam-3442	164	1	then	then	ADV
ejpam-3442	164	2	,	,	PUNCT
ejpam-3442	164	3	(	(	PUNCT
ejpam-3442	164	4	(	(	PUNCT
ejpam-3442	164	5	f	f	X
ejpam-3442	164	6	,	,	PUNCT
ejpam-3442	164	7	e	e	NOUN
ejpam-3442	164	8	)	)	PUNCT
ejpam-3442	164	9	−	−	PROPN
ejpam-3442	164	10	(	(	PUNCT
ejpam-3442	164	11	g	g	NOUN
ejpam-3442	164	12	,	,	PUNCT
ejpam-3442	164	13	e))∗s⊆̃(f	e))∗s⊆̃(f	PROPN
ejpam-3442	164	14	,	,	PUNCT
ejpam-3442	164	15	e)∗s	e)∗s	PROPN
ejpam-3442	164	16	.	.	PUNCT
ejpam-3442	165	1	hence	hence	ADV
ejpam-3442	165	2	,	,	PUNCT
ejpam-3442	165	3	(	(	PUNCT
ejpam-3442	165	4	(	(	PUNCT
ejpam-3442	165	5	f	f	X
ejpam-3442	165	6	,	,	PUNCT
ejpam-3442	165	7	e	e	NOUN
ejpam-3442	165	8	)	)	PUNCT
ejpam-3442	165	9	−	−	PROPN
ejpam-3442	165	10	(	(	PUNCT
ejpam-3442	165	11	g	g	NOUN
ejpam-3442	165	12	,	,	PUNCT
ejpam-3442	165	13	e))∗s	e))∗s	NOUN
ejpam-3442	165	14	−	−	NOUN
ejpam-3442	166	1	(	(	PUNCT
ejpam-3442	166	2	g	g	PROPN
ejpam-3442	166	3	,	,	PUNCT
ejpam-3442	166	4	e)∗s⊆̃(f	e)∗s⊆̃(f	PROPN
ejpam-3442	166	5	,	,	PUNCT
ejpam-3442	166	6	e)∗s	e)∗s	PROPN
ejpam-3442	166	7	−	−	PROPN
ejpam-3442	166	8	(	(	PUNCT
ejpam-3442	166	9	g	g	NOUN
ejpam-3442	166	10	,	,	PUNCT
ejpam-3442	166	11	e)∗s	e)∗s	PROPN
ejpam-3442	166	12	.	.	PUNCT
ejpam-3442	167	1	for	for	ADP
ejpam-3442	167	2	the	the	DET
ejpam-3442	167	3	reverse	reverse	ADJ
ejpam-3442	167	4	inclusion	inclusion	NOUN
ejpam-3442	167	5	,	,	PUNCT
ejpam-3442	167	6	since	since	SCONJ
ejpam-3442	167	7	(	(	PUNCT
ejpam-3442	167	8	f	f	X
ejpam-3442	167	9	,	,	PUNCT
ejpam-3442	167	10	e	e	NOUN
ejpam-3442	167	11	)	)	PUNCT
ejpam-3442	167	12	=	=	SYM
ejpam-3442	168	1	[	[	X
ejpam-3442	168	2	(	(	PUNCT
ejpam-3442	168	3	f	f	X
ejpam-3442	168	4	,	,	PUNCT
ejpam-3442	168	5	e	e	NOUN
ejpam-3442	168	6	)	)	PUNCT
ejpam-3442	168	7	−	−	PROPN
ejpam-3442	168	8	(	(	PUNCT
ejpam-3442	168	9	g	g	NOUN
ejpam-3442	168	10	,	,	PUNCT
ejpam-3442	168	11	e)]∪̃[(f	e)]∪̃[(f	PROPN
ejpam-3442	168	12	,	,	PUNCT
ejpam-3442	168	13	e)∩̃(g	e)∩̃(g	PROPN
ejpam-3442	168	14	,	,	PUNCT
ejpam-3442	168	15	e	e	NOUN
ejpam-3442	168	16	)	)	PUNCT
ejpam-3442	168	17	]	]	PUNCT
ejpam-3442	168	18	.	.	PUNCT
ejpam-3442	169	1	then	then	ADV
ejpam-3442	169	2	,	,	PUNCT
ejpam-3442	169	3	(	(	PUNCT
ejpam-3442	169	4	f	f	X
ejpam-3442	169	5	,	,	PUNCT
ejpam-3442	169	6	e)∗s	e)∗s	PROPN
ejpam-3442	169	7	=	=	PUNCT
ejpam-3442	170	1	[	[	X
ejpam-3442	170	2	[	[	X
ejpam-3442	170	3	(	(	PUNCT
ejpam-3442	170	4	f	f	X
ejpam-3442	170	5	,	,	PUNCT
ejpam-3442	170	6	e)−	e)−	PROPN
ejpam-3442	170	7	(	(	PUNCT
ejpam-3442	170	8	g	g	NOUN
ejpam-3442	170	9	,	,	PUNCT
ejpam-3442	170	10	e)]∪̃[(f	e)]∪̃[(f	PROPN
ejpam-3442	170	11	,	,	PUNCT
ejpam-3442	170	12	e)∩̃(g	e)∩̃(g	PROPN
ejpam-3442	170	13	,	,	PUNCT
ejpam-3442	170	14	e)]]∗s	e)]]∗s	X
ejpam-3442	170	15	.	.	PUNCT
ejpam-3442	171	1	it	it	PRON
ejpam-3442	171	2	follows	follow	VERB
ejpam-3442	171	3	,	,	PUNCT
ejpam-3442	171	4	(	(	PUNCT
ejpam-3442	171	5	f	f	X
ejpam-3442	171	6	,	,	PUNCT
ejpam-3442	171	7	e)∗s	e)∗s	PROPN
ejpam-3442	172	1	=	=	PUNCT
ejpam-3442	173	1	[	[	X
ejpam-3442	173	2	[	[	X
ejpam-3442	173	3	(	(	PUNCT
ejpam-3442	173	4	f	f	X
ejpam-3442	173	5	,	,	PUNCT
ejpam-3442	173	6	e)−(g	e)−(g	NOUN
ejpam-3442	173	7	,	,	PUNCT
ejpam-3442	173	8	e)]∪̃[(f	e)]∪̃[(f	PROPN
ejpam-3442	173	9	,	,	PUNCT
ejpam-3442	173	10	e)∩̃(g	e)∩̃(g	PROPN
ejpam-3442	173	11	,	,	PUNCT
ejpam-3442	173	12	e)]]∗s	e)]]∗s	X
ejpam-3442	173	13	=	=	PUNCT
ejpam-3442	174	1	[	[	X
ejpam-3442	174	2	(	(	PUNCT
ejpam-3442	174	3	f	f	X
ejpam-3442	174	4	,	,	PUNCT
ejpam-3442	174	5	e)−(g	e)−(g	NOUN
ejpam-3442	174	6	,	,	PUNCT
ejpam-3442	174	7	e)]∗s∪̃[(f	e)]∗s∪̃[(f	NOUN
ejpam-3442	174	8	,	,	PUNCT
ejpam-3442	174	9	e)∩̃	e)∩̃	PROPN
ejpam-3442	174	10	(	(	PUNCT
ejpam-3442	174	11	g	g	NOUN
ejpam-3442	174	12	,	,	PUNCT
ejpam-3442	174	13	e)]∗s⊆̃[(f	e)]∗s⊆̃[(f	NOUN
ejpam-3442	174	14	,	,	PUNCT
ejpam-3442	174	15	e)−(g	e)−(g	NOUN
ejpam-3442	174	16	,	,	PUNCT
ejpam-3442	174	17	e)]∗s∪̃(g	e)]∗s∪̃(g	NOUN
ejpam-3442	174	18	,	,	PUNCT
ejpam-3442	174	19	e)∗s	e)∗s	PROPN
ejpam-3442	174	20	from	from	ADP
ejpam-3442	174	21	(	(	PUNCT
ejpam-3442	174	22	6	6	NUM
ejpam-3442	174	23	)	)	PUNCT
ejpam-3442	174	24	.	.	PUNCT
ejpam-3442	175	1	hence	hence	ADV
ejpam-3442	175	2	,	,	PUNCT
ejpam-3442	175	3	(	(	PUNCT
ejpam-3442	175	4	f	f	X
ejpam-3442	175	5	,	,	PUNCT
ejpam-3442	175	6	e)∗s−(g	e)∗s−(g	NOUN
ejpam-3442	175	7	,	,	PUNCT
ejpam-3442	175	8	e)∗s⊆̃[[(f	e)∗s⊆̃[[(f	X
ejpam-3442	175	9	,	,	PUNCT
ejpam-3442	175	10	e)−	e)−	PROPN
ejpam-3442	175	11	(	(	PUNCT
ejpam-3442	175	12	g	g	NOUN
ejpam-3442	175	13	,	,	PUNCT
ejpam-3442	175	14	e)]∗s∪̃(g	e)]∗s∪̃(g	NOUN
ejpam-3442	175	15	,	,	PUNCT
ejpam-3442	175	16	e)∗s	e)∗s	PROPN
ejpam-3442	175	17	]	]	X
ejpam-3442	175	18	−	−	PROPN
ejpam-3442	175	19	(	(	PUNCT
ejpam-3442	175	20	g	g	NOUN
ejpam-3442	175	21	,	,	PUNCT
ejpam-3442	175	22	e)∗s	e)∗s	PROPN
ejpam-3442	175	23	=	=	PUNCT
ejpam-3442	176	1	[	[	X
ejpam-3442	176	2	[	[	X
ejpam-3442	176	3	(	(	PUNCT
ejpam-3442	176	4	f	f	X
ejpam-3442	176	5	,	,	PUNCT
ejpam-3442	176	6	e)−	e)−	PROPN
ejpam-3442	176	7	(	(	PUNCT
ejpam-3442	176	8	g	g	NOUN
ejpam-3442	176	9	,	,	PUNCT
ejpam-3442	176	10	e)]∗s∪̃(g	e)]∗s∪̃(g	NOUN
ejpam-3442	176	11	,	,	PUNCT
ejpam-3442	176	12	e)∗s	e)∗s	PROPN
ejpam-3442	176	13	]	]	X
ejpam-3442	176	14	∩̃(g	∩̃(g	X
ejpam-3442	176	15	,	,	PUNCT
ejpam-3442	176	16	e)∗	e)∗	PROPN
ejpam-3442	176	17	′	′	NUM
ejpam-3442	177	1	=	=	PUNCT
ejpam-3442	178	1	[	[	X
ejpam-3442	178	2	(	(	PUNCT
ejpam-3442	178	3	f	f	X
ejpam-3442	178	4	,	,	PUNCT
ejpam-3442	178	5	e)−	e)−	PROPN
ejpam-3442	178	6	(	(	PUNCT
ejpam-3442	178	7	g	g	NOUN
ejpam-3442	178	8	,	,	PUNCT
ejpam-3442	178	9	e)]∗s	e)]∗s	PROPN
ejpam-3442	178	10	−	−	NOUN
ejpam-3442	178	11	(	(	PUNCT
ejpam-3442	178	12	g	g	NOUN
ejpam-3442	178	13	,	,	PUNCT
ejpam-3442	178	14	e)∗s	e)∗s	PROPN
ejpam-3442	178	15	.	.	PUNCT
ejpam-3442	179	1	thus	thus	ADV
ejpam-3442	179	2	,	,	PUNCT
ejpam-3442	179	3	(	(	PUNCT
ejpam-3442	179	4	f	f	X
ejpam-3442	179	5	,	,	PUNCT
ejpam-3442	179	6	e)∗s	e)∗s	PROPN
ejpam-3442	179	7	−	−	PROPN
ejpam-3442	179	8	(	(	PUNCT
ejpam-3442	179	9	g	g	NOUN
ejpam-3442	179	10	,	,	PUNCT
ejpam-3442	179	11	e)∗s	e)∗s	PROPN
ejpam-3442	179	12	=	=	SYM
ejpam-3442	179	13	(	(	PUNCT
ejpam-3442	179	14	(	(	PUNCT
ejpam-3442	179	15	f	f	X
ejpam-3442	179	16	,	,	PUNCT
ejpam-3442	179	17	e)−	e)−	PROPN
ejpam-3442	179	18	(	(	PUNCT
ejpam-3442	179	19	g	g	NOUN
ejpam-3442	179	20	,	,	PUNCT
ejpam-3442	179	21	e))∗s	e))∗s	NOUN
ejpam-3442	179	22	−	−	NOUN
ejpam-3442	179	23	(	(	PUNCT
ejpam-3442	179	24	g	g	NOUN
ejpam-3442	179	25	,	,	PUNCT
ejpam-3442	179	26	e)∗s	e)∗s	PROPN
ejpam-3442	179	27	.	.	PUNCT
ejpam-3442	180	1	now	now	ADV
ejpam-3442	180	2	,	,	PUNCT
ejpam-3442	180	3	if	if	SCONJ
ejpam-3442	180	4	xe∈̃((f	xe∈̃((f	NOUN
ejpam-3442	180	5	,	,	PUNCT
ejpam-3442	180	6	e)−	e)−	PROPN
ejpam-3442	180	7	(	(	PUNCT
ejpam-3442	180	8	g	g	NOUN
ejpam-3442	180	9	,	,	PUNCT
ejpam-3442	180	10	e))∗s	e))∗s	NOUN
ejpam-3442	180	11	−	−	NOUN
ejpam-3442	180	12	(	(	PUNCT
ejpam-3442	180	13	g	g	NOUN
ejpam-3442	180	14	,	,	PUNCT
ejpam-3442	180	15	e)∗s	e)∗s	PROPN
ejpam-3442	180	16	.	.	PUNCT
ejpam-3442	181	1	then	then	ADV
ejpam-3442	181	2	,	,	PUNCT
ejpam-3442	181	3	xe∈̃((f	xe∈̃((f	PROPN
ejpam-3442	181	4	,	,	PUNCT
ejpam-3442	181	5	e)−	e)−	PROPN
ejpam-3442	181	6	(	(	PUNCT
ejpam-3442	181	7	g	g	NOUN
ejpam-3442	181	8	,	,	PUNCT
ejpam-3442	181	9	e))∗s	e))∗s	NOUN
ejpam-3442	181	10	and	and	CCONJ
ejpam-3442	181	11	consequently	consequently	ADV
ejpam-3442	181	12	(	(	PUNCT
ejpam-3442	181	13	f	f	X
ejpam-3442	181	14	,	,	PUNCT
ejpam-3442	181	15	e)∗s	e)∗s	PROPN
ejpam-3442	181	16	−	−	PROPN
ejpam-3442	181	17	(	(	PUNCT
ejpam-3442	181	18	g	g	NOUN
ejpam-3442	181	19	,	,	PUNCT
ejpam-3442	181	20	e)∗s	e)∗s	PROPN
ejpam-3442	181	21	=	=	SYM
ejpam-3442	181	22	(	(	PUNCT
ejpam-3442	181	23	(	(	PUNCT
ejpam-3442	181	24	f	f	X
ejpam-3442	181	25	,	,	PUNCT
ejpam-3442	181	26	e)−	e)−	PROPN
ejpam-3442	181	27	(	(	PUNCT
ejpam-3442	181	28	g	g	NOUN
ejpam-3442	181	29	,	,	PUNCT
ejpam-3442	181	30	e))∗s	e))∗s	NOUN
ejpam-3442	181	31	−	−	NOUN
ejpam-3442	181	32	(	(	PUNCT
ejpam-3442	181	33	g	g	NOUN
ejpam-3442	181	34	,	,	PUNCT
ejpam-3442	181	35	e)∗s⊆̃((f	e)∗s⊆̃((f	NUM
ejpam-3442	181	36	,	,	PUNCT
ejpam-3442	181	37	e	e	NOUN
ejpam-3442	181	38	)	)	PUNCT
ejpam-3442	181	39	−	−	PROPN
ejpam-3442	181	40	(	(	PUNCT
ejpam-3442	181	41	g	g	NOUN
ejpam-3442	181	42	,	,	PUNCT
ejpam-3442	181	43	e))∗s	e))∗s	NOUN
ejpam-3442	181	44	.	.	PUNCT
ejpam-3442	182	1	(	(	PUNCT
ejpam-3442	182	2	10	10	NUM
ejpam-3442	182	3	)	)	PUNCT
ejpam-3442	182	4	we	we	PRON
ejpam-3442	182	5	first	first	ADV
ejpam-3442	182	6	prove	prove	VERB
ejpam-3442	182	7	that	that	SCONJ
ejpam-3442	182	8	(	(	PUNCT
ejpam-3442	182	9	f	f	X
ejpam-3442	182	10	,	,	PUNCT
ejpam-3442	182	11	e)∗s	e)∗s	PROPN
ejpam-3442	182	12	=	=	SYM
ejpam-3442	182	13	(	(	PUNCT
ejpam-3442	182	14	(	(	PUNCT
ejpam-3442	182	15	f	f	X
ejpam-3442	182	16	,	,	PUNCT
ejpam-3442	182	17	e	e	NOUN
ejpam-3442	182	18	)	)	PUNCT
ejpam-3442	182	19	−	−	PROPN
ejpam-3442	183	1	(	(	PUNCT
ejpam-3442	183	2	i	i	NOUN
ejpam-3442	183	3	,	,	PUNCT
ejpam-3442	183	4	e))∗s	e))∗s	NOUN
ejpam-3442	183	5	.	.	PUNCT
ejpam-3442	184	1	since	since	SCONJ
ejpam-3442	184	2	(	(	PUNCT
ejpam-3442	184	3	(	(	PUNCT
ejpam-3442	184	4	f	f	X
ejpam-3442	184	5	,	,	PUNCT
ejpam-3442	184	6	e	e	NOUN
ejpam-3442	184	7	)	)	PUNCT
ejpam-3442	184	8	−	−	PROPN
ejpam-3442	185	1	(	(	PUNCT
ejpam-3442	185	2	i	i	INTJ
ejpam-3442	185	3	,	,	PUNCT
ejpam-3442	185	4	e))⊆̃(f	e))⊆̃(f	ADV
ejpam-3442	185	5	,	,	PUNCT
ejpam-3442	185	6	e	e	NOUN
ejpam-3442	185	7	)	)	PUNCT
ejpam-3442	185	8	,	,	PUNCT
ejpam-3442	185	9	(	(	PUNCT
ejpam-3442	185	10	(	(	PUNCT
ejpam-3442	185	11	f	f	X
ejpam-3442	185	12	,	,	PUNCT
ejpam-3442	185	13	e	e	NOUN
ejpam-3442	185	14	)	)	PUNCT
ejpam-3442	185	15	−	−	PROPN
ejpam-3442	186	1	(	(	PUNCT
ejpam-3442	186	2	i	i	PROPN
ejpam-3442	186	3	,	,	PUNCT
ejpam-3442	186	4	e))∗s⊆̃(f	e))∗s⊆̃(f	PROPN
ejpam-3442	186	5	,	,	PUNCT
ejpam-3442	186	6	e)∗s	e)∗s	PROPN
ejpam-3442	186	7	from	from	ADP
ejpam-3442	186	8	(	(	PUNCT
ejpam-3442	186	9	2	2	NUM
ejpam-3442	186	10	)	)	PUNCT
ejpam-3442	186	11	.	.	PUNCT
ejpam-3442	187	1	for	for	ADP
ejpam-3442	187	2	the	the	DET
ejpam-3442	187	3	reverse	reverse	ADJ
ejpam-3442	187	4	inclusion	inclusion	NOUN
ejpam-3442	187	5	,	,	PUNCT
ejpam-3442	187	6	let	let	VERB
ejpam-3442	187	7	xe˜6∈((f	xe˜6∈((f	PROPN
ejpam-3442	187	8	,	,	PUNCT
ejpam-3442	187	9	e	e	NOUN
ejpam-3442	187	10	)	)	PUNCT
ejpam-3442	187	11	−	−	PROPN
ejpam-3442	188	1	(	(	PUNCT
ejpam-3442	188	2	i	i	NOUN
ejpam-3442	188	3	,	,	PUNCT
ejpam-3442	188	4	e))∗s	e))∗s	NOUN
ejpam-3442	188	5	.	.	PUNCT
ejpam-3442	189	1	then	then	ADV
ejpam-3442	189	2	,	,	PUNCT
ejpam-3442	189	3	there	there	PRON
ejpam-3442	189	4	exists	exist	VERB
ejpam-3442	189	5	oxe	oxe	PRON
ejpam-3442	189	6	∈	∈	PROPN
ejpam-3442	189	7	sos(x	sos(x	PROPN
ejpam-3442	189	8	)	)	PUNCT
ejpam-3442	189	9	such	such	ADJ
ejpam-3442	189	10	that	that	SCONJ
ejpam-3442	189	11	oxe∩̃((f	oxe∩̃((f	NOUN
ejpam-3442	189	12	,	,	PUNCT
ejpam-3442	189	13	e	e	NOUN
ejpam-3442	189	14	)	)	PUNCT
ejpam-3442	189	15	−	−	PROPN
ejpam-3442	190	1	(	(	PUNCT
ejpam-3442	190	2	i	i	NOUN
ejpam-3442	190	3	,	,	PUNCT
ejpam-3442	190	4	e	e	NOUN
ejpam-3442	190	5	)	)	PUNCT
ejpam-3442	190	6	)	)	PUNCT
ejpam-3442	191	1	∈	∈	PROPN
ejpam-3442	191	2	ĩ.	ĩ.	PROPN
ejpam-3442	191	3	since	since	SCONJ
ejpam-3442	191	4	(	(	PUNCT
ejpam-3442	191	5	i	i	PRON
ejpam-3442	191	6	,	,	PUNCT
ejpam-3442	191	7	e	e	NOUN
ejpam-3442	191	8	)	)	PUNCT
ejpam-3442	191	9	∈	∈	PROPN
ejpam-3442	191	10	ĩ.	ĩ.	PROPN
ejpam-3442	191	11	then	then	ADV
ejpam-3442	191	12	,	,	PUNCT
ejpam-3442	191	13	(	(	PUNCT
ejpam-3442	191	14	i	i	INTJ
ejpam-3442	191	15	,	,	PUNCT
ejpam-3442	191	16	e)∪̃(oxe∩̃((f	e)∪̃(oxe∩̃((f	PROPN
ejpam-3442	191	17	,	,	PUNCT
ejpam-3442	191	18	e)−(i	e)−(i	VERB
ejpam-3442	191	19	,	,	PUNCT
ejpam-3442	191	20	e	e	NOUN
ejpam-3442	191	21	)	)	PUNCT
ejpam-3442	191	22	)	)	PUNCT
ejpam-3442	191	23	)	)	PUNCT
ejpam-3442	192	1	∈	∈	PROPN
ejpam-3442	192	2	ĩ.	ĩ.	PROPN
ejpam-3442	192	3	hence	hence	ADV
ejpam-3442	192	4	,	,	PUNCT
ejpam-3442	192	5	(	(	PUNCT
ejpam-3442	192	6	i	i	PRON
ejpam-3442	192	7	,	,	PUNCT
ejpam-3442	192	8	e)∪̃(oxe∩̃(f	e)∪̃(oxe∩̃(f	PROPN
ejpam-3442	192	9	,	,	PUNCT
ejpam-3442	192	10	e	e	NOUN
ejpam-3442	192	11	)	)	PUNCT
ejpam-3442	192	12	)	)	PUNCT
ejpam-3442	193	1	∈	∈	PROPN
ejpam-3442	193	2	ĩ.	ĩ.	PROPN
ejpam-3442	193	3	thus	thus	ADV
ejpam-3442	193	4	,	,	PUNCT
ejpam-3442	193	5	oxe∩̃(f	oxe∩̃(f	ADV
ejpam-3442	193	6	,	,	PUNCT
ejpam-3442	193	7	e	e	NOUN
ejpam-3442	193	8	)	)	PUNCT
ejpam-3442	193	9	)	)	PUNCT
ejpam-3442	194	1	∈	∈	PROPN
ejpam-3442	194	2	ĩ	ĩ	PROPN
ejpam-3442	194	3	for	for	ADP
ejpam-3442	194	4	some	some	DET
ejpam-3442	194	5	oxe	oxe	NOUN
ejpam-3442	194	6	∈	∈	PROPN
ejpam-3442	194	7	sos(x	sos(x	PROPN
ejpam-3442	194	8	)	)	PUNCT
ejpam-3442	194	9	.	.	PUNCT
ejpam-3442	195	1	it	it	PRON
ejpam-3442	195	2	follows	follow	VERB
ejpam-3442	195	3	that	that	SCONJ
ejpam-3442	195	4	,	,	PUNCT
ejpam-3442	195	5	xe˜6∈(f	xe˜6∈(f	PROPN
ejpam-3442	195	6	,	,	PUNCT
ejpam-3442	195	7	e)∗s	e)∗s	PROPN
ejpam-3442	195	8	.	.	PUNCT
ejpam-3442	196	1	this	this	PRON
ejpam-3442	196	2	means	mean	VERB
ejpam-3442	196	3	that	that	SCONJ
ejpam-3442	196	4	,	,	PUNCT
ejpam-3442	196	5	(	(	PUNCT
ejpam-3442	196	6	f	f	X
ejpam-3442	196	7	,	,	PUNCT
ejpam-3442	196	8	e)∗s⊆̃((f	e)∗s⊆̃((f	NUM
ejpam-3442	196	9	,	,	PUNCT
ejpam-3442	196	10	e)−	e)−	PROPN
ejpam-3442	196	11	(	(	PUNCT
ejpam-3442	196	12	i	i	NOUN
ejpam-3442	196	13	,	,	PUNCT
ejpam-3442	196	14	e))∗s	e))∗s	NOUN
ejpam-3442	196	15	.	.	PUNCT
ejpam-3442	197	1	now	now	ADV
ejpam-3442	197	2	,	,	PUNCT
ejpam-3442	197	3	we	we	PRON
ejpam-3442	197	4	prove	prove	VERB
ejpam-3442	197	5	that	that	SCONJ
ejpam-3442	197	6	(	(	PUNCT
ejpam-3442	197	7	(	(	PUNCT
ejpam-3442	197	8	f	f	X
ejpam-3442	197	9	,	,	PUNCT
ejpam-3442	197	10	e)∪̃(i	e)∪̃(i	NOUN
ejpam-3442	197	11	,	,	PUNCT
ejpam-3442	197	12	e))∗s	e))∗s	NOUN
ejpam-3442	197	13	=	=	SYM
ejpam-3442	197	14	(	(	PUNCT
ejpam-3442	197	15	f	f	NOUN
ejpam-3442	197	16	,	,	PUNCT
ejpam-3442	197	17	e)∗s	e)∗s	PROPN
ejpam-3442	197	18	.	.	PUNCT
ejpam-3442	198	1	from	from	ADP
ejpam-3442	198	2	(	(	PUNCT
ejpam-3442	198	3	2	2	NUM
ejpam-3442	198	4	)	)	PUNCT
ejpam-3442	198	5	,	,	PUNCT
ejpam-3442	198	6	(	(	PUNCT
ejpam-3442	198	7	(	(	PUNCT
ejpam-3442	198	8	f	f	X
ejpam-3442	198	9	,	,	PUNCT
ejpam-3442	198	10	e)∪̃(i	e)∪̃(i	NOUN
ejpam-3442	198	11	,	,	PUNCT
ejpam-3442	198	12	e))∗s	e))∗s	NOUN
ejpam-3442	198	13	=	=	SYM
ejpam-3442	198	14	(	(	PUNCT
ejpam-3442	198	15	f	f	X
ejpam-3442	198	16	,	,	PUNCT
ejpam-3442	198	17	e)∗s∪̃(i	e)∗s∪̃(i	X
ejpam-3442	198	18	,	,	PUNCT
ejpam-3442	198	19	e)∗s	e)∗s	PROPN
ejpam-3442	198	20	=	=	SYM
ejpam-3442	198	21	(	(	PUNCT
ejpam-3442	198	22	f	f	X
ejpam-3442	198	23	,	,	PUNCT
ejpam-3442	198	24	e)∗s∪̃φ̃	e)∗s∪̃φ̃	PUNCT
ejpam-3442	198	25	=	=	SYM
ejpam-3442	198	26	(	(	PUNCT
ejpam-3442	198	27	f	f	X
ejpam-3442	198	28	,	,	PUNCT
ejpam-3442	198	29	e)∗s	e)∗s	PROPN
ejpam-3442	198	30	from	from	ADP
ejpam-3442	198	31	remark	remark	NOUN
ejpam-3442	198	32	3	3	NUM
ejpam-3442	198	33	(	(	PUNCT
ejpam-3442	198	34	1	1	NUM
ejpam-3442	198	35	)	)	PUNCT
ejpam-3442	198	36	.	.	PUNCT
ejpam-3442	199	1	this	this	PRON
ejpam-3442	199	2	completes	complete	VERB
ejpam-3442	199	3	the	the	DET
ejpam-3442	199	4	proof	proof	NOUN
ejpam-3442	199	5	.	.	PUNCT
ejpam-3442	200	1	corollary	corollary	ADJ
ejpam-3442	200	2	1	1	NUM
ejpam-3442	200	3	.	.	PUNCT
ejpam-3442	201	1	let	let	VERB
ejpam-3442	201	2	ĩ	ĩ	PROPN
ejpam-3442	201	3	be	be	AUX
ejpam-3442	201	4	a	a	DET
ejpam-3442	201	5	soft	soft	ADJ
ejpam-3442	201	6	ideal	ideal	NOUN
ejpam-3442	201	7	with	with	ADP
ejpam-3442	201	8	the	the	DET
ejpam-3442	201	9	same	same	ADJ
ejpam-3442	201	10	set	set	NOUN
ejpam-3442	201	11	of	of	ADP
ejpam-3442	201	12	parameters	parameter	NOUN
ejpam-3442	201	13	e	e	X
ejpam-3442	201	14	on	on	ADP
ejpam-3442	201	15	a	a	DET
ejpam-3442	201	16	soft	soft	ADJ
ejpam-3442	201	17	topological	topological	ADJ
ejpam-3442	201	18	space	space	NOUN
ejpam-3442	201	19	(	(	PUNCT
ejpam-3442	201	20	x	x	X
ejpam-3442	201	21	,	,	PUNCT
ejpam-3442	201	22	τ	τ	PROPN
ejpam-3442	201	23	,	,	PUNCT
ejpam-3442	201	24	e	e	NOUN
ejpam-3442	201	25	)	)	PUNCT
ejpam-3442	201	26	.	.	PUNCT
ejpam-3442	202	1	let	let	VERB
ejpam-3442	202	2	(	(	PUNCT
ejpam-3442	202	3	f	f	X
ejpam-3442	202	4	,	,	PUNCT
ejpam-3442	202	5	e	e	NOUN
ejpam-3442	202	6	)	)	PUNCT
ejpam-3442	202	7	,	,	PUNCT
ejpam-3442	202	8	(	(	PUNCT
ejpam-3442	202	9	g	g	NOUN
ejpam-3442	202	10	,	,	PUNCT
ejpam-3442	202	11	e	e	NOUN
ejpam-3442	202	12	)	)	PUNCT
ejpam-3442	202	13	∈	∈	PROPN
ejpam-3442	203	1	ss(x)e	ss(x)e	PROPN
ejpam-3442	203	2	.	.	PUNCT
ejpam-3442	204	1	then	then	ADV
ejpam-3442	204	2	,	,	PUNCT
ejpam-3442	204	3	(	(	PUNCT
ejpam-3442	204	4	1	1	X
ejpam-3442	204	5	)	)	PUNCT
ejpam-3442	204	6	(	(	PUNCT
ejpam-3442	204	7	f	f	X
ejpam-3442	204	8	,	,	PUNCT
ejpam-3442	204	9	e)∗s	e)∗s	PROPN
ejpam-3442	204	10	is	be	AUX
ejpam-3442	204	11	semi	semi	ADV
ejpam-3442	204	12	closed	closed	ADJ
ejpam-3442	204	13	soft	soft	ADJ
ejpam-3442	204	14	set	set	NOUN
ejpam-3442	204	15	.	.	PUNCT
ejpam-3442	205	1	(	(	PUNCT
ejpam-3442	205	2	2	2	NUM
ejpam-3442	205	3	)	)	PUNCT
ejpam-3442	205	4	(	(	PUNCT
ejpam-3442	205	5	(	(	PUNCT
ejpam-3442	205	6	f	f	X
ejpam-3442	205	7	,	,	PUNCT
ejpam-3442	205	8	e)∗s)∗s⊆̃(f	e)∗s)∗s⊆̃(f	PROPN
ejpam-3442	205	9	,	,	PUNCT
ejpam-3442	205	10	e)∗	e)∗	PROPN
ejpam-3442	205	11	,	,	PUNCT
ejpam-3442	205	12	(	(	PUNCT
ejpam-3442	205	13	3	3	X
ejpam-3442	205	14	)	)	PUNCT
ejpam-3442	205	15	(	(	PUNCT
ejpam-3442	205	16	(	(	PUNCT
ejpam-3442	205	17	f	f	X
ejpam-3442	205	18	,	,	PUNCT
ejpam-3442	205	19	e)∗s)∗⊆̃(f	e)∗s)∗⊆̃(f	PROPN
ejpam-3442	205	20	,	,	PUNCT
ejpam-3442	205	21	e)∗	e)∗	PROPN
ejpam-3442	205	22	,	,	PUNCT
ejpam-3442	205	23	(	(	PUNCT
ejpam-3442	205	24	4	4	NUM
ejpam-3442	205	25	)	)	PUNCT
ejpam-3442	205	26	(	(	PUNCT
ejpam-3442	205	27	(	(	PUNCT
ejpam-3442	205	28	f	f	X
ejpam-3442	205	29	,	,	PUNCT
ejpam-3442	205	30	e)∗)∗s⊆̃(f	e)∗)∗s⊆̃(f	PROPN
ejpam-3442	205	31	,	,	PUNCT
ejpam-3442	205	32	e)∗	e)∗	PROPN
ejpam-3442	205	33	,	,	PUNCT
ejpam-3442	205	34	f.	f.	PROPN
ejpam-3442	205	35	a.	a.	PROPN
ejpam-3442	205	36	gharib	gharib	PROPN
ejpam-3442	205	37	,	,	PUNCT
ejpam-3442	206	1	a.	a.	PROPN
ejpam-3442	206	2	m.	m.	PROPN
ejpam-3442	206	3	abd	abd	PROPN
ejpam-3442	206	4	el	el	PROPN
ejpam-3442	206	5	-	-	PROPN
ejpam-3442	206	6	latif	latif	PROPN
ejpam-3442	206	7	/	/	SYM
ejpam-3442	206	8	eur	eur	PROPN
ejpam-3442	206	9	.	.	PUNCT
ejpam-3442	207	1	j.	j.	PROPN
ejpam-3442	207	2	pure	pure	PROPN
ejpam-3442	207	3	appl	appl	PROPN
ejpam-3442	207	4	.	.	PROPN
ejpam-3442	207	5	math	math	PROPN
ejpam-3442	207	6	,	,	PUNCT
ejpam-3442	207	7	12	12	NUM
ejpam-3442	207	8	(	(	PUNCT
ejpam-3442	207	9	3	3	NUM
ejpam-3442	207	10	)	)	PUNCT
ejpam-3442	207	11	(	(	PUNCT
ejpam-3442	207	12	2019	2019	NUM
ejpam-3442	207	13	)	)	PUNCT
ejpam-3442	207	14	,	,	PUNCT
ejpam-3442	207	15	857	857	NUM
ejpam-3442	207	16	-	-	SYM
ejpam-3442	207	17	869	869	NUM
ejpam-3442	207	18	863	863	NUM
ejpam-3442	207	19	(	(	PUNCT
ejpam-3442	207	20	5	5	NUM
ejpam-3442	207	21	)	)	PUNCT
ejpam-3442	207	22	scl(f	scl(f	PROPN
ejpam-3442	207	23	,	,	PUNCT
ejpam-3442	207	24	e)∗s⊆̃cl(f	e)∗s⊆̃cl(f	PROPN
ejpam-3442	207	25	,	,	PUNCT
ejpam-3442	207	26	e	e	NOUN
ejpam-3442	207	27	)	)	PUNCT
ejpam-3442	207	28	,	,	PUNCT
ejpam-3442	207	29	(	(	PUNCT
ejpam-3442	207	30	6	6	NUM
ejpam-3442	207	31	)	)	PUNCT
ejpam-3442	207	32	(	(	PUNCT
ejpam-3442	207	33	f	f	X
ejpam-3442	207	34	,	,	PUNCT
ejpam-3442	207	35	e)∗s⊆̃(f	e)∗s⊆̃(f	PROPN
ejpam-3442	207	36	,	,	PUNCT
ejpam-3442	207	37	e)∗⊆̃cl(f	e)∗⊆̃cl(f	PROPN
ejpam-3442	207	38	,	,	PUNCT
ejpam-3442	207	39	e	e	NOUN
ejpam-3442	207	40	)	)	PUNCT
ejpam-3442	207	41	,	,	PUNCT
ejpam-3442	207	42	(	(	PUNCT
ejpam-3442	207	43	7	7	X
ejpam-3442	207	44	)	)	PUNCT
ejpam-3442	207	45	if	if	SCONJ
ejpam-3442	207	46	(	(	PUNCT
ejpam-3442	207	47	i	i	NOUN
ejpam-3442	207	48	,	,	PUNCT
ejpam-3442	207	49	e	e	NOUN
ejpam-3442	207	50	)	)	PUNCT
ejpam-3442	207	51	∈	∈	PROPN
ejpam-3442	207	52	ĩ	ĩ	PROPN
ejpam-3442	207	53	,	,	PUNCT
ejpam-3442	207	54	then	then	ADV
ejpam-3442	207	55	[	[	X
ejpam-3442	207	56	x̃	x̃	PROPN
