id	sid	tid	token	lemma	pos
ejpam-2312	1	1	european	european	PROPN
ejpam-2312	1	2	journal	journal	PROPN
ejpam-2312	1	3	of	of	ADP
ejpam-2312	1	4	pure	pure	ADJ
ejpam-2312	1	5	and	and	CCONJ
ejpam-2312	1	6	applied	apply	VERB
ejpam-2312	1	7	mathematics	mathematic	NOUN
ejpam-2312	1	8	vol	vol	NOUN
ejpam-2312	1	9	.	.	PROPN
ejpam-2312	2	1	10	10	NUM
ejpam-2312	2	2	,	,	PUNCT
ejpam-2312	2	3	no	no	INTJ
ejpam-2312	2	4	.	.	NOUN
ejpam-2312	2	5	2	2	NUM
ejpam-2312	2	6	,	,	PUNCT
ejpam-2312	2	7	2017	2017	NUM
ejpam-2312	2	8	,	,	PUNCT
ejpam-2312	2	9	199	199	NUM
ejpam-2312	2	10	-	-	SYM
ejpam-2312	2	11	210	210	NUM
ejpam-2312	2	12	issn	issn	PROPN
ejpam-2312	2	13	1307	1307	NUM
ejpam-2312	2	14	-	-	SYM
ejpam-2312	2	15	5543	5543	NUM
ejpam-2312	2	16	–	–	PUNCT
ejpam-2312	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2312	2	18	published	publish	VERB
ejpam-2312	2	19	by	by	ADP
ejpam-2312	2	20	new	new	PROPN
ejpam-2312	2	21	york	york	PROPN
ejpam-2312	2	22	business	business	PROPN
ejpam-2312	2	23	global	global	ADJ
ejpam-2312	2	24	on	on	ADP
ejpam-2312	2	25	some	some	DET
ejpam-2312	2	26	properties	property	NOUN
ejpam-2312	2	27	of	of	ADP
ejpam-2312	2	28	weak	weak	ADJ
ejpam-2312	2	29	soft	soft	ADJ
ejpam-2312	2	30	axioms	axiom	NOUN
ejpam-2312	2	31	sabir	sabir	PROPN
ejpam-2312	2	32	hussain	hussain	PROPN
ejpam-2312	2	33	department	department	PROPN
ejpam-2312	2	34	of	of	ADP
ejpam-2312	2	35	mathematics	mathematics	PROPN
ejpam-2312	2	36	,	,	PUNCT
ejpam-2312	2	37	college	college	NOUN
ejpam-2312	2	38	of	of	ADP
ejpam-2312	2	39	science	science	NOUN
ejpam-2312	2	40	,	,	PUNCT
ejpam-2312	2	41	qassim	qassim	PROPN
ejpam-2312	2	42	university	university	PROPN
ejpam-2312	2	43	,	,	PUNCT
ejpam-2312	2	44	buraydah	buraydah	NOUN
ejpam-2312	2	45	51482	51482	NUM
ejpam-2312	3	1	,	,	PUNCT
ejpam-2312	3	2	saudi	saudi	PROPN
ejpam-2312	3	3	arabia	arabia	PROPN
ejpam-2312	3	4	abstract	abstract	NOUN
ejpam-2312	3	5	.	.	PUNCT
ejpam-2312	4	1	the	the	DET
ejpam-2312	4	2	aim	aim	NOUN
ejpam-2312	4	3	of	of	ADP
ejpam-2312	4	4	this	this	DET
ejpam-2312	4	5	paper	paper	NOUN
ejpam-2312	4	6	is	be	AUX
ejpam-2312	4	7	to	to	PART
ejpam-2312	4	8	initiate	initiate	VERB
ejpam-2312	4	9	and	and	CCONJ
ejpam-2312	4	10	discuss	discuss	VERB
ejpam-2312	4	11	the	the	DET
ejpam-2312	4	12	properties	property	NOUN
ejpam-2312	4	13	and	and	CCONJ
ejpam-2312	4	14	characterizations	characterization	NOUN
ejpam-2312	4	15	of	of	ADP
ejpam-2312	4	16	soft	soft	ADJ
ejpam-2312	4	17	semi	semi	NOUN
ejpam-2312	4	18	-	-	ADJ
ejpam-2312	4	19	ti	ti	ADJ
ejpam-2312	4	20	and	and	CCONJ
ejpam-2312	4	21	soft	soft	ADJ
ejpam-2312	4	22	semi	semi	NOUN
ejpam-2312	4	23	-	-	NOUN
ejpam-2312	4	24	di	di	ADJ
ejpam-2312	4	25	(	(	PUNCT
ejpam-2312	4	26	for	for	ADP
ejpam-2312	4	27	i	i	PRON
ejpam-2312	4	28	=	=	SYM
ejpam-2312	4	29	0	0	NUM
ejpam-2312	4	30	,	,	PUNCT
ejpam-2312	4	31	1	1	NUM
ejpam-2312	4	32	,	,	PUNCT
ejpam-2312	4	33	2	2	X
ejpam-2312	4	34	)	)	PUNCT
ejpam-2312	4	35	spaces	space	NOUN
ejpam-2312	4	36	at	at	ADP
ejpam-2312	4	37	soft	soft	ADJ
ejpam-2312	4	38	point	point	NOUN
ejpam-2312	4	39	by	by	ADP
ejpam-2312	4	40	analyzing	analyze	VERB
ejpam-2312	4	41	the	the	DET
ejpam-2312	4	42	relationship	relationship	NOUN
ejpam-2312	4	43	among	among	ADP
ejpam-2312	4	44	them	they	PRON
ejpam-2312	4	45	.	.	PUNCT
ejpam-2312	5	1	we	we	PRON
ejpam-2312	5	2	also	also	ADV
ejpam-2312	5	3	introduce	introduce	VERB
ejpam-2312	5	4	and	and	CCONJ
ejpam-2312	5	5	explore	explore	VERB
ejpam-2312	5	6	the	the	DET
ejpam-2312	5	7	properties	property	NOUN
ejpam-2312	5	8	of	of	ADP
ejpam-2312	5	9	soft	soft	ADJ
ejpam-2312	5	10	s	s	NOUN
ejpam-2312	5	11	-	-	ADJ
ejpam-2312	5	12	continuous	continuous	ADJ
ejpam-2312	5	13	functions	function	NOUN
ejpam-2312	5	14	.	.	PUNCT
ejpam-2312	6	1	these	these	DET
ejpam-2312	6	2	results	result	NOUN
ejpam-2312	6	3	will	will	AUX
ejpam-2312	6	4	be	be	AUX
ejpam-2312	6	5	useful	useful	ADJ
ejpam-2312	6	6	to	to	PART
ejpam-2312	6	7	enhance	enhance	VERB
ejpam-2312	6	8	the	the	DET
ejpam-2312	6	9	theoretical	theoretical	ADJ
ejpam-2312	6	10	framework	framework	NOUN
ejpam-2312	6	11	and	and	CCONJ
ejpam-2312	6	12	to	to	PART
ejpam-2312	6	13	promote	promote	VERB
ejpam-2312	6	14	further	further	ADJ
ejpam-2312	6	15	study	study	NOUN
ejpam-2312	6	16	towards	towards	ADP
ejpam-2312	6	17	the	the	DET
ejpam-2312	6	18	daily	daily	ADJ
ejpam-2312	6	19	life	life	NOUN
ejpam-2312	6	20	applications	application	NOUN
ejpam-2312	6	21	.	.	PUNCT
ejpam-2312	7	1	2010	2010	NUM
ejpam-2312	7	2	mathematics	mathematic	NOUN
ejpam-2312	7	3	subject	subject	NOUN
ejpam-2312	7	4	classifications	classification	NOUN
ejpam-2312	7	5	:	:	PUNCT
ejpam-2312	7	6	06d72	06d72	NOUN
ejpam-2312	7	7	,	,	PUNCT
ejpam-2312	7	8	54a10	54a10	NUM
ejpam-2312	7	9	,	,	PUNCT
ejpam-2312	7	10	54d10	54d10	NUM
ejpam-2312	7	11	key	key	ADJ
ejpam-2312	7	12	words	word	NOUN
ejpam-2312	7	13	and	and	CCONJ
ejpam-2312	7	14	phrases	phrase	NOUN
ejpam-2312	7	15	:	:	PUNCT
ejpam-2312	7	16	soft	soft	ADJ
ejpam-2312	7	17	sets	set	NOUN
ejpam-2312	7	18	,	,	PUNCT
ejpam-2312	7	19	soft	soft	ADJ
ejpam-2312	7	20	topology	topology	NOUN
ejpam-2312	7	21	,	,	PUNCT
ejpam-2312	7	22	soft	soft	ADJ
ejpam-2312	7	23	semi	semi	ADJ
ejpam-2312	7	24	-	-	ADJ
ejpam-2312	7	25	open(closed	open(close	VERB
ejpam-2312	7	26	)	)	PUNCT
ejpam-2312	7	27	,	,	PUNCT
ejpam-2312	7	28	soft	soft	ADJ
ejpam-2312	7	29	semi	semi	ADJ
ejpam-2312	7	30	-	-	ADJ
ejpam-2312	7	31	closure	closure	ADJ
ejpam-2312	7	32	,	,	PUNCT
ejpam-2312	7	33	soft	soft	ADJ
ejpam-2312	7	34	semi	semi	NOUN
ejpam-2312	7	35	-	-	NOUN
ejpam-2312	7	36	di	di	ADJ
ejpam-2312	7	37	(	(	PUNCT
ejpam-2312	7	38	for	for	ADP
ejpam-2312	7	39	i	i	PRON
ejpam-2312	7	40	=	=	SYM
ejpam-2312	7	41	0	0	NUM
ejpam-2312	7	42	,	,	PUNCT
ejpam-2312	7	43	1	1	NUM
ejpam-2312	7	44	,	,	PUNCT
ejpam-2312	7	45	2	2	NUM
ejpam-2312	7	46	)	)	PUNCT
ejpam-2312	7	47	spaces	space	NOUN
ejpam-2312	7	48	,	,	PUNCT
ejpam-2312	7	49	soft	soft	ADJ
ejpam-2312	7	50	semi	semi	NOUN
ejpam-2312	7	51	-	-	ADJ
ejpam-2312	7	52	ti(for	ti(for	ADP
ejpam-2312	7	53	i	i	PROPN
ejpam-2312	7	54	=	=	NOUN
ejpam-2312	7	55	0	0	NUM
ejpam-2312	7	56	,	,	PUNCT
ejpam-2312	7	57	1	1	NUM
ejpam-2312	7	58	,	,	PUNCT
ejpam-2312	7	59	2	2	NUM
ejpam-2312	7	60	)	)	PUNCT
ejpam-2312	7	61	spaces	space	NOUN
ejpam-2312	7	62	,	,	PUNCT
ejpam-2312	7	63	soft	soft	ADJ
ejpam-2312	7	64	s	s	NOUN
ejpam-2312	7	65	-	-	ADJ
ejpam-2312	7	66	continuous	continuous	ADJ
ejpam-2312	7	67	function	function	NOUN
ejpam-2312	7	68	1	1	NUM
ejpam-2312	7	69	.	.	X
ejpam-2312	7	70	introduction	introduction	NOUN
ejpam-2312	7	71	an	an	DET
ejpam-2312	7	72	application	application	NOUN
ejpam-2312	7	73	of	of	ADP
ejpam-2312	7	74	soft	soft	ADJ
ejpam-2312	7	75	sets	set	NOUN
ejpam-2312	7	76	in	in	ADP
ejpam-2312	7	77	decision	decision	NOUN
ejpam-2312	7	78	making	make	VERB
ejpam-2312	7	79	problems	problem	NOUN
ejpam-2312	7	80	that	that	PRON
ejpam-2312	7	81	is	be	AUX
ejpam-2312	7	82	based	base	VERB
ejpam-2312	7	83	on	on	ADP
ejpam-2312	7	84	the	the	DET
ejpam-2312	7	85	reduction	reduction	NOUN
ejpam-2312	7	86	of	of	ADP
ejpam-2312	7	87	parameters	parameter	NOUN
ejpam-2312	7	88	to	to	PART
ejpam-2312	7	89	keep	keep	VERB
ejpam-2312	7	90	the	the	DET
ejpam-2312	7	91	optimal	optimal	ADJ
ejpam-2312	7	92	choice	choice	NOUN
ejpam-2312	7	93	objects	object	NOUN
ejpam-2312	7	94	can	can	AUX
ejpam-2312	7	95	be	be	AUX
ejpam-2312	7	96	seen	see	VERB
ejpam-2312	7	97	.	.	PUNCT
ejpam-2312	8	1	this	this	PRON
ejpam-2312	8	2	is	be	AUX
ejpam-2312	8	3	also	also	ADV
ejpam-2312	8	4	useful	useful	ADJ
ejpam-2312	8	5	in	in	ADP
ejpam-2312	8	6	the	the	DET
ejpam-2312	8	7	process	process	NOUN
ejpam-2312	8	8	to	to	PART
ejpam-2312	8	9	construct	construct	VERB
ejpam-2312	8	10	models	model	NOUN
ejpam-2312	8	11	during	during	ADP
ejpam-2312	8	12	the	the	DET
ejpam-2312	8	13	modelling	modelling	NOUN
ejpam-2312	8	14	process	process	NOUN
ejpam-2312	8	15	in	in	ADP
ejpam-2312	8	16	different	different	ADJ
ejpam-2312	8	17	fields	field	NOUN
ejpam-2312	8	18	of	of	ADP
ejpam-2312	8	19	life	life	NOUN
ejpam-2312	8	20	.	.	PUNCT
ejpam-2312	9	1	the	the	DET
ejpam-2312	9	2	real	real	ADJ
ejpam-2312	9	3	world	world	NOUN
ejpam-2312	9	4	is	be	AUX
ejpam-2312	9	5	inherently	inherently	ADV
ejpam-2312	9	6	uncertain	uncertain	ADJ
ejpam-2312	9	7	,	,	PUNCT
ejpam-2312	9	8	imprecise	imprecise	ADJ
ejpam-2312	9	9	and	and	CCONJ
ejpam-2312	9	10	vague	vague	ADJ
ejpam-2312	9	11	.	.	PUNCT
ejpam-2312	10	1	because	because	SCONJ
ejpam-2312	10	2	of	of	ADP
ejpam-2312	10	3	various	various	ADJ
ejpam-2312	10	4	uncertainties	uncertainty	NOUN
ejpam-2312	10	5	,	,	PUNCT
ejpam-2312	10	6	classical	classical	ADJ
ejpam-2312	10	7	methods	method	NOUN
ejpam-2312	10	8	are	be	AUX
ejpam-2312	10	9	not	not	PART
ejpam-2312	10	10	successful	successful	ADJ
ejpam-2312	10	11	for	for	ADP
ejpam-2312	10	12	solving	solve	VERB
ejpam-2312	10	13	complicated	complicated	ADJ
ejpam-2312	10	14	problems	problem	NOUN
ejpam-2312	10	15	in	in	ADP
ejpam-2312	10	16	economics	economic	NOUN
ejpam-2312	10	17	,	,	PUNCT
ejpam-2312	10	18	engineering	engineering	NOUN
ejpam-2312	10	19	and	and	CCONJ
ejpam-2312	10	20	environment	environment	NOUN
ejpam-2312	10	21	.	.	PUNCT
ejpam-2312	11	1	a	a	DET
ejpam-2312	11	2	soft	soft	ADJ
ejpam-2312	11	3	set	set	NOUN
ejpam-2312	11	4	is	be	AUX
ejpam-2312	11	5	a	a	DET
ejpam-2312	11	6	collection	collection	NOUN
ejpam-2312	11	7	of	of	ADP
ejpam-2312	11	8	approximate	approximate	ADJ
ejpam-2312	11	9	descriptions	description	NOUN
ejpam-2312	11	10	of	of	ADP
ejpam-2312	11	11	an	an	DET
ejpam-2312	11	12	object	object	NOUN
ejpam-2312	11	13	and	and	CCONJ
ejpam-2312	11	14	is	be	AUX
ejpam-2312	11	15	free	free	ADJ
ejpam-2312	11	16	from	from	ADP
ejpam-2312	11	17	the	the	DET
ejpam-2312	11	18	parameterizations	parameterization	NOUN
ejpam-2312	11	19	inadequacy	inadequacy	NOUN
ejpam-2312	11	20	syndrome	syndrome	NOUN
ejpam-2312	11	21	of	of	ADP
ejpam-2312	11	22	fuzzy	fuzzy	ADJ
ejpam-2312	11	23	set	set	NOUN
ejpam-2312	11	24	theory	theory	NOUN
ejpam-2312	11	25	,	,	PUNCT
ejpam-2312	11	26	rough	rough	ADJ
ejpam-2312	11	27	set	set	NOUN
ejpam-2312	11	28	theory	theory	NOUN
ejpam-2312	11	29	,	,	PUNCT
ejpam-2312	11	30	probability	probability	NOUN
ejpam-2312	11	31	theory	theory	NOUN
ejpam-2312	11	32	and	and	CCONJ
ejpam-2312	11	33	game	game	NOUN
ejpam-2312	11	34	theory	theory	NOUN
ejpam-2312	11	35	.	.	PUNCT
ejpam-2312	12	1	soft	soft	ADJ
ejpam-2312	12	2	systems	system	NOUN
ejpam-2312	12	3	provide	provide	VERB
ejpam-2312	12	4	a	a	DET
ejpam-2312	12	5	very	very	ADV
ejpam-2312	12	6	general	general	ADJ
ejpam-2312	12	7	framework	framework	NOUN
ejpam-2312	12	8	with	with	ADP
ejpam-2312	12	9	the	the	DET
ejpam-2312	12	10	involvement	involvement	NOUN
ejpam-2312	12	11	of	of	ADP
ejpam-2312	12	12	parameters	parameter	NOUN
ejpam-2312	12	13	.	.	PUNCT
ejpam-2312	13	1	research	research	NOUN
ejpam-2312	13	2	works	work	VERB
ejpam-2312	13	3	on	on	ADP
ejpam-2312	13	4	soft	soft	ADJ
ejpam-2312	13	5	set	set	NOUN
ejpam-2312	13	6	theory	theory	NOUN
ejpam-2312	13	7	,	,	PUNCT
ejpam-2312	13	8	its	its	PRON
ejpam-2312	13	9	generalized	generalized	ADJ
ejpam-2312	13	10	structures	structure	NOUN
ejpam-2312	13	11	and	and	CCONJ
ejpam-2312	13	12	its	its	PRON
ejpam-2312	13	13	applications	application	NOUN
ejpam-2312	13	14	in	in	ADP
ejpam-2312	13	15	various	various	ADJ
ejpam-2312	13	16	fields	field	NOUN
ejpam-2312	13	17	are	be	AUX
ejpam-2312	13	18	progressing	progress	VERB
ejpam-2312	13	19	rapidly	rapidly	ADV
ejpam-2312	13	20	now	now	ADV
ejpam-2312	13	21	a	a	DET
ejpam-2312	13	22	days	day	NOUN
ejpam-2312	13	23	.	.	PUNCT
ejpam-2312	14	1	molodtsov	molodtsov	PROPN
ejpam-2312	15	1	[	[	X
ejpam-2312	15	2	14	14	NUM
ejpam-2312	15	3	,	,	PUNCT
ejpam-2312	15	4	15	15	NUM
ejpam-2312	15	5	]	]	PUNCT
ejpam-2312	15	6	initiated	initiate	VERB
ejpam-2312	15	7	and	and	CCONJ
ejpam-2312	15	8	applied	apply	VERB
ejpam-2312	15	9	soft	soft	ADJ
ejpam-2312	15	10	sets	set	NOUN
ejpam-2312	15	11	theory	theory	NOUN
ejpam-2312	15	12	,	,	PUNCT
ejpam-2312	15	13	while	while	SCONJ
ejpam-2312	15	14	modelling	model	VERB
ejpam-2312	15	15	the	the	DET
ejpam-2312	15	16	problems	problem	NOUN
ejpam-2312	15	17	in	in	ADP
ejpam-2312	15	18	the	the	DET
ejpam-2312	15	19	field	field	NOUN
ejpam-2312	15	20	of	of	ADP
ejpam-2312	15	21	science	science	NOUN
ejpam-2312	15	22	including	include	VERB
ejpam-2312	15	23	engineering	engineering	NOUN
ejpam-2312	15	24	physics	physic	NOUN
ejpam-2312	15	25	,	,	PUNCT
ejpam-2312	15	26	computer	computer	NOUN
ejpam-2312	15	27	science	science	NOUN
ejpam-2312	15	28	,	,	PUNCT
ejpam-2312	15	29	economics	economic	NOUN
ejpam-2312	15	30	,	,	PUNCT
ejpam-2312	15	31	social	social	ADJ
ejpam-2312	15	32	sciences	science	NOUN
ejpam-2312	15	33	and	and	CCONJ
ejpam-2312	15	34	medical	medical	ADJ
ejpam-2312	15	35	sciences	science	NOUN
ejpam-2312	15	36	,	,	PUNCT
ejpam-2312	15	37	to	to	PART
ejpam-2312	15	38	deal	deal	VERB
ejpam-2312	15	39	with	with	ADP
ejpam-2312	15	40	uncertain	uncertain	ADJ
ejpam-2312	15	41	data	datum	NOUN
ejpam-2312	15	42	and	and	CCONJ
ejpam-2312	15	43	not	not	PART
ejpam-2312	15	44	clear	clear	ADJ
ejpam-2312	15	45	objects	object	NOUN
ejpam-2312	15	46	without	without	ADP
ejpam-2312	15	47	complete	complete	ADJ
ejpam-2312	15	48	information	information	NOUN
ejpam-2312	15	49	.	.	PUNCT
ejpam-2312	16	1	maji	maji	PROPN
ejpam-2312	16	2	et	et	PROPN
ejpam-2312	16	3	al	al	PROPN
ejpam-2312	16	4	.	.	PUNCT
ejpam-2312	17	1	[	[	X
ejpam-2312	17	2	12	12	NUM
ejpam-2312	17	3	,	,	PUNCT
ejpam-2312	17	4	13	13	NUM
ejpam-2312	17	5	]	]	PUNCT
ejpam-2312	17	6	discussed	discuss	VERB
ejpam-2312	17	7	and	and	CCONJ
ejpam-2312	17	8	applied	apply	VERB
ejpam-2312	17	9	the	the	DET
ejpam-2312	17	10	soft	soft	ADJ
ejpam-2312	17	11	set	set	NOUN
ejpam-2312	17	12	theory	theory	NOUN
ejpam-2312	17	13	in	in	ADP
ejpam-2312	17	14	decision	decision	NOUN
ejpam-2312	17	15	making	make	VERB
ejpam-2312	17	16	problems	problem	NOUN
ejpam-2312	17	17	.	.	PUNCT
ejpam-2312	18	1	in	in	ADP
ejpam-2312	18	2	[	[	X
ejpam-2312	18	3	17	17	NUM
ejpam-2312	18	4	]	]	PUNCT
ejpam-2312	18	5	and	and	CCONJ
ejpam-2312	18	6	[	[	X
ejpam-2312	18	7	19	19	NUM
ejpam-2312	18	8	]	]	PUNCT
ejpam-2312	18	9	,	,	PUNCT
ejpam-2312	18	10	xiao	xiao	PROPN
ejpam-2312	18	11	et	et	PROPN
ejpam-2312	18	12	al	al	PROPN
ejpam-2312	18	13	.	.	PROPN
ejpam-2312	19	1	and	and	CCONJ
ejpam-2312	19	2	pei	pei	PROPN
ejpam-2312	19	3	et	et	PROPN
ejpam-2312	19	4	al	al	PROPN
ejpam-2312	19	5	.	.	PROPN
ejpam-2312	19	6	respectively	respectively	ADV
ejpam-2312	19	7	explored	explore	VERB
ejpam-2312	19	8	the	the	DET
ejpam-2312	19	9	soft	soft	ADJ
ejpam-2312	19	10	sets	set	NOUN
ejpam-2312	19	11	in	in	ADP
ejpam-2312	19	12	information	information	NOUN
ejpam-2312	19	13	systems	system	NOUN
ejpam-2312	19	14	.	.	PUNCT
ejpam-2312	20	1	the	the	DET
ejpam-2312	20	2	criteria	criterion	NOUN
ejpam-2312	20	3	of	of	ADP
ejpam-2312	20	4	measuring	measure	VERB
ejpam-2312	20	5	the	the	DET
ejpam-2312	20	6	sound	sound	ADJ
ejpam-2312	20	7	quality	quality	NOUN
ejpam-2312	20	8	through	through	ADP
ejpam-2312	20	9	the	the	DET
ejpam-2312	20	10	soft	soft	ADJ
ejpam-2312	20	11	sets	set	NOUN
ejpam-2312	20	12	studied	study	VERB
ejpam-2312	20	13	by	by	ADP
ejpam-2312	20	14	kostek	kostek	PROPN
ejpam-2312	21	1	[	[	X
ejpam-2312	21	2	11	11	NUM
ejpam-2312	21	3	]	]	PUNCT
ejpam-2312	21	4	.	.	PUNCT
ejpam-2312	22	1	mushrif	mushrif	PROPN
ejpam-2312	22	2	et	et	PROPN
ejpam-2312	22	3	al	al	PROPN
ejpam-2312	22	4	.	.	PUNCT
ejpam-2312	23	1	[	[	X
ejpam-2312	23	2	16	16	NUM
ejpam-2312	23	3	]	]	PUNCT
ejpam-2312	23	4	established	establish	VERB
ejpam-2312	23	5	the	the	DET
ejpam-2312	23	6	remarkable	remarkable	ADJ
ejpam-2312	23	7	method	method	NOUN
ejpam-2312	23	8	for	for	ADP
ejpam-2312	23	9	the	the	DET
ejpam-2312	23	10	classification	classification	NOUN
ejpam-2312	23	11	of	of	ADP
ejpam-2312	23	12	natural	natural	ADJ
ejpam-2312	23	13	textures	texture	NOUN
ejpam-2312	23	14	by	by	ADP
ejpam-2312	23	15	applying	apply	VERB
ejpam-2312	23	16	the	the	DET
ejpam-2312	23	17	concept	concept	NOUN
ejpam-2312	23	18	of	of	ADP
ejpam-2312	23	19	soft	soft	ADJ
ejpam-2312	23	20	set	set	NOUN
ejpam-2312	23	21	.	.	PUNCT
ejpam-2312	24	1	email	email	NOUN
ejpam-2312	24	2	addresses	address	NOUN
ejpam-2312	24	3	:	:	PUNCT
ejpam-2312	24	4	sabiriub@yahoo.com	sabiriub@yahoo.com	X
ejpam-2312	24	5	;	;	PUNCT
ejpam-2312	24	6	sh.hussain@qu.edu.sa	sh.hussain@qu.edu.sa	PROPN
ejpam-2312	24	7	(	(	PUNCT
ejpam-2312	24	8	s.	s.	PROPN
ejpam-2312	24	9	hussain	hussain	PROPN
ejpam-2312	24	10	)	)	PUNCT
ejpam-2312	24	11	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2312	25	1	199	199	NUM
ejpam-2312	25	2	c	c	X
ejpam-2312	25	3	©	©	PROPN
ejpam-2312	25	4	2017	2017	NUM
ejpam-2312	25	5	ejpam	ejpam	VERB
ejpam-2312	25	6	all	all	DET
ejpam-2312	25	7	rights	right	NOUN
ejpam-2312	25	8	reserved	reserve	VERB
ejpam-2312	25	9	.	.	PUNCT
ejpam-2312	26	1	s.	s.	PROPN
ejpam-2312	26	2	hussain	hussain	PROPN
ejpam-2312	26	3	/	/	SYM
ejpam-2312	26	4	eur	eur	PROPN
ejpam-2312	26	5	.	.	PUNCT
ejpam-2312	27	1	j.	j.	PROPN
ejpam-2312	27	2	pure	pure	PROPN
ejpam-2312	27	3	appl	appl	PROPN
ejpam-2312	27	4	.	.	PROPN
ejpam-2312	27	5	math	math	PROPN
ejpam-2312	27	6	,	,	PUNCT
ejpam-2312	27	7	10	10	NUM
ejpam-2312	27	8	(	(	PUNCT
ejpam-2312	27	9	2	2	NUM
ejpam-2312	27	10	)	)	PUNCT
ejpam-2312	27	11	(	(	PUNCT
ejpam-2312	27	12	2017	2017	NUM
ejpam-2312	27	13	)	)	PUNCT
ejpam-2312	27	14	,	,	PUNCT
ejpam-2312	27	15	199	199	NUM
ejpam-2312	27	16	-	-	SYM
ejpam-2312	27	17	210	210	NUM
ejpam-2312	27	18	200	200	NUM
ejpam-2312	27	19	in	in	ADP
ejpam-2312	27	20	[	[	X
ejpam-2312	27	21	18	18	NUM
ejpam-2312	27	22	]	]	PUNCT
ejpam-2312	27	23	,	,	PUNCT
ejpam-2312	27	24	shabir	shabir	PROPN
ejpam-2312	27	25	and	and	CCONJ
ejpam-2312	27	26	naz	naz	PROPN
ejpam-2312	27	27	introduced	introduce	VERB
ejpam-2312	27	28	and	and	CCONJ
ejpam-2312	27	29	studied	study	VERB
ejpam-2312	27	30	the	the	DET
ejpam-2312	27	31	primary	primary	ADJ
ejpam-2312	27	32	concepts	concept	NOUN
ejpam-2312	27	33	of	of	ADP
ejpam-2312	27	34	soft	soft	ADJ
ejpam-2312	27	35	topological	topological	ADJ
ejpam-2312	27	36	spaces	space	NOUN
ejpam-2312	27	37	.	.	PUNCT
ejpam-2312	28	1	after	after	ADP
ejpam-2312	28	2	that	that	DET
ejpam-2312	28	3	hussain	hussain	PROPN
ejpam-2312	29	1	[	[	X
ejpam-2312	29	2	6	6	NUM
ejpam-2312	29	3	,	,	PUNCT
ejpam-2312	29	4	7	7	NUM
ejpam-2312	29	5	]	]	PUNCT
ejpam-2312	29	6	,	,	PUNCT
ejpam-2312	29	7	hussain	hussain	PROPN
ejpam-2312	29	8	and	and	CCONJ
ejpam-2312	29	9	ahmad	ahmad	PROPN
ejpam-2312	29	10	[	[	X
ejpam-2312	29	11	8	8	NUM
ejpam-2312	29	12	,	,	PUNCT
ejpam-2312	29	13	9	9	NUM
ejpam-2312	29	14	]	]	PUNCT
ejpam-2312	29	15	and	and	CCONJ
ejpam-2312	29	16	[	[	X
ejpam-2312	29	17	1	1	NUM
ejpam-2312	29	18	]	]	PUNCT
ejpam-2312	29	19	,	,	PUNCT
ejpam-2312	29	20	aygunoglu	aygunoglu	PROPN
ejpam-2312	29	21	et	et	PROPN
ejpam-2312	29	22	al	al	PROPN
ejpam-2312	29	23	.	.	PUNCT
ejpam-2312	30	1	[	[	X
ejpam-2312	30	2	2	2	NUM
ejpam-2312	30	3	]	]	PUNCT
ejpam-2312	30	4	,	,	PUNCT
ejpam-2312	30	5	zorlutana	zorlutana	PROPN
ejpam-2312	30	6	et	et	PROPN
ejpam-2312	30	7	al	al	PROPN
ejpam-2312	30	8	.	.	PUNCT
ejpam-2312	31	1	[	[	X
ejpam-2312	31	2	20	20	NUM
ejpam-2312	31	3	]	]	PUNCT
ejpam-2312	31	4	continued	continue	VERB
ejpam-2312	31	5	to	to	PART
ejpam-2312	31	6	add	add	VERB
ejpam-2312	31	7	many	many	ADJ
ejpam-2312	31	8	basic	basic	ADJ
ejpam-2312	31	9	concepts	concept	NOUN
ejpam-2312	31	10	in	in	ADP
ejpam-2312	31	11	soft	soft	ADJ
ejpam-2312	31	12	topological	topological	ADJ
ejpam-2312	31	13	spaces	space	NOUN
ejpam-2312	31	14	.	.	PUNCT
ejpam-2312	32	1	in	in	ADP
ejpam-2312	32	2	[	[	X
ejpam-2312	32	3	3	3	NUM
ejpam-2312	32	4	,	,	PUNCT
ejpam-2312	32	5	4	4	NUM
ejpam-2312	32	6	]	]	PUNCT
ejpam-2312	32	7	,	,	PUNCT
ejpam-2312	32	8	chen	chen	PROPN
ejpam-2312	32	9	introduced	introduce	VERB
ejpam-2312	32	10	and	and	CCONJ
ejpam-2312	32	11	explored	explore	VERB
ejpam-2312	32	12	soft	soft	ADJ
ejpam-2312	32	13	semi	semi	ADJ
ejpam-2312	32	14	-	-	ADJ
ejpam-2312	32	15	open(closed	open(closed	ADJ
ejpam-2312	32	16	)	)	PUNCT
ejpam-2312	32	17	sets	set	NOUN
ejpam-2312	32	18	in	in	ADP
ejpam-2312	32	19	soft	soft	ADJ
ejpam-2312	32	20	topological	topological	ADJ
ejpam-2312	32	21	spaces	space	NOUN
ejpam-2312	32	22	.	.	PUNCT
ejpam-2312	33	1	in	in	ADP
ejpam-2312	33	2	[	[	X
ejpam-2312	33	3	5	5	NUM
ejpam-2312	33	4	]	]	PUNCT
ejpam-2312	33	5	,	,	PUNCT
ejpam-2312	33	6	hussain	hussain	PROPN
ejpam-2312	33	7	added	add	VERB
ejpam-2312	33	8	many	many	ADJ
ejpam-2312	33	9	concepts	concept	NOUN
ejpam-2312	33	10	toward	toward	ADP
ejpam-2312	33	11	soft	soft	ADJ
ejpam-2312	33	12	semi	semi	ADJ
ejpam-2312	33	13	-	-	ADJ
ejpam-2312	33	14	open	open	ADJ
ejpam-2312	33	15	sets	set	NOUN
ejpam-2312	33	16	and	and	CCONJ
ejpam-2312	33	17	soft	soft	ADJ
ejpam-2312	33	18	semi	semi	ADJ
ejpam-2312	33	19	-	-	ADJ
ejpam-2312	33	20	closed	closed	ADJ
ejpam-2312	33	21	sets	set	NOUN
ejpam-2312	33	22	in	in	ADP
ejpam-2312	33	23	soft	soft	ADJ
ejpam-2312	33	24	topological	topological	ADJ
ejpam-2312	33	25	spaces	space	NOUN
ejpam-2312	33	26	.	.	PUNCT
ejpam-2312	34	1	kharral	kharral	PROPN
ejpam-2312	34	2	and	and	CCONJ
ejpam-2312	34	3	ahmad	ahmad	PROPN
ejpam-2312	34	4	[	[	X
ejpam-2312	34	5	10	10	NUM
ejpam-2312	34	6	]	]	PUNCT
ejpam-2312	34	7	and	and	CCONJ
ejpam-2312	34	8	then	then	ADV
ejpam-2312	34	9	zorlutana	zorlutana	PROPN
ejpam-2312	35	1	[	[	X
ejpam-2312	35	2	20	20	NUM
ejpam-2312	35	3	]	]	PUNCT
ejpam-2312	35	4	discussed	discuss	VERB
ejpam-2312	35	5	the	the	DET
ejpam-2312	35	6	mappings	mapping	NOUN
ejpam-2312	35	7	of	of	ADP
ejpam-2312	35	8	soft	soft	ADJ
ejpam-2312	35	9	classes	class	NOUN
ejpam-2312	35	10	and	and	CCONJ
ejpam-2312	35	11	their	their	PRON
ejpam-2312	35	12	properties	property	NOUN
ejpam-2312	35	13	in	in	ADP
ejpam-2312	35	14	soft	soft	ADJ
ejpam-2312	35	15	topological	topological	ADJ
ejpam-2312	35	16	spaces	space	NOUN
ejpam-2312	35	17	.	.	PUNCT
ejpam-2312	36	1	recently	recently	ADV
ejpam-2312	36	2	in	in	ADP
ejpam-2312	36	3	[	[	X
ejpam-2312	36	4	7	7	NUM
ejpam-2312	36	5	]	]	PUNCT
ejpam-2312	36	6	,	,	PUNCT
ejpam-2312	36	7	hussain	hussain	PROPN
ejpam-2312	36	8	presented	present	VERB
ejpam-2312	36	9	and	and	CCONJ
ejpam-2312	36	10	discussed	discuss	VERB
ejpam-2312	36	11	basic	basic	ADJ
ejpam-2312	36	12	properties	property	NOUN
ejpam-2312	36	13	and	and	CCONJ
ejpam-2312	36	14	characterizations	characterization	NOUN
ejpam-2312	36	15	of	of	ADP
ejpam-2312	36	16	soft	soft	ADJ
ejpam-2312	36	17	pu	pu	ADJ
ejpam-2312	36	18	-	-	ADJ
ejpam-2312	36	19	continuous	continuous	ADJ
ejpam-2312	36	20	functions	function	NOUN
ejpam-2312	36	21	and	and	CCONJ
ejpam-2312	36	22	soft	soft	ADJ
ejpam-2312	36	23	pu	pu	PROPN
ejpam-2312	36	24	-	-	PUNCT
ejpam-2312	36	25	open(closed	open(close	VERB
ejpam-2312	36	26	)	)	PUNCT
ejpam-2312	36	27	functions	function	NOUN
ejpam-2312	36	28	.	.	PUNCT
ejpam-2312	37	1	2	2	X
ejpam-2312	37	2	.	.	X
ejpam-2312	37	3	preliminaries	preliminary	NOUN
ejpam-2312	37	4	first	first	ADV
ejpam-2312	37	5	we	we	PRON
ejpam-2312	37	6	recall	recall	VERB
ejpam-2312	37	7	some	some	DET
ejpam-2312	37	8	definitions	definition	NOUN
ejpam-2312	37	9	and	and	CCONJ
ejpam-2312	37	10	results	result	NOUN
ejpam-2312	37	11	which	which	PRON
ejpam-2312	37	12	will	will	AUX
ejpam-2312	37	13	use	use	VERB
ejpam-2312	37	14	in	in	ADP
ejpam-2312	37	15	the	the	DET
ejpam-2312	37	16	sequel	sequel	NOUN
ejpam-2312	37	17	.	.	PUNCT
ejpam-2312	38	1	definition	definition	NOUN
ejpam-2312	38	2	1	1	NUM
ejpam-2312	38	3	(	(	PUNCT
ejpam-2312	38	4	[	[	X
ejpam-2312	38	5	14	14	NUM
ejpam-2312	38	6	]	]	NUM
ejpam-2312	38	7	)	)	PUNCT
ejpam-2312	38	8	.	.	PUNCT
ejpam-2312	39	1	let	let	VERB
ejpam-2312	39	2	x	x	PRON
ejpam-2312	39	3	be	be	AUX
ejpam-2312	39	4	an	an	DET
ejpam-2312	39	5	initial	initial	ADJ
ejpam-2312	39	6	universe	universe	NOUN
ejpam-2312	39	7	and	and	CCONJ
ejpam-2312	39	8	e	e	NOUN
ejpam-2312	39	9	be	be	AUX
ejpam-2312	39	10	a	a	DET
ejpam-2312	39	11	set	set	NOUN
ejpam-2312	39	12	of	of	ADP
ejpam-2312	39	13	parameters	parameter	NOUN
ejpam-2312	39	14	.	.	PUNCT
ejpam-2312	40	1	let	let	VERB
ejpam-2312	40	2	p	p	NOUN
ejpam-2312	40	3	(	(	PUNCT
ejpam-2312	40	4	x	x	NOUN
ejpam-2312	40	5	)	)	PUNCT
ejpam-2312	40	6	denotes	denote	VERB
ejpam-2312	40	7	the	the	DET
ejpam-2312	40	8	power	power	NOUN
ejpam-2312	40	9	set	set	NOUN
ejpam-2312	40	10	of	of	ADP
ejpam-2312	40	11	x	x	PROPN
ejpam-2312	40	12	and	and	CCONJ
ejpam-2312	40	13	a	a	DET
ejpam-2312	40	14	be	be	AUX
ejpam-2312	40	15	a	a	DET
ejpam-2312	40	16	non	non	ADJ
ejpam-2312	40	17	-	-	ADJ
ejpam-2312	40	18	empty	empty	ADJ
ejpam-2312	40	19	subset	subset	NOUN
ejpam-2312	40	20	of	of	ADP
ejpam-2312	40	21	e.	e.	PROPN
ejpam-2312	40	22	a	a	DET
ejpam-2312	40	23	pair	pair	NOUN
ejpam-2312	40	24	(	(	PUNCT
ejpam-2312	40	25	f	f	X
ejpam-2312	40	26	,	,	PUNCT
ejpam-2312	40	27	a	a	PRON
ejpam-2312	40	28	)	)	PUNCT
ejpam-2312	40	29	is	be	AUX
ejpam-2312	40	30	called	call	VERB
ejpam-2312	40	31	a	a	DET
ejpam-2312	40	32	soft	soft	ADJ
ejpam-2312	40	33	set	set	NOUN
ejpam-2312	40	34	over	over	ADP
ejpam-2312	40	35	x	x	NOUN
ejpam-2312	40	36	,	,	PUNCT
ejpam-2312	40	37	where	where	SCONJ
ejpam-2312	40	38	f	f	PROPN
ejpam-2312	40	39	is	be	AUX
ejpam-2312	40	40	a	a	DET
ejpam-2312	40	41	mapping	mapping	NOUN
ejpam-2312	40	42	given	give	VERB
ejpam-2312	40	43	by	by	ADP
ejpam-2312	40	44	f	f	PROPN
ejpam-2312	40	45	:	:	PUNCT
ejpam-2312	40	46	a→	a→	PUNCT
ejpam-2312	40	47	p	p	X
ejpam-2312	40	48	(	(	PUNCT
ejpam-2312	40	49	x	x	NOUN
ejpam-2312	40	50	)	)	PUNCT
ejpam-2312	40	51	.	.	PUNCT
ejpam-2312	41	1	in	in	ADP
ejpam-2312	41	2	other	other	ADJ
ejpam-2312	41	3	words	word	NOUN
ejpam-2312	41	4	,	,	PUNCT
ejpam-2312	41	5	a	a	DET
ejpam-2312	41	6	soft	soft	ADJ
ejpam-2312	41	7	set	set	NOUN
ejpam-2312	41	8	over	over	ADP
ejpam-2312	41	9	x	x	PUNCT
ejpam-2312	41	10	is	be	AUX
ejpam-2312	41	11	a	a	DET
ejpam-2312	41	12	parameterized	parameterized	ADJ
ejpam-2312	41	13	family	family	NOUN
ejpam-2312	41	14	of	of	ADP
ejpam-2312	41	15	subsets	subset	NOUN
ejpam-2312	41	16	of	of	ADP
ejpam-2312	41	17	the	the	DET
ejpam-2312	41	18	universe	universe	NOUN
ejpam-2312	41	19	x.	x.	NOUN
ejpam-2312	41	20	for	for	ADP
ejpam-2312	41	21	e	e	PROPN
ejpam-2312	41	22	∈	∈	PROPN
ejpam-2312	41	23	a	a	PROPN
ejpam-2312	41	24	,	,	PUNCT
ejpam-2312	41	25	f	f	PROPN
ejpam-2312	41	26	(	(	PUNCT
ejpam-2312	41	27	e	e	NOUN
ejpam-2312	41	28	)	)	PUNCT
ejpam-2312	41	29	may	may	AUX
ejpam-2312	41	30	be	be	AUX
ejpam-2312	41	31	considered	consider	VERB
ejpam-2312	41	32	as	as	ADP
ejpam-2312	41	33	the	the	DET
ejpam-2312	41	34	set	set	NOUN
ejpam-2312	41	35	of	of	ADP
ejpam-2312	41	36	e	e	NOUN
ejpam-2312	41	37	-	-	ADJ
ejpam-2312	41	38	approximate	approximate	ADJ
ejpam-2312	41	39	elements	element	NOUN
ejpam-2312	41	40	of	of	ADP
ejpam-2312	41	41	the	the	DET
ejpam-2312	41	42	soft	soft	ADJ
ejpam-2312	41	43	set	set	NOUN
ejpam-2312	41	44	(	(	PUNCT
ejpam-2312	41	45	f	f	X
ejpam-2312	41	46	,	,	PUNCT
ejpam-2312	41	47	a	a	PRON
ejpam-2312	41	48	)	)	PUNCT
ejpam-2312	41	49	.	.	PUNCT
ejpam-2312	42	1	clearly	clearly	ADV
ejpam-2312	42	2	,	,	PUNCT
ejpam-2312	42	3	a	a	DET
ejpam-2312	42	4	soft	soft	ADJ
ejpam-2312	42	5	set	set	NOUN
ejpam-2312	42	6	is	be	AUX
ejpam-2312	42	7	not	not	PART
ejpam-2312	42	8	a	a	DET
ejpam-2312	42	9	set	set	NOUN
ejpam-2312	42	10	.	.	PUNCT
ejpam-2312	43	1	here	here	ADV
ejpam-2312	43	2	we	we	PRON
ejpam-2312	43	3	consider	consider	VERB
ejpam-2312	43	4	only	only	ADV
ejpam-2312	43	5	soft	soft	ADJ
ejpam-2312	43	6	sets	set	NOUN
ejpam-2312	43	7	(	(	PUNCT
ejpam-2312	43	8	f	f	X
ejpam-2312	43	9	,	,	PUNCT
ejpam-2312	43	10	a	a	PRON
ejpam-2312	43	11	)	)	PUNCT
ejpam-2312	43	12	over	over	ADP
ejpam-2312	43	13	a	a	DET
ejpam-2312	43	14	universe	universe	NOUN
ejpam-2312	43	15	x	x	PUNCT
ejpam-2312	43	16	in	in	ADP
ejpam-2312	43	17	which	which	PRON
ejpam-2312	43	18	all	all	DET
ejpam-2312	43	19	the	the	DET
ejpam-2312	43	20	parameters	parameter	NOUN
ejpam-2312	43	21	of	of	ADP
ejpam-2312	43	22	set	set	NOUN
ejpam-2312	43	23	a	a	PRON
ejpam-2312	43	24	are	be	AUX
ejpam-2312	43	25	same	same	ADJ
ejpam-2312	43	26	.	.	PUNCT
ejpam-2312	44	1	we	we	PRON
ejpam-2312	44	2	denote	denote	VERB
ejpam-2312	44	3	the	the	DET
ejpam-2312	44	4	family	family	NOUN
ejpam-2312	44	5	of	of	ADP
ejpam-2312	44	6	these	these	DET
ejpam-2312	44	7	soft	soft	ADJ
ejpam-2312	44	8	sets	set	NOUN
ejpam-2312	44	9	by	by	ADP
ejpam-2312	44	10	ss(x)a	ss(x)a	PROPN
ejpam-2312	44	11	.	.	PROPN
ejpam-2312	44	12	for	for	ADP
ejpam-2312	44	13	soft	soft	ADJ
ejpam-2312	44	14	subsets	subset	NOUN
ejpam-2312	44	15	,	,	PUNCT
ejpam-2312	44	16	soft	soft	ADJ
ejpam-2312	44	17	union	union	NOUN
ejpam-2312	44	18	,	,	PUNCT
ejpam-2312	44	19	soft	soft	ADJ
ejpam-2312	44	20	intersection	intersection	NOUN
ejpam-2312	44	21	,	,	PUNCT
ejpam-2312	44	22	soft	soft	ADJ
ejpam-2312	44	23	complement	complement	NOUN
ejpam-2312	44	24	,	,	PUNCT
ejpam-2312	44	25	their	their	PRON
ejpam-2312	44	26	properties	property	NOUN
ejpam-2312	44	27	and	and	CCONJ
ejpam-2312	44	28	the	the	DET
ejpam-2312	44	29	relations	relation	NOUN
ejpam-2312	44	30	to	to	ADP
ejpam-2312	44	31	each	each	DET
ejpam-2312	44	32	other	other	ADJ
ejpam-2312	44	33	;	;	PUNCT
ejpam-2312	44	34	the	the	DET
ejpam-2312	44	35	interested	interested	ADJ
ejpam-2312	44	36	reader	reader	NOUN
ejpam-2312	44	37	is	be	AUX
ejpam-2312	44	38	refer	refer	VERB
ejpam-2312	44	39	to	to	ADP
ejpam-2312	44	40	[	[	X
ejpam-2312	44	41	12	12	NUM
ejpam-2312	44	42	,	,	PUNCT
ejpam-2312	44	43	13	13	NUM
ejpam-2312	44	44	,	,	PUNCT
ejpam-2312	44	45	14	14	NUM
ejpam-2312	44	46	,	,	PUNCT
ejpam-2312	44	47	15	15	NUM
ejpam-2312	44	48	]	]	PUNCT
ejpam-2312	44	49	.	.	PUNCT
ejpam-2312	45	1	definition	definition	NOUN
ejpam-2312	45	2	2	2	NUM
ejpam-2312	45	3	(	(	PUNCT
ejpam-2312	45	4	[	[	X
ejpam-2312	45	5	18	18	NUM
ejpam-2312	45	6	]	]	NUM
ejpam-2312	45	7	)	)	PUNCT
ejpam-2312	45	8	.	.	PUNCT
ejpam-2312	46	1	let	let	VERB
ejpam-2312	46	2	τ	τ	PROPN
ejpam-2312	46	3	be	be	AUX
ejpam-2312	46	4	the	the	DET
ejpam-2312	46	5	collection	collection	NOUN
ejpam-2312	46	6	of	of	ADP
ejpam-2312	46	7	soft	soft	ADJ
ejpam-2312	46	8	sets	set	NOUN
ejpam-2312	46	9	over	over	ADP
ejpam-2312	46	10	x	x	NOUN
ejpam-2312	46	11	,	,	PUNCT
ejpam-2312	46	12	then	then	ADV
ejpam-2312	46	13	τ	τ	PROPN
ejpam-2312	46	14	is	be	AUX
ejpam-2312	46	15	said	say	VERB
ejpam-2312	46	16	to	to	PART
ejpam-2312	46	17	be	be	AUX
ejpam-2312	46	18	a	a	DET
ejpam-2312	46	19	soft	soft	ADJ
ejpam-2312	46	20	topology	topology	NOUN
ejpam-2312	46	21	on	on	ADP
ejpam-2312	46	22	x	x	SYM
ejpam-2312	46	23	,	,	PUNCT
ejpam-2312	46	24	if	if	SCONJ
ejpam-2312	46	25	(	(	PUNCT
ejpam-2312	46	26	1	1	X
ejpam-2312	46	27	)	)	PUNCT
ejpam-2312	46	28	φ	φ	NUM
ejpam-2312	46	29	,	,	PUNCT
ejpam-2312	46	30	x̃	x̃	PROPN
ejpam-2312	46	31	belong	belong	VERB
ejpam-2312	46	32	to	to	ADP
ejpam-2312	46	33	τ	τ	PROPN
ejpam-2312	46	34	.	.	PUNCT
ejpam-2312	47	1	(	(	PUNCT
ejpam-2312	47	2	2	2	X
ejpam-2312	47	3	)	)	PUNCT
ejpam-2312	47	4	the	the	DET
ejpam-2312	47	5	union	union	NOUN
ejpam-2312	47	6	of	of	ADP
ejpam-2312	47	7	any	any	DET
ejpam-2312	47	8	number	number	NOUN
ejpam-2312	47	9	of	of	ADP
ejpam-2312	47	10	soft	soft	ADJ
ejpam-2312	47	11	sets	set	NOUN
ejpam-2312	47	12	in	in	ADP
ejpam-2312	47	13	τ	τ	PROPN
ejpam-2312	47	14	belongs	belong	VERB
ejpam-2312	47	15	to	to	ADP
ejpam-2312	47	16	τ	τ	PROPN
ejpam-2312	47	17	.	.	PUNCT
ejpam-2312	48	1	(	(	PUNCT
ejpam-2312	48	2	3	3	X
ejpam-2312	48	3	)	)	PUNCT
ejpam-2312	48	4	the	the	DET
ejpam-2312	48	5	intersection	intersection	NOUN
ejpam-2312	48	6	of	of	ADP
ejpam-2312	48	7	any	any	DET
ejpam-2312	48	8	two	two	NUM
ejpam-2312	48	9	soft	soft	ADJ
ejpam-2312	48	10	sets	set	NOUN
ejpam-2312	48	11	in	in	ADP
ejpam-2312	48	12	τ	τ	PROPN
ejpam-2312	48	13	belongs	belong	VERB
ejpam-2312	48	14	to	to	ADP
ejpam-2312	48	15	τ	τ	PROPN
ejpam-2312	48	16	.	.	PUNCT
ejpam-2312	49	1	the	the	DET
ejpam-2312	49	2	triplet	triplet	NOUN
ejpam-2312	49	3	(	(	PUNCT
ejpam-2312	49	4	x	x	NOUN
ejpam-2312	49	5	,	,	PUNCT
ejpam-2312	49	6	τ	τ	PROPN
ejpam-2312	49	7	,	,	PUNCT
ejpam-2312	49	8	e	e	NOUN
ejpam-2312	49	9	)	)	PUNCT
ejpam-2312	49	10	is	be	AUX
ejpam-2312	49	11	called	call	VERB
ejpam-2312	49	12	a	a	DET
ejpam-2312	49	13	soft	soft	ADJ
ejpam-2312	49	14	topological	topological	ADJ
ejpam-2312	49	15	space	space	NOUN
