id	sid	tid	token	lemma	pos
ejpam-4972	1	1	european	european	PROPN
ejpam-4972	1	2	journal	journal	PROPN
ejpam-4972	1	3	of	of	ADP
ejpam-4972	1	4	pure	pure	ADJ
ejpam-4972	1	5	and	and	CCONJ
ejpam-4972	1	6	applied	apply	VERB
ejpam-4972	1	7	mathematics	mathematic	NOUN
ejpam-4972	1	8	vol	vol	NOUN
ejpam-4972	1	9	.	.	PUNCT
ejpam-4972	2	1	16	16	NUM
ejpam-4972	2	2	,	,	PUNCT
ejpam-4972	2	3	no	no	INTJ
ejpam-4972	2	4	.	.	NOUN
ejpam-4972	2	5	4	4	NUM
ejpam-4972	2	6	,	,	PUNCT
ejpam-4972	2	7	2023	2023	NUM
ejpam-4972	2	8	,	,	PUNCT
ejpam-4972	2	9	2613	2613	NUM
ejpam-4972	2	10	-	-	SYM
ejpam-4972	2	11	2631	2631	NUM
ejpam-4972	2	12	issn	issn	PROPN
ejpam-4972	2	13	1307	1307	NUM
ejpam-4972	2	14	-	-	SYM
ejpam-4972	2	15	5543	5543	NUM
ejpam-4972	2	16	–	–	PUNCT
ejpam-4972	3	1	ejpam.com	ejpam.com	X
ejpam-4972	3	2	published	publish	VERB
ejpam-4972	3	3	by	by	ADP
ejpam-4972	3	4	new	new	PROPN
ejpam-4972	3	5	york	york	PROPN
ejpam-4972	3	6	business	business	PROPN
ejpam-4972	3	7	global	global	ADJ
ejpam-4972	3	8	generalized	generalize	VERB
ejpam-4972	3	9	different	different	ADJ
ejpam-4972	3	10	types	type	NOUN
ejpam-4972	3	11	of	of	ADP
ejpam-4972	3	12	mappings	mapping	NOUN
ejpam-4972	3	13	in	in	ADP
ejpam-4972	3	14	fuzzy	fuzzy	ADJ
ejpam-4972	3	15	bitopological	bitopological	ADJ
ejpam-4972	3	16	spaces	space	NOUN
ejpam-4972	3	17	ahlam	ahlam	PROPN
ejpam-4972	3	18	ahmed	ahme	VERB
ejpam-4972	3	19	alharbi1,2	alharbi1,2	PROPN
ejpam-4972	3	20	,	,	PUNCT
ejpam-4972	3	21	adem	adem	PROPN
ejpam-4972	3	22	kilicman2,∗	kilicman2,∗	PROPN
ejpam-4972	3	23	1	1	NUM
ejpam-4972	3	24	department	department	NOUN
ejpam-4972	3	25	of	of	ADP
ejpam-4972	3	26	mathematics	mathematic	NOUN
ejpam-4972	3	27	,	,	PUNCT
ejpam-4972	3	28	faculty	faculty	NOUN
ejpam-4972	3	29	of	of	ADP
ejpam-4972	3	30	science	science	NOUN
ejpam-4972	3	31	,	,	PUNCT
ejpam-4972	3	32	taibah	taibah	PROPN
ejpam-4972	3	33	university	university	PROPN
ejpam-4972	3	34	,	,	PUNCT
ejpam-4972	3	35	madinah	madinah	PROPN
ejpam-4972	3	36	42353	42353	NUM
ejpam-4972	3	37	,	,	PUNCT
ejpam-4972	3	38	kingdom	kingdom	NOUN
ejpam-4972	3	39	of	of	ADP
ejpam-4972	3	40	saudi	saudi	PROPN
ejpam-4972	3	41	arabia	arabia	PROPN
ejpam-4972	3	42	2	2	NUM
ejpam-4972	3	43	department	department	NOUN
ejpam-4972	3	44	of	of	ADP
ejpam-4972	3	45	mathematics	mathematic	NOUN
ejpam-4972	3	46	,	,	PUNCT
ejpam-4972	3	47	faculty	faculty	NOUN
ejpam-4972	3	48	of	of	ADP
ejpam-4972	3	49	science	science	PROPN
ejpam-4972	3	50	university	university	PROPN
ejpam-4972	3	51	putra	putra	PROPN
ejpam-4972	3	52	malaysia	malaysia	PROPN
ejpam-4972	3	53	,	,	PUNCT
ejpam-4972	3	54	43400	43400	NUM
ejpam-4972	3	55	upm	upm	PROPN
ejpam-4972	3	56	serdang	serdang	PROPN
ejpam-4972	3	57	,	,	PUNCT
ejpam-4972	3	58	selangor	selangor	PROPN
ejpam-4972	3	59	,	,	PUNCT
ejpam-4972	3	60	malaysia	malaysia	PROPN
ejpam-4972	3	61	abstract	abstract	NOUN
ejpam-4972	3	62	.	.	PUNCT
ejpam-4972	4	1	the	the	DET
ejpam-4972	4	2	principal	principal	ADJ
ejpam-4972	4	3	objective	objective	NOUN
ejpam-4972	4	4	of	of	ADP
ejpam-4972	4	5	this	this	DET
ejpam-4972	4	6	research	research	NOUN
ejpam-4972	4	7	is	be	AUX
ejpam-4972	4	8	to	to	PART
ejpam-4972	4	9	present	present	VERB
ejpam-4972	4	10	generalized	generalized	ADJ
ejpam-4972	4	11	function	function	NOUN
ejpam-4972	4	12	ideas	idea	NOUN
ejpam-4972	4	13	including	include	VERB
ejpam-4972	4	14	:	:	PUNCT
ejpam-4972	4	15	fuzzy	fuzzy	ADJ
ejpam-4972	4	16	generalized	generalize	VERB
ejpam-4972	4	17	continuity	continuity	NOUN
ejpam-4972	4	18	,	,	PUNCT
ejpam-4972	4	19	generalized	generalize	VERB
ejpam-4972	4	20	strong	strong	ADJ
ejpam-4972	4	21	continuity	continuity	NOUN
ejpam-4972	4	22	,	,	PUNCT
ejpam-4972	4	23	generalized	generalized	ADJ
ejpam-4972	4	24	irresoluteness	irresoluteness	NOUN
ejpam-4972	4	25	,	,	PUNCT
ejpam-4972	4	26	generalized	generalize	VERB
ejpam-4972	4	27	open	open	ADJ
ejpam-4972	4	28	and	and	CCONJ
ejpam-4972	4	29	closed	closed	ADJ
ejpam-4972	4	30	mappings	mapping	NOUN
ejpam-4972	4	31	.	.	PUNCT
ejpam-4972	5	1	the	the	DET
ejpam-4972	5	2	last	last	ADJ
ejpam-4972	5	3	part	part	NOUN
ejpam-4972	5	4	of	of	ADP
ejpam-4972	5	5	our	our	PRON
ejpam-4972	5	6	study	study	NOUN
ejpam-4972	5	7	focuses	focus	VERB
ejpam-4972	5	8	on	on	ADP
ejpam-4972	5	9	homomorphisms	homomorphism	NOUN
ejpam-4972	5	10	in	in	ADP
ejpam-4972	5	11	fuzzy	fuzzy	ADJ
ejpam-4972	5	12	bitopological	bitopological	ADJ
ejpam-4972	5	13	spaces	space	NOUN
ejpam-4972	5	14	.	.	PUNCT
ejpam-4972	6	1	we	we	PRON
ejpam-4972	6	2	also	also	ADV
ejpam-4972	6	3	explore	explore	VERB
ejpam-4972	6	4	the	the	DET
ejpam-4972	6	5	relationships	relationship	NOUN
ejpam-4972	6	6	between	between	ADP
ejpam-4972	6	7	these	these	DET
ejpam-4972	6	8	concepts	concept	NOUN
ejpam-4972	6	9	,	,	PUNCT
ejpam-4972	6	10	their	their	PRON
ejpam-4972	6	11	characteristics	characteristic	NOUN
ejpam-4972	6	12	,	,	PUNCT
ejpam-4972	6	13	compositions	composition	NOUN
ejpam-4972	6	14	,	,	PUNCT
ejpam-4972	6	15	and	and	CCONJ
ejpam-4972	6	16	important	important	ADJ
ejpam-4972	6	17	theories	theory	NOUN
ejpam-4972	6	18	,	,	PUNCT
ejpam-4972	6	19	along	along	ADP
ejpam-4972	6	20	with	with	ADP
ejpam-4972	6	21	some	some	DET
ejpam-4972	6	22	relevant	relevant	ADJ
ejpam-4972	6	23	counterexamples	counterexample	NOUN
ejpam-4972	6	24	.	.	PUNCT
ejpam-4972	7	1	2020	2020	NUM
ejpam-4972	7	2	mathematics	mathematic	NOUN
ejpam-4972	7	3	subject	subject	NOUN
ejpam-4972	7	4	classifications	classification	NOUN
ejpam-4972	7	5	:	:	PUNCT
ejpam-4972	7	6	54a40	54a40	NUM
ejpam-4972	7	7	,	,	PUNCT
ejpam-4972	7	8	03e72	03e72	NUM
ejpam-4972	7	9	,	,	PUNCT
ejpam-4972	7	10	47s40	47s40	NUM
ejpam-4972	7	11	,	,	PUNCT
ejpam-4972	7	12	94d05	94d05	NUM
ejpam-4972	7	13	,	,	PUNCT
ejpam-4972	7	14	03b52	03b52	NUM
ejpam-4972	7	15	,	,	PUNCT
ejpam-4972	7	16	28e10	28e10	NUM
ejpam-4972	7	17	key	key	ADJ
ejpam-4972	7	18	words	word	NOUN
ejpam-4972	7	19	and	and	CCONJ
ejpam-4972	7	20	phrases	phrase	NOUN
ejpam-4972	7	21	:	:	PUNCT
ejpam-4972	7	22	fuzzy	fuzzy	ADJ
ejpam-4972	7	23	bitopology	bitopology	NOUN
ejpam-4972	7	24	space	space	NOUN
ejpam-4972	7	25	(	(	PUNCT
ejpam-4972	7	26	fbts	fbt	NOUN
ejpam-4972	7	27	)	)	PUNCT
ejpam-4972	7	28	,	,	PUNCT
ejpam-4972	7	29	fuzzy	fuzzy	ADJ
ejpam-4972	7	30	generalized	generalize	VERB
ejpam-4972	7	31	closed	closed	ADJ
ejpam-4972	7	32	groups	group	NOUN
ejpam-4972	7	33	(	(	PUNCT
ejpam-4972	7	34	(	(	PUNCT
ejpam-4972	7	35	i	i	PROPN
ejpam-4972	7	36	,	,	PUNCT
ejpam-4972	7	37	j	j	PROPN
ejpam-4972	7	38	)	)	PUNCT
ejpam-4972	7	39	−	−	PROPN
ejpam-4972	7	40	gψ	gψ	VERB
ejpam-4972	7	41	−	−	PROPN
ejpam-4972	7	42	cld	cld	NOUN
ejpam-4972	7	43	)	)	PUNCT
ejpam-4972	7	44	,	,	PUNCT
ejpam-4972	7	45	fuzzy	fuzzy	ADJ
ejpam-4972	7	46	generalized	generalize	VERB
ejpam-4972	7	47	continuous	continuous	ADJ
ejpam-4972	7	48	(	(	PUNCT
ejpam-4972	7	49	(	(	PUNCT
ejpam-4972	7	50	i	i	PROPN
ejpam-4972	7	51	,	,	PUNCT
ejpam-4972	7	52	j	j	PROPN
ejpam-4972	7	53	)	)	PUNCT
ejpam-4972	7	54	−	−	PROPN
ejpam-4972	7	55	gψ	gψ	VERB
ejpam-4972	7	56	−	−	PROPN
ejpam-4972	7	57	conts	cont	NOUN
ejpam-4972	7	58	)	)	PUNCT
ejpam-4972	7	59	,	,	PUNCT
ejpam-4972	7	60	fuzzy	fuzzy	ADJ
ejpam-4972	7	61	generalized	generalize	VERB
ejpam-4972	7	62	irresolute	irresolute	NOUN
ejpam-4972	7	63	(	(	PUNCT
ejpam-4972	7	64	(	(	PUNCT
ejpam-4972	7	65	i	i	NOUN
ejpam-4972	7	66	,	,	PUNCT
ejpam-4972	7	67	j)−	j)−	PROPN
ejpam-4972	7	68	gψ−	gψ−	PUNCT
ejpam-4972	7	69	irresolute	irresolute	ADJ
ejpam-4972	7	70	)	)	PUNCT
ejpam-4972	7	71	,	,	PUNCT
ejpam-4972	7	72	fuzzy	fuzzy	ADJ
ejpam-4972	7	73	generalized	generalize	VERB
ejpam-4972	7	74	strongly	strongly	ADV
ejpam-4972	7	75	continuous	continuous	ADJ
ejpam-4972	7	76	(	(	PUNCT
ejpam-4972	7	77	(	(	PUNCT
ejpam-4972	7	78	i	i	NOUN
ejpam-4972	7	79	,	,	PUNCT
ejpam-4972	7	80	j)−	j)−	PROPN
ejpam-4972	7	81	gψ−	gψ−	PUNCT
ejpam-4972	7	82	strongly	strongly	ADV
ejpam-4972	7	83	conts	cont	NOUN
ejpam-4972	7	84	)	)	PUNCT
ejpam-4972	7	85	,	,	PUNCT
ejpam-4972	7	86	fuzzy	fuzzy	ADJ
ejpam-4972	7	87	generalized	generalize	VERB
ejpam-4972	7	88	open	open	ADJ
ejpam-4972	7	89	mapping	mapping	NOUN
ejpam-4972	7	90	(	(	PUNCT
ejpam-4972	7	91	(	(	PUNCT
ejpam-4972	7	92	i	i	PROPN
ejpam-4972	7	93	,	,	PUNCT
ejpam-4972	7	94	j	j	PROPN
ejpam-4972	7	95	)	)	PUNCT
ejpam-4972	7	96	−	−	PROPN
ejpam-4972	7	97	gψ	gψ	VERB
ejpam-4972	7	98	−	−	PRON
ejpam-4972	7	99	open	open	ADJ
ejpam-4972	7	100	mapping	mapping	NOUN
ejpam-4972	7	101	)	)	PUNCT
ejpam-4972	7	102	,	,	PUNCT
ejpam-4972	7	103	fuzzy	fuzzy	ADJ
ejpam-4972	7	104	generalized	generalize	VERB
ejpam-4972	7	105	closed	closed	ADJ
ejpam-4972	7	106	mapping	mapping	NOUN
ejpam-4972	7	107	(	(	PUNCT
ejpam-4972	7	108	(	(	PUNCT
ejpam-4972	7	109	i	i	PROPN
ejpam-4972	7	110	,	,	PUNCT
ejpam-4972	7	111	j)−	j)−	PROPN
ejpam-4972	7	112	gψ	gψ	VERB
ejpam-4972	7	113	−	−	PROPN
ejpam-4972	7	114	closed	closed	ADJ
ejpam-4972	7	115	mapping	mapping	NOUN
ejpam-4972	7	116	)	)	PUNCT
ejpam-4972	7	117	.	.	PUNCT
ejpam-4972	8	1	1	1	X
ejpam-4972	8	2	.	.	X
ejpam-4972	8	3	introduction	introduction	NOUN
ejpam-4972	8	4	our	our	PRON
ejpam-4972	8	5	focus	focus	NOUN
ejpam-4972	8	6	in	in	ADP
ejpam-4972	8	7	this	this	DET
ejpam-4972	8	8	study	study	NOUN
ejpam-4972	8	9	is	be	AUX
ejpam-4972	8	10	on	on	ADP
ejpam-4972	8	11	fuzzy	fuzzy	ADJ
ejpam-4972	8	12	bitopology	bitopology	NOUN
ejpam-4972	8	13	filed	file	VERB
ejpam-4972	8	14	,	,	PUNCT
ejpam-4972	8	15	that	that	PRON
ejpam-4972	8	16	was	be	AUX
ejpam-4972	8	17	developed	develop	VERB
ejpam-4972	8	18	of	of	ADP
ejpam-4972	8	19	fuzzy	fuzzy	ADJ
ejpam-4972	8	20	topology	topology	NOUN
ejpam-4972	8	21	and	and	CCONJ
ejpam-4972	8	22	presented	present	VERB
ejpam-4972	8	23	for	for	ADP
ejpam-4972	8	24	the	the	DET
ejpam-4972	8	25	first	first	ADJ
ejpam-4972	8	26	time	time	NOUN
ejpam-4972	8	27	in	in	ADP
ejpam-4972	8	28	1965	1965	NUM
ejpam-4972	8	29	by	by	ADP
ejpam-4972	8	30	scientist	scientist	NOUN
ejpam-4972	8	31	zadeh	zadeh	PROPN
ejpam-4972	9	1	[	[	X
ejpam-4972	9	2	14	14	NUM
ejpam-4972	9	3	]	]	PUNCT
ejpam-4972	9	4	.	.	PUNCT
ejpam-4972	10	1	after	after	ADP
ejpam-4972	10	2	that	that	PRON
ejpam-4972	10	3	,	,	PUNCT
ejpam-4972	10	4	some	some	DET
ejpam-4972	10	5	scientists	scientist	NOUN
ejpam-4972	10	6	developed	develop	VERB
ejpam-4972	10	7	the	the	DET
ejpam-4972	10	8	concepts	concept	NOUN
ejpam-4972	10	9	of	of	ADP
ejpam-4972	10	10	fuzzy	fuzzy	ADJ
ejpam-4972	10	11	topology	topology	NOUN
ejpam-4972	10	12	by	by	ADP
ejpam-4972	10	13	adapting	adapt	VERB
ejpam-4972	10	14	fundamental	fundamental	ADJ
ejpam-4972	10	15	ideas	idea	NOUN
ejpam-4972	10	16	from	from	ADP
ejpam-4972	10	17	general	general	ADJ
ejpam-4972	10	18	topology	topology	NOUN
ejpam-4972	10	19	to	to	ADP
ejpam-4972	10	20	fuzzy	fuzzy	ADJ
ejpam-4972	10	21	topology	topology	NOUN
ejpam-4972	10	22	.	.	PUNCT
ejpam-4972	11	1	for	for	ADP
ejpam-4972	11	2	example	example	NOUN
ejpam-4972	11	3	,	,	PUNCT
ejpam-4972	11	4	in	in	ADP
ejpam-4972	11	5	1968	1968	NUM
ejpam-4972	11	6	chang	chang	PROPN
ejpam-4972	11	7	created	create	VERB
ejpam-4972	11	8	several	several	ADJ
ejpam-4972	11	9	fuzzy	fuzzy	ADJ
ejpam-4972	11	10	concepts	concept	NOUN
ejpam-4972	11	11	[	[	X
ejpam-4972	11	12	8	8	NUM
ejpam-4972	11	13	]	]	PUNCT
ejpam-4972	11	14	.	.	PUNCT
ejpam-4972	12	1	then	then	ADV
ejpam-4972	12	2	,	,	PUNCT
ejpam-4972	12	3	fuzzy	fuzzy	ADJ
ejpam-4972	12	4	bitopological	bitopological	ADJ
ejpam-4972	12	5	spaces	space	NOUN
ejpam-4972	12	6	were	be	AUX
ejpam-4972	12	7	introduced	introduce	VERB
ejpam-4972	12	8	by	by	ADP
ejpam-4972	12	9	kandil	kandil	NOUN
ejpam-4972	12	10	in	in	ADP
ejpam-4972	12	11	1989[4	1989[4	NUM
ejpam-4972	12	12	]	]	PUNCT
ejpam-4972	12	13	.	.	PUNCT
ejpam-4972	13	1	and	and	CCONJ
ejpam-4972	13	2	hence	hence	ADV
ejpam-4972	13	3	,	,	PUNCT
ejpam-4972	13	4	balasubramanian	balasubramanian	PROPN
ejpam-4972	13	5	and	and	CCONJ
ejpam-4972	13	6	sundaram	sundaram	PROPN
ejpam-4972	13	7	created	create	VERB
ejpam-4972	13	8	generalized	generalize	VERB
ejpam-4972	13	9	fuzzy	fuzzy	ADJ
ejpam-4972	13	10	closed	closed	ADJ
ejpam-4972	13	11	groups	group	NOUN
ejpam-4972	13	12	in	in	ADP
ejpam-4972	13	13	fuzzy	fuzzy	ADJ
ejpam-4972	13	14	topology	topology	NOUN
ejpam-4972	13	15	space	space	NOUN
ejpam-4972	13	16	in	in	ADP
ejpam-4972	13	17	1997	1997	NUM
ejpam-4972	13	18	[	[	X
ejpam-4972	13	19	11	11	NUM
ejpam-4972	13	20	]	]	PUNCT
ejpam-4972	13	21	.	.	PUNCT
ejpam-4972	14	1	in	in	ADP
ejpam-4972	14	2	addition	addition	NOUN
ejpam-4972	14	3	,	,	PUNCT
ejpam-4972	14	4	some	some	DET
ejpam-4972	14	5	scientists	scientist	NOUN
ejpam-4972	14	6	presented	present	VERB
ejpam-4972	14	7	several	several	ADJ
ejpam-4972	14	8	studies	study	NOUN
ejpam-4972	14	9	on	on	ADP
ejpam-4972	14	10	generalized	generalized	ADJ
ejpam-4972	14	11	closed	closed	ADJ
ejpam-4972	14	12	group	group	NOUN
ejpam-4972	14	13	in	in	ADP
ejpam-4972	14	14	fuzzy	fuzzy	ADJ
ejpam-4972	14	15	space	space	NOUN
ejpam-4972	14	16	[	[	X
ejpam-4972	14	17	16	16	NUM
ejpam-4972	14	18	,	,	PUNCT
ejpam-4972	14	19	18	18	NUM
ejpam-4972	14	20	,	,	PUNCT
ejpam-4972	14	21	24	24	NUM
ejpam-4972	14	22	]	]	PUNCT
ejpam-4972	14	23	.	.	PUNCT
ejpam-4972	15	1	many	many	ADJ
ejpam-4972	15	2	studies	study	NOUN
ejpam-4972	15	3	about	about	ADP
ejpam-4972	15	4	mappings	mapping	NOUN
ejpam-4972	15	5	in	in	ADP
ejpam-4972	15	6	general	general	ADJ
ejpam-4972	15	7	topological	topological	ADJ
ejpam-4972	15	8	space	space	NOUN
ejpam-4972	15	9	have	have	AUX
ejpam-4972	15	10	been	be	AUX
ejpam-4972	15	11	made	make	VERB
ejpam-4972	15	12	by	by	ADP
ejpam-4972	15	13	scientists	scientist	NOUN
ejpam-4972	15	14	,	,	PUNCT
ejpam-4972	15	15	including	include	VERB
ejpam-4972	15	16	[	[	X
ejpam-4972	15	17	6	6	NUM
ejpam-4972	15	18	,	,	PUNCT
ejpam-4972	15	19	12	12	NUM
ejpam-4972	15	20	,	,	PUNCT
ejpam-4972	15	21	23	23	NUM
ejpam-4972	15	22	]	]	PUNCT
ejpam-4972	15	23	.	.	PUNCT
ejpam-4972	16	1	as	as	SCONJ
ejpam-4972	16	2	are	be	AUX
ejpam-4972	16	3	some	some	DET
ejpam-4972	16	4	scholars	scholar	NOUN
ejpam-4972	16	5	also	also	ADV
ejpam-4972	16	6	presented	present	VERB
ejpam-4972	16	7	different	different	ADJ
ejpam-4972	16	8	types	type	NOUN
ejpam-4972	16	9	of	of	ADP
ejpam-4972	16	10	studies	study	NOUN
ejpam-4972	16	11	on	on	ADP
ejpam-4972	16	12	functions	function	NOUN
ejpam-4972	16	13	in	in	ADP
ejpam-4972	16	14	fuzzy	fuzzy	ADJ
ejpam-4972	16	15	topology	topology	NOUN
ejpam-4972	16	16	space	space	NOUN
ejpam-4972	16	17	[	[	X
ejpam-4972	16	18	5	5	NUM
ejpam-4972	16	19	,	,	PUNCT
ejpam-4972	16	20	7	7	NUM
ejpam-4972	16	21	,	,	PUNCT
ejpam-4972	16	22	10	10	NUM
ejpam-4972	16	23	,	,	PUNCT
ejpam-4972	16	24	13	13	NUM
ejpam-4972	16	25	,	,	PUNCT
ejpam-4972	16	26	15	15	NUM
ejpam-4972	16	27	,	,	PUNCT
ejpam-4972	16	28	17	17	NUM
ejpam-4972	16	29	]	]	PUNCT
ejpam-4972	16	30	.	.	PUNCT
ejpam-4972	17	1	also	also	ADV
ejpam-4972	17	2	,	,	PUNCT
ejpam-4972	17	3	there	there	PRON
ejpam-4972	17	4	has	have	AUX
ejpam-4972	17	5	been	be	AUX
ejpam-4972	17	6	research	research	NOUN
ejpam-4972	17	7	that	that	PRON
ejpam-4972	17	8	showed	show	VERB
ejpam-4972	17	9	several	several	ADJ
ejpam-4972	17	10	mapping	mapping	NOUN
ejpam-4972	17	11	forms	form	NOUN
ejpam-4972	17	12	,	,	PUNCT
ejpam-4972	17	13	∗corresponding	∗corresponde	VERB
ejpam-4972	17	14	author	author	NOUN
ejpam-4972	17	15	.	.	PUNCT
ejpam-4972	18	1	doi	doi	NOUN
ejpam-4972	18	2	:	:	PUNCT
ejpam-4972	18	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4972	https://doi.org/10.29020/nybg.ejpam.v16i4.4972	NUM
ejpam-4972	18	4	email	email	NOUN
ejpam-4972	18	5	addresses	address	NOUN
ejpam-4972	18	6	:	:	PUNCT
ejpam-4972	18	7	aasehli@taibahu.edu.sa	aasehli@taibahu.edu.sa	NOUN
ejpam-4972	18	8	(	(	PUNCT
ejpam-4972	18	9	a.	a.	NOUN
ejpam-4972	18	10	a.	a.	NOUN
ejpam-4972	18	11	alharbi	alharbi	PROPN
ejpam-4972	18	12	)	)	PUNCT
ejpam-4972	18	13	,	,	PUNCT
ejpam-4972	18	14	akilic@upm.edu.my	akilic@upm.edu.my	PROPN
ejpam-4972	18	15	(	(	PUNCT
ejpam-4972	18	16	a.	a.	NOUN
ejpam-4972	18	17	kilicman	kilicman	PROPN
ejpam-4972	18	18	)	)	PUNCT
ejpam-4972	18	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4972	18	20	2613	2613	NUM
ejpam-4972	19	1	©	©	ADP
ejpam-4972	19	2	2023	2023	NUM
ejpam-4972	19	3	ejpam	ejpam	NOUN
ejpam-4972	19	4	all	all	DET
ejpam-4972	19	5	rights	right	NOUN
ejpam-4972	19	6	reserved	reserve	VERB
ejpam-4972	19	7	.	.	PUNCT
ejpam-4972	20	1	a.	a.	NOUN
ejpam-4972	20	2	a.	a.	PROPN
ejpam-4972	20	3	alharbi	alharbi	PROPN
ejpam-4972	20	4	,	,	PUNCT
ejpam-4972	20	5	a.	a.	NOUN
ejpam-4972	20	6	kilicman	kilicman	PROPN
ejpam-4972	20	7	/	/	SYM
ejpam-4972	20	8	eur	eur	PROPN
ejpam-4972	20	9	.	.	PUNCT
ejpam-4972	21	1	j.	j.	PROPN
ejpam-4972	21	2	pure	pure	PROPN
ejpam-4972	21	3	appl	appl	PROPN
ejpam-4972	21	4	.	.	PROPN
ejpam-4972	21	5	math	math	PROPN
ejpam-4972	21	6	,	,	PUNCT
ejpam-4972	21	7	16	16	NUM
ejpam-4972	21	8	(	(	PUNCT
ejpam-4972	21	9	4	4	NUM
ejpam-4972	21	10	)	)	PUNCT
ejpam-4972	21	11	(	(	PUNCT
ejpam-4972	21	12	2023	2023	NUM
ejpam-4972	21	13	)	)	PUNCT
ejpam-4972	21	14	,	,	PUNCT
ejpam-4972	21	15	2613	2613	NUM
ejpam-4972	21	16	-	-	SYM
ejpam-4972	21	17	2631	2631	NUM
ejpam-4972	21	18	2614	2614	NUM
ejpam-4972	21	19	including	include	VERB
ejpam-4972	21	20	irresolute	irresolute	ADJ
ejpam-4972	21	21	and	and	CCONJ
ejpam-4972	21	22	strong	strong	ADJ
ejpam-4972	21	23	functions	function	NOUN
ejpam-4972	21	24	,	,	PUNCT
ejpam-4972	21	25	such	such	ADJ
ejpam-4972	21	26	as	as	ADP
ejpam-4972	21	27	[	[	X
ejpam-4972	21	28	20–22	20–22	NUM
ejpam-4972	21	29	]	]	X
ejpam-4972	21	30	.	.	PUNCT
ejpam-4972	22	1	there	there	PRON
ejpam-4972	22	2	is	be	VERB
ejpam-4972	22	3	also	also	ADV
ejpam-4972	22	4	a	a	DET
ejpam-4972	22	5	lot	lot	NOUN
ejpam-4972	22	6	of	of	ADP
ejpam-4972	22	7	research	research	NOUN
ejpam-4972	22	8	related	relate	VERB
ejpam-4972	22	9	to	to	ADP
ejpam-4972	22	10	the	the	DET
ejpam-4972	22	11	topic	topic	NOUN
ejpam-4972	22	12	of	of	ADP
ejpam-4972	22	13	this	this	DET
ejpam-4972	22	14	manuscript	manuscript	NOUN
ejpam-4972	22	15	but	but	CCONJ
ejpam-4972	22	16	with	with	ADP
ejpam-4972	22	17	practical	practical	ADJ
ejpam-4972	22	18	application	application	NOUN
ejpam-4972	22	19	in	in	ADP
ejpam-4972	22	20	real	real	ADJ
ejpam-4972	22	21	-	-	PUNCT
ejpam-4972	22	22	life	life	NOUN
ejpam-4972	22	23	scenarios	scenario	NOUN
ejpam-4972	22	24	,	,	PUNCT
ejpam-4972	22	25	such	such	ADJ
ejpam-4972	22	26	as	as	ADP
ejpam-4972	22	27	”	"	PUNCT
ejpam-4972	22	28	a	a	DET
ejpam-4972	22	29	comparison	comparison	NOUN
ejpam-4972	22	30	of	of	ADP
ejpam-4972	22	31	three	three	NUM
ejpam-4972	22	32	types	type	NOUN
ejpam-4972	22	33	of	of	ADP
ejpam-4972	22	34	rough	rough	ADJ
ejpam-4972	22	35	fuzzy	fuzzy	ADJ
ejpam-4972	22	36	sets	set	NOUN
ejpam-4972	22	37	based	base	VERB
ejpam-4972	22	38	on	on	ADP
ejpam-4972	22	39	two	two	NUM
ejpam-4972	22	40	universal	universal	ADJ
ejpam-4972	22	41	sets	set	NOUN
ejpam-4972	22	42	”	"	PUNCT
ejpam-4972	22	43	[	[	X
ejpam-4972	22	44	1	1	NUM
ejpam-4972	22	45	]	]	PUNCT
ejpam-4972	22	46	.	.	PUNCT
ejpam-4972	23	1	also	also	ADV
ejpam-4972	23	2	,	,	PUNCT
ejpam-4972	23	3	”	"	PUNCT
ejpam-4972	23	4	on	on	ADP
ejpam-4972	23	5	fuzzy	fuzzy	ADJ
ejpam-4972	23	6	point	point	NOUN
ejpam-4972	23	7	applications	application	NOUN
ejpam-4972	23	8	of	of	ADP
ejpam-4972	23	9	fuzzy	fuzzy	ADJ
ejpam-4972	23	10	topological	topological	ADJ
ejpam-4972	23	11	spaces	space	NOUN
ejpam-4972	23	12	”	"	PUNCT
ejpam-4972	23	13	[	[	X
ejpam-4972	23	14	2	2	NUM
ejpam-4972	23	15	]	]	PUNCT
ejpam-4972	23	16	.	.	PUNCT
ejpam-4972	24	1	since	since	SCONJ
ejpam-4972	24	2	,	,	PUNCT
ejpam-4972	24	3	generalized	generalize	VERB
ejpam-4972	24	4	closed	closed	ADJ
ejpam-4972	24	5	sets	set	NOUN
ejpam-4972	24	6	in	in	ADP
ejpam-4972	24	7	fuzzy	fuzzy	ADJ
ejpam-4972	24	8	bitopology	bitopology	NOUN
ejpam-4972	24	9	spaces	space	NOUN
ejpam-4972	24	10	are	be	AUX
ejpam-4972	24	11	essential	essential	ADJ
ejpam-4972	24	12	for	for	ADP
ejpam-4972	24	13	incorporating	incorporate	VERB
ejpam-4972	24	14	flexibility	flexibility	NOUN
ejpam-4972	24	15	,	,	PUNCT
ejpam-4972	24	16	granularity	granularity	NOUN
ejpam-4972	24	17	,	,	PUNCT
ejpam-4972	24	18	and	and	CCONJ
ejpam-4972	24	19	uncertainty	uncertainty	NOUN
ejpam-4972	24	20	in	in	ADP
ejpam-4972	24	21	the	the	DET
ejpam-4972	24	22	study	study	NOUN
ejpam-4972	24	23	of	of	ADP
ejpam-4972	24	24	fuzzy	fuzzy	ADJ
ejpam-4972	24	25	sets	set	NOUN
ejpam-4972	24	26	and	and	CCONJ
ejpam-4972	24	27	various	various	ADJ
ejpam-4972	24	28	topological	topological	ADJ
ejpam-4972	24	29	properties	property	NOUN
ejpam-4972	24	30	,	,	PUNCT
ejpam-4972	24	31	such	such	ADJ
ejpam-4972	24	32	as	as	ADP
ejpam-4972	24	33	continuity	continuity	NOUN
ejpam-4972	24	34	.	.	PUNCT
ejpam-4972	25	1	this	this	DET
ejpam-4972	25	2	use	use	NOUN
ejpam-4972	25	3	has	have	VERB
ejpam-4972	25	4	several	several	ADJ
ejpam-4972	25	5	advantages	advantage	NOUN
ejpam-4972	25	6	,	,	PUNCT
ejpam-4972	25	7	it	it	PRON
ejpam-4972	25	8	gives	give	VERB
ejpam-4972	25	9	a	a	DET
ejpam-4972	25	10	more	more	ADV
ejpam-4972	25	11	precise	precise	ADJ
ejpam-4972	25	12	description	description	NOUN
ejpam-4972	25	13	of	of	ADP
ejpam-4972	25	14	the	the	DET
ejpam-4972	25	15	behavior	behavior	NOUN
ejpam-4972	25	16	of	of	ADP
ejpam-4972	25	17	fuzzy	fuzzy	ADJ
ejpam-4972	25	18	functions	function	NOUN
ejpam-4972	25	19	.	.	PUNCT
ejpam-4972	26	1	so	so	ADV
ejpam-4972	26	2	,	,	PUNCT
ejpam-4972	26	3	this	this	DET
ejpam-4972	26	4	study	study	NOUN
ejpam-4972	26	5	aims	aim	VERB
ejpam-4972	26	6	to	to	PART
ejpam-4972	26	7	introduce	introduce	VERB
ejpam-4972	26	8	and	and	CCONJ
ejpam-4972	26	9	explore	explore	VERB
ejpam-4972	26	10	a	a	DET
ejpam-4972	26	11	range	range	NOUN
ejpam-4972	26	12	of	of	ADP
ejpam-4972	26	13	generalized	generalized	ADJ
ejpam-4972	26	14	function	function	NOUN
ejpam-4972	26	15	concepts	concept	NOUN
ejpam-4972	26	16	within	within	ADP
ejpam-4972	26	17	the	the	DET
ejpam-4972	26	18	framework	framework	NOUN
ejpam-4972	26	19	of	of	ADP
ejpam-4972	26	20	fuzzy	fuzzy	ADJ
ejpam-4972	26	21	bitopological	bitopological	ADJ
ejpam-4972	26	22	spaces	space	NOUN
ejpam-4972	26	23	.	.	PUNCT
ejpam-4972	27	1	more	more	ADV
ejpam-4972	27	2	precisely	precisely	ADV
ejpam-4972	27	3	,	,	PUNCT
ejpam-4972	27	4	in	in	ADP
ejpam-4972	27	5	the	the	DET
ejpam-4972	27	6	concepts	concept	NOUN
ejpam-4972	27	7	of	of	ADP
ejpam-4972	27	8	fuzzy	fuzzy	ADJ
ejpam-4972	27	9	generalized	generalized	ADJ
ejpam-4972	27	10	continuity	continuity	NOUN
ejpam-4972	27	11	,	,	PUNCT
ejpam-4972	27	12	generalized	generalize	VERB
ejpam-4972	27	13	strong	strong	ADJ
ejpam-4972	27	14	continuity	continuity	NOUN
ejpam-4972	27	15	,	,	PUNCT
ejpam-4972	27	16	generalized	generalized	ADJ
ejpam-4972	27	17	irresoluteness	irresoluteness	NOUN
ejpam-4972	27	18	,	,	PUNCT
ejpam-4972	27	19	as	as	ADV
ejpam-4972	27	20	well	well	ADV
ejpam-4972	27	21	as	as	ADP
ejpam-4972	27	22	generalized	generalize	VERB
ejpam-4972	27	23	open	open	ADJ
ejpam-4972	27	24	and	and	CCONJ
ejpam-4972	27	25	closed	closed	ADJ
ejpam-4972	27	26	mappings	mapping	NOUN
ejpam-4972	27	27	.	.	PUNCT
ejpam-4972	28	1	furthermore	furthermore	ADV
ejpam-4972	28	2	,	,	PUNCT
ejpam-4972	28	3	we	we	PRON
ejpam-4972	28	4	investigate	investigate	VERB
ejpam-4972	28	5	the	the	DET
ejpam-4972	28	6	concept	concept	NOUN
ejpam-4972	28	7	of	of	ADP
ejpam-4972	28	8	homomorphism	homomorphism	NOUN
ejpam-4972	28	9	in	in	ADP
ejpam-4972	28	10	the	the	DET
ejpam-4972	28	11	context	context	NOUN
ejpam-4972	28	12	of	of	ADP
ejpam-4972	28	13	fuzzy	fuzzy	ADJ
ejpam-4972	28	14	bitopological	bitopological	ADJ
ejpam-4972	28	15	spaces	space	NOUN
ejpam-4972	28	16	.	.	PUNCT
ejpam-4972	29	1	our	our	PRON
ejpam-4972	29	2	study	study	NOUN
ejpam-4972	29	3	not	not	PART
ejpam-4972	29	4	only	only	ADV
ejpam-4972	29	5	introduces	introduce	VERB
ejpam-4972	29	6	these	these	DET
ejpam-4972	29	7	concepts	concept	NOUN
ejpam-4972	29	8	but	but	CCONJ
ejpam-4972	29	9	also	also	ADV
ejpam-4972	29	10	delves	delve	VERB
ejpam-4972	29	11	into	into	ADP
ejpam-4972	29	12	their	their	PRON
ejpam-4972	29	13	interrelationships	interrelationship	NOUN
ejpam-4972	29	14	,	,	PUNCT
ejpam-4972	29	15	characteristics	characteristic	NOUN
ejpam-4972	29	16	,	,	PUNCT
ejpam-4972	29	17	composition	composition	NOUN
ejpam-4972	29	18	,	,	PUNCT
ejpam-4972	29	19	and	and	CCONJ
ejpam-4972	29	20	highlights	highlight	VERB
ejpam-4972	29	21	important	important	ADJ
ejpam-4972	29	22	theories	theory	NOUN
ejpam-4972	29	23	and	and	CCONJ
ejpam-4972	29	24	counterexamples	counterexample	NOUN
ejpam-4972	29	25	.	.	PUNCT
ejpam-4972	30	1	through	through	ADP
ejpam-4972	30	2	this	this	DET
ejpam-4972	30	3	comprehensive	comprehensive	ADJ
ejpam-4972	30	4	review	review	NOUN
ejpam-4972	30	5	,	,	PUNCT
ejpam-4972	30	6	we	we	PRON
ejpam-4972	30	7	contribute	contribute	VERB
ejpam-4972	30	8	to	to	ADP
ejpam-4972	30	9	a	a	DET
ejpam-4972	30	10	deeper	deep	ADJ
ejpam-4972	30	11	understanding	understanding	NOUN
ejpam-4972	30	12	of	of	ADP
ejpam-4972	30	13	these	these	DET
ejpam-4972	30	14	fundamental	fundamental	ADJ
ejpam-4972	30	15	concepts	concept	NOUN
ejpam-4972	30	16	and	and	CCONJ
ejpam-4972	30	17	their	their	PRON
ejpam-4972	30	18	applications	application	NOUN
ejpam-4972	30	19	in	in	ADP
ejpam-4972	30	20	the	the	DET
ejpam-4972	30	21	context	context	NOUN
ejpam-4972	30	22	of	of	ADP
ejpam-4972	30	23	fuzzy	fuzzy	ADJ
ejpam-4972	30	24	bitopological	bitopological	ADJ
ejpam-4972	30	25	spaces	space	NOUN
ejpam-4972	30	26	.	.	PUNCT
ejpam-4972	31	1	the	the	DET
ejpam-4972	31	2	study	study	NOUN
ejpam-4972	31	3	is	be	AUX
ejpam-4972	31	4	set	set	VERB
ejpam-4972	31	5	up	up	ADP
ejpam-4972	31	6	as	as	SCONJ
ejpam-4972	31	7	follows	follow	VERB
ejpam-4972	31	8	:	:	PUNCT
ejpam-4972	31	9	the	the	DET
ejpam-4972	31	10	history	history	NOUN
ejpam-4972	31	11	,	,	PUNCT
ejpam-4972	31	12	importance	importance	NOUN
ejpam-4972	31	13	,	,	PUNCT
ejpam-4972	31	14	and	and	CCONJ
ejpam-4972	31	15	related	related	ADJ
ejpam-4972	31	16	research	research	NOUN
ejpam-4972	31	17	of	of	ADP
ejpam-4972	31	18	the	the	DET
ejpam-4972	31	19	subject	subject	NOUN
ejpam-4972	31	20	are	be	AUX
ejpam-4972	31	21	examined	examine	VERB
ejpam-4972	31	22	in	in	ADP
ejpam-4972	31	23	section	section	NOUN
ejpam-4972	31	24	1	1	NUM
ejpam-4972	31	25	(	(	PUNCT
ejpam-4972	31	26	introduction	introduction	NOUN
ejpam-4972	31	27	)	)	PUNCT
ejpam-4972	31	28	.	.	PUNCT
ejpam-4972	32	1	in	in	ADP
ejpam-4972	32	2	section	section	NOUN
ejpam-4972	32	3	2	2	NUM
ejpam-4972	32	4	(	(	PUNCT
ejpam-4972	32	5	preliminaries	preliminary	NOUN
ejpam-4972	32	6	)	)	PUNCT
ejpam-4972	32	7	,	,	PUNCT
ejpam-4972	32	8	we	we	PRON
ejpam-4972	32	9	outline	outline	VERB
ejpam-4972	32	10	a	a	DET
ejpam-4972	32	11	few	few	ADJ
ejpam-4972	32	12	key	key	ADJ
ejpam-4972	32	13	antecedent	antecedent	NOUN
ejpam-4972	32	14	ideas	idea	NOUN
ejpam-4972	32	15	that	that	PRON
ejpam-4972	32	16	are	be	AUX
ejpam-4972	32	17	relevant	relevant	ADJ
ejpam-4972	32	18	to	to	ADP
ejpam-4972	32	19	our	our	PRON
ejpam-4972	32	20	research	research	NOUN
ejpam-4972	32	21	.	.	PUNCT
ejpam-4972	33	1	the	the	DET
ejpam-4972	33	2	concept	concept	NOUN
ejpam-4972	33	3	of	of	ADP
ejpam-4972	33	4	generalized	generalized	ADJ
ejpam-4972	33	5	continuous	continuous	ADJ
ejpam-4972	33	6	concepts	concept	NOUN
ejpam-4972	33	7	is	be	AUX
ejpam-4972	33	8	presented	present	VERB
ejpam-4972	33	9	in	in	ADP
ejpam-4972	33	10	section	section	NOUN
ejpam-4972	33	11	3	3	NUM
ejpam-4972	33	12	(	(	PUNCT
ejpam-4972	33	13	types	type	NOUN
ejpam-4972	33	14	of	of	ADP
ejpam-4972	33	15	fuzzy	fuzzy	ADJ
ejpam-4972	33	16	generalized	generalize	VERB
ejpam-4972	33	17	continuous	continuous	ADJ
ejpam-4972	33	18	mappings	mapping	NOUN
ejpam-4972	33	19	)	)	PUNCT
ejpam-4972	33	20	,	,	PUNCT
ejpam-4972	33	21	which	which	PRON
ejpam-4972	33	22	also	also	ADV
ejpam-4972	33	23	discusses	discuss	VERB
ejpam-4972	33	24	them	they	PRON
ejpam-4972	33	25	in	in	ADP
ejpam-4972	33	26	connection	connection	NOUN
ejpam-4972	33	27	to	to	ADP
ejpam-4972	33	28	important	important	ADJ
ejpam-4972	33	29	theorems	theorem	NOUN
ejpam-4972	33	30	and	and	CCONJ
ejpam-4972	33	31	distinctive	distinctive	ADJ
ejpam-4972	33	32	characteristics	characteristic	NOUN
ejpam-4972	33	33	.	.	PUNCT
ejpam-4972	34	1	however	however	ADV
ejpam-4972	34	2	,	,	PUNCT
ejpam-4972	34	3	the	the	DET
ejpam-4972	34	4	types	type	NOUN
ejpam-4972	34	5	of	of	ADP
ejpam-4972	34	6	strong	strong	ADJ
ejpam-4972	34	7	continuity	continuity	NOUN
ejpam-4972	34	8	and	and	CCONJ
ejpam-4972	34	9	irresoluteness	irresoluteness	NOUN
ejpam-4972	34	10	functions	function	NOUN
ejpam-4972	34	11	are	be	AUX
ejpam-4972	34	12	defined	define	VERB
ejpam-4972	34	13	in	in	ADP
ejpam-4972	34	14	section	section	NOUN
ejpam-4972	34	15	4	4	NUM
ejpam-4972	34	16	(	(	PUNCT
ejpam-4972	34	17	types	type	NOUN
ejpam-4972	34	18	of	of	ADP
ejpam-4972	34	19	fuzzy	fuzzy	ADJ
ejpam-4972	34	20	generalized	generalize	VERB
ejpam-4972	34	21	strongly	strongly	ADV
ejpam-4972	34	22	continuity	continuity	NOUN
ejpam-4972	34	23	and	and	CCONJ
ejpam-4972	34	24	irresolute	irresolute	ADJ
ejpam-4972	34	25	mapping	mapping	NOUN
ejpam-4972	34	26	)	)	PUNCT
ejpam-4972	34	27	,	,	PUNCT
ejpam-4972	34	28	which	which	PRON
ejpam-4972	34	29	also	also	ADV
ejpam-4972	34	30	examines	examine	VERB
ejpam-4972	34	31	how	how	SCONJ
ejpam-4972	34	32	these	these	DET
ejpam-4972	34	33	definitions	definition	NOUN
ejpam-4972	34	34	relate	relate	VERB
ejpam-4972	34	35	to	to	ADP
ejpam-4972	34	36	the	the	DET
ejpam-4972	34	37	major	major	ADJ
ejpam-4972	34	38	theories	theory	NOUN
ejpam-4972	34	39	and	and	CCONJ
ejpam-4972	34	40	some	some	DET
ejpam-4972	34	41	significant	significant	ADJ
ejpam-4972	34	42	examples	example	NOUN
ejpam-4972	34	43	.	.	PUNCT
ejpam-4972	35	1	we	we	PRON
ejpam-4972	35	2	also	also	ADV
ejpam-4972	35	3	provided	provide	VERB
ejpam-4972	35	4	crucial	crucial	ADJ
ejpam-4972	35	5	definitions	definition	NOUN
ejpam-4972	35	6	and	and	CCONJ
ejpam-4972	35	7	theorems	theorem	NOUN
ejpam-4972	35	8	for	for	ADP
ejpam-4972	35	9	open	open	ADJ
ejpam-4972	35	10	and	and	CCONJ
ejpam-4972	35	11	closed	closed	ADJ
ejpam-4972	35	12	mappings	mapping	NOUN
ejpam-4972	35	13	in	in	ADP
ejpam-4972	35	14	section	section	NOUN
ejpam-4972	35	15	5	5	NUM
ejpam-4972	35	16	(	(	PUNCT
ejpam-4972	35	17	types	type	NOUN
ejpam-4972	35	18	of	of	ADP
ejpam-4972	35	19	fuzzy	fuzzy	ADJ
ejpam-4972	35	20	generalized	generalize	VERB
ejpam-4972	35	21	open	open	ADJ
ejpam-4972	35	22	and	and	CCONJ
ejpam-4972	35	23	closed	closed	ADJ
ejpam-4972	35	24	mappings	mapping	NOUN
ejpam-4972	35	25	)	)	PUNCT
ejpam-4972	35	26	.	.	PUNCT
ejpam-4972	36	1	in	in	ADP
ejpam-4972	36	2	section	section	NOUN
ejpam-4972	36	3	6	6	NUM
ejpam-4972	36	4	(	(	PUNCT
ejpam-4972	36	5	fuzzy	fuzzy	ADJ
ejpam-4972	36	6	generalized	generalize	VERB
ejpam-4972	36	7	homomorphism	homomorphism	PROPN
ejpam-4972	36	8	mapping	mapping	NOUN
ejpam-4972	36	9	)	)	PUNCT
ejpam-4972	36	10	we	we	PRON
ejpam-4972	36	11	have	have	AUX
ejpam-4972	36	12	presented	present	VERB
ejpam-4972	36	13	a	a	DET
ejpam-4972	36	14	definition	definition	NOUN
ejpam-4972	36	15	of	of	ADP
ejpam-4972	36	16	homomorphism	homomorphism	NOUN
ejpam-4972	36	17	and	and	CCONJ
ejpam-4972	36	18	reviewed	review	VERB
ejpam-4972	36	19	the	the	DET
ejpam-4972	36	20	main	main	ADJ
ejpam-4972	36	21	theories	theory	NOUN
ejpam-4972	36	22	and	and	CCONJ
ejpam-4972	36	23	their	their	PRON
ejpam-4972	36	24	relationship	relationship	NOUN
ejpam-4972	36	25	to	to	ADP
ejpam-4972	36	26	the	the	DET
ejpam-4972	36	27	above	above	ADJ
ejpam-4972	36	28	functions	function	NOUN
ejpam-4972	36	29	.	.	PUNCT
ejpam-4972	37	1	finally	finally	ADV
ejpam-4972	37	2	,	,	PUNCT
ejpam-4972	37	3	in	in	ADP
ejpam-4972	37	4	section	section	NOUN
ejpam-4972	37	5	7	7	NUM
ejpam-4972	37	6	(	(	PUNCT
ejpam-4972	37	7	conclusion	conclusion	NOUN
ejpam-4972	37	8	)	)	PUNCT
ejpam-4972	37	9	,	,	PUNCT
ejpam-4972	37	10	we	we	PRON
ejpam-4972	37	11	compile	compile	VERB
ejpam-4972	37	12	our	our	PRON
ejpam-4972	37	13	findings	finding	NOUN
ejpam-4972	37	14	.	.	PUNCT
ejpam-4972	38	1	2	2	X
ejpam-4972	38	2	.	.	X
ejpam-4972	38	3	preliminaries	preliminary	NOUN
ejpam-4972	38	4	in	in	ADP
ejpam-4972	38	5	the	the	DET
ejpam-4972	38	6	next	next	ADJ
ejpam-4972	38	7	section	section	NOUN
ejpam-4972	38	8	,	,	PUNCT
ejpam-4972	38	9	we	we	PRON
ejpam-4972	38	10	mention	mention	VERB
ejpam-4972	38	11	a	a	DET
ejpam-4972	38	12	few	few	ADJ
ejpam-4972	38	13	previous	previous	ADJ
ejpam-4972	38	14	concepts	concept	NOUN
ejpam-4972	38	15	which	which	PRON
ejpam-4972	38	16	are	be	AUX
ejpam-4972	38	17	fundamental	fundamental	ADJ
ejpam-4972	38	18	to	to	ADP
ejpam-4972	38	19	this	this	DET
ejpam-4972	38	20	study	study	NOUN
ejpam-4972	38	21	.	.	PUNCT
ejpam-4972	39	1	definition	definition	NOUN
ejpam-4972	39	2	1	1	NUM
ejpam-4972	39	3	.	.	PUNCT
ejpam-4972	40	1	[	[	X
ejpam-4972	40	2	19	19	NUM
ejpam-4972	40	3	]	]	PUNCT
ejpam-4972	40	4	assume	assume	VERB
ejpam-4972	40	5	i	i	PRON
ejpam-4972	40	6	stands	stand	VERB
ejpam-4972	40	7	for	for	ADP
ejpam-4972	40	8	the	the	DET
ejpam-4972	40	9	unit	unit	NOUN
ejpam-4972	40	10	period	period	NOUN
ejpam-4972	41	1	[	[	X
ejpam-4972	41	2	0	0	NUM
ejpam-4972	41	3	,	,	PUNCT
ejpam-4972	41	4	1	1	NUM
ejpam-4972	41	5	]	]	PUNCT
ejpam-4972	41	6	and	and	CCONJ
ejpam-4972	41	7	x	x	X
ejpam-4972	41	8	is	be	AUX
ejpam-4972	41	9	not	not	PART
ejpam-4972	41	10	a	a	DET
ejpam-4972	41	11	blank	blank	NOUN
ejpam-4972	41	12	,	,	PUNCT
ejpam-4972	41	13	then	then	ADV
ejpam-4972	41	14	:	:	PUNCT
ejpam-4972	41	15	(	(	PUNCT
ejpam-4972	41	16	1	1	X
ejpam-4972	41	17	)	)	PUNCT
ejpam-4972	41	18	a	a	DET
ejpam-4972	41	19	fuzzy	fuzzy	ADJ
ejpam-4972	41	20	set	set	NOUN
ejpam-4972	41	21	m	m	VERB
ejpam-4972	41	22	is	be	AUX
ejpam-4972	41	23	referred	refer	VERB
ejpam-4972	41	24	to	to	ADP
ejpam-4972	41	25	a	a	DET
ejpam-4972	41	26	function	function	NOUN
ejpam-4972	41	27	with	with	ADP
ejpam-4972	41	28	domain	domain	NOUN
ejpam-4972	41	29	x	x	PUNCT
ejpam-4972	41	30	and	and	CCONJ
ejpam-4972	41	31	range	range	VERB
ejpam-4972	41	32	i	i	PRON
ejpam-4972	41	33	,	,	PUNCT
ejpam-4972	41	34	m(t	m(t	NOUN
ejpam-4972	41	35	)	)	PUNCT
ejpam-4972	41	36	∈	∈	PROPN
ejpam-4972	41	37	(	(	PUNCT
ejpam-4972	41	38	0	0	NUM
ejpam-4972	41	39	,	,	PUNCT
ejpam-4972	41	40	1	1	NUM
ejpam-4972	41	41	]	]	PUNCT
ejpam-4972	41	42	if	if	SCONJ
ejpam-4972	41	43	t	t	PROPN
ejpam-4972	41	44	∈m	∈m	NOUN
ejpam-4972	41	45	,	,	PUNCT
ejpam-4972	41	46	as	as	ADP
ejpam-4972	41	47	m(t	m(t	NOUN
ejpam-4972	41	48	)	)	PUNCT
ejpam-4972	42	1	=	=	SYM
ejpam-4972	42	2	0	0	PUNCT
ejpam-4972	42	3	when	when	SCONJ
ejpam-4972	42	4	t	t	PROPN
ejpam-4972	42	5	̸∈m	̸∈m	VERB
ejpam-4972	42	6	.	.	PUNCT
ejpam-4972	43	1	(	(	PUNCT
ejpam-4972	43	2	2	2	X
ejpam-4972	43	3	)	)	PUNCT
ejpam-4972	43	4	m	m	VERB
ejpam-4972	43	5	is	be	AUX
ejpam-4972	43	6	included	include	VERB
ejpam-4972	43	7	in	in	ADP
ejpam-4972	43	8	l	l	NOUN
ejpam-4972	43	9	as	as	SCONJ
ejpam-4972	43	10	shown	show	VERB
ejpam-4972	43	11	by	by	ADP
ejpam-4972	43	12	m	m	PROPN
ejpam-4972	43	13	⊆	⊆	NUM
ejpam-4972	43	14	l	l	NOUN
ejpam-4972	43	15	if	if	SCONJ
ejpam-4972	43	16	m(t	m(t	NOUN
ejpam-4972	43	17	)	)	PUNCT
ejpam-4972	43	18	≤	≤	NUM
ejpam-4972	43	19	l(t	l(t	NOUN
ejpam-4972	43	20	)	)	PUNCT
ejpam-4972	43	21	,	,	PUNCT
ejpam-4972	43	22	while	while	SCONJ
ejpam-4972	43	23	t	t	PROPN
ejpam-4972	43	24	∈	∈	PROPN
ejpam-4972	43	25	x	x	X
ejpam-4972	43	26	(	(	PUNCT
ejpam-4972	43	27	3	3	NUM
ejpam-4972	43	28	)	)	PUNCT
ejpam-4972	43	29	m	m	NOUN
ejpam-4972	44	1	∨	∨	NOUN
ejpam-4972	44	2	l	l	NOUN
ejpam-4972	44	3	is	be	AUX
ejpam-4972	44	4	the	the	DET
ejpam-4972	44	5	combination	combination	NOUN
ejpam-4972	44	6	of	of	ADP
ejpam-4972	44	7	groups	group	NOUN
ejpam-4972	44	8	defined	define	VERB
ejpam-4972	44	9	as	as	ADP
ejpam-4972	44	10	(	(	PUNCT
ejpam-4972	44	11	m	m	PROPN
ejpam-4972	44	12	∨	∨	NOUN
ejpam-4972	44	13	l)(t	l)(t	X
ejpam-4972	44	14	)	)	PUNCT
ejpam-4972	44	15	=	=	SYM
ejpam-4972	44	16	upper{m(t	upper{m(t	PROPN
ejpam-4972	44	17	)	)	PUNCT
ejpam-4972	44	18	,	,	PUNCT
ejpam-4972	44	19	l(t	l(t	PROPN
ejpam-4972	44	20	)	)	PUNCT
ejpam-4972	44	21	}	}	PUNCT
ejpam-4972	44	22	∀	∀	PUNCT
ejpam-4972	44	23	t	t	NOUN
ejpam-4972	44	24	∈	∈	PROPN
ejpam-4972	44	25	x.	x.	NOUN
ejpam-4972	44	26	a.	a.	PROPN
ejpam-4972	44	27	a.	a.	PROPN
ejpam-4972	44	28	alharbi	alharbi	PROPN
ejpam-4972	44	29	,	,	PUNCT
ejpam-4972	44	30	a.	a.	NOUN
ejpam-4972	44	31	kilicman	kilicman	PROPN
ejpam-4972	44	32	/	/	SYM
ejpam-4972	44	33	eur	eur	PROPN
ejpam-4972	44	34	.	.	PUNCT
ejpam-4972	45	1	j.	j.	PROPN
ejpam-4972	45	2	pure	pure	PROPN
ejpam-4972	45	3	appl	appl	PROPN
ejpam-4972	45	4	.	.	PROPN
ejpam-4972	45	5	math	math	PROPN
ejpam-4972	45	6	,	,	PUNCT
ejpam-4972	45	7	16	16	NUM
ejpam-4972	45	8	(	(	PUNCT
ejpam-4972	45	9	4	4	NUM
ejpam-4972	45	10	)	)	PUNCT
ejpam-4972	45	11	(	(	PUNCT
ejpam-4972	45	12	2023	2023	NUM
ejpam-4972	45	13	)	)	PUNCT
ejpam-4972	45	14	,	,	PUNCT
ejpam-4972	45	15	2613	2613	NUM
ejpam-4972	45	16	-	-	SYM
ejpam-4972	45	17	2631	2631	NUM
ejpam-4972	45	18	2615	2615	NUM
ejpam-4972	45	19	(	(	PUNCT
ejpam-4972	45	20	4	4	NUM
ejpam-4972	45	21	)	)	PUNCT
ejpam-4972	45	22	m	m	NOUN
ejpam-4972	45	23	∧	∧	PROPN
ejpam-4972	45	24	l	l	NOUN
ejpam-4972	45	25	is	be	AUX
ejpam-4972	45	26	the	the	DET
ejpam-4972	45	27	intersection	intersection	NOUN
ejpam-4972	45	28	that	that	PRON
ejpam-4972	45	29	defiend	defiend	VERB
ejpam-4972	45	30	as	as	ADP
ejpam-4972	45	31	(	(	PUNCT
ejpam-4972	45	32	m	m	PROPN
ejpam-4972	45	33	∧	∧	NOUN
ejpam-4972	45	34	l)(t	l)(t	ADJ
ejpam-4972	45	35	)	)	PUNCT
ejpam-4972	45	36	=	=	SYM
ejpam-4972	45	37	lower{m(t	lower{m(t	ADJ
ejpam-4972	45	38	)	)	PUNCT
ejpam-4972	45	39	,	,	PUNCT
ejpam-4972	45	40	l(t	l(t	PROPN
ejpam-4972	45	41	)	)	PUNCT
ejpam-4972	45	42	}	}	PUNCT
ejpam-4972	45	43	∀	∀	PUNCT
ejpam-4972	45	44	t	t	NOUN
ejpam-4972	45	45	∈	∈	NOUN
ejpam-4972	45	46	x.	x.	NOUN
ejpam-4972	46	1	(	(	PUNCT
ejpam-4972	46	2	5	5	X
ejpam-4972	46	3	)	)	PUNCT
ejpam-4972	46	4	m	m	VERB
ejpam-4972	46	5	c	c	NOUN
ejpam-4972	46	6	is	be	AUX
ejpam-4972	46	7	the	the	DET
ejpam-4972	46	8	completeness	completeness	NOUN
ejpam-4972	46	9	that	that	PRON
ejpam-4972	46	10	defiend	defiend	VERB
ejpam-4972	46	11	as	as	ADP
ejpam-4972	46	12	(	(	PUNCT
ejpam-4972	46	13	m(t))c	m(t))c	PROPN
ejpam-4972	46	14	=	=	NOUN
ejpam-4972	46	15	1−m(t	1−m(t	NUM
ejpam-4972	46	16	)	)	PUNCT
ejpam-4972	46	17	,	,	PUNCT
ejpam-4972	46	18	∀	∀	X
ejpam-4972	46	19	t	t	NOUN
ejpam-4972	46	20	∈	∈	PROPN
ejpam-4972	46	21	x.	x.	NOUN
ejpam-4972	47	1	the	the	DET
ejpam-4972	47	2	concepts	concept	NOUN
ejpam-4972	47	3	of	of	ADP