ejpam-3442	207	57	−	−	PROPN
ejpam-3442	207	58	(	(	PUNCT
ejpam-3442	207	59	i	i	NOUN
ejpam-3442	207	60	,	,	PUNCT
ejpam-3442	207	61	e)]∗s	e)]∗s	PROPN
ejpam-3442	207	62	=	=	PUNCT
ejpam-3442	208	1	x̃∗s	x̃∗s	X
ejpam-3442	208	2	.	.	PUNCT
ejpam-3442	208	3	proof	proof	NOUN
ejpam-3442	208	4	.	.	PUNCT
ejpam-3442	209	1	it	it	PRON
ejpam-3442	209	2	is	be	AUX
ejpam-3442	209	3	follows	follow	VERB
ejpam-3442	209	4	from	from	ADP
ejpam-3442	209	5	theorem	theorem	ADJ
ejpam-3442	209	6	1	1	NUM
ejpam-3442	209	7	and	and	CCONJ
ejpam-3442	209	8	theorem	theorem	VERB
ejpam-3442	209	9	2	2	NUM
ejpam-3442	209	10	.	.	PUNCT
ejpam-3442	209	11	theorem	theorem	NOUN
ejpam-3442	209	12	3	3	X
ejpam-3442	209	13	.	.	PUNCT
ejpam-3442	210	1	let	let	VERB
ejpam-3442	210	2	ĩ	ĩ	PROPN
ejpam-3442	210	3	and	and	CCONJ
ejpam-3442	210	4	j̃	j̃	PROPN
ejpam-3442	210	5	be	be	VERB
ejpam-3442	210	6	two	two	NUM
ejpam-3442	210	7	soft	soft	ADJ
ejpam-3442	210	8	ideals	ideal	NOUN
ejpam-3442	210	9	with	with	ADP
ejpam-3442	210	10	the	the	DET
ejpam-3442	210	11	same	same	ADJ
ejpam-3442	210	12	set	set	NOUN
ejpam-3442	210	13	of	of	ADP
ejpam-3442	210	14	parameters	parameter	NOUN
ejpam-3442	210	15	e	e	X
ejpam-3442	210	16	on	on	ADP
ejpam-3442	210	17	a	a	DET
ejpam-3442	210	18	soft	soft	ADJ
ejpam-3442	210	19	topological	topological	ADJ
ejpam-3442	210	20	space	space	NOUN
ejpam-3442	210	21	(	(	PUNCT
ejpam-3442	210	22	x	x	X
ejpam-3442	210	23	,	,	PUNCT
ejpam-3442	210	24	τ	τ	PROPN
ejpam-3442	210	25	,	,	PUNCT
ejpam-3442	210	26	e	e	NOUN
ejpam-3442	210	27	)	)	PUNCT
ejpam-3442	210	28	and	and	CCONJ
ejpam-3442	211	1	(	(	PUNCT
ejpam-3442	211	2	f	f	X
ejpam-3442	211	3	,	,	PUNCT
ejpam-3442	211	4	e	e	NOUN
ejpam-3442	211	5	)	)	PUNCT
ejpam-3442	211	6	∈	∈	PROPN
ejpam-3442	211	7	ss(x)e	ss(x)e	PROPN
ejpam-3442	211	8	.	.	PUNCT
ejpam-3442	212	1	then	then	ADV
ejpam-3442	212	2	,	,	PUNCT
ejpam-3442	212	3	(	(	PUNCT
ejpam-3442	212	4	f	f	X
ejpam-3442	212	5	,	,	PUNCT
ejpam-3442	212	6	e)∗s(ĩ∩j̃	e)∗s(ĩ∩j̃	PROPN
ejpam-3442	212	7	)	)	PUNCT
ejpam-3442	212	8	=	=	PUNCT
ejpam-3442	212	9	(	(	PUNCT
ejpam-3442	212	10	f	f	X
ejpam-3442	212	11	,	,	PUNCT
ejpam-3442	212	12	e)∗(ĩ)∪̃(f	e)∗(ĩ)∪̃(f	PROPN
ejpam-3442	212	13	,	,	PUNCT
ejpam-3442	212	14	e)∗(j̃	e)∗(j̃	NOUN
ejpam-3442	212	15	)	)	PUNCT
ejpam-3442	212	16	.	.	PUNCT
ejpam-3442	213	1	proof	proof	NOUN
ejpam-3442	213	2	.	.	PUNCT
ejpam-3442	214	1	since	since	SCONJ
ejpam-3442	214	2	ĩ	ĩ	PROPN
ejpam-3442	214	3	∩	∩	NOUN
ejpam-3442	214	4	j̃	j̃	PROPN
ejpam-3442	214	5	⊆	⊆	NUM
ejpam-3442	214	6	ĩ	ĩ	PROPN
ejpam-3442	214	7	and	and	CCONJ
ejpam-3442	214	8	ĩ	ĩ	NOUN
ejpam-3442	214	9	∩	∩	NOUN
ejpam-3442	214	10	j̃	j̃	PROPN
ejpam-3442	214	11	⊆	⊆	NUM
ejpam-3442	214	12	j̃	j̃	PROPN
ejpam-3442	214	13	,	,	PUNCT
ejpam-3442	214	14	(	(	PUNCT
ejpam-3442	214	15	f	f	X
ejpam-3442	214	16	,	,	PUNCT
ejpam-3442	214	17	e)∗(ĩ	e)∗(ĩ	NOUN
ejpam-3442	214	18	)	)	PUNCT
ejpam-3442	214	19	,	,	PUNCT
ejpam-3442	214	20	(	(	PUNCT
ejpam-3442	214	21	f	f	X
ejpam-3442	214	22	,	,	PUNCT
ejpam-3442	214	23	e)∗(j̃)⊆̃(f	e)∗(j̃)⊆̃(f	PROPN
ejpam-3442	214	24	,	,	PUNCT
ejpam-3442	214	25	e)∗s(ĩ	e)∗s(ĩ	PROPN
ejpam-3442	214	26	∩	∩	NOUN
ejpam-3442	214	27	(	(	PUNCT
ejpam-3442	214	28	j̃	j̃	PROPN
ejpam-3442	214	29	)	)	PUNCT
ejpam-3442	214	30	)	)	PUNCT
ejpam-3442	214	31	from	from	ADP
ejpam-3442	214	32	theorem	theorem	ADJ
ejpam-3442	214	33	2	2	NUM
ejpam-3442	214	34	(	(	PUNCT
ejpam-3442	214	35	3	3	NUM
ejpam-3442	214	36	)	)	PUNCT
ejpam-3442	214	37	.	.	PUNCT
ejpam-3442	215	1	therefore	therefore	ADV
ejpam-3442	215	2	,	,	PUNCT
ejpam-3442	215	3	(	(	PUNCT
ejpam-3442	215	4	f	f	X
ejpam-3442	215	5	,	,	PUNCT
ejpam-3442	215	6	e)∗(ĩ)∪̃(f	e)∗(ĩ)∪̃(f	PROPN
ejpam-3442	215	7	,	,	PUNCT
ejpam-3442	215	8	e)∗(j̃)⊆̃(f	e)∗(j̃)⊆̃(f	PROPN
ejpam-3442	215	9	,	,	PUNCT
ejpam-3442	215	10	e)∗s(ĩ	e)∗s(ĩ	PROPN
ejpam-3442	215	11	∩	∩	ADJ
ejpam-3442	215	12	j̃	j̃	PROPN
ejpam-3442	215	13	)	)	PUNCT
ejpam-3442	215	14	.	.	PUNCT
ejpam-3442	216	1	for	for	ADP
ejpam-3442	216	2	the	the	DET
ejpam-3442	216	3	reverse	reverse	ADJ
ejpam-3442	216	4	inclusion	inclusion	NOUN
ejpam-3442	216	5	,	,	PUNCT
ejpam-3442	216	6	let	let	VERB
ejpam-3442	216	7	xe∈̃(f	xe∈̃(f	PRON
ejpam-3442	216	8	,	,	PUNCT
ejpam-3442	216	9	e)∗s(ĩ	e)∗s(ĩ	PROPN
ejpam-3442	216	10	∩	∩	ADJ
ejpam-3442	216	11	j̃	j̃	PROPN
ejpam-3442	216	12	)	)	PUNCT
ejpam-3442	216	13	.	.	PUNCT
ejpam-3442	217	1	then	then	ADV
ejpam-3442	217	2	,	,	PUNCT
ejpam-3442	217	3	oxe∩̃(f	oxe∩̃(f	ADV
ejpam-3442	217	4	,	,	PUNCT
ejpam-3442	217	5	e	e	NOUN
ejpam-3442	217	6	)	)	PUNCT
ejpam-3442	217	7	6∈	6∈	NOUN
ejpam-3442	217	8	(	(	PUNCT
ejpam-3442	217	9	ĩ	ĩ	PROPN
ejpam-3442	217	10	∩	∩	ADJ
ejpam-3442	217	11	j̃	j̃	NOUN
ejpam-3442	217	12	)	)	PUNCT
ejpam-3442	217	13	∀	∀	PUNCT
ejpam-3442	217	14	oxe	oxe	PRON
ejpam-3442	217	15	∈	∈	PROPN
ejpam-3442	217	16	sos(x	sos(x	PROPN
ejpam-3442	217	17	)	)	PUNCT
ejpam-3442	217	18	and	and	CCONJ
ejpam-3442	217	19	so	so	ADV
ejpam-3442	217	20	oxe∩̃(f	oxe∩̃(f	ADV
ejpam-3442	217	21	,	,	PUNCT
ejpam-3442	217	22	e	e	NOUN
ejpam-3442	217	23	)	)	PUNCT
ejpam-3442	217	24	6∈	6∈	NOUN
ejpam-3442	217	25	ĩ	ĩ	PROPN
ejpam-3442	217	26	or	or	CCONJ
ejpam-3442	217	27	oxe∩̃(f	oxe∩̃(f	NUM
ejpam-3442	217	28	,	,	PUNCT
ejpam-3442	217	29	e	e	NOUN
ejpam-3442	217	30	)	)	PUNCT
ejpam-3442	217	31	6∈	6∈	NOUN
ejpam-3442	218	1	j̃	j̃	PROPN
ejpam-3442	218	2	.	.	PUNCT
ejpam-3442	219	1	it	it	PRON
ejpam-3442	219	2	follows	follow	VERB
ejpam-3442	219	3	,	,	PUNCT
ejpam-3442	219	4	xe∈̃(f	xe∈̃(f	PROPN
ejpam-3442	219	5	,	,	PUNCT
ejpam-3442	219	6	e)∗s(ĩ	e)∗s(ĩ	NOUN
ejpam-3442	219	7	)	)	PUNCT
ejpam-3442	219	8	or	or	CCONJ
ejpam-3442	219	9	xe∈̃(f	xe∈̃(f	PROPN
ejpam-3442	219	10	,	,	PUNCT
ejpam-3442	219	11	e)∗s(j̃	e)∗s(j̃	NUM
ejpam-3442	219	12	)	)	PUNCT
ejpam-3442	219	13	and	and	CCONJ
ejpam-3442	219	14	consequently	consequently	ADV
ejpam-3442	219	15	xe∈̃(f	xe∈̃(f	PROPN
ejpam-3442	219	16	,	,	PUNCT
ejpam-3442	219	17	e)∗s(ĩ)∪̃(f	e)∗s(ĩ)∪̃(f	PRON
ejpam-3442	219	18	,	,	PUNCT
ejpam-3442	219	19	e)∗s(j̃	e)∗s(j̃	NOUN
ejpam-3442	219	20	)	)	PUNCT
ejpam-3442	219	21	.	.	PUNCT
ejpam-3442	220	1	thus	thus	ADV
ejpam-3442	220	2	,	,	PUNCT
ejpam-3442	220	3	(	(	PUNCT
ejpam-3442	220	4	f	f	X
ejpam-3442	220	5	,	,	PUNCT
ejpam-3442	220	6	e)∗s(ĩ	e)∗s(ĩ	PROPN
ejpam-3442	220	7	∩	∩	PROPN
ejpam-3442	220	8	j̃)⊆̃(f	j̃)⊆̃(f	PROPN
ejpam-3442	220	9	,	,	PUNCT
ejpam-3442	220	10	e)∗(ĩ)∪̃(f	e)∗(ĩ)∪̃(f	NUM
ejpam-3442	220	11	,	,	PUNCT
ejpam-3442	220	12	e)∗(j̃	e)∗(j̃	NOUN
ejpam-3442	220	13	)	)	PUNCT
ejpam-3442	220	14	.	.	PUNCT
ejpam-3442	221	1	this	this	PRON
ejpam-3442	221	2	completes	complete	VERB
ejpam-3442	221	3	the	the	DET
ejpam-3442	221	4	proof	proof	NOUN
ejpam-3442	221	5	.	.	PUNCT
ejpam-3442	222	1	theorem	theorem	ADJ
ejpam-3442	222	2	4	4	NUM
ejpam-3442	222	3	.	.	PUNCT
ejpam-3442	223	1	let	let	AUX
ejpam-3442	223	2	(	(	PUNCT
ejpam-3442	223	3	x	x	X
ejpam-3442	223	4	,	,	PUNCT
ejpam-3442	223	5	τ	τ	PROPN
ejpam-3442	223	6	,	,	PUNCT
ejpam-3442	223	7	e	e	NOUN
ejpam-3442	223	8	)	)	PUNCT
ejpam-3442	223	9	be	be	AUX
ejpam-3442	223	10	a	a	DET
ejpam-3442	223	11	soft	soft	ADJ
ejpam-3442	223	12	topological	topological	ADJ
ejpam-3442	223	13	space	space	NOUN
ejpam-3442	223	14	and	and	CCONJ
ejpam-3442	223	15	ĩ	ĩ	PROPN
ejpam-3442	223	16	be	be	VERB
ejpam-3442	223	17	a	a	DET
ejpam-3442	223	18	soft	soft	ADJ
ejpam-3442	223	19	ideal	ideal	NOUN
ejpam-3442	223	20	over	over	ADP
ejpam-3442	223	21	x	x	PUNCT
ejpam-3442	223	22	with	with	ADP
ejpam-3442	223	23	the	the	DET
ejpam-3442	223	24	same	same	ADJ
ejpam-3442	223	25	set	set	NOUN
ejpam-3442	223	26	of	of	ADP
ejpam-3442	223	27	parameters	parameter	NOUN
ejpam-3442	224	1	e.	e.	PROPN
ejpam-3442	224	2	then	then	ADV
ejpam-3442	224	3	the	the	DET
ejpam-3442	224	4	operator	operator	NOUN
ejpam-3442	224	5	cl∗s	cl∗	NOUN
ejpam-3442	224	6	:	:	PUNCT
ejpam-3442	224	7	ss(x)e	ss(x)e	PROPN
ejpam-3442	224	8	→	→	PUNCT
ejpam-3442	224	9	ss(x)e	ss(x)e	NOUN
ejpam-3442	224	10	defined	define	VERB
ejpam-3442	224	11	by	by	ADP
ejpam-3442	224	12	:	:	PUNCT
ejpam-3442	224	13	cl∗s(f	cl∗s(f	PROPN
ejpam-3442	224	14	,	,	PUNCT
ejpam-3442	224	15	e	e	NOUN
ejpam-3442	224	16	)	)	PUNCT
ejpam-3442	224	17	=	=	SYM
ejpam-3442	224	18	(	(	PUNCT
ejpam-3442	224	19	f	f	X
ejpam-3442	224	20	,	,	PUNCT
ejpam-3442	224	21	e)∪̃(f	e)∪̃(f	PROPN
ejpam-3442	224	22	,	,	PUNCT
ejpam-3442	224	23	e)∗s	e)∗s	PROPN
ejpam-3442	224	24	.	.	PUNCT
ejpam-3442	225	1	(	(	PUNCT
ejpam-3442	225	2	1	1	X
ejpam-3442	225	3	)	)	PUNCT
ejpam-3442	225	4	is	be	AUX
ejpam-3442	225	5	a	a	DET
ejpam-3442	225	6	soft	soft	ADJ
ejpam-3442	225	7	closure	closure	NOUN
ejpam-3442	225	8	operator	operator	NOUN
ejpam-3442	225	9	.	.	PUNCT
ejpam-3442	226	1	proof	proof	NOUN
ejpam-3442	226	2	.	.	PUNCT
ejpam-3442	227	1	cl∗s(φ̃	cl∗s(φ̃	NOUN
ejpam-3442	227	2	)	)	PUNCT
ejpam-3442	227	3	=	=	SYM
ejpam-3442	228	1	φ̃∪̃(φ̃)∗s	φ̃∪̃(φ̃)∗s	ADJ
ejpam-3442	228	2	=	=	PUNCT
ejpam-3442	228	3	φ̃∪̃φ̃	φ̃∪̃φ̃	NOUN
ejpam-3442	228	4	=	=	PUNCT
ejpam-3442	228	5	φ̃	φ̃	PROPN
ejpam-3442	228	6	from	from	ADP
ejpam-3442	228	7	theorem	theorem	ADJ
ejpam-3442	228	8	1	1	NUM
ejpam-3442	228	9	(	(	PUNCT
ejpam-3442	228	10	1	1	NUM
ejpam-3442	228	11	)	)	PUNCT
ejpam-3442	228	12	,	,	PUNCT
ejpam-3442	228	13	and	and	CCONJ
ejpam-3442	228	14	obviously	obviously	ADV
ejpam-3442	228	15	(	(	PUNCT
ejpam-3442	228	16	f	f	X
ejpam-3442	228	17	,	,	PUNCT
ejpam-3442	228	18	e)⊆̃cl∗s(f	e)⊆̃cl∗s(f	PROPN
ejpam-3442	228	19	,	,	PUNCT
ejpam-3442	228	20	e	e	NOUN
ejpam-3442	228	21	)	)	PUNCT
ejpam-3442	228	22	∀(f	∀(f	PROPN
ejpam-3442	228	23	,	,	PUNCT
ejpam-3442	228	24	e	e	NOUN
ejpam-3442	228	25	)	)	PUNCT
ejpam-3442	228	26	∈	∈	PROPN
ejpam-3442	228	27	ss(x)e	ss(x)e	PROPN
ejpam-3442	228	28	.	.	PUNCT
ejpam-3442	229	1	now	now	ADV
ejpam-3442	229	2	,	,	PUNCT
ejpam-3442	229	3	cl∗s((f	cl∗s((f	VERB
ejpam-3442	229	4	,	,	PUNCT
ejpam-3442	229	5	e)∪̃(g	e)∪̃(g	NOUN
ejpam-3442	229	6	,	,	PUNCT
ejpam-3442	229	7	e	e	NOUN
ejpam-3442	229	8	)	)	PUNCT
ejpam-3442	229	9	)	)	PUNCT
ejpam-3442	230	1	=	=	SYM
ejpam-3442	230	2	(	(	PUNCT
ejpam-3442	230	3	(	(	PUNCT
ejpam-3442	230	4	f	f	X
ejpam-3442	230	5	,	,	PUNCT
ejpam-3442	230	6	e)∪̃(g	e)∪̃(g	NOUN
ejpam-3442	230	7	,	,	PUNCT
ejpam-3442	230	8	e))∪̃((f	e))∪̃((f	X
ejpam-3442	230	9	,	,	PUNCT
ejpam-3442	230	10	e)∪̃(g	e)∪̃(g	NOUN
ejpam-3442	230	11	,	,	PUNCT
ejpam-3442	230	12	e))∗s	e))∗s	NOUN
ejpam-3442	230	13	=	=	SYM
ejpam-3442	230	14	(	(	PUNCT
ejpam-3442	230	15	(	(	PUNCT
ejpam-3442	230	16	f	f	X
ejpam-3442	230	17	,	,	PUNCT
ejpam-3442	230	18	e)∪̃(g	e)∪̃(g	NOUN
ejpam-3442	230	19	,	,	PUNCT
ejpam-3442	230	20	e))∪̃((f	e))∪̃((f	X
ejpam-3442	230	21	,	,	PUNCT
ejpam-3442	230	22	e)∗s∪̃(g	e)∗s∪̃(g	X
ejpam-3442	230	23	,	,	PUNCT
ejpam-3442	230	24	e)∗s	e)∗s	NOUN
ejpam-3442	230	25	)	)	PUNCT
ejpam-3442	230	26	=	=	SYM
ejpam-3442	230	27	(	(	PUNCT
ejpam-3442	230	28	(	(	PUNCT
ejpam-3442	230	29	f	f	X
ejpam-3442	230	30	,	,	PUNCT
ejpam-3442	230	31	e)∪̃(f	e)∪̃(f	PROPN
ejpam-3442	230	32	,	,	PUNCT
ejpam-3442	230	33	e)∗s)∪̃((g	e)∗s)∪̃((g	PROPN
ejpam-3442	230	34	,	,	PUNCT
ejpam-3442	230	35	e)∪̃(g	e)∪̃(g	NOUN
ejpam-3442	230	36	,	,	PUNCT
ejpam-3442	230	37	e)∗s	e)∗s	NUM
ejpam-3442	230	38	)	)	PUNCT
ejpam-3442	230	39	=	=	SYM
ejpam-3442	230	40	cl∗s(f	cl∗s(f	NOUN
ejpam-3442	230	41	,	,	PUNCT
ejpam-3442	230	42	e)∪̃cl∗s	e)∪̃cl∗s	X
ejpam-3442	230	43	(	(	PUNCT
ejpam-3442	230	44	g	g	NOUN
ejpam-3442	230	45	,	,	PUNCT
ejpam-3442	230	46	e	e	NOUN
ejpam-3442	230	47	)	)	PUNCT
ejpam-3442	230	48	from	from	ADP
ejpam-3442	230	49	theorem	theorem	ADJ
ejpam-3442	230	50	2	2	NUM
ejpam-3442	230	51	(	(	PUNCT
ejpam-3442	230	52	6	6	NUM
ejpam-3442	230	53	)	)	PUNCT
ejpam-3442	230	54	.	.	PUNCT
ejpam-3442	231	1	also	also	ADV
ejpam-3442	231	2	,	,	PUNCT
ejpam-3442	231	3	for	for	ADP
ejpam-3442	231	4	any	any	DET
ejpam-3442	231	5	(	(	PUNCT
ejpam-3442	231	6	f	f	X
ejpam-3442	231	7	,	,	PUNCT
ejpam-3442	231	8	e	e	NOUN
ejpam-3442	231	9	)	)	PUNCT
ejpam-3442	231	10	∈	∈	PROPN
ejpam-3442	231	11	ss(x)e	ss(x)e	PROPN
ejpam-3442	231	12	,	,	PUNCT
ejpam-3442	231	13	cl∗s(cl∗s(f	cl∗s(cl∗s(f	NOUN
ejpam-3442	231	14	,	,	PUNCT
ejpam-3442	231	15	e	e	NOUN
ejpam-3442	231	16	)	)	PUNCT
ejpam-3442	231	17	)	)	PUNCT
ejpam-3442	231	18	=	=	SYM
ejpam-3442	231	19	cl∗s((f	cl∗s((f	VERB
ejpam-3442	231	20	,	,	PUNCT
ejpam-3442	231	21	e)∪̃(f	e)∪̃(f	PROPN
ejpam-3442	231	22	,	,	PUNCT
ejpam-3442	231	23	e)∗s	e)∗s	PROPN
ejpam-3442	231	24	)	)	PUNCT
ejpam-3442	231	25	=	=	SYM
ejpam-3442	231	26	(	(	PUNCT
ejpam-3442	231	27	(	(	PUNCT
ejpam-3442	231	28	f	f	X
ejpam-3442	231	29	,	,	PUNCT
ejpam-3442	231	30	e)∪̃(f	e)∪̃(f	PROPN
ejpam-3442	231	31	,	,	PUNCT
ejpam-3442	231	32	e)∗s)∪̃((f	e)∗s)∪̃((f	ADJ
ejpam-3442	231	33	,	,	PUNCT
ejpam-3442	231	34	e)∪̃(f	e)∪̃(f	PROPN
ejpam-3442	231	35	,	,	PUNCT
ejpam-3442	231	36	e)∗s)∗s	e)∗s)∗s	PROPN
ejpam-3442	231	37	=	=	SYM
ejpam-3442	231	38	(	(	PUNCT
ejpam-3442	231	39	(	(	PUNCT
ejpam-3442	231	40	f	f	X
ejpam-3442	231	41	,	,	PUNCT
ejpam-3442	231	42	e)∪̃(f	e)∪̃(f	PROPN
ejpam-3442	231	43	,	,	PUNCT
ejpam-3442	231	44	e)∗s)∪̃((f	e)∗s)∪̃((f	ADJ
ejpam-3442	231	45	,	,	PUNCT
ejpam-3442	231	46	e)∗s∪̃((f	e)∗s∪̃((f	PROPN
ejpam-3442	231	47	,	,	PUNCT
ejpam-3442	231	48	e)∗s)∗s)⊆̃((f	e)∗s)∗s)⊆̃((f	NOUN
ejpam-3442	231	49	,	,	PUNCT
ejpam-3442	231	50	e)∪̃	e)∪̃	PROPN
ejpam-3442	231	51	(	(	PUNCT
ejpam-3442	231	52	f	f	PROPN
ejpam-3442	231	53	,	,	PUNCT
ejpam-3442	231	54	e)∗s))∪̃((f	e)∗s))∪̃((f	NOUN
ejpam-3442	231	55	,	,	PUNCT
ejpam-3442	231	56	e)∗s∪̃((f	e)∗s∪̃((f	PROPN
ejpam-3442	231	57	,	,	PUNCT
ejpam-3442	231	58	e)∗s	e)∗s	NUM
ejpam-3442	231	59	)	)	PUNCT
ejpam-3442	231	60	)	)	PUNCT
ejpam-3442	232	1	=	=	SYM
ejpam-3442	232	2	cl∗s(f	cl∗s(f	PROPN
ejpam-3442	232	3	,	,	PUNCT
ejpam-3442	232	4	e	e	NOUN
ejpam-3442	232	5	)	)	PUNCT
ejpam-3442	232	6	from	from	ADP
ejpam-3442	232	7	theorem	theorem	ADJ
ejpam-3442	232	8	2	2	NUM
ejpam-3442	232	9	(	(	PUNCT
ejpam-3442	232	10	5	5	NUM
ejpam-3442	232	11	)	)	PUNCT
ejpam-3442	232	12	.	.	PUNCT
ejpam-3442	233	1	definition	definition	NOUN
ejpam-3442	233	2	13	13	NUM
ejpam-3442	233	3	.	.	PUNCT
ejpam-3442	234	1	let	let	VERB
ejpam-3442	234	2	(	(	PUNCT
ejpam-3442	234	3	x	x	X
ejpam-3442	234	4	,	,	PUNCT
ejpam-3442	234	5	τ	τ	PROPN
ejpam-3442	234	6	,	,	PUNCT
ejpam-3442	234	7	e	e	NOUN
ejpam-3442	234	8	)	)	PUNCT
ejpam-3442	234	9	be	be	AUX
ejpam-3442	234	10	a	a	DET
ejpam-3442	234	11	soft	soft	ADJ
ejpam-3442	234	12	topological	topological	ADJ
ejpam-3442	234	13	space	space	NOUN
ejpam-3442	234	14	,	,	PUNCT
ejpam-3442	234	15	ĩ	ĩ	PROPN
ejpam-3442	234	16	be	be	VERB
ejpam-3442	234	17	a	a	DET
ejpam-3442	234	18	soft	soft	ADJ
ejpam-3442	234	19	ideal	ideal	NOUN
ejpam-3442	234	20	over	over	ADP
ejpam-3442	234	21	x	x	PUNCT
ejpam-3442	234	22	with	with	ADP
ejpam-3442	234	23	the	the	DET
ejpam-3442	234	24	same	same	ADJ
ejpam-3442	234	25	set	set	NOUN
ejpam-3442	234	26	of	of	ADP
ejpam-3442	234	27	parameters	parameter	NOUN
ejpam-3442	234	28	e	e	NOUN
ejpam-3442	234	29	and	and	CCONJ
ejpam-3442	234	30	cl∗s	cl∗	NOUN
ejpam-3442	234	31	:	:	PUNCT
ejpam-3442	234	32	ss(x)e	ss(x)e	PROPN
ejpam-3442	234	33	→	→	PUNCT
ejpam-3442	234	34	ss(x)e	ss(x)e	NOUN
ejpam-3442	234	35	be	be	AUX
ejpam-3442	234	36	the	the	DET
ejpam-3442	234	37	soft	soft	ADJ
ejpam-3442	234	38	closure	closure	NOUN
ejpam-3442	234	39	operator	operator	NOUN
ejpam-3442	234	40	.	.	PUNCT
ejpam-3442	235	1	then	then	ADV
ejpam-3442	235	2	there	there	PRON
ejpam-3442	235	3	exists	exist	VERB
ejpam-3442	235	4	a	a	DET
ejpam-3442	235	5	unique	unique	ADJ
ejpam-3442	235	6	soft	soft	ADJ
ejpam-3442	235	7	topology	topology	NOUN
ejpam-3442	235	8	over	over	ADP
ejpam-3442	235	9	x	x	PUNCT
ejpam-3442	235	10	with	with	ADP
ejpam-3442	235	11	the	the	DET
ejpam-3442	235	12	same	same	ADJ
ejpam-3442	235	13	set	set	NOUN
ejpam-3442	235	14	of	of	ADP
ejpam-3442	235	15	parameters	parameter	NOUN
ejpam-3442	235	16	e	e	NOUN
ejpam-3442	235	17	,	,	PUNCT
ejpam-3442	235	18	finer	fine	ADJ
ejpam-3442	235	19	than	than	ADP
ejpam-3442	235	20	τ	τ	PROPN
ejpam-3442	235	21	,	,	PUNCT
ejpam-3442	235	22	called	call	VERB
ejpam-3442	235	23	the	the	DET
ejpam-3442	235	24	∗-soft	∗-soft	ADJ
ejpam-3442	235	25	topology	topology	NOUN
ejpam-3442	235	26	,	,	PUNCT
ejpam-3442	235	27	denoted	denote	VERB
ejpam-3442	235	28	by	by	ADP
ejpam-3442	235	29	τ∗s(ĩ	τ∗s(ĩ	NOUN
ejpam-3442	235	30	)	)	PUNCT
ejpam-3442	235	31	or	or	CCONJ
ejpam-3442	235	32	τ∗s	τ∗s	NUM
ejpam-3442	235	33	,	,	PUNCT
ejpam-3442	235	34	given	give	VERB
ejpam-3442	235	35	by	by	ADP
ejpam-3442	235	36	τ∗s(ĩ	τ∗s(ĩ	NOUN
ejpam-3442	235	37	)	)	PUNCT
ejpam-3442	235	38	=	=	PRON
ejpam-3442	235	39	{	{	PUNCT
ejpam-3442	235	40	(	(	PUNCT
ejpam-3442	235	41	f	f	X
ejpam-3442	235	42	,	,	PUNCT
ejpam-3442	235	43	e	e	NOUN
ejpam-3442	235	44	)	)	PUNCT
ejpam-3442	235	45	∈	∈	PROPN
ejpam-3442	235	46	ss(x)e	ss(x)e	NOUN
ejpam-3442	235	47	:	:	PUNCT
ejpam-3442	235	48	cl∗s(f	cl∗s(f	NOUN
ejpam-3442	235	49	,	,	PUNCT
ejpam-3442	235	50	e)′	e)′	NOUN
ejpam-3442	235	51	=	=	PRON
ejpam-3442	235	52	(	(	PUNCT
ejpam-3442	235	53	f	f	X
ejpam-3442	235	54	,	,	PUNCT
ejpam-3442	235	55	e)′	e)′	PROPN
ejpam-3442	235	56	}	}	PUNCT
ejpam-3442	235	57	.	.	PUNCT
ejpam-3442	236	1	(	(	PUNCT
ejpam-3442	236	2	2	2	X
ejpam-3442	236	3	)	)	PUNCT
ejpam-3442	236	4	example	example	NOUN
ejpam-3442	236	5	3	3	NUM
ejpam-3442	236	6	.	.	PUNCT
ejpam-3442	237	1	(	(	PUNCT
ejpam-3442	237	2	1	1	X
ejpam-3442	237	3	)	)	PUNCT
ejpam-3442	237	4	if	if	SCONJ
ejpam-3442	237	5	ĩ	ĩ	PROPN
ejpam-3442	237	6	=	=	SYM
ejpam-3442	237	7	{	{	PUNCT
ejpam-3442	237	8	φ̃	φ̃	PROPN
ejpam-3442	237	9	}	}	PUNCT
ejpam-3442	237	10	,	,	PUNCT
ejpam-3442	237	11	then	then	ADV
ejpam-3442	237	12	(	(	PUNCT
ejpam-3442	237	13	f	f	X
ejpam-3442	237	14	,	,	PUNCT
ejpam-3442	237	15	e)∗s(ĩ	e)∗s(ĩ	PROPN
ejpam-3442	237	16	,	,	PUNCT
ejpam-3442	237	17	τ	τ	X
ejpam-3442	237	18	)	)	PUNCT
ejpam-3442	237	19	=	=	SYM
ejpam-3442	237	20	scl(f	scl(f	PROPN
ejpam-3442	237	21	,	,	PUNCT
ejpam-3442	237	22	e	e	NOUN
ejpam-3442	237	23	)	)	PUNCT
ejpam-3442	237	24	∀(f	∀(f	PROPN
ejpam-3442	237	25	,	,	PUNCT
ejpam-3442	237	26	e	e	NOUN
ejpam-3442	237	27	)	)	PUNCT
ejpam-3442	237	28	∈	∈	PROPN
ejpam-3442	238	1	ss(x)e	ss(x)e	NOUN
ejpam-3442	238	2	.	.	PUNCT
ejpam-3442	239	1	hence	hence	ADV
ejpam-3442	239	2	,	,	PUNCT
ejpam-3442	239	3	cl∗s(f	cl∗s(f	PROPN
ejpam-3442	239	4	,	,	PUNCT
ejpam-3442	239	5	e	e	NOUN
ejpam-3442	239	6	)	)	PUNCT
ejpam-3442	239	7	=	=	SYM
ejpam-3442	239	8	scl(f	scl(f	PROPN
ejpam-3442	239	9	,	,	PUNCT
ejpam-3442	239	10	e	e	NOUN
ejpam-3442	239	11	)	)	PUNCT
ejpam-3442	239	12	.	.	PUNCT
ejpam-3442	240	1	(	(	PUNCT
ejpam-3442	240	2	2	2	X
ejpam-3442	240	3	)	)	PUNCT
ejpam-3442	240	4	if	if	SCONJ
ejpam-3442	240	5	ĩ	ĩ	PROPN
ejpam-3442	240	6	=	=	SYM
ejpam-3442	240	7	ss(x)e	ss(x)e	NOUN
ejpam-3442	240	8	,	,	PUNCT
ejpam-3442	240	9	then	then	ADV
ejpam-3442	240	10	(	(	PUNCT
ejpam-3442	240	11	f	f	X
ejpam-3442	240	12	,	,	PUNCT
ejpam-3442	240	13	e)∗s(ĩ	e)∗s(ĩ	PROPN
ejpam-3442	240	14	,	,	PUNCT
ejpam-3442	240	15	τ	τ	X
ejpam-3442	240	16	)	)	PUNCT
ejpam-3442	240	17	=	=	PUNCT
ejpam-3442	240	18	φ̃	φ̃	PROPN
ejpam-3442	240	19	∀(f	∀(f	PROPN
ejpam-3442	240	20	,	,	PUNCT
ejpam-3442	240	21	e	e	NOUN
ejpam-3442	240	22	)	)	PUNCT
ejpam-3442	240	23	∈	∈	PROPN
ejpam-3442	240	24	ss(x)e	ss(x)e	NOUN
ejpam-3442	240	25	.	.	PUNCT
ejpam-3442	241	1	hence	hence	ADV
ejpam-3442	241	2	,	,	PUNCT
ejpam-3442	241	3	cl∗s(f	cl∗s(f	PROPN
ejpam-3442	241	4	,	,	PUNCT
ejpam-3442	241	5	e	e	NOUN
ejpam-3442	241	6	)	)	PUNCT
ejpam-3442	241	7	=	=	SYM
ejpam-3442	241	8	(	(	PUNCT
ejpam-3442	241	9	f	f	X
ejpam-3442	241	10	,	,	PUNCT
ejpam-3442	241	11	e	e	NOUN
ejpam-3442	241	12	)	)	PUNCT
ejpam-3442	241	13	and	and	CCONJ
ejpam-3442	241	14	τ∗s	τ∗s	PUNCT
ejpam-3442	241	15	=	=	SYM
ejpam-3442	241	16	ss(x)e	ss(x)e	PROPN
ejpam-3442	241	17	(	(	PUNCT
ejpam-3442	241	18	the	the	DET
ejpam-3442	241	19	soft	soft	ADJ
ejpam-3442	241	20	discrete	discrete	ADJ
ejpam-3442	241	21	topology	topology	NOUN
ejpam-3442	241	22	)	)	PUNCT
ejpam-3442	241	23	.	.	PUNCT
ejpam-3442	242	1	theorem	theorem	NOUN
ejpam-3442	242	2	5	5	NUM
ejpam-3442	242	3	.	.	PUNCT
ejpam-3442	243	1	let	let	VERB
ejpam-3442	243	2	ĩ	ĩ	PROPN
ejpam-3442	243	3	and	and	CCONJ
ejpam-3442	243	4	j̃	j̃	PROPN
ejpam-3442	243	5	be	be	VERB