ejpam-2312	49	16	over	over	ADP
ejpam-2312	49	17	x.	x.	NOUN
ejpam-2312	50	1	every	every	DET
ejpam-2312	50	2	member	member	NOUN
ejpam-2312	50	3	of	of	ADP
ejpam-2312	50	4	τ	τ	PROPN
ejpam-2312	50	5	is	be	AUX
ejpam-2312	50	6	called	call	VERB
ejpam-2312	50	7	soft	soft	ADJ
ejpam-2312	50	8	open	open	ADJ
ejpam-2312	50	9	set	set	NOUN
ejpam-2312	50	10	.	.	PUNCT
ejpam-2312	51	1	a	a	DET
ejpam-2312	51	2	soft	soft	ADJ
ejpam-2312	51	3	set	set	NOUN
ejpam-2312	51	4	is	be	AUX
ejpam-2312	51	5	called	call	VERB
ejpam-2312	51	6	soft	soft	ADJ
ejpam-2312	51	7	closed	closed	ADJ
ejpam-2312	51	8	if	if	SCONJ
ejpam-2312	52	1	and	and	CCONJ
ejpam-2312	52	2	only	only	ADV
ejpam-2312	52	3	if	if	SCONJ
ejpam-2312	52	4	its	its	PRON
ejpam-2312	52	5	complement	complement	NOUN
ejpam-2312	52	6	is	be	AUX
ejpam-2312	52	7	soft	soft	ADJ
ejpam-2312	52	8	open	open	ADJ
ejpam-2312	52	9	.	.	PUNCT
ejpam-2312	53	1	definition	definition	NOUN
ejpam-2312	53	2	3	3	NUM
ejpam-2312	53	3	(	(	PUNCT
ejpam-2312	53	4	[	[	X
ejpam-2312	53	5	8	8	NUM
ejpam-2312	53	6	,	,	PUNCT
ejpam-2312	53	7	18	18	NUM
ejpam-2312	53	8	]	]	PUNCT
ejpam-2312	53	9	)	)	PUNCT
ejpam-2312	53	10	.	.	PUNCT
ejpam-2312	54	1	let	let	VERB
ejpam-2312	54	2	(	(	PUNCT
ejpam-2312	54	3	x	x	X
ejpam-2312	54	4	,	,	PUNCT
ejpam-2312	54	5	τ	τ	PROPN
ejpam-2312	54	6	,	,	PUNCT
ejpam-2312	54	7	e	e	NOUN
ejpam-2312	54	8	)	)	PUNCT
ejpam-2312	54	9	be	be	AUX
ejpam-2312	54	10	a	a	DET
ejpam-2312	54	11	soft	soft	ADJ
ejpam-2312	54	12	topological	topological	ADJ
ejpam-2312	54	13	space	space	NOUN
ejpam-2312	54	14	over	over	ADP
ejpam-2312	54	15	x	x	PUNCT
ejpam-2312	54	16	and	and	CCONJ
ejpam-2312	54	17	a	a	DET
ejpam-2312	54	18	⊆	⊆	NUM
ejpam-2312	54	19	x.	x.	NOUN
ejpam-2312	54	20	then	then	ADV
ejpam-2312	54	21	(	(	PUNCT
ejpam-2312	54	22	1	1	X
ejpam-2312	54	23	)	)	PUNCT
ejpam-2312	54	24	soft	soft	ADJ
ejpam-2312	54	25	interior	interior	NOUN
ejpam-2312	54	26	of	of	ADP
ejpam-2312	54	27	soft	soft	ADJ
ejpam-2312	54	28	set	set	NOUN
ejpam-2312	54	29	(	(	PUNCT
ejpam-2312	54	30	f	f	X
ejpam-2312	54	31	,	,	PUNCT
ejpam-2312	54	32	a	a	PRON
ejpam-2312	54	33	)	)	PUNCT
ejpam-2312	54	34	over	over	ADP
ejpam-2312	54	35	x	x	PUNCT
ejpam-2312	54	36	denoted	denote	VERB
ejpam-2312	54	37	by	by	ADP
ejpam-2312	54	38	(	(	PUNCT
ejpam-2312	54	39	f	f	X
ejpam-2312	54	40	,	,	PUNCT
ejpam-2312	54	41	a	a	PRON
ejpam-2312	54	42	)	)	PUNCT
ejpam-2312	54	43	◦	◦	NOUN
ejpam-2312	54	44	and	and	CCONJ
ejpam-2312	54	45	is	be	AUX
ejpam-2312	54	46	defined	define	VERB
ejpam-2312	54	47	as	as	ADP
ejpam-2312	54	48	the	the	DET
ejpam-2312	54	49	union	union	NOUN
ejpam-2312	54	50	of	of	ADP
ejpam-2312	54	51	all	all	DET
ejpam-2312	54	52	soft	soft	ADJ
ejpam-2312	54	53	open	open	ADJ
ejpam-2312	54	54	sets	set	NOUN
ejpam-2312	54	55	contained	contain	VERB
ejpam-2312	54	56	in	in	ADP
ejpam-2312	54	57	(	(	PUNCT
ejpam-2312	54	58	f	f	X
ejpam-2312	54	59	,	,	PUNCT
ejpam-2312	54	60	a	a	PRON
ejpam-2312	54	61	)	)	PUNCT
ejpam-2312	54	62	.	.	PUNCT
ejpam-2312	55	1	thus	thus	ADV
ejpam-2312	55	2	(	(	PUNCT
ejpam-2312	55	3	f	f	X
ejpam-2312	55	4	,	,	PUNCT
ejpam-2312	55	5	a	a	PRON
ejpam-2312	55	6	)	)	PUNCT
ejpam-2312	55	7	◦	◦	NOUN
ejpam-2312	55	8	is	be	AUX
ejpam-2312	55	9	the	the	DET
ejpam-2312	55	10	largest	large	ADJ
ejpam-2312	55	11	soft	soft	ADJ
ejpam-2312	55	12	open	open	ADJ
ejpam-2312	55	13	set	set	NOUN
ejpam-2312	55	14	contained	contain	VERB
ejpam-2312	55	15	in	in	ADP
ejpam-2312	55	16	(	(	PUNCT
ejpam-2312	55	17	f	f	X
ejpam-2312	55	18	,	,	PUNCT
ejpam-2312	55	19	a	a	PRON
ejpam-2312	55	20	)	)	PUNCT
ejpam-2312	55	21	.	.	PUNCT
ejpam-2312	56	1	(	(	PUNCT
ejpam-2312	56	2	2	2	X
ejpam-2312	56	3	)	)	PUNCT
ejpam-2312	56	4	soft	soft	ADJ
ejpam-2312	56	5	closure	closure	NOUN
ejpam-2312	56	6	of	of	ADP
ejpam-2312	56	7	(	(	PUNCT
ejpam-2312	56	8	f	f	X
ejpam-2312	56	9	,	,	PUNCT
ejpam-2312	56	10	a	a	PRON
ejpam-2312	56	11	)	)	PUNCT
ejpam-2312	56	12	,	,	PUNCT
ejpam-2312	56	13	denoted	denote	VERB
ejpam-2312	56	14	by	by	ADP
ejpam-2312	56	15	(	(	PUNCT
ejpam-2312	56	16	f	f	X
ejpam-2312	56	17	,	,	PUNCT
ejpam-2312	56	18	a	a	PRON
ejpam-2312	56	19	)	)	PUNCT
ejpam-2312	56	20	is	be	AUX
ejpam-2312	56	21	the	the	DET
ejpam-2312	56	22	intersection	intersection	NOUN
ejpam-2312	56	23	of	of	ADP
ejpam-2312	56	24	all	all	DET
ejpam-2312	56	25	soft	soft	ADJ
ejpam-2312	56	26	closed	closed	ADJ
ejpam-2312	56	27	super	super	ADJ
ejpam-2312	56	28	sets	set	NOUN
ejpam-2312	56	29	of	of	ADP
ejpam-2312	56	30	(	(	PUNCT
ejpam-2312	56	31	f	f	X
ejpam-2312	56	32	,	,	PUNCT
ejpam-2312	56	33	a	a	PRON
ejpam-2312	56	34	)	)	PUNCT
ejpam-2312	56	35	.	.	PUNCT
ejpam-2312	57	1	clearly	clearly	ADV
ejpam-2312	57	2	(	(	PUNCT
ejpam-2312	57	3	f	f	X
ejpam-2312	57	4	,	,	PUNCT
ejpam-2312	57	5	a	a	PRON
ejpam-2312	57	6	)	)	PUNCT
ejpam-2312	57	7	is	be	AUX
ejpam-2312	57	8	the	the	DET
ejpam-2312	57	9	smallest	small	ADJ
ejpam-2312	57	10	soft	soft	ADJ
ejpam-2312	57	11	closed	closed	ADJ
ejpam-2312	57	12	set	set	VERB
ejpam-2312	57	13	over	over	ADP
ejpam-2312	57	14	x	x	ADP
ejpam-2312	57	15	which	which	PRON
ejpam-2312	57	16	contains	contain	VERB
ejpam-2312	57	17	(	(	PUNCT
ejpam-2312	57	18	f	f	X
ejpam-2312	57	19	,	,	PUNCT
ejpam-2312	57	20	a	a	PRON
ejpam-2312	57	21	)	)	PUNCT
ejpam-2312	57	22	.	.	PUNCT
ejpam-2312	58	1	s.	s.	PROPN
ejpam-2312	58	2	hussain	hussain	PROPN
ejpam-2312	58	3	/	/	SYM
ejpam-2312	58	4	eur	eur	PROPN
ejpam-2312	58	5	.	.	PUNCT
ejpam-2312	59	1	j.	j.	PROPN
ejpam-2312	59	2	pure	pure	PROPN
ejpam-2312	59	3	appl	appl	PROPN
ejpam-2312	59	4	.	.	PROPN
ejpam-2312	59	5	math	math	PROPN
ejpam-2312	59	6	,	,	PUNCT
ejpam-2312	59	7	10	10	NUM
ejpam-2312	59	8	(	(	PUNCT
ejpam-2312	59	9	2	2	NUM
ejpam-2312	59	10	)	)	PUNCT
ejpam-2312	59	11	(	(	PUNCT
ejpam-2312	59	12	2017	2017	NUM
ejpam-2312	59	13	)	)	PUNCT
ejpam-2312	59	14	,	,	PUNCT
ejpam-2312	59	15	199	199	NUM
ejpam-2312	59	16	-	-	SYM
ejpam-2312	59	17	210	210	NUM
ejpam-2312	59	18	201	201	NUM
ejpam-2312	59	19	(	(	PUNCT
ejpam-2312	59	20	3	3	NUM
ejpam-2312	59	21	)	)	PUNCT
ejpam-2312	59	22	soft	soft	ADJ
ejpam-2312	59	23	boundary	boundary	NOUN
ejpam-2312	59	24	of	of	ADP
ejpam-2312	59	25	soft	soft	ADJ
ejpam-2312	59	26	set	set	NOUN
ejpam-2312	59	27	(	(	PUNCT
ejpam-2312	59	28	f	f	X
ejpam-2312	59	29	,	,	PUNCT
ejpam-2312	59	30	a	a	PRON
ejpam-2312	59	31	)	)	PUNCT
ejpam-2312	59	32	over	over	ADP
ejpam-2312	59	33	x	x	PUNCT
ejpam-2312	59	34	denoted	denote	VERB
ejpam-2312	59	35	by	by	ADP
ejpam-2312	59	36	(	(	PUNCT
ejpam-2312	59	37	f	f	X
ejpam-2312	59	38	,	,	PUNCT
ejpam-2312	59	39	a	a	PRON
ejpam-2312	59	40	)	)	PUNCT
ejpam-2312	59	41	and	and	CCONJ
ejpam-2312	59	42	is	be	AUX
ejpam-2312	59	43	defined	define	VERB
ejpam-2312	59	44	as	as	ADP
ejpam-2312	59	45	(	(	PUNCT
ejpam-2312	59	46	f	f	X
ejpam-2312	59	47	,	,	PUNCT
ejpam-2312	59	48	a	a	PRON
ejpam-2312	59	49	)	)	PUNCT
ejpam-2312	59	50	=	=	SYM
ejpam-2312	59	51	(	(	PUNCT
ejpam-2312	59	52	f	f	X
ejpam-2312	59	53	,	,	PUNCT
ejpam-2312	59	54	a	a	PRON
ejpam-2312	59	55	)	)	PUNCT
ejpam-2312	59	56	∩	∩	NOUN
ejpam-2312	59	57	(	(	PUNCT
ejpam-2312	59	58	(	(	PUNCT
ejpam-2312	59	59	f	f	X
ejpam-2312	59	60	,	,	PUNCT
ejpam-2312	59	61	a)′	a)′	PROPN
ejpam-2312	59	62	)	)	PUNCT
ejpam-2312	59	63	.	.	PUNCT
ejpam-2312	60	1	obviously	obviously	ADV
ejpam-2312	60	2	(	(	PUNCT
ejpam-2312	60	3	f	f	X
ejpam-2312	60	4	,	,	PUNCT
ejpam-2312	60	5	a	a	PRON
ejpam-2312	60	6	)	)	PUNCT
ejpam-2312	60	7	is	be	AUX
ejpam-2312	60	8	a	a	DET
ejpam-2312	60	9	smallest	small	ADJ
ejpam-2312	60	10	soft	soft	ADJ
ejpam-2312	60	11	closed	closed	ADJ
ejpam-2312	60	12	set	set	VERB
ejpam-2312	60	13	over	over	ADP
ejpam-2312	60	14	x	x	PUNCT
ejpam-2312	60	15	containing	contain	VERB
ejpam-2312	60	16	(	(	PUNCT
ejpam-2312	60	17	f	f	X
ejpam-2312	60	18	,	,	PUNCT
ejpam-2312	60	19	a	a	PRON
ejpam-2312	60	20	)	)	PUNCT
ejpam-2312	60	21	.	.	PUNCT
ejpam-2312	61	1	for	for	ADP
ejpam-2312	61	2	detailed	detailed	ADJ
ejpam-2312	61	3	properties	property	NOUN
ejpam-2312	61	4	of	of	ADP
ejpam-2312	61	5	soft	soft	ADJ
ejpam-2312	61	6	interior	interior	NOUN
ejpam-2312	61	7	,	,	PUNCT
ejpam-2312	61	8	soft	soft	ADJ
ejpam-2312	61	9	closure	closure	NOUN
ejpam-2312	61	10	and	and	CCONJ
ejpam-2312	61	11	soft	soft	ADJ
ejpam-2312	61	12	boundary	boundary	NOUN
ejpam-2312	61	13	,	,	PUNCT
ejpam-2312	61	14	we	we	PRON
ejpam-2312	61	15	refer	refer	VERB
ejpam-2312	61	16	to	to	ADP
ejpam-2312	61	17	[	[	X
ejpam-2312	61	18	8	8	NUM
ejpam-2312	61	19	]	]	PUNCT
ejpam-2312	61	20	.	.	PUNCT
ejpam-2312	62	1	definition	definition	NOUN
ejpam-2312	62	2	4	4	NUM
ejpam-2312	62	3	(	(	PUNCT
ejpam-2312	62	4	[	[	X
ejpam-2312	62	5	3	3	NUM
ejpam-2312	62	6	]	]	NUM
ejpam-2312	62	7	)	)	PUNCT
ejpam-2312	62	8	.	.	PUNCT
ejpam-2312	63	1	let	let	VERB
ejpam-2312	63	2	(	(	PUNCT
ejpam-2312	63	3	x	x	X
ejpam-2312	63	4	,	,	PUNCT
ejpam-2312	63	5	τ	τ	PROPN
ejpam-2312	63	6	,	,	PUNCT
ejpam-2312	63	7	e	e	NOUN
ejpam-2312	63	8	)	)	PUNCT
ejpam-2312	63	9	be	be	AUX
ejpam-2312	63	10	a	a	DET
ejpam-2312	63	11	soft	soft	ADJ
ejpam-2312	63	12	topological	topological	ADJ
ejpam-2312	63	13	space	space	NOUN
ejpam-2312	63	14	over	over	ADP
ejpam-2312	63	15	x	x	PUNCT
ejpam-2312	63	16	with	with	ADP
ejpam-2312	63	17	a	a	DET
ejpam-2312	63	18	⊆	⊆	NUM
ejpam-2312	63	19	x	x	PUNCT
ejpam-2312	63	20	and	and	CCONJ
ejpam-2312	63	21	(	(	PUNCT
ejpam-2312	63	22	f	f	X
ejpam-2312	63	23	,	,	PUNCT
ejpam-2312	63	24	a	a	PRON
ejpam-2312	63	25	)	)	PUNCT
ejpam-2312	63	26	be	be	AUX
ejpam-2312	63	27	a	a	DET
ejpam-2312	63	28	soft	soft	ADJ
ejpam-2312	63	29	set	set	NOUN
ejpam-2312	63	30	over	over	ADP
ejpam-2312	63	31	x.	x.	NOUN
ejpam-2312	63	32	then	then	ADV
ejpam-2312	63	33	(	(	PUNCT
ejpam-2312	63	34	f	f	X
ejpam-2312	63	35	,	,	PUNCT
ejpam-2312	63	36	a	a	PRON
ejpam-2312	63	37	)	)	PUNCT
ejpam-2312	63	38	is	be	AUX
ejpam-2312	63	39	called	call	VERB
ejpam-2312	63	40	soft	soft	ADJ
ejpam-2312	63	41	semi	semi	ADJ
ejpam-2312	63	42	-	-	ADJ
ejpam-2312	63	43	open	open	ADJ
ejpam-2312	63	44	set	set	NOUN
ejpam-2312	63	45	if	if	SCONJ
ejpam-2312	63	46	and	and	CCONJ
ejpam-2312	63	47	only	only	ADV
ejpam-2312	63	48	if	if	SCONJ
ejpam-2312	63	49	there	there	PRON
ejpam-2312	63	50	exists	exist	VERB
ejpam-2312	63	51	a	a	DET
ejpam-2312	63	52	soft	soft	ADJ
ejpam-2312	63	53	open	open	ADJ
ejpam-2312	63	54	set	set	NOUN
ejpam-2312	63	55	(	(	PUNCT
ejpam-2312	63	56	g	g	NOUN
ejpam-2312	63	57	,	,	PUNCT
ejpam-2312	63	58	a	a	PRON
ejpam-2312	63	59	)	)	PUNCT
ejpam-2312	63	60	such	such	ADJ
ejpam-2312	63	61	that	that	SCONJ
ejpam-2312	63	62	(	(	PUNCT
ejpam-2312	63	63	g	g	NOUN
ejpam-2312	63	64	,	,	PUNCT
ejpam-2312	63	65	a)⊆̃(f	a)⊆̃(f	PROPN
ejpam-2312	63	66	,	,	PUNCT
ejpam-2312	63	67	a)⊆̃(g	a)⊆̃(g	PROPN
ejpam-2312	63	68	,	,	PUNCT
ejpam-2312	63	69	a	a	PRON
ejpam-2312	63	70	)	)	PUNCT
ejpam-2312	63	71	.	.	PUNCT
ejpam-2312	64	1	the	the	DET
ejpam-2312	64	2	set	set	NOUN
ejpam-2312	64	3	of	of	ADP
ejpam-2312	64	4	all	all	DET
ejpam-2312	64	5	soft	soft	ADJ
ejpam-2312	64	6	semi	semi	ADJ
ejpam-2312	64	7	-	-	ADJ
ejpam-2312	64	8	open	open	ADJ
ejpam-2312	64	9	sets	set	NOUN
ejpam-2312	64	10	is	be	AUX
ejpam-2312	64	11	denoted	denote	VERB
ejpam-2312	64	12	by	by	ADP
ejpam-2312	64	13	s.s.o(x	s.s.o(x	NOUN
ejpam-2312	64	14	)	)	PUNCT
ejpam-2312	64	15	.	.	PUNCT
ejpam-2312	65	1	note	note	VERB
ejpam-2312	65	2	that	that	SCONJ
ejpam-2312	65	3	every	every	DET
ejpam-2312	65	4	soft	soft	ADJ
ejpam-2312	65	5	open	open	ADJ
ejpam-2312	65	6	set	set	NOUN
ejpam-2312	65	7	is	be	AUX
ejpam-2312	65	8	soft	soft	ADJ
ejpam-2312	65	9	semi	semi	ADJ
ejpam-2312	65	10	-	-	ADJ
ejpam-2312	65	11	open	open	ADJ
ejpam-2312	65	12	set	set	NOUN
ejpam-2312	65	13	.	.	PUNCT
ejpam-2312	66	1	a	a	DET
ejpam-2312	66	2	soft	soft	ADJ
ejpam-2312	66	3	set	set	NOUN
ejpam-2312	66	4	(	(	PUNCT
ejpam-2312	66	5	f	f	X
ejpam-2312	66	6	,	,	PUNCT
ejpam-2312	66	7	a	a	PRON
ejpam-2312	66	8	)	)	PUNCT
ejpam-2312	66	9	is	be	AUX
ejpam-2312	66	10	said	say	VERB
ejpam-2312	66	11	to	to	PART
ejpam-2312	66	12	be	be	AUX
ejpam-2312	66	13	soft	soft	ADJ
ejpam-2312	66	14	semi	semi	ADJ
ejpam-2312	66	15	-	-	ADJ
ejpam-2312	66	16	closed	closed	ADJ
ejpam-2312	66	17	if	if	SCONJ
ejpam-2312	66	18	its	its	PRON
ejpam-2312	66	19	soft	soft	ADJ
ejpam-2312	66	20	relative	relative	ADJ
ejpam-2312	66	21	complement	complement	NOUN
ejpam-2312	66	22	is	be	AUX
ejpam-2312	66	23	soft	soft	ADJ
ejpam-2312	66	24	semi	semi	ADJ
ejpam-2312	66	25	-	-	ADJ
ejpam-2312	66	26	open	open	ADJ
ejpam-2312	66	27	.	.	PUNCT
ejpam-2312	67	1	equivalently	equivalently	ADV
ejpam-2312	67	2	,	,	PUNCT
ejpam-2312	67	3	there	there	PRON
ejpam-2312	67	4	exists	exist	VERB
ejpam-2312	67	5	a	a	DET
ejpam-2312	67	6	soft	soft	ADJ
ejpam-2312	67	7	closed	closed	ADJ
ejpam-2312	67	8	set	set	NOUN
ejpam-2312	67	9	(	(	PUNCT
ejpam-2312	67	10	g	g	NOUN
ejpam-2312	67	11	,	,	PUNCT
ejpam-2312	67	12	a	a	PRON
ejpam-2312	67	13	)	)	PUNCT
ejpam-2312	67	14	such	such	ADJ
ejpam-2312	67	15	that	that	SCONJ
ejpam-2312	67	16	(	(	PUNCT
ejpam-2312	67	17	g	g	NOUN
ejpam-2312	67	18	,	,	PUNCT
ejpam-2312	67	19	a)	a)	NOUN
ejpam-2312	67	20	◦	◦	NOUN
ejpam-2312	67	21	⊆̃(f	⊆̃(f	NOUN
ejpam-2312	67	22	,	,	PUNCT
ejpam-2312	67	23	a)⊆̃(g	a)⊆̃(g	PROPN
ejpam-2312	67	24	,	,	PUNCT
ejpam-2312	67	25	a	a	PRON
ejpam-2312	67	26	)	)	PUNCT
ejpam-2312	67	27	.	.	PUNCT
ejpam-2312	68	1	note	note	VERB
ejpam-2312	68	2	that	that	SCONJ
ejpam-2312	68	3	every	every	DET
ejpam-2312	68	4	soft	soft	ADJ
ejpam-2312	68	5	closed	closed	ADJ
ejpam-2312	68	6	set	set	NOUN
ejpam-2312	68	7	is	be	AUX
ejpam-2312	68	8	soft	soft	ADJ
ejpam-2312	68	9	semi	semi	ADJ
ejpam-2312	68	10	-	-	ADJ
ejpam-2312	68	11	closed	closed	ADJ
ejpam-2312	68	12	set	set	NOUN
ejpam-2312	68	13	.	.	PUNCT
ejpam-2312	69	1	definition	definition	NOUN
ejpam-2312	69	2	5	5	NUM
ejpam-2312	69	3	(	(	PUNCT
ejpam-2312	69	4	[	[	X
ejpam-2312	69	5	5	5	NUM
ejpam-2312	69	6	]	]	PUNCT
ejpam-2312	69	7	)	)	PUNCT
ejpam-2312	69	8	.	.	PUNCT
ejpam-2312	70	1	let	let	VERB
ejpam-2312	70	2	(	(	PUNCT
ejpam-2312	70	3	x	x	X
ejpam-2312	70	4	,	,	PUNCT
ejpam-2312	70	5	τ	τ	PROPN
ejpam-2312	70	6	,	,	PUNCT
ejpam-2312	70	7	e	e	NOUN
ejpam-2312	70	8	)	)	PUNCT
ejpam-2312	70	9	be	be	AUX
ejpam-2312	70	10	a	a	DET
ejpam-2312	70	11	soft	soft	ADJ
ejpam-2312	70	12	topological	topological	ADJ
ejpam-2312	70	13	space	space	NOUN
ejpam-2312	70	14	over	over	ADP
ejpam-2312	70	15	x	x	PUNCT
ejpam-2312	70	16	with	with	ADP
ejpam-2312	70	17	a	a	DET
ejpam-2312	70	18	⊆	⊆	NUM
ejpam-2312	70	19	x.	x.	NOUN
ejpam-2312	71	1	[	[	X
ejpam-2312	71	2	(	(	PUNCT
ejpam-2312	71	3	i)]soft	i)]soft	PROPN
ejpam-2312	71	4	semi	semi	NOUN
ejpam-2312	71	5	-	-	ADJ
ejpam-2312	71	6	interior	interior	ADJ
ejpam-2312	71	7	of	of	ADP
ejpam-2312	71	8	soft	soft	ADJ
ejpam-2312	71	9	set	set	NOUN
ejpam-2312	71	10	(	(	PUNCT
ejpam-2312	71	11	f	f	X
ejpam-2312	71	12	,	,	PUNCT
ejpam-2312	71	13	a	a	PRON
ejpam-2312	71	14	)	)	PUNCT
ejpam-2312	71	15	over	over	ADP
ejpam-2312	71	16	x	x	PUNCT
ejpam-2312	71	17	denoted	denote	VERB
ejpam-2312	71	18	by	by	ADP
ejpam-2312	71	19	ints(f	ints(f	PROPN
ejpam-2312	71	20	,	,	PUNCT
ejpam-2312	71	21	a	a	PRON
ejpam-2312	71	22	)	)	PUNCT
ejpam-2312	71	23	and	and	CCONJ
ejpam-2312	71	24	is	be	AUX
ejpam-2312	71	25	defined	define	VERB
ejpam-2312	71	26	as	as	ADP
ejpam-2312	71	27	the	the	DET
ejpam-2312	71	28	union	union	NOUN
ejpam-2312	71	29	of	of	ADP
ejpam-2312	71	30	all	all	DET
ejpam-2312	71	31	soft	soft	ADJ
ejpam-2312	71	32	semi	semi	ADJ
ejpam-2312	71	33	-	-	ADJ
ejpam-2312	71	34	open	open	ADJ
ejpam-2312	71	35	sets	set	NOUN
ejpam-2312	71	36	contained	contain	VERB
ejpam-2312	71	37	in	in	ADP
ejpam-2312	71	38	(	(	PUNCT
ejpam-2312	71	39	f	f	X
ejpam-2312	71	40	,	,	PUNCT
ejpam-2312	71	41	a	a	PRON
ejpam-2312	71	42	)	)	PUNCT
ejpam-2312	71	43	.	.	PUNCT
ejpam-2312	72	1	soft	soft	ADJ
ejpam-2312	72	2	semi	semi	NOUN
ejpam-2312	72	3	-	-	NOUN
ejpam-2312	72	4	closure	closure	NOUN
ejpam-2312	72	5	of	of	ADP
ejpam-2312	72	6	(	(	PUNCT
ejpam-2312	72	7	f	f	X
ejpam-2312	72	8	,	,	PUNCT
ejpam-2312	72	9	a	a	NOUN
ejpam-2312	72	10	)	)	PUNCT
ejpam-2312	72	11	over	over	ADP
ejpam-2312	72	12	x	x	PUNCT
ejpam-2312	72	13	denoted	denote	VERB
ejpam-2312	72	14	by	by	ADP
ejpam-2312	72	15	cls(f	cls(f	PROPN
ejpam-2312	72	16	,	,	PUNCT
ejpam-2312	72	17	a	a	PRON
ejpam-2312	72	18	)	)	PUNCT
ejpam-2312	72	19	is	be	AUX
ejpam-2312	72	20	the	the	DET
ejpam-2312	72	21	intersection	intersection	NOUN
ejpam-2312	72	22	of	of	ADP
ejpam-2312	72	23	all	all	DET
ejpam-2312	72	24	soft	soft	ADJ
ejpam-2312	72	25	semi	semi	ADJ
ejpam-2312	72	26	-	-	ADJ
ejpam-2312	72	27	closed	closed	ADJ
ejpam-2312	72	28	super	super	ADJ
ejpam-2312	72	29	sets	set	NOUN
ejpam-2312	72	30	of	of	ADP
ejpam-2312	72	31	(	(	PUNCT
ejpam-2312	72	32	f	f	X
ejpam-2312	72	33	,	,	PUNCT
ejpam-2312	72	34	a	a	PRON
ejpam-2312	72	35	)	)	PUNCT
ejpam-2312	72	36	.	.	PUNCT
ejpam-2312	73	1	for	for	ADP
ejpam-2312	73	2	detailed	detailed	ADJ
ejpam-2312	73	3	properties	property	NOUN
ejpam-2312	73	4	of	of	ADP
ejpam-2312	73	5	soft	soft	ADJ
ejpam-2312	73	6	semi	semi	ADJ
ejpam-2312	73	7	-	-	ADJ
ejpam-2312	73	8	open(closed	open(close	VERB
ejpam-2312	73	9	)	)	PUNCT
ejpam-2312	73	10	and	and	CCONJ
ejpam-2312	73	11	soft	soft	ADJ
ejpam-2312	73	12	semi	semi	ADJ
ejpam-2312	73	13	-	-	ADJ
ejpam-2312	73	14	interior(closure	interior(closure	ADJ
ejpam-2312	73	15	)	)	PUNCT
ejpam-2312	73	16	we	we	PRON
ejpam-2312	73	17	refer	refer	VERB
ejpam-2312	73	18	to	to	ADP
ejpam-2312	73	19	[	[	X
ejpam-2312	73	20	3	3	NUM
ejpam-2312	73	21	,	,	PUNCT
ejpam-2312	73	22	4	4	NUM
ejpam-2312	73	23	,	,	PUNCT
ejpam-2312	73	24	5	5	NUM
ejpam-2312	73	25	]	]	PUNCT
ejpam-2312	73	26	.	.	PUNCT
ejpam-2312	74	1	3	3	X
ejpam-2312	74	2	.	.	NOUN
ejpam-2312	74	3	soft	soft	ADJ
ejpam-2312	74	4	semi	semi	ADJ
ejpam-2312	74	5	-	-	ADJ
ejpam-2312	74	6	separation	separation	NOUN
ejpam-2312	74	7	axioms	axiom	NOUN
ejpam-2312	74	8	hereafter	hereafter	ADV
ejpam-2312	74	9	,	,	PUNCT
ejpam-2312	74	10	ss(x)a	ss(x)a	PROPN
ejpam-2312	74	11	denotes	denote	VERB
ejpam-2312	74	12	the	the	DET
ejpam-2312	74	13	family	family	NOUN
ejpam-2312	74	14	of	of	ADP
ejpam-2312	74	15	soft	soft	ADJ
ejpam-2312	74	16	sets	set	NOUN
ejpam-2312	74	17	over	over	ADP
ejpam-2312	74	18	x	x	PUNCT
ejpam-2312	74	19	with	with	ADP
ejpam-2312	74	20	the	the	DET
ejpam-2312	74	21	set	set	NOUN
ejpam-2312	74	22	of	of	ADP
ejpam-2312	74	23	parameters	parameter	NOUN
ejpam-2312	74	24	a.	a.	NOUN
ejpam-2312	74	25	definition	definition	NOUN
ejpam-2312	74	26	6	6	NUM
ejpam-2312	74	27	(	(	PUNCT
ejpam-2312	74	28	[	[	X
ejpam-2312	74	29	13	13	NUM
ejpam-2312	74	30	]	]	NUM
ejpam-2312	74	31	)	)	PUNCT
ejpam-2312	74	32	.	.	PUNCT
ejpam-2312	75	1	a	a	DET
ejpam-2312	75	2	soft	soft	ADJ
ejpam-2312	75	3	set	set	NOUN
ejpam-2312	75	4	(	(	PUNCT
ejpam-2312	75	5	f	f	X
ejpam-2312	75	6	,	,	PUNCT
ejpam-2312	75	7	a	a	PRON
ejpam-2312	75	8	)	)	PUNCT
ejpam-2312	75	9	over	over	ADP
ejpam-2312	75	10	x	x	VERB
ejpam-2312	75	11	is	be	AUX
ejpam-2312	75	12	said	say	VERB
ejpam-2312	75	13	to	to	PART
ejpam-2312	75	14	be	be	AUX
ejpam-2312	75	15	an	an	DET
ejpam-2312	75	16	absolute	absolute	ADJ
ejpam-2312	75	17	soft	soft	ADJ
ejpam-2312	75	18	set	set	NOUN
ejpam-2312	75	19	,	,	PUNCT
ejpam-2312	75	20	denoted	denote	VERB
ejpam-2312	75	21	by	by	ADP
ejpam-2312	75	22	x̃a	x̃a	NOUN
ejpam-2312	75	23	,	,	PUNCT
ejpam-2312	75	24	if	if	SCONJ
ejpam-2312	75	25	for	for	ADP
ejpam-2312	75	26	all	all	DET
ejpam-2312	75	27	e	e	PROPN
ejpam-2312	75	28	∈	∈	PROPN
ejpam-2312	75	29	a	a	X
ejpam-2312	75	30	,	,	PUNCT
ejpam-2312	75	31	f	f	PROPN
ejpam-2312	75	32	(	(	PUNCT
ejpam-2312	75	33	e	e	NOUN
ejpam-2312	75	34	)	)	PUNCT
ejpam-2312	75	35	=	=	PUNCT
ejpam-2312	76	1	x.	x.	NOUN
ejpam-2312	76	2	clearly	clearly	ADV
ejpam-2312	76	3	,	,	PUNCT
ejpam-2312	76	4	x̃c	x̃c	PROPN
ejpam-2312	77	1	a	a	DET
ejpam-2312	77	2	=	=	X
ejpam-2312	77	3	φa	φa	NOUN
ejpam-2312	77	4	and	and	CCONJ
ejpam-2312	77	5	φc	φc	VERB
ejpam-2312	77	6	a	a	PRON
ejpam-2312	77	7	=	=	NOUN
ejpam-2312	77	8	x̃a	x̃a	PROPN
ejpam-2312	77	9	.	.	PUNCT
ejpam-2312	78	1	definition	definition	NOUN
ejpam-2312	78	2	7	7	NUM
ejpam-2312	78	3	(	(	PUNCT
ejpam-2312	78	4	[	[	X
ejpam-2312	78	5	13	13	NUM
ejpam-2312	78	6	]	]	NUM
ejpam-2312	78	7	)	)	PUNCT
ejpam-2312	78	8	.	.	PUNCT
ejpam-2312	79	1	a	a	DET
ejpam-2312	79	2	soft	soft	ADJ
ejpam-2312	79	3	set	set	NOUN
ejpam-2312	79	4	(	(	PUNCT
ejpam-2312	79	5	f	f	X
ejpam-2312	79	6	,	,	PUNCT
ejpam-2312	79	7	a	a	PRON
ejpam-2312	79	8	)	)	PUNCT
ejpam-2312	79	9	over	over	ADP
ejpam-2312	79	10	x	x	VERB
ejpam-2312	79	11	is	be	AUX
ejpam-2312	79	12	said	say	VERB
ejpam-2312	79	13	to	to	PART
ejpam-2312	79	14	be	be	AUX
ejpam-2312	79	15	null	null	ADJ
ejpam-2312	79	16	soft	soft	ADJ
ejpam-2312	79	17	set	set	NOUN
ejpam-2312	79	18	,	,	PUNCT
ejpam-2312	79	19	denoted	denote	VERB
ejpam-2312	79	20	by	by	ADP
ejpam-2312	79	21	φ̃a	φ̃a	ADV
ejpam-2312	79	22	,	,	PUNCT
ejpam-2312	79	23	if	if	SCONJ
ejpam-2312	79	24	for	for	ADP
ejpam-2312	79	25	all	all	DET
ejpam-2312	79	26	e	e	PROPN
ejpam-2312	79	27	∈	∈	PROPN
ejpam-2312	79	28	a	a	X
ejpam-2312	79	29	,	,	PUNCT
ejpam-2312	79	30	f	f	PROPN
ejpam-2312	79	31	(	(	PUNCT
ejpam-2312	79	32	e	e	NOUN
ejpam-2312	79	33	)	)	PUNCT
ejpam-2312	79	34	=	=	SYM
ejpam-2312	80	1	φ	φ	PROPN
ejpam-2312	80	2	.	.	PUNCT
ejpam-2312	80	3	proposition	proposition	NOUN
ejpam-2312	80	4	1	1	NUM
ejpam-2312	80	5	(	(	PUNCT
ejpam-2312	80	6	[	[	X
ejpam-2312	80	7	20	20	NUM
ejpam-2312	80	8	]	]	NUM
ejpam-2312	80	9	)	)	PUNCT
ejpam-2312	80	10	.	.	PUNCT
ejpam-2312	81	1	let	let	VERB
ejpam-2312	81	2	ef	ef	VERB
ejpam-2312	81	3	∈̃x̃a	∈̃x̃a	PRON
ejpam-2312	82	1	and	and	CCONJ
ejpam-2312	82	2	(	(	PUNCT
ejpam-2312	82	3	g	g	NOUN
ejpam-2312	82	4	,	,	PUNCT
ejpam-2312	82	5	a)∈̃ss(x)a	a)∈̃ss(x)a	PROPN
ejpam-2312	82	6	.	.	PUNCT
ejpam-2312	83	1	if	if	SCONJ
ejpam-2312	83	2	ef	ef	PROPN
ejpam-2312	83	3	∈̃(g	∈̃(g	NOUN
ejpam-2312	83	4	,	,	PUNCT
ejpam-2312	83	5	a	a	PRON
ejpam-2312	83	6	)	)	PUNCT
ejpam-2312	83	7	,	,	PUNCT
ejpam-2312	83	8	then	then	ADV
ejpam-2312	83	9	ef	ef	X
ejpam-2312	83	10	/̃∈(g	/̃∈(g	PROPN
ejpam-2312	83	11	,	,	PUNCT
ejpam-2312	83	12	a)c	a)c	PUNCT
ejpam-2312	83	13	.	.	PUNCT
ejpam-2312	84	1	definition	definition	NOUN
ejpam-2312	84	2	8	8	NUM
ejpam-2312	84	3	(	(	PUNCT
ejpam-2312	84	4	[	[	X
ejpam-2312	84	5	20	20	NUM
ejpam-2312	84	6	]	]	NUM
ejpam-2312	84	7	)	)	PUNCT
ejpam-2312	84	8	.	.	PUNCT
ejpam-2312	85	1	the	the	DET
ejpam-2312	85	2	soft	soft	ADJ
ejpam-2312	85	3	set	set	NOUN
ejpam-2312	85	4	(	(	PUNCT
ejpam-2312	85	5	f	f	X
ejpam-2312	85	6	,	,	PUNCT
ejpam-2312	85	7	a)∈̃ss(x)a	a)∈̃ss(x)a	PROPN
ejpam-2312	85	8	is	be	AUX
ejpam-2312	85	9	called	call	VERB
ejpam-2312	85	10	soft	soft	ADJ
ejpam-2312	85	11	point	point	NOUN
ejpam-2312	85	12	in	in	ADP
ejpam-2312	85	13	x̃a	x̃a	NUM
ejpam-2312	85	14	,	,	PUNCT
ejpam-2312	85	15	denoted	denote	VERB
ejpam-2312	85	16	by	by	ADP
ejpam-2312	85	17	ef	ef	PROPN
ejpam-2312	85	18	,	,	PUNCT
ejpam-2312	85	19	if	if	SCONJ
ejpam-2312	85	20	for	for	ADP
ejpam-2312	85	21	the	the	DET
ejpam-2312	85	22	element	element	NOUN
ejpam-2312	85	23	e	e	PROPN
ejpam-2312	85	24	∈	∈	PROPN
ejpam-2312	85	25	a	a	PROPN
ejpam-2312	85	26	,	,	PUNCT
ejpam-2312	85	27	f	f	PROPN
ejpam-2312	85	28	(	(	PUNCT
ejpam-2312	85	29	e	e	NOUN
ejpam-2312	85	30	)	)	PUNCT
ejpam-2312	85	31	6=	6=	ADP
ejpam-2312	85	32	φ	φ	PROPN
ejpam-2312	85	33	and	and	CCONJ
ejpam-2312	85	34	f	f	PROPN
ejpam-2312	85	35	(	(	PUNCT
ejpam-2312	85	36	e	e	NOUN
ejpam-2312	85	37	′	′	NUM
ejpam-2312	85	38	)	)	PUNCT
ejpam-2312	86	1	=	=	SYM
ejpam-2312	86	2	φ	φ	PROPN
ejpam-2312	86	3	,	,	PUNCT
ejpam-2312	86	4	for	for	ADP
ejpam-2312	86	5	all	all	DET
ejpam-2312	86	6	e	e	NOUN
ejpam-2312	86	7	′	′	NUM
ejpam-2312	86	8	∈	∈	PROPN
ejpam-2312	86	9	a−	a−	PROPN
ejpam-2312	86	10	{	{	PUNCT
ejpam-2312	86	11	e	e	NOUN
ejpam-2312	86	12	}	}	PUNCT
ejpam-2312	86	13	.	.	PUNCT
ejpam-2312	87	1	definition	definition	NOUN
ejpam-2312	87	2	9	9	NUM
ejpam-2312	87	3	(	(	PUNCT
ejpam-2312	87	4	[	[	X
ejpam-2312	87	5	20	20	NUM
ejpam-2312	87	6	]	]	NUM
ejpam-2312	87	7	)	)	PUNCT
ejpam-2312	87	8	.	.	PUNCT
ejpam-2312	88	1	the	the	DET
ejpam-2312	88	2	soft	soft	ADJ
ejpam-2312	88	3	point	point	NOUN
ejpam-2312	88	4	ef	ef	PROPN
ejpam-2312	88	5	is	be	AUX
ejpam-2312	88	6	said	say	VERB
ejpam-2312	88	7	to	to	PART
ejpam-2312	88	8	be	be	AUX
ejpam-2312	88	9	in	in	ADP
ejpam-2312	88	10	the	the	DET
ejpam-2312	88	11	soft	soft	ADJ
ejpam-2312	88	12	set	set	NOUN
ejpam-2312	88	13	(	(	PUNCT
ejpam-2312	88	14	g	g	NOUN
ejpam-2312	88	15	,	,	PUNCT
ejpam-2312	88	16	a	a	PRON
ejpam-2312	88	17	)	)	PUNCT
ejpam-2312	88	18	,	,	PUNCT
ejpam-2312	88	19	denoted	denote	VERB
ejpam-2312	88	20	by	by	ADP
ejpam-2312	88	21	ef	ef	PROPN
ejpam-2312	88	22	∈̃(g	∈̃(g	NOUN
ejpam-2312	88	23	,	,	PUNCT
ejpam-2312	88	24	a	a	PRON
ejpam-2312	88	25	)	)	PUNCT
ejpam-2312	88	26	,	,	PUNCT
ejpam-2312	88	27	if	if	SCONJ
ejpam-2312	88	28	for	for	ADP
ejpam-2312	88	29	the	the	DET
ejpam-2312	88	30	element	element	NOUN
ejpam-2312	88	31	e	e	PROPN
ejpam-2312	88	32	∈	∈	PROPN
ejpam-2312	88	33	a	a	PROPN
ejpam-2312	88	34	,	,	PUNCT
ejpam-2312	88	35	f	f	PROPN
ejpam-2312	88	36	(	(	PUNCT
ejpam-2312	88	37	e	e	NOUN
ejpam-2312	88	38	)	)	PUNCT
ejpam-2312	88	39	⊆	⊆	NUM
ejpam-2312	88	40	g(e	g(e	PROPN
ejpam-2312	88	41	)	)	PUNCT
ejpam-2312	88	42	.	.	PUNCT
ejpam-2312	89	1	definition	definition	NOUN
ejpam-2312	89	2	10	10	NUM
ejpam-2312	89	3	(	(	PUNCT
ejpam-2312	89	4	[	[	X
ejpam-2312	89	5	6	6	NUM
ejpam-2312	89	6	]	]	NUM
ejpam-2312	89	7	)	)	PUNCT
ejpam-2312	89	8	.	.	PUNCT
ejpam-2312	90	1	two	two	NUM
ejpam-2312	90	2	soft	soft	ADJ
ejpam-2312	90	3	sets	set	NOUN
ejpam-2312	90	4	(	(	PUNCT
ejpam-2312	90	5	g	g	NOUN
ejpam-2312	90	6	,	,	PUNCT
ejpam-2312	90	7	a	a	PRON
ejpam-2312	90	8	)	)	PUNCT
ejpam-2312	90	9	,	,	PUNCT
ejpam-2312	90	10	(	(	PUNCT
ejpam-2312	90	11	h	h	NOUN
ejpam-2312	90	12	,	,	PUNCT
ejpam-2312	90	13	a	a	PRON
ejpam-2312	90	14	)	)	PUNCT
ejpam-2312	90	15	in	in	ADP
ejpam-2312	90	16	ss(x)a	ss(x)a	PROPN
ejpam-2312	90	17	are	be	AUX
ejpam-2312	90	18	said	say	VERB
ejpam-2312	90	19	to	to	PART
ejpam-2312	90	20	be	be	AUX
ejpam-2312	90	21	soft	soft	ADJ
ejpam-2312	90	22	disjoint	disjoint	NOUN
ejpam-2312	90	23	,	,	PUNCT
ejpam-2312	90	24	written	write	VERB
ejpam-2312	90	25	(	(	PUNCT
ejpam-2312	90	26	g	g	NOUN
ejpam-2312	90	27	,	,	PUNCT
ejpam-2312	90	28	a)∩̃(h	a)∩̃(h	PROPN
ejpam-2312	90	29	,	,	PUNCT
ejpam-2312	90	30	a	a	PRON
ejpam-2312	90	31	)	)	PUNCT
ejpam-2312	91	1	=	=	SYM
ejpam-2312	91	2	φa	φa	ADP
ejpam-2312	91	3	,	,	PUNCT
ejpam-2312	91	4	if	if	SCONJ
ejpam-2312	91	5	g(e	g(e	PROPN
ejpam-2312	91	6	)	)	PUNCT
ejpam-2312	91	7	∩h(e	∩h(e	NOUN
ejpam-2312	91	8	)	)	PUNCT
ejpam-2312	91	9	=	=	SYM
ejpam-2312	92	1	φ	φ	PROPN
ejpam-2312	92	2	,	,	PUNCT
ejpam-2312	92	3	for	for	ADP
ejpam-2312	92	4	all	all	DET
ejpam-2312	92	5	e	e	PROPN
ejpam-2312	92	6	∈	∈	PROPN
ejpam-2312	92	7	a.	a.	NOUN
ejpam-2312	92	8	definition	definition	NOUN
ejpam-2312	92	9	11	11	NUM
ejpam-2312	92	10	(	(	PUNCT
ejpam-2312	92	11	[	[	X
ejpam-2312	92	12	6	6	NUM
ejpam-2312	92	13	]	]	NUM
ejpam-2312	92	14	)	)	PUNCT
ejpam-2312	92	15	.	.	PUNCT
ejpam-2312	93	1	two	two	NUM
ejpam-2312	93	2	soft	soft	ADJ
ejpam-2312	93	3	points	point	NOUN
ejpam-2312	93	4	eg	eg	NOUN
ejpam-2312	93	5	,	,	PUNCT
ejpam-2312	93	6	eh	eh	INTJ
ejpam-2312	93	7	in	in	SCONJ
ejpam-2312	93	8	x̃a	x̃a	NOUN
ejpam-2312	93	9	are	be	AUX
ejpam-2312	93	10	distinct	distinct	ADJ
ejpam-2312	93	11	,	,	PUNCT
ejpam-2312	93	12	written	write	VERB
ejpam-2312	93	13	eg	eg	PROPN
ejpam-2312	93	14	6=	6=	PROPN
ejpam-2312	93	15	eh	eh	INTJ
ejpam-2312	93	16	,	,	PUNCT
ejpam-2312	93	17	if	if	SCONJ
ejpam-2312	93	18	there	there	PRON
ejpam-2312	93	19	corresponding	correspond	VERB
ejpam-2312	93	20	soft	soft	ADJ
ejpam-2312	93	21	sets	set	NOUN
ejpam-2312	93	22	(	(	PUNCT
ejpam-2312	93	23	g	g	NOUN
ejpam-2312	93	24	,	,	PUNCT
ejpam-2312	93	25	a	a	PRON
ejpam-2312	93	26	)	)	PUNCT
ejpam-2312	93	27	and	and	CCONJ
ejpam-2312	93	28	(	(	PUNCT
ejpam-2312	93	29	h	h	NOUN
ejpam-2312	93	30	,	,	PUNCT
ejpam-2312	93	31	a	a	PRON
ejpam-2312	93	32	)	)	PUNCT
ejpam-2312	93	33	are	be	AUX
ejpam-2312	93	34	soft	soft	ADJ
ejpam-2312	93	35	disjoint	disjoint	NOUN
ejpam-2312	93	36	.	.	PUNCT
ejpam-2312	94	1	s.	s.	PROPN
ejpam-2312	94	2	hussain	hussain	PROPN
ejpam-2312	94	3	/	/	SYM
ejpam-2312	94	4	eur	eur	PROPN
ejpam-2312	94	5	.	.	PUNCT
ejpam-2312	95	1	j.	j.	PROPN
ejpam-2312	95	2	pure	pure	PROPN
ejpam-2312	95	3	appl	appl	PROPN
ejpam-2312	95	4	.	.	PROPN
ejpam-2312	95	5	math	math	PROPN
ejpam-2312	95	6	,	,	PUNCT
ejpam-2312	95	7	10	10	NUM
ejpam-2312	95	8	(	(	PUNCT
ejpam-2312	95	9	2	2	NUM
ejpam-2312	95	10	)	)	PUNCT
ejpam-2312	95	11	(	(	PUNCT
ejpam-2312	95	12	2017	2017	NUM
ejpam-2312	95	13	)	)	PUNCT
ejpam-2312	95	14	,	,	PUNCT
ejpam-2312	95	15	199	199	NUM
ejpam-2312	95	16	-	-	SYM
ejpam-2312	95	17	210	210	NUM
ejpam-2312	95	18	202	202	NUM
ejpam-2312	95	19	definition	definition	NOUN
ejpam-2312	95	20	12	12	NUM
ejpam-2312	95	21	.	.	PUNCT
ejpam-2312	96	1	let	let	VERB
ejpam-2312	96	2	(	(	PUNCT
ejpam-2312	96	3	x	x	X
ejpam-2312	96	4	,	,	PUNCT
ejpam-2312	96	5	τ	τ	PROPN
ejpam-2312	96	6	,	,	PUNCT
ejpam-2312	96	7	a	a	PRON
ejpam-2312	96	8	)	)	PUNCT
ejpam-2312	96	9	be	be	AUX
ejpam-2312	96	10	a	a	DET
ejpam-2312	96	11	soft	soft	ADJ
ejpam-2312	96	12	topological	topological	ADJ
ejpam-2312	96	13	space	space	NOUN
ejpam-2312	96	14	over	over	ADP
ejpam-2312	96	15	x	x	PUNCT
ejpam-2312	96	16	and	and	CCONJ
ejpam-2312	96	17	(	(	PUNCT
ejpam-2312	96	18	f	f	X
ejpam-2312	96	19	,	,	PUNCT
ejpam-2312	96	20	a)∈̃ss(x)a	a)∈̃ss(x)a	PROPN
ejpam-2312	96	21	.	.	PUNCT
ejpam-2312	97	1	then	then	ADV
ejpam-2312	97	2	(	(	PUNCT
ejpam-2312	97	3	f	f	X
ejpam-2312	97	4	,	,	PUNCT
ejpam-2312	97	5	a	a	PRON
ejpam-2312	97	6	)	)	PUNCT
ejpam-2312	97	7	is	be	AUX
ejpam-2312	97	8	soft	soft	ADJ
ejpam-2312	97	9	semi	semi	ADJ
ejpam-2312	97	10	-	-	ADJ
ejpam-2312	97	11	d	d	ADJ
ejpam-2312	97	12	-	-	PUNCT
ejpam-2312	97	13	set	set	ADJ
ejpam-2312	97	14	,	,	PUNCT
ejpam-2312	97	15	if	if	SCONJ
ejpam-2312	97	16	there	there	PRON
ejpam-2312	97	17	exists	exist	VERB
ejpam-2312	97	18	two	two	NUM
ejpam-2312	97	19	soft	soft	ADJ
ejpam-2312	97	20	semi	semi	ADJ
ejpam-2312	97	21	-	-	ADJ
ejpam-2312	97	22	open	open	ADJ
ejpam-2312	97	23	sets	set	NOUN
ejpam-2312	97	24	(	(	PUNCT
ejpam-2312	97	25	g	g	NOUN
ejpam-2312	97	26	,	,	PUNCT
ejpam-2312	97	27	a	a	PRON
ejpam-2312	97	28	)	)	PUNCT
ejpam-2312	97	29	and	and	CCONJ
ejpam-2312	97	30	(	(	PUNCT
ejpam-2312	97	31	h	h	NOUN
ejpam-2312	97	32	,	,	PUNCT
ejpam-2312	97	33	a	a	PRON
ejpam-2312	97	34	)	)	PUNCT
ejpam-2312	97	35	such	such	ADJ
ejpam-2312	97	36	that	that	SCONJ
ejpam-2312	97	37	(	(	PUNCT
ejpam-2312	97	38	g	g	NOUN
ejpam-2312	97	39	,	,	PUNCT
ejpam-2312	97	40	a	a	PRON
ejpam-2312	97	41	)	)	PUNCT
ejpam-2312	97	42	˜6	˜6	PROPN
ejpam-2312	97	43	=	=	SYM
ejpam-2312	97	44	x̃	x̃	PROPN
ejpam-2312	97	45	and	and	CCONJ
ejpam-2312	97	46	(	(	PUNCT
ejpam-2312	97	47	f	f	X
ejpam-2312	97	48	,	,	PUNCT
ejpam-2312	97	49	a)=̃(g	a)=̃(g	VERB
ejpam-2312	97	50	,	,	PUNCT
ejpam-2312	97	51	a)\̃(h	a)\̃(h	ADV
ejpam-2312	97	52	,	,	PUNCT
ejpam-2312	97	53	a	a	PRON
ejpam-2312	97	54	)	)	PUNCT
ejpam-2312	97	55	.	.	PUNCT
ejpam-2312	98	1	from	from	ADP
ejpam-2312	98	2	the	the	DET
ejpam-2312	98	3	definition	definition	NOUN
ejpam-2312	98	4	,	,	PUNCT
ejpam-2312	98	5	it	it	PRON
ejpam-2312	98	6	is	be	AUX
ejpam-2312	98	7	clear	clear	ADJ
ejpam-2312	98	8	that	that	SCONJ
ejpam-2312	98	9	every	every	DET
ejpam-2312	98	10	soft	soft	ADJ
ejpam-2312	98	11	semi	semi	ADJ
ejpam-2312	98	12	-	-	ADJ
ejpam-2312	98	13	open	open	ADJ
ejpam-2312	98	14	set	set	NOUN
ejpam-2312	98	15	(	(	PUNCT
ejpam-2312	98	16	g	g	NOUN
ejpam-2312	98	17	,	,	PUNCT
ejpam-2312	98	18	a	a	PRON
ejpam-2312	98	19	)	)	PUNCT
ejpam-2312	98	20	˜6	˜6	PROPN
ejpam-2312	98	21	=	=	SYM
ejpam-2312	98	22	x̃	x̃	PROPN
ejpam-2312	98	23	is	be	AUX
ejpam-2312	98	24	soft	soft	ADJ
ejpam-2312	98	25	semi	semi	ADJ
ejpam-2312	98	26	-	-	ADJ
ejpam-2312	98	27	dset	dset	ADJ
ejpam-2312	98	28	,	,	PUNCT
ejpam-2312	99	1	if	if	SCONJ
ejpam-2312	99	2	(	(	PUNCT
ejpam-2312	99	3	f	f	X
ejpam-2312	99	4	,	,	PUNCT
ejpam-2312	99	5	a)=̃(g	a)=̃(g	VERB
ejpam-2312	99	6	,	,	PUNCT
ejpam-2312	99	7	a	a	PRON
ejpam-2312	99	8	)	)	PUNCT
ejpam-2312	99	9	and	and	CCONJ
ejpam-2312	99	10	(	(	PUNCT
ejpam-2312	99	11	h	h	NOUN
ejpam-2312	99	12	,	,	PUNCT
ejpam-2312	99	13	a)=̃φ̃.	a)=̃φ̃.	NUM
ejpam-2312	99	14	example	example	NOUN
ejpam-2312	99	15	1	1	X
ejpam-2312	99	16	.	.	PUNCT
ejpam-2312	100	1	let	let	VERB
ejpam-2312	100	2	x	x	PUNCT
