id	sid	tid	token	lemma	pos
ejpam-5330	1	1	european	european	PROPN
ejpam-5330	1	2	journal	journal	PROPN
ejpam-5330	1	3	of	of	ADP
ejpam-5330	1	4	pure	pure	ADJ
ejpam-5330	1	5	and	and	CCONJ
ejpam-5330	1	6	applied	apply	VERB
ejpam-5330	1	7	mathematics	mathematic	NOUN
ejpam-5330	1	8	vol	vol	NOUN
ejpam-5330	1	9	.	.	PROPN
ejpam-5330	2	1	17	17	NUM
ejpam-5330	2	2	,	,	PUNCT
ejpam-5330	2	3	no	no	INTJ
ejpam-5330	2	4	.	.	NOUN
ejpam-5330	2	5	4	4	NUM
ejpam-5330	2	6	,	,	PUNCT
ejpam-5330	2	7	2024	2024	NUM
ejpam-5330	2	8	,	,	PUNCT
ejpam-5330	2	9	4112	4112	NUM
ejpam-5330	2	10	-	-	SYM
ejpam-5330	2	11	4134	4134	NUM
ejpam-5330	2	12	issn	issn	PROPN
ejpam-5330	2	13	1307	1307	NUM
ejpam-5330	2	14	-	-	SYM
ejpam-5330	2	15	5543	5543	NUM
ejpam-5330	2	16	–	–	PUNCT
ejpam-5330	3	1	ejpam.com	ejpam.com	X
ejpam-5330	3	2	published	publish	VERB
ejpam-5330	3	3	by	by	ADP
ejpam-5330	3	4	new	new	PROPN
ejpam-5330	3	5	york	york	PROPN
ejpam-5330	3	6	business	business	PROPN
ejpam-5330	3	7	global	global	ADJ
ejpam-5330	3	8	on	on	ADP
ejpam-5330	3	9	fuzzy	fuzzy	ADJ
ejpam-5330	3	10	soft	soft	ADJ
ejpam-5330	3	11	α	α	NOUN
ejpam-5330	3	12	-	-	ADJ
ejpam-5330	3	13	open	open	ADJ
ejpam-5330	3	14	sets	set	NOUN
ejpam-5330	3	15	,	,	PUNCT
ejpam-5330	3	16	α	α	NOUN
ejpam-5330	3	17	-	-	NOUN
ejpam-5330	3	18	continuity	continuity	NOUN
ejpam-5330	3	19	,	,	PUNCT
ejpam-5330	3	20	and	and	CCONJ
ejpam-5330	3	21	α	α	NOUN
ejpam-5330	3	22	-	-	NOUN
ejpam-5330	3	23	compactness	compactness	NOUN
ejpam-5330	3	24	:	:	PUNCT
ejpam-5330	3	25	some	some	DET
ejpam-5330	3	26	novel	novel	ADJ
ejpam-5330	3	27	results	result	NOUN
ejpam-5330	3	28	wafa	wafa	NOUN
ejpam-5330	3	29	alqurashi1	alqurashi1	PROPN
ejpam-5330	3	30	,	,	PUNCT
ejpam-5330	3	31	islam	islam	PROPN
ejpam-5330	3	32	m.	m.	PROPN
ejpam-5330	3	33	taha2,3,∗	taha2,3,∗	PROPN
ejpam-5330	3	34	1	1	NUM
ejpam-5330	3	35	department	department	NOUN
ejpam-5330	3	36	of	of	ADP
ejpam-5330	3	37	mathematics	mathematic	NOUN
ejpam-5330	3	38	,	,	PUNCT
ejpam-5330	3	39	faculty	faculty	NOUN
ejpam-5330	3	40	of	of	ADP
ejpam-5330	3	41	science	science	NOUN
ejpam-5330	3	42	,	,	PUNCT
ejpam-5330	3	43	umm	umm	INTJ
ejpam-5330	3	44	al	al	PROPN
ejpam-5330	3	45	-	-	PUNCT
ejpam-5330	3	46	qura	qura	PROPN
ejpam-5330	3	47	university	university	PROPN
ejpam-5330	3	48	,	,	PUNCT
ejpam-5330	3	49	makkah	makkah	PROPN
ejpam-5330	3	50	,	,	PUNCT
ejpam-5330	3	51	saudi	saudi	PROPN
ejpam-5330	3	52	arabia	arabia	PROPN
ejpam-5330	3	53	2	2	NUM
ejpam-5330	3	54	department	department	NOUN
ejpam-5330	3	55	of	of	ADP
ejpam-5330	3	56	basic	basic	ADJ
ejpam-5330	3	57	sciences	science	NOUN
ejpam-5330	3	58	,	,	PUNCT
ejpam-5330	3	59	higher	high	ADJ
ejpam-5330	3	60	institute	institute	NOUN
ejpam-5330	3	61	of	of	ADP
ejpam-5330	3	62	engineering	engineering	NOUN
ejpam-5330	3	63	and	and	CCONJ
ejpam-5330	3	64	technology	technology	NOUN
ejpam-5330	3	65	,	,	PUNCT
ejpam-5330	3	66	menoufia	menoufia	PROPN
ejpam-5330	3	67	,	,	PUNCT
ejpam-5330	3	68	egypt	egypt	PROPN
ejpam-5330	3	69	3	3	NUM
ejpam-5330	3	70	department	department	NOUN
ejpam-5330	3	71	of	of	ADP
ejpam-5330	3	72	mathematics	mathematic	NOUN
ejpam-5330	3	73	,	,	PUNCT
ejpam-5330	3	74	faculty	faculty	NOUN
ejpam-5330	3	75	of	of	ADP
ejpam-5330	3	76	science	science	NOUN
ejpam-5330	3	77	,	,	PUNCT
ejpam-5330	3	78	sohag	sohag	NOUN
ejpam-5330	3	79	university	university	NOUN
ejpam-5330	3	80	,	,	PUNCT
ejpam-5330	3	81	sohag	sohag	NOUN
ejpam-5330	3	82	,	,	PUNCT
ejpam-5330	3	83	egypt	egypt	PROPN
ejpam-5330	3	84	abstract	abstract	NOUN
ejpam-5330	3	85	.	.	PUNCT
ejpam-5330	4	1	in	in	ADP
ejpam-5330	4	2	this	this	DET
ejpam-5330	4	3	paper	paper	NOUN
ejpam-5330	4	4	,	,	PUNCT
ejpam-5330	4	5	we	we	PRON
ejpam-5330	4	6	defined	define	VERB
ejpam-5330	4	7	the	the	DET
ejpam-5330	4	8	notions	notion	NOUN
ejpam-5330	4	9	of	of	ADP
ejpam-5330	4	10	fuzzy	fuzzy	ADJ
ejpam-5330	4	11	soft	soft	ADJ
ejpam-5330	4	12	α	α	NOUN
ejpam-5330	4	13	-	-	ADJ
ejpam-5330	4	14	interior	interior	ADJ
ejpam-5330	4	15	(	(	PUNCT
ejpam-5330	4	16	α	α	NOUN
ejpam-5330	4	17	-	-	PUNCT
ejpam-5330	4	18	closure	closure	NOUN
ejpam-5330	4	19	)	)	PUNCT
ejpam-5330	4	20	operators	operator	NOUN
ejpam-5330	4	21	via	via	ADP
ejpam-5330	4	22	fuzzy	fuzzy	ADJ
ejpam-5330	4	23	soft	soft	ADJ
ejpam-5330	4	24	topologies	topology	NOUN
ejpam-5330	4	25	based	base	VERB
ejpam-5330	4	26	on	on	ADP
ejpam-5330	4	27	the	the	DET
ejpam-5330	4	28	sense	sense	NOUN
ejpam-5330	4	29	of	of	ADP
ejpam-5330	4	30	šostak	šostak	NOUN
ejpam-5330	4	31	and	and	CCONJ
ejpam-5330	4	32	studied	study	VERB
ejpam-5330	4	33	some	some	DET
ejpam-5330	4	34	topological	topological	ADJ
ejpam-5330	4	35	properties	property	NOUN
ejpam-5330	4	36	of	of	ADP
ejpam-5330	4	37	them	they	PRON
ejpam-5330	4	38	.	.	PUNCT
ejpam-5330	5	1	also	also	ADV
ejpam-5330	5	2	,	,	PUNCT
ejpam-5330	5	3	the	the	DET
ejpam-5330	5	4	notion	notion	NOUN
ejpam-5330	5	5	of	of	ADP
ejpam-5330	5	6	r	r	NOUN
ejpam-5330	5	7	-	-	PUNCT
ejpam-5330	5	8	fuzzy	fuzzy	ADJ
ejpam-5330	5	9	soft	soft	ADJ
ejpam-5330	5	10	α	α	NOUN
ejpam-5330	5	11	-	-	PUNCT
ejpam-5330	5	12	connected	connect	VERB
ejpam-5330	5	13	sets	set	NOUN
ejpam-5330	5	14	was	be	AUX
ejpam-5330	5	15	introduced	introduce	VERB
ejpam-5330	5	16	and	and	CCONJ
ejpam-5330	5	17	investigated	investigate	VERB
ejpam-5330	5	18	.	.	PUNCT
ejpam-5330	6	1	thereafter	thereafter	ADV
ejpam-5330	6	2	,	,	PUNCT
ejpam-5330	6	3	we	we	PRON
ejpam-5330	6	4	defined	define	VERB
ejpam-5330	6	5	and	and	CCONJ
ejpam-5330	6	6	characterized	characterize	VERB
ejpam-5330	6	7	the	the	DET
ejpam-5330	6	8	notions	notion	NOUN
ejpam-5330	6	9	of	of	ADP
ejpam-5330	6	10	fuzzy	fuzzy	ADJ
ejpam-5330	6	11	soft	soft	ADJ
ejpam-5330	6	12	weakly	weakly	ADJ
ejpam-5330	6	13	(	(	PUNCT
ejpam-5330	6	14	almost	almost	ADV
ejpam-5330	6	15	)	)	PUNCT
ejpam-5330	6	16	α	α	NUM
ejpam-5330	6	17	-	-	ADJ
ejpam-5330	6	18	continuous	continuous	ADJ
ejpam-5330	6	19	mappings	mapping	NOUN
ejpam-5330	6	20	,	,	PUNCT
ejpam-5330	6	21	which	which	PRON
ejpam-5330	6	22	are	be	AUX
ejpam-5330	6	23	weaker	weak	ADJ
ejpam-5330	6	24	forms	form	NOUN
ejpam-5330	6	25	of	of	ADP
ejpam-5330	6	26	fuzzy	fuzzy	ADJ
ejpam-5330	6	27	soft	soft	ADJ
ejpam-5330	6	28	α	α	ADJ
ejpam-5330	6	29	-	-	ADJ
ejpam-5330	6	30	continuous	continuous	ADJ
ejpam-5330	6	31	mappings	mapping	NOUN
ejpam-5330	6	32	.	.	PUNCT
ejpam-5330	7	1	moreover	moreover	ADV
ejpam-5330	7	2	,	,	PUNCT
ejpam-5330	7	3	we	we	PRON
ejpam-5330	7	4	showed	show	VERB
ejpam-5330	7	5	that	that	SCONJ
ejpam-5330	7	6	fuzzy	fuzzy	ADJ
ejpam-5330	7	7	soft	soft	ADJ
ejpam-5330	7	8	α	α	NOUN
ejpam-5330	7	9	-	-	PUNCT
ejpam-5330	7	10	continuity	continuity	NOUN
ejpam-5330	7	11	⇒	⇒	NOUN
ejpam-5330	7	12	fuzzy	fuzzy	ADJ
ejpam-5330	7	13	soft	soft	ADJ
ejpam-5330	7	14	almost	almost	ADV
ejpam-5330	7	15	α	α	NOUN
ejpam-5330	7	16	-	-	PUNCT
ejpam-5330	7	17	continuity	continuity	NOUN
ejpam-5330	7	18	⇒	⇒	NOUN
ejpam-5330	7	19	fuzzy	fuzzy	ADJ
ejpam-5330	7	20	soft	soft	ADJ
ejpam-5330	7	21	weakly	weakly	ADJ
ejpam-5330	7	22	α	α	NOUN
ejpam-5330	7	23	-	-	NOUN
ejpam-5330	7	24	continuity	continuity	NOUN
ejpam-5330	7	25	,	,	PUNCT
ejpam-5330	7	26	but	but	CCONJ
ejpam-5330	7	27	the	the	DET
ejpam-5330	7	28	converse	converse	NOUN
ejpam-5330	7	29	may	may	AUX
ejpam-5330	7	30	not	not	PART
ejpam-5330	7	31	be	be	AUX
ejpam-5330	7	32	true	true	ADJ
ejpam-5330	7	33	.	.	PUNCT
ejpam-5330	8	1	in	in	ADP
ejpam-5330	8	2	addition	addition	NOUN
ejpam-5330	8	3	,	,	PUNCT
ejpam-5330	8	4	we	we	PRON
ejpam-5330	8	5	investigated	investigate	VERB
ejpam-5330	8	6	some	some	DET
ejpam-5330	8	7	properties	property	NOUN
ejpam-5330	8	8	of	of	ADP
ejpam-5330	8	9	fuzzy	fuzzy	ADJ
ejpam-5330	8	10	soft	soft	ADJ
ejpam-5330	8	11	α	α	NOUN
ejpam-5330	8	12	-	-	NOUN
ejpam-5330	8	13	continuity	continuity	NOUN
ejpam-5330	8	14	.	.	PUNCT
ejpam-5330	9	1	finally	finally	ADV
ejpam-5330	9	2	,	,	PUNCT
ejpam-5330	9	3	several	several	ADJ
ejpam-5330	9	4	types	type	NOUN
ejpam-5330	9	5	of	of	ADP
ejpam-5330	9	6	fuzzy	fuzzy	ADJ
ejpam-5330	9	7	soft	soft	ADJ
ejpam-5330	9	8	compactness	compactness	NOUN
ejpam-5330	9	9	via	via	ADP
ejpam-5330	9	10	r	r	NOUN
ejpam-5330	9	11	-	-	PUNCT
ejpam-5330	9	12	fuzzy	fuzzy	ADJ
ejpam-5330	9	13	soft	soft	ADJ
ejpam-5330	9	14	α	α	NOUN
ejpam-5330	9	15	-	-	ADJ
ejpam-5330	9	16	open	open	ADJ
ejpam-5330	9	17	sets	set	NOUN
ejpam-5330	9	18	were	be	AUX
ejpam-5330	9	19	given	give	VERB
ejpam-5330	9	20	and	and	CCONJ
ejpam-5330	9	21	the	the	DET
ejpam-5330	9	22	relationships	relationship	NOUN
ejpam-5330	9	23	between	between	ADP
ejpam-5330	9	24	them	they	PRON
ejpam-5330	9	25	were	be	AUX
ejpam-5330	9	26	studied	study	VERB
ejpam-5330	9	27	with	with	ADP
ejpam-5330	9	28	the	the	DET
ejpam-5330	9	29	help	help	NOUN
ejpam-5330	9	30	of	of	ADP
ejpam-5330	9	31	some	some	DET
ejpam-5330	9	32	examples	example	NOUN
ejpam-5330	9	33	.	.	PUNCT
ejpam-5330	10	1	2020	2020	NUM
ejpam-5330	10	2	mathematics	mathematic	NOUN
ejpam-5330	10	3	subject	subject	NOUN
ejpam-5330	10	4	classifications	classification	NOUN
ejpam-5330	10	5	:	:	PUNCT
ejpam-5330	10	6	54a05	54a05	NUM
ejpam-5330	10	7	,	,	PUNCT
ejpam-5330	10	8	54a40	54a40	NUM
ejpam-5330	10	9	,	,	PUNCT
ejpam-5330	10	10	54c05	54c05	NUM
ejpam-5330	10	11	,	,	PUNCT
ejpam-5330	10	12	54c10	54c10	NUM
ejpam-5330	10	13	,	,	PUNCT
ejpam-5330	10	14	54d30	54d30	ADJ
ejpam-5330	10	15	key	key	ADJ
ejpam-5330	10	16	words	word	NOUN
ejpam-5330	10	17	and	and	CCONJ
ejpam-5330	10	18	phrases	phrase	NOUN
ejpam-5330	10	19	:	:	PUNCT
ejpam-5330	10	20	fuzzy	fuzzy	ADJ
ejpam-5330	10	21	soft	soft	ADJ
ejpam-5330	10	22	topology	topology	NOUN
ejpam-5330	10	23	,	,	PUNCT
ejpam-5330	10	24	r	r	NOUN
ejpam-5330	10	25	-	-	PUNCT
ejpam-5330	10	26	fuzzy	fuzzy	ADJ
ejpam-5330	10	27	soft	soft	ADJ
ejpam-5330	10	28	α	α	NOUN
ejpam-5330	10	29	-	-	ADJ
ejpam-5330	10	30	open	open	ADJ
ejpam-5330	10	31	(	(	PUNCT
ejpam-5330	10	32	α	α	NOUN
ejpam-5330	10	33	-	-	ADJ
ejpam-5330	10	34	closed	closed	ADJ
ejpam-5330	10	35	)	)	PUNCT
ejpam-5330	10	36	set	set	NOUN
ejpam-5330	10	37	,	,	PUNCT
ejpam-5330	10	38	fuzzy	fuzzy	ADJ
ejpam-5330	10	39	soft	soft	ADJ
ejpam-5330	10	40	αinterior	αinterior	NOUN
ejpam-5330	10	41	(	(	PUNCT
ejpam-5330	10	42	α	α	NOUN
ejpam-5330	10	43	-	-	PUNCT
ejpam-5330	10	44	closure	closure	NOUN
ejpam-5330	10	45	)	)	PUNCT
ejpam-5330	10	46	operator	operator	NOUN
ejpam-5330	10	47	,	,	PUNCT
ejpam-5330	10	48	connectedness	connectedness	NOUN
ejpam-5330	10	49	,	,	PUNCT
ejpam-5330	10	50	fuzzy	fuzzy	ADJ
ejpam-5330	10	51	soft	soft	ADJ
ejpam-5330	10	52	weakly	weakly	ADJ
ejpam-5330	10	53	(	(	PUNCT
ejpam-5330	10	54	almost	almost	ADV
ejpam-5330	10	55	)	)	PUNCT
ejpam-5330	10	56	α	α	NOUN
ejpam-5330	10	57	-	-	PUNCT
ejpam-5330	10	58	continuity	continuity	NOUN
ejpam-5330	10	59	,	,	PUNCT
ejpam-5330	10	60	compactness	compactness	NOUN
ejpam-5330	10	61	1	1	NUM
ejpam-5330	10	62	.	.	PUNCT
ejpam-5330	11	1	introduction	introduction	NOUN
ejpam-5330	11	2	and	and	CCONJ
ejpam-5330	11	3	preliminaries	preliminary	NOUN
ejpam-5330	11	4	the	the	DET
ejpam-5330	11	5	theory	theory	NOUN
ejpam-5330	11	6	of	of	ADP
ejpam-5330	11	7	soft	soft	ADJ
ejpam-5330	11	8	sets	set	NOUN
ejpam-5330	11	9	was	be	AUX
ejpam-5330	11	10	first	first	ADV
ejpam-5330	11	11	introduced	introduce	VERB
ejpam-5330	11	12	by	by	ADP
ejpam-5330	11	13	molodtsov	molodtsov	NOUN
ejpam-5330	11	14	[	[	X
ejpam-5330	11	15	24	24	NUM
ejpam-5330	11	16	]	]	PUNCT
ejpam-5330	11	17	,	,	PUNCT
ejpam-5330	11	18	which	which	PRON
ejpam-5330	11	19	is	be	AUX
ejpam-5330	11	20	a	a	DET
ejpam-5330	11	21	completely	completely	ADV
ejpam-5330	11	22	new	new	ADJ
ejpam-5330	11	23	approach	approach	NOUN
ejpam-5330	11	24	for	for	ADP
ejpam-5330	11	25	vagueness	vagueness	NOUN
ejpam-5330	11	26	and	and	CCONJ
ejpam-5330	11	27	modeling	model	VERB
ejpam-5330	11	28	uncertainty	uncertainty	NOUN
ejpam-5330	11	29	.	.	PUNCT
ejpam-5330	12	1	he	he	PRON
ejpam-5330	12	2	demonstrated	demonstrate	VERB
ejpam-5330	12	3	many	many	ADJ
ejpam-5330	12	4	applications	application	NOUN
ejpam-5330	12	5	of	of	ADP
ejpam-5330	12	6	this	this	DET
ejpam-5330	12	7	theory	theory	NOUN
ejpam-5330	12	8	in	in	ADP
ejpam-5330	12	9	solving	solve	VERB
ejpam-5330	12	10	several	several	ADJ
ejpam-5330	12	11	practical	practical	ADJ
ejpam-5330	12	12	problems	problem	NOUN
ejpam-5330	12	13	in	in	ADP
ejpam-5330	12	14	mathematics	mathematic	NOUN
ejpam-5330	12	15	,	,	PUNCT
ejpam-5330	12	16	engineering	engineering	NOUN
ejpam-5330	12	17	,	,	PUNCT
ejpam-5330	12	18	economics	economic	NOUN
ejpam-5330	12	19	,	,	PUNCT
ejpam-5330	12	20	social	social	ADJ
ejpam-5330	12	21	science	science	NOUN
ejpam-5330	12	22	,	,	PUNCT
ejpam-5330	12	23	etc	etc	X
ejpam-5330	12	24	.	.	X
ejpam-5330	13	1	in	in	ADP
ejpam-5330	13	2	[	[	X
ejpam-5330	13	3	28	28	NUM
ejpam-5330	13	4	]	]	PUNCT
ejpam-5330	13	5	,	,	PUNCT
ejpam-5330	13	6	the	the	DET
ejpam-5330	13	7	notion	notion	NOUN
ejpam-5330	13	8	of	of	ADP
ejpam-5330	13	9	soft	soft	ADJ
ejpam-5330	13	10	sets	set	NOUN
ejpam-5330	13	11	was	be	AUX
ejpam-5330	13	12	used	use	VERB
ejpam-5330	13	13	to	to	PART
ejpam-5330	13	14	introduced	introduce	VERB
ejpam-5330	13	15	soft	soft	ADJ
ejpam-5330	13	16	topologies	topology	NOUN
ejpam-5330	13	17	.	.	PUNCT
ejpam-5330	14	1	moreover	moreover	ADV
ejpam-5330	14	2	,	,	PUNCT
ejpam-5330	14	3	the	the	DET
ejpam-5330	14	4	study	study	NOUN
ejpam-5330	14	5	in	in	ADP
ejpam-5330	14	6	[	[	X
ejpam-5330	14	7	28	28	NUM
ejpam-5330	14	8	]	]	PUNCT
ejpam-5330	14	9	was	be	AUX
ejpam-5330	14	10	particularly	particularly	ADV
ejpam-5330	14	11	important	important	ADJ
ejpam-5330	14	12	in	in	ADP
ejpam-5330	14	13	the	the	DET
ejpam-5330	14	14	development	development	NOUN
ejpam-5330	14	15	of	of	ADP
ejpam-5330	14	16	the	the	DET
ejpam-5330	14	17	field	field	NOUN
ejpam-5330	14	18	of	of	ADP
ejpam-5330	14	19	soft	soft	ADJ
ejpam-5330	14	20	topology	topology	NOUN
ejpam-5330	14	21	,	,	PUNCT
ejpam-5330	14	22	see	see	VERB
ejpam-5330	14	23	[	[	X
ejpam-5330	14	24	10	10	NUM
ejpam-5330	14	25	,	,	PUNCT
ejpam-5330	14	26	18	18	NUM
ejpam-5330	14	27	,	,	PUNCT
ejpam-5330	14	28	33	33	NUM
ejpam-5330	14	29	,	,	PUNCT
ejpam-5330	14	30	38	38	NUM
ejpam-5330	14	31	]	]	PUNCT
ejpam-5330	14	32	.	.	PUNCT
ejpam-5330	15	1	generalizations	generalization	NOUN
ejpam-5330	15	2	of	of	ADP
ejpam-5330	15	3	soft	soft	ADJ
ejpam-5330	15	4	open	open	ADJ
ejpam-5330	15	5	subsets	subset	NOUN
ejpam-5330	15	6	play	play	VERB
ejpam-5330	15	7	an	an	DET
ejpam-5330	15	8	effective	effective	ADJ
ejpam-5330	15	9	role	role	NOUN
ejpam-5330	15	10	in	in	ADP
ejpam-5330	15	11	soft	soft	ADJ
ejpam-5330	15	12	topologies	topology	NOUN
ejpam-5330	15	13	through	through	ADP
ejpam-5330	15	14	their	their	PRON
ejpam-5330	15	15	use	use	NOUN
ejpam-5330	15	16	to	to	PART
ejpam-5330	15	17	improve	improve	VERB
ejpam-5330	15	18	on	on	ADP
ejpam-5330	15	19	some	some	DET
ejpam-5330	15	20	known	know	VERB
ejpam-5330	15	21	results	result	NOUN
ejpam-5330	15	22	or	or	CCONJ
ejpam-5330	15	23	to	to	PART
ejpam-5330	15	24	open	open	VERB
ejpam-5330	15	25	the	the	DET
ejpam-5330	15	26	door	door	NOUN
ejpam-5330	15	27	to	to	PART
ejpam-5330	15	28	reintroduce	reintroduce	VERB
ejpam-5330	15	29	and	and	CCONJ
ejpam-5330	15	30	establish	establish	VERB
ejpam-5330	15	31	many	many	ADJ
ejpam-5330	15	32	of	of	ADP
ejpam-5330	15	33	the	the	DET
ejpam-5330	15	34	soft	soft	ADJ
ejpam-5330	15	35	topological	topological	ADJ
ejpam-5330	15	36	notions	notion	NOUN
ejpam-5330	15	37	such	such	ADJ
ejpam-5330	15	38	as	as	ADP
ejpam-5330	15	39	soft	soft	ADJ
ejpam-5330	15	40	separation	separation	NOUN
ejpam-5330	15	41	axioms	axiom	NOUN
ejpam-5330	15	42	[	[	X
ejpam-5330	15	43	7	7	NUM
ejpam-5330	15	44	,	,	PUNCT
ejpam-5330	15	45	20	20	NUM
ejpam-5330	15	46	]	]	PUNCT
ejpam-5330	15	47	,	,	PUNCT
ejpam-5330	15	48	soft	soft	ADJ
ejpam-5330	15	49	continuity	continuity	NOUN
ejpam-5330	15	50	[	[	X
ejpam-5330	15	51	25	25	NUM
ejpam-5330	15	52	]	]	PUNCT
ejpam-5330	15	53	,	,	PUNCT
ejpam-5330	15	54	soft	soft	ADJ
ejpam-5330	15	55	connectedness	connectedness	NOUN
ejpam-5330	16	1	[	[	X
ejpam-5330	16	2	34	34	NUM
ejpam-5330	16	3	,	,	PUNCT
ejpam-5330	16	4	36	36	NUM
ejpam-5330	16	5	]	]	PUNCT
ejpam-5330	16	6	,	,	PUNCT
ejpam-5330	16	7	etc	etc	X
ejpam-5330	16	8	.	.	X
ejpam-5330	16	9	akdag	akdag	PROPN
ejpam-5330	16	10	∗corresponding	∗corresponde	VERB
ejpam-5330	16	11	author	author	NOUN
ejpam-5330	16	12	.	.	PUNCT
ejpam-5330	17	1	doi	doi	NOUN
ejpam-5330	17	2	:	:	PUNCT
ejpam-5330	17	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5330	https://doi.org/10.29020/nybg.ejpam.v17i4.5330	VERB
ejpam-5330	17	4	email	email	NOUN
ejpam-5330	17	5	addresses	address	NOUN
ejpam-5330	17	6	:	:	PUNCT
ejpam-5330	17	7	wkqurashi@uqu.edu.sa	wkqurashi@uqu.edu.sa	PROPN
ejpam-5330	17	8	(	(	PUNCT
ejpam-5330	17	9	w.	w.	PROPN
ejpam-5330	17	10	alqurashi	alqurashi	PROPN
ejpam-5330	17	11	)	)	PUNCT
ejpam-5330	17	12	,	,	PUNCT
ejpam-5330	17	13	imtaha2010@yahoo.com	imtaha2010@yahoo.com	X
ejpam-5330	17	14	(	(	PUNCT
ejpam-5330	17	15	i.	i.	PROPN
ejpam-5330	17	16	m.	m.	PROPN
ejpam-5330	17	17	taha	taha	PROPN
ejpam-5330	17	18	)	)	PUNCT
ejpam-5330	17	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5330	18	1	4112	4112	NUM
ejpam-5330	18	2	copyright	copyright	NOUN
ejpam-5330	18	3	:	:	PUNCT
ejpam-5330	18	4	©	©	PROPN
ejpam-5330	18	5	2024	2024	NUM
ejpam-5330	18	6	the	the	DET
ejpam-5330	18	7	author(s	author(s	NOUN
ejpam-5330	18	8	)	)	PUNCT
ejpam-5330	18	9	.	.	PUNCT
ejpam-5330	19	1	(	(	PUNCT
ejpam-5330	19	2	cc	cc	NOUN
ejpam-5330	19	3	by	by	ADP
ejpam-5330	19	4	-	-	PUNCT
ejpam-5330	19	5	nc	nc	PROPN
ejpam-5330	19	6	4.0	4.0	NUM
ejpam-5330	19	7	)	)	PUNCT
ejpam-5330	19	8	w.	w.	PROPN
ejpam-5330	19	9	alqurashi	alqurashi	PROPN
ejpam-5330	19	10	,	,	PUNCT
ejpam-5330	19	11	i.	i.	PROPN
ejpam-5330	19	12	m.	m.	PROPN
ejpam-5330	19	13	taha	taha	PROPN
ejpam-5330	19	14	/	/	PUNCT
ejpam-5330	19	15	eur	eur	PROPN
ejpam-5330	19	16	.	.	PUNCT
ejpam-5330	20	1	j.	j.	PROPN
ejpam-5330	20	2	pure	pure	PROPN
ejpam-5330	20	3	appl	appl	PROPN
ejpam-5330	20	4	.	.	PROPN
ejpam-5330	20	5	math	math	PROPN
ejpam-5330	20	6	,	,	PUNCT
ejpam-5330	20	7	17	17	NUM
ejpam-5330	20	8	(	(	PUNCT
ejpam-5330	20	9	4	4	NUM
ejpam-5330	20	10	)	)	PUNCT
ejpam-5330	20	11	(	(	PUNCT
ejpam-5330	20	12	2024	2024	NUM
ejpam-5330	20	13	)	)	PUNCT
ejpam-5330	20	14	,	,	PUNCT
ejpam-5330	20	15	4112	4112	NUM
ejpam-5330	20	16	-	-	SYM
ejpam-5330	20	17	4134	4134	NUM
ejpam-5330	20	18	4113	4113	NUM
ejpam-5330	20	19	and	and	CCONJ
ejpam-5330	20	20	ozkan	ozkan	X
ejpam-5330	21	1	[	[	X
ejpam-5330	21	2	3	3	NUM
ejpam-5330	21	3	]	]	PUNCT
ejpam-5330	21	4	defined	define	VERB
ejpam-5330	21	5	the	the	DET
ejpam-5330	21	6	notion	notion	NOUN
ejpam-5330	21	7	of	of	ADP
ejpam-5330	21	8	soft	soft	ADJ
ejpam-5330	21	9	α	α	NOUN
ejpam-5330	21	10	-	-	ADJ
ejpam-5330	21	11	open	open	ADJ
ejpam-5330	21	12	sets	set	NOUN
ejpam-5330	21	13	on	on	ADP
ejpam-5330	21	14	soft	soft	ADJ
ejpam-5330	21	15	topological	topological	ADJ
ejpam-5330	21	16	spaces	space	NOUN
ejpam-5330	21	17	and	and	CCONJ
ejpam-5330	21	18	some	some	DET
ejpam-5330	21	19	properties	property	NOUN
ejpam-5330	21	20	are	be	AUX
ejpam-5330	21	21	specified	specify	VERB
ejpam-5330	21	22	.	.	PUNCT
ejpam-5330	22	1	the	the	DET
ejpam-5330	22	2	notion	notion	NOUN
ejpam-5330	22	3	of	of	ADP
ejpam-5330	22	4	soft	soft	ADJ
ejpam-5330	22	5	β	β	NOUN
ejpam-5330	22	6	-	-	ADJ
ejpam-5330	22	7	open	open	ADJ
ejpam-5330	22	8	sets	set	NOUN
ejpam-5330	22	9	was	be	AUX
ejpam-5330	22	10	defined	define	VERB
ejpam-5330	22	11	and	and	CCONJ
ejpam-5330	22	12	studied	study	VERB
ejpam-5330	22	13	by	by	ADP
ejpam-5330	22	14	the	the	DET
ejpam-5330	22	15	authors	author	NOUN
ejpam-5330	22	16	of	of	ADP
ejpam-5330	22	17	[	[	X
ejpam-5330	22	18	2	2	NUM
ejpam-5330	22	19	,	,	PUNCT
ejpam-5330	22	20	17	17	NUM
ejpam-5330	22	21	]	]	PUNCT
ejpam-5330	22	22	.	.	PUNCT
ejpam-5330	23	1	also	also	ADV
ejpam-5330	23	2	,	,	PUNCT
ejpam-5330	23	3	the	the	DET
ejpam-5330	23	4	concepts	concept	NOUN
ejpam-5330	23	5	of	of	ADP
ejpam-5330	23	6	soft	soft	ADJ
ejpam-5330	23	7	semi	semi	ADJ
ejpam-5330	23	8	-	-	ADJ
ejpam-5330	23	9	open	open	ADJ
ejpam-5330	23	10	,	,	PUNCT
ejpam-5330	23	11	somewhere	somewhere	ADV
ejpam-5330	23	12	dense	dense	ADJ
ejpam-5330	23	13	and	and	CCONJ
ejpam-5330	23	14	q	q	NOUN
ejpam-5330	23	15	-	-	PUNCT
ejpam-5330	23	16	sets	set	NOUN
ejpam-5330	23	17	were	be	AUX
ejpam-5330	23	18	studied	study	VERB
ejpam-5330	23	19	by	by	ADP
ejpam-5330	23	20	the	the	DET
ejpam-5330	23	21	authors	author	NOUN
ejpam-5330	23	22	of	of	ADP
ejpam-5330	23	23	[	[	X
ejpam-5330	23	24	4	4	NUM
ejpam-5330	23	25	,	,	PUNCT
ejpam-5330	23	26	6	6	NUM
ejpam-5330	23	27	]	]	PUNCT
ejpam-5330	23	28	.	.	PUNCT
ejpam-5330	24	1	moreover	moreover	ADV
ejpam-5330	24	2	,	,	PUNCT
ejpam-5330	24	3	al	al	PROPN
ejpam-5330	24	4	-	-	PUNCT
ejpam-5330	24	5	shami	shami	PROPN
ejpam-5330	24	6	et	et	PROPN
ejpam-5330	24	7	al	al	PROPN
ejpam-5330	24	8	.	.	PUNCT
ejpam-5330	25	1	[	[	X
ejpam-5330	25	2	8	8	NUM
ejpam-5330	25	3	]	]	PUNCT
ejpam-5330	25	4	initiated	initiate	VERB
ejpam-5330	25	5	the	the	DET
ejpam-5330	25	6	notion	notion	NOUN
ejpam-5330	25	7	of	of	ADP
ejpam-5330	25	8	weakly	weakly	ADJ
ejpam-5330	25	9	soft	soft	ADJ
ejpam-5330	25	10	β	β	ADJ
ejpam-5330	25	11	-	-	ADJ
ejpam-5330	25	12	open	open	ADJ
ejpam-5330	25	13	sets	set	NOUN
ejpam-5330	25	14	and	and	CCONJ
ejpam-5330	25	15	examined	examine	VERB
ejpam-5330	25	16	weakly	weakly	ADV
ejpam-5330	25	17	soft	soft	ADJ
ejpam-5330	25	18	β	β	NOUN
ejpam-5330	25	19	-	-	NOUN
ejpam-5330	25	20	continuity	continuity	NOUN
ejpam-5330	25	21	.	.	PUNCT
ejpam-5330	26	1	kaur	kaur	PROPN
ejpam-5330	26	2	et	et	PROPN
ejpam-5330	26	3	al	al	PROPN
ejpam-5330	26	4	.	.	PUNCT
ejpam-5330	27	1	[	[	X
ejpam-5330	27	2	21	21	NUM
ejpam-5330	27	3	]	]	PUNCT
ejpam-5330	27	4	introduced	introduce	VERB
ejpam-5330	27	5	a	a	DET
ejpam-5330	27	6	new	new	ADJ
ejpam-5330	27	7	approach	approach	NOUN
ejpam-5330	27	8	to	to	ADP
ejpam-5330	27	9	studying	study	VERB
ejpam-5330	27	10	soft	soft	ADJ
ejpam-5330	27	11	continuous	continuous	ADJ
ejpam-5330	27	12	mappings	mapping	NOUN
ejpam-5330	27	13	using	use	VERB
ejpam-5330	27	14	an	an	DET
ejpam-5330	27	15	induced	induced	ADJ
ejpam-5330	27	16	mapping	mapping	NOUN
ejpam-5330	27	17	based	base	VERB
ejpam-5330	27	18	on	on	ADP
ejpam-5330	27	19	soft	soft	ADJ
ejpam-5330	27	20	sets	set	NOUN
ejpam-5330	27	21	.	.	PUNCT
ejpam-5330	28	1	al	al	PROPN
ejpam-5330	28	2	ghour	ghour	PROPN
ejpam-5330	28	3	and	and	CCONJ
ejpam-5330	28	4	al	al	PROPN
ejpam-5330	28	5	-	-	PUNCT
ejpam-5330	28	6	mufarrij	mufarrij	PROPN
ejpam-5330	29	1	[	[	X
ejpam-5330	29	2	5	5	NUM
ejpam-5330	29	3	]	]	PUNCT
ejpam-5330	29	4	defined	define	VERB
ejpam-5330	29	5	two	two	NUM
ejpam-5330	29	6	new	new	ADJ
ejpam-5330	29	7	notions	notion	NOUN
ejpam-5330	29	8	of	of	ADP
ejpam-5330	29	9	mappings	mapping	NOUN
ejpam-5330	29	10	over	over	ADP
ejpam-5330	29	11	soft	soft	ADJ
ejpam-5330	29	12	topological	topological	ADJ
ejpam-5330	29	13	spaces	space	NOUN
ejpam-5330	29	14	:	:	PUNCT
ejpam-5330	29	15	soft	soft	ADJ
ejpam-5330	29	16	somewhat	somewhat	ADV
ejpam-5330	29	17	-	-	PUNCT
ejpam-5330	29	18	r	r	NOUN
ejpam-5330	29	19	-	-	PUNCT
ejpam-5330	29	20	continuity	continuity	NOUN
ejpam-5330	29	21	and	and	CCONJ
ejpam-5330	29	22	soft	soft	ADJ
ejpam-5330	29	23	somewhat	somewhat	ADV
ejpam-5330	29	24	-	-	PUNCT
ejpam-5330	29	25	r	r	NOUN
ejpam-5330	29	26	-	-	NOUN
ejpam-5330	29	27	openness	openness	NOUN
ejpam-5330	29	28	.	.	PUNCT
ejpam-5330	30	1	the	the	DET
ejpam-5330	30	2	concept	concept	NOUN
ejpam-5330	30	3	of	of	ADP
ejpam-5330	30	4	fuzzy	fuzzy	ADJ
ejpam-5330	30	5	soft	soft	ADJ
ejpam-5330	30	6	sets	set	NOUN
ejpam-5330	30	7	was	be	AUX
ejpam-5330	30	8	defined	define	VERB
ejpam-5330	30	9	by	by	ADP
ejpam-5330	30	10	maji	maji	PROPN
ejpam-5330	30	11	et	et	PROPN
ejpam-5330	30	12	al	al	PROPN
ejpam-5330	30	13	.	.	PUNCT
ejpam-5330	31	1	[	[	X
ejpam-5330	31	2	22	22	NUM
ejpam-5330	31	3	]	]	PUNCT
ejpam-5330	31	4	,	,	PUNCT
ejpam-5330	31	5	which	which	PRON
ejpam-5330	31	6	combines	combine	VERB
ejpam-5330	31	7	soft	soft	ADJ
ejpam-5330	31	8	sets	set	NOUN
ejpam-5330	31	9	[	[	X
ejpam-5330	31	10	24	24	NUM
ejpam-5330	31	11	]	]	PUNCT
ejpam-5330	31	12	and	and	CCONJ
ejpam-5330	31	13	fuzzy	fuzzy	ADJ
ejpam-5330	31	14	sets	set	NOUN
ejpam-5330	31	15	[	[	X
ejpam-5330	31	16	37	37	NUM
ejpam-5330	31	17	]	]	PUNCT
ejpam-5330	31	18	.	.	PUNCT
ejpam-5330	32	1	the	the	DET
ejpam-5330	32	2	concept	concept	NOUN
ejpam-5330	32	3	of	of	ADP
ejpam-5330	32	4	fuzzy	fuzzy	ADJ
ejpam-5330	32	5	soft	soft	ADJ
ejpam-5330	32	6	topology	topology	NOUN
ejpam-5330	32	7	was	be	AUX
ejpam-5330	32	8	introduced	introduce	VERB
ejpam-5330	32	9	and	and	CCONJ
ejpam-5330	32	10	some	some	PRON
ejpam-5330	32	11	characterized	characterize	VERB
ejpam-5330	32	12	such	such	ADJ
ejpam-5330	32	13	as	as	ADP
ejpam-5330	32	14	fuzzy	fuzzy	ADJ
ejpam-5330	32	15	soft	soft	ADJ
ejpam-5330	32	16	interior	interior	NOUN
ejpam-5330	32	17	(	(	PUNCT
ejpam-5330	32	18	closure	closure	NOUN
ejpam-5330	32	19	)	)	PUNCT
ejpam-5330	32	20	set	set	NOUN
ejpam-5330	32	21	,	,	PUNCT
ejpam-5330	32	22	fuzzy	fuzzy	ADJ
ejpam-5330	32	23	soft	soft	ADJ
ejpam-5330	32	24	continuity	continuity	NOUN
ejpam-5330	32	25	,	,	PUNCT
ejpam-5330	32	26	and	and	CCONJ
ejpam-5330	32	27	fuzzy	fuzzy	ADJ
ejpam-5330	32	28	soft	soft	ADJ
ejpam-5330	32	29	subspace	subspace	NOUN
ejpam-5330	32	30	were	be	AUX
ejpam-5330	32	31	studied	study	VERB
ejpam-5330	32	32	in	in	ADP
ejpam-5330	32	33	[	[	X
ejpam-5330	32	34	16	16	NUM
ejpam-5330	32	35	,	,	PUNCT
ejpam-5330	32	36	19	19	NUM
ejpam-5330	32	37	]	]	PUNCT
ejpam-5330	32	38	based	base	VERB
ejpam-5330	32	39	on	on	ADP
ejpam-5330	32	40	fuzzy	fuzzy	ADJ
ejpam-5330	32	41	topologies	topology	NOUN
ejpam-5330	32	42	in	in	ADP
ejpam-5330	32	43	the	the	DET
ejpam-5330	32	44	sense	sense	NOUN
ejpam-5330	32	45	of	of	ADP
ejpam-5330	32	46	šostak	šostak	NOUN
ejpam-5330	32	47	[	[	X
ejpam-5330	32	48	35	35	NUM
ejpam-5330	32	49	]	]	PUNCT
ejpam-5330	32	50	.	.	PUNCT
ejpam-5330	33	1	a	a	DET
ejpam-5330	33	2	new	new	ADJ
ejpam-5330	33	3	approach	approach	NOUN
ejpam-5330	33	4	to	to	ADP
ejpam-5330	33	5	studying	study	VERB
ejpam-5330	33	6	separation	separation	NOUN
ejpam-5330	33	7	and	and	CCONJ
ejpam-5330	33	8	regularity	regularity	NOUN
ejpam-5330	33	9	axioms	axiom	NOUN
ejpam-5330	33	10	via	via	ADP
ejpam-5330	33	11	fuzzy	fuzzy	ADJ
ejpam-5330	33	12	soft	soft	ADJ
ejpam-5330	33	13	sets	set	NOUN
ejpam-5330	33	14	was	be	AUX
ejpam-5330	33	15	introduced	introduce	VERB
ejpam-5330	33	16	by	by	ADP
ejpam-5330	33	17	the	the	DET
ejpam-5330	33	18	author	author	NOUN
ejpam-5330	33	19	of	of	ADP
ejpam-5330	33	20	[	[	X
ejpam-5330	33	21	29	29	NUM
ejpam-5330	33	22	,	,	PUNCT
ejpam-5330	33	23	31	31	NUM
ejpam-5330	33	24	]	]	PUNCT
ejpam-5330	33	25	based	base	VERB
ejpam-5330	33	26	on	on	ADP
ejpam-5330	33	27	the	the	DET
ejpam-5330	33	28	paper	paper	NOUN
ejpam-5330	33	29	by	by	ADP
ejpam-5330	33	30	aygünoǧlu	aygünoǧlu	PROPN
ejpam-5330	33	31	et	et	PROPN
ejpam-5330	33	32	al	al	PROPN
ejpam-5330	33	33	.	.	PUNCT
ejpam-5330	34	1	[	[	X
ejpam-5330	34	2	19	19	NUM
ejpam-5330	34	3	]	]	PUNCT
ejpam-5330	34	4	.	.	PUNCT
ejpam-5330	35	1	the	the	DET
ejpam-5330	35	2	concept	concept	NOUN
ejpam-5330	35	3	of	of	ADP
ejpam-5330	35	4	r	r	NOUN
ejpam-5330	35	5	-	-	PUNCT
ejpam-5330	35	6	fuzzy	fuzzy	ADJ
ejpam-5330	35	7	soft	soft	ADJ
ejpam-5330	35	8	regularly	regularly	ADV
ejpam-5330	35	9	open	open	ADJ
ejpam-5330	35	10	sets	set	NOUN
ejpam-5330	35	11	was	be	AUX
ejpam-5330	35	12	introduced	introduce	VERB
ejpam-5330	35	13	by	by	ADP
ejpam-5330	35	14	çetkin	çetkin	PROPN
ejpam-5330	35	15	and	and	CCONJ
ejpam-5330	35	16	aygün	aygün	NOUN
ejpam-5330	35	17	[	[	X
ejpam-5330	35	18	15	15	NUM
ejpam-5330	35	19	]	]	PUNCT
ejpam-5330	35	20	.	.	PUNCT
ejpam-5330	36	1	also	also	ADV
ejpam-5330	36	2	,	,	PUNCT
ejpam-5330	36	3	the	the	DET
ejpam-5330	36	4	concepts	concept	NOUN
ejpam-5330	36	5	of	of	ADP
ejpam-5330	36	6	r	r	NOUN
ejpam-5330	36	7	-	-	PUNCT
ejpam-5330	36	8	fuzzy	fuzzy	ADJ
ejpam-5330	36	9	soft	soft	ADJ
ejpam-5330	36	10	pre	pre	ADJ
ejpam-5330	36	11	-	-	ADJ
ejpam-5330	36	12	open	open	ADJ
ejpam-5330	36	13	(	(	PUNCT
ejpam-5330	36	14	resp	resp	NOUN
ejpam-5330	36	15	.	.	PUNCT
ejpam-5330	37	1	β	β	X
ejpam-5330	37	2	-	-	ADJ
ejpam-5330	37	3	open	open	ADJ
ejpam-5330	37	4	)	)	PUNCT
ejpam-5330	37	5	sets	set	NOUN
ejpam-5330	37	6	were	be	AUX
ejpam-5330	37	7	defined	define	VERB
ejpam-5330	37	8	by	by	ADP
ejpam-5330	37	9	taha	taha	PROPN
ejpam-5330	38	1	[	[	X
ejpam-5330	38	2	30	30	NUM
ejpam-5330	38	3	]	]	PUNCT
ejpam-5330	38	4	.	.	PUNCT
ejpam-5330	39	1	in	in	ADP
ejpam-5330	39	2	2024	2024	NUM
ejpam-5330	39	3	,	,	PUNCT
ejpam-5330	39	4	alshammari	alshammari	NOUN
ejpam-5330	39	5	and	and	CCONJ
ejpam-5330	39	6	taha	taha	NOUN
ejpam-5330	39	7	[	[	X
ejpam-5330	39	8	12	12	NUM
ejpam-5330	39	9	]	]	PUNCT
ejpam-5330	39	10	introduced	introduce	VERB
ejpam-5330	39	11	and	and	CCONJ
ejpam-5330	39	12	studied	study	VERB
ejpam-5330	39	13	the	the	DET
ejpam-5330	39	14	notions	notion	NOUN
ejpam-5330	39	15	of	of	ADP
ejpam-5330	39	16	fuzzy	fuzzy	ADJ
ejpam-5330	39	17	soft	soft	ADJ
ejpam-5330	39	18	almost	almost	ADV
ejpam-5330	39	19	(	(	PUNCT
ejpam-5330	39	20	weakly	weakly	ADJ
ejpam-5330	39	21	)	)	PUNCT
ejpam-5330	39	22	β	β	X
ejpam-5330	39	23	-	-	ADJ
ejpam-5330	39	24	continuous	continuous	ADJ
ejpam-5330	39	25	mappings	mapping	NOUN
ejpam-5330	39	26	,	,	PUNCT
ejpam-5330	39	27	which	which	PRON
ejpam-5330	39	28	are	be	AUX
ejpam-5330	39	29	weaker	weak	ADJ
ejpam-5330	39	30	forms	form	NOUN
ejpam-5330	39	31	of	of	ADP
ejpam-5330	39	32	a	a	DET
ejpam-5330	39	33	fuzzy	fuzzy	ADJ
ejpam-5330	39	34	soft	soft	ADJ
ejpam-5330	39	35	β	β	NOUN
ejpam-5330	39	36	-	-	NOUN
ejpam-5330	39	37	continuity	continuity	NOUN
ejpam-5330	39	38	in	in	ADP
ejpam-5330	39	39	fuzzy	fuzzy	ADJ
ejpam-5330	39	40	soft	soft	ADJ
ejpam-5330	39	41	topological	topological	ADJ
ejpam-5330	39	42	spaces	space	NOUN
ejpam-5330	39	43	.	.	PUNCT
ejpam-5330	40	1	in	in	ADP
ejpam-5330	40	2	addition	addition	NOUN
ejpam-5330	40	3	,	,	PUNCT
ejpam-5330	40	4	many	many	ADJ
ejpam-5330	40	5	authors	author	NOUN
ejpam-5330	40	6	have	have	AUX
ejpam-5330	40	7	contributed	contribute	VERB
ejpam-5330	40	8	to	to	ADP
ejpam-5330	40	9	fuzzy	fuzzy	ADJ
ejpam-5330	40	10	soft	soft	ADJ
ejpam-5330	40	11	set	set	NOUN
ejpam-5330	40	12	theory	theory	NOUN
ejpam-5330	40	13	in	in	ADP
ejpam-5330	40	14	the	the	DET
ejpam-5330	40	15	different	different	ADJ
ejpam-5330	40	16	fields	field	NOUN
ejpam-5330	40	17	such	such	ADJ
ejpam-5330	40	18	as	as	ADP
ejpam-5330	40	19	topology	topology	NOUN
ejpam-5330	40	20	,	,	PUNCT
ejpam-5330	40	21	see	see	VERB
ejpam-5330	40	22	e.g.	e.g.	ADV
ejpam-5330	40	23	[	[	X
ejpam-5330	40	24	9	9	NUM
ejpam-5330	40	25	,	,	PUNCT
ejpam-5330	40	26	26	26	NUM
ejpam-5330	40	27	,	,	PUNCT
ejpam-5330	40	28	27	27	NUM
ejpam-5330	40	29	]	]	PUNCT
ejpam-5330	40	30	.	.	PUNCT
ejpam-5330	41	1	in	in	ADP
ejpam-5330	41	2	our	our	PRON
ejpam-5330	41	3	study	study	NOUN
ejpam-5330	41	4	,	,	PUNCT
ejpam-5330	41	5	the	the	DET
ejpam-5330	41	6	layout	layout	NOUN
ejpam-5330	41	7	is	be	AUX
ejpam-5330	41	8	designed	design	VERB
ejpam-5330	41	9	as	as	SCONJ
ejpam-5330	41	10	follows	follow	VERB
ejpam-5330	41	11	.	.	PUNCT
ejpam-5330	42	1	•	•	NUM
ejpam-5330	42	2	in	in	ADP
ejpam-5330	42	3	section	section	NOUN
ejpam-5330	42	4	2	2	NUM
ejpam-5330	42	5	,	,	PUNCT
ejpam-5330	42	6	we	we	PRON
ejpam-5330	42	7	introduce	introduce	VERB
ejpam-5330	42	8	the	the	DET
ejpam-5330	42	9	concepts	concept	NOUN
ejpam-5330	42	10	of	of	ADP
ejpam-5330	42	11	fuzzy	fuzzy	ADJ
ejpam-5330	42	12	soft	soft	ADJ
ejpam-5330	42	13	α	α	NOUN
ejpam-5330	42	14	-	-	NOUN
ejpam-5330	42	15	closure	closure	NOUN
ejpam-5330	42	16	(	(	PUNCT
ejpam-5330	42	17	α	α	NOUN
ejpam-5330	42	18	-	-	ADJ
ejpam-5330	42	19	interior	interior	ADJ
ejpam-5330	42	20	)	)	PUNCT
ejpam-5330	42	21	operators	operator	NOUN
ejpam-5330	42	22	in	in	ADP
ejpam-5330	42	23	fuzzy	fuzzy	ADJ
ejpam-5330	42	24	soft	soft	ADJ
ejpam-5330	42	25	topological	topological	ADJ
ejpam-5330	42	26	space	space	NOUN
ejpam-5330	42	27	(	(	PUNCT
ejpam-5330	42	28	w	w	NOUN
ejpam-5330	42	29	,	,	PUNCT
ejpam-5330	42	30	τn	τn	NOUN
ejpam-5330	42	31	)	)	PUNCT
ejpam-5330	42	32	based	base	VERB
ejpam-5330	42	33	on	on	ADP
ejpam-5330	42	34	the	the	DET
ejpam-5330	42	35	paper	paper	NOUN
ejpam-5330	42	36	by	by	ADP
ejpam-5330	42	37	aygünoǧlu	aygünoǧlu	PROPN
ejpam-5330	42	38	et	et	PROPN
ejpam-5330	42	39	al	al	PROPN
ejpam-5330	42	40	.	.	PUNCT
ejpam-5330	43	1	[	[	X
ejpam-5330	43	2	19	19	NUM
ejpam-5330	43	3	]	]	PUNCT
ejpam-5330	43	4	and	and	CCONJ
ejpam-5330	43	5	examine	examine	VERB
ejpam-5330	43	6	some	some	PRON
ejpam-5330	43	7	of	of	ADP
ejpam-5330	43	8	its	its	PRON
ejpam-5330	43	9	properties	property	NOUN
ejpam-5330	43	10	.	.	PUNCT
ejpam-5330	44	1	also	also	ADV
ejpam-5330	44	2	,	,	PUNCT
ejpam-5330	44	3	the	the	DET
ejpam-5330	44	4	concept	concept	NOUN
ejpam-5330	44	5	of	of	ADP
ejpam-5330	44	6	r	r	NOUN
ejpam-5330	44	7	-	-	PUNCT
ejpam-5330	44	8	fuzzy	fuzzy	ADJ
ejpam-5330	44	9	soft	soft	ADJ
ejpam-5330	44	10	α	α	NOUN
ejpam-5330	44	11	-	-	PUNCT
ejpam-5330	44	12	connected	connect	VERB
ejpam-5330	44	13	sets	set	NOUN
ejpam-5330	44	14	is	be	AUX
ejpam-5330	44	15	introduced	introduce	VERB
ejpam-5330	44	16	and	and	CCONJ
ejpam-5330	44	17	studied	study	VERB
ejpam-5330	44	18	.	.	PUNCT
ejpam-5330	45	1	•	•	NUM
ejpam-5330	45	2	in	in	ADP
ejpam-5330	45	3	section	section	NOUN
ejpam-5330	45	4	3	3	NUM
ejpam-5330	45	5	,	,	PUNCT
ejpam-5330	45	6	we	we	PRON
ejpam-5330	45	7	are	be	AUX
ejpam-5330	45	8	going	go	VERB
ejpam-5330	45	9	to	to	PART
ejpam-5330	45	10	investigate	investigate	VERB
ejpam-5330	45	11	some	some	DET
ejpam-5330	45	12	properties	property	NOUN
ejpam-5330	45	13	of	of	ADP
ejpam-5330	45	14	fuzzy	fuzzy	ADJ
ejpam-5330	45	15	soft	soft	ADJ
ejpam-5330	45	16	α	α	ADJ
ejpam-5330	45	17	-	-	ADJ
ejpam-5330	45	18	continuous	continuous	ADJ
ejpam-5330	45	19	mappings	mapping	NOUN
ejpam-5330	45	20	between	between	ADP
ejpam-5330	45	21	two	two	NUM
ejpam-5330	45	22	fuzzy	fuzzy	ADJ
ejpam-5330	45	23	soft	soft	ADJ
ejpam-5330	45	24	topological	topological	ADJ
ejpam-5330	45	25	spaces	space	NOUN
ejpam-5330	45	26	(	(	PUNCT
ejpam-5330	45	27	w	w	NOUN
ejpam-5330	45	28	,	,	PUNCT
ejpam-5330	45	29	τn	τn	PROPN
ejpam-5330	45	30	)	)	PUNCT
ejpam-5330	46	1	and	and	CCONJ
ejpam-5330	46	2	(	(	PUNCT
ejpam-5330	46	3	v	v	NOUN
ejpam-5330	46	4	,	,	PUNCT
ejpam-5330	46	5	ηf	ηf	PROPN
ejpam-5330	46	6	)	)	PUNCT
ejpam-5330	46	7	.	.	PUNCT
ejpam-5330	47	1	moreover	moreover	ADV
ejpam-5330	47	2	,	,	PUNCT
ejpam-5330	47	3	we	we	PRON
ejpam-5330	47	4	define	define	VERB
ejpam-5330	47	5	and	and	CCONJ
ejpam-5330	47	6	study	study	VERB
ejpam-5330	47	7	the	the	DET
ejpam-5330	47	8	concepts	concept	NOUN
ejpam-5330	47	9	of	of	ADP
ejpam-5330	47	10	fuzzy	fuzzy	ADJ
ejpam-5330	47	11	soft	soft	ADJ
ejpam-5330	47	12	weakly	weakly	ADJ
ejpam-5330	47	13	(	(	PUNCT
ejpam-5330	47	14	almost	almost	ADV
ejpam-5330	47	15	)	)	PUNCT
ejpam-5330	47	16	α	α	NUM
ejpam-5330	47	17	-	-	ADJ
ejpam-5330	47	18	continuous	continuous	ADJ
ejpam-5330	47	19	mappings	mapping	NOUN
ejpam-5330	47	20	,	,	PUNCT
ejpam-5330	47	21	which	which	PRON
ejpam-5330	47	22	are	be	AUX
ejpam-5330	47	23	weaker	weak	ADJ
ejpam-5330	47	24	forms	form	NOUN
ejpam-5330	47	25	of	of	ADP
ejpam-5330	47	26	fuzzy	fuzzy	ADJ
ejpam-5330	47	27	soft	soft	ADJ
ejpam-5330	47	28	α	α	ADJ
ejpam-5330	47	29	-	-	ADJ
ejpam-5330	47	30	continuous	continuous	ADJ
ejpam-5330	47	31	mappings	mapping	NOUN
ejpam-5330	47	32	.	.	PUNCT
ejpam-5330	48	1	also	also	ADV
ejpam-5330	48	2	,	,	PUNCT
ejpam-5330	48	3	the	the	DET
ejpam-5330	48	4	relationships	relationship	NOUN
ejpam-5330	48	5	between	between	ADP
ejpam-5330	48	6	these	these	DET
ejpam-5330	48	7	classes	class	NOUN
ejpam-5330	48	8	of	of	ADP
ejpam-5330	48	9	mappings	mapping	NOUN
ejpam-5330	48	10	are	be	AUX
ejpam-5330	48	11	investigated	investigate	VERB
ejpam-5330	48	12	with	with	ADP
ejpam-5330	48	13	the	the	DET
ejpam-5330	48	14	help	help	NOUN
ejpam-5330	48	15	of	of	ADP
ejpam-5330	48	16	some	some	DET
ejpam-5330	48	17	examples	example	NOUN
ejpam-5330	48	18	.	.	PUNCT
ejpam-5330	49	1	•	•	NOUN
ejpam-5330	49	2	in	in	ADP
ejpam-5330	49	3	section	section	NOUN
ejpam-5330	49	4	4	4	NUM
ejpam-5330	49	5	,	,	PUNCT
ejpam-5330	49	6	several	several	ADJ
ejpam-5330	49	7	types	type	NOUN
ejpam-5330	49	8	of	of	ADP
ejpam-5330	49	9	fuzzy	fuzzy	ADJ
ejpam-5330	49	10	soft	soft	ADJ
ejpam-5330	49	11	compactness	compactness	NOUN
ejpam-5330	49	12	via	via	ADP
ejpam-5330	49	13	r	r	NOUN
ejpam-5330	49	14	-	-	PUNCT
ejpam-5330	49	15	fuzzy	fuzzy	ADJ
ejpam-5330	49	16	soft	soft	ADJ
ejpam-5330	49	17	α	α	NOUN
ejpam-5330	49	18	-	-	ADJ
ejpam-5330	49	19	open	open	ADJ
ejpam-5330	49	20	sets	set	NOUN
ejpam-5330	49	21	are	be	AUX
ejpam-5330	49	22	defined	define	VERB
ejpam-5330	49	23	,	,	PUNCT
ejpam-5330	49	24	and	and	CCONJ
ejpam-5330	49	25	the	the	DET
ejpam-5330	49	26	relationships	relationship	NOUN
ejpam-5330	49	27	between	between	ADP
ejpam-5330	49	28	them	they	PRON
ejpam-5330	49	29	are	be	AUX
ejpam-5330	49	30	specified	specify	VERB
ejpam-5330	49	31	.	.	PUNCT
ejpam-5330	50	1	•	•	NUM
ejpam-5330	50	2	finally	finally	ADV
ejpam-5330	50	3	,	,	PUNCT
ejpam-5330	50	4	we	we	PRON
ejpam-5330	50	5	close	close	VERB
ejpam-5330	50	6	this	this	DET
ejpam-5330	50	7	manuscript	manuscript	NOUN
ejpam-5330	50	8	with	with	ADP
ejpam-5330	50	9	some	some	DET
ejpam-5330	50	10	conclusions	conclusion	NOUN
ejpam-5330	50	11	and	and	CCONJ
ejpam-5330	50	12	proposed	propose	VERB
ejpam-5330	50	13	some	some	DET
ejpam-5330	50	14	future	future	ADJ
ejpam-5330	50	15	works	work	NOUN
ejpam-5330	50	16	in	in	ADP
ejpam-5330	50	17	section	section	NOUN
ejpam-5330	50	18	5	5	NUM
ejpam-5330	50	19	.	.	PUNCT
ejpam-5330	51	1	in	in	ADP
ejpam-5330	51	2	this	this	DET
ejpam-5330	51	3	work	work	NOUN
ejpam-5330	51	4	,	,	PUNCT
ejpam-5330	51	5	nonempty	nonempty	NOUN
ejpam-5330	51	6	sets	set	NOUN
ejpam-5330	51	7	will	will	AUX
ejpam-5330	51	8	be	be	AUX
ejpam-5330	51	9	denoted	denote	VERB
ejpam-5330	51	10	byw	byw	PROPN
ejpam-5330	51	11	,	,	PUNCT
ejpam-5330	51	12	v	v	NOUN
ejpam-5330	51	13	,	,	PUNCT
ejpam-5330	51	14	etc	etc	X
ejpam-5330	51	15	.	.	X
ejpam-5330	52	1	n	n	X
ejpam-5330	52	2	is	be	AUX
ejpam-5330	52	3	the	the	DET
ejpam-5330	52	4	set	set	NOUN
ejpam-5330	52	5	of	of	ADP
ejpam-5330	52	6	all	all	DET
ejpam-5330	52	7	parameters	parameter	NOUN
ejpam-5330	52	8	for	for	ADP
ejpam-5330	52	9	w	w	PROPN
ejpam-5330	52	10	and	and	CCONJ
ejpam-5330	52	11	c	c	NOUN
ejpam-5330	52	12	⊆	⊆	NUM
ejpam-5330	52	13	n	n	NOUN
ejpam-5330	52	14	.	.	PUNCT
ejpam-5330	53	1	the	the	DET
ejpam-5330	53	2	family	family	NOUN
ejpam-5330	53	3	of	of	ADP
ejpam-5330	53	4	all	all	DET
ejpam-5330	53	5	fuzzy	fuzzy	ADJ
ejpam-5330	53	6	sets	set	NOUN
ejpam-5330	53	7	on	on	ADP
ejpam-5330	53	8	w	w	PROPN
ejpam-5330	53	9	is	be	AUX
ejpam-5330	53	10	denoted	denote	VERB
ejpam-5330	53	11	by	by	ADP
ejpam-5330	53	12	iw	iw	PROPN
ejpam-5330	53	13	(	(	PUNCT
ejpam-5330	53	14	where	where	SCONJ
ejpam-5330	53	15	i	i	PRON
ejpam-5330	53	16	◦	◦	VERB
ejpam-5330	53	17	=	=	SYM
ejpam-5330	53	18	(	(	PUNCT
ejpam-5330	53	19	0	0	NUM
ejpam-5330	53	20	,	,	PUNCT
ejpam-5330	53	21	1	1	NUM
ejpam-5330	53	22	]	]	PUNCT
ejpam-5330	53	23	,	,	PUNCT
ejpam-5330	53	24	i	i	PRON
ejpam-5330	53	25	=	=	PUNCT
ejpam-5330	54	1	[	[	X
ejpam-5330	54	2	0	0	NUM
ejpam-5330	54	3	,	,	PUNCT
ejpam-5330	54	4	1	1	NUM
ejpam-5330	54	5	]	]	NUM
ejpam-5330	54	6	)	)	PUNCT
ejpam-5330	54	7	,	,	PUNCT
ejpam-5330	54	8	and	and	CCONJ
ejpam-5330	54	9	for	for	ADP
ejpam-5330	54	10	s	s	PROPN
ejpam-5330	54	11	∈	∈	PROPN
ejpam-5330	54	12	i	i	PRON
ejpam-5330	54	13	,	,	PUNCT
ejpam-5330	54	14	s(w	s(w	NOUN
ejpam-5330	54	15	)	)	PUNCT
ejpam-5330	54	16	=	=	SYM
ejpam-5330	54	17	s	s	NOUN
ejpam-5330	54	18	,	,	PUNCT
ejpam-5330	54	19	for	for	ADP
ejpam-5330	54	20	all	all	DET
ejpam-5330	54	21	w	w	NOUN
ejpam-5330	54	22	∈w	∈w	NOUN
ejpam-5330	54	23	.	.	PUNCT
ejpam-5330	55	1	w.	w.	PROPN
ejpam-5330	55	2	alqurashi	alqurashi	PROPN
ejpam-5330	55	3	,	,	PUNCT
ejpam-5330	55	4	i.	i.	PROPN
ejpam-5330	55	5	m.	m.	PROPN
ejpam-5330	55	6	taha	taha	PROPN
ejpam-5330	55	7	/	/	PUNCT
ejpam-5330	55	8	eur	eur	PROPN
ejpam-5330	55	9	.	.	PUNCT
ejpam-5330	56	1	j.	j.	PROPN
ejpam-5330	56	2	pure	pure	PROPN
ejpam-5330	56	3	appl	appl	PROPN
ejpam-5330	56	4	.	.	PROPN
ejpam-5330	56	5	math	math	PROPN
ejpam-5330	56	6	,	,	PUNCT
ejpam-5330	56	7	17	17	NUM
ejpam-5330	56	8	(	(	PUNCT
ejpam-5330	56	9	4	4	NUM
ejpam-5330	56	10	)	)	PUNCT
ejpam-5330	56	11	(	(	PUNCT
ejpam-5330	56	12	2024	2024	NUM
ejpam-5330	56	13	)	)	PUNCT
ejpam-5330	56	14	,	,	PUNCT
ejpam-5330	56	15	4112	4112	NUM
ejpam-5330	56	16	-	-	SYM
ejpam-5330	56	17	4134	4134	NUM
ejpam-5330	56	18	4114	4114	NUM
ejpam-5330	56	19	the	the	DET
ejpam-5330	56	20	following	follow	VERB
ejpam-5330	56	21	concepts	concept	NOUN
ejpam-5330	56	22	and	and	CCONJ
ejpam-5330	56	23	results	result	NOUN
ejpam-5330	56	24	will	will	AUX
ejpam-5330	56	25	be	be	AUX
ejpam-5330	56	26	used	use	VERB
ejpam-5330	56	27	in	in	ADP
ejpam-5330	56	28	the	the	DET
ejpam-5330	56	29	next	next	ADJ
ejpam-5330	56	30	sections	section	NOUN
ejpam-5330	56	31	.	.	PUNCT
ejpam-5330	57	1	definition	definition	NOUN
ejpam-5330	57	2	1	1	NUM
ejpam-5330	57	3	.	.	PUNCT
ejpam-5330	58	1	[	[	X
ejpam-5330	58	2	1	1	NUM
ejpam-5330	58	3	,	,	PUNCT
ejpam-5330	58	4	14	14	NUM
ejpam-5330	58	5	,	,	PUNCT
ejpam-5330	58	6	19	19	NUM
ejpam-5330	58	7	]	]	PUNCT
ejpam-5330	58	8	a	a	DET
ejpam-5330	58	9	fuzzy	fuzzy	ADJ
ejpam-5330	58	10	soft	soft	ADJ
ejpam-5330	58	11	set	set	NOUN
ejpam-5330	58	12	hc	hc	PRON
ejpam-5330	58	13	on	on	ADP
ejpam-5330	58	14	w	w	PROPN
ejpam-5330	58	15	is	be	AUX
ejpam-5330	58	16	a	a	DET
ejpam-5330	58	17	mapping	mapping	NOUN
ejpam-5330	58	18	from	from	ADP
ejpam-5330	58	19	n	n	PROPN
ejpam-5330	58	20	to	to	ADP
ejpam-5330	58	21	iw	iw	INTJ
ejpam-5330	58	22	,	,	PUNCT
ejpam-5330	58	23	such	such	ADJ
ejpam-5330	58	24	that	that	SCONJ
ejpam-5330	58	25	hc(n	hc(n	NUM
ejpam-5330	58	26	)	)	PUNCT
ejpam-5330	59	1	is	be	AUX
ejpam-5330	59	2	a	a	DET
ejpam-5330	59	3	fuzzy	fuzzy	ADJ
ejpam-5330	59	4	set	set	NOUN
ejpam-5330	59	5	on	on	ADP
ejpam-5330	59	6	w	w	PROPN
ejpam-5330	59	7	,	,	PUNCT
ejpam-5330	59	8	for	for	ADP
ejpam-5330	59	9	each	each	DET
ejpam-5330	59	10	n	n	PRON
ejpam-5330	59	11	∈	∈	PROPN
ejpam-5330	59	12	c	c	NOUN
ejpam-5330	59	13	and	and	CCONJ
ejpam-5330	59	14	hc(n	hc(n	NUM
ejpam-5330	59	15	)	)	PUNCT
ejpam-5330	60	1	=	=	SYM
ejpam-5330	60	2	0	0	NUM
ejpam-5330	60	3	,	,	PUNCT
ejpam-5330	60	4	if	if	SCONJ
ejpam-5330	60	5	n	n	PROPN
ejpam-5330	60	6	̸∈	̸∈	PROPN
ejpam-5330	60	7	c.	c.	PROPN
ejpam-5330	60	8	the	the	DET
ejpam-5330	60	9	family	family	NOUN
ejpam-5330	60	10	of	of	ADP
ejpam-5330	60	11	all	all	DET
ejpam-5330	60	12	fuzzy	fuzzy	ADJ
ejpam-5330	60	13	soft	soft	ADJ
ejpam-5330	60	14	sets	set	NOUN
ejpam-5330	60	15	on	on	ADP
ejpam-5330	60	16	w	w	PROPN
ejpam-5330	60	17	is	be	AUX
ejpam-5330	60	18	denoted	denote	VERB
ejpam-5330	60	19	by	by	ADP
ejpam-5330	60	20	˜(w	˜(w	PROPN
ejpam-5330	60	21	,	,	PUNCT
ejpam-5330	60	22	n	n	CCONJ
ejpam-5330	60	23	)	)	PUNCT
ejpam-5330	60	24	.	.	PUNCT
ejpam-5330	61	1	definition	definition	NOUN
ejpam-5330	61	2	2	2	NUM
ejpam-5330	61	3	.	.	PUNCT
ejpam-5330	62	1	[	[	X
ejpam-5330	62	2	32	32	NUM
ejpam-5330	62	3	]	]	PUNCT
ejpam-5330	62	4	the	the	DET
ejpam-5330	62	5	difference	difference	NOUN
ejpam-5330	62	6	between	between	ADP
ejpam-5330	62	7	two	two	NUM
ejpam-5330	62	8	fuzzy	fuzzy	ADJ
ejpam-5330	62	9	soft	soft	ADJ
ejpam-5330	62	10	sets	set	NOUN
ejpam-5330	62	11	hc	hc	PRON
ejpam-5330	62	12	and	and	CCONJ
ejpam-5330	62	13	gb	gb	NOUN
ejpam-5330	62	14	is	be	AUX
ejpam-5330	62	15	a	a	DET
ejpam-5330	62	16	fuzzy	fuzzy	ADJ
ejpam-5330	62	17	soft	soft	ADJ
ejpam-5330	62	18	set	set	NOUN
ejpam-5330	62	19	,	,	PUNCT
ejpam-5330	62	20	defined	define	VERB
ejpam-5330	62	21	as	as	ADP
ejpam-5330	62	22	follows	follow	VERB
ejpam-5330	62	23	,	,	PUNCT
ejpam-5330	62	24	for	for	ADP
ejpam-5330	62	25	each	each	DET
ejpam-5330	62	26	n	n	PRON
ejpam-5330	62	27	∈	∈	PROPN
ejpam-5330	62	28	n	n	NOUN
ejpam-5330	62	29	:	:	PUNCT
ejpam-5330	62	30	(	(	PUNCT
ejpam-5330	62	31	hc	hc	PROPN
ejpam-5330	62	32	⊓	⊓	PROPN
ejpam-5330	62	33	gb)(n	gb)(n	PROPN
ejpam-5330	62	34	)	)	PUNCT
ejpam-5330	62	35	=	=	PRON
ejpam-5330	63	1	{	{	PUNCT
ejpam-5330	63	2	0	0	NUM
ejpam-5330	63	3	,	,	PUNCT
ejpam-5330	63	4	if	if	SCONJ
ejpam-5330	63	5	hc(n	hc(n	NUM
ejpam-5330	63	6	)	)	PUNCT
ejpam-5330	63	7	≤	≤	NOUN
ejpam-5330	63	8	gb(n	gb(n	NOUN
ejpam-5330	63	9	)	)	PUNCT
ejpam-5330	63	10	,	,	PUNCT
ejpam-5330	63	11	hc(n	hc(n	NUM
ejpam-5330	63	12	)	)	PUNCT
ejpam-5330	64	1	∧	∧	NOUN
ejpam-5330	64	2	(	(	PUNCT
ejpam-5330	64	3	gb(n	gb(n	NOUN
ejpam-5330	64	4	)	)	PUNCT
ejpam-5330	64	5	)	)	PUNCT
ejpam-5330	65	1	c	c	X
ejpam-5330	65	2	,	,	PUNCT
ejpam-5330	65	3	otherwise	otherwise	ADV
ejpam-5330	65	4	.	.	PUNCT
ejpam-5330	66	1	definition	definition	NOUN
ejpam-5330	66	2	3	3	NUM
ejpam-5330	66	3	.	.	PUNCT
ejpam-5330	67	1	[	[	X
ejpam-5330	67	2	23	23	NUM
ejpam-5330	67	3	]	]	PUNCT
ejpam-5330	67	4	a	a	DET
ejpam-5330	67	5	fuzzy	fuzzy	ADJ
ejpam-5330	67	6	soft	soft	ADJ
ejpam-5330	67	7	point	point	NOUN
ejpam-5330	67	8	nws	nws	PROPN
ejpam-5330	67	9	on	on	ADP
ejpam-5330	67	10	w	w	PROPN
ejpam-5330	67	11	is	be	AUX
ejpam-5330	67	12	a	a	DET
ejpam-5330	67	13	fuzzy	fuzzy	ADJ
ejpam-5330	67	14	soft	soft	ADJ
ejpam-5330	67	15	set	set	NOUN
ejpam-5330	67	16	,	,	PUNCT
ejpam-5330	67	17	defined	define	VERB
ejpam-5330	67	18	as	as	SCONJ
ejpam-5330	67	19	follows	follow	VERB
ejpam-5330	67	20	:	:	PUNCT
ejpam-5330	67	21	nws(k	nws(k	X
ejpam-5330	67	22	)	)	PUNCT
ejpam-5330	67	23	=	=	PRON
ejpam-5330	67	24	{	{	PUNCT
ejpam-5330	67	25	ws	ws	NOUN
ejpam-5330	67	26	,	,	PUNCT
ejpam-5330	67	27	if	if	SCONJ
ejpam-5330	67	28	k	k	PROPN
ejpam-5330	67	29	=	=	PUNCT
ejpam-5330	67	30	n	n	CCONJ
ejpam-5330	67	31	,	,	PUNCT
ejpam-5330	67	32	0	0	NUM
ejpam-5330	67	33	,	,	PUNCT
ejpam-5330	67	34	if	if	SCONJ
ejpam-5330	67	35	k	k	PROPN
ejpam-5330	67	36	∈	∈	PROPN
ejpam-5330	67	37	n	n	PRON
ejpam-5330	67	38	−	−	PROPN
ejpam-5330	67	39	{	{	PUNCT
ejpam-5330	67	40	n	n	CCONJ
ejpam-5330	67	41	}	}	PUNCT
ejpam-5330	67	42	,	,	PUNCT
ejpam-5330	67	43	where	where	SCONJ
ejpam-5330	67	44	ws	ws	PROPN
ejpam-5330	67	45	is	be	AUX
ejpam-5330	67	46	a	a	DET
ejpam-5330	67	47	fuzzy	fuzzy	ADJ
ejpam-5330	67	48	point	point	NOUN
ejpam-5330	67	49	on	on	ADP
ejpam-5330	67	50	w	w	PROPN
ejpam-5330	67	51	.	.	PUNCT
ejpam-5330	68	1	a	a	DET
ejpam-5330	68	2	fuzzy	fuzzy	ADJ
ejpam-5330	68	3	soft	soft	ADJ
ejpam-5330	68	4	point	point	NOUN
ejpam-5330	68	5	nws	nws	PROPN
ejpam-5330	68	6	is	be	AUX
ejpam-5330	68	7	called	call	VERB
ejpam-5330	68	8	belong	belong	VERB
ejpam-5330	68	9	to	to	ADP
ejpam-5330	68	10	a	a	DET
ejpam-5330	68	11	fuzzy	fuzzy	ADJ
ejpam-5330	68	12	soft	soft	ADJ
ejpam-5330	68	13	set	set	NOUN
ejpam-5330	68	14	fa	fa	NOUN
ejpam-5330	68	15	,	,	PUNCT
ejpam-5330	68	16	denoted	denote	VERB
ejpam-5330	68	17	by	by	ADP
ejpam-5330	68	18	nws∈̃fa	nws∈̃fa	PROPN
ejpam-5330	68	19	,	,	PUNCT
ejpam-5330	68	20	if	if	SCONJ
ejpam-5330	68	21	s	s	NOUN
ejpam-5330	68	22	≤	≤	NUM
ejpam-5330	68	23	fa(n)(w	fa(n)(w	NOUN
ejpam-5330	68	24	)	)	PUNCT
ejpam-5330	68	25	.	.	PUNCT
ejpam-5330	69	1	the	the	DET
ejpam-5330	69	2	family	family	NOUN
ejpam-5330	69	3	of	of	ADP
ejpam-5330	69	4	all	all	DET
ejpam-5330	69	5	fuzzy	fuzzy	ADJ
ejpam-5330	69	6	soft	soft	ADJ
ejpam-5330	69	7	points	point	NOUN
ejpam-5330	69	8	on	on	ADP
ejpam-5330	69	9	w	w	PROPN
ejpam-5330	69	10	is	be	AUX
ejpam-5330	69	11	denoted	denote	VERB
ejpam-5330	69	12	by	by	ADP
ejpam-5330	69	13	p̃s(w	p̃s(w	PROPN
ejpam-5330	69	14	)	)	PUNCT
ejpam-5330	69	15	.	.	PUNCT
ejpam-5330	70	1	definition	definition	NOUN
ejpam-5330	70	2	4	4	NUM
ejpam-5330	70	3	.	.	PUNCT
ejpam-5330	71	1	[	[	X
ejpam-5330	71	2	13	13	NUM
ejpam-5330	71	3	]	]	PUNCT
ejpam-5330	71	4	a	a	DET
ejpam-5330	71	5	fuzzy	fuzzy	ADJ
ejpam-5330	71	6	soft	soft	ADJ
ejpam-5330	71	7	point	point	NOUN
ejpam-5330	71	8	nws	nws	PROPN
ejpam-5330	71	9	∈	∈	PROPN
ejpam-5330	71	10	p̃s(w	p̃s(w	NOUN
ejpam-5330	71	11	)	)	PUNCT
ejpam-5330	71	12	is	be	AUX
ejpam-5330	71	13	called	call	VERB
ejpam-5330	71	14	a	a	DET
ejpam-5330	71	15	soft	soft	ADJ
ejpam-5330	71	16	quasi	quasi	NOUN
ejpam-5330	71	17	-	-	NOUN
ejpam-5330	71	18	coincident	coincident	ADJ
ejpam-5330	71	19	with	with	ADP
ejpam-5330	71	20	hc	hc	PROPN
ejpam-5330	71	21	∈	∈	PROPN
ejpam-5330	71	22	˜(w	˜(w	PROPN
ejpam-5330	71	23	,	,	PUNCT
ejpam-5330	71	24	n	n	CCONJ
ejpam-5330	71	25	)	)	PUNCT
ejpam-5330	71	26	and	and	CCONJ
ejpam-5330	71	27	denoted	denote	VERB
ejpam-5330	71	28	by	by	ADP
ejpam-5330	71	29	nws	nws	PROPN
ejpam-5330	71	30	q̃hc	q̃hc	PROPN
ejpam-5330	71	31	,	,	PUNCT
ejpam-5330	71	32	if	if	SCONJ
ejpam-5330	71	33	s+hc(n)(w	s+hc(n)(w	NOUN
ejpam-5330	71	34	)	)	PUNCT
ejpam-5330	71	35	>	>	X
ejpam-5330	72	1	1	1	X
ejpam-5330	72	2	.	.	PUNCT
ejpam-5330	72	3	a	a	DET
ejpam-5330	72	4	fuzzy	fuzzy	ADJ
ejpam-5330	72	5	soft	soft	ADJ
ejpam-5330	72	6	set	set	NOUN
ejpam-5330	72	7	hc	hc	PROPN
ejpam-5330	72	8	∈	∈	PROPN
ejpam-5330	72	9	˜(w	˜(w	PROPN
ejpam-5330	72	10	,	,	PUNCT
ejpam-5330	72	11	n	n	CCONJ
ejpam-5330	72	12	)	)	PUNCT
ejpam-5330	72	13	is	be	AUX
ejpam-5330	72	14	called	call	VERB
ejpam-5330	72	15	a	a	DET
ejpam-5330	72	16	soft	soft	ADJ
ejpam-5330	72	17	quasi	quasi	NOUN
ejpam-5330	72	18	-	-	NOUN
ejpam-5330	72	19	coincident	coincident	ADJ
ejpam-5330	72	20	with	with	ADP
ejpam-5330	72	21	gb	gb	PROPN
ejpam-5330	72	22	∈	∈	PROPN
ejpam-5330	72	23	˜(w	˜(w	PROPN
ejpam-5330	72	24	,	,	PUNCT
ejpam-5330	72	25	n	n	CCONJ
ejpam-5330	72	26	)	)	PUNCT
ejpam-5330	72	27	and	and	CCONJ
ejpam-5330	72	28	denoted	denote	VERB
ejpam-5330	72	29	by	by	ADP
ejpam-5330	72	30	hc	hc	PROPN
ejpam-5330	72	31	q̃gb	q̃gb	PROPN
ejpam-5330	72	32	,	,	PUNCT
ejpam-5330	72	33	if	if	SCONJ
ejpam-5330	72	34	there	there	PRON
ejpam-5330	72	35	is	be	VERB
ejpam-5330	72	36	n	n	DET
ejpam-5330	72	37	∈	∈	PROPN
ejpam-5330	72	38	n	n	NOUN
ejpam-5330	72	39	and	and	CCONJ
ejpam-5330	72	40	w	w	PROPN
ejpam-5330	72	41	∈w	∈w	NOUN
ejpam-5330	72	42	,	,	PUNCT
ejpam-5330	73	1	such	such	ADJ
ejpam-5330	73	2	that	that	SCONJ
ejpam-5330	73	3	hc(n)(w	hc(n)(w	NOUN
ejpam-5330	73	4	)	)	PUNCT
ejpam-5330	73	5	+	+	CCONJ
ejpam-5330	73	6	gb(n)(w	gb(n)(w	NOUN
ejpam-5330	73	7	)	)	PUNCT
ejpam-5330	73	8	>	>	X
ejpam-5330	73	9	1	1	NUM
ejpam-5330	73	10	,	,	PUNCT
ejpam-5330	73	11	if	if	SCONJ
ejpam-5330	73	12	hc	hc	PROPN
ejpam-5330	73	13	is	be	AUX
ejpam-5330	73	14	not	not	PART
ejpam-5330	73	15	soft	soft	ADJ
ejpam-5330	73	16	quasi	quasi	NOUN
ejpam-5330	73	17	-	-	NOUN
ejpam-5330	73	18	coincident	coincident	ADJ
ejpam-5330	73	19	with	with	ADP
ejpam-5330	73	20	gb	gb	PRON
ejpam-5330	73	21	,	,	PUNCT
ejpam-5330	73	22	hc	hc	PROPN
ejpam-5330	73	23	̸	̸	PUNCT
ejpam-5330	73	24	q̃gb	q̃gb	PROPN
ejpam-5330	73	25	.	.	PUNCT
ejpam-5330	74	1	definition	definition	NOUN
ejpam-5330	74	2	5	5	NUM
ejpam-5330	74	3	.	.	PUNCT
ejpam-5330	75	1	[	[	X
ejpam-5330	75	2	19	19	NUM
ejpam-5330	75	3	]	]	PUNCT
ejpam-5330	75	4	a	a	DET
ejpam-5330	75	5	mapping	mapping	NOUN
ejpam-5330	75	6	τ	τ	X
ejpam-5330	75	7	:	:	PUNCT
ejpam-5330	75	8	n	n	CCONJ
ejpam-5330	75	9	−→	−→	NOUN
ejpam-5330	76	1	[	[	X
ejpam-5330	76	2	0	0	NUM
ejpam-5330	76	3	,	,	PUNCT
ejpam-5330	76	4	1	1	NUM
ejpam-5330	76	5	]	]	PUNCT
ejpam-5330	76	6	˜(w	˜(w	PROPN
ejpam-5330	76	7	,	,	PUNCT
ejpam-5330	76	8	n	n	CCONJ
ejpam-5330	76	9	)	)	PUNCT
ejpam-5330	76	10	is	be	AUX
ejpam-5330	76	11	called	call	VERB
ejpam-5330	76	12	a	a	DET
ejpam-5330	76	13	fuzzy	fuzzy	ADJ
ejpam-5330	76	14	soft	soft	ADJ
ejpam-5330	76	15	topology	topology	NOUN
ejpam-5330	76	16	on	on	ADP
ejpam-5330	76	17	w	w	NOUN
ejpam-5330	76	18	if	if	SCONJ
ejpam-5330	76	19	it	it	PRON
ejpam-5330	76	20	satisfies	satisfy	VERB
ejpam-5330	76	21	the	the	DET
ejpam-5330	76	22	following	following	NOUN
ejpam-5330	76	23	,	,	PUNCT
ejpam-5330	76	24	for	for	ADP
ejpam-5330	76	25	each	each	DET
ejpam-5330	76	26	n	n	PRON
ejpam-5330	76	27	∈	∈	PROPN
ejpam-5330	76	28	n	n	NOUN
ejpam-5330	76	29	:	:	PUNCT
ejpam-5330	76	30	(	(	PUNCT
ejpam-5330	76	31	1	1	NUM
ejpam-5330	76	32	)	)	PUNCT
ejpam-5330	76	33	τn(φ	τn(φ	ADV
ejpam-5330	76	34	)	)	PUNCT
ejpam-5330	76	35	=	=	SYM
ejpam-5330	76	36	τn(ñ	τn(ñ	X
ejpam-5330	76	37	)	)	PUNCT
ejpam-5330	77	1	=	=	SYM
ejpam-5330	77	2	1	1	NUM
ejpam-5330	77	3	,	,	PUNCT
ejpam-5330	77	4	(	(	PUNCT
ejpam-5330	77	5	2	2	NUM
ejpam-5330	77	6	)	)	PUNCT
ejpam-5330	77	7	τn(hc	τn(hc	PUNCT
ejpam-5330	77	8	⊓	⊓	PROPN
ejpam-5330	77	9	gb	gb	NOUN
ejpam-5330	77	10	)	)	PUNCT
ejpam-5330	77	11	≥	≥	NOUN
ejpam-5330	77	12	τn(hc	τn(hc	NUM
ejpam-5330	77	13	)	)	PUNCT
ejpam-5330	78	1	∧	∧	NOUN
ejpam-5330	78	2	τn(gb	τn(gb	NOUN
ejpam-5330	78	3	)	)	PUNCT
ejpam-5330	78	4	,	,	PUNCT
ejpam-5330	78	5	for	for	ADP
ejpam-5330	78	6	each	each	DET
ejpam-5330	78	7	hc	hc	PROPN
ejpam-5330	78	8	,	,	PUNCT
ejpam-5330	78	9	gb	gb	PROPN
ejpam-5330	78	10	∈	∈	PROPN
ejpam-5330	78	11	˜(w	˜(w	PROPN
ejpam-5330	78	12	,	,	PUNCT
ejpam-5330	78	13	n	n	CCONJ
ejpam-5330	78	14	)	)	PUNCT
ejpam-5330	78	15	,	,	PUNCT
ejpam-5330	78	16	(	(	PUNCT
ejpam-5330	78	17	3	3	X
ejpam-5330	78	18	)	)	PUNCT
ejpam-5330	78	19	τn(⊔δ∈∆(hc)δ	τn(⊔δ∈∆(hc)δ	PROPN
ejpam-5330	78	20	)	)	PUNCT
ejpam-5330	78	21	≥	≥	NOUN
ejpam-5330	78	22	∧δ∈∆τn((hc)δ	∧δ∈∆τn((hc)δ	NUM
ejpam-5330	78	23	)	)	PUNCT
ejpam-5330	78	24	,	,	PUNCT
ejpam-5330	78	25	for	for	ADP
ejpam-5330	78	26	each	each	PRON
ejpam-5330	78	27	(	(	PUNCT
ejpam-5330	78	28	hc)δ	hc)δ	PROPN
ejpam-5330	78	29	∈	∈	PROPN
