id	sid	tid	token	lemma	pos
ejpam-2422	1	1	european	european	PROPN
ejpam-2422	1	2	journal	journal	PROPN
ejpam-2422	1	3	of	of	ADP
ejpam-2422	1	4	pure	pure	ADJ
ejpam-2422	1	5	and	and	CCONJ
ejpam-2422	1	6	applied	apply	VERB
ejpam-2422	1	7	mathematics	mathematic	NOUN
ejpam-2422	1	8	vol	vol	NOUN
ejpam-2422	1	9	.	.	PROPN
ejpam-2422	2	1	9	9	NUM
ejpam-2422	2	2	,	,	PUNCT
ejpam-2422	2	3	no	no	INTJ
ejpam-2422	2	4	.	.	NOUN
ejpam-2422	2	5	4	4	NUM
ejpam-2422	2	6	,	,	PUNCT
ejpam-2422	2	7	2016	2016	NUM
ejpam-2422	2	8	,	,	PUNCT
ejpam-2422	2	9	419	419	NUM
ejpam-2422	2	10	-	-	SYM
ejpam-2422	2	11	433	433	NUM
ejpam-2422	2	12	issn	issn	PROPN
ejpam-2422	2	13	1307	1307	NUM
ejpam-2422	2	14	-	-	SYM
ejpam-2422	2	15	5543	5543	NUM
ejpam-2422	2	16	–	–	PUNCT
ejpam-2422	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2422	2	18	hutton	hutton	PROPN
ejpam-2422	2	19	uniformity	uniformity	NOUN
ejpam-2422	2	20	in	in	ADP
ejpam-2422	2	21	the	the	DET
ejpam-2422	2	22	context	context	NOUN
ejpam-2422	2	23	of	of	ADP
ejpam-2422	2	24	fuzzy	fuzzy	ADJ
ejpam-2422	2	25	soft	soft	ADJ
ejpam-2422	2	26	sets	set	NOUN
ejpam-2422	2	27	vildan	vildan	PROPN
ejpam-2422	2	28	çetkin	çetkin	PROPN
ejpam-2422	2	29	∗	∗	NOUN
ejpam-2422	2	30	,	,	PUNCT
ejpam-2422	2	31	halis	halis	ADJ
ejpam-2422	2	32	aygün	aygün	NOUN
ejpam-2422	2	33	department	department	NOUN
ejpam-2422	2	34	of	of	ADP
ejpam-2422	2	35	mathematics	mathematic	NOUN
ejpam-2422	2	36	,	,	PUNCT
ejpam-2422	2	37	kocaeli	kocaeli	PROPN
ejpam-2422	2	38	university	university	PROPN
ejpam-2422	2	39	,	,	PUNCT
ejpam-2422	2	40	umuttepe	umuttepe	NOUN
ejpam-2422	2	41	campus	campus	NOUN
ejpam-2422	2	42	,	,	PUNCT
ejpam-2422	2	43	41380	41380	NUM
ejpam-2422	2	44	,	,	PUNCT
ejpam-2422	2	45	kocaeli	kocaeli	ADJ
ejpam-2422	2	46	,	,	PUNCT
ejpam-2422	2	47	turkey	turkey	PROPN
ejpam-2422	2	48	abstract	abstract	NOUN
ejpam-2422	2	49	.	.	PUNCT
ejpam-2422	3	1	in	in	ADP
ejpam-2422	3	2	this	this	DET
ejpam-2422	3	3	paper	paper	NOUN
ejpam-2422	3	4	,	,	PUNCT
ejpam-2422	3	5	we	we	PRON
ejpam-2422	3	6	introduce	introduce	VERB
ejpam-2422	3	7	the	the	DET
ejpam-2422	3	8	concept	concept	NOUN
ejpam-2422	3	9	of	of	ADP
ejpam-2422	3	10	fuzzy	fuzzy	ADJ
ejpam-2422	3	11	soft	soft	ADJ
ejpam-2422	3	12	uniformity	uniformity	NOUN
ejpam-2422	3	13	in	in	ADP
ejpam-2422	3	14	hutton	hutton	PROPN
ejpam-2422	3	15	’s	’s	PART
ejpam-2422	3	16	sense	sense	NOUN
ejpam-2422	3	17	.	.	PUNCT
ejpam-2422	4	1	we	we	PRON
ejpam-2422	4	2	define	define	VERB
ejpam-2422	4	3	topological	topological	ADJ
ejpam-2422	4	4	fuzzy	fuzzy	ADJ
ejpam-2422	4	5	soft	soft	ADJ
ejpam-2422	4	6	remote	remote	ADJ
ejpam-2422	4	7	neighborhood	neighborhood	NOUN
ejpam-2422	4	8	system	system	NOUN
ejpam-2422	4	9	and	and	CCONJ
ejpam-2422	4	10	use	use	VERB
ejpam-2422	4	11	this	this	PRON
ejpam-2422	4	12	for	for	ADP
ejpam-2422	4	13	investigating	investigate	VERB
ejpam-2422	4	14	the	the	DET
ejpam-2422	4	15	relationship	relationship	NOUN
ejpam-2422	4	16	between	between	ADP
ejpam-2422	4	17	fuzzy	fuzzy	ADJ
ejpam-2422	4	18	soft	soft	ADJ
ejpam-2422	4	19	cotopology	cotopology	NOUN
ejpam-2422	4	20	and	and	CCONJ
ejpam-2422	4	21	fuzzy	fuzzy	ADJ
ejpam-2422	4	22	soft	soft	ADJ
ejpam-2422	4	23	(	(	PUNCT
ejpam-2422	4	24	quasi-)uniformity	quasi-)uniformity	NOUN
ejpam-2422	4	25	.	.	PUNCT
ejpam-2422	5	1	we	we	PRON
ejpam-2422	5	2	show	show	VERB
ejpam-2422	5	3	the	the	DET
ejpam-2422	5	4	existence	existence	NOUN
ejpam-2422	5	5	of	of	ADP
ejpam-2422	5	6	the	the	DET
ejpam-2422	5	7	initial	initial	ADJ
ejpam-2422	5	8	structure	structure	NOUN
ejpam-2422	5	9	of	of	ADP
ejpam-2422	5	10	fuzzy	fuzzy	ADJ
ejpam-2422	5	11	soft	soft	ADJ
ejpam-2422	5	12	uniformities	uniformity	NOUN
ejpam-2422	5	13	and	and	CCONJ
ejpam-2422	5	14	also	also	ADV
ejpam-2422	5	15	we	we	PRON
ejpam-2422	5	16	prove	prove	VERB
ejpam-2422	5	17	the	the	DET
ejpam-2422	5	18	category	category	NOUN
ejpam-2422	5	19	of	of	ADP
ejpam-2422	5	20	fuzzy	fuzzy	ADJ
ejpam-2422	5	21	soft	soft	ADJ
ejpam-2422	5	22	uniform	uniform	ADJ
ejpam-2422	5	23	spaces	space	NOUN
ejpam-2422	5	24	is	be	AUX
ejpam-2422	5	25	a	a	DET
ejpam-2422	5	26	topological	topological	ADJ
ejpam-2422	5	27	category	category	NOUN
ejpam-2422	5	28	over	over	ADP
ejpam-2422	5	29	set3	set3	PROPN
ejpam-2422	5	30	.	.	PUNCT
ejpam-2422	6	1	2010	2010	NUM
ejpam-2422	6	2	mathematics	mathematic	NOUN
ejpam-2422	6	3	subject	subject	NOUN
ejpam-2422	6	4	classifications	classification	NOUN
ejpam-2422	6	5	:	:	PUNCT
ejpam-2422	6	6	54a05,54a40,54e15	54a05,54a40,54e15	NUM
ejpam-2422	6	7	key	key	ADJ
ejpam-2422	6	8	words	word	NOUN
ejpam-2422	6	9	and	and	CCONJ
ejpam-2422	6	10	phrases	phrase	NOUN
ejpam-2422	6	11	:	:	PUNCT
ejpam-2422	6	12	fuzzy	fuzzy	ADJ
ejpam-2422	6	13	soft	soft	ADJ
ejpam-2422	6	14	set	set	NOUN
ejpam-2422	6	15	,	,	PUNCT
ejpam-2422	6	16	fuzzy	fuzzy	ADJ
ejpam-2422	6	17	soft	soft	ADJ
ejpam-2422	6	18	topology	topology	NOUN
ejpam-2422	6	19	,	,	PUNCT
ejpam-2422	6	20	fuzzy	fuzzy	ADJ
ejpam-2422	6	21	soft	soft	ADJ
ejpam-2422	6	22	remote	remote	ADJ
ejpam-2422	6	23	neighborhood	neighborhood	NOUN
ejpam-2422	6	24	,	,	PUNCT
ejpam-2422	6	25	fuzzy	fuzzy	ADJ
ejpam-2422	6	26	soft	soft	ADJ
ejpam-2422	6	27	uniformity	uniformity	NOUN
ejpam-2422	6	28	1	1	NUM
ejpam-2422	6	29	.	.	PUNCT
ejpam-2422	6	30	introduction	introduction	NOUN
ejpam-2422	6	31	in	in	ADP
ejpam-2422	6	32	1999	1999	NUM
ejpam-2422	6	33	,	,	PUNCT
ejpam-2422	6	34	molodtsov	molodtsov	NOUN
ejpam-2422	7	1	[	[	X
ejpam-2422	7	2	12	12	NUM
ejpam-2422	7	3	]	]	PUNCT
ejpam-2422	7	4	proposed	propose	VERB
ejpam-2422	7	5	a	a	DET
ejpam-2422	7	6	completely	completely	ADV
ejpam-2422	7	7	new	new	ADJ
ejpam-2422	7	8	concept	concept	NOUN
ejpam-2422	7	9	called	call	VERB
ejpam-2422	7	10	soft	soft	ADJ
ejpam-2422	7	11	set	set	NOUN
ejpam-2422	7	12	theory	theory	NOUN
ejpam-2422	7	13	to	to	ADP
ejpam-2422	7	14	model	model	NOUN
ejpam-2422	7	15	uncertainty	uncertainty	NOUN
ejpam-2422	7	16	,	,	PUNCT
ejpam-2422	7	17	which	which	PRON
ejpam-2422	7	18	associates	associate	VERB
ejpam-2422	7	19	a	a	DET
ejpam-2422	7	20	set	set	NOUN
ejpam-2422	7	21	with	with	ADP
ejpam-2422	7	22	a	a	DET
ejpam-2422	7	23	set	set	NOUN
ejpam-2422	7	24	of	of	ADP
ejpam-2422	7	25	parameters	parameter	NOUN
ejpam-2422	7	26	.	.	PUNCT
ejpam-2422	8	1	later	later	ADV
ejpam-2422	8	2	,	,	PUNCT
ejpam-2422	8	3	maji	maji	PROPN
ejpam-2422	8	4	et	et	PROPN
ejpam-2422	8	5	al	al	PROPN
ejpam-2422	8	6	.	.	PUNCT
ejpam-2422	9	1	[	[	X
ejpam-2422	9	2	11	11	NUM
ejpam-2422	9	3	]	]	PUNCT
ejpam-2422	9	4	introduced	introduce	VERB
ejpam-2422	9	5	the	the	DET
ejpam-2422	9	6	concept	concept	NOUN
ejpam-2422	9	7	of	of	ADP
ejpam-2422	9	8	fuzzy	fuzzy	ADJ
ejpam-2422	9	9	soft	soft	ADJ
ejpam-2422	9	10	set	set	NOUN
ejpam-2422	9	11	which	which	PRON
ejpam-2422	9	12	combines	combine	VERB
ejpam-2422	9	13	fuzzy	fuzzy	ADJ
ejpam-2422	9	14	sets	set	NOUN
ejpam-2422	9	15	and	and	CCONJ
ejpam-2422	9	16	soft	soft	ADJ
ejpam-2422	9	17	sets	set	NOUN
ejpam-2422	9	18	.	.	PUNCT
ejpam-2422	10	1	soft	soft	ADJ
ejpam-2422	10	2	set	set	NOUN
ejpam-2422	10	3	and	and	CCONJ
ejpam-2422	10	4	fuzzy	fuzzy	ADJ
ejpam-2422	10	5	soft	soft	ADJ
ejpam-2422	10	6	set	set	NOUN
ejpam-2422	10	7	theories	theory	NOUN
ejpam-2422	10	8	have	have	VERB
ejpam-2422	10	9	a	a	DET
ejpam-2422	10	10	rich	rich	ADJ
ejpam-2422	10	11	potential	potential	NOUN
ejpam-2422	10	12	for	for	ADP
ejpam-2422	10	13	applications	application	NOUN
ejpam-2422	10	14	in	in	ADP
ejpam-2422	10	15	several	several	ADJ
ejpam-2422	10	16	directions	direction	NOUN
ejpam-2422	10	17	.	.	PUNCT
ejpam-2422	11	1	up	up	ADV
ejpam-2422	11	2	till	till	SCONJ
ejpam-2422	11	3	now	now	ADV
ejpam-2422	11	4	there	there	PRON
ejpam-2422	11	5	are	be	VERB
ejpam-2422	11	6	many	many	ADJ
ejpam-2422	11	7	spectacular	spectacular	ADJ
ejpam-2422	11	8	and	and	CCONJ
ejpam-2422	11	9	creative	creative	ADJ
ejpam-2422	11	10	works	work	NOUN
ejpam-2422	11	11	about	about	ADP
ejpam-2422	11	12	the	the	DET
ejpam-2422	11	13	theories	theory	NOUN
ejpam-2422	11	14	of	of	ADP
ejpam-2422	11	15	soft	soft	ADJ
ejpam-2422	11	16	set	set	NOUN
ejpam-2422	11	17	and	and	CCONJ
ejpam-2422	11	18	fuzzy	fuzzy	ADJ
ejpam-2422	11	19	soft	soft	ADJ
ejpam-2422	11	20	set	set	NOUN
ejpam-2422	11	21	in	in	ADP
ejpam-2422	11	22	the	the	DET
ejpam-2422	11	23	literature	literature	NOUN
ejpam-2422	11	24	(	(	PUNCT
ejpam-2422	11	25	see	see	VERB
ejpam-2422	11	26	[	[	X
ejpam-2422	11	27	2	2	NUM
ejpam-2422	11	28	,	,	PUNCT
ejpam-2422	11	29	3	3	NUM
ejpam-2422	11	30	,	,	PUNCT
ejpam-2422	11	31	8	8	NUM
ejpam-2422	11	32	,	,	PUNCT
ejpam-2422	11	33	9	9	NUM
ejpam-2422	11	34	,	,	PUNCT
ejpam-2422	11	35	11	11	NUM
ejpam-2422	11	36	,	,	PUNCT
ejpam-2422	11	37	13	13	NUM
ejpam-2422	11	38	,	,	PUNCT
ejpam-2422	11	39	17	17	NUM
ejpam-2422	11	40	]	]	PUNCT
ejpam-2422	11	41	)	)	PUNCT
ejpam-2422	11	42	.	.	PUNCT
ejpam-2422	12	1	furthermore	furthermore	ADV
ejpam-2422	12	2	,	,	PUNCT
ejpam-2422	12	3	aygünoğlu	aygünoğlu	PROPN
ejpam-2422	12	4	et	et	PROPN
ejpam-2422	12	5	al	al	PROPN
ejpam-2422	12	6	.	.	PUNCT
ejpam-2422	13	1	[	[	X
ejpam-2422	13	2	4	4	X
ejpam-2422	13	3	]	]	PUNCT
ejpam-2422	13	4	studied	study	VERB
ejpam-2422	13	5	the	the	DET
ejpam-2422	13	6	topological	topological	ADJ
ejpam-2422	13	7	structure	structure	NOUN
ejpam-2422	13	8	of	of	ADP
ejpam-2422	13	9	fuzzy	fuzzy	ADJ
ejpam-2422	13	10	soft	soft	ADJ
ejpam-2422	13	11	sets	set	NOUN
ejpam-2422	13	12	based	base	VERB
ejpam-2422	13	13	on	on	ADP
ejpam-2422	13	14	the	the	DET
ejpam-2422	13	15	sense	sense	NOUN
ejpam-2422	13	16	of	of	ADP
ejpam-2422	13	17	šostak	šostak	NOUN
ejpam-2422	14	1	[	[	X
ejpam-2422	14	2	16	16	NUM
ejpam-2422	14	3	]	]	PUNCT
ejpam-2422	14	4	.	.	PUNCT
ejpam-2422	15	1	it	it	PRON
ejpam-2422	15	2	is	be	AUX
ejpam-2422	15	3	well	well	ADV
ejpam-2422	15	4	-	-	PUNCT
ejpam-2422	15	5	known	know	VERB
ejpam-2422	15	6	that	that	SCONJ
ejpam-2422	15	7	uniformity	uniformity	NOUN
ejpam-2422	15	8	is	be	AUX
ejpam-2422	15	9	a	a	DET
ejpam-2422	15	10	very	very	ADV
ejpam-2422	15	11	important	important	ADJ
ejpam-2422	15	12	concept	concept	NOUN
ejpam-2422	15	13	close	close	ADV
ejpam-2422	15	14	to	to	ADP
ejpam-2422	15	15	topology	topology	NOUN
ejpam-2422	15	16	and	and	CCONJ
ejpam-2422	15	17	a	a	DET
ejpam-2422	15	18	convenient	convenient	ADJ
ejpam-2422	15	19	tool	tool	NOUN
ejpam-2422	15	20	for	for	ADP
ejpam-2422	15	21	investigating	investigate	VERB
ejpam-2422	15	22	topology	topology	NOUN
ejpam-2422	15	23	.	.	PUNCT
ejpam-2422	16	1	fuzzy	fuzzy	ADJ
ejpam-2422	16	2	versions	version	NOUN
ejpam-2422	16	3	of	of	ADP
ejpam-2422	16	4	(	(	PUNCT
ejpam-2422	16	5	quasi-)uniformity	quasi-)uniformity	NOUN
ejpam-2422	16	6	theory	theory	NOUN
ejpam-2422	16	7	were	be	AUX
ejpam-2422	16	8	established	establish	VERB
ejpam-2422	16	9	by	by	ADP
ejpam-2422	16	10	hutton	hutton	PROPN
ejpam-2422	16	11	[	[	X
ejpam-2422	16	12	7	7	NUM
ejpam-2422	16	13	]	]	PUNCT
ejpam-2422	16	14	,	,	PUNCT
ejpam-2422	16	15	lowen	lowen	PROPN
ejpam-2422	17	1	[	[	X
ejpam-2422	17	2	10	10	NUM
ejpam-2422	17	3	]	]	PUNCT
ejpam-2422	17	4	,	,	PUNCT
ejpam-2422	17	5	höhle	höhle	PROPN
ejpam-2422	18	1	[	[	X
ejpam-2422	18	2	6	6	NUM
ejpam-2422	18	3	]	]	PUNCT
ejpam-2422	18	4	and	and	CCONJ
ejpam-2422	18	5	shi	shi	PROPN
ejpam-2422	19	1	[	[	X
ejpam-2422	19	2	14	14	NUM
ejpam-2422	19	3	,	,	PUNCT
ejpam-2422	19	4	15	15	NUM
ejpam-2422	19	5	]	]	PUNCT
ejpam-2422	19	6	.	.	PUNCT
ejpam-2422	20	1	fuzzy	fuzzy	ADJ
ejpam-2422	20	2	(	(	PUNCT
ejpam-2422	20	3	quasi-)uniformity	quasi-)uniformity	NOUN
ejpam-2422	20	4	in	in	ADP
ejpam-2422	20	5	hutton	hutton	PROPN
ejpam-2422	20	6	’s	’s	PART
ejpam-2422	20	7	sense	sense	NOUN
ejpam-2422	20	8	has	have	AUX
ejpam-2422	20	9	been	be	AUX
ejpam-2422	20	10	accepted	accept	VERB
ejpam-2422	20	11	by	by	ADP
ejpam-2422	20	12	many	many	ADJ
ejpam-2422	20	13	authors	author	NOUN
ejpam-2422	20	14	and	and	CCONJ
ejpam-2422	20	15	has	have	AUX
ejpam-2422	20	16	attracted	attract	VERB
ejpam-2422	20	17	wide	wide	ADJ
ejpam-2422	20	18	attention	attention	NOUN
ejpam-2422	20	19	in	in	ADP
ejpam-2422	20	20	the	the	DET
ejpam-2422	20	21	literature	literature	NOUN
ejpam-2422	20	22	,	,	PUNCT
ejpam-2422	20	23	despite	despite	SCONJ
ejpam-2422	20	24	this	this	PRON
ejpam-2422	20	25	.	.	PUNCT
ejpam-2422	21	1	in	in	ADP
ejpam-2422	21	2	this	this	DET
ejpam-2422	21	3	paper	paper	NOUN
ejpam-2422	21	4	,	,	PUNCT
ejpam-2422	21	5	we	we	PRON
ejpam-2422	21	6	give	give	VERB
ejpam-2422	21	7	an	an	DET
ejpam-2422	21	8	approach	approach	NOUN
ejpam-2422	21	9	to	to	ADP
ejpam-2422	21	10	the	the	DET
ejpam-2422	21	11	concept	concept	NOUN
ejpam-2422	21	12	of	of	ADP
ejpam-2422	21	13	fuzzy	fuzzy	ADJ
ejpam-2422	21	14	soft	soft	ADJ
ejpam-2422	21	15	uniformity	uniformity	NOUN
ejpam-2422	21	16	in	in	ADP
ejpam-2422	21	17	the	the	DET
ejpam-2422	21	18	sense	sense	NOUN
ejpam-2422	21	19	of	of	ADP
ejpam-2422	21	20	hutton	hutton	PROPN
ejpam-2422	21	21	which	which	PRON
ejpam-2422	21	22	is	be	AUX
ejpam-2422	21	23	compatible	compatible	ADJ
ejpam-2422	21	24	with	with	ADP
ejpam-2422	21	25	the	the	DET
ejpam-2422	21	26	fuzzy	fuzzy	ADJ
ejpam-2422	21	27	soft	soft	ADJ
ejpam-2422	21	28	topology	topology	NOUN
ejpam-2422	21	29	.	.	PUNCT
ejpam-2422	22	1	the	the	DET
ejpam-2422	22	2	structure	structure	NOUN
ejpam-2422	22	3	of	of	ADP
ejpam-2422	22	4	this	this	DET
ejpam-2422	22	5	paper	paper	NOUN
ejpam-2422	22	6	is	be	AUX
ejpam-2422	22	7	organized	organize	VERB
ejpam-2422	22	8	as	as	SCONJ
ejpam-2422	22	9	follows	follow	VERB
ejpam-2422	22	10	.	.	PUNCT
ejpam-2422	23	1	in	in	ADP
ejpam-2422	23	2	section	section	NOUN
ejpam-2422	23	3	2	2	NUM
ejpam-2422	23	4	,	,	PUNCT
ejpam-2422	23	5	we	we	PRON
ejpam-2422	23	6	give	give	VERB
ejpam-2422	23	7	some	some	DET
ejpam-2422	23	8	preliminary	preliminary	ADJ
ejpam-2422	23	9	concepts	concept	NOUN
ejpam-2422	23	10	and	and	CCONJ
ejpam-2422	23	11	properties	property	NOUN
ejpam-2422	23	12	.	.	PUNCT
ejpam-2422	24	1	in	in	ADP
ejpam-2422	24	2	section	section	NOUN
ejpam-2422	24	3	3	3	NUM
ejpam-2422	24	4	,	,	PUNCT
ejpam-2422	24	5	we	we	PRON
ejpam-2422	24	6	give	give	VERB
ejpam-2422	24	7	the	the	DET
ejpam-2422	24	8	definition	definition	NOUN
ejpam-2422	24	9	of	of	ADP
ejpam-2422	24	10	fuzzy	fuzzy	ADJ
ejpam-2422	24	11	soft	soft	ADJ
ejpam-2422	24	12	remote	remote	ADJ
ejpam-2422	24	13	neighborhood	neighborhood	NOUN
ejpam-2422	24	14	system	system	NOUN
ejpam-2422	24	15	and	and	CCONJ
ejpam-2422	24	16	investigate	investigate	VERB
ejpam-2422	24	17	relations	relation	NOUN
ejpam-2422	24	18	∗corresponding	∗corresponde	VERB
ejpam-2422	24	19	author	author	NOUN
ejpam-2422	24	20	.	.	PUNCT
ejpam-2422	25	1	email	email	NOUN
ejpam-2422	25	2	addresses	address	NOUN
ejpam-2422	25	3	:	:	PUNCT
ejpam-2422	25	4	vcetkin@gmail.com	vcetkin@gmail.com	X
ejpam-2422	25	5	(	(	PUNCT
ejpam-2422	25	6	v.	v.	ADP
ejpam-2422	25	7	çetkin	çetkin	PROPN
ejpam-2422	25	8	)	)	PUNCT
ejpam-2422	25	9	,	,	PUNCT
ejpam-2422	26	1	halis@kocaeli.edu.tr	halis@kocaeli.edu.tr	INTJ
ejpam-2422	26	2	(	(	PUNCT
ejpam-2422	26	3	h.	h.	PROPN
ejpam-2422	26	4	aygün	aygün	PROPN
ejpam-2422	26	5	)	)	PUNCT
ejpam-2422	26	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2422	27	1	419	419	NUM
ejpam-2422	28	1	c	c	NOUN
ejpam-2422	28	2	©	©	PROPN
ejpam-2422	28	3	2016	2016	NUM
ejpam-2422	28	4	ejpam	ejpam	VERB
ejpam-2422	28	5	all	all	DET
ejpam-2422	28	6	rights	right	NOUN
ejpam-2422	28	7	reserved	reserve	VERB
ejpam-2422	28	8	.	.	PUNCT
ejpam-2422	29	1	v.	v.	ADP
ejpam-2422	29	2	çetkin	çetkin	PROPN
ejpam-2422	29	3	,	,	PUNCT
ejpam-2422	29	4	h.	h.	PROPN
ejpam-2422	29	5	aygün	aygün	PROPN
ejpam-2422	29	6	/	/	SYM
ejpam-2422	29	7	eur	eur	PROPN
ejpam-2422	29	8	.	.	PUNCT
ejpam-2422	30	1	j.	j.	PROPN
ejpam-2422	30	2	pure	pure	PROPN
ejpam-2422	30	3	appl	appl	PROPN
ejpam-2422	30	4	.	.	PROPN
ejpam-2422	30	5	math	math	PROPN
ejpam-2422	30	6	,	,	PUNCT
ejpam-2422	30	7	9	9	NUM
ejpam-2422	30	8	(	(	PUNCT
ejpam-2422	30	9	2016	2016	NUM
ejpam-2422	30	10	)	)	PUNCT
ejpam-2422	30	11	,	,	PUNCT
ejpam-2422	30	12	419	419	NUM
ejpam-2422	30	13	-	-	SYM
ejpam-2422	30	14	433	433	NUM
ejpam-2422	30	15	420	420	NUM
ejpam-2422	30	16	between	between	ADP
ejpam-2422	30	17	fuzzy	fuzzy	ADJ
ejpam-2422	30	18	soft	soft	ADJ
ejpam-2422	30	19	cotopological	cotopological	ADJ
ejpam-2422	30	20	space	space	NOUN
ejpam-2422	30	21	and	and	CCONJ
ejpam-2422	30	22	fuzzy	fuzzy	ADJ
ejpam-2422	30	23	soft	soft	ADJ
ejpam-2422	30	24	remote	remote	ADJ
ejpam-2422	30	25	neighborhood	neighborhood	NOUN
ejpam-2422	30	26	system	system	NOUN
ejpam-2422	30	27	.	.	PUNCT
ejpam-2422	31	1	in	in	ADP
ejpam-2422	31	2	section	section	NOUN
ejpam-2422	31	3	4	4	NUM
ejpam-2422	31	4	,	,	PUNCT
ejpam-2422	31	5	we	we	PRON
ejpam-2422	31	6	define	define	VERB
ejpam-2422	31	7	fuzzy	fuzzy	ADJ
ejpam-2422	31	8	soft	soft	ADJ
ejpam-2422	31	9	uniformity	uniformity	NOUN
ejpam-2422	31	10	in	in	ADP
ejpam-2422	31	11	the	the	DET
ejpam-2422	31	12	sense	sense	NOUN
ejpam-2422	31	13	of	of	ADP
ejpam-2422	31	14	hutton	hutton	PROPN
ejpam-2422	31	15	and	and	CCONJ
ejpam-2422	31	16	we	we	PRON
ejpam-2422	31	17	study	study	VERB
ejpam-2422	31	18	the	the	DET
ejpam-2422	31	19	relationship	relationship	NOUN
ejpam-2422	31	20	between	between	ADP
ejpam-2422	31	21	fuzzy	fuzzy	ADJ
ejpam-2422	31	22	soft	soft	ADJ
ejpam-2422	31	23	cotopology	cotopology	NOUN
ejpam-2422	31	24	and	and	CCONJ
ejpam-2422	31	25	fuzzy	fuzzy	ADJ
ejpam-2422	31	26	soft	soft	ADJ
ejpam-2422	31	27	uniformity	uniformity	NOUN
ejpam-2422	31	28	by	by	ADP
ejpam-2422	31	29	using	use	VERB
ejpam-2422	31	30	fuzzy	fuzzy	ADJ
ejpam-2422	31	31	soft	soft	ADJ
ejpam-2422	31	32	remote	remote	ADJ
ejpam-2422	31	33	neighborhood	neighborhood	NOUN
ejpam-2422	31	34	system	system	NOUN
ejpam-2422	31	35	.	.	PUNCT
ejpam-2422	32	1	in	in	ADP
ejpam-2422	32	2	the	the	DET
ejpam-2422	32	3	last	last	ADJ
ejpam-2422	32	4	section	section	NOUN
ejpam-2422	32	5	,	,	PUNCT
ejpam-2422	32	6	we	we	PRON
ejpam-2422	32	7	introduce	introduce	VERB
ejpam-2422	32	8	and	and	CCONJ
ejpam-2422	32	9	characterize	characterize	VERB
ejpam-2422	32	10	the	the	DET
ejpam-2422	32	11	initial	initial	ADJ
ejpam-2422	32	12	structure	structure	NOUN
ejpam-2422	32	13	of	of	ADP
ejpam-2422	32	14	fuzzy	fuzzy	ADJ
ejpam-2422	32	15	soft	soft	ADJ
ejpam-2422	32	16	uniform	uniform	NOUN
ejpam-2422	32	17	spaces	space	NOUN
ejpam-2422	32	18	.	.	PUNCT
ejpam-2422	33	1	2	2	X
ejpam-2422	33	2	.	.	NUM
ejpam-2422	33	3	preliminaries	preliminary	NOUN
ejpam-2422	33	4	throughout	throughout	ADP
ejpam-2422	33	5	this	this	DET
ejpam-2422	33	6	paper	paper	NOUN
ejpam-2422	33	7	,	,	PUNCT
ejpam-2422	33	8	l	l	NOUN
ejpam-2422	33	9	is	be	AUX
ejpam-2422	33	10	a	a	DET
ejpam-2422	33	11	complete	complete	ADJ
ejpam-2422	33	12	lattice	lattice	NOUN
ejpam-2422	33	13	,	,	PUNCT
ejpam-2422	33	14	m	m	VERB
ejpam-2422	33	15	is	be	AUX
ejpam-2422	33	16	a	a	DET
ejpam-2422	33	17	completely	completely	ADV
ejpam-2422	33	18	distributive	distributive	ADJ
ejpam-2422	33	19	lattice	lattice	NOUN
ejpam-2422	33	20	and	and	CCONJ
ejpam-2422	33	21	there	there	PRON
ejpam-2422	33	22	is	be	VERB
ejpam-2422	33	23	an	an	DET
ejpam-2422	33	24	order	order	NOUN
ejpam-2422	33	25	-	-	PUNCT
ejpam-2422	33	26	reversing	reverse	VERB
ejpam-2422	33	27	involution	involution	NOUN
ejpam-2422	33	28	′	′	NUM
ejpam-2422	33	29	on	on	ADP
ejpam-2422	33	30	l.	l.	PROPN
ejpam-2422	33	31	let	let	VERB
ejpam-2422	33	32	a	a	DET
ejpam-2422	33	33	,	,	PUNCT
ejpam-2422	33	34	b	b	NOUN
ejpam-2422	33	35	be	be	AUX
ejpam-2422	33	36	elements	element	NOUN
ejpam-2422	33	37	in	in	ADP
ejpam-2422	33	38	l.	l.	PROPN
ejpam-2422	33	39	an	an	DET
ejpam-2422	33	40	element	element	NOUN
ejpam-2422	33	41	a	a	PRON
ejpam-2422	33	42	in	in	ADP
ejpam-2422	33	43	l	l	NOUN
ejpam-2422	33	44	is	be	AUX
ejpam-2422	33	45	said	say	VERB
ejpam-2422	33	46	to	to	PART
ejpam-2422	33	47	be	be	AUX
ejpam-2422	33	48	coprime	coprime	ADJ
ejpam-2422	33	49	if	if	SCONJ
ejpam-2422	33	50	a	a	DET
ejpam-2422	33	51	≤	≤	NUM
ejpam-2422	33	52	b	b	NOUN
ejpam-2422	33	53	∨	∨	NUM
ejpam-2422	33	54	c	c	PROPN
ejpam-2422	33	55	implies	imply	VERB
ejpam-2422	33	56	that	that	SCONJ
ejpam-2422	33	57	a	a	DET
ejpam-2422	33	58	≤	≤	PROPN
ejpam-2422	33	59	b	b	NOUN
ejpam-2422	33	60	or	or	CCONJ
ejpam-2422	33	61	a	a	DET
ejpam-2422	33	62	≤	≤	ADJ
ejpam-2422	33	63	c.	c.	NOUN
ejpam-2422	33	64	the	the	DET
ejpam-2422	33	65	set	set	NOUN
ejpam-2422	33	66	of	of	ADP
ejpam-2422	33	67	all	all	DET
ejpam-2422	33	68	coprimes	coprime	NOUN
ejpam-2422	33	69	of	of	ADP
ejpam-2422	33	70	l	l	NOUN
ejpam-2422	33	71	is	be	AUX
ejpam-2422	33	72	denoted	denote	VERB
ejpam-2422	33	73	by	by	ADP
ejpam-2422	33	74	c(l	c(l	NOUN
ejpam-2422	33	75	)	)	PUNCT
ejpam-2422	33	76	.	.	PUNCT
ejpam-2422	34	1	we	we	PRON
ejpam-2422	34	2	say	say	VERB
ejpam-2422	34	3	a	a	PRON
ejpam-2422	34	4	is	be	AUX
ejpam-2422	34	5	way	way	NOUN
ejpam-2422	34	6	below	below	ADV
ejpam-2422	34	7	(	(	PUNCT
ejpam-2422	34	8	wedge	wedge	NOUN
ejpam-2422	34	9	below	below	ADP
ejpam-2422	34	10	)	)	PUNCT
ejpam-2422	34	11	b	b	NOUN
ejpam-2422	34	12	,	,	PUNCT
ejpam-2422	34	13	in	in	ADP
ejpam-2422	34	14	symbols	symbol	NOUN
ejpam-2422	34	15	,	,	PUNCT
ejpam-2422	34	16	a	a	DET
ejpam-2422	34	17	�	�	PROPN
ejpam-2422	34	18	b	b	PROPN
ejpam-2422	34	19	(	(	PUNCT
ejpam-2422	34	20	a	a	DET
ejpam-2422	34	21	ã	ã	X
ejpam-2422	34	22	b	b	NOUN
ejpam-2422	34	23	)	)	PUNCT
ejpam-2422	34	24	or	or	CCONJ
ejpam-2422	34	25	b	b	X
ejpam-2422	34	26	�	�	PROPN
ejpam-2422	34	27	a	a	DET
ejpam-2422	34	28	(	(	PUNCT
ejpam-2422	34	29	b	b	PROPN
ejpam-2422	34	30	â	â	X
ejpam-2422	34	31	a	a	NOUN
ejpam-2422	34	32	)	)	PUNCT
ejpam-2422	34	33	,	,	PUNCT
ejpam-2422	34	34	if	if	SCONJ
ejpam-2422	34	35	for	for	ADP
ejpam-2422	34	36	every	every	DET
ejpam-2422	34	37	directed	direct	VERB
ejpam-2422	34	38	(	(	PUNCT
ejpam-2422	34	39	arbitrary	arbitrary	ADJ
ejpam-2422	34	40	)	)	PUNCT
ejpam-2422	34	41	subset	subset	NOUN
ejpam-2422	35	1	d	d	NOUN
ejpam-2422	35	2	⊆	⊆	NUM
ejpam-2422	35	3	l	l	NOUN
ejpam-2422	35	4	,	,	PUNCT
ejpam-2422	35	5	∨d	∨d	PROPN
ejpam-2422	35	6	≥	≥	PROPN
ejpam-2422	35	7	b	b	PROPN
ejpam-2422	35	8	implies	imply	VERB
ejpam-2422	35	9	a	a	DET
ejpam-2422	35	10	≤	≤	NUM
ejpam-2422	35	11	d	d	NOUN
ejpam-2422	35	12	for	for	ADP
ejpam-2422	35	13	some	some	DET
ejpam-2422	35	14	d	d	PROPN
ejpam-2422	35	15	∈	∈	PROPN
ejpam-2422	35	16	d.	d.	NOUN
ejpam-2422	35	17	clearly	clearly	ADV
ejpam-2422	35	18	if	if	SCONJ
ejpam-2422	35	19	a	a	DET
ejpam-2422	35	20	∈	∈	PROPN
ejpam-2422	35	21	l	l	NOUN
ejpam-2422	35	22	is	be	AUX
ejpam-2422	35	23	coprime	coprime	ADJ
ejpam-2422	35	24	,	,	PUNCT
ejpam-2422	36	1	then	then	ADV
ejpam-2422	36	2	a	a	DET
ejpam-2422	36	3	�	�	PROPN
ejpam-2422	36	4	b	b	PROPN
ejpam-2422	36	5	if	if	SCONJ
ejpam-2422	37	1	and	and	CCONJ
ejpam-2422	37	2	only	only	ADV
ejpam-2422	37	3	if	if	SCONJ
ejpam-2422	37	4	a	a	DET
ejpam-2422	37	5	ã	ã	X
ejpam-2422	37	6	b.	b.	NOUN
ejpam-2422	37	7	a	a	DET
ejpam-2422	37	8	complete	complete	ADJ
ejpam-2422	37	9	lattice	lattice	NOUN
ejpam-2422	37	10	l	l	NOUN
ejpam-2422	37	11	is	be	AUX
ejpam-2422	37	12	said	say	VERB
ejpam-2422	37	13	to	to	PART
ejpam-2422	37	14	be	be	AUX
ejpam-2422	37	15	continuous	continuous	ADJ
ejpam-2422	37	16	(	(	PUNCT
ejpam-2422	37	17	completely	completely	ADV
ejpam-2422	37	18	distributive	distributive	ADJ
ejpam-2422	37	19	)	)	PUNCT
ejpam-2422	37	20	if	if	SCONJ
ejpam-2422	37	21	every	every	DET
ejpam-2422	37	22	element	element	NOUN
ejpam-2422	37	23	in	in	ADP
ejpam-2422	37	24	l	l	PROPN
ejpam-2422	37	25	is	be	AUX
ejpam-2422	37	26	the	the	DET
ejpam-2422	37	27	supremum	supremum	NOUN
ejpam-2422	37	28	of	of	ADP
ejpam-2422	37	29	all	all	DET
ejpam-2422	37	30	elements	element	NOUN
ejpam-2422	37	31	way	way	ADV
ejpam-2422	37	32	below	below	ADV
ejpam-2422	37	33	(	(	PUNCT
ejpam-2422	37	34	wedge	wedge	NOUN
ejpam-2422	37	35	below	below	ADV
ejpam-2422	37	36	)	)	PUNCT
ejpam-2422	37	37	it	it	PRON
ejpam-2422	37	38	.	.	PUNCT
ejpam-2422	38	1	proposition	proposition	NOUN
ejpam-2422	38	2	1	1	NUM
ejpam-2422	38	3	.	.	PUNCT
ejpam-2422	39	1	[	[	X
ejpam-2422	39	2	5	5	X
ejpam-2422	39	3	]	]	PUNCT
ejpam-2422	39	4	let	let	AUX
ejpam-2422	39	5	l	l	NOUN
ejpam-2422	39	6	be	be	AUX
ejpam-2422	39	7	a	a	DET
ejpam-2422	39	8	complete	complete	ADJ
ejpam-2422	39	9	lattice	lattice	NOUN
ejpam-2422	39	10	.	.	PUNCT
ejpam-2422	40	1	the	the	DET
ejpam-2422	40	2	following	follow	VERB
ejpam-2422	40	3	conditions	condition	NOUN
ejpam-2422	40	4	are	be	AUX
ejpam-2422	40	5	equivalent	equivalent	ADJ
ejpam-2422	40	6	:	:	PUNCT
ejpam-2422	40	7	(	(	PUNCT
ejpam-2422	40	8	i	i	NOUN
ejpam-2422	40	9	)	)	PUNCT
ejpam-2422	40	10	l	l	NOUN
ejpam-2422	40	11	is	be	AUX
ejpam-2422	40	12	completely	completely	ADV
ejpam-2422	40	13	distributive	distributive	ADJ
ejpam-2422	40	14	.	.	PUNCT
ejpam-2422	41	1	(	(	PUNCT
ejpam-2422	41	2	ii	ii	NOUN
ejpam-2422	41	3	)	)	PUNCT
ejpam-2422	41	4	l	l	NOUN
ejpam-2422	41	5	is	be	AUX
ejpam-2422	41	6	distributive	distributive	ADJ
ejpam-2422	41	7	continuous	continuous	ADJ
ejpam-2422	41	8	lattice	lattice	NOUN
ejpam-2422	41	9	with	with	ADP
ejpam-2422	41	10	enough	enough	ADJ
ejpam-2422	41	11	coprimes	coprime	NOUN
ejpam-2422	41	12	.	.	PUNCT
ejpam-2422	42	1	(	(	PUNCT
ejpam-2422	42	2	iii	iii	X
ejpam-2422	42	3	)	)	PUNCT
ejpam-2422	42	4	the	the	DET
ejpam-2422	42	5	operator	operator	NOUN
ejpam-2422	42	6	∨	∨	NOUN
ejpam-2422	42	7	:	:	PUNCT
ejpam-2422	43	1	low(l)→	low(l)→	PROPN
ejpam-2422	43	2	l	l	NOUN
ejpam-2422	43	3	sending	send	VERB
ejpam-2422	43	4	every	every	DET
ejpam-2422	43	5	lower	low	ADJ
ejpam-2422	43	6	set	set	NOUN
ejpam-2422	43	7	to	to	ADP
ejpam-2422	43	8	its	its	PRON
ejpam-2422	43	9	supremum	supremum	NOUN
ejpam-2422	43	10	has	have	VERB
ejpam-2422	43	11	a	a	DET
ejpam-2422	43	12	left	left	ADJ
ejpam-2422	43	13	adjoint	adjoint	NOUN
ejpam-2422	43	14	β	β	X
ejpam-2422	43	15	,	,	PUNCT
ejpam-2422	43	16	and	and	CCONJ
ejpam-2422	43	17	in	in	ADP
ejpam-2422	43	18	this	this	DET
ejpam-2422	43	19	case	case	NOUN
ejpam-2422	43	20	β(a	β(a	PROPN
ejpam-2422	43	21	)	)	PUNCT
ejpam-2422	43	22	=	=	PRON
ejpam-2422	44	1	{	{	PUNCT
ejpam-2422	44	2	b	b	PROPN
ejpam-2422	44	3	|	|	NOUN
ejpam-2422	44	4	b	b	PROPN
ejpam-2422	45	1	ã	ã	X
ejpam-2422	45	2	a	a	X
ejpam-2422	45	3	}	}	PUNCT
ejpam-2422	45	4	.	.	PUNCT
ejpam-2422	46	1	from	from	ADP
ejpam-2422	46	2	(	(	PUNCT
ejpam-2422	46	3	iii	iii	NOUN
ejpam-2422	46	4	)	)	PUNCT
ejpam-2422	46	5	in	in	ADP
ejpam-2422	46	6	the	the	DET
ejpam-2422	46	7	above	above	ADJ
ejpam-2422	46	8	proposition	proposition	NOUN
ejpam-2422	46	9	it	it	PRON
ejpam-2422	46	10	is	be	AUX
ejpam-2422	46	11	easy	easy	ADJ
ejpam-2422	46	12	to	to	PART
ejpam-2422	46	13	see	see	VERB
ejpam-2422	46	14	that	that	SCONJ
ejpam-2422	46	15	the	the	DET
ejpam-2422	46	16	wedge	wedge	NOUN
ejpam-2422	46	17	below	below	ADP
ejpam-2422	46	18	relation	relation	NOUN
ejpam-2422	46	19	has	have	VERB
ejpam-2422	46	20	the	the	DET
ejpam-2422	46	21	interpolation	interpolation	NOUN
ejpam-2422	46	22	property	property	NOUN
ejpam-2422	46	23	in	in	ADP
ejpam-2422	46	24	a	a	DET
ejpam-2422	46	25	completely	completely	ADV
ejpam-2422	46	26	distributive	distributive	ADJ
ejpam-2422	46	27	lattice	lattice	NOUN
ejpam-2422	46	28	,	,	PUNCT
ejpam-2422	46	29	this	this	PRON
ejpam-2422	46	30	is	be	AUX
ejpam-2422	46	31	to	to	PART
ejpam-2422	46	32	say	say	VERB
ejpam-2422	46	33	,	,	PUNCT
ejpam-2422	46	34	a	a	DET
ejpam-2422	46	35	ã	ã	X
ejpam-2422	46	36	b	b	NOUN
ejpam-2422	46	37	implies	imply	VERB
ejpam-2422	46	38	there	there	PRON
ejpam-2422	46	39	is	be	VERB
ejpam-2422	46	40	some	some	DET
ejpam-2422	46	41	c	c	NOUN
ejpam-2422	46	42	∈	∈	NOUN
ejpam-2422	46	43	l	l	NOUN
ejpam-2422	46	44	such	such	ADJ
ejpam-2422	46	45	that	that	SCONJ
ejpam-2422	46	46	a	a	DET
ejpam-2422	46	47	ã	ã	X
ejpam-2422	46	48	c	c	X
ejpam-2422	46	49	ã	ã	X
ejpam-2422	46	50	b.	b.	PROPN
ejpam-2422	46	51	let	let	VERB
ejpam-2422	46	52	e	e	PROPN
ejpam-2422	46	53	and	and	CCONJ
ejpam-2422	46	54	k	k	PROPN
ejpam-2422	46	55	be	be	AUX
ejpam-2422	46	56	arbitrary	arbitrary	ADJ
ejpam-2422	46	57	nonempty	nonempty	ADJ
ejpam-2422	46	58	sets	set	NOUN
ejpam-2422	46	59	viewed	view	VERB
ejpam-2422	46	60	on	on	ADP
ejpam-2422	46	61	the	the	DET
ejpam-2422	46	62	sets	set	NOUN
ejpam-2422	46	63	of	of	ADP
ejpam-2422	46	64	parameters	parameter	NOUN
ejpam-2422	46	65	.	.	PUNCT
ejpam-2422	47	1	a	a	DET
ejpam-2422	47	2	fuzzy	fuzzy	ADJ
ejpam-2422	47	3	soft	soft	ADJ
ejpam-2422	47	4	set	set	NOUN
ejpam-2422	47	5	f	f	PROPN
ejpam-2422	47	6	on	on	ADP
ejpam-2422	47	7	x	x	X
ejpam-2422	47	8	,	,	PUNCT
ejpam-2422	47	9	is	be	AUX
ejpam-2422	47	10	a	a	DET
ejpam-2422	47	11	mapping	mapping	NOUN
ejpam-2422	47	12	from	from	ADP
ejpam-2422	47	13	e	e	NOUN
ejpam-2422	47	14	into	into	ADP
ejpam-2422	47	15	lx	lx	NOUN
ejpam-2422	47	16	,	,	PUNCT
ejpam-2422	47	17	i.e.	i.e.	X
ejpam-2422	47	18	,	,	PUNCT
ejpam-2422	47	19	fe	fe	X
ejpam-2422	47	20	:	:	PUNCT
ejpam-2422	47	21	=	=	SYM
ejpam-2422	47	22	f	f	X
ejpam-2422	47	23	(	(	PUNCT
ejpam-2422	47	24	e	e	NOUN
ejpam-2422	47	25	)	)	PUNCT
ejpam-2422	47	26	is	be	AUX
ejpam-2422	47	27	an	an	DET
ejpam-2422	47	28	l	l	NOUN
ejpam-2422	47	29	-	-	ADJ
ejpam-2422	47	30	fuzzy	fuzzy	ADJ
ejpam-2422	47	31	set	set	NOUN
ejpam-2422	47	32	on	on	ADP
ejpam-2422	47	33	x	x	X
ejpam-2422	47	34	,	,	PUNCT
ejpam-2422	47	35	for	for	ADP
ejpam-2422	47	36	each	each	DET
ejpam-2422	47	37	e	e	PROPN
ejpam-2422	47	38	∈	∈	PROPN
ejpam-2422	47	39	e	e	X
ejpam-2422	47	40	(	(	PUNCT
ejpam-2422	47	41	see	see	VERB
ejpam-2422	47	42	figure	figure	NOUN
ejpam-2422	47	43	1	1	NUM
ejpam-2422	47	44	)	)	PUNCT
ejpam-2422	47	45	.	.	PUNCT
ejpam-2422	48	1	the	the	DET
ejpam-2422	48	2	family	family	NOUN
ejpam-2422	48	3	of	of	ADP
ejpam-2422	48	4	all	all	DET
ejpam-2422	48	5	l	l	ADJ
ejpam-2422	48	6	-	-	ADJ
ejpam-2422	48	7	fuzzy	fuzzy	ADJ
ejpam-2422	48	8	soft	soft	ADJ
ejpam-2422	48	9	sets	set	NOUN
ejpam-2422	48	10	on	on	ADP
ejpam-2422	48	11	x	x	PUNCT
ejpam-2422	48	12	is	be	AUX
ejpam-2422	48	13	denoted	denote	VERB
ejpam-2422	48	14	by	by	ADP
ejpam-2422	48	15	(	(	PUNCT
ejpam-2422	48	16	lx	lx	NOUN
ejpam-2422	48	17	)	)	PUNCT
ejpam-2422	48	18	e	e	X
ejpam-2422	48	19	.	.	PUNCT
ejpam-2422	49	1	by	by	ADP
ejpam-2422	49	2	0x	0x	NOUN
ejpam-2422	49	3	and	and	CCONJ
ejpam-2422	49	4	1x	1x	NUM
ejpam-2422	49	5	,	,	PUNCT
ejpam-2422	49	6	we	we	PRON
ejpam-2422	49	7	denote	denote	VERB
ejpam-2422	49	8	respectively	respectively	ADV
ejpam-2422	49	9	the	the	DET
ejpam-2422	49	10	null	null	ADJ
ejpam-2422	49	11	fuzzy	fuzzy	ADJ
ejpam-2422	49	12	soft	soft	ADJ
ejpam-2422	49	13	set	set	NOUN
ejpam-2422	49	14	and	and	CCONJ
ejpam-2422	49	15	absolute	absolute	ADJ
ejpam-2422	49	16	fuzzy	fuzzy	ADJ
ejpam-2422	49	17	soft	soft	ADJ
ejpam-2422	49	18	set	set	NOUN
ejpam-2422	49	19	.	.	PUNCT
ejpam-2422	50	1	the	the	DET
ejpam-2422	50	2	complement	complement	NOUN
ejpam-2422	50	3	of	of	ADP
ejpam-2422	50	4	an	an	DET
ejpam-2422	50	5	l	l	ADJ
ejpam-2422	50	6	-	-	ADJ
ejpam-2422	50	7	fuzzy	fuzzy	ADJ
ejpam-2422	50	8	soft	soft	ADJ
ejpam-2422	50	9	set	set	NOUN
ejpam-2422	50	10	f	f	X
ejpam-2422	50	11	is	be	AUX
ejpam-2422	50	12	denoted	denote	VERB
ejpam-2422	50	13	by	by	ADP
ejpam-2422	50	14	f	f	PROPN
ejpam-2422	50	15	′	′	PROPN
ejpam-2422	50	16	,	,	PUNCT
ejpam-2422	50	17	where	where	SCONJ
ejpam-2422	50	18	f	f	PROPN
ejpam-2422	50	19	′e	′e	PROPN
ejpam-2422	50	20	(	(	PUNCT
ejpam-2422	50	21	x	x	NOUN
ejpam-2422	50	22	)	)	PUNCT
ejpam-2422	50	23	=	=	SYM
ejpam-2422	50	24	(	(	PUNCT
ejpam-2422	50	25	fe(x))′.	fe(x))′.	ADP
ejpam-2422	50	26	the	the	DET
ejpam-2422	50	27	set	set	NOUN
ejpam-2422	50	28	of	of	ADP
ejpam-2422	50	29	all	all	DET
ejpam-2422	50	30	coprimes	coprime	NOUN
ejpam-2422	50	31	of	of	ADP
ejpam-2422	50	32	(	(	PUNCT
ejpam-2422	50	33	lx	lx	NOUN
ejpam-2422	50	34	)	)	PUNCT
ejpam-2422	50	35	e	e	NOUN
ejpam-2422	50	36	is	be	AUX
ejpam-2422	50	37	denoted	denote	VERB
ejpam-2422	50	38	by	by	ADP
ejpam-2422	50	39	c((lx	c((lx	NOUN
ejpam-2422	50	40	)	)	PUNCT
ejpam-2422	50	41	e	e	NOUN
ejpam-2422	50	42	)	)	PUNCT
ejpam-2422	50	43	.	.	PUNCT
ejpam-2422	51	1	definition	definition	NOUN
ejpam-2422	51	2	1	1	NUM
ejpam-2422	51	3	(	(	PUNCT
ejpam-2422	51	4	[	[	X
ejpam-2422	51	5	1	1	NUM
ejpam-2422	51	6	,	,	PUNCT
ejpam-2422	51	7	11	11	NUM
ejpam-2422	51	8	]	]	NUM
ejpam-2422	51	9	)	)	PUNCT
ejpam-2422	51	10	.	.	PUNCT
ejpam-2422	52	1	(	(	PUNCT
ejpam-2422	52	2	i	i	NOUN
ejpam-2422	52	3	)	)	PUNCT
ejpam-2422	52	4	we	we	PRON
ejpam-2422	52	5	say	say	VERB
ejpam-2422	52	6	that	that	SCONJ
ejpam-2422	52	7	f	f	PROPN
ejpam-2422	52	8	is	be	AUX
ejpam-2422	52	9	a	a	DET
ejpam-2422	52	10	fuzzy	fuzzy	ADJ
ejpam-2422	52	11	soft	soft	ADJ
ejpam-2422	52	12	subset	subset	NOUN
ejpam-2422	52	13	of	of	ADP
ejpam-2422	52	14	g	g	PROPN
ejpam-2422	52	15	and	and	CCONJ
ejpam-2422	52	16	write	write	VERB
ejpam-2422	52	17	f	f	PROPN
ejpam-2422	52	18	v	v	ADP
ejpam-2422	52	19	g	g	PROPN
ejpam-2422	52	20	if	if	SCONJ
ejpam-2422	52	21	fe	fe	X
ejpam-2422	52	22	≤	≤	X
ejpam-2422	52	23	ge	ge	PROPN
ejpam-2422	52	24	,	,	PUNCT
ejpam-2422	52	25	for	for	ADP
ejpam-2422	52	26	each	each	DET
ejpam-2422	52	27	e	e	PROPN
ejpam-2422	52	28	∈	∈	PROPN
ejpam-2422	52	29	e.	e.	PROPN
ejpam-2422	52	30	(	(	PUNCT
ejpam-2422	52	31	ii	ii	PROPN
ejpam-2422	52	32	)	)	PUNCT
ejpam-2422	52	33	union	union	NOUN
ejpam-2422	52	34	of	of	ADP
ejpam-2422	52	35	f	f	PROPN
ejpam-2422	52	36	and	and	CCONJ
ejpam-2422	52	37	g	g	PROPN
ejpam-2422	52	38	is	be	AUX
ejpam-2422	52	39	the	the	DET
ejpam-2422	52	40	fuzzy	fuzzy	ADJ
ejpam-2422	52	41	soft	soft	ADJ
ejpam-2422	52	42	set	set	NOUN
ejpam-2422	52	43	h=	h=	PRON
ejpam-2422	53	1	f	f	PROPN
ejpam-2422	53	2	t	t	PROPN
ejpam-2422	53	3	g	g	PROPN
ejpam-2422	53	4	,	,	PUNCT
ejpam-2422	53	5	where	where	SCONJ
ejpam-2422	53	6	he	he	PRON
ejpam-2422	53	7	=	=	SYM
ejpam-2422	53	8	fe	fe	X
ejpam-2422	53	9	∨	∨	NUM
ejpam-2422	53	10	ge	ge	PROPN
ejpam-2422	53	11	,	,	PUNCT
ejpam-2422	53	12	for	for	ADP
ejpam-2422	53	13	each	each	DET
ejpam-2422	53	14	e	e	PROPN
ejpam-2422	53	15	∈	∈	PROPN
ejpam-2422	53	16	e.	e.	PROPN
ejpam-2422	53	17	(	(	PUNCT
ejpam-2422	53	18	iii	iii	NOUN
ejpam-2422	53	19	)	)	PUNCT
ejpam-2422	53	20	intersection	intersection	NOUN
ejpam-2422	53	21	of	of	ADP
ejpam-2422	53	22	f	f	PROPN
ejpam-2422	53	23	and	and	CCONJ
ejpam-2422	53	24	g	g	PROPN
ejpam-2422	53	25	is	be	AUX
ejpam-2422	53	26	the	the	DET
ejpam-2422	53	27	fuzzy	fuzzy	ADJ
ejpam-2422	53	28	soft	soft	ADJ
ejpam-2422	53	29	set	set	NOUN
ejpam-2422	53	30	h=	h=	X
ejpam-2422	53	31	f	f	X
ejpam-2422	53	32	u	u	NOUN
ejpam-2422	53	33	g	g	PROPN
ejpam-2422	53	34	,	,	PUNCT
ejpam-2422	53	35	where	where	SCONJ
ejpam-2422	53	36	he	he	PRON
ejpam-2422	53	37	=	=	SYM
ejpam-2422	53	38	fe	fe	X
ejpam-2422	53	39	∧	∧	PROPN
ejpam-2422	53	40	ge	ge	PROPN
ejpam-2422	53	41	,	,	PUNCT
ejpam-2422	53	42	for	for	ADP
ejpam-2422	53	43	each	each	DET
ejpam-2422	53	44	e	e	PROPN
ejpam-2422	53	45	∈	∈	PROPN
ejpam-2422	53	46	e.	e.	PROPN
ejpam-2422	53	47	let	let	VERB