ejpam-2312	100	3	=	=	PRON
ejpam-2312	100	4	{	{	PUNCT
ejpam-2312	100	5	h1	h1	PROPN
ejpam-2312	100	6	,	,	PUNCT
ejpam-2312	100	7	h2	h2	PROPN
ejpam-2312	100	8	,	,	PUNCT
ejpam-2312	100	9	h3	h3	NOUN
ejpam-2312	100	10	}	}	PUNCT
ejpam-2312	100	11	,	,	PUNCT
ejpam-2312	100	12	a	a	DET
ejpam-2312	100	13	=	=	X
ejpam-2312	100	14	{	{	PUNCT
ejpam-2312	100	15	e1	e1	PROPN
ejpam-2312	100	16	,	,	PUNCT
ejpam-2312	100	17	e2	e2	PROPN
ejpam-2312	100	18	}	}	PUNCT
ejpam-2312	100	19	and	and	CCONJ
ejpam-2312	100	20	τ	τ	PROPN
ejpam-2312	100	21	=	=	PUNCT
ejpam-2312	100	22	{	{	PUNCT
ejpam-2312	100	23	φ̃	φ̃	PROPN
ejpam-2312	100	24	,	,	PUNCT
ejpam-2312	100	25	x̃	x̃	PROPN
ejpam-2312	100	26	,	,	PUNCT
ejpam-2312	100	27	(	(	PUNCT
ejpam-2312	100	28	k1	k1	PROPN
ejpam-2312	100	29	,	,	PUNCT
ejpam-2312	100	30	a	a	PRON
ejpam-2312	100	31	)	)	PUNCT
ejpam-2312	100	32	,	,	PUNCT
ejpam-2312	100	33	(	(	PUNCT
ejpam-2312	100	34	k2	k2	PROPN
ejpam-2312	100	35	,	,	PUNCT
ejpam-2312	100	36	a	a	PRON
ejpam-2312	100	37	)	)	PUNCT
ejpam-2312	100	38	,	,	PUNCT
ejpam-2312	100	39	(	(	PUNCT
ejpam-2312	100	40	k3	k3	PROPN
ejpam-2312	100	41	,	,	PUNCT
ejpam-2312	100	42	a	a	PRON
ejpam-2312	100	43	)	)	PUNCT
ejpam-2312	100	44	,	,	PUNCT
ejpam-2312	100	45	(	(	PUNCT
ejpam-2312	100	46	k4	k4	PROPN
ejpam-2312	100	47	,	,	PUNCT
ejpam-2312	100	48	a	a	PRON
ejpam-2312	100	49	)	)	PUNCT
ejpam-2312	100	50	,	,	PUNCT
ejpam-2312	100	51	(	(	PUNCT
ejpam-2312	100	52	k5	k5	PROPN
ejpam-2312	100	53	,	,	PUNCT
ejpam-2312	100	54	a	a	PRON
ejpam-2312	100	55	)	)	PUNCT
ejpam-2312	100	56	,	,	PUNCT
ejpam-2312	100	57	(	(	PUNCT
ejpam-2312	100	58	k6	k6	PROPN
ejpam-2312	100	59	,	,	PUNCT
ejpam-2312	100	60	a	a	PRON
ejpam-2312	100	61	)	)	PUNCT
ejpam-2312	100	62	,	,	PUNCT
ejpam-2312	100	63	(	(	PUNCT
ejpam-2312	100	64	k7	k7	PROPN
ejpam-2312	100	65	,	,	PUNCT
ejpam-2312	100	66	a	a	PRON
ejpam-2312	100	67	)	)	PUNCT
ejpam-2312	100	68	}	}	PUNCT
ejpam-2312	100	69	where	where	SCONJ
ejpam-2312	100	70	(	(	PUNCT
ejpam-2312	100	71	k1	k1	NOUN
ejpam-2312	100	72	,	,	PUNCT
ejpam-2312	100	73	a	a	PRON
ejpam-2312	100	74	)	)	PUNCT
ejpam-2312	100	75	,	,	PUNCT
ejpam-2312	100	76	(	(	PUNCT
ejpam-2312	100	77	k2	k2	PROPN
ejpam-2312	100	78	,	,	PUNCT
ejpam-2312	100	79	a	a	PRON
ejpam-2312	100	80	)	)	PUNCT
ejpam-2312	100	81	,	,	PUNCT
ejpam-2312	100	82	(	(	PUNCT
ejpam-2312	100	83	k3	k3	PROPN
ejpam-2312	100	84	,	,	PUNCT
ejpam-2312	100	85	a	a	PRON
ejpam-2312	100	86	)	)	PUNCT
ejpam-2312	100	87	,	,	PUNCT
ejpam-2312	100	88	(	(	PUNCT
ejpam-2312	100	89	k4	k4	PROPN
ejpam-2312	100	90	,	,	PUNCT
ejpam-2312	100	91	a	a	PRON
ejpam-2312	100	92	)	)	PUNCT
ejpam-2312	100	93	,	,	PUNCT
ejpam-2312	100	94	(	(	PUNCT
ejpam-2312	100	95	k5	k5	PROPN
ejpam-2312	100	96	,	,	PUNCT
ejpam-2312	100	97	a	a	PRON
ejpam-2312	100	98	)	)	PUNCT
ejpam-2312	100	99	,	,	PUNCT
ejpam-2312	100	100	(	(	PUNCT
ejpam-2312	100	101	k6	k6	PROPN
ejpam-2312	100	102	,	,	PUNCT
ejpam-2312	100	103	a	a	PRON
ejpam-2312	100	104	)	)	PUNCT
ejpam-2312	100	105	and	and	CCONJ
ejpam-2312	100	106	(	(	PUNCT
ejpam-2312	100	107	k7	k7	PROPN
ejpam-2312	100	108	,	,	PUNCT
ejpam-2312	100	109	a	a	PRON
ejpam-2312	100	110	)	)	PUNCT
ejpam-2312	100	111	are	be	AUX
ejpam-2312	100	112	soft	soft	ADJ
ejpam-2312	100	113	sets	set	NOUN
ejpam-2312	100	114	over	over	ADP
ejpam-2312	100	115	x	x	NOUN
ejpam-2312	100	116	,	,	PUNCT
ejpam-2312	100	117	defined	define	VERB
ejpam-2312	100	118	as	as	SCONJ
ejpam-2312	100	119	follows	follow	VERB
ejpam-2312	100	120	:	:	PUNCT
ejpam-2312	100	121	k1(e1	k1(e1	NOUN
ejpam-2312	100	122	)	)	PUNCT
ejpam-2312	101	1	=	=	NOUN
ejpam-2312	101	2	{	{	PUNCT
ejpam-2312	101	3	h1	h1	PROPN
ejpam-2312	101	4	,	,	PUNCT
ejpam-2312	101	5	h2},k1(e2	h2},k1(e2	PROPN
ejpam-2312	101	6	)	)	PUNCT
ejpam-2312	101	7	=	=	PRON
ejpam-2312	101	8	{	{	PUNCT
ejpam-2312	101	9	h1	h1	PROPN
ejpam-2312	101	10	,	,	PUNCT
ejpam-2312	101	11	h2},k2(e1	h2},k2(e1	NOUN
ejpam-2312	101	12	)	)	PUNCT
ejpam-2312	101	13	=	=	PRON
ejpam-2312	101	14	{	{	PUNCT
ejpam-2312	101	15	h2},k2(e2	h2},k2(e2	NOUN
ejpam-2312	101	16	)	)	PUNCT
ejpam-2312	101	17	=	=	PRON
ejpam-2312	101	18	{	{	PUNCT
ejpam-2312	101	19	h1	h1	PROPN
ejpam-2312	101	20	,	,	PUNCT
ejpam-2312	101	21	h3},k3(e1	h3},k3(e1	NOUN
ejpam-2312	101	22	)	)	PUNCT
ejpam-2312	101	23	=	=	SYM
ejpam-2312	101	24	{	{	PUNCT
ejpam-2312	101	25	h2	h2	PROPN
ejpam-2312	101	26	,	,	PUNCT
ejpam-2312	101	27	h3	h3	NOUN
ejpam-2312	101	28	}	}	PUNCT
ejpam-2312	101	29	,	,	PUNCT
ejpam-2312	101	30	k3(e2	k3(e2	NOUN
ejpam-2312	101	31	)	)	PUNCT
ejpam-2312	101	32	=	=	NOUN
ejpam-2312	101	33	{	{	PUNCT
ejpam-2312	101	34	h1},k4(e1	h1},k4(e1	NOUN
ejpam-2312	101	35	)	)	PUNCT
ejpam-2312	101	36	=	=	PRON
ejpam-2312	101	37	{	{	PUNCT
ejpam-2312	101	38	h2},k4(e2	h2},k4(e2	PROPN
ejpam-2312	101	39	)	)	PUNCT
ejpam-2312	101	40	=	=	SYM
ejpam-2312	101	41	{	{	PUNCT
ejpam-2312	101	42	h1},k5(e1	h1},k5(e1	NOUN
ejpam-2312	101	43	)	)	PUNCT
ejpam-2312	101	44	=	=	PRON
ejpam-2312	101	45	{	{	PUNCT
ejpam-2312	101	46	h1	h1	PROPN
ejpam-2312	101	47	,	,	PUNCT
ejpam-2312	101	48	h2},k5(e2	h2},k5(e2	PROPN
ejpam-2312	101	49	)	)	PUNCT
ejpam-2312	101	50	=	=	SYM
ejpam-2312	102	1	x	x	X
ejpam-2312	102	2	,	,	PUNCT
ejpam-2312	102	3	k6(e1	k6(e1	NOUN
ejpam-2312	102	4	)	)	PUNCT
ejpam-2312	102	5	=	=	SYM
ejpam-2312	102	6	x	x	NOUN
ejpam-2312	102	7	,	,	PUNCT
ejpam-2312	102	8	k6(e2	k6(e2	PROPN
ejpam-2312	102	9	)	)	PUNCT
ejpam-2312	102	10	=	=	NOUN
ejpam-2312	102	11	{	{	PUNCT
ejpam-2312	102	12	h1	h1	PROPN
ejpam-2312	102	13	,	,	PUNCT
ejpam-2312	102	14	h2},k7(e1	h2},k7(e1	PROPN
ejpam-2312	102	15	)	)	PUNCT
ejpam-2312	102	16	=	=	SYM
ejpam-2312	102	17	{	{	PUNCT
ejpam-2312	102	18	h2	h2	NOUN
ejpam-2312	102	19	,	,	PUNCT
ejpam-2312	102	20	h3},k7(e2	h3},k7(e2	PROPN
ejpam-2312	102	21	)	)	PUNCT
ejpam-2312	102	22	=	=	PRON
ejpam-2312	102	23	{	{	PUNCT
ejpam-2312	102	24	h1	h1	PROPN
ejpam-2312	102	25	,	,	PUNCT
ejpam-2312	102	26	h3	h3	NOUN
ejpam-2312	102	27	}	}	PUNCT
ejpam-2312	102	28	.	.	PUNCT
ejpam-2312	103	1	then	then	ADV
ejpam-2312	103	2	τ	τ	PROPN
ejpam-2312	103	3	defines	define	VERB
ejpam-2312	103	4	a	a	DET
ejpam-2312	103	5	soft	soft	ADJ
ejpam-2312	103	6	topology	topology	NOUN
ejpam-2312	103	7	on	on	ADP
ejpam-2312	103	8	x	x	PUNCT
ejpam-2312	103	9	and	and	CCONJ
ejpam-2312	103	10	hence	hence	ADV
ejpam-2312	103	11	(	(	PUNCT
ejpam-2312	103	12	x	x	X
ejpam-2312	103	13	,	,	PUNCT
ejpam-2312	103	14	τ	τ	PROPN
ejpam-2312	103	15	,	,	PUNCT
ejpam-2312	103	16	a	a	PRON
ejpam-2312	103	17	)	)	PUNCT
ejpam-2312	103	18	is	be	AUX
ejpam-2312	103	19	a	a	DET
ejpam-2312	103	20	soft	soft	ADJ
ejpam-2312	103	21	topological	topological	ADJ
ejpam-2312	103	22	space	space	NOUN
ejpam-2312	103	23	over	over	ADP
ejpam-2312	103	24	x.	x.	NOUN
ejpam-2312	103	25	clearly	clearly	ADV
ejpam-2312	103	26	(	(	PUNCT
ejpam-2312	103	27	f	f	X
ejpam-2312	103	28	,	,	PUNCT
ejpam-2312	103	29	a)=̃{{h1	a)=̃{{h1	PUNCT
ejpam-2312	103	30	}	}	PUNCT
ejpam-2312	103	31	,	,	PUNCT
ejpam-2312	103	32	{	{	PUNCT
ejpam-2312	103	33	h2	h2	NOUN
ejpam-2312	103	34	,	,	PUNCT
ejpam-2312	103	35	h3	h3	NOUN
ejpam-2312	103	36	}	}	PUNCT
ejpam-2312	103	37	}	}	PUNCT
ejpam-2312	103	38	is	be	AUX
ejpam-2312	103	39	a	a	DET
ejpam-2312	103	40	soft	soft	ADJ
ejpam-2312	103	41	semi	semi	ADJ
ejpam-2312	103	42	-	-	ADJ
ejpam-2312	103	43	d	d	ADJ
ejpam-2312	103	44	-	-	PUNCT
ejpam-2312	103	45	set	set	NOUN
ejpam-2312	103	46	,	,	PUNCT
ejpam-2312	103	47	because	because	SCONJ
ejpam-2312	103	48	(	(	PUNCT
ejpam-2312	103	49	f	f	X
ejpam-2312	103	50	,	,	PUNCT
ejpam-2312	103	51	a)=̃(k5	a)=̃(k5	PROPN
ejpam-2312	103	52	,	,	PUNCT
ejpam-2312	103	53	a)\̃(k4	a)\̃(k4	PROPN
ejpam-2312	103	54	,	,	PUNCT
ejpam-2312	103	55	a	a	PRON
ejpam-2312	103	56	)	)	PUNCT
ejpam-2312	103	57	.	.	PUNCT
ejpam-2312	104	1	similarly	similarly	ADV
ejpam-2312	104	2	,	,	PUNCT
ejpam-2312	104	3	(	(	PUNCT
ejpam-2312	104	4	k	k	NOUN
ejpam-2312	104	5	,	,	PUNCT
ejpam-2312	104	6	a)=̃{{h1	a)=̃{{h1	PUNCT
ejpam-2312	104	7	}	}	PUNCT
ejpam-2312	104	8	,	,	PUNCT
ejpam-2312	104	9	{	{	PUNCT
ejpam-2312	104	10	h2	h2	NOUN
ejpam-2312	104	11	}	}	PUNCT
ejpam-2312	104	12	}	}	PUNCT
ejpam-2312	104	13	is	be	AUX
ejpam-2312	104	14	soft	soft	ADJ
ejpam-2312	104	15	semi	semi	ADJ
ejpam-2312	104	16	-	-	ADJ
ejpam-2312	104	17	d	d	ADJ
ejpam-2312	104	18	-	-	PUNCT
ejpam-2312	104	19	set	set	NOUN
ejpam-2312	104	20	,	,	PUNCT
ejpam-2312	104	21	because	because	SCONJ
ejpam-2312	104	22	(	(	PUNCT
ejpam-2312	104	23	k	k	NOUN
ejpam-2312	104	24	,	,	PUNCT
ejpam-2312	104	25	a)=̃(k1	a)=̃(k1	PROPN
ejpam-2312	104	26	,	,	PUNCT
ejpam-2312	104	27	a)\̃(k2	a)\̃(k2	PROPN
ejpam-2312	104	28	,	,	PUNCT
ejpam-2312	104	29	a	a	PRON
ejpam-2312	104	30	)	)	PUNCT
ejpam-2312	104	31	.	.	PUNCT
ejpam-2312	105	1	definition	definition	NOUN
ejpam-2312	105	2	13	13	NUM
ejpam-2312	105	3	.	.	PUNCT
ejpam-2312	106	1	let	let	VERB
ejpam-2312	106	2	(	(	PUNCT
ejpam-2312	106	3	x	x	X
ejpam-2312	106	4	,	,	PUNCT
ejpam-2312	106	5	τ	τ	PROPN
ejpam-2312	106	6	,	,	PUNCT
ejpam-2312	106	7	a	a	PRON
ejpam-2312	106	8	)	)	PUNCT
ejpam-2312	106	9	be	be	AUX
ejpam-2312	106	10	a	a	DET
ejpam-2312	106	11	soft	soft	ADJ
ejpam-2312	106	12	topological	topological	ADJ
ejpam-2312	106	13	space	space	NOUN
ejpam-2312	106	14	over	over	ADP
ejpam-2312	106	15	x.	x.	NOUN
ejpam-2312	106	16	then	then	ADV
ejpam-2312	106	17	(	(	PUNCT
ejpam-2312	106	18	x	x	X
ejpam-2312	106	19	,	,	PUNCT
ejpam-2312	106	20	τ	τ	PROPN
ejpam-2312	106	21	,	,	PUNCT
ejpam-2312	106	22	a	a	PRON
ejpam-2312	106	23	)	)	PUNCT
ejpam-2312	106	24	is	be	AUX
ejpam-2312	106	25	called	call	VERB
ejpam-2312	106	26	soft	soft	ADJ
ejpam-2312	106	27	semi	semi	ADJ
ejpam-2312	106	28	-	-	ADJ
ejpam-2312	106	29	d0	d0	ADJ
ejpam-2312	106	30	space	space	NOUN
ejpam-2312	106	31	,	,	PUNCT
ejpam-2312	106	32	if	if	SCONJ
ejpam-2312	106	33	for	for	ADP
ejpam-2312	106	34	any	any	DET
ejpam-2312	106	35	two	two	NUM
ejpam-2312	106	36	distinct	distinct	ADJ
ejpam-2312	106	37	soft	soft	ADJ
ejpam-2312	106	38	points	point	NOUN
ejpam-2312	106	39	ef	ef	NOUN
ejpam-2312	106	40	and	and	CCONJ
ejpam-2312	106	41	eg	eg	NOUN
ejpam-2312	106	42	in	in	ADP
ejpam-2312	106	43	x̃a	x̃a	NUM
ejpam-2312	106	44	,	,	PUNCT
ejpam-2312	106	45	there	there	PRON
ejpam-2312	106	46	exists	exist	VERB
ejpam-2312	106	47	soft	soft	ADJ
ejpam-2312	106	48	semi	semi	ADJ
ejpam-2312	106	49	-	-	ADJ
ejpam-2312	106	50	d	d	ADJ
ejpam-2312	106	51	-	-	PUNCT
ejpam-2312	106	52	set	set	ADJ
ejpam-2312	106	53	(	(	PUNCT
ejpam-2312	106	54	h	h	NOUN
ejpam-2312	106	55	,	,	PUNCT
ejpam-2312	106	56	a	a	PRON
ejpam-2312	106	57	)	)	PUNCT
ejpam-2312	106	58	in	in	ADP
ejpam-2312	106	59	ss(x)a	ss(x)a	PROPN
ejpam-2312	107	1	such	such	ADJ
ejpam-2312	107	2	that	that	SCONJ
ejpam-2312	107	3	ef	ef	PROPN
ejpam-2312	107	4	∈̃(h	∈̃(h	NOUN
ejpam-2312	107	5	,	,	PUNCT
ejpam-2312	107	6	a	a	PRON
ejpam-2312	107	7	)	)	PUNCT
ejpam-2312	107	8	and	and	CCONJ
ejpam-2312	107	9	eg	eg	PROPN
ejpam-2312	107	10	/̃∈(h	/̃∈(h	PROPN
ejpam-2312	107	11	,	,	PUNCT
ejpam-2312	107	12	a	a	PRON
ejpam-2312	107	13	)	)	PUNCT
ejpam-2312	107	14	or	or	CCONJ
ejpam-2312	107	15	soft	soft	ADJ
ejpam-2312	107	16	semi	semi	ADJ
ejpam-2312	107	17	-	-	ADJ
ejpam-2312	107	18	d	d	ADJ
ejpam-2312	107	19	-	-	PUNCT
ejpam-2312	107	20	set	set	ADJ
ejpam-2312	107	21	(	(	PUNCT
ejpam-2312	107	22	k	k	NOUN
ejpam-2312	107	23	,	,	PUNCT
ejpam-2312	107	24	a	a	PRON
ejpam-2312	107	25	)	)	PUNCT
ejpam-2312	107	26	in	in	ADP
ejpam-2312	107	27	ss(x)a	ss(x)a	PROPN
ejpam-2312	107	28	such	such	ADJ
ejpam-2312	107	29	that	that	SCONJ
ejpam-2312	107	30	eg∈̃(k	eg∈̃(k	NOUN
ejpam-2312	107	31	,	,	PUNCT
ejpam-2312	107	32	a	a	PRON
ejpam-2312	107	33	)	)	PUNCT
ejpam-2312	107	34	and	and	CCONJ
ejpam-2312	107	35	ef	ef	X
ejpam-2312	107	36	/̃∈(k	/̃∈(k	NOUN
ejpam-2312	107	37	,	,	PUNCT
ejpam-2312	107	38	a	a	PRON
ejpam-2312	107	39	)	)	PUNCT
ejpam-2312	107	40	.	.	PUNCT
ejpam-2312	108	1	definition	definition	NOUN
ejpam-2312	108	2	14	14	NUM
ejpam-2312	108	3	.	.	PUNCT
ejpam-2312	109	1	let	let	VERB
ejpam-2312	109	2	(	(	PUNCT
ejpam-2312	109	3	x	x	X
ejpam-2312	109	4	,	,	PUNCT
ejpam-2312	109	5	τ	τ	PROPN
ejpam-2312	109	6	,	,	PUNCT
ejpam-2312	109	7	a	a	PRON
ejpam-2312	109	8	)	)	PUNCT
ejpam-2312	109	9	be	be	AUX
ejpam-2312	109	10	a	a	DET
ejpam-2312	109	11	soft	soft	ADJ
ejpam-2312	109	12	topological	topological	ADJ
ejpam-2312	109	13	space	space	NOUN
ejpam-2312	109	14	over	over	ADP
ejpam-2312	109	15	x.	x.	NOUN
ejpam-2312	109	16	then	then	ADV
ejpam-2312	109	17	(	(	PUNCT
ejpam-2312	109	18	x	x	X
ejpam-2312	109	19	,	,	PUNCT
ejpam-2312	109	20	τ	τ	PROPN
ejpam-2312	109	21	,	,	PUNCT
ejpam-2312	109	22	a	a	PRON
ejpam-2312	109	23	)	)	PUNCT
ejpam-2312	109	24	is	be	AUX
ejpam-2312	109	25	called	call	VERB
ejpam-2312	109	26	soft	soft	ADJ
ejpam-2312	109	27	semi	semi	ADJ
ejpam-2312	109	28	-	-	ADJ
ejpam-2312	109	29	d1	d1	ADJ
ejpam-2312	109	30	space	space	NOUN
ejpam-2312	109	31	,	,	PUNCT
ejpam-2312	109	32	if	if	SCONJ
ejpam-2312	109	33	for	for	ADP
ejpam-2312	109	34	any	any	DET
ejpam-2312	109	35	two	two	NUM
ejpam-2312	109	36	distinct	distinct	ADJ
ejpam-2312	109	37	soft	soft	ADJ
ejpam-2312	109	38	points	point	NOUN
ejpam-2312	109	39	ef	ef	NOUN
ejpam-2312	109	40	and	and	CCONJ
ejpam-2312	109	41	eg	eg	NOUN
ejpam-2312	109	42	in	in	ADP
ejpam-2312	109	43	x̃a	x̃a	NUM
ejpam-2312	109	44	,	,	PUNCT
ejpam-2312	109	45	there	there	PRON
ejpam-2312	109	46	exists	exist	VERB
ejpam-2312	109	47	soft	soft	ADJ
ejpam-2312	109	48	semi	semi	ADJ
ejpam-2312	109	49	-	-	ADJ
ejpam-2312	109	50	d	d	ADJ
ejpam-2312	109	51	-	-	PUNCT
ejpam-2312	109	52	set	set	ADJ
ejpam-2312	109	53	(	(	PUNCT
ejpam-2312	109	54	h	h	NOUN
ejpam-2312	109	55	,	,	PUNCT
ejpam-2312	109	56	a	a	PRON
ejpam-2312	109	57	)	)	PUNCT
ejpam-2312	109	58	in	in	ADP
ejpam-2312	109	59	ss(x)a	ss(x)a	PROPN
ejpam-2312	110	1	such	such	ADJ
ejpam-2312	110	2	that	that	SCONJ
ejpam-2312	110	3	ef	ef	PROPN
ejpam-2312	110	4	∈̃(h	∈̃(h	NOUN
ejpam-2312	110	5	,	,	PUNCT
ejpam-2312	110	6	a	a	PRON
ejpam-2312	110	7	)	)	PUNCT
ejpam-2312	110	8	and	and	CCONJ
ejpam-2312	110	9	eg	eg	PROPN
ejpam-2312	110	10	/̃∈(h	/̃∈(h	PROPN
ejpam-2312	110	11	,	,	PUNCT
ejpam-2312	110	12	a	a	PRON
ejpam-2312	110	13	)	)	PUNCT
ejpam-2312	110	14	and	and	CCONJ
ejpam-2312	110	15	soft	soft	ADJ
ejpam-2312	110	16	semi	semi	ADJ
ejpam-2312	110	17	-	-	ADJ
ejpam-2312	110	18	d	d	ADJ
ejpam-2312	110	19	-	-	PUNCT
ejpam-2312	110	20	set	set	ADJ
ejpam-2312	110	21	(	(	PUNCT
ejpam-2312	110	22	k	k	NOUN
ejpam-2312	110	23	,	,	PUNCT
ejpam-2312	110	24	a	a	PRON
ejpam-2312	110	25	)	)	PUNCT
ejpam-2312	110	26	in	in	ADP
ejpam-2312	110	27	ss(x)a	ss(x)a	PROPN
ejpam-2312	110	28	such	such	ADJ
ejpam-2312	110	29	that	that	SCONJ
ejpam-2312	110	30	eg∈̃(k	eg∈̃(k	NOUN
ejpam-2312	110	31	,	,	PUNCT
ejpam-2312	110	32	a	a	PRON
ejpam-2312	110	33	)	)	PUNCT
ejpam-2312	110	34	and	and	CCONJ
ejpam-2312	110	35	ef	ef	X
ejpam-2312	110	36	/̃∈(k	/̃∈(k	NOUN
ejpam-2312	110	37	,	,	PUNCT
ejpam-2312	110	38	a	a	PRON
ejpam-2312	110	39	)	)	PUNCT
ejpam-2312	110	40	.	.	PUNCT
ejpam-2312	111	1	definition	definition	NOUN
ejpam-2312	111	2	15	15	NUM
ejpam-2312	111	3	.	.	PUNCT
ejpam-2312	112	1	let	let	VERB
ejpam-2312	112	2	(	(	PUNCT
ejpam-2312	112	3	x	x	X
ejpam-2312	112	4	,	,	PUNCT
ejpam-2312	112	5	τ	τ	PROPN
ejpam-2312	112	6	,	,	PUNCT
ejpam-2312	112	7	a	a	PRON
ejpam-2312	112	8	)	)	PUNCT
ejpam-2312	112	9	be	be	AUX
ejpam-2312	112	10	a	a	DET
ejpam-2312	112	11	soft	soft	ADJ
ejpam-2312	112	12	topological	topological	ADJ
ejpam-2312	112	13	space	space	NOUN
ejpam-2312	112	14	over	over	ADP
ejpam-2312	112	15	x.	x.	NOUN
ejpam-2312	112	16	then	then	ADV
ejpam-2312	112	17	(	(	PUNCT
ejpam-2312	112	18	x	x	X
ejpam-2312	112	19	,	,	PUNCT
ejpam-2312	112	20	τ	τ	PROPN
ejpam-2312	112	21	,	,	PUNCT
ejpam-2312	112	22	a	a	PRON
ejpam-2312	112	23	)	)	PUNCT
ejpam-2312	112	24	is	be	AUX
ejpam-2312	112	25	called	call	VERB
ejpam-2312	112	26	soft	soft	ADJ
ejpam-2312	112	27	semi	semi	ADJ
ejpam-2312	112	28	-	-	ADJ
ejpam-2312	112	29	d2	d2	ADJ
ejpam-2312	112	30	space	space	NOUN
ejpam-2312	112	31	,	,	PUNCT
ejpam-2312	112	32	if	if	SCONJ
ejpam-2312	112	33	for	for	ADP
ejpam-2312	112	34	any	any	DET
ejpam-2312	112	35	two	two	NUM
ejpam-2312	112	36	distinct	distinct	ADJ
ejpam-2312	112	37	soft	soft	ADJ
ejpam-2312	112	38	points	point	NOUN
ejpam-2312	112	39	ef	ef	NOUN
ejpam-2312	112	40	and	and	CCONJ
ejpam-2312	112	41	eg	eg	NOUN
ejpam-2312	112	42	in	in	ADP
ejpam-2312	112	43	x̃a	x̃a	NUM
ejpam-2312	112	44	,	,	PUNCT
ejpam-2312	112	45	there	there	PRON
ejpam-2312	112	46	exists	exist	VERB
ejpam-2312	112	47	disjoint	disjoint	VERB
ejpam-2312	112	48	soft	soft	ADJ
ejpam-2312	112	49	semi	semi	ADJ
ejpam-2312	112	50	-	-	ADJ
ejpam-2312	112	51	d	d	ADJ
ejpam-2312	112	52	-	-	PUNCT
ejpam-2312	112	53	sets	set	NOUN
ejpam-2312	112	54	(	(	PUNCT
ejpam-2312	112	55	h	h	NOUN
ejpam-2312	112	56	,	,	PUNCT
ejpam-2312	112	57	a	a	PRON
ejpam-2312	112	58	)	)	PUNCT
ejpam-2312	112	59	and	and	CCONJ
ejpam-2312	112	60	(	(	PUNCT
ejpam-2312	112	61	k	k	NOUN
ejpam-2312	112	62	,	,	PUNCT
ejpam-2312	112	63	a	a	PRON
ejpam-2312	112	64	)	)	PUNCT
ejpam-2312	112	65	in	in	ADP
ejpam-2312	112	66	ss(x)a	ss(x)a	PROPN
ejpam-2312	112	67	such	such	ADJ
ejpam-2312	112	68	that	that	SCONJ
ejpam-2312	112	69	ef	ef	PROPN
ejpam-2312	112	70	∈̃(h	∈̃(h	NOUN
ejpam-2312	112	71	,	,	PUNCT
ejpam-2312	112	72	a	a	PRON
ejpam-2312	112	73	)	)	PUNCT
ejpam-2312	112	74	and	and	CCONJ
ejpam-2312	112	75	eg∈̃(k	eg∈̃(k	PROPN
ejpam-2312	112	76	,	,	PUNCT
ejpam-2312	112	77	a	a	PRON
ejpam-2312	112	78	)	)	PUNCT
ejpam-2312	112	79	.	.	PUNCT
ejpam-2312	113	1	remark	remark	PROPN
ejpam-2312	113	2	1	1	NUM
ejpam-2312	113	3	.	.	PUNCT
ejpam-2312	114	1	it	it	PRON
ejpam-2312	114	2	is	be	AUX
ejpam-2312	114	3	clear	clear	ADJ
ejpam-2312	114	4	from	from	ADP
ejpam-2312	114	5	the	the	DET
ejpam-2312	114	6	above	above	ADJ
ejpam-2312	114	7	definitions	definition	NOUN
ejpam-2312	114	8	that	that	PRON
ejpam-2312	114	9	soft	soft	ADJ
ejpam-2312	114	10	semi	semi	ADJ
ejpam-2312	114	11	-	-	ADJ
ejpam-2312	114	12	d2	d2	ADJ
ejpam-2312	114	13	⇒	⇒	NOUN
ejpam-2312	114	14	soft	soft	ADJ
ejpam-2312	114	15	semi	semi	ADJ
ejpam-2312	114	16	-	-	ADJ
ejpam-2312	114	17	d1	d1	ADJ
ejpam-2312	114	18	⇒	⇒	NOUN
ejpam-2312	114	19	soft	soft	ADJ
ejpam-2312	114	20	semi	semi	NOUN
ejpam-2312	114	21	-	-	NOUN
ejpam-2312	114	22	d0	d0	NOUN
ejpam-2312	114	23	.	.	PUNCT
ejpam-2312	115	1	the	the	DET
ejpam-2312	115	2	interested	interested	ADJ
ejpam-2312	115	3	reader	reader	NOUN
ejpam-2312	115	4	can	can	AUX
ejpam-2312	115	5	easily	easily	ADV
ejpam-2312	115	6	check	check	VERB
ejpam-2312	115	7	that	that	SCONJ
ejpam-2312	115	8	the	the	DET
ejpam-2312	115	9	converse	converse	NOUN
ejpam-2312	115	10	is	be	AUX
ejpam-2312	115	11	not	not	PART
ejpam-2312	115	12	true	true	ADJ
ejpam-2312	115	13	in	in	ADP
ejpam-2312	115	14	general	general	ADJ
ejpam-2312	115	15	.	.	PUNCT
ejpam-2312	116	1	definition	definition	NOUN
ejpam-2312	116	2	16	16	NUM
ejpam-2312	116	3	.	.	PUNCT
ejpam-2312	117	1	let	let	VERB
ejpam-2312	117	2	(	(	PUNCT
ejpam-2312	117	3	x	x	X
ejpam-2312	117	4	,	,	PUNCT
ejpam-2312	117	5	τ	τ	PROPN
ejpam-2312	117	6	,	,	PUNCT
ejpam-2312	117	7	a	a	PRON
ejpam-2312	117	8	)	)	PUNCT
ejpam-2312	117	9	be	be	AUX
ejpam-2312	117	10	a	a	DET
ejpam-2312	117	11	soft	soft	ADJ
ejpam-2312	117	12	topological	topological	ADJ
ejpam-2312	117	13	space	space	NOUN
ejpam-2312	117	14	over	over	ADP
ejpam-2312	117	15	x.	x.	NOUN
ejpam-2312	117	16	if	if	SCONJ
ejpam-2312	117	17	for	for	ADP
ejpam-2312	117	18	any	any	DET
ejpam-2312	117	19	two	two	NUM
ejpam-2312	117	20	distinct	distinct	ADJ
ejpam-2312	117	21	soft	soft	ADJ
ejpam-2312	117	22	points	point	NOUN
ejpam-2312	117	23	eg	eg	NOUN
ejpam-2312	117	24	,	,	PUNCT
ejpam-2312	117	25	eh	eh	INTJ
ejpam-2312	117	26	in	in	ADP
ejpam-2312	117	27	x̃a	x̃a	NUM
ejpam-2312	117	28	,	,	PUNCT
ejpam-2312	117	29	there	there	PRON
ejpam-2312	117	30	exist	exist	VERB
ejpam-2312	117	31	soft	soft	ADJ
ejpam-2312	117	32	semi	semi	ADJ
ejpam-2312	117	33	-	-	ADJ
ejpam-2312	117	34	open	open	ADJ
ejpam-2312	117	35	sets	set	NOUN
ejpam-2312	117	36	(	(	PUNCT
ejpam-2312	117	37	f1	f1	NOUN
ejpam-2312	117	38	,	,	PUNCT
ejpam-2312	117	39	a	a	PRON
ejpam-2312	117	40	)	)	PUNCT
ejpam-2312	117	41	or	or	CCONJ
ejpam-2312	117	42	(	(	PUNCT
ejpam-2312	117	43	f2	f2	PROPN
ejpam-2312	117	44	,	,	PUNCT
ejpam-2312	117	45	a	a	PRON
ejpam-2312	117	46	)	)	PUNCT
ejpam-2312	117	47	such	such	ADJ
ejpam-2312	117	48	that	that	SCONJ
ejpam-2312	117	49	eg∈̃(f1	eg∈̃(f1	PROPN
ejpam-2312	117	50	,	,	PUNCT
ejpam-2312	117	51	a	a	PRON
ejpam-2312	117	52	)	)	PUNCT
ejpam-2312	117	53	,	,	PUNCT
ejpam-2312	117	54	eh	eh	INTJ
ejpam-2312	117	55	/̃∈(f1	/̃∈(f1	PROPN
ejpam-2312	117	56	,	,	PUNCT
ejpam-2312	117	57	a	a	PRON
ejpam-2312	117	58	)	)	PUNCT
ejpam-2312	117	59	,	,	PUNCT
ejpam-2312	117	60	eh	eh	INTJ
ejpam-2312	117	61	∈̃(f2	∈̃(f2	PRON
ejpam-2312	117	62	,	,	PUNCT
ejpam-2312	117	63	a	a	PRON
ejpam-2312	117	64	)	)	PUNCT
ejpam-2312	117	65	,	,	PUNCT
ejpam-2312	117	66	eg	eg	PROPN
ejpam-2312	117	67	/̃∈(f2	/̃∈(f2	PROPN
ejpam-2312	117	68	,	,	PUNCT
ejpam-2312	117	69	a	a	PRON
ejpam-2312	117	70	)	)	PUNCT
ejpam-2312	117	71	,	,	PUNCT
ejpam-2312	117	72	then	then	ADV
ejpam-2312	117	73	(	(	PUNCT
ejpam-2312	117	74	x	x	X
ejpam-2312	117	75	,	,	PUNCT
ejpam-2312	117	76	τ	τ	PROPN
ejpam-2312	117	77	,	,	PUNCT
ejpam-2312	117	78	a	a	PRON
ejpam-2312	117	79	)	)	PUNCT
ejpam-2312	117	80	is	be	AUX
ejpam-2312	117	81	called	call	VERB
ejpam-2312	117	82	soft	soft	ADJ
ejpam-2312	117	83	semi	semi	ADJ
ejpam-2312	117	84	-	-	NOUN
ejpam-2312	117	85	t0space	t0space	ADJ
ejpam-2312	117	86	.	.	PUNCT
ejpam-2312	118	1	s.	s.	PROPN
ejpam-2312	118	2	hussain	hussain	PROPN
ejpam-2312	118	3	/	/	SYM
ejpam-2312	118	4	eur	eur	PROPN
ejpam-2312	118	5	.	.	PUNCT
ejpam-2312	119	1	j.	j.	PROPN
ejpam-2312	119	2	pure	pure	PROPN
ejpam-2312	119	3	appl	appl	PROPN
ejpam-2312	119	4	.	.	PROPN
ejpam-2312	119	5	math	math	PROPN
ejpam-2312	119	6	,	,	PUNCT
ejpam-2312	119	7	10	10	NUM
ejpam-2312	119	8	(	(	PUNCT
ejpam-2312	119	9	2	2	NUM
ejpam-2312	119	10	)	)	PUNCT
ejpam-2312	119	11	(	(	PUNCT
ejpam-2312	119	12	2017	2017	NUM
ejpam-2312	119	13	)	)	PUNCT
ejpam-2312	119	14	,	,	PUNCT
ejpam-2312	119	15	199	199	NUM
ejpam-2312	119	16	-	-	SYM
ejpam-2312	119	17	210	210	NUM
ejpam-2312	119	18	203	203	NUM
ejpam-2312	119	19	example	example	NOUN
ejpam-2312	119	20	2	2	NUM
ejpam-2312	119	21	.	.	PUNCT
ejpam-2312	120	1	let	let	VERB
ejpam-2312	120	2	x	x	PUNCT
ejpam-2312	120	3	=	=	PRON
ejpam-2312	120	4	{	{	PUNCT
ejpam-2312	120	5	h1	h1	PROPN
ejpam-2312	120	6	,	,	PUNCT
ejpam-2312	120	7	h2	h2	PROPN
ejpam-2312	120	8	,	,	PUNCT
ejpam-2312	120	9	h3	h3	NOUN
ejpam-2312	120	10	}	}	PUNCT
ejpam-2312	120	11	,	,	PUNCT
ejpam-2312	120	12	a	a	DET
ejpam-2312	120	13	=	=	X
ejpam-2312	120	14	{	{	PUNCT
ejpam-2312	120	15	e1	e1	PROPN
ejpam-2312	120	16	,	,	PUNCT
ejpam-2312	120	17	e2	e2	PROPN
ejpam-2312	120	18	,	,	PUNCT
ejpam-2312	120	19	e3	e3	NOUN
ejpam-2312	120	20	}	}	PUNCT
ejpam-2312	120	21	and	and	CCONJ
ejpam-2312	120	22	τ	τ	X
ejpam-2312	121	1	=	=	PUNCT
ejpam-2312	121	2	{	{	PUNCT
ejpam-2312	121	3	φ̃	φ̃	PROPN
ejpam-2312	121	4	,	,	PUNCT
ejpam-2312	121	5	x̃	x̃	PROPN
ejpam-2312	121	6	,	,	PUNCT
ejpam-2312	121	7	(	(	PUNCT
ejpam-2312	121	8	k1	k1	PROPN
ejpam-2312	121	9	,	,	PUNCT
ejpam-2312	121	10	a	a	NOUN
ejpam-2312	121	11	)	)	PUNCT
ejpam-2312	121	12	}	}	PUNCT
ejpam-2312	121	13	,	,	PUNCT
ejpam-2312	121	14	where	where	SCONJ
ejpam-2312	121	15	(	(	PUNCT
ejpam-2312	121	16	k1	k1	NOUN
ejpam-2312	121	17	,	,	PUNCT
ejpam-2312	121	18	a)=̃{(e1	a)=̃{(e1	PROPN
ejpam-2312	121	19	,	,	PUNCT
ejpam-2312	121	20	{	{	PUNCT
ejpam-2312	121	21	h1	h1	PROPN
ejpam-2312	121	22	}	}	PUNCT
ejpam-2312	121	23	)	)	PUNCT
ejpam-2312	121	24	,	,	PUNCT
ejpam-2312	121	25	(	(	PUNCT
ejpam-2312	121	26	e2	e2	PROPN
ejpam-2312	121	27	,	,	PUNCT
ejpam-2312	121	28	{	{	PUNCT
ejpam-2312	121	29	h2	h2	NOUN
ejpam-2312	121	30	}	}	PUNCT
ejpam-2312	121	31	)	)	PUNCT
ejpam-2312	121	32	,	,	PUNCT
ejpam-2312	121	33	(	(	PUNCT
ejpam-2312	121	34	e3	e3	NOUN
ejpam-2312	121	35	,	,	PUNCT
ejpam-2312	121	36	{	{	PUNCT
ejpam-2312	121	37	h3	h3	NOUN
ejpam-2312	121	38	}	}	PUNCT
ejpam-2312	121	39	)	)	PUNCT
ejpam-2312	121	40	}	}	PUNCT
ejpam-2312	121	41	is	be	AUX
ejpam-2312	121	42	a	a	DET
ejpam-2312	121	43	soft	soft	ADJ
ejpam-2312	121	44	sets	set	NOUN
ejpam-2312	121	45	over	over	ADP
ejpam-2312	121	46	x	x	PUNCT
ejpam-2312	121	47	with	with	ADP
ejpam-2312	121	48	soft	soft	ADJ
ejpam-2312	121	49	points	point	NOUN
ejpam-2312	121	50	:	:	PUNCT
ejpam-2312	121	51	e1(k1	e1(k1	NUM
ejpam-2312	121	52	)	)	PUNCT
ejpam-2312	121	53	=	=	PRON
ejpam-2312	121	54	{	{	PUNCT
ejpam-2312	121	55	h1	h1	PROPN
ejpam-2312	121	56	}	}	PUNCT
ejpam-2312	121	57	,	,	PUNCT
ejpam-2312	121	58	e2(k1	e2(k1	ADJ
ejpam-2312	121	59	)	)	PUNCT
ejpam-2312	121	60	=	=	PRON
ejpam-2312	121	61	{	{	PUNCT
ejpam-2312	121	62	h2	h2	NOUN
ejpam-2312	121	63	}	}	PUNCT
ejpam-2312	121	64	,	,	PUNCT
ejpam-2312	121	65	e3(k1	e3(k1	NUM
ejpam-2312	121	66	)	)	PUNCT
ejpam-2312	121	67	=	=	PRON
ejpam-2312	121	68	{	{	PUNCT
ejpam-2312	121	69	h3	h3	NOUN
ejpam-2312	121	70	}	}	PUNCT
ejpam-2312	121	71	.	.	PUNCT
ejpam-2312	122	1	then	then	ADV
ejpam-2312	122	2	τ	τ	PROPN
ejpam-2312	122	3	defines	define	VERB
ejpam-2312	122	4	a	a	DET
ejpam-2312	122	5	soft	soft	ADJ
ejpam-2312	122	6	topology	topology	NOUN
ejpam-2312	122	7	on	on	ADP
ejpam-2312	122	8	x	x	PUNCT
ejpam-2312	122	9	and	and	CCONJ
ejpam-2312	122	10	hence	hence	ADV
ejpam-2312	122	11	(	(	PUNCT
ejpam-2312	122	12	x	x	X
ejpam-2312	122	13	,	,	PUNCT
ejpam-2312	122	14	τ	τ	PROPN
ejpam-2312	122	15	,	,	PUNCT
ejpam-2312	122	16	a	a	PRON
ejpam-2312	122	17	)	)	PUNCT
ejpam-2312	122	18	is	be	AUX
ejpam-2312	122	19	a	a	DET
ejpam-2312	122	20	soft	soft	ADJ
ejpam-2312	122	21	topological	topological	ADJ
ejpam-2312	122	22	space	space	NOUN
ejpam-2312	122	23	over	over	ADP
ejpam-2312	122	24	x.	x.	NOUN
ejpam-2312	123	1	moreover	moreover	ADV
ejpam-2312	123	2	(	(	PUNCT
ejpam-2312	123	3	x	x	X
ejpam-2312	123	4	,	,	PUNCT
ejpam-2312	123	5	τ	τ	PROPN
ejpam-2312	123	6	,	,	PUNCT
ejpam-2312	123	7	a	a	PRON
ejpam-2312	123	8	)	)	PUNCT
ejpam-2312	123	9	is	be	AUX
ejpam-2312	123	10	soft	soft	ADJ
ejpam-2312	123	11	semi	semi	ADJ
ejpam-2312	123	12	-	-	ADJ
ejpam-2312	123	13	t0	t0	NOUN
ejpam-2312	123	14	-	-	NOUN
ejpam-2312	123	15	space	space	NOUN
ejpam-2312	123	16	.	.	PUNCT
ejpam-2312	124	1	definition	definition	NOUN
ejpam-2312	124	2	17	17	NUM
ejpam-2312	124	3	.	.	PUNCT
ejpam-2312	125	1	let	let	VERB
ejpam-2312	125	2	(	(	PUNCT
ejpam-2312	125	3	x	x	X
ejpam-2312	125	4	,	,	PUNCT
ejpam-2312	125	5	τ	τ	PROPN
ejpam-2312	125	6	,	,	PUNCT
ejpam-2312	125	7	a	a	PRON
ejpam-2312	125	8	)	)	PUNCT
ejpam-2312	125	9	be	be	AUX
ejpam-2312	125	10	a	a	DET
ejpam-2312	125	11	soft	soft	ADJ
ejpam-2312	125	12	topological	topological	ADJ
ejpam-2312	125	13	space	space	NOUN
ejpam-2312	125	14	over	over	ADP
ejpam-2312	125	15	x.	x.	NOUN
ejpam-2312	126	1	(	(	PUNCT
ejpam-2312	126	2	g	g	PROPN
ejpam-2312	126	3	,	,	PUNCT
ejpam-2312	126	4	a	a	PRON
ejpam-2312	126	5	)	)	PUNCT
ejpam-2312	126	6	be	be	AUX
ejpam-2312	126	7	soft	soft	ADJ
ejpam-2312	126	8	set	set	NOUN
ejpam-2312	126	9	in	in	ADP
ejpam-2312	126	10	ss(x)a	ss(x)a	PROPN
ejpam-2312	126	11	,	,	PUNCT
ejpam-2312	126	12	and	and	CCONJ
ejpam-2312	126	13	ef	ef	PROPN
ejpam-2312	126	14	be	be	AUX
ejpam-2312	126	15	a	a	DET
ejpam-2312	126	16	soft	soft	ADJ
ejpam-2312	126	17	point	point	NOUN
ejpam-2312	126	18	in	in	ADP
ejpam-2312	126	19	x̃a	x̃a	PROPN
ejpam-2312	126	20	.	.	PUNCT
ejpam-2312	127	1	then	then	ADV
ejpam-2312	127	2	(	(	PUNCT
ejpam-2312	127	3	g	g	NOUN
ejpam-2312	127	4	,	,	PUNCT
ejpam-2312	127	5	a	a	PRON
ejpam-2312	127	6	)	)	PUNCT
ejpam-2312	127	7	is	be	AUX
ejpam-2312	127	8	said	say	VERB
ejpam-2312	127	9	to	to	PART
ejpam-2312	127	10	be	be	AUX
ejpam-2312	127	11	soft	soft	ADJ
ejpam-2312	127	12	semi	semi	ADJ
ejpam-2312	127	13	-	-	ADJ
ejpam-2312	127	14	neighborhood	neighborhood	NOUN
ejpam-2312	127	15	of	of	ADP
ejpam-2312	127	16	soft	soft	ADJ
ejpam-2312	127	17	point	point	NOUN
ejpam-2312	127	18	ef	ef	NOUN
ejpam-2312	127	19	,	,	PUNCT
ejpam-2312	127	20	if	if	SCONJ
ejpam-2312	127	21	there	there	PRON
ejpam-2312	127	22	exists	exist	VERB
ejpam-2312	127	23	a	a	DET
ejpam-2312	127	24	soft	soft	ADJ
ejpam-2312	127	25	open	open	ADJ
ejpam-2312	127	26	set	set	NOUN
ejpam-2312	127	27	(	(	PUNCT
ejpam-2312	127	28	k	k	NOUN
ejpam-2312	127	29	,	,	PUNCT
ejpam-2312	127	30	a	a	PRON
ejpam-2312	127	31	)	)	PUNCT
ejpam-2312	127	32	such	such	ADJ
ejpam-2312	127	33	that	that	SCONJ
ejpam-2312	127	34	ef	ef	PROPN
ejpam-2312	127	35	∈̃(k	∈̃(k	NOUN
ejpam-2312	127	36	,	,	PUNCT
ejpam-2312	127	37	a)⊂̃(g	a)⊂̃(g	PRON
ejpam-2312	127	38	,	,	PUNCT
ejpam-2312	127	39	a	a	PRON
ejpam-2312	127	40	)	)	PUNCT
ejpam-2312	127	41	.	.	PUNCT
ejpam-2312	128	1	definition	definition	NOUN
ejpam-2312	128	2	18	18	NUM
ejpam-2312	128	3	.	.	PUNCT
ejpam-2312	129	1	let	let	VERB
ejpam-2312	129	2	(	(	PUNCT
ejpam-2312	129	3	x	x	X
ejpam-2312	129	4	,	,	PUNCT
ejpam-2312	129	5	τ	τ	PROPN
ejpam-2312	129	6	,	,	PUNCT
ejpam-2312	129	7	a	a	PRON
ejpam-2312	129	8	)	)	PUNCT
ejpam-2312	129	9	be	be	AUX
ejpam-2312	129	10	a	a	DET
ejpam-2312	129	11	soft	soft	ADJ
ejpam-2312	129	12	topological	topological	ADJ
ejpam-2312	129	13	space	space	NOUN
ejpam-2312	129	14	over	over	ADP
ejpam-2312	129	15	x.	x.	NOUN
ejpam-2312	130	1	(	(	PUNCT
ejpam-2312	130	2	f	f	X
ejpam-2312	130	3	,	,	PUNCT
ejpam-2312	130	4	a	a	PRON
ejpam-2312	130	5	)	)	PUNCT
ejpam-2312	130	6	be	be	AUX
ejpam-2312	130	7	soft	soft	ADJ
ejpam-2312	130	8	set	set	NOUN
ejpam-2312	130	9	in	in	ADP
ejpam-2312	130	10	ss(x)a	ss(x)a	PROPN
ejpam-2312	130	11	,	,	PUNCT
ejpam-2312	130	12	and	and	CCONJ
ejpam-2312	130	13	ef	ef	PROPN
ejpam-2312	130	14	be	be	AUX
ejpam-2312	130	15	a	a	DET
ejpam-2312	130	16	soft	soft	ADJ
ejpam-2312	130	17	point	point	NOUN
ejpam-2312	130	18	in	in	ADP
ejpam-2312	130	19	x̃a	x̃a	PROPN
ejpam-2312	130	20	.	.	PUNCT
ejpam-2312	131	1	if	if	SCONJ
ejpam-2312	131	2	every	every	DET
ejpam-2312	131	3	soft	soft	ADJ
ejpam-2312	131	4	neighborhood	neighborhood	NOUN
ejpam-2312	131	5	of	of	ADP
ejpam-2312	131	6	ef	ef	VERB
ejpam-2312	131	7	soft	soft	ADJ
ejpam-2312	131	8	intersects	intersect	NOUN
ejpam-2312	131	9	(	(	PUNCT
ejpam-2312	131	10	f	f	X
ejpam-2312	131	11	,	,	PUNCT
ejpam-2312	131	12	a	a	PRON
ejpam-2312	131	13	)	)	PUNCT
ejpam-2312	131	14	in	in	ADP
ejpam-2312	131	15	some	some	DET
ejpam-2312	131	16	soft	soft	ADJ
ejpam-2312	131	17	points	point	NOUN
ejpam-2312	131	18	other	other	ADJ
ejpam-2312	131	19	than	than	ADP
ejpam-2312	131	20	ef	ef	PROPN
ejpam-2312	131	21	itself	itself	PRON
ejpam-2312	131	22	,	,	PUNCT
ejpam-2312	131	23	then	then	ADV
ejpam-2312	131	24	ef	ef	PROPN
ejpam-2312	131	25	is	be	AUX
ejpam-2312	131	26	called	call	VERB
ejpam-2312	131	27	soft	soft	ADJ
ejpam-2312	131	28	semi	semi	ADJ
ejpam-2312	131	29	-	-	ADJ
ejpam-2312	131	30	limit	limit	ADJ
ejpam-2312	131	31	point	point	NOUN
ejpam-2312	131	32	of	of	ADP
ejpam-2312	131	33	(	(	PUNCT
ejpam-2312	131	34	f	f	X
ejpam-2312	131	35	,	,	PUNCT
ejpam-2312	131	36	e	e	NOUN
ejpam-2312	131	37	)	)	PUNCT
ejpam-2312	131	38	.	.	PUNCT
ejpam-2312	132	1	the	the	DET
ejpam-2312	132	2	set	set	NOUN
ejpam-2312	132	3	of	of	ADP
ejpam-2312	132	4	all	all	DET
ejpam-2312	132	5	soft	soft	ADJ
ejpam-2312	132	6	semi	semi	ADJ
ejpam-2312	132	7	-	-	ADJ
ejpam-2312	132	8	limit	limit	ADJ
ejpam-2312	132	9	points	point	NOUN
ejpam-2312	132	10	of	of	ADP
ejpam-2312	132	11	(	(	PUNCT
ejpam-2312	132	12	f	f	X
ejpam-2312	132	13	,	,	PUNCT
ejpam-2312	132	14	a	a	PRON
ejpam-2312	132	15	)	)	PUNCT
ejpam-2312	132	16	is	be	AUX
ejpam-2312	132	17	denoted	denote	VERB
ejpam-2312	132	18	by	by	ADP
ejpam-2312	132	19	(	(	PUNCT
ejpam-2312	132	20	f	f	X
ejpam-2312	132	21	,	,	PUNCT
ejpam-2312	132	22	a)ssd	a)ssd	PROPN
ejpam-2312	132	23	.	.	PUNCT
ejpam-2312	133	1	in	in	ADP
ejpam-2312	133	2	other	other	ADJ
ejpam-2312	133	3	words	word	NOUN
ejpam-2312	133	4	,	,	PUNCT
ejpam-2312	133	5	if	if	SCONJ
ejpam-2312	133	6	(	(	PUNCT
ejpam-2312	133	7	x	x	NOUN
ejpam-2312	133	8	,	,	PUNCT
ejpam-2312	133	9	τ	τ	PROPN
ejpam-2312	133	10	,	,	PUNCT
ejpam-2312	133	11	a	a	PRON
ejpam-2312	133	12	)	)	PUNCT
ejpam-2312	133	13	is	be	AUX
ejpam-2312	133	14	a	a	DET
ejpam-2312	133	15	soft	soft	ADJ
ejpam-2312	133	16	topological	topological	ADJ
ejpam-2312	133	17	space	space	NOUN
ejpam-2312	133	18	,	,	PUNCT
ejpam-2312	133	19	(	(	PUNCT
ejpam-2312	133	20	f	f	X
ejpam-2312	133	21	,	,	PUNCT
ejpam-2312	133	22	a	a	PRON