ejpam-5330	78	30	˜(w	˜(w	PROPN
ejpam-5330	78	31	,	,	PUNCT
ejpam-5330	78	32	n	n	CCONJ
ejpam-5330	78	33	)	)	PUNCT
ejpam-5330	78	34	,	,	PUNCT
ejpam-5330	78	35	δ	δ	PROPN
ejpam-5330	78	36	∈	∈	PROPN
ejpam-5330	79	1	∆.	∆.	X
ejpam-5330	79	2	thus	thus	ADV
ejpam-5330	79	3	,	,	PUNCT
ejpam-5330	79	4	(	(	PUNCT
ejpam-5330	79	5	w	w	NOUN
ejpam-5330	79	6	,	,	PUNCT
ejpam-5330	79	7	τn	τn	NOUN
ejpam-5330	79	8	)	)	PUNCT
ejpam-5330	79	9	is	be	AUX
ejpam-5330	79	10	called	call	VERB
ejpam-5330	79	11	a	a	DET
ejpam-5330	79	12	fuzzy	fuzzy	ADJ
ejpam-5330	79	13	soft	soft	ADJ
ejpam-5330	79	14	topological	topological	ADJ
ejpam-5330	79	15	space	space	NOUN
ejpam-5330	79	16	(	(	PUNCT
ejpam-5330	79	17	briefly	briefly	ADV
ejpam-5330	79	18	,	,	PUNCT
ejpam-5330	79	19	fsts	fst	NOUN
ejpam-5330	79	20	)	)	PUNCT
ejpam-5330	79	21	in	in	ADP
ejpam-5330	79	22	the	the	DET
ejpam-5330	79	23	sense	sense	NOUN
ejpam-5330	79	24	of	of	ADP
ejpam-5330	79	25	šostak	šostak	NOUN
ejpam-5330	79	26	[	[	X
ejpam-5330	79	27	35	35	NUM
ejpam-5330	79	28	]	]	PUNCT
ejpam-5330	79	29	.	.	PUNCT
ejpam-5330	80	1	w.	w.	PROPN
ejpam-5330	80	2	alqurashi	alqurashi	PROPN
ejpam-5330	80	3	,	,	PUNCT
ejpam-5330	80	4	i.	i.	PROPN
ejpam-5330	80	5	m.	m.	PROPN
ejpam-5330	80	6	taha	taha	PROPN
ejpam-5330	80	7	/	/	PUNCT
ejpam-5330	80	8	eur	eur	PROPN
ejpam-5330	80	9	.	.	PUNCT
ejpam-5330	81	1	j.	j.	PROPN
ejpam-5330	81	2	pure	pure	PROPN
ejpam-5330	81	3	appl	appl	PROPN
ejpam-5330	81	4	.	.	PROPN
ejpam-5330	81	5	math	math	PROPN
ejpam-5330	81	6	,	,	PUNCT
ejpam-5330	81	7	17	17	NUM
ejpam-5330	81	8	(	(	PUNCT
ejpam-5330	81	9	4	4	NUM
ejpam-5330	81	10	)	)	PUNCT
ejpam-5330	81	11	(	(	PUNCT
ejpam-5330	81	12	2024	2024	NUM
ejpam-5330	81	13	)	)	PUNCT
ejpam-5330	81	14	,	,	PUNCT
ejpam-5330	81	15	4112	4112	NUM
ejpam-5330	81	16	-	-	SYM
ejpam-5330	81	17	4134	4134	NUM
ejpam-5330	81	18	4115	4115	NUM
ejpam-5330	81	19	definition	definition	NOUN
ejpam-5330	81	20	6	6	NUM
ejpam-5330	81	21	.	.	PUNCT
ejpam-5330	82	1	[	[	X
ejpam-5330	82	2	19	19	NUM
ejpam-5330	82	3	]	]	X
ejpam-5330	82	4	let	let	ADJ
ejpam-5330	82	5	(	(	PUNCT
ejpam-5330	82	6	w	w	NOUN
ejpam-5330	82	7	,	,	PUNCT
ejpam-5330	82	8	τn	τn	PROPN
ejpam-5330	82	9	)	)	PUNCT
ejpam-5330	82	10	and	and	CCONJ
ejpam-5330	82	11	(	(	PUNCT
ejpam-5330	82	12	v	v	NOUN
ejpam-5330	82	13	,	,	PUNCT
ejpam-5330	82	14	ηf	ηf	PROPN
ejpam-5330	82	15	)	)	PUNCT
ejpam-5330	82	16	be	be	AUX
ejpam-5330	82	17	an	an	DET
ejpam-5330	82	18	fstss	fstss	NOUN
ejpam-5330	82	19	.	.	PUNCT
ejpam-5330	83	1	a	a	DET
ejpam-5330	83	2	fuzzy	fuzzy	ADJ
ejpam-5330	83	3	soft	soft	ADJ
ejpam-5330	83	4	mapping	mapping	NOUN
ejpam-5330	83	5	φψ	φψ	X
ejpam-5330	83	6	:	:	PUNCT
ejpam-5330	83	7	˜(w	˜(w	PROPN
ejpam-5330	83	8	,	,	PUNCT
ejpam-5330	83	9	n	n	CCONJ
ejpam-5330	83	10	)	)	PUNCT
ejpam-5330	83	11	−→	−→	NOUN
ejpam-5330	83	12	(	(	PUNCT
ejpam-5330	83	13	̃v	̃v	NOUN
ejpam-5330	83	14	,	,	PUNCT
ejpam-5330	83	15	f	f	PROPN
ejpam-5330	83	16	)	)	PUNCT
ejpam-5330	83	17	is	be	AUX
ejpam-5330	83	18	called	call	VERB
ejpam-5330	83	19	fuzzy	fuzzy	ADJ
ejpam-5330	83	20	soft	soft	ADJ
ejpam-5330	83	21	continuous	continuous	ADJ
ejpam-5330	83	22	if	if	SCONJ
ejpam-5330	83	23	τn(φ	τn(φ	PUNCT
ejpam-5330	83	24	−1	−1	NOUN
ejpam-5330	83	25	ψ	ψ	X
ejpam-5330	83	26	(	(	PUNCT
ejpam-5330	83	27	hc	hc	NOUN
ejpam-5330	83	28	)	)	PUNCT
ejpam-5330	83	29	)	)	PUNCT
ejpam-5330	83	30	≥	≥	PROPN
ejpam-5330	83	31	ηk(hc	ηk(hc	PROPN
ejpam-5330	83	32	)	)	PUNCT
ejpam-5330	83	33	for	for	ADP
ejpam-5330	83	34	each	each	DET
ejpam-5330	83	35	hc	hc	PROPN
ejpam-5330	83	36	∈	∈	PROPN
ejpam-5330	83	37	(	(	PUNCT
ejpam-5330	83	38	̃v	̃v	NOUN
ejpam-5330	83	39	,	,	PUNCT
ejpam-5330	83	40	f	f	PROPN
ejpam-5330	83	41	)	)	PUNCT
ejpam-5330	83	42	,	,	PUNCT
ejpam-5330	83	43	n	n	PROPN
ejpam-5330	83	44	∈	∈	PROPN
ejpam-5330	83	45	n	n	CCONJ
ejpam-5330	83	46	,	,	PUNCT
ejpam-5330	83	47	and	and	CCONJ
ejpam-5330	83	48	(	(	PUNCT
ejpam-5330	83	49	k	k	X
ejpam-5330	83	50	=	=	SYM
ejpam-5330	83	51	ψ(n	ψ(n	PROPN
ejpam-5330	83	52	)	)	PUNCT
ejpam-5330	83	53	)	)	PUNCT
ejpam-5330	84	1	∈	∈	PROPN
ejpam-5330	84	2	f	f	X
ejpam-5330	84	3	.	.	PUNCT
ejpam-5330	85	1	definition	definition	NOUN
ejpam-5330	85	2	7	7	NUM
ejpam-5330	85	3	.	.	PUNCT
ejpam-5330	86	1	[	[	X
ejpam-5330	86	2	15	15	NUM
ejpam-5330	86	3	,	,	PUNCT
ejpam-5330	86	4	16	16	NUM
ejpam-5330	86	5	]	]	PUNCT
ejpam-5330	86	6	in	in	ADP
ejpam-5330	86	7	an	an	DET
ejpam-5330	86	8	fsts	fst	NOUN
ejpam-5330	86	9	(	(	PUNCT
ejpam-5330	86	10	w	w	NOUN
ejpam-5330	86	11	,	,	PUNCT
ejpam-5330	86	12	τn	τn	NOUN
ejpam-5330	86	13	)	)	PUNCT
ejpam-5330	86	14	,	,	PUNCT
ejpam-5330	86	15	for	for	ADP
ejpam-5330	86	16	each	each	DET
ejpam-5330	86	17	hc	hc	PROPN
ejpam-5330	86	18	∈	∈	PROPN
ejpam-5330	86	19	˜(w	˜(w	PROPN
ejpam-5330	86	20	,	,	PUNCT
ejpam-5330	86	21	n	n	CCONJ
ejpam-5330	86	22	)	)	PUNCT
ejpam-5330	86	23	,	,	PUNCT
ejpam-5330	86	24	n	n	PROPN
ejpam-5330	86	25	∈	∈	PROPN
ejpam-5330	86	26	n	n	NOUN
ejpam-5330	86	27	,	,	PUNCT
ejpam-5330	86	28	and	and	CCONJ
ejpam-5330	86	29	r	r	NOUN
ejpam-5330	86	30	∈	∈	PROPN
ejpam-5330	86	31	i0	i0	PROPN
ejpam-5330	86	32	,	,	PUNCT
ejpam-5330	86	33	we	we	PRON
ejpam-5330	86	34	define	define	VERB
ejpam-5330	86	35	the	the	DET
ejpam-5330	86	36	fuzzy	fuzzy	ADJ
ejpam-5330	86	37	soft	soft	ADJ
ejpam-5330	86	38	operators	operator	NOUN
ejpam-5330	86	39	cτ	cτ	VERB
ejpam-5330	86	40	and	and	CCONJ
ejpam-5330	86	41	iτ	iτ	INTJ
ejpam-5330	86	42	:	:	PUNCT
ejpam-5330	86	43	n	n	NUM
ejpam-5330	86	44	×	×	PROPN
ejpam-5330	86	45	˜(w	˜(w	PROPN
ejpam-5330	86	46	,	,	PUNCT
ejpam-5330	86	47	n)×	n)×	PRON
ejpam-5330	86	48	i	i	PROPN
ejpam-5330	86	49	◦	◦	PROPN
ejpam-5330	86	50	→	→	SYM
ejpam-5330	86	51	˜(w	˜(w	PROPN
ejpam-5330	86	52	,	,	PUNCT
ejpam-5330	86	53	n	n	CCONJ
ejpam-5330	86	54	)	)	PUNCT
ejpam-5330	86	55	as	as	SCONJ
ejpam-5330	86	56	follows	follow	VERB
ejpam-5330	86	57	:	:	PUNCT
ejpam-5330	86	58	cτ	cτ	INTJ
ejpam-5330	86	59	(	(	PUNCT
ejpam-5330	86	60	n	n	X
ejpam-5330	86	61	,	,	PUNCT
ejpam-5330	86	62	hc	hc	PROPN
ejpam-5330	86	63	,	,	PUNCT
ejpam-5330	86	64	r	r	NOUN
ejpam-5330	86	65	)	)	PUNCT
ejpam-5330	86	66	=	=	SYM
ejpam-5330	86	67	⊓	⊓	NOUN
ejpam-5330	86	68	{	{	PUNCT
ejpam-5330	86	69	gb	gb	NOUN
ejpam-5330	86	70	∈	∈	PROPN
ejpam-5330	86	71	˜(w	˜(w	PROPN
ejpam-5330	86	72	,	,	PUNCT
ejpam-5330	86	73	n	n	CCONJ
ejpam-5330	86	74	)	)	PUNCT
ejpam-5330	86	75	:	:	PUNCT
ejpam-5330	86	76	hc	hc	ADP
ejpam-5330	86	77	⊑	⊑	X
ejpam-5330	86	78	gb	gb	PROPN
ejpam-5330	86	79	,	,	PUNCT
ejpam-5330	86	80	τn(g	τn(g	X
ejpam-5330	86	81	c	c	PROPN
ejpam-5330	86	82	b	b	X
ejpam-5330	86	83	)	)	PUNCT
ejpam-5330	86	84	≥	≥	NOUN
ejpam-5330	86	85	r	r	NOUN
ejpam-5330	86	86	}	}	PUNCT
ejpam-5330	86	87	,	,	PUNCT
ejpam-5330	86	88	iτ	iτ	X
ejpam-5330	86	89	(	(	PUNCT
ejpam-5330	86	90	n	n	CCONJ
ejpam-5330	86	91	,	,	PUNCT
ejpam-5330	86	92	hc	hc	PROPN
ejpam-5330	86	93	,	,	PUNCT
ejpam-5330	86	94	r	r	NOUN
ejpam-5330	86	95	)	)	PUNCT
ejpam-5330	86	96	=	=	SYM
ejpam-5330	87	1	⊔	⊔	X
ejpam-5330	87	2	{	{	PUNCT
ejpam-5330	87	3	gb	gb	NOUN
ejpam-5330	87	4	∈	∈	PROPN
ejpam-5330	87	5	˜(w	˜(w	PROPN
ejpam-5330	87	6	,	,	PUNCT
ejpam-5330	87	7	n	n	CCONJ
ejpam-5330	87	8	)	)	PUNCT
ejpam-5330	87	9	:	:	PUNCT
ejpam-5330	88	1	gb	gb	ADP
ejpam-5330	88	2	⊑	⊑	DET
ejpam-5330	88	3	hc	hc	PROPN
ejpam-5330	88	4	,	,	PUNCT
ejpam-5330	88	5	τn(gb	τn(gb	PROPN
ejpam-5330	88	6	)	)	PUNCT
ejpam-5330	88	7	≥	≥	NOUN
ejpam-5330	88	8	r	r	NOUN
ejpam-5330	88	9	}	}	PUNCT
ejpam-5330	88	10	.	.	PUNCT
ejpam-5330	89	1	definition	definition	NOUN
ejpam-5330	89	2	8	8	NUM
ejpam-5330	89	3	.	.	PUNCT
ejpam-5330	90	1	let	let	AUX
ejpam-5330	90	2	(	(	PUNCT
ejpam-5330	90	3	w	w	NOUN
ejpam-5330	90	4	,	,	PUNCT
ejpam-5330	90	5	τn	τn	PART
ejpam-5330	90	6	)	)	PUNCT
ejpam-5330	90	7	be	be	AUX
ejpam-5330	90	8	an	an	DET
ejpam-5330	90	9	fsts	fst	NOUN
ejpam-5330	90	10	and	and	CCONJ
ejpam-5330	90	11	r	r	NOUN
ejpam-5330	90	12	∈	∈	PROPN
ejpam-5330	90	13	i0	i0	PROPN
ejpam-5330	90	14	.	.	PUNCT
ejpam-5330	91	1	a	a	DET
ejpam-5330	91	2	fuzzy	fuzzy	ADJ
ejpam-5330	91	3	soft	soft	ADJ
ejpam-5330	91	4	set	set	NOUN
ejpam-5330	91	5	hc	hc	PROPN
ejpam-5330	91	6	∈	∈	PROPN
ejpam-5330	91	7	˜(w	˜(w	PROPN
ejpam-5330	91	8	,	,	PUNCT
ejpam-5330	91	9	n	n	CCONJ
ejpam-5330	91	10	)	)	PUNCT
ejpam-5330	91	11	is	be	AUX
ejpam-5330	91	12	called	call	VERB
ejpam-5330	91	13	r	r	NOUN
ejpam-5330	91	14	-	-	PUNCT
ejpam-5330	91	15	fuzzy	fuzzy	ADJ
ejpam-5330	91	16	soft	soft	ADJ
ejpam-5330	91	17	regularly	regularly	ADV
ejpam-5330	91	18	open	open	ADJ
ejpam-5330	91	19	[	[	X
ejpam-5330	91	20	15	15	NUM
ejpam-5330	91	21	]	]	X
ejpam-5330	91	22	(	(	PUNCT
ejpam-5330	91	23	resp	resp	NOUN
ejpam-5330	91	24	.	.	PUNCT
ejpam-5330	91	25	,	,	PUNCT
ejpam-5330	91	26	β	β	X
ejpam-5330	91	27	-	-	VERB
ejpam-5330	91	28	open	open	ADJ
ejpam-5330	91	29	[	[	X
ejpam-5330	91	30	30	30	NUM
ejpam-5330	91	31	]	]	PUNCT
ejpam-5330	91	32	,	,	PUNCT
ejpam-5330	91	33	pre	pre	ADJ
ejpam-5330	91	34	-	-	ADJ
ejpam-5330	91	35	open	open	ADJ
ejpam-5330	91	36	[	[	X
ejpam-5330	91	37	30	30	NUM
ejpam-5330	91	38	]	]	PUNCT
ejpam-5330	91	39	,	,	PUNCT
ejpam-5330	91	40	α	α	X
ejpam-5330	91	41	-	-	ADJ
ejpam-5330	91	42	open	open	ADJ
ejpam-5330	91	43	[	[	X
ejpam-5330	91	44	11	11	NUM
ejpam-5330	91	45	]	]	PUNCT
ejpam-5330	91	46	,	,	PUNCT
ejpam-5330	91	47	and	and	CCONJ
ejpam-5330	91	48	semiopen	semiopen	VERB
ejpam-5330	91	49	[	[	X
ejpam-5330	91	50	11	11	NUM
ejpam-5330	91	51	]	]	SYM
ejpam-5330	91	52	)	)	PUNCT
ejpam-5330	91	53	if	if	SCONJ
ejpam-5330	91	54	hc	hc	X
ejpam-5330	91	55	=	=	VERB
ejpam-5330	91	56	iτ	iτ	X
ejpam-5330	91	57	(	(	PUNCT
ejpam-5330	91	58	n	n	CCONJ
ejpam-5330	91	59	,	,	PUNCT
ejpam-5330	91	60	cτ	cτ	INTJ
ejpam-5330	91	61	(	(	PUNCT
ejpam-5330	91	62	n	n	X
ejpam-5330	91	63	,	,	PUNCT
ejpam-5330	91	64	hc	hc	PROPN
ejpam-5330	91	65	,	,	PUNCT
ejpam-5330	91	66	r	r	NOUN
ejpam-5330	91	67	)	)	PUNCT
ejpam-5330	91	68	,	,	PUNCT
ejpam-5330	91	69	r	r	NOUN
ejpam-5330	91	70	)	)	PUNCT
ejpam-5330	91	71	(	(	PUNCT
ejpam-5330	91	72	resp	resp	NOUN
ejpam-5330	91	73	.	.	PUNCT
ejpam-5330	91	74	,	,	PUNCT
ejpam-5330	91	75	hc	hc	PROPN
ejpam-5330	91	76	⊑	⊑	X
ejpam-5330	91	77	cτ	cτ	PROPN
ejpam-5330	91	78	(	(	PUNCT
ejpam-5330	91	79	n	n	CCONJ
ejpam-5330	91	80	,	,	PUNCT
ejpam-5330	91	81	iτ	iτ	X
ejpam-5330	91	82	(	(	PUNCT
ejpam-5330	91	83	n	n	CCONJ
ejpam-5330	91	84	,	,	PUNCT
ejpam-5330	91	85	cτ	cτ	INTJ
ejpam-5330	91	86	(	(	PUNCT
ejpam-5330	91	87	n	n	X
ejpam-5330	91	88	,	,	PUNCT
ejpam-5330	91	89	hc	hc	PROPN
ejpam-5330	91	90	,	,	PUNCT
ejpam-5330	91	91	r	r	NOUN
ejpam-5330	91	92	)	)	PUNCT
ejpam-5330	91	93	,	,	PUNCT
ejpam-5330	91	94	r	r	NOUN
ejpam-5330	91	95	)	)	PUNCT
ejpam-5330	91	96	,	,	PUNCT
ejpam-5330	91	97	r	r	NOUN
ejpam-5330	91	98	)	)	PUNCT
ejpam-5330	91	99	,	,	PUNCT
ejpam-5330	91	100	hc	hc	PROPN
ejpam-5330	91	101	⊑	⊑	X
ejpam-5330	91	102	iτ	iτ	X
ejpam-5330	91	103	(	(	PUNCT
ejpam-5330	91	104	n	n	CCONJ
ejpam-5330	91	105	,	,	PUNCT
ejpam-5330	91	106	cτ	cτ	INTJ
ejpam-5330	91	107	(	(	PUNCT
ejpam-5330	91	108	n	n	X
ejpam-5330	91	109	,	,	PUNCT
ejpam-5330	91	110	hc	hc	PROPN
ejpam-5330	91	111	,	,	PUNCT
ejpam-5330	91	112	r	r	NOUN
ejpam-5330	91	113	)	)	PUNCT
ejpam-5330	91	114	,	,	PUNCT
ejpam-5330	91	115	r	r	NOUN
ejpam-5330	91	116	)	)	PUNCT
ejpam-5330	91	117	,	,	PUNCT
ejpam-5330	91	118	hc	hc	PROPN
ejpam-5330	91	119	⊑	⊑	X
ejpam-5330	91	120	iτ	iτ	X
ejpam-5330	91	121	(	(	PUNCT
ejpam-5330	91	122	n	n	CCONJ
ejpam-5330	91	123	,	,	PUNCT
ejpam-5330	91	124	cτ	cτ	INTJ
ejpam-5330	91	125	(	(	PUNCT
ejpam-5330	91	126	n	n	CCONJ
ejpam-5330	91	127	,	,	PUNCT
ejpam-5330	91	128	iτ	iτ	X
ejpam-5330	91	129	(	(	PUNCT
ejpam-5330	91	130	n	n	CCONJ
ejpam-5330	91	131	,	,	PUNCT
ejpam-5330	91	132	hc	hc	PROPN
ejpam-5330	91	133	,	,	PUNCT
ejpam-5330	91	134	r	r	NOUN
ejpam-5330	91	135	)	)	PUNCT
ejpam-5330	91	136	,	,	PUNCT
ejpam-5330	91	137	r	r	NOUN
ejpam-5330	91	138	)	)	PUNCT
ejpam-5330	91	139	,	,	PUNCT
ejpam-5330	91	140	r	r	NOUN
ejpam-5330	91	141	)	)	PUNCT
ejpam-5330	91	142	,	,	PUNCT
ejpam-5330	91	143	and	and	CCONJ
ejpam-5330	91	144	hc	hc	X
ejpam-5330	91	145	⊑	⊑	X
ejpam-5330	91	146	cτ	cτ	PROPN
ejpam-5330	91	147	(	(	PUNCT
ejpam-5330	91	148	n	n	CCONJ
ejpam-5330	91	149	,	,	PUNCT
ejpam-5330	91	150	iτ	iτ	X
ejpam-5330	91	151	(	(	PUNCT
ejpam-5330	91	152	n	n	CCONJ
ejpam-5330	91	153	,	,	PUNCT
ejpam-5330	91	154	hc	hc	PROPN
ejpam-5330	91	155	,	,	PUNCT
ejpam-5330	91	156	r	r	NOUN
ejpam-5330	91	157	)	)	PUNCT
ejpam-5330	91	158	,	,	PUNCT
ejpam-5330	91	159	r	r	NOUN
ejpam-5330	91	160	)	)	PUNCT
ejpam-5330	91	161	)	)	PUNCT
ejpam-5330	91	162	for	for	ADP
ejpam-5330	91	163	each	each	DET
ejpam-5330	91	164	n	n	PRON
ejpam-5330	91	165	∈	∈	PROPN
ejpam-5330	91	166	n	n	NOUN
ejpam-5330	91	167	.	.	PUNCT
ejpam-5330	92	1	definition	definition	NOUN
ejpam-5330	92	2	9	9	NUM
ejpam-5330	92	3	.	.	PUNCT
ejpam-5330	93	1	[	[	X
ejpam-5330	93	2	15	15	NUM
ejpam-5330	93	3	]	]	X
ejpam-5330	93	4	let	let	AUX
ejpam-5330	93	5	(	(	PUNCT
ejpam-5330	93	6	w	w	NOUN
ejpam-5330	93	7	,	,	PUNCT
ejpam-5330	93	8	τn	τn	PART
ejpam-5330	93	9	)	)	PUNCT
ejpam-5330	93	10	be	be	AUX
ejpam-5330	93	11	an	an	DET
ejpam-5330	93	12	fsts	fst	NOUN
ejpam-5330	93	13	and	and	CCONJ
ejpam-5330	93	14	r	r	NOUN
ejpam-5330	93	15	∈	∈	PROPN
ejpam-5330	93	16	i0	i0	PROPN
ejpam-5330	93	17	.	.	PUNCT
ejpam-5330	94	1	a	a	DET
ejpam-5330	94	2	fuzzy	fuzzy	ADJ
ejpam-5330	94	3	soft	soft	ADJ
ejpam-5330	94	4	set	set	NOUN
ejpam-5330	94	5	hc	hc	PROPN
ejpam-5330	94	6	∈	∈	PROPN
ejpam-5330	94	7	˜(w	˜(w	PROPN
ejpam-5330	94	8	,	,	PUNCT
ejpam-5330	94	9	n	n	CCONJ
ejpam-5330	94	10	)	)	PUNCT
ejpam-5330	94	11	is	be	AUX
ejpam-5330	94	12	called	call	VERB
ejpam-5330	94	13	r	r	NOUN
ejpam-5330	94	14	-	-	PUNCT
ejpam-5330	94	15	fuzzy	fuzzy	ADJ
ejpam-5330	94	16	soft	soft	ADJ
ejpam-5330	94	17	regularly	regularly	ADV
ejpam-5330	94	18	closed	close	VERB
ejpam-5330	94	19	if	if	SCONJ
ejpam-5330	94	20	hc	hc	X
ejpam-5330	94	21	=	=	PUNCT
ejpam-5330	94	22	cτ	cτ	X
ejpam-5330	94	23	(	(	PUNCT
ejpam-5330	94	24	n	n	CCONJ
ejpam-5330	94	25	,	,	PUNCT
ejpam-5330	94	26	iτ	iτ	X
ejpam-5330	94	27	(	(	PUNCT
ejpam-5330	94	28	n	n	CCONJ
ejpam-5330	94	29	,	,	PUNCT
ejpam-5330	94	30	hc	hc	PROPN
ejpam-5330	94	31	,	,	PUNCT
ejpam-5330	94	32	r	r	NOUN
ejpam-5330	94	33	)	)	PUNCT
ejpam-5330	94	34	,	,	PUNCT
ejpam-5330	94	35	r	r	NOUN
ejpam-5330	94	36	)	)	PUNCT
ejpam-5330	94	37	for	for	ADP
ejpam-5330	94	38	each	each	DET
ejpam-5330	94	39	n	n	PRON
ejpam-5330	94	40	∈	∈	PROPN
ejpam-5330	94	41	n	n	NOUN
ejpam-5330	94	42	.	.	PUNCT
ejpam-5330	95	1	definition	definition	NOUN
ejpam-5330	95	2	10	10	NUM
ejpam-5330	95	3	.	.	PUNCT
ejpam-5330	96	1	[	[	X
ejpam-5330	96	2	11	11	NUM
ejpam-5330	96	3	]	]	X
ejpam-5330	96	4	let	let	VERB
ejpam-5330	96	5	(	(	PUNCT
ejpam-5330	96	6	w	w	NOUN
ejpam-5330	96	7	,	,	PUNCT
ejpam-5330	96	8	τn	τn	PROPN
ejpam-5330	96	9	)	)	PUNCT
ejpam-5330	96	10	and	and	CCONJ
ejpam-5330	96	11	(	(	PUNCT
ejpam-5330	96	12	v	v	NOUN
ejpam-5330	96	13	,	,	PUNCT
ejpam-5330	96	14	ηf	ηf	PROPN
ejpam-5330	96	15	)	)	PUNCT
ejpam-5330	96	16	be	be	AUX
ejpam-5330	96	17	an	an	DET
ejpam-5330	96	18	fstss	fstss	NOUN
ejpam-5330	96	19	and	and	CCONJ
ejpam-5330	96	20	r	r	NOUN
ejpam-5330	96	21	∈	∈	PROPN
ejpam-5330	96	22	i0	i0	PROPN
ejpam-5330	96	23	.	.	PUNCT
ejpam-5330	97	1	a	a	DET
ejpam-5330	97	2	fuzzy	fuzzy	ADJ
ejpam-5330	97	3	soft	soft	ADJ
ejpam-5330	97	4	mapping	mapping	NOUN
ejpam-5330	97	5	φψ	φψ	X
ejpam-5330	97	6	:	:	PUNCT
ejpam-5330	97	7	˜(w	˜(w	PROPN
ejpam-5330	97	8	,	,	PUNCT
ejpam-5330	97	9	n	n	CCONJ
ejpam-5330	97	10	)	)	PUNCT
ejpam-5330	97	11	−→	−→	NOUN
ejpam-5330	97	12	(	(	PUNCT
ejpam-5330	97	13	̃v	̃v	NOUN
ejpam-5330	97	14	,	,	PUNCT
ejpam-5330	97	15	f	f	PROPN
ejpam-5330	97	16	)	)	PUNCT
ejpam-5330	97	17	is	be	AUX
ejpam-5330	97	18	called	call	VERB
ejpam-5330	97	19	fuzzy	fuzzy	ADJ
ejpam-5330	97	20	soft	soft	ADJ
ejpam-5330	97	21	almost	almost	ADV
ejpam-5330	97	22	(	(	PUNCT
ejpam-5330	97	23	resp	resp	NOUN
ejpam-5330	97	24	.	.	PUNCT
ejpam-5330	97	25	,	,	PUNCT
ejpam-5330	97	26	weakly	weakly	ADJ
ejpam-5330	97	27	)	)	PUNCT
ejpam-5330	97	28	continuous	continuous	ADJ
ejpam-5330	97	29	if	if	SCONJ
ejpam-5330	97	30	for	for	ADP
ejpam-5330	97	31	any	any	DET
ejpam-5330	97	32	nws	nws	PROPN
ejpam-5330	97	33	∈	∈	PROPN
ejpam-5330	97	34	p̃s(w	p̃s(w	NOUN
ejpam-5330	97	35	)	)	PUNCT
ejpam-5330	97	36	and	and	CCONJ
ejpam-5330	97	37	any	any	DET
ejpam-5330	97	38	fa	fa	NOUN
ejpam-5330	97	39	∈	∈	PROPN
ejpam-5330	97	40	(	(	PUNCT
ejpam-5330	97	41	̃v	̃v	NOUN
ejpam-5330	97	42	,	,	PUNCT
ejpam-5330	97	43	f	f	PROPN
ejpam-5330	97	44	)	)	PUNCT
ejpam-5330	97	45	with	with	ADP
ejpam-5330	97	46	ηk(fa	ηk(fa	PROPN
ejpam-5330	97	47	)	)	PUNCT
ejpam-5330	97	48	≥	≥	NOUN
ejpam-5330	97	49	r	r	NOUN
ejpam-5330	97	50	containing	contain	VERB
ejpam-5330	97	51	φψ(nws	φψ(nws	NOUN
ejpam-5330	97	52	)	)	PUNCT
ejpam-5330	97	53	,	,	PUNCT
ejpam-5330	97	54	there	there	PRON
ejpam-5330	97	55	is	be	VERB
ejpam-5330	97	56	hc	hc	PROPN
ejpam-5330	97	57	∈	∈	PROPN
ejpam-5330	97	58	˜(w	˜(w	PROPN
ejpam-5330	97	59	,	,	PUNCT
ejpam-5330	97	60	n	n	CCONJ
ejpam-5330	97	61	)	)	PUNCT
ejpam-5330	97	62	with	with	ADP
ejpam-5330	97	63	τn(hc	τn(hc	PROPN
ejpam-5330	97	64	)	)	PUNCT
ejpam-5330	97	65	≥	≥	NOUN
ejpam-5330	97	66	r	r	NOUN
ejpam-5330	97	67	containing	contain	VERB
ejpam-5330	97	68	nws	nws	NOUN
ejpam-5330	97	69	,	,	PUNCT
ejpam-5330	97	70	such	such	ADJ
ejpam-5330	97	71	that	that	DET
ejpam-5330	97	72	φψ(hc	φψ(hc	NOUN
ejpam-5330	97	73	)	)	PUNCT
ejpam-5330	97	74	⊑	⊑	PRON
ejpam-5330	97	75	iη(k	iη(k	PROPN
ejpam-5330	97	76	,	,	PUNCT
ejpam-5330	97	77	cη(k	cη(k	PROPN
ejpam-5330	97	78	,	,	PUNCT
ejpam-5330	97	79	fa	fa	NOUN
ejpam-5330	97	80	,	,	PUNCT
ejpam-5330	97	81	r	r	NOUN
ejpam-5330	97	82	)	)	PUNCT
ejpam-5330	97	83	,	,	PUNCT
ejpam-5330	97	84	r	r	NOUN
ejpam-5330	97	85	)	)	PUNCT
ejpam-5330	97	86	(	(	PUNCT
ejpam-5330	97	87	resp	resp	NOUN
ejpam-5330	97	88	.	.	PUNCT
ejpam-5330	97	89	,	,	PUNCT
ejpam-5330	97	90	φψ(hc	φψ(hc	NOUN
ejpam-5330	97	91	)	)	PUNCT
ejpam-5330	97	92	⊑	⊑	PRON
ejpam-5330	97	93	cη(k	cη(k	PROPN
ejpam-5330	97	94	,	,	PUNCT
ejpam-5330	97	95	fa	fa	NOUN
ejpam-5330	97	96	,	,	PUNCT
ejpam-5330	97	97	r	r	NOUN
ejpam-5330	97	98	)	)	PUNCT
ejpam-5330	97	99	)	)	PUNCT
ejpam-5330	97	100	.	.	PUNCT
ejpam-5330	98	1	remark	remark	PROPN
ejpam-5330	98	2	1	1	NUM
ejpam-5330	98	3	.	.	PUNCT
ejpam-5330	99	1	[	[	X
ejpam-5330	99	2	11	11	NUM
ejpam-5330	99	3	]	]	PUNCT
ejpam-5330	99	4	from	from	ADP
ejpam-5330	99	5	definitions	definition	NOUN
ejpam-5330	99	6	6	6	NUM
ejpam-5330	99	7	and	and	CCONJ
ejpam-5330	99	8	10	10	NUM
ejpam-5330	99	9	,	,	PUNCT
ejpam-5330	99	10	we	we	PRON
ejpam-5330	99	11	have	have	VERB
ejpam-5330	99	12	:	:	PUNCT
ejpam-5330	99	13	fuzzy	fuzzy	ADJ
ejpam-5330	99	14	soft	soft	ADJ
ejpam-5330	99	15	continuity	continuity	NOUN
ejpam-5330	99	16	⇒	⇒	NOUN
ejpam-5330	99	17	fuzzy	fuzzy	ADJ
ejpam-5330	99	18	soft	soft	ADJ
ejpam-5330	99	19	almost	almost	ADV
ejpam-5330	99	20	continuity	continuity	NOUN
ejpam-5330	99	21	⇒	⇒	NOUN
ejpam-5330	99	22	fuzzy	fuzzy	ADJ
ejpam-5330	99	23	soft	soft	ADJ
ejpam-5330	99	24	weakly	weakly	ADJ
ejpam-5330	99	25	continuity	continuity	NOUN
ejpam-5330	99	26	,	,	PUNCT
ejpam-5330	99	27	but	but	CCONJ
ejpam-5330	99	28	the	the	DET
ejpam-5330	99	29	converse	converse	NOUN
ejpam-5330	99	30	may	may	AUX
ejpam-5330	99	31	not	not	PART
ejpam-5330	99	32	be	be	AUX
ejpam-5330	99	33	true	true	ADJ
ejpam-5330	99	34	.	.	PUNCT
ejpam-5330	100	1	lemma	lemma	PROPN
ejpam-5330	100	2	1	1	X
ejpam-5330	100	3	.	.	PUNCT
ejpam-5330	101	1	let	let	VERB
ejpam-5330	101	2	(	(	PUNCT
ejpam-5330	101	3	w	w	NOUN
ejpam-5330	101	4	,	,	PUNCT
ejpam-5330	101	5	τn	τn	PROPN
ejpam-5330	101	6	)	)	PUNCT
ejpam-5330	101	7	and	and	CCONJ
ejpam-5330	101	8	(	(	PUNCT
ejpam-5330	101	9	v	v	NOUN
ejpam-5330	101	10	,	,	PUNCT
ejpam-5330	101	11	ηf	ηf	PROPN
ejpam-5330	101	12	)	)	PUNCT
ejpam-5330	101	13	be	be	AUX
ejpam-5330	101	14	an	an	DET
ejpam-5330	101	15	fstss	fstss	NOUN
ejpam-5330	101	16	and	and	CCONJ
ejpam-5330	101	17	r	r	NOUN
ejpam-5330	101	18	∈	∈	PROPN
ejpam-5330	101	19	i0	i0	PROPN
ejpam-5330	101	20	.	.	PUNCT
ejpam-5330	102	1	a	a	DET
ejpam-5330	102	2	fuzzy	fuzzy	ADJ
ejpam-5330	102	3	soft	soft	ADJ
ejpam-5330	102	4	mapping	mapping	NOUN
ejpam-5330	102	5	φψ	φψ	X
ejpam-5330	102	6	:	:	PUNCT
ejpam-5330	102	7	˜(w	˜(w	PROPN
ejpam-5330	102	8	,	,	PUNCT
ejpam-5330	102	9	n	n	CCONJ
ejpam-5330	102	10	)	)	PUNCT
ejpam-5330	102	11	−→	−→	NOUN
ejpam-5330	102	12	(	(	PUNCT
ejpam-5330	102	13	̃v	̃v	NOUN
ejpam-5330	102	14	,	,	PUNCT
ejpam-5330	102	15	f	f	PROPN
ejpam-5330	102	16	)	)	PUNCT
ejpam-5330	102	17	is	be	AUX
ejpam-5330	102	18	fuzzy	fuzzy	ADJ
ejpam-5330	102	19	soft	soft	ADJ
ejpam-5330	102	20	almost	almost	ADV
ejpam-5330	102	21	continuous	continuous	ADJ
ejpam-5330	102	22	if	if	SCONJ
ejpam-5330	102	23	τn(φ	τn(φ	PUNCT
ejpam-5330	102	24	−1	−1	NOUN
ejpam-5330	102	25	ψ	ψ	X
ejpam-5330	102	26	(	(	PUNCT
ejpam-5330	102	27	hc	hc	NOUN
ejpam-5330	102	28	)	)	PUNCT
ejpam-5330	102	29	)	)	PUNCT
ejpam-5330	102	30	≥	≥	NOUN
ejpam-5330	103	1	r	r	NOUN
ejpam-5330	103	2	for	for	ADP
ejpam-5330	103	3	each	each	DET
ejpam-5330	103	4	hc	hc	PROPN
ejpam-5330	103	5	∈	∈	PROPN
ejpam-5330	103	6	(	(	PUNCT
ejpam-5330	103	7	̃v	̃v	NOUN
ejpam-5330	103	8	,	,	PUNCT
ejpam-5330	103	9	f	f	PROPN
ejpam-5330	103	10	)	)	PUNCT
ejpam-5330	103	11	is	be	AUX
ejpam-5330	103	12	r	r	NOUN
ejpam-5330	103	13	-	-	PUNCT
ejpam-5330	103	14	fuzzy	fuzzy	ADJ
ejpam-5330	103	15	soft	soft	ADJ
ejpam-5330	103	16	regularly	regularly	ADV
ejpam-5330	103	17	open	open	ADJ
ejpam-5330	103	18	,	,	PUNCT
ejpam-5330	103	19	n	n	NOUN
ejpam-5330	103	20	∈	∈	PROPN
ejpam-5330	103	21	n	n	NOUN
ejpam-5330	103	22	,	,	PUNCT
ejpam-5330	103	23	and	and	CCONJ
ejpam-5330	103	24	(	(	PUNCT
ejpam-5330	103	25	k	k	X
ejpam-5330	103	26	=	=	SYM
ejpam-5330	103	27	ψ(n	ψ(n	PROPN
ejpam-5330	103	28	)	)	PUNCT
ejpam-5330	103	29	)	)	PUNCT
ejpam-5330	104	1	∈	∈	PROPN
ejpam-5330	104	2	f	f	X
ejpam-5330	104	3	.	.	PUNCT
ejpam-5330	105	1	proof	proof	NOUN
ejpam-5330	105	2	.	.	PUNCT
ejpam-5330	106	1	easily	easily	ADV
ejpam-5330	106	2	proved	prove	VERB
ejpam-5330	106	3	from	from	ADP
ejpam-5330	106	4	definition	definition	NOUN
ejpam-5330	106	5	10	10	NUM
ejpam-5330	106	6	.	.	PUNCT
ejpam-5330	107	1	definition	definition	NOUN
ejpam-5330	107	2	11	11	NUM
ejpam-5330	107	3	.	.	PUNCT
ejpam-5330	108	1	let	let	VERB
ejpam-5330	108	2	(	(	PUNCT
ejpam-5330	108	3	w	w	NOUN
ejpam-5330	108	4	,	,	PUNCT
ejpam-5330	108	5	τn	τn	PROPN
ejpam-5330	108	6	)	)	PUNCT
ejpam-5330	108	7	and	and	CCONJ
ejpam-5330	108	8	(	(	PUNCT
ejpam-5330	108	9	v	v	NOUN
ejpam-5330	108	10	,	,	PUNCT
ejpam-5330	108	11	ηf	ηf	PROPN
ejpam-5330	108	12	)	)	PUNCT
ejpam-5330	108	13	be	be	AUX
ejpam-5330	108	14	an	an	DET
ejpam-5330	108	15	fstss	fstss	NOUN
ejpam-5330	108	16	.	.	PUNCT
ejpam-5330	109	1	a	a	DET
ejpam-5330	109	2	fuzzy	fuzzy	ADJ
ejpam-5330	109	3	soft	soft	ADJ
ejpam-5330	109	4	mapping	mapping	NOUN
ejpam-5330	109	5	φψ	φψ	X
ejpam-5330	109	6	:	:	PUNCT
ejpam-5330	109	7	˜(w	˜(w	PROPN
ejpam-5330	109	8	,	,	PUNCT
ejpam-5330	109	9	n	n	CCONJ
ejpam-5330	109	10	)	)	PUNCT
ejpam-5330	109	11	−→	−→	NOUN
ejpam-5330	109	12	(	(	PUNCT
ejpam-5330	109	13	̃v	̃v	NOUN
ejpam-5330	109	14	,	,	PUNCT
ejpam-5330	109	15	f	f	PROPN
ejpam-5330	109	16	)	)	PUNCT
ejpam-5330	109	17	is	be	AUX
ejpam-5330	109	18	called	call	VERB
ejpam-5330	109	19	fuzzy	fuzzy	ADJ
ejpam-5330	109	20	soft	soft	ADJ
ejpam-5330	109	21	open	open	ADJ
ejpam-5330	109	22	if	if	SCONJ
ejpam-5330	109	23	ηk(φψ(hc	ηk(φψ(hc	X
ejpam-5330	109	24	)	)	PUNCT
ejpam-5330	109	25	)	)	PUNCT
ejpam-5330	109	26	≥	≥	X
ejpam-5330	109	27	τn(hc	τn(hc	NUM
ejpam-5330	109	28	)	)	PUNCT
ejpam-5330	109	29	for	for	ADP
ejpam-5330	109	30	each	each	DET
ejpam-5330	109	31	hc	hc	PROPN
ejpam-5330	109	32	∈	∈	PROPN
ejpam-5330	109	33	˜(w	˜(w	PROPN
ejpam-5330	109	34	,	,	PUNCT
ejpam-5330	109	35	n	n	CCONJ
ejpam-5330	109	36	)	)	PUNCT
ejpam-5330	109	37	,	,	PUNCT
ejpam-5330	109	38	n	n	PROPN
ejpam-5330	109	39	∈	∈	PROPN
ejpam-5330	109	40	n	n	CCONJ
ejpam-5330	109	41	,	,	PUNCT
ejpam-5330	109	42	and	and	CCONJ
ejpam-5330	109	43	(	(	PUNCT
ejpam-5330	109	44	k	k	X
ejpam-5330	109	45	=	=	SYM
ejpam-5330	109	46	ψ(n	ψ(n	PROPN
ejpam-5330	109	47	)	)	PUNCT
ejpam-5330	109	48	)	)	PUNCT
ejpam-5330	110	1	∈	∈	PROPN
ejpam-5330	110	2	f	f	X
ejpam-5330	110	3	.	.	PUNCT
ejpam-5330	111	1	the	the	DET
ejpam-5330	111	2	basic	basic	ADJ
ejpam-5330	111	3	concepts	concept	NOUN
ejpam-5330	111	4	and	and	CCONJ
ejpam-5330	111	5	results	result	NOUN
ejpam-5330	111	6	that	that	SCONJ
ejpam-5330	111	7	we	we	PRON
ejpam-5330	111	8	need	need	VERB
ejpam-5330	111	9	in	in	ADP
ejpam-5330	111	10	the	the	DET
ejpam-5330	111	11	next	next	ADJ
ejpam-5330	111	12	sections	section	NOUN
ejpam-5330	111	13	are	be	AUX
ejpam-5330	111	14	found	find	VERB
ejpam-5330	111	15	in	in	ADP
ejpam-5330	111	16	[	[	X
ejpam-5330	111	17	16	16	NUM
ejpam-5330	111	18	,	,	PUNCT
ejpam-5330	111	19	19	19	NUM
ejpam-5330	111	20	]	]	PUNCT
ejpam-5330	111	21	.	.	PUNCT
ejpam-5330	112	1	w.	w.	PROPN
ejpam-5330	112	2	alqurashi	alqurashi	PROPN
ejpam-5330	112	3	,	,	PUNCT
ejpam-5330	112	4	i.	i.	PROPN
ejpam-5330	112	5	m.	m.	PROPN
ejpam-5330	112	6	taha	taha	PROPN
ejpam-5330	112	7	/	/	PUNCT
ejpam-5330	112	8	eur	eur	PROPN
ejpam-5330	112	9	.	.	PUNCT
ejpam-5330	113	1	j.	j.	PROPN
ejpam-5330	113	2	pure	pure	PROPN
ejpam-5330	113	3	appl	appl	PROPN
ejpam-5330	113	4	.	.	PROPN
ejpam-5330	113	5	math	math	PROPN
ejpam-5330	113	6	,	,	PUNCT
ejpam-5330	113	7	17	17	NUM
ejpam-5330	113	8	(	(	PUNCT
ejpam-5330	113	9	4	4	NUM
ejpam-5330	113	10	)	)	PUNCT
ejpam-5330	113	11	(	(	PUNCT
ejpam-5330	113	12	2024	2024	NUM
ejpam-5330	113	13	)	)	PUNCT
ejpam-5330	113	14	,	,	PUNCT
ejpam-5330	113	15	4112	4112	NUM
ejpam-5330	113	16	-	-	SYM
ejpam-5330	113	17	4134	4134	NUM
ejpam-5330	113	18	4116	4116	NUM
ejpam-5330	113	19	2	2	NUM
ejpam-5330	113	20	.	.	PUNCT
ejpam-5330	114	1	on	on	ADP
ejpam-5330	114	2	r	r	NOUN
ejpam-5330	114	3	-	-	PUNCT
ejpam-5330	114	4	fuzzy	fuzzy	ADJ
ejpam-5330	114	5	soft	soft	ADJ
ejpam-5330	114	6	α	α	NOUN
ejpam-5330	114	7	-	-	ADJ
ejpam-5330	114	8	open	open	ADJ
ejpam-5330	114	9	sets	set	NOUN
ejpam-5330	114	10	here	here	ADV
ejpam-5330	114	11	,	,	PUNCT
ejpam-5330	114	12	we	we	PRON
ejpam-5330	114	13	introduce	introduce	VERB
ejpam-5330	114	14	and	and	CCONJ
ejpam-5330	114	15	discuss	discuss	VERB
ejpam-5330	114	16	the	the	DET
ejpam-5330	114	17	notions	notion	NOUN
ejpam-5330	114	18	of	of	ADP
ejpam-5330	114	19	fuzzy	fuzzy	ADJ
ejpam-5330	114	20	soft	soft	ADJ
ejpam-5330	114	21	α	α	NOUN
ejpam-5330	114	22	-	-	NOUN
ejpam-5330	114	23	closure	closure	NOUN
ejpam-5330	114	24	(	(	PUNCT
ejpam-5330	114	25	α	α	NOUN
ejpam-5330	114	26	-	-	ADJ
ejpam-5330	114	27	interior	interior	ADJ
ejpam-5330	114	28	)	)	PUNCT
ejpam-5330	114	29	operators	operator	NOUN
ejpam-5330	114	30	in	in	ADP
ejpam-5330	114	31	an	an	DET
ejpam-5330	114	32	fstss	fstss	NOUN
ejpam-5330	114	33	based	base	VERB
ejpam-5330	114	34	on	on	ADP
ejpam-5330	114	35	the	the	DET
ejpam-5330	114	36	paper	paper	NOUN
ejpam-5330	114	37	by	by	ADP
ejpam-5330	114	38	aygünoǧlu	aygünoǧlu	PROPN
ejpam-5330	114	39	et	et	PROPN
ejpam-5330	114	40	al	al	PROPN
ejpam-5330	114	41	.	.	PUNCT
ejpam-5330	115	1	[	[	X
ejpam-5330	115	2	19	19	NUM
ejpam-5330	115	3	]	]	PUNCT
ejpam-5330	115	4	.	.	PUNCT
ejpam-5330	116	1	also	also	ADV
ejpam-5330	116	2	,	,	PUNCT
ejpam-5330	116	3	the	the	DET
ejpam-5330	116	4	notion	notion	NOUN
ejpam-5330	116	5	of	of	ADP
ejpam-5330	116	6	r	r	NOUN
ejpam-5330	116	7	-	-	PUNCT
ejpam-5330	116	8	fuzzy	fuzzy	ADJ
ejpam-5330	116	9	soft	soft	ADJ
ejpam-5330	116	10	α	α	NOUN
ejpam-5330	116	11	-	-	PUNCT
ejpam-5330	116	12	connected	connect	VERB
ejpam-5330	116	13	sets	set	NOUN
ejpam-5330	116	14	has	have	AUX
ejpam-5330	116	15	been	be	AUX
ejpam-5330	116	16	defined	define	VERB
ejpam-5330	116	17	and	and	CCONJ
ejpam-5330	116	18	studied	study	VERB
ejpam-5330	116	19	with	with	ADP
ejpam-5330	116	20	help	help	NOUN
ejpam-5330	116	21	of	of	ADP
ejpam-5330	116	22	fuzzy	fuzzy	ADJ
ejpam-5330	116	23	soft	soft	ADJ
ejpam-5330	116	24	α	α	NOUN
ejpam-5330	116	25	-	-	PUNCT
ejpam-5330	116	26	closure	closure	NOUN
ejpam-5330	116	27	operators	operator	NOUN
ejpam-5330	116	28	.	.	PUNCT
ejpam-5330	117	1	definition	definition	NOUN
ejpam-5330	117	2	12	12	NUM
ejpam-5330	117	3	.	.	PUNCT
ejpam-5330	118	1	let	let	AUX
ejpam-5330	118	2	(	(	PUNCT
ejpam-5330	118	3	w	w	NOUN
ejpam-5330	118	4	,	,	PUNCT
ejpam-5330	118	5	τn	τn	PART
ejpam-5330	118	6	)	)	PUNCT
ejpam-5330	118	7	be	be	AUX
ejpam-5330	118	8	an	an	DET
ejpam-5330	118	9	fsts	fst	NOUN
ejpam-5330	118	10	and	and	CCONJ
ejpam-5330	118	11	r	r	NOUN
ejpam-5330	118	12	∈	∈	PROPN
ejpam-5330	118	13	i0	i0	PROPN
ejpam-5330	118	14	.	.	PUNCT
ejpam-5330	119	1	a	a	DET
ejpam-5330	119	2	fuzzy	fuzzy	ADJ
ejpam-5330	119	3	soft	soft	ADJ
ejpam-5330	119	4	set	set	NOUN
ejpam-5330	119	5	hc	hc	NOUN
ejpam-5330	119	6	is	be	AUX
ejpam-5330	119	7	called	call	VERB
ejpam-5330	119	8	r	r	NOUN
ejpam-5330	119	9	-	-	PUNCT
ejpam-5330	119	10	fuzzy	fuzzy	ADJ
ejpam-5330	119	11	soft	soft	ADJ
ejpam-5330	119	12	α	α	NOUN
ejpam-5330	119	13	-	-	ADJ
ejpam-5330	119	14	closed	closed	ADJ
ejpam-5330	119	15	(	(	PUNCT
ejpam-5330	119	16	resp	resp	NOUN
ejpam-5330	119	17	.	.	PUNCT
ejpam-5330	120	1	,	,	PUNCT
ejpam-5330	120	2	semi	semi	ADJ
ejpam-5330	120	3	-	-	ADJ
ejpam-5330	120	4	closed	closed	ADJ
ejpam-5330	120	5	,	,	PUNCT
ejpam-5330	120	6	β	β	NOUN
ejpam-5330	120	7	-	-	VERB
ejpam-5330	120	8	closed	closed	ADJ
ejpam-5330	120	9	,	,	PUNCT
ejpam-5330	120	10	and	and	CCONJ
ejpam-5330	120	11	pre	pre	ADJ
ejpam-5330	120	12	-	-	ADJ
ejpam-5330	120	13	closed	closed	ADJ
ejpam-5330	120	14	)	)	PUNCT
ejpam-5330	120	15	if	if	SCONJ
ejpam-5330	120	16	cτ	cτ	INTJ
ejpam-5330	120	17	(	(	PUNCT
ejpam-5330	120	18	n	n	CCONJ
ejpam-5330	120	19	,	,	PUNCT
ejpam-5330	120	20	iτ	iτ	X
ejpam-5330	120	21	(	(	PUNCT
ejpam-5330	120	22	n	n	CCONJ
ejpam-5330	120	23	,	,	PUNCT
ejpam-5330	120	24	cτ	cτ	INTJ
ejpam-5330	120	25	(	(	PUNCT
ejpam-5330	120	26	n	n	X
ejpam-5330	120	27	,	,	PUNCT
ejpam-5330	120	28	hc	hc	PROPN
ejpam-5330	120	29	,	,	PUNCT
ejpam-5330	120	30	r	r	NOUN
ejpam-5330	120	31	)	)	PUNCT
ejpam-5330	120	32	,	,	PUNCT
ejpam-5330	120	33	r	r	NOUN
ejpam-5330	120	34	)	)	PUNCT
ejpam-5330	120	35	,	,	PUNCT
ejpam-5330	120	36	r	r	X
ejpam-5330	120	37	)	)	PUNCT
ejpam-5330	120	38	⊑	⊑	PROPN
ejpam-5330	120	39	hc	hc	PROPN
ejpam-5330	120	40	(	(	PUNCT
ejpam-5330	120	41	resp	resp	PROPN
ejpam-5330	120	42	.	.	PUNCT
ejpam-5330	120	43	,	,	PUNCT
ejpam-5330	120	44	iτ	iτ	X
ejpam-5330	120	45	(	(	PUNCT
ejpam-5330	120	46	n	n	CCONJ
ejpam-5330	120	47	,	,	PUNCT
ejpam-5330	120	48	cτ	cτ	INTJ
ejpam-5330	120	49	(	(	PUNCT
ejpam-5330	120	50	n	n	X
ejpam-5330	120	51	,	,	PUNCT
ejpam-5330	120	52	hc	hc	PROPN
ejpam-5330	120	53	,	,	PUNCT
ejpam-5330	120	54	r	r	NOUN
ejpam-5330	120	55	)	)	PUNCT
ejpam-5330	120	56	,	,	PUNCT
ejpam-5330	120	57	r	r	X
ejpam-5330	120	58	)	)	PUNCT
ejpam-5330	120	59	⊑	⊑	PROPN
ejpam-5330	120	60	hc	hc	PROPN
ejpam-5330	120	61	,	,	PUNCT
ejpam-5330	120	62	iτ	iτ	X
ejpam-5330	120	63	(	(	PUNCT
ejpam-5330	120	64	n	n	CCONJ
ejpam-5330	120	65	,	,	PUNCT
ejpam-5330	120	66	cτ	cτ	INTJ
ejpam-5330	120	67	(	(	PUNCT
ejpam-5330	120	68	n	n	CCONJ
ejpam-5330	120	69	,	,	PUNCT
ejpam-5330	120	70	iτ	iτ	X
ejpam-5330	120	71	(	(	PUNCT
ejpam-5330	120	72	n	n	CCONJ
ejpam-5330	120	73	,	,	PUNCT
ejpam-5330	120	74	hc	hc	PROPN
ejpam-5330	120	75	,	,	PUNCT
ejpam-5330	120	76	r	r	NOUN
ejpam-5330	120	77	)	)	PUNCT
ejpam-5330	120	78	,	,	PUNCT
ejpam-5330	120	79	r	r	NOUN
ejpam-5330	120	80	)	)	PUNCT
ejpam-5330	120	81	,	,	PUNCT
ejpam-5330	120	82	r	r	X
ejpam-5330	120	83	)	)	PUNCT
ejpam-5330	120	84	⊑	⊑	PROPN
ejpam-5330	120	85	hc	hc	PROPN
ejpam-5330	120	86	,	,	PUNCT
ejpam-5330	120	87	and	and	CCONJ
ejpam-5330	120	88	cτ	cτ	INTJ
ejpam-5330	120	89	(	(	PUNCT
ejpam-5330	120	90	n	n	CCONJ
ejpam-5330	120	91	,	,	PUNCT
ejpam-5330	120	92	iτ	iτ	X
ejpam-5330	120	93	(	(	PUNCT
ejpam-5330	120	94	n	n	CCONJ
ejpam-5330	120	95	,	,	PUNCT
ejpam-5330	120	96	hc	hc	PROPN
ejpam-5330	120	97	,	,	PUNCT
ejpam-5330	120	98	r	r	NOUN
ejpam-5330	120	99	)	)	PUNCT
ejpam-5330	120	100	,	,	PUNCT
ejpam-5330	120	101	r	r	X
ejpam-5330	120	102	)	)	PUNCT
ejpam-5330	120	103	⊑	⊑	PROPN
ejpam-5330	120	104	hc	hc	PROPN
ejpam-5330	120	105	)	)	PUNCT
ejpam-5330	120	106	for	for	ADP
ejpam-5330	120	107	each	each	DET
ejpam-5330	120	108	n	n	PRON
ejpam-5330	120	109	∈	∈	PROPN
ejpam-5330	120	110	n	n	X
ejpam-5330	120	111	.	.	PUNCT
ejpam-5330	121	1	remark	remark	PROPN
ejpam-5330	121	2	2	2	NUM
ejpam-5330	121	3	.	.	PUNCT
ejpam-5330	122	1	the	the	DET
ejpam-5330	122	2	complement	complement	NOUN
ejpam-5330	122	3	of	of	ADP
ejpam-5330	122	4	r	r	NOUN
ejpam-5330	122	5	-	-	PUNCT
ejpam-5330	122	6	fuzzy	fuzzy	ADJ
ejpam-5330	122	7	soft	soft	ADJ
ejpam-5330	122	8	α	α	NOUN
ejpam-5330	122	9	-	-	ADJ
ejpam-5330	122	10	closed	closed	ADJ
ejpam-5330	122	11	(	(	PUNCT
ejpam-5330	122	12	resp	resp	NOUN
ejpam-5330	122	13	.	.	PUNCT
ejpam-5330	122	14	,	,	PUNCT
ejpam-5330	122	15	semi	semi	ADJ
ejpam-5330	122	16	-	-	ADJ
ejpam-5330	122	17	closed	closed	ADJ
ejpam-5330	122	18	,	,	PUNCT
ejpam-5330	122	19	β	β	NOUN
ejpam-5330	122	20	-	-	VERB
ejpam-5330	122	21	closed	closed	ADJ
ejpam-5330	122	22	,	,	PUNCT
ejpam-5330	122	23	and	and	CCONJ
ejpam-5330	122	24	pre	pre	ADJ
ejpam-5330	122	25	-	-	ADJ
ejpam-5330	122	26	closed	closed	ADJ
ejpam-5330	122	27	)	)	PUNCT
ejpam-5330	122	28	set	set	NOUN
ejpam-5330	122	29	is	be	AUX
ejpam-5330	122	30	r	r	NOUN
ejpam-5330	122	31	-	-	PUNCT
ejpam-5330	122	32	fuzzy	fuzzy	ADJ
ejpam-5330	122	33	soft	soft	ADJ
ejpam-5330	122	34	α	α	NOUN
ejpam-5330	122	35	-	-	ADJ
ejpam-5330	122	36	open	open	ADJ
ejpam-5330	123	1	[	[	X
ejpam-5330	123	2	11	11	NUM
ejpam-5330	123	3	]	]	PUNCT
ejpam-5330	123	4	(	(	PUNCT
ejpam-5330	123	5	resp	resp	NOUN
ejpam-5330	123	6	.	.	PUNCT
ejpam-5330	123	7	,	,	PUNCT
ejpam-5330	123	8	semi	semi	ADJ
ejpam-5330	123	9	-	-	ADJ
ejpam-5330	123	10	open	open	ADJ
ejpam-5330	123	11	[	[	X
ejpam-5330	123	12	11	11	NUM
ejpam-5330	123	13	]	]	PUNCT
ejpam-5330	123	14	,	,	PUNCT
ejpam-5330	123	15	β	β	X
ejpam-5330	123	16	-	-	VERB
ejpam-5330	123	17	open	open	ADJ
ejpam-5330	123	18	[	[	X
ejpam-5330	123	19	30	30	NUM
ejpam-5330	123	20	]	]	PUNCT
ejpam-5330	123	21	,	,	PUNCT
ejpam-5330	123	22	and	and	CCONJ
ejpam-5330	123	23	pre	pre	ADJ
ejpam-5330	123	24	-	-	ADJ
ejpam-5330	123	25	open	open	ADJ
ejpam-5330	123	26	[	[	X
ejpam-5330	123	27	30	30	NUM
ejpam-5330	123	28	]	]	PUNCT
ejpam-5330	123	29	)	)	PUNCT
ejpam-5330	123	30	set	set	NOUN
ejpam-5330	123	31	.	.	PUNCT
ejpam-5330	124	1	lemma	lemma	PROPN
ejpam-5330	124	2	2	2	X
ejpam-5330	124	3	.	.	PUNCT
ejpam-5330	125	1	let	let	AUX
ejpam-5330	125	2	(	(	PUNCT
ejpam-5330	125	3	w	w	NOUN
ejpam-5330	125	4	,	,	PUNCT
ejpam-5330	125	5	τn	τn	PART
ejpam-5330	125	6	)	)	PUNCT
ejpam-5330	125	7	be	be	AUX
ejpam-5330	125	8	an	an	DET
ejpam-5330	125	9	fsts	fst	NOUN
ejpam-5330	125	10	and	and	CCONJ
ejpam-5330	125	11	r	r	NOUN
ejpam-5330	125	12	∈	∈	PROPN
ejpam-5330	125	13	i0	i0	PROPN
ejpam-5330	125	14	,	,	PUNCT
ejpam-5330	125	15	then	then	ADV
ejpam-5330	125	16	any	any	DET
ejpam-5330	125	17	intersection	intersection	NOUN
ejpam-5330	125	18	(	(	PUNCT
ejpam-5330	125	19	resp	resp	NOUN
ejpam-5330	125	20	.	.	PUNCT
ejpam-5330	125	21	,	,	PUNCT
ejpam-5330	125	22	union	union	NOUN
ejpam-5330	125	23	)	)	PUNCT
ejpam-5330	125	24	of	of	ADP
ejpam-5330	125	25	r	r	NOUN
ejpam-5330	125	26	-	-	PUNCT
ejpam-5330	125	27	fuzzy	fuzzy	ADJ
ejpam-5330	125	28	soft	soft	ADJ
ejpam-5330	125	29	α	α	NOUN
ejpam-5330	125	30	-	-	ADJ
ejpam-5330	125	31	closed	closed	ADJ
ejpam-5330	125	32	(	(	PUNCT
ejpam-5330	125	33	resp	resp	NOUN
ejpam-5330	125	34	.	.	PUNCT
ejpam-5330	125	35	,	,	PUNCT
ejpam-5330	125	36	α	α	X
ejpam-5330	125	37	-	-	ADJ
ejpam-5330	125	38	open	open	ADJ
ejpam-5330	125	39	)	)	PUNCT
ejpam-5330	125	40	sets	set	NOUN
ejpam-5330	125	41	is	be	AUX
ejpam-5330	125	42	an	an	DET
ejpam-5330	125	43	r	r	NOUN
ejpam-5330	125	44	-	-	PUNCT
ejpam-5330	125	45	fuzzy	fuzzy	ADJ
ejpam-5330	125	46	soft	soft	ADJ
ejpam-5330	125	47	α	α	NOUN
ejpam-5330	125	48	-	-	ADJ
ejpam-5330	125	49	closed	closed	ADJ
ejpam-5330	125	50	(	(	PUNCT
ejpam-5330	125	51	resp	resp	NOUN
ejpam-5330	125	52	.	.	PUNCT
ejpam-5330	125	53	,	,	PUNCT
ejpam-5330	125	54	α	α	X
ejpam-5330	125	55	-	-	ADJ
ejpam-5330	125	56	open	open	ADJ
ejpam-5330	125	57	)	)	PUNCT
ejpam-5330	125	58	set	set	NOUN
ejpam-5330	125	59	.	.	PUNCT
ejpam-5330	126	1	proof	proof	NOUN
ejpam-5330	126	2	.	.	PUNCT
ejpam-5330	127	1	easily	easily	ADV
ejpam-5330	127	2	proved	prove	VERB
ejpam-5330	127	3	from	from	ADP
ejpam-5330	127	4	definitions	definition	NOUN
ejpam-5330	127	5	8	8	NUM
ejpam-5330	127	6	and	and	CCONJ
ejpam-5330	127	7	12	12	NUM
ejpam-5330	127	8	.	.	PUNCT
ejpam-5330	128	1	proposition	proposition	NOUN
ejpam-5330	128	2	1	1	NUM
ejpam-5330	128	3	.	.	PUNCT
ejpam-5330	129	1	let	let	AUX
ejpam-5330	129	2	(	(	PUNCT
ejpam-5330	129	3	w	w	NOUN
ejpam-5330	129	4	,	,	PUNCT
ejpam-5330	129	5	τn	τn	PART
ejpam-5330	129	6	)	)	PUNCT
ejpam-5330	129	7	be	be	AUX
ejpam-5330	129	8	an	an	DET
ejpam-5330	129	9	fsts	fst	NOUN
ejpam-5330	129	10	,	,	PUNCT
ejpam-5330	129	11	hc	hc	PROPN
ejpam-5330	129	12	∈	∈	PROPN
ejpam-5330	129	13	˜(w	˜(w	PROPN
ejpam-5330	129	14	,	,	PUNCT
ejpam-5330	129	15	n	n	CCONJ
ejpam-5330	129	16	)	)	PUNCT
ejpam-5330	129	17	,	,	PUNCT
ejpam-5330	129	18	n	n	PROPN
ejpam-5330	129	19	∈	∈	PROPN
ejpam-5330	129	20	n	n	NOUN
ejpam-5330	129	21	,	,	PUNCT
ejpam-5330	129	22	and	and	CCONJ
ejpam-5330	129	23	r	r	NOUN
ejpam-5330	129	24	∈	∈	PROPN
ejpam-5330	129	25	i0	i0	PROPN
ejpam-5330	129	26	,	,	PUNCT
ejpam-5330	129	27	then	then	ADV
ejpam-5330	129	28	the	the	DET
ejpam-5330	129	29	following	following	ADJ
ejpam-5330	129	30	statements	statement	NOUN
ejpam-5330	129	31	are	be	AUX
ejpam-5330	129	32	equivalent	equivalent	ADJ
ejpam-5330	129	33	.	.	PUNCT
ejpam-5330	130	1	(	(	PUNCT
ejpam-5330	130	2	1	1	X
ejpam-5330	130	3	)	)	PUNCT
ejpam-5330	130	4	hc	hc	PROPN
ejpam-5330	130	5	is	be	AUX
ejpam-5330	130	6	r	r	NOUN
ejpam-5330	130	7	-	-	PUNCT
ejpam-5330	130	8	fuzzy	fuzzy	ADJ
ejpam-5330	130	9	soft	soft	ADJ
ejpam-5330	130	10	α	α	NOUN
ejpam-5330	130	11	-	-	VERB
ejpam-5330	130	12	closed	closed	ADJ
ejpam-5330	130	13	.	.	PUNCT
ejpam-5330	131	1	(	(	PUNCT
ejpam-5330	131	2	2	2	X
ejpam-5330	131	3	)	)	PUNCT
ejpam-5330	131	4	hc	hc	PROPN
ejpam-5330	131	5	is	be	AUX
ejpam-5330	131	6	r	r	NOUN
ejpam-5330	131	7	-	-	PUNCT
ejpam-5330	131	8	fuzzy	fuzzy	ADJ
ejpam-5330	131	9	soft	soft	ADJ
ejpam-5330	131	10	semi	semi	ADJ
ejpam-5330	131	11	-	-	ADJ
ejpam-5330	131	12	closed	closed	ADJ
ejpam-5330	131	13	and	and	CCONJ
ejpam-5330	131	14	r	r	NOUN
ejpam-5330	131	15	-	-	PUNCT
ejpam-5330	131	16	fuzzy	fuzzy	ADJ
ejpam-5330	131	17	soft	soft	ADJ
ejpam-5330	131	18	pre	pre	ADJ
ejpam-5330	131	19	-	-	ADJ
ejpam-5330	131	20	closed	closed	ADJ
ejpam-5330	131	21	.	.	PUNCT
ejpam-5330	132	1	proof	proof	NOUN
ejpam-5330	132	2	.	.	PUNCT
ejpam-5330	133	1	(	(	PUNCT
ejpam-5330	133	2	1	1	X
ejpam-5330	133	3	)	)	PUNCT
ejpam-5330	133	4	⇒	⇒	NOUN
ejpam-5330	133	5	(	(	PUNCT
ejpam-5330	133	6	2	2	X
ejpam-5330	133	7	)	)	PUNCT
ejpam-5330	133	8	let	let	VERB
ejpam-5330	133	9	hc	hc	PRON
ejpam-5330	133	10	be	be	AUX
ejpam-5330	133	11	an	an	DET
ejpam-5330	133	12	r	r	NOUN
ejpam-5330	133	13	-	-	PUNCT
ejpam-5330	133	14	fuzzy	fuzzy	ADJ
ejpam-5330	133	15	soft	soft	ADJ
ejpam-5330	133	16	α	α	NOUN
ejpam-5330	133	17	-	-	VERB
ejpam-5330	133	18	closed	closed	ADJ
ejpam-5330	133	19	,	,	PUNCT
ejpam-5330	133	20	hc	hc	PROPN
ejpam-5330	133	21	⊒	⊒	PROPN
ejpam-5330	133	22	cτ	cτ	PROPN
ejpam-5330	133	23	(	(	PUNCT
ejpam-5330	133	24	n	n	CCONJ
ejpam-5330	133	25	,	,	PUNCT
ejpam-5330	133	26	iτ	iτ	X
ejpam-5330	133	27	(	(	PUNCT
ejpam-5330	133	28	n	n	CCONJ
ejpam-5330	133	29	,	,	PUNCT
ejpam-5330	133	30	cτ	cτ	INTJ
ejpam-5330	133	31	(	(	PUNCT
ejpam-5330	133	32	n	n	X
ejpam-5330	133	33	,	,	PUNCT
ejpam-5330	133	34	hc	hc	PROPN
ejpam-5330	133	35	,	,	PUNCT
ejpam-5330	133	36	r	r	NOUN
ejpam-5330	133	37	)	)	PUNCT
ejpam-5330	133	38	,	,	PUNCT
ejpam-5330	133	39	r	r	NOUN
ejpam-5330	133	40	)	)	PUNCT
ejpam-5330	133	41	,	,	PUNCT
ejpam-5330	133	42	r	r	NOUN
ejpam-5330	133	43	)	)	PUNCT
ejpam-5330	133	44	⊒	⊒	NOUN
ejpam-5330	133	45	iτ	iτ	X
ejpam-5330	133	46	(	(	PUNCT
ejpam-5330	133	47	n	n	CCONJ
ejpam-5330	133	48	,	,	PUNCT
ejpam-5330	133	49	cτ	cτ	INTJ
ejpam-5330	133	50	(	(	PUNCT
ejpam-5330	133	51	n	n	X
ejpam-5330	133	52	,	,	PUNCT
ejpam-5330	133	53	hc	hc	PROPN
ejpam-5330	133	54	,	,	PUNCT
ejpam-5330	133	55	r	r	NOUN
ejpam-5330	133	56	)	)	PUNCT
ejpam-5330	133	57	,	,	PUNCT
ejpam-5330	133	58	r	r	NOUN
ejpam-5330	133	59	)	)	PUNCT
ejpam-5330	133	60	.	.	PUNCT
ejpam-5330	134	1	this	this	PRON
ejpam-5330	134	2	shows	show	VERB
ejpam-5330	134	3	that	that	SCONJ
ejpam-5330	134	4	hc	hc	PROPN
ejpam-5330	134	5	is	be	AUX
ejpam-5330	134	6	r	r	NOUN
ejpam-5330	134	7	-	-	PUNCT
ejpam-5330	134	8	fuzzy	fuzzy	ADJ
ejpam-5330	134	9	soft	soft	ADJ
ejpam-5330	134	10	semi	semi	ADJ
ejpam-5330	134	11	-	-	ADJ
ejpam-5330	134	12	closed	closed	ADJ
ejpam-5330	134	13	.	.	PUNCT
ejpam-5330	135	1	since	since	SCONJ
ejpam-5330	135	2	hc	hc	PROPN
ejpam-5330	135	3	⊒	⊒	PROPN
ejpam-5330	135	4	cτ	cτ	X
ejpam-5330	135	5	(	(	PUNCT
ejpam-5330	135	6	n	n	CCONJ
ejpam-5330	135	7	,	,	PUNCT
ejpam-5330	135	8	iτ	iτ	X
ejpam-5330	135	9	(	(	PUNCT
ejpam-5330	135	10	n	n	CCONJ
ejpam-5330	135	11	,	,	PUNCT
ejpam-5330	135	12	cτ	cτ	INTJ
ejpam-5330	135	13	(	(	PUNCT
ejpam-5330	135	14	n	n	X
ejpam-5330	135	15	,	,	PUNCT
ejpam-5330	135	16	hc	hc	PROPN
ejpam-5330	135	17	,	,	PUNCT
ejpam-5330	135	18	r	r	NOUN
ejpam-5330	135	19	)	)	PUNCT
ejpam-5330	135	20	,	,	PUNCT
ejpam-5330	135	21	r	r	NOUN
ejpam-5330	135	22	)	)	PUNCT
ejpam-5330	135	23	,	,	PUNCT
ejpam-5330	135	24	r	r	NOUN
ejpam-5330	135	25	)	)	PUNCT
ejpam-5330	135	26	and	and	CCONJ
ejpam-5330	135	27	cτ	cτ	INTJ
ejpam-5330	135	28	(	(	PUNCT
ejpam-5330	135	29	n	n	CCONJ
ejpam-5330	135	30	,	,	PUNCT
ejpam-5330	135	31	hc	hc	PROPN
ejpam-5330	135	32	,	,	PUNCT
ejpam-5330	135	33	r	r	NOUN
ejpam-5330	135	34	)	)	PUNCT
ejpam-5330	135	35	⊒	⊒	PROPN
ejpam-5330	135	36	hc	hc	PROPN
ejpam-5330	135	37	,	,	PUNCT
ejpam-5330	135	38	then	then	ADV
ejpam-5330	135	39	hc	hc	PROPN
ejpam-5330	135	40	⊒	⊒	PROPN
ejpam-5330	135	41	cτ	cτ	PROPN
ejpam-5330	135	42	(	(	PUNCT
ejpam-5330	135	43	n	n	CCONJ
ejpam-5330	135	44	,	,	PUNCT
ejpam-5330	135	45	iτ	iτ	X
ejpam-5330	135	46	(	(	PUNCT
ejpam-5330	135	47	n	n	CCONJ
ejpam-5330	135	48	,	,	PUNCT
ejpam-5330	135	49	hc	hc	PROPN
ejpam-5330	135	50	,	,	PUNCT
ejpam-5330	135	51	r	r	NOUN
ejpam-5330	135	52	)	)	PUNCT
ejpam-5330	135	53	,	,	PUNCT
ejpam-5330	135	54	r	r	NOUN
ejpam-5330	135	55	)	)	PUNCT
ejpam-5330	135	56	.	.	PUNCT
ejpam-5330	136	1	therefore	therefore	ADV
ejpam-5330	136	2	,	,	PUNCT
ejpam-5330	136	3	hc	hc	PROPN
ejpam-5330	136	4	is	be	AUX
ejpam-5330	136	5	r	r	NOUN
ejpam-5330	136	6	-	-	PUNCT
ejpam-5330	136	7	fuzzy	fuzzy	ADJ
ejpam-5330	136	8	soft	soft	ADJ
ejpam-5330	136	9	pre	pre	ADJ
ejpam-5330	136	10	-	-	ADJ
ejpam-5330	136	11	closed	closed	ADJ
ejpam-5330	136	12	(	(	PUNCT
ejpam-5330	136	13	2	2	NUM
ejpam-5330	136	14	)	)	PUNCT
ejpam-5330	136	15	⇒	⇒	NOUN
ejpam-5330	136	16	(	(	PUNCT
ejpam-5330	136	17	1	1	X
ejpam-5330	136	18	)	)	PUNCT
ejpam-5330	136	19	let	let	VERB
ejpam-5330	136	20	hc	hc	PRON
ejpam-5330	136	21	be	be	AUX
ejpam-5330	136	22	an	an	DET
ejpam-5330	136	23	r	r	NOUN
ejpam-5330	136	24	-	-	PUNCT
ejpam-5330	136	25	fuzzy	fuzzy	ADJ
ejpam-5330	136	26	soft	soft	ADJ
ejpam-5330	136	27	semi	semi	ADJ
ejpam-5330	136	28	-	-	ADJ
ejpam-5330	136	29	closed	closed	ADJ
ejpam-5330	136	30	and	and	CCONJ
ejpam-5330	136	31	r	r	NOUN
ejpam-5330	136	32	-	-	PUNCT
ejpam-5330	136	33	fuzzy	fuzzy	ADJ
ejpam-5330	136	34	soft	soft	ADJ
ejpam-5330	136	35	pre	pre	ADJ
ejpam-5330	136	36	-	-	ADJ
ejpam-5330	136	37	closed	closed	ADJ
ejpam-5330	136	38	,	,	PUNCT
ejpam-5330	136	39	then	then	ADV
ejpam-5330	136	40	hc	hc	PROPN
ejpam-5330	136	41	⊒	⊒	PROPN
ejpam-5330	136	42	cτ	cτ	PROPN
ejpam-5330	136	43	(	(	PUNCT
ejpam-5330	136	44	n	n	CCONJ
ejpam-5330	136	45	,	,	PUNCT
ejpam-5330	136	46	iτ	iτ	X
ejpam-5330	136	47	(	(	PUNCT
ejpam-5330	136	48	n	n	CCONJ
ejpam-5330	136	49	,	,	PUNCT
ejpam-5330	136	50	iτ	iτ	X
ejpam-5330	136	51	(	(	PUNCT
ejpam-5330	136	52	n	n	CCONJ
ejpam-5330	136	53	,	,	PUNCT
ejpam-5330	136	54	cτ	cτ	INTJ
ejpam-5330	136	55	(	(	PUNCT
ejpam-5330	136	56	n	n	X
ejpam-5330	136	57	,	,	PUNCT
ejpam-5330	136	58	hc	hc	PROPN
ejpam-5330	136	59	,	,	PUNCT
ejpam-5330	136	60	r	r	NOUN
ejpam-5330	136	61	)	)	PUNCT
ejpam-5330	136	62	,	,	PUNCT
ejpam-5330	136	63	r	r	NOUN
ejpam-5330	136	64	)	)	PUNCT
ejpam-5330	136	65	,	,	PUNCT
ejpam-5330	136	66	r	r	NOUN
ejpam-5330	136	67	)	)	PUNCT
ejpam-5330	136	68	,	,	PUNCT
ejpam-5330	136	69	r	r	NOUN
ejpam-5330	136	70	)	)	PUNCT
ejpam-5330	136	71	=	=	NOUN
ejpam-5330	136	72	cτ	cτ	INTJ
ejpam-5330	136	73	(	(	PUNCT
ejpam-5330	136	74	n	n	CCONJ
ejpam-5330	136	75	,	,	PUNCT
ejpam-5330	136	76	iτ	iτ	X
ejpam-5330	136	77	(	(	PUNCT
ejpam-5330	136	78	n	n	CCONJ
ejpam-5330	136	79	,	,	PUNCT
ejpam-5330	136	80	cτ	cτ	INTJ
ejpam-5330	136	81	(	(	PUNCT
ejpam-5330	136	82	n	n	X
ejpam-5330	136	83	,	,	PUNCT
ejpam-5330	136	84	hc	hc	PROPN
ejpam-5330	136	85	,	,	PUNCT
ejpam-5330	136	86	r	r	NOUN
ejpam-5330	136	87	)	)	PUNCT
ejpam-5330	136	88	,	,	PUNCT
ejpam-5330	136	89	r	r	NOUN
ejpam-5330	136	90	)	)	PUNCT
ejpam-5330	136	91	,	,	PUNCT
ejpam-5330	136	92	r	r	NOUN
ejpam-5330	136	93	)	)	PUNCT
ejpam-5330	136	94	.	.	PUNCT
ejpam-5330	137	1	this	this	PRON
ejpam-5330	137	2	shows	show	VERB
ejpam-5330	137	3	that	that	SCONJ
ejpam-5330	137	4	hc	hc	PROPN
ejpam-5330	137	5	is	be	AUX
ejpam-5330	137	6	r	r	NOUN
ejpam-5330	137	7	-	-	PUNCT
ejpam-5330	137	8	fuzzy	fuzzy	ADJ
ejpam-5330	137	9	soft	soft	ADJ
ejpam-5330	137	10	α	α	NOUN
ejpam-5330	137	11	-	-	PUNCT
ejpam-5330	137	12	closed	closed	ADJ
ejpam-5330	137	13	.	.	PUNCT
ejpam-5330	138	1	proposition	proposition	NOUN
ejpam-5330	138	2	2	2	NUM
ejpam-5330	138	3	.	.	PUNCT
ejpam-5330	139	1	let	let	AUX
ejpam-5330	139	2	(	(	PUNCT
ejpam-5330	139	3	w	w	NOUN
ejpam-5330	139	4	,	,	PUNCT
ejpam-5330	139	5	τn	τn	PART
ejpam-5330	139	6	)	)	PUNCT
ejpam-5330	139	7	be	be	AUX
ejpam-5330	139	8	an	an	DET
ejpam-5330	139	9	fsts	fst	NOUN
ejpam-5330	139	10	,	,	PUNCT
ejpam-5330	139	11	gb	gb	PRON
ejpam-5330	139	12	,	,	PUNCT
ejpam-5330	139	13	hc	hc	PROPN
ejpam-5330	139	14	∈	∈	PROPN
ejpam-5330	139	15	˜(w	˜(w	PROPN
ejpam-5330	139	16	,	,	PUNCT
ejpam-5330	139	17	n	n	CCONJ
ejpam-5330	139	18	)	)	PUNCT
ejpam-5330	139	19	,	,	PUNCT
ejpam-5330	139	20	n	n	PROPN
ejpam-5330	139	21	∈	∈	PROPN
ejpam-5330	139	22	n	n	NOUN
ejpam-5330	139	23	,	,	PUNCT
ejpam-5330	139	24	and	and	CCONJ
ejpam-5330	139	25	r	r	NOUN
ejpam-5330	139	26	∈	∈	PROPN
ejpam-5330	139	27	i0	i0	PROPN
ejpam-5330	139	28	.	.	PUNCT
ejpam-5330	140	1	if	if	SCONJ
ejpam-5330	140	2	gb	gb	PRON
ejpam-5330	140	3	is	be	AUX
ejpam-5330	140	4	an	an	DET
ejpam-5330	140	5	r	r	NOUN
ejpam-5330	140	6	-	-	PUNCT
ejpam-5330	140	7	fuzzy	fuzzy	ADJ
ejpam-5330	140	8	soft	soft	ADJ
ejpam-5330	140	9	semi	semi	ADJ
ejpam-5330	140	10	-	-	ADJ
ejpam-5330	140	11	closed	closed	ADJ
ejpam-5330	140	12	set	set	NOUN
ejpam-5330	140	13	,	,	PUNCT
ejpam-5330	140	14	such	such	ADJ
ejpam-5330	140	15	that	that	PRON
ejpam-5330	140	16	gb	gb	PROPN
ejpam-5330	140	17	⊒	⊒	PROPN
ejpam-5330	140	18	hc	hc	PROPN
ejpam-5330	140	19	⊒	⊒	PROPN
ejpam-5330	140	20	cτ	cτ	PROPN
ejpam-5330	140	21	(	(	PUNCT
ejpam-5330	140	22	n	n	CCONJ
ejpam-5330	140	23	,	,	PUNCT
ejpam-5330	140	24	iτ	iτ	X
ejpam-5330	140	25	(	(	PUNCT
ejpam-5330	140	26	n	n	CCONJ
ejpam-5330	140	27	,	,	PUNCT
ejpam-5330	140	28	gb	gb	ADJ
ejpam-5330	140	29	,	,	PUNCT
ejpam-5330	140	30	r	r	NOUN
ejpam-5330	140	31	)	)	PUNCT
ejpam-5330	140	32	,	,	PUNCT
ejpam-5330	140	33	r	r	NOUN
ejpam-5330	140	34	)	)	PUNCT
ejpam-5330	140	35	,	,	PUNCT
ejpam-5330	140	36	then	then	ADV
ejpam-5330	140	37	hc	hc	PROPN
ejpam-5330	140	38	is	be	AUX
ejpam-5330	140	39	r	r	NOUN
ejpam-5330	140	40	-	-	PUNCT
ejpam-5330	140	41	fuzzy	fuzzy	ADJ
ejpam-5330	140	42	soft	soft	ADJ
ejpam-5330	140	43	α	α	NOUN
ejpam-5330	140	44	-	-	PUNCT
ejpam-5330	140	45	closed	closed	ADJ
ejpam-5330	140	46	.	.	PUNCT
ejpam-5330	141	1	w.	w.	PROPN
ejpam-5330	141	2	alqurashi	alqurashi	PROPN
ejpam-5330	141	3	,	,	PUNCT
ejpam-5330	141	4	i.	i.	PROPN
ejpam-5330	141	5	m.	m.	PROPN
ejpam-5330	141	6	taha	taha	PROPN
ejpam-5330	141	7	/	/	PUNCT
ejpam-5330	141	8	eur	eur	PROPN
ejpam-5330	141	9	.	.	PUNCT
ejpam-5330	142	1	j.	j.	PROPN
ejpam-5330	142	2	pure	pure	PROPN
ejpam-5330	142	3	appl	appl	PROPN
ejpam-5330	142	4	.	.	PROPN
ejpam-5330	142	5	math	math	PROPN
ejpam-5330	142	6	,	,	PUNCT
ejpam-5330	142	7	17	17	NUM
ejpam-5330	142	8	(	(	PUNCT
ejpam-5330	142	9	4	4	NUM
ejpam-5330	142	10	)	)	PUNCT
ejpam-5330	142	11	(	(	PUNCT
ejpam-5330	142	12	2024	2024	NUM
ejpam-5330	142	13	)	)	PUNCT
ejpam-5330	142	14	,	,	PUNCT
ejpam-5330	142	15	4112	4112	NUM
ejpam-5330	142	16	-	-	SYM
ejpam-5330	142	17	4134	4134	NUM
ejpam-5330	142	18	4117	4117	NUM
ejpam-5330	142	19	proof	proof	NOUN
ejpam-5330	142	20	.	.	PUNCT
ejpam-5330	143	1	let	let	VERB
ejpam-5330	143	2	gb	gb	PRON
ejpam-5330	143	3	be	be	AUX
ejpam-5330	143	4	an	an	DET
ejpam-5330	143	5	r	r	NOUN
ejpam-5330	143	6	-	-	PUNCT
ejpam-5330	143	7	fuzzy	fuzzy	ADJ
ejpam-5330	143	8	soft	soft	ADJ
ejpam-5330	143	9	semi	semi	ADJ
ejpam-5330	143	10	-	-	ADJ
ejpam-5330	143	11	closed	closed	ADJ
ejpam-5330	143	12	and	and	CCONJ
ejpam-5330	143	13	gb	gb	PROPN
ejpam-5330	143	14	⊒	⊒	PROPN
ejpam-5330	143	15	hc	hc	PROPN
ejpam-5330	143	16	,	,	PUNCT
ejpam-5330	143	17	then	then	ADV
ejpam-5330	143	18	gb	gb	ADP
ejpam-5330	143	19	⊒	⊒	PROPN
ejpam-5330	143	20	iτ	iτ	X
ejpam-5330	143	21	(	(	PUNCT
ejpam-5330	143	22	n	n	CCONJ
ejpam-5330	143	23	,	,	PUNCT
ejpam-5330	143	24	cτ	cτ	INTJ
ejpam-5330	143	25	(	(	PUNCT
ejpam-5330	143	26	n	n	CCONJ
ejpam-5330	143	27	,	,	PUNCT
ejpam-5330	143	28	gb	gb	ADJ
ejpam-5330	143	29	,	,	PUNCT
ejpam-5330	143	30	r	r	NOUN
ejpam-5330	143	31	)	)	PUNCT
ejpam-5330	143	32	,	,	PUNCT
ejpam-5330	143	33	r	r	NOUN
ejpam-5330	143	34	)	)	PUNCT
ejpam-5330	143	35	⊒	⊒	NOUN
ejpam-5330	143	36	iτ	iτ	X
ejpam-5330	143	37	(	(	PUNCT
ejpam-5330	143	38	n	n	CCONJ
ejpam-5330	143	39	,	,	PUNCT
ejpam-5330	143	40	cτ	cτ	INTJ
ejpam-5330	143	41	(	(	PUNCT
ejpam-5330	143	42	n	n	X
ejpam-5330	143	43	,	,	PUNCT
ejpam-5330	143	44	hc	hc	PROPN
ejpam-5330	143	45	,	,	PUNCT
ejpam-5330	143	46	r	r	NOUN
ejpam-5330	143	47	)	)	PUNCT
ejpam-5330	143	48	,	,	PUNCT
ejpam-5330	143	49	r	r	NOUN
ejpam-5330	143	50	)	)	PUNCT
ejpam-5330	143	51	.	.	PUNCT
ejpam-5330	144	1	let	let	VERB
ejpam-5330	144	2	hc	hc	PROPN
ejpam-5330	144	3	⊒	⊒	VERB
ejpam-5330	144	4	cτ	cτ	VERB
ejpam-5330	144	5	(	(	PUNCT
ejpam-5330	144	6	n	n	CCONJ
ejpam-5330	144	7	,	,	PUNCT
ejpam-5330	144	8	iτ	iτ	X
ejpam-5330	144	9	(	(	PUNCT
ejpam-5330	144	10	n	n	CCONJ
ejpam-5330	144	11	,	,	PUNCT
ejpam-5330	144	12	gb	gb	ADJ
ejpam-5330	144	13	,	,	PUNCT
ejpam-5330	144	14	r	r	NOUN
ejpam-5330	144	15	)	)	PUNCT
ejpam-5330	144	16	,	,	PUNCT
ejpam-5330	144	17	r	r	NOUN
ejpam-5330	144	18	)	)	PUNCT
ejpam-5330	144	19	,	,	PUNCT
ejpam-5330	144	20	then	then	ADV
ejpam-5330	144	21	hc	hc	PROPN
ejpam-5330	144	22	⊒	⊒	PROPN
ejpam-5330	144	23	cτ	cτ	PROPN
ejpam-5330	144	24	(	(	PUNCT
ejpam-5330	144	25	n	n	CCONJ
ejpam-5330	144	26	,	,	PUNCT
ejpam-5330	144	27	iτ	iτ	X
ejpam-5330	144	28	(	(	PUNCT
ejpam-5330	144	29	n	n	CCONJ
ejpam-5330	144	30	,	,	PUNCT
ejpam-5330	144	31	iτ	iτ	X
ejpam-5330	144	32	(	(	PUNCT
ejpam-5330	144	33	n	n	CCONJ
ejpam-5330	144	34	,	,	PUNCT
ejpam-5330	144	35	cτ	cτ	INTJ
ejpam-5330	144	36	(	(	PUNCT
ejpam-5330	144	37	n	n	X
ejpam-5330	144	38	,	,	PUNCT
ejpam-5330	144	39	hc	hc	PROPN
ejpam-5330	144	40	,	,	PUNCT
ejpam-5330	144	41	r	r	NOUN
ejpam-5330	144	42	)	)	PUNCT
ejpam-5330	144	43	,	,	PUNCT
ejpam-5330	144	44	r	r	NOUN
ejpam-5330	144	45	)	)	PUNCT
ejpam-5330	144	46	,	,	PUNCT
ejpam-5330	144	47	r	r	NOUN
ejpam-5330	144	48	)	)	PUNCT
ejpam-5330	144	49	,	,	PUNCT
ejpam-5330	144	50	r	r	NOUN
ejpam-5330	144	51	)	)	PUNCT
ejpam-5330	144	52	=	=	NOUN
ejpam-5330	144	53	cτ	cτ	INTJ
ejpam-5330	144	54	(	(	PUNCT
ejpam-5330	144	55	n	n	CCONJ
ejpam-5330	144	56	,	,	PUNCT
ejpam-5330	144	57	iτ	iτ	X
ejpam-5330	144	58	(	(	PUNCT
ejpam-5330	144	59	n	n	CCONJ
ejpam-5330	144	60	,	,	PUNCT
ejpam-5330	144	61	cτ	cτ	INTJ
ejpam-5330	144	62	(	(	PUNCT
ejpam-5330	144	63	n	n	X
ejpam-5330	144	64	,	,	PUNCT
ejpam-5330	144	65	hc	hc	PROPN
ejpam-5330	144	66	,	,	PUNCT
ejpam-5330	144	67	r	r	NOUN
ejpam-5330	144	68	)	)	PUNCT
ejpam-5330	144	69	,	,	PUNCT
ejpam-5330	144	70	r	r	NOUN
ejpam-5330	144	71	)	)	PUNCT
ejpam-5330	144	72	,	,	PUNCT
ejpam-5330	144	73	r	r	NOUN
ejpam-5330	144	74	)	)	PUNCT
ejpam-5330	144	75	.	.	PUNCT
ejpam-5330	145	1	therefore	therefore	ADV
ejpam-5330	145	2	,	,	PUNCT
ejpam-5330	145	3	hc	hc	PROPN
ejpam-5330	145	4	is	be	AUX
ejpam-5330	145	5	r	r	NOUN
ejpam-5330	145	6	-	-	PUNCT
ejpam-5330	145	7	fuzzy	fuzzy	ADJ
ejpam-5330	145	8	soft	soft	ADJ
ejpam-5330	145	9	α	α	NOUN
ejpam-5330	145	10	-	-	PUNCT
ejpam-5330	145	11	closed	closed	ADJ
ejpam-5330	145	12	.	.	PUNCT
ejpam-5330	146	1	lemma	lemma	PROPN
ejpam-5330	146	2	3	3	X
ejpam-5330	146	3	.	.	PUNCT
ejpam-5330	147	1	let	let	AUX
ejpam-5330	147	2	(	(	PUNCT
ejpam-5330	147	3	w	w	NOUN
ejpam-5330	147	4	,	,	PUNCT
ejpam-5330	147	5	τn	τn	PART
ejpam-5330	147	6	)	)	PUNCT
ejpam-5330	147	7	be	be	AUX
ejpam-5330	147	8	an	an	DET
ejpam-5330	147	9	fsts	fst	NOUN
ejpam-5330	147	10	,	,	PUNCT
ejpam-5330	147	11	gb	gb	PRON
ejpam-5330	147	12	,	,	PUNCT
ejpam-5330	147	13	hc	hc	PROPN
ejpam-5330	147	14	∈	∈	PROPN
ejpam-5330	147	15	˜(w	˜(w	PROPN
ejpam-5330	147	16	,	,	PUNCT
ejpam-5330	147	17	n	n	CCONJ