ejpam-3442	243	6	any	any	DET
ejpam-3442	243	7	two	two	NUM
ejpam-3442	243	8	soft	soft	ADJ
ejpam-3442	243	9	ideals	ideal	NOUN
ejpam-3442	243	10	with	with	ADP
ejpam-3442	243	11	the	the	DET
ejpam-3442	243	12	same	same	ADJ
ejpam-3442	243	13	set	set	NOUN
ejpam-3442	243	14	of	of	ADP
ejpam-3442	243	15	parameters	parameter	NOUN
ejpam-3442	243	16	e	e	X
ejpam-3442	243	17	on	on	ADP
ejpam-3442	243	18	a	a	DET
ejpam-3442	243	19	soft	soft	ADJ
ejpam-3442	243	20	topological	topological	ADJ
ejpam-3442	243	21	space	space	NOUN
ejpam-3442	243	22	(	(	PUNCT
ejpam-3442	243	23	x	x	X
ejpam-3442	243	24	,	,	PUNCT
ejpam-3442	243	25	τ	τ	PROPN
ejpam-3442	243	26	,	,	PUNCT
ejpam-3442	243	27	e	e	NOUN
ejpam-3442	243	28	)	)	PUNCT
ejpam-3442	243	29	.	.	PUNCT
ejpam-3442	244	1	if	if	SCONJ
ejpam-3442	244	2	ĩ	ĩ	PROPN
ejpam-3442	244	3	⊆	⊆	NUM
ejpam-3442	244	4	j̃	j̃	PROPN
ejpam-3442	244	5	,	,	PUNCT
ejpam-3442	244	6	then	then	ADV
ejpam-3442	244	7	τ∗s(ĩ	τ∗s(ĩ	NOUN
ejpam-3442	244	8	)	)	PUNCT
ejpam-3442	244	9	⊆	⊆	NUM
ejpam-3442	244	10	τ∗s(j̃	τ∗s(j̃	NOUN
ejpam-3442	244	11	)	)	PUNCT
ejpam-3442	244	12	.	.	PUNCT
ejpam-3442	245	1	f.	f.	PROPN
ejpam-3442	245	2	a.	a.	PROPN
ejpam-3442	245	3	gharib	gharib	PROPN
ejpam-3442	245	4	,	,	PUNCT
ejpam-3442	245	5	a.	a.	PROPN
ejpam-3442	245	6	m.	m.	PROPN
ejpam-3442	245	7	abd	abd	PROPN
ejpam-3442	245	8	el	el	PROPN
ejpam-3442	245	9	-	-	PROPN
ejpam-3442	245	10	latif	latif	PROPN
ejpam-3442	245	11	/	/	SYM
ejpam-3442	245	12	eur	eur	PROPN
ejpam-3442	245	13	.	.	PUNCT
ejpam-3442	246	1	j.	j.	PROPN
ejpam-3442	246	2	pure	pure	PROPN
ejpam-3442	246	3	appl	appl	PROPN
ejpam-3442	246	4	.	.	PROPN
ejpam-3442	246	5	math	math	PROPN
ejpam-3442	246	6	,	,	PUNCT
ejpam-3442	246	7	12	12	NUM
ejpam-3442	246	8	(	(	PUNCT
ejpam-3442	246	9	3	3	NUM
ejpam-3442	246	10	)	)	PUNCT
ejpam-3442	246	11	(	(	PUNCT
ejpam-3442	246	12	2019	2019	NUM
ejpam-3442	246	13	)	)	PUNCT
ejpam-3442	246	14	,	,	PUNCT
ejpam-3442	246	15	857	857	NUM
ejpam-3442	246	16	-	-	SYM
ejpam-3442	246	17	869	869	NUM
ejpam-3442	246	18	864	864	NUM
ejpam-3442	246	19	proof	proof	NOUN
ejpam-3442	246	20	.	.	PUNCT
ejpam-3442	247	1	let	let	VERB
ejpam-3442	247	2	(	(	PUNCT
ejpam-3442	247	3	f	f	X
ejpam-3442	247	4	,	,	PUNCT
ejpam-3442	247	5	e	e	NOUN
ejpam-3442	247	6	)	)	PUNCT
ejpam-3442	247	7	be	be	AUX
ejpam-3442	247	8	a	a	DET
ejpam-3442	247	9	τ∗s(ĩ)-closed	τ∗s(ĩ)-close	VERB
ejpam-3442	247	10	soft	soft	ADJ
ejpam-3442	247	11	set	set	NOUN
ejpam-3442	247	12	.	.	PUNCT
ejpam-3442	248	1	since	since	SCONJ
ejpam-3442	248	2	ĩ	ĩ	PROPN
ejpam-3442	248	3	⊆	⊆	NUM
ejpam-3442	248	4	j̃	j̃	PROPN
ejpam-3442	248	5	,	,	PUNCT
ejpam-3442	248	6	(	(	PUNCT
ejpam-3442	248	7	f	f	X
ejpam-3442	248	8	,	,	PUNCT
ejpam-3442	248	9	e)∗s(j̃	e)∗s(j̃	INTJ
ejpam-3442	248	10	,	,	PUNCT
ejpam-3442	248	11	τ)⊆̃(f	τ)⊆̃(f	PROPN
ejpam-3442	248	12	,	,	PUNCT
ejpam-3442	248	13	e)∗s(ĩ	e)∗s(ĩ	PROPN
ejpam-3442	248	14	,	,	PUNCT
ejpam-3442	248	15	τ	τ	PROPN
ejpam-3442	248	16	)	)	PUNCT
ejpam-3442	248	17	.	.	PUNCT
ejpam-3442	249	1	therefore	therefore	ADV
ejpam-3442	249	2	,	,	PUNCT
ejpam-3442	249	3	cl∗s	cl∗s	X
ejpam-3442	249	4	j̃	j̃	PROPN
ejpam-3442	249	5	(	(	PUNCT
ejpam-3442	249	6	f	f	X
ejpam-3442	249	7	,	,	PUNCT
ejpam-3442	249	8	e)⊆̃cl∗s	e)⊆̃cl∗s	CCONJ
ejpam-3442	249	9	ĩ	ĩ	PROPN
ejpam-3442	249	10	(	(	PUNCT
ejpam-3442	249	11	f	f	X
ejpam-3442	249	12	,	,	PUNCT
ejpam-3442	249	13	e	e	NOUN
ejpam-3442	249	14	)	)	PUNCT
ejpam-3442	249	15	.	.	PUNCT
ejpam-3442	250	1	hence	hence	ADV
ejpam-3442	250	2	,	,	PUNCT
ejpam-3442	250	3	(	(	PUNCT
ejpam-3442	250	4	f	f	X
ejpam-3442	250	5	,	,	PUNCT
ejpam-3442	250	6	e)⊆̃cl∗s	e)⊆̃cl∗s	NUM
ejpam-3442	250	7	j̃	j̃	PROPN
ejpam-3442	250	8	(	(	PUNCT
ejpam-3442	250	9	f	f	X
ejpam-3442	250	10	,	,	PUNCT
ejpam-3442	250	11	e)⊆̃cl∗s	e)⊆̃cl∗s	CCONJ
ejpam-3442	250	12	ĩ	ĩ	PROPN
ejpam-3442	250	13	(	(	PUNCT
ejpam-3442	250	14	f	f	X
ejpam-3442	250	15	,	,	PUNCT
ejpam-3442	250	16	e	e	NOUN
ejpam-3442	250	17	)	)	PUNCT
ejpam-3442	250	18	=	=	SYM
ejpam-3442	250	19	(	(	PUNCT
ejpam-3442	250	20	f	f	X
ejpam-3442	250	21	,	,	PUNCT
ejpam-3442	250	22	e	e	NOUN
ejpam-3442	250	23	)	)	PUNCT
ejpam-3442	250	24	and	and	CCONJ
ejpam-3442	250	25	consequently	consequently	ADV
ejpam-3442	250	26	(	(	PUNCT
ejpam-3442	250	27	f	f	X
ejpam-3442	250	28	,	,	PUNCT
ejpam-3442	250	29	e	e	NOUN
ejpam-3442	250	30	)	)	PUNCT
ejpam-3442	250	31	is	be	AUX
ejpam-3442	250	32	τ∗s(j̃)-closed	τ∗s(j̃)-close	VERB
ejpam-3442	250	33	soft	soft	ADJ
ejpam-3442	250	34	.	.	PUNCT
ejpam-3442	251	1	proposition	proposition	NOUN
ejpam-3442	251	2	1	1	NUM
ejpam-3442	251	3	.	.	PUNCT
ejpam-3442	252	1	let	let	VERB
ejpam-3442	252	2	(	(	PUNCT
ejpam-3442	252	3	x	x	X
ejpam-3442	252	4	,	,	PUNCT
ejpam-3442	252	5	τ	τ	PROPN
ejpam-3442	252	6	,	,	PUNCT
ejpam-3442	252	7	e	e	NOUN
ejpam-3442	252	8	)	)	PUNCT
ejpam-3442	252	9	be	be	AUX
ejpam-3442	252	10	a	a	DET
ejpam-3442	252	11	soft	soft	ADJ
ejpam-3442	252	12	topological	topological	ADJ
ejpam-3442	252	13	space	space	NOUN
ejpam-3442	252	14	and	and	CCONJ
ejpam-3442	252	15	ĩ	ĩ	PROPN
ejpam-3442	252	16	be	be	VERB
ejpam-3442	252	17	a	a	DET
ejpam-3442	252	18	soft	soft	ADJ
ejpam-3442	252	19	ideal	ideal	NOUN
ejpam-3442	252	20	over	over	ADP
ejpam-3442	252	21	x	x	PUNCT
ejpam-3442	252	22	with	with	ADP
ejpam-3442	252	23	the	the	DET
ejpam-3442	252	24	same	same	ADJ
ejpam-3442	252	25	set	set	NOUN
ejpam-3442	252	26	of	of	ADP
ejpam-3442	252	27	parameters	parameter	NOUN
ejpam-3442	253	1	e.	e.	PROPN
ejpam-3442	253	2	then	then	ADV
ejpam-3442	253	3	,	,	PUNCT
ejpam-3442	253	4	β(ĩ	β(ĩ	PROPN
ejpam-3442	253	5	,	,	PUNCT
ejpam-3442	253	6	τ	τ	PROPN
ejpam-3442	253	7	)	)	PUNCT
ejpam-3442	253	8	=	=	PRON
ejpam-3442	253	9	{	{	PUNCT
ejpam-3442	253	10	(	(	PUNCT
ejpam-3442	253	11	f	f	X
ejpam-3442	253	12	,	,	PUNCT
ejpam-3442	253	13	e)−	e)−	PROPN
ejpam-3442	253	14	(	(	PUNCT
ejpam-3442	253	15	g	g	NOUN
ejpam-3442	253	16	,	,	PUNCT
ejpam-3442	253	17	e	e	NOUN
ejpam-3442	253	18	)	)	PUNCT
ejpam-3442	253	19	:	:	PUNCT
ejpam-3442	253	20	(	(	PUNCT
ejpam-3442	253	21	f	f	X
ejpam-3442	253	22	,	,	PUNCT
ejpam-3442	253	23	e	e	NOUN
ejpam-3442	253	24	)	)	PUNCT
ejpam-3442	253	25	∈	∈	PROPN
ejpam-3442	253	26	sos(x	sos(x	PROPN
ejpam-3442	253	27	)	)	PUNCT
ejpam-3442	253	28	,	,	PUNCT
ejpam-3442	253	29	(	(	PUNCT
ejpam-3442	253	30	g	g	NOUN
ejpam-3442	253	31	,	,	PUNCT
ejpam-3442	253	32	e	e	NOUN
ejpam-3442	253	33	)	)	PUNCT
ejpam-3442	253	34	∈	∈	PROPN
ejpam-3442	253	35	ĩ	ĩ	PROPN
ejpam-3442	253	36	}	}	PUNCT
ejpam-3442	253	37	is	be	AUX
ejpam-3442	253	38	a	a	DET
ejpam-3442	253	39	soft	soft	ADJ
ejpam-3442	253	40	basis	basis	NOUN
ejpam-3442	253	41	for	for	ADP
ejpam-3442	253	42	the	the	DET
ejpam-3442	253	43	soft	soft	ADJ
ejpam-3442	253	44	topology	topology	NOUN
ejpam-3442	253	45	τ∗s(ĩ	τ∗s(ĩ	ADP
ejpam-3442	253	46	)	)	PUNCT
ejpam-3442	253	47	.	.	PUNCT
ejpam-3442	254	1	proof	proof	NOUN
ejpam-3442	254	2	.	.	PUNCT
ejpam-3442	255	1	since	since	SCONJ
ejpam-3442	255	2	x̃	x̃	PROPN
ejpam-3442	255	3	∈	∈	PROPN
ejpam-3442	255	4	τ	τ	PROPN
ejpam-3442	255	5	,	,	PUNCT
ejpam-3442	255	6	φ̃	φ̃	PROPN
ejpam-3442	255	7	∈	∈	PROPN
ejpam-3442	255	8	ĩ.	ĩ.	PROPN
ejpam-3442	255	9	then	then	ADV
ejpam-3442	255	10	,	,	PUNCT
ejpam-3442	255	11	x̃	x̃	PROPN
ejpam-3442	255	12	−	−	PROPN
ejpam-3442	255	13	φ̃	φ̃	PROPN
ejpam-3442	255	14	∈	∈	PROPN
ejpam-3442	255	15	β	β	NOUN
ejpam-3442	255	16	.	.	PUNCT
ejpam-3442	255	17	hence	hence	ADV
ejpam-3442	255	18	,	,	PUNCT
ejpam-3442	255	19	x̃	x̃	PROPN
ejpam-3442	255	20	∈	∈	PROPN
ejpam-3442	255	21	β	β	X
ejpam-3442	255	22	and	and	CCONJ
ejpam-3442	255	23	⋃̃	⋃̃	PROPN
ejpam-3442	255	24	j∈j((fj	j∈j((fj	PROPN
ejpam-3442	255	25	,	,	PUNCT
ejpam-3442	255	26	e	e	NOUN
ejpam-3442	255	27	)	)	PUNCT
ejpam-3442	255	28	−	−	PROPN
ejpam-3442	255	29	(	(	PUNCT
ejpam-3442	255	30	gj	gj	NOUN
ejpam-3442	255	31	,	,	PUNCT
ejpam-3442	255	32	e	e	NOUN
ejpam-3442	255	33	)	)	PUNCT
ejpam-3442	255	34	)	)	PUNCT
ejpam-3442	256	1	=	=	PUNCT
ejpam-3442	257	1	x̃.	x̃.	ADV
ejpam-3442	257	2	also	also	ADV
ejpam-3442	257	3	,	,	PUNCT
ejpam-3442	257	4	let	let	VERB
ejpam-3442	257	5	(	(	PUNCT
ejpam-3442	257	6	(	(	PUNCT
ejpam-3442	257	7	f1	f1	NOUN
ejpam-3442	257	8	,	,	PUNCT
ejpam-3442	257	9	e)−(g1	e)−(g1	PROPN
ejpam-3442	257	10	,	,	PUNCT
ejpam-3442	257	11	e	e	NOUN
ejpam-3442	257	12	)	)	PUNCT
ejpam-3442	257	13	)	)	PUNCT
ejpam-3442	257	14	,	,	PUNCT
ejpam-3442	257	15	(	(	PUNCT
ejpam-3442	257	16	(	(	PUNCT
ejpam-3442	257	17	f2	f2	PROPN
ejpam-3442	257	18	,	,	PUNCT
ejpam-3442	257	19	e)−(g2	e)−(g2	PROPN
ejpam-3442	257	20	,	,	PUNCT
ejpam-3442	257	21	e	e	NOUN
ejpam-3442	257	22	)	)	PUNCT
ejpam-3442	257	23	)	)	PUNCT
ejpam-3442	258	1	∈	∈	PROPN
ejpam-3442	258	2	β	β	NOUN
ejpam-3442	258	3	such	such	ADJ
ejpam-3442	258	4	that	that	SCONJ
ejpam-3442	258	5	xe∈̃((f1	xe∈̃((f1	PROPN
ejpam-3442	258	6	,	,	PUNCT
ejpam-3442	258	7	e)−	e)−	PROPN
ejpam-3442	258	8	(	(	PUNCT
ejpam-3442	258	9	g1	g1	PROPN
ejpam-3442	258	10	,	,	PUNCT
ejpam-3442	258	11	e))∩̃((f2	e))∩̃((f2	PROPN
ejpam-3442	258	12	,	,	PUNCT
ejpam-3442	258	13	e)−(g2	e)−(g2	PROPN
ejpam-3442	258	14	,	,	PUNCT
ejpam-3442	258	15	e	e	NOUN
ejpam-3442	258	16	)	)	PUNCT
ejpam-3442	258	17	)	)	PUNCT
ejpam-3442	258	18	.	.	PUNCT
ejpam-3442	259	1	then	then	ADV
ejpam-3442	259	2	xe∈̃((f1	xe∈̃((f1	PROPN
ejpam-3442	259	3	,	,	PUNCT
ejpam-3442	259	4	e)−(g1	e)−(g1	PROPN
ejpam-3442	259	5	,	,	PUNCT
ejpam-3442	259	6	e))∩̃((f2	e))∩̃((f2	PROPN
ejpam-3442	259	7	,	,	PUNCT
ejpam-3442	259	8	e)−(g2	e)−(g2	PROPN
ejpam-3442	259	9	,	,	PUNCT
ejpam-3442	259	10	e	e	NOUN
ejpam-3442	259	11	)	)	PUNCT
ejpam-3442	259	12	)	)	PUNCT
ejpam-3442	260	1	=	=	SYM
ejpam-3442	260	2	(	(	PUNCT
ejpam-3442	260	3	(	(	PUNCT
ejpam-3442	260	4	f1	f1	NOUN
ejpam-3442	260	5	,	,	PUNCT
ejpam-3442	260	6	e)∩̃(f2	e)∩̃(f2	PROPN
ejpam-3442	260	7	,	,	PUNCT
ejpam-3442	260	8	e))−	e))−	PRON
ejpam-3442	260	9	(	(	PUNCT
ejpam-3442	260	10	(	(	PUNCT
ejpam-3442	260	11	g1	g1	PROPN
ejpam-3442	260	12	,	,	PUNCT
ejpam-3442	260	13	e)∪̃(g2	e)∪̃(g2	PROPN
ejpam-3442	260	14	,	,	PUNCT
ejpam-3442	260	15	e	e	NOUN
ejpam-3442	260	16	)	)	PUNCT
ejpam-3442	260	17	)	)	PUNCT
ejpam-3442	261	1	∈	∈	PROPN
ejpam-3442	261	2	β(ĩ	β(ĩ	PROPN
ejpam-3442	261	3	,	,	PUNCT
ejpam-3442	261	4	τ	τ	PROPN
ejpam-3442	261	5	)	)	PUNCT
ejpam-3442	261	6	.	.	PUNCT
ejpam-3442	262	1	thus	thus	ADV
ejpam-3442	262	2	,	,	PUNCT
ejpam-3442	262	3	β	β	X
ejpam-3442	262	4	is	be	AUX
ejpam-3442	262	5	a	a	DET
ejpam-3442	262	6	soft	soft	ADJ
ejpam-3442	262	7	basis	basis	NOUN
ejpam-3442	262	8	of	of	ADP
ejpam-3442	262	9	τ∗s	τ∗s	PUNCT
ejpam-3442	262	10	.	.	PUNCT
ejpam-3442	263	1	corollary	corollary	ADJ
ejpam-3442	263	2	2	2	NUM
ejpam-3442	263	3	.	.	PUNCT
ejpam-3442	264	1	let	let	VERB
ejpam-3442	264	2	(	(	PUNCT
ejpam-3442	264	3	x	x	X
ejpam-3442	264	4	,	,	PUNCT
ejpam-3442	264	5	τ	τ	PROPN
ejpam-3442	264	6	,	,	PUNCT
ejpam-3442	264	7	e	e	NOUN
ejpam-3442	264	8	)	)	PUNCT
ejpam-3442	264	9	be	be	AUX
ejpam-3442	264	10	a	a	DET
ejpam-3442	264	11	soft	soft	ADJ
ejpam-3442	264	12	topological	topological	ADJ
ejpam-3442	264	13	space	space	NOUN
ejpam-3442	264	14	and	and	CCONJ
ejpam-3442	264	15	ĩ	ĩ	PROPN
ejpam-3442	264	16	be	be	VERB
ejpam-3442	264	17	a	a	DET
ejpam-3442	264	18	soft	soft	ADJ
ejpam-3442	264	19	ideal	ideal	NOUN
ejpam-3442	264	20	over	over	ADP
ejpam-3442	264	21	x	x	PUNCT
ejpam-3442	264	22	with	with	ADP
ejpam-3442	264	23	the	the	DET
ejpam-3442	264	24	same	same	ADJ
ejpam-3442	264	25	set	set	NOUN
ejpam-3442	264	26	of	of	ADP
ejpam-3442	264	27	parameters	parameter	NOUN
ejpam-3442	265	1	e.	e.	PROPN
ejpam-3442	265	2	then	then	ADV
ejpam-3442	265	3	,	,	PUNCT
ejpam-3442	265	4	τ	τ	PROPN
ejpam-3442	265	5	⊆	⊆	NUM
ejpam-3442	265	6	β(ĩ	β(ĩ	PROPN
ejpam-3442	265	7	,	,	PUNCT
ejpam-3442	265	8	τ	τ	PROPN
ejpam-3442	265	9	)	)	PUNCT
ejpam-3442	265	10	⊆	⊆	NUM
ejpam-3442	265	11	τ∗(ĩ	τ∗(ĩ	SYM
ejpam-3442	265	12	)	)	PUNCT
ejpam-3442	265	13	⊆	⊆	NUM
ejpam-3442	265	14	τ∗s(ĩ	τ∗s(ĩ	NUM
ejpam-3442	265	15	)	)	PUNCT
ejpam-3442	265	16	.	.	PUNCT
ejpam-3442	266	1	proof	proof	NOUN
ejpam-3442	266	2	.	.	PUNCT
ejpam-3442	267	1	it	it	PRON
ejpam-3442	267	2	is	be	AUX
ejpam-3442	267	3	obvious	obvious	ADJ
ejpam-3442	267	4	from	from	ADP
ejpam-3442	267	5	theorem	theorem	ADJ
ejpam-3442	267	6	2(3	2(3	NUM
ejpam-3442	267	7	)	)	PUNCT
ejpam-3442	267	8	and	and	CCONJ
ejpam-3442	267	9	proposition	proposition	NOUN
ejpam-3442	267	10	1	1	NUM
ejpam-3442	267	11	.	.	NOUN
ejpam-3442	267	12	4	4	NUM
ejpam-3442	267	13	.	.	NOUN
ejpam-3442	267	14	soft	soft	ADJ
ejpam-3442	267	15	semi	semi	NOUN
ejpam-3442	267	16	-	-	NOUN
ejpam-3442	267	17	compatibility	compatibility	NOUN
ejpam-3442	267	18	of	of	ADP
ejpam-3442	267	19	τ	τ	PROPN
ejpam-3442	267	20	with	with	ADP
ejpam-3442	267	21	ĩ	ĩ	PROPN
ejpam-3442	267	22	in	in	ADP
ejpam-3442	267	23	this	this	DET
ejpam-3442	267	24	section	section	NOUN
ejpam-3442	267	25	,	,	PUNCT
ejpam-3442	267	26	we	we	PRON
ejpam-3442	267	27	will	will	AUX
ejpam-3442	267	28	introduce	introduce	VERB
ejpam-3442	267	29	the	the	DET
ejpam-3442	267	30	notion	notion	NOUN
ejpam-3442	267	31	of	of	ADP
ejpam-3442	267	32	soft	soft	ADJ
ejpam-3442	267	33	semi	semi	ADJ
ejpam-3442	267	34	compatibility	compatibility	NOUN
ejpam-3442	267	35	of	of	ADP
ejpam-3442	267	36	soft	soft	ADJ
ejpam-3442	267	37	ideals	ideal	NOUN
ejpam-3442	267	38	with	with	ADP
ejpam-3442	267	39	soft	soft	ADJ
ejpam-3442	267	40	topologies	topology	NOUN
ejpam-3442	267	41	and	and	CCONJ
ejpam-3442	267	42	some	some	DET
ejpam-3442	267	43	equivalent	equivalent	ADJ
ejpam-3442	267	44	conditions	condition	NOUN
ejpam-3442	267	45	concerning	concern	VERB
ejpam-3442	267	46	this	this	DET
ejpam-3442	267	47	topic	topic	NOUN
ejpam-3442	267	48	will	will	AUX
ejpam-3442	267	49	be	be	AUX
ejpam-3442	267	50	investigated	investigate	VERB
ejpam-3442	267	51	here	here	ADV
ejpam-3442	267	52	.	.	PUNCT
ejpam-3442	268	1	definition	definition	NOUN
ejpam-3442	268	2	14	14	NUM
ejpam-3442	268	3	.	.	PUNCT
ejpam-3442	269	1	let	let	VERB
ejpam-3442	269	2	(	(	PUNCT
ejpam-3442	269	3	x	x	X
ejpam-3442	269	4	,	,	PUNCT
ejpam-3442	269	5	τ	τ	PROPN
ejpam-3442	269	6	,	,	PUNCT
ejpam-3442	269	7	e	e	NOUN
ejpam-3442	269	8	)	)	PUNCT
ejpam-3442	269	9	be	be	AUX
ejpam-3442	269	10	a	a	DET
ejpam-3442	269	11	soft	soft	ADJ
ejpam-3442	269	12	topological	topological	ADJ
ejpam-3442	269	13	space	space	NOUN
ejpam-3442	269	14	and	and	CCONJ
ejpam-3442	269	15	ĩ	ĩ	PROPN
ejpam-3442	269	16	be	be	VERB
ejpam-3442	269	17	a	a	DET
ejpam-3442	269	18	soft	soft	ADJ
ejpam-3442	269	19	ideal	ideal	NOUN
ejpam-3442	269	20	over	over	ADP
ejpam-3442	269	21	x	x	PUNCT
ejpam-3442	269	22	with	with	ADP
ejpam-3442	269	23	the	the	DET
ejpam-3442	269	24	same	same	ADJ
ejpam-3442	269	25	set	set	NOUN
ejpam-3442	269	26	of	of	ADP
ejpam-3442	269	27	parameters	parameter	NOUN
ejpam-3442	269	28	e.	e.	PROPN
ejpam-3442	270	1	we	we	PRON
ejpam-3442	270	2	say	say	VERB
ejpam-3442	270	3	that	that	SCONJ
ejpam-3442	270	4	τ	τ	PROPN
ejpam-3442	270	5	is	be	AUX
ejpam-3442	270	6	semi	semi	ADV
ejpam-3442	270	7	compatible	compatible	ADJ
ejpam-3442	270	8	with	with	ADP
ejpam-3442	270	9	ĩ	ĩ	PROPN
ejpam-3442	270	10	,	,	PUNCT
ejpam-3442	270	11	denoted	denote	VERB
ejpam-3442	270	12	by	by	ADP
ejpam-3442	270	13	τ	τ	PROPN
ejpam-3442	270	14	∼s	∼s	NUM
ejpam-3442	271	1	ĩ	ĩ	PROPN
ejpam-3442	271	2	,	,	PUNCT
ejpam-3442	271	3	if	if	SCONJ
ejpam-3442	271	4	the	the	DET
ejpam-3442	271	5	following	follow	VERB
ejpam-3442	271	6	holds	hold	VERB
ejpam-3442	271	7	for	for	ADP
ejpam-3442	271	8	each	each	DET
ejpam-3442	271	9	(	(	PUNCT
ejpam-3442	271	10	f	f	X
ejpam-3442	271	11	,	,	PUNCT
ejpam-3442	271	12	e	e	NOUN
ejpam-3442	271	13	)	)	PUNCT
ejpam-3442	271	14	∈	∈	PROPN
ejpam-3442	272	1	ss(x)e	ss(x)e	NOUN
ejpam-3442	272	2	:	:	PUNCT
ejpam-3442	272	3	if	if	SCONJ
ejpam-3442	272	4	for	for	ADP
ejpam-3442	272	5	each	each	DET
ejpam-3442	272	6	soft	soft	ADJ
ejpam-3442	272	7	point	point	NOUN
ejpam-3442	272	8	xe	xe	PROPN
ejpam-3442	272	9	and	and	CCONJ
ejpam-3442	272	10	xe∈̃(f	xe∈̃(f	PROPN
ejpam-3442	272	11	,	,	PUNCT
ejpam-3442	272	12	e	e	X
ejpam-3442	272	13	)	)	PUNCT
ejpam-3442	272	14	there	there	PRON
ejpam-3442	272	15	exists	exist	VERB
ejpam-3442	272	16	oxe	oxe	PRON
ejpam-3442	272	17	∈	∈	PROPN
ejpam-3442	272	18	sos(x	sos(x	PROPN
ejpam-3442	272	19	)	)	PUNCT
ejpam-3442	272	20	such	such	ADJ
ejpam-3442	272	21	that	that	SCONJ
ejpam-3442	272	22	oxe∩̃(f	oxe∩̃(f	NUM
ejpam-3442	272	23	,	,	PUNCT
ejpam-3442	272	24	e	e	NOUN
ejpam-3442	272	25	)	)	PUNCT
ejpam-3442	272	26	∈	∈	PROPN
ejpam-3442	272	27	ĩ	ĩ	PROPN
ejpam-3442	272	28	,	,	PUNCT
ejpam-3442	272	29	then	then	ADV
ejpam-3442	272	30	(	(	PUNCT
ejpam-3442	272	31	f	f	X
ejpam-3442	272	32	,	,	PUNCT
ejpam-3442	272	33	e	e	NOUN
ejpam-3442	272	34	)	)	PUNCT
ejpam-3442	272	35	∈	∈	PROPN
ejpam-3442	272	36	ĩ.	ĩ.	NOUN
ejpam-3442	272	37	theorem	theorem	VERB
ejpam-3442	272	38	6	6	NUM
ejpam-3442	272	39	.	.	PUNCT
ejpam-3442	273	1	let	let	AUX
ejpam-3442	273	2	(	(	PUNCT
ejpam-3442	273	3	x	x	X
ejpam-3442	273	4	,	,	PUNCT
ejpam-3442	273	5	τ	τ	PROPN
ejpam-3442	273	6	,	,	PUNCT
ejpam-3442	273	7	e	e	NOUN
ejpam-3442	273	8	)	)	PUNCT
ejpam-3442	273	9	be	be	AUX
ejpam-3442	273	10	a	a	DET
ejpam-3442	273	11	soft	soft	ADJ
ejpam-3442	273	12	topological	topological	ADJ
ejpam-3442	273	13	space	space	NOUN
ejpam-3442	273	14	,	,	PUNCT
ejpam-3442	273	15	ĩ	ĩ	PROPN
ejpam-3442	273	16	be	be	VERB
ejpam-3442	273	17	a	a	DET
ejpam-3442	273	18	soft	soft	ADJ
ejpam-3442	273	19	ideal	ideal	NOUN
ejpam-3442	273	20	over	over	ADP
ejpam-3442	273	21	x	x	PUNCT
ejpam-3442	273	22	with	with	ADP
ejpam-3442	273	23	the	the	DET
ejpam-3442	273	24	same	same	ADJ
ejpam-3442	273	25	set	set	NOUN
ejpam-3442	273	26	of	of	ADP
ejpam-3442	273	27	parameters	parameter	NOUN
ejpam-3442	273	28	e	e	PROPN
ejpam-3442	273	29	and	and	CCONJ
ejpam-3442	273	30	τ	τ	PROPN
ejpam-3442	273	31	∼s	∼s	PROPN
ejpam-3442	273	32	ĩ.	ĩ.	PROPN
ejpam-3442	273	33	then	then	ADV
ejpam-3442	273	34	,	,	PUNCT
ejpam-3442	273	35	the	the	DET
ejpam-3442	273	36	following	follow	VERB
ejpam-3442	273	37	are	be	AUX
ejpam-3442	273	38	equivalent	equivalent	ADJ
ejpam-3442	273	39	for	for	ADP
ejpam-3442	273	40	each	each	DET
ejpam-3442	273	41	(	(	PUNCT
ejpam-3442	273	42	f	f	X
ejpam-3442	273	43	,	,	PUNCT
ejpam-3442	273	44	e	e	NOUN
ejpam-3442	273	45	)	)	PUNCT
ejpam-3442	273	46	∈	∈	PROPN
ejpam-3442	274	1	ss(x)e	ss(x)e	NOUN
ejpam-3442	274	2	:	:	PUNCT
ejpam-3442	274	3	(	(	PUNCT
ejpam-3442	274	4	1	1	X
ejpam-3442	274	5	)	)	PUNCT
ejpam-3442	274	6	if	if	SCONJ
ejpam-3442	274	7	(	(	PUNCT
ejpam-3442	274	8	f	f	X
ejpam-3442	274	9	,	,	PUNCT
ejpam-3442	274	10	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	274	11	,	,	PUNCT
ejpam-3442	274	12	e)∗s	e)∗s	X
ejpam-3442	274	13	=	=	SYM
ejpam-3442	274	14	φ̃	φ̃	PROPN
ejpam-3442	274	15	,	,	PUNCT
ejpam-3442	274	16	then	then	ADV
ejpam-3442	274	17	(	(	PUNCT
ejpam-3442	274	18	f	f	X
ejpam-3442	274	19	,	,	PUNCT
ejpam-3442	274	20	e)∗s	e)∗s	PROPN
ejpam-3442	274	21	=	=	SYM
ejpam-3442	274	22	φ̃.	φ̃.	PROPN
ejpam-3442	274	23	(	(	PUNCT
ejpam-3442	274	24	2	2	NUM
ejpam-3442	274	25	)	)	PUNCT
ejpam-3442	274	26	(	(	PUNCT
ejpam-3442	274	27	(	(	PUNCT
ejpam-3442	274	28	f	f	X
ejpam-3442	274	29	,	,	PUNCT
ejpam-3442	274	30	e)−	e)−	PROPN
ejpam-3442	274	31	(	(	PUNCT
ejpam-3442	274	32	f	f	X
ejpam-3442	274	33	,	,	PUNCT
ejpam-3442	274	34	e)∗s)∗s	e)∗s)∗s	PROPN
ejpam-3442	274	35	=	=	SYM
ejpam-3442	274	36	φ̃.	φ̃.	PROPN
ejpam-3442	274	37	(	(	PUNCT
ejpam-3442	274	38	3	3	NUM
ejpam-3442	274	39	)	)	PUNCT
ejpam-3442	274	40	(	(	PUNCT
ejpam-3442	274	41	(	(	PUNCT
ejpam-3442	274	42	f	f	X
ejpam-3442	274	43	,	,	PUNCT
ejpam-3442	274	44	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	274	45	,	,	PUNCT
ejpam-3442	274	46	e)∗s)∗s	e)∗s)∗s	PROPN
ejpam-3442	274	47	=	=	SYM
ejpam-3442	274	48	(	(	PUNCT
ejpam-3442	274	49	f	f	NOUN
ejpam-3442	274	50	,	,	PUNCT
ejpam-3442	274	51	e)∗s	e)∗s	NOUN
ejpam-3442	274	52	.	.	PUNCT
ejpam-3442	275	1	proof	proof	NOUN
ejpam-3442	275	2	.	.	PUNCT
ejpam-3442	276	1	(	(	PUNCT
ejpam-3442	276	2	1	1	X
ejpam-3442	276	3	)	)	PUNCT
ejpam-3442	276	4	=	=	NOUN
ejpam-3442	276	5	⇒	⇒	NOUN
ejpam-3442	276	6	(	(	PUNCT
ejpam-3442	276	7	2	2	X
ejpam-3442	276	8	)	)	PUNCT
ejpam-3442	276	9	let	let	VERB
ejpam-3442	276	10	(	(	PUNCT