ejpam-2312	133	23	)	)	PUNCT
ejpam-2312	133	24	be	be	AUX
ejpam-2312	133	25	soft	soft	ADJ
ejpam-2312	133	26	set	set	NOUN
ejpam-2312	133	27	in	in	ADP
ejpam-2312	133	28	ss(x)a	ss(x)a	PROPN
ejpam-2312	133	29	,	,	PUNCT
ejpam-2312	133	30	and	and	CCONJ
ejpam-2312	133	31	ef	ef	PROPN
ejpam-2312	133	32	be	be	AUX
ejpam-2312	133	33	soft	soft	ADJ
ejpam-2312	133	34	point	point	NOUN
ejpam-2312	133	35	in	in	ADP
ejpam-2312	133	36	x̃a	x̃a	NUM
ejpam-2312	133	37	,	,	PUNCT
ejpam-2312	133	38	then	then	ADV
ejpam-2312	133	39	ef	ef	VERB
ejpam-2312	133	40	∈̃(f	∈̃(f	NOUN
ejpam-2312	133	41	,	,	PUNCT
ejpam-2312	133	42	a)ssd	a)ssd	NOUN
ejpam-2312	133	43	if	if	SCONJ
ejpam-2312	133	44	and	and	CCONJ
ejpam-2312	133	45	only	only	ADV
ejpam-2312	133	46	if	if	SCONJ
ejpam-2312	133	47	(	(	PUNCT
ejpam-2312	133	48	g	g	NOUN
ejpam-2312	133	49	,	,	PUNCT
ejpam-2312	133	50	a)∩̃((f	a)∩̃((f	VERB
ejpam-2312	133	51	,	,	PUNCT
ejpam-2312	133	52	a)\̃{ef	a)\̃{ef	NUM
ejpam-2312	133	53	}	}	PUNCT
ejpam-2312	133	54	)	)	PUNCT
ejpam-2312	133	55	˜6	˜6	PROPN
ejpam-2312	133	56	=	=	SYM
ejpam-2312	133	57	φ̃	φ̃	PROPN
ejpam-2312	133	58	,	,	PUNCT
ejpam-2312	133	59	for	for	ADP
ejpam-2312	133	60	all	all	DET
ejpam-2312	133	61	soft	soft	ADJ
ejpam-2312	133	62	semi	semi	ADJ
ejpam-2312	133	63	-	-	ADJ
ejpam-2312	133	64	open	open	ADJ
ejpam-2312	133	65	neighborhoods	neighborhood	NOUN
ejpam-2312	133	66	(	(	PUNCT
ejpam-2312	133	67	g	g	NOUN
ejpam-2312	133	68	,	,	PUNCT
ejpam-2312	133	69	a	a	PRON
ejpam-2312	133	70	)	)	PUNCT
ejpam-2312	133	71	of	of	ADP
ejpam-2312	133	72	ef	ef	PROPN
ejpam-2312	133	73	.	.	PUNCT
ejpam-2312	134	1	remark	remark	PROPN
ejpam-2312	134	2	2	2	NUM
ejpam-2312	134	3	.	.	PUNCT
ejpam-2312	135	1	form	form	VERB
ejpam-2312	135	2	the	the	DET
ejpam-2312	135	3	definition	definition	NOUN
ejpam-2312	135	4	,	,	PUNCT
ejpam-2312	135	5	it	it	PRON
ejpam-2312	135	6	follows	follow	VERB
ejpam-2312	135	7	that	that	SCONJ
ejpam-2312	135	8	the	the	DET
ejpam-2312	135	9	soft	soft	ADJ
ejpam-2312	135	10	point	point	NOUN
ejpam-2312	135	11	ef	ef	PROPN
ejpam-2312	135	12	is	be	AUX
ejpam-2312	135	13	a	a	DET
ejpam-2312	135	14	soft	soft	ADJ
ejpam-2312	135	15	semi	semi	ADJ
ejpam-2312	135	16	-	-	ADJ
ejpam-2312	135	17	limit	limit	ADJ
ejpam-2312	135	18	point	point	NOUN
ejpam-2312	135	19	of	of	ADP
ejpam-2312	135	20	(	(	PUNCT
ejpam-2312	135	21	f	f	X
ejpam-2312	135	22	,	,	PUNCT
ejpam-2312	135	23	a	a	PRON
ejpam-2312	135	24	)	)	PUNCT
ejpam-2312	135	25	if	if	SCONJ
ejpam-2312	136	1	and	and	CCONJ
ejpam-2312	136	2	only	only	ADV
ejpam-2312	136	3	if	if	SCONJ
ejpam-2312	136	4	ef	ef	PROPN
ejpam-2312	136	5	∈̃cls((f	∈̃cls((f	NOUN
ejpam-2312	136	6	,	,	PUNCT
ejpam-2312	136	7	a)\̃{ef	a)\̃{ef	NOUN
ejpam-2312	136	8	}	}	PUNCT
ejpam-2312	136	9	)	)	PUNCT
ejpam-2312	136	10	.	.	PUNCT
ejpam-2312	137	1	theorem	theorem	NOUN
ejpam-2312	137	2	1	1	X
ejpam-2312	137	3	.	.	PUNCT
ejpam-2312	138	1	let	let	VERB
ejpam-2312	138	2	(	(	PUNCT
ejpam-2312	138	3	x	x	X
ejpam-2312	138	4	,	,	PUNCT
ejpam-2312	138	5	τ	τ	PROPN
ejpam-2312	138	6	,	,	PUNCT
ejpam-2312	138	7	a	a	PRON
ejpam-2312	138	8	)	)	PUNCT
ejpam-2312	138	9	be	be	AUX
ejpam-2312	138	10	a	a	DET
ejpam-2312	138	11	soft	soft	ADJ
ejpam-2312	138	12	topological	topological	ADJ
ejpam-2312	138	13	space	space	NOUN
ejpam-2312	138	14	over	over	ADP
ejpam-2312	138	15	x.	x.	NOUN
ejpam-2312	138	16	then	then	ADV
ejpam-2312	138	17	the	the	DET
ejpam-2312	138	18	following	following	NOUN
ejpam-2312	138	19	are	be	AUX
ejpam-2312	138	20	equivalent	equivalent	ADJ
ejpam-2312	138	21	:	:	PUNCT
ejpam-2312	138	22	(	(	PUNCT
ejpam-2312	138	23	1	1	X
ejpam-2312	138	24	)	)	PUNCT
ejpam-2312	138	25	(	(	PUNCT
ejpam-2312	138	26	x	x	X
ejpam-2312	138	27	,	,	PUNCT
ejpam-2312	138	28	τ	τ	PROPN
ejpam-2312	138	29	,	,	PUNCT
ejpam-2312	138	30	a	a	PRON
ejpam-2312	138	31	)	)	PUNCT
ejpam-2312	138	32	is	be	AUX
ejpam-2312	138	33	soft	soft	ADJ
ejpam-2312	138	34	semi	semi	ADJ
ejpam-2312	138	35	-	-	ADJ
ejpam-2312	138	36	t0	t0	ADJ
ejpam-2312	138	37	space	space	NOUN
ejpam-2312	138	38	.	.	PUNCT
ejpam-2312	139	1	(	(	PUNCT
ejpam-2312	139	2	2	2	X
ejpam-2312	139	3	)	)	PUNCT
ejpam-2312	139	4	for	for	ADP
ejpam-2312	139	5	any	any	DET
ejpam-2312	139	6	distinct	distinct	ADJ
ejpam-2312	139	7	soft	soft	ADJ
ejpam-2312	139	8	points	point	NOUN
ejpam-2312	139	9	eg	eg	NOUN
ejpam-2312	139	10	and	and	CCONJ
ejpam-2312	139	11	eh	eh	INTJ
ejpam-2312	139	12	in	in	ADP
ejpam-2312	139	13	x̃a	x̃a	NUM
ejpam-2312	139	14	,	,	PUNCT
ejpam-2312	139	15	cls(eg	cls(eg	X
ejpam-2312	139	16	)	)	PUNCT
ejpam-2312	139	17	˜6	˜6	NOUN
ejpam-2312	139	18	=	=	NOUN
ejpam-2312	139	19	cls(eh	cls(eh	X
ejpam-2312	139	20	)	)	PUNCT
ejpam-2312	139	21	.	.	PUNCT
ejpam-2312	140	1	proof	proof	NOUN
ejpam-2312	140	2	.	.	PUNCT
ejpam-2312	141	1	(	(	PUNCT
ejpam-2312	141	2	1	1	X
ejpam-2312	141	3	)	)	PUNCT
ejpam-2312	141	4	⇒	⇒	NOUN
ejpam-2312	141	5	(	(	PUNCT
ejpam-2312	141	6	2	2	X
ejpam-2312	141	7	)	)	PUNCT
ejpam-2312	141	8	suppose	suppose	VERB
ejpam-2312	141	9	that	that	SCONJ
ejpam-2312	141	10	(	(	PUNCT
ejpam-2312	141	11	x	x	X
ejpam-2312	141	12	,	,	PUNCT
ejpam-2312	141	13	τ	τ	PROPN
ejpam-2312	141	14	,	,	PUNCT
ejpam-2312	141	15	a	a	PRON
ejpam-2312	141	16	)	)	PUNCT
ejpam-2312	141	17	is	be	AUX
ejpam-2312	141	18	soft	soft	ADJ
ejpam-2312	141	19	semi	semi	ADJ
ejpam-2312	141	20	-	-	ADJ
ejpam-2312	141	21	t0	t0	ADJ
ejpam-2312	141	22	space	space	NOUN
ejpam-2312	141	23	and	and	CCONJ
ejpam-2312	141	24	eg	eg	NOUN
ejpam-2312	141	25	and	and	CCONJ
ejpam-2312	141	26	eh	eh	INTJ
ejpam-2312	141	27	are	be	AUX
ejpam-2312	141	28	distinct	distinct	ADJ
ejpam-2312	141	29	soft	soft	ADJ
ejpam-2312	141	30	points	point	NOUN
ejpam-2312	141	31	in	in	ADP
ejpam-2312	141	32	x̃a	x̃a	PROPN
ejpam-2312	141	33	.	.	PUNCT
ejpam-2312	142	1	then	then	ADV
ejpam-2312	142	2	there	there	PRON
ejpam-2312	142	3	exists	exist	VERB
ejpam-2312	142	4	at	at	ADP
ejpam-2312	142	5	least	least	ADV
ejpam-2312	142	6	one	one	NUM
ejpam-2312	142	7	soft	soft	ADJ
ejpam-2312	142	8	semi	semi	ADJ
ejpam-2312	142	9	-	-	ADJ
ejpam-2312	142	10	open	open	ADJ
ejpam-2312	142	11	set	set	NOUN
ejpam-2312	142	12	(	(	PUNCT
ejpam-2312	142	13	k	k	NOUN
ejpam-2312	142	14	,	,	PUNCT
ejpam-2312	142	15	a	a	PRON
ejpam-2312	142	16	)	)	PUNCT
ejpam-2312	142	17	(	(	PUNCT
ejpam-2312	142	18	say	say	INTJ
ejpam-2312	142	19	)	)	PUNCT
ejpam-2312	142	20	,	,	PUNCT
ejpam-2312	142	21	which	which	PRON
ejpam-2312	142	22	contains	contain	VERB
ejpam-2312	142	23	eg	eg	NOUN
ejpam-2312	142	24	but	but	CCONJ
ejpam-2312	142	25	not	not	PART
ejpam-2312	142	26	eh	eh	INTJ
ejpam-2312	142	27	.	.	PUNCT
ejpam-2312	143	1	but	but	CCONJ
ejpam-2312	143	2	then	then	ADV
ejpam-2312	143	3	eg	eg	NOUN
ejpam-2312	143	4	is	be	AUX
ejpam-2312	143	5	not	not	PART
ejpam-2312	143	6	soft	soft	ADJ
ejpam-2312	143	7	semi	semi	ADJ
ejpam-2312	143	8	-	-	ADJ
ejpam-2312	143	9	limit	limit	ADJ
ejpam-2312	143	10	point	point	NOUN
ejpam-2312	143	11	of	of	ADP
ejpam-2312	143	12	eh	eh	INTJ
ejpam-2312	143	13	.	.	PUNCT
ejpam-2312	144	1	since	since	SCONJ
ejpam-2312	144	2	eg	eg	NOUN
ejpam-2312	144	3	is	be	AUX
ejpam-2312	144	4	not	not	PART
ejpam-2312	144	5	in	in	ADP
ejpam-2312	144	6	eh	eh	INTJ
ejpam-2312	144	7	,	,	PUNCT
ejpam-2312	144	8	cls(eg	cls(eg	X
ejpam-2312	144	9	)	)	PUNCT
ejpam-2312	144	10	˜6	˜6	NOUN
ejpam-2312	144	11	=	=	NOUN
ejpam-2312	144	12	cls(eh	cls(eh	NOUN
ejpam-2312	144	13	)	)	PUNCT
ejpam-2312	144	14	.	.	PUNCT
ejpam-2312	145	1	(	(	PUNCT
ejpam-2312	145	2	2)⇒	2)⇒	NUM
ejpam-2312	145	3	(	(	PUNCT
ejpam-2312	145	4	1	1	X
ejpam-2312	145	5	)	)	PUNCT
ejpam-2312	145	6	suppose	suppose	VERB
ejpam-2312	145	7	that	that	SCONJ
ejpam-2312	145	8	for	for	ADP
ejpam-2312	145	9	any	any	DET
ejpam-2312	145	10	distinct	distinct	ADJ
ejpam-2312	145	11	soft	soft	ADJ
ejpam-2312	145	12	points	point	NOUN
ejpam-2312	145	13	eg	eg	NOUN
ejpam-2312	145	14	and	and	CCONJ
ejpam-2312	145	15	eh	eh	INTJ
ejpam-2312	145	16	in	in	ADP
ejpam-2312	145	17	xa	xa	PROPN
ejpam-2312	145	18	,	,	PUNCT
ejpam-2312	145	19	cls(eg	cls(eg	X
ejpam-2312	145	20	)	)	PUNCT
ejpam-2312	145	21	˜6	˜6	NOUN
ejpam-2312	145	22	=	=	NOUN
ejpam-2312	145	23	cls(eh	cls(eh	NOUN
ejpam-2312	145	24	)	)	PUNCT
ejpam-2312	145	25	.	.	PUNCT
ejpam-2312	146	1	contrarily	contrarily	ADV
ejpam-2312	146	2	suppose	suppose	VERB
ejpam-2312	146	3	that	that	SCONJ
ejpam-2312	146	4	x̃a	x̃a	PRON
ejpam-2312	146	5	is	be	AUX
ejpam-2312	146	6	not	not	PART
ejpam-2312	146	7	soft	soft	ADJ
ejpam-2312	146	8	semi	semi	ADJ
ejpam-2312	146	9	-	-	ADJ
ejpam-2312	146	10	t0	t0	ADJ
ejpam-2312	146	11	space	space	NOUN
ejpam-2312	146	12	.	.	PUNCT
ejpam-2312	147	1	then	then	ADV
ejpam-2312	147	2	every	every	DET
ejpam-2312	147	3	soft	soft	ADJ
ejpam-2312	147	4	semi	semi	ADJ
ejpam-2312	147	5	-	-	ADJ
ejpam-2312	147	6	open	open	ADJ
ejpam-2312	147	7	set	set	NOUN
ejpam-2312	147	8	which	which	PRON
ejpam-2312	147	9	contains	contain	VERB
ejpam-2312	147	10	eg	eg	NOUN
ejpam-2312	147	11	also	also	ADV
ejpam-2312	147	12	contains	contain	VERB
ejpam-2312	147	13	eh	eh	INTJ
ejpam-2312	147	14	.	.	PUNCT
ejpam-2312	148	1	then	then	ADV
ejpam-2312	148	2	by	by	ADP
ejpam-2312	148	3	the	the	DET
ejpam-2312	148	4	property	property	NOUN
ejpam-2312	148	5	of	of	ADP
ejpam-2312	148	6	soft	soft	ADJ
ejpam-2312	148	7	semi	semi	ADJ
ejpam-2312	148	8	-	-	ADJ
ejpam-2312	148	9	limit	limit	ADJ
ejpam-2312	148	10	point	point	NOUN
ejpam-2312	148	11	,	,	PUNCT
ejpam-2312	148	12	eg	eg	NOUN
ejpam-2312	148	13	is	be	AUX
ejpam-2312	148	14	in	in	ADP
ejpam-2312	148	15	cls(eh	cls(eh	NUM
ejpam-2312	148	16	)	)	PUNCT
ejpam-2312	148	17	so	so	SCONJ
ejpam-2312	148	18	that	that	SCONJ
ejpam-2312	148	19	cls(eg)⊆̃cls(eh	cls(eg)⊆̃cls(eh	NOUN
ejpam-2312	148	20	)	)	PUNCT
ejpam-2312	148	21	.	.	PUNCT
ejpam-2312	149	1	similarly	similarly	ADV
ejpam-2312	149	2	every	every	DET
ejpam-2312	149	3	soft	soft	ADJ
ejpam-2312	149	4	semi	semi	ADJ
ejpam-2312	149	5	-	-	ADJ
ejpam-2312	149	6	pen	pen	ADJ
ejpam-2312	149	7	set	set	NOUN
ejpam-2312	149	8	which	which	PRON
ejpam-2312	149	9	contains	contain	VERB
ejpam-2312	149	10	eh	eh	INTJ
ejpam-2312	149	11	also	also	ADV
ejpam-2312	149	12	contains	contain	VERB
ejpam-2312	149	13	eg	eg	NOUN
ejpam-2312	149	14	(	(	PUNCT
ejpam-2312	149	15	otherwise	otherwise	ADV
ejpam-2312	149	16	x̃a	x̃a	X
ejpam-2312	149	17	would	would	AUX
ejpam-2312	149	18	be	be	AUX
ejpam-2312	149	19	a	a	DET
ejpam-2312	149	20	soft	soft	ADJ
ejpam-2312	149	21	semi	semi	ADJ
ejpam-2312	149	22	-	-	ADJ
ejpam-2312	149	23	t0	t0	ADJ
ejpam-2312	149	24	space	space	NOUN
ejpam-2312	149	25	)	)	PUNCT
ejpam-2312	149	26	.	.	PUNCT
ejpam-2312	150	1	so	so	ADV
ejpam-2312	150	2	cls(eh)⊆̃cls(eg	cls(eh)⊆̃cls(eg	PROPN
ejpam-2312	150	3	)	)	PUNCT
ejpam-2312	150	4	.	.	PUNCT
ejpam-2312	151	1	thus	thus	ADV
ejpam-2312	151	2	cls(eg)=̃cls(eh	cls(eg)=̃cls(eh	NOUN
ejpam-2312	151	3	)	)	PUNCT
ejpam-2312	151	4	.	.	PUNCT
ejpam-2312	152	1	this	this	DET
ejpam-2312	152	2	contradiction	contradiction	NOUN
ejpam-2312	152	3	proves	prove	VERB
ejpam-2312	152	4	as	as	SCONJ
ejpam-2312	152	5	required	require	VERB
ejpam-2312	152	6	.	.	PUNCT
ejpam-2312	153	1	definition	definition	NOUN
ejpam-2312	153	2	19	19	NUM
ejpam-2312	153	3	.	.	PUNCT
ejpam-2312	154	1	let	let	VERB
ejpam-2312	154	2	(	(	PUNCT
ejpam-2312	154	3	x	x	X
ejpam-2312	154	4	,	,	PUNCT
ejpam-2312	154	5	τ	τ	PROPN
ejpam-2312	154	6	,	,	PUNCT
ejpam-2312	154	7	a	a	PRON
ejpam-2312	154	8	)	)	PUNCT
ejpam-2312	154	9	be	be	AUX
ejpam-2312	154	10	a	a	DET
ejpam-2312	154	11	soft	soft	ADJ
ejpam-2312	154	12	topological	topological	ADJ
ejpam-2312	154	13	space	space	NOUN
ejpam-2312	154	14	over	over	ADP
ejpam-2312	154	15	x	x	PUNCT
ejpam-2312	154	16	and	and	CCONJ
ejpam-2312	154	17	eg	eg	NOUN
ejpam-2312	154	18	,	,	PUNCT
ejpam-2312	154	19	eh	eh	INTJ
ejpam-2312	154	20	are	be	AUX
ejpam-2312	154	21	two	two	NUM
ejpam-2312	154	22	distinct	distinct	ADJ
ejpam-2312	154	23	soft	soft	ADJ
ejpam-2312	154	24	points	point	NOUN
ejpam-2312	154	25	in	in	ADP
ejpam-2312	154	26	x̃a	x̃a	PROPN
ejpam-2312	154	27	.	.	PUNCT
ejpam-2312	155	1	if	if	SCONJ
ejpam-2312	155	2	there	there	PRON
ejpam-2312	155	3	exists	exist	VERB
ejpam-2312	155	4	a	a	DET
ejpam-2312	155	5	soft	soft	ADJ
ejpam-2312	155	6	semi	semi	ADJ
ejpam-2312	155	7	-	-	ADJ
ejpam-2312	155	8	open	open	ADJ
ejpam-2312	155	9	set	set	NOUN
ejpam-2312	155	10	(	(	PUNCT
ejpam-2312	155	11	f1	f1	NOUN
ejpam-2312	155	12	,	,	PUNCT
ejpam-2312	155	13	a	a	NOUN
ejpam-2312	155	14	)	)	PUNCT
ejpam-2312	155	15	such	such	ADJ
ejpam-2312	155	16	that	that	SCONJ
ejpam-2312	155	17	eg∈̃(f1	eg∈̃(f1	PROPN
ejpam-2312	155	18	,	,	PUNCT
ejpam-2312	155	19	a	a	PRON
ejpam-2312	155	20	)	)	PUNCT
ejpam-2312	155	21	,	,	PUNCT
ejpam-2312	155	22	eh	eh	INTJ
ejpam-2312	155	23	/̃∈(f1	/̃∈(f1	PROPN
ejpam-2312	155	24	,	,	PUNCT
ejpam-2312	155	25	a	a	PRON
ejpam-2312	155	26	)	)	PUNCT
ejpam-2312	155	27	and	and	CCONJ
ejpam-2312	155	28	a	a	DET
ejpam-2312	155	29	soft	soft	ADJ
ejpam-2312	155	30	semi	semi	ADJ
ejpam-2312	155	31	-	-	ADJ
ejpam-2312	155	32	open	open	ADJ
ejpam-2312	155	33	set	set	NOUN
ejpam-2312	155	34	(	(	PUNCT
ejpam-2312	155	35	f2	f2	PROPN
ejpam-2312	155	36	,	,	PUNCT
ejpam-2312	155	37	a	a	PRON
ejpam-2312	155	38	)	)	PUNCT
ejpam-2312	155	39	such	such	ADJ
ejpam-2312	155	40	that	that	SCONJ
ejpam-2312	155	41	eh	eh	INTJ
ejpam-2312	155	42	∈̃(f2	∈̃(f2	PRON
ejpam-2312	155	43	,	,	PUNCT
ejpam-2312	155	44	a	a	PRON
ejpam-2312	155	45	)	)	PUNCT
ejpam-2312	155	46	,	,	PUNCT
ejpam-2312	155	47	eg	eg	PROPN
ejpam-2312	155	48	/̃∈(f2	/̃∈(f2	PROPN
ejpam-2312	155	49	,	,	PUNCT
ejpam-2312	155	50	a	a	PRON
ejpam-2312	155	51	)	)	PUNCT
ejpam-2312	155	52	,	,	PUNCT
ejpam-2312	155	53	then	then	ADV
ejpam-2312	155	54	(	(	PUNCT
ejpam-2312	155	55	x	x	X
ejpam-2312	155	56	,	,	PUNCT
ejpam-2312	155	57	τ	τ	PROPN
ejpam-2312	155	58	,	,	PUNCT
ejpam-2312	155	59	a	a	PRON
ejpam-2312	155	60	)	)	PUNCT
ejpam-2312	155	61	is	be	AUX
ejpam-2312	155	62	called	call	VERB
ejpam-2312	155	63	soft	soft	ADJ
ejpam-2312	155	64	semi	semi	ADJ
ejpam-2312	155	65	-	-	ADJ
ejpam-2312	155	66	t1	t1	ADJ
ejpam-2312	155	67	-	-	PUNCT
ejpam-2312	155	68	space	space	NOUN
ejpam-2312	155	69	.	.	PUNCT
ejpam-2312	155	70	example	example	NOUN
ejpam-2312	156	1	3	3	NUM
ejpam-2312	156	2	.	.	PUNCT
ejpam-2312	157	1	in	in	ADP
ejpam-2312	157	2	example	example	NOUN
ejpam-2312	157	3	2	2	NUM
ejpam-2312	157	4	,	,	PUNCT
ejpam-2312	157	5	(	(	PUNCT
ejpam-2312	157	6	x	x	X
ejpam-2312	157	7	,	,	PUNCT
ejpam-2312	157	8	τ	τ	PROPN
ejpam-2312	157	9	,	,	PUNCT
ejpam-2312	157	10	a	a	PRON
ejpam-2312	157	11	)	)	PUNCT
ejpam-2312	157	12	is	be	AUX
ejpam-2312	157	13	not	not	PART
ejpam-2312	157	14	soft	soft	ADJ
ejpam-2312	157	15	semi	semi	ADJ
ejpam-2312	157	16	-	-	ADJ
ejpam-2312	157	17	t1	t1	ADJ
ejpam-2312	157	18	space	space	NOUN
ejpam-2312	157	19	.	.	PUNCT
ejpam-2312	158	1	s.	s.	PROPN
ejpam-2312	158	2	hussain	hussain	PROPN
ejpam-2312	158	3	/	/	SYM
ejpam-2312	158	4	eur	eur	PROPN
ejpam-2312	158	5	.	.	PUNCT
ejpam-2312	159	1	j.	j.	PROPN
ejpam-2312	159	2	pure	pure	PROPN
ejpam-2312	159	3	appl	appl	PROPN
ejpam-2312	159	4	.	.	PROPN
ejpam-2312	159	5	math	math	PROPN
ejpam-2312	159	6	,	,	PUNCT
ejpam-2312	159	7	10	10	NUM
ejpam-2312	159	8	(	(	PUNCT
ejpam-2312	159	9	2	2	NUM
ejpam-2312	159	10	)	)	PUNCT
ejpam-2312	159	11	(	(	PUNCT
ejpam-2312	159	12	2017	2017	NUM
ejpam-2312	159	13	)	)	PUNCT
ejpam-2312	159	14	,	,	PUNCT
ejpam-2312	159	15	199	199	NUM
ejpam-2312	159	16	-	-	SYM
ejpam-2312	159	17	210	210	NUM
ejpam-2312	159	18	204	204	NUM
ejpam-2312	159	19	theorem	theorem	NOUN
ejpam-2312	159	20	2	2	NUM
ejpam-2312	159	21	.	.	PUNCT
ejpam-2312	160	1	let	let	VERB
ejpam-2312	160	2	(	(	PUNCT
ejpam-2312	160	3	x	x	X
ejpam-2312	160	4	,	,	PUNCT
ejpam-2312	160	5	τ	τ	PROPN
ejpam-2312	160	6	,	,	PUNCT
ejpam-2312	160	7	a	a	PRON
ejpam-2312	160	8	)	)	PUNCT
ejpam-2312	160	9	be	be	AUX
ejpam-2312	160	10	a	a	DET
ejpam-2312	160	11	soft	soft	ADJ
ejpam-2312	160	12	topological	topological	ADJ
ejpam-2312	160	13	space	space	NOUN
ejpam-2312	160	14	over	over	ADP
ejpam-2312	160	15	x.	x.	NOUN
ejpam-2312	160	16	then	then	ADV
ejpam-2312	160	17	the	the	DET
ejpam-2312	160	18	following	follow	VERB
ejpam-2312	160	19	are	be	AUX
ejpam-2312	160	20	equivalent	equivalent	ADJ
ejpam-2312	160	21	to	to	ADP
ejpam-2312	160	22	each	each	DET
ejpam-2312	160	23	other	other	ADJ
ejpam-2312	160	24	:	:	PUNCT
ejpam-2312	160	25	(	(	PUNCT
ejpam-2312	160	26	1	1	X
ejpam-2312	160	27	)	)	PUNCT
ejpam-2312	160	28	(	(	PUNCT
ejpam-2312	160	29	x	x	X
ejpam-2312	160	30	,	,	PUNCT
ejpam-2312	160	31	τ	τ	PROPN
ejpam-2312	160	32	,	,	PUNCT
ejpam-2312	160	33	a	a	PRON
ejpam-2312	160	34	)	)	PUNCT
ejpam-2312	160	35	is	be	AUX
ejpam-2312	160	36	soft	soft	ADJ
ejpam-2312	160	37	semi	semi	ADJ
ejpam-2312	160	38	-	-	ADJ
ejpam-2312	160	39	t1	t1	ADJ
ejpam-2312	160	40	.	.	PUNCT
ejpam-2312	161	1	(	(	PUNCT
ejpam-2312	161	2	2	2	X
ejpam-2312	161	3	)	)	PUNCT
ejpam-2312	161	4	{	{	PUNCT
ejpam-2312	161	5	ef	ef	PROPN
ejpam-2312	161	6	}	}	PUNCT
ejpam-2312	161	7	is	be	AUX
ejpam-2312	161	8	soft	soft	ADJ
ejpam-2312	161	9	semi	semi	ADJ
ejpam-2312	161	10	-	-	ADJ
ejpam-2312	161	11	closed	closed	ADJ
ejpam-2312	161	12	,	,	PUNCT
ejpam-2312	161	13	for	for	ADP
ejpam-2312	161	14	each	each	DET
ejpam-2312	161	15	soft	soft	ADJ
ejpam-2312	161	16	point	point	NOUN
ejpam-2312	161	17	ef	ef	NOUN
ejpam-2312	161	18	in	in	ADP
ejpam-2312	161	19	x̃a	x̃a	PRON
ejpam-2312	161	20	.	.	PUNCT
ejpam-2312	162	1	proof	proof	NOUN
ejpam-2312	162	2	.	.	PUNCT
ejpam-2312	163	1	(	(	PUNCT
ejpam-2312	163	2	1	1	X
ejpam-2312	163	3	)	)	PUNCT
ejpam-2312	163	4	⇒	⇒	NOUN
ejpam-2312	163	5	(	(	PUNCT
ejpam-2312	163	6	2	2	X
ejpam-2312	163	7	)	)	PUNCT
ejpam-2312	163	8	let	let	VERB
ejpam-2312	163	9	(	(	PUNCT
ejpam-2312	163	10	x	x	NOUN
ejpam-2312	163	11	,	,	PUNCT
ejpam-2312	163	12	τ	τ	PROPN
ejpam-2312	163	13	,	,	PUNCT
ejpam-2312	163	14	a	a	PRON
ejpam-2312	163	15	)	)	PUNCT
ejpam-2312	163	16	be	be	AUX
ejpam-2312	163	17	a	a	DET
ejpam-2312	163	18	soft	soft	ADJ
ejpam-2312	163	19	topological	topological	ADJ
ejpam-2312	163	20	space	space	NOUN
ejpam-2312	163	21	over	over	ADP
ejpam-2312	163	22	x.	x.	NOUN
ejpam-2312	163	23	let	let	VERB
ejpam-2312	163	24	ef	ef	PART
ejpam-2312	163	25	be	be	AUX
ejpam-2312	163	26	soft	soft	ADJ
ejpam-2312	163	27	point	point	NOUN
ejpam-2312	163	28	in	in	ADP
ejpam-2312	163	29	x̃a	x̃a	X
ejpam-2312	163	30	and	and	CCONJ
ejpam-2312	163	31	eg	eg	PROPN
ejpam-2312	163	32	∈	∈	PROPN
ejpam-2312	163	33	{	{	PUNCT
ejpam-2312	163	34	ef	ef	PROPN
ejpam-2312	163	35	}	}	PUNCT
ejpam-2312	163	36	c.	c.	PROPN
ejpam-2312	163	37	then	then	ADV
ejpam-2312	163	38	ef	ef	PROPN
ejpam-2312	163	39	and	and	CCONJ
ejpam-2312	163	40	eg	eg	NOUN
ejpam-2312	163	41	are	be	AUX
ejpam-2312	163	42	distinct	distinct	ADJ
ejpam-2312	163	43	soft	soft	ADJ
ejpam-2312	163	44	points	point	NOUN
ejpam-2312	163	45	.	.	PUNCT
ejpam-2312	164	1	since	since	SCONJ
ejpam-2312	164	2	(	(	PUNCT
ejpam-2312	164	3	x	x	X
ejpam-2312	164	4	,	,	PUNCT
ejpam-2312	164	5	τ	τ	PROPN
ejpam-2312	164	6	,	,	PUNCT
ejpam-2312	164	7	a	a	PRON
ejpam-2312	164	8	)	)	PUNCT
ejpam-2312	164	9	is	be	AUX
ejpam-2312	164	10	a	a	DET
ejpam-2312	164	11	soft	soft	ADJ
ejpam-2312	164	12	semi	semi	ADJ
ejpam-2312	164	13	-	-	ADJ
ejpam-2312	164	14	t1	t1	ADJ
ejpam-2312	164	15	space	space	NOUN
ejpam-2312	164	16	,	,	PUNCT
ejpam-2312	164	17	then	then	ADV
ejpam-2312	164	18	there	there	PRON
ejpam-2312	164	19	exists	exist	VERB
ejpam-2312	164	20	a	a	DET
ejpam-2312	164	21	soft	soft	ADJ
ejpam-2312	164	22	semi	semi	ADJ
ejpam-2312	164	23	-	-	ADJ
ejpam-2312	164	24	open	open	ADJ
ejpam-2312	164	25	set	set	NOUN
ejpam-2312	164	26	(	(	PUNCT
ejpam-2312	164	27	h	h	NOUN
ejpam-2312	164	28	,	,	PUNCT
ejpam-2312	164	29	a	a	PRON
ejpam-2312	164	30	)	)	PUNCT
ejpam-2312	164	31	with	with	ADP
ejpam-2312	164	32	eg∈̃(h	eg∈̃(h	NOUN
ejpam-2312	164	33	,	,	PUNCT
ejpam-2312	164	34	a	a	PRON
ejpam-2312	164	35	)	)	PUNCT
ejpam-2312	164	36	and	and	CCONJ
ejpam-2312	164	37	ef	ef	PROPN
ejpam-2312	164	38	/̃∈(h	/̃∈(h	PROPN
ejpam-2312	164	39	,	,	PUNCT
ejpam-2312	164	40	a	a	PRON
ejpam-2312	164	41	)	)	PUNCT
ejpam-2312	164	42	.	.	PUNCT
ejpam-2312	165	1	thus	thus	ADV
ejpam-2312	165	2	,	,	PUNCT
ejpam-2312	165	3	eg∈̃(h	eg∈̃(h	NOUN
ejpam-2312	165	4	,	,	PUNCT
ejpam-2312	165	5	a)⊆̃{ef	a)⊆̃{ef	PUNCT
ejpam-2312	165	6	}	}	PUNCT
ejpam-2312	165	7	c.	c.	NOUN
ejpam-2312	165	8	this	this	PRON
ejpam-2312	165	9	follows	follow	VERB
ejpam-2312	165	10	that	that	SCONJ
ejpam-2312	165	11	{	{	PUNCT
ejpam-2312	165	12	ef	ef	PROPN
ejpam-2312	165	13	}	}	PUNCT
ejpam-2312	165	14	c	c	PROPN
ejpam-2312	165	15	can	can	AUX
ejpam-2312	165	16	be	be	AUX
ejpam-2312	165	17	written	write	VERB
ejpam-2312	165	18	as	as	ADP
ejpam-2312	165	19	the	the	DET
ejpam-2312	165	20	soft	soft	ADJ
ejpam-2312	165	21	union	union	NOUN
ejpam-2312	165	22	of	of	ADP
ejpam-2312	165	23	soft	soft	ADJ
ejpam-2312	165	24	semi	semi	ADJ
ejpam-2312	165	25	-	-	ADJ
ejpam-2312	165	26	open	open	ADJ
ejpam-2312	165	27	sets	set	NOUN
ejpam-2312	165	28	(	(	PUNCT
ejpam-2312	165	29	hi	hi	INTJ
ejpam-2312	165	30	,	,	PUNCT
ejpam-2312	165	31	a	a	PRON
ejpam-2312	165	32	)	)	PUNCT
ejpam-2312	165	33	with	with	ADP
ejpam-2312	165	34	ehi∈̃{ef	ehi∈̃{ef	PRON
ejpam-2312	165	35	}	}	PUNCT
ejpam-2312	165	36	c.	c.	NOUN
ejpam-2312	165	37	hence	hence	ADV
ejpam-2312	165	38	{	{	PUNCT
ejpam-2312	165	39	ef	ef	PROPN
ejpam-2312	165	40	}	}	PUNCT
ejpam-2312	165	41	c	c	PROPN
ejpam-2312	165	42	is	be	AUX
ejpam-2312	165	43	soft	soft	ADJ
ejpam-2312	165	44	semi	semi	ADJ
ejpam-2312	165	45	-	-	ADJ
ejpam-2312	165	46	open	open	ADJ
ejpam-2312	165	47	which	which	PRON
ejpam-2312	165	48	implies	imply	VERB
ejpam-2312	165	49	that	that	SCONJ
ejpam-2312	165	50	{	{	PUNCT
ejpam-2312	165	51	ef	ef	PROPN
ejpam-2312	165	52	}	}	PUNCT
ejpam-2312	165	53	is	be	AUX
ejpam-2312	165	54	soft	soft	ADJ
ejpam-2312	165	55	semi	semi	ADJ
ejpam-2312	165	56	-	-	ADJ
ejpam-2312	165	57	closed	closed	ADJ
ejpam-2312	165	58	.	.	PUNCT
ejpam-2312	166	1	(	(	PUNCT
ejpam-2312	166	2	2)⇒	2)⇒	NUM
ejpam-2312	166	3	(	(	PUNCT
ejpam-2312	166	4	1	1	X
ejpam-2312	166	5	)	)	PUNCT
ejpam-2312	166	6	let	let	AUX
ejpam-2312	166	7	{	{	PUNCT
ejpam-2312	166	8	ef	ef	VERB
ejpam-2312	166	9	}	}	PUNCT
ejpam-2312	166	10	is	be	AUX
ejpam-2312	166	11	soft	soft	ADJ
ejpam-2312	166	12	semi	semi	ADJ
ejpam-2312	166	13	-	-	ADJ
ejpam-2312	166	14	closed	closed	ADJ
ejpam-2312	166	15	,	,	PUNCT
ejpam-2312	166	16	for	for	ADP
ejpam-2312	166	17	each	each	DET
ejpam-2312	166	18	soft	soft	ADJ
ejpam-2312	166	19	point	point	NOUN
ejpam-2312	166	20	ef	ef	NOUN
ejpam-2312	166	21	in	in	ADP
ejpam-2312	166	22	x̃a	x̃a	PRON
ejpam-2312	166	23	.	.	PUNCT
ejpam-2312	167	1	suppose	suppose	VERB
ejpam-2312	167	2	ef	ef	PROPN
ejpam-2312	167	3	and	and	CCONJ
ejpam-2312	167	4	eg	eg	NOUN
ejpam-2312	167	5	be	be	AUX
ejpam-2312	167	6	distinct	distinct	ADJ
ejpam-2312	167	7	soft	soft	ADJ
ejpam-2312	167	8	points	point	NOUN
ejpam-2312	167	9	in	in	ADP
ejpam-2312	167	10	x̃a	x̃a	PROPN
ejpam-2312	167	11	.	.	PUNCT
ejpam-2312	168	1	then	then	ADV
ejpam-2312	168	2	eg∈̃{ef	eg∈̃{ef	PUNCT
ejpam-2312	168	3	}	}	PUNCT
ejpam-2312	168	4	c.	c.	PROPN
ejpam-2312	168	5	thus	thus	ADV
ejpam-2312	168	6	{	{	PUNCT
ejpam-2312	168	7	ef	ef	PROPN
ejpam-2312	168	8	}	}	PUNCT
ejpam-2312	168	9	c	c	PROPN
ejpam-2312	168	10	is	be	AUX
ejpam-2312	168	11	a	a	DET
ejpam-2312	168	12	soft	soft	ADJ
ejpam-2312	168	13	semi	semi	ADJ
ejpam-2312	168	14	-	-	ADJ
ejpam-2312	168	15	open	open	ADJ
ejpam-2312	168	16	set	set	VERB
ejpam-2312	168	17	with	with	ADP
ejpam-2312	168	18	eg∈̃{ef	eg∈̃{ef	PUNCT
ejpam-2312	168	19	}	}	PUNCT
ejpam-2312	168	20	c	c	PROPN
ejpam-2312	168	21	and	and	CCONJ
ejpam-2312	168	22	ef	ef	X
ejpam-2312	168	23	/̃∈{ef	/̃∈{ef	PUNCT
ejpam-2312	168	24	}	}	PUNCT
ejpam-2312	168	25	c.	c.	NOUN
ejpam-2312	168	26	also	also	ADV
ejpam-2312	168	27	{	{	PUNCT
ejpam-2312	168	28	eg}c	eg}c	PROPN
ejpam-2312	168	29	is	be	AUX
ejpam-2312	168	30	a	a	DET
ejpam-2312	168	31	soft	soft	ADJ
ejpam-2312	168	32	semi	semi	ADJ
ejpam-2312	168	33	-	-	ADJ
ejpam-2312	168	34	open	open	ADJ
ejpam-2312	168	35	set	set	VERB
ejpam-2312	168	36	with	with	ADP
ejpam-2312	168	37	ef	ef	PROPN
ejpam-2312	168	38	∈̃{eg}c	∈̃{eg}c	ADV
ejpam-2312	168	39	and	and	CCONJ
ejpam-2312	168	40	eg	eg	PROPN
ejpam-2312	168	41	/̃∈{eg}c	/̃∈{eg}c	PROPN
ejpam-2312	168	42	.	.	PUNCT
ejpam-2312	169	1	this	this	PRON
ejpam-2312	169	2	implies	imply	VERB
ejpam-2312	169	3	that	that	SCONJ
ejpam-2312	169	4	(	(	PUNCT
ejpam-2312	169	5	x	x	X
ejpam-2312	169	6	,	,	PUNCT
ejpam-2312	169	7	τ	τ	PROPN
ejpam-2312	169	8	,	,	PUNCT
ejpam-2312	169	9	a	a	PRON
ejpam-2312	169	10	)	)	PUNCT
ejpam-2312	169	11	is	be	AUX
ejpam-2312	169	12	soft	soft	ADJ
ejpam-2312	169	13	semi	semi	ADJ
ejpam-2312	169	14	-	-	ADJ
ejpam-2312	169	15	t1	t1	ADJ
ejpam-2312	169	16	space	space	NOUN
ejpam-2312	169	17	.	.	PUNCT
ejpam-2312	170	1	definition	definition	NOUN
ejpam-2312	170	2	20	20	NUM
ejpam-2312	170	3	.	.	PUNCT
ejpam-2312	171	1	let	let	VERB
ejpam-2312	171	2	(	(	PUNCT
ejpam-2312	171	3	x	x	X
ejpam-2312	171	4	,	,	PUNCT
ejpam-2312	171	5	τ	τ	PROPN
ejpam-2312	171	6	,	,	PUNCT
ejpam-2312	171	7	a	a	PRON
ejpam-2312	171	8	)	)	PUNCT
ejpam-2312	171	9	be	be	AUX
ejpam-2312	171	10	a	a	DET
ejpam-2312	171	11	soft	soft	ADJ
ejpam-2312	171	12	topological	topological	ADJ
ejpam-2312	171	13	space	space	NOUN
ejpam-2312	171	14	over	over	ADP
ejpam-2312	171	15	x	x	PUNCT
ejpam-2312	171	16	and	and	CCONJ
ejpam-2312	171	17	eg	eg	NOUN
ejpam-2312	171	18	,	,	PUNCT
ejpam-2312	171	19	eh	eh	INTJ
ejpam-2312	171	20	are	be	AUX
ejpam-2312	171	21	two	two	NUM
ejpam-2312	171	22	distinct	distinct	ADJ
ejpam-2312	171	23	soft	soft	ADJ
ejpam-2312	171	24	points	point	NOUN
ejpam-2312	171	25	in	in	ADP
ejpam-2312	171	26	x̃a	x̃a	PROPN
ejpam-2312	171	27	.	.	PUNCT
ejpam-2312	172	1	if	if	SCONJ
ejpam-2312	172	2	there	there	PRON
ejpam-2312	172	3	exist	exist	VERB
ejpam-2312	172	4	soft	soft	ADJ
ejpam-2312	172	5	disjoint	disjoint	NOUN
ejpam-2312	172	6	soft	soft	ADJ
ejpam-2312	172	7	semi	semi	ADJ
ejpam-2312	172	8	-	-	ADJ
ejpam-2312	172	9	open	open	ADJ
ejpam-2312	172	10	sets	set	NOUN
ejpam-2312	172	11	(	(	PUNCT
ejpam-2312	172	12	f1	f1	NOUN
ejpam-2312	172	13	,	,	PUNCT
ejpam-2312	172	14	a	a	PRON
ejpam-2312	172	15	)	)	PUNCT
ejpam-2312	172	16	and	and	CCONJ
ejpam-2312	172	17	(	(	PUNCT
ejpam-2312	172	18	f2	f2	PROPN
ejpam-2312	172	19	,	,	PUNCT
ejpam-2312	172	20	a	a	PRON
ejpam-2312	172	21	)	)	PUNCT
ejpam-2312	172	22	such	such	ADJ
ejpam-2312	172	23	that	that	SCONJ
ejpam-2312	172	24	eg∈̃(f1	eg∈̃(f1	PROPN
ejpam-2312	172	25	,	,	PUNCT
ejpam-2312	172	26	a	a	PRON
ejpam-2312	172	27	)	)	PUNCT
ejpam-2312	172	28	,	,	PUNCT
ejpam-2312	172	29	eh	eh	INTJ
ejpam-2312	172	30	∈̃(f2	∈̃(f2	PRON
ejpam-2312	172	31	,	,	PUNCT
ejpam-2312	172	32	a	a	PRON
ejpam-2312	172	33	)	)	PUNCT
ejpam-2312	172	34	,	,	PUNCT
ejpam-2312	172	35	then	then	ADV
ejpam-2312	172	36	(	(	PUNCT
ejpam-2312	172	37	x	x	X
ejpam-2312	172	38	,	,	PUNCT
ejpam-2312	172	39	τ	τ	PROPN
ejpam-2312	172	40	,	,	PUNCT
ejpam-2312	172	41	a	a	PRON
ejpam-2312	172	42	)	)	PUNCT
ejpam-2312	172	43	is	be	AUX
ejpam-2312	172	44	called	call	VERB
ejpam-2312	172	45	soft	soft	ADJ
ejpam-2312	172	46	semi	semi	ADJ
ejpam-2312	172	47	-	-	ADJ
ejpam-2312	172	48	t2	t2	ADJ
ejpam-2312	172	49	-	-	PUNCT
ejpam-2312	172	50	space	space	NOUN
ejpam-2312	172	51	.	.	PUNCT
ejpam-2312	173	1	example	example	NOUN
ejpam-2312	174	1	4	4	NUM
ejpam-2312	174	2	.	.	PUNCT
ejpam-2312	175	1	let	let	VERB
ejpam-2312	175	2	(	(	PUNCT
ejpam-2312	175	3	x	x	X
ejpam-2312	175	4	,	,	PUNCT
ejpam-2312	175	5	τ	τ	PROPN
ejpam-2312	175	6	,	,	PUNCT
ejpam-2312	175	7	a	a	PRON
ejpam-2312	175	8	)	)	PUNCT
ejpam-2312	175	9	be	be	AUX
ejpam-2312	175	10	a	a	DET
ejpam-2312	175	11	soft	soft	ADJ
ejpam-2312	175	12	discrete	discrete	ADJ
ejpam-2312	175	13	soft	soft	ADJ
ejpam-2312	175	14	topological	topological	ADJ
ejpam-2312	175	15	space	space	NOUN
ejpam-2312	176	1	[	[	X
ejpam-2312	176	2	18	18	NUM
ejpam-2312	176	3	]	]	PUNCT
ejpam-2312	176	4	.	.	PUNCT
ejpam-2312	177	1	then	then	ADV
ejpam-2312	177	2	(	(	PUNCT
ejpam-2312	177	3	x	x	X
ejpam-2312	177	4	,	,	PUNCT
ejpam-2312	177	5	τ	τ	PROPN
ejpam-2312	177	6	,	,	PUNCT
ejpam-2312	177	7	a	a	PRON
ejpam-2312	177	8	)	)	PUNCT
ejpam-2312	177	9	is	be	AUX
ejpam-2312	177	10	soft	soft	ADJ
ejpam-2312	177	11	semi	semi	ADJ
ejpam-2312	177	12	-	-	ADJ
ejpam-2312	177	13	t2	t2	ADJ
ejpam-2312	177	14	space	space	NOUN
ejpam-2312	177	15	.	.	PUNCT
ejpam-2312	178	1	theorem	theorem	NOUN
ejpam-2312	178	2	3	3	X
ejpam-2312	178	3	.	.	PUNCT
ejpam-2312	179	1	let	let	VERB
ejpam-2312	179	2	(	(	PUNCT
ejpam-2312	179	3	x	x	X
ejpam-2312	179	4	,	,	PUNCT
ejpam-2312	179	5	τ	τ	PROPN
ejpam-2312	179	6	,	,	PUNCT
ejpam-2312	179	7	a	a	PRON
ejpam-2312	179	8	)	)	PUNCT
ejpam-2312	179	9	be	be	AUX
ejpam-2312	179	10	a	a	DET
ejpam-2312	179	11	soft	soft	ADJ
ejpam-2312	179	12	topological	topological	ADJ
ejpam-2312	179	13	space	space	NOUN
ejpam-2312	179	14	over	over	ADP
ejpam-2312	179	15	x	x	PUNCT
ejpam-2312	179	16	and	and	CCONJ
ejpam-2312	179	17	eg	eg	NOUN
ejpam-2312	179	18	,	,	PUNCT
ejpam-2312	179	19	eh	eh	INTJ
ejpam-2312	179	20	are	be	AUX
ejpam-2312	179	21	distinct	distinct	ADJ
ejpam-2312	179	22	soft	soft	ADJ
ejpam-2312	179	23	points	point	NOUN
ejpam-2312	179	24	in	in	ADP
ejpam-2312	179	25	x̃a	x̃a	PROPN
ejpam-2312	179	26	.	.	PUNCT
ejpam-2312	180	1	then	then	ADV
ejpam-2312	180	2	(	(	PUNCT
ejpam-2312	180	3	x	x	X
ejpam-2312	180	4	,	,	PUNCT
ejpam-2312	180	5	τ	τ	PROPN
ejpam-2312	180	6	,	,	PUNCT
ejpam-2312	180	7	a	a	PRON
ejpam-2312	180	8	)	)	PUNCT
ejpam-2312	180	9	is	be	AUX
ejpam-2312	180	10	soft	soft	ADJ
ejpam-2312	180	11	semi	semi	ADJ
ejpam-2312	180	12	-	-	ADJ
ejpam-2312	180	13	t2	t2	ADJ
ejpam-2312	180	14	-	-	PUNCT
ejpam-2312	180	15	space	space	NOUN
ejpam-2312	180	16	,	,	PUNCT
ejpam-2312	180	17	implies	imply	VERB
ejpam-2312	180	18	that	that	SCONJ
ejpam-2312	180	19	there	there	PRON
ejpam-2312	180	20	exist	exist	VERB
ejpam-2312	180	21	soft	soft	ADJ
ejpam-2312	180	22	semi	semi	ADJ
ejpam-2312	180	23	-	-	ADJ
ejpam-2312	180	24	closed	closed	ADJ
ejpam-2312	180	25	sets	set	NOUN
ejpam-2312	180	26	(	(	PUNCT
ejpam-2312	180	27	h	h	NOUN
ejpam-2312	180	28	,	,	PUNCT
ejpam-2312	180	29	a	a	PRON
ejpam-2312	180	30	)	)	PUNCT
ejpam-2312	180	31	and	and	CCONJ
ejpam-2312	180	32	(	(	PUNCT
ejpam-2312	180	33	k	k	NOUN
ejpam-2312	180	34	,	,	PUNCT
ejpam-2312	180	35	a	a	NOUN
ejpam-2312	180	36	)	)	PUNCT
ejpam-2312	180	37	such	such	ADJ
ejpam-2312	180	38	that	that	SCONJ
ejpam-2312	180	39	eg∈̃(h	eg∈̃(h	NOUN
ejpam-2312	180	40	,	,	PUNCT
ejpam-2312	180	41	a	a	PRON
ejpam-2312	180	42	)	)	PUNCT
ejpam-2312	180	43	,	,	PUNCT
ejpam-2312	181	1	eh	eh	INTJ
ejpam-2312	181	2	/̃∈(h	/̃∈(h	INTJ
ejpam-2312	181	3	,	,	PUNCT
ejpam-2312	181	4	a	a	PRON
ejpam-2312	181	5	)	)	PUNCT
ejpam-2312	181	6	and	and	CCONJ
ejpam-2312	181	7	eg	eg	PROPN
ejpam-2312	181	8	/̃∈(k	/̃∈(k	PROPN
ejpam-2312	181	9	,	,	PUNCT
ejpam-2312	181	10	a	a	PRON
ejpam-2312	181	11	)	)	PUNCT
ejpam-2312	181	12	,	,	PUNCT
ejpam-2312	181	13	eh	eh	INTJ
ejpam-2312	181	14	∈̃(k	∈̃(k	NOUN
ejpam-2312	181	15	,	,	PUNCT
ejpam-2312	181	16	a	a	PRON
ejpam-2312	181	17	)	)	PUNCT
ejpam-2312	181	18	,	,	PUNCT
ejpam-2312	181	19	and	and	CCONJ
ejpam-2312	181	20	(	(	PUNCT
ejpam-2312	181	21	h	h	NOUN
ejpam-2312	181	22	,	,	PUNCT
ejpam-2312	181	23	a)∪̃(k	a)∪̃(k	NOUN
ejpam-2312	181	24	,	,	PUNCT
ejpam-2312	181	25	a	a	PRON
ejpam-2312	181	26	)	)	PUNCT
ejpam-2312	181	27	=	=	SYM
ejpam-2312	181	28	x̃a	x̃a	ADJ
ejpam-2312	181	29	.	.	PUNCT
ejpam-2312	181	30	proof	proof	NOUN
ejpam-2312	181	31	.	.	PUNCT
ejpam-2312	182	1	since	since	SCONJ
ejpam-2312	182	2	(	(	PUNCT
ejpam-2312	182	3	x	x	X
ejpam-2312	182	4	,	,	PUNCT
ejpam-2312	182	5	τ	τ	PROPN
ejpam-2312	182	6	,	,	PUNCT
ejpam-2312	182	7	a	a	PRON
ejpam-2312	182	8	)	)	PUNCT
ejpam-2312	182	9	is	be	AUX
ejpam-2312	182	10	soft	soft	ADJ
ejpam-2312	182	11	semi	semi	ADJ
ejpam-2312	182	12	-	-	ADJ
ejpam-2312	182	13	t2	t2	ADJ
ejpam-2312	182	14	-	-	PUNCT
ejpam-2312	182	15	space	space	NOUN
ejpam-2312	182	16	and	and	CCONJ
ejpam-2312	182	17	eg	eg	NOUN
ejpam-2312	182	18	and	and	CCONJ
ejpam-2312	182	19	eh	eh	INTJ
ejpam-2312	182	20	are	be	AUX
ejpam-2312	182	21	distinct	distinct	ADJ
ejpam-2312	182	22	soft	soft	ADJ
ejpam-2312	182	23	points	point	NOUN
ejpam-2312	182	24	in	in	ADP
ejpam-2312	182	25	x̃a	x̃a	NUM
ejpam-2312	182	26	,	,	PUNCT
ejpam-2312	182	27	then	then	ADV
ejpam-2312	182	28	there	there	PRON
ejpam-2312	182	29	exist	exist	VERB
ejpam-2312	182	30	soft	soft	ADJ