ejpam-5330	147	18	)	)	PUNCT
ejpam-5330	147	19	,	,	PUNCT
ejpam-5330	147	20	n	n	PROPN
ejpam-5330	147	21	∈	∈	PROPN
ejpam-5330	147	22	n	n	NOUN
ejpam-5330	147	23	,	,	PUNCT
ejpam-5330	147	24	and	and	CCONJ
ejpam-5330	147	25	r	r	NOUN
ejpam-5330	147	26	∈	∈	PROPN
ejpam-5330	147	27	i0	i0	PROPN
ejpam-5330	147	28	.	.	PUNCT
ejpam-5330	148	1	if	if	SCONJ
ejpam-5330	148	2	gb	gb	PRON
ejpam-5330	148	3	is	be	AUX
ejpam-5330	148	4	an	an	DET
ejpam-5330	148	5	r	r	NOUN
ejpam-5330	148	6	-	-	PUNCT
ejpam-5330	148	7	fuzzy	fuzzy	ADJ
ejpam-5330	148	8	soft	soft	ADJ
ejpam-5330	148	9	α	α	NOUN
ejpam-5330	148	10	-	-	PUNCT
ejpam-5330	148	11	closed	closed	ADJ
ejpam-5330	148	12	set	set	NOUN
ejpam-5330	148	13	,	,	PUNCT
ejpam-5330	148	14	such	such	ADJ
ejpam-5330	148	15	that	that	PRON
ejpam-5330	148	16	gb	gb	PROPN
ejpam-5330	148	17	⊒	⊒	PROPN
ejpam-5330	148	18	hc	hc	PROPN
ejpam-5330	148	19	⊒	⊒	PROPN
ejpam-5330	148	20	cτ	cτ	PROPN
ejpam-5330	148	21	(	(	PUNCT
ejpam-5330	148	22	n	n	CCONJ
ejpam-5330	148	23	,	,	PUNCT
ejpam-5330	148	24	iτ	iτ	X
ejpam-5330	148	25	(	(	PUNCT
ejpam-5330	148	26	n	n	CCONJ
ejpam-5330	148	27	,	,	PUNCT
ejpam-5330	148	28	gb	gb	ADJ
ejpam-5330	148	29	,	,	PUNCT
ejpam-5330	148	30	r	r	NOUN
ejpam-5330	148	31	)	)	PUNCT
ejpam-5330	148	32	,	,	PUNCT
ejpam-5330	148	33	r	r	NOUN
ejpam-5330	148	34	)	)	PUNCT
ejpam-5330	148	35	,	,	PUNCT
ejpam-5330	148	36	then	then	ADV
ejpam-5330	148	37	hc	hc	PROPN
ejpam-5330	148	38	is	be	AUX
ejpam-5330	148	39	r	r	NOUN
ejpam-5330	148	40	-	-	PUNCT
ejpam-5330	148	41	fuzzy	fuzzy	ADJ
ejpam-5330	148	42	soft	soft	ADJ
ejpam-5330	148	43	α	α	NOUN
ejpam-5330	148	44	-	-	PUNCT
ejpam-5330	148	45	closed	closed	ADJ
ejpam-5330	148	46	.	.	PUNCT
ejpam-5330	149	1	proof	proof	NOUN
ejpam-5330	149	2	.	.	PUNCT
ejpam-5330	150	1	it	it	PRON
ejpam-5330	150	2	is	be	AUX
ejpam-5330	150	3	easily	easily	ADV
ejpam-5330	150	4	proved	prove	VERB
ejpam-5330	150	5	from	from	ADP
ejpam-5330	150	6	every	every	DET
ejpam-5330	150	7	r	r	NOUN
ejpam-5330	150	8	-	-	PUNCT
ejpam-5330	150	9	fuzzy	fuzzy	ADJ
ejpam-5330	150	10	soft	soft	ADJ
ejpam-5330	150	11	α	α	NOUN
ejpam-5330	150	12	-	-	PUNCT
ejpam-5330	150	13	closed	closed	ADJ
ejpam-5330	150	14	set	set	NOUN
ejpam-5330	150	15	that	that	PRON
ejpam-5330	150	16	is	be	AUX
ejpam-5330	150	17	an	an	DET
ejpam-5330	150	18	r	r	NOUN
ejpam-5330	150	19	-	-	PUNCT
ejpam-5330	150	20	fuzzy	fuzzy	ADJ
ejpam-5330	150	21	soft	soft	ADJ
ejpam-5330	150	22	semi	semi	ADJ
ejpam-5330	150	23	-	-	ADJ
ejpam-5330	150	24	closed	closed	ADJ
ejpam-5330	150	25	set	set	NOUN
ejpam-5330	150	26	.	.	PUNCT
ejpam-5330	151	1	remark	remark	PROPN
ejpam-5330	151	2	3	3	NUM
ejpam-5330	151	3	.	.	PUNCT
ejpam-5330	152	1	from	from	ADP
ejpam-5330	152	2	the	the	DET
ejpam-5330	152	3	previous	previous	ADJ
ejpam-5330	152	4	definition	definition	NOUN
ejpam-5330	152	5	,	,	PUNCT
ejpam-5330	152	6	we	we	PRON
ejpam-5330	152	7	can	can	AUX
ejpam-5330	152	8	summarize	summarize	VERB
ejpam-5330	152	9	the	the	DET
ejpam-5330	152	10	relationships	relationship	NOUN
ejpam-5330	152	11	among	among	ADP
ejpam-5330	152	12	different	different	ADJ
ejpam-5330	152	13	types	type	NOUN
ejpam-5330	152	14	of	of	ADP
ejpam-5330	152	15	fuzzy	fuzzy	ADJ
ejpam-5330	152	16	soft	soft	ADJ
ejpam-5330	152	17	sets	set	NOUN
ejpam-5330	152	18	as	as	ADP
ejpam-5330	152	19	in	in	ADP
ejpam-5330	152	20	the	the	DET
ejpam-5330	152	21	next	next	ADJ
ejpam-5330	152	22	diagram	diagram	NOUN
ejpam-5330	152	23	.	.	PUNCT
ejpam-5330	153	1	fuzzy	fuzzy	ADJ
ejpam-5330	153	2	soft	soft	ADJ
ejpam-5330	153	3	α−	α−	ADP
ejpam-5330	153	4	closed	closed	ADJ
ejpam-5330	153	5	set	set	VERB
ejpam-5330	153	6	⇓	⇓	PROPN
ejpam-5330	153	7	⇓	⇓	PROPN
ejpam-5330	153	8	fuzzy	fuzzy	ADJ
ejpam-5330	153	9	soft	soft	ADJ
ejpam-5330	153	10	semi−closed	semi−close	VERB
ejpam-5330	153	11	set	set	VERB
ejpam-5330	153	12	fuzzy	fuzzy	ADJ
ejpam-5330	153	13	soft	soft	ADJ
ejpam-5330	153	14	pre−closed	pre−close	VERB
ejpam-5330	153	15	set	set	NOUN
ejpam-5330	153	16	⇓	⇓	PROPN
ejpam-5330	153	17	⇓	⇓	PROPN
ejpam-5330	153	18	fuzzy	fuzzy	ADJ
ejpam-5330	153	19	soft	soft	ADJ
ejpam-5330	153	20	β	β	NOUN
ejpam-5330	153	21	−	−	NOUN
ejpam-5330	153	22	closed	close	VERB
ejpam-5330	153	23	set	set	VERB
ejpam-5330	153	24	remark	remark	NOUN
ejpam-5330	153	25	4	4	NUM
ejpam-5330	153	26	.	.	PUNCT
ejpam-5330	154	1	the	the	DET
ejpam-5330	154	2	converses	converse	NOUN
ejpam-5330	154	3	of	of	ADP
ejpam-5330	154	4	the	the	DET
ejpam-5330	154	5	above	above	ADJ
ejpam-5330	154	6	relationships	relationship	NOUN
ejpam-5330	154	7	may	may	AUX
ejpam-5330	154	8	not	not	PART
ejpam-5330	154	9	be	be	AUX
ejpam-5330	154	10	true	true	ADJ
ejpam-5330	154	11	,	,	PUNCT
ejpam-5330	154	12	as	as	SCONJ
ejpam-5330	154	13	shown	show	VERB
ejpam-5330	154	14	by	by	ADP
ejpam-5330	154	15	examples	example	NOUN
ejpam-5330	154	16	1	1	NUM
ejpam-5330	154	17	and	and	CCONJ
ejpam-5330	154	18	2	2	NUM
ejpam-5330	154	19	.	.	NOUN
ejpam-5330	154	20	example	example	NOUN
ejpam-5330	155	1	1	1	NUM
ejpam-5330	155	2	.	.	PUNCT
ejpam-5330	156	1	let	let	VERB
ejpam-5330	156	2	w	w	VERB
ejpam-5330	156	3	=	=	PUNCT
ejpam-5330	156	4	{	{	PUNCT
ejpam-5330	156	5	w1	w1	NOUN
ejpam-5330	156	6	,	,	PUNCT
ejpam-5330	156	7	w2	w2	NOUN
ejpam-5330	156	8	}	}	PUNCT
ejpam-5330	156	9	,	,	PUNCT
ejpam-5330	156	10	n	n	NOUN
ejpam-5330	156	11	=	=	SYM
ejpam-5330	156	12	{	{	PUNCT
ejpam-5330	156	13	n1	n1	NOUN
ejpam-5330	156	14	,	,	PUNCT
ejpam-5330	156	15	n2	n2	ADJ
ejpam-5330	156	16	}	}	PUNCT
ejpam-5330	156	17	,	,	PUNCT
ejpam-5330	156	18	and	and	CCONJ
ejpam-5330	156	19	define	define	VERB
ejpam-5330	156	20	fn	fn	NOUN
ejpam-5330	156	21	,	,	PUNCT
ejpam-5330	156	22	gn	gn	PROPN
ejpam-5330	156	23	,	,	PUNCT
ejpam-5330	156	24	hn	hn	PROPN
ejpam-5330	156	25	∈	∈	PROPN
ejpam-5330	156	26	˜(w	˜(w	PROPN
ejpam-5330	156	27	,	,	PUNCT
ejpam-5330	156	28	n	n	CCONJ
ejpam-5330	156	29	)	)	PUNCT
ejpam-5330	156	30	as	as	SCONJ
ejpam-5330	156	31	follows	follow	VERB
ejpam-5330	156	32	:	:	PUNCT
ejpam-5330	156	33	fn	fn	NOUN
ejpam-5330	156	34	=	=	SYM
ejpam-5330	156	35	{	{	PUNCT
ejpam-5330	156	36	(	(	PUNCT
ejpam-5330	156	37	n1	n1	NOUN
ejpam-5330	156	38	,	,	PUNCT
ejpam-5330	156	39	{	{	PUNCT
ejpam-5330	156	40	w1	w1	NOUN
ejpam-5330	156	41	0.3	0.3	NUM
ejpam-5330	156	42	,	,	PUNCT
ejpam-5330	156	43	w2	w2	NOUN
ejpam-5330	156	44	0.4	0.4	NUM
ejpam-5330	156	45	}	}	PUNCT
ejpam-5330	156	46	)	)	PUNCT
ejpam-5330	156	47	,	,	PUNCT
ejpam-5330	156	48	(	(	PUNCT
ejpam-5330	156	49	n2	n2	ADJ
ejpam-5330	156	50	,	,	PUNCT
ejpam-5330	156	51	{	{	PUNCT
ejpam-5330	156	52	w1	w1	NOUN
ejpam-5330	156	53	0.3	0.3	NUM
ejpam-5330	156	54	,	,	PUNCT
ejpam-5330	156	55	w2	w2	NOUN
ejpam-5330	156	56	0.4	0.4	NUM
ejpam-5330	156	57	}	}	PUNCT
ejpam-5330	156	58	)	)	PUNCT
ejpam-5330	156	59	}	}	PUNCT
ejpam-5330	156	60	,	,	PUNCT
ejpam-5330	156	61	gn	gn	PROPN
ejpam-5330	156	62	=	=	PUNCT
ejpam-5330	156	63	{	{	PUNCT
ejpam-5330	156	64	(	(	PUNCT
ejpam-5330	156	65	n1	n1	NOUN
ejpam-5330	156	66	,	,	PUNCT
ejpam-5330	156	67	{	{	PUNCT
ejpam-5330	156	68	w1	w1	NOUN
ejpam-5330	156	69	0.6	0.6	NUM
ejpam-5330	156	70	,	,	PUNCT
ejpam-5330	156	71	w2	w2	NOUN
ejpam-5330	156	72	0.2	0.2	NUM
ejpam-5330	156	73	}	}	PUNCT
ejpam-5330	156	74	)	)	PUNCT
ejpam-5330	156	75	,	,	PUNCT
ejpam-5330	156	76	(	(	PUNCT
ejpam-5330	156	77	n2	n2	ADJ
ejpam-5330	156	78	,	,	PUNCT
ejpam-5330	156	79	{	{	PUNCT
ejpam-5330	156	80	w1	w1	NOUN
ejpam-5330	156	81	0.6	0.6	NUM
ejpam-5330	156	82	,	,	PUNCT
ejpam-5330	156	83	w2	w2	NOUN
ejpam-5330	156	84	0.2	0.2	NUM
ejpam-5330	156	85	}	}	PUNCT
ejpam-5330	156	86	)	)	PUNCT
ejpam-5330	156	87	}	}	PUNCT
ejpam-5330	156	88	,	,	PUNCT
ejpam-5330	156	89	hn	hn	PROPN
ejpam-5330	156	90	=	=	PRON
ejpam-5330	156	91	{	{	PUNCT
ejpam-5330	156	92	(	(	PUNCT
ejpam-5330	156	93	n1	n1	NOUN
ejpam-5330	156	94	,	,	PUNCT
ejpam-5330	156	95	{	{	PUNCT
ejpam-5330	156	96	w1	w1	NOUN
ejpam-5330	156	97	0.3	0.3	NUM
ejpam-5330	156	98	,	,	PUNCT
ejpam-5330	156	99	w2	w2	NOUN
ejpam-5330	156	100	0.5	0.5	NUM
ejpam-5330	156	101	}	}	PUNCT
ejpam-5330	156	102	)	)	PUNCT
ejpam-5330	156	103	,	,	PUNCT
ejpam-5330	156	104	(	(	PUNCT
ejpam-5330	156	105	n2	n2	ADJ
ejpam-5330	156	106	,	,	PUNCT
ejpam-5330	156	107	{	{	PUNCT
ejpam-5330	156	108	w1	w1	NOUN
ejpam-5330	156	109	0.3	0.3	NUM
ejpam-5330	156	110	,	,	PUNCT
ejpam-5330	156	111	w2	w2	NOUN
ejpam-5330	156	112	0.5	0.5	NUM
ejpam-5330	156	113	}	}	PUNCT
ejpam-5330	156	114	)	)	PUNCT
ejpam-5330	156	115	}	}	PUNCT
ejpam-5330	156	116	.	.	PUNCT
ejpam-5330	157	1	define	define	VERB
ejpam-5330	157	2	fuzzy	fuzzy	ADJ
ejpam-5330	157	3	soft	soft	ADJ
ejpam-5330	157	4	topology	topology	NOUN
ejpam-5330	157	5	τn	τn	NOUN
ejpam-5330	157	6	:	:	PUNCT
ejpam-5330	157	7	n	n	CCONJ
ejpam-5330	157	8	−→	−→	NOUN
ejpam-5330	158	1	[	[	X
ejpam-5330	158	2	0	0	NUM
ejpam-5330	158	3	,	,	PUNCT
ejpam-5330	158	4	1	1	NUM
ejpam-5330	158	5	]	]	PUNCT
ejpam-5330	158	6	˜(w	˜(w	PROPN
ejpam-5330	158	7	,	,	PUNCT
ejpam-5330	158	8	n	n	CCONJ
ejpam-5330	158	9	)	)	PUNCT
ejpam-5330	158	10	as	as	SCONJ
ejpam-5330	158	11	follows	follow	VERB
ejpam-5330	158	12	:	:	PUNCT
ejpam-5330	158	13	τn1(tn	τn1(tn	PUNCT
ejpam-5330	158	14	)	)	PUNCT
ejpam-5330	159	1	=	=	PUNCT
ejpam-5330	159	2			NUM
ejpam-5330	159	3	1	1	NUM
ejpam-5330	159	4	,	,	PUNCT
ejpam-5330	159	5	if	if	SCONJ
ejpam-5330	159	6	tn	tn	PROPN
ejpam-5330	159	7	∈	∈	PROPN
ejpam-5330	159	8	{	{	PUNCT
ejpam-5330	159	9	φ	φ	NOUN
ejpam-5330	159	10	,	,	PUNCT
ejpam-5330	159	11	ñ	ñ	PROPN
ejpam-5330	159	12	}	}	PUNCT
ejpam-5330	159	13	,	,	PUNCT
ejpam-5330	159	14	1	1	NUM
ejpam-5330	159	15	2	2	NUM
ejpam-5330	159	16	,	,	PUNCT
ejpam-5330	159	17	if	if	SCONJ
ejpam-5330	159	18	tn	tn	NUM
ejpam-5330	159	19	=	=	SYM
ejpam-5330	159	20	fn	fn	NOUN
ejpam-5330	159	21	,	,	PUNCT
ejpam-5330	159	22	2	2	NUM
ejpam-5330	159	23	3	3	NUM
ejpam-5330	159	24	,	,	PUNCT
ejpam-5330	159	25	if	if	SCONJ
ejpam-5330	159	26	tn	tn	NUM
ejpam-5330	159	27	=	=	SYM
ejpam-5330	159	28	gn	gn	PROPN
ejpam-5330	159	29	,	,	PUNCT
ejpam-5330	159	30	2	2	NUM
ejpam-5330	159	31	3	3	NUM
ejpam-5330	159	32	,	,	PUNCT
ejpam-5330	159	33	if	if	SCONJ
ejpam-5330	159	34	tn	tn	NUM
ejpam-5330	159	35	=	=	SYM
ejpam-5330	159	36	fn	fn	NOUN
ejpam-5330	159	37	⊓	⊓	PROPN
ejpam-5330	159	38	gn	gn	PROPN
ejpam-5330	159	39	,	,	PUNCT
ejpam-5330	159	40	1	1	NUM
ejpam-5330	159	41	2	2	NUM
ejpam-5330	159	42	,	,	PUNCT
ejpam-5330	159	43	if	if	SCONJ
ejpam-5330	159	44	tn	tn	NUM
ejpam-5330	159	45	=	=	SYM
ejpam-5330	159	46	fn	fn	PROPN
ejpam-5330	159	47	⊔	⊔	PROPN
ejpam-5330	159	48	gn	gn	PROPN
ejpam-5330	159	49	,	,	PUNCT
ejpam-5330	159	50	0	0	NUM
ejpam-5330	159	51	,	,	PUNCT
ejpam-5330	159	52	otherwise	otherwise	ADV
ejpam-5330	159	53	,	,	PUNCT
ejpam-5330	159	54	τn2(tn	τn2(tn	PUNCT
ejpam-5330	159	55	)	)	PUNCT
ejpam-5330	160	1	=	=	PUNCT
ejpam-5330	160	2			NUM
ejpam-5330	160	3	1	1	NUM
ejpam-5330	160	4	,	,	PUNCT
ejpam-5330	160	5	if	if	SCONJ
ejpam-5330	160	6	tn	tn	PROPN
ejpam-5330	160	7	∈	∈	PROPN
ejpam-5330	160	8	{	{	PUNCT
ejpam-5330	160	9	φ	φ	NOUN
ejpam-5330	160	10	,	,	PUNCT
ejpam-5330	160	11	ñ	ñ	PROPN
ejpam-5330	160	12	}	}	PUNCT
ejpam-5330	160	13	,	,	PUNCT
ejpam-5330	160	14	1	1	NUM
ejpam-5330	160	15	4	4	NUM
ejpam-5330	160	16	,	,	PUNCT
ejpam-5330	160	17	if	if	SCONJ
ejpam-5330	160	18	tn	tn	NUM
ejpam-5330	160	19	=	=	SYM
ejpam-5330	160	20	fn	fn	NOUN
ejpam-5330	160	21	,	,	PUNCT
ejpam-5330	160	22	1	1	NUM
ejpam-5330	160	23	2	2	NUM
ejpam-5330	160	24	,	,	PUNCT
ejpam-5330	160	25	if	if	SCONJ
ejpam-5330	160	26	tn	tn	NUM
ejpam-5330	160	27	=	=	SYM
ejpam-5330	160	28	gn	gn	PROPN
ejpam-5330	160	29	,	,	PUNCT
ejpam-5330	160	30	1	1	NUM
ejpam-5330	160	31	2	2	NUM
ejpam-5330	160	32	,	,	PUNCT
ejpam-5330	160	33	if	if	SCONJ
ejpam-5330	160	34	tn	tn	NUM
ejpam-5330	160	35	=	=	SYM
ejpam-5330	160	36	fn	fn	NOUN
ejpam-5330	160	37	⊓	⊓	PROPN
ejpam-5330	160	38	gn	gn	PROPN
ejpam-5330	160	39	,	,	PUNCT
ejpam-5330	160	40	1	1	NUM
ejpam-5330	160	41	4	4	NUM
ejpam-5330	160	42	,	,	PUNCT
ejpam-5330	160	43	if	if	SCONJ
ejpam-5330	160	44	tn	tn	NUM
ejpam-5330	160	45	=	=	SYM
ejpam-5330	160	46	fn	fn	PROPN
ejpam-5330	160	47	⊔	⊔	PROPN
ejpam-5330	160	48	gn	gn	PROPN
ejpam-5330	160	49	,	,	PUNCT
ejpam-5330	160	50	0	0	NUM
ejpam-5330	160	51	,	,	PUNCT
ejpam-5330	160	52	otherwise	otherwise	ADV
ejpam-5330	160	53	.	.	PUNCT
ejpam-5330	161	1	thus	thus	ADV
ejpam-5330	161	2	,	,	PUNCT
ejpam-5330	161	3	hn	hn	PROPN
ejpam-5330	161	4	is	be	AUX
ejpam-5330	161	5	1	1	NUM
ejpam-5330	161	6	4	4	NUM
ejpam-5330	161	7	-fuzzy	-fuzzy	NOUN
ejpam-5330	161	8	soft	soft	ADJ
ejpam-5330	161	9	semi	semi	ADJ
ejpam-5330	161	10	-	-	ADJ
ejpam-5330	161	11	closed	closed	ADJ
ejpam-5330	161	12	and	and	CCONJ
ejpam-5330	161	13	1	1	NUM
ejpam-5330	161	14	4	4	NUM
ejpam-5330	161	15	-fuzzy	-fuzzy	NOUN
ejpam-5330	161	16	soft	soft	ADJ
ejpam-5330	161	17	β	β	NOUN
ejpam-5330	161	18	-	-	VERB
ejpam-5330	161	19	closed	closed	ADJ
ejpam-5330	161	20	,	,	PUNCT
ejpam-5330	161	21	but	but	CCONJ
ejpam-5330	161	22	it	it	PRON
ejpam-5330	161	23	is	be	AUX
ejpam-5330	161	24	neither	neither	CCONJ
ejpam-5330	161	25	1	1	NUM
ejpam-5330	161	26	4	4	NUM
ejpam-5330	161	27	-fuzzy	-fuzzy	NOUN
ejpam-5330	161	28	soft	soft	ADJ
ejpam-5330	161	29	α	α	NOUN
ejpam-5330	161	30	-	-	PUNCT
ejpam-5330	161	31	closed	closed	ADJ
ejpam-5330	161	32	nor	nor	CCONJ
ejpam-5330	161	33	1	1	NUM
ejpam-5330	161	34	4	4	NUM
ejpam-5330	161	35	-fuzzy	-fuzzy	NOUN
ejpam-5330	161	36	soft	soft	ADJ
ejpam-5330	161	37	pre	pre	ADJ
ejpam-5330	161	38	-	-	ADJ
ejpam-5330	161	39	closed	closed	ADJ
ejpam-5330	161	40	.	.	PUNCT
ejpam-5330	162	1	w.	w.	PROPN
ejpam-5330	162	2	alqurashi	alqurashi	PROPN
ejpam-5330	162	3	,	,	PUNCT
ejpam-5330	162	4	i.	i.	PROPN
ejpam-5330	162	5	m.	m.	PROPN
ejpam-5330	162	6	taha	taha	PROPN
ejpam-5330	162	7	/	/	PUNCT
ejpam-5330	162	8	eur	eur	PROPN
ejpam-5330	162	9	.	.	PUNCT
ejpam-5330	163	1	j.	j.	PROPN
ejpam-5330	163	2	pure	pure	PROPN
ejpam-5330	163	3	appl	appl	PROPN
ejpam-5330	163	4	.	.	PROPN
ejpam-5330	163	5	math	math	PROPN
ejpam-5330	163	6	,	,	PUNCT
ejpam-5330	163	7	17	17	NUM
ejpam-5330	163	8	(	(	PUNCT
ejpam-5330	163	9	4	4	NUM
ejpam-5330	163	10	)	)	PUNCT
ejpam-5330	163	11	(	(	PUNCT
ejpam-5330	163	12	2024	2024	NUM
ejpam-5330	163	13	)	)	PUNCT
ejpam-5330	163	14	,	,	PUNCT
ejpam-5330	163	15	4112	4112	NUM
ejpam-5330	163	16	-	-	SYM
ejpam-5330	163	17	4134	4134	NUM
ejpam-5330	163	18	4118	4118	NUM
ejpam-5330	163	19	example	example	NOUN
ejpam-5330	164	1	2	2	NUM
ejpam-5330	164	2	.	.	X
ejpam-5330	164	3	let	let	VERB
ejpam-5330	164	4	w	w	VERB
ejpam-5330	164	5	=	=	PUNCT
ejpam-5330	164	6	{	{	PUNCT
ejpam-5330	164	7	w1	w1	NOUN
ejpam-5330	164	8	,	,	PUNCT
ejpam-5330	164	9	w2	w2	NOUN
ejpam-5330	164	10	}	}	PUNCT
ejpam-5330	164	11	,	,	PUNCT
ejpam-5330	164	12	n	n	NOUN
ejpam-5330	164	13	=	=	SYM
ejpam-5330	164	14	{	{	PUNCT
ejpam-5330	164	15	n1	n1	NOUN
ejpam-5330	164	16	,	,	PUNCT
ejpam-5330	164	17	n2	n2	ADJ
ejpam-5330	164	18	}	}	PUNCT
ejpam-5330	164	19	,	,	PUNCT
ejpam-5330	164	20	and	and	CCONJ
ejpam-5330	164	21	define	define	VERB
ejpam-5330	164	22	fn	fn	NOUN
ejpam-5330	164	23	,	,	PUNCT
ejpam-5330	164	24	hn	hn	PROPN
ejpam-5330	164	25	∈	∈	PROPN
ejpam-5330	164	26	˜(w	˜(w	PROPN
ejpam-5330	164	27	,	,	PUNCT
ejpam-5330	164	28	n	n	CCONJ
ejpam-5330	164	29	)	)	PUNCT
ejpam-5330	164	30	as	as	SCONJ
ejpam-5330	164	31	follows	follow	VERB
ejpam-5330	164	32	:	:	PUNCT
ejpam-5330	164	33	fn	fn	NOUN
ejpam-5330	164	34	=	=	SYM
ejpam-5330	164	35	{	{	PUNCT
ejpam-5330	164	36	(	(	PUNCT
ejpam-5330	164	37	n1	n1	NOUN
ejpam-5330	164	38	,	,	PUNCT
ejpam-5330	164	39	{	{	PUNCT
ejpam-5330	164	40	w1	w1	NOUN
ejpam-5330	164	41	0.4	0.4	NUM
ejpam-5330	164	42	,	,	PUNCT
ejpam-5330	164	43	w2	w2	NOUN
ejpam-5330	164	44	0.5	0.5	NUM
ejpam-5330	164	45	}	}	PUNCT
ejpam-5330	164	46	)	)	PUNCT
ejpam-5330	164	47	,	,	PUNCT
ejpam-5330	164	48	(	(	PUNCT
ejpam-5330	164	49	n2	n2	ADJ
ejpam-5330	164	50	,	,	PUNCT
ejpam-5330	164	51	{	{	PUNCT
ejpam-5330	164	52	w1	w1	NOUN
ejpam-5330	164	53	0.4	0.4	NUM
ejpam-5330	164	54	,	,	PUNCT
ejpam-5330	164	55	w2	w2	NOUN
ejpam-5330	164	56	0.5	0.5	NUM
ejpam-5330	164	57	}	}	PUNCT
ejpam-5330	164	58	)	)	PUNCT
ejpam-5330	164	59	}	}	PUNCT
ejpam-5330	164	60	,	,	PUNCT
ejpam-5330	164	61	hn	hn	PROPN
ejpam-5330	164	62	=	=	PRON
ejpam-5330	164	63	{	{	PUNCT
ejpam-5330	164	64	(	(	PUNCT
ejpam-5330	164	65	n1	n1	NOUN
ejpam-5330	164	66	,	,	PUNCT
ejpam-5330	164	67	{	{	PUNCT
ejpam-5330	164	68	w1	w1	NOUN
ejpam-5330	164	69	0.7	0.7	NUM
ejpam-5330	164	70	,	,	PUNCT
ejpam-5330	164	71	w2	w2	NOUN
ejpam-5330	164	72	0.6	0.6	NUM
ejpam-5330	164	73	}	}	PUNCT
ejpam-5330	164	74	)	)	PUNCT
ejpam-5330	164	75	,	,	PUNCT
ejpam-5330	164	76	(	(	PUNCT
ejpam-5330	164	77	n2	n2	ADJ
ejpam-5330	164	78	,	,	PUNCT
ejpam-5330	164	79	{	{	PUNCT
ejpam-5330	164	80	w1	w1	NOUN
ejpam-5330	164	81	0.7	0.7	NUM
ejpam-5330	164	82	,	,	PUNCT
ejpam-5330	164	83	w2	w2	NOUN
ejpam-5330	164	84	0.6	0.6	NUM
ejpam-5330	164	85	}	}	PUNCT
ejpam-5330	164	86	)	)	PUNCT
ejpam-5330	164	87	}	}	PUNCT
ejpam-5330	164	88	.	.	PUNCT
ejpam-5330	165	1	define	define	VERB
ejpam-5330	165	2	fuzzy	fuzzy	ADJ
ejpam-5330	165	3	soft	soft	ADJ
ejpam-5330	165	4	topology	topology	NOUN
ejpam-5330	165	5	τn	τn	NOUN
ejpam-5330	165	6	:	:	PUNCT
ejpam-5330	165	7	n	n	CCONJ
ejpam-5330	165	8	−→	−→	NOUN
ejpam-5330	166	1	[	[	X
ejpam-5330	166	2	0	0	NUM
ejpam-5330	166	3	,	,	PUNCT
ejpam-5330	166	4	1	1	NUM
ejpam-5330	166	5	]	]	PUNCT
ejpam-5330	166	6	˜(w	˜(w	PROPN
ejpam-5330	166	7	,	,	PUNCT
ejpam-5330	166	8	n	n	CCONJ
ejpam-5330	166	9	)	)	PUNCT
ejpam-5330	166	10	as	as	SCONJ
ejpam-5330	166	11	follows	follow	VERB
ejpam-5330	166	12	:	:	PUNCT
ejpam-5330	166	13	τn1(tn	τn1(tn	PUNCT
ejpam-5330	166	14	)	)	PUNCT
ejpam-5330	167	1	=	=	PUNCT
ejpam-5330	168	1			NOUN
ejpam-5330	168	2	1	1	NUM
ejpam-5330	168	3	,	,	PUNCT
ejpam-5330	168	4	if	if	SCONJ
ejpam-5330	168	5	tn	tn	PROPN
ejpam-5330	168	6	∈	∈	PROPN
ejpam-5330	168	7	{	{	PUNCT
ejpam-5330	168	8	φ	φ	NOUN
ejpam-5330	168	9	,	,	PUNCT
ejpam-5330	168	10	ñ	ñ	PROPN
ejpam-5330	168	11	}	}	PUNCT
ejpam-5330	168	12	,	,	PUNCT
ejpam-5330	168	13	1	1	NUM
ejpam-5330	168	14	3	3	NUM
ejpam-5330	168	15	,	,	PUNCT
ejpam-5330	168	16	if	if	SCONJ
ejpam-5330	168	17	tn	tn	NUM
ejpam-5330	168	18	=	=	SYM
ejpam-5330	168	19	fn	fn	NOUN
ejpam-5330	168	20	,	,	PUNCT
ejpam-5330	168	21	0	0	NUM
ejpam-5330	168	22	,	,	PUNCT
ejpam-5330	168	23	otherwise	otherwise	ADV
ejpam-5330	168	24	,	,	PUNCT
ejpam-5330	168	25	τn2(tn	τn2(tn	PUNCT
ejpam-5330	168	26	)	)	PUNCT
ejpam-5330	169	1	=	=	PUNCT
ejpam-5330	169	2			NOUN
ejpam-5330	169	3	1	1	NUM
ejpam-5330	169	4	,	,	PUNCT
ejpam-5330	169	5	if	if	SCONJ
ejpam-5330	169	6	tn	tn	PROPN
ejpam-5330	169	7	∈	∈	PROPN
ejpam-5330	169	8	{	{	PUNCT
ejpam-5330	169	9	φ	φ	NOUN
ejpam-5330	169	10	,	,	PUNCT
ejpam-5330	169	11	ñ	ñ	PROPN
ejpam-5330	169	12	}	}	PUNCT
ejpam-5330	169	13	,	,	PUNCT
ejpam-5330	169	14	1	1	NUM
ejpam-5330	169	15	2	2	NUM
ejpam-5330	169	16	,	,	PUNCT
ejpam-5330	169	17	if	if	SCONJ
ejpam-5330	169	18	tn	tn	NUM
ejpam-5330	169	19	=	=	SYM
ejpam-5330	169	20	fn	fn	NOUN
ejpam-5330	169	21	,	,	PUNCT
ejpam-5330	169	22	0	0	NUM
ejpam-5330	169	23	,	,	PUNCT
ejpam-5330	169	24	otherwise	otherwise	ADV
ejpam-5330	169	25	.	.	PUNCT
ejpam-5330	170	1	thus	thus	ADV
ejpam-5330	170	2	,	,	PUNCT
ejpam-5330	170	3	hn	hn	PROPN
ejpam-5330	170	4	is	be	AUX
ejpam-5330	170	5	1	1	NUM
ejpam-5330	170	6	3	3	NUM
ejpam-5330	170	7	-fuzzy	-fuzzy	NOUN
ejpam-5330	170	8	soft	soft	ADJ
ejpam-5330	170	9	pre	pre	ADJ
ejpam-5330	170	10	-	-	ADJ
ejpam-5330	170	11	closed	closed	ADJ
ejpam-5330	170	12	and	and	CCONJ
ejpam-5330	170	13	1	1	NUM
ejpam-5330	170	14	3	3	NUM
ejpam-5330	170	15	-fuzzy	-fuzzy	NOUN
ejpam-5330	170	16	soft	soft	ADJ
ejpam-5330	170	17	β	β	NOUN
ejpam-5330	170	18	-	-	VERB
ejpam-5330	170	19	closed	closed	ADJ
ejpam-5330	170	20	,	,	PUNCT
ejpam-5330	170	21	but	but	CCONJ
ejpam-5330	170	22	it	it	PRON
ejpam-5330	170	23	is	be	AUX
ejpam-5330	170	24	neither	neither	CCONJ
ejpam-5330	170	25	1	1	NUM
ejpam-5330	170	26	3	3	NUM
ejpam-5330	170	27	-fuzzy	-fuzzy	NOUN
ejpam-5330	170	28	soft	soft	ADJ
ejpam-5330	170	29	semi	semi	ADJ
ejpam-5330	170	30	-	-	ADJ
ejpam-5330	170	31	closed	closed	ADJ
ejpam-5330	170	32	nor	nor	CCONJ
ejpam-5330	170	33	1	1	NUM
ejpam-5330	170	34	3	3	NUM
ejpam-5330	170	35	-fuzzy	-fuzzy	NOUN
ejpam-5330	170	36	soft	soft	ADJ
ejpam-5330	170	37	α	α	NOUN
ejpam-5330	170	38	-	-	PUNCT
ejpam-5330	170	39	closed	closed	ADJ
ejpam-5330	170	40	.	.	PUNCT
ejpam-5330	171	1	definition	definition	NOUN
ejpam-5330	171	2	13	13	NUM
ejpam-5330	171	3	.	.	PUNCT
ejpam-5330	172	1	in	in	ADP
ejpam-5330	172	2	an	an	DET
ejpam-5330	172	3	fsts	fst	NOUN
ejpam-5330	172	4	(	(	PUNCT
ejpam-5330	172	5	w	w	NOUN
ejpam-5330	172	6	,	,	PUNCT
ejpam-5330	172	7	τn	τn	NOUN
ejpam-5330	172	8	)	)	PUNCT
ejpam-5330	172	9	,	,	PUNCT
ejpam-5330	172	10	for	for	ADP
ejpam-5330	172	11	each	each	DET
ejpam-5330	172	12	hc	hc	PROPN
ejpam-5330	172	13	∈	∈	PROPN
ejpam-5330	172	14	˜(w	˜(w	PROPN
ejpam-5330	172	15	,	,	PUNCT
ejpam-5330	172	16	n	n	CCONJ
ejpam-5330	172	17	)	)	PUNCT
ejpam-5330	172	18	,	,	PUNCT
ejpam-5330	172	19	n	n	PROPN
ejpam-5330	172	20	∈	∈	PROPN
ejpam-5330	172	21	n	n	NOUN
ejpam-5330	172	22	,	,	PUNCT
ejpam-5330	172	23	and	and	CCONJ
ejpam-5330	172	24	r	r	NOUN
ejpam-5330	172	25	∈	∈	PROPN
ejpam-5330	172	26	i0	i0	PROPN
ejpam-5330	172	27	,	,	PUNCT
ejpam-5330	172	28	we	we	PRON
ejpam-5330	172	29	define	define	VERB
ejpam-5330	172	30	a	a	DET
ejpam-5330	172	31	fuzzy	fuzzy	ADJ
ejpam-5330	172	32	soft	soft	ADJ
ejpam-5330	172	33	α	α	NOUN
ejpam-5330	172	34	-	-	PUNCT
ejpam-5330	172	35	closure	closure	NOUN
ejpam-5330	172	36	operator	operator	NOUN
ejpam-5330	172	37	αcτ	αcτ	NOUN
ejpam-5330	172	38	:	:	PUNCT
ejpam-5330	172	39	n	n	X
ejpam-5330	172	40	×	×	PROPN
ejpam-5330	172	41	˜(w	˜(w	PROPN
ejpam-5330	172	42	,	,	PUNCT
ejpam-5330	172	43	n)×	n)×	PRON
ejpam-5330	172	44	i	i	PROPN
ejpam-5330	172	45	◦	◦	PROPN
ejpam-5330	172	46	→	→	SYM
ejpam-5330	172	47	˜(w	˜(w	PROPN
ejpam-5330	172	48	,	,	PUNCT
ejpam-5330	172	49	n	n	CCONJ
ejpam-5330	172	50	)	)	PUNCT
ejpam-5330	172	51	as	as	SCONJ
ejpam-5330	172	52	follows	follow	VERB
ejpam-5330	172	53	:	:	PUNCT
ejpam-5330	172	54	αcτ	αcτ	X
ejpam-5330	172	55	(	(	PUNCT
ejpam-5330	172	56	n	n	X
ejpam-5330	172	57	,	,	PUNCT
ejpam-5330	172	58	hc	hc	PROPN
ejpam-5330	172	59	,	,	PUNCT
ejpam-5330	172	60	r	r	NOUN
ejpam-5330	172	61	)	)	PUNCT
ejpam-5330	172	62	=	=	SYM
ejpam-5330	172	63	⊓	⊓	NOUN
ejpam-5330	172	64	{	{	PUNCT
ejpam-5330	172	65	fa	fa	PROPN
ejpam-5330	172	66	∈	∈	PROPN
ejpam-5330	172	67	˜(w	˜(w	PROPN
ejpam-5330	172	68	,	,	PUNCT
ejpam-5330	172	69	n	n	CCONJ
ejpam-5330	172	70	)	)	PUNCT
ejpam-5330	172	71	:	:	PUNCT
ejpam-5330	172	72	hc	hc	ADP
ejpam-5330	172	73	⊑	⊑	X
ejpam-5330	172	74	fa	fa	PROPN
ejpam-5330	172	75	,	,	PUNCT
ejpam-5330	172	76	fa	fa	PROPN
ejpam-5330	172	77	is	be	AUX
ejpam-5330	172	78	r	r	NOUN
ejpam-5330	172	79	-	-	PUNCT
ejpam-5330	172	80	fuzzy	fuzzy	ADJ
ejpam-5330	172	81	soft	soft	ADJ
ejpam-5330	172	82	α	α	NOUN
ejpam-5330	172	83	-	-	VERB
ejpam-5330	172	84	closed	closed	ADJ
ejpam-5330	172	85	}	}	PUNCT
ejpam-5330	172	86	.	.	PUNCT
ejpam-5330	173	1	theorem	theorem	NOUN
ejpam-5330	173	2	1	1	NUM
ejpam-5330	173	3	.	.	PUNCT
ejpam-5330	174	1	in	in	ADP
ejpam-5330	174	2	an	an	DET
ejpam-5330	174	3	fsts	fst	NOUN
ejpam-5330	174	4	(	(	PUNCT
ejpam-5330	174	5	w	w	NOUN
ejpam-5330	174	6	,	,	PUNCT
ejpam-5330	174	7	τn	τn	NOUN
ejpam-5330	174	8	)	)	PUNCT
ejpam-5330	174	9	,	,	PUNCT
ejpam-5330	174	10	for	for	ADP
ejpam-5330	174	11	each	each	DET
ejpam-5330	174	12	gb	gb	NOUN
ejpam-5330	174	13	,	,	PUNCT
ejpam-5330	174	14	hc	hc	PROPN
ejpam-5330	174	15	∈	∈	PROPN
ejpam-5330	174	16	˜(w	˜(w	PROPN
ejpam-5330	174	17	,	,	PUNCT
ejpam-5330	174	18	n	n	CCONJ
ejpam-5330	174	19	)	)	PUNCT
ejpam-5330	174	20	,	,	PUNCT
ejpam-5330	174	21	n	n	PROPN
ejpam-5330	174	22	∈	∈	PROPN
ejpam-5330	174	23	n	n	NOUN
ejpam-5330	174	24	,	,	PUNCT
ejpam-5330	174	25	and	and	CCONJ
ejpam-5330	174	26	r	r	NOUN
ejpam-5330	174	27	∈	∈	PROPN
ejpam-5330	174	28	i0	i0	PROPN
ejpam-5330	174	29	,	,	PUNCT
ejpam-5330	174	30	the	the	DET
ejpam-5330	174	31	operator	operator	NOUN
ejpam-5330	174	32	αcτ	αcτ	VERB
ejpam-5330	174	33	:	:	PUNCT
ejpam-5330	174	34	n	n	X
ejpam-5330	174	35	×	×	PROPN
ejpam-5330	174	36	˜(w	˜(w	PROPN
ejpam-5330	174	37	,	,	PUNCT
ejpam-5330	174	38	n)×	n)×	PRON
ejpam-5330	174	39	i	i	PROPN
ejpam-5330	174	40	◦	◦	PROPN
ejpam-5330	174	41	→	→	SYM
ejpam-5330	174	42	˜(w	˜(w	PROPN
ejpam-5330	174	43	,	,	PUNCT
ejpam-5330	174	44	n	n	CCONJ
ejpam-5330	174	45	)	)	PUNCT
ejpam-5330	174	46	satisfies	satisfy	VERB
ejpam-5330	174	47	the	the	DET
ejpam-5330	174	48	following	follow	VERB
ejpam-5330	174	49	properties	property	NOUN
ejpam-5330	174	50	.	.	PUNCT
ejpam-5330	175	1	(	(	PUNCT
ejpam-5330	175	2	1	1	X
ejpam-5330	175	3	)	)	PUNCT
ejpam-5330	175	4	αcτ	αcτ	NOUN
ejpam-5330	175	5	(	(	PUNCT
ejpam-5330	175	6	n	n	CCONJ
ejpam-5330	175	7	,	,	PUNCT
ejpam-5330	175	8	φ	φ	NOUN
ejpam-5330	175	9	,	,	PUNCT
ejpam-5330	175	10	r	r	NOUN
ejpam-5330	175	11	)	)	PUNCT
ejpam-5330	175	12	=	=	SYM
ejpam-5330	176	1	φ	φ	PROPN
ejpam-5330	176	2	.	.	PUNCT
ejpam-5330	177	1	(	(	PUNCT
ejpam-5330	177	2	2	2	X
ejpam-5330	177	3	)	)	PUNCT
ejpam-5330	177	4	hc	hc	ADP
ejpam-5330	177	5	⊑	⊑	X
ejpam-5330	177	6	αcτ	αcτ	X
ejpam-5330	177	7	(	(	PUNCT
ejpam-5330	177	8	n	n	X
ejpam-5330	177	9	,	,	PUNCT
ejpam-5330	177	10	hc	hc	PROPN
ejpam-5330	177	11	,	,	PUNCT
ejpam-5330	177	12	r	r	NOUN
ejpam-5330	177	13	)	)	PUNCT
ejpam-5330	177	14	⊑	⊑	PROPN
ejpam-5330	177	15	cτ	cτ	PROPN
ejpam-5330	177	16	(	(	PUNCT
ejpam-5330	177	17	n	n	X
ejpam-5330	177	18	,	,	PUNCT
ejpam-5330	177	19	hc	hc	PROPN
ejpam-5330	177	20	,	,	PUNCT
ejpam-5330	177	21	r	r	NOUN
ejpam-5330	177	22	)	)	PUNCT
ejpam-5330	177	23	.	.	PUNCT
ejpam-5330	178	1	(	(	PUNCT
ejpam-5330	178	2	3	3	X
ejpam-5330	178	3	)	)	PUNCT
ejpam-5330	178	4	αcτ	αcτ	NOUN
ejpam-5330	178	5	(	(	PUNCT
ejpam-5330	178	6	n	n	X
ejpam-5330	178	7	,	,	PUNCT
ejpam-5330	178	8	hc	hc	PROPN
ejpam-5330	178	9	,	,	PUNCT
ejpam-5330	178	10	r	r	NOUN
ejpam-5330	178	11	)	)	PUNCT
ejpam-5330	178	12	⊑	⊑	X
ejpam-5330	178	13	αcτ	αcτ	X
ejpam-5330	178	14	(	(	PUNCT
ejpam-5330	178	15	n	n	CCONJ
ejpam-5330	178	16	,	,	PUNCT
ejpam-5330	178	17	gb	gb	ADJ
ejpam-5330	178	18	,	,	PUNCT
ejpam-5330	178	19	r	r	NOUN
ejpam-5330	178	20	)	)	PUNCT
ejpam-5330	178	21	if	if	SCONJ
ejpam-5330	178	22	,	,	PUNCT
ejpam-5330	178	23	hc	hc	PROPN
ejpam-5330	178	24	⊑	⊑	X
ejpam-5330	178	25	gb	gb	PROPN
ejpam-5330	178	26	.	.	PUNCT
ejpam-5330	179	1	(	(	PUNCT
ejpam-5330	179	2	4	4	X
ejpam-5330	179	3	)	)	PUNCT
ejpam-5330	179	4	αcτ	αcτ	NOUN
ejpam-5330	179	5	(	(	PUNCT
ejpam-5330	179	6	n	n	CCONJ
ejpam-5330	179	7	,	,	PUNCT
ejpam-5330	179	8	αcτ	αcτ	X
ejpam-5330	179	9	(	(	PUNCT
ejpam-5330	179	10	n	n	X
ejpam-5330	179	11	,	,	PUNCT
ejpam-5330	179	12	hc	hc	PROPN
ejpam-5330	179	13	,	,	PUNCT
ejpam-5330	179	14	r	r	NOUN
ejpam-5330	179	15	)	)	PUNCT
ejpam-5330	179	16	,	,	PUNCT
ejpam-5330	179	17	r	r	NOUN
ejpam-5330	179	18	)	)	PUNCT
ejpam-5330	179	19	=	=	NOUN
ejpam-5330	179	20	αcτ	αcτ	X
ejpam-5330	179	21	(	(	PUNCT
ejpam-5330	179	22	n	n	X
ejpam-5330	179	23	,	,	PUNCT
ejpam-5330	179	24	hc	hc	PROPN
ejpam-5330	179	25	,	,	PUNCT
ejpam-5330	179	26	r	r	NOUN
ejpam-5330	179	27	)	)	PUNCT
ejpam-5330	179	28	.	.	PUNCT
ejpam-5330	180	1	(	(	PUNCT
ejpam-5330	180	2	5	5	X
ejpam-5330	180	3	)	)	PUNCT
ejpam-5330	180	4	αcτ	αcτ	NOUN
ejpam-5330	180	5	(	(	PUNCT
ejpam-5330	180	6	n	n	X
ejpam-5330	180	7	,	,	PUNCT
ejpam-5330	180	8	hc	hc	PROPN
ejpam-5330	180	9	⊔	⊔	PROPN
ejpam-5330	180	10	gb	gb	PROPN
ejpam-5330	180	11	,	,	PUNCT
ejpam-5330	180	12	r	r	NOUN
ejpam-5330	180	13	)	)	PUNCT
ejpam-5330	180	14	⊒	⊒	NOUN
ejpam-5330	180	15	αcτ	αcτ	X
ejpam-5330	180	16	(	(	PUNCT
ejpam-5330	180	17	n	n	X
ejpam-5330	180	18	,	,	PUNCT
ejpam-5330	180	19	hc	hc	PROPN
ejpam-5330	180	20	,	,	PUNCT
ejpam-5330	180	21	r	r	NOUN
ejpam-5330	180	22	)	)	PUNCT
ejpam-5330	180	23	⊔	⊔	NOUN
ejpam-5330	180	24	αcτ	αcτ	NOUN
ejpam-5330	180	25	(	(	PUNCT
ejpam-5330	180	26	n	n	CCONJ
ejpam-5330	180	27	,	,	PUNCT
ejpam-5330	180	28	gb	gb	ADJ
ejpam-5330	180	29	,	,	PUNCT
ejpam-5330	180	30	r	r	NOUN
ejpam-5330	180	31	)	)	PUNCT
ejpam-5330	180	32	.	.	PUNCT
ejpam-5330	181	1	(	(	PUNCT
ejpam-5330	181	2	6	6	NUM
ejpam-5330	181	3	)	)	PUNCT
ejpam-5330	181	4	αcτ	αcτ	NOUN
ejpam-5330	181	5	(	(	PUNCT
ejpam-5330	181	6	n	n	X
ejpam-5330	181	7	,	,	PUNCT
ejpam-5330	181	8	hc	hc	PROPN
ejpam-5330	181	9	,	,	PUNCT
ejpam-5330	181	10	r	r	NOUN
ejpam-5330	181	11	)	)	PUNCT
ejpam-5330	181	12	=	=	SYM
ejpam-5330	182	1	hc	hc	PROPN
ejpam-5330	182	2	iff	iff	PROPN
ejpam-5330	182	3	hc	hc	PROPN
ejpam-5330	182	4	is	be	AUX
ejpam-5330	182	5	r	r	NOUN
ejpam-5330	182	6	-	-	PUNCT
ejpam-5330	182	7	fuzzy	fuzzy	ADJ
ejpam-5330	182	8	soft	soft	ADJ
ejpam-5330	182	9	α	α	NOUN
ejpam-5330	182	10	-	-	VERB
ejpam-5330	182	11	closed	closed	ADJ
ejpam-5330	182	12	.	.	PUNCT
ejpam-5330	183	1	(	(	PUNCT
ejpam-5330	183	2	7	7	X
ejpam-5330	183	3	)	)	PUNCT
ejpam-5330	183	4	αcτ	αcτ	NOUN
ejpam-5330	183	5	(	(	PUNCT
ejpam-5330	183	6	n	n	CCONJ
ejpam-5330	183	7	,	,	PUNCT
ejpam-5330	183	8	cτ	cτ	INTJ
ejpam-5330	183	9	(	(	PUNCT
ejpam-5330	183	10	n	n	X
ejpam-5330	183	11	,	,	PUNCT
ejpam-5330	183	12	hc	hc	PROPN
ejpam-5330	183	13	,	,	PUNCT
ejpam-5330	183	14	r	r	NOUN
ejpam-5330	183	15	)	)	PUNCT
ejpam-5330	183	16	,	,	PUNCT
ejpam-5330	183	17	r	r	NOUN
ejpam-5330	183	18	)	)	PUNCT
ejpam-5330	183	19	=	=	NOUN
ejpam-5330	183	20	cτ	cτ	INTJ
ejpam-5330	183	21	(	(	PUNCT
ejpam-5330	183	22	n	n	X
ejpam-5330	183	23	,	,	PUNCT
ejpam-5330	183	24	hc	hc	PROPN
ejpam-5330	183	25	,	,	PUNCT
ejpam-5330	183	26	r	r	NOUN
ejpam-5330	183	27	)	)	PUNCT
ejpam-5330	183	28	.	.	PUNCT
ejpam-5330	184	1	proof	proof	NOUN
ejpam-5330	184	2	.	.	PUNCT
ejpam-5330	185	1	(	(	PUNCT
ejpam-5330	185	2	1	1	NUM
ejpam-5330	185	3	)	)	PUNCT
ejpam-5330	185	4	,	,	PUNCT
ejpam-5330	185	5	(	(	PUNCT
ejpam-5330	185	6	2	2	NUM
ejpam-5330	185	7	)	)	PUNCT
ejpam-5330	185	8	,	,	PUNCT
ejpam-5330	185	9	(	(	PUNCT
ejpam-5330	185	10	3	3	NUM
ejpam-5330	185	11	)	)	PUNCT
ejpam-5330	185	12	,	,	PUNCT
ejpam-5330	185	13	and	and	CCONJ
ejpam-5330	185	14	(	(	PUNCT
ejpam-5330	185	15	6	6	NUM
ejpam-5330	185	16	)	)	PUNCT
ejpam-5330	185	17	are	be	AUX
ejpam-5330	185	18	easily	easily	ADV
ejpam-5330	185	19	proved	prove	VERB
ejpam-5330	185	20	from	from	ADP
ejpam-5330	185	21	definition	definition	NOUN
ejpam-5330	185	22	13	13	NUM
ejpam-5330	185	23	.	.	PUNCT
ejpam-5330	186	1	(	(	PUNCT
ejpam-5330	186	2	4	4	NUM
ejpam-5330	186	3	)	)	PUNCT
ejpam-5330	186	4	from	from	ADP
ejpam-5330	186	5	(	(	PUNCT
ejpam-5330	186	6	2	2	NUM
ejpam-5330	186	7	)	)	PUNCT
ejpam-5330	186	8	and	and	CCONJ
ejpam-5330	186	9	(	(	PUNCT
ejpam-5330	186	10	3	3	NUM
ejpam-5330	186	11	)	)	PUNCT
ejpam-5330	186	12	,	,	PUNCT
ejpam-5330	186	13	αcτ	αcτ	X
ejpam-5330	186	14	(	(	PUNCT
ejpam-5330	186	15	n	n	X
ejpam-5330	186	16	,	,	PUNCT
ejpam-5330	186	17	hc	hc	PROPN
ejpam-5330	186	18	,	,	PUNCT
ejpam-5330	186	19	r	r	NOUN
ejpam-5330	186	20	)	)	PUNCT
ejpam-5330	186	21	⊑	⊑	X
ejpam-5330	186	22	αcτ	αcτ	X
ejpam-5330	186	23	(	(	PUNCT
ejpam-5330	186	24	n	n	CCONJ
ejpam-5330	186	25	,	,	PUNCT
ejpam-5330	186	26	αcτ	αcτ	X
ejpam-5330	186	27	(	(	PUNCT
ejpam-5330	186	28	n	n	X
ejpam-5330	186	29	,	,	PUNCT
ejpam-5330	186	30	hc	hc	PROPN
ejpam-5330	186	31	,	,	PUNCT
ejpam-5330	186	32	r	r	NOUN
ejpam-5330	186	33	)	)	PUNCT
ejpam-5330	186	34	,	,	PUNCT
ejpam-5330	186	35	r	r	NOUN
ejpam-5330	186	36	)	)	PUNCT
ejpam-5330	186	37	.	.	PUNCT
ejpam-5330	187	1	now	now	ADV
ejpam-5330	187	2	,	,	PUNCT
ejpam-5330	187	3	we	we	PRON
ejpam-5330	187	4	show	show	VERB
ejpam-5330	187	5	that	that	SCONJ
ejpam-5330	187	6	αcτ	αcτ	NOUN
ejpam-5330	187	7	(	(	PUNCT
ejpam-5330	187	8	n	n	X
ejpam-5330	187	9	,	,	PUNCT
ejpam-5330	187	10	hc	hc	PROPN
ejpam-5330	187	11	,	,	PUNCT
ejpam-5330	187	12	r	r	NOUN
ejpam-5330	187	13	)	)	PUNCT
ejpam-5330	187	14	⊒	⊒	NOUN
ejpam-5330	187	15	αcτ	αcτ	X
ejpam-5330	187	16	(	(	PUNCT
ejpam-5330	187	17	n	n	CCONJ
ejpam-5330	187	18	,	,	PUNCT
ejpam-5330	187	19	αcτ	αcτ	X
ejpam-5330	187	20	(	(	PUNCT
ejpam-5330	187	21	n	n	X
ejpam-5330	187	22	,	,	PUNCT
ejpam-5330	187	23	hc	hc	PROPN
ejpam-5330	187	24	,	,	PUNCT
ejpam-5330	187	25	r	r	NOUN
ejpam-5330	187	26	)	)	PUNCT
ejpam-5330	187	27	,	,	PUNCT
ejpam-5330	187	28	r	r	NOUN
ejpam-5330	187	29	)	)	PUNCT
ejpam-5330	187	30	.	.	PUNCT
ejpam-5330	187	31	suppose	suppose	VERB
ejpam-5330	187	32	that	that	SCONJ
ejpam-5330	187	33	αcτ	αcτ	NOUN
ejpam-5330	187	34	(	(	PUNCT
ejpam-5330	187	35	n	n	X
ejpam-5330	187	36	,	,	PUNCT
ejpam-5330	187	37	hc	hc	PROPN
ejpam-5330	187	38	,	,	PUNCT
ejpam-5330	187	39	r	r	NOUN
ejpam-5330	187	40	)	)	PUNCT
ejpam-5330	187	41	does	do	AUX
ejpam-5330	187	42	not	not	PART
ejpam-5330	187	43	contain	contain	VERB
ejpam-5330	187	44	αcτ	αcτ	NOUN
ejpam-5330	187	45	(	(	PUNCT
ejpam-5330	187	46	n	n	CCONJ
ejpam-5330	187	47	,	,	PUNCT
ejpam-5330	187	48	αcτ	αcτ	X
ejpam-5330	187	49	(	(	PUNCT
ejpam-5330	187	50	n	n	X
ejpam-5330	187	51	,	,	PUNCT
ejpam-5330	187	52	hc	hc	PROPN
ejpam-5330	187	53	,	,	PUNCT
ejpam-5330	187	54	r	r	NOUN
ejpam-5330	187	55	)	)	PUNCT
ejpam-5330	187	56	,	,	PUNCT
ejpam-5330	187	57	r	r	NOUN
ejpam-5330	187	58	)	)	PUNCT
ejpam-5330	187	59	,	,	PUNCT
ejpam-5330	187	60	then	then	ADV
ejpam-5330	187	61	there	there	PRON
ejpam-5330	187	62	is	be	VERB
ejpam-5330	187	63	w	w	NOUN
ejpam-5330	187	64	∈w	∈w	NOUN
ejpam-5330	187	65	and	and	CCONJ
ejpam-5330	187	66	s	s	NOUN
ejpam-5330	187	67	∈	∈	PROPN
ejpam-5330	187	68	(	(	PUNCT
ejpam-5330	187	69	0	0	NUM
ejpam-5330	187	70	,	,	PUNCT
ejpam-5330	187	71	1	1	NUM
ejpam-5330	187	72	)	)	PUNCT
ejpam-5330	187	73	,	,	PUNCT
ejpam-5330	188	1	such	such	ADJ
ejpam-5330	188	2	that	that	SCONJ
ejpam-5330	188	3	αcτ	αcτ	NOUN
ejpam-5330	188	4	(	(	PUNCT
ejpam-5330	188	5	n	n	X
ejpam-5330	188	6	,	,	PUNCT
ejpam-5330	188	7	hc	hc	PROPN
ejpam-5330	188	8	,	,	PUNCT
ejpam-5330	188	9	r)(n)(w	r)(n)(w	PROPN
ejpam-5330	188	10	)	)	PUNCT
ejpam-5330	188	11	<	<	X
ejpam-5330	188	12	s	s	X
ejpam-5330	188	13	<	<	X
ejpam-5330	188	14	αcτ	αcτ	X
ejpam-5330	188	15	(	(	PUNCT
ejpam-5330	188	16	n	n	CCONJ
ejpam-5330	188	17	,	,	PUNCT
ejpam-5330	188	18	αcτ	αcτ	X
ejpam-5330	188	19	(	(	PUNCT
ejpam-5330	188	20	n	n	X
ejpam-5330	188	21	,	,	PUNCT
ejpam-5330	188	22	hc	hc	PROPN
ejpam-5330	188	23	,	,	PUNCT
ejpam-5330	188	24	r	r	NOUN
ejpam-5330	188	25	)	)	PUNCT
ejpam-5330	188	26	,	,	PUNCT
ejpam-5330	188	27	r)(n)(w	r)(n)(w	PROPN
ejpam-5330	188	28	)	)	PUNCT
ejpam-5330	188	29	.	.	PUNCT
ejpam-5330	189	1	(	(	PUNCT
ejpam-5330	189	2	a	a	X
ejpam-5330	189	3	)	)	PUNCT
ejpam-5330	189	4	since	since	SCONJ
ejpam-5330	189	5	αcτ	αcτ	X
ejpam-5330	189	6	(	(	PUNCT
ejpam-5330	189	7	n	n	X
ejpam-5330	189	8	,	,	PUNCT
ejpam-5330	189	9	hc	hc	PROPN
ejpam-5330	189	10	,	,	PUNCT
ejpam-5330	189	11	r)(n)(w	r)(n)(w	PROPN
ejpam-5330	189	12	)	)	PUNCT
ejpam-5330	189	13	<	<	X
ejpam-5330	189	14	s	s	X
ejpam-5330	189	15	,	,	PUNCT
ejpam-5330	189	16	by	by	ADP
ejpam-5330	189	17	the	the	DET
ejpam-5330	189	18	definition	definition	NOUN
ejpam-5330	189	19	of	of	ADP
ejpam-5330	189	20	αcτ	αcτ	NOUN
ejpam-5330	189	21	,	,	PUNCT
ejpam-5330	189	22	there	there	PRON
ejpam-5330	189	23	is	be	VERB
ejpam-5330	189	24	gb	gb	ADP
ejpam-5330	189	25	as	as	ADP
ejpam-5330	189	26	an	an	DET
ejpam-5330	189	27	r	r	NOUN
ejpam-5330	189	28	-	-	PUNCT
ejpam-5330	189	29	fuzzy	fuzzy	ADJ
ejpam-5330	189	30	soft	soft	ADJ
ejpam-5330	189	31	α	α	NOUN
ejpam-5330	189	32	-	-	VERB
ejpam-5330	189	33	closed	closed	ADJ
ejpam-5330	189	34	with	with	ADP
ejpam-5330	189	35	hc	hc	PROPN
ejpam-5330	189	36	⊑	⊑	PRON
ejpam-5330	189	37	gb	gb	PROPN
ejpam-5330	189	38	,	,	PUNCT
ejpam-5330	189	39	such	such	ADJ
ejpam-5330	189	40	that	that	SCONJ
ejpam-5330	189	41	αcτ	αcτ	NOUN
ejpam-5330	189	42	(	(	PUNCT
ejpam-5330	189	43	n	n	X
ejpam-5330	189	44	,	,	PUNCT
ejpam-5330	189	45	hc	hc	PROPN
ejpam-5330	189	46	,	,	PUNCT
ejpam-5330	189	47	r)(n)(w	r)(n)(w	PROPN
ejpam-5330	189	48	)	)	PUNCT
ejpam-5330	189	49	≤	≤	NUM
ejpam-5330	189	50	gb(n)(w	gb(n)(w	NOUN
ejpam-5330	189	51	)	)	PUNCT
ejpam-5330	189	52	<	<	X
ejpam-5330	189	53	s.	s.	PROPN
ejpam-5330	189	54	since	since	SCONJ
ejpam-5330	189	55	w.	w.	PROPN
ejpam-5330	189	56	alqurashi	alqurashi	PROPN
ejpam-5330	189	57	,	,	PUNCT
ejpam-5330	189	58	i.	i.	PROPN
ejpam-5330	189	59	m.	m.	PROPN
ejpam-5330	189	60	taha	taha	PROPN
ejpam-5330	189	61	/	/	PUNCT
ejpam-5330	189	62	eur	eur	PROPN
ejpam-5330	189	63	.	.	PUNCT
ejpam-5330	190	1	j.	j.	PROPN
ejpam-5330	190	2	pure	pure	PROPN
ejpam-5330	190	3	appl	appl	PROPN
ejpam-5330	190	4	.	.	PROPN
ejpam-5330	190	5	math	math	PROPN
ejpam-5330	190	6	,	,	PUNCT
ejpam-5330	190	7	17	17	NUM
ejpam-5330	190	8	(	(	PUNCT
ejpam-5330	190	9	4	4	NUM
ejpam-5330	190	10	)	)	PUNCT
ejpam-5330	190	11	(	(	PUNCT
ejpam-5330	190	12	2024	2024	NUM
ejpam-5330	190	13	)	)	PUNCT
ejpam-5330	190	14	,	,	PUNCT
ejpam-5330	190	15	4112	4112	NUM
ejpam-5330	190	16	-	-	SYM
ejpam-5330	190	17	4134	4134	NUM
ejpam-5330	190	18	4119	4119	NUM
ejpam-5330	190	19	hc	hc	ADP
ejpam-5330	190	20	⊑	⊑	X
ejpam-5330	190	21	gb	gb	PROPN
ejpam-5330	190	22	,	,	PUNCT
ejpam-5330	190	23	we	we	PRON
ejpam-5330	190	24	have	have	AUX
ejpam-5330	190	25	αcτ	αcτ	NOUN
ejpam-5330	190	26	(	(	PUNCT
ejpam-5330	190	27	n	n	X
ejpam-5330	190	28	,	,	PUNCT
ejpam-5330	190	29	hc	hc	PROPN
ejpam-5330	190	30	,	,	PUNCT
ejpam-5330	190	31	r	r	NOUN
ejpam-5330	190	32	)	)	PUNCT
ejpam-5330	190	33	⊑	⊑	PRON
ejpam-5330	191	1	gb	gb	PROPN
ejpam-5330	191	2	.	.	PUNCT
ejpam-5330	191	3	again	again	ADV
ejpam-5330	191	4	,	,	PUNCT
ejpam-5330	191	5	by	by	ADP
ejpam-5330	191	6	the	the	DET
ejpam-5330	191	7	definition	definition	NOUN
ejpam-5330	191	8	of	of	ADP
ejpam-5330	191	9	αcτ	αcτ	NOUN
ejpam-5330	191	10	,	,	PUNCT
ejpam-5330	191	11	we	we	PRON
ejpam-5330	191	12	have	have	VERB
ejpam-5330	191	13	αcτ	αcτ	NOUN
ejpam-5330	191	14	(	(	PUNCT
ejpam-5330	191	15	n	n	CCONJ
ejpam-5330	191	16	,	,	PUNCT
ejpam-5330	191	17	αcτ	αcτ	X
ejpam-5330	191	18	(	(	PUNCT
ejpam-5330	191	19	n	n	X
ejpam-5330	191	20	,	,	PUNCT
ejpam-5330	191	21	hc	hc	PROPN
ejpam-5330	191	22	,	,	PUNCT
ejpam-5330	191	23	r	r	NOUN
ejpam-5330	191	24	)	)	PUNCT
ejpam-5330	191	25	,	,	PUNCT
ejpam-5330	192	1	r	r	X
ejpam-5330	192	2	)	)	PUNCT
ejpam-5330	192	3	⊑	⊑	PRON
ejpam-5330	192	4	gb	gb	PROPN
ejpam-5330	192	5	.	.	PUNCT
ejpam-5330	193	1	hence	hence	ADV
ejpam-5330	193	2	,	,	PUNCT
ejpam-5330	193	3	αcτ	αcτ	X
ejpam-5330	193	4	(	(	PUNCT
ejpam-5330	193	5	n	n	CCONJ
ejpam-5330	193	6	,	,	PUNCT
ejpam-5330	193	7	αcτ	αcτ	X
ejpam-5330	193	8	(	(	PUNCT
ejpam-5330	193	9	n	n	X
ejpam-5330	193	10	,	,	PUNCT
ejpam-5330	193	11	hc	hc	PROPN
ejpam-5330	193	12	,	,	PUNCT
ejpam-5330	193	13	r	r	NOUN
ejpam-5330	193	14	)	)	PUNCT
ejpam-5330	193	15	,	,	PUNCT
ejpam-5330	193	16	r)(n)(w	r)(n)(w	PROPN
ejpam-5330	193	17	)	)	PUNCT
ejpam-5330	193	18	≤	≤	NUM
ejpam-5330	193	19	gb(n)(w	gb(n)(w	NOUN
ejpam-5330	193	20	)	)	PUNCT
ejpam-5330	193	21	<	<	X
ejpam-5330	193	22	s	s	PROPN
ejpam-5330	193	23	,	,	PUNCT
ejpam-5330	193	24	which	which	PRON
ejpam-5330	193	25	is	be	AUX
ejpam-5330	193	26	a	a	DET
ejpam-5330	193	27	contradiction	contradiction	NOUN
ejpam-5330	193	28	for	for	ADP
ejpam-5330	193	29	(	(	PUNCT
ejpam-5330	193	30	a	a	NOUN
ejpam-5330	193	31	)	)	PUNCT
ejpam-5330	193	32	.	.	PUNCT
ejpam-5330	194	1	thus	thus	ADV
ejpam-5330	194	2	,	,	PUNCT
ejpam-5330	194	3	αcτ	αcτ	X
ejpam-5330	194	4	(	(	PUNCT
ejpam-5330	194	5	n	n	X
ejpam-5330	194	6	,	,	PUNCT
ejpam-5330	194	7	hc	hc	PROPN
ejpam-5330	194	8	,	,	PUNCT
ejpam-5330	194	9	r	r	NOUN
ejpam-5330	194	10	)	)	PUNCT
ejpam-5330	194	11	⊒	⊒	NOUN
ejpam-5330	194	12	αcτ	αcτ	X
ejpam-5330	194	13	(	(	PUNCT
ejpam-5330	194	14	n	n	CCONJ
ejpam-5330	194	15	,	,	PUNCT
ejpam-5330	194	16	αcτ	αcτ	X
ejpam-5330	194	17	(	(	PUNCT
ejpam-5330	194	18	n	n	X
ejpam-5330	194	19	,	,	PUNCT
ejpam-5330	194	20	hc	hc	PROPN
ejpam-5330	194	21	,	,	PUNCT
ejpam-5330	194	22	r	r	NOUN
ejpam-5330	194	23	)	)	PUNCT
ejpam-5330	194	24	,	,	PUNCT
ejpam-5330	194	25	r	r	NOUN
ejpam-5330	194	26	)	)	PUNCT
ejpam-5330	194	27	,	,	PUNCT
ejpam-5330	194	28	then	then	ADV
ejpam-5330	194	29	αcτ	αcτ	X
ejpam-5330	194	30	(	(	PUNCT
ejpam-5330	194	31	n	n	CCONJ
ejpam-5330	194	32	,	,	PUNCT
ejpam-5330	194	33	αcτ	αcτ	X
ejpam-5330	194	34	(	(	PUNCT
ejpam-5330	194	35	n	n	X
ejpam-5330	194	36	,	,	PUNCT
ejpam-5330	194	37	hc	hc	PROPN
ejpam-5330	194	38	,	,	PUNCT
ejpam-5330	194	39	r	r	NOUN
ejpam-5330	194	40	)	)	PUNCT
ejpam-5330	194	41	,	,	PUNCT
ejpam-5330	194	42	r	r	NOUN
ejpam-5330	194	43	)	)	PUNCT
ejpam-5330	194	44	=	=	NOUN
ejpam-5330	194	45	αcτ	αcτ	X
ejpam-5330	194	46	(	(	PUNCT
ejpam-5330	194	47	n	n	X
ejpam-5330	194	48	,	,	PUNCT
ejpam-5330	194	49	hc	hc	PROPN
ejpam-5330	194	50	,	,	PUNCT
ejpam-5330	194	51	r	r	NOUN
ejpam-5330	194	52	)	)	PUNCT
ejpam-5330	194	53	.	.	PUNCT
ejpam-5330	195	1	(	(	PUNCT
ejpam-5330	195	2	5	5	NUM
ejpam-5330	195	3	)	)	PUNCT
ejpam-5330	195	4	since	since	SCONJ
ejpam-5330	195	5	hc	hc	PROPN
ejpam-5330	195	6	and	and	CCONJ
ejpam-5330	195	7	gb	gb	NOUN
ejpam-5330	195	8	⊑	⊑	DET
ejpam-5330	195	9	hc	hc	PROPN
ejpam-5330	195	10	⊔	⊔	PROPN
ejpam-5330	195	11	gb	gb	PROPN
ejpam-5330	195	12	,	,	PUNCT
ejpam-5330	195	13	hence	hence	ADV
ejpam-5330	195	14	by	by	ADP
ejpam-5330	195	15	(	(	PUNCT
ejpam-5330	195	16	3	3	NUM
ejpam-5330	195	17	)	)	PUNCT
ejpam-5330	195	18	,	,	PUNCT
ejpam-5330	195	19	αcτ	αcτ	X
ejpam-5330	195	20	(	(	PUNCT
ejpam-5330	195	21	n	n	X
ejpam-5330	195	22	,	,	PUNCT
ejpam-5330	195	23	hc	hc	PROPN
ejpam-5330	195	24	,	,	PUNCT
ejpam-5330	195	25	r	r	NOUN
ejpam-5330	195	26	)	)	PUNCT
ejpam-5330	195	27	⊑	⊑	X
ejpam-5330	195	28	αcτ	αcτ	X
ejpam-5330	195	29	(	(	PUNCT
ejpam-5330	195	30	n	n	X
ejpam-5330	195	31	,	,	PUNCT
ejpam-5330	195	32	hc	hc	PROPN
ejpam-5330	195	33	⊔	⊔	PROPN
ejpam-5330	195	34	gb	gb	PROPN
ejpam-5330	195	35	,	,	PUNCT
ejpam-5330	195	36	r	r	NOUN
ejpam-5330	195	37	)	)	PUNCT
ejpam-5330	195	38	and	and	CCONJ
ejpam-5330	195	39	αcτ	αcτ	PROPN
ejpam-5330	195	40	(	(	PUNCT
ejpam-5330	195	41	n	n	CCONJ
ejpam-5330	195	42	,	,	PUNCT
ejpam-5330	195	43	gb	gb	ADJ
ejpam-5330	195	44	,	,	PUNCT
ejpam-5330	195	45	r	r	NOUN
ejpam-5330	195	46	)	)	PUNCT
ejpam-5330	195	47	⊑	⊑	X
ejpam-5330	195	48	αcτ	αcτ	X
ejpam-5330	195	49	(	(	PUNCT
ejpam-5330	195	50	n	n	X
ejpam-5330	195	51	,	,	PUNCT
ejpam-5330	195	52	hc	hc	PROPN
ejpam-5330	195	53	⊔	⊔	PROPN
ejpam-5330	195	54	gb	gb	NOUN
ejpam-5330	195	55	,	,	PUNCT
ejpam-5330	195	56	r	r	NOUN
ejpam-5330	195	57	)	)	PUNCT
ejpam-5330	195	58	.	.	PUNCT
ejpam-5330	196	1	thus	thus	ADV
ejpam-5330	196	2	,	,	PUNCT
ejpam-5330	196	3	αcτ	αcτ	X
ejpam-5330	196	4	(	(	PUNCT
ejpam-5330	196	5	n	n	X
ejpam-5330	196	6	,	,	PUNCT
ejpam-5330	196	7	hc	hc	PROPN
ejpam-5330	196	8	⊔	⊔	PROPN
ejpam-5330	196	9	gb	gb	PROPN
ejpam-5330	196	10	,	,	PUNCT
ejpam-5330	196	11	r	r	NOUN
ejpam-5330	196	12	)	)	PUNCT
ejpam-5330	196	13	⊒	⊒	NOUN
ejpam-5330	196	14	αcτ	αcτ	X
ejpam-5330	196	15	(	(	PUNCT
ejpam-5330	196	16	n	n	X
ejpam-5330	196	17	,	,	PUNCT
ejpam-5330	196	18	hc	hc	PROPN
ejpam-5330	196	19	,	,	PUNCT
ejpam-5330	196	20	r	r	NOUN
ejpam-5330	196	21	)	)	PUNCT
ejpam-5330	196	22	⊔	⊔	NOUN
ejpam-5330	196	23	αcτ	αcτ	NOUN
ejpam-5330	196	24	(	(	PUNCT
ejpam-5330	196	25	n	n	CCONJ
ejpam-5330	196	26	,	,	PUNCT
ejpam-5330	196	27	gb	gb	ADJ
ejpam-5330	196	28	,	,	PUNCT
ejpam-5330	196	29	r	r	NOUN
ejpam-5330	196	30	)	)	PUNCT
ejpam-5330	196	31	.	.	PUNCT
ejpam-5330	197	1	(	(	PUNCT
ejpam-5330	197	2	7	7	X
ejpam-5330	197	3	)	)	PUNCT
ejpam-5330	197	4	from	from	ADP
ejpam-5330	197	5	(	(	PUNCT
ejpam-5330	197	6	6	6	NUM
ejpam-5330	197	7	)	)	PUNCT
ejpam-5330	197	8	and	and	CCONJ
ejpam-5330	197	9	cτ	cτ	INTJ
ejpam-5330	197	10	(	(	PUNCT
ejpam-5330	197	11	n	n	CCONJ
ejpam-5330	197	12	,	,	PUNCT
ejpam-5330	197	13	hc	hc	PROPN
ejpam-5330	197	14	,	,	PUNCT
ejpam-5330	197	15	r	r	NOUN
ejpam-5330	197	16	)	)	PUNCT
ejpam-5330	197	17	is	be	AUX
ejpam-5330	197	18	r	r	NOUN
ejpam-5330	197	19	-	-	PUNCT
ejpam-5330	197	20	fuzzy	fuzzy	ADJ
ejpam-5330	197	21	soft	soft	ADJ
ejpam-5330	197	22	α	α	NOUN
ejpam-5330	197	23	-	-	PUNCT
ejpam-5330	197	24	closed	closed	ADJ
ejpam-5330	197	25	set	set	NOUN
ejpam-5330	197	26	,	,	PUNCT
ejpam-5330	197	27	then	then	ADV
ejpam-5330	197	28	αcτ	αcτ	X
ejpam-5330	197	29	(	(	PUNCT
ejpam-5330	197	30	n	n	CCONJ
ejpam-5330	197	31	,	,	PUNCT
ejpam-5330	197	32	cτ	cτ	INTJ
ejpam-5330	197	33	(	(	PUNCT
ejpam-5330	197	34	n	n	X
ejpam-5330	197	35	,	,	PUNCT
ejpam-5330	197	36	hc	hc	PROPN
ejpam-5330	197	37	,	,	PUNCT
ejpam-5330	197	38	r	r	NOUN
ejpam-5330	197	39	)	)	PUNCT
ejpam-5330	197	40	,	,	PUNCT
ejpam-5330	197	41	r	r	NOUN
ejpam-5330	197	42	)	)	PUNCT
ejpam-5330	197	43	=	=	NOUN
ejpam-5330	197	44	cτ	cτ	INTJ
ejpam-5330	197	45	(	(	PUNCT
ejpam-5330	197	46	n	n	X
ejpam-5330	197	47	,	,	PUNCT
ejpam-5330	197	48	hc	hc	PROPN
ejpam-5330	197	49	,	,	PUNCT
ejpam-5330	197	50	r	r	NOUN
ejpam-5330	197	51	)	)	PUNCT
ejpam-5330	197	52	.	.	PUNCT
ejpam-5330	198	1	theorem	theorem	NOUN
ejpam-5330	198	2	2	2	NUM
ejpam-5330	198	3	.	.	PUNCT
ejpam-5330	198	4	in	in	ADP
ejpam-5330	198	5	an	an	DET
ejpam-5330	198	6	fsts	fst	NOUN
ejpam-5330	198	7	(	(	PUNCT
ejpam-5330	198	8	w	w	NOUN
ejpam-5330	198	9	,	,	PUNCT
ejpam-5330	198	10	τn	τn	NOUN
ejpam-5330	198	11	)	)	PUNCT
ejpam-5330	198	12	,	,	PUNCT
ejpam-5330	198	13	for	for	ADP
ejpam-5330	198	14	each	each	DET
ejpam-5330	198	15	hc	hc	PROPN
ejpam-5330	198	16	∈	∈	PROPN
ejpam-5330	198	17	˜(w	˜(w	PROPN
ejpam-5330	198	18	,	,	PUNCT
ejpam-5330	198	19	n	n	CCONJ
ejpam-5330	198	20	)	)	PUNCT
ejpam-5330	198	21	,	,	PUNCT
ejpam-5330	198	22	n	n	PROPN
ejpam-5330	198	23	∈	∈	PROPN
ejpam-5330	198	24	n	n	NOUN
ejpam-5330	198	25	,	,	PUNCT
ejpam-5330	198	26	and	and	CCONJ
ejpam-5330	198	27	r	r	NOUN
ejpam-5330	198	28	∈	∈	PROPN
ejpam-5330	198	29	i0	i0	PROPN
ejpam-5330	198	30	,	,	PUNCT
ejpam-5330	198	31	we	we	PRON
ejpam-5330	198	32	define	define	VERB
ejpam-5330	198	33	a	a	DET
ejpam-5330	198	34	fuzzy	fuzzy	ADJ
ejpam-5330	198	35	soft	soft	ADJ
ejpam-5330	198	36	α	α	ADJ
ejpam-5330	198	37	-	-	ADJ
ejpam-5330	198	38	interior	interior	ADJ
ejpam-5330	198	39	operator	operator	NOUN
ejpam-5330	198	40	αiτ	αiτ	NOUN
ejpam-5330	198	41	:	:	PUNCT
ejpam-5330	198	42	n	n	PROPN
ejpam-5330	198	43	×	×	PROPN
ejpam-5330	198	44	˜(w	˜(w	PROPN
ejpam-5330	198	45	,	,	PUNCT
ejpam-5330	198	46	n)×	n)×	PRON
ejpam-5330	198	47	i	i	PROPN
ejpam-5330	198	48	◦	◦	PROPN
ejpam-5330	198	49	→	→	SYM
ejpam-5330	198	50	˜(w	˜(w	PROPN
ejpam-5330	198	51	,	,	PUNCT
ejpam-5330	198	52	n	n	CCONJ
ejpam-5330	198	53	)	)	PUNCT
ejpam-5330	198	54	as	as	SCONJ
ejpam-5330	198	55	follows	follow	VERB
ejpam-5330	198	56	:	:	PUNCT
ejpam-5330	198	57	αiτ	αiτ	PROPN
ejpam-5330	198	58	(	(	PUNCT
ejpam-5330	198	59	n	n	CCONJ
ejpam-5330	198	60	,	,	PUNCT
ejpam-5330	198	61	hc	hc	PROPN
ejpam-5330	198	62	,	,	PUNCT
ejpam-5330	198	63	r	r	NOUN
ejpam-5330	198	64	)	)	PUNCT
ejpam-5330	198	65	=	=	SYM
ejpam-5330	198	66	⊔	⊔	X
ejpam-5330	198	67	{	{	PUNCT
ejpam-5330	198	68	fa	fa	PROPN
ejpam-5330	198	69	∈	∈	PROPN
ejpam-5330	198	70	˜(w	˜(w	PROPN
ejpam-5330	198	71	,	,	PUNCT
ejpam-5330	198	72	n	n	CCONJ
ejpam-5330	198	73	)	)	PUNCT
ejpam-5330	198	74	:	:	PUNCT
ejpam-5330	199	1	fa	fa	X
ejpam-5330	199	2	⊑	⊑	DET
ejpam-5330	199	3	hc	hc	PROPN
ejpam-5330	199	4	,	,	PUNCT
ejpam-5330	199	5	fa	fa	PROPN
ejpam-5330	199	6	is	be	AUX
ejpam-5330	199	7	r	r	NOUN
ejpam-5330	199	8	-	-	PUNCT
ejpam-5330	199	9	fuzzy	fuzzy	ADJ
ejpam-5330	199	10	soft	soft	ADJ
ejpam-5330	199	11	α	α	NOUN
ejpam-5330	199	12	-	-	NOUN
ejpam-5330	199	13	open	open	ADJ
ejpam-5330	199	14	}	}	PUNCT
ejpam-5330	199	15	.	.	PUNCT
ejpam-5330	200	1	for	for	ADP
ejpam-5330	200	2	each	each	DET
ejpam-5330	200	3	gb	gb	NOUN
ejpam-5330	200	4	and	and	CCONJ
ejpam-5330	200	5	hc	hc	PROPN
ejpam-5330	200	6	∈	∈	PROPN
ejpam-5330	200	7	˜(w	˜(w	PROPN
ejpam-5330	200	8	,	,	PUNCT
ejpam-5330	200	9	n	n	CCONJ
ejpam-5330	200	10	)	)	PUNCT
ejpam-5330	200	11	,	,	PUNCT
ejpam-5330	200	12	the	the	DET
ejpam-5330	200	13	operator	operator	NOUN
ejpam-5330	200	14	αiτ	αiτ	PROPN
ejpam-5330	200	15	satisfies	satisfy	VERB
ejpam-5330	200	16	the	the	DET
ejpam-5330	200	17	following	follow	VERB
ejpam-5330	200	18	properties	property	NOUN
ejpam-5330	200	19	.	.	PUNCT
ejpam-5330	201	1	(	(	PUNCT
ejpam-5330	201	2	1	1	X
ejpam-5330	201	3	)	)	PUNCT
ejpam-5330	201	4	αiτ	αiτ	NOUN
ejpam-5330	201	5	(	(	PUNCT
ejpam-5330	201	6	n	n	CCONJ
ejpam-5330	201	7	,	,	PUNCT
ejpam-5330	201	8	ñ	ñ	VERB
ejpam-5330	201	9	,	,	PUNCT
ejpam-5330	201	10	r	r	NOUN
ejpam-5330	201	11	)	)	PUNCT
ejpam-5330	201	12	=	=	SYM
ejpam-5330	201	13	ñ	ñ	VERB
ejpam-5330	201	14	.	.	PUNCT
ejpam-5330	202	1	(	(	PUNCT
ejpam-5330	202	2	2	2	X
ejpam-5330	202	3	)	)	PUNCT
ejpam-5330	202	4	iτ	iτ	NOUN
ejpam-5330	202	5	(	(	PUNCT
ejpam-5330	202	6	n	n	X
ejpam-5330	202	7	,	,	PUNCT
ejpam-5330	202	8	hc	hc	PROPN
ejpam-5330	202	9	,	,	PUNCT
ejpam-5330	202	10	r	r	NOUN
ejpam-5330	202	11	)	)	PUNCT
ejpam-5330	202	12	⊑	⊑	PROPN
ejpam-5330	202	13	αiτ	αiτ	PROPN
ejpam-5330	202	14	(	(	PUNCT
ejpam-5330	202	15	n	n	CCONJ
ejpam-5330	202	16	,	,	PUNCT
ejpam-5330	202	17	hc	hc	PROPN
ejpam-5330	202	18	,	,	PUNCT
ejpam-5330	202	19	r	r	NOUN
ejpam-5330	202	20	)	)	PUNCT
ejpam-5330	202	21	⊑	⊑	PROPN
ejpam-5330	202	22	hc	hc	PROPN
ejpam-5330	202	23	.	.	PUNCT
ejpam-5330	203	1	(	(	PUNCT
ejpam-5330	203	2	3	3	X
ejpam-5330	203	3	)	)	PUNCT
ejpam-5330	203	4	αiτ	αiτ	NOUN
ejpam-5330	203	5	(	(	PUNCT
ejpam-5330	203	6	n	n	CCONJ
ejpam-5330	203	7	,	,	PUNCT
ejpam-5330	203	8	hc	hc	PROPN
ejpam-5330	203	9	,	,	PUNCT
ejpam-5330	203	10	r	r	NOUN
ejpam-5330	203	11	)	)	PUNCT
ejpam-5330	204	1	⊑	⊑	PROPN
ejpam-5330	204	2	αiτ	αiτ	PROPN
ejpam-5330	204	3	(	(	PUNCT
ejpam-5330	204	4	n	n	CCONJ
ejpam-5330	204	5	,	,	PUNCT
ejpam-5330	204	6	gb	gb	ADJ
ejpam-5330	204	7	,	,	PUNCT
ejpam-5330	204	8	r	r	NOUN
ejpam-5330	204	9	)	)	PUNCT
ejpam-5330	204	10	if	if	SCONJ
ejpam-5330	204	11	,	,	PUNCT
ejpam-5330	204	12	hc	hc	PROPN
ejpam-5330	204	13	⊑	⊑	X
ejpam-5330	204	14	gb	gb	PROPN
ejpam-5330	204	15	.	.	PUNCT
ejpam-5330	205	1	(	(	PUNCT
ejpam-5330	205	2	4	4	X
ejpam-5330	205	3	)	)	PUNCT
ejpam-5330	205	4	αiτ	αiτ	NOUN
ejpam-5330	205	5	(	(	PUNCT
ejpam-5330	205	6	n	n	CCONJ
ejpam-5330	205	7	,	,	PUNCT
ejpam-5330	205	8	αiτ	αiτ	PROPN
ejpam-5330	205	9	(	(	PUNCT
ejpam-5330	205	10	n	n	CCONJ
ejpam-5330	205	11	,	,	PUNCT
ejpam-5330	205	12	hc	hc	PROPN
ejpam-5330	205	13	,	,	PUNCT
ejpam-5330	205	14	r	r	NOUN
ejpam-5330	205	15	)	)	PUNCT
ejpam-5330	205	16	,	,	PUNCT
ejpam-5330	205	17	r	r	NOUN
ejpam-5330	205	18	)	)	PUNCT
ejpam-5330	205	19	=	=	SYM
ejpam-5330	205	20	αiτ	αiτ	NOUN
ejpam-5330	205	21	(	(	PUNCT
ejpam-5330	205	22	n	n	CCONJ
ejpam-5330	205	23	,	,	PUNCT
ejpam-5330	205	24	hc	hc	PROPN
ejpam-5330	205	25	,	,	PUNCT
ejpam-5330	205	26	r	r	NOUN
ejpam-5330	205	27	)	)	PUNCT
ejpam-5330	205	28	.	.	PUNCT
ejpam-5330	206	1	(	(	PUNCT
ejpam-5330	206	2	5	5	X
ejpam-5330	206	3	)	)	PUNCT
ejpam-5330	206	4	αiτ	αiτ	NOUN
ejpam-5330	206	5	(	(	PUNCT
ejpam-5330	206	6	n	n	CCONJ
ejpam-5330	206	7	,	,	PUNCT
ejpam-5330	206	8	hc	hc	PROPN
ejpam-5330	206	9	,	,	PUNCT
ejpam-5330	206	10	r	r	NOUN
ejpam-5330	206	11	)	)	PUNCT
ejpam-5330	206	12	⊓	⊓	PROPN
ejpam-5330	206	13	αiτ	αiτ	NOUN
ejpam-5330	206	14	(	(	PUNCT
ejpam-5330	206	15	n	n	CCONJ
ejpam-5330	206	16	,	,	PUNCT
ejpam-5330	206	17	gb	gb	ADJ
ejpam-5330	206	18	,	,	PUNCT
ejpam-5330	206	19	r	r	NOUN
ejpam-5330	206	20	)	)	PUNCT
ejpam-5330	206	21	⊒	⊒	PROPN
ejpam-5330	206	22	αiτ	αiτ	PROPN
ejpam-5330	206	23	(	(	PUNCT
ejpam-5330	206	24	n	n	CCONJ
ejpam-5330	206	25	,	,	PUNCT
ejpam-5330	206	26	hc	hc	PROPN
ejpam-5330	206	27	⊓	⊓	PROPN
ejpam-5330	206	28	gb	gb	NOUN
ejpam-5330	206	29	,	,	PUNCT
ejpam-5330	206	30	r	r	NOUN
ejpam-5330	206	31	)	)	PUNCT
ejpam-5330	206	32	.	.	PUNCT
ejpam-5330	207	1	(	(	PUNCT
ejpam-5330	207	2	6	6	X
ejpam-5330	207	3	)	)	PUNCT
ejpam-5330	207	4	αiτ	αiτ	NOUN
ejpam-5330	207	5	(	(	PUNCT
ejpam-5330	207	6	n	n	CCONJ
ejpam-5330	207	7	,	,	PUNCT
ejpam-5330	207	8	hc	hc	PROPN
ejpam-5330	207	9	,	,	PUNCT
ejpam-5330	207	10	r	r	NOUN
ejpam-5330	207	11	)	)	PUNCT
ejpam-5330	207	12	=	=	SYM
ejpam-5330	208	1	hc	hc	PROPN
ejpam-5330	208	2	iff	iff	PROPN
ejpam-5330	208	3	hc	hc	PROPN
ejpam-5330	208	4	is	be	AUX
ejpam-5330	208	5	r	r	NOUN
ejpam-5330	208	6	-	-	PUNCT
ejpam-5330	208	7	fuzzy	fuzzy	ADJ
ejpam-5330	208	8	soft	soft	ADJ
ejpam-5330	208	9	α	α	NOUN
ejpam-5330	208	10	-	-	NOUN
ejpam-5330	208	11	open	open	ADJ
ejpam-5330	208	12	.	.	PUNCT
ejpam-5330	209	1	(	(	PUNCT
ejpam-5330	209	2	7	7	X
ejpam-5330	209	3	)	)	PUNCT
ejpam-5330	209	4	αiτ	αiτ	NOUN
ejpam-5330	209	5	(	(	PUNCT
ejpam-5330	209	6	n	n	CCONJ
ejpam-5330	209	7	,	,	PUNCT
ejpam-5330	209	8	h	h	NOUN
ejpam-5330	209	9	c	c	NOUN
ejpam-5330	209	10	c	c	NOUN
ejpam-5330	209	11	,	,	PUNCT
ejpam-5330	209	12	r	r	NOUN
ejpam-5330	209	13	)	)	PUNCT
ejpam-5330	209	14	=	=	SYM
ejpam-5330	209	15	(	(	PUNCT
ejpam-5330	209	16	αcτ	αcτ	X
ejpam-5330	209	17	(	(	PUNCT
ejpam-5330	209	18	n	n	X
ejpam-5330	209	19	,	,	PUNCT
ejpam-5330	209	20	hc	hc	PROPN
ejpam-5330	209	21	,	,	PUNCT
ejpam-5330	209	22	r	r	NOUN
ejpam-5330	209	23	)	)	PUNCT
ejpam-5330	209	24	)	)	PUNCT
ejpam-5330	209	25	c.	c.	NOUN
ejpam-5330	209	26	proof	proof	NOUN
ejpam-5330	209	27	.	.	PUNCT
ejpam-5330	210	1	(	(	PUNCT
ejpam-5330	210	2	1	1	NUM
ejpam-5330	210	3	)	)	PUNCT
ejpam-5330	210	4	,	,	PUNCT
ejpam-5330	210	5	(	(	PUNCT
ejpam-5330	210	6	2	2	NUM
ejpam-5330	210	7	)	)	PUNCT
ejpam-5330	210	8	,	,	PUNCT
ejpam-5330	210	9	(	(	PUNCT
ejpam-5330	210	10	3	3	NUM
ejpam-5330	210	11	)	)	PUNCT
ejpam-5330	210	12	,	,	PUNCT
ejpam-5330	210	13	and	and	CCONJ
ejpam-5330	210	14	(	(	PUNCT
ejpam-5330	210	15	6	6	NUM
ejpam-5330	210	16	)	)	PUNCT
ejpam-5330	210	17	are	be	AUX
ejpam-5330	210	18	easily	easily	ADV
ejpam-5330	210	19	proved	prove	VERB
ejpam-5330	210	20	from	from	ADP
ejpam-5330	210	21	the	the	DET
ejpam-5330	210	22	definition	definition	NOUN