ejpam-3442	276	11	f	f	X
ejpam-3442	276	12	,	,	PUNCT
ejpam-3442	276	13	e	e	NOUN
ejpam-3442	276	14	)	)	PUNCT
ejpam-3442	276	15	∈	∈	PROPN
ejpam-3442	276	16	ss(x)e	ss(x)e	PROPN
ejpam-3442	276	17	.	.	PUNCT
ejpam-3442	277	1	since	since	SCONJ
ejpam-3442	277	2	(	(	PUNCT
ejpam-3442	277	3	(	(	PUNCT
ejpam-3442	277	4	f	f	X
ejpam-3442	277	5	,	,	PUNCT
ejpam-3442	277	6	e	e	NOUN
ejpam-3442	277	7	)	)	PUNCT
ejpam-3442	277	8	−	−	PROPN
ejpam-3442	277	9	(	(	PUNCT
ejpam-3442	277	10	f	f	X
ejpam-3442	277	11	,	,	PUNCT
ejpam-3442	277	12	e)∗s)∩̃((f	e)∗s)∩̃((f	PROPN
ejpam-3442	277	13	,	,	PUNCT
ejpam-3442	277	14	e	e	NOUN
ejpam-3442	277	15	)	)	PUNCT
ejpam-3442	277	16	−	−	PROPN
ejpam-3442	277	17	(	(	PUNCT
ejpam-3442	277	18	f	f	X
ejpam-3442	277	19	,	,	PUNCT
ejpam-3442	277	20	e)∗s)∗s	e)∗s)∗s	PROPN
ejpam-3442	277	21	=	=	SYM
ejpam-3442	278	1	[	[	X
ejpam-3442	278	2	(	(	PUNCT
ejpam-3442	278	3	(	(	PUNCT
ejpam-3442	278	4	f	f	X
ejpam-3442	278	5	,	,	PUNCT
ejpam-3442	278	6	e)−	e)−	PROPN
ejpam-3442	278	7	(	(	PUNCT
ejpam-3442	278	8	f	f	X
ejpam-3442	278	9	,	,	PUNCT
ejpam-3442	278	10	e)∗s)∩̃(f	e)∗s)∩̃(f	X
ejpam-3442	278	11	,	,	PUNCT
ejpam-3442	278	12	e)∗s	e)∗s	PROPN
ejpam-3442	278	13	]	]	X
ejpam-3442	278	14	∩̃[((f	∩̃[((f	ADJ
ejpam-3442	278	15	,	,	PUNCT
ejpam-3442	278	16	e)−	e)−	PROPN
ejpam-3442	278	17	(	(	PUNCT
ejpam-3442	278	18	f	f	X
ejpam-3442	278	19	,	,	PUNCT
ejpam-3442	278	20	e)∗s)∩̃(x̃−	e)∗s)∩̃(x̃−	PROPN
ejpam-3442	278	21	(	(	PUNCT
ejpam-3442	278	22	f	f	X
ejpam-3442	278	23	,	,	PUNCT
ejpam-3442	278	24	e)∗s)∗s	e)∗s)∗s	PROPN
ejpam-3442	278	25	]	]	X
ejpam-3442	278	26	=	=	SYM
ejpam-3442	278	27	φ̃∩̃[((f	φ̃∩̃[((f	NOUN
ejpam-3442	278	28	,	,	PUNCT
ejpam-3442	278	29	e)−	e)−	PROPN
ejpam-3442	278	30	(	(	PUNCT
ejpam-3442	278	31	f	f	X
ejpam-3442	278	32	,	,	PUNCT
ejpam-3442	278	33	e)∗s)∩̃(x̃	e)∗s)∩̃(x̃	PROPN
ejpam-3442	278	34	−	−	PROPN
ejpam-3442	278	35	(	(	PUNCT
ejpam-3442	278	36	f	f	X
ejpam-3442	278	37	,	,	PUNCT
ejpam-3442	278	38	e)∗s)∗s	e)∗s)∗s	PROPN
ejpam-3442	278	39	]	]	X
ejpam-3442	279	1	=	=	PUNCT
ejpam-3442	279	2	φ̃	φ̃	PROPN
ejpam-3442	279	3	,	,	PUNCT
ejpam-3442	279	4	(	(	PUNCT
ejpam-3442	279	5	(	(	PUNCT
ejpam-3442	279	6	f	f	X
ejpam-3442	279	7	,	,	PUNCT
ejpam-3442	279	8	e)−	e)−	PROPN
ejpam-3442	279	9	(	(	PUNCT
ejpam-3442	279	10	f	f	X
ejpam-3442	279	11	,	,	PUNCT
ejpam-3442	279	12	e)∗s)∗s	e)∗s)∗s	PROPN
ejpam-3442	279	13	=	=	SYM
ejpam-3442	279	14	φ̃	φ̃	PROPN
ejpam-3442	279	15	by	by	ADP
ejpam-3442	279	16	(	(	PUNCT
ejpam-3442	279	17	1	1	NUM
ejpam-3442	279	18	)	)	PUNCT
ejpam-3442	279	19	.	.	PUNCT
ejpam-3442	280	1	f.	f.	PROPN
ejpam-3442	280	2	a.	a.	PROPN
ejpam-3442	280	3	gharib	gharib	PROPN
ejpam-3442	280	4	,	,	PUNCT
ejpam-3442	280	5	a.	a.	PROPN
ejpam-3442	280	6	m.	m.	PROPN
ejpam-3442	280	7	abd	abd	PROPN
ejpam-3442	280	8	el	el	PROPN
ejpam-3442	280	9	-	-	PROPN
ejpam-3442	280	10	latif	latif	PROPN
ejpam-3442	280	11	/	/	SYM
ejpam-3442	280	12	eur	eur	PROPN
ejpam-3442	280	13	.	.	PUNCT
ejpam-3442	281	1	j.	j.	PROPN
ejpam-3442	281	2	pure	pure	PROPN
ejpam-3442	281	3	appl	appl	PROPN
ejpam-3442	281	4	.	.	PROPN
ejpam-3442	281	5	math	math	PROPN
ejpam-3442	281	6	,	,	PUNCT
ejpam-3442	281	7	12	12	NUM
ejpam-3442	281	8	(	(	PUNCT
ejpam-3442	281	9	3	3	NUM
ejpam-3442	281	10	)	)	PUNCT
ejpam-3442	281	11	(	(	PUNCT
ejpam-3442	281	12	2019	2019	NUM
ejpam-3442	281	13	)	)	PUNCT
ejpam-3442	281	14	,	,	PUNCT
ejpam-3442	281	15	857	857	NUM
ejpam-3442	281	16	-	-	SYM
ejpam-3442	281	17	869	869	NUM
ejpam-3442	281	18	865	865	NUM
ejpam-3442	281	19	(	(	PUNCT
ejpam-3442	281	20	2	2	NUM
ejpam-3442	281	21	)	)	PUNCT
ejpam-3442	282	1	=	=	NOUN
ejpam-3442	282	2	⇒	⇒	NOUN
ejpam-3442	282	3	(	(	PUNCT
ejpam-3442	282	4	3	3	X
ejpam-3442	282	5	)	)	PUNCT
ejpam-3442	282	6	let	let	VERB
ejpam-3442	282	7	(	(	PUNCT
ejpam-3442	282	8	f	f	X
ejpam-3442	282	9	,	,	PUNCT
ejpam-3442	282	10	e	e	NOUN
ejpam-3442	282	11	)	)	PUNCT
ejpam-3442	282	12	∈	∈	PROPN
ejpam-3442	282	13	ss(x)e	ss(x)e	PROPN
ejpam-3442	282	14	.	.	PUNCT
ejpam-3442	283	1	since	since	SCONJ
ejpam-3442	283	2	(	(	PUNCT
ejpam-3442	283	3	f	f	X
ejpam-3442	283	4	,	,	PUNCT
ejpam-3442	283	5	e	e	NOUN
ejpam-3442	283	6	)	)	PUNCT
ejpam-3442	283	7	=	=	SYM
ejpam-3442	283	8	(	(	PUNCT
ejpam-3442	283	9	(	(	PUNCT
ejpam-3442	283	10	f	f	X
ejpam-3442	283	11	,	,	PUNCT
ejpam-3442	283	12	e)−((f	e)−((f	PROPN
ejpam-3442	283	13	,	,	PUNCT
ejpam-3442	283	14	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	283	15	,	,	PUNCT
ejpam-3442	283	16	e)∗s))∪̃((f	e)∗s))∪̃((f	NOUN
ejpam-3442	283	17	,	,	PUNCT
ejpam-3442	283	18	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	283	19	,	,	PUNCT
ejpam-3442	283	20	e)∗s	e)∗s	PROPN
ejpam-3442	283	21	)	)	PUNCT
ejpam-3442	283	22	,	,	PUNCT
ejpam-3442	283	23	(	(	PUNCT
ejpam-3442	283	24	f	f	X
ejpam-3442	283	25	,	,	PUNCT
ejpam-3442	283	26	e)∗s	e)∗s	PROPN
ejpam-3442	283	27	=	=	SYM
ejpam-3442	284	1	[	[	X
ejpam-3442	284	2	(	(	PUNCT
ejpam-3442	284	3	f	f	NUM
ejpam-3442	284	4	,	,	PUNCT
ejpam-3442	284	5	e)−((f	e)−((f	NOUN
ejpam-3442	284	6	,	,	PUNCT
ejpam-3442	284	7	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	284	8	,	,	PUNCT
ejpam-3442	284	9	e)∗s)∪̃((f	e)∗s)∪̃((f	X
ejpam-3442	284	10	,	,	PUNCT
ejpam-3442	284	11	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	284	12	,	,	PUNCT
ejpam-3442	284	13	e)∗s)]∗s	e)∗s)]∗s	NOUN
ejpam-3442	284	14	=	=	PUNCT
ejpam-3442	285	1	[	[	X
ejpam-3442	285	2	(	(	PUNCT
ejpam-3442	285	3	f	f	NUM
ejpam-3442	285	4	,	,	PUNCT
ejpam-3442	285	5	e)−((f	e)−((f	PROPN
ejpam-3442	285	6	,	,	PUNCT
ejpam-3442	285	7	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	285	8	,	,	PUNCT
ejpam-3442	285	9	e)∗s)]∗s	e)∗s)]∗s	NOUN
ejpam-3442	285	10	∪̃[(f	∪̃[(f	ADV
ejpam-3442	285	11	,	,	PUNCT
ejpam-3442	285	12	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	285	13	,	,	PUNCT
ejpam-3442	285	14	e)∗s	e)∗s	PROPN
ejpam-3442	285	15	]	]	X
ejpam-3442	285	16	∗s	∗s	ADP
ejpam-3442	285	17	=	=	SYM
ejpam-3442	286	1	[	[	X
ejpam-3442	286	2	φ̃∪̃((f	φ̃∪̃((f	NUM
ejpam-3442	286	3	,	,	PUNCT
ejpam-3442	286	4	e)−(f	e)−(f	NUM
ejpam-3442	286	5	,	,	PUNCT
ejpam-3442	286	6	e)∗s)]∗s∪̃[(f	e)∗s)]∗s∪̃[(f	PROPN
ejpam-3442	286	7	,	,	PUNCT
ejpam-3442	286	8	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	286	9	,	,	PUNCT
ejpam-3442	286	10	e)∗s	e)∗s	PROPN
ejpam-3442	286	11	]	]	X
ejpam-3442	287	1	∗s	∗s	ADP
ejpam-3442	287	2	=	=	SYM
ejpam-3442	288	1	[	[	X
ejpam-3442	288	2	(	(	PUNCT
ejpam-3442	288	3	f	f	X
ejpam-3442	288	4	,	,	PUNCT
ejpam-3442	288	5	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	288	6	,	,	PUNCT
ejpam-3442	288	7	e)∗s	e)∗s	PROPN
ejpam-3442	288	8	]	]	X
ejpam-3442	288	9	∗s	∗s	ADP
ejpam-3442	288	10	from	from	ADP
ejpam-3442	288	11	(	(	PUNCT
ejpam-3442	288	12	2	2	NUM
ejpam-3442	288	13	)	)	PUNCT
ejpam-3442	288	14	.	.	PUNCT
ejpam-3442	289	1	(	(	PUNCT
ejpam-3442	289	2	3	3	X
ejpam-3442	289	3	)	)	PUNCT
ejpam-3442	289	4	=	=	NOUN
ejpam-3442	289	5	⇒	⇒	NOUN
ejpam-3442	289	6	(	(	PUNCT
ejpam-3442	289	7	1	1	X
ejpam-3442	289	8	)	)	PUNCT
ejpam-3442	289	9	let	let	VERB
ejpam-3442	289	10	(	(	PUNCT
ejpam-3442	289	11	f	f	X
ejpam-3442	289	12	,	,	PUNCT
ejpam-3442	289	13	e	e	NOUN
ejpam-3442	289	14	)	)	PUNCT
ejpam-3442	289	15	∈	∈	PROPN
ejpam-3442	289	16	ss(x)e	ss(x)e	PROPN
ejpam-3442	290	1	and	and	CCONJ
ejpam-3442	290	2	(	(	PUNCT
ejpam-3442	290	3	f	f	X
ejpam-3442	290	4	,	,	PUNCT
ejpam-3442	290	5	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	290	6	,	,	PUNCT
ejpam-3442	290	7	e)∗s	e)∗s	PROPN
ejpam-3442	290	8	=	=	SYM
ejpam-3442	290	9	φ̃.	φ̃.	PROPN
ejpam-3442	290	10	then	then	ADV
ejpam-3442	290	11	,	,	PUNCT
ejpam-3442	290	12	(	(	PUNCT
ejpam-3442	290	13	f	f	X
ejpam-3442	290	14	,	,	PUNCT
ejpam-3442	290	15	e)∗s	e)∗s	PROPN
ejpam-3442	291	1	=	=	SYM
ejpam-3442	292	1	[	[	X
ejpam-3442	292	2	(	(	PUNCT
ejpam-3442	292	3	f	f	X
ejpam-3442	292	4	,	,	PUNCT
ejpam-3442	292	5	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	292	6	,	,	PUNCT
ejpam-3442	292	7	e)∗s	e)∗s	PROPN
ejpam-3442	292	8	]	]	X
ejpam-3442	292	9	∗s	∗s	NOUN
ejpam-3442	292	10	=	=	SYM
ejpam-3442	292	11	(	(	PUNCT
ejpam-3442	292	12	φ̃)∗s	φ̃)∗s	PROPN
ejpam-3442	292	13	=	=	PROPN
ejpam-3442	292	14	φ̃.	φ̃.	PROPN
ejpam-3442	292	15	corollary	corollary	NOUN
ejpam-3442	292	16	3	3	X
ejpam-3442	292	17	.	.	PUNCT
ejpam-3442	293	1	let	let	AUX
ejpam-3442	293	2	(	(	PUNCT
ejpam-3442	293	3	x	x	X
ejpam-3442	293	4	,	,	PUNCT
ejpam-3442	293	5	τ	τ	PROPN
ejpam-3442	293	6	,	,	PUNCT
ejpam-3442	293	7	e	e	NOUN
ejpam-3442	293	8	)	)	PUNCT
ejpam-3442	293	9	be	be	AUX
ejpam-3442	293	10	a	a	DET
ejpam-3442	293	11	soft	soft	ADJ
ejpam-3442	293	12	topological	topological	ADJ
ejpam-3442	293	13	space	space	NOUN
ejpam-3442	293	14	,	,	PUNCT
ejpam-3442	293	15	ĩ	ĩ	PROPN
ejpam-3442	293	16	be	be	VERB
ejpam-3442	293	17	a	a	DET
ejpam-3442	293	18	soft	soft	ADJ
ejpam-3442	293	19	ideal	ideal	NOUN
ejpam-3442	293	20	over	over	ADP
ejpam-3442	293	21	x	x	PUNCT
ejpam-3442	293	22	with	with	ADP
ejpam-3442	293	23	the	the	DET
ejpam-3442	293	24	same	same	ADJ
ejpam-3442	293	25	set	set	NOUN
ejpam-3442	293	26	of	of	ADP
ejpam-3442	293	27	parameters	parameter	NOUN
ejpam-3442	293	28	e	e	NOUN
ejpam-3442	293	29	,	,	PUNCT
ejpam-3442	293	30	(	(	PUNCT
ejpam-3442	293	31	f	f	X
ejpam-3442	293	32	,	,	PUNCT
ejpam-3442	293	33	e	e	NOUN
ejpam-3442	293	34	)	)	PUNCT
ejpam-3442	293	35	∈	∈	PROPN
ejpam-3442	293	36	ss(x)e	ss(x)e	PROPN
ejpam-3442	294	1	and	and	CCONJ
ejpam-3442	294	2	τ	τ	PROPN
ejpam-3442	294	3	∼s	∼s	PROPN
ejpam-3442	294	4	ĩ.	ĩ.	PROPN
ejpam-3442	294	5	then	then	ADV
ejpam-3442	294	6	,	,	PUNCT
ejpam-3442	294	7	(	(	PUNCT
ejpam-3442	294	8	(	(	PUNCT
ejpam-3442	294	9	f	f	X
ejpam-3442	294	10	,	,	PUNCT
ejpam-3442	294	11	e)∗s)∗s	e)∗s)∗s	PROPN
ejpam-3442	294	12	=	=	SYM
ejpam-3442	294	13	(	(	PUNCT
ejpam-3442	294	14	f	f	NOUN
ejpam-3442	294	15	,	,	PUNCT
ejpam-3442	294	16	e)∗s	e)∗s	NOUN
ejpam-3442	294	17	.	.	PUNCT
ejpam-3442	295	1	proof	proof	NOUN
ejpam-3442	295	2	.	.	PUNCT
ejpam-3442	296	1	let	let	VERB
ejpam-3442	296	2	(	(	PUNCT
ejpam-3442	296	3	f	f	X
ejpam-3442	296	4	,	,	PUNCT
ejpam-3442	296	5	e	e	NOUN
ejpam-3442	296	6	)	)	PUNCT
ejpam-3442	296	7	∈	∈	PROPN
ejpam-3442	296	8	ss(x)e	ss(x)e	PROPN
ejpam-3442	296	9	.	.	PUNCT
ejpam-3442	297	1	since	since	SCONJ
ejpam-3442	297	2	(	(	PUNCT
ejpam-3442	297	3	f	f	X
ejpam-3442	297	4	,	,	PUNCT
ejpam-3442	297	5	e)∗s	e)∗s	PROPN
ejpam-3442	297	6	=	=	SYM
ejpam-3442	297	7	(	(	PUNCT
ejpam-3442	297	8	(	(	PUNCT
ejpam-3442	297	9	f	f	X
ejpam-3442	297	10	,	,	PUNCT
ejpam-3442	297	11	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	297	12	,	,	PUNCT
ejpam-3442	297	13	e)∗s)∗s⊆̃(f	e)∗s)∗s⊆̃(f	PROPN
ejpam-3442	297	14	,	,	PUNCT
ejpam-3442	297	15	e)∗s)∗s	e)∗s)∗s	PROPN
ejpam-3442	297	16	from	from	ADP
ejpam-3442	297	17	theorem	theorem	ADJ
ejpam-3442	297	18	6	6	NUM
ejpam-3442	297	19	.	.	PUNCT
ejpam-3442	298	1	but	but	CCONJ
ejpam-3442	298	2	,	,	PUNCT
ejpam-3442	298	3	we	we	PRON
ejpam-3442	298	4	have	have	VERB
ejpam-3442	298	5	(	(	PUNCT
ejpam-3442	298	6	(	(	PUNCT
ejpam-3442	298	7	f	f	X
ejpam-3442	298	8	,	,	PUNCT
ejpam-3442	298	9	e)∗s)∗s⊆̃(f	e)∗s)∗s⊆̃(f	PROPN
ejpam-3442	298	10	,	,	PUNCT
ejpam-3442	298	11	e)∗s	e)∗s	PROPN
ejpam-3442	298	12	from	from	ADP
ejpam-3442	298	13	theorem	theorem	ADJ
ejpam-3442	298	14	2	2	NUM
ejpam-3442	298	15	(	(	PUNCT
ejpam-3442	298	16	5	5	NUM
ejpam-3442	298	17	)	)	PUNCT
ejpam-3442	298	18	.	.	PUNCT
ejpam-3442	299	1	thus	thus	ADV
ejpam-3442	299	2	,	,	PUNCT
ejpam-3442	299	3	(	(	PUNCT
ejpam-3442	299	4	(	(	PUNCT
ejpam-3442	299	5	f	f	X
ejpam-3442	299	6	,	,	PUNCT
ejpam-3442	299	7	e)∗s)∗s	e)∗s)∗s	PROPN
ejpam-3442	299	8	=	=	SYM
ejpam-3442	299	9	(	(	PUNCT
ejpam-3442	299	10	f	f	NOUN
ejpam-3442	299	11	,	,	PUNCT
ejpam-3442	299	12	e)∗s	e)∗s	PROPN
ejpam-3442	299	13	.	.	PUNCT
ejpam-3442	300	1	theorem	theorem	VERB
ejpam-3442	300	2	7	7	NUM
ejpam-3442	300	3	.	.	PUNCT
ejpam-3442	301	1	let	let	AUX
ejpam-3442	301	2	(	(	PUNCT
ejpam-3442	301	3	x	x	X
ejpam-3442	301	4	,	,	PUNCT
ejpam-3442	301	5	τ	τ	PROPN
ejpam-3442	301	6	,	,	PUNCT
ejpam-3442	301	7	e	e	NOUN
ejpam-3442	301	8	)	)	PUNCT
ejpam-3442	301	9	be	be	AUX
ejpam-3442	301	10	a	a	DET
ejpam-3442	301	11	soft	soft	ADJ
ejpam-3442	301	12	topological	topological	ADJ
ejpam-3442	301	13	space	space	NOUN
ejpam-3442	301	14	and	and	CCONJ
ejpam-3442	301	15	ĩ	ĩ	PROPN
ejpam-3442	301	16	be	be	VERB
ejpam-3442	301	17	a	a	DET
ejpam-3442	301	18	soft	soft	ADJ
ejpam-3442	301	19	ideal	ideal	NOUN
ejpam-3442	301	20	over	over	ADP
ejpam-3442	301	21	x	x	PUNCT
ejpam-3442	301	22	with	with	ADP
ejpam-3442	301	23	the	the	DET
ejpam-3442	301	24	same	same	ADJ
ejpam-3442	301	25	set	set	NOUN
ejpam-3442	301	26	of	of	ADP
ejpam-3442	301	27	parameters	parameter	NOUN
ejpam-3442	302	1	e.	e.	PROPN
ejpam-3442	302	2	then	then	ADV
ejpam-3442	302	3	,	,	PUNCT
ejpam-3442	302	4	the	the	DET
ejpam-3442	302	5	following	follow	VERB
ejpam-3442	302	6	are	be	AUX
ejpam-3442	302	7	equivalent	equivalent	ADJ
ejpam-3442	302	8	:	:	PUNCT
ejpam-3442	302	9	(	(	PUNCT
ejpam-3442	302	10	1	1	X
ejpam-3442	302	11	)	)	PUNCT
ejpam-3442	302	12	τ	τ	PROPN
ejpam-3442	303	1	∼s	∼s	PROPN
ejpam-3442	303	2	ĩ.	ĩ.	PROPN
ejpam-3442	303	3	(	(	PUNCT
ejpam-3442	303	4	2	2	X
ejpam-3442	303	5	)	)	PUNCT
ejpam-3442	303	6	if	if	SCONJ
ejpam-3442	303	7	(	(	PUNCT
ejpam-3442	303	8	f	f	X
ejpam-3442	303	9	,	,	PUNCT
ejpam-3442	303	10	e	e	NOUN
ejpam-3442	303	11	)	)	PUNCT
ejpam-3442	303	12	∈	∈	PROPN
ejpam-3442	303	13	ss(x)e	ss(x)e	PROPN
ejpam-3442	303	14	has	have	VERB
ejpam-3442	303	15	a	a	DET
ejpam-3442	303	16	cover	cover	NOUN
ejpam-3442	303	17	of	of	ADP
ejpam-3442	303	18	semi	semi	ADJ
ejpam-3442	303	19	open	open	ADJ
ejpam-3442	303	20	soft	soft	ADJ
ejpam-3442	303	21	sets	set	NOUN
ejpam-3442	303	22	each	each	PRON
ejpam-3442	303	23	of	of	ADP
ejpam-3442	303	24	whose	whose	DET
ejpam-3442	303	25	soft	soft	ADJ
ejpam-3442	303	26	intersection	intersection	NOUN
ejpam-3442	303	27	with	with	ADP
ejpam-3442	303	28	(	(	PUNCT
ejpam-3442	303	29	f	f	X
ejpam-3442	303	30	,	,	PUNCT
ejpam-3442	303	31	e	e	NOUN
ejpam-3442	303	32	)	)	PUNCT
ejpam-3442	303	33	is	be	AUX
ejpam-3442	303	34	in	in	ADP
ejpam-3442	303	35	ĩ	ĩ	PROPN
ejpam-3442	303	36	,	,	PUNCT
ejpam-3442	303	37	then	then	ADV
ejpam-3442	303	38	(	(	PUNCT
ejpam-3442	303	39	f	f	X
ejpam-3442	303	40	,	,	PUNCT
ejpam-3442	303	41	e	e	NOUN
ejpam-3442	303	42	)	)	PUNCT
ejpam-3442	303	43	∈	∈	PROPN
ejpam-3442	303	44	ĩ.	ĩ.	NOUN
ejpam-3442	303	45	(	(	PUNCT
ejpam-3442	303	46	3	3	X
ejpam-3442	303	47	)	)	PUNCT
ejpam-3442	303	48	for	for	ADP
ejpam-3442	303	49	every	every	DET
ejpam-3442	303	50	(	(	PUNCT
ejpam-3442	303	51	f	f	X
ejpam-3442	303	52	,	,	PUNCT
ejpam-3442	303	53	e	e	NOUN
ejpam-3442	303	54	)	)	PUNCT
ejpam-3442	303	55	∈	∈	PROPN
ejpam-3442	303	56	ss(x)e	ss(x)e	VERB
ejpam-3442	303	57	such	such	ADJ
ejpam-3442	303	58	that	that	SCONJ
ejpam-3442	303	59	(	(	PUNCT
ejpam-3442	303	60	f	f	X
ejpam-3442	303	61	,	,	PUNCT
ejpam-3442	303	62	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	303	63	,	,	PUNCT
ejpam-3442	303	64	e)∗s	e)∗s	PRON
ejpam-3442	303	65	=	=	SYM
ejpam-3442	303	66	φ̃	φ̃	PROPN
ejpam-3442	303	67	implies	imply	VERB
ejpam-3442	303	68	(	(	PUNCT
ejpam-3442	303	69	f	f	X
ejpam-3442	303	70	,	,	PUNCT
ejpam-3442	303	71	e	e	NOUN
ejpam-3442	303	72	)	)	PUNCT
ejpam-3442	303	73	∈	∈	PROPN
ejpam-3442	303	74	ĩ.	ĩ.	NOUN
ejpam-3442	303	75	(	(	PUNCT
ejpam-3442	303	76	4	4	NUM
ejpam-3442	303	77	)	)	PUNCT
ejpam-3442	303	78	for	for	ADP
ejpam-3442	303	79	every	every	DET
ejpam-3442	303	80	(	(	PUNCT
ejpam-3442	303	81	f	f	X
ejpam-3442	303	82	,	,	PUNCT
ejpam-3442	303	83	e	e	NOUN
ejpam-3442	303	84	)	)	PUNCT
ejpam-3442	303	85	∈	∈	PROPN
ejpam-3442	303	86	ss(x)e	ss(x)e	NOUN
ejpam-3442	303	87	,	,	PUNCT
ejpam-3442	303	88	(	(	PUNCT
ejpam-3442	303	89	f	f	X
ejpam-3442	303	90	,	,	PUNCT
ejpam-3442	303	91	e)−	e)−	PROPN
ejpam-3442	303	92	(	(	PUNCT
ejpam-3442	303	93	f	f	X
ejpam-3442	303	94	,	,	PUNCT
ejpam-3442	303	95	e)∗s	e)∗	VERB
ejpam-3442	303	96	∈	∈	PROPN
ejpam-3442	303	97	ĩ.	ĩ.	NOUN
ejpam-3442	303	98	(	(	PUNCT
ejpam-3442	303	99	5	5	NUM
ejpam-3442	303	100	)	)	PUNCT
ejpam-3442	303	101	for	for	ADP
ejpam-3442	303	102	every	every	DET
ejpam-3442	303	103	τ∗s	τ∗s	NUM
ejpam-3442	303	104	-	-	PUNCT
ejpam-3442	303	105	closed	closed	ADJ
ejpam-3442	303	106	soft	soft	ADJ
ejpam-3442	303	107	subset	subset	NOUN
ejpam-3442	303	108	(	(	PUNCT
ejpam-3442	303	109	f	f	X
ejpam-3442	303	110	,	,	PUNCT
ejpam-3442	303	111	e	e	NOUN
ejpam-3442	303	112	)	)	PUNCT
ejpam-3442	303	113	,	,	PUNCT
ejpam-3442	303	114	(	(	PUNCT
ejpam-3442	303	115	f	f	X
ejpam-3442	303	116	,	,	PUNCT
ejpam-3442	303	117	e)−	e)−	PROPN
ejpam-3442	303	118	(	(	PUNCT
ejpam-3442	303	119	f	f	X
ejpam-3442	303	120	,	,	PUNCT
ejpam-3442	303	121	e)∗s	e)∗	VERB
ejpam-3442	303	122	∈	∈	PROPN
ejpam-3442	303	123	ĩ.	ĩ.	NOUN
ejpam-3442	303	124	(	(	PUNCT
ejpam-3442	303	125	6	6	NUM
ejpam-3442	303	126	)	)	PUNCT
ejpam-3442	303	127	for	for	ADP
ejpam-3442	303	128	every	every	DET
ejpam-3442	303	129	(	(	PUNCT
ejpam-3442	303	130	f	f	X
ejpam-3442	303	131	,	,	PUNCT
ejpam-3442	303	132	e	e	NOUN
ejpam-3442	303	133	)	)	PUNCT
ejpam-3442	303	134	∈	∈	PROPN
ejpam-3442	304	1	ss(x)e	ss(x)e	NOUN
ejpam-3442	304	2	,	,	PUNCT
ejpam-3442	304	3	if	if	SCONJ
ejpam-3442	304	4	(	(	PUNCT
ejpam-3442	304	5	f	f	X
ejpam-3442	304	6	,	,	PUNCT
ejpam-3442	304	7	e	e	NOUN
ejpam-3442	304	8	)	)	PUNCT
ejpam-3442	304	9	contains	contain	VERB
ejpam-3442	304	10	no	no	DET
ejpam-3442	304	11	non	non	ADJ
ejpam-3442	304	12	-	-	ADJ
ejpam-3442	304	13	null	null	ADJ
ejpam-3442	304	14	soft	soft	ADJ
ejpam-3442	304	15	set	set	NOUN
ejpam-3442	304	16	(	(	PUNCT
ejpam-3442	304	17	g	g	NOUN
ejpam-3442	304	18	,	,	PUNCT
ejpam-3442	304	19	e	e	NOUN
ejpam-3442	304	20	)	)	PUNCT
ejpam-3442	304	21	with	with	ADP
ejpam-3442	304	22	(	(	PUNCT
ejpam-3442	304	23	g	g	NOUN
ejpam-3442	304	24	,	,	PUNCT
ejpam-3442	304	25	e)⊆̃(g	e)⊆̃(g	PROPN
ejpam-3442	304	26	,	,	PUNCT
ejpam-3442	304	27	e)∗s	e)∗s	PROPN
ejpam-3442	304	28	,	,	PUNCT
ejpam-3442	304	29	then	then	ADV
ejpam-3442	304	30	(	(	PUNCT
ejpam-3442	304	31	f	f	X
ejpam-3442	304	32	,	,	PUNCT
ejpam-3442	304	33	e	e	NOUN
ejpam-3442	304	34	)	)	PUNCT
ejpam-3442	304	35	∈	∈	PROPN
ejpam-3442	304	36	ĩ.	ĩ.	PROPN
ejpam-3442	304	37	proof	proof	NOUN
ejpam-3442	304	38	.	.	PUNCT
ejpam-3442	305	1	(	(	PUNCT
ejpam-3442	305	2	1	1	X
ejpam-3442	305	3	)	)	PUNCT
ejpam-3442	305	4	=	=	NOUN
ejpam-3442	305	5	⇒	⇒	NOUN
ejpam-3442	305	6	(	(	PUNCT
ejpam-3442	305	7	2	2	NUM
ejpam-3442	305	8	)	)	PUNCT
ejpam-3442	305	9	obvious	obvious	ADJ
ejpam-3442	305	10	from	from	ADP
ejpam-3442	305	11	definition	definition	NOUN
ejpam-3442	305	12	14	14	NUM
ejpam-3442	305	13	.	.	PUNCT
ejpam-3442	306	1	(	(	PUNCT
ejpam-3442	306	2	2	2	X
ejpam-3442	306	3	)	)	PUNCT
ejpam-3442	306	4	=	=	NOUN
ejpam-3442	306	5	⇒	⇒	NOUN
ejpam-3442	306	6	(	(	PUNCT
ejpam-3442	306	7	3	3	X
ejpam-3442	306	8	)	)	PUNCT
ejpam-3442	306	9	let	let	VERB
ejpam-3442	306	10	(	(	PUNCT
ejpam-3442	306	11	f	f	X
ejpam-3442	306	12	,	,	PUNCT
ejpam-3442	306	13	e	e	NOUN
ejpam-3442	306	14	)	)	PUNCT
ejpam-3442	306	15	∈	∈	PROPN
ejpam-3442	306	16	ss(x)e	ss(x)e	VERB
ejpam-3442	306	17	such	such	ADJ
ejpam-3442	306	18	that	that	SCONJ
ejpam-3442	306	19	(	(	PUNCT
ejpam-3442	306	20	f	f	X
ejpam-3442	306	21	,	,	PUNCT
ejpam-3442	306	22	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	306	23	,	,	PUNCT
ejpam-3442	306	24	e)∗s	e)∗s	PROPN
ejpam-3442	306	25	=	=	SYM
ejpam-3442	306	26	φ̃	φ̃	PROPN
ejpam-3442	306	27	and	and	CCONJ
ejpam-3442	306	28	xe∈̃(f	xe∈̃(f	PROPN
ejpam-3442	306	29	,	,	PUNCT
ejpam-3442	306	30	e	e	NOUN
ejpam-3442	306	31	)	)	PUNCT
ejpam-3442	306	32	.	.	PUNCT
ejpam-3442	307	1	then	then	ADV
ejpam-3442	307	2	,	,	PUNCT
ejpam-3442	307	3	xe˜6∈(f	xe˜6∈(f	PROPN
ejpam-3442	307	4	,	,	PUNCT
ejpam-3442	307	5	e)∗s	e)∗s	PROPN
ejpam-3442	307	6	and	and	CCONJ
ejpam-3442	307	7	thenoxe∩̃(f	thenoxe∩̃(f	NUM
ejpam-3442	307	8	,	,	PUNCT
ejpam-3442	307	9	e	e	NOUN
ejpam-3442	307	10	)	)	PUNCT
ejpam-3442	307	11	∈	∈	PROPN
ejpam-3442	307	12	ĩ	ĩ	PROPN
ejpam-3442	307	13	for	for	ADP
ejpam-3442	307	14	someoxe	someoxe	NOUN
ejpam-3442	307	15	∈	∈	PROPN
ejpam-3442	307	16	sos(x	sos(x	PROPN
ejpam-3442	307	17	)	)	PUNCT
ejpam-3442	307	18	.	.	PUNCT