ejpam-2422	53	48	p	p	PRON
ejpam-2422	53	49	|	|	ADV
ejpam-2422	53	50	f	f	PROPN
ejpam-2422	53	51	denote	denote	VERB
ejpam-2422	53	52	the	the	DET
ejpam-2422	53	53	set	set	NOUN
ejpam-2422	53	54	{	{	PUNCT
ejpam-2422	53	55	g	g	NOUN
ejpam-2422	53	56	∈	∈	PROPN
ejpam-2422	53	57	(	(	PUNCT
ejpam-2422	53	58	lx	lx	NOUN
ejpam-2422	53	59	)	)	PUNCT
ejpam-2422	54	1	e	e	X
ejpam-2422	54	2	|	|	ADV
ejpam-2422	54	3	p	p	X
ejpam-2422	54	4	6v	6v	VERB
ejpam-2422	54	5	g	g	PROPN
ejpam-2422	54	6	v	v	NUM
ejpam-2422	54	7	f	f	X
ejpam-2422	54	8	}	}	PUNCT
ejpam-2422	54	9	for	for	ADP
ejpam-2422	54	10	p	p	PROPN
ejpam-2422	54	11	∈	∈	PROPN
ejpam-2422	54	12	c((lx	c((lx	PROPN
ejpam-2422	54	13	)	)	PUNCT
ejpam-2422	54	14	e	e	X
ejpam-2422	54	15	)	)	PUNCT
ejpam-2422	54	16	and	and	CCONJ
ejpam-2422	54	17	f	f	PROPN
ejpam-2422	54	18	∈	∈	PROPN
ejpam-2422	54	19	(	(	PUNCT
ejpam-2422	54	20	lx	lx	NOUN
ejpam-2422	54	21	)	)	PUNCT
ejpam-2422	54	22	e	e	X
ejpam-2422	54	23	.	.	PUNCT
ejpam-2422	55	1	v.	v.	ADP
ejpam-2422	55	2	çetkin	çetkin	PROPN
ejpam-2422	55	3	,	,	PUNCT
ejpam-2422	55	4	h.	h.	PROPN
ejpam-2422	55	5	aygün	aygün	PROPN
ejpam-2422	55	6	/	/	SYM
ejpam-2422	55	7	eur	eur	PROPN
ejpam-2422	55	8	.	.	PUNCT
ejpam-2422	56	1	j.	j.	PROPN
ejpam-2422	56	2	pure	pure	PROPN
ejpam-2422	56	3	appl	appl	PROPN
ejpam-2422	56	4	.	.	PROPN
ejpam-2422	56	5	math	math	PROPN
ejpam-2422	56	6	,	,	PUNCT
ejpam-2422	56	7	9	9	NUM
ejpam-2422	56	8	(	(	PUNCT
ejpam-2422	56	9	2016	2016	NUM
ejpam-2422	56	10	)	)	PUNCT
ejpam-2422	56	11	,	,	PUNCT
ejpam-2422	56	12	419	419	NUM
ejpam-2422	56	13	-	-	SYM
ejpam-2422	56	14	433	433	NUM
ejpam-2422	56	15	421	421	NUM
ejpam-2422	56	16	figure	figure	NOUN
ejpam-2422	56	17	1	1	NUM
ejpam-2422	56	18	:	:	PUNCT
ejpam-2422	56	19	a	a	DET
ejpam-2422	56	20	fuzzy	fuzzy	ADJ
ejpam-2422	56	21	soft	soft	ADJ
ejpam-2422	56	22	set	set	NOUN
ejpam-2422	56	23	f	f	PROPN
ejpam-2422	56	24	let	let	VERB
ejpam-2422	56	25	ϕ	ϕ	NOUN
ejpam-2422	56	26	:	:	PUNCT
ejpam-2422	57	1	x1	x1	PROPN
ejpam-2422	57	2	−→	−→	NOUN
ejpam-2422	57	3	x2	x2	PROPN
ejpam-2422	57	4	and	and	CCONJ
ejpam-2422	57	5	ψ	ψ	NOUN
ejpam-2422	57	6	:	:	PUNCT
ejpam-2422	57	7	e1	e1	VERB
ejpam-2422	57	8	−→	−→	NOUN
ejpam-2422	57	9	e2	e2	NOUN
ejpam-2422	57	10	be	be	VERB
ejpam-2422	57	11	two	two	NUM
ejpam-2422	57	12	functions	function	NOUN
ejpam-2422	57	13	,	,	PUNCT
ejpam-2422	57	14	where	where	SCONJ
ejpam-2422	57	15	e1	e1	PROPN
ejpam-2422	57	16	and	and	CCONJ
ejpam-2422	57	17	e2	e2	PROPN
ejpam-2422	57	18	are	be	AUX
ejpam-2422	57	19	parameter	parameter	NOUN
ejpam-2422	57	20	sets	set	NOUN
ejpam-2422	57	21	for	for	ADP
ejpam-2422	57	22	the	the	DET
ejpam-2422	57	23	crisp	crisp	ADJ
ejpam-2422	57	24	sets	set	NOUN
ejpam-2422	57	25	x1	x1	PROPN
ejpam-2422	57	26	and	and	CCONJ
ejpam-2422	57	27	x2	x2	PROPN
ejpam-2422	57	28	,	,	PUNCT
ejpam-2422	57	29	respectively	respectively	ADV
ejpam-2422	57	30	.	.	PUNCT
ejpam-2422	58	1	define	define	VERB
ejpam-2422	58	2	l	l	ADJ
ejpam-2422	58	3	-	-	ADJ
ejpam-2422	58	4	fuzzy	fuzzy	ADJ
ejpam-2422	58	5	soft	soft	ADJ
ejpam-2422	58	6	mapping	mapping	NOUN
ejpam-2422	58	7	ϕψ	ϕψ	ADP
ejpam-2422	58	8	→	→	SYM
ejpam-2422	58	9	:	:	PUNCT
ejpam-2422	58	10	(	(	PUNCT
ejpam-2422	58	11	lx1)e1	lx1)e1	X
ejpam-2422	58	12	→	→	PUNCT
ejpam-2422	58	13	(	(	PUNCT
ejpam-2422	58	14	lx2)e2	lx2)e2	PROPN
ejpam-2422	58	15	and	and	CCONJ
ejpam-2422	58	16	its	its	PRON
ejpam-2422	58	17	l	l	ADJ
ejpam-2422	58	18	-	-	ADJ
ejpam-2422	58	19	fuzzy	fuzzy	ADJ
ejpam-2422	58	20	soft	soft	ADJ
ejpam-2422	58	21	inverse	inverse	NOUN
ejpam-2422	58	22	mapping	mapping	NOUN
ejpam-2422	58	23	ϕψ	ϕψ	ADP
ejpam-2422	58	24	←	←	PROPN
ejpam-2422	58	25	:	:	PUNCT
ejpam-2422	58	26	(	(	PUNCT
ejpam-2422	58	27	lx2)e2	lx2)e2	PROPN
ejpam-2422	58	28	→	→	SYM
ejpam-2422	58	29	(	(	PUNCT
ejpam-2422	58	30	lx1)e1	lx1)e1	ADV
ejpam-2422	58	31	by	by	ADP
ejpam-2422	58	32	(	(	PUNCT
ejpam-2422	58	33	ϕψ→	ϕψ→	PROPN
ejpam-2422	58	34	(	(	PUNCT
ejpam-2422	58	35	f	f	PROPN
ejpam-2422	58	36	)	)	PUNCT
ejpam-2422	58	37	)	)	PUNCT
ejpam-2422	58	38	e2	e2	PROPN
ejpam-2422	58	39	(	(	PUNCT
ejpam-2422	58	40	y	y	NOUN
ejpam-2422	58	41	)	)	PUNCT
ejpam-2422	58	42	=	=	PUNCT
ejpam-2422	58	43	∨	∨	NUM
ejpam-2422	58	44	ϕ(x)=y	ϕ(x)=y	PROPN
ejpam-2422	58	45	∨	∨	PROPN
ejpam-2422	58	46	ψ(e1)=e2	ψ(e1)=e2	PROPN
ejpam-2422	58	47	fe1	fe1	PROPN
ejpam-2422	58	48	(	(	PUNCT
ejpam-2422	58	49	x	x	NOUN
ejpam-2422	58	50	)	)	PUNCT
ejpam-2422	58	51	,	,	PUNCT
ejpam-2422	58	52	for	for	ADP
ejpam-2422	58	53	all	all	DET
ejpam-2422	58	54	f	f	PROPN
ejpam-2422	58	55	∈	∈	PROPN
ejpam-2422	58	56	(	(	PUNCT
ejpam-2422	58	57	lx1)e1	lx1)e1	INTJ
ejpam-2422	58	58	,	,	PUNCT
ejpam-2422	58	59	y	y	PROPN
ejpam-2422	58	60	∈	∈	PROPN
ejpam-2422	58	61	x2	x2	PROPN
ejpam-2422	58	62	,	,	PUNCT
ejpam-2422	58	63	e2	e2	PROPN
ejpam-2422	58	64	∈	∈	PROPN
ejpam-2422	58	65	e2	e2	PROPN
ejpam-2422	58	66	and	and	CCONJ
ejpam-2422	58	67	(	(	PUNCT
ejpam-2422	58	68	ϕψ←(g))e1	ϕψ←(g))e1	INTJ
ejpam-2422	58	69	(	(	PUNCT
ejpam-2422	58	70	x	x	NOUN
ejpam-2422	58	71	)	)	PUNCT
ejpam-2422	58	72	=	=	SYM
ejpam-2422	58	73	gψ(e1)(ϕ(x	gψ(e1)(ϕ(x	NOUN
ejpam-2422	58	74	)	)	PUNCT
ejpam-2422	58	75	)	)	PUNCT
ejpam-2422	58	76	,	,	PUNCT
ejpam-2422	58	77	for	for	ADP
ejpam-2422	58	78	all	all	DET
ejpam-2422	58	79	e1	e1	PROPN
ejpam-2422	58	80	∈	∈	PROPN
ejpam-2422	58	81	e1	e1	NOUN
ejpam-2422	58	82	,	,	PUNCT
ejpam-2422	58	83	x	x	SYM
ejpam-2422	58	84	∈	∈	NOUN
ejpam-2422	58	85	x1	x1	NOUN
ejpam-2422	58	86	and	and	CCONJ
ejpam-2422	58	87	g	g	PROPN
ejpam-2422	58	88	∈	∈	PROPN
ejpam-2422	58	89	(	(	PUNCT
ejpam-2422	58	90	lx2)e2	lx2)e2	PROPN
ejpam-2422	58	91	.	.	PUNCT
ejpam-2422	59	1	we	we	PRON
ejpam-2422	59	2	refer	refer	VERB
ejpam-2422	59	3	to	to	ADP
ejpam-2422	59	4	[	[	X
ejpam-2422	59	5	3	3	NUM
ejpam-2422	59	6	,	,	PUNCT
ejpam-2422	59	7	4	4	NUM
ejpam-2422	59	8	,	,	PUNCT
ejpam-2422	59	9	9	9	NUM
ejpam-2422	59	10	,	,	PUNCT
ejpam-2422	59	11	11	11	NUM
ejpam-2422	59	12	]	]	PUNCT
ejpam-2422	59	13	for	for	ADP
ejpam-2422	59	14	all	all	DET
ejpam-2422	59	15	the	the	DET
ejpam-2422	59	16	basic	basic	ADJ
ejpam-2422	59	17	definitions	definition	NOUN
ejpam-2422	59	18	and	and	CCONJ
ejpam-2422	59	19	notations	notation	NOUN
ejpam-2422	59	20	related	relate	VERB
ejpam-2422	59	21	to	to	ADP
ejpam-2422	59	22	fuzzy	fuzzy	ADJ
ejpam-2422	59	23	soft	soft	ADJ
ejpam-2422	59	24	sets	set	NOUN
ejpam-2422	59	25	and	and	CCONJ
ejpam-2422	59	26	fuzzy	fuzzy	ADJ
ejpam-2422	59	27	soft	soft	ADJ
ejpam-2422	59	28	mappings	mapping	NOUN
ejpam-2422	59	29	.	.	PUNCT
ejpam-2422	60	1	definition	definition	NOUN
ejpam-2422	60	2	2	2	NUM
ejpam-2422	60	3	(	(	PUNCT
ejpam-2422	60	4	[	[	X
ejpam-2422	60	5	4	4	NUM
ejpam-2422	60	6	]	]	NUM
ejpam-2422	60	7	)	)	PUNCT
ejpam-2422	60	8	.	.	PUNCT
ejpam-2422	61	1	a	a	DET
ejpam-2422	61	2	mapping	mapping	NOUN
ejpam-2422	61	3	τ	τ	X
ejpam-2422	61	4	:	:	PUNCT
ejpam-2422	61	5	k	k	X
ejpam-2422	61	6	→	→	PUNCT
ejpam-2422	61	7	m	m	PROPN
ejpam-2422	61	8	(	(	PUNCT
ejpam-2422	61	9	l	l	NOUN
ejpam-2422	61	10	x	x	X
ejpam-2422	61	11	)	)	PUNCT
ejpam-2422	61	12	e	e	X
ejpam-2422	61	13	is	be	AUX
ejpam-2422	61	14	called	call	VERB
ejpam-2422	61	15	an	an	DET
ejpam-2422	61	16	(	(	PUNCT
ejpam-2422	61	17	l	l	NOUN
ejpam-2422	61	18	,	,	PUNCT
ejpam-2422	61	19	m)-fuzzy	m)-fuzzy	X
ejpam-2422	61	20	(	(	PUNCT
ejpam-2422	61	21	e	e	NOUN
ejpam-2422	61	22	,	,	PUNCT
ejpam-2422	61	23	k)-soft	k)-soft	NOUN
ejpam-2422	61	24	topology	topology	NOUN
ejpam-2422	61	25	on	on	ADP
ejpam-2422	61	26	x	x	SYM
ejpam-2422	61	27	if	if	SCONJ
ejpam-2422	61	28	it	it	PRON
ejpam-2422	61	29	satisfies	satisfy	VERB
ejpam-2422	61	30	the	the	DET
ejpam-2422	61	31	following	follow	VERB
ejpam-2422	61	32	conditions	condition	NOUN
ejpam-2422	61	33	for	for	ADP
ejpam-2422	61	34	each	each	DET
ejpam-2422	61	35	k	k	PROPN
ejpam-2422	61	36	∈	∈	PROPN
ejpam-2422	61	37	k	k	PROPN
ejpam-2422	61	38	,	,	PUNCT
ejpam-2422	61	39	(	(	PUNCT
ejpam-2422	61	40	t1	t1	NOUN
ejpam-2422	61	41	)	)	PUNCT
ejpam-2422	61	42	τk(0x	τk(0x	PUNCT
ejpam-2422	61	43	)	)	PUNCT
ejpam-2422	62	1	=	=	SYM
ejpam-2422	62	2	τk(1x	τk(1x	PRON
ejpam-2422	62	3	)	)	PUNCT
ejpam-2422	62	4	=	=	PUNCT
ejpam-2422	63	1	1	1	NUM
ejpam-2422	63	2	m	m	NOUN
ejpam-2422	63	3	.	.	PUNCT
ejpam-2422	64	1	(	(	PUNCT
ejpam-2422	64	2	t2	t2	NOUN
ejpam-2422	64	3	)	)	PUNCT
ejpam-2422	64	4	τk	τk	ADP
ejpam-2422	64	5	(	(	PUNCT
ejpam-2422	64	6	f	f	PROPN
ejpam-2422	64	7	u	u	PROPN
ejpam-2422	65	1	g)≥	g)≥	ADJ
ejpam-2422	65	2	τk	τk	ADP
ejpam-2422	65	3	(	(	PUNCT
ejpam-2422	65	4	f	f	X
ejpam-2422	65	5	)	)	PUNCT
ejpam-2422	65	6	∧τk(g	∧τk(g	X
ejpam-2422	65	7	)	)	PUNCT
ejpam-2422	65	8	for	for	ADP
ejpam-2422	65	9	each	each	DET
ejpam-2422	65	10	f	f	NOUN
ejpam-2422	65	11	,	,	PUNCT
ejpam-2422	65	12	g	g	PROPN
ejpam-2422	65	13	∈	∈	PROPN
ejpam-2422	65	14	(	(	PUNCT
ejpam-2422	65	15	lx	lx	NOUN
ejpam-2422	65	16	)	)	PUNCT
ejpam-2422	65	17	e	e	X
ejpam-2422	65	18	.	.	PUNCT
ejpam-2422	66	1	(	(	PUNCT
ejpam-2422	66	2	t3	t3	PROPN
ejpam-2422	66	3	)	)	PUNCT
ejpam-2422	66	4	τk	τk	ADP
ejpam-2422	66	5	(	(	PUNCT
ejpam-2422	66	6	⊔	⊔	PROPN
ejpam-2422	66	7	i∈λ	i∈λ	NOUN
ejpam-2422	66	8	fi)≥	fi)≥	PROPN
ejpam-2422	66	9	∧	∧	PROPN
ejpam-2422	66	10	i∈λτk	i∈λτk	PROPN
ejpam-2422	66	11	(	(	PUNCT
ejpam-2422	66	12	fi	fi	NOUN
ejpam-2422	66	13	)	)	PUNCT
ejpam-2422	66	14	for	for	ADP
ejpam-2422	66	15	each	each	PRON
ejpam-2422	66	16	{	{	PUNCT
ejpam-2422	66	17	fi}i∈λ	fi}i∈λ	PROPN
ejpam-2422	66	18	⊆	⊆	NUM
ejpam-2422	66	19	(	(	PUNCT
ejpam-2422	66	20	lx	lx	NOUN
ejpam-2422	66	21	)	)	PUNCT
ejpam-2422	66	22	e	e	X
ejpam-2422	66	23	.	.	PUNCT
ejpam-2422	67	1	the	the	DET
ejpam-2422	67	2	pair	pair	NOUN
ejpam-2422	67	3	(	(	PUNCT
ejpam-2422	67	4	x	x	X
ejpam-2422	67	5	,	,	PUNCT
ejpam-2422	67	6	τ	τ	X
ejpam-2422	67	7	)	)	PUNCT
ejpam-2422	67	8	is	be	AUX
ejpam-2422	67	9	called	call	VERB
ejpam-2422	67	10	an	an	DET
ejpam-2422	67	11	(	(	PUNCT
ejpam-2422	67	12	l	l	NOUN
ejpam-2422	67	13	,	,	PUNCT
ejpam-2422	67	14	m)-fuzzy	m)-fuzzy	X
ejpam-2422	67	15	(	(	PUNCT
ejpam-2422	67	16	e	e	NOUN
ejpam-2422	67	17	,	,	PUNCT
ejpam-2422	67	18	k)-soft	k)-soft	PROPN
ejpam-2422	67	19	topological	topological	ADJ
ejpam-2422	67	20	space	space	NOUN
ejpam-2422	67	21	example	example	NOUN
ejpam-2422	68	1	1	1	X
ejpam-2422	68	2	.	.	PUNCT
ejpam-2422	69	1	let	let	VERB
ejpam-2422	69	2	e	e	PRON
ejpam-2422	69	3	be	be	AUX
ejpam-2422	69	4	a	a	DET
ejpam-2422	69	5	parameter	parameter	NOUN
ejpam-2422	69	6	set	set	NOUN
ejpam-2422	69	7	,	,	PUNCT
ejpam-2422	69	8	i	i	PRON
ejpam-2422	69	9	=	=	PUNCT
ejpam-2422	70	1	[	[	X
ejpam-2422	70	2	0,1	0,1	NUM
ejpam-2422	70	3	]	]	PUNCT
ejpam-2422	70	4	,	,	PUNCT
ejpam-2422	70	5	k	k	PROPN
ejpam-2422	70	6	=	=	PUNCT
ejpam-2422	71	1	n	n	CCONJ
ejpam-2422	71	2	be	be	AUX
ejpam-2422	71	3	the	the	DET
ejpam-2422	71	4	set	set	NOUN
ejpam-2422	71	5	of	of	ADP
ejpam-2422	71	6	natural	natural	ADJ
ejpam-2422	71	7	numbers	number	NOUN
ejpam-2422	71	8	and	and	CCONJ
ejpam-2422	71	9	τ	τ	PROPN
ejpam-2422	71	10	:	:	PUNCT
ejpam-2422	71	11	k	k	X
ejpam-2422	71	12	→	→	PUNCT
ejpam-2422	71	13	i	i	PROPN
ejpam-2422	71	14	(	(	PUNCT
ejpam-2422	71	15	i	i	NOUN
ejpam-2422	71	16	x	x	X
ejpam-2422	71	17	)	)	PUNCT
ejpam-2422	71	18	e	e	AUX
ejpam-2422	71	19	be	be	AUX
ejpam-2422	71	20	defined	define	VERB
ejpam-2422	71	21	as	as	SCONJ
ejpam-2422	71	22	follows	follow	VERB
ejpam-2422	71	23	:	:	PUNCT
ejpam-2422	71	24	for	for	ADP
ejpam-2422	71	25	all	all	DET
ejpam-2422	71	26	k	k	PROPN
ejpam-2422	71	27	∈	∈	PROPN
ejpam-2422	71	28	k	k	NOUN
ejpam-2422	71	29	,	,	PUNCT
ejpam-2422	71	30	τk	τk	ADP
ejpam-2422	71	31	(	(	PUNCT
ejpam-2422	71	32	f	f	NOUN
ejpam-2422	71	33	)	)	PUNCT
ejpam-2422	71	34	=	=	PUNCT
ejpam-2422	72	1	¨	¨	NOUN
ejpam-2422	72	2	1	1	NUM
ejpam-2422	72	3	,	,	PUNCT
ejpam-2422	72	4	if	if	SCONJ
ejpam-2422	72	5	f	f	PROPN
ejpam-2422	72	6	=	=	SYM
ejpam-2422	72	7	0x	0x	PROPN
ejpam-2422	72	8	,	,	PUNCT
ejpam-2422	72	9	1x	1x	NUM
ejpam-2422	72	10	,	,	PUNCT
ejpam-2422	72	11	1	1	NUM
ejpam-2422	72	12	k	k	NOUN
ejpam-2422	72	13	,	,	PUNCT
ejpam-2422	72	14	otherwise	otherwise	ADV
ejpam-2422	72	15	.	.	PUNCT
ejpam-2422	73	1	(	(	PUNCT
ejpam-2422	73	2	1	1	X
ejpam-2422	73	3	)	)	PUNCT
ejpam-2422	73	4	it	it	PRON
ejpam-2422	73	5	is	be	AUX
ejpam-2422	73	6	easy	easy	ADJ
ejpam-2422	73	7	to	to	PART
ejpam-2422	73	8	testify	testify	VERB
ejpam-2422	73	9	that	that	SCONJ
ejpam-2422	73	10	τ	τ	PROPN
ejpam-2422	73	11	is	be	AUX
ejpam-2422	73	12	a	a	DET
ejpam-2422	73	13	fuzzy	fuzzy	ADJ
ejpam-2422	73	14	soft	soft	ADJ
ejpam-2422	73	15	topology	topology	NOUN
ejpam-2422	73	16	on	on	ADP
ejpam-2422	73	17	x	x	PROPN
ejpam-2422	73	18	.	.	PUNCT
ejpam-2422	74	1	definition	definition	NOUN
ejpam-2422	74	2	3	3	NUM
ejpam-2422	74	3	(	(	PUNCT
ejpam-2422	74	4	[	[	X
ejpam-2422	74	5	4	4	NUM
ejpam-2422	74	6	]	]	NUM
ejpam-2422	74	7	)	)	PUNCT
ejpam-2422	74	8	.	.	PUNCT
ejpam-2422	75	1	a	a	DET
ejpam-2422	75	2	mapping	mapping	NOUN
ejpam-2422	75	3	t	t	NOUN
ejpam-2422	75	4	:	:	PUNCT
ejpam-2422	75	5	k	k	X
ejpam-2422	75	6	→	→	PUNCT
ejpam-2422	75	7	m	m	PROPN
ejpam-2422	75	8	(	(	PUNCT
ejpam-2422	75	9	l	l	NOUN
ejpam-2422	75	10	x	x	X
ejpam-2422	75	11	)	)	PUNCT
ejpam-2422	75	12	e	e	X
ejpam-2422	75	13	is	be	AUX
ejpam-2422	75	14	called	call	VERB
ejpam-2422	75	15	an	an	DET
ejpam-2422	75	16	(	(	PUNCT
ejpam-2422	75	17	l	l	NOUN
ejpam-2422	75	18	,	,	PUNCT
ejpam-2422	75	19	m)-fuzzy	m)-fuzzy	X
ejpam-2422	75	20	(	(	PUNCT
ejpam-2422	75	21	e	e	NOUN
ejpam-2422	75	22	,	,	PUNCT
ejpam-2422	75	23	k)-soft	k)-soft	PROPN
ejpam-2422	75	24	cotopology	cotopology	NOUN
ejpam-2422	75	25	on	on	ADP
ejpam-2422	75	26	x	x	SYM
ejpam-2422	75	27	if	if	SCONJ
ejpam-2422	75	28	it	it	PRON
ejpam-2422	75	29	satisfies	satisfy	VERB
ejpam-2422	75	30	the	the	DET
ejpam-2422	75	31	following	follow	VERB
ejpam-2422	75	32	conditions	condition	NOUN
ejpam-2422	75	33	for	for	ADP
ejpam-2422	75	34	each	each	DET
ejpam-2422	75	35	k	k	PROPN
ejpam-2422	75	36	∈	∈	PROPN
ejpam-2422	75	37	k	k	PROPN
ejpam-2422	75	38	,	,	PUNCT
ejpam-2422	75	39	(	(	PUNCT
ejpam-2422	75	40	c1	c1	NOUN
ejpam-2422	75	41	)	)	PUNCT
ejpam-2422	75	42	tk(0x	tk(0x	NOUN
ejpam-2422	75	43	)	)	PUNCT
ejpam-2422	76	1	=	=	SYM
ejpam-2422	76	2	tk(1x	tk(1x	NOUN
ejpam-2422	76	3	)	)	PUNCT
ejpam-2422	76	4	=	=	PUNCT
ejpam-2422	77	1	1	1	NUM
ejpam-2422	77	2	m	m	NOUN
ejpam-2422	77	3	.	.	PUNCT
ejpam-2422	78	1	(	(	PUNCT
ejpam-2422	78	2	c2	c2	PROPN
ejpam-2422	78	3	)	)	PUNCT
ejpam-2422	78	4	tk	tk	PROPN
ejpam-2422	78	5	(	(	PUNCT
ejpam-2422	78	6	f	f	PROPN
ejpam-2422	78	7	t	t	PROPN
ejpam-2422	78	8	g)≥	g)≥	PROPN
ejpam-2422	78	9	tk	tk	PROPN
ejpam-2422	78	10	(	(	PUNCT
ejpam-2422	78	11	f	f	PROPN
ejpam-2422	78	12	)	)	PUNCT
ejpam-2422	78	13	∧tk(g	∧tk(g	PROPN
ejpam-2422	78	14	)	)	PUNCT
ejpam-2422	78	15	for	for	ADP
ejpam-2422	78	16	all	all	DET
ejpam-2422	78	17	f	f	PROPN
ejpam-2422	78	18	,	,	PUNCT
ejpam-2422	78	19	g	g	PROPN
ejpam-2422	78	20	∈	∈	PROPN
ejpam-2422	78	21	(	(	PUNCT
ejpam-2422	78	22	lx	lx	NOUN
ejpam-2422	78	23	)	)	PUNCT
ejpam-2422	79	1	e	e	X
ejpam-2422	79	2	.	.	PUNCT
ejpam-2422	80	1	v.	v.	ADP
ejpam-2422	80	2	çetkin	çetkin	PROPN
ejpam-2422	80	3	,	,	PUNCT
ejpam-2422	80	4	h.	h.	PROPN
ejpam-2422	80	5	aygün	aygün	PROPN
ejpam-2422	80	6	/	/	SYM
ejpam-2422	80	7	eur	eur	PROPN
ejpam-2422	80	8	.	.	PUNCT
ejpam-2422	81	1	j.	j.	PROPN
ejpam-2422	81	2	pure	pure	PROPN
ejpam-2422	81	3	appl	appl	PROPN
ejpam-2422	81	4	.	.	PROPN
ejpam-2422	81	5	math	math	PROPN
ejpam-2422	81	6	,	,	PUNCT
ejpam-2422	81	7	9	9	NUM
ejpam-2422	81	8	(	(	PUNCT
ejpam-2422	81	9	2016	2016	NUM
ejpam-2422	81	10	)	)	PUNCT
ejpam-2422	81	11	,	,	PUNCT
ejpam-2422	81	12	419	419	NUM
ejpam-2422	81	13	-	-	SYM
ejpam-2422	81	14	433	433	NUM
ejpam-2422	81	15	422	422	NUM
ejpam-2422	81	16	(	(	PUNCT
ejpam-2422	81	17	c3	c3	PROPN
ejpam-2422	81	18	)	)	PUNCT
ejpam-2422	81	19	tk(ui∈λ	tk(ui∈λ	PROPN
ejpam-2422	81	20	fi)≥	fi)≥	ADJ
ejpam-2422	81	21	∧	∧	PROPN
ejpam-2422	81	22	i∈λtk	i∈λtk	PROPN
ejpam-2422	81	23	(	(	PUNCT
ejpam-2422	81	24	fi	fi	NOUN
ejpam-2422	81	25	)	)	PUNCT
ejpam-2422	81	26	for	for	ADP
ejpam-2422	81	27	all	all	PRON
ejpam-2422	81	28	{	{	PUNCT
ejpam-2422	81	29	fi}i∈λ	fi}i∈λ	PROPN
ejpam-2422	81	30	⊆	⊆	NUM
ejpam-2422	81	31	(	(	PUNCT
ejpam-2422	81	32	lx	lx	NOUN
ejpam-2422	81	33	)	)	PUNCT
ejpam-2422	82	1	e	e	X
ejpam-2422	82	2	.	.	PUNCT
ejpam-2422	83	1	the	the	DET
ejpam-2422	83	2	pair	pair	NOUN
ejpam-2422	83	3	(	(	PUNCT
ejpam-2422	83	4	x	x	X
ejpam-2422	83	5	,	,	PUNCT
ejpam-2422	83	6	t	t	PROPN
ejpam-2422	83	7	)	)	PUNCT
ejpam-2422	83	8	is	be	AUX
ejpam-2422	83	9	called	call	VERB
ejpam-2422	83	10	an	an	DET
ejpam-2422	83	11	(	(	PUNCT
ejpam-2422	83	12	l	l	NOUN
ejpam-2422	83	13	,	,	PUNCT
ejpam-2422	83	14	m)-fuzzy	m)-fuzzy	X
ejpam-2422	83	15	(	(	PUNCT
ejpam-2422	83	16	e	e	NOUN
ejpam-2422	83	17	,	,	PUNCT
ejpam-2422	83	18	k)-soft	k)-soft	VERB
ejpam-2422	83	19	cotopological	cotopological	ADJ
ejpam-2422	83	20	space	space	NOUN
ejpam-2422	83	21	.	.	PUNCT
ejpam-2422	84	1	let	let	VERB
ejpam-2422	84	2	(	(	PUNCT
ejpam-2422	84	3	x1,t	x1,t	PROPN
ejpam-2422	84	4	1	1	NUM
ejpam-2422	84	5	)	)	PUNCT
ejpam-2422	84	6	and	and	CCONJ
ejpam-2422	84	7	(	(	PUNCT
ejpam-2422	84	8	x2,t	x2,t	PROPN
ejpam-2422	84	9	2	2	NUM
ejpam-2422	84	10	)	)	PUNCT
ejpam-2422	84	11	be	be	AUX
ejpam-2422	84	12	an	an	DET
ejpam-2422	84	13	(	(	PUNCT
ejpam-2422	84	14	l	l	NOUN
ejpam-2422	84	15	,	,	PUNCT
ejpam-2422	84	16	m)-fuzzy	m)-fuzzy	X
ejpam-2422	84	17	(	(	PUNCT
ejpam-2422	84	18	e1	e1	PROPN
ejpam-2422	84	19	,	,	PUNCT
ejpam-2422	84	20	k1)-soft	k1)-soft	ADJ
ejpam-2422	84	21	cotopological	cotopological	ADJ
ejpam-2422	84	22	space	space	NOUN
ejpam-2422	84	23	and	and	CCONJ
ejpam-2422	84	24	an	an	DET
ejpam-2422	84	25	(	(	PUNCT
ejpam-2422	84	26	l	l	NOUN
ejpam-2422	84	27	,	,	PUNCT
ejpam-2422	84	28	m)-fuzzy	m)-fuzzy	X
ejpam-2422	84	29	(	(	PUNCT
ejpam-2422	84	30	e2	e2	PROPN
ejpam-2422	84	31	,	,	PUNCT
ejpam-2422	84	32	k2)-soft	k2)-soft	ADJ
ejpam-2422	84	33	cotopological	cotopological	ADJ
ejpam-2422	84	34	space	space	NOUN
ejpam-2422	84	35	,	,	PUNCT
ejpam-2422	84	36	respectively	respectively	ADV
ejpam-2422	84	37	.	.	PUNCT
ejpam-2422	85	1	a	a	DET
ejpam-2422	85	2	fuzzy	fuzzy	ADJ
ejpam-2422	85	3	soft	soft	ADJ
ejpam-2422	85	4	mapping	mapping	NOUN
ejpam-2422	85	5	ϕψ	ϕψ	ADP
ejpam-2422	85	6	,	,	PUNCT
ejpam-2422	85	7	η	η	PROPN
ejpam-2422	85	8	:	:	PUNCT
ejpam-2422	85	9	(	(	PUNCT
ejpam-2422	85	10	x1,t	x1,t	PROPN
ejpam-2422	85	11	1)→	1)→	NUM
ejpam-2422	85	12	(	(	PUNCT
ejpam-2422	85	13	x2,t	x2,t	PROPN
ejpam-2422	85	14	2	2	NUM
ejpam-2422	85	15	)	)	PUNCT
ejpam-2422	85	16	is	be	AUX
ejpam-2422	85	17	said	say	VERB
ejpam-2422	85	18	to	to	PART
ejpam-2422	85	19	be	be	AUX
ejpam-2422	85	20	continuous	continuous	ADJ
ejpam-2422	85	21	if	if	SCONJ
ejpam-2422	85	22	t	t	PROPN
ejpam-2422	85	23	1	1	NUM
ejpam-2422	85	24	k	k	X
ejpam-2422	85	25	(	(	PUNCT
ejpam-2422	85	26	ϕ	ϕ	PROPN
ejpam-2422	85	27	←	←	PROPN
ejpam-2422	85	28	ψ	ψ	X
ejpam-2422	85	29	(	(	PUNCT
ejpam-2422	85	30	g))≥	g))≥	PROPN
ejpam-2422	85	31	t	t	PROPN
ejpam-2422	85	32	2	2	NUM
ejpam-2422	85	33	η(k)(g	η(k)(g	NUM
ejpam-2422	85	34	)	)	PUNCT
ejpam-2422	85	35	for	for	ADP
ejpam-2422	85	36	each	each	DET
ejpam-2422	85	37	g	g	PROPN
ejpam-2422	85	38	∈	∈	PROPN
ejpam-2422	85	39	(	(	PUNCT
ejpam-2422	85	40	lx2)e2	lx2)e2	PROPN
ejpam-2422	85	41	,	,	PUNCT
ejpam-2422	85	42	k	k	PROPN
ejpam-2422	85	43	∈	∈	PROPN
ejpam-2422	85	44	k1	k1	PROPN
ejpam-2422	85	45	,	,	PUNCT
ejpam-2422	85	46	where	where	SCONJ
ejpam-2422	85	47	ϕ	ϕ	X
ejpam-2422	85	48	:	:	PUNCT
ejpam-2422	85	49	x1	x1	PROPN
ejpam-2422	85	50	→	→	SYM
ejpam-2422	85	51	x2	x2	PROPN
ejpam-2422	85	52	,	,	PUNCT
ejpam-2422	85	53	ψ	ψ	X
ejpam-2422	85	54	:	:	PUNCT
ejpam-2422	85	55	e1	e1	PROPN
ejpam-2422	85	56	→	→	SYM
ejpam-2422	85	57	e2	e2	PROPN
ejpam-2422	85	58	and	and	CCONJ
ejpam-2422	85	59	η	η	PROPN
ejpam-2422	85	60	:	:	PUNCT
ejpam-2422	85	61	k1	k1	PROPN
ejpam-2422	85	62	→	→	SYM
ejpam-2422	85	63	k2	k2	PROPN
ejpam-2422	85	64	are	be	AUX
ejpam-2422	85	65	classical	classical	ADJ
ejpam-2422	85	66	functions	function	NOUN
ejpam-2422	85	67	.	.	PUNCT
ejpam-2422	86	1	let	let	VERB
ejpam-2422	86	2	fsctop(l	fsctop(l	NOUN
ejpam-2422	86	3	,	,	PUNCT
ejpam-2422	86	4	m	m	VERB
ejpam-2422	86	5	)	)	PUNCT
ejpam-2422	86	6	denote	denote	VERB
ejpam-2422	86	7	the	the	DET
ejpam-2422	86	8	category	category	NOUN
ejpam-2422	86	9	of	of	ADP
ejpam-2422	86	10	(	(	PUNCT
ejpam-2422	86	11	l	l	NOUN
ejpam-2422	86	12	,	,	PUNCT
ejpam-2422	86	13	m)-fuzzy	m)-fuzzy	X
ejpam-2422	86	14	(	(	PUNCT
ejpam-2422	86	15	e	e	NOUN
ejpam-2422	86	16	,	,	PUNCT
ejpam-2422	86	17	k)-soft	k)-soft	VERB
ejpam-2422	86	18	cotopological	cotopological	ADJ
ejpam-2422	86	19	spaces	space	NOUN
ejpam-2422	86	20	and	and	CCONJ
ejpam-2422	86	21	continuous	continuous	ADJ
ejpam-2422	86	22	mappings	mapping	NOUN
ejpam-2422	86	23	.	.	PUNCT
ejpam-2422	87	1	if	if	SCONJ
ejpam-2422	87	2	t	t	PROPN
ejpam-2422	87	3	is	be	AUX
ejpam-2422	87	4	an	an	DET
ejpam-2422	87	5	(	(	PUNCT
ejpam-2422	87	6	l	l	NOUN
ejpam-2422	87	7	,	,	PUNCT
ejpam-2422	87	8	m)-fuzzy	m)-fuzzy	X
ejpam-2422	87	9	(	(	PUNCT
ejpam-2422	87	10	e	e	NOUN
ejpam-2422	87	11	,	,	PUNCT
ejpam-2422	87	12	k)-soft	k)-soft	PROPN
ejpam-2422	87	13	cotopology	cotopology	NOUN
ejpam-2422	87	14	on	on	ADP
ejpam-2422	87	15	x	x	X
ejpam-2422	87	16	,	,	PUNCT
ejpam-2422	87	17	then	then	ADV
ejpam-2422	87	18	τ	τ	PROPN
ejpam-2422	87	19	is	be	AUX
ejpam-2422	87	20	an	an	DET
ejpam-2422	87	21	(	(	PUNCT
ejpam-2422	87	22	l	l	NOUN
ejpam-2422	87	23	,	,	PUNCT
ejpam-2422	87	24	m)-fuzzy	m)-fuzzy	X
ejpam-2422	87	25	(	(	PUNCT
ejpam-2422	87	26	e	e	NOUN
ejpam-2422	87	27	,	,	PUNCT
ejpam-2422	87	28	k)-soft	k)-soft	NOUN
ejpam-2422	87	29	topology	topology	NOUN
ejpam-2422	87	30	on	on	ADP
ejpam-2422	87	31	x	x	SYM
ejpam-2422	87	32	,	,	PUNCT
ejpam-2422	87	33	where	where	SCONJ
ejpam-2422	87	34	τ	τ	PROPN
ejpam-2422	87	35	:	:	PUNCT
ejpam-2422	87	36	k	k	X
ejpam-2422	87	37	→	→	PUNCT
ejpam-2422	87	38	m	m	PROPN
ejpam-2422	87	39	(	(	PUNCT
ejpam-2422	87	40	l	l	NOUN
ejpam-2422	87	41	x	x	X
ejpam-2422	87	42	)	)	PUNCT
ejpam-2422	87	43	e	e	NOUN
ejpam-2422	87	44	is	be	AUX
ejpam-2422	87	45	defined	define	VERB
ejpam-2422	87	46	by	by	ADP
ejpam-2422	87	47	τk	τk	ADP
ejpam-2422	87	48	(	(	PUNCT
ejpam-2422	87	49	f	f	PROPN
ejpam-2422	87	50	)	)	PUNCT
ejpam-2422	87	51	=	=	SYM
ejpam-2422	87	52	tk	tk	PROPN
ejpam-2422	87	53	(	(	PUNCT
ejpam-2422	87	54	f	f	PROPN
ejpam-2422	87	55	′	′	NUM
ejpam-2422	87	56	)	)	PUNCT
ejpam-2422	87	57	,	,	PUNCT
ejpam-2422	87	58	for	for	ADP
ejpam-2422	87	59	each	each	DET
ejpam-2422	87	60	k	k	PROPN
ejpam-2422	87	61	∈	∈	PROPN
ejpam-2422	88	1	k	k	PROPN
ejpam-2422	88	2	.	.	PUNCT
ejpam-2422	88	3	example	example	NOUN
ejpam-2422	89	1	2	2	NUM
ejpam-2422	89	2	.	.	PUNCT
ejpam-2422	89	3	let	let	VERB
ejpam-2422	89	4	x	x	PUNCT
ejpam-2422	89	5	=	=	PRON
ejpam-2422	89	6	{	{	PUNCT
ejpam-2422	89	7	x	x	INTJ
ejpam-2422	89	8	,	,	PUNCT
ejpam-2422	89	9	y	y	PROPN
ejpam-2422	89	10	}	}	PUNCT
ejpam-2422	89	11	be	be	AUX
ejpam-2422	89	12	a	a	DET
ejpam-2422	89	13	classical	classical	ADJ
ejpam-2422	89	14	set	set	NOUN
ejpam-2422	89	15	,	,	PUNCT
ejpam-2422	89	16	e	e	X
ejpam-2422	89	17	=	=	PRON
ejpam-2422	89	18	{	{	PUNCT
ejpam-2422	89	19	e1	e1	PROPN
ejpam-2422	89	20	,	,	PUNCT
ejpam-2422	89	21	e2	e2	PROPN
ejpam-2422	89	22	}	}	PUNCT
ejpam-2422	89	23	,	,	PUNCT
ejpam-2422	89	24	k	k	X
ejpam-2422	89	25	=	=	PRON
ejpam-2422	89	26	{	{	PUNCT
ejpam-2422	89	27	k1	k1	PROPN
ejpam-2422	89	28	,	,	PUNCT
ejpam-2422	89	29	k2	k2	NOUN
ejpam-2422	89	30	}	}	PUNCT
ejpam-2422	89	31	be	be	VERB
ejpam-2422	89	32	parameter	parameter	NOUN
ejpam-2422	89	33	sets	set	NOUN
ejpam-2422	89	34	,	,	PUNCT
ejpam-2422	89	35	l	l	NOUN
ejpam-2422	89	36	=	=	PUNCT
ejpam-2422	90	1	m	m	VERB
ejpam-2422	90	2	=	=	ADJ
ejpam-2422	91	1	i	i	NOUN
ejpam-2422	91	2	=	=	PUNCT
ejpam-2422	92	1	[	[	X
ejpam-2422	92	2	0,1	0,1	NUM
ejpam-2422	92	3	]	]	PUNCT
ejpam-2422	92	4	.	.	PUNCT
ejpam-2422	93	1	define	define	VERB
ejpam-2422	93	2	h	h	NOUN
ejpam-2422	93	3	∈	∈	PROPN
ejpam-2422	93	4	(	(	PUNCT
ejpam-2422	93	5	ix	ix	ADJ
ejpam-2422	93	6	)	)	PUNCT
ejpam-2422	93	7	e	e	NOUN
ejpam-2422	93	8	as	as	SCONJ
ejpam-2422	93	9	follows	follow	VERB
ejpam-2422	93	10	:	:	PUNCT
ejpam-2422	93	11	he1	he1	PROPN
ejpam-2422	93	12	(	(	PUNCT
ejpam-2422	93	13	x	x	NOUN
ejpam-2422	93	14	)	)	PUNCT
ejpam-2422	93	15	=	=	SYM
ejpam-2422	93	16	0.6	0.6	NUM
ejpam-2422	93	17	,	,	PUNCT
ejpam-2422	93	18	he1	he1	PROPN
ejpam-2422	93	19	(	(	PUNCT
ejpam-2422	93	20	y	y	NOUN
ejpam-2422	93	21	)	)	PUNCT
ejpam-2422	93	22	=	=	SYM
ejpam-2422	93	23	0.5	0.5	NUM
ejpam-2422	93	24	,	,	PUNCT
ejpam-2422	93	25	he2	he2	PROPN
ejpam-2422	93	26	(	(	PUNCT
ejpam-2422	93	27	x	x	NOUN
ejpam-2422	93	28	)	)	PUNCT
ejpam-2422	93	29	=	=	SYM
ejpam-2422	93	30	0.8	0.8	NUM
ejpam-2422	93	31	and	and	CCONJ
ejpam-2422	93	32	he2	he2	PROPN
ejpam-2422	93	33	(	(	PUNCT
ejpam-2422	93	34	y	y	NOUN
ejpam-2422	93	35	)	)	PUNCT
ejpam-2422	93	36	=	=	SYM
ejpam-2422	93	37	0.6	0.6	X
ejpam-2422	93	38	.	.	PUNCT
ejpam-2422	94	1	then	then	ADV
ejpam-2422	94	2	the	the	DET
ejpam-2422	94	3	mapping	mapping	NOUN
ejpam-2422	94	4	t	t	NOUN
ejpam-2422	94	5	:	:	PUNCT
ejpam-2422	95	1	k	k	X
ejpam-2422	95	2	→	→	PUNCT
ejpam-2422	95	3	i	i	PROPN
ejpam-2422	95	4	(	(	PUNCT
ejpam-2422	95	5	i	i	NOUN
ejpam-2422	95	6	x	x	X
ejpam-2422	95	7	)	)	PUNCT
ejpam-2422	95	8	e	e	NOUN
ejpam-2422	95	9	which	which	PRON
ejpam-2422	95	10	is	be	AUX
ejpam-2422	95	11	defined	define	VERB
ejpam-2422	95	12	as	as	SCONJ
ejpam-2422	95	13	follows	follow	VERB
ejpam-2422	95	14	is	be	AUX
ejpam-2422	95	15	a	a	DET
ejpam-2422	95	16	fuzzy	fuzzy	ADJ
ejpam-2422	95	17	soft	soft	ADJ
ejpam-2422	95	18	cotopology	cotopology	NOUN
ejpam-2422	95	19	on	on	ADP
ejpam-2422	95	20	x	x	X
ejpam-2422	95	21	:	:	PUNCT
ejpam-2422	95	22	tk	tk	PROPN
ejpam-2422	95	23	(	(	PUNCT
ejpam-2422	95	24	f	f	PROPN
ejpam-2422	95	25	)	)	PUNCT
ejpam-2422	95	26	=	=	PUNCT
ejpam-2422	96	1			PROPN
ejpam-2422	96	2			ADV
ejpam-2422	96	3			PRON
ejpam-2422	96	4			ADJ
ejpam-2422	96	5			NOUN
ejpam-2422	96	6	1	1	NUM
ejpam-2422	96	7	,	,	PUNCT
ejpam-2422	96	8	if	if	SCONJ
ejpam-2422	96	9	f	f	PROPN
ejpam-2422	96	10	=	=	SYM
ejpam-2422	96	11	0x	0x	PROPN
ejpam-2422	96	12	,	,	PUNCT
ejpam-2422	96	13	1x	1x	NUM
ejpam-2422	96	14	,	,	PUNCT
ejpam-2422	96	15	k	k	PROPN
ejpam-2422	96	16	∈	∈	PROPN
ejpam-2422	96	17	k	k	X
ejpam-2422	96	18	0.7	0.7	NUM
ejpam-2422	96	19	,	,	PUNCT
ejpam-2422	96	20	if	if	SCONJ
ejpam-2422	96	21	f	f	PROPN
ejpam-2422	96	22	=	=	SYM
ejpam-2422	96	23	h	h	PROPN
ejpam-2422	96	24	,	,	PUNCT
ejpam-2422	96	25	k	k	PROPN
ejpam-2422	96	26	=	=	SYM
ejpam-2422	96	27	k1	k1	PROPN
ejpam-2422	96	28	,	,	PUNCT
ejpam-2422	96	29	0	0	NUM
ejpam-2422	96	30	,	,	PUNCT
ejpam-2422	96	31	otherwise	otherwise	ADV
ejpam-2422	96	32	.	.	PUNCT
ejpam-2422	97	1	(	(	PUNCT
ejpam-2422	97	2	2	2	NUM
ejpam-2422	97	3	)	)	PUNCT
ejpam-2422	97	4	3	3	NUM
ejpam-2422	97	5	.	.	X
ejpam-2422	97	6	fuzzy	fuzzy	ADJ
ejpam-2422	97	7	soft	soft	ADJ
ejpam-2422	97	8	remote	remote	ADJ
ejpam-2422	97	9	neighborhood	neighborhood	NOUN
ejpam-2422	97	10	system	system	NOUN
ejpam-2422	97	11	in	in	ADP
ejpam-2422	97	12	this	this	DET
ejpam-2422	97	13	section	section	NOUN
ejpam-2422	97	14	,	,	PUNCT
ejpam-2422	97	15	we	we	PRON
ejpam-2422	97	16	define	define	VERB
ejpam-2422	97	17	fuzzy	fuzzy	ADJ
ejpam-2422	97	18	soft	soft	ADJ
ejpam-2422	97	19	remote	remote	ADJ
ejpam-2422	97	20	neighborhood	neighborhood	NOUN
ejpam-2422	97	21	system	system	NOUN
ejpam-2422	97	22	and	and	CCONJ
ejpam-2422	97	23	give	give	VERB
ejpam-2422	97	24	the	the	DET
ejpam-2422	97	25	relationships	relationship	NOUN
ejpam-2422	97	26	between	between	ADP
ejpam-2422	97	27	fuzzy	fuzzy	ADJ
ejpam-2422	97	28	soft	soft	ADJ
ejpam-2422	97	29	remote	remote	ADJ
ejpam-2422	97	30	neighborhood	neighborhood	NOUN
ejpam-2422	97	31	system	system	NOUN
ejpam-2422	97	32	and	and	CCONJ
ejpam-2422	97	33	fuzzy	fuzzy	ADJ
ejpam-2422	97	34	soft	soft	ADJ
ejpam-2422	97	35	cotopological	cotopological	ADJ
ejpam-2422	97	36	space	space	NOUN
ejpam-2422	97	37	.	.	PUNCT
ejpam-2422	98	1	if	if	SCONJ
ejpam-2422	98	2	the	the	DET
ejpam-2422	98	3	parameter	parameter	NOUN
ejpam-2422	98	4	sets	set	VERB
ejpam-2422	98	5	e	e	NOUN
ejpam-2422	98	6	and	and	CCONJ
ejpam-2422	98	7	k	k	PROPN
ejpam-2422	98	8	are	be	AUX
ejpam-2422	98	9	both	both	DET
ejpam-2422	98	10	one	one	NUM
ejpam-2422	98	11	pointed	point	VERB
ejpam-2422	98	12	,	,	PUNCT
ejpam-2422	98	13	then	then	ADV
ejpam-2422	98	14	we	we	PRON
ejpam-2422	98	15	obtain	obtain	VERB
ejpam-2422	98	16	the	the	DET
ejpam-2422	98	17	results	result	NOUN
ejpam-2422	98	18	given	give	VERB
ejpam-2422	98	19	in	in	ADP
ejpam-2422	98	20	the	the	DET
ejpam-2422	98	21	paper	paper	NOUN
ejpam-2422	98	22	of	of	ADP
ejpam-2422	98	23	[	[	X
ejpam-2422	98	24	18	18	NUM
ejpam-2422	98	25	]	]	PUNCT
ejpam-2422	98	26	.	.	PUNCT
ejpam-2422	99	1	definition	definition	NOUN
ejpam-2422	99	2	4	4	NUM
ejpam-2422	99	3	.	.	PUNCT
ejpam-2422	100	1	a	a	DET
ejpam-2422	100	2	topological	topological	ADJ
ejpam-2422	100	3	fuzzy	fuzzy	ADJ
ejpam-2422	100	4	soft	soft	ADJ
ejpam-2422	100	5	remote	remote	ADJ
ejpam-2422	100	6	neighborhood	neighborhood	NOUN
ejpam-2422	100	7	system	system	NOUN
ejpam-2422	100	8	is	be	AUX
ejpam-2422	100	9	a	a	DET
ejpam-2422	100	10	set	set	NOUN
ejpam-2422	100	11	r	r	NOUN
ejpam-2422	100	12	=	=	PUNCT
ejpam-2422	100	13	{	{	PUNCT
ejpam-2422	100	14	rp	rp	NOUN
ejpam-2422	100	15	|	|	ADV
ejpam-2422	100	16	p	p	X
ejpam-2422	100	17	∈	∈	PROPN
ejpam-2422	100	18	c((lx	c((lx	PROPN
ejpam-2422	100	19	)	)	PUNCT
ejpam-2422	100	20	e	e	NOUN
ejpam-2422	100	21	)	)	PUNCT
ejpam-2422	100	22	}	}	PUNCT
ejpam-2422	100	23	of	of	ADP
ejpam-2422	100	24	mappings	mapping	NOUN
ejpam-2422	100	25	rp	rp	NOUN
ejpam-2422	100	26	:	:	PUNCT
ejpam-2422	100	27	k	k	X
ejpam-2422	100	28	→	→	PUNCT
ejpam-2422	100	29	m	m	PROPN
ejpam-2422	100	30	(	(	PUNCT
ejpam-2422	100	31	l	l	NOUN
ejpam-2422	100	32	x	x	X
ejpam-2422	100	33	)	)	PUNCT
ejpam-2422	100	34	e	e	X
ejpam-2422	100	35	such	such	ADJ
ejpam-2422	100	36	that	that	PRON
ejpam-2422	100	37	for	for	ADP
ejpam-2422	100	38	each	each	DET
ejpam-2422	100	39	k	k	PROPN
ejpam-2422	100	40	∈	∈	PROPN
ejpam-2422	100	41	k	k	NOUN
ejpam-2422	100	42	:	:	PUNCT
ejpam-2422	100	43	(	(	PUNCT
ejpam-2422	100	44	rn1	rn1	NOUN
ejpam-2422	100	45	)	)	PUNCT
ejpam-2422	100	46	rp	rp	NOUN
ejpam-2422	100	47	k(1x	k(1x	NOUN
ejpam-2422	100	48	)	)	PUNCT
ejpam-2422	101	1	=	=	PUNCT
ejpam-2422	101	2	0	0	NUM
ejpam-2422	101	3	m	m	NOUN
ejpam-2422	101	4	,	,	PUNCT
ejpam-2422	101	5	rp	rp	NOUN
ejpam-2422	101	6	k(0x	k(0x	X
ejpam-2422	101	7	)	)	PUNCT
ejpam-2422	102	1	=	=	PUNCT
ejpam-2422	102	2	1	1	NUM
ejpam-2422	102	3	m	m	NOUN
ejpam-2422	102	4	.	.	PUNCT
ejpam-2422	103	1	(	(	PUNCT
ejpam-2422	103	2	rn2	rn2	PROPN
ejpam-2422	103	3	)	)	PUNCT
ejpam-2422	104	1	rp	rp	PROPN
ejpam-2422	105	1	k	k	PROPN
ejpam-2422	105	2	(	(	PUNCT
ejpam-2422	105	3	f	f	PROPN
ejpam-2422	105	4	)	)	PUNCT
ejpam-2422	105	5	6=	6=	ADP
ejpam-2422	105	6	0	0	NUM
ejpam-2422	105	7	m	m	NOUN
ejpam-2422	105	8	implies	imply	VERB
ejpam-2422	105	9	p	p	NOUN
ejpam-2422	105	10	6v	6v	PROPN
ejpam-2422	105	11	f	f	X
ejpam-2422	105	12	.	.	PUNCT
ejpam-2422	106	1	(	(	PUNCT
ejpam-2422	106	2	rn3	rn3	NOUN
ejpam-2422	106	3	)	)	PUNCT
ejpam-2422	106	4	rp	rp	NOUN
ejpam-2422	107	1	k	k	PROPN
ejpam-2422	107	2	(	(	PUNCT
ejpam-2422	107	3	f	f	PROPN
ejpam-2422	107	4	t	t	PROPN
ejpam-2422	107	5	g	g	NOUN
ejpam-2422	107	6	)	)	PUNCT
ejpam-2422	108	1	=	=	SYM
ejpam-2422	108	2	rp	rp	NOUN
ejpam-2422	109	1	k	k	PROPN
ejpam-2422	109	2	(	(	PUNCT
ejpam-2422	109	3	f	f	NOUN
ejpam-2422	109	4	)	)	PUNCT
ejpam-2422	109	5	∧	∧	PROPN
ejpam-2422	109	6	rp	rp	ADP
ejpam-2422	109	7	k(g	k(g	PROPN
ejpam-2422	109	8	)	)	PUNCT
ejpam-2422	109	9	.	.	PUNCT
ejpam-2422	110	1	(	(	PUNCT
ejpam-2422	110	2	rn4	rn4	NOUN
ejpam-2422	110	3	)	)	PUNCT
ejpam-2422	110	4	rp	rp	NOUN
ejpam-2422	111	1	k	k	PROPN
ejpam-2422	111	2	(	(	PUNCT
ejpam-2422	111	3	f	f	PROPN
ejpam-2422	111	4	)	)	PUNCT
ejpam-2422	111	5	=	=	SYM
ejpam-2422	111	6	∨	∨	NUM
ejpam-2422	111	7	g∈p|	g∈p|	PROPN
ejpam-2422	111	8	f	f	PROPN
ejpam-2422	111	9	∧	∧	PROPN
ejpam-2422	111	10	r	r	PROPN
ejpam-2422	111	11	6vg	6vg	PROPN
ejpam-2422	111	12	rr	rr	PROPN
ejpam-2422	111	13	k(g	k(g	PROPN
ejpam-2422	111	14	)	)	PUNCT
ejpam-2422	111	15	.	.	PUNCT
ejpam-2422	112	1	lemma	lemma	PROPN
ejpam-2422	112	2	1	1	X
ejpam-2422	112	3	.	.	PUNCT
ejpam-2422	113	1	let	let	VERB
ejpam-2422	113	2	t	t	NOUN
ejpam-2422	113	3	:	:	PUNCT
ejpam-2422	113	4	k	k	PROPN
ejpam-2422	113	5	→	→	PUNCT
ejpam-2422	113	6	m	m	PROPN
ejpam-2422	113	7	(	(	PUNCT
ejpam-2422	113	8	l	l	NOUN
ejpam-2422	113	9	x	x	X
ejpam-2422	113	10	)	)	PUNCT
ejpam-2422	113	11	e	e	X
ejpam-2422	113	12	be	be	AUX
ejpam-2422	113	13	an	an	DET
ejpam-2422	113	14	(	(	PUNCT
ejpam-2422	113	15	l	l	NOUN
ejpam-2422	113	16	,	,	PUNCT
ejpam-2422	113	17	m)-fuzzy	m)-fuzzy	X
ejpam-2422	113	18	(	(	PUNCT
ejpam-2422	113	19	e	e	NOUN
ejpam-2422	113	20	,	,	PUNCT
ejpam-2422	113	21	k)-soft	k)-soft	PROPN
ejpam-2422	113	22	cotopology	cotopology	PROPN
ejpam-2422	113	23	.	.	PUNCT
ejpam-2422	114	1	then	then	ADV
ejpam-2422	114	2	the	the	DET
ejpam-2422	114	3	followings	following	NOUN
ejpam-2422	114	4	are	be	AUX
ejpam-2422	114	5	valid	valid	ADJ
ejpam-2422	114	6	.	.	PUNCT
ejpam-2422	115	1	v.	v.	ADP
ejpam-2422	115	2	çetkin	çetkin	PROPN
ejpam-2422	115	3	,	,	PUNCT
ejpam-2422	115	4	h.	h.	PROPN
ejpam-2422	115	5	aygün	aygün	PROPN
ejpam-2422	115	6	/	/	SYM
ejpam-2422	115	7	eur	eur	PROPN
ejpam-2422	115	8	.	.	PUNCT
ejpam-2422	116	1	j.	j.	PROPN
ejpam-2422	116	2	pure	pure	PROPN
ejpam-2422	116	3	appl	appl	PROPN
ejpam-2422	116	4	.	.	PROPN
ejpam-2422	116	5	math	math	PROPN
ejpam-2422	116	6	,	,	PUNCT
ejpam-2422	116	7	9	9	NUM
ejpam-2422	116	8	(	(	PUNCT
ejpam-2422	116	9	2016	2016	NUM
ejpam-2422	116	10	)	)	PUNCT
ejpam-2422	116	11	,	,	PUNCT
ejpam-2422	116	12	419	419	NUM
ejpam-2422	116	13	-	-	SYM
ejpam-2422	116	14	433	433	NUM
ejpam-2422	116	15	423	423	NUM
ejpam-2422	116	16	(	(	PUNCT
ejpam-2422	116	17	1	1	NUM
ejpam-2422	116	18	)	)	PUNCT
ejpam-2422	116	19	rt	rt	NOUN
ejpam-2422	116	20	=	=	PUNCT
ejpam-2422	116	21	{	{	PUNCT
ejpam-2422	116	22	r	r	NOUN
ejpam-2422	116	23	p	p	NOUN
ejpam-2422	116	24	t	t	NOUN
ejpam-2422	117	1	|	|	ADV
ejpam-2422	117	2	p	p	PROPN
ejpam-2422	117	3	∈	∈	PROPN
ejpam-2422	117	4	c((lx	c((lx	PROPN
ejpam-2422	117	5	)	)	PUNCT
ejpam-2422	117	6	e	e	X
ejpam-2422	117	7	)	)	PUNCT
ejpam-2422	117	8	}	}	PUNCT
ejpam-2422	117	9	is	be	AUX
ejpam-2422	117	10	a	a	DET
ejpam-2422	117	11	topological	topological	ADJ
ejpam-2422	117	12	fuzzy	fuzzy	ADJ
ejpam-2422	117	13	soft	soft	ADJ
ejpam-2422	117	14	remote	remote	ADJ
ejpam-2422	117	15	neighborhood	neighborhood	NOUN
ejpam-2422	117	16	system	system	NOUN
ejpam-2422	117	17	,	,	PUNCT
ejpam-2422	117	18	where	where	SCONJ
ejpam-2422	117	19	rp	rp	NOUN
ejpam-2422	117	20	t	t	PROPN
ejpam-2422	117	21	is	be	AUX
ejpam-2422	117	22	defined	define	VERB