ejpam-5330	210	23	of	of	ADP
ejpam-5330	210	24	αiτ	αiτ	PROPN
ejpam-5330	210	25	.	.	PUNCT
ejpam-5330	211	1	(	(	PUNCT
ejpam-5330	211	2	4	4	NUM
ejpam-5330	211	3	)	)	PUNCT
ejpam-5330	211	4	and	and	CCONJ
ejpam-5330	211	5	(	(	PUNCT
ejpam-5330	211	6	5	5	X
ejpam-5330	211	7	)	)	PUNCT
ejpam-5330	211	8	are	be	AUX
ejpam-5330	211	9	easily	easily	ADV
ejpam-5330	211	10	proved	prove	VERB
ejpam-5330	211	11	by	by	ADP
ejpam-5330	211	12	a	a	DET
ejpam-5330	211	13	similar	similar	ADJ
ejpam-5330	211	14	way	way	NOUN
ejpam-5330	211	15	in	in	ADP
ejpam-5330	211	16	theorem	theorem	NOUN
ejpam-5330	211	17	1	1	NUM
ejpam-5330	211	18	.	.	PUNCT
ejpam-5330	212	1	(	(	PUNCT
ejpam-5330	212	2	7	7	NUM
ejpam-5330	212	3	)	)	PUNCT
ejpam-5330	212	4	for	for	ADP
ejpam-5330	212	5	each	each	DET
ejpam-5330	212	6	hc	hc	PROPN
ejpam-5330	212	7	∈	∈	PROPN
ejpam-5330	212	8	˜(w	˜(w	PROPN
ejpam-5330	212	9	,	,	PUNCT
ejpam-5330	212	10	n	n	CCONJ
ejpam-5330	212	11	)	)	PUNCT
ejpam-5330	212	12	,	,	PUNCT
ejpam-5330	212	13	n	n	PROPN
ejpam-5330	212	14	∈	∈	PROPN
ejpam-5330	212	15	n	n	NOUN
ejpam-5330	212	16	,	,	PUNCT
ejpam-5330	212	17	and	and	CCONJ
ejpam-5330	212	18	r	r	NOUN
ejpam-5330	212	19	∈	∈	PROPN
ejpam-5330	212	20	i0	i0	PROPN
ejpam-5330	212	21	,	,	PUNCT
ejpam-5330	212	22	we	we	PRON
ejpam-5330	212	23	have	have	VERB
ejpam-5330	212	24	αiτ	αiτ	PROPN
ejpam-5330	212	25	(	(	PUNCT
ejpam-5330	212	26	n	n	CCONJ
ejpam-5330	212	27	,	,	PUNCT
ejpam-5330	212	28	h	h	NOUN
ejpam-5330	212	29	c	c	NOUN
ejpam-5330	212	30	c	c	NOUN
ejpam-5330	212	31	,	,	PUNCT
ejpam-5330	212	32	r	r	NOUN
ejpam-5330	212	33	)	)	PUNCT
ejpam-5330	212	34	=	=	SYM
ejpam-5330	212	35	⊔{fa	⊔{fa	PUNCT
ejpam-5330	212	36	∈	∈	PROPN
ejpam-5330	212	37	˜(w	˜(w	PROPN
ejpam-5330	212	38	,	,	PUNCT
ejpam-5330	212	39	n	n	CCONJ
ejpam-5330	212	40	)	)	PUNCT
ejpam-5330	212	41	:	:	PUNCT
ejpam-5330	213	1	fa	fa	X
ejpam-5330	213	2	⊑	⊑	PRON
ejpam-5330	213	3	hcc	hcc	PROPN
ejpam-5330	213	4	,	,	PUNCT
ejpam-5330	213	5	fa	fa	PROPN
ejpam-5330	213	6	is	be	AUX
ejpam-5330	213	7	r	r	NOUN
ejpam-5330	213	8	-	-	PUNCT
ejpam-5330	213	9	fuzzy	fuzzy	ADJ
ejpam-5330	213	10	soft	soft	ADJ
ejpam-5330	213	11	α	α	NOUN
ejpam-5330	213	12	-	-	NOUN
ejpam-5330	213	13	open}=	open}=	NOUN
ejpam-5330	214	1	[	[	X
ejpam-5330	214	2	⊓{f	⊓{f	X
ejpam-5330	214	3	ca	ca	NOUN
ejpam-5330	214	4	∈	∈	PROPN
ejpam-5330	214	5	˜(w	˜(w	PROPN
ejpam-5330	214	6	,	,	PUNCT
ejpam-5330	214	7	n	n	CCONJ
ejpam-5330	214	8	)	)	PUNCT
ejpam-5330	214	9	:	:	PUNCT
ejpam-5330	214	10	hc	hc	ADP
ejpam-5330	214	11	⊑	⊑	X
ejpam-5330	214	12	f	f	PROPN
ejpam-5330	214	13	ca	ca	PROPN
ejpam-5330	214	14	,	,	PUNCT
ejpam-5330	214	15	f	f	PROPN
ejpam-5330	214	16	c	c	PROPN
ejpam-5330	214	17	a	a	PRON
ejpam-5330	214	18	is	be	AUX
ejpam-5330	214	19	r	r	NOUN
ejpam-5330	214	20	-	-	PUNCT
ejpam-5330	214	21	fuzzy	fuzzy	ADJ
ejpam-5330	214	22	soft	soft	ADJ
ejpam-5330	214	23	α	α	NOUN
ejpam-5330	214	24	-	-	PUNCT
ejpam-5330	214	25	closed}]c	closed}]c	NOUN
ejpam-5330	214	26	=	=	SYM
ejpam-5330	214	27	(	(	PUNCT
ejpam-5330	214	28	αcτ	αcτ	X
ejpam-5330	214	29	(	(	PUNCT
ejpam-5330	214	30	n	n	X
ejpam-5330	214	31	,	,	PUNCT
ejpam-5330	214	32	hc	hc	PROPN
ejpam-5330	214	33	,	,	PUNCT
ejpam-5330	214	34	r	r	NOUN
ejpam-5330	214	35	)	)	PUNCT
ejpam-5330	214	36	)	)	PUNCT
ejpam-5330	214	37	c.	c.	NOUN
ejpam-5330	214	38	definition	definition	NOUN
ejpam-5330	214	39	14	14	NUM
ejpam-5330	214	40	.	.	PUNCT
ejpam-5330	215	1	let	let	AUX
ejpam-5330	215	2	(	(	PUNCT
ejpam-5330	215	3	w	w	NOUN
ejpam-5330	215	4	,	,	PUNCT
ejpam-5330	215	5	τn	τn	PART
ejpam-5330	215	6	)	)	PUNCT
ejpam-5330	215	7	be	be	AUX
ejpam-5330	215	8	an	an	DET
ejpam-5330	215	9	fsts	fst	NOUN
ejpam-5330	215	10	,	,	PUNCT
ejpam-5330	215	11	r	r	NOUN
ejpam-5330	215	12	∈	∈	PROPN
ejpam-5330	215	13	i0	i0	PROPN
ejpam-5330	215	14	,	,	PUNCT
ejpam-5330	215	15	and	and	CCONJ
ejpam-5330	215	16	gb	gb	NOUN
ejpam-5330	215	17	,	,	PUNCT
ejpam-5330	215	18	hc	hc	PROPN
ejpam-5330	215	19	∈	∈	PROPN
ejpam-5330	215	20	˜(w	˜(w	PROPN
ejpam-5330	215	21	,	,	PUNCT
ejpam-5330	215	22	n	n	CCONJ
ejpam-5330	215	23	)	)	PUNCT
ejpam-5330	215	24	,	,	PUNCT
ejpam-5330	215	25	then	then	ADV
ejpam-5330	215	26	we	we	PRON
ejpam-5330	215	27	have	have	VERB
ejpam-5330	215	28	w.	w.	PROPN
ejpam-5330	215	29	alqurashi	alqurashi	PROPN
ejpam-5330	215	30	,	,	PUNCT
ejpam-5330	215	31	i.	i.	PROPN
ejpam-5330	215	32	m.	m.	PROPN
ejpam-5330	215	33	taha	taha	PROPN
ejpam-5330	215	34	/	/	PUNCT
ejpam-5330	215	35	eur	eur	PROPN
ejpam-5330	215	36	.	.	PUNCT
ejpam-5330	216	1	j.	j.	PROPN
ejpam-5330	216	2	pure	pure	PROPN
ejpam-5330	216	3	appl	appl	PROPN
ejpam-5330	216	4	.	.	PROPN
ejpam-5330	216	5	math	math	PROPN
ejpam-5330	216	6	,	,	PUNCT
ejpam-5330	216	7	17	17	NUM
ejpam-5330	216	8	(	(	PUNCT
ejpam-5330	216	9	4	4	NUM
ejpam-5330	216	10	)	)	PUNCT
ejpam-5330	216	11	(	(	PUNCT
ejpam-5330	216	12	2024	2024	NUM
ejpam-5330	216	13	)	)	PUNCT
ejpam-5330	216	14	,	,	PUNCT
ejpam-5330	216	15	4112	4112	NUM
ejpam-5330	216	16	-	-	SYM
ejpam-5330	216	17	4134	4134	NUM
ejpam-5330	216	18	4120	4120	NUM
ejpam-5330	216	19	(	(	PUNCT
ejpam-5330	216	20	1	1	NUM
ejpam-5330	216	21	)	)	PUNCT
ejpam-5330	216	22	two	two	NUM
ejpam-5330	216	23	fuzzy	fuzzy	ADJ
ejpam-5330	216	24	soft	soft	ADJ
ejpam-5330	216	25	sets	set	NOUN
ejpam-5330	216	26	gb	gb	ADP
ejpam-5330	217	1	and	and	CCONJ
ejpam-5330	217	2	hc	hc	PROPN
ejpam-5330	217	3	are	be	AUX
ejpam-5330	217	4	called	call	VERB
ejpam-5330	217	5	r	r	NOUN
ejpam-5330	217	6	-	-	PUNCT
ejpam-5330	217	7	fuzzy	fuzzy	ADJ
ejpam-5330	217	8	soft	soft	ADJ
ejpam-5330	217	9	α	α	NOUN
ejpam-5330	217	10	-	-	PUNCT
ejpam-5330	217	11	separated	separate	VERB
ejpam-5330	217	12	iff	iff	PROPN
ejpam-5330	217	13	gb	gb	PRON
ejpam-5330	217	14	̸	̸	PUNCT
ejpam-5330	217	15	q̃	q̃	PROPN
ejpam-5330	217	16	αcτ	αcτ	X
ejpam-5330	217	17	(	(	PUNCT
ejpam-5330	217	18	n	n	X
ejpam-5330	217	19	,	,	PUNCT
ejpam-5330	217	20	hc	hc	PROPN
ejpam-5330	217	21	,	,	PUNCT
ejpam-5330	217	22	r	r	NOUN
ejpam-5330	217	23	)	)	PUNCT
ejpam-5330	217	24	and	and	CCONJ
ejpam-5330	217	25	hc	hc	PROPN
ejpam-5330	217	26	̸	̸	PUNCT
ejpam-5330	217	27	q̃	q̃	PROPN
ejpam-5330	217	28	αcτ	αcτ	X
ejpam-5330	217	29	(	(	PUNCT
ejpam-5330	217	30	n	n	CCONJ
ejpam-5330	217	31	,	,	PUNCT
ejpam-5330	217	32	gb	gb	ADJ
ejpam-5330	217	33	,	,	PUNCT
ejpam-5330	217	34	r	r	NOUN
ejpam-5330	217	35	)	)	PUNCT
ejpam-5330	217	36	for	for	ADP
ejpam-5330	217	37	each	each	DET
ejpam-5330	217	38	n	n	PRON
ejpam-5330	217	39	∈	∈	PROPN
ejpam-5330	217	40	n	n	NOUN
ejpam-5330	217	41	.	.	PUNCT
ejpam-5330	218	1	(	(	PUNCT
ejpam-5330	218	2	2	2	X
ejpam-5330	218	3	)	)	PUNCT
ejpam-5330	218	4	any	any	DET
ejpam-5330	218	5	fuzzy	fuzzy	ADJ
ejpam-5330	218	6	soft	soft	ADJ
ejpam-5330	218	7	set	set	NOUN
ejpam-5330	218	8	which	which	PRON
ejpam-5330	218	9	can	can	AUX
ejpam-5330	218	10	not	not	PART
ejpam-5330	218	11	be	be	AUX
ejpam-5330	218	12	expressed	express	VERB
ejpam-5330	218	13	as	as	SCONJ
ejpam-5330	218	14	the	the	DET
ejpam-5330	218	15	union	union	NOUN
ejpam-5330	218	16	of	of	ADP
ejpam-5330	218	17	two	two	NUM
ejpam-5330	218	18	r	r	NOUN
ejpam-5330	218	19	-	-	PUNCT
ejpam-5330	218	20	fuzzy	fuzzy	ADJ
ejpam-5330	218	21	soft	soft	ADJ
ejpam-5330	218	22	α	α	NOUN
ejpam-5330	218	23	-	-	PUNCT
ejpam-5330	218	24	separated	separate	VERB
ejpam-5330	218	25	sets	set	NOUN
ejpam-5330	218	26	is	be	AUX
ejpam-5330	218	27	called	call	VERB
ejpam-5330	218	28	an	an	DET
ejpam-5330	218	29	r	r	NOUN
ejpam-5330	218	30	-	-	PUNCT
ejpam-5330	218	31	fuzzy	fuzzy	ADJ
ejpam-5330	218	32	soft	soft	ADJ
ejpam-5330	218	33	α	α	NOUN
ejpam-5330	218	34	-	-	PUNCT
ejpam-5330	218	35	connected	connect	VERB
ejpam-5330	218	36	.	.	PUNCT
ejpam-5330	219	1	theorem	theorem	VERB
ejpam-5330	219	2	3	3	NUM
ejpam-5330	219	3	.	.	PUNCT
ejpam-5330	220	1	in	in	ADP
ejpam-5330	220	2	an	an	DET
ejpam-5330	220	3	fsts	fst	NOUN
ejpam-5330	220	4	(	(	PUNCT
ejpam-5330	220	5	w	w	NOUN
ejpam-5330	220	6	,	,	PUNCT
ejpam-5330	220	7	τn	τn	NOUN
ejpam-5330	220	8	)	)	PUNCT
ejpam-5330	220	9	,	,	PUNCT
ejpam-5330	220	10	we	we	PRON
ejpam-5330	220	11	have	have	VERB
ejpam-5330	220	12	:	:	PUNCT
ejpam-5330	220	13	(	(	PUNCT
ejpam-5330	220	14	1	1	X
ejpam-5330	220	15	)	)	PUNCT
ejpam-5330	220	16	if	if	SCONJ
ejpam-5330	220	17	fa	fa	PROPN
ejpam-5330	220	18	and	and	CCONJ
ejpam-5330	220	19	gb	gb	PROPN
ejpam-5330	220	20	∈	∈	PROPN
ejpam-5330	220	21	˜(w	˜(w	PROPN
ejpam-5330	220	22	,	,	PUNCT
ejpam-5330	220	23	n	n	CCONJ
ejpam-5330	220	24	)	)	PUNCT
ejpam-5330	220	25	are	be	AUX
ejpam-5330	220	26	r	r	NOUN
ejpam-5330	220	27	-	-	PUNCT
ejpam-5330	220	28	fuzzy	fuzzy	ADJ
ejpam-5330	220	29	soft	soft	ADJ
ejpam-5330	220	30	α	α	NOUN
ejpam-5330	220	31	-	-	PUNCT
ejpam-5330	220	32	separated	separate	VERB
ejpam-5330	220	33	and	and	CCONJ
ejpam-5330	220	34	hc	hc	X
ejpam-5330	220	35	,	,	PUNCT
ejpam-5330	220	36	td	td	PROPN
ejpam-5330	220	37	∈	∈	PROPN
ejpam-5330	220	38	˜(w	˜(w	PROPN
ejpam-5330	220	39	,	,	PUNCT
ejpam-5330	220	40	n	n	CCONJ
ejpam-5330	220	41	)	)	PUNCT
ejpam-5330	220	42	such	such	ADJ
ejpam-5330	220	43	that	that	SCONJ
ejpam-5330	220	44	hc	hc	PROPN
ejpam-5330	220	45	⊑	⊑	DET
ejpam-5330	220	46	fa	fa	PROPN
ejpam-5330	220	47	and	and	CCONJ
ejpam-5330	220	48	td	td	VERB
ejpam-5330	220	49	⊑	⊑	PRON
ejpam-5330	220	50	gb	gb	NOUN
ejpam-5330	220	51	,	,	PUNCT
ejpam-5330	220	52	then	then	ADV
ejpam-5330	220	53	hc	hc	PROPN
ejpam-5330	220	54	and	and	CCONJ
ejpam-5330	220	55	td	td	NOUN
ejpam-5330	220	56	are	be	AUX
ejpam-5330	220	57	r	r	NOUN
ejpam-5330	220	58	-	-	PUNCT
ejpam-5330	220	59	fuzzy	fuzzy	ADJ
ejpam-5330	220	60	soft	soft	ADJ
ejpam-5330	220	61	α	α	NOUN
ejpam-5330	220	62	-	-	PUNCT
ejpam-5330	220	63	separated	separate	VERB
ejpam-5330	220	64	.	.	PUNCT
ejpam-5330	221	1	(	(	PUNCT
ejpam-5330	221	2	2	2	X
ejpam-5330	221	3	)	)	PUNCT
ejpam-5330	221	4	if	if	SCONJ
ejpam-5330	221	5	fa	fa	PROPN
ejpam-5330	221	6	̸	̸	PUNCT
ejpam-5330	221	7	q̃	q̃	PROPN
ejpam-5330	221	8	gb	gb	ADV
ejpam-5330	221	9	and	and	CCONJ
ejpam-5330	221	10	either	either	CCONJ
ejpam-5330	221	11	both	both	PRON
ejpam-5330	221	12	are	be	AUX
ejpam-5330	221	13	r	r	NOUN
ejpam-5330	221	14	-	-	PUNCT
ejpam-5330	221	15	fuzzy	fuzzy	ADJ
ejpam-5330	221	16	soft	soft	ADJ
ejpam-5330	221	17	α	α	NOUN
ejpam-5330	221	18	-	-	ADJ
ejpam-5330	221	19	open	open	ADJ
ejpam-5330	221	20	or	or	CCONJ
ejpam-5330	221	21	both	both	PRON
ejpam-5330	221	22	are	be	AUX
ejpam-5330	221	23	r	r	NOUN
ejpam-5330	221	24	-	-	PUNCT
ejpam-5330	221	25	fuzzy	fuzzy	ADJ
ejpam-5330	221	26	soft	soft	ADJ
ejpam-5330	221	27	α	α	NOUN
ejpam-5330	221	28	-	-	VERB
ejpam-5330	221	29	closed	closed	ADJ
ejpam-5330	221	30	,	,	PUNCT
ejpam-5330	221	31	then	then	ADV
ejpam-5330	221	32	fa	fa	PROPN
ejpam-5330	221	33	and	and	CCONJ
ejpam-5330	221	34	gb	gb	PROPN
ejpam-5330	221	35	are	be	AUX
ejpam-5330	221	36	r	r	NOUN
ejpam-5330	221	37	-	-	PUNCT
ejpam-5330	221	38	fuzzy	fuzzy	ADJ
ejpam-5330	221	39	soft	soft	ADJ
ejpam-5330	221	40	α	α	NOUN
ejpam-5330	221	41	-	-	PUNCT
ejpam-5330	221	42	separated	separate	VERB
ejpam-5330	221	43	.	.	PUNCT
ejpam-5330	222	1	(	(	PUNCT
ejpam-5330	222	2	3	3	X
ejpam-5330	222	3	)	)	PUNCT
ejpam-5330	222	4	if	if	SCONJ
ejpam-5330	222	5	fa	fa	PROPN
ejpam-5330	222	6	and	and	CCONJ
ejpam-5330	222	7	gb	gb	PRON
ejpam-5330	222	8	are	be	AUX
ejpam-5330	222	9	either	either	CCONJ
ejpam-5330	222	10	both	both	CCONJ
ejpam-5330	222	11	r	r	NOUN
ejpam-5330	222	12	-	-	PUNCT
ejpam-5330	222	13	fuzzy	fuzzy	ADJ
ejpam-5330	222	14	soft	soft	ADJ
ejpam-5330	222	15	α	α	NOUN
ejpam-5330	222	16	-	-	ADJ
ejpam-5330	222	17	open	open	ADJ
ejpam-5330	222	18	or	or	CCONJ
ejpam-5330	222	19	both	both	CCONJ
ejpam-5330	222	20	r	r	NOUN
ejpam-5330	222	21	-	-	PUNCT
ejpam-5330	222	22	fuzzy	fuzzy	ADJ
ejpam-5330	222	23	soft	soft	ADJ
ejpam-5330	222	24	α	α	NOUN
ejpam-5330	222	25	-	-	VERB
ejpam-5330	222	26	closed	closed	ADJ
ejpam-5330	222	27	,	,	PUNCT
ejpam-5330	222	28	then	then	ADV
ejpam-5330	222	29	fa	fa	PROPN
ejpam-5330	222	30	⊓	⊓	PROPN
ejpam-5330	222	31	gcb	gcb	X
ejpam-5330	222	32	and	and	CCONJ
ejpam-5330	222	33	gb	gb	ADJ
ejpam-5330	222	34	⊓	⊓	PROPN
ejpam-5330	222	35	f	f	PROPN
ejpam-5330	222	36	ca	can	AUX
ejpam-5330	222	37	are	be	AUX
ejpam-5330	222	38	r	r	NOUN
ejpam-5330	222	39	-	-	PUNCT
ejpam-5330	222	40	fuzzy	fuzzy	ADJ
ejpam-5330	222	41	soft	soft	ADJ
ejpam-5330	222	42	α	α	NOUN
ejpam-5330	222	43	-	-	PUNCT
ejpam-5330	222	44	separated	separate	VERB
ejpam-5330	222	45	.	.	PUNCT
ejpam-5330	223	1	proof	proof	NOUN
ejpam-5330	223	2	.	.	PUNCT
ejpam-5330	224	1	(	(	PUNCT
ejpam-5330	224	2	1	1	X
ejpam-5330	224	3	)	)	PUNCT
ejpam-5330	224	4	and	and	CCONJ
ejpam-5330	224	5	(	(	PUNCT
ejpam-5330	224	6	2	2	X
ejpam-5330	224	7	)	)	PUNCT
ejpam-5330	224	8	are	be	AUX
ejpam-5330	224	9	obvious	obvious	ADJ
ejpam-5330	224	10	.	.	PUNCT
ejpam-5330	225	1	(	(	PUNCT
ejpam-5330	225	2	3	3	X
ejpam-5330	225	3	)	)	PUNCT
ejpam-5330	225	4	let	let	VERB
ejpam-5330	225	5	fa	fa	INTJ
ejpam-5330	225	6	and	and	CCONJ
ejpam-5330	225	7	gb	gb	PRON
ejpam-5330	225	8	be	be	AUX
ejpam-5330	225	9	an	an	DET
ejpam-5330	225	10	r	r	NOUN
ejpam-5330	225	11	-	-	PUNCT
ejpam-5330	225	12	fuzzy	fuzzy	ADJ
ejpam-5330	225	13	soft	soft	ADJ
ejpam-5330	225	14	α	α	NOUN
ejpam-5330	225	15	-	-	NOUN
ejpam-5330	225	16	open	open	ADJ
ejpam-5330	225	17	.	.	PUNCT
ejpam-5330	226	1	since	since	SCONJ
ejpam-5330	226	2	fa	fa	PROPN
ejpam-5330	226	3	⊓	⊓	PROPN
ejpam-5330	226	4	gcb	gcb	PROPN
ejpam-5330	226	5	⊑	⊑	X
ejpam-5330	226	6	gcb	gcb	PROPN
ejpam-5330	226	7	,	,	PUNCT
ejpam-5330	226	8	αcτ	αcτ	X
ejpam-5330	226	9	(	(	PUNCT
ejpam-5330	226	10	n	n	CCONJ
ejpam-5330	226	11	,	,	PUNCT
ejpam-5330	226	12	fa⊓gcb	fa⊓gcb	ADV
ejpam-5330	226	13	,	,	PUNCT
ejpam-5330	226	14	r	r	X
ejpam-5330	226	15	)	)	PUNCT
ejpam-5330	226	16	⊑	⊑	X
ejpam-5330	226	17	gcb	gcb	PROPN
ejpam-5330	226	18	and	and	CCONJ
ejpam-5330	226	19	hence	hence	ADV
ejpam-5330	226	20	αcτ	αcτ	X
ejpam-5330	226	21	(	(	PUNCT
ejpam-5330	226	22	n	n	CCONJ
ejpam-5330	226	23	,	,	PUNCT
ejpam-5330	226	24	fa	fa	X
ejpam-5330	226	25	⊓	⊓	PROPN
ejpam-5330	226	26	gcb	gcb	PROPN
ejpam-5330	226	27	,	,	PUNCT
ejpam-5330	226	28	r)̸	r)̸	PROPN
ejpam-5330	226	29	q̃	q̃	PROPN
ejpam-5330	226	30	gb	gb	PRON
ejpam-5330	226	31	.	.	PUNCT
ejpam-5330	227	1	then	then	ADV
ejpam-5330	227	2	,	,	PUNCT
ejpam-5330	227	3	αcτ	αcτ	X
ejpam-5330	227	4	(	(	PUNCT
ejpam-5330	227	5	n	n	X
ejpam-5330	227	6	,	,	PUNCT
ejpam-5330	227	7	fa	fa	X
ejpam-5330	227	8	⊓	⊓	PROPN
ejpam-5330	227	9	gcb	gcb	PROPN
ejpam-5330	227	10	,	,	PUNCT
ejpam-5330	227	11	r)̸	r)̸	PROPN
ejpam-5330	227	12	q̃	q̃	PROPN
ejpam-5330	227	13	(	(	PUNCT
ejpam-5330	227	14	gb	gb	NOUN
ejpam-5330	227	15	⊓	⊓	PROPN
ejpam-5330	227	16	f	f	PROPN
ejpam-5330	227	17	ca	ca	NOUN
ejpam-5330	227	18	)	)	PUNCT
ejpam-5330	227	19	.	.	PUNCT
ejpam-5330	228	1	again	again	ADV
ejpam-5330	228	2	,	,	PUNCT
ejpam-5330	228	3	since	since	SCONJ
ejpam-5330	228	4	gb	gb	DET
ejpam-5330	228	5	⊓	⊓	PROPN
ejpam-5330	228	6	f	f	PROPN
ejpam-5330	228	7	ca	ca	NOUN
ejpam-5330	228	8	⊑	⊑	X
ejpam-5330	228	9	f	f	PROPN
ejpam-5330	228	10	ca	can	AUX
ejpam-5330	228	11	,	,	PUNCT
ejpam-5330	228	12	αcτ	αcτ	X
ejpam-5330	228	13	(	(	PUNCT
ejpam-5330	228	14	n	n	CCONJ
ejpam-5330	228	15	,	,	PUNCT
ejpam-5330	228	16	gb	gb	ADP
ejpam-5330	228	17	⊓	⊓	PROPN
ejpam-5330	228	18	f	f	PROPN
ejpam-5330	228	19	ca	can	AUX
ejpam-5330	228	20	,	,	PUNCT
ejpam-5330	228	21	r	r	NOUN
ejpam-5330	228	22	)	)	PUNCT
ejpam-5330	228	23	⊑	⊑	X
ejpam-5330	229	1	f	f	PROPN
ejpam-5330	229	2	ca	can	AUX
ejpam-5330	229	3	and	and	CCONJ
ejpam-5330	229	4	hence	hence	ADV
ejpam-5330	229	5	αcτ	αcτ	VERB
ejpam-5330	229	6	(	(	PUNCT
ejpam-5330	229	7	n	n	CCONJ
ejpam-5330	229	8	,	,	PUNCT
ejpam-5330	229	9	gb	gb	ADP
ejpam-5330	229	10	⊓f	⊓f	ADV
ejpam-5330	229	11	ca	ca	NOUN
ejpam-5330	229	12	,	,	PUNCT
ejpam-5330	229	13	r)̸	r)̸	PROPN
ejpam-5330	229	14	q̃	q̃	PROPN
ejpam-5330	229	15	fa	fa	PROPN
ejpam-5330	229	16	.	.	PUNCT
ejpam-5330	230	1	then	then	ADV
ejpam-5330	230	2	,	,	PUNCT
ejpam-5330	230	3	αcτ	αcτ	X
ejpam-5330	230	4	(	(	PUNCT
ejpam-5330	230	5	n	n	CCONJ
ejpam-5330	230	6	,	,	PUNCT
ejpam-5330	230	7	gb	gb	ADP
ejpam-5330	230	8	⊓	⊓	PROPN
ejpam-5330	230	9	f	f	PROPN
ejpam-5330	230	10	ca	ca	NOUN
ejpam-5330	230	11	,	,	PUNCT
ejpam-5330	230	12	r)̸	r)̸	PROPN
ejpam-5330	230	13	q̃	q̃	PROPN
ejpam-5330	230	14	(	(	PUNCT
ejpam-5330	230	15	fa	fa	PROPN
ejpam-5330	230	16	⊓	⊓	PROPN
ejpam-5330	230	17	gcb	gcb	PROPN
ejpam-5330	230	18	)	)	PUNCT
ejpam-5330	230	19	.	.	PUNCT
ejpam-5330	231	1	thus	thus	ADV
ejpam-5330	231	2	,	,	PUNCT
ejpam-5330	231	3	fa	fa	X
ejpam-5330	231	4	⊓	⊓	PROPN
ejpam-5330	231	5	gcb	gcb	X
ejpam-5330	231	6	and	and	CCONJ
ejpam-5330	231	7	gb	gb	ADJ
ejpam-5330	231	8	⊓	⊓	PROPN
ejpam-5330	231	9	f	f	PROPN
ejpam-5330	231	10	ca	can	AUX
ejpam-5330	231	11	are	be	AUX
ejpam-5330	231	12	r	r	NOUN
ejpam-5330	231	13	-	-	PUNCT
ejpam-5330	231	14	fuzzy	fuzzy	ADJ
ejpam-5330	231	15	soft	soft	ADJ
ejpam-5330	231	16	α	α	NOUN
ejpam-5330	231	17	-	-	PUNCT
ejpam-5330	231	18	separated	separate	VERB
ejpam-5330	231	19	.	.	PUNCT
ejpam-5330	232	1	the	the	DET
ejpam-5330	232	2	other	other	ADJ
ejpam-5330	232	3	case	case	NOUN
ejpam-5330	232	4	follows	follow	VERB
ejpam-5330	232	5	similar	similar	ADJ
ejpam-5330	232	6	lines	line	NOUN
ejpam-5330	232	7	.	.	PUNCT
ejpam-5330	233	1	theorem	theorem	ADJ
ejpam-5330	233	2	4	4	NUM
ejpam-5330	233	3	.	.	PUNCT
ejpam-5330	234	1	in	in	ADP
ejpam-5330	234	2	an	an	DET
ejpam-5330	234	3	fsts	fst	NOUN
ejpam-5330	234	4	(	(	PUNCT
ejpam-5330	234	5	w	w	NOUN
ejpam-5330	234	6	,	,	PUNCT
ejpam-5330	234	7	τn	τn	NOUN
ejpam-5330	234	8	)	)	PUNCT
ejpam-5330	234	9	,	,	PUNCT
ejpam-5330	234	10	then	then	ADV
ejpam-5330	234	11	fa	fa	INTJ
ejpam-5330	234	12	,	,	PUNCT
ejpam-5330	234	13	gb	gb	PROPN
ejpam-5330	234	14	∈	∈	PROPN
ejpam-5330	234	15	˜(w	˜(w	PROPN
ejpam-5330	234	16	,	,	PUNCT
ejpam-5330	234	17	n	n	CCONJ
ejpam-5330	234	18	)	)	PUNCT
ejpam-5330	234	19	are	be	AUX
ejpam-5330	234	20	r	r	NOUN
ejpam-5330	234	21	-	-	PUNCT
ejpam-5330	234	22	fuzzy	fuzzy	ADJ
ejpam-5330	234	23	soft	soft	ADJ
ejpam-5330	234	24	α	α	NOUN
ejpam-5330	234	25	-	-	PUNCT
ejpam-5330	234	26	separated	separate	VERB
ejpam-5330	234	27	iff	iff	NOUN
ejpam-5330	234	28	there	there	ADV
ejpam-5330	234	29	exist	exist	VERB
ejpam-5330	234	30	two	two	NUM
ejpam-5330	234	31	r	r	NOUN
ejpam-5330	234	32	-	-	PUNCT
ejpam-5330	234	33	fuzzy	fuzzy	ADJ
ejpam-5330	234	34	soft	soft	ADJ
ejpam-5330	234	35	α	α	NOUN
ejpam-5330	234	36	-	-	ADJ
ejpam-5330	234	37	open	open	ADJ
ejpam-5330	234	38	sets	set	NOUN
ejpam-5330	234	39	hc	hc	NOUN
ejpam-5330	234	40	and	and	CCONJ
ejpam-5330	234	41	td	td	NOUN
ejpam-5330	234	42	such	such	ADJ
ejpam-5330	234	43	that	that	SCONJ
ejpam-5330	234	44	fa	fa	PROPN
ejpam-5330	234	45	⊑	⊑	PRON
ejpam-5330	234	46	hc	hc	PROPN
ejpam-5330	234	47	,	,	PUNCT
ejpam-5330	234	48	gb	gb	ADP
ejpam-5330	234	49	⊑	⊑	PRON
ejpam-5330	234	50	td	td	PROPN
ejpam-5330	234	51	,	,	PUNCT
ejpam-5330	234	52	fa	fa	PROPN
ejpam-5330	234	53	̸	̸	PUNCT
ejpam-5330	234	54	q̃	q̃	PROPN
ejpam-5330	234	55	td	td	NOUN
ejpam-5330	234	56	,	,	PUNCT
ejpam-5330	234	57	and	and	CCONJ
ejpam-5330	234	58	gb	gb	PRON
ejpam-5330	234	59	̸	̸	PUNCT
ejpam-5330	234	60	q̃	q̃	PROPN
ejpam-5330	234	61	hc	hc	NOUN
ejpam-5330	234	62	.	.	PUNCT
ejpam-5330	235	1	proof	proof	NOUN
ejpam-5330	235	2	.	.	PUNCT
ejpam-5330	236	1	(	(	PUNCT
ejpam-5330	236	2	⇒	⇒	NOUN
ejpam-5330	236	3	)	)	PUNCT
ejpam-5330	236	4	let	let	AUX
ejpam-5330	236	5	fa	fa	NOUN
ejpam-5330	236	6	and	and	CCONJ
ejpam-5330	236	7	gb	gb	NOUN
ejpam-5330	236	8	∈	∈	PROPN
ejpam-5330	236	9	˜(w	˜(w	PROPN
ejpam-5330	236	10	,	,	PUNCT
ejpam-5330	236	11	n	n	CCONJ
ejpam-5330	236	12	)	)	PUNCT
ejpam-5330	236	13	be	be	AUX
ejpam-5330	236	14	an	an	DET
ejpam-5330	236	15	r	r	NOUN
ejpam-5330	236	16	-	-	PUNCT
ejpam-5330	236	17	fuzzy	fuzzy	ADJ
ejpam-5330	236	18	soft	soft	ADJ
ejpam-5330	236	19	α	α	NOUN
ejpam-5330	236	20	-	-	VERB
ejpam-5330	236	21	separated	separate	VERB
ejpam-5330	236	22	,	,	PUNCT
ejpam-5330	236	23	fa	fa	X
ejpam-5330	236	24	⊑	⊑	X
ejpam-5330	236	25	(	(	PUNCT
ejpam-5330	236	26	αcτ	αcτ	X
ejpam-5330	236	27	(	(	PUNCT
ejpam-5330	236	28	n	n	CCONJ
ejpam-5330	236	29	,	,	PUNCT
ejpam-5330	236	30	gb	gb	ADJ
ejpam-5330	236	31	,	,	PUNCT
ejpam-5330	236	32	r	r	NOUN
ejpam-5330	236	33	)	)	PUNCT
ejpam-5330	236	34	)	)	PUNCT
ejpam-5330	237	1	c	c	NOUN
ejpam-5330	237	2	=	=	SYM
ejpam-5330	237	3	hc	hc	PROPN
ejpam-5330	237	4	and	and	CCONJ
ejpam-5330	237	5	gb	gb	ADP
ejpam-5330	237	6	⊑	⊑	X
ejpam-5330	237	7	(	(	PUNCT
ejpam-5330	237	8	αcτ	αcτ	X
ejpam-5330	237	9	(	(	PUNCT
ejpam-5330	237	10	n	n	X
ejpam-5330	237	11	,	,	PUNCT
ejpam-5330	237	12	fa	fa	NOUN
ejpam-5330	237	13	,	,	PUNCT
ejpam-5330	237	14	r	r	NOUN
ejpam-5330	237	15	)	)	PUNCT
ejpam-5330	237	16	)	)	PUNCT
ejpam-5330	238	1	c	c	NOUN
ejpam-5330	239	1	=	=	SYM
ejpam-5330	239	2	td	td	NOUN
ejpam-5330	239	3	,	,	PUNCT
ejpam-5330	239	4	where	where	SCONJ
ejpam-5330	239	5	td	td	NOUN
ejpam-5330	239	6	and	and	CCONJ
ejpam-5330	239	7	hc	hc	PROPN
ejpam-5330	239	8	are	be	AUX
ejpam-5330	239	9	r	r	NOUN
ejpam-5330	239	10	-	-	PUNCT
ejpam-5330	239	11	fuzzy	fuzzy	ADJ
ejpam-5330	239	12	soft	soft	ADJ
ejpam-5330	239	13	α	α	NOUN
ejpam-5330	239	14	-	-	ADJ
ejpam-5330	239	15	open	open	ADJ
ejpam-5330	239	16	,	,	PUNCT
ejpam-5330	239	17	then	then	ADV
ejpam-5330	239	18	td	td	NOUN
ejpam-5330	239	19	̸	̸	ADV
ejpam-5330	239	20	q̃αcτ	q̃αcτ	NOUN
ejpam-5330	239	21	(	(	PUNCT
ejpam-5330	239	22	n	n	X
ejpam-5330	239	23	,	,	PUNCT
ejpam-5330	239	24	fa	fa	NOUN
ejpam-5330	239	25	,	,	PUNCT
ejpam-5330	239	26	r	r	NOUN
ejpam-5330	239	27	)	)	PUNCT
ejpam-5330	239	28	and	and	CCONJ
ejpam-5330	239	29	hc	hc	PRON
ejpam-5330	239	30	̸	̸	ADV
ejpam-5330	239	31	q̃αcτ	q̃αcτ	NOUN
ejpam-5330	239	32	(	(	PUNCT
ejpam-5330	239	33	n	n	CCONJ
ejpam-5330	239	34	,	,	PUNCT
ejpam-5330	239	35	gb	gb	ADJ
ejpam-5330	239	36	,	,	PUNCT
ejpam-5330	239	37	r	r	NOUN
ejpam-5330	239	38	)	)	PUNCT
ejpam-5330	239	39	.	.	PUNCT
ejpam-5330	240	1	thus	thus	ADV
ejpam-5330	240	2	,	,	PUNCT
ejpam-5330	240	3	gb	gb	ADP
ejpam-5330	240	4	̸	̸	PUNCT
ejpam-5330	240	5	q̃	q̃	PROPN
ejpam-5330	240	6	hc	hc	PROPN
ejpam-5330	240	7	and	and	CCONJ
ejpam-5330	240	8	fa	fa	PROPN
ejpam-5330	240	9	̸	̸	PUNCT
ejpam-5330	240	10	q̃	q̃	PROPN
ejpam-5330	240	11	td	td	NOUN
ejpam-5330	240	12	.	.	PUNCT
ejpam-5330	241	1	hence	hence	ADV
ejpam-5330	241	2	,	,	PUNCT
ejpam-5330	241	3	we	we	PRON
ejpam-5330	241	4	obtain	obtain	VERB
ejpam-5330	241	5	the	the	DET
ejpam-5330	241	6	required	require	VERB
ejpam-5330	241	7	result	result	NOUN
ejpam-5330	241	8	.	.	PUNCT
ejpam-5330	242	1	(	(	PUNCT
ejpam-5330	242	2	⇐	⇐	ADJ
ejpam-5330	242	3	)	)	PUNCT
ejpam-5330	242	4	let	let	VERB
ejpam-5330	242	5	hc	hc	PRON
ejpam-5330	242	6	and	and	CCONJ
ejpam-5330	242	7	td	td	NOUN
ejpam-5330	242	8	be	be	AUX
ejpam-5330	242	9	an	an	DET
ejpam-5330	242	10	r	r	NOUN
ejpam-5330	242	11	-	-	PUNCT
ejpam-5330	242	12	fuzzy	fuzzy	ADJ
ejpam-5330	242	13	soft	soft	ADJ
ejpam-5330	242	14	α	α	NOUN
ejpam-5330	242	15	-	-	NOUN
ejpam-5330	242	16	open	open	ADJ
ejpam-5330	242	17	such	such	ADJ
ejpam-5330	242	18	that	that	PRON
ejpam-5330	242	19	gb	gb	ADP
ejpam-5330	242	20	⊑	⊑	PRON
ejpam-5330	242	21	td	td	PROPN
ejpam-5330	242	22	,	,	PUNCT
ejpam-5330	242	23	fa	fa	X
ejpam-5330	242	24	⊑	⊑	DET
ejpam-5330	242	25	hc	hc	PROPN
ejpam-5330	242	26	,	,	PUNCT
ejpam-5330	242	27	gb	gb	ADP
ejpam-5330	242	28	̸	̸	PUNCT
ejpam-5330	242	29	q̃	q̃	PROPN
ejpam-5330	242	30	hc	hc	PROPN
ejpam-5330	242	31	and	and	CCONJ
ejpam-5330	242	32	fa	fa	PROPN
ejpam-5330	242	33	̸	̸	PUNCT
ejpam-5330	242	34	q̃	q̃	PROPN
ejpam-5330	242	35	td	td	NOUN
ejpam-5330	242	36	.	.	PUNCT
ejpam-5330	243	1	then	then	ADV
ejpam-5330	243	2	,	,	PUNCT
ejpam-5330	243	3	gb	gb	ADP
ejpam-5330	243	4	⊑	⊑	DET
ejpam-5330	243	5	hcc	hcc	PROPN
ejpam-5330	243	6	and	and	CCONJ
ejpam-5330	243	7	fa	fa	PROPN
ejpam-5330	243	8	⊑	⊑	DET
ejpam-5330	243	9	tcd	tcd	PROPN
ejpam-5330	243	10	.	.	PUNCT
ejpam-5330	244	1	hence	hence	ADV
ejpam-5330	244	2	,	,	PUNCT
ejpam-5330	244	3	αcτ	αcτ	X
ejpam-5330	244	4	(	(	PUNCT
ejpam-5330	244	5	n	n	CCONJ
ejpam-5330	244	6	,	,	PUNCT
ejpam-5330	244	7	gb	gb	ADJ
ejpam-5330	244	8	,	,	PUNCT
ejpam-5330	244	9	r	r	NOUN
ejpam-5330	244	10	)	)	PUNCT
ejpam-5330	244	11	⊑	⊑	PROPN
ejpam-5330	244	12	hcc	hcc	PROPN
ejpam-5330	244	13	and	and	CCONJ
ejpam-5330	244	14	αcτ	αcτ	PROPN
ejpam-5330	244	15	(	(	PUNCT
ejpam-5330	244	16	n	n	X
ejpam-5330	244	17	,	,	PUNCT
ejpam-5330	244	18	fa	fa	NOUN
ejpam-5330	244	19	,	,	PUNCT
ejpam-5330	244	20	r	r	NOUN
ejpam-5330	244	21	)	)	PUNCT
ejpam-5330	244	22	⊑	⊑	PRON
ejpam-5330	244	23	tcd	tcd	PROPN
ejpam-5330	244	24	.	.	PUNCT
ejpam-5330	245	1	then	then	ADV
ejpam-5330	245	2	,	,	PUNCT
ejpam-5330	245	3	αcτ	αcτ	X
ejpam-5330	245	4	(	(	PUNCT
ejpam-5330	245	5	n	n	CCONJ
ejpam-5330	245	6	,	,	PUNCT
ejpam-5330	245	7	gb	gb	ADJ
ejpam-5330	245	8	,	,	PUNCT
ejpam-5330	245	9	r)̸	r)̸	PROPN
ejpam-5330	245	10	q̃	q̃	PROPN
ejpam-5330	245	11	fa	fa	PROPN
ejpam-5330	245	12	and	and	CCONJ
ejpam-5330	245	13	αcτ	αcτ	PROPN
ejpam-5330	245	14	(	(	PUNCT
ejpam-5330	245	15	n	n	X
ejpam-5330	245	16	,	,	PUNCT
ejpam-5330	245	17	fa	fa	NOUN
ejpam-5330	245	18	,	,	PUNCT
ejpam-5330	245	19	r	r	NOUN
ejpam-5330	245	20	)	)	PUNCT
ejpam-5330	245	21	̸	̸	PUNCT
ejpam-5330	245	22	q̃	q̃	PROPN
ejpam-5330	245	23	gb	gb	PRON
ejpam-5330	245	24	.	.	PUNCT
ejpam-5330	246	1	thus	thus	ADV
ejpam-5330	246	2	,	,	PUNCT
ejpam-5330	246	3	gb	gb	PRON
ejpam-5330	246	4	and	and	CCONJ
ejpam-5330	246	5	fa	fa	PROPN
ejpam-5330	246	6	are	be	AUX
ejpam-5330	246	7	rfuzzy	rfuzzy	ADJ
ejpam-5330	246	8	soft	soft	ADJ
ejpam-5330	246	9	αseparated	αseparate	VERB
ejpam-5330	246	10	.	.	PUNCT
ejpam-5330	247	1	hence	hence	ADV
ejpam-5330	247	2	,	,	PUNCT
ejpam-5330	247	3	we	we	PRON
ejpam-5330	247	4	obtain	obtain	VERB
ejpam-5330	247	5	the	the	DET
ejpam-5330	247	6	required	require	VERB
ejpam-5330	247	7	result	result	NOUN
ejpam-5330	247	8	.	.	PUNCT
ejpam-5330	248	1	theorem	theorem	ADJ
ejpam-5330	248	2	5	5	NUM
ejpam-5330	248	3	.	.	PUNCT
ejpam-5330	249	1	in	in	ADP
ejpam-5330	249	2	an	an	DET
ejpam-5330	249	3	fsts	fst	NOUN
ejpam-5330	249	4	(	(	PUNCT
ejpam-5330	249	5	w	w	NOUN
ejpam-5330	249	6	,	,	PUNCT
ejpam-5330	249	7	τn	τn	NOUN
ejpam-5330	249	8	)	)	PUNCT
ejpam-5330	249	9	,	,	PUNCT
ejpam-5330	249	10	if	if	SCONJ
ejpam-5330	249	11	gb	gb	ADP
ejpam-5330	249	12	∈	∈	PROPN
ejpam-5330	249	13	˜(w	˜(w	PROPN
ejpam-5330	249	14	,	,	PUNCT
ejpam-5330	249	15	n	n	CCONJ
ejpam-5330	249	16	)	)	PUNCT
ejpam-5330	249	17	is	be	AUX
ejpam-5330	249	18	r	r	NOUN
ejpam-5330	249	19	-	-	PUNCT
ejpam-5330	249	20	fuzzy	fuzzy	ADJ
ejpam-5330	249	21	soft	soft	ADJ
ejpam-5330	249	22	α	α	NOUN
ejpam-5330	249	23	-	-	VERB
ejpam-5330	249	24	connected	connect	VERB
ejpam-5330	249	25	such	such	ADJ
ejpam-5330	249	26	that	that	DET
ejpam-5330	249	27	gb	gb	ADP
ejpam-5330	249	28	⊑	⊑	X
ejpam-5330	249	29	fa	fa	X
ejpam-5330	249	30	⊑	⊑	X
ejpam-5330	249	31	αcτ	αcτ	X
ejpam-5330	249	32	(	(	PUNCT
ejpam-5330	249	33	n	n	CCONJ
ejpam-5330	249	34	,	,	PUNCT
ejpam-5330	249	35	gb	gb	ADJ
ejpam-5330	249	36	,	,	PUNCT
ejpam-5330	249	37	r	r	NOUN
ejpam-5330	249	38	)	)	PUNCT
ejpam-5330	249	39	,	,	PUNCT
ejpam-5330	249	40	then	then	ADV
ejpam-5330	249	41	fa	fa	PROPN
ejpam-5330	249	42	is	be	AUX
ejpam-5330	249	43	r	r	NOUN
ejpam-5330	249	44	-	-	PUNCT
ejpam-5330	249	45	fuzzy	fuzzy	ADJ
ejpam-5330	249	46	soft	soft	ADJ
ejpam-5330	249	47	α	α	NOUN
ejpam-5330	249	48	-	-	PUNCT
ejpam-5330	249	49	connected	connect	VERB
ejpam-5330	249	50	.	.	PUNCT
ejpam-5330	250	1	w.	w.	PROPN
ejpam-5330	250	2	alqurashi	alqurashi	PROPN
ejpam-5330	250	3	,	,	PUNCT
ejpam-5330	250	4	i.	i.	PROPN
ejpam-5330	250	5	m.	m.	PROPN
ejpam-5330	250	6	taha	taha	PROPN
ejpam-5330	250	7	/	/	PUNCT
ejpam-5330	250	8	eur	eur	PROPN
ejpam-5330	250	9	.	.	PUNCT
ejpam-5330	251	1	j.	j.	PROPN
ejpam-5330	251	2	pure	pure	PROPN
ejpam-5330	251	3	appl	appl	PROPN
ejpam-5330	251	4	.	.	PROPN
ejpam-5330	251	5	math	math	PROPN
ejpam-5330	251	6	,	,	PUNCT
ejpam-5330	251	7	17	17	NUM
ejpam-5330	251	8	(	(	PUNCT
ejpam-5330	251	9	4	4	NUM
ejpam-5330	251	10	)	)	PUNCT
ejpam-5330	251	11	(	(	PUNCT
ejpam-5330	251	12	2024	2024	NUM
ejpam-5330	251	13	)	)	PUNCT
ejpam-5330	251	14	,	,	PUNCT
ejpam-5330	251	15	4112	4112	NUM
ejpam-5330	251	16	-	-	SYM
ejpam-5330	251	17	4134	4134	NUM
ejpam-5330	251	18	4121	4121	NUM
ejpam-5330	251	19	proof	proof	NOUN
ejpam-5330	251	20	.	.	PUNCT
ejpam-5330	251	21	suppose	suppose	VERB
ejpam-5330	251	22	that	that	SCONJ
ejpam-5330	251	23	fa	fa	PROPN
ejpam-5330	251	24	is	be	AUX
ejpam-5330	251	25	not	not	PART
ejpam-5330	251	26	r	r	NOUN
ejpam-5330	251	27	-	-	PUNCT
ejpam-5330	251	28	fuzzy	fuzzy	ADJ
ejpam-5330	251	29	soft	soft	ADJ
ejpam-5330	251	30	α	α	NOUN
ejpam-5330	251	31	-	-	VERB
ejpam-5330	251	32	connected	connect	VERB
ejpam-5330	251	33	,	,	PUNCT
ejpam-5330	251	34	then	then	ADV
ejpam-5330	251	35	there	there	PRON
ejpam-5330	251	36	is	be	VERB
ejpam-5330	251	37	r	r	NOUN
ejpam-5330	251	38	-	-	PUNCT
ejpam-5330	251	39	fuzzy	fuzzy	ADJ
ejpam-5330	251	40	soft	soft	ADJ
ejpam-5330	251	41	α	α	NOUN
ejpam-5330	251	42	-	-	PUNCT
ejpam-5330	251	43	separated	separate	VERB
ejpam-5330	251	44	sets	set	NOUN
ejpam-5330	251	45	h∗c	h∗c	VERB
ejpam-5330	251	46	and	and	CCONJ
ejpam-5330	251	47	t∗d	t∗d	PROPN
ejpam-5330	251	48	∈	∈	PROPN
ejpam-5330	251	49	˜(w	˜(w	PROPN
ejpam-5330	251	50	,	,	PUNCT
ejpam-5330	251	51	n	n	CCONJ
ejpam-5330	251	52	)	)	PUNCT
ejpam-5330	252	1	such	such	ADJ
ejpam-5330	252	2	that	that	PRON
ejpam-5330	252	3	fa	fa	PROPN
ejpam-5330	253	1	=	=	SYM
ejpam-5330	253	2	h∗c	h∗c	X
ejpam-5330	253	3	⊔	⊔	PROPN
ejpam-5330	253	4	t∗d	t∗d	NOUN
ejpam-5330	253	5	.	.	PUNCT
ejpam-5330	254	1	let	let	VERB
ejpam-5330	254	2	hc	hc	VERB
ejpam-5330	254	3	=	=	PUNCT
ejpam-5330	254	4	gb	gb	PROPN
ejpam-5330	254	5	⊓	⊓	PROPN
ejpam-5330	254	6	h∗c	h∗c	PUNCT
ejpam-5330	254	7	and	and	CCONJ
ejpam-5330	254	8	td	td	NOUN
ejpam-5330	254	9	=	=	PUNCT
ejpam-5330	254	10	gb	gb	ADJ
ejpam-5330	254	11	⊓	⊓	PROPN
ejpam-5330	254	12	t∗d	t∗d	NOUN
ejpam-5330	254	13	,	,	PUNCT
ejpam-5330	254	14	then	then	ADV
ejpam-5330	254	15	gb	gb	NOUN
ejpam-5330	254	16	=	=	NOUN
ejpam-5330	254	17	td	td	NOUN
ejpam-5330	254	18	⊔	⊔	PROPN
ejpam-5330	254	19	hc	hc	PROPN
ejpam-5330	254	20	.	.	PUNCT
ejpam-5330	255	1	since	since	SCONJ
ejpam-5330	255	2	hc	hc	PROPN
ejpam-5330	255	3	⊑	⊑	PRON
ejpam-5330	255	4	h∗c	h∗c	PUNCT
ejpam-5330	255	5	and	and	CCONJ
ejpam-5330	255	6	td	td	VERB
ejpam-5330	255	7	⊑	⊑	PRON
ejpam-5330	255	8	t∗d	t∗d	NOUN
ejpam-5330	255	9	,	,	PUNCT
ejpam-5330	255	10	by	by	ADP
ejpam-5330	255	11	theorem	theorem	NOUN
ejpam-5330	255	12	3(1	3(1	NUM
ejpam-5330	255	13	)	)	PUNCT
ejpam-5330	255	14	,	,	PUNCT
ejpam-5330	255	15	hc	hc	PROPN
ejpam-5330	255	16	and	and	CCONJ
ejpam-5330	255	17	td	td	NOUN
ejpam-5330	255	18	are	be	AUX
ejpam-5330	255	19	r	r	NOUN
ejpam-5330	255	20	-	-	PUNCT
ejpam-5330	255	21	fuzzy	fuzzy	ADJ
ejpam-5330	255	22	soft	soft	ADJ
ejpam-5330	255	23	α	α	NOUN
ejpam-5330	255	24	-	-	VERB
ejpam-5330	255	25	separated	separate	VERB
ejpam-5330	255	26	,	,	PUNCT
ejpam-5330	255	27	which	which	PRON
ejpam-5330	255	28	is	be	AUX
ejpam-5330	255	29	a	a	DET
ejpam-5330	255	30	contradiction	contradiction	NOUN
ejpam-5330	255	31	.	.	PUNCT
ejpam-5330	256	1	thus	thus	ADV
ejpam-5330	256	2	,	,	PUNCT
ejpam-5330	256	3	fa	fa	PROPN
ejpam-5330	256	4	is	be	AUX
ejpam-5330	256	5	r	r	NOUN
ejpam-5330	256	6	-	-	PUNCT
ejpam-5330	256	7	fuzzy	fuzzy	ADJ
ejpam-5330	256	8	soft	soft	ADJ
ejpam-5330	256	9	α	α	NOUN
ejpam-5330	256	10	-	-	VERB
ejpam-5330	256	11	connected	connect	VERB
ejpam-5330	256	12	,	,	PUNCT
ejpam-5330	256	13	as	as	SCONJ
ejpam-5330	256	14	required	require	VERB
ejpam-5330	256	15	.	.	PUNCT
ejpam-5330	257	1	3	3	X
ejpam-5330	257	2	.	.	X
ejpam-5330	257	3	on	on	ADP
ejpam-5330	257	4	fuzzy	fuzzy	ADJ
ejpam-5330	257	5	soft	soft	ADJ
ejpam-5330	257	6	α	α	NOUN
ejpam-5330	257	7	-	-	NOUN
ejpam-5330	257	8	continuity	continuity	NOUN
ejpam-5330	257	9	here	here	ADV
ejpam-5330	257	10	,	,	PUNCT
ejpam-5330	257	11	we	we	PRON
ejpam-5330	257	12	investigate	investigate	VERB
ejpam-5330	257	13	some	some	DET
ejpam-5330	257	14	properties	property	NOUN
ejpam-5330	257	15	of	of	ADP
ejpam-5330	257	16	fuzzy	fuzzy	ADJ
ejpam-5330	257	17	soft	soft	ADJ
ejpam-5330	257	18	α	α	ADJ
ejpam-5330	257	19	-	-	ADJ
ejpam-5330	257	20	continuous	continuous	ADJ
ejpam-5330	257	21	mappings	mapping	NOUN
ejpam-5330	257	22	.	.	PUNCT
ejpam-5330	258	1	additionally	additionally	ADV
ejpam-5330	258	2	,	,	PUNCT
ejpam-5330	258	3	we	we	PRON
ejpam-5330	258	4	introduce	introduce	VERB
ejpam-5330	258	5	and	and	CCONJ
ejpam-5330	258	6	study	study	VERB
ejpam-5330	258	7	the	the	DET
ejpam-5330	258	8	notions	notion	NOUN
ejpam-5330	258	9	of	of	ADP
ejpam-5330	258	10	fuzzy	fuzzy	ADJ
ejpam-5330	258	11	soft	soft	ADJ
ejpam-5330	258	12	almost	almost	ADV
ejpam-5330	258	13	(	(	PUNCT
ejpam-5330	258	14	weakly	weakly	ADJ
ejpam-5330	258	15	)	)	PUNCT
ejpam-5330	258	16	α	α	NUM
ejpam-5330	258	17	-	-	ADJ
ejpam-5330	258	18	continuous	continuous	ADJ
ejpam-5330	258	19	mappings	mapping	NOUN
ejpam-5330	258	20	,	,	PUNCT
ejpam-5330	258	21	which	which	PRON
ejpam-5330	258	22	are	be	AUX
ejpam-5330	258	23	weaker	weak	ADJ
ejpam-5330	258	24	forms	form	NOUN
ejpam-5330	258	25	of	of	ADP
ejpam-5330	258	26	fuzzy	fuzzy	ADJ
ejpam-5330	258	27	soft	soft	ADJ
ejpam-5330	258	28	α	α	ADJ
ejpam-5330	258	29	-	-	ADJ
ejpam-5330	258	30	continuous	continuous	ADJ
ejpam-5330	258	31	mappings	mapping	NOUN
ejpam-5330	258	32	.	.	PUNCT
ejpam-5330	259	1	also	also	ADV
ejpam-5330	259	2	,	,	PUNCT
ejpam-5330	259	3	we	we	PRON
ejpam-5330	259	4	show	show	VERB
ejpam-5330	259	5	that	that	SCONJ
ejpam-5330	259	6	fuzzy	fuzzy	ADJ
ejpam-5330	259	7	soft	soft	ADJ
ejpam-5330	259	8	α	α	NOUN
ejpam-5330	259	9	-	-	PUNCT
ejpam-5330	259	10	continuity	continuity	NOUN
ejpam-5330	259	11	⇒	⇒	NOUN
ejpam-5330	259	12	fuzzy	fuzzy	ADJ
ejpam-5330	259	13	soft	soft	ADJ
ejpam-5330	259	14	almost	almost	ADV
ejpam-5330	259	15	α	α	NOUN
ejpam-5330	259	16	-	-	PUNCT
ejpam-5330	259	17	continuity	continuity	NOUN
ejpam-5330	259	18	⇒	⇒	NOUN
ejpam-5330	259	19	fuzzy	fuzzy	ADJ
ejpam-5330	259	20	soft	soft	ADJ
ejpam-5330	259	21	weakly	weakly	ADJ
ejpam-5330	259	22	α	α	NOUN
ejpam-5330	259	23	-	-	NOUN
ejpam-5330	259	24	continuity	continuity	NOUN
ejpam-5330	259	25	.	.	PUNCT
ejpam-5330	260	1	definition	definition	NOUN
ejpam-5330	260	2	15	15	NUM
ejpam-5330	260	3	.	.	PUNCT
ejpam-5330	261	1	[	[	X
ejpam-5330	261	2	11	11	NUM
ejpam-5330	261	3	]	]	X
ejpam-5330	261	4	let	let	VERB
ejpam-5330	261	5	(	(	PUNCT
ejpam-5330	261	6	w	w	NOUN
ejpam-5330	261	7	,	,	PUNCT
ejpam-5330	261	8	τn	τn	PROPN
ejpam-5330	261	9	)	)	PUNCT
ejpam-5330	261	10	and	and	CCONJ
ejpam-5330	261	11	(	(	PUNCT
ejpam-5330	261	12	v	v	NOUN
ejpam-5330	261	13	,	,	PUNCT
ejpam-5330	261	14	ηf	ηf	PROPN
ejpam-5330	261	15	)	)	PUNCT
ejpam-5330	261	16	be	be	AUX
ejpam-5330	261	17	an	an	DET
ejpam-5330	261	18	fstss	fstss	NOUN
ejpam-5330	261	19	and	and	CCONJ
ejpam-5330	261	20	r	r	NOUN
ejpam-5330	261	21	∈	∈	PROPN
ejpam-5330	261	22	io	io	X
ejpam-5330	261	23	.	.	PUNCT
ejpam-5330	262	1	a	a	DET
ejpam-5330	262	2	fuzzy	fuzzy	ADJ
ejpam-5330	262	3	soft	soft	ADJ
ejpam-5330	262	4	mapping	mapping	NOUN
ejpam-5330	262	5	φψ	φψ	X
ejpam-5330	262	6	:	:	PUNCT
ejpam-5330	262	7	˜(w	˜(w	PROPN
ejpam-5330	262	8	,	,	PUNCT
ejpam-5330	262	9	n	n	CCONJ
ejpam-5330	262	10	)	)	PUNCT
ejpam-5330	262	11	−→	−→	NOUN
ejpam-5330	262	12	(	(	PUNCT
ejpam-5330	262	13	̃v	̃v	NOUN
ejpam-5330	262	14	,	,	PUNCT
ejpam-5330	262	15	f	f	PROPN
ejpam-5330	262	16	)	)	PUNCT
ejpam-5330	262	17	is	be	AUX
ejpam-5330	262	18	called	call	VERB
ejpam-5330	262	19	fuzzy	fuzzy	ADJ
ejpam-5330	262	20	soft	soft	ADJ
ejpam-5330	262	21	α	α	NOUN
ejpam-5330	262	22	-	-	ADJ
ejpam-5330	262	23	continuous	continuous	ADJ
ejpam-5330	262	24	if	if	SCONJ
ejpam-5330	262	25	φ−1	φ−1	PROPN
ejpam-5330	262	26	ψ	ψ	X
ejpam-5330	262	27	(	(	PUNCT
ejpam-5330	262	28	hc	hc	NOUN
ejpam-5330	262	29	)	)	PUNCT
ejpam-5330	262	30	is	be	AUX
ejpam-5330	262	31	r	r	NOUN
ejpam-5330	262	32	-	-	PUNCT
ejpam-5330	262	33	fuzzy	fuzzy	ADJ
ejpam-5330	262	34	soft	soft	ADJ
ejpam-5330	262	35	α	α	NOUN
ejpam-5330	262	36	-	-	ADJ
ejpam-5330	262	37	open	open	ADJ
ejpam-5330	262	38	set	set	NOUN
ejpam-5330	262	39	for	for	ADP
ejpam-5330	262	40	each	each	DET
ejpam-5330	262	41	hc	hc	PROPN
ejpam-5330	262	42	∈	∈	PROPN
ejpam-5330	262	43	(	(	PUNCT
ejpam-5330	262	44	̃v	̃v	NOUN
ejpam-5330	262	45	,	,	PUNCT
ejpam-5330	262	46	f	f	PROPN
ejpam-5330	262	47	)	)	PUNCT
ejpam-5330	262	48	with	with	ADP
ejpam-5330	262	49	ηk(hc	ηk(hc	PROPN
ejpam-5330	262	50	)	)	PUNCT
ejpam-5330	263	1	≥	≥	PROPN
ejpam-5330	263	2	r	r	NOUN
ejpam-5330	263	3	,	,	PUNCT
ejpam-5330	263	4	n	n	NOUN
ejpam-5330	263	5	∈	∈	NOUN
ejpam-5330	263	6	n	n	NOUN
ejpam-5330	263	7	,	,	PUNCT
ejpam-5330	263	8	and	and	CCONJ
ejpam-5330	263	9	(	(	PUNCT
ejpam-5330	263	10	k	k	X
ejpam-5330	263	11	=	=	SYM
ejpam-5330	263	12	ψ(n	ψ(n	PROPN
ejpam-5330	263	13	)	)	PUNCT
ejpam-5330	263	14	)	)	PUNCT
ejpam-5330	264	1	∈	∈	PROPN
ejpam-5330	264	2	f	f	PROPN
ejpam-5330	264	3	.	.	PUNCT
ejpam-5330	265	1	theorem	theorem	ADJ
ejpam-5330	265	2	6	6	NUM
ejpam-5330	265	3	.	.	PUNCT
ejpam-5330	266	1	let	let	VERB
ejpam-5330	266	2	(	(	PUNCT
ejpam-5330	266	3	w	w	NOUN
ejpam-5330	266	4	,	,	PUNCT
ejpam-5330	266	5	τn	τn	PROPN
ejpam-5330	266	6	)	)	PUNCT
ejpam-5330	266	7	and	and	CCONJ
ejpam-5330	266	8	(	(	PUNCT
ejpam-5330	266	9	v	v	NOUN
ejpam-5330	266	10	,	,	PUNCT
ejpam-5330	266	11	ηf	ηf	PROPN
ejpam-5330	266	12	)	)	PUNCT
ejpam-5330	266	13	be	be	AUX
ejpam-5330	266	14	an	an	DET
ejpam-5330	266	15	fstss	fstss	NOUN
ejpam-5330	266	16	,	,	PUNCT
ejpam-5330	266	17	and	and	CCONJ
ejpam-5330	266	18	φψ	φψ	PROPN
ejpam-5330	266	19	:	:	PUNCT
ejpam-5330	266	20	˜(w	˜(w	PROPN
ejpam-5330	266	21	,	,	PUNCT
ejpam-5330	266	22	n	n	CCONJ
ejpam-5330	266	23	)	)	PUNCT
ejpam-5330	266	24	−→	−→	NOUN
ejpam-5330	266	25	(	(	PUNCT
ejpam-5330	266	26	̃v	̃v	NOUN
ejpam-5330	266	27	,	,	PUNCT
ejpam-5330	266	28	f	f	PROPN
ejpam-5330	266	29	)	)	PUNCT
ejpam-5330	266	30	be	be	AUX
ejpam-5330	266	31	a	a	DET
ejpam-5330	266	32	fuzzy	fuzzy	ADJ
ejpam-5330	266	33	soft	soft	ADJ
ejpam-5330	266	34	mapping	mapping	NOUN
ejpam-5330	266	35	.	.	PUNCT
ejpam-5330	267	1	the	the	DET
ejpam-5330	267	2	following	follow	VERB
ejpam-5330	267	3	statements	statement	NOUN
ejpam-5330	267	4	are	be	AUX
ejpam-5330	267	5	equivalent	equivalent	ADJ
ejpam-5330	267	6	for	for	ADP
ejpam-5330	267	7	each	each	DET
ejpam-5330	267	8	fa	fa	X
ejpam-5330	267	9	∈	∈	PROPN
ejpam-5330	267	10	(	(	PUNCT
ejpam-5330	267	11	̃v	̃v	NOUN
ejpam-5330	267	12	,	,	PUNCT
ejpam-5330	267	13	f	f	PROPN
ejpam-5330	267	14	)	)	PUNCT
ejpam-5330	267	15	,	,	PUNCT
ejpam-5330	267	16	n	n	PROPN
ejpam-5330	267	17	∈	∈	PROPN
ejpam-5330	267	18	n	n	NOUN
ejpam-5330	267	19	,	,	PUNCT
ejpam-5330	267	20	(	(	PUNCT
ejpam-5330	267	21	k	k	NOUN
ejpam-5330	267	22	=	=	SYM
ejpam-5330	267	23	ψ(n	ψ(n	PROPN
ejpam-5330	267	24	)	)	PUNCT
ejpam-5330	267	25	)	)	PUNCT
ejpam-5330	268	1	∈	∈	PROPN
ejpam-5330	268	2	f	f	X
ejpam-5330	268	3	,	,	PUNCT
ejpam-5330	268	4	and	and	CCONJ
ejpam-5330	268	5	r	r	NOUN
ejpam-5330	268	6	∈	∈	PROPN
ejpam-5330	268	7	i	i	PRON
ejpam-5330	268	8	◦	◦	NOUN
ejpam-5330	268	9	:	:	PUNCT
ejpam-5330	268	10	(	(	PUNCT
ejpam-5330	268	11	1	1	X
ejpam-5330	268	12	)	)	PUNCT
ejpam-5330	268	13	φψ	φψ	NOUN
ejpam-5330	268	14	is	be	AUX
ejpam-5330	268	15	fuzzy	fuzzy	ADJ
ejpam-5330	268	16	soft	soft	ADJ
ejpam-5330	268	17	α	α	NOUN
ejpam-5330	268	18	-	-	ADJ
ejpam-5330	268	19	continuous	continuous	ADJ
ejpam-5330	268	20	.	.	PUNCT
ejpam-5330	269	1	(	(	PUNCT
ejpam-5330	269	2	2	2	NUM
ejpam-5330	269	3	)	)	PUNCT
ejpam-5330	269	4	for	for	ADP
ejpam-5330	269	5	each	each	DET
ejpam-5330	269	6	fa	fa	NOUN
ejpam-5330	269	7	with	with	ADP
ejpam-5330	269	8	ηk(f	ηk(f	X
ejpam-5330	269	9	c	c	PROPN
ejpam-5330	269	10	a	a	PRON
ejpam-5330	269	11	)	)	PUNCT
ejpam-5330	269	12	≥	≥	NOUN
ejpam-5330	269	13	r	r	NOUN
ejpam-5330	269	14	,	,	PUNCT
ejpam-5330	269	15	φ−1	φ−1	PROPN
ejpam-5330	269	16	ψ	ψ	SYM
ejpam-5330	269	17	(	(	PUNCT
ejpam-5330	269	18	fa	fa	NOUN
ejpam-5330	269	19	)	)	PUNCT
ejpam-5330	269	20	is	be	AUX
ejpam-5330	269	21	r	r	NOUN
ejpam-5330	269	22	-	-	PUNCT
ejpam-5330	269	23	fuzzy	fuzzy	ADJ
ejpam-5330	269	24	soft	soft	ADJ
ejpam-5330	269	25	α	α	NOUN
ejpam-5330	269	26	-	-	VERB
ejpam-5330	269	27	closed	closed	ADJ
ejpam-5330	269	28	.	.	PUNCT
ejpam-5330	270	1	(	(	PUNCT
ejpam-5330	270	2	3	3	X
ejpam-5330	270	3	)	)	PUNCT
ejpam-5330	270	4	αcτ	αcτ	NOUN
ejpam-5330	270	5	(	(	PUNCT
ejpam-5330	270	6	n	n	X
ejpam-5330	270	7	,	,	PUNCT
ejpam-5330	270	8	φ	φ	PROPN
ejpam-5330	270	9	−1	−1	NOUN
ejpam-5330	270	10	ψ	ψ	X
ejpam-5330	270	11	(	(	PUNCT
ejpam-5330	270	12	fa	fa	NOUN
ejpam-5330	270	13	)	)	PUNCT
ejpam-5330	270	14	,	,	PUNCT
ejpam-5330	270	15	r	r	X
ejpam-5330	270	16	)	)	PUNCT
ejpam-5330	270	17	⊑	⊑	X
ejpam-5330	270	18	φ−1	φ−1	PROPN
ejpam-5330	270	19	ψ	ψ	X
ejpam-5330	270	20	(	(	PUNCT
ejpam-5330	270	21	cη(k	cη(k	PROPN
ejpam-5330	270	22	,	,	PUNCT
ejpam-5330	270	23	fa	fa	NOUN
ejpam-5330	270	24	,	,	PUNCT
ejpam-5330	270	25	r	r	NOUN
ejpam-5330	270	26	)	)	PUNCT
ejpam-5330	270	27	)	)	PUNCT
ejpam-5330	270	28	.	.	PUNCT
ejpam-5330	271	1	(	(	PUNCT
ejpam-5330	271	2	4	4	X
ejpam-5330	271	3	)	)	PUNCT
ejpam-5330	271	4	φ−1	φ−1	PROPN
ejpam-5330	271	5	ψ	ψ	SYM
ejpam-5330	271	6	(	(	PUNCT
ejpam-5330	271	7	iη(k	iη(k	PROPN
ejpam-5330	271	8	,	,	PUNCT
ejpam-5330	271	9	fa	fa	NOUN
ejpam-5330	271	10	,	,	PUNCT
ejpam-5330	271	11	r	r	NOUN
ejpam-5330	271	12	)	)	PUNCT
ejpam-5330	271	13	)	)	PUNCT
ejpam-5330	272	1	⊑	⊑	PROPN
ejpam-5330	272	2	αiτ	αiτ	PROPN
ejpam-5330	272	3	(	(	PUNCT
ejpam-5330	272	4	n	n	CCONJ
ejpam-5330	272	5	,	,	PUNCT
ejpam-5330	272	6	φ	φ	PROPN
ejpam-5330	272	7	−1	−1	NOUN
ejpam-5330	272	8	ψ	ψ	X
ejpam-5330	272	9	(	(	PUNCT
ejpam-5330	272	10	fa	fa	NOUN
ejpam-5330	272	11	)	)	PUNCT
ejpam-5330	272	12	,	,	PUNCT
ejpam-5330	272	13	r	r	NOUN
ejpam-5330	272	14	)	)	PUNCT
ejpam-5330	272	15	.	.	PUNCT
ejpam-5330	273	1	(	(	PUNCT
ejpam-5330	273	2	5	5	X
ejpam-5330	273	3	)	)	PUNCT
ejpam-5330	273	4	cτ	cτ	NOUN
ejpam-5330	273	5	(	(	PUNCT
ejpam-5330	273	6	n	n	CCONJ
ejpam-5330	273	7	,	,	PUNCT
ejpam-5330	273	8	iτ	iτ	X
ejpam-5330	273	9	(	(	PUNCT
ejpam-5330	273	10	n	n	CCONJ
ejpam-5330	273	11	,	,	PUNCT
ejpam-5330	273	12	cτ	cτ	INTJ
ejpam-5330	273	13	(	(	PUNCT
ejpam-5330	273	14	n	n	CCONJ
ejpam-5330	273	15	,	,	PUNCT
ejpam-5330	273	16	φ	φ	PROPN
ejpam-5330	273	17	−1	−1	NOUN
ejpam-5330	273	18	ψ	ψ	X
ejpam-5330	273	19	(	(	PUNCT
ejpam-5330	273	20	fa	fa	NOUN
ejpam-5330	273	21	)	)	PUNCT
ejpam-5330	273	22	,	,	PUNCT
ejpam-5330	273	23	r	r	NOUN
ejpam-5330	273	24	)	)	PUNCT
ejpam-5330	273	25	,	,	PUNCT
ejpam-5330	273	26	r	r	NOUN
ejpam-5330	273	27	)	)	PUNCT
ejpam-5330	273	28	,	,	PUNCT
ejpam-5330	273	29	r	r	X
ejpam-5330	273	30	)	)	PUNCT
ejpam-5330	273	31	⊑	⊑	X
ejpam-5330	273	32	φ−1	φ−1	PROPN
ejpam-5330	273	33	ψ	ψ	X
ejpam-5330	273	34	(	(	PUNCT
ejpam-5330	273	35	cη(k	cη(k	PROPN
ejpam-5330	273	36	,	,	PUNCT
ejpam-5330	273	37	fa	fa	NOUN
ejpam-5330	273	38	,	,	PUNCT
ejpam-5330	273	39	r	r	NOUN
ejpam-5330	273	40	)	)	PUNCT
ejpam-5330	273	41	)	)	PUNCT
ejpam-5330	273	42	.	.	PUNCT
ejpam-5330	274	1	proof	proof	NOUN
ejpam-5330	274	2	.	.	PUNCT
ejpam-5330	275	1	(	(	PUNCT
ejpam-5330	275	2	1	1	X
ejpam-5330	275	3	)	)	PUNCT
ejpam-5330	275	4	⇔	⇔	NOUN
ejpam-5330	275	5	(	(	PUNCT
ejpam-5330	275	6	2	2	NUM
ejpam-5330	275	7	)	)	PUNCT
ejpam-5330	275	8	follows	follow	VERB
ejpam-5330	275	9	from	from	ADP
ejpam-5330	275	10	remark	remark	NOUN
ejpam-5330	275	11	2	2	NUM
ejpam-5330	275	12	and	and	CCONJ
ejpam-5330	275	13	φ−1	φ−1	PROPN
ejpam-5330	275	14	ψ	ψ	X
ejpam-5330	275	15	(	(	PUNCT
ejpam-5330	275	16	f	f	PROPN
ejpam-5330	275	17	ca	ca	NOUN
ejpam-5330	275	18	)	)	PUNCT
ejpam-5330	275	19	=	=	PUNCT
ejpam-5330	276	1	(	(	PUNCT
ejpam-5330	276	2	φ−1	φ−1	PROPN
ejpam-5330	276	3	ψ	ψ	SYM
ejpam-5330	276	4	(	(	PUNCT
ejpam-5330	276	5	fa	fa	NOUN
ejpam-5330	276	6	)	)	PUNCT
ejpam-5330	276	7	)	)	PUNCT
ejpam-5330	276	8	c.	c.	NOUN
ejpam-5330	276	9	(	(	PUNCT
ejpam-5330	276	10	2	2	NUM
ejpam-5330	276	11	)	)	PUNCT
ejpam-5330	276	12	⇒	⇒	NOUN
ejpam-5330	276	13	(	(	PUNCT
ejpam-5330	276	14	3	3	X
ejpam-5330	276	15	)	)	PUNCT
ejpam-5330	276	16	let	let	VERB
ejpam-5330	276	17	fa	fa	X
ejpam-5330	276	18	∈	∈	PROPN
ejpam-5330	276	19	(	(	PUNCT
ejpam-5330	276	20	̃v	̃v	NOUN
ejpam-5330	276	21	,	,	PUNCT
ejpam-5330	276	22	f	f	PROPN
ejpam-5330	276	23	)	)	PUNCT
ejpam-5330	276	24	,	,	PUNCT
ejpam-5330	276	25	hence	hence	ADV
ejpam-5330	276	26	by	by	ADP
ejpam-5330	276	27	(	(	PUNCT
ejpam-5330	276	28	2	2	NUM
ejpam-5330	276	29	)	)	PUNCT
ejpam-5330	276	30	,	,	PUNCT
ejpam-5330	276	31	φ−1	φ−1	PROPN
ejpam-5330	276	32	ψ	ψ	X
ejpam-5330	276	33	(	(	PUNCT
ejpam-5330	276	34	cη(k	cη(k	PROPN
ejpam-5330	276	35	,	,	PUNCT
ejpam-5330	276	36	fa	fa	NOUN
ejpam-5330	276	37	,	,	PUNCT
ejpam-5330	276	38	r	r	NOUN
ejpam-5330	276	39	)	)	PUNCT
ejpam-5330	276	40	)	)	PUNCT
ejpam-5330	276	41	is	be	AUX
ejpam-5330	276	42	r	r	NOUN
ejpam-5330	276	43	-	-	PUNCT
ejpam-5330	276	44	fuzzy	fuzzy	ADJ
ejpam-5330	276	45	soft	soft	ADJ
ejpam-5330	276	46	α	α	NOUN
ejpam-5330	276	47	-	-	PUNCT
ejpam-5330	276	48	closed	closed	ADJ
ejpam-5330	276	49	.	.	PUNCT
ejpam-5330	277	1	then	then	ADV
ejpam-5330	277	2	,	,	PUNCT
ejpam-5330	277	3	we	we	PRON
ejpam-5330	277	4	obtain	obtain	VERB
ejpam-5330	277	5	αcτ	αcτ	X
ejpam-5330	277	6	(	(	PUNCT
ejpam-5330	277	7	n	n	X
ejpam-5330	277	8	,	,	PUNCT
ejpam-5330	277	9	φ	φ	PROPN
ejpam-5330	277	10	−1	−1	NOUN
ejpam-5330	277	11	ψ	ψ	X
ejpam-5330	277	12	(	(	PUNCT
ejpam-5330	277	13	fa	fa	NOUN
ejpam-5330	277	14	)	)	PUNCT
ejpam-5330	277	15	,	,	PUNCT
ejpam-5330	277	16	r	r	X
ejpam-5330	277	17	)	)	PUNCT
ejpam-5330	277	18	⊑	⊑	X
ejpam-5330	277	19	φ−1	φ−1	PROPN
ejpam-5330	277	20	ψ	ψ	X
ejpam-5330	277	21	(	(	PUNCT
ejpam-5330	277	22	cη(k	cη(k	PROPN
ejpam-5330	277	23	,	,	PUNCT
ejpam-5330	277	24	fa	fa	NOUN
ejpam-5330	277	25	,	,	PUNCT
ejpam-5330	277	26	r	r	NOUN
ejpam-5330	277	27	)	)	PUNCT
ejpam-5330	277	28	)	)	PUNCT
ejpam-5330	277	29	.	.	PUNCT
ejpam-5330	278	1	(	(	PUNCT
ejpam-5330	278	2	3	3	X
ejpam-5330	278	3	)	)	PUNCT
ejpam-5330	278	4	⇔	⇔	X
ejpam-5330	278	5	(	(	PUNCT
ejpam-5330	278	6	4	4	NUM
ejpam-5330	278	7	)	)	PUNCT
ejpam-5330	278	8	follows	follow	VERB
ejpam-5330	278	9	from	from	ADP
ejpam-5330	278	10	theorem	theorem	ADJ
ejpam-5330	278	11	2(7	2(7	NUM
ejpam-5330	278	12	)	)	PUNCT
ejpam-5330	278	13	.	.	PUNCT
ejpam-5330	279	1	w.	w.	PROPN
ejpam-5330	279	2	alqurashi	alqurashi	PROPN
ejpam-5330	279	3	,	,	PUNCT
ejpam-5330	279	4	i.	i.	PROPN
ejpam-5330	279	5	m.	m.	PROPN
ejpam-5330	279	6	taha	taha	PROPN
ejpam-5330	279	7	/	/	PUNCT
ejpam-5330	279	8	eur	eur	PROPN
ejpam-5330	279	9	.	.	PUNCT
ejpam-5330	280	1	j.	j.	PROPN
ejpam-5330	280	2	pure	pure	PROPN
ejpam-5330	280	3	appl	appl	PROPN
ejpam-5330	280	4	.	.	PROPN
ejpam-5330	280	5	math	math	PROPN
ejpam-5330	280	6	,	,	PUNCT
ejpam-5330	280	7	17	17	NUM
ejpam-5330	280	8	(	(	PUNCT
ejpam-5330	280	9	4	4	NUM
ejpam-5330	280	10	)	)	PUNCT
ejpam-5330	280	11	(	(	PUNCT
ejpam-5330	280	12	2024	2024	NUM
ejpam-5330	280	13	)	)	PUNCT
ejpam-5330	280	14	,	,	PUNCT
ejpam-5330	280	15	4112	4112	NUM
ejpam-5330	280	16	-	-	SYM
ejpam-5330	280	17	4134	4134	NUM
ejpam-5330	280	18	4122	4122	NUM
ejpam-5330	280	19	(	(	PUNCT
ejpam-5330	280	20	3)⇒	3)⇒	NUM
ejpam-5330	280	21	(	(	PUNCT
ejpam-5330	280	22	5	5	NUM
ejpam-5330	280	23	)	)	PUNCT
ejpam-5330	280	24	let	let	VERB
ejpam-5330	280	25	fa	fa	X
ejpam-5330	280	26	∈	∈	PROPN
ejpam-5330	280	27	(	(	PUNCT
ejpam-5330	280	28	̃v	̃v	NOUN
ejpam-5330	280	29	,	,	PUNCT
ejpam-5330	280	30	f	f	PROPN
ejpam-5330	280	31	)	)	PUNCT
ejpam-5330	280	32	,	,	PUNCT
ejpam-5330	280	33	hence	hence	ADV
ejpam-5330	280	34	by	by	ADP
ejpam-5330	280	35	(	(	PUNCT
ejpam-5330	280	36	3	3	NUM
ejpam-5330	280	37	)	)	PUNCT
ejpam-5330	280	38	,	,	PUNCT
ejpam-5330	280	39	we	we	PRON
ejpam-5330	280	40	obtain	obtain	VERB
ejpam-5330	280	41	cτ	cτ	ADP
ejpam-5330	280	42	(	(	PUNCT
ejpam-5330	280	43	n	n	CCONJ
ejpam-5330	280	44	,	,	PUNCT
ejpam-5330	280	45	iτ	iτ	X
ejpam-5330	280	46	(	(	PUNCT
ejpam-5330	280	47	n	n	CCONJ
ejpam-5330	280	48	,	,	PUNCT
ejpam-5330	280	49	cτ	cτ	INTJ
ejpam-5330	280	50	(	(	PUNCT
ejpam-5330	280	51	n	n	CCONJ
ejpam-5330	280	52	,	,	PUNCT
ejpam-5330	280	53	φ	φ	PROPN
ejpam-5330	280	54	−1	−1	NOUN
ejpam-5330	280	55	ψ	ψ	X
ejpam-5330	280	56	(	(	PUNCT
ejpam-5330	280	57	fa	fa	NOUN
ejpam-5330	280	58	)	)	PUNCT
ejpam-5330	280	59	,	,	PUNCT
ejpam-5330	280	60	r	r	NOUN
ejpam-5330	280	61	)	)	PUNCT
ejpam-5330	280	62	,	,	PUNCT
ejpam-5330	280	63	r	r	NOUN
ejpam-5330	280	64	)	)	PUNCT
ejpam-5330	280	65	,	,	PUNCT
ejpam-5330	280	66	r	r	X
ejpam-5330	280	67	)	)	PUNCT
ejpam-5330	280	68	⊑	⊑	X
ejpam-5330	280	69	αcτ	αcτ	X
ejpam-5330	280	70	(	(	PUNCT
ejpam-5330	280	71	n	n	X
ejpam-5330	280	72	,	,	PUNCT
ejpam-5330	280	73	φ	φ	PROPN
ejpam-5330	280	74	−1	−1	NOUN
ejpam-5330	280	75	ψ	ψ	X
ejpam-5330	280	76	(	(	PUNCT
ejpam-5330	280	77	fa	fa	NOUN
ejpam-5330	280	78	)	)	PUNCT
ejpam-5330	280	79	,	,	PUNCT
ejpam-5330	280	80	r	r	X
ejpam-5330	280	81	)	)	PUNCT
ejpam-5330	280	82	⊑	⊑	X
ejpam-5330	280	83	φ−1	φ−1	PROPN
ejpam-5330	280	84	ψ	ψ	X
ejpam-5330	280	85	(	(	PUNCT
ejpam-5330	280	86	cη(k	cη(k	PROPN
ejpam-5330	280	87	,	,	PUNCT
ejpam-5330	280	88	fa	fa	NOUN
ejpam-5330	280	89	,	,	PUNCT
ejpam-5330	280	90	r	r	NOUN
ejpam-5330	280	91	)	)	PUNCT
ejpam-5330	280	92	)	)	PUNCT
ejpam-5330	280	93	.	.	PUNCT
ejpam-5330	281	1	(	(	PUNCT
ejpam-5330	281	2	5	5	X
ejpam-5330	281	3	)	)	PUNCT
ejpam-5330	281	4	⇒	⇒	NOUN
ejpam-5330	281	5	(	(	PUNCT
ejpam-5330	281	6	1	1	X
ejpam-5330	281	7	)	)	PUNCT
ejpam-5330	281	8	let	let	VERB
ejpam-5330	281	9	fa	fa	X
ejpam-5330	281	10	∈	∈	PROPN
ejpam-5330	281	11	(	(	PUNCT
ejpam-5330	281	12	̃v	̃v	NOUN
ejpam-5330	281	13	,	,	PUNCT
ejpam-5330	281	14	f	f	PROPN
ejpam-5330	281	15	)	)	PUNCT
ejpam-5330	281	16	with	with	ADP
ejpam-5330	281	17	ηk(fa	ηk(fa	PROPN
ejpam-5330	281	18	)	)	PUNCT
ejpam-5330	281	19	≥	≥	NOUN
ejpam-5330	281	20	r	r	NOUN
ejpam-5330	281	21	,	,	PUNCT
ejpam-5330	281	22	hence	hence	ADV
ejpam-5330	281	23	by	by	ADP
ejpam-5330	281	24	(	(	PUNCT
ejpam-5330	281	25	3	3	NUM
ejpam-5330	281	26	)	)	PUNCT
ejpam-5330	281	27	,	,	PUNCT
ejpam-5330	281	28	we	we	PRON
ejpam-5330	281	29	obtain	obtain	VERB
ejpam-5330	281	30	(	(	PUNCT
ejpam-5330	281	31	φ−1	φ−1	PROPN
ejpam-5330	281	32	ψ	ψ	SYM
ejpam-5330	281	33	(	(	PUNCT
ejpam-5330	281	34	fa	fa	NOUN
ejpam-5330	281	35	)	)	PUNCT
ejpam-5330	281	36	)	)	PUNCT
ejpam-5330	282	1	c	c	X
ejpam-5330	283	1	=	=	SYM
ejpam-5330	283	2	φ−1	φ−1	PROPN
ejpam-5330	283	3	ψ	ψ	X
ejpam-5330	283	4	(	(	PUNCT
ejpam-5330	283	5	f	f	PROPN
ejpam-5330	283	6	ca	ca	PROPN
ejpam-5330	283	7	)	)	PUNCT
ejpam-5330	283	8	⊒	⊒	PROPN
ejpam-5330	283	9	cτ	cτ	X
ejpam-5330	283	10	(	(	PUNCT
ejpam-5330	283	11	n	n	CCONJ
ejpam-5330	283	12	,	,	PUNCT
ejpam-5330	283	13	iτ	iτ	X
ejpam-5330	283	14	(	(	PUNCT
ejpam-5330	283	15	n	n	CCONJ
ejpam-5330	283	16	,	,	PUNCT
ejpam-5330	283	17	cτ	cτ	INTJ
ejpam-5330	283	18	(	(	PUNCT
ejpam-5330	283	19	n	n	CCONJ
ejpam-5330	283	20	,	,	PUNCT
ejpam-5330	283	21	φ	φ	PROPN
ejpam-5330	283	22	−1	−1	NOUN
ejpam-5330	283	23	ψ	ψ	PROPN
ejpam-5330	283	24	(	(	PUNCT
ejpam-5330	283	25	f	f	PROPN
ejpam-5330	283	26	ca	ca	PROPN
ejpam-5330	283	27	)	)	PUNCT
ejpam-5330	283	28	,	,	PUNCT
ejpam-5330	283	29	r	r	NOUN
ejpam-5330	283	30	)	)	PUNCT
ejpam-5330	283	31	,	,	PUNCT
ejpam-5330	283	32	r	r	NOUN
ejpam-5330	283	33	)	)	PUNCT
ejpam-5330	283	34	,	,	PUNCT
ejpam-5330	283	35	r	r	NOUN
ejpam-5330	283	36	)	)	PUNCT
ejpam-5330	283	37	=	=	SYM
ejpam-5330	283	38	(	(	PUNCT
ejpam-5330	283	39	iτ	iτ	INTJ
ejpam-5330	283	40	(	(	PUNCT
ejpam-5330	283	41	n	n	CCONJ
ejpam-5330	283	42	,	,	PUNCT
ejpam-5330	283	43	cτ	cτ	INTJ
ejpam-5330	283	44	(	(	PUNCT
ejpam-5330	283	45	n	n	CCONJ
ejpam-5330	283	46	,	,	PUNCT
ejpam-5330	283	47	iτ	iτ	X
ejpam-5330	283	48	(	(	PUNCT
ejpam-5330	283	49	n	n	CCONJ
ejpam-5330	283	50	,	,	PUNCT
ejpam-5330	283	51	φ	φ	PROPN
ejpam-5330	283	52	−1	−1	NOUN
ejpam-5330	283	53	ψ	ψ	X
ejpam-5330	283	54	(	(	PUNCT
ejpam-5330	283	55	fa	fa	NOUN
ejpam-5330	283	56	)	)	PUNCT
ejpam-5330	283	57	,	,	PUNCT
ejpam-5330	283	58	r	r	NOUN
ejpam-5330	283	59	)	)	PUNCT
ejpam-5330	283	60	,	,	PUNCT
ejpam-5330	283	61	r	r	NOUN
ejpam-5330	283	62	)	)	PUNCT
ejpam-5330	283	63	,	,	PUNCT
ejpam-5330	283	64	r	r	NOUN
ejpam-5330	283	65	)	)	PUNCT
ejpam-5330	283	66	)	)	PUNCT
ejpam-5330	283	67	c.	c.	NOUN
ejpam-5330	284	1	then	then	ADV
ejpam-5330	284	2	,	,	PUNCT
ejpam-5330	284	3	φ−1	φ−1	PROPN
ejpam-5330	284	4	ψ	ψ	SYM
ejpam-5330	284	5	(	(	PUNCT
ejpam-5330	284	6	fa	fa	INTJ
ejpam-5330	284	7	)	)	PUNCT
ejpam-5330	284	8	⊑	⊑	X
ejpam-5330	284	9	iτ	iτ	X
ejpam-5330	284	10	(	(	PUNCT
ejpam-5330	284	11	n	n	CCONJ
ejpam-5330	284	12	,	,	PUNCT
ejpam-5330	284	13	cτ	cτ	INTJ
ejpam-5330	284	14	(	(	PUNCT
ejpam-5330	284	15	n	n	CCONJ
ejpam-5330	284	16	,	,	PUNCT
ejpam-5330	284	17	iτ	iτ	X
ejpam-5330	284	18	(	(	PUNCT
ejpam-5330	284	19	n	n	CCONJ
ejpam-5330	284	20	,	,	PUNCT
ejpam-5330	284	21	φ	φ	PROPN
ejpam-5330	284	22	−1	−1	NOUN
ejpam-5330	284	23	ψ	ψ	X
ejpam-5330	284	24	(	(	PUNCT
ejpam-5330	284	25	fa	fa	NOUN
ejpam-5330	284	26	)	)	PUNCT
ejpam-5330	284	27	,	,	PUNCT
ejpam-5330	284	28	r	r	NOUN
ejpam-5330	284	29	)	)	PUNCT
ejpam-5330	284	30	,	,	PUNCT
ejpam-5330	284	31	r	r	NOUN
ejpam-5330	284	32	)	)	PUNCT
ejpam-5330	284	33	,	,	PUNCT
ejpam-5330	284	34	r	r	NOUN
ejpam-5330	284	35	)	)	PUNCT
ejpam-5330	284	36	,	,	PUNCT
ejpam-5330	284	37	so	so	ADV
ejpam-5330	284	38	φ	φ	PROPN
ejpam-5330	284	39	−1	−1	PROPN
ejpam-5330	284	40	ψ	ψ	X
ejpam-5330	284	41	(	(	PUNCT
ejpam-5330	284	42	fa	fa	NOUN
ejpam-5330	284	43	)	)	PUNCT
ejpam-5330	284	44	is	be	AUX
ejpam-5330	284	45	r	r	NOUN