ejpam-3442	308	1	therefore	therefore	ADV
ejpam-3442	308	2	,	,	PUNCT
ejpam-3442	308	3	(	(	PUNCT
ejpam-3442	308	4	f	f	X
ejpam-3442	308	5	,	,	PUNCT
ejpam-3442	308	6	e)⊆̃∪̃{oxe	e)⊆̃∪̃{oxe	PROPN
ejpam-3442	308	7	:	:	PUNCT
ejpam-3442	308	8	xe∈̃(f	xe∈̃(f	X
ejpam-3442	308	9	,	,	PUNCT
ejpam-3442	308	10	e	e	NOUN
ejpam-3442	308	11	)	)	PUNCT
ejpam-3442	308	12	and	and	CCONJ
ejpam-3442	308	13	oxe	oxe	PRON
ejpam-3442	308	14	∈	∈	PROPN
ejpam-3442	308	15	sos(x	sos(x	PROPN
ejpam-3442	308	16	)	)	PUNCT
ejpam-3442	308	17	}	}	PUNCT
ejpam-3442	308	18	.	.	PUNCT
ejpam-3442	309	1	by	by	ADP
ejpam-3442	309	2	(	(	PUNCT
ejpam-3442	309	3	2	2	NUM
ejpam-3442	309	4	)	)	PUNCT
ejpam-3442	309	5	,	,	PUNCT
ejpam-3442	309	6	(	(	PUNCT
ejpam-3442	309	7	f	f	X
ejpam-3442	309	8	,	,	PUNCT
ejpam-3442	309	9	e	e	NOUN
ejpam-3442	309	10	)	)	PUNCT
ejpam-3442	309	11	∈	∈	PROPN
ejpam-3442	309	12	ĩ.	ĩ.	NOUN
ejpam-3442	309	13	(	(	PUNCT
ejpam-3442	309	14	3	3	X
ejpam-3442	309	15	)	)	PUNCT
ejpam-3442	310	1	=	=	NOUN
ejpam-3442	310	2	⇒	⇒	NOUN
ejpam-3442	310	3	(	(	PUNCT
ejpam-3442	310	4	4	4	X
ejpam-3442	310	5	)	)	PUNCT
ejpam-3442	310	6	let	let	VERB
ejpam-3442	310	7	(	(	PUNCT
ejpam-3442	310	8	f	f	X
ejpam-3442	310	9	,	,	PUNCT
ejpam-3442	310	10	e	e	NOUN
ejpam-3442	310	11	)	)	PUNCT
ejpam-3442	310	12	∈	∈	PROPN
ejpam-3442	310	13	ss(x)e	ss(x)e	PROPN
ejpam-3442	310	14	.	.	PUNCT
ejpam-3442	311	1	since	since	SCONJ
ejpam-3442	311	2	(	(	PUNCT
ejpam-3442	311	3	(	(	PUNCT
ejpam-3442	311	4	f	f	X
ejpam-3442	311	5	,	,	PUNCT
ejpam-3442	311	6	e	e	NOUN
ejpam-3442	311	7	)	)	PUNCT
ejpam-3442	311	8	−	−	PROPN
ejpam-3442	311	9	(	(	PUNCT
ejpam-3442	311	10	f	f	X
ejpam-3442	311	11	,	,	PUNCT
ejpam-3442	311	12	e)∗s)∩̃((f	e)∗s)∩̃((f	PROPN
ejpam-3442	311	13	,	,	PUNCT
ejpam-3442	311	14	e	e	NOUN
ejpam-3442	311	15	)	)	PUNCT
ejpam-3442	311	16	−	−	PROPN
ejpam-3442	311	17	(	(	PUNCT
ejpam-3442	311	18	f	f	X
ejpam-3442	311	19	,	,	PUNCT
ejpam-3442	311	20	e)∗s)∗s	e)∗s)∗s	PROPN
ejpam-3442	311	21	=	=	SYM
ejpam-3442	311	22	(	(	PUNCT
ejpam-3442	311	23	(	(	PUNCT
ejpam-3442	311	24	f	f	X
ejpam-3442	311	25	,	,	PUNCT
ejpam-3442	311	26	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	311	27	,	,	PUNCT
ejpam-3442	311	28	e)∗	e)∗	PROPN
ejpam-3442	311	29	′	′	NUM
ejpam-3442	311	30	)	)	PUNCT
ejpam-3442	311	31	∩̃((f	∩̃((f	PROPN
ejpam-3442	311	32	,	,	PUNCT
ejpam-3442	311	33	e)−(f	e)−(f	NUM
ejpam-3442	311	34	,	,	PUNCT
ejpam-3442	311	35	e)∗s)∗s⊆̃((f	e)∗s)∗s⊆̃((f	VERB
ejpam-3442	311	36	,	,	PUNCT
ejpam-3442	311	37	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	311	38	,	,	PUNCT
ejpam-3442	311	39	e)∗	e)∗	PROPN
ejpam-3442	311	40	′	′	NUM
ejpam-3442	311	41	)	)	PUNCT
ejpam-3442	311	42	∩̃(f	∩̃(f	PUNCT
ejpam-3442	311	43	,	,	PUNCT
ejpam-3442	311	44	e)∗s	e)∗s	PROPN
ejpam-3442	311	45	=	=	SYM
ejpam-3442	311	46	φ̃.	φ̃.	PROPN
ejpam-3442	311	47	then	then	ADV
ejpam-3442	311	48	,	,	PUNCT
ejpam-3442	311	49	(	(	PUNCT
ejpam-3442	311	50	f	f	X
ejpam-3442	311	51	,	,	PUNCT
ejpam-3442	311	52	e)−(f	e)−(f	PROPN
ejpam-3442	311	53	,	,	PUNCT
ejpam-3442	311	54	e)∗s	e)∗s	PRON
ejpam-3442	311	55	∈	∈	PROPN
ejpam-3442	311	56	ĩ	ĩ	PROPN
ejpam-3442	311	57	by	by	ADP
ejpam-3442	311	58	(	(	PUNCT
ejpam-3442	311	59	3	3	NUM
ejpam-3442	311	60	)	)	PUNCT
ejpam-3442	311	61	.	.	PUNCT
ejpam-3442	312	1	(	(	PUNCT
ejpam-3442	312	2	4	4	X
ejpam-3442	312	3	)	)	PUNCT
ejpam-3442	312	4	=	=	NOUN
ejpam-3442	312	5	⇒	⇒	NOUN
ejpam-3442	312	6	(	(	PUNCT
ejpam-3442	312	7	5	5	NUM
ejpam-3442	312	8	)	)	PUNCT
ejpam-3442	312	9	immediate	immediate	ADJ
ejpam-3442	312	10	.	.	PUNCT
ejpam-3442	313	1	f.	f.	PROPN
ejpam-3442	313	2	a.	a.	PROPN
ejpam-3442	313	3	gharib	gharib	PROPN
ejpam-3442	313	4	,	,	PUNCT
ejpam-3442	313	5	a.	a.	PROPN
ejpam-3442	313	6	m.	m.	PROPN
ejpam-3442	313	7	abd	abd	PROPN
ejpam-3442	313	8	el	el	PROPN
ejpam-3442	313	9	-	-	PROPN
ejpam-3442	313	10	latif	latif	PROPN
ejpam-3442	313	11	/	/	SYM
ejpam-3442	313	12	eur	eur	PROPN
ejpam-3442	313	13	.	.	PUNCT
ejpam-3442	314	1	j.	j.	PROPN
ejpam-3442	314	2	pure	pure	PROPN
ejpam-3442	314	3	appl	appl	PROPN
ejpam-3442	314	4	.	.	PROPN
ejpam-3442	314	5	math	math	PROPN
ejpam-3442	314	6	,	,	PUNCT
ejpam-3442	314	7	12	12	NUM
ejpam-3442	314	8	(	(	PUNCT
ejpam-3442	314	9	3	3	NUM
ejpam-3442	314	10	)	)	PUNCT
ejpam-3442	314	11	(	(	PUNCT
ejpam-3442	314	12	2019	2019	NUM
ejpam-3442	314	13	)	)	PUNCT
ejpam-3442	314	14	,	,	PUNCT
ejpam-3442	314	15	857	857	NUM
ejpam-3442	314	16	-	-	SYM
ejpam-3442	314	17	869	869	NUM
ejpam-3442	314	18	866	866	NUM
ejpam-3442	314	19	(	(	PUNCT
ejpam-3442	314	20	5	5	NUM
ejpam-3442	314	21	)	)	PUNCT
ejpam-3442	315	1	=	=	NOUN
ejpam-3442	315	2	⇒	⇒	NOUN
ejpam-3442	315	3	(	(	PUNCT
ejpam-3442	315	4	1	1	X
ejpam-3442	315	5	)	)	PUNCT
ejpam-3442	315	6	let	let	VERB
ejpam-3442	315	7	(	(	PUNCT
ejpam-3442	315	8	f	f	X
ejpam-3442	315	9	,	,	PUNCT
ejpam-3442	315	10	e	e	NOUN
ejpam-3442	315	11	)	)	PUNCT
ejpam-3442	315	12	∈	∈	PROPN
ejpam-3442	315	13	ss(x)e	ss(x)e	PROPN
ejpam-3442	315	14	and	and	CCONJ
ejpam-3442	315	15	assume	assume	VERB
ejpam-3442	315	16	that	that	SCONJ
ejpam-3442	315	17	for	for	ADP
ejpam-3442	315	18	every	every	DET
ejpam-3442	315	19	xe∈̃(f	xe∈̃(f	PROPN
ejpam-3442	315	20	,	,	PUNCT
ejpam-3442	315	21	e	e	NOUN
ejpam-3442	315	22	)	)	PUNCT
ejpam-3442	315	23	there	there	PRON
ejpam-3442	315	24	exists	exist	VERB
ejpam-3442	315	25	oxe	oxe	PRON
ejpam-3442	315	26	∈	∈	PROPN
ejpam-3442	315	27	sos(x	sos(x	PROPN
ejpam-3442	315	28	)	)	PUNCT
ejpam-3442	315	29	such	such	ADJ
ejpam-3442	315	30	that	that	SCONJ
ejpam-3442	315	31	oxe∩̃(f	oxe∩̃(f	NUM
ejpam-3442	315	32	,	,	PUNCT
ejpam-3442	315	33	e	e	NOUN
ejpam-3442	315	34	)	)	PUNCT
ejpam-3442	315	35	∈	∈	PROPN
ejpam-3442	315	36	ĩ.	ĩ.	PROPN
ejpam-3442	315	37	then	then	ADV
ejpam-3442	315	38	,	,	PUNCT
ejpam-3442	315	39	xe˜6∈(f	xe˜6∈(f	PROPN
ejpam-3442	315	40	,	,	PUNCT
ejpam-3442	315	41	e)∗s	e)∗s	PROPN
ejpam-3442	315	42	.	.	PUNCT
ejpam-3442	316	1	hence	hence	ADV
ejpam-3442	316	2	,	,	PUNCT
ejpam-3442	316	3	(	(	PUNCT
ejpam-3442	316	4	(	(	PUNCT
ejpam-3442	316	5	f	f	X
ejpam-3442	316	6	,	,	PUNCT
ejpam-3442	316	7	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	316	8	,	,	PUNCT
ejpam-3442	316	9	e)∗s	e)∗s	PROPN
ejpam-3442	316	10	)	)	PUNCT
ejpam-3442	316	11	=	=	SYM
ejpam-3442	316	12	φ̃	φ̃	PROPN
ejpam-3442	316	13	and	and	CCONJ
ejpam-3442	316	14	since	since	SCONJ
ejpam-3442	316	15	(	(	PUNCT
ejpam-3442	316	16	f	f	X
ejpam-3442	316	17	,	,	PUNCT
ejpam-3442	316	18	e)∪̃(f	e)∪̃(f	PROPN
ejpam-3442	316	19	,	,	PUNCT
ejpam-3442	316	20	e)∗s	e)∗s	PROPN
ejpam-3442	316	21	is	be	AUX
ejpam-3442	316	22	τ∗s	τ∗s	NUM
ejpam-3442	316	23	-	-	PUNCT
ejpam-3442	316	24	closed	close	VERB
ejpam-3442	316	25	soft	soft	ADJ
ejpam-3442	316	26	,	,	PUNCT
ejpam-3442	316	27	we	we	PRON
ejpam-3442	316	28	have	have	VERB
ejpam-3442	316	29	(	(	PUNCT
ejpam-3442	316	30	(	(	PUNCT
ejpam-3442	316	31	f	f	X
ejpam-3442	316	32	,	,	PUNCT
ejpam-3442	316	33	e)∪̃(f	e)∪̃(f	PROPN
ejpam-3442	316	34	,	,	PUNCT
ejpam-3442	316	35	e)∗s)−((f	e)∗s)−((f	PROPN
ejpam-3442	316	36	,	,	PUNCT
ejpam-3442	316	37	e)∪̃(f	e)∪̃(f	PROPN
ejpam-3442	316	38	,	,	PUNCT
ejpam-3442	316	39	e)∗s)∗s	e)∗s)∗s	PROPN
ejpam-3442	316	40	∈	∈	PROPN
ejpam-3442	316	41	ĩ	ĩ	PROPN
ejpam-3442	316	42	by	by	ADP
ejpam-3442	316	43	(	(	PUNCT
ejpam-3442	316	44	5	5	NUM
ejpam-3442	316	45	)	)	PUNCT
ejpam-3442	316	46	.	.	PUNCT
ejpam-3442	317	1	hence	hence	ADV
ejpam-3442	317	2	,	,	PUNCT
ejpam-3442	317	3	(	(	PUNCT
ejpam-3442	317	4	(	(	PUNCT
ejpam-3442	317	5	f	f	X
ejpam-3442	317	6	,	,	PUNCT
ejpam-3442	317	7	e)∪̃(f	e)∪̃(f	PROPN
ejpam-3442	317	8	,	,	PUNCT
ejpam-3442	317	9	e)∗s)−((f	e)∗s)−((f	PROPN
ejpam-3442	317	10	,	,	PUNCT
ejpam-3442	317	11	e)∗s∪̃((f	e)∗s∪̃((f	PROPN
ejpam-3442	317	12	,	,	PUNCT
ejpam-3442	317	13	e)∗s)∗s	e)∗s)∗s	NUM
ejpam-3442	317	14	)	)	PUNCT
ejpam-3442	317	15	=	=	SYM
ejpam-3442	317	16	(	(	PUNCT
ejpam-3442	317	17	(	(	PUNCT
ejpam-3442	317	18	f	f	X
ejpam-3442	317	19	,	,	PUNCT
ejpam-3442	317	20	e)∪̃(f	e)∪̃(f	PROPN
ejpam-3442	317	21	,	,	PUNCT
ejpam-3442	317	22	e)∗s)−	e)∗s)−	PROPN
ejpam-3442	317	23	(	(	PUNCT
ejpam-3442	317	24	(	(	PUNCT
ejpam-3442	317	25	f	f	X
ejpam-3442	317	26	,	,	PUNCT
ejpam-3442	317	27	e)∗s	e)∗s	PROPN
ejpam-3442	317	28	)	)	PUNCT
ejpam-3442	317	29	=	=	PUNCT
ejpam-3442	317	30	(	(	PUNCT
ejpam-3442	317	31	f	f	X
ejpam-3442	317	32	,	,	PUNCT
ejpam-3442	317	33	e	e	NOUN
ejpam-3442	317	34	)	)	PUNCT
ejpam-3442	317	35	∈	∈	PROPN
ejpam-3442	317	36	ĩ	ĩ	PROPN
ejpam-3442	317	37	by	by	ADP
ejpam-3442	317	38	theorem	theorem	ADJ
ejpam-3442	317	39	2	2	NUM
ejpam-3442	317	40	(	(	PUNCT
ejpam-3442	317	41	5,6	5,6	NUM
ejpam-3442	317	42	)	)	PUNCT
ejpam-3442	317	43	.	.	PUNCT
ejpam-3442	318	1	therefore	therefore	ADV
ejpam-3442	318	2	,	,	PUNCT
ejpam-3442	318	3	τ	τ	PROPN
ejpam-3442	318	4	∼s	∼s	PROPN
ejpam-3442	318	5	ĩ.	ĩ.	PROPN
ejpam-3442	318	6	(	(	PUNCT
ejpam-3442	318	7	4	4	X
ejpam-3442	318	8	)	)	PUNCT
ejpam-3442	319	1	=	=	NOUN
ejpam-3442	319	2	⇒	⇒	NOUN
ejpam-3442	319	3	(	(	PUNCT
ejpam-3442	319	4	6	6	NUM
ejpam-3442	319	5	)	)	PUNCT
ejpam-3442	319	6	let	let	VERB
ejpam-3442	319	7	(	(	PUNCT
ejpam-3442	319	8	f	f	X
ejpam-3442	319	9	,	,	PUNCT
ejpam-3442	319	10	e	e	NOUN
ejpam-3442	319	11	)	)	PUNCT
ejpam-3442	319	12	∈	∈	PROPN
ejpam-3442	319	13	ss(x)e	ss(x)e	VERB
ejpam-3442	319	14	such	such	ADJ
ejpam-3442	319	15	that	that	SCONJ
ejpam-3442	319	16	(	(	PUNCT
ejpam-3442	319	17	f	f	X
ejpam-3442	319	18	,	,	PUNCT
ejpam-3442	319	19	e	e	NOUN
ejpam-3442	319	20	)	)	PUNCT
ejpam-3442	319	21	contains	contain	VERB
ejpam-3442	319	22	no	no	DET
ejpam-3442	319	23	non	non	ADJ
ejpam-3442	319	24	-	-	ADJ
ejpam-3442	319	25	null	null	ADJ
ejpam-3442	319	26	soft	soft	ADJ
ejpam-3442	319	27	set	set	NOUN
ejpam-3442	319	28	(	(	PUNCT
ejpam-3442	319	29	g	g	NOUN
ejpam-3442	319	30	,	,	PUNCT
ejpam-3442	319	31	e	e	NOUN
ejpam-3442	319	32	)	)	PUNCT
ejpam-3442	319	33	with	with	ADP
ejpam-3442	319	34	(	(	PUNCT
ejpam-3442	319	35	g	g	NOUN
ejpam-3442	319	36	,	,	PUNCT
ejpam-3442	319	37	e)⊆̃(g	e)⊆̃(g	PROPN
ejpam-3442	319	38	,	,	PUNCT
ejpam-3442	319	39	e)∗s	e)∗s	PROPN
ejpam-3442	319	40	.	.	PUNCT
ejpam-3442	320	1	since	since	SCONJ
ejpam-3442	320	2	(	(	PUNCT
ejpam-3442	320	3	f	f	X
ejpam-3442	320	4	,	,	PUNCT
ejpam-3442	320	5	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	320	6	,	,	PUNCT
ejpam-3442	320	7	e)∗s⊆̃(f	e)∗s⊆̃(f	PROPN
ejpam-3442	320	8	,	,	PUNCT
ejpam-3442	320	9	e)∗s	e)∗s	PROPN
ejpam-3442	320	10	=	=	SYM
ejpam-3442	320	11	(	(	PUNCT
ejpam-3442	320	12	(	(	PUNCT
ejpam-3442	320	13	f	f	X
ejpam-3442	320	14	,	,	PUNCT
ejpam-3442	320	15	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	320	16	,	,	PUNCT
ejpam-3442	320	17	e)∗s)∗s	e)∗s)∗s	PROPN
ejpam-3442	320	18	from	from	ADP
ejpam-3442	320	19	theorem	theorem	ADJ
ejpam-3442	320	20	6	6	NUM
ejpam-3442	320	21	(	(	PUNCT
ejpam-3442	320	22	3	3	NUM
ejpam-3442	320	23	)	)	PUNCT
ejpam-3442	320	24	.	.	PUNCT
ejpam-3442	321	1	it	it	PRON
ejpam-3442	321	2	follows	follow	VERB
ejpam-3442	321	3	,	,	PUNCT
ejpam-3442	321	4	(	(	PUNCT
ejpam-3442	321	5	f	f	X
ejpam-3442	321	6	,	,	PUNCT
ejpam-3442	321	7	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	321	8	,	,	PUNCT
ejpam-3442	321	9	e)∗s⊆̃((f	e)∗s⊆̃((f	NUM
ejpam-3442	321	10	,	,	PUNCT
ejpam-3442	321	11	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	321	12	,	,	PUNCT
ejpam-3442	321	13	e)∗s)∗s	e)∗s)∗s	PROPN
ejpam-3442	321	14	.	.	PUNCT
ejpam-3442	322	1	by	by	ADP
ejpam-3442	322	2	assumption	assumption	NOUN
ejpam-3442	322	3	,	,	PUNCT
ejpam-3442	322	4	(	(	PUNCT
ejpam-3442	322	5	f	f	X
ejpam-3442	322	6	,	,	PUNCT
ejpam-3442	322	7	e)∩̃(f	e)∩̃(f	PROPN
ejpam-3442	322	8	,	,	PUNCT
ejpam-3442	322	9	e)∗s	e)∗s	PROPN
ejpam-3442	322	10	=	=	SYM
ejpam-3442	322	11	φ̃.	φ̃.	PROPN
ejpam-3442	322	12	thus	thus	ADV
ejpam-3442	322	13	,	,	PUNCT
ejpam-3442	322	14	(	(	PUNCT
ejpam-3442	322	15	f	f	X
ejpam-3442	322	16	,	,	PUNCT
ejpam-3442	322	17	e	e	NOUN
ejpam-3442	322	18	)	)	PUNCT
ejpam-3442	322	19	=	=	SYM
ejpam-3442	322	20	(	(	PUNCT
ejpam-3442	322	21	f	f	X
ejpam-3442	322	22	,	,	PUNCT
ejpam-3442	322	23	e)−	e)−	PROPN
ejpam-3442	322	24	(	(	PUNCT
ejpam-3442	322	25	f	f	X
ejpam-3442	322	26	,	,	PUNCT
ejpam-3442	322	27	e)∗s	e)∗s	PRON
ejpam-3442	322	28	∈	∈	PROPN
ejpam-3442	322	29	ĩ	ĩ	PROPN
ejpam-3442	322	30	by	by	ADP
ejpam-3442	322	31	(	(	PUNCT
ejpam-3442	322	32	4	4	NUM
ejpam-3442	322	33	)	)	PUNCT
ejpam-3442	322	34	.	.	PUNCT
ejpam-3442	323	1	(	(	PUNCT
ejpam-3442	323	2	6	6	X
ejpam-3442	323	3	)	)	PUNCT
ejpam-3442	323	4	=	=	NOUN
ejpam-3442	323	5	⇒	⇒	NOUN
ejpam-3442	323	6	(	(	PUNCT
ejpam-3442	323	7	4	4	X
ejpam-3442	323	8	)	)	PUNCT
ejpam-3442	323	9	let	let	VERB
ejpam-3442	323	10	(	(	PUNCT
ejpam-3442	323	11	f	f	X
ejpam-3442	323	12	,	,	PUNCT
ejpam-3442	323	13	e	e	NOUN
ejpam-3442	323	14	)	)	PUNCT
ejpam-3442	323	15	∈	∈	PROPN
ejpam-3442	323	16	ss(x)e	ss(x)e	PROPN
ejpam-3442	323	17	.	.	PUNCT
ejpam-3442	324	1	since	since	SCONJ
ejpam-3442	324	2	(	(	PUNCT
ejpam-3442	324	3	(	(	PUNCT
ejpam-3442	324	4	f	f	X
ejpam-3442	324	5	,	,	PUNCT
ejpam-3442	324	6	e)−(f	e)−(f	PROPN
ejpam-3442	324	7	,	,	PUNCT
ejpam-3442	324	8	e)∗s)∩̃((f	e)∗s)∩̃((f	PROPN
ejpam-3442	324	9	,	,	PUNCT
ejpam-3442	324	10	e)−(f	e)−(f	NUM
ejpam-3442	324	11	,	,	PUNCT
ejpam-3442	324	12	e)∗s)∗s	e)∗s)∗s	PROPN
ejpam-3442	324	13	=	=	SYM
ejpam-3442	324	14	φ̃	φ̃	PROPN
ejpam-3442	324	15	and	and	CCONJ
ejpam-3442	324	16	(	(	PUNCT
ejpam-3442	324	17	f	f	X
ejpam-3442	324	18	,	,	PUNCT
ejpam-3442	324	19	e)−	e)−	PROPN
ejpam-3442	324	20	(	(	PUNCT
ejpam-3442	324	21	f	f	NOUN
ejpam-3442	324	22	,	,	PUNCT
ejpam-3442	324	23	e)∗s	e)∗s	PROPN
ejpam-3442	324	24	)	)	PUNCT
ejpam-3442	324	25	contains	contain	VERB
ejpam-3442	324	26	no	no	DET
ejpam-3442	324	27	non	non	ADJ
ejpam-3442	324	28	-	-	ADJ
ejpam-3442	324	29	null	null	ADJ
ejpam-3442	324	30	soft	soft	ADJ
ejpam-3442	324	31	set	set	NOUN
ejpam-3442	324	32	(	(	PUNCT
ejpam-3442	324	33	g	g	NOUN
ejpam-3442	324	34	,	,	PUNCT
ejpam-3442	324	35	e	e	NOUN
ejpam-3442	324	36	)	)	PUNCT
ejpam-3442	324	37	with	with	ADP
ejpam-3442	324	38	(	(	PUNCT
ejpam-3442	324	39	g	g	NOUN
ejpam-3442	324	40	,	,	PUNCT
ejpam-3442	324	41	e)⊆̃(g	e)⊆̃(g	PROPN
ejpam-3442	324	42	,	,	PUNCT
ejpam-3442	324	43	e)∗s	e)∗s	PROPN
ejpam-3442	324	44	.	.	PUNCT
ejpam-3442	325	1	hence	hence	ADV
ejpam-3442	325	2	,	,	PUNCT
ejpam-3442	325	3	(	(	PUNCT
ejpam-3442	325	4	f	f	X
ejpam-3442	325	5	,	,	PUNCT
ejpam-3442	325	6	e)−	e)−	PROPN
ejpam-3442	325	7	(	(	PUNCT
ejpam-3442	325	8	f	f	X
ejpam-3442	325	9	,	,	PUNCT
ejpam-3442	325	10	e)∗s	e)∗s	PRON
ejpam-3442	325	11	∈	∈	PROPN
ejpam-3442	325	12	ĩ	ĩ	PROPN
ejpam-3442	325	13	by	by	ADP
ejpam-3442	325	14	(	(	PUNCT
ejpam-3442	325	15	6	6	NUM
ejpam-3442	325	16	)	)	PUNCT
ejpam-3442	325	17	.	.	PUNCT
ejpam-3442	325	18	theorem	theorem	ADJ
ejpam-3442	325	19	8	8	NUM
ejpam-3442	325	20	.	.	PUNCT
ejpam-3442	326	1	if	if	SCONJ
ejpam-3442	326	2	(	(	PUNCT
ejpam-3442	326	3	x	x	X
ejpam-3442	326	4	,	,	PUNCT
ejpam-3442	326	5	τ	τ	PROPN
ejpam-3442	326	6	,	,	PUNCT
ejpam-3442	326	7	e	e	NOUN
ejpam-3442	326	8	)	)	PUNCT
ejpam-3442	326	9	is	be	AUX
ejpam-3442	326	10	a	a	DET
ejpam-3442	326	11	soft	soft	ADJ
ejpam-3442	326	12	topological	topological	ADJ
ejpam-3442	326	13	space	space	NOUN
ejpam-3442	326	14	,	,	PUNCT
ejpam-3442	326	15	ĩ	ĩ	PROPN
ejpam-3442	326	16	be	be	VERB
ejpam-3442	326	17	a	a	DET
ejpam-3442	326	18	soft	soft	ADJ
ejpam-3442	326	19	ideal	ideal	NOUN
ejpam-3442	326	20	over	over	ADP
ejpam-3442	326	21	x	x	PUNCT
ejpam-3442	326	22	with	with	ADP
ejpam-3442	326	23	the	the	DET
ejpam-3442	326	24	same	same	ADJ
ejpam-3442	326	25	set	set	NOUN
ejpam-3442	326	26	of	of	ADP
ejpam-3442	326	27	parameters	parameter	NOUN
ejpam-3442	326	28	e	e	NOUN
ejpam-3442	326	29	and	and	CCONJ
ejpam-3442	326	30	semi	semi	ADV
ejpam-3442	326	31	compatible	compatible	ADJ
ejpam-3442	326	32	with	with	ADP
ejpam-3442	326	33	τ	τ	PROPN
ejpam-3442	326	34	.	.	PUNCT
ejpam-3442	327	1	then	then	ADV
ejpam-3442	327	2	,	,	PUNCT
ejpam-3442	327	3	a	a	DET
ejpam-3442	327	4	soft	soft	ADJ
ejpam-3442	327	5	set	set	NOUN
ejpam-3442	327	6	is	be	AUX
ejpam-3442	327	7	τ∗s	τ∗s	NUM
ejpam-3442	327	8	-	-	PUNCT
ejpam-3442	327	9	closed	closed	ADJ
ejpam-3442	327	10	if	if	SCONJ
ejpam-3442	327	11	and	and	CCONJ
ejpam-3442	327	12	only	only	ADV
ejpam-3442	327	13	if	if	SCONJ
ejpam-3442	327	14	it	it	PRON
ejpam-3442	327	15	is	be	AUX
ejpam-3442	327	16	the	the	DET
ejpam-3442	327	17	union	union	NOUN
ejpam-3442	327	18	of	of	ADP
ejpam-3442	327	19	a	a	DET
ejpam-3442	327	20	τ	τ	PROPN
ejpam-3442	327	21	-semi	-semi	NOUN
ejpam-3442	327	22	closed	close	VERB
ejpam-3442	327	23	soft	soft	ADJ
ejpam-3442	327	24	set	set	NOUN
ejpam-3442	327	25	and	and	CCONJ
ejpam-3442	327	26	a	a	DET
ejpam-3442	327	27	soft	soft	ADJ
ejpam-3442	327	28	set	set	NOUN
ejpam-3442	327	29	in	in	ADP
ejpam-3442	327	30	ĩ.	ĩ.	PROPN
ejpam-3442	327	31	proof	proof	NOUN
ejpam-3442	327	32	.	.	PUNCT
ejpam-3442	328	1	let	let	VERB
ejpam-3442	328	2	(	(	PUNCT
ejpam-3442	328	3	f	f	X
ejpam-3442	328	4	,	,	PUNCT
ejpam-3442	328	5	e	e	NOUN
ejpam-3442	328	6	)	)	PUNCT
ejpam-3442	328	7	be	be	AUX
ejpam-3442	328	8	a	a	DET
ejpam-3442	328	9	τ∗s	τ∗s	NUM
ejpam-3442	328	10	-	-	PUNCT
ejpam-3442	328	11	closed	closed	ADJ
ejpam-3442	328	12	soft	soft	ADJ
ejpam-3442	328	13	set	set	NOUN
ejpam-3442	328	14	.	.	PUNCT
ejpam-3442	329	1	then	then	ADV
ejpam-3442	329	2	,	,	PUNCT
ejpam-3442	329	3	cl∗s(f	cl∗s(f	PROPN
ejpam-3442	329	4	,	,	PUNCT
ejpam-3442	329	5	e	e	NOUN
ejpam-3442	329	6	)	)	PUNCT
ejpam-3442	329	7	=	=	SYM
ejpam-3442	330	1	(	(	PUNCT
ejpam-3442	330	2	f	f	X
ejpam-3442	330	3	,	,	PUNCT
ejpam-3442	330	4	e	e	NOUN
ejpam-3442	330	5	)	)	PUNCT
ejpam-3442	330	6	=	=	SYM
ejpam-3442	330	7	(	(	PUNCT
ejpam-3442	330	8	f	f	X
ejpam-3442	330	9	,	,	PUNCT
ejpam-3442	330	10	e)∪̃(f	e)∪̃(f	PROPN
ejpam-3442	330	11	,	,	PUNCT
ejpam-3442	330	12	e)∗s	e)∗s	PROPN
ejpam-3442	330	13	=	=	SYM
ejpam-3442	330	14	(	(	PUNCT
ejpam-3442	330	15	f	f	X
ejpam-3442	330	16	,	,	PUNCT
ejpam-3442	330	17	e	e	NOUN
ejpam-3442	330	18	)	)	PUNCT
ejpam-3442	330	19	.	.	PUNCT
ejpam-3442	331	1	it	it	PRON
ejpam-3442	331	2	follows	follow	VERB
ejpam-3442	331	3	,	,	PUNCT
ejpam-3442	331	4	(	(	PUNCT
ejpam-3442	331	5	f	f	X
ejpam-3442	331	6	,	,	PUNCT
ejpam-3442	331	7	e)∗s⊆̃(f	e)∗s⊆̃(f	PROPN
ejpam-3442	331	8	,	,	PUNCT
ejpam-3442	331	9	e	e	NOUN
ejpam-3442	331	10	)	)	PUNCT
ejpam-3442	331	11	.	.	PUNCT
ejpam-3442	332	1	hence	hence	ADV
ejpam-3442	332	2	,	,	PUNCT
ejpam-3442	332	3	(	(	PUNCT
ejpam-3442	332	4	f	f	X
ejpam-3442	332	5	,	,	PUNCT
ejpam-3442	332	6	e	e	NOUN
ejpam-3442	332	7	)	)	PUNCT
ejpam-3442	332	8	=	=	SYM
ejpam-3442	332	9	(	(	PUNCT
ejpam-3442	332	10	(	(	PUNCT
ejpam-3442	332	11	f	f	X
ejpam-3442	332	12	,	,	PUNCT
ejpam-3442	332	13	e	e	NOUN
ejpam-3442	332	14	)	)	PUNCT
ejpam-3442	332	15	−	−	PROPN
ejpam-3442	332	16	(	(	PUNCT
ejpam-3442	332	17	f	f	X
ejpam-3442	332	18	,	,	PUNCT
ejpam-3442	332	19	e)∗s)∪̃(f	e)∗s)∪̃(f	PROPN
ejpam-3442	332	20	,	,	PUNCT
ejpam-3442	332	21	e)∗s	e)∗s	PROPN
ejpam-3442	332	22	,	,	PUNCT
ejpam-3442	332	23	where	where	SCONJ
ejpam-3442	332	24	(	(	PUNCT
ejpam-3442	332	25	f	f	X
ejpam-3442	332	26	,	,	PUNCT
ejpam-3442	332	27	e	e	NOUN
ejpam-3442	332	28	)	)	PUNCT
ejpam-3442	332	29	−	−	PROPN
ejpam-3442	333	1	(	(	PUNCT
ejpam-3442	333	2	f	f	X
ejpam-3442	333	3	,	,	PUNCT
ejpam-3442	333	4	e)∗s	e)∗s	PRON
ejpam-3442	333	5	∈	∈	PROPN
ejpam-3442	333	6	ĩ	ĩ	PROPN
ejpam-3442	333	7	from	from	ADP
ejpam-3442	333	8	theorem	theorem	ADJ
ejpam-3442	333	9	7	7	NUM
ejpam-3442	333	10	and	and	CCONJ
ejpam-3442	333	11	(	(	PUNCT
ejpam-3442	333	12	f	f	X
ejpam-3442	333	13	,	,	PUNCT
ejpam-3442	333	14	e)∗s	e)∗s	PROPN
ejpam-3442	333	15	is	be	AUX
ejpam-3442	333	16	τ	τ	PROPN
ejpam-3442	333	17	-semi	-semi	NOUN
ejpam-3442	333	18	closed	close	VERB
ejpam-3442	333	19	soft	soft	ADJ
ejpam-3442	333	20	from	from	ADP
ejpam-3442	333	21	corollary	corollary	ADJ
ejpam-3442	333	22	1	1	NUM
ejpam-3442	333	23	.	.	PUNCT
ejpam-3442	334	1	conversely	conversely	ADV
ejpam-3442	334	2	,	,	PUNCT
ejpam-3442	334	3	let	let	VERB
ejpam-3442	334	4	(	(	PUNCT
ejpam-3442	334	5	f	f	X
ejpam-3442	334	6	,	,	PUNCT
ejpam-3442	334	7	e	e	NOUN
ejpam-3442	334	8	)	)	PUNCT
ejpam-3442	334	9	=	=	SYM
ejpam-3442	334	10	(	(	PUNCT