ejpam-2312	182	31	disjoint	disjoint	NOUN
ejpam-2312	182	32	soft	soft	ADJ
ejpam-2312	182	33	semi	semi	ADJ
ejpam-2312	182	34	-	-	ADJ
ejpam-2312	182	35	open	open	ADJ
ejpam-2312	182	36	sets	set	NOUN
ejpam-2312	182	37	(	(	PUNCT
ejpam-2312	182	38	g1	g1	PROPN
ejpam-2312	182	39	,	,	PUNCT
ejpam-2312	182	40	a	a	PRON
ejpam-2312	182	41	)	)	PUNCT
ejpam-2312	182	42	and	and	CCONJ
ejpam-2312	182	43	(	(	PUNCT
ejpam-2312	182	44	g2	g2	PROPN
ejpam-2312	182	45	,	,	PUNCT
ejpam-2312	182	46	a	a	PRON
ejpam-2312	182	47	)	)	PUNCT
ejpam-2312	182	48	such	such	ADJ
ejpam-2312	182	49	that	that	SCONJ
ejpam-2312	182	50	eg∈̃(g1	eg∈̃(g1	NOUN
ejpam-2312	182	51	,	,	PUNCT
ejpam-2312	182	52	a	a	PRON
ejpam-2312	182	53	)	)	PUNCT
ejpam-2312	182	54	and	and	CCONJ
ejpam-2312	182	55	eh	eh	INTJ
ejpam-2312	182	56	∈̃(g2	∈̃(g2	NUM
ejpam-2312	182	57	,	,	PUNCT
ejpam-2312	182	58	a	a	PRON
ejpam-2312	182	59	)	)	PUNCT
ejpam-2312	182	60	.	.	PUNCT
ejpam-2312	183	1	clearly	clearly	ADV
ejpam-2312	183	2	(	(	PUNCT
ejpam-2312	183	3	g1	g1	PROPN
ejpam-2312	183	4	,	,	PUNCT
ejpam-2312	183	5	a)⊆̃(g2	a)⊆̃(g2	PROPN
ejpam-2312	183	6	,	,	PUNCT
ejpam-2312	183	7	a)c	a)c	PUNCT
ejpam-2312	183	8	and	and	CCONJ
ejpam-2312	183	9	(	(	PUNCT
ejpam-2312	183	10	g2	g2	PROPN
ejpam-2312	183	11	,	,	PUNCT
ejpam-2312	183	12	a)⊆̃(g1	a)⊆̃(g1	PROPN
ejpam-2312	183	13	,	,	PUNCT
ejpam-2312	183	14	a)c	a)c	PUNCT
ejpam-2312	183	15	.	.	PUNCT
ejpam-2312	184	1	hence	hence	ADV
ejpam-2312	184	2	eg∈̃(g2	eg∈̃(g2	NOUN
ejpam-2312	184	3	,	,	PUNCT
ejpam-2312	184	4	a)c	a)c	PUNCT
ejpam-2312	184	5	.	.	PUNCT
ejpam-2312	185	1	put	put	NOUN
ejpam-2312	185	2	(	(	PUNCT
ejpam-2312	185	3	g2	g2	PROPN
ejpam-2312	185	4	,	,	PUNCT
ejpam-2312	185	5	a)c	a)c	PUNCT
ejpam-2312	185	6	=	=	PUNCT
ejpam-2312	185	7	(	(	PUNCT
ejpam-2312	185	8	h	h	NOUN
ejpam-2312	185	9	,	,	PUNCT
ejpam-2312	185	10	a	a	PRON
ejpam-2312	185	11	)	)	PUNCT
ejpam-2312	185	12	.	.	PUNCT
ejpam-2312	186	1	this	this	PRON
ejpam-2312	186	2	gives	give	VERB
ejpam-2312	186	3	eg∈̃(h	eg∈̃(h	NOUN
ejpam-2312	186	4	,	,	PUNCT
ejpam-2312	186	5	a	a	PRON
ejpam-2312	186	6	)	)	PUNCT
ejpam-2312	186	7	and	and	CCONJ
ejpam-2312	186	8	eh	eh	INTJ
ejpam-2312	186	9	/̃∈(h	/̃∈(h	INTJ
ejpam-2312	186	10	,	,	PUNCT
ejpam-2312	186	11	a	a	PRON
ejpam-2312	186	12	)	)	PUNCT
ejpam-2312	186	13	.	.	PUNCT
ejpam-2312	187	1	also	also	ADV
ejpam-2312	187	2	eh	eh	INTJ
ejpam-2312	187	3	∈̃(g1	∈̃(g1	NUM
ejpam-2312	187	4	,	,	PUNCT
ejpam-2312	187	5	a)c	a)c	PUNCT
ejpam-2312	187	6	.	.	PUNCT
ejpam-2312	188	1	put	put	NOUN
ejpam-2312	188	2	(	(	PUNCT
ejpam-2312	188	3	g1	g1	NOUN
ejpam-2312	188	4	,	,	PUNCT
ejpam-2312	188	5	a)c=̃(k	a)c=̃(k	NOUN
ejpam-2312	188	6	,	,	PUNCT
ejpam-2312	188	7	a	a	PRON
ejpam-2312	188	8	)	)	PUNCT
ejpam-2312	188	9	.	.	PUNCT
ejpam-2312	189	1	therefore	therefore	ADV
ejpam-2312	189	2	eg∈̃(h	eg∈̃(h	VERB
ejpam-2312	189	3	,	,	PUNCT
ejpam-2312	189	4	a	a	PRON
ejpam-2312	189	5	)	)	PUNCT
ejpam-2312	189	6	and	and	CCONJ
ejpam-2312	189	7	eh	eh	INTJ
ejpam-2312	189	8	∈̃(k	∈̃(k	NOUN
ejpam-2312	189	9	,	,	PUNCT
ejpam-2312	189	10	a	a	PRON
ejpam-2312	189	11	)	)	PUNCT
ejpam-2312	189	12	.	.	PUNCT
ejpam-2312	190	1	moreover	moreover	ADV
ejpam-2312	190	2	(	(	PUNCT
ejpam-2312	190	3	h	h	NOUN
ejpam-2312	190	4	,	,	PUNCT
ejpam-2312	190	5	a)∪̃(k	a)∪̃(k	NOUN
ejpam-2312	190	6	,	,	PUNCT
ejpam-2312	190	7	a)=̃(g2	a)=̃(g2	ADV
ejpam-2312	190	8	,	,	PUNCT
ejpam-2312	190	9	a)c∪̃(g1	a)c∪̃(g1	NOUN
ejpam-2312	190	10	,	,	PUNCT
ejpam-2312	190	11	a)c=̃x̃a	a)c=̃x̃a	NUM
ejpam-2312	190	12	.	.	PUNCT
ejpam-2312	191	1	remark	remark	NOUN
ejpam-2312	191	2	3	3	NUM
ejpam-2312	191	3	.	.	PUNCT
ejpam-2312	191	4	from	from	ADP
ejpam-2312	191	5	the	the	DET
ejpam-2312	191	6	above	above	ADJ
ejpam-2312	191	7	theorem	theorem	NOUN
ejpam-2312	191	8	and	and	CCONJ
ejpam-2312	191	9	by	by	ADP
ejpam-2312	191	10	definitions	definition	NOUN
ejpam-2312	191	11	of	of	ADP
ejpam-2312	191	12	soft	soft	ADJ
ejpam-2312	191	13	semi	semi	ADJ
ejpam-2312	191	14	-	-	ADJ
ejpam-2312	191	15	di	di	ADJ
ejpam-2312	191	16	and	and	CCONJ
ejpam-2312	191	17	soft	soft	ADJ
ejpam-2312	191	18	semiti(for	semiti(for	ADP
ejpam-2312	191	19	i	i	PROPN
ejpam-2312	191	20	=	=	NOUN
ejpam-2312	191	21	0	0	NUM
ejpam-2312	191	22	,	,	PUNCT
ejpam-2312	191	23	1	1	NUM
ejpam-2312	191	24	,	,	PUNCT
ejpam-2312	191	25	2	2	NUM
ejpam-2312	191	26	)	)	PUNCT
ejpam-2312	191	27	spaces	space	NOUN
ejpam-2312	191	28	,	,	PUNCT
ejpam-2312	191	29	clearly	clearly	ADV
ejpam-2312	191	30	we	we	PRON
ejpam-2312	191	31	have	have	VERB
ejpam-2312	191	32	:	:	PUNCT
ejpam-2312	191	33	(	(	PUNCT
ejpam-2312	191	34	1	1	X
ejpam-2312	191	35	)	)	PUNCT
ejpam-2312	191	36	soft	soft	ADJ
ejpam-2312	191	37	semi	semi	ADJ
ejpam-2312	191	38	-	-	ADJ
ejpam-2312	191	39	t2	t2	ADJ
ejpam-2312	191	40	⇒	⇒	NOUN
ejpam-2312	191	41	soft	soft	ADJ
ejpam-2312	191	42	semi	semi	ADJ
ejpam-2312	191	43	-	-	ADJ
ejpam-2312	191	44	t1	t1	ADJ
ejpam-2312	191	45	⇒	⇒	NOUN
ejpam-2312	191	46	soft	soft	ADJ
ejpam-2312	191	47	semi	semi	NOUN
ejpam-2312	191	48	-	-	ADJ
ejpam-2312	191	49	t0	t0	NOUN
ejpam-2312	191	50	(	(	PUNCT
ejpam-2312	191	51	2	2	NUM
ejpam-2312	191	52	)	)	PUNCT
ejpam-2312	191	53	soft	soft	ADJ
ejpam-2312	191	54	semi	semi	ADJ
ejpam-2312	191	55	-	-	ADJ
ejpam-2312	191	56	ti	ti	ADJ
ejpam-2312	191	57	⇒	⇒	NOUN
ejpam-2312	191	58	soft	soft	ADJ
ejpam-2312	191	59	semi	semi	NOUN
ejpam-2312	191	60	-	-	NOUN
ejpam-2312	191	61	di	di	ADJ
ejpam-2312	191	62	(	(	PUNCT
ejpam-2312	191	63	for	for	ADP
ejpam-2312	191	64	i	i	PRON
ejpam-2312	191	65	=	=	SYM
ejpam-2312	191	66	0	0	NUM
ejpam-2312	191	67	,	,	PUNCT
ejpam-2312	191	68	1	1	NUM
ejpam-2312	191	69	,	,	PUNCT
ejpam-2312	191	70	2	2	NUM
ejpam-2312	191	71	)	)	PUNCT
ejpam-2312	191	72	.	.	PUNCT
ejpam-2312	192	1	s.	s.	PROPN
ejpam-2312	192	2	hussain	hussain	PROPN
ejpam-2312	192	3	/	/	SYM
ejpam-2312	192	4	eur	eur	PROPN
ejpam-2312	192	5	.	.	PUNCT
ejpam-2312	193	1	j.	j.	PROPN
ejpam-2312	193	2	pure	pure	PROPN
ejpam-2312	193	3	appl	appl	PROPN
ejpam-2312	193	4	.	.	PROPN
ejpam-2312	193	5	math	math	PROPN
ejpam-2312	193	6	,	,	PUNCT
ejpam-2312	193	7	10	10	NUM
ejpam-2312	193	8	(	(	PUNCT
ejpam-2312	193	9	2	2	NUM
ejpam-2312	193	10	)	)	PUNCT
ejpam-2312	193	11	(	(	PUNCT
ejpam-2312	193	12	2017	2017	NUM
ejpam-2312	193	13	)	)	PUNCT
ejpam-2312	193	14	,	,	PUNCT
ejpam-2312	193	15	199	199	NUM
ejpam-2312	193	16	-	-	SYM
ejpam-2312	193	17	210	210	NUM
ejpam-2312	193	18	205	205	NUM
ejpam-2312	193	19	theorem	theorem	NOUN
ejpam-2312	193	20	4	4	NUM
ejpam-2312	193	21	.	.	PUNCT
ejpam-2312	194	1	let	let	VERB
ejpam-2312	194	2	(	(	PUNCT
ejpam-2312	194	3	x	x	X
ejpam-2312	194	4	,	,	PUNCT
ejpam-2312	194	5	τ	τ	PROPN
ejpam-2312	194	6	,	,	PUNCT
ejpam-2312	194	7	a	a	PRON
ejpam-2312	194	8	)	)	PUNCT
ejpam-2312	194	9	be	be	AUX
ejpam-2312	194	10	a	a	DET
ejpam-2312	194	11	soft	soft	ADJ
ejpam-2312	194	12	topological	topological	ADJ
ejpam-2312	194	13	space	space	NOUN
ejpam-2312	194	14	over	over	ADP
ejpam-2312	194	15	x	x	PUNCT
ejpam-2312	194	16	and	and	CCONJ
ejpam-2312	194	17	ef	ef	PROPN
ejpam-2312	194	18	,	,	PUNCT
ejpam-2312	194	19	eg	eg	PROPN
ejpam-2312	194	20	are	be	AUX
ejpam-2312	194	21	distinct	distinct	ADJ
ejpam-2312	194	22	soft	soft	ADJ
ejpam-2312	194	23	points	point	NOUN
ejpam-2312	194	24	in	in	ADP
ejpam-2312	194	25	x̃a	x̃a	PROPN
ejpam-2312	194	26	.	.	PUNCT
ejpam-2312	195	1	then	then	ADV
ejpam-2312	195	2	(	(	PUNCT
ejpam-2312	195	3	x	x	X
ejpam-2312	195	4	,	,	PUNCT
ejpam-2312	195	5	τ	τ	PROPN
ejpam-2312	195	6	,	,	PUNCT
ejpam-2312	195	7	a	a	PRON
ejpam-2312	195	8	)	)	PUNCT
ejpam-2312	195	9	is	be	AUX
ejpam-2312	195	10	soft	soft	ADJ
ejpam-2312	195	11	semi	semi	ADJ
ejpam-2312	195	12	-	-	ADJ
ejpam-2312	195	13	d0	d0	ADJ
ejpam-2312	195	14	space	space	NOUN
ejpam-2312	195	15	if	if	SCONJ
ejpam-2312	195	16	and	and	CCONJ
ejpam-2312	195	17	only	only	ADV
ejpam-2312	195	18	if	if	SCONJ
ejpam-2312	195	19	(	(	PUNCT
ejpam-2312	195	20	x	x	NOUN
ejpam-2312	195	21	,	,	PUNCT
ejpam-2312	195	22	τ	τ	PROPN
ejpam-2312	195	23	,	,	PUNCT
ejpam-2312	195	24	a	a	PRON
ejpam-2312	195	25	)	)	PUNCT
ejpam-2312	195	26	is	be	AUX
ejpam-2312	195	27	soft	soft	ADJ
ejpam-2312	195	28	semi	semi	ADJ
ejpam-2312	195	29	-	-	ADJ
ejpam-2312	195	30	t0	t0	ADJ
ejpam-2312	195	31	space	space	NOUN
ejpam-2312	195	32	.	.	PUNCT
ejpam-2312	196	1	proof	proof	NOUN
ejpam-2312	196	2	.	.	PUNCT
ejpam-2312	197	1	(	(	PUNCT
ejpam-2312	197	2	⇒	⇒	NOUN
ejpam-2312	197	3	)	)	PUNCT
ejpam-2312	197	4	let	let	VERB
ejpam-2312	197	5	(	(	PUNCT
ejpam-2312	197	6	x	x	NOUN
ejpam-2312	197	7	,	,	PUNCT
ejpam-2312	197	8	τ	τ	PROPN
ejpam-2312	197	9	,	,	PUNCT
ejpam-2312	197	10	a	a	PRON
ejpam-2312	197	11	)	)	PUNCT
ejpam-2312	197	12	be	be	AUX
ejpam-2312	197	13	a	a	DET
ejpam-2312	197	14	soft	soft	ADJ
ejpam-2312	197	15	semi	semi	ADJ
ejpam-2312	197	16	-	-	ADJ
ejpam-2312	197	17	d0	d0	ADJ
ejpam-2312	197	18	space	space	NOUN
ejpam-2312	197	19	.	.	PUNCT
ejpam-2312	198	1	then	then	ADV
ejpam-2312	198	2	for	for	ADP
ejpam-2312	198	3	each	each	DET
ejpam-2312	198	4	distinct	distinct	ADJ
ejpam-2312	198	5	soft	soft	ADJ
ejpam-2312	198	6	point	point	NOUN
ejpam-2312	198	7	ef	ef	NOUN
ejpam-2312	198	8	,	,	PUNCT
ejpam-2312	198	9	eg	eg	NOUN
ejpam-2312	198	10	in	in	ADP
ejpam-2312	198	11	x̃a	x̃a	NUM
ejpam-2312	198	12	,	,	PUNCT
ejpam-2312	198	13	there	there	PRON
ejpam-2312	198	14	exists	exist	VERB
ejpam-2312	198	15	a	a	DET
ejpam-2312	198	16	soft	soft	ADJ
ejpam-2312	198	17	semi	semi	ADJ
ejpam-2312	198	18	-	-	ADJ
ejpam-2312	198	19	d	d	ADJ
ejpam-2312	198	20	-	-	PUNCT
ejpam-2312	198	21	set	set	ADJ
ejpam-2312	198	22	(	(	PUNCT
ejpam-2312	198	23	h	h	NOUN
ejpam-2312	198	24	,	,	PUNCT
ejpam-2312	198	25	a	a	PRON
ejpam-2312	198	26	)	)	PUNCT
ejpam-2312	198	27	in	in	ADP
ejpam-2312	198	28	ss(x)a	ss(x)a	PROPN
ejpam-2312	198	29	such	such	ADJ
ejpam-2312	198	30	that	that	SCONJ
ejpam-2312	198	31	ef	ef	PROPN
ejpam-2312	198	32	∈̃(h	∈̃(h	NOUN
ejpam-2312	198	33	,	,	PUNCT
ejpam-2312	198	34	a	a	PRON
ejpam-2312	198	35	)	)	PUNCT
ejpam-2312	198	36	and	and	CCONJ
ejpam-2312	198	37	eg	eg	PROPN
ejpam-2312	198	38	/̃∈(h	/̃∈(h	PROPN
ejpam-2312	198	39	,	,	PUNCT
ejpam-2312	198	40	a	a	PRON
ejpam-2312	198	41	)	)	PUNCT
ejpam-2312	198	42	.	.	PUNCT
ejpam-2312	199	1	suppose	suppose	VERB
ejpam-2312	199	2	that	that	SCONJ
ejpam-2312	199	3	(	(	PUNCT
ejpam-2312	199	4	h	h	NOUN
ejpam-2312	199	5	,	,	PUNCT
ejpam-2312	199	6	a)=̃(f	a)=̃(f	X
ejpam-2312	199	7	,	,	PUNCT
ejpam-2312	199	8	a)\̃(g	a)\̃(g	ADP
ejpam-2312	199	9	,	,	PUNCT
ejpam-2312	199	10	a	a	PRON
ejpam-2312	199	11	)	)	PUNCT
ejpam-2312	199	12	,	,	PUNCT
ejpam-2312	199	13	where	where	SCONJ
ejpam-2312	199	14	(	(	PUNCT
ejpam-2312	199	15	f	f	X
ejpam-2312	199	16	,	,	PUNCT
ejpam-2312	199	17	a	a	PRON
ejpam-2312	199	18	)	)	PUNCT
ejpam-2312	199	19	and	and	CCONJ
ejpam-2312	199	20	(	(	PUNCT
ejpam-2312	199	21	g	g	NOUN
ejpam-2312	199	22	,	,	PUNCT
ejpam-2312	199	23	a	a	PRON
ejpam-2312	199	24	)	)	PUNCT
ejpam-2312	199	25	are	be	AUX
ejpam-2312	199	26	soft	soft	ADJ
ejpam-2312	199	27	semiopen	semiopen	ADJ
ejpam-2312	199	28	sets	set	NOUN
ejpam-2312	199	29	and	and	CCONJ
ejpam-2312	199	30	(	(	PUNCT
ejpam-2312	199	31	f	f	X
ejpam-2312	199	32	,	,	PUNCT
ejpam-2312	199	33	a	a	PRON
ejpam-2312	199	34	)	)	PUNCT
ejpam-2312	199	35	˜6	˜6	NOUN
ejpam-2312	200	1	=	=	SYM
ejpam-2312	200	2	x̃.	x̃.	ADJ
ejpam-2312	200	3	this	this	PRON
ejpam-2312	200	4	follows	follow	VERB
ejpam-2312	200	5	that	that	SCONJ
ejpam-2312	200	6	ef	ef	VERB
ejpam-2312	200	7	∈̃(f	∈̃(f	NOUN
ejpam-2312	200	8	,	,	PUNCT
ejpam-2312	200	9	a	a	PRON
ejpam-2312	200	10	)	)	PUNCT
ejpam-2312	200	11	and	and	CCONJ
ejpam-2312	200	12	for	for	ADP
ejpam-2312	200	13	eg	eg	PROPN
ejpam-2312	200	14	/̃∈(h	/̃∈(h	PROPN
ejpam-2312	200	15	,	,	PUNCT
ejpam-2312	200	16	a	a	PRON
ejpam-2312	200	17	)	)	PUNCT
ejpam-2312	200	18	,	,	PUNCT
ejpam-2312	200	19	we	we	PRON
ejpam-2312	200	20	have	have	VERB
ejpam-2312	200	21	two	two	NUM
ejpam-2312	200	22	possibilities	possibility	NOUN
ejpam-2312	200	23	:	:	PUNCT
ejpam-2312	201	1	[	[	X
ejpam-2312	201	2	1.]eg	1.]eg	NUM
ejpam-2312	201	3	/̃∈(f	/̃∈(f	NOUN
ejpam-2312	201	4	,	,	PUNCT
ejpam-2312	201	5	a	a	PRON
ejpam-2312	201	6	)	)	PUNCT
ejpam-2312	201	7	.	.	PUNCT
ejpam-2312	202	1	therefore	therefore	ADV
ejpam-2312	202	2	,	,	PUNCT
ejpam-2312	202	3	ef	ef	VERB
ejpam-2312	202	4	∈̃(f	∈̃(f	ADJ
ejpam-2312	202	5	,	,	PUNCT
ejpam-2312	202	6	a	a	PRON
ejpam-2312	202	7	)	)	PUNCT
ejpam-2312	202	8	and	and	CCONJ
ejpam-2312	202	9	eg	eg	NOUN
ejpam-2312	202	10	/̃∈(f	/̃∈(f	PROPN
ejpam-2312	202	11	,	,	PUNCT
ejpam-2312	202	12	a	a	PRON
ejpam-2312	202	13	)	)	PUNCT
ejpam-2312	202	14	.	.	PUNCT
ejpam-2312	203	1	eg∈̃(f	eg∈̃(f	PROPN
ejpam-2312	203	2	,	,	PUNCT
ejpam-2312	203	3	a	a	PRON
ejpam-2312	203	4	)	)	PUNCT
ejpam-2312	203	5	and	and	CCONJ
ejpam-2312	203	6	eg∈̃(g	eg∈̃(g	PROPN
ejpam-2312	203	7	,	,	PUNCT
ejpam-2312	203	8	a	a	PRON
ejpam-2312	203	9	)	)	PUNCT
ejpam-2312	203	10	.	.	PUNCT
ejpam-2312	204	1	hence	hence	ADV
ejpam-2312	204	2	eg∈̃(g	eg∈̃(g	PROPN
ejpam-2312	204	3	,	,	PUNCT
ejpam-2312	204	4	a	a	PRON
ejpam-2312	204	5	)	)	PUNCT
ejpam-2312	204	6	and	and	CCONJ
ejpam-2312	204	7	ef	ef	X
ejpam-2312	204	8	/̃∈(g	/̃∈(g	PROPN
ejpam-2312	204	9	,	,	PUNCT
ejpam-2312	204	10	a	a	PRON
ejpam-2312	204	11	)	)	PUNCT
ejpam-2312	204	12	.	.	PUNCT
ejpam-2312	205	1	this	this	PRON
ejpam-2312	205	2	follows	follow	VERB
ejpam-2312	205	3	that	that	SCONJ
ejpam-2312	205	4	(	(	PUNCT
ejpam-2312	205	5	x	x	X
ejpam-2312	205	6	,	,	PUNCT
ejpam-2312	205	7	τ	τ	PROPN
ejpam-2312	205	8	,	,	PUNCT
ejpam-2312	205	9	a	a	PRON
ejpam-2312	205	10	)	)	PUNCT
ejpam-2312	205	11	is	be	AUX
ejpam-2312	205	12	soft	soft	ADJ
ejpam-2312	205	13	semi	semi	ADJ
ejpam-2312	205	14	-	-	ADJ
ejpam-2312	205	15	t0	t0	ADJ
ejpam-2312	205	16	space	space	NOUN
ejpam-2312	205	17	.	.	PUNCT
ejpam-2312	206	1	(	(	PUNCT
ejpam-2312	206	2	⇐	⇐	PROPN
ejpam-2312	206	3	)	)	PUNCT
ejpam-2312	206	4	the	the	DET
ejpam-2312	206	5	proof	proof	NOUN
ejpam-2312	206	6	follows	follow	VERB
ejpam-2312	206	7	from	from	ADP
ejpam-2312	206	8	remark	remark	NOUN
ejpam-2312	206	9	3(2	3(2	NUM
ejpam-2312	206	10	)	)	PUNCT
ejpam-2312	206	11	.	.	PUNCT
ejpam-2312	207	1	theorem	theorem	NOUN
ejpam-2312	207	2	5	5	NUM
ejpam-2312	207	3	.	.	PUNCT
ejpam-2312	208	1	let	let	VERB
ejpam-2312	208	2	(	(	PUNCT
ejpam-2312	208	3	x	x	X
ejpam-2312	208	4	,	,	PUNCT
ejpam-2312	208	5	τ	τ	PROPN
ejpam-2312	208	6	,	,	PUNCT
ejpam-2312	208	7	a	a	PRON
ejpam-2312	208	8	)	)	PUNCT
ejpam-2312	208	9	be	be	AUX
ejpam-2312	208	10	a	a	DET
ejpam-2312	208	11	soft	soft	ADJ
ejpam-2312	208	12	topological	topological	ADJ
ejpam-2312	208	13	space	space	NOUN
ejpam-2312	208	14	over	over	ADP
ejpam-2312	208	15	x	x	PUNCT
ejpam-2312	208	16	and	and	CCONJ
ejpam-2312	208	17	ef	ef	PROPN
ejpam-2312	208	18	,	,	PUNCT
ejpam-2312	208	19	eg	eg	PROPN
ejpam-2312	208	20	are	be	AUX
ejpam-2312	208	21	distinct	distinct	ADJ
ejpam-2312	208	22	soft	soft	ADJ
ejpam-2312	208	23	points	point	NOUN
ejpam-2312	208	24	in	in	ADP
ejpam-2312	208	25	x̃a	x̃a	PROPN
ejpam-2312	208	26	.	.	PUNCT
ejpam-2312	209	1	then	then	ADV
ejpam-2312	209	2	(	(	PUNCT
ejpam-2312	209	3	x	x	X
ejpam-2312	209	4	,	,	PUNCT
ejpam-2312	209	5	τ	τ	PROPN
ejpam-2312	209	6	,	,	PUNCT
ejpam-2312	209	7	a	a	PRON
ejpam-2312	209	8	)	)	PUNCT
ejpam-2312	209	9	is	be	AUX
ejpam-2312	209	10	soft	soft	ADJ
ejpam-2312	209	11	semi	semi	ADJ
ejpam-2312	209	12	-	-	ADJ
ejpam-2312	209	13	d1	d1	ADJ
ejpam-2312	209	14	space	space	NOUN
ejpam-2312	209	15	if	if	SCONJ
ejpam-2312	209	16	and	and	CCONJ
ejpam-2312	209	17	only	only	ADV
ejpam-2312	209	18	if	if	SCONJ
ejpam-2312	209	19	(	(	PUNCT
ejpam-2312	209	20	x	x	NOUN
ejpam-2312	209	21	,	,	PUNCT
ejpam-2312	209	22	τ	τ	PROPN
ejpam-2312	209	23	,	,	PUNCT
ejpam-2312	209	24	a	a	PRON
ejpam-2312	209	25	)	)	PUNCT
ejpam-2312	209	26	is	be	AUX
ejpam-2312	209	27	soft	soft	ADJ
ejpam-2312	209	28	semi	semi	ADJ
ejpam-2312	209	29	-	-	ADJ
ejpam-2312	209	30	d2	d2	ADJ
ejpam-2312	209	31	space	space	NOUN
ejpam-2312	209	32	.	.	PUNCT
ejpam-2312	210	1	proof	proof	NOUN
ejpam-2312	210	2	.	.	PUNCT
ejpam-2312	211	1	(	(	PUNCT
ejpam-2312	211	2	⇒	⇒	NOUN
ejpam-2312	211	3	)	)	PUNCT
ejpam-2312	211	4	let	let	VERB
ejpam-2312	211	5	(	(	PUNCT
ejpam-2312	211	6	x	x	NOUN
ejpam-2312	211	7	,	,	PUNCT
ejpam-2312	211	8	τ	τ	PROPN
ejpam-2312	211	9	,	,	PUNCT
ejpam-2312	211	10	a	a	PRON
ejpam-2312	211	11	)	)	PUNCT
ejpam-2312	211	12	be	be	AUX
ejpam-2312	211	13	soft	soft	ADJ
ejpam-2312	211	14	semi	semi	ADJ
ejpam-2312	211	15	-	-	ADJ
ejpam-2312	211	16	d1	d1	ADJ
ejpam-2312	211	17	space	space	NOUN
ejpam-2312	211	18	.	.	PUNCT
ejpam-2312	212	1	then	then	ADV
ejpam-2312	212	2	for	for	ADP
ejpam-2312	212	3	any	any	DET
ejpam-2312	212	4	two	two	NUM
ejpam-2312	212	5	distinct	distinct	ADJ
ejpam-2312	212	6	soft	soft	ADJ
ejpam-2312	212	7	points	point	NOUN
ejpam-2312	212	8	ef	ef	NOUN
ejpam-2312	212	9	and	and	CCONJ
ejpam-2312	212	10	eg	eg	NOUN
ejpam-2312	212	11	in	in	ADP
ejpam-2312	212	12	x̃a	x̃a	NUM
ejpam-2312	212	13	,	,	PUNCT
ejpam-2312	212	14	there	there	PRON
ejpam-2312	212	15	exists	exist	VERB
ejpam-2312	212	16	soft	soft	ADJ
ejpam-2312	212	17	semi	semi	ADJ
ejpam-2312	212	18	-	-	ADJ
ejpam-2312	212	19	d	d	ADJ
ejpam-2312	212	20	-	-	PUNCT
ejpam-2312	212	21	sets	set	NOUN
ejpam-2312	212	22	(	(	PUNCT
ejpam-2312	212	23	h	h	NOUN
ejpam-2312	212	24	,	,	PUNCT
ejpam-2312	212	25	a	a	PRON
ejpam-2312	212	26	)	)	PUNCT
ejpam-2312	212	27	and	and	CCONJ
ejpam-2312	212	28	(	(	PUNCT
ejpam-2312	212	29	k	k	NOUN
ejpam-2312	212	30	,	,	PUNCT
ejpam-2312	212	31	a	a	PRON
ejpam-2312	212	32	)	)	PUNCT
ejpam-2312	212	33	in	in	ADP
ejpam-2312	212	34	ss(x)a	ss(x)a	PROPN
ejpam-2312	212	35	such	such	ADJ
ejpam-2312	212	36	that	that	SCONJ
ejpam-2312	212	37	ef	ef	PROPN
ejpam-2312	212	38	∈̃(h	∈̃(h	NOUN
ejpam-2312	212	39	,	,	PUNCT
ejpam-2312	212	40	a	a	PRON
ejpam-2312	212	41	)	)	PUNCT
ejpam-2312	212	42	,	,	PUNCT
ejpam-2312	212	43	eg	eg	PROPN
ejpam-2312	212	44	/̃∈(h	/̃∈(h	PROPN
ejpam-2312	212	45	,	,	PUNCT
ejpam-2312	212	46	a	a	PRON
ejpam-2312	212	47	)	)	PUNCT
ejpam-2312	212	48	,	,	PUNCT
ejpam-2312	212	49	eg∈̃(k	eg∈̃(k	PROPN
ejpam-2312	212	50	,	,	PUNCT
ejpam-2312	212	51	a	a	PRON
ejpam-2312	212	52	)	)	PUNCT
ejpam-2312	212	53	,	,	PUNCT
ejpam-2312	212	54	ef	ef	PROPN
ejpam-2312	212	55	/̃∈(k	/̃∈(k	NOUN
ejpam-2312	212	56	,	,	PUNCT
ejpam-2312	212	57	a	a	PRON
ejpam-2312	212	58	)	)	PUNCT
ejpam-2312	212	59	.	.	PUNCT
ejpam-2312	213	1	consider	consider	VERB
ejpam-2312	213	2	soft	soft	ADJ
ejpam-2312	213	3	sets	set	NOUN
ejpam-2312	213	4	(	(	PUNCT
ejpam-2312	213	5	f	f	X
ejpam-2312	213	6	,	,	PUNCT
ejpam-2312	213	7	a	a	PRON
ejpam-2312	213	8	)	)	PUNCT
ejpam-2312	213	9	,	,	PUNCT
ejpam-2312	213	10	(	(	PUNCT
ejpam-2312	213	11	g	g	NOUN
ejpam-2312	213	12	,	,	PUNCT
ejpam-2312	213	13	a	a	PRON
ejpam-2312	213	14	)	)	PUNCT
ejpam-2312	213	15	,	,	PUNCT
ejpam-2312	213	16	(	(	PUNCT
ejpam-2312	213	17	l	l	NOUN
ejpam-2312	213	18	,	,	PUNCT
ejpam-2312	213	19	a	a	PRON
ejpam-2312	213	20	)	)	PUNCT
ejpam-2312	213	21	and	and	CCONJ
ejpam-2312	213	22	(	(	PUNCT
ejpam-2312	213	23	m	m	PROPN
ejpam-2312	213	24	,	,	PUNCT
ejpam-2312	213	25	a	a	PRON
ejpam-2312	213	26	)	)	PUNCT
ejpam-2312	213	27	such	such	ADJ
ejpam-2312	213	28	that	that	SCONJ
ejpam-2312	213	29	(	(	PUNCT
ejpam-2312	213	30	h	h	NOUN
ejpam-2312	213	31	,	,	PUNCT
ejpam-2312	213	32	a)=̃(f	a)=̃(f	X
ejpam-2312	213	33	,	,	PUNCT
ejpam-2312	213	34	a)\̃(g	a)\̃(g	ADP
ejpam-2312	213	35	,	,	PUNCT
ejpam-2312	213	36	a	a	PRON
ejpam-2312	213	37	)	)	PUNCT
ejpam-2312	213	38	and	and	CCONJ
ejpam-2312	213	39	(	(	PUNCT
ejpam-2312	213	40	k	k	NOUN
ejpam-2312	213	41	,	,	PUNCT
ejpam-2312	213	42	a)=̃(l	a)=̃(l	ADJ
ejpam-2312	213	43	,	,	PUNCT
ejpam-2312	213	44	a)\̃(m	a)\̃(m	PROPN
ejpam-2312	213	45	,	,	PUNCT
ejpam-2312	213	46	a	a	PRON
ejpam-2312	213	47	)	)	PUNCT
ejpam-2312	213	48	.	.	PUNCT
ejpam-2312	214	1	ef	ef	PROPN
ejpam-2312	214	2	/̃∈(k	/̃∈(k	NOUN
ejpam-2312	214	3	,	,	PUNCT
ejpam-2312	214	4	a	a	PRON
ejpam-2312	214	5	)	)	PUNCT
ejpam-2312	214	6	,	,	PUNCT
ejpam-2312	214	7	implies	imply	VERB
ejpam-2312	214	8	that	that	SCONJ
ejpam-2312	214	9	either	either	CCONJ
ejpam-2312	214	10	ef	ef	PROPN
ejpam-2312	214	11	/̃∈(l	/̃∈(l	PROPN
ejpam-2312	214	12	,	,	PUNCT
ejpam-2312	214	13	a	a	PRON
ejpam-2312	214	14	)	)	PUNCT
ejpam-2312	214	15	or	or	CCONJ
ejpam-2312	214	16	ef	ef	VERB
ejpam-2312	214	17	∈̃(l	∈̃(l	NOUN
ejpam-2312	214	18	,	,	PUNCT
ejpam-2312	214	19	a	a	PRON
ejpam-2312	214	20	)	)	PUNCT
ejpam-2312	214	21	and	and	CCONJ
ejpam-2312	214	22	ef	ef	PROPN
ejpam-2312	214	23	∈̃(m	∈̃(m	PROPN
ejpam-2312	214	24	,	,	PUNCT
ejpam-2312	214	25	a	a	PRON
ejpam-2312	214	26	)	)	PUNCT
ejpam-2312	214	27	.	.	PUNCT
ejpam-2312	215	1	we	we	PRON
ejpam-2312	215	2	suppose	suppose	VERB
ejpam-2312	215	3	two	two	NUM
ejpam-2312	215	4	cases	case	NOUN
ejpam-2312	215	5	:	:	PUNCT
ejpam-2312	215	6	[	[	X
ejpam-2312	215	7	case	case	NOUN
ejpam-2312	215	8	(	(	PUNCT
ejpam-2312	215	9	1).]if	1).]if	NUM
ejpam-2312	215	10	ef	ef	X
ejpam-2312	215	11	/̃∈(l	/̃∈(l	PROPN
ejpam-2312	215	12	,	,	PUNCT
ejpam-2312	215	13	a	a	PRON
ejpam-2312	215	14	)	)	PUNCT
ejpam-2312	215	15	.	.	PUNCT
ejpam-2312	216	1	as	as	ADP
ejpam-2312	216	2	eg∈̃(h	eg∈̃(h	NOUN
ejpam-2312	216	3	,	,	PUNCT
ejpam-2312	216	4	a	a	PRON
ejpam-2312	216	5	)	)	PUNCT
ejpam-2312	216	6	then	then	ADV
ejpam-2312	216	7	either	either	CCONJ
ejpam-2312	216	8	eg∈̃(f	eg∈̃(f	PROPN
ejpam-2312	216	9	,	,	PUNCT
ejpam-2312	216	10	a	a	PRON
ejpam-2312	216	11	)	)	PUNCT
ejpam-2312	216	12	and	and	CCONJ
ejpam-2312	216	13	eg∈̃(g	eg∈̃(g	PROPN
ejpam-2312	216	14	,	,	PUNCT
ejpam-2312	216	15	a	a	PRON
ejpam-2312	216	16	)	)	PUNCT
ejpam-2312	216	17	or	or	CCONJ
ejpam-2312	216	18	eg	eg	NOUN
ejpam-2312	216	19	/̃∈(f	/̃∈(f	INTJ
ejpam-2312	216	20	,	,	PUNCT
ejpam-2312	216	21	a	a	PRON
ejpam-2312	216	22	)	)	PUNCT
ejpam-2312	216	23	.	.	PUNCT
ejpam-2312	217	1	if	if	SCONJ
ejpam-2312	217	2	eg∈̃(f	eg∈̃(f	PROPN
ejpam-2312	217	3	,	,	PUNCT
ejpam-2312	217	4	a	a	PRON
ejpam-2312	217	5	)	)	PUNCT
ejpam-2312	217	6	and	and	CCONJ
ejpam-2312	217	7	eg∈̃(g	eg∈̃(g	PROPN
ejpam-2312	217	8	,	,	PUNCT
ejpam-2312	217	9	a	a	PRON
ejpam-2312	217	10	)	)	PUNCT
ejpam-2312	217	11	.	.	PUNCT
ejpam-2312	218	1	then	then	ADV
ejpam-2312	218	2	ef	ef	VERB
ejpam-2312	218	3	∈̃(f	∈̃(f	PROPN
ejpam-2312	218	4	,	,	PUNCT
ejpam-2312	218	5	a)\̃(g	a)\̃(g	ADP
ejpam-2312	218	6	,	,	PUNCT
ejpam-2312	218	7	a	a	PRON
ejpam-2312	218	8	)	)	PUNCT
ejpam-2312	218	9	,	,	PUNCT
ejpam-2312	218	10	eg∈̃(g	eg∈̃(g	PROPN
ejpam-2312	218	11	,	,	PUNCT
ejpam-2312	218	12	a	a	PRON
ejpam-2312	218	13	)	)	PUNCT
ejpam-2312	218	14	and	and	CCONJ
ejpam-2312	218	15	(	(	PUNCT
ejpam-2312	218	16	(	(	PUNCT
ejpam-2312	218	17	f	f	X
ejpam-2312	218	18	,	,	PUNCT
ejpam-2312	218	19	a)\̃(g	a)\̃(g	PROPN
ejpam-2312	218	20	,	,	PUNCT
ejpam-2312	218	21	a))∩̃(g	a))∩̃(g	NOUN
ejpam-2312	218	22	,	,	PUNCT
ejpam-2312	218	23	a)=̃φ̃.	a)=̃φ̃.	NUM
ejpam-2312	218	24	if	if	SCONJ
ejpam-2312	218	25	eg	eg	PROPN
ejpam-2312	218	26	/̃∈(f	/̃∈(f	NOUN
ejpam-2312	218	27	,	,	PUNCT
ejpam-2312	218	28	a	a	PRON
ejpam-2312	218	29	)	)	PUNCT
ejpam-2312	218	30	.	.	PUNCT
ejpam-2312	219	1	as	as	SCONJ
ejpam-2312	219	2	ef	ef	PROPN
ejpam-2312	219	3	∈̃(f	∈̃(f	PROPN
ejpam-2312	219	4	,	,	PUNCT
ejpam-2312	219	5	a)\̃(g	a)\̃(g	ADP
ejpam-2312	219	6	,	,	PUNCT
ejpam-2312	219	7	a	a	PRON
ejpam-2312	219	8	)	)	PUNCT
ejpam-2312	219	9	,	,	PUNCT
ejpam-2312	219	10	we	we	PRON
ejpam-2312	219	11	have	have	VERB
ejpam-2312	219	12	that	that	PRON
ejpam-2312	219	13	ef	ef	VERB
ejpam-2312	219	14	∈̃(f	∈̃(f	ADJ
ejpam-2312	219	15	,	,	PUNCT
ejpam-2312	219	16	a)\̃((g	a)\̃((g	ADJ
ejpam-2312	219	17	,	,	PUNCT
ejpam-2312	219	18	a)∪̃(l	a)∪̃(l	ADJ
ejpam-2312	219	19	,	,	PUNCT
ejpam-2312	219	20	a	a	PRON
ejpam-2312	219	21	)	)	PUNCT
ejpam-2312	219	22	)	)	PUNCT
ejpam-2312	219	23	and	and	CCONJ
ejpam-2312	219	24	from	from	ADP
ejpam-2312	219	25	eg∈̃(l	eg∈̃(l	ADP
ejpam-2312	219	26	,	,	PUNCT
ejpam-2312	219	27	a)\̃(m	a)\̃(m	PROPN
ejpam-2312	219	28	,	,	PUNCT
ejpam-2312	219	29	a	a	PRON
ejpam-2312	219	30	)	)	PUNCT
ejpam-2312	219	31	,	,	PUNCT
ejpam-2312	219	32	we	we	PRON
ejpam-2312	219	33	have	have	VERB
ejpam-2312	219	34	eg∈̃(l	eg∈̃(l	NOUN
ejpam-2312	219	35	,	,	PUNCT
ejpam-2312	219	36	a)\̃((f	a)\̃((f	ADV
ejpam-2312	219	37	,	,	PUNCT
ejpam-2312	219	38	a)∪̃(m	a)∪̃(m	NOUN
ejpam-2312	219	39	,	,	PUNCT
ejpam-2312	219	40	a	a	PRON
ejpam-2312	219	41	)	)	PUNCT
ejpam-2312	219	42	)	)	PUNCT
ejpam-2312	219	43	.	.	PUNCT
ejpam-2312	220	1	clearly	clearly	ADV
ejpam-2312	220	2	(	(	PUNCT
ejpam-2312	220	3	(	(	PUNCT
ejpam-2312	220	4	f	f	X
ejpam-2312	220	5	,	,	PUNCT
ejpam-2312	220	6	a)\̃((g	a)\̃((g	ADJ
ejpam-2312	220	7	,	,	PUNCT
ejpam-2312	220	8	a)∪̃(l	a)∪̃(l	ADV
ejpam-2312	220	9	,	,	PUNCT
ejpam-2312	220	10	a)))∩̃((l	a)))∩̃((l	PROPN
ejpam-2312	220	11	,	,	PUNCT
ejpam-2312	220	12	a)\̃((f	a)\̃((f	ADV
ejpam-2312	220	13	,	,	PUNCT
ejpam-2312	220	14	a)∪̃(m	a)∪̃(m	NOUN
ejpam-2312	220	15	,	,	PUNCT
ejpam-2312	220	16	a)))=̃φ̃.	a)))=̃φ̃.	VERB
ejpam-2312	220	17	if	if	SCONJ
ejpam-2312	220	18	ef	ef	ADP
ejpam-2312	220	19	∈̃(l	∈̃(l	NOUN
ejpam-2312	220	20	,	,	PUNCT
ejpam-2312	220	21	a	a	PRON
ejpam-2312	220	22	)	)	PUNCT
ejpam-2312	220	23	and	and	CCONJ
ejpam-2312	220	24	ef	ef	PROPN
ejpam-2312	220	25	∈̃(m	∈̃(m	PROPN
ejpam-2312	220	26	,	,	PUNCT
ejpam-2312	220	27	a	a	PRON
ejpam-2312	220	28	)	)	PUNCT
ejpam-2312	220	29	.	.	PUNCT
ejpam-2312	221	1	then	then	ADV
ejpam-2312	221	2	eg∈̃(l	eg∈̃(l	ADP
ejpam-2312	221	3	,	,	PUNCT
ejpam-2312	221	4	a)\̃(m	a)\̃(m	PROPN
ejpam-2312	221	5	,	,	PUNCT
ejpam-2312	221	6	a	a	PRON
ejpam-2312	221	7	)	)	PUNCT
ejpam-2312	221	8	,	,	PUNCT
ejpam-2312	221	9	ef	ef	PROPN
ejpam-2312	221	10	∈̃(m	∈̃(m	PROPN
ejpam-2312	221	11	,	,	PUNCT
ejpam-2312	221	12	a	a	PRON
ejpam-2312	221	13	)	)	PUNCT
ejpam-2312	221	14	and	and	CCONJ
ejpam-2312	221	15	(	(	PUNCT
ejpam-2312	221	16	(	(	PUNCT
ejpam-2312	221	17	l	l	NOUN
ejpam-2312	221	18	,	,	PUNCT
ejpam-2312	221	19	a)\̃(m	a)\̃(m	NOUN
ejpam-2312	221	20	,	,	PUNCT
ejpam-2312	221	21	a))∩̃(m	a))∩̃(m	NOUN
ejpam-2312	221	22	,	,	PUNCT
ejpam-2312	221	23	a)=̃φ̃.	a)=̃φ̃.	NUM
ejpam-2312	221	24	thus	thus	ADV
ejpam-2312	221	25	in	in	ADP
ejpam-2312	221	26	each	each	DET
ejpam-2312	221	27	case	case	NOUN
ejpam-2312	221	28	,	,	PUNCT
ejpam-2312	221	29	(	(	PUNCT
ejpam-2312	221	30	x	x	X
ejpam-2312	221	31	,	,	PUNCT
ejpam-2312	221	32	τ	τ	PROPN
ejpam-2312	221	33	,	,	PUNCT
ejpam-2312	221	34	a	a	PRON
ejpam-2312	221	35	)	)	PUNCT
ejpam-2312	221	36	is	be	AUX
ejpam-2312	221	37	soft	soft	ADJ
ejpam-2312	221	38	semi	semi	ADJ
ejpam-2312	221	39	-	-	ADJ
ejpam-2312	221	40	d2	d2	ADJ
ejpam-2312	221	41	space	space	NOUN
ejpam-2312	221	42	.	.	PUNCT
ejpam-2312	222	1	(	(	PUNCT
ejpam-2312	222	2	⇐	⇐	NOUN
ejpam-2312	222	3	)	)	PUNCT
ejpam-2312	222	4	this	this	PRON
ejpam-2312	222	5	follows	follow	VERB
ejpam-2312	222	6	from	from	ADP
ejpam-2312	222	7	remark	remark	NOUN
ejpam-2312	222	8	1	1	NUM
ejpam-2312	222	9	.	.	PUNCT
ejpam-2312	223	1	hence	hence	ADV
ejpam-2312	223	2	the	the	DET
ejpam-2312	223	3	proof	proof	NOUN
ejpam-2312	223	4	.	.	PUNCT
ejpam-2312	224	1	proposition	proposition	NOUN
ejpam-2312	224	2	2	2	NUM
ejpam-2312	224	3	.	.	PUNCT
ejpam-2312	225	1	let	let	VERB
ejpam-2312	225	2	(	(	PUNCT
ejpam-2312	225	3	x	x	X
ejpam-2312	225	4	,	,	PUNCT
ejpam-2312	225	5	τ	τ	PROPN
ejpam-2312	225	6	,	,	PUNCT
ejpam-2312	225	7	a	a	PRON
ejpam-2312	225	8	)	)	PUNCT
ejpam-2312	225	9	be	be	AUX
ejpam-2312	225	10	a	a	DET
ejpam-2312	225	11	soft	soft	ADJ
ejpam-2312	225	12	topological	topological	ADJ
ejpam-2312	225	13	space	space	NOUN
ejpam-2312	225	14	over	over	ADP
ejpam-2312	225	15	x.	x.	NOUN
ejpam-2312	226	1	if	if	SCONJ
ejpam-2312	226	2	(	(	PUNCT
ejpam-2312	226	3	x	x	NOUN
ejpam-2312	226	4	,	,	PUNCT
ejpam-2312	226	5	τ	τ	PROPN
ejpam-2312	226	6	,	,	PUNCT
ejpam-2312	226	7	a	a	PRON
ejpam-2312	226	8	)	)	PUNCT
ejpam-2312	226	9	is	be	AUX
ejpam-2312	226	10	soft	soft	ADJ
ejpam-2312	226	11	semid1	semid1	NOUN
ejpam-2312	226	12	space	space	NOUN
ejpam-2312	226	13	,	,	PUNCT
ejpam-2312	226	14	then	then	ADV
ejpam-2312	226	15	x	x	PUNCT
ejpam-2312	226	16	is	be	AUX
ejpam-2312	226	17	soft	soft	ADJ
ejpam-2312	226	18	semi	semi	ADJ
ejpam-2312	226	19	-	-	ADJ
ejpam-2312	226	20	t0	t0	ADJ
ejpam-2312	226	21	space	space	NOUN
ejpam-2312	226	22	.	.	PUNCT
ejpam-2312	227	1	proof	proof	NOUN
ejpam-2312	227	2	.	.	PUNCT
ejpam-2312	228	1	the	the	DET
ejpam-2312	228	2	proof	proof	NOUN
ejpam-2312	228	3	follows	follows	AUX
ejpam-2312	228	4	directly	directly	ADV
ejpam-2312	228	5	form	form	VERB
ejpam-2312	228	6	remark	remark	NOUN
ejpam-2312	228	7	1	1	NUM
ejpam-2312	228	8	and	and	CCONJ
ejpam-2312	228	9	theorem	theorem	VERB
ejpam-2312	228	10	4	4	NUM
ejpam-2312	228	11	.	.	PUNCT
ejpam-2312	228	12	definition	definition	NOUN
ejpam-2312	228	13	21	21	NUM
ejpam-2312	228	14	.	.	PUNCT
ejpam-2312	229	1	let	let	VERB
ejpam-2312	229	2	(	(	PUNCT
ejpam-2312	229	3	x	x	X
ejpam-2312	229	4	,	,	PUNCT
ejpam-2312	229	5	τ	τ	PROPN
ejpam-2312	229	6	,	,	PUNCT
ejpam-2312	229	7	a	a	PRON
ejpam-2312	229	8	)	)	PUNCT
ejpam-2312	229	9	be	be	AUX
ejpam-2312	229	10	a	a	DET
ejpam-2312	229	11	soft	soft	ADJ
ejpam-2312	229	12	topological	topological	ADJ
ejpam-2312	229	13	space	space	NOUN
ejpam-2312	229	14	over	over	ADP
ejpam-2312	229	15	x	x	PUNCT
ejpam-2312	229	16	and	and	CCONJ
ejpam-2312	229	17	ef	ef	PROPN
ejpam-2312	229	18	,	,	PUNCT
ejpam-2312	229	19	eg	eg	NOUN
ejpam-2312	229	20	be	be	AUX
ejpam-2312	229	21	any	any	DET
ejpam-2312	229	22	soft	soft	ADJ
ejpam-2312	229	23	points	point	NOUN
ejpam-2312	229	24	in	in	ADP
ejpam-2312	229	25	x̃a	x̃a	PROPN
ejpam-2312	229	26	.	.	PUNCT
ejpam-2312	230	1	if	if	SCONJ
ejpam-2312	230	2	ef	ef	VERB
ejpam-2312	230	3	∈̃cls({eg	∈̃cls({eg	NOUN
ejpam-2312	230	4	}	}	PUNCT
ejpam-2312	230	5	)	)	PUNCT
ejpam-2312	230	6	implies	imply	VERB
ejpam-2312	230	7	eg∈̃cls({ef	eg∈̃cls({ef	NOUN
ejpam-2312	230	8	}	}	PUNCT
ejpam-2312	230	9	)	)	PUNCT
ejpam-2312	230	10	,	,	PUNCT
ejpam-2312	230	11	then	then	ADV
ejpam-2312	230	12	(	(	PUNCT
ejpam-2312	230	13	x	x	X
ejpam-2312	230	14	,	,	PUNCT
ejpam-2312	230	15	τ	τ	PROPN
ejpam-2312	230	16	,	,	PUNCT
ejpam-2312	230	17	a	a	PRON
ejpam-2312	230	18	)	)	PUNCT
ejpam-2312	230	19	is	be	AUX
ejpam-2312	230	20	called	call	VERB
ejpam-2312	230	21	soft	soft	ADJ
ejpam-2312	230	22	semisymmetric	semisymmetric	NOUN
ejpam-2312	230	23	.	.	PUNCT
ejpam-2312	231	1	s.	s.	PROPN
ejpam-2312	231	2	hussain	hussain	PROPN
ejpam-2312	231	3	/	/	SYM
ejpam-2312	231	4	eur	eur	PROPN
ejpam-2312	231	5	.	.	PUNCT
ejpam-2312	232	1	j.	j.	PROPN
ejpam-2312	232	2	pure	pure	PROPN
ejpam-2312	232	3	appl	appl	PROPN
ejpam-2312	232	4	.	.	PROPN
ejpam-2312	232	5	math	math	PROPN
ejpam-2312	232	6	,	,	PUNCT
ejpam-2312	232	7	10	10	NUM
ejpam-2312	232	8	(	(	PUNCT
ejpam-2312	232	9	2	2	NUM
ejpam-2312	232	10	)	)	PUNCT
ejpam-2312	232	11	(	(	PUNCT
ejpam-2312	232	12	2017	2017	NUM
ejpam-2312	232	13	)	)	PUNCT
ejpam-2312	232	14	,	,	PUNCT
ejpam-2312	232	15	199	199	NUM
ejpam-2312	232	16	-	-	SYM
ejpam-2312	232	17	210	210	NUM
ejpam-2312	232	18	206	206	NUM
ejpam-2312	232	19	definition	definition	NOUN
ejpam-2312	232	20	22	22	NUM
ejpam-2312	232	21	.	.	PUNCT
ejpam-2312	233	1	let	let	VERB
ejpam-2312	233	2	(	(	PUNCT
ejpam-2312	233	3	x	x	X
ejpam-2312	233	4	,	,	PUNCT
ejpam-2312	233	5	τ	τ	PROPN
ejpam-2312	233	6	,	,	PUNCT
ejpam-2312	233	7	a	a	PRON
ejpam-2312	233	8	)	)	PUNCT
ejpam-2312	233	9	be	be	AUX
ejpam-2312	233	10	a	a	DET
ejpam-2312	233	11	soft	soft	ADJ
ejpam-2312	233	12	topological	topological	ADJ
ejpam-2312	233	13	space	space	NOUN
ejpam-2312	233	14	over	over	ADP
ejpam-2312	233	15	x	x	PUNCT
ejpam-2312	233	16	and	and	CCONJ
ejpam-2312	233	17	(	(	PUNCT
ejpam-2312	233	18	f	f	X
ejpam-2312	233	19	,	,	PUNCT
ejpam-2312	233	20	a	a	PRON
ejpam-2312	233	21	)	)	PUNCT
ejpam-2312	233	22	be	be	AUX
ejpam-2312	233	23	a	a	DET
ejpam-2312	233	24	soft	soft	ADJ
ejpam-2312	233	25	set	set	NOUN
ejpam-2312	233	26	in	in	ADP
ejpam-2312	233	27	ss(x)a	ss(x)a	PROPN
ejpam-2312	233	28	.	.	PUNCT
ejpam-2312	234	1	if	if	SCONJ
ejpam-2312	234	2	for	for	ADP
ejpam-2312	234	3	any	any	DET
ejpam-2312	234	4	soft	soft	ADJ
ejpam-2312	234	5	semi	semi	ADJ
ejpam-2312	234	6	-	-	ADJ
ejpam-2312	234	7	open	open	ADJ
ejpam-2312	234	8	set	set	NOUN
ejpam-2312	234	9	(	(	PUNCT
ejpam-2312	234	10	h	h	NOUN
ejpam-2312	234	11	,	,	PUNCT
ejpam-2312	234	12	a	a	PRON
ejpam-2312	234	13	)	)	PUNCT
ejpam-2312	234	14	in	in	ADP
ejpam-2312	234	15	ss(x)a	ss(x)a	PROPN
ejpam-2312	234	16	and	and	CCONJ
ejpam-2312	234	17	(	(	PUNCT
ejpam-2312	234	18	f	f	X
ejpam-2312	234	19	,	,	PUNCT