ejpam-4972	47	4	fuzzy	fuzzy	ADJ
ejpam-4972	47	5	topology	topology	NOUN
ejpam-4972	47	6	as	as	ADV
ejpam-4972	47	7	well	well	ADV
ejpam-4972	47	8	as	as	ADP
ejpam-4972	47	9	fuzzy	fuzzy	ADJ
ejpam-4972	47	10	bitopological	bitopological	ADJ
ejpam-4972	47	11	spaces	space	NOUN
ejpam-4972	47	12	are	be	AUX
ejpam-4972	47	13	shown	show	VERB
ejpam-4972	47	14	below	below	ADP
ejpam-4972	47	15	:	:	PUNCT
ejpam-4972	47	16	definition	definition	NOUN
ejpam-4972	47	17	2	2	NUM
ejpam-4972	47	18	.	.	PUNCT
ejpam-4972	48	1	[	[	X
ejpam-4972	48	2	19	19	NUM
ejpam-4972	48	3	]	]	PUNCT
ejpam-4972	48	4	the	the	DET
ejpam-4972	48	5	pair	pair	NOUN
ejpam-4972	48	6	(	(	PUNCT
ejpam-4972	48	7	x	x	NOUN
ejpam-4972	48	8	,	,	PUNCT
ejpam-4972	48	9	δ	δ	PROPN
ejpam-4972	48	10	)	)	PUNCT
ejpam-4972	48	11	is	be	AUX
ejpam-4972	48	12	consider	consider	VERB
ejpam-4972	48	13	fuzzy	fuzzy	ADJ
ejpam-4972	48	14	topology	topology	NOUN
ejpam-4972	48	15	if	if	SCONJ
ejpam-4972	48	16	the	the	DET
ejpam-4972	48	17	next	next	ADJ
ejpam-4972	48	18	three	three	NUM
ejpam-4972	48	19	conditions	condition	NOUN
ejpam-4972	48	20	holds	hold	VERB
ejpam-4972	48	21	:	:	PUNCT
ejpam-4972	48	22	1	1	NUM
ejpam-4972	48	23	.	.	NOUN
ejpam-4972	48	24	0	0	NUM
ejpam-4972	48	25	,	,	PUNCT
ejpam-4972	48	26	1	1	NUM
ejpam-4972	48	27	∈	∈	PROPN
ejpam-4972	48	28	δ	δ	PROPN
ejpam-4972	48	29	,	,	PUNCT
ejpam-4972	48	30	since	since	SCONJ
ejpam-4972	48	31	0(t	0(t	NUM
ejpam-4972	48	32	)	)	PUNCT
ejpam-4972	48	33	=	=	SYM
ejpam-4972	48	34	0	0	NUM
ejpam-4972	48	35	,	,	PUNCT
ejpam-4972	48	36	1(t	1(t	NUM
ejpam-4972	48	37	)	)	PUNCT
ejpam-4972	48	38	=	=	SYM
ejpam-4972	48	39	1	1	NUM
ejpam-4972	48	40	,	,	PUNCT
ejpam-4972	48	41	as	as	ADP
ejpam-4972	48	42	t	t	PROPN
ejpam-4972	48	43	∈	∈	PROPN
ejpam-4972	48	44	x.	x.	NOUN
ejpam-4972	49	1	2	2	X
ejpam-4972	49	2	.	.	X
ejpam-4972	50	1	m	m	VERB
ejpam-4972	50	2	∧	∧	PROPN
ejpam-4972	50	3	l	l	NOUN
ejpam-4972	50	4	∈	∈	PROPN
ejpam-4972	50	5	δ	δ	PROPN
ejpam-4972	50	6	,	,	PUNCT
ejpam-4972	50	7	∀m	∀m	PROPN
ejpam-4972	50	8	,	,	PUNCT
ejpam-4972	50	9	l	l	PROPN
ejpam-4972	50	10	∈	∈	PROPN
ejpam-4972	50	11	δ	δ	PROPN
ejpam-4972	50	12	,	,	PUNCT
ejpam-4972	50	13	.	.	PUNCT
ejpam-4972	51	1	3	3	X
ejpam-4972	51	2	.	.	X
ejpam-4972	51	3	∨i∈imi	∨i∈imi	PROPN
ejpam-4972	51	4	∈	∈	PROPN
ejpam-4972	51	5	δ	δ	PROPN
ejpam-4972	51	6	,	,	PUNCT
ejpam-4972	51	7	∀(mi∈i	∀(mi∈i	PROPN
ejpam-4972	51	8	)	)	PUNCT
ejpam-4972	51	9	∈	∈	PROPN
ejpam-4972	51	10	δ	δ	PROPN
ejpam-4972	51	11	,	,	PUNCT
ejpam-4972	51	12	.	.	PUNCT
ejpam-4972	52	1	the	the	DET
ejpam-4972	52	2	pair	pair	NOUN
ejpam-4972	52	3	(	(	PUNCT
ejpam-4972	52	4	x	x	NOUN
ejpam-4972	52	5	,	,	PUNCT
ejpam-4972	52	6	δ	δ	PROPN
ejpam-4972	52	7	)	)	PUNCT
ejpam-4972	52	8	is	be	AUX
ejpam-4972	52	9	referred	refer	VERB
ejpam-4972	52	10	to	to	ADP
ejpam-4972	52	11	as	as	ADP
ejpam-4972	52	12	”	"	PUNCT
ejpam-4972	52	13	fuzzy	fuzzy	ADJ
ejpam-4972	52	14	topology	topology	NOUN
ejpam-4972	52	15	space	space	NOUN
ejpam-4972	52	16	,	,	PUNCT
ejpam-4972	52	17	”	"	PUNCT
ejpam-4972	52	18	or	or	CCONJ
ejpam-4972	52	19	”	"	PUNCT
ejpam-4972	52	20	fts	fts	X
ejpam-4972	52	21	”	"	PUNCT
ejpam-4972	52	22	shortly	shortly	ADV
ejpam-4972	52	23	.	.	PUNCT
ejpam-4972	53	1	also	also	ADV
ejpam-4972	53	2	,	,	PUNCT
ejpam-4972	53	3	the	the	DET
ejpam-4972	53	4	parts	part	NOUN
ejpam-4972	53	5	of	of	ADP
ejpam-4972	53	6	δ	δ	PROPN
ejpam-4972	53	7	are	be	AUX
ejpam-4972	53	8	known	know	VERB
ejpam-4972	53	9	as	as	ADP
ejpam-4972	53	10	open	open	ADJ
ejpam-4972	53	11	fuzzy	fuzzy	ADJ
ejpam-4972	53	12	groups	group	NOUN
ejpam-4972	53	13	.	.	PUNCT
ejpam-4972	54	1	when	when	SCONJ
ejpam-4972	54	2	f	f	PROPN
ejpam-4972	54	3	∈	∈	PROPN
ejpam-4972	54	4	δ	δ	PROPN
ejpam-4972	54	5	,	,	PUNCT
ejpam-4972	54	6	thus	thus	ADV
ejpam-4972	54	7	f	f	X
ejpam-4972	54	8	c	c	PROPN
ejpam-4972	54	9	is	be	AUX
ejpam-4972	54	10	regarded	regard	VERB
ejpam-4972	54	11	as	as	ADP
ejpam-4972	54	12	closed	close	VERB
ejpam-4972	54	13	fuzzy	fuzzy	ADJ
ejpam-4972	54	14	group	group	NOUN
ejpam-4972	54	15	,	,	PUNCT
ejpam-4972	54	16	and	and	CCONJ
ejpam-4972	54	17	the	the	DET
ejpam-4972	54	18	set	set	NOUN
ejpam-4972	54	19	of	of	ADP
ejpam-4972	54	20	all	all	DET
ejpam-4972	54	21	closed	closed	ADJ
ejpam-4972	54	22	fuzzy	fuzzy	ADJ
ejpam-4972	54	23	groups	group	NOUN
ejpam-4972	54	24	denoted	denote	VERB
ejpam-4972	54	25	by	by	ADP
ejpam-4972	54	26	fδ	fδ	X
ejpam-4972	54	27	.	.	NOUN
ejpam-4972	54	28	definition	definition	NOUN
ejpam-4972	54	29	3	3	NUM
ejpam-4972	54	30	.	.	PUNCT
ejpam-4972	55	1	[	[	X
ejpam-4972	55	2	4	4	X
ejpam-4972	55	3	]	]	X
ejpam-4972	55	4	a	a	DET
ejpam-4972	55	5	bitopology	bitopology	NOUN
ejpam-4972	55	6	fuzzy	fuzzy	ADJ
ejpam-4972	55	7	spaces	space	NOUN
ejpam-4972	55	8	,	,	PUNCT
ejpam-4972	55	9	often	often	ADV
ejpam-4972	55	10	known	know	VERB
ejpam-4972	55	11	as	as	ADP
ejpam-4972	55	12	fbts	fbt	NOUN
ejpam-4972	55	13	,	,	PUNCT
ejpam-4972	55	14	(	(	PUNCT
ejpam-4972	55	15	x	x	NOUN
ejpam-4972	55	16	,	,	PUNCT
ejpam-4972	55	17	δ1	δ1	NOUN
ejpam-4972	55	18	,	,	PUNCT
ejpam-4972	55	19	δ2	δ2	PROPN
ejpam-4972	55	20	)	)	PUNCT
ejpam-4972	55	21	as	as	SCONJ
ejpam-4972	55	22	x	x	PRON
ejpam-4972	55	23	is	be	AUX
ejpam-4972	55	24	not	not	PART
ejpam-4972	55	25	empty	empty	ADJ
ejpam-4972	55	26	,	,	PUNCT
ejpam-4972	55	27	and	and	CCONJ
ejpam-4972	55	28	δ1	δ1	NOUN
ejpam-4972	55	29	,	,	PUNCT
ejpam-4972	55	30	δ2	δ2	PROPN
ejpam-4972	55	31	are	be	AUX
ejpam-4972	55	32	fuzzy	fuzzy	ADJ
ejpam-4972	55	33	topological	topological	ADJ
ejpam-4972	55	34	spaces	space	NOUN
ejpam-4972	55	35	on	on	ADP
ejpam-4972	55	36	x.	x.	NOUN
ejpam-4972	55	37	during	during	ADP
ejpam-4972	55	38	the	the	DET
ejpam-4972	55	39	course	course	NOUN
ejpam-4972	55	40	of	of	ADP
ejpam-4972	55	41	this	this	DET
ejpam-4972	55	42	research	research	NOUN
ejpam-4972	55	43	,	,	PUNCT
ejpam-4972	55	44	x	x	PRON
ejpam-4972	55	45	conducts	conduct	VERB
ejpam-4972	55	46	fuzzy	fuzzy	ADJ
ejpam-4972	55	47	bitopology	bitopology	NOUN
ejpam-4972	55	48	(	(	PUNCT
ejpam-4972	55	49	x	x	NOUN
ejpam-4972	55	50	,	,	PUNCT
ejpam-4972	55	51	δ1	δ1	NOUN
ejpam-4972	55	52	,	,	PUNCT
ejpam-4972	55	53	δ2	δ2	ADJ
ejpam-4972	55	54	)	)	PUNCT
ejpam-4972	55	55	and	and	CCONJ
ejpam-4972	55	56	y	y	PROPN
ejpam-4972	55	57	takes	take	VERB
ejpam-4972	55	58	(	(	PUNCT
ejpam-4972	55	59	y	y	PROPN
ejpam-4972	55	60	,	,	PUNCT
ejpam-4972	55	61	σ1	σ1	PROPN
ejpam-4972	55	62	,	,	PUNCT
ejpam-4972	55	63	σ2	σ2	NOUN
ejpam-4972	55	64	)	)	PUNCT
ejpam-4972	55	65	so	so	SCONJ
ejpam-4972	55	66	that	that	SCONJ
ejpam-4972	55	67	i	i	PRON
ejpam-4972	55	68	̸=	̸=	PROPN
ejpam-4972	55	69	j	j	PROPN
ejpam-4972	55	70	,	,	PUNCT
ejpam-4972	55	71	as	as	ADP
ejpam-4972	55	72	i	i	PRON
ejpam-4972	55	73	,	,	PUNCT
ejpam-4972	55	74	j	j	PROPN
ejpam-4972	55	75	∈	∈	PROPN
ejpam-4972	55	76	{	{	PUNCT
ejpam-4972	55	77	1	1	NUM
ejpam-4972	55	78	,	,	PUNCT
ejpam-4972	55	79	2	2	NUM
ejpam-4972	55	80	}	}	PUNCT
ejpam-4972	55	81	definition	definition	NOUN
ejpam-4972	55	82	4	4	NUM
ejpam-4972	55	83	.	.	PUNCT
ejpam-4972	56	1	[	[	X
ejpam-4972	56	2	9	9	NUM
ejpam-4972	56	3	]	]	PUNCT
ejpam-4972	56	4	.	.	PUNCT
ejpam-4972	57	1	a	a	DET
ejpam-4972	57	2	fuzzy	fuzzy	ADJ
ejpam-4972	57	3	group	group	NOUN
ejpam-4972	57	4	µ	µ	X
ejpam-4972	57	5	of	of	ADP
ejpam-4972	57	6	x	x	PROPN
ejpam-4972	57	7	is	be	AUX
ejpam-4972	57	8	referred	refer	VERB
ejpam-4972	57	9	to	to	ADP
ejpam-4972	57	10	fuzzy	fuzzy	ADJ
ejpam-4972	57	11	point	point	NOUN
ejpam-4972	57	12	(	(	PUNCT
ejpam-4972	57	13	singleton	singleton	NOUN
ejpam-4972	57	14	)	)	PUNCT
ejpam-4972	57	15	iff	iff	PROPN
ejpam-4972	57	16	µ(t	µ(t	ADJ
ejpam-4972	57	17	)	)	PUNCT
ejpam-4972	58	1	=	=	SYM
ejpam-4972	58	2	r	r	NOUN
ejpam-4972	58	3	,	,	PUNCT
ejpam-4972	58	4	(	(	PUNCT
ejpam-4972	58	5	0	0	NUM
ejpam-4972	58	6	<	<	X
ejpam-4972	58	7	r	r	NOUN
ejpam-4972	58	8	≤	≤	NUM
ejpam-4972	58	9	1	1	NUM
ejpam-4972	58	10	)	)	PUNCT
ejpam-4972	58	11	with	with	ADP
ejpam-4972	58	12	a	a	DET
ejpam-4972	58	13	specific	specific	ADJ
ejpam-4972	58	14	t	t	NOUN
ejpam-4972	58	15	∈	∈	PROPN
ejpam-4972	58	16	x	x	X
ejpam-4972	58	17	,	,	PUNCT
ejpam-4972	58	18	µ(h	µ(h	PROPN
ejpam-4972	58	19	)	)	PUNCT
ejpam-4972	58	20	=	=	SYM
ejpam-4972	58	21	0	0	NUM
ejpam-4972	58	22	with	with	ADP
ejpam-4972	58	23	each	each	DET
ejpam-4972	58	24	elements	element	NOUN
ejpam-4972	58	25	h	h	NOUN
ejpam-4972	58	26	of	of	ADP
ejpam-4972	58	27	x	x	PUNCT
ejpam-4972	58	28	excluding	exclude	VERB
ejpam-4972	58	29	t	t	PROPN
ejpam-4972	58	30	,	,	PUNCT
ejpam-4972	58	31	and	and	CCONJ
ejpam-4972	58	32	it	it	PRON
ejpam-4972	58	33	is	be	AUX
ejpam-4972	58	34	indicated	indicate	VERB
ejpam-4972	58	35	by	by	ADP
ejpam-4972	58	36	tr	tr	VERB
ejpam-4972	58	37	.	.	VERB
ejpam-4972	59	1	sometimes	sometimes	ADV
ejpam-4972	59	2	we	we	PRON
ejpam-4972	59	3	refer	refer	VERB
ejpam-4972	59	4	to	to	ADP
ejpam-4972	59	5	tr	tr	VERB
ejpam-4972	59	6	as	as	ADP
ejpam-4972	59	7	a	a	DET
ejpam-4972	59	8	fuzzy	fuzzy	ADJ
ejpam-4972	59	9	point	point	NOUN
ejpam-4972	59	10	if	if	SCONJ
ejpam-4972	59	11	0	0	NUM
ejpam-4972	59	12	<	<	X
ejpam-4972	59	13	r	r	X
ejpam-4972	59	14	<	<	X
ejpam-4972	59	15	1	1	NUM
ejpam-4972	59	16	.	.	PUNCT
ejpam-4972	59	17	additionally	additionally	ADV
ejpam-4972	59	18	,	,	PUNCT
ejpam-4972	59	19	s(x	s(x	PROPN
ejpam-4972	59	20	)	)	PUNCT
ejpam-4972	59	21	refers	refer	VERB
ejpam-4972	59	22	to	to	ADP
ejpam-4972	59	23	the	the	DET
ejpam-4972	59	24	set	set	NOUN
ejpam-4972	59	25	of	of	ADP
ejpam-4972	59	26	each	each	DET
ejpam-4972	59	27	fuzzy	fuzzy	ADJ
ejpam-4972	59	28	points	point	NOUN
ejpam-4972	59	29	(	(	PUNCT
ejpam-4972	59	30	singletons	singleton	NOUN
ejpam-4972	59	31	)	)	PUNCT
ejpam-4972	59	32	included	include	VERB
ejpam-4972	59	33	in	in	ADP
ejpam-4972	59	34	x.	x.	PROPN
ejpam-4972	59	35	one	one	NUM
ejpam-4972	59	36	of	of	ADP
ejpam-4972	59	37	the	the	DET
ejpam-4972	59	38	fundamental	fundamental	ADJ
ejpam-4972	59	39	ideas	idea	NOUN
ejpam-4972	59	40	is	be	AUX
ejpam-4972	59	41	the	the	DET
ejpam-4972	59	42	continuous	continuous	ADJ
ejpam-4972	59	43	and	and	CCONJ
ejpam-4972	59	44	irresolute	irresolute	ADJ
ejpam-4972	59	45	mapping	mapping	NOUN
ejpam-4972	59	46	,	,	PUNCT
ejpam-4972	59	47	which	which	PRON
ejpam-4972	59	48	were	be	AUX
ejpam-4972	59	49	defined	define	VERB
ejpam-4972	59	50	as	as	ADP
ejpam-4972	59	51	:	:	PUNCT
ejpam-4972	59	52	definition	definition	NOUN
ejpam-4972	59	53	5	5	NUM
ejpam-4972	59	54	.	.	PUNCT
ejpam-4972	60	1	[	[	X
ejpam-4972	60	2	19	19	NUM
ejpam-4972	60	3	]	]	X
ejpam-4972	60	4	if	if	SCONJ
ejpam-4972	60	5	t	t	PROPN
ejpam-4972	60	6	is	be	AUX
ejpam-4972	60	7	a	a	DET
ejpam-4972	60	8	function	function	NOUN
ejpam-4972	60	9	from	from	ADP
ejpam-4972	60	10	(	(	PUNCT
ejpam-4972	60	11	x	x	NOUN
ejpam-4972	60	12	,	,	PUNCT
ejpam-4972	60	13	δ	δ	PROPN
ejpam-4972	60	14	)	)	PUNCT
ejpam-4972	60	15	to	to	ADP
ejpam-4972	60	16	(	(	PUNCT
ejpam-4972	60	17	y	y	PROPN
ejpam-4972	60	18	,	,	PUNCT
ejpam-4972	60	19	σ).then	σ).then	PROPN
ejpam-4972	60	20	t	t	PROPN
ejpam-4972	60	21	is	be	AUX
ejpam-4972	60	22	fuzzy	fuzzy	ADJ
ejpam-4972	60	23	δ−continuous	δ−continuous	ADJ
ejpam-4972	60	24	iff	iff	PROPN
ejpam-4972	60	25	t−1(w	t−1(w	NOUN
ejpam-4972	60	26	)	)	PUNCT
ejpam-4972	60	27	∈	∈	PROPN
ejpam-4972	60	28	δ	δ	PROPN
ejpam-4972	60	29	,	,	PUNCT
ejpam-4972	60	30	∀w	∀w	PROPN
ejpam-4972	60	31	∈	∈	PROPN
ejpam-4972	60	32	σ	σ	PROPN
ejpam-4972	60	33	.	.	PUNCT
ejpam-4972	60	34	definition	definition	NOUN
ejpam-4972	60	35	6	6	NUM
ejpam-4972	60	36	.	.	PUNCT
ejpam-4972	61	1	[	[	X
ejpam-4972	61	2	23	23	NUM
ejpam-4972	61	3	]	]	PUNCT
ejpam-4972	61	4	a	a	DET
ejpam-4972	61	5	function	function	NOUN
ejpam-4972	61	6	t	t	NOUN
ejpam-4972	61	7	:	:	PUNCT
ejpam-4972	61	8	(	(	PUNCT
ejpam-4972	61	9	x	x	NOUN
ejpam-4972	61	10	,	,	PUNCT
ejpam-4972	61	11	δ	δ	PROPN
ejpam-4972	61	12	)	)	PUNCT
ejpam-4972	61	13	−→	−→	NOUN
ejpam-4972	61	14	(	(	PUNCT
ejpam-4972	61	15	y	y	PROPN
ejpam-4972	61	16	,	,	PUNCT
ejpam-4972	61	17	σ	σ	PROPN
ejpam-4972	61	18	)	)	PUNCT
ejpam-4972	61	19	is	be	AUX
ejpam-4972	61	20	known	know	VERB
ejpam-4972	61	21	as	as	ADP
ejpam-4972	61	22	fuzzy	fuzzy	ADJ
ejpam-4972	61	23	α−	α−	ADP
ejpam-4972	61	24	irresolute	irresolute	ADJ
ejpam-4972	61	25	when	when	SCONJ
ejpam-4972	61	26	t−1(w	t−1(w	NOUN
ejpam-4972	61	27	)	)	PUNCT
ejpam-4972	61	28	is	be	AUX
ejpam-4972	61	29	fuzzy	fuzzy	ADJ
ejpam-4972	61	30	α−open	α−open	NOUN
ejpam-4972	61	31	of	of	ADP
ejpam-4972	61	32	x	x	PUNCT
ejpam-4972	61	33	on	on	ADP
ejpam-4972	61	34	all	all	PRON
ejpam-4972	61	35	fuzzy	fuzzy	ADJ
ejpam-4972	61	36	α−open	α−open	X
ejpam-4972	61	37	w	w	NOUN
ejpam-4972	61	38	of	of	ADP
ejpam-4972	61	39	y	y	PROPN
ejpam-4972	61	40	.	.	PUNCT
ejpam-4972	62	1	one	one	NUM
ejpam-4972	62	2	of	of	ADP
ejpam-4972	62	3	the	the	DET
ejpam-4972	62	4	fundamental	fundamental	ADJ
ejpam-4972	62	5	ideas	idea	NOUN
ejpam-4972	62	6	in	in	ADP
ejpam-4972	62	7	the	the	DET
ejpam-4972	62	8	research	research	NOUN
ejpam-4972	62	9	is	be	AUX
ejpam-4972	62	10	the	the	DET
ejpam-4972	62	11	generalized	generalize	VERB
ejpam-4972	62	12	fuzzy	fuzzy	ADJ
ejpam-4972	62	13	closed	closed	ADJ
ejpam-4972	62	14	group	group	NOUN
ejpam-4972	62	15	,	,	PUNCT
ejpam-4972	62	16	that	that	PRON
ejpam-4972	62	17	is	be	AUX
ejpam-4972	62	18	known	know	VERB
ejpam-4972	62	19	as	as	SCONJ
ejpam-4972	62	20	follows	follow	VERB
ejpam-4972	62	21	:	:	PUNCT
ejpam-4972	62	22	definition	definition	NOUN
ejpam-4972	62	23	7	7	NUM
ejpam-4972	62	24	.	.	PUNCT
ejpam-4972	63	1	[	[	X
ejpam-4972	63	2	11	11	NUM
ejpam-4972	63	3	]	]	X
ejpam-4972	63	4	k	k	X
ejpam-4972	63	5	is	be	AUX
ejpam-4972	63	6	named	name	VERB
ejpam-4972	63	7	generalized	generalized	ADJ
ejpam-4972	63	8	fuzzy	fuzzy	ADJ
ejpam-4972	63	9	closed	close	VERB
ejpam-4972	63	10	if	if	SCONJ
ejpam-4972	63	11	closure	closure	NOUN
ejpam-4972	63	12	k	k	PROPN
ejpam-4972	63	13	is	be	AUX
ejpam-4972	63	14	subgroup	subgroup	NOUN
ejpam-4972	63	15	of	of	ADP
ejpam-4972	63	16	r	r	NOUN
ejpam-4972	63	17	,	,	PUNCT
ejpam-4972	63	18	as	as	SCONJ
ejpam-4972	63	19	k	k	PROPN
ejpam-4972	63	20	is	be	AUX
ejpam-4972	63	21	subgroup	subgroup	NOUN
ejpam-4972	63	22	of	of	ADP
ejpam-4972	63	23	r	r	NOUN
ejpam-4972	63	24	,	,	PUNCT
ejpam-4972	63	25	which	which	PRON
ejpam-4972	63	26	is	be	AUX
ejpam-4972	63	27	fuzzy	fuzzy	ADJ
ejpam-4972	63	28	open	open	ADJ
ejpam-4972	63	29	.	.	PUNCT
ejpam-4972	64	1	i.e.	i.e.	X
ejpam-4972	64	2	,	,	PUNCT
ejpam-4972	64	3	k	k	PROPN
ejpam-4972	64	4	is	be	AUX
ejpam-4972	64	5	generalized	generalize	VERB
ejpam-4972	64	6	fuzzy	fuzzy	ADJ
ejpam-4972	64	7	closed	close	VERB
ejpam-4972	64	8	when	when	SCONJ
ejpam-4972	64	9	cl(k	cl(k	NOUN
ejpam-4972	64	10	)	)	PUNCT
ejpam-4972	64	11	≤	≤	NOUN
ejpam-4972	64	12	r	r	NOUN
ejpam-4972	64	13	,	,	PUNCT
ejpam-4972	64	14	whatever	whatever	PRON
ejpam-4972	64	15	k	k	PROPN
ejpam-4972	64	16	≤	≤	PROPN
ejpam-4972	64	17	r	r	NOUN
ejpam-4972	64	18	,	,	PUNCT
ejpam-4972	64	19	r	r	NOUN
ejpam-4972	64	20	is	be	AUX
ejpam-4972	64	21	fuzzy	fuzzy	ADJ
ejpam-4972	64	22	open	open	ADJ
ejpam-4972	64	23	.	.	PUNCT
ejpam-4972	65	1	in	in	ADP
ejpam-4972	65	2	the	the	DET
ejpam-4972	65	3	following	follow	VERB
ejpam-4972	65	4	sections	section	NOUN
ejpam-4972	65	5	,	,	PUNCT
ejpam-4972	65	6	we	we	PRON
ejpam-4972	65	7	divided	divide	VERB
ejpam-4972	65	8	the	the	DET
ejpam-4972	65	9	work	work	NOUN
ejpam-4972	65	10	into	into	ADP
ejpam-4972	65	11	four	four	NUM
ejpam-4972	65	12	parts	part	NOUN
ejpam-4972	65	13	:	:	PUNCT
ejpam-4972	65	14	fuzzy	fuzzy	ADJ
ejpam-4972	65	15	(	(	PUNCT
ejpam-4972	65	16	i	i	PROPN
ejpam-4972	65	17	,	,	PUNCT
ejpam-4972	65	18	j)−	j)−	PROPN
ejpam-4972	65	19	generalized	generalize	VERB
ejpam-4972	65	20	ψ	ψ	ADP
ejpam-4972	65	21	continuity	continuity	NOUN
ejpam-4972	65	22	,	,	PUNCT
ejpam-4972	65	23	(	(	PUNCT
ejpam-4972	65	24	i	i	PRON
ejpam-4972	65	25	,	,	PUNCT
ejpam-4972	65	26	j)−	j)−	PROPN
ejpam-4972	65	27	generalized	generalize	VERB
ejpam-4972	65	28	ψ	ψ	ADP
ejpam-4972	65	29	strongly	strongly	ADV
ejpam-4972	65	30	continuity	continuity	NOUN
ejpam-4972	65	31	and	and	CCONJ
ejpam-4972	65	32	irresolute	irresolute	ADJ
ejpam-4972	65	33	,	,	PUNCT
ejpam-4972	65	34	(	(	PUNCT
ejpam-4972	65	35	i	i	PRON
ejpam-4972	65	36	,	,	PUNCT
ejpam-4972	65	37	j)−generalized	j)−generalize	VERB
ejpam-4972	65	38	ψ	ψ	ADP
ejpam-4972	65	39	open	open	ADJ
ejpam-4972	65	40	and	and	CCONJ
ejpam-4972	65	41	closed	close	VERB
ejpam-4972	65	42	mapping	mapping	NOUN
ejpam-4972	65	43	and	and	CCONJ
ejpam-4972	65	44	last	last	ADJ
ejpam-4972	65	45	part	part	NOUN
ejpam-4972	65	46	is	be	AUX
ejpam-4972	65	47	the	the	DET
ejpam-4972	65	48	fuzzy	fuzzy	ADJ
ejpam-4972	65	49	homomorphism	homomorphism	NOUN
ejpam-4972	65	50	.	.	PUNCT
ejpam-4972	66	1	also	also	ADV
ejpam-4972	66	2	,	,	PUNCT
ejpam-4972	66	3	we	we	PRON
ejpam-4972	66	4	apply	apply	VERB
ejpam-4972	66	5	some	some	DET
ejpam-4972	66	6	theorems	theorem	NOUN
ejpam-4972	66	7	,	,	PUNCT
ejpam-4972	66	8	some	some	DET
ejpam-4972	66	9	corollaries	corollary	NOUN
ejpam-4972	66	10	.	.	PUNCT
ejpam-4972	67	1	as	as	SCONJ
ejpam-4972	67	2	it	it	PRON
ejpam-4972	67	3	includes	include	VERB
ejpam-4972	67	4	important	important	ADJ
ejpam-4972	67	5	examples	example	NOUN
ejpam-4972	67	6	and	and	CCONJ
ejpam-4972	67	7	diagrams	diagram	NOUN
ejpam-4972	67	8	to	to	PART
ejpam-4972	67	9	explain	explain	VERB
ejpam-4972	67	10	the	the	DET
ejpam-4972	67	11	relations	relation	NOUN
ejpam-4972	67	12	via	via	ADP
ejpam-4972	67	13	instructors	instructor	NOUN
ejpam-4972	67	14	.	.	PUNCT
ejpam-4972	68	1	a.	a.	NOUN
ejpam-4972	68	2	a.	a.	PROPN
ejpam-4972	68	3	alharbi	alharbi	PROPN
ejpam-4972	68	4	,	,	PUNCT
ejpam-4972	68	5	a.	a.	NOUN
ejpam-4972	68	6	kilicman	kilicman	PROPN
ejpam-4972	68	7	/	/	SYM
ejpam-4972	68	8	eur	eur	PROPN
ejpam-4972	68	9	.	.	PUNCT
ejpam-4972	69	1	j.	j.	PROPN
ejpam-4972	69	2	pure	pure	PROPN
ejpam-4972	69	3	appl	appl	PROPN
ejpam-4972	69	4	.	.	PROPN
ejpam-4972	69	5	math	math	PROPN
ejpam-4972	69	6	,	,	PUNCT
ejpam-4972	69	7	16	16	NUM
ejpam-4972	69	8	(	(	PUNCT
ejpam-4972	69	9	4	4	NUM
ejpam-4972	69	10	)	)	PUNCT
ejpam-4972	69	11	(	(	PUNCT
ejpam-4972	69	12	2023	2023	NUM
ejpam-4972	69	13	)	)	PUNCT
ejpam-4972	69	14	,	,	PUNCT
ejpam-4972	69	15	2613	2613	NUM
ejpam-4972	69	16	-	-	SYM
ejpam-4972	69	17	2631	2631	NUM
ejpam-4972	69	18	2616	2616	NUM
ejpam-4972	69	19	3	3	NUM
ejpam-4972	69	20	.	.	PUNCT
ejpam-4972	69	21	types	type	NOUN
ejpam-4972	69	22	of	of	ADP
ejpam-4972	69	23	fuzzy	fuzzy	ADJ
ejpam-4972	69	24	generalized	generalize	VERB
ejpam-4972	69	25	continuous	continuous	ADJ
ejpam-4972	69	26	mappings	mapping	NOUN
ejpam-4972	69	27	we	we	PRON
ejpam-4972	69	28	define	define	VERB
ejpam-4972	69	29	and	and	CCONJ
ejpam-4972	69	30	investigate	investigate	VERB
ejpam-4972	69	31	some	some	DET
ejpam-4972	69	32	concepts	concept	NOUN
ejpam-4972	69	33	of	of	ADP
ejpam-4972	69	34	fuzzy	fuzzy	ADJ
ejpam-4972	69	35	generalized	generalize	VERB
ejpam-4972	69	36	continuous	continuous	ADJ
ejpam-4972	69	37	mapping	mapping	NOUN
ejpam-4972	69	38	which	which	PRON
ejpam-4972	69	39	includes	include	VERB
ejpam-4972	69	40	fuzzy	fuzzy	ADJ
ejpam-4972	69	41	(	(	PUNCT
ejpam-4972	69	42	i	i	NOUN
ejpam-4972	69	43	,	,	PUNCT
ejpam-4972	69	44	j)−gα−conts	j)−gα−conts	PROPN
ejpam-4972	69	45	,	,	PUNCT
ejpam-4972	69	46	(	(	PUNCT
ejpam-4972	69	47	i	i	PROPN
ejpam-4972	69	48	,	,	PUNCT
ejpam-4972	69	49	j)−gs−conts	j)−gs−conts	PROPN
ejpam-4972	69	50	,	,	PUNCT
ejpam-4972	69	51	(	(	PUNCT
ejpam-4972	69	52	i	i	PROPN
ejpam-4972	69	53	,	,	PUNCT
ejpam-4972	69	54	j)−gp−conts	j)−gp−conts	PROPN
ejpam-4972	69	55	,	,	PUNCT
ejpam-4972	69	56	(	(	PUNCT
ejpam-4972	69	57	i	i	PROPN
ejpam-4972	69	58	,	,	PUNCT
ejpam-4972	69	59	j)−gβ−conts	j)−gβ−conts	PROPN
ejpam-4972	69	60	,	,	PUNCT
ejpam-4972	69	61	and	and	CCONJ
ejpam-4972	69	62	we	we	PRON
ejpam-4972	69	63	denote	denote	VERB
ejpam-4972	69	64	for	for	ADP
ejpam-4972	69	65	them	they	PRON
ejpam-4972	69	66	by	by	ADP
ejpam-4972	69	67	(	(	PUNCT
ejpam-4972	69	68	i	i	NOUN
ejpam-4972	69	69	,	,	PUNCT
ejpam-4972	69	70	j)−	j)−	PROPN
ejpam-4972	69	71	gψ−conts	gψ−cont	NOUN
ejpam-4972	69	72	.	.	PUNCT
ejpam-4972	70	1	definition	definition	NOUN
ejpam-4972	70	2	8	8	NUM
ejpam-4972	70	3	.	.	PUNCT
ejpam-4972	71	1	any	any	DET
ejpam-4972	71	2	subgroup	subgroup	NOUN
ejpam-4972	71	3	k	k	PROPN
ejpam-4972	71	4	of	of	ADP
ejpam-4972	71	5	fbts	fbt	NOUN
ejpam-4972	71	6	(	(	PUNCT
ejpam-4972	71	7	x	x	NOUN
ejpam-4972	71	8	,	,	PUNCT
ejpam-4972	71	9	δ1	δ1	NOUN
ejpam-4972	71	10	,	,	PUNCT
ejpam-4972	71	11	δ2	δ2	PROPN
ejpam-4972	71	12	)	)	PUNCT
ejpam-4972	71	13	is	be	AUX
ejpam-4972	71	14	named	name	VERB
ejpam-4972	71	15	as	as	ADP
ejpam-4972	71	16	:	:	PUNCT
ejpam-4972	71	17	(	(	PUNCT
ejpam-4972	71	18	1	1	X
ejpam-4972	71	19	)	)	PUNCT
ejpam-4972	71	20	(	(	PUNCT
ejpam-4972	71	21	i	i	NOUN
ejpam-4972	71	22	,	,	PUNCT
ejpam-4972	71	23	j)−generalized	j)−generalized	PROPN
ejpam-4972	71	24	ψ−closed	ψ−close	VERB
ejpam-4972	71	25	(	(	PUNCT
ejpam-4972	71	26	simply	simply	ADV
ejpam-4972	71	27	,	,	PUNCT
ejpam-4972	71	28	(	(	PUNCT
ejpam-4972	71	29	i	i	PRON
ejpam-4972	71	30	,	,	PUNCT
ejpam-4972	71	31	j)−gψ−	j)−gψ−	X
ejpam-4972	71	32	cld	cld	PROPN
ejpam-4972	71	33	)	)	PUNCT
ejpam-4972	71	34	when	when	SCONJ
ejpam-4972	71	35	δj−ψ−	δj−ψ−	NOUN
ejpam-4972	71	36	cl(k	cl(k	NOUN
ejpam-4972	71	37	)	)	PUNCT
ejpam-4972	71	38	≤w	≤w	NOUN
ejpam-4972	71	39	,	,	PUNCT
ejpam-4972	71	40	while	while	SCONJ
ejpam-4972	71	41	k	k	PROPN
ejpam-4972	71	42	≤	≤	PROPN
ejpam-4972	71	43	w	w	ADP
ejpam-4972	71	44	,	,	PUNCT
ejpam-4972	71	45	w	w	PROPN
ejpam-4972	71	46	∈	∈	PROPN
ejpam-4972	71	47	δi	δi	NOUN
ejpam-4972	71	48	,	,	PUNCT
ejpam-4972	71	49	as	as	ADP
ejpam-4972	71	50	ψ	ψ	PRON
ejpam-4972	71	51	containing	contain	VERB
ejpam-4972	71	52	the	the	DET
ejpam-4972	71	53	kinds	kind	NOUN
ejpam-4972	71	54	(	(	PUNCT
ejpam-4972	71	55	alpha	alpha	NOUN
ejpam-4972	71	56	(	(	PUNCT
ejpam-4972	71	57	α	α	NOUN
ejpam-4972	71	58	)	)	PUNCT
ejpam-4972	71	59	,	,	PUNCT
ejpam-4972	71	60	semi	semi	ADV
ejpam-4972	71	61	(	(	PUNCT
ejpam-4972	71	62	s	s	NOUN
ejpam-4972	71	63	)	)	PUNCT
ejpam-4972	71	64	,	,	PUNCT
ejpam-4972	71	65	pre	pre	X
ejpam-4972	71	66	(	(	PUNCT
ejpam-4972	71	67	p	p	NOUN
ejpam-4972	71	68	)	)	PUNCT
ejpam-4972	71	69	,	,	PUNCT
ejpam-4972	71	70	and	and	CCONJ
ejpam-4972	71	71	beta	beta	NOUN
ejpam-4972	71	72	(	(	PUNCT
ejpam-4972	71	73	β	β	NOUN
ejpam-4972	71	74	)	)	PUNCT
ejpam-4972	71	75	)	)	PUNCT
ejpam-4972	71	76	.	.	PUNCT
ejpam-4972	72	1	(	(	PUNCT
ejpam-4972	72	2	2	2	X
ejpam-4972	72	3	)	)	PUNCT
ejpam-4972	72	4	(	(	PUNCT
ejpam-4972	72	5	i	i	PROPN
ejpam-4972	72	6	,	,	PUNCT
ejpam-4972	72	7	j)−	j)−	PROPN
ejpam-4972	72	8	gψ	gψ	VERB
ejpam-4972	72	9	−	−	PROPN
ejpam-4972	72	10	open	open	ADJ
ejpam-4972	72	11	is	be	AUX
ejpam-4972	72	12	the	the	DET
ejpam-4972	72	13	complement	complement	NOUN
ejpam-4972	72	14	of	of	ADP
ejpam-4972	72	15	the	the	DET
ejpam-4972	72	16	group	group	NOUN
ejpam-4972	72	17	(	(	PUNCT
ejpam-4972	72	18	i	i	PROPN
ejpam-4972	72	19	,	,	PUNCT
ejpam-4972	72	20	j)−	j)−	PROPN
ejpam-4972	72	21	gψ	gψ	VERB
ejpam-4972	72	22	−	−	PROPN
ejpam-4972	72	23	cld	cld	PROPN
ejpam-4972	72	24	.	.	PUNCT
ejpam-4972	72	25	remark	remark	PROPN
ejpam-4972	72	26	1	1	NUM
ejpam-4972	72	27	.	.	PUNCT
ejpam-4972	73	1	(	(	PUNCT
ejpam-4972	73	2	1	1	X
ejpam-4972	73	3	)	)	PUNCT
ejpam-4972	73	4	a	a	DET
ejpam-4972	73	5	class	class	NOUN
ejpam-4972	73	6	of	of	ADP
ejpam-4972	73	7	each	each	DET
ejpam-4972	73	8	fuzzy	fuzzy	ADJ
ejpam-4972	73	9	(	(	PUNCT
ejpam-4972	73	10	i	i	PROPN
ejpam-4972	73	11	,	,	PUNCT
ejpam-4972	73	12	j	j	PROPN
ejpam-4972	73	13	)	)	PUNCT
ejpam-4972	73	14	−	−	PROPN
ejpam-4972	73	15	gψ−open	gψ−open	NOUN
ejpam-4972	73	16	,	,	PUNCT
ejpam-4972	73	17	(	(	PUNCT
ejpam-4972	73	18	i	i	PROPN
ejpam-4972	73	19	,	,	PUNCT
ejpam-4972	73	20	j	j	PROPN
ejpam-4972	73	21	)	)	PUNCT
ejpam-4972	73	22	−	−	PROPN
ejpam-4972	73	23	gψ	gψ	VERB
ejpam-4972	73	24	−	−	PROPN
ejpam-4972	73	25	cld	cld	NOUN
ejpam-4972	73	26	of	of	ADP
ejpam-4972	73	27	(	(	PUNCT
ejpam-4972	73	28	x	x	NOUN
ejpam-4972	73	29	,	,	PUNCT
ejpam-4972	73	30	δ1	δ1	NOUN
ejpam-4972	73	31	,	,	PUNCT
ejpam-4972	73	32	δ2	δ2	PROPN
ejpam-4972	73	33	)	)	PUNCT
ejpam-4972	73	34	is	be	AUX
ejpam-4972	73	35	represented	represent	VERB
ejpam-4972	73	36	by	by	ADP
ejpam-4972	73	37	ofgψ	ofgψ	PROPN
ejpam-4972	73	38	(	(	PUNCT
ejpam-4972	73	39	i	i	PROPN
ejpam-4972	73	40	,	,	PUNCT
ejpam-4972	73	41	j	j	PROPN
ejpam-4972	73	42	)	)	PUNCT
ejpam-4972	73	43	,	,	PUNCT
ejpam-4972	74	1	f	f	PROPN
ejpam-4972	74	2	fgψ	fgψ	X
ejpam-4972	74	3	(	(	PUNCT
ejpam-4972	74	4	i	i	PROPN
ejpam-4972	74	5	,	,	PUNCT
ejpam-4972	74	6	j	j	PROPN
ejpam-4972	74	7	)	)	PUNCT
ejpam-4972	74	8	,	,	PUNCT
ejpam-4972	74	9	and	and	CCONJ
ejpam-4972	74	10	so	so	ADV
ejpam-4972	74	11	forth	forth	ADV
ejpam-4972	74	12	.	.	PUNCT
ejpam-4972	75	1	(	(	PUNCT
ejpam-4972	75	2	2	2	X
ejpam-4972	75	3	)	)	PUNCT
ejpam-4972	75	4	the	the	DET
ejpam-4972	75	5	class	class	NOUN
ejpam-4972	75	6	of	of	ADP
ejpam-4972	75	7	each	each	DET
ejpam-4972	75	8	gψ−open	gψ−open	NOUN
ejpam-4972	75	9	,	,	PUNCT
ejpam-4972	75	10	gψ	gψ	VERB
ejpam-4972	75	11	−	−	PROPN
ejpam-4972	75	12	cld	cld	PROPN
ejpam-4972	75	13	subgroups	subgroup	NOUN
ejpam-4972	75	14	of	of	ADP
ejpam-4972	75	15	x	x	PUNCT
ejpam-4972	75	16	in	in	ADP
ejpam-4972	75	17	relation	relation	NOUN
ejpam-4972	75	18	to	to	PART
ejpam-4972	75	19	δi	δi	VERB
ejpam-4972	75	20	represented	represent	VERB
ejpam-4972	75	21	by	by	ADP
ejpam-4972	75	22	ofgψ	ofgψ	PROPN
ejpam-4972	75	23	i	i	NOUN
ejpam-4972	75	24	,	,	PUNCT
ejpam-4972	75	25	and	and	CCONJ
ejpam-4972	76	1	ffgψ	ffgψ	NOUN
ejpam-4972	76	2	i	i	PRON
ejpam-4972	76	3	,	,	PUNCT
ejpam-4972	76	4	i	i	PRON
ejpam-4972	76	5	=	=	NOUN
ejpam-4972	76	6	1	1	NUM
ejpam-4972	76	7	,	,	PUNCT
ejpam-4972	76	8	2	2	NUM
ejpam-4972	76	9	.	.	X
ejpam-4972	77	1	in	in	ADP
ejpam-4972	77	2	the	the	DET
ejpam-4972	77	3	following	following	NOUN
ejpam-4972	77	4	,	,	PUNCT
ejpam-4972	77	5	we	we	PRON
ejpam-4972	77	6	introduce	introduce	VERB
ejpam-4972	77	7	the	the	DET
ejpam-4972	77	8	most	most	ADV
ejpam-4972	77	9	important	important	ADJ
ejpam-4972	77	10	definitions	definition	NOUN
ejpam-4972	77	11	and	and	CCONJ
ejpam-4972	77	12	theories	theory	NOUN
ejpam-4972	77	13	of	of	ADP
ejpam-4972	77	14	the	the	DET
ejpam-4972	77	15	concept	concept	NOUN
ejpam-4972	77	16	of	of	ADP
ejpam-4972	77	17	generalized	generalized	ADJ
ejpam-4972	77	18	continuous	continuous	ADJ
ejpam-4972	77	19	:	:	PUNCT
ejpam-4972	77	20	definition	definition	NOUN
ejpam-4972	77	21	9	9	NUM
ejpam-4972	77	22	.	.	PUNCT
ejpam-4972	78	1	a	a	DET
ejpam-4972	78	2	function	function	NOUN
ejpam-4972	78	3	t	t	NOUN
ejpam-4972	78	4	:	:	PUNCT
ejpam-4972	78	5	(	(	PUNCT
ejpam-4972	78	6	x	x	X
ejpam-4972	78	7	,	,	PUNCT
ejpam-4972	78	8	δ1	δ1	NOUN
ejpam-4972	78	9	,	,	PUNCT
ejpam-4972	78	10	δ2	δ2	ADJ
ejpam-4972	78	11	)	)	PUNCT
ejpam-4972	78	12	→	→	SYM
ejpam-4972	78	13	(	(	PUNCT
ejpam-4972	78	14	y	y	PROPN
ejpam-4972	78	15	,	,	PUNCT
ejpam-4972	78	16	σ1	σ1	PROPN
ejpam-4972	78	17	,	,	PUNCT
ejpam-4972	78	18	σ2	σ2	PROPN
ejpam-4972	78	19	)	)	PUNCT
ejpam-4972	78	20	is	be	AUX
ejpam-4972	78	21	named	name	VERB
ejpam-4972	78	22	fuzzy	fuzzy	ADJ
ejpam-4972	78	23	(	(	PUNCT
ejpam-4972	78	24	i	i	NOUN
ejpam-4972	78	25	,	,	PUNCT
ejpam-4972	78	26	j)−generalized	j)−generalize	VERB
ejpam-4972	78	27	ψ−	ψ−	VERB
ejpam-4972	78	28	continuous	continuous	ADJ
ejpam-4972	78	29	(	(	PUNCT
ejpam-4972	78	30	briefly	briefly	ADV
ejpam-4972	78	31	,	,	PUNCT
ejpam-4972	78	32	(	(	PUNCT
ejpam-4972	78	33	i	i	PROPN
ejpam-4972	78	34	,	,	PUNCT
ejpam-4972	78	35	j	j	PROPN
ejpam-4972	78	36	)	)	PUNCT
ejpam-4972	78	37	−	−	PROPN
ejpam-4972	78	38	gψ	gψ	VERB
ejpam-4972	78	39	−	−	PROPN
ejpam-4972	78	40	conts	cont	NOUN
ejpam-4972	78	41	)	)	PUNCT
ejpam-4972	78	42	when	when	SCONJ
ejpam-4972	78	43	the	the	DET
ejpam-4972	78	44	opposite	opposite	ADJ
ejpam-4972	78	45	image	image	NOUN
ejpam-4972	78	46	of	of	ADP
ejpam-4972	78	47	all	all	DET
ejpam-4972	78	48	fuzzy	fuzzy	ADJ
ejpam-4972	78	49	open	open	ADJ
ejpam-4972	78	50	group	group	NOUN
ejpam-4972	78	51	of	of	ADP
ejpam-4972	78	52	(	(	PUNCT
ejpam-4972	78	53	y	y	PROPN
ejpam-4972	78	54	,	,	PUNCT
ejpam-4972	78	55	σj	σj	VERB
ejpam-4972	78	56	)	)	PUNCT
ejpam-4972	78	57	is	be	AUX
ejpam-4972	78	58	fuzzy	fuzzy	ADJ
ejpam-4972	78	59	(	(	PUNCT
ejpam-4972	78	60	i	i	PROPN
ejpam-4972	78	61	,	,	PUNCT
ejpam-4972	78	62	j)−	j)−	PROPN
ejpam-4972	78	63	gψ	gψ	VERB
ejpam-4972	78	64	−	−	DET
ejpam-4972	78	65	open	open	ADJ
ejpam-4972	78	66	group	group	NOUN
ejpam-4972	78	67	of	of	ADP
ejpam-4972	78	68	(	(	PUNCT
ejpam-4972	78	69	x	x	NOUN
ejpam-4972	78	70	,	,	PUNCT
ejpam-4972	78	71	δ1	δ1	NOUN
ejpam-4972	78	72	,	,	PUNCT
ejpam-4972	78	73	δ2	δ2	PROPN
ejpam-4972	78	74	)	)	PUNCT
ejpam-4972	78	75	.	.	PUNCT
ejpam-4972	79	1	by	by	ADP
ejpam-4972	79	2	using	use	VERB
ejpam-4972	79	3	the	the	DET
ejpam-4972	79	4	complement	complement	NOUN
ejpam-4972	79	5	of	of	ADP
ejpam-4972	79	6	the	the	DET
ejpam-4972	79	7	above	above	ADJ
ejpam-4972	79	8	definition	definition	NOUN
ejpam-4972	79	9	we	we	PRON
ejpam-4972	79	10	get	get	VERB
ejpam-4972	79	11	the	the	DET
ejpam-4972	79	12	coming	come	VERB
ejpam-4972	79	13	remark	remark	NOUN
ejpam-4972	79	14	:	:	PUNCT
ejpam-4972	79	15	remark	remark	NOUN
ejpam-4972	79	16	2	2	NUM
ejpam-4972	79	17	.	.	PUNCT
ejpam-4972	80	1	(	(	PUNCT
ejpam-4972	80	2	i	i	NOUN
ejpam-4972	80	3	)	)	PUNCT
ejpam-4972	80	4	suppose	suppose	VERB
ejpam-4972	80	5	t	t	NOUN
ejpam-4972	80	6	:	:	PUNCT
ejpam-4972	80	7	(	(	PUNCT
ejpam-4972	80	8	x	x	X
ejpam-4972	80	9	,	,	PUNCT
ejpam-4972	80	10	δ1	δ1	NOUN
ejpam-4972	80	11	,	,	PUNCT
ejpam-4972	80	12	δ2	δ2	ADJ
ejpam-4972	80	13	)	)	PUNCT
ejpam-4972	80	14	→	→	SYM
ejpam-4972	80	15	(	(	PUNCT
ejpam-4972	80	16	y	y	PROPN
ejpam-4972	80	17	,	,	PUNCT
ejpam-4972	80	18	σ1	σ1	PROPN
ejpam-4972	80	19	,	,	PUNCT
ejpam-4972	80	20	σ2	σ2	NOUN
ejpam-4972	80	21	)	)	PUNCT
ejpam-4972	80	22	.	.	PUNCT
ejpam-4972	81	1	hence	hence	ADV
ejpam-4972	81	2	t	t	PROPN
ejpam-4972	81	3	is	be	AUX
ejpam-4972	81	4	fuzzy	fuzzy	ADJ
ejpam-4972	81	5	(	(	PUNCT
ejpam-4972	81	6	i	i	NOUN
ejpam-4972	81	7	,	,	PUNCT
ejpam-4972	81	8	j)−	j)−	PROPN
ejpam-4972	81	9	gψ−	gψ−	PUNCT
ejpam-4972	81	10	conts	conts	PROPN
ejpam-4972	81	11	iff	iff	PROPN
ejpam-4972	81	12	∀	∀	X
ejpam-4972	81	13	fuzzy	fuzzy	ADJ
ejpam-4972	81	14	closed	close	VERB
ejpam-4972	81	15	group	group	NOUN
ejpam-4972	81	16	v	v	NOUN
ejpam-4972	81	17	of	of	ADP
ejpam-4972	81	18	(	(	PUNCT
ejpam-4972	81	19	y	y	PROPN
ejpam-4972	81	20	,	,	PUNCT
ejpam-4972	81	21	σj	σj	NOUN
ejpam-4972	81	22	)	)	PUNCT
ejpam-4972	81	23	,	,	PUNCT
ejpam-4972	81	24	t	t	PROPN
ejpam-4972	81	25	−1(v	−1(v	PROPN
ejpam-4972	81	26	)	)	PUNCT
ejpam-4972	81	27	is	be	AUX
ejpam-4972	81	28	fuzzy	fuzzy	ADJ
ejpam-4972	81	29	(	(	PUNCT
ejpam-4972	81	30	i	i	PROPN
ejpam-4972	81	31	,	,	PUNCT
ejpam-4972	81	32	j)−	j)−	PROPN
ejpam-4972	81	33	gψ	gψ	VERB
ejpam-4972	81	34	−	−	PROPN
ejpam-4972	81	35	cld	cld	PROPN
ejpam-4972	81	36	group	group	NOUN
ejpam-4972	81	37	of	of	ADP
ejpam-4972	81	38	x.	x.	PROPN
ejpam-4972	81	39	(	(	PUNCT
ejpam-4972	81	40	ii	ii	PROPN
ejpam-4972	81	41	)	)	PUNCT
ejpam-4972	81	42	by	by	ADP
ejpam-4972	81	43	setting	set	VERB
ejpam-4972	81	44	δi	δi	ADP
ejpam-4972	81	45	=	=	SYM
ejpam-4972	81	46	δj	δj	NOUN
ejpam-4972	81	47	,	,	PUNCT
ejpam-4972	81	48	σi	σi	NOUN
ejpam-4972	81	49	=	=	PUNCT
ejpam-4972	81	50	σj	σj	VERB
ejpam-4972	81	51	in	in	ADP
ejpam-4972	81	52	definition	definition	NOUN
ejpam-4972	81	53	9	9	NUM
ejpam-4972	81	54	,	,	PUNCT
ejpam-4972	81	55	we	we	PRON
ejpam-4972	81	56	find	find	VERB
ejpam-4972	81	57	any	any	DET
ejpam-4972	81	58	fuzzy	fuzzy	ADJ
ejpam-4972	81	59	(	(	PUNCT
ejpam-4972	81	60	i	i	PROPN
ejpam-4972	81	61	,	,	PUNCT
ejpam-4972	81	62	j	j	PROPN
ejpam-4972	81	63	)	)	PUNCT
ejpam-4972	81	64	−	−	PROPN
ejpam-4972	81	65	gψ	gψ	ADV
ejpam-4972	82	1	−	−	PROPN
ejpam-4972	82	2	conts	cont	NOUN
ejpam-4972	82	3	is	be	AUX
ejpam-4972	82	4	fuzzy	fuzzy	ADJ
ejpam-4972	82	5	gψ	gψ	ADP
ejpam-4972	82	6	−	−	PROPN
ejpam-4972	82	7	conts	cont	NOUN
ejpam-4972	82	8	.	.	PUNCT
ejpam-4972	83	1	theorem	theorem	NOUN
ejpam-4972	83	2	1	1	NUM
ejpam-4972	83	3	.	.	PUNCT
ejpam-4972	84	1	suppose	suppose	VERB
ejpam-4972	84	2	t	t	NOUN
ejpam-4972	84	3	:	:	PUNCT
ejpam-4972	84	4	(	(	PUNCT
ejpam-4972	84	5	x	x	X
ejpam-4972	84	6	,	,	PUNCT
ejpam-4972	84	7	δ1	δ1	NOUN
ejpam-4972	84	8	,	,	PUNCT
ejpam-4972	84	9	δ2	δ2	ADJ
ejpam-4972	84	10	)	)	PUNCT
ejpam-4972	84	11	→	→	SYM
ejpam-4972	84	12	(	(	PUNCT
ejpam-4972	84	13	y	y	PROPN
ejpam-4972	84	14	,	,	PUNCT
ejpam-4972	84	15	σ1	σ1	PROPN
ejpam-4972	84	16	,	,	PUNCT
ejpam-4972	84	17	σ2	σ2	NOUN
ejpam-4972	84	18	)	)	PUNCT
ejpam-4972	84	19	is	be	AUX
ejpam-4972	84	20	fuzzy	fuzzy	ADJ
ejpam-4972	84	21	(	(	PUNCT
ejpam-4972	84	22	i	i	PROPN
ejpam-4972	84	23	,	,	PUNCT
ejpam-4972	84	24	j	j	PROPN
ejpam-4972	84	25	)	)	PUNCT
ejpam-4972	84	26	−	−	PROPN
ejpam-4972	84	27	gψ	gψ	VERB
ejpam-4972	84	28	−	−	PROPN
ejpam-4972	84	29	conts	cont	NOUN
ejpam-4972	84	30	.	.	PUNCT
ejpam-4972	85	1	then	then	ADV
ejpam-4972	85	2	any	any	DET
ejpam-4972	85	3	fuzzy	fuzzy	ADJ
ejpam-4972	85	4	point	point	NOUN
ejpam-4972	85	5	xr	xr	PROPN
ejpam-4972	85	6	in	in	ADP
ejpam-4972	85	7	x	x	PUNCT
ejpam-4972	85	8	with	with	ADP
ejpam-4972	85	9	σj	σj	ADJ
ejpam-4972	85	10	−q−	−q−	PROPN
ejpam-4972	85	11	nbd	nbd	PROPN
ejpam-4972	85	12	h	h	PROPN
ejpam-4972	85	13	of	of	ADP
ejpam-4972	85	14	t(xr	t(xr	ADV
ejpam-4972	85	15	)	)	PUNCT
ejpam-4972	85	16	,	,	PUNCT
ejpam-4972	85	17	∃	∃	PROPN
ejpam-4972	85	18	fuzzy	fuzzy	ADJ
ejpam-4972	85	19	(	(	PUNCT
ejpam-4972	85	20	i	i	PROPN
ejpam-4972	85	21	,	,	PUNCT
ejpam-4972	85	22	j)−	j)−	PROPN
ejpam-4972	85	23	gψ	gψ	VERB
ejpam-4972	85	24	−q−	−q−	NOUN
ejpam-4972	85	25	nbd	nbd	PROPN
ejpam-4972	85	26	r	r	PROPN
ejpam-4972	85	27	of	of	ADP
ejpam-4972	85	28	xr	xr	PROPN
ejpam-4972	85	29	as	as	ADP
ejpam-4972	85	30	t(r	t(r	PROPN
ejpam-4972	85	31	)	)	PUNCT
ejpam-4972	85	32	≤	≤	NOUN
ejpam-4972	85	33	h.	h.	NOUN
ejpam-4972	85	34	proof	proof	NOUN
ejpam-4972	85	35	.	.	PUNCT
ejpam-4972	86	1	let	let	VERB
ejpam-4972	86	2	xr	xr	PROPN
ejpam-4972	86	3	∈	∈	PROPN
ejpam-4972	86	4	ix	ix	X
ejpam-4972	87	1	and	and	CCONJ
ejpam-4972	87	2	h	h	PROPN
ejpam-4972	87	3	∈	∈	PROPN
ejpam-4972	87	4	nq	nq	PROPN
ejpam-4972	87	5	j	j	PROPN
ejpam-4972	87	6	(	(	PUNCT
ejpam-4972	87	7	t(xr	t(xr	ADV
ejpam-4972	87	8	)	)	PUNCT
ejpam-4972	87	9	)	)	PUNCT
ejpam-4972	87	10	.	.	PUNCT
ejpam-4972	88	1	then	then	ADV
ejpam-4972	88	2	∃	∃	PROPN
ejpam-4972	88	3	w	w	PROPN
ejpam-4972	88	4	∈	∈	PROPN
ejpam-4972	88	5	σj	σj	VERB
ejpam-4972	88	6	as	as	ADP
ejpam-4972	88	7	t(xr	t(xr	ADV
ejpam-4972	88	8	)	)	PUNCT
ejpam-4972	88	9	qw	qw	CCONJ
ejpam-4972	88	10	≤	≤	NUM
ejpam-4972	88	11	h	h	NOUN
ejpam-4972	88	12	,	,	PUNCT
ejpam-4972	88	13	and	and	CCONJ
ejpam-4972	88	14	hence	hence	ADV
ejpam-4972	88	15	t−1(w	t−1(w	NOUN
ejpam-4972	88	16	)	)	PUNCT
ejpam-4972	88	17	is	be	AUX
ejpam-4972	88	18	fuzzy	fuzzy	ADJ
ejpam-4972	88	19	(	(	PUNCT
ejpam-4972	88	20	i	i	PROPN
ejpam-4972	88	21	,	,	PUNCT
ejpam-4972	88	22	j	j	PROPN
ejpam-4972	88	23	)	)	PUNCT
ejpam-4972	88	24	−	−	PROPN
ejpam-4972	88	25	gψ	gψ	VERB
ejpam-4972	88	26	−	−	ADV
ejpam-4972	88	27	open	open	ADJ
ejpam-4972	88	28	in	in	ADP
ejpam-4972	88	29	x	x	PUNCT
ejpam-4972	88	30	with	with	ADP
ejpam-4972	88	31	xr	xr	PROPN
ejpam-4972	88	32	q	q	PROPN
ejpam-4972	88	33	t	t	PROPN
ejpam-4972	88	34	−1(w	−1(w	ADV
ejpam-4972	88	35	)	)	PUNCT
ejpam-4972	88	36	≤	≤	NUM
ejpam-4972	88	37	t−1(h	t−1(h	NOUN
ejpam-4972	88	38	)	)	PUNCT
ejpam-4972	88	39	.	.	PUNCT
ejpam-4972	89	1	if	if	SCONJ
ejpam-4972	89	2	we	we	PRON
ejpam-4972	89	3	take	take	VERB
ejpam-4972	89	4	t−1(w	t−1(w	NOUN
ejpam-4972	89	5	)	)	PUNCT
ejpam-4972	90	1	=	=	SYM
ejpam-4972	90	2	r	r	NOUN
ejpam-4972	90	3	,	,	PUNCT
ejpam-4972	90	4	then	then	ADV
ejpam-4972	90	5	∃r	∃r	PROPN
ejpam-4972	90	6	∈	∈	PROPN
ejpam-4972	90	7	ngψq	ngψq	ADV
ejpam-4972	91	1	(	(	PUNCT
ejpam-4972	91	2	i	i	PROPN
ejpam-4972	91	3	,	,	PUNCT
ejpam-4972	91	4	j	j	PROPN
ejpam-4972	91	5	)	)	PUNCT
ejpam-4972	91	6	(	(	PUNCT
ejpam-4972	91	7	xr	xr	X
ejpam-4972	91	8	)	)	PUNCT
ejpam-4972	91	9	,	,	PUNCT
ejpam-4972	91	10	as	as	ADP
ejpam-4972	91	11	r	r	NOUN
ejpam-4972	91	12	≤	≤	NUM
ejpam-4972	91	13	t−1(h	t−1(h	NOUN
ejpam-4972	91	14	)	)	PUNCT
ejpam-4972	91	15	.	.	PUNCT
ejpam-4972	92	1	so	so	ADV
ejpam-4972	92	2	t(r	t(r	NOUN
ejpam-4972	92	3	)	)	PUNCT
ejpam-4972	92	4	≤	≤	NOUN
ejpam-4972	92	5	h.	h.	NOUN
ejpam-4972	92	6	by	by	ADP
ejpam-4972	92	7	using	use	VERB
ejpam-4972	92	8	the	the	DET
ejpam-4972	92	9	relations	relation	NOUN
ejpam-4972	92	10	via	via	ADP
ejpam-4972	92	11	ngψ	ngψ	NOUN
ejpam-4972	92	12	(	(	PUNCT
ejpam-4972	92	13	i	i	PROPN
ejpam-4972	92	14	,	,	PUNCT
ejpam-4972	92	15	j	j	PROPN
ejpam-4972	92	16	)	)	PUNCT
ejpam-4972	92	17	,	,	PUNCT
ejpam-4972	92	18	n	n	X
ejpam-4972	92	19	gψq	gψq	X
ejpam-4972	92	20	(	(	PUNCT
ejpam-4972	92	21	i	i	PROPN
ejpam-4972	92	22	,	,	PUNCT
ejpam-4972	92	23	j	j	PROPN
ejpam-4972	92	24	)	)	PUNCT
ejpam-4972	92	25	in	in	ADP
ejpam-4972	92	26	[	[	X
ejpam-4972	92	27	3	3	NUM
ejpam-4972	92	28	]	]	PUNCT
ejpam-4972	92	29	,	,	PUNCT
ejpam-4972	92	30	and	and	CCONJ
ejpam-4972	92	31	the	the	DET
ejpam-4972	92	32	above	above	ADJ
ejpam-4972	92	33	theorem	theorem	NOUN
ejpam-4972	92	34	we	we	PRON
ejpam-4972	92	35	get	get	VERB
ejpam-4972	92	36	the	the	DET
ejpam-4972	92	37	next	next	ADJ
ejpam-4972	92	38	corollary	corollary	NOUN
ejpam-4972	92	39	:	:	PUNCT
ejpam-4972	92	40	corollary	corollary	ADJ
ejpam-4972	92	41	1	1	PROPN
ejpam-4972	92	42	.	.	PUNCT
ejpam-4972	92	43	suppose	suppose	VERB
ejpam-4972	92	44	t	t	NOUN
ejpam-4972	92	45	:	:	PUNCT
ejpam-4972	92	46	(	(	PUNCT
ejpam-4972	92	47	x	x	X
ejpam-4972	92	48	,	,	PUNCT
ejpam-4972	92	49	δ1	δ1	NOUN
ejpam-4972	92	50	,	,	PUNCT
ejpam-4972	92	51	δ2	δ2	ADJ
ejpam-4972	92	52	)	)	PUNCT
ejpam-4972	92	53	→	→	SYM
ejpam-4972	92	54	(	(	PUNCT
ejpam-4972	92	55	y	y	PROPN
ejpam-4972	92	56	,	,	PUNCT
ejpam-4972	92	57	σ1	σ1	PROPN
ejpam-4972	92	58	,	,	PUNCT
ejpam-4972	92	59	σ2	σ2	PROPN
ejpam-4972	92	60	)	)	PUNCT
ejpam-4972	92	61	be	be	VERB
ejpam-4972	92	62	fuzzy	fuzzy	ADJ
ejpam-4972	92	63	(	(	PUNCT
ejpam-4972	92	64	i	i	PROPN
ejpam-4972	92	65	,	,	PUNCT
ejpam-4972	92	66	j)−	j)−	PROPN
ejpam-4972	92	67	gψ	gψ	VERB
ejpam-4972	92	68	−	−	PROPN
ejpam-4972	92	69	conts	cont	NOUN
ejpam-4972	92	70	.	.	PUNCT
ejpam-4972	93	1	then	then	ADV
ejpam-4972	93	2	∀	∀	PUNCT
ejpam-4972	93	3	xr	xr	PROPN
ejpam-4972	93	4	∈	∈	PROPN
ejpam-4972	93	5	ix	ix	X
ejpam-4972	93	6	and	and	CCONJ
ejpam-4972	93	7	∀	∀	NUM
ejpam-4972	93	8	h	h	NOUN
ejpam-4972	93	9	∈	∈	PROPN
ejpam-4972	93	10	nj(t(xr	nj(t(xr	PROPN
ejpam-4972	93	11	)	)	PUNCT