ejpam-3442	334	11	g	g	NOUN
ejpam-3442	334	12	,	,	PUNCT
ejpam-3442	334	13	e)∪̃(i	e)∪̃(i	NOUN
ejpam-3442	334	14	,	,	PUNCT
ejpam-3442	334	15	e	e	NOUN
ejpam-3442	334	16	)	)	PUNCT
ejpam-3442	334	17	,	,	PUNCT
ejpam-3442	334	18	for	for	ADP
ejpam-3442	334	19	some	some	DET
ejpam-3442	334	20	τ	τ	NUM
ejpam-3442	334	21	-semi	-semi	NOUN
ejpam-3442	334	22	closed	close	VERB
ejpam-3442	334	23	soft	soft	ADJ
ejpam-3442	334	24	set	set	NOUN
ejpam-3442	334	25	(	(	PUNCT
ejpam-3442	334	26	g	g	NOUN
ejpam-3442	334	27	,	,	PUNCT
ejpam-3442	334	28	e	e	NOUN
ejpam-3442	334	29	)	)	PUNCT
ejpam-3442	334	30	and	and	CCONJ
ejpam-3442	334	31	(	(	PUNCT
ejpam-3442	334	32	i	i	NOUN
ejpam-3442	334	33	,	,	PUNCT
ejpam-3442	334	34	e	e	NOUN
ejpam-3442	334	35	)	)	PUNCT
ejpam-3442	334	36	∈	∈	PROPN
ejpam-3442	334	37	ĩ.	ĩ.	PROPN
ejpam-3442	334	38	then	then	ADV
ejpam-3442	334	39	,	,	PUNCT
ejpam-3442	334	40	(	(	PUNCT
ejpam-3442	334	41	f	f	X
ejpam-3442	334	42	,	,	PUNCT
ejpam-3442	334	43	e)∗s	e)∗s	PROPN
ejpam-3442	334	44	=	=	SYM
ejpam-3442	334	45	(	(	PUNCT
ejpam-3442	334	46	(	(	PUNCT
ejpam-3442	334	47	g	g	NOUN
ejpam-3442	334	48	,	,	PUNCT
ejpam-3442	334	49	e	e	NOUN
ejpam-3442	334	50	)	)	PUNCT
ejpam-3442	334	51	−	−	PROPN
ejpam-3442	335	1	(	(	PUNCT
ejpam-3442	335	2	i	i	NOUN
ejpam-3442	335	3	,	,	PUNCT
ejpam-3442	335	4	e))∗s	e))∗s	NOUN
ejpam-3442	335	5	=	=	SYM
ejpam-3442	335	6	(	(	PUNCT
ejpam-3442	335	7	g	g	NOUN
ejpam-3442	335	8	,	,	PUNCT
ejpam-3442	335	9	e)∗s⊆̃scl(g	e)∗s⊆̃scl(g	NOUN
ejpam-3442	335	10	,	,	PUNCT
ejpam-3442	335	11	e	e	NOUN
ejpam-3442	335	12	)	)	PUNCT
ejpam-3442	335	13	=	=	SYM
ejpam-3442	335	14	(	(	PUNCT
ejpam-3442	335	15	g	g	NOUN
ejpam-3442	335	16	,	,	PUNCT
ejpam-3442	335	17	e)⊆̃(f	e)⊆̃(f	PROPN
ejpam-3442	335	18	,	,	PUNCT
ejpam-3442	335	19	e	e	NOUN
ejpam-3442	335	20	)	)	PUNCT
ejpam-3442	335	21	from	from	ADP
ejpam-3442	335	22	theorem	theorem	ADJ
ejpam-3442	335	23	2	2	NUM
ejpam-3442	335	24	(	(	PUNCT
ejpam-3442	335	25	4,12	4,12	NOUN
ejpam-3442	335	26	)	)	PUNCT
ejpam-3442	335	27	.	.	PUNCT
ejpam-3442	336	1	it	it	PRON
ejpam-3442	336	2	follows	follow	VERB
ejpam-3442	336	3	,	,	PUNCT
ejpam-3442	336	4	(	(	PUNCT
ejpam-3442	336	5	f	f	X
ejpam-3442	336	6	,	,	PUNCT
ejpam-3442	336	7	e)∪̃(f	e)∪̃(f	PROPN
ejpam-3442	336	8	,	,	PUNCT
ejpam-3442	336	9	e)∗s	e)∗s	PROPN
ejpam-3442	336	10	=	=	SYM
ejpam-3442	336	11	(	(	PUNCT
ejpam-3442	336	12	f	f	X
ejpam-3442	336	13	,	,	PUNCT
ejpam-3442	336	14	e	e	NOUN
ejpam-3442	336	15	)	)	PUNCT
ejpam-3442	336	16	.	.	PUNCT
ejpam-3442	337	1	hence	hence	ADV
ejpam-3442	337	2	,	,	PUNCT
ejpam-3442	337	3	cl∗s(f	cl∗s(f	PROPN
ejpam-3442	337	4	,	,	PUNCT
ejpam-3442	337	5	e	e	NOUN
ejpam-3442	337	6	)	)	PUNCT
ejpam-3442	337	7	=	=	SYM
ejpam-3442	337	8	(	(	PUNCT
ejpam-3442	337	9	f	f	X
ejpam-3442	337	10	,	,	PUNCT
ejpam-3442	337	11	e	e	NOUN
ejpam-3442	337	12	)	)	PUNCT
ejpam-3442	337	13	.	.	PUNCT
ejpam-3442	338	1	therefore	therefore	ADV
ejpam-3442	338	2	,	,	PUNCT
ejpam-3442	338	3	(	(	PUNCT
ejpam-3442	338	4	f	f	X
ejpam-3442	338	5	,	,	PUNCT
ejpam-3442	338	6	e	e	NOUN
ejpam-3442	338	7	)	)	PUNCT
ejpam-3442	338	8	is	be	AUX
ejpam-3442	338	9	τ∗s	τ∗s	NUM
ejpam-3442	338	10	-	-	PUNCT
ejpam-3442	338	11	closed	closed	ADJ
ejpam-3442	338	12	soft	soft	ADJ
ejpam-3442	338	13	.	.	PUNCT
ejpam-3442	339	1	definition	definition	NOUN
ejpam-3442	339	2	15	15	NUM
ejpam-3442	339	3	.	.	PUNCT
ejpam-3442	340	1	[	[	X
ejpam-3442	340	2	19	19	NUM
ejpam-3442	340	3	]	]	PUNCT
ejpam-3442	340	4	a	a	DET
ejpam-3442	340	5	soft	soft	ADJ
ejpam-3442	340	6	topological	topological	ADJ
ejpam-3442	340	7	space	space	NOUN
ejpam-3442	340	8	(	(	PUNCT
ejpam-3442	340	9	x	x	X
ejpam-3442	340	10	,	,	PUNCT
ejpam-3442	340	11	τ	τ	PROPN
ejpam-3442	340	12	,	,	PUNCT
ejpam-3442	340	13	e	e	NOUN
ejpam-3442	340	14	)	)	PUNCT
ejpam-3442	340	15	is	be	AUX
ejpam-3442	340	16	called	call	VERB
ejpam-3442	340	17	a	a	DET
ejpam-3442	340	18	soft	soft	ADJ
ejpam-3442	340	19	semi	semi	ADJ
ejpam-3442	340	20	compact	compact	ADJ
ejpam-3442	340	21	space	space	NOUN
ejpam-3442	340	22	if	if	SCONJ
ejpam-3442	340	23	each	each	DET
ejpam-3442	340	24	semi	semi	ADV
ejpam-3442	340	25	open	open	VERB
ejpam-3442	340	26	soft	soft	ADJ
ejpam-3442	340	27	cover	cover	NOUN
ejpam-3442	340	28	of	of	ADP
ejpam-3442	340	29	x̃	x̃	PROPN
ejpam-3442	340	30	has	have	VERB
ejpam-3442	340	31	a	a	DET
ejpam-3442	340	32	finite	finite	ADJ
ejpam-3442	340	33	soft	soft	ADJ
ejpam-3442	340	34	subcover	subcover	PROPN
ejpam-3442	340	35	.	.	PUNCT
ejpam-3442	341	1	theorem	theorem	VERB
ejpam-3442	341	2	9	9	NUM
ejpam-3442	341	3	.	.	PUNCT
ejpam-3442	342	1	[	[	X
ejpam-3442	342	2	19	19	NUM
ejpam-3442	342	3	]	]	X
ejpam-3442	342	4	each	each	DET
ejpam-3442	342	5	semi	semi	ADV
ejpam-3442	342	6	closed	close	VERB
ejpam-3442	342	7	soft	soft	ADJ
ejpam-3442	342	8	subspace	subspace	NOUN
ejpam-3442	342	9	of	of	ADP
ejpam-3442	342	10	a	a	DET
ejpam-3442	342	11	soft	soft	ADJ
ejpam-3442	342	12	semi	semi	ADJ
ejpam-3442	342	13	compact	compact	ADJ
ejpam-3442	342	14	topological	topological	ADJ
ejpam-3442	342	15	space	space	NOUN
ejpam-3442	342	16	is	be	AUX
ejpam-3442	342	17	a	a	DET
ejpam-3442	342	18	soft	soft	ADJ
ejpam-3442	342	19	semi	semi	ADJ
ejpam-3442	342	20	compact	compact	ADJ
ejpam-3442	342	21	.	.	PUNCT
ejpam-3442	343	1	theorem	theorem	ADJ
ejpam-3442	343	2	10	10	NUM
ejpam-3442	343	3	.	.	PUNCT
ejpam-3442	344	1	let	let	VERB
ejpam-3442	344	2	(	(	PUNCT
ejpam-3442	344	3	x	x	X
ejpam-3442	344	4	,	,	PUNCT
ejpam-3442	344	5	τ	τ	PROPN
ejpam-3442	344	6	,	,	PUNCT
ejpam-3442	344	7	e	e	NOUN
ejpam-3442	344	8	)	)	PUNCT
ejpam-3442	344	9	be	be	AUX
ejpam-3442	344	10	a	a	DET
ejpam-3442	344	11	soft	soft	ADJ
ejpam-3442	344	12	semi	semi	ADJ
ejpam-3442	344	13	compact	compact	ADJ
ejpam-3442	344	14	space	space	NOUN
ejpam-3442	344	15	in	in	ADP
ejpam-3442	344	16	which	which	PRON
ejpam-3442	344	17	every	every	DET
ejpam-3442	344	18	soft	soft	ADJ
ejpam-3442	344	19	subset	subset	NOUN
ejpam-3442	344	20	of	of	ADP
ejpam-3442	344	21	x̃	x̃	PROPN
ejpam-3442	344	22	is	be	AUX
ejpam-3442	344	23	a	a	DET
ejpam-3442	344	24	semi	semi	ADV
ejpam-3442	344	25	closed	closed	ADJ
ejpam-3442	344	26	soft	soft	ADJ
ejpam-3442	344	27	and	and	CCONJ
ejpam-3442	344	28	ĩ	ĩ	PROPN
ejpam-3442	344	29	be	be	VERB
ejpam-3442	344	30	a	a	DET
ejpam-3442	344	31	soft	soft	ADJ
ejpam-3442	344	32	ideal	ideal	NOUN
ejpam-3442	344	33	over	over	ADP
ejpam-3442	344	34	x	x	PUNCT
ejpam-3442	344	35	with	with	ADP
ejpam-3442	344	36	the	the	DET
ejpam-3442	344	37	same	same	ADJ
ejpam-3442	344	38	set	set	NOUN
ejpam-3442	344	39	of	of	ADP
ejpam-3442	344	40	parameters	parameter	NOUN
ejpam-3442	345	1	e.	e.	PROPN
ejpam-3442	345	2	then	then	ADV
ejpam-3442	345	3	,	,	PUNCT
ejpam-3442	345	4	τ	τ	PROPN
ejpam-3442	345	5	∼s	∼s	NUM
ejpam-3442	345	6	ĩ.	ĩ.	NOUN
ejpam-3442	345	7	proof	proof	NOUN
ejpam-3442	345	8	.	.	PUNCT
ejpam-3442	346	1	let	let	AUX
ejpam-3442	346	2	(	(	PUNCT
ejpam-3442	346	3	f	f	X
ejpam-3442	346	4	,	,	PUNCT
ejpam-3442	346	5	e	e	NOUN
ejpam-3442	346	6	)	)	PUNCT
ejpam-3442	346	7	be	be	AUX
ejpam-3442	346	8	a	a	DET
ejpam-3442	346	9	soft	soft	ADJ
ejpam-3442	346	10	subset	subset	NOUN
ejpam-3442	346	11	of	of	ADP
ejpam-3442	346	12	x̃.	x̃.	PROPN
ejpam-3442	346	13	assume	assume	VERB
ejpam-3442	346	14	that	that	SCONJ
ejpam-3442	346	15	,	,	PUNCT
ejpam-3442	346	16	for	for	ADP
ejpam-3442	346	17	each	each	DET
ejpam-3442	346	18	xe∈̃(f	xe∈̃(f	PROPN
ejpam-3442	346	19	,	,	PUNCT
ejpam-3442	346	20	e	e	NOUN
ejpam-3442	346	21	)	)	PUNCT
ejpam-3442	346	22	,	,	PUNCT
ejpam-3442	346	23	there	there	PRON
ejpam-3442	346	24	exists	exist	VERB
ejpam-3442	346	25	a	a	DET
ejpam-3442	346	26	semi	semi	ADJ
ejpam-3442	346	27	open	open	ADJ
ejpam-3442	346	28	soft	soft	ADJ
ejpam-3442	346	29	set	set	NOUN
ejpam-3442	346	30	oxe	oxe	PRON
ejpam-3442	346	31	such	such	ADJ
ejpam-3442	346	32	that	that	PRON
ejpam-3442	346	33	oxe∩̃(f	oxe∩̃(f	NUM
ejpam-3442	346	34	,	,	PUNCT
ejpam-3442	346	35	e	e	NOUN
ejpam-3442	346	36	)	)	PUNCT
ejpam-3442	346	37	∈	∈	PROPN
ejpam-3442	346	38	ĩ.	ĩ.	PROPN
ejpam-3442	346	39	then	then	ADV
ejpam-3442	346	40	,	,	PUNCT
ejpam-3442	346	41	(	(	PUNCT
ejpam-3442	346	42	f	f	X
ejpam-3442	346	43	,	,	PUNCT
ejpam-3442	346	44	e)⊆̃∪̃{oxe	e)⊆̃∪̃{oxe	PROPN
ejpam-3442	346	45	:	:	PUNCT
ejpam-3442	346	46	xe∈̃(f	xe∈̃(f	X
ejpam-3442	346	47	,	,	PUNCT
ejpam-3442	346	48	e	e	NOUN
ejpam-3442	346	49	)	)	PUNCT
ejpam-3442	346	50	and	and	CCONJ
ejpam-3442	346	51	oxe	oxe	PRON
ejpam-3442	346	52	∈	∈	PROPN
ejpam-3442	346	53	sos(x	sos(x	PROPN
ejpam-3442	346	54	)	)	PUNCT
ejpam-3442	346	55	}	}	PUNCT
ejpam-3442	346	56	.	.	PUNCT
ejpam-3442	347	1	it	it	PRON
ejpam-3442	347	2	follows	follow	VERB
ejpam-3442	347	3	,	,	PUNCT
ejpam-3442	347	4	the	the	DET
ejpam-3442	347	5	family	family	NOUN
ejpam-3442	347	6	∪̃{oxe	∪̃{oxe	PROPN
ejpam-3442	347	7	:	:	PUNCT
ejpam-3442	347	8	xe∈̃(f	xe∈̃(f	X
ejpam-3442	347	9	,	,	PUNCT
ejpam-3442	347	10	e	e	NOUN
ejpam-3442	347	11	)	)	PUNCT
ejpam-3442	347	12	}	}	PUNCT
ejpam-3442	347	13	is	be	AUX
ejpam-3442	347	14	a	a	DET
ejpam-3442	347	15	semi	semi	ADJ
ejpam-3442	347	16	open	open	ADJ
ejpam-3442	347	17	soft	soft	ADJ
ejpam-3442	347	18	cover	cover	NOUN
ejpam-3442	347	19	of	of	ADP
ejpam-3442	347	20	(	(	PUNCT
ejpam-3442	347	21	f	f	X
ejpam-3442	347	22	,	,	PUNCT
ejpam-3442	347	23	e	e	NOUN
ejpam-3442	347	24	)	)	PUNCT
ejpam-3442	347	25	.	.	PUNCT
ejpam-3442	348	1	by	by	ADP
ejpam-3442	348	2	assumption	assumption	NOUN
ejpam-3442	348	3	,	,	PUNCT
ejpam-3442	348	4	(	(	PUNCT
ejpam-3442	348	5	f	f	X
ejpam-3442	348	6	,	,	PUNCT
ejpam-3442	348	7	e	e	NOUN
ejpam-3442	348	8	)	)	PUNCT
ejpam-3442	348	9	is	be	AUX
ejpam-3442	348	10	a	a	DET
ejpam-3442	348	11	semi	semi	ADV
ejpam-3442	348	12	closed	closed	ADJ
ejpam-3442	348	13	soft	soft	ADJ
ejpam-3442	348	14	set	set	NOUN
ejpam-3442	348	15	.	.	PUNCT
ejpam-3442	349	1	by	by	ADP
ejpam-3442	349	2	theorem	theorem	NOUN
ejpam-3442	349	3	9	9	NUM
ejpam-3442	349	4	,	,	PUNCT
ejpam-3442	349	5	(	(	PUNCT
ejpam-3442	349	6	f	f	X
ejpam-3442	349	7	,	,	PUNCT
ejpam-3442	349	8	e	e	NOUN
ejpam-3442	349	9	)	)	PUNCT
ejpam-3442	349	10	is	be	AUX
ejpam-3442	349	11	a	a	DET
ejpam-3442	349	12	soft	soft	ADJ
ejpam-3442	349	13	semi	semi	ADJ
ejpam-3442	349	14	compact	compact	ADJ
ejpam-3442	349	15	.	.	PUNCT
ejpam-3442	350	1	hence	hence	ADV
ejpam-3442	350	2	,	,	PUNCT
ejpam-3442	350	3	there	there	PRON
ejpam-3442	350	4	exist	exist	VERB
ejpam-3442	350	5	a	a	DET
ejpam-3442	350	6	finite	finite	ADJ
ejpam-3442	350	7	number	number	NOUN
ejpam-3442	350	8	of	of	ADP
ejpam-3442	350	9	soft	soft	ADJ
ejpam-3442	350	10	points	point	NOUN
ejpam-3442	350	11	,	,	PUNCT
ejpam-3442	350	12	say	say	VERB
ejpam-3442	350	13	,	,	PUNCT
ejpam-3442	350	14	x1e1	x1e1	AUX
ejpam-3442	350	15	,	,	PUNCT
ejpam-3442	350	16	x2e2	x2e2	PROPN
ejpam-3442	350	17	,	,	PUNCT
ejpam-3442	350	18	...	...	PUNCT
ejpam-3442	350	19	,	,	PUNCT
ejpam-3442	350	20	xnen	xnen	PROPN
ejpam-3442	350	21	in	in	ADP
ejpam-3442	350	22	(	(	PUNCT
ejpam-3442	350	23	f	f	X
ejpam-3442	350	24	,	,	PUNCT
ejpam-3442	350	25	e	e	NOUN
ejpam-3442	350	26	)	)	PUNCT
ejpam-3442	350	27	such	such	ADJ
ejpam-3442	350	28	that	that	SCONJ
ejpam-3442	350	29	(	(	PUNCT
ejpam-3442	350	30	f	f	X
ejpam-3442	350	31	,	,	PUNCT
ejpam-3442	350	32	e)⊆̃∪̃ni=1oxiei	e)⊆̃∪̃ni=1oxiei	PROPN
ejpam-3442	350	33	and	and	CCONJ
ejpam-3442	350	34	hence	hence	ADV
ejpam-3442	350	35	(	(	PUNCT
ejpam-3442	350	36	f	f	X
ejpam-3442	350	37	,	,	PUNCT
ejpam-3442	350	38	e	e	NOUN
ejpam-3442	350	39	)	)	PUNCT
ejpam-3442	350	40	=	=	SYM
ejpam-3442	350	41	(	(	PUNCT
ejpam-3442	350	42	f	f	X
ejpam-3442	350	43	,	,	PUNCT
ejpam-3442	350	44	e)∩̃[∪̃ni=1oxiei	e)∩̃[∪̃ni=1oxiei	X
ejpam-3442	350	45	]	]	PUNCT
ejpam-3442	351	1	=	=	SYM
ejpam-3442	351	2	∪̃ni=1[(f	∪̃ni=1[(f	PROPN
ejpam-3442	351	3	,	,	PUNCT
ejpam-3442	351	4	e)∩̃oxiei	e)∩̃oxiei	X
ejpam-3442	351	5	]	]	PUNCT
ejpam-3442	351	6	.	.	PUNCT
ejpam-3442	352	1	since	since	SCONJ
ejpam-3442	352	2	oxiei	oxiei	ADV
ejpam-3442	352	3	∩̃(f	∩̃(f	NOUN
ejpam-3442	352	4	,	,	PUNCT
ejpam-3442	352	5	e	e	X
ejpam-3442	352	6	)	)	PUNCT
ejpam-3442	352	7	∈	∈	PROPN
ejpam-3442	352	8	ĩ	ĩ	PROPN
ejpam-3442	352	9	for	for	ADP
ejpam-3442	352	10	each	each	DET
ejpam-3442	352	11	i	i	PRON
ejpam-3442	352	12	,	,	PUNCT
ejpam-3442	352	13	(	(	PUNCT
ejpam-3442	352	14	f	f	X
ejpam-3442	352	15	,	,	PUNCT
ejpam-3442	352	16	e	e	NOUN
ejpam-3442	352	17	)	)	PUNCT
ejpam-3442	352	18	∈	∈	PROPN
ejpam-3442	352	19	ĩ.	ĩ.	PROPN
ejpam-3442	352	20	therefore	therefore	ADV
ejpam-3442	352	21	,	,	PUNCT
ejpam-3442	352	22	τ	τ	PROPN
ejpam-3442	353	1	∼s	∼s	NUM
ejpam-3442	353	2	ĩ.	ĩ.	PROPN
ejpam-3442	353	3	references	reference	VERB
ejpam-3442	353	4	867	867	NUM
ejpam-3442	353	5	5	5	NUM
ejpam-3442	353	6	.	.	PUNCT
ejpam-3442	353	7	conclusion	conclusion	NOUN
ejpam-3442	353	8	in	in	ADP
ejpam-3442	353	9	this	this	DET
ejpam-3442	353	10	paper	paper	NOUN
ejpam-3442	353	11	,	,	PUNCT
ejpam-3442	353	12	we	we	PRON
ejpam-3442	353	13	will	will	AUX
ejpam-3442	353	14	introduce	introduce	VERB
ejpam-3442	353	15	and	and	CCONJ
ejpam-3442	353	16	study	study	VERB
ejpam-3442	353	17	two	two	NUM
ejpam-3442	353	18	different	different	ADJ
ejpam-3442	353	19	notions	notion	NOUN
ejpam-3442	353	20	via	via	ADP
ejpam-3442	353	21	soft	soft	ADJ
ejpam-3442	353	22	ideals	ideal	NOUN
ejpam-3442	353	23	namely	namely	ADV
ejpam-3442	353	24	,	,	PUNCT
ejpam-3442	353	25	soft	soft	ADJ
ejpam-3442	353	26	semi	semi	ADJ
ejpam-3442	353	27	local	local	ADJ
ejpam-3442	353	28	function	function	NOUN
ejpam-3442	353	29	and	and	CCONJ
ejpam-3442	353	30	soft	soft	ADJ
ejpam-3442	353	31	semi	semi	ADJ
ejpam-3442	353	32	compatibility	compatibility	NOUN
ejpam-3442	353	33	of	of	ADP
ejpam-3442	353	34	τ	τ	PROPN
ejpam-3442	353	35	with	with	ADP
ejpam-3442	353	36	ĩ	ĩ	PROPN
ejpam-3442	353	37	and	and	CCONJ
ejpam-3442	353	38	investigate	investigate	VERB
ejpam-3442	353	39	their	their	PRON
ejpam-3442	353	40	relationships	relationship	NOUN
ejpam-3442	353	41	with	with	ADP
ejpam-3442	353	42	other	other	ADJ
ejpam-3442	353	43	types	type	NOUN
ejpam-3442	353	44	of	of	ADP
ejpam-3442	353	45	similar	similar	ADJ
ejpam-3442	353	46	operators	operator	NOUN
ejpam-3442	353	47	.	.	PUNCT
ejpam-3442	354	1	some	some	DET
ejpam-3442	354	2	properties	property	NOUN
ejpam-3442	354	3	and	and	CCONJ
ejpam-3442	354	4	characterizations	characterization	NOUN
ejpam-3442	354	5	of	of	ADP
ejpam-3442	354	6	soft	soft	ADJ
ejpam-3442	354	7	semi	semi	ADJ
ejpam-3442	354	8	local	local	ADJ
ejpam-3442	354	9	function	function	NOUN
ejpam-3442	354	10	are	be	AUX
ejpam-3442	354	11	explored	explore	VERB
ejpam-3442	354	12	.	.	PUNCT
ejpam-3442	355	1	in	in	ADP
ejpam-3442	355	2	future	future	NOUN
ejpam-3442	355	3	,	,	PUNCT
ejpam-3442	355	4	we	we	PRON
ejpam-3442	355	5	will	will	AUX
ejpam-3442	355	6	introduce	introduce	VERB
ejpam-3442	355	7	the	the	DET
ejpam-3442	355	8	notions	notion	NOUN
ejpam-3442	355	9	of	of	ADP
ejpam-3442	355	10	soft	soft	ADJ
ejpam-3442	355	11	θ	θ	NOUN
ejpam-3442	355	12	-	-	ADJ
ejpam-3442	355	13	open	open	ADJ
ejpam-3442	355	14	and	and	CCONJ
ejpam-3442	355	15	soft	soft	ADJ
ejpam-3442	355	16	θ	θ	ADJ
ejpam-3442	355	17	-	-	PUNCT
ejpam-3442	355	18	closed	closed	ADJ
ejpam-3442	355	19	sets	set	NOUN
ejpam-3442	355	20	and	and	CCONJ
ejpam-3442	355	21	soft	soft	ADJ
ejpam-3442	355	22	θ	θ	NOUN
ejpam-3442	355	23	-	-	NOUN
ejpam-3442	355	24	closure	closure	NOUN
ejpam-3442	355	25	.	.	PUNCT
ejpam-3442	356	1	also	also	ADV
ejpam-3442	356	2	,	,	PUNCT
ejpam-3442	356	3	we	we	PRON
ejpam-3442	356	4	introduce	introduce	VERB
ejpam-3442	356	5	the	the	DET
ejpam-3442	356	6	notion	notion	NOUN
ejpam-3442	356	7	of	of	ADP
ejpam-3442	356	8	soft	soft	ADJ
ejpam-3442	356	9	local	local	ADJ
ejpam-3442	356	10	closure	closure	NOUN
ejpam-3442	356	11	functions	function	NOUN
ejpam-3442	356	12	as	as	ADP
ejpam-3442	356	13	a	a	DET
ejpam-3442	356	14	generalization	generalization	NOUN
ejpam-3442	356	15	of	of	ADP
ejpam-3442	356	16	the	the	DET
ejpam-3442	356	17	soft	soft	ADJ
ejpam-3442	356	18	θ	θ	NOUN
ejpam-3442	356	19	-	-	NOUN
ejpam-3442	356	20	closure	closure	NOUN
ejpam-3442	356	21	and	and	CCONJ
ejpam-3442	356	22	the	the	DET
ejpam-3442	356	23	soft	soft	ADJ
ejpam-3442	356	24	(	(	PUNCT
ejpam-3442	356	25	semi	semi	ADJ
ejpam-3442	356	26	)	)	PUNCT
ejpam-3442	356	27	local	local	ADJ
ejpam-3442	356	28	function	function	NOUN
ejpam-3442	356	29	in	in	ADP
ejpam-3442	356	30	a	a	DET
ejpam-3442	356	31	soft	soft	ADJ
ejpam-3442	356	32	ideal	ideal	ADJ
ejpam-3442	356	33	topological	topological	ADJ
ejpam-3442	356	34	space	space	NOUN
ejpam-3442	356	35	and	and	CCONJ
ejpam-3442	356	36	the	the	DET
ejpam-3442	356	37	future	future	ADJ
ejpam-3442	356	38	research	research	NOUN
ejpam-3442	356	39	will	will	AUX
ejpam-3442	356	40	be	be	AUX
ejpam-3442	356	41	undertaken	undertake	VERB
ejpam-3442	356	42	in	in	ADP
ejpam-3442	356	43	this	this	DET
ejpam-3442	356	44	direction	direction	NOUN
ejpam-3442	356	45	.	.	PUNCT
ejpam-3442	357	1	conflict	conflict	NOUN
ejpam-3442	357	2	of	of	ADP
ejpam-3442	357	3	interest	interest	NOUN
ejpam-3442	357	4	we	we	PRON
ejpam-3442	357	5	declare	declare	VERB
ejpam-3442	357	6	that	that	SCONJ
ejpam-3442	357	7	,	,	PUNCT
ejpam-3442	357	8	there	there	PRON
ejpam-3442	357	9	is	be	VERB
ejpam-3442	357	10	no	no	DET
ejpam-3442	357	11	conflict	conflict	NOUN
ejpam-3442	357	12	of	of	ADP
ejpam-3442	357	13	interest	interest	NOUN
ejpam-3442	357	14	regarding	regard	VERB
ejpam-3442	357	15	the	the	DET
ejpam-3442	357	16	publication	publication	NOUN
ejpam-3442	357	17	of	of	ADP
ejpam-3442	357	18	this	this	DET
ejpam-3442	357	19	manuscript	manuscript	NOUN
ejpam-3442	357	20	.	.	PUNCT
ejpam-3442	358	1	acknowledgements	acknowledgement	NOUN
ejpam-3442	358	2	the	the	DET
ejpam-3442	358	3	authors	author	NOUN
ejpam-3442	358	4	gratefully	gratefully	ADV
ejpam-3442	358	5	acknowledge	acknowledge	VERB
ejpam-3442	358	6	the	the	DET
ejpam-3442	358	7	approval	approval	NOUN
ejpam-3442	358	8	and	and	CCONJ
ejpam-3442	358	9	the	the	DET
ejpam-3442	358	10	support	support	NOUN
ejpam-3442	358	11	of	of	ADP
ejpam-3442	358	12	this	this	DET
ejpam-3442	358	13	research	research	NOUN
ejpam-3442	358	14	study	study	NOUN
ejpam-3442	358	15	by	by	ADP
ejpam-3442	358	16	the	the	DET
ejpam-3442	358	17	grant	grant	PROPN
ejpam-3442	358	18	no	no	PROPN
ejpam-3442	358	19	.	.	PUNCT
ejpam-3442	358	20	sar-2017	sar-2017	NOUN
ejpam-3442	358	21	-	-	PUNCT
ejpam-3442	358	22	1	1	NUM
ejpam-3442	358	23	-	-	PUNCT
ejpam-3442	358	24	8	8	NUM
ejpam-3442	358	25	-	-	PUNCT
ejpam-3442	358	26	f-7213	f-7213	NOUN
ejpam-3442	358	27	,	,	PUNCT
ejpam-3442	358	28	k.	k.	PROPN
ejpam-3442	358	29	s.	s.	PROPN
ejpam-3442	358	30	a.	a.	PROPN
ejpam-3442	358	31	from	from	ADP
ejpam-3442	358	32	the	the	DET
ejpam-3442	358	33	deanship	deanship	NOUN
ejpam-3442	358	34	of	of	ADP
ejpam-3442	358	35	scientific	scientific	ADJ
ejpam-3442	358	36	research	research	NOUN
ejpam-3442	358	37	at	at	ADP
ejpam-3442	358	38	northern	northern	ADJ
ejpam-3442	358	39	border	border	NOUN
ejpam-3442	358	40	university	university	PROPN
ejpam-3442	358	41	,	,	PUNCT
ejpam-3442	358	42	arar	arar	PROPN
ejpam-3442	358	43	,	,	PUNCT
ejpam-3442	358	44	k.	k.	PROPN
ejpam-3442	358	45	s.	s.	PROPN
ejpam-3442	358	46	a.	a.	PROPN
ejpam-3442	358	47	references	reference	NOUN
ejpam-3442	359	1	[	[	X
ejpam-3442	359	2	1	1	NUM
ejpam-3442	359	3	]	]	PUNCT
ejpam-3442	359	4	m.	m.	NOUN
ejpam-3442	359	5	e.	e.	PROPN
ejpam-3442	359	6	abd	abd	PROPN
ejpam-3442	359	7	ei	ei	PROPN
ejpam-3442	359	8	mosef	mosef	PROPN
ejpam-3442	359	9	,	,	PUNCT
ejpam-3442	359	10	e.	e.	PROPN
ejpam-3442	359	11	f.	f.	PROPN
ejpam-3442	359	12	lashien	lashien	PROPN
ejpam-3442	359	13	and	and	CCONJ
ejpam-3442	359	14	a.	a.	NOUN
ejpam-3442	359	15	a.	a.	PROPN
ejpam-3442	359	16	nasef	nasef	PROPN
ejpam-3442	359	17	,	,	PUNCT
ejpam-3442	359	18	some	some	DET
ejpam-3442	359	19	topological	topological	ADJ
ejpam-3442	359	20	operators	operator	NOUN
ejpam-3442	359	21	via	via	ADP
ejpam-3442	359	22	ideals	ideal	NOUN
ejpam-3442	359	23	,	,	PUNCT
ejpam-3442	359	24	kyungpook	kyungpook	NOUN
ejpam-3442	359	25	math	math	NOUN
ejpam-3442	359	26	.	.	PUNCT
ejpam-3442	360	1	j.	j.	PROPN
ejpam-3442	360	2	,	,	PUNCT
ejpam-3442	360	3	32	32	NUM