ejpam-2422	117	23	by	by	ADP
ejpam-2422	117	24	for	for	ADP
ejpam-2422	117	25	all	all	DET
ejpam-2422	117	26	k	k	PROPN
ejpam-2422	117	27	∈	∈	PROPN
ejpam-2422	117	28	k	k	NOUN
ejpam-2422	117	29	,	,	PUNCT
ejpam-2422	117	30	p	p	PROPN
ejpam-2422	117	31	∈	∈	PROPN
ejpam-2422	117	32	c((lx	c((lx	PROPN
ejpam-2422	117	33	)	)	PUNCT
ejpam-2422	117	34	e	e	X
ejpam-2422	117	35	)	)	PUNCT
ejpam-2422	117	36	and	and	CCONJ
ejpam-2422	117	37	f	f	PROPN
ejpam-2422	117	38	∈	∈	PROPN
ejpam-2422	117	39	(	(	PUNCT
ejpam-2422	117	40	lx	lx	NOUN
ejpam-2422	117	41	)	)	PUNCT
ejpam-2422	117	42	e	e	NOUN
ejpam-2422	117	43	,	,	PUNCT
ejpam-2422	117	44	as	as	ADP
ejpam-2422	117	45	(	(	PUNCT
ejpam-2422	117	46	rp	rp	NOUN
ejpam-2422	117	47	t	t	PROPN
ejpam-2422	117	48	)	)	PUNCT
ejpam-2422	118	1	k	k	PROPN
ejpam-2422	118	2	(	(	PUNCT
ejpam-2422	118	3	f	f	PROPN
ejpam-2422	118	4	)	)	PUNCT
ejpam-2422	118	5	=	=	SYM
ejpam-2422	118	6	¨	¨	ADJ
ejpam-2422	118	7	∨	∨	NUM
ejpam-2422	118	8	g∈p|	g∈p|	PROPN
ejpam-2422	118	9	f	f	PROPN
ejpam-2422	118	10	tk(g	tk(g	PROPN
ejpam-2422	118	11	)	)	PUNCT
ejpam-2422	118	12	,	,	PUNCT
ejpam-2422	118	13	if	if	SCONJ
ejpam-2422	118	14	p	p	PRON
ejpam-2422	118	15	6v	6v	VERB
ejpam-2422	118	16	f	f	X
ejpam-2422	118	17	;	;	PUNCT
ejpam-2422	118	18	0	0	NUM
ejpam-2422	118	19	m	m	NOUN
ejpam-2422	118	20	,	,	PUNCT
ejpam-2422	118	21	otherwise	otherwise	ADV
ejpam-2422	118	22	.	.	PUNCT
ejpam-2422	119	1	(	(	PUNCT
ejpam-2422	119	2	3	3	X
ejpam-2422	119	3	)	)	PUNCT
ejpam-2422	119	4	(	(	PUNCT
ejpam-2422	119	5	2	2	X
ejpam-2422	119	6	)	)	PUNCT
ejpam-2422	119	7	if	if	SCONJ
ejpam-2422	119	8	t	t	PROPN
ejpam-2422	119	9	and	and	CCONJ
ejpam-2422	119	10	s	s	PRON
ejpam-2422	119	11	are	be	AUX
ejpam-2422	119	12	two	two	NUM
ejpam-2422	119	13	(	(	PUNCT
ejpam-2422	119	14	l	l	NOUN
ejpam-2422	119	15	,	,	PUNCT
ejpam-2422	119	16	m)-fuzzy	m)-fuzzy	X
ejpam-2422	119	17	(	(	PUNCT
ejpam-2422	119	18	e	e	NOUN
ejpam-2422	119	19	,	,	PUNCT
ejpam-2422	119	20	k)-soft	k)-soft	PROPN
ejpam-2422	119	21	cotopologies	cotopologie	NOUN
ejpam-2422	119	22	which	which	PRON
ejpam-2422	119	23	determine	determine	VERB
ejpam-2422	119	24	the	the	DET
ejpam-2422	119	25	same	same	ADJ
ejpam-2422	119	26	topological	topological	ADJ
ejpam-2422	119	27	fuzzy	fuzzy	ADJ
ejpam-2422	119	28	soft	soft	ADJ
ejpam-2422	119	29	remote	remote	ADJ
ejpam-2422	119	30	neighborhood	neighborhood	NOUN
ejpam-2422	119	31	system	system	NOUN
ejpam-2422	119	32	,	,	PUNCT
ejpam-2422	119	33	then	then	ADV
ejpam-2422	119	34	t	t	PROPN
ejpam-2422	119	35	=	=	SYM
ejpam-2422	119	36	s	s	PART
ejpam-2422	119	37	.	.	PUNCT
ejpam-2422	120	1	proof	proof	NOUN
ejpam-2422	120	2	.	.	PUNCT
ejpam-2422	121	1	by	by	ADP
ejpam-2422	121	2	definition	definition	NOUN
ejpam-2422	121	3	4	4	NUM
ejpam-2422	121	4	,	,	PUNCT
ejpam-2422	121	5	we	we	PRON
ejpam-2422	121	6	need	need	VERB
ejpam-2422	121	7	to	to	PART
ejpam-2422	121	8	show	show	VERB
ejpam-2422	121	9	(	(	PUNCT
ejpam-2422	121	10	rn1)-(rn4	rn1)-(rn4	NOUN
ejpam-2422	121	11	)	)	PUNCT
ejpam-2422	121	12	in	in	ADP
ejpam-2422	121	13	the	the	DET
ejpam-2422	121	14	following	following	NOUN
ejpam-2422	121	15	.	.	PUNCT
ejpam-2422	122	1	first	first	ADV
ejpam-2422	122	2	of	of	ADP
ejpam-2422	122	3	all	all	PRON
ejpam-2422	122	4	,	,	PUNCT
ejpam-2422	122	5	(	(	PUNCT
ejpam-2422	122	6	rn1)(rn2	rn1)(rn2	NOUN
ejpam-2422	122	7	)	)	PUNCT
ejpam-2422	122	8	are	be	AUX
ejpam-2422	122	9	trivial	trivial	ADJ
ejpam-2422	122	10	.	.	PUNCT
ejpam-2422	123	1	(	(	PUNCT
ejpam-2422	123	2	rn3	rn3	NOUN
ejpam-2422	123	3	):	):	PUNCT
ejpam-2422	123	4	let	let	VERB
ejpam-2422	123	5	k	k	PROPN
ejpam-2422	123	6	∈	∈	PROPN
ejpam-2422	123	7	k	k	PROPN
ejpam-2422	123	8	and	and	CCONJ
ejpam-2422	123	9	f	f	PROPN
ejpam-2422	123	10	,	,	PUNCT
ejpam-2422	123	11	g	g	PROPN
ejpam-2422	123	12	∈	∈	PROPN
ejpam-2422	123	13	(	(	PUNCT
ejpam-2422	123	14	lx	lx	NOUN
ejpam-2422	123	15	)	)	PUNCT
ejpam-2422	124	1	e	e	X
ejpam-2422	124	2	.	.	PUNCT
ejpam-2422	125	1	from	from	ADP
ejpam-2422	125	2	the	the	DET
ejpam-2422	125	3	definition	definition	NOUN
ejpam-2422	125	4	of	of	ADP
ejpam-2422	125	5	rp	rp	PROPN
ejpam-2422	125	6	t	t	PROPN
ejpam-2422	125	7	,	,	PUNCT
ejpam-2422	125	8	we	we	PRON
ejpam-2422	125	9	have	have	VERB
ejpam-2422	125	10	f	f	PROPN
ejpam-2422	125	11	v	v	ADP
ejpam-2422	125	12	g	g	PROPN
ejpam-2422	125	13	implies	imply	VERB
ejpam-2422	125	14	(	(	PUNCT
ejpam-2422	125	15	rp	rp	NOUN
ejpam-2422	125	16	t	t	PROPN
ejpam-2422	125	17	)	)	PUNCT
ejpam-2422	126	1	k	k	PROPN
ejpam-2422	126	2	(	(	PUNCT
ejpam-2422	126	3	f	f	PROPN
ejpam-2422	126	4	)	)	PUNCT
ejpam-2422	126	5	≥	≥	PROPN
ejpam-2422	126	6	(	(	PUNCT
ejpam-2422	126	7	r	r	NOUN
ejpam-2422	126	8	p	p	PROPN
ejpam-2422	126	9	t	t	NOUN
ejpam-2422	126	10	)	)	PUNCT
ejpam-2422	126	11	k(g	k(g	PROPN
ejpam-2422	126	12	)	)	PUNCT
ejpam-2422	126	13	.	.	PUNCT
ejpam-2422	127	1	this	this	PRON
ejpam-2422	127	2	is	be	AUX
ejpam-2422	127	3	to	to	PART
ejpam-2422	127	4	say	say	VERB
ejpam-2422	127	5	(	(	PUNCT
ejpam-2422	127	6	rp	rp	NOUN
ejpam-2422	127	7	t	t	PROPN
ejpam-2422	127	8	)	)	PUNCT
ejpam-2422	128	1	k	k	PROPN
ejpam-2422	128	2	(	(	PUNCT
ejpam-2422	128	3	f	f	PROPN
ejpam-2422	128	4	t	t	PROPN
ejpam-2422	128	5	g	g	NOUN
ejpam-2422	128	6	)	)	PUNCT
ejpam-2422	128	7	≤	≤	NOUN
ejpam-2422	128	8	(	(	PUNCT
ejpam-2422	128	9	rp	rp	NOUN
ejpam-2422	128	10	t	t	PROPN
ejpam-2422	128	11	)	)	PUNCT
ejpam-2422	129	1	k	k	PROPN
ejpam-2422	129	2	(	(	PUNCT
ejpam-2422	129	3	f	f	X
ejpam-2422	129	4	)	)	PUNCT
ejpam-2422	129	5	∧	∧	PROPN
ejpam-2422	129	6	(	(	PUNCT
ejpam-2422	129	7	r	r	NOUN
ejpam-2422	129	8	p	p	PROPN
ejpam-2422	129	9	t	t	NOUN
ejpam-2422	129	10	)	)	PUNCT
ejpam-2422	129	11	k(g	k(g	PROPN
ejpam-2422	129	12	)	)	PUNCT
ejpam-2422	129	13	.	.	PUNCT
ejpam-2422	129	14	suppose	suppose	VERB
ejpam-2422	129	15	that	that	SCONJ
ejpam-2422	129	16	α	α	PRON
ejpam-2422	129	17	ã	ã	X
ejpam-2422	129	18	(	(	PUNCT
ejpam-2422	129	19	(	(	PUNCT
ejpam-2422	129	20	rp	rp	NOUN
ejpam-2422	129	21	t	t	PROPN
ejpam-2422	129	22	)	)	PUNCT
ejpam-2422	129	23	k	k	PROPN
ejpam-2422	129	24	(	(	PUNCT
ejpam-2422	129	25	f	f	X
ejpam-2422	129	26	)	)	PUNCT
ejpam-2422	129	27	∧	∧	PROPN
ejpam-2422	129	28	(	(	PUNCT
ejpam-2422	129	29	r	r	NOUN
ejpam-2422	129	30	p	p	PROPN
ejpam-2422	129	31	t	t	NOUN
ejpam-2422	129	32	)	)	PUNCT
ejpam-2422	129	33	k(g	k(g	PROPN
ejpam-2422	129	34	)	)	PUNCT
ejpam-2422	129	35	)	)	PUNCT
ejpam-2422	129	36	,	,	PUNCT
ejpam-2422	129	37	where	where	SCONJ
ejpam-2422	129	38	α	α	X
ejpam-2422	129	39	∈	∈	PROPN
ejpam-2422	129	40	c(m	c(m	PROPN
ejpam-2422	129	41	)	)	PUNCT
ejpam-2422	129	42	.	.	PUNCT
ejpam-2422	130	1	then	then	ADV
ejpam-2422	130	2	α	α	PRON
ejpam-2422	130	3	ã	ã	X
ejpam-2422	130	4	(	(	PUNCT
ejpam-2422	130	5	rp	rp	NOUN
ejpam-2422	130	6	t	t	PROPN
ejpam-2422	130	7	)	)	PUNCT
ejpam-2422	131	1	k	k	PROPN
ejpam-2422	131	2	(	(	PUNCT
ejpam-2422	131	3	f	f	PROPN
ejpam-2422	131	4	)	)	PUNCT
ejpam-2422	131	5	and	and	CCONJ
ejpam-2422	131	6	α	α	PRON
ejpam-2422	131	7	ã	ã	X
ejpam-2422	131	8	(	(	PUNCT
ejpam-2422	131	9	rp	rp	NOUN
ejpam-2422	131	10	t	t	PROPN
ejpam-2422	131	11	)	)	PUNCT
ejpam-2422	131	12	k(g	k(g	PROPN
ejpam-2422	131	13	)	)	PUNCT
ejpam-2422	131	14	.	.	PUNCT
ejpam-2422	132	1	then	then	ADV
ejpam-2422	132	2	there	there	PRON
ejpam-2422	132	3	exist	exist	VERB
ejpam-2422	132	4	u	u	NOUN
ejpam-2422	132	5	∈	∈	PROPN
ejpam-2422	132	6	p	p	NOUN
ejpam-2422	133	1	|	|	NOUN
ejpam-2422	133	2	f	f	PROPN
ejpam-2422	133	3	and	and	CCONJ
ejpam-2422	133	4	v	v	ADP
ejpam-2422	133	5	∈	∈	NOUN
ejpam-2422	134	1	p	p	NOUN
ejpam-2422	134	2	|	|	ADV
ejpam-2422	134	3	g	g	NOUN
ejpam-2422	134	4	such	such	ADJ
ejpam-2422	134	5	that	that	DET
ejpam-2422	134	6	α≤	α≤	NOUN
ejpam-2422	134	7	tk(u	tk(u	NOUN
ejpam-2422	134	8	)	)	PUNCT
ejpam-2422	134	9	and	and	CCONJ
ejpam-2422	134	10	α≤	α≤	PROPN
ejpam-2422	134	11	tk(v	tk(v	NUM
ejpam-2422	134	12	)	)	PUNCT
ejpam-2422	134	13	.	.	PUNCT
ejpam-2422	135	1	therefore	therefore	ADV
ejpam-2422	135	2	,	,	PUNCT
ejpam-2422	135	3	α≤	α≤	PROPN
ejpam-2422	135	4	tk(u)∧tk(v)≤	tk(u)∧tk(v)≤	NOUN
ejpam-2422	135	5	tk(ut	tk(ut	PROPN
ejpam-2422	135	6	v	v	NOUN
ejpam-2422	135	7	)	)	PUNCT
ejpam-2422	135	8	.	.	PUNCT
ejpam-2422	136	1	it	it	PRON
ejpam-2422	136	2	is	be	AUX
ejpam-2422	136	3	clear	clear	ADJ
ejpam-2422	136	4	that	that	SCONJ
ejpam-2422	136	5	p	p	NOUN
ejpam-2422	136	6	6v	6v	NOUN
ejpam-2422	136	7	(	(	PUNCT
ejpam-2422	136	8	ut	ut	PROPN
ejpam-2422	136	9	v	v	NOUN
ejpam-2422	136	10	)	)	PUNCT
ejpam-2422	136	11	,	,	PUNCT
ejpam-2422	136	12	f	f	PROPN
ejpam-2422	136	13	t	t	PROPN
ejpam-2422	136	14	g	g	PROPN
ejpam-2422	136	15	v	v	X
ejpam-2422	136	16	ut	ut	PROPN
ejpam-2422	136	17	v.	v.	CCONJ
ejpam-2422	136	18	hence	hence	ADV
ejpam-2422	136	19	by	by	ADP
ejpam-2422	136	20	the	the	DET
ejpam-2422	136	21	definition	definition	NOUN
ejpam-2422	136	22	of	of	ADP
ejpam-2422	136	23	rp	rp	PROPN
ejpam-2422	136	24	t	t	PROPN
ejpam-2422	136	25	,	,	PUNCT
ejpam-2422	136	26	we	we	PRON
ejpam-2422	136	27	have	have	VERB
ejpam-2422	136	28	α≤	α≤	NOUN
ejpam-2422	136	29	(	(	PUNCT
ejpam-2422	136	30	rp	rp	NOUN
ejpam-2422	136	31	t	t	PROPN
ejpam-2422	136	32	)	)	PUNCT
ejpam-2422	137	1	k	k	PROPN
ejpam-2422	137	2	(	(	PUNCT
ejpam-2422	137	3	f	f	PROPN
ejpam-2422	137	4	t	t	PROPN
ejpam-2422	137	5	g	g	PROPN
ejpam-2422	137	6	)	)	PUNCT
ejpam-2422	137	7	.	.	PUNCT
ejpam-2422	138	1	from	from	ADP
ejpam-2422	138	2	the	the	DET
ejpam-2422	138	3	arbitrariness	arbitrariness	NOUN
ejpam-2422	138	4	of	of	ADP
ejpam-2422	138	5	α	α	NOUN
ejpam-2422	138	6	,	,	PUNCT
ejpam-2422	138	7	we	we	PRON
ejpam-2422	138	8	get	get	VERB
ejpam-2422	138	9	for	for	ADP
ejpam-2422	138	10	each	each	DET
ejpam-2422	138	11	k	k	PROPN
ejpam-2422	138	12	∈	∈	PROPN
ejpam-2422	138	13	k	k	X
ejpam-2422	138	14	,	,	PUNCT
ejpam-2422	138	15	(	(	PUNCT
ejpam-2422	138	16	rp	rp	NOUN
ejpam-2422	138	17	t	t	PROPN
ejpam-2422	138	18	)	)	PUNCT
ejpam-2422	139	1	k	k	PROPN
ejpam-2422	139	2	(	(	PUNCT
ejpam-2422	139	3	f	f	PROPN
ejpam-2422	139	4	t	t	PROPN
ejpam-2422	139	5	g)≥	g)≥	PROPN
ejpam-2422	139	6	(	(	PUNCT
ejpam-2422	139	7	rp	rp	NOUN
ejpam-2422	139	8	t	t	PROPN
ejpam-2422	139	9	)	)	PUNCT
ejpam-2422	140	1	k	k	PROPN
ejpam-2422	140	2	(	(	PUNCT
ejpam-2422	140	3	f	f	NOUN
ejpam-2422	140	4	)	)	PUNCT
ejpam-2422	140	5	∧	∧	PROPN
ejpam-2422	140	6	(	(	PUNCT
ejpam-2422	140	7	r	r	NOUN
ejpam-2422	140	8	p	p	PROPN
ejpam-2422	140	9	t	t	NOUN
ejpam-2422	140	10	)	)	PUNCT
ejpam-2422	140	11	k(g	k(g	PROPN
ejpam-2422	140	12	)	)	PUNCT
ejpam-2422	140	13	.	.	PUNCT
ejpam-2422	141	1	(	(	PUNCT
ejpam-2422	141	2	rn4	rn4	NOUN
ejpam-2422	141	3	):	):	PUNCT
ejpam-2422	141	4	for	for	ADP
ejpam-2422	141	5	each	each	DET
ejpam-2422	141	6	g	g	PROPN
ejpam-2422	141	7	∈	∈	PROPN
ejpam-2422	141	8	p	p	NOUN
ejpam-2422	142	1	|	|	NOUN
ejpam-2422	142	2	f	f	PROPN
ejpam-2422	142	3	and	and	CCONJ
ejpam-2422	142	4	k	k	PROPN
ejpam-2422	142	5	∈	∈	PROPN
ejpam-2422	143	1	k	k	NOUN
ejpam-2422	143	2	,	,	PUNCT
ejpam-2422	143	3	we	we	PRON
ejpam-2422	143	4	have	have	VERB
ejpam-2422	143	5	tk(g)≤	tk(g)≤	NOUN
ejpam-2422	143	6	∧	∧	PROPN
ejpam-2422	144	1	p	p	PROPN
ejpam-2422	145	1	6vg	6vg	ADJ
ejpam-2422	146	1	(	(	PUNCT
ejpam-2422	146	2	rp	rp	NOUN
ejpam-2422	146	3	t	t	PROPN
ejpam-2422	146	4	)	)	PUNCT
ejpam-2422	146	5	k(g)≤	k(g)≤	NOUN
ejpam-2422	146	6	(	(	PUNCT
ejpam-2422	146	7	r	r	NOUN
ejpam-2422	146	8	p	p	PROPN
ejpam-2422	146	9	t	t	PROPN
ejpam-2422	146	10	)	)	PUNCT
ejpam-2422	146	11	k(g)≤	k(g)≤	NOUN
ejpam-2422	146	12	(	(	PUNCT
ejpam-2422	146	13	r	r	NOUN
ejpam-2422	146	14	p	p	PROPN
ejpam-2422	146	15	t	t	PROPN
ejpam-2422	146	16	)	)	PUNCT
ejpam-2422	147	1	k	k	PROPN
ejpam-2422	147	2	(	(	PUNCT
ejpam-2422	147	3	f	f	PROPN
ejpam-2422	147	4	)	)	PUNCT
ejpam-2422	147	5	.	.	PUNCT
ejpam-2422	148	1	therefore	therefore	ADV
ejpam-2422	148	2	,	,	PUNCT
ejpam-2422	148	3	(	(	PUNCT
ejpam-2422	148	4	rp	rp	NOUN
ejpam-2422	148	5	t	t	PROPN
ejpam-2422	148	6	)	)	PUNCT
ejpam-2422	149	1	k	k	PROPN
ejpam-2422	149	2	(	(	PUNCT
ejpam-2422	149	3	f	f	PROPN
ejpam-2422	149	4	)	)	PUNCT
ejpam-2422	149	5	=	=	SYM
ejpam-2422	149	6	∨	∨	NUM
ejpam-2422	149	7	g∈p|	g∈p|	PROPN
ejpam-2422	149	8	f	f	PROPN
ejpam-2422	149	9	tk(g)≤	tk(g)≤	PROPN
ejpam-2422	149	10	∨	∨	NUM
ejpam-2422	149	11	g∈p|	g∈p|	PROPN
ejpam-2422	149	12	f	f	PROPN
ejpam-2422	149	13	∧	∧	PROPN
ejpam-2422	149	14	r	r	NOUN
ejpam-2422	149	15	6vg(r	6vg(r	NUM
ejpam-2422	149	16	r	r	NOUN
ejpam-2422	149	17	t	t	NOUN
ejpam-2422	149	18	)	)	PUNCT
ejpam-2422	149	19	k(g)≤	k(g)≤	NOUN
ejpam-2422	149	20	(	(	PUNCT
ejpam-2422	149	21	r	r	NOUN
ejpam-2422	149	22	p	p	PROPN
ejpam-2422	149	23	t	t	PROPN
ejpam-2422	149	24	)	)	PUNCT
ejpam-2422	150	1	k	k	PROPN
ejpam-2422	150	2	(	(	PUNCT
ejpam-2422	150	3	f	f	PROPN
ejpam-2422	150	4	)	)	PUNCT
ejpam-2422	150	5	.	.	PUNCT
ejpam-2422	151	1	this	this	PRON
ejpam-2422	151	2	means	mean	VERB
ejpam-2422	151	3	that	that	SCONJ
ejpam-2422	151	4	for	for	ADP
ejpam-2422	151	5	each	each	DET
ejpam-2422	151	6	k	k	PROPN
ejpam-2422	151	7	∈	∈	PROPN
ejpam-2422	151	8	k	k	X
ejpam-2422	151	9	,	,	PUNCT
ejpam-2422	151	10	(	(	PUNCT
ejpam-2422	151	11	rp	rp	NOUN
ejpam-2422	151	12	t	t	PROPN
ejpam-2422	151	13	)	)	PUNCT
ejpam-2422	151	14	k	k	PROPN
ejpam-2422	151	15	(	(	PUNCT
ejpam-2422	151	16	f	f	PROPN
ejpam-2422	151	17	)	)	PUNCT
ejpam-2422	151	18	=	=	SYM
ejpam-2422	152	1	∨	∨	NUM
ejpam-2422	152	2	g∈p|	g∈p|	PROPN
ejpam-2422	152	3	f	f	PROPN
ejpam-2422	152	4	∧	∧	PROPN
ejpam-2422	152	5	r	r	NOUN
ejpam-2422	152	6	6vg(r	6vg(r	NUM
ejpam-2422	152	7	r	r	NOUN
ejpam-2422	152	8	t	t	NOUN
ejpam-2422	152	9	)	)	PUNCT
ejpam-2422	152	10	k(g	k(g	PROPN
ejpam-2422	152	11	)	)	PUNCT
ejpam-2422	152	12	.	.	PUNCT
ejpam-2422	153	1	(	(	PUNCT
ejpam-2422	153	2	2	2	X
ejpam-2422	153	3	)	)	PUNCT
ejpam-2422	153	4	for	for	ADP
ejpam-2422	153	5	the	the	DET
ejpam-2422	153	6	proof	proof	NOUN
ejpam-2422	153	7	of	of	ADP
ejpam-2422	153	8	the	the	DET
ejpam-2422	153	9	second	second	ADJ
ejpam-2422	153	10	claim	claim	NOUN
ejpam-2422	153	11	of	of	ADP
ejpam-2422	153	12	lemma	lemma	PROPN
ejpam-2422	153	13	1	1	NUM
ejpam-2422	153	14	,	,	PUNCT
ejpam-2422	153	15	it	it	PRON
ejpam-2422	153	16	is	be	AUX
ejpam-2422	153	17	sufficient	sufficient	ADJ
ejpam-2422	153	18	to	to	PART
ejpam-2422	153	19	show	show	VERB
ejpam-2422	153	20	the	the	DET
ejpam-2422	153	21	validity	validity	NOUN
ejpam-2422	153	22	of	of	ADP
ejpam-2422	153	23	the	the	DET
ejpam-2422	153	24	following	follow	VERB
ejpam-2422	153	25	equality	equality	NOUN
ejpam-2422	153	26	;	;	PUNCT
ejpam-2422	153	27	tk	tk	PROPN
ejpam-2422	153	28	(	(	PUNCT
ejpam-2422	153	29	f	f	NOUN
ejpam-2422	153	30	)	)	PUNCT
ejpam-2422	154	1	=	=	PUNCT
ejpam-2422	154	2	∧	∧	PROPN
ejpam-2422	154	3	p	p	NOUN
ejpam-2422	154	4	6v	6v	X
ejpam-2422	154	5	f	f	X
ejpam-2422	154	6	(	(	PUNCT
ejpam-2422	154	7	r	r	NOUN
ejpam-2422	154	8	p	p	PROPN
ejpam-2422	154	9	t	t	PROPN
ejpam-2422	154	10	)	)	PUNCT
ejpam-2422	155	1	k	k	PROPN
ejpam-2422	155	2	(	(	PUNCT
ejpam-2422	155	3	f	f	PROPN
ejpam-2422	155	4	)	)	PUNCT
ejpam-2422	155	5	for	for	ADP
ejpam-2422	155	6	all	all	DET
ejpam-2422	155	7	f	f	PROPN
ejpam-2422	155	8	∈	∈	PROPN
ejpam-2422	155	9	(	(	PUNCT
ejpam-2422	155	10	lx	lx	NOUN
ejpam-2422	155	11	)	)	PUNCT
ejpam-2422	155	12	e	e	NOUN
ejpam-2422	155	13	and	and	CCONJ
ejpam-2422	155	14	k	k	PROPN
ejpam-2422	155	15	∈	∈	PROPN
ejpam-2422	156	1	k	k	X
ejpam-2422	156	2	.	.	PUNCT
ejpam-2422	157	1	obviously	obviously	ADV
ejpam-2422	157	2	,	,	PUNCT
ejpam-2422	157	3	tk	tk	PROPN
ejpam-2422	157	4	(	(	PUNCT
ejpam-2422	157	5	f	f	PROPN
ejpam-2422	157	6	)	)	PUNCT
ejpam-2422	157	7	≤	≤	NUM
ejpam-2422	157	8	∧	∧	PROPN
ejpam-2422	157	9	p	p	NOUN
ejpam-2422	157	10	6v	6v	X
ejpam-2422	157	11	f	f	X
ejpam-2422	157	12	(	(	PUNCT
ejpam-2422	157	13	r	r	NOUN
ejpam-2422	157	14	p	p	PROPN
ejpam-2422	157	15	t	t	PROPN
ejpam-2422	157	16	)	)	PUNCT
ejpam-2422	158	1	k	k	PROPN
ejpam-2422	158	2	(	(	PUNCT
ejpam-2422	158	3	f	f	PROPN
ejpam-2422	158	4	)	)	PUNCT
ejpam-2422	158	5	for	for	ADP
ejpam-2422	158	6	all	all	DET
ejpam-2422	158	7	f	f	PROPN
ejpam-2422	158	8	∈	∈	PROPN
ejpam-2422	158	9	(	(	PUNCT
ejpam-2422	158	10	lx	lx	NOUN
ejpam-2422	158	11	)	)	PUNCT
ejpam-2422	158	12	e	e	NOUN
ejpam-2422	158	13	and	and	CCONJ
ejpam-2422	158	14	k	k	PROPN
ejpam-2422	158	15	∈	∈	PROPN
ejpam-2422	159	1	k	k	X
ejpam-2422	159	2	.	.	PUNCT
ejpam-2422	160	1	so	so	ADV
ejpam-2422	160	2	it	it	PRON
ejpam-2422	160	3	is	be	AUX
ejpam-2422	160	4	enough	enough	ADJ
ejpam-2422	160	5	to	to	PART
ejpam-2422	160	6	prove	prove	VERB
ejpam-2422	160	7	tk	tk	PROPN
ejpam-2422	160	8	(	(	PUNCT
ejpam-2422	160	9	f	f	PROPN
ejpam-2422	160	10	)	)	PUNCT
ejpam-2422	160	11	≥	≥	PROPN
ejpam-2422	161	1	∧	∧	PROPN
ejpam-2422	161	2	p	p	NOUN
ejpam-2422	161	3	6v	6v	X
ejpam-2422	161	4	f	f	X
ejpam-2422	161	5	(	(	PUNCT
ejpam-2422	161	6	r	r	NOUN
ejpam-2422	161	7	p	p	PROPN
ejpam-2422	161	8	t	t	PROPN
ejpam-2422	161	9	)	)	PUNCT
ejpam-2422	162	1	k	k	PROPN
ejpam-2422	162	2	(	(	PUNCT
ejpam-2422	162	3	f	f	PROPN
ejpam-2422	162	4	)	)	PUNCT
ejpam-2422	162	5	.	.	PUNCT
ejpam-2422	163	1	in	in	ADP
ejpam-2422	163	2	fact	fact	NOUN
ejpam-2422	163	3	,	,	PUNCT
ejpam-2422	163	4	we	we	PRON
ejpam-2422	163	5	have	have	VERB
ejpam-2422	163	6	∧	∧	PROPN
ejpam-2422	163	7	p	p	NOUN
ejpam-2422	163	8	6v	6v	NOUN
ejpam-2422	163	9	f	f	X
ejpam-2422	163	10	(	(	PUNCT
ejpam-2422	163	11	rp	rp	PROPN
ejpam-2422	163	12	t	t	PROPN
ejpam-2422	163	13	)	)	PUNCT
ejpam-2422	164	1	k	k	PROPN
ejpam-2422	164	2	(	(	PUNCT
ejpam-2422	164	3	f	f	NOUN
ejpam-2422	164	4	)	)	PUNCT
ejpam-2422	164	5	=	=	PUNCT
ejpam-2422	165	1	∧	∧	PROPN
ejpam-2422	165	2	p	p	NOUN
ejpam-2422	165	3	6v	6v	X
ejpam-2422	165	4	f	f	PROPN
ejpam-2422	165	5	∨	∨	NUM
ejpam-2422	165	6	g∈p|	g∈p|	PROPN
ejpam-2422	165	7	f	f	PROPN
ejpam-2422	165	8	tk(g	tk(g	PROPN
ejpam-2422	165	9	)	)	PUNCT
ejpam-2422	165	10	=	=	PUNCT
ejpam-2422	166	1	∨	∨	NUM
ejpam-2422	166	2	a∈πp	a∈πp	PROPN
ejpam-2422	166	3	6v	6v	VERB
ejpam-2422	166	4	f	f	PROPN
ejpam-2422	166	5	p|	p|	NOUN
ejpam-2422	166	6	f	f	NOUN
ejpam-2422	166	7	∧	∧	PROPN
ejpam-2422	166	8	p	p	PROPN
ejpam-2422	166	9	6v	6v	NUM
ejpam-2422	166	10	f	f	PROPN
ejpam-2422	166	11	tk(a(p))≤	tk(a(p))≤	NUM
ejpam-2422	166	12	∨	∨	NUM
ejpam-2422	166	13	a∈πp	a∈πp	PROPN
ejpam-2422	166	14	6v	6v	VERB
ejpam-2422	166	15	f	f	PROPN
ejpam-2422	166	16	p|	p|	PROPN
ejpam-2422	166	17	f	f	NOUN
ejpam-2422	166	18	tk(up	tk(up	VERB
ejpam-2422	166	19	6v	6v	VERB
ejpam-2422	166	20	f	f	PROPN
ejpam-2422	166	21	a(p	a(p	NOUN
ejpam-2422	166	22	)	)	PUNCT
ejpam-2422	166	23	)	)	PUNCT
ejpam-2422	167	1	=	=	SYM
ejpam-2422	167	2	tk	tk	PROPN
ejpam-2422	167	3	(	(	PUNCT
ejpam-2422	167	4	f	f	PROPN
ejpam-2422	167	5	)	)	PUNCT
ejpam-2422	167	6	.	.	PUNCT
ejpam-2422	168	1	the	the	DET
ejpam-2422	168	2	last	last	ADJ
ejpam-2422	168	3	equality	equality	NOUN
ejpam-2422	168	4	is	be	AUX
ejpam-2422	168	5	due	due	ADJ
ejpam-2422	168	6	to	to	PART
ejpam-2422	168	7	up	up	ADP
ejpam-2422	168	8	6v	6v	PROPN
ejpam-2422	168	9	f	f	PROPN
ejpam-2422	168	10	a(p	a(p	PROPN
ejpam-2422	168	11	)	)	PUNCT
ejpam-2422	168	12	=	=	SYM
ejpam-2422	168	13	f	f	PROPN
ejpam-2422	168	14	for	for	ADP
ejpam-2422	168	15	every	every	DET
ejpam-2422	168	16	a∈	a∈	PROPN
ejpam-2422	168	17	πp	πp	ADP
ejpam-2422	168	18	6v	6v	VERB
ejpam-2422	169	1	f	f	PROPN
ejpam-2422	170	1	p	p	NOUN
ejpam-2422	170	2	|	|	INTJ
ejpam-2422	170	3	f	f	PROPN
ejpam-2422	170	4	.	.	PUNCT
ejpam-2422	171	1	lemma	lemma	PROPN
ejpam-2422	171	2	2	2	X
ejpam-2422	171	3	.	.	PUNCT
ejpam-2422	172	1	let	let	VERB
ejpam-2422	172	2	r	r	NOUN
ejpam-2422	172	3	=	=	PUNCT
ejpam-2422	172	4	{	{	PUNCT
ejpam-2422	172	5	rp	rp	NOUN
ejpam-2422	172	6	|	|	ADV
ejpam-2422	172	7	p	p	X
ejpam-2422	172	8	∈	∈	PROPN
ejpam-2422	172	9	c((lx	c((lx	PROPN
ejpam-2422	172	10	)	)	PUNCT
ejpam-2422	172	11	e	e	X
ejpam-2422	172	12	)	)	PUNCT
ejpam-2422	172	13	}	}	PUNCT
ejpam-2422	172	14	be	be	AUX
ejpam-2422	172	15	a	a	DET
ejpam-2422	172	16	topological	topological	ADJ
ejpam-2422	172	17	fuzzy	fuzzy	ADJ
ejpam-2422	172	18	soft	soft	ADJ
ejpam-2422	172	19	remote	remote	ADJ
ejpam-2422	172	20	neighborhood	neighborhood	NOUN
ejpam-2422	172	21	system	system	NOUN
ejpam-2422	172	22	and	and	CCONJ
ejpam-2422	172	23	t	t	NOUN
ejpam-2422	172	24	:	:	PUNCT
ejpam-2422	173	1	k	k	X
ejpam-2422	173	2	→	→	PUNCT
ejpam-2422	173	3	m	m	PROPN
ejpam-2422	173	4	(	(	PUNCT
ejpam-2422	173	5	l	l	NOUN
ejpam-2422	173	6	x	x	X
ejpam-2422	173	7	)	)	PUNCT
ejpam-2422	173	8	e	e	AUX
ejpam-2422	173	9	be	be	AUX
ejpam-2422	173	10	defined	define	VERB
ejpam-2422	173	11	by	by	ADP
ejpam-2422	173	12	for	for	ADP
ejpam-2422	173	13	all	all	DET
ejpam-2422	173	14	k	k	PROPN
ejpam-2422	173	15	∈	∈	PROPN
ejpam-2422	173	16	k	k	PROPN
ejpam-2422	173	17	and	and	CCONJ
ejpam-2422	173	18	f	f	PROPN
ejpam-2422	173	19	∈	∈	PROPN
ejpam-2422	173	20	(	(	PUNCT
ejpam-2422	173	21	lx	lx	NOUN
ejpam-2422	173	22	)	)	PUNCT
ejpam-2422	173	23	e	e	NOUN
ejpam-2422	173	24	,	,	PUNCT
ejpam-2422	173	25	tk	tk	PROPN
ejpam-2422	173	26	(	(	PUNCT
ejpam-2422	173	27	f	f	PROPN
ejpam-2422	173	28	)	)	PUNCT
ejpam-2422	174	1	=	=	PUNCT
ejpam-2422	174	2	∧	∧	PROPN
ejpam-2422	174	3	p	p	NOUN
ejpam-2422	174	4	6v	6v	NOUN
ejpam-2422	174	5	f	f	PROPN
ejpam-2422	174	6	rp	rp	PROPN
ejpam-2422	174	7	k	k	PROPN
ejpam-2422	175	1	(	(	PUNCT
ejpam-2422	175	2	f	f	PROPN
ejpam-2422	175	3	)	)	PUNCT
ejpam-2422	175	4	.	.	PUNCT
ejpam-2422	176	1	then	then	ADV
ejpam-2422	176	2	t	t	PROPN
ejpam-2422	176	3	is	be	AUX
ejpam-2422	176	4	an	an	DET
ejpam-2422	176	5	(	(	PUNCT
ejpam-2422	176	6	l	l	NOUN
ejpam-2422	176	7	,	,	PUNCT
ejpam-2422	176	8	m)-fuzzy	m)-fuzzy	X
ejpam-2422	176	9	(	(	PUNCT
ejpam-2422	176	10	e	e	NOUN
ejpam-2422	176	11	,	,	PUNCT
ejpam-2422	176	12	k)-soft	k)-soft	PROPN
ejpam-2422	176	13	cotopology	cotopology	NOUN
ejpam-2422	176	14	on	on	ADP
ejpam-2422	176	15	x	x	X
ejpam-2422	176	16	.	.	PUNCT
ejpam-2422	177	1	furthermore	furthermore	ADV
ejpam-2422	177	2	,	,	PUNCT
ejpam-2422	177	3	if	if	SCONJ
ejpam-2422	177	4	r	r	NOUN
ejpam-2422	177	5	and	and	CCONJ
ejpam-2422	177	6	p	p	NOUN
ejpam-2422	177	7	are	be	AUX
ejpam-2422	177	8	two	two	NUM
ejpam-2422	177	9	topological	topological	ADJ
ejpam-2422	177	10	fuzzy	fuzzy	ADJ
ejpam-2422	177	11	soft	soft	ADJ
ejpam-2422	177	12	remote	remote	ADJ
ejpam-2422	177	13	neighborhood	neighborhood	NOUN
ejpam-2422	177	14	systems	system	NOUN
ejpam-2422	177	15	which	which	PRON
ejpam-2422	177	16	determine	determine	VERB
ejpam-2422	177	17	the	the	DET
ejpam-2422	177	18	same	same	ADJ
ejpam-2422	177	19	(	(	PUNCT
ejpam-2422	177	20	l	l	NOUN
ejpam-2422	177	21	,	,	PUNCT
ejpam-2422	177	22	m)-fuzzy	m)-fuzzy	X
ejpam-2422	177	23	(	(	PUNCT
ejpam-2422	177	24	e	e	NOUN
ejpam-2422	177	25	,	,	PUNCT
ejpam-2422	177	26	k)-soft	k)-soft	PROPN
ejpam-2422	177	27	cotopology	cotopology	PROPN
ejpam-2422	177	28	,	,	PUNCT
ejpam-2422	177	29	then	then	ADV
ejpam-2422	177	30	r	r	NOUN
ejpam-2422	177	31	=	=	NOUN
ejpam-2422	177	32	p	p	NOUN
ejpam-2422	177	33	.	.	PUNCT
ejpam-2422	178	1	v.	v.	ADP
ejpam-2422	178	2	çetkin	çetkin	PROPN
ejpam-2422	178	3	,	,	PUNCT
ejpam-2422	178	4	h.	h.	PROPN
ejpam-2422	178	5	aygün	aygün	PROPN
ejpam-2422	178	6	/	/	SYM
ejpam-2422	178	7	eur	eur	PROPN
ejpam-2422	178	8	.	.	PUNCT
ejpam-2422	179	1	j.	j.	PROPN
ejpam-2422	179	2	pure	pure	PROPN
ejpam-2422	179	3	appl	appl	PROPN
ejpam-2422	179	4	.	.	PROPN
ejpam-2422	179	5	math	math	PROPN
ejpam-2422	179	6	,	,	PUNCT
ejpam-2422	179	7	9	9	NUM
ejpam-2422	179	8	(	(	PUNCT
ejpam-2422	179	9	2016	2016	NUM
ejpam-2422	179	10	)	)	PUNCT
ejpam-2422	179	11	,	,	PUNCT
ejpam-2422	179	12	419	419	NUM
ejpam-2422	179	13	-	-	SYM
ejpam-2422	179	14	433	433	NUM
ejpam-2422	179	15	424	424	NUM
ejpam-2422	179	16	proof	proof	NOUN
ejpam-2422	179	17	.	.	PUNCT
ejpam-2422	180	1	by	by	ADP
ejpam-2422	180	2	definition	definition	NOUN
ejpam-2422	180	3	3	3	NUM
ejpam-2422	180	4	,	,	PUNCT
ejpam-2422	180	5	(	(	PUNCT
ejpam-2422	180	6	c1	c1	NOUN
ejpam-2422	180	7	)	)	PUNCT
ejpam-2422	180	8	is	be	AUX
ejpam-2422	180	9	trivial	trivial	ADJ
ejpam-2422	180	10	.	.	PUNCT
ejpam-2422	181	1	(	(	PUNCT
ejpam-2422	181	2	c2	c2	PROPN
ejpam-2422	181	3	)	)	PUNCT
ejpam-2422	181	4	is	be	AUX
ejpam-2422	181	5	proved	prove	VERB
ejpam-2422	181	6	by	by	ADP
ejpam-2422	181	7	the	the	DET
ejpam-2422	181	8	following	follow	VERB
ejpam-2422	181	9	equations	equation	NOUN
ejpam-2422	181	10	:	:	PUNCT
ejpam-2422	181	11	for	for	ADP
ejpam-2422	181	12	each	each	DET
ejpam-2422	181	13	k	k	PROPN
ejpam-2422	181	14	∈	∈	PROPN
ejpam-2422	181	15	k	k	PROPN
ejpam-2422	181	16	,	,	PUNCT
ejpam-2422	181	17	tk	tk	PROPN
ejpam-2422	181	18	(	(	PUNCT
ejpam-2422	181	19	f	f	PROPN
ejpam-2422	181	20	t	t	PROPN
ejpam-2422	181	21	g	g	NOUN
ejpam-2422	181	22	)	)	PUNCT
ejpam-2422	182	1	=	=	SYM
ejpam-2422	183	1	∧	∧	PROPN
ejpam-2422	183	2	p	p	NOUN
ejpam-2422	183	3	6v	6v	NOUN
ejpam-2422	183	4	(	(	PUNCT
ejpam-2422	183	5	f	f	PROPN
ejpam-2422	183	6	tg	tg	PROPN
ejpam-2422	183	7	)	)	PUNCT
ejpam-2422	183	8	rp	rp	NOUN
ejpam-2422	184	1	k	k	PROPN
ejpam-2422	184	2	(	(	PUNCT
ejpam-2422	184	3	f	f	PROPN
ejpam-2422	184	4	t	t	PROPN
ejpam-2422	184	5	g)≥	g)≥	PROPN
ejpam-2422	184	6	(	(	PUNCT
ejpam-2422	184	7	∧	∧	PROPN
ejpam-2422	184	8	p	p	NOUN
ejpam-2422	184	9	6v	6v	NOUN
ejpam-2422	184	10	f	f	PROPN
ejpam-2422	184	11	rp	rp	PROPN
ejpam-2422	184	12	k	k	PROPN
ejpam-2422	184	13	(	(	PUNCT
ejpam-2422	184	14	f	f	PROPN
ejpam-2422	184	15	)	)	PUNCT
ejpam-2422	184	16	)	)	PUNCT
ejpam-2422	185	1	∧	∧	NOUN
ejpam-2422	185	2	(	(	PUNCT
ejpam-2422	185	3	∧	∧	PROPN
ejpam-2422	185	4	p	p	PRON
ejpam-2422	185	5	6vg	6vg	ADJ
ejpam-2422	185	6	rp	rp	NOUN
ejpam-2422	185	7	k(g	k(g	NOUN
ejpam-2422	185	8	)	)	PUNCT
ejpam-2422	185	9	)	)	PUNCT
ejpam-2422	186	1	=	=	SYM
ejpam-2422	186	2	tk	tk	PROPN
ejpam-2422	186	3	(	(	PUNCT
ejpam-2422	186	4	f	f	PROPN
ejpam-2422	186	5	)	)	PUNCT
ejpam-2422	186	6	∧tk(g	∧tk(g	PROPN
ejpam-2422	186	7	)	)	PUNCT
ejpam-2422	186	8	.	.	PUNCT
ejpam-2422	187	1	finally	finally	ADV
ejpam-2422	187	2	,	,	PUNCT
ejpam-2422	187	3	(	(	PUNCT
ejpam-2422	187	4	c3	c3	NOUN
ejpam-2422	187	5	)	)	PUNCT
ejpam-2422	187	6	is	be	AUX
ejpam-2422	187	7	shown	show	VERB
ejpam-2422	187	8	by	by	ADP
ejpam-2422	187	9	the	the	DET
ejpam-2422	187	10	following	follow	VERB
ejpam-2422	187	11	computation	computation	NOUN
ejpam-2422	187	12	:	:	PUNCT
ejpam-2422	187	13	for	for	ADP
ejpam-2422	187	14	each	each	DET
ejpam-2422	187	15	k	k	PROPN
ejpam-2422	187	16	∈	∈	PROPN
ejpam-2422	187	17	k	k	PROPN
ejpam-2422	187	18	,	,	PUNCT
ejpam-2422	187	19	tk(u	tk(u	X
ejpam-2422	187	20	j∈j	j∈j	PROPN
ejpam-2422	187	21	f	f	PROPN
ejpam-2422	187	22	j	j	PROPN
ejpam-2422	187	23	)	)	PUNCT
ejpam-2422	188	1	=	=	PUNCT
ejpam-2422	188	2	∧	∧	PROPN
ejpam-2422	188	3	p	p	PRON
ejpam-2422	188	4	6vu	6vu	ADJ
ejpam-2422	188	5	j∈j	j∈j	NOUN
ejpam-2422	188	6	f	f	PROPN
ejpam-2422	188	7	j	j	PROPN
ejpam-2422	188	8	rp	rp	PROPN
ejpam-2422	188	9	k(u	k(u	PROPN
ejpam-2422	188	10	j∈j	j∈j	PROPN
ejpam-2422	188	11	f	f	PROPN
ejpam-2422	188	12	j	j	PROPN
ejpam-2422	188	13	)	)	PUNCT
ejpam-2422	189	1	=	=	SYM
ejpam-2422	189	2	∧	∧	PROPN
ejpam-2422	189	3	j∈j	j∈j	NOUN
ejpam-2422	189	4	∧	∧	PROPN
ejpam-2422	189	5	p	p	PROPN
ejpam-2422	189	6	6v	6v	VERB
ejpam-2422	189	7	f	f	PROPN
ejpam-2422	189	8	j	j	PROPN
ejpam-2422	189	9	rp	rp	PROPN
ejpam-2422	189	10	k(u	k(u	PROPN
ejpam-2422	189	11	j∈j	j∈j	PROPN
ejpam-2422	189	12	f	f	PROPN
ejpam-2422	189	13	j)≥	j)≥	PROPN
ejpam-2422	189	14	∧	∧	PROPN
ejpam-2422	189	15	j∈j	j∈j	NOUN
ejpam-2422	189	16	∧	∧	PROPN
ejpam-2422	189	17	p	p	PROPN
ejpam-2422	189	18	6v	6v	VERB
ejpam-2422	189	19	f	f	PROPN
ejpam-2422	189	20	j	j	PROPN
ejpam-2422	189	21	rp	rp	PROPN
ejpam-2422	190	1	k	k	PROPN
ejpam-2422	191	1	(	(	PUNCT
ejpam-2422	191	2	f	f	PROPN
ejpam-2422	191	3	j	j	PROPN
ejpam-2422	191	4	)	)	PUNCT
ejpam-2422	191	5	=	=	SYM
ejpam-2422	192	1	∧	∧	PROPN
ejpam-2422	192	2	j∈j	j∈j	NOUN
ejpam-2422	192	3	tk	tk	PROPN
ejpam-2422	192	4	(	(	PUNCT
ejpam-2422	192	5	f	f	PROPN
ejpam-2422	192	6	j	j	PROPN
ejpam-2422	192	7	)	)	PUNCT
ejpam-2422	192	8	.	.	PUNCT
ejpam-2422	193	1	this	this	PRON
ejpam-2422	193	2	completes	complete	VERB
ejpam-2422	193	3	the	the	DET
ejpam-2422	193	4	proof	proof	NOUN
ejpam-2422	193	5	.	.	PUNCT
ejpam-2422	194	1	moreover	moreover	ADV
ejpam-2422	194	2	,	,	PUNCT
ejpam-2422	194	3	it	it	PRON
ejpam-2422	194	4	is	be	AUX
ejpam-2422	194	5	obvious	obvious	ADJ
ejpam-2422	194	6	that	that	SCONJ
ejpam-2422	194	7	r	r	NOUN
ejpam-2422	194	8	=	=	PUNCT
ejpam-2422	194	9	p	p	NOUN
ejpam-2422	194	10	if	if	SCONJ
ejpam-2422	194	11	r	r	NOUN
ejpam-2422	194	12	and	and	CCONJ
ejpam-2422	194	13	p	p	NOUN
ejpam-2422	194	14	are	be	AUX
ejpam-2422	194	15	two	two	NUM
ejpam-2422	194	16	topological	topological	ADJ
ejpam-2422	194	17	fuzzy	fuzzy	ADJ
ejpam-2422	194	18	soft	soft	ADJ
ejpam-2422	194	19	remote	remote	ADJ
ejpam-2422	194	20	neighborhood	neighborhood	NOUN
ejpam-2422	194	21	systems	system	NOUN
ejpam-2422	194	22	which	which	PRON
ejpam-2422	194	23	determine	determine	VERB
ejpam-2422	194	24	the	the	DET
ejpam-2422	194	25	same	same	ADJ
ejpam-2422	194	26	fuzzy	fuzzy	ADJ
ejpam-2422	194	27	soft	soft	ADJ
ejpam-2422	194	28	cotopology	cotopology	NOUN
ejpam-2422	194	29	.	.	PUNCT
ejpam-2422	195	1	lemma	lemma	PROPN
ejpam-2422	195	2	3	3	X
ejpam-2422	195	3	.	.	PUNCT
ejpam-2422	196	1	let	let	AUX
ejpam-2422	196	2	r	r	NOUN
ejpam-2422	196	3	=	=	PUNCT
ejpam-2422	196	4	{	{	PUNCT
ejpam-2422	196	5	rp	rp	NOUN
ejpam-2422	196	6	|	|	ADV
ejpam-2422	196	7	p	p	X
ejpam-2422	196	8	∈	∈	PROPN
ejpam-2422	196	9	c((lx	c((lx	PROPN
ejpam-2422	196	10	)	)	PUNCT
ejpam-2422	196	11	e	e	X
ejpam-2422	196	12	)	)	PUNCT
ejpam-2422	196	13	}	}	PUNCT
ejpam-2422	196	14	be	be	AUX
ejpam-2422	196	15	a	a	DET
ejpam-2422	196	16	set	set	NOUN
ejpam-2422	196	17	satisfying	satisfying	NOUN
ejpam-2422	196	18	(	(	PUNCT
ejpam-2422	196	19	rn1)-(rn3	rn1)-(rn3	NOUN
ejpam-2422	196	20	)	)	PUNCT
ejpam-2422	196	21	.	.	PUNCT
ejpam-2422	197	1	then	then	ADV
ejpam-2422	197	2	the	the	DET
ejpam-2422	197	3	following	follow	VERB
ejpam-2422	197	4	statements	statement	NOUN
ejpam-2422	197	5	are	be	AUX
ejpam-2422	197	6	equivalent	equivalent	ADJ
ejpam-2422	197	7	:	:	PUNCT
ejpam-2422	197	8	(	(	PUNCT
ejpam-2422	197	9	rn4	rn4	NOUN
ejpam-2422	197	10	)	)	PUNCT
ejpam-2422	197	11	rp	rp	NOUN
ejpam-2422	198	1	k	k	PROPN
ejpam-2422	198	2	(	(	PUNCT
ejpam-2422	198	3	f	f	PROPN
ejpam-2422	198	4	)	)	PUNCT
ejpam-2422	198	5	=	=	SYM
ejpam-2422	198	6	∨	∨	NUM
ejpam-2422	198	7	g∈p|	g∈p|	PROPN
ejpam-2422	198	8	f	f	PROPN
ejpam-2422	198	9	∧	∧	PROPN
ejpam-2422	198	10	r	r	PROPN
ejpam-2422	198	11	6vg	6vg	PROPN
ejpam-2422	198	12	rr	rr	PROPN
ejpam-2422	198	13	k(g	k(g	PROPN
ejpam-2422	198	14	)	)	PUNCT
ejpam-2422	198	15	.	.	PUNCT
ejpam-2422	199	1	(	(	PUNCT
ejpam-2422	199	2	rn4	rn4	NOUN
ejpam-2422	199	3	*	*	NOUN
ejpam-2422	199	4	)	)	PUNCT
ejpam-2422	199	5	rp	rp	NOUN
ejpam-2422	200	1	k	k	PROPN
ejpam-2422	200	2	(	(	PUNCT
ejpam-2422	200	3	f	f	PROPN
ejpam-2422	200	4	)	)	PUNCT
ejpam-2422	200	5	=	=	SYM
ejpam-2422	200	6	∨	∨	NUM
ejpam-2422	200	7	g∈p|	g∈p|	PROPN
ejpam-2422	200	8	f	f	PROPN
ejpam-2422	200	9	(	(	PUNCT
ejpam-2422	200	10	r	r	NOUN
ejpam-2422	200	11	p	p	PROPN
ejpam-2422	200	12	k(g)∧	k(g)∧	PROPN
ejpam-2422	200	13	∧	∧	PROPN
ejpam-2422	200	14	r	r	PROPN
ejpam-2422	200	15	6vg	6vg	PROPN
ejpam-2422	200	16	rr	rr	PROPN
ejpam-2422	201	1	k	k	PROPN
ejpam-2422	201	2	(	(	PUNCT
ejpam-2422	201	3	f	f	PROPN
ejpam-2422	201	4	)	)	PUNCT
ejpam-2422	201	5	)	)	PUNCT
ejpam-2422	201	6	.	.	PUNCT
ejpam-2422	202	1	proof	proof	NOUN
ejpam-2422	202	2	.	.	PUNCT
ejpam-2422	203	1	suppose	suppose	VERB
ejpam-2422	203	2	(	(	PUNCT
ejpam-2422	203	3	rn4	rn4	NOUN
ejpam-2422	203	4	*	*	PRON
ejpam-2422	203	5	)	)	PUNCT
ejpam-2422	203	6	holds	hold	NOUN
ejpam-2422	203	7	,	,	PUNCT
ejpam-2422	203	8	i.e.	i.e.	X
ejpam-2422	203	9	,	,	PUNCT
ejpam-2422	203	10	rp	rp	NOUN
ejpam-2422	203	11	k	k	PROPN
ejpam-2422	203	12	(	(	PUNCT
ejpam-2422	203	13	f	f	PROPN
ejpam-2422	203	14	)	)	PUNCT
ejpam-2422	204	1	=	=	SYM
ejpam-2422	204	2	∨	∨	NUM
ejpam-2422	204	3	g∈p|	g∈p|	PROPN
ejpam-2422	204	4	f	f	PROPN
ejpam-2422	204	5	(	(	PUNCT
ejpam-2422	204	6	r	r	PROPN
ejpam-2422	204	7	p	p	X
ejpam-2422	204	8	k(g	k(g	PROPN
ejpam-2422	204	9	)	)	PUNCT
ejpam-2422	204	10	∧	∧	NOUN
ejpam-2422	204	11	∧	∧	PROPN
ejpam-2422	204	12	r	r	NOUN
ejpam-2422	204	13	6vg	6vg	PROPN
ejpam-2422	204	14	rr	rr	PROPN
ejpam-2422	205	1	k	k	PROPN
ejpam-2422	205	2	(	(	PUNCT
ejpam-2422	205	3	f	f	PROPN
ejpam-2422	205	4	)	)	PUNCT
ejpam-2422	205	5	)	)	PUNCT
ejpam-2422	205	6	.	.	PUNCT
ejpam-2422	206	1	let	let	VERB
ejpam-2422	206	2	α	α	PRON
ejpam-2422	206	3	∈	∈	PROPN
ejpam-2422	206	4	c(m	c(m	PROPN
ejpam-2422	206	5	)	)	PUNCT
ejpam-2422	207	1	such	such	ADJ
ejpam-2422	207	2	that	that	SCONJ
ejpam-2422	207	3	α	α	PROPN
ejpam-2422	207	4	ã	ã	X
ejpam-2422	207	5	rp	rp	NOUN
ejpam-2422	207	6	k	k	PROPN
ejpam-2422	207	7	(	(	PUNCT
ejpam-2422	207	8	f	f	PROPN
ejpam-2422	207	9	)	)	PUNCT
ejpam-2422	207	10	=	=	SYM
ejpam-2422	207	11	∨	∨	NUM
ejpam-2422	207	12	g∈p|	g∈p|	PROPN
ejpam-2422	207	13	f	f	PROPN
ejpam-2422	207	14	(	(	PUNCT
ejpam-2422	207	15	r	r	PROPN
ejpam-2422	207	16	p	p	X
ejpam-2422	207	17	k(g	k(g	PROPN
ejpam-2422	207	18	)	)	PUNCT
ejpam-2422	207	19	∧	∧	NOUN
ejpam-2422	207	20	∧	∧	PROPN
ejpam-2422	207	21	r	r	NOUN
ejpam-2422	207	22	6vg	6vg	PROPN
ejpam-2422	207	23	rr	rr	PROPN
ejpam-2422	207	24	k	k	PROPN
ejpam-2422	207	25	(	(	PUNCT
ejpam-2422	207	26	f	f	PROPN
ejpam-2422	207	27	)	)	PUNCT
ejpam-2422	207	28	)	)	PUNCT
ejpam-2422	207	29	.	.	PUNCT
ejpam-2422	208	1	then	then	ADV
ejpam-2422	208	2	there	there	PRON
ejpam-2422	208	3	exists	exist	VERB
ejpam-2422	208	4	some	some	DET
ejpam-2422	208	5	g	g	NOUN
ejpam-2422	208	6	∈	∈	PROPN
ejpam-2422	208	7	p	p	NOUN
ejpam-2422	209	1	|	|	NOUN
ejpam-2422	209	2	f	f	PROPN
ejpam-2422	210	1	such	such	ADJ
ejpam-2422	210	2	that	that	SCONJ
ejpam-2422	210	3	(	(	PUNCT
ejpam-2422	210	4	1	1	NUM
ejpam-2422	210	5	)	)	PUNCT
ejpam-2422	210	6	αã	αã	NUM
ejpam-2422	210	7	rp	rp	NOUN
ejpam-2422	210	8	k(g	k(g	PROPN
ejpam-2422	210	9	)	)	PUNCT
ejpam-2422	210	10	;	;	PUNCT
ejpam-2422	210	11	(	(	PUNCT
ejpam-2422	210	12	2	2	X
ejpam-2422	210	13	)	)	PUNCT
ejpam-2422	210	14	αã	αã	NUM
ejpam-2422	210	15	rr	rr	NOUN
ejpam-2422	211	1	k	k	PROPN
ejpam-2422	211	2	(	(	PUNCT
ejpam-2422	211	3	f	f	PROPN
ejpam-2422	211	4	)	)	PUNCT
ejpam-2422	211	5	,	,	PUNCT
ejpam-2422	211	6	for	for	ADP
ejpam-2422	211	7	each	each	DET
ejpam-2422	211	8	r	r	NOUN
ejpam-2422	211	9	6v	6v	NOUN
ejpam-2422	211	10	g.	g.	NOUN
ejpam-2422	211	11	it	it	PRON
ejpam-2422	211	12	is	be	AUX
ejpam-2422	211	13	clear	clear	ADJ
ejpam-2422	211	14	that	that	SCONJ
ejpam-2422	211	15	the	the	DET
ejpam-2422	211	16	meet	meet	NOUN
ejpam-2422	211	17	of	of	ADP
ejpam-2422	211	18	fuzzy	fuzzy	ADJ
ejpam-2422	211	19	soft	soft	ADJ
ejpam-2422	211	20	sets	set	NOUN
ejpam-2422	211	21	containing	contain	VERB
ejpam-2422	211	22	f	f	PROPN
ejpam-2422	211	23	and	and	CCONJ
ejpam-2422	211	24	fulfilling	fulfil	VERB
ejpam-2422	211	25	(	(	PUNCT