ejpam-4972	93	12	)	)	PUNCT
ejpam-4972	93	13	,	,	PUNCT
ejpam-4972	93	14	∃	∃	PROPN
ejpam-4972	93	15	r	r	NOUN
ejpam-4972	93	16	∈	∈	PROPN
ejpam-4972	93	17	ngψ	ngψ	NOUN
ejpam-4972	93	18	(	(	PUNCT
ejpam-4972	93	19	i	i	NOUN
ejpam-4972	93	20	,	,	PUNCT
ejpam-4972	93	21	j)(xr	j)(xr	PROPN
ejpam-4972	93	22	)	)	PUNCT
ejpam-4972	93	23	as	as	ADP
ejpam-4972	93	24	t(r	t(r	NOUN
ejpam-4972	93	25	)	)	PUNCT
ejpam-4972	93	26	≤	≤	NOUN
ejpam-4972	93	27	h.	h.	PROPN
ejpam-4972	93	28	a.	a.	NOUN
ejpam-4972	93	29	a.	a.	PROPN
ejpam-4972	93	30	alharbi	alharbi	PROPN
ejpam-4972	93	31	,	,	PUNCT
ejpam-4972	93	32	a.	a.	NOUN
ejpam-4972	93	33	kilicman	kilicman	PROPN
ejpam-4972	93	34	/	/	SYM
ejpam-4972	93	35	eur	eur	PROPN
ejpam-4972	93	36	.	.	PUNCT
ejpam-4972	94	1	j.	j.	PROPN
ejpam-4972	94	2	pure	pure	PROPN
ejpam-4972	94	3	appl	appl	PROPN
ejpam-4972	94	4	.	.	PROPN
ejpam-4972	94	5	math	math	PROPN
ejpam-4972	94	6	,	,	PUNCT
ejpam-4972	94	7	16	16	NUM
ejpam-4972	94	8	(	(	PUNCT
ejpam-4972	94	9	4	4	NUM
ejpam-4972	94	10	)	)	PUNCT
ejpam-4972	94	11	(	(	PUNCT
ejpam-4972	94	12	2023	2023	NUM
ejpam-4972	94	13	)	)	PUNCT
ejpam-4972	94	14	,	,	PUNCT
ejpam-4972	94	15	2613	2613	NUM
ejpam-4972	94	16	-	-	SYM
ejpam-4972	94	17	2631	2631	NUM
ejpam-4972	94	18	2617	2617	NUM
ejpam-4972	94	19	theorem	theorem	NOUN
ejpam-4972	94	20	2	2	NUM
ejpam-4972	94	21	.	.	PUNCT
ejpam-4972	94	22	suppose	suppose	VERB
ejpam-4972	94	23	t	t	NOUN
ejpam-4972	94	24	:	:	PUNCT
ejpam-4972	94	25	(	(	PUNCT
ejpam-4972	94	26	x	x	X
ejpam-4972	94	27	,	,	PUNCT
ejpam-4972	94	28	δ1	δ1	NOUN
ejpam-4972	94	29	,	,	PUNCT
ejpam-4972	94	30	δ2	δ2	ADJ
ejpam-4972	94	31	)	)	PUNCT
ejpam-4972	94	32	→	→	SYM
ejpam-4972	94	33	(	(	PUNCT
ejpam-4972	94	34	y	y	PROPN
ejpam-4972	94	35	,	,	PUNCT
ejpam-4972	94	36	σ1	σ1	PROPN
ejpam-4972	94	37	,	,	PUNCT
ejpam-4972	94	38	σ2	σ2	NOUN
ejpam-4972	94	39	)	)	PUNCT
ejpam-4972	94	40	.	.	PUNCT
ejpam-4972	95	1	then	then	ADV
ejpam-4972	95	2	the	the	DET
ejpam-4972	95	3	coming	come	VERB
ejpam-4972	95	4	claims	claim	NOUN
ejpam-4972	95	5	are	be	AUX
ejpam-4972	95	6	hold	hold	ADJ
ejpam-4972	95	7	:	:	PUNCT
ejpam-4972	95	8	(	(	PUNCT
ejpam-4972	95	9	1	1	X
ejpam-4972	95	10	)	)	PUNCT
ejpam-4972	95	11	if	if	SCONJ
ejpam-4972	95	12	t	t	PROPN
ejpam-4972	95	13	is	be	AUX
ejpam-4972	95	14	fuzzy	fuzzy	ADJ
ejpam-4972	95	15	(	(	PUNCT
ejpam-4972	95	16	i	i	NOUN
ejpam-4972	95	17	,	,	PUNCT
ejpam-4972	95	18	j)−	j)−	PROPN
ejpam-4972	95	19	g	g	PROPN
ejpam-4972	95	20	−	−	PROPN
ejpam-4972	95	21	conts	cont	NOUN
ejpam-4972	95	22	,	,	PUNCT
ejpam-4972	95	23	hence	hence	ADV
ejpam-4972	95	24	it	it	PRON
ejpam-4972	95	25	is	be	AUX
ejpam-4972	95	26	(	(	PUNCT
ejpam-4972	95	27	i	i	PROPN
ejpam-4972	95	28	,	,	PUNCT
ejpam-4972	95	29	j)−	j)−	PROPN
ejpam-4972	95	30	gα−	gα−	PROPN
ejpam-4972	95	31	conts	cont	NOUN
ejpam-4972	95	32	(	(	PUNCT
ejpam-4972	95	33	2	2	X
ejpam-4972	95	34	)	)	PUNCT
ejpam-4972	95	35	if	if	SCONJ
ejpam-4972	95	36	t	t	PROPN
ejpam-4972	95	37	is	be	AUX
ejpam-4972	95	38	fuzzy	fuzzy	ADJ
ejpam-4972	95	39	(	(	PUNCT
ejpam-4972	95	40	i	i	NOUN
ejpam-4972	95	41	,	,	PUNCT
ejpam-4972	95	42	j)−	j)−	PROPN
ejpam-4972	95	43	gα−	gα−	PUNCT
ejpam-4972	95	44	conts	cont	NOUN
ejpam-4972	95	45	,	,	PUNCT
ejpam-4972	95	46	hence	hence	ADV
ejpam-4972	95	47	it	it	PRON
ejpam-4972	95	48	is	be	AUX
ejpam-4972	95	49	(	(	PUNCT
ejpam-4972	95	50	i	i	PROPN
ejpam-4972	95	51	,	,	PUNCT
ejpam-4972	95	52	j)−	j)−	PROPN
ejpam-4972	95	53	gp−	gp−	PROPN
ejpam-4972	95	54	conts	cont	NOUN
ejpam-4972	95	55	also	also	ADV
ejpam-4972	95	56	(	(	PUNCT
ejpam-4972	95	57	i	i	PROPN
ejpam-4972	95	58	,	,	PUNCT
ejpam-4972	95	59	j)−	j)−	PROPN
ejpam-4972	95	60	gs−	gs−	PROPN
ejpam-4972	95	61	conts	cont	NOUN
ejpam-4972	95	62	.	.	PUNCT
ejpam-4972	96	1	(	(	PUNCT
ejpam-4972	96	2	3	3	X
ejpam-4972	96	3	)	)	PUNCT
ejpam-4972	96	4	if	if	SCONJ
ejpam-4972	96	5	t	t	PROPN
ejpam-4972	96	6	is	be	AUX
ejpam-4972	96	7	fuzzy	fuzzy	ADJ
ejpam-4972	96	8	(	(	PUNCT
ejpam-4972	96	9	i	i	NOUN
ejpam-4972	96	10	,	,	PUNCT
ejpam-4972	96	11	j)−	j)−	PROPN
ejpam-4972	96	12	gp−	gp−	PROPN
ejpam-4972	96	13	conts	cont	NOUN
ejpam-4972	96	14	or	or	CCONJ
ejpam-4972	96	15	(	(	PUNCT
ejpam-4972	96	16	i	i	PROPN
ejpam-4972	96	17	,	,	PUNCT
ejpam-4972	96	18	j)−	j)−	PROPN
ejpam-4972	96	19	gs−	gs−	NUM
ejpam-4972	96	20	conts	cont	NOUN
ejpam-4972	96	21	,	,	PUNCT
ejpam-4972	96	22	hence	hence	ADV
ejpam-4972	96	23	it	it	PRON
ejpam-4972	96	24	is	be	AUX
ejpam-4972	96	25	(	(	PUNCT
ejpam-4972	96	26	i	i	PROPN
ejpam-4972	96	27	,	,	PUNCT
ejpam-4972	96	28	j)−	j)−	PROPN
ejpam-4972	96	29	gβ	gβ	PROPN
ejpam-4972	96	30	−	−	PROPN
ejpam-4972	96	31	conts	cont	NOUN
ejpam-4972	96	32	.	.	PUNCT
ejpam-4972	97	1	proof	proof	NOUN
ejpam-4972	97	2	.	.	PUNCT
ejpam-4972	98	1	it	it	PRON
ejpam-4972	98	2	is	be	AUX
ejpam-4972	98	3	clear	clear	ADJ
ejpam-4972	98	4	from	from	ADP
ejpam-4972	98	5	definition	definition	NOUN
ejpam-4972	98	6	9	9	NUM
ejpam-4972	98	7	,	,	PUNCT
ejpam-4972	98	8	relationships	relationship	NOUN
ejpam-4972	98	9	via	via	ADP
ejpam-4972	98	10	each	each	DET
ejpam-4972	98	11	kinds	kind	NOUN
ejpam-4972	98	12	of	of	ADP
ejpam-4972	98	13	fuzzy	fuzzy	ADJ
ejpam-4972	98	14	(	(	PUNCT
ejpam-4972	98	15	i	i	PROPN
ejpam-4972	98	16	,	,	PUNCT
ejpam-4972	98	17	j	j	PROPN
ejpam-4972	98	18	)	)	PUNCT
ejpam-4972	98	19	generalized	generalize	VERB
ejpam-4972	98	20	neigborhoods	neigborhood	NOUN
ejpam-4972	98	21	in	in	ADP
ejpam-4972	98	22	the	the	DET
ejpam-4972	98	23	refrence	refrence	NOUN
ejpam-4972	98	24	[	[	X
ejpam-4972	98	25	3	3	NUM
ejpam-4972	98	26	]	]	PUNCT
ejpam-4972	98	27	.	.	PUNCT
ejpam-4972	99	1	remark	remark	PROPN
ejpam-4972	99	2	3	3	NUM
ejpam-4972	99	3	.	.	PUNCT
ejpam-4972	100	1	the	the	DET
ejpam-4972	100	2	following	follow	VERB
ejpam-4972	100	3	diagram	diagram	NOUN
ejpam-4972	100	4	explain	explain	VERB
ejpam-4972	100	5	the	the	DET
ejpam-4972	100	6	relation	relation	NOUN
ejpam-4972	100	7	between	between	ADP
ejpam-4972	100	8	statements	statement	NOUN
ejpam-4972	100	9	in	in	ADP
ejpam-4972	100	10	the	the	DET
ejpam-4972	100	11	above	above	ADJ
ejpam-4972	100	12	theorem	theorem	NOUN
ejpam-4972	100	13	.	.	PROPN
ejpam-4972	100	14	figure	figure	NOUN
ejpam-4972	100	15	1	1	NUM
ejpam-4972	100	16	:	:	PUNCT
ejpam-4972	100	17	presents	present	VERB
ejpam-4972	100	18	the	the	DET
ejpam-4972	100	19	relationships	relationship	NOUN
ejpam-4972	100	20	via	via	ADP
ejpam-4972	100	21	all	all	DET
ejpam-4972	100	22	varieties	variety	NOUN
ejpam-4972	100	23	of	of	ADP
ejpam-4972	100	24	fuzzy	fuzzy	ADJ
ejpam-4972	100	25	(	(	PUNCT
ejpam-4972	100	26	i	i	PROPN
ejpam-4972	100	27	,	,	PUNCT
ejpam-4972	100	28	j)−	j)−	PROPN
ejpam-4972	100	29	gψ	gψ	VERB
ejpam-4972	100	30	−	−	PROPN
ejpam-4972	100	31	conts	cont	NOUN
ejpam-4972	100	32	.	.	PUNCT
ejpam-4972	101	1	the	the	DET
ejpam-4972	101	2	examples	example	NOUN
ejpam-4972	101	3	below	below	ADP
ejpam-4972	101	4	demonstrate	demonstrate	VERB
ejpam-4972	101	5	that	that	SCONJ
ejpam-4972	101	6	the	the	DET
ejpam-4972	101	7	reverse	reverse	ADJ
ejpam-4972	101	8	implications	implication	NOUN
ejpam-4972	101	9	of	of	ADP
ejpam-4972	101	10	figure	figure	NOUN
ejpam-4972	101	11	(	(	PUNCT
ejpam-4972	101	12	1	1	NUM
ejpam-4972	101	13	)	)	PUNCT
ejpam-4972	101	14	are	be	AUX
ejpam-4972	101	15	generally	generally	ADV
ejpam-4972	101	16	not	not	PART
ejpam-4972	101	17	true	true	ADJ
ejpam-4972	101	18	:	:	PUNCT
ejpam-4972	101	19	example	example	NOUN
ejpam-4972	101	20	1	1	X
ejpam-4972	101	21	.	.	PUNCT
ejpam-4972	101	22	suppose	suppose	VERB
ejpam-4972	101	23	e	e	NOUN
ejpam-4972	101	24	,	,	PUNCT
ejpam-4972	101	25	f	f	PROPN
ejpam-4972	101	26	,	,	PUNCT
ejpam-4972	101	27	and	and	CCONJ
ejpam-4972	101	28	g	g	NOUN
ejpam-4972	101	29	are	be	AUX
ejpam-4972	101	30	fuzzy	fuzzy	ADJ
ejpam-4972	101	31	subgroups	subgroup	NOUN
ejpam-4972	101	32	of	of	ADP
ejpam-4972	101	33	x	x	SYM
ejpam-4972	101	34	=	=	X
ejpam-4972	101	35	{	{	PUNCT
ejpam-4972	101	36	a	a	DET
ejpam-4972	101	37	,	,	PUNCT
ejpam-4972	101	38	b	b	NOUN
ejpam-4972	101	39	}	}	PUNCT
ejpam-4972	101	40	.	.	PUNCT
ejpam-4972	102	1	we	we	PRON
ejpam-4972	102	2	determine	determine	VERB
ejpam-4972	102	3	them	they	PRON
ejpam-4972	102	4	as	as	ADP
ejpam-4972	102	5	:	:	PUNCT
ejpam-4972	102	6	e(a	e(a	NOUN
ejpam-4972	102	7	,	,	PUNCT
ejpam-4972	102	8	b	b	X
ejpam-4972	102	9	)	)	PUNCT
ejpam-4972	102	10	=	=	SYM
ejpam-4972	102	11	{	{	PUNCT
ejpam-4972	102	12	0.5	0.5	NUM
ejpam-4972	102	13	,	,	PUNCT
ejpam-4972	102	14	0.4	0.4	NUM
ejpam-4972	102	15	}	}	PUNCT
ejpam-4972	102	16	,	,	PUNCT
ejpam-4972	102	17	f	f	PROPN
ejpam-4972	102	18	(	(	PUNCT
ejpam-4972	102	19	a	a	DET
ejpam-4972	102	20	,	,	PUNCT
ejpam-4972	102	21	b	b	NOUN
ejpam-4972	102	22	)	)	PUNCT
ejpam-4972	102	23	=	=	NOUN
ejpam-4972	102	24	{	{	PUNCT
ejpam-4972	102	25	0.7	0.7	NUM
ejpam-4972	102	26	,	,	PUNCT
ejpam-4972	102	27	0.5	0.5	NUM
ejpam-4972	102	28	}	}	PUNCT
ejpam-4972	102	29	,	,	PUNCT
ejpam-4972	102	30	and	and	CCONJ
ejpam-4972	102	31	g(a	g(a	PROPN
ejpam-4972	102	32	,	,	PUNCT
ejpam-4972	102	33	b	b	NOUN
ejpam-4972	102	34	)	)	PUNCT
ejpam-4972	102	35	=	=	SYM
ejpam-4972	102	36	{	{	PUNCT
ejpam-4972	102	37	0.4	0.4	NUM
ejpam-4972	102	38	,	,	PUNCT
ejpam-4972	102	39	0.4	0.4	NUM
ejpam-4972	102	40	}	}	PUNCT
ejpam-4972	102	41	.	.	PUNCT
ejpam-4972	103	1	consider	consider	VERB
ejpam-4972	103	2	the	the	DET
ejpam-4972	103	3	fuzzy	fuzzy	ADJ
ejpam-4972	103	4	bitopology	bitopology	NOUN
ejpam-4972	103	5	δ1	δ1	NOUN
ejpam-4972	103	6	=	=	PUNCT
ejpam-4972	103	7	{	{	PUNCT
ejpam-4972	103	8	0	0	NUM
ejpam-4972	103	9	,	,	PUNCT
ejpam-4972	103	10	1	1	NUM
ejpam-4972	103	11	,	,	PUNCT
ejpam-4972	103	12	e	e	NOUN
ejpam-4972	103	13	}	}	PUNCT
ejpam-4972	103	14	also	also	ADV
ejpam-4972	103	15	δ2	δ2	VERB
ejpam-4972	103	16	=	=	SYM
ejpam-4972	103	17	{	{	PUNCT
ejpam-4972	103	18	0	0	NUM
ejpam-4972	103	19	,	,	PUNCT
ejpam-4972	103	20	1	1	NUM
ejpam-4972	103	21	,	,	PUNCT
ejpam-4972	103	22	f	f	X
ejpam-4972	103	23	,	,	PUNCT
ejpam-4972	103	24	g	g	NOUN
ejpam-4972	103	25	}	}	PUNCT
ejpam-4972	103	26	on	on	ADP
ejpam-4972	103	27	x.	x.	NOUN
ejpam-4972	103	28	suppose	suppose	VERB
ejpam-4972	103	29	n	n	ADP
ejpam-4972	103	30	with	with	ADP
ejpam-4972	103	31	m	m	PROPN
ejpam-4972	103	32	are	be	AUX
ejpam-4972	103	33	fuzzy	fuzzy	ADJ
ejpam-4972	103	34	subgroups	subgroup	NOUN
ejpam-4972	103	35	of	of	ADP
ejpam-4972	103	36	y	y	PROPN
ejpam-4972	103	37	=	=	PUNCT
ejpam-4972	103	38	{	{	PUNCT
ejpam-4972	103	39	r	r	NOUN
ejpam-4972	103	40	,	,	PUNCT
ejpam-4972	103	41	h	h	NOUN
ejpam-4972	103	42	}	}	PUNCT
ejpam-4972	103	43	defined	define	VERB
ejpam-4972	103	44	as	as	ADP
ejpam-4972	103	45	:	:	PUNCT
ejpam-4972	103	46	n(r	n(r	NOUN
ejpam-4972	103	47	,	,	PUNCT
ejpam-4972	103	48	h	h	NOUN
ejpam-4972	103	49	)	)	PUNCT
ejpam-4972	103	50	=	=	PRON
ejpam-4972	103	51	{	{	PUNCT
ejpam-4972	103	52	0.2	0.2	NUM
ejpam-4972	103	53	,	,	PUNCT
ejpam-4972	103	54	0.5	0.5	NUM
ejpam-4972	103	55	}	}	PUNCT
ejpam-4972	103	56	,	,	PUNCT
ejpam-4972	103	57	m(r	m(r	PROPN
ejpam-4972	103	58	,	,	PUNCT
ejpam-4972	103	59	h	h	NOUN
ejpam-4972	103	60	)	)	PUNCT
ejpam-4972	103	61	=	=	PUNCT
ejpam-4972	103	62	{	{	PUNCT
ejpam-4972	103	63	0.7	0.7	NUM
ejpam-4972	103	64	,	,	PUNCT
ejpam-4972	103	65	0.6	0.6	NUM
ejpam-4972	103	66	}	}	PUNCT
ejpam-4972	103	67	.	.	PUNCT
ejpam-4972	104	1	consider	consider	VERB
ejpam-4972	104	2	the	the	DET
ejpam-4972	104	3	fuzzy	fuzzy	ADJ
ejpam-4972	104	4	bitopology	bitopology	NOUN
ejpam-4972	104	5	σ1	σ1	NOUN
ejpam-4972	104	6	=	=	PUNCT
ejpam-4972	104	7	{	{	PUNCT
ejpam-4972	104	8	0	0	NUM
ejpam-4972	104	9	,	,	PUNCT
ejpam-4972	104	10	1	1	NUM
ejpam-4972	104	11	,	,	PUNCT
ejpam-4972	104	12	n	n	CCONJ
ejpam-4972	104	13	}	}	PUNCT
ejpam-4972	104	14	with	with	ADP
ejpam-4972	104	15	σ2	σ2	PROPN
ejpam-4972	104	16	=	=	SYM
ejpam-4972	104	17	{	{	PUNCT
ejpam-4972	104	18	0	0	NUM
ejpam-4972	104	19	,	,	PUNCT
ejpam-4972	104	20	1,m	1,m	NOUN
ejpam-4972	104	21	}	}	PUNCT
ejpam-4972	104	22	on	on	ADP
ejpam-4972	104	23	y	y	PROPN
ejpam-4972	104	24	and	and	CCONJ
ejpam-4972	104	25	t(a	t(a	NOUN
ejpam-4972	104	26	)	)	PUNCT
ejpam-4972	105	1	=	=	SYM
ejpam-4972	105	2	r	r	NOUN
ejpam-4972	105	3	,	,	PUNCT
ejpam-4972	105	4	t(b	t(b	NOUN
ejpam-4972	105	5	)	)	PUNCT
ejpam-4972	105	6	=	=	SYM
ejpam-4972	106	1	h.	h.	NOUN
ejpam-4972	106	2	one	one	PRON
ejpam-4972	106	3	may	may	AUX
ejpam-4972	106	4	notice	notice	VERB
ejpam-4972	106	5	that	that	SCONJ
ejpam-4972	106	6	t	t	PROPN
ejpam-4972	106	7	is	be	AUX
ejpam-4972	106	8	fuzzy	fuzzy	ADJ
ejpam-4972	106	9	(	(	PUNCT
ejpam-4972	106	10	1	1	NUM
ejpam-4972	106	11	,	,	PUNCT
ejpam-4972	106	12	2	2	NUM
ejpam-4972	106	13	)	)	PUNCT
ejpam-4972	106	14	−	−	NOUN
ejpam-4972	106	15	gα	gα	ADP
ejpam-4972	106	16	−	−	PROPN
ejpam-4972	106	17	conts	cont	NOUN
ejpam-4972	106	18	,	,	PUNCT
ejpam-4972	106	19	but	but	CCONJ
ejpam-4972	106	20	not	not	PART
ejpam-4972	106	21	fuzzy	fuzzy	ADJ
ejpam-4972	106	22	(	(	PUNCT
ejpam-4972	106	23	1	1	NUM
ejpam-4972	106	24	,	,	PUNCT
ejpam-4972	106	25	2	2	NUM
ejpam-4972	106	26	)	)	PUNCT
ejpam-4972	106	27	−	−	NOUN
ejpam-4972	107	1	g	g	PROPN
ejpam-4972	107	2	−	−	PROPN
ejpam-4972	107	3	conts	cont	NOUN
ejpam-4972	107	4	as	as	ADP
ejpam-4972	107	5	t−1(m	t−1(m	PROPN
ejpam-4972	107	6	c	c	PROPN
ejpam-4972	107	7	)	)	PUNCT
ejpam-4972	107	8	≤	≤	NUM
ejpam-4972	107	9	e	e	X
ejpam-4972	107	10	∈	∈	NOUN
ejpam-4972	107	11	δ1	δ1	NOUN
ejpam-4972	107	12	but	but	CCONJ
ejpam-4972	107	13	δ2	δ2	VERB
ejpam-4972	107	14	−	−	PROPN
ejpam-4972	107	15	cl(t−1(m	cl(t−1(m	PROPN
ejpam-4972	107	16	c	c	NOUN
ejpam-4972	107	17	)	)	PUNCT
ejpam-4972	107	18	)	)	PUNCT
ejpam-4972	108	1	≰	≰	PROPN
ejpam-4972	108	2	e.	e.	PROPN
ejpam-4972	108	3	the	the	DET
ejpam-4972	108	4	next	next	ADJ
ejpam-4972	108	5	example	example	NOUN
ejpam-4972	108	6	clear	clear	ADJ
ejpam-4972	108	7	that	that	SCONJ
ejpam-4972	108	8	(	(	PUNCT
ejpam-4972	108	9	1	1	NUM
ejpam-4972	108	10	,	,	PUNCT
ejpam-4972	108	11	2)−	2)−	PROPN
ejpam-4972	108	12	gp−	gp−	PROPN
ejpam-4972	108	13	conts	cont	NOUN
ejpam-4972	108	14	⇏	⇏	VERB
ejpam-4972	108	15	(	(	PUNCT
ejpam-4972	108	16	1	1	NUM
ejpam-4972	108	17	,	,	PUNCT
ejpam-4972	108	18	2)−	2)−	PROPN
ejpam-4972	108	19	gα−	gα−	PROPN
ejpam-4972	108	20	conts	cont	NOUN
ejpam-4972	108	21	.	.	PUNCT
ejpam-4972	108	22	example	example	NOUN
ejpam-4972	108	23	2	2	NUM
ejpam-4972	108	24	.	.	PUNCT
ejpam-4972	108	25	suppose	suppose	VERB
ejpam-4972	108	26	e	e	NOUN
ejpam-4972	108	27	,	,	PUNCT
ejpam-4972	108	28	f	f	PROPN
ejpam-4972	108	29	,	,	PUNCT
ejpam-4972	108	30	and	and	CCONJ
ejpam-4972	108	31	g	g	NOUN
ejpam-4972	108	32	are	be	AUX
ejpam-4972	108	33	fuzzy	fuzzy	ADJ
ejpam-4972	108	34	subgroups	subgroup	NOUN
ejpam-4972	108	35	of	of	ADP
ejpam-4972	108	36	x	x	SYM
ejpam-4972	108	37	=	=	X
ejpam-4972	108	38	{	{	PUNCT
ejpam-4972	108	39	a	a	DET
ejpam-4972	108	40	,	,	PUNCT
ejpam-4972	108	41	b	b	NOUN
ejpam-4972	108	42	}	}	PUNCT
ejpam-4972	108	43	.	.	PUNCT
ejpam-4972	109	1	we	we	PRON
ejpam-4972	109	2	determine	determine	VERB
ejpam-4972	109	3	them	they	PRON
ejpam-4972	109	4	as	as	ADP
ejpam-4972	109	5	:	:	PUNCT
ejpam-4972	109	6	e(a	e(a	NOUN
ejpam-4972	109	7	,	,	PUNCT
ejpam-4972	109	8	b	b	X
ejpam-4972	109	9	)	)	PUNCT
ejpam-4972	109	10	=	=	NOUN
ejpam-4972	109	11	{	{	PUNCT
ejpam-4972	109	12	0.7	0.7	NUM
ejpam-4972	109	13	,	,	PUNCT
ejpam-4972	109	14	0.5	0.5	NUM
ejpam-4972	109	15	}	}	PUNCT
ejpam-4972	109	16	,	,	PUNCT
ejpam-4972	109	17	f	f	PROPN
ejpam-4972	109	18	(	(	PUNCT
ejpam-4972	109	19	a	a	DET
ejpam-4972	109	20	,	,	PUNCT
ejpam-4972	109	21	b	b	NOUN
ejpam-4972	109	22	)	)	PUNCT
ejpam-4972	109	23	=	=	SYM
ejpam-4972	109	24	{	{	PUNCT
ejpam-4972	109	25	0.6	0.6	NUM
ejpam-4972	109	26	,	,	PUNCT
ejpam-4972	109	27	0.8	0.8	NUM
ejpam-4972	109	28	}	}	PUNCT
ejpam-4972	109	29	,	,	PUNCT
ejpam-4972	109	30	and	and	CCONJ
ejpam-4972	109	31	g(a	g(a	PROPN
ejpam-4972	109	32	,	,	PUNCT
ejpam-4972	109	33	b	b	NOUN
ejpam-4972	109	34	)	)	PUNCT
ejpam-4972	109	35	=	=	SYM
ejpam-4972	109	36	{	{	PUNCT
ejpam-4972	109	37	0.4	0.4	NUM
ejpam-4972	109	38	,	,	PUNCT
ejpam-4972	109	39	0.3	0.3	NUM
ejpam-4972	109	40	}	}	PUNCT
ejpam-4972	109	41	.	.	PUNCT
ejpam-4972	110	1	consider	consider	VERB
ejpam-4972	110	2	the	the	DET
ejpam-4972	110	3	fuzzy	fuzzy	ADJ
ejpam-4972	110	4	bitopology	bitopology	NOUN
ejpam-4972	110	5	δ1	δ1	NOUN
ejpam-4972	110	6	=	=	PUNCT
ejpam-4972	110	7	{	{	PUNCT
ejpam-4972	110	8	0	0	NUM
ejpam-4972	110	9	,	,	PUNCT
ejpam-4972	110	10	1	1	NUM
ejpam-4972	110	11	,	,	PUNCT
ejpam-4972	110	12	e	e	NOUN
ejpam-4972	110	13	}	}	PUNCT
ejpam-4972	110	14	also	also	ADV
ejpam-4972	110	15	δ2	δ2	VERB
ejpam-4972	110	16	=	=	SYM
ejpam-4972	110	17	{	{	PUNCT
ejpam-4972	110	18	0	0	NUM
ejpam-4972	110	19	,	,	PUNCT
ejpam-4972	110	20	1	1	NUM
ejpam-4972	110	21	,	,	PUNCT
ejpam-4972	110	22	f	f	X
ejpam-4972	110	23	,	,	PUNCT
ejpam-4972	110	24	g	g	NOUN
ejpam-4972	110	25	}	}	PUNCT
ejpam-4972	110	26	on	on	ADP
ejpam-4972	110	27	x.	x.	NOUN
ejpam-4972	110	28	suppose	suppose	VERB
ejpam-4972	110	29	n	n	ADP
ejpam-4972	110	30	with	with	ADP
ejpam-4972	110	31	m	m	PROPN
ejpam-4972	110	32	are	be	AUX
ejpam-4972	110	33	fuzzy	fuzzy	ADJ
ejpam-4972	110	34	subgroups	subgroup	NOUN
ejpam-4972	110	35	of	of	ADP
ejpam-4972	110	36	y	y	PROPN
ejpam-4972	110	37	=	=	PUNCT
ejpam-4972	110	38	{	{	PUNCT
ejpam-4972	110	39	r	r	NOUN
ejpam-4972	110	40	,	,	PUNCT
ejpam-4972	110	41	h	h	NOUN
ejpam-4972	110	42	}	}	PUNCT
ejpam-4972	110	43	defined	define	VERB
ejpam-4972	110	44	as	as	ADP
ejpam-4972	110	45	:	:	PUNCT
ejpam-4972	110	46	n(r	n(r	NOUN
ejpam-4972	110	47	,	,	PUNCT
ejpam-4972	110	48	h	h	NOUN
ejpam-4972	110	49	)	)	PUNCT
ejpam-4972	110	50	=	=	PRON
ejpam-4972	110	51	{	{	PUNCT
ejpam-4972	110	52	0.2	0.2	NUM
ejpam-4972	110	53	,	,	PUNCT
ejpam-4972	110	54	0.5	0.5	NUM
ejpam-4972	110	55	}	}	PUNCT
ejpam-4972	110	56	,	,	PUNCT
ejpam-4972	110	57	m(r	m(r	PROPN
ejpam-4972	110	58	,	,	PUNCT
ejpam-4972	110	59	h	h	NOUN
ejpam-4972	110	60	)	)	PUNCT
ejpam-4972	110	61	=	=	NOUN
ejpam-4972	110	62	{	{	PUNCT
ejpam-4972	110	63	0.8	0.8	NUM
ejpam-4972	110	64	,	,	PUNCT
ejpam-4972	110	65	0.6	0.6	NUM
ejpam-4972	110	66	}	}	PUNCT
ejpam-4972	110	67	.	.	PUNCT
ejpam-4972	111	1	consider	consider	VERB
ejpam-4972	111	2	the	the	DET
ejpam-4972	111	3	fuzzy	fuzzy	ADJ
ejpam-4972	111	4	bitopology	bitopology	NOUN
ejpam-4972	111	5	σ1	σ1	NOUN
ejpam-4972	111	6	=	=	PUNCT
ejpam-4972	111	7	{	{	PUNCT
ejpam-4972	111	8	0	0	NUM
ejpam-4972	111	9	,	,	PUNCT
ejpam-4972	111	10	1	1	NUM
ejpam-4972	111	11	,	,	PUNCT
ejpam-4972	111	12	n	n	CCONJ
ejpam-4972	111	13	}	}	PUNCT
ejpam-4972	111	14	with	with	ADP
ejpam-4972	111	15	σ2	σ2	PROPN
ejpam-4972	111	16	=	=	SYM
ejpam-4972	111	17	{	{	PUNCT
ejpam-4972	111	18	0	0	NUM
ejpam-4972	111	19	,	,	PUNCT
ejpam-4972	111	20	1,m	1,m	NOUN
ejpam-4972	111	21	}	}	PUNCT
ejpam-4972	111	22	on	on	ADP
ejpam-4972	111	23	y	y	PROPN
ejpam-4972	111	24	and	and	CCONJ
ejpam-4972	111	25	t(a	t(a	NOUN
ejpam-4972	111	26	)	)	PUNCT
ejpam-4972	112	1	=	=	SYM
ejpam-4972	112	2	r	r	NOUN
ejpam-4972	112	3	,	,	PUNCT
ejpam-4972	112	4	t(b	t(b	NOUN
ejpam-4972	112	5	)	)	PUNCT
ejpam-4972	112	6	=	=	SYM
ejpam-4972	113	1	h.	h.	NOUN
ejpam-4972	113	2	one	one	PRON
ejpam-4972	113	3	may	may	AUX
ejpam-4972	113	4	notice	notice	VERB
ejpam-4972	113	5	that	that	SCONJ
ejpam-4972	113	6	t	t	PROPN
ejpam-4972	113	7	is	be	AUX
ejpam-4972	113	8	fuzzy	fuzzy	ADJ
ejpam-4972	113	9	(	(	PUNCT
ejpam-4972	113	10	1	1	NUM
ejpam-4972	113	11	,	,	PUNCT
ejpam-4972	113	12	2	2	NUM
ejpam-4972	113	13	)	)	PUNCT
ejpam-4972	113	14	−	−	NOUN
ejpam-4972	113	15	gp	gp	NOUN
ejpam-4972	113	16	−	−	NOUN
ejpam-4972	113	17	conts	cont	NOUN
ejpam-4972	113	18	,	,	PUNCT
ejpam-4972	113	19	but	but	CCONJ
ejpam-4972	113	20	not	not	PART
ejpam-4972	113	21	fuzzy	fuzzy	ADJ
ejpam-4972	113	22	(	(	PUNCT
ejpam-4972	113	23	1	1	NUM
ejpam-4972	113	24	,	,	PUNCT
ejpam-4972	113	25	2	2	NUM
ejpam-4972	113	26	)	)	PUNCT
ejpam-4972	113	27	−	−	NOUN
ejpam-4972	113	28	gα	gα	ADP
ejpam-4972	113	29	−	−	PROPN
ejpam-4972	113	30	conts	cont	NOUN
ejpam-4972	113	31	as	as	ADP
ejpam-4972	113	32	t−1(m	t−1(m	PROPN
ejpam-4972	113	33	c	c	PROPN
ejpam-4972	113	34	)	)	PUNCT
ejpam-4972	113	35	≤	≤	NUM
ejpam-4972	113	36	e	e	X
ejpam-4972	113	37	∈	∈	NOUN
ejpam-4972	113	38	δ1	δ1	NOUN
ejpam-4972	113	39	but	but	CCONJ
ejpam-4972	113	40	δ2	δ2	VERB
ejpam-4972	113	41	−	−	PROPN
ejpam-4972	113	42	α−	α−	ADP
ejpam-4972	113	43	cl(t−1(m	cl(t−1(m	PROPN
ejpam-4972	113	44	c	c	NOUN
ejpam-4972	113	45	)	)	PUNCT
ejpam-4972	113	46	)	)	PUNCT
ejpam-4972	114	1	≰	≰	PROPN
ejpam-4972	114	2	e.	e.	PROPN
ejpam-4972	114	3	the	the	DET
ejpam-4972	114	4	next	next	ADJ
ejpam-4972	114	5	example	example	NOUN
ejpam-4972	114	6	proves	prove	VERB
ejpam-4972	114	7	(	(	PUNCT
ejpam-4972	114	8	1	1	NUM
ejpam-4972	114	9	,	,	PUNCT
ejpam-4972	114	10	2)−	2)−	NUM
ejpam-4972	114	11	gs−	gs−	PROPN
ejpam-4972	114	12	conts	cont	NOUN
ejpam-4972	114	13	⇏	⇏	VERB
ejpam-4972	114	14	(	(	PUNCT
ejpam-4972	114	15	1	1	NUM
ejpam-4972	114	16	,	,	PUNCT
ejpam-4972	114	17	2)−	2)−	PROPN
ejpam-4972	114	18	gα−	gα−	ADJ
ejpam-4972	114	19	conts	cont	NOUN
ejpam-4972	114	20	.	.	PUNCT
ejpam-4972	115	1	a.	a.	NOUN
ejpam-4972	115	2	a.	a.	PROPN
ejpam-4972	115	3	alharbi	alharbi	PROPN
ejpam-4972	115	4	,	,	PUNCT
ejpam-4972	115	5	a.	a.	NOUN
ejpam-4972	115	6	kilicman	kilicman	PROPN
ejpam-4972	115	7	/	/	SYM
ejpam-4972	115	8	eur	eur	PROPN
ejpam-4972	115	9	.	.	PUNCT
ejpam-4972	116	1	j.	j.	PROPN
ejpam-4972	116	2	pure	pure	PROPN
ejpam-4972	116	3	appl	appl	PROPN
ejpam-4972	116	4	.	.	PROPN
ejpam-4972	116	5	math	math	PROPN
ejpam-4972	116	6	,	,	PUNCT
ejpam-4972	116	7	16	16	NUM
ejpam-4972	116	8	(	(	PUNCT
ejpam-4972	116	9	4	4	NUM
ejpam-4972	116	10	)	)	PUNCT
ejpam-4972	116	11	(	(	PUNCT
ejpam-4972	116	12	2023	2023	NUM
ejpam-4972	116	13	)	)	PUNCT
ejpam-4972	116	14	,	,	PUNCT
ejpam-4972	116	15	2613	2613	NUM
ejpam-4972	116	16	-	-	SYM
ejpam-4972	116	17	2631	2631	NUM
ejpam-4972	116	18	2618	2618	NUM
ejpam-4972	116	19	example	example	NOUN
ejpam-4972	117	1	3	3	NUM
ejpam-4972	117	2	.	.	PUNCT
ejpam-4972	117	3	suppose	suppose	VERB
ejpam-4972	117	4	e	e	NOUN
ejpam-4972	117	5	,	,	PUNCT
ejpam-4972	117	6	f	f	PROPN
ejpam-4972	117	7	,	,	PUNCT
ejpam-4972	117	8	g	g	PROPN
ejpam-4972	117	9	,	,	PUNCT
ejpam-4972	117	10	and	and	CCONJ
ejpam-4972	117	11	h	h	NOUN
ejpam-4972	117	12	are	be	AUX
ejpam-4972	117	13	fuzzy	fuzzy	ADJ
ejpam-4972	117	14	subgroups	subgroup	NOUN
ejpam-4972	117	15	of	of	ADP
ejpam-4972	117	16	x	x	SYM
ejpam-4972	117	17	=	=	X
ejpam-4972	117	18	{	{	PUNCT
ejpam-4972	117	19	a	a	DET
ejpam-4972	117	20	,	,	PUNCT
ejpam-4972	117	21	b	b	NOUN
ejpam-4972	117	22	}	}	PUNCT
ejpam-4972	117	23	.	.	PUNCT
ejpam-4972	118	1	we	we	PRON
ejpam-4972	118	2	determine	determine	VERB
ejpam-4972	118	3	them	they	PRON
ejpam-4972	118	4	as	as	ADP
ejpam-4972	118	5	:	:	PUNCT
ejpam-4972	118	6	e(a	e(a	NOUN
ejpam-4972	118	7	,	,	PUNCT
ejpam-4972	118	8	b	b	X
ejpam-4972	118	9	)	)	PUNCT
ejpam-4972	118	10	=	=	NOUN
ejpam-4972	118	11	{	{	PUNCT
ejpam-4972	118	12	0.7	0.7	NUM
ejpam-4972	118	13	,	,	PUNCT
ejpam-4972	118	14	0.5	0.5	NUM
ejpam-4972	118	15	}	}	PUNCT
ejpam-4972	118	16	f	f	NOUN
ejpam-4972	118	17	(	(	PUNCT
ejpam-4972	118	18	a	a	DET
ejpam-4972	118	19	,	,	PUNCT
ejpam-4972	118	20	b	b	NOUN
ejpam-4972	118	21	)	)	PUNCT
ejpam-4972	118	22	=	=	SYM
ejpam-4972	118	23	{	{	PUNCT
ejpam-4972	118	24	0.5	0.5	NUM
ejpam-4972	118	25	,	,	PUNCT
ejpam-4972	118	26	0.4	0.4	NUM
ejpam-4972	118	27	}	}	PUNCT
ejpam-4972	118	28	,	,	PUNCT
ejpam-4972	118	29	g(a	g(a	PROPN
ejpam-4972	118	30	,	,	PUNCT
ejpam-4972	118	31	b	b	NOUN
ejpam-4972	118	32	)	)	PUNCT
ejpam-4972	118	33	=	=	SYM
ejpam-4972	118	34	{	{	PUNCT
ejpam-4972	118	35	0.4	0.4	NUM
ejpam-4972	118	36	,	,	PUNCT
ejpam-4972	118	37	0.3	0.3	NUM
ejpam-4972	118	38	}	}	PUNCT
ejpam-4972	118	39	,	,	PUNCT
ejpam-4972	118	40	and	and	CCONJ
ejpam-4972	118	41	h(a	h(a	PROPN
ejpam-4972	118	42	,	,	PUNCT
ejpam-4972	118	43	b	b	NOUN
ejpam-4972	118	44	)	)	PUNCT
ejpam-4972	118	45	=	=	SYM
ejpam-4972	118	46	{	{	PUNCT
ejpam-4972	118	47	0.5	0.5	NUM
ejpam-4972	118	48	,	,	PUNCT
ejpam-4972	118	49	0.6	0.6	NUM
ejpam-4972	118	50	}	}	PUNCT
ejpam-4972	118	51	.	.	PUNCT
ejpam-4972	119	1	consider	consider	VERB
ejpam-4972	119	2	the	the	DET
ejpam-4972	119	3	fuzzy	fuzzy	ADJ
ejpam-4972	119	4	bitopology	bitopology	NOUN
ejpam-4972	119	5	δ1	δ1	NOUN
ejpam-4972	119	6	=	=	PUNCT
ejpam-4972	119	7	{	{	PUNCT
ejpam-4972	119	8	0	0	NUM
ejpam-4972	119	9	,	,	PUNCT
ejpam-4972	119	10	1	1	NUM
ejpam-4972	119	11	,	,	PUNCT
ejpam-4972	119	12	e	e	NOUN
ejpam-4972	119	13	}	}	PUNCT
ejpam-4972	119	14	with	with	ADP
ejpam-4972	119	15	δ2	δ2	VERB
ejpam-4972	119	16	=	=	SYM
ejpam-4972	119	17	{	{	PUNCT
ejpam-4972	119	18	0	0	NUM
ejpam-4972	119	19	,	,	PUNCT
ejpam-4972	119	20	1	1	NUM
ejpam-4972	119	21	,	,	PUNCT
ejpam-4972	119	22	f	f	X
ejpam-4972	119	23	,	,	PUNCT
ejpam-4972	119	24	g	g	NOUN
ejpam-4972	119	25	}	}	PUNCT
ejpam-4972	119	26	on	on	ADP
ejpam-4972	119	27	x.	x.	NOUN
ejpam-4972	119	28	suppose	suppose	VERB
ejpam-4972	119	29	n	n	ADP
ejpam-4972	119	30	with	with	ADP
ejpam-4972	119	31	m	m	PROPN
ejpam-4972	119	32	are	be	AUX
ejpam-4972	119	33	fuzzy	fuzzy	ADJ
ejpam-4972	119	34	subgroups	subgroup	NOUN
ejpam-4972	119	35	of	of	ADP
ejpam-4972	119	36	y	y	PROPN
ejpam-4972	119	37	=	=	PUNCT
ejpam-4972	119	38	{	{	PUNCT
ejpam-4972	119	39	r	r	NOUN
ejpam-4972	119	40	,	,	PUNCT
ejpam-4972	119	41	h	h	NOUN
ejpam-4972	119	42	}	}	PUNCT
ejpam-4972	119	43	defined	define	VERB
ejpam-4972	119	44	as	as	ADP
ejpam-4972	119	45	:	:	PUNCT
ejpam-4972	119	46	n(r	n(r	NOUN
ejpam-4972	119	47	,	,	PUNCT
ejpam-4972	119	48	h	h	NOUN
ejpam-4972	119	49	)	)	PUNCT
ejpam-4972	119	50	=	=	PRON
ejpam-4972	119	51	{	{	PUNCT
ejpam-4972	119	52	0.2	0.2	NUM
ejpam-4972	119	53	,	,	PUNCT
ejpam-4972	119	54	0.5	0.5	NUM
ejpam-4972	119	55	}	}	PUNCT
ejpam-4972	119	56	,	,	PUNCT
ejpam-4972	119	57	m(r	m(r	PROPN
ejpam-4972	119	58	,	,	PUNCT
ejpam-4972	119	59	h	h	NOUN
ejpam-4972	119	60	)	)	PUNCT
ejpam-4972	119	61	=	=	SYM
ejpam-4972	119	62	{	{	PUNCT
ejpam-4972	119	63	0.5	0.5	NUM
ejpam-4972	119	64	,	,	PUNCT
ejpam-4972	119	65	0.5	0.5	NUM
ejpam-4972	119	66	}	}	PUNCT
ejpam-4972	119	67	.	.	PUNCT
ejpam-4972	120	1	consider	consider	VERB
ejpam-4972	120	2	the	the	DET
ejpam-4972	120	3	fuzzy	fuzzy	ADJ
ejpam-4972	120	4	bitopology	bitopology	NOUN
ejpam-4972	120	5	σ1	σ1	NOUN
ejpam-4972	120	6	=	=	PUNCT
ejpam-4972	120	7	{	{	PUNCT
ejpam-4972	120	8	0	0	NUM
ejpam-4972	120	9	,	,	PUNCT
ejpam-4972	120	10	1	1	NUM
ejpam-4972	120	11	,	,	PUNCT
ejpam-4972	120	12	n	n	CCONJ
ejpam-4972	120	13	}	}	PUNCT
ejpam-4972	120	14	also	also	ADV
ejpam-4972	120	15	σ2	σ2	PROPN
ejpam-4972	120	16	=	=	SYM
ejpam-4972	120	17	{	{	PUNCT
ejpam-4972	120	18	0	0	NUM
ejpam-4972	120	19	,	,	PUNCT
ejpam-4972	120	20	1,m	1,m	NOUN
ejpam-4972	120	21	}	}	PUNCT
ejpam-4972	120	22	on	on	ADP
ejpam-4972	120	23	y	y	PROPN
ejpam-4972	120	24	and	and	CCONJ
ejpam-4972	120	25	t(a	t(a	NOUN
ejpam-4972	120	26	)	)	PUNCT
ejpam-4972	121	1	=	=	SYM
ejpam-4972	121	2	r	r	NOUN
ejpam-4972	121	3	,	,	PUNCT
ejpam-4972	121	4	t(b	t(b	NOUN
ejpam-4972	121	5	)	)	PUNCT
ejpam-4972	121	6	=	=	SYM
ejpam-4972	122	1	h.	h.	NOUN
ejpam-4972	122	2	one	one	PRON
ejpam-4972	122	3	may	may	AUX
ejpam-4972	122	4	notice	notice	VERB
ejpam-4972	122	5	that	that	SCONJ
ejpam-4972	122	6	t	t	PROPN
ejpam-4972	122	7	is	be	AUX
ejpam-4972	122	8	fuzzy	fuzzy	ADJ
ejpam-4972	122	9	(	(	PUNCT
ejpam-4972	122	10	1	1	NUM
ejpam-4972	122	11	,	,	PUNCT
ejpam-4972	122	12	2)−	2)−	NUM
ejpam-4972	122	13	gs−	gs−	NUM
ejpam-4972	122	14	conts	cont	NOUN
ejpam-4972	122	15	,	,	PUNCT
ejpam-4972	122	16	but	but	CCONJ
ejpam-4972	122	17	not	not	PART
ejpam-4972	122	18	fuzzy	fuzzy	ADJ
ejpam-4972	122	19	(	(	PUNCT
ejpam-4972	122	20	1	1	NUM
ejpam-4972	122	21	,	,	PUNCT
ejpam-4972	122	22	2)−	2)−	PROPN
ejpam-4972	122	23	gα−	gα−	NOUN
ejpam-4972	122	24	conts	cont	NOUN
ejpam-4972	122	25	since	since	SCONJ
ejpam-4972	122	26	t−1(m	t−1(m	PROPN
ejpam-4972	122	27	c	c	PROPN
ejpam-4972	122	28	)	)	PUNCT
ejpam-4972	122	29	≤	≤	NUM
ejpam-4972	122	30	e	e	X
ejpam-4972	122	31	∈	∈	NOUN
ejpam-4972	122	32	δ1	δ1	NOUN
ejpam-4972	122	33	but	but	CCONJ
ejpam-4972	122	34	δ2	δ2	VERB
ejpam-4972	122	35	−	−	PROPN
ejpam-4972	122	36	α−	α−	ADP
ejpam-4972	122	37	cl(t−1(m	cl(t−1(m	PROPN
ejpam-4972	122	38	c	c	NOUN
ejpam-4972	122	39	)	)	PUNCT
ejpam-4972	122	40	)	)	PUNCT
ejpam-4972	123	1	≰	≰	PROPN
ejpam-4972	123	2	e.	e.	PROPN
ejpam-4972	123	3	the	the	DET
ejpam-4972	123	4	following	follow	VERB
ejpam-4972	123	5	example	example	NOUN
ejpam-4972	123	6	clear	clear	ADJ
ejpam-4972	123	7	that	that	SCONJ
ejpam-4972	123	8	(	(	PUNCT
ejpam-4972	123	9	1	1	NUM
ejpam-4972	123	10	,	,	PUNCT
ejpam-4972	123	11	2)−	2)−	NUM
ejpam-4972	123	12	gβ	gβ	AUX
ejpam-4972	123	13	−	−	PROPN
ejpam-4972	123	14	conts	cont	NOUN
ejpam-4972	123	15	⇏	⇏	VERB
ejpam-4972	123	16	(	(	PUNCT
ejpam-4972	123	17	1	1	NUM
ejpam-4972	123	18	,	,	PUNCT
ejpam-4972	123	19	2)−	2)−	NUM
ejpam-4972	123	20	gs−	gs−	NUM
ejpam-4972	123	21	conts	cont	NOUN
ejpam-4972	123	22	.	.	PUNCT
ejpam-4972	123	23	example	example	NOUN
ejpam-4972	123	24	4	4	NUM
ejpam-4972	123	25	.	.	PUNCT
ejpam-4972	123	26	suppose	suppose	VERB
ejpam-4972	123	27	e	e	NOUN
ejpam-4972	123	28	,	,	PUNCT
ejpam-4972	123	29	f	f	PROPN
ejpam-4972	123	30	,	,	PUNCT
ejpam-4972	123	31	g	g	PROPN
ejpam-4972	123	32	,	,	PUNCT
ejpam-4972	123	33	and	and	CCONJ
ejpam-4972	123	34	h	h	NOUN
ejpam-4972	123	35	are	be	AUX
ejpam-4972	123	36	fuzzy	fuzzy	ADJ
ejpam-4972	123	37	subgroups	subgroup	NOUN
ejpam-4972	123	38	of	of	ADP
ejpam-4972	123	39	x	x	SYM
ejpam-4972	123	40	=	=	X
ejpam-4972	123	41	{	{	PUNCT
ejpam-4972	123	42	a	a	DET
ejpam-4972	123	43	,	,	PUNCT
ejpam-4972	123	44	b	b	NOUN
ejpam-4972	123	45	}	}	PUNCT
ejpam-4972	123	46	.	.	PUNCT
ejpam-4972	124	1	we	we	PRON
ejpam-4972	124	2	determine	determine	VERB
ejpam-4972	124	3	them	they	PRON
ejpam-4972	124	4	as	as	ADP
ejpam-4972	124	5	:	:	PUNCT
ejpam-4972	124	6	e(a	e(a	NOUN
ejpam-4972	124	7	,	,	PUNCT
ejpam-4972	124	8	b	b	X
ejpam-4972	124	9	)	)	PUNCT
ejpam-4972	124	10	=	=	SYM
ejpam-4972	124	11	{	{	PUNCT
ejpam-4972	124	12	0.5	0.5	NUM
ejpam-4972	124	13	,	,	PUNCT
ejpam-4972	124	14	0.7	0.7	NUM
ejpam-4972	124	15	}	}	PUNCT
ejpam-4972	124	16	f	f	NOUN
ejpam-4972	124	17	(	(	PUNCT
ejpam-4972	124	18	a	a	DET
ejpam-4972	124	19	,	,	PUNCT
ejpam-4972	124	20	b	b	NOUN
ejpam-4972	124	21	)	)	PUNCT
ejpam-4972	124	22	=	=	SYM
ejpam-4972	124	23	{	{	PUNCT
ejpam-4972	124	24	0.6	0.6	NUM
ejpam-4972	124	25	,	,	PUNCT
ejpam-4972	124	26	0.5	0.5	NUM
ejpam-4972	124	27	}	}	PUNCT
ejpam-4972	124	28	,	,	PUNCT
ejpam-4972	124	29	g(a	g(a	PROPN
ejpam-4972	124	30	,	,	PUNCT
ejpam-4972	124	31	b	b	NOUN
ejpam-4972	124	32	)	)	PUNCT
ejpam-4972	124	33	=	=	SYM
ejpam-4972	124	34	{	{	PUNCT
ejpam-4972	124	35	0.4	0.4	NUM
ejpam-4972	124	36	,	,	PUNCT
ejpam-4972	124	37	0.3	0.3	NUM
ejpam-4972	124	38	}	}	PUNCT
ejpam-4972	124	39	,	,	PUNCT
ejpam-4972	124	40	and	and	CCONJ
ejpam-4972	124	41	h(a	h(a	PROPN
ejpam-4972	124	42	,	,	PUNCT
ejpam-4972	124	43	b	b	NOUN
ejpam-4972	124	44	)	)	PUNCT
ejpam-4972	124	45	=	=	SYM
ejpam-4972	124	46	{	{	PUNCT
ejpam-4972	124	47	0.6	0.6	NUM
ejpam-4972	124	48	,	,	PUNCT
ejpam-4972	124	49	0.5	0.5	NUM
ejpam-4972	124	50	}	}	PUNCT
ejpam-4972	124	51	.	.	PUNCT
ejpam-4972	125	1	consider	consider	VERB
ejpam-4972	125	2	the	the	DET
ejpam-4972	125	3	fuzzy	fuzzy	ADJ
ejpam-4972	125	4	bitopology	bitopology	NOUN
ejpam-4972	125	5	δ1	δ1	NOUN
ejpam-4972	125	6	=	=	PUNCT
ejpam-4972	125	7	{	{	PUNCT
ejpam-4972	125	8	0	0	NUM
ejpam-4972	125	9	,	,	PUNCT
ejpam-4972	125	10	1	1	NUM
ejpam-4972	125	11	,	,	PUNCT
ejpam-4972	125	12	e	e	NOUN
ejpam-4972	125	13	}	}	PUNCT
ejpam-4972	125	14	,	,	PUNCT
ejpam-4972	125	15	δ2	δ2	VERB
ejpam-4972	125	16	=	=	SYM
ejpam-4972	125	17	{	{	PUNCT
ejpam-4972	125	18	0	0	NUM
ejpam-4972	125	19	,	,	PUNCT
ejpam-4972	125	20	1	1	NUM
ejpam-4972	125	21	,	,	PUNCT
ejpam-4972	125	22	f	f	X
ejpam-4972	125	23	,	,	PUNCT
ejpam-4972	125	24	g	g	NOUN
ejpam-4972	125	25	}	}	PUNCT
ejpam-4972	125	26	on	on	ADP
ejpam-4972	125	27	x.	x.	NOUN
ejpam-4972	125	28	suppose	suppose	VERB
ejpam-4972	125	29	n	n	X
ejpam-4972	125	30	,	,	PUNCT
ejpam-4972	125	31	m	m	VERB
ejpam-4972	125	32	are	be	AUX
ejpam-4972	125	33	fuzzy	fuzzy	ADJ
ejpam-4972	125	34	subgroups	subgroup	NOUN
ejpam-4972	125	35	of	of	ADP
ejpam-4972	125	36	y	y	PROPN
ejpam-4972	125	37	=	=	PUNCT
ejpam-4972	125	38	{	{	PUNCT
ejpam-4972	125	39	r	r	NOUN
ejpam-4972	125	40	,	,	PUNCT
ejpam-4972	125	41	h	h	NOUN
ejpam-4972	125	42	}	}	PUNCT
ejpam-4972	125	43	defined	define	VERB
ejpam-4972	125	44	as	as	ADP
ejpam-4972	125	45	:	:	PUNCT
ejpam-4972	125	46	n(r	n(r	NOUN
ejpam-4972	125	47	,	,	PUNCT
ejpam-4972	125	48	h	h	NOUN
ejpam-4972	125	49	)	)	PUNCT
ejpam-4972	125	50	=	=	PRON
ejpam-4972	125	51	{	{	PUNCT
ejpam-4972	125	52	0.2	0.2	NUM
ejpam-4972	125	53	,	,	PUNCT
ejpam-4972	125	54	0.5	0.5	NUM
ejpam-4972	125	55	}	}	PUNCT
ejpam-4972	125	56	,	,	PUNCT
ejpam-4972	125	57	m(r	m(r	PROPN
ejpam-4972	125	58	,	,	PUNCT
ejpam-4972	125	59	h	h	NOUN
ejpam-4972	125	60	)	)	PUNCT
ejpam-4972	125	61	=	=	SYM
ejpam-4972	125	62	{	{	PUNCT
ejpam-4972	125	63	0.5	0.5	NUM
ejpam-4972	125	64	,	,	PUNCT
ejpam-4972	125	65	0.5	0.5	NUM
ejpam-4972	125	66	}	}	PUNCT
ejpam-4972	125	67	.	.	PUNCT
ejpam-4972	126	1	consider	consider	VERB
ejpam-4972	126	2	the	the	DET
ejpam-4972	126	3	fuzzy	fuzzy	ADJ
ejpam-4972	126	4	bitopology	bitopology	NOUN
ejpam-4972	126	5	σ1	σ1	NOUN
ejpam-4972	126	6	=	=	PUNCT
ejpam-4972	126	7	{	{	PUNCT
ejpam-4972	126	8	0	0	NUM
ejpam-4972	126	9	,	,	PUNCT
ejpam-4972	126	10	1	1	NUM
ejpam-4972	126	11	,	,	PUNCT
ejpam-4972	126	12	n	n	CCONJ
ejpam-4972	126	13	}	}	PUNCT
ejpam-4972	126	14	,	,	PUNCT
ejpam-4972	126	15	σ2	σ2	PROPN
ejpam-4972	126	16	=	=	SYM
ejpam-4972	126	17	{	{	PUNCT
ejpam-4972	126	18	0	0	NUM
ejpam-4972	126	19	,	,	PUNCT
ejpam-4972	126	20	1,m	1,m	NOUN
ejpam-4972	126	21	}	}	PUNCT
ejpam-4972	126	22	on	on	ADP
ejpam-4972	126	23	y	y	PROPN
ejpam-4972	126	24	and	and	CCONJ
ejpam-4972	126	25	t(a	t(a	NOUN
ejpam-4972	126	26	)	)	PUNCT
ejpam-4972	126	27	=	=	SYM
ejpam-4972	126	28	r	r	NOUN
ejpam-4972	126	29	,	,	PUNCT
ejpam-4972	126	30	t(b	t(b	NOUN
ejpam-4972	126	31	)	)	PUNCT
ejpam-4972	126	32	=	=	SYM
ejpam-4972	127	1	h.	h.	NOUN
ejpam-4972	127	2	one	one	PRON
ejpam-4972	127	3	may	may	AUX
ejpam-4972	127	4	notice	notice	VERB
ejpam-4972	127	5	that	that	SCONJ
ejpam-4972	127	6	t	t	PROPN
ejpam-4972	127	7	is	be	AUX
ejpam-4972	127	8	fuzzy	fuzzy	ADJ
ejpam-4972	127	9	(	(	PUNCT
ejpam-4972	127	10	1	1	NUM
ejpam-4972	127	11	,	,	PUNCT
ejpam-4972	127	12	2)−gβ−	2)−gβ−	NUM
ejpam-4972	127	13	conts	cont	NOUN
ejpam-4972	127	14	,	,	PUNCT
ejpam-4972	127	15	but	but	CCONJ
ejpam-4972	127	16	not	not	PART
ejpam-4972	127	17	(	(	PUNCT
ejpam-4972	127	18	1	1	NUM
ejpam-4972	127	19	,	,	PUNCT
ejpam-4972	127	20	2)−gs−	2)−gs−	NUM
ejpam-4972	127	21	conts	cont	NOUN
ejpam-4972	127	22	as	as	ADP
ejpam-4972	127	23	t−1(m	t−1(m	PROPN
ejpam-4972	127	24	c	c	PROPN
ejpam-4972	127	25	)	)	PUNCT
ejpam-4972	127	26	≤	≤	NUM
ejpam-4972	127	27	e	e	X
ejpam-4972	127	28	∈	∈	NOUN
ejpam-4972	127	29	δ1	δ1	NOUN
ejpam-4972	127	30	but	but	CCONJ
ejpam-4972	127	31	δ2	δ2	VERB
ejpam-4972	127	32	−	−	PROPN
ejpam-4972	127	33	s−	s−	PROPN
ejpam-4972	127	34	cl(t−1(m	cl(t−1(m	PROPN
ejpam-4972	127	35	c	c	NOUN
ejpam-4972	127	36	)	)	PUNCT
ejpam-4972	127	37	)	)	PUNCT
ejpam-4972	128	1	≰	≰	PROPN
ejpam-4972	128	2	e.	e.	PROPN
ejpam-4972	128	3	the	the	DET
ejpam-4972	128	4	example	example	NOUN
ejpam-4972	128	5	follow	follow	NOUN
ejpam-4972	128	6	indicates	indicate	VERB
ejpam-4972	128	7	that	that	SCONJ
ejpam-4972	128	8	(	(	PUNCT
ejpam-4972	128	9	1	1	NUM
ejpam-4972	128	10	,	,	PUNCT
ejpam-4972	128	11	2)−	2)−	NUM
ejpam-4972	128	12	gβ	gβ	AUX
ejpam-4972	128	13	−	−	PROPN
ejpam-4972	128	14	conts	cont	NOUN
ejpam-4972	128	15	⇏	⇏	VERB
ejpam-4972	128	16	(	(	PUNCT
ejpam-4972	128	17	1	1	NUM
ejpam-4972	128	18	,	,	PUNCT
ejpam-4972	128	19	2)−	2)−	NUM
ejpam-4972	128	20	gp−	gp−	PROPN
ejpam-4972	128	21	conts	cont	NOUN
ejpam-4972	128	22	.	.	PUNCT
ejpam-4972	128	23	example	example	NOUN
ejpam-4972	128	24	5	5	NUM
ejpam-4972	128	25	.	.	PUNCT
ejpam-4972	128	26	suppose	suppose	VERB
ejpam-4972	128	27	e	e	NOUN
ejpam-4972	128	28	,	,	PUNCT
ejpam-4972	128	29	f	f	PROPN
ejpam-4972	128	30	,	,	PUNCT
ejpam-4972	128	31	g	g	PROPN
ejpam-4972	128	32	,	,	PUNCT
ejpam-4972	128	33	and	and	CCONJ
ejpam-4972	128	34	h	h	NOUN
ejpam-4972	128	35	are	be	AUX
ejpam-4972	128	36	fuzzy	fuzzy	ADJ
ejpam-4972	128	37	subgroups	subgroup	NOUN
ejpam-4972	128	38	of	of	ADP
ejpam-4972	128	39	x	x	SYM
ejpam-4972	128	40	=	=	X
ejpam-4972	128	41	{	{	PUNCT
ejpam-4972	128	42	a	a	DET
ejpam-4972	128	43	,	,	PUNCT
ejpam-4972	128	44	b	b	NOUN
ejpam-4972	128	45	}	}	PUNCT
ejpam-4972	128	46	.	.	PUNCT
ejpam-4972	129	1	we	we	PRON
ejpam-4972	129	2	determine	determine	VERB
ejpam-4972	129	3	them	they	PRON
ejpam-4972	129	4	as	as	ADP
ejpam-4972	129	5	:	:	PUNCT
ejpam-4972	129	6	e(a	e(a	NOUN
ejpam-4972	129	7	,	,	PUNCT
ejpam-4972	129	8	b	b	X
ejpam-4972	129	9	)	)	PUNCT
ejpam-4972	129	10	=	=	SYM
ejpam-4972	129	11	{	{	PUNCT
ejpam-4972	129	12	0.5	0.5	NUM
ejpam-4972	129	13	,	,	PUNCT
ejpam-4972	129	14	0.7	0.7	NUM
ejpam-4972	129	15	}	}	PUNCT
ejpam-4972	129	16	f	f	NOUN
ejpam-4972	129	17	(	(	PUNCT
ejpam-4972	129	18	a	a	DET
ejpam-4972	129	19	,	,	PUNCT
ejpam-4972	129	20	b	b	NOUN
ejpam-4972	129	21	)	)	PUNCT
ejpam-4972	129	22	=	=	SYM
ejpam-4972	129	23	{	{	PUNCT
ejpam-4972	129	24	0.4	0.4	NUM
ejpam-4972	129	25	,	,	PUNCT
ejpam-4972	129	26	0.6	0.6	NUM
ejpam-4972	129	27	}	}	PUNCT
ejpam-4972	129	28	,	,	PUNCT
ejpam-4972	129	29	g(a	g(a	PROPN
ejpam-4972	129	30	,	,	PUNCT
ejpam-4972	129	31	b	b	NOUN
ejpam-4972	129	32	)	)	PUNCT
ejpam-4972	129	33	=	=	PUNCT
ejpam-4972	129	34	{	{	PUNCT
ejpam-4972	129	35	0.3	0.3	NUM
ejpam-4972	129	36	,	,	PUNCT
ejpam-4972	129	37	0.4	0.4	NUM
ejpam-4972	129	38	}	}	PUNCT
ejpam-4972	129	39	,	,	PUNCT
ejpam-4972	129	40	and	and	CCONJ
ejpam-4972	129	41	h(a	h(a	PROPN
ejpam-4972	129	42	,	,	PUNCT
ejpam-4972	129	43	b	b	NOUN
ejpam-4972	129	44	)	)	PUNCT
ejpam-4972	129	45	=	=	SYM
ejpam-4972	129	46	{	{	PUNCT
ejpam-4972	129	47	0.6	0.6	NUM
ejpam-4972	129	48	,	,	PUNCT
ejpam-4972	129	49	0.5	0.5	NUM
ejpam-4972	129	50	}	}	PUNCT
ejpam-4972	129	51	.	.	PUNCT
ejpam-4972	130	1	consider	consider	VERB
ejpam-4972	130	2	the	the	DET
ejpam-4972	130	3	fuzzy	fuzzy	ADJ
ejpam-4972	130	4	bitopology	bitopology	NOUN
ejpam-4972	130	5	δ1	δ1	NOUN
ejpam-4972	130	6	=	=	PUNCT
ejpam-4972	130	7	{	{	PUNCT
ejpam-4972	130	8	0	0	NUM
ejpam-4972	130	9	,	,	PUNCT
ejpam-4972	130	10	1	1	NUM
ejpam-4972	130	11	,	,	PUNCT
ejpam-4972	130	12	e	e	NOUN
ejpam-4972	130	13	}	}	PUNCT
ejpam-4972	130	14	,	,	PUNCT
ejpam-4972	130	15	δ2	δ2	VERB
ejpam-4972	130	16	=	=	SYM