ejpam-3442	360	4	(	(	PUNCT
ejpam-3442	360	5	2	2	NUM
ejpam-3442	360	6	)	)	PUNCT
ejpam-3442	360	7	(	(	PUNCT
ejpam-3442	360	8	1992	1992	NUM
ejpam-3442	360	9	)	)	PUNCT
ejpam-3442	360	10	,	,	PUNCT
ejpam-3442	360	11	273	273	NUM
ejpam-3442	360	12	-	-	SYM
ejpam-3442	360	13	284	284	NUM
ejpam-3442	360	14	.	.	PUNCT
ejpam-3442	361	1	[	[	X
ejpam-3442	361	2	2	2	NUM
ejpam-3442	361	3	]	]	PUNCT
ejpam-3442	361	4	a.	a.	PROPN
ejpam-3442	361	5	al	al	PROPN
ejpam-3442	361	6	-	-	PUNCT
ejpam-3442	361	7	omari	omari	PROPN
ejpam-3442	361	8	and	and	CCONJ
ejpam-3442	361	9	t.	t.	PROPN
ejpam-3442	361	10	noiri	noiri	PROPN
ejpam-3442	361	11	,	,	PUNCT
ejpam-3442	361	12	local	local	ADJ
ejpam-3442	361	13	closure	closure	NOUN
ejpam-3442	361	14	functions	function	NOUN
ejpam-3442	361	15	in	in	ADP
ejpam-3442	361	16	ideal	ideal	ADJ
ejpam-3442	361	17	topological	topological	ADJ
ejpam-3442	361	18	spaces	space	NOUN
ejpam-3442	361	19	,	,	PUNCT
ejpam-3442	361	20	novi	novi	PROPN
ejpam-3442	361	21	sad	sad	PROPN
ejpam-3442	361	22	j.	j.	PROPN
ejpam-3442	361	23	math	math	PROPN
ejpam-3442	361	24	.	.	PUNCT
ejpam-3442	362	1	,	,	PUNCT
ejpam-3442	362	2	43	43	NUM
ejpam-3442	362	3	(	(	PUNCT
ejpam-3442	362	4	2	2	NUM
ejpam-3442	362	5	)	)	PUNCT
ejpam-3442	362	6	(	(	PUNCT
ejpam-3442	362	7	2013	2013	NUM
ejpam-3442	362	8	)	)	PUNCT
ejpam-3442	362	9	,	,	PUNCT
ejpam-3442	362	10	139	139	NUM
ejpam-3442	362	11	-	-	SYM
ejpam-3442	362	12	149	149	NUM
ejpam-3442	362	13	.	.	PUNCT
ejpam-3442	363	1	[	[	X
ejpam-3442	363	2	3	3	X
ejpam-3442	363	3	]	]	X
ejpam-3442	363	4	m.	m.	PROPN
ejpam-3442	363	5	i.	i.	PROPN
ejpam-3442	363	6	ali	ali	PROPN
ejpam-3442	363	7	,	,	PUNCT
ejpam-3442	363	8	f.	f.	PROPN
ejpam-3442	363	9	feng	feng	PROPN
ejpam-3442	363	10	,	,	PUNCT
ejpam-3442	363	11	x.	x.	PROPN
ejpam-3442	363	12	liu	liu	PROPN
ejpam-3442	363	13	,	,	PUNCT
ejpam-3442	363	14	w.	w.	PROPN
ejpam-3442	363	15	k.	k.	PROPN
ejpam-3442	363	16	min	min	PROPN
ejpam-3442	363	17	and	and	CCONJ
ejpam-3442	363	18	m.	m.	NOUN
ejpam-3442	363	19	shabir	shabir	PROPN
ejpam-3442	363	20	,	,	PUNCT
ejpam-3442	363	21	on	on	ADP
ejpam-3442	363	22	some	some	DET
ejpam-3442	363	23	new	new	ADJ
ejpam-3442	363	24	operations	operation	NOUN
ejpam-3442	363	25	in	in	ADP
ejpam-3442	363	26	soft	soft	ADJ
ejpam-3442	363	27	set	set	NOUN
ejpam-3442	363	28	theory	theory	NOUN
ejpam-3442	363	29	,	,	PUNCT
ejpam-3442	363	30	comput	comput	NOUN
ejpam-3442	363	31	.	.	PUNCT
ejpam-3442	364	1	math	math	NOUN
ejpam-3442	364	2	.	.	PUNCT
ejpam-3442	365	1	appl	appl	PROPN
ejpam-3442	365	2	.	.	PROPN
ejpam-3442	365	3	,	,	PUNCT
ejpam-3442	365	4	57	57	NUM
ejpam-3442	365	5	(	(	PUNCT
ejpam-3442	365	6	2009	2009	NUM
ejpam-3442	365	7	)	)	PUNCT
ejpam-3442	365	8	,	,	PUNCT
ejpam-3442	365	9	1547	1547	NUM
ejpam-3442	365	10	-	-	SYM
ejpam-3442	365	11	1553	1553	NUM
ejpam-3442	365	12	.	.	PUNCT
ejpam-3442	366	1	[	[	X
ejpam-3442	366	2	4	4	X
ejpam-3442	366	3	]	]	PUNCT
ejpam-3442	366	4	b.	b.	PROPN
ejpam-3442	366	5	chen	chen	PROPN
ejpam-3442	366	6	,	,	PUNCT
ejpam-3442	366	7	soft	soft	ADJ
ejpam-3442	366	8	semi	semi	ADJ
ejpam-3442	366	9	open	open	ADJ
ejpam-3442	366	10	sets	set	NOUN
ejpam-3442	366	11	and	and	CCONJ
ejpam-3442	366	12	related	related	ADJ
ejpam-3442	366	13	properties	property	NOUN
ejpam-3442	366	14	in	in	ADP
ejpam-3442	366	15	soft	soft	ADJ
ejpam-3442	366	16	topological	topological	ADJ
ejpam-3442	366	17	spaces	space	NOUN
ejpam-3442	366	18	,	,	PUNCT
ejpam-3442	366	19	appl	appl	PROPN
ejpam-3442	366	20	.	.	PROPN
ejpam-3442	366	21	math	math	PROPN
ejpam-3442	366	22	.	.	PUNCT
ejpam-3442	366	23	inf	inf	PROPN
ejpam-3442	366	24	.	.	PUNCT
ejpam-3442	367	1	sci	sci	PROPN
ejpam-3442	367	2	,	,	PUNCT
ejpam-3442	367	3	7	7	NUM
ejpam-3442	367	4	(	(	PUNCT
ejpam-3442	367	5	1	1	NUM
ejpam-3442	367	6	)	)	PUNCT
ejpam-3442	367	7	(	(	PUNCT
ejpam-3442	367	8	2013	2013	NUM
ejpam-3442	367	9	)	)	PUNCT
ejpam-3442	367	10	,	,	PUNCT
ejpam-3442	367	11	287	287	NUM
ejpam-3442	367	12	-	-	SYM
ejpam-3442	367	13	294	294	NUM
ejpam-3442	367	14	.	.	PUNCT
ejpam-3442	368	1	[	[	X
ejpam-3442	368	2	5	5	X
ejpam-3442	368	3	]	]	PUNCT
ejpam-3442	368	4	s.	s.	PROPN
ejpam-3442	368	5	jafari	jafari	PROPN
ejpam-3442	368	6	and	and	CCONJ
ejpam-3442	368	7	n.	n.	PROPN
ejpam-3442	368	8	rajesh	rajesh	PROPN
ejpam-3442	368	9	,	,	PUNCT
ejpam-3442	368	10	generalized	generalize	VERB
ejpam-3442	368	11	closed	close	VERB
ejpam-3442	368	12	sets	set	NOUN
ejpam-3442	368	13	with	with	ADP
ejpam-3442	368	14	respect	respect	NOUN
ejpam-3442	368	15	to	to	ADP
ejpam-3442	368	16	an	an	DET
ejpam-3442	368	17	ideal	ideal	ADJ
ejpam-3442	368	18	,	,	PUNCT
ejpam-3442	368	19	eur	eur	PROPN
ejpam-3442	368	20	.	.	PUNCT
ejpam-3442	369	1	j.	j.	PROPN
ejpam-3442	369	2	pure	pure	PROPN
ejpam-3442	369	3	appl	appl	PROPN
ejpam-3442	369	4	.	.	PUNCT
ejpam-3442	369	5	math	math	PROPN
ejpam-3442	369	6	.	.	PUNCT
ejpam-3442	370	1	,	,	PUNCT
ejpam-3442	370	2	4	4	NUM
ejpam-3442	370	3	(	(	PUNCT
ejpam-3442	370	4	2	2	NUM
ejpam-3442	370	5	)	)	PUNCT
ejpam-3442	370	6	(	(	PUNCT
ejpam-3442	370	7	2011	2011	NUM
ejpam-3442	370	8	)	)	PUNCT
ejpam-3442	370	9	,	,	PUNCT
ejpam-3442	370	10	147	147	NUM
ejpam-3442	370	11	-	-	SYM
ejpam-3442	370	12	151	151	NUM
ejpam-3442	370	13	.	.	PUNCT
ejpam-3442	371	1	[	[	X
ejpam-3442	371	2	6	6	NUM
ejpam-3442	371	3	]	]	PUNCT
ejpam-3442	371	4	d.	d.	PROPN
ejpam-3442	371	5	jankovic	jankovic	PROPN
ejpam-3442	371	6	and	and	CCONJ
ejpam-3442	371	7	t.r	t.r	PROPN
ejpam-3442	371	8	.	.	PROPN
ejpam-3442	371	9	hamlet	hamlet	PROPN
ejpam-3442	371	10	,	,	PUNCT
ejpam-3442	371	11	new	new	ADJ
ejpam-3442	371	12	topologies	topology	NOUN
ejpam-3442	371	13	from	from	ADP
ejpam-3442	371	14	old	old	ADJ
ejpam-3442	371	15	via	via	ADP
ejpam-3442	371	16	ideals	ideal	NOUN
ejpam-3442	371	17	,	,	PUNCT
ejpam-3442	371	18	amer	amer	PROPN
ejpam-3442	371	19	.	.	PROPN
ejpam-3442	371	20	math	math	PROPN
ejpam-3442	371	21	.	.	PUNCT
ejpam-3442	372	1	monthly	monthly	ADV
ejpam-3442	372	2	,	,	PUNCT
ejpam-3442	372	3	97	97	NUM
ejpam-3442	372	4	(	(	PUNCT
ejpam-3442	372	5	4	4	NUM
ejpam-3442	372	6	)	)	PUNCT
ejpam-3442	372	7	(	(	PUNCT
ejpam-3442	372	8	1990	1990	NUM
ejpam-3442	372	9	)	)	PUNCT
ejpam-3442	372	10	,	,	PUNCT
ejpam-3442	372	11	295	295	NUM
ejpam-3442	372	12	-	-	SYM
ejpam-3442	372	13	310	310	NUM
ejpam-3442	372	14	.	.	PUNCT
ejpam-3442	373	1	[	[	X
ejpam-3442	373	2	7	7	NUM
ejpam-3442	373	3	]	]	PUNCT
ejpam-3442	373	4	a.	a.	NOUN
ejpam-3442	373	5	kandil	kandil	PROPN
ejpam-3442	373	6	,	,	PUNCT
ejpam-3442	373	7	o.	o.	PROPN
ejpam-3442	373	8	a.	a.	PROPN
ejpam-3442	373	9	e.	e.	PROPN
ejpam-3442	373	10	tantawy	tantawy	PROPN
ejpam-3442	373	11	,	,	PUNCT
ejpam-3442	373	12	s.	s.	PROPN
ejpam-3442	373	13	a.	a.	PROPN
ejpam-3442	373	14	el	el	PROPN
ejpam-3442	373	15	-	-	PUNCT
ejpam-3442	373	16	sheikh	sheikh	PROPN
ejpam-3442	373	17	and	and	CCONJ
ejpam-3442	373	18	a.	a.	NOUN
ejpam-3442	373	19	m.	m.	NOUN
ejpam-3442	373	20	abd	abd	PROPN
ejpam-3442	373	21	el	el	PROPN
ejpam-3442	373	22	-	-	PROPN
ejpam-3442	373	23	latif	latif	PROPN
ejpam-3442	373	24	,	,	PUNCT
ejpam-3442	373	25	γ	γ	PROPN
ejpam-3442	373	26	-	-	PUNCT
ejpam-3442	373	27	operation	operation	NOUN
ejpam-3442	373	28	and	and	CCONJ
ejpam-3442	373	29	decompositions	decomposition	NOUN
ejpam-3442	373	30	of	of	ADP
ejpam-3442	373	31	some	some	DET
ejpam-3442	373	32	forms	form	NOUN
ejpam-3442	373	33	of	of	ADP
ejpam-3442	373	34	soft	soft	ADJ
ejpam-3442	373	35	continuity	continuity	NOUN
ejpam-3442	373	36	in	in	ADP
ejpam-3442	373	37	soft	soft	ADJ
ejpam-3442	373	38	topological	topological	ADJ
ejpam-3442	373	39	spaces	space	NOUN
ejpam-3442	373	40	,	,	PUNCT
ejpam-3442	373	41	ann	ann	PROPN
ejpam-3442	373	42	.	.	PROPN
ejpam-3442	373	43	fuzzy	fuzzy	ADJ
ejpam-3442	373	44	math	math	NOUN
ejpam-3442	373	45	.	.	PUNCT
ejpam-3442	374	1	inform	inform	NOUN
ejpam-3442	374	2	.	.	PUNCT
ejpam-3442	375	1	,	,	PUNCT
ejpam-3442	375	2	7	7	NUM
ejpam-3442	375	3	(	(	PUNCT
ejpam-3442	375	4	2	2	NUM
ejpam-3442	375	5	)	)	PUNCT
ejpam-3442	375	6	(	(	PUNCT
ejpam-3442	375	7	2014	2014	NUM
ejpam-3442	375	8	)	)	PUNCT
ejpam-3442	375	9	,	,	PUNCT
ejpam-3442	375	10	181	181	NUM
ejpam-3442	375	11	-	-	SYM
ejpam-3442	375	12	196	196	NUM
ejpam-3442	375	13	.	.	PUNCT
ejpam-3442	376	1	references	reference	NOUN
ejpam-3442	376	2	868	868	NUM
ejpam-3442	376	3	[	[	SYM
ejpam-3442	376	4	8	8	NUM
ejpam-3442	376	5	]	]	PUNCT
ejpam-3442	376	6	a.	a.	NOUN
ejpam-3442	376	7	kandil	kandil	PROPN
ejpam-3442	376	8	,	,	PUNCT
ejpam-3442	376	9	o.	o.	PROPN
ejpam-3442	376	10	a.	a.	PROPN
ejpam-3442	376	11	e.	e.	PROPN
ejpam-3442	376	12	tantawy	tantawy	PROPN
ejpam-3442	376	13	,	,	PUNCT
ejpam-3442	376	14	s.	s.	PROPN
ejpam-3442	376	15	a.	a.	PROPN
ejpam-3442	376	16	el	el	PROPN
ejpam-3442	376	17	-	-	PUNCT
ejpam-3442	376	18	sheikh	sheikh	PROPN
ejpam-3442	376	19	and	and	CCONJ
ejpam-3442	376	20	a.	a.	NOUN
ejpam-3442	376	21	m.	m.	NOUN
ejpam-3442	376	22	abd	abd	PROPN
ejpam-3442	376	23	el	el	PROPN
ejpam-3442	376	24	-	-	PROPN
ejpam-3442	376	25	latif	latif	PROPN
ejpam-3442	376	26	,	,	PUNCT
ejpam-3442	376	27	γ	γ	PROPN
ejpam-3442	376	28	-	-	PUNCT
ejpam-3442	376	29	operation	operation	NOUN
ejpam-3442	376	30	and	and	CCONJ
ejpam-3442	376	31	decompositions	decomposition	NOUN
ejpam-3442	376	32	of	of	ADP
ejpam-3442	376	33	some	some	DET
ejpam-3442	376	34	forms	form	NOUN
ejpam-3442	376	35	of	of	ADP
ejpam-3442	376	36	soft	soft	ADJ
ejpam-3442	376	37	continuity	continuity	NOUN
ejpam-3442	376	38	of	of	ADP
ejpam-3442	376	39	soft	soft	ADJ
ejpam-3442	376	40	topological	topological	ADJ
ejpam-3442	376	41	spaces	space	NOUN
ejpam-3442	376	42	via	via	ADP
ejpam-3442	376	43	soft	soft	ADJ
ejpam-3442	376	44	ideal	ideal	NOUN
ejpam-3442	376	45	,	,	PUNCT
ejpam-3442	376	46	ann	ann	PROPN
ejpam-3442	376	47	.	.	PROPN
ejpam-3442	376	48	fuzzy	fuzzy	ADJ
ejpam-3442	376	49	math	math	NOUN
ejpam-3442	376	50	.	.	PUNCT
ejpam-3442	377	1	inform	inform	NOUN
ejpam-3442	377	2	.	.	PUNCT
ejpam-3442	377	3	,	,	PUNCT
ejpam-3442	377	4	9	9	NUM
ejpam-3442	377	5	(	(	PUNCT
ejpam-3442	377	6	3	3	NUM
ejpam-3442	377	7	)	)	PUNCT
ejpam-3442	377	8	(	(	PUNCT
ejpam-3442	377	9	2015	2015	NUM
ejpam-3442	377	10	)	)	PUNCT
ejpam-3442	377	11	,	,	PUNCT
ejpam-3442	377	12	385	385	NUM
ejpam-3442	377	13	-	-	SYM
ejpam-3442	377	14	402	402	NUM
ejpam-3442	377	15	.	.	PUNCT
ejpam-3442	378	1	[	[	X
ejpam-3442	378	2	9	9	NUM
ejpam-3442	378	3	]	]	PUNCT
ejpam-3442	378	4	a.	a.	NOUN
ejpam-3442	378	5	kandil	kandil	PROPN
ejpam-3442	378	6	,	,	PUNCT
ejpam-3442	378	7	o.	o.	PROPN
ejpam-3442	378	8	a.	a.	PROPN
ejpam-3442	378	9	e.	e.	PROPN
ejpam-3442	378	10	tantawy	tantawy	PROPN
ejpam-3442	378	11	,	,	PUNCT
ejpam-3442	378	12	s.	s.	PROPN
ejpam-3442	378	13	a.	a.	PROPN
ejpam-3442	378	14	el	el	PROPN
ejpam-3442	378	15	-	-	PUNCT
ejpam-3442	378	16	sheikh	sheikh	PROPN
ejpam-3442	378	17	and	and	CCONJ
ejpam-3442	378	18	a.	a.	NOUN
ejpam-3442	378	19	m.	m.	NOUN
ejpam-3442	378	20	abd	abd	PROPN
ejpam-3442	378	21	el	el	PROPN
ejpam-3442	378	22	-	-	PROPN
ejpam-3442	378	23	latif	latif	PROPN
ejpam-3442	378	24	,	,	PUNCT
ejpam-3442	378	25	soft	soft	ADJ
ejpam-3442	378	26	connectedness	connectedness	NOUN
ejpam-3442	378	27	via	via	ADP
ejpam-3442	378	28	soft	soft	ADJ
ejpam-3442	378	29	ideals	ideal	NOUN
ejpam-3442	378	30	,	,	PUNCT
ejpam-3442	378	31	journal	journal	NOUN
ejpam-3442	378	32	of	of	ADP
ejpam-3442	378	33	new	new	ADJ
ejpam-3442	378	34	results	result	NOUN
ejpam-3442	378	35	in	in	ADP
ejpam-3442	378	36	science	science	NOUN
ejpam-3442	378	37	,	,	PUNCT
ejpam-3442	378	38	4	4	NUM
ejpam-3442	378	39	(	(	PUNCT
ejpam-3442	378	40	2014	2014	NUM
ejpam-3442	378	41	)	)	PUNCT
ejpam-3442	378	42	,	,	PUNCT
ejpam-3442	378	43	90	90	NUM
ejpam-3442	378	44	-	-	SYM
ejpam-3442	378	45	108	108	NUM
ejpam-3442	378	46	.	.	PUNCT
ejpam-3442	379	1	[	[	X
ejpam-3442	379	2	10	10	NUM
ejpam-3442	379	3	]	]	X
ejpam-3442	379	4	a.	a.	NOUN
ejpam-3442	379	5	kandil	kandil	PROPN
ejpam-3442	379	6	,	,	PUNCT
ejpam-3442	379	7	o.	o.	PROPN
ejpam-3442	379	8	a.	a.	PROPN
ejpam-3442	379	9	e.	e.	PROPN
ejpam-3442	379	10	tantawy	tantawy	PROPN
ejpam-3442	379	11	,	,	PUNCT
ejpam-3442	379	12	s.	s.	PROPN
ejpam-3442	379	13	a.	a.	PROPN
ejpam-3442	379	14	el	el	PROPN
ejpam-3442	379	15	-	-	PUNCT
ejpam-3442	379	16	sheikh	sheikh	PROPN
ejpam-3442	379	17	and	and	CCONJ
ejpam-3442	379	18	a.	a.	NOUN
ejpam-3442	379	19	m.	m.	NOUN
ejpam-3442	379	20	abd	abd	PROPN
ejpam-3442	379	21	el	el	PROPN
ejpam-3442	379	22	-	-	PROPN
ejpam-3442	379	23	latif	latif	PROPN
ejpam-3442	379	24	,	,	PUNCT
ejpam-3442	379	25	soft	soft	ADJ
ejpam-3442	379	26	ideal	ideal	ADJ
ejpam-3442	379	27	theory	theory	NOUN
ejpam-3442	379	28	,	,	PUNCT
ejpam-3442	379	29	soft	soft	ADJ
ejpam-3442	379	30	local	local	ADJ
ejpam-3442	379	31	function	function	NOUN
ejpam-3442	379	32	and	and	CCONJ
ejpam-3442	379	33	generated	generate	VERB
ejpam-3442	379	34	soft	soft	ADJ
ejpam-3442	379	35	topological	topological	ADJ
ejpam-3442	379	36	spaces	space	NOUN
ejpam-3442	379	37	,	,	PUNCT
ejpam-3442	379	38	appl	appl	PROPN
ejpam-3442	379	39	.	.	PROPN
ejpam-3442	379	40	math	math	PROPN
ejpam-3442	379	41	.	.	PUNCT
ejpam-3442	380	1	inf	inf	PROPN
ejpam-3442	380	2	.	.	PUNCT
ejpam-3442	381	1	sci	sci	PROPN
ejpam-3442	381	2	.	.	PROPN
ejpam-3442	381	3	,	,	PUNCT
ejpam-3442	381	4	8	8	NUM
ejpam-3442	381	5	(	(	PUNCT
ejpam-3442	381	6	4	4	NUM
ejpam-3442	381	7	)	)	PUNCT
ejpam-3442	381	8	(	(	PUNCT
ejpam-3442	381	9	2014	2014	NUM
ejpam-3442	381	10	)	)	PUNCT
ejpam-3442	381	11	,	,	PUNCT
ejpam-3442	381	12	1595	1595	NUM
ejpam-3442	381	13	-	-	SYM
ejpam-3442	381	14	1603	1603	NUM
ejpam-3442	381	15	.	.	PUNCT
ejpam-3442	382	1	[	[	X
ejpam-3442	382	2	11	11	NUM
ejpam-3442	382	3	]	]	PUNCT
ejpam-3442	382	4	a.	a.	NOUN
ejpam-3442	382	5	kandil	kandil	PROPN
ejpam-3442	382	6	,	,	PUNCT
ejpam-3442	382	7	o.	o.	PROPN
ejpam-3442	382	8	a.	a.	PROPN
ejpam-3442	382	9	e.	e.	PROPN
ejpam-3442	382	10	tantawy	tantawy	PROPN
ejpam-3442	382	11	,	,	PUNCT
ejpam-3442	382	12	s.	s.	PROPN
ejpam-3442	382	13	a.	a.	PROPN
ejpam-3442	382	14	el	el	PROPN
ejpam-3442	382	15	-	-	PUNCT
ejpam-3442	382	16	sheikh	sheikh	PROPN
ejpam-3442	382	17	and	and	CCONJ
ejpam-3442	382	18	a.	a.	NOUN
ejpam-3442	382	19	m.	m.	NOUN
ejpam-3442	382	20	abd	abd	PROPN
ejpam-3442	382	21	el	el	PROPN
ejpam-3442	382	22	-	-	PROPN
ejpam-3442	382	23	latif	latif	PROPN
ejpam-3442	382	24	,	,	PUNCT
ejpam-3442	382	25	soft	soft	ADJ
ejpam-3442	382	26	regularity	regularity	NOUN
ejpam-3442	382	27	and	and	CCONJ
ejpam-3442	382	28	normality	normality	NOUN
ejpam-3442	382	29	based	base	VERB
ejpam-3442	382	30	on	on	ADP
ejpam-3442	382	31	semi	semi	ADJ
ejpam-3442	382	32	open	open	ADJ
ejpam-3442	382	33	soft	soft	ADJ
ejpam-3442	382	34	sets	set	NOUN
ejpam-3442	382	35	and	and	CCONJ
ejpam-3442	382	36	soft	soft	ADJ
ejpam-3442	382	37	ideals	ideal	NOUN
ejpam-3442	382	38	,	,	PUNCT
ejpam-3442	382	39	appl	appl	PROPN
ejpam-3442	382	40	.	.	PROPN
ejpam-3442	382	41	math	math	PROPN
ejpam-3442	382	42	.	.	PUNCT
ejpam-3442	383	1	inf	inf	PROPN
ejpam-3442	383	2	.	.	PUNCT
ejpam-3442	384	1	sci	sci	PROPN
ejpam-3442	384	2	.	.	PUNCT
ejpam-3442	384	3	lett	lett	PROPN
ejpam-3442	384	4	.	.	PROPN
ejpam-3442	384	5	,	,	PUNCT
ejpam-3442	384	6	3	3	NUM
ejpam-3442	384	7	(	(	PUNCT
ejpam-3442	384	8	2	2	NUM
ejpam-3442	384	9	)	)	PUNCT
ejpam-3442	384	10	(	(	PUNCT
ejpam-3442	384	11	2015	2015	NUM
ejpam-3442	384	12	)	)	PUNCT
ejpam-3442	384	13	,	,	PUNCT
ejpam-3442	384	14	47	47	NUM
ejpam-3442	384	15	-	-	SYM
ejpam-3442	384	16	55	55	NUM
ejpam-3442	384	17	.	.	PUNCT
ejpam-3442	385	1	[	[	X
ejpam-3442	385	2	12	12	NUM
ejpam-3442	385	3	]	]	PUNCT
ejpam-3442	385	4	a.	a.	NOUN
ejpam-3442	385	5	kandil	kandil	PROPN
ejpam-3442	385	6	,	,	PUNCT
ejpam-3442	385	7	o.	o.	PROPN
ejpam-3442	385	8	a.	a.	PROPN
ejpam-3442	385	9	e.	e.	PROPN
ejpam-3442	385	10	tantawy	tantawy	PROPN
ejpam-3442	385	11	,	,	PUNCT
ejpam-3442	385	12	s.	s.	PROPN
ejpam-3442	385	13	a.	a.	PROPN
ejpam-3442	385	14	el	el	PROPN
ejpam-3442	385	15	-	-	PUNCT
ejpam-3442	385	16	sheikh	sheikh	PROPN
ejpam-3442	385	17	and	and	CCONJ
ejpam-3442	385	18	a.	a.	NOUN
ejpam-3442	385	19	m.	m.	NOUN
ejpam-3442	385	20	abd	abd	PROPN
ejpam-3442	385	21	el	el	PROPN
ejpam-3442	385	22	-	-	PROPN
ejpam-3442	385	23	latif	latif	PROPN
ejpam-3442	385	24	,	,	PUNCT
ejpam-3442	385	25	soft	soft	ADJ
ejpam-3442	385	26	semi	semi	ADJ
ejpam-3442	385	27	compactness	compactness	NOUN
ejpam-3442	385	28	via	via	ADP
ejpam-3442	385	29	soft	soft	ADJ
ejpam-3442	385	30	ideals	ideal	NOUN
ejpam-3442	385	31	,	,	PUNCT
ejpam-3442	385	32	appl	appl	PROPN
ejpam-3442	385	33	.	.	PROPN
ejpam-3442	385	34	math	math	PROPN
ejpam-3442	385	35	.	.	PUNCT
ejpam-3442	386	1	inf	inf	PROPN
ejpam-3442	386	2	.	.	PUNCT
ejpam-3442	387	1	sci	sci	PROPN
ejpam-3442	387	2	.	.	PROPN
ejpam-3442	387	3	,	,	PUNCT
ejpam-3442	387	4	8	8	NUM
ejpam-3442	387	5	(	(	PUNCT
ejpam-3442	387	6	5	5	NUM
ejpam-3442	387	7	)	)	PUNCT
ejpam-3442	387	8	(	(	PUNCT
ejpam-3442	387	9	2014	2014	NUM
ejpam-3442	387	10	)	)	PUNCT
ejpam-3442	387	11	,	,	PUNCT
ejpam-3442	387	12	2297	2297	NUM
ejpam-3442	387	13	-	-	SYM
ejpam-3442	387	14	2306	2306	NUM
ejpam-3442	387	15	.	.	PUNCT
ejpam-3442	388	1	[	[	X
ejpam-3442	388	2	13	13	NUM
ejpam-3442	388	3	]	]	PUNCT
ejpam-3442	388	4	a.	a.	NOUN
ejpam-3442	388	5	kandil	kandil	PROPN
ejpam-3442	388	6	,	,	PUNCT
ejpam-3442	388	7	o.	o.	PROPN
ejpam-3442	388	8	a.	a.	PROPN
ejpam-3442	388	9	e.	e.	PROPN
ejpam-3442	388	10	tantawy	tantawy	PROPN
ejpam-3442	388	11	,	,	PUNCT
ejpam-3442	388	12	s.	s.	PROPN
ejpam-3442	388	13	a.	a.	PROPN
ejpam-3442	388	14	el	el	PROPN
ejpam-3442	388	15	-	-	PUNCT
ejpam-3442	388	16	sheikh	sheikh	PROPN
ejpam-3442	388	17	and	and	CCONJ
ejpam-3442	388	18	a.	a.	NOUN
ejpam-3442	388	19	m.	m.	NOUN
ejpam-3442	388	20	abd	abd	PROPN
ejpam-3442	388	21	el	el	PROPN
ejpam-3442	388	22	-	-	PROPN
ejpam-3442	388	23	latif	latif	PROPN
ejpam-3442	388	24	,	,	PUNCT
ejpam-3442	388	25	soft	soft	ADJ
ejpam-3442	388	26	semi	semi	ADJ
ejpam-3442	388	27	(	(	PUNCT
ejpam-3442	388	28	quasi	quasi	ADJ
ejpam-3442	388	29	)	)	PUNCT
ejpam-3442	388	30	hausdorff	hausdorff	NOUN
ejpam-3442	388	31	spaces	space	NOUN
ejpam-3442	388	32	via	via	ADP
ejpam-3442	388	33	soft	soft	ADJ
ejpam-3442	388	34	ideals	ideal	NOUN
ejpam-3442	388	35	,	,	PUNCT
ejpam-3442	388	36	south	south	ADJ
ejpam-3442	388	37	asian	asian	PROPN
ejpam-3442	388	38	j.	j.	PROPN
ejpam-3442	388	39	math	math	PROPN
ejpam-3442	388	40	.	.	PUNCT
ejpam-3442	388	41	,	,	PUNCT
ejpam-3442	388	42	4	4	NUM
ejpam-3442	388	43	(	(	PUNCT
ejpam-3442	388	44	6	6	NUM
ejpam-3442	388	45	)	)	PUNCT
ejpam-3442	388	46	(	(	PUNCT
ejpam-3442	388	47	2014	2014	NUM
ejpam-3442	388	48	)	)	PUNCT
ejpam-3442	388	49	,	,	PUNCT
ejpam-3442	388	50	265	265	NUM
ejpam-3442	388	51	-	-	SYM
ejpam-3442	388	52	284	284	NUM
ejpam-3442	388	53	.	.	PUNCT
ejpam-3442	389	1	[	[	X
ejpam-3442	389	2	14	14	NUM
ejpam-3442	389	3	]	]	PUNCT
ejpam-3442	389	4	a.	a.	NOUN
ejpam-3442	389	5	kandil	kandil	PROPN
ejpam-3442	389	6	,	,	PUNCT
ejpam-3442	389	7	o.	o.	PROPN
ejpam-3442	389	8	a.	a.	PROPN
ejpam-3442	389	9	e.	e.	PROPN
ejpam-3442	389	10	tantawy	tantawy	PROPN
ejpam-3442	389	11	,	,	PUNCT
ejpam-3442	389	12	s.	s.	PROPN
ejpam-3442	389	13	a.	a.	PROPN
ejpam-3442	389	14	el	el	PROPN
ejpam-3442	389	15	-	-	PUNCT
ejpam-3442	389	16	sheikh	sheikh	PROPN
ejpam-3442	389	17	and	and	CCONJ
ejpam-3442	389	18	a.	a.	NOUN
ejpam-3442	389	19	m.	m.	NOUN
ejpam-3442	389	20	abd	abd	PROPN
ejpam-3442	389	21	el	el	PROPN
ejpam-3442	389	22	-	-	PROPN
ejpam-3442	389	23	latif	latif	PROPN
ejpam-3442	389	24	,	,	PUNCT
ejpam-3442	389	25	supra	supra	PROPN
ejpam-3442	389	26	generalized	generalize	VERB
ejpam-3442	389	27	closed	close	VERB
ejpam-3442	389	28	soft	soft	ADJ
ejpam-3442	389	29	sets	set	NOUN
ejpam-3442	389	30	with	with	ADP
ejpam-3442	389	31	respect	respect	NOUN
ejpam-3442	389	32	to	to	ADP
ejpam-3442	389	33	an	an	DET
ejpam-3442	389	34	soft	soft	ADJ
ejpam-3442	389	35	ideal	ideal	NOUN
ejpam-3442	389	36	in	in	ADP
ejpam-3442	389	37	supra	supra	PROPN
ejpam-3442	389	38	soft	soft	ADJ
ejpam-3442	389	39	topological	topological	ADJ
ejpam-3442	389	40	spaces	space	NOUN
ejpam-3442	389	41	,	,	PUNCT
ejpam-3442	389	42	appl	appl	PROPN
ejpam-3442	389	43	.	.	PROPN