ejpam-2422	211	26	1	1	NUM
ejpam-2422	211	27	)	)	PUNCT
ejpam-2422	211	28	and	and	CCONJ
ejpam-2422	211	29	(	(	PUNCT
ejpam-2422	211	30	2	2	X
ejpam-2422	211	31	)	)	PUNCT
ejpam-2422	211	32	is	be	AUX
ejpam-2422	211	33	still	still	ADV
ejpam-2422	211	34	of	of	ADP
ejpam-2422	211	35	such	such	ADJ
ejpam-2422	211	36	kind	kind	NOUN
ejpam-2422	211	37	.	.	PUNCT
ejpam-2422	212	1	so	so	ADV
ejpam-2422	212	2	we	we	PRON
ejpam-2422	212	3	can	can	AUX
ejpam-2422	212	4	define	define	VERB
ejpam-2422	212	5	g∗	g∗	PROPN
ejpam-2422	212	6	to	to	PART
ejpam-2422	212	7	be	be	AUX
ejpam-2422	212	8	the	the	DET
ejpam-2422	212	9	minimal	minimal	ADJ
ejpam-2422	212	10	fuzzy	fuzzy	ADJ
ejpam-2422	212	11	soft	soft	ADJ
ejpam-2422	212	12	set	set	NOUN
ejpam-2422	212	13	containing	contain	VERB
ejpam-2422	212	14	f	f	PROPN
ejpam-2422	212	15	and	and	CCONJ
ejpam-2422	212	16	fulfilling	fulfil	VERB
ejpam-2422	212	17	(	(	PUNCT
ejpam-2422	212	18	1	1	NUM
ejpam-2422	212	19	)	)	PUNCT
ejpam-2422	212	20	,	,	PUNCT
ejpam-2422	212	21	(	(	PUNCT
ejpam-2422	212	22	2	2	NUM
ejpam-2422	212	23	)	)	PUNCT
ejpam-2422	212	24	,	,	PUNCT
ejpam-2422	212	25	i.e.	i.e.	X
ejpam-2422	212	26	,	,	PUNCT
ejpam-2422	212	27	αã	αã	X
ejpam-2422	212	28	rp	rp	NOUN
ejpam-2422	212	29	k(g∗	k(g∗	NOUN
ejpam-2422	212	30	)	)	PUNCT
ejpam-2422	212	31	and	and	CCONJ
ejpam-2422	212	32	αã	αã	NUM
ejpam-2422	212	33	rr	rr	NOUN
ejpam-2422	212	34	k	k	PROPN
ejpam-2422	212	35	(	(	PUNCT
ejpam-2422	212	36	f	f	PROPN
ejpam-2422	212	37	)	)	PUNCT
ejpam-2422	212	38	for	for	ADP
ejpam-2422	212	39	all	all	DET
ejpam-2422	212	40	r	r	NOUN
ejpam-2422	212	41	6v	6v	NOUN
ejpam-2422	212	42	g∗.	g∗.	NOUN
ejpam-2422	212	43	thus	thus	ADV
ejpam-2422	212	44	,	,	PUNCT
ejpam-2422	212	45	for	for	ADP
ejpam-2422	212	46	each	each	DET
ejpam-2422	212	47	r	r	NOUN
ejpam-2422	212	48	6v	6v	NUM
ejpam-2422	212	49	g∗	g∗	NOUN
ejpam-2422	212	50	,	,	PUNCT
ejpam-2422	212	51	it	it	PRON
ejpam-2422	212	52	follows	follow	VERB
ejpam-2422	212	53	from	from	ADP
ejpam-2422	212	54	αã	αã	NUM
ejpam-2422	212	55	rr	rr	NOUN
ejpam-2422	212	56	k	k	PROPN
ejpam-2422	212	57	(	(	PUNCT
ejpam-2422	212	58	f	f	PROPN
ejpam-2422	212	59	)	)	PUNCT
ejpam-2422	212	60	that	that	SCONJ
ejpam-2422	212	61	there	there	PRON
ejpam-2422	212	62	exists	exist	VERB
ejpam-2422	212	63	hr	hr	NOUN
ejpam-2422	212	64	∈	∈	PROPN
ejpam-2422	212	65	r	r	NOUN
ejpam-2422	212	66	|	|	NOUN
ejpam-2422	212	67	f	f	PROPN
ejpam-2422	212	68	such	such	ADJ
ejpam-2422	212	69	that	that	PRON
ejpam-2422	212	70	(	(	PUNCT
ejpam-2422	212	71	3	3	X
ejpam-2422	212	72	)	)	PUNCT
ejpam-2422	212	73	rr	rr	NOUN
ejpam-2422	212	74	k(h	k(h	PROPN
ejpam-2422	212	75	r)â	r)â	VERB
ejpam-2422	212	76	α	α	X
ejpam-2422	212	77	;	;	PUNCT
ejpam-2422	212	78	(	(	PUNCT
ejpam-2422	212	79	4	4	X
ejpam-2422	212	80	)	)	PUNCT
ejpam-2422	212	81	rr	rr	NOUN
ejpam-2422	213	1	k	k	PROPN
ejpam-2422	213	2	(	(	PUNCT
ejpam-2422	213	3	f	f	PROPN
ejpam-2422	213	4	)	)	PUNCT
ejpam-2422	213	5	â	â	PROPN
ejpam-2422	213	6	α	α	NOUN
ejpam-2422	213	7	,	,	PUNCT
ejpam-2422	213	8	for	for	SCONJ
ejpam-2422	213	9	each	each	DET
ejpam-2422	213	10	g	g	NOUN
ejpam-2422	213	11	6v	6v	NOUN
ejpam-2422	213	12	hr	hr	NOUN
ejpam-2422	213	13	.	.	PUNCT
ejpam-2422	214	1	it	it	PRON
ejpam-2422	214	2	is	be	AUX
ejpam-2422	214	3	easy	easy	ADJ
ejpam-2422	214	4	to	to	PART
ejpam-2422	214	5	check	check	VERB
ejpam-2422	214	6	that	that	DET
ejpam-2422	214	7	g	g	NOUN
ejpam-2422	214	8	∗uhr	∗uhr	PROPN
ejpam-2422	214	9	satisfies	satisfie	NOUN
ejpam-2422	214	10	(	(	PUNCT
ejpam-2422	214	11	1	1	NUM
ejpam-2422	214	12	)	)	PUNCT
ejpam-2422	214	13	and	and	CCONJ
ejpam-2422	214	14	(	(	PUNCT
ejpam-2422	214	15	2	2	NUM
ejpam-2422	214	16	)	)	PUNCT
ejpam-2422	214	17	.	.	PUNCT
ejpam-2422	215	1	hence	hence	ADV
ejpam-2422	215	2	,	,	PUNCT
ejpam-2422	215	3	by	by	ADP
ejpam-2422	215	4	the	the	DET
ejpam-2422	215	5	minimality	minimality	NOUN
ejpam-2422	215	6	of	of	ADP
ejpam-2422	215	7	g∗	g∗	PROPN
ejpam-2422	215	8	,	,	PUNCT
ejpam-2422	215	9	it	it	PRON
ejpam-2422	215	10	follows	follow	VERB
ejpam-2422	215	11	that	that	PRON
ejpam-2422	215	12	g∗	g∗	VERB
ejpam-2422	215	13	v	v	ADP
ejpam-2422	215	14	g	g	NOUN
ejpam-2422	215	15	∗	∗	NOUN
ejpam-2422	215	16	uhr	uhr	NOUN
ejpam-2422	215	17	.	.	PUNCT
ejpam-2422	216	1	therefore	therefore	ADV
ejpam-2422	216	2	,	,	PUNCT
ejpam-2422	216	3	g∗	g∗	VERB
ejpam-2422	216	4	v	v	ADP
ejpam-2422	216	5	hr	hr	NOUN
ejpam-2422	216	6	.	.	PUNCT
ejpam-2422	217	1	then	then	ADV
ejpam-2422	217	2	we	we	PRON
ejpam-2422	217	3	get	get	VERB
ejpam-2422	217	4	that	that	SCONJ
ejpam-2422	217	5	α	α	PRON
ejpam-2422	217	6	ã	ã	X
ejpam-2422	217	7	rr	rr	PROPN
ejpam-2422	217	8	k(h	k(h	PROPN
ejpam-2422	217	9	r	r	PROPN
ejpam-2422	217	10	)	)	PUNCT
ejpam-2422	217	11	≤	≤	NUM
ejpam-2422	217	12	rr	rr	NOUN
ejpam-2422	217	13	k(g∗	k(g∗	PROPN
ejpam-2422	217	14	)	)	PUNCT
ejpam-2422	217	15	for	for	ADP
ejpam-2422	217	16	all	all	DET
ejpam-2422	217	17	r	r	NOUN
ejpam-2422	217	18	6v	6v	NOUN
ejpam-2422	217	19	g∗.	g∗.	NOUN
ejpam-2422	217	20	thus	thus	ADV
ejpam-2422	217	21	,	,	PUNCT
ejpam-2422	217	22	α≤	α≤	PROPN
ejpam-2422	217	23	∧	∧	PROPN
ejpam-2422	217	24	r	r	NOUN
ejpam-2422	217	25	6vg∗	6vg∗	NUM
ejpam-2422	217	26	rr	rr	NOUN
ejpam-2422	217	27	k(g∗	k(g∗	NOUN
ejpam-2422	217	28	)	)	PUNCT
ejpam-2422	217	29	.	.	PUNCT
ejpam-2422	218	1	therefore	therefore	ADV
ejpam-2422	218	2	,	,	PUNCT
ejpam-2422	218	3	α≤	α≤	PROPN
ejpam-2422	218	4	∨	∨	NUM
ejpam-2422	218	5	g∈p|	g∈p|	PROPN
ejpam-2422	218	6	f	f	PROPN
ejpam-2422	218	7	∧	∧	PROPN
ejpam-2422	218	8	r	r	PROPN
ejpam-2422	218	9	6vg	6vg	PROPN
ejpam-2422	218	10	rr	rr	PROPN
ejpam-2422	218	11	k(g	k(g	PROPN
ejpam-2422	218	12	)	)	PUNCT
ejpam-2422	218	13	.	.	PUNCT
ejpam-2422	219	1	from	from	ADP
ejpam-2422	219	2	the	the	DET
ejpam-2422	219	3	arbitrariness	arbitrariness	NOUN
ejpam-2422	219	4	of	of	ADP
ejpam-2422	219	5	α	α	NOUN
ejpam-2422	219	6	,	,	PUNCT
ejpam-2422	219	7	we	we	PRON
ejpam-2422	219	8	have	have	VERB
ejpam-2422	219	9	rp	rp	ADP
ejpam-2422	219	10	k	k	X
ejpam-2422	219	11	(	(	PUNCT
ejpam-2422	219	12	f	f	PROPN
ejpam-2422	219	13	)	)	PUNCT
ejpam-2422	219	14	≤	≤	PROPN
ejpam-2422	219	15	∨	∨	NUM
ejpam-2422	219	16	g∈p|	g∈p|	PROPN
ejpam-2422	219	17	f	f	PROPN
ejpam-2422	219	18	∧	∧	PROPN
ejpam-2422	219	19	r	r	PROPN
ejpam-2422	219	20	6vg	6vg	PROPN
ejpam-2422	219	21	rr	rr	PROPN
ejpam-2422	219	22	k(g	k(g	PROPN
ejpam-2422	219	23	)	)	PUNCT
ejpam-2422	219	24	,	,	PUNCT
ejpam-2422	219	25	for	for	ADP
ejpam-2422	219	26	each	each	DET
ejpam-2422	219	27	k	k	PROPN
ejpam-2422	219	28	∈	∈	PROPN
ejpam-2422	219	29	k	k	PROPN
ejpam-2422	219	30	.	.	PUNCT
ejpam-2422	220	1	since	since	SCONJ
ejpam-2422	220	2	for	for	ADP
ejpam-2422	220	3	each	each	DET
ejpam-2422	220	4	k	k	PROPN
ejpam-2422	220	5	∈	∈	PROPN
ejpam-2422	220	6	k	k	PROPN
ejpam-2422	220	7	,	,	PUNCT
ejpam-2422	220	8	rp	rp	PROPN
ejpam-2422	220	9	k	k	PROPN
ejpam-2422	220	10	(	(	PUNCT
ejpam-2422	220	11	f	f	PROPN
ejpam-2422	220	12	)	)	PUNCT
ejpam-2422	220	13	≥	≥	PROPN
ejpam-2422	220	14	∨	∨	NUM
ejpam-2422	220	15	g∈p|	g∈p|	PROPN
ejpam-2422	220	16	f	f	PROPN
ejpam-2422	220	17	∧	∧	PROPN
ejpam-2422	220	18	r	r	PROPN
ejpam-2422	220	19	6vg	6vg	ADJ
ejpam-2422	220	20	rr	rr	PROPN
ejpam-2422	220	21	k(g	k(g	PROPN
ejpam-2422	220	22	)	)	PUNCT
ejpam-2422	220	23	is	be	AUX
ejpam-2422	220	24	obvious	obvious	ADJ
ejpam-2422	220	25	.	.	PUNCT
ejpam-2422	221	1	we	we	PRON
ejpam-2422	221	2	have	have	VERB
ejpam-2422	221	3	rp	rp	ADP
ejpam-2422	221	4	k	k	X
ejpam-2422	221	5	(	(	PUNCT
ejpam-2422	221	6	f	f	PROPN
ejpam-2422	221	7	)	)	PUNCT
ejpam-2422	222	1	=	=	SYM
ejpam-2422	222	2	∨	∨	NUM
ejpam-2422	222	3	g∈p|	g∈p|	PROPN
ejpam-2422	222	4	f	f	PROPN
ejpam-2422	222	5	∧	∧	PROPN
ejpam-2422	222	6	r	r	PROPN
ejpam-2422	222	7	6vg	6vg	PROPN
ejpam-2422	222	8	rr	rr	PROPN
ejpam-2422	222	9	k(g	k(g	PROPN
ejpam-2422	222	10	)	)	PUNCT
ejpam-2422	222	11	,	,	PUNCT
ejpam-2422	222	12	as	as	SCONJ
ejpam-2422	222	13	desired	desire	VERB
ejpam-2422	222	14	.	.	PUNCT
ejpam-2422	223	1	v.	v.	ADP
ejpam-2422	223	2	çetkin	çetkin	PROPN
ejpam-2422	223	3	,	,	PUNCT
ejpam-2422	223	4	h.	h.	PROPN
ejpam-2422	223	5	aygün	aygün	PROPN
ejpam-2422	223	6	/	/	SYM
ejpam-2422	223	7	eur	eur	PROPN
ejpam-2422	223	8	.	.	PUNCT
ejpam-2422	224	1	j.	j.	PROPN
ejpam-2422	224	2	pure	pure	PROPN
ejpam-2422	224	3	appl	appl	PROPN
ejpam-2422	224	4	.	.	PROPN
ejpam-2422	224	5	math	math	PROPN
ejpam-2422	224	6	,	,	PUNCT
ejpam-2422	224	7	9	9	NUM
ejpam-2422	224	8	(	(	PUNCT
ejpam-2422	224	9	2016	2016	NUM
ejpam-2422	224	10	)	)	PUNCT
ejpam-2422	224	11	,	,	PUNCT
ejpam-2422	224	12	419	419	NUM
ejpam-2422	224	13	-	-	SYM
ejpam-2422	224	14	433	433	NUM
ejpam-2422	224	15	425	425	NUM
ejpam-2422	224	16	4	4	NUM
ejpam-2422	224	17	.	.	PUNCT
ejpam-2422	224	18	fuzzy	fuzzy	ADJ
ejpam-2422	224	19	soft	soft	ADJ
ejpam-2422	224	20	uniform	uniform	ADJ
ejpam-2422	224	21	spaces	space	NOUN
ejpam-2422	224	22	in	in	ADP
ejpam-2422	224	23	this	this	DET
ejpam-2422	224	24	section	section	NOUN
ejpam-2422	224	25	,	,	PUNCT
ejpam-2422	224	26	we	we	PRON
ejpam-2422	224	27	introduce	introduce	VERB
ejpam-2422	224	28	the	the	DET
ejpam-2422	224	29	concept	concept	NOUN
ejpam-2422	224	30	of	of	ADP
ejpam-2422	224	31	fuzzy	fuzzy	ADJ
ejpam-2422	224	32	soft	soft	ADJ
ejpam-2422	224	33	uniformity	uniformity	NOUN
ejpam-2422	224	34	as	as	ADP
ejpam-2422	224	35	a	a	DET
ejpam-2422	224	36	parameterized	parameterized	ADJ
ejpam-2422	224	37	family	family	NOUN
ejpam-2422	224	38	of	of	ADP
ejpam-2422	224	39	hutton	hutton	PROPN
ejpam-2422	224	40	uniformity	uniformity	NOUN
ejpam-2422	224	41	in	in	ADP
ejpam-2422	224	42	the	the	DET
ejpam-2422	224	43	spirit	spirit	NOUN
ejpam-2422	224	44	of	of	ADP
ejpam-2422	224	45	fuzzy	fuzzy	ADJ
ejpam-2422	224	46	soft	soft	ADJ
ejpam-2422	224	47	topology	topology	NOUN
ejpam-2422	224	48	.	.	PUNCT
ejpam-2422	225	1	also	also	ADV
ejpam-2422	225	2	,	,	PUNCT
ejpam-2422	225	3	we	we	PRON
ejpam-2422	225	4	consider	consider	VERB
ejpam-2422	225	5	the	the	DET
ejpam-2422	225	6	categorical	categorical	ADJ
ejpam-2422	225	7	relationship	relationship	NOUN
ejpam-2422	225	8	between	between	ADP
ejpam-2422	225	9	the	the	DET
ejpam-2422	225	10	fuzzy	fuzzy	ADJ
ejpam-2422	225	11	soft	soft	ADJ
ejpam-2422	225	12	remote	remote	ADJ
ejpam-2422	225	13	neighborhood	neighborhood	NOUN
ejpam-2422	225	14	system	system	NOUN
ejpam-2422	225	15	and	and	CCONJ
ejpam-2422	225	16	fuzzy	fuzzy	ADJ
ejpam-2422	225	17	soft	soft	ADJ
ejpam-2422	225	18	uniform	uniform	ADJ
ejpam-2422	225	19	space	space	NOUN
ejpam-2422	225	20	.	.	PUNCT
ejpam-2422	226	1	leth	leth	PROPN
ejpam-2422	226	2	(	(	PUNCT
ejpam-2422	226	3	x	x	X
ejpam-2422	226	4	,	,	PUNCT
ejpam-2422	226	5	e	e	NOUN
ejpam-2422	226	6	)	)	PUNCT
ejpam-2422	226	7	denote	denote	VERB
ejpam-2422	226	8	the	the	DET
ejpam-2422	226	9	family	family	NOUN
ejpam-2422	226	10	of	of	ADP
ejpam-2422	226	11	all	all	DET
ejpam-2422	226	12	mappings	mapping	NOUN
ejpam-2422	227	1	λ	λ	INTJ
ejpam-2422	227	2	:	:	PUNCT
ejpam-2422	227	3	(	(	PUNCT
ejpam-2422	227	4	lx	lx	NOUN
ejpam-2422	227	5	)	)	PUNCT
ejpam-2422	227	6	e	e	X
ejpam-2422	227	7	→	→	PUNCT
ejpam-2422	227	8	(	(	PUNCT
ejpam-2422	227	9	lx	lx	NOUN
ejpam-2422	227	10	)	)	PUNCT
ejpam-2422	227	11	e	e	X
ejpam-2422	227	12	such	such	ADJ
ejpam-2422	227	13	that	that	PRON
ejpam-2422	227	14	:	:	PUNCT
ejpam-2422	227	15	(	(	PUNCT
ejpam-2422	227	16	1	1	X
ejpam-2422	227	17	)	)	PUNCT
ejpam-2422	227	18	f	f	PROPN
ejpam-2422	227	19	v	v	X
ejpam-2422	227	20	λ	λ	PROPN
ejpam-2422	227	21	(	(	PUNCT
ejpam-2422	227	22	f	f	PROPN
ejpam-2422	227	23	)	)	PUNCT
ejpam-2422	227	24	for	for	ADP
ejpam-2422	227	25	all	all	DET
ejpam-2422	227	26	f	f	PROPN
ejpam-2422	227	27	∈	∈	PROPN
ejpam-2422	227	28	(	(	PUNCT
ejpam-2422	227	29	lx	lx	NOUN
ejpam-2422	227	30	)	)	PUNCT
ejpam-2422	227	31	e	e	X
ejpam-2422	227	32	.	.	PUNCT
ejpam-2422	228	1	(	(	PUNCT
ejpam-2422	228	2	2	2	X
ejpam-2422	228	3	)	)	PUNCT
ejpam-2422	228	4	λ	λ	PROPN
ejpam-2422	228	5	(	(	PUNCT
ejpam-2422	228	6	⊔	⊔	PROPN
ejpam-2422	228	7	j∈j	j∈j	PROPN
ejpam-2422	228	8	f	f	PROPN
ejpam-2422	228	9	j	j	PROPN
ejpam-2422	228	10	)	)	PUNCT
ejpam-2422	228	11	=	=	SYM
ejpam-2422	229	1	⊔	⊔	PROPN
ejpam-2422	229	2	j∈j	j∈j	PROPN
ejpam-2422	229	3	λ	λ	PROPN
ejpam-2422	229	4	(	(	PUNCT
ejpam-2422	229	5	f	f	PROPN
ejpam-2422	229	6	j	j	PROPN
ejpam-2422	229	7	)	)	PUNCT
ejpam-2422	229	8	for	for	ADP
ejpam-2422	229	9	all	all	PRON
ejpam-2422	229	10	{	{	PUNCT
ejpam-2422	229	11	f	f	PROPN
ejpam-2422	229	12	j	j	PROPN
ejpam-2422	229	13	}	}	PUNCT
ejpam-2422	229	14	j∈j	j∈j	NOUN
ejpam-2422	229	15	⊆	⊆	NUM
ejpam-2422	229	16	(	(	PUNCT
ejpam-2422	229	17	lx	lx	NOUN
ejpam-2422	229	18	)	)	PUNCT
ejpam-2422	229	19	e	e	X
ejpam-2422	229	20	.	.	PUNCT
ejpam-2422	230	1	λ∗	λ∗	PROPN
ejpam-2422	230	2	denotes	denote	VERB
ejpam-2422	230	3	the	the	DET
ejpam-2422	230	4	biggest	big	ADJ
ejpam-2422	230	5	element	element	NOUN
ejpam-2422	230	6	of	of	ADP
ejpam-2422	230	7	h	h	NOUN
ejpam-2422	230	8	(	(	PUNCT
ejpam-2422	230	9	x	x	NOUN
ejpam-2422	230	10	,	,	PUNCT
ejpam-2422	230	11	e	e	NOUN
ejpam-2422	230	12	)	)	PUNCT
ejpam-2422	230	13	,	,	PUNCT
ejpam-2422	230	14	i.e.	i.e.	X
ejpam-2422	230	15	,	,	PUNCT
ejpam-2422	230	16	λ∗	λ∗	PROPN
ejpam-2422	230	17	(	(	PUNCT
ejpam-2422	230	18	f	f	PROPN
ejpam-2422	230	19	)	)	PUNCT
ejpam-2422	231	1	=	=	PUNCT
ejpam-2422	231	2	0x	0x	NOUN
ejpam-2422	231	3	when	when	SCONJ
ejpam-2422	231	4	f	f	PROPN
ejpam-2422	231	5	=	=	SYM
ejpam-2422	231	6	0x	0x	PROPN
ejpam-2422	231	7	and	and	CCONJ
ejpam-2422	231	8	λ∗	λ∗	PROPN
ejpam-2422	231	9	(	(	PUNCT
ejpam-2422	231	10	f	f	PROPN
ejpam-2422	231	11	)	)	PUNCT
ejpam-2422	231	12	=	=	SYM
ejpam-2422	232	1	1x	1x	NUM
ejpam-2422	232	2	otherwise	otherwise	ADV
ejpam-2422	232	3	.	.	PUNCT
ejpam-2422	233	1	for	for	ADP
ejpam-2422	233	2	λ,µ	λ,µ	PROPN
ejpam-2422	233	3	∈h	∈h	NOUN
ejpam-2422	233	4	(	(	PUNCT
ejpam-2422	233	5	x	x	X
ejpam-2422	233	6	,	,	PUNCT
ejpam-2422	233	7	e	e	NOUN
ejpam-2422	233	8	)	)	PUNCT
ejpam-2422	233	9	,	,	PUNCT
ejpam-2422	233	10	we	we	PRON
ejpam-2422	233	11	have	have	VERB
ejpam-2422	233	12	that	that	PRON
ejpam-2422	233	13	λ∆µ	λ∆µ	VERB
ejpam-2422	233	14	∈h	∈h	NOUN
ejpam-2422	233	15	(	(	PUNCT
ejpam-2422	233	16	x	x	X
ejpam-2422	233	17	,	,	PUNCT
ejpam-2422	233	18	e	e	NOUN
ejpam-2422	233	19	)	)	PUNCT
ejpam-2422	233	20	and	and	CCONJ
ejpam-2422	233	21	λ	λ	X
ejpam-2422	233	22	◦	◦	NOUN
ejpam-2422	233	23	µ	µ	X
ejpam-2422	233	24	∈h	∈h	NOUN
ejpam-2422	233	25	(	(	PUNCT
ejpam-2422	233	26	x	x	X
ejpam-2422	233	27	,	,	PUNCT
ejpam-2422	233	28	e	e	NOUN
ejpam-2422	233	29	)	)	PUNCT
ejpam-2422	233	30	,	,	PUNCT
ejpam-2422	233	31	where	where	SCONJ
ejpam-2422	233	32	λ∆µ	λ∆µ	VERB
ejpam-2422	233	33	(	(	PUNCT
ejpam-2422	233	34	f	f	PROPN
ejpam-2422	233	35	)	)	PUNCT
ejpam-2422	233	36	=	=	SYM
ejpam-2422	233	37	u{λ(g	u{λ(g	PROPN
ejpam-2422	233	38	)	)	PUNCT
ejpam-2422	233	39	t	t	PROPN
ejpam-2422	233	40	µ(h	µ(h	PROPN
ejpam-2422	233	41	)	)	PUNCT
ejpam-2422	234	1	|	|	ADV
ejpam-2422	234	2	f	f	X
ejpam-2422	234	3	=	=	SYM
ejpam-2422	234	4	g	g	PROPN
ejpam-2422	234	5	t	t	PROPN
ejpam-2422	234	6	h	h	NOUN
ejpam-2422	234	7	}	}	PUNCT
ejpam-2422	234	8	and	and	CCONJ
ejpam-2422	234	9	λ	λ	X
ejpam-2422	234	10	◦	◦	NOUN
ejpam-2422	234	11	µ	µ	X
ejpam-2422	234	12	(	(	PUNCT
ejpam-2422	234	13	f	f	NOUN
ejpam-2422	234	14	)	)	PUNCT
ejpam-2422	235	1	=	=	SYM
ejpam-2422	235	2	λ(µ	λ(µ	X
ejpam-2422	235	3	(	(	PUNCT
ejpam-2422	235	4	f	f	PROPN
ejpam-2422	235	5	)	)	PUNCT
ejpam-2422	235	6	)	)	PUNCT
ejpam-2422	235	7	.	.	PUNCT
ejpam-2422	236	1	for	for	ADP
ejpam-2422	236	2	each	each	DET
ejpam-2422	236	3	λ	λ	PROPN
ejpam-2422	236	4	∈	∈	PROPN
ejpam-2422	236	5	h	h	NOUN
ejpam-2422	236	6	(	(	PUNCT
ejpam-2422	236	7	x	x	NOUN
ejpam-2422	236	8	,	,	PUNCT
ejpam-2422	236	9	e	e	NOUN
ejpam-2422	236	10	)	)	PUNCT
ejpam-2422	236	11	,	,	PUNCT
ejpam-2422	236	12	let	let	VERB
ejpam-2422	236	13	λã(g	λã(g	PUNCT
ejpam-2422	236	14	)	)	PUNCT
ejpam-2422	237	1	=	=	PUNCT
ejpam-2422	238	1	u{h	u{h	ADJ
ejpam-2422	238	2	∈	∈	NOUN
ejpam-2422	238	3	(	(	PUNCT
ejpam-2422	238	4	lx	lx	NOUN
ejpam-2422	238	5	)	)	PUNCT
ejpam-2422	238	6	e	e	X
ejpam-2422	239	1	|	|	ADV
ejpam-2422	239	2	λ(h′)v	λ(h′)v	PRON
ejpam-2422	239	3	g	g	PROPN
ejpam-2422	239	4	′	′	NUM
ejpam-2422	239	5	}	}	PUNCT
ejpam-2422	239	6	.	.	PUNCT
ejpam-2422	240	1	proposition	proposition	NOUN
ejpam-2422	240	2	2	2	NUM
ejpam-2422	240	3	.	.	PUNCT
ejpam-2422	241	1	(	(	PUNCT
ejpam-2422	241	2	i	i	NOUN
ejpam-2422	241	3	)	)	PUNCT
ejpam-2422	241	4	λã	λã	PROPN
ejpam-2422	241	5	∈h	∈h	NOUN
ejpam-2422	241	6	(	(	PUNCT
ejpam-2422	241	7	x	x	X
ejpam-2422	241	8	,	,	PUNCT
ejpam-2422	241	9	e	e	NOUN
ejpam-2422	241	10	)	)	PUNCT
ejpam-2422	241	11	.	.	PUNCT
ejpam-2422	242	1	(	(	PUNCT
ejpam-2422	242	2	ii	ii	NOUN
ejpam-2422	242	3	)	)	PUNCT
ejpam-2422	242	4	(	(	PUNCT
ejpam-2422	242	5	λã)ã	λã)ã	PROPN
ejpam-2422	242	6	=	=	SYM
ejpam-2422	242	7	λ	λ	PROPN
ejpam-2422	242	8	.	.	PUNCT
ejpam-2422	243	1	(	(	PUNCT
ejpam-2422	243	2	iii	iii	NOUN
ejpam-2422	243	3	)	)	PUNCT
ejpam-2422	243	4	(	(	PUNCT
ejpam-2422	243	5	λ	λ	NOUN
ejpam-2422	243	6	◦	◦	NOUN
ejpam-2422	243	7	µ)ã	µ)ã	PUNCT
ejpam-2422	243	8	=	=	SYM
ejpam-2422	243	9	µã	µã	ADP
ejpam-2422	243	10	◦	◦	NOUN
ejpam-2422	243	11	λã	λã	PROPN
ejpam-2422	243	12	.	.	PUNCT
ejpam-2422	244	1	(	(	PUNCT
ejpam-2422	244	2	iv	iv	X
ejpam-2422	244	3	)	)	PUNCT
ejpam-2422	244	4	λ≤	λ≤	X
ejpam-2422	244	5	µ	µ	X
ejpam-2422	244	6	implies	imply	VERB
ejpam-2422	244	7	λã	λã	PROPN
ejpam-2422	244	8	≤	≤	NUM
ejpam-2422	244	9	µã	µã	ADP
ejpam-2422	244	10	.	.	PUNCT
ejpam-2422	245	1	(	(	PUNCT
ejpam-2422	245	2	v	v	NOUN
ejpam-2422	245	3	)	)	PUNCT
ejpam-2422	245	4	(	(	PUNCT
ejpam-2422	245	5	λ∆µ)ã	λ∆µ)ã	X
ejpam-2422	245	6	=	=	SYM
ejpam-2422	245	7	λã∆µã	λã∆µã	PROPN
ejpam-2422	245	8	.	.	PUNCT
ejpam-2422	246	1	(	(	PUNCT
ejpam-2422	246	2	vi	vi	NOUN
ejpam-2422	246	3	)	)	PUNCT
ejpam-2422	246	4	(	(	PUNCT
ejpam-2422	247	1	∨	∨	NUM
ejpam-2422	247	2	i∈γλi)ã	i∈γλi)ã	PROPN
ejpam-2422	247	3	=	=	SYM
ejpam-2422	247	4	∨	∨	NUM
ejpam-2422	247	5	i∈γλ	i∈γλ	NOUN
ejpam-2422	247	6	ã	ã	X
ejpam-2422	247	7	i	i	NOUN
ejpam-2422	247	8	.	.	PUNCT
ejpam-2422	248	1	(	(	PUNCT
ejpam-2422	248	2	vii	vii	PROPN
ejpam-2422	248	3	)	)	PUNCT
ejpam-2422	248	4	if	if	SCONJ
ejpam-2422	248	5	λ1	λ1	ADJ
ejpam-2422	248	6	≤	≤	ADJ
ejpam-2422	248	7	λ2	λ2	NOUN
ejpam-2422	248	8	and	and	CCONJ
ejpam-2422	248	9	µ1	µ1	PROPN
ejpam-2422	248	10	≤	≤	PROPN
ejpam-2422	248	11	µ2	µ2	PROPN
ejpam-2422	248	12	,	,	PUNCT
ejpam-2422	248	13	then	then	ADV
ejpam-2422	248	14	λ1∆µ1	λ1∆µ1	PROPN
ejpam-2422	248	15	≤	≤	NUM
ejpam-2422	249	1	λ2∆µ2	λ2∆µ2	PROPN
ejpam-2422	249	2	.	.	PUNCT
ejpam-2422	249	3	suppose	suppose	VERB
ejpam-2422	249	4	ϕψ	ϕψ	ADP
ejpam-2422	249	5	:	:	PUNCT
ejpam-2422	249	6	(	(	PUNCT
ejpam-2422	249	7	lx	lx	NOUN
ejpam-2422	249	8	)	)	PUNCT
ejpam-2422	249	9	e	e	X
ejpam-2422	249	10	→	→	PUNCT
ejpam-2422	249	11	(	(	PUNCT
ejpam-2422	249	12	ly	ly	X
ejpam-2422	249	13	)	)	PUNCT
ejpam-2422	249	14	f	f	X
ejpam-2422	249	15	be	be	AUX
ejpam-2422	249	16	a	a	DET
ejpam-2422	249	17	fuzzy	fuzzy	ADJ
ejpam-2422	249	18	soft	soft	ADJ
ejpam-2422	249	19	mapping	mapping	NOUN
ejpam-2422	249	20	and	and	CCONJ
ejpam-2422	249	21	λ	λ	PROPN
ejpam-2422	249	22	∈h	∈h	NOUN
ejpam-2422	249	23	(	(	PUNCT
ejpam-2422	249	24	y	y	PROPN
ejpam-2422	249	25	,	,	PUNCT
ejpam-2422	249	26	f	f	PROPN
ejpam-2422	249	27	)	)	PUNCT
ejpam-2422	249	28	,	,	PUNCT
ejpam-2422	249	29	define	define	VERB
ejpam-2422	249	30	ϕ	ϕ	NOUN
ejpam-2422	249	31	⇐	⇐	PROPN
ejpam-2422	249	32	ψ	ψ	X
ejpam-2422	249	33	(	(	PUNCT
ejpam-2422	249	34	λ	λ	X
ejpam-2422	249	35	)	)	PUNCT
ejpam-2422	249	36	:	:	PUNCT
ejpam-2422	249	37	(	(	PUNCT
ejpam-2422	249	38	lx	lx	NOUN
ejpam-2422	249	39	)	)	PUNCT
ejpam-2422	249	40	e	e	X
ejpam-2422	249	41	→	→	PUNCT
ejpam-2422	249	42	(	(	PUNCT
ejpam-2422	249	43	lx	lx	NOUN
ejpam-2422	249	44	)	)	PUNCT
ejpam-2422	249	45	e	e	X
ejpam-2422	249	46	by	by	ADP
ejpam-2422	249	47	ϕ	ϕ	PROPN
ejpam-2422	249	48	⇐	⇐	PROPN
ejpam-2422	249	49	ψ	ψ	X
ejpam-2422	249	50	(	(	PUNCT
ejpam-2422	249	51	λ	λ	NOUN
ejpam-2422	249	52	)	)	PUNCT
ejpam-2422	249	53	(	(	PUNCT
ejpam-2422	249	54	f	f	PROPN
ejpam-2422	249	55	)	)	PUNCT
ejpam-2422	249	56	=	=	PUNCT
ejpam-2422	250	1	ϕ←	ϕ←	PUNCT
ejpam-2422	251	1	ψ	ψ	X
ejpam-2422	251	2	◦	◦	NOUN
ejpam-2422	251	3	λ	λ	X
ejpam-2422	251	4	◦	◦	NOUN
ejpam-2422	251	5	ϕ→	ϕ→	X
ejpam-2422	251	6	ψ	ψ	X
ejpam-2422	251	7	(	(	PUNCT
ejpam-2422	251	8	f	f	PROPN
ejpam-2422	251	9	)	)	PUNCT
ejpam-2422	251	10	for	for	ADP
ejpam-2422	251	11	all	all	DET
ejpam-2422	251	12	f	f	PROPN
ejpam-2422	251	13	∈	∈	PROPN
ejpam-2422	251	14	(	(	PUNCT
ejpam-2422	251	15	lx	lx	NOUN
ejpam-2422	251	16	)	)	PUNCT
ejpam-2422	251	17	e	e	X
ejpam-2422	251	18	.	.	PUNCT
ejpam-2422	252	1	proposition	proposition	NOUN
ejpam-2422	252	2	3	3	NUM
ejpam-2422	252	3	.	.	PUNCT
ejpam-2422	253	1	(	(	PUNCT
ejpam-2422	253	2	i	i	NOUN
ejpam-2422	253	3	)	)	PUNCT
ejpam-2422	253	4	ϕ	ϕ	NOUN
ejpam-2422	253	5	⇐	⇐	PROPN
ejpam-2422	253	6	ψ	ψ	X
ejpam-2422	253	7	(	(	PUNCT
ejpam-2422	253	8	λ	λ	NOUN
ejpam-2422	253	9	)	)	PUNCT
ejpam-2422	253	10	∈h	∈h	NOUN
ejpam-2422	253	11	(	(	PUNCT
ejpam-2422	253	12	x	x	X
ejpam-2422	253	13	,	,	PUNCT
ejpam-2422	253	14	e	e	NOUN
ejpam-2422	253	15	)	)	PUNCT
ejpam-2422	253	16	.	.	PUNCT
ejpam-2422	254	1	(	(	PUNCT
ejpam-2422	254	2	ii	ii	NOUN
ejpam-2422	254	3	)	)	PUNCT
ejpam-2422	254	4	λ≤	λ≤	VERB
ejpam-2422	254	5	µ	µ	PROPN
ejpam-2422	254	6	implies	imply	VERB
ejpam-2422	254	7	ϕ	ϕ	NOUN
ejpam-2422	254	8	⇐	⇐	ADP
ejpam-2422	254	9	ψ	ψ	X
ejpam-2422	254	10	(	(	PUNCT
ejpam-2422	254	11	λ)≤	λ)≤	X
ejpam-2422	254	12	ϕ	ϕ	NOUN
ejpam-2422	254	13	⇐	⇐	NOUN
ejpam-2422	254	14	ψ	ψ	X
ejpam-2422	254	15	(	(	PUNCT
ejpam-2422	254	16	µ	µ	NOUN
ejpam-2422	254	17	)	)	PUNCT
ejpam-2422	254	18	.	.	PUNCT
ejpam-2422	255	1	(	(	PUNCT
ejpam-2422	255	2	iii	iii	X
ejpam-2422	255	3	)	)	PUNCT
ejpam-2422	255	4	ϕ	ϕ	NOUN
ejpam-2422	255	5	⇐	⇐	PROPN
ejpam-2422	255	6	ψ	ψ	X
ejpam-2422	255	7	(	(	PUNCT
ejpam-2422	255	8	λã	λã	PROPN
ejpam-2422	255	9	)	)	PUNCT
ejpam-2422	255	10	=	=	SYM
ejpam-2422	256	1	(	(	PUNCT
ejpam-2422	256	2	ϕ	ϕ	X
ejpam-2422	256	3	⇐	⇐	X
ejpam-2422	256	4	ψ	ψ	X
ejpam-2422	256	5	(	(	PUNCT
ejpam-2422	256	6	λ))ã	λ))ã	ADJ
ejpam-2422	256	7	.	.	PUNCT
ejpam-2422	257	1	(	(	PUNCT
ejpam-2422	257	2	iv	iv	X
ejpam-2422	257	3	)	)	PUNCT
ejpam-2422	257	4	ϕ	ϕ	NOUN
ejpam-2422	257	5	⇐	⇐	PROPN
ejpam-2422	257	6	ψ	ψ	X
ejpam-2422	257	7	(	(	PUNCT
ejpam-2422	257	8	λ	λ	PART
ejpam-2422	257	9	◦	◦	NOUN
ejpam-2422	257	10	µ)≤	µ)≤	VERB
ejpam-2422	257	11	ϕ	ϕ	NOUN
ejpam-2422	257	12	⇐	⇐	NOUN
ejpam-2422	257	13	ψ	ψ	X
ejpam-2422	257	14	(	(	PUNCT
ejpam-2422	257	15	λ	λ	NOUN
ejpam-2422	257	16	)	)	PUNCT
ejpam-2422	257	17	◦	◦	NOUN
ejpam-2422	257	18	ϕ	ϕ	NOUN
ejpam-2422	257	19	⇐	⇐	ADP
ejpam-2422	257	20	ψ	ψ	X
ejpam-2422	257	21	(	(	PUNCT
ejpam-2422	257	22	µ	µ	NOUN
ejpam-2422	257	23	)	)	PUNCT
ejpam-2422	257	24	.	.	PUNCT
ejpam-2422	258	1	definition	definition	NOUN
ejpam-2422	258	2	5	5	NUM
ejpam-2422	258	3	.	.	PUNCT
ejpam-2422	259	1	an	an	DET
ejpam-2422	259	2	(	(	PUNCT
ejpam-2422	259	3	l	l	NOUN
ejpam-2422	259	4	,	,	PUNCT
ejpam-2422	259	5	m)-fuzzy	m)-fuzzy	X
ejpam-2422	259	6	(	(	PUNCT
ejpam-2422	259	7	e	e	NOUN
ejpam-2422	259	8	,	,	PUNCT
ejpam-2422	259	9	k)-soft	k)-soft	ADJ
ejpam-2422	259	10	quasi	quasi	NOUN
ejpam-2422	259	11	-	-	NOUN
ejpam-2422	259	12	uniformity	uniformity	NOUN
ejpam-2422	259	13	is	be	AUX
ejpam-2422	259	14	a	a	DET
ejpam-2422	259	15	mapping	mapping	NOUN
ejpam-2422	259	16	u	u	NOUN
ejpam-2422	259	17	:	:	PUNCT
ejpam-2422	259	18	k	k	PROPN
ejpam-2422	259	19	→	→	SYM
ejpam-2422	259	20	mh	mh	PROPN
ejpam-2422	259	21	(	(	PUNCT
ejpam-2422	259	22	x	x	X
ejpam-2422	259	23	,	,	PUNCT
ejpam-2422	259	24	e	e	NOUN
ejpam-2422	259	25	)	)	PUNCT
ejpam-2422	259	26	which	which	PRON
ejpam-2422	259	27	satisfies	satisfy	VERB
ejpam-2422	259	28	the	the	DET
ejpam-2422	259	29	following	follow	VERB
ejpam-2422	259	30	conditions	condition	NOUN
ejpam-2422	259	31	:	:	PUNCT
ejpam-2422	259	32	for	for	ADP
ejpam-2422	259	33	each	each	DET
ejpam-2422	259	34	k	k	PROPN
ejpam-2422	259	35	∈	∈	PROPN
ejpam-2422	259	36	k	k	X
ejpam-2422	259	37	,	,	PUNCT
ejpam-2422	259	38	(	(	PUNCT
ejpam-2422	259	39	u1	u1	NOUN
ejpam-2422	259	40	)	)	PUNCT
ejpam-2422	259	41	uk(λ∗	uk(λ∗	NUM
ejpam-2422	259	42	)	)	PUNCT
ejpam-2422	260	1	=	=	PUNCT
ejpam-2422	260	2	1	1	NUM
ejpam-2422	260	3	m	m	NOUN
ejpam-2422	260	4	.	.	PUNCT
ejpam-2422	261	1	v.	v.	ADP
ejpam-2422	261	2	çetkin	çetkin	PROPN
ejpam-2422	261	3	,	,	PUNCT
ejpam-2422	261	4	h.	h.	PROPN
ejpam-2422	261	5	aygün	aygün	PROPN
ejpam-2422	261	6	/	/	SYM
ejpam-2422	261	7	eur	eur	PROPN
ejpam-2422	261	8	.	.	PUNCT
ejpam-2422	262	1	j.	j.	PROPN
ejpam-2422	262	2	pure	pure	PROPN
ejpam-2422	262	3	appl	appl	PROPN
ejpam-2422	262	4	.	.	PROPN
ejpam-2422	262	5	math	math	PROPN
ejpam-2422	262	6	,	,	PUNCT
ejpam-2422	262	7	9	9	NUM
ejpam-2422	262	8	(	(	PUNCT
ejpam-2422	262	9	2016	2016	NUM
ejpam-2422	262	10	)	)	PUNCT
ejpam-2422	262	11	,	,	PUNCT
ejpam-2422	262	12	419	419	NUM
ejpam-2422	262	13	-	-	SYM
ejpam-2422	262	14	433	433	NUM
ejpam-2422	262	15	426	426	NUM
ejpam-2422	262	16	(	(	PUNCT
ejpam-2422	262	17	u2	u2	PROPN
ejpam-2422	262	18	)	)	PUNCT
ejpam-2422	262	19	uk(λ∆µ)≥uk(λ)∧uk(µ	uk(λ∆µ)≥uk(λ)∧uk(µ	PROPN
ejpam-2422	262	20	)	)	PUNCT
ejpam-2422	262	21	for	for	ADP
ejpam-2422	262	22	each	each	DET
ejpam-2422	262	23	λ,µ	λ,µ	NOUN
ejpam-2422	262	24	∈h	∈h	NOUN
ejpam-2422	262	25	(	(	PUNCT
ejpam-2422	262	26	x	x	X
ejpam-2422	262	27	,	,	PUNCT
ejpam-2422	262	28	e	e	NOUN
ejpam-2422	262	29	)	)	PUNCT
ejpam-2422	262	30	.	.	PUNCT
ejpam-2422	263	1	(	(	PUNCT
ejpam-2422	263	2	u3	u3	PROPN
ejpam-2422	263	3	)	)	PUNCT
ejpam-2422	263	4	if	if	SCONJ
ejpam-2422	263	5	λ≥	λ≥	PROPN
ejpam-2422	263	6	µ	µ	NUM
ejpam-2422	263	7	,	,	PUNCT
ejpam-2422	263	8	then	then	ADV
ejpam-2422	263	9	uk(λ)≥uk(µ	uk(λ)≥uk(µ	NOUN
ejpam-2422	263	10	)	)	PUNCT
ejpam-2422	263	11	.	.	PUNCT
ejpam-2422	264	1	(	(	PUNCT
ejpam-2422	264	2	u4	u4	PROPN
ejpam-2422	264	3	)	)	PUNCT
ejpam-2422	264	4	uk(λ)≤	uk(λ)≤	NOUN
ejpam-2422	264	5	∨	∨	NOUN
ejpam-2422	264	6	{	{	PUNCT
ejpam-2422	264	7	uk(µ	uk(µ	PROPN
ejpam-2422	264	8	)	)	PUNCT
ejpam-2422	265	1	|	|	ADV
ejpam-2422	265	2	µ	µ	PRON
ejpam-2422	265	3	◦	◦	NOUN
ejpam-2422	265	4	µ≤	µ≤	ADJ
ejpam-2422	265	5	λ	λ	NOUN
ejpam-2422	265	6	}	}	PUNCT
ejpam-2422	265	7	for	for	ADP
ejpam-2422	265	8	all	all	DET
ejpam-2422	265	9	λ	λ	NOUN
ejpam-2422	265	10	∈h	∈h	NOUN
ejpam-2422	265	11	(	(	PUNCT
ejpam-2422	265	12	x	x	X
ejpam-2422	265	13	,	,	PUNCT
ejpam-2422	265	14	e	e	NOUN
ejpam-2422	265	15	)	)	PUNCT
ejpam-2422	265	16	.	.	PUNCT
ejpam-2422	266	1	the	the	DET
ejpam-2422	266	2	pair	pair	NOUN
ejpam-2422	266	3	(	(	PUNCT
ejpam-2422	266	4	x	x	X
ejpam-2422	266	5	,	,	PUNCT
ejpam-2422	266	6	u	u	NOUN
ejpam-2422	266	7	)	)	PUNCT
ejpam-2422	266	8	is	be	AUX
ejpam-2422	266	9	called	call	VERB
ejpam-2422	266	10	an	an	DET
ejpam-2422	266	11	(	(	PUNCT
ejpam-2422	266	12	l	l	NOUN
ejpam-2422	266	13	,	,	PUNCT
ejpam-2422	266	14	m)-fuzzy	m)-fuzzy	X
ejpam-2422	266	15	(	(	PUNCT
ejpam-2422	266	16	e	e	NOUN
ejpam-2422	266	17	,	,	PUNCT
ejpam-2422	266	18	k)-soft	k)-soft	ADJ
ejpam-2422	266	19	quasi	quasi	ADJ
ejpam-2422	266	20	-	-	ADJ
ejpam-2422	266	21	uniform	uniform	ADJ
ejpam-2422	266	22	space	space	NOUN
ejpam-2422	266	23	.	.	PUNCT
ejpam-2422	267	1	an	an	DET
ejpam-2422	267	2	(	(	PUNCT
ejpam-2422	267	3	l	l	NOUN
ejpam-2422	267	4	,	,	PUNCT
ejpam-2422	267	5	m)-fuzzy	m)-fuzzy	X
ejpam-2422	267	6	(	(	PUNCT
ejpam-2422	267	7	e	e	NOUN
ejpam-2422	267	8	,	,	PUNCT
ejpam-2422	267	9	k)soft	k)soft	ADV
ejpam-2422	267	10	quasi	quasi	ADJ
ejpam-2422	267	11	-	-	ADJ
ejpam-2422	267	12	uniform	uniform	ADJ
ejpam-2422	267	13	space	space	NOUN
ejpam-2422	267	14	(	(	PUNCT
ejpam-2422	267	15	x	x	X
ejpam-2422	267	16	,	,	PUNCT
ejpam-2422	267	17	u	u	NOUN
ejpam-2422	267	18	)	)	PUNCT
ejpam-2422	267	19	is	be	AUX
ejpam-2422	267	20	said	say	VERB
ejpam-2422	267	21	to	to	PART
ejpam-2422	267	22	be	be	AUX
ejpam-2422	267	23	an	an	DET
ejpam-2422	267	24	(	(	PUNCT
ejpam-2422	267	25	l	l	NOUN
ejpam-2422	267	26	,	,	PUNCT
ejpam-2422	267	27	m)-fuzzy	m)-fuzzy	X
ejpam-2422	267	28	(	(	PUNCT
ejpam-2422	267	29	e	e	NOUN
ejpam-2422	267	30	,	,	PUNCT
ejpam-2422	267	31	k)-soft	k)-soft	PROPN
ejpam-2422	267	32	uniform	uniform	ADJ
ejpam-2422	267	33	space	space	NOUN
ejpam-2422	267	34	if	if	SCONJ
ejpam-2422	267	35	u	u	PRON
ejpam-2422	267	36	provides	provide	VERB
ejpam-2422	267	37	the	the	DET
ejpam-2422	267	38	condition	condition	NOUN
ejpam-2422	267	39	:	:	PUNCT
ejpam-2422	267	40	(	(	PUNCT
ejpam-2422	267	41	u	u	NOUN
ejpam-2422	267	42	)	)	PUNCT
ejpam-2422	267	43	uk(λ)≤	uk(λ)≤	NOUN
ejpam-2422	267	44	∨	∨	NOUN
ejpam-2422	267	45	{	{	PUNCT
ejpam-2422	267	46	uk(µ	uk(µ	PROPN
ejpam-2422	267	47	)	)	PUNCT
ejpam-2422	267	48	|	|	ADV
ejpam-2422	267	49	µ≤	µ≤	ADJ
ejpam-2422	267	50	λ/	λ/	NOUN
ejpam-2422	267	51	}	}	PUNCT
ejpam-2422	267	52	for	for	ADP
ejpam-2422	267	53	each	each	DET
ejpam-2422	267	54	k	k	PROPN
ejpam-2422	267	55	∈	∈	PROPN
ejpam-2422	267	56	k	k	PROPN
ejpam-2422	267	57	,	,	PUNCT
ejpam-2422	267	58	λ	λ	PROPN
ejpam-2422	267	59	∈h	∈h	NOUN
ejpam-2422	267	60	(	(	PUNCT
ejpam-2422	267	61	x	x	X
ejpam-2422	267	62	,	,	PUNCT
ejpam-2422	267	63	e	e	NOUN
ejpam-2422	267	64	)	)	PUNCT
ejpam-2422	267	65	.	.	PUNCT
ejpam-2422	268	1	given	give	VERB
ejpam-2422	268	2	two	two	NUM
ejpam-2422	268	3	u	u	NOUN
ejpam-2422	268	4	1	1	NUM
ejpam-2422	268	5	and	and	CCONJ
ejpam-2422	268	6	u	u	NOUN
ejpam-2422	268	7	2	2	NUM
ejpam-2422	268	8	uniformities	uniformity	NOUN
ejpam-2422	268	9	on	on	ADP
ejpam-2422	268	10	x	x	SYM
ejpam-2422	268	11	,	,	PUNCT
ejpam-2422	268	12	we	we	PRON
ejpam-2422	268	13	say	say	VERB
ejpam-2422	268	14	u	u	NOUN
ejpam-2422	268	15	1	1	NUM
ejpam-2422	268	16	is	be	AUX
ejpam-2422	268	17	finer	fine	ADJ
ejpam-2422	268	18	than	than	ADP
ejpam-2422	268	19	u	u	NOUN
ejpam-2422	268	20	2	2	NUM
ejpam-2422	268	21	(	(	PUNCT
ejpam-2422	268	22	or	or	CCONJ
ejpam-2422	268	23	u	u	NOUN
ejpam-2422	268	24	2	2	NUM
ejpam-2422	268	25	is	be	AUX
ejpam-2422	268	26	coarser	coarse	ADJ
ejpam-2422	268	27	than	than	ADP
ejpam-2422	268	28	u	u	NOUN
ejpam-2422	268	29	1	1	NUM
ejpam-2422	268	30	)	)	PUNCT
ejpam-2422	268	31	iff	iff	NOUN
ejpam-2422	268	32	u	u	NOUN
ejpam-2422	268	33	1	1	NUM
ejpam-2422	268	34	k	k	X
ejpam-2422	268	35	(	(	PUNCT
ejpam-2422	268	36	λ)≥u	λ)≥u	NUM
ejpam-2422	268	37	2	2	NUM
ejpam-2422	268	38	k	k	X
ejpam-2422	268	39	(	(	PUNCT
ejpam-2422	268	40	λ	λ	NOUN
ejpam-2422	268	41	)	)	PUNCT
ejpam-2422	268	42	for	for	ADP
ejpam-2422	268	43	each	each	DET
ejpam-2422	268	44	k	k	PROPN
ejpam-2422	268	45	∈	∈	PROPN
ejpam-2422	268	46	k	k	PROPN
ejpam-2422	268	47	and	and	CCONJ
ejpam-2422	268	48	λ	λ	PROPN
ejpam-2422	268	49	∈h	∈h	NOUN
ejpam-2422	268	50	(	(	PUNCT
ejpam-2422	268	51	x	x	X
ejpam-2422	268	52	,	,	PUNCT
ejpam-2422	268	53	e	e	NOUN
ejpam-2422	268	54	)	)	PUNCT
ejpam-2422	268	55	.	.	PUNCT
ejpam-2422	269	1	a	a	DET
ejpam-2422	269	2	fuzzy	fuzzy	ADJ
ejpam-2422	269	3	soft	soft	ADJ
ejpam-2422	269	4	mapping	mapping	NOUN
ejpam-2422	269	5	ϕψ	ϕψ	ADP
ejpam-2422	269	6	,	,	PUNCT
ejpam-2422	269	7	η	η	PROPN
ejpam-2422	269	8	:	:	PUNCT
ejpam-2422	269	9	(	(	PUNCT
ejpam-2422	269	10	x1,u	x1,u	PROPN
ejpam-2422	269	11	1)→	1)→	NUM
ejpam-2422	269	12	(	(	PUNCT
ejpam-2422	269	13	x2,u	x2,u	NOUN
ejpam-2422	269	14	2	2	NUM
ejpam-2422	269	15	)	)	PUNCT
ejpam-2422	269	16	is	be	AUX
ejpam-2422	269	17	called	call	VERB
ejpam-2422	269	18	(	(	PUNCT
ejpam-2422	269	19	quasi-	quasi-	X
ejpam-2422	269	20	)	)	PUNCT
ejpam-2422	269	21	uniformly	uniformly	ADV
ejpam-2422	269	22	continuous	continuous	ADJ
ejpam-2422	269	23	if	if	SCONJ
ejpam-2422	269	24	u	u	PROPN
ejpam-2422	269	25	1	1	NUM
ejpam-2422	269	26	k	k	X
ejpam-2422	269	27	(	(	PUNCT
ejpam-2422	269	28	ϕ	ϕ	X
ejpam-2422	269	29	⇐	⇐	PROPN
ejpam-2422	269	30	ψ	ψ	X
ejpam-2422	269	31	(	(	PUNCT
ejpam-2422	269	32	µ	µ	NOUN
ejpam-2422	269	33	)	)	PUNCT
ejpam-2422	269	34	)	)	PUNCT
ejpam-2422	269	35	≥	≥	NOUN
ejpam-2422	269	36	u	u	NOUN
ejpam-2422	269	37	2	2	NUM
ejpam-2422	269	38	η(k)(µ	η(k)(µ	NUM
ejpam-2422	269	39	)	)	PUNCT
ejpam-2422	269	40	for	for	ADP
ejpam-2422	269	41	all	all	PRON
ejpam-2422	269	42	µ	µ	PRON
ejpam-2422	269	43	∈	∈	NOUN
ejpam-2422	269	44	h	h	NOUN
ejpam-2422	269	45	(	(	PUNCT
ejpam-2422	269	46	x2	x2	PROPN
ejpam-2422	269	47	,	,	PUNCT
ejpam-2422	269	48	e2	e2	PROPN
ejpam-2422	269	49	)	)	PUNCT
ejpam-2422	269	50	,	,	PUNCT
ejpam-2422	269	51	k	k	PROPN
ejpam-2422	269	52	∈	∈	PROPN
ejpam-2422	269	53	k1	k1	PROPN
ejpam-2422	269	54	,	,	PUNCT
ejpam-2422	269	55	where	where	SCONJ
ejpam-2422	269	56	(	(	PUNCT
ejpam-2422	269	57	x1,u	x1,u	PROPN
ejpam-2422	269	58	1	1	NUM
ejpam-2422	269	59	)	)	PUNCT
ejpam-2422	269	60	and	and	CCONJ
ejpam-2422	269	61	(	(	PUNCT
ejpam-2422	269	62	x2,u	x2,u	NOUN
ejpam-2422	269	63	2	2	NUM
ejpam-2422	269	64	)	)	PUNCT
ejpam-2422	269	65	is	be	AUX
ejpam-2422	269	66	an	an	DET
ejpam-2422	269	67	(	(	PUNCT
ejpam-2422	269	68	l	l	NOUN
ejpam-2422	269	69	,	,	PUNCT
ejpam-2422	269	70	m)-fuzzy	m)-fuzzy	X
ejpam-2422	269	71	(	(	PUNCT
ejpam-2422	269	72	e1	e1	PROPN
ejpam-2422	269	73	,	,	PUNCT
ejpam-2422	269	74	k1)-soft	k1)-soft	X
ejpam-2422	269	75	uniform	uniform	NOUN
ejpam-2422	269	76	space	space	NOUN
ejpam-2422	269	77	and	and	CCONJ
ejpam-2422	269	78	an	an	DET
ejpam-2422	269	79	(	(	PUNCT
ejpam-2422	269	80	l	l	NOUN
ejpam-2422	269	81	,	,	PUNCT
ejpam-2422	269	82	m)-fuzzy	m)-fuzzy	X
ejpam-2422	269	83	(	(	PUNCT
ejpam-2422	269	84	e2	e2	PROPN
ejpam-2422	269	85	,	,	PUNCT
ejpam-2422	269	86	k2)-soft	k2)-soft	X
ejpam-2422	269	87	uniform	uniform	ADJ
ejpam-2422	269	88	space	space	NOUN
ejpam-2422	269	89	,	,	PUNCT
ejpam-2422	269	90	respectively	respectively	ADV
ejpam-2422	269	91	.	.	PUNCT
ejpam-2422	270	1	theorem	theorem	NOUN
ejpam-2422	270	2	1	1	NUM
ejpam-2422	270	3	.	.	PUNCT
ejpam-2422	271	1	let	let	VERB
ejpam-2422	271	2	(	(	PUNCT
ejpam-2422	271	3	x1,u	x1,u	PROPN
ejpam-2422	271	4	1	1	NUM
ejpam-2422	271	5	)	)	PUNCT
ejpam-2422	271	6	,	,	PUNCT
ejpam-2422	271	7	(	(	PUNCT
ejpam-2422	271	8	x2,u	x2,u	NOUN
ejpam-2422	271	9	2	2	NUM
ejpam-2422	271	10	)	)	PUNCT
ejpam-2422	271	11	and	and	CCONJ
ejpam-2422	271	12	(	(	PUNCT
ejpam-2422	271	13	x3,u	x3,u	PROPN
ejpam-2422	271	14	3	3	X
ejpam-2422	271	15	)	)	PUNCT
ejpam-2422	271	16	be	be	AUX
ejpam-2422	271	17	(	(	PUNCT
ejpam-2422	271	18	l	l	NOUN
ejpam-2422	271	19	,	,	PUNCT
ejpam-2422	271	20	m)-fuzzy	m)-fuzzy	X
ejpam-2422	271	21	(	(	PUNCT
ejpam-2422	271	22	ei	ei	X
ejpam-2422	271	23	,	,	PUNCT
ejpam-2422	271	24	ki)-soft	ki)-soft	PROPN
ejpam-2422	271	25	uniform	uniform	NOUN
ejpam-2422	271	26	spaces	space	NOUN
ejpam-2422	271	27	,	,	PUNCT
ejpam-2422	271	28	respectively	respectively	ADV
ejpam-2422	271	29	for	for	ADP
ejpam-2422	271	30	i	i	PROPN
ejpam-2422	271	31	=	=	SYM
ejpam-2422	271	32	1	1	NUM
ejpam-2422	271	33	,	,	PUNCT
ejpam-2422	271	34	2,3	2,3	NUM
ejpam-2422	271	35	.	.	PUNCT
ejpam-2422	272	1	if	if	SCONJ
ejpam-2422	272	2	ϕψ	ϕψ	PROPN