ejpam-5330	284	46	-	-	PUNCT
ejpam-5330	284	47	fuzzy	fuzzy	ADJ
ejpam-5330	284	48	soft	soft	ADJ
ejpam-5330	284	49	α	α	NOUN
ejpam-5330	284	50	-	-	NOUN
ejpam-5330	284	51	open	open	ADJ
ejpam-5330	284	52	.	.	PUNCT
ejpam-5330	285	1	hence	hence	ADV
ejpam-5330	285	2	,	,	PUNCT
ejpam-5330	285	3	φψ	φψ	X
ejpam-5330	285	4	is	be	AUX
ejpam-5330	285	5	fuzzy	fuzzy	ADJ
ejpam-5330	285	6	soft	soft	ADJ
ejpam-5330	285	7	α	α	NOUN
ejpam-5330	285	8	-	-	ADJ
ejpam-5330	285	9	continuous	continuous	ADJ
ejpam-5330	285	10	.	.	PUNCT
ejpam-5330	286	1	lemma	lemma	PROPN
ejpam-5330	286	2	4	4	NUM
ejpam-5330	286	3	.	.	PUNCT
ejpam-5330	287	1	every	every	DET
ejpam-5330	287	2	fuzzy	fuzzy	ADJ
ejpam-5330	287	3	soft	soft	ADJ
ejpam-5330	287	4	continuous	continuous	ADJ
ejpam-5330	287	5	mapping	mapping	NOUN
ejpam-5330	287	6	[	[	X
ejpam-5330	287	7	19	19	NUM
ejpam-5330	287	8	]	]	PUNCT
ejpam-5330	287	9	is	be	AUX
ejpam-5330	287	10	fuzzy	fuzzy	ADJ
ejpam-5330	287	11	soft	soft	ADJ
ejpam-5330	287	12	α	α	NOUN
ejpam-5330	287	13	-	-	ADJ
ejpam-5330	287	14	continuous	continuous	ADJ
ejpam-5330	287	15	.	.	PUNCT
ejpam-5330	288	1	proof	proof	NOUN
ejpam-5330	288	2	.	.	PUNCT
ejpam-5330	289	1	follows	follow	VERB
ejpam-5330	289	2	from	from	ADP
ejpam-5330	289	3	definitions	definition	NOUN
ejpam-5330	289	4	6	6	NUM
ejpam-5330	289	5	and	and	CCONJ
ejpam-5330	289	6	15	15	NUM
ejpam-5330	289	7	.	.	PUNCT
ejpam-5330	290	1	remark	remark	NOUN
ejpam-5330	290	2	5	5	NUM
ejpam-5330	290	3	.	.	PUNCT
ejpam-5330	291	1	the	the	DET
ejpam-5330	291	2	converse	converse	NOUN
ejpam-5330	291	3	of	of	ADP
ejpam-5330	291	4	lemma	lemma	PROPN
ejpam-5330	291	5	4	4	NUM
ejpam-5330	291	6	is	be	AUX
ejpam-5330	291	7	not	not	PART
ejpam-5330	291	8	true	true	ADJ
ejpam-5330	291	9	,	,	PUNCT
ejpam-5330	291	10	as	as	SCONJ
ejpam-5330	291	11	shown	show	VERB
ejpam-5330	291	12	by	by	ADP
ejpam-5330	291	13	example	example	NOUN
ejpam-5330	291	14	3	3	NUM
ejpam-5330	291	15	.	.	NOUN
ejpam-5330	291	16	example	example	NOUN
ejpam-5330	292	1	3	3	X
ejpam-5330	292	2	.	.	PUNCT
ejpam-5330	292	3	let	let	VERB
ejpam-5330	292	4	w	w	VERB
ejpam-5330	292	5	=	=	PUNCT
ejpam-5330	292	6	{	{	PUNCT
ejpam-5330	292	7	w1	w1	NOUN
ejpam-5330	292	8	,	,	PUNCT
ejpam-5330	292	9	w2	w2	NOUN
ejpam-5330	292	10	,	,	PUNCT
ejpam-5330	292	11	w3	w3	PROPN
ejpam-5330	292	12	}	}	PUNCT
ejpam-5330	292	13	,	,	PUNCT
ejpam-5330	292	14	n	n	NOUN
ejpam-5330	292	15	=	=	SYM
ejpam-5330	292	16	{	{	PUNCT
ejpam-5330	292	17	n1	n1	NOUN
ejpam-5330	292	18	,	,	PUNCT
ejpam-5330	292	19	n2	n2	ADJ
ejpam-5330	292	20	}	}	PUNCT
ejpam-5330	292	21	,	,	PUNCT
ejpam-5330	292	22	and	and	CCONJ
ejpam-5330	292	23	define	define	VERB
ejpam-5330	292	24	fn	fn	NOUN
ejpam-5330	292	25	,	,	PUNCT
ejpam-5330	292	26	gn	gn	PROPN
ejpam-5330	292	27	,	,	PUNCT
ejpam-5330	292	28	hn	hn	PROPN
ejpam-5330	292	29	∈	∈	PROPN
ejpam-5330	292	30	˜(w	˜(w	PROPN
ejpam-5330	292	31	,	,	PUNCT
ejpam-5330	292	32	n	n	CCONJ
ejpam-5330	292	33	)	)	PUNCT
ejpam-5330	292	34	as	as	ADP
ejpam-5330	292	35	:	:	PUNCT
ejpam-5330	292	36	fn	fn	NOUN
ejpam-5330	292	37	=	=	SYM
ejpam-5330	292	38	{	{	PUNCT
ejpam-5330	292	39	(	(	PUNCT
ejpam-5330	292	40	n1	n1	NOUN
ejpam-5330	292	41	,	,	PUNCT
ejpam-5330	292	42	{	{	PUNCT
ejpam-5330	292	43	w1	w1	NOUN
ejpam-5330	292	44	0.4	0.4	NUM
ejpam-5330	292	45	,	,	PUNCT
ejpam-5330	292	46	w2	w2	NOUN
ejpam-5330	292	47	0.5	0.5	NUM
ejpam-5330	292	48	,	,	PUNCT
ejpam-5330	292	49	w3	w3	PROPN
ejpam-5330	292	50	0.5	0.5	NUM
ejpam-5330	292	51	}	}	PUNCT
ejpam-5330	292	52	)	)	PUNCT
ejpam-5330	292	53	,	,	PUNCT
ejpam-5330	292	54	(	(	PUNCT
ejpam-5330	292	55	n2	n2	ADJ
ejpam-5330	292	56	,	,	PUNCT
ejpam-5330	292	57	{	{	PUNCT
ejpam-5330	292	58	w1	w1	NOUN
ejpam-5330	292	59	0.4	0.4	NUM
ejpam-5330	292	60	,	,	PUNCT
ejpam-5330	292	61	w2	w2	NOUN
ejpam-5330	292	62	0.5	0.5	NUM
ejpam-5330	292	63	,	,	PUNCT
ejpam-5330	292	64	w3	w3	PROPN
ejpam-5330	292	65	0.5	0.5	NUM
ejpam-5330	292	66	}	}	PUNCT
ejpam-5330	292	67	)	)	PUNCT
ejpam-5330	292	68	}	}	PUNCT
ejpam-5330	292	69	,	,	PUNCT
ejpam-5330	292	70	gn	gn	PROPN
ejpam-5330	292	71	=	=	PUNCT
ejpam-5330	292	72	{	{	PUNCT
ejpam-5330	292	73	(	(	PUNCT
ejpam-5330	292	74	n1	n1	NOUN
ejpam-5330	292	75	,	,	PUNCT
ejpam-5330	292	76	{	{	PUNCT
ejpam-5330	292	77	w1	w1	NOUN
ejpam-5330	292	78	0.3	0.3	NUM
ejpam-5330	292	79	,	,	PUNCT
ejpam-5330	292	80	w2	w2	NOUN
ejpam-5330	292	81	0.3	0.3	NUM
ejpam-5330	292	82	,	,	PUNCT
ejpam-5330	292	83	w3	w3	PROPN
ejpam-5330	292	84	0.4	0.4	NUM
ejpam-5330	292	85	}	}	PUNCT
ejpam-5330	292	86	)	)	PUNCT
ejpam-5330	292	87	,	,	PUNCT
ejpam-5330	292	88	(	(	PUNCT
ejpam-5330	292	89	n2	n2	ADJ
ejpam-5330	292	90	,	,	PUNCT
ejpam-5330	292	91	{	{	PUNCT
ejpam-5330	292	92	w1	w1	NOUN
ejpam-5330	292	93	0.3	0.3	NUM
ejpam-5330	292	94	,	,	PUNCT
ejpam-5330	292	95	w2	w2	NOUN
ejpam-5330	292	96	0.3	0.3	NUM
ejpam-5330	292	97	,	,	PUNCT
ejpam-5330	292	98	w3	w3	PROPN
ejpam-5330	292	99	0.4	0.4	NUM
ejpam-5330	292	100	}	}	PUNCT
ejpam-5330	292	101	)	)	PUNCT
ejpam-5330	292	102	}	}	PUNCT
ejpam-5330	292	103	,	,	PUNCT
ejpam-5330	292	104	hn	hn	PROPN
ejpam-5330	292	105	=	=	PRON
ejpam-5330	292	106	{	{	PUNCT
ejpam-5330	292	107	(	(	PUNCT
ejpam-5330	292	108	n1	n1	NOUN
ejpam-5330	292	109	,	,	PUNCT
ejpam-5330	292	110	{	{	PUNCT
ejpam-5330	292	111	w1	w1	NOUN
ejpam-5330	292	112	0.3	0.3	NUM
ejpam-5330	292	113	,	,	PUNCT
ejpam-5330	292	114	w2	w2	NOUN
ejpam-5330	292	115	0.4	0.4	NUM
ejpam-5330	292	116	,	,	PUNCT
ejpam-5330	292	117	w3	w3	PROPN
ejpam-5330	292	118	0.4	0.4	NUM
ejpam-5330	292	119	}	}	PUNCT
ejpam-5330	292	120	)	)	PUNCT
ejpam-5330	292	121	,	,	PUNCT
ejpam-5330	292	122	(	(	PUNCT
ejpam-5330	292	123	n2	n2	ADJ
ejpam-5330	292	124	,	,	PUNCT
ejpam-5330	292	125	{	{	PUNCT
ejpam-5330	292	126	w1	w1	NOUN
ejpam-5330	292	127	0.3	0.3	NUM
ejpam-5330	292	128	,	,	PUNCT
ejpam-5330	292	129	w2	w2	NOUN
ejpam-5330	292	130	0.4	0.4	NUM
ejpam-5330	292	131	,	,	PUNCT
ejpam-5330	292	132	w3	w3	PROPN
ejpam-5330	292	133	0.4	0.4	NUM
ejpam-5330	292	134	}	}	PUNCT
ejpam-5330	292	135	)	)	PUNCT
ejpam-5330	292	136	}	}	PUNCT
ejpam-5330	292	137	.	.	PUNCT
ejpam-5330	293	1	define	define	VERB
ejpam-5330	293	2	fuzzy	fuzzy	ADJ
ejpam-5330	293	3	soft	soft	ADJ
ejpam-5330	293	4	topologies	topology	NOUN
ejpam-5330	293	5	τn	τn	ADP
ejpam-5330	293	6	,	,	PUNCT
ejpam-5330	293	7	ηn	ηn	INTJ
ejpam-5330	293	8	:	:	PUNCT
ejpam-5330	293	9	n	n	X
ejpam-5330	293	10	−→	−→	NOUN
ejpam-5330	293	11	[	[	X
ejpam-5330	293	12	0	0	NUM
ejpam-5330	293	13	,	,	PUNCT
ejpam-5330	293	14	1	1	NUM
ejpam-5330	293	15	]	]	PUNCT
ejpam-5330	293	16	˜(w	˜(w	PROPN
ejpam-5330	293	17	,	,	PUNCT
ejpam-5330	293	18	n	n	CCONJ
ejpam-5330	293	19	)	)	PUNCT
ejpam-5330	293	20	as	as	SCONJ
ejpam-5330	293	21	follows	follow	VERB
ejpam-5330	293	22	:	:	PUNCT
ejpam-5330	293	23	∀n	∀n	NUM
ejpam-5330	293	24	∈	∈	PROPN
ejpam-5330	293	25	n	n	PRON
ejpam-5330	293	26	,	,	PUNCT
ejpam-5330	293	27	τn(tn	τn(tn	PROPN
ejpam-5330	293	28	)	)	PUNCT
ejpam-5330	294	1	=	=	PUNCT
ejpam-5330	294	2			NOUN
ejpam-5330	294	3	1	1	NUM
ejpam-5330	294	4	,	,	PUNCT
ejpam-5330	294	5	if	if	SCONJ
ejpam-5330	294	6	tn	tn	PROPN
ejpam-5330	294	7	∈	∈	PROPN
ejpam-5330	294	8	{	{	PUNCT
ejpam-5330	294	9	φ	φ	NOUN
ejpam-5330	294	10	,	,	PUNCT
ejpam-5330	294	11	ñ	ñ	PROPN
ejpam-5330	294	12	}	}	PUNCT
ejpam-5330	294	13	,	,	PUNCT
ejpam-5330	294	14	1	1	NUM
ejpam-5330	294	15	2	2	NUM
ejpam-5330	294	16	,	,	PUNCT
ejpam-5330	294	17	if	if	SCONJ
ejpam-5330	294	18	tn	tn	NUM
ejpam-5330	294	19	=	=	SYM
ejpam-5330	294	20	fn	fn	NOUN
ejpam-5330	294	21	,	,	PUNCT
ejpam-5330	294	22	2	2	NUM
ejpam-5330	294	23	3	3	NUM
ejpam-5330	294	24	,	,	PUNCT
ejpam-5330	294	25	if	if	SCONJ
ejpam-5330	294	26	tn	tn	PROPN
ejpam-5330	294	27	=	=	SYM
ejpam-5330	294	28	gn	gn	PROPN
ejpam-5330	294	29	,	,	PUNCT
ejpam-5330	294	30	0	0	NUM
ejpam-5330	294	31	,	,	PUNCT
ejpam-5330	294	32	otherwise	otherwise	ADV
ejpam-5330	294	33	,	,	PUNCT
ejpam-5330	294	34	ηn(tn	ηn(tn	PROPN
ejpam-5330	294	35	)	)	PUNCT
ejpam-5330	294	36	=	=	PUNCT
ejpam-5330	295	1			NOUN
ejpam-5330	295	2	1	1	NUM
ejpam-5330	295	3	,	,	PUNCT
ejpam-5330	295	4	if	if	SCONJ
ejpam-5330	295	5	tn	tn	PROPN
ejpam-5330	295	6	∈	∈	PROPN
ejpam-5330	295	7	{	{	PUNCT
ejpam-5330	295	8	φ	φ	NOUN
ejpam-5330	295	9	,	,	PUNCT
ejpam-5330	295	10	ñ	ñ	PROPN
ejpam-5330	295	11	}	}	PUNCT
ejpam-5330	295	12	,	,	PUNCT
ejpam-5330	295	13	1	1	NUM
ejpam-5330	295	14	2	2	NUM
ejpam-5330	295	15	,	,	PUNCT
ejpam-5330	295	16	if	if	SCONJ
ejpam-5330	295	17	tn	tn	NUM
ejpam-5330	295	18	=	=	SYM
ejpam-5330	295	19	fn	fn	NOUN
ejpam-5330	295	20	,	,	PUNCT
ejpam-5330	295	21	1	1	NUM
ejpam-5330	295	22	3	3	NUM
ejpam-5330	295	23	,	,	PUNCT
ejpam-5330	295	24	if	if	SCONJ
ejpam-5330	295	25	tn	tn	NUM
ejpam-5330	295	26	=	=	SYM
ejpam-5330	295	27	hn	hn	PROPN
ejpam-5330	295	28	,	,	PUNCT
ejpam-5330	295	29	0	0	NUM
ejpam-5330	295	30	,	,	PUNCT
ejpam-5330	295	31	otherwise	otherwise	ADV
ejpam-5330	295	32	.	.	PUNCT
ejpam-5330	296	1	thus	thus	ADV
ejpam-5330	296	2	,	,	PUNCT
ejpam-5330	296	3	the	the	DET
ejpam-5330	296	4	identity	identity	NOUN
ejpam-5330	296	5	fuzzy	fuzzy	ADJ
ejpam-5330	296	6	soft	soft	ADJ
ejpam-5330	296	7	mapping	mapping	NOUN
ejpam-5330	296	8	φψ	φψ	X
ejpam-5330	296	9	:	:	PUNCT
ejpam-5330	296	10	(	(	PUNCT
ejpam-5330	296	11	w	w	INTJ
ejpam-5330	296	12	,	,	PUNCT
ejpam-5330	296	13	τn	τn	NOUN
ejpam-5330	296	14	)	)	PUNCT
ejpam-5330	296	15	−→	−→	NOUN
ejpam-5330	296	16	(	(	PUNCT
ejpam-5330	296	17	w	w	NOUN
ejpam-5330	296	18	,	,	PUNCT
ejpam-5330	296	19	ηn	ηn	INTJ
ejpam-5330	296	20	)	)	PUNCT
ejpam-5330	296	21	is	be	AUX
ejpam-5330	296	22	fuzzy	fuzzy	ADJ
ejpam-5330	296	23	soft	soft	ADJ
ejpam-5330	296	24	αcontinuous	αcontinuous	ADJ
ejpam-5330	296	25	,	,	PUNCT
ejpam-5330	296	26	but	but	CCONJ
ejpam-5330	296	27	it	it	PRON
ejpam-5330	296	28	is	be	AUX
ejpam-5330	296	29	not	not	PART
ejpam-5330	296	30	fuzzy	fuzzy	ADJ
ejpam-5330	296	31	soft	soft	ADJ
ejpam-5330	296	32	continuous	continuous	ADJ
ejpam-5330	296	33	.	.	PUNCT
ejpam-5330	297	1	definition	definition	NOUN
ejpam-5330	297	2	16	16	NUM
ejpam-5330	297	3	.	.	PUNCT
ejpam-5330	298	1	let	let	VERB
ejpam-5330	298	2	(	(	PUNCT
ejpam-5330	298	3	w	w	NOUN
ejpam-5330	298	4	,	,	PUNCT
ejpam-5330	298	5	τn	τn	PROPN
ejpam-5330	298	6	)	)	PUNCT
ejpam-5330	298	7	and	and	CCONJ
ejpam-5330	298	8	(	(	PUNCT
ejpam-5330	298	9	v	v	NOUN
ejpam-5330	298	10	,	,	PUNCT
ejpam-5330	298	11	ηf	ηf	PROPN
ejpam-5330	298	12	)	)	PUNCT
ejpam-5330	298	13	be	be	AUX
ejpam-5330	298	14	an	an	DET
ejpam-5330	298	15	fstss	fstss	NOUN
ejpam-5330	298	16	.	.	PUNCT
ejpam-5330	299	1	a	a	DET
ejpam-5330	299	2	fuzzy	fuzzy	ADJ
ejpam-5330	299	3	soft	soft	ADJ
ejpam-5330	299	4	mapping	mapping	NOUN
ejpam-5330	299	5	φψ	φψ	X
ejpam-5330	299	6	:	:	PUNCT
ejpam-5330	299	7	˜(w	˜(w	PROPN
ejpam-5330	299	8	,	,	PUNCT
ejpam-5330	299	9	n	n	CCONJ
ejpam-5330	299	10	)	)	PUNCT
ejpam-5330	299	11	−→	−→	NOUN
ejpam-5330	299	12	(	(	PUNCT
ejpam-5330	299	13	̃v	̃v	NOUN
ejpam-5330	299	14	,	,	PUNCT
ejpam-5330	299	15	f	f	PROPN
ejpam-5330	299	16	)	)	PUNCT
ejpam-5330	299	17	is	be	AUX
ejpam-5330	299	18	called	call	VERB
ejpam-5330	299	19	fuzzy	fuzzy	ADJ
ejpam-5330	299	20	soft	soft	ADJ
ejpam-5330	299	21	almost	almost	ADV
ejpam-5330	299	22	(	(	PUNCT
ejpam-5330	299	23	resp	resp	NOUN
ejpam-5330	299	24	.	.	PUNCT
ejpam-5330	299	25	,	,	PUNCT
ejpam-5330	299	26	weakly	weakly	ADJ
ejpam-5330	299	27	)	)	PUNCT
ejpam-5330	299	28	α	α	NOUN
ejpam-5330	299	29	-	-	ADJ
ejpam-5330	299	30	continuous	continuous	ADJ
ejpam-5330	299	31	if	if	SCONJ
ejpam-5330	299	32	for	for	ADP
ejpam-5330	299	33	each	each	DET
ejpam-5330	299	34	nws	nws	PROPN
ejpam-5330	299	35	∈	∈	PROPN
ejpam-5330	299	36	p̃s(w	p̃s(w	NOUN
ejpam-5330	299	37	)	)	PUNCT
ejpam-5330	299	38	and	and	CCONJ
ejpam-5330	299	39	each	each	DET
ejpam-5330	299	40	gb	gb	NOUN
ejpam-5330	299	41	∈	∈	PROPN
ejpam-5330	299	42	(	(	PUNCT
ejpam-5330	299	43	̃v	̃v	NOUN
ejpam-5330	299	44	,	,	PUNCT
ejpam-5330	299	45	f	f	PROPN
ejpam-5330	299	46	)	)	PUNCT
ejpam-5330	299	47	with	with	ADP
ejpam-5330	299	48	ηk(gb	ηk(gb	NOUN
ejpam-5330	299	49	)	)	PUNCT
ejpam-5330	299	50	≥	≥	NOUN
ejpam-5330	299	51	r	r	NOUN
ejpam-5330	299	52	containing	contain	VERB
ejpam-5330	299	53	φψ(nws	φψ(nws	NOUN
ejpam-5330	299	54	)	)	PUNCT
ejpam-5330	299	55	,	,	PUNCT
ejpam-5330	299	56	there	there	PRON
ejpam-5330	299	57	is	be	VERB
ejpam-5330	299	58	hc	hc	PROPN
ejpam-5330	299	59	∈	∈	PROPN
ejpam-5330	299	60	˜(w	˜(w	PROPN
ejpam-5330	299	61	,	,	PUNCT
ejpam-5330	299	62	n	n	CCONJ
ejpam-5330	299	63	)	)	PUNCT
ejpam-5330	299	64	that	that	PRON
ejpam-5330	299	65	is	be	AUX
ejpam-5330	299	66	an	an	DET
ejpam-5330	299	67	r	r	NOUN
ejpam-5330	299	68	-	-	PUNCT
ejpam-5330	299	69	fuzzy	fuzzy	ADJ
ejpam-5330	299	70	soft	soft	ADJ
ejpam-5330	299	71	α	α	NOUN
ejpam-5330	299	72	-	-	ADJ
ejpam-5330	299	73	open	open	ADJ
ejpam-5330	299	74	set	set	NOUN
ejpam-5330	299	75	containing	contain	VERB
ejpam-5330	299	76	nws	nws	PROPN
ejpam-5330	299	77	,	,	PUNCT
ejpam-5330	299	78	such	such	ADJ
ejpam-5330	299	79	that	that	DET
ejpam-5330	299	80	φψ(hc	φψ(hc	NOUN
ejpam-5330	299	81	)	)	PUNCT
ejpam-5330	299	82	⊑	⊑	PRON
ejpam-5330	299	83	iη(k	iη(k	PROPN
ejpam-5330	299	84	,	,	PUNCT
ejpam-5330	299	85	cη(k	cη(k	PROPN
ejpam-5330	299	86	,	,	PUNCT
ejpam-5330	299	87	gb	gb	PRON
ejpam-5330	299	88	,	,	PUNCT
ejpam-5330	299	89	r	r	NOUN
ejpam-5330	299	90	)	)	PUNCT
ejpam-5330	299	91	,	,	PUNCT
ejpam-5330	299	92	r	r	NOUN
ejpam-5330	299	93	)	)	PUNCT
ejpam-5330	299	94	(	(	PUNCT
ejpam-5330	299	95	resp	resp	NOUN
ejpam-5330	299	96	.	.	PUNCT
ejpam-5330	299	97	,	,	PUNCT
ejpam-5330	299	98	φψ(hc	φψ(hc	NOUN
ejpam-5330	299	99	)	)	PUNCT
ejpam-5330	299	100	⊑	⊑	PRON
ejpam-5330	299	101	cη(k	cη(k	PROPN
ejpam-5330	299	102	,	,	PUNCT
ejpam-5330	299	103	gb	gb	PROPN
ejpam-5330	299	104	,	,	PUNCT
ejpam-5330	299	105	r	r	NOUN
ejpam-5330	299	106	)	)	PUNCT
ejpam-5330	299	107	)	)	PUNCT
ejpam-5330	299	108	,	,	PUNCT
ejpam-5330	299	109	n	n	PROPN
ejpam-5330	299	110	∈	∈	PROPN
ejpam-5330	299	111	n	n	NOUN
ejpam-5330	299	112	,	,	PUNCT
ejpam-5330	299	113	(	(	PUNCT
ejpam-5330	299	114	k	k	NOUN
ejpam-5330	299	115	=	=	SYM
ejpam-5330	299	116	ψ(n	ψ(n	PROPN
ejpam-5330	299	117	)	)	PUNCT
ejpam-5330	299	118	)	)	PUNCT
ejpam-5330	300	1	∈	∈	PROPN
ejpam-5330	300	2	f	f	X
ejpam-5330	300	3	,	,	PUNCT
ejpam-5330	300	4	and	and	CCONJ
ejpam-5330	300	5	r	r	NOUN
ejpam-5330	300	6	∈	∈	PROPN
ejpam-5330	300	7	i	i	PROPN
ejpam-5330	300	8	◦	◦	NOUN
ejpam-5330	300	9	.	.	PUNCT
ejpam-5330	301	1	lemma	lemma	PROPN
ejpam-5330	301	2	5	5	NUM
ejpam-5330	301	3	.	.	PUNCT
ejpam-5330	302	1	(	(	PUNCT
ejpam-5330	302	2	1	1	X
ejpam-5330	302	3	)	)	PUNCT
ejpam-5330	302	4	every	every	DET
ejpam-5330	302	5	fuzzy	fuzzy	ADJ
ejpam-5330	302	6	soft	soft	ADJ
ejpam-5330	302	7	α	α	NOUN
ejpam-5330	302	8	-	-	ADJ
ejpam-5330	302	9	continuous	continuous	ADJ
ejpam-5330	302	10	mapping	mapping	NOUN
ejpam-5330	302	11	is	be	AUX
ejpam-5330	302	12	fuzzy	fuzzy	ADJ
ejpam-5330	302	13	soft	soft	ADJ
ejpam-5330	302	14	almost	almost	ADV
ejpam-5330	302	15	α	α	NOUN
ejpam-5330	302	16	-	-	ADJ
ejpam-5330	302	17	continuous	continuous	ADJ
ejpam-5330	302	18	.	.	PUNCT
ejpam-5330	303	1	(	(	PUNCT
ejpam-5330	303	2	2	2	X
ejpam-5330	303	3	)	)	PUNCT
ejpam-5330	303	4	every	every	DET
ejpam-5330	303	5	fuzzy	fuzzy	ADJ
ejpam-5330	303	6	soft	soft	ADJ
ejpam-5330	303	7	almost	almost	ADV
ejpam-5330	303	8	α	α	ADJ
ejpam-5330	303	9	-	-	ADJ
ejpam-5330	303	10	continuous	continuous	ADJ
ejpam-5330	303	11	mapping	mapping	NOUN
ejpam-5330	303	12	is	be	AUX
ejpam-5330	303	13	fuzzy	fuzzy	ADJ
ejpam-5330	304	1	soft	soft	ADJ
ejpam-5330	304	2	weakly	weakly	ADJ
ejpam-5330	304	3	α	α	NOUN
ejpam-5330	304	4	-	-	ADJ
ejpam-5330	304	5	continuous	continuous	ADJ
ejpam-5330	304	6	.	.	PUNCT
ejpam-5330	304	7	proof	proof	NOUN
ejpam-5330	304	8	.	.	PUNCT
ejpam-5330	305	1	follows	follow	VERB
ejpam-5330	305	2	from	from	ADP
ejpam-5330	305	3	definitions	definition	NOUN
ejpam-5330	305	4	15	15	NUM
ejpam-5330	305	5	and	and	CCONJ
ejpam-5330	305	6	16	16	NUM
ejpam-5330	305	7	.	.	PUNCT
ejpam-5330	306	1	remark	remark	PROPN
ejpam-5330	306	2	6	6	NUM
ejpam-5330	306	3	.	.	PUNCT
ejpam-5330	307	1	the	the	DET
ejpam-5330	307	2	converse	converse	NOUN
ejpam-5330	307	3	of	of	ADP
ejpam-5330	307	4	lemma	lemma	PROPN
ejpam-5330	307	5	5	5	NUM
ejpam-5330	307	6	is	be	AUX
ejpam-5330	307	7	not	not	PART
ejpam-5330	307	8	true	true	ADJ
ejpam-5330	307	9	,	,	PUNCT
ejpam-5330	307	10	as	as	SCONJ
ejpam-5330	307	11	shown	show	VERB
ejpam-5330	307	12	by	by	ADP
ejpam-5330	307	13	examples	example	NOUN
ejpam-5330	307	14	4	4	NUM
ejpam-5330	307	15	and	and	CCONJ
ejpam-5330	307	16	5	5	NUM
ejpam-5330	307	17	.	.	X
ejpam-5330	307	18	w.	w.	PROPN
ejpam-5330	307	19	alqurashi	alqurashi	PROPN
ejpam-5330	307	20	,	,	PUNCT
ejpam-5330	307	21	i.	i.	PROPN
ejpam-5330	307	22	m.	m.	PROPN
ejpam-5330	307	23	taha	taha	PROPN
ejpam-5330	307	24	/	/	PUNCT
ejpam-5330	307	25	eur	eur	PROPN
ejpam-5330	307	26	.	.	PUNCT
ejpam-5330	308	1	j.	j.	PROPN
ejpam-5330	308	2	pure	pure	PROPN
ejpam-5330	308	3	appl	appl	PROPN
ejpam-5330	308	4	.	.	PROPN
ejpam-5330	308	5	math	math	PROPN
ejpam-5330	308	6	,	,	PUNCT
ejpam-5330	308	7	17	17	NUM
ejpam-5330	308	8	(	(	PUNCT
ejpam-5330	308	9	4	4	NUM
ejpam-5330	308	10	)	)	PUNCT
ejpam-5330	308	11	(	(	PUNCT
ejpam-5330	308	12	2024	2024	NUM
ejpam-5330	308	13	)	)	PUNCT
ejpam-5330	308	14	,	,	PUNCT
ejpam-5330	308	15	4112	4112	NUM
ejpam-5330	308	16	-	-	SYM
ejpam-5330	308	17	4134	4134	NUM
ejpam-5330	308	18	4123	4123	NUM
ejpam-5330	308	19	example	example	NOUN
ejpam-5330	308	20	4	4	NUM
ejpam-5330	308	21	.	.	PUNCT
ejpam-5330	309	1	letw	letw	NOUN
ejpam-5330	309	2	=	=	CCONJ
ejpam-5330	309	3	{	{	PUNCT
ejpam-5330	309	4	w1	w1	NOUN
ejpam-5330	309	5	,	,	PUNCT
ejpam-5330	309	6	w2	w2	NOUN
ejpam-5330	309	7	,	,	PUNCT
ejpam-5330	309	8	w3	w3	PROPN
ejpam-5330	309	9	}	}	PUNCT
ejpam-5330	309	10	,	,	PUNCT
ejpam-5330	309	11	n	n	NOUN
ejpam-5330	309	12	=	=	SYM
ejpam-5330	309	13	{	{	PUNCT
ejpam-5330	309	14	n1	n1	NOUN
ejpam-5330	309	15	,	,	PUNCT
ejpam-5330	309	16	n2	n2	ADJ
ejpam-5330	309	17	}	}	PUNCT
ejpam-5330	309	18	,	,	PUNCT
ejpam-5330	309	19	and	and	CCONJ
ejpam-5330	309	20	define	define	VERB
ejpam-5330	309	21	gn	gn	PROPN
ejpam-5330	309	22	,	,	PUNCT
ejpam-5330	309	23	hn	hn	PROPN
ejpam-5330	309	24	∈	∈	PROPN
ejpam-5330	309	25	˜(w	˜(w	PROPN
ejpam-5330	309	26	,	,	PUNCT
ejpam-5330	309	27	n	n	CCONJ
ejpam-5330	309	28	)	)	PUNCT
ejpam-5330	309	29	as	as	SCONJ
ejpam-5330	309	30	follows	follow	VERB
ejpam-5330	309	31	:	:	PUNCT
ejpam-5330	309	32	gn	gn	PROPN
ejpam-5330	309	33	=	=	PUNCT
ejpam-5330	309	34	{	{	PUNCT
ejpam-5330	309	35	(	(	PUNCT
ejpam-5330	309	36	n1	n1	NOUN
ejpam-5330	309	37	,	,	PUNCT
ejpam-5330	309	38	{	{	PUNCT
ejpam-5330	309	39	w1	w1	NOUN
ejpam-5330	309	40	0.5	0.5	NUM
ejpam-5330	309	41	,	,	PUNCT
ejpam-5330	309	42	w2	w2	NOUN
ejpam-5330	309	43	0.5	0.5	NUM
ejpam-5330	309	44	,	,	PUNCT
ejpam-5330	309	45	w3	w3	PROPN
ejpam-5330	309	46	0.4	0.4	NUM
ejpam-5330	309	47	}	}	PUNCT
ejpam-5330	309	48	)	)	PUNCT
ejpam-5330	309	49	,	,	PUNCT
ejpam-5330	309	50	(	(	PUNCT
ejpam-5330	309	51	n2	n2	ADJ
ejpam-5330	309	52	,	,	PUNCT
ejpam-5330	309	53	{	{	PUNCT
ejpam-5330	309	54	w1	w1	NOUN
ejpam-5330	309	55	0.5	0.5	NUM
ejpam-5330	309	56	,	,	PUNCT
ejpam-5330	309	57	w2	w2	NOUN
ejpam-5330	309	58	0.5	0.5	NUM
ejpam-5330	309	59	,	,	PUNCT
ejpam-5330	309	60	w3	w3	PROPN
ejpam-5330	309	61	0.4	0.4	NUM
ejpam-5330	309	62	}	}	PUNCT
ejpam-5330	309	63	)	)	PUNCT
ejpam-5330	309	64	}	}	PUNCT
ejpam-5330	309	65	,	,	PUNCT
ejpam-5330	309	66	hn	hn	PROPN
ejpam-5330	309	67	=	=	PRON
ejpam-5330	309	68	{	{	PUNCT
ejpam-5330	309	69	(	(	PUNCT
ejpam-5330	309	70	n1	n1	NOUN
ejpam-5330	309	71	,	,	PUNCT
ejpam-5330	309	72	{	{	PUNCT
ejpam-5330	309	73	w1	w1	NOUN
ejpam-5330	309	74	0.3	0.3	NUM
ejpam-5330	309	75	,	,	PUNCT
ejpam-5330	309	76	w2	w2	NOUN
ejpam-5330	309	77	0.3	0.3	NUM
ejpam-5330	309	78	,	,	PUNCT
ejpam-5330	309	79	w3	w3	PROPN
ejpam-5330	309	80	0.4	0.4	NUM
ejpam-5330	309	81	}	}	PUNCT
ejpam-5330	309	82	)	)	PUNCT
ejpam-5330	309	83	,	,	PUNCT
ejpam-5330	309	84	(	(	PUNCT
ejpam-5330	309	85	n2	n2	ADJ
ejpam-5330	309	86	,	,	PUNCT
ejpam-5330	309	87	{	{	PUNCT
ejpam-5330	309	88	w1	w1	NOUN
ejpam-5330	309	89	0.3	0.3	NUM
ejpam-5330	309	90	,	,	PUNCT
ejpam-5330	309	91	w2	w2	NOUN
ejpam-5330	309	92	0.3	0.3	NUM
ejpam-5330	309	93	,	,	PUNCT
ejpam-5330	309	94	w3	w3	PROPN
ejpam-5330	309	95	0.4	0.4	NUM
ejpam-5330	309	96	}	}	PUNCT
ejpam-5330	309	97	)	)	PUNCT
ejpam-5330	309	98	}	}	PUNCT
ejpam-5330	309	99	.	.	PUNCT
ejpam-5330	310	1	define	define	VERB
ejpam-5330	310	2	fuzzy	fuzzy	ADJ
ejpam-5330	310	3	soft	soft	ADJ
ejpam-5330	310	4	topologies	topology	NOUN
ejpam-5330	310	5	τn	τn	ADP
ejpam-5330	310	6	,	,	PUNCT
ejpam-5330	310	7	ηn	ηn	INTJ
ejpam-5330	310	8	:	:	PUNCT
ejpam-5330	310	9	n	n	X
ejpam-5330	310	10	−→	−→	NOUN
ejpam-5330	310	11	[	[	X
ejpam-5330	310	12	0	0	NUM
ejpam-5330	310	13	,	,	PUNCT
ejpam-5330	310	14	1	1	NUM
ejpam-5330	310	15	]	]	PUNCT
ejpam-5330	310	16	˜(w	˜(w	PROPN
ejpam-5330	310	17	,	,	PUNCT
ejpam-5330	310	18	n	n	CCONJ
ejpam-5330	310	19	)	)	PUNCT
ejpam-5330	310	20	as	as	SCONJ
ejpam-5330	310	21	follows	follow	VERB
ejpam-5330	310	22	:	:	PUNCT
ejpam-5330	310	23	∀n	∀n	NUM
ejpam-5330	310	24	∈	∈	PROPN
ejpam-5330	310	25	n	n	PRON
ejpam-5330	310	26	,	,	PUNCT
ejpam-5330	310	27	τn(tn	τn(tn	PROPN
ejpam-5330	310	28	)	)	PUNCT
ejpam-5330	311	1	=	=	PUNCT
ejpam-5330	312	1			NOUN
ejpam-5330	312	2	1	1	NUM
ejpam-5330	312	3	,	,	PUNCT
ejpam-5330	312	4	if	if	SCONJ
ejpam-5330	312	5	tn	tn	PROPN
ejpam-5330	312	6	∈	∈	PROPN
ejpam-5330	312	7	{	{	PUNCT
ejpam-5330	312	8	φ	φ	NOUN
ejpam-5330	312	9	,	,	PUNCT
ejpam-5330	312	10	ñ	ñ	PROPN
ejpam-5330	312	11	}	}	PUNCT
ejpam-5330	312	12	,	,	PUNCT
ejpam-5330	312	13	1	1	NUM
ejpam-5330	312	14	2	2	NUM
ejpam-5330	312	15	,	,	PUNCT
ejpam-5330	312	16	if	if	SCONJ
ejpam-5330	312	17	tn	tn	PROPN
ejpam-5330	312	18	=	=	SYM
ejpam-5330	312	19	gn	gn	PROPN
ejpam-5330	312	20	,	,	PUNCT
ejpam-5330	312	21	0	0	NUM
ejpam-5330	312	22	,	,	PUNCT
ejpam-5330	312	23	otherwise	otherwise	ADV
ejpam-5330	312	24	,	,	PUNCT
ejpam-5330	312	25	ηn(tn	ηn(tn	PROPN
ejpam-5330	312	26	)	)	PUNCT
ejpam-5330	312	27	=	=	PUNCT
ejpam-5330	312	28			NOUN
ejpam-5330	312	29	1	1	NUM
ejpam-5330	312	30	,	,	PUNCT
ejpam-5330	312	31	if	if	SCONJ
ejpam-5330	312	32	tn	tn	PROPN
ejpam-5330	312	33	∈	∈	PROPN
ejpam-5330	312	34	{	{	PUNCT
ejpam-5330	312	35	φ	φ	NOUN
ejpam-5330	312	36	,	,	PUNCT
ejpam-5330	312	37	ñ	ñ	PROPN
ejpam-5330	312	38	}	}	PUNCT
ejpam-5330	312	39	,	,	PUNCT
ejpam-5330	312	40	1	1	NUM
ejpam-5330	312	41	2	2	NUM
ejpam-5330	312	42	,	,	PUNCT
ejpam-5330	312	43	if	if	SCONJ
ejpam-5330	312	44	tn	tn	NUM
ejpam-5330	312	45	=	=	SYM
ejpam-5330	312	46	gn	gn	PROPN
ejpam-5330	312	47	,	,	PUNCT
ejpam-5330	312	48	1	1	NUM
ejpam-5330	312	49	3	3	NUM
ejpam-5330	312	50	,	,	PUNCT
ejpam-5330	312	51	if	if	SCONJ
ejpam-5330	312	52	tn	tn	NUM
ejpam-5330	312	53	=	=	SYM
ejpam-5330	312	54	hn	hn	PROPN
ejpam-5330	312	55	,	,	PUNCT
ejpam-5330	312	56	0	0	NUM
ejpam-5330	312	57	,	,	PUNCT
ejpam-5330	312	58	otherwise	otherwise	ADV
ejpam-5330	312	59	.	.	PUNCT
ejpam-5330	313	1	thus	thus	ADV
ejpam-5330	313	2	,	,	PUNCT
ejpam-5330	313	3	the	the	DET
ejpam-5330	313	4	identity	identity	NOUN
ejpam-5330	313	5	fuzzy	fuzzy	ADJ
ejpam-5330	313	6	soft	soft	ADJ
ejpam-5330	313	7	mapping	mapping	NOUN
ejpam-5330	313	8	φψ	φψ	X
ejpam-5330	313	9	:	:	PUNCT
ejpam-5330	313	10	(	(	PUNCT
ejpam-5330	313	11	w	w	INTJ
ejpam-5330	313	12	,	,	PUNCT
ejpam-5330	313	13	τn	τn	NOUN
ejpam-5330	313	14	)	)	PUNCT
ejpam-5330	313	15	−→	−→	NOUN
ejpam-5330	313	16	(	(	PUNCT
ejpam-5330	313	17	w	w	NOUN
ejpam-5330	313	18	,	,	PUNCT
ejpam-5330	313	19	ηn	ηn	INTJ
ejpam-5330	313	20	)	)	PUNCT
ejpam-5330	313	21	is	be	AUX
ejpam-5330	313	22	fuzzy	fuzzy	ADJ
ejpam-5330	313	23	soft	soft	ADJ
ejpam-5330	313	24	almost	almost	ADV
ejpam-5330	313	25	α	α	NOUN
ejpam-5330	313	26	-	-	ADJ
ejpam-5330	313	27	continuous	continuous	ADJ
ejpam-5330	313	28	,	,	PUNCT
ejpam-5330	313	29	but	but	CCONJ
ejpam-5330	313	30	it	it	PRON
ejpam-5330	313	31	is	be	AUX
ejpam-5330	313	32	not	not	PART
ejpam-5330	313	33	fuzzy	fuzzy	ADJ
ejpam-5330	313	34	soft	soft	ADJ
ejpam-5330	313	35	α	α	NOUN
ejpam-5330	313	36	-	-	ADJ
ejpam-5330	313	37	continuous	continuous	ADJ
ejpam-5330	313	38	.	.	PUNCT
ejpam-5330	313	39	example	example	NOUN
ejpam-5330	314	1	5	5	NUM
ejpam-5330	314	2	.	.	PUNCT
ejpam-5330	314	3	letw	letw	NOUN
ejpam-5330	314	4	=	=	CCONJ
ejpam-5330	314	5	{	{	PUNCT
ejpam-5330	314	6	w1	w1	NOUN
ejpam-5330	314	7	,	,	PUNCT
ejpam-5330	314	8	w2	w2	NOUN
ejpam-5330	314	9	,	,	PUNCT
ejpam-5330	314	10	w3	w3	PROPN
ejpam-5330	314	11	}	}	PUNCT
ejpam-5330	314	12	,	,	PUNCT
ejpam-5330	314	13	n	n	NOUN
ejpam-5330	314	14	=	=	SYM
ejpam-5330	314	15	{	{	PUNCT
ejpam-5330	314	16	n1	n1	NOUN
ejpam-5330	314	17	,	,	PUNCT
ejpam-5330	314	18	n2	n2	ADJ
ejpam-5330	314	19	}	}	PUNCT
ejpam-5330	314	20	,	,	PUNCT
ejpam-5330	314	21	and	and	CCONJ
ejpam-5330	314	22	define	define	VERB
ejpam-5330	314	23	gn	gn	PROPN
ejpam-5330	314	24	,	,	PUNCT
ejpam-5330	314	25	hn	hn	PROPN
ejpam-5330	314	26	∈	∈	PROPN
ejpam-5330	314	27	˜(w	˜(w	PROPN
ejpam-5330	314	28	,	,	PUNCT
ejpam-5330	314	29	n	n	CCONJ
ejpam-5330	314	30	)	)	PUNCT
ejpam-5330	314	31	as	as	SCONJ
ejpam-5330	314	32	follows	follow	VERB
ejpam-5330	314	33	:	:	PUNCT
ejpam-5330	314	34	gn	gn	PROPN
ejpam-5330	314	35	=	=	PUNCT
ejpam-5330	314	36	{	{	PUNCT
ejpam-5330	314	37	(	(	PUNCT
ejpam-5330	314	38	n1	n1	NOUN
ejpam-5330	314	39	,	,	PUNCT
ejpam-5330	314	40	{	{	PUNCT
ejpam-5330	314	41	w1	w1	NOUN
ejpam-5330	314	42	0.5	0.5	NUM
ejpam-5330	314	43	,	,	PUNCT
ejpam-5330	314	44	w2	w2	NOUN
ejpam-5330	314	45	0.5	0.5	NUM
ejpam-5330	314	46	,	,	PUNCT
ejpam-5330	314	47	w3	w3	PROPN
ejpam-5330	314	48	0.5	0.5	NUM
ejpam-5330	314	49	}	}	PUNCT
ejpam-5330	314	50	)	)	PUNCT
ejpam-5330	314	51	,	,	PUNCT
ejpam-5330	314	52	(	(	PUNCT
ejpam-5330	314	53	n2	n2	ADJ
ejpam-5330	314	54	,	,	PUNCT
ejpam-5330	314	55	{	{	PUNCT
ejpam-5330	314	56	w1	w1	NOUN
ejpam-5330	314	57	0.5	0.5	NUM
ejpam-5330	314	58	,	,	PUNCT
ejpam-5330	314	59	w2	w2	NOUN
ejpam-5330	314	60	0.5	0.5	NUM
ejpam-5330	314	61	,	,	PUNCT
ejpam-5330	314	62	w3	w3	PROPN
ejpam-5330	314	63	0.5	0.5	NUM
ejpam-5330	314	64	}	}	PUNCT
ejpam-5330	314	65	)	)	PUNCT
ejpam-5330	314	66	}	}	PUNCT
ejpam-5330	314	67	,	,	PUNCT
ejpam-5330	314	68	hn	hn	PROPN
ejpam-5330	314	69	=	=	PRON
ejpam-5330	314	70	{	{	PUNCT
ejpam-5330	314	71	(	(	PUNCT
ejpam-5330	314	72	n1	n1	NOUN
ejpam-5330	314	73	,	,	PUNCT
ejpam-5330	314	74	{	{	PUNCT
ejpam-5330	314	75	w1	w1	NOUN
ejpam-5330	314	76	0.3	0.3	NUM
ejpam-5330	314	77	,	,	PUNCT
ejpam-5330	314	78	w2	w2	NOUN
ejpam-5330	314	79	0	0	NUM
ejpam-5330	314	80	,	,	PUNCT
ejpam-5330	314	81	w3	w3	PROPN
ejpam-5330	314	82	0.5	0.5	NUM
ejpam-5330	314	83	}	}	PUNCT
ejpam-5330	314	84	)	)	PUNCT
ejpam-5330	314	85	,	,	PUNCT
ejpam-5330	314	86	(	(	PUNCT
ejpam-5330	314	87	n2	n2	ADJ
ejpam-5330	314	88	,	,	PUNCT
ejpam-5330	314	89	{	{	PUNCT
ejpam-5330	314	90	w1	w1	NOUN
ejpam-5330	314	91	0.3	0.3	NUM
ejpam-5330	314	92	,	,	PUNCT
ejpam-5330	314	93	w2	w2	NOUN
ejpam-5330	314	94	0	0	NUM
ejpam-5330	314	95	,	,	PUNCT
ejpam-5330	314	96	w3	w3	PROPN
ejpam-5330	314	97	0.5	0.5	NUM
ejpam-5330	314	98	}	}	PUNCT
ejpam-5330	314	99	)	)	PUNCT
ejpam-5330	314	100	}	}	PUNCT
ejpam-5330	314	101	.	.	PUNCT
ejpam-5330	315	1	define	define	VERB
ejpam-5330	315	2	fuzzy	fuzzy	ADJ
ejpam-5330	315	3	soft	soft	ADJ
ejpam-5330	315	4	topologies	topology	NOUN
ejpam-5330	315	5	τn	τn	ADP
ejpam-5330	315	6	,	,	PUNCT
ejpam-5330	315	7	ηn	ηn	INTJ
ejpam-5330	315	8	:	:	PUNCT
ejpam-5330	315	9	n	n	X
ejpam-5330	315	10	−→	−→	NOUN
ejpam-5330	315	11	[	[	X
ejpam-5330	315	12	0	0	NUM
ejpam-5330	315	13	,	,	PUNCT
ejpam-5330	315	14	1	1	NUM
ejpam-5330	315	15	]	]	PUNCT
ejpam-5330	315	16	˜(w	˜(w	PROPN
ejpam-5330	315	17	,	,	PUNCT
ejpam-5330	315	18	n	n	CCONJ
ejpam-5330	315	19	)	)	PUNCT
ejpam-5330	315	20	as	as	SCONJ
ejpam-5330	315	21	follows	follow	VERB
ejpam-5330	315	22	:	:	PUNCT
ejpam-5330	315	23	∀n	∀n	NUM
ejpam-5330	315	24	∈	∈	PROPN
ejpam-5330	315	25	n	n	PRON
ejpam-5330	315	26	,	,	PUNCT
ejpam-5330	315	27	τn(tn	τn(tn	PROPN
ejpam-5330	315	28	)	)	PUNCT
ejpam-5330	316	1	=	=	PUNCT
ejpam-5330	317	1			NOUN
ejpam-5330	317	2	1	1	NUM
ejpam-5330	317	3	,	,	PUNCT
ejpam-5330	317	4	if	if	SCONJ
ejpam-5330	317	5	tn	tn	PROPN
ejpam-5330	317	6	∈	∈	PROPN
ejpam-5330	317	7	{	{	PUNCT
ejpam-5330	317	8	φ	φ	NOUN
ejpam-5330	317	9	,	,	PUNCT
ejpam-5330	317	10	ñ	ñ	PROPN
ejpam-5330	317	11	}	}	PUNCT
ejpam-5330	317	12	,	,	PUNCT
ejpam-5330	317	13	2	2	NUM
ejpam-5330	317	14	3	3	NUM
ejpam-5330	317	15	,	,	PUNCT
ejpam-5330	317	16	if	if	SCONJ
ejpam-5330	317	17	tn	tn	PROPN
ejpam-5330	317	18	=	=	SYM
ejpam-5330	317	19	gn	gn	PROPN
ejpam-5330	317	20	,	,	PUNCT
ejpam-5330	317	21	0	0	NUM
ejpam-5330	317	22	,	,	PUNCT
ejpam-5330	317	23	otherwise	otherwise	ADV
ejpam-5330	317	24	,	,	PUNCT
ejpam-5330	317	25	ηn(tn	ηn(tn	PROPN
ejpam-5330	317	26	)	)	PUNCT
ejpam-5330	318	1	=	=	PUNCT
ejpam-5330	319	1			NOUN
ejpam-5330	319	2	1	1	NUM
ejpam-5330	319	3	,	,	PUNCT
ejpam-5330	319	4	if	if	SCONJ
ejpam-5330	319	5	tn	tn	PROPN
ejpam-5330	319	6	∈	∈	PROPN
ejpam-5330	319	7	{	{	PUNCT
ejpam-5330	319	8	φ	φ	NOUN
ejpam-5330	319	9	,	,	PUNCT
ejpam-5330	319	10	ñ	ñ	PROPN
ejpam-5330	319	11	}	}	PUNCT
ejpam-5330	319	12	,	,	PUNCT
ejpam-5330	319	13	1	1	NUM
ejpam-5330	319	14	3	3	NUM
ejpam-5330	319	15	,	,	PUNCT
ejpam-5330	319	16	if	if	SCONJ
ejpam-5330	319	17	tn	tn	NUM
ejpam-5330	319	18	=	=	SYM
ejpam-5330	319	19	hn	hn	PROPN
ejpam-5330	319	20	,	,	PUNCT
ejpam-5330	319	21	0	0	NUM
ejpam-5330	319	22	,	,	PUNCT
ejpam-5330	319	23	otherwise	otherwise	ADV
ejpam-5330	319	24	.	.	PUNCT
ejpam-5330	320	1	thus	thus	ADV
ejpam-5330	320	2	,	,	PUNCT
ejpam-5330	320	3	the	the	DET
ejpam-5330	320	4	identity	identity	NOUN
ejpam-5330	320	5	fuzzy	fuzzy	ADJ
ejpam-5330	320	6	soft	soft	ADJ
ejpam-5330	320	7	mapping	mapping	NOUN
ejpam-5330	320	8	φψ	φψ	X
ejpam-5330	320	9	:	:	PUNCT
ejpam-5330	320	10	(	(	PUNCT
ejpam-5330	320	11	w	w	INTJ
ejpam-5330	320	12	,	,	PUNCT
ejpam-5330	320	13	τn	τn	NOUN
ejpam-5330	320	14	)	)	PUNCT
ejpam-5330	320	15	−→	−→	NOUN
ejpam-5330	320	16	(	(	PUNCT
ejpam-5330	320	17	w	w	NOUN
ejpam-5330	320	18	,	,	PUNCT
ejpam-5330	320	19	ηn	ηn	INTJ
ejpam-5330	320	20	)	)	PUNCT
ejpam-5330	320	21	is	be	AUX
ejpam-5330	320	22	fuzzy	fuzzy	ADJ
ejpam-5330	320	23	soft	soft	ADJ
ejpam-5330	320	24	weakly	weakly	ADJ
ejpam-5330	320	25	α	α	NOUN
ejpam-5330	320	26	-	-	ADJ
ejpam-5330	320	27	continuous	continuous	ADJ
ejpam-5330	320	28	,	,	PUNCT
ejpam-5330	320	29	but	but	CCONJ
ejpam-5330	320	30	it	it	PRON
ejpam-5330	320	31	is	be	AUX
ejpam-5330	320	32	not	not	PART
ejpam-5330	320	33	fuzzy	fuzzy	ADJ
ejpam-5330	320	34	soft	soft	ADJ
ejpam-5330	320	35	almost	almost	ADV
ejpam-5330	320	36	α	α	NOUN
ejpam-5330	320	37	-	-	ADJ
ejpam-5330	320	38	continuous	continuous	ADJ
ejpam-5330	320	39	.	.	PUNCT
ejpam-5330	321	1	theorem	theorem	ADJ
ejpam-5330	321	2	7	7	NUM
ejpam-5330	321	3	.	.	PUNCT
ejpam-5330	322	1	let	let	VERB
ejpam-5330	322	2	(	(	PUNCT
ejpam-5330	322	3	w	w	NOUN
ejpam-5330	322	4	,	,	PUNCT
ejpam-5330	322	5	τn	τn	PROPN
ejpam-5330	322	6	)	)	PUNCT
ejpam-5330	322	7	and	and	CCONJ
ejpam-5330	322	8	(	(	PUNCT
ejpam-5330	322	9	v	v	NOUN
ejpam-5330	322	10	,	,	PUNCT
ejpam-5330	322	11	ηf	ηf	PROPN
ejpam-5330	322	12	)	)	PUNCT
ejpam-5330	322	13	be	be	AUX
ejpam-5330	322	14	an	an	DET
ejpam-5330	322	15	fstss	fstss	NOUN
ejpam-5330	322	16	,	,	PUNCT
ejpam-5330	322	17	and	and	CCONJ
ejpam-5330	322	18	φψ	φψ	PROPN
ejpam-5330	322	19	:	:	PUNCT
ejpam-5330	322	20	˜(w	˜(w	PROPN
ejpam-5330	322	21	,	,	PUNCT
ejpam-5330	322	22	n	n	CCONJ
ejpam-5330	322	23	)	)	PUNCT
ejpam-5330	322	24	−→	−→	NOUN
ejpam-5330	322	25	(	(	PUNCT
ejpam-5330	322	26	̃v	̃v	NOUN
ejpam-5330	322	27	,	,	PUNCT
ejpam-5330	322	28	f	f	PROPN
ejpam-5330	322	29	)	)	PUNCT
ejpam-5330	322	30	be	be	AUX
ejpam-5330	322	31	a	a	DET
ejpam-5330	322	32	fuzzy	fuzzy	ADJ
ejpam-5330	322	33	soft	soft	ADJ
ejpam-5330	322	34	mapping	mapping	NOUN
ejpam-5330	322	35	.	.	PUNCT
ejpam-5330	323	1	the	the	DET
ejpam-5330	323	2	following	follow	VERB
ejpam-5330	323	3	statements	statement	NOUN
ejpam-5330	323	4	are	be	AUX
ejpam-5330	323	5	equivalent	equivalent	ADJ
ejpam-5330	323	6	for	for	ADP
ejpam-5330	323	7	each	each	DET
ejpam-5330	323	8	fa	fa	X
ejpam-5330	323	9	∈	∈	PROPN
ejpam-5330	323	10	(	(	PUNCT
ejpam-5330	323	11	̃v	̃v	NOUN
ejpam-5330	323	12	,	,	PUNCT
ejpam-5330	323	13	f	f	PROPN
ejpam-5330	323	14	)	)	PUNCT
ejpam-5330	323	15	,	,	PUNCT
ejpam-5330	323	16	n	n	PROPN
ejpam-5330	323	17	∈	∈	PROPN
ejpam-5330	323	18	n	n	NOUN
ejpam-5330	323	19	,	,	PUNCT
ejpam-5330	323	20	(	(	PUNCT
ejpam-5330	323	21	k	k	NOUN
ejpam-5330	323	22	=	=	SYM
ejpam-5330	323	23	ψ(n	ψ(n	PROPN
ejpam-5330	323	24	)	)	PUNCT
ejpam-5330	323	25	)	)	PUNCT
ejpam-5330	324	1	∈	∈	PROPN
ejpam-5330	324	2	f	f	X
ejpam-5330	324	3	,	,	PUNCT
ejpam-5330	324	4	and	and	CCONJ
ejpam-5330	324	5	r	r	NOUN
ejpam-5330	324	6	∈	∈	PROPN
ejpam-5330	324	7	i	i	PRON
ejpam-5330	324	8	◦	◦	NOUN
ejpam-5330	324	9	:	:	PUNCT
ejpam-5330	324	10	(	(	PUNCT
ejpam-5330	324	11	1	1	X
ejpam-5330	324	12	)	)	PUNCT
ejpam-5330	324	13	φψ	φψ	NOUN
ejpam-5330	324	14	is	be	AUX
ejpam-5330	324	15	fuzzy	fuzzy	ADJ
ejpam-5330	324	16	soft	soft	ADJ
ejpam-5330	324	17	almost	almost	ADV
ejpam-5330	324	18	α	α	NOUN
ejpam-5330	324	19	-	-	ADJ
ejpam-5330	324	20	continuous	continuous	ADJ
ejpam-5330	324	21	.	.	PUNCT
ejpam-5330	325	1	(	(	PUNCT
ejpam-5330	325	2	2	2	X
ejpam-5330	325	3	)	)	PUNCT
ejpam-5330	325	4	φ−1	φ−1	PROPN
ejpam-5330	325	5	ψ	ψ	SYM
ejpam-5330	325	6	(	(	PUNCT
ejpam-5330	325	7	fa	fa	NOUN
ejpam-5330	325	8	)	)	PUNCT
ejpam-5330	325	9	is	be	AUX
ejpam-5330	325	10	r	r	NOUN
ejpam-5330	325	11	-	-	PUNCT
ejpam-5330	325	12	fuzzy	fuzzy	ADJ
ejpam-5330	325	13	soft	soft	ADJ
ejpam-5330	325	14	α	α	NOUN
ejpam-5330	325	15	-	-	NOUN
ejpam-5330	325	16	open	open	ADJ
ejpam-5330	325	17	,	,	PUNCT
ejpam-5330	325	18	for	for	SCONJ
ejpam-5330	325	19	each	each	DET
ejpam-5330	325	20	fa	fa	NOUN
ejpam-5330	325	21	is	be	AUX
ejpam-5330	325	22	r	r	NOUN
ejpam-5330	325	23	-	-	PUNCT
ejpam-5330	325	24	fuzzy	fuzzy	ADJ
ejpam-5330	325	25	soft	soft	ADJ
ejpam-5330	325	26	regularly	regularly	ADV
ejpam-5330	325	27	open	open	ADJ
ejpam-5330	325	28	.	.	PUNCT
ejpam-5330	326	1	(	(	PUNCT
ejpam-5330	326	2	3	3	X
ejpam-5330	326	3	)	)	PUNCT
ejpam-5330	326	4	φ−1	φ−1	PROPN
ejpam-5330	326	5	ψ	ψ	SYM
ejpam-5330	326	6	(	(	PUNCT
ejpam-5330	326	7	fa	fa	NOUN
ejpam-5330	326	8	)	)	PUNCT
ejpam-5330	326	9	is	be	AUX
ejpam-5330	326	10	r	r	NOUN
ejpam-5330	326	11	-	-	PUNCT
ejpam-5330	326	12	fuzzy	fuzzy	ADJ
ejpam-5330	326	13	soft	soft	ADJ
ejpam-5330	326	14	α	α	NOUN
ejpam-5330	326	15	-	-	VERB
ejpam-5330	326	16	closed	closed	ADJ
ejpam-5330	326	17	,	,	PUNCT
ejpam-5330	326	18	for	for	SCONJ
ejpam-5330	326	19	each	each	DET
ejpam-5330	326	20	fa	fa	NOUN
ejpam-5330	326	21	is	be	AUX
ejpam-5330	326	22	r	r	NOUN
ejpam-5330	326	23	-	-	PUNCT
ejpam-5330	326	24	fuzzy	fuzzy	ADJ
ejpam-5330	326	25	soft	soft	ADJ
ejpam-5330	326	26	regularly	regularly	ADV
ejpam-5330	326	27	closed	closed	ADJ
ejpam-5330	326	28	.	.	PUNCT
ejpam-5330	327	1	(	(	PUNCT
ejpam-5330	327	2	4	4	X
ejpam-5330	327	3	)	)	PUNCT
ejpam-5330	327	4	αcτ	αcτ	NOUN
ejpam-5330	327	5	(	(	PUNCT
ejpam-5330	327	6	n	n	X
ejpam-5330	327	7	,	,	PUNCT
ejpam-5330	327	8	φ	φ	PROPN
ejpam-5330	327	9	−1	−1	NOUN
ejpam-5330	327	10	ψ	ψ	X
ejpam-5330	327	11	(	(	PUNCT
ejpam-5330	327	12	fa	fa	NOUN
ejpam-5330	327	13	)	)	PUNCT
ejpam-5330	327	14	,	,	PUNCT
ejpam-5330	327	15	r	r	X
ejpam-5330	327	16	)	)	PUNCT
ejpam-5330	327	17	⊑	⊑	X
ejpam-5330	327	18	φ−1	φ−1	PROPN
ejpam-5330	327	19	ψ	ψ	X
ejpam-5330	327	20	(	(	PUNCT
ejpam-5330	327	21	cη(k	cη(k	PROPN
ejpam-5330	327	22	,	,	PUNCT
ejpam-5330	327	23	fa	fa	NOUN
ejpam-5330	327	24	,	,	PUNCT
ejpam-5330	327	25	r	r	NOUN
ejpam-5330	327	26	)	)	PUNCT
ejpam-5330	327	27	)	)	PUNCT
ejpam-5330	327	28	,	,	PUNCT
ejpam-5330	327	29	for	for	SCONJ
ejpam-5330	327	30	each	each	DET
ejpam-5330	327	31	fa	fa	NOUN
ejpam-5330	327	32	is	be	AUX
ejpam-5330	327	33	r	r	NOUN
ejpam-5330	327	34	-	-	PUNCT
ejpam-5330	327	35	fuzzy	fuzzy	ADJ
ejpam-5330	327	36	soft	soft	ADJ
ejpam-5330	327	37	β	β	NOUN
ejpam-5330	327	38	-	-	ADJ
ejpam-5330	327	39	open	open	ADJ
ejpam-5330	327	40	.	.	PUNCT
ejpam-5330	328	1	(	(	PUNCT
ejpam-5330	328	2	5	5	NUM
ejpam-5330	328	3	)	)	PUNCT
ejpam-5330	328	4	αcτ	αcτ	NOUN
ejpam-5330	328	5	(	(	PUNCT
ejpam-5330	328	6	n	n	X
ejpam-5330	328	7	,	,	PUNCT
ejpam-5330	328	8	φ	φ	PROPN
ejpam-5330	328	9	−1	−1	NOUN
ejpam-5330	328	10	ψ	ψ	X
ejpam-5330	328	11	(	(	PUNCT
ejpam-5330	328	12	fa	fa	NOUN
ejpam-5330	328	13	)	)	PUNCT
ejpam-5330	328	14	,	,	PUNCT
ejpam-5330	328	15	r	r	X
ejpam-5330	328	16	)	)	PUNCT
ejpam-5330	328	17	⊑	⊑	X
ejpam-5330	328	18	φ−1	φ−1	PROPN
ejpam-5330	328	19	ψ	ψ	X
ejpam-5330	328	20	(	(	PUNCT
ejpam-5330	328	21	cη(k	cη(k	PROPN
ejpam-5330	328	22	,	,	PUNCT
ejpam-5330	328	23	fa	fa	NOUN
ejpam-5330	328	24	,	,	PUNCT
ejpam-5330	328	25	r	r	NOUN
ejpam-5330	328	26	)	)	PUNCT
ejpam-5330	328	27	)	)	PUNCT
ejpam-5330	328	28	,	,	PUNCT
ejpam-5330	328	29	for	for	SCONJ
ejpam-5330	328	30	each	each	DET
ejpam-5330	328	31	fa	fa	NOUN
ejpam-5330	328	32	is	be	AUX
ejpam-5330	328	33	r	r	NOUN
ejpam-5330	328	34	-	-	PUNCT
ejpam-5330	328	35	fuzzy	fuzzy	ADJ
ejpam-5330	328	36	soft	soft	ADJ
ejpam-5330	328	37	semi	semi	ADJ
ejpam-5330	328	38	-	-	ADJ
ejpam-5330	328	39	open	open	ADJ
ejpam-5330	328	40	.	.	PUNCT
ejpam-5330	329	1	(	(	PUNCT
ejpam-5330	329	2	6	6	X
ejpam-5330	329	3	)	)	PUNCT
ejpam-5330	329	4	αiτ	αiτ	NOUN
ejpam-5330	329	5	(	(	PUNCT
ejpam-5330	329	6	n	n	CCONJ
ejpam-5330	329	7	,	,	PUNCT
ejpam-5330	329	8	φ	φ	PROPN
ejpam-5330	329	9	−1	−1	NOUN
ejpam-5330	329	10	ψ	ψ	X
ejpam-5330	329	11	(	(	PUNCT
ejpam-5330	329	12	iη(k	iη(k	NOUN
ejpam-5330	329	13	,	,	PUNCT
ejpam-5330	329	14	cη(k	cη(k	PROPN
ejpam-5330	329	15	,	,	PUNCT
ejpam-5330	329	16	fa	fa	NOUN
ejpam-5330	329	17	,	,	PUNCT
ejpam-5330	329	18	r	r	NOUN
ejpam-5330	329	19	)	)	PUNCT
ejpam-5330	329	20	,	,	PUNCT
ejpam-5330	329	21	r	r	NOUN
ejpam-5330	329	22	)	)	PUNCT
ejpam-5330	329	23	)	)	PUNCT
ejpam-5330	329	24	,	,	PUNCT
ejpam-5330	329	25	r	r	NOUN
ejpam-5330	329	26	)	)	PUNCT
ejpam-5330	329	27	⊒	⊒	PUNCT
ejpam-5330	329	28	φ−1	φ−1	PROPN
ejpam-5330	329	29	ψ	ψ	PROPN
ejpam-5330	329	30	(	(	PUNCT
ejpam-5330	329	31	fa	fa	NOUN
ejpam-5330	329	32	)	)	PUNCT
ejpam-5330	329	33	,	,	PUNCT
ejpam-5330	329	34	for	for	ADP
ejpam-5330	329	35	each	each	DET
ejpam-5330	329	36	fa	fa	NOUN
ejpam-5330	329	37	with	with	ADP
ejpam-5330	329	38	ηk(fa	ηk(fa	PROPN
ejpam-5330	329	39	)	)	PUNCT
ejpam-5330	329	40	≥	≥	PROPN
ejpam-5330	329	41	r.	r.	PROPN
ejpam-5330	329	42	w.	w.	PROPN
ejpam-5330	329	43	alqurashi	alqurashi	PROPN
ejpam-5330	329	44	,	,	PUNCT
ejpam-5330	329	45	i.	i.	PROPN
ejpam-5330	329	46	m.	m.	PROPN
ejpam-5330	329	47	taha	taha	PROPN
ejpam-5330	329	48	/	/	PUNCT
ejpam-5330	329	49	eur	eur	PROPN
ejpam-5330	329	50	.	.	PUNCT
ejpam-5330	330	1	j.	j.	PROPN
ejpam-5330	330	2	pure	pure	PROPN
ejpam-5330	330	3	appl	appl	PROPN
ejpam-5330	330	4	.	.	PROPN
ejpam-5330	330	5	math	math	PROPN
ejpam-5330	330	6	,	,	PUNCT
ejpam-5330	330	7	17	17	NUM
ejpam-5330	330	8	(	(	PUNCT
ejpam-5330	330	9	4	4	NUM
ejpam-5330	330	10	)	)	PUNCT
ejpam-5330	330	11	(	(	PUNCT
ejpam-5330	330	12	2024	2024	NUM
ejpam-5330	330	13	)	)	PUNCT
ejpam-5330	330	14	,	,	PUNCT
ejpam-5330	330	15	4112	4112	NUM
ejpam-5330	330	16	-	-	SYM
ejpam-5330	330	17	4134	4134	NUM
ejpam-5330	330	18	4124	4124	NUM
ejpam-5330	330	19	proof	proof	NOUN
ejpam-5330	330	20	.	.	PUNCT
ejpam-5330	331	1	(	(	PUNCT
ejpam-5330	331	2	1	1	X
ejpam-5330	331	3	)	)	PUNCT
ejpam-5330	331	4	⇒	⇒	NOUN
ejpam-5330	331	5	(	(	PUNCT
ejpam-5330	331	6	2	2	X
ejpam-5330	331	7	)	)	PUNCT
ejpam-5330	331	8	let	let	VERB
ejpam-5330	331	9	nws	nws	PROPN
ejpam-5330	331	10	∈	∈	PROPN
ejpam-5330	331	11	p̃s(w	p̃s(w	NOUN
ejpam-5330	331	12	)	)	PUNCT
ejpam-5330	331	13	and	and	CCONJ
ejpam-5330	331	14	fa	fa	NUM
ejpam-5330	331	15	∈	∈	PROPN
ejpam-5330	331	16	(	(	PUNCT
ejpam-5330	331	17	̃v	̃v	NOUN
ejpam-5330	331	18	,	,	PUNCT
ejpam-5330	331	19	f	f	PROPN
ejpam-5330	331	20	)	)	PUNCT
ejpam-5330	331	21	be	be	AUX
ejpam-5330	331	22	an	an	DET
ejpam-5330	331	23	r	r	NOUN
ejpam-5330	331	24	-	-	PUNCT
ejpam-5330	331	25	fuzzy	fuzzy	ADJ
ejpam-5330	331	26	soft	soft	ADJ
ejpam-5330	331	27	regularly	regularly	ADV
ejpam-5330	331	28	open	open	ADJ
ejpam-5330	331	29	set	set	NOUN
ejpam-5330	331	30	containing	contain	VERB
ejpam-5330	331	31	φψ(nws	φψ(nws	NOUN
ejpam-5330	331	32	)	)	PUNCT
ejpam-5330	331	33	,	,	PUNCT
ejpam-5330	331	34	hence	hence	ADV
ejpam-5330	331	35	by	by	ADP
ejpam-5330	331	36	(	(	PUNCT
ejpam-5330	331	37	1	1	NUM
ejpam-5330	331	38	)	)	PUNCT
ejpam-5330	331	39	,	,	PUNCT
ejpam-5330	331	40	there	there	PRON
ejpam-5330	331	41	is	be	VERB
ejpam-5330	331	42	hc	hc	PROPN
ejpam-5330	331	43	∈	∈	PROPN
ejpam-5330	331	44	˜(w	˜(w	PROPN
ejpam-5330	331	45	,	,	PUNCT
ejpam-5330	331	46	n	n	CCONJ
ejpam-5330	331	47	)	)	PUNCT
ejpam-5330	331	48	is	be	AUX
ejpam-5330	331	49	r	r	NOUN
ejpam-5330	331	50	-	-	PUNCT
ejpam-5330	331	51	fuzzy	fuzzy	ADJ
ejpam-5330	331	52	soft	soft	ADJ
ejpam-5330	331	53	α	α	NOUN
ejpam-5330	331	54	-	-	ADJ
ejpam-5330	331	55	open	open	ADJ
ejpam-5330	331	56	set	set	NOUN
ejpam-5330	331	57	containing	contain	VERB
ejpam-5330	331	58	nws	nws	PROPN
ejpam-5330	331	59	such	such	ADJ
ejpam-5330	331	60	that	that	DET
ejpam-5330	331	61	φψ(hc	φψ(hc	NOUN
ejpam-5330	331	62	)	)	PUNCT
ejpam-5330	331	63	⊑	⊑	PRON
ejpam-5330	331	64	iη(k	iη(k	PROPN
ejpam-5330	331	65	,	,	PUNCT
ejpam-5330	331	66	cη(k	cη(k	PROPN
ejpam-5330	331	67	,	,	PUNCT
ejpam-5330	331	68	fa	fa	NOUN
ejpam-5330	331	69	,	,	PUNCT
ejpam-5330	331	70	r	r	NOUN
ejpam-5330	331	71	)	)	PUNCT
ejpam-5330	331	72	,	,	PUNCT
ejpam-5330	331	73	r	r	NOUN
ejpam-5330	331	74	)	)	PUNCT
ejpam-5330	331	75	.	.	PUNCT
ejpam-5330	332	1	thus	thus	ADV
ejpam-5330	332	2	,	,	PUNCT
ejpam-5330	332	3	hc	hc	PROPN
ejpam-5330	332	4	⊑	⊑	DET
ejpam-5330	332	5	φ−1	φ−1	PROPN
ejpam-5330	332	6	ψ	ψ	SYM
ejpam-5330	332	7	(	(	PUNCT
ejpam-5330	332	8	iη(k	iη(k	NOUN
ejpam-5330	332	9	,	,	PUNCT
ejpam-5330	332	10	cη(k	cη(k	PROPN
ejpam-5330	332	11	,	,	PUNCT
ejpam-5330	332	12	fa	fa	NOUN
ejpam-5330	332	13	,	,	PUNCT
ejpam-5330	332	14	r	r	NOUN
ejpam-5330	332	15	)	)	PUNCT
ejpam-5330	332	16	,	,	PUNCT
ejpam-5330	332	17	r	r	NOUN
ejpam-5330	332	18	)	)	PUNCT
ejpam-5330	332	19	)	)	PUNCT
ejpam-5330	333	1	=	=	PUNCT
ejpam-5330	333	2	φ−1	φ−1	PROPN
ejpam-5330	333	3	ψ	ψ	X
ejpam-5330	333	4	(	(	PUNCT
ejpam-5330	333	5	fa	fa	NOUN
ejpam-5330	333	6	)	)	PUNCT
ejpam-5330	333	7	and	and	CCONJ
ejpam-5330	333	8	nws∈̃hc	nws∈̃hc	ADJ
ejpam-5330	333	9	⊑	⊑	PRON
ejpam-5330	333	10	φ−1	φ−1	PROPN
ejpam-5330	333	11	ψ	ψ	X
ejpam-5330	333	12	(	(	PUNCT
ejpam-5330	333	13	fa	fa	NOUN
ejpam-5330	333	14	)	)	PUNCT
ejpam-5330	333	15	.	.	PUNCT
ejpam-5330	334	1	then	then	ADV
ejpam-5330	334	2	,	,	PUNCT
ejpam-5330	334	3	nws∈̃iτ	nws∈̃iτ	X
ejpam-5330	334	4	(	(	PUNCT
ejpam-5330	334	5	n	n	CCONJ
ejpam-5330	334	6	,	,	PUNCT
ejpam-5330	334	7	cτ	cτ	INTJ
ejpam-5330	334	8	(	(	PUNCT
ejpam-5330	334	9	n	n	CCONJ
ejpam-5330	334	10	,	,	PUNCT
ejpam-5330	334	11	iτ	iτ	X
ejpam-5330	334	12	(	(	PUNCT
ejpam-5330	334	13	n	n	CCONJ
ejpam-5330	334	14	,	,	PUNCT
ejpam-5330	334	15	φ−1	φ−1	PROPN
ejpam-5330	334	16	ψ	ψ	SYM
ejpam-5330	334	17	(	(	PUNCT
ejpam-5330	334	18	fa	fa	NOUN
ejpam-5330	334	19	)	)	PUNCT
ejpam-5330	334	20	,	,	PUNCT
ejpam-5330	334	21	r	r	NOUN
ejpam-5330	334	22	)	)	PUNCT
ejpam-5330	334	23	,	,	PUNCT
ejpam-5330	334	24	r	r	NOUN
ejpam-5330	334	25	)	)	PUNCT
ejpam-5330	334	26	,	,	PUNCT
ejpam-5330	334	27	r	r	NOUN
ejpam-5330	334	28	)	)	PUNCT
ejpam-5330	334	29	and	and	CCONJ
ejpam-5330	334	30	φ	φ	NUM
ejpam-5330	334	31	−1	−1	NOUN
ejpam-5330	334	32	ψ	ψ	PROPN
ejpam-5330	334	33	(	(	PUNCT
ejpam-5330	334	34	fa	fa	X
ejpam-5330	334	35	)	)	PUNCT
ejpam-5330	334	36	⊑	⊑	X
ejpam-5330	334	37	iτ	iτ	X
ejpam-5330	334	38	(	(	PUNCT
ejpam-5330	334	39	n	n	CCONJ
ejpam-5330	334	40	,	,	PUNCT
ejpam-5330	334	41	cτ	cτ	INTJ
ejpam-5330	334	42	(	(	PUNCT
ejpam-5330	334	43	n	n	CCONJ
ejpam-5330	334	44	,	,	PUNCT
ejpam-5330	334	45	iτ	iτ	X
ejpam-5330	334	46	(	(	PUNCT
ejpam-5330	334	47	n	n	CCONJ
ejpam-5330	334	48	,	,	PUNCT
ejpam-5330	334	49	φ	φ	PROPN
ejpam-5330	334	50	−1	−1	NOUN
ejpam-5330	334	51	ψ	ψ	X
ejpam-5330	334	52	(	(	PUNCT
ejpam-5330	334	53	fa	fa	NOUN
ejpam-5330	334	54	)	)	PUNCT
ejpam-5330	334	55	,	,	PUNCT
ejpam-5330	334	56	r	r	NOUN
ejpam-5330	334	57	)	)	PUNCT
ejpam-5330	334	58	,	,	PUNCT
ejpam-5330	334	59	r	r	NOUN
ejpam-5330	334	60	)	)	PUNCT
ejpam-5330	334	61	,	,	PUNCT
ejpam-5330	334	62	r	r	NOUN
ejpam-5330	334	63	)	)	PUNCT
ejpam-5330	334	64	.	.	PUNCT
ejpam-5330	335	1	therefore	therefore	ADV
ejpam-5330	335	2	,	,	PUNCT
ejpam-5330	335	3	φ−1	φ−1	PROPN
ejpam-5330	335	4	ψ	ψ	SYM
ejpam-5330	335	5	(	(	PUNCT
ejpam-5330	335	6	fa	fa	NOUN
ejpam-5330	335	7	)	)	PUNCT
ejpam-5330	335	8	is	be	AUX
ejpam-5330	335	9	r	r	NOUN
ejpam-5330	335	10	-	-	PUNCT
ejpam-5330	335	11	fuzzy	fuzzy	ADJ
ejpam-5330	335	12	soft	soft	ADJ
ejpam-5330	335	13	α	α	NOUN
ejpam-5330	335	14	-	-	ADJ
ejpam-5330	335	15	open	open	ADJ
ejpam-5330	335	16	set	set	NOUN
ejpam-5330	335	17	.	.	PUNCT
ejpam-5330	336	1	(	(	PUNCT
ejpam-5330	336	2	2	2	X
ejpam-5330	336	3	)	)	PUNCT
ejpam-5330	336	4	⇒	⇒	NOUN
ejpam-5330	336	5	(	(	PUNCT
ejpam-5330	336	6	3	3	X
ejpam-5330	336	7	)	)	PUNCT
ejpam-5330	336	8	let	let	VERB
ejpam-5330	336	9	fa	fa	PART
ejpam-5330	336	10	be	be	AUX
ejpam-5330	336	11	an	an	DET
ejpam-5330	336	12	r	r	NOUN
ejpam-5330	336	13	-	-	PUNCT
ejpam-5330	336	14	fuzzy	fuzzy	ADJ
ejpam-5330	336	15	soft	soft	ADJ
ejpam-5330	336	16	regularly	regularly	ADV
ejpam-5330	336	17	closed	close	VERB
ejpam-5330	336	18	set	set	VERB
ejpam-5330	336	19	,	,	PUNCT
ejpam-5330	336	20	hence	hence	ADV
ejpam-5330	336	21	by	by	ADP
ejpam-5330	336	22	(	(	PUNCT
ejpam-5330	336	23	2	2	NUM
ejpam-5330	336	24	)	)	PUNCT
ejpam-5330	336	25	,	,	PUNCT
ejpam-5330	336	26	φ−1	φ−1	PROPN
ejpam-5330	336	27	ψ	ψ	X
ejpam-5330	336	28	(	(	PUNCT
ejpam-5330	336	29	f	f	PROPN
ejpam-5330	336	30	ca	ca	NOUN
ejpam-5330	336	31	)	)	PUNCT
ejpam-5330	336	32	=	=	PUNCT
ejpam-5330	337	1	(	(	PUNCT
ejpam-5330	337	2	φ−1	φ−1	PROPN
ejpam-5330	337	3	ψ	ψ	SYM
ejpam-5330	337	4	(	(	PUNCT
ejpam-5330	337	5	fa	fa	NOUN
ejpam-5330	337	6	)	)	PUNCT
ejpam-5330	337	7	)	)	PUNCT
ejpam-5330	338	1	c	c	NOUN
ejpam-5330	338	2	is	be	AUX
ejpam-5330	338	3	r	r	NOUN
ejpam-5330	338	4	-	-	PUNCT
ejpam-5330	338	5	fuzzy	fuzzy	ADJ
ejpam-5330	338	6	soft	soft	ADJ
ejpam-5330	338	7	α	α	NOUN
ejpam-5330	338	8	-	-	ADJ
ejpam-5330	338	9	open	open	ADJ
ejpam-5330	338	10	set	set	NOUN
ejpam-5330	338	11	.	.	PUNCT
ejpam-5330	339	1	then	then	ADV
ejpam-5330	339	2	,	,	PUNCT
ejpam-5330	339	3	φ−1	φ−1	PROPN
ejpam-5330	339	4	ψ	ψ	SYM
ejpam-5330	339	5	(	(	PUNCT
ejpam-5330	339	6	fa	fa	NOUN
ejpam-5330	339	7	)	)	PUNCT
ejpam-5330	339	8	is	be	AUX
ejpam-5330	339	9	r	r	NOUN
ejpam-5330	339	10	-	-	PUNCT
ejpam-5330	339	11	fuzzy	fuzzy	ADJ
ejpam-5330	339	12	soft	soft	ADJ
ejpam-5330	339	13	α	α	NOUN
ejpam-5330	339	14	-	-	PUNCT
ejpam-5330	339	15	closed	closed	ADJ
ejpam-5330	339	16	set	set	NOUN
ejpam-5330	339	17	.	.	PUNCT
ejpam-5330	340	1	(	(	PUNCT
ejpam-5330	340	2	3	3	X
ejpam-5330	340	3	)	)	PUNCT
ejpam-5330	340	4	⇒	⇒	NOUN
ejpam-5330	340	5	(	(	PUNCT
ejpam-5330	340	6	4	4	X
ejpam-5330	340	7	)	)	PUNCT
ejpam-5330	340	8	let	let	VERB
ejpam-5330	340	9	fa	fa	PART
ejpam-5330	340	10	be	be	AUX
ejpam-5330	340	11	an	an	DET
ejpam-5330	340	12	r	r	NOUN
ejpam-5330	340	13	-	-	PUNCT
ejpam-5330	340	14	fuzzy	fuzzy	ADJ
ejpam-5330	340	15	soft	soft	ADJ
ejpam-5330	340	16	β	β	NOUN
ejpam-5330	340	17	-	-	ADJ
ejpam-5330	340	18	open	open	ADJ
ejpam-5330	340	19	set	set	NOUN
ejpam-5330	340	20	.	.	PUNCT
ejpam-5330	341	1	since	since	SCONJ
ejpam-5330	341	2	cη(k	cη(k	PROPN
ejpam-5330	341	3	,	,	PUNCT
ejpam-5330	341	4	fa	fa	NOUN
ejpam-5330	341	5	,	,	PUNCT
ejpam-5330	341	6	r	r	NOUN
ejpam-5330	341	7	)	)	PUNCT
ejpam-5330	341	8	is	be	AUX
ejpam-5330	341	9	r	r	NOUN
ejpam-5330	341	10	-	-	PUNCT
ejpam-5330	341	11	fuzzy	fuzzy	ADJ
ejpam-5330	341	12	soft	soft	ADJ
ejpam-5330	341	13	regularly	regularly	ADV
ejpam-5330	341	14	closed	close	VERB
ejpam-5330	341	15	set	set	VERB
ejpam-5330	341	16	,	,	PUNCT
ejpam-5330	341	17	hence	hence	ADV
ejpam-5330	341	18	by	by	ADP
ejpam-5330	341	19	(	(	PUNCT
ejpam-5330	341	20	3	3	NUM
ejpam-5330	341	21	)	)	PUNCT
ejpam-5330	341	22	,	,	PUNCT
ejpam-5330	341	23	φ−1	φ−1	PROPN
ejpam-5330	341	24	ψ	ψ	X
ejpam-5330	341	25	(	(	PUNCT
ejpam-5330	341	26	cη(k	cη(k	PROPN
ejpam-5330	341	27	,	,	PUNCT
ejpam-5330	341	28	fa	fa	NOUN
ejpam-5330	341	29	,	,	PUNCT
ejpam-5330	341	30	r	r	NOUN
ejpam-5330	341	31	)	)	PUNCT
ejpam-5330	341	32	)	)	PUNCT
ejpam-5330	341	33	is	be	AUX
ejpam-5330	341	34	r	r	NOUN
ejpam-5330	341	35	-	-	PUNCT
ejpam-5330	341	36	fuzzy	fuzzy	ADJ
ejpam-5330	341	37	soft	soft	ADJ
ejpam-5330	341	38	α	α	NOUN
ejpam-5330	341	39	-	-	PUNCT
ejpam-5330	341	40	closed	closed	ADJ
ejpam-5330	341	41	set	set	NOUN
ejpam-5330	341	42	.	.	PUNCT
ejpam-5330	342	1	since	since	SCONJ
ejpam-5330	342	2	φ−1	φ−1	PROPN
ejpam-5330	342	3	ψ	ψ	X
ejpam-5330	342	4	(	(	PUNCT
ejpam-5330	342	5	fa	fa	INTJ
ejpam-5330	342	6	)	)	PUNCT
ejpam-5330	342	7	⊑	⊑	X
ejpam-5330	342	8	φ−1	φ−1	PROPN
ejpam-5330	342	9	ψ	ψ	X
ejpam-5330	342	10	(	(	PUNCT
ejpam-5330	342	11	cη(k	cη(k	PROPN
ejpam-5330	342	12	,	,	PUNCT
ejpam-5330	342	13	fa	fa	NOUN
ejpam-5330	342	14	,	,	PUNCT
ejpam-5330	342	15	r	r	NOUN
ejpam-5330	342	16	)	)	PUNCT
ejpam-5330	342	17	)	)	PUNCT
ejpam-5330	342	18	,	,	PUNCT
ejpam-5330	342	19	then	then	ADV
ejpam-5330	342	20	we	we	PRON
ejpam-5330	342	21	have	have	VERB
ejpam-5330	342	22	αcτ	αcτ	NOUN
ejpam-5330	342	23	(	(	PUNCT
ejpam-5330	342	24	n	n	X
ejpam-5330	342	25	,	,	PUNCT
ejpam-5330	342	26	φ	φ	PROPN
ejpam-5330	342	27	−1	−1	NOUN
ejpam-5330	342	28	ψ	ψ	X
ejpam-5330	342	29	(	(	PUNCT
ejpam-5330	342	30	fa	fa	NOUN
ejpam-5330	342	31	)	)	PUNCT
ejpam-5330	342	32	,	,	PUNCT
ejpam-5330	342	33	r	r	X
ejpam-5330	342	34	)	)	PUNCT
ejpam-5330	342	35	⊑	⊑	X
ejpam-5330	342	36	φ−1	φ−1	PROPN
ejpam-5330	342	37	ψ	ψ	X
ejpam-5330	342	38	(	(	PUNCT
ejpam-5330	342	39	cη(k	cη(k	PROPN
ejpam-5330	342	40	,	,	PUNCT
ejpam-5330	342	41	fa	fa	NOUN
ejpam-5330	342	42	,	,	PUNCT
ejpam-5330	342	43	r	r	NOUN
ejpam-5330	342	44	)	)	PUNCT
ejpam-5330	342	45	)	)	PUNCT
ejpam-5330	342	46	.	.	PUNCT
ejpam-5330	343	1	(	(	PUNCT
ejpam-5330	343	2	4	4	X
ejpam-5330	343	3	)	)	PUNCT
ejpam-5330	343	4	⇒	⇒	NOUN
ejpam-5330	343	5	(	(	PUNCT
ejpam-5330	343	6	5	5	X
ejpam-5330	343	7	)	)	PUNCT
ejpam-5330	343	8	this	this	PRON
ejpam-5330	343	9	is	be	AUX
ejpam-5330	343	10	obvious	obvious	ADJ
ejpam-5330	343	11	from	from	ADP
ejpam-5330	343	12	each	each	DET
ejpam-5330	343	13	r	r	NOUN
ejpam-5330	343	14	-	-	PUNCT
ejpam-5330	343	15	fuzzy	fuzzy	ADJ
ejpam-5330	343	16	soft	soft	ADJ
ejpam-5330	343	17	semi	semi	ADJ
ejpam-5330	343	18	-	-	ADJ
ejpam-5330	343	19	open	open	ADJ
ejpam-5330	343	20	set	set	NOUN
ejpam-5330	343	21	that	that	PRON
ejpam-5330	343	22	is	be	AUX
ejpam-5330	343	23	an	an	DET
ejpam-5330	343	24	r	r	NOUN
ejpam-5330	343	25	-	-	PUNCT
ejpam-5330	343	26	fuzzy	fuzzy	ADJ
ejpam-5330	343	27	soft	soft	ADJ
ejpam-5330	343	28	β	β	NOUN
ejpam-5330	343	29	-	-	ADJ
ejpam-5330	343	30	open	open	ADJ
ejpam-5330	343	31	.	.	PUNCT
ejpam-5330	344	1	(	(	PUNCT
ejpam-5330	344	2	5	5	X
ejpam-5330	344	3	)	)	PUNCT
ejpam-5330	344	4	⇒	⇒	NOUN
ejpam-5330	344	5	(	(	PUNCT
ejpam-5330	344	6	3	3	X
ejpam-5330	344	7	)	)	PUNCT
ejpam-5330	344	8	let	let	VERB
ejpam-5330	344	9	fa	fa	PART
ejpam-5330	344	10	be	be	AUX
ejpam-5330	344	11	an	an	DET
ejpam-5330	344	12	r	r	NOUN
ejpam-5330	344	13	-	-	PUNCT
ejpam-5330	344	14	fuzzy	fuzzy	ADJ
ejpam-5330	344	15	soft	soft	ADJ
ejpam-5330	344	16	regularly	regularly	ADV
ejpam-5330	344	17	closed	close	VERB
ejpam-5330	344	18	set	set	NOUN
ejpam-5330	344	19	,	,	PUNCT
ejpam-5330	344	20	hence	hence	ADV
ejpam-5330	344	21	fa	fa	PROPN
ejpam-5330	344	22	is	be	AUX
ejpam-5330	344	23	r	r	NOUN
ejpam-5330	344	24	-	-	PUNCT
ejpam-5330	344	25	fuzzy	fuzzy	ADJ
ejpam-5330	344	26	soft	soft	ADJ
ejpam-5330	344	27	semi	semi	ADJ
ejpam-5330	344	28	-	-	ADJ
ejpam-5330	344	29	open	open	ADJ
ejpam-5330	344	30	.	.	PUNCT
ejpam-5330	345	1	then	then	ADV
ejpam-5330	345	2	by	by	ADP
ejpam-5330	345	3	(	(	PUNCT
ejpam-5330	345	4	5	5	NUM
ejpam-5330	345	5	)	)	PUNCT
ejpam-5330	345	6	,	,	PUNCT
ejpam-5330	345	7	αcτ	αcτ	X
ejpam-5330	345	8	(	(	PUNCT
ejpam-5330	345	9	n	n	X
ejpam-5330	345	10	,	,	PUNCT
ejpam-5330	345	11	φ	φ	PROPN
ejpam-5330	345	12	−1	−1	NOUN
ejpam-5330	345	13	ψ	ψ	X
ejpam-5330	345	14	(	(	PUNCT
ejpam-5330	345	15	fa	fa	NOUN
ejpam-5330	345	16	)	)	PUNCT
ejpam-5330	345	17	,	,	PUNCT
ejpam-5330	345	18	r	r	X
ejpam-5330	345	19	)	)	PUNCT
ejpam-5330	345	20	⊑	⊑	X
ejpam-5330	345	21	φ−1	φ−1	PROPN
ejpam-5330	345	22	ψ	ψ	X
ejpam-5330	345	23	(	(	PUNCT
ejpam-5330	345	24	cη(k	cη(k	PROPN
ejpam-5330	345	25	,	,	PUNCT
ejpam-5330	345	26	fa	fa	NOUN
ejpam-5330	345	27	,	,	PUNCT
ejpam-5330	345	28	r	r	NOUN
ejpam-5330	345	29	)	)	PUNCT
ejpam-5330	345	30	)	)	PUNCT
ejpam-5330	346	1	=	=	PUNCT
ejpam-5330	346	2	φ−1	φ−1	PROPN
ejpam-5330	346	3	ψ	ψ	X
ejpam-5330	346	4	(	(	PUNCT
ejpam-5330	346	5	fa	fa	NOUN
ejpam-5330	346	6	)	)	PUNCT
ejpam-5330	346	7	.	.	PUNCT
ejpam-5330	347	1	therefore	therefore	ADV
ejpam-5330	347	2	,	,	PUNCT
ejpam-5330	347	3	φ−1	φ−1	PROPN
ejpam-5330	347	4	ψ	ψ	SYM
ejpam-5330	347	5	(	(	PUNCT
ejpam-5330	347	6	fa	fa	NOUN
ejpam-5330	347	7	)	)	PUNCT
ejpam-5330	347	8	is	be	AUX
ejpam-5330	347	9	r	r	NOUN
ejpam-5330	347	10	-	-	PUNCT
ejpam-5330	347	11	fuzzy	fuzzy	ADJ
ejpam-5330	347	12	soft	soft	ADJ
ejpam-5330	347	13	α	α	NOUN
ejpam-5330	347	14	-	-	PUNCT
ejpam-5330	347	15	closed	closed	ADJ