ejpam-2312	234	20	a)⊆̃(h	a)⊆̃(h	PROPN
ejpam-2312	234	21	,	,	PUNCT
ejpam-2312	234	22	a	a	PRON
ejpam-2312	234	23	)	)	PUNCT
ejpam-2312	234	24	implies	imply	VERB
ejpam-2312	234	25	cls(f	cls(f	PROPN
ejpam-2312	234	26	,	,	PUNCT
ejpam-2312	234	27	a)⊆̃(h	a)⊆̃(h	PROPN
ejpam-2312	234	28	,	,	PUNCT
ejpam-2312	234	29	a	a	PRON
ejpam-2312	234	30	)	)	PUNCT
ejpam-2312	234	31	,	,	PUNCT
ejpam-2312	234	32	then	then	ADV
ejpam-2312	234	33	(	(	PUNCT
ejpam-2312	234	34	f	f	X
ejpam-2312	234	35	,	,	PUNCT
ejpam-2312	234	36	a	a	PRON
ejpam-2312	234	37	)	)	PUNCT
ejpam-2312	234	38	is	be	AUX
ejpam-2312	234	39	called	call	VERB
ejpam-2312	234	40	soft	soft	ADJ
ejpam-2312	234	41	semi	semi	ADJ
ejpam-2312	234	42	-	-	ADJ
ejpam-2312	234	43	generalized	generalized	ADJ
ejpam-2312	234	44	closed	close	VERB
ejpam-2312	234	45	(	(	PUNCT
ejpam-2312	234	46	in	in	ADP
ejpam-2312	234	47	short	short	ADJ
ejpam-2312	234	48	soft	soft	ADJ
ejpam-2312	234	49	sg	sg	NOUN
ejpam-2312	234	50	-	-	PUNCT
ejpam-2312	234	51	closed	closed	ADJ
ejpam-2312	234	52	)	)	PUNCT
ejpam-2312	234	53	set	set	NOUN
ejpam-2312	234	54	.	.	PUNCT
ejpam-2312	235	1	the	the	DET
ejpam-2312	235	2	proof	proof	NOUN
ejpam-2312	235	3	of	of	ADP
ejpam-2312	235	4	the	the	DET
ejpam-2312	235	5	following	follow	VERB
ejpam-2312	235	6	proposition	proposition	NOUN
ejpam-2312	235	7	is	be	AUX
ejpam-2312	235	8	straightforward	straightforward	ADJ
ejpam-2312	235	9	form	form	NOUN
ejpam-2312	235	10	the	the	DET
ejpam-2312	235	11	definition	definition	NOUN
ejpam-2312	235	12	of	of	ADP
ejpam-2312	235	13	soft	soft	ADJ
ejpam-2312	235	14	semi	semi	ADJ
ejpam-2312	235	15	-	-	ADJ
ejpam-2312	235	16	closed	closed	ADJ
ejpam-2312	235	17	and	and	CCONJ
ejpam-2312	235	18	soft	soft	ADJ
ejpam-2312	235	19	sg	sg	NOUN
ejpam-2312	235	20	-	-	PUNCT
ejpam-2312	235	21	closed	close	VERB
ejpam-2312	235	22	set	set	NOUN
ejpam-2312	235	23	.	.	PUNCT
ejpam-2312	236	1	proposition	proposition	NOUN
ejpam-2312	236	2	3	3	NUM
ejpam-2312	236	3	.	.	PUNCT
ejpam-2312	237	1	in	in	ADP
ejpam-2312	237	2	a	a	DET
ejpam-2312	237	3	soft	soft	ADJ
ejpam-2312	237	4	topological	topological	ADJ
ejpam-2312	237	5	space	space	NOUN
ejpam-2312	237	6	(	(	PUNCT
ejpam-2312	237	7	x	x	X
ejpam-2312	237	8	,	,	PUNCT
ejpam-2312	237	9	τ	τ	PROPN
ejpam-2312	237	10	,	,	PUNCT
ejpam-2312	237	11	a	a	PRON
ejpam-2312	237	12	)	)	PUNCT
ejpam-2312	237	13	over	over	ADP
ejpam-2312	237	14	x	x	NOUN
ejpam-2312	237	15	,	,	PUNCT
ejpam-2312	237	16	every	every	DET
ejpam-2312	237	17	soft	soft	ADJ
ejpam-2312	237	18	semi	semi	ADJ
ejpam-2312	237	19	closed	closed	ADJ
ejpam-2312	237	20	set	set	NOUN
ejpam-2312	237	21	(	(	PUNCT
ejpam-2312	237	22	f	f	X
ejpam-2312	237	23	,	,	PUNCT
ejpam-2312	237	24	a	a	PRON
ejpam-2312	237	25	)	)	PUNCT
ejpam-2312	237	26	is	be	AUX
ejpam-2312	237	27	soft	soft	ADJ
ejpam-2312	237	28	sg	sg	NOUN
ejpam-2312	237	29	-	-	PUNCT
ejpam-2312	237	30	closed	closed	ADJ
ejpam-2312	237	31	.	.	PUNCT
ejpam-2312	238	1	theorem	theorem	NOUN
ejpam-2312	238	2	6	6	NUM
ejpam-2312	238	3	.	.	PUNCT
ejpam-2312	239	1	let	let	VERB
ejpam-2312	239	2	(	(	PUNCT
ejpam-2312	239	3	x	x	X
ejpam-2312	239	4	,	,	PUNCT
ejpam-2312	239	5	τ	τ	PROPN
ejpam-2312	239	6	,	,	PUNCT
ejpam-2312	239	7	a	a	PRON
ejpam-2312	239	8	)	)	PUNCT
ejpam-2312	239	9	be	be	AUX
ejpam-2312	239	10	a	a	DET
ejpam-2312	239	11	soft	soft	ADJ
ejpam-2312	239	12	topological	topological	ADJ
ejpam-2312	239	13	space	space	NOUN
ejpam-2312	239	14	over	over	ADP
ejpam-2312	239	15	x.	x.	NOUN
ejpam-2312	239	16	then	then	ADV
ejpam-2312	239	17	the	the	DET
ejpam-2312	239	18	following	follow	VERB
ejpam-2312	239	19	statements	statement	NOUN
ejpam-2312	239	20	are	be	AUX
ejpam-2312	239	21	equivalent	equivalent	ADJ
ejpam-2312	239	22	:	:	PUNCT
ejpam-2312	239	23	(	(	PUNCT
ejpam-2312	239	24	1	1	X
ejpam-2312	239	25	)	)	PUNCT
ejpam-2312	239	26	{	{	PUNCT
ejpam-2312	239	27	ef	ef	PROPN
ejpam-2312	239	28	}	}	PUNCT
ejpam-2312	239	29	is	be	AUX
ejpam-2312	239	30	soft	soft	ADJ
ejpam-2312	239	31	sg	sg	NOUN
ejpam-2312	239	32	-	-	PUNCT
ejpam-2312	239	33	closed	closed	ADJ
ejpam-2312	239	34	,	,	PUNCT
ejpam-2312	239	35	for	for	ADP
ejpam-2312	239	36	any	any	DET
ejpam-2312	239	37	soft	soft	ADJ
ejpam-2312	239	38	point	point	NOUN
ejpam-2312	239	39	ef	ef	NOUN
ejpam-2312	239	40	in	in	ADP
ejpam-2312	239	41	x̃a	x̃a	PROPN
ejpam-2312	239	42	.	.	PUNCT
ejpam-2312	240	1	(	(	PUNCT
ejpam-2312	240	2	2	2	NUM
ejpam-2312	240	3	)	)	PUNCT
ejpam-2312	240	4	(	(	PUNCT
ejpam-2312	240	5	x	x	X
ejpam-2312	240	6	,	,	PUNCT
ejpam-2312	240	7	τ	τ	PROPN
ejpam-2312	240	8	,	,	PUNCT
ejpam-2312	240	9	a	a	PRON
ejpam-2312	240	10	)	)	PUNCT
ejpam-2312	240	11	is	be	AUX
ejpam-2312	240	12	soft	soft	ADJ
ejpam-2312	240	13	semi	semi	ADJ
ejpam-2312	240	14	-	-	ADJ
ejpam-2312	240	15	symmetric	symmetric	ADJ
ejpam-2312	240	16	.	.	PUNCT
ejpam-2312	241	1	proof	proof	NOUN
ejpam-2312	241	2	.	.	PUNCT
ejpam-2312	242	1	(	(	PUNCT
ejpam-2312	242	2	1)⇒	1)⇒	NUM
ejpam-2312	242	3	(	(	PUNCT
ejpam-2312	242	4	2	2	NUM
ejpam-2312	242	5	)	)	PUNCT
ejpam-2312	242	6	assume	assume	VERB
ejpam-2312	242	7	that	that	SCONJ
ejpam-2312	242	8	ef	ef	VERB
ejpam-2312	242	9	∈̃cls({eg	∈̃cls({eg	NOUN
ejpam-2312	242	10	}	}	PUNCT
ejpam-2312	242	11	)	)	PUNCT
ejpam-2312	242	12	.	.	PUNCT
ejpam-2312	243	1	suppose	suppose	VERB
ejpam-2312	243	2	on	on	ADP
ejpam-2312	243	3	the	the	DET
ejpam-2312	243	4	contrarily	contrarily	ADV
ejpam-2312	243	5	that	that	SCONJ
ejpam-2312	243	6	eg	eg	NOUN
ejpam-2312	243	7	/̃∈cls({ef	/̃∈cls({ef	PUNCT
ejpam-2312	243	8	}	}	PUNCT
ejpam-2312	243	9	)	)	PUNCT
ejpam-2312	243	10	.	.	PUNCT
ejpam-2312	244	1	then	then	ADV
ejpam-2312	244	2	eg∈̃(cls({eg}))c	eg∈̃(cls({eg}))c	PROPN
ejpam-2312	244	3	.	.	PUNCT
ejpam-2312	245	1	this	this	PRON
ejpam-2312	245	2	follows	follow	VERB
ejpam-2312	245	3	that	that	SCONJ
ejpam-2312	245	4	{	{	PUNCT
ejpam-2312	245	5	eg}⊆̃(cls({ef	eg}⊆̃(cls({ef	ADJ
ejpam-2312	245	6	}	}	PUNCT
ejpam-2312	245	7	)	)	PUNCT
ejpam-2312	245	8	)	)	PUNCT
ejpam-2312	245	9	c.	c.	PROPN
ejpam-2312	245	10	therefore	therefore	ADV
ejpam-2312	245	11	,	,	PUNCT
ejpam-2312	245	12	cls({eg})⊆̃(cls({ef	cls({eg})⊆̃(cls({ef	PROPN
ejpam-2312	245	13	}	}	PUNCT
ejpam-2312	245	14	)	)	PUNCT
ejpam-2312	245	15	)	)	PUNCT
ejpam-2312	245	16	c.	c.	NOUN
ejpam-2312	245	17	hence	hence	ADV
ejpam-2312	245	18	eg∈̃(cls({ef	eg∈̃(cls({ef	NOUN
ejpam-2312	245	19	}	}	PUNCT
ejpam-2312	245	20	)	)	PUNCT
ejpam-2312	245	21	)	)	PUNCT
ejpam-2312	246	1	c.	c.	NOUN
ejpam-2312	246	2	this	this	DET
ejpam-2312	246	3	contradiction	contradiction	NOUN
ejpam-2312	246	4	proves	prove	VERB
ejpam-2312	246	5	the	the	DET
ejpam-2312	246	6	required	require	VERB
ejpam-2312	246	7	result	result	NOUN
ejpam-2312	246	8	.	.	PUNCT
ejpam-2312	247	1	(	(	PUNCT
ejpam-2312	247	2	2	2	X
ejpam-2312	247	3	)	)	PUNCT
ejpam-2312	247	4	⇒	⇒	NOUN
ejpam-2312	247	5	(	(	PUNCT
ejpam-2312	247	6	1	1	X
ejpam-2312	247	7	)	)	PUNCT
ejpam-2312	247	8	assume	assume	VERB
ejpam-2312	247	9	on	on	ADP
ejpam-2312	247	10	the	the	DET
ejpam-2312	247	11	contrary	contrary	NOUN
ejpam-2312	248	1	that	that	SCONJ
ejpam-2312	248	2	for	for	ADP
ejpam-2312	248	3	soft	soft	ADJ
ejpam-2312	248	4	point	point	NOUN
ejpam-2312	248	5	ef	ef	NOUN
ejpam-2312	248	6	in	in	ADP
ejpam-2312	248	7	x̃a	x̃a	PROPN
ejpam-2312	248	8	and	and	CCONJ
ejpam-2312	248	9	a	a	DET
ejpam-2312	248	10	soft	soft	ADJ
ejpam-2312	248	11	semiopen	semiopen	ADJ
ejpam-2312	248	12	set	set	NOUN
ejpam-2312	248	13	(	(	PUNCT
ejpam-2312	248	14	h	h	NOUN
ejpam-2312	248	15	,	,	PUNCT
ejpam-2312	248	16	a	a	PRON
ejpam-2312	248	17	)	)	PUNCT
ejpam-2312	248	18	in	in	ADP
ejpam-2312	248	19	ss(x)a	ss(x)a	PROPN
ejpam-2312	248	20	such	such	ADJ
ejpam-2312	248	21	that	that	SCONJ
ejpam-2312	248	22	{	{	PUNCT
ejpam-2312	248	23	ef	ef	NOUN
ejpam-2312	248	24	}	}	PUNCT
ejpam-2312	248	25	⊆̃(h	⊆̃(h	PROPN
ejpam-2312	248	26	,	,	PUNCT
ejpam-2312	248	27	a	a	PRON
ejpam-2312	248	28	)	)	PUNCT
ejpam-2312	248	29	and	and	CCONJ
ejpam-2312	248	30	cls({ef	cls({ef	NOUN
ejpam-2312	248	31	}	}	PUNCT
ejpam-2312	248	32	)	)	PUNCT
ejpam-2312	248	33	˜6⊆(g	˜6⊆(g	NOUN
ejpam-2312	248	34	,	,	PUNCT
ejpam-2312	248	35	a	a	PRON
ejpam-2312	248	36	)	)	PUNCT
ejpam-2312	248	37	.	.	PUNCT
ejpam-2312	249	1	this	this	PRON
ejpam-2312	249	2	follows	follow	VERB
ejpam-2312	249	3	that	that	DET
ejpam-2312	249	4	cls({ef	cls({ef	NOUN
ejpam-2312	249	5	}	}	PUNCT
ejpam-2312	249	6	)	)	PUNCT
ejpam-2312	249	7	∩̃(h	∩̃(h	PROPN
ejpam-2312	249	8	,	,	PUNCT
ejpam-2312	249	9	a)c	a)c	X
ejpam-2312	249	10	˜6	˜6	PROPN
ejpam-2312	249	11	=	=	SYM
ejpam-2312	249	12	φ̃.	φ̃.	NOUN
ejpam-2312	249	13	let	let	VERB
ejpam-2312	249	14	us	we	PRON
ejpam-2312	249	15	take	take	VERB
ejpam-2312	249	16	a	a	DET
ejpam-2312	249	17	soft	soft	ADJ
ejpam-2312	249	18	point	point	NOUN
ejpam-2312	249	19	eg	eg	NOUN
ejpam-2312	249	20	in	in	ADP
ejpam-2312	249	21	x̃a	x̃a	PRON
ejpam-2312	249	22	and	and	CCONJ
ejpam-2312	249	23	assume	assume	VERB
ejpam-2312	249	24	that	that	SCONJ
ejpam-2312	249	25	eg∈̃(cls({ef	eg∈̃(cls({ef	NOUN
ejpam-2312	249	26	}	}	PUNCT
ejpam-2312	249	27	)	)	PUNCT
ejpam-2312	249	28	∩̃(h	∩̃(h	NOUN
ejpam-2312	249	29	,	,	PUNCT
ejpam-2312	249	30	a)c	a)c	PUNCT
ejpam-2312	249	31	)	)	PUNCT
ejpam-2312	249	32	.	.	PUNCT
ejpam-2312	250	1	here	here	ADV
ejpam-2312	250	2	we	we	PRON
ejpam-2312	250	3	have	have	AUX
ejpam-2312	250	4	ef	ef	ADP
ejpam-2312	250	5	∈̃cls({eg	∈̃cls({eg	NOUN
ejpam-2312	250	6	}	}	PUNCT
ejpam-2312	250	7	)	)	PUNCT
ejpam-2312	250	8	.	.	PUNCT
ejpam-2312	251	1	this	this	PRON
ejpam-2312	251	2	implies	imply	VERB
ejpam-2312	251	3	that	that	SCONJ
ejpam-2312	251	4	cls({eg})⊆̃(h	cls({eg})⊆̃(h	ADV
ejpam-2312	251	5	,	,	PUNCT
ejpam-2312	251	6	a)c	a)c	ADV
ejpam-2312	251	7	and	and	CCONJ
ejpam-2312	251	8	ef	ef	PROPN
ejpam-2312	251	9	/̃∈(h	/̃∈(h	PROPN
ejpam-2312	251	10	,	,	PUNCT
ejpam-2312	251	11	a	a	PRON
ejpam-2312	251	12	)	)	PUNCT
ejpam-2312	251	13	.	.	PUNCT
ejpam-2312	252	1	a	a	DET
ejpam-2312	252	2	contradiction	contradiction	NOUN
ejpam-2312	252	3	.	.	PUNCT
ejpam-2312	253	1	hence	hence	ADV
ejpam-2312	253	2	the	the	DET
ejpam-2312	253	3	proof	proof	NOUN
ejpam-2312	253	4	.	.	PUNCT
ejpam-2312	254	1	theorem	theorem	VERB
ejpam-2312	254	2	7	7	NUM
ejpam-2312	254	3	.	.	PUNCT
ejpam-2312	255	1	any	any	DET
ejpam-2312	255	2	soft	soft	ADJ
ejpam-2312	255	3	semi	semi	ADJ
ejpam-2312	255	4	-	-	ADJ
ejpam-2312	255	5	t1	t1	ADJ
ejpam-2312	255	6	space	space	NOUN
ejpam-2312	255	7	is	be	AUX
ejpam-2312	255	8	soft	soft	ADJ
ejpam-2312	255	9	semi	semi	ADJ
ejpam-2312	255	10	-	-	ADJ
ejpam-2312	255	11	symmetric	symmetric	ADJ
ejpam-2312	255	12	in	in	ADP
ejpam-2312	255	13	a	a	DET
ejpam-2312	255	14	soft	soft	ADJ
ejpam-2312	255	15	topological	topological	ADJ
ejpam-2312	255	16	space	space	NOUN
ejpam-2312	255	17	(	(	PUNCT
ejpam-2312	255	18	x	x	X
ejpam-2312	255	19	,	,	PUNCT
ejpam-2312	255	20	τ	τ	PROPN
ejpam-2312	255	21	,	,	PUNCT
ejpam-2312	255	22	a	a	PRON
ejpam-2312	255	23	)	)	PUNCT
ejpam-2312	255	24	over	over	ADP
ejpam-2312	255	25	x.	x.	NOUN
ejpam-2312	255	26	proof	proof	NOUN
ejpam-2312	255	27	.	.	PUNCT
ejpam-2312	256	1	let	let	VERB
ejpam-2312	256	2	(	(	PUNCT
ejpam-2312	256	3	x	x	X
ejpam-2312	256	4	,	,	PUNCT
ejpam-2312	256	5	τ	τ	PROPN
ejpam-2312	256	6	,	,	PUNCT
ejpam-2312	256	7	a	a	PRON
ejpam-2312	256	8	)	)	PUNCT
ejpam-2312	256	9	be	be	AUX
ejpam-2312	256	10	soft	soft	ADJ
ejpam-2312	256	11	semi	semi	ADJ
ejpam-2312	256	12	-	-	ADJ
ejpam-2312	256	13	t1	t1	ADJ
ejpam-2312	256	14	space	space	NOUN
ejpam-2312	256	15	.	.	PUNCT
ejpam-2312	257	1	then	then	ADV
ejpam-2312	257	2	theorem	theorem	VERB
ejpam-2312	257	3	2	2	NUM
ejpam-2312	257	4	follows	follow	VERB
ejpam-2312	257	5	that	that	SCONJ
ejpam-2312	257	6	{	{	PUNCT
ejpam-2312	257	7	ef	ef	PROPN
ejpam-2312	257	8	}	}	PUNCT
ejpam-2312	257	9	is	be	AUX
ejpam-2312	257	10	soft	soft	ADJ
ejpam-2312	257	11	semi	semi	ADJ
ejpam-2312	257	12	-	-	ADJ
ejpam-2312	257	13	closed	closed	ADJ
ejpam-2312	257	14	,	,	PUNCT
ejpam-2312	257	15	for	for	ADP
ejpam-2312	257	16	any	any	DET
ejpam-2312	257	17	soft	soft	ADJ
ejpam-2312	257	18	point	point	NOUN
ejpam-2312	257	19	ef	ef	NOUN
ejpam-2312	257	20	in	in	ADP
ejpam-2312	257	21	x̃a	x̃a	PRON
ejpam-2312	257	22	.	.	PUNCT
ejpam-2312	258	1	thus	thus	ADV
ejpam-2312	258	2	{	{	PUNCT
ejpam-2312	258	3	ef	ef	PROPN
ejpam-2312	258	4	}	}	PUNCT
ejpam-2312	258	5	is	be	AUX
ejpam-2312	258	6	soft	soft	ADJ
ejpam-2312	258	7	sg	sg	NOUN
ejpam-2312	258	8	-	-	PUNCT
ejpam-2312	258	9	closed	closed	ADJ
ejpam-2312	258	10	,	,	PUNCT
ejpam-2312	258	11	by	by	ADP
ejpam-2312	258	12	proposition	proposition	NOUN
ejpam-2312	258	13	3	3	NUM
ejpam-2312	258	14	.	.	PUNCT
ejpam-2312	258	15	therefore	therefore	ADV
ejpam-2312	258	16	theorem	theorem	VERB
ejpam-2312	258	17	6	6	NUM
ejpam-2312	258	18	implies	imply	VERB
ejpam-2312	258	19	that	that	SCONJ
ejpam-2312	258	20	{	{	PUNCT
ejpam-2312	258	21	ef	ef	PROPN
ejpam-2312	258	22	}	}	PUNCT
ejpam-2312	258	23	is	be	AUX
ejpam-2312	258	24	soft	soft	ADJ
ejpam-2312	258	25	semi	semi	ADJ
ejpam-2312	258	26	-	-	ADJ
ejpam-2312	258	27	symmetric	symmetric	ADJ
ejpam-2312	258	28	.	.	PUNCT
ejpam-2312	259	1	this	this	PRON
ejpam-2312	259	2	completes	complete	VERB
ejpam-2312	259	3	the	the	DET
ejpam-2312	259	4	proof	proof	NOUN
ejpam-2312	259	5	.	.	PUNCT
ejpam-2312	260	1	theorem	theorem	ADJ
ejpam-2312	260	2	8	8	NUM
ejpam-2312	260	3	.	.	PUNCT
ejpam-2312	261	1	let	let	VERB
ejpam-2312	261	2	(	(	PUNCT
ejpam-2312	261	3	x	x	X
ejpam-2312	261	4	,	,	PUNCT
ejpam-2312	261	5	τ	τ	PROPN
ejpam-2312	261	6	,	,	PUNCT
ejpam-2312	261	7	a	a	PRON
ejpam-2312	261	8	)	)	PUNCT
ejpam-2312	261	9	be	be	AUX
ejpam-2312	261	10	a	a	DET
ejpam-2312	261	11	soft	soft	ADJ
ejpam-2312	261	12	topological	topological	ADJ
ejpam-2312	261	13	space	space	NOUN
ejpam-2312	261	14	over	over	ADP
ejpam-2312	261	15	x.	x.	NOUN
ejpam-2312	261	16	then	then	ADV
ejpam-2312	261	17	(	(	PUNCT
ejpam-2312	261	18	x	x	X
ejpam-2312	261	19	,	,	PUNCT
ejpam-2312	261	20	τ	τ	PROPN
ejpam-2312	261	21	,	,	PUNCT
ejpam-2312	261	22	a	a	PRON
ejpam-2312	261	23	)	)	PUNCT
ejpam-2312	261	24	is	be	AUX
ejpam-2312	261	25	a	a	DET
ejpam-2312	261	26	soft	soft	ADJ
ejpam-2312	261	27	semi	semi	ADJ
ejpam-2312	261	28	-	-	ADJ
ejpam-2312	261	29	symmetric	symmetric	ADJ
ejpam-2312	261	30	and	and	CCONJ
ejpam-2312	261	31	soft	soft	ADJ
ejpam-2312	261	32	semi	semi	ADJ
ejpam-2312	261	33	-	-	ADJ
ejpam-2312	261	34	t0	t0	ADJ
ejpam-2312	261	35	space	space	NOUN
ejpam-2312	261	36	if	if	SCONJ
ejpam-2312	261	37	and	and	CCONJ
ejpam-2312	261	38	only	only	ADV
ejpam-2312	261	39	if	if	SCONJ
ejpam-2312	261	40	it	it	PRON
ejpam-2312	261	41	is	be	AUX
ejpam-2312	261	42	soft	soft	ADJ
ejpam-2312	261	43	semi	semi	ADJ
ejpam-2312	261	44	-	-	ADJ
ejpam-2312	261	45	t1	t1	ADJ
ejpam-2312	261	46	.	.	PUNCT
ejpam-2312	262	1	proof	proof	NOUN
ejpam-2312	262	2	.	.	PUNCT
ejpam-2312	263	1	(	(	PUNCT
ejpam-2312	263	2	⇒	⇒	PROPN
ejpam-2312	263	3	)	)	PUNCT
ejpam-2312	263	4	suppose	suppose	VERB
ejpam-2312	263	5	(	(	PUNCT
ejpam-2312	263	6	x	x	X
ejpam-2312	263	7	,	,	PUNCT
ejpam-2312	263	8	τ	τ	PROPN
ejpam-2312	263	9	,	,	PUNCT
ejpam-2312	263	10	a	a	PRON
ejpam-2312	263	11	)	)	PUNCT
ejpam-2312	263	12	is	be	AUX
ejpam-2312	263	13	soft	soft	ADJ
ejpam-2312	263	14	semi	semi	ADJ
ejpam-2312	263	15	-	-	ADJ
ejpam-2312	263	16	t0	t0	ADJ
ejpam-2312	263	17	space	space	NOUN
ejpam-2312	263	18	.	.	PUNCT
ejpam-2312	264	1	then	then	ADV
ejpam-2312	264	2	for	for	ADP
ejpam-2312	264	3	any	any	DET
ejpam-2312	264	4	two	two	NUM
ejpam-2312	264	5	distinct	distinct	ADJ
ejpam-2312	264	6	soft	soft	ADJ
ejpam-2312	264	7	point	point	NOUN
ejpam-2312	264	8	ef	ef	NOUN
ejpam-2312	264	9	and	and	CCONJ
ejpam-2312	264	10	eg	eg	NOUN
ejpam-2312	264	11	in	in	ADP
ejpam-2312	264	12	x̃a	x̃a	NUM
ejpam-2312	264	13	,	,	PUNCT
ejpam-2312	264	14	there	there	PRON
ejpam-2312	264	15	exists	exist	VERB
ejpam-2312	264	16	soft	soft	ADJ
ejpam-2312	264	17	semi	semi	ADJ
ejpam-2312	264	18	-	-	ADJ
ejpam-2312	264	19	open	open	ADJ
ejpam-2312	264	20	set	set	NOUN
ejpam-2312	264	21	(	(	PUNCT
ejpam-2312	264	22	h	h	NOUN
ejpam-2312	264	23	,	,	PUNCT
ejpam-2312	264	24	a	a	PRON
ejpam-2312	264	25	)	)	PUNCT
ejpam-2312	264	26	in	in	ADP
ejpam-2312	264	27	ss(x)a	ss(x)a	PROPN
ejpam-2312	264	28	such	such	ADJ
ejpam-2312	264	29	that	that	SCONJ
ejpam-2312	264	30	ef	ef	PROPN
ejpam-2312	264	31	∈̃(h	∈̃(h	NOUN
ejpam-2312	264	32	,	,	PUNCT
ejpam-2312	264	33	a)⊆̃({eg})c	a)⊆̃({eg})c	PROPN
ejpam-2312	264	34	.	.	PROPN
ejpam-2312	265	1	this	this	PRON
ejpam-2312	265	2	implies	imply	VERB
ejpam-2312	265	3	that	that	SCONJ
ejpam-2312	265	4	ef	ef	VERB
ejpam-2312	265	5	/̃∈cls({eg	/̃∈cls({eg	PUNCT
ejpam-2312	265	6	}	}	PUNCT
ejpam-2312	265	7	)	)	PUNCT
ejpam-2312	265	8	.	.	PUNCT
ejpam-2312	266	1	therefore	therefore	ADV
ejpam-2312	266	2	,	,	PUNCT
ejpam-2312	266	3	eg	eg	NOUN
ejpam-2312	266	4	/∈	/∈	PUNCT
ejpam-2312	266	5	cls({ef	cls({ef	NOUN
ejpam-2312	266	6	}	}	PUNCT
ejpam-2312	266	7	)	)	PUNCT
ejpam-2312	266	8	.	.	PUNCT
ejpam-2312	267	1	this	this	PRON
ejpam-2312	267	2	follows	follow	VERB
ejpam-2312	267	3	that	that	SCONJ
ejpam-2312	267	4	there	there	PRON
ejpam-2312	267	5	exists	exist	VERB
ejpam-2312	267	6	a	a	DET
ejpam-2312	267	7	soft	soft	ADJ
ejpam-2312	267	8	semi	semi	ADJ
ejpam-2312	267	9	-	-	ADJ
ejpam-2312	267	10	open	open	ADJ
ejpam-2312	267	11	set	set	NOUN
ejpam-2312	267	12	(	(	PUNCT
ejpam-2312	267	13	k	k	NOUN
ejpam-2312	267	14	,	,	PUNCT
ejpam-2312	267	15	a	a	PRON
ejpam-2312	267	16	)	)	PUNCT
ejpam-2312	267	17	such	such	ADJ
ejpam-2312	267	18	that	that	SCONJ
ejpam-2312	267	19	eg∈̃(k	eg∈̃(k	NOUN
ejpam-2312	267	20	,	,	PUNCT
ejpam-2312	267	21	a)⊆̃({ef	a)⊆̃({ef	X
ejpam-2312	267	22	}	}	PUNCT
ejpam-2312	267	23	)	)	PUNCT
ejpam-2312	268	1	c.	c.	NOUN
ejpam-2312	268	2	therefore	therefore	ADV
ejpam-2312	268	3	(	(	PUNCT
ejpam-2312	268	4	x	x	X
ejpam-2312	268	5	,	,	PUNCT
ejpam-2312	268	6	τ	τ	PROPN
ejpam-2312	268	7	,	,	PUNCT
ejpam-2312	268	8	a	a	PRON
ejpam-2312	268	9	)	)	PUNCT
ejpam-2312	268	10	is	be	AUX
ejpam-2312	268	11	soft	soft	ADJ
ejpam-2312	268	12	semi	semi	ADJ
ejpam-2312	268	13	-	-	ADJ
ejpam-2312	268	14	t1	t1	ADJ
ejpam-2312	268	15	space	space	NOUN
ejpam-2312	268	16	.	.	PUNCT
ejpam-2312	269	1	(	(	PUNCT
ejpam-2312	269	2	⇐	⇐	NOUN
ejpam-2312	269	3	)	)	PUNCT
ejpam-2312	269	4	using	use	VERB
ejpam-2312	269	5	theorem	theorem	NOUN
ejpam-2312	269	6	6	6	NUM
ejpam-2312	269	7	and	and	CCONJ
ejpam-2312	269	8	remark	remark	NOUN
ejpam-2312	269	9	3(1	3(1	NUM
ejpam-2312	269	10	)	)	PUNCT
ejpam-2312	269	11	,	,	PUNCT
ejpam-2312	269	12	proof	proof	NOUN
ejpam-2312	269	13	follows	follow	VERB
ejpam-2312	269	14	directly	directly	ADV
ejpam-2312	269	15	.	.	PUNCT
ejpam-2312	270	1	hence	hence	ADV
ejpam-2312	270	2	the	the	DET
ejpam-2312	270	3	proof	proof	NOUN
ejpam-2312	270	4	.	.	PUNCT
ejpam-2312	271	1	the	the	DET
ejpam-2312	271	2	following	follow	VERB
ejpam-2312	271	3	theorem	theorem	NOUN
ejpam-2312	271	4	follows	follow	VERB
ejpam-2312	271	5	from	from	ADP
ejpam-2312	271	6	remark	remark	NOUN
ejpam-2312	271	7	3(1	3(1	NUM
ejpam-2312	271	8	)	)	PUNCT
ejpam-2312	271	9	,	,	PUNCT
ejpam-2312	271	10	theorem	theorem	VERB
ejpam-2312	271	11	5	5	NUM
ejpam-2312	271	12	,	,	PUNCT
ejpam-2312	271	13	proposition	proposition	NOUN
ejpam-2312	271	14	2	2	NUM
ejpam-2312	271	15	and	and	CCONJ
ejpam-2312	271	16	theorem	theorem	VERB
ejpam-2312	271	17	8	8	NUM
ejpam-2312	271	18	.	.	PUNCT
ejpam-2312	272	1	s.	s.	PROPN
ejpam-2312	272	2	hussain	hussain	PROPN
ejpam-2312	272	3	/	/	SYM
ejpam-2312	272	4	eur	eur	PROPN
ejpam-2312	272	5	.	.	PUNCT
ejpam-2312	273	1	j.	j.	PROPN
ejpam-2312	273	2	pure	pure	PROPN
ejpam-2312	273	3	appl	appl	PROPN
ejpam-2312	273	4	.	.	PROPN
ejpam-2312	273	5	math	math	PROPN
ejpam-2312	273	6	,	,	PUNCT
ejpam-2312	273	7	10	10	NUM
ejpam-2312	273	8	(	(	PUNCT
ejpam-2312	273	9	2	2	NUM
ejpam-2312	273	10	)	)	PUNCT
ejpam-2312	273	11	(	(	PUNCT
ejpam-2312	273	12	2017	2017	NUM
ejpam-2312	273	13	)	)	PUNCT
ejpam-2312	273	14	,	,	PUNCT
ejpam-2312	273	15	199	199	NUM
ejpam-2312	273	16	-	-	SYM
ejpam-2312	273	17	210	210	NUM
ejpam-2312	273	18	207	207	NUM
ejpam-2312	273	19	theorem	theorem	NOUN
ejpam-2312	273	20	9	9	NUM
ejpam-2312	273	21	.	.	PUNCT
ejpam-2312	274	1	if	if	SCONJ
ejpam-2312	274	2	a	a	DET
ejpam-2312	274	3	soft	soft	ADJ
ejpam-2312	274	4	topological	topological	ADJ
ejpam-2312	274	5	space	space	NOUN
ejpam-2312	274	6	(	(	PUNCT
ejpam-2312	274	7	x	x	X
ejpam-2312	274	8	,	,	PUNCT
ejpam-2312	274	9	τ	τ	PROPN
ejpam-2312	274	10	,	,	PUNCT
ejpam-2312	274	11	a	a	PRON
ejpam-2312	274	12	)	)	PUNCT
ejpam-2312	274	13	over	over	ADV
ejpam-2312	274	14	x	x	VERB
ejpam-2312	274	15	is	be	AUX
ejpam-2312	274	16	soft	soft	ADJ
ejpam-2312	274	17	semi	semi	ADJ
ejpam-2312	274	18	-	-	ADJ
ejpam-2312	274	19	symmetric	symmetric	ADJ
ejpam-2312	274	20	,	,	PUNCT
ejpam-2312	274	21	then	then	ADV
ejpam-2312	274	22	we	we	PRON
ejpam-2312	274	23	have	have	VERB
ejpam-2312	274	24	:	:	PUNCT
ejpam-2312	274	25	(	(	PUNCT
ejpam-2312	274	26	x	x	X
ejpam-2312	274	27	,	,	PUNCT
ejpam-2312	274	28	τ	τ	PROPN
ejpam-2312	274	29	,	,	PUNCT
ejpam-2312	274	30	a	a	PRON
ejpam-2312	274	31	)	)	PUNCT
ejpam-2312	274	32	is	be	AUX
ejpam-2312	274	33	soft	soft	ADJ
ejpam-2312	274	34	semi	semi	ADJ
ejpam-2312	274	35	-	-	ADJ
ejpam-2312	274	36	t0	t0	ADJ
ejpam-2312	274	37	space	space	NOUN
ejpam-2312	274	38	⇔	⇔	X
ejpam-2312	274	39	(	(	PUNCT
ejpam-2312	274	40	x	x	PROPN
ejpam-2312	274	41	,	,	PUNCT
ejpam-2312	274	42	τ	τ	PROPN
ejpam-2312	274	43	,	,	PUNCT
ejpam-2312	274	44	a	a	PRON
ejpam-2312	274	45	)	)	PUNCT
ejpam-2312	274	46	is	be	AUX
ejpam-2312	274	47	soft	soft	ADJ
ejpam-2312	274	48	semi	semi	ADJ
ejpam-2312	274	49	-	-	ADJ
ejpam-2312	274	50	d1	d1	ADJ
ejpam-2312	274	51	space	space	NOUN
ejpam-2312	274	52	⇔	⇔	X
ejpam-2312	274	53	(	(	PUNCT
ejpam-2312	274	54	x	x	PROPN
ejpam-2312	274	55	,	,	PUNCT
ejpam-2312	274	56	τ	τ	PROPN
ejpam-2312	274	57	,	,	PUNCT
ejpam-2312	274	58	a	a	PRON
ejpam-2312	274	59	)	)	PUNCT
ejpam-2312	274	60	is	be	AUX
ejpam-2312	274	61	soft	soft	ADJ
ejpam-2312	274	62	semi	semi	ADJ
ejpam-2312	274	63	-	-	ADJ
ejpam-2312	274	64	t1	t1	ADJ
ejpam-2312	274	65	space	space	NOUN
ejpam-2312	274	66	.	.	PUNCT
ejpam-2312	275	1	4	4	X
ejpam-2312	275	2	.	.	X
ejpam-2312	275	3	properties	property	NOUN
ejpam-2312	275	4	of	of	ADP
ejpam-2312	275	5	soft	soft	ADJ
ejpam-2312	275	6	s	s	NOUN
ejpam-2312	275	7	-	-	ADJ
ejpam-2312	275	8	continuous	continuous	ADJ
ejpam-2312	275	9	functions	function	NOUN
ejpam-2312	275	10	definition	definition	NOUN
ejpam-2312	275	11	23	23	NUM
ejpam-2312	275	12	(	(	PUNCT
ejpam-2312	275	13	[	[	X
ejpam-2312	275	14	10	10	NUM
ejpam-2312	275	15	]	]	NUM
ejpam-2312	275	16	)	)	PUNCT
ejpam-2312	275	17	.	.	PUNCT
ejpam-2312	276	1	let	let	VERB
ejpam-2312	276	2	ss(x)a	ss(x)a	PROPN
ejpam-2312	276	3	and	and	CCONJ
ejpam-2312	276	4	ss(y	ss(y	ADJ
ejpam-2312	276	5	)	)	PUNCT
ejpam-2312	276	6	b	b	X
ejpam-2312	276	7	be	be	AUX
ejpam-2312	276	8	two	two	NUM
ejpam-2312	276	9	families	family	NOUN
ejpam-2312	276	10	of	of	ADP
ejpam-2312	276	11	soft	soft	ADJ
ejpam-2312	276	12	sets	set	NOUN
ejpam-2312	276	13	.	.	PUNCT
ejpam-2312	277	1	u	u	NOUN
ejpam-2312	277	2	:	:	PUNCT
ejpam-2312	277	3	x	x	X
ejpam-2312	277	4	→	→	SYM
ejpam-2312	277	5	y	y	PROPN
ejpam-2312	277	6	and	and	CCONJ
ejpam-2312	277	7	p	p	X
ejpam-2312	277	8	:	:	PUNCT
ejpam-2312	277	9	a→	a→	PROPN
ejpam-2312	277	10	b	b	NOUN
ejpam-2312	277	11	be	be	AUX
ejpam-2312	277	12	mappings	mapping	NOUN
ejpam-2312	277	13	.	.	PUNCT
ejpam-2312	278	1	then	then	ADV
ejpam-2312	278	2	the	the	DET
ejpam-2312	278	3	image	image	NOUN
ejpam-2312	278	4	and	and	CCONJ
ejpam-2312	278	5	the	the	DET
ejpam-2312	278	6	inverse	inverse	ADJ
ejpam-2312	278	7	image	image	NOUN
ejpam-2312	278	8	of	of	ADP
ejpam-2312	278	9	a	a	DET
ejpam-2312	278	10	function	function	NOUN
ejpam-2312	278	11	fpu	fpu	NOUN
ejpam-2312	278	12	:	:	PUNCT
ejpam-2312	278	13	ss(x)a	ss(x)a	PROPN
ejpam-2312	278	14	→	→	SYM
ejpam-2312	278	15	ss(y	ss(y	NUM
ejpam-2312	278	16	)	)	PUNCT
ejpam-2312	278	17	b	b	NOUN
ejpam-2312	278	18	is	be	AUX
ejpam-2312	278	19	defined	define	VERB
ejpam-2312	278	20	as	as	SCONJ
ejpam-2312	278	21	follows	follow	VERB
ejpam-2312	278	22	:	:	PUNCT
ejpam-2312	278	23	(	(	PUNCT
ejpam-2312	278	24	1	1	X
ejpam-2312	278	25	)	)	PUNCT
ejpam-2312	278	26	let	let	VERB
ejpam-2312	278	27	(	(	PUNCT
ejpam-2312	278	28	f	f	X
ejpam-2312	278	29	,	,	PUNCT
ejpam-2312	278	30	a	a	PRON
ejpam-2312	278	31	)	)	PUNCT
ejpam-2312	278	32	be	be	AUX
ejpam-2312	278	33	soft	soft	ADJ
ejpam-2312	278	34	set	set	NOUN
ejpam-2312	278	35	in	in	ADP
ejpam-2312	278	36	ss(x)a	ss(x)a	PROPN
ejpam-2312	278	37	.	.	PUNCT
ejpam-2312	279	1	the	the	DET
ejpam-2312	279	2	image	image	NOUN
ejpam-2312	279	3	of	of	ADP
ejpam-2312	279	4	(	(	PUNCT
ejpam-2312	279	5	f	f	X
ejpam-2312	279	6	,	,	PUNCT
ejpam-2312	279	7	a	a	PRON
ejpam-2312	279	8	)	)	PUNCT
ejpam-2312	279	9	under	under	ADP
ejpam-2312	279	10	fpu	fpu	PROPN
ejpam-2312	279	11	,	,	PUNCT
ejpam-2312	279	12	written	write	VERB
ejpam-2312	279	13	as	as	ADP
ejpam-2312	279	14	fpu(f	fpu(f	PROPN
ejpam-2312	279	15	,	,	PUNCT
ejpam-2312	279	16	a	a	PRON
ejpam-2312	279	17	)	)	PUNCT
ejpam-2312	279	18	=	=	SYM
ejpam-2312	279	19	(	(	PUNCT
ejpam-2312	279	20	fpu(f	fpu(f	PROPN
ejpam-2312	279	21	)	)	PUNCT
ejpam-2312	279	22	,	,	PUNCT
ejpam-2312	279	23	p(a	p(a	PROPN
ejpam-2312	279	24	)	)	PUNCT
ejpam-2312	279	25	)	)	PUNCT
ejpam-2312	279	26	,	,	PUNCT
ejpam-2312	279	27	is	be	AUX
ejpam-2312	279	28	a	a	DET
ejpam-2312	279	29	soft	soft	ADJ
ejpam-2312	279	30	set	set	NOUN
ejpam-2312	279	31	in	in	ADP
ejpam-2312	279	32	ss(y	ss(y	ADJ
ejpam-2312	279	33	)	)	PUNCT
ejpam-2312	279	34	b	b	X
ejpam-2312	279	35	such	such	ADJ
ejpam-2312	279	36	that	that	PRON
ejpam-2312	279	37	fpu(f	fpu(f	PROPN
ejpam-2312	279	38	)	)	PUNCT
ejpam-2312	279	39	(	(	PUNCT
ejpam-2312	279	40	y	y	X
ejpam-2312	279	41	)	)	PUNCT
ejpam-2312	279	42	=	=	SYM
ejpam-2312	280	1	{	{	PUNCT
ejpam-2312	280	2	⋃	⋃	NOUN
ejpam-2312	280	3	x∈p−1(y)∩a	x∈p−1(y)∩a	NUM
ejpam-2312	280	4	u(f	u(f	PROPN
ejpam-2312	280	5	(	(	PUNCT
ejpam-2312	280	6	x	x	NOUN
ejpam-2312	280	7	)	)	PUNCT
ejpam-2312	280	8	)	)	PUNCT
ejpam-2312	280	9	,	,	PUNCT
ejpam-2312	280	10	p−1(y	p−1(y	PROPN
ejpam-2312	280	11	)	)	PUNCT
ejpam-2312	281	1	∩a	∩a	PROPN
ejpam-2312	281	2	6=	6=	PROPN
ejpam-2312	281	3	φ	φ	PROPN
ejpam-2312	281	4	φ	φ	PROPN
ejpam-2312	281	5	,	,	PUNCT
ejpam-2312	281	6	otherwise	otherwise	ADV
ejpam-2312	281	7	for	for	ADP
ejpam-2312	281	8	all	all	DET
ejpam-2312	281	9	y	y	PROPN
ejpam-2312	281	10	∈	∈	PROPN
ejpam-2312	281	11	b.	b.	PROPN
ejpam-2312	281	12	(	(	PUNCT
ejpam-2312	281	13	2	2	X
ejpam-2312	281	14	)	)	PUNCT
ejpam-2312	281	15	let	let	VERB
ejpam-2312	281	16	(	(	PUNCT
ejpam-2312	281	17	g	g	NOUN
ejpam-2312	281	18	,	,	PUNCT
ejpam-2312	281	19	b	b	NOUN
ejpam-2312	281	20	)	)	PUNCT
ejpam-2312	281	21	be	be	AUX
ejpam-2312	281	22	soft	soft	ADJ
ejpam-2312	281	23	set	set	NOUN
ejpam-2312	281	24	in	in	ADP
ejpam-2312	281	25	ss(y	ss(y	PROPN
ejpam-2312	281	26	)	)	PUNCT
ejpam-2312	282	1	b.	b.	PROPN
ejpam-2312	282	2	then	then	ADV
ejpam-2312	282	3	the	the	DET
ejpam-2312	282	4	inverse	inverse	ADJ
ejpam-2312	282	5	image	image	NOUN
ejpam-2312	282	6	of	of	ADP
ejpam-2312	282	7	(	(	PUNCT
ejpam-2312	282	8	g	g	PROPN
ejpam-2312	282	9	,	,	PUNCT
ejpam-2312	282	10	b	b	NOUN
ejpam-2312	282	11	)	)	PUNCT
ejpam-2312	282	12	under	under	ADP
ejpam-2312	282	13	fpu	fpu	PROPN
ejpam-2312	282	14	,	,	PUNCT
ejpam-2312	282	15	written	write	VERB
ejpam-2312	282	16	as	as	ADP
ejpam-2312	282	17	f−1pu	f−1pu	NOUN
ejpam-2312	282	18	(	(	PUNCT
ejpam-2312	282	19	g	g	PROPN
ejpam-2312	282	20	,	,	PUNCT
ejpam-2312	282	21	b	b	NOUN
ejpam-2312	282	22	)	)	PUNCT
ejpam-2312	282	23	=	=	SYM
ejpam-2312	282	24	(	(	PUNCT
ejpam-2312	282	25	f−1pu	f−1pu	NOUN
ejpam-2312	282	26	(	(	PUNCT
ejpam-2312	282	27	g	g	NOUN
ejpam-2312	282	28	)	)	PUNCT
ejpam-2312	282	29	,	,	PUNCT
ejpam-2312	282	30	p−1(b	p−1(b	PROPN
ejpam-2312	282	31	)	)	PUNCT
ejpam-2312	282	32	)	)	PUNCT
ejpam-2312	282	33	,	,	PUNCT
ejpam-2312	282	34	is	be	AUX
ejpam-2312	282	35	a	a	DET
ejpam-2312	282	36	soft	soft	ADJ
ejpam-2312	282	37	set	set	NOUN
ejpam-2312	282	38	in	in	ADP
ejpam-2312	282	39	ss(x)a	ss(x)a	PROPN
ejpam-2312	282	40	such	such	ADJ
ejpam-2312	282	41	that	that	DET
ejpam-2312	282	42	f−1pu	f−1pu	NOUN
ejpam-2312	282	43	(	(	PUNCT
ejpam-2312	282	44	g)(x	g)(x	PROPN
ejpam-2312	282	45	)	)	PUNCT
ejpam-2312	282	46	=	=	PRON
ejpam-2312	282	47	{	{	PUNCT
ejpam-2312	282	48	u−1(g(p(x	u−1(g(p(x	PROPN
ejpam-2312	282	49	)	)	PUNCT
ejpam-2312	282	50	)	)	PUNCT
ejpam-2312	282	51	)	)	PUNCT
ejpam-2312	282	52	,	,	PUNCT
ejpam-2312	282	53	p(x	p(x	PROPN
ejpam-2312	282	54	)	)	PUNCT
ejpam-2312	282	55	∈	∈	PROPN
ejpam-2312	282	56	b	b	PROPN
ejpam-2312	282	57	φ	φ	PROPN
ejpam-2312	282	58	,	,	PUNCT
ejpam-2312	282	59	otherwise	otherwise	ADV
ejpam-2312	282	60	for	for	ADP
ejpam-2312	282	61	all	all	DET
ejpam-2312	282	62	x	x	SYM
ejpam-2312	282	63	∈	∈	NOUN
ejpam-2312	282	64	a.	a.	NOUN
ejpam-2312	282	65	the	the	DET
ejpam-2312	282	66	soft	soft	ADJ
ejpam-2312	282	67	function	function	NOUN
ejpam-2312	282	68	fpu	fpu	NOUN
ejpam-2312	282	69	is	be	AUX
ejpam-2312	282	70	called	call	VERB
ejpam-2312	282	71	soft	soft	ADJ
ejpam-2312	282	72	surjective	surjective	ADJ
ejpam-2312	282	73	,	,	PUNCT
ejpam-2312	282	74	if	if	SCONJ
ejpam-2312	282	75	p	p	NOUN
ejpam-2312	282	76	and	and	CCONJ
ejpam-2312	282	77	u	u	NOUN
ejpam-2312	282	78	are	be	AUX
ejpam-2312	282	79	surjective	surjective	ADJ
ejpam-2312	282	80	.	.	PUNCT
ejpam-2312	283	1	the	the	DET
ejpam-2312	283	2	soft	soft	ADJ
ejpam-2312	283	3	function	function	NOUN
ejpam-2312	283	4	fpu	fpu	NOUN
ejpam-2312	283	5	is	be	AUX
ejpam-2312	283	6	called	call	VERB
ejpam-2312	283	7	soft	soft	ADJ
ejpam-2312	283	8	injective	injective	ADJ
ejpam-2312	283	9	,	,	PUNCT
ejpam-2312	283	10	if	if	SCONJ
ejpam-2312	283	11	p	p	NOUN
ejpam-2312	283	12	and	and	CCONJ
ejpam-2312	283	13	u	u	NOUN
ejpam-2312	283	14	are	be	AUX
ejpam-2312	283	15	injective	injective	ADJ
ejpam-2312	283	16	.	.	PUNCT
ejpam-2312	284	1	for	for	ADP
ejpam-2312	284	2	detailed	detailed	ADJ
ejpam-2312	284	3	properties	property	NOUN
ejpam-2312	284	4	of	of	ADP
ejpam-2312	284	5	soft	soft	ADJ
ejpam-2312	284	6	functions	function	NOUN
ejpam-2312	284	7	,	,	PUNCT
ejpam-2312	284	8	we	we	PRON
ejpam-2312	284	9	refer	refer	VERB
ejpam-2312	284	10	to	to	ADP
ejpam-2312	284	11	[	[	X
ejpam-2312	284	12	7	7	NUM
ejpam-2312	284	13	,	,	PUNCT
ejpam-2312	284	14	10	10	NUM
ejpam-2312	284	15	,	,	PUNCT
ejpam-2312	284	16	20	20	NUM
ejpam-2312	284	17	]	]	PUNCT
ejpam-2312	284	18	.	.	PUNCT
ejpam-2312	285	1	definition	definition	NOUN
ejpam-2312	285	2	24	24	NUM
ejpam-2312	285	3	.	.	PUNCT
ejpam-2312	286	1	let	let	VERB
ejpam-2312	286	2	(	(	PUNCT
ejpam-2312	286	3	x	x	X
ejpam-2312	286	4	,	,	PUNCT
ejpam-2312	286	5	τ	τ	PROPN
ejpam-2312	286	6	,	,	PUNCT
ejpam-2312	286	7	a	a	PRON
ejpam-2312	286	8	)	)	PUNCT
ejpam-2312	286	9	and	and	CCONJ
ejpam-2312	286	10	(	(	PUNCT
ejpam-2312	286	11	y	y	PROPN
ejpam-2312	286	12	,	,	PUNCT
ejpam-2312	286	13	τ∗	τ∗	PROPN
ejpam-2312	286	14	,	,	PUNCT
ejpam-2312	286	15	b	b	NOUN
ejpam-2312	286	16	)	)	PUNCT
ejpam-2312	286	17	be	be	AUX
ejpam-2312	286	18	soft	soft	ADJ
ejpam-2312	286	19	topological	topological	ADJ
ejpam-2312	286	20	spaces	space	NOUN
ejpam-2312	286	21	over	over	ADP
ejpam-2312	286	22	x	x	PUNCT
ejpam-2312	286	23	and	and	CCONJ
ejpam-2312	286	24	y	y	PROPN
ejpam-2312	286	25	respectively	respectively	ADV
ejpam-2312	286	26	and	and	CCONJ
ejpam-2312	286	27	u	u	X
ejpam-2312	286	28	:	:	PUNCT
ejpam-2312	287	1	x	x	X
ejpam-2312	287	2	→	→	SYM
ejpam-2312	287	3	y	y	PROPN
ejpam-2312	287	4	and	and	CCONJ
ejpam-2312	287	5	p	p	X
ejpam-2312	287	6	:	:	PUNCT
ejpam-2312	287	7	a	a	DET
ejpam-2312	287	8	→	→	SYM
ejpam-2312	287	9	b	b	NOUN
ejpam-2312	287	10	be	be	AUX
ejpam-2312	287	11	mappings	mapping	NOUN
ejpam-2312	287	12	.	.	PUNCT
ejpam-2312	288	1	then	then	ADV
ejpam-2312	288	2	the	the	DET
ejpam-2312	288	3	soft	soft	ADJ
ejpam-2312	288	4	function	function	NOUN
ejpam-2312	288	5	fpu	fpu	NOUN
ejpam-2312	288	6	:	:	PUNCT
ejpam-2312	288	7	ss(x)a	ss(x)a	PROPN
ejpam-2312	288	8	→	→	SYM
ejpam-2312	288	9	ss(y	ss(y	NUM
ejpam-2312	288	10	)	)	PUNCT
ejpam-2312	288	11	b	b	NOUN
ejpam-2312	288	12	is	be	AUX
ejpam-2312	288	13	soft	soft	ADJ
ejpam-2312	288	14	s	s	NOUN
ejpam-2312	288	15	-	-	ADJ
ejpam-2312	288	16	continuous	continuous	ADJ
ejpam-2312	288	17	,	,	PUNCT
ejpam-2312	288	18	if	if	SCONJ
ejpam-2312	288	19	for	for	ADP
ejpam-2312	288	20	any	any	DET