ejpam-2422	272	3	,	,	PUNCT
ejpam-2422	272	4	η	η	PROPN
ejpam-2422	272	5	:	:	PUNCT
ejpam-2422	272	6	(	(	PUNCT
ejpam-2422	272	7	x1,u	x1,u	PROPN
ejpam-2422	272	8	1)→	1)→	NUM
ejpam-2422	272	9	(	(	PUNCT
ejpam-2422	272	10	x2,u	x2,u	NOUN
ejpam-2422	272	11	2	2	NUM
ejpam-2422	272	12	)	)	PUNCT
ejpam-2422	272	13	and	and	CCONJ
ejpam-2422	272	14	ϕ∗	ϕ∗	ADJ
ejpam-2422	272	15	ψ∗,η∗	ψ∗,η∗	PROPN
ejpam-2422	272	16	:	:	PUNCT
ejpam-2422	272	17	(	(	PUNCT
ejpam-2422	272	18	x2,u	x2,u	NOUN
ejpam-2422	272	19	2)→	2)→	NUM
ejpam-2422	272	20	(	(	PUNCT
ejpam-2422	272	21	x3,u	x3,u	PROPN
ejpam-2422	272	22	3	3	NUM
ejpam-2422	272	23	)	)	PUNCT
ejpam-2422	272	24	are	be	AUX
ejpam-2422	272	25	uniformly	uniformly	ADV
ejpam-2422	272	26	continuous	continuous	ADJ
ejpam-2422	272	27	,	,	PUNCT
ejpam-2422	272	28	then	then	ADV
ejpam-2422	272	29	the	the	DET
ejpam-2422	272	30	composition	composition	NOUN
ejpam-2422	272	31	is	be	AUX
ejpam-2422	272	32	uniformly	uniformly	ADV
ejpam-2422	272	33	continuous	continuous	ADJ
ejpam-2422	272	34	.	.	PUNCT
ejpam-2422	273	1	the	the	DET
ejpam-2422	273	2	category	category	NOUN
ejpam-2422	273	3	of	of	ADP
ejpam-2422	273	4	(	(	PUNCT
ejpam-2422	273	5	l	l	NOUN
ejpam-2422	273	6	,	,	PUNCT
ejpam-2422	273	7	m)-fuzzy	m)-fuzzy	X
ejpam-2422	273	8	(	(	PUNCT
ejpam-2422	273	9	e	e	NOUN
ejpam-2422	273	10	,	,	PUNCT
ejpam-2422	273	11	k)-soft	k)-soft	ADJ
ejpam-2422	273	12	quasi	quasi	ADJ
ejpam-2422	273	13	-	-	ADJ
ejpam-2422	273	14	uniform	uniform	ADJ
ejpam-2422	273	15	spaces	space	NOUN
ejpam-2422	273	16	and	and	CCONJ
ejpam-2422	273	17	continuous	continuous	ADJ
ejpam-2422	273	18	mappings	mapping	NOUN
ejpam-2422	273	19	is	be	AUX
ejpam-2422	273	20	denoted	denote	VERB
ejpam-2422	273	21	by	by	ADP
ejpam-2422	273	22	hfsu(l	hfsu(l	PROPN
ejpam-2422	273	23	,	,	PUNCT
ejpam-2422	273	24	m	m	PROPN
ejpam-2422	273	25	)	)	PUNCT
ejpam-2422	273	26	.	.	PUNCT
ejpam-2422	274	1	theorem	theorem	NOUN
ejpam-2422	274	2	2	2	NUM
ejpam-2422	274	3	.	.	X
ejpam-2422	275	1	let	let	AUX
ejpam-2422	275	2	(	(	PUNCT
ejpam-2422	275	3	x	x	X
ejpam-2422	275	4	,	,	PUNCT
ejpam-2422	275	5	u	u	NOUN
ejpam-2422	275	6	)	)	PUNCT
ejpam-2422	275	7	be	be	VERB
ejpam-2422	275	8	an	an	DET
ejpam-2422	275	9	(	(	PUNCT
ejpam-2422	275	10	l	l	NOUN
ejpam-2422	275	11	,	,	PUNCT
ejpam-2422	275	12	m)-fuzzy	m)-fuzzy	X
ejpam-2422	275	13	(	(	PUNCT
ejpam-2422	275	14	e	e	NOUN
ejpam-2422	275	15	,	,	PUNCT
ejpam-2422	275	16	k)-soft	k)-soft	ADJ
ejpam-2422	275	17	quasi	quasi	ADJ
ejpam-2422	275	18	-	-	ADJ
ejpam-2422	275	19	uniform	uniform	ADJ
ejpam-2422	275	20	space	space	NOUN
ejpam-2422	275	21	and	and	CCONJ
ejpam-2422	275	22	rp	rp	NOUN
ejpam-2422	275	23	u	u	NOUN
ejpam-2422	275	24	:	:	PUNCT
ejpam-2422	275	25	k	k	X
ejpam-2422	275	26	→	→	PUNCT
ejpam-2422	275	27	m	m	PROPN
ejpam-2422	275	28	(	(	PUNCT
ejpam-2422	275	29	l	l	NOUN
ejpam-2422	275	30	x	x	X
ejpam-2422	275	31	)	)	PUNCT
ejpam-2422	275	32	e	e	AUX
ejpam-2422	275	33	be	be	AUX
ejpam-2422	275	34	defined	define	VERB
ejpam-2422	275	35	by	by	ADP
ejpam-2422	275	36	for	for	ADP
ejpam-2422	275	37	all	all	DET
ejpam-2422	275	38	f	f	PROPN
ejpam-2422	275	39	∈	∈	PROPN
ejpam-2422	275	40	(	(	PUNCT
ejpam-2422	275	41	lx	lx	NOUN
ejpam-2422	275	42	)	)	PUNCT
ejpam-2422	275	43	e	e	NOUN
ejpam-2422	275	44	,	,	PUNCT
ejpam-2422	275	45	(	(	PUNCT
ejpam-2422	275	46	rp	rp	NOUN
ejpam-2422	275	47	u	u	NOUN
ejpam-2422	275	48	)	)	PUNCT
ejpam-2422	275	49	k	k	PROPN
ejpam-2422	275	50	(	(	PUNCT
ejpam-2422	275	51	f	f	PROPN
ejpam-2422	275	52	)	)	PUNCT
ejpam-2422	276	1	=	=	PUNCT
ejpam-2422	277	1	∨	∨	PROPN
ejpam-2422	277	2	p	p	NOUN
ejpam-2422	277	3	6vh	6vh	ADJ
ejpam-2422	277	4	∨	∨	NOUN
ejpam-2422	277	5	λ(h′)v	λ(h′)v	PRON
ejpam-2422	278	1	f	f	NOUN
ejpam-2422	278	2	′	′	NUM
ejpam-2422	278	3	uk(λ	uk(λ	NOUN
ejpam-2422	278	4	)	)	PUNCT
ejpam-2422	278	5	.	.	PUNCT
ejpam-2422	279	1	then	then	ADV
ejpam-2422	279	2	ru	ru	NOUN
ejpam-2422	279	3	=	=	PUNCT
ejpam-2422	279	4	{	{	PUNCT
ejpam-2422	279	5	r	r	NOUN
ejpam-2422	279	6	p	p	NOUN
ejpam-2422	279	7	u	u	NOUN
ejpam-2422	279	8	|	|	ADV
ejpam-2422	279	9	p	p	PROPN
ejpam-2422	279	10	∈	∈	PROPN
ejpam-2422	279	11	c((lx	c((lx	PROPN
ejpam-2422	279	12	)	)	PUNCT
ejpam-2422	279	13	e	e	X
ejpam-2422	279	14	)	)	PUNCT
ejpam-2422	279	15	}	}	PUNCT
ejpam-2422	279	16	is	be	AUX
ejpam-2422	279	17	a	a	DET
ejpam-2422	279	18	topological	topological	ADJ
ejpam-2422	279	19	fuzzy	fuzzy	ADJ
ejpam-2422	279	20	soft	soft	ADJ
ejpam-2422	279	21	remote	remote	ADJ
ejpam-2422	279	22	neighborhood	neighborhood	NOUN
ejpam-2422	279	23	system	system	NOUN
ejpam-2422	279	24	.	.	PUNCT
ejpam-2422	280	1	proof	proof	NOUN
ejpam-2422	280	2	.	.	PUNCT
ejpam-2422	281	1	we	we	PRON
ejpam-2422	281	2	need	need	VERB
ejpam-2422	281	3	to	to	PART
ejpam-2422	281	4	check	check	VERB
ejpam-2422	281	5	(	(	PUNCT
ejpam-2422	281	6	rn1)-(rn4	rn1)-(rn4	NOUN
ejpam-2422	281	7	)	)	PUNCT
ejpam-2422	281	8	.	.	PUNCT
ejpam-2422	282	1	(	(	PUNCT
ejpam-2422	282	2	rn1	rn1	NOUN
ejpam-2422	282	3	)	)	PUNCT
ejpam-2422	282	4	,	,	PUNCT
ejpam-2422	282	5	(	(	PUNCT
ejpam-2422	282	6	rn2	rn2	PROPN
ejpam-2422	282	7	)	)	PUNCT
ejpam-2422	282	8	and	and	CCONJ
ejpam-2422	282	9	(	(	PUNCT
ejpam-2422	282	10	rn3	rn3	NOUN
ejpam-2422	282	11	)	)	PUNCT
ejpam-2422	282	12	are	be	AUX
ejpam-2422	282	13	straightforward	straightforward	ADJ
ejpam-2422	282	14	,	,	PUNCT
ejpam-2422	282	15	what	what	PRON
ejpam-2422	282	16	remains	remain	VERB
ejpam-2422	282	17	is	be	AUX
ejpam-2422	282	18	to	to	PART
ejpam-2422	282	19	prove	prove	VERB
ejpam-2422	282	20	.	.	PUNCT
ejpam-2422	283	1	(	(	PUNCT
ejpam-2422	283	2	rn4	rn4	NOUN
ejpam-2422	283	3	):	):	PUNCT
ejpam-2422	283	4	from	from	ADP
ejpam-2422	283	5	lemma	lemma	PROPN
ejpam-2422	283	6	3	3	NUM
ejpam-2422	283	7	,	,	PUNCT
ejpam-2422	283	8	we	we	PRON
ejpam-2422	283	9	know	know	VERB
ejpam-2422	283	10	that	that	SCONJ
ejpam-2422	283	11	it	it	PRON
ejpam-2422	283	12	is	be	AUX
ejpam-2422	283	13	equivalent	equivalent	ADJ
ejpam-2422	283	14	to	to	PART
ejpam-2422	283	15	check	check	VERB
ejpam-2422	283	16	(	(	PUNCT
ejpam-2422	283	17	rn4	rn4	NOUN
ejpam-2422	283	18	*	*	NUM
ejpam-2422	283	19	)	)	PUNCT
ejpam-2422	283	20	.	.	PUNCT
ejpam-2422	284	1	since	since	SCONJ
ejpam-2422	284	2	(	(	PUNCT
ejpam-2422	284	3	rp	rp	NOUN
ejpam-2422	284	4	u	u	NOUN
ejpam-2422	284	5	)	)	PUNCT
ejpam-2422	284	6	k	k	PROPN
ejpam-2422	284	7	(	(	PUNCT
ejpam-2422	284	8	f	f	PROPN
ejpam-2422	284	9	)	)	PUNCT
ejpam-2422	284	10	≥	≥	PROPN
ejpam-2422	284	11	∨	∨	NUM
ejpam-2422	284	12	g∈p|	g∈p|	PROPN
ejpam-2422	284	13	f	f	PROPN
ejpam-2422	284	14	�	�	PROPN
ejpam-2422	284	15	(	(	PUNCT
ejpam-2422	284	16	rp	rp	NOUN
ejpam-2422	284	17	u	u	NOUN
ejpam-2422	284	18	)	)	PUNCT
ejpam-2422	284	19	k(g)∧	k(g)∧	PROPN
ejpam-2422	284	20	∧	∧	PROPN
ejpam-2422	284	21	r	r	NOUN
ejpam-2422	284	22	6vg(r	6vg(r	NUM
ejpam-2422	284	23	r	r	NOUN
ejpam-2422	284	24	u	u	NOUN
ejpam-2422	284	25	)	)	PUNCT
ejpam-2422	284	26	k	k	PROPN
ejpam-2422	284	27	(	(	PUNCT
ejpam-2422	284	28	f	f	PROPN
ejpam-2422	284	29	)	)	PUNCT
ejpam-2422	284	30	�	�	PROPN
ejpam-2422	284	31	,	,	PUNCT
ejpam-2422	284	32	for	for	ADP
ejpam-2422	284	33	all	all	DET
ejpam-2422	284	34	k	k	PROPN
ejpam-2422	284	35	∈	∈	PROPN
ejpam-2422	284	36	k	k	X
ejpam-2422	284	37	,	,	PUNCT
ejpam-2422	284	38	is	be	AUX
ejpam-2422	284	39	obvious	obvious	ADJ
ejpam-2422	284	40	.	.	PUNCT
ejpam-2422	285	1	it	it	PRON
ejpam-2422	285	2	is	be	AUX
ejpam-2422	285	3	sufficient	sufficient	ADJ
ejpam-2422	285	4	to	to	PART
ejpam-2422	285	5	show	show	VERB
ejpam-2422	285	6	that	that	SCONJ
ejpam-2422	285	7	(	(	PUNCT
ejpam-2422	285	8	rp	rp	NOUN
ejpam-2422	285	9	u	u	NOUN
ejpam-2422	285	10	)	)	PUNCT
ejpam-2422	286	1	k	k	PROPN
ejpam-2422	286	2	(	(	PUNCT
ejpam-2422	286	3	f	f	PROPN
ejpam-2422	286	4	)	)	PUNCT
ejpam-2422	286	5	≤	≤	PROPN
ejpam-2422	286	6	∨	∨	NUM
ejpam-2422	286	7	g∈p|	g∈p|	PROPN
ejpam-2422	286	8	f	f	PROPN
ejpam-2422	286	9	�	�	PROPN
ejpam-2422	286	10	(	(	PUNCT
ejpam-2422	286	11	rp	rp	NOUN
ejpam-2422	286	12	u	u	NOUN
ejpam-2422	286	13	)	)	PUNCT
ejpam-2422	286	14	k(g)∧	k(g)∧	PROPN
ejpam-2422	286	15	∧	∧	PROPN
ejpam-2422	286	16	r	r	NOUN
ejpam-2422	286	17	6vg(r	6vg(r	NUM
ejpam-2422	286	18	r	r	NOUN
ejpam-2422	286	19	u	u	NOUN
ejpam-2422	286	20	)	)	PUNCT
ejpam-2422	286	21	k	k	PROPN
ejpam-2422	286	22	(	(	PUNCT
ejpam-2422	286	23	f	f	PROPN
ejpam-2422	286	24	)	)	PUNCT
ejpam-2422	286	25	�	�	PROPN
ejpam-2422	286	26	,	,	PUNCT
ejpam-2422	286	27	for	for	ADP
ejpam-2422	286	28	each	each	DET
ejpam-2422	286	29	k	k	PROPN
ejpam-2422	286	30	∈	∈	PROPN
ejpam-2422	286	31	k	k	X
ejpam-2422	286	32	.	.	PUNCT
ejpam-2422	287	1	let	let	VERB
ejpam-2422	287	2	k	k	PROPN
ejpam-2422	287	3	∈	∈	PROPN
ejpam-2422	287	4	k	k	PROPN
ejpam-2422	287	5	and	and	CCONJ
ejpam-2422	287	6	α	α	PROPN
ejpam-2422	287	7	∈	∈	PROPN
ejpam-2422	287	8	c(m	c(m	PROPN
ejpam-2422	287	9	)	)	PUNCT
ejpam-2422	287	10	such	such	ADJ
ejpam-2422	287	11	that	that	DET
ejpam-2422	287	12	αã	αã	INTJ
ejpam-2422	287	13	(	(	PUNCT
ejpam-2422	287	14	rp	rp	NOUN
ejpam-2422	287	15	u	u	NOUN
ejpam-2422	287	16	)	)	PUNCT
ejpam-2422	287	17	k	k	PROPN
ejpam-2422	287	18	(	(	PUNCT
ejpam-2422	287	19	f	f	PROPN
ejpam-2422	287	20	)	)	PUNCT
ejpam-2422	287	21	,	,	PUNCT
ejpam-2422	287	22	that	that	ADV
ejpam-2422	287	23	is	is	ADV
ejpam-2422	287	24	,	,	PUNCT
ejpam-2422	287	25	αã	αã	INTJ
ejpam-2422	287	26	(	(	PUNCT
ejpam-2422	287	27	rp	rp	NOUN
ejpam-2422	287	28	u	u	NOUN
ejpam-2422	287	29	)	)	PUNCT
ejpam-2422	288	1	k	k	PROPN
ejpam-2422	288	2	(	(	PUNCT
ejpam-2422	288	3	f	f	PROPN
ejpam-2422	288	4	)	)	PUNCT
ejpam-2422	288	5	=	=	PUNCT
ejpam-2422	289	1	∨	∨	PROPN
ejpam-2422	289	2	p	p	NOUN
ejpam-2422	289	3	6vh	6vh	ADJ
ejpam-2422	289	4	∨	∨	NOUN
ejpam-2422	289	5	λ(h′)v	λ(h′)v	PRON
ejpam-2422	290	1	f	f	NOUN
ejpam-2422	290	2	′	′	NUM
ejpam-2422	290	3	uk(λ)≤	uk(λ)≤	NOUN
ejpam-2422	290	4	∨	∨	PROPN
ejpam-2422	290	5	p	p	NOUN
ejpam-2422	290	6	6vh	6vh	ADJ
ejpam-2422	290	7	∨	∨	NOUN
ejpam-2422	290	8	λ(h′)v	λ(h′)v	PRON
ejpam-2422	291	1	f	f	PROPN
ejpam-2422	291	2	′	′	NUM
ejpam-2422	291	3	∨	∨	NUM
ejpam-2422	291	4	µ	µ	PRON
ejpam-2422	291	5	◦	◦	NOUN
ejpam-2422	291	6	µ≤λ	µ≤λ	NOUN
ejpam-2422	291	7	uk(µ	uk(µ	NUM
ejpam-2422	291	8	)	)	PUNCT
ejpam-2422	291	9	.	.	PUNCT
ejpam-2422	292	1	then	then	ADV
ejpam-2422	292	2	there	there	PRON
ejpam-2422	292	3	exist	exist	VERB
ejpam-2422	292	4	h	h	NOUN
ejpam-2422	292	5	∈	∈	NOUN
ejpam-2422	292	6	(	(	PUNCT
ejpam-2422	292	7	lx	lx	NOUN
ejpam-2422	292	8	)	)	PUNCT
ejpam-2422	292	9	e	e	NOUN
ejpam-2422	292	10	,	,	PUNCT
ejpam-2422	292	11	λ	λ	X
ejpam-2422	292	12	∈h	∈h	NOUN
ejpam-2422	292	13	(	(	PUNCT
ejpam-2422	292	14	x	x	X
ejpam-2422	292	15	,	,	PUNCT
ejpam-2422	292	16	e	e	NOUN
ejpam-2422	292	17	)	)	PUNCT
ejpam-2422	292	18	and	and	CCONJ
ejpam-2422	292	19	µ	µ	X
ejpam-2422	292	20	∈h	∈h	NOUN
ejpam-2422	292	21	(	(	PUNCT
ejpam-2422	292	22	x	x	X
ejpam-2422	292	23	,	,	PUNCT
ejpam-2422	292	24	e	e	NOUN
ejpam-2422	292	25	)	)	PUNCT
ejpam-2422	292	26	such	such	ADJ
ejpam-2422	292	27	that	that	SCONJ
ejpam-2422	292	28	p	p	PROPN
ejpam-2422	292	29	6v	6v	NUM
ejpam-2422	292	30	hw	hw	PROPN
ejpam-2422	292	31	(	(	PUNCT
ejpam-2422	292	32	µ(h′))′	µ(h′))′	SYM
ejpam-2422	292	33	w	w	NOUN
ejpam-2422	292	34	(	(	PUNCT
ejpam-2422	292	35	(	(	PUNCT
ejpam-2422	292	36	µ	µ	X
ejpam-2422	292	37	◦	◦	NOUN
ejpam-2422	292	38	µ)(h′))′	µ)(h′))′	NUM
ejpam-2422	292	39	w	w	NOUN
ejpam-2422	292	40	(	(	PUNCT
ejpam-2422	292	41	λ(h′))′	λ(h′))′	PROPN
ejpam-2422	292	42	w	w	PROPN
ejpam-2422	292	43	f	f	PROPN
ejpam-2422	292	44	v.	v.	PROPN
ejpam-2422	292	45	çetkin	çetkin	PROPN
ejpam-2422	292	46	,	,	PUNCT
ejpam-2422	292	47	h.	h.	PROPN
ejpam-2422	292	48	aygün	aygün	PROPN
ejpam-2422	292	49	/	/	SYM
ejpam-2422	292	50	eur	eur	PROPN
ejpam-2422	292	51	.	.	PUNCT
ejpam-2422	293	1	j.	j.	PROPN
ejpam-2422	293	2	pure	pure	PROPN
ejpam-2422	293	3	appl	appl	PROPN
ejpam-2422	293	4	.	.	PROPN
ejpam-2422	293	5	math	math	PROPN
ejpam-2422	293	6	,	,	PUNCT
ejpam-2422	293	7	9	9	NUM
ejpam-2422	293	8	(	(	PUNCT
ejpam-2422	293	9	2016	2016	NUM
ejpam-2422	293	10	)	)	PUNCT
ejpam-2422	293	11	,	,	PUNCT
ejpam-2422	293	12	419	419	NUM
ejpam-2422	293	13	-	-	SYM
ejpam-2422	293	14	433	433	NUM
ejpam-2422	293	15	427	427	NUM
ejpam-2422	293	16	and	and	CCONJ
ejpam-2422	293	17	α≤uk(µ	α≤uk(µ	NUM
ejpam-2422	293	18	)	)	PUNCT
ejpam-2422	293	19	.	.	PUNCT
ejpam-2422	294	1	let	let	VERB
ejpam-2422	294	2	g	g	NOUN
ejpam-2422	294	3	=	=	PUNCT
ejpam-2422	294	4	(	(	PUNCT
ejpam-2422	294	5	µ(h′))′.	µ(h′))′.	ADV
ejpam-2422	294	6	then	then	ADV
ejpam-2422	294	7	g	g	PROPN
ejpam-2422	294	8	∈	∈	PROPN
ejpam-2422	295	1	p	p	NOUN
ejpam-2422	296	1	|	|	NOUN
ejpam-2422	296	2	f	f	PROPN
ejpam-2422	296	3	.	.	PUNCT
ejpam-2422	297	1	furthermore	furthermore	ADV
ejpam-2422	297	2	,	,	PUNCT
ejpam-2422	297	3	we	we	PRON
ejpam-2422	297	4	have	have	VERB
ejpam-2422	297	5	(	(	PUNCT
ejpam-2422	297	6	rp	rp	NOUN
ejpam-2422	297	7	u	u	NOUN
ejpam-2422	297	8	)	)	PUNCT
ejpam-2422	297	9	k(g	k(g	PROPN
ejpam-2422	297	10	)	)	PUNCT
ejpam-2422	297	11	=	=	PUNCT
ejpam-2422	298	1	∨	∨	PROPN
ejpam-2422	298	2	p	p	PROPN
ejpam-2422	298	3	6vd	6vd	ADJ
ejpam-2422	298	4	∨	∨	PROPN
ejpam-2422	298	5	ν(d	ν(d	PROPN
ejpam-2422	298	6	′)vg	′)vg	PROPN
ejpam-2422	298	7	′	′	NUM
ejpam-2422	298	8	uk(ν)≥	uk(ν)≥	PROPN
ejpam-2422	298	9	∨	∨	NUM
ejpam-2422	298	10	ν(h′)vg	ν(h′)vg	ADP
ejpam-2422	298	11	′	′	NUM
ejpam-2422	298	12	uk(ν)≥uk(µ)≥	uk(ν)≥uk(µ)≥	PROPN
ejpam-2422	298	13	α	α	PROPN
ejpam-2422	298	14	and	and	CCONJ
ejpam-2422	298	15	∧	∧	PROPN
ejpam-2422	298	16	r	r	NOUN
ejpam-2422	298	17	6vg	6vg	NOUN
ejpam-2422	298	18	(	(	PUNCT
ejpam-2422	298	19	rr	rr	NOUN
ejpam-2422	298	20	u	u	NOUN
ejpam-2422	298	21	)	)	PUNCT
ejpam-2422	298	22	k	k	PROPN
ejpam-2422	298	23	(	(	PUNCT
ejpam-2422	298	24	f	f	NOUN
ejpam-2422	298	25	)	)	PUNCT
ejpam-2422	299	1	=	=	PUNCT
ejpam-2422	299	2	∧	∧	NOUN
ejpam-2422	299	3	r	r	NOUN
ejpam-2422	299	4	6vg	6vg	ADJ
ejpam-2422	299	5	∨	∨	NOUN
ejpam-2422	299	6	r	r	NOUN
ejpam-2422	299	7	6vd	6vd	ADJ
ejpam-2422	299	8	∨	∨	NOUN
ejpam-2422	299	9	ν(d	ν(d	NOUN
ejpam-2422	299	10	′)v	′)v	NOUN
ejpam-2422	299	11	f	f	NOUN
ejpam-2422	299	12	′	′	NOUN
ejpam-2422	299	13	uk(ν)≥	uk(ν)≥	PROPN
ejpam-2422	300	1	∧	∧	PROPN
ejpam-2422	300	2	r	r	NOUN
ejpam-2422	300	3	6vg	6vg	ADJ
ejpam-2422	300	4	∨	∨	NUM
ejpam-2422	300	5	ν(g	ν(g	PROPN
ejpam-2422	300	6	′)v	′)v	NOUN
ejpam-2422	300	7	f	f	PROPN
ejpam-2422	300	8	′	′	NOUN
ejpam-2422	300	9	uk(ν)≥	uk(ν)≥	PROPN
ejpam-2422	300	10	∧	∧	PROPN
ejpam-2422	300	11	r	r	NOUN
ejpam-2422	300	12	6vg	6vg	ADJ
ejpam-2422	301	1	uk(µ)≥	uk(µ)≥	PROPN
ejpam-2422	301	2	α	α	PROPN
ejpam-2422	301	3	.	.	PUNCT
ejpam-2422	302	1	then	then	ADV
ejpam-2422	302	2	α≤	α≤	PROPN
ejpam-2422	302	3	(	(	PUNCT
ejpam-2422	302	4	rp	rp	NOUN
ejpam-2422	302	5	u	u	NOUN
ejpam-2422	302	6	)	)	PUNCT
ejpam-2422	302	7	k(g)∧	k(g)∧	PROPN
ejpam-2422	302	8	∧	∧	PROPN
ejpam-2422	302	9	r	r	NOUN
ejpam-2422	302	10	6vg(r	6vg(r	NUM
ejpam-2422	302	11	r	r	NOUN
ejpam-2422	302	12	u	u	NOUN
ejpam-2422	302	13	)	)	PUNCT
ejpam-2422	302	14	k	k	PROPN
ejpam-2422	302	15	(	(	PUNCT
ejpam-2422	302	16	f	f	PROPN
ejpam-2422	302	17	)	)	PUNCT
ejpam-2422	302	18	.	.	PUNCT
ejpam-2422	303	1	therefore	therefore	ADV
ejpam-2422	303	2	,	,	PUNCT
ejpam-2422	303	3	α≤	α≤	PROPN
ejpam-2422	303	4	∨	∨	NUM
ejpam-2422	303	5	g∈p|	g∈p|	PROPN
ejpam-2422	303	6	f	f	PROPN
ejpam-2422	303	7	�	�	PROPN
ejpam-2422	303	8	(	(	PUNCT
ejpam-2422	303	9	rp	rp	NOUN
ejpam-2422	303	10	u	u	NOUN
ejpam-2422	303	11	)	)	PUNCT
ejpam-2422	303	12	k(g)∧	k(g)∧	PROPN
ejpam-2422	303	13	∧	∧	PROPN
ejpam-2422	303	14	r	r	NOUN
ejpam-2422	303	15	6vg(r	6vg(r	NUM
ejpam-2422	303	16	r	r	NOUN
ejpam-2422	303	17	u	u	NOUN
ejpam-2422	303	18	)	)	PUNCT
ejpam-2422	303	19	k	k	PROPN
ejpam-2422	303	20	(	(	PUNCT
ejpam-2422	303	21	f	f	PROPN
ejpam-2422	303	22	)	)	PUNCT
ejpam-2422	303	23	�	�	PROPN
ejpam-2422	303	24	.	.	PUNCT
ejpam-2422	304	1	from	from	ADP
ejpam-2422	304	2	the	the	DET
ejpam-2422	304	3	arbitrariness	arbitrariness	NOUN
ejpam-2422	304	4	of	of	ADP
ejpam-2422	304	5	α	α	NOUN
ejpam-2422	304	6	,	,	PUNCT
ejpam-2422	304	7	we	we	PRON
ejpam-2422	304	8	have	have	VERB
ejpam-2422	304	9	(	(	PUNCT
ejpam-2422	304	10	r	r	NOUN
ejpam-2422	304	11	p	p	PROPN
ejpam-2422	304	12	u	u	NOUN
ejpam-2422	304	13	)	)	PUNCT
ejpam-2422	305	1	k	k	PROPN
ejpam-2422	305	2	(	(	PUNCT
ejpam-2422	305	3	f	f	PROPN
ejpam-2422	305	4	)	)	PUNCT
ejpam-2422	305	5	≤	≤	PROPN
ejpam-2422	305	6	∨	∨	NUM
ejpam-2422	305	7	g∈p|	g∈p|	PROPN
ejpam-2422	305	8	f	f	PROPN
ejpam-2422	305	9	�	�	PROPN
ejpam-2422	305	10	(	(	PUNCT
ejpam-2422	305	11	rp	rp	NOUN
ejpam-2422	305	12	u	u	NOUN
ejpam-2422	305	13	)	)	PUNCT
ejpam-2422	305	14	k(g)∧	k(g)∧	PROPN
ejpam-2422	305	15	∧	∧	PROPN
ejpam-2422	305	16	r	r	NOUN
ejpam-2422	305	17	6vg(r	6vg(r	NUM
ejpam-2422	305	18	r	r	NOUN
ejpam-2422	305	19	u	u	NOUN
ejpam-2422	305	20	)	)	PUNCT
ejpam-2422	305	21	k	k	PROPN
ejpam-2422	305	22	(	(	PUNCT
ejpam-2422	305	23	f	f	PROPN
ejpam-2422	305	24	)	)	PUNCT
ejpam-2422	305	25	�	�	PROPN
ejpam-2422	305	26	.	.	PUNCT
ejpam-2422	306	1	theorem	theorem	VERB
ejpam-2422	306	2	3	3	X
ejpam-2422	306	3	.	.	PUNCT
ejpam-2422	307	1	let	let	AUX
ejpam-2422	307	2	(	(	PUNCT
ejpam-2422	307	3	x	x	X
ejpam-2422	307	4	,	,	PUNCT
ejpam-2422	307	5	u	u	NOUN
ejpam-2422	307	6	)	)	PUNCT
ejpam-2422	307	7	be	be	VERB
ejpam-2422	307	8	an	an	DET
ejpam-2422	307	9	(	(	PUNCT
ejpam-2422	307	10	l	l	NOUN
ejpam-2422	307	11	,	,	PUNCT
ejpam-2422	307	12	m)-fuzzy	m)-fuzzy	X
ejpam-2422	307	13	(	(	PUNCT
ejpam-2422	307	14	e	e	NOUN
ejpam-2422	307	15	,	,	PUNCT
ejpam-2422	307	16	k)-soft	k)-soft	ADJ
ejpam-2422	307	17	quasi	quasi	ADJ
ejpam-2422	307	18	-	-	ADJ
ejpam-2422	307	19	uniform	uniform	ADJ
ejpam-2422	307	20	space	space	NOUN
ejpam-2422	307	21	.	.	PUNCT
ejpam-2422	308	1	then	then	ADV
ejpam-2422	308	2	,	,	PUNCT
ejpam-2422	308	3	r	r	PROPN
ejpam-2422	308	4	p	p	NOUN
ejpam-2422	308	5	u	u	NOUN
ejpam-2422	308	6	can	can	AUX
ejpam-2422	308	7	also	also	ADV
ejpam-2422	308	8	be	be	AUX
ejpam-2422	308	9	written	write	VERB
ejpam-2422	308	10	as	as	SCONJ
ejpam-2422	308	11	follows	follow	VERB
ejpam-2422	308	12	:	:	PUNCT
ejpam-2422	308	13	(	(	PUNCT
ejpam-2422	308	14	i	i	NOUN
ejpam-2422	308	15	)	)	PUNCT
ejpam-2422	309	1	(	(	PUNCT
ejpam-2422	309	2	r	r	NOUN
ejpam-2422	309	3	p	p	X
ejpam-2422	309	4	u	u	NOUN
ejpam-2422	309	5	)	)	PUNCT
ejpam-2422	309	6	k	k	PROPN
ejpam-2422	309	7	(	(	PUNCT
ejpam-2422	309	8	f	f	PROPN
ejpam-2422	309	9	)	)	PUNCT
ejpam-2422	309	10	=	=	PUNCT
ejpam-2422	310	1	∨	∨	PROPN
ejpam-2422	310	2	p	p	NOUN
ejpam-2422	310	3	6vh	6vh	ADJ
ejpam-2422	310	4	∨	∨	NUM
ejpam-2422	310	5	λ	λ	NOUN
ejpam-2422	310	6	◦	◦	NOUN
ejpam-2422	310	7	λ(h′)v	λ(h′)v	PRON
ejpam-2422	310	8	f	f	NOUN
ejpam-2422	310	9	′uk(λ	′uk(λ	PROPN
ejpam-2422	310	10	)	)	PUNCT
ejpam-2422	310	11	.	.	PUNCT
ejpam-2422	311	1	(	(	PUNCT
ejpam-2422	311	2	ii	ii	NOUN
ejpam-2422	311	3	)	)	PUNCT
ejpam-2422	311	4	(	(	PUNCT
ejpam-2422	311	5	r	r	NOUN
ejpam-2422	311	6	p	p	X
ejpam-2422	311	7	u	u	NOUN
ejpam-2422	311	8	)	)	PUNCT
ejpam-2422	311	9	k	k	PROPN
ejpam-2422	311	10	(	(	PUNCT
ejpam-2422	311	11	f	f	PROPN
ejpam-2422	311	12	)	)	PUNCT
ejpam-2422	311	13	=	=	SYM
ejpam-2422	311	14	∨	∨	NUM
ejpam-2422	311	15	h∈(lx	h∈(lx	NOUN
ejpam-2422	311	16	)	)	PUNCT
ejpam-2422	311	17	e	e	NOUN
ejpam-2422	311	18	∨	∨	NUM
ejpam-2422	311	19	p	p	PROPN
ejpam-2422	311	20	6vλ(h′)w(λ	6vλ(h′)w(λ	NUM
ejpam-2422	311	21	◦	◦	NOUN
ejpam-2422	311	22	λ(h′))′w	λ(h′))′w	NOUN
ejpam-2422	311	23	f	f	NOUN
ejpam-2422	311	24	uk(λ	uk(λ	NOUN
ejpam-2422	311	25	)	)	PUNCT
ejpam-2422	311	26	.	.	PUNCT
ejpam-2422	312	1	(	(	PUNCT
ejpam-2422	312	2	iii	iii	X
ejpam-2422	312	3	)	)	PUNCT
ejpam-2422	312	4	(	(	PUNCT
ejpam-2422	312	5	r	r	NOUN
ejpam-2422	312	6	p	p	X
ejpam-2422	312	7	u	u	NOUN
ejpam-2422	312	8	)	)	PUNCT
ejpam-2422	312	9	k	k	PROPN
ejpam-2422	312	10	(	(	PUNCT
ejpam-2422	312	11	f	f	PROPN
ejpam-2422	312	12	)	)	PUNCT
ejpam-2422	312	13	=	=	PUNCT
ejpam-2422	313	1	∨	∨	NUM
ejpam-2422	313	2	p	p	NOUN
ejpam-2422	313	3	6vλ/	6vλ/	NUM
ejpam-2422	313	4	(	(	PUNCT
ejpam-2422	313	5	f	f	PROPN
ejpam-2422	313	6	)	)	PUNCT
ejpam-2422	313	7	uk(λ	uk(λ	NOUN
ejpam-2422	313	8	)	)	PUNCT
ejpam-2422	313	9	.	.	PUNCT
ejpam-2422	314	1	proof	proof	NOUN
ejpam-2422	314	2	.	.	PUNCT
ejpam-2422	315	1	(	(	PUNCT
ejpam-2422	315	2	i	i	NOUN
ejpam-2422	315	3	)	)	PUNCT
ejpam-2422	315	4	and	and	CCONJ
ejpam-2422	315	5	(	(	PUNCT
ejpam-2422	315	6	ii	ii	NOUN
ejpam-2422	315	7	)	)	PUNCT
ejpam-2422	315	8	are	be	AUX
ejpam-2422	315	9	trivial	trivial	ADJ
ejpam-2422	315	10	.	.	PUNCT
ejpam-2422	316	1	(	(	PUNCT
ejpam-2422	316	2	iii	iii	X
ejpam-2422	316	3	)	)	PUNCT
ejpam-2422	316	4	can	can	AUX
ejpam-2422	316	5	be	be	AUX
ejpam-2422	316	6	obtained	obtain	VERB
ejpam-2422	316	7	by	by	ADP
ejpam-2422	316	8	the	the	DET
ejpam-2422	316	9	definition	definition	NOUN
ejpam-2422	316	10	of	of	ADP
ejpam-2422	316	11	λ/.	λ/.	NOUN
ejpam-2422	316	12	from	from	ADP
ejpam-2422	316	13	lemma	lemma	PROPN
ejpam-2422	316	14	2	2	NUM
ejpam-2422	316	15	,	,	PUNCT
ejpam-2422	316	16	we	we	PRON
ejpam-2422	316	17	know	know	VERB
ejpam-2422	316	18	that	that	SCONJ
ejpam-2422	316	19	tu	tu	PROPN
ejpam-2422	316	20	is	be	AUX
ejpam-2422	316	21	an	an	DET
ejpam-2422	316	22	(	(	PUNCT
ejpam-2422	316	23	l	l	NOUN
ejpam-2422	316	24	,	,	PUNCT
ejpam-2422	316	25	m)-fuzzy	m)-fuzzy	X
ejpam-2422	316	26	(	(	PUNCT
ejpam-2422	316	27	e	e	NOUN
ejpam-2422	316	28	,	,	PUNCT
ejpam-2422	316	29	k)-soft	k)-soft	PROPN
ejpam-2422	316	30	cotopology	cotopology	NOUN
ejpam-2422	316	31	on	on	ADP
ejpam-2422	316	32	x	x	PUNCT
ejpam-2422	316	33	and	and	CCONJ
ejpam-2422	316	34	call	call	VERB
ejpam-2422	316	35	it	it	PRON
ejpam-2422	316	36	the	the	DET
ejpam-2422	316	37	generated	generate	VERB
ejpam-2422	316	38	(	(	PUNCT
ejpam-2422	316	39	l	l	NOUN
ejpam-2422	316	40	,	,	PUNCT
ejpam-2422	316	41	m)-fuzzy	m)-fuzzy	X
ejpam-2422	316	42	(	(	PUNCT
ejpam-2422	316	43	e	e	NOUN
ejpam-2422	316	44	,	,	PUNCT
ejpam-2422	316	45	k)-soft	k)-soft	PROPN
ejpam-2422	316	46	cotopology	cotopology	NOUN
ejpam-2422	316	47	by	by	ADP
ejpam-2422	316	48	u	u	PROPN
ejpam-2422	316	49	.	.	PUNCT
ejpam-2422	317	1	theorem	theorem	ADJ
ejpam-2422	317	2	4	4	NUM
ejpam-2422	317	3	.	.	PUNCT
ejpam-2422	318	1	let	let	AUX
ejpam-2422	318	2	(	(	PUNCT
ejpam-2422	318	3	x	x	X
ejpam-2422	318	4	,	,	PUNCT
ejpam-2422	318	5	t	t	PROPN
ejpam-2422	318	6	)	)	PUNCT
ejpam-2422	318	7	be	be	AUX
ejpam-2422	318	8	an	an	DET
ejpam-2422	318	9	(	(	PUNCT
ejpam-2422	318	10	l	l	NOUN
ejpam-2422	318	11	,	,	PUNCT
ejpam-2422	318	12	m)-fuzzy	m)-fuzzy	X
ejpam-2422	318	13	(	(	PUNCT
ejpam-2422	318	14	e	e	NOUN
ejpam-2422	318	15	,	,	PUNCT
ejpam-2422	318	16	k)-soft	k)-soft	VERB
ejpam-2422	318	17	cotopological	cotopological	ADJ
ejpam-2422	318	18	space	space	NOUN
ejpam-2422	318	19	.	.	PUNCT
ejpam-2422	319	1	then	then	ADV
ejpam-2422	319	2	there	there	PRON
ejpam-2422	319	3	is	be	VERB
ejpam-2422	319	4	one	one	NUM
ejpam-2422	319	5	(	(	PUNCT
ejpam-2422	319	6	l	l	NOUN
ejpam-2422	319	7	,	,	PUNCT
ejpam-2422	319	8	m)-fuzzy	m)-fuzzy	X
ejpam-2422	319	9	(	(	PUNCT
ejpam-2422	319	10	e	e	NOUN
ejpam-2422	319	11	,	,	PUNCT
ejpam-2422	319	12	k)-soft	k)-soft	X
ejpam-2422	319	13	quasi	quasi	NOUN
ejpam-2422	319	14	uniformity	uniformity	PROPN
ejpam-2422	319	15	ut	ut	PROPN
ejpam-2422	319	16	on	on	ADP
ejpam-2422	319	17	x	x	SYM
ejpam-2422	319	18	such	such	ADJ
ejpam-2422	319	19	that	that	SCONJ
ejpam-2422	319	20	the	the	DET
ejpam-2422	319	21	generated	generate	VERB
ejpam-2422	319	22	(	(	PUNCT
ejpam-2422	319	23	l	l	NOUN
ejpam-2422	319	24	,	,	PUNCT
ejpam-2422	319	25	m)-fuzzy	m)-fuzzy	X
ejpam-2422	319	26	(	(	PUNCT
ejpam-2422	319	27	e	e	NOUN
ejpam-2422	319	28	,	,	PUNCT
ejpam-2422	319	29	k)soft	k)soft	PROPN
ejpam-2422	319	30	cotopology	cotopology	NOUN
ejpam-2422	319	31	by	by	ADP
ejpam-2422	319	32	ut	ut	PROPN
ejpam-2422	319	33	is	be	AUX
ejpam-2422	319	34	just	just	ADV
ejpam-2422	319	35	t	t	PROPN
ejpam-2422	319	36	,	,	PUNCT
ejpam-2422	319	37	i.e.	i.e.	X
ejpam-2422	319	38	,	,	PUNCT
ejpam-2422	319	39	t	t	NOUN
ejpam-2422	319	40	=	=	SYM
ejpam-2422	319	41	tut	tut	PROPN
ejpam-2422	319	42	.	.	PUNCT
ejpam-2422	320	1	this	this	PRON
ejpam-2422	320	2	is	be	AUX
ejpam-2422	320	3	to	to	PART
ejpam-2422	320	4	say	say	VERB
ejpam-2422	320	5	that	that	SCONJ
ejpam-2422	320	6	each	each	DET
ejpam-2422	320	7	(	(	PUNCT
ejpam-2422	320	8	l	l	NOUN
ejpam-2422	320	9	,	,	PUNCT
ejpam-2422	320	10	m)-fuzzy	m)-fuzzy	X
ejpam-2422	320	11	(	(	PUNCT
ejpam-2422	320	12	e	e	NOUN
ejpam-2422	320	13	,	,	PUNCT
ejpam-2422	320	14	k)-soft	k)-soft	VERB
ejpam-2422	320	15	cotopological	cotopological	ADJ
ejpam-2422	320	16	space	space	NOUN
ejpam-2422	320	17	is	be	AUX
ejpam-2422	320	18	(	(	PUNCT
ejpam-2422	320	19	l	l	NOUN
ejpam-2422	320	20	,	,	PUNCT
ejpam-2422	320	21	m)-fuzzy	m)-fuzzy	X
ejpam-2422	320	22	(	(	PUNCT
ejpam-2422	320	23	e	e	NOUN
ejpam-2422	320	24	,	,	PUNCT
ejpam-2422	320	25	k)-soft	k)-soft	VERB
ejpam-2422	320	26	quasi	quasi	ADJ
ejpam-2422	320	27	-	-	ADJ
ejpam-2422	320	28	uniformizable	uniformizable	ADJ
ejpam-2422	320	29	.	.	PUNCT
ejpam-2422	321	1	proof	proof	NOUN
ejpam-2422	321	2	.	.	PUNCT
ejpam-2422	322	1	let	let	VERB
ejpam-2422	322	2	g	g	PROPN
ejpam-2422	322	3	∈	∈	PROPN
ejpam-2422	322	4	(	(	PUNCT
ejpam-2422	322	5	lx	lx	NOUN
ejpam-2422	322	6	)	)	PUNCT
ejpam-2422	322	7	e	e	NOUN
ejpam-2422	322	8	and	and	CCONJ
ejpam-2422	322	9	λg	λg	X
ejpam-2422	322	10	:	:	PUNCT
ejpam-2422	322	11	(	(	PUNCT
ejpam-2422	322	12	lx	lx	NOUN
ejpam-2422	322	13	)	)	PUNCT
ejpam-2422	322	14	e	e	X
ejpam-2422	322	15	→	→	PUNCT
ejpam-2422	322	16	(	(	PUNCT
ejpam-2422	322	17	lx	lx	NOUN
ejpam-2422	322	18	)	)	PUNCT
ejpam-2422	322	19	e	e	X
ejpam-2422	322	20	be	be	AUX
ejpam-2422	322	21	defined	define	VERB
ejpam-2422	322	22	as	as	SCONJ
ejpam-2422	322	23	follows	follow	VERB
ejpam-2422	322	24	:	:	PUNCT
ejpam-2422	322	25	λg	λg	PROPN
ejpam-2422	322	26	(	(	PUNCT
ejpam-2422	322	27	f	f	PROPN
ejpam-2422	322	28	)	)	PUNCT
ejpam-2422	322	29	=	=	PUNCT
ejpam-2422	323	1			PROPN
ejpam-2422	323	2			VERB
ejpam-2422	323	3			PRON
ejpam-2422	323	4			PROPN
ejpam-2422	323	5			PROPN
ejpam-2422	323	6	1x	1x	NOUN
ejpam-2422	323	7	,	,	PUNCT
ejpam-2422	323	8	if	if	SCONJ
ejpam-2422	323	9	f	f	PROPN
ejpam-2422	323	10	6v	6v	VERB
ejpam-2422	323	11	g	g	NOUN
ejpam-2422	323	12	;	;	PUNCT
ejpam-2422	323	13	g	g	NOUN
ejpam-2422	323	14	,	,	PUNCT
ejpam-2422	323	15	if	if	SCONJ
ejpam-2422	323	16	0x	0x	PROPN
ejpam-2422	323	17	6=	6=	NUM
ejpam-2422	323	18	f	f	PROPN
ejpam-2422	323	19	v	v	ADP
ejpam-2422	323	20	g	g	NOUN
ejpam-2422	323	21	;	;	PUNCT
ejpam-2422	323	22	0x	0x	X
ejpam-2422	323	23	,	,	PUNCT
ejpam-2422	323	24	otherwise	otherwise	ADV
ejpam-2422	323	25	.	.	PUNCT
ejpam-2422	324	1	then	then	ADV
ejpam-2422	324	2	λ	λ	X
ejpam-2422	324	3	f	f	PROPN
ejpam-2422	324	4	∈h	∈h	NOUN
ejpam-2422	324	5	(	(	PUNCT
ejpam-2422	324	6	x	x	X
ejpam-2422	324	7	,	,	PUNCT
ejpam-2422	324	8	e	e	NOUN
ejpam-2422	324	9	)	)	PUNCT
ejpam-2422	324	10	and	and	CCONJ
ejpam-2422	324	11	λ	λ	X
ejpam-2422	324	12	f	f	PROPN
ejpam-2422	324	13	◦	◦	NOUN
ejpam-2422	324	14	λ	λ	X
ejpam-2422	324	15	f	f	NOUN
ejpam-2422	325	1	=	=	SYM
ejpam-2422	325	2	λ	λ	X
ejpam-2422	325	3	f	f	PROPN
ejpam-2422	325	4	.	.	PUNCT
ejpam-2422	326	1	define	define	VERB
ejpam-2422	326	2	ut	ut	PROPN
ejpam-2422	326	3	:	:	PUNCT
ejpam-2422	326	4	k	k	PROPN
ejpam-2422	326	5	→	→	SYM
ejpam-2422	326	6	mh	mh	PROPN
ejpam-2422	326	7	(	(	PUNCT
ejpam-2422	326	8	x	x	X
ejpam-2422	326	9	,	,	PUNCT
ejpam-2422	326	10	e	e	NOUN
ejpam-2422	326	11	)	)	PUNCT
ejpam-2422	326	12	by	by	ADP
ejpam-2422	326	13	(	(	PUNCT
ejpam-2422	326	14	ut	ut	PROPN
ejpam-2422	326	15	)	)	PUNCT
ejpam-2422	326	16	k(λ	k(λ	X
ejpam-2422	326	17	)	)	PUNCT
ejpam-2422	326	18	=	=	SYM
ejpam-2422	326	19	∨	∨	X
ejpam-2422	326	20	{	{	PUNCT
ejpam-2422	326	21	n	n	CCONJ
ejpam-2422	326	22	∧	∧	PROPN
ejpam-2422	326	23	i=1	i=1	PROPN
ejpam-2422	326	24	tk(gi	tk(gi	PROPN
ejpam-2422	326	25	)	)	PUNCT
ejpam-2422	327	1	|	|	ADV
ejpam-2422	327	2	λ≥∆n	λ≥∆n	PROPN
ejpam-2422	327	3	i=1λg	i=1λg	VERB
ejpam-2422	327	4	′i	′i	NOUN
ejpam-2422	327	5	,	,	PUNCT
ejpam-2422	327	6	n	n	PRON
ejpam-2422	327	7	∈	∈	PROPN
ejpam-2422	327	8	n	n	CCONJ
ejpam-2422	327	9	}	}	PUNCT
ejpam-2422	327	10	.	.	PUNCT
ejpam-2422	328	1	it	it	PRON
ejpam-2422	328	2	is	be	AUX
ejpam-2422	328	3	easy	easy	ADJ
ejpam-2422	328	4	to	to	PART
ejpam-2422	328	5	verify	verify	VERB
ejpam-2422	328	6	that	that	SCONJ
ejpam-2422	328	7	ut	ut	PROPN
ejpam-2422	328	8	is	be	AUX
ejpam-2422	328	9	an	an	DET
ejpam-2422	328	10	(	(	PUNCT
ejpam-2422	328	11	l	l	NOUN
ejpam-2422	328	12	,	,	PUNCT
ejpam-2422	328	13	m)-fuzzy	m)-fuzzy	X
ejpam-2422	328	14	(	(	PUNCT
ejpam-2422	328	15	e	e	NOUN
ejpam-2422	328	16	,	,	PUNCT
ejpam-2422	328	17	k)-soft	k)-soft	X
ejpam-2422	328	18	quasi	quasi	NOUN
ejpam-2422	328	19	uniformity	uniformity	NOUN
ejpam-2422	328	20	on	on	ADP
ejpam-2422	328	21	x	x	X
ejpam-2422	328	22	.	.	PUNCT
ejpam-2422	329	1	now	now	ADV
ejpam-2422	329	2	we	we	PRON
ejpam-2422	329	3	prove	prove	VERB
ejpam-2422	329	4	that	that	SCONJ
ejpam-2422	329	5	t	t	NOUN
ejpam-2422	329	6	=	=	SYM
ejpam-2422	329	7	tut	tut	NOUN
ejpam-2422	329	8	.	.	PUNCT
ejpam-2422	330	1	noting	note	VERB
ejpam-2422	330	2	that	that	SCONJ
ejpam-2422	330	3	λ/	λ/	ADJ
ejpam-2422	330	4	g	g	NOUN
ejpam-2422	330	5	′i	′i	NOUN
ejpam-2422	330	6	(	(	PUNCT
ejpam-2422	330	7	f	f	X
ejpam-2422	330	8	)	)	PUNCT
ejpam-2422	330	9	=	=	SYM
ejpam-2422	330	10	f	f	PROPN
ejpam-2422	330	11	,	,	PUNCT
ejpam-2422	330	12	from	from	ADP
ejpam-2422	330	13	the	the	DET
ejpam-2422	330	14	definition	definition	NOUN
ejpam-2422	330	15	of	of	ADP
ejpam-2422	330	16	tut	tut	NOUN
ejpam-2422	330	17	,	,	PUNCT
ejpam-2422	330	18	we	we	PRON
ejpam-2422	330	19	have	have	VERB
ejpam-2422	330	20	for	for	ADP
ejpam-2422	330	21	k	k	PROPN
ejpam-2422	330	22	∈	∈	PROPN
ejpam-2422	330	23	k	k	PROPN
ejpam-2422	330	24	(	(	PUNCT
ejpam-2422	330	25	tut	tut	NOUN
ejpam-2422	330	26	)	)	PUNCT
ejpam-2422	330	27	k	k	PROPN
ejpam-2422	330	28	(	(	PUNCT
ejpam-2422	330	29	f	f	NOUN
ejpam-2422	330	30	)	)	PUNCT
ejpam-2422	331	1	=	=	PUNCT
ejpam-2422	331	2	∧	∧	PROPN
ejpam-2422	331	3	p	p	NOUN
ejpam-2422	331	4	6v	6v	X
ejpam-2422	331	5	f	f	PROPN
ejpam-2422	331	6	∨	∨	NUM
ejpam-2422	331	7	p	p	PROPN
ejpam-2422	331	8	6vλ/	6vλ/	NUM
ejpam-2422	331	9	(	(	PUNCT
ejpam-2422	331	10	f	f	PROPN
ejpam-2422	331	11	)	)	PUNCT
ejpam-2422	331	12	∨	∨	X
ejpam-2422	331	13	{	{	PUNCT
ejpam-2422	331	14	n	n	CCONJ
ejpam-2422	331	15	∧	∧	PROPN
ejpam-2422	331	16	i=1	i=1	PROPN
ejpam-2422	331	17	tk(gi	tk(gi	PROPN
ejpam-2422	331	18	)	)	PUNCT
ejpam-2422	332	1	|	|	ADV
ejpam-2422	332	2	λ≥∆n	λ≥∆n	PROPN
ejpam-2422	332	3	i=1λg	i=1λg	VERB
ejpam-2422	332	4	′i	′i	NOUN
ejpam-2422	332	5	,	,	PUNCT
ejpam-2422	332	6	n	n	PRON
ejpam-2422	332	7	∈	∈	PROPN
ejpam-2422	332	8	n	n	CCONJ
ejpam-2422	332	9	}	}	PUNCT
ejpam-2422	332	10	≥	≥	NUM
ejpam-2422	332	11	∧	∧	PROPN
ejpam-2422	332	12	p	p	NOUN
ejpam-2422	332	13	6v	6v	PROPN
ejpam-2422	332	14	f	f	PROPN
ejpam-2422	332	15	tk	tk	PROPN
ejpam-2422	332	16	(	(	PUNCT
ejpam-2422	332	17	f	f	PROPN
ejpam-2422	332	18	)	)	PUNCT
ejpam-2422	332	19	=	=	SYM
ejpam-2422	332	20	tk	tk	PROPN
ejpam-2422	332	21	(	(	PUNCT
ejpam-2422	332	22	f	f	PROPN
ejpam-2422	332	23	)	)	PUNCT
ejpam-2422	332	24	.	.	PUNCT
ejpam-2422	333	1	v.	v.	ADP
ejpam-2422	333	2	çetkin	çetkin	PROPN
ejpam-2422	333	3	,	,	PUNCT
ejpam-2422	333	4	h.	h.	PROPN
ejpam-2422	333	5	aygün	aygün	PROPN
ejpam-2422	333	6	/	/	SYM
ejpam-2422	333	7	eur	eur	PROPN
ejpam-2422	333	8	.	.	PUNCT
ejpam-2422	334	1	j.	j.	PROPN
ejpam-2422	334	2	pure	pure	PROPN
ejpam-2422	334	3	appl	appl	PROPN
ejpam-2422	334	4	.	.	PROPN
ejpam-2422	334	5	math	math	PROPN
ejpam-2422	334	6	,	,	PUNCT
ejpam-2422	334	7	9	9	NUM
ejpam-2422	334	8	(	(	PUNCT
ejpam-2422	334	9	2016	2016	NUM
ejpam-2422	334	10	)	)	PUNCT
ejpam-2422	334	11	,	,	PUNCT
ejpam-2422	334	12	419	419	NUM
ejpam-2422	334	13	-	-	SYM
ejpam-2422	334	14	433	433	NUM
ejpam-2422	334	15	428	428	NUM
ejpam-2422	334	16	this	this	PRON
ejpam-2422	334	17	is	be	AUX
ejpam-2422	334	18	to	to	PART
ejpam-2422	334	19	say	say	VERB
ejpam-2422	334	20	tut	tut	PROPN
ejpam-2422	334	21	≥	≥	NOUN
ejpam-2422	334	22	t	t	NOUN
ejpam-2422	334	23	.	.	PUNCT
ejpam-2422	335	1	on	on	ADP
ejpam-2422	335	2	the	the	DET
ejpam-2422	335	3	other	other	ADJ
ejpam-2422	335	4	hand	hand	NOUN
ejpam-2422	335	5	,	,	PUNCT
ejpam-2422	335	6	we	we	PRON
ejpam-2422	335	7	have	have	VERB
ejpam-2422	335	8	(	(	PUNCT
ejpam-2422	335	9	tut	tut	NOUN
ejpam-2422	335	10	)	)	PUNCT
ejpam-2422	336	1	k	k	PROPN
ejpam-2422	336	2	(	(	PUNCT
ejpam-2422	336	3	f	f	NOUN
ejpam-2422	336	4	)	)	PUNCT
ejpam-2422	337	1	=	=	PUNCT
ejpam-2422	337	2	∧	∧	PROPN
ejpam-2422	337	3	p	p	NOUN
ejpam-2422	337	4	6v	6v	X
ejpam-2422	337	5	f	f	PROPN
ejpam-2422	337	6	∨	∨	NUM
ejpam-2422	337	7	p	p	PROPN
ejpam-2422	337	8	6vλ/	6vλ/	NUM
ejpam-2422	337	9	(	(	PUNCT
ejpam-2422	337	10	f	f	PROPN
ejpam-2422	337	11	)	)	PUNCT
ejpam-2422	337	12	∨	∨	X
ejpam-2422	337	13	{	{	PUNCT
ejpam-2422	337	14	n	n	CCONJ
ejpam-2422	337	15	∧	∧	PROPN
ejpam-2422	337	16	i=1	i=1	PROPN
ejpam-2422	337	17	tk(gi	tk(gi	PROPN
ejpam-2422	337	18	)	)	PUNCT
ejpam-2422	338	1	|	|	ADV
ejpam-2422	338	2	λ≥∆n	λ≥∆n	PROPN
ejpam-2422	338	3	i=1λg	i=1λg	VERB
ejpam-2422	338	4	′i	′i	NOUN
ejpam-2422	338	5	,	,	PUNCT
ejpam-2422	338	6	n	n	PRON
ejpam-2422	338	7	∈	∈	PROPN
ejpam-2422	338	8	n	n	CCONJ
ejpam-2422	338	9	}	}	PUNCT
ejpam-2422	338	10	≤	≤	NUM
ejpam-2422	338	11	∧	∧	PROPN
ejpam-2422	338	12	p	p	NOUN
ejpam-2422	338	13	6v	6v	NOUN
ejpam-2422	338	14	f	f	PROPN
ejpam-2422	338	15	∨	∨	NUM
ejpam-2422	338	16	p	p	PROPN
ejpam-2422	338	17	6vλ/	6vλ/	NUM
ejpam-2422	338	18	(	(	PUNCT
ejpam-2422	338	19	f	f	PROPN
ejpam-2422	338	20	)	)	PUNCT
ejpam-2422	338	21	∨	∨	X
ejpam-2422	338	22	{	{	PUNCT
ejpam-2422	338	23	n	n	CCONJ
ejpam-2422	338	24	∧	∧	PROPN
ejpam-2422	338	25	i=1	i=1	PROPN
ejpam-2422	338	26	tk(gi	tk(gi	PROPN
ejpam-2422	338	27	)	)	PUNCT
ejpam-2422	339	1	|	|	ADV
ejpam-2422	339	2	λ/	λ/	PROPN
ejpam-2422	339	3	≥∆n	≥∆n	NOUN
ejpam-2422	339	4	i=1λ	i=1λ	PROPN
ejpam-2422	339	5	/	/	SYM
ejpam-2422	339	6	g	g	NOUN
ejpam-2422	339	7	′i	′i	NOUN
ejpam-2422	339	8	,	,	PUNCT
ejpam-2422	339	9	n	n	X
ejpam-2422	339	10	∈	∈	PROPN
ejpam-2422	339	11	n	n	CCONJ
ejpam-2422	339	12	}	}	PUNCT
ejpam-2422	339	13	≤	≤	NUM
ejpam-2422	339	14	∧	∧	PROPN
ejpam-2422	339	15	p	p	NOUN
ejpam-2422	339	16	6v	6v	NOUN
ejpam-2422	339	17	f	f	PROPN
ejpam-2422	339	18	∨	∨	NUM
ejpam-2422	339	19	p	p	PROPN
ejpam-2422	339	20	6vλ/	6vλ/	NUM
ejpam-2422	339	21	(	(	PUNCT
ejpam-2422	339	22	f	f	PROPN
ejpam-2422	339	23	)	)	PUNCT
ejpam-2422	339	24	∨	∨	X
ejpam-2422	339	25	{	{	PUNCT
ejpam-2422	339	26	n	n	CCONJ
ejpam-2422	339	27	∧	∧	PROPN
ejpam-2422	339	28	i=1	i=1	PROPN
ejpam-2422	339	29	tk(gi	tk(gi	PROPN
ejpam-2422	339	30	)	)	PUNCT
ejpam-2422	340	1	|	|	ADV
ejpam-2422	340	2	λ/	λ/	ADJ
ejpam-2422	340	3	(	(	PUNCT
ejpam-2422	340	4	f	f	X
ejpam-2422	340	5	)	)	PUNCT
ejpam-2422	340	6	≥∆n	≥∆n	PROPN