ejpam-5330	347	16	set	set	NOUN
ejpam-5330	347	17	.	.	PUNCT
ejpam-5330	348	1	(	(	PUNCT
ejpam-5330	348	2	3	3	X
ejpam-5330	348	3	)	)	PUNCT
ejpam-5330	348	4	⇒	⇒	NOUN
ejpam-5330	348	5	(	(	PUNCT
ejpam-5330	348	6	6	6	X
ejpam-5330	348	7	)	)	PUNCT
ejpam-5330	348	8	let	let	VERB
ejpam-5330	348	9	fa	fa	X
ejpam-5330	348	10	∈	∈	PROPN
ejpam-5330	348	11	(	(	PUNCT
ejpam-5330	348	12	̃v	̃v	NOUN
ejpam-5330	348	13	,	,	PUNCT
ejpam-5330	348	14	f	f	PROPN
ejpam-5330	348	15	)	)	PUNCT
ejpam-5330	348	16	with	with	ADP
ejpam-5330	348	17	ηk(fa	ηk(fa	PROPN
ejpam-5330	348	18	)	)	PUNCT
ejpam-5330	348	19	≥	≥	NOUN
ejpam-5330	348	20	r	r	NOUN
ejpam-5330	348	21	and	and	CCONJ
ejpam-5330	348	22	nws∈̃φ−1	nws∈̃φ−1	PROPN
ejpam-5330	348	23	ψ	ψ	X
ejpam-5330	348	24	(	(	PUNCT
ejpam-5330	348	25	fa	fa	NOUN
ejpam-5330	348	26	)	)	PUNCT
ejpam-5330	348	27	,	,	PUNCT
ejpam-5330	348	28	then	then	ADV
ejpam-5330	348	29	we	we	PRON
ejpam-5330	348	30	have	have	VERB
ejpam-5330	348	31	nws∈̃φ−1	nws∈̃φ−1	PROPN
ejpam-5330	348	32	ψ	ψ	X
ejpam-5330	348	33	(	(	PUNCT
ejpam-5330	348	34	iη(k	iη(k	NOUN
ejpam-5330	348	35	,	,	PUNCT
ejpam-5330	348	36	cη(k	cη(k	PROPN
ejpam-5330	348	37	,	,	PUNCT
ejpam-5330	348	38	fa	fa	NOUN
ejpam-5330	348	39	,	,	PUNCT
ejpam-5330	348	40	r	r	NOUN
ejpam-5330	348	41	)	)	PUNCT
ejpam-5330	348	42	,	,	PUNCT
ejpam-5330	348	43	r	r	NOUN
ejpam-5330	348	44	)	)	PUNCT
ejpam-5330	348	45	)	)	PUNCT
ejpam-5330	348	46	.	.	PUNCT
ejpam-5330	349	1	since	since	SCONJ
ejpam-5330	349	2	[	[	X
ejpam-5330	349	3	iη(k	iη(k	NOUN
ejpam-5330	349	4	,	,	PUNCT
ejpam-5330	349	5	cη(k	cη(k	PROPN
ejpam-5330	349	6	,	,	PUNCT
ejpam-5330	349	7	fa	fa	NOUN
ejpam-5330	349	8	,	,	PUNCT
ejpam-5330	349	9	r	r	NOUN
ejpam-5330	349	10	)	)	PUNCT
ejpam-5330	349	11	,	,	PUNCT
ejpam-5330	349	12	r	r	NOUN
ejpam-5330	349	13	)	)	PUNCT
ejpam-5330	349	14	]	]	PUNCT
ejpam-5330	349	15	c	c	NOUN
ejpam-5330	349	16	is	be	AUX
ejpam-5330	349	17	r	r	NOUN
ejpam-5330	349	18	-	-	PUNCT
ejpam-5330	349	19	fuzzy	fuzzy	ADJ
ejpam-5330	349	20	soft	soft	ADJ
ejpam-5330	349	21	regularly	regularly	ADV
ejpam-5330	349	22	closed	close	VERB
ejpam-5330	349	23	set	set	NOUN
ejpam-5330	349	24	,	,	PUNCT
ejpam-5330	349	25	φ−1	φ−1	PROPN
ejpam-5330	349	26	ψ	ψ	X
ejpam-5330	349	27	(	(	PUNCT
ejpam-5330	349	28	[	[	X
ejpam-5330	349	29	iη(k	iη(k	NOUN
ejpam-5330	349	30	,	,	PUNCT
ejpam-5330	349	31	cη(k	cη(k	PROPN
ejpam-5330	349	32	,	,	PUNCT
ejpam-5330	349	33	fa	fa	NOUN
ejpam-5330	349	34	,	,	PUNCT
ejpam-5330	349	35	r	r	NOUN
ejpam-5330	349	36	)	)	PUNCT
ejpam-5330	349	37	,	,	PUNCT
ejpam-5330	349	38	r	r	NOUN
ejpam-5330	349	39	)	)	PUNCT
ejpam-5330	349	40	]	]	PUNCT
ejpam-5330	350	1	c	c	X
ejpam-5330	350	2	)	)	PUNCT
ejpam-5330	350	3	is	be	AUX
ejpam-5330	350	4	r	r	NOUN
ejpam-5330	350	5	-	-	PUNCT
ejpam-5330	350	6	fuzzy	fuzzy	ADJ
ejpam-5330	350	7	soft	soft	ADJ
ejpam-5330	350	8	α	α	NOUN
ejpam-5330	350	9	-	-	PUNCT
ejpam-5330	350	10	closed	closed	ADJ
ejpam-5330	350	11	set	set	NOUN
ejpam-5330	350	12	(	(	PUNCT
ejpam-5330	350	13	from	from	ADP
ejpam-5330	350	14	(	(	PUNCT
ejpam-5330	350	15	3	3	NUM
ejpam-5330	350	16	)	)	PUNCT
ejpam-5330	350	17	)	)	PUNCT
ejpam-5330	350	18	.	.	PUNCT
ejpam-5330	351	1	thus	thus	ADV
ejpam-5330	351	2	,	,	PUNCT
ejpam-5330	351	3	φ−1	φ−1	PROPN
ejpam-5330	351	4	ψ	ψ	SYM
ejpam-5330	351	5	(	(	PUNCT
ejpam-5330	351	6	iη(k	iη(k	NOUN
ejpam-5330	351	7	,	,	PUNCT
ejpam-5330	351	8	cη(k	cη(k	PROPN
ejpam-5330	351	9	,	,	PUNCT
ejpam-5330	351	10	fa	fa	NOUN
ejpam-5330	351	11	,	,	PUNCT
ejpam-5330	351	12	r	r	NOUN
ejpam-5330	351	13	)	)	PUNCT
ejpam-5330	351	14	,	,	PUNCT
ejpam-5330	351	15	r	r	NOUN
ejpam-5330	351	16	)	)	PUNCT
ejpam-5330	351	17	)	)	PUNCT
ejpam-5330	351	18	is	be	AUX
ejpam-5330	351	19	r	r	NOUN
ejpam-5330	351	20	-	-	PUNCT
ejpam-5330	351	21	fuzzy	fuzzy	ADJ
ejpam-5330	351	22	soft	soft	ADJ
ejpam-5330	351	23	αopen	αopen	NOUN
ejpam-5330	351	24	set	set	NOUN
ejpam-5330	351	25	and	and	CCONJ
ejpam-5330	351	26	nws∈̃αiτ	nws∈̃αiτ	PROPN
ejpam-5330	351	27	(	(	PUNCT
ejpam-5330	351	28	n	n	CCONJ
ejpam-5330	351	29	,	,	PUNCT
ejpam-5330	351	30	φ−1	φ−1	PROPN
ejpam-5330	351	31	ψ	ψ	SYM
ejpam-5330	351	32	(	(	PUNCT
ejpam-5330	351	33	iη(k	iη(k	NOUN
ejpam-5330	351	34	,	,	PUNCT
ejpam-5330	351	35	cη(k	cη(k	PROPN
ejpam-5330	351	36	,	,	PUNCT
ejpam-5330	351	37	fa	fa	NOUN
ejpam-5330	351	38	,	,	PUNCT
ejpam-5330	351	39	r	r	NOUN
ejpam-5330	351	40	)	)	PUNCT
ejpam-5330	351	41	,	,	PUNCT
ejpam-5330	351	42	r	r	NOUN
ejpam-5330	351	43	)	)	PUNCT
ejpam-5330	351	44	)	)	PUNCT
ejpam-5330	351	45	,	,	PUNCT
ejpam-5330	351	46	r	r	NOUN
ejpam-5330	351	47	)	)	PUNCT
ejpam-5330	351	48	.	.	PUNCT
ejpam-5330	352	1	then	then	ADV
ejpam-5330	352	2	,	,	PUNCT
ejpam-5330	352	3	φ−1	φ−1	PROPN
ejpam-5330	352	4	ψ	ψ	SYM
ejpam-5330	352	5	(	(	PUNCT
ejpam-5330	352	6	fa	fa	X
ejpam-5330	352	7	)	)	PUNCT
ejpam-5330	352	8	⊑	⊑	PROPN
ejpam-5330	352	9	αiτ	αiτ	PROPN
ejpam-5330	352	10	(	(	PUNCT
ejpam-5330	352	11	n	n	CCONJ
ejpam-5330	352	12	,	,	PUNCT
ejpam-5330	352	13	φ	φ	PROPN
ejpam-5330	352	14	−1	−1	NOUN
ejpam-5330	352	15	ψ	ψ	X
ejpam-5330	352	16	(	(	PUNCT
ejpam-5330	352	17	iη(k	iη(k	NOUN
ejpam-5330	352	18	,	,	PUNCT
ejpam-5330	352	19	cη(k	cη(k	PROPN
ejpam-5330	352	20	,	,	PUNCT
ejpam-5330	352	21	fa	fa	NOUN
ejpam-5330	352	22	,	,	PUNCT
ejpam-5330	352	23	r	r	NOUN
ejpam-5330	352	24	)	)	PUNCT
ejpam-5330	352	25	,	,	PUNCT
ejpam-5330	352	26	r	r	NOUN
ejpam-5330	352	27	)	)	PUNCT
ejpam-5330	352	28	)	)	PUNCT
ejpam-5330	352	29	,	,	PUNCT
ejpam-5330	352	30	r	r	NOUN
ejpam-5330	352	31	)	)	PUNCT
ejpam-5330	352	32	.	.	PUNCT
ejpam-5330	353	1	(	(	PUNCT
ejpam-5330	353	2	6	6	X
ejpam-5330	353	3	)	)	PUNCT
ejpam-5330	353	4	⇒	⇒	NOUN
ejpam-5330	353	5	(	(	PUNCT
ejpam-5330	353	6	1	1	X
ejpam-5330	353	7	)	)	PUNCT
ejpam-5330	353	8	let	let	VERB
ejpam-5330	353	9	nws	nws	PROPN
ejpam-5330	353	10	∈	∈	PROPN
ejpam-5330	353	11	p̃s(w	p̃s(w	NOUN
ejpam-5330	353	12	)	)	PUNCT
ejpam-5330	353	13	and	and	CCONJ
ejpam-5330	353	14	fa	fa	NUM
ejpam-5330	353	15	∈	∈	PROPN
ejpam-5330	353	16	(	(	PUNCT
ejpam-5330	353	17	̃v	̃v	NOUN
ejpam-5330	353	18	,	,	PUNCT
ejpam-5330	353	19	f	f	PROPN
ejpam-5330	353	20	)	)	PUNCT
ejpam-5330	353	21	with	with	ADP
ejpam-5330	353	22	ηk(fa	ηk(fa	PROPN
ejpam-5330	353	23	)	)	PUNCT
ejpam-5330	353	24	≥	≥	NOUN
ejpam-5330	354	1	r	r	NOUN
ejpam-5330	354	2	containing	contain	VERB
ejpam-5330	354	3	φψ(nws	φψ(nws	NOUN
ejpam-5330	354	4	)	)	PUNCT
ejpam-5330	354	5	,	,	PUNCT
ejpam-5330	354	6	hence	hence	ADV
ejpam-5330	354	7	by	by	ADP
ejpam-5330	354	8	(	(	PUNCT
ejpam-5330	354	9	6	6	NUM
ejpam-5330	354	10	)	)	PUNCT
ejpam-5330	354	11	,	,	PUNCT
ejpam-5330	354	12	φ−1	φ−1	PROPN
ejpam-5330	354	13	ψ	ψ	SYM
ejpam-5330	354	14	(	(	PUNCT
ejpam-5330	354	15	fa	fa	X
ejpam-5330	354	16	)	)	PUNCT
ejpam-5330	354	17	⊑	⊑	PROPN
ejpam-5330	354	18	αiτ	αiτ	PROPN
ejpam-5330	354	19	(	(	PUNCT
ejpam-5330	354	20	n	n	CCONJ
ejpam-5330	354	21	,	,	PUNCT
ejpam-5330	354	22	φ	φ	PROPN
ejpam-5330	354	23	−1	−1	NOUN
ejpam-5330	354	24	ψ	ψ	X
ejpam-5330	354	25	(	(	PUNCT
ejpam-5330	354	26	iη(k	iη(k	NOUN
ejpam-5330	354	27	,	,	PUNCT
ejpam-5330	354	28	cη(k	cη(k	PROPN
ejpam-5330	354	29	,	,	PUNCT
ejpam-5330	354	30	fa	fa	NOUN
ejpam-5330	354	31	,	,	PUNCT
ejpam-5330	354	32	r	r	NOUN
ejpam-5330	354	33	)	)	PUNCT
ejpam-5330	354	34	,	,	PUNCT
ejpam-5330	354	35	r	r	NOUN
ejpam-5330	354	36	)	)	PUNCT
ejpam-5330	354	37	)	)	PUNCT
ejpam-5330	354	38	,	,	PUNCT
ejpam-5330	354	39	r	r	NOUN
ejpam-5330	354	40	)	)	PUNCT
ejpam-5330	354	41	.	.	PUNCT
ejpam-5330	355	1	since	since	SCONJ
ejpam-5330	355	2	nws∈̃φ−1	nws∈̃φ−1	PROPN
ejpam-5330	355	3	ψ	ψ	X
ejpam-5330	355	4	(	(	PUNCT
ejpam-5330	355	5	fa	fa	NOUN
ejpam-5330	355	6	)	)	PUNCT
ejpam-5330	355	7	,	,	PUNCT
ejpam-5330	355	8	then	then	ADV
ejpam-5330	355	9	we	we	PRON
ejpam-5330	355	10	obtain	obtain	VERB
ejpam-5330	355	11	nws∈̃αiτ	nws∈̃αiτ	NOUN
ejpam-5330	355	12	(	(	PUNCT
ejpam-5330	355	13	n	n	CCONJ
ejpam-5330	355	14	,	,	PUNCT
ejpam-5330	355	15	φ−1	φ−1	PROPN
ejpam-5330	355	16	ψ	ψ	SYM
ejpam-5330	355	17	(	(	PUNCT
ejpam-5330	355	18	iη(k	iη(k	NOUN
ejpam-5330	355	19	,	,	PUNCT
ejpam-5330	355	20	cη(k	cη(k	PROPN
ejpam-5330	355	21	,	,	PUNCT
ejpam-5330	355	22	fa	fa	NOUN
ejpam-5330	355	23	,	,	PUNCT
ejpam-5330	355	24	r	r	NOUN
ejpam-5330	355	25	)	)	PUNCT
ejpam-5330	355	26	,	,	PUNCT
ejpam-5330	355	27	r	r	NOUN
ejpam-5330	355	28	)	)	PUNCT
ejpam-5330	355	29	)	)	PUNCT
ejpam-5330	355	30	,	,	PUNCT
ejpam-5330	355	31	r	r	X
ejpam-5330	355	32	)	)	PUNCT
ejpam-5330	355	33	=	=	SYM
ejpam-5330	355	34	hc	hc	PROPN
ejpam-5330	355	35	(	(	PUNCT
ejpam-5330	355	36	say	say	INTJ
ejpam-5330	355	37	)	)	PUNCT
ejpam-5330	355	38	.	.	PUNCT
ejpam-5330	356	1	hence	hence	ADV
ejpam-5330	356	2	,	,	PUNCT
ejpam-5330	356	3	there	there	PRON
ejpam-5330	356	4	is	be	VERB
ejpam-5330	356	5	hc	hc	PROPN
ejpam-5330	356	6	∈	∈	PROPN
ejpam-5330	356	7	˜(w	˜(w	PROPN
ejpam-5330	356	8	,	,	PUNCT
ejpam-5330	356	9	n	n	CCONJ
ejpam-5330	356	10	)	)	PUNCT
ejpam-5330	356	11	is	be	AUX
ejpam-5330	356	12	r	r	NOUN
ejpam-5330	356	13	-	-	PUNCT
ejpam-5330	356	14	fuzzy	fuzzy	ADJ
ejpam-5330	356	15	soft	soft	ADJ
ejpam-5330	356	16	α	α	NOUN
ejpam-5330	356	17	-	-	ADJ
ejpam-5330	356	18	open	open	ADJ
ejpam-5330	356	19	set	set	NOUN
ejpam-5330	356	20	containing	contain	VERB
ejpam-5330	356	21	nws	nws	PROPN
ejpam-5330	356	22	such	such	ADJ
ejpam-5330	356	23	that	that	DET
ejpam-5330	356	24	φψ(hc	φψ(hc	NOUN
ejpam-5330	356	25	)	)	PUNCT
ejpam-5330	356	26	⊑	⊑	PRON
ejpam-5330	356	27	iη(k	iη(k	PROPN
ejpam-5330	356	28	,	,	PUNCT
ejpam-5330	356	29	cη(k	cη(k	PROPN
ejpam-5330	356	30	,	,	PUNCT
ejpam-5330	356	31	fa	fa	NOUN
ejpam-5330	356	32	,	,	PUNCT
ejpam-5330	356	33	r	r	NOUN
ejpam-5330	356	34	)	)	PUNCT
ejpam-5330	356	35	,	,	PUNCT
ejpam-5330	356	36	r	r	NOUN
ejpam-5330	356	37	)	)	PUNCT
ejpam-5330	356	38	.	.	PUNCT
ejpam-5330	357	1	therefore	therefore	ADV
ejpam-5330	357	2	,	,	PUNCT
ejpam-5330	357	3	φψ	φψ	X
ejpam-5330	357	4	is	be	AUX
ejpam-5330	357	5	fuzzy	fuzzy	ADJ
ejpam-5330	357	6	soft	soft	ADJ
ejpam-5330	357	7	almost	almost	ADV
ejpam-5330	357	8	α	α	NOUN
ejpam-5330	357	9	-	-	ADJ
ejpam-5330	357	10	continuous	continuous	ADJ
ejpam-5330	357	11	.	.	PUNCT
ejpam-5330	358	1	in	in	ADP
ejpam-5330	358	2	a	a	DET
ejpam-5330	358	3	similar	similar	ADJ
ejpam-5330	358	4	way	way	NOUN
ejpam-5330	358	5	,	,	PUNCT
ejpam-5330	358	6	we	we	PRON
ejpam-5330	358	7	can	can	AUX
ejpam-5330	358	8	prove	prove	VERB
ejpam-5330	358	9	the	the	DET
ejpam-5330	358	10	following	follow	VERB
ejpam-5330	358	11	theorem	theorem	PROPN
ejpam-5330	358	12	.	.	PUNCT
ejpam-5330	359	1	w.	w.	PROPN
ejpam-5330	359	2	alqurashi	alqurashi	PROPN
ejpam-5330	359	3	,	,	PUNCT
ejpam-5330	359	4	i.	i.	PROPN
ejpam-5330	359	5	m.	m.	PROPN
ejpam-5330	359	6	taha	taha	PROPN
ejpam-5330	359	7	/	/	PUNCT
ejpam-5330	359	8	eur	eur	PROPN
ejpam-5330	359	9	.	.	PUNCT
ejpam-5330	360	1	j.	j.	PROPN
ejpam-5330	360	2	pure	pure	PROPN
ejpam-5330	360	3	appl	appl	PROPN
ejpam-5330	360	4	.	.	PROPN
ejpam-5330	360	5	math	math	PROPN
ejpam-5330	360	6	,	,	PUNCT
ejpam-5330	360	7	17	17	NUM
ejpam-5330	360	8	(	(	PUNCT
ejpam-5330	360	9	4	4	NUM
ejpam-5330	360	10	)	)	PUNCT
ejpam-5330	360	11	(	(	PUNCT
ejpam-5330	360	12	2024	2024	NUM
ejpam-5330	360	13	)	)	PUNCT
ejpam-5330	360	14	,	,	PUNCT
ejpam-5330	360	15	4112	4112	NUM
ejpam-5330	360	16	-	-	SYM
ejpam-5330	360	17	4134	4134	NUM
ejpam-5330	360	18	4125	4125	NUM
ejpam-5330	360	19	theorem	theorem	VERB
ejpam-5330	360	20	8	8	NUM
ejpam-5330	360	21	.	.	PUNCT
ejpam-5330	361	1	let	let	VERB
ejpam-5330	361	2	(	(	PUNCT
ejpam-5330	361	3	w	w	NOUN
ejpam-5330	361	4	,	,	PUNCT
ejpam-5330	361	5	τn	τn	PROPN
ejpam-5330	361	6	)	)	PUNCT
ejpam-5330	361	7	and	and	CCONJ
ejpam-5330	361	8	(	(	PUNCT
ejpam-5330	361	9	v	v	NOUN
ejpam-5330	361	10	,	,	PUNCT
ejpam-5330	361	11	ηf	ηf	PROPN
ejpam-5330	361	12	)	)	PUNCT
ejpam-5330	361	13	be	be	AUX
ejpam-5330	361	14	an	an	DET
ejpam-5330	361	15	fstss	fstss	NOUN
ejpam-5330	361	16	,	,	PUNCT
ejpam-5330	361	17	and	and	CCONJ
ejpam-5330	361	18	φψ	φψ	PROPN
ejpam-5330	361	19	:	:	PUNCT
ejpam-5330	361	20	˜(w	˜(w	PROPN
ejpam-5330	361	21	,	,	PUNCT
ejpam-5330	361	22	n	n	CCONJ
ejpam-5330	361	23	)	)	PUNCT
ejpam-5330	361	24	−→	−→	NOUN
ejpam-5330	361	25	(	(	PUNCT
ejpam-5330	361	26	̃v	̃v	NOUN
ejpam-5330	361	27	,	,	PUNCT
ejpam-5330	361	28	f	f	PROPN
ejpam-5330	361	29	)	)	PUNCT
ejpam-5330	361	30	be	be	AUX
ejpam-5330	361	31	a	a	DET
ejpam-5330	361	32	fuzzy	fuzzy	ADJ
ejpam-5330	361	33	soft	soft	ADJ
ejpam-5330	361	34	mapping	mapping	NOUN
ejpam-5330	361	35	.	.	PUNCT
ejpam-5330	362	1	the	the	DET
ejpam-5330	362	2	following	follow	VERB
ejpam-5330	362	3	statements	statement	NOUN
ejpam-5330	362	4	are	be	AUX
ejpam-5330	362	5	equivalent	equivalent	ADJ
ejpam-5330	362	6	for	for	ADP
ejpam-5330	362	7	each	each	DET
ejpam-5330	362	8	fa	fa	X
ejpam-5330	362	9	∈	∈	PROPN
ejpam-5330	362	10	(	(	PUNCT
ejpam-5330	362	11	̃v	̃v	NOUN
ejpam-5330	362	12	,	,	PUNCT
ejpam-5330	362	13	f	f	PROPN
ejpam-5330	362	14	)	)	PUNCT
ejpam-5330	362	15	,	,	PUNCT
ejpam-5330	362	16	n	n	PROPN
ejpam-5330	362	17	∈	∈	PROPN
ejpam-5330	362	18	n	n	NOUN
ejpam-5330	362	19	,	,	PUNCT
ejpam-5330	362	20	(	(	PUNCT
ejpam-5330	362	21	k	k	NOUN
ejpam-5330	362	22	=	=	SYM
ejpam-5330	362	23	ψ(n	ψ(n	PROPN
ejpam-5330	362	24	)	)	PUNCT
ejpam-5330	362	25	)	)	PUNCT
ejpam-5330	363	1	∈	∈	PROPN
ejpam-5330	363	2	f	f	X
ejpam-5330	363	3	,	,	PUNCT
ejpam-5330	363	4	and	and	CCONJ
ejpam-5330	363	5	r	r	NOUN
ejpam-5330	363	6	∈	∈	PROPN
ejpam-5330	363	7	i	i	PRON
ejpam-5330	363	8	◦	◦	NOUN
ejpam-5330	363	9	:	:	PUNCT
ejpam-5330	363	10	(	(	PUNCT
ejpam-5330	363	11	1	1	X
ejpam-5330	363	12	)	)	PUNCT
ejpam-5330	363	13	φψ	φψ	NOUN
ejpam-5330	363	14	is	be	AUX
ejpam-5330	363	15	fuzzy	fuzzy	ADJ
ejpam-5330	363	16	soft	soft	ADJ
ejpam-5330	363	17	weakly	weakly	ADJ
ejpam-5330	364	1	α	α	NOUN
ejpam-5330	364	2	-	-	ADJ
ejpam-5330	364	3	continuous	continuous	ADJ
ejpam-5330	364	4	.	.	PUNCT
ejpam-5330	365	1	(	(	PUNCT
ejpam-5330	365	2	2	2	X
ejpam-5330	365	3	)	)	PUNCT
ejpam-5330	365	4	iτ	iτ	NOUN
ejpam-5330	365	5	(	(	PUNCT
ejpam-5330	365	6	n	n	CCONJ
ejpam-5330	365	7	,	,	PUNCT
ejpam-5330	365	8	cτ	cτ	INTJ
ejpam-5330	365	9	(	(	PUNCT
ejpam-5330	365	10	n	n	CCONJ
ejpam-5330	365	11	,	,	PUNCT
ejpam-5330	365	12	iτ	iτ	X
ejpam-5330	365	13	(	(	PUNCT
ejpam-5330	365	14	n	n	CCONJ
ejpam-5330	365	15	,	,	PUNCT
ejpam-5330	365	16	φ	φ	PROPN
ejpam-5330	365	17	−1	−1	NOUN
ejpam-5330	365	18	ψ	ψ	X
ejpam-5330	365	19	(	(	PUNCT
ejpam-5330	365	20	cη(k	cη(k	PROPN
ejpam-5330	365	21	,	,	PUNCT
ejpam-5330	365	22	fa	fa	NOUN
ejpam-5330	365	23	,	,	PUNCT
ejpam-5330	365	24	r	r	NOUN
ejpam-5330	365	25	)	)	PUNCT
ejpam-5330	365	26	)	)	PUNCT
ejpam-5330	365	27	,	,	PUNCT
ejpam-5330	365	28	r	r	NOUN
ejpam-5330	365	29	)	)	PUNCT
ejpam-5330	365	30	,	,	PUNCT
ejpam-5330	365	31	r	r	NOUN
ejpam-5330	365	32	)	)	PUNCT
ejpam-5330	365	33	,	,	PUNCT
ejpam-5330	365	34	r	r	NOUN
ejpam-5330	365	35	)	)	PUNCT
ejpam-5330	365	36	⊒	⊒	PUNCT
ejpam-5330	365	37	φ−1	φ−1	PROPN
ejpam-5330	365	38	ψ	ψ	PROPN
ejpam-5330	365	39	(	(	PUNCT
ejpam-5330	365	40	fa	fa	NOUN
ejpam-5330	365	41	)	)	PUNCT
ejpam-5330	365	42	,	,	PUNCT
ejpam-5330	365	43	if	if	SCONJ
ejpam-5330	365	44	ηk(fa	ηk(fa	PROPN
ejpam-5330	365	45	)	)	PUNCT
ejpam-5330	365	46	≥	≥	PROPN
ejpam-5330	365	47	r.	r.	PROPN
ejpam-5330	365	48	(	(	PUNCT
ejpam-5330	365	49	3	3	X
ejpam-5330	365	50	)	)	PUNCT
ejpam-5330	365	51	cτ	cτ	NOUN
ejpam-5330	365	52	(	(	PUNCT
ejpam-5330	365	53	n	n	CCONJ
ejpam-5330	365	54	,	,	PUNCT
ejpam-5330	365	55	iτ	iτ	X
ejpam-5330	365	56	(	(	PUNCT
ejpam-5330	365	57	n	n	CCONJ
ejpam-5330	365	58	,	,	PUNCT
ejpam-5330	365	59	cτ	cτ	INTJ
ejpam-5330	365	60	(	(	PUNCT
ejpam-5330	365	61	n	n	CCONJ
ejpam-5330	365	62	,	,	PUNCT
ejpam-5330	365	63	φ	φ	PROPN
ejpam-5330	365	64	−1	−1	NOUN
ejpam-5330	365	65	ψ	ψ	X
ejpam-5330	365	66	(	(	PUNCT
ejpam-5330	365	67	iη(k	iη(k	PROPN
ejpam-5330	365	68	,	,	PUNCT
ejpam-5330	365	69	fa	fa	NOUN
ejpam-5330	365	70	,	,	PUNCT
ejpam-5330	365	71	r	r	NOUN
ejpam-5330	365	72	)	)	PUNCT
ejpam-5330	365	73	)	)	PUNCT
ejpam-5330	365	74	,	,	PUNCT
ejpam-5330	365	75	r	r	NOUN
ejpam-5330	365	76	)	)	PUNCT
ejpam-5330	365	77	,	,	PUNCT
ejpam-5330	365	78	r	r	NOUN
ejpam-5330	365	79	)	)	PUNCT
ejpam-5330	365	80	,	,	PUNCT
ejpam-5330	365	81	r	r	X
ejpam-5330	365	82	)	)	PUNCT
ejpam-5330	365	83	⊑	⊑	X
ejpam-5330	365	84	φ−1	φ−1	PROPN
ejpam-5330	365	85	ψ	ψ	X
ejpam-5330	365	86	(	(	PUNCT
ejpam-5330	365	87	fa	fa	NOUN
ejpam-5330	365	88	)	)	PUNCT
ejpam-5330	365	89	,	,	PUNCT
ejpam-5330	365	90	if	if	SCONJ
ejpam-5330	365	91	ηk(f	ηk(f	VERB
ejpam-5330	365	92	c	c	PROPN
ejpam-5330	365	93	a	a	PRON
ejpam-5330	365	94	)	)	PUNCT
ejpam-5330	365	95	≥	≥	PROPN
ejpam-5330	365	96	r.	r.	PROPN
ejpam-5330	365	97	(	(	PUNCT
ejpam-5330	365	98	4	4	NUM
ejpam-5330	365	99	)	)	PUNCT
ejpam-5330	365	100	αcτ	αcτ	NOUN
ejpam-5330	365	101	(	(	PUNCT
ejpam-5330	365	102	n	n	X
ejpam-5330	365	103	,	,	PUNCT
ejpam-5330	365	104	φ	φ	PROPN
ejpam-5330	365	105	−1	−1	NOUN
ejpam-5330	365	106	ψ	ψ	X
ejpam-5330	365	107	(	(	PUNCT
ejpam-5330	365	108	iη(k	iη(k	PROPN
ejpam-5330	365	109	,	,	PUNCT
ejpam-5330	365	110	fa	fa	NOUN
ejpam-5330	365	111	,	,	PUNCT
ejpam-5330	365	112	r	r	NOUN
ejpam-5330	365	113	)	)	PUNCT
ejpam-5330	365	114	)	)	PUNCT
ejpam-5330	365	115	,	,	PUNCT
ejpam-5330	366	1	r	r	X
ejpam-5330	366	2	)	)	PUNCT
ejpam-5330	366	3	⊑	⊑	X
ejpam-5330	366	4	φ−1	φ−1	PROPN
ejpam-5330	366	5	ψ	ψ	X
ejpam-5330	366	6	(	(	PUNCT
ejpam-5330	366	7	fa	fa	NOUN
ejpam-5330	366	8	)	)	PUNCT
ejpam-5330	366	9	,	,	PUNCT
ejpam-5330	366	10	if	if	SCONJ
ejpam-5330	366	11	ηk(f	ηk(f	VERB
ejpam-5330	366	12	c	c	PROPN
ejpam-5330	366	13	a	a	PRON
ejpam-5330	366	14	)	)	PUNCT
ejpam-5330	366	15	≥	≥	PROPN
ejpam-5330	366	16	r.	r.	PROPN
ejpam-5330	366	17	(	(	PUNCT
ejpam-5330	366	18	5	5	NUM
ejpam-5330	366	19	)	)	PUNCT
ejpam-5330	366	20	αcτ	αcτ	NOUN
ejpam-5330	366	21	(	(	PUNCT
ejpam-5330	366	22	n	n	X
ejpam-5330	366	23	,	,	PUNCT
ejpam-5330	366	24	φ	φ	PROPN
ejpam-5330	366	25	−1	−1	NOUN
ejpam-5330	366	26	ψ	ψ	X
ejpam-5330	366	27	(	(	PUNCT
ejpam-5330	366	28	iη(k	iη(k	NOUN
ejpam-5330	366	29	,	,	PUNCT
ejpam-5330	366	30	cη(k	cη(k	PROPN
ejpam-5330	366	31	,	,	PUNCT
ejpam-5330	366	32	fa	fa	NOUN
ejpam-5330	366	33	,	,	PUNCT
ejpam-5330	366	34	r	r	NOUN
ejpam-5330	366	35	)	)	PUNCT
ejpam-5330	366	36	,	,	PUNCT
ejpam-5330	366	37	r	r	NOUN
ejpam-5330	366	38	)	)	PUNCT
ejpam-5330	366	39	)	)	PUNCT
ejpam-5330	366	40	,	,	PUNCT
ejpam-5330	366	41	r	r	X
ejpam-5330	366	42	)	)	PUNCT
ejpam-5330	366	43	⊑	⊑	X
ejpam-5330	366	44	φ−1	φ−1	PROPN
ejpam-5330	366	45	ψ	ψ	X
ejpam-5330	366	46	(	(	PUNCT
ejpam-5330	366	47	cη(k	cη(k	PROPN
ejpam-5330	366	48	,	,	PUNCT
ejpam-5330	366	49	fa	fa	NOUN
ejpam-5330	366	50	,	,	PUNCT
ejpam-5330	366	51	r	r	NOUN
ejpam-5330	366	52	)	)	PUNCT
ejpam-5330	366	53	)	)	PUNCT
ejpam-5330	366	54	.	.	PUNCT
ejpam-5330	367	1	(	(	PUNCT
ejpam-5330	367	2	6	6	X
ejpam-5330	367	3	)	)	PUNCT
ejpam-5330	367	4	αiτ	αiτ	NOUN
ejpam-5330	367	5	(	(	PUNCT
ejpam-5330	367	6	n	n	CCONJ
ejpam-5330	367	7	,	,	PUNCT
ejpam-5330	367	8	φ	φ	PROPN
ejpam-5330	367	9	−1	−1	NOUN
ejpam-5330	367	10	ψ	ψ	X
ejpam-5330	367	11	(	(	PUNCT
ejpam-5330	367	12	cη(k	cη(k	PROPN
ejpam-5330	367	13	,	,	PUNCT
ejpam-5330	367	14	iη(k	iη(k	NOUN
ejpam-5330	367	15	,	,	PUNCT
ejpam-5330	367	16	fa	fa	NOUN
ejpam-5330	367	17	,	,	PUNCT
ejpam-5330	367	18	r	r	NOUN
ejpam-5330	367	19	)	)	PUNCT
ejpam-5330	367	20	,	,	PUNCT
ejpam-5330	367	21	r	r	NOUN
ejpam-5330	367	22	)	)	PUNCT
ejpam-5330	367	23	)	)	PUNCT
ejpam-5330	367	24	,	,	PUNCT
ejpam-5330	367	25	r	r	NOUN
ejpam-5330	367	26	)	)	PUNCT
ejpam-5330	367	27	⊒	⊒	PUNCT
ejpam-5330	367	28	φ−1	φ−1	PROPN
ejpam-5330	367	29	ψ	ψ	PROPN
ejpam-5330	367	30	(	(	PUNCT
ejpam-5330	367	31	iη(k	iη(k	PROPN
ejpam-5330	367	32	,	,	PUNCT
ejpam-5330	367	33	fa	fa	NOUN
ejpam-5330	367	34	,	,	PUNCT
ejpam-5330	367	35	r	r	NOUN
ejpam-5330	367	36	)	)	PUNCT
ejpam-5330	367	37	)	)	PUNCT
ejpam-5330	367	38	.	.	PUNCT
ejpam-5330	368	1	(	(	PUNCT
ejpam-5330	368	2	7	7	X
ejpam-5330	368	3	)	)	PUNCT
ejpam-5330	368	4	φ−1	φ−1	PROPN
ejpam-5330	368	5	ψ	ψ	SYM
ejpam-5330	368	6	(	(	PUNCT
ejpam-5330	368	7	fa	fa	INTJ
ejpam-5330	368	8	)	)	PUNCT
ejpam-5330	368	9	⊑	⊑	PROPN
ejpam-5330	368	10	αiτ	αiτ	PROPN
ejpam-5330	368	11	(	(	PUNCT
ejpam-5330	368	12	n	n	CCONJ
ejpam-5330	368	13	,	,	PUNCT
ejpam-5330	368	14	φ	φ	PROPN
ejpam-5330	368	15	−1	−1	NOUN
ejpam-5330	368	16	ψ	ψ	X
ejpam-5330	368	17	(	(	PUNCT
ejpam-5330	368	18	cη(k	cη(k	PROPN
ejpam-5330	368	19	,	,	PUNCT
ejpam-5330	368	20	fa	fa	NOUN
ejpam-5330	368	21	,	,	PUNCT
ejpam-5330	368	22	r	r	NOUN
ejpam-5330	368	23	)	)	PUNCT
ejpam-5330	368	24	)	)	PUNCT
ejpam-5330	368	25	,	,	PUNCT
ejpam-5330	368	26	r	r	NOUN
ejpam-5330	368	27	)	)	PUNCT
ejpam-5330	368	28	,	,	PUNCT
ejpam-5330	368	29	if	if	SCONJ
ejpam-5330	368	30	ηk(fa	ηk(fa	PROPN
ejpam-5330	368	31	)	)	PUNCT
ejpam-5330	368	32	≥	≥	PROPN
ejpam-5330	368	33	r.	r.	PROPN
ejpam-5330	368	34	remark	remark	PROPN
ejpam-5330	368	35	7	7	NUM
ejpam-5330	368	36	.	.	PUNCT
ejpam-5330	368	37	from	from	ADP
ejpam-5330	368	38	the	the	DET
ejpam-5330	368	39	previous	previous	ADJ
ejpam-5330	368	40	definitions	definition	NOUN
ejpam-5330	368	41	and	and	CCONJ
ejpam-5330	368	42	results	result	NOUN
ejpam-5330	368	43	,	,	PUNCT
ejpam-5330	368	44	we	we	PRON
ejpam-5330	368	45	can	can	AUX
ejpam-5330	368	46	summarize	summarize	VERB
ejpam-5330	368	47	the	the	DET
ejpam-5330	368	48	relationships	relationship	NOUN
ejpam-5330	368	49	among	among	ADP
ejpam-5330	368	50	different	different	ADJ
ejpam-5330	368	51	types	type	NOUN
ejpam-5330	368	52	of	of	ADP
ejpam-5330	368	53	fuzzy	fuzzy	ADJ
ejpam-5330	368	54	soft	soft	ADJ
ejpam-5330	368	55	continuity	continuity	NOUN
ejpam-5330	368	56	as	as	ADP
ejpam-5330	368	57	in	in	ADP
ejpam-5330	368	58	the	the	DET
ejpam-5330	368	59	next	next	ADJ
ejpam-5330	368	60	diagram	diagram	NOUN
ejpam-5330	368	61	.	.	PUNCT
ejpam-5330	369	1	fuzzy	fuzzy	ADJ
ejpam-5330	369	2	soft	soft	ADJ
ejpam-5330	369	3	continuity	continuity	NOUN
ejpam-5330	369	4	⇒	⇒	NOUN
ejpam-5330	369	5	fuzzy	fuzzy	ADJ
ejpam-5330	369	6	soft	soft	ADJ
ejpam-5330	369	7	α	α	NOUN
ejpam-5330	369	8	-	-	PUNCT
ejpam-5330	369	9	continuity	continuity	NOUN
ejpam-5330	369	10	⇓	⇓	PROPN
ejpam-5330	369	11	⇓	⇓	PROPN
ejpam-5330	369	12	fuzzy	fuzzy	ADJ
ejpam-5330	369	13	soft	soft	ADJ
ejpam-5330	369	14	almost	almost	ADV
ejpam-5330	369	15	continuity	continuity	NOUN
ejpam-5330	369	16	⇒	⇒	NOUN
ejpam-5330	369	17	fuzzy	fuzzy	ADJ
ejpam-5330	369	18	soft	soft	ADJ
ejpam-5330	369	19	almost	almost	ADV
ejpam-5330	369	20	α	α	NOUN
ejpam-5330	369	21	-	-	PUNCT
ejpam-5330	369	22	continuity	continuity	NOUN
ejpam-5330	369	23	⇓	⇓	PROPN
ejpam-5330	369	24	⇓	⇓	PROPN
ejpam-5330	369	25	fuzzy	fuzzy	ADJ
ejpam-5330	369	26	soft	soft	ADJ
ejpam-5330	369	27	weakly	weakly	ADJ
ejpam-5330	369	28	continuity	continuity	NOUN
ejpam-5330	369	29	⇒	⇒	NOUN
ejpam-5330	369	30	fuzzy	fuzzy	ADJ
ejpam-5330	369	31	soft	soft	ADJ
ejpam-5330	369	32	weakly	weakly	ADJ
ejpam-5330	369	33	α	α	NOUN
ejpam-5330	369	34	-	-	PUNCT
ejpam-5330	369	35	continuity	continuity	NOUN
ejpam-5330	369	36	proposition	proposition	NOUN
ejpam-5330	369	37	3	3	X
ejpam-5330	369	38	.	.	PUNCT
ejpam-5330	370	1	let	let	VERB
ejpam-5330	370	2	(	(	PUNCT
ejpam-5330	370	3	w	w	NOUN
ejpam-5330	370	4	,	,	PUNCT
ejpam-5330	370	5	τn	τn	NOUN
ejpam-5330	370	6	)	)	PUNCT
ejpam-5330	370	7	,	,	PUNCT
ejpam-5330	370	8	(	(	PUNCT
ejpam-5330	370	9	v	v	NOUN
ejpam-5330	370	10	,	,	PUNCT
ejpam-5330	370	11	ηf	ηf	PROPN
ejpam-5330	370	12	)	)	PUNCT
ejpam-5330	370	13	and	and	CCONJ
ejpam-5330	370	14	(	(	PUNCT
ejpam-5330	370	15	u	u	NOUN
ejpam-5330	370	16	,	,	PUNCT
ejpam-5330	370	17	γe	γe	PRON
ejpam-5330	370	18	)	)	PUNCT
ejpam-5330	370	19	be	be	VERB
ejpam-5330	370	20	an	an	DET
ejpam-5330	370	21	fstss	fstss	NOUN
ejpam-5330	370	22	,	,	PUNCT
ejpam-5330	370	23	and	and	CCONJ
ejpam-5330	370	24	φψ	φψ	PROPN
ejpam-5330	370	25	:	:	PUNCT
ejpam-5330	370	26	˜(w	˜(w	PROPN
ejpam-5330	370	27	,	,	PUNCT
ejpam-5330	370	28	n	n	CCONJ
ejpam-5330	370	29	)	)	PUNCT
ejpam-5330	370	30	−→	−→	NOUN
ejpam-5330	370	31	(	(	PUNCT
ejpam-5330	370	32	̃v	̃v	NOUN
ejpam-5330	370	33	,	,	PUNCT
ejpam-5330	370	34	f	f	PROPN
ejpam-5330	370	35	)	)	PUNCT
ejpam-5330	370	36	,	,	PUNCT
ejpam-5330	370	37	φ∗	φ∗	NOUN
ejpam-5330	370	38	ψ∗	ψ∗	NOUN
ejpam-5330	370	39	:	:	PUNCT
ejpam-5330	370	40	(	(	PUNCT
ejpam-5330	370	41	̃v	̃v	NOUN
ejpam-5330	370	42	,	,	PUNCT
ejpam-5330	370	43	f	f	PROPN
ejpam-5330	370	44	)	)	PUNCT
ejpam-5330	371	1	−→	−→	NOUN
ejpam-5330	371	2	(	(	PUNCT
ejpam-5330	371	3	̃u	̃u	PROPN
ejpam-5330	371	4	,	,	PUNCT
ejpam-5330	371	5	e	e	NOUN
ejpam-5330	371	6	)	)	PUNCT
ejpam-5330	371	7	be	be	VERB
ejpam-5330	371	8	two	two	NUM
ejpam-5330	371	9	fuzzy	fuzzy	ADJ
ejpam-5330	371	10	soft	soft	ADJ
ejpam-5330	371	11	functions	function	NOUN
ejpam-5330	371	12	.	.	PUNCT
ejpam-5330	372	1	then	then	ADV
ejpam-5330	372	2	,	,	PUNCT
ejpam-5330	372	3	the	the	DET
ejpam-5330	372	4	composition	composition	NOUN
ejpam-5330	372	5	φ∗	φ∗	NOUN
ejpam-5330	372	6	ψ∗	ψ∗	NOUN
ejpam-5330	372	7	◦	◦	NOUN
ejpam-5330	372	8	φψ	φψ	NOUN
ejpam-5330	372	9	is	be	AUX
ejpam-5330	372	10	fuzzy	fuzzy	ADJ
ejpam-5330	372	11	soft	soft	ADJ
ejpam-5330	372	12	almost	almost	ADV
ejpam-5330	372	13	α	α	NOUN
ejpam-5330	372	14	-	-	ADJ
ejpam-5330	372	15	continuous	continuous	ADJ
ejpam-5330	372	16	if	if	SCONJ
ejpam-5330	372	17	φψ	φψ	NOUN
ejpam-5330	372	18	is	be	AUX
ejpam-5330	372	19	fuzzy	fuzzy	ADJ
ejpam-5330	372	20	soft	soft	ADJ
ejpam-5330	372	21	α	α	NOUN
ejpam-5330	372	22	-	-	ADJ
ejpam-5330	372	23	continuous	continuous	ADJ
ejpam-5330	372	24	and	and	CCONJ
ejpam-5330	372	25	φ∗	φ∗	NOUN
ejpam-5330	372	26	ψ∗	ψ∗	NOUN
ejpam-5330	372	27	is	be	AUX
ejpam-5330	372	28	fuzzy	fuzzy	ADJ
ejpam-5330	372	29	soft	soft	ADJ
ejpam-5330	372	30	almost	almost	ADV
ejpam-5330	372	31	continuous	continuous	ADJ
ejpam-5330	372	32	(	(	PUNCT
ejpam-5330	372	33	resp	resp	NOUN
ejpam-5330	372	34	.	.	PUNCT
ejpam-5330	372	35	,	,	PUNCT
ejpam-5330	372	36	continuous	continuous	ADJ
ejpam-5330	372	37	)	)	PUNCT
ejpam-5330	372	38	.	.	PUNCT
ejpam-5330	373	1	proof	proof	NOUN
ejpam-5330	373	2	.	.	PUNCT
ejpam-5330	374	1	the	the	DET
ejpam-5330	374	2	proof	proof	NOUN
ejpam-5330	374	3	is	be	AUX
ejpam-5330	374	4	obvious	obvious	ADJ
ejpam-5330	374	5	.	.	PUNCT
ejpam-5330	375	1	let	let	VERB
ejpam-5330	375	2	h	h	NOUN
ejpam-5330	375	3	and	and	CCONJ
ejpam-5330	375	4	i	i	PRON
ejpam-5330	375	5	:	:	PUNCT
ejpam-5330	375	6	n	n	NUM
ejpam-5330	375	7	×	×	PROPN
ejpam-5330	375	8	˜(w	˜(w	PROPN
ejpam-5330	375	9	,	,	PUNCT
ejpam-5330	375	10	n	n	CCONJ
ejpam-5330	375	11	)	)	PUNCT
ejpam-5330	375	12	×	×	NOUN
ejpam-5330	375	13	i	i	PROPN
ejpam-5330	375	14	◦	◦	NOUN
ejpam-5330	375	15	→	→	SYM
ejpam-5330	375	16	˜(w	˜(w	PROPN
ejpam-5330	375	17	,	,	PUNCT
ejpam-5330	375	18	n	n	CCONJ
ejpam-5330	375	19	)	)	PUNCT
ejpam-5330	375	20	be	be	AUX
ejpam-5330	375	21	operators	operator	NOUN
ejpam-5330	375	22	on	on	ADP
ejpam-5330	375	23	˜(w	˜(w	PROPN
ejpam-5330	375	24	,	,	PUNCT
ejpam-5330	375	25	n	n	CCONJ
ejpam-5330	375	26	)	)	PUNCT
ejpam-5330	375	27	,	,	PUNCT
ejpam-5330	375	28	and	and	CCONJ
ejpam-5330	375	29	j	j	PROPN
ejpam-5330	375	30	and	and	CCONJ
ejpam-5330	375	31	k	k	NOUN
ejpam-5330	376	1	:	:	PUNCT
ejpam-5330	376	2	f	f	X
ejpam-5330	376	3	×	×	NOUN
ejpam-5330	376	4	(	(	PUNCT
ejpam-5330	376	5	̃v	̃v	NOUN
ejpam-5330	376	6	,	,	PUNCT
ejpam-5330	376	7	f	f	PROPN
ejpam-5330	376	8	)	)	PUNCT
ejpam-5330	376	9	×	×	PROPN
ejpam-5330	376	10	i	i	PROPN
ejpam-5330	376	11	◦	◦	NOUN
ejpam-5330	376	12	→	→	PUNCT
ejpam-5330	376	13	(	(	PUNCT
ejpam-5330	376	14	̃v	̃v	NOUN
ejpam-5330	376	15	,	,	PUNCT
ejpam-5330	376	16	f	f	PROPN
ejpam-5330	376	17	)	)	PUNCT
ejpam-5330	376	18	be	be	AUX
ejpam-5330	376	19	operators	operator	NOUN
ejpam-5330	376	20	on	on	ADP
ejpam-5330	376	21	(	(	PUNCT
ejpam-5330	376	22	̃v	̃v	NOUN
ejpam-5330	376	23	,	,	PUNCT
ejpam-5330	376	24	f	f	PROPN
ejpam-5330	376	25	)	)	PUNCT
ejpam-5330	376	26	.	.	PUNCT
ejpam-5330	377	1	w.	w.	PROPN
ejpam-5330	377	2	alqurashi	alqurashi	PROPN
ejpam-5330	377	3	,	,	PUNCT
ejpam-5330	377	4	i.	i.	PROPN
ejpam-5330	377	5	m.	m.	PROPN
ejpam-5330	377	6	taha	taha	PROPN
ejpam-5330	377	7	/	/	PUNCT
ejpam-5330	377	8	eur	eur	PROPN
ejpam-5330	377	9	.	.	PUNCT
ejpam-5330	378	1	j.	j.	PROPN
ejpam-5330	378	2	pure	pure	PROPN
ejpam-5330	378	3	appl	appl	PROPN
ejpam-5330	378	4	.	.	PROPN
ejpam-5330	378	5	math	math	PROPN
ejpam-5330	378	6	,	,	PUNCT
ejpam-5330	378	7	17	17	NUM
ejpam-5330	378	8	(	(	PUNCT
ejpam-5330	378	9	4	4	NUM
ejpam-5330	378	10	)	)	PUNCT
ejpam-5330	378	11	(	(	PUNCT
ejpam-5330	378	12	2024	2024	NUM
ejpam-5330	378	13	)	)	PUNCT
ejpam-5330	378	14	,	,	PUNCT
ejpam-5330	378	15	4112	4112	NUM
ejpam-5330	378	16	-	-	SYM
ejpam-5330	378	17	4134	4134	NUM
ejpam-5330	378	18	4126	4126	NUM
ejpam-5330	378	19	definition	definition	NOUN
ejpam-5330	378	20	17	17	NUM
ejpam-5330	378	21	.	.	PUNCT
ejpam-5330	379	1	[	[	X
ejpam-5330	379	2	11	11	NUM
ejpam-5330	379	3	]	]	X
ejpam-5330	379	4	let	let	VERB
ejpam-5330	379	5	(	(	PUNCT
ejpam-5330	379	6	w	w	NOUN
ejpam-5330	379	7	,	,	PUNCT
ejpam-5330	379	8	τn	τn	PROPN
ejpam-5330	379	9	)	)	PUNCT
ejpam-5330	379	10	and	and	CCONJ
ejpam-5330	379	11	(	(	PUNCT
ejpam-5330	379	12	v	v	NOUN
ejpam-5330	379	13	,	,	PUNCT
ejpam-5330	379	14	ηf	ηf	PROPN
ejpam-5330	379	15	)	)	PUNCT
ejpam-5330	379	16	be	be	AUX
ejpam-5330	379	17	an	an	DET
ejpam-5330	379	18	fstss	fstss	NOUN
ejpam-5330	379	19	.	.	PUNCT
ejpam-5330	380	1	φψ	φψ	PROPN
ejpam-5330	380	2	:	:	PUNCT
ejpam-5330	381	1	˜(w	˜(w	PROPN
ejpam-5330	381	2	,	,	PUNCT
ejpam-5330	381	3	n	n	CCONJ
ejpam-5330	381	4	)	)	PUNCT
ejpam-5330	381	5	−→	−→	NOUN
ejpam-5330	381	6	(	(	PUNCT
ejpam-5330	381	7	̃v	̃v	NOUN
ejpam-5330	381	8	,	,	PUNCT
ejpam-5330	381	9	f	f	PROPN
ejpam-5330	381	10	)	)	PUNCT
ejpam-5330	381	11	is	be	AUX
ejpam-5330	381	12	said	say	VERB
ejpam-5330	381	13	to	to	PART
ejpam-5330	381	14	be	be	AUX
ejpam-5330	381	15	a	a	DET
ejpam-5330	381	16	fuzzy	fuzzy	ADJ
ejpam-5330	381	17	soft	soft	ADJ
ejpam-5330	381	18	(	(	PUNCT
ejpam-5330	381	19	h	h	NOUN
ejpam-5330	381	20	,	,	PUNCT
ejpam-5330	381	21	i	i	PRON
ejpam-5330	381	22	,	,	PUNCT
ejpam-5330	381	23	j	j	PROPN
ejpam-5330	381	24	,	,	PUNCT
ejpam-5330	381	25	k)-continuous	k)-continuous	ADJ
ejpam-5330	381	26	mapping	mapping	NOUN
ejpam-5330	381	27	if	if	SCONJ
ejpam-5330	381	28	h[n	h[n	PROPN
ejpam-5330	381	29	,	,	PUNCT
ejpam-5330	381	30	φ−1	φ−1	PROPN
ejpam-5330	381	31	ψ	ψ	X
ejpam-5330	381	32	(	(	PUNCT
ejpam-5330	381	33	k(k	k(k	PROPN
ejpam-5330	381	34	,	,	PUNCT
ejpam-5330	381	35	hc	hc	PROPN
ejpam-5330	381	36	,	,	PUNCT
ejpam-5330	381	37	r	r	NOUN
ejpam-5330	381	38	)	)	PUNCT
ejpam-5330	381	39	)	)	PUNCT
ejpam-5330	381	40	,	,	PUNCT
ejpam-5330	381	41	r	r	X
ejpam-5330	381	42	]	]	X
ejpam-5330	381	43	⊓	⊓	PROPN
ejpam-5330	381	44	i[n	i[n	NOUN
ejpam-5330	381	45	,	,	PUNCT
ejpam-5330	381	46	φ−1	φ−1	PROPN
ejpam-5330	381	47	ψ	ψ	X
ejpam-5330	381	48	(	(	PUNCT
ejpam-5330	381	49	j	j	PROPN
ejpam-5330	381	50	(	(	PUNCT
ejpam-5330	381	51	k	k	PROPN
ejpam-5330	381	52	,	,	PUNCT
ejpam-5330	381	53	hc	hc	PROPN
ejpam-5330	381	54	,	,	PUNCT
ejpam-5330	381	55	r	r	NOUN
ejpam-5330	381	56	)	)	PUNCT
ejpam-5330	381	57	)	)	PUNCT
ejpam-5330	381	58	,	,	PUNCT
ejpam-5330	381	59	r	r	X
ejpam-5330	381	60	]	]	X
ejpam-5330	381	61	=	=	PUNCT
ejpam-5330	381	62	φ	φ	PROPN
ejpam-5330	381	63	for	for	ADP
ejpam-5330	381	64	each	each	DET
ejpam-5330	381	65	hc	hc	PROPN
ejpam-5330	381	66	∈	∈	PROPN
ejpam-5330	381	67	(	(	PUNCT
ejpam-5330	381	68	̃v	̃v	NOUN
ejpam-5330	381	69	,	,	PUNCT
ejpam-5330	381	70	f	f	PROPN
ejpam-5330	381	71	)	)	PUNCT
ejpam-5330	381	72	with	with	ADP
ejpam-5330	381	73	ηk(hc	ηk(hc	PROPN
ejpam-5330	381	74	)	)	PUNCT
ejpam-5330	381	75	≥	≥	PROPN
ejpam-5330	381	76	r	r	NOUN
ejpam-5330	381	77	,	,	PUNCT
ejpam-5330	381	78	n	n	NOUN
ejpam-5330	381	79	∈	∈	NOUN
ejpam-5330	381	80	n	n	NOUN
ejpam-5330	381	81	,	,	PUNCT
ejpam-5330	381	82	and	and	CCONJ
ejpam-5330	381	83	(	(	PUNCT
ejpam-5330	381	84	k	k	X
ejpam-5330	381	85	=	=	SYM
ejpam-5330	381	86	ψ(n	ψ(n	PROPN
ejpam-5330	381	87	)	)	PUNCT
ejpam-5330	381	88	)	)	PUNCT
ejpam-5330	382	1	∈	∈	PROPN
ejpam-5330	382	2	f	f	INTJ
ejpam-5330	382	3	.	.	PUNCT
ejpam-5330	383	1	in	in	ADP
ejpam-5330	383	2	(	(	PUNCT
ejpam-5330	383	3	2023	2023	NUM
ejpam-5330	383	4	)	)	PUNCT
ejpam-5330	383	5	,	,	PUNCT
ejpam-5330	383	6	alshammari	alshammari	PROPN
ejpam-5330	383	7	et	et	PROPN
ejpam-5330	383	8	al	al	PROPN
ejpam-5330	383	9	.	.	PUNCT
ejpam-5330	384	1	[	[	X
ejpam-5330	384	2	11	11	NUM
ejpam-5330	384	3	]	]	PUNCT
ejpam-5330	384	4	defined	define	VERB
ejpam-5330	384	5	the	the	DET
ejpam-5330	384	6	notion	notion	NOUN
ejpam-5330	384	7	of	of	ADP
ejpam-5330	384	8	fuzzy	fuzzy	ADJ
ejpam-5330	384	9	soft	soft	ADJ
ejpam-5330	384	10	α	α	ADJ
ejpam-5330	384	11	-	-	ADJ
ejpam-5330	384	12	continuous	continuous	ADJ
ejpam-5330	384	13	mappings	mapping	NOUN
ejpam-5330	384	14	:	:	PUNCT
ejpam-5330	384	15	φ−1	φ−1	PROPN
ejpam-5330	384	16	ψ	ψ	X
ejpam-5330	384	17	(	(	PUNCT
ejpam-5330	384	18	hc	hc	PROPN
ejpam-5330	384	19	)	)	PUNCT
ejpam-5330	384	20	⊑	⊑	X
ejpam-5330	384	21	iτ	iτ	X
ejpam-5330	384	22	(	(	PUNCT
ejpam-5330	384	23	n	n	CCONJ
ejpam-5330	384	24	,	,	PUNCT
ejpam-5330	384	25	cτ	cτ	INTJ
ejpam-5330	384	26	(	(	PUNCT
ejpam-5330	384	27	n	n	CCONJ
ejpam-5330	384	28	,	,	PUNCT
ejpam-5330	384	29	iτ	iτ	X
ejpam-5330	384	30	(	(	PUNCT
ejpam-5330	384	31	n	n	CCONJ
ejpam-5330	384	32	,	,	PUNCT
ejpam-5330	384	33	φ	φ	PROPN
ejpam-5330	384	34	−1	−1	NOUN
ejpam-5330	384	35	ψ	ψ	X
ejpam-5330	384	36	(	(	PUNCT
ejpam-5330	384	37	hc	hc	PROPN
ejpam-5330	384	38	)	)	PUNCT
ejpam-5330	384	39	,	,	PUNCT
ejpam-5330	384	40	r	r	NOUN
ejpam-5330	384	41	)	)	PUNCT
ejpam-5330	384	42	,	,	PUNCT
ejpam-5330	384	43	r	r	NOUN
ejpam-5330	384	44	)	)	PUNCT
ejpam-5330	384	45	,	,	PUNCT
ejpam-5330	384	46	r	r	NOUN
ejpam-5330	384	47	)	)	PUNCT
ejpam-5330	384	48	,	,	PUNCT
ejpam-5330	384	49	for	for	ADP
ejpam-5330	384	50	each	each	DET
ejpam-5330	384	51	hc	hc	PROPN
ejpam-5330	384	52	∈	∈	PROPN
ejpam-5330	384	53	(	(	PUNCT
ejpam-5330	384	54	̃v	̃v	NOUN
ejpam-5330	384	55	,	,	PUNCT
ejpam-5330	384	56	f	f	PROPN
ejpam-5330	384	57	)	)	PUNCT
ejpam-5330	384	58	with	with	ADP
ejpam-5330	384	59	ηk(hc	ηk(hc	PROPN
ejpam-5330	384	60	)	)	PUNCT
ejpam-5330	384	61	≥	≥	PROPN
ejpam-5330	384	62	r.	r.	NOUN
ejpam-5330	385	1	we	we	PRON
ejpam-5330	385	2	can	can	AUX
ejpam-5330	385	3	see	see	VERB
ejpam-5330	385	4	that	that	DET
ejpam-5330	385	5	definition	definition	NOUN
ejpam-5330	385	6	17	17	NUM
ejpam-5330	385	7	generalizes	generalize	VERB
ejpam-5330	385	8	the	the	DET
ejpam-5330	385	9	concept	concept	NOUN
ejpam-5330	385	10	of	of	ADP
ejpam-5330	385	11	fuzzy	fuzzy	ADJ
ejpam-5330	385	12	soft	soft	ADJ
ejpam-5330	385	13	continuous	continuous	ADJ
ejpam-5330	385	14	functions	function	NOUN
ejpam-5330	385	15	when	when	SCONJ
ejpam-5330	385	16	we	we	PRON
ejpam-5330	385	17	choose	choose	VERB
ejpam-5330	385	18	h	h	NOUN
ejpam-5330	385	19	=	=	NOUN
ejpam-5330	385	20	identity	identity	NOUN
ejpam-5330	385	21	operator	operator	NOUN
ejpam-5330	385	22	,	,	PUNCT
ejpam-5330	386	1	i	i	PRON
ejpam-5330	386	2	=	=	SYM
ejpam-5330	386	3	interior	interior	ADJ
ejpam-5330	386	4	closure	closure	ADJ
ejpam-5330	386	5	interior	interior	ADJ
ejpam-5330	386	6	operator	operator	NOUN
ejpam-5330	386	7	,	,	PUNCT
ejpam-5330	386	8	j	j	NOUN
ejpam-5330	386	9	=	=	SYM
ejpam-5330	386	10	identity	identity	NOUN
ejpam-5330	386	11	operator	operator	NOUN
ejpam-5330	386	12	,	,	PUNCT
ejpam-5330	386	13	and	and	CCONJ
ejpam-5330	386	14	k	k	NOUN
ejpam-5330	386	15	=	=	SYM
ejpam-5330	386	16	identity	identity	NOUN
ejpam-5330	386	17	operator	operator	NOUN
ejpam-5330	386	18	.	.	PUNCT
ejpam-5330	387	1	a	a	DET
ejpam-5330	387	2	historical	historical	ADJ
ejpam-5330	387	3	justification	justification	NOUN
ejpam-5330	387	4	of	of	ADP
ejpam-5330	387	5	definition	definition	NOUN
ejpam-5330	387	6	17	17	NUM
ejpam-5330	387	7	:	:	PUNCT
ejpam-5330	387	8	(	(	PUNCT
ejpam-5330	387	9	1	1	X
ejpam-5330	387	10	)	)	PUNCT
ejpam-5330	387	11	in	in	ADP
ejpam-5330	387	12	section	section	NOUN
ejpam-5330	387	13	3	3	NUM
ejpam-5330	387	14	,	,	PUNCT
ejpam-5330	387	15	we	we	PRON
ejpam-5330	387	16	obtained	obtain	VERB
ejpam-5330	387	17	the	the	DET
ejpam-5330	387	18	notion	notion	NOUN
ejpam-5330	387	19	of	of	ADP
ejpam-5330	387	20	fuzzy	fuzzy	ADJ
ejpam-5330	387	21	soft	soft	ADJ
ejpam-5330	387	22	almost	almost	ADV
ejpam-5330	387	23	α	α	NUM
ejpam-5330	387	24	-	-	ADJ
ejpam-5330	387	25	continuous	continuous	ADJ
ejpam-5330	387	26	mappings	mapping	NOUN
ejpam-5330	387	27	:	:	PUNCT
ejpam-5330	387	28	φ−1	φ−1	PROPN
ejpam-5330	387	29	ψ	ψ	X
ejpam-5330	387	30	(	(	PUNCT
ejpam-5330	387	31	hc	hc	PROPN
ejpam-5330	387	32	)	)	PUNCT
ejpam-5330	387	33	⊑	⊑	PROPN
ejpam-5330	387	34	αiτ	αiτ	PROPN
ejpam-5330	387	35	(	(	PUNCT
ejpam-5330	387	36	n	n	CCONJ
ejpam-5330	387	37	,	,	PUNCT
ejpam-5330	387	38	φ	φ	PROPN
ejpam-5330	387	39	−1	−1	NOUN
ejpam-5330	387	40	ψ	ψ	X
ejpam-5330	387	41	(	(	PUNCT
ejpam-5330	387	42	iη(k	iη(k	NOUN
ejpam-5330	387	43	,	,	PUNCT
ejpam-5330	387	44	cη(k	cη(k	PROPN
ejpam-5330	387	45	,	,	PUNCT
ejpam-5330	387	46	hc	hc	PROPN
ejpam-5330	387	47	,	,	PUNCT
ejpam-5330	387	48	r	r	NOUN
ejpam-5330	387	49	)	)	PUNCT
ejpam-5330	387	50	,	,	PUNCT
ejpam-5330	387	51	r	r	NOUN
ejpam-5330	387	52	)	)	PUNCT
ejpam-5330	387	53	)	)	PUNCT
ejpam-5330	387	54	,	,	PUNCT
ejpam-5330	387	55	r	r	NOUN
ejpam-5330	387	56	)	)	PUNCT
ejpam-5330	387	57	,	,	PUNCT
ejpam-5330	387	58	for	for	ADP
ejpam-5330	387	59	each	each	DET
ejpam-5330	387	60	hc	hc	PROPN
ejpam-5330	387	61	∈	∈	PROPN
ejpam-5330	387	62	(	(	PUNCT
ejpam-5330	387	63	̃v	̃v	NOUN
ejpam-5330	387	64	,	,	PUNCT
ejpam-5330	387	65	f	f	PROPN
ejpam-5330	387	66	)	)	PUNCT
ejpam-5330	387	67	with	with	ADP
ejpam-5330	387	68	ηk(hc	ηk(hc	PROPN
ejpam-5330	387	69	)	)	PUNCT
ejpam-5330	387	70	≥	≥	PROPN
ejpam-5330	387	71	r.	r.	PROPN
ejpam-5330	387	72	here	here	ADV
ejpam-5330	387	73	,	,	PUNCT
ejpam-5330	387	74	h	h	NOUN
ejpam-5330	387	75	=	=	NOUN
ejpam-5330	387	76	identity	identity	NOUN
ejpam-5330	387	77	operator	operator	NOUN
ejpam-5330	387	78	,	,	PUNCT
ejpam-5330	387	79	i	i	PRON
ejpam-5330	387	80	=	=	NOUN
ejpam-5330	387	81	α	α	X
ejpam-5330	387	82	-	-	ADJ
ejpam-5330	387	83	interior	interior	ADJ
ejpam-5330	387	84	operator	operator	NOUN
ejpam-5330	387	85	,	,	PUNCT
ejpam-5330	387	86	j	j	NOUN
ejpam-5330	388	1	=	=	SYM
ejpam-5330	388	2	interior	interior	ADJ
ejpam-5330	388	3	closure	closure	NOUN
ejpam-5330	388	4	operator	operator	NOUN
ejpam-5330	388	5	,	,	PUNCT
ejpam-5330	388	6	and	and	CCONJ
ejpam-5330	388	7	k	k	NOUN
ejpam-5330	388	8	=	=	SYM
ejpam-5330	388	9	identity	identity	NOUN
ejpam-5330	388	10	operator	operator	NOUN
ejpam-5330	388	11	.	.	PUNCT
ejpam-5330	389	1	(	(	PUNCT
ejpam-5330	389	2	2	2	X
ejpam-5330	389	3	)	)	PUNCT
ejpam-5330	389	4	in	in	ADP
ejpam-5330	389	5	section	section	NOUN
ejpam-5330	389	6	3	3	NUM
ejpam-5330	389	7	,	,	PUNCT
ejpam-5330	389	8	we	we	PRON
ejpam-5330	389	9	obtained	obtain	VERB
ejpam-5330	389	10	the	the	DET
ejpam-5330	389	11	notion	notion	NOUN
ejpam-5330	389	12	of	of	ADP
ejpam-5330	389	13	fuzzy	fuzzy	ADJ
ejpam-5330	389	14	soft	soft	ADJ
ejpam-5330	389	15	weakly	weakly	ADJ
ejpam-5330	389	16	α	α	ADJ
ejpam-5330	389	17	-	-	ADJ
ejpam-5330	389	18	continuous	continuous	ADJ
ejpam-5330	389	19	mappings	mapping	NOUN
ejpam-5330	389	20	:	:	PUNCT
ejpam-5330	389	21	φ−1	φ−1	PROPN
ejpam-5330	389	22	ψ	ψ	X
ejpam-5330	389	23	(	(	PUNCT
ejpam-5330	389	24	hc	hc	PROPN
ejpam-5330	389	25	)	)	PUNCT
ejpam-5330	389	26	⊑	⊑	PROPN
ejpam-5330	389	27	αiτ	αiτ	PROPN
ejpam-5330	389	28	(	(	PUNCT
ejpam-5330	389	29	n	n	CCONJ
ejpam-5330	389	30	,	,	PUNCT
ejpam-5330	389	31	φ	φ	PROPN
ejpam-5330	389	32	−1	−1	NOUN
ejpam-5330	389	33	ψ	ψ	X
ejpam-5330	389	34	(	(	PUNCT
ejpam-5330	389	35	cη(k	cη(k	PROPN
ejpam-5330	389	36	,	,	PUNCT
ejpam-5330	389	37	hc	hc	PROPN
ejpam-5330	389	38	,	,	PUNCT
ejpam-5330	389	39	r	r	NOUN
ejpam-5330	389	40	)	)	PUNCT
ejpam-5330	389	41	)	)	PUNCT
ejpam-5330	389	42	,	,	PUNCT
ejpam-5330	389	43	r	r	NOUN
ejpam-5330	389	44	)	)	PUNCT
ejpam-5330	389	45	,	,	PUNCT
ejpam-5330	389	46	for	for	ADP
ejpam-5330	389	47	each	each	DET
ejpam-5330	389	48	hc	hc	PROPN
ejpam-5330	389	49	∈	∈	PROPN
ejpam-5330	389	50	(	(	PUNCT
ejpam-5330	389	51	̃v	̃v	NOUN
ejpam-5330	389	52	,	,	PUNCT
ejpam-5330	389	53	f	f	PROPN
ejpam-5330	389	54	)	)	PUNCT
ejpam-5330	389	55	with	with	ADP
ejpam-5330	389	56	ηk(hc	ηk(hc	PROPN
ejpam-5330	389	57	)	)	PUNCT
ejpam-5330	389	58	≥	≥	PROPN
ejpam-5330	389	59	r.	r.	PROPN
ejpam-5330	389	60	here	here	ADV
ejpam-5330	389	61	,	,	PUNCT
ejpam-5330	389	62	h	h	NOUN
ejpam-5330	389	63	=	=	NOUN
ejpam-5330	389	64	identity	identity	NOUN
ejpam-5330	389	65	operator	operator	NOUN
ejpam-5330	389	66	,	,	PUNCT
ejpam-5330	389	67	i	i	PRON
ejpam-5330	389	68	=	=	NOUN
ejpam-5330	389	69	α	α	X
ejpam-5330	389	70	-	-	ADJ
ejpam-5330	389	71	interior	interior	ADJ
ejpam-5330	389	72	operator	operator	NOUN
ejpam-5330	389	73	,	,	PUNCT
ejpam-5330	389	74	j	j	NOUN
ejpam-5330	390	1	=	=	SYM
ejpam-5330	390	2	closure	closure	NOUN
ejpam-5330	390	3	operator	operator	NOUN
ejpam-5330	390	4	,	,	PUNCT
ejpam-5330	390	5	and	and	CCONJ
ejpam-5330	390	6	k	k	NOUN
ejpam-5330	390	7	=	=	SYM
ejpam-5330	390	8	identity	identity	NOUN
ejpam-5330	390	9	operator	operator	NOUN
ejpam-5330	390	10	.	.	PUNCT
ejpam-5330	391	1	4	4	X
ejpam-5330	391	2	.	.	X
ejpam-5330	391	3	fuzzy	fuzzy	ADJ
ejpam-5330	391	4	soft	soft	ADJ
ejpam-5330	391	5	α	α	NOUN
ejpam-5330	391	6	-	-	NOUN
ejpam-5330	391	7	compactness	compactness	NOUN
ejpam-5330	391	8	here	here	ADV
ejpam-5330	391	9	,	,	PUNCT
ejpam-5330	391	10	some	some	DET
ejpam-5330	391	11	novel	novel	ADJ
ejpam-5330	391	12	types	type	NOUN
ejpam-5330	391	13	of	of	ADP
ejpam-5330	391	14	fuzzy	fuzzy	ADJ
ejpam-5330	391	15	soft	soft	ADJ
ejpam-5330	391	16	compactness	compactness	NOUN
ejpam-5330	391	17	via	via	ADP
ejpam-5330	391	18	r	r	NOUN
ejpam-5330	391	19	-	-	PUNCT
ejpam-5330	391	20	fuzzy	fuzzy	ADJ
ejpam-5330	391	21	soft	soft	ADJ
ejpam-5330	391	22	α	α	NOUN
ejpam-5330	391	23	-	-	ADJ
ejpam-5330	391	24	open	open	ADJ
ejpam-5330	391	25	sets	set	NOUN
ejpam-5330	391	26	were	be	AUX
ejpam-5330	391	27	introduced	introduce	VERB
ejpam-5330	391	28	and	and	CCONJ
ejpam-5330	391	29	the	the	DET
ejpam-5330	391	30	relationships	relationship	NOUN
ejpam-5330	391	31	between	between	ADP
ejpam-5330	391	32	them	they	PRON
ejpam-5330	391	33	were	be	AUX
ejpam-5330	391	34	explored	explore	VERB
ejpam-5330	391	35	with	with	ADP
ejpam-5330	391	36	the	the	DET
ejpam-5330	391	37	help	help	NOUN
ejpam-5330	391	38	of	of	ADP
ejpam-5330	391	39	some	some	DET
ejpam-5330	391	40	examples	example	NOUN
ejpam-5330	391	41	.	.	PUNCT
ejpam-5330	392	1	definition	definition	NOUN
ejpam-5330	392	2	18	18	NUM
ejpam-5330	392	3	.	.	PUNCT
ejpam-5330	393	1	let	let	AUX
ejpam-5330	393	2	(	(	PUNCT
ejpam-5330	393	3	w	w	NOUN
ejpam-5330	393	4	,	,	PUNCT
ejpam-5330	393	5	τn	τn	PART
ejpam-5330	393	6	)	)	PUNCT
ejpam-5330	393	7	be	be	AUX
ejpam-5330	393	8	an	an	DET
ejpam-5330	393	9	fsts	fst	NOUN
ejpam-5330	393	10	and	and	CCONJ
ejpam-5330	393	11	r	r	NOUN
ejpam-5330	393	12	∈	∈	PROPN
ejpam-5330	393	13	i	i	PRON
ejpam-5330	393	14	◦	◦	NOUN
ejpam-5330	393	15	,	,	PUNCT
ejpam-5330	393	16	then	then	ADV
ejpam-5330	393	17	hc	hc	PROPN
ejpam-5330	393	18	∈	∈	PROPN
ejpam-5330	393	19	˜(w	˜(w	PROPN
ejpam-5330	393	20	,	,	PUNCT
ejpam-5330	393	21	n	n	CCONJ
ejpam-5330	393	22	)	)	PUNCT
ejpam-5330	393	23	is	be	AUX
ejpam-5330	393	24	called	call	VERB
ejpam-5330	393	25	an	an	DET
ejpam-5330	393	26	r	r	NOUN
ejpam-5330	393	27	-	-	PUNCT
ejpam-5330	393	28	fuzzy	fuzzy	ADJ
ejpam-5330	393	29	soft	soft	ADJ
ejpam-5330	393	30	compact	compact	ADJ
ejpam-5330	393	31	iff	iff	NOUN
ejpam-5330	393	32	for	for	ADP
ejpam-5330	393	33	every	every	DET
ejpam-5330	393	34	family	family	NOUN
ejpam-5330	393	35	{	{	PUNCT
ejpam-5330	393	36	(	(	PUNCT
ejpam-5330	393	37	gb)δ	gb)δ	PROPN
ejpam-5330	393	38	∈	∈	PROPN
ejpam-5330	393	39	˜(w	˜(w	PROPN
ejpam-5330	393	40	,	,	PUNCT
ejpam-5330	393	41	n	n	CCONJ
ejpam-5330	393	42	)	)	PUNCT
ejpam-5330	393	43	|	|	ADV
ejpam-5330	393	44	τn((gb)δ	τn((gb)δ	NOUN
ejpam-5330	393	45	)	)	PUNCT
ejpam-5330	393	46	≥	≥	NOUN
ejpam-5330	393	47	r	r	NOUN
ejpam-5330	393	48	for	for	ADP
ejpam-5330	393	49	each	each	DET
ejpam-5330	393	50	n	n	PRON
ejpam-5330	393	51	∈	∈	PROPN
ejpam-5330	393	52	n}δ∈∆	n}δ∈∆	NOUN
ejpam-5330	393	53	,	,	PUNCT
ejpam-5330	393	54	such	such	ADJ
ejpam-5330	393	55	that	that	SCONJ
ejpam-5330	393	56	hc	hc	PROPN
ejpam-5330	393	57	⊑	⊑	PROPN
ejpam-5330	393	58	⊔δ∈∆(gb)δ	⊔δ∈∆(gb)δ	PROPN
ejpam-5330	393	59	,	,	PUNCT
ejpam-5330	393	60	there	there	PRON
ejpam-5330	393	61	is	be	VERB
ejpam-5330	393	62	a	a	DET
ejpam-5330	393	63	finite	finite	NOUN
ejpam-5330	393	64	subset	subset	NOUN
ejpam-5330	393	65	∆	∆	ADJ
ejpam-5330	393	66	◦	◦	NOUN
ejpam-5330	393	67	of	of	ADP
ejpam-5330	393	68	∆	∆	PROPN
ejpam-5330	393	69	,	,	PUNCT
ejpam-5330	393	70	such	such	ADJ
ejpam-5330	393	71	that	that	SCONJ
ejpam-5330	393	72	hc	hc	PROPN
ejpam-5330	393	73	⊑	⊑	PRON
ejpam-5330	393	74	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	393	75	◦	◦	NOUN
ejpam-5330	393	76	(gb)δ	(gb)δ	NUM
ejpam-5330	393	77	.	.	PUNCT
ejpam-5330	393	78	definition	definition	NOUN
ejpam-5330	393	79	19	19	NUM
ejpam-5330	393	80	.	.	PUNCT
ejpam-5330	394	1	let	let	AUX
ejpam-5330	394	2	(	(	PUNCT
ejpam-5330	394	3	w	w	NOUN
ejpam-5330	394	4	,	,	PUNCT
ejpam-5330	394	5	τn	τn	PART
ejpam-5330	394	6	)	)	PUNCT
ejpam-5330	394	7	be	be	AUX
ejpam-5330	394	8	an	an	DET
ejpam-5330	394	9	fsts	fst	NOUN
ejpam-5330	394	10	and	and	CCONJ
ejpam-5330	394	11	r	r	NOUN
ejpam-5330	394	12	∈	∈	PROPN
ejpam-5330	394	13	i	i	PRON
ejpam-5330	394	14	◦	◦	NOUN
ejpam-5330	394	15	,	,	PUNCT
ejpam-5330	394	16	then	then	ADV
ejpam-5330	394	17	hc	hc	PROPN
ejpam-5330	394	18	∈	∈	PROPN
ejpam-5330	394	19	˜(w	˜(w	PROPN
ejpam-5330	394	20	,	,	PUNCT
ejpam-5330	394	21	n	n	CCONJ
ejpam-5330	394	22	)	)	PUNCT
ejpam-5330	394	23	is	be	AUX
ejpam-5330	394	24	called	call	VERB
ejpam-5330	394	25	an	an	DET
ejpam-5330	394	26	r	r	NOUN
ejpam-5330	394	27	-	-	PUNCT
ejpam-5330	394	28	fuzzy	fuzzy	ADJ
ejpam-5330	394	29	soft	soft	ADJ
ejpam-5330	394	30	α	α	ADJ
ejpam-5330	394	31	-	-	ADJ
ejpam-5330	394	32	compact	compact	ADJ
ejpam-5330	394	33	iff	iff	NOUN
ejpam-5330	394	34	for	for	ADP
ejpam-5330	394	35	every	every	DET
ejpam-5330	394	36	family	family	NOUN
ejpam-5330	394	37	{	{	PUNCT
ejpam-5330	394	38	(	(	PUNCT
ejpam-5330	394	39	gb)δ	gb)δ	PROPN
ejpam-5330	394	40	∈	∈	PROPN
ejpam-5330	394	41	˜(w	˜(w	PROPN
ejpam-5330	394	42	,	,	PUNCT
ejpam-5330	394	43	n	n	CCONJ
ejpam-5330	394	44	)	)	PUNCT
ejpam-5330	395	1	|	|	ADV
ejpam-5330	395	2	(	(	PUNCT
ejpam-5330	395	3	gb)δ	gb)δ	PROPN
ejpam-5330	395	4	is	be	AUX
ejpam-5330	395	5	r	r	NOUN
ejpam-5330	395	6	-	-	PUNCT
ejpam-5330	395	7	fuzzy	fuzzy	ADJ
ejpam-5330	395	8	soft	soft	ADJ
ejpam-5330	395	9	α	α	NOUN
ejpam-5330	395	10	-	-	PUNCT
ejpam-5330	395	11	open}δ∈∆	open}δ∈∆	NOUN
ejpam-5330	395	12	,	,	PUNCT
ejpam-5330	395	13	such	such	ADJ
ejpam-5330	395	14	that	that	SCONJ
ejpam-5330	395	15	hc	hc	PROPN
ejpam-5330	395	16	⊑	⊑	PROPN
ejpam-5330	395	17	⊔δ∈∆(gb)δ	⊔δ∈∆(gb)δ	PROPN
ejpam-5330	395	18	,	,	PUNCT
ejpam-5330	395	19	there	there	PRON
ejpam-5330	395	20	is	be	VERB
ejpam-5330	395	21	a	a	DET
ejpam-5330	395	22	finite	finite	NOUN
ejpam-5330	395	23	subset	subset	NOUN
ejpam-5330	395	24	∆	∆	ADJ
ejpam-5330	395	25	◦	◦	NOUN
ejpam-5330	395	26	of	of	ADP
ejpam-5330	395	27	∆	∆	PROPN
ejpam-5330	395	28	,	,	PUNCT
ejpam-5330	395	29	such	such	ADJ
ejpam-5330	395	30	that	that	SCONJ
ejpam-5330	395	31	hc	hc	PROPN
ejpam-5330	395	32	⊑	⊑	PRON
ejpam-5330	395	33	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	395	34	◦	◦	NOUN
ejpam-5330	395	35	(gb)δ	(gb)δ	PROPN
ejpam-5330	395	36	.	.	PUNCT
ejpam-5330	396	1	w.	w.	PROPN
ejpam-5330	396	2	alqurashi	alqurashi	PROPN
ejpam-5330	396	3	,	,	PUNCT
ejpam-5330	396	4	i.	i.	PROPN
ejpam-5330	396	5	m.	m.	PROPN
ejpam-5330	396	6	taha	taha	PROPN
ejpam-5330	396	7	/	/	PUNCT
ejpam-5330	396	8	eur	eur	PROPN
ejpam-5330	396	9	.	.	PUNCT
ejpam-5330	397	1	j.	j.	PROPN
ejpam-5330	397	2	pure	pure	PROPN
ejpam-5330	397	3	appl	appl	PROPN
ejpam-5330	397	4	.	.	PROPN
ejpam-5330	397	5	math	math	PROPN
ejpam-5330	397	6	,	,	PUNCT
ejpam-5330	397	7	17	17	NUM
ejpam-5330	397	8	(	(	PUNCT
ejpam-5330	397	9	4	4	NUM
ejpam-5330	397	10	)	)	PUNCT
ejpam-5330	397	11	(	(	PUNCT
ejpam-5330	397	12	2024	2024	NUM
ejpam-5330	397	13	)	)	PUNCT
ejpam-5330	397	14	,	,	PUNCT
ejpam-5330	397	15	4112	4112	NUM
ejpam-5330	397	16	-	-	SYM
ejpam-5330	397	17	4134	4134	NUM
ejpam-5330	397	18	4127	4127	NUM
ejpam-5330	397	19	lemma	lemma	PROPN
ejpam-5330	397	20	6	6	NUM
ejpam-5330	397	21	.	.	PUNCT
ejpam-5330	398	1	let	let	AUX
ejpam-5330	398	2	(	(	PUNCT
ejpam-5330	398	3	w	w	NOUN
ejpam-5330	398	4	,	,	PUNCT
ejpam-5330	398	5	τn	τn	PART
ejpam-5330	398	6	)	)	PUNCT
ejpam-5330	398	7	be	be	AUX
ejpam-5330	398	8	an	an	DET
ejpam-5330	398	9	fsts	fst	NOUN
ejpam-5330	398	10	and	and	CCONJ
ejpam-5330	398	11	r	r	NOUN
ejpam-5330	398	12	∈	∈	PROPN
ejpam-5330	398	13	i	i	X
ejpam-5330	398	14	◦	◦	NOUN
ejpam-5330	398	15	.	.	PUNCT
ejpam-5330	399	1	if	if	SCONJ
ejpam-5330	399	2	hc	hc	PROPN
ejpam-5330	399	3	∈	∈	PROPN
ejpam-5330	399	4	˜(w	˜(w	PROPN
ejpam-5330	399	5	,	,	PUNCT
ejpam-5330	399	6	n	n	CCONJ
ejpam-5330	399	7	)	)	PUNCT
ejpam-5330	399	8	is	be	AUX
ejpam-5330	399	9	r	r	NOUN
ejpam-5330	399	10	-	-	PUNCT
ejpam-5330	399	11	fuzzy	fuzzy	ADJ
ejpam-5330	399	12	soft	soft	ADJ
ejpam-5330	399	13	α	α	NOUN
ejpam-5330	399	14	-	-	ADJ
ejpam-5330	399	15	compact	compact	ADJ
ejpam-5330	399	16	,	,	PUNCT
ejpam-5330	399	17	then	then	ADV
ejpam-5330	399	18	hc	hc	PROPN
ejpam-5330	399	19	is	be	AUX
ejpam-5330	399	20	r	r	NOUN
ejpam-5330	399	21	-	-	PUNCT
ejpam-5330	399	22	fuzzy	fuzzy	ADJ
ejpam-5330	399	23	soft	soft	ADJ
ejpam-5330	399	24	compact	compact	ADJ
ejpam-5330	399	25	.	.	PUNCT
ejpam-5330	400	1	proof	proof	NOUN
ejpam-5330	400	2	.	.	PUNCT
ejpam-5330	401	1	follows	follow	VERB
ejpam-5330	401	2	from	from	ADP
ejpam-5330	401	3	definitions	definition	NOUN
ejpam-5330	401	4	18	18	NUM
ejpam-5330	401	5	and	and	CCONJ
ejpam-5330	401	6	19	19	NUM
ejpam-5330	401	7	.	.	PUNCT
ejpam-5330	401	8	theorem	theorem	NOUN
ejpam-5330	401	9	9	9	NUM
ejpam-5330	401	10	.	.	PUNCT
ejpam-5330	402	1	let	let	VERB
ejpam-5330	402	2	φψ	φψ	NOUN
ejpam-5330	402	3	:	:	PUNCT
ejpam-5330	402	4	(	(	PUNCT
ejpam-5330	402	5	w	w	INTJ
ejpam-5330	402	6	,	,	PUNCT
ejpam-5330	402	7	τn	τn	NOUN
ejpam-5330	402	8	)	)	PUNCT
ejpam-5330	402	9	−→	−→	NOUN
ejpam-5330	402	10	(	(	PUNCT
ejpam-5330	402	11	v	v	NOUN
ejpam-5330	402	12	,	,	PUNCT
ejpam-5330	402	13	ηf	ηf	PROPN
ejpam-5330	402	14	)	)	PUNCT
ejpam-5330	402	15	be	be	AUX
ejpam-5330	402	16	a	a	DET
ejpam-5330	402	17	fuzzy	fuzzy	ADJ
ejpam-5330	402	18	soft	soft	ADJ
ejpam-5330	402	19	α	α	NOUN
ejpam-5330	402	20	-	-	ADJ
ejpam-5330	402	21	continuous	continuous	ADJ
ejpam-5330	402	22	mapping	mapping	NOUN
ejpam-5330	402	23	.	.	PUNCT
ejpam-5330	403	1	if	if	SCONJ
ejpam-5330	403	2	hc	hc	PROPN
ejpam-5330	403	3	∈	∈	PROPN
ejpam-5330	403	4	˜(w	˜(w	PROPN
ejpam-5330	403	5	,	,	PUNCT
ejpam-5330	403	6	n	n	CCONJ
ejpam-5330	403	7	)	)	PUNCT
ejpam-5330	403	8	is	be	AUX
ejpam-5330	403	9	r	r	NOUN
ejpam-5330	403	10	-	-	PUNCT
ejpam-5330	403	11	fuzzy	fuzzy	ADJ
ejpam-5330	403	12	soft	soft	ADJ
ejpam-5330	403	13	α	α	NOUN
ejpam-5330	403	14	-	-	ADJ
ejpam-5330	403	15	compact	compact	ADJ
ejpam-5330	403	16	,	,	PUNCT
ejpam-5330	403	17	then	then	ADV
ejpam-5330	403	18	φψ(hc	φψ(hc	NOUN
ejpam-5330	403	19	)	)	PUNCT
ejpam-5330	403	20	is	be	AUX
ejpam-5330	403	21	r	r	NOUN
ejpam-5330	403	22	-	-	PUNCT
ejpam-5330	403	23	fuzzy	fuzzy	ADJ
ejpam-5330	403	24	soft	soft	ADJ
ejpam-5330	403	25	compact	compact	ADJ
ejpam-5330	403	26	.	.	PUNCT
ejpam-5330	404	1	proof	proof	NOUN
ejpam-5330	404	2	.	.	PUNCT
ejpam-5330	405	1	let	let	VERB
ejpam-5330	405	2	{	{	PUNCT
ejpam-5330	405	3	(	(	PUNCT
ejpam-5330	405	4	gb)δ	gb)δ	PROPN
ejpam-5330	405	5	∈	∈	PROPN
ejpam-5330	405	6	(	(	PUNCT
ejpam-5330	405	7	̃v	̃v	NOUN
ejpam-5330	405	8	,	,	PUNCT
ejpam-5330	405	9	f	f	PROPN
ejpam-5330	405	10	)	)	PUNCT
ejpam-5330	406	1	|	|	ADV
ejpam-5330	406	2	ηk((gb)δ	ηk((gb)δ	NOUN
ejpam-5330	406	3	)	)	PUNCT
ejpam-5330	406	4	≥	≥	X
ejpam-5330	406	5	r}δ∈∆	r}δ∈∆	VERB
ejpam-5330	406	6	with	with	ADP
ejpam-5330	406	7	φψ(hc	φψ(hc	NOUN
ejpam-5330	406	8	)	)	PUNCT
ejpam-5330	406	9	⊑	⊑	X
ejpam-5330	406	10	⊔δ∈∆(gb)δ	⊔δ∈∆(gb)δ	PROPN
ejpam-5330	406	11	for	for	ADP
ejpam-5330	406	12	each	each	DET
ejpam-5330	406	13	k	k	PROPN
ejpam-5330	406	14	∈	∈	PROPN
ejpam-5330	406	15	f	f	X
ejpam-5330	406	16	.	.	PUNCT
ejpam-5330	407	1	then	then	ADV
ejpam-5330	407	2	,	,	PUNCT
ejpam-5330	407	3	{	{	PUNCT
ejpam-5330	407	4	φ−1	φ−1	PROPN
ejpam-5330	407	5	ψ	ψ	X
ejpam-5330	407	6	(	(	PUNCT
ejpam-5330	407	7	(	(	PUNCT
ejpam-5330	407	8	gb)δ	gb)δ	PROPN
ejpam-5330	407	9	)	)	PUNCT
ejpam-5330	407	10	∈	∈	PROPN
ejpam-5330	407	11	˜(w	˜(w	PROPN
ejpam-5330	407	12	,	,	PUNCT
ejpam-5330	407	13	n	n	CCONJ
ejpam-5330	407	14	)	)	PUNCT
ejpam-5330	407	15	|	|	ADV
ejpam-5330	407	16	φ−1	φ−1	PROPN
ejpam-5330	407	17	ψ	ψ	X
ejpam-5330	407	18	(	(	PUNCT
ejpam-5330	407	19	(	(	PUNCT
ejpam-5330	407	20	gb)δ	gb)δ	NOUN
ejpam-5330	407	21	)	)	PUNCT
ejpam-5330	407	22	is	be	AUX
ejpam-5330	407	23	r	r	NOUN
ejpam-5330	407	24	-	-	PUNCT
ejpam-5330	407	25	fuzzy	fuzzy	ADJ
ejpam-5330	407	26	soft	soft	ADJ
ejpam-5330	407	27	α	α	NOUN
ejpam-5330	407	28	-	-	NOUN
ejpam-5330	407	29	open}δ∈∆	open}δ∈∆	PROPN
ejpam-5330	407	30	(	(	PUNCT
ejpam-5330	407	31	by	by	ADP
ejpam-5330	407	32	φψ	φψ	PROPN
ejpam-5330	407	33	is	be	AUX
ejpam-5330	407	34	fuzzy	fuzzy	ADJ
ejpam-5330	407	35	soft	soft	ADJ
ejpam-5330	407	36	α	α	NOUN