ejpam-4972	130	17	{	{	PUNCT
ejpam-4972	130	18	0	0	NUM
ejpam-4972	130	19	,	,	PUNCT
ejpam-4972	130	20	1	1	NUM
ejpam-4972	130	21	,	,	PUNCT
ejpam-4972	130	22	f	f	X
ejpam-4972	130	23	,	,	PUNCT
ejpam-4972	130	24	g	g	NOUN
ejpam-4972	130	25	}	}	PUNCT
ejpam-4972	130	26	on	on	ADP
ejpam-4972	130	27	x.	x.	NOUN
ejpam-4972	130	28	suppose	suppose	VERB
ejpam-4972	130	29	n	n	X
ejpam-4972	130	30	,	,	PUNCT
ejpam-4972	130	31	m	m	VERB
ejpam-4972	130	32	are	be	AUX
ejpam-4972	130	33	fuzzy	fuzzy	ADJ
ejpam-4972	130	34	subgroups	subgroup	NOUN
ejpam-4972	130	35	of	of	ADP
ejpam-4972	130	36	y	y	PROPN
ejpam-4972	130	37	=	=	PUNCT
ejpam-4972	130	38	{	{	PUNCT
ejpam-4972	130	39	r	r	NOUN
ejpam-4972	130	40	,	,	PUNCT
ejpam-4972	130	41	h	h	NOUN
ejpam-4972	130	42	}	}	PUNCT
ejpam-4972	130	43	defined	define	VERB
ejpam-4972	130	44	as	as	ADP
ejpam-4972	130	45	:	:	PUNCT
ejpam-4972	130	46	n(r	n(r	NOUN
ejpam-4972	130	47	,	,	PUNCT
ejpam-4972	130	48	h	h	NOUN
ejpam-4972	130	49	)	)	PUNCT
ejpam-4972	130	50	=	=	VERB
ejpam-4972	130	51	{	{	PUNCT
ejpam-4972	130	52	0.7	0.7	NUM
ejpam-4972	130	53	,	,	PUNCT
ejpam-4972	130	54	0.5	0.5	NUM
ejpam-4972	130	55	}	}	PUNCT
ejpam-4972	130	56	,	,	PUNCT
ejpam-4972	130	57	m(r	m(r	PROPN
ejpam-4972	130	58	,	,	PUNCT
ejpam-4972	130	59	h	h	NOUN
ejpam-4972	130	60	)	)	PUNCT
ejpam-4972	130	61	=	=	SYM
ejpam-4972	130	62	{	{	PUNCT
ejpam-4972	130	63	0.5	0.5	NUM
ejpam-4972	130	64	,	,	PUNCT
ejpam-4972	130	65	0.5	0.5	NUM
ejpam-4972	130	66	}	}	PUNCT
ejpam-4972	130	67	.	.	PUNCT
ejpam-4972	131	1	consider	consider	VERB
ejpam-4972	131	2	the	the	DET
ejpam-4972	131	3	fuzzy	fuzzy	ADJ
ejpam-4972	131	4	bitopology	bitopology	NOUN
ejpam-4972	131	5	σ1	σ1	NOUN
ejpam-4972	131	6	=	=	PUNCT
ejpam-4972	131	7	{	{	PUNCT
ejpam-4972	131	8	0	0	NUM
ejpam-4972	131	9	,	,	PUNCT
ejpam-4972	131	10	1	1	NUM
ejpam-4972	131	11	,	,	PUNCT
ejpam-4972	131	12	n	n	CCONJ
ejpam-4972	131	13	}	}	PUNCT
ejpam-4972	131	14	,	,	PUNCT
ejpam-4972	131	15	σ2	σ2	PROPN
ejpam-4972	131	16	=	=	SYM
ejpam-4972	131	17	{	{	PUNCT
ejpam-4972	131	18	0	0	NUM
ejpam-4972	131	19	,	,	PUNCT
ejpam-4972	131	20	1,m	1,m	NOUN
ejpam-4972	131	21	}	}	PUNCT
ejpam-4972	131	22	on	on	ADP
ejpam-4972	131	23	y	y	PROPN
ejpam-4972	131	24	and	and	CCONJ
ejpam-4972	131	25	t(a	t(a	NOUN
ejpam-4972	131	26	)	)	PUNCT
ejpam-4972	131	27	=	=	SYM
ejpam-4972	131	28	r	r	NOUN
ejpam-4972	131	29	,	,	PUNCT
ejpam-4972	131	30	t(b	t(b	NOUN
ejpam-4972	131	31	)	)	PUNCT
ejpam-4972	131	32	=	=	SYM
ejpam-4972	132	1	h.	h.	NOUN
ejpam-4972	132	2	one	one	PRON
ejpam-4972	132	3	may	may	AUX
ejpam-4972	132	4	notice	notice	VERB
ejpam-4972	132	5	that	that	SCONJ
ejpam-4972	132	6	t	t	PROPN
ejpam-4972	132	7	is	be	AUX
ejpam-4972	132	8	fuzzy	fuzzy	ADJ
ejpam-4972	132	9	(	(	PUNCT
ejpam-4972	132	10	1	1	NUM
ejpam-4972	132	11	,	,	PUNCT
ejpam-4972	132	12	2)−gβ−conts	2)−gβ−conts	NUM
ejpam-4972	132	13	,	,	PUNCT
ejpam-4972	132	14	but	but	CCONJ
ejpam-4972	132	15	not	not	PART
ejpam-4972	132	16	(	(	PUNCT
ejpam-4972	132	17	1	1	NUM
ejpam-4972	132	18	,	,	PUNCT
ejpam-4972	132	19	2)−gp−conts	2)−gp−conts	NUM
ejpam-4972	132	20	as	as	ADP
ejpam-4972	132	21	t−1(m	t−1(m	PROPN
ejpam-4972	132	22	c	c	PROPN
ejpam-4972	132	23	)	)	PUNCT
ejpam-4972	132	24	≤	≤	NUM
ejpam-4972	132	25	e	e	X
ejpam-4972	132	26	∈	∈	NOUN
ejpam-4972	132	27	δ1	δ1	NOUN
ejpam-4972	132	28	but	but	CCONJ
ejpam-4972	132	29	δ2	δ2	VERB
ejpam-4972	132	30	−	−	PROPN
ejpam-4972	132	31	p−	p−	NOUN
ejpam-4972	132	32	cl(t−1(m	cl(t−1(m	NOUN
ejpam-4972	132	33	c	c	NOUN
ejpam-4972	132	34	)	)	PUNCT
ejpam-4972	132	35	)	)	PUNCT
ejpam-4972	133	1	≰	≰	PROPN
ejpam-4972	133	2	e.	e.	PROPN
ejpam-4972	133	3	theorem	theorem	PROPN
ejpam-4972	133	4	3	3	X
ejpam-4972	133	5	.	.	PUNCT
ejpam-4972	133	6	suppose	suppose	VERB
ejpam-4972	133	7	t	t	NOUN
ejpam-4972	133	8	:	:	PUNCT
ejpam-4972	133	9	(	(	PUNCT
ejpam-4972	133	10	x	x	X
ejpam-4972	133	11	,	,	PUNCT
ejpam-4972	133	12	δ1	δ1	NOUN
ejpam-4972	133	13	,	,	PUNCT
ejpam-4972	133	14	δ2	δ2	ADJ
ejpam-4972	133	15	)	)	PUNCT
ejpam-4972	133	16	→	→	SYM
ejpam-4972	133	17	(	(	PUNCT
ejpam-4972	133	18	y	y	PROPN
ejpam-4972	133	19	,	,	PUNCT
ejpam-4972	133	20	σ1	σ1	PROPN
ejpam-4972	133	21	,	,	PUNCT
ejpam-4972	133	22	σ2	σ2	NOUN
ejpam-4972	133	23	)	)	PUNCT
ejpam-4972	133	24	is	be	AUX
ejpam-4972	133	25	fuzzy	fuzzy	ADJ
ejpam-4972	133	26	δj	δj	ADP
ejpam-4972	133	27	−	−	PROPN
ejpam-4972	133	28	ψ	ψ	NOUN
ejpam-4972	133	29	−	−	PROPN
ejpam-4972	133	30	conts	cont	NOUN
ejpam-4972	133	31	.	.	PUNCT
ejpam-4972	134	1	thus	thus	ADV
ejpam-4972	134	2	t	t	PROPN
ejpam-4972	134	3	is	be	AUX
ejpam-4972	134	4	fuzzy	fuzzy	ADJ
ejpam-4972	134	5	(	(	PUNCT
ejpam-4972	134	6	i	i	PROPN
ejpam-4972	134	7	,	,	PUNCT
ejpam-4972	134	8	j)−	j)−	PROPN
ejpam-4972	134	9	gψ	gψ	VERB
ejpam-4972	134	10	−	−	PROPN
ejpam-4972	134	11	conts	cont	NOUN
ejpam-4972	134	12	.	.	PUNCT
ejpam-4972	135	1	proof	proof	NOUN
ejpam-4972	135	2	.	.	PUNCT
ejpam-4972	136	1	suppose	suppose	VERB
ejpam-4972	136	2	t	t	PROPN
ejpam-4972	136	3	is	be	AUX
ejpam-4972	136	4	fuzzy	fuzzy	ADJ
ejpam-4972	136	5	δj	δj	ADP
ejpam-4972	136	6	−	−	PROPN
ejpam-4972	136	7	ψ	ψ	NOUN
ejpam-4972	136	8	−	−	PROPN
ejpam-4972	136	9	conts	cont	NOUN
ejpam-4972	136	10	and	and	CCONJ
ejpam-4972	136	11	u	u	NOUN
ejpam-4972	136	12	∈	∈	PROPN
ejpam-4972	136	13	fσj	fσj	NOUN
ejpam-4972	136	14	.	.	PUNCT
ejpam-4972	137	1	then	then	ADV
ejpam-4972	137	2	t−1(u	t−1(u	PROPN
ejpam-4972	137	3	)	)	PUNCT
ejpam-4972	137	4	∈	∈	PROPN
ejpam-4972	137	5	fψc(x	fψc(x	PROPN
ejpam-4972	137	6	,	,	PUNCT
ejpam-4972	137	7	δj	δj	NOUN
ejpam-4972	137	8	)	)	PUNCT
ejpam-4972	137	9	,	,	PUNCT
ejpam-4972	137	10	and	and	CCONJ
ejpam-4972	137	11	hence	hence	ADV
ejpam-4972	137	12	t−1(u	t−1(u	NUM
ejpam-4972	137	13	)	)	PUNCT
ejpam-4972	137	14	is	be	AUX
ejpam-4972	137	15	fuzzy	fuzzy	ADJ
ejpam-4972	137	16	(	(	PUNCT
ejpam-4972	137	17	i	i	PROPN
ejpam-4972	137	18	,	,	PUNCT
ejpam-4972	137	19	j)−	j)−	PROPN
ejpam-4972	137	20	gψ	gψ	VERB
ejpam-4972	137	21	−	−	PROPN
ejpam-4972	137	22	cld	cld	NOUN
ejpam-4972	137	23	of	of	ADP
ejpam-4972	137	24	x.	x.	PROPN
ejpam-4972	137	25	therefore	therefore	ADV
ejpam-4972	137	26	t	t	PROPN
ejpam-4972	137	27	is	be	AUX
ejpam-4972	137	28	fuzzy	fuzzy	ADJ
ejpam-4972	137	29	(	(	PUNCT
ejpam-4972	137	30	i	i	PROPN
ejpam-4972	137	31	,	,	PUNCT
ejpam-4972	137	32	j)−	j)−	PROPN
ejpam-4972	137	33	gψ	gψ	VERB
ejpam-4972	137	34	−	−	PROPN
ejpam-4972	137	35	conts	cont	NOUN
ejpam-4972	137	36	.	.	PUNCT
ejpam-4972	138	1	remark	remark	PROPN
ejpam-4972	138	2	4	4	NUM
ejpam-4972	138	3	.	.	PUNCT
ejpam-4972	139	1	the	the	DET
ejpam-4972	139	2	inverse	inverse	NOUN
ejpam-4972	139	3	of	of	ADP
ejpam-4972	139	4	the	the	DET
ejpam-4972	139	5	above	above	ADJ
ejpam-4972	139	6	theorem	theorem	NOUN
ejpam-4972	139	7	is	be	AUX
ejpam-4972	139	8	incorrect	incorrect	ADJ
ejpam-4972	139	9	.	.	PUNCT
ejpam-4972	140	1	the	the	DET
ejpam-4972	140	2	next	next	ADJ
ejpam-4972	140	3	example	example	NOUN
ejpam-4972	140	4	is	be	AUX
ejpam-4972	140	5	evidenced	evidence	VERB
ejpam-4972	140	6	that	that	SCONJ
ejpam-4972	140	7	:	:	PUNCT
ejpam-4972	140	8	suppose	suppose	VERB
ejpam-4972	140	9	e	e	X
ejpam-4972	140	10	,	,	PUNCT
ejpam-4972	140	11	f	f	PROPN
ejpam-4972	140	12	are	be	AUX
ejpam-4972	140	13	fuzzy	fuzzy	ADJ
ejpam-4972	140	14	subgroups	subgroup	NOUN
ejpam-4972	140	15	of	of	ADP
ejpam-4972	140	16	x	x	SYM
ejpam-4972	140	17	=	=	X
ejpam-4972	140	18	{	{	PUNCT
ejpam-4972	140	19	a	a	DET
ejpam-4972	140	20	,	,	PUNCT
ejpam-4972	140	21	b	b	NOUN
ejpam-4972	140	22	}	}	PUNCT
ejpam-4972	140	23	.	.	PUNCT
ejpam-4972	141	1	we	we	PRON
ejpam-4972	141	2	determine	determine	VERB
ejpam-4972	141	3	them	they	PRON
ejpam-4972	141	4	as	as	ADP
ejpam-4972	141	5	:	:	PUNCT
ejpam-4972	141	6	e(a	e(a	NOUN
ejpam-4972	141	7	,	,	PUNCT
ejpam-4972	141	8	b	b	X
ejpam-4972	141	9	)	)	PUNCT
ejpam-4972	141	10	=	=	PUNCT
ejpam-4972	141	11	{	{	PUNCT
ejpam-4972	141	12	0.3	0.3	NUM
ejpam-4972	141	13	,	,	PUNCT
ejpam-4972	141	14	0.4	0.4	NUM
ejpam-4972	141	15	}	}	PUNCT
ejpam-4972	141	16	,	,	PUNCT
ejpam-4972	141	17	f	f	PROPN
ejpam-4972	141	18	(	(	PUNCT
ejpam-4972	141	19	a	a	DET
ejpam-4972	141	20	,	,	PUNCT
ejpam-4972	141	21	b	b	NOUN
ejpam-4972	141	22	)	)	PUNCT
ejpam-4972	141	23	=	=	PUNCT
ejpam-4972	141	24	{	{	PUNCT
ejpam-4972	141	25	0.3	0.3	NUM
ejpam-4972	141	26	,	,	PUNCT
ejpam-4972	141	27	0.2	0.2	NUM
ejpam-4972	141	28	}	}	PUNCT
ejpam-4972	141	29	.	.	PUNCT
ejpam-4972	142	1	consider	consider	VERB
ejpam-4972	142	2	the	the	DET
ejpam-4972	142	3	fuzzy	fuzzy	ADJ
ejpam-4972	142	4	bitopology	bitopology	NOUN
ejpam-4972	142	5	δ1	δ1	NOUN
ejpam-4972	142	6	=	=	PUNCT
ejpam-4972	142	7	{	{	PUNCT
ejpam-4972	142	8	0	0	NUM
ejpam-4972	142	9	,	,	PUNCT
ejpam-4972	142	10	1	1	NUM
ejpam-4972	142	11	,	,	PUNCT
ejpam-4972	142	12	e	e	NOUN
ejpam-4972	142	13	}	}	PUNCT
ejpam-4972	142	14	,	,	PUNCT
ejpam-4972	142	15	δ2	δ2	VERB
ejpam-4972	142	16	=	=	SYM
ejpam-4972	142	17	{	{	PUNCT
ejpam-4972	142	18	0	0	NUM
ejpam-4972	142	19	,	,	PUNCT
ejpam-4972	142	20	1	1	NUM
ejpam-4972	142	21	,	,	PUNCT
ejpam-4972	142	22	f	f	X
ejpam-4972	142	23	}	}	PUNCT
ejpam-4972	142	24	on	on	ADP
ejpam-4972	142	25	x.	x.	NOUN
ejpam-4972	142	26	suppose	suppose	VERB
ejpam-4972	142	27	n	n	X
ejpam-4972	142	28	,	,	PUNCT
ejpam-4972	142	29	m	m	VERB
ejpam-4972	142	30	are	be	AUX
ejpam-4972	142	31	fuzzy	fuzzy	ADJ
ejpam-4972	142	32	subgroups	subgroup	NOUN
ejpam-4972	142	33	of	of	ADP
ejpam-4972	142	34	y	y	PROPN
ejpam-4972	142	35	=	=	PUNCT
ejpam-4972	142	36	{	{	PUNCT
ejpam-4972	142	37	r	r	NOUN
ejpam-4972	142	38	,	,	PUNCT
ejpam-4972	142	39	h	h	NOUN
ejpam-4972	142	40	}	}	PUNCT
ejpam-4972	142	41	defined	define	VERB
ejpam-4972	142	42	as	as	ADP
ejpam-4972	142	43	:	:	PUNCT
ejpam-4972	142	44	n(r	n(r	NOUN
ejpam-4972	142	45	,	,	PUNCT
ejpam-4972	142	46	h	h	NOUN
ejpam-4972	142	47	)	)	PUNCT
ejpam-4972	142	48	=	=	PUNCT
ejpam-4972	142	49	{	{	PUNCT
ejpam-4972	142	50	0.6	0.6	NUM
ejpam-4972	142	51	,	,	PUNCT
ejpam-4972	142	52	0.7	0.7	NUM
ejpam-4972	142	53	}	}	PUNCT
ejpam-4972	142	54	,	,	PUNCT
ejpam-4972	142	55	m(r	m(r	PROPN
ejpam-4972	142	56	,	,	PUNCT
ejpam-4972	142	57	h	h	NOUN
ejpam-4972	142	58	)	)	PUNCT
ejpam-4972	142	59	=	=	PUNCT
ejpam-4972	142	60	{	{	PUNCT
ejpam-4972	142	61	0.3	0.3	NUM
ejpam-4972	142	62	,	,	PUNCT
ejpam-4972	142	63	0.3	0.3	NUM
ejpam-4972	142	64	}	}	PUNCT
ejpam-4972	142	65	.	.	PUNCT
ejpam-4972	143	1	consider	consider	VERB
ejpam-4972	143	2	the	the	DET
ejpam-4972	143	3	fuzzy	fuzzy	ADJ
ejpam-4972	143	4	bitopology	bitopology	NOUN
ejpam-4972	143	5	σ1	σ1	NOUN
ejpam-4972	143	6	=	=	PUNCT
ejpam-4972	143	7	{	{	PUNCT
ejpam-4972	143	8	0	0	NUM
ejpam-4972	143	9	,	,	PUNCT
ejpam-4972	143	10	1	1	NUM
ejpam-4972	143	11	,	,	PUNCT
ejpam-4972	143	12	n	n	CCONJ
ejpam-4972	143	13	}	}	PUNCT
ejpam-4972	143	14	,	,	PUNCT
ejpam-4972	143	15	σ2	σ2	PROPN
ejpam-4972	143	16	=	=	SYM
ejpam-4972	143	17	{	{	PUNCT
ejpam-4972	143	18	0	0	NUM
ejpam-4972	143	19	,	,	PUNCT
ejpam-4972	143	20	1,m	1,m	NOUN
ejpam-4972	143	21	}	}	PUNCT
ejpam-4972	143	22	on	on	ADP
ejpam-4972	143	23	y	y	PROPN
ejpam-4972	143	24	and	and	CCONJ
ejpam-4972	143	25	t(a	t(a	NOUN
ejpam-4972	143	26	)	)	PUNCT
ejpam-4972	143	27	=	=	SYM
ejpam-4972	143	28	r	r	NOUN
ejpam-4972	143	29	,	,	PUNCT
ejpam-4972	143	30	t(b	t(b	NOUN
ejpam-4972	143	31	)	)	PUNCT
ejpam-4972	143	32	=	=	SYM
ejpam-4972	144	1	h.	h.	NOUN
ejpam-4972	144	2	one	one	PRON
ejpam-4972	144	3	may	may	AUX
ejpam-4972	144	4	notice	notice	VERB
ejpam-4972	144	5	that	that	SCONJ
ejpam-4972	144	6	t	t	PROPN
ejpam-4972	144	7	is	be	AUX
ejpam-4972	144	8	fuzzy	fuzzy	ADJ
ejpam-4972	144	9	(	(	PUNCT
ejpam-4972	144	10	1	1	NUM
ejpam-4972	144	11	,	,	PUNCT
ejpam-4972	144	12	2)−	2)−	NUM
ejpam-4972	144	13	g−	g−	PROPN
ejpam-4972	144	14	conts	cont	NOUN
ejpam-4972	144	15	,	,	PUNCT
ejpam-4972	144	16	so	so	ADV
ejpam-4972	144	17	by	by	ADP
ejpam-4972	144	18	theorem	theorem	NOUN
ejpam-4972	144	19	2	2	NUM
ejpam-4972	144	20	,	,	PUNCT
ejpam-4972	144	21	t	t	PROPN
ejpam-4972	144	22	is	be	AUX
ejpam-4972	144	23	fuzzy	fuzzy	ADJ
ejpam-4972	144	24	(	(	PUNCT
ejpam-4972	144	25	1	1	NUM
ejpam-4972	144	26	,	,	PUNCT
ejpam-4972	144	27	2)−	2)−	PROPN
ejpam-4972	144	28	gα−	gα−	NOUN
ejpam-4972	144	29	conts	cont	NOUN
ejpam-4972	144	30	but	but	CCONJ
ejpam-4972	144	31	not	not	PART
ejpam-4972	144	32	δ2−α−	δ2−α−	ADJ
ejpam-4972	144	33	conts	cont	NOUN
ejpam-4972	144	34	since	since	SCONJ
ejpam-4972	144	35	δ2−α−	δ2−α−	ADJ
ejpam-4972	144	36	cl(t−1(m	cl(t−1(m	PROPN
ejpam-4972	144	37	c	c	NOUN
ejpam-4972	144	38	)	)	PUNCT
ejpam-4972	144	39	)	)	PUNCT
ejpam-4972	145	1	≰	≰	X
ejpam-4972	145	2	t−1(m	t−1(m	PROPN
ejpam-4972	145	3	c	c	PROPN
ejpam-4972	145	4	)	)	PUNCT
ejpam-4972	145	5	.	.	PUNCT
ejpam-4972	146	1	corollary	corollary	ADJ
ejpam-4972	146	2	2	2	PROPN
ejpam-4972	146	3	.	.	PUNCT
ejpam-4972	146	4	suppose	suppose	VERB
ejpam-4972	146	5	t	t	NOUN
ejpam-4972	146	6	:	:	PUNCT
ejpam-4972	146	7	(	(	PUNCT
ejpam-4972	146	8	x	x	X
ejpam-4972	146	9	,	,	PUNCT
ejpam-4972	146	10	δ1	δ1	NOUN
ejpam-4972	146	11	,	,	PUNCT
ejpam-4972	146	12	δ2	δ2	ADJ
ejpam-4972	146	13	)	)	PUNCT
ejpam-4972	146	14	→	→	SYM
ejpam-4972	146	15	(	(	PUNCT
ejpam-4972	146	16	y	y	PROPN
ejpam-4972	146	17	,	,	PUNCT
ejpam-4972	146	18	σ1	σ1	PROPN
ejpam-4972	146	19	,	,	PUNCT
ejpam-4972	146	20	σ2	σ2	NOUN
ejpam-4972	146	21	)	)	PUNCT
ejpam-4972	146	22	is	be	AUX
ejpam-4972	146	23	fuzzy	fuzzy	ADJ
ejpam-4972	146	24	δj	δj	ADP
ejpam-4972	146	25	−	−	PROPN
ejpam-4972	146	26	conts	cont	NOUN
ejpam-4972	146	27	.	.	PUNCT
ejpam-4972	147	1	then	then	ADV
ejpam-4972	147	2	t	t	PROPN
ejpam-4972	147	3	is	be	AUX
ejpam-4972	147	4	(	(	PUNCT
ejpam-4972	147	5	i	i	PROPN
ejpam-4972	147	6	,	,	PUNCT
ejpam-4972	147	7	j	j	PROPN
ejpam-4972	147	8	)	)	PUNCT
ejpam-4972	147	9	−	−	PROPN
ejpam-4972	147	10	gψ	gψ	VERB
ejpam-4972	147	11	−	−	PROPN
ejpam-4972	147	12	conts	cont	NOUN
ejpam-4972	147	13	.	.	PUNCT
ejpam-4972	148	1	theorem	theorem	NOUN
ejpam-4972	148	2	4	4	NUM
ejpam-4972	148	3	.	.	PUNCT
ejpam-4972	149	1	suppose	suppose	VERB
ejpam-4972	149	2	t	t	NOUN
ejpam-4972	149	3	:	:	PUNCT
ejpam-4972	149	4	(	(	PUNCT
ejpam-4972	149	5	x	x	X
ejpam-4972	149	6	,	,	PUNCT
ejpam-4972	149	7	δ1	δ1	NOUN
ejpam-4972	149	8	,	,	PUNCT
ejpam-4972	149	9	δ2	δ2	ADJ
ejpam-4972	149	10	)	)	PUNCT
ejpam-4972	149	11	→	→	SYM
ejpam-4972	149	12	(	(	PUNCT
ejpam-4972	149	13	y	y	PROPN
ejpam-4972	149	14	,	,	PUNCT
ejpam-4972	149	15	σ1	σ1	PROPN
ejpam-4972	149	16	,	,	PUNCT
ejpam-4972	149	17	σ2	σ2	PROPN
ejpam-4972	149	18	)	)	PUNCT
ejpam-4972	149	19	is	be	AUX
ejpam-4972	149	20	injection	injection	NOUN
ejpam-4972	149	21	mapping	mapping	NOUN
ejpam-4972	149	22	.	.	PUNCT
ejpam-4972	150	1	hence	hence	ADV
ejpam-4972	150	2	the	the	DET
ejpam-4972	150	3	next	next	ADJ
ejpam-4972	150	4	statements	statement	NOUN
ejpam-4972	150	5	are	be	AUX
ejpam-4972	150	6	equivalent	equivalent	ADJ
ejpam-4972	150	7	:	:	PUNCT
ejpam-4972	150	8	a.	a.	NOUN
ejpam-4972	150	9	a.	a.	NOUN
ejpam-4972	150	10	alharbi	alharbi	PROPN
ejpam-4972	150	11	,	,	PUNCT
ejpam-4972	150	12	a.	a.	NOUN
ejpam-4972	150	13	kilicman	kilicman	PROPN
ejpam-4972	150	14	/	/	SYM
ejpam-4972	150	15	eur	eur	PROPN
ejpam-4972	150	16	.	.	PUNCT
ejpam-4972	151	1	j.	j.	PROPN
ejpam-4972	151	2	pure	pure	PROPN
ejpam-4972	151	3	appl	appl	PROPN
ejpam-4972	151	4	.	.	PROPN
ejpam-4972	151	5	math	math	PROPN
ejpam-4972	151	6	,	,	PUNCT
ejpam-4972	151	7	16	16	NUM
ejpam-4972	151	8	(	(	PUNCT
ejpam-4972	151	9	4	4	NUM
ejpam-4972	151	10	)	)	PUNCT
ejpam-4972	151	11	(	(	PUNCT
ejpam-4972	151	12	2023	2023	NUM
ejpam-4972	151	13	)	)	PUNCT
ejpam-4972	151	14	,	,	PUNCT
ejpam-4972	151	15	2613	2613	NUM
ejpam-4972	151	16	-	-	SYM
ejpam-4972	151	17	2631	2631	NUM
ejpam-4972	151	18	2619	2619	NUM
ejpam-4972	151	19	(	(	PUNCT
ejpam-4972	151	20	i	i	NOUN
ejpam-4972	151	21	)	)	PUNCT
ejpam-4972	151	22	t((i	t((i	PROPN
ejpam-4972	151	23	,	,	PUNCT
ejpam-4972	151	24	j)−	j)−	PROPN
ejpam-4972	151	25	gψ	gψ	VERB
ejpam-4972	151	26	−	−	NOUN
ejpam-4972	151	27	cl(e	cl(e	NUM
ejpam-4972	151	28	)	)	PUNCT
ejpam-4972	151	29	)	)	PUNCT
ejpam-4972	152	1	≤	≤	NUM
ejpam-4972	152	2	σj	σj	VERB
ejpam-4972	152	3	−	−	PROPN
ejpam-4972	152	4	cl(t(e	cl(t(e	NOUN
ejpam-4972	152	5	)	)	PUNCT
ejpam-4972	152	6	)	)	PUNCT
ejpam-4972	152	7	,	,	PUNCT
ejpam-4972	152	8	∀e	∀e	PROPN
ejpam-4972	152	9	∈	∈	NOUN
ejpam-4972	152	10	ix	ix	X
ejpam-4972	152	11	.	.	PUNCT
ejpam-4972	153	1	(	(	PUNCT
ejpam-4972	153	2	ii	ii	NOUN
ejpam-4972	153	3	)	)	PUNCT
ejpam-4972	153	4	(	(	PUNCT
ejpam-4972	153	5	i	i	PROPN
ejpam-4972	153	6	,	,	PUNCT
ejpam-4972	153	7	j)−	j)−	PROPN
ejpam-4972	153	8	gψ	gψ	VERB
ejpam-4972	153	9	−	−	PROPN
ejpam-4972	153	10	cl(t−1(f	cl(t−1(f	NOUN
ejpam-4972	153	11	)	)	PUNCT
ejpam-4972	153	12	)	)	PUNCT
ejpam-4972	154	1	≤	≤	PUNCT
ejpam-4972	155	1	t−1(σj	t−1(σj	ADP
ejpam-4972	155	2	−	−	PROPN
ejpam-4972	155	3	cl(f	cl(f	NOUN
ejpam-4972	155	4	)	)	PUNCT
ejpam-4972	155	5	)	)	PUNCT
ejpam-4972	155	6	,	,	PUNCT
ejpam-4972	155	7	∀f	∀f	PROPN
ejpam-4972	155	8	∈	∈	PROPN
ejpam-4972	155	9	iy	iy	INTJ
ejpam-4972	155	10	.	.	PUNCT
ejpam-4972	156	1	(	(	PUNCT
ejpam-4972	156	2	iii	iii	X
ejpam-4972	156	3	)	)	PUNCT
ejpam-4972	156	4	t−1(σj	t−1(σj	ADP
ejpam-4972	156	5	−	−	PROPN
ejpam-4972	156	6	int(f	int(f	PROPN
ejpam-4972	156	7	)	)	PUNCT
ejpam-4972	156	8	)	)	PUNCT
ejpam-4972	157	1	≤	≤	NOUN
ejpam-4972	157	2	(	(	PUNCT
ejpam-4972	157	3	i	i	PRON
ejpam-4972	157	4	,	,	PUNCT
ejpam-4972	157	5	j)−	j)−	PROPN
ejpam-4972	157	6	gψ	gψ	VERB
ejpam-4972	157	7	−	−	PROPN
ejpam-4972	157	8	int(t−1(f	int(t−1(f	PROPN
ejpam-4972	157	9	)	)	PUNCT
ejpam-4972	157	10	)	)	PUNCT
ejpam-4972	157	11	,	,	PUNCT
ejpam-4972	157	12	∀f	∀f	PROPN
ejpam-4972	157	13	∈	∈	PROPN
ejpam-4972	157	14	iy	iy	X
ejpam-4972	157	15	.	.	PUNCT
ejpam-4972	158	1	proof	proof	NOUN
ejpam-4972	158	2	.	.	PUNCT
ejpam-4972	159	1	(	(	PUNCT
ejpam-4972	159	2	i	i	NOUN
ejpam-4972	159	3	)	)	PUNCT
ejpam-4972	159	4	→	→	SYM
ejpam-4972	159	5	(	(	PUNCT
ejpam-4972	159	6	ii	ii	NOUN
ejpam-4972	159	7	)	)	PUNCT
ejpam-4972	159	8	suppose	suppose	VERB
ejpam-4972	160	1	f	f	PROPN
ejpam-4972	160	2	∈	∈	PROPN
ejpam-4972	160	3	iy	iy	PROPN
ejpam-4972	160	4	.	.	PUNCT
ejpam-4972	161	1	then	then	ADV
ejpam-4972	161	2	t−1(f	t−1(f	PROPN
ejpam-4972	161	3	)	)	PUNCT
ejpam-4972	161	4	∈	∈	PROPN
ejpam-4972	161	5	ix	ix	VERB
ejpam-4972	161	6	by	by	ADP
ejpam-4972	161	7	(	(	PUNCT
ejpam-4972	161	8	i	i	NOUN
ejpam-4972	161	9	)	)	PUNCT
ejpam-4972	161	10	we	we	PRON
ejpam-4972	161	11	find	find	VERB
ejpam-4972	161	12	t((i	t((i	NOUN
ejpam-4972	161	13	,	,	PUNCT
ejpam-4972	161	14	j)−	j)−	PROPN
ejpam-4972	161	15	gψ−	gψ−	PUNCT
ejpam-4972	161	16	cl(t−1(f	cl(t−1(f	PROPN
ejpam-4972	161	17	)	)	PUNCT
ejpam-4972	161	18	)	)	PUNCT
ejpam-4972	161	19	)	)	PUNCT
ejpam-4972	162	1	≤	≤	NUM
ejpam-4972	162	2	σj	σj	VERB
ejpam-4972	162	3	−	−	PROPN
ejpam-4972	162	4	cl(t(t−1(f	cl(t(t−1(f	PROPN
ejpam-4972	162	5	)	)	PUNCT
ejpam-4972	162	6	)	)	PUNCT
ejpam-4972	162	7	)	)	PUNCT
ejpam-4972	163	1	≤	≤	NUM
ejpam-4972	163	2	σj	σj	VERB
ejpam-4972	163	3	−	−	PROPN
ejpam-4972	163	4	cl(f	cl(f	PROPN
ejpam-4972	163	5	)	)	PUNCT
ejpam-4972	163	6	.	.	PUNCT
ejpam-4972	164	1	so	so	ADV
ejpam-4972	164	2	,	,	PUNCT
ejpam-4972	164	3	(	(	PUNCT
ejpam-4972	164	4	i	i	PROPN
ejpam-4972	164	5	,	,	PUNCT
ejpam-4972	164	6	j)−	j)−	PROPN
ejpam-4972	164	7	gψ	gψ	VERB
ejpam-4972	164	8	−	−	PROPN
ejpam-4972	164	9	cl(t−1(f	cl(t−1(f	NOUN
ejpam-4972	164	10	)	)	PUNCT
ejpam-4972	164	11	)	)	PUNCT
ejpam-4972	165	1	≤	≤	PUNCT
ejpam-4972	166	1	t−1(σj	t−1(σj	ADP
ejpam-4972	166	2	−	−	PROPN
ejpam-4972	166	3	cl(f	cl(f	NOUN
ejpam-4972	166	4	)	)	PUNCT
ejpam-4972	166	5	)	)	PUNCT
ejpam-4972	166	6	.	.	PUNCT
ejpam-4972	167	1	(	(	PUNCT
ejpam-4972	167	2	ii	ii	NOUN
ejpam-4972	167	3	)	)	PUNCT
ejpam-4972	167	4	→	→	SYM
ejpam-4972	167	5	(	(	PUNCT
ejpam-4972	167	6	iii	iii	X
ejpam-4972	167	7	)	)	PUNCT
ejpam-4972	167	8	suppose	suppose	VERB
ejpam-4972	167	9	f	f	PROPN
ejpam-4972	167	10	∈	∈	PROPN
ejpam-4972	167	11	iy	iy	PROPN
ejpam-4972	167	12	.	.	PUNCT
ejpam-4972	168	1	by	by	ADP
ejpam-4972	168	2	(	(	PUNCT
ejpam-4972	168	3	ii	ii	NOUN
ejpam-4972	168	4	)	)	PUNCT
ejpam-4972	168	5	(	(	PUNCT
ejpam-4972	168	6	i	i	PROPN
ejpam-4972	168	7	,	,	PUNCT
ejpam-4972	168	8	j	j	PROPN
ejpam-4972	168	9	)	)	PUNCT
ejpam-4972	168	10	−	−	PROPN
ejpam-4972	168	11	gψ	gψ	VERB
ejpam-4972	168	12	−	−	PROPN
ejpam-4972	168	13	cl(t−1(f	cl(t−1(f	NOUN
ejpam-4972	168	14	)	)	PUNCT
ejpam-4972	168	15	)	)	PUNCT
ejpam-4972	169	1	≤	≤	PUNCT
ejpam-4972	170	1	t−1(σj	t−1(σj	ADP
ejpam-4972	170	2	−	−	NOUN
ejpam-4972	170	3	cl(e	cl(e	NUM
ejpam-4972	170	4	)	)	PUNCT
ejpam-4972	170	5	)	)	PUNCT
ejpam-4972	170	6	.	.	PUNCT
ejpam-4972	171	1	after	after	ADP
ejpam-4972	171	2	that	that	PRON
ejpam-4972	171	3	(	(	PUNCT
ejpam-4972	171	4	t−1(σj	t−1(σj	ADP
ejpam-4972	171	5	−	−	PROPN
ejpam-4972	171	6	cl(e)))c	cl(e)))c	ADJ
ejpam-4972	171	7	≤	≤	X
ejpam-4972	171	8	(	(	PUNCT
ejpam-4972	171	9	(	(	PUNCT
ejpam-4972	171	10	i	i	NOUN
ejpam-4972	171	11	,	,	PUNCT
ejpam-4972	171	12	j)−	j)−	PROPN
ejpam-4972	171	13	gψ	gψ	VERB
ejpam-4972	171	14	−	−	NOUN
ejpam-4972	171	15	cl(t−1(e)))c	cl(t−1(e)))c	PROPN
ejpam-4972	171	16	,	,	PUNCT
ejpam-4972	171	17	and	and	CCONJ
ejpam-4972	171	18	hence	hence	ADV
ejpam-4972	171	19	t−1(σj	t−1(σj	ADP
ejpam-4972	171	20	−	−	PROPN
ejpam-4972	171	21	int(e)c	int(e)c	NOUN
ejpam-4972	171	22	)	)	PUNCT
ejpam-4972	171	23	≤	≤	NOUN
ejpam-4972	171	24	(	(	PUNCT
ejpam-4972	171	25	i	i	NOUN
ejpam-4972	171	26	,	,	PUNCT
ejpam-4972	171	27	j)−	j)−	PROPN
ejpam-4972	171	28	gψ	gψ	VERB
ejpam-4972	171	29	−	−	PROPN
ejpam-4972	171	30	int(t−1(e)c	int(t−1(e)c	PROPN
ejpam-4972	171	31	)	)	PUNCT
ejpam-4972	171	32	.	.	PUNCT
ejpam-4972	172	1	(	(	PUNCT
ejpam-4972	172	2	iii	iii	NOUN
ejpam-4972	172	3	)	)	PUNCT
ejpam-4972	172	4	→	→	SYM
ejpam-4972	172	5	(	(	PUNCT
ejpam-4972	172	6	i	i	NOUN
ejpam-4972	172	7	)	)	PUNCT
ejpam-4972	172	8	suppose	suppose	VERB
ejpam-4972	172	9	e	e	X
ejpam-4972	172	10	∈	∈	PROPN
ejpam-4972	172	11	ix	ix	ADV
ejpam-4972	172	12	.	.	PUNCT
ejpam-4972	173	1	then	then	ADV
ejpam-4972	173	2	t(e	t(e	X
ejpam-4972	173	3	)	)	PUNCT
ejpam-4972	174	1	∈	∈	PROPN
ejpam-4972	174	2	iy	iy	PROPN
ejpam-4972	174	3	by	by	ADP
ejpam-4972	174	4	(	(	PUNCT
ejpam-4972	174	5	iii	iii	X
ejpam-4972	174	6	)	)	PUNCT
ejpam-4972	174	7	t−1(σj	t−1(σj	ADP
ejpam-4972	174	8	−	−	PROPN
ejpam-4972	174	9	int(t(e	int(t(e	NOUN
ejpam-4972	174	10	)	)	PUNCT
ejpam-4972	174	11	)	)	PUNCT
ejpam-4972	174	12	≤	≤	NOUN
ejpam-4972	174	13	(	(	PUNCT
ejpam-4972	174	14	i	i	PRON
ejpam-4972	174	15	,	,	PUNCT
ejpam-4972	174	16	j	j	PROPN
ejpam-4972	174	17	)	)	PUNCT
ejpam-4972	174	18	−	−	PROPN
ejpam-4972	174	19	gψ	gψ	VERB
ejpam-4972	174	20	−	−	PROPN
ejpam-4972	174	21	int(t−1(t(e	int(t−1(t(e	PROPN
ejpam-4972	174	22	)	)	PUNCT
ejpam-4972	174	23	)	)	PUNCT
ejpam-4972	174	24	.	.	PUNCT
ejpam-4972	175	1	as	as	SCONJ
ejpam-4972	175	2	t	t	PROPN
ejpam-4972	175	3	is	be	AUX
ejpam-4972	175	4	injection	injection	NOUN
ejpam-4972	175	5	then	then	ADV
ejpam-4972	175	6	,	,	PUNCT
ejpam-4972	175	7	t−1(σj	t−1(σj	ADP
ejpam-4972	176	1	−	−	PROPN
ejpam-4972	176	2	int(t(e	int(t(e	NOUN
ejpam-4972	176	3	)	)	PUNCT
ejpam-4972	176	4	)	)	PUNCT
ejpam-4972	177	1	≤	≤	NOUN
ejpam-4972	177	2	(	(	PUNCT
ejpam-4972	177	3	i	i	PRON
ejpam-4972	177	4	,	,	PUNCT
ejpam-4972	177	5	j	j	PROPN
ejpam-4972	177	6	)	)	PUNCT
ejpam-4972	177	7	−	−	PROPN
ejpam-4972	177	8	gψ	gψ	VERB
ejpam-4972	177	9	−	−	PROPN
ejpam-4972	177	10	int(e	int(e	PROPN
ejpam-4972	177	11	)	)	PUNCT
ejpam-4972	177	12	.	.	PUNCT
ejpam-4972	178	1	after	after	ADP
ejpam-4972	178	2	that	that	PRON
ejpam-4972	178	3	(	(	PUNCT
ejpam-4972	178	4	i	i	NOUN
ejpam-4972	178	5	,	,	PUNCT
ejpam-4972	178	6	j)−	j)−	PROPN
ejpam-4972	178	7	gψ−	gψ−	PUNCT
ejpam-4972	178	8	cl((e)c	cl((e)c	PROPN
ejpam-4972	178	9	)	)	PUNCT
ejpam-4972	178	10	≤	≤	PUNCT
ejpam-4972	179	1	t−1(σj	t−1(σj	ADP
ejpam-4972	179	2	−	−	PROPN
ejpam-4972	179	3	cl(t(e)c	cl(t(e)c	NOUN
ejpam-4972	179	4	)	)	PUNCT
ejpam-4972	179	5	.	.	PUNCT
ejpam-4972	180	1	so	so	ADV
ejpam-4972	180	2	,	,	PUNCT
ejpam-4972	180	3	t((i	t((i	PROPN
ejpam-4972	180	4	,	,	PUNCT
ejpam-4972	180	5	j)−	j)−	PROPN
ejpam-4972	180	6	gψ−	gψ−	PUNCT
ejpam-4972	180	7	cl((e)c	cl((e)c	PROPN
ejpam-4972	180	8	)	)	PUNCT
ejpam-4972	180	9	)	)	PUNCT
ejpam-4972	180	10	≤	≤	NUM
ejpam-4972	180	11	t(t−1(σj	t(t−1(σj	ADP
ejpam-4972	180	12	−	−	PROPN
ejpam-4972	180	13	cl(t(e)c	cl(t(e)c	NOUN
ejpam-4972	180	14	)	)	PUNCT
ejpam-4972	180	15	)	)	PUNCT
ejpam-4972	181	1	≤	≤	NUM
ejpam-4972	181	2	σj	σj	VERB
ejpam-4972	181	3	−	−	PROPN
ejpam-4972	181	4	cl(t(e)c	cl(t(e)c	NOUN
ejpam-4972	181	5	)	)	PUNCT
ejpam-4972	181	6	.	.	PUNCT
ejpam-4972	182	1	theorem	theorem	NOUN
ejpam-4972	182	2	5	5	NUM
ejpam-4972	182	3	.	.	PUNCT
ejpam-4972	183	1	suppose	suppose	VERB
ejpam-4972	183	2	t	t	NOUN
ejpam-4972	183	3	:	:	PUNCT
ejpam-4972	183	4	(	(	PUNCT
ejpam-4972	183	5	x	x	X
ejpam-4972	183	6	,	,	PUNCT
ejpam-4972	183	7	δ1	δ1	NOUN
ejpam-4972	183	8	,	,	PUNCT
ejpam-4972	183	9	δ2	δ2	ADJ
ejpam-4972	183	10	)	)	PUNCT
ejpam-4972	183	11	→	→	SYM
ejpam-4972	183	12	(	(	PUNCT
ejpam-4972	183	13	y	y	PROPN
ejpam-4972	183	14	,	,	PUNCT
ejpam-4972	183	15	σ1	σ1	PROPN
ejpam-4972	183	16	,	,	PUNCT
ejpam-4972	183	17	σ2	σ2	NOUN
ejpam-4972	183	18	)	)	PUNCT
ejpam-4972	183	19	is	be	AUX
ejpam-4972	183	20	fuzzy	fuzzy	ADJ
ejpam-4972	183	21	(	(	PUNCT
ejpam-4972	183	22	i	i	PROPN
ejpam-4972	183	23	,	,	PUNCT
ejpam-4972	183	24	j	j	PROPN
ejpam-4972	183	25	)	)	PUNCT
ejpam-4972	183	26	−	−	PROPN
ejpam-4972	183	27	gψ	gψ	VERB
ejpam-4972	183	28	−	−	PROPN
ejpam-4972	183	29	conts	cont	NOUN
ejpam-4972	183	30	.	.	PUNCT
ejpam-4972	184	1	hence	hence	ADV
ejpam-4972	184	2	t((i	t((i	PROPN
ejpam-4972	184	3	,	,	PUNCT
ejpam-4972	184	4	j)−	j)−	PROPN
ejpam-4972	184	5	gψ	gψ	VERB
ejpam-4972	184	6	−	−	NOUN
ejpam-4972	184	7	cl(e	cl(e	NUM
ejpam-4972	184	8	)	)	PUNCT
ejpam-4972	184	9	)	)	PUNCT
ejpam-4972	185	1	≤	≤	NUM
ejpam-4972	185	2	σj	σj	VERB
ejpam-4972	185	3	−	−	PROPN
ejpam-4972	185	4	cl(t(e	cl(t(e	NOUN
ejpam-4972	185	5	)	)	PUNCT
ejpam-4972	185	6	)	)	PUNCT
ejpam-4972	185	7	,	,	PUNCT
ejpam-4972	185	8	for	for	ADP
ejpam-4972	185	9	each	each	DET
ejpam-4972	185	10	e	e	NOUN
ejpam-4972	185	11	∈	∈	PROPN
ejpam-4972	185	12	ix	ix	ADV
ejpam-4972	185	13	.	.	PUNCT
ejpam-4972	186	1	proof	proof	NOUN
ejpam-4972	186	2	.	.	PUNCT
ejpam-4972	187	1	assume	assume	VERB
ejpam-4972	187	2	t	t	PROPN
ejpam-4972	187	3	is	be	AUX
ejpam-4972	187	4	fuzzy	fuzzy	ADJ
ejpam-4972	187	5	(	(	PUNCT
ejpam-4972	187	6	i	i	NOUN
ejpam-4972	187	7	,	,	PUNCT
ejpam-4972	187	8	j)−gψ−	j)−gψ−	PROPN
ejpam-4972	187	9	conts	cont	NOUN
ejpam-4972	187	10	and	and	CCONJ
ejpam-4972	187	11	e	e	NOUN
ejpam-4972	187	12	∈	∈	PROPN
ejpam-4972	187	13	ix	ix	ADV
ejpam-4972	187	14	.	.	PUNCT
ejpam-4972	188	1	then	then	ADV
ejpam-4972	188	2	e	e	X
ejpam-4972	188	3	≤	≤	ADV
ejpam-4972	188	4	t−1(σj−	t−1(σj−	PROPN
ejpam-4972	188	5	cl(t(e	cl(t(e	NOUN
ejpam-4972	188	6	)	)	PUNCT
ejpam-4972	188	7	)	)	PUNCT
ejpam-4972	188	8	)	)	PUNCT
ejpam-4972	188	9	.	.	PUNCT
ejpam-4972	189	1	as	as	SCONJ
ejpam-4972	189	2	σj	σj	ADP
ejpam-4972	189	3	−	−	PROPN
ejpam-4972	189	4	cl(t(e	cl(t(e	NOUN
ejpam-4972	189	5	)	)	PUNCT
ejpam-4972	189	6	)	)	PUNCT
ejpam-4972	190	1	∈	∈	PROPN
ejpam-4972	190	2	fc(y	fc(y	NOUN
ejpam-4972	190	3	,	,	PUNCT
ejpam-4972	190	4	σj	σj	NOUN
ejpam-4972	190	5	)	)	PUNCT
ejpam-4972	190	6	,	,	PUNCT
ejpam-4972	190	7	t	t	PROPN
ejpam-4972	190	8	is	be	AUX
ejpam-4972	190	9	fuzzy	fuzzy	ADJ
ejpam-4972	190	10	(	(	PUNCT
ejpam-4972	190	11	i	i	NOUN
ejpam-4972	190	12	,	,	PUNCT
ejpam-4972	190	13	j)−	j)−	PROPN
ejpam-4972	190	14	gψ−	gψ−	PUNCT
ejpam-4972	190	15	conts	cont	NOUN
ejpam-4972	190	16	,	,	PUNCT
ejpam-4972	190	17	thus	thus	ADV
ejpam-4972	190	18	t−1(σj	t−1(σj	ADP
ejpam-4972	190	19	−	−	PROPN
ejpam-4972	190	20	cl(t(e	cl(t(e	NOUN
ejpam-4972	190	21	)	)	PUNCT
ejpam-4972	190	22	)	)	PUNCT
ejpam-4972	190	23	)	)	PUNCT
ejpam-4972	191	1	is	be	AUX
ejpam-4972	191	2	fuzzy	fuzzy	ADJ
ejpam-4972	191	3	(	(	PUNCT
ejpam-4972	191	4	i	i	PROPN
ejpam-4972	191	5	,	,	PUNCT
ejpam-4972	191	6	j)−gψ−cld	j)−gψ−cld	PROPN
ejpam-4972	191	7	of	of	ADP
ejpam-4972	191	8	x	x	PRON
ejpam-4972	191	9	,	,	PUNCT
ejpam-4972	191	10	so	so	CCONJ
ejpam-4972	191	11	(	(	PUNCT
ejpam-4972	191	12	i	i	NOUN
ejpam-4972	191	13	,	,	PUNCT
ejpam-4972	191	14	j)−gψ−cl(e	j)−gψ−cl(e	ADJ
ejpam-4972	191	15	)	)	PUNCT
ejpam-4972	191	16	≤	≤	NOUN
ejpam-4972	191	17	t−1(σj−cl(t(e	t−1(σj−cl(t(e	PROPN
ejpam-4972	191	18	)	)	PUNCT
ejpam-4972	191	19	)	)	PUNCT
ejpam-4972	191	20	)	)	PUNCT
ejpam-4972	191	21	.	.	PUNCT
ejpam-4972	192	1	so	so	ADV
ejpam-4972	192	2	,	,	PUNCT
ejpam-4972	192	3	t((i	t((i	NOUN
ejpam-4972	192	4	,	,	PUNCT
ejpam-4972	192	5	j)−gψ−cl(e	j)−gψ−cl(e	NOUN
ejpam-4972	192	6	)	)	PUNCT
ejpam-4972	192	7	)	)	PUNCT
ejpam-4972	192	8	≤	≤	NUM
ejpam-4972	192	9	σj	σj	VERB
ejpam-4972	192	10	−	−	PROPN
ejpam-4972	192	11	cl(t(e	cl(t(e	NOUN
ejpam-4972	192	12	)	)	PUNCT
ejpam-4972	192	13	)	)	PUNCT
ejpam-4972	192	14	.	.	PUNCT
ejpam-4972	193	1	remark	remark	PROPN
ejpam-4972	193	2	5	5	NUM
ejpam-4972	193	3	.	.	PUNCT
ejpam-4972	194	1	(	(	PUNCT
ejpam-4972	194	2	1	1	X
ejpam-4972	194	3	)	)	PUNCT
ejpam-4972	194	4	if	if	SCONJ
ejpam-4972	194	5	t	t	PROPN
ejpam-4972	194	6	is	be	AUX
ejpam-4972	194	7	an	an	DET
ejpam-4972	194	8	injective	injective	ADJ
ejpam-4972	194	9	and	and	CCONJ
ejpam-4972	194	10	fuzzy	fuzzy	ADJ
ejpam-4972	194	11	(	(	PUNCT
ejpam-4972	194	12	i	i	PROPN
ejpam-4972	194	13	,	,	PUNCT
ejpam-4972	194	14	j	j	PROPN
ejpam-4972	194	15	)	)	PUNCT
ejpam-4972	194	16	−	−	PROPN
ejpam-4972	194	17	gψ	gψ	VERB
ejpam-4972	194	18	−	−	PROPN
ejpam-4972	194	19	conts	cont	NOUN
ejpam-4972	194	20	mapping	mapping	NOUN
ejpam-4972	194	21	.	.	PUNCT
ejpam-4972	195	1	then	then	ADV
ejpam-4972	195	2	any	any	DET
ejpam-4972	195	3	statement	statement	NOUN
ejpam-4972	195	4	of	of	ADP
ejpam-4972	195	5	theorem	theorem	NOUN
ejpam-4972	195	6	4	4	NUM
ejpam-4972	195	7	is	be	AUX
ejpam-4972	195	8	hold	hold	VERB
ejpam-4972	195	9	in	in	ADP
ejpam-4972	195	10	theorem	theorem	NOUN
ejpam-4972	195	11	5	5	NUM
ejpam-4972	195	12	since	since	SCONJ
ejpam-4972	195	13	they	they	PRON
ejpam-4972	195	14	are	be	AUX
ejpam-4972	195	15	equivalent	equivalent	ADJ
ejpam-4972	195	16	.	.	PUNCT
ejpam-4972	196	1	(	(	PUNCT
ejpam-4972	196	2	2	2	X
ejpam-4972	196	3	)	)	PUNCT
ejpam-4972	196	4	the	the	DET
ejpam-4972	196	5	converse	converse	NOUN
ejpam-4972	196	6	of	of	ADP
ejpam-4972	196	7	theorem	theorem	ADJ
ejpam-4972	196	8	5	5	NUM
ejpam-4972	196	9	,	,	PUNCT
ejpam-4972	196	10	corollary	corollary	ADJ
ejpam-4972	196	11	5	5	NUM
ejpam-4972	196	12	is	be	AUX
ejpam-4972	196	13	incorrect	incorrect	ADJ
ejpam-4972	196	14	because	because	SCONJ
ejpam-4972	196	15	if	if	SCONJ
ejpam-4972	196	16	we	we	PRON
ejpam-4972	196	17	have	have	VERB
ejpam-4972	196	18	a	a	DET
ejpam-4972	196	19	fuzzy	fuzzy	ADJ
ejpam-4972	196	20	set	set	VERB
ejpam-4972	196	21	f	f	PROPN
ejpam-4972	196	22	∈	∈	PROPN
ejpam-4972	196	23	fσj	fσj	NOUN
ejpam-4972	196	24	,	,	PUNCT
ejpam-4972	196	25	then	then	ADV
ejpam-4972	196	26	by	by	ADP
ejpam-4972	196	27	(	(	PUNCT
ejpam-4972	196	28	ii	ii	NOUN
ejpam-4972	196	29	)	)	PUNCT
ejpam-4972	196	30	for	for	ADP
ejpam-4972	196	31	example	example	NOUN
ejpam-4972	196	32	in	in	ADP
ejpam-4972	196	33	theorem	theorem	NOUN
ejpam-4972	196	34	4	4	NUM
ejpam-4972	196	35	we	we	PRON
ejpam-4972	196	36	find	find	VERB
ejpam-4972	196	37	(	(	PUNCT
ejpam-4972	196	38	i	i	PROPN
ejpam-4972	196	39	,	,	PUNCT
ejpam-4972	196	40	j	j	PROPN
ejpam-4972	196	41	)	)	PUNCT
ejpam-4972	196	42	−	−	PROPN
ejpam-4972	196	43	gψ	gψ	VERB
ejpam-4972	196	44	−	−	PROPN
ejpam-4972	196	45	cl(t−1(f	cl(t−1(f	NOUN
ejpam-4972	196	46	)	)	PUNCT
ejpam-4972	196	47	)	)	PUNCT
ejpam-4972	197	1	=	=	SYM
ejpam-4972	197	2	t−1((f	t−1((f	INTJ
ejpam-4972	197	3	)	)	PUNCT
ejpam-4972	197	4	)	)	PUNCT
ejpam-4972	198	1	but	but	CCONJ
ejpam-4972	198	2	t−1((f	t−1((f	INTJ
ejpam-4972	198	3	)	)	PUNCT
ejpam-4972	198	4	)	)	PUNCT
ejpam-4972	198	5	is	be	AUX
ejpam-4972	198	6	not	not	PART
ejpam-4972	198	7	fuzzy	fuzzy	ADJ
ejpam-4972	198	8	(	(	PUNCT
ejpam-4972	198	9	i	i	PROPN
ejpam-4972	198	10	,	,	PUNCT
ejpam-4972	198	11	j)−	j)−	PROPN
ejpam-4972	198	12	gψ	gψ	VERB
ejpam-4972	198	13	−	−	PROPN
ejpam-4972	198	14	cld	cld	NOUN
ejpam-4972	198	15	group	group	NOUN
ejpam-4972	198	16	in	in	ADP
ejpam-4972	198	17	x.	x.	PROPN
ejpam-4972	198	18	theorem	theorem	VERB
ejpam-4972	198	19	6	6	NUM
ejpam-4972	198	20	.	.	PUNCT
ejpam-4972	199	1	suppose	suppose	VERB
ejpam-4972	199	2	t	t	NOUN
ejpam-4972	199	3	:	:	PUNCT
ejpam-4972	199	4	(	(	PUNCT
ejpam-4972	199	5	x	x	X
ejpam-4972	199	6	,	,	PUNCT
ejpam-4972	199	7	δ1	δ1	NOUN
ejpam-4972	199	8	,	,	PUNCT
ejpam-4972	199	9	δ2	δ2	ADJ
ejpam-4972	199	10	)	)	PUNCT
ejpam-4972	199	11	→	→	SYM
ejpam-4972	199	12	(	(	PUNCT
ejpam-4972	199	13	y	y	PROPN
ejpam-4972	199	14	,	,	PUNCT
ejpam-4972	199	15	σ1	σ1	PROPN
ejpam-4972	199	16	,	,	PUNCT
ejpam-4972	199	17	σ2	σ2	NOUN
ejpam-4972	199	18	)	)	PUNCT
ejpam-4972	199	19	,	,	PUNCT
ejpam-4972	199	20	g	g	NOUN
ejpam-4972	199	21	:	:	PUNCT
ejpam-4972	199	22	(	(	PUNCT
ejpam-4972	199	23	y	y	PROPN
ejpam-4972	199	24	,	,	PUNCT
ejpam-4972	199	25	σ1	σ1	PROPN
ejpam-4972	199	26	,	,	PUNCT
ejpam-4972	199	27	σ2	σ2	NOUN
ejpam-4972	199	28	)	)	PUNCT
ejpam-4972	199	29	→	→	SYM
ejpam-4972	199	30	(	(	PUNCT
ejpam-4972	199	31	z	z	NOUN
ejpam-4972	199	32	,	,	PUNCT
ejpam-4972	199	33	η1	η1	NOUN
ejpam-4972	199	34	,	,	PUNCT
ejpam-4972	199	35	η2	η2	PROPN
ejpam-4972	199	36	)	)	PUNCT
ejpam-4972	199	37	are	be	AUX
ejpam-4972	199	38	fuzzy	fuzzy	ADJ
ejpam-4972	199	39	(	(	PUNCT
ejpam-4972	199	40	i	i	PROPN
ejpam-4972	199	41	,	,	PUNCT
ejpam-4972	199	42	j)−	j)−	PROPN
ejpam-4972	199	43	gψ	gψ	VERB
ejpam-4972	199	44	−	−	PROPN
ejpam-4972	199	45	conts	cont	NOUN
ejpam-4972	199	46	,	,	PUNCT
ejpam-4972	199	47	hence	hence	ADV
ejpam-4972	199	48	g	g	PROPN
ejpam-4972	199	49	◦	◦	NOUN
ejpam-4972	199	50	t	t	PROPN
ejpam-4972	199	51	:	:	PUNCT
ejpam-4972	199	52	(	(	PUNCT
ejpam-4972	199	53	x	x	X
ejpam-4972	199	54	,	,	PUNCT
ejpam-4972	199	55	δ1	δ1	NOUN
ejpam-4972	199	56	,	,	PUNCT
ejpam-4972	199	57	δ2	δ2	ADJ
ejpam-4972	199	58	)	)	PUNCT
ejpam-4972	199	59	→	→	SYM
ejpam-4972	199	60	(	(	PUNCT
ejpam-4972	199	61	z	z	NOUN
ejpam-4972	199	62	,	,	PUNCT
ejpam-4972	199	63	η1	η1	NOUN
ejpam-4972	199	64	,	,	PUNCT
ejpam-4972	199	65	η2	η2	PROPN
ejpam-4972	199	66	)	)	PUNCT
ejpam-4972	199	67	is	be	AUX
ejpam-4972	199	68	not	not	PART
ejpam-4972	199	69	fuzzy	fuzzy	ADJ
ejpam-4972	199	70	(	(	PUNCT
ejpam-4972	199	71	i	i	PROPN
ejpam-4972	199	72	,	,	PUNCT
ejpam-4972	199	73	j)−	j)−	PROPN
ejpam-4972	199	74	gψ	gψ	VERB
ejpam-4972	199	75	−	−	PROPN
ejpam-4972	199	76	conts	cont	NOUN
ejpam-4972	199	77	.	.	PUNCT
ejpam-4972	200	1	we	we	PRON
ejpam-4972	200	2	show	show	VERB
ejpam-4972	200	3	that	that	SCONJ
ejpam-4972	200	4	if	if	SCONJ
ejpam-4972	200	5	the	the	DET
ejpam-4972	200	6	functions	function	NOUN
ejpam-4972	200	7	t	t	NOUN
ejpam-4972	200	8	with	with	ADP
ejpam-4972	200	9	g	g	PROPN
ejpam-4972	200	10	are	be	AUX
ejpam-4972	200	11	fuzzy	fuzzy	ADJ
ejpam-4972	200	12	(	(	PUNCT
ejpam-4972	200	13	i	i	PROPN
ejpam-4972	200	14	,	,	PUNCT
ejpam-4972	200	15	j	j	PROPN
ejpam-4972	200	16	)	)	PUNCT
ejpam-4972	200	17	−	−	PROPN
ejpam-4972	200	18	gα	gα	ADP
ejpam-4972	200	19	−	−	PROPN
ejpam-4972	200	20	conts	cont	NOUN
ejpam-4972	200	21	by	by	ADP
ejpam-4972	200	22	the	the	DET
ejpam-4972	200	23	coming	come	VERB
ejpam-4972	200	24	example	example	NOUN
ejpam-4972	200	25	:	:	PUNCT
ejpam-4972	200	26	example	example	NOUN
ejpam-4972	200	27	6	6	NUM
ejpam-4972	200	28	.	.	PUNCT
ejpam-4972	200	29	suppose	suppose	VERB
ejpam-4972	200	30	e	e	NOUN
ejpam-4972	200	31	,	,	PUNCT
ejpam-4972	200	32	f	f	PROPN
ejpam-4972	200	33	,	,	PUNCT
ejpam-4972	200	34	and	and	CCONJ
ejpam-4972	200	35	g	g	NOUN
ejpam-4972	200	36	are	be	AUX
ejpam-4972	200	37	fuzzy	fuzzy	ADJ
ejpam-4972	200	38	subgroups	subgroup	NOUN
ejpam-4972	200	39	of	of	ADP
ejpam-4972	200	40	x	x	SYM
ejpam-4972	200	41	=	=	X
ejpam-4972	200	42	{	{	PUNCT
ejpam-4972	200	43	a	a	DET
ejpam-4972	200	44	,	,	PUNCT
ejpam-4972	200	45	b	b	NOUN
ejpam-4972	200	46	}	}	PUNCT
ejpam-4972	200	47	known	know	VERB
ejpam-4972	200	48	as	as	ADP
ejpam-4972	200	49	:	:	PUNCT
ejpam-4972	200	50	e(a	e(a	NOUN
ejpam-4972	200	51	,	,	PUNCT
ejpam-4972	200	52	b	b	X
ejpam-4972	200	53	)	)	PUNCT
ejpam-4972	200	54	=	=	PUNCT
ejpam-4972	200	55	{	{	PUNCT
ejpam-4972	200	56	0.3	0.3	NUM
ejpam-4972	200	57	,	,	PUNCT
ejpam-4972	200	58	0.4	0.4	NUM
ejpam-4972	200	59	}	}	PUNCT
ejpam-4972	200	60	,	,	PUNCT
ejpam-4972	200	61	f	f	PROPN
ejpam-4972	200	62	(	(	PUNCT
ejpam-4972	200	63	a	a	DET
ejpam-4972	200	64	,	,	PUNCT
ejpam-4972	200	65	b	b	NOUN
ejpam-4972	200	66	)	)	PUNCT
ejpam-4972	200	67	=	=	SYM
ejpam-4972	200	68	{	{	PUNCT
ejpam-4972	200	69	0.4	0.4	NUM
ejpam-4972	200	70	,	,	PUNCT
ejpam-4972	200	71	0.5	0.5	NUM
ejpam-4972	200	72	}	}	PUNCT
ejpam-4972	200	73	,	,	PUNCT
ejpam-4972	200	74	g(a	g(a	PROPN
ejpam-4972	200	75	,	,	PUNCT
ejpam-4972	200	76	b	b	NOUN
ejpam-4972	200	77	)	)	PUNCT
ejpam-4972	200	78	=	=	SYM
ejpam-4972	200	79	{	{	PUNCT
ejpam-4972	200	80	0.4	0.4	NUM
ejpam-4972	200	81	,	,	PUNCT
ejpam-4972	200	82	0.4	0.4	NUM
ejpam-4972	200	83	}	}	PUNCT
ejpam-4972	200	84	.	.	PUNCT
ejpam-4972	201	1	consider	consider	VERB
ejpam-4972	201	2	the	the	DET
ejpam-4972	201	3	fuzzy	fuzzy	ADJ
ejpam-4972	201	4	bitopology	bitopology	NOUN
ejpam-4972	201	5	δ1	δ1	NOUN
ejpam-4972	201	6	=	=	PUNCT
ejpam-4972	201	7	{	{	PUNCT
ejpam-4972	201	8	0	0	NUM
ejpam-4972	201	9	,	,	PUNCT
ejpam-4972	201	10	1	1	NUM
ejpam-4972	201	11	,	,	PUNCT
ejpam-4972	201	12	e	e	NOUN
ejpam-4972	201	13	}	}	PUNCT
ejpam-4972	201	14	also	also	ADV
ejpam-4972	201	15	δ2	δ2	VERB
ejpam-4972	201	16	=	=	SYM
ejpam-4972	201	17	{	{	PUNCT
ejpam-4972	201	18	0	0	NUM
ejpam-4972	201	19	,	,	PUNCT
ejpam-4972	201	20	1	1	NUM
ejpam-4972	201	21	,	,	PUNCT
ejpam-4972	201	22	f	f	X
ejpam-4972	201	23	,	,	PUNCT
ejpam-4972	201	24	g	g	NOUN
ejpam-4972	201	25	}	}	PUNCT
ejpam-4972	201	26	on	on	ADP
ejpam-4972	201	27	x.	x.	NOUN
ejpam-4972	201	28	suppose	suppose	VERB
ejpam-4972	201	29	n	n	ADP
ejpam-4972	201	30	with	with	ADP
ejpam-4972	201	31	m	m	PROPN
ejpam-4972	201	32	are	be	AUX
ejpam-4972	201	33	fuzzy	fuzzy	ADJ
ejpam-4972	201	34	subgroups	subgroup	NOUN
ejpam-4972	201	35	of	of	ADP
ejpam-4972	201	36	y	y	PROPN
ejpam-4972	201	37	=	=	PUNCT
ejpam-4972	201	38	{	{	PUNCT
ejpam-4972	201	39	r	r	NOUN
ejpam-4972	201	40	,	,	PUNCT
ejpam-4972	201	41	h	h	NOUN
ejpam-4972	201	42	}	}	PUNCT
ejpam-4972	201	43	defined	define	VERB
ejpam-4972	201	44	as	as	ADP
ejpam-4972	201	45	:	:	PUNCT
ejpam-4972	201	46	n(r	n(r	NOUN
ejpam-4972	201	47	,	,	PUNCT
ejpam-4972	201	48	h	h	NOUN
ejpam-4972	201	49	)	)	PUNCT
ejpam-4972	201	50	=	=	SYM
ejpam-4972	201	51	{	{	PUNCT