ejpam-2312	288	21	soft	soft	ADJ
ejpam-2312	288	22	semi	semi	ADJ
ejpam-2312	288	23	-	-	ADJ
ejpam-2312	288	24	open	open	ADJ
ejpam-2312	288	25	set	set	NOUN
ejpam-2312	288	26	(	(	PUNCT
ejpam-2312	288	27	g	g	PROPN
ejpam-2312	288	28	,	,	PUNCT
ejpam-2312	288	29	b	b	NOUN
ejpam-2312	288	30	)	)	PUNCT
ejpam-2312	288	31	in	in	ADP
ejpam-2312	288	32	ss(y	ss(y	NUM
ejpam-2312	288	33	)	)	PUNCT
ejpam-2312	288	34	b	b	NOUN
ejpam-2312	288	35	,	,	PUNCT
ejpam-2312	288	36	f−1pu	f−1pu	NOUN
ejpam-2312	288	37	(	(	PUNCT
ejpam-2312	288	38	g	g	PROPN
ejpam-2312	288	39	,	,	PUNCT
ejpam-2312	288	40	b	b	NOUN
ejpam-2312	288	41	)	)	PUNCT
ejpam-2312	288	42	)	)	PUNCT
ejpam-2312	288	43	is	be	AUX
ejpam-2312	288	44	soft	soft	ADJ
ejpam-2312	288	45	semi	semi	ADJ
ejpam-2312	288	46	-	-	ADJ
ejpam-2312	288	47	open	open	ADJ
ejpam-2312	288	48	in	in	ADP
ejpam-2312	288	49	ss(x)a	ss(x)a	PROPN
ejpam-2312	288	50	.	.	PUNCT
ejpam-2312	288	51	theorem	theorem	PROPN
ejpam-2312	288	52	10	10	NUM
ejpam-2312	288	53	.	.	PUNCT
ejpam-2312	289	1	let	let	VERB
ejpam-2312	289	2	(	(	PUNCT
ejpam-2312	289	3	x	x	X
ejpam-2312	289	4	,	,	PUNCT
ejpam-2312	289	5	τ	τ	PROPN
ejpam-2312	289	6	,	,	PUNCT
ejpam-2312	289	7	a	a	PRON
ejpam-2312	289	8	)	)	PUNCT
ejpam-2312	289	9	and	and	CCONJ
ejpam-2312	289	10	(	(	PUNCT
ejpam-2312	289	11	y	y	PROPN
ejpam-2312	289	12	,	,	PUNCT
ejpam-2312	289	13	τ∗	τ∗	PROPN
ejpam-2312	289	14	,	,	PUNCT
ejpam-2312	289	15	b	b	NOUN
ejpam-2312	289	16	)	)	PUNCT
ejpam-2312	289	17	be	be	AUX
ejpam-2312	289	18	soft	soft	ADJ
ejpam-2312	289	19	topological	topological	ADJ
ejpam-2312	289	20	spaces	space	NOUN
ejpam-2312	289	21	over	over	ADP
ejpam-2312	289	22	x	x	PUNCT
ejpam-2312	289	23	and	and	CCONJ
ejpam-2312	289	24	y	y	PROPN
ejpam-2312	289	25	respectively	respectively	ADV
ejpam-2312	289	26	.	.	PUNCT
ejpam-2312	290	1	if	if	SCONJ
ejpam-2312	290	2	a	a	DET
ejpam-2312	290	3	soft	soft	ADJ
ejpam-2312	290	4	function	function	NOUN
ejpam-2312	290	5	fpu	fpu	NOUN
ejpam-2312	290	6	:	:	PUNCT
ejpam-2312	290	7	ss(x)a	ss(x)a	PROPN
ejpam-2312	290	8	→	→	SYM
ejpam-2312	290	9	ss(y	ss(y	NUM
ejpam-2312	290	10	)	)	PUNCT
ejpam-2312	290	11	b	b	NOUN
ejpam-2312	290	12	is	be	AUX
ejpam-2312	290	13	soft	soft	ADJ
ejpam-2312	290	14	surjective	surjective	ADJ
ejpam-2312	290	15	soft	soft	ADJ
ejpam-2312	290	16	s	s	NOUN
ejpam-2312	290	17	-	-	ADJ
ejpam-2312	290	18	continuous	continuous	ADJ
ejpam-2312	290	19	,	,	PUNCT
ejpam-2312	290	20	then	then	ADV
ejpam-2312	290	21	for	for	ADP
ejpam-2312	290	22	each	each	DET
ejpam-2312	290	23	soft	soft	ADJ
ejpam-2312	290	24	semi	semi	ADJ
ejpam-2312	290	25	-	-	ADJ
ejpam-2312	290	26	d	d	ADJ
ejpam-2312	290	27	set	set	NOUN
ejpam-2312	290	28	(	(	PUNCT
ejpam-2312	290	29	g	g	NOUN
ejpam-2312	290	30	,	,	PUNCT
ejpam-2312	290	31	b	b	NOUN
ejpam-2312	290	32	)	)	PUNCT
ejpam-2312	290	33	in	in	ADP
ejpam-2312	290	34	ss(y	ss(y	NUM
ejpam-2312	290	35	)	)	PUNCT
ejpam-2312	290	36	b	b	NOUN
ejpam-2312	290	37	,	,	PUNCT
ejpam-2312	290	38	f−1pu	f−1pu	NOUN
ejpam-2312	290	39	(	(	PUNCT
ejpam-2312	290	40	g	g	PROPN
ejpam-2312	290	41	,	,	PUNCT
ejpam-2312	290	42	b	b	NOUN
ejpam-2312	290	43	)	)	PUNCT
ejpam-2312	290	44	is	be	AUX
ejpam-2312	290	45	soft	soft	ADJ
ejpam-2312	290	46	semi	semi	ADJ
ejpam-2312	290	47	-	-	ADJ
ejpam-2312	290	48	d	d	ADJ
ejpam-2312	290	49	set	set	NOUN
ejpam-2312	290	50	in	in	ADP
ejpam-2312	290	51	ss(x)a	ss(x)a	PROPN
ejpam-2312	290	52	.	.	PUNCT
ejpam-2312	291	1	proof	proof	NOUN
ejpam-2312	291	2	.	.	PUNCT
ejpam-2312	292	1	suppose	suppose	VERB
ejpam-2312	292	2	that	that	SCONJ
ejpam-2312	292	3	soft	soft	ADJ
ejpam-2312	292	4	function	function	NOUN
ejpam-2312	292	5	fpu	fpu	NOUN
ejpam-2312	292	6	is	be	AUX
ejpam-2312	292	7	soft	soft	ADJ
ejpam-2312	292	8	surjective	surjective	ADJ
ejpam-2312	292	9	soft	soft	ADJ
ejpam-2312	292	10	s	s	NOUN
ejpam-2312	292	11	-	-	ADJ
ejpam-2312	292	12	continuous	continuous	ADJ
ejpam-2312	292	13	and	and	CCONJ
ejpam-2312	292	14	(	(	PUNCT
ejpam-2312	292	15	g	g	PROPN
ejpam-2312	292	16	,	,	PUNCT
ejpam-2312	292	17	b	b	NOUN
ejpam-2312	292	18	)	)	PUNCT
ejpam-2312	292	19	be	be	AUX
ejpam-2312	292	20	soft	soft	ADJ
ejpam-2312	292	21	semi	semi	ADJ
ejpam-2312	292	22	-	-	ADJ
ejpam-2312	292	23	d	d	ADJ
ejpam-2312	292	24	set	set	NOUN
ejpam-2312	292	25	in	in	ADP
ejpam-2312	292	26	ss(y	ss(y	PROPN
ejpam-2312	292	27	)	)	PUNCT
ejpam-2312	293	1	b.	b.	PROPN
ejpam-2312	293	2	then	then	ADV
ejpam-2312	293	3	there	there	PRON
ejpam-2312	293	4	exist	exist	VERB
ejpam-2312	293	5	soft	soft	ADJ
ejpam-2312	293	6	semi	semi	ADJ
ejpam-2312	293	7	-	-	ADJ
ejpam-2312	293	8	open	open	ADJ
ejpam-2312	293	9	sets	set	NOUN
ejpam-2312	293	10	(	(	PUNCT
ejpam-2312	293	11	h	h	NOUN
ejpam-2312	293	12	,	,	PUNCT
ejpam-2312	293	13	b	b	NOUN
ejpam-2312	293	14	)	)	PUNCT
ejpam-2312	293	15	and	and	CCONJ
ejpam-2312	293	16	(	(	PUNCT
ejpam-2312	293	17	k	k	X
ejpam-2312	293	18	,	,	PUNCT
ejpam-2312	293	19	b	b	NOUN
ejpam-2312	293	20	)	)	PUNCT
ejpam-2312	293	21	in	in	ADP
ejpam-2312	293	22	ss(y	ss(y	ADJ
ejpam-2312	293	23	)	)	PUNCT
ejpam-2312	293	24	b	b	X
ejpam-2312	293	25	such	such	ADJ
ejpam-2312	293	26	that	that	PRON
ejpam-2312	293	27	(	(	PUNCT
ejpam-2312	293	28	h	h	NOUN
ejpam-2312	293	29	,	,	PUNCT
ejpam-2312	293	30	b	b	NOUN
ejpam-2312	293	31	)	)	PUNCT
ejpam-2312	293	32	˜6	˜6	NOUN
ejpam-2312	293	33	=	=	SYM
ejpam-2312	293	34	ỹ	ỹ	PROPN
ejpam-2312	293	35	and	and	CCONJ
ejpam-2312	293	36	(	(	PUNCT
ejpam-2312	293	37	g	g	NOUN
ejpam-2312	293	38	,	,	PUNCT
ejpam-2312	293	39	b)=̃(h	b)=̃(h	ADV
ejpam-2312	293	40	,	,	PUNCT
ejpam-2312	293	41	b)\̃(k	b)\̃(k	PROPN
ejpam-2312	293	42	,	,	PUNCT
ejpam-2312	293	43	b	b	NOUN
ejpam-2312	293	44	)	)	PUNCT
ejpam-2312	293	45	.	.	PUNCT
ejpam-2312	294	1	since	since	SCONJ
ejpam-2312	294	2	fpu	fpu	PROPN
ejpam-2312	294	3	is	be	AUX
ejpam-2312	294	4	soft	soft	ADJ
ejpam-2312	294	5	s	s	NOUN
ejpam-2312	294	6	-	-	ADJ
ejpam-2312	294	7	continuous	continuous	ADJ
ejpam-2312	294	8	,	,	PUNCT
ejpam-2312	294	9	implies	imply	VERB
ejpam-2312	294	10	that	that	DET
ejpam-2312	294	11	f−1pu	f−1pu	PROPN
ejpam-2312	294	12	(	(	PUNCT
ejpam-2312	294	13	(	(	PUNCT
ejpam-2312	294	14	h	h	NOUN
ejpam-2312	294	15	,	,	PUNCT
ejpam-2312	294	16	b	b	NOUN
ejpam-2312	294	17	)	)	PUNCT
ejpam-2312	294	18	)	)	PUNCT
ejpam-2312	294	19	and	and	CCONJ
ejpam-2312	294	20	f−1pu	f−1pu	NOUN
ejpam-2312	294	21	(	(	PUNCT
ejpam-2312	294	22	(	(	PUNCT
ejpam-2312	294	23	k	k	X
ejpam-2312	294	24	,	,	PUNCT
ejpam-2312	294	25	b	b	NOUN
ejpam-2312	294	26	)	)	PUNCT
ejpam-2312	294	27	)	)	PUNCT
ejpam-2312	294	28	are	be	AUX
ejpam-2312	294	29	soft	soft	ADJ
ejpam-2312	294	30	semi	semi	ADJ
ejpam-2312	294	31	-	-	ADJ
ejpam-2312	294	32	open	open	ADJ
ejpam-2312	294	33	in	in	ADP
ejpam-2312	294	34	ss(x)b	ss(x)b	PROPN
ejpam-2312	294	35	.	.	PUNCT
ejpam-2312	295	1	as	as	SCONJ
ejpam-2312	295	2	fpu	fpu	PROPN
ejpam-2312	295	3	is	be	AUX
ejpam-2312	295	4	soft	soft	ADJ
ejpam-2312	295	5	surjective	surjective	ADJ
ejpam-2312	295	6	,	,	PUNCT
ejpam-2312	295	7	therefore	therefore	ADV
ejpam-2312	295	8	(	(	PUNCT
ejpam-2312	295	9	h	h	NOUN
ejpam-2312	295	10	,	,	PUNCT
ejpam-2312	295	11	b	b	NOUN
ejpam-2312	295	12	)	)	PUNCT
ejpam-2312	295	13	˜6	˜6	NOUN
ejpam-2312	295	14	=	=	SYM
ejpam-2312	295	15	ỹ	ỹ	PROPN
ejpam-2312	295	16	follows	follow	VERB
ejpam-2312	295	17	f−1pu	f−1pu	NOUN
ejpam-2312	295	18	(	(	PUNCT
ejpam-2312	295	19	(	(	PUNCT
ejpam-2312	295	20	h	h	NOUN
ejpam-2312	295	21	,	,	PUNCT
ejpam-2312	295	22	b	b	NOUN
ejpam-2312	295	23	)	)	PUNCT
ejpam-2312	295	24	)	)	PUNCT
ejpam-2312	296	1	˜6	˜6	NOUN
ejpam-2312	296	2	=	=	SYM
ejpam-2312	296	3	x̃.	x̃.	ADJ
ejpam-2312	296	4	therefore	therefore	ADV
ejpam-2312	296	5	f−1pu	f−1pu	PROPN
ejpam-2312	296	6	(	(	PUNCT
ejpam-2312	296	7	(	(	PUNCT
ejpam-2312	296	8	g	g	NOUN
ejpam-2312	296	9	,	,	PUNCT
ejpam-2312	296	10	b))=̃f−1pu	b))=̃f−1pu	NOUN
ejpam-2312	296	11	(	(	PUNCT
ejpam-2312	296	12	(	(	PUNCT
ejpam-2312	296	13	h	h	NOUN
ejpam-2312	296	14	,	,	PUNCT
ejpam-2312	296	15	b))\̃f−1pu	b))\̃f−1pu	X
ejpam-2312	296	16	(	(	PUNCT
ejpam-2312	296	17	(	(	PUNCT
ejpam-2312	296	18	k	k	X
ejpam-2312	296	19	,	,	PUNCT
ejpam-2312	296	20	b	b	NOUN
ejpam-2312	296	21	)	)	PUNCT
ejpam-2312	296	22	)	)	PUNCT
ejpam-2312	296	23	is	be	AUX
ejpam-2312	296	24	soft	soft	ADJ
ejpam-2312	296	25	semi	semi	ADJ
ejpam-2312	296	26	-	-	ADJ
ejpam-2312	296	27	d	d	ADJ
ejpam-2312	296	28	set	set	NOUN
ejpam-2312	296	29	.	.	PUNCT
ejpam-2312	297	1	hence	hence	ADV
ejpam-2312	297	2	the	the	DET
ejpam-2312	297	3	proof	proof	NOUN
ejpam-2312	297	4	.	.	PUNCT
ejpam-2312	298	1	s.	s.	PROPN
ejpam-2312	298	2	hussain	hussain	PROPN
ejpam-2312	298	3	/	/	SYM
ejpam-2312	298	4	eur	eur	PROPN
ejpam-2312	298	5	.	.	PUNCT
ejpam-2312	299	1	j.	j.	PROPN
ejpam-2312	299	2	pure	pure	PROPN
ejpam-2312	299	3	appl	appl	PROPN
ejpam-2312	299	4	.	.	PROPN
ejpam-2312	299	5	math	math	PROPN
ejpam-2312	299	6	,	,	PUNCT
ejpam-2312	299	7	10	10	NUM
ejpam-2312	299	8	(	(	PUNCT
ejpam-2312	299	9	2	2	NUM
ejpam-2312	299	10	)	)	PUNCT
ejpam-2312	299	11	(	(	PUNCT
ejpam-2312	299	12	2017	2017	NUM
ejpam-2312	299	13	)	)	PUNCT
ejpam-2312	299	14	,	,	PUNCT
ejpam-2312	299	15	199	199	NUM
ejpam-2312	299	16	-	-	SYM
ejpam-2312	299	17	210	210	NUM
ejpam-2312	299	18	208	208	NUM
ejpam-2312	299	19	theorem	theorem	NOUN
ejpam-2312	299	20	11	11	NUM
ejpam-2312	299	21	.	.	PUNCT
ejpam-2312	300	1	let	let	VERB
ejpam-2312	300	2	(	(	PUNCT
ejpam-2312	300	3	x	x	X
ejpam-2312	300	4	,	,	PUNCT
ejpam-2312	300	5	τ	τ	PROPN
ejpam-2312	300	6	,	,	PUNCT
ejpam-2312	300	7	a	a	PRON
ejpam-2312	300	8	)	)	PUNCT
ejpam-2312	300	9	and	and	CCONJ
ejpam-2312	300	10	(	(	PUNCT
ejpam-2312	300	11	y	y	PROPN
ejpam-2312	300	12	,	,	PUNCT
ejpam-2312	300	13	τ∗	τ∗	PROPN
ejpam-2312	300	14	,	,	PUNCT
ejpam-2312	300	15	b	b	NOUN
ejpam-2312	300	16	)	)	PUNCT
ejpam-2312	300	17	be	be	AUX
ejpam-2312	300	18	soft	soft	ADJ
ejpam-2312	300	19	topological	topological	ADJ
ejpam-2312	300	20	spaces	space	NOUN
ejpam-2312	300	21	over	over	ADP
ejpam-2312	300	22	x	x	PUNCT
ejpam-2312	300	23	and	and	CCONJ
ejpam-2312	300	24	y	y	PROPN
ejpam-2312	300	25	respectively	respectively	ADV
ejpam-2312	300	26	.	.	PUNCT
ejpam-2312	301	1	then	then	ADV
ejpam-2312	301	2	the	the	DET
ejpam-2312	301	3	following	follow	VERB
ejpam-2312	301	4	statements	statement	NOUN
ejpam-2312	301	5	are	be	AUX
ejpam-2312	301	6	equivalent	equivalent	ADJ
ejpam-2312	301	7	:	:	PUNCT
ejpam-2312	301	8	(	(	PUNCT
ejpam-2312	301	9	1	1	X
ejpam-2312	301	10	)	)	PUNCT
ejpam-2312	301	11	for	for	ADP
ejpam-2312	301	12	any	any	DET
ejpam-2312	301	13	two	two	NUM
ejpam-2312	301	14	distinct	distinct	ADJ
ejpam-2312	301	15	soft	soft	ADJ
ejpam-2312	301	16	points	point	NOUN
ejpam-2312	301	17	ef	ef	NOUN
ejpam-2312	301	18	,	,	PUNCT
ejpam-2312	301	19	eg	eg	NOUN
ejpam-2312	301	20	in	in	ADP
ejpam-2312	301	21	x̃a	x̃a	NUM
ejpam-2312	301	22	,	,	PUNCT
ejpam-2312	301	23	there	there	PRON
ejpam-2312	301	24	exists	exist	VERB
ejpam-2312	301	25	soft	soft	ADJ
ejpam-2312	301	26	surjective	surjective	ADJ
ejpam-2312	301	27	soft	soft	ADJ
ejpam-2312	301	28	scontinuous	scontinuous	ADJ
ejpam-2312	301	29	function	function	NOUN
ejpam-2312	301	30	fpu	fpu	NOUN
ejpam-2312	301	31	:	:	PUNCT
ejpam-2312	301	32	ss(x)a	ss(x)a	PROPN
ejpam-2312	301	33	→	→	SYM
ejpam-2312	301	34	ss(y	ss(y	NUM
ejpam-2312	301	35	)	)	PUNCT
ejpam-2312	301	36	b	b	NOUN
ejpam-2312	301	37	,	,	PUNCT
ejpam-2312	301	38	where	where	SCONJ
ejpam-2312	301	39	ỹ	ỹ	PROPN
ejpam-2312	301	40	is	be	AUX
ejpam-2312	301	41	soft	soft	ADJ
ejpam-2312	301	42	semi	semi	ADJ
ejpam-2312	301	43	-	-	ADJ
ejpam-2312	301	44	d1	d1	ADJ
ejpam-2312	301	45	space	space	NOUN
ejpam-2312	301	46	with	with	ADP
ejpam-2312	301	47	fpu(ef	fpu(ef	NOUN
ejpam-2312	301	48	)	)	PUNCT
ejpam-2312	302	1	˜6	˜6	NOUN
ejpam-2312	302	2	=	=	SYM
ejpam-2312	302	3	fpu(eg	fpu(eg	X
ejpam-2312	302	4	)	)	PUNCT
ejpam-2312	302	5	.	.	PUNCT
ejpam-2312	303	1	(	(	PUNCT
ejpam-2312	303	2	2	2	X
ejpam-2312	303	3	)	)	PUNCT
ejpam-2312	303	4	x̃	x̃	PROPN
ejpam-2312	303	5	is	be	AUX
ejpam-2312	303	6	soft	soft	ADJ
ejpam-2312	303	7	semi	semi	ADJ
ejpam-2312	303	8	-	-	ADJ
ejpam-2312	303	9	d1	d1	ADJ
ejpam-2312	303	10	space	space	NOUN
ejpam-2312	303	11	.	.	PUNCT
ejpam-2312	304	1	proof	proof	NOUN
ejpam-2312	304	2	.	.	PUNCT
ejpam-2312	305	1	(	(	PUNCT
ejpam-2312	305	2	1	1	X
ejpam-2312	305	3	)	)	PUNCT
ejpam-2312	305	4	⇒	⇒	NOUN
ejpam-2312	305	5	(	(	PUNCT
ejpam-2312	305	6	2	2	NUM
ejpam-2312	305	7	)	)	PUNCT
ejpam-2312	305	8	since	since	SCONJ
ejpam-2312	305	9	for	for	ADP
ejpam-2312	305	10	any	any	DET
ejpam-2312	305	11	two	two	NUM
ejpam-2312	305	12	distinct	distinct	ADJ
ejpam-2312	305	13	soft	soft	ADJ
ejpam-2312	305	14	points	point	NOUN
ejpam-2312	305	15	ef	ef	NOUN
ejpam-2312	305	16	,	,	PUNCT
ejpam-2312	305	17	eg	eg	NOUN
ejpam-2312	305	18	in	in	ADP
ejpam-2312	305	19	x̃a	x̃a	NUM
ejpam-2312	305	20	,	,	PUNCT
ejpam-2312	305	21	there	there	PRON
ejpam-2312	305	22	exists	exist	VERB
ejpam-2312	305	23	soft	soft	ADJ
ejpam-2312	305	24	surjective	surjective	ADJ
ejpam-2312	305	25	soft	soft	ADJ
ejpam-2312	305	26	s	s	NOUN
ejpam-2312	305	27	-	-	ADJ
ejpam-2312	305	28	continuous	continuous	ADJ
ejpam-2312	305	29	fpu	fpu	NOUN
ejpam-2312	305	30	:	:	PUNCT
ejpam-2312	305	31	ss(x)a	ss(x)a	PROPN
ejpam-2312	305	32	→	→	SYM
ejpam-2312	305	33	ss(y	ss(y	NUM
ejpam-2312	305	34	)	)	PUNCT
ejpam-2312	305	35	b	b	NOUN
ejpam-2312	305	36	,	,	PUNCT
ejpam-2312	305	37	where	where	SCONJ
ejpam-2312	305	38	ỹ	ỹ	PROPN
ejpam-2312	305	39	is	be	AUX
ejpam-2312	305	40	soft	soft	ADJ
ejpam-2312	305	41	semi	semi	ADJ
ejpam-2312	305	42	-	-	ADJ
ejpam-2312	305	43	d1	d1	ADJ
ejpam-2312	305	44	space	space	NOUN
ejpam-2312	305	45	with	with	ADP
ejpam-2312	305	46	fpu(ef	fpu(ef	NOUN
ejpam-2312	305	47	)	)	PUNCT
ejpam-2312	306	1	˜6	˜6	NOUN
ejpam-2312	306	2	=	=	SYM
ejpam-2312	306	3	fpu(eg	fpu(eg	X
ejpam-2312	306	4	)	)	PUNCT
ejpam-2312	306	5	.	.	PUNCT
ejpam-2312	307	1	then	then	ADV
ejpam-2312	307	2	there	there	PRON
ejpam-2312	307	3	exist	exist	VERB
ejpam-2312	307	4	soft	soft	ADJ
ejpam-2312	307	5	disjoint	disjoint	NOUN
ejpam-2312	307	6	soft	soft	ADJ
ejpam-2312	307	7	semi	semi	ADJ
ejpam-2312	307	8	-	-	ADJ
ejpam-2312	307	9	d	d	ADJ
ejpam-2312	307	10	sets	set	NOUN
ejpam-2312	307	11	(	(	PUNCT
ejpam-2312	307	12	g	g	NOUN
ejpam-2312	307	13	,	,	PUNCT
ejpam-2312	307	14	b	b	NOUN
ejpam-2312	307	15	)	)	PUNCT
ejpam-2312	307	16	and	and	CCONJ
ejpam-2312	307	17	(	(	PUNCT
ejpam-2312	307	18	h	h	NOUN
ejpam-2312	307	19	,	,	PUNCT
ejpam-2312	307	20	b	b	NOUN
ejpam-2312	307	21	)	)	PUNCT
ejpam-2312	307	22	in	in	ADP
ejpam-2312	307	23	ỹ	ỹ	PROPN
ejpam-2312	307	24	with	with	ADP
ejpam-2312	307	25	fpu(ef	fpu(ef	NOUN
ejpam-2312	307	26	)	)	PUNCT
ejpam-2312	307	27	∈̃(g	∈̃(g	NOUN
ejpam-2312	307	28	,	,	PUNCT
ejpam-2312	307	29	b	b	NOUN
ejpam-2312	307	30	)	)	PUNCT
ejpam-2312	307	31	,	,	PUNCT
ejpam-2312	307	32	fpu(eg)∈̃(h	fpu(eg)∈̃(h	PROPN
ejpam-2312	307	33	,	,	PUNCT
ejpam-2312	307	34	b	b	NOUN
ejpam-2312	307	35	)	)	PUNCT
ejpam-2312	307	36	.	.	PUNCT
ejpam-2312	308	1	as	as	SCONJ
ejpam-2312	308	2	fpu	fpu	PROPN
ejpam-2312	308	3	is	be	AUX
ejpam-2312	308	4	soft	soft	ADJ
ejpam-2312	308	5	surjective	surjective	ADJ
ejpam-2312	308	6	soft	soft	ADJ
ejpam-2312	308	7	s	s	NOUN
ejpam-2312	308	8	-	-	ADJ
ejpam-2312	308	9	continuous	continuous	ADJ
ejpam-2312	308	10	,	,	PUNCT
ejpam-2312	308	11	so	so	ADV
ejpam-2312	308	12	theorem	theorem	ADJ
ejpam-2312	308	13	10	10	NUM
ejpam-2312	308	14	follows	follow	VERB
ejpam-2312	308	15	that	that	DET
ejpam-2312	308	16	f−1pu	f−1pu	NOUN
ejpam-2312	308	17	(	(	PUNCT
ejpam-2312	308	18	(	(	PUNCT
ejpam-2312	308	19	g	g	NOUN
ejpam-2312	308	20	,	,	PUNCT
ejpam-2312	308	21	b	b	NOUN
ejpam-2312	308	22	)	)	PUNCT
ejpam-2312	308	23	)	)	PUNCT
ejpam-2312	308	24	and	and	CCONJ
ejpam-2312	308	25	f−1pu	f−1pu	NOUN
ejpam-2312	308	26	(	(	PUNCT
ejpam-2312	308	27	(	(	PUNCT
ejpam-2312	308	28	h	h	NOUN
ejpam-2312	308	29	,	,	PUNCT
ejpam-2312	308	30	b	b	NOUN
ejpam-2312	308	31	)	)	PUNCT
ejpam-2312	308	32	)	)	PUNCT
ejpam-2312	308	33	are	be	AUX
ejpam-2312	308	34	soft	soft	ADJ
ejpam-2312	308	35	disjoint	disjoint	ADJ
ejpam-2312	308	36	soft	soft	ADJ
ejpam-2312	308	37	semi	semi	ADJ
ejpam-2312	308	38	-	-	ADJ
ejpam-2312	308	39	d	d	ADJ
ejpam-2312	308	40	sets	set	NOUN
ejpam-2312	308	41	in	in	ADP
ejpam-2312	308	42	x̃	x̃	PROPN
ejpam-2312	308	43	with	with	ADP
ejpam-2312	308	44	ef	ef	PROPN
ejpam-2312	308	45	∈̃f−1pu	∈̃f−1pu	PROPN
ejpam-2312	308	46	(	(	PUNCT
ejpam-2312	308	47	(	(	PUNCT
ejpam-2312	308	48	g	g	NOUN
ejpam-2312	308	49	,	,	PUNCT
ejpam-2312	308	50	b	b	NOUN
ejpam-2312	308	51	)	)	PUNCT
ejpam-2312	308	52	)	)	PUNCT
ejpam-2312	308	53	,	,	PUNCT
ejpam-2312	308	54	eg∈̃f−1pu	eg∈̃f−1pu	X
ejpam-2312	308	55	(	(	PUNCT
ejpam-2312	308	56	(	(	PUNCT
ejpam-2312	308	57	h	h	NOUN
ejpam-2312	308	58	,	,	PUNCT
ejpam-2312	308	59	b	b	NOUN
ejpam-2312	308	60	)	)	PUNCT
ejpam-2312	308	61	)	)	PUNCT
ejpam-2312	308	62	.	.	PUNCT
ejpam-2312	309	1	hence	hence	ADV
ejpam-2312	309	2	again	again	ADV
ejpam-2312	309	3	theorem	theorem	VERB
ejpam-2312	309	4	10	10	NUM
ejpam-2312	309	5	implies	imply	VERB
ejpam-2312	309	6	that	that	SCONJ
ejpam-2312	309	7	x̃	x̃	PROPN
ejpam-2312	309	8	is	be	AUX
ejpam-2312	309	9	soft	soft	ADJ
ejpam-2312	309	10	semi	semi	ADJ
ejpam-2312	309	11	-	-	ADJ
ejpam-2312	309	12	d1	d1	ADJ
ejpam-2312	309	13	space	space	NOUN
ejpam-2312	309	14	.	.	PUNCT
ejpam-2312	310	1	(	(	PUNCT
ejpam-2312	310	2	2	2	X
ejpam-2312	310	3	)	)	PUNCT
ejpam-2312	310	4	⇒	⇒	NOUN
ejpam-2312	310	5	(	(	PUNCT
ejpam-2312	310	6	1	1	X
ejpam-2312	310	7	)	)	PUNCT
ejpam-2312	310	8	this	this	PRON
ejpam-2312	310	9	follows	follow	VERB
ejpam-2312	310	10	by	by	ADP
ejpam-2312	310	11	letting	let	VERB
ejpam-2312	310	12	the	the	DET
ejpam-2312	310	13	identity	identity	NOUN
ejpam-2312	310	14	soft	soft	ADJ
ejpam-2312	310	15	function	function	NOUN
ejpam-2312	310	16	,	,	PUNCT
ejpam-2312	310	17	which	which	PRON
ejpam-2312	310	18	fulfills	fulfill	VERB
ejpam-2312	310	19	the	the	DET
ejpam-2312	310	20	desired	desire	VERB
ejpam-2312	310	21	properties	property	NOUN
ejpam-2312	310	22	.	.	PUNCT
ejpam-2312	311	1	hence	hence	ADV
ejpam-2312	311	2	the	the	DET
ejpam-2312	311	3	proof	proof	NOUN
ejpam-2312	311	4	.	.	PUNCT
ejpam-2312	312	1	theorem	theorem	NOUN
ejpam-2312	312	2	12	12	NUM
ejpam-2312	312	3	.	.	PUNCT
ejpam-2312	313	1	let	let	VERB
ejpam-2312	313	2	(	(	PUNCT
ejpam-2312	313	3	x	x	X
ejpam-2312	313	4	,	,	PUNCT
ejpam-2312	313	5	τ	τ	PROPN
ejpam-2312	313	6	,	,	PUNCT
ejpam-2312	313	7	a	a	PRON
ejpam-2312	313	8	)	)	PUNCT
ejpam-2312	313	9	and	and	CCONJ
ejpam-2312	313	10	(	(	PUNCT
ejpam-2312	313	11	y	y	PROPN
ejpam-2312	313	12	,	,	PUNCT
ejpam-2312	313	13	τ∗	τ∗	PROPN
ejpam-2312	313	14	,	,	PUNCT
ejpam-2312	313	15	b	b	NOUN
ejpam-2312	313	16	)	)	PUNCT
ejpam-2312	313	17	be	be	AUX
ejpam-2312	313	18	soft	soft	ADJ
ejpam-2312	313	19	topological	topological	ADJ
ejpam-2312	313	20	spaces	space	NOUN
ejpam-2312	313	21	over	over	ADP
ejpam-2312	313	22	x	x	PUNCT
ejpam-2312	313	23	and	and	CCONJ
ejpam-2312	313	24	y	y	PROPN
ejpam-2312	313	25	respectively	respectively	ADV
ejpam-2312	313	26	and	and	CCONJ
ejpam-2312	313	27	soft	soft	ADJ
ejpam-2312	313	28	function	function	NOUN
ejpam-2312	313	29	fpu	fpu	NOUN
ejpam-2312	313	30	:	:	PUNCT
ejpam-2312	313	31	ss(x)a	ss(x)a	PROPN
ejpam-2312	313	32	→	→	SYM
ejpam-2312	313	33	ss(y	ss(y	NUM
ejpam-2312	313	34	)	)	PUNCT
ejpam-2312	313	35	b	b	NOUN
ejpam-2312	313	36	is	be	AUX
ejpam-2312	313	37	soft	soft	ADJ
ejpam-2312	313	38	bijective	bijective	ADJ
ejpam-2312	313	39	soft	soft	ADJ
ejpam-2312	313	40	s	s	NOUN
ejpam-2312	313	41	-	-	NOUN
ejpam-2312	313	42	continuous	continuous	ADJ
ejpam-2312	313	43	.	.	PUNCT
ejpam-2312	314	1	if	if	SCONJ
ejpam-2312	314	2	ỹ	ỹ	PROPN
ejpam-2312	314	3	is	be	AUX
ejpam-2312	314	4	soft	soft	ADJ
ejpam-2312	314	5	semi	semi	ADJ
ejpam-2312	314	6	-	-	ADJ
ejpam-2312	314	7	d1	d1	ADJ
ejpam-2312	314	8	space	space	NOUN
ejpam-2312	314	9	then	then	ADV
ejpam-2312	314	10	x̃	x̃	PROPN
ejpam-2312	314	11	is	be	AUX
ejpam-2312	314	12	soft	soft	ADJ
ejpam-2312	314	13	semi	semi	ADJ
ejpam-2312	314	14	-	-	ADJ
ejpam-2312	314	15	d1	d1	ADJ
ejpam-2312	314	16	space	space	NOUN
ejpam-2312	314	17	.	.	PUNCT
ejpam-2312	315	1	proof	proof	NOUN
ejpam-2312	315	2	.	.	PUNCT
ejpam-2312	316	1	suppose	suppose	VERB
ejpam-2312	316	2	ef	ef	PROPN
ejpam-2312	316	3	and	and	CCONJ
ejpam-2312	316	4	eg	eg	NOUN
ejpam-2312	316	5	be	be	AUX
ejpam-2312	316	6	two	two	NUM
ejpam-2312	316	7	distinct	distinct	ADJ
ejpam-2312	316	8	soft	soft	ADJ
ejpam-2312	316	9	points	point	NOUN
ejpam-2312	316	10	in	in	ADP
ejpam-2312	316	11	x̃a	x̃a	PROPN
ejpam-2312	316	12	.	.	PUNCT
ejpam-2312	317	1	since	since	SCONJ
ejpam-2312	317	2	fpu	fpu	PROPN
ejpam-2312	317	3	is	be	AUX
ejpam-2312	317	4	soft	soft	ADJ
ejpam-2312	317	5	injective	injective	ADJ
ejpam-2312	317	6	and	and	CCONJ
ejpam-2312	317	7	ỹ	ỹ	PROPN
ejpam-2312	317	8	is	be	AUX
ejpam-2312	317	9	soft	soft	ADJ
ejpam-2312	317	10	semi	semi	ADJ
ejpam-2312	317	11	-	-	ADJ
ejpam-2312	317	12	d1	d1	ADJ
ejpam-2312	317	13	,	,	PUNCT
ejpam-2312	317	14	then	then	ADV
ejpam-2312	317	15	there	there	PRON
ejpam-2312	317	16	exist	exist	VERB
ejpam-2312	317	17	soft	soft	ADJ
ejpam-2312	317	18	semi	semi	ADJ
ejpam-2312	317	19	-	-	ADJ
ejpam-2312	317	20	d	d	ADJ
ejpam-2312	317	21	sets	set	NOUN
ejpam-2312	317	22	(	(	PUNCT
ejpam-2312	317	23	g	g	NOUN
ejpam-2312	317	24	,	,	PUNCT
ejpam-2312	317	25	b	b	NOUN
ejpam-2312	317	26	)	)	PUNCT
ejpam-2312	317	27	and	and	CCONJ
ejpam-2312	317	28	(	(	PUNCT
ejpam-2312	317	29	h	h	NOUN
ejpam-2312	317	30	,	,	PUNCT
ejpam-2312	317	31	b	b	NOUN
ejpam-2312	317	32	)	)	PUNCT
ejpam-2312	317	33	in	in	ADP
ejpam-2312	317	34	ss(y	ss(y	ADJ
ejpam-2312	317	35	)	)	PUNCT
ejpam-2312	318	1	b	b	X
ejpam-2312	318	2	such	such	ADJ
ejpam-2312	318	3	that	that	PRON
ejpam-2312	318	4	fpu(ef	fpu(ef	VERB
ejpam-2312	318	5	)	)	PUNCT
ejpam-2312	318	6	∈̃(g	∈̃(g	NOUN
ejpam-2312	318	7	,	,	PUNCT
ejpam-2312	318	8	b	b	NOUN
ejpam-2312	318	9	)	)	PUNCT
ejpam-2312	318	10	,	,	PUNCT
ejpam-2312	318	11	fpu(eg)∈̃(h	fpu(eg)∈̃(h	PROPN
ejpam-2312	318	12	,	,	PUNCT
ejpam-2312	318	13	b	b	NOUN
ejpam-2312	318	14	)	)	PUNCT
ejpam-2312	318	15	and	and	CCONJ
ejpam-2312	318	16	fpu(eg	fpu(eg	X
ejpam-2312	318	17	)	)	PUNCT
ejpam-2312	318	18	/̃∈(g	/̃∈(g	PUNCT
ejpam-2312	318	19	,	,	PUNCT
ejpam-2312	318	20	b	b	NOUN
ejpam-2312	318	21	)	)	PUNCT
ejpam-2312	318	22	,	,	PUNCT
ejpam-2312	318	23	fpu(ef	fpu(ef	X
ejpam-2312	318	24	)	)	PUNCT
ejpam-2312	318	25	/̃∈(h	/̃∈(h	PUNCT
ejpam-2312	318	26	,	,	PUNCT
ejpam-2312	318	27	b	b	NOUN
ejpam-2312	318	28	)	)	PUNCT
ejpam-2312	318	29	.	.	PUNCT
ejpam-2312	319	1	therefore	therefore	ADV
ejpam-2312	319	2	,	,	PUNCT
ejpam-2312	319	3	by	by	ADP
ejpam-2312	319	4	theorem	theorem	NOUN
ejpam-2312	319	5	10	10	NUM
ejpam-2312	319	6	,	,	PUNCT
ejpam-2312	319	7	f−1pu	f−1pu	NOUN
ejpam-2312	319	8	(	(	PUNCT
ejpam-2312	319	9	(	(	PUNCT
ejpam-2312	319	10	g	g	NOUN
ejpam-2312	319	11	,	,	PUNCT
ejpam-2312	319	12	b	b	NOUN
ejpam-2312	319	13	)	)	PUNCT
ejpam-2312	319	14	)	)	PUNCT
ejpam-2312	319	15	and	and	CCONJ
ejpam-2312	319	16	f−1pu	f−1pu	NOUN
ejpam-2312	319	17	(	(	PUNCT
ejpam-2312	319	18	h	h	NOUN
ejpam-2312	319	19	,	,	PUNCT
ejpam-2312	319	20	b	b	NOUN
ejpam-2312	319	21	)	)	PUNCT
ejpam-2312	319	22	are	be	AUX
ejpam-2312	319	23	soft	soft	ADJ
ejpam-2312	319	24	semi	semi	ADJ
ejpam-2312	319	25	-	-	ADJ
ejpam-2312	319	26	d	d	ADJ
ejpam-2312	319	27	sets	set	NOUN
ejpam-2312	319	28	in	in	ADP
ejpam-2312	319	29	ss(x)a	ss(x)a	PROPN
ejpam-2312	319	30	with	with	ADP
ejpam-2312	319	31	ef	ef	PROPN
ejpam-2312	319	32	∈̃f−1pu	∈̃f−1pu	PROPN
ejpam-2312	319	33	(	(	PUNCT
ejpam-2312	319	34	(	(	PUNCT
ejpam-2312	319	35	g	g	NOUN
ejpam-2312	319	36	,	,	PUNCT
ejpam-2312	319	37	b	b	NOUN
ejpam-2312	319	38	)	)	PUNCT
ejpam-2312	319	39	)	)	PUNCT
ejpam-2312	320	1	and	and	CCONJ
ejpam-2312	320	2	eg∈̃f−1pu	eg∈̃f−1pu	PROPN
ejpam-2312	320	3	(	(	PUNCT
ejpam-2312	320	4	h	h	NOUN
ejpam-2312	320	5	,	,	PUNCT
ejpam-2312	320	6	b	b	NOUN
ejpam-2312	320	7	)	)	PUNCT
ejpam-2312	320	8	.	.	PUNCT
ejpam-2312	321	1	this	this	PRON
ejpam-2312	321	2	implies	imply	VERB
ejpam-2312	321	3	that	that	SCONJ
ejpam-2312	321	4	x̃	x̃	PROPN
ejpam-2312	321	5	is	be	AUX
ejpam-2312	321	6	soft	soft	ADJ
ejpam-2312	321	7	semi	semi	ADJ
ejpam-2312	321	8	-	-	ADJ
ejpam-2312	321	9	d1	d1	ADJ
ejpam-2312	321	10	space	space	NOUN
ejpam-2312	321	11	.	.	PUNCT
ejpam-2312	322	1	this	this	PRON
ejpam-2312	322	2	completes	complete	VERB
ejpam-2312	322	3	the	the	DET
ejpam-2312	322	4	proof	proof	NOUN
ejpam-2312	322	5	.	.	PUNCT
ejpam-2312	323	1	theorem	theorem	VERB
ejpam-2312	323	2	13	13	NUM
ejpam-2312	323	3	.	.	PUNCT
ejpam-2312	324	1	let	let	VERB
ejpam-2312	324	2	(	(	PUNCT
ejpam-2312	324	3	x	x	X
ejpam-2312	324	4	,	,	PUNCT
ejpam-2312	324	5	τ	τ	PROPN
ejpam-2312	324	6	,	,	PUNCT
ejpam-2312	324	7	a	a	PRON
ejpam-2312	324	8	)	)	PUNCT
ejpam-2312	324	9	and	and	CCONJ
ejpam-2312	324	10	(	(	PUNCT
ejpam-2312	324	11	y	y	PROPN
ejpam-2312	324	12	,	,	PUNCT
ejpam-2312	324	13	τ∗	τ∗	PROPN
ejpam-2312	324	14	,	,	PUNCT
ejpam-2312	324	15	b	b	NOUN
ejpam-2312	324	16	)	)	PUNCT
ejpam-2312	324	17	be	be	AUX
ejpam-2312	324	18	soft	soft	ADJ
ejpam-2312	324	19	topological	topological	ADJ
ejpam-2312	324	20	spaces	space	NOUN
ejpam-2312	324	21	over	over	ADP
ejpam-2312	324	22	x	x	PUNCT
ejpam-2312	324	23	and	and	CCONJ
ejpam-2312	324	24	y	y	PROPN
ejpam-2312	324	25	respectively	respectively	ADV
ejpam-2312	324	26	.	.	PUNCT
ejpam-2312	325	1	a	a	DET
ejpam-2312	325	2	soft	soft	ADJ
ejpam-2312	325	3	function	function	NOUN
ejpam-2312	325	4	fpu	fpu	NOUN
ejpam-2312	325	5	:	:	PUNCT
ejpam-2312	325	6	ss(x)a	ss(x)a	PROPN
ejpam-2312	325	7	→	→	SYM
ejpam-2312	325	8	ss(y	ss(y	NUM
ejpam-2312	325	9	)	)	PUNCT
ejpam-2312	325	10	b	b	NOUN
ejpam-2312	325	11	is	be	AUX
ejpam-2312	325	12	soft	soft	ADJ
ejpam-2312	325	13	s	s	NOUN
ejpam-2312	325	14	-	-	ADJ
ejpam-2312	325	15	continuous	continuous	ADJ
ejpam-2312	325	16	,	,	PUNCT
ejpam-2312	325	17	if	if	SCONJ
ejpam-2312	325	18	for	for	ADP
ejpam-2312	325	19	each	each	DET
ejpam-2312	325	20	soft	soft	ADJ
ejpam-2312	325	21	point	point	NOUN
ejpam-2312	325	22	ef	ef	NOUN
ejpam-2312	325	23	in	in	ADP
ejpam-2312	325	24	x̃a	x̃a	PROPN
ejpam-2312	325	25	and	and	CCONJ
ejpam-2312	325	26	each	each	DET
ejpam-2312	325	27	soft	soft	ADJ
ejpam-2312	325	28	semi	semi	ADJ
ejpam-2312	325	29	-	-	ADJ
ejpam-2312	325	30	open	open	ADJ
ejpam-2312	325	31	set	set	NOUN
ejpam-2312	325	32	(	(	PUNCT
ejpam-2312	325	33	g	g	PROPN
ejpam-2312	325	34	,	,	PUNCT
ejpam-2312	325	35	b	b	NOUN
ejpam-2312	325	36	)	)	PUNCT
ejpam-2312	325	37	in	in	ADP
ejpam-2312	325	38	ss(y	ss(y	ADJ
ejpam-2312	325	39	)	)	PUNCT
ejpam-2312	325	40	b	b	X
ejpam-2312	325	41	such	such	ADJ
ejpam-2312	325	42	that	that	PRON
ejpam-2312	325	43	fpu(ef	fpu(ef	VERB
ejpam-2312	325	44	)	)	PUNCT
ejpam-2312	325	45	∈̃(g	∈̃(g	NOUN
ejpam-2312	325	46	,	,	PUNCT
ejpam-2312	325	47	b	b	NOUN
ejpam-2312	325	48	)	)	PUNCT
ejpam-2312	325	49	,	,	PUNCT
ejpam-2312	325	50	there	there	PRON
ejpam-2312	325	51	exists	exist	VERB
ejpam-2312	325	52	a	a	DET
ejpam-2312	325	53	soft	soft	ADJ
ejpam-2312	325	54	semi	semi	ADJ
ejpam-2312	325	55	-	-	ADJ
ejpam-2312	325	56	open	open	ADJ
ejpam-2312	325	57	set	set	NOUN
ejpam-2312	325	58	(	(	PUNCT
ejpam-2312	325	59	f	f	X
ejpam-2312	325	60	,	,	PUNCT
ejpam-2312	325	61	a	a	PRON
ejpam-2312	325	62	)	)	PUNCT
ejpam-2312	325	63	in	in	ADP
ejpam-2312	325	64	ss(x)a	ss(x)a	PROPN
ejpam-2312	325	65	such	such	ADJ
ejpam-2312	325	66	that	that	SCONJ
ejpam-2312	325	67	fpu(f	fpu(f	PROPN
ejpam-2312	325	68	,	,	PUNCT
ejpam-2312	325	69	a)⊆̃(g	a)⊆̃(g	PROPN
ejpam-2312	325	70	,	,	PUNCT
ejpam-2312	325	71	b	b	NOUN
ejpam-2312	325	72	)	)	PUNCT
ejpam-2312	325	73	.	.	PUNCT
ejpam-2312	326	1	proof	proof	NOUN
ejpam-2312	326	2	.	.	PUNCT
ejpam-2312	327	1	(	(	PUNCT
ejpam-2312	327	2	⇒	⇒	PROPN
ejpam-2312	327	3	)	)	PUNCT
ejpam-2312	327	4	since	since	SCONJ
ejpam-2312	327	5	fpu	fpu	PROPN
ejpam-2312	327	6	is	be	AUX
ejpam-2312	327	7	soft	soft	ADJ
ejpam-2312	327	8	s	s	NOUN
ejpam-2312	327	9	-	-	ADJ
ejpam-2312	327	10	continuous	continuous	ADJ
ejpam-2312	327	11	,	,	PUNCT
ejpam-2312	327	12	implies	imply	VERB
ejpam-2312	327	13	that	that	PRON
ejpam-2312	327	14	f−1pu	f−1pu	NOUN
ejpam-2312	327	15	(	(	PUNCT
ejpam-2312	327	16	g	g	PROPN
ejpam-2312	327	17	,	,	PUNCT
ejpam-2312	327	18	b	b	NOUN
ejpam-2312	327	19	)	)	PUNCT
ejpam-2312	327	20	is	be	AUX
ejpam-2312	327	21	soft	soft	ADJ
ejpam-2312	327	22	semi	semi	ADJ
ejpam-2312	327	23	-	-	ADJ
ejpam-2312	327	24	open	open	ADJ
ejpam-2312	327	25	in	in	ADP
ejpam-2312	327	26	ss(x)a	ss(x)a	PROPN
ejpam-2312	327	27	,	,	PUNCT
ejpam-2312	327	28	for	for	ADP
ejpam-2312	327	29	soft	soft	ADJ
ejpam-2312	327	30	semi	semi	ADJ
ejpam-2312	327	31	-	-	ADJ
ejpam-2312	327	32	open	open	ADJ
ejpam-2312	327	33	set	set	NOUN
ejpam-2312	327	34	(	(	PUNCT
ejpam-2312	327	35	g	g	PROPN
ejpam-2312	327	36	,	,	PUNCT
ejpam-2312	327	37	b	b	NOUN
ejpam-2312	327	38	)	)	PUNCT
ejpam-2312	327	39	in	in	ADP
ejpam-2312	327	40	ss(y	ss(y	PROPN
ejpam-2312	327	41	)	)	PUNCT
ejpam-2312	328	1	b.	b.	NOUN
ejpam-2312	328	2	we	we	PRON
ejpam-2312	328	3	need	need	VERB
ejpam-2312	328	4	to	to	PART
ejpam-2312	328	5	show	show	VERB
ejpam-2312	328	6	that	that	SCONJ
ejpam-2312	328	7	there	there	PRON
ejpam-2312	328	8	exists	exist	VERB
ejpam-2312	328	9	a	a	DET
ejpam-2312	328	10	soft	soft	ADJ
ejpam-2312	328	11	semi	semi	ADJ
ejpam-2312	328	12	-	-	ADJ
ejpam-2312	328	13	open	open	ADJ
ejpam-2312	328	14	set	set	NOUN
ejpam-2312	328	15	(	(	PUNCT
ejpam-2312	328	16	f	f	X
ejpam-2312	328	17	,	,	PUNCT
ejpam-2312	328	18	a	a	PRON
ejpam-2312	328	19	)	)	PUNCT
ejpam-2312	328	20	in	in	ADP
ejpam-2312	328	21	ss(x)a	ss(x)a	PROPN
ejpam-2312	328	22	such	such	ADJ
ejpam-2312	328	23	that	that	SCONJ
ejpam-2312	328	24	fpu(f	fpu(f	PROPN
ejpam-2312	328	25	,	,	PUNCT
ejpam-2312	328	26	a)⊆̃(g	a)⊆̃(g	PROPN
ejpam-2312	328	27	,	,	PUNCT
ejpam-2312	328	28	b	b	NOUN
ejpam-2312	328	29	)	)	PUNCT
ejpam-2312	328	30	,	,	PUNCT
ejpam-2312	328	31	for	for	ADP
ejpam-2312	328	32	each	each	DET
ejpam-2312	328	33	soft	soft	ADJ
ejpam-2312	328	34	point	point	NOUN
ejpam-2312	328	35	ef	ef	NOUN
ejpam-2312	328	36	in	in	ADP
ejpam-2312	328	37	x̃a	x̃a	PROPN
ejpam-2312	328	38	and	and	CCONJ
ejpam-2312	328	39	each	each	DET
ejpam-2312	328	40	soft	soft	ADJ
ejpam-2312	328	41	semi	semi	ADJ
ejpam-2312	328	42	-	-	ADJ
ejpam-2312	328	43	open	open	ADJ
ejpam-2312	328	44	set	set	NOUN
ejpam-2312	328	45	(	(	PUNCT
ejpam-2312	328	46	g	g	PROPN
ejpam-2312	328	47	,	,	PUNCT
ejpam-2312	328	48	b	b	NOUN
ejpam-2312	328	49	)	)	PUNCT
ejpam-2312	328	50	in	in	ADP
ejpam-2312	328	51	ss(y	ss(y	ADJ
ejpam-2312	328	52	)	)	PUNCT
ejpam-2312	328	53	b	b	X
ejpam-2312	328	54	such	such	ADJ
ejpam-2312	328	55	that	that	PRON
ejpam-2312	328	56	fpu(ef	fpu(ef	VERB
ejpam-2312	328	57	)	)	PUNCT
ejpam-2312	328	58	∈̃(g	∈̃(g	NOUN
ejpam-2312	328	59	,	,	PUNCT
ejpam-2312	328	60	b	b	NOUN
ejpam-2312	328	61	)	)	PUNCT
ejpam-2312	328	62	.	.	PUNCT
ejpam-2312	329	1	consider	consider	VERB
ejpam-2312	329	2	the	the	DET
ejpam-2312	329	3	soft	soft	ADJ
ejpam-2312	329	4	point	point	NOUN
ejpam-2312	329	5	ef	ef	NOUN
ejpam-2312	329	6	in	in	ADP
ejpam-2312	329	7	x̃a	x̃a	PRON
ejpam-2312	329	8	with	with	ADP
ejpam-2312	329	9	ef	ef	PROPN
ejpam-2312	329	10	∈̃f−1pu	∈̃f−1pu	PROPN
ejpam-2312	329	11	(	(	PUNCT
ejpam-2312	329	12	g	g	PROPN
ejpam-2312	329	13	,	,	PUNCT
ejpam-2312	329	14	b	b	NOUN
ejpam-2312	329	15	)	)	PUNCT
ejpam-2312	329	16	and	and	CCONJ
ejpam-2312	329	17	(	(	PUNCT
ejpam-2312	329	18	f	f	X
ejpam-2312	329	19	,	,	PUNCT
ejpam-2312	329	20	a	a	PRON
ejpam-2312	329	21	)	)	PUNCT
ejpam-2312	329	22	=	=	SYM
ejpam-2312	329	23	f−1pu	f−1pu	NOUN
ejpam-2312	329	24	(	(	PUNCT
ejpam-2312	329	25	g	g	PROPN
ejpam-2312	329	26	,	,	PUNCT
ejpam-2312	329	27	b	b	NOUN
ejpam-2312	329	28	)	)	PUNCT
ejpam-2312	329	29	.	.	PUNCT
ejpam-2312	330	1	this	this	PRON
ejpam-2312	330	2	implies	imply	VERB
ejpam-2312	330	3	that	that	SCONJ
ejpam-2312	330	4	for	for	ADP
ejpam-2312	330	5	soft	soft	ADJ
ejpam-2312	330	6	semi	semi	ADJ
ejpam-2312	330	7	-	-	ADJ
ejpam-2312	330	8	open	open	ADJ
ejpam-2312	330	9	set	set	NOUN
ejpam-2312	330	10	(	(	PUNCT
ejpam-2312	330	11	g	g	NOUN
ejpam-2312	330	12	,	,	PUNCT
ejpam-2312	330	13	b	b	NOUN
ejpam-2312	330	14	)	)	PUNCT
ejpam-2312	330	15	,	,	PUNCT
ejpam-2312	330	16	ef	ef	ADP
ejpam-2312	330	17	∈̃(f	∈̃(f	PROPN
ejpam-2312	330	18	,	,	PUNCT
ejpam-2312	330	19	a	a	PRON
ejpam-2312	330	20	)	)	PUNCT
ejpam-2312	330	21	and	and	CCONJ
ejpam-2312	330	22	fpu(f	fpu(f	PROPN