ejpam-5330	407	37	-	-	ADJ
ejpam-5330	407	38	continuous	continuous	ADJ
ejpam-5330	407	39	)	)	PUNCT
ejpam-5330	407	40	such	such	ADJ
ejpam-5330	407	41	that	that	SCONJ
ejpam-5330	407	42	hc	hc	PROPN
ejpam-5330	407	43	⊑	⊑	PROPN
ejpam-5330	407	44	⊔δ∈∆φ−1	⊔δ∈∆φ−1	PROPN
ejpam-5330	407	45	ψ	ψ	X
ejpam-5330	407	46	(	(	PUNCT
ejpam-5330	407	47	(	(	PUNCT
ejpam-5330	407	48	gb)δ	gb)δ	PROPN
ejpam-5330	407	49	)	)	PUNCT
ejpam-5330	407	50	.	.	PUNCT
ejpam-5330	408	1	since	since	SCONJ
ejpam-5330	408	2	hc	hc	PROPN
ejpam-5330	408	3	is	be	AUX
ejpam-5330	408	4	r	r	NOUN
ejpam-5330	408	5	-	-	PUNCT
ejpam-5330	408	6	fuzzy	fuzzy	ADJ
ejpam-5330	409	1	soft	soft	ADJ
ejpam-5330	409	2	α	α	NOUN
ejpam-5330	409	3	-	-	ADJ
ejpam-5330	409	4	compact	compact	ADJ
ejpam-5330	409	5	,	,	PUNCT
ejpam-5330	409	6	there	there	PRON
ejpam-5330	409	7	is	be	VERB
ejpam-5330	409	8	a	a	DET
ejpam-5330	409	9	finite	finite	NOUN
ejpam-5330	409	10	subset	subset	NOUN
ejpam-5330	409	11	∆	∆	ADJ
ejpam-5330	409	12	◦	◦	NOUN
ejpam-5330	409	13	of	of	ADP
ejpam-5330	409	14	∆	∆	PROPN
ejpam-5330	409	15	such	such	ADJ
ejpam-5330	409	16	that	that	SCONJ
ejpam-5330	409	17	hc	hc	PROPN
ejpam-5330	409	18	⊑	⊑	PRON
ejpam-5330	409	19	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	409	20	◦	◦	NOUN
ejpam-5330	409	21	φ	φ	NUM
ejpam-5330	409	22	−1	−1	NOUN
ejpam-5330	409	23	ψ	ψ	PROPN
ejpam-5330	409	24	(	(	PUNCT
ejpam-5330	409	25	(	(	PUNCT
ejpam-5330	409	26	gb)δ	gb)δ	PROPN
ejpam-5330	409	27	)	)	PUNCT
ejpam-5330	409	28	.	.	PUNCT
ejpam-5330	410	1	then	then	ADV
ejpam-5330	410	2	,	,	PUNCT
ejpam-5330	410	3	φψ(hc	φψ(hc	NOUN
ejpam-5330	410	4	)	)	PUNCT
ejpam-5330	410	5	⊑	⊑	PART
ejpam-5330	411	1	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	411	2	◦	◦	NOUN
ejpam-5330	411	3	(gb)δ	(gb)δ	NOUN
ejpam-5330	411	4	.	.	PUNCT
ejpam-5330	412	1	hence	hence	ADV
ejpam-5330	412	2	,	,	PUNCT
ejpam-5330	412	3	the	the	DET
ejpam-5330	412	4	proof	proof	NOUN
ejpam-5330	412	5	is	be	AUX
ejpam-5330	412	6	completed	complete	VERB
ejpam-5330	412	7	.	.	PUNCT
ejpam-5330	413	1	definition	definition	NOUN
ejpam-5330	413	2	20	20	NUM
ejpam-5330	413	3	.	.	PUNCT
ejpam-5330	414	1	let	let	AUX
ejpam-5330	414	2	(	(	PUNCT
ejpam-5330	414	3	w	w	NOUN
ejpam-5330	414	4	,	,	PUNCT
ejpam-5330	414	5	τn	τn	PART
ejpam-5330	414	6	)	)	PUNCT
ejpam-5330	414	7	be	be	AUX
ejpam-5330	414	8	an	an	DET
ejpam-5330	414	9	fsts	fst	NOUN
ejpam-5330	414	10	and	and	CCONJ
ejpam-5330	414	11	r	r	NOUN
ejpam-5330	414	12	∈	∈	PROPN
ejpam-5330	414	13	i	i	PRON
ejpam-5330	414	14	◦	◦	NOUN
ejpam-5330	414	15	,	,	PUNCT
ejpam-5330	414	16	then	then	ADV
ejpam-5330	414	17	hc	hc	PROPN
ejpam-5330	414	18	∈	∈	PROPN
ejpam-5330	414	19	˜(w	˜(w	PROPN
ejpam-5330	414	20	,	,	PUNCT
ejpam-5330	414	21	n	n	CCONJ
ejpam-5330	414	22	)	)	PUNCT
ejpam-5330	414	23	is	be	AUX
ejpam-5330	414	24	called	call	VERB
ejpam-5330	414	25	an	an	DET
ejpam-5330	414	26	r	r	NOUN
ejpam-5330	414	27	-	-	PUNCT
ejpam-5330	414	28	fuzzy	fuzzy	ADJ
ejpam-5330	414	29	soft	soft	ADJ
ejpam-5330	414	30	almost	almost	ADV
ejpam-5330	414	31	compact	compact	ADJ
ejpam-5330	414	32	iff	iff	NOUN
ejpam-5330	414	33	for	for	ADP
ejpam-5330	414	34	every	every	DET
ejpam-5330	414	35	family	family	NOUN
ejpam-5330	414	36	{	{	PUNCT
ejpam-5330	414	37	(	(	PUNCT
ejpam-5330	414	38	gb)δ	gb)δ	PROPN
ejpam-5330	414	39	∈	∈	PROPN
ejpam-5330	414	40	˜(w	˜(w	PROPN
ejpam-5330	414	41	,	,	PUNCT
ejpam-5330	414	42	n	n	CCONJ
ejpam-5330	414	43	)	)	PUNCT
ejpam-5330	414	44	|	|	ADV
ejpam-5330	414	45	τn((gb)δ	τn((gb)δ	ADP
ejpam-5330	414	46	)	)	PUNCT
ejpam-5330	414	47	≥	≥	NOUN
ejpam-5330	414	48	r}δ∈∆	r}δ∈∆	NOUN
ejpam-5330	414	49	,	,	PUNCT
ejpam-5330	414	50	such	such	ADJ
ejpam-5330	414	51	that	that	SCONJ
ejpam-5330	414	52	hc	hc	PROPN
ejpam-5330	414	53	⊑	⊑	PROPN
ejpam-5330	414	54	⊔δ∈∆(gb)δ	⊔δ∈∆(gb)δ	PROPN
ejpam-5330	414	55	,	,	PUNCT
ejpam-5330	414	56	there	there	PRON
ejpam-5330	414	57	is	be	VERB
ejpam-5330	414	58	a	a	DET
ejpam-5330	414	59	finite	finite	NOUN
ejpam-5330	414	60	subset	subset	NOUN
ejpam-5330	414	61	∆	∆	ADJ
ejpam-5330	414	62	◦	◦	NOUN
ejpam-5330	414	63	of	of	ADP
ejpam-5330	414	64	∆	∆	PROPN
ejpam-5330	414	65	,	,	PUNCT
ejpam-5330	414	66	such	such	ADJ
ejpam-5330	414	67	that	that	SCONJ
ejpam-5330	414	68	hc	hc	PROPN
ejpam-5330	414	69	⊑	⊑	PRON
ejpam-5330	414	70	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	414	71	◦	◦	NOUN
ejpam-5330	414	72	cτ	cτ	NOUN
ejpam-5330	414	73	(	(	PUNCT
ejpam-5330	414	74	n	n	X
ejpam-5330	414	75	,	,	PUNCT
ejpam-5330	414	76	(	(	PUNCT
ejpam-5330	414	77	gb)δ	gb)δ	PROPN
ejpam-5330	414	78	,	,	PUNCT
ejpam-5330	414	79	r	r	NOUN
ejpam-5330	414	80	)	)	PUNCT
ejpam-5330	414	81	for	for	ADP
ejpam-5330	414	82	each	each	DET
ejpam-5330	414	83	n	n	PRON
ejpam-5330	414	84	∈	∈	PROPN
ejpam-5330	414	85	n	n	X
ejpam-5330	414	86	.	.	PUNCT
ejpam-5330	415	1	definition	definition	NOUN
ejpam-5330	415	2	21	21	NUM
ejpam-5330	415	3	.	.	PUNCT
ejpam-5330	416	1	let	let	AUX
ejpam-5330	416	2	(	(	PUNCT
ejpam-5330	416	3	w	w	NOUN
ejpam-5330	416	4	,	,	PUNCT
ejpam-5330	416	5	τn	τn	PART
ejpam-5330	416	6	)	)	PUNCT
ejpam-5330	416	7	be	be	AUX
ejpam-5330	416	8	an	an	DET
ejpam-5330	416	9	fsts	fst	NOUN
ejpam-5330	416	10	and	and	CCONJ
ejpam-5330	416	11	r	r	NOUN
ejpam-5330	416	12	∈	∈	PROPN
ejpam-5330	416	13	i	i	PRON
ejpam-5330	416	14	◦	◦	NOUN
ejpam-5330	416	15	,	,	PUNCT
ejpam-5330	416	16	then	then	ADV
ejpam-5330	416	17	hc	hc	PROPN
ejpam-5330	416	18	∈	∈	PROPN
ejpam-5330	416	19	˜(w	˜(w	PROPN
ejpam-5330	416	20	,	,	PUNCT
ejpam-5330	416	21	n	n	CCONJ
ejpam-5330	416	22	)	)	PUNCT
ejpam-5330	416	23	is	be	AUX
ejpam-5330	416	24	called	call	VERB
ejpam-5330	416	25	an	an	DET
ejpam-5330	416	26	r	r	NOUN
ejpam-5330	416	27	-	-	PUNCT
ejpam-5330	416	28	fuzzy	fuzzy	ADJ
ejpam-5330	416	29	soft	soft	ADJ
ejpam-5330	416	30	almost	almost	ADV
ejpam-5330	416	31	α	α	ADJ
ejpam-5330	416	32	-	-	ADJ
ejpam-5330	416	33	compact	compact	ADJ
ejpam-5330	416	34	iff	iff	NOUN
ejpam-5330	416	35	for	for	ADP
ejpam-5330	416	36	every	every	DET
ejpam-5330	416	37	family	family	NOUN
ejpam-5330	416	38	{	{	PUNCT
ejpam-5330	416	39	(	(	PUNCT
ejpam-5330	416	40	gb)δ	gb)δ	PROPN
ejpam-5330	416	41	∈	∈	PROPN
ejpam-5330	416	42	˜(w	˜(w	PROPN
ejpam-5330	416	43	,	,	PUNCT
ejpam-5330	416	44	n	n	CCONJ
ejpam-5330	416	45	)	)	PUNCT
ejpam-5330	417	1	|	|	ADV
ejpam-5330	417	2	(	(	PUNCT
ejpam-5330	417	3	gb)δ	gb)δ	PROPN
ejpam-5330	417	4	is	be	AUX
ejpam-5330	417	5	r	r	NOUN
ejpam-5330	417	6	-	-	PUNCT
ejpam-5330	417	7	fuzzy	fuzzy	ADJ
ejpam-5330	417	8	soft	soft	ADJ
ejpam-5330	417	9	α	α	NOUN
ejpam-5330	417	10	-	-	PUNCT
ejpam-5330	417	11	open}δ∈∆	open}δ∈∆	NOUN
ejpam-5330	417	12	,	,	PUNCT
ejpam-5330	417	13	such	such	ADJ
ejpam-5330	417	14	that	that	SCONJ
ejpam-5330	417	15	hc	hc	PROPN
ejpam-5330	417	16	⊑	⊑	PROPN
ejpam-5330	417	17	⊔δ∈∆(gb)δ	⊔δ∈∆(gb)δ	PROPN
ejpam-5330	417	18	,	,	PUNCT
ejpam-5330	417	19	there	there	PRON
ejpam-5330	417	20	is	be	VERB
ejpam-5330	417	21	a	a	DET
ejpam-5330	417	22	finite	finite	NOUN
ejpam-5330	417	23	subset	subset	NOUN
ejpam-5330	417	24	∆	∆	ADJ
ejpam-5330	417	25	◦	◦	NOUN
ejpam-5330	417	26	of	of	ADP
ejpam-5330	417	27	∆	∆	PROPN
ejpam-5330	417	28	,	,	PUNCT
ejpam-5330	417	29	such	such	ADJ
ejpam-5330	417	30	that	that	SCONJ
ejpam-5330	417	31	hc	hc	PROPN
ejpam-5330	417	32	⊑	⊑	PRON
ejpam-5330	417	33	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	417	34	◦	◦	NOUN
ejpam-5330	417	35	cτ	cτ	NOUN
ejpam-5330	417	36	(	(	PUNCT
ejpam-5330	417	37	n	n	X
ejpam-5330	417	38	,	,	PUNCT
ejpam-5330	417	39	(	(	PUNCT
ejpam-5330	417	40	gb)δ	gb)δ	PROPN
ejpam-5330	417	41	,	,	PUNCT
ejpam-5330	417	42	r	r	NOUN
ejpam-5330	417	43	)	)	PUNCT
ejpam-5330	417	44	for	for	ADP
ejpam-5330	417	45	each	each	DET
ejpam-5330	417	46	n	n	PRON
ejpam-5330	417	47	∈	∈	PROPN
ejpam-5330	417	48	n	n	X
ejpam-5330	417	49	.	.	PUNCT
ejpam-5330	418	1	lemma	lemma	PROPN
ejpam-5330	418	2	7	7	X
ejpam-5330	418	3	.	.	PUNCT
ejpam-5330	419	1	let	let	AUX
ejpam-5330	419	2	(	(	PUNCT
ejpam-5330	419	3	w	w	NOUN
ejpam-5330	419	4	,	,	PUNCT
ejpam-5330	419	5	τn	τn	PART
ejpam-5330	419	6	)	)	PUNCT
ejpam-5330	419	7	be	be	AUX
ejpam-5330	419	8	an	an	DET
ejpam-5330	419	9	fsts	fst	NOUN
ejpam-5330	419	10	and	and	CCONJ
ejpam-5330	419	11	r	r	NOUN
ejpam-5330	419	12	∈	∈	PROPN
ejpam-5330	419	13	i	i	X
ejpam-5330	419	14	◦	◦	NOUN
ejpam-5330	419	15	.	.	PUNCT
ejpam-5330	420	1	if	if	SCONJ
ejpam-5330	420	2	hc	hc	PROPN
ejpam-5330	420	3	∈	∈	PROPN
ejpam-5330	420	4	˜(w	˜(w	PROPN
ejpam-5330	420	5	,	,	PUNCT
ejpam-5330	420	6	n	n	CCONJ
ejpam-5330	420	7	)	)	PUNCT
ejpam-5330	420	8	is	be	AUX
ejpam-5330	420	9	r	r	NOUN
ejpam-5330	420	10	-	-	PUNCT
ejpam-5330	420	11	fuzzy	fuzzy	ADJ
ejpam-5330	420	12	soft	soft	ADJ
ejpam-5330	420	13	almost	almost	ADV
ejpam-5330	420	14	α	α	NOUN
ejpam-5330	420	15	-	-	ADJ
ejpam-5330	420	16	compact	compact	ADJ
ejpam-5330	420	17	,	,	PUNCT
ejpam-5330	420	18	then	then	ADV
ejpam-5330	420	19	hc	hc	PROPN
ejpam-5330	420	20	is	be	AUX
ejpam-5330	420	21	r	r	NOUN
ejpam-5330	420	22	-	-	PUNCT
ejpam-5330	420	23	fuzzy	fuzzy	ADJ
ejpam-5330	420	24	soft	soft	ADJ
ejpam-5330	420	25	almost	almost	ADV
ejpam-5330	420	26	compact	compact	ADJ
ejpam-5330	420	27	.	.	PUNCT
ejpam-5330	421	1	proof	proof	NOUN
ejpam-5330	421	2	.	.	PUNCT
ejpam-5330	422	1	follows	follow	VERB
ejpam-5330	422	2	from	from	ADP
ejpam-5330	422	3	definitions	definition	NOUN
ejpam-5330	422	4	20	20	NUM
ejpam-5330	422	5	and	and	CCONJ
ejpam-5330	422	6	21	21	NUM
ejpam-5330	422	7	.	.	PUNCT
ejpam-5330	423	1	lemma	lemma	PROPN
ejpam-5330	423	2	8	8	NUM
ejpam-5330	423	3	.	.	PUNCT
ejpam-5330	424	1	let	let	AUX
ejpam-5330	424	2	(	(	PUNCT
ejpam-5330	424	3	w	w	NOUN
ejpam-5330	424	4	,	,	PUNCT
ejpam-5330	424	5	τn	τn	PART
ejpam-5330	424	6	)	)	PUNCT
ejpam-5330	424	7	be	be	AUX
ejpam-5330	424	8	an	an	DET
ejpam-5330	424	9	fsts	fst	NOUN
ejpam-5330	424	10	and	and	CCONJ
ejpam-5330	424	11	r	r	NOUN
ejpam-5330	424	12	∈	∈	PROPN
ejpam-5330	424	13	i	i	X
ejpam-5330	424	14	◦	◦	NOUN
ejpam-5330	424	15	.	.	PUNCT
ejpam-5330	425	1	if	if	SCONJ
ejpam-5330	425	2	hc	hc	PROPN
ejpam-5330	425	3	∈	∈	PROPN
ejpam-5330	425	4	˜(w	˜(w	PROPN
ejpam-5330	425	5	,	,	PUNCT
ejpam-5330	425	6	n	n	CCONJ
ejpam-5330	425	7	)	)	PUNCT
ejpam-5330	425	8	is	be	AUX
ejpam-5330	425	9	r	r	NOUN
ejpam-5330	425	10	-	-	PUNCT
ejpam-5330	425	11	fuzzy	fuzzy	ADJ
ejpam-5330	425	12	soft	soft	ADJ
ejpam-5330	425	13	compact	compact	ADJ
ejpam-5330	425	14	(	(	PUNCT
ejpam-5330	425	15	resp	resp	NOUN
ejpam-5330	425	16	.	.	PUNCT
ejpam-5330	425	17	,	,	PUNCT
ejpam-5330	425	18	α	α	NOUN
ejpam-5330	425	19	-	-	ADJ
ejpam-5330	425	20	compact	compact	ADJ
ejpam-5330	425	21	)	)	PUNCT
ejpam-5330	425	22	,	,	PUNCT
ejpam-5330	425	23	then	then	ADV
ejpam-5330	425	24	hc	hc	PROPN
ejpam-5330	425	25	is	be	AUX
ejpam-5330	425	26	r	r	NOUN
ejpam-5330	425	27	-	-	PUNCT
ejpam-5330	425	28	fuzzy	fuzzy	ADJ
ejpam-5330	425	29	soft	soft	ADJ
ejpam-5330	425	30	almost	almost	ADV
ejpam-5330	425	31	compact	compact	ADJ
ejpam-5330	425	32	(	(	PUNCT
ejpam-5330	425	33	resp	resp	NOUN
ejpam-5330	425	34	.	.	PUNCT
ejpam-5330	425	35	,	,	PUNCT
ejpam-5330	425	36	almost	almost	ADV
ejpam-5330	425	37	α	α	NOUN
ejpam-5330	425	38	-	-	ADJ
ejpam-5330	425	39	compact	compact	ADJ
ejpam-5330	425	40	)	)	PUNCT
ejpam-5330	425	41	.	.	PUNCT
ejpam-5330	426	1	proof	proof	NOUN
ejpam-5330	426	2	.	.	PUNCT
ejpam-5330	427	1	follows	follow	VERB
ejpam-5330	427	2	from	from	ADP
ejpam-5330	427	3	definitions	definition	NOUN
ejpam-5330	427	4	18	18	NUM
ejpam-5330	427	5	,	,	PUNCT
ejpam-5330	427	6	19	19	NUM
ejpam-5330	427	7	,	,	PUNCT
ejpam-5330	427	8	20	20	NUM
ejpam-5330	427	9	,	,	PUNCT
ejpam-5330	427	10	and	and	CCONJ
ejpam-5330	428	1	21	21	NUM
ejpam-5330	428	2	.	.	PUNCT
ejpam-5330	428	3	remark	remark	PROPN
ejpam-5330	428	4	8	8	NUM
ejpam-5330	428	5	.	.	PUNCT
ejpam-5330	429	1	the	the	DET
ejpam-5330	429	2	converse	converse	NOUN
ejpam-5330	429	3	of	of	ADP
ejpam-5330	429	4	lemma	lemma	PROPN
ejpam-5330	429	5	8	8	NUM
ejpam-5330	429	6	may	may	AUX
ejpam-5330	429	7	not	not	PART
ejpam-5330	429	8	be	be	AUX
ejpam-5330	429	9	true	true	ADJ
ejpam-5330	429	10	,	,	PUNCT
ejpam-5330	429	11	as	as	SCONJ
ejpam-5330	429	12	shown	show	VERB
ejpam-5330	429	13	by	by	ADP
ejpam-5330	429	14	example	example	NOUN
ejpam-5330	429	15	6	6	NUM
ejpam-5330	429	16	.	.	PUNCT
ejpam-5330	429	17	w.	w.	PROPN
ejpam-5330	429	18	alqurashi	alqurashi	PROPN
ejpam-5330	429	19	,	,	PUNCT
ejpam-5330	429	20	i.	i.	PROPN
ejpam-5330	429	21	m.	m.	PROPN
ejpam-5330	429	22	taha	taha	PROPN
ejpam-5330	429	23	/	/	PUNCT
ejpam-5330	429	24	eur	eur	PROPN
ejpam-5330	429	25	.	.	PUNCT
ejpam-5330	430	1	j.	j.	PROPN
ejpam-5330	430	2	pure	pure	PROPN
ejpam-5330	430	3	appl	appl	PROPN
ejpam-5330	430	4	.	.	PROPN
ejpam-5330	430	5	math	math	PROPN
ejpam-5330	430	6	,	,	PUNCT
ejpam-5330	430	7	17	17	NUM
ejpam-5330	430	8	(	(	PUNCT
ejpam-5330	430	9	4	4	NUM
ejpam-5330	430	10	)	)	PUNCT
ejpam-5330	430	11	(	(	PUNCT
ejpam-5330	430	12	2024	2024	NUM
ejpam-5330	430	13	)	)	PUNCT
ejpam-5330	430	14	,	,	PUNCT
ejpam-5330	430	15	4112	4112	NUM
ejpam-5330	430	16	-	-	SYM
ejpam-5330	430	17	4134	4134	NUM
ejpam-5330	430	18	4128	4128	NUM
ejpam-5330	430	19	example	example	NOUN
ejpam-5330	430	20	6	6	NUM
ejpam-5330	430	21	.	.	PUNCT
ejpam-5330	431	1	let	let	AUX
ejpam-5330	431	2	v	v	VERB
ejpam-5330	431	3	=	=	SYM
ejpam-5330	431	4	i	i	PROPN
ejpam-5330	431	5	,	,	PUNCT
ejpam-5330	431	6	n	n	PROPN
ejpam-5330	431	7	∈	∈	PROPN
ejpam-5330	431	8	n	n	PRON
ejpam-5330	431	9	−{1	−{1	NUM
ejpam-5330	431	10	}	}	PUNCT
ejpam-5330	431	11	,	,	PUNCT
ejpam-5330	431	12	and	and	CCONJ
ejpam-5330	431	13	f	f	X
ejpam-5330	431	14	=	=	SYM
ejpam-5330	431	15	{	{	PUNCT
ejpam-5330	431	16	k1	k1	PROPN
ejpam-5330	431	17	,	,	PUNCT
ejpam-5330	431	18	k2	k2	NOUN
ejpam-5330	431	19	}	}	PUNCT
ejpam-5330	431	20	be	be	VERB
ejpam-5330	431	21	the	the	DET
ejpam-5330	431	22	parameter	parameter	NOUN
ejpam-5330	431	23	set	set	NOUN
ejpam-5330	431	24	of	of	ADP
ejpam-5330	431	25	v.	v.	ADP
ejpam-5330	431	26	define	define	VERB
ejpam-5330	431	27	gfn	gfn	NOUN
ejpam-5330	431	28	and	and	CCONJ
ejpam-5330	431	29	ff1	ff1	PROPN
ejpam-5330	431	30	∈	∈	PROPN
ejpam-5330	431	31	(	(	PUNCT
ejpam-5330	431	32	̃v	̃v	NOUN
ejpam-5330	431	33	,	,	PUNCT
ejpam-5330	431	34	f	f	PROPN
ejpam-5330	431	35	)	)	PUNCT
ejpam-5330	431	36	as	as	SCONJ
ejpam-5330	431	37	follows	follow	VERB
ejpam-5330	431	38	∀	∀	X
ejpam-5330	432	1	k	k	PROPN
ejpam-5330	432	2	∈	∈	PROPN
ejpam-5330	432	3	f	f	X
ejpam-5330	432	4	:	:	PUNCT
ejpam-5330	432	5	gfn(k)(v	gfn(k)(v	X
ejpam-5330	432	6	)	)	PUNCT
ejpam-5330	432	7	=	=	SYM
ejpam-5330	433	1			NOUN
ejpam-5330	433	2	0.8	0.8	NUM
ejpam-5330	433	3	,	,	PUNCT
ejpam-5330	433	4	if	if	SCONJ
ejpam-5330	433	5	v	v	NOUN
ejpam-5330	433	6	=	=	SYM
ejpam-5330	433	7	0	0	NUM
ejpam-5330	433	8	,	,	PUNCT
ejpam-5330	433	9	nv	nv	PROPN
ejpam-5330	433	10	,	,	PUNCT
ejpam-5330	433	11	if	if	SCONJ
ejpam-5330	433	12	0	0	NUM
ejpam-5330	433	13	<	<	X
ejpam-5330	433	14	v	v	X
ejpam-5330	433	15	≤	≤	NUM
ejpam-5330	433	16	1	1	NUM
ejpam-5330	433	17	n	n	NOUN
ejpam-5330	433	18	,	,	PUNCT
ejpam-5330	433	19	1	1	NUM
ejpam-5330	433	20	,	,	PUNCT
ejpam-5330	433	21	if	if	SCONJ
ejpam-5330	433	22	1	1	NUM
ejpam-5330	433	23	n	n	ADV
ejpam-5330	433	24	<	<	X
ejpam-5330	433	25	v	v	X
ejpam-5330	433	26	≤	≤	NUM
ejpam-5330	433	27	1	1	NUM
ejpam-5330	433	28	,	,	PUNCT
ejpam-5330	433	29	ff1(k)(v	ff1(k)(v	X
ejpam-5330	433	30	)	)	PUNCT
ejpam-5330	434	1	=	=	PRON
ejpam-5330	434	2	{	{	PUNCT
ejpam-5330	434	3	1	1	NUM
ejpam-5330	434	4	,	,	PUNCT
ejpam-5330	434	5	if	if	SCONJ
ejpam-5330	434	6	v	v	NOUN
ejpam-5330	434	7	=	=	SYM
ejpam-5330	434	8	0	0	NUM
ejpam-5330	434	9	,	,	PUNCT
ejpam-5330	434	10	1	1	NUM
ejpam-5330	434	11	2	2	NUM
ejpam-5330	434	12	,	,	PUNCT
ejpam-5330	434	13	otherwise	otherwise	ADV
ejpam-5330	434	14	.	.	PUNCT
ejpam-5330	435	1	define	define	VERB
ejpam-5330	435	2	fuzzy	fuzzy	ADJ
ejpam-5330	435	3	soft	soft	ADJ
ejpam-5330	435	4	topology	topology	NOUN
ejpam-5330	435	5	ηf	ηf	NOUN
ejpam-5330	435	6	:	:	PUNCT
ejpam-5330	435	7	f	f	X
ejpam-5330	436	1	−→	−→	NOUN
ejpam-5330	436	2	[	[	X
ejpam-5330	436	3	0	0	NUM
ejpam-5330	436	4	,	,	PUNCT
ejpam-5330	436	5	1](̃v	1](̃v	NUM
ejpam-5330	436	6	,	,	PUNCT
ejpam-5330	436	7	f	f	PROPN
ejpam-5330	436	8	)	)	PUNCT
ejpam-5330	436	9	as	as	SCONJ
ejpam-5330	436	10	follows	follow	VERB
ejpam-5330	436	11	:	:	PUNCT
ejpam-5330	436	12	∀k	∀k	X
ejpam-5330	436	13	∈	∈	PROPN
ejpam-5330	436	14	f	f	PROPN
ejpam-5330	436	15	,	,	PUNCT
ejpam-5330	436	16	ηk(tf	ηk(tf	PROPN
ejpam-5330	436	17	)	)	PUNCT
ejpam-5330	437	1	=	=	PUNCT
ejpam-5330	437	2			VERB
ejpam-5330	437	3	4	4	NUM
ejpam-5330	437	4	5	5	NUM
ejpam-5330	437	5	,	,	PUNCT
ejpam-5330	437	6	if	if	SCONJ
ejpam-5330	437	7	tf	tf	PROPN
ejpam-5330	437	8	∈	∈	PROPN
ejpam-5330	437	9	{	{	PUNCT
ejpam-5330	437	10	φ	φ	PROPN
ejpam-5330	437	11	,	,	PUNCT
ejpam-5330	437	12	f̃	f̃	PROPN
ejpam-5330	437	13	}	}	PUNCT
ejpam-5330	437	14	,	,	PUNCT
ejpam-5330	437	15	2	2	NUM
ejpam-5330	437	16	3	3	NUM
ejpam-5330	437	17	,	,	PUNCT
ejpam-5330	437	18	if	if	SCONJ
ejpam-5330	437	19	tf	tf	PROPN
ejpam-5330	437	20	≤	≤	NUM
ejpam-5330	437	21	ff1	ff1	NOUN
ejpam-5330	437	22	,	,	PUNCT
ejpam-5330	437	23	n	n	PROPN
ejpam-5330	437	24	n+1	n+1	PROPN
ejpam-5330	437	25	,	,	PUNCT
ejpam-5330	437	26	if	if	SCONJ
ejpam-5330	437	27	tf	tf	PROPN
ejpam-5330	437	28	≤	≤	PROPN
ejpam-5330	437	29	gfn	gfn	NOUN
ejpam-5330	437	30	,	,	PUNCT
ejpam-5330	437	31	0	0	NUM
ejpam-5330	437	32	,	,	PUNCT
ejpam-5330	437	33	otherwise	otherwise	ADV
ejpam-5330	437	34	.	.	PUNCT
ejpam-5330	438	1	thus	thus	ADV
ejpam-5330	438	2	,	,	PUNCT
ejpam-5330	438	3	v	v	NOUN
ejpam-5330	438	4	is	be	AUX
ejpam-5330	438	5	1	1	NUM
ejpam-5330	438	6	2	2	NUM
ejpam-5330	438	7	-fuzzy	-fuzzy	NOUN
ejpam-5330	438	8	soft	soft	ADJ
ejpam-5330	438	9	almost	almost	ADV
ejpam-5330	438	10	compact	compact	ADJ
ejpam-5330	438	11	,	,	PUNCT
ejpam-5330	438	12	but	but	CCONJ
ejpam-5330	438	13	it	it	PRON
ejpam-5330	438	14	is	be	AUX
ejpam-5330	438	15	not	not	PART
ejpam-5330	438	16	1	1	NUM
ejpam-5330	438	17	2	2	NUM
ejpam-5330	438	18	-fuzzy	-fuzzy	NOUN
ejpam-5330	438	19	soft	soft	ADJ
ejpam-5330	438	20	compact	compact	ADJ
ejpam-5330	438	21	.	.	PUNCT
ejpam-5330	439	1	theorem	theorem	ADJ
ejpam-5330	439	2	10	10	NUM
ejpam-5330	439	3	.	.	PUNCT
ejpam-5330	440	1	let	let	VERB
ejpam-5330	440	2	φψ	φψ	NOUN
ejpam-5330	440	3	:	:	PUNCT
ejpam-5330	440	4	(	(	PUNCT
ejpam-5330	440	5	w	w	INTJ
ejpam-5330	440	6	,	,	PUNCT
ejpam-5330	440	7	τn	τn	NOUN
ejpam-5330	440	8	)	)	PUNCT
ejpam-5330	440	9	−→	−→	NOUN
ejpam-5330	440	10	(	(	PUNCT
ejpam-5330	440	11	v	v	NOUN
ejpam-5330	440	12	,	,	PUNCT
ejpam-5330	440	13	ηf	ηf	PROPN
ejpam-5330	440	14	)	)	PUNCT
ejpam-5330	440	15	be	be	AUX
ejpam-5330	440	16	a	a	DET
ejpam-5330	440	17	fuzzy	fuzzy	ADJ
ejpam-5330	440	18	soft	soft	ADJ
ejpam-5330	440	19	continuous	continuous	ADJ
ejpam-5330	440	20	mapping	mapping	NOUN
ejpam-5330	440	21	.	.	PUNCT
ejpam-5330	441	1	if	if	SCONJ
ejpam-5330	441	2	hc	hc	PROPN
ejpam-5330	441	3	∈	∈	PROPN
ejpam-5330	441	4	˜(w	˜(w	PROPN
ejpam-5330	441	5	,	,	PUNCT
ejpam-5330	441	6	n	n	CCONJ
ejpam-5330	441	7	)	)	PUNCT
ejpam-5330	441	8	is	be	AUX
ejpam-5330	441	9	r	r	NOUN
ejpam-5330	441	10	-	-	PUNCT
ejpam-5330	441	11	fuzzy	fuzzy	ADJ
ejpam-5330	441	12	soft	soft	ADJ
ejpam-5330	441	13	almost	almost	ADV
ejpam-5330	441	14	α	α	NOUN
ejpam-5330	441	15	-	-	ADJ
ejpam-5330	441	16	compact	compact	ADJ
ejpam-5330	441	17	,	,	PUNCT
ejpam-5330	441	18	then	then	ADV
ejpam-5330	441	19	φψ(hc	φψ(hc	NOUN
ejpam-5330	441	20	)	)	PUNCT
ejpam-5330	441	21	is	be	AUX
ejpam-5330	441	22	r	r	NOUN
ejpam-5330	441	23	-	-	PUNCT
ejpam-5330	441	24	fuzzy	fuzzy	ADJ
ejpam-5330	441	25	soft	soft	ADJ
ejpam-5330	441	26	almost	almost	ADV
ejpam-5330	441	27	compact	compact	ADJ
ejpam-5330	441	28	.	.	PUNCT
ejpam-5330	442	1	proof	proof	NOUN
ejpam-5330	442	2	.	.	PUNCT
ejpam-5330	443	1	let	let	VERB
ejpam-5330	443	2	{	{	PUNCT
ejpam-5330	443	3	(	(	PUNCT
ejpam-5330	443	4	gb)δ	gb)δ	PROPN
ejpam-5330	443	5	∈	∈	PROPN
ejpam-5330	443	6	(	(	PUNCT
ejpam-5330	443	7	̃v	̃v	NOUN
ejpam-5330	443	8	,	,	PUNCT
ejpam-5330	443	9	f	f	PROPN
ejpam-5330	443	10	)	)	PUNCT
ejpam-5330	444	1	|	|	ADV
ejpam-5330	444	2	ηk((gb)δ	ηk((gb)δ	NOUN
ejpam-5330	444	3	)	)	PUNCT
ejpam-5330	444	4	≥	≥	X
ejpam-5330	444	5	r}δ∈∆	r}δ∈∆	VERB
ejpam-5330	444	6	with	with	ADP
ejpam-5330	444	7	φψ(hc	φψ(hc	NOUN
ejpam-5330	444	8	)	)	PUNCT
ejpam-5330	444	9	⊑	⊑	X
ejpam-5330	444	10	⊔δ∈∆(gb)δ	⊔δ∈∆(gb)δ	PROPN
ejpam-5330	444	11	for	for	ADP
ejpam-5330	444	12	each	each	DET
ejpam-5330	444	13	k	k	PROPN
ejpam-5330	444	14	∈	∈	PROPN
ejpam-5330	444	15	f	f	X
ejpam-5330	444	16	.	.	PUNCT
ejpam-5330	445	1	then	then	ADV
ejpam-5330	445	2	,	,	PUNCT
ejpam-5330	445	3	{	{	PUNCT
ejpam-5330	445	4	φ−1	φ−1	PROPN
ejpam-5330	445	5	ψ	ψ	X
ejpam-5330	445	6	(	(	PUNCT
ejpam-5330	445	7	(	(	PUNCT
ejpam-5330	445	8	gb)δ	gb)δ	PROPN
ejpam-5330	445	9	)	)	PUNCT
ejpam-5330	445	10	∈	∈	PROPN
ejpam-5330	445	11	˜(w	˜(w	PROPN
ejpam-5330	445	12	,	,	PUNCT
ejpam-5330	445	13	n	n	CCONJ
ejpam-5330	445	14	)	)	PUNCT
ejpam-5330	445	15	|	|	ADV
ejpam-5330	445	16	φ−1	φ−1	PROPN
ejpam-5330	445	17	ψ	ψ	X
ejpam-5330	445	18	(	(	PUNCT
ejpam-5330	445	19	(	(	PUNCT
ejpam-5330	445	20	gb)δ	gb)δ	NOUN
ejpam-5330	445	21	)	)	PUNCT
ejpam-5330	445	22	is	be	AUX
ejpam-5330	445	23	r	r	NOUN
ejpam-5330	445	24	-	-	PUNCT
ejpam-5330	445	25	fuzzy	fuzzy	ADJ
ejpam-5330	445	26	soft	soft	ADJ
ejpam-5330	445	27	α	α	NOUN
ejpam-5330	445	28	-	-	NOUN
ejpam-5330	445	29	open}δ∈∆	open}δ∈∆	PROPN
ejpam-5330	445	30	(	(	PUNCT
ejpam-5330	445	31	by	by	ADP
ejpam-5330	445	32	φψ	φψ	PROPN
ejpam-5330	445	33	is	be	AUX
ejpam-5330	445	34	fuzzy	fuzzy	ADJ
ejpam-5330	445	35	soft	soft	ADJ
ejpam-5330	445	36	α	α	NOUN
ejpam-5330	445	37	-	-	ADJ
ejpam-5330	445	38	continuous	continuous	ADJ
ejpam-5330	445	39	)	)	PUNCT
ejpam-5330	445	40	such	such	ADJ
ejpam-5330	445	41	that	that	SCONJ
ejpam-5330	445	42	hc	hc	PROPN
ejpam-5330	445	43	⊑	⊑	PROPN
ejpam-5330	445	44	⊔δ∈∆φ−1	⊔δ∈∆φ−1	PROPN
ejpam-5330	445	45	ψ	ψ	X
ejpam-5330	445	46	(	(	PUNCT
ejpam-5330	445	47	(	(	PUNCT
ejpam-5330	445	48	gb)δ	gb)δ	PROPN
ejpam-5330	445	49	)	)	PUNCT
ejpam-5330	445	50	.	.	PUNCT
ejpam-5330	446	1	since	since	SCONJ
ejpam-5330	446	2	hc	hc	PROPN
ejpam-5330	446	3	is	be	AUX
ejpam-5330	446	4	r	r	NOUN
ejpam-5330	446	5	-	-	PUNCT
ejpam-5330	446	6	fuzzy	fuzzy	ADJ
ejpam-5330	446	7	soft	soft	ADJ
ejpam-5330	446	8	almost	almost	ADV
ejpam-5330	446	9	α	α	NOUN
ejpam-5330	446	10	-	-	ADJ
ejpam-5330	446	11	compact	compact	ADJ
ejpam-5330	446	12	,	,	PUNCT
ejpam-5330	446	13	there	there	PRON
ejpam-5330	446	14	is	be	VERB
ejpam-5330	446	15	a	a	DET
ejpam-5330	446	16	finite	finite	NOUN
ejpam-5330	446	17	subset	subset	NOUN
ejpam-5330	446	18	∆	∆	ADJ
ejpam-5330	446	19	◦	◦	NOUN
ejpam-5330	446	20	of	of	ADP
ejpam-5330	446	21	∆	∆	PROPN
ejpam-5330	446	22	such	such	ADJ
ejpam-5330	446	23	that	that	SCONJ
ejpam-5330	446	24	hc	hc	PROPN
ejpam-5330	446	25	⊑	⊑	PRON
ejpam-5330	446	26	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	446	27	◦	◦	NOUN
ejpam-5330	446	28	cτ	cτ	NOUN
ejpam-5330	446	29	(	(	PUNCT
ejpam-5330	446	30	n	n	CCONJ
ejpam-5330	446	31	,	,	PUNCT
ejpam-5330	446	32	φ	φ	PROPN
ejpam-5330	446	33	−1	−1	NOUN
ejpam-5330	446	34	ψ	ψ	X
ejpam-5330	446	35	(	(	PUNCT
ejpam-5330	446	36	(	(	PUNCT
ejpam-5330	446	37	gb)δ	gb)δ	PROPN
ejpam-5330	446	38	)	)	PUNCT
ejpam-5330	446	39	,	,	PUNCT
ejpam-5330	446	40	r	r	NOUN
ejpam-5330	446	41	)	)	PUNCT
ejpam-5330	446	42	.	.	PUNCT
ejpam-5330	447	1	since	since	SCONJ
ejpam-5330	447	2	φψ	φψ	PROPN
ejpam-5330	447	3	is	be	AUX
ejpam-5330	447	4	fuzzy	fuzzy	ADJ
ejpam-5330	447	5	soft	soft	ADJ
ejpam-5330	447	6	continuous	continuous	ADJ
ejpam-5330	447	7	mapping	mapping	NOUN
ejpam-5330	447	8	,	,	PUNCT
ejpam-5330	447	9	it	it	PRON
ejpam-5330	447	10	follows	follow	VERB
ejpam-5330	447	11	⊔δ∈∆	⊔δ∈∆	ADP
ejpam-5330	447	12	◦	◦	NOUN
ejpam-5330	447	13	cτ	cτ	NOUN
ejpam-5330	447	14	(	(	PUNCT
ejpam-5330	447	15	n	n	CCONJ
ejpam-5330	447	16	,	,	PUNCT
ejpam-5330	447	17	φ	φ	PROPN
ejpam-5330	447	18	−1	−1	NOUN
ejpam-5330	447	19	ψ	ψ	X
ejpam-5330	447	20	(	(	PUNCT
ejpam-5330	447	21	(	(	PUNCT
ejpam-5330	447	22	gb)δ	gb)δ	PROPN
ejpam-5330	447	23	)	)	PUNCT
ejpam-5330	447	24	,	,	PUNCT
ejpam-5330	448	1	r	r	X
ejpam-5330	448	2	)	)	PUNCT
ejpam-5330	448	3	⊑	⊑	PRON
ejpam-5330	448	4	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	448	5	◦	◦	NOUN
ejpam-5330	448	6	φ	φ	NUM
ejpam-5330	448	7	−1	−1	NOUN
ejpam-5330	448	8	ψ	ψ	PROPN
ejpam-5330	448	9	(	(	PUNCT
ejpam-5330	448	10	cη(k	cη(k	PROPN
ejpam-5330	448	11	,	,	PUNCT
ejpam-5330	448	12	(	(	PUNCT
ejpam-5330	448	13	gb)δ	gb)δ	PROPN
ejpam-5330	448	14	,	,	PUNCT
ejpam-5330	448	15	r	r	NOUN
ejpam-5330	448	16	)	)	PUNCT
ejpam-5330	448	17	)	)	PUNCT
ejpam-5330	449	1	=	=	PUNCT
ejpam-5330	449	2	φ−1	φ−1	PROPN
ejpam-5330	449	3	ψ	ψ	SYM
ejpam-5330	449	4	(	(	PUNCT
ejpam-5330	449	5	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	449	6	◦	◦	NOUN
ejpam-5330	449	7	cη(k	cη(k	NOUN
ejpam-5330	449	8	,	,	PUNCT
ejpam-5330	449	9	(	(	PUNCT
ejpam-5330	449	10	gb)δ	gb)δ	PROPN
ejpam-5330	449	11	,	,	PUNCT
ejpam-5330	449	12	r	r	NOUN
ejpam-5330	449	13	)	)	PUNCT
ejpam-5330	449	14	)	)	PUNCT
ejpam-5330	449	15	.	.	PUNCT
ejpam-5330	450	1	then	then	ADV
ejpam-5330	450	2	,	,	PUNCT
ejpam-5330	450	3	φψ(hc	φψ(hc	NOUN
ejpam-5330	450	4	)	)	PUNCT
ejpam-5330	450	5	⊑	⊑	PRON
ejpam-5330	451	1	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	451	2	◦	◦	NOUN
ejpam-5330	451	3	cη(k	cη(k	NOUN
ejpam-5330	451	4	,	,	PUNCT
ejpam-5330	451	5	(	(	PUNCT
ejpam-5330	451	6	gb)δ	gb)δ	PROPN
ejpam-5330	451	7	,	,	PUNCT
ejpam-5330	451	8	r	r	NOUN
ejpam-5330	451	9	)	)	PUNCT
ejpam-5330	451	10	.	.	PUNCT
ejpam-5330	452	1	hence	hence	ADV
ejpam-5330	452	2	,	,	PUNCT
ejpam-5330	452	3	the	the	DET
ejpam-5330	452	4	proof	proof	NOUN
ejpam-5330	452	5	is	be	AUX
ejpam-5330	452	6	completed	complete	VERB
ejpam-5330	452	7	.	.	PUNCT
ejpam-5330	453	1	definition	definition	NOUN
ejpam-5330	453	2	22	22	NUM
ejpam-5330	453	3	.	.	PUNCT
ejpam-5330	454	1	let	let	AUX
ejpam-5330	454	2	(	(	PUNCT
ejpam-5330	454	3	w	w	NOUN
ejpam-5330	454	4	,	,	PUNCT
ejpam-5330	454	5	τn	τn	PART
ejpam-5330	454	6	)	)	PUNCT
ejpam-5330	454	7	be	be	AUX
ejpam-5330	454	8	an	an	DET
ejpam-5330	454	9	fsts	fst	NOUN
ejpam-5330	454	10	and	and	CCONJ
ejpam-5330	454	11	r	r	NOUN
ejpam-5330	454	12	∈	∈	PROPN
ejpam-5330	454	13	i	i	PRON
ejpam-5330	454	14	◦	◦	NOUN
ejpam-5330	454	15	,	,	PUNCT
ejpam-5330	454	16	then	then	ADV
ejpam-5330	454	17	hc	hc	PROPN
ejpam-5330	454	18	∈	∈	PROPN
ejpam-5330	454	19	˜(w	˜(w	PROPN
ejpam-5330	454	20	,	,	PUNCT
ejpam-5330	454	21	n	n	CCONJ
ejpam-5330	454	22	)	)	PUNCT
ejpam-5330	454	23	is	be	AUX
ejpam-5330	454	24	called	call	VERB
ejpam-5330	454	25	an	an	DET
ejpam-5330	454	26	r	r	NOUN
ejpam-5330	454	27	-	-	PUNCT
ejpam-5330	454	28	fuzzy	fuzzy	ADJ
ejpam-5330	454	29	soft	soft	ADJ
ejpam-5330	454	30	nearly	nearly	ADV
ejpam-5330	454	31	compact	compact	ADJ
ejpam-5330	454	32	iff	iff	NOUN
ejpam-5330	454	33	for	for	ADP
ejpam-5330	454	34	every	every	DET
ejpam-5330	454	35	family	family	NOUN
ejpam-5330	454	36	{	{	PUNCT
ejpam-5330	454	37	(	(	PUNCT
ejpam-5330	454	38	gb)δ	gb)δ	PROPN
ejpam-5330	454	39	∈	∈	PROPN
ejpam-5330	454	40	˜(w	˜(w	PROPN
ejpam-5330	454	41	,	,	PUNCT
ejpam-5330	454	42	n	n	CCONJ
ejpam-5330	454	43	)	)	PUNCT
ejpam-5330	454	44	|	|	ADV
ejpam-5330	454	45	τn((gb)δ	τn((gb)δ	ADP
ejpam-5330	454	46	)	)	PUNCT
ejpam-5330	454	47	≥	≥	NOUN
ejpam-5330	454	48	r}δ∈∆	r}δ∈∆	NOUN
ejpam-5330	454	49	,	,	PUNCT
ejpam-5330	454	50	such	such	ADJ
ejpam-5330	454	51	that	that	SCONJ
ejpam-5330	454	52	hc	hc	PROPN
ejpam-5330	454	53	⊑	⊑	PROPN
ejpam-5330	454	54	⊔δ∈∆(gb)δ	⊔δ∈∆(gb)δ	PROPN
ejpam-5330	454	55	,	,	PUNCT
ejpam-5330	454	56	there	there	PRON
ejpam-5330	454	57	is	be	VERB
ejpam-5330	454	58	a	a	DET
ejpam-5330	454	59	finite	finite	NOUN
ejpam-5330	454	60	subset	subset	NOUN
ejpam-5330	454	61	∆	∆	ADJ
ejpam-5330	454	62	◦	◦	NOUN
ejpam-5330	454	63	of	of	ADP
ejpam-5330	454	64	∆	∆	PROPN
ejpam-5330	454	65	,	,	PUNCT
ejpam-5330	454	66	such	such	ADJ
ejpam-5330	454	67	that	that	SCONJ
ejpam-5330	454	68	hc	hc	PROPN
ejpam-5330	454	69	⊑	⊑	PRON
ejpam-5330	454	70	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	454	71	◦	◦	NOUN
ejpam-5330	454	72	iτ	iτ	NOUN
ejpam-5330	454	73	(	(	PUNCT
ejpam-5330	454	74	n	n	CCONJ
ejpam-5330	454	75	,	,	PUNCT
ejpam-5330	454	76	cτ	cτ	INTJ
ejpam-5330	454	77	(	(	PUNCT
ejpam-5330	454	78	n	n	CCONJ
ejpam-5330	454	79	,	,	PUNCT
ejpam-5330	454	80	(	(	PUNCT
ejpam-5330	454	81	gb)δ	gb)δ	PROPN
ejpam-5330	454	82	,	,	PUNCT
ejpam-5330	454	83	r	r	NOUN
ejpam-5330	454	84	)	)	PUNCT
ejpam-5330	454	85	,	,	PUNCT
ejpam-5330	454	86	r	r	NOUN
ejpam-5330	454	87	)	)	PUNCT
ejpam-5330	454	88	for	for	ADP
ejpam-5330	454	89	each	each	DET
ejpam-5330	454	90	n	n	PRON
ejpam-5330	454	91	∈	∈	PROPN
ejpam-5330	454	92	n.	n.	PROPN
ejpam-5330	454	93	w.	w.	PROPN
ejpam-5330	454	94	alqurashi	alqurashi	PROPN
ejpam-5330	454	95	,	,	PUNCT
ejpam-5330	454	96	i.	i.	PROPN
ejpam-5330	454	97	m.	m.	PROPN
ejpam-5330	454	98	taha	taha	PROPN
ejpam-5330	454	99	/	/	PUNCT
ejpam-5330	454	100	eur	eur	PROPN
ejpam-5330	454	101	.	.	PUNCT
ejpam-5330	455	1	j.	j.	PROPN
ejpam-5330	455	2	pure	pure	PROPN
ejpam-5330	455	3	appl	appl	PROPN
ejpam-5330	455	4	.	.	PROPN
ejpam-5330	455	5	math	math	PROPN
ejpam-5330	455	6	,	,	PUNCT
ejpam-5330	455	7	17	17	NUM
ejpam-5330	455	8	(	(	PUNCT
ejpam-5330	455	9	4	4	NUM
ejpam-5330	455	10	)	)	PUNCT
ejpam-5330	455	11	(	(	PUNCT
ejpam-5330	455	12	2024	2024	NUM
ejpam-5330	455	13	)	)	PUNCT
ejpam-5330	455	14	,	,	PUNCT
ejpam-5330	455	15	4112	4112	NUM
ejpam-5330	455	16	-	-	SYM
ejpam-5330	455	17	4134	4134	NUM
ejpam-5330	455	18	4129	4129	NUM
ejpam-5330	455	19	definition	definition	NOUN
ejpam-5330	455	20	23	23	NUM
ejpam-5330	455	21	.	.	PUNCT
ejpam-5330	456	1	let	let	AUX
ejpam-5330	456	2	(	(	PUNCT
ejpam-5330	456	3	w	w	NOUN
ejpam-5330	456	4	,	,	PUNCT
ejpam-5330	456	5	τn	τn	PART
ejpam-5330	456	6	)	)	PUNCT
ejpam-5330	456	7	be	be	AUX
ejpam-5330	456	8	an	an	DET
ejpam-5330	456	9	fsts	fst	NOUN
ejpam-5330	456	10	and	and	CCONJ
ejpam-5330	456	11	r	r	NOUN
ejpam-5330	456	12	∈	∈	PROPN
ejpam-5330	456	13	i	i	PRON
ejpam-5330	456	14	◦	◦	NOUN
ejpam-5330	456	15	,	,	PUNCT
ejpam-5330	456	16	then	then	ADV
ejpam-5330	456	17	hc	hc	PROPN
ejpam-5330	456	18	∈	∈	PROPN
ejpam-5330	456	19	˜(w	˜(w	PROPN
ejpam-5330	456	20	,	,	PUNCT
ejpam-5330	456	21	n	n	CCONJ
ejpam-5330	456	22	)	)	PUNCT
ejpam-5330	456	23	is	be	AUX
ejpam-5330	456	24	called	call	VERB
ejpam-5330	456	25	an	an	DET
ejpam-5330	456	26	r	r	NOUN
ejpam-5330	456	27	-	-	PUNCT
ejpam-5330	456	28	fuzzy	fuzzy	ADJ
ejpam-5330	456	29	soft	soft	ADJ
ejpam-5330	456	30	nearly	nearly	ADV
ejpam-5330	456	31	α	α	ADJ
ejpam-5330	456	32	-	-	ADJ
ejpam-5330	456	33	compact	compact	ADJ
ejpam-5330	456	34	iff	iff	NOUN
ejpam-5330	456	35	for	for	ADP
ejpam-5330	456	36	every	every	DET
ejpam-5330	456	37	family	family	NOUN
ejpam-5330	456	38	{	{	PUNCT
ejpam-5330	456	39	(	(	PUNCT
ejpam-5330	456	40	gb)δ	gb)δ	PROPN
ejpam-5330	456	41	∈	∈	PROPN
ejpam-5330	456	42	˜(w	˜(w	PROPN
ejpam-5330	456	43	,	,	PUNCT
ejpam-5330	456	44	n	n	CCONJ
ejpam-5330	456	45	)	)	PUNCT
ejpam-5330	457	1	|	|	ADV
ejpam-5330	457	2	(	(	PUNCT
ejpam-5330	457	3	gb)δ	gb)δ	PROPN
ejpam-5330	457	4	is	be	AUX
ejpam-5330	457	5	r	r	NOUN
ejpam-5330	457	6	-	-	PUNCT
ejpam-5330	457	7	fuzzy	fuzzy	ADJ
ejpam-5330	457	8	soft	soft	ADJ
ejpam-5330	457	9	α	α	NOUN
ejpam-5330	457	10	-	-	PUNCT
ejpam-5330	457	11	open}δ∈∆	open}δ∈∆	NOUN
ejpam-5330	457	12	,	,	PUNCT
ejpam-5330	457	13	such	such	ADJ
ejpam-5330	457	14	that	that	SCONJ
ejpam-5330	457	15	hc	hc	PROPN
ejpam-5330	457	16	⊑	⊑	PROPN
ejpam-5330	457	17	⊔δ∈∆(gb)δ	⊔δ∈∆(gb)δ	PROPN
ejpam-5330	457	18	,	,	PUNCT
ejpam-5330	457	19	there	there	PRON
ejpam-5330	457	20	is	be	VERB
ejpam-5330	457	21	a	a	DET
ejpam-5330	457	22	finite	finite	NOUN
ejpam-5330	457	23	subset	subset	NOUN
ejpam-5330	457	24	∆	∆	ADJ
ejpam-5330	457	25	◦	◦	NOUN
ejpam-5330	457	26	of	of	ADP
ejpam-5330	457	27	∆	∆	PROPN
ejpam-5330	457	28	,	,	PUNCT
ejpam-5330	457	29	such	such	ADJ
ejpam-5330	457	30	that	that	SCONJ
ejpam-5330	457	31	hc	hc	PROPN
ejpam-5330	457	32	⊑	⊑	PRON
ejpam-5330	457	33	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	457	34	◦	◦	NOUN
ejpam-5330	457	35	iτ	iτ	NOUN
ejpam-5330	457	36	(	(	PUNCT
ejpam-5330	457	37	n	n	CCONJ
ejpam-5330	457	38	,	,	PUNCT
ejpam-5330	457	39	cτ	cτ	INTJ
ejpam-5330	457	40	(	(	PUNCT
ejpam-5330	457	41	n	n	CCONJ
ejpam-5330	457	42	,	,	PUNCT
ejpam-5330	457	43	(	(	PUNCT
ejpam-5330	457	44	gb)δ	gb)δ	PROPN
ejpam-5330	457	45	,	,	PUNCT
ejpam-5330	457	46	r	r	NOUN
ejpam-5330	457	47	)	)	PUNCT
ejpam-5330	457	48	,	,	PUNCT
ejpam-5330	457	49	r	r	NOUN
ejpam-5330	457	50	)	)	PUNCT
ejpam-5330	457	51	for	for	ADP
ejpam-5330	457	52	each	each	DET
ejpam-5330	457	53	n	n	PRON
ejpam-5330	457	54	∈	∈	PROPN
ejpam-5330	457	55	n.	n.	NOUN
ejpam-5330	457	56	lemma	lemma	PROPN
ejpam-5330	457	57	9	9	X
ejpam-5330	457	58	.	.	PUNCT
ejpam-5330	458	1	let	let	AUX
ejpam-5330	458	2	(	(	PUNCT
ejpam-5330	458	3	w	w	NOUN
ejpam-5330	458	4	,	,	PUNCT
ejpam-5330	458	5	τn	τn	PART
ejpam-5330	458	6	)	)	PUNCT
ejpam-5330	458	7	be	be	AUX
ejpam-5330	458	8	an	an	DET
ejpam-5330	458	9	fsts	fst	NOUN
ejpam-5330	458	10	and	and	CCONJ
ejpam-5330	458	11	r	r	NOUN
ejpam-5330	458	12	∈	∈	PROPN
ejpam-5330	458	13	i	i	X
ejpam-5330	458	14	◦	◦	NOUN
ejpam-5330	458	15	.	.	PUNCT
ejpam-5330	459	1	if	if	SCONJ
ejpam-5330	459	2	hc	hc	PROPN
ejpam-5330	459	3	∈	∈	PROPN
ejpam-5330	459	4	˜(w	˜(w	PROPN
ejpam-5330	459	5	,	,	PUNCT
ejpam-5330	459	6	n	n	CCONJ
ejpam-5330	459	7	)	)	PUNCT
ejpam-5330	459	8	is	be	AUX
ejpam-5330	459	9	r	r	NOUN
ejpam-5330	459	10	-	-	PUNCT
ejpam-5330	459	11	fuzzy	fuzzy	ADJ
ejpam-5330	459	12	soft	soft	ADJ
ejpam-5330	459	13	nearly	nearly	ADV
ejpam-5330	459	14	α	α	NOUN
ejpam-5330	459	15	-	-	ADJ
ejpam-5330	459	16	compact	compact	ADJ
ejpam-5330	459	17	,	,	PUNCT
ejpam-5330	459	18	then	then	ADV
ejpam-5330	459	19	hc	hc	PROPN
ejpam-5330	459	20	is	be	AUX
ejpam-5330	459	21	r	r	NOUN
ejpam-5330	459	22	-	-	PUNCT
ejpam-5330	459	23	fuzzy	fuzzy	ADJ
ejpam-5330	459	24	soft	soft	ADJ
ejpam-5330	459	25	nearly	nearly	ADV
ejpam-5330	459	26	compact	compact	ADJ
ejpam-5330	459	27	.	.	PUNCT
ejpam-5330	460	1	proof	proof	NOUN
ejpam-5330	460	2	.	.	PUNCT
ejpam-5330	461	1	follows	follow	VERB
ejpam-5330	461	2	from	from	ADP
ejpam-5330	461	3	definitions	definition	NOUN
ejpam-5330	461	4	22	22	NUM
ejpam-5330	461	5	and	and	CCONJ
ejpam-5330	461	6	23	23	NUM
ejpam-5330	461	7	.	.	PUNCT
ejpam-5330	462	1	lemma	lemma	PROPN
ejpam-5330	462	2	10	10	NUM
ejpam-5330	462	3	.	.	PUNCT
ejpam-5330	463	1	let	let	AUX
ejpam-5330	463	2	(	(	PUNCT
ejpam-5330	463	3	w	w	NOUN
ejpam-5330	463	4	,	,	PUNCT
ejpam-5330	463	5	τn	τn	PART
ejpam-5330	463	6	)	)	PUNCT
ejpam-5330	463	7	be	be	AUX
ejpam-5330	463	8	an	an	DET
ejpam-5330	463	9	fsts	fst	NOUN
ejpam-5330	463	10	and	and	CCONJ
ejpam-5330	463	11	r	r	NOUN
ejpam-5330	463	12	∈	∈	PROPN
ejpam-5330	463	13	i	i	X
ejpam-5330	463	14	◦	◦	NOUN
ejpam-5330	463	15	.	.	PUNCT
ejpam-5330	464	1	if	if	SCONJ
ejpam-5330	464	2	hc	hc	PROPN
ejpam-5330	464	3	∈	∈	PROPN
ejpam-5330	464	4	˜(w	˜(w	PROPN
ejpam-5330	464	5	,	,	PUNCT
ejpam-5330	464	6	n	n	CCONJ
ejpam-5330	464	7	)	)	PUNCT
ejpam-5330	464	8	is	be	AUX
ejpam-5330	464	9	r	r	NOUN
ejpam-5330	464	10	-	-	PUNCT
ejpam-5330	464	11	fuzzy	fuzzy	ADJ
ejpam-5330	464	12	soft	soft	ADJ
ejpam-5330	464	13	compact	compact	ADJ
ejpam-5330	464	14	(	(	PUNCT
ejpam-5330	464	15	resp	resp	NOUN
ejpam-5330	464	16	.	.	PUNCT
ejpam-5330	464	17	,	,	PUNCT
ejpam-5330	464	18	α	α	NOUN
ejpam-5330	464	19	-	-	ADJ
ejpam-5330	464	20	compact	compact	ADJ
ejpam-5330	464	21	)	)	PUNCT
ejpam-5330	464	22	,	,	PUNCT
ejpam-5330	464	23	then	then	ADV
ejpam-5330	464	24	hc	hc	PROPN
ejpam-5330	464	25	is	be	AUX
ejpam-5330	464	26	r	r	NOUN
ejpam-5330	464	27	-	-	PUNCT
ejpam-5330	464	28	fuzzy	fuzzy	ADJ
ejpam-5330	464	29	soft	soft	ADJ
ejpam-5330	464	30	nearly	nearly	ADV
ejpam-5330	464	31	compact	compact	ADJ
ejpam-5330	464	32	(	(	PUNCT
ejpam-5330	464	33	resp	resp	NOUN
ejpam-5330	464	34	.	.	PUNCT
ejpam-5330	464	35	,	,	PUNCT
ejpam-5330	464	36	nearly	nearly	ADV
ejpam-5330	464	37	α	α	NOUN
ejpam-5330	464	38	-	-	ADJ
ejpam-5330	464	39	compact	compact	ADJ
ejpam-5330	464	40	)	)	PUNCT
ejpam-5330	464	41	.	.	PUNCT
ejpam-5330	465	1	proof	proof	NOUN
ejpam-5330	465	2	.	.	PUNCT
ejpam-5330	466	1	follows	follow	VERB
ejpam-5330	466	2	from	from	ADP
ejpam-5330	466	3	definitions	definition	NOUN
ejpam-5330	466	4	18	18	NUM
ejpam-5330	466	5	,	,	PUNCT
ejpam-5330	466	6	19	19	NUM
ejpam-5330	466	7	,	,	PUNCT
ejpam-5330	466	8	22	22	NUM
ejpam-5330	466	9	,	,	PUNCT
ejpam-5330	466	10	and	and	CCONJ
ejpam-5330	466	11	23	23	NUM
ejpam-5330	466	12	.	.	PUNCT
ejpam-5330	467	1	remark	remark	NOUN
ejpam-5330	467	2	9	9	NUM
ejpam-5330	467	3	.	.	PUNCT
ejpam-5330	468	1	the	the	DET
ejpam-5330	468	2	converse	converse	NOUN
ejpam-5330	468	3	of	of	ADP
ejpam-5330	468	4	lemma	lemma	PROPN
ejpam-5330	468	5	10	10	NUM
ejpam-5330	468	6	may	may	AUX
ejpam-5330	468	7	not	not	PART
ejpam-5330	468	8	be	be	AUX
ejpam-5330	468	9	true	true	ADJ
ejpam-5330	468	10	,	,	PUNCT
ejpam-5330	468	11	as	as	SCONJ
ejpam-5330	468	12	shown	show	VERB
ejpam-5330	468	13	by	by	ADP
ejpam-5330	468	14	example	example	NOUN
ejpam-5330	468	15	7	7	NUM
ejpam-5330	468	16	.	.	NOUN
ejpam-5330	468	17	example	example	NOUN
ejpam-5330	469	1	7	7	NUM
ejpam-5330	469	2	.	.	PUNCT
ejpam-5330	470	1	let	let	VERB
ejpam-5330	470	2	v	v	VERB
ejpam-5330	470	3	=	=	PUNCT
ejpam-5330	470	4	i	i	PROPN
ejpam-5330	470	5	,	,	PUNCT
ejpam-5330	470	6	0	0	PUNCT
ejpam-5330	470	7	<	<	X
ejpam-5330	470	8	n	n	X
ejpam-5330	470	9	<	<	X
ejpam-5330	470	10	1	1	NUM
ejpam-5330	470	11	,	,	PUNCT
ejpam-5330	470	12	and	and	CCONJ
ejpam-5330	470	13	f	f	X
ejpam-5330	470	14	=	=	SYM
ejpam-5330	470	15	{	{	PUNCT
ejpam-5330	470	16	k1	k1	PROPN
ejpam-5330	470	17	,	,	PUNCT
ejpam-5330	470	18	k2	k2	NOUN
ejpam-5330	470	19	}	}	PUNCT
ejpam-5330	470	20	be	be	VERB
ejpam-5330	470	21	the	the	DET
ejpam-5330	470	22	parameter	parameter	NOUN
ejpam-5330	470	23	set	set	NOUN
ejpam-5330	470	24	of	of	ADP
ejpam-5330	470	25	v.	v.	ADP
ejpam-5330	470	26	define	define	VERB
ejpam-5330	470	27	gfn	gfn	NOUN
ejpam-5330	470	28	,	,	PUNCT
ejpam-5330	470	29	gf	gf	NOUN
ejpam-5330	470	30	,	,	PUNCT
ejpam-5330	470	31	and	and	CCONJ
ejpam-5330	470	32	ff	ff	PROPN
ejpam-5330	470	33	∈	∈	PROPN
ejpam-5330	470	34	(	(	PUNCT
ejpam-5330	470	35	̃v	̃v	NOUN
ejpam-5330	470	36	,	,	PUNCT
ejpam-5330	470	37	f	f	PROPN
ejpam-5330	470	38	)	)	PUNCT
ejpam-5330	470	39	as	as	SCONJ
ejpam-5330	470	40	follows	follow	VERB
ejpam-5330	470	41	∀	∀	X
ejpam-5330	471	1	k	k	PROPN
ejpam-5330	471	2	∈	∈	PROPN
ejpam-5330	471	3	f	f	X
ejpam-5330	471	4	:	:	PUNCT
ejpam-5330	471	5	gfn(k)(v	gfn(k)(v	X
ejpam-5330	471	6	)	)	PUNCT
ejpam-5330	471	7	=	=	PRON
ejpam-5330	471	8	{	{	PUNCT
ejpam-5330	471	9	v	v	NOUN
ejpam-5330	471	10	n	n	NOUN
ejpam-5330	471	11	,	,	PUNCT
ejpam-5330	471	12	if	if	SCONJ
ejpam-5330	471	13	0	0	NUM
ejpam-5330	471	14	≤	≤	NUM
ejpam-5330	471	15	v	v	NOUN
ejpam-5330	471	16	≤	≤	NUM
ejpam-5330	471	17	n	n	CCONJ
ejpam-5330	471	18	,	,	PUNCT
ejpam-5330	471	19	1−v	1−v	PROPN
ejpam-5330	471	20	1−n	1−n	NUM
ejpam-5330	471	21	,	,	PUNCT
ejpam-5330	471	22	if	if	SCONJ
ejpam-5330	471	23	n	n	CCONJ
ejpam-5330	471	24	<	<	X
ejpam-5330	471	25	v	v	X
ejpam-5330	471	26	≤	≤	NUM
ejpam-5330	471	27	1	1	NUM
ejpam-5330	471	28	,	,	PUNCT
ejpam-5330	471	29	gf	gf	X
ejpam-5330	471	30	(	(	PUNCT
ejpam-5330	471	31	k)(v	k)(v	X
ejpam-5330	471	32	)	)	PUNCT
ejpam-5330	472	1	=	=	PRON
ejpam-5330	472	2	{	{	PUNCT
ejpam-5330	472	3	1	1	NUM
ejpam-5330	472	4	,	,	PUNCT
ejpam-5330	472	5	if	if	SCONJ
ejpam-5330	472	6	v	v	NOUN
ejpam-5330	472	7	=	=	SYM
ejpam-5330	472	8	0	0	NUM
ejpam-5330	472	9	,	,	PUNCT
ejpam-5330	472	10	1	1	NUM
ejpam-5330	472	11	2	2	NUM
ejpam-5330	472	12	,	,	PUNCT
ejpam-5330	472	13	if	if	SCONJ
ejpam-5330	472	14	0	0	NUM
ejpam-5330	472	15	<	<	X
ejpam-5330	472	16	v	v	X
ejpam-5330	472	17	≤	≤	NUM
ejpam-5330	472	18	1	1	NUM
ejpam-5330	472	19	,	,	PUNCT
ejpam-5330	472	20	ff	ff	INTJ
ejpam-5330	472	21	(	(	PUNCT
ejpam-5330	472	22	k)(v	k)(v	X
ejpam-5330	472	23	)	)	PUNCT
ejpam-5330	472	24	=	=	PRON
ejpam-5330	472	25	{	{	PUNCT
ejpam-5330	472	26	1	1	NUM
ejpam-5330	472	27	2	2	NUM
ejpam-5330	472	28	,	,	PUNCT
ejpam-5330	472	29	if	if	SCONJ
ejpam-5330	472	30	0	0	NUM
ejpam-5330	472	31	≤	≤	NUM
ejpam-5330	472	32	v	v	ADP
ejpam-5330	472	33	<	<	X
ejpam-5330	472	34	1	1	NUM
ejpam-5330	472	35	,	,	PUNCT
ejpam-5330	472	36	1	1	NUM
ejpam-5330	472	37	,	,	PUNCT
ejpam-5330	472	38	if	if	SCONJ
ejpam-5330	472	39	v	v	NOUN
ejpam-5330	472	40	=	=	SYM
ejpam-5330	472	41	1	1	X
ejpam-5330	472	42	.	.	X
ejpam-5330	472	43	define	define	VERB
ejpam-5330	472	44	fuzzy	fuzzy	ADJ
ejpam-5330	472	45	soft	soft	ADJ
ejpam-5330	472	46	topology	topology	NOUN
ejpam-5330	472	47	ηf	ηf	NOUN
ejpam-5330	472	48	:	:	PUNCT
ejpam-5330	472	49	f	f	X
ejpam-5330	473	1	−→	−→	NOUN
ejpam-5330	473	2	[	[	X
ejpam-5330	473	3	0	0	NUM
ejpam-5330	473	4	,	,	PUNCT
ejpam-5330	473	5	1](̃v	1](̃v	NUM
ejpam-5330	473	6	,	,	PUNCT
ejpam-5330	473	7	f	f	PROPN
ejpam-5330	473	8	)	)	PUNCT
ejpam-5330	473	9	as	as	SCONJ
ejpam-5330	473	10	follows	follow	VERB
ejpam-5330	473	11	:	:	PUNCT
ejpam-5330	473	12	∀k	∀k	X
ejpam-5330	473	13	∈	∈	PROPN
ejpam-5330	473	14	f	f	PROPN
ejpam-5330	473	15	,	,	PUNCT
ejpam-5330	473	16	ηk(tf	ηk(tf	PROPN
ejpam-5330	473	17	)	)	PUNCT
ejpam-5330	474	1	=	=	PUNCT
ejpam-5330	475	1			NOUN
ejpam-5330	475	2	1	1	NUM
ejpam-5330	475	3	,	,	PUNCT
ejpam-5330	475	4	if	if	SCONJ
ejpam-5330	475	5	tf	tf	PROPN
ejpam-5330	475	6	∈	∈	PROPN
ejpam-5330	475	7	{	{	PUNCT
ejpam-5330	475	8	gf	gf	NOUN
ejpam-5330	475	9	,	,	PUNCT
ejpam-5330	475	10	ff	ff	INTJ
ejpam-5330	475	11	,	,	PUNCT
ejpam-5330	475	12	φ	φ	PROPN
ejpam-5330	475	13	,	,	PUNCT
ejpam-5330	475	14	f̃	f̃	PROPN
ejpam-5330	475	15	}	}	PUNCT
ejpam-5330	475	16	,	,	PUNCT
ejpam-5330	475	17	max({1−	max({1−	PROPN
ejpam-5330	475	18	n	n	CCONJ
ejpam-5330	475	19	,	,	PUNCT
ejpam-5330	475	20	n	n	CCONJ
ejpam-5330	475	21	}	}	PUNCT
ejpam-5330	475	22	)	)	PUNCT
ejpam-5330	475	23	,	,	PUNCT
ejpam-5330	475	24	if	if	SCONJ
ejpam-5330	475	25	tf	tf	PROPN
ejpam-5330	475	26	=	=	PUNCT
ejpam-5330	475	27	gfn	gfn	NOUN
ejpam-5330	475	28	,	,	PUNCT
ejpam-5330	475	29	0	0	NUM
ejpam-5330	475	30	,	,	PUNCT
ejpam-5330	475	31	otherwise	otherwise	ADV
ejpam-5330	475	32	.	.	PUNCT
ejpam-5330	476	1	thus	thus	ADV
ejpam-5330	476	2	,	,	PUNCT
ejpam-5330	476	3	v	v	NOUN
ejpam-5330	476	4	is	be	AUX
ejpam-5330	476	5	1	1	NUM
ejpam-5330	476	6	2	2	NUM
ejpam-5330	476	7	-fuzzy	-fuzzy	NOUN
ejpam-5330	476	8	soft	soft	ADJ
ejpam-5330	476	9	nearly	nearly	ADV
ejpam-5330	476	10	compact	compact	ADJ
ejpam-5330	476	11	,	,	PUNCT
ejpam-5330	476	12	but	but	CCONJ
ejpam-5330	476	13	it	it	PRON
ejpam-5330	476	14	is	be	AUX
ejpam-5330	476	15	not	not	PART
ejpam-5330	476	16	1	1	NUM
ejpam-5330	476	17	2	2	NUM
ejpam-5330	476	18	-fuzzy	-fuzzy	NOUN
ejpam-5330	476	19	soft	soft	ADJ
ejpam-5330	476	20	compact	compact	ADJ
ejpam-5330	476	21	.	.	PUNCT
ejpam-5330	477	1	w.	w.	PROPN
ejpam-5330	477	2	alqurashi	alqurashi	PROPN
ejpam-5330	477	3	,	,	PUNCT
ejpam-5330	477	4	i.	i.	PROPN
ejpam-5330	477	5	m.	m.	PROPN
ejpam-5330	477	6	taha	taha	PROPN
ejpam-5330	477	7	/	/	PUNCT
ejpam-5330	477	8	eur	eur	PROPN
ejpam-5330	477	9	.	.	PUNCT
ejpam-5330	478	1	j.	j.	PROPN
ejpam-5330	478	2	pure	pure	PROPN
ejpam-5330	478	3	appl	appl	PROPN
ejpam-5330	478	4	.	.	PROPN
ejpam-5330	478	5	math	math	PROPN
ejpam-5330	478	6	,	,	PUNCT
ejpam-5330	478	7	17	17	NUM
ejpam-5330	478	8	(	(	PUNCT
ejpam-5330	478	9	4	4	NUM
ejpam-5330	478	10	)	)	PUNCT
ejpam-5330	478	11	(	(	PUNCT
ejpam-5330	478	12	2024	2024	NUM
ejpam-5330	478	13	)	)	PUNCT
ejpam-5330	478	14	,	,	PUNCT
ejpam-5330	478	15	4112	4112	NUM
ejpam-5330	478	16	-	-	SYM
ejpam-5330	478	17	4134	4134	NUM
ejpam-5330	478	18	4130	4130	NUM
ejpam-5330	478	19	theorem	theorem	NOUN
ejpam-5330	478	20	11	11	NUM
ejpam-5330	478	21	.	.	PUNCT
ejpam-5330	479	1	let	let	VERB
ejpam-5330	479	2	φψ	φψ	NOUN
ejpam-5330	479	3	:	:	PUNCT
ejpam-5330	479	4	(	(	PUNCT
ejpam-5330	479	5	w	w	INTJ
ejpam-5330	479	6	,	,	PUNCT
ejpam-5330	479	7	τn	τn	NOUN
ejpam-5330	479	8	)	)	PUNCT
ejpam-5330	479	9	−→	−→	NOUN
ejpam-5330	479	10	(	(	PUNCT
ejpam-5330	479	11	v	v	NOUN
ejpam-5330	479	12	,	,	PUNCT
ejpam-5330	479	13	ηf	ηf	PROPN
ejpam-5330	479	14	)	)	PUNCT
ejpam-5330	479	15	be	be	AUX
ejpam-5330	479	16	a	a	DET
ejpam-5330	479	17	fuzzy	fuzzy	ADJ
ejpam-5330	479	18	soft	soft	ADJ
ejpam-5330	479	19	continuous	continuous	ADJ
ejpam-5330	479	20	and	and	CCONJ
ejpam-5330	479	21	fuzzy	fuzzy	ADJ
ejpam-5330	479	22	soft	soft	ADJ
ejpam-5330	479	23	open	open	ADJ
ejpam-5330	479	24	mapping	mapping	NOUN
ejpam-5330	479	25	.	.	PUNCT
ejpam-5330	480	1	if	if	SCONJ
ejpam-5330	480	2	hc	hc	PROPN
ejpam-5330	480	3	∈	∈	PROPN
ejpam-5330	480	4	˜(w	˜(w	PROPN
ejpam-5330	480	5	,	,	PUNCT
ejpam-5330	480	6	n	n	CCONJ
ejpam-5330	480	7	)	)	PUNCT
ejpam-5330	480	8	is	be	AUX
ejpam-5330	480	9	r	r	NOUN
ejpam-5330	480	10	-	-	PUNCT
ejpam-5330	480	11	fuzzy	fuzzy	ADJ
ejpam-5330	480	12	soft	soft	ADJ
ejpam-5330	480	13	nearly	nearly	ADV
ejpam-5330	480	14	α	α	NOUN
ejpam-5330	480	15	-	-	ADJ
ejpam-5330	480	16	compact	compact	ADJ
ejpam-5330	480	17	,	,	PUNCT
ejpam-5330	480	18	then	then	ADV
ejpam-5330	480	19	φψ(hc	φψ(hc	NOUN
ejpam-5330	480	20	)	)	PUNCT
ejpam-5330	480	21	is	be	AUX
ejpam-5330	480	22	r	r	NOUN
ejpam-5330	480	23	-	-	PUNCT
ejpam-5330	480	24	fuzzy	fuzzy	ADJ
ejpam-5330	480	25	soft	soft	ADJ
ejpam-5330	480	26	nearly	nearly	ADV
ejpam-5330	480	27	compact	compact	ADJ
ejpam-5330	480	28	.	.	PUNCT
ejpam-5330	481	1	proof	proof	NOUN
ejpam-5330	481	2	.	.	PUNCT
ejpam-5330	482	1	let	let	VERB
ejpam-5330	482	2	{	{	PUNCT
ejpam-5330	482	3	(	(	PUNCT
ejpam-5330	482	4	gb)δ	gb)δ	PROPN
ejpam-5330	482	5	∈	∈	PROPN
ejpam-5330	482	6	(	(	PUNCT
ejpam-5330	482	7	̃v	̃v	NOUN
ejpam-5330	482	8	,	,	PUNCT
ejpam-5330	482	9	f	f	PROPN
ejpam-5330	482	10	)	)	PUNCT
ejpam-5330	483	1	|	|	ADV
ejpam-5330	483	2	ηk((gb)δ	ηk((gb)δ	NOUN
ejpam-5330	483	3	)	)	PUNCT
ejpam-5330	483	4	≥	≥	X
ejpam-5330	483	5	r}δ∈∆	r}δ∈∆	VERB
ejpam-5330	483	6	with	with	ADP
ejpam-5330	483	7	φψ(hc	φψ(hc	NOUN
ejpam-5330	483	8	)	)	PUNCT
ejpam-5330	483	9	⊑	⊑	X
ejpam-5330	483	10	⊔δ∈∆(gb)δ	⊔δ∈∆(gb)δ	PROPN
ejpam-5330	483	11	for	for	ADP
ejpam-5330	483	12	each	each	DET
ejpam-5330	483	13	k	k	PROPN
ejpam-5330	483	14	∈	∈	PROPN
ejpam-5330	483	15	f	f	X
ejpam-5330	483	16	.	.	PUNCT
ejpam-5330	484	1	then	then	ADV
ejpam-5330	484	2	,	,	PUNCT
ejpam-5330	484	3	{	{	PUNCT
ejpam-5330	484	4	φ−1	φ−1	PROPN
ejpam-5330	484	5	ψ	ψ	X
ejpam-5330	484	6	(	(	PUNCT
ejpam-5330	484	7	(	(	PUNCT
ejpam-5330	484	8	gb)δ	gb)δ	PROPN
ejpam-5330	484	9	)	)	PUNCT
ejpam-5330	484	10	∈	∈	PROPN
ejpam-5330	484	11	˜(w	˜(w	PROPN
ejpam-5330	484	12	,	,	PUNCT
ejpam-5330	484	13	n	n	CCONJ
ejpam-5330	484	14	)	)	PUNCT
ejpam-5330	484	15	|	|	ADV
ejpam-5330	484	16	φ−1	φ−1	PROPN
ejpam-5330	484	17	ψ	ψ	X
ejpam-5330	484	18	(	(	PUNCT
ejpam-5330	484	19	(	(	PUNCT
ejpam-5330	484	20	gb)δ	gb)δ	NOUN
ejpam-5330	484	21	)	)	PUNCT
ejpam-5330	484	22	is	be	AUX
ejpam-5330	484	23	r	r	NOUN
ejpam-5330	484	24	-	-	PUNCT
ejpam-5330	484	25	fuzzy	fuzzy	ADJ
ejpam-5330	484	26	soft	soft	ADJ
ejpam-5330	484	27	α	α	NOUN
ejpam-5330	484	28	-	-	NOUN
ejpam-5330	484	29	open}δ∈∆	open}δ∈∆	PROPN
ejpam-5330	484	30	(	(	PUNCT
ejpam-5330	484	31	by	by	ADP
ejpam-5330	484	32	φψ	φψ	PROPN
ejpam-5330	484	33	is	be	AUX
ejpam-5330	484	34	fuzzy	fuzzy	ADJ
ejpam-5330	484	35	soft	soft	ADJ
ejpam-5330	484	36	α	α	NOUN
ejpam-5330	484	37	-	-	ADJ
ejpam-5330	484	38	continuous	continuous	ADJ
ejpam-5330	484	39	)	)	PUNCT
ejpam-5330	484	40	such	such	ADJ
ejpam-5330	484	41	that	that	SCONJ
ejpam-5330	484	42	hc	hc	PROPN
ejpam-5330	484	43	⊑	⊑	PROPN
ejpam-5330	484	44	⊔δ∈∆φ−1	⊔δ∈∆φ−1	PROPN
ejpam-5330	484	45	ψ	ψ	X
ejpam-5330	484	46	(	(	PUNCT
ejpam-5330	484	47	(	(	PUNCT
ejpam-5330	484	48	gb)δ	gb)δ	PROPN
ejpam-5330	484	49	)	)	PUNCT
ejpam-5330	484	50	.	.	PUNCT
ejpam-5330	485	1	since	since	SCONJ
ejpam-5330	485	2	hc	hc	PROPN
ejpam-5330	485	3	is	be	AUX
ejpam-5330	485	4	r	r	NOUN
ejpam-5330	485	5	-	-	PUNCT
ejpam-5330	485	6	fuzzy	fuzzy	ADJ
ejpam-5330	485	7	soft	soft	ADJ
ejpam-5330	485	8	nearly	nearly	ADV
ejpam-5330	485	9	αcompact	αcompact	ADJ
ejpam-5330	485	10	,	,	PUNCT
ejpam-5330	485	11	there	there	PRON
ejpam-5330	485	12	is	be	VERB
ejpam-5330	485	13	a	a	DET
ejpam-5330	485	14	finite	finite	NOUN
ejpam-5330	485	15	subset	subset	NOUN
ejpam-5330	485	16	∆	∆	ADJ
ejpam-5330	485	17	◦	◦	NOUN
ejpam-5330	485	18	of	of	ADP
ejpam-5330	485	19	∆	∆	PROPN
ejpam-5330	485	20	such	such	ADJ
ejpam-5330	485	21	that	that	SCONJ
ejpam-5330	485	22	hc	hc	PROPN
ejpam-5330	485	23	⊑	⊑	PRON
ejpam-5330	485	24	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	485	25	◦	◦	NOUN
ejpam-5330	485	26	iτ	iτ	NOUN
ejpam-5330	485	27	(	(	PUNCT
ejpam-5330	485	28	n	n	CCONJ
ejpam-5330	485	29	,	,	PUNCT
ejpam-5330	485	30	cτ	cτ	INTJ
ejpam-5330	485	31	(	(	PUNCT
ejpam-5330	485	32	n	n	CCONJ
ejpam-5330	485	33	,	,	PUNCT
ejpam-5330	485	34	φ	φ	PROPN
ejpam-5330	485	35	−1	−1	NOUN
ejpam-5330	485	36	ψ	ψ	X
ejpam-5330	485	37	(	(	PUNCT
ejpam-5330	485	38	(	(	PUNCT
ejpam-5330	485	39	gb)δ	gb)δ	PROPN
ejpam-5330	485	40	)	)	PUNCT
ejpam-5330	485	41	,	,	PUNCT
ejpam-5330	485	42	r	r	NOUN
ejpam-5330	485	43	)	)	PUNCT
ejpam-5330	485	44	,	,	PUNCT
ejpam-5330	485	45	r	r	NOUN
ejpam-5330	485	46	)	)	PUNCT
ejpam-5330	485	47	.	.	PUNCT
ejpam-5330	486	1	since	since	SCONJ
ejpam-5330	486	2	φψ	φψ	PROPN
ejpam-5330	486	3	is	be	AUX
ejpam-5330	486	4	fuzzy	fuzzy	ADJ
ejpam-5330	486	5	soft	soft	ADJ
ejpam-5330	486	6	continuous	continuous	ADJ
ejpam-5330	486	7	and	and	CCONJ
ejpam-5330	486	8	fuzzy	fuzzy	ADJ
ejpam-5330	486	9	soft	soft	ADJ
ejpam-5330	486	10	open	open	ADJ
ejpam-5330	486	11	mapping	mapping	NOUN
ejpam-5330	486	12	,	,	PUNCT
ejpam-5330	486	13	it	it	PRON
ejpam-5330	486	14	follows	follow	VERB
ejpam-5330	486	15	φψ(hc	φψ(hc	NOUN
ejpam-5330	486	16	)	)	PUNCT
ejpam-5330	487	1	⊑	⊑	PRON
ejpam-5330	488	1	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	488	2	◦	◦	NOUN
ejpam-5330	488	3	φψ(iτ	φψ(iτ	PROPN
ejpam-5330	488	4	(	(	PUNCT
ejpam-5330	488	5	n	n	CCONJ
ejpam-5330	488	6	,	,	PUNCT
ejpam-5330	488	7	cτ	cτ	INTJ
ejpam-5330	488	8	(	(	PUNCT
ejpam-5330	488	9	n	n	CCONJ
ejpam-5330	488	10	,	,	PUNCT
ejpam-5330	488	11	φ	φ	PROPN
ejpam-5330	488	12	−1	−1	NOUN
ejpam-5330	488	13	ψ	ψ	X
ejpam-5330	488	14	(	(	PUNCT
ejpam-5330	488	15	(	(	PUNCT
ejpam-5330	488	16	gb)δ	gb)δ	PROPN
ejpam-5330	488	17	)	)	PUNCT
ejpam-5330	488	18	,	,	PUNCT
ejpam-5330	488	19	r	r	NOUN
ejpam-5330	488	20	)	)	PUNCT
ejpam-5330	488	21	,	,	PUNCT
ejpam-5330	488	22	r	r	NOUN
ejpam-5330	488	23	)	)	PUNCT
ejpam-5330	488	24	)	)	PUNCT
ejpam-5330	488	25	⊑	⊑	PRON
ejpam-5330	489	1	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	489	2	◦	◦	NOUN
ejpam-5330	489	3	iη(k	iη(k	NOUN
ejpam-5330	489	4	,	,	PUNCT
ejpam-5330	489	5	φψ(cτ	φψ(cτ	PROPN
ejpam-5330	489	6	(	(	PUNCT
ejpam-5330	489	7	n	n	CCONJ
ejpam-5330	489	8	,	,	PUNCT
ejpam-5330	489	9	φ	φ	PROPN
ejpam-5330	489	10	−1	−1	NOUN
ejpam-5330	489	11	ψ	ψ	X
ejpam-5330	489	12	(	(	PUNCT
ejpam-5330	489	13	(	(	PUNCT
ejpam-5330	489	14	gb)δ	gb)δ	PROPN
ejpam-5330	489	15	)	)	PUNCT
ejpam-5330	489	16	,	,	PUNCT
ejpam-5330	489	17	r	r	NOUN
ejpam-5330	489	18	)	)	PUNCT
ejpam-5330	489	19	)	)	PUNCT
ejpam-5330	489	20	,	,	PUNCT
ejpam-5330	489	21	r	r	X
ejpam-5330	489	22	)	)	PUNCT
ejpam-5330	489	23	⊑	⊑	PRON
ejpam-5330	489	24	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	489	25	◦	◦	NOUN
ejpam-5330	489	26	iη(k	iη(k	NOUN
ejpam-5330	489	27	,	,	PUNCT
ejpam-5330	489	28	φψ(φ	φψ(φ	NUM
ejpam-5330	489	29	−1	−1	NOUN
ejpam-5330	489	30	ψ	ψ	X
ejpam-5330	489	31	(	(	PUNCT
ejpam-5330	489	32	cη(k	cη(k	PROPN
ejpam-5330	489	33	,	,	PUNCT
ejpam-5330	489	34	(	(	PUNCT
ejpam-5330	489	35	gb)δ	gb)δ	PROPN
ejpam-5330	489	36	,	,	PUNCT
ejpam-5330	489	37	r	r	NOUN
ejpam-5330	489	38	)	)	PUNCT
ejpam-5330	489	39	)	)	PUNCT
ejpam-5330	489	40	)	)	PUNCT
ejpam-5330	489	41	,	,	PUNCT
ejpam-5330	489	42	r	r	X
ejpam-5330	489	43	)	)	PUNCT
ejpam-5330	489	44	⊑	⊑	PRON
ejpam-5330	489	45	⊔δ∈∆	⊔δ∈∆	PROPN
ejpam-5330	489	46	◦	◦	NOUN
ejpam-5330	489	47	iη(k	iη(k	NOUN
ejpam-5330	489	48	,	,	PUNCT
ejpam-5330	489	49	cη(k	cη(k	PROPN
ejpam-5330	489	50	,	,	PUNCT
ejpam-5330	489	51	(	(	PUNCT
ejpam-5330	489	52	gb)δ	gb)δ	PROPN
ejpam-5330	489	53	,	,	PUNCT
ejpam-5330	489	54	r	r	NOUN
ejpam-5330	489	55	)	)	PUNCT
ejpam-5330	489	56	,	,	PUNCT
ejpam-5330	489	57	r	r	NOUN
ejpam-5330	489	58	)	)	PUNCT
ejpam-5330	489	59	.	.	PUNCT
ejpam-5330	490	1	hence	hence	ADV
ejpam-5330	490	2	,	,	PUNCT
ejpam-5330	490	3	the	the	DET
ejpam-5330	490	4	proof	proof	NOUN
ejpam-5330	490	5	is	be	AUX
ejpam-5330	490	6	completed	complete	VERB
ejpam-5330	490	7	.	.	PUNCT
ejpam-5330	491	1	lemma	lemma	PROPN
ejpam-5330	491	2	11	11	NUM
ejpam-5330	491	3	.	.	PUNCT
ejpam-5330	492	1	let	let	AUX
ejpam-5330	492	2	(	(	PUNCT
ejpam-5330	492	3	w	w	NOUN
ejpam-5330	492	4	,	,	PUNCT
ejpam-5330	492	5	τn	τn	PART
ejpam-5330	492	6	)	)	PUNCT
ejpam-5330	492	7	be	be	AUX
ejpam-5330	492	8	an	an	DET
ejpam-5330	492	9	fsts	fst	NOUN
ejpam-5330	492	10	and	and	CCONJ
ejpam-5330	492	11	r	r	NOUN
ejpam-5330	492	12	∈	∈	PROPN
ejpam-5330	492	13	i	i	X
ejpam-5330	492	14	◦	◦	NOUN
ejpam-5330	492	15	.	.	PUNCT
ejpam-5330	493	1	if	if	SCONJ
ejpam-5330	493	2	hc	hc	PROPN
ejpam-5330	493	3	∈	∈	PROPN
ejpam-5330	493	4	˜(w	˜(w	PROPN
ejpam-5330	493	5	,	,	PUNCT
ejpam-5330	493	6	n	n	CCONJ
ejpam-5330	493	7	)	)	PUNCT
ejpam-5330	493	8	is	be	AUX
ejpam-5330	493	9	r	r	NOUN
ejpam-5330	493	10	-	-	PUNCT
ejpam-5330	493	11	fuzzy	fuzzy	ADJ