ejpam-2422	340	7	i=1λg	i=1λg	VERB
ejpam-2422	340	8	′i	′i	NOUN
ejpam-2422	340	9	(	(	PUNCT
ejpam-2422	340	10	f	f	PROPN
ejpam-2422	340	11	)	)	PUNCT
ejpam-2422	340	12	,	,	PUNCT
ejpam-2422	340	13	n	n	PROPN
ejpam-2422	340	14	∈	∈	PROPN
ejpam-2422	340	15	n	n	CCONJ
ejpam-2422	340	16	}	}	PUNCT
ejpam-2422	340	17	≤	≤	NUM
ejpam-2422	340	18	∧	∧	PROPN
ejpam-2422	340	19	p	p	NOUN
ejpam-2422	340	20	6v	6v	X
ejpam-2422	340	21	f	f	PROPN
ejpam-2422	340	22	∨	∨	NUM
ejpam-2422	340	23	{	{	PUNCT
ejpam-2422	340	24	tk(um	tk(um	NOUN
ejpam-2422	340	25	j=1	j=1	NOUN
ejpam-2422	340	26	g	g	PROPN
ejpam-2422	340	27	j	j	PROPN
ejpam-2422	340	28	)	)	PUNCT
ejpam-2422	341	1	|	|	ADV
ejpam-2422	341	2	p	p	NOUN
ejpam-2422	341	3	6v	6v	NUM
ejpam-2422	341	4	um	um	INTJ
ejpam-2422	341	5	j=1	j=1	PROPN
ejpam-2422	341	6	g	g	PROPN
ejpam-2422	341	7	j	j	PROPN
ejpam-2422	341	8	w	w	PROPN
ejpam-2422	341	9	f	f	PROPN
ejpam-2422	341	10	,	,	PUNCT
ejpam-2422	342	1	m	m	PROPN
ejpam-2422	342	2	∈	∈	PROPN
ejpam-2422	342	3	n	n	CCONJ
ejpam-2422	342	4	}	}	PUNCT
ejpam-2422	342	5	≤	≤	NUM
ejpam-2422	342	6	∧	∧	PROPN
ejpam-2422	342	7	p	p	NOUN
ejpam-2422	342	8	6v	6v	X
ejpam-2422	342	9	f	f	PROPN
ejpam-2422	342	10	∨	∨	NUM
ejpam-2422	342	11	{	{	PUNCT
ejpam-2422	342	12	tk(g	tk(g	NOUN
ejpam-2422	342	13	)	)	PUNCT
ejpam-2422	343	1	|	|	ADV
ejpam-2422	343	2	p	p	NOUN
ejpam-2422	343	3	6v	6v	VERB
ejpam-2422	343	4	g	g	PROPN
ejpam-2422	343	5	w	w	PROPN
ejpam-2422	343	6	f	f	PROPN
ejpam-2422	343	7	}	}	PUNCT
ejpam-2422	343	8	=	=	SYM
ejpam-2422	343	9	tk	tk	PROPN
ejpam-2422	343	10	(	(	PUNCT
ejpam-2422	343	11	f	f	PROPN
ejpam-2422	343	12	)	)	PUNCT
ejpam-2422	343	13	.	.	PUNCT
ejpam-2422	344	1	this	this	PRON
ejpam-2422	344	2	completes	complete	VERB
ejpam-2422	344	3	the	the	DET
ejpam-2422	344	4	proof	proof	NOUN
ejpam-2422	344	5	.	.	PUNCT
ejpam-2422	345	1	theorem	theorem	ADJ
ejpam-2422	345	2	5	5	NUM
ejpam-2422	345	3	.	.	PUNCT
ejpam-2422	346	1	if	if	SCONJ
ejpam-2422	346	2	ϕψ	ϕψ	PROPN
ejpam-2422	346	3	,	,	PUNCT
ejpam-2422	346	4	η	η	PROPN
ejpam-2422	346	5	:	:	PUNCT
ejpam-2422	346	6	(	(	PUNCT
ejpam-2422	346	7	x1,u	x1,u	PROPN
ejpam-2422	346	8	1)→	1)→	NUM
ejpam-2422	346	9	(	(	PUNCT
ejpam-2422	346	10	x2,u	x2,u	NOUN
ejpam-2422	346	11	2	2	NUM
ejpam-2422	346	12	)	)	PUNCT
ejpam-2422	346	13	is	be	AUX
ejpam-2422	346	14	quasi	quasi	ADJ
ejpam-2422	346	15	uniformly	uniformly	ADV
ejpam-2422	346	16	continuous	continuous	ADJ
ejpam-2422	346	17	,	,	PUNCT
ejpam-2422	346	18	then	then	ADV
ejpam-2422	346	19	ϕψ	ϕψ	INTJ
ejpam-2422	346	20	,	,	PUNCT
ejpam-2422	346	21	η	η	PROPN
ejpam-2422	346	22	:	:	PUNCT
ejpam-2422	346	23	(	(	PUNCT
ejpam-2422	346	24	x1,tu	x1,tu	PROPN
ejpam-2422	346	25	1)→	1)→	NUM
ejpam-2422	346	26	(	(	PUNCT
ejpam-2422	346	27	x2,tu	x2,tu	NOUN
ejpam-2422	346	28	2	2	NUM
ejpam-2422	346	29	)	)	PUNCT
ejpam-2422	346	30	is	be	AUX
ejpam-2422	346	31	fuzzy	fuzzy	ADJ
ejpam-2422	346	32	soft	soft	ADJ
ejpam-2422	346	33	continuous	continuous	ADJ
ejpam-2422	346	34	.	.	PUNCT
ejpam-2422	347	1	proof	proof	NOUN
ejpam-2422	347	2	.	.	PUNCT
ejpam-2422	348	1	let	let	VERB
ejpam-2422	348	2	g	g	PROPN
ejpam-2422	348	3	∈	∈	PROPN
ejpam-2422	348	4	(	(	PUNCT
ejpam-2422	348	5	lx2)e2	lx2)e2	PROPN
ejpam-2422	348	6	,	,	PUNCT
ejpam-2422	348	7	k	k	PROPN
ejpam-2422	348	8	∈	∈	PROPN
ejpam-2422	348	9	k1	k1	NOUN
ejpam-2422	348	10	and	and	CCONJ
ejpam-2422	348	11	α	α	PRON
ejpam-2422	348	12	ã	ã	X
ejpam-2422	348	13	(	(	PUNCT
ejpam-2422	348	14	tu	tu	PROPN
ejpam-2422	348	15	2)η(k)(g	2)η(k)(g	NUM
ejpam-2422	348	16	)	)	PUNCT
ejpam-2422	348	17	.	.	PUNCT
ejpam-2422	349	1	since	since	SCONJ
ejpam-2422	349	2	ϕψ	ϕψ	PROPN
ejpam-2422	349	3	,	,	PUNCT
ejpam-2422	349	4	η	η	PROPN
ejpam-2422	349	5	:	:	PUNCT
ejpam-2422	349	6	(	(	PUNCT
ejpam-2422	349	7	x1,u	x1,u	PROPN
ejpam-2422	349	8	1)→	1)→	NUM
ejpam-2422	349	9	(	(	PUNCT
ejpam-2422	349	10	x2,u	x2,u	NOUN
ejpam-2422	349	11	2	2	NUM
ejpam-2422	349	12	)	)	PUNCT
ejpam-2422	349	13	is	be	AUX
ejpam-2422	349	14	quasi	quasi	ADJ
ejpam-2422	349	15	uniformly	uniformly	ADV
ejpam-2422	349	16	continuous	continuous	ADJ
ejpam-2422	349	17	,	,	PUNCT
ejpam-2422	349	18	we	we	PRON
ejpam-2422	349	19	have	have	VERB
ejpam-2422	349	20	u	u	PROPN
ejpam-2422	349	21	1	1	NUM
ejpam-2422	349	22	k	k	X
ejpam-2422	349	23	(	(	PUNCT
ejpam-2422	349	24	ϕ	ϕ	X
ejpam-2422	349	25	⇐	⇐	PROPN
ejpam-2422	349	26	ψ	ψ	X
ejpam-2422	349	27	(	(	PUNCT
ejpam-2422	349	28	µ	µ	NOUN
ejpam-2422	349	29	)	)	PUNCT
ejpam-2422	349	30	)	)	PUNCT
ejpam-2422	349	31	≥	≥	NOUN
ejpam-2422	349	32	u	u	NOUN
ejpam-2422	349	33	2	2	NUM
ejpam-2422	349	34	η(k)(µ	η(k)(µ	NUM
ejpam-2422	349	35	)	)	PUNCT
ejpam-2422	349	36	for	for	ADP
ejpam-2422	349	37	all	all	DET
ejpam-2422	349	38	µ	µ	PRON
ejpam-2422	349	39	∈	∈	NOUN
ejpam-2422	349	40	h	h	NOUN
ejpam-2422	349	41	(	(	PUNCT
ejpam-2422	349	42	x2	x2	PROPN
ejpam-2422	349	43	,	,	PUNCT
ejpam-2422	349	44	e2	e2	PROPN
ejpam-2422	349	45	)	)	PUNCT
ejpam-2422	349	46	,	,	PUNCT
ejpam-2422	349	47	k	k	PROPN
ejpam-2422	349	48	∈	∈	PROPN
ejpam-2422	349	49	k1	k1	PROPN
ejpam-2422	349	50	.	.	PUNCT
ejpam-2422	350	1	hence	hence	ADV
ejpam-2422	350	2	,	,	PUNCT
ejpam-2422	350	3	αã	αã	INTJ
ejpam-2422	350	4	(	(	PUNCT
ejpam-2422	350	5	tu	tu	PROPN
ejpam-2422	350	6	2)η(k)(g	2)η(k)(g	NUM
ejpam-2422	350	7	)	)	PUNCT
ejpam-2422	350	8	=	=	SYM
ejpam-2422	350	9	∧	∧	PROPN
ejpam-2422	350	10	p	p	PROPN
ejpam-2422	350	11	6vg	6vg	ADJ
ejpam-2422	350	12	∨	∨	PROPN
ejpam-2422	350	13	p	p	PROPN
ejpam-2422	350	14	6vλ/(g	6vλ/(g	PROPN
ejpam-2422	350	15	)	)	PUNCT
ejpam-2422	350	16	u	u	NOUN
ejpam-2422	350	17	2	2	NUM
ejpam-2422	350	18	η(k)(λ)≤	η(k)(λ)≤	PROPN
ejpam-2422	350	19	∧	∧	PROPN
ejpam-2422	350	20	p	p	PROPN
ejpam-2422	350	21	6vg	6vg	ADJ
ejpam-2422	350	22	∨	∨	PROPN
ejpam-2422	350	23	p	p	PROPN
ejpam-2422	350	24	6vλ/(g	6vλ/(g	PROPN
ejpam-2422	350	25	)	)	PUNCT
ejpam-2422	350	26	u	u	NOUN
ejpam-2422	350	27	1	1	NUM
ejpam-2422	350	28	k	k	X
ejpam-2422	350	29	(	(	PUNCT
ejpam-2422	350	30	ϕ	ϕ	X
ejpam-2422	350	31	⇐	⇐	PROPN
ejpam-2422	350	32	ψ	ψ	X
ejpam-2422	350	33	(	(	PUNCT
ejpam-2422	350	34	λ	λ	NOUN
ejpam-2422	350	35	)	)	PUNCT
ejpam-2422	350	36	)	)	PUNCT
ejpam-2422	350	37	.	.	PUNCT
ejpam-2422	351	1	noting	note	VERB
ejpam-2422	351	2	that	that	SCONJ
ejpam-2422	351	3	ϕ→	ϕ→	PROPN
ejpam-2422	351	4	ψ	ψ	X
ejpam-2422	351	5	(	(	PUNCT
ejpam-2422	351	6	h	h	NOUN
ejpam-2422	351	7	)	)	PUNCT
ejpam-2422	351	8	6v	6v	NOUN
ejpam-2422	351	9	g	g	NOUN
ejpam-2422	351	10	when	when	SCONJ
ejpam-2422	351	11	h	h	PROPN
ejpam-2422	351	12	6v	6v	VERB
ejpam-2422	351	13	ϕ←	ϕ←	NOUN
ejpam-2422	351	14	ψ	ψ	X
ejpam-2422	351	15	(	(	PUNCT
ejpam-2422	351	16	g	g	NOUN
ejpam-2422	351	17	)	)	PUNCT
ejpam-2422	351	18	,	,	PUNCT
ejpam-2422	351	19	we	we	PRON
ejpam-2422	351	20	can	can	AUX
ejpam-2422	351	21	find	find	VERB
ejpam-2422	351	22	some	some	DET
ejpam-2422	351	23	λ(h	λ(h	ADJ
ejpam-2422	351	24	)	)	PUNCT
ejpam-2422	351	25	∈	∈	PROPN
ejpam-2422	351	26	h	h	NOUN
ejpam-2422	351	27	(	(	PUNCT
ejpam-2422	351	28	x2	x2	PROPN
ejpam-2422	351	29	,	,	PUNCT
ejpam-2422	351	30	e2	e2	PROPN
ejpam-2422	351	31	)	)	PUNCT
ejpam-2422	351	32	such	such	ADJ
ejpam-2422	351	33	that	that	SCONJ
ejpam-2422	351	34	ϕ→	ϕ→	PROPN
ejpam-2422	351	35	ψ	ψ	X
ejpam-2422	351	36	(	(	PUNCT
ejpam-2422	351	37	h	h	NOUN
ejpam-2422	351	38	)	)	PUNCT
ejpam-2422	351	39	6v	6v	NOUN
ejpam-2422	351	40	λ(h)(g	λ(h)(g	NUM
ejpam-2422	351	41	)	)	PUNCT
ejpam-2422	351	42	and	and	CCONJ
ejpam-2422	351	43	α	α	PRON
ejpam-2422	351	44	≤	≤	NOUN
ejpam-2422	351	45	u	u	NOUN
ejpam-2422	351	46	1	1	NUM
ejpam-2422	351	47	k	k	X
ejpam-2422	351	48	(	(	PUNCT
ejpam-2422	351	49	ϕ	ϕ	X
ejpam-2422	351	50	⇐	⇐	PROPN
ejpam-2422	351	51	ψ	ψ	X
ejpam-2422	351	52	(	(	PUNCT
ejpam-2422	351	53	λ(h	λ(h	NOUN
ejpam-2422	351	54	)	)	PUNCT
ejpam-2422	351	55	)	)	PUNCT
ejpam-2422	351	56	)	)	PUNCT
ejpam-2422	351	57	.	.	PUNCT
ejpam-2422	352	1	now	now	ADV
ejpam-2422	352	2	let	let	VERB
ejpam-2422	352	3	ν(h	ν(h	PROPN
ejpam-2422	352	4	)	)	PUNCT
ejpam-2422	352	5	=	=	PUNCT
ejpam-2422	353	1	ϕ	ϕ	PRON
ejpam-2422	353	2	⇐	⇐	NOUN
ejpam-2422	353	3	ψ	ψ	X
ejpam-2422	353	4	(	(	PUNCT
ejpam-2422	353	5	λ(h	λ(h	NOUN
ejpam-2422	353	6	)	)	PUNCT
ejpam-2422	353	7	)	)	PUNCT
ejpam-2422	353	8	.	.	PUNCT
ejpam-2422	354	1	then	then	ADV
ejpam-2422	354	2	ν(h	ν(h	PROPN
ejpam-2422	354	3	)	)	PUNCT
ejpam-2422	354	4	∈	∈	PROPN
ejpam-2422	354	5	h	h	NOUN
ejpam-2422	354	6	(	(	PUNCT
ejpam-2422	354	7	x1	x1	PROPN
ejpam-2422	354	8	,	,	PUNCT
ejpam-2422	354	9	e1	e1	PROPN
ejpam-2422	354	10	)	)	PUNCT
ejpam-2422	354	11	and	and	CCONJ
ejpam-2422	354	12	h	h	NOUN
ejpam-2422	354	13	6v	6v	NOUN
ejpam-2422	354	14	ν/(h)(ϕ	ν/(h)(ϕ	PART
ejpam-2422	354	15	←	←	PROPN
ejpam-2422	354	16	ψ	ψ	X
ejpam-2422	354	17	(	(	PUNCT
ejpam-2422	354	18	g	g	NOUN
ejpam-2422	354	19	)	)	PUNCT
ejpam-2422	354	20	)	)	PUNCT
ejpam-2422	354	21	.	.	PUNCT
ejpam-2422	355	1	hence	hence	ADV
ejpam-2422	355	2	,	,	PUNCT
ejpam-2422	355	3	α≤	α≤	PROPN
ejpam-2422	355	4	∧	∧	PROPN
ejpam-2422	355	5	h	h	NOUN
ejpam-2422	355	6	6vϕ←	6vϕ←	NUM
ejpam-2422	355	7	ψ	ψ	X
ejpam-2422	355	8	(	(	PUNCT
ejpam-2422	355	9	g	g	NOUN
ejpam-2422	355	10	)	)	PUNCT
ejpam-2422	355	11	u	u	NOUN
ejpam-2422	355	12	1	1	NUM
ejpam-2422	355	13	k	k	NOUN
ejpam-2422	355	14	(	(	PUNCT
ejpam-2422	355	15	ν(h))≤	ν(h))≤	ADJ
ejpam-2422	355	16	∧	∧	PROPN
ejpam-2422	355	17	h	h	NOUN
ejpam-2422	355	18	6vϕ←	6vϕ←	NUM
ejpam-2422	355	19	ψ	ψ	X
ejpam-2422	355	20	(	(	PUNCT
ejpam-2422	355	21	g	g	NOUN
ejpam-2422	355	22	)	)	PUNCT
ejpam-2422	355	23	∨	∨	NUM
ejpam-2422	355	24	h	h	NOUN
ejpam-2422	355	25	6vν/(ϕ←	6vν/(ϕ←	NUM
ejpam-2422	355	26	ψ	ψ	X
ejpam-2422	355	27	(	(	PUNCT
ejpam-2422	355	28	g	g	NOUN
ejpam-2422	355	29	)	)	PUNCT
ejpam-2422	355	30	)	)	PUNCT
ejpam-2422	355	31	u	u	NOUN
ejpam-2422	355	32	1	1	NUM
ejpam-2422	355	33	k	k	X
ejpam-2422	355	34	(	(	PUNCT
ejpam-2422	355	35	ν	ν	NOUN
ejpam-2422	355	36	)	)	PUNCT
ejpam-2422	355	37	=	=	SYM
ejpam-2422	355	38	(	(	PUNCT
ejpam-2422	355	39	tu	tu	PROPN
ejpam-2422	355	40	1)k(ϕ	1)k(ϕ	NUM
ejpam-2422	355	41	←	←	PROPN
ejpam-2422	355	42	ψ	ψ	X
ejpam-2422	355	43	(	(	PUNCT
ejpam-2422	355	44	g	g	NOUN
ejpam-2422	355	45	)	)	PUNCT
ejpam-2422	355	46	)	)	PUNCT
ejpam-2422	355	47	.	.	PUNCT
ejpam-2422	356	1	therefore	therefore	ADV
ejpam-2422	356	2	,	,	PUNCT
ejpam-2422	356	3	(	(	PUNCT
ejpam-2422	356	4	tu	tu	PROPN
ejpam-2422	356	5	2)η(k)(g)≤	2)η(k)(g)≤	NUM
ejpam-2422	356	6	(	(	PUNCT
ejpam-2422	356	7	tu	tu	PROPN
ejpam-2422	356	8	1)k(ϕ←ψ	1)k(ϕ←ψ	PROPN
ejpam-2422	356	9	(	(	PUNCT
ejpam-2422	356	10	g	g	NOUN
ejpam-2422	356	11	)	)	PUNCT
ejpam-2422	356	12	)	)	PUNCT
ejpam-2422	356	13	from	from	ADP
ejpam-2422	356	14	the	the	DET
ejpam-2422	356	15	arbitrariness	arbitrariness	NOUN
ejpam-2422	356	16	of	of	ADP
ejpam-2422	356	17	α	α	NOUN
ejpam-2422	356	18	.	.	PUNCT
ejpam-2422	357	1	so	so	ADV
ejpam-2422	357	2	,	,	PUNCT
ejpam-2422	357	3	ϕψ	ϕψ	INTJ
ejpam-2422	357	4	,	,	PUNCT
ejpam-2422	357	5	η	η	PROPN
ejpam-2422	357	6	:	:	PUNCT
ejpam-2422	357	7	(	(	PUNCT
ejpam-2422	357	8	x1,tu	x1,tu	PROPN
ejpam-2422	357	9	1)→	1)→	NUM
ejpam-2422	357	10	(	(	PUNCT
ejpam-2422	357	11	x2,tu	x2,tu	NOUN
ejpam-2422	357	12	2	2	NUM
ejpam-2422	357	13	)	)	PUNCT
ejpam-2422	357	14	is	be	AUX
ejpam-2422	357	15	fuzzy	fuzzy	ADJ
ejpam-2422	357	16	soft	soft	ADJ
ejpam-2422	357	17	continuous	continuous	ADJ
ejpam-2422	357	18	.	.	PUNCT
ejpam-2422	358	1	theorem	theorem	NOUN
ejpam-2422	358	2	6	6	NUM
ejpam-2422	358	3	.	.	PUNCT
ejpam-2422	359	1	if	if	SCONJ
ejpam-2422	359	2	ϕψ	ϕψ	PROPN
ejpam-2422	359	3	,	,	PUNCT
ejpam-2422	359	4	η	η	PROPN
ejpam-2422	359	5	:	:	PUNCT
ejpam-2422	359	6	(	(	PUNCT
ejpam-2422	359	7	x1,t	x1,t	PROPN
ejpam-2422	359	8	1)→	1)→	NUM
ejpam-2422	359	9	(	(	PUNCT
ejpam-2422	359	10	x2,t	x2,t	PROPN
ejpam-2422	359	11	2	2	NUM
ejpam-2422	359	12	)	)	PUNCT
ejpam-2422	359	13	is	be	AUX
ejpam-2422	359	14	fuzzy	fuzzy	ADJ
ejpam-2422	359	15	soft	soft	ADJ
ejpam-2422	359	16	continuous	continuous	ADJ
ejpam-2422	359	17	,	,	PUNCT
ejpam-2422	359	18	then	then	ADV
ejpam-2422	359	19	ϕψ	ϕψ	INTJ
ejpam-2422	359	20	,	,	PUNCT
ejpam-2422	359	21	η	η	PROPN
ejpam-2422	359	22	:	:	PUNCT
ejpam-2422	359	23	(	(	PUNCT
ejpam-2422	359	24	x1,ut	x1,ut	PROPN
ejpam-2422	359	25	1)→	1)→	NUM
ejpam-2422	359	26	(	(	PUNCT
ejpam-2422	359	27	x2,ut	x2,ut	PROPN
ejpam-2422	359	28	2	2	NUM
ejpam-2422	359	29	)	)	PUNCT
ejpam-2422	359	30	is	be	AUX
ejpam-2422	359	31	quasi	quasi	ADJ
ejpam-2422	359	32	uniformly	uniformly	ADV
ejpam-2422	359	33	continuous	continuous	ADJ
ejpam-2422	359	34	.	.	PUNCT
ejpam-2422	360	1	proof	proof	NOUN
ejpam-2422	360	2	.	.	PUNCT
ejpam-2422	361	1	let	let	VERB
ejpam-2422	361	2	ϕψ	ϕψ	INTJ
ejpam-2422	361	3	,	,	PUNCT
ejpam-2422	361	4	η	η	PROPN
ejpam-2422	361	5	:	:	PUNCT
ejpam-2422	361	6	(	(	PUNCT
ejpam-2422	361	7	x1,t	x1,t	PROPN
ejpam-2422	361	8	1)→	1)→	NUM
ejpam-2422	361	9	(	(	PUNCT
ejpam-2422	361	10	x2,t	x2,t	PROPN
ejpam-2422	361	11	2	2	NUM
ejpam-2422	361	12	)	)	PUNCT
ejpam-2422	361	13	be	be	AUX
ejpam-2422	361	14	continuous	continuous	ADJ
ejpam-2422	361	15	.	.	PUNCT
ejpam-2422	362	1	from	from	ADP
ejpam-2422	362	2	the	the	DET
ejpam-2422	362	3	definition	definition	NOUN
ejpam-2422	362	4	ofut	ofut	NOUN
ejpam-2422	362	5	1	1	NUM
ejpam-2422	362	6	,	,	PUNCT
ejpam-2422	362	7	we	we	PRON
ejpam-2422	362	8	know	know	VERB
ejpam-2422	362	9	that	that	SCONJ
ejpam-2422	362	10	for	for	ADP
ejpam-2422	362	11	each	each	DET
ejpam-2422	362	12	k	k	PROPN
ejpam-2422	362	13	∈	∈	PROPN
ejpam-2422	362	14	k	k	X
ejpam-2422	362	15	,	,	PUNCT
ejpam-2422	362	16	(	(	PUNCT
ejpam-2422	362	17	ut	ut	PROPN
ejpam-2422	362	18	2)η(k)(λ	2)η(k)(λ	NUM
ejpam-2422	362	19	)	)	PUNCT
ejpam-2422	363	1	=	=	SYM
ejpam-2422	363	2	∨	∨	X
ejpam-2422	363	3	{	{	PUNCT
ejpam-2422	363	4	∧n	∧n	X
ejpam-2422	363	5	i=1	i=1	PROPN
ejpam-2422	363	6	t	t	PROPN
ejpam-2422	363	7	2	2	NUM
ejpam-2422	363	8	η(k)(gi	η(k)(gi	PROPN
ejpam-2422	363	9	)	)	PUNCT
ejpam-2422	364	1	|	|	ADV
ejpam-2422	364	2	λ	λ	X
ejpam-2422	364	3	≥	≥	PROPN
ejpam-2422	364	4	∆n	∆n	PROPN
ejpam-2422	364	5	i=1λg	i=1λg	VERB
ejpam-2422	364	6	′i	′i	NOUN
ejpam-2422	364	7	,	,	PUNCT
ejpam-2422	364	8	n	n	PRON
ejpam-2422	364	9	∈	∈	PROPN
ejpam-2422	364	10	n	n	CCONJ
ejpam-2422	364	11	}	}	PUNCT
ejpam-2422	364	12	.	.	PUNCT
ejpam-2422	365	1	moreover	moreover	ADV
ejpam-2422	365	2	,	,	PUNCT
ejpam-2422	365	3	if	if	SCONJ
ejpam-2422	365	4	λ≥∆n	λ≥∆n	PROPN
ejpam-2422	365	5	i=1λg	i=1λg	VERB
ejpam-2422	365	6	′i	′i	NOUN
ejpam-2422	365	7	,	,	PUNCT
ejpam-2422	365	8	then	then	ADV
ejpam-2422	365	9	we	we	PRON
ejpam-2422	365	10	have	have	VERB
ejpam-2422	365	11	ϕ	ϕ	NOUN
ejpam-2422	365	12	⇐	⇐	NOUN
ejpam-2422	365	13	ψ	ψ	X
ejpam-2422	365	14	(	(	PUNCT
ejpam-2422	365	15	λ)≥	λ)≥	NOUN
ejpam-2422	365	16	ϕ	ϕ	NOUN
ejpam-2422	365	17	⇐	⇐	PROPN
ejpam-2422	365	18	ψ	ψ	X
ejpam-2422	365	19	(	(	PUNCT
ejpam-2422	365	20	∆	∆	PROPN
ejpam-2422	365	21	n	n	PART
ejpam-2422	365	22	i=1λg	i=1λg	VERB
ejpam-2422	365	23	′i	′i	PROPN
ejpam-2422	365	24	)	)	PUNCT
ejpam-2422	365	25	=	=	SYM
ejpam-2422	365	26	n	n	NUM
ejpam-2422	365	27	∧	∧	PROPN
ejpam-2422	365	28	i=1	i=1	PROPN
ejpam-2422	366	1	(	(	PUNCT
ejpam-2422	366	2	ϕ	ϕ	NOUN
ejpam-2422	366	3	⇐	⇐	NOUN
ejpam-2422	366	4	ψ	ψ	X
ejpam-2422	366	5	(	(	PUNCT
ejpam-2422	366	6	λ(g	λ(g	NOUN
ejpam-2422	366	7	′	′	NUM
ejpam-2422	366	8	i	i	NOUN
ejpam-2422	366	9	)	)	PUNCT
ejpam-2422	366	10	)	)	PUNCT
ejpam-2422	366	11	)	)	PUNCT
ejpam-2422	367	1	=	=	PUNCT
ejpam-2422	368	1	n	n	NUM
ejpam-2422	368	2	∧	∧	PROPN
ejpam-2422	368	3	i=1	i=1	PROPN
ejpam-2422	368	4	λϕ←	λϕ←	NOUN
ejpam-2422	368	5	ψ	ψ	X
ejpam-2422	368	6	(	(	PUNCT
ejpam-2422	368	7	gi)′	gi)′	PROPN
ejpam-2422	368	8	.	.	PUNCT
ejpam-2422	369	1	v.	v.	ADP
ejpam-2422	369	2	çetkin	çetkin	PROPN
ejpam-2422	369	3	,	,	PUNCT
ejpam-2422	369	4	h.	h.	PROPN
ejpam-2422	369	5	aygün	aygün	PROPN
ejpam-2422	369	6	/	/	SYM
ejpam-2422	369	7	eur	eur	PROPN
ejpam-2422	369	8	.	.	PUNCT
ejpam-2422	370	1	j.	j.	PROPN
ejpam-2422	370	2	pure	pure	PROPN
ejpam-2422	370	3	appl	appl	PROPN
ejpam-2422	370	4	.	.	PROPN
ejpam-2422	370	5	math	math	PROPN
ejpam-2422	370	6	,	,	PUNCT
ejpam-2422	370	7	9	9	NUM
ejpam-2422	370	8	(	(	PUNCT
ejpam-2422	370	9	2016	2016	NUM
ejpam-2422	370	10	)	)	PUNCT
ejpam-2422	370	11	,	,	PUNCT
ejpam-2422	370	12	419	419	NUM
ejpam-2422	370	13	-	-	SYM
ejpam-2422	370	14	433	433	NUM
ejpam-2422	370	15	429	429	NUM
ejpam-2422	370	16	sinceϕψ	sinceϕψ	NOUN
ejpam-2422	370	17	,	,	PUNCT
ejpam-2422	370	18	η	η	NOUN
ejpam-2422	370	19	:	:	PUNCT
ejpam-2422	370	20	(	(	PUNCT
ejpam-2422	370	21	x1,t	x1,t	PROPN
ejpam-2422	370	22	1)→	1)→	NUM
ejpam-2422	370	23	(	(	PUNCT
ejpam-2422	370	24	x2,t	x2,t	PROPN
ejpam-2422	370	25	2	2	NUM
ejpam-2422	370	26	)	)	PUNCT
ejpam-2422	370	27	is	be	AUX
ejpam-2422	370	28	continuous	continuous	ADJ
ejpam-2422	370	29	,	,	PUNCT
ejpam-2422	370	30	we	we	PRON
ejpam-2422	370	31	have	have	VERB
ejpam-2422	370	32	∧n	∧n	X
ejpam-2422	370	33	i=1	i=1	ADP
ejpam-2422	370	34	t	t	PROPN
ejpam-2422	370	35	2	2	NUM
ejpam-2422	370	36	η(k)(gi)≤	η(k)(gi)≤	NOUN
ejpam-2422	370	37	∧n	∧n	ADP
ejpam-2422	370	38	i=1	i=1	PROPN
ejpam-2422	370	39	t	t	PROPN
ejpam-2422	370	40	1	1	NUM
ejpam-2422	370	41	k	k	X
ejpam-2422	370	42	(	(	PUNCT
ejpam-2422	370	43	ϕ	ϕ	PROPN
ejpam-2422	370	44	←	←	PROPN
ejpam-2422	370	45	ψ	ψ	X
ejpam-2422	370	46	(	(	PUNCT
ejpam-2422	370	47	gi	gi	INTJ
ejpam-2422	370	48	)	)	PUNCT
ejpam-2422	370	49	)	)	PUNCT
ejpam-2422	370	50	.	.	PUNCT
ejpam-2422	371	1	hence	hence	ADV
ejpam-2422	371	2	,	,	PUNCT
ejpam-2422	371	3	(	(	PUNCT
ejpam-2422	371	4	ut	ut	PROPN
ejpam-2422	371	5	2)η(k)(λ)≥	2)η(k)(λ)≥	PROPN
ejpam-2422	371	6	(	(	PUNCT
ejpam-2422	371	7	ut	ut	PROPN
ejpam-2422	371	8	1)k(ϕ	1)k(ϕ	NUM
ejpam-2422	371	9	⇐	⇐	PROPN
ejpam-2422	371	10	ψ	ψ	X
ejpam-2422	371	11	(	(	PUNCT
ejpam-2422	371	12	λ	λ	NOUN
ejpam-2422	371	13	)	)	PUNCT
ejpam-2422	371	14	)	)	PUNCT
ejpam-2422	371	15	.	.	PUNCT
ejpam-2422	372	1	therefore	therefore	ADV
ejpam-2422	372	2	,	,	PUNCT
ejpam-2422	372	3	ϕψ	ϕψ	INTJ
ejpam-2422	372	4	,	,	PUNCT
ejpam-2422	372	5	η	η	PROPN
ejpam-2422	372	6	:	:	PUNCT
ejpam-2422	372	7	(	(	PUNCT
ejpam-2422	372	8	x1,ut	x1,ut	PROPN
ejpam-2422	372	9	1)→	1)→	NUM
ejpam-2422	372	10	(	(	PUNCT
ejpam-2422	372	11	x2,ut	x2,ut	PROPN
ejpam-2422	372	12	2	2	NUM
ejpam-2422	372	13	)	)	PUNCT
ejpam-2422	372	14	is	be	AUX
ejpam-2422	372	15	quasi	quasi	ADJ
ejpam-2422	372	16	uniformly	uniformly	ADV
ejpam-2422	372	17	continuous	continuous	ADJ
ejpam-2422	372	18	.	.	PUNCT
ejpam-2422	373	1	theorem	theorem	ADJ
ejpam-2422	373	2	7	7	NUM
ejpam-2422	373	3	.	.	PUNCT
ejpam-2422	374	1	let	let	VERB
ejpam-2422	374	2	g	g	NOUN
ejpam-2422	374	3	:	:	PUNCT
ejpam-2422	374	4	fsctop(l	fsctop(l	NOUN
ejpam-2422	374	5	,	,	PUNCT
ejpam-2422	374	6	m)→	m)→	VERB
ejpam-2422	374	7	hfsu(l	hfsu(l	PROPN
ejpam-2422	374	8	,	,	PUNCT
ejpam-2422	374	9	m	m	VERB
ejpam-2422	374	10	)	)	PUNCT
ejpam-2422	374	11	be	be	AUX
ejpam-2422	374	12	defined	define	VERB
ejpam-2422	374	13	by	by	ADP
ejpam-2422	374	14	g((x	g((x	NOUN
ejpam-2422	374	15	,	,	PUNCT
ejpam-2422	374	16	t	t	NOUN
ejpam-2422	374	17	)	)	PUNCT
ejpam-2422	374	18	)	)	PUNCT
ejpam-2422	375	1	=	=	PUNCT
ejpam-2422	375	2	(	(	PUNCT
ejpam-2422	375	3	x	x	INTJ
ejpam-2422	375	4	,	,	PUNCT
ejpam-2422	375	5	ut	ut	PROPN
ejpam-2422	375	6	)	)	PUNCT
ejpam-2422	375	7	.	.	PUNCT
ejpam-2422	376	1	then	then	ADV
ejpam-2422	376	2	g	g	PROPN
ejpam-2422	376	3	is	be	AUX
ejpam-2422	376	4	an	an	DET
ejpam-2422	376	5	embedding	embed	VERB
ejpam-2422	376	6	functor	functor	NOUN
ejpam-2422	376	7	from	from	ADP
ejpam-2422	376	8	fsctop(l	fsctop(l	PROPN
ejpam-2422	376	9	,	,	PUNCT
ejpam-2422	376	10	m	m	NOUN
ejpam-2422	376	11	)	)	PUNCT
ejpam-2422	376	12	to	to	PART
ejpam-2422	376	13	hfsu(l	hfsu(l	PROPN
ejpam-2422	376	14	,	,	PUNCT
ejpam-2422	376	15	m	m	PROPN
ejpam-2422	376	16	)	)	PUNCT
ejpam-2422	376	17	.	.	PUNCT
ejpam-2422	377	1	5	5	X
ejpam-2422	377	2	.	.	X
ejpam-2422	377	3	category	category	NOUN
ejpam-2422	377	4	of	of	ADP
ejpam-2422	377	5	fuzzy	fuzzy	ADJ
ejpam-2422	377	6	soft	soft	ADJ
ejpam-2422	377	7	uniform	uniform	ADJ
ejpam-2422	377	8	spaces	space	NOUN
ejpam-2422	377	9	in	in	ADP
ejpam-2422	377	10	this	this	DET
ejpam-2422	377	11	section	section	NOUN
ejpam-2422	377	12	,	,	PUNCT
ejpam-2422	377	13	we	we	PRON
ejpam-2422	377	14	will	will	AUX
ejpam-2422	377	15	show	show	VERB
ejpam-2422	377	16	that	that	SCONJ
ejpam-2422	377	17	the	the	DET
ejpam-2422	377	18	category	category	NOUN
ejpam-2422	377	19	hfsu(l	hfsu(l	NOUN
ejpam-2422	377	20	,	,	PUNCT
ejpam-2422	377	21	m	m	PROPN
ejpam-2422	377	22	)	)	PUNCT
ejpam-2422	377	23	of	of	ADP
ejpam-2422	377	24	(	(	PUNCT
ejpam-2422	377	25	l	l	NOUN
ejpam-2422	377	26	,	,	PUNCT
ejpam-2422	377	27	m)-fuzzy	m)-fuzzy	X
ejpam-2422	377	28	(	(	PUNCT
ejpam-2422	377	29	e	e	NOUN
ejpam-2422	377	30	,	,	PUNCT
ejpam-2422	377	31	k)-soft	k)-soft	PROPN
ejpam-2422	377	32	uniform	uniform	ADJ
ejpam-2422	377	33	spaces	space	NOUN
ejpam-2422	377	34	and	and	CCONJ
ejpam-2422	377	35	continuous	continuous	ADJ
ejpam-2422	377	36	functions	function	NOUN
ejpam-2422	377	37	is	be	AUX
ejpam-2422	377	38	a	a	DET
ejpam-2422	377	39	topological	topological	ADJ
ejpam-2422	377	40	category	category	NOUN
ejpam-2422	377	41	over	over	ADP
ejpam-2422	377	42	set3	set3	PROPN
ejpam-2422	377	43	.	.	PUNCT
ejpam-2422	378	1	theorem	theorem	ADJ
ejpam-2422	378	2	8	8	NUM
ejpam-2422	378	3	.	.	PUNCT
ejpam-2422	379	1	let	let	VERB
ejpam-2422	379	2	{	{	PUNCT
ejpam-2422	379	3	(	(	PUNCT
ejpam-2422	379	4	x	x	PROPN
ejpam-2422	379	5	i	i	PRON
ejpam-2422	379	6	,	,	PUNCT
ejpam-2422	379	7	u	u	PRON
ejpam-2422	379	8	i)}i∈γ	i)}i∈γ	PROPN
ejpam-2422	379	9	be	be	VERB
ejpam-2422	379	10	a	a	DET
ejpam-2422	379	11	family	family	NOUN
ejpam-2422	379	12	of	of	ADP
ejpam-2422	379	13	(	(	PUNCT
ejpam-2422	379	14	l	l	NOUN
ejpam-2422	379	15	,	,	PUNCT
ejpam-2422	379	16	m)-fuzzy	m)-fuzzy	X
ejpam-2422	379	17	(	(	PUNCT
ejpam-2422	379	18	ei	ei	X
ejpam-2422	379	19	,	,	PUNCT
ejpam-2422	379	20	ki)-soft	ki)-soft	PROPN
ejpam-2422	379	21	uniform	uniform	NOUN
ejpam-2422	379	22	spaces	space	VERB
ejpam-2422	379	23	,	,	PUNCT
ejpam-2422	379	24	x	x	ADJ
ejpam-2422	379	25	be	be	AUX
ejpam-2422	379	26	a	a	DET
ejpam-2422	379	27	set	set	NOUN
ejpam-2422	379	28	,	,	PUNCT
ejpam-2422	379	29	e	e	X
ejpam-2422	379	30	,	,	PUNCT
ejpam-2422	379	31	k	k	X
ejpam-2422	379	32	be	be	VERB
ejpam-2422	379	33	the	the	DET
ejpam-2422	379	34	parameter	parameter	NOUN
ejpam-2422	379	35	sets	set	NOUN
ejpam-2422	379	36	and	and	CCONJ
ejpam-2422	379	37	for	for	ADP
ejpam-2422	379	38	each	each	DET
ejpam-2422	379	39	i	i	PRON
ejpam-2422	379	40	∈	∈	PROPN
ejpam-2422	379	41	γ	γ	X
ejpam-2422	379	42	,	,	PUNCT
ejpam-2422	379	43	ϕi	ϕi	ADP
ejpam-2422	379	44	:	:	PUNCT
ejpam-2422	379	45	x	x	X
ejpam-2422	379	46	→	→	PUNCT
ejpam-2422	379	47	x	x	PUNCT
ejpam-2422	379	48	i	i	PRON
ejpam-2422	379	49	,	,	PUNCT
ejpam-2422	379	50	ψi	ψi	ADP
ejpam-2422	379	51	:	:	PUNCT
ejpam-2422	379	52	e→	e→	NOUN
ejpam-2422	379	53	ei	ei	PROPN
ejpam-2422	379	54	and	and	CCONJ
ejpam-2422	379	55	ηi	ηi	INTJ
ejpam-2422	379	56	:	:	PUNCT
ejpam-2422	379	57	k	k	PROPN
ejpam-2422	379	58	→	→	PUNCT
ejpam-2422	379	59	ki	ki	PROPN
ejpam-2422	379	60	be	be	AUX
ejpam-2422	379	61	a	a	DET
ejpam-2422	379	62	function	function	NOUN
ejpam-2422	379	63	.	.	PUNCT
ejpam-2422	380	1	we	we	PRON
ejpam-2422	380	2	define	define	VERB
ejpam-2422	380	3	the	the	DET
ejpam-2422	380	4	mapping	mapping	NOUN
ejpam-2422	380	5	u	u	NOUN
ejpam-2422	380	6	:	:	PUNCT
ejpam-2422	380	7	k	k	PROPN
ejpam-2422	380	8	→	→	SYM
ejpam-2422	380	9	mh	mh	PROPN
ejpam-2422	380	10	(	(	PUNCT
ejpam-2422	380	11	x	x	X
ejpam-2422	380	12	,	,	PUNCT
ejpam-2422	380	13	e	e	NOUN
ejpam-2422	380	14	)	)	PUNCT
ejpam-2422	380	15	by	by	ADP
ejpam-2422	380	16	:	:	PUNCT
ejpam-2422	380	17	uk(λ	uk(λ	NOUN
ejpam-2422	380	18	)	)	PUNCT
ejpam-2422	380	19	=	=	SYM
ejpam-2422	380	20	∨	∨	X
ejpam-2422	380	21	{	{	PUNCT
ejpam-2422	380	22	n	n	CCONJ
ejpam-2422	380	23	∧	∧	PROPN
ejpam-2422	380	24	j=1	j=1	NOUN
ejpam-2422	380	25	u	u	NOUN
ejpam-2422	381	1	i	i	PRON
ejpam-2422	381	2	j	j	PROPN
ejpam-2422	381	3	ηi	ηi	PROPN
ejpam-2422	381	4	j	j	PROPN
ejpam-2422	381	5	(	(	PUNCT
ejpam-2422	381	6	k)(λi	k)(λi	PROPN
ejpam-2422	381	7	j	j	PROPN
ejpam-2422	381	8	)	)	PUNCT
ejpam-2422	382	1	|∆n	|∆n	PROPN
ejpam-2422	382	2	j=1(ϕψ	j=1(ϕψ	PROPN
ejpam-2422	382	3	)	)	PUNCT
ejpam-2422	383	1	⇐	⇐	INTJ
ejpam-2422	383	2	i	i	PRON
ejpam-2422	383	3	j	j	PROPN
ejpam-2422	383	4	(	(	PUNCT
ejpam-2422	383	5	λi	λi	ADP
ejpam-2422	383	6	j	j	PROPN
ejpam-2422	383	7	)	)	PUNCT
ejpam-2422	383	8	≤	≤	PROPN
ejpam-2422	383	9	λ	λ	PROPN
ejpam-2422	383	10	}	}	PUNCT
ejpam-2422	383	11	,	,	PUNCT
ejpam-2422	383	12	for	for	ADP
ejpam-2422	383	13	each	each	DET
ejpam-2422	383	14	k	k	PROPN
ejpam-2422	383	15	∈	∈	PROPN
ejpam-2422	383	16	k	k	NOUN
ejpam-2422	383	17	,	,	PUNCT
ejpam-2422	383	18	where	where	SCONJ
ejpam-2422	383	19	∨	∨	NOUN
ejpam-2422	383	20	is	be	AUX
ejpam-2422	383	21	taken	take	VERB
ejpam-2422	383	22	over	over	ADP
ejpam-2422	383	23	the	the	DET
ejpam-2422	383	24	finite	finite	ADJ
ejpam-2422	383	25	index	index	NOUN
ejpam-2422	383	26	set	set	NOUN
ejpam-2422	383	27	{	{	PUNCT
ejpam-2422	383	28	i1	i1	PROPN
ejpam-2422	383	29	,	,	PUNCT
ejpam-2422	383	30	.	.	PUNCT
ejpam-2422	383	31	.	.	PUNCT
ejpam-2422	384	1	.	.	PUNCT
ejpam-2422	385	1	,	,	PUNCT
ejpam-2422	385	2	in	in	ADP
ejpam-2422	385	3	}	}	PUNCT
ejpam-2422	385	4	⊆	⊆	NUM
ejpam-2422	385	5	γ	γ	X
ejpam-2422	385	6	.	.	PROPN
ejpam-2422	386	1	then	then	ADV
ejpam-2422	386	2	the	the	DET
ejpam-2422	386	3	following	follow	VERB
ejpam-2422	386	4	items	item	NOUN
ejpam-2422	386	5	are	be	AUX
ejpam-2422	386	6	satisfied	satisfied	ADJ
ejpam-2422	386	7	.	.	PUNCT
ejpam-2422	387	1	(	(	PUNCT
ejpam-2422	387	2	1	1	X
ejpam-2422	387	3	)	)	PUNCT
ejpam-2422	387	4	u	u	NOUN
ejpam-2422	387	5	is	be	AUX
ejpam-2422	387	6	the	the	DET
ejpam-2422	387	7	coarsest	coarse	ADJ
ejpam-2422	387	8	(	(	PUNCT
ejpam-2422	387	9	l	l	NOUN
ejpam-2422	387	10	,	,	PUNCT
ejpam-2422	387	11	m)-fuzzy	m)-fuzzy	X
ejpam-2422	387	12	(	(	PUNCT
ejpam-2422	387	13	e	e	NOUN
ejpam-2422	387	14	,	,	PUNCT
ejpam-2422	387	15	k)-soft	k)-soft	NOUN
ejpam-2422	387	16	uniformity	uniformity	NOUN
ejpam-2422	387	17	on	on	ADP
ejpam-2422	387	18	x	x	PUNCT
ejpam-2422	387	19	for	for	ADP
ejpam-2422	387	20	which	which	PRON
ejpam-2422	387	21	each	each	DET
ejpam-2422	387	22	(	(	PUNCT
ejpam-2422	387	23	ϕψ	ϕψ	INTJ
ejpam-2422	387	24	,	,	PUNCT
ejpam-2422	387	25	η)i	η)i	ADJ
ejpam-2422	387	26	is	be	AUX
ejpam-2422	387	27	uniformly	uniformly	ADV
ejpam-2422	387	28	continuous	continuous	ADJ
ejpam-2422	387	29	function	function	NOUN
ejpam-2422	387	30	.	.	PUNCT
ejpam-2422	388	1	(	(	PUNCT
ejpam-2422	388	2	2	2	X
ejpam-2422	388	3	)	)	PUNCT
ejpam-2422	388	4	a	a	DET
ejpam-2422	388	5	function	function	NOUN
ejpam-2422	388	6	ϕψ	ϕψ	ADP
ejpam-2422	388	7	,	,	PUNCT
ejpam-2422	388	8	η	η	PROPN
ejpam-2422	388	9	:	:	PUNCT
ejpam-2422	388	10	(	(	PUNCT
ejpam-2422	388	11	z	z	NOUN
ejpam-2422	388	12	,	,	PUNCT
ejpam-2422	388	13	v	v	NOUN
ejpam-2422	388	14	)	)	PUNCT
ejpam-2422	388	15	→	→	SYM
ejpam-2422	388	16	(	(	PUNCT
ejpam-2422	388	17	x	x	X
ejpam-2422	388	18	,	,	PUNCT
ejpam-2422	388	19	u	u	NOUN
ejpam-2422	388	20	)	)	PUNCT
ejpam-2422	388	21	is	be	AUX
ejpam-2422	388	22	uniformly	uniformly	ADV
ejpam-2422	388	23	continuous	continuous	ADJ
ejpam-2422	388	24	iff	iff	PROPN
ejpam-2422	388	25	(	(	PUNCT
ejpam-2422	388	26	ϕψ	ϕψ	INTJ
ejpam-2422	388	27	,	,	PUNCT
ejpam-2422	388	28	η)i	η)i	ADJ
ejpam-2422	388	29	◦	◦	NOUN
ejpam-2422	388	30	ϕψ	ϕψ	PROPN
ejpam-2422	388	31	,	,	PUNCT
ejpam-2422	388	32	η	η	PROPN
ejpam-2422	388	33	:	:	PUNCT
ejpam-2422	388	34	(	(	PUNCT
ejpam-2422	388	35	z	z	NOUN
ejpam-2422	388	36	,	,	PUNCT
ejpam-2422	388	37	v	v	NOUN
ejpam-2422	388	38	)	)	PUNCT
ejpam-2422	388	39	→	→	SYM
ejpam-2422	388	40	(	(	PUNCT
ejpam-2422	388	41	x	x	X
ejpam-2422	388	42	i	i	PRON
ejpam-2422	388	43	,	,	PUNCT
ejpam-2422	388	44	u	u	PROPN
ejpam-2422	388	45	i	i	PROPN
ejpam-2422	388	46	)	)	PUNCT
ejpam-2422	388	47	is	be	AUX
ejpam-2422	388	48	uniformly	uniformly	ADV
ejpam-2422	388	49	continuous	continuous	ADJ
ejpam-2422	388	50	for	for	ADP
ejpam-2422	388	51	all	all	DET
ejpam-2422	388	52	i	i	PRON
ejpam-2422	388	53	∈	∈	PROPN
ejpam-2422	388	54	γ	γ	X
ejpam-2422	388	55	.	.	PUNCT
ejpam-2422	388	56	proof	proof	NOUN
ejpam-2422	388	57	.	.	PUNCT
ejpam-2422	389	1	(	(	PUNCT
ejpam-2422	389	2	1	1	X
ejpam-2422	389	3	)	)	PUNCT
ejpam-2422	389	4	firstly	firstly	ADV
ejpam-2422	389	5	,	,	PUNCT
ejpam-2422	389	6	we	we	PRON
ejpam-2422	389	7	will	will	AUX
ejpam-2422	389	8	prove	prove	VERB
ejpam-2422	389	9	that	that	SCONJ
ejpam-2422	389	10	u	u	NOUN
ejpam-2422	389	11	is	be	AUX
ejpam-2422	389	12	an	an	DET
ejpam-2422	389	13	(	(	PUNCT
ejpam-2422	389	14	l	l	NOUN
ejpam-2422	389	15	,	,	PUNCT
ejpam-2422	389	16	m)-fuzzy	m)-fuzzy	X
ejpam-2422	389	17	(	(	PUNCT
ejpam-2422	389	18	e	e	NOUN
ejpam-2422	389	19	,	,	PUNCT
ejpam-2422	389	20	k)-soft	k)-soft	NOUN
ejpam-2422	389	21	uniformity	uniformity	NOUN
ejpam-2422	389	22	on	on	ADP
ejpam-2422	389	23	x	x	X
ejpam-2422	389	24	.	.	PUNCT
ejpam-2422	390	1	(	(	PUNCT
ejpam-2422	390	2	u1	u1	NOUN
ejpam-2422	390	3	)	)	PUNCT
ejpam-2422	390	4	and	and	CCONJ
ejpam-2422	390	5	(	(	PUNCT
ejpam-2422	390	6	u3	u3	NOUN
ejpam-2422	390	7	)	)	PUNCT
ejpam-2422	390	8	are	be	AUX
ejpam-2422	390	9	clear	clear	ADJ
ejpam-2422	390	10	.	.	PUNCT
ejpam-2422	391	1	(	(	PUNCT
ejpam-2422	391	2	u2	u2	NOUN
ejpam-2422	391	3	):	):	PUNCT
ejpam-2422	391	4	suppose	suppose	VERB
ejpam-2422	391	5	there	there	PRON
ejpam-2422	391	6	exist	exist	VERB
ejpam-2422	391	7	λ,µ	λ,µ	NOUN
ejpam-2422	391	8	∈h	∈h	NOUN
ejpam-2422	391	9	(	(	PUNCT
ejpam-2422	391	10	x	x	X
ejpam-2422	391	11	,	,	PUNCT
ejpam-2422	391	12	e	e	NOUN
ejpam-2422	391	13	)	)	PUNCT
ejpam-2422	391	14	and	and	CCONJ
ejpam-2422	391	15	k	k	PROPN
ejpam-2422	391	16	∈	∈	PROPN
ejpam-2422	391	17	k	k	PROPN
ejpam-2422	391	18	s.t	s.t	PROPN
ejpam-2422	391	19	.	.	PUNCT
ejpam-2422	391	20	uk(λ∆µ	uk(λ∆µ	PROPN
ejpam-2422	391	21	)	)	PUNCT
ejpam-2422	391	22	6≥	6≥	NUM
ejpam-2422	391	23	uk(λ)∧uk(µ	uk(λ)∧uk(µ	PROPN
ejpam-2422	391	24	)	)	PUNCT
ejpam-2422	391	25	.	.	PUNCT
ejpam-2422	392	1	by	by	ADP
ejpam-2422	392	2	the	the	DET
ejpam-2422	392	3	definition	definition	NOUN
ejpam-2422	392	4	of	of	ADP
ejpam-2422	392	5	u	u	NOUN
ejpam-2422	392	6	,	,	PUNCT
ejpam-2422	392	7	there	there	PRON
ejpam-2422	392	8	exist	exist	VERB
ejpam-2422	392	9	finite	finite	ADJ
ejpam-2422	392	10	index	index	NOUN
ejpam-2422	392	11	sets	set	NOUN
ejpam-2422	392	12	{	{	PUNCT
ejpam-2422	392	13	i1	i1	NOUN
ejpam-2422	392	14	,	,	PUNCT
ejpam-2422	392	15	.	.	PUNCT
ejpam-2422	392	16	.	.	PUNCT
ejpam-2422	393	1	.	.	PUNCT
ejpam-2422	394	1	,	,	PUNCT
ejpam-2422	394	2	in	in	ADP
ejpam-2422	394	3	}	}	PUNCT
ejpam-2422	394	4	,	,	PUNCT
ejpam-2422	394	5	{	{	PUNCT
ejpam-2422	394	6	j1	j1	PROPN
ejpam-2422	394	7	,	,	PUNCT
ejpam-2422	394	8	.	.	PUNCT
ejpam-2422	394	9	.	.	PUNCT
ejpam-2422	394	10	.	.	PUNCT
ejpam-2422	395	1	,	,	PUNCT
ejpam-2422	395	2	jm	jm	NOUN
ejpam-2422	395	3	}	}	PUNCT
ejpam-2422	395	4	⊆	⊆	NUM
ejpam-2422	395	5	γ	γ	NOUN
ejpam-2422	395	6	such	such	ADJ
ejpam-2422	395	7	that	that	DET
ejpam-2422	395	8	uk(λ∆µ	uk(λ∆µ	NOUN
ejpam-2422	395	9	)	)	PUNCT
ejpam-2422	395	10	6≥	6≥	NUM
ejpam-2422	395	11	�	�	PROPN
ejpam-2422	395	12	∧n	∧n	PRON
ejpam-2422	395	13	r=1u	r=1u	ADJ
ejpam-2422	395	14	ir	ir	NOUN
ejpam-2422	395	15	ηir	ηir	NOUN
ejpam-2422	395	16	(	(	PUNCT
ejpam-2422	395	17	k	k	NOUN
ejpam-2422	395	18	)	)	PUNCT
ejpam-2422	395	19	(	(	PUNCT
ejpam-2422	395	20	λir	λir	NOUN
ejpam-2422	395	21	)	)	PUNCT
ejpam-2422	395	22	�	�	PROPN
ejpam-2422	395	23	∧	∧	PROPN
ejpam-2422	395	24	�	�	PROPN
ejpam-2422	395	25	∧m	∧m	PROPN
ejpam-2422	395	26	s=1u	s=1u	VERB
ejpam-2422	395	27	js	js	PROPN
ejpam-2422	395	28	η	η	PROPN
ejpam-2422	395	29	js	js	PROPN
ejpam-2422	395	30	(	(	PUNCT
ejpam-2422	395	31	k	k	NOUN
ejpam-2422	395	32	)	)	PUNCT
ejpam-2422	395	33	(	(	PUNCT
ejpam-2422	395	34	µ	µ	X
ejpam-2422	395	35	js	js	ADJ
ejpam-2422	395	36	)	)	PUNCT
ejpam-2422	395	37	�	�	PROPN
ejpam-2422	395	38	where	where	SCONJ
ejpam-2422	395	39	∆n	∆n	PROPN
ejpam-2422	395	40	r=1(ϕψ	r=1(ϕψ	NOUN
ejpam-2422	395	41	)	)	PUNCT
ejpam-2422	395	42	⇐	⇐	PROPN
ejpam-2422	395	43	ir	ir	PROPN
ejpam-2422	395	44	(	(	PUNCT
ejpam-2422	395	45	λir	λir	NOUN
ejpam-2422	395	46	)	)	PUNCT
ejpam-2422	395	47	≤	≤	NOUN
ejpam-2422	395	48	λ	λ	PROPN
ejpam-2422	395	49	and	and	CCONJ
ejpam-2422	395	50	∆m	∆m	PROPN
ejpam-2422	395	51	s=1(ϕψ	s=1(ϕψ	NOUN
ejpam-2422	395	52	)	)	PUNCT
ejpam-2422	395	53	⇐	⇐	ADJ
ejpam-2422	395	54	js	js	PROPN
ejpam-2422	395	55	(	(	PUNCT
ejpam-2422	395	56	µ	µ	X
ejpam-2422	395	57	js)≤	js)≤	X
ejpam-2422	395	58	µ.	µ.	NOUN
ejpam-2422	395	59	since	since	SCONJ
ejpam-2422	395	60	(	(	PUNCT
ejpam-2422	395	61	∆n	∆n	PROPN
ejpam-2422	395	62	r=1(ϕψ	r=1(ϕψ	NOUN
ejpam-2422	395	63	)	)	PUNCT
ejpam-2422	395	64	⇐	⇐	PROPN
ejpam-2422	395	65	ir	ir	PROPN
ejpam-2422	395	66	(	(	PUNCT
ejpam-2422	395	67	λir	λir	NOUN
ejpam-2422	395	68	)	)	PUNCT
ejpam-2422	395	69	)	)	PUNCT
ejpam-2422	395	70	∆(∆	∆(∆	NOUN
ejpam-2422	395	71	m	m	VERB
ejpam-2422	395	72	s=1(ϕψ	s=1(ϕψ	PRON
ejpam-2422	395	73	)	)	PUNCT
ejpam-2422	395	74	⇐	⇐	ADJ
ejpam-2422	395	75	js	js	PROPN
ejpam-2422	395	76	(	(	PUNCT
ejpam-2422	395	77	µ	µ	X
ejpam-2422	395	78	js))≤	js))≤	X
ejpam-2422	395	79	λ∆µ.	λ∆µ.	ADV
ejpam-2422	395	80	by	by	ADP
ejpam-2422	395	81	proposition	proposition	NOUN
ejpam-2422	395	82	2	2	NUM
ejpam-2422	395	83	(	(	PUNCT
ejpam-2422	395	84	vii	vii	PROPN
ejpam-2422	395	85	)	)	PUNCT
ejpam-2422	395	86	,	,	PUNCT
ejpam-2422	395	87	we	we	PRON
ejpam-2422	395	88	have	have	VERB
ejpam-2422	395	89	uk(λ∆µ)≥	uk(λ∆µ)≥	PROPN
ejpam-2422	395	90	�	�	PROPN
ejpam-2422	395	91	∧n	∧n	PRON
ejpam-2422	395	92	r=1u	r=1u	ADJ
ejpam-2422	395	93	ir	ir	NOUN
ejpam-2422	395	94	ηir	ηir	NOUN
ejpam-2422	395	95	(	(	PUNCT
ejpam-2422	395	96	k	k	NOUN
ejpam-2422	395	97	)	)	PUNCT
ejpam-2422	395	98	(	(	PUNCT
ejpam-2422	395	99	λir	λir	NOUN
ejpam-2422	395	100	)	)	PUNCT
ejpam-2422	395	101	�	�	PROPN
ejpam-2422	395	102	∧	∧	PROPN
ejpam-2422	395	103	�	�	PROPN
ejpam-2422	395	104	∧m	∧m	PROPN
ejpam-2422	395	105	s=1u	s=1u	VERB
ejpam-2422	395	106	js	js	PROPN
ejpam-2422	395	107	η	η	PROPN
ejpam-2422	395	108	js	js	PROPN
ejpam-2422	395	109	(	(	PUNCT
ejpam-2422	395	110	k	k	NOUN
ejpam-2422	395	111	)	)	PUNCT
ejpam-2422	395	112	(	(	PUNCT
ejpam-2422	395	113	µ	µ	X
ejpam-2422	395	114	js	js	ADJ
ejpam-2422	395	115	)	)	PUNCT
ejpam-2422	395	116	�	�	PROPN
ejpam-2422	395	117	.	.	PUNCT
ejpam-2422	396	1	this	this	PRON
ejpam-2422	396	2	is	be	AUX
ejpam-2422	396	3	a	a	DET
ejpam-2422	396	4	contradiction	contradiction	NOUN
ejpam-2422	396	5	.	.	PUNCT
ejpam-2422	397	1	hence	hence	ADV
ejpam-2422	397	2	for	for	ADP
ejpam-2422	397	3	each	each	DET
ejpam-2422	397	4	k	k	PROPN
ejpam-2422	397	5	∈	∈	PROPN
ejpam-2422	397	6	k	k	PROPN
ejpam-2422	397	7	and	and	CCONJ
ejpam-2422	397	8	λ,µ	λ,µ	VERB
ejpam-2422	397	9	∈h	∈h	NOUN
ejpam-2422	397	10	(	(	PUNCT