ejpam-4972	201	52	0.5	0.5	NUM
ejpam-4972	201	53	,	,	PUNCT
ejpam-4972	201	54	0.4	0.4	NUM
ejpam-4972	201	55	}	}	PUNCT
ejpam-4972	201	56	,	,	PUNCT
ejpam-4972	201	57	m(r	m(r	PROPN
ejpam-4972	201	58	,	,	PUNCT
ejpam-4972	201	59	h	h	NOUN
ejpam-4972	201	60	)	)	PUNCT
ejpam-4972	201	61	=	=	SYM
ejpam-4972	201	62	{	{	PUNCT
ejpam-4972	201	63	0.5	0.5	NUM
ejpam-4972	201	64	,	,	PUNCT
ejpam-4972	201	65	0.5	0.5	NUM
ejpam-4972	201	66	}	}	PUNCT
ejpam-4972	201	67	.	.	PUNCT
ejpam-4972	202	1	consider	consider	VERB
ejpam-4972	202	2	the	the	DET
ejpam-4972	202	3	fuzzy	fuzzy	ADJ
ejpam-4972	202	4	bitopology	bitopology	NOUN
ejpam-4972	202	5	σ1	σ1	NOUN
ejpam-4972	202	6	=	=	PUNCT
ejpam-4972	202	7	{	{	PUNCT
ejpam-4972	202	8	0	0	NUM
ejpam-4972	202	9	,	,	PUNCT
ejpam-4972	202	10	1	1	NUM
ejpam-4972	202	11	,	,	PUNCT
ejpam-4972	202	12	n	n	CCONJ
ejpam-4972	202	13	}	}	PUNCT
ejpam-4972	202	14	,	,	PUNCT
ejpam-4972	202	15	σ2	σ2	PROPN
ejpam-4972	202	16	=	=	SYM
ejpam-4972	202	17	{	{	PUNCT
ejpam-4972	202	18	0	0	NUM
ejpam-4972	202	19	,	,	PUNCT
ejpam-4972	202	20	1,m	1,m	NOUN
ejpam-4972	202	21	}	}	PUNCT
ejpam-4972	202	22	on	on	ADP
ejpam-4972	202	23	y	y	PROPN
ejpam-4972	202	24	,	,	PUNCT
ejpam-4972	202	25	and	and	CCONJ
ejpam-4972	202	26	t(a	t(a	NOUN
ejpam-4972	202	27	)	)	PUNCT
ejpam-4972	202	28	=	=	SYM
ejpam-4972	202	29	r	r	NOUN
ejpam-4972	202	30	,	,	PUNCT
ejpam-4972	202	31	t(b	t(b	NOUN
ejpam-4972	202	32	)	)	PUNCT
ejpam-4972	202	33	=	=	SYM
ejpam-4972	202	34	h.	h.	PROPN
ejpam-4972	202	35	a.	a.	NOUN
ejpam-4972	202	36	a.	a.	PROPN
ejpam-4972	202	37	alharbi	alharbi	PROPN
ejpam-4972	202	38	,	,	PUNCT
ejpam-4972	202	39	a.	a.	NOUN
ejpam-4972	202	40	kilicman	kilicman	PROPN
ejpam-4972	202	41	/	/	SYM
ejpam-4972	202	42	eur	eur	PROPN
ejpam-4972	202	43	.	.	PUNCT
ejpam-4972	203	1	j.	j.	PROPN
ejpam-4972	203	2	pure	pure	PROPN
ejpam-4972	203	3	appl	appl	PROPN
ejpam-4972	203	4	.	.	PROPN
ejpam-4972	203	5	math	math	PROPN
ejpam-4972	203	6	,	,	PUNCT
ejpam-4972	203	7	16	16	NUM
ejpam-4972	203	8	(	(	PUNCT
ejpam-4972	203	9	4	4	NUM
ejpam-4972	203	10	)	)	PUNCT
ejpam-4972	203	11	(	(	PUNCT
ejpam-4972	203	12	2023	2023	NUM
ejpam-4972	203	13	)	)	PUNCT
ejpam-4972	203	14	,	,	PUNCT
ejpam-4972	203	15	2613	2613	NUM
ejpam-4972	203	16	-	-	SYM
ejpam-4972	203	17	2631	2631	NUM
ejpam-4972	203	18	2620	2620	NUM
ejpam-4972	203	19	suppose	suppose	VERB
ejpam-4972	203	20	l	l	NOUN
ejpam-4972	203	21	and	and	CCONJ
ejpam-4972	203	22	k	k	PROPN
ejpam-4972	203	23	are	be	AUX
ejpam-4972	203	24	fuzzy	fuzzy	ADJ
ejpam-4972	203	25	subgroups	subgroup	NOUN
ejpam-4972	203	26	of	of	ADP
ejpam-4972	203	27	z	z	NOUN
ejpam-4972	203	28	=	=	PUNCT
ejpam-4972	203	29	{	{	PUNCT
ejpam-4972	203	30	a	a	DET
ejpam-4972	203	31	,	,	PUNCT
ejpam-4972	203	32	b	b	NOUN
ejpam-4972	203	33	}	}	PUNCT
ejpam-4972	203	34	defined	define	VERB
ejpam-4972	203	35	as	as	ADP
ejpam-4972	203	36	:	:	PUNCT
ejpam-4972	203	37	l(a	l(a	PROPN
ejpam-4972	203	38	,	,	PUNCT
ejpam-4972	203	39	b	b	NOUN
ejpam-4972	203	40	)	)	PUNCT
ejpam-4972	203	41	=	=	NOUN
ejpam-4972	203	42	{	{	PUNCT
ejpam-4972	203	43	0.2	0.2	NUM
ejpam-4972	203	44	,	,	PUNCT
ejpam-4972	203	45	0.3	0.3	NUM
ejpam-4972	203	46	}	}	PUNCT
ejpam-4972	203	47	,	,	PUNCT
ejpam-4972	203	48	k(a	k(a	PROPN
ejpam-4972	203	49	,	,	PUNCT
ejpam-4972	203	50	b	b	NOUN
ejpam-4972	203	51	)	)	PUNCT
ejpam-4972	203	52	=	=	NOUN
ejpam-4972	203	53	{	{	PUNCT
ejpam-4972	203	54	0.7	0.7	NUM
ejpam-4972	203	55	,	,	PUNCT
ejpam-4972	203	56	0.5	0.5	NUM
ejpam-4972	203	57	}	}	PUNCT
ejpam-4972	203	58	.	.	PUNCT
ejpam-4972	204	1	consider	consider	VERB
ejpam-4972	204	2	the	the	DET
ejpam-4972	204	3	fuzzy	fuzzy	ADJ
ejpam-4972	204	4	bitopology	bitopology	NOUN
ejpam-4972	204	5	η1	η1	NOUN
ejpam-4972	204	6	=	=	SYM
ejpam-4972	204	7	{	{	PUNCT
ejpam-4972	204	8	0	0	NUM
ejpam-4972	204	9	,	,	PUNCT
ejpam-4972	204	10	1	1	NUM
ejpam-4972	204	11	,	,	PUNCT
ejpam-4972	204	12	l	l	NOUN
ejpam-4972	204	13	}	}	PUNCT
ejpam-4972	204	14	and	and	CCONJ
ejpam-4972	204	15	η2	η2	ADJ
ejpam-4972	204	16	=	=	PUNCT
ejpam-4972	204	17	{	{	PUNCT
ejpam-4972	204	18	0	0	NUM
ejpam-4972	204	19	,	,	PUNCT
ejpam-4972	204	20	1,k	1,k	NUM
ejpam-4972	204	21	}	}	PUNCT
ejpam-4972	204	22	on	on	ADP
ejpam-4972	204	23	z	z	PROPN
ejpam-4972	204	24	,	,	PUNCT
ejpam-4972	204	25	g	g	PROPN
ejpam-4972	204	26	:	:	PUNCT
ejpam-4972	204	27	(	(	PUNCT
ejpam-4972	204	28	y	y	PROPN
ejpam-4972	204	29	,	,	PUNCT
ejpam-4972	204	30	σ1	σ1	PROPN
ejpam-4972	204	31	,	,	PUNCT
ejpam-4972	204	32	σ2	σ2	NOUN
ejpam-4972	204	33	)	)	PUNCT
ejpam-4972	204	34	→	→	SYM
ejpam-4972	204	35	(	(	PUNCT
ejpam-4972	204	36	z	z	NOUN
ejpam-4972	204	37	,	,	PUNCT
ejpam-4972	204	38	η1	η1	NOUN
ejpam-4972	204	39	,	,	PUNCT
ejpam-4972	204	40	η2	η2	NOUN
ejpam-4972	204	41	)	)	PUNCT
ejpam-4972	204	42	such	such	ADJ
ejpam-4972	204	43	that	that	PRON
ejpam-4972	204	44	g(a	g(a	PROPN
ejpam-4972	204	45	)	)	PUNCT
ejpam-4972	205	1	=	=	SYM
ejpam-4972	205	2	a	a	X
ejpam-4972	205	3	,	,	PUNCT
ejpam-4972	205	4	g(b	g(b	PROPN
ejpam-4972	205	5	)	)	PUNCT
ejpam-4972	205	6	=	=	SYM
ejpam-4972	205	7	b.	b.	PROPN
ejpam-4972	205	8	one	one	PRON
ejpam-4972	205	9	may	may	AUX
ejpam-4972	205	10	notice	notice	VERB
ejpam-4972	205	11	that	that	SCONJ
ejpam-4972	205	12	t	t	PROPN
ejpam-4972	205	13	,	,	PUNCT
ejpam-4972	205	14	g	g	PROPN
ejpam-4972	205	15	are	be	AUX
ejpam-4972	205	16	fuzzy	fuzzy	ADJ
ejpam-4972	205	17	(	(	PUNCT
ejpam-4972	205	18	1	1	NUM
ejpam-4972	205	19	,	,	PUNCT
ejpam-4972	205	20	2	2	NUM
ejpam-4972	205	21	)	)	PUNCT
ejpam-4972	205	22	−	−	NOUN
ejpam-4972	205	23	g	g	NOUN
ejpam-4972	205	24	−	−	PROPN
ejpam-4972	205	25	conts	cont	NOUN
ejpam-4972	205	26	,	,	PUNCT
ejpam-4972	205	27	and	and	CCONJ
ejpam-4972	205	28	hence	hence	ADV
ejpam-4972	205	29	by	by	ADP
ejpam-4972	205	30	theorem	theorem	NOUN
ejpam-4972	205	31	2	2	NUM
ejpam-4972	205	32	they	they	PRON
ejpam-4972	205	33	are	be	AUX
ejpam-4972	205	34	(	(	PUNCT
ejpam-4972	205	35	i	i	PROPN
ejpam-4972	205	36	,	,	PUNCT
ejpam-4972	205	37	j	j	PROPN
ejpam-4972	205	38	)	)	PUNCT
ejpam-4972	205	39	−	−	PROPN
ejpam-4972	205	40	gα	gα	ADP
ejpam-4972	205	41	−	−	PROPN
ejpam-4972	205	42	conts	cont	NOUN
ejpam-4972	205	43	,	,	PUNCT
ejpam-4972	205	44	but	but	CCONJ
ejpam-4972	205	45	g	g	PROPN
ejpam-4972	205	46	◦	◦	PROPN
ejpam-4972	205	47	t	t	PROPN
ejpam-4972	205	48	is	be	AUX
ejpam-4972	205	49	not	not	PART
ejpam-4972	205	50	fuzzy	fuzzy	ADJ
ejpam-4972	205	51	(	(	PUNCT
ejpam-4972	205	52	1	1	NUM
ejpam-4972	205	53	,	,	PUNCT
ejpam-4972	205	54	2)−	2)−	PROPN
ejpam-4972	205	55	gα−	gα−	NOUN
ejpam-4972	205	56	conts	cont	NOUN
ejpam-4972	205	57	since	since	SCONJ
ejpam-4972	205	58	(	(	PUNCT
ejpam-4972	205	59	g	g	PROPN
ejpam-4972	205	60	◦	◦	NOUN
ejpam-4972	205	61	t)−1(kc	t)−1(kc	NOUN
ejpam-4972	205	62	)	)	PUNCT
ejpam-4972	205	63	≤	≤	NUM
ejpam-4972	205	64	e	e	X
ejpam-4972	205	65	≤	≤	NUM
ejpam-4972	205	66	δ1	δ1	NOUN
ejpam-4972	205	67	,	,	PUNCT
ejpam-4972	205	68	but	but	CCONJ
ejpam-4972	206	1	δ2	δ2	VERB
ejpam-4972	206	2	−α−	−α−	VERB
ejpam-4972	206	3	cl((g	cl((g	ADJ
ejpam-4972	206	4	◦	◦	PROPN
ejpam-4972	206	5	t)−1(kc	t)−1(kc	NUM
ejpam-4972	206	6	)	)	PUNCT
ejpam-4972	206	7	)	)	PUNCT
ejpam-4972	207	1	≰	≰	PROPN
ejpam-4972	207	2	e.	e.	PROPN
ejpam-4972	207	3	theorem	theorem	VERB
ejpam-4972	207	4	7	7	PROPN
ejpam-4972	207	5	.	.	PUNCT
ejpam-4972	207	6	suppose	suppose	VERB
ejpam-4972	207	7	t	t	NOUN
ejpam-4972	207	8	:	:	PUNCT
ejpam-4972	207	9	(	(	PUNCT
ejpam-4972	207	10	x	x	X
ejpam-4972	207	11	,	,	PUNCT
ejpam-4972	207	12	δ1	δ1	NOUN
ejpam-4972	207	13	,	,	PUNCT
ejpam-4972	207	14	δ2	δ2	ADJ
ejpam-4972	207	15	)	)	PUNCT
ejpam-4972	207	16	→	→	SYM
ejpam-4972	207	17	(	(	PUNCT
ejpam-4972	207	18	y	y	PROPN
ejpam-4972	207	19	,	,	PUNCT
ejpam-4972	207	20	σ1	σ1	PROPN
ejpam-4972	207	21	,	,	PUNCT
ejpam-4972	207	22	σ2	σ2	PROPN
ejpam-4972	207	23	)	)	PUNCT
ejpam-4972	207	24	is	be	AUX
ejpam-4972	207	25	δj	δj	ADP
ejpam-4972	207	26	−	−	PROPN
ejpam-4972	207	27	ψ	ψ	NOUN
ejpam-4972	207	28	−	−	PROPN
ejpam-4972	207	29	conts	cont	NOUN
ejpam-4972	207	30	,	,	PUNCT
ejpam-4972	207	31	g	g	NOUN
ejpam-4972	207	32	:	:	PUNCT
ejpam-4972	207	33	(	(	PUNCT
ejpam-4972	207	34	y	y	PROPN
ejpam-4972	207	35	,	,	PUNCT
ejpam-4972	207	36	σ1	σ1	PROPN
ejpam-4972	207	37	,	,	PUNCT
ejpam-4972	207	38	σ2	σ2	NOUN
ejpam-4972	207	39	)	)	PUNCT
ejpam-4972	207	40	→	→	SYM
ejpam-4972	207	41	(	(	PUNCT
ejpam-4972	207	42	z	z	NOUN
ejpam-4972	207	43	,	,	PUNCT
ejpam-4972	207	44	η1	η1	NOUN
ejpam-4972	207	45	,	,	PUNCT
ejpam-4972	207	46	η2	η2	PROPN
ejpam-4972	207	47	)	)	PUNCT
ejpam-4972	207	48	is	be	AUX
ejpam-4972	207	49	(	(	PUNCT
ejpam-4972	207	50	i	i	NOUN
ejpam-4972	207	51	,	,	PUNCT
ejpam-4972	207	52	j)−gψ−conts	j)−gψ−cont	NOUN
ejpam-4972	207	53	,	,	PUNCT
ejpam-4972	207	54	and	and	CCONJ
ejpam-4972	207	55	any	any	DET
ejpam-4972	207	56	fuzzy	fuzzy	ADJ
ejpam-4972	207	57	(	(	PUNCT
ejpam-4972	207	58	i	i	PROPN
ejpam-4972	207	59	,	,	PUNCT
ejpam-4972	207	60	j)−gψ−cld	j)−gψ−cld	PRON
ejpam-4972	207	61	of	of	ADP
ejpam-4972	207	62	y	y	PROPN
ejpam-4972	207	63	is	be	AUX
ejpam-4972	207	64	fuzzy	fuzzy	ADJ
ejpam-4972	207	65	open	open	ADJ
ejpam-4972	207	66	of	of	ADP
ejpam-4972	207	67	(	(	PUNCT
ejpam-4972	207	68	y	y	PROPN
ejpam-4972	207	69	,	,	PUNCT
ejpam-4972	207	70	σi	σi	NOUN
ejpam-4972	207	71	)	)	PUNCT
ejpam-4972	207	72	.	.	PUNCT
ejpam-4972	208	1	thus	thus	ADV
ejpam-4972	208	2	g	g	ADP
ejpam-4972	208	3	◦	◦	PROPN
ejpam-4972	208	4	t	t	PROPN
ejpam-4972	208	5	:	:	PUNCT
ejpam-4972	208	6	(	(	PUNCT
ejpam-4972	208	7	x	x	X
ejpam-4972	208	8	,	,	PUNCT
ejpam-4972	208	9	δ1	δ1	NOUN
ejpam-4972	208	10	,	,	PUNCT
ejpam-4972	208	11	δ2	δ2	ADJ
ejpam-4972	208	12	)	)	PUNCT
ejpam-4972	208	13	→	→	SYM
ejpam-4972	208	14	(	(	PUNCT
ejpam-4972	208	15	z	z	NOUN
ejpam-4972	208	16	,	,	PUNCT
ejpam-4972	208	17	η1	η1	NOUN
ejpam-4972	208	18	,	,	PUNCT
ejpam-4972	208	19	η2	η2	PROPN
ejpam-4972	208	20	)	)	PUNCT
ejpam-4972	208	21	is	be	AUX
ejpam-4972	208	22	(	(	PUNCT
ejpam-4972	208	23	i	i	PROPN
ejpam-4972	208	24	,	,	PUNCT
ejpam-4972	208	25	j)−	j)−	PROPN
ejpam-4972	208	26	gψ	gψ	VERB
ejpam-4972	208	27	−	−	PROPN
ejpam-4972	208	28	conts	cont	NOUN
ejpam-4972	208	29	.	.	PUNCT
ejpam-4972	209	1	proof	proof	NOUN
ejpam-4972	209	2	.	.	PUNCT
ejpam-4972	210	1	assume	assume	VERB
ejpam-4972	210	2	w	w	NOUN
ejpam-4972	210	3	is	be	AUX
ejpam-4972	210	4	fuzzy	fuzzy	ADJ
ejpam-4972	210	5	closed	closed	ADJ
ejpam-4972	210	6	of	of	ADP
ejpam-4972	210	7	(	(	PUNCT
ejpam-4972	210	8	z	z	NOUN
ejpam-4972	210	9	,	,	PUNCT
ejpam-4972	210	10	ηj	ηj	NOUN
ejpam-4972	210	11	)	)	PUNCT
ejpam-4972	210	12	.	.	PUNCT
ejpam-4972	211	1	as	as	SCONJ
ejpam-4972	211	2	g	g	PROPN
ejpam-4972	211	3	is	be	AUX
ejpam-4972	211	4	fuzzy	fuzzy	ADJ
ejpam-4972	211	5	(	(	PUNCT
ejpam-4972	211	6	i	i	PROPN
ejpam-4972	211	7	,	,	PUNCT
ejpam-4972	211	8	j	j	PROPN
ejpam-4972	211	9	)	)	PUNCT
ejpam-4972	211	10	−	−	PROPN
ejpam-4972	211	11	gψ	gψ	VERB
ejpam-4972	211	12	−	−	PROPN
ejpam-4972	211	13	conts	cont	NOUN
ejpam-4972	211	14	,	,	PUNCT
ejpam-4972	211	15	then	then	ADV
ejpam-4972	211	16	g−1(w	g−1(w	PROPN
ejpam-4972	211	17	)	)	PUNCT
ejpam-4972	211	18	is	be	AUX
ejpam-4972	211	19	fuzzy	fuzzy	ADJ
ejpam-4972	211	20	(	(	PUNCT
ejpam-4972	211	21	i	i	PROPN
ejpam-4972	211	22	,	,	PUNCT
ejpam-4972	211	23	j)−	j)−	PROPN
ejpam-4972	211	24	gψ	gψ	VERB
ejpam-4972	211	25	−	−	PROPN
ejpam-4972	211	26	cld	cld	NOUN
ejpam-4972	211	27	of	of	ADP
ejpam-4972	211	28	y	y	PROPN
ejpam-4972	211	29	.	.	PUNCT
ejpam-4972	212	1	so	so	ADV
ejpam-4972	212	2	by	by	ADP
ejpam-4972	212	3	hypotheses	hypothesis	NOUN
ejpam-4972	212	4	g−1(w	g−1(w	NOUN
ejpam-4972	212	5	)	)	PUNCT
ejpam-4972	212	6	is	be	AUX
ejpam-4972	212	7	fuzzy	fuzzy	ADJ
ejpam-4972	212	8	open	open	ADJ
ejpam-4972	212	9	of	of	ADP
ejpam-4972	212	10	(	(	PUNCT
ejpam-4972	212	11	y	y	PROPN
ejpam-4972	212	12	,	,	PUNCT
ejpam-4972	212	13	σi	σi	NOUN
ejpam-4972	212	14	)	)	PUNCT
ejpam-4972	212	15	,	,	PUNCT
ejpam-4972	212	16	so	so	ADV
ejpam-4972	212	17	g−1(w	g−1(w	PROPN
ejpam-4972	212	18	)	)	PUNCT
ejpam-4972	212	19	is	be	AUX
ejpam-4972	212	20	fuzzy	fuzzy	ADJ
ejpam-4972	212	21	δj	δj	ADP
ejpam-4972	212	22	−ψ−	−ψ−	NOUN
ejpam-4972	212	23	cld	cld	PROPN
ejpam-4972	212	24	of	of	ADP
ejpam-4972	212	25	(	(	PUNCT
ejpam-4972	212	26	y	y	PROPN
ejpam-4972	212	27	,	,	PUNCT
ejpam-4972	212	28	σj	σj	NOUN
ejpam-4972	212	29	)	)	PUNCT
ejpam-4972	212	30	.	.	PUNCT
ejpam-4972	213	1	as	as	SCONJ
ejpam-4972	213	2	t	t	PROPN
ejpam-4972	213	3	is	be	AUX
ejpam-4972	213	4	fuzzy	fuzzy	ADJ
ejpam-4972	213	5	δj	δj	ADJ
ejpam-4972	213	6	−ψ−	−ψ−	NOUN
ejpam-4972	213	7	conts	cont	NOUN
ejpam-4972	213	8	,	,	PUNCT
ejpam-4972	213	9	then	then	ADV
ejpam-4972	213	10	t−1(g−1(w	t−1(g−1(w	NUM
ejpam-4972	213	11	)	)	PUNCT
ejpam-4972	213	12	)	)	PUNCT
ejpam-4972	213	13	is	be	AUX
ejpam-4972	213	14	fuzzy	fuzzy	ADJ
ejpam-4972	213	15	δj	δj	ADJ
ejpam-4972	213	16	−ψ−	−ψ−	NOUN
ejpam-4972	213	17	cld	cld	NOUN
ejpam-4972	213	18	of	of	ADP
ejpam-4972	213	19	x	x	PRON
ejpam-4972	213	20	,	,	PUNCT
ejpam-4972	213	21	thus	thus	ADV
ejpam-4972	213	22	(	(	PUNCT
ejpam-4972	213	23	g	g	PROPN
ejpam-4972	213	24	◦	◦	NOUN
ejpam-4972	213	25	t)−1(w	t)−1(w	PROPN
ejpam-4972	213	26	)	)	PUNCT
ejpam-4972	213	27	is	be	AUX
ejpam-4972	213	28	fuzzy	fuzzy	ADJ
ejpam-4972	213	29	(	(	PUNCT
ejpam-4972	213	30	i	i	NOUN
ejpam-4972	213	31	,	,	PUNCT
ejpam-4972	213	32	j)−	j)−	PROPN
ejpam-4972	213	33	gψ−	gψ−	PUNCT
ejpam-4972	213	34	cld	cld	PROPN
ejpam-4972	213	35	of	of	ADP
ejpam-4972	213	36	x.	x.	NOUN
ejpam-4972	213	37	therefore	therefore	ADV
ejpam-4972	213	38	g	g	PROPN
ejpam-4972	213	39	◦	◦	PROPN
ejpam-4972	213	40	t	t	PROPN
ejpam-4972	213	41	is	be	AUX
ejpam-4972	213	42	fuzzy	fuzzy	ADJ
ejpam-4972	213	43	(	(	PUNCT
ejpam-4972	213	44	i	i	PROPN
ejpam-4972	213	45	,	,	PUNCT
ejpam-4972	213	46	j)−	j)−	PROPN
ejpam-4972	213	47	gψ	gψ	VERB
ejpam-4972	213	48	−	−	PROPN
ejpam-4972	213	49	conts	cont	NOUN
ejpam-4972	213	50	.	.	PUNCT
ejpam-4972	214	1	theorem	theorem	ADJ
ejpam-4972	214	2	8	8	NUM
ejpam-4972	214	3	.	.	PUNCT
ejpam-4972	215	1	suppose	suppose	VERB
ejpam-4972	215	2	t	t	NOUN
ejpam-4972	215	3	:	:	PUNCT
ejpam-4972	215	4	(	(	PUNCT
ejpam-4972	215	5	x	x	X
ejpam-4972	215	6	,	,	PUNCT
ejpam-4972	215	7	δ1	δ1	NOUN
ejpam-4972	215	8	,	,	PUNCT
ejpam-4972	215	9	δ2	δ2	ADJ
ejpam-4972	215	10	)	)	PUNCT
ejpam-4972	215	11	→	→	SYM
ejpam-4972	215	12	(	(	PUNCT
ejpam-4972	215	13	y	y	PROPN
ejpam-4972	215	14	,	,	PUNCT
ejpam-4972	215	15	σ1	σ1	PROPN
ejpam-4972	215	16	,	,	PUNCT
ejpam-4972	215	17	σ2	σ2	NOUN
ejpam-4972	215	18	)	)	PUNCT
ejpam-4972	215	19	is	be	AUX
ejpam-4972	215	20	fuzzy	fuzzy	ADJ
ejpam-4972	215	21	(	(	PUNCT
ejpam-4972	215	22	i	i	NOUN
ejpam-4972	215	23	,	,	PUNCT
ejpam-4972	215	24	j)−gψ−conts	j)−gψ−cont	NOUN
ejpam-4972	215	25	,	,	PUNCT
ejpam-4972	215	26	g	g	NOUN
ejpam-4972	215	27	:	:	PUNCT
ejpam-4972	215	28	(	(	PUNCT
ejpam-4972	215	29	y	y	PROPN
ejpam-4972	215	30	,	,	PUNCT
ejpam-4972	215	31	σ1	σ1	PROPN
ejpam-4972	215	32	,	,	PUNCT
ejpam-4972	215	33	σ2	σ2	NOUN
ejpam-4972	215	34	)	)	PUNCT
ejpam-4972	215	35	→	→	SYM
ejpam-4972	215	36	(	(	PUNCT
ejpam-4972	215	37	z	z	NOUN
ejpam-4972	215	38	,	,	PUNCT
ejpam-4972	215	39	η1	η1	NOUN
ejpam-4972	215	40	,	,	PUNCT
ejpam-4972	215	41	η2	η2	PROPN
ejpam-4972	215	42	)	)	PUNCT
ejpam-4972	215	43	is	be	AUX
ejpam-4972	215	44	σj	σj	VERB
ejpam-4972	215	45	−	−	PROPN
ejpam-4972	215	46	conts	cont	NOUN
ejpam-4972	215	47	.	.	PUNCT
ejpam-4972	216	1	therefore	therefore	ADV
ejpam-4972	216	2	g	g	PROPN
ejpam-4972	216	3	◦	◦	PROPN
ejpam-4972	216	4	t	t	PROPN
ejpam-4972	216	5	:	:	PUNCT
ejpam-4972	216	6	(	(	PUNCT
ejpam-4972	216	7	x	x	X
ejpam-4972	216	8	,	,	PUNCT
ejpam-4972	216	9	δ1	δ1	NOUN
ejpam-4972	216	10	,	,	PUNCT
ejpam-4972	216	11	δ2	δ2	ADJ
ejpam-4972	216	12	)	)	PUNCT
ejpam-4972	216	13	→	→	SYM
ejpam-4972	216	14	(	(	PUNCT
ejpam-4972	216	15	z	z	NOUN
ejpam-4972	216	16	,	,	PUNCT
ejpam-4972	216	17	η1	η1	NOUN
ejpam-4972	216	18	,	,	PUNCT
ejpam-4972	216	19	η2	η2	PROPN
ejpam-4972	216	20	)	)	PUNCT
ejpam-4972	216	21	is	be	AUX
ejpam-4972	216	22	(	(	PUNCT
ejpam-4972	216	23	i	i	PROPN
ejpam-4972	216	24	,	,	PUNCT
ejpam-4972	216	25	j)−	j)−	PROPN
ejpam-4972	216	26	gψ	gψ	VERB
ejpam-4972	216	27	−	−	PROPN
ejpam-4972	216	28	conts	cont	NOUN
ejpam-4972	216	29	.	.	PUNCT
ejpam-4972	217	1	proof	proof	NOUN
ejpam-4972	217	2	.	.	PUNCT
ejpam-4972	218	1	assume	assume	VERB
ejpam-4972	218	2	w	w	NOUN
ejpam-4972	218	3	is	be	AUX
ejpam-4972	218	4	fuzzy	fuzzy	ADJ
ejpam-4972	218	5	closed	closed	ADJ
ejpam-4972	218	6	of	of	ADP
ejpam-4972	218	7	(	(	PUNCT
ejpam-4972	218	8	z	z	NOUN
ejpam-4972	218	9	,	,	PUNCT
ejpam-4972	218	10	ηj	ηj	NOUN
ejpam-4972	218	11	)	)	PUNCT
ejpam-4972	218	12	.	.	PUNCT
ejpam-4972	219	1	as	as	SCONJ
ejpam-4972	219	2	g	g	PROPN
ejpam-4972	219	3	is	be	AUX
ejpam-4972	219	4	fuzzy	fuzzy	ADJ
ejpam-4972	219	5	σj	σj	ADP
ejpam-4972	219	6	−	−	PROPN
ejpam-4972	219	7	conts	cont	NOUN
ejpam-4972	219	8	,	,	PUNCT
ejpam-4972	219	9	then	then	ADV
ejpam-4972	219	10	g−1(w	g−1(w	PROPN
ejpam-4972	219	11	)	)	PUNCT
ejpam-4972	219	12	is	be	AUX
ejpam-4972	219	13	fuzzy	fuzzy	ADJ
ejpam-4972	219	14	closed	closed	ADJ
ejpam-4972	219	15	of	of	ADP
ejpam-4972	219	16	(	(	PUNCT
ejpam-4972	219	17	y	y	PROPN
ejpam-4972	219	18	,	,	PUNCT
ejpam-4972	219	19	σj	σj	NOUN
ejpam-4972	219	20	)	)	PUNCT
ejpam-4972	219	21	.	.	PUNCT
ejpam-4972	220	1	as	as	SCONJ
ejpam-4972	220	2	t	t	PROPN
ejpam-4972	220	3	is	be	AUX
ejpam-4972	220	4	fuzzy	fuzzy	ADJ
ejpam-4972	220	5	(	(	PUNCT
ejpam-4972	220	6	i	i	PROPN
ejpam-4972	220	7	,	,	PUNCT
ejpam-4972	220	8	j	j	PROPN
ejpam-4972	220	9	)	)	PUNCT
ejpam-4972	220	10	−	−	PROPN
ejpam-4972	220	11	gψ	gψ	VERB
ejpam-4972	220	12	−	−	PROPN
ejpam-4972	220	13	conts	cont	NOUN
ejpam-4972	220	14	,	,	PUNCT
ejpam-4972	220	15	then	then	ADV
ejpam-4972	220	16	t−1(g−1(w	t−1(g−1(w	NUM
ejpam-4972	220	17	)	)	PUNCT
ejpam-4972	220	18	)	)	PUNCT
ejpam-4972	221	1	is	be	AUX
ejpam-4972	221	2	fuzzy	fuzzy	ADJ
ejpam-4972	221	3	(	(	PUNCT
ejpam-4972	221	4	i	i	PROPN
ejpam-4972	221	5	,	,	PUNCT
ejpam-4972	221	6	j)−	j)−	PROPN
ejpam-4972	221	7	gψ	gψ	VERB
ejpam-4972	221	8	−	−	PROPN
ejpam-4972	221	9	cld	cld	NOUN
ejpam-4972	221	10	of	of	ADP
ejpam-4972	221	11	x.	x.	NOUN
ejpam-4972	221	12	therefore	therefore	ADV
ejpam-4972	221	13	g	g	PROPN
ejpam-4972	221	14	◦	◦	PROPN
ejpam-4972	221	15	t	t	PROPN
ejpam-4972	221	16	is	be	AUX
ejpam-4972	221	17	fuzzy	fuzzy	ADJ
ejpam-4972	221	18	(	(	PUNCT
ejpam-4972	221	19	i	i	PROPN
ejpam-4972	221	20	,	,	PUNCT
ejpam-4972	221	21	j)−	j)−	PROPN
ejpam-4972	221	22	gψ	gψ	VERB
ejpam-4972	221	23	−	−	PROPN
ejpam-4972	221	24	conts	cont	NOUN
ejpam-4972	221	25	.	.	PUNCT
ejpam-4972	222	1	theorem	theorem	NOUN
ejpam-4972	222	2	9	9	NUM
ejpam-4972	222	3	.	.	PUNCT
ejpam-4972	223	1	suppose	suppose	VERB
ejpam-4972	223	2	t	t	NOUN
ejpam-4972	223	3	:	:	PUNCT
ejpam-4972	223	4	(	(	PUNCT
ejpam-4972	223	5	x	x	X
ejpam-4972	223	6	,	,	PUNCT
ejpam-4972	223	7	δ1	δ1	NOUN
ejpam-4972	223	8	,	,	PUNCT
ejpam-4972	223	9	δ2	δ2	ADJ
ejpam-4972	223	10	)	)	PUNCT
ejpam-4972	223	11	→	→	SYM
ejpam-4972	223	12	(	(	PUNCT
ejpam-4972	223	13	y	y	PROPN
ejpam-4972	223	14	,	,	PUNCT
ejpam-4972	223	15	σ1	σ1	PROPN
ejpam-4972	223	16	,	,	PUNCT
ejpam-4972	223	17	σ2	σ2	NOUN
ejpam-4972	223	18	)	)	PUNCT
ejpam-4972	223	19	is	be	AUX
ejpam-4972	223	20	fuzzy	fuzzy	ADJ
ejpam-4972	223	21	δj	δj	ADP
ejpam-4972	223	22	−	−	PROPN
ejpam-4972	223	23	ψ	ψ	NOUN
ejpam-4972	223	24	−	−	PROPN
ejpam-4972	223	25	conts	cont	NOUN
ejpam-4972	223	26	and	and	CCONJ
ejpam-4972	223	27	δi	δi	VERB
ejpam-4972	223	28	−	−	NOUN
ejpam-4972	223	29	open	open	ADJ
ejpam-4972	223	30	mapping	mapping	NOUN
ejpam-4972	223	31	.	.	PUNCT
ejpam-4972	224	1	then	then	ADV
ejpam-4972	224	2	any	any	DET
ejpam-4972	224	3	fuzzy	fuzzy	ADJ
ejpam-4972	224	4	(	(	PUNCT
ejpam-4972	224	5	i	i	NOUN
ejpam-4972	224	6	,	,	PUNCT
ejpam-4972	224	7	j)−	j)−	PROPN
ejpam-4972	224	8	gψ−	gψ−	PROPN
ejpam-4972	224	9	cld	cld	PROPN
ejpam-4972	224	10	group	group	NOUN
ejpam-4972	224	11	f	f	PROPN
ejpam-4972	224	12	of	of	ADP
ejpam-4972	224	13	y	y	PROPN
ejpam-4972	224	14	,	,	PUNCT
ejpam-4972	224	15	t−1(f	t−1(f	PROPN
ejpam-4972	224	16	)	)	PUNCT
ejpam-4972	224	17	is	be	AUX
ejpam-4972	224	18	(	(	PUNCT
ejpam-4972	224	19	i	i	NOUN
ejpam-4972	224	20	,	,	PUNCT
ejpam-4972	224	21	j)−	j)−	PROPN
ejpam-4972	224	22	gψ−	gψ−	PUNCT
ejpam-4972	224	23	cld	cld	PROPN
ejpam-4972	224	24	of	of	ADP
ejpam-4972	224	25	x.	x.	PROPN
ejpam-4972	224	26	proof	proof	PROPN
ejpam-4972	224	27	.	.	PUNCT
ejpam-4972	225	1	assume	assume	VERB
ejpam-4972	225	2	f	f	PROPN
ejpam-4972	225	3	is	be	AUX
ejpam-4972	225	4	fuzzy	fuzzy	ADJ
ejpam-4972	225	5	(	(	PUNCT
ejpam-4972	225	6	i	i	PROPN
ejpam-4972	225	7	,	,	PUNCT
ejpam-4972	225	8	j	j	PROPN
ejpam-4972	225	9	)	)	PUNCT
ejpam-4972	225	10	−	−	PROPN
ejpam-4972	225	11	gψ	gψ	VERB
ejpam-4972	225	12	−	−	PROPN
ejpam-4972	225	13	cld	cld	NOUN
ejpam-4972	225	14	group	group	NOUN
ejpam-4972	225	15	of	of	ADP
ejpam-4972	225	16	y	y	PROPN
ejpam-4972	225	17	,	,	PUNCT
ejpam-4972	225	18	w	w	PROPN
ejpam-4972	225	19	is	be	AUX
ejpam-4972	225	20	fuzzy	fuzzy	ADJ
ejpam-4972	225	21	open	open	ADJ
ejpam-4972	225	22	of	of	ADP
ejpam-4972	225	23	(	(	PUNCT
ejpam-4972	225	24	x	x	NOUN
ejpam-4972	225	25	,	,	PUNCT
ejpam-4972	225	26	δi	δi	PROPN
ejpam-4972	225	27	)	)	PUNCT
ejpam-4972	225	28	including	include	VERB
ejpam-4972	225	29	t−1(f	t−1(f	NOUN
ejpam-4972	225	30	)	)	PUNCT
ejpam-4972	225	31	.	.	PUNCT
ejpam-4972	226	1	since	since	SCONJ
ejpam-4972	226	2	t	t	PROPN
ejpam-4972	226	3	is	be	AUX
ejpam-4972	226	4	fuzzy	fuzzy	ADJ
ejpam-4972	226	5	δi	δi	ADP
ejpam-4972	226	6	−	−	PROPN
ejpam-4972	226	7	open	open	ADJ
ejpam-4972	226	8	,	,	PUNCT
ejpam-4972	226	9	then	then	ADV
ejpam-4972	226	10	t(w	t(w	NOUN
ejpam-4972	226	11	)	)	PUNCT
ejpam-4972	226	12	is	be	AUX
ejpam-4972	226	13	fuzzy	fuzzy	ADJ
ejpam-4972	226	14	open	open	ADJ
ejpam-4972	226	15	of	of	ADP
ejpam-4972	226	16	(	(	PUNCT
ejpam-4972	226	17	y	y	PROPN
ejpam-4972	226	18	,	,	PUNCT
ejpam-4972	226	19	σi	σi	NOUN
ejpam-4972	226	20	)	)	PUNCT
ejpam-4972	226	21	.	.	PUNCT
ejpam-4972	227	1	as	as	ADP
ejpam-4972	227	2	f	f	PROPN
ejpam-4972	227	3	≤	≤	PROPN
ejpam-4972	227	4	t(w	t(w	NOUN
ejpam-4972	227	5	)	)	PUNCT
ejpam-4972	227	6	,	,	PUNCT
ejpam-4972	227	7	f	f	PROPN
ejpam-4972	227	8	is	be	AUX
ejpam-4972	227	9	fuzzy	fuzzy	ADJ
ejpam-4972	227	10	(	(	PUNCT
ejpam-4972	227	11	i	i	PROPN
ejpam-4972	227	12	,	,	PUNCT
ejpam-4972	227	13	j	j	PROPN
ejpam-4972	227	14	)	)	PUNCT
ejpam-4972	227	15	−	−	PROPN
ejpam-4972	227	16	gψ	gψ	VERB
ejpam-4972	227	17	−	−	PROPN
ejpam-4972	227	18	cld	cld	NOUN
ejpam-4972	227	19	of	of	ADP
ejpam-4972	227	20	y	y	PROPN
ejpam-4972	227	21	,	,	PUNCT
ejpam-4972	227	22	then	then	ADV
ejpam-4972	227	23	σj	σj	VERB
ejpam-4972	227	24	−	−	PROPN
ejpam-4972	227	25	ψ	ψ	NOUN
ejpam-4972	227	26	−	−	PROPN
ejpam-4972	227	27	cl(f	cl(f	NOUN
ejpam-4972	227	28	)	)	PUNCT
ejpam-4972	227	29	≤	≤	NUM
ejpam-4972	227	30	t(w	t(w	NOUN
ejpam-4972	227	31	)	)	PUNCT
ejpam-4972	227	32	which	which	PRON
ejpam-4972	227	33	implies	imply	VERB
ejpam-4972	227	34	t−1(σj	t−1(σj	ADP
ejpam-4972	227	35	−	−	NOUN
ejpam-4972	227	36	ψ	ψ	NOUN
ejpam-4972	227	37	−	−	PROPN
ejpam-4972	227	38	cl(f	cl(f	PROPN
ejpam-4972	227	39	)	)	PUNCT
ejpam-4972	227	40	)	)	PUNCT
ejpam-4972	228	1	≤	≤	NUM
ejpam-4972	228	2	w	w	X
ejpam-4972	228	3	.	.	PUNCT
ejpam-4972	229	1	since	since	SCONJ
ejpam-4972	229	2	t	t	PROPN
ejpam-4972	229	3	is	be	AUX
ejpam-4972	229	4	fuzzy	fuzzy	ADJ
ejpam-4972	229	5	δj	δj	ADP
ejpam-4972	229	6	−	−	PROPN
ejpam-4972	229	7	ψ	ψ	NOUN
ejpam-4972	229	8	−	−	PROPN
ejpam-4972	229	9	conts	cont	NOUN
ejpam-4972	229	10	,	,	PUNCT
ejpam-4972	229	11	hence	hence	ADV
ejpam-4972	229	12	t−1(σj	t−1(σj	ADP
ejpam-4972	229	13	−	−	NOUN
ejpam-4972	229	14	ψ	ψ	NOUN
ejpam-4972	229	15	−	−	PROPN
ejpam-4972	229	16	cl(f	cl(f	NOUN
ejpam-4972	229	17	)	)	PUNCT
ejpam-4972	229	18	)	)	PUNCT
ejpam-4972	230	1	=	=	PRON
ejpam-4972	230	2	δj	δj	ADP
ejpam-4972	230	3	−	−	PROPN
ejpam-4972	230	4	ψ	ψ	NOUN
ejpam-4972	230	5	−	−	PROPN
ejpam-4972	230	6	cl(t−1(σjψ	cl(t−1(σjψ	NOUN
ejpam-4972	230	7	−	−	PROPN
ejpam-4972	230	8	cl(f	cl(f	NOUN
ejpam-4972	230	9	)	)	PUNCT
ejpam-4972	230	10	)	)	PUNCT
ejpam-4972	230	11	)	)	PUNCT
ejpam-4972	230	12	.	.	PUNCT
ejpam-4972	231	1	then	then	ADV
ejpam-4972	231	2	δj	δj	ADP
ejpam-4972	231	3	−	−	PROPN
ejpam-4972	231	4	ψ	ψ	NOUN
ejpam-4972	231	5	−	−	PROPN
ejpam-4972	231	6	cl(t−1(f	cl(t−1(f	NOUN
ejpam-4972	231	7	)	)	PUNCT
ejpam-4972	231	8	)	)	PUNCT
ejpam-4972	231	9	≤	≤	PUNCT
ejpam-4972	232	1	t−1(σj	t−1(σj	ADP
ejpam-4972	232	2	−	−	NOUN
ejpam-4972	232	3	ψ	ψ	NOUN
ejpam-4972	232	4	−	−	PROPN
ejpam-4972	232	5	cl(f	cl(f	PROPN
ejpam-4972	232	6	)	)	PUNCT
ejpam-4972	232	7	)	)	PUNCT
ejpam-4972	233	1	≤w	≤w	NOUN
ejpam-4972	233	2	.	.	PUNCT
ejpam-4972	234	1	so	so	ADV
ejpam-4972	234	2	,	,	PUNCT
ejpam-4972	234	3	t−1(f	t−1(f	PROPN
ejpam-4972	234	4	)	)	PUNCT
ejpam-4972	234	5	is	be	AUX
ejpam-4972	234	6	fuzzy	fuzzy	ADJ
ejpam-4972	234	7	(	(	PUNCT
ejpam-4972	234	8	i	i	PROPN
ejpam-4972	234	9	,	,	PUNCT
ejpam-4972	234	10	j)−	j)−	PROPN
ejpam-4972	234	11	gψ	gψ	VERB
ejpam-4972	234	12	−	−	PROPN
ejpam-4972	234	13	cld	cld	NOUN
ejpam-4972	234	14	of	of	ADP
ejpam-4972	234	15	x.	x.	PROPN
ejpam-4972	234	16	4	4	NUM
ejpam-4972	234	17	.	.	NOUN
ejpam-4972	234	18	types	type	NOUN
ejpam-4972	234	19	of	of	ADP
ejpam-4972	234	20	fuzzy	fuzzy	ADJ
ejpam-4972	234	21	generalized	generalize	VERB
ejpam-4972	234	22	strongly	strongly	ADV
ejpam-4972	234	23	continuity	continuity	NOUN
ejpam-4972	234	24	and	and	CCONJ
ejpam-4972	234	25	irresolute	irresolute	ADJ
ejpam-4972	234	26	mapping	mapping	NOUN
ejpam-4972	234	27	in	in	ADP
ejpam-4972	234	28	the	the	DET
ejpam-4972	234	29	coming	come	VERB
ejpam-4972	234	30	part	part	NOUN
ejpam-4972	234	31	,	,	PUNCT
ejpam-4972	234	32	we	we	PRON
ejpam-4972	234	33	define	define	VERB
ejpam-4972	234	34	fuzzy	fuzzy	ADJ
ejpam-4972	234	35	generalized	generalize	VERB
ejpam-4972	234	36	strong	strong	ADJ
ejpam-4972	234	37	continuity	continuity	NOUN
ejpam-4972	234	38	and	and	CCONJ
ejpam-4972	234	39	irresolute	irresolute	ADJ
ejpam-4972	234	40	mapping	mapping	NOUN
ejpam-4972	234	41	of	of	ADP
ejpam-4972	234	42	generalized	generalize	VERB
ejpam-4972	234	43	closed	close	VERB
ejpam-4972	234	44	sets	set	NOUN
ejpam-4972	234	45	and	and	CCONJ
ejpam-4972	234	46	we	we	PRON
ejpam-4972	234	47	denote	denote	VERB
ejpam-4972	234	48	by	by	ADP
ejpam-4972	234	49	(	(	PUNCT
ejpam-4972	234	50	i	i	PROPN
ejpam-4972	234	51	,	,	PUNCT
ejpam-4972	234	52	j	j	PROPN
ejpam-4972	234	53	)	)	PUNCT
ejpam-4972	234	54	−	−	PROPN
ejpam-4972	234	55	gψ−strongly	gψ−strongly	ADV
ejpam-4972	234	56	conts	cont	NOUN
ejpam-4972	234	57	,	,	PUNCT
ejpam-4972	234	58	and	and	CCONJ
ejpam-4972	234	59	(	(	PUNCT
ejpam-4972	234	60	i	i	PROPN
ejpam-4972	234	61	,	,	PUNCT
ejpam-4972	234	62	j	j	PROPN
ejpam-4972	234	63	)	)	PUNCT
ejpam-4972	235	1	−	−	NOUN
ejpam-4972	236	1	gψ−irresolute	gψ−irresolute	NOUN
ejpam-4972	236	2	respectively	respectively	ADV
ejpam-4972	236	3	after	after	ADP
ejpam-4972	236	4	that	that	SCONJ
ejpam-4972	236	5	we	we	PRON
ejpam-4972	236	6	study	study	VERB
ejpam-4972	236	7	some	some	DET
ejpam-4972	236	8	properties	property	NOUN
ejpam-4972	236	9	and	and	CCONJ
ejpam-4972	236	10	theorem	theorem	VERB
ejpam-4972	236	11	for	for	ADP
ejpam-4972	236	12	them	they	PRON
ejpam-4972	236	13	and	and	CCONJ
ejpam-4972	236	14	presented	present	VERB
ejpam-4972	236	15	counter	counter	ADJ
ejpam-4972	236	16	examples	example	NOUN
ejpam-4972	236	17	too	too	ADV
ejpam-4972	236	18	.	.	PUNCT
ejpam-4972	237	1	definition	definition	NOUN
ejpam-4972	237	2	10	10	NUM
ejpam-4972	237	3	.	.	PUNCT
ejpam-4972	238	1	a	a	DET
ejpam-4972	238	2	function	function	NOUN
ejpam-4972	238	3	t	t	NOUN
ejpam-4972	238	4	:	:	PUNCT
ejpam-4972	238	5	(	(	PUNCT
ejpam-4972	238	6	x	x	X
ejpam-4972	238	7	,	,	PUNCT
ejpam-4972	238	8	δ1	δ1	NOUN
ejpam-4972	238	9	,	,	PUNCT
ejpam-4972	238	10	δ2	δ2	ADJ
ejpam-4972	238	11	)	)	PUNCT
ejpam-4972	238	12	→	→	SYM
ejpam-4972	238	13	(	(	PUNCT
ejpam-4972	238	14	y	y	PROPN
ejpam-4972	238	15	,	,	PUNCT
ejpam-4972	238	16	σ1	σ1	PROPN
ejpam-4972	238	17	,	,	PUNCT
ejpam-4972	238	18	σ2	σ2	PROPN
ejpam-4972	238	19	)	)	PUNCT
ejpam-4972	238	20	is	be	AUX
ejpam-4972	238	21	claimed	claim	VERB
ejpam-4972	238	22	:	:	PUNCT
ejpam-4972	238	23	(	(	PUNCT
ejpam-4972	238	24	1	1	X
ejpam-4972	238	25	)	)	PUNCT
ejpam-4972	238	26	fuzzy	fuzzy	NOUN
ejpam-4972	238	27	(	(	PUNCT
ejpam-4972	238	28	i	i	NOUN
ejpam-4972	238	29	,	,	PUNCT
ejpam-4972	238	30	j)−generalizedψ−strongly	j)−generalizedψ−strongly	ADV
ejpam-4972	238	31	continuous	continuous	ADJ
ejpam-4972	238	32	(	(	PUNCT
ejpam-4972	238	33	briefly	briefly	ADV
ejpam-4972	238	34	,	,	PUNCT
ejpam-4972	238	35	(	(	PUNCT
ejpam-4972	238	36	i	i	PRON
ejpam-4972	238	37	,	,	PUNCT
ejpam-4972	238	38	j)−gψ−strongly	j)−gψ−strongly	ADV
ejpam-4972	238	39	conts	cont	NOUN
ejpam-4972	238	40	)	)	PUNCT
ejpam-4972	238	41	when	when	SCONJ
ejpam-4972	238	42	t−1(w	t−1(w	NOUN
ejpam-4972	238	43	)	)	PUNCT
ejpam-4972	238	44	is	be	AUX
ejpam-4972	238	45	fuzzy	fuzzy	ADJ
ejpam-4972	238	46	δj	δj	ADP
ejpam-4972	238	47	−	−	PROPN
ejpam-4972	238	48	closed	closed	ADJ
ejpam-4972	238	49	group	group	NOUN
ejpam-4972	238	50	of	of	ADP
ejpam-4972	238	51	x	x	PUNCT
ejpam-4972	238	52	for	for	SCONJ
ejpam-4972	238	53	all	all	DET
ejpam-4972	238	54	w	w	NOUN
ejpam-4972	238	55	is	be	AUX
ejpam-4972	238	56	(	(	PUNCT
ejpam-4972	238	57	i	i	PROPN
ejpam-4972	238	58	,	,	PUNCT
ejpam-4972	238	59	j)−	j)−	PROPN
ejpam-4972	238	60	gψ	gψ	VERB
ejpam-4972	238	61	−	−	PROPN
ejpam-4972	238	62	cld	cld	NOUN
ejpam-4972	238	63	of	of	ADP
ejpam-4972	238	64	y	y	PROPN
ejpam-4972	238	65	.	.	PUNCT
ejpam-4972	239	1	a.	a.	NOUN
ejpam-4972	239	2	a.	a.	PROPN
ejpam-4972	239	3	alharbi	alharbi	PROPN
ejpam-4972	239	4	,	,	PUNCT
ejpam-4972	239	5	a.	a.	NOUN
ejpam-4972	239	6	kilicman	kilicman	PROPN
ejpam-4972	239	7	/	/	SYM
ejpam-4972	239	8	eur	eur	PROPN
ejpam-4972	239	9	.	.	PUNCT
ejpam-4972	240	1	j.	j.	PROPN
ejpam-4972	240	2	pure	pure	PROPN
ejpam-4972	240	3	appl	appl	PROPN
ejpam-4972	240	4	.	.	PROPN
ejpam-4972	240	5	math	math	PROPN
ejpam-4972	240	6	,	,	PUNCT
ejpam-4972	240	7	16	16	NUM
ejpam-4972	240	8	(	(	PUNCT
ejpam-4972	240	9	4	4	NUM
ejpam-4972	240	10	)	)	PUNCT
ejpam-4972	240	11	(	(	PUNCT
ejpam-4972	240	12	2023	2023	NUM
ejpam-4972	240	13	)	)	PUNCT
ejpam-4972	240	14	,	,	PUNCT
ejpam-4972	240	15	2613	2613	NUM
ejpam-4972	240	16	-	-	SYM
ejpam-4972	240	17	2631	2631	NUM
ejpam-4972	240	18	2621	2621	NUM
ejpam-4972	240	19	(	(	PUNCT
ejpam-4972	240	20	2	2	NUM
ejpam-4972	240	21	)	)	PUNCT
ejpam-4972	240	22	fuzzy	fuzzy	NOUN
ejpam-4972	240	23	(	(	PUNCT
ejpam-4972	240	24	i	i	PROPN
ejpam-4972	240	25	,	,	PUNCT
ejpam-4972	240	26	j	j	PROPN
ejpam-4972	240	27	)	)	PUNCT
ejpam-4972	240	28	−	−	PROPN
ejpam-4972	240	29	generalizedψ	generalizedψ	NOUN
ejpam-4972	240	30	−	−	PROPN
ejpam-4972	240	31	irresolute	irresolute	ADJ
ejpam-4972	240	32	mapping	mapping	NOUN
ejpam-4972	240	33	(	(	PUNCT
ejpam-4972	240	34	briefly	briefly	ADV
ejpam-4972	240	35	,	,	PUNCT
ejpam-4972	240	36	(	(	PUNCT
ejpam-4972	240	37	i	i	PROPN
ejpam-4972	240	38	,	,	PUNCT
ejpam-4972	240	39	j	j	PROPN
ejpam-4972	240	40	)	)	PUNCT
ejpam-4972	240	41	−	−	PROPN
ejpam-4972	240	42	gψ	gψ	VERB
ejpam-4972	240	43	−	−	NOUN
ejpam-4972	240	44	irresolute	irresolute	ADJ
ejpam-4972	240	45	)	)	PUNCT
ejpam-4972	240	46	when	when	SCONJ
ejpam-4972	240	47	t−1(w	t−1(w	NOUN
ejpam-4972	240	48	)	)	PUNCT
ejpam-4972	240	49	is	be	AUX
ejpam-4972	240	50	fuzzy	fuzzy	ADJ
ejpam-4972	240	51	(	(	PUNCT
ejpam-4972	240	52	i	i	PROPN
ejpam-4972	240	53	,	,	PUNCT
ejpam-4972	240	54	j)−	j)−	PROPN
ejpam-4972	240	55	gψ	gψ	VERB
ejpam-4972	240	56	−	−	PROPN
ejpam-4972	240	57	cld	cld	NOUN
ejpam-4972	240	58	of	of	ADP
ejpam-4972	240	59	x	x	PUNCT
ejpam-4972	240	60	for	for	SCONJ
ejpam-4972	240	61	all	all	DET
ejpam-4972	240	62	w	w	NOUN
ejpam-4972	240	63	is	be	AUX
ejpam-4972	240	64	(	(	PUNCT
ejpam-4972	240	65	i	i	PROPN
ejpam-4972	240	66	,	,	PUNCT
ejpam-4972	240	67	j)−	j)−	PROPN
ejpam-4972	240	68	gψ	gψ	VERB
ejpam-4972	240	69	−	−	PROPN
ejpam-4972	240	70	cld	cld	NOUN
ejpam-4972	240	71	of	of	ADP
ejpam-4972	240	72	y	y	PROPN
ejpam-4972	240	73	.	.	PUNCT
ejpam-4972	241	1	theorem	theorem	ADJ
ejpam-4972	241	2	10	10	NUM
ejpam-4972	241	3	.	.	PUNCT
ejpam-4972	242	1	suppose	suppose	VERB
ejpam-4972	242	2	t	t	NOUN
ejpam-4972	242	3	:	:	PUNCT
ejpam-4972	242	4	(	(	PUNCT
ejpam-4972	242	5	x	x	X
ejpam-4972	242	6	,	,	PUNCT
ejpam-4972	242	7	δ1	δ1	NOUN
ejpam-4972	242	8	,	,	PUNCT
ejpam-4972	242	9	δ2	δ2	ADJ
ejpam-4972	242	10	)	)	PUNCT
ejpam-4972	242	11	→	→	SYM
ejpam-4972	242	12	(	(	PUNCT
ejpam-4972	242	13	y	y	PROPN
ejpam-4972	242	14	,	,	PUNCT
ejpam-4972	242	15	σ1	σ1	PROPN
ejpam-4972	242	16	,	,	PUNCT
ejpam-4972	242	17	σ2	σ2	NOUN
ejpam-4972	242	18	)	)	PUNCT
ejpam-4972	242	19	.	.	PUNCT
ejpam-4972	243	1	thus	thus	ADV
ejpam-4972	243	2	,	,	PUNCT
ejpam-4972	243	3	the	the	DET
ejpam-4972	243	4	next	next	ADJ
ejpam-4972	243	5	claims	claim	NOUN
ejpam-4972	243	6	are	be	AUX
ejpam-4972	243	7	accurate	accurate	ADJ
ejpam-4972	243	8	:	:	PUNCT
ejpam-4972	243	9	(	(	PUNCT
ejpam-4972	243	10	1	1	X
ejpam-4972	243	11	)	)	PUNCT
ejpam-4972	243	12	if	if	SCONJ
ejpam-4972	243	13	t	t	PROPN
ejpam-4972	243	14	is	be	AUX
ejpam-4972	243	15	fuzzy	fuzzy	ADJ
ejpam-4972	243	16	(	(	PUNCT
ejpam-4972	243	17	i	i	PROPN
ejpam-4972	243	18	,	,	PUNCT
ejpam-4972	243	19	j)−	j)−	PROPN
ejpam-4972	243	20	gψ	gψ	VERB
ejpam-4972	243	21	−	−	NOUN
ejpam-4972	243	22	strongly	strongly	ADV
ejpam-4972	243	23	conts	cont	NOUN
ejpam-4972	243	24	,	,	PUNCT
ejpam-4972	243	25	thus	thus	ADV
ejpam-4972	243	26	it	it	PRON
ejpam-4972	243	27	is	be	AUX
ejpam-4972	243	28	δj	δj	ADP
ejpam-4972	243	29	−	−	PROPN
ejpam-4972	243	30	conts	cont	NOUN
ejpam-4972	243	31	.	.	PUNCT
ejpam-4972	244	1	(	(	PUNCT
ejpam-4972	244	2	2	2	X
ejpam-4972	244	3	)	)	PUNCT
ejpam-4972	244	4	if	if	SCONJ
ejpam-4972	244	5	t	t	PROPN
ejpam-4972	244	6	is	be	AUX
ejpam-4972	244	7	(	(	PUNCT
ejpam-4972	244	8	i	i	PROPN
ejpam-4972	244	9	,	,	PUNCT
ejpam-4972	244	10	j)−	j)−	PROPN
ejpam-4972	244	11	gψ	gψ	VERB
ejpam-4972	244	12	−	−	NOUN
ejpam-4972	244	13	strongly	strongly	ADV
ejpam-4972	244	14	conts	cont	NOUN
ejpam-4972	244	15	,	,	PUNCT
ejpam-4972	244	16	thus	thus	ADV
ejpam-4972	244	17	it	it	PRON
ejpam-4972	244	18	is	be	AUX
ejpam-4972	244	19	(	(	PUNCT
ejpam-4972	244	20	i	i	PROPN
ejpam-4972	244	21	,	,	PUNCT
ejpam-4972	244	22	j)−	j)−	PROPN
ejpam-4972	244	23	gψ	gψ	VERB
ejpam-4972	244	24	−	−	PROPN
ejpam-4972	244	25	irresolute	irresolute	ADJ
ejpam-4972	244	26	.	.	PUNCT
ejpam-4972	245	1	(	(	PUNCT
ejpam-4972	245	2	3	3	X
ejpam-4972	245	3	)	)	PUNCT
ejpam-4972	245	4	if	if	SCONJ
ejpam-4972	245	5	t	t	PROPN
ejpam-4972	245	6	is	be	AUX
ejpam-4972	245	7	(	(	PUNCT
ejpam-4972	245	8	i	i	PROPN
ejpam-4972	245	9	,	,	PUNCT
ejpam-4972	245	10	j)−	j)−	PROPN
ejpam-4972	245	11	gψ	gψ	VERB
ejpam-4972	245	12	−	−	PROPN
ejpam-4972	245	13	irresolute	irresolute	ADJ
ejpam-4972	245	14	,	,	PUNCT
ejpam-4972	245	15	thus	thus	ADV
ejpam-4972	245	16	it	it	PRON
ejpam-4972	245	17	is	be	AUX
ejpam-4972	245	18	(	(	PUNCT
ejpam-4972	245	19	i	i	PROPN
ejpam-4972	245	20	,	,	PUNCT
ejpam-4972	245	21	j)−	j)−	PROPN
ejpam-4972	245	22	gψ	gψ	VERB
ejpam-4972	245	23	−	−	PROPN
ejpam-4972	245	24	conts	cont	NOUN
ejpam-4972	245	25	.	.	PUNCT
ejpam-4972	246	1	proof	proof	NOUN
ejpam-4972	246	2	.	.	PUNCT
ejpam-4972	247	1	(	(	PUNCT
ejpam-4972	247	2	1	1	X
ejpam-4972	247	3	)	)	PUNCT
ejpam-4972	247	4	assume	assume	VERB
ejpam-4972	247	5	t	t	PROPN
ejpam-4972	247	6	is	be	AUX
ejpam-4972	247	7	(	(	PUNCT
ejpam-4972	247	8	i	i	PROPN
ejpam-4972	247	9	,	,	PUNCT
ejpam-4972	247	10	j)−	j)−	PROPN
ejpam-4972	247	11	gψ−	gψ−	PUNCT
ejpam-4972	247	12	strongly	strongly	ADV
ejpam-4972	247	13	conts	cont	NOUN
ejpam-4972	247	14	,	,	PUNCT
ejpam-4972	247	15	w	w	PROPN
ejpam-4972	247	16	∈	∈	PROPN
ejpam-4972	247	17	fσj	fσj	NOUN
ejpam-4972	247	18	.	.	PUNCT
ejpam-4972	248	1	since	since	SCONJ
ejpam-4972	248	2	w	w	NOUN
ejpam-4972	248	3	is	be	AUX
ejpam-4972	248	4	fuzzy	fuzzy	ADJ
ejpam-4972	248	5	closed	closed	ADJ
ejpam-4972	248	6	of	of	ADP
ejpam-4972	248	7	(	(	PUNCT
ejpam-4972	248	8	y	y	PROPN
ejpam-4972	248	9	,	,	PUNCT
ejpam-4972	248	10	σj	σj	NOUN
ejpam-4972	248	11	)	)	PUNCT
ejpam-4972	248	12	,	,	PUNCT
ejpam-4972	248	13	then	then	ADV
ejpam-4972	248	14	w	w	NOUN
ejpam-4972	248	15	is	be	AUX
ejpam-4972	248	16	(	(	PUNCT
ejpam-4972	248	17	i	i	PROPN
ejpam-4972	248	18	,	,	PUNCT
ejpam-4972	248	19	j	j	PROPN
ejpam-4972	248	20	)	)	PUNCT
ejpam-4972	248	21	−	−	PROPN
ejpam-4972	248	22	gψ	gψ	VERB
ejpam-4972	248	23	−	−	PROPN
ejpam-4972	248	24	cld	cld	NOUN
ejpam-4972	248	25	group	group	NOUN
ejpam-4972	248	26	of	of	ADP
ejpam-4972	248	27	y	y	PROPN
ejpam-4972	248	28	.	.	PUNCT
ejpam-4972	249	1	as	as	SCONJ
ejpam-4972	249	2	t	t	PROPN
ejpam-4972	249	3	is	be	AUX
ejpam-4972	249	4	fuzzy	fuzzy	ADJ
ejpam-4972	249	5	(	(	PUNCT
ejpam-4972	249	6	i	i	PROPN
ejpam-4972	249	7	,	,	PUNCT
ejpam-4972	249	8	j	j	PROPN
ejpam-4972	249	9	)	)	PUNCT
ejpam-4972	249	10	−	−	PROPN
ejpam-4972	249	11	gψ	gψ	VERB
ejpam-4972	249	12	−	−	NOUN
ejpam-4972	249	13	strongly	strongly	ADV
ejpam-4972	249	14	conts	cont	NOUN
ejpam-4972	249	15	,	,	PUNCT
ejpam-4972	249	16	thus	thus	ADV
ejpam-4972	249	17	t−1(w	t−1(w	ADJ
ejpam-4972	249	18	)	)	PUNCT
ejpam-4972	249	19	∈	∈	PROPN
ejpam-4972	249	20	fδj	fδj	NOUN
ejpam-4972	249	21	.	.	PUNCT
ejpam-4972	250	1	therefore	therefore	ADV
ejpam-4972	250	2	t	t	PROPN
ejpam-4972	250	3	is	be	AUX
ejpam-4972	250	4	δj	δj	ADP
ejpam-4972	250	5	−	−	PROPN
ejpam-4972	250	6	conts	cont	NOUN
ejpam-4972	250	7	.	.	PUNCT
ejpam-4972	251	1	(	(	PUNCT
ejpam-4972	251	2	2	2	X
ejpam-4972	251	3	)	)	PUNCT
ejpam-4972	251	4	assume	assume	VERB
ejpam-4972	251	5	t	t	PROPN
ejpam-4972	251	6	is	be	AUX
ejpam-4972	251	7	(	(	PUNCT
ejpam-4972	251	8	i	i	PROPN
ejpam-4972	251	9	,	,	PUNCT
ejpam-4972	251	10	j	j	PROPN
ejpam-4972	251	11	)	)	PUNCT
ejpam-4972	251	12	−	−	PROPN
ejpam-4972	251	13	gψ	gψ	VERB
ejpam-4972	251	14	−	−	NOUN
ejpam-4972	251	15	strongly	strongly	ADV
ejpam-4972	251	16	conts	cont	NOUN
ejpam-4972	251	17	and	and	CCONJ
ejpam-4972	251	18	w	w	NOUN
ejpam-4972	251	19	is	be	AUX
ejpam-4972	251	20	(	(	PUNCT
ejpam-4972	251	21	i	i	PROPN
ejpam-4972	251	22	,	,	PUNCT
ejpam-4972	251	23	j	j	PROPN
ejpam-4972	251	24	)	)	PUNCT
ejpam-4972	251	25	−	−	PROPN
ejpam-4972	251	26	gψ	gψ	VERB
ejpam-4972	251	27	−	−	PROPN
ejpam-4972	251	28	cld	cld	NOUN
ejpam-4972	251	29	group	group	NOUN
ejpam-4972	251	30	of	of	ADP
ejpam-4972	251	31	y	y	PROPN
ejpam-4972	251	32	.	.	PUNCT
ejpam-4972	252	1	thus	thus	ADV
ejpam-4972	252	2	t−1(w	t−1(w	ADV
ejpam-4972	252	3	)	)	PUNCT
ejpam-4972	252	4	∈	∈	PROPN