ejpam-5330	493	12	soft	soft	ADJ
ejpam-5330	493	13	nearly	nearly	ADV
ejpam-5330	493	14	αcompact	αcompact	NOUN
ejpam-5330	493	15	(	(	PUNCT
ejpam-5330	493	16	resp	resp	NOUN
ejpam-5330	493	17	.	.	PUNCT
ejpam-5330	493	18	,	,	PUNCT
ejpam-5330	493	19	nearly	nearly	ADV
ejpam-5330	493	20	compact	compact	ADJ
ejpam-5330	493	21	)	)	PUNCT
ejpam-5330	493	22	,	,	PUNCT
ejpam-5330	493	23	then	then	ADV
ejpam-5330	493	24	hc	hc	PROPN
ejpam-5330	493	25	is	be	AUX
ejpam-5330	493	26	r	r	NOUN
ejpam-5330	493	27	-	-	PUNCT
ejpam-5330	493	28	fuzzy	fuzzy	ADJ
ejpam-5330	493	29	soft	soft	ADJ
ejpam-5330	493	30	almost	almost	ADV
ejpam-5330	493	31	α	α	NOUN
ejpam-5330	493	32	-	-	ADJ
ejpam-5330	493	33	compact	compact	ADJ
ejpam-5330	493	34	(	(	PUNCT
ejpam-5330	493	35	resp	resp	NOUN
ejpam-5330	493	36	.	.	PUNCT
ejpam-5330	493	37	,	,	PUNCT
ejpam-5330	493	38	almost	almost	ADV
ejpam-5330	493	39	compact	compact	ADJ
ejpam-5330	493	40	)	)	PUNCT
ejpam-5330	493	41	.	.	PUNCT
ejpam-5330	494	1	proof	proof	NOUN
ejpam-5330	494	2	.	.	PUNCT
ejpam-5330	495	1	follows	follow	VERB
ejpam-5330	495	2	from	from	ADP
ejpam-5330	495	3	definitions	definition	NOUN
ejpam-5330	495	4	20	20	NUM
ejpam-5330	495	5	,	,	PUNCT
ejpam-5330	495	6	21	21	NUM
ejpam-5330	495	7	,	,	PUNCT
ejpam-5330	495	8	22	22	NUM
ejpam-5330	495	9	,	,	PUNCT
ejpam-5330	495	10	and	and	CCONJ
ejpam-5330	495	11	23	23	NUM
ejpam-5330	495	12	.	.	PUNCT
ejpam-5330	496	1	remark	remark	PROPN
ejpam-5330	496	2	10	10	NUM
ejpam-5330	496	3	.	.	PUNCT
ejpam-5330	497	1	from	from	ADP
ejpam-5330	497	2	the	the	DET
ejpam-5330	497	3	previous	previous	ADJ
ejpam-5330	497	4	definitions	definition	NOUN
ejpam-5330	497	5	and	and	CCONJ
ejpam-5330	497	6	results	result	NOUN
ejpam-5330	497	7	,	,	PUNCT
ejpam-5330	497	8	we	we	PRON
ejpam-5330	497	9	can	can	AUX
ejpam-5330	497	10	summarize	summarize	VERB
ejpam-5330	497	11	the	the	DET
ejpam-5330	497	12	relationships	relationship	NOUN
ejpam-5330	497	13	among	among	ADP
ejpam-5330	497	14	different	different	ADJ
ejpam-5330	497	15	types	type	NOUN
ejpam-5330	497	16	of	of	ADP
ejpam-5330	497	17	fuzzy	fuzzy	ADJ
ejpam-5330	497	18	soft	soft	ADJ
ejpam-5330	497	19	compactness	compactness	NOUN
ejpam-5330	497	20	as	as	ADP
ejpam-5330	497	21	in	in	ADP
ejpam-5330	497	22	the	the	DET
ejpam-5330	497	23	next	next	ADJ
ejpam-5330	497	24	diagram	diagram	NOUN
ejpam-5330	497	25	.	.	PUNCT
ejpam-5330	498	1	fuzzy	fuzzy	ADJ
ejpam-5330	498	2	soft	soft	ADJ
ejpam-5330	498	3	α	α	NOUN
ejpam-5330	498	4	-	-	PUNCT
ejpam-5330	498	5	compactness	compactness	NOUN
ejpam-5330	498	6	⇒	⇒	NOUN
ejpam-5330	498	7	fuzzy	fuzzy	ADJ
ejpam-5330	498	8	soft	soft	ADJ
ejpam-5330	498	9	compactness	compactness	NOUN
ejpam-5330	498	10	⇓	⇓	PROPN
ejpam-5330	498	11	⇓	⇓	PROPN
ejpam-5330	498	12	fuzzy	fuzzy	ADV
ejpam-5330	498	13	soft	soft	ADJ
ejpam-5330	498	14	nearly	nearly	ADV
ejpam-5330	498	15	α	α	NOUN
ejpam-5330	498	16	-	-	PUNCT
ejpam-5330	498	17	compactness	compactness	NOUN
ejpam-5330	498	18	⇒	⇒	NOUN
ejpam-5330	498	19	fuzzy	fuzzy	ADJ
ejpam-5330	498	20	soft	soft	ADJ
ejpam-5330	498	21	nearly	nearly	ADV
ejpam-5330	498	22	compactness	compactness	NOUN
ejpam-5330	498	23	⇓	⇓	PROPN
ejpam-5330	498	24	⇓	⇓	PROPN
ejpam-5330	498	25	fuzzy	fuzzy	ADJ
ejpam-5330	498	26	soft	soft	ADJ
ejpam-5330	498	27	almost	almost	ADV
ejpam-5330	498	28	α	α	NOUN
ejpam-5330	498	29	-	-	PUNCT
ejpam-5330	498	30	compactness	compactness	NOUN
ejpam-5330	498	31	⇒	⇒	NOUN
ejpam-5330	498	32	fuzzy	fuzzy	ADJ
ejpam-5330	498	33	soft	soft	ADJ
ejpam-5330	498	34	almost	almost	ADV
ejpam-5330	498	35	compactness	compactness	NOUN
ejpam-5330	498	36	references	reference	NOUN
ejpam-5330	498	37	4131	4131	NUM
ejpam-5330	498	38	5	5	NUM
ejpam-5330	498	39	.	.	PUNCT
ejpam-5330	498	40	conclusion	conclusion	NOUN
ejpam-5330	498	41	and	and	CCONJ
ejpam-5330	498	42	future	future	ADJ
ejpam-5330	498	43	work	work	NOUN
ejpam-5330	498	44	in	in	ADP
ejpam-5330	498	45	this	this	DET
ejpam-5330	498	46	study	study	NOUN
ejpam-5330	498	47	,	,	PUNCT
ejpam-5330	498	48	the	the	DET
ejpam-5330	498	49	concepts	concept	NOUN
ejpam-5330	498	50	of	of	ADP
ejpam-5330	498	51	fuzzy	fuzzy	ADJ
ejpam-5330	498	52	soft	soft	ADJ
ejpam-5330	498	53	α	α	NOUN
ejpam-5330	498	54	-	-	NOUN
ejpam-5330	498	55	closure	closure	NOUN
ejpam-5330	498	56	(	(	PUNCT
ejpam-5330	498	57	α	α	NOUN
ejpam-5330	498	58	-	-	ADJ
ejpam-5330	498	59	interior	interior	ADJ
ejpam-5330	498	60	)	)	PUNCT
ejpam-5330	498	61	operators	operator	NOUN
ejpam-5330	498	62	have	have	AUX
ejpam-5330	498	63	been	be	AUX
ejpam-5330	498	64	introduced	introduce	VERB
ejpam-5330	498	65	in	in	ADP
ejpam-5330	498	66	an	an	DET
ejpam-5330	498	67	fstss	fstss	NOUN
ejpam-5330	498	68	based	base	VERB
ejpam-5330	498	69	on	on	ADP
ejpam-5330	498	70	the	the	DET
ejpam-5330	498	71	paper	paper	NOUN
ejpam-5330	498	72	by	by	ADP
ejpam-5330	498	73	aygünoǧlu	aygünoǧlu	PROPN
ejpam-5330	498	74	et	et	PROPN
ejpam-5330	498	75	al	al	PROPN
ejpam-5330	498	76	.	.	PUNCT
ejpam-5330	499	1	[	[	X
ejpam-5330	499	2	19	19	NUM
ejpam-5330	499	3	]	]	PUNCT
ejpam-5330	499	4	and	and	CCONJ
ejpam-5330	499	5	some	some	PRON
ejpam-5330	499	6	of	of	ADP
ejpam-5330	499	7	their	their	PRON
ejpam-5330	499	8	basic	basic	ADJ
ejpam-5330	499	9	properties	property	NOUN
ejpam-5330	499	10	have	have	AUX
ejpam-5330	499	11	been	be	AUX
ejpam-5330	499	12	investigated	investigate	VERB
ejpam-5330	499	13	.	.	PUNCT
ejpam-5330	500	1	thereafter	thereafter	ADV
ejpam-5330	500	2	,	,	PUNCT
ejpam-5330	500	3	the	the	DET
ejpam-5330	500	4	notion	notion	NOUN
ejpam-5330	500	5	of	of	ADP
ejpam-5330	500	6	r	r	NOUN
ejpam-5330	500	7	-	-	PUNCT
ejpam-5330	500	8	fuzzy	fuzzy	ADJ
ejpam-5330	500	9	soft	soft	ADJ
ejpam-5330	500	10	α	α	NOUN
ejpam-5330	500	11	-	-	PUNCT
ejpam-5330	500	12	connected	connect	VERB
ejpam-5330	500	13	sets	set	NOUN
ejpam-5330	500	14	has	have	AUX
ejpam-5330	500	15	been	be	AUX
ejpam-5330	500	16	defined	define	VERB
ejpam-5330	500	17	and	and	CCONJ
ejpam-5330	500	18	studied	study	VERB
ejpam-5330	500	19	.	.	PUNCT
ejpam-5330	501	1	furthermore	furthermore	ADV
ejpam-5330	501	2	,	,	PUNCT
ejpam-5330	501	3	some	some	DET
ejpam-5330	501	4	properties	property	NOUN
ejpam-5330	501	5	of	of	ADP
ejpam-5330	501	6	fuzzy	fuzzy	ADJ
ejpam-5330	501	7	soft	soft	ADJ
ejpam-5330	501	8	α	α	ADJ
ejpam-5330	501	9	-	-	ADJ
ejpam-5330	501	10	continuous	continuous	ADJ
ejpam-5330	501	11	mappings	mapping	NOUN
ejpam-5330	501	12	have	have	AUX
ejpam-5330	501	13	been	be	AUX
ejpam-5330	501	14	obtained	obtain	VERB
ejpam-5330	501	15	between	between	ADP
ejpam-5330	501	16	two	two	NUM
ejpam-5330	501	17	fstss	fstss	NOUN
ejpam-5330	501	18	(	(	PUNCT
ejpam-5330	501	19	w	w	PROPN
ejpam-5330	501	20	,	,	PUNCT
ejpam-5330	501	21	τn	τn	PROPN
ejpam-5330	501	22	)	)	PUNCT
ejpam-5330	501	23	and	and	CCONJ
ejpam-5330	501	24	(	(	PUNCT
ejpam-5330	501	25	v	v	NOUN
ejpam-5330	501	26	,	,	PUNCT
ejpam-5330	501	27	ηf	ηf	PROPN
ejpam-5330	501	28	)	)	PUNCT
ejpam-5330	501	29	.	.	PUNCT
ejpam-5330	502	1	moreover	moreover	ADV
ejpam-5330	502	2	,	,	PUNCT
ejpam-5330	502	3	as	as	ADP
ejpam-5330	502	4	a	a	DET
ejpam-5330	502	5	weaker	weak	ADJ
ejpam-5330	502	6	form	form	NOUN
ejpam-5330	502	7	of	of	ADP
ejpam-5330	502	8	the	the	DET
ejpam-5330	502	9	notion	notion	NOUN
ejpam-5330	502	10	of	of	ADP
ejpam-5330	502	11	fuzzy	fuzzy	ADJ
ejpam-5330	502	12	soft	soft	ADJ
ejpam-5330	502	13	α	α	ADJ
ejpam-5330	502	14	-	-	ADJ
ejpam-5330	502	15	continuous	continuous	ADJ
ejpam-5330	502	16	mappings	mapping	NOUN
ejpam-5330	502	17	,	,	PUNCT
ejpam-5330	502	18	the	the	DET
ejpam-5330	502	19	notions	notion	NOUN
ejpam-5330	502	20	of	of	ADP
ejpam-5330	502	21	fuzzy	fuzzy	ADJ
ejpam-5330	502	22	soft	soft	ADJ
ejpam-5330	502	23	almost	almost	ADV
ejpam-5330	502	24	(	(	PUNCT
ejpam-5330	502	25	weakly	weakly	ADJ
ejpam-5330	502	26	)	)	PUNCT
ejpam-5330	502	27	α	α	X
ejpam-5330	502	28	-	-	ADJ
ejpam-5330	502	29	continuous	continuous	ADJ
ejpam-5330	502	30	mappings	mapping	NOUN
ejpam-5330	502	31	have	have	AUX
ejpam-5330	502	32	been	be	AUX
ejpam-5330	502	33	introduced	introduce	VERB
ejpam-5330	502	34	and	and	CCONJ
ejpam-5330	502	35	some	some	PRON
ejpam-5330	502	36	of	of	ADP
ejpam-5330	502	37	their	their	PRON
ejpam-5330	502	38	characterizations	characterization	NOUN
ejpam-5330	502	39	have	have	AUX
ejpam-5330	502	40	been	be	AUX
ejpam-5330	502	41	investigated	investigate	VERB
ejpam-5330	502	42	.	.	PUNCT
ejpam-5330	503	1	also	also	ADV
ejpam-5330	503	2	,	,	PUNCT
ejpam-5330	503	3	we	we	PRON
ejpam-5330	503	4	have	have	AUX
ejpam-5330	503	5	shown	show	VERB
ejpam-5330	503	6	that	that	DET
ejpam-5330	503	7	fuzzy	fuzzy	ADJ
ejpam-5330	503	8	soft	soft	ADJ
ejpam-5330	503	9	α	α	NOUN
ejpam-5330	503	10	-	-	PUNCT
ejpam-5330	503	11	continuity	continuity	NOUN
ejpam-5330	503	12	⇒	⇒	NOUN
ejpam-5330	503	13	fuzzy	fuzzy	ADJ
ejpam-5330	503	14	soft	soft	ADJ
ejpam-5330	503	15	almost	almost	ADV
ejpam-5330	503	16	α	α	NOUN
ejpam-5330	503	17	-	-	PUNCT
ejpam-5330	503	18	continuity	continuity	NOUN
ejpam-5330	503	19	⇒	⇒	NOUN
ejpam-5330	503	20	fuzzy	fuzzy	ADJ
ejpam-5330	503	21	soft	soft	ADJ
ejpam-5330	503	22	weakly	weakly	ADJ
ejpam-5330	503	23	α	α	NOUN
ejpam-5330	503	24	-	-	NOUN
ejpam-5330	503	25	continuity	continuity	NOUN
ejpam-5330	504	1	and	and	CCONJ
ejpam-5330	504	2	we	we	PRON
ejpam-5330	504	3	have	have	VERB
ejpam-5330	504	4	the	the	DET
ejpam-5330	504	5	following	follow	VERB
ejpam-5330	504	6	:	:	PUNCT
ejpam-5330	504	7	•	•	NUM
ejpam-5330	504	8	fuzzy	fuzzy	ADJ
ejpam-5330	504	9	soft	soft	ADJ
ejpam-5330	504	10	(	(	PUNCT
ejpam-5330	504	11	idw	idw	PROPN
ejpam-5330	504	12	,	,	PUNCT
ejpam-5330	504	13	iτ	iτ	INTJ
ejpam-5330	504	14	(	(	PUNCT
ejpam-5330	504	15	cτ	cτ	INTJ
ejpam-5330	504	16	(	(	PUNCT
ejpam-5330	504	17	iτ	iτ	NOUN
ejpam-5330	504	18	)	)	PUNCT
ejpam-5330	504	19	)	)	PUNCT
ejpam-5330	504	20	,	,	PUNCT
ejpam-5330	504	21	idv	idv	PROPN
ejpam-5330	504	22	,	,	PUNCT
ejpam-5330	504	23	idv	idv	PROPN
ejpam-5330	504	24	)	)	PUNCT
ejpam-5330	504	25	-continuous	-continuous	ADJ
ejpam-5330	504	26	mapping	mapping	NOUN
ejpam-5330	504	27	is	be	AUX
ejpam-5330	504	28	fuzzy	fuzzy	ADJ
ejpam-5330	504	29	soft	soft	ADJ
ejpam-5330	504	30	α	α	NOUN
ejpam-5330	504	31	-	-	ADJ
ejpam-5330	504	32	continuous	continuous	ADJ
ejpam-5330	504	33	.	.	PUNCT
ejpam-5330	505	1	•	•	NUM
ejpam-5330	505	2	fuzzy	fuzzy	ADJ
ejpam-5330	505	3	soft	soft	ADJ
ejpam-5330	505	4	(	(	PUNCT
ejpam-5330	505	5	idw	idw	PROPN
ejpam-5330	505	6	,	,	PUNCT
ejpam-5330	505	7	αiτ	αiτ	NOUN
ejpam-5330	505	8	,	,	PUNCT
ejpam-5330	505	9	iη(cη	iη(cη	PROPN
ejpam-5330	505	10	)	)	PUNCT
ejpam-5330	505	11	,	,	PUNCT
ejpam-5330	505	12	idv	idv	PROPN
ejpam-5330	505	13	)	)	PUNCT
ejpam-5330	505	14	-continuous	-continuous	ADJ
ejpam-5330	505	15	mapping	mapping	NOUN
ejpam-5330	505	16	is	be	AUX
ejpam-5330	505	17	fuzzy	fuzzy	ADJ
ejpam-5330	505	18	soft	soft	ADJ
ejpam-5330	505	19	almost	almost	ADV
ejpam-5330	505	20	α	α	NOUN
ejpam-5330	505	21	-	-	ADJ
ejpam-5330	505	22	continuous	continuous	ADJ
ejpam-5330	505	23	.	.	PUNCT
ejpam-5330	505	24	•	•	NUM
ejpam-5330	505	25	fuzzy	fuzzy	ADJ
ejpam-5330	505	26	soft	soft	ADJ
ejpam-5330	505	27	(	(	PUNCT
ejpam-5330	505	28	idw	idw	PROPN
ejpam-5330	505	29	,	,	PUNCT
ejpam-5330	505	30	αiτ	αiτ	NOUN
ejpam-5330	505	31	,	,	PUNCT
ejpam-5330	505	32	cη	cη	PROPN
ejpam-5330	505	33	,	,	PUNCT
ejpam-5330	505	34	idv	idv	NOUN
ejpam-5330	505	35	)	)	PUNCT
ejpam-5330	505	36	-continuous	-continuous	ADJ
ejpam-5330	505	37	mapping	mapping	NOUN
ejpam-5330	505	38	is	be	AUX
ejpam-5330	505	39	fuzzy	fuzzy	ADJ
ejpam-5330	505	40	soft	soft	ADJ
ejpam-5330	505	41	weakly	weakly	ADJ
ejpam-5330	506	1	α	α	NOUN
ejpam-5330	506	2	-	-	ADJ
ejpam-5330	506	3	continuous	continuous	ADJ
ejpam-5330	506	4	.	.	PUNCT
ejpam-5330	507	1	in	in	ADP
ejpam-5330	507	2	the	the	DET
ejpam-5330	507	3	end	end	NOUN
ejpam-5330	507	4	,	,	PUNCT
ejpam-5330	507	5	new	new	ADJ
ejpam-5330	507	6	types	type	NOUN
ejpam-5330	507	7	of	of	ADP
ejpam-5330	507	8	soft	soft	ADJ
ejpam-5330	507	9	compactness	compactness	NOUN
ejpam-5330	507	10	via	via	ADP
ejpam-5330	507	11	r	r	NOUN
ejpam-5330	507	12	-	-	PUNCT
ejpam-5330	507	13	fuzzy	fuzzy	ADJ
ejpam-5330	507	14	soft	soft	ADJ
ejpam-5330	507	15	α	α	NOUN
ejpam-5330	507	16	-	-	ADJ
ejpam-5330	507	17	open	open	ADJ
ejpam-5330	507	18	sets	set	NOUN
ejpam-5330	507	19	have	have	AUX
ejpam-5330	507	20	been	be	AUX
ejpam-5330	507	21	explored	explore	VERB
ejpam-5330	507	22	and	and	CCONJ
ejpam-5330	507	23	the	the	DET
ejpam-5330	507	24	relationships	relationship	NOUN
ejpam-5330	507	25	between	between	ADP
ejpam-5330	507	26	them	they	PRON
ejpam-5330	507	27	have	have	AUX
ejpam-5330	507	28	been	be	AUX
ejpam-5330	507	29	studied	study	VERB
ejpam-5330	507	30	.	.	PUNCT
ejpam-5330	508	1	in	in	ADP
ejpam-5330	508	2	upcoming	upcoming	ADJ
ejpam-5330	508	3	papers	paper	NOUN
ejpam-5330	508	4	,	,	PUNCT
ejpam-5330	508	5	we	we	PRON
ejpam-5330	508	6	will	will	AUX
ejpam-5330	508	7	use	use	VERB
ejpam-5330	508	8	the	the	DET
ejpam-5330	508	9	fuzzy	fuzzy	ADJ
ejpam-5330	508	10	soft	soft	ADJ
ejpam-5330	508	11	α	α	NOUN
ejpam-5330	508	12	-	-	PUNCT
ejpam-5330	508	13	closure	closure	NOUN
ejpam-5330	508	14	operator	operator	NOUN
ejpam-5330	508	15	to	to	PART
ejpam-5330	508	16	define	define	VERB
ejpam-5330	508	17	some	some	DET
ejpam-5330	508	18	new	new	ADJ
ejpam-5330	508	19	separation	separation	NOUN
ejpam-5330	508	20	axioms	axiom	NOUN
ejpam-5330	508	21	in	in	ADP
ejpam-5330	508	22	an	an	DET
ejpam-5330	508	23	fsts	fst	NOUN
ejpam-5330	508	24	based	base	VERB
ejpam-5330	508	25	on	on	ADP
ejpam-5330	508	26	the	the	DET
ejpam-5330	508	27	paper	paper	NOUN
ejpam-5330	508	28	by	by	ADP
ejpam-5330	508	29	aygünoǧlu	aygünoǧlu	PROPN
ejpam-5330	508	30	et	et	PROPN
ejpam-5330	508	31	al	al	PROPN
ejpam-5330	508	32	.	.	PUNCT
ejpam-5330	509	1	[	[	X
ejpam-5330	509	2	19	19	NUM
ejpam-5330	509	3	]	]	PUNCT
ejpam-5330	509	4	.	.	PUNCT
ejpam-5330	510	1	also	also	ADV
ejpam-5330	510	2	,	,	PUNCT
ejpam-5330	510	3	we	we	PRON
ejpam-5330	510	4	shall	shall	AUX
ejpam-5330	510	5	discuss	discuss	VERB
ejpam-5330	510	6	some	some	PRON
ejpam-5330	510	7	of	of	ADP
ejpam-5330	510	8	the	the	DET
ejpam-5330	510	9	notions	notion	NOUN
ejpam-5330	510	10	given	give	VERB
ejpam-5330	510	11	here	here	ADV
ejpam-5330	510	12	in	in	ADP
ejpam-5330	510	13	the	the	DET
ejpam-5330	510	14	frames	frame	NOUN
ejpam-5330	510	15	of	of	ADP
ejpam-5330	510	16	fuzzy	fuzzy	ADJ
ejpam-5330	510	17	soft	soft	ADJ
ejpam-5330	510	18	r	r	NOUN
ejpam-5330	510	19	-	-	PUNCT
ejpam-5330	510	20	minimal	minimal	ADJ
ejpam-5330	510	21	structures	structure	NOUN
ejpam-5330	510	22	[	[	X
ejpam-5330	510	23	30	30	NUM
ejpam-5330	510	24	]	]	PUNCT
ejpam-5330	510	25	.	.	PUNCT
ejpam-5330	511	1	acknowledgements	acknowledgement	NOUN
ejpam-5330	511	2	we	we	PRON
ejpam-5330	511	3	would	would	AUX
ejpam-5330	511	4	like	like	VERB
ejpam-5330	511	5	to	to	PART
ejpam-5330	511	6	thank	thank	VERB
ejpam-5330	511	7	the	the	DET
ejpam-5330	511	8	reviewers	reviewer	NOUN
ejpam-5330	511	9	and	and	CCONJ
ejpam-5330	511	10	editors	editor	NOUN
ejpam-5330	511	11	whose	whose	DET
ejpam-5330	511	12	constructive	constructive	ADJ
ejpam-5330	511	13	comments	comment	NOUN
ejpam-5330	511	14	and	and	CCONJ
ejpam-5330	511	15	suggestions	suggestion	NOUN
ejpam-5330	511	16	helped	help	VERB
ejpam-5330	511	17	to	to	PART
ejpam-5330	511	18	improve	improve	VERB
ejpam-5330	511	19	this	this	DET
ejpam-5330	511	20	paper	paper	NOUN
ejpam-5330	511	21	.	.	PUNCT
ejpam-5330	512	1	references	reference	NOUN
ejpam-5330	512	2	[	[	X
ejpam-5330	512	3	1	1	NUM
ejpam-5330	512	4	]	]	PUNCT
ejpam-5330	512	5	b.	b.	PROPN
ejpam-5330	512	6	ahmad	ahmad	PROPN
ejpam-5330	512	7	and	and	CCONJ
ejpam-5330	512	8	a.	a.	PROPN
ejpam-5330	512	9	kharal	kharal	PROPN
ejpam-5330	512	10	.	.	PUNCT
ejpam-5330	513	1	on	on	ADP
ejpam-5330	513	2	fuzzy	fuzzy	ADJ
ejpam-5330	513	3	soft	soft	ADJ
ejpam-5330	513	4	sets	set	NOUN
ejpam-5330	513	5	.	.	PUNCT
ejpam-5330	514	1	adv	adv	PROPN
ejpam-5330	514	2	.	.	PUNCT
ejpam-5330	514	3	fuzzy	fuzzy	ADJ
ejpam-5330	514	4	syst	syst	PROPN
ejpam-5330	514	5	.	.	PUNCT
ejpam-5330	514	6	,	,	PUNCT
ejpam-5330	514	7	page	page	NOUN
ejpam-5330	514	8	586507	586507	NUM
ejpam-5330	514	9	,	,	PUNCT
ejpam-5330	514	10	2009	2009	NUM
ejpam-5330	514	11	.	.	PUNCT
ejpam-5330	515	1	[	[	X
ejpam-5330	515	2	2	2	NUM
ejpam-5330	515	3	]	]	PUNCT
ejpam-5330	515	4	m.	m.	NOUN
ejpam-5330	515	5	akdag	akdag	PROPN
ejpam-5330	515	6	and	and	CCONJ
ejpam-5330	515	7	a.	a.	NOUN
ejpam-5330	515	8	ozkan	ozkan	PROPN
ejpam-5330	515	9	.	.	PUNCT
ejpam-5330	516	1	on	on	ADP
ejpam-5330	516	2	soft	soft	ADJ
ejpam-5330	516	3	β	β	ADJ
ejpam-5330	516	4	-	-	ADJ
ejpam-5330	516	5	open	open	ADJ
ejpam-5330	516	6	sets	set	NOUN
ejpam-5330	516	7	and	and	CCONJ
ejpam-5330	516	8	soft	soft	ADJ
ejpam-5330	516	9	β	β	ADJ
ejpam-5330	516	10	-	-	ADJ
ejpam-5330	516	11	continuous	continuous	ADJ
ejpam-5330	516	12	functions	function	NOUN
ejpam-5330	516	13	.	.	PUNCT
ejpam-5330	517	1	sci	sci	PROPN
ejpam-5330	517	2	.	.	PROPN
ejpam-5330	517	3	world	world	PROPN
ejpam-5330	517	4	j.	j.	PROPN
ejpam-5330	517	5	,	,	PUNCT
ejpam-5330	517	6	page	page	NOUN
ejpam-5330	517	7	843456	843456	NUM
ejpam-5330	517	8	,	,	PUNCT
ejpam-5330	517	9	2014	2014	NUM
ejpam-5330	517	10	.	.	PUNCT
ejpam-5330	518	1	[	[	X
ejpam-5330	518	2	3	3	X
ejpam-5330	518	3	]	]	X
ejpam-5330	518	4	m.	m.	NOUN
ejpam-5330	518	5	akdag	akdag	PROPN
ejpam-5330	518	6	and	and	CCONJ
ejpam-5330	518	7	a.	a.	NOUN
ejpam-5330	518	8	ozkan	ozkan	PROPN
ejpam-5330	518	9	.	.	PUNCT
ejpam-5330	519	1	soft	soft	ADJ
ejpam-5330	519	2	α	α	NOUN
ejpam-5330	519	3	-	-	ADJ
ejpam-5330	519	4	open	open	ADJ
ejpam-5330	519	5	sets	set	NOUN
ejpam-5330	519	6	and	and	CCONJ
ejpam-5330	519	7	soft	soft	ADJ
ejpam-5330	519	8	α	α	PRON
ejpam-5330	519	9	-	-	ADJ
ejpam-5330	519	10	continuous	continuous	ADJ
ejpam-5330	519	11	functions	function	NOUN
ejpam-5330	519	12	.	.	PUNCT
ejpam-5330	520	1	abst	abst	PROPN
ejpam-5330	520	2	.	.	PROPN
ejpam-5330	520	3	appl	appl	PROPN
ejpam-5330	520	4	.	.	PUNCT
ejpam-5330	521	1	anal	anal	PROPN
ejpam-5330	521	2	.	.	PUNCT
ejpam-5330	521	3	,	,	PUNCT
ejpam-5330	521	4	page	page	NOUN
ejpam-5330	521	5	891341	891341	NUM
ejpam-5330	521	6	,	,	PUNCT
ejpam-5330	521	7	2014	2014	NUM
ejpam-5330	521	8	.	.	PUNCT
ejpam-5330	522	1	[	[	X
ejpam-5330	522	2	4	4	X
ejpam-5330	522	3	]	]	PUNCT
ejpam-5330	522	4	s.	s.	PROPN
ejpam-5330	522	5	al	al	PROPN
ejpam-5330	522	6	-	-	PROPN
ejpam-5330	522	7	ghour	ghour	PROPN
ejpam-5330	522	8	.	.	PUNCT
ejpam-5330	523	1	boolean	boolean	ADJ
ejpam-5330	523	2	algebra	algebra	NOUN
ejpam-5330	523	3	of	of	ADP
ejpam-5330	523	4	soft	soft	ADJ
ejpam-5330	523	5	q	q	NOUN
ejpam-5330	523	6	-	-	PUNCT
ejpam-5330	523	7	sets	set	NOUN
ejpam-5330	523	8	in	in	ADP
ejpam-5330	523	9	soft	soft	ADJ
ejpam-5330	523	10	topological	topological	ADJ
ejpam-5330	523	11	spaces	space	NOUN
ejpam-5330	523	12	.	.	PUNCT
ejpam-5330	524	1	appl	appl	PROPN
ejpam-5330	524	2	.	.	PUNCT
ejpam-5330	525	1	comput	comput	PROPN
ejpam-5330	525	2	.	.	PUNCT
ejpam-5330	526	1	intell	intell	PROPN
ejpam-5330	526	2	.	.	PUNCT
ejpam-5330	527	1	soft	soft	ADJ
ejpam-5330	527	2	comput	comput	NOUN
ejpam-5330	527	3	.	.	PUNCT
ejpam-5330	527	4	,	,	PUNCT
ejpam-5330	527	5	page	page	NOUN
ejpam-5330	527	6	5200590	5200590	NUM
ejpam-5330	527	7	,	,	PUNCT
ejpam-5330	527	8	2022	2022	NUM
ejpam-5330	527	9	.	.	PUNCT
ejpam-5330	528	1	references	reference	NOUN
ejpam-5330	528	2	4132	4132	NUM
ejpam-5330	529	1	[	[	X
ejpam-5330	529	2	5	5	NUM
ejpam-5330	529	3	]	]	PUNCT
ejpam-5330	529	4	s.	s.	PROPN
ejpam-5330	529	5	al	al	PROPN
ejpam-5330	529	6	-	-	PROPN
ejpam-5330	529	7	ghour	ghour	PROPN
ejpam-5330	529	8	and	and	CCONJ
ejpam-5330	529	9	j.	j.	PROPN
ejpam-5330	529	10	al	al	PROPN
ejpam-5330	529	11	-	-	PUNCT
ejpam-5330	529	12	mufarrij	mufarrij	PROPN
ejpam-5330	529	13	.	.	PUNCT
ejpam-5330	530	1	between	between	ADP
ejpam-5330	530	2	soft	soft	ADJ
ejpam-5330	530	3	complete	complete	ADJ
ejpam-5330	530	4	continuity	continuity	NOUN
ejpam-5330	530	5	and	and	CCONJ
ejpam-5330	530	6	soft	soft	ADJ
ejpam-5330	530	7	somewhatcontinuity	somewhatcontinuity	NOUN
ejpam-5330	530	8	.	.	PUNCT
ejpam-5330	530	9	symmetry	symmetry	PROPN
ejpam-5330	530	10	,	,	PUNCT
ejpam-5330	530	11	15:1–14	15:1–14	NUM
ejpam-5330	530	12	,	,	PUNCT
ejpam-5330	530	13	2023	2023	NUM
ejpam-5330	530	14	.	.	PUNCT
ejpam-5330	531	1	[	[	X
ejpam-5330	531	2	6	6	NUM
ejpam-5330	531	3	]	]	PUNCT
ejpam-5330	531	4	t.	t.	PROPN
ejpam-5330	531	5	m.	m.	PROPN
ejpam-5330	531	6	al	al	PROPN
ejpam-5330	531	7	-	-	PUNCT
ejpam-5330	531	8	shami	shami	PROPN
ejpam-5330	531	9	.	.	PUNCT
ejpam-5330	532	1	soft	soft	ADJ
ejpam-5330	532	2	somewhere	somewhere	ADV
ejpam-5330	532	3	dense	dense	ADJ
ejpam-5330	532	4	sets	set	NOUN
ejpam-5330	532	5	on	on	ADP
ejpam-5330	532	6	soft	soft	ADJ
ejpam-5330	532	7	topological	topological	ADJ
ejpam-5330	532	8	spaces	space	NOUN
ejpam-5330	532	9	.	.	PUNCT
ejpam-5330	533	1	commun	commun	PROPN
ejpam-5330	533	2	.	.	PUNCT
ejpam-5330	534	1	korean	korean	ADJ
ejpam-5330	534	2	math	math	PROPN
ejpam-5330	534	3	.	.	PUNCT
ejpam-5330	535	1	soc	soc	PROPN
ejpam-5330	535	2	.	.	PUNCT
ejpam-5330	535	3	,	,	PUNCT
ejpam-5330	535	4	33:1341–1356	33:1341–1356	NUM
ejpam-5330	535	5	,	,	PUNCT
ejpam-5330	535	6	2018	2018	NUM
ejpam-5330	535	7	.	.	PUNCT
ejpam-5330	536	1	[	[	X
ejpam-5330	536	2	7	7	X
ejpam-5330	536	3	]	]	PUNCT
ejpam-5330	536	4	t.	t.	PROPN
ejpam-5330	536	5	m.	m.	PROPN
ejpam-5330	536	6	al	al	PROPN
ejpam-5330	536	7	-	-	PUNCT
ejpam-5330	536	8	shami	shami	PROPN
ejpam-5330	536	9	.	.	PUNCT
ejpam-5330	537	1	on	on	ADP
ejpam-5330	537	2	soft	soft	ADJ
ejpam-5330	537	3	separation	separation	NOUN
ejpam-5330	537	4	axioms	axiom	NOUN
ejpam-5330	537	5	and	and	CCONJ
ejpam-5330	537	6	their	their	PRON
ejpam-5330	537	7	applications	application	NOUN
ejpam-5330	537	8	on	on	ADP
ejpam-5330	537	9	decision	decision	NOUN
ejpam-5330	537	10	-	-	PUNCT
ejpam-5330	537	11	making	make	VERB
ejpam-5330	537	12	problem	problem	NOUN
ejpam-5330	537	13	.	.	PUNCT
ejpam-5330	538	1	math	math	NOUN
ejpam-5330	538	2	.	.	PUNCT
ejpam-5330	539	1	probl	probl	PROPN
ejpam-5330	539	2	.	.	PUNCT
ejpam-5330	540	1	eng	eng	PROPN
ejpam-5330	540	2	.	.	PROPN
ejpam-5330	540	3	,	,	PUNCT
ejpam-5330	540	4	pages	page	NOUN
ejpam-5330	540	5	1–12	1–12	PROPN
ejpam-5330	540	6	,	,	PUNCT
ejpam-5330	540	7	2021	2021	NUM
ejpam-5330	540	8	.	.	PUNCT
ejpam-5330	541	1	[	[	X
ejpam-5330	541	2	8	8	NUM
ejpam-5330	541	3	]	]	PUNCT
ejpam-5330	541	4	t.	t.	PROPN
ejpam-5330	541	5	m.	m.	PROPN
ejpam-5330	541	6	al	al	PROPN
ejpam-5330	541	7	-	-	PUNCT
ejpam-5330	541	8	shami	shami	PROPN
ejpam-5330	541	9	,	,	PUNCT
ejpam-5330	541	10	m.	m.	NOUN
ejpam-5330	541	11	arar	arar	PROPN
ejpam-5330	541	12	,	,	PUNCT
ejpam-5330	541	13	r.	r.	PROPN
ejpam-5330	541	14	abu	abu	PROPN
ejpam-5330	541	15	-	-	PUNCT
ejpam-5330	541	16	gdairi	gdairi	PROPN
ejpam-5330	541	17	,	,	PUNCT
ejpam-5330	541	18	and	and	CCONJ
ejpam-5330	541	19	z.	z.	PROPN
ejpam-5330	541	20	a.	a.	PROPN
ejpam-5330	541	21	ameen	ameen	PROPN
ejpam-5330	541	22	.	.	PUNCT
ejpam-5330	542	1	on	on	ADP
ejpam-5330	542	2	weakly	weakly	ADJ
ejpam-5330	542	3	soft	soft	ADJ
ejpam-5330	542	4	β	β	NOUN
ejpam-5330	542	5	-	-	ADJ
ejpam-5330	542	6	open	open	ADJ
ejpam-5330	542	7	sets	set	NOUN
ejpam-5330	542	8	and	and	CCONJ
ejpam-5330	542	9	weakly	weakly	ADJ
ejpam-5330	542	10	soft	soft	ADJ
ejpam-5330	542	11	β	β	NOUN
ejpam-5330	542	12	-	-	NOUN
ejpam-5330	542	13	continuity	continuity	NOUN
ejpam-5330	542	14	.	.	PUNCT
ejpam-5330	543	1	j.	j.	PROPN
ejpam-5330	543	2	inte	inte	PROPN
ejpam-5330	543	3	.	.	PUNCT
ejpam-5330	544	1	fuzzy	fuzzy	ADJ
ejpam-5330	544	2	syst	syst	PROPN
ejpam-5330	544	3	.	.	PUNCT
ejpam-5330	544	4	,	,	PUNCT
ejpam-5330	544	5	45:6351–6363	45:6351–6363	NUM
ejpam-5330	544	6	,	,	PUNCT
ejpam-5330	544	7	2023	2023	NUM
ejpam-5330	544	8	.	.	PUNCT
ejpam-5330	545	1	[	[	X
ejpam-5330	545	2	9	9	NUM
ejpam-5330	545	3	]	]	PUNCT
ejpam-5330	545	4	t.	t.	PROPN
ejpam-5330	545	5	m.	m.	PROPN
ejpam-5330	545	6	al	al	PROPN
ejpam-5330	545	7	-	-	PUNCT
ejpam-5330	545	8	shami	shami	PROPN
ejpam-5330	545	9	,	,	PUNCT
ejpam-5330	545	10	s.	s.	PROPN
ejpam-5330	545	11	saleh	saleh	PROPN
ejpam-5330	545	12	,	,	PUNCT
ejpam-5330	545	13	a.	a.	PROPN
ejpam-5330	545	14	m.	m.	PROPN
ejpam-5330	545	15	abd	abd	PROPN
ejpam-5330	545	16	el	el	PROPN
ejpam-5330	545	17	-	-	PROPN
ejpam-5330	545	18	latif	latif	PROPN
ejpam-5330	545	19	,	,	PUNCT
ejpam-5330	545	20	and	and	CCONJ
ejpam-5330	545	21	a.	a.	NOUN
ejpam-5330	545	22	mhemdi	mhemdi	PROPN
ejpam-5330	545	23	.	.	PUNCT
ejpam-5330	546	1	novel	novel	ADJ
ejpam-5330	546	2	categories	category	NOUN
ejpam-5330	546	3	of	of	ADP
ejpam-5330	546	4	spaces	space	NOUN
ejpam-5330	546	5	in	in	ADP
ejpam-5330	546	6	the	the	DET
ejpam-5330	546	7	frame	frame	NOUN
ejpam-5330	546	8	of	of	ADP
ejpam-5330	546	9	fuzzy	fuzzy	ADJ
ejpam-5330	546	10	soft	soft	ADJ
ejpam-5330	546	11	topologies	topology	NOUN
ejpam-5330	546	12	.	.	PUNCT
ejpam-5330	547	1	aims	aim	VERB
ejpam-5330	547	2	mathematics	mathematic	NOUN
ejpam-5330	547	3	,	,	PUNCT
ejpam-5330	547	4	9(3):6305–6320	9(3):6305–6320	NUM
ejpam-5330	547	5	,	,	PUNCT
ejpam-5330	547	6	2024	2024	NUM
ejpam-5330	547	7	.	.	PUNCT
ejpam-5330	548	1	[	[	X
ejpam-5330	548	2	10	10	NUM
ejpam-5330	548	3	]	]	X
ejpam-5330	548	4	j.	j.	PROPN
ejpam-5330	548	5	c.	c.	PROPN
ejpam-5330	548	6	r.	r.	PROPN
ejpam-5330	548	7	alcantud	alcantud	PROPN
ejpam-5330	548	8	.	.	PUNCT
ejpam-5330	549	1	soft	soft	ADJ
ejpam-5330	549	2	open	open	ADJ
ejpam-5330	549	3	bases	basis	NOUN
ejpam-5330	549	4	and	and	CCONJ
ejpam-5330	549	5	a	a	DET
ejpam-5330	549	6	novel	novel	ADJ
ejpam-5330	549	7	construction	construction	NOUN
ejpam-5330	549	8	of	of	ADP
ejpam-5330	549	9	soft	soft	ADJ
ejpam-5330	549	10	topologies	topology	NOUN
ejpam-5330	549	11	from	from	ADP
ejpam-5330	549	12	bases	basis	NOUN
ejpam-5330	549	13	for	for	ADP
ejpam-5330	549	14	topologies	topology	NOUN
ejpam-5330	549	15	.	.	PUNCT
ejpam-5330	550	1	mathematics	mathematic	NOUN
ejpam-5330	550	2	,	,	PUNCT
ejpam-5330	550	3	8:672	8:672	NUM
ejpam-5330	550	4	,	,	PUNCT
ejpam-5330	550	5	2020	2020	NUM
ejpam-5330	550	6	.	.	PUNCT
ejpam-5330	551	1	[	[	X
ejpam-5330	551	2	11	11	NUM
ejpam-5330	551	3	]	]	X
ejpam-5330	551	4	i.	i.	NOUN
ejpam-5330	551	5	alshammari	alshammari	PROPN
ejpam-5330	551	6	,	,	PUNCT
ejpam-5330	551	7	m.	m.	PROPN
ejpam-5330	551	8	h.	h.	PROPN
ejpam-5330	551	9	alqahtani	alqahtani	PROPN
ejpam-5330	551	10	,	,	PUNCT
ejpam-5330	551	11	and	and	CCONJ
ejpam-5330	551	12	i.	i.	PROPN
ejpam-5330	551	13	m.	m.	PROPN
ejpam-5330	551	14	taha	taha	PROPN
ejpam-5330	551	15	.	.	PUNCT
ejpam-5330	552	1	on	on	ADP
ejpam-5330	552	2	r	r	NOUN
ejpam-5330	552	3	-	-	PUNCT
ejpam-5330	552	4	fuzzy	fuzzy	ADJ
ejpam-5330	552	5	soft	soft	ADJ
ejpam-5330	552	6	δ	δ	NOUN
ejpam-5330	552	7	-	-	ADJ
ejpam-5330	552	8	open	open	ADJ
ejpam-5330	552	9	sets	set	NOUN
ejpam-5330	552	10	and	and	CCONJ
ejpam-5330	552	11	applications	application	NOUN
ejpam-5330	552	12	via	via	ADP
ejpam-5330	552	13	fuzzy	fuzzy	ADJ
ejpam-5330	552	14	soft	soft	ADJ
ejpam-5330	552	15	topologies	topology	NOUN
ejpam-5330	552	16	.	.	PUNCT
ejpam-5330	553	1	preprints	preprint	NOUN
ejpam-5330	553	2	,	,	PUNCT
ejpam-5330	553	3	page	page	NOUN
ejpam-5330	553	4	2023121240	2023121240	NUM
ejpam-5330	553	5	,	,	PUNCT
ejpam-5330	553	6	2023	2023	NUM
ejpam-5330	553	7	.	.	PUNCT
ejpam-5330	554	1	[	[	X
ejpam-5330	554	2	12	12	NUM
ejpam-5330	554	3	]	]	X
ejpam-5330	554	4	i.	i.	NOUN
ejpam-5330	554	5	alshammari	alshammari	PROPN
ejpam-5330	554	6	and	and	CCONJ
ejpam-5330	554	7	i.	i.	PROPN
ejpam-5330	554	8	m.	m.	PROPN
ejpam-5330	554	9	taha	taha	PROPN
ejpam-5330	554	10	.	.	PUNCT
ejpam-5330	555	1	on	on	ADP
ejpam-5330	555	2	fuzzy	fuzzy	ADJ
ejpam-5330	555	3	soft	soft	ADJ
ejpam-5330	555	4	β	β	NOUN
ejpam-5330	555	5	-	-	NOUN
ejpam-5330	555	6	continuity	continuity	NOUN
ejpam-5330	555	7	and	and	CCONJ
ejpam-5330	555	8	β	β	NOUN
ejpam-5330	555	9	-	-	NOUN
ejpam-5330	555	10	irresoluteness	irresoluteness	NOUN
ejpam-5330	555	11	:	:	PUNCT
ejpam-5330	555	12	some	some	DET
ejpam-5330	555	13	new	new	ADJ
ejpam-5330	555	14	results	result	NOUN
ejpam-5330	555	15	.	.	PUNCT
ejpam-5330	556	1	aims	aim	VERB
ejpam-5330	556	2	mathematics	mathematic	NOUN
ejpam-5330	556	3	,	,	PUNCT
ejpam-5330	556	4	9(5):11304–11319	9(5):11304–11319	PROPN
ejpam-5330	556	5	,	,	PUNCT
ejpam-5330	556	6	2024	2024	NUM
ejpam-5330	556	7	.	.	PUNCT
ejpam-5330	557	1	[	[	X
ejpam-5330	557	2	13	13	NUM
ejpam-5330	557	3	]	]	PUNCT
ejpam-5330	557	4	s.	s.	PROPN
ejpam-5330	557	5	atmaca	atmaca	PROPN
ejpam-5330	557	6	and	and	CCONJ
ejpam-5330	557	7	i.	i.	PROPN
ejpam-5330	557	8	zorlutuna	zorlutuna	PROPN
ejpam-5330	557	9	.	.	PUNCT
ejpam-5330	558	1	on	on	ADP
ejpam-5330	558	2	fuzzy	fuzzy	ADJ
ejpam-5330	558	3	soft	soft	ADJ
ejpam-5330	558	4	topological	topological	ADJ
ejpam-5330	558	5	spaces	space	NOUN
ejpam-5330	558	6	.	.	PUNCT
ejpam-5330	559	1	ann	ann	PROPN
ejpam-5330	559	2	.	.	PUNCT
ejpam-5330	559	3	fuzzy	fuzzy	ADJ
ejpam-5330	559	4	math	math	NOUN
ejpam-5330	559	5	.	.	PUNCT
ejpam-5330	560	1	inform	inform	NOUN
ejpam-5330	560	2	.	.	PUNCT
ejpam-5330	560	3	,	,	PUNCT
ejpam-5330	560	4	5:377–386	5:377–386	NUM
ejpam-5330	560	5	,	,	PUNCT
ejpam-5330	560	6	2013	2013	NUM
ejpam-5330	560	7	.	.	PUNCT
ejpam-5330	561	1	[	[	X
ejpam-5330	561	2	14	14	NUM
ejpam-5330	561	3	]	]	X
ejpam-5330	561	4	n.	n.	PROPN
ejpam-5330	561	5	çaǧman	çaǧman	PROPN
ejpam-5330	561	6	,	,	PUNCT
ejpam-5330	561	7	s.	s.	PROPN
ejpam-5330	561	8	enginoǧlu	enginoǧlu	PROPN
ejpam-5330	561	9	,	,	PUNCT
ejpam-5330	561	10	and	and	CCONJ
ejpam-5330	561	11	f.	f.	PROPN
ejpam-5330	561	12	çitak	çitak	PROPN
ejpam-5330	561	13	.	.	PUNCT
ejpam-5330	562	1	fuzzy	fuzzy	ADJ
ejpam-5330	562	2	soft	soft	ADJ
ejpam-5330	562	3	set	set	NOUN
ejpam-5330	562	4	theory	theory	NOUN
ejpam-5330	562	5	and	and	CCONJ
ejpam-5330	562	6	its	its	PRON
ejpam-5330	562	7	applications	application	NOUN
ejpam-5330	562	8	.	.	PUNCT
ejpam-5330	563	1	iran	iran	PROPN
ejpam-5330	563	2	.	.	PUNCT
ejpam-5330	564	1	j.	j.	PROPN
ejpam-5330	564	2	fuzzy	fuzzy	PROPN
ejpam-5330	564	3	syst	syst	PROPN
ejpam-5330	564	4	.	.	PUNCT
ejpam-5330	564	5	,	,	PUNCT
ejpam-5330	564	6	8:137–147	8:137–147	NUM
ejpam-5330	564	7	,	,	PUNCT
ejpam-5330	564	8	2011	2011	NUM
ejpam-5330	564	9	.	.	PUNCT
ejpam-5330	565	1	[	[	X
ejpam-5330	565	2	15	15	X
ejpam-5330	565	3	]	]	X
ejpam-5330	565	4	v.	v.	CCONJ
ejpam-5330	565	5	çetkin	çetkin	PROPN
ejpam-5330	565	6	and	and	CCONJ
ejpam-5330	565	7	h.	h.	PROPN
ejpam-5330	565	8	aygün	aygün	PROPN
ejpam-5330	565	9	.	.	PUNCT
ejpam-5330	566	1	fuzzy	fuzzy	ADJ
ejpam-5330	566	2	soft	soft	ADJ
ejpam-5330	566	3	semiregularization	semiregularization	NOUN
ejpam-5330	566	4	spaces	space	NOUN
ejpam-5330	566	5	.	.	PUNCT
ejpam-5330	567	1	ann	ann	PROPN
ejpam-5330	567	2	.	.	PUNCT
ejpam-5330	567	3	fuzzy	fuzzy	ADJ
ejpam-5330	567	4	math	math	NOUN
ejpam-5330	567	5	.	.	PUNCT
ejpam-5330	568	1	inform	inform	NOUN
ejpam-5330	568	2	.	.	PUNCT
ejpam-5330	568	3	,	,	PUNCT
ejpam-5330	568	4	7:687–697	7:687–697	NOUN
ejpam-5330	568	5	,	,	PUNCT
ejpam-5330	568	6	2014	2014	NUM
ejpam-5330	568	7	.	.	PUNCT
ejpam-5330	569	1	[	[	X
ejpam-5330	569	2	16	16	X
ejpam-5330	569	3	]	]	X
ejpam-5330	569	4	v.	v.	PROPN
ejpam-5330	569	5	çetkin	çetkin	PROPN
ejpam-5330	569	6	,	,	PUNCT
ejpam-5330	569	7	a.	a.	NOUN
ejpam-5330	569	8	aygünoǧlu	aygünoǧlu	PROPN
ejpam-5330	569	9	,	,	PUNCT
ejpam-5330	569	10	and	and	CCONJ
ejpam-5330	569	11	h.	h.	PROPN
ejpam-5330	569	12	aygün	aygün	PROPN
ejpam-5330	569	13	.	.	PUNCT
ejpam-5330	570	1	on	on	ADP
ejpam-5330	570	2	soft	soft	ADJ
ejpam-5330	570	3	fuzzy	fuzzy	ADJ
ejpam-5330	570	4	closure	closure	NOUN
ejpam-5330	570	5	and	and	CCONJ
ejpam-5330	570	6	interior	interior	ADJ
ejpam-5330	570	7	operators	operator	NOUN
ejpam-5330	570	8	.	.	PUNCT
ejpam-5330	571	1	util	util	PROPN
ejpam-5330	571	2	.	.	PUNCT
ejpam-5330	572	1	math	math	NOUN
ejpam-5330	572	2	.	.	PUNCT
ejpam-5330	573	1	,	,	PUNCT
ejpam-5330	573	2	99:341–367	99:341–367	PROPN
ejpam-5330	573	3	,	,	PUNCT
ejpam-5330	573	4	2016	2016	NUM
ejpam-5330	573	5	.	.	PUNCT
ejpam-5330	574	1	[	[	X
ejpam-5330	574	2	17	17	NUM
ejpam-5330	574	3	]	]	PUNCT
ejpam-5330	574	4	s.	s.	PROPN
ejpam-5330	574	5	a.	a.	PROPN
ejpam-5330	574	6	el	el	PROPN
ejpam-5330	574	7	-	-	PUNCT
ejpam-5330	574	8	sheikh	sheikh	PROPN
ejpam-5330	574	9	,	,	PUNCT
ejpam-5330	574	10	r.	r.	PROPN
ejpam-5330	574	11	a.	a.	PROPN
ejpam-5330	574	12	hosny	hosny	PROPN
ejpam-5330	574	13	,	,	PUNCT
ejpam-5330	574	14	and	and	CCONJ
ejpam-5330	574	15	a.	a.	NOUN
ejpam-5330	574	16	m.	m.	PROPN
ejpam-5330	574	17	abd	abd	PROPN
ejpam-5330	574	18	el	el	PROPN
ejpam-5330	574	19	-	-	PROPN
ejpam-5330	574	20	latif	latif	PROPN
ejpam-5330	574	21	.	.	PUNCT
ejpam-5330	575	1	characterizations	characterization	NOUN
ejpam-5330	575	2	of	of	ADP
ejpam-5330	575	3	β	β	NOUN
ejpam-5330	575	4	-	-	ADJ
ejpam-5330	575	5	soft	soft	ADJ
ejpam-5330	575	6	separation	separation	NOUN
ejpam-5330	575	7	axioms	axiom	NOUN
ejpam-5330	575	8	in	in	ADP
ejpam-5330	575	9	soft	soft	ADJ
ejpam-5330	575	10	topological	topological	ADJ
ejpam-5330	575	11	spaces	space	NOUN
ejpam-5330	575	12	.	.	PUNCT
ejpam-5330	576	1	inf	inf	PROPN
ejpam-5330	576	2	.	.	PUNCT
ejpam-5330	577	1	sci	sci	PROPN
ejpam-5330	577	2	.	.	PUNCT
ejpam-5330	577	3	lett	lett	PROPN
ejpam-5330	577	4	.	.	PROPN
ejpam-5330	577	5	,	,	PUNCT
ejpam-5330	577	6	4:125–133	4:125–133	NUM
ejpam-5330	577	7	,	,	PUNCT
ejpam-5330	577	8	2015	2015	NUM
ejpam-5330	577	9	.	.	PUNCT
ejpam-5330	578	1	[	[	X
ejpam-5330	578	2	18	18	NUM
ejpam-5330	578	3	]	]	PUNCT
ejpam-5330	578	4	a.	a.	NOUN
ejpam-5330	578	5	aygünoǧlu	aygünoǧlu	PROPN
ejpam-5330	578	6	and	and	CCONJ
ejpam-5330	578	7	h.	h.	PROPN
ejpam-5330	578	8	aygün	aygün	PROPN
ejpam-5330	578	9	.	.	PUNCT
ejpam-5330	579	1	some	some	DET
ejpam-5330	579	2	notes	note	NOUN
ejpam-5330	579	3	on	on	ADP
ejpam-5330	579	4	soft	soft	ADJ
ejpam-5330	579	5	topological	topological	ADJ
ejpam-5330	579	6	spaces	space	NOUN
ejpam-5330	579	7	.	.	PUNCT
ejpam-5330	580	1	neural	neural	ADJ
ejpam-5330	580	2	comput	comput	NOUN
ejpam-5330	580	3	.	.	PUNCT
ejpam-5330	581	1	appl	appl	PROPN
ejpam-5330	581	2	.	.	PROPN
ejpam-5330	581	3	,	,	PUNCT
ejpam-5330	581	4	21:113–119	21:113–119	PROPN
ejpam-5330	581	5	,	,	PUNCT
ejpam-5330	581	6	2012	2012	NUM
ejpam-5330	581	7	.	.	PUNCT
ejpam-5330	582	1	[	[	X
ejpam-5330	582	2	19	19	NUM
ejpam-5330	582	3	]	]	X
ejpam-5330	582	4	a.	a.	NOUN
ejpam-5330	582	5	aygünoǧlu	aygünoǧlu	PROPN
ejpam-5330	582	6	,	,	PUNCT
ejpam-5330	582	7	v.	v.	PROPN
ejpam-5330	582	8	çetkin	çetkin	PROPN
ejpam-5330	582	9	,	,	PUNCT
ejpam-5330	582	10	and	and	CCONJ
ejpam-5330	582	11	h.	h.	PROPN
ejpam-5330	582	12	aygün	aygün	PROPN
ejpam-5330	582	13	.	.	PUNCT
ejpam-5330	583	1	an	an	DET
ejpam-5330	583	2	introduction	introduction	NOUN
ejpam-5330	583	3	to	to	ADP
ejpam-5330	583	4	fuzzy	fuzzy	ADJ
ejpam-5330	583	5	soft	soft	ADJ
ejpam-5330	583	6	topological	topological	ADJ
ejpam-5330	583	7	spaces	space	NOUN
ejpam-5330	583	8	.	.	PUNCT
ejpam-5330	584	1	hacet	hacet	PROPN
ejpam-5330	584	2	.	.	PUNCT
ejpam-5330	585	1	j.	j.	PROPN
ejpam-5330	585	2	math	math	PROPN
ejpam-5330	585	3	.	.	PUNCT
ejpam-5330	586	1	stat	stat	PROPN
ejpam-5330	586	2	.	.	PUNCT
ejpam-5330	586	3	,	,	PUNCT
ejpam-5330	586	4	43:193–208	43:193–208	NOUN
ejpam-5330	586	5	,	,	PUNCT
ejpam-5330	586	6	2014	2014	NUM
ejpam-5330	586	7	.	.	PUNCT
ejpam-5330	587	1	[	[	X
ejpam-5330	587	2	20	20	NUM
ejpam-5330	587	3	]	]	PUNCT
ejpam-5330	587	4	s.	s.	PROPN
ejpam-5330	587	5	hussain	hussain	PROPN
ejpam-5330	587	6	and	and	CCONJ
ejpam-5330	587	7	b.	b.	PROPN
ejpam-5330	587	8	ahmad	ahmad	PROPN
ejpam-5330	587	9	.	.	PUNCT
ejpam-5330	587	10	soft	soft	ADJ
ejpam-5330	587	11	separation	separation	NOUN
ejpam-5330	587	12	axioms	axiom	NOUN
ejpam-5330	587	13	in	in	ADP
ejpam-5330	587	14	soft	soft	ADJ
ejpam-5330	587	15	topological	topological	ADJ
ejpam-5330	587	16	spaces	space	NOUN
ejpam-5330	587	17	.	.	PUNCT
ejpam-5330	588	1	hacet	hacet	PROPN
ejpam-5330	588	2	.	.	PUNCT
ejpam-5330	589	1	j.	j.	PROPN
ejpam-5330	589	2	math	math	PROPN
ejpam-5330	589	3	.	.	PUNCT
ejpam-5330	590	1	stat	stat	PROPN
ejpam-5330	590	2	.	.	PUNCT
ejpam-5330	590	3	,	,	PUNCT
ejpam-5330	590	4	44:559–568	44:559–568	PROPN
ejpam-5330	590	5	,	,	PUNCT
ejpam-5330	590	6	2015	2015	NUM
ejpam-5330	590	7	.	.	PUNCT
ejpam-5330	591	1	references	reference	NOUN
ejpam-5330	591	2	4133	4133	NUM
ejpam-5330	592	1	[	[	X
ejpam-5330	592	2	21	21	NUM
ejpam-5330	592	3	]	]	X
ejpam-5330	592	4	s.	s.	PROPN
ejpam-5330	592	5	kaur	kaur	PROPN
ejpam-5330	592	6	,	,	PUNCT
ejpam-5330	592	7	t.	t.	PROPN
ejpam-5330	592	8	m.	m.	PROPN
ejpam-5330	592	9	al	al	PROPN
ejpam-5330	592	10	-	-	PUNCT
ejpam-5330	592	11	shami	shami	PROPN
ejpam-5330	592	12	,	,	PUNCT
ejpam-5330	592	13	a.	a.	NOUN
ejpam-5330	592	14	ozkan	ozkan	PROPN
ejpam-5330	592	15	,	,	PUNCT
ejpam-5330	592	16	and	and	CCONJ
ejpam-5330	592	17	m.	m.	PROPN
ejpam-5330	592	18	hosny	hosny	PROPN
ejpam-5330	592	19	.	.	PUNCT
ejpam-5330	593	1	a	a	DET
ejpam-5330	593	2	new	new	ADJ
ejpam-5330	593	3	approach	approach	NOUN
ejpam-5330	593	4	to	to	ADP
ejpam-5330	593	5	soft	soft	ADJ
ejpam-5330	593	6	continuity	continuity	NOUN
ejpam-5330	593	7	.	.	PUNCT
ejpam-5330	594	1	mathematics	mathematic	NOUN
ejpam-5330	594	2	,	,	PUNCT
ejpam-5330	594	3	11:3164	11:3164	NUM
ejpam-5330	594	4	,	,	PUNCT
ejpam-5330	594	5	2023	2023	NUM
ejpam-5330	594	6	.	.	PUNCT
ejpam-5330	595	1	[	[	X
ejpam-5330	595	2	22	22	NUM
ejpam-5330	595	3	]	]	PUNCT
ejpam-5330	595	4	p.	p.	PROPN
ejpam-5330	595	5	k.	k.	PROPN
ejpam-5330	596	1	maji	maji	PROPN
ejpam-5330	596	2	,	,	PUNCT
ejpam-5330	596	3	r.	r.	PROPN
ejpam-5330	596	4	biswas	biswas	PROPN
ejpam-5330	596	5	,	,	PUNCT
ejpam-5330	596	6	and	and	CCONJ
ejpam-5330	597	1	a.	a.	PROPN
ejpam-5330	597	2	r.	r.	PROPN
ejpam-5330	597	3	roy	roy	PROPN
ejpam-5330	597	4	.	.	PROPN
ejpam-5330	597	5	fuzzy	fuzzy	ADJ
ejpam-5330	597	6	soft	soft	ADJ
ejpam-5330	597	7	sets	set	NOUN
ejpam-5330	597	8	.	.	PUNCT
ejpam-5330	598	1	j.	j.	PROPN
ejpam-5330	598	2	fuzzy	fuzzy	PROPN
ejpam-5330	598	3	math	math	PROPN
ejpam-5330	598	4	.	.	PUNCT
ejpam-5330	598	5	,	,	PUNCT
ejpam-5330	598	6	9:589–602	9:589–602	NUM
ejpam-5330	598	7	,	,	PUNCT
ejpam-5330	598	8	2001	2001	NUM
ejpam-5330	598	9	.	.	PUNCT
ejpam-5330	599	1	[	[	X
ejpam-5330	599	2	23	23	NUM
ejpam-5330	599	3	]	]	PUNCT
ejpam-5330	599	4	s.	s.	PROPN
ejpam-5330	599	5	mishra	mishra	PROPN
ejpam-5330	599	6	and	and	CCONJ
ejpam-5330	599	7	r.	r.	PROPN
ejpam-5330	599	8	srivastava	srivastava	PROPN
ejpam-5330	599	9	.	.	PUNCT
ejpam-5330	600	1	hausdorff	hausdorff	PROPN
ejpam-5330	600	2	fuzzy	fuzzy	ADJ
ejpam-5330	600	3	soft	soft	ADJ
ejpam-5330	600	4	topological	topological	ADJ
ejpam-5330	600	5	spaces	space	NOUN
ejpam-5330	600	6	.	.	PUNCT
ejpam-5330	601	1	ann	ann	PROPN
ejpam-5330	601	2	.	.	PUNCT
ejpam-5330	601	3	fuzzy	fuzzy	ADJ
ejpam-5330	601	4	math	math	NOUN
ejpam-5330	601	5	.	.	PUNCT
ejpam-5330	602	1	inform	inform	NOUN
ejpam-5330	602	2	.	.	PUNCT
ejpam-5330	602	3	,	,	PUNCT
ejpam-5330	602	4	9:247–260	9:247–260	NOUN
ejpam-5330	602	5	,	,	PUNCT
ejpam-5330	602	6	2015	2015	NUM
ejpam-5330	602	7	.	.	PUNCT
ejpam-5330	603	1	[	[	X
ejpam-5330	603	2	24	24	NUM
ejpam-5330	603	3	]	]	X
ejpam-5330	603	4	d.	d.	PROPN
ejpam-5330	603	5	molodtsov	molodtsov	PROPN
ejpam-5330	603	6	.	.	PUNCT
ejpam-5330	604	1	soft	soft	ADJ
ejpam-5330	604	2	set	set	NOUN
ejpam-5330	604	3	theory	theory	NOUN
ejpam-5330	604	4	-	-	PUNCT
ejpam-5330	604	5	first	first	ADJ
ejpam-5330	604	6	results	result	NOUN
ejpam-5330	604	7	.	.	PUNCT
ejpam-5330	605	1	comput	comput	NOUN
ejpam-5330	605	2	.	.	PUNCT
ejpam-5330	606	1	math	math	NOUN
ejpam-5330	606	2	.	.	PUNCT
ejpam-5330	607	1	appl	appl	PROPN
ejpam-5330	607	2	.	.	PROPN
ejpam-5330	607	3	,	,	PUNCT
ejpam-5330	607	4	37:19–31	37:19–31	PROPN
ejpam-5330	607	5	,	,	PUNCT
ejpam-5330	607	6	1999	1999	NUM
ejpam-5330	607	7	.	.	PUNCT
ejpam-5330	608	1	[	[	X
ejpam-5330	608	2	25	25	NUM
ejpam-5330	608	3	]	]	PUNCT
ejpam-5330	608	4	s.	s.	PROPN
ejpam-5330	608	5	k.	k.	PROPN
ejpam-5330	608	6	nazmul	nazmul	PROPN
ejpam-5330	608	7	and	and	CCONJ
ejpam-5330	608	8	s.	s.	PROPN
ejpam-5330	608	9	k.	k.	PROPN
ejpam-5330	608	10	samanta	samanta	PROPN
ejpam-5330	608	11	.	.	PUNCT
ejpam-5330	609	1	neighbourhood	neighbourhood	NOUN
ejpam-5330	609	2	properties	property	NOUN
ejpam-5330	609	3	of	of	ADP
ejpam-5330	609	4	soft	soft	ADJ
ejpam-5330	609	5	topological	topological	ADJ
ejpam-5330	609	6	spaces	space	NOUN
ejpam-5330	609	7	.	.	PUNCT
ejpam-5330	610	1	ann	ann	PROPN
ejpam-5330	610	2	.	.	PUNCT
ejpam-5330	610	3	fuzzy	fuzzy	ADJ
ejpam-5330	610	4	math	math	NOUN
ejpam-5330	610	5	.	.	PUNCT
ejpam-5330	611	1	inform	inform	NOUN
ejpam-5330	611	2	.	.	PUNCT
ejpam-5330	611	3	,	,	PUNCT
ejpam-5330	611	4	6:1–15	6:1–15	NUM
ejpam-5330	611	5	,	,	PUNCT
ejpam-5330	611	6	2013	2013	NUM
ejpam-5330	611	7	.	.	PUNCT
ejpam-5330	612	1	[	[	X
ejpam-5330	612	2	26	26	NUM
ejpam-5330	612	3	]	]	PUNCT
ejpam-5330	612	4	s.	s.	PROPN
ejpam-5330	612	5	saleh	saleh	PROPN
ejpam-5330	612	6	and	and	CCONJ
ejpam-5330	612	7	j.	j.	PROPN
ejpam-5330	612	8	al	al	PROPN
ejpam-5330	612	9	-	-	PUNCT
ejpam-5330	612	10	mufarrij	mufarrij	PROPN
ejpam-5330	612	11	.	.	PUNCT
ejpam-5330	613	1	on	on	ADP
ejpam-5330	613	2	g	g	NOUN
ejpam-5330	613	3	-	-	PUNCT
ejpam-5330	613	4	regularity	regularity	NOUN
ejpam-5330	613	5	and	and	CCONJ
ejpam-5330	613	6	g	g	NOUN
ejpam-5330	613	7	-	-	PUNCT
ejpam-5330	613	8	normality	normality	NOUN
ejpam-5330	613	9	in	in	ADP
ejpam-5330	613	10	fuzzy	fuzzy	ADJ
ejpam-5330	613	11	soft	soft	ADJ
ejpam-5330	613	12	topological	topological	ADJ
ejpam-5330	613	13	spaces	space	NOUN
ejpam-5330	613	14	.	.	PUNCT
ejpam-5330	614	1	europ	europ	PROPN
ejpam-5330	614	2	.	.	PUNCT
ejpam-5330	615	1	j.	j.	PROPN
ejpam-5330	615	2	pure	pure	PROPN
ejpam-5330	615	3	appl	appl	PROPN
ejpam-5330	615	4	.	.	PUNCT
ejpam-5330	615	5	math	math	PROPN
ejpam-5330	615	6	.	.	PUNCT
ejpam-5330	615	7	,	,	PUNCT
ejpam-5330	615	8	16(1):180–191	16(1):180–191	PROPN
ejpam-5330	615	9	,	,	PUNCT
ejpam-5330	615	10	2023	2023	NUM
ejpam-5330	615	11	.	.	PUNCT
ejpam-5330	616	1	[	[	X
ejpam-5330	616	2	27	27	NUM
ejpam-5330	616	3	]	]	X
ejpam-5330	616	4	s.	s.	PROPN
ejpam-5330	616	5	saleh	saleh	PROPN
ejpam-5330	616	6	,	,	PUNCT
ejpam-5330	616	7	t.	t.	PROPN
ejpam-5330	616	8	m.	m.	PROPN
ejpam-5330	616	9	al	al	PROPN
ejpam-5330	616	10	-	-	PUNCT
ejpam-5330	616	11	shami	shami	PROPN
ejpam-5330	616	12	,	,	PUNCT
ejpam-5330	616	13	and	and	CCONJ
ejpam-5330	616	14	a.	a.	NOUN
ejpam-5330	616	15	mhemdi	mhemdi	PROPN
ejpam-5330	616	16	.	.	PUNCT
ejpam-5330	617	1	on	on	ADP
ejpam-5330	617	2	some	some	DET
ejpam-5330	617	3	new	new	ADJ
ejpam-5330	617	4	types	type	NOUN
ejpam-5330	617	5	of	of	ADP
ejpam-5330	617	6	fuzzy	fuzzy	ADJ
ejpam-5330	617	7	soft	soft	ADJ
ejpam-5330	617	8	compact	compact	ADJ
ejpam-5330	617	9	spaces	space	NOUN
ejpam-5330	617	10	.	.	PUNCT
ejpam-5330	618	1	j.	j.	PROPN
ejpam-5330	618	2	math	math	PROPN
ejpam-5330	618	3	.	.	PUNCT
ejpam-5330	618	4	,	,	PUNCT
ejpam-5330	618	5	page	page	NOUN
ejpam-5330	618	6	5065592	5065592	NUM
ejpam-5330	618	7	,	,	PUNCT
ejpam-5330	618	8	2023	2023	NUM
ejpam-5330	618	9	.	.	PUNCT
ejpam-5330	619	1	[	[	X
ejpam-5330	619	2	28	28	NUM
ejpam-5330	619	3	]	]	X
ejpam-5330	619	4	m.	m.	NOUN
ejpam-5330	619	5	shabir	shabir	PROPN
ejpam-5330	619	6	and	and	CCONJ
ejpam-5330	619	7	m.	m.	PROPN
ejpam-5330	619	8	naz	naz	PROPN
ejpam-5330	619	9	.	.	PUNCT
ejpam-5330	620	1	on	on	ADP
ejpam-5330	620	2	soft	soft	ADJ
ejpam-5330	620	3	topological	topological	ADJ
ejpam-5330	620	4	spaces	space	NOUN
ejpam-5330	620	5	.	.	PUNCT
ejpam-5330	621	1	comput	comput	NOUN
ejpam-5330	621	2	.	.	PUNCT
ejpam-5330	622	1	math	math	NOUN
ejpam-5330	622	2	.	.	PUNCT
ejpam-5330	623	1	appl	appl	PROPN
ejpam-5330	623	2	.	.	PROPN
ejpam-5330	623	3	,	,	PUNCT
ejpam-5330	623	4	61:1786	61:1786	X
ejpam-5330	623	5	–	–	PUNCT
ejpam-5330	623	6	1799	1799	NUM
ejpam-5330	623	7	,	,	PUNCT
ejpam-5330	623	8	2011	2011	NUM
ejpam-5330	623	9	.	.	PUNCT
ejpam-5330	624	1	[	[	X
ejpam-5330	624	2	29	29	NUM
ejpam-5330	624	3	]	]	X
ejpam-5330	624	4	i.	i.	PROPN
ejpam-5330	624	5	m.	m.	PROPN
ejpam-5330	624	6	taha	taha	PROPN
ejpam-5330	624	7	.	.	PUNCT
ejpam-5330	625	1	a	a	DET
ejpam-5330	625	2	new	new	ADJ
ejpam-5330	625	3	approach	approach	NOUN
ejpam-5330	625	4	to	to	ADP
ejpam-5330	625	5	separation	separation	NOUN
ejpam-5330	625	6	and	and	CCONJ
ejpam-5330	625	7	regularity	regularity	NOUN
ejpam-5330	625	8	axioms	axiom	NOUN
ejpam-5330	625	9	via	via	ADP
ejpam-5330	625	10	fuzzy	fuzzy	ADJ
ejpam-5330	625	11	soft	soft	ADJ
ejpam-5330	625	12	sets	set	NOUN
ejpam-5330	625	13	.	.	PUNCT
ejpam-5330	626	1	ann	ann	PROPN
ejpam-5330	626	2	.	.	PUNCT
ejpam-5330	626	3	fuzzy	fuzzy	ADJ
ejpam-5330	626	4	math	math	NOUN
ejpam-5330	626	5	.	.	PUNCT
ejpam-5330	627	1	inform	inform	NOUN
ejpam-5330	627	2	.	.	PUNCT
ejpam-5330	627	3	,	,	PUNCT
ejpam-5330	627	4	20:115–123	20:115–123	NOUN
ejpam-5330	627	5	,	,	PUNCT
ejpam-5330	627	6	2020	2020	NUM
ejpam-5330	627	7	.	.	PUNCT
ejpam-5330	628	1	[	[	X
ejpam-5330	628	2	30	30	NUM
ejpam-5330	628	3	]	]	X
ejpam-5330	628	4	i.	i.	PROPN
ejpam-5330	628	5	m.	m.	PROPN
ejpam-5330	628	6	taha	taha	PROPN
ejpam-5330	628	7	.	.	PUNCT
ejpam-5330	629	1	compactness	compactness	NOUN
ejpam-5330	629	2	on	on	ADP
ejpam-5330	629	3	fuzzy	fuzzy	ADJ
ejpam-5330	629	4	soft	soft	ADJ
ejpam-5330	629	5	r	r	NOUN
ejpam-5330	629	6	-	-	PUNCT
ejpam-5330	629	7	minimal	minimal	ADJ
ejpam-5330	629	8	spaces	space	NOUN
ejpam-5330	629	9	.	.	PUNCT
ejpam-5330	630	1	int	int	NOUN
ejpam-5330	630	2	.	.	PUNCT
ejpam-5330	631	1	j.	j.	PROPN
ejpam-5330	631	2	fuzzy	fuzzy	PROPN
ejpam-5330	631	3	logic	logic	PROPN
ejpam-5330	631	4	intell	intell	PROPN
ejpam-5330	631	5	.	.	PUNCT
ejpam-5330	632	1	syst	syst	PROPN
ejpam-5330	632	2	.	.	PROPN
ejpam-5330	632	3	,	,	PUNCT
ejpam-5330	632	4	21:251–258	21:251–258	PROPN
ejpam-5330	632	5	,	,	PUNCT
ejpam-5330	632	6	2021	2021	NUM
ejpam-5330	632	7	.	.	PUNCT
ejpam-5330	633	1	[	[	X
ejpam-5330	633	2	31	31	NUM
ejpam-5330	633	3	]	]	PUNCT
ejpam-5330	633	4	i.	i.	PROPN
ejpam-5330	633	5	m.	m.	PROPN
ejpam-5330	633	6	taha	taha	PROPN
ejpam-5330	633	7	.	.	PUNCT
ejpam-5330	634	1	some	some	DET
ejpam-5330	634	2	new	new	ADJ
ejpam-5330	634	3	separation	separation	NOUN
ejpam-5330	634	4	axioms	axiom	VERB
ejpam-5330	634	5	in	in	ADP
ejpam-5330	634	6	fuzzy	fuzzy	ADJ
ejpam-5330	634	7	soft	soft	ADJ
ejpam-5330	634	8	topological	topological	ADJ
ejpam-5330	634	9	spaces	space	NOUN
ejpam-5330	634	10	.	.	PUNCT
ejpam-5330	635	1	filomat	filomat	PROPN
ejpam-5330	635	2	,	,	PUNCT
ejpam-5330	635	3	35:1775–1783	35:1775–1783	PROPN
ejpam-5330	635	4	,	,	PUNCT
ejpam-5330	635	5	2021	2021	NUM
ejpam-5330	635	6	.	.	PUNCT
ejpam-5330	636	1	[	[	X
ejpam-5330	636	2	32	32	NUM
ejpam-5330	636	3	]	]	PUNCT
ejpam-5330	636	4	i.	i.	PROPN
ejpam-5330	636	5	m.	m.	PROPN
ejpam-5330	636	6	taha	taha	PROPN
ejpam-5330	636	7	.	.	PUNCT
ejpam-5330	637	1	some	some	DET
ejpam-5330	637	2	new	new	ADJ
ejpam-5330	637	3	results	result	NOUN
ejpam-5330	637	4	on	on	ADP
ejpam-5330	637	5	fuzzy	fuzzy	ADJ
ejpam-5330	637	6	soft	soft	ADJ
ejpam-5330	637	7	r	r	NOUN
ejpam-5330	637	8	-	-	PUNCT
ejpam-5330	637	9	minimal	minimal	ADJ
ejpam-5330	637	10	spaces	space	NOUN
ejpam-5330	637	11	.	.	PUNCT
ejpam-5330	638	1	aims	aim	VERB
ejpam-5330	638	2	mathematics	mathematic	NOUN
ejpam-5330	638	3	,	,	PUNCT
ejpam-5330	638	4	7:12458–12470	7:12458–12470	NUM
ejpam-5330	638	5	,	,	PUNCT
ejpam-5330	638	6	2022	2022	NUM
ejpam-5330	638	7	.	.	PUNCT
ejpam-5330	639	1	[	[	X
ejpam-5330	639	2	33	33	NUM
ejpam-5330	639	3	]	]	PUNCT
ejpam-5330	639	4	m.	m.	NOUN
ejpam-5330	639	5	terepeta	terepeta	PROPN
ejpam-5330	639	6	.	.	PUNCT
ejpam-5330	640	1	on	on	ADP
ejpam-5330	640	2	separating	separate	VERB
ejpam-5330	640	3	axioms	axiom	NOUN
ejpam-5330	640	4	and	and	CCONJ
ejpam-5330	640	5	similarity	similarity	NOUN
ejpam-5330	640	6	of	of	ADP
ejpam-5330	640	7	soft	soft	ADJ
ejpam-5330	640	8	topological	topological	ADJ
ejpam-5330	640	9	spaces	space	NOUN
ejpam-5330	640	10	.	.	PUNCT
ejpam-5330	641	1	soft	soft	ADJ
ejpam-5330	641	2	computing	computing	NOUN
ejpam-5330	641	3	,	,	PUNCT
ejpam-5330	641	4	23(3):1049–1057	23(3):1049–1057	NUM
ejpam-5330	641	5	,	,	PUNCT
ejpam-5330	641	6	2019	2019	NUM
ejpam-5330	641	7	.	.	PUNCT
ejpam-5330	642	1	[	[	X
ejpam-5330	642	2	34	34	NUM
ejpam-5330	642	3	]	]	PUNCT
ejpam-5330	642	4	s.	s.	PROPN
ejpam-5330	642	5	s.	s.	PROPN
ejpam-5330	642	6	thakur	thakur	PROPN
ejpam-5330	642	7	and	and	CCONJ
ejpam-5330	642	8	a.	a.	NOUN
ejpam-5330	642	9	s.	s.	PROPN
ejpam-5330	642	10	rajput	rajput	PROPN
ejpam-5330	642	11	.	.	PUNCT
ejpam-5330	643	1	connectedness	connectedness	NOUN
ejpam-5330	643	2	between	between	ADP
ejpam-5330	643	3	soft	soft	ADJ
ejpam-5330	643	4	sets	set	NOUN
ejpam-5330	643	5	.	.	PUNCT
ejpam-5330	644	1	new	new	ADJ
ejpam-5330	644	2	math	math	NOUN
ejpam-5330	644	3	.	.	PUNCT
ejpam-5330	645	1	nat	nat	PROPN
ejpam-5330	645	2	.	.	PUNCT
ejpam-5330	646	1	comput	comput	PROPN
ejpam-5330	646	2	.	.	PUNCT
ejpam-5330	646	3	,	,	PUNCT
ejpam-5330	646	4	14:53–71	14:53–71	PROPN
ejpam-5330	646	5	,	,	PUNCT
ejpam-5330	646	6	2018	2018	NUM
ejpam-5330	646	7	.	.	PUNCT
ejpam-5330	647	1	[	[	X
ejpam-5330	647	2	35	35	NUM
ejpam-5330	647	3	]	]	PUNCT
ejpam-5330	647	4	a.	a.	NOUN
ejpam-5330	647	5	p.	p.	NOUN
ejpam-5330	647	6	šostak	šostak	NOUN
ejpam-5330	647	7	.	.	PUNCT
ejpam-5330	648	1	on	on	ADP
ejpam-5330	648	2	a	a	DET
ejpam-5330	648	3	fuzzy	fuzzy	ADJ
ejpam-5330	648	4	topological	topological	ADJ
ejpam-5330	648	5	structure	structure	NOUN
ejpam-5330	648	6	.	.	PUNCT
ejpam-5330	649	1	in	in	ADP
ejpam-5330	649	2	in	in	ADP
ejpam-5330	649	3	:	:	PUNCT
ejpam-5330	649	4	proceedings	proceeding	NOUN
ejpam-5330	649	5	of	of	ADP
ejpam-5330	649	6	the	the	DET
ejpam-5330	649	7	13th	13th	NOUN
ejpam-5330	649	8	winter	winter	NOUN
ejpam-5330	649	9	school	school	NOUN
ejpam-5330	649	10	on	on	ADP
ejpam-5330	649	11	abstract	abstract	ADJ
ejpam-5330	649	12	analysis	analysis	NOUN
ejpam-5330	649	13	,	,	PUNCT
ejpam-5330	649	14	section	section	NOUN
ejpam-5330	649	15	of	of	ADP
ejpam-5330	649	16	topology	topology	NOUN
ejpam-5330	649	17	,	,	PUNCT
ejpam-5330	649	18	palermo	palermo	NOUN
ejpam-5330	649	19	:	:	PUNCT
ejpam-5330	649	20	circolo	circolo	PROPN
ejpam-5330	649	21	matematico	matematico	NOUN
ejpam-5330	649	22	di	di	X
ejpam-5330	649	23	palermo	palermo	NOUN
ejpam-5330	649	24	,	,	PUNCT
ejpam-5330	649	25	pages	page	NOUN
ejpam-5330	649	26	89–103	89–103	PROPN
ejpam-5330	649	27	,	,	PUNCT
ejpam-5330	649	28	1985	1985	NUM
ejpam-5330	649	29	.	.	PUNCT
ejpam-5330	650	1	[	[	X
ejpam-5330	650	2	36	36	NUM
ejpam-5330	650	3	]	]	X
ejpam-5330	650	4	h.	h.	PROPN
ejpam-5330	650	5	l.	l.	PROPN
ejpam-5330	650	6	yang	yang	PROPN
ejpam-5330	650	7	,	,	PUNCT
ejpam-5330	650	8	x.	x.	PROPN
ejpam-5330	650	9	liao	liao	PROPN
ejpam-5330	650	10	,	,	PUNCT
ejpam-5330	650	11	and	and	CCONJ
ejpam-5330	650	12	s.	s.	PROPN
ejpam-5330	650	13	g.	g.	PROPN
ejpam-5330	650	14	li	li	PROPN
ejpam-5330	650	15	.	.	PROPN
ejpam-5330	651	1	on	on	ADP
ejpam-5330	651	2	soft	soft	ADJ
ejpam-5330	651	3	continuous	continuous	ADJ
ejpam-5330	651	4	mappings	mapping	NOUN
ejpam-5330	651	5	and	and	CCONJ
ejpam-5330	651	6	soft	soft	ADJ
ejpam-5330	651	7	connectedness	connectedness	NOUN
ejpam-5330	651	8	of	of	ADP
ejpam-5330	651	9	soft	soft	ADJ
ejpam-5330	651	10	topological	topological	ADJ
ejpam-5330	651	11	spaces	space	NOUN
ejpam-5330	651	12	.	.	PUNCT
ejpam-5330	652	1	hacet	hacet	PROPN
ejpam-5330	652	2	.	.	PUNCT
ejpam-5330	653	1	j.	j.	PROPN
ejpam-5330	653	2	math	math	PROPN
ejpam-5330	653	3	.	.	PUNCT
ejpam-5330	654	1	stat	stat	PROPN
ejpam-5330	654	2	.	.	PUNCT
ejpam-5330	654	3	,	,	PUNCT
ejpam-5330	654	4	44:385–398	44:385–398	PROPN
ejpam-5330	654	5	,	,	PUNCT
ejpam-5330	654	6	2015	2015	NUM
ejpam-5330	654	7	.	.	PUNCT
ejpam-5330	655	1	[	[	X
ejpam-5330	655	2	37	37	NUM
ejpam-5330	655	3	]	]	PUNCT
ejpam-5330	655	4	l.	l.	PROPN
ejpam-5330	655	5	a.	a.	PROPN
ejpam-5330	655	6	zadeh	zadeh	PROPN
ejpam-5330	655	7	.	.	PUNCT
ejpam-5330	655	8	fuzzy	fuzzy	ADJ
ejpam-5330	655	9	sets	set	NOUN
ejpam-5330	655	10	.	.	PUNCT
ejpam-5330	656	1	inform	inform	NOUN
ejpam-5330	656	2	.	.	PUNCT
ejpam-5330	657	1	control	control	NOUN
ejpam-5330	657	2	,	,	PUNCT
ejpam-5330	657	3	8:338–353	8:338–353	NUM
ejpam-5330	657	4	,	,	PUNCT
ejpam-5330	657	5	1965	1965	NUM
ejpam-5330	657	6	.	.	PUNCT
ejpam-5330	658	1	references	reference	NOUN
ejpam-5330	658	2	4134	4134	NUM
ejpam-5330	658	3	[	[	X
ejpam-5330	658	4	38	38	NUM
ejpam-5330	658	5	]	]	PUNCT
ejpam-5330	658	6	i.	i.	PROPN
ejpam-5330	658	7	zorlutuna	zorlutuna	PROPN
ejpam-5330	658	8	,	,	PUNCT
ejpam-5330	658	9	m.	m.	NOUN
ejpam-5330	658	10	akdag	akdag	PROPN
ejpam-5330	658	11	,	,	PUNCT
ejpam-5330	658	12	w.	w.	PROPN
ejpam-5330	658	13	k.	k.	PROPN
ejpam-5330	658	14	min	min	PROPN
ejpam-5330	658	15	,	,	PUNCT
ejpam-5330	658	16	and	and	CCONJ
ejpam-5330	658	17	s.	s.	PROPN
ejpam-5330	658	18	atmaca	atmaca	PROPN
ejpam-5330	658	19	.	.	PUNCT
ejpam-5330	659	1	remarks	remark	NOUN
ejpam-5330	659	2	on	on	ADP
ejpam-5330	659	3	soft	soft	ADJ
ejpam-5330	659	4	topological	topological	ADJ
ejpam-5330	659	5	spaces	space	NOUN
ejpam-5330	659	6	.	.	PUNCT
ejpam-5330	660	1	ann	ann	PROPN
ejpam-5330	660	2	.	.	PUNCT
ejpam-5330	660	3	fuzzy	fuzzy	ADJ
ejpam-5330	660	4	math	math	NOUN
ejpam-5330	660	5	.	.	PUNCT
ejpam-5330	661	1	inform	inform	NOUN
ejpam-5330	661	2	.	.	PUNCT
ejpam-5330	661	3	,	,	PUNCT
ejpam-5330	661	4	3:171–185	3:171–185	NUM
ejpam-5330	661	5	,	,	PUNCT
ejpam-5330	661	6	2012	2012	NUM
ejpam-5330	661	7	.	.	PUNCT