ejpam-2422	397	11	x	x	X
ejpam-2422	397	12	,	,	PUNCT
ejpam-2422	397	13	e	e	NOUN
ejpam-2422	397	14	)	)	PUNCT
ejpam-2422	397	15	,	,	PUNCT
ejpam-2422	397	16	we	we	PRON
ejpam-2422	397	17	obtain	obtain	VERB
ejpam-2422	397	18	uk(λ∆µ)≥uk(λ)∧uk(µ	uk(λ∆µ)≥uk(λ)∧uk(µ	PROPN
ejpam-2422	397	19	)	)	PUNCT
ejpam-2422	397	20	.	.	PUNCT
ejpam-2422	398	1	(	(	PUNCT
ejpam-2422	398	2	u4	u4	NOUN
ejpam-2422	398	3	):	):	PUNCT
ejpam-2422	398	4	suppose	suppose	VERB
ejpam-2422	398	5	there	there	PRON
ejpam-2422	398	6	exist	exist	VERB
ejpam-2422	398	7	k	k	PROPN
ejpam-2422	398	8	∈	∈	PROPN
ejpam-2422	398	9	k	k	PROPN
ejpam-2422	398	10	and	and	CCONJ
ejpam-2422	398	11	λ	λ	PROPN
ejpam-2422	398	12	∈h	∈h	NOUN
ejpam-2422	398	13	(	(	PUNCT
ejpam-2422	398	14	x	x	X
ejpam-2422	398	15	,	,	PUNCT
ejpam-2422	398	16	e	e	NOUN
ejpam-2422	398	17	)	)	PUNCT
ejpam-2422	398	18	such	such	ADJ
ejpam-2422	398	19	that	that	SCONJ
ejpam-2422	398	20	uk(λ	uk(λ	NOUN
ejpam-2422	398	21	)	)	PUNCT
ejpam-2422	398	22	6≤	6≤	NUM
ejpam-2422	398	23	∨	∨	NOUN
ejpam-2422	398	24	{	{	PUNCT
ejpam-2422	398	25	uk(µ	uk(µ	PROPN
ejpam-2422	398	26	)	)	PUNCT
ejpam-2422	398	27	|	|	ADV
ejpam-2422	398	28	µ	µ	DET
ejpam-2422	398	29	◦	◦	NOUN
ejpam-2422	398	30	µ≤	µ≤	ADJ
ejpam-2422	398	31	λ	λ	NOUN
ejpam-2422	398	32	}	}	PUNCT
ejpam-2422	398	33	.	.	PUNCT
ejpam-2422	399	1	by	by	ADP
ejpam-2422	399	2	the	the	DET
ejpam-2422	399	3	definition	definition	NOUN
ejpam-2422	399	4	of	of	ADP
ejpam-2422	399	5	uk(λ	uk(λ	NOUN
ejpam-2422	399	6	)	)	PUNCT
ejpam-2422	399	7	,	,	PUNCT
ejpam-2422	399	8	there	there	PRON
ejpam-2422	399	9	exists	exist	VERB
ejpam-2422	399	10	a	a	DET
ejpam-2422	399	11	finite	finite	ADJ
ejpam-2422	399	12	index	index	NOUN
ejpam-2422	399	13	set	set	VERB
ejpam-2422	399	14	j	j	PROPN
ejpam-2422	399	15	=	=	PUNCT
ejpam-2422	399	16	{	{	PUNCT
ejpam-2422	399	17	i1	i1	PROPN
ejpam-2422	399	18	,	,	PUNCT
ejpam-2422	399	19	.	.	PUNCT
ejpam-2422	399	20	.	.	PUNCT
ejpam-2422	400	1	.	.	PUNCT
ejpam-2422	401	1	,	,	PUNCT
ejpam-2422	401	2	in	in	ADP
ejpam-2422	401	3	}	}	PUNCT
ejpam-2422	401	4	⊆	⊆	NUM
ejpam-2422	401	5	γ	γ	NOUN
ejpam-2422	401	6	such	such	ADJ
ejpam-2422	401	7	that	that	SCONJ
ejpam-2422	401	8	∧n	∧n	PRON
ejpam-2422	401	9	j=1u	j=1u	NOUN
ejpam-2422	402	1	i	i	PRON
ejpam-2422	402	2	j	j	PROPN
ejpam-2422	403	1	ηi	ηi	PROPN
ejpam-2422	403	2	j	j	PROPN
ejpam-2422	403	3	(	(	PUNCT
ejpam-2422	403	4	k)(λi	k)(λi	PROPN
ejpam-2422	403	5	j	j	PROPN
ejpam-2422	403	6	)	)	PUNCT
ejpam-2422	403	7	6≤	6≤	NUM
ejpam-2422	403	8	∨	∨	NOUN
ejpam-2422	403	9	{	{	PUNCT
ejpam-2422	403	10	uk(µ	uk(µ	PROPN
ejpam-2422	403	11	)	)	PUNCT
ejpam-2422	403	12	|	|	ADV
ejpam-2422	403	13	µ	µ	X
ejpam-2422	403	14	◦	◦	NOUN
ejpam-2422	403	15	µ	µ	PRON
ejpam-2422	403	16	≤	≤	X
ejpam-2422	403	17	λ	λ	NOUN
ejpam-2422	403	18	}	}	PUNCT
ejpam-2422	403	19	,	,	PUNCT
ejpam-2422	403	20	where	where	SCONJ
ejpam-2422	403	21	∆n	∆n	PROPN
ejpam-2422	403	22	j=1(ϕψ	j=1(ϕψ	NOUN
ejpam-2422	403	23	)	)	PUNCT
ejpam-2422	404	1	⇐	⇐	INTJ
ejpam-2422	405	1	i	i	PRON
ejpam-2422	405	2	j	j	PROPN
ejpam-2422	405	3	(	(	PUNCT
ejpam-2422	405	4	λi	λi	ADP
ejpam-2422	405	5	j	j	PROPN
ejpam-2422	405	6	)	)	PUNCT
ejpam-2422	405	7	≤	≤	PROPN
ejpam-2422	405	8	λ	λ	PROPN
ejpam-2422	405	9	.	.	PUNCT
ejpam-2422	406	1	since	since	SCONJ
ejpam-2422	406	2	(	(	PUNCT
ejpam-2422	406	3	x	x	X
ejpam-2422	406	4	i	i	PRON
ejpam-2422	406	5	j	j	PROPN
ejpam-2422	406	6	,	,	PUNCT
ejpam-2422	406	7	u	u	PROPN
ejpam-2422	406	8	i	i	PROPN
ejpam-2422	406	9	j	j	PROPN
ejpam-2422	406	10	)	)	PUNCT
ejpam-2422	406	11	is	be	AUX
ejpam-2422	406	12	an	an	DET
ejpam-2422	406	13	v.	v.	X
ejpam-2422	406	14	çetkin	çetkin	NOUN
ejpam-2422	406	15	,	,	PUNCT
ejpam-2422	406	16	h.	h.	PROPN
ejpam-2422	406	17	aygün	aygün	PROPN
ejpam-2422	406	18	/	/	SYM
ejpam-2422	406	19	eur	eur	PROPN
ejpam-2422	406	20	.	.	PUNCT
ejpam-2422	407	1	j.	j.	PROPN
ejpam-2422	407	2	pure	pure	PROPN
ejpam-2422	407	3	appl	appl	PROPN
ejpam-2422	407	4	.	.	PROPN
ejpam-2422	407	5	math	math	PROPN
ejpam-2422	407	6	,	,	PUNCT
ejpam-2422	407	7	9	9	NUM
ejpam-2422	407	8	(	(	PUNCT
ejpam-2422	407	9	2016	2016	NUM
ejpam-2422	407	10	)	)	PUNCT
ejpam-2422	407	11	,	,	PUNCT
ejpam-2422	407	12	419	419	NUM
ejpam-2422	407	13	-	-	SYM
ejpam-2422	407	14	433	433	NUM
ejpam-2422	407	15	430	430	NUM
ejpam-2422	407	16	(	(	PUNCT
ejpam-2422	407	17	l	l	NOUN
ejpam-2422	407	18	,	,	PUNCT
ejpam-2422	407	19	m)-fuzzy	m)-fuzzy	X
ejpam-2422	407	20	(	(	PUNCT
ejpam-2422	407	21	ei	ei	PROPN
ejpam-2422	407	22	j	j	PROPN
ejpam-2422	407	23	,	,	PUNCT
ejpam-2422	407	24	ki	ki	PROPN
ejpam-2422	407	25	j	j	PROPN
ejpam-2422	407	26	)	)	PUNCT
ejpam-2422	407	27	-soft	-soft	ADJ
ejpam-2422	407	28	uniformity	uniformity	NOUN
ejpam-2422	407	29	for	for	ADP
ejpam-2422	407	30	each	each	DET
ejpam-2422	407	31	i	i	PRON
ejpam-2422	407	32	j	j	PROPN
ejpam-2422	407	33	∈	∈	PROPN
ejpam-2422	407	34	{	{	PUNCT
ejpam-2422	407	35	i1	i1	PROPN
ejpam-2422	407	36	,	,	PUNCT
ejpam-2422	407	37	.	.	PUNCT
ejpam-2422	407	38	.	.	PUNCT
ejpam-2422	408	1	.	.	PUNCT
ejpam-2422	409	1	,	,	PUNCT
ejpam-2422	409	2	in	in	ADP
ejpam-2422	409	3	}	}	PUNCT
ejpam-2422	409	4	,	,	PUNCT
ejpam-2422	409	5	by	by	ADP
ejpam-2422	409	6	definition	definition	NOUN
ejpam-2422	409	7	5	5	NUM
ejpam-2422	409	8	,	,	PUNCT
ejpam-2422	409	9	u	u	NOUN
ejpam-2422	410	1	i	i	PRON
ejpam-2422	410	2	j	j	PROPN
ejpam-2422	410	3	ηi	ηi	PROPN
ejpam-2422	410	4	j	j	PROPN
ejpam-2422	410	5	(	(	PUNCT
ejpam-2422	410	6	k)(λi	k)(λi	PROPN
ejpam-2422	410	7	j	j	PROPN
ejpam-2422	410	8	)	)	PUNCT
ejpam-2422	410	9	≤	≤	PROPN
ejpam-2422	410	10	∨	∨	NUM
ejpam-2422	410	11	{	{	PUNCT
ejpam-2422	410	12	u	u	NOUN
ejpam-2422	411	1	i	i	NOUN
ejpam-2422	411	2	j	j	PROPN
ejpam-2422	411	3	ηi	ηi	PROPN
ejpam-2422	411	4	j	j	PROPN
ejpam-2422	411	5	(	(	PUNCT
ejpam-2422	411	6	k)(ν	k)(ν	PROPN
ejpam-2422	411	7	)	)	PUNCT
ejpam-2422	412	1	|	|	ADV
ejpam-2422	412	2	ν	ν	X
ejpam-2422	412	3	◦	◦	NOUN
ejpam-2422	412	4	ν≤	ν≤	PROPN
ejpam-2422	412	5	λi	λi	ADP
ejpam-2422	412	6	j	j	PROPN
ejpam-2422	412	7	}	}	PUNCT
ejpam-2422	412	8	.	.	PUNCT
ejpam-2422	413	1	for	for	ADP
ejpam-2422	413	2	each	each	DET
ejpam-2422	413	3	i	i	PRON
ejpam-2422	413	4	j	j	PROPN
ejpam-2422	413	5	∈	∈	PROPN
ejpam-2422	413	6	{	{	PUNCT
ejpam-2422	413	7	i1	i1	PROPN
ejpam-2422	413	8	,	,	PUNCT
ejpam-2422	413	9	.	.	PUNCT
ejpam-2422	413	10	.	.	PUNCT
ejpam-2422	413	11	.	.	PUNCT
ejpam-2422	414	1	,	,	PUNCT
ejpam-2422	414	2	in	in	ADP
ejpam-2422	414	3	}	}	PUNCT
ejpam-2422	414	4	,	,	PUNCT
ejpam-2422	414	5	there	there	PRON
ejpam-2422	414	6	exists	exist	VERB
ejpam-2422	414	7	νi	νi	DET
ejpam-2422	414	8	j	j	PROPN
ejpam-2422	414	9	∈	∈	PROPN
ejpam-2422	414	10	h	h	NOUN
ejpam-2422	414	11	(	(	PUNCT
ejpam-2422	414	12	x	x	PROPN
ejpam-2422	414	13	i	i	PRON
ejpam-2422	414	14	j	j	PROPN
ejpam-2422	414	15	,	,	PUNCT
ejpam-2422	414	16	ei	ei	PROPN
ejpam-2422	414	17	j	j	PROPN
ejpam-2422	414	18	)	)	PUNCT
ejpam-2422	414	19	with	with	ADP
ejpam-2422	414	20	νi	νi	DET
ejpam-2422	414	21	j	j	NOUN
ejpam-2422	414	22	◦	◦	NOUN
ejpam-2422	414	23	νi	νi	DET
ejpam-2422	414	24	j	j	PROPN
ejpam-2422	414	25	≤	≤	PROPN
ejpam-2422	415	1	λi	λi	ADP
ejpam-2422	415	2	j	j	PROPN
ejpam-2422	415	3	such	such	ADJ
ejpam-2422	415	4	that	that	SCONJ
ejpam-2422	415	5	∧n	∧n	AUX
ejpam-2422	415	6	j=1u	j=1u	NOUN
ejpam-2422	416	1	i	i	PRON
ejpam-2422	416	2	j	j	PROPN
ejpam-2422	417	1	ηi	ηi	PROPN
ejpam-2422	417	2	j	j	PROPN
ejpam-2422	417	3	(	(	PUNCT
ejpam-2422	417	4	k)(νi	k)(νi	PROPN
ejpam-2422	417	5	j	j	PROPN
ejpam-2422	417	6	)	)	PUNCT
ejpam-2422	417	7	6≤	6≤	NUM
ejpam-2422	417	8	∨	∨	NOUN
ejpam-2422	417	9	{	{	PUNCT
ejpam-2422	417	10	uk(µ	uk(µ	PROPN
ejpam-2422	417	11	)	)	PUNCT
ejpam-2422	417	12	|	|	ADV
ejpam-2422	417	13	µ	µ	X
ejpam-2422	417	14	◦	◦	NOUN
ejpam-2422	417	15	µ	µ	PRON
ejpam-2422	417	16	≤	≤	X
ejpam-2422	417	17	λ	λ	NOUN
ejpam-2422	417	18	}	}	PUNCT
ejpam-2422	417	19	.	.	PUNCT
ejpam-2422	418	1	put	put	VERB
ejpam-2422	418	2	ν∗	ν∗	NOUN
ejpam-2422	419	1	=	=	SYM
ejpam-2422	419	2	∆n	∆n	PROPN
ejpam-2422	419	3	j=1(ϕψ	j=1(ϕψ	PROPN
ejpam-2422	419	4	)	)	PUNCT
ejpam-2422	420	1	⇐	⇐	INTJ
ejpam-2422	420	2	i	i	PRON
ejpam-2422	420	3	j	j	PROPN
ejpam-2422	420	4	(	(	PUNCT
ejpam-2422	420	5	νi	νi	DET
ejpam-2422	420	6	j	j	PROPN
ejpam-2422	420	7	)	)	PUNCT
ejpam-2422	420	8	.	.	PUNCT
ejpam-2422	421	1	for	for	ADP
ejpam-2422	421	2	each	each	DET
ejpam-2422	421	3	i	i	PRON
ejpam-2422	421	4	j	j	PROPN
ejpam-2422	421	5	∈	∈	PROPN
ejpam-2422	421	6	j	j	PROPN
ejpam-2422	421	7	,	,	PUNCT
ejpam-2422	421	8	we	we	PRON
ejpam-2422	421	9	have	have	AUX
ejpam-2422	421	10	ν∗	ν∗	VERB
ejpam-2422	421	11	◦	◦	NOUN
ejpam-2422	421	12	ν∗	ν∗	NOUN
ejpam-2422	422	1	=	=	SYM
ejpam-2422	422	2	(	(	PUNCT
ejpam-2422	422	3	∆n	∆n	PROPN
ejpam-2422	422	4	j=1(ϕψ	j=1(ϕψ	PROPN
ejpam-2422	422	5	)	)	PUNCT
ejpam-2422	423	1	⇐	⇐	INTJ
ejpam-2422	423	2	i	i	PRON
ejpam-2422	423	3	j	j	PROPN
ejpam-2422	423	4	(	(	PUNCT
ejpam-2422	423	5	νi	νi	DET
ejpam-2422	423	6	j	j	NOUN
ejpam-2422	423	7	)	)	PUNCT
ejpam-2422	423	8	)	)	PUNCT
ejpam-2422	424	1	◦	◦	NOUN
ejpam-2422	424	2	(	(	PUNCT
ejpam-2422	424	3	∆n	∆n	PROPN
ejpam-2422	424	4	j=1(ϕψ	j=1(ϕψ	PROPN
ejpam-2422	424	5	)	)	PUNCT
ejpam-2422	424	6	⇐	⇐	INTJ
ejpam-2422	424	7	i	i	PRON
ejpam-2422	424	8	j	j	PROPN
ejpam-2422	424	9	(	(	PUNCT
ejpam-2422	424	10	νi	νi	DET
ejpam-2422	424	11	j	j	PROPN
ejpam-2422	424	12	)	)	PUNCT
ejpam-2422	424	13	)	)	PUNCT
ejpam-2422	424	14	.	.	PUNCT
ejpam-2422	425	1	hence	hence	ADV
ejpam-2422	425	2	,	,	PUNCT
ejpam-2422	425	3	ν∗	ν∗	VERB
ejpam-2422	425	4	◦	◦	NOUN
ejpam-2422	425	5	ν∗	ν∗	VERB
ejpam-2422	426	1	≤∆n	≤∆n	PROPN
ejpam-2422	426	2	j=1((ϕψ	j=1((ϕψ	PROPN
ejpam-2422	426	3	)	)	PUNCT
ejpam-2422	426	4	⇐	⇐	PROPN
ejpam-2422	426	5	i	i	PRON
ejpam-2422	426	6	j	j	PROPN
ejpam-2422	426	7	(	(	PUNCT
ejpam-2422	426	8	νi	νi	PRON
ejpam-2422	426	9	j	j	NOUN
ejpam-2422	426	10	)	)	PUNCT
ejpam-2422	426	11	◦	◦	NOUN
ejpam-2422	426	12	(	(	PUNCT
ejpam-2422	426	13	ϕψ)	ϕψ)	X
ejpam-2422	426	14	⇐	⇐	NOUN
ejpam-2422	426	15	i	i	PRON
ejpam-2422	426	16	j	j	X
ejpam-2422	426	17	(	(	PUNCT
ejpam-2422	426	18	νi	νi	PRON
ejpam-2422	426	19	j	j	PROPN
ejpam-2422	426	20	)	)	PUNCT
ejpam-2422	426	21	)	)	PUNCT
ejpam-2422	427	1	≤∆n	≤∆n	PROPN
ejpam-2422	427	2	j=1((ϕψ	j=1((ϕψ	PROPN
ejpam-2422	427	3	)	)	PUNCT
ejpam-2422	427	4	⇐	⇐	PROPN
ejpam-2422	427	5	i	i	PRON
ejpam-2422	428	1	j	j	PROPN
ejpam-2422	428	2	(	(	PUNCT
ejpam-2422	428	3	νi	νi	DET
ejpam-2422	428	4	j	j	NOUN
ejpam-2422	428	5	◦	◦	VERB
ejpam-2422	428	6	νi	νi	DET
ejpam-2422	428	7	j	j	PROPN
ejpam-2422	428	8	)	)	PUNCT
ejpam-2422	428	9	)	)	PUNCT
ejpam-2422	429	1	≤∆n	≤∆n	PROPN
ejpam-2422	429	2	j=1(ϕψ	j=1(ϕψ	NOUN
ejpam-2422	429	3	)	)	PUNCT
ejpam-2422	430	1	⇐	⇐	INTJ
ejpam-2422	430	2	i	i	PRON
ejpam-2422	430	3	j	j	PROPN
ejpam-2422	430	4	(	(	PUNCT
ejpam-2422	430	5	λi	λi	ADP
ejpam-2422	430	6	j	j	PROPN
ejpam-2422	430	7	)	)	PUNCT
ejpam-2422	430	8	≤	≤	PROPN
ejpam-2422	431	1	λ	λ	PROPN
ejpam-2422	431	2	.	.	PUNCT
ejpam-2422	432	1	then	then	ADV
ejpam-2422	432	2	we	we	PRON
ejpam-2422	432	3	have	have	AUX
ejpam-2422	432	4	ν∗	ν∗	VERB
ejpam-2422	432	5	◦	◦	NOUN
ejpam-2422	432	6	ν∗	ν∗	VERB
ejpam-2422	432	7	≤	≤	NUM
ejpam-2422	432	8	λ	λ	PROPN
ejpam-2422	432	9	and	and	CCONJ
ejpam-2422	432	10	uk(ν∗)≥	uk(ν∗)≥	PROPN
ejpam-2422	433	1	∧n	∧n	PRON
ejpam-2422	434	1	j=1u	j=1u	NOUN
ejpam-2422	435	1	i	i	PRON
ejpam-2422	435	2	j	j	PROPN
ejpam-2422	436	1	ηi	ηi	PROPN
ejpam-2422	436	2	j	j	PROPN
ejpam-2422	436	3	(	(	PUNCT
ejpam-2422	436	4	k)(νi	k)(νi	PROPN
ejpam-2422	436	5	j	j	PROPN
ejpam-2422	436	6	)	)	PUNCT
ejpam-2422	436	7	.	.	PUNCT
ejpam-2422	437	1	this	this	PRON
ejpam-2422	437	2	is	be	AUX
ejpam-2422	437	3	a	a	DET
ejpam-2422	437	4	contradiction	contradiction	NOUN
ejpam-2422	437	5	.	.	PUNCT
ejpam-2422	438	1	(	(	PUNCT
ejpam-2422	438	2	u4	u4	NOUN
ejpam-2422	438	3	):	):	PUNCT
ejpam-2422	438	4	let	let	VERB
ejpam-2422	438	5	{	{	PUNCT
ejpam-2422	438	6	(	(	PUNCT
ejpam-2422	438	7	x	x	PROPN
ejpam-2422	438	8	i	i	PRON
ejpam-2422	438	9	,	,	PUNCT
ejpam-2422	438	10	u	u	PRON
ejpam-2422	438	11	i)}i∈γ	i)}i∈γ	PROPN
ejpam-2422	438	12	be	be	VERB
ejpam-2422	438	13	a	a	DET
ejpam-2422	438	14	family	family	NOUN
ejpam-2422	438	15	of	of	ADP
ejpam-2422	438	16	(	(	PUNCT
ejpam-2422	438	17	l	l	NOUN
ejpam-2422	438	18	,	,	PUNCT
ejpam-2422	438	19	m)-fuzzy	m)-fuzzy	X
ejpam-2422	438	20	(	(	PUNCT
ejpam-2422	438	21	ei	ei	X
ejpam-2422	438	22	,	,	PUNCT
ejpam-2422	438	23	ki)-soft	ki)-soft	PROPN
ejpam-2422	438	24	uniform	uniform	NOUN
ejpam-2422	438	25	spaces	space	VERB
ejpam-2422	438	26	.	.	PUNCT
ejpam-2422	439	1	suppose	suppose	VERB
ejpam-2422	439	2	there	there	PRON
ejpam-2422	439	3	exists	exist	VERB
ejpam-2422	439	4	λ	λ	PROPN
ejpam-2422	439	5	∈	∈	PROPN
ejpam-2422	439	6	h	h	NOUN
ejpam-2422	439	7	(	(	PUNCT
ejpam-2422	439	8	x	x	NOUN
ejpam-2422	439	9	,	,	PUNCT
ejpam-2422	439	10	e	e	NOUN
ejpam-2422	439	11	)	)	PUNCT
ejpam-2422	439	12	and	and	CCONJ
ejpam-2422	439	13	k	k	PROPN
ejpam-2422	439	14	∈	∈	PROPN
ejpam-2422	440	1	k	k	X
ejpam-2422	440	2	such	such	ADJ
ejpam-2422	440	3	that	that	SCONJ
ejpam-2422	440	4	uk(λ	uk(λ	NOUN
ejpam-2422	440	5	)	)	PUNCT
ejpam-2422	440	6	6≤	6≤	NUM
ejpam-2422	440	7	∨	∨	NOUN
ejpam-2422	440	8	{	{	PUNCT
ejpam-2422	440	9	uk(µ	uk(µ	PROPN
ejpam-2422	440	10	)	)	PUNCT
ejpam-2422	440	11	|	|	ADV
ejpam-2422	440	12	µ	µ	X
ejpam-2422	440	13	≤	≤	NOUN
ejpam-2422	440	14	λ/	λ/	NOUN
ejpam-2422	440	15	}	}	PUNCT
ejpam-2422	440	16	.	.	PUNCT
ejpam-2422	441	1	by	by	ADP
ejpam-2422	441	2	using	use	VERB
ejpam-2422	441	3	the	the	DET
ejpam-2422	441	4	definition	definition	NOUN
ejpam-2422	441	5	of	of	ADP
ejpam-2422	441	6	uk(λ	uk(λ	NOUN
ejpam-2422	441	7	)	)	PUNCT
ejpam-2422	441	8	,	,	PUNCT
ejpam-2422	441	9	there	there	PRON
ejpam-2422	441	10	exists	exist	VERB
ejpam-2422	441	11	a	a	DET
ejpam-2422	441	12	finite	finite	ADJ
ejpam-2422	441	13	index	index	NOUN
ejpam-2422	441	14	set	set	VERB
ejpam-2422	441	15	j	j	PROPN
ejpam-2422	441	16	=	=	PRON
ejpam-2422	441	17	{	{	PUNCT
ejpam-2422	441	18	j1	j1	PROPN
ejpam-2422	441	19	,	,	PUNCT
ejpam-2422	441	20	.	.	PUNCT
ejpam-2422	441	21	.	.	PUNCT
ejpam-2422	442	1	.	.	PUNCT
ejpam-2422	443	1	,	,	PUNCT
ejpam-2422	443	2	jn	jn	PROPN
ejpam-2422	443	3	}	}	PUNCT
ejpam-2422	443	4	of	of	ADP
ejpam-2422	443	5	γ	γ	PROPN
ejpam-2422	443	6	such	such	ADJ
ejpam-2422	443	7	that	that	SCONJ
ejpam-2422	443	8	∨	∨	NOUN
ejpam-2422	443	9	{	{	PUNCT
ejpam-2422	443	10	uk(µ	uk(µ	PROPN
ejpam-2422	443	11	)	)	PUNCT
ejpam-2422	443	12	|	|	ADV
ejpam-2422	443	13	µ≤	µ≤	ADJ
ejpam-2422	443	14	λ/	λ/	ADJ
ejpam-2422	443	15	}	}	PUNCT
ejpam-2422	443	16	6≥	6≥	NUM
ejpam-2422	443	17	∧n	∧n	NOUN
ejpam-2422	443	18	i=1u	i=1u	VERB
ejpam-2422	443	19	ji	ji	PROPN
ejpam-2422	443	20	η	η	PROPN
ejpam-2422	443	21	ji	ji	PROPN
ejpam-2422	443	22	(	(	PUNCT
ejpam-2422	443	23	k)(λ	k)(λ	X
ejpam-2422	443	24	ji	ji	PROPN
ejpam-2422	443	25	)	)	PUNCT
ejpam-2422	443	26	,	,	PUNCT
ejpam-2422	443	27	where	where	SCONJ
ejpam-2422	443	28	∆n	∆n	PROPN
ejpam-2422	443	29	i=1(ϕψ	i=1(ϕψ	NOUN
ejpam-2422	443	30	)	)	PUNCT
ejpam-2422	444	1	⇐	⇐	PROPN
ejpam-2422	444	2	ji	ji	PROPN
ejpam-2422	444	3	(	(	PUNCT
ejpam-2422	444	4	λ	λ	X
ejpam-2422	444	5	ji	ji	X
ejpam-2422	444	6	)	)	PUNCT
ejpam-2422	444	7	≤	≤	PROPN
ejpam-2422	444	8	λ	λ	PROPN
ejpam-2422	444	9	.	.	PUNCT
ejpam-2422	445	1	since	since	SCONJ
ejpam-2422	445	2	u	u	PROPN
ejpam-2422	445	3	ji	ji	PROPN
ejpam-2422	445	4	is	be	AUX
ejpam-2422	445	5	an	an	DET
ejpam-2422	445	6	(	(	PUNCT
ejpam-2422	445	7	l	l	NOUN
ejpam-2422	445	8	,	,	PUNCT
ejpam-2422	445	9	m)-fuzzy	m)-fuzzy	PUNCT
ejpam-2422	445	10	(	(	PUNCT
ejpam-2422	445	11	e	e	X
ejpam-2422	445	12	ji	ji	PROPN
ejpam-2422	445	13	,	,	PUNCT
ejpam-2422	445	14	k	k	PROPN
ejpam-2422	445	15	ji	ji	ADJ
ejpam-2422	445	16	)	)	PUNCT
ejpam-2422	445	17	-soft	-soft	ADJ
ejpam-2422	445	18	uniformity	uniformity	NOUN
ejpam-2422	445	19	on	on	ADP
ejpam-2422	445	20	x	x	PROPN
ejpam-2422	445	21	ji	ji	PROPN
ejpam-2422	445	22	,	,	PUNCT
ejpam-2422	445	23	then	then	ADV
ejpam-2422	445	24	∨	∨	NUM
ejpam-2422	445	25	{	{	PUNCT
ejpam-2422	445	26	u	u	PROPN
ejpam-2422	445	27	ji	ji	PROPN
ejpam-2422	445	28	η	η	PROPN
ejpam-2422	445	29	ji	ji	PROPN
ejpam-2422	445	30	(	(	PUNCT
ejpam-2422	445	31	k)(ν	k)(ν	PROPN
ejpam-2422	445	32	)	)	PUNCT
ejpam-2422	445	33	|	|	ADV
ejpam-2422	445	34	ν	ν	X
ejpam-2422	445	35	≤	≤	ADJ
ejpam-2422	445	36	λ	λ	PROPN
ejpam-2422	445	37	/	/	SYM
ejpam-2422	445	38	ji	ji	PROPN
ejpam-2422	445	39	}	}	PUNCT
ejpam-2422	445	40	≥	≥	PROPN
ejpam-2422	445	41	u	u	NOUN
ejpam-2422	445	42	ji	ji	PROPN
ejpam-2422	445	43	η	η	PROPN
ejpam-2422	445	44	ji	ji	PROPN
ejpam-2422	445	45	(	(	PUNCT
ejpam-2422	445	46	k)(λ	k)(λ	X
ejpam-2422	445	47	ji	ji	PROPN
ejpam-2422	445	48	)	)	PUNCT
ejpam-2422	445	49	.	.	PUNCT
ejpam-2422	446	1	for	for	ADP
ejpam-2422	446	2	each	each	DET
ejpam-2422	446	3	ji	ji	PROPN
ejpam-2422	446	4	∈	∈	PROPN
ejpam-2422	446	5	j	j	PROPN
ejpam-2422	446	6	,	,	PUNCT
ejpam-2422	446	7	there	there	PRON
ejpam-2422	446	8	exists	exist	VERB
ejpam-2422	446	9	ν∗ji	ν∗ji	PROPN
ejpam-2422	446	10	∈	∈	PROPN
ejpam-2422	446	11	h	h	NOUN
ejpam-2422	446	12	(	(	PUNCT
ejpam-2422	446	13	x	x	SYM
ejpam-2422	446	14	ji	ji	PROPN
ejpam-2422	446	15	,	,	PUNCT
ejpam-2422	446	16	e	e	X
ejpam-2422	446	17	ji	ji	PROPN
ejpam-2422	446	18	)	)	PUNCT
ejpam-2422	446	19	with	with	ADP
ejpam-2422	446	20	ν∗ji	ν∗ji	NOUN
ejpam-2422	446	21	≤	≤	NUM
ejpam-2422	446	22	λ	λ	PROPN
ejpam-2422	446	23	/	/	SYM
ejpam-2422	446	24	ji	ji	PROPN
ejpam-2422	446	25	such	such	ADJ
ejpam-2422	446	26	that	that	SCONJ
ejpam-2422	446	27	∨	∨	PROPN
ejpam-2422	446	28	{	{	PUNCT
ejpam-2422	446	29	uk(µ	uk(µ	PROPN
ejpam-2422	446	30	)	)	PUNCT
ejpam-2422	446	31	|	|	ADV
ejpam-2422	446	32	µ≤	µ≤	ADJ
ejpam-2422	446	33	λ/	λ/	ADJ
ejpam-2422	446	34	}	}	PUNCT
ejpam-2422	446	35	6≥	6≥	NUM
ejpam-2422	446	36	∧n	∧n	NOUN
ejpam-2422	446	37	i=1u	i=1u	VERB
ejpam-2422	446	38	ji	ji	PROPN
ejpam-2422	446	39	η	η	PROPN
ejpam-2422	446	40	ji	ji	PROPN
ejpam-2422	446	41	(	(	PUNCT
ejpam-2422	446	42	k)(ν	k)(ν	PROPN
ejpam-2422	446	43	∗	∗	X
ejpam-2422	446	44	ji	ji	PROPN
ejpam-2422	446	45	)	)	PUNCT
ejpam-2422	446	46	.	.	PUNCT
ejpam-2422	447	1	on	on	ADP
ejpam-2422	447	2	the	the	DET
ejpam-2422	447	3	other	other	ADJ
ejpam-2422	447	4	hand	hand	NOUN
ejpam-2422	447	5	,	,	PUNCT
ejpam-2422	447	6	we	we	PRON
ejpam-2422	447	7	have	have	VERB
ejpam-2422	447	8	∆n	∆n	PROPN
ejpam-2422	447	9	i=1(ϕψ	i=1(ϕψ	NOUN
ejpam-2422	447	10	)	)	PUNCT
ejpam-2422	447	11	⇐	⇐	PROPN
ejpam-2422	447	12	ji	ji	PROPN
ejpam-2422	447	13	(	(	PUNCT
ejpam-2422	447	14	ν∗ji	ν∗ji	PROPN
ejpam-2422	447	15	)	)	PUNCT
ejpam-2422	448	1	≤∆	≤∆	PROPN
ejpam-2422	448	2	n	n	NUM
ejpam-2422	448	3	i=1(ϕψ	i=1(ϕψ	NOUN
ejpam-2422	448	4	)	)	PUNCT
ejpam-2422	448	5	⇐	⇐	PROPN
ejpam-2422	448	6	ji	ji	PROPN
ejpam-2422	448	7	(	(	PUNCT
ejpam-2422	448	8	λ	λ	PROPN
ejpam-2422	448	9	/	/	SYM
ejpam-2422	448	10	ji	ji	NOUN
ejpam-2422	448	11	)	)	PUNCT
ejpam-2422	448	12	=	=	SYM
ejpam-2422	449	1	∆	∆	PROPN
ejpam-2422	449	2	n	n	PRON
ejpam-2422	449	3	i=1((ϕψ	i=1((ϕψ	NOUN
ejpam-2422	449	4	)	)	PUNCT
ejpam-2422	449	5	⇐	⇐	PROPN
ejpam-2422	449	6	ji	ji	PROPN
ejpam-2422	449	7	(	(	PUNCT
ejpam-2422	449	8	λ	λ	X
ejpam-2422	449	9	ji	ji	PROPN
ejpam-2422	449	10	)	)	PUNCT
ejpam-2422	449	11	)	)	PUNCT
ejpam-2422	449	12	/	/	PUNCT
ejpam-2422	450	1	=	=	SYM
ejpam-2422	450	2	(	(	PUNCT
ejpam-2422	450	3	∆n	∆n	PROPN
ejpam-2422	450	4	i=1(ϕψ	i=1(ϕψ	NOUN
ejpam-2422	450	5	)	)	PUNCT
ejpam-2422	450	6	⇐	⇐	PROPN
ejpam-2422	450	7	ji	ji	PROPN
ejpam-2422	450	8	(	(	PUNCT
ejpam-2422	450	9	λ	λ	X
ejpam-2422	450	10	ji	ji	PROPN
ejpam-2422	450	11	)	)	PUNCT
ejpam-2422	450	12	)	)	PUNCT
ejpam-2422	450	13	/	/	SYM
ejpam-2422	450	14	≤	≤	NUM
ejpam-2422	450	15	λ/.	λ/.	NOUN
ejpam-2422	450	16	put	put	VERB
ejpam-2422	450	17	ν∗	ν∗	NOUN
ejpam-2422	451	1	=	=	X
ejpam-2422	451	2	∆n	∆n	NOUN
ejpam-2422	451	3	i=1(ϕψ	i=1(ϕψ	NOUN
ejpam-2422	451	4	)	)	PUNCT
ejpam-2422	451	5	⇐	⇐	PROPN
ejpam-2422	451	6	ji	ji	PROPN
ejpam-2422	451	7	(	(	PUNCT
ejpam-2422	451	8	ν∗ji	ν∗ji	PROPN
ejpam-2422	451	9	)	)	PUNCT
ejpam-2422	451	10	.	.	PUNCT
ejpam-2422	452	1	then	then	ADV
ejpam-2422	452	2	there	there	PRON
ejpam-2422	452	3	exists	exist	VERB
ejpam-2422	452	4	ν∗	ν∗	VERB
ejpam-2422	452	5	∈h	∈h	NOUN
ejpam-2422	452	6	(	(	PUNCT
ejpam-2422	452	7	x	x	X
ejpam-2422	452	8	,	,	PUNCT
ejpam-2422	452	9	e	e	NOUN
ejpam-2422	452	10	)	)	PUNCT
ejpam-2422	452	11	such	such	ADJ
ejpam-2422	452	12	that	that	DET
ejpam-2422	452	13	ν∗	ν∗	PROPN
ejpam-2422	452	14	≤	≤	X
ejpam-2422	452	15	λ/	λ/	ADJ
ejpam-2422	452	16	and	and	CCONJ
ejpam-2422	452	17	uk(ν∗)≥	uk(ν∗)≥	ADJ
ejpam-2422	452	18	∧n	∧n	X
ejpam-2422	452	19	i=1u	i=1u	VERB
ejpam-2422	452	20	ji	ji	PROPN
ejpam-2422	452	21	η	η	PROPN
ejpam-2422	452	22	ji	ji	PROPN
ejpam-2422	452	23	(	(	PUNCT
ejpam-2422	452	24	k)(ν	k)(ν	PROPN
ejpam-2422	452	25	∗	∗	X
ejpam-2422	452	26	ji	ji	PROPN
ejpam-2422	452	27	)	)	PUNCT
ejpam-2422	452	28	.	.	PUNCT
ejpam-2422	453	1	thus	thus	ADV
ejpam-2422	453	2	n	n	PRON
ejpam-2422	453	3	∧	∧	NOUN
ejpam-2422	453	4	i=1	i=1	PROPN
ejpam-2422	453	5	u	u	PROPN
ejpam-2422	453	6	ji	ji	PROPN
ejpam-2422	453	7	η	η	PROPN
ejpam-2422	453	8	ji	ji	PROPN
ejpam-2422	453	9	(	(	PUNCT
ejpam-2422	453	10	k)(ν	k)(ν	PROPN
ejpam-2422	453	11	∗	∗	PROPN
ejpam-2422	453	12	ji	ji	PROPN
ejpam-2422	453	13	)	)	PUNCT
ejpam-2422	453	14	≤uk(ν	≤uk(ν	PROPN
ejpam-2422	453	15	∗)≤	∗)≤	PROPN
ejpam-2422	453	16	∨	∨	NOUN
ejpam-2422	453	17	{	{	PUNCT
ejpam-2422	453	18	uk(µ	uk(µ	PROPN
ejpam-2422	453	19	)	)	PUNCT
ejpam-2422	453	20	|	|	ADV
ejpam-2422	453	21	µ≤	µ≤	ADJ
ejpam-2422	453	22	λ/	λ/	ADJ
ejpam-2422	453	23	}	}	PUNCT
ejpam-2422	453	24	.	.	PUNCT
ejpam-2422	454	1	this	this	PRON
ejpam-2422	454	2	is	be	AUX
ejpam-2422	454	3	a	a	DET
ejpam-2422	454	4	contradiction	contradiction	NOUN
ejpam-2422	454	5	.	.	PUNCT
ejpam-2422	455	1	hence	hence	ADV
ejpam-2422	455	2	for	for	ADP
ejpam-2422	455	3	each	each	DET
ejpam-2422	455	4	k	k	PROPN
ejpam-2422	455	5	∈	∈	PROPN
ejpam-2422	455	6	k	k	PROPN
ejpam-2422	455	7	and	and	CCONJ
ejpam-2422	455	8	λ	λ	PROPN
ejpam-2422	455	9	∈h	∈h	NOUN
ejpam-2422	455	10	(	(	PUNCT
ejpam-2422	455	11	x	x	X
ejpam-2422	455	12	,	,	PUNCT
ejpam-2422	455	13	e	e	NOUN
ejpam-2422	455	14	)	)	PUNCT
ejpam-2422	455	15	,	,	PUNCT
ejpam-2422	455	16	we	we	PRON
ejpam-2422	455	17	have	have	VERB
ejpam-2422	455	18	uk(λ	uk(λ	NOUN
ejpam-2422	455	19	)	)	PUNCT
ejpam-2422	455	20	≤	≤	NUM
ejpam-2422	455	21	∨	∨	NUM
ejpam-2422	455	22	{	{	PUNCT
ejpam-2422	455	23	uk(µ	uk(µ	PROPN
ejpam-2422	455	24	)	)	PUNCT
ejpam-2422	455	25	|	|	ADV
ejpam-2422	455	26	µ≤	µ≤	ADJ
ejpam-2422	455	27	λ/	λ/	ADJ
ejpam-2422	455	28	}	}	PUNCT
ejpam-2422	455	29	.	.	PUNCT
ejpam-2422	456	1	secondly	secondly	ADV
ejpam-2422	456	2	by	by	ADP
ejpam-2422	456	3	using	use	VERB
ejpam-2422	456	4	the	the	DET
ejpam-2422	456	5	definition	definition	NOUN
ejpam-2422	456	6	of	of	ADP
ejpam-2422	456	7	u	u	NOUN
ejpam-2422	456	8	,	,	PUNCT
ejpam-2422	456	9	we	we	PRON
ejpam-2422	456	10	have	have	VERB
ejpam-2422	456	11	uk((ϕψ)	uk((ϕψ)	ADJ
ejpam-2422	456	12	⇐	⇐	ADJ
ejpam-2422	456	13	i	i	PROPN
ejpam-2422	456	14	(	(	PUNCT
ejpam-2422	456	15	λi	λi	NOUN
ejpam-2422	456	16	)	)	PUNCT
ejpam-2422	456	17	)	)	PUNCT
ejpam-2422	456	18	≥	≥	NOUN
ejpam-2422	456	19	u	u	NOUN
ejpam-2422	456	20	i	i	PRON
ejpam-2422	456	21	ηi(k	ηi(k	PROPN
ejpam-2422	456	22	)	)	PUNCT
ejpam-2422	456	23	(	(	PUNCT
ejpam-2422	456	24	λi	λi	X
ejpam-2422	456	25	)	)	PUNCT
ejpam-2422	456	26	for	for	ADP
ejpam-2422	456	27	each	each	DET
ejpam-2422	456	28	k	k	PROPN
ejpam-2422	456	29	∈	∈	PROPN
ejpam-2422	456	30	k	k	NOUN
ejpam-2422	456	31	,	,	PUNCT
ejpam-2422	456	32	i	i	PRON
ejpam-2422	456	33	∈	∈	VERB
ejpam-2422	456	34	γ	γ	X
ejpam-2422	456	35	and	and	CCONJ
ejpam-2422	456	36	λi	λi	X
ejpam-2422	456	37	∈h	∈h	NOUN
ejpam-2422	456	38	(	(	PUNCT
ejpam-2422	456	39	x	x	X
ejpam-2422	456	40	i	i	PRON
ejpam-2422	456	41	,	,	PUNCT
ejpam-2422	456	42	ei	ei	NOUN
ejpam-2422	456	43	)	)	PUNCT
ejpam-2422	456	44	.	.	PUNCT
ejpam-2422	457	1	hence	hence	ADV
ejpam-2422	457	2	(	(	PUNCT
ejpam-2422	457	3	ϕψ	ϕψ	INTJ
ejpam-2422	457	4	,	,	PUNCT
ejpam-2422	457	5	η)i	η)i	ADJ
ejpam-2422	457	6	is	be	AUX
ejpam-2422	457	7	uniformly	uniformly	ADV
ejpam-2422	457	8	continuous	continuous	ADJ
ejpam-2422	457	9	function	function	NOUN
ejpam-2422	457	10	.	.	PUNCT
ejpam-2422	458	1	finally	finally	ADV
ejpam-2422	458	2	,	,	PUNCT
ejpam-2422	458	3	if	if	SCONJ
ejpam-2422	458	4	(	(	PUNCT
ejpam-2422	458	5	ϕψ	ϕψ	INTJ
ejpam-2422	458	6	,	,	PUNCT
ejpam-2422	458	7	η)i	η)i	ADJ
ejpam-2422	458	8	:	:	PUNCT
ejpam-2422	458	9	(	(	PUNCT
ejpam-2422	458	10	x	x	X
ejpam-2422	458	11	,	,	PUNCT
ejpam-2422	458	12	v	v	NOUN
ejpam-2422	458	13	)	)	PUNCT
ejpam-2422	458	14	→	→	SYM
ejpam-2422	458	15	(	(	PUNCT
ejpam-2422	458	16	x	x	X
ejpam-2422	458	17	i	i	PRON
ejpam-2422	458	18	,	,	PUNCT
ejpam-2422	458	19	u	u	PROPN
ejpam-2422	458	20	i	i	PROPN
ejpam-2422	458	21	)	)	PUNCT
ejpam-2422	458	22	is	be	AUX
ejpam-2422	458	23	uniformly	uniformly	ADV
ejpam-2422	458	24	continuous	continuous	ADJ
ejpam-2422	458	25	,	,	PUNCT
ejpam-2422	458	26	i.e.	i.e.	X
ejpam-2422	458	27	,	,	PUNCT
ejpam-2422	458	28	vk((ϕψ)	vk((ϕψ)	NOUN
ejpam-2422	458	29	⇐	⇐	VERB
ejpam-2422	458	30	i	i	PROPN
ejpam-2422	458	31	(	(	PUNCT
ejpam-2422	458	32	λi	λi	NOUN
ejpam-2422	458	33	)	)	PUNCT
ejpam-2422	458	34	)	)	PUNCT
ejpam-2422	458	35	≥	≥	NOUN
ejpam-2422	458	36	u	u	NOUN
ejpam-2422	458	37	i	i	PRON
ejpam-2422	458	38	ηi(k	ηi(k	PROPN
ejpam-2422	458	39	)	)	PUNCT
ejpam-2422	458	40	(	(	PUNCT
ejpam-2422	458	41	λi	λi	X
ejpam-2422	458	42	)	)	PUNCT
ejpam-2422	458	43	for	for	ADP
ejpam-2422	458	44	each	each	DET
ejpam-2422	458	45	k	k	PROPN
ejpam-2422	458	46	∈	∈	PROPN
ejpam-2422	458	47	k	k	NOUN
ejpam-2422	458	48	,	,	PUNCT
ejpam-2422	458	49	i	i	PRON
ejpam-2422	458	50	∈	∈	VERB
ejpam-2422	458	51	γ	γ	NOUN
ejpam-2422	458	52	and	and	CCONJ
ejpam-2422	458	53	λi	λi	ADP
ejpam-2422	458	54	∈	∈	PROPN
ejpam-2422	458	55	h	h	NOUN
ejpam-2422	458	56	(	(	PUNCT
ejpam-2422	458	57	x	x	PROPN
ejpam-2422	458	58	i	i	PRON
ejpam-2422	458	59	,	,	PUNCT
ejpam-2422	458	60	ei	ei	PROPN
ejpam-2422	458	61	)	)	PUNCT
ejpam-2422	458	62	.	.	PUNCT
ejpam-2422	459	1	then	then	ADV
ejpam-2422	459	2	for	for	ADP
ejpam-2422	459	3	k	k	PROPN
ejpam-2422	459	4	∈	∈	PROPN
ejpam-2422	459	5	k	k	PROPN
ejpam-2422	459	6	,	,	PUNCT
ejpam-2422	459	7	we	we	PRON
ejpam-2422	459	8	have	have	VERB
ejpam-2422	459	9	uk	uk	PROPN
ejpam-2422	459	10	(	(	PUNCT
ejpam-2422	459	11	f	f	PROPN
ejpam-2422	459	12	)	)	PUNCT
ejpam-2422	460	1	=	=	SYM
ejpam-2422	460	2	∨	∨	X
ejpam-2422	460	3	{	{	PUNCT
ejpam-2422	460	4	n	n	CCONJ
ejpam-2422	460	5	∧	∧	PROPN
ejpam-2422	460	6	j=1	j=1	NOUN
ejpam-2422	460	7	u	u	NOUN
ejpam-2422	461	1	i	i	PRON
ejpam-2422	461	2	j	j	PROPN
ejpam-2422	461	3	ηi	ηi	PROPN
ejpam-2422	461	4	j	j	PROPN
ejpam-2422	461	5	(	(	PUNCT
ejpam-2422	461	6	k)(λi	k)(λi	PROPN
ejpam-2422	461	7	j	j	PROPN
ejpam-2422	461	8	)	)	PUNCT
ejpam-2422	462	1	|∆n	|∆n	PROPN
ejpam-2422	462	2	j=1(ϕψ	j=1(ϕψ	PROPN
ejpam-2422	462	3	)	)	PUNCT
ejpam-2422	463	1	⇐	⇐	INTJ
ejpam-2422	463	2	i	i	PRON
ejpam-2422	463	3	j	j	PROPN
ejpam-2422	463	4	(	(	PUNCT
ejpam-2422	463	5	λi	λi	ADP
ejpam-2422	463	6	j	j	PROPN
ejpam-2422	463	7	)	)	PUNCT
ejpam-2422	463	8	≤	≤	PROPN
ejpam-2422	463	9	λ	λ	PROPN
ejpam-2422	463	10	}	}	PUNCT
ejpam-2422	463	11	≤	≤	NUM
ejpam-2422	463	12	∨	∨	NOUN
ejpam-2422	463	13	{	{	PUNCT
ejpam-2422	463	14	n	n	CCONJ
ejpam-2422	463	15	∧	∧	PROPN
ejpam-2422	463	16	j=1	j=1	PROPN
ejpam-2422	463	17	vk((ϕψ	vk((ϕψ	PROPN
ejpam-2422	463	18	)	)	PUNCT
ejpam-2422	464	1	⇐	⇐	NOUN
ejpam-2422	464	2	i	i	PRON
ejpam-2422	464	3	j	j	PROPN
ejpam-2422	464	4	(	(	PUNCT
ejpam-2422	464	5	λi	λi	ADP
ejpam-2422	464	6	j	j	PROPN
ejpam-2422	464	7	)	)	PUNCT
ejpam-2422	464	8	)	)	PUNCT
ejpam-2422	465	1	|∆n	|∆n	PROPN
ejpam-2422	465	2	j=1(ϕψ	j=1(ϕψ	PROPN
ejpam-2422	465	3	)	)	PUNCT
ejpam-2422	466	1	⇐	⇐	INTJ
ejpam-2422	466	2	i	i	PRON
ejpam-2422	466	3	j	j	PROPN
ejpam-2422	466	4	(	(	PUNCT
ejpam-2422	466	5	λi	λi	ADP
ejpam-2422	466	6	j	j	PROPN
ejpam-2422	466	7	)	)	PUNCT
ejpam-2422	466	8	≤	≤	PROPN
ejpam-2422	466	9	λ	λ	PROPN
ejpam-2422	466	10	}	}	PUNCT
ejpam-2422	466	11	≤	≤	NUM
ejpam-2422	466	12	∨	∨	NOUN
ejpam-2422	466	13	{	{	PUNCT
ejpam-2422	466	14	vk(∆	vk(∆	PROPN
ejpam-2422	466	15	n	n	PRON
ejpam-2422	466	16	j=1(ϕψ	j=1(ϕψ	NOUN
ejpam-2422	466	17	)	)	PUNCT
ejpam-2422	467	1	⇐	⇐	INTJ
ejpam-2422	467	2	i	i	PRON
ejpam-2422	467	3	j	j	PROPN
ejpam-2422	467	4	(	(	PUNCT
ejpam-2422	467	5	λi	λi	ADP
ejpam-2422	467	6	j	j	PROPN
ejpam-2422	467	7	)	)	PUNCT
ejpam-2422	467	8	)	)	PUNCT
ejpam-2422	468	1	|∆n	|∆n	PROPN
ejpam-2422	468	2	j=1(ϕψ	j=1(ϕψ	PROPN
ejpam-2422	468	3	)	)	PUNCT
ejpam-2422	469	1	⇐	⇐	INTJ
ejpam-2422	469	2	i	i	PRON
ejpam-2422	469	3	j	j	PROPN
ejpam-2422	469	4	(	(	PUNCT
ejpam-2422	469	5	λi	λi	ADP
ejpam-2422	469	6	j	j	PROPN
ejpam-2422	469	7	)	)	PUNCT
ejpam-2422	469	8	≤	≤	PROPN
ejpam-2422	469	9	λ	λ	PROPN
ejpam-2422	469	10	}	}	PUNCT
ejpam-2422	469	11	≤	≤	NOUN
ejpam-2422	469	12	vk(λ	vk(λ	NOUN
ejpam-2422	469	13	)	)	PUNCT
ejpam-2422	469	14	.	.	PUNCT
ejpam-2422	470	1	v.	v.	ADP
ejpam-2422	470	2	çetkin	çetkin	PROPN
ejpam-2422	470	3	,	,	PUNCT
ejpam-2422	470	4	h.	h.	PROPN
ejpam-2422	470	5	aygün	aygün	PROPN
ejpam-2422	470	6	/	/	SYM
ejpam-2422	470	7	eur	eur	PROPN
ejpam-2422	470	8	.	.	PUNCT
ejpam-2422	471	1	j.	j.	PROPN
ejpam-2422	471	2	pure	pure	PROPN
ejpam-2422	471	3	appl	appl	PROPN
ejpam-2422	471	4	.	.	PROPN
ejpam-2422	471	5	math	math	PROPN
ejpam-2422	471	6	,	,	PUNCT
ejpam-2422	471	7	9	9	NUM
ejpam-2422	471	8	(	(	PUNCT
ejpam-2422	471	9	2016	2016	NUM
ejpam-2422	471	10	)	)	PUNCT
ejpam-2422	471	11	,	,	PUNCT
ejpam-2422	471	12	419	419	NUM
ejpam-2422	471	13	-	-	SYM
ejpam-2422	471	14	433	433	NUM
ejpam-2422	471	15	431	431	NUM
ejpam-2422	471	16	(	(	PUNCT
ejpam-2422	471	17	2	2	NUM
ejpam-2422	471	18	)	)	PUNCT
ejpam-2422	471	19	necessity	necessity	NOUN
ejpam-2422	471	20	of	of	ADP
ejpam-2422	471	21	the	the	DET
ejpam-2422	471	22	composition	composition	NOUN
ejpam-2422	471	23	condition	condition	NOUN
ejpam-2422	471	24	is	be	AUX
ejpam-2422	471	25	clear	clear	ADJ
ejpam-2422	471	26	.	.	PUNCT
ejpam-2422	472	1	suppose	suppose	VERB
ejpam-2422	472	2	that	that	SCONJ
ejpam-2422	472	3	for	for	ADP
ejpam-2422	472	4	(	(	PUNCT
ejpam-2422	472	5	l	l	NOUN
ejpam-2422	472	6	,	,	PUNCT
ejpam-2422	472	7	m)-fuzzy	m)-fuzzy	X
ejpam-2422	472	8	(	(	PUNCT
ejpam-2422	472	9	e∗	e∗	PROPN
ejpam-2422	472	10	,	,	PUNCT
ejpam-2422	472	11	k∗	k∗	PROPN
ejpam-2422	472	12	)	)	PUNCT
ejpam-2422	472	13	-soft	-soft	ADJ
ejpam-2422	472	14	uniform	uniform	ADJ
ejpam-2422	472	15	space	space	NOUN
ejpam-2422	472	16	(	(	PUNCT
ejpam-2422	472	17	z	z	NOUN
ejpam-2422	472	18	,	,	PUNCT
ejpam-2422	472	19	v	v	NOUN
ejpam-2422	472	20	)	)	PUNCT
ejpam-2422	472	21	,	,	PUNCT
ejpam-2422	472	22	ϕψ	ϕψ	INTJ
ejpam-2422	472	23	,	,	PUNCT
ejpam-2422	472	24	η	η	PROPN
ejpam-2422	472	25	:	:	PUNCT
ejpam-2422	472	26	(	(	PUNCT
ejpam-2422	472	27	z	z	NOUN
ejpam-2422	472	28	,	,	PUNCT
ejpam-2422	472	29	v	v	NOUN
ejpam-2422	472	30	)	)	PUNCT
ejpam-2422	472	31	→	→	SYM
ejpam-2422	472	32	(	(	PUNCT
ejpam-2422	472	33	x	x	X
ejpam-2422	472	34	,	,	PUNCT
ejpam-2422	472	35	u	u	NOUN
ejpam-2422	472	36	)	)	PUNCT
ejpam-2422	472	37	is	be	AUX
ejpam-2422	472	38	not	not	PART
ejpam-2422	472	39	uniformly	uniformly	ADV
ejpam-2422	472	40	continuous	continuous	ADJ
ejpam-2422	472	41	.	.	PUNCT
ejpam-2422	473	1	then	then	ADV
ejpam-2422	473	2	there	there	PRON
ejpam-2422	473	3	exist	exist	VERB
ejpam-2422	473	4	k∗	k∗	PROPN
ejpam-2422	473	5	∈	∈	PROPN
ejpam-2422	473	6	k∗	k∗	PROPN
ejpam-2422	473	7	and	and	CCONJ
ejpam-2422	473	8	λ	λ	PROPN
ejpam-2422	473	9	∈h	∈h	NOUN
ejpam-2422	473	10	(	(	PUNCT
ejpam-2422	473	11	x	x	X
ejpam-2422	473	12	,	,	PUNCT
ejpam-2422	473	13	e	e	NOUN
ejpam-2422	473	14	)	)	PUNCT
ejpam-2422	473	15	such	such	ADJ
ejpam-2422	473	16	that	that	DET
ejpam-2422	473	17	vk∗((ϕψ)	vk∗((ϕψ)	VERB
ejpam-2422	473	18	⇐	⇐	ADJ
ejpam-2422	473	19	(λ	(λ	NOUN
ejpam-2422	473	20	)	)	PUNCT
ejpam-2422	473	21	)	)	PUNCT
ejpam-2422	473	22	6≥	6≥	NUM
ejpam-2422	473	23	uη(k∗)(λ	uη(k∗)(λ	NOUN
ejpam-2422	473	24	)	)	PUNCT
ejpam-2422	473	25	.	.	PUNCT
ejpam-2422	474	1	by	by	ADP
ejpam-2422	474	2	the	the	DET
ejpam-2422	474	3	definition	definition	NOUN
ejpam-2422	474	4	of	of	ADP
ejpam-2422	474	5	u	u	NOUN
ejpam-2422	474	6	,	,	PUNCT
ejpam-2422	474	7	there	there	PRON
ejpam-2422	474	8	exists	exist	VERB
ejpam-2422	474	9	a	a	DET
ejpam-2422	474	10	finite	finite	ADJ
ejpam-2422	474	11	index	index	NOUN
ejpam-2422	474	12	set	set	VERB
ejpam-2422	474	13	j	j	PROPN
ejpam-2422	474	14	=	=	PRON
ejpam-2422	474	15	{	{	PUNCT
ejpam-2422	474	16	j1	j1	PROPN
ejpam-2422	474	17	,	,	PUNCT
ejpam-2422	474	18	.	.	PUNCT
ejpam-2422	474	19	.	.	PUNCT
ejpam-2422	475	1	.	.	PUNCT
ejpam-2422	476	1	,	,	PUNCT
ejpam-2422	476	2	jn	jn	PROPN
ejpam-2422	476	3	}	}	PUNCT
ejpam-2422	476	4	of	of	ADP
ejpam-2422	476	5	γ	γ	DET
ejpam-2422	476	6	such	such	ADJ
ejpam-2422	476	7	thatvk∗((ϕψ)	thatvk∗((ϕψ)	NOUN
ejpam-2422	476	8	⇐	⇐	NOUN
ejpam-2422	476	9	(λ	(λ	NOUN
ejpam-2422	476	10	)	)	PUNCT
ejpam-2422	476	11	)	)	PUNCT
ejpam-2422	477	1	6≥	6≥	NUM
ejpam-2422	477	2	∧n	∧n	PUNCT
ejpam-2422	477	3	i=1u	i=1u	VERB
ejpam-2422	477	4	ji	ji	PROPN
ejpam-2422	477	5	η	η	PROPN
ejpam-2422	477	6	ji	ji	PROPN
ejpam-2422	477	7	(	(	PUNCT
ejpam-2422	477	8	η(k∗))(λ	η(k∗))(λ	NOUN
ejpam-2422	477	9	ji	ji	PROPN
ejpam-2422	477	10	)	)	PUNCT
ejpam-2422	477	11	,	,	PUNCT
ejpam-2422	477	12	where	where	SCONJ
ejpam-2422	477	13	∆n	∆n	PROPN
ejpam-2422	477	14	i=1(ϕψ	i=1(ϕψ	NOUN
ejpam-2422	477	15	)	)	PUNCT
ejpam-2422	477	16	⇐	⇐	PROPN
ejpam-2422	477	17	ji	ji	PROPN
ejpam-2422	477	18	(	(	PUNCT
ejpam-2422	477	19	λ	λ	X
ejpam-2422	477	20	ji	ji	X
ejpam-2422	477	21	)	)	PUNCT
ejpam-2422	477	22	≤	≤	PROPN
ejpam-2422	477	23	λ	λ	PROPN
ejpam-2422	477	24	.	.	PUNCT
ejpam-2422	478	1	on	on	ADP
ejpam-2422	478	2	the	the	DET
ejpam-2422	478	3	other	other	ADJ
ejpam-2422	478	4	hand	hand	NOUN
ejpam-2422	478	5	,	,	PUNCT
ejpam-2422	478	6	since	since	SCONJ
ejpam-2422	478	7	(	(	PUNCT
ejpam-2422	478	8	ϕψ	ϕψ	INTJ
ejpam-2422	478	9	,	,	PUNCT
ejpam-2422	478	10	η	η	NOUN
ejpam-2422	478	11	)	)	PUNCT
ejpam-2422	478	12	ji	ji	PROPN
ejpam-2422	478	13	◦	◦	NOUN
ejpam-2422	478	14	ϕψ	ϕψ	PROPN
ejpam-2422	478	15	,	,	PUNCT
ejpam-2422	478	16	η	η	PROPN
ejpam-2422	478	17	is	be	AUX
ejpam-2422	478	18	uniformly	uniformly	ADV
ejpam-2422	478	19	continuous	continuous	ADJ
ejpam-2422	478	20	,	,	PUNCT
ejpam-2422	478	21	we	we	PRON
ejpam-2422	478	22	have	have	VERB
ejpam-2422	478	23	n	n	NUM
ejpam-2422	478	24	∧	∧	NOUN
ejpam-2422	478	25	i=1	i=1	PROPN
ejpam-2422	478	26	u	u	PROPN
ejpam-2422	478	27	ji	ji	PROPN
ejpam-2422	478	28	η	η	PROPN
ejpam-2422	478	29	ji	ji	PROPN
ejpam-2422	478	30	(	(	PUNCT
ejpam-2422	478	31	η(k∗))(λ	η(k∗))(λ	NOUN
ejpam-2422	478	32	ji	ji	PROPN
ejpam-2422	478	33	)	)	PUNCT
ejpam-2422	478	34	≤	≤	PROPN
ejpam-2422	479	1	n	n	CCONJ
ejpam-2422	479	2	∧	∧	PROPN
ejpam-2422	479	3	i=1	i=1	PROPN