ejpam-2312	330	23	,	,	PUNCT
ejpam-2312	330	24	a)⊆̃fpuf−1pu	a)⊆̃fpuf−1pu	PROPN
ejpam-2312	330	25	(	(	PUNCT
ejpam-2312	330	26	g	g	NOUN
ejpam-2312	330	27	,	,	PUNCT
ejpam-2312	330	28	b)⊆̃(g	b)⊆̃(g	PROPN
ejpam-2312	330	29	,	,	PUNCT
ejpam-2312	330	30	b	b	NOUN
ejpam-2312	330	31	)	)	PUNCT
ejpam-2312	330	32	.	.	PUNCT
ejpam-2312	331	1	(	(	PUNCT
ejpam-2312	331	2	⇐	⇐	NOUN
ejpam-2312	331	3	)	)	PUNCT
ejpam-2312	331	4	suppose	suppose	VERB
ejpam-2312	331	5	that	that	SCONJ
ejpam-2312	331	6	for	for	ADP
ejpam-2312	331	7	each	each	DET
ejpam-2312	331	8	soft	soft	ADJ
ejpam-2312	331	9	point	point	NOUN
ejpam-2312	331	10	ef	ef	NOUN
ejpam-2312	331	11	in	in	ADP
ejpam-2312	331	12	x̃a	x̃a	PROPN
ejpam-2312	331	13	and	and	CCONJ
ejpam-2312	331	14	each	each	DET
ejpam-2312	331	15	soft	soft	ADJ
ejpam-2312	331	16	semi	semi	ADJ
ejpam-2312	331	17	-	-	ADJ
ejpam-2312	331	18	open	open	ADJ
ejpam-2312	331	19	set	set	NOUN
ejpam-2312	331	20	(	(	PUNCT
ejpam-2312	331	21	g	g	PROPN
ejpam-2312	331	22	,	,	PUNCT
ejpam-2312	331	23	b	b	NOUN
ejpam-2312	331	24	)	)	PUNCT
ejpam-2312	331	25	in	in	ADP
ejpam-2312	331	26	ss(y	ss(y	ADJ
ejpam-2312	331	27	)	)	PUNCT
ejpam-2312	331	28	b	b	X
ejpam-2312	331	29	such	such	ADJ
ejpam-2312	331	30	that	that	PRON
ejpam-2312	331	31	f(ef	f(ef	ADJ
ejpam-2312	331	32	)	)	PUNCT
ejpam-2312	331	33	∈̃(g	∈̃(g	NOUN
ejpam-2312	331	34	,	,	PUNCT
ejpam-2312	331	35	b	b	NOUN
ejpam-2312	331	36	)	)	PUNCT
ejpam-2312	331	37	,	,	PUNCT
ejpam-2312	331	38	there	there	PRON
ejpam-2312	331	39	exists	exist	VERB
ejpam-2312	331	40	a	a	DET
ejpam-2312	331	41	soft	soft	ADJ
ejpam-2312	331	42	semi	semi	ADJ
ejpam-2312	331	43	-	-	ADJ
ejpam-2312	331	44	open	open	ADJ
ejpam-2312	331	45	set	set	NOUN
ejpam-2312	331	46	(	(	PUNCT
ejpam-2312	331	47	f	f	X
ejpam-2312	331	48	,	,	PUNCT
ejpam-2312	331	49	a	a	PRON
ejpam-2312	331	50	)	)	PUNCT
ejpam-2312	331	51	in	in	ADP
ejpam-2312	331	52	ss(x)a	ss(x)a	PROPN
ejpam-2312	331	53	such	such	ADJ
ejpam-2312	331	54	that	that	SCONJ
ejpam-2312	331	55	fpu(f	fpu(f	PROPN
ejpam-2312	331	56	,	,	PUNCT
ejpam-2312	331	57	a)⊆̃(g	a)⊆̃(g	PROPN
ejpam-2312	331	58	,	,	PUNCT
ejpam-2312	331	59	b	b	NOUN
ejpam-2312	331	60	)	)	PUNCT
ejpam-2312	331	61	.	.	PUNCT
ejpam-2312	332	1	to	to	PART
ejpam-2312	332	2	prove	prove	VERB
ejpam-2312	332	3	that	that	SCONJ
ejpam-2312	332	4	soft	soft	ADJ
ejpam-2312	332	5	function	function	NOUN
ejpam-2312	332	6	fpu	fpu	NOUN
ejpam-2312	332	7	is	be	AUX
ejpam-2312	332	8	soft	soft	ADJ
ejpam-2312	332	9	s	s	NOUN
ejpam-2312	332	10	-	-	NOUN
ejpam-2312	332	11	continuous	continuous	ADJ
ejpam-2312	332	12	.	.	PUNCT
ejpam-2312	333	1	we	we	PRON
ejpam-2312	333	2	references	reference	VERB
ejpam-2312	333	3	209	209	NUM
ejpam-2312	333	4	show	show	VERB
ejpam-2312	333	5	that	that	SCONJ
ejpam-2312	333	6	the	the	DET
ejpam-2312	333	7	inverse	inverse	ADJ
ejpam-2312	333	8	image	image	NOUN
ejpam-2312	333	9	of	of	ADP
ejpam-2312	333	10	soft	soft	ADJ
ejpam-2312	333	11	semi	semi	ADJ
ejpam-2312	333	12	-	-	ADJ
ejpam-2312	333	13	open	open	ADJ
ejpam-2312	333	14	set	set	NOUN
ejpam-2312	333	15	in	in	ADP
ejpam-2312	333	16	ss(y	ss(y	ADJ
ejpam-2312	333	17	)	)	PUNCT
ejpam-2312	333	18	b	b	NOUN
ejpam-2312	333	19	is	be	AUX
ejpam-2312	333	20	soft	soft	ADJ
ejpam-2312	333	21	semi	semi	ADJ
ejpam-2312	333	22	-	-	ADJ
ejpam-2312	333	23	open	open	ADJ
ejpam-2312	333	24	set	set	NOUN
ejpam-2312	333	25	in	in	ADP
ejpam-2312	333	26	ss(x)a	ss(x)a	PROPN
ejpam-2312	333	27	.	.	PUNCT
ejpam-2312	334	1	now	now	ADV
ejpam-2312	334	2	ef	ef	PROPN
ejpam-2312	334	3	∈̃f−1pu	∈̃f−1pu	PROPN
ejpam-2312	334	4	(	(	PUNCT
ejpam-2312	334	5	g	g	PROPN
ejpam-2312	334	6	,	,	PUNCT
ejpam-2312	334	7	b	b	NOUN
ejpam-2312	334	8	)	)	PUNCT
ejpam-2312	334	9	follows	follow	VERB
ejpam-2312	334	10	fpu(ef	fpu(ef	NOUN
ejpam-2312	334	11	)	)	PUNCT
ejpam-2312	334	12	∈̃(g	∈̃(g	NOUN
ejpam-2312	334	13	,	,	PUNCT
ejpam-2312	334	14	b	b	NOUN
ejpam-2312	334	15	)	)	PUNCT
ejpam-2312	334	16	.	.	PUNCT
ejpam-2312	335	1	thus	thus	ADV
ejpam-2312	335	2	by	by	ADP
ejpam-2312	335	3	hypothesis	hypothesis	NOUN
ejpam-2312	335	4	,	,	PUNCT
ejpam-2312	335	5	there	there	PRON
ejpam-2312	335	6	exists	exist	VERB
ejpam-2312	335	7	a	a	DET
ejpam-2312	335	8	soft	soft	ADJ
ejpam-2312	335	9	semi	semi	ADJ
ejpam-2312	335	10	-	-	ADJ
ejpam-2312	335	11	open	open	ADJ
ejpam-2312	335	12	set	set	NOUN
ejpam-2312	335	13	(	(	PUNCT
ejpam-2312	335	14	f	f	X
ejpam-2312	335	15	,	,	PUNCT
ejpam-2312	335	16	a)ef	a)ef	VERB
ejpam-2312	335	17	such	such	ADJ
ejpam-2312	335	18	that	that	SCONJ
ejpam-2312	335	19	ef	ef	VERB
ejpam-2312	335	20	∈̃(f	∈̃(f	ADJ
ejpam-2312	335	21	,	,	PUNCT
ejpam-2312	335	22	a)ef	a)ef	PROPN
ejpam-2312	335	23	and	and	CCONJ
ejpam-2312	335	24	fpu((f	fpu((f	NOUN
ejpam-2312	335	25	,	,	PUNCT
ejpam-2312	335	26	a)ef	a)ef	PROPN
ejpam-2312	335	27	)	)	PUNCT
ejpam-2312	335	28	∈̃(g	∈̃(g	NOUN
ejpam-2312	335	29	,	,	PUNCT
ejpam-2312	335	30	b	b	NOUN
ejpam-2312	335	31	)	)	PUNCT
ejpam-2312	335	32	.	.	PUNCT
ejpam-2312	336	1	thus	thus	ADV
ejpam-2312	336	2	ef	ef	VERB
ejpam-2312	336	3	∈̃(f	∈̃(f	ADJ
ejpam-2312	336	4	,	,	PUNCT
ejpam-2312	336	5	a)ef	a)ef	PROPN
ejpam-2312	336	6	⊆̃f−1pu	⊆̃f−1pu	PROPN
ejpam-2312	336	7	(	(	PUNCT
ejpam-2312	336	8	g	g	NOUN
ejpam-2312	336	9	,	,	PUNCT
ejpam-2312	336	10	b	b	NOUN
ejpam-2312	336	11	)	)	PUNCT
ejpam-2312	336	12	and	and	CCONJ
ejpam-2312	336	13	f−1pu	f−1pu	NOUN
ejpam-2312	336	14	(	(	PUNCT
ejpam-2312	336	15	g	g	PROPN
ejpam-2312	336	16	,	,	PUNCT
ejpam-2312	336	17	b)=̃	b)=̃	PROPN
ejpam-2312	336	18	⋃̃	⋃̃	PROPN
ejpam-2312	336	19	ef	ef	PROPN
ejpam-2312	336	20	∈̃f−1	∈̃f−1	PROPN
ejpam-2312	336	21	pu	pu	PROPN
ejpam-2312	336	22	(	(	PUNCT
ejpam-2312	336	23	g	g	NOUN
ejpam-2312	336	24	,	,	PUNCT
ejpam-2312	336	25	b)(f	b)(f	PROPN
ejpam-2312	336	26	,	,	PUNCT
ejpam-2312	336	27	a)ef	a)ef	PROPN
ejpam-2312	336	28	,	,	PUNCT
ejpam-2312	336	29	for	for	ADP
ejpam-2312	336	30	which	which	PRON
ejpam-2312	336	31	f−1pu	f−1pu	NOUN
ejpam-2312	336	32	(	(	PUNCT
ejpam-2312	336	33	g	g	PROPN
ejpam-2312	336	34	,	,	PUNCT
ejpam-2312	336	35	b	b	NOUN
ejpam-2312	336	36	)	)	PUNCT
ejpam-2312	336	37	is	be	AUX
ejpam-2312	336	38	soft	soft	ADJ
ejpam-2312	336	39	semi	semi	ADJ
ejpam-2312	336	40	-	-	ADJ
ejpam-2312	336	41	open	open	ADJ
ejpam-2312	336	42	set	set	NOUN
ejpam-2312	336	43	in	in	ADP
ejpam-2312	336	44	ss(x)a	ss(x)a	PROPN
ejpam-2312	336	45	.	.	PUNCT
ejpam-2312	337	1	hence	hence	PROPN
ejpam-2312	337	2	fpu	fpu	PROPN
ejpam-2312	337	3	is	be	AUX
ejpam-2312	337	4	soft	soft	ADJ
ejpam-2312	337	5	s	s	NOUN
ejpam-2312	337	6	-	-	ADJ
ejpam-2312	337	7	continuous	continuous	ADJ
ejpam-2312	337	8	.	.	PUNCT
ejpam-2312	338	1	this	this	PRON
ejpam-2312	338	2	completes	complete	VERB
ejpam-2312	338	3	the	the	DET
ejpam-2312	338	4	proof	proof	NOUN
ejpam-2312	338	5	.	.	PUNCT
ejpam-2312	339	1	5	5	X
ejpam-2312	339	2	.	.	X
ejpam-2312	339	3	conclusion	conclusion	NOUN
ejpam-2312	339	4	in	in	ADP
ejpam-2312	339	5	the	the	DET
ejpam-2312	339	6	present	present	ADJ
ejpam-2312	339	7	work	work	NOUN
ejpam-2312	339	8	,	,	PUNCT
ejpam-2312	339	9	we	we	PRON
ejpam-2312	339	10	initiated	initiate	VERB
ejpam-2312	339	11	and	and	CCONJ
ejpam-2312	339	12	explored	explore	VERB
ejpam-2312	339	13	the	the	DET
ejpam-2312	339	14	properties	property	NOUN
ejpam-2312	339	15	and	and	CCONJ
ejpam-2312	339	16	characterizations	characterization	NOUN
ejpam-2312	339	17	of	of	ADP
ejpam-2312	339	18	soft	soft	ADJ
ejpam-2312	339	19	semi	semi	NOUN
ejpam-2312	339	20	-	-	NOUN
ejpam-2312	339	21	ti	ti	X
ejpam-2312	339	22	(	(	PUNCT
ejpam-2312	339	23	for	for	ADP
ejpam-2312	339	24	i	i	PRON
ejpam-2312	339	25	=	=	SYM
ejpam-2312	339	26	0	0	NUM
ejpam-2312	339	27	,	,	PUNCT
ejpam-2312	339	28	1	1	NUM
ejpam-2312	339	29	,	,	PUNCT
ejpam-2312	339	30	2	2	NUM
ejpam-2312	339	31	)	)	PUNCT
ejpam-2312	339	32	spaces	space	NOUN
ejpam-2312	339	33	.	.	PUNCT
ejpam-2312	340	1	we	we	PRON
ejpam-2312	340	2	also	also	ADV
ejpam-2312	340	3	introduced	introduce	VERB
ejpam-2312	340	4	and	and	CCONJ
ejpam-2312	340	5	discussed	discuss	VERB
ejpam-2312	340	6	the	the	DET
ejpam-2312	340	7	concepts	concept	NOUN
ejpam-2312	340	8	of	of	ADP
ejpam-2312	340	9	soft	soft	ADJ
ejpam-2312	340	10	semi	semi	NOUN
ejpam-2312	340	11	-	-	NOUN
ejpam-2312	340	12	di	di	ADJ
ejpam-2312	340	13	(	(	PUNCT
ejpam-2312	340	14	for	for	ADP
ejpam-2312	340	15	i	i	PRON
ejpam-2312	340	16	=	=	SYM
ejpam-2312	340	17	0	0	NUM
ejpam-2312	340	18	,	,	PUNCT
ejpam-2312	340	19	1	1	NUM
ejpam-2312	340	20	,	,	PUNCT
ejpam-2312	340	21	2	2	NUM
ejpam-2312	340	22	)	)	PUNCT
ejpam-2312	340	23	spaces	space	NOUN
ejpam-2312	340	24	by	by	ADP
ejpam-2312	340	25	analyzing	analyze	VERB
ejpam-2312	340	26	the	the	DET
ejpam-2312	340	27	relationship	relationship	NOUN
ejpam-2312	340	28	among	among	ADP
ejpam-2312	340	29	these	these	DET
ejpam-2312	340	30	spaces	space	NOUN
ejpam-2312	340	31	.	.	PUNCT
ejpam-2312	341	1	moreover	moreover	ADV
ejpam-2312	341	2	,	,	PUNCT
ejpam-2312	341	3	we	we	PRON
ejpam-2312	341	4	introduced	introduce	VERB
ejpam-2312	341	5	and	and	CCONJ
ejpam-2312	341	6	studied	study	VERB
ejpam-2312	341	7	soft	soft	ADJ
ejpam-2312	341	8	s	s	NOUN
ejpam-2312	341	9	-	-	ADJ
ejpam-2312	341	10	continuous	continuous	ADJ
ejpam-2312	341	11	function	function	NOUN
ejpam-2312	341	12	and	and	CCONJ
ejpam-2312	341	13	explore	explore	VERB
ejpam-2312	341	14	the	the	DET
ejpam-2312	341	15	properties	property	NOUN
ejpam-2312	341	16	of	of	ADP
ejpam-2312	341	17	soft	soft	ADJ
ejpam-2312	341	18	semi	semi	ADJ
ejpam-2312	341	19	-	-	ADJ
ejpam-2312	341	20	d1	d1	ADJ
ejpam-2312	341	21	space	space	NOUN
ejpam-2312	341	22	in	in	ADP
ejpam-2312	341	23	soft	soft	ADJ
ejpam-2312	341	24	s	s	NOUN
ejpam-2312	341	25	-	-	ADJ
ejpam-2312	341	26	continuous	continuous	ADJ
ejpam-2312	341	27	function	function	NOUN
ejpam-2312	341	28	.	.	PUNCT
ejpam-2312	342	1	there	there	PRON
ejpam-2312	342	2	is	be	VERB
ejpam-2312	342	3	a	a	DET
ejpam-2312	342	4	wide	wide	ADJ
ejpam-2312	342	5	space	space	NOUN
ejpam-2312	342	6	to	to	PART
ejpam-2312	342	7	work	work	VERB
ejpam-2312	342	8	further	far	ADV
ejpam-2312	342	9	in	in	ADP
ejpam-2312	342	10	this	this	DET
ejpam-2312	342	11	field	field	NOUN
ejpam-2312	342	12	using	use	VERB
ejpam-2312	342	13	defined	define	VERB
ejpam-2312	342	14	concepts	concept	NOUN
ejpam-2312	342	15	,	,	PUNCT
ejpam-2312	342	16	properties	property	NOUN
ejpam-2312	342	17	and	and	CCONJ
ejpam-2312	342	18	characterizations	characterization	NOUN
ejpam-2312	342	19	to	to	PART
ejpam-2312	342	20	enhance	enhance	VERB
ejpam-2312	342	21	the	the	DET
ejpam-2312	342	22	general	general	ADJ
ejpam-2312	342	23	framework	framework	NOUN
ejpam-2312	342	24	which	which	PRON
ejpam-2312	342	25	will	will	AUX
ejpam-2312	342	26	be	be	AUX
ejpam-2312	342	27	applicable	applicable	ADJ
ejpam-2312	342	28	towards	towards	ADP
ejpam-2312	342	29	daily	daily	ADJ
ejpam-2312	342	30	life	life	NOUN
ejpam-2312	342	31	to	to	PART
ejpam-2312	342	32	solve	solve	VERB
ejpam-2312	342	33	the	the	DET
ejpam-2312	342	34	problems	problem	NOUN
ejpam-2312	342	35	having	have	VERB
ejpam-2312	342	36	uncertainties	uncertainty	NOUN
ejpam-2312	342	37	.	.	PUNCT
ejpam-2312	343	1	references	reference	NOUN
ejpam-2312	343	2	[	[	X
ejpam-2312	343	3	1	1	NUM
ejpam-2312	343	4	]	]	PUNCT
ejpam-2312	343	5	b.	b.	PROPN
ejpam-2312	343	6	ahmad	ahmad	PROPN
ejpam-2312	343	7	and	and	CCONJ
ejpam-2312	343	8	s.	s.	PROPN
ejpam-2312	343	9	hussain	hussain	PROPN
ejpam-2312	343	10	.	.	PUNCT
ejpam-2312	344	1	on	on	ADP
ejpam-2312	344	2	some	some	DET
ejpam-2312	344	3	structures	structure	NOUN
ejpam-2312	344	4	of	of	ADP
ejpam-2312	344	5	soft	soft	ADJ
ejpam-2312	344	6	topology	topology	NOUN
ejpam-2312	344	7	.	.	PUNCT
ejpam-2312	345	1	mathematical	mathematical	ADJ
ejpam-2312	345	2	sciences	sciences	PROPN
ejpam-2312	345	3	,	,	PUNCT
ejpam-2312	345	4	6(64	6(64	NUM
ejpam-2312	345	5	)	)	PUNCT
ejpam-2312	345	6	,	,	PUNCT
ejpam-2312	345	7	1	1	NUM
ejpam-2312	345	8	-	-	SYM
ejpam-2312	345	9	7	7	NUM
ejpam-2312	345	10	.	.	NOUN
ejpam-2312	345	11	2012	2012	NUM
ejpam-2312	345	12	.	.	PUNCT
ejpam-2312	346	1	[	[	X
ejpam-2312	346	2	2	2	NUM
ejpam-2312	346	3	]	]	PUNCT
ejpam-2312	346	4	a.	a.	NOUN
ejpam-2312	346	5	ayguoglu	ayguoglu	NOUN
ejpam-2312	346	6	and	and	CCONJ
ejpam-2312	346	7	h.	h.	PROPN
ejpam-2312	346	8	aygun	aygun	PROPN
ejpam-2312	346	9	.	.	PUNCT
ejpam-2312	347	1	some	some	DET
ejpam-2312	347	2	notes	note	NOUN
ejpam-2312	347	3	on	on	ADP
ejpam-2312	347	4	soft	soft	ADJ
ejpam-2312	347	5	topological	topological	ADJ
ejpam-2312	347	6	spaces	space	NOUN
ejpam-2312	347	7	.	.	PUNCT
ejpam-2312	348	1	neural	neural	ADJ
ejpam-2312	348	2	computing	computing	NOUN
ejpam-2312	348	3	and	and	CCONJ
ejpam-2312	348	4	applications	application	NOUN
ejpam-2312	348	5	,	,	PUNCT
ejpam-2312	348	6	21	21	NUM
ejpam-2312	348	7	,	,	PUNCT
ejpam-2312	348	8	113–119	113–119	NUM
ejpam-2312	348	9	.	.	NOUN
ejpam-2312	348	10	2012	2012	NUM
ejpam-2312	348	11	.	.	PUNCT
ejpam-2312	349	1	[	[	X
ejpam-2312	349	2	3	3	X
ejpam-2312	349	3	]	]	X
ejpam-2312	349	4	b.	b.	PROPN
ejpam-2312	349	5	chen	chen	PROPN
ejpam-2312	349	6	.	.	PUNCT
ejpam-2312	350	1	soft	soft	ADJ
ejpam-2312	350	2	semi	semi	ADJ
ejpam-2312	350	3	-	-	ADJ
ejpam-2312	350	4	open	open	ADJ
ejpam-2312	350	5	sets	set	NOUN
ejpam-2312	350	6	and	and	CCONJ
ejpam-2312	350	7	related	related	ADJ
ejpam-2312	350	8	properties	property	NOUN
ejpam-2312	350	9	in	in	ADP
ejpam-2312	350	10	soft	soft	ADJ
ejpam-2312	350	11	topological	topological	ADJ
ejpam-2312	350	12	spaces	space	NOUN
ejpam-2312	350	13	.	.	PUNCT
ejpam-2312	351	1	applied	apply	VERB
ejpam-2312	351	2	mathematics	mathematic	NOUN
ejpam-2312	351	3	and	and	CCONJ
ejpam-2312	351	4	information	information	NOUN
ejpam-2312	351	5	sciences	science	NOUN
ejpam-2312	351	6	,	,	PUNCT
ejpam-2312	351	7	7(1	7(1	NUM
ejpam-2312	351	8	)	)	PUNCT
ejpam-2312	351	9	,	,	PUNCT
ejpam-2312	351	10	287–294	287–294	NUM
ejpam-2312	351	11	.	.	PUNCT
ejpam-2312	351	12	2013	2013	NUM
ejpam-2312	351	13	.	.	PUNCT
ejpam-2312	352	1	[	[	X
ejpam-2312	352	2	4	4	X
ejpam-2312	352	3	]	]	PUNCT
ejpam-2312	352	4	b.	b.	PROPN
ejpam-2312	352	5	chen	chen	PROPN
ejpam-2312	352	6	.	.	PUNCT
ejpam-2312	353	1	soft	soft	ADJ
ejpam-2312	353	2	local	local	ADJ
ejpam-2312	353	3	properties	property	NOUN
ejpam-2312	353	4	of	of	ADP
ejpam-2312	353	5	soft	soft	ADJ
ejpam-2312	353	6	semi	semi	ADJ
ejpam-2312	353	7	-	-	ADJ
ejpam-2312	353	8	open	open	ADJ
ejpam-2312	353	9	sets	set	NOUN
ejpam-2312	353	10	.	.	PUNCT
ejpam-2312	354	1	discrete	discrete	ADJ
ejpam-2312	354	2	dynamics	dynamic	NOUN
ejpam-2312	354	3	in	in	ADP
ejpam-2312	354	4	nature	nature	NOUN
ejpam-2312	354	5	and	and	CCONJ
ejpam-2312	354	6	society	society	NOUN
ejpam-2312	354	7	,	,	PUNCT
ejpam-2312	354	8	article	article	NOUN
ejpam-2312	354	9	i	i	PROPN
ejpam-2312	354	10	d	d	PROPN
ejpam-2312	354	11	298032	298032	NUM
ejpam-2312	354	12	,	,	PUNCT
ejpam-2312	354	13	1	1	NUM
ejpam-2312	354	14	-	-	SYM
ejpam-2312	354	15	6	6	NUM
ejpam-2312	354	16	.	.	NOUN
ejpam-2312	354	17	2013	2013	NUM
ejpam-2312	354	18	.	.	PUNCT
ejpam-2312	355	1	[	[	X
ejpam-2312	355	2	5	5	X
ejpam-2312	355	3	]	]	PUNCT
ejpam-2312	355	4	s.	s.	PROPN
ejpam-2312	355	5	hussain	hussain	PROPN
ejpam-2312	355	6	.	.	PUNCT
ejpam-2312	356	1	properties	property	NOUN
ejpam-2312	356	2	of	of	ADP
ejpam-2312	356	3	soft	soft	ADJ
ejpam-2312	356	4	semi	semi	ADJ
ejpam-2312	356	5	-	-	ADJ
ejpam-2312	356	6	open	open	ADJ
ejpam-2312	356	7	and	and	CCONJ
ejpam-2312	356	8	soft	soft	ADJ
ejpam-2312	356	9	semi	semi	ADJ
ejpam-2312	356	10	-	-	ADJ
ejpam-2312	356	11	closed	closed	ADJ
ejpam-2312	356	12	sets	set	NOUN
ejpam-2312	356	13	.	.	PUNCT
ejpam-2312	357	1	pensee	pensee	PROPN
ejpam-2312	357	2	journal	journal	PROPN
ejpam-2312	357	3	,	,	PUNCT
ejpam-2312	357	4	76(2	76(2	NUM
ejpam-2312	357	5	)	)	PUNCT
ejpam-2312	357	6	,	,	PUNCT
ejpam-2312	357	7	133–143	133–143	NUM
ejpam-2312	357	8	.	.	PUNCT
ejpam-2312	357	9	2014	2014	NUM
ejpam-2312	357	10	.	.	PUNCT
ejpam-2312	358	1	[	[	X
ejpam-2312	358	2	6	6	NUM
ejpam-2312	358	3	]	]	PUNCT
ejpam-2312	358	4	s.	s.	PROPN
ejpam-2312	358	5	hussain	hussain	PROPN
ejpam-2312	358	6	.	.	PUNCT
ejpam-2312	359	1	a	a	DET
ejpam-2312	359	2	note	note	NOUN
ejpam-2312	359	3	on	on	ADP
ejpam-2312	359	4	soft	soft	ADJ
ejpam-2312	359	5	connectedness	connectedness	NOUN
ejpam-2312	359	6	.	.	PUNCT
ejpam-2312	360	1	journal	journal	PROPN
ejpam-2312	360	2	of	of	ADP
ejpam-2312	360	3	egyptian	egyptian	PROPN
ejpam-2312	360	4	mathematical	mathematical	PROPN
ejpam-2312	360	5	society	society	NOUN
ejpam-2312	360	6	,	,	PUNCT
ejpam-2312	360	7	23(1	23(1	NUM
ejpam-2312	360	8	)	)	PUNCT
ejpam-2312	360	9	,	,	PUNCT
ejpam-2312	360	10	6–11	6–11	NOUN
ejpam-2312	360	11	.	.	PUNCT
ejpam-2312	360	12	2015	2015	NUM
ejpam-2312	360	13	.	.	PUNCT
ejpam-2312	361	1	http://dx.doi.org/10.1016/j.joems.2014.02.003	http://dx.doi.org/10.1016/j.joems.2014.02.003	NOUN
ejpam-2312	361	2	.	.	PUNCT
ejpam-2312	362	1	[	[	X
ejpam-2312	362	2	7	7	X
ejpam-2312	362	3	]	]	PUNCT
ejpam-2312	362	4	s.	s.	PROPN
ejpam-2312	362	5	hussain	hussain	PROPN
ejpam-2312	362	6	.	.	PUNCT
ejpam-2312	363	1	on	on	ADP
ejpam-2312	363	2	some	some	DET
ejpam-2312	363	3	soft	soft	ADJ
ejpam-2312	363	4	functions	function	NOUN
ejpam-2312	363	5	.	.	PUNCT
ejpam-2312	364	1	mathematical	mathematical	ADJ
ejpam-2312	364	2	science	science	NOUN
ejpam-2312	364	3	letters	letter	NOUN
ejpam-2312	364	4	,	,	PUNCT
ejpam-2312	364	5	4(1	4(1	NOUN
ejpam-2312	364	6	)	)	PUNCT
ejpam-2312	364	7	,	,	PUNCT
ejpam-2312	364	8	55–61	55–61	NUM
ejpam-2312	364	9	.	.	NOUN
ejpam-2312	364	10	2015	2015	NUM
ejpam-2312	364	11	.	.	PUNCT
ejpam-2312	365	1	[	[	X
ejpam-2312	365	2	8	8	X
ejpam-2312	365	3	]	]	PUNCT
ejpam-2312	365	4	s.	s.	PROPN
ejpam-2312	365	5	hussain	hussain	PROPN
ejpam-2312	365	6	and	and	CCONJ
ejpam-2312	365	7	b.	b.	PROPN
ejpam-2312	365	8	ahmad	ahmad	PROPN
ejpam-2312	365	9	.	.	PUNCT
ejpam-2312	366	1	some	some	DET
ejpam-2312	366	2	properties	property	NOUN
ejpam-2312	366	3	of	of	ADP
ejpam-2312	366	4	soft	soft	ADJ
ejpam-2312	366	5	topological	topological	ADJ
ejpam-2312	366	6	spaces	space	NOUN
ejpam-2312	366	7	.	.	PUNCT
ejpam-2312	367	1	computers	computer	NOUN
ejpam-2312	367	2	and	and	CCONJ
ejpam-2312	367	3	mathematics	mathematic	NOUN
ejpam-2312	367	4	with	with	ADP
ejpam-2312	367	5	applications	application	NOUN
ejpam-2312	367	6	,	,	PUNCT
ejpam-2312	367	7	62(11	62(11	NUM
ejpam-2312	367	8	)	)	PUNCT
ejpam-2312	367	9	,	,	PUNCT
ejpam-2312	367	10	4058–4067	4058–4067	NUM
ejpam-2312	367	11	.	.	PUNCT
ejpam-2312	367	12	2011	2011	NUM
ejpam-2312	367	13	.	.	PUNCT
ejpam-2312	368	1	[	[	X
ejpam-2312	368	2	9	9	NUM
ejpam-2312	368	3	]	]	PUNCT
ejpam-2312	368	4	s.	s.	PROPN
ejpam-2312	368	5	hussain	hussain	PROPN
ejpam-2312	368	6	and	and	CCONJ
ejpam-2312	368	7	b.	b.	PROPN
ejpam-2312	368	8	ahmad	ahmad	PROPN
ejpam-2312	368	9	.	.	PUNCT
ejpam-2312	369	1	soft	soft	ADJ
ejpam-2312	369	2	separation	separation	NOUN
ejpam-2312	369	3	axioms	axiom	NOUN
ejpam-2312	369	4	in	in	ADP
ejpam-2312	369	5	soft	soft	ADJ
ejpam-2312	369	6	topological	topological	ADJ
ejpam-2312	369	7	spaces	space	NOUN
ejpam-2312	369	8	.	.	PUNCT
ejpam-2312	370	1	hacettepe	hacettepe	PROPN
ejpam-2312	370	2	journal	journal	PROPN
ejpam-2312	370	3	of	of	ADP
ejpam-2312	370	4	mathematics	mathematic	NOUN
ejpam-2312	370	5	and	and	CCONJ
ejpam-2312	370	6	statistics	statistic	NOUN
ejpam-2312	370	7	,	,	PUNCT
ejpam-2312	370	8	44(3	44(3	NOUN
ejpam-2312	370	9	)	)	PUNCT
ejpam-2312	370	10	,	,	PUNCT
ejpam-2312	370	11	559–568	559–568	NUM
ejpam-2312	370	12	.	.	NOUN
ejpam-2312	370	13	2015	2015	NUM
ejpam-2312	370	14	.	.	PUNCT
ejpam-2312	371	1	references	reference	NOUN
ejpam-2312	371	2	210	210	NUM
ejpam-2312	371	3	[	[	X
ejpam-2312	371	4	10	10	NUM
ejpam-2312	371	5	]	]	PUNCT
ejpam-2312	371	6	a.	a.	NOUN
ejpam-2312	371	7	kharal	kharal	PROPN
ejpam-2312	371	8	and	and	CCONJ
ejpam-2312	371	9	b.	b.	PROPN
ejpam-2312	371	10	ahmad	ahmad	PROPN
ejpam-2312	371	11	.	.	PUNCT
ejpam-2312	372	1	mappings	mapping	NOUN
ejpam-2312	372	2	on	on	ADP
ejpam-2312	372	3	soft	soft	ADJ
ejpam-2312	372	4	classes	class	NOUN
ejpam-2312	372	5	.	.	PUNCT
ejpam-2312	373	1	new	new	ADJ
ejpam-2312	373	2	mathematics	mathematic	NOUN
ejpam-2312	373	3	and	and	CCONJ
ejpam-2312	373	4	natural	natural	ADJ
ejpam-2312	373	5	computations	computation	NOUN
ejpam-2312	373	6	,	,	PUNCT
ejpam-2312	373	7	7(3	7(3	NUM
ejpam-2312	373	8	)	)	PUNCT
ejpam-2312	373	9	,	,	PUNCT
ejpam-2312	373	10	471–481	471–481	NUM
ejpam-2312	373	11	.	.	PUNCT
ejpam-2312	373	12	2011	2011	NUM
ejpam-2312	373	13	.	.	PUNCT
ejpam-2312	374	1	[	[	X
ejpam-2312	374	2	11	11	NUM
ejpam-2312	374	3	]	]	X
ejpam-2312	374	4	b.	b.	PROPN
ejpam-2312	374	5	kostek	kostek	PROPN
ejpam-2312	374	6	.	.	PUNCT
ejpam-2312	374	7	soft	soft	ADJ
ejpam-2312	374	8	set	set	ADJ
ejpam-2312	374	9	approach	approach	NOUN
ejpam-2312	374	10	to	to	ADP
ejpam-2312	374	11	subjective	subjective	ADJ
ejpam-2312	374	12	assesment	assesment	NOUN
ejpam-2312	374	13	of	of	ADP
ejpam-2312	374	14	sound	sound	ADJ
ejpam-2312	374	15	quality	quality	NOUN
ejpam-2312	374	16	.	.	PUNCT
ejpam-2312	375	1	fuzzy	fuzzy	ADJ
ejpam-2312	375	2	systems	system	NOUN
ejpam-2312	375	3	proceeding	proceeding	NOUN
ejpam-2312	375	4	,	,	PUNCT
ejpam-2312	375	5	1998	1998	NUM
ejpam-2312	375	6	,	,	PUNCT
ejpam-2312	375	7	ieee	ieee	PROPN
ejpam-2312	375	8	world	world	PROPN
ejpam-2312	375	9	congress	congress	PROPN
ejpam-2312	375	10	on	on	ADP
ejpam-2312	375	11	computational	computational	ADJ
ejpam-2312	375	12	intelegence	intelegence	NOUN
ejpam-2312	375	13	,	,	PUNCT
ejpam-2312	375	14	4–9	4–9	PROPN
ejpam-2312	375	15	may	may	AUX
ejpam-2312	375	16	,	,	PUNCT
ejpam-2312	375	17	669–676	669–676	NUM
ejpam-2312	375	18	.	.	PUNCT
ejpam-2312	375	19	1998	1998	NUM
ejpam-2312	375	20	.	.	PUNCT
ejpam-2312	376	1	doi	doi	NOUN
ejpam-2312	376	2	:	:	PUNCT
ejpam-2312	376	3	10.1109	10.1109	NUM
ejpam-2312	376	4	/	/	SYM
ejpam-2312	376	5	fuzzy.1998.687568	fuzzy.1998.687568	NOUN
ejpam-2312	377	1	[	[	X
ejpam-2312	377	2	12	12	NUM
ejpam-2312	377	3	]	]	PUNCT
ejpam-2312	377	4	p.	p.	PROPN
ejpam-2312	377	5	k.	k.	PROPN
ejpam-2312	378	1	maji	maji	PROPN
ejpam-2312	378	2	,	,	PUNCT
ejpam-2312	378	3	r.	r.	PROPN
ejpam-2312	378	4	biswas	biswas	PROPN
ejpam-2312	378	5	,	,	PUNCT
ejpam-2312	378	6	and	and	CCONJ
ejpam-2312	378	7	r.	r.	PROPN
ejpam-2312	378	8	roy	roy	PROPN
ejpam-2312	378	9	.	.	PUNCT
ejpam-2312	379	1	an	an	DET
ejpam-2312	379	2	application	application	NOUN
ejpam-2312	379	3	of	of	ADP
ejpam-2312	379	4	soft	soft	ADJ
ejpam-2312	379	5	sets	set	NOUN
ejpam-2312	379	6	in	in	ADP
ejpam-2312	379	7	a	a	DET
ejpam-2312	379	8	decision	decision	NOUN
ejpam-2312	379	9	making	making	NOUN
ejpam-2312	379	10	problem	problem	NOUN
ejpam-2312	379	11	,	,	PUNCT
ejpam-2312	379	12	computers	computer	NOUN
ejpam-2312	379	13	and	and	CCONJ
ejpam-2312	379	14	mathematics	mathematic	NOUN
ejpam-2312	379	15	with	with	ADP
ejpam-2312	379	16	applications	application	NOUN
ejpam-2312	379	17	,	,	PUNCT
ejpam-2312	379	18	44(8	44(8	NOUN
ejpam-2312	379	19	-	-	SYM
ejpam-2312	379	20	9	9	NUM
ejpam-2312	379	21	)	)	PUNCT
ejpam-2312	379	22	,	,	PUNCT
ejpam-2312	379	23	1077	1077	NUM
ejpam-2312	379	24	-	-	SYM
ejpam-2312	379	25	1083	1083	NUM
ejpam-2312	379	26	.	.	PUNCT
ejpam-2312	379	27	2002	2002	NUM
ejpam-2312	379	28	.	.	PUNCT
ejpam-2312	380	1	[	[	X
ejpam-2312	380	2	13	13	NUM
ejpam-2312	380	3	]	]	PUNCT
ejpam-2312	380	4	p.	p.	PROPN
ejpam-2312	380	5	k.	k.	PROPN
ejpam-2312	381	1	maji	maji	PROPN
ejpam-2312	381	2	,	,	PUNCT
ejpam-2312	381	3	r.	r.	PROPN
ejpam-2312	381	4	biswas	biswas	PROPN
ejpam-2312	381	5	and	and	CCONJ
ejpam-2312	381	6	r.	r.	PROPN
ejpam-2312	381	7	roy	roy	PROPN
ejpam-2312	381	8	.	.	PROPN
ejpam-2312	381	9	soft	soft	ADJ
ejpam-2312	381	10	set	set	NOUN
ejpam-2312	381	11	theory	theory	NOUN
ejpam-2312	381	12	.	.	PUNCT
ejpam-2312	382	1	computers	computer	NOUN
ejpam-2312	382	2	and	and	CCONJ
ejpam-2312	382	3	mathematics	mathematic	NOUN
ejpam-2312	382	4	with	with	ADP
ejpam-2312	382	5	applications	application	NOUN
ejpam-2312	382	6	,	,	PUNCT
ejpam-2312	382	7	45(4	45(4	NOUN
ejpam-2312	382	8	-	-	SYM
ejpam-2312	382	9	5	5	NUM
ejpam-2312	382	10	)	)	PUNCT
ejpam-2312	382	11	,	,	PUNCT
ejpam-2312	382	12	555	555	NUM
ejpam-2312	382	13	-	-	SYM
ejpam-2312	382	14	562	562	NUM
ejpam-2312	382	15	.	.	PUNCT
ejpam-2312	382	16	2003	2003	NUM
ejpam-2312	382	17	.	.	PUNCT
ejpam-2312	383	1	[	[	X
ejpam-2312	383	2	14	14	NUM
ejpam-2312	383	3	]	]	X
ejpam-2312	383	4	d.	d.	PROPN
ejpam-2312	383	5	molodtsov	molodtsov	PROPN
ejpam-2312	383	6	.	.	PUNCT
ejpam-2312	384	1	soft	soft	ADJ
ejpam-2312	384	2	set	set	ADJ
ejpam-2312	384	3	theory	theory	NOUN
ejpam-2312	384	4	first	first	ADJ
ejpam-2312	384	5	results	result	NOUN
ejpam-2312	384	6	,	,	PUNCT
ejpam-2312	384	7	computers	computer	NOUN
ejpam-2312	384	8	and	and	CCONJ
ejpam-2312	384	9	mathematics	mathematic	NOUN
ejpam-2312	384	10	with	with	ADP
ejpam-2312	384	11	applications	application	NOUN
ejpam-2312	384	12	,	,	PUNCT
ejpam-2312	384	13	37(4	37(4	PROPN
ejpam-2312	384	14	-	-	PUNCT
ejpam-2312	384	15	5	5	NUM
ejpam-2312	384	16	)	)	PUNCT
ejpam-2312	384	17	,	,	PUNCT
ejpam-2312	384	18	19	19	NUM
ejpam-2312	384	19	-	-	SYM
ejpam-2312	384	20	31	31	NUM
ejpam-2312	384	21	.	.	PUNCT
ejpam-2312	384	22	1999	1999	NUM
ejpam-2312	384	23	.	.	PUNCT
ejpam-2312	385	1	[	[	X
ejpam-2312	385	2	15	15	NUM
ejpam-2312	385	3	]	]	X
ejpam-2312	385	4	d.	d.	PROPN
ejpam-2312	385	5	molodtsov	molodtsov	PROPN
ejpam-2312	385	6	,	,	PUNCT
ejpam-2312	385	7	v.y	v.y	PROPN
ejpam-2312	385	8	.	.	PROPN
ejpam-2312	385	9	leonov	leonov	PROPN
ejpam-2312	385	10	,	,	PUNCT
ejpam-2312	385	11	and	and	CCONJ
ejpam-2312	385	12	d.v	d.v	PROPN
ejpam-2312	385	13	.	.	PROPN
ejpam-2312	385	14	kovkov	kovkov	PROPN
ejpam-2312	385	15	.	.	PUNCT
ejpam-2312	386	1	soft	soft	ADJ
ejpam-2312	386	2	sets	set	NOUN
ejpam-2312	386	3	technique	technique	NOUN
ejpam-2312	386	4	and	and	CCONJ
ejpam-2312	386	5	its	its	PRON
ejpam-2312	386	6	application	application	NOUN
ejpam-2312	386	7	,	,	PUNCT
ejpam-2312	386	8	nechetkie	nechetkie	ADJ
ejpam-2312	386	9	sistemy	sistemy	PROPN
ejpam-2312	387	1	i	i	PROPN
ejpam-2312	387	2	myagkie	myagkie	PROPN
ejpam-2312	387	3	vychisleniya	vychisleniya	PROPN
ejpam-2312	387	4	,	,	PUNCT
ejpam-2312	387	5	9(1	9(1	NUM
ejpam-2312	387	6	)	)	PUNCT
ejpam-2312	387	7	,	,	PUNCT
ejpam-2312	387	8	8	8	NUM
ejpam-2312	387	9	-	-	SYM
ejpam-2312	387	10	39	39	NUM
ejpam-2312	387	11	.	.	PUNCT
ejpam-2312	388	1	2006	2006	NUM
ejpam-2312	388	2	.	.	PUNCT
ejpam-2312	389	1	[	[	X
ejpam-2312	389	2	16	16	NUM
ejpam-2312	389	3	]	]	PUNCT
ejpam-2312	389	4	m.	m.	NOUN
ejpam-2312	389	5	mushrif	mushrif	NOUN
ejpam-2312	389	6	,	,	PUNCT
ejpam-2312	389	7	s.	s.	PROPN
ejpam-2312	389	8	sengupta	sengupta	PROPN
ejpam-2312	389	9	,	,	PUNCT
ejpam-2312	389	10	and	and	CCONJ
ejpam-2312	389	11	a.	a.	PROPN
ejpam-2312	389	12	k.	k.	PROPN
ejpam-2312	389	13	ray	ray	PROPN
ejpam-2312	389	14	.	.	PUNCT
ejpam-2312	390	1	texture	texture	ADJ
ejpam-2312	390	2	classification	classification	NOUN
ejpam-2312	390	3	using	use	VERB
ejpam-2312	390	4	a	a	DET
ejpam-2312	390	5	novel	novel	NOUN
ejpam-2312	390	6	,	,	PUNCT
ejpam-2312	390	7	soft	soft	ADJ
ejpam-2312	390	8	set	set	NOUN
ejpam-2312	390	9	theory	theory	NOUN
ejpam-2312	390	10	based	base	VERB
ejpam-2312	390	11	classification	classification	NOUN
ejpam-2312	390	12	algorithm	algorithm	NOUN
ejpam-2312	390	13	,	,	PUNCT
ejpam-2312	390	14	springer	springer	NOUN
ejpam-2312	390	15	,	,	PUNCT
ejpam-2312	390	16	berlin	berlin	PROPN
ejpam-2312	390	17	.	.	PUNCT
ejpam-2312	391	1	254–264	254–264	NUM
ejpam-2312	391	2	.	.	PUNCT
ejpam-2312	392	1	2006	2006	NUM
ejpam-2312	392	2	.	.	PUNCT
ejpam-2312	393	1	[	[	X
ejpam-2312	393	2	17	17	NUM
ejpam-2312	393	3	]	]	PUNCT
ejpam-2312	393	4	x.	x.	PROPN
ejpam-2312	393	5	hu	hu	PROPN
ejpam-2312	393	6	,	,	PUNCT
ejpam-2312	393	7	q.	q.	PROPN
ejpam-2312	393	8	liu	liu	PROPN
ejpam-2312	393	9	,	,	PUNCT
ejpam-2312	393	10	a.	a.	NOUN
ejpam-2312	393	11	skowron	skowron	PROPN
ejpam-2312	393	12	,	,	PUNCT
ejpam-2312	393	13	y.	y.	PROPN
ejpam-2312	393	14	y.	y.	PROPN
ejpam-2312	393	15	lin	lin	PROPN
ejpam-2312	393	16	,	,	PUNCT
ejpam-2312	393	17	r.	r.	PROPN
ejpam-2312	393	18	r.	r.	PROPN
ejpam-2312	393	19	yager	yager	PROPN
ejpam-2312	393	20	,	,	PUNCT
ejpam-2312	393	21	b.	b.	PROPN
ejpam-2312	393	22	zhang(eds	zhang(ed	NOUN
ejpam-2312	393	23	.	.	PUNCT
ejpam-2312	393	24	)	)	PUNCT
ejpam-2312	393	25	proceedings	proceeding	NOUN
ejpam-2312	393	26	of	of	ADP
ejpam-2312	393	27	granular	granular	ADJ
ejpam-2312	393	28	computing	computing	NOUN
ejpam-2312	393	29	vol	vol	NOUN
ejpam-2312	393	30	.	.	PROPN
ejpam-2312	393	31	2	2	NUM
ejpam-2312	393	32	,	,	PUNCT
ejpam-2312	393	33	ieee(2005	ieee(2005	NUM
ejpam-2312	393	34	)	)	PUNCT
ejpam-2312	393	35	,	,	PUNCT
ejpam-2312	393	36	617–621	617–621	NUM
ejpam-2312	393	37	.	.	PUNCT
ejpam-2312	393	38	2005	2005	NUM
ejpam-2312	393	39	.	.	PUNCT
ejpam-2312	394	1	[	[	X
ejpam-2312	394	2	18	18	NUM
ejpam-2312	394	3	]	]	PUNCT
ejpam-2312	394	4	m.	m.	NOUN
ejpam-2312	394	5	shabir	shabir	PROPN
ejpam-2312	394	6	and	and	CCONJ
ejpam-2312	394	7	m.	m.	PROPN
ejpam-2312	394	8	naz	naz	PROPN
ejpam-2312	394	9	.	.	PUNCT
ejpam-2312	395	1	on	on	ADP
ejpam-2312	395	2	soft	soft	ADJ
ejpam-2312	395	3	topological	topological	ADJ
ejpam-2312	395	4	spaces	space	NOUN
ejpam-2312	395	5	,	,	PUNCT
ejpam-2312	395	6	computers	computer	NOUN
ejpam-2312	395	7	and	and	CCONJ
ejpam-2312	395	8	mathematics	mathematic	NOUN
ejpam-2312	395	9	with	with	ADP
ejpam-2312	395	10	applications	application	NOUN
ejpam-2312	395	11	,	,	PUNCT
ejpam-2312	395	12	61(7	61(7	PROPN
ejpam-2312	395	13	)	)	PUNCT
ejpam-2312	395	14	,	,	PUNCT
ejpam-2312	395	15	1786–1799	1786–1799	NUM
ejpam-2312	395	16	.	.	PUNCT
ejpam-2312	395	17	2011	2011	NUM
ejpam-2312	395	18	.	.	PUNCT
ejpam-2312	396	1	[	[	X
ejpam-2312	396	2	19	19	NUM
ejpam-2312	396	3	]	]	PUNCT
ejpam-2312	396	4	z.	z.	PROPN
ejpam-2312	396	5	xio	xio	PROPN
ejpam-2312	396	6	,	,	PUNCT
ejpam-2312	396	7	l.	l.	PROPN
ejpam-2312	396	8	chen	chen	PROPN
ejpam-2312	396	9	,	,	PUNCT
ejpam-2312	396	10	b.	b.	PROPN
ejpam-2312	396	11	zhong	zhong	PROPN
ejpam-2312	396	12	,	,	PUNCT
ejpam-2312	396	13	and	and	CCONJ
ejpam-2312	396	14	s.	s.	PROPN
ejpam-2312	396	15	ye	ye	PROPN
ejpam-2312	396	16	.	.	PROPN
ejpam-2312	396	17	recognition	recognition	NOUN
ejpam-2312	396	18	for	for	ADP
ejpam-2312	396	19	information	information	NOUN
ejpam-2312	396	20	based	base	VERB
ejpam-2312	396	21	on	on	ADP
ejpam-2312	396	22	the	the	DET
ejpam-2312	396	23	theory	theory	NOUN
ejpam-2312	396	24	of	of	ADP
ejpam-2312	396	25	soft	soft	ADJ
ejpam-2312	396	26	sets	set	NOUN
ejpam-2312	396	27	,	,	PUNCT
ejpam-2312	396	28	j.	j.	PROPN
ejpam-2312	396	29	chen(ed	chen(ed	PROPN
ejpam-2312	396	30	.	.	PUNCT
ejpam-2312	396	31	)	)	PUNCT
ejpam-2312	396	32	,	,	PUNCT
ejpam-2312	396	33	proceedings	proceeding	NOUN
ejpam-2312	396	34	of	of	ADP
ejpam-2312	396	35	icsssm-05	icsssm-05	PROPN
ejpam-2312	396	36	,	,	PUNCT
ejpam-2312	396	37	vol	vol	NOUN
ejpam-2312	396	38	.	.	NOUN
ejpam-2312	396	39	2	2	NUM
ejpam-2312	396	40	,	,	PUNCT
ejpam-2312	396	41	ieee(2005	ieee(2005	NUM
ejpam-2312	396	42	)	)	PUNCT
ejpam-2312	396	43	,	,	PUNCT
ejpam-2312	396	44	1104–1106	1104–1106	NUM
ejpam-2312	396	45	.	.	PUNCT
ejpam-2312	396	46	2005	2005	NUM
ejpam-2312	396	47	.	.	PUNCT
ejpam-2312	397	1	[	[	X
ejpam-2312	397	2	20	20	NUM
ejpam-2312	397	3	]	]	X
ejpam-2312	397	4	i.	i.	PROPN
ejpam-2312	397	5	zorlutana	zorlutana	PROPN
ejpam-2312	397	6	,	,	PUNCT
ejpam-2312	397	7	n.	n.	PROPN
ejpam-2312	397	8	akdag	akdag	PROPN
ejpam-2312	397	9	,	,	PUNCT
ejpam-2312	397	10	and	and	CCONJ
ejpam-2312	397	11	w.	w.	PROPN
ejpam-2312	397	12	k.	k.	PROPN
ejpam-2312	397	13	min	min	PROPN
ejpam-2312	397	14	.	.	PROPN
ejpam-2312	397	15	remarks	remark	NOUN
ejpam-2312	397	16	on	on	ADP
ejpam-2312	397	17	soft	soft	ADJ
ejpam-2312	397	18	topological	topological	ADJ
ejpam-2312	397	19	spaces	space	NOUN
ejpam-2312	397	20	,	,	PUNCT
ejpam-2312	397	21	annals	annal	NOUN
ejpam-2312	397	22	of	of	ADP
ejpam-2312	397	23	fuzzy	fuzzy	ADJ
ejpam-2312	397	24	mathematics	mathematic	NOUN
ejpam-2312	397	25	and	and	CCONJ
ejpam-2312	397	26	informatics	informatic	NOUN
ejpam-2312	397	27	,	,	PUNCT
ejpam-2312	397	28	3(2	3(2	NUM
ejpam-2312	397	29	)	)	PUNCT
ejpam-2312	397	30	,	,	PUNCT
ejpam-2312	397	31	171–185	171–185	NUM
ejpam-2312	397	32	.	.	PUNCT
ejpam-2312	397	33	2012	2012	NUM
ejpam-2312	397	34	.	.	PUNCT