ejpam-4972	252	5	fδj	fδj	NOUN
ejpam-4972	252	6	,	,	PUNCT
ejpam-4972	252	7	so	so	CCONJ
ejpam-4972	252	8	t−1(w	t−1(w	NOUN
ejpam-4972	252	9	)	)	PUNCT
ejpam-4972	252	10	is	be	AUX
ejpam-4972	252	11	(	(	PUNCT
ejpam-4972	252	12	i	i	PROPN
ejpam-4972	252	13	,	,	PUNCT
ejpam-4972	252	14	j	j	PROPN
ejpam-4972	252	15	)	)	PUNCT
ejpam-4972	252	16	−	−	PROPN
ejpam-4972	252	17	gψ	gψ	VERB
ejpam-4972	252	18	−	−	PROPN
ejpam-4972	252	19	cld	cld	NOUN
ejpam-4972	252	20	group	group	NOUN
ejpam-4972	252	21	of	of	ADP
ejpam-4972	252	22	x.	x.	PROPN
ejpam-4972	252	23	consequently	consequently	ADV
ejpam-4972	252	24	,	,	PUNCT
ejpam-4972	252	25	t	t	PROPN
ejpam-4972	252	26	is	be	AUX
ejpam-4972	252	27	(	(	PUNCT
ejpam-4972	252	28	i	i	PROPN
ejpam-4972	252	29	,	,	PUNCT
ejpam-4972	252	30	j)−	j)−	PROPN
ejpam-4972	252	31	gψ	gψ	VERB
ejpam-4972	252	32	−	−	PROPN
ejpam-4972	252	33	irresolute	irresolute	ADJ
ejpam-4972	252	34	mapping	mapping	NOUN
ejpam-4972	252	35	.	.	PUNCT
ejpam-4972	253	1	(	(	PUNCT
ejpam-4972	253	2	3	3	X
ejpam-4972	253	3	)	)	PUNCT
ejpam-4972	253	4	assume	assume	VERB
ejpam-4972	253	5	t	t	PROPN
ejpam-4972	253	6	is	be	AUX
ejpam-4972	253	7	(	(	PUNCT
ejpam-4972	253	8	i	i	PROPN
ejpam-4972	253	9	,	,	PUNCT
ejpam-4972	253	10	j	j	PROPN
ejpam-4972	253	11	)	)	PUNCT
ejpam-4972	253	12	−	−	PROPN
ejpam-4972	253	13	gψ	gψ	VERB
ejpam-4972	253	14	−	−	NOUN
ejpam-4972	253	15	irresolute	irresolute	ADJ
ejpam-4972	253	16	,	,	PUNCT
ejpam-4972	253	17	w	w	PROPN
ejpam-4972	253	18	∈	∈	PROPN
ejpam-4972	253	19	fσj	fσj	NOUN
ejpam-4972	253	20	.	.	PUNCT
ejpam-4972	254	1	since	since	SCONJ
ejpam-4972	254	2	w	w	NOUN
ejpam-4972	254	3	is	be	AUX
ejpam-4972	254	4	fuzzy	fuzzy	ADJ
ejpam-4972	254	5	closed	closed	ADJ
ejpam-4972	254	6	of	of	ADP
ejpam-4972	254	7	(	(	PUNCT
ejpam-4972	254	8	y	y	PROPN
ejpam-4972	254	9	,	,	PUNCT
ejpam-4972	254	10	σj	σj	NOUN
ejpam-4972	254	11	)	)	PUNCT
ejpam-4972	254	12	,	,	PUNCT
ejpam-4972	254	13	then	then	ADV
ejpam-4972	254	14	w	w	NOUN
ejpam-4972	254	15	is	be	AUX
ejpam-4972	254	16	(	(	PUNCT
ejpam-4972	254	17	i	i	PROPN
ejpam-4972	254	18	,	,	PUNCT
ejpam-4972	254	19	j	j	PROPN
ejpam-4972	254	20	)	)	PUNCT
ejpam-4972	254	21	−	−	PROPN
ejpam-4972	254	22	gψ	gψ	VERB
ejpam-4972	254	23	−	−	PROPN
ejpam-4972	254	24	cld	cld	NOUN
ejpam-4972	254	25	of	of	ADP
ejpam-4972	254	26	y	y	PROPN
ejpam-4972	254	27	.	.	PUNCT
ejpam-4972	255	1	as	as	SCONJ
ejpam-4972	255	2	t	t	PROPN
ejpam-4972	255	3	is	be	AUX
ejpam-4972	255	4	(	(	PUNCT
ejpam-4972	255	5	i	i	PROPN
ejpam-4972	255	6	,	,	PUNCT
ejpam-4972	255	7	j	j	PROPN
ejpam-4972	255	8	)	)	PUNCT
ejpam-4972	255	9	−	−	PROPN
ejpam-4972	255	10	gψ	gψ	VERB
ejpam-4972	255	11	−	−	NOUN
ejpam-4972	255	12	irresolute	irresolute	ADJ
ejpam-4972	255	13	,	,	PUNCT
ejpam-4972	255	14	thus	thus	ADV
ejpam-4972	255	15	t−1(w	t−1(w	NOUN
ejpam-4972	255	16	)	)	PUNCT
ejpam-4972	255	17	is	be	AUX
ejpam-4972	255	18	(	(	PUNCT
ejpam-4972	255	19	i	i	PROPN
ejpam-4972	255	20	,	,	PUNCT
ejpam-4972	255	21	j)−	j)−	PROPN
ejpam-4972	255	22	gψ	gψ	VERB
ejpam-4972	255	23	−	−	PROPN
ejpam-4972	255	24	cld	cld	NOUN
ejpam-4972	255	25	of	of	ADP
ejpam-4972	255	26	x.	x.	NOUN
ejpam-4972	256	1	so	so	ADV
ejpam-4972	256	2	,	,	PUNCT
ejpam-4972	256	3	t	t	PROPN
ejpam-4972	256	4	is	be	AUX
ejpam-4972	256	5	(	(	PUNCT
ejpam-4972	256	6	i	i	PROPN
ejpam-4972	256	7	,	,	PUNCT
ejpam-4972	256	8	j)−	j)−	PROPN
ejpam-4972	256	9	gψ	gψ	VERB
ejpam-4972	256	10	−	−	PROPN
ejpam-4972	256	11	conts	cont	NOUN
ejpam-4972	256	12	.	.	PUNCT
ejpam-4972	257	1	remark	remark	PROPN
ejpam-4972	257	2	6	6	NUM
ejpam-4972	257	3	.	.	PUNCT
ejpam-4972	258	1	the	the	DET
ejpam-4972	258	2	next	next	ADJ
ejpam-4972	258	3	diagram	diagram	NOUN
ejpam-4972	258	4	explaining	explain	VERB
ejpam-4972	258	5	the	the	DET
ejpam-4972	258	6	relation	relation	NOUN
ejpam-4972	258	7	in	in	ADP
ejpam-4972	258	8	each	each	DET
ejpam-4972	258	9	statements	statement	NOUN
ejpam-4972	258	10	in	in	ADP
ejpam-4972	258	11	the	the	DET
ejpam-4972	258	12	above	above	ADJ
ejpam-4972	258	13	theorem	theorem	NOUN
ejpam-4972	258	14	:	:	PUNCT
ejpam-4972	258	15	figure	figure	NOUN
ejpam-4972	258	16	2	2	NUM
ejpam-4972	258	17	:	:	PUNCT
ejpam-4972	258	18	presents	present	VERB
ejpam-4972	258	19	the	the	DET
ejpam-4972	258	20	relationships	relationship	NOUN
ejpam-4972	258	21	via	via	ADP
ejpam-4972	258	22	all	all	DET
ejpam-4972	258	23	varieties	variety	NOUN
ejpam-4972	258	24	of	of	ADP
ejpam-4972	258	25	fuzzy	fuzzy	ADJ
ejpam-4972	258	26	(	(	PUNCT
ejpam-4972	258	27	i	i	PROPN
ejpam-4972	258	28	,	,	PUNCT
ejpam-4972	258	29	j)−	j)−	PROPN
ejpam-4972	258	30	gψ	gψ	VERB
ejpam-4972	258	31	−mappings	−mapping	NOUN
ejpam-4972	258	32	.	.	PUNCT
ejpam-4972	259	1	the	the	DET
ejpam-4972	259	2	coming	come	VERB
ejpam-4972	259	3	examples	example	NOUN
ejpam-4972	259	4	clear	clear	VERB
ejpam-4972	259	5	the	the	DET
ejpam-4972	259	6	opposite	opposite	ADJ
ejpam-4972	259	7	implications	implication	NOUN
ejpam-4972	259	8	of	of	ADP
ejpam-4972	259	9	figure	figure	NOUN
ejpam-4972	259	10	(	(	PUNCT
ejpam-4972	259	11	2	2	NUM
ejpam-4972	259	12	)	)	PUNCT
ejpam-4972	259	13	are	be	AUX
ejpam-4972	259	14	generally	generally	ADV
ejpam-4972	259	15	not	not	PART
ejpam-4972	259	16	true	true	ADJ
ejpam-4972	259	17	and	and	CCONJ
ejpam-4972	259	18	also	also	ADV
ejpam-4972	259	19	clear	clear	ADJ
ejpam-4972	259	20	that	that	SCONJ
ejpam-4972	259	21	the	the	DET
ejpam-4972	259	22	fuzzy	fuzzy	ADJ
ejpam-4972	259	23	δj	δj	ADP
ejpam-4972	259	24	−	−	PROPN
ejpam-4972	259	25	conts	cont	NOUN
ejpam-4972	259	26	and	and	CCONJ
ejpam-4972	259	27	(	(	PUNCT
ejpam-4972	259	28	i	i	PROPN
ejpam-4972	259	29	,	,	PUNCT
ejpam-4972	259	30	j)−	j)−	PROPN
ejpam-4972	259	31	gψ	gψ	VERB
ejpam-4972	259	32	−	−	PROPN
ejpam-4972	259	33	irresolute	irresolute	ADJ
ejpam-4972	259	34	are	be	AUX
ejpam-4972	259	35	independent	independent	ADJ
ejpam-4972	259	36	as	as	SCONJ
ejpam-4972	259	37	we	we	PRON
ejpam-4972	259	38	explain	explain	VERB
ejpam-4972	259	39	that	that	SCONJ
ejpam-4972	259	40	for	for	ADP
ejpam-4972	259	41	type	type	NOUN
ejpam-4972	259	42	ψ	ψ	NOUN
ejpam-4972	259	43	is	be	AUX
ejpam-4972	259	44	fuzzy	fuzzy	ADJ
ejpam-4972	259	45	α−open	α−open	NOUN
ejpam-4972	259	46	.	.	PUNCT
ejpam-4972	259	47	example	example	NOUN
ejpam-4972	260	1	7	7	NUM
ejpam-4972	260	2	.	.	PUNCT
ejpam-4972	260	3	suppose	suppose	VERB
ejpam-4972	260	4	e	e	NOUN
ejpam-4972	260	5	,	,	PUNCT
ejpam-4972	260	6	b	b	NOUN
ejpam-4972	260	7	,	,	PUNCT
ejpam-4972	260	8	g	g	NOUN
ejpam-4972	260	9	,	,	PUNCT
ejpam-4972	260	10	and	and	CCONJ
ejpam-4972	260	11	h	h	NOUN
ejpam-4972	260	12	are	be	AUX
ejpam-4972	260	13	subgroups	subgroup	NOUN
ejpam-4972	260	14	of	of	ADP
ejpam-4972	260	15	x	x	X
ejpam-4972	260	16	=	=	X
ejpam-4972	260	17	{	{	PUNCT
ejpam-4972	260	18	a	a	DET
ejpam-4972	260	19	,	,	PUNCT
ejpam-4972	260	20	b	b	NOUN
ejpam-4972	260	21	}	}	PUNCT
ejpam-4972	260	22	defined	define	VERB
ejpam-4972	260	23	as	as	ADP
ejpam-4972	260	24	:	:	PUNCT
ejpam-4972	260	25	e(a	e(a	NOUN
ejpam-4972	260	26	,	,	PUNCT
ejpam-4972	260	27	b	b	X
ejpam-4972	260	28	)	)	PUNCT
ejpam-4972	260	29	=	=	SYM
ejpam-4972	260	30	{	{	PUNCT
ejpam-4972	260	31	0.5	0.5	NUM
ejpam-4972	260	32	,	,	PUNCT
ejpam-4972	260	33	0.4	0.4	NUM
ejpam-4972	260	34	}	}	PUNCT
ejpam-4972	260	35	,	,	PUNCT
ejpam-4972	260	36	f	f	PROPN
ejpam-4972	260	37	(	(	PUNCT
ejpam-4972	260	38	a	a	DET
ejpam-4972	260	39	,	,	PUNCT
ejpam-4972	260	40	b	b	NOUN
ejpam-4972	260	41	)	)	PUNCT
ejpam-4972	260	42	=	=	NOUN
ejpam-4972	260	43	{	{	PUNCT
ejpam-4972	260	44	0.7	0.7	NUM
ejpam-4972	260	45	,	,	PUNCT
ejpam-4972	260	46	0.5	0.5	NUM
ejpam-4972	260	47	}	}	PUNCT
ejpam-4972	260	48	,	,	PUNCT
ejpam-4972	260	49	g(a	g(a	PROPN
ejpam-4972	260	50	,	,	PUNCT
ejpam-4972	260	51	b	b	NOUN
ejpam-4972	260	52	)	)	PUNCT
ejpam-4972	260	53	=	=	SYM
ejpam-4972	260	54	{	{	PUNCT
ejpam-4972	260	55	0.4	0.4	NUM
ejpam-4972	260	56	,	,	PUNCT
ejpam-4972	260	57	0.3	0.3	NUM
ejpam-4972	260	58	}	}	PUNCT
ejpam-4972	260	59	.	.	PUNCT
ejpam-4972	261	1	consider	consider	VERB
ejpam-4972	261	2	the	the	DET
ejpam-4972	261	3	fuzzy	fuzzy	ADJ
ejpam-4972	261	4	bitopology	bitopology	NOUN
ejpam-4972	261	5	δ1	δ1	NOUN
ejpam-4972	261	6	=	=	PUNCT
ejpam-4972	261	7	{	{	PUNCT
ejpam-4972	261	8	0	0	NUM
ejpam-4972	261	9	,	,	PUNCT
ejpam-4972	261	10	1	1	NUM
ejpam-4972	261	11	,	,	PUNCT
ejpam-4972	261	12	e	e	NOUN
ejpam-4972	261	13	}	}	PUNCT
ejpam-4972	261	14	,	,	PUNCT
ejpam-4972	261	15	δ2	δ2	VERB
ejpam-4972	261	16	=	=	SYM
ejpam-4972	261	17	{	{	PUNCT
ejpam-4972	261	18	0	0	NUM
ejpam-4972	261	19	,	,	PUNCT
ejpam-4972	261	20	1	1	NUM
ejpam-4972	261	21	,	,	PUNCT
ejpam-4972	261	22	f	f	X
ejpam-4972	261	23	,	,	PUNCT
ejpam-4972	261	24	g	g	NOUN
ejpam-4972	261	25	}	}	PUNCT
ejpam-4972	261	26	on	on	ADP
ejpam-4972	261	27	x.	x.	NOUN
ejpam-4972	261	28	suppose	suppose	VERB
ejpam-4972	261	29	n	n	X
ejpam-4972	261	30	,	,	PUNCT
ejpam-4972	261	31	m	m	VERB
ejpam-4972	261	32	are	be	AUX
ejpam-4972	261	33	fuzzy	fuzzy	ADJ
ejpam-4972	261	34	subgroups	subgroup	NOUN
ejpam-4972	261	35	of	of	ADP
ejpam-4972	261	36	y	y	PROPN
ejpam-4972	261	37	=	=	PUNCT
ejpam-4972	261	38	{	{	PUNCT
ejpam-4972	261	39	r	r	NOUN
ejpam-4972	261	40	,	,	PUNCT
ejpam-4972	261	41	h	h	NOUN
ejpam-4972	261	42	}	}	PUNCT
ejpam-4972	261	43	defined	define	VERB
ejpam-4972	261	44	as	as	SCONJ
ejpam-4972	261	45	follows	follow	VERB
ejpam-4972	261	46	:	:	PUNCT
ejpam-4972	261	47	n(r	n(r	NOUN
ejpam-4972	261	48	,	,	PUNCT
ejpam-4972	261	49	h	h	NOUN
ejpam-4972	261	50	)	)	PUNCT
ejpam-4972	261	51	=	=	PUNCT
ejpam-4972	261	52	{	{	PUNCT
ejpam-4972	261	53	0.3	0.3	NUM
ejpam-4972	261	54	,	,	PUNCT
ejpam-4972	261	55	0.1	0.1	NUM
ejpam-4972	261	56	}	}	PUNCT
ejpam-4972	261	57	,	,	PUNCT
ejpam-4972	261	58	m(r	m(r	PROPN
ejpam-4972	261	59	,	,	PUNCT
ejpam-4972	261	60	h	h	NOUN
ejpam-4972	261	61	)	)	PUNCT
ejpam-4972	261	62	=	=	PUNCT
ejpam-4972	261	63	{	{	PUNCT
ejpam-4972	261	64	0.7	0.7	NUM
ejpam-4972	261	65	,	,	PUNCT
ejpam-4972	261	66	0.6	0.6	NUM
ejpam-4972	261	67	}	}	PUNCT
ejpam-4972	261	68	.	.	PUNCT
ejpam-4972	262	1	consider	consider	VERB
ejpam-4972	262	2	the	the	DET
ejpam-4972	262	3	fuzzy	fuzzy	ADJ
ejpam-4972	262	4	bitopology	bitopology	NOUN
ejpam-4972	262	5	σ1	σ1	NOUN
ejpam-4972	262	6	=	=	PUNCT
ejpam-4972	262	7	{	{	PUNCT
ejpam-4972	262	8	0	0	NUM
ejpam-4972	262	9	,	,	PUNCT
ejpam-4972	262	10	1	1	NUM
ejpam-4972	262	11	,	,	PUNCT
ejpam-4972	262	12	n	n	CCONJ
ejpam-4972	262	13	}	}	PUNCT
ejpam-4972	262	14	,	,	PUNCT
ejpam-4972	262	15	σ2	σ2	PROPN
ejpam-4972	262	16	=	=	SYM
ejpam-4972	262	17	{	{	PUNCT
ejpam-4972	262	18	0	0	NUM
ejpam-4972	262	19	,	,	PUNCT
ejpam-4972	262	20	1,m	1,m	NOUN
ejpam-4972	262	21	}	}	PUNCT
ejpam-4972	262	22	on	on	ADP
ejpam-4972	262	23	y	y	PROPN
ejpam-4972	262	24	and	and	CCONJ
ejpam-4972	262	25	t(a	t(a	NOUN
ejpam-4972	262	26	)	)	PUNCT
ejpam-4972	262	27	=	=	SYM
ejpam-4972	262	28	r	r	NOUN
ejpam-4972	262	29	,	,	PUNCT
ejpam-4972	262	30	t(b	t(b	NOUN
ejpam-4972	262	31	)	)	PUNCT
ejpam-4972	262	32	=	=	SYM
ejpam-4972	263	1	h.	h.	NOUN
ejpam-4972	263	2	one	one	PRON
ejpam-4972	263	3	may	may	AUX
ejpam-4972	263	4	notice	notice	VERB
ejpam-4972	263	5	that	that	SCONJ
ejpam-4972	263	6	m	m	VERB
ejpam-4972	263	7	c	c	NOUN
ejpam-4972	263	8	is	be	AUX
ejpam-4972	263	9	fuzzy	fuzzy	ADJ
ejpam-4972	263	10	σ2	σ2	PROPN
ejpam-4972	263	11	−	−	PROPN
ejpam-4972	263	12	closed	close	VERB
ejpam-4972	263	13	of	of	ADP
ejpam-4972	263	14	y	y	PROPN
ejpam-4972	263	15	and	and	CCONJ
ejpam-4972	264	1	t−1(m	t−1(m	PROPN
ejpam-4972	264	2	c	c	X
ejpam-4972	264	3	)	)	PUNCT
ejpam-4972	264	4	is	be	AUX
ejpam-4972	264	5	fuzzy	fuzzy	ADJ
ejpam-4972	264	6	(	(	PUNCT
ejpam-4972	264	7	1	1	NUM
ejpam-4972	264	8	,	,	PUNCT
ejpam-4972	264	9	2	2	NUM
ejpam-4972	264	10	)	)	PUNCT
ejpam-4972	264	11	−	−	PROPN
ejpam-4972	264	12	gα	gα	ADP
ejpam-4972	264	13	−	−	PROPN
ejpam-4972	264	14	cld	cld	NOUN
ejpam-4972	264	15	of	of	ADP
ejpam-4972	264	16	x	x	PRON
ejpam-4972	264	17	,	,	PUNCT
ejpam-4972	264	18	so	so	SCONJ
ejpam-4972	264	19	t	t	PROPN
ejpam-4972	264	20	is	be	AUX
ejpam-4972	264	21	(	(	PUNCT
ejpam-4972	264	22	1	1	NUM
ejpam-4972	264	23	,	,	PUNCT
ejpam-4972	264	24	2	2	NUM
ejpam-4972	264	25	)	)	PUNCT
ejpam-4972	264	26	−	−	NOUN
ejpam-4972	264	27	gα	gα	ADP
ejpam-4972	264	28	−	−	PROPN
ejpam-4972	264	29	conts	cont	NOUN
ejpam-4972	264	30	,	,	PUNCT
ejpam-4972	264	31	but	but	CCONJ
ejpam-4972	264	32	not	not	PART
ejpam-4972	264	33	δ2	δ2	VERB
ejpam-4972	264	34	−	−	PROPN
ejpam-4972	264	35	conts	cont	NOUN
ejpam-4972	264	36	since	since	SCONJ
ejpam-4972	264	37	δ2	δ2	VERB
ejpam-4972	264	38	−	−	PROPN
ejpam-4972	264	39	cl(t−1(m	cl(t−1(m	PROPN
ejpam-4972	264	40	c	c	NOUN
ejpam-4972	264	41	)	)	PUNCT
ejpam-4972	264	42	)	)	PUNCT
ejpam-4972	264	43	not	not	PART
ejpam-4972	264	44	closed	close	VERB
ejpam-4972	264	45	of	of	ADP
ejpam-4972	264	46	x.	x.	NOUN
ejpam-4972	264	47	also	also	ADV
ejpam-4972	264	48	,	,	PUNCT
ejpam-4972	264	49	we	we	PRON
ejpam-4972	264	50	find	find	VERB
ejpam-4972	264	51	t	t	PROPN
ejpam-4972	264	52	is	be	AUX
ejpam-4972	264	53	(	(	PUNCT
ejpam-4972	264	54	i	i	PROPN
ejpam-4972	264	55	,	,	PUNCT
ejpam-4972	264	56	j)−	j)−	PROPN
ejpam-4972	264	57	gψ	gψ	VERB
ejpam-4972	264	58	−	−	NOUN
ejpam-4972	264	59	irresolute	irresolute	ADJ
ejpam-4972	264	60	but	but	CCONJ
ejpam-4972	264	61	not	not	PART
ejpam-4972	264	62	fuzzy	fuzzy	ADJ
ejpam-4972	264	63	(	(	PUNCT
ejpam-4972	264	64	1	1	NUM
ejpam-4972	264	65	,	,	PUNCT
ejpam-4972	264	66	2)−	2)−	PROPN
ejpam-4972	264	67	gα−	gα−	PRON
ejpam-4972	264	68	strongly	strongly	ADV
ejpam-4972	264	69	conts	cont	NOUN
ejpam-4972	264	70	since	since	SCONJ
ejpam-4972	264	71	m	m	PROPN
ejpam-4972	264	72	c	c	NOUN
ejpam-4972	264	73	is	be	AUX
ejpam-4972	264	74	fuzzy	fuzzy	ADJ
ejpam-4972	264	75	(	(	PUNCT
ejpam-4972	264	76	1	1	NUM
ejpam-4972	264	77	,	,	PUNCT
ejpam-4972	264	78	2)−	2)−	PROPN
ejpam-4972	264	79	gα−	gα−	NUM
ejpam-4972	264	80	cld	cld	NOUN
ejpam-4972	264	81	of	of	ADP
ejpam-4972	264	82	y	y	PROPN
ejpam-4972	265	1	but	but	CCONJ
ejpam-4972	265	2	t−1	t−1	PROPN
ejpam-4972	265	3	is	be	AUX
ejpam-4972	265	4	not	not	PART
ejpam-4972	265	5	closed	close	VERB
ejpam-4972	265	6	of	of	ADP
ejpam-4972	265	7	x.	x.	PROPN
ejpam-4972	265	8	a.	a.	PROPN
ejpam-4972	265	9	a.	a.	PROPN
ejpam-4972	265	10	alharbi	alharbi	PROPN
ejpam-4972	265	11	,	,	PUNCT
ejpam-4972	265	12	a.	a.	NOUN
ejpam-4972	265	13	kilicman	kilicman	PROPN
ejpam-4972	265	14	/	/	SYM
ejpam-4972	265	15	eur	eur	PROPN
ejpam-4972	265	16	.	.	PUNCT
ejpam-4972	266	1	j.	j.	PROPN
ejpam-4972	266	2	pure	pure	PROPN
ejpam-4972	266	3	appl	appl	PROPN
ejpam-4972	266	4	.	.	PROPN
ejpam-4972	266	5	math	math	PROPN
ejpam-4972	266	6	,	,	PUNCT
ejpam-4972	266	7	16	16	NUM
ejpam-4972	266	8	(	(	PUNCT
ejpam-4972	266	9	4	4	NUM
ejpam-4972	266	10	)	)	PUNCT
ejpam-4972	266	11	(	(	PUNCT
ejpam-4972	266	12	2023	2023	NUM
ejpam-4972	266	13	)	)	PUNCT
ejpam-4972	266	14	,	,	PUNCT
ejpam-4972	266	15	2613	2613	NUM
ejpam-4972	266	16	-	-	SYM
ejpam-4972	266	17	2631	2631	NUM
ejpam-4972	266	18	2622	2622	NUM
ejpam-4972	266	19	theorem	theorem	VERB
ejpam-4972	266	20	11	11	NUM
ejpam-4972	266	21	.	.	PUNCT
ejpam-4972	267	1	suppose	suppose	VERB
ejpam-4972	267	2	t	t	NOUN
ejpam-4972	267	3	:	:	PUNCT
ejpam-4972	267	4	(	(	PUNCT
ejpam-4972	267	5	x	x	X
ejpam-4972	267	6	,	,	PUNCT
ejpam-4972	267	7	δ1	δ1	NOUN
ejpam-4972	267	8	,	,	PUNCT
ejpam-4972	267	9	δ2	δ2	ADJ
ejpam-4972	267	10	)	)	PUNCT
ejpam-4972	267	11	→	→	SYM
ejpam-4972	267	12	(	(	PUNCT
ejpam-4972	267	13	y	y	PROPN
ejpam-4972	267	14	,	,	PUNCT
ejpam-4972	267	15	σ1	σ1	PROPN
ejpam-4972	267	16	,	,	PUNCT
ejpam-4972	267	17	σ2	σ2	NOUN
ejpam-4972	267	18	)	)	PUNCT
ejpam-4972	267	19	is	be	AUX
ejpam-4972	267	20	fuzzy	fuzzy	ADJ
ejpam-4972	267	21	(	(	PUNCT
ejpam-4972	267	22	i	i	NOUN
ejpam-4972	267	23	,	,	PUNCT
ejpam-4972	267	24	j)−gψ−irresolute	j)−gψ−irresolute	PROPN
ejpam-4972	267	25	mapping	mapping	NOUN
ejpam-4972	267	26	,	,	PUNCT
ejpam-4972	267	27	with	with	SCONJ
ejpam-4972	267	28	all	all	PRON
ejpam-4972	267	29	(	(	PUNCT
ejpam-4972	267	30	i	i	PROPN
ejpam-4972	267	31	,	,	PUNCT
ejpam-4972	267	32	j)−	j)−	PROPN
ejpam-4972	267	33	gψ−	gψ−	PUNCT
ejpam-4972	267	34	cld	cld	PROPN
ejpam-4972	267	35	of	of	ADP
ejpam-4972	267	36	x	x	PUNCT
ejpam-4972	267	37	is	be	AUX
ejpam-4972	267	38	fuzzy	fuzzy	ADJ
ejpam-4972	267	39	open	open	ADJ
ejpam-4972	267	40	in	in	ADP
ejpam-4972	267	41	(	(	PUNCT
ejpam-4972	267	42	x	x	NOUN
ejpam-4972	267	43	,	,	PUNCT
ejpam-4972	267	44	δi	δi	NOUN
ejpam-4972	267	45	)	)	PUNCT
ejpam-4972	267	46	.	.	PUNCT
ejpam-4972	268	1	hence	hence	ADV
ejpam-4972	268	2	t	t	PROPN
ejpam-4972	268	3	is	be	AUX
ejpam-4972	268	4	δj	δj	ADJ
ejpam-4972	268	5	−ψ−	−ψ−	NOUN
ejpam-4972	268	6	conts	cont	NOUN
ejpam-4972	268	7	mapping	mapping	NOUN
ejpam-4972	268	8	.	.	PUNCT
ejpam-4972	269	1	proof	proof	NOUN
ejpam-4972	269	2	.	.	PUNCT
ejpam-4972	270	1	assumew	assumew	PROPN
ejpam-4972	270	2	∈	∈	PROPN
ejpam-4972	270	3	fσj	fσj	NOUN
ejpam-4972	270	4	.	.	PUNCT
ejpam-4972	271	1	thenw	thenw	NOUN
ejpam-4972	271	2	is	be	AUX
ejpam-4972	271	3	(	(	PUNCT
ejpam-4972	271	4	i	i	PROPN
ejpam-4972	271	5	,	,	PUNCT
ejpam-4972	271	6	j)−gψ−cld	j)−gψ−cld	PROPN
ejpam-4972	271	7	of	of	ADP
ejpam-4972	271	8	y	y	PROPN
ejpam-4972	271	9	.	.	PUNCT
ejpam-4972	272	1	as	as	SCONJ
ejpam-4972	272	2	t	t	PROPN
ejpam-4972	272	3	is	be	AUX
ejpam-4972	272	4	(	(	PUNCT
ejpam-4972	272	5	i	i	PROPN
ejpam-4972	272	6	,	,	PUNCT
ejpam-4972	272	7	j)−gψ−irresolute	j)−gψ−irresolute	PROPN
ejpam-4972	272	8	,	,	PUNCT
ejpam-4972	272	9	then	then	ADV
ejpam-4972	272	10	t−1(w	t−1(w	INTJ
ejpam-4972	272	11	)	)	PUNCT
ejpam-4972	272	12	is	be	AUX
ejpam-4972	272	13	(	(	PUNCT
ejpam-4972	272	14	i	i	PROPN
ejpam-4972	272	15	,	,	PUNCT
ejpam-4972	272	16	j	j	PROPN
ejpam-4972	272	17	)	)	PUNCT
ejpam-4972	272	18	−	−	PROPN
ejpam-4972	272	19	gψ	gψ	VERB
ejpam-4972	272	20	−	−	PROPN
ejpam-4972	272	21	cld	cld	NOUN
ejpam-4972	272	22	of	of	ADP
ejpam-4972	272	23	x.	x.	NOUN
ejpam-4972	272	24	thus	thus	ADV
ejpam-4972	272	25	by	by	ADP
ejpam-4972	272	26	hypotheses	hypothesis	NOUN
ejpam-4972	272	27	t−1(w	t−1(w	NOUN
ejpam-4972	272	28	)	)	PUNCT
ejpam-4972	272	29	∈	∈	PROPN
ejpam-4972	272	30	fo(x	fo(x	PUNCT
ejpam-4972	272	31	,	,	PUNCT
ejpam-4972	272	32	δi	δi	NOUN
ejpam-4972	272	33	)	)	PUNCT
ejpam-4972	272	34	,	,	PUNCT
ejpam-4972	272	35	so	so	CCONJ
ejpam-4972	272	36	t−1(w	t−1(w	X
ejpam-4972	272	37	)	)	PUNCT
ejpam-4972	272	38	∈	∈	PROPN
ejpam-4972	272	39	fψc(x	fψc(x	PROPN
ejpam-4972	272	40	,	,	PUNCT
ejpam-4972	272	41	δj	δj	NOUN
ejpam-4972	272	42	)	)	PUNCT
ejpam-4972	272	43	.	.	PUNCT
ejpam-4972	273	1	theretore	theretore	NOUN
ejpam-4972	273	2	t	t	PROPN
ejpam-4972	273	3	is	be	AUX
ejpam-4972	273	4	fuzzy	fuzzy	ADJ
ejpam-4972	273	5	δj	δj	ADP
ejpam-4972	273	6	−	−	PROPN
ejpam-4972	273	7	ψ	ψ	SYM
ejpam-4972	273	8	−	−	PROPN
ejpam-4972	273	9	conts	cont	NOUN
ejpam-4972	273	10	mapping	mapping	NOUN
ejpam-4972	273	11	.	.	PUNCT
ejpam-4972	274	1	theorem	theorem	ADJ
ejpam-4972	274	2	12	12	NUM
ejpam-4972	274	3	.	.	PUNCT
ejpam-4972	275	1	suppose	suppose	VERB
ejpam-4972	275	2	t	t	NOUN
ejpam-4972	275	3	:	:	PUNCT
ejpam-4972	275	4	(	(	PUNCT
ejpam-4972	275	5	x	x	X
ejpam-4972	275	6	,	,	PUNCT
ejpam-4972	275	7	δ1	δ1	NOUN
ejpam-4972	275	8	,	,	PUNCT
ejpam-4972	275	9	δ2	δ2	ADJ
ejpam-4972	275	10	)	)	PUNCT
ejpam-4972	275	11	→	→	SYM
ejpam-4972	275	12	(	(	PUNCT
ejpam-4972	275	13	y	y	PROPN
ejpam-4972	275	14	,	,	PUNCT
ejpam-4972	275	15	σ1	σ1	PROPN
ejpam-4972	275	16	,	,	PUNCT
ejpam-4972	275	17	σ2	σ2	NOUN
ejpam-4972	275	18	)	)	PUNCT
ejpam-4972	275	19	is	be	AUX
ejpam-4972	275	20	fuzzy	fuzzy	ADJ
ejpam-4972	275	21	δj−ψ−irresolute	δj−ψ−irresolute	NUM
ejpam-4972	276	1	mapping	mapping	NOUN
ejpam-4972	276	2	,	,	PUNCT
ejpam-4972	276	3	and	and	CCONJ
ejpam-4972	276	4	every	every	DET
ejpam-4972	276	5	fuzzy	fuzzy	ADJ
ejpam-4972	276	6	(	(	PUNCT
ejpam-4972	276	7	i	i	PROPN
ejpam-4972	276	8	,	,	PUNCT
ejpam-4972	276	9	j)−gψ−cld	j)−gψ−cld	PRON
ejpam-4972	276	10	of	of	ADP
ejpam-4972	276	11	y	y	PROPN
ejpam-4972	276	12	is	be	AUX
ejpam-4972	276	13	fuzzy	fuzzy	ADJ
ejpam-4972	276	14	open	open	ADJ
ejpam-4972	276	15	of	of	ADP
ejpam-4972	276	16	(	(	PUNCT
ejpam-4972	276	17	y	y	PROPN
ejpam-4972	276	18	,	,	PUNCT
ejpam-4972	276	19	σi	σi	NOUN
ejpam-4972	276	20	)	)	PUNCT
ejpam-4972	276	21	.	.	PUNCT
ejpam-4972	277	1	hence	hence	ADV
ejpam-4972	277	2	t	t	PROPN
ejpam-4972	277	3	is	be	AUX
ejpam-4972	277	4	(	(	PUNCT
ejpam-4972	277	5	i	i	PROPN
ejpam-4972	277	6	,	,	PUNCT
ejpam-4972	277	7	j)−gψ−	j)−gψ−	PROPN
ejpam-4972	277	8	irresolute	irresolute	VERB
ejpam-4972	277	9	mapping	mapping	NOUN
ejpam-4972	277	10	.	.	PUNCT
ejpam-4972	278	1	proof	proof	NOUN
ejpam-4972	278	2	.	.	PUNCT
ejpam-4972	279	1	suppose	suppose	VERB
ejpam-4972	279	2	w	w	NOUN
ejpam-4972	279	3	is	be	AUX
ejpam-4972	279	4	(	(	PUNCT
ejpam-4972	279	5	i	i	PROPN
ejpam-4972	279	6	,	,	PUNCT
ejpam-4972	279	7	j	j	PROPN
ejpam-4972	279	8	)	)	PUNCT
ejpam-4972	279	9	−	−	PROPN
ejpam-4972	279	10	gψ	gψ	VERB
ejpam-4972	279	11	−	−	PROPN
ejpam-4972	279	12	cld	cld	NOUN
ejpam-4972	279	13	group	group	NOUN
ejpam-4972	279	14	of	of	ADP
ejpam-4972	279	15	y	y	PROPN
ejpam-4972	279	16	.	.	PUNCT
ejpam-4972	280	1	then	then	ADV
ejpam-4972	280	2	by	by	ADP
ejpam-4972	280	3	hypotheses	hypothesis	NOUN
ejpam-4972	280	4	w	w	PROPN
ejpam-4972	280	5	∈	∈	PROPN
ejpam-4972	280	6	(	(	PUNCT
ejpam-4972	280	7	x	x	NOUN
ejpam-4972	280	8	,	,	PUNCT
ejpam-4972	280	9	δi	δi	NOUN
ejpam-4972	280	10	)	)	PUNCT
ejpam-4972	280	11	,	,	PUNCT
ejpam-4972	280	12	and	and	CCONJ
ejpam-4972	280	13	hence	hence	ADV
ejpam-4972	280	14	w	w	PROPN
ejpam-4972	280	15	∈	∈	PROPN
ejpam-4972	280	16	fψc(y	fψc(y	NOUN
ejpam-4972	280	17	,	,	PUNCT
ejpam-4972	280	18	σj	σj	NOUN
ejpam-4972	280	19	)	)	PUNCT
ejpam-4972	280	20	.	.	PUNCT
ejpam-4972	281	1	as	as	SCONJ
ejpam-4972	281	2	t	t	PROPN
ejpam-4972	281	3	is	be	AUX
ejpam-4972	281	4	δj	δj	ADP
ejpam-4972	281	5	−	−	PROPN
ejpam-4972	281	6	ψ	ψ	NOUN
ejpam-4972	281	7	−	−	NOUN
ejpam-4972	281	8	irresolute	irresolute	ADJ
ejpam-4972	281	9	,	,	PUNCT
ejpam-4972	281	10	then	then	ADV
ejpam-4972	281	11	t−1(w	t−1(w	ADV
ejpam-4972	281	12	)	)	PUNCT
ejpam-4972	281	13	∈	∈	PROPN
ejpam-4972	281	14	fψc(x	fψc(x	PROPN
ejpam-4972	281	15	,	,	PUNCT
ejpam-4972	281	16	δj	δj	NOUN
ejpam-4972	281	17	)	)	PUNCT
ejpam-4972	281	18	,	,	PUNCT
ejpam-4972	281	19	and	and	CCONJ
ejpam-4972	281	20	hence	hence	ADV
ejpam-4972	281	21	t−1(w	t−1(w	NOUN
ejpam-4972	281	22	)	)	PUNCT
ejpam-4972	281	23	is	be	AUX
ejpam-4972	281	24	fuzzy	fuzzy	ADJ
ejpam-4972	281	25	(	(	PUNCT
ejpam-4972	281	26	i	i	PROPN
ejpam-4972	281	27	,	,	PUNCT
ejpam-4972	281	28	j	j	PROPN
ejpam-4972	281	29	)	)	PUNCT
ejpam-4972	281	30	−	−	PROPN
ejpam-4972	281	31	gψ	gψ	VERB
ejpam-4972	281	32	−	−	PROPN
ejpam-4972	281	33	cld	cld	NOUN
ejpam-4972	281	34	of	of	ADP
ejpam-4972	281	35	x.	x.	PROPN
ejpam-4972	281	36	hence	hence	ADV
ejpam-4972	281	37	,	,	PUNCT
ejpam-4972	281	38	t	t	PROPN
ejpam-4972	281	39	is	be	AUX
ejpam-4972	281	40	fuzzy	fuzzy	ADJ
ejpam-4972	281	41	(	(	PUNCT
ejpam-4972	281	42	i	i	PROPN
ejpam-4972	281	43	,	,	PUNCT
ejpam-4972	281	44	j	j	PROPN
ejpam-4972	281	45	)	)	PUNCT
ejpam-4972	281	46	−	−	PROPN
ejpam-4972	281	47	gψ	gψ	VERB
ejpam-4972	281	48	−	−	NOUN
ejpam-4972	281	49	irresolute	irresolute	ADJ
ejpam-4972	281	50	mapping	mapping	NOUN
ejpam-4972	281	51	.	.	PUNCT
ejpam-4972	282	1	theorem	theorem	VERB
ejpam-4972	282	2	13	13	NUM
ejpam-4972	282	3	.	.	PUNCT
ejpam-4972	283	1	suppose	suppose	VERB
ejpam-4972	283	2	t	t	NOUN
ejpam-4972	283	3	:	:	PUNCT
ejpam-4972	283	4	(	(	PUNCT
ejpam-4972	283	5	x	x	X
ejpam-4972	283	6	,	,	PUNCT
ejpam-4972	283	7	δ1	δ1	NOUN
ejpam-4972	283	8	,	,	PUNCT
ejpam-4972	283	9	δ2	δ2	ADJ
ejpam-4972	283	10	)	)	PUNCT
ejpam-4972	283	11	→	→	SYM
ejpam-4972	283	12	(	(	PUNCT
ejpam-4972	283	13	y	y	PROPN
ejpam-4972	283	14	,	,	PUNCT
ejpam-4972	283	15	σ1	σ1	PROPN
ejpam-4972	283	16	,	,	PUNCT
ejpam-4972	283	17	σ2	σ2	NOUN
ejpam-4972	283	18	)	)	PUNCT
ejpam-4972	283	19	.	.	PUNCT
ejpam-4972	284	1	thus	thus	ADV
ejpam-4972	284	2	,	,	PUNCT
ejpam-4972	284	3	the	the	DET
ejpam-4972	284	4	next	next	ADJ
ejpam-4972	284	5	claims	claim	NOUN
ejpam-4972	284	6	are	be	AUX
ejpam-4972	284	7	accurate	accurate	ADJ
ejpam-4972	284	8	:	:	PUNCT
ejpam-4972	284	9	(	(	PUNCT
ejpam-4972	284	10	1	1	X
ejpam-4972	284	11	)	)	PUNCT
ejpam-4972	284	12	if	if	SCONJ
ejpam-4972	284	13	t	t	PROPN
ejpam-4972	284	14	is	be	AUX
ejpam-4972	284	15	(	(	PUNCT
ejpam-4972	284	16	i	i	PROPN
ejpam-4972	284	17	,	,	PUNCT
ejpam-4972	284	18	j)−	j)−	PROPN
ejpam-4972	284	19	gβ−	gβ−	PROPN
ejpam-4972	284	20	strongly	strongly	ADV
ejpam-4972	284	21	conts	cont	NOUN
ejpam-4972	284	22	,	,	PUNCT
ejpam-4972	284	23	so	so	SCONJ
ejpam-4972	284	24	it	it	PRON
ejpam-4972	284	25	is	be	AUX
ejpam-4972	284	26	(	(	PUNCT
ejpam-4972	284	27	i	i	PROPN
ejpam-4972	284	28	,	,	PUNCT
ejpam-4972	284	29	j)−	j)−	PROPN
ejpam-4972	284	30	gs−	gs−	NUM
ejpam-4972	284	31	strongly	strongly	ADV
ejpam-4972	284	32	conts	cont	VERB
ejpam-4972	284	33	also	also	ADV
ejpam-4972	284	34	(	(	PUNCT
ejpam-4972	284	35	i	i	PROPN
ejpam-4972	284	36	,	,	PUNCT
ejpam-4972	284	37	j)−	j)−	PROPN
ejpam-4972	284	38	gp−	gp−	PRON
ejpam-4972	284	39	strongly	strongly	ADV
ejpam-4972	284	40	conts	cont	NOUN
ejpam-4972	284	41	.	.	PUNCT
ejpam-4972	285	1	(	(	PUNCT
ejpam-4972	285	2	2	2	X
ejpam-4972	285	3	)	)	PUNCT
ejpam-4972	285	4	if	if	SCONJ
ejpam-4972	285	5	t	t	PROPN
ejpam-4972	285	6	is	be	AUX
ejpam-4972	285	7	(	(	PUNCT
ejpam-4972	285	8	i	i	PROPN
ejpam-4972	285	9	,	,	PUNCT
ejpam-4972	285	10	j)−	j)−	PROPN
ejpam-4972	285	11	gs−	gs−	NUM
ejpam-4972	285	12	strongly	strongly	ADV
ejpam-4972	285	13	conts	cont	NOUN
ejpam-4972	285	14	or	or	CCONJ
ejpam-4972	285	15	(	(	PUNCT
ejpam-4972	285	16	i	i	PROPN
ejpam-4972	285	17	,	,	PUNCT
ejpam-4972	285	18	j)−	j)−	PROPN
ejpam-4972	285	19	gp−	gp−	PROPN
ejpam-4972	285	20	strongly	strongly	ADV
ejpam-4972	285	21	conts	cont	NOUN
ejpam-4972	285	22	,	,	PUNCT
ejpam-4972	285	23	so	so	SCONJ
ejpam-4972	285	24	it	it	PRON
ejpam-4972	285	25	is	be	AUX
ejpam-4972	285	26	(	(	PUNCT
ejpam-4972	285	27	i	i	PROPN
ejpam-4972	285	28	,	,	PUNCT
ejpam-4972	285	29	j)−	j)−	PROPN
ejpam-4972	285	30	gα−	gα−	PUNCT
ejpam-4972	285	31	strongly	strongly	ADV
ejpam-4972	285	32	conts	cont	NOUN
ejpam-4972	285	33	.	.	PUNCT
ejpam-4972	286	1	(	(	PUNCT
ejpam-4972	286	2	3	3	X
ejpam-4972	286	3	)	)	PUNCT
ejpam-4972	286	4	if	if	SCONJ
ejpam-4972	286	5	t	t	PROPN
ejpam-4972	286	6	is	be	AUX
ejpam-4972	286	7	(	(	PUNCT
ejpam-4972	286	8	i	i	PROPN
ejpam-4972	286	9	,	,	PUNCT
ejpam-4972	286	10	j)−	j)−	PROPN
ejpam-4972	286	11	gα−	gα−	PUNCT
ejpam-4972	286	12	strongly	strongly	ADV
ejpam-4972	286	13	conts	cont	NOUN
ejpam-4972	286	14	,	,	PUNCT
ejpam-4972	286	15	so	so	SCONJ
ejpam-4972	286	16	it	it	PRON
ejpam-4972	286	17	is	be	AUX
ejpam-4972	286	18	(	(	PUNCT
ejpam-4972	286	19	i	i	PROPN
ejpam-4972	286	20	,	,	PUNCT
ejpam-4972	286	21	j)−	j)−	PROPN
ejpam-4972	286	22	g	g	PROPN
ejpam-4972	286	23	−	−	PROPN
ejpam-4972	286	24	strongly	strongly	ADV
ejpam-4972	286	25	conts	cont	NOUN
ejpam-4972	286	26	.	.	PUNCT
ejpam-4972	287	1	proof	proof	NOUN
ejpam-4972	287	2	.	.	PUNCT
ejpam-4972	288	1	it	it	PRON
ejpam-4972	288	2	is	be	AUX
ejpam-4972	288	3	clear	clear	ADJ
ejpam-4972	288	4	by	by	ADP
ejpam-4972	288	5	uses	use	VERB
ejpam-4972	288	6	theorems	theorem	NOUN
ejpam-4972	288	7	in	in	ADP
ejpam-4972	288	8	[	[	X
ejpam-4972	288	9	3	3	NUM
ejpam-4972	288	10	]	]	PUNCT
ejpam-4972	288	11	.	.	PUNCT
ejpam-4972	289	1	remark	remark	PROPN
ejpam-4972	289	2	7	7	NUM
ejpam-4972	289	3	.	.	PUNCT
ejpam-4972	290	1	the	the	DET
ejpam-4972	290	2	following	follow	VERB
ejpam-4972	290	3	diagram	diagram	NOUN
ejpam-4972	290	4	explaining	explain	VERB
ejpam-4972	290	5	the	the	DET
ejpam-4972	290	6	relation	relation	NOUN
ejpam-4972	290	7	in	in	ADP
ejpam-4972	290	8	each	each	DET
ejpam-4972	290	9	statements	statement	NOUN
ejpam-4972	290	10	in	in	ADP
ejpam-4972	290	11	the	the	DET
ejpam-4972	290	12	above	above	ADJ
ejpam-4972	290	13	theorem	theorem	NOUN
ejpam-4972	290	14	:	:	PUNCT
ejpam-4972	290	15	figure	figure	NOUN
ejpam-4972	290	16	3	3	NUM
ejpam-4972	290	17	:	:	PUNCT
ejpam-4972	290	18	presents	present	VERB
ejpam-4972	290	19	the	the	DET
ejpam-4972	290	20	relationships	relationship	NOUN
ejpam-4972	290	21	via	via	ADP
ejpam-4972	290	22	all	all	DET
ejpam-4972	290	23	varieties	variety	NOUN
ejpam-4972	290	24	of	of	ADP
ejpam-4972	290	25	fuzzy	fuzzy	ADJ
ejpam-4972	290	26	(	(	PUNCT
ejpam-4972	290	27	i	i	PROPN
ejpam-4972	290	28	,	,	PUNCT
ejpam-4972	290	29	j)−	j)−	PROPN
ejpam-4972	290	30	gψ	gψ	VERB
ejpam-4972	290	31	−	−	NOUN
ejpam-4972	290	32	strongly	strongly	ADV
ejpam-4972	290	33	conts	cont	NOUN
ejpam-4972	290	34	.	.	PUNCT
ejpam-4972	291	1	the	the	DET
ejpam-4972	291	2	converses	converse	NOUN
ejpam-4972	291	3	of	of	ADP
ejpam-4972	291	4	the	the	DET
ejpam-4972	291	5	above	above	ADJ
ejpam-4972	291	6	relations	relation	NOUN
ejpam-4972	291	7	are	be	AUX
ejpam-4972	291	8	not	not	PART
ejpam-4972	291	9	valid	valid	ADJ
ejpam-4972	291	10	in	in	ADP
ejpam-4972	291	11	general	general	ADJ
ejpam-4972	291	12	and	and	CCONJ
ejpam-4972	291	13	this	this	PRON
ejpam-4972	291	14	is	be	AUX
ejpam-4972	291	15	based	base	VERB
ejpam-4972	291	16	on	on	ADP
ejpam-4972	291	17	the	the	DET
ejpam-4972	291	18	relationships	relationship	NOUN
ejpam-4972	291	19	between	between	ADP
ejpam-4972	291	20	the	the	DET
ejpam-4972	291	21	(	(	PUNCT
ejpam-4972	291	22	i	i	PROPN
ejpam-4972	291	23	,	,	PUNCT
ejpam-4972	291	24	j	j	PROPN
ejpam-4972	291	25	)	)	PUNCT
ejpam-4972	291	26	−	−	PROPN
ejpam-4972	291	27	gψ	gψ	VERB
ejpam-4972	292	1	−	−	PROPN
ejpam-4972	292	2	cld	cld	NOUN
ejpam-4972	292	3	groups	group	NOUN
ejpam-4972	292	4	that	that	PRON
ejpam-4972	292	5	were	be	AUX
ejpam-4972	292	6	explained	explain	VERB
ejpam-4972	292	7	with	with	ADP
ejpam-4972	292	8	examples	example	NOUN
ejpam-4972	292	9	in	in	ADP
ejpam-4972	292	10	reference	reference	NOUN
ejpam-4972	292	11	no	no	PRON
ejpam-4972	292	12	[	[	X
ejpam-4972	292	13	3	3	NUM
ejpam-4972	292	14	]	]	PUNCT
ejpam-4972	292	15	.	.	PUNCT
ejpam-4972	292	16	a.	a.	NOUN
ejpam-4972	292	17	a.	a.	PROPN
ejpam-4972	292	18	alharbi	alharbi	PROPN
ejpam-4972	292	19	,	,	PUNCT
ejpam-4972	292	20	a.	a.	NOUN
ejpam-4972	292	21	kilicman	kilicman	PROPN
ejpam-4972	292	22	/	/	SYM
ejpam-4972	292	23	eur	eur	PROPN
ejpam-4972	292	24	.	.	PUNCT
ejpam-4972	293	1	j.	j.	PROPN
ejpam-4972	293	2	pure	pure	PROPN
ejpam-4972	293	3	appl	appl	PROPN
ejpam-4972	293	4	.	.	PROPN
ejpam-4972	293	5	math	math	PROPN
ejpam-4972	293	6	,	,	PUNCT
ejpam-4972	293	7	16	16	NUM
ejpam-4972	293	8	(	(	PUNCT
ejpam-4972	293	9	4	4	NUM
ejpam-4972	293	10	)	)	PUNCT
ejpam-4972	293	11	(	(	PUNCT
ejpam-4972	293	12	2023	2023	NUM
ejpam-4972	293	13	)	)	PUNCT
ejpam-4972	293	14	,	,	PUNCT
ejpam-4972	293	15	2613	2613	NUM
ejpam-4972	293	16	-	-	SYM
ejpam-4972	293	17	2631	2631	NUM
ejpam-4972	293	18	2623	2623	NUM
ejpam-4972	293	19	theorem	theorem	VERB
ejpam-4972	293	20	14	14	NUM
ejpam-4972	293	21	.	.	PUNCT
ejpam-4972	294	1	suppose	suppose	VERB
ejpam-4972	294	2	t	t	NOUN
ejpam-4972	294	3	:	:	PUNCT
ejpam-4972	294	4	(	(	PUNCT
ejpam-4972	294	5	x	x	X
ejpam-4972	294	6	,	,	PUNCT
ejpam-4972	294	7	δ1	δ1	NOUN
ejpam-4972	294	8	,	,	PUNCT
ejpam-4972	294	9	δ2	δ2	ADJ
ejpam-4972	294	10	)	)	PUNCT
ejpam-4972	294	11	→	→	SYM
ejpam-4972	294	12	(	(	PUNCT
ejpam-4972	294	13	y	y	PROPN
ejpam-4972	294	14	,	,	PUNCT
ejpam-4972	294	15	σ1	σ1	PROPN
ejpam-4972	294	16	,	,	PUNCT
ejpam-4972	294	17	σ2	σ2	NOUN
ejpam-4972	294	18	)	)	PUNCT
ejpam-4972	294	19	is	be	AUX
ejpam-4972	294	20	fuzzy	fuzzy	ADJ
ejpam-4972	294	21	(	(	PUNCT
ejpam-4972	294	22	i	i	NOUN
ejpam-4972	294	23	,	,	PUNCT
ejpam-4972	294	24	j)−gψ−irresolute	j)−gψ−irresolute	PROPN
ejpam-4972	294	25	mapping	mapping	NOUN
ejpam-4972	294	26	.	.	PUNCT
ejpam-4972	295	1	after	after	ADP
ejpam-4972	295	2	that	that	DET
ejpam-4972	295	3	t((i	t((i	PROPN
ejpam-4972	295	4	,	,	PUNCT
ejpam-4972	295	5	j)−	j)−	PROPN
ejpam-4972	295	6	gψ	gψ	VERB
ejpam-4972	295	7	−	−	NOUN
ejpam-4972	295	8	cl(e	cl(e	NUM
ejpam-4972	295	9	)	)	PUNCT
ejpam-4972	295	10	)	)	PUNCT
ejpam-4972	296	1	≤	≤	NUM
ejpam-4972	296	2	σj	σj	VERB
ejpam-4972	296	3	−	−	PROPN
ejpam-4972	296	4	ψ	ψ	SYM
ejpam-4972	296	5	−	−	PROPN
ejpam-4972	296	6	cl(t(e	cl(t(e	NOUN
ejpam-4972	296	7	)	)	PUNCT
ejpam-4972	296	8	)	)	PUNCT
ejpam-4972	296	9	,	,	PUNCT
ejpam-4972	296	10	∀e	∀e	PROPN
ejpam-4972	296	11	∈	∈	NOUN
ejpam-4972	296	12	ix	ix	X
ejpam-4972	296	13	.	.	PUNCT
ejpam-4972	297	1	proof	proof	NOUN
ejpam-4972	297	2	.	.	PUNCT
ejpam-4972	298	1	assume	assume	VERB
ejpam-4972	298	2	t	t	PROPN
ejpam-4972	298	3	is	be	AUX
ejpam-4972	298	4	(	(	PUNCT
ejpam-4972	298	5	i	i	PROPN
ejpam-4972	298	6	,	,	PUNCT
ejpam-4972	298	7	j)−gψ−irresolute	j)−gψ−irresolute	PROPN
ejpam-4972	298	8	,	,	PUNCT
ejpam-4972	298	9	e	e	NOUN
ejpam-4972	298	10	∈	∈	PROPN
ejpam-4972	298	11	ix	ix	ADV
ejpam-4972	298	12	.	.	PUNCT
ejpam-4972	299	1	thus	thus	ADV
ejpam-4972	299	2	e	e	X
ejpam-4972	299	3	≤	≤	NOUN
ejpam-4972	299	4	t−1(σj−ψ−cl(t(e	t−1(σj−ψ−cl(t(e	NOUN
ejpam-4972	299	5	)	)	PUNCT
ejpam-4972	299	6	)	)	PUNCT
ejpam-4972	299	7	)	)	PUNCT
ejpam-4972	299	8	,	,	PUNCT
ejpam-4972	299	9	and	and	CCONJ
ejpam-4972	299	10	hence	hence	ADV
ejpam-4972	299	11	σj−ψ−	σj−ψ−	PROPN
ejpam-4972	299	12	cl(t(e	cl(t(e	X
ejpam-4972	299	13	)	)	PUNCT
ejpam-4972	299	14	)	)	PUNCT
ejpam-4972	299	15	is	be	AUX
ejpam-4972	299	16	fuzzy	fuzzy	ADJ
ejpam-4972	299	17	(	(	PUNCT
ejpam-4972	299	18	i	i	PROPN
ejpam-4972	299	19	,	,	PUNCT
ejpam-4972	299	20	j)−gψ−	j)−gψ−	PROPN
ejpam-4972	299	21	cld	cld	PROPN
ejpam-4972	299	22	of	of	ADP
ejpam-4972	299	23	y	y	PROPN
ejpam-4972	299	24	.	.	PUNCT
ejpam-4972	300	1	as	as	SCONJ
ejpam-4972	300	2	t	t	PROPN
ejpam-4972	300	3	is	be	AUX
ejpam-4972	300	4	fuzzy	fuzzy	ADJ
ejpam-4972	300	5	(	(	PUNCT
ejpam-4972	300	6	i	i	NOUN
ejpam-4972	300	7	,	,	PUNCT
ejpam-4972	300	8	j)−gψ−	j)−gψ−	PROPN
ejpam-4972	300	9	irresolute	irresolute	PROPN
ejpam-4972	300	10	,	,	PUNCT
ejpam-4972	300	11	so	so	SCONJ
ejpam-4972	301	1	t−1(σj	t−1(σj	ADP
ejpam-4972	301	2	−	−	PROPN
ejpam-4972	301	3	ψ	ψ	NOUN
ejpam-4972	301	4	−	−	PROPN
ejpam-4972	301	5	cl(t(e	cl(t(e	NOUN
ejpam-4972	301	6	)	)	PUNCT
ejpam-4972	301	7	)	)	PUNCT
ejpam-4972	301	8	)	)	PUNCT
ejpam-4972	301	9	is	be	AUX
ejpam-4972	301	10	fuzzy	fuzzy	ADJ
ejpam-4972	301	11	(	(	PUNCT
ejpam-4972	301	12	i	i	PROPN
ejpam-4972	301	13	,	,	PUNCT
ejpam-4972	301	14	j	j	PROPN
ejpam-4972	301	15	)	)	PUNCT
ejpam-4972	301	16	−	−	PROPN
ejpam-4972	301	17	gψ	gψ	VERB
ejpam-4972	301	18	−	−	PROPN
ejpam-4972	301	19	cld	cld	NOUN
ejpam-4972	301	20	of	of	ADP
ejpam-4972	301	21	x	x	PRON
ejpam-4972	301	22	,	,	PUNCT
ejpam-4972	301	23	thus	thus	ADV
ejpam-4972	301	24	(	(	PUNCT
ejpam-4972	301	25	i	i	PROPN
ejpam-4972	301	26	,	,	PUNCT
ejpam-4972	301	27	j	j	PROPN
ejpam-4972	301	28	)	)	PUNCT
ejpam-4972	301	29	−	−	PROPN
ejpam-4972	301	30	gψ	gψ	VERB
ejpam-4972	301	31	−	−	NOUN
ejpam-4972	301	32	cl(e	cl(e	NOUN
ejpam-4972	301	33	)	)	PUNCT
ejpam-4972	301	34	≤	≤	PUNCT
ejpam-4972	302	1	t−1(σj	t−1(σj	ADP
ejpam-4972	302	2	−	−	NOUN
ejpam-4972	302	3	ψ	ψ	NOUN
ejpam-4972	302	4	−	−	PROPN
ejpam-4972	302	5	cl(t(e	cl(t(e	NOUN
ejpam-4972	302	6	)	)	PUNCT
ejpam-4972	302	7	)	)	PUNCT
ejpam-4972	302	8	)	)	PUNCT
ejpam-4972	302	9	.	.	PUNCT
ejpam-4972	303	1	therefore	therefore	ADV
ejpam-4972	303	2	t((i	t((i	PROPN
ejpam-4972	303	3	,	,	PUNCT
ejpam-4972	303	4	j)−	j)−	PROPN
ejpam-4972	303	5	gψ	gψ	VERB
ejpam-4972	303	6	−	−	NOUN
ejpam-4972	303	7	cl(e	cl(e	NUM
ejpam-4972	303	8	)	)	PUNCT
ejpam-4972	303	9	)	)	PUNCT
ejpam-4972	304	1	≤	≤	NUM
ejpam-4972	304	2	σj	σj	VERB
ejpam-4972	304	3	−	−	PROPN
ejpam-4972	304	4	ψ	ψ	SYM
ejpam-4972	304	5	−	−	PROPN
ejpam-4972	304	6	cl(t(e	cl(t(e	NOUN
ejpam-4972	304	7	)	)	PUNCT
ejpam-4972	304	8	)	)	PUNCT
ejpam-4972	304	9	.	.	PUNCT
ejpam-4972	305	1	corollary	corollary	ADJ
ejpam-4972	305	2	3	3	X
ejpam-4972	305	3	.	.	PUNCT
ejpam-4972	305	4	suppose	suppose	VERB
ejpam-4972	305	5	t	t	NOUN
ejpam-4972	305	6	:	:	PUNCT
ejpam-4972	305	7	(	(	PUNCT
ejpam-4972	305	8	x	x	X
ejpam-4972	305	9	,	,	PUNCT
ejpam-4972	305	10	δ1	δ1	NOUN
ejpam-4972	305	11	,	,	PUNCT
ejpam-4972	305	12	δ2	δ2	ADJ
ejpam-4972	305	13	)	)	PUNCT
ejpam-4972	305	14	→	→	SYM
ejpam-4972	305	15	(	(	PUNCT
ejpam-4972	305	16	y	y	PROPN
ejpam-4972	305	17	,	,	PUNCT
ejpam-4972	305	18	σ1	σ1	PROPN
ejpam-4972	305	19	,	,	PUNCT
ejpam-4972	305	20	σ2	σ2	NOUN
ejpam-4972	305	21	)	)	PUNCT
ejpam-4972	305	22	is	be	AUX
ejpam-4972	305	23	fuzzy	fuzzy	ADJ
ejpam-4972	305	24	(	(	PUNCT
ejpam-4972	305	25	i	i	PROPN
ejpam-4972	305	26	,	,	PUNCT
ejpam-4972	305	27	j	j	PROPN
ejpam-4972	305	28	)	)	PUNCT
ejpam-4972	305	29	−	−	PROPN
ejpam-4972	305	30	gψ	gψ	VERB
ejpam-4972	305	31	−	−	NOUN
ejpam-4972	305	32	strongly	strongly	ADV
ejpam-4972	305	33	conts	cont	VERB
ejpam-4972	305	34	mapping	mapping	NOUN
ejpam-4972	305	35	.	.	PUNCT
ejpam-4972	306	1	hence	hence	ADV
ejpam-4972	306	2	t((i	t((i	PROPN
ejpam-4972	306	3	,	,	PUNCT
ejpam-4972	306	4	j)−	j)−	PROPN
ejpam-4972	306	5	gψ	gψ	VERB
ejpam-4972	306	6	−	−	NOUN
ejpam-4972	306	7	cl(e	cl(e	NUM
ejpam-4972	306	8	)	)	PUNCT
ejpam-4972	306	9	)	)	PUNCT
ejpam-4972	307	1	≤	≤	NUM
ejpam-4972	307	2	σj	σj	VERB
ejpam-4972	307	3	−	−	PROPN
ejpam-4972	307	4	ψ	ψ	SYM
ejpam-4972	307	5	−	−	PROPN
ejpam-4972	307	6	cl(t(e	cl(t(e	NOUN
ejpam-4972	307	7	)	)	PUNCT
ejpam-4972	307	8	)	)	PUNCT
ejpam-4972	307	9	,	,	PUNCT
ejpam-4972	307	10	∀e	∀e	PROPN
ejpam-4972	307	11	∈	∈	PROPN
ejpam-4972	307	12	ix	ix	X
ejpam-4972	307	13	.	.	PUNCT
ejpam-4972	308	1	theorem	theorem	ADJ
ejpam-4972	308	2	15	15	NUM
ejpam-4972	308	3	.	.	PUNCT
ejpam-4972	309	1	suppose	suppose	VERB
ejpam-4972	309	2	t	t	NOUN
ejpam-4972	309	3	:	:	PUNCT
ejpam-4972	309	4	(	(	PUNCT
ejpam-4972	309	5	x	x	X
ejpam-4972	309	6	,	,	PUNCT
ejpam-4972	309	7	δ1	δ1	NOUN
ejpam-4972	309	8	,	,	PUNCT
ejpam-4972	309	9	δ2	δ2	ADJ
ejpam-4972	309	10	)	)	PUNCT
ejpam-4972	309	11	→	→	SYM
ejpam-4972	309	12	(	(	PUNCT
ejpam-4972	309	13	y	y	PROPN
ejpam-4972	309	14	,	,	PUNCT
ejpam-4972	309	15	σ1	σ1	PROPN
ejpam-4972	309	16	,	,	PUNCT
ejpam-4972	309	17	σ2	σ2	NOUN
ejpam-4972	309	18	)	)	PUNCT
ejpam-4972	309	19	is	be	AUX
ejpam-4972	309	20	fuzzy	fuzzy	ADJ
ejpam-4972	309	21	(	(	PUNCT
ejpam-4972	309	22	i	i	PROPN
ejpam-4972	309	23	,	,	PUNCT
ejpam-4972	309	24	j)−	j)−	PROPN
ejpam-4972	309	25	gψ	gψ	VERB
ejpam-4972	309	26	−	−	PROPN
ejpam-4972	309	27	irresolute	irresolute	ADJ
ejpam-4972	309	28	(	(	PUNCT
ejpam-4972	309	29	resp	resp	NOUN
ejpam-4972	309	30	,	,	PUNCT
ejpam-4972	309	31	(	(	PUNCT
ejpam-4972	309	32	i	i	PRON
ejpam-4972	309	33	,	,	PUNCT
ejpam-4972	309	34	j)−gψ−strongly	j)−gψ−strongly	ADV
ejpam-4972	309	35	conts	cont	NOUN
ejpam-4972	309	36	)	)	PUNCT