ejpam-3442	389	44	math	math	PROPN
ejpam-3442	389	45	.	.	PUNCT
ejpam-3442	390	1	inf	inf	PROPN
ejpam-3442	390	2	.	.	PUNCT
ejpam-3442	391	1	sci	sci	PROPN
ejpam-3442	391	2	.	.	PROPN
ejpam-3442	391	3	,	,	PUNCT
ejpam-3442	391	4	8	8	NUM
ejpam-3442	391	5	(	(	PUNCT
ejpam-3442	391	6	4	4	NUM
ejpam-3442	391	7	)	)	PUNCT
ejpam-3442	391	8	(	(	PUNCT
ejpam-3442	391	9	2014	2014	NUM
ejpam-3442	391	10	)	)	PUNCT
ejpam-3442	391	11	,	,	PUNCT
ejpam-3442	391	12	1731	1731	NUM
ejpam-3442	391	13	-	-	SYM
ejpam-3442	391	14	1740	1740	NUM
ejpam-3442	391	15	.	.	PUNCT
ejpam-3442	392	1	[	[	X
ejpam-3442	392	2	15	15	NUM
ejpam-3442	392	3	]	]	X
ejpam-3442	392	4	m.	m.	NOUN
ejpam-3442	392	5	khan	khan	PROPN
ejpam-3442	392	6	and	and	CCONJ
ejpam-3442	392	7	t.	t.	PROPN
ejpam-3442	392	8	noiri	noiri	PROPN
ejpam-3442	392	9	,	,	PUNCT
ejpam-3442	392	10	semi	semi	ADJ
ejpam-3442	392	11	-	-	ADJ
ejpam-3442	392	12	local	local	ADJ
ejpam-3442	392	13	functions	function	NOUN
ejpam-3442	392	14	in	in	ADP
ejpam-3442	392	15	ideal	ideal	ADJ
ejpam-3442	392	16	topological	topological	ADJ
ejpam-3442	392	17	spaces	space	NOUN
ejpam-3442	392	18	,	,	PUNCT
ejpam-3442	392	19	journal	journal	NOUN
ejpam-3442	392	20	of	of	ADP
ejpam-3442	392	21	advanced	advanced	ADJ
ejpam-3442	392	22	research	research	NOUN
ejpam-3442	392	23	in	in	ADP
ejpam-3442	392	24	pure	pure	ADJ
ejpam-3442	392	25	mathematics	mathematic	NOUN
ejpam-3442	392	26	,	,	PUNCT
ejpam-3442	392	27	2	2	NUM
ejpam-3442	392	28	(	(	PUNCT
ejpam-3442	392	29	1	1	NUM
ejpam-3442	392	30	)	)	PUNCT
ejpam-3442	392	31	(	(	PUNCT
ejpam-3442	392	32	2010	2010	NUM
ejpam-3442	392	33	)	)	PUNCT
ejpam-3442	392	34	,	,	PUNCT
ejpam-3442	392	35	36	36	NUM
ejpam-3442	392	36	-	-	SYM
ejpam-3442	392	37	42	42	NUM
ejpam-3442	392	38	.	.	PUNCT
ejpam-3442	393	1	[	[	X
ejpam-3442	393	2	16	16	NUM
ejpam-3442	393	3	]	]	PUNCT
ejpam-3442	393	4	k.	k.	PROPN
ejpam-3442	393	5	kuratowski	kuratowski	PROPN
ejpam-3442	393	6	.	.	PUNCT
ejpam-3442	394	1	topology	topology	PROPN
ejpam-3442	395	1	i	i	PRON
ejpam-3442	395	2	,	,	PUNCT
ejpam-3442	395	3	warszawa	warszawa	PROPN
ejpam-3442	395	4	,	,	PUNCT
ejpam-3442	395	5	1933	1933	NUM
ejpam-3442	395	6	.	.	PUNCT
ejpam-3442	396	1	[	[	X
ejpam-3442	396	2	17	17	NUM
ejpam-3442	396	3	]	]	PUNCT
ejpam-3442	396	4	k.	k.	PROPN
ejpam-3442	396	5	kuratowski	kuratowski	PROPN
ejpam-3442	396	6	,	,	PUNCT
ejpam-3442	396	7	topology	topology	NOUN
ejpam-3442	396	8	,	,	PUNCT
ejpam-3442	396	9	vol	vol	NOUN
ejpam-3442	396	10	.	.	PUNCT
ejpam-3442	397	1	i	i	PRON
ejpam-3442	397	2	,	,	PUNCT
ejpam-3442	397	3	academic	academic	ADJ
ejpam-3442	397	4	press	press	NOUN
ejpam-3442	397	5	,	,	PUNCT
ejpam-3442	397	6	new	new	PROPN
ejpam-3442	397	7	york	york	PROPN
ejpam-3442	397	8	,	,	PUNCT
ejpam-3442	397	9	london	london	PROPN
ejpam-3442	397	10	,	,	PUNCT
ejpam-3442	397	11	1966	1966	NUM
ejpam-3442	397	12	.	.	PUNCT
ejpam-3442	398	1	[	[	X
ejpam-3442	398	2	18	18	NUM
ejpam-3442	398	3	]	]	X
ejpam-3442	398	4	d.	d.	PROPN
ejpam-3442	398	5	v.	v.	PROPN
ejpam-3442	398	6	kovkov	kovkov	PROPN
ejpam-3442	398	7	,	,	PUNCT
ejpam-3442	398	8	v.	v.	ADP
ejpam-3442	398	9	m.	m.	NOUN
ejpam-3442	398	10	kolbanov	kolbanov	PROPN
ejpam-3442	398	11	and	and	CCONJ
ejpam-3442	398	12	d.	d.	PROPN
ejpam-3442	398	13	a.	a.	PROPN
ejpam-3442	398	14	molodtsov	molodtsov	PROPN
ejpam-3442	398	15	,	,	PUNCT
ejpam-3442	398	16	soft	soft	ADJ
ejpam-3442	398	17	sets	set	NOUN
ejpam-3442	398	18	theory	theory	NOUN
ejpam-3442	398	19	-	-	PUNCT
ejpam-3442	398	20	based	base	VERB
ejpam-3442	398	21	optimization	optimization	NOUN
ejpam-3442	398	22	,	,	PUNCT
ejpam-3442	398	23	journal	journal	NOUN
ejpam-3442	398	24	of	of	ADP
ejpam-3442	398	25	computer	computer	NOUN
ejpam-3442	398	26	and	and	CCONJ
ejpam-3442	398	27	systems	systems	PROPN
ejpam-3442	398	28	sciences	sciences	PROPN
ejpam-3442	398	29	international	international	PROPN
ejpam-3442	398	30	,	,	PUNCT
ejpam-3442	398	31	46	46	NUM
ejpam-3442	398	32	(	(	PUNCT
ejpam-3442	398	33	6	6	NUM
ejpam-3442	398	34	)	)	PUNCT
ejpam-3442	398	35	(	(	PUNCT
ejpam-3442	398	36	2007	2007	NUM
ejpam-3442	398	37	)	)	PUNCT
ejpam-3442	398	38	,	,	PUNCT
ejpam-3442	398	39	872	872	NUM
ejpam-3442	398	40	-	-	SYM
ejpam-3442	398	41	880	880	NUM
ejpam-3442	398	42	.	.	PUNCT
ejpam-3442	399	1	[	[	X
ejpam-3442	399	2	19	19	NUM
ejpam-3442	399	3	]	]	PUNCT
ejpam-3442	399	4	j.	j.	PROPN
ejpam-3442	399	5	mahanta	mahanta	PROPN
ejpam-3442	399	6	and	and	CCONJ
ejpam-3442	399	7	p.	p.	PROPN
ejpam-3442	399	8	k.	k.	PROPN
ejpam-3442	400	1	das	das	PROPN
ejpam-3442	400	2	,	,	PUNCT
ejpam-3442	400	3	on	on	ADP
ejpam-3442	400	4	soft	soft	ADJ
ejpam-3442	400	5	topological	topological	ADJ
ejpam-3442	400	6	space	space	NOUN
ejpam-3442	400	7	via	via	ADP
ejpam-3442	400	8	semi	semi	ADV
ejpam-3442	400	9	open	open	ADJ
ejpam-3442	400	10	and	and	CCONJ
ejpam-3442	400	11	semi	semi	ADV
ejpam-3442	400	12	closed	closed	ADJ
ejpam-3442	400	13	soft	soft	ADJ
ejpam-3442	400	14	sets	set	NOUN
ejpam-3442	400	15	,	,	PUNCT
ejpam-3442	400	16	kyungpook	kyungpook	NOUN
ejpam-3442	400	17	math	math	NOUN
ejpam-3442	400	18	.	.	PUNCT
ejpam-3442	401	1	j.	j.	PROPN
ejpam-3442	401	2	,	,	PUNCT
ejpam-3442	401	3	54	54	NUM
ejpam-3442	401	4	(	(	PUNCT
ejpam-3442	401	5	2014	2014	NUM
ejpam-3442	401	6	)	)	PUNCT
ejpam-3442	401	7	,	,	PUNCT
ejpam-3442	401	8	221	221	NUM
ejpam-3442	401	9	-	-	SYM
ejpam-3442	401	10	236	236	NUM
ejpam-3442	401	11	.	.	PUNCT
ejpam-3442	402	1	[	[	X
ejpam-3442	402	2	20	20	NUM
ejpam-3442	402	3	]	]	PUNCT
ejpam-3442	402	4	s.	s.	PROPN
ejpam-3442	402	5	mistry	mistry	PROPN
ejpam-3442	402	6	and	and	CCONJ
ejpam-3442	402	7	s.	s.	PROPN
ejpam-3442	402	8	modak	modak	PROPN
ejpam-3442	402	9	,	,	PUNCT
ejpam-3442	402	10	(	(	PUNCT
ejpam-3442	402	11	)	)	PUNCT
ejpam-3442	402	12	∗p	∗p	NOUN
ejpam-3442	402	13	and	and	CCONJ
ejpam-3442	402	14	ψp	ψp	NOUN
ejpam-3442	402	15	-	-	PUNCT
ejpam-3442	402	16	operator	operator	NOUN
ejpam-3442	402	17	,	,	PUNCT
ejpam-3442	402	18	international	international	PROPN
ejpam-3442	402	19	mathematical	mathematical	ADJ
ejpam-3442	402	20	forum	forum	PROPN
ejpam-3442	402	21	,	,	PUNCT
ejpam-3442	402	22	7	7	NUM
ejpam-3442	402	23	(	(	PUNCT
ejpam-3442	402	24	2	2	NUM
ejpam-3442	402	25	)	)	PUNCT
ejpam-3442	402	26	(	(	PUNCT
ejpam-3442	402	27	2012	2012	NUM
ejpam-3442	402	28	,	,	PUNCT
ejpam-3442	402	29	89	89	NUM
ejpam-3442	402	30	-	-	SYM
ejpam-3442	402	31	96	96	NUM
ejpam-3442	402	32	.	.	PUNCT
ejpam-3442	403	1	[	[	X
ejpam-3442	403	2	21	21	NUM
ejpam-3442	403	3	]	]	PUNCT
ejpam-3442	403	4	p.	p.	PROPN
ejpam-3442	403	5	k.	k.	PROPN
ejpam-3442	404	1	maji	maji	PROPN
ejpam-3442	404	2	,	,	PUNCT
ejpam-3442	404	3	r.	r.	PROPN
ejpam-3442	404	4	biswas	biswas	PROPN
ejpam-3442	404	5	and	and	CCONJ
ejpam-3442	404	6	a.	a.	PROPN
ejpam-3442	404	7	r.	r.	PROPN
ejpam-3442	404	8	roy	roy	PROPN
ejpam-3442	404	9	,	,	PUNCT
ejpam-3442	404	10	soft	soft	ADJ
ejpam-3442	404	11	set	set	NOUN
ejpam-3442	404	12	theory	theory	NOUN
ejpam-3442	404	13	,	,	PUNCT
ejpam-3442	404	14	comput	comput	NOUN
ejpam-3442	404	15	.	.	PUNCT
ejpam-3442	405	1	math	math	NOUN
ejpam-3442	405	2	.	.	PUNCT
ejpam-3442	406	1	appl	appl	PROPN
ejpam-3442	406	2	.	.	PROPN
ejpam-3442	407	1	,	,	PUNCT
ejpam-3442	407	2	45	45	NUM
ejpam-3442	407	3	(	(	PUNCT
ejpam-3442	407	4	2003	2003	NUM
ejpam-3442	407	5	)	)	PUNCT
ejpam-3442	407	6	,	,	PUNCT
ejpam-3442	407	7	555	555	NUM
ejpam-3442	407	8	-	-	SYM
ejpam-3442	407	9	562	562	NUM
ejpam-3442	407	10	.	.	PUNCT
ejpam-3442	408	1	[	[	X
ejpam-3442	408	2	22	22	NUM
ejpam-3442	408	3	]	]	X
ejpam-3442	408	4	r.	r.	PROPN
ejpam-3442	408	5	manoharan	manoharan	PROPN
ejpam-3442	408	6	and	and	CCONJ
ejpam-3442	408	7	p.	p.	NOUN
ejpam-3442	408	8	thangavelu	thangavelu	NOUN
ejpam-3442	408	9	,	,	PUNCT
ejpam-3442	408	10	some	some	DET
ejpam-3442	408	11	new	new	ADJ
ejpam-3442	408	12	sets	set	NOUN
ejpam-3442	408	13	and	and	CCONJ
ejpam-3442	408	14	topologies	topology	NOUN
ejpam-3442	408	15	in	in	ADP
ejpam-3442	408	16	ideal	ideal	ADJ
ejpam-3442	408	17	topological	topological	ADJ
ejpam-3442	408	18	spaces	space	NOUN
ejpam-3442	408	19	,	,	PUNCT
ejpam-3442	408	20	chinese	chinese	ADJ
ejpam-3442	408	21	journal	journal	NOUN
ejpam-3442	408	22	of	of	ADP
ejpam-3442	408	23	mathematics	mathematic	NOUN
ejpam-3442	408	24	,	,	PUNCT
ejpam-3442	408	25	volume	volume	NOUN
ejpam-3442	408	26	(	(	PUNCT
ejpam-3442	408	27	2013	2013	NUM
ejpam-3442	408	28	)	)	PUNCT
ejpam-3442	408	29	,	,	PUNCT
ejpam-3442	408	30	article	article	NOUN
ejpam-3442	408	31	i	i	PROPN
ejpam-3442	408	32	d	d	PROPN
ejpam-3442	408	33	973608	973608	NUM
ejpam-3442	408	34	,	,	PUNCT
ejpam-3442	408	35	6	6	NUM
ejpam-3442	408	36	pages	page	NOUN
ejpam-3442	408	37	.	.	PUNCT
ejpam-3442	409	1	references	reference	NOUN
ejpam-3442	409	2	869	869	NUM
ejpam-3442	410	1	[	[	X
ejpam-3442	410	2	23	23	NUM
ejpam-3442	410	3	]	]	X
ejpam-3442	410	4	d.	d.	PROPN
ejpam-3442	410	5	molodtsov	molodtsov	PROPN
ejpam-3442	410	6	,	,	PUNCT
ejpam-3442	410	7	v.	v.	PROPN
ejpam-3442	410	8	y.	y.	PROPN
ejpam-3442	410	9	leonov	leonov	PROPN
ejpam-3442	410	10	and	and	CCONJ
ejpam-3442	410	11	d.	d.	PROPN
ejpam-3442	410	12	v.	v.	PROPN
ejpam-3442	410	13	kovkov	kovkov	PROPN
ejpam-3442	410	14	,	,	PUNCT
ejpam-3442	410	15	soft	soft	ADJ
ejpam-3442	410	16	sets	set	NOUN
ejpam-3442	410	17	technique	technique	NOUN
ejpam-3442	410	18	and	and	CCONJ
ejpam-3442	410	19	its	its	PRON
ejpam-3442	410	20	application	application	NOUN
ejpam-3442	410	21	,	,	PUNCT
ejpam-3442	410	22	nechetkie	nechetkie	ADJ
ejpam-3442	410	23	sistemy	sistemy	PROPN
ejpam-3442	411	1	i	i	PROPN
ejpam-3442	411	2	myagkie	myagkie	PROPN
ejpam-3442	411	3	vychisleniya	vychisleniya	PROPN
ejpam-3442	411	4	,	,	PUNCT
ejpam-3442	411	5	1	1	NUM
ejpam-3442	411	6	(	(	PUNCT
ejpam-3442	411	7	1	1	NUM
ejpam-3442	411	8	)	)	PUNCT
ejpam-3442	411	9	(	(	PUNCT
ejpam-3442	411	10	2006	2006	NUM
ejpam-3442	411	11	)	)	PUNCT
ejpam-3442	411	12	,	,	PUNCT
ejpam-3442	411	13	8	8	NUM
ejpam-3442	411	14	-	-	SYM
ejpam-3442	411	15	39	39	NUM
ejpam-3442	411	16	.	.	PUNCT
ejpam-3442	412	1	[	[	X
ejpam-3442	412	2	24	24	NUM
ejpam-3442	412	3	]	]	PUNCT
ejpam-3442	412	4	d.	d.	PROPN
ejpam-3442	412	5	a.	a.	PROPN
ejpam-3442	412	6	molodtsov	molodtsov	PROPN
ejpam-3442	412	7	,	,	PUNCT
ejpam-3442	412	8	soft	soft	ADJ
ejpam-3442	412	9	set	set	NOUN
ejpam-3442	412	10	theory	theory	NOUN
ejpam-3442	412	11	-	-	PUNCT
ejpam-3442	412	12	first	first	ADJ
ejpam-3442	412	13	results	result	NOUN
ejpam-3442	412	14	,	,	PUNCT
ejpam-3442	412	15	comput	comput	NOUN
ejpam-3442	412	16	.	.	PUNCT
ejpam-3442	413	1	math	math	NOUN
ejpam-3442	413	2	.	.	PUNCT
ejpam-3442	414	1	appl	appl	PROPN
ejpam-3442	414	2	.	.	PROPN
ejpam-3442	414	3	,	,	PUNCT
ejpam-3442	414	4	37	37	NUM
ejpam-3442	414	5	(	(	PUNCT
ejpam-3442	414	6	1999	1999	NUM
ejpam-3442	414	7	)	)	PUNCT
ejpam-3442	414	8	,	,	PUNCT
ejpam-3442	414	9	19	19	NUM
ejpam-3442	414	10	-	-	SYM
ejpam-3442	414	11	31	31	NUM
ejpam-3442	414	12	.	.	PUNCT
ejpam-3442	415	1	[	[	X
ejpam-3442	415	2	25	25	NUM
ejpam-3442	415	3	]	]	PUNCT
ejpam-3442	415	4	sk	sk	PROPN
ejpam-3442	415	5	.	.	PROPN
ejpam-3442	415	6	nazmul	nazmul	PROPN
ejpam-3442	415	7	and	and	CCONJ
ejpam-3442	415	8	s.	s.	PROPN
ejpam-3442	415	9	k.	k.	PROPN
ejpam-3442	415	10	samanta	samanta	PROPN
ejpam-3442	415	11	,	,	PUNCT
ejpam-3442	415	12	neighbourhood	neighbourhood	NOUN
ejpam-3442	415	13	properties	property	NOUN
ejpam-3442	415	14	of	of	ADP
ejpam-3442	415	15	soft	soft	ADJ
ejpam-3442	415	16	topological	topological	ADJ
ejpam-3442	415	17	spaces	space	NOUN
ejpam-3442	415	18	,	,	PUNCT
ejpam-3442	415	19	ann	ann	PROPN
ejpam-3442	415	20	.	.	PROPN
ejpam-3442	415	21	fuzzy	fuzzy	ADJ
ejpam-3442	415	22	math	math	NOUN
ejpam-3442	415	23	.	.	PUNCT
ejpam-3442	416	1	inform	inform	NOUN
ejpam-3442	416	2	.	.	PUNCT
ejpam-3442	416	3	,	,	PUNCT
ejpam-3442	416	4	6	6	NUM
ejpam-3442	416	5	(	(	PUNCT
ejpam-3442	416	6	2012	2012	NUM
ejpam-3442	416	7	)	)	PUNCT
ejpam-3442	416	8	,	,	PUNCT
ejpam-3442	416	9	1	1	NUM
ejpam-3442	416	10	-	-	SYM
ejpam-3442	416	11	15	15	NUM
ejpam-3442	416	12	.	.	PUNCT
ejpam-3442	417	1	[	[	X
ejpam-3442	417	2	26	26	NUM
ejpam-3442	417	3	]	]	X
ejpam-3442	417	4	d.	d.	PROPN
ejpam-3442	417	5	pei	pei	PROPN
ejpam-3442	417	6	and	and	CCONJ
ejpam-3442	417	7	d.	d.	PROPN
ejpam-3442	417	8	miao	miao	PROPN
ejpam-3442	417	9	,	,	PUNCT
ejpam-3442	417	10	from	from	ADP
ejpam-3442	417	11	soft	soft	ADJ
ejpam-3442	417	12	sets	set	NOUN
ejpam-3442	417	13	to	to	ADP
ejpam-3442	417	14	information	information	NOUN
ejpam-3442	417	15	systems	system	NOUN
ejpam-3442	417	16	,	,	PUNCT
ejpam-3442	417	17	in	in	ADP
ejpam-3442	417	18	:	:	PUNCT
ejpam-3442	417	19	x.	x.	PROPN
ejpam-3442	417	20	hu	hu	PROPN
ejpam-3442	417	21	,	,	PUNCT
ejpam-3442	417	22	q.	q.	PROPN
ejpam-3442	417	23	liu	liu	PROPN
ejpam-3442	417	24	,	,	PUNCT
ejpam-3442	417	25	a.	a.	NOUN
ejpam-3442	417	26	skowron	skowron	PROPN
ejpam-3442	417	27	,	,	PUNCT
ejpam-3442	417	28	t.	t.	PROPN
ejpam-3442	417	29	y.	y.	PROPN
ejpam-3442	417	30	lin	lin	PROPN
ejpam-3442	417	31	,	,	PUNCT
ejpam-3442	417	32	r.	r.	PROPN
ejpam-3442	417	33	r.	r.	PROPN
ejpam-3442	417	34	yager	yager	PROPN
ejpam-3442	417	35	,	,	PUNCT
ejpam-3442	417	36	b.	b.	PROPN
ejpam-3442	417	37	zhang	zhang	PROPN
ejpam-3442	417	38	(	(	PUNCT
ejpam-3442	417	39	eds	eds	PROPN
ejpam-3442	417	40	.	.	PUNCT
ejpam-3442	417	41	)	)	PUNCT
ejpam-3442	417	42	,	,	PUNCT
ejpam-3442	417	43	proceedings	proceeding	NOUN
ejpam-3442	417	44	of	of	ADP
ejpam-3442	417	45	granular	granular	ADJ
ejpam-3442	417	46	computing	computing	NOUN
ejpam-3442	417	47	,	,	PUNCT
ejpam-3442	417	48	in	in	ADP
ejpam-3442	417	49	:	:	PUNCT
ejpam-3442	417	50	ieee	ieee	NOUN
ejpam-3442	417	51	,	,	PUNCT
ejpam-3442	417	52	vol.2	vol.2	PROPN
ejpam-3442	417	53	,	,	PUNCT
ejpam-3442	417	54	2005	2005	NUM
ejpam-3442	417	55	,	,	PUNCT
ejpam-3442	417	56	pp	pp	ADJ
ejpam-3442	417	57	.	.	PUNCT
ejpam-3442	418	1	617	617	NUM
ejpam-3442	418	2	-	-	SYM
ejpam-3442	418	3	621	621	NUM
ejpam-3442	418	4	.	.	PUNCT
ejpam-3442	419	1	[	[	X
ejpam-3442	419	2	27	27	NUM
ejpam-3442	419	3	]	]	PUNCT
ejpam-3442	419	4	s.	s.	PROPN
ejpam-3442	419	5	scheinberg	scheinberg	PROPN
ejpam-3442	419	6	,	,	PUNCT
ejpam-3442	419	7	topologies	topology	NOUN
ejpam-3442	419	8	which	which	PRON
ejpam-3442	419	9	generate	generate	VERB
ejpam-3442	419	10	a	a	DET
ejpam-3442	419	11	complete	complete	ADJ
ejpam-3442	419	12	measure	measure	NOUN
ejpam-3442	419	13	algebra	algebra	NOUN
ejpam-3442	419	14	,	,	PUNCT
ejpam-3442	419	15	advances	advance	NOUN
ejpam-3442	419	16	in	in	ADP
ejpam-3442	419	17	math	math	NOUN
ejpam-3442	419	18	.	.	PUNCT
ejpam-3442	420	1	,	,	PUNCT
ejpam-3442	420	2	7	7	NUM
ejpam-3442	420	3	(	(	PUNCT
ejpam-3442	420	4	1971	1971	NUM
ejpam-3442	420	5	)	)	PUNCT
ejpam-3442	420	6	,	,	PUNCT
ejpam-3442	420	7	231	231	NUM
ejpam-3442	420	8	-	-	SYM
ejpam-3442	420	9	239	239	NUM
ejpam-3442	420	10	.	.	PUNCT
ejpam-3442	421	1	[	[	X
ejpam-3442	421	2	28	28	NUM
ejpam-3442	421	3	]	]	X
ejpam-3442	421	4	m.	m.	NOUN
ejpam-3442	421	5	shabir	shabir	PROPN
ejpam-3442	421	6	and	and	CCONJ
ejpam-3442	421	7	m.	m.	PROPN
ejpam-3442	421	8	naz	naz	PROPN
ejpam-3442	421	9	,	,	PUNCT
ejpam-3442	421	10	on	on	ADP
ejpam-3442	421	11	soft	soft	ADJ
ejpam-3442	421	12	topological	topological	ADJ
ejpam-3442	421	13	spaces	space	NOUN
ejpam-3442	421	14	,	,	PUNCT
ejpam-3442	421	15	comput	comput	NOUN
ejpam-3442	421	16	.	.	PUNCT
ejpam-3442	422	1	math	math	NOUN
ejpam-3442	422	2	.	.	PUNCT
ejpam-3442	423	1	appl	appl	PROPN
ejpam-3442	423	2	.	.	PROPN
ejpam-3442	423	3	,	,	PUNCT
ejpam-3442	423	4	61	61	NUM
ejpam-3442	423	5	(	(	PUNCT
ejpam-3442	423	6	2011	2011	NUM
ejpam-3442	423	7	)	)	PUNCT
ejpam-3442	423	8	,	,	PUNCT
ejpam-3442	423	9	1786	1786	NUM
ejpam-3442	423	10	-	-	SYM
ejpam-3442	423	11	1799	1799	NUM
ejpam-3442	423	12	.	.	PUNCT
ejpam-3442	424	1	[	[	X
ejpam-3442	424	2	29	29	NUM
ejpam-3442	424	3	]	]	X
ejpam-3442	424	4	r.	r.	PROPN
ejpam-3442	424	5	vaidyanathaswamy	vaidyanathaswamy	PROPN
ejpam-3442	424	6	,	,	PUNCT
ejpam-3442	424	7	the	the	DET
ejpam-3442	424	8	localisation	localisation	NOUN
ejpam-3442	424	9	theory	theory	NOUN
ejpam-3442	424	10	in	in	ADP
ejpam-3442	424	11	set	set	NOUN
ejpam-3442	424	12	-	-	PUNCT
ejpam-3442	424	13	topology	topology	NOUN
ejpam-3442	424	14	,	,	PUNCT
ejpam-3442	424	15	proc	proc	NOUN
ejpam-3442	424	16	.	.	PUNCT
ejpam-3442	425	1	indian	indian	PROPN
ejpam-3442	425	2	acad	acad	PROPN
ejpam-3442	425	3	.	.	PUNCT
ejpam-3442	426	1	sci	sci	PROPN
ejpam-3442	426	2	.	.	PROPN
ejpam-3442	426	3	,	,	PUNCT
ejpam-3442	426	4	sect	sect	NOUN
ejpam-3442	426	5	.	.	PUNCT
ejpam-3442	427	1	a.	a.	NOUN
ejpam-3442	427	2	,	,	PUNCT
ejpam-3442	427	3	20	20	NUM
ejpam-3442	427	4	(	(	PUNCT
ejpam-3442	427	5	1944	1944	NUM
ejpam-3442	427	6	)	)	PUNCT
ejpam-3442	427	7	,	,	PUNCT
ejpam-3442	427	8	51	51	NUM
ejpam-3442	427	9	-	-	SYM
ejpam-3442	427	10	61	61	NUM
ejpam-3442	427	11	.	.	PUNCT
ejpam-3442	428	1	[	[	X
ejpam-3442	428	2	30	30	NUM
ejpam-3442	428	3	]	]	X
ejpam-3442	428	4	n.	n.	NOUN
ejpam-3442	428	5	v.	v.	ADP
ejpam-3442	428	6	velicko	velicko	ADJ
ejpam-3442	428	7	,	,	PUNCT
ejpam-3442	428	8	h	h	NOUN
ejpam-3442	428	9	-	-	PUNCT
ejpam-3442	428	10	closed	closed	ADJ
ejpam-3442	428	11	topological	topological	ADJ
ejpam-3442	428	12	spaces	space	NOUN
ejpam-3442	428	13	,	,	PUNCT
ejpam-3442	428	14	mat	mat	PROPN
ejpam-3442	428	15	.	.	PUNCT
ejpam-3442	428	16	sb	sb	PROPN
ejpam-3442	428	17	.	.	PROPN
ejpam-3442	429	1	(	(	PUNCT
ejpam-3442	429	2	n.s	n.s	PROPN
ejpam-3442	429	3	.	.	PROPN
ejpam-3442	429	4	)	)	PUNCT
ejpam-3442	429	5	,	,	PUNCT
ejpam-3442	429	6	70	70	NUM
ejpam-3442	429	7	(	(	PUNCT
ejpam-3442	429	8	112	112	NUM
ejpam-3442	429	9	)	)	PUNCT
ejpam-3442	429	10	(	(	PUNCT
ejpam-3442	429	11	1966	1966	NUM
ejpam-3442	429	12	)	)	PUNCT
ejpam-3442	429	13	,	,	PUNCT
ejpam-3442	429	14	98	98	NUM
ejpam-3442	429	15	-	-	SYM
ejpam-3442	429	16	112	112	NUM
ejpam-3442	429	17	.	.	PUNCT
ejpam-3442	430	1	(	(	PUNCT
ejpam-3442	430	2	in	in	ADP
ejpam-3442	430	3	russian	russian	PROPN
ejpam-3442	430	4	)	)	PUNCT
ejpam-3442	430	5	;	;	PUNCT
ejpam-3442	430	6	in	in	ADP
ejpam-3442	430	7	:	:	PUNCT
ejpam-3442	430	8	american	american	PROPN
ejpam-3442	430	9	mathematical	mathematical	ADJ
ejpam-3442	430	10	society	society	NOUN
ejpam-3442	430	11	translations	translation	NOUN
ejpam-3442	430	12	,	,	PUNCT
ejpam-3442	430	13	vol	vol	NOUN
ejpam-3442	430	14	.	.	PROPN
ejpam-3442	430	15	78	78	NUM
ejpam-3442	430	16	,	,	PUNCT
ejpam-3442	430	17	american	american	PROPN
ejpam-3442	430	18	mathematical	mathematical	ADJ
ejpam-3442	430	19	society	society	NOUN
ejpam-3442	430	20	,	,	PUNCT
ejpam-3442	430	21	providence	providence	NOUN
ejpam-3442	430	22	,	,	PUNCT
ejpam-3442	430	23	ri	ri	NOUN
ejpam-3442	430	24	,	,	PUNCT
ejpam-3442	430	25	1969	1969	NUM
ejpam-3442	430	26	,	,	PUNCT
ejpam-3442	430	27	103	103	NUM
ejpam-3442	430	28	-	-	SYM
ejpam-3442	430	29	118	118	NUM
ejpam-3442	430	30	.	.	PUNCT
ejpam-3442	431	1	[	[	X
ejpam-3442	431	2	31	31	NUM
ejpam-3442	431	3	]	]	X
ejpam-3442	431	4	i.	i.	PROPN
ejpam-3442	431	5	zorlutuna	zorlutuna	PROPN
ejpam-3442	431	6	,	,	PUNCT
ejpam-3442	431	7	m.	m.	NOUN
ejpam-3442	431	8	akdag	akdag	PROPN
ejpam-3442	431	9	,	,	PUNCT
ejpam-3442	431	10	w.k	w.k	PROPN
ejpam-3442	431	11	.	.	PROPN
ejpam-3442	431	12	min	min	PROPN
ejpam-3442	431	13	and	and	CCONJ
ejpam-3442	431	14	s.	s.	PROPN
ejpam-3442	431	15	atmaca	atmaca	PROPN
ejpam-3442	431	16	,	,	PUNCT
ejpam-3442	431	17	remarks	remark	NOUN
ejpam-3442	431	18	on	on	ADP
ejpam-3442	431	19	soft	soft	ADJ
ejpam-3442	431	20	topological	topological	ADJ
ejpam-3442	431	21	spaces	space	NOUN
ejpam-3442	431	22	,	,	PUNCT
ejpam-3442	431	23	ann	ann	PROPN
ejpam-3442	431	24	.	.	PROPN
ejpam-3442	431	25	fuzzy	fuzzy	ADJ
ejpam-3442	431	26	math	math	NOUN
ejpam-3442	431	27	.	.	PUNCT
ejpam-3442	432	1	inform	inform	NOUN
ejpam-3442	432	2	.	.	PUNCT
ejpam-3442	432	3	,	,	PUNCT
ejpam-3442	432	4	3	3	NUM
ejpam-3442	432	5	(	(	PUNCT
ejpam-3442	432	6	2	2	NUM
ejpam-3442	432	7	)	)	PUNCT
ejpam-3442	432	8	(	(	PUNCT
ejpam-3442	432	9	2012	2012	NUM
ejpam-3442	432	10	)	)	PUNCT
ejpam-3442	432	11	,	,	PUNCT
ejpam-3442	432	12	171	171	NUM
ejpam-3442	432	13	-	-	SYM
ejpam-3442	432	14	185	185	NUM
ejpam-3442	432	15	.	.	PUNCT