ejpam-2422	479	4	vk∗(ϕ	vk∗(ϕ	NOUN
ejpam-2422	479	5	⇐	⇐	PROPN
ejpam-2422	479	6	ψ	ψ	PROPN
ejpam-2422	479	7	,	,	PUNCT
ejpam-2422	479	8	η	η	PROPN
ejpam-2422	479	9	◦	◦	NOUN
ejpam-2422	479	10	(	(	PUNCT
ejpam-2422	479	11	ϕψ	ϕψ	INTJ
ejpam-2422	479	12	,	,	PUNCT
ejpam-2422	479	13	η	η	NOUN
ejpam-2422	479	14	)	)	PUNCT
ejpam-2422	479	15	⇐	⇐	PROPN
ejpam-2422	479	16	ji	ji	PROPN
ejpam-2422	480	1	(	(	PUNCT
ejpam-2422	480	2	λ	λ	X
ejpam-2422	480	3	ji	ji	PROPN
ejpam-2422	480	4	)	)	PUNCT
ejpam-2422	480	5	)	)	PUNCT
ejpam-2422	481	1	≤vk∗(∆	≤vk∗(∆	ADJ
ejpam-2422	481	2	n	n	PRON
ejpam-2422	481	3	i=1ϕ	i=1ϕ	VERB
ejpam-2422	481	4	⇐	⇐	ADJ
ejpam-2422	481	5	ψ	ψ	PROPN
ejpam-2422	481	6	,	,	PUNCT
ejpam-2422	481	7	η((ϕψ	η((ϕψ	PROPN
ejpam-2422	481	8	,	,	PUNCT
ejpam-2422	481	9	η	η	NOUN
ejpam-2422	481	10	)	)	PUNCT
ejpam-2422	481	11	⇐	⇐	PROPN
ejpam-2422	481	12	ji	ji	PROPN
ejpam-2422	481	13	(	(	PUNCT
ejpam-2422	481	14	λ	λ	X
ejpam-2422	481	15	ji	ji	PROPN
ejpam-2422	481	16	)	)	PUNCT
ejpam-2422	481	17	)	)	PUNCT
ejpam-2422	481	18	)	)	PUNCT
ejpam-2422	482	1	=	=	PRON
ejpam-2422	482	2	vk∗(ϕ	vk∗(ϕ	ADJ
ejpam-2422	482	3	⇐	⇐	PROPN
ejpam-2422	482	4	ψ	ψ	NOUN
ejpam-2422	482	5	,	,	PUNCT
ejpam-2422	482	6	η(∆	η(∆	NOUN
ejpam-2422	482	7	n	n	PRON
ejpam-2422	482	8	i=1(ϕψ	i=1(ϕψ	NOUN
ejpam-2422	482	9	,	,	PUNCT
ejpam-2422	482	10	η	η	NOUN
ejpam-2422	482	11	)	)	PUNCT
ejpam-2422	482	12	⇐	⇐	PROPN
ejpam-2422	482	13	ji	ji	PROPN
ejpam-2422	483	1	(	(	PUNCT
ejpam-2422	483	2	λ	λ	X
ejpam-2422	483	3	ji	ji	PROPN
ejpam-2422	483	4	)	)	PUNCT
ejpam-2422	483	5	)	)	PUNCT
ejpam-2422	483	6	)	)	PUNCT
ejpam-2422	484	1	≤vk∗(ϕ	≤vk∗(ϕ	NOUN
ejpam-2422	484	2	⇐	⇐	ADJ
ejpam-2422	484	3	ψ	ψ	PROPN
ejpam-2422	484	4	,	,	PUNCT
ejpam-2422	484	5	η(λ	η(λ	NOUN
ejpam-2422	484	6	)	)	PUNCT
ejpam-2422	484	7	)	)	PUNCT
ejpam-2422	484	8	.	.	PUNCT
ejpam-2422	485	1	this	this	PRON
ejpam-2422	485	2	is	be	AUX
ejpam-2422	485	3	a	a	DET
ejpam-2422	485	4	contradiction	contradiction	NOUN
ejpam-2422	485	5	.	.	PUNCT
ejpam-2422	486	1	definition	definition	NOUN
ejpam-2422	486	2	6	6	NUM
ejpam-2422	486	3	.	.	PUNCT
ejpam-2422	487	1	let	let	VERB
ejpam-2422	487	2	{	{	PUNCT
ejpam-2422	487	3	(	(	PUNCT
ejpam-2422	487	4	x	x	PROPN
ejpam-2422	487	5	i	i	PRON
ejpam-2422	487	6	,	,	PUNCT
ejpam-2422	487	7	u	u	PRON
ejpam-2422	487	8	i)}i∈γ	i)}i∈γ	PROPN
ejpam-2422	487	9	be	be	VERB
ejpam-2422	487	10	a	a	DET
ejpam-2422	487	11	family	family	NOUN
ejpam-2422	487	12	of	of	ADP
ejpam-2422	487	13	(	(	PUNCT
ejpam-2422	487	14	l	l	NOUN
ejpam-2422	487	15	,	,	PUNCT
ejpam-2422	487	16	m)-fuzzy	m)-fuzzy	X
ejpam-2422	487	17	(	(	PUNCT
ejpam-2422	487	18	ei	ei	X
ejpam-2422	487	19	,	,	PUNCT
ejpam-2422	487	20	ki)-soft	ki)-soft	PROPN
ejpam-2422	487	21	uniform	uniform	NOUN
ejpam-2422	487	22	spaces	space	VERB
ejpam-2422	487	23	,	,	PUNCT
ejpam-2422	487	24	x	x	ADJ
ejpam-2422	487	25	be	be	AUX
ejpam-2422	487	26	a	a	DET
ejpam-2422	487	27	set	set	NOUN
ejpam-2422	487	28	,	,	PUNCT
ejpam-2422	487	29	e	e	X
ejpam-2422	487	30	,	,	PUNCT
ejpam-2422	487	31	k	k	X
ejpam-2422	487	32	be	be	VERB
ejpam-2422	487	33	the	the	DET
ejpam-2422	487	34	parameter	parameter	NOUN
ejpam-2422	487	35	sets	set	NOUN
ejpam-2422	487	36	and	and	CCONJ
ejpam-2422	487	37	ϕi	ϕi	ADP
ejpam-2422	487	38	:	:	PUNCT
ejpam-2422	487	39	x	x	X
ejpam-2422	487	40	→	→	PUNCT
ejpam-2422	487	41	x	x	SYM
ejpam-2422	487	42	i	i	PRON
ejpam-2422	487	43	,	,	PUNCT
ejpam-2422	487	44	ψi	ψi	ADP
ejpam-2422	487	45	:	:	PUNCT
ejpam-2422	487	46	e	e	X
ejpam-2422	487	47	→	→	SYM
ejpam-2422	487	48	ei	ei	NOUN
ejpam-2422	487	49	and	and	CCONJ
ejpam-2422	487	50	ηi	ηi	INTJ
ejpam-2422	487	51	:	:	PUNCT
ejpam-2422	487	52	k	k	PROPN
ejpam-2422	487	53	→	→	PUNCT
ejpam-2422	487	54	ki	ki	PROPN
ejpam-2422	487	55	be	be	AUX
ejpam-2422	487	56	functions	function	NOUN
ejpam-2422	487	57	for	for	ADP
ejpam-2422	487	58	each	each	DET
ejpam-2422	487	59	i	i	PRON
ejpam-2422	487	60	∈	∈	PROPN
ejpam-2422	487	61	γ	γ	X
ejpam-2422	487	62	.	.	PUNCT
ejpam-2422	488	1	the	the	DET
ejpam-2422	488	2	initial	initial	ADJ
ejpam-2422	488	3	(	(	PUNCT
ejpam-2422	488	4	l	l	NOUN
ejpam-2422	488	5	,	,	PUNCT
ejpam-2422	488	6	m)-fuzzy	m)-fuzzy	X
ejpam-2422	488	7	(	(	PUNCT
ejpam-2422	488	8	e	e	NOUN
ejpam-2422	488	9	,	,	PUNCT
ejpam-2422	488	10	k)-soft	k)-soft	PROPN
ejpam-2422	488	11	uniform	uniform	ADJ
ejpam-2422	488	12	structure	structure	NOUN
ejpam-2422	488	13	on	on	ADP
ejpam-2422	488	14	x	x	PUNCT
ejpam-2422	488	15	with	with	ADP
ejpam-2422	488	16	respect	respect	NOUN
ejpam-2422	488	17	to	to	ADP
ejpam-2422	488	18	(	(	PUNCT
ejpam-2422	488	19	x	x	X
ejpam-2422	488	20	,	,	PUNCT
ejpam-2422	488	21	(	(	PUNCT
ejpam-2422	488	22	ϕψ	ϕψ	INTJ
ejpam-2422	488	23	,	,	PUNCT
ejpam-2422	488	24	η)i	η)i	ADJ
ejpam-2422	488	25	,	,	PUNCT
ejpam-2422	488	26	(	(	PUNCT
ejpam-2422	488	27	x	x	X
ejpam-2422	488	28	i	i	PRON
ejpam-2422	488	29	,	,	PUNCT
ejpam-2422	488	30	u	u	PROPN
ejpam-2422	488	31	i),γ	i),γ	PROPN
ejpam-2422	488	32	)	)	PUNCT
ejpam-2422	488	33	is	be	AUX
ejpam-2422	488	34	the	the	DET
ejpam-2422	488	35	coarsest	coarse	ADJ
ejpam-2422	488	36	(	(	PUNCT
ejpam-2422	488	37	l	l	NOUN
ejpam-2422	488	38	,	,	PUNCT
ejpam-2422	488	39	m)-fuzzy	m)-fuzzy	X
ejpam-2422	488	40	(	(	PUNCT
ejpam-2422	488	41	e	e	NOUN
ejpam-2422	488	42	,	,	PUNCT
ejpam-2422	488	43	k)-soft	k)-soft	PROPN
ejpam-2422	488	44	uniform	uniform	ADJ
ejpam-2422	488	45	structure	structure	NOUN
ejpam-2422	488	46	on	on	ADP
ejpam-2422	488	47	x	x	PUNCT
ejpam-2422	488	48	for	for	ADP
ejpam-2422	488	49	which	which	PRON
ejpam-2422	488	50	all	all	PRON
ejpam-2422	488	51	i	i	PRON
ejpam-2422	488	52	∈	∈	PROPN
ejpam-2422	488	53	γ	γ	X
ejpam-2422	488	54	,	,	PUNCT
ejpam-2422	488	55	(	(	PUNCT
ejpam-2422	488	56	ϕψ	ϕψ	INTJ
ejpam-2422	488	57	,	,	PUNCT
ejpam-2422	488	58	η)i	η)i	ADJ
ejpam-2422	488	59	are	be	AUX
ejpam-2422	488	60	uniformly	uniformly	ADV
ejpam-2422	488	61	continuous	continuous	ADJ
ejpam-2422	488	62	.	.	PUNCT
ejpam-2422	489	1	from	from	ADP
ejpam-2422	489	2	theorem	theorem	ADJ
ejpam-2422	489	3	8	8	NUM
ejpam-2422	489	4	and	and	CCONJ
ejpam-2422	489	5	definition	definition	NOUN
ejpam-2422	489	6	6	6	NUM
ejpam-2422	489	7	,	,	PUNCT
ejpam-2422	489	8	we	we	PRON
ejpam-2422	489	9	have	have	VERB
ejpam-2422	489	10	the	the	DET
ejpam-2422	489	11	following	follow	VERB
ejpam-2422	489	12	theorem	theorem	NOUN
ejpam-2422	489	13	:	:	PUNCT
ejpam-2422	489	14	theorem	theorem	NOUN
ejpam-2422	489	15	9	9	NUM
ejpam-2422	489	16	.	.	PUNCT
ejpam-2422	490	1	the	the	DET
ejpam-2422	490	2	category	category	NOUN
ejpam-2422	490	3	hfsu(l	hfsu(l	NOUN
ejpam-2422	490	4	,	,	PUNCT
ejpam-2422	490	5	m	m	PROPN
ejpam-2422	490	6	)	)	PUNCT
ejpam-2422	490	7	of	of	ADP
ejpam-2422	490	8	(	(	PUNCT
ejpam-2422	490	9	l	l	NOUN
ejpam-2422	490	10	,	,	PUNCT
ejpam-2422	490	11	m)-fuzzy	m)-fuzzy	X
ejpam-2422	490	12	(	(	PUNCT
ejpam-2422	490	13	e	e	NOUN
ejpam-2422	490	14	,	,	PUNCT
ejpam-2422	490	15	k)-soft	k)-soft	PROPN
ejpam-2422	490	16	uniform	uniform	ADJ
ejpam-2422	490	17	spaces	space	NOUN
ejpam-2422	490	18	and	and	CCONJ
ejpam-2422	490	19	uniformly	uniformly	ADV
ejpam-2422	490	20	continuous	continuous	ADJ
ejpam-2422	490	21	functions	function	NOUN
ejpam-2422	490	22	is	be	AUX
ejpam-2422	490	23	a	a	DET
ejpam-2422	490	24	topological	topological	ADJ
ejpam-2422	490	25	category	category	NOUN
ejpam-2422	490	26	over	over	ADP
ejpam-2422	490	27	the	the	DET
ejpam-2422	490	28	category	category	NOUN
ejpam-2422	490	29	set3	set3	VERB
ejpam-2422	490	30	with	with	ADP
ejpam-2422	490	31	respect	respect	NOUN
ejpam-2422	490	32	to	to	ADP
ejpam-2422	490	33	the	the	DET
ejpam-2422	490	34	usual	usual	ADJ
ejpam-2422	490	35	forgetful	forgetful	ADJ
ejpam-2422	490	36	functor	functor	NOUN
ejpam-2422	490	37	v	v	NOUN
ejpam-2422	490	38	:	:	PUNCT
ejpam-2422	490	39	hfsu(l	hfsu(l	ADJ
ejpam-2422	490	40	,	,	PUNCT
ejpam-2422	490	41	m)→	m)→	VERB
ejpam-2422	490	42	set3	set3	NOUN
ejpam-2422	490	43	which	which	PRON
ejpam-2422	490	44	is	be	AUX
ejpam-2422	490	45	defined	define	VERB
ejpam-2422	490	46	by	by	ADP
ejpam-2422	490	47	v	v	NUM
ejpam-2422	490	48	(	(	PUNCT
ejpam-2422	490	49	x	x	NOUN
ejpam-2422	490	50	,	,	PUNCT
ejpam-2422	490	51	u	u	NOUN
ejpam-2422	490	52	)	)	PUNCT
ejpam-2422	490	53	=	=	SYM
ejpam-2422	491	1	(	(	PUNCT
ejpam-2422	491	2	x	x	X
ejpam-2422	491	3	,	,	PUNCT
ejpam-2422	491	4	e	e	NOUN
ejpam-2422	491	5	,	,	PUNCT
ejpam-2422	491	6	k	k	NOUN
ejpam-2422	491	7	)	)	PUNCT
ejpam-2422	491	8	and	and	CCONJ
ejpam-2422	491	9	v	v	NOUN
ejpam-2422	491	10	(	(	PUNCT
ejpam-2422	491	11	ϕψ	ϕψ	INTJ
ejpam-2422	491	12	,	,	PUNCT
ejpam-2422	491	13	η	η	NOUN
ejpam-2422	491	14	)	)	PUNCT
ejpam-2422	491	15	=	=	SYM
ejpam-2422	491	16	(	(	PUNCT
ejpam-2422	491	17	ϕ,ψ	ϕ,ψ	PROPN
ejpam-2422	491	18	,	,	PUNCT
ejpam-2422	491	19	η	η	NOUN
ejpam-2422	491	20	)	)	PUNCT
ejpam-2422	491	21	.	.	PUNCT
ejpam-2422	492	1	definition	definition	NOUN
ejpam-2422	492	2	7	7	NUM
ejpam-2422	492	3	.	.	PUNCT
ejpam-2422	493	1	let	let	VERB
ejpam-2422	493	2	x	x	PUNCT
ejpam-2422	493	3	=	=	PUNCT
ejpam-2422	493	4	πi∈γx	πi∈γx	PUNCT
ejpam-2422	493	5	i	i	PRON
ejpam-2422	493	6	,	,	PUNCT
ejpam-2422	494	1	e	e	X
ejpam-2422	494	2	=	=	PUNCT
ejpam-2422	494	3	πi∈γei	πi∈γei	NOUN
ejpam-2422	494	4	and	and	CCONJ
ejpam-2422	494	5	k	k	PROPN
ejpam-2422	494	6	=	=	PROPN
ejpam-2422	494	7	πi∈γki	πi∈γki	PROPN
ejpam-2422	494	8	be	be	AUX
ejpam-2422	494	9	the	the	DET
ejpam-2422	494	10	product	product	NOUN
ejpam-2422	494	11	sets	set	NOUN
ejpam-2422	494	12	and	and	CCONJ
ejpam-2422	494	13	{	{	PUNCT
ejpam-2422	494	14	(	(	PUNCT
ejpam-2422	494	15	x	x	X
ejpam-2422	494	16	i	i	PRON
ejpam-2422	494	17	,	,	PUNCT
ejpam-2422	494	18	u	u	PRON
ejpam-2422	494	19	i)}i∈γ	i)}i∈γ	PROPN
ejpam-2422	494	20	be	be	VERB
ejpam-2422	494	21	a	a	DET
ejpam-2422	494	22	family	family	NOUN
ejpam-2422	494	23	of	of	ADP
ejpam-2422	494	24	(	(	PUNCT
ejpam-2422	494	25	l	l	NOUN
ejpam-2422	494	26	,	,	PUNCT
ejpam-2422	494	27	m)-fuzzy	m)-fuzzy	X
ejpam-2422	494	28	(	(	PUNCT
ejpam-2422	494	29	ei	ei	X
ejpam-2422	494	30	,	,	PUNCT
ejpam-2422	494	31	ki)-soft	ki)-soft	PROPN
ejpam-2422	494	32	uniform	uniform	NOUN
ejpam-2422	494	33	spaces	space	NOUN
ejpam-2422	494	34	,	,	PUNCT
ejpam-2422	494	35	for	for	ADP
ejpam-2422	494	36	each	each	DET
ejpam-2422	494	37	i	i	PRON
ejpam-2422	494	38	∈	∈	PROPN
ejpam-2422	494	39	γ	γ	X
ejpam-2422	494	40	.	.	PUNCT
ejpam-2422	495	1	the	the	DET
ejpam-2422	495	2	initial	initial	ADJ
ejpam-2422	495	3	(	(	PUNCT
ejpam-2422	495	4	l	l	NOUN
ejpam-2422	495	5	,	,	PUNCT
ejpam-2422	495	6	m)-fuzzy	m)-fuzzy	X
ejpam-2422	495	7	(	(	PUNCT
ejpam-2422	495	8	e	e	NOUN
ejpam-2422	495	9	,	,	PUNCT
ejpam-2422	495	10	k)-soft	k)-soft	NOUN
ejpam-2422	495	11	uniformity	uniformity	NOUN
ejpam-2422	495	12	structure	structure	NOUN
ejpam-2422	495	13	u	u	NOUN
ejpam-2422	495	14	on	on	ADP
ejpam-2422	495	15	x	x	PUNCT
ejpam-2422	495	16	with	with	ADP
ejpam-2422	495	17	respect	respect	NOUN
ejpam-2422	495	18	to	to	ADP
ejpam-2422	495	19	the	the	DET
ejpam-2422	495	20	family	family	NOUN
ejpam-2422	495	21	{	{	PUNCT
ejpam-2422	495	22	(	(	PUNCT
ejpam-2422	495	23	pq	pq	INTJ
ejpam-2422	495	24	,	,	PUNCT
ejpam-2422	495	25	r)i	r)i	PUNCT
ejpam-2422	495	26	:	:	PUNCT
ejpam-2422	495	27	x	x	X
ejpam-2422	495	28	→	→	X
ejpam-2422	495	29	(	(	PUNCT
ejpam-2422	495	30	x	x	X
ejpam-2422	495	31	i	i	PRON
ejpam-2422	495	32	,	,	PUNCT
ejpam-2422	495	33	u	u	NOUN
ejpam-2422	495	34	i)}i∈γ	i)}i∈γ	ADJ
ejpam-2422	495	35	of	of	ADP
ejpam-2422	495	36	all	all	DET
ejpam-2422	495	37	projection	projection	NOUN
ejpam-2422	495	38	functions	function	NOUN
ejpam-2422	495	39	is	be	AUX
ejpam-2422	495	40	called	call	VERB
ejpam-2422	495	41	the	the	DET
ejpam-2422	495	42	product	product	NOUN
ejpam-2422	495	43	of	of	ADP
ejpam-2422	495	44	(	(	PUNCT
ejpam-2422	495	45	l	l	NOUN
ejpam-2422	495	46	,	,	PUNCT
ejpam-2422	495	47	m)-fuzzy	m)-fuzzy	X
ejpam-2422	495	48	(	(	PUNCT
ejpam-2422	495	49	ei	ei	X
ejpam-2422	495	50	,	,	PUNCT
ejpam-2422	495	51	ki)-soft	ki)-soft	ADJ
ejpam-2422	495	52	uniformity	uniformity	NOUN
ejpam-2422	495	53	{	{	PUNCT
ejpam-2422	495	54	u	u	NOUN
ejpam-2422	495	55	i}i∈γ	i}i∈γ	NOUN
ejpam-2422	495	56	.	.	PUNCT
ejpam-2422	496	1	the	the	DET
ejpam-2422	496	2	pair	pair	NOUN
ejpam-2422	496	3	(	(	PUNCT
ejpam-2422	496	4	x	x	X
ejpam-2422	496	5	,	,	PUNCT
ejpam-2422	496	6	u	u	NOUN
ejpam-2422	496	7	)	)	PUNCT
ejpam-2422	496	8	is	be	AUX
ejpam-2422	496	9	called	call	VERB
ejpam-2422	496	10	the	the	DET
ejpam-2422	496	11	product	product	NOUN
ejpam-2422	496	12	(	(	PUNCT
ejpam-2422	496	13	l	l	NOUN
ejpam-2422	496	14	,	,	PUNCT
ejpam-2422	496	15	m)-fuzzy	m)-fuzzy	X
ejpam-2422	496	16	(	(	PUNCT
ejpam-2422	496	17	e	e	NOUN
ejpam-2422	496	18	,	,	PUNCT
ejpam-2422	496	19	k)-soft	k)-soft	PROPN
ejpam-2422	496	20	uniform	uniform	ADJ
ejpam-2422	496	21	space	space	NOUN
ejpam-2422	496	22	.	.	PUNCT
ejpam-2422	497	1	6	6	X
ejpam-2422	497	2	.	.	X
ejpam-2422	497	3	conclusion	conclusion	NOUN
ejpam-2422	497	4	since	since	SCONJ
ejpam-2422	497	5	uniformity	uniformity	NOUN
ejpam-2422	497	6	plays	play	VERB
ejpam-2422	497	7	an	an	DET
ejpam-2422	497	8	important	important	ADJ
ejpam-2422	497	9	role	role	NOUN
ejpam-2422	497	10	in	in	ADP
ejpam-2422	497	11	classical	classical	ADJ
ejpam-2422	497	12	topology	topology	NOUN
ejpam-2422	497	13	and	and	CCONJ
ejpam-2422	497	14	fuzzy	fuzzy	ADJ
ejpam-2422	497	15	topology	topology	NOUN
ejpam-2422	497	16	,	,	PUNCT
ejpam-2422	497	17	a	a	DET
ejpam-2422	497	18	great	great	ADJ
ejpam-2422	497	19	number	number	NOUN
ejpam-2422	497	20	of	of	ADP
ejpam-2422	497	21	interesting	interesting	ADJ
ejpam-2422	497	22	works	work	NOUN
ejpam-2422	497	23	has	have	AUX
ejpam-2422	497	24	been	be	AUX
ejpam-2422	497	25	done	do	VERB
ejpam-2422	497	26	on	on	ADP
ejpam-2422	497	27	the	the	DET
ejpam-2422	497	28	uniformity	uniformity	NOUN
ejpam-2422	497	29	theory	theory	NOUN
ejpam-2422	497	30	for	for	ADP
ejpam-2422	497	31	classical	classical	ADJ
ejpam-2422	497	32	sets	set	NOUN
ejpam-2422	497	33	and	and	CCONJ
ejpam-2422	497	34	fuzzy	fuzzy	ADJ
ejpam-2422	497	35	sets	set	NOUN
ejpam-2422	497	36	.	.	PUNCT
ejpam-2422	498	1	so	so	ADV
ejpam-2422	498	2	,	,	PUNCT
ejpam-2422	498	3	we	we	PRON
ejpam-2422	498	4	found	find	VERB
ejpam-2422	498	5	it	it	PRON
ejpam-2422	498	6	reasonable	reasonable	ADJ
ejpam-2422	498	7	to	to	PART
ejpam-2422	498	8	investigate	investigate	VERB
ejpam-2422	498	9	hutton	hutton	NOUN
ejpam-2422	498	10	uniformity	uniformity	NOUN
ejpam-2422	498	11	in	in	ADP
ejpam-2422	498	12	the	the	DET
ejpam-2422	498	13	context	context	NOUN
ejpam-2422	498	14	of	of	ADP
ejpam-2422	498	15	fuzzy	fuzzy	ADJ
ejpam-2422	498	16	soft	soft	ADJ
ejpam-2422	498	17	sets	set	NOUN
ejpam-2422	498	18	.	.	PUNCT
ejpam-2422	499	1	for	for	ADP
ejpam-2422	499	2	this	this	DET
ejpam-2422	499	3	reason	reason	NOUN
ejpam-2422	499	4	,	,	PUNCT
ejpam-2422	499	5	we	we	PRON
ejpam-2422	499	6	defined	define	VERB
ejpam-2422	499	7	fuzzy	fuzzy	ADJ
ejpam-2422	499	8	soft	soft	ADJ
ejpam-2422	499	9	remote	remote	ADJ
ejpam-2422	499	10	neighborhood	neighborhood	NOUN
ejpam-2422	499	11	system	system	NOUN
ejpam-2422	499	12	and	and	CCONJ
ejpam-2422	499	13	used	use	VERB
ejpam-2422	499	14	this	this	PRON
ejpam-2422	499	15	to	to	PART
ejpam-2422	499	16	investigate	investigate	VERB
ejpam-2422	499	17	the	the	DET
ejpam-2422	499	18	relation	relation	NOUN
ejpam-2422	499	19	between	between	ADP
ejpam-2422	499	20	fuzzy	fuzzy	ADJ
ejpam-2422	499	21	soft	soft	ADJ
ejpam-2422	499	22	cotopology	cotopology	NOUN
ejpam-2422	499	23	and	and	CCONJ
ejpam-2422	499	24	fuzzy	fuzzy	ADJ
ejpam-2422	499	25	soft	soft	ADJ
ejpam-2422	499	26	(	(	PUNCT
ejpam-2422	499	27	quasi-)uniformity	quasi-)uniformity	NOUN
ejpam-2422	499	28	.	.	PUNCT
ejpam-2422	500	1	we	we	PRON
ejpam-2422	500	2	proved	prove	VERB
ejpam-2422	500	3	the	the	DET
ejpam-2422	500	4	existence	existence	NOUN
ejpam-2422	500	5	of	of	ADP
ejpam-2422	500	6	the	the	DET
ejpam-2422	500	7	initial	initial	ADJ
ejpam-2422	500	8	structure	structure	NOUN
ejpam-2422	500	9	of	of	ADP
ejpam-2422	500	10	fuzzy	fuzzy	ADJ
ejpam-2422	500	11	soft	soft	ADJ
ejpam-2422	500	12	uniformities	uniformity	NOUN
ejpam-2422	500	13	.	.	PUNCT
ejpam-2422	501	1	therefore	therefore	ADV
ejpam-2422	501	2	we	we	PRON
ejpam-2422	501	3	defined	define	VERB
ejpam-2422	501	4	the	the	DET
ejpam-2422	501	5	product	product	NOUN
ejpam-2422	501	6	fuzzy	fuzzy	ADJ
ejpam-2422	501	7	soft	soft	ADJ
ejpam-2422	501	8	uniformity	uniformity	NOUN
ejpam-2422	501	9	.	.	PUNCT
ejpam-2422	502	1	also	also	ADV
ejpam-2422	502	2	,	,	PUNCT
ejpam-2422	502	3	we	we	PRON
ejpam-2422	502	4	showed	show	VERB
ejpam-2422	502	5	that	that	SCONJ
ejpam-2422	502	6	hfsu(l	hfsu(l	NOUN
ejpam-2422	502	7	,	,	PUNCT
ejpam-2422	502	8	m	m	VERB
ejpam-2422	502	9	)	)	PUNCT
ejpam-2422	502	10	is	be	AUX
ejpam-2422	502	11	a	a	DET
ejpam-2422	502	12	topological	topological	ADJ
ejpam-2422	502	13	category	category	NOUN
ejpam-2422	502	14	over	over	ADP
ejpam-2422	502	15	set3	set3	PROPN
ejpam-2422	502	16	.	.	PUNCT
ejpam-2422	503	1	references	reference	NOUN
ejpam-2422	503	2	432	432	NUM
ejpam-2422	503	3	references	reference	NOUN
ejpam-2422	503	4	[	[	X
ejpam-2422	503	5	1	1	NUM
ejpam-2422	503	6	]	]	PUNCT
ejpam-2422	503	7	b.	b.	PROPN
ejpam-2422	503	8	ahmad	ahmad	PROPN
ejpam-2422	503	9	and	and	CCONJ
ejpam-2422	503	10	a.	a.	PROPN
ejpam-2422	503	11	kharal	kharal	PROPN
ejpam-2422	503	12	.	.	PUNCT
ejpam-2422	504	1	on	on	ADP
ejpam-2422	504	2	fuzzy	fuzzy	ADJ
ejpam-2422	504	3	soft	soft	ADJ
ejpam-2422	504	4	sets	set	NOUN
ejpam-2422	504	5	,	,	PUNCT
ejpam-2422	504	6	advances	advance	NOUN
ejpam-2422	504	7	in	in	ADP
ejpam-2422	504	8	fuzzy	fuzzy	ADJ
ejpam-2422	504	9	systems	system	NOUN
ejpam-2422	504	10	,	,	PUNCT
ejpam-2422	504	11	article	article	NOUN
ejpam-2422	504	12	i	i	PROPN
ejpam-2422	504	13	d	d	PROPN
ejpam-2422	504	14	586507	586507	NUM
ejpam-2422	504	15	,	,	PUNCT
ejpam-2422	504	16	2009	2009	NUM
ejpam-2422	504	17	.	.	PUNCT
ejpam-2422	505	1	[	[	X
ejpam-2422	505	2	2	2	X
ejpam-2422	505	3	]	]	PUNCT
ejpam-2422	505	4	h.	h.	PROPN
ejpam-2422	505	5	aktaş	aktaş	PROPN
ejpam-2422	505	6	and	and	CCONJ
ejpam-2422	505	7	n.	n.	PROPN
ejpam-2422	505	8	çaǧman	çaǧman	PROPN
ejpam-2422	505	9	.	.	PUNCT
ejpam-2422	505	10	soft	soft	ADJ
ejpam-2422	505	11	sets	set	NOUN
ejpam-2422	505	12	and	and	CCONJ
ejpam-2422	505	13	soft	soft	ADJ
ejpam-2422	505	14	groups	group	NOUN
ejpam-2422	505	15	,	,	PUNCT
ejpam-2422	505	16	information	information	NOUN
ejpam-2422	505	17	sciences	science	NOUN
ejpam-2422	505	18	,	,	PUNCT
ejpam-2422	505	19	177(13	177(13	NUM
ejpam-2422	505	20	)	)	PUNCT
ejpam-2422	505	21	,	,	PUNCT
ejpam-2422	505	22	27262735	27262735	NUM
ejpam-2422	505	23	.	.	PUNCT
ejpam-2422	505	24	2007	2007	NUM
ejpam-2422	505	25	.	.	PUNCT
ejpam-2422	506	1	[	[	X
ejpam-2422	506	2	3	3	NUM
ejpam-2422	506	3	]	]	PUNCT
ejpam-2422	506	4	a.	a.	NOUN
ejpam-2422	506	5	aygünoǧlu	aygünoǧlu	PROPN
ejpam-2422	506	6	and	and	CCONJ
ejpam-2422	506	7	h.	h.	PROPN
ejpam-2422	506	8	aygün	aygün	PROPN
ejpam-2422	506	9	.	.	PUNCT
ejpam-2422	507	1	introduction	introduction	NOUN
ejpam-2422	507	2	to	to	ADP
ejpam-2422	507	3	fuzzy	fuzzy	ADJ
ejpam-2422	507	4	soft	soft	ADJ
ejpam-2422	507	5	groups	group	NOUN
ejpam-2422	507	6	,	,	PUNCT
ejpam-2422	507	7	computers	computer	NOUN
ejpam-2422	507	8	and	and	CCONJ
ejpam-2422	507	9	mathematics	mathematic	NOUN
ejpam-2422	507	10	with	with	ADP
ejpam-2422	507	11	applications	application	NOUN
ejpam-2422	507	12	,	,	PUNCT
ejpam-2422	507	13	58	58	NUM
ejpam-2422	507	14	,	,	PUNCT
ejpam-2422	507	15	1279	1279	NUM
ejpam-2422	507	16	-	-	SYM
ejpam-2422	507	17	1286	1286	NUM
ejpam-2422	507	18	.	.	PUNCT
ejpam-2422	508	1	2009	2009	NUM
ejpam-2422	508	2	.	.	PUNCT
ejpam-2422	509	1	[	[	X
ejpam-2422	509	2	4	4	NUM
ejpam-2422	509	3	]	]	PUNCT
ejpam-2422	509	4	a.	a.	NOUN
ejpam-2422	509	5	aygünoǧlu	aygünoǧlu	PROPN
ejpam-2422	509	6	,	,	PUNCT
ejpam-2422	509	7	v.	v.	ADP
ejpam-2422	509	8	çetkin	çetkin	PROPN
ejpam-2422	509	9	,	,	PUNCT
ejpam-2422	509	10	and	and	CCONJ
ejpam-2422	509	11	h.	h.	PROPN
ejpam-2422	509	12	aygün	aygün	PROPN
ejpam-2422	509	13	.	.	PUNCT
ejpam-2422	510	1	an	an	DET
ejpam-2422	510	2	introduction	introduction	NOUN
ejpam-2422	510	3	to	to	ADP
ejpam-2422	510	4	fuzzy	fuzzy	ADJ
ejpam-2422	510	5	soft	soft	ADJ
ejpam-2422	510	6	topological	topological	ADJ
ejpam-2422	510	7	spaces	space	NOUN
ejpam-2422	510	8	,	,	PUNCT
ejpam-2422	510	9	hacettepe	hacettepe	PROPN
ejpam-2422	510	10	journal	journal	NOUN
ejpam-2422	510	11	of	of	ADP
ejpam-2422	510	12	mathematics	mathematic	NOUN
ejpam-2422	510	13	and	and	CCONJ
ejpam-2422	510	14	statistics	statistic	NOUN
ejpam-2422	510	15	,	,	PUNCT
ejpam-2422	510	16	43(2	43(2	PROPN
ejpam-2422	510	17	)	)	PUNCT
ejpam-2422	510	18	,	,	PUNCT
ejpam-2422	510	19	197	197	NUM
ejpam-2422	510	20	-	-	SYM
ejpam-2422	510	21	208	208	NUM
ejpam-2422	510	22	.	.	PUNCT
ejpam-2422	510	23	2014	2014	NUM
ejpam-2422	510	24	.	.	PUNCT
ejpam-2422	511	1	[	[	X
ejpam-2422	511	2	5	5	NUM
ejpam-2422	511	3	]	]	PUNCT
ejpam-2422	511	4	g.	g.	NOUN
ejpam-2422	511	5	gierz	gierz	PROPN
ejpam-2422	511	6	,	,	PUNCT
ejpam-2422	511	7	k.	k.	PROPN
ejpam-2422	511	8	h.	h.	PROPN
ejpam-2422	511	9	hofmann	hofmann	PROPN
ejpam-2422	511	10	,	,	PUNCT
ejpam-2422	511	11	k.	k.	PROPN
ejpam-2422	511	12	keimel	keimel	PROPN
ejpam-2422	511	13	,	,	PUNCT
ejpam-2422	511	14	j.	j.	PROPN
ejpam-2422	511	15	d.	d.	PROPN
ejpam-2422	511	16	lawson	lawson	PROPN
ejpam-2422	511	17	,	,	PUNCT
ejpam-2422	511	18	m.	m.	NOUN
ejpam-2422	511	19	mislove	mislove	NOUN
ejpam-2422	511	20	and	and	CCONJ
ejpam-2422	511	21	d.	d.	PROPN
ejpam-2422	511	22	s.	s.	PROPN
ejpam-2422	511	23	scott	scott	PROPN
ejpam-2422	511	24	.	.	PUNCT
ejpam-2422	512	1	a	a	DET
ejpam-2422	512	2	compendium	compendium	NOUN
ejpam-2422	512	3	of	of	ADP
ejpam-2422	512	4	continuous	continuous	ADJ
ejpam-2422	512	5	lattices	lattice	NOUN
ejpam-2422	512	6	,	,	PUNCT
ejpam-2422	512	7	springer	springer	NOUN
ejpam-2422	512	8	,	,	PUNCT
ejpam-2422	512	9	berlin	berlin	PROPN
ejpam-2422	512	10	,	,	PUNCT
ejpam-2422	512	11	heidelberg	heidelberg	PROPN
ejpam-2422	512	12	,	,	PUNCT
ejpam-2422	512	13	new	new	PROPN
ejpam-2422	512	14	york	york	PROPN
ejpam-2422	512	15	,	,	PUNCT
ejpam-2422	512	16	1980	1980	NUM
ejpam-2422	512	17	.	.	PUNCT
ejpam-2422	513	1	[	[	X
ejpam-2422	513	2	6	6	NUM
ejpam-2422	513	3	]	]	X
ejpam-2422	513	4	u.	u.	NOUN
ejpam-2422	513	5	höhle	höhle	PROPN
ejpam-2422	513	6	.	.	PUNCT
ejpam-2422	514	1	probabilistic	probabilistic	ADJ
ejpam-2422	514	2	topologies	topology	NOUN
ejpam-2422	514	3	induced	induce	VERB
ejpam-2422	514	4	by	by	ADP
ejpam-2422	514	5	l	l	ADJ
ejpam-2422	514	6	-	-	ADJ
ejpam-2422	514	7	fuzzy	fuzzy	ADJ
ejpam-2422	514	8	uniformities	uniformity	NOUN
ejpam-2422	514	9	,	,	PUNCT
ejpam-2422	514	10	manuscripta	manuscripta	PROPN
ejpam-2422	514	11	mathematica	mathematica	PROPN
ejpam-2422	514	12	,	,	PUNCT
ejpam-2422	514	13	38(3	38(3	NUM
ejpam-2422	514	14	)	)	PUNCT
ejpam-2422	514	15	,	,	PUNCT
ejpam-2422	514	16	289	289	NUM
ejpam-2422	514	17	-	-	SYM
ejpam-2422	514	18	323	323	NUM
ejpam-2422	514	19	.	.	PUNCT
ejpam-2422	514	20	1982	1982	NUM
ejpam-2422	514	21	.	.	PUNCT
ejpam-2422	515	1	[	[	X
ejpam-2422	515	2	7	7	X
ejpam-2422	515	3	]	]	X
ejpam-2422	515	4	b.	b.	PROPN
ejpam-2422	515	5	hutton	hutton	PROPN
ejpam-2422	515	6	.	.	PUNCT
ejpam-2422	516	1	uniformities	uniformity	NOUN
ejpam-2422	516	2	on	on	ADP
ejpam-2422	516	3	fuzzy	fuzzy	ADJ
ejpam-2422	516	4	topological	topological	ADJ
ejpam-2422	516	5	spaces	space	NOUN
ejpam-2422	516	6	,	,	PUNCT
ejpam-2422	516	7	journal	journal	NOUN
ejpam-2422	516	8	of	of	ADP
ejpam-2422	516	9	mathematical	mathematical	ADJ
ejpam-2422	516	10	analysis	analysis	NOUN
ejpam-2422	516	11	and	and	CCONJ
ejpam-2422	516	12	applications	application	NOUN
ejpam-2422	516	13	,	,	PUNCT
ejpam-2422	516	14	58	58	NUM
ejpam-2422	516	15	,	,	PUNCT
ejpam-2422	516	16	559	559	NUM
ejpam-2422	516	17	-	-	SYM
ejpam-2422	516	18	571	571	NUM
ejpam-2422	516	19	.	.	PUNCT
ejpam-2422	516	20	1977	1977	NUM
ejpam-2422	516	21	.	.	PUNCT
ejpam-2422	517	1	[	[	X
ejpam-2422	517	2	8	8	NUM
ejpam-2422	517	3	]	]	X
ejpam-2422	518	1	y.	y.	PROPN
ejpam-2422	518	2	b.	b.	PROPN
ejpam-2422	518	3	jun	jun	PROPN
ejpam-2422	518	4	.	.	PROPN
ejpam-2422	518	5	soft	soft	ADJ
ejpam-2422	518	6	bck	bck	PROPN
ejpam-2422	518	7	/	/	SYM
ejpam-2422	518	8	bci	bci	PROPN
ejpam-2422	518	9	algebras	algebra	NOUN
ejpam-2422	518	10	,	,	PUNCT
ejpam-2422	518	11	computers	computer	NOUN
ejpam-2422	518	12	and	and	CCONJ
ejpam-2422	518	13	mathematics	mathematic	NOUN
ejpam-2422	518	14	with	with	ADP
ejpam-2422	518	15	applications	application	NOUN
ejpam-2422	518	16	,	,	PUNCT
ejpam-2422	518	17	56(5	56(5	NUM
ejpam-2422	518	18	)	)	PUNCT
ejpam-2422	518	19	,	,	PUNCT
ejpam-2422	518	20	1408	1408	NUM
ejpam-2422	518	21	-	-	SYM
ejpam-2422	518	22	1413	1413	NUM
ejpam-2422	518	23	.	.	PUNCT
ejpam-2422	518	24	2008	2008	NUM
ejpam-2422	518	25	.	.	PUNCT
ejpam-2422	519	1	[	[	X
ejpam-2422	519	2	9	9	NUM
ejpam-2422	519	3	]	]	PUNCT
ejpam-2422	519	4	a.	a.	NOUN
ejpam-2422	519	5	kharal	kharal	PROPN
ejpam-2422	519	6	and	and	CCONJ
ejpam-2422	519	7	b.	b.	PROPN
ejpam-2422	519	8	ahmad	ahmad	PROPN
ejpam-2422	519	9	.	.	PUNCT
ejpam-2422	520	1	mappings	mapping	NOUN
ejpam-2422	520	2	on	on	ADP
ejpam-2422	520	3	fuzzy	fuzzy	ADJ
ejpam-2422	520	4	soft	soft	ADJ
ejpam-2422	520	5	classes	class	NOUN
ejpam-2422	520	6	,	,	PUNCT
ejpam-2422	520	7	advances	advance	NOUN
ejpam-2422	520	8	in	in	ADP
ejpam-2422	520	9	fuzzy	fuzzy	ADJ
ejpam-2422	520	10	systems	system	NOUN
ejpam-2422	520	11	,	,	PUNCT
ejpam-2422	520	12	article	article	NOUN
ejpam-2422	520	13	i	i	PROPN
ejpam-2422	520	14	d	d	PROPN
ejpam-2422	520	15	407890	407890	NUM
ejpam-2422	520	16	,	,	PUNCT
ejpam-2422	520	17	2009	2009	NUM
ejpam-2422	520	18	.	.	PUNCT
ejpam-2422	521	1	[	[	X
ejpam-2422	521	2	10	10	NUM
ejpam-2422	521	3	]	]	X
ejpam-2422	521	4	r.	r.	PROPN
ejpam-2422	521	5	lowen	lowen	PROPN
ejpam-2422	521	6	.	.	PUNCT
ejpam-2422	522	1	fuzzy	fuzzy	ADJ
ejpam-2422	522	2	uniform	uniform	ADJ
ejpam-2422	522	3	spaces	space	NOUN
ejpam-2422	522	4	,	,	PUNCT
ejpam-2422	522	5	journal	journal	NOUN
ejpam-2422	522	6	of	of	ADP
ejpam-2422	522	7	mathematical	mathematical	ADJ
ejpam-2422	522	8	analysis	analysis	NOUN
ejpam-2422	522	9	and	and	CCONJ
ejpam-2422	522	10	applications	application	NOUN
ejpam-2422	522	11	,	,	PUNCT
ejpam-2422	522	12	82(2	82(2	NUM
ejpam-2422	522	13	)	)	PUNCT
ejpam-2422	522	14	,	,	PUNCT
ejpam-2422	522	15	370	370	NUM
ejpam-2422	522	16	-	-	SYM
ejpam-2422	522	17	385	385	NUM
ejpam-2422	522	18	.	.	PUNCT
ejpam-2422	522	19	1981	1981	NUM
ejpam-2422	522	20	.	.	PUNCT
ejpam-2422	523	1	[	[	X
ejpam-2422	523	2	11	11	NUM
ejpam-2422	523	3	]	]	X
ejpam-2422	523	4	p.k	p.k	PROPN
ejpam-2422	523	5	.	.	PROPN
ejpam-2422	523	6	maji	maji	PROPN
ejpam-2422	523	7	,	,	PUNCT
ejpam-2422	523	8	r.	r.	PROPN
ejpam-2422	523	9	biswas	biswas	PROPN
ejpam-2422	523	10	,	,	PUNCT
ejpam-2422	523	11	and	and	CCONJ
ejpam-2422	523	12	a.r	a.r	PROPN
ejpam-2422	523	13	.	.	PROPN
ejpam-2422	523	14	roy	roy	PROPN
ejpam-2422	523	15	.	.	PROPN
ejpam-2422	523	16	fuzzy	fuzzy	ADJ
ejpam-2422	523	17	soft	soft	ADJ
ejpam-2422	523	18	sets	set	NOUN
ejpam-2422	523	19	,	,	PUNCT
ejpam-2422	523	20	journal	journal	NOUN
ejpam-2422	523	21	of	of	ADP
ejpam-2422	523	22	fuzzy	fuzzy	ADJ
ejpam-2422	523	23	mathematics	mathematic	NOUN
ejpam-2422	523	24	,	,	PUNCT
ejpam-2422	523	25	9(3	9(3	NUM
ejpam-2422	523	26	)	)	PUNCT
ejpam-2422	523	27	,	,	PUNCT
ejpam-2422	523	28	589	589	NUM
ejpam-2422	523	29	-	-	SYM
ejpam-2422	523	30	602	602	NUM
ejpam-2422	523	31	.	.	PUNCT
ejpam-2422	523	32	2001	2001	NUM
ejpam-2422	523	33	.	.	PUNCT
ejpam-2422	524	1	[	[	X
ejpam-2422	524	2	12	12	NUM
ejpam-2422	524	3	]	]	X
ejpam-2422	524	4	d.	d.	PROPN
ejpam-2422	524	5	molodtsov	molodtsov	PROPN
ejpam-2422	524	6	.	.	PUNCT
ejpam-2422	525	1	soft	soft	ADJ
ejpam-2422	525	2	set	set	NOUN
ejpam-2422	525	3	theory	theory	NOUN
ejpam-2422	525	4	-	-	PUNCT
ejpam-2422	525	5	first	first	ADJ
ejpam-2422	525	6	results	result	NOUN
ejpam-2422	525	7	,	,	PUNCT
ejpam-2422	525	8	computers	computer	NOUN
ejpam-2422	525	9	and	and	CCONJ
ejpam-2422	525	10	mathematics	mathematic	NOUN
ejpam-2422	525	11	with	with	ADP
ejpam-2422	525	12	applications	application	NOUN
ejpam-2422	525	13	,	,	PUNCT
ejpam-2422	525	14	37(4/5	37(4/5	NOUN
ejpam-2422	525	15	)	)	PUNCT
ejpam-2422	525	16	,	,	PUNCT
ejpam-2422	525	17	19	19	NUM
ejpam-2422	525	18	-	-	SYM
ejpam-2422	525	19	31	31	NUM
ejpam-2422	525	20	.	.	PUNCT
ejpam-2422	525	21	1999	1999	NUM
ejpam-2422	525	22	.	.	PUNCT
ejpam-2422	526	1	[	[	X
ejpam-2422	526	2	13	13	NUM
ejpam-2422	526	3	]	]	SYM
ejpam-2422	526	4	a.r	a.r	PROPN
ejpam-2422	526	5	.	.	PROPN
ejpam-2422	526	6	roy	roy	PROPN
ejpam-2422	526	7	and	and	CCONJ
ejpam-2422	526	8	p.k	p.k	PROPN
ejpam-2422	526	9	.	.	PROPN
ejpam-2422	526	10	maji	maji	PROPN
ejpam-2422	526	11	.	.	PUNCT
ejpam-2422	527	1	a	a	DET
ejpam-2422	527	2	fuzzy	fuzzy	ADJ
ejpam-2422	527	3	soft	soft	ADJ
ejpam-2422	527	4	set	set	ADJ
ejpam-2422	527	5	theoretic	theoretic	ADJ
ejpam-2422	527	6	approach	approach	NOUN
ejpam-2422	527	7	to	to	ADP
ejpam-2422	527	8	decision	decision	NOUN
ejpam-2422	527	9	making	making	NOUN
ejpam-2422	527	10	problems	problem	NOUN
ejpam-2422	527	11	,	,	PUNCT
ejpam-2422	527	12	journal	journal	NOUN
ejpam-2422	527	13	of	of	ADP
ejpam-2422	527	14	computational	computational	ADJ
ejpam-2422	527	15	and	and	CCONJ
ejpam-2422	527	16	applied	applied	ADJ
ejpam-2422	527	17	mathematics	mathematic	NOUN
ejpam-2422	527	18	,	,	PUNCT
ejpam-2422	527	19	203	203	NUM
ejpam-2422	527	20	,	,	PUNCT
ejpam-2422	527	21	412	412	NUM
ejpam-2422	527	22	-	-	SYM
ejpam-2422	527	23	418	418	NUM
ejpam-2422	527	24	.	.	PUNCT
ejpam-2422	527	25	2007	2007	NUM
ejpam-2422	527	26	.	.	PUNCT
ejpam-2422	528	1	[	[	X
ejpam-2422	528	2	14	14	NUM
ejpam-2422	528	3	]	]	X
ejpam-2422	528	4	f.	f.	PROPN
ejpam-2422	528	5	g.	g.	PROPN
ejpam-2422	528	6	shi	shi	PROPN
ejpam-2422	528	7	.	.	PUNCT
ejpam-2422	529	1	pointwise	pointwise	VERB
ejpam-2422	529	2	uniformities	uniformity	NOUN
ejpam-2422	529	3	in	in	ADP
ejpam-2422	529	4	fuzzy	fuzzy	ADJ
ejpam-2422	529	5	set	set	NOUN
ejpam-2422	529	6	theory	theory	NOUN
ejpam-2422	529	7	,	,	PUNCT
ejpam-2422	529	8	fuzzy	fuzzy	ADJ
ejpam-2422	529	9	sets	set	NOUN
ejpam-2422	529	10	and	and	CCONJ
ejpam-2422	529	11	systems	system	NOUN
ejpam-2422	529	12	,	,	PUNCT
ejpam-2422	529	13	98(1	98(1	NOUN
ejpam-2422	529	14	)	)	PUNCT
ejpam-2422	529	15	,	,	PUNCT
ejpam-2422	529	16	141146	141146	NUM
ejpam-2422	529	17	.	.	PUNCT
ejpam-2422	530	1	1998	1998	NUM
ejpam-2422	530	2	.	.	PUNCT
ejpam-2422	531	1	[	[	X
ejpam-2422	531	2	15	15	NUM
ejpam-2422	531	3	]	]	X
ejpam-2422	531	4	f.	f.	PROPN
ejpam-2422	531	5	g.	g.	PROPN
ejpam-2422	531	6	shi	shi	PROPN
ejpam-2422	531	7	,	,	PUNCT
ejpam-2422	531	8	j.	j.	PROPN
ejpam-2422	531	9	zhang	zhang	PROPN
ejpam-2422	531	10	,	,	PUNCT
ejpam-2422	531	11	and	and	CCONJ
ejpam-2422	531	12	c.	c.	PROPN
ejpam-2422	531	13	y.	y.	PROPN
ejpam-2422	531	14	zheng	zheng	PROPN
ejpam-2422	531	15	.	.	PUNCT
ejpam-2422	532	1	l	l	NOUN
ejpam-2422	532	2	-	-	NOUN
ejpam-2422	532	3	proximities	proximity	NOUN
ejpam-2422	532	4	and	and	CCONJ
ejpam-2422	532	5	totally	totally	ADV
ejpam-2422	532	6	bounded	bound	VERB
ejpam-2422	532	7	pointwise	pointwise	PROPN
ejpam-2422	532	8	luniformities	luniformitie	NOUN
ejpam-2422	532	9	,	,	PUNCT
ejpam-2422	532	10	fuzzy	fuzzy	ADJ
ejpam-2422	532	11	sets	set	NOUN
ejpam-2422	532	12	and	and	CCONJ
ejpam-2422	532	13	systems	system	NOUN
ejpam-2422	532	14	,	,	PUNCT
ejpam-2422	532	15	133(3	133(3	NUM
ejpam-2422	532	16	)	)	PUNCT
ejpam-2422	532	17	,	,	PUNCT
ejpam-2422	532	18	321	321	NUM
ejpam-2422	532	19	-	-	SYM
ejpam-2422	532	20	331	331	NUM
ejpam-2422	532	21	.	.	PUNCT
ejpam-2422	532	22	2003	2003	NUM
ejpam-2422	532	23	.	.	PUNCT
ejpam-2422	533	1	[	[	X
ejpam-2422	533	2	16	16	NUM
ejpam-2422	533	3	]	]	PUNCT
ejpam-2422	533	4	a.	a.	NOUN
ejpam-2422	533	5	p.	p.	NOUN
ejpam-2422	533	6	s̆ostak	s̆ostak	PROPN
ejpam-2422	533	7	.	.	PUNCT
ejpam-2422	534	1	on	on	ADP
ejpam-2422	534	2	a	a	DET
ejpam-2422	534	3	fuzzy	fuzzy	ADJ
ejpam-2422	534	4	topological	topological	ADJ
ejpam-2422	534	5	structure	structure	NOUN
ejpam-2422	534	6	,	,	PUNCT
ejpam-2422	534	7	rendiconti	rendiconti	VERB
ejpam-2422	534	8	del	del	PROPN
ejpam-2422	534	9	circolo	circolo	PROPN
ejpam-2422	534	10	matematico	matematico	NOUN
ejpam-2422	534	11	di	di	X
ejpam-2422	534	12	palermo	palermo	PROPN
ejpam-2422	534	13	serie	serie	PROPN
ejpam-2422	534	14	ii	ii	PROPN
ejpam-2422	534	15	,	,	PUNCT
ejpam-2422	534	16	supplemento	supplemento	NOUN
ejpam-2422	534	17	,	,	PUNCT
ejpam-2422	534	18	11	11	NUM
ejpam-2422	534	19	,	,	PUNCT
ejpam-2422	534	20	89	89	NUM
ejpam-2422	534	21	-	-	SYM
ejpam-2422	534	22	103	103	NUM
ejpam-2422	534	23	.	.	PUNCT
ejpam-2422	534	24	1985	1985	NUM
ejpam-2422	534	25	.	.	PUNCT
ejpam-2422	535	1	references	reference	NOUN
ejpam-2422	535	2	433	433	NUM
ejpam-2422	535	3	[	[	X
ejpam-2422	535	4	17	17	NUM
ejpam-2422	535	5	]	]	PUNCT
ejpam-2422	535	6	b.	b.	PROPN
ejpam-2422	535	7	tanay	tanay	PROPN
ejpam-2422	535	8	and	and	CCONJ
ejpam-2422	535	9	m.	m.	PROPN
ejpam-2422	535	10	b.	b.	PROPN
ejpam-2422	535	11	kandemir	kandemir	PROPN
ejpam-2422	535	12	.	.	PUNCT
ejpam-2422	536	1	topological	topological	ADJ
ejpam-2422	536	2	structures	structure	NOUN
ejpam-2422	536	3	of	of	ADP
ejpam-2422	536	4	fuzzy	fuzzy	ADJ
ejpam-2422	536	5	soft	soft	ADJ
ejpam-2422	536	6	sets	set	NOUN
ejpam-2422	536	7	,	,	PUNCT
ejpam-2422	536	8	computers	computer	NOUN
ejpam-2422	536	9	and	and	CCONJ
ejpam-2422	536	10	mathematics	mathematic	NOUN
ejpam-2422	536	11	with	with	ADP
ejpam-2422	536	12	applications	application	NOUN
ejpam-2422	536	13	,	,	PUNCT
ejpam-2422	536	14	61	61	NUM
ejpam-2422	536	15	,	,	PUNCT
ejpam-2422	536	16	412	412	NUM
ejpam-2422	536	17	-	-	SYM
ejpam-2422	536	18	418	418	NUM
ejpam-2422	536	19	.	.	PUNCT
ejpam-2422	536	20	2011	2011	NUM
ejpam-2422	536	21	.	.	PUNCT
ejpam-2422	537	1	[	[	X
ejpam-2422	537	2	18	18	NUM
ejpam-2422	537	3	]	]	X
ejpam-2422	537	4	y.	y.	PROPN
ejpam-2422	537	5	yue	yue	PROPN
ejpam-2422	537	6	and	and	CCONJ
ejpam-2422	537	7	f.	f.	PROPN
ejpam-2422	537	8	shi	shi	PROPN
ejpam-2422	537	9	.	.	PUNCT
ejpam-2422	538	1	l	l	ADJ
ejpam-2422	538	2	-	-	ADJ
ejpam-2422	538	3	fuzzy	fuzzy	ADJ
ejpam-2422	538	4	uniform	uniform	ADJ
ejpam-2422	538	5	spaces	space	NOUN
ejpam-2422	538	6	,	,	PUNCT
ejpam-2422	538	7	journal	journal	NOUN
ejpam-2422	538	8	of	of	ADP
ejpam-2422	538	9	the	the	DET
ejpam-2422	538	10	korean	korean	PROPN
ejpam-2422	538	11	mathematical	mathematical	ADJ
ejpam-2422	538	12	society	society	NOUN
ejpam-2422	538	13	,	,	PUNCT
ejpam-2422	538	14	44(6	44(6	NOUN
ejpam-2422	538	15	)	)	PUNCT
ejpam-2422	538	16	,	,	PUNCT
ejpam-2422	538	17	1383	1383	NUM
ejpam-2422	538	18	-	-	SYM
ejpam-2422	538	19	1396	1396	NUM
ejpam-2422	538	20	.	.	PUNCT
ejpam-2422	539	1	2007	2007	NUM
ejpam-2422	539	2	.	.	PUNCT