ejpam-4972	309	37	mapping	mapping	NOUN
ejpam-4972	309	38	.	.	PUNCT
ejpam-4972	310	1	thus	thus	ADV
ejpam-4972	310	2	t((i	t((i	PROPN
ejpam-4972	310	3	,	,	PUNCT
ejpam-4972	310	4	j)−gψ−cl(e	j)−gψ−cl(e	NOUN
ejpam-4972	310	5	)	)	PUNCT
ejpam-4972	310	6	)	)	PUNCT
ejpam-4972	311	1	≤	≤	NUM
ejpam-4972	311	2	σj−cl(t(e	σj−cl(t(e	PROPN
ejpam-4972	311	3	)	)	PUNCT
ejpam-4972	311	4	)	)	PUNCT
ejpam-4972	311	5	,	,	PUNCT
ejpam-4972	311	6	∀e	∀e	PROPN
ejpam-4972	311	7	∈	∈	NOUN
ejpam-4972	311	8	ix	ix	X
ejpam-4972	311	9	.	.	PUNCT
ejpam-4972	312	1	proof	proof	NOUN
ejpam-4972	312	2	.	.	PUNCT
ejpam-4972	313	1	it	it	PRON
ejpam-4972	313	2	is	be	AUX
ejpam-4972	313	3	clear	clear	ADJ
ejpam-4972	313	4	from	from	ADP
ejpam-4972	313	5	theorem	theorem	ADJ
ejpam-4972	313	6	10	10	NUM
ejpam-4972	313	7	and	and	CCONJ
ejpam-4972	313	8	theorem	theorem	VERB
ejpam-4972	313	9	5	5	NUM
ejpam-4972	313	10	.	.	NOUN
ejpam-4972	313	11	remark	remark	PROPN
ejpam-4972	313	12	8	8	NUM
ejpam-4972	313	13	.	.	PUNCT
ejpam-4972	313	14	from	from	ADP
ejpam-4972	313	15	remark	remark	NOUN
ejpam-4972	313	16	5	5	NUM
ejpam-4972	313	17	and	and	CCONJ
ejpam-4972	313	18	theorem	theorem	VERB
ejpam-4972	313	19	10	10	NUM
ejpam-4972	313	20	we	we	PRON
ejpam-4972	313	21	find	find	VERB
ejpam-4972	313	22	when	when	SCONJ
ejpam-4972	313	23	t	t	NOUN
ejpam-4972	313	24	:	:	PUNCT
ejpam-4972	313	25	(	(	PUNCT
ejpam-4972	313	26	x	x	X
ejpam-4972	313	27	,	,	PUNCT
ejpam-4972	313	28	δ1	δ1	NOUN
ejpam-4972	313	29	,	,	PUNCT
ejpam-4972	313	30	δ2	δ2	ADJ
ejpam-4972	313	31	)	)	PUNCT
ejpam-4972	313	32	→	→	SYM
ejpam-4972	313	33	(	(	PUNCT
ejpam-4972	313	34	y	y	PROPN
ejpam-4972	313	35	,	,	PUNCT
ejpam-4972	313	36	σ1	σ1	PROPN
ejpam-4972	313	37	,	,	PUNCT
ejpam-4972	313	38	σ2	σ2	PROPN
ejpam-4972	313	39	)	)	PUNCT
ejpam-4972	313	40	is	be	AUX
ejpam-4972	313	41	an	an	DET
ejpam-4972	313	42	injective	injective	ADJ
ejpam-4972	313	43	and	and	CCONJ
ejpam-4972	313	44	fuzzy	fuzzy	ADJ
ejpam-4972	313	45	(	(	PUNCT
ejpam-4972	313	46	i	i	NOUN
ejpam-4972	313	47	,	,	PUNCT
ejpam-4972	313	48	j)−gψ−	j)−gψ−	PROPN
ejpam-4972	313	49	irresolute	irresolute	PROPN
ejpam-4972	313	50	(	(	PUNCT
ejpam-4972	313	51	resp	resp	NOUN
ejpam-4972	313	52	,	,	PUNCT
ejpam-4972	313	53	(	(	PUNCT
ejpam-4972	313	54	i	i	PRON
ejpam-4972	313	55	,	,	PUNCT
ejpam-4972	313	56	j)−gψ−strongly	j)−gψ−strongly	ADV
ejpam-4972	313	57	conts	cont	NOUN
ejpam-4972	313	58	)	)	PUNCT
ejpam-4972	313	59	mapping	mapping	NOUN
ejpam-4972	313	60	.	.	PUNCT
ejpam-4972	314	1	hence	hence	ADV
ejpam-4972	314	2	any	any	DET
ejpam-4972	314	3	statement	statement	NOUN
ejpam-4972	314	4	of	of	ADP
ejpam-4972	314	5	theorem	theorem	NOUN
ejpam-4972	314	6	4	4	NUM
ejpam-4972	314	7	is	be	AUX
ejpam-4972	314	8	hold	hold	VERB
ejpam-4972	314	9	in	in	ADP
ejpam-4972	314	10	theorem	theorem	ADJ
ejpam-4972	314	11	15	15	NUM
ejpam-4972	314	12	.	.	PUNCT
ejpam-4972	315	1	theorem	theorem	NOUN
ejpam-4972	315	2	16	16	NUM
ejpam-4972	315	3	.	.	PUNCT
ejpam-4972	316	1	suppose	suppose	VERB
ejpam-4972	316	2	t	t	NOUN
ejpam-4972	316	3	:	:	PUNCT
ejpam-4972	316	4	(	(	PUNCT
ejpam-4972	316	5	x	x	X
ejpam-4972	316	6	,	,	PUNCT
ejpam-4972	316	7	δ1	δ1	NOUN
ejpam-4972	316	8	,	,	PUNCT
ejpam-4972	316	9	δ2	δ2	ADJ
ejpam-4972	316	10	)	)	PUNCT
ejpam-4972	316	11	→	→	SYM
ejpam-4972	316	12	(	(	PUNCT
ejpam-4972	316	13	y	y	PROPN
ejpam-4972	316	14	,	,	PUNCT
ejpam-4972	316	15	σ1	σ1	PROPN
ejpam-4972	316	16	,	,	PUNCT
ejpam-4972	316	17	σ2	σ2	NOUN
ejpam-4972	316	18	)	)	PUNCT
ejpam-4972	316	19	,	,	PUNCT
ejpam-4972	316	20	g	g	NOUN
ejpam-4972	316	21	:	:	PUNCT
ejpam-4972	316	22	(	(	PUNCT
ejpam-4972	316	23	y	y	PROPN
ejpam-4972	316	24	,	,	PUNCT
ejpam-4972	316	25	σ1	σ1	PROPN
ejpam-4972	316	26	,	,	PUNCT
ejpam-4972	316	27	σ2	σ2	NOUN
ejpam-4972	316	28	)	)	PUNCT
ejpam-4972	316	29	→	→	SYM
ejpam-4972	316	30	(	(	PUNCT
ejpam-4972	316	31	z	z	NOUN
ejpam-4972	316	32	,	,	PUNCT
ejpam-4972	316	33	η1	η1	NOUN
ejpam-4972	316	34	,	,	PUNCT
ejpam-4972	316	35	η2	η2	NOUN
ejpam-4972	316	36	)	)	PUNCT
ejpam-4972	316	37	.	.	PUNCT
ejpam-4972	317	1	hence	hence	ADV
ejpam-4972	317	2	the	the	DET
ejpam-4972	317	3	next	next	ADJ
ejpam-4972	317	4	cliams	cliam	NOUN
ejpam-4972	317	5	are	be	AUX
ejpam-4972	317	6	true	true	ADJ
ejpam-4972	317	7	:	:	PUNCT
ejpam-4972	317	8	(	(	PUNCT
ejpam-4972	317	9	1	1	X
ejpam-4972	317	10	)	)	PUNCT
ejpam-4972	317	11	g	g	NOUN
ejpam-4972	317	12	◦	◦	PROPN
ejpam-4972	317	13	t	t	PROPN
ejpam-4972	317	14	is	be	AUX
ejpam-4972	317	15	fuzzy	fuzzy	ADJ
ejpam-4972	317	16	(	(	PUNCT
ejpam-4972	317	17	i	i	PROPN
ejpam-4972	317	18	,	,	PUNCT
ejpam-4972	317	19	j)−	j)−	PROPN
ejpam-4972	317	20	gψ	gψ	VERB
ejpam-4972	317	21	−	−	PROPN
ejpam-4972	317	22	strongly	strongly	ADV
ejpam-4972	317	23	conts	cont	VERB
ejpam-4972	317	24	if	if	SCONJ
ejpam-4972	317	25	t	t	PROPN
ejpam-4972	317	26	,	,	PUNCT
ejpam-4972	317	27	g	g	PROPN
ejpam-4972	317	28	are	be	AUX
ejpam-4972	317	29	fuzzy	fuzzy	ADJ
ejpam-4972	317	30	(	(	PUNCT
ejpam-4972	317	31	i	i	PROPN
ejpam-4972	317	32	,	,	PUNCT
ejpam-4972	317	33	j)−	j)−	PROPN
ejpam-4972	317	34	gψ	gψ	VERB
ejpam-4972	317	35	−	−	NOUN
ejpam-4972	317	36	strongly	strongly	ADV
ejpam-4972	317	37	conts	cont	NOUN
ejpam-4972	317	38	.	.	PUNCT
ejpam-4972	318	1	(	(	PUNCT
ejpam-4972	318	2	2	2	X
ejpam-4972	318	3	)	)	PUNCT
ejpam-4972	318	4	g	g	NOUN
ejpam-4972	318	5	◦	◦	PROPN
ejpam-4972	318	6	t	t	PROPN
ejpam-4972	318	7	is	be	AUX
ejpam-4972	318	8	fuzzy	fuzzy	ADJ
ejpam-4972	318	9	(	(	PUNCT
ejpam-4972	318	10	i	i	PROPN
ejpam-4972	318	11	,	,	PUNCT
ejpam-4972	318	12	j)−	j)−	PROPN
ejpam-4972	318	13	gψ	gψ	VERB
ejpam-4972	318	14	−	−	PROPN
ejpam-4972	318	15	irresolute	irresolute	ADJ
ejpam-4972	318	16	if	if	SCONJ
ejpam-4972	318	17	t	t	PROPN
ejpam-4972	318	18	,	,	PUNCT
ejpam-4972	318	19	g	g	PROPN
ejpam-4972	318	20	are	be	AUX
ejpam-4972	318	21	fuzzy	fuzzy	ADJ
ejpam-4972	318	22	(	(	PUNCT
ejpam-4972	318	23	i	i	PROPN
ejpam-4972	318	24	,	,	PUNCT
ejpam-4972	318	25	j)−	j)−	PROPN
ejpam-4972	318	26	gψ	gψ	VERB
ejpam-4972	318	27	−	−	PROPN
ejpam-4972	318	28	irresolute	irresolute	ADJ
ejpam-4972	318	29	.	.	PUNCT
ejpam-4972	319	1	(	(	PUNCT
ejpam-4972	319	2	3	3	X
ejpam-4972	319	3	)	)	PUNCT
ejpam-4972	319	4	g	g	NOUN
ejpam-4972	319	5	◦	◦	PROPN
ejpam-4972	319	6	t	t	PROPN
ejpam-4972	319	7	is	be	AUX
ejpam-4972	319	8	fuzzy	fuzzy	ADJ
ejpam-4972	319	9	(	(	PUNCT
ejpam-4972	319	10	i	i	NOUN
ejpam-4972	319	11	,	,	PUNCT
ejpam-4972	319	12	j)−	j)−	PROPN
ejpam-4972	319	13	gψ−	gψ−	PUNCT
ejpam-4972	319	14	conts	cont	NOUN
ejpam-4972	319	15	if	if	SCONJ
ejpam-4972	319	16	g	g	PROPN
ejpam-4972	319	17	is	be	AUX
ejpam-4972	319	18	(	(	PUNCT
ejpam-4972	319	19	i	i	PROPN
ejpam-4972	319	20	,	,	PUNCT
ejpam-4972	319	21	j)−	j)−	PROPN
ejpam-4972	319	22	gψ−	gψ−	PUNCT
ejpam-4972	319	23	conts	cont	NOUN
ejpam-4972	319	24	,	,	PUNCT
ejpam-4972	319	25	t	t	PROPN
ejpam-4972	319	26	is	be	AUX
ejpam-4972	319	27	(	(	PUNCT
ejpam-4972	319	28	i	i	PROPN
ejpam-4972	319	29	,	,	PUNCT
ejpam-4972	319	30	j)−	j)−	PROPN
ejpam-4972	319	31	gψ−	gψ−	PUNCT
ejpam-4972	319	32	irresolute	irresolute	ADJ
ejpam-4972	319	33	.	.	PUNCT
ejpam-4972	320	1	proof	proof	NOUN
ejpam-4972	320	2	.	.	PUNCT
ejpam-4972	321	1	(	(	PUNCT
ejpam-4972	321	2	1	1	X
ejpam-4972	321	3	)	)	PUNCT
ejpam-4972	321	4	assume	assume	VERB
ejpam-4972	321	5	w	w	NOUN
ejpam-4972	321	6	is	be	AUX
ejpam-4972	321	7	fuzzy	fuzzy	ADJ
ejpam-4972	321	8	(	(	PUNCT
ejpam-4972	321	9	i	i	PROPN
ejpam-4972	321	10	,	,	PUNCT
ejpam-4972	321	11	j	j	PROPN
ejpam-4972	321	12	)	)	PUNCT
ejpam-4972	321	13	−	−	PROPN
ejpam-4972	321	14	gψ	gψ	VERB
ejpam-4972	321	15	−	−	PROPN
ejpam-4972	321	16	cld	cld	NOUN
ejpam-4972	321	17	of	of	ADP
ejpam-4972	321	18	z.	z.	PROPN
ejpam-4972	321	19	as	as	SCONJ
ejpam-4972	321	20	g	g	PROPN
ejpam-4972	321	21	is	be	AUX
ejpam-4972	321	22	fuzzy	fuzzy	ADJ
ejpam-4972	321	23	(	(	PUNCT
ejpam-4972	321	24	i	i	PROPN
ejpam-4972	321	25	,	,	PUNCT
ejpam-4972	321	26	j	j	PROPN
ejpam-4972	321	27	)	)	PUNCT
ejpam-4972	321	28	−	−	PROPN
ejpam-4972	321	29	gψ	gψ	VERB
ejpam-4972	321	30	−	−	NOUN
ejpam-4972	321	31	strongly	strongly	ADV
ejpam-4972	321	32	conts	cont	NOUN
ejpam-4972	321	33	,	,	PUNCT
ejpam-4972	321	34	hence	hence	ADV
ejpam-4972	321	35	g−1(w	g−1(w	PROPN
ejpam-4972	321	36	)	)	PUNCT
ejpam-4972	321	37	is	be	AUX
ejpam-4972	321	38	fuzzy	fuzzy	ADJ
ejpam-4972	321	39	closed	closed	ADJ
ejpam-4972	321	40	of	of	ADP
ejpam-4972	321	41	y	y	PROPN
ejpam-4972	321	42	,	,	PUNCT
ejpam-4972	321	43	so	so	ADV
ejpam-4972	321	44	g−1(w	g−1(w	PROPN
ejpam-4972	321	45	)	)	PUNCT
ejpam-4972	321	46	is	be	AUX
ejpam-4972	321	47	(	(	PUNCT
ejpam-4972	321	48	i	i	PROPN
ejpam-4972	321	49	,	,	PUNCT
ejpam-4972	321	50	j)−	j)−	PROPN
ejpam-4972	321	51	gψ	gψ	VERB
ejpam-4972	321	52	−	−	PROPN
ejpam-4972	321	53	cld	cld	NOUN
ejpam-4972	321	54	group	group	NOUN
ejpam-4972	321	55	of	of	ADP
ejpam-4972	321	56	y	y	PROPN
ejpam-4972	321	57	.	.	PUNCT
ejpam-4972	322	1	as	as	SCONJ
ejpam-4972	322	2	t	t	PROPN
ejpam-4972	322	3	is	be	AUX
ejpam-4972	322	4	(	(	PUNCT
ejpam-4972	322	5	i	i	PROPN
ejpam-4972	322	6	,	,	PUNCT
ejpam-4972	322	7	j	j	PROPN
ejpam-4972	322	8	)	)	PUNCT
ejpam-4972	322	9	−	−	PROPN
ejpam-4972	322	10	gψ	gψ	VERB
ejpam-4972	322	11	−	−	NOUN
ejpam-4972	322	12	strongly	strongly	ADV
ejpam-4972	322	13	conts	cont	NOUN
ejpam-4972	322	14	,	,	PUNCT
ejpam-4972	322	15	then	then	ADV
ejpam-4972	322	16	t−1(g−1(w	t−1(g−1(w	NUM
ejpam-4972	322	17	)	)	PUNCT
ejpam-4972	322	18	)	)	PUNCT
ejpam-4972	323	1	=	=	PRON
ejpam-4972	323	2	(	(	PUNCT
ejpam-4972	323	3	g	g	PROPN
ejpam-4972	323	4	◦	◦	NOUN
ejpam-4972	323	5	t)−1(w	t)−1(w	PROPN
ejpam-4972	323	6	)	)	PUNCT
ejpam-4972	323	7	is	be	AUX
ejpam-4972	323	8	fuzzy	fuzzy	ADJ
ejpam-4972	323	9	closed	closed	ADJ
ejpam-4972	323	10	of	of	ADP
ejpam-4972	323	11	x.	x.	NOUN
ejpam-4972	323	12	therefore	therefore	ADV
ejpam-4972	323	13	g	g	PROPN
ejpam-4972	323	14	◦	◦	PROPN
ejpam-4972	323	15	t	t	PROPN
ejpam-4972	323	16	is	be	AUX
ejpam-4972	323	17	fuzzy	fuzzy	ADJ
ejpam-4972	323	18	(	(	PUNCT
ejpam-4972	323	19	i	i	PROPN
ejpam-4972	323	20	,	,	PUNCT
ejpam-4972	323	21	j)−	j)−	PROPN
ejpam-4972	323	22	gψ	gψ	VERB
ejpam-4972	323	23	−	−	NOUN
ejpam-4972	323	24	strongly	strongly	ADV
ejpam-4972	323	25	conts	cont	NOUN
ejpam-4972	323	26	.	.	PUNCT
ejpam-4972	324	1	(	(	PUNCT
ejpam-4972	324	2	2	2	X
ejpam-4972	324	3	)	)	PUNCT
ejpam-4972	324	4	assume	assume	VERB
ejpam-4972	324	5	w	w	NOUN
ejpam-4972	324	6	is	be	AUX
ejpam-4972	324	7	fuzzy	fuzzy	ADJ
ejpam-4972	324	8	(	(	PUNCT
ejpam-4972	324	9	i	i	PROPN
ejpam-4972	324	10	,	,	PUNCT
ejpam-4972	324	11	j	j	PROPN
ejpam-4972	324	12	)	)	PUNCT
ejpam-4972	324	13	−	−	PROPN
ejpam-4972	324	14	gψ	gψ	VERB
ejpam-4972	324	15	−	−	PROPN
ejpam-4972	324	16	cld	cld	NOUN
ejpam-4972	324	17	of	of	ADP
ejpam-4972	324	18	z.	z.	PROPN
ejpam-4972	324	19	as	as	SCONJ
ejpam-4972	324	20	g	g	PROPN
ejpam-4972	324	21	is	be	AUX
ejpam-4972	324	22	fuzzy	fuzzy	ADJ
ejpam-4972	324	23	(	(	PUNCT
ejpam-4972	324	24	i	i	PROPN
ejpam-4972	324	25	,	,	PUNCT
ejpam-4972	324	26	j	j	PROPN
ejpam-4972	324	27	)	)	PUNCT
ejpam-4972	324	28	−	−	PROPN
ejpam-4972	324	29	gψ	gψ	VERB
ejpam-4972	324	30	−	−	NOUN
ejpam-4972	324	31	irresolute	irresolute	ADJ
ejpam-4972	324	32	,	,	PUNCT
ejpam-4972	324	33	hence	hence	ADV
ejpam-4972	324	34	g−1(w	g−1(w	PROPN
ejpam-4972	324	35	)	)	PUNCT
ejpam-4972	324	36	is	be	AUX
ejpam-4972	324	37	fuzzy	fuzzy	ADJ
ejpam-4972	324	38	(	(	PUNCT
ejpam-4972	324	39	i	i	PROPN
ejpam-4972	324	40	,	,	PUNCT
ejpam-4972	324	41	j	j	PROPN
ejpam-4972	324	42	)	)	PUNCT
ejpam-4972	324	43	−	−	PROPN
ejpam-4972	324	44	gψ	gψ	VERB
ejpam-4972	324	45	−	−	PROPN
ejpam-4972	324	46	cld	cld	NOUN
ejpam-4972	324	47	of	of	ADP
ejpam-4972	324	48	y	y	PROPN
ejpam-4972	324	49	.	.	PUNCT
ejpam-4972	325	1	as	as	SCONJ
ejpam-4972	325	2	t	t	PROPN
ejpam-4972	325	3	is	be	AUX
ejpam-4972	325	4	(	(	PUNCT
ejpam-4972	325	5	i	i	PROPN
ejpam-4972	325	6	,	,	PUNCT
ejpam-4972	325	7	j	j	PROPN
ejpam-4972	325	8	)	)	PUNCT
ejpam-4972	325	9	−	−	PROPN
ejpam-4972	325	10	gψ	gψ	VERB
ejpam-4972	325	11	−	−	NOUN
ejpam-4972	325	12	irresolute	irresolute	ADJ
ejpam-4972	325	13	,	,	PUNCT
ejpam-4972	325	14	then	then	ADV
ejpam-4972	325	15	t−1(g−1(w	t−1(g−1(w	NUM
ejpam-4972	325	16	)	)	PUNCT
ejpam-4972	325	17	)	)	PUNCT
ejpam-4972	326	1	=	=	PRON
ejpam-4972	326	2	(	(	PUNCT
ejpam-4972	326	3	g	g	PROPN
ejpam-4972	326	4	◦	◦	NOUN
ejpam-4972	326	5	t)−1(w	t)−1(w	PROPN
ejpam-4972	326	6	)	)	PUNCT
ejpam-4972	326	7	is	be	AUX
ejpam-4972	326	8	fuzzy	fuzzy	ADJ
ejpam-4972	326	9	(	(	PUNCT
ejpam-4972	326	10	i	i	PROPN
ejpam-4972	326	11	,	,	PUNCT
ejpam-4972	326	12	j)−	j)−	PROPN
ejpam-4972	326	13	gψ	gψ	VERB
ejpam-4972	326	14	−	−	PROPN
ejpam-4972	326	15	cld	cld	NOUN
ejpam-4972	326	16	of	of	ADP
ejpam-4972	326	17	x.	x.	NOUN
ejpam-4972	326	18	therefore	therefore	ADV
ejpam-4972	326	19	g	g	PROPN
ejpam-4972	326	20	◦	◦	PROPN
ejpam-4972	326	21	t	t	PROPN
ejpam-4972	326	22	is	be	AUX
ejpam-4972	326	23	fuzzy	fuzzy	ADJ
ejpam-4972	326	24	(	(	PUNCT
ejpam-4972	326	25	i	i	PROPN
ejpam-4972	326	26	,	,	PUNCT
ejpam-4972	326	27	j)−	j)−	PROPN
ejpam-4972	326	28	gψ	gψ	VERB
ejpam-4972	326	29	−	−	PROPN
ejpam-4972	326	30	irresolute	irresolute	ADJ
ejpam-4972	326	31	.	.	PUNCT
ejpam-4972	327	1	(	(	PUNCT
ejpam-4972	327	2	3	3	X
ejpam-4972	327	3	)	)	PUNCT
ejpam-4972	327	4	suppose	suppose	VERB
ejpam-4972	327	5	w	w	PROPN
ejpam-4972	327	6	∈	∈	PROPN
ejpam-4972	327	7	fηj	fηj	NOUN
ejpam-4972	327	8	.	.	PUNCT
ejpam-4972	328	1	since	since	SCONJ
ejpam-4972	328	2	g	g	PROPN
ejpam-4972	328	3	is	be	AUX
ejpam-4972	328	4	fuzzy	fuzzy	ADJ
ejpam-4972	328	5	(	(	PUNCT
ejpam-4972	328	6	i	i	PROPN
ejpam-4972	328	7	,	,	PUNCT
ejpam-4972	328	8	j	j	PROPN
ejpam-4972	328	9	)	)	PUNCT
ejpam-4972	328	10	−	−	PROPN
ejpam-4972	328	11	gψ	gψ	VERB
ejpam-4972	328	12	−	−	PROPN
ejpam-4972	328	13	conts	cont	NOUN
ejpam-4972	328	14	,	,	PUNCT
ejpam-4972	328	15	then	then	ADV
ejpam-4972	328	16	g−1(w	g−1(w	PROPN
ejpam-4972	328	17	)	)	PUNCT
ejpam-4972	328	18	is	be	AUX
ejpam-4972	328	19	fuzzy	fuzzy	ADJ
ejpam-4972	328	20	(	(	PUNCT
ejpam-4972	328	21	i	i	PROPN
ejpam-4972	328	22	,	,	PUNCT
ejpam-4972	328	23	j	j	PROPN
ejpam-4972	328	24	)	)	PUNCT
ejpam-4972	329	1	−	−	PROPN
ejpam-4972	329	2	gψ−cld	gψ−cld	NOUN
ejpam-4972	329	3	of	of	ADP
ejpam-4972	329	4	y	y	PROPN
ejpam-4972	329	5	.	.	PUNCT
ejpam-4972	330	1	as	as	SCONJ
ejpam-4972	330	2	t	t	PROPN
ejpam-4972	330	3	is	be	AUX
ejpam-4972	330	4	fuzzy	fuzzy	ADJ
ejpam-4972	330	5	(	(	PUNCT
ejpam-4972	330	6	i	i	NOUN
ejpam-4972	330	7	,	,	PUNCT
ejpam-4972	330	8	j)−gψ−	j)−gψ−	PROPN
ejpam-4972	330	9	irresolute	irresolute	PROPN
ejpam-4972	330	10	,	,	PUNCT
ejpam-4972	330	11	thus	thus	ADV
ejpam-4972	330	12	t−1(g−1(w	t−1(g−1(w	NUM
ejpam-4972	330	13	)	)	PUNCT
ejpam-4972	330	14	)	)	PUNCT
ejpam-4972	331	1	=	=	PUNCT
ejpam-4972	331	2	(	(	PUNCT
ejpam-4972	331	3	g	g	ADP
ejpam-4972	331	4	◦	◦	NOUN
ejpam-4972	331	5	t)−1(w	t)−1(w	NUM
ejpam-4972	331	6	)	)	PUNCT
ejpam-4972	331	7	is	be	AUX
ejpam-4972	331	8	fuzzy	fuzzy	ADJ
ejpam-4972	331	9	(	(	PUNCT
ejpam-4972	331	10	i	i	PROPN
ejpam-4972	331	11	,	,	PUNCT
ejpam-4972	331	12	j)−	j)−	PROPN
ejpam-4972	331	13	gψ	gψ	VERB
ejpam-4972	331	14	−	−	PROPN
ejpam-4972	331	15	cld	cld	NOUN
ejpam-4972	331	16	of	of	ADP
ejpam-4972	331	17	x.	x.	NOUN
ejpam-4972	331	18	therefore	therefore	ADV
ejpam-4972	331	19	g	g	PROPN
ejpam-4972	331	20	◦	◦	PROPN
ejpam-4972	331	21	t	t	PROPN
ejpam-4972	331	22	is	be	AUX
ejpam-4972	331	23	fuzzy	fuzzy	ADJ
ejpam-4972	331	24	(	(	PUNCT
ejpam-4972	331	25	i	i	PROPN
ejpam-4972	331	26	,	,	PUNCT
ejpam-4972	331	27	j)−	j)−	PROPN
ejpam-4972	331	28	gψ	gψ	VERB
ejpam-4972	331	29	−	−	PROPN
ejpam-4972	331	30	conts	cont	NOUN
ejpam-4972	331	31	.	.	PUNCT
ejpam-4972	332	1	theorem	theorem	NOUN
ejpam-4972	332	2	17	17	NUM
ejpam-4972	332	3	.	.	PUNCT
ejpam-4972	333	1	suppose	suppose	VERB
ejpam-4972	333	2	t	t	NOUN
ejpam-4972	333	3	:	:	PUNCT
ejpam-4972	333	4	(	(	PUNCT
ejpam-4972	333	5	x	x	X
ejpam-4972	333	6	,	,	PUNCT
ejpam-4972	333	7	δ1	δ1	NOUN
ejpam-4972	333	8	,	,	PUNCT
ejpam-4972	333	9	δ2	δ2	ADJ
ejpam-4972	333	10	)	)	PUNCT
ejpam-4972	333	11	→	→	SYM
ejpam-4972	333	12	(	(	PUNCT
ejpam-4972	333	13	y	y	PROPN
ejpam-4972	333	14	,	,	PUNCT
ejpam-4972	333	15	σ1	σ1	PROPN
ejpam-4972	333	16	,	,	PUNCT
ejpam-4972	333	17	σ2	σ2	NOUN
ejpam-4972	333	18	)	)	PUNCT
ejpam-4972	333	19	is	be	AUX
ejpam-4972	333	20	fuzzy	fuzzy	ADJ
ejpam-4972	333	21	δj	δj	ADP
ejpam-4972	333	22	−	−	PROPN
ejpam-4972	333	23	ψ	ψ	NOUN
ejpam-4972	333	24	−	−	PROPN
ejpam-4972	333	25	conts	cont	NOUN
ejpam-4972	333	26	and	and	CCONJ
ejpam-4972	333	27	δi	δi	VERB
ejpam-4972	333	28	−	−	PUNCT
ejpam-4972	333	29	open	open	ADJ
ejpam-4972	333	30	mapping	mapping	NOUN
ejpam-4972	333	31	(	(	PUNCT
ejpam-4972	333	32	resp	resp	NOUN
ejpam-4972	333	33	,	,	PUNCT
ejpam-4972	333	34	δi	δi	ADP
ejpam-4972	333	35	−	−	PROPN
ejpam-4972	333	36	closed	closed	ADJ
ejpam-4972	333	37	)	)	PUNCT
ejpam-4972	333	38	.	.	PUNCT
ejpam-4972	334	1	hence	hence	ADV
ejpam-4972	334	2	t	t	PROPN
ejpam-4972	334	3	is	be	AUX
ejpam-4972	334	4	fuzzy	fuzzy	ADJ
ejpam-4972	334	5	(	(	PUNCT
ejpam-4972	334	6	i	i	PROPN
ejpam-4972	334	7	,	,	PUNCT
ejpam-4972	334	8	j)−	j)−	PROPN
ejpam-4972	334	9	gψ	gψ	VERB
ejpam-4972	334	10	−	−	PROPN
ejpam-4972	334	11	irresolute	irresolute	ADJ
ejpam-4972	334	12	mapping	mapping	NOUN
ejpam-4972	334	13	.	.	PUNCT
ejpam-4972	335	1	a.	a.	NOUN
ejpam-4972	335	2	a.	a.	PROPN
ejpam-4972	335	3	alharbi	alharbi	PROPN
ejpam-4972	335	4	,	,	PUNCT
ejpam-4972	335	5	a.	a.	NOUN
ejpam-4972	335	6	kilicman	kilicman	PROPN
ejpam-4972	335	7	/	/	SYM
ejpam-4972	335	8	eur	eur	PROPN
ejpam-4972	335	9	.	.	PUNCT
ejpam-4972	336	1	j.	j.	PROPN
ejpam-4972	336	2	pure	pure	PROPN
ejpam-4972	336	3	appl	appl	PROPN
ejpam-4972	336	4	.	.	PROPN
ejpam-4972	336	5	math	math	PROPN
ejpam-4972	336	6	,	,	PUNCT
ejpam-4972	336	7	16	16	NUM
ejpam-4972	336	8	(	(	PUNCT
ejpam-4972	336	9	4	4	NUM
ejpam-4972	336	10	)	)	PUNCT
ejpam-4972	336	11	(	(	PUNCT
ejpam-4972	336	12	2023	2023	NUM
ejpam-4972	336	13	)	)	PUNCT
ejpam-4972	336	14	,	,	PUNCT
ejpam-4972	336	15	2613	2613	NUM
ejpam-4972	336	16	-	-	SYM
ejpam-4972	336	17	2631	2631	NUM
ejpam-4972	336	18	2624	2624	NUM
ejpam-4972	336	19	proof	proof	NOUN
ejpam-4972	336	20	.	.	PUNCT
ejpam-4972	337	1	it	it	PRON
ejpam-4972	337	2	is	be	AUX
ejpam-4972	337	3	clear	clear	ADJ
ejpam-4972	337	4	from	from	ADP
ejpam-4972	337	5	theorem	theorem	ADJ
ejpam-4972	337	6	9	9	NUM
ejpam-4972	337	7	and	and	CCONJ
ejpam-4972	337	8	definition	definition	NOUN
ejpam-4972	337	9	10	10	NUM
ejpam-4972	337	10	.	.	PUNCT
ejpam-4972	338	1	theorem	theorem	NOUN
ejpam-4972	338	2	18	18	NUM
ejpam-4972	338	3	.	.	PUNCT
ejpam-4972	339	1	suppose	suppose	VERB
ejpam-4972	339	2	t	t	NOUN
ejpam-4972	339	3	:	:	PUNCT
ejpam-4972	339	4	(	(	PUNCT
ejpam-4972	339	5	x	x	X
ejpam-4972	339	6	,	,	PUNCT
ejpam-4972	339	7	δ1	δ1	NOUN
ejpam-4972	339	8	,	,	PUNCT
ejpam-4972	339	9	δ2	δ2	ADJ
ejpam-4972	339	10	)	)	PUNCT
ejpam-4972	339	11	→	→	SYM
ejpam-4972	339	12	(	(	PUNCT
ejpam-4972	339	13	y	y	PROPN
ejpam-4972	339	14	,	,	PUNCT
ejpam-4972	339	15	σ1	σ1	PROPN
ejpam-4972	339	16	,	,	PUNCT
ejpam-4972	339	17	σ2	σ2	NOUN
ejpam-4972	339	18	)	)	PUNCT
ejpam-4972	339	19	.	.	PUNCT
ejpam-4972	340	1	consequently	consequently	ADV
ejpam-4972	340	2	,	,	PUNCT
ejpam-4972	340	3	the	the	DET
ejpam-4972	340	4	claims	claim	NOUN
ejpam-4972	340	5	below	below	ADV
ejpam-4972	340	6	are	be	AUX
ejpam-4972	340	7	equivalent	equivalent	ADJ
ejpam-4972	340	8	:	:	PUNCT
ejpam-4972	340	9	(	(	PUNCT
ejpam-4972	340	10	i	i	NOUN
ejpam-4972	340	11	)	)	PUNCT
ejpam-4972	340	12	t	t	PROPN
ejpam-4972	340	13	is	be	AUX
ejpam-4972	340	14	fuzzy	fuzzy	ADJ
ejpam-4972	340	15	(	(	PUNCT
ejpam-4972	340	16	i	i	PROPN
ejpam-4972	340	17	,	,	PUNCT
ejpam-4972	340	18	j)−	j)−	PROPN
ejpam-4972	340	19	gψ	gψ	VERB
ejpam-4972	340	20	−	−	PROPN
ejpam-4972	340	21	irresolute	irresolute	ADJ
ejpam-4972	340	22	mapping	mapping	NOUN
ejpam-4972	340	23	.	.	PUNCT
ejpam-4972	341	1	(	(	PUNCT
ejpam-4972	341	2	ii	ii	NOUN
ejpam-4972	341	3	)	)	PUNCT
ejpam-4972	341	4	the	the	DET
ejpam-4972	341	5	converse	converse	NOUN
ejpam-4972	341	6	of	of	ADP
ejpam-4972	341	7	all	all	DET
ejpam-4972	341	8	fuzzy	fuzzy	ADJ
ejpam-4972	341	9	(	(	PUNCT
ejpam-4972	341	10	i	i	PROPN
ejpam-4972	341	11	,	,	PUNCT
ejpam-4972	341	12	j)−	j)−	PROPN
ejpam-4972	341	13	gψ	gψ	VERB
ejpam-4972	341	14	−	−	PROPN
ejpam-4972	341	15	open	open	ADJ
ejpam-4972	341	16	of	of	ADP
ejpam-4972	341	17	y	y	PROPN
ejpam-4972	341	18	is	be	AUX
ejpam-4972	341	19	(	(	PUNCT
ejpam-4972	341	20	i	i	PROPN
ejpam-4972	341	21	,	,	PUNCT
ejpam-4972	341	22	j)−	j)−	PROPN
ejpam-4972	341	23	gψ	gψ	VERB
ejpam-4972	341	24	−	−	PROPN
ejpam-4972	341	25	open	open	ADJ
ejpam-4972	341	26	of	of	ADP
ejpam-4972	341	27	x.	x.	NOUN
ejpam-4972	341	28	proof	proof	NOUN
ejpam-4972	341	29	.	.	PUNCT
ejpam-4972	342	1	it	it	PRON
ejpam-4972	342	2	’s	’	VERB
ejpam-4972	342	3	clear	clear	ADJ
ejpam-4972	342	4	by	by	ADP
ejpam-4972	342	5	taking	take	VERB
ejpam-4972	342	6	the	the	DET
ejpam-4972	342	7	complement	complement	NOUN
ejpam-4972	342	8	of	of	ADP
ejpam-4972	342	9	definition	definition	NOUN
ejpam-4972	342	10	10	10	NUM
ejpam-4972	342	11	.	.	PUNCT
ejpam-4972	343	1	theorem	theorem	NOUN
ejpam-4972	343	2	19	19	NUM
ejpam-4972	343	3	.	.	PUNCT
ejpam-4972	344	1	suppose	suppose	VERB
ejpam-4972	344	2	t	t	NOUN
ejpam-4972	344	3	:	:	PUNCT
ejpam-4972	344	4	(	(	PUNCT
ejpam-4972	344	5	x	x	X
ejpam-4972	344	6	,	,	PUNCT
ejpam-4972	344	7	δ1	δ1	NOUN
ejpam-4972	344	8	,	,	PUNCT
ejpam-4972	344	9	δ2	δ2	ADJ
ejpam-4972	344	10	)	)	PUNCT
ejpam-4972	344	11	→	→	SYM
ejpam-4972	344	12	(	(	PUNCT
ejpam-4972	344	13	y	y	PROPN
ejpam-4972	344	14	,	,	PUNCT
ejpam-4972	344	15	σ1	σ1	PROPN
ejpam-4972	344	16	,	,	PUNCT
ejpam-4972	344	17	σ2	σ2	NOUN
ejpam-4972	344	18	)	)	PUNCT
ejpam-4972	344	19	.	.	PUNCT
ejpam-4972	345	1	consequently	consequently	ADV
ejpam-4972	345	2	,	,	PUNCT
ejpam-4972	345	3	the	the	DET
ejpam-4972	345	4	next	next	ADJ
ejpam-4972	345	5	claims	claim	NOUN
ejpam-4972	345	6	are	be	AUX
ejpam-4972	345	7	equivalent	equivalent	ADJ
ejpam-4972	345	8	:	:	PUNCT
ejpam-4972	345	9	(	(	PUNCT
ejpam-4972	345	10	i	i	NOUN
ejpam-4972	345	11	)	)	PUNCT
ejpam-4972	345	12	t	t	PROPN
ejpam-4972	345	13	is	be	AUX
ejpam-4972	345	14	fuzzy	fuzzy	ADJ
ejpam-4972	345	15	(	(	PUNCT
ejpam-4972	345	16	i	i	PROPN
ejpam-4972	345	17	,	,	PUNCT
ejpam-4972	345	18	j)−	j)−	PROPN
ejpam-4972	345	19	gψ	gψ	VERB
ejpam-4972	345	20	−	−	NOUN
ejpam-4972	345	21	strongly	strongly	ADV
ejpam-4972	345	22	conts	cont	NOUN
ejpam-4972	345	23	.	.	PUNCT
ejpam-4972	346	1	(	(	PUNCT
ejpam-4972	346	2	ii	ii	NOUN
ejpam-4972	346	3	)	)	PUNCT
ejpam-4972	346	4	the	the	DET
ejpam-4972	346	5	inverse	inverse	NOUN
ejpam-4972	346	6	of	of	ADP
ejpam-4972	346	7	every	every	DET
ejpam-4972	346	8	fuzzy	fuzzy	ADJ
ejpam-4972	346	9	(	(	PUNCT
ejpam-4972	346	10	i	i	PROPN
ejpam-4972	346	11	,	,	PUNCT
ejpam-4972	346	12	j)−	j)−	PROPN
ejpam-4972	346	13	gψ	gψ	VERB
ejpam-4972	346	14	−	−	DET
ejpam-4972	346	15	open	open	ADJ
ejpam-4972	346	16	group	group	NOUN
ejpam-4972	346	17	of	of	ADP
ejpam-4972	346	18	y	y	PROPN
ejpam-4972	346	19	is	be	AUX
ejpam-4972	346	20	δj	δj	ADP
ejpam-4972	346	21	−	−	NUM
ejpam-4972	346	22	open	open	ADJ
ejpam-4972	346	23	group	group	NOUN
ejpam-4972	346	24	of	of	ADP
ejpam-4972	346	25	x.	x.	NOUN
ejpam-4972	346	26	proof	proof	NOUN
ejpam-4972	346	27	.	.	PUNCT
ejpam-4972	347	1	it	it	PRON
ejpam-4972	347	2	is	be	AUX
ejpam-4972	347	3	clear	clear	ADJ
ejpam-4972	347	4	by	by	ADP
ejpam-4972	347	5	taking	take	VERB
ejpam-4972	347	6	the	the	DET
ejpam-4972	347	7	complement	complement	NOUN
ejpam-4972	347	8	of	of	ADP
ejpam-4972	347	9	definition	definition	NOUN
ejpam-4972	347	10	10	10	NUM
ejpam-4972	347	11	.	.	PUNCT
ejpam-4972	348	1	theorem	theorem	NOUN
ejpam-4972	348	2	20	20	NUM
ejpam-4972	348	3	.	.	PUNCT
ejpam-4972	349	1	suppose	suppose	VERB
ejpam-4972	349	2	t	t	NOUN
ejpam-4972	349	3	:	:	PUNCT
ejpam-4972	349	4	(	(	PUNCT
ejpam-4972	349	5	x	x	X
ejpam-4972	349	6	,	,	PUNCT
ejpam-4972	349	7	δ1	δ1	NOUN
ejpam-4972	349	8	,	,	PUNCT
ejpam-4972	349	9	δ2	δ2	ADJ
ejpam-4972	349	10	)	)	PUNCT
ejpam-4972	349	11	→	→	SYM
ejpam-4972	349	12	(	(	PUNCT
ejpam-4972	349	13	y	y	PROPN
ejpam-4972	349	14	,	,	PUNCT
ejpam-4972	349	15	σ1	σ1	PROPN
ejpam-4972	349	16	,	,	PUNCT
ejpam-4972	349	17	σ2	σ2	NOUN
ejpam-4972	349	18	)	)	PUNCT
ejpam-4972	349	19	,	,	PUNCT
ejpam-4972	349	20	g	g	NOUN
ejpam-4972	349	21	:	:	PUNCT
ejpam-4972	349	22	(	(	PUNCT
ejpam-4972	349	23	y	y	PROPN
ejpam-4972	349	24	,	,	PUNCT
ejpam-4972	349	25	σ1	σ1	PROPN
ejpam-4972	349	26	,	,	PUNCT
ejpam-4972	349	27	σ2	σ2	NOUN
ejpam-4972	349	28	)	)	PUNCT
ejpam-4972	349	29	→	→	SYM
ejpam-4972	349	30	(	(	PUNCT
ejpam-4972	349	31	z	z	NOUN
ejpam-4972	349	32	,	,	PUNCT
ejpam-4972	349	33	η1	η1	NOUN
ejpam-4972	349	34	,	,	PUNCT
ejpam-4972	349	35	η2	η2	NOUN
ejpam-4972	349	36	)	)	PUNCT
ejpam-4972	349	37	.	.	PUNCT
ejpam-4972	350	1	hence	hence	ADV
ejpam-4972	350	2	the	the	DET
ejpam-4972	350	3	next	next	ADJ
ejpam-4972	350	4	claims	claim	NOUN
ejpam-4972	350	5	are	be	AUX
ejpam-4972	350	6	true	true	ADJ
ejpam-4972	350	7	:	:	PUNCT
ejpam-4972	350	8	(	(	PUNCT
ejpam-4972	350	9	1	1	X
ejpam-4972	350	10	)	)	PUNCT
ejpam-4972	350	11	g	g	NOUN
ejpam-4972	350	12	◦	◦	NOUN
ejpam-4972	350	13	t	t	PROPN
ejpam-4972	350	14	is	be	AUX
ejpam-4972	350	15	fuzzy	fuzzy	ADJ
ejpam-4972	350	16	δj	δj	ADP
ejpam-4972	350	17	−	−	PROPN
ejpam-4972	350	18	conts	cont	NOUN
ejpam-4972	350	19	when	when	SCONJ
ejpam-4972	350	20	g	g	PROPN
ejpam-4972	350	21	is	be	AUX
ejpam-4972	350	22	fuzzy	fuzzy	ADJ
ejpam-4972	350	23	(	(	PUNCT
ejpam-4972	350	24	i	i	PROPN
ejpam-4972	350	25	,	,	PUNCT
ejpam-4972	350	26	j	j	PROPN
ejpam-4972	350	27	)	)	PUNCT
ejpam-4972	350	28	−	−	PROPN
ejpam-4972	350	29	gψ	gψ	VERB
ejpam-4972	350	30	−	−	PROPN
ejpam-4972	350	31	conts	cont	NOUN
ejpam-4972	350	32	and	and	CCONJ
ejpam-4972	350	33	t	t	PROPN
ejpam-4972	350	34	is	be	AUX
ejpam-4972	350	35	(	(	PUNCT
ejpam-4972	350	36	i	i	PROPN
ejpam-4972	350	37	,	,	PUNCT
ejpam-4972	350	38	j	j	PROPN
ejpam-4972	350	39	)	)	PUNCT
ejpam-4972	350	40	−	−	PROPN
ejpam-4972	350	41	gψ	gψ	VERB
ejpam-4972	350	42	−	−	NOUN
ejpam-4972	350	43	strongly	strongly	ADV
ejpam-4972	350	44	conts	cont	NOUN
ejpam-4972	350	45	.	.	PUNCT
ejpam-4972	351	1	(	(	PUNCT
ejpam-4972	351	2	2	2	X
ejpam-4972	351	3	)	)	PUNCT
ejpam-4972	351	4	g	g	NOUN
ejpam-4972	351	5	◦	◦	PROPN
ejpam-4972	351	6	t	t	PROPN
ejpam-4972	351	7	is	be	AUX
ejpam-4972	351	8	fuzzy	fuzzy	ADJ
ejpam-4972	351	9	(	(	PUNCT
ejpam-4972	351	10	i	i	PROPN
ejpam-4972	351	11	,	,	PUNCT
ejpam-4972	351	12	j)−	j)−	PROPN
ejpam-4972	351	13	gψ	gψ	VERB
ejpam-4972	351	14	−	−	ADV
ejpam-4972	351	15	strongly	strongly	ADV
ejpam-4972	351	16	conts	cont	VERB
ejpam-4972	351	17	when	when	SCONJ
ejpam-4972	351	18	g	g	PROPN
ejpam-4972	351	19	is	be	AUX
ejpam-4972	351	20	(	(	PUNCT
ejpam-4972	351	21	i	i	PROPN
ejpam-4972	351	22	,	,	PUNCT
ejpam-4972	351	23	j)−	j)−	PROPN
ejpam-4972	351	24	gψ	gψ	VERB
ejpam-4972	351	25	−	−	NOUN
ejpam-4972	351	26	strongly	strongly	ADV
ejpam-4972	351	27	conts	cont	NOUN
ejpam-4972	351	28	and	and	CCONJ
ejpam-4972	351	29	t	t	PROPN
ejpam-4972	351	30	is	be	AUX
ejpam-4972	351	31	δj	δj	ADP
ejpam-4972	351	32	−	−	PROPN
ejpam-4972	351	33	conts	cont	NOUN
ejpam-4972	351	34	.	.	PUNCT
ejpam-4972	352	1	(	(	PUNCT
ejpam-4972	352	2	3	3	X
ejpam-4972	352	3	)	)	PUNCT
ejpam-4972	352	4	g	g	NOUN
ejpam-4972	352	5	◦	◦	PROPN
ejpam-4972	352	6	t	t	PROPN
ejpam-4972	352	7	is	be	AUX
ejpam-4972	352	8	fuzzy	fuzzy	ADJ
ejpam-4972	352	9	(	(	PUNCT
ejpam-4972	352	10	i	i	PROPN
ejpam-4972	352	11	,	,	PUNCT
ejpam-4972	352	12	j	j	PROPN
ejpam-4972	352	13	)	)	PUNCT
ejpam-4972	352	14	−	−	PROPN
ejpam-4972	352	15	gψ	gψ	VERB
ejpam-4972	352	16	−	−	NOUN
ejpam-4972	352	17	strongly	strongly	ADV
ejpam-4972	352	18	conts	cont	VERB
ejpam-4972	352	19	when	when	SCONJ
ejpam-4972	352	20	g	g	PROPN
ejpam-4972	352	21	is	be	AUX
ejpam-4972	352	22	(	(	PUNCT
ejpam-4972	352	23	i	i	PROPN
ejpam-4972	352	24	,	,	PUNCT
ejpam-4972	352	25	j	j	PROPN
ejpam-4972	352	26	)	)	PUNCT
ejpam-4972	352	27	−	−	PROPN
ejpam-4972	352	28	gψ	gψ	VERB
ejpam-4972	352	29	−	−	PROPN
ejpam-4972	352	30	irresolute	irresolute	ADJ
ejpam-4972	352	31	,	,	PUNCT
ejpam-4972	352	32	t	t	PROPN
ejpam-4972	352	33	is	be	AUX
ejpam-4972	352	34	(	(	PUNCT
ejpam-4972	352	35	i	i	PROPN
ejpam-4972	352	36	,	,	PUNCT
ejpam-4972	352	37	j)−	j)−	PROPN
ejpam-4972	352	38	gψ	gψ	VERB
ejpam-4972	352	39	−	−	NOUN
ejpam-4972	352	40	strongly	strongly	ADV
ejpam-4972	352	41	conts	cont	NOUN
ejpam-4972	352	42	.	.	PUNCT
ejpam-4972	353	1	proof	proof	NOUN
ejpam-4972	353	2	.	.	PUNCT
ejpam-4972	354	1	(	(	PUNCT
ejpam-4972	354	2	1	1	X
ejpam-4972	354	3	)	)	PUNCT
ejpam-4972	354	4	assume	assume	VERB
ejpam-4972	354	5	w	w	PROPN
ejpam-4972	354	6	∈	∈	PROPN
ejpam-4972	354	7	fηj	fηj	NOUN
ejpam-4972	354	8	.	.	PUNCT
ejpam-4972	355	1	as	as	SCONJ
ejpam-4972	355	2	g	g	PROPN
ejpam-4972	355	3	is	be	AUX
ejpam-4972	355	4	(	(	PUNCT
ejpam-4972	355	5	i	i	PROPN
ejpam-4972	355	6	,	,	PUNCT
ejpam-4972	355	7	j)−	j)−	PROPN
ejpam-4972	355	8	gψ	gψ	VERB
ejpam-4972	355	9	−	−	PROPN
ejpam-4972	355	10	conts	cont	NOUN
ejpam-4972	355	11	,	,	PUNCT
ejpam-4972	355	12	thus	thus	ADV
ejpam-4972	355	13	g−1(w	g−1(w	NOUN
ejpam-4972	355	14	)	)	PUNCT
ejpam-4972	355	15	is	be	AUX
ejpam-4972	355	16	(	(	PUNCT
ejpam-4972	355	17	i	i	PROPN
ejpam-4972	355	18	,	,	PUNCT
ejpam-4972	355	19	j)−	j)−	PROPN
ejpam-4972	355	20	gψ	gψ	VERB
ejpam-4972	355	21	−	−	PROPN
ejpam-4972	355	22	cld	cld	NOUN
ejpam-4972	355	23	group	group	NOUN
ejpam-4972	355	24	of	of	ADP
ejpam-4972	355	25	y	y	PROPN
ejpam-4972	355	26	.	.	PUNCT
ejpam-4972	356	1	since	since	SCONJ
ejpam-4972	356	2	t	t	PROPN
ejpam-4972	356	3	is	be	AUX
ejpam-4972	356	4	fuzzy	fuzzy	ADJ
ejpam-4972	356	5	(	(	PUNCT
ejpam-4972	356	6	i	i	NOUN
ejpam-4972	356	7	,	,	PUNCT
ejpam-4972	356	8	j)−	j)−	PROPN
ejpam-4972	356	9	gψ−	gψ−	PUNCT
ejpam-4972	356	10	strongly	strongly	ADV
ejpam-4972	356	11	conts	cont	NOUN
ejpam-4972	356	12	,	,	PUNCT
ejpam-4972	356	13	then	then	ADV
ejpam-4972	356	14	t−1(g−1(w	t−1(g−1(w	NUM
ejpam-4972	356	15	)	)	PUNCT
ejpam-4972	356	16	)	)	PUNCT
ejpam-4972	357	1	=	=	PRON
ejpam-4972	357	2	(	(	PUNCT
ejpam-4972	357	3	g	g	PROPN
ejpam-4972	357	4	◦	◦	NOUN
ejpam-4972	357	5	t)−1(w	t)−1(w	PROPN
ejpam-4972	357	6	)	)	PUNCT
ejpam-4972	357	7	is	be	AUX
ejpam-4972	357	8	fuzzy	fuzzy	ADJ
ejpam-4972	357	9	δj	δj	ADP
ejpam-4972	357	10	−	−	PROPN
ejpam-4972	357	11	closed	close	VERB
ejpam-4972	357	12	of	of	ADP
ejpam-4972	357	13	x.	x.	NOUN
ejpam-4972	357	14	therefore	therefore	ADV
ejpam-4972	357	15	g	g	PROPN
ejpam-4972	357	16	◦	◦	PROPN
ejpam-4972	357	17	t	t	PROPN
ejpam-4972	357	18	is	be	AUX
ejpam-4972	357	19	fuzzy	fuzzy	ADJ
ejpam-4972	357	20	δj	δj	ADP
ejpam-4972	357	21	−	−	PROPN
ejpam-4972	357	22	conts	cont	NOUN
ejpam-4972	357	23	.	.	PUNCT
ejpam-4972	358	1	(	(	PUNCT
ejpam-4972	358	2	2	2	X
ejpam-4972	358	3	)	)	PUNCT
ejpam-4972	358	4	assumew	assumew	NOUN
ejpam-4972	358	5	is	be	AUX
ejpam-4972	358	6	fuzzy	fuzzy	ADJ
ejpam-4972	358	7	(	(	PUNCT
ejpam-4972	358	8	i	i	PROPN
ejpam-4972	358	9	,	,	PUNCT
ejpam-4972	358	10	j)−gψ−cld	j)−gψ−cld	PROPN
ejpam-4972	358	11	group	group	NOUN
ejpam-4972	358	12	of	of	ADP
ejpam-4972	358	13	z.	z.	PROPN
ejpam-4972	358	14	as	as	SCONJ
ejpam-4972	358	15	g	g	PROPN
ejpam-4972	358	16	is	be	AUX
ejpam-4972	358	17	fuzzy	fuzzy	ADJ
ejpam-4972	358	18	(	(	PUNCT
ejpam-4972	358	19	i	i	NOUN
ejpam-4972	358	20	,	,	PUNCT
ejpam-4972	358	21	j)−gψ−strongly	j)−gψ−strongly	ADV
ejpam-4972	358	22	conts	cont	NOUN
ejpam-4972	358	23	,	,	PUNCT
ejpam-4972	358	24	thus	thus	ADV
ejpam-4972	358	25	g−1(w	g−1(w	NOUN
ejpam-4972	358	26	)	)	PUNCT
ejpam-4972	358	27	is	be	AUX
ejpam-4972	358	28	fuzzy	fuzzy	ADJ
ejpam-4972	358	29	closed	closed	ADJ
ejpam-4972	358	30	(	(	PUNCT
ejpam-4972	358	31	y	y	NOUN
ejpam-4972	358	32	,	,	PUNCT
ejpam-4972	358	33	σj	σj	NOUN
ejpam-4972	358	34	)	)	PUNCT
ejpam-4972	358	35	.	.	PUNCT
ejpam-4972	359	1	as	as	SCONJ
ejpam-4972	359	2	t	t	PROPN
ejpam-4972	359	3	is	be	AUX
ejpam-4972	359	4	fuzzy	fuzzy	ADJ
ejpam-4972	359	5	δj	δj	ADP
ejpam-4972	359	6	−	−	PROPN
ejpam-4972	359	7	conts	cont	NOUN
ejpam-4972	359	8	,	,	PUNCT
ejpam-4972	359	9	then	then	ADV
ejpam-4972	359	10	t−1(g−1(w	t−1(g−1(w	NUM
ejpam-4972	359	11	)	)	PUNCT
ejpam-4972	359	12	)	)	PUNCT
ejpam-4972	360	1	=	=	PRON
ejpam-4972	360	2	(	(	PUNCT
ejpam-4972	360	3	g	g	PROPN
ejpam-4972	360	4	◦	◦	NOUN
ejpam-4972	360	5	t)−1(w	t)−1(w	X
ejpam-4972	360	6	)	)	PUNCT
ejpam-4972	360	7	∈	∈	PROPN
ejpam-4972	360	8	fδj	fδj	NOUN
ejpam-4972	360	9	.	.	PUNCT
ejpam-4972	361	1	so	so	ADV
ejpam-4972	361	2	,	,	PUNCT
ejpam-4972	361	3	g	g	PROPN
ejpam-4972	361	4	◦	◦	PROPN
ejpam-4972	361	5	t	t	PROPN
ejpam-4972	361	6	is	be	AUX
ejpam-4972	361	7	fuzzy	fuzzy	ADJ
ejpam-4972	361	8	(	(	PUNCT
ejpam-4972	361	9	i	i	PROPN
ejpam-4972	361	10	,	,	PUNCT
ejpam-4972	361	11	j)−	j)−	PROPN
ejpam-4972	361	12	gψ	gψ	VERB
ejpam-4972	361	13	−	−	NOUN
ejpam-4972	361	14	strongly	strongly	ADV
ejpam-4972	361	15	conts	cont	NOUN
ejpam-4972	361	16	.	.	PUNCT
ejpam-4972	362	1	(	(	PUNCT
ejpam-4972	362	2	3	3	X
ejpam-4972	362	3	)	)	PUNCT
ejpam-4972	362	4	assumew	assumew	NOUN
ejpam-4972	362	5	is	be	AUX
ejpam-4972	362	6	fuzzy	fuzzy	ADJ
ejpam-4972	362	7	(	(	PUNCT
ejpam-4972	362	8	i	i	PROPN
ejpam-4972	362	9	,	,	PUNCT
ejpam-4972	362	10	j)−gψ−cld	j)−gψ−cld	PROPN
ejpam-4972	362	11	group	group	NOUN
ejpam-4972	362	12	of	of	ADP
ejpam-4972	362	13	z.	z.	PROPN
ejpam-4972	362	14	as	as	SCONJ
ejpam-4972	362	15	g	g	PROPN
ejpam-4972	362	16	is	be	AUX
ejpam-4972	362	17	fuzzy	fuzzy	ADJ
ejpam-4972	362	18	(	(	PUNCT
ejpam-4972	362	19	i	i	NOUN
ejpam-4972	362	20	,	,	PUNCT
ejpam-4972	362	21	j)−gψ−irresolute	j)−gψ−irresolute	PROPN
ejpam-4972	362	22	,	,	PUNCT
ejpam-4972	362	23	thus	thus	ADV
ejpam-4972	362	24	g−1(w	g−1(w	NOUN
ejpam-4972	362	25	)	)	PUNCT
ejpam-4972	362	26	is	be	AUX
ejpam-4972	362	27	fuzzy	fuzzy	ADJ
ejpam-4972	362	28	(	(	PUNCT
ejpam-4972	362	29	i	i	PROPN
ejpam-4972	362	30	,	,	PUNCT
ejpam-4972	362	31	j)−gψ−cld	j)−gψ−cld	PROPN
ejpam-4972	363	1	group	group	NOUN
ejpam-4972	363	2	of	of	ADP
ejpam-4972	363	3	y	y	PROPN
ejpam-4972	363	4	.	.	PUNCT
ejpam-4972	364	1	as	as	SCONJ
ejpam-4972	364	2	t	t	PROPN
ejpam-4972	364	3	is	be	AUX
ejpam-4972	364	4	fuzzy	fuzzy	ADJ
ejpam-4972	364	5	(	(	PUNCT
ejpam-4972	364	6	i	i	NOUN
ejpam-4972	364	7	,	,	PUNCT
ejpam-4972	364	8	j)−gψ−strongly	j)−gψ−strongly	ADV
ejpam-4972	364	9	conts	cont	NOUN
ejpam-4972	364	10	,	,	PUNCT
ejpam-4972	364	11	hence	hence	ADV
ejpam-4972	364	12	t−1(g−1(w	t−1(g−1(w	ADV
ejpam-4972	364	13	)	)	PUNCT
ejpam-4972	364	14	)	)	PUNCT
ejpam-4972	365	1	=	=	PRON
ejpam-4972	365	2	(	(	PUNCT
ejpam-4972	365	3	g	g	PROPN
ejpam-4972	365	4	◦	◦	NOUN
ejpam-4972	365	5	t)−1(w	t)−1(w	NOUN
ejpam-4972	365	6	)	)	PUNCT
ejpam-4972	365	7	∈	∈	PROPN
ejpam-4972	365	8	fδj	fδj	NOUN
ejpam-4972	365	9	.	.	PUNCT
ejpam-4972	366	1	so	so	ADV
ejpam-4972	366	2	,	,	PUNCT
ejpam-4972	366	3	g	g	ADP
ejpam-4972	366	4	◦	◦	NOUN
ejpam-4972	366	5	t	t	NOUN
ejpam-4972	366	6	is	be	AUX
ejpam-4972	366	7	fuzzy	fuzzy	ADJ
ejpam-4972	366	8	(	(	PUNCT
ejpam-4972	366	9	i	i	NOUN
ejpam-4972	366	10	,	,	PUNCT
ejpam-4972	366	11	j)−gψ−strongly	j)−gψ−strongly	ADV
ejpam-4972	366	12	conts	cont	NOUN
ejpam-4972	366	13	.	.	PUNCT
ejpam-4972	367	1	a.	a.	NOUN
ejpam-4972	367	2	a.	a.	PROPN
ejpam-4972	367	3	alharbi	alharbi	PROPN
ejpam-4972	367	4	,	,	PUNCT
ejpam-4972	367	5	a.	a.	NOUN
ejpam-4972	367	6	kilicman	kilicman	PROPN
ejpam-4972	367	7	/	/	SYM
ejpam-4972	367	8	eur	eur	PROPN
ejpam-4972	367	9	.	.	PUNCT
ejpam-4972	368	1	j.	j.	PROPN
ejpam-4972	368	2	pure	pure	PROPN
ejpam-4972	368	3	appl	appl	PROPN
ejpam-4972	368	4	.	.	PROPN
ejpam-4972	368	5	math	math	PROPN
ejpam-4972	368	6	,	,	PUNCT
ejpam-4972	368	7	16	16	NUM
ejpam-4972	368	8	(	(	PUNCT
ejpam-4972	368	9	4	4	NUM
ejpam-4972	368	10	)	)	PUNCT
ejpam-4972	368	11	(	(	PUNCT
ejpam-4972	368	12	2023	2023	NUM
ejpam-4972	368	13	)	)	PUNCT
ejpam-4972	368	14	,	,	PUNCT
ejpam-4972	368	15	2613	2613	NUM
ejpam-4972	368	16	-	-	SYM
ejpam-4972	368	17	2631	2631	NUM
ejpam-4972	368	18	2625	2625	NUM
ejpam-4972	368	19	5	5	NUM
ejpam-4972	368	20	.	.	PUNCT
ejpam-4972	368	21	types	type	NOUN
ejpam-4972	368	22	of	of	ADP
ejpam-4972	368	23	fuzzy	fuzzy	ADJ
ejpam-4972	368	24	generalized	generalize	VERB
ejpam-4972	368	25	open	open	ADJ
ejpam-4972	368	26	and	and	CCONJ
ejpam-4972	368	27	closed	closed	ADJ
ejpam-4972	368	28	mappings	mapping	NOUN
ejpam-4972	368	29	in	in	ADP
ejpam-4972	368	30	the	the	DET
ejpam-4972	368	31	third	third	ADJ
ejpam-4972	368	32	part	part	NOUN
ejpam-4972	368	33	,	,	PUNCT
ejpam-4972	368	34	we	we	PRON
ejpam-4972	368	35	introduce	introduce	VERB
ejpam-4972	368	36	some	some	DET
ejpam-4972	368	37	concepts	concept	NOUN
ejpam-4972	368	38	for	for	ADP
ejpam-4972	368	39	fuzzy	fuzzy	ADJ
ejpam-4972	368	40	(	(	PUNCT
ejpam-4972	368	41	i	i	NOUN
ejpam-4972	368	42	,	,	PUNCT
ejpam-4972	368	43	j)−generalized	j)−generalized	ADJ
ejpam-4972	368	44	ψ−open	ψ−open	ADV
ejpam-4972	368	45	and	and	CCONJ
ejpam-4972	368	46	closed	close	VERB
ejpam-4972	368	47	mapping	mapping	NOUN
ejpam-4972	368	48	then	then	ADV
ejpam-4972	368	49	we	we	PRON
ejpam-4972	368	50	study	study	VERB
ejpam-4972	368	51	some	some	DET
ejpam-4972	368	52	properties	property	NOUN
ejpam-4972	368	53	and	and	CCONJ
ejpam-4972	368	54	important	important	ADJ
ejpam-4972	368	55	theorems	theorem	NOUN
ejpam-4972	368	56	.	.	PUNCT
ejpam-4972	369	1	definition	definition	NOUN
ejpam-4972	369	2	11	11	NUM
ejpam-4972	369	3	.	.	PUNCT
ejpam-4972	370	1	suppose	suppose	VERB
ejpam-4972	370	2	t	t	NOUN
ejpam-4972	370	3	:	:	PUNCT
ejpam-4972	370	4	(	(	PUNCT
ejpam-4972	370	5	x	x	X
ejpam-4972	370	6	,	,	PUNCT
ejpam-4972	370	7	δ1	δ1	NOUN
ejpam-4972	370	8	,	,	PUNCT
ejpam-4972	370	9	δ2	δ2	ADJ
ejpam-4972	370	10	)	)	PUNCT
ejpam-4972	370	11	→	→	SYM
ejpam-4972	370	12	(	(	PUNCT
ejpam-4972	370	13	y	y	PROPN
ejpam-4972	370	14	,	,	PUNCT
ejpam-4972	370	15	σ1	σ1	PROPN
ejpam-4972	370	16	,	,	PUNCT
ejpam-4972	370	17	σ2	σ2	NOUN
ejpam-4972	370	18	)	)	PUNCT
ejpam-4972	370	19	.	.	PUNCT
ejpam-4972	371	1	thus	thus	ADV
ejpam-4972	371	2	t	t	PROPN
ejpam-4972	371	3	is	be	AUX
ejpam-4972	371	4	referred	refer	VERB
ejpam-4972	371	5	to	to	ADP
ejpam-4972	371	6	as	as	ADP
ejpam-4972	371	7	:	:	PUNCT
ejpam-4972	371	8	(	(	PUNCT
ejpam-4972	371	9	1	1	X
ejpam-4972	371	10	)	)	PUNCT
ejpam-4972	371	11	fuzzy	fuzzy	NOUN
ejpam-4972	371	12	(	(	PUNCT
ejpam-4972	371	13	i	i	PROPN
ejpam-4972	371	14	,	,	PUNCT
ejpam-4972	371	15	j)−	j)−	PROPN
ejpam-4972	371	16	generalized	generalize	VERB
ejpam-4972	371	17	ψ	ψ	ADP
ejpam-4972	371	18	−	−	NOUN
ejpam-4972	371	19	open	open	ADJ
ejpam-4972	371	20	mapping	mapping	NOUN
ejpam-4972	371	21	(	(	PUNCT
ejpam-4972	371	22	briefly	briefly	ADV
ejpam-4972	371	23	,	,	PUNCT
ejpam-4972	371	24	(	(	PUNCT
ejpam-4972	371	25	i	i	PROPN
ejpam-4972	371	26	,	,	PUNCT
ejpam-4972	371	27	j)−	j)−	PROPN
ejpam-4972	371	28	gψ	gψ	VERB
ejpam-4972	371	29	−	−	PROPN
ejpam-4972	371	30	open	open	ADJ
ejpam-4972	371	31	)	)	PUNCT
ejpam-4972	371	32	when	when	SCONJ
ejpam-4972	371	33	t(v	t(v	PROPN
ejpam-4972	371	34	)	)	PUNCT
ejpam-4972	371	35	is	be	AUX
ejpam-4972	371	36	fuzzy	fuzzy	ADJ
ejpam-4972	371	37	(	(	PUNCT
ejpam-4972	371	38	i	i	PROPN
ejpam-4972	371	39	,	,	PUNCT
ejpam-4972	371	40	j)−	j)−	PROPN
ejpam-4972	371	41	gψ	gψ	VERB
ejpam-4972	371	42	−	−	PROPN
ejpam-4972	371	43	open	open	ADJ
ejpam-4972	371	44	in	in	ADP
ejpam-4972	371	45	y	y	PROPN
ejpam-4972	371	46	for	for	ADP
ejpam-4972	371	47	any	any	DET
ejpam-4972	371	48	v	v	NOUN
ejpam-4972	371	49	is	be	AUX
ejpam-4972	371	50	(	(	PUNCT
ejpam-4972	371	51	i	i	PROPN
ejpam-4972	371	52	,	,	PUNCT
ejpam-4972	371	53	j)−	j)−	PROPN
ejpam-4972	371	54	gψ	gψ	VERB
ejpam-4972	371	55	−	−	PROPN
ejpam-4972	371	56	open	open	ADJ
ejpam-4972	371	57	of	of	ADP
ejpam-4972	371	58	x.	x.	NOUN
ejpam-4972	371	59	(	(	PUNCT
ejpam-4972	371	60	2	2	NUM
ejpam-4972	371	61	)	)	PUNCT
ejpam-4972	371	62	fuzzy	fuzzy	NOUN
ejpam-4972	371	63	(	(	PUNCT
ejpam-4972	371	64	i	i	PROPN
ejpam-4972	371	65	,	,	PUNCT
ejpam-4972	371	66	j)−	j)−	PROPN
ejpam-4972	371	67	generalized	generalize	VERB
ejpam-4972	371	68	ψ−	ψ−	VERB
ejpam-4972	371	69	closed	closed	ADJ
ejpam-4972	371	70	mapping	mapping	NOUN
ejpam-4972	371	71	(	(	PUNCT
ejpam-4972	371	72	briefly	briefly	ADV
ejpam-4972	371	73	,	,	PUNCT
ejpam-4972	371	74	(	(	PUNCT
ejpam-4972	371	75	i	i	NOUN
ejpam-4972	371	76	,	,	PUNCT
ejpam-4972	371	77	j)−	j)−	PROPN
ejpam-4972	371	78	gψ−	gψ−	PUNCT
ejpam-4972	371	79	closed	closed	ADJ
ejpam-4972	371	80	)	)	PUNCT
ejpam-4972	371	81	when	when	SCONJ
ejpam-4972	371	82	t(v	t(v	PROPN
ejpam-4972	371	83	)	)	PUNCT
ejpam-4972	371	84	is	be	AUX
ejpam-4972	371	85	fuzzy	fuzzy	ADJ
ejpam-4972	371	86	(	(	PUNCT
ejpam-4972	371	87	i	i	PROPN
ejpam-4972	371	88	,	,	PUNCT
ejpam-4972	371	89	j)−	j)−	PROPN
ejpam-4972	371	90	gψ	gψ	VERB
ejpam-4972	371	91	−	−	PROPN
ejpam-4972	371	92	cld	cld	NOUN
ejpam-4972	371	93	of	of	ADP
ejpam-4972	371	94	y	y	PROPN
ejpam-4972	371	95	for	for	ADP
ejpam-4972	371	96	any	any	DET
ejpam-4972	371	97	v	v	NOUN
ejpam-4972	371	98	is	be	AUX
ejpam-4972	371	99	(	(	PUNCT
ejpam-4972	371	100	i	i	PROPN
ejpam-4972	371	101	,	,	PUNCT
ejpam-4972	371	102	j)−	j)−	PROPN
ejpam-4972	371	103	gψ	gψ	VERB
ejpam-4972	371	104	−	−	PROPN
ejpam-4972	371	105	cld	cld	NOUN
ejpam-4972	371	106	of	of	ADP
ejpam-4972	371	107	x.	x.	PROPN
ejpam-4972	371	108	theorem	theorem	VERB
ejpam-4972	371	109	21	21	NUM
ejpam-4972	371	110	.	.	PUNCT
ejpam-4972	372	1	suppose	suppose	VERB
ejpam-4972	372	2	t	t	NOUN
ejpam-4972	372	3	:	:	PUNCT
ejpam-4972	372	4	(	(	PUNCT
ejpam-4972	372	5	x	x	X
ejpam-4972	372	6	,	,	PUNCT
ejpam-4972	372	7	δ1	δ1	NOUN
ejpam-4972	372	8	,	,	PUNCT
ejpam-4972	372	9	δ2	δ2	ADJ
ejpam-4972	372	10	)	)	PUNCT
ejpam-4972	372	11	→	→	SYM
ejpam-4972	372	12	(	(	PUNCT
ejpam-4972	372	13	y	y	PROPN
ejpam-4972	372	14	,	,	PUNCT
ejpam-4972	372	15	σ1	σ1	PROPN
ejpam-4972	372	16	,	,	PUNCT
ejpam-4972	372	17	σ2	σ2	NOUN
ejpam-4972	372	18	)	)	PUNCT
ejpam-4972	372	19	is	be	AUX
ejpam-4972	372	20	fuzzy	fuzzy	ADJ
ejpam-4972	372	21	σj−open	σj−open	NOUN
ejpam-4972	372	22	function	function	NOUN
ejpam-4972	372	23	.	.	PUNCT
ejpam-4972	373	1	thus	thus	ADV
ejpam-4972	373	2	t(k	t(k	NOUN
ejpam-4972	373	3	)	)	PUNCT
ejpam-4972	373	4	is	be	AUX
ejpam-4972	373	5	fuzzy	fuzzy	ADJ
ejpam-4972	373	6	(	(	PUNCT
ejpam-4972	373	7	i	i	PROPN
ejpam-4972	373	8	,	,	PUNCT
ejpam-4972	373	9	j)−	j)−	PROPN
ejpam-4972	373	10	gψ	gψ	VERB
ejpam-4972	373	11	−	−	PROPN
ejpam-4972	373	12	open	open	ADJ
ejpam-4972	373	13	in	in	ADP
ejpam-4972	373	14	y	y	PROPN
ejpam-4972	373	15	for	for	ADP
ejpam-4972	373	16	any	any	DET
ejpam-4972	373	17	k	k	PROPN
ejpam-4972	373	18	∈	∈	PROPN
ejpam-4972	373	19	(	(	PUNCT
ejpam-4972	373	20	x	x	NOUN
ejpam-4972	373	21	,	,	PUNCT
ejpam-4972	373	22	δj	δj	ADJ
ejpam-4972	373	23	)	)	PUNCT
ejpam-4972	373	24	.	.	PUNCT
ejpam-4972	374	1	proof	proof	NOUN
ejpam-4972	374	2	.	.	PUNCT
ejpam-4972	375	1	assume	assume	VERB
ejpam-4972	375	2	t	t	PROPN
ejpam-4972	375	3	is	be	AUX
ejpam-4972	375	4	σj	σj	VERB
ejpam-4972	375	5	−	−	PROPN
ejpam-4972	375	6	open	open	ADJ
ejpam-4972	375	7	,	,	PUNCT
ejpam-4972	375	8	k	k	PROPN
ejpam-4972	375	9	∈	∈	PROPN
ejpam-4972	375	10	oδj	oδj	NOUN
ejpam-4972	375	11	.	.	PUNCT
ejpam-4972	376	1	so	so	ADV
ejpam-4972	376	2	t(k	t(k	NOUN
ejpam-4972	376	3	)	)	PUNCT
ejpam-4972	376	4	∈	∈	PROPN
ejpam-4972	376	5	(	(	PUNCT
ejpam-4972	376	6	y	y	NOUN
ejpam-4972	376	7	,	,	PUNCT
ejpam-4972	376	8	σj	σj	NOUN
ejpam-4972	376	9	)	)	PUNCT
ejpam-4972	376	10	,	,	PUNCT
ejpam-4972	376	11	and	and	CCONJ
ejpam-4972	376	12	hence	hence	ADV
ejpam-4972	376	13	by	by	ADP
ejpam-4972	376	14	relation	relation	NOUN
ejpam-4972	376	15	via	via	ADP
ejpam-4972	376	16	open	open	ADJ
ejpam-4972	376	17	group	group	NOUN
ejpam-4972	376	18	and	and	CCONJ
ejpam-4972	376	19	(	(	PUNCT
ejpam-4972	376	20	i	i	PROPN
ejpam-4972	376	21	,	,	PUNCT
ejpam-4972	376	22	j	j	PROPN
ejpam-4972	376	23	)	)	PUNCT
ejpam-4972	376	24	−	−	PROPN
ejpam-4972	376	25	gψ	gψ	VERB
ejpam-4972	376	26	−	−	DET
ejpam-4972	376	27	open	open	ADJ
ejpam-4972	376	28	group	group	NOUN
ejpam-4972	376	29	which	which	PRON
ejpam-4972	376	30	was	be	AUX
ejpam-4972	376	31	clear	clear	ADJ
ejpam-4972	376	32	in	in	ADP
ejpam-4972	376	33	refrence	refrence	NOUN
ejpam-4972	376	34	[	[	X
ejpam-4972	376	35	3	3	NUM
ejpam-4972	376	36	]	]	PUNCT
ejpam-4972	376	37	,	,	PUNCT
ejpam-4972	376	38	we	we	PRON
ejpam-4972	376	39	find	find	VERB
ejpam-4972	376	40	t(k	t(k	NOUN
ejpam-4972	376	41	)	)	PUNCT
ejpam-4972	376	42	is	be	AUX
ejpam-4972	376	43	fuzzy	fuzzy	ADJ
ejpam-4972	376	44	(	(	PUNCT
ejpam-4972	376	45	i	i	PROPN
ejpam-4972	376	46	,	,	PUNCT
ejpam-4972	376	47	j)−	j)−	PROPN
ejpam-4972	376	48	gψ	gψ	VERB
ejpam-4972	376	49	−	−	PROPN
ejpam-4972	376	50	open	open	ADJ
ejpam-4972	376	51	in	in	ADP
ejpam-4972	376	52	y	y	PROPN
ejpam-4972	376	53	.	.	PUNCT
ejpam-4972	377	1	theorem	theorem	PROPN
ejpam-4972	377	2	22	22	NUM
ejpam-4972	377	3	.	.	PUNCT
ejpam-4972	378	1	suppose	suppose	VERB
ejpam-4972	378	2	t	t	NOUN
ejpam-4972	378	3	:	:	PUNCT
ejpam-4972	378	4	(	(	PUNCT
ejpam-4972	378	5	x	x	X
ejpam-4972	378	6	,	,	PUNCT
ejpam-4972	378	7	δ1	δ1	NOUN
ejpam-4972	378	8	,	,	PUNCT
ejpam-4972	378	9	δ2	δ2	ADJ
ejpam-4972	378	10	)	)	PUNCT
ejpam-4972	378	11	→	→	SYM
ejpam-4972	378	12	(	(	PUNCT
ejpam-4972	378	13	y	y	PROPN
ejpam-4972	378	14	,	,	PUNCT
ejpam-4972	378	15	σ1	σ1	PROPN
ejpam-4972	378	16	,	,	PUNCT
ejpam-4972	378	17	σ2	σ2	NOUN
ejpam-4972	378	18	)	)	PUNCT
ejpam-4972	378	19	,	,	PUNCT
ejpam-4972	378	20	g	g	NOUN
ejpam-4972	378	21	:	:	PUNCT
ejpam-4972	378	22	(	(	PUNCT
ejpam-4972	378	23	y	y	PROPN
ejpam-4972	378	24	,	,	PUNCT
ejpam-4972	378	25	σ1	σ1	PROPN
ejpam-4972	378	26	,	,	PUNCT
ejpam-4972	378	27	σ2	σ2	NOUN
ejpam-4972	378	28	)	)	PUNCT
ejpam-4972	378	29	→	→	SYM
ejpam-4972	378	30	(	(	PUNCT
ejpam-4972	378	31	z	z	NOUN
ejpam-4972	378	32	,	,	PUNCT
ejpam-4972	378	33	η1	η1	NOUN
ejpam-4972	378	34	,	,	PUNCT
ejpam-4972	378	35	η2	η2	NOUN
ejpam-4972	378	36	)	)	PUNCT
ejpam-4972	378	37	.	.	PUNCT
ejpam-4972	379	1	then	then	ADV
ejpam-4972	379	2	the	the	DET
ejpam-4972	379	3	claims	claim	NOUN
ejpam-4972	379	4	below	below	ADV
ejpam-4972	379	5	are	be	AUX
ejpam-4972	379	6	true	true	ADJ
ejpam-4972	379	7	:	:	PUNCT
ejpam-4972	379	8	(	(	PUNCT
ejpam-4972	379	9	1	1	X
ejpam-4972	379	10	)	)	PUNCT
ejpam-4972	379	11	g	g	NOUN
ejpam-4972	379	12	◦	◦	NOUN
ejpam-4972	379	13	t	t	NOUN
ejpam-4972	379	14	is	be	AUX
ejpam-4972	379	15	fuzzy	fuzzy	ADJ
ejpam-4972	379	16	(	(	PUNCT
ejpam-4972	379	17	i	i	NOUN
ejpam-4972	379	18	,	,	PUNCT
ejpam-4972	379	19	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	379	20	(	(	PUNCT
ejpam-4972	379	21	resp	resp	NOUN
ejpam-4972	379	22	,	,	PUNCT
ejpam-4972	379	23	(	(	PUNCT
ejpam-4972	379	24	i	i	NOUN
ejpam-4972	379	25	,	,	PUNCT
ejpam-4972	379	26	j)−gψ−closed	j)−gψ−close	VERB
ejpam-4972	379	27	)	)	PUNCT
ejpam-4972	379	28	if	if	SCONJ
ejpam-4972	379	29	t	t	PROPN
ejpam-4972	379	30	,	,	PUNCT
ejpam-4972	379	31	g	g	PROPN
ejpam-4972	379	32	are	be	AUX
ejpam-4972	379	33	(	(	PUNCT
ejpam-4972	379	34	i	i	NOUN
ejpam-4972	379	35	,	,	PUNCT
ejpam-4972	379	36	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	379	37	(	(	PUNCT
ejpam-4972	379	38	resp	resp	NOUN
ejpam-4972	379	39	,	,	PUNCT
ejpam-4972	379	40	(	(	PUNCT
ejpam-4972	379	41	i	i	PROPN
ejpam-4972	379	42	,	,	PUNCT
ejpam-4972	379	43	j)−	j)−	PROPN
ejpam-4972	379	44	gψ	gψ	VERB
ejpam-4972	379	45	−	−	PROPN
ejpam-4972	379	46	closed	closed	ADJ
ejpam-4972	379	47	)	)	PUNCT
ejpam-4972	379	48	mapping	mapping	NOUN
ejpam-4972	379	49	.	.	PUNCT
ejpam-4972	380	1	(	(	PUNCT
ejpam-4972	380	2	2	2	X
ejpam-4972	380	3	)	)	PUNCT
ejpam-4972	380	4	t	t	NOUN
ejpam-4972	380	5	is	be	AUX
ejpam-4972	380	6	fuzzy	fuzzy	ADJ
ejpam-4972	380	7	(	(	PUNCT
ejpam-4972	380	8	i	i	NOUN
ejpam-4972	380	9	,	,	PUNCT
ejpam-4972	380	10	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	380	11	(	(	PUNCT
ejpam-4972	380	12	resp	resp	NOUN
ejpam-4972	380	13	,	,	PUNCT
ejpam-4972	380	14	(	(	PUNCT
ejpam-4972	380	15	i	i	PRON
ejpam-4972	380	16	,	,	PUNCT
ejpam-4972	380	17	j)−gψ−	j)−gψ−	PROPN
ejpam-4972	380	18	closed	close	VERB
ejpam-4972	380	19	)	)	PUNCT
ejpam-4972	380	20	if	if	SCONJ
ejpam-4972	380	21	g	g	PROPN
ejpam-4972	380	22	◦	◦	PROPN
ejpam-4972	380	23	t	t	PROPN
ejpam-4972	380	24	is	be	AUX
ejpam-4972	380	25	(	(	PUNCT
ejpam-4972	380	26	i	i	NOUN
ejpam-4972	380	27	,	,	PUNCT
ejpam-4972	380	28	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	380	29	(	(	PUNCT
ejpam-4972	380	30	resp	resp	NOUN
ejpam-4972	380	31	,	,	PUNCT
ejpam-4972	380	32	(	(	PUNCT
ejpam-4972	380	33	i	i	PROPN
ejpam-4972	380	34	,	,	PUNCT
ejpam-4972	380	35	j)−	j)−	PROPN
ejpam-4972	380	36	gψ	gψ	VERB
ejpam-4972	380	37	−	−	PROPN
ejpam-4972	380	38	closed	closed	ADJ
ejpam-4972	380	39	)	)	PUNCT
ejpam-4972	380	40	,	,	PUNCT
ejpam-4972	380	41	g	g	PROPN
ejpam-4972	380	42	is	be	AUX
ejpam-4972	380	43	(	(	PUNCT
ejpam-4972	380	44	i	i	PROPN
ejpam-4972	380	45	,	,	PUNCT
ejpam-4972	380	46	j)−	j)−	PROPN
ejpam-4972	380	47	gψ	gψ	VERB
ejpam-4972	380	48	−	−	NOUN
ejpam-4972	380	49	irresolute	irresolute	ADJ
ejpam-4972	380	50	and	and	CCONJ
ejpam-4972	380	51	injective	injective	ADJ
ejpam-4972	380	52	mapping	mapping	NOUN
ejpam-4972	380	53	.	.	PUNCT
ejpam-4972	381	1	(	(	PUNCT
ejpam-4972	381	2	3	3	X
ejpam-4972	381	3	)	)	PUNCT
ejpam-4972	381	4	t	t	NOUN
ejpam-4972	381	5	is	be	AUX
ejpam-4972	381	6	fuzzy	fuzzy	ADJ
ejpam-4972	381	7	δj−open	δj−open	NOUN
ejpam-4972	381	8	(	(	PUNCT
ejpam-4972	381	9	resp	resp	NOUN
ejpam-4972	381	10	,	,	PUNCT
ejpam-4972	381	11	δj−closed	δj−close	VERB
ejpam-4972	381	12	)	)	PUNCT
ejpam-4972	381	13	if	if	SCONJ
ejpam-4972	381	14	g	g	PROPN
ejpam-4972	381	15	◦	◦	NOUN
ejpam-4972	381	16	t	t	NOUN
ejpam-4972	381	17	is	be	AUX
ejpam-4972	381	18	(	(	PUNCT
ejpam-4972	381	19	i	i	NOUN
ejpam-4972	381	20	,	,	PUNCT
ejpam-4972	381	21	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	381	22	(	(	PUNCT
ejpam-4972	381	23	resp	resp	NOUN
ejpam-4972	381	24	,	,	PUNCT
ejpam-4972	381	25	(	(	PUNCT
ejpam-4972	381	26	i	i	NOUN
ejpam-4972	381	27	,	,	PUNCT
ejpam-4972	381	28	j)−gψ−closed	j)−gψ−close	VERB
ejpam-4972	381	29	)	)	PUNCT
ejpam-4972	381	30	,	,	PUNCT
ejpam-4972	381	31	g	g	PROPN
ejpam-4972	381	32	is	be	AUX
ejpam-4972	381	33	(	(	PUNCT
ejpam-4972	381	34	i	i	PROPN
ejpam-4972	381	35	,	,	PUNCT
ejpam-4972	381	36	j)−	j)−	PROPN
ejpam-4972	381	37	gψ	gψ	VERB
ejpam-4972	381	38	−	−	NOUN
ejpam-4972	381	39	strongly	strongly	ADV
ejpam-4972	381	40	conts	cont	NOUN
ejpam-4972	381	41	and	and	CCONJ
ejpam-4972	381	42	injective	injective	ADJ
ejpam-4972	381	43	mapping	mapping	NOUN
ejpam-4972	381	44	.	.	PUNCT
ejpam-4972	382	1	(	(	PUNCT
ejpam-4972	382	2	4	4	X
ejpam-4972	382	3	)	)	PUNCT
ejpam-4972	382	4	g	g	NOUN
ejpam-4972	382	5	is	be	AUX
ejpam-4972	382	6	fuzzy	fuzzy	ADJ
ejpam-4972	382	7	(	(	PUNCT
ejpam-4972	382	8	i	i	NOUN
ejpam-4972	382	9	,	,	PUNCT
ejpam-4972	382	10	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	382	11	(	(	PUNCT
ejpam-4972	382	12	resp	resp	NOUN
ejpam-4972	382	13	,	,	PUNCT
ejpam-4972	382	14	(	(	PUNCT
ejpam-4972	382	15	i	i	NOUN
ejpam-4972	382	16	,	,	PUNCT
ejpam-4972	382	17	j)−gψ−closed	j)−gψ−close	VERB
ejpam-4972	382	18	)	)	PUNCT
ejpam-4972	382	19	if	if	SCONJ
ejpam-4972	382	20	g	g	PROPN
ejpam-4972	382	21	◦	◦	PROPN
ejpam-4972	382	22	t	t	PROPN
ejpam-4972	382	23	is	be	AUX
ejpam-4972	382	24	(	(	PUNCT
ejpam-4972	382	25	i	i	NOUN
ejpam-4972	382	26	,	,	PUNCT
ejpam-4972	382	27	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	382	28	(	(	PUNCT
ejpam-4972	382	29	resp	resp	NOUN
ejpam-4972	382	30	,	,	PUNCT
ejpam-4972	382	31	(	(	PUNCT
ejpam-4972	382	32	i	i	PROPN
ejpam-4972	382	33	,	,	PUNCT
ejpam-4972	382	34	j)−	j)−	PROPN
ejpam-4972	382	35	gψ	gψ	VERB
ejpam-4972	382	36	−	−	PROPN
ejpam-4972	382	37	closed	closed	ADJ
ejpam-4972	382	38	)	)	PUNCT
ejpam-4972	382	39	,	,	PUNCT
ejpam-4972	382	40	t	t	PROPN
ejpam-4972	382	41	is	be	AUX
ejpam-4972	382	42	(	(	PUNCT
ejpam-4972	382	43	i	i	PROPN
ejpam-4972	382	44	,	,	PUNCT
ejpam-4972	382	45	j)−	j)−	PROPN
ejpam-4972	382	46	gψ	gψ	VERB
ejpam-4972	382	47	−	−	PROPN
ejpam-4972	382	48	irresolute	irresolute	ADJ
ejpam-4972	382	49	and	and	CCONJ
ejpam-4972	382	50	surjective	surjective	ADJ
ejpam-4972	382	51	mapping	mapping	NOUN
ejpam-4972	382	52	.	.	PUNCT
ejpam-4972	383	1	(	(	PUNCT
ejpam-4972	383	2	5	5	X
ejpam-4972	383	3	)	)	PUNCT
ejpam-4972	383	4	g	g	NOUN
ejpam-4972	383	5	is	be	AUX
ejpam-4972	383	6	fuzzy	fuzzy	ADJ
ejpam-4972	383	7	σj	σj	ADP
ejpam-4972	383	8	−	−	PROPN
ejpam-4972	383	9	open	open	ADJ
ejpam-4972	383	10	(	(	PUNCT
ejpam-4972	383	11	resp	resp	NOUN
ejpam-4972	383	12	,	,	PUNCT
ejpam-4972	383	13	σj	σj	VERB
ejpam-4972	383	14	−	−	PROPN
ejpam-4972	383	15	closed	closed	ADJ
ejpam-4972	383	16	)	)	PUNCT
ejpam-4972	383	17	if	if	SCONJ
ejpam-4972	383	18	g	g	PROPN
ejpam-4972	383	19	◦	◦	PROPN
ejpam-4972	383	20	t	t	PROPN
ejpam-4972	383	21	is	be	AUX
ejpam-4972	383	22	δj	δj	ADP
ejpam-4972	383	23	−	−	PROPN
ejpam-4972	383	24	open	open	ADJ
ejpam-4972	383	25	(	(	PUNCT
ejpam-4972	383	26	resp	resp	NOUN
ejpam-4972	383	27	,	,	PUNCT
ejpam-4972	383	28	δj	δj	ADP
ejpam-4972	383	29	−	−	PROPN
ejpam-4972	383	30	closed	closed	ADJ
ejpam-4972	383	31	)	)	PUNCT
ejpam-4972	383	32	,	,	PUNCT
ejpam-4972	383	33	t	t	PROPN
ejpam-4972	383	34	is	be	AUX
ejpam-4972	383	35	(	(	PUNCT
ejpam-4972	383	36	i	i	PROPN
ejpam-4972	383	37	,	,	PUNCT
ejpam-4972	383	38	j)−	j)−	PROPN
ejpam-4972	383	39	gψ	gψ	VERB
ejpam-4972	383	40	−	−	NOUN
ejpam-4972	383	41	strongly	strongly	ADV
ejpam-4972	383	42	conts	cont	NOUN
ejpam-4972	383	43	and	and	CCONJ
ejpam-4972	383	44	surjective	surjective	ADJ
ejpam-4972	383	45	mapping	mapping	NOUN
ejpam-4972	383	46	.	.	PUNCT
ejpam-4972	384	1	proof	proof	NOUN
ejpam-4972	384	2	.	.	PUNCT
ejpam-4972	385	1	(	(	PUNCT
ejpam-4972	385	2	1	1	X
ejpam-4972	385	3	)	)	PUNCT
ejpam-4972	385	4	assume	assume	VERB
ejpam-4972	385	5	k	k	PROPN
ejpam-4972	385	6	is	be	AUX
ejpam-4972	385	7	fuzzy	fuzzy	ADJ
ejpam-4972	385	8	(	(	PUNCT
ejpam-4972	385	9	i	i	NOUN
ejpam-4972	385	10	,	,	PUNCT
ejpam-4972	385	11	j)−	j)−	PROPN
ejpam-4972	385	12	gψ−	gψ−	PUNCT
ejpam-4972	385	13	open	open	ADJ
ejpam-4972	385	14	group	group	NOUN
ejpam-4972	385	15	of	of	ADP
ejpam-4972	385	16	x.	x.	PROPN
ejpam-4972	385	17	as	as	ADP
ejpam-4972	385	18	t	t	PROPN
ejpam-4972	385	19	is	be	AUX
ejpam-4972	385	20	(	(	PUNCT
ejpam-4972	385	21	i	i	PROPN
ejpam-4972	385	22	,	,	PUNCT
ejpam-4972	385	23	j)−	j)−	PROPN
ejpam-4972	385	24	gψ−	gψ−	PUNCT
ejpam-4972	385	25	open	open	ADJ
ejpam-4972	385	26	mapping	mapping	NOUN
ejpam-4972	385	27	,	,	PUNCT
ejpam-4972	385	28	thus	thus	ADV
ejpam-4972	385	29	t(k	t(k	NOUN
ejpam-4972	385	30	)	)	PUNCT
ejpam-4972	385	31	is	be	AUX
ejpam-4972	385	32	(	(	PUNCT
ejpam-4972	385	33	i	i	PROPN
ejpam-4972	385	34	,	,	PUNCT
ejpam-4972	385	35	j)−	j)−	PROPN
ejpam-4972	385	36	gψ−	gψ−	PUNCT
ejpam-4972	385	37	open	open	ADJ
ejpam-4972	385	38	group	group	NOUN
ejpam-4972	385	39	of	of	ADP
ejpam-4972	385	40	y	y	PROPN
ejpam-4972	385	41	.	.	PUNCT
ejpam-4972	386	1	as	as	SCONJ
ejpam-4972	386	2	g	g	PROPN
ejpam-4972	386	3	is	be	AUX
ejpam-4972	386	4	(	(	PUNCT
ejpam-4972	386	5	i	i	PROPN
ejpam-4972	386	6	,	,	PUNCT
ejpam-4972	386	7	j)−	j)−	PROPN
ejpam-4972	386	8	gψ−	gψ−	PUNCT
ejpam-4972	386	9	open	open	ADJ
ejpam-4972	386	10	mapping	mapping	NOUN
ejpam-4972	386	11	,	,	PUNCT
ejpam-4972	386	12	hence	hence	ADV
ejpam-4972	386	13	g(t(k	g(t(k	PROPN
ejpam-4972	386	14	)	)	PUNCT
ejpam-4972	386	15	)	)	PUNCT
ejpam-4972	386	16	is	be	AUX
ejpam-4972	386	17	(	(	PUNCT
ejpam-4972	386	18	i	i	PROPN
ejpam-4972	386	19	,	,	PUNCT
ejpam-4972	386	20	j)−	j)−	PROPN
ejpam-4972	386	21	gψ−	gψ−	PUNCT
ejpam-4972	386	22	open	open	ADJ
ejpam-4972	386	23	group	group	NOUN
ejpam-4972	386	24	of	of	ADP
ejpam-4972	386	25	z.	z.	PROPN
ejpam-4972	387	1	so	so	ADV
ejpam-4972	387	2	(	(	PUNCT
ejpam-4972	387	3	g	g	NOUN
ejpam-4972	387	4	◦	◦	NOUN
ejpam-4972	387	5	t)(k	t)(k	NOUN
ejpam-4972	387	6	)	)	PUNCT
ejpam-4972	387	7	is	be	AUX
ejpam-4972	387	8	(	(	PUNCT
ejpam-4972	387	9	i	i	PROPN
ejpam-4972	387	10	,	,	PUNCT
ejpam-4972	387	11	j)−	j)−	PROPN
ejpam-4972	387	12	gψ−	gψ−	PUNCT
ejpam-4972	387	13	open	open	ADJ
ejpam-4972	387	14	of	of	ADP
ejpam-4972	387	15	z.	z.	PROPN
ejpam-4972	388	1	so	so	ADV
ejpam-4972	388	2	,	,	PUNCT
ejpam-4972	388	3	g	g	PROPN
ejpam-4972	388	4	◦	◦	PROPN
ejpam-4972	388	5	t	t	PROPN
ejpam-4972	388	6	is	be	AUX
ejpam-4972	388	7	(	(	PUNCT
ejpam-4972	388	8	i	i	PROPN
ejpam-4972	388	9	,	,	PUNCT
ejpam-4972	388	10	j)−	j)−	PROPN
ejpam-4972	388	11	gψ	gψ	VERB
ejpam-4972	388	12	−	−	DET
ejpam-4972	388	13	open	open	ADJ
ejpam-4972	388	14	mapping	mapping	NOUN
ejpam-4972	388	15	.	.	PUNCT
ejpam-4972	389	1	(	(	PUNCT
ejpam-4972	389	2	2	2	X
ejpam-4972	389	3	)	)	PUNCT
ejpam-4972	389	4	assume	assume	VERB
ejpam-4972	389	5	k	k	PROPN
ejpam-4972	389	6	is	be	AUX
ejpam-4972	389	7	(	(	PUNCT
ejpam-4972	389	8	i	i	NOUN
ejpam-4972	389	9	,	,	PUNCT
ejpam-4972	389	10	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	389	11	group	group	NOUN
ejpam-4972	389	12	of	of	ADP
ejpam-4972	389	13	x.	x.	PROPN
ejpam-4972	389	14	as	as	SCONJ
ejpam-4972	389	15	g	g	PROPN
ejpam-4972	389	16	◦	◦	PROPN
ejpam-4972	389	17	t	t	PROPN
ejpam-4972	389	18	is	be	AUX
ejpam-4972	389	19	(	(	PUNCT
ejpam-4972	389	20	i	i	NOUN
ejpam-4972	389	21	,	,	PUNCT
ejpam-4972	389	22	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	389	23	mapping	mapping	NOUN
ejpam-4972	389	24	,	,	PUNCT
ejpam-4972	389	25	then	then	ADV
ejpam-4972	389	26	g(t(k	g(t(k	PROPN
ejpam-4972	389	27	)	)	PUNCT
ejpam-4972	389	28	)	)	PUNCT
ejpam-4972	390	1	is	be	AUX
ejpam-4972	390	2	(	(	PUNCT
ejpam-4972	390	3	i	i	PROPN
ejpam-4972	390	4	,	,	PUNCT
ejpam-4972	390	5	j	j	PROPN
ejpam-4972	390	6	)	)	PUNCT
ejpam-4972	390	7	−	−	PROPN
ejpam-4972	390	8	gψ	gψ	VERB
ejpam-4972	390	9	−	−	DET
ejpam-4972	390	10	open	open	ADJ
ejpam-4972	390	11	group	group	NOUN
ejpam-4972	390	12	of	of	ADP
ejpam-4972	390	13	z.	z.	PROPN
ejpam-4972	390	14	as	as	SCONJ
ejpam-4972	390	15	g	g	PROPN
ejpam-4972	390	16	is	be	AUX
ejpam-4972	390	17	(	(	PUNCT
ejpam-4972	390	18	i	i	PROPN
ejpam-4972	390	19	,	,	PUNCT
ejpam-4972	390	20	j	j	PROPN
ejpam-4972	390	21	)	)	PUNCT
ejpam-4972	390	22	−	−	PROPN
ejpam-4972	390	23	gψ	gψ	VERB
ejpam-4972	390	24	−	−	NOUN
ejpam-4972	390	25	irresolute	irresolute	ADJ
ejpam-4972	390	26	mapping	mapping	NOUN
ejpam-4972	390	27	,	,	PUNCT
ejpam-4972	390	28	injective	injective	ADJ
ejpam-4972	390	29	,	,	PUNCT
ejpam-4972	390	30	then	then	ADV
ejpam-4972	390	31	t(k	t(k	PROPN
ejpam-4972	390	32	)	)	PUNCT
ejpam-4972	390	33	is	be	AUX
ejpam-4972	390	34	(	(	PUNCT
ejpam-4972	390	35	i	i	PROPN
ejpam-4972	390	36	,	,	PUNCT
ejpam-4972	390	37	j)−	j)−	PROPN
ejpam-4972	390	38	gψ−	gψ−	PUNCT
ejpam-4972	390	39	open	open	ADJ
ejpam-4972	390	40	group	group	NOUN
ejpam-4972	390	41	of	of	ADP
ejpam-4972	390	42	y	y	PROPN
ejpam-4972	390	43	.	.	PUNCT
ejpam-4972	391	1	so	so	ADV
ejpam-4972	391	2	,	,	PUNCT
ejpam-4972	391	3	t	t	PROPN
ejpam-4972	391	4	is	be	AUX
ejpam-4972	391	5	fuzzy	fuzzy	ADJ
ejpam-4972	391	6	(	(	PUNCT
ejpam-4972	391	7	i	i	NOUN
ejpam-4972	391	8	,	,	PUNCT
ejpam-4972	391	9	j)−	j)−	PROPN
ejpam-4972	391	10	gψ−	gψ−	PUNCT
ejpam-4972	391	11	open	open	ADJ
ejpam-4972	391	12	mapping	mapping	NOUN
ejpam-4972	391	13	.	.	PUNCT
ejpam-4972	392	1	a.	a.	NOUN
ejpam-4972	392	2	a.	a.	PROPN
ejpam-4972	392	3	alharbi	alharbi	PROPN
ejpam-4972	392	4	,	,	PUNCT
ejpam-4972	392	5	a.	a.	NOUN
ejpam-4972	392	6	kilicman	kilicman	PROPN
ejpam-4972	392	7	/	/	SYM
ejpam-4972	392	8	eur	eur	PROPN
ejpam-4972	392	9	.	.	PUNCT
ejpam-4972	393	1	j.	j.	PROPN
ejpam-4972	393	2	pure	pure	PROPN
ejpam-4972	393	3	appl	appl	PROPN
ejpam-4972	393	4	.	.	PROPN
ejpam-4972	393	5	math	math	PROPN
ejpam-4972	393	6	,	,	PUNCT
ejpam-4972	393	7	16	16	NUM
ejpam-4972	393	8	(	(	PUNCT
ejpam-4972	393	9	4	4	NUM
ejpam-4972	393	10	)	)	PUNCT
ejpam-4972	393	11	(	(	PUNCT
ejpam-4972	393	12	2023	2023	NUM
ejpam-4972	393	13	)	)	PUNCT
ejpam-4972	393	14	,	,	PUNCT
ejpam-4972	393	15	2613	2613	NUM
ejpam-4972	393	16	-	-	SYM
ejpam-4972	393	17	2631	2631	NUM
ejpam-4972	393	18	2626	2626	NUM
ejpam-4972	393	19	(	(	PUNCT
ejpam-4972	393	20	3	3	X
ejpam-4972	393	21	)	)	PUNCT
ejpam-4972	393	22	assume	assume	VERB
ejpam-4972	393	23	k	k	PROPN
ejpam-4972	393	24	∈	∈	PROPN
ejpam-4972	393	25	δj	δj	ADP
ejpam-4972	393	26	.	.	PUNCT
ejpam-4972	394	1	after	after	ADP
ejpam-4972	394	2	that	that	PRON
ejpam-4972	394	3	k	k	PROPN
ejpam-4972	394	4	considers	consider	VERB
ejpam-4972	394	5	(	(	PUNCT
ejpam-4972	394	6	i	i	NOUN
ejpam-4972	394	7	,	,	PUNCT
ejpam-4972	394	8	j	j	PROPN
ejpam-4972	394	9	)	)	PUNCT
ejpam-4972	394	10	−	−	PROPN
ejpam-4972	394	11	gψ	gψ	VERB
ejpam-4972	394	12	−	−	DET
ejpam-4972	394	13	open	open	ADJ
ejpam-4972	394	14	group	group	NOUN
ejpam-4972	394	15	of	of	ADP
ejpam-4972	394	16	x.	x.	PROPN
ejpam-4972	394	17	as	as	SCONJ
ejpam-4972	394	18	g	g	PROPN
ejpam-4972	394	19	◦	◦	PROPN
ejpam-4972	394	20	t	t	PROPN
ejpam-4972	394	21	is	be	AUX
ejpam-4972	394	22	(	(	PUNCT
ejpam-4972	394	23	i	i	PROPN
ejpam-4972	394	24	,	,	PUNCT
ejpam-4972	394	25	j	j	PROPN
ejpam-4972	394	26	)	)	PUNCT
ejpam-4972	394	27	−	−	PROPN
ejpam-4972	394	28	gψ	gψ	VERB
ejpam-4972	394	29	−	−	DET
ejpam-4972	394	30	open	open	ADJ
ejpam-4972	394	31	mapping	mapping	NOUN
ejpam-4972	394	32	,	,	PUNCT
ejpam-4972	394	33	thus	thus	ADV
ejpam-4972	394	34	g(t(k	g(t(k	NOUN
ejpam-4972	394	35	)	)	PUNCT
ejpam-4972	394	36	)	)	PUNCT
ejpam-4972	395	1	is	be	AUX
ejpam-4972	395	2	(	(	PUNCT
ejpam-4972	395	3	i	i	PROPN
ejpam-4972	395	4	,	,	PUNCT
ejpam-4972	395	5	j	j	PROPN
ejpam-4972	395	6	)	)	PUNCT
ejpam-4972	395	7	−	−	PROPN
ejpam-4972	395	8	gψ	gψ	VERB
ejpam-4972	395	9	−	−	DET
ejpam-4972	395	10	open	open	ADJ
ejpam-4972	395	11	group	group	NOUN
ejpam-4972	395	12	of	of	ADP
ejpam-4972	395	13	z.	z.	PROPN
ejpam-4972	395	14	as	as	SCONJ
ejpam-4972	395	15	g	g	PROPN
ejpam-4972	395	16	is	be	AUX
ejpam-4972	395	17	(	(	PUNCT
ejpam-4972	395	18	i	i	PROPN
ejpam-4972	395	19	,	,	PUNCT
ejpam-4972	395	20	j	j	PROPN
ejpam-4972	395	21	)	)	PUNCT
ejpam-4972	395	22	−	−	PROPN
ejpam-4972	395	23	gψ	gψ	VERB
ejpam-4972	395	24	−	−	PROPN
ejpam-4972	395	25	stongly	stongly	ADV
ejpam-4972	395	26	conts	cont	VERB
ejpam-4972	395	27	mapping	mapping	NOUN
ejpam-4972	395	28	with	with	ADP
ejpam-4972	395	29	injective	injective	ADJ
ejpam-4972	395	30	,	,	PUNCT
ejpam-4972	395	31	then	then	ADV
ejpam-4972	395	32	t(k	t(k	PROPN
ejpam-4972	395	33	)	)	PUNCT
ejpam-4972	395	34	∈	∈	PROPN
ejpam-4972	395	35	σj	σj	NOUN
ejpam-4972	395	36	.	.	PUNCT
ejpam-4972	396	1	therefore	therefore	ADV
ejpam-4972	396	2	t	t	PROPN
ejpam-4972	396	3	is	be	AUX
ejpam-4972	396	4	fuzzy	fuzzy	ADJ
ejpam-4972	396	5	δj	δj	ADP
ejpam-4972	396	6	−	−	PUNCT
ejpam-4972	396	7	open	open	ADJ
ejpam-4972	396	8	mapping	mapping	NOUN
ejpam-4972	396	9	.	.	PUNCT
ejpam-4972	397	1	(	(	PUNCT
ejpam-4972	397	2	4	4	X
ejpam-4972	397	3	)	)	PUNCT
ejpam-4972	397	4	assume	assume	VERB
ejpam-4972	397	5	w	w	NOUN
ejpam-4972	397	6	is	be	AUX
ejpam-4972	397	7	fuzzy	fuzzy	ADJ
ejpam-4972	397	8	(	(	PUNCT
ejpam-4972	397	9	i	i	PROPN
ejpam-4972	397	10	,	,	PUNCT
ejpam-4972	397	11	j	j	PROPN
ejpam-4972	397	12	)	)	PUNCT
ejpam-4972	397	13	−	−	PROPN
ejpam-4972	397	14	gψ	gψ	VERB
ejpam-4972	397	15	−	−	DET
ejpam-4972	397	16	open	open	ADJ
ejpam-4972	397	17	group	group	NOUN
ejpam-4972	397	18	of	of	ADP
ejpam-4972	397	19	y	y	PROPN
ejpam-4972	397	20	.as	.as	PROPN
ejpam-4972	398	1	t	t	PROPN
ejpam-4972	398	2	is	be	AUX
ejpam-4972	398	3	(	(	PUNCT
ejpam-4972	398	4	i	i	PROPN
ejpam-4972	398	5	,	,	PUNCT
ejpam-4972	398	6	j	j	PROPN
ejpam-4972	398	7	)	)	PUNCT
ejpam-4972	398	8	−	−	PROPN
ejpam-4972	398	9	gψ	gψ	VERB
ejpam-4972	398	10	−	−	NOUN
ejpam-4972	398	11	irresolute	irresolute	ADJ
ejpam-4972	398	12	mapping	mapping	NOUN
ejpam-4972	398	13	,	,	PUNCT
ejpam-4972	398	14	thus	thus	ADV
ejpam-4972	398	15	t−1(w	t−1(w	NOUN
ejpam-4972	398	16	)	)	PUNCT
ejpam-4972	399	1	is	be	AUX
ejpam-4972	399	2	(	(	PUNCT
ejpam-4972	399	3	i	i	NOUN
ejpam-4972	399	4	,	,	PUNCT
ejpam-4972	399	5	j)−	j)−	PROPN
ejpam-4972	399	6	gψ−	gψ−	PUNCT
ejpam-4972	399	7	open	open	ADJ
ejpam-4972	399	8	group	group	NOUN
ejpam-4972	399	9	of	of	ADP
ejpam-4972	399	10	x.	x.	PROPN
ejpam-4972	399	11	as	as	ADP
ejpam-4972	399	12	g	g	PROPN
ejpam-4972	399	13	◦	◦	PROPN
ejpam-4972	399	14	t	t	PROPN
ejpam-4972	399	15	is	be	AUX
ejpam-4972	399	16	(	(	PUNCT
ejpam-4972	399	17	i	i	PROPN
ejpam-4972	399	18	,	,	PUNCT
ejpam-4972	399	19	j)−	j)−	PROPN
ejpam-4972	399	20	gψ−	gψ−	PUNCT
ejpam-4972	399	21	open	open	ADJ
ejpam-4972	399	22	mapping	mapping	NOUN
ejpam-4972	399	23	,	,	PUNCT
ejpam-4972	399	24	t	t	PROPN
ejpam-4972	399	25	is	be	AUX
ejpam-4972	399	26	surjective	surjective	ADJ
ejpam-4972	399	27	,	,	PUNCT
ejpam-4972	399	28	then	then	ADV
ejpam-4972	399	29	g(w	g(w	ADJ
ejpam-4972	400	1	)	)	PUNCT
ejpam-4972	400	2	is	be	AUX
ejpam-4972	400	3	(	(	PUNCT
ejpam-4972	400	4	i	i	PROPN
ejpam-4972	400	5	,	,	PUNCT
ejpam-4972	400	6	j)−	j)−	PROPN
ejpam-4972	400	7	gψ	gψ	VERB
ejpam-4972	400	8	−	−	DET
ejpam-4972	400	9	open	open	ADJ
ejpam-4972	400	10	group	group	NOUN
ejpam-4972	400	11	of	of	ADP
ejpam-4972	400	12	z.	z.	PROPN
ejpam-4972	401	1	so	so	ADV
ejpam-4972	401	2	,	,	PUNCT
ejpam-4972	401	3	g	g	PROPN
ejpam-4972	401	4	is	be	AUX
ejpam-4972	401	5	fuzzy	fuzzy	ADJ
ejpam-4972	401	6	(	(	PUNCT
ejpam-4972	401	7	i	i	PROPN
ejpam-4972	401	8	,	,	PUNCT
ejpam-4972	401	9	j)−	j)−	PROPN
ejpam-4972	401	10	gψ	gψ	VERB
ejpam-4972	401	11	−	−	DET
ejpam-4972	401	12	open	open	ADJ
ejpam-4972	401	13	mapping	mapping	NOUN
ejpam-4972	401	14	.	.	PUNCT
ejpam-4972	402	1	(	(	PUNCT
ejpam-4972	402	2	5	5	X
ejpam-4972	402	3	)	)	PUNCT
ejpam-4972	402	4	assume	assume	VERB
ejpam-4972	402	5	w	w	PROPN
ejpam-4972	402	6	∈	∈	PROPN
ejpam-4972	402	7	σj	σj	NOUN
ejpam-4972	402	8	.	.	PUNCT
ejpam-4972	403	1	then	then	ADV
ejpam-4972	403	2	w	w	NOUN
ejpam-4972	403	3	is	be	AUX
ejpam-4972	403	4	(	(	PUNCT
ejpam-4972	403	5	i	i	PROPN
ejpam-4972	403	6	,	,	PUNCT
ejpam-4972	403	7	j	j	PROPN
ejpam-4972	403	8	)	)	PUNCT
ejpam-4972	403	9	−	−	PROPN
ejpam-4972	403	10	gψ	gψ	VERB
ejpam-4972	403	11	−	−	DET
ejpam-4972	403	12	open	open	ADJ
ejpam-4972	403	13	group	group	NOUN
ejpam-4972	403	14	of	of	ADP
ejpam-4972	403	15	y	y	PROPN
ejpam-4972	403	16	.	.	PUNCT
ejpam-4972	404	1	as	as	SCONJ
ejpam-4972	404	2	t	t	PROPN
ejpam-4972	404	3	is	be	AUX
ejpam-4972	404	4	(	(	PUNCT
ejpam-4972	404	5	i	i	PROPN
ejpam-4972	404	6	,	,	PUNCT
ejpam-4972	404	7	j	j	PROPN
ejpam-4972	404	8	)	)	PUNCT
ejpam-4972	404	9	−	−	PROPN
ejpam-4972	404	10	gψ	gψ	VERB
ejpam-4972	404	11	−	−	PROPN
ejpam-4972	404	12	stongly	stongly	ADV
ejpam-4972	404	13	conts	cont	VERB
ejpam-4972	404	14	mapping	mapping	NOUN
ejpam-4972	404	15	,	,	PUNCT
ejpam-4972	404	16	then	then	ADV
ejpam-4972	404	17	t−1(w	t−1(w	ADV
ejpam-4972	404	18	)	)	PUNCT
ejpam-4972	404	19	∈	∈	PROPN
ejpam-4972	404	20	δj	δj	ADP
ejpam-4972	404	21	.	.	PUNCT
ejpam-4972	405	1	as	as	SCONJ
ejpam-4972	405	2	g	g	PROPN
ejpam-4972	405	3	◦	◦	PROPN
ejpam-4972	405	4	t	t	PROPN
ejpam-4972	405	5	is	be	AUX
ejpam-4972	405	6	δj	δj	ADP
ejpam-4972	405	7	−	−	NOUN
ejpam-4972	405	8	open	open	ADJ
ejpam-4972	405	9	,	,	PUNCT
ejpam-4972	405	10	with	with	SCONJ
ejpam-4972	405	11	t	t	PROPN
ejpam-4972	405	12	is	be	AUX
ejpam-4972	405	13	surjective	surjective	ADJ
ejpam-4972	405	14	,	,	PUNCT
ejpam-4972	406	1	thus	thus	ADV
ejpam-4972	406	2	g(w	g(w	ADJ
ejpam-4972	406	3	)	)	PUNCT
ejpam-4972	406	4	∈	∈	PROPN
ejpam-4972	406	5	ηj	ηj	NOUN
ejpam-4972	406	6	.	.	PUNCT
ejpam-4972	407	1	so	so	ADV
ejpam-4972	407	2	,	,	PUNCT
ejpam-4972	407	3	g	g	PROPN
ejpam-4972	407	4	is	be	AUX
ejpam-4972	407	5	σj	σj	VERB
ejpam-4972	407	6	−	−	PRON
ejpam-4972	407	7	open	open	ADJ
ejpam-4972	407	8	mapping	mapping	NOUN
ejpam-4972	407	9	corollary	corollary	ADJ
ejpam-4972	407	10	4	4	NUM
ejpam-4972	407	11	.	.	PUNCT
ejpam-4972	408	1	(	(	PUNCT
ejpam-4972	408	2	1	1	X
ejpam-4972	408	3	)	)	PUNCT
ejpam-4972	408	4	suppose	suppose	VERB
ejpam-4972	408	5	t	t	NOUN
ejpam-4972	408	6	:	:	PUNCT
ejpam-4972	408	7	(	(	PUNCT
ejpam-4972	408	8	x	x	X
ejpam-4972	408	9	,	,	PUNCT
ejpam-4972	408	10	δ1	δ1	NOUN
ejpam-4972	408	11	,	,	PUNCT
ejpam-4972	408	12	δ2	δ2	ADJ
ejpam-4972	408	13	)	)	PUNCT
ejpam-4972	408	14	→	→	SYM
ejpam-4972	408	15	(	(	PUNCT
ejpam-4972	408	16	y	y	PROPN
ejpam-4972	408	17	,	,	PUNCT
ejpam-4972	408	18	σ1	σ1	PROPN
ejpam-4972	408	19	,	,	PUNCT
ejpam-4972	408	20	σ2	σ2	NOUN
ejpam-4972	408	21	)	)	PUNCT
ejpam-4972	408	22	,	,	PUNCT
ejpam-4972	408	23	g	g	NOUN
ejpam-4972	408	24	:	:	PUNCT
ejpam-4972	408	25	(	(	PUNCT
ejpam-4972	408	26	y	y	PROPN
ejpam-4972	408	27	,	,	PUNCT
ejpam-4972	408	28	σ1	σ1	PROPN
ejpam-4972	408	29	,	,	PUNCT
ejpam-4972	408	30	σ2	σ2	NOUN
ejpam-4972	408	31	)	)	PUNCT
ejpam-4972	408	32	→	→	SYM
ejpam-4972	408	33	(	(	PUNCT
ejpam-4972	408	34	z	z	NOUN
ejpam-4972	408	35	,	,	PUNCT
ejpam-4972	408	36	η1	η1	NOUN
ejpam-4972	408	37	,	,	PUNCT
ejpam-4972	408	38	η2	η2	PROPN
ejpam-4972	408	39	)	)	PUNCT
ejpam-4972	408	40	is	be	AUX
ejpam-4972	408	41	(	(	PUNCT
ejpam-4972	408	42	i	i	PROPN
ejpam-4972	408	43	,	,	PUNCT
ejpam-4972	408	44	j)−	j)−	PROPN
ejpam-4972	408	45	gψ	gψ	VERB
ejpam-4972	408	46	−	−	NOUN
ejpam-4972	408	47	strongly	strongly	ADV
ejpam-4972	408	48	conts	cont	NOUN
ejpam-4972	408	49	,	,	PUNCT
ejpam-4972	408	50	injective	injective	ADJ
ejpam-4972	408	51	mapping	mapping	NOUN
ejpam-4972	408	52	,	,	PUNCT
ejpam-4972	408	53	also	also	ADV
ejpam-4972	408	54	g	g	PROPN
ejpam-4972	408	55	◦	◦	PROPN
ejpam-4972	408	56	t	t	PROPN
ejpam-4972	408	57	is	be	AUX
ejpam-4972	408	58	(	(	PUNCT
ejpam-4972	408	59	i	i	PROPN
ejpam-4972	408	60	,	,	PUNCT
ejpam-4972	408	61	j)−	j)−	PROPN
ejpam-4972	408	62	gψ	gψ	VERB
ejpam-4972	408	63	−	−	PROPN
ejpam-4972	408	64	open	open	ADJ
ejpam-4972	408	65	(	(	PUNCT
ejpam-4972	408	66	resp	resp	NOUN
ejpam-4972	408	67	,	,	PUNCT
ejpam-4972	408	68	(	(	PUNCT
ejpam-4972	408	69	i	i	NOUN
ejpam-4972	408	70	,	,	PUNCT
ejpam-4972	408	71	j)−gψ−closed	j)−gψ−close	VERB
ejpam-4972	408	72	)	)	PUNCT
ejpam-4972	408	73	.	.	PUNCT
ejpam-4972	409	1	thus	thus	ADV
ejpam-4972	409	2	,	,	PUNCT
ejpam-4972	409	3	t	t	PROPN
ejpam-4972	409	4	is	be	AUX
ejpam-4972	409	5	(	(	PUNCT
ejpam-4972	409	6	i	i	NOUN
ejpam-4972	409	7	,	,	PUNCT
ejpam-4972	409	8	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	409	9	(	(	PUNCT
ejpam-4972	409	10	resp	resp	NOUN
ejpam-4972	409	11	,	,	PUNCT
ejpam-4972	409	12	(	(	PUNCT
ejpam-4972	409	13	i	i	PRON
ejpam-4972	409	14	,	,	PUNCT
ejpam-4972	409	15	j)−gψ−closed	j)−gψ−closed	ADJ
ejpam-4972	409	16	)	)	PUNCT
ejpam-4972	409	17	mapping	mapping	NOUN
ejpam-4972	409	18	.	.	PUNCT
ejpam-4972	410	1	(	(	PUNCT
ejpam-4972	410	2	2	2	X
ejpam-4972	410	3	)	)	PUNCT
ejpam-4972	410	4	suppose	suppose	VERB
ejpam-4972	410	5	t	t	NOUN
ejpam-4972	410	6	:	:	PUNCT
ejpam-4972	410	7	(	(	PUNCT
ejpam-4972	410	8	x	x	X
ejpam-4972	410	9	,	,	PUNCT
ejpam-4972	410	10	δ1	δ1	NOUN
ejpam-4972	410	11	,	,	PUNCT
ejpam-4972	410	12	δ2	δ2	ADJ
ejpam-4972	410	13	)	)	PUNCT
ejpam-4972	410	14	→	→	SYM
ejpam-4972	410	15	(	(	PUNCT
ejpam-4972	410	16	y	y	PROPN
ejpam-4972	410	17	,	,	PUNCT
ejpam-4972	410	18	σ1	σ1	PROPN
ejpam-4972	410	19	,	,	PUNCT
ejpam-4972	410	20	σ2	σ2	PROPN
ejpam-4972	410	21	)	)	PUNCT
ejpam-4972	410	22	is	be	AUX
ejpam-4972	410	23	(	(	PUNCT
ejpam-4972	410	24	i	i	PROPN
ejpam-4972	410	25	,	,	PUNCT
ejpam-4972	410	26	j)−	j)−	PROPN
ejpam-4972	410	27	gψ−	gψ−	PUNCT
ejpam-4972	410	28	strongly	strongly	ADV
ejpam-4972	410	29	conts	cont	NOUN
ejpam-4972	410	30	,	,	PUNCT
ejpam-4972	410	31	surjective	surjective	ADJ
ejpam-4972	410	32	function	function	NOUN
ejpam-4972	410	33	,	,	PUNCT
ejpam-4972	410	34	g	g	PROPN
ejpam-4972	410	35	:	:	PUNCT
ejpam-4972	410	36	(	(	PUNCT
ejpam-4972	410	37	y	y	PROPN
ejpam-4972	410	38	,	,	PUNCT
ejpam-4972	410	39	σ1	σ1	PROPN
ejpam-4972	410	40	,	,	PUNCT
ejpam-4972	410	41	σ2	σ2	NOUN
ejpam-4972	410	42	)	)	PUNCT
ejpam-4972	410	43	→	→	SYM
ejpam-4972	410	44	(	(	PUNCT
ejpam-4972	410	45	z	z	NOUN
ejpam-4972	410	46	,	,	PUNCT
ejpam-4972	410	47	η1	η1	NOUN
ejpam-4972	410	48	,	,	PUNCT
ejpam-4972	410	49	η2	η2	NOUN
ejpam-4972	410	50	)	)	PUNCT
ejpam-4972	410	51	,	,	PUNCT
ejpam-4972	410	52	also	also	ADV
ejpam-4972	410	53	g	g	PROPN
ejpam-4972	410	54	◦	◦	PROPN
ejpam-4972	410	55	t	t	PROPN
ejpam-4972	410	56	is	be	AUX
ejpam-4972	410	57	(	(	PUNCT
ejpam-4972	410	58	i	i	PROPN
ejpam-4972	410	59	,	,	PUNCT
ejpam-4972	410	60	j)−	j)−	PROPN
ejpam-4972	410	61	gψ−	gψ−	PUNCT
ejpam-4972	410	62	open	open	ADJ
ejpam-4972	410	63	(	(	PUNCT
ejpam-4972	410	64	resp	resp	NOUN
ejpam-4972	410	65	,	,	PUNCT
ejpam-4972	410	66	(	(	PUNCT
ejpam-4972	410	67	i	i	PROPN
ejpam-4972	410	68	,	,	PUNCT
ejpam-4972	410	69	j)−	j)−	PROPN
ejpam-4972	410	70	gψ−	gψ−	PROPN
ejpam-4972	410	71	closed	closed	ADJ
ejpam-4972	410	72	)	)	PUNCT
ejpam-4972	410	73	.	.	PUNCT
ejpam-4972	411	1	thus	thus	ADV
ejpam-4972	411	2	g	g	PROPN
ejpam-4972	411	3	is	be	AUX
ejpam-4972	411	4	(	(	PUNCT
ejpam-4972	411	5	i	i	PROPN
ejpam-4972	411	6	,	,	PUNCT
ejpam-4972	411	7	j)−	j)−	PROPN
ejpam-4972	411	8	gψ	gψ	VERB
ejpam-4972	411	9	−	−	PROPN
ejpam-4972	411	10	open	open	ADJ
ejpam-4972	411	11	(	(	PUNCT
ejpam-4972	411	12	resp	resp	NOUN
ejpam-4972	411	13	,	,	PUNCT
ejpam-4972	411	14	(	(	PUNCT
ejpam-4972	411	15	i	i	PROPN
ejpam-4972	411	16	,	,	PUNCT
ejpam-4972	411	17	j)−	j)−	PROPN
ejpam-4972	411	18	gψ	gψ	VERB
ejpam-4972	411	19	−	−	PROPN
ejpam-4972	411	20	closed	closed	ADJ
ejpam-4972	411	21	)	)	PUNCT
ejpam-4972	411	22	mapping	mapping	NOUN
ejpam-4972	411	23	.	.	PUNCT
ejpam-4972	412	1	(	(	PUNCT
ejpam-4972	412	2	3	3	X
ejpam-4972	412	3	)	)	PUNCT
ejpam-4972	412	4	suppose	suppose	VERB
ejpam-4972	412	5	t	t	NOUN
ejpam-4972	412	6	:	:	PUNCT
ejpam-4972	412	7	(	(	PUNCT
ejpam-4972	412	8	x	x	X
ejpam-4972	412	9	,	,	PUNCT
ejpam-4972	412	10	δ1	δ1	NOUN
ejpam-4972	412	11	,	,	PUNCT
ejpam-4972	412	12	δ2	δ2	ADJ
ejpam-4972	412	13	)	)	PUNCT
ejpam-4972	412	14	→	→	SYM
ejpam-4972	412	15	(	(	PUNCT
ejpam-4972	412	16	y	y	PROPN
ejpam-4972	412	17	,	,	PUNCT
ejpam-4972	412	18	σ1	σ1	PROPN
ejpam-4972	412	19	,	,	PUNCT
ejpam-4972	412	20	σ2	σ2	NOUN
ejpam-4972	412	21	)	)	PUNCT
ejpam-4972	412	22	,	,	PUNCT
ejpam-4972	412	23	g	g	NOUN
ejpam-4972	412	24	:	:	PUNCT
ejpam-4972	412	25	(	(	PUNCT
ejpam-4972	412	26	y	y	PROPN
ejpam-4972	412	27	,	,	PUNCT
ejpam-4972	412	28	σ1	σ1	PROPN
ejpam-4972	412	29	,	,	PUNCT
ejpam-4972	412	30	σ2	σ2	NOUN
ejpam-4972	412	31	)	)	PUNCT
ejpam-4972	412	32	→	→	SYM
ejpam-4972	412	33	(	(	PUNCT
ejpam-4972	412	34	z	z	NOUN
ejpam-4972	412	35	,	,	PUNCT
ejpam-4972	412	36	η1	η1	NOUN
ejpam-4972	412	37	,	,	PUNCT
ejpam-4972	412	38	η2	η2	PROPN
ejpam-4972	412	39	)	)	PUNCT
ejpam-4972	412	40	is	be	AUX
ejpam-4972	412	41	(	(	PUNCT
ejpam-4972	412	42	i	i	PROPN
ejpam-4972	412	43	,	,	PUNCT
ejpam-4972	412	44	j	j	PROPN
ejpam-4972	412	45	)	)	PUNCT
ejpam-4972	412	46	−	−	PROPN
ejpam-4972	413	1	gβ	gβ	NOUN
ejpam-4972	413	2	−	−	NOUN
ejpam-4972	413	3	strongly	strongly	ADV
ejpam-4972	413	4	conts	cont	NOUN
ejpam-4972	413	5	,	,	PUNCT
ejpam-4972	413	6	injective	injective	ADJ
ejpam-4972	413	7	mapping	mapping	NOUN
ejpam-4972	413	8	,	,	PUNCT
ejpam-4972	413	9	also	also	ADV
ejpam-4972	413	10	g	g	PROPN
ejpam-4972	413	11	◦	◦	PROPN
ejpam-4972	413	12	t	t	PROPN
ejpam-4972	413	13	is	be	AUX
ejpam-4972	413	14	(	(	PUNCT
ejpam-4972	413	15	i	i	PROPN
ejpam-4972	413	16	,	,	PUNCT
ejpam-4972	413	17	j)−	j)−	PROPN
ejpam-4972	413	18	gψ	gψ	VERB
ejpam-4972	413	19	−	−	PROPN
ejpam-4972	413	20	open	open	ADJ
ejpam-4972	413	21	(	(	PUNCT
ejpam-4972	413	22	resp	resp	NOUN
ejpam-4972	413	23	,	,	PUNCT
ejpam-4972	413	24	(	(	PUNCT
ejpam-4972	413	25	i	i	PROPN
ejpam-4972	413	26	,	,	PUNCT
ejpam-4972	413	27	j)−	j)−	PROPN
ejpam-4972	413	28	gψ	gψ	VERB
ejpam-4972	413	29	−	−	PROPN
ejpam-4972	413	30	closed	closed	ADJ
ejpam-4972	413	31	)	)	PUNCT
ejpam-4972	413	32	.	.	PUNCT
ejpam-4972	414	1	thus	thus	ADV
ejpam-4972	414	2	t	t	PROPN
ejpam-4972	414	3	is	be	AUX
ejpam-4972	414	4	δj	δj	ADP
ejpam-4972	414	5	−	−	PROPN
ejpam-4972	414	6	open	open	ADJ
ejpam-4972	414	7	(	(	PUNCT
ejpam-4972	414	8	resp	resp	NOUN
ejpam-4972	414	9	,	,	PUNCT
ejpam-4972	414	10	δj	δj	ADP
ejpam-4972	414	11	−	−	PROPN
ejpam-4972	414	12	closed	closed	ADJ
ejpam-4972	414	13	)	)	PUNCT
ejpam-4972	414	14	mapping	mapping	NOUN
ejpam-4972	414	15	.	.	PUNCT
ejpam-4972	415	1	theorem	theorem	VERB
ejpam-4972	415	2	23	23	NUM
ejpam-4972	415	3	.	.	PUNCT
ejpam-4972	416	1	suppose	suppose	VERB
ejpam-4972	416	2	t	t	NOUN
ejpam-4972	416	3	:	:	PUNCT
ejpam-4972	416	4	(	(	PUNCT
ejpam-4972	416	5	x	x	X
ejpam-4972	416	6	,	,	PUNCT
ejpam-4972	416	7	δ1	δ1	NOUN
ejpam-4972	416	8	,	,	PUNCT
ejpam-4972	416	9	δ2	δ2	ADJ
ejpam-4972	416	10	)	)	PUNCT
ejpam-4972	416	11	→	→	SYM
ejpam-4972	416	12	(	(	PUNCT
ejpam-4972	416	13	y	y	PROPN
ejpam-4972	416	14	,	,	PUNCT
ejpam-4972	416	15	σ1	σ1	PROPN
ejpam-4972	416	16	,	,	PUNCT
ejpam-4972	416	17	σ2	σ2	NOUN
ejpam-4972	416	18	)	)	PUNCT
ejpam-4972	416	19	is	be	AUX
ejpam-4972	416	20	fuzzy	fuzzy	ADJ
ejpam-4972	416	21	(	(	PUNCT
ejpam-4972	416	22	i	i	NOUN
ejpam-4972	416	23	,	,	PUNCT
ejpam-4972	416	24	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	416	25	(	(	PUNCT
ejpam-4972	416	26	resp	resp	NOUN
ejpam-4972	416	27	,	,	PUNCT
ejpam-4972	416	28	(	(	PUNCT
ejpam-4972	416	29	i	i	PROPN
ejpam-4972	416	30	,	,	PUNCT
ejpam-4972	416	31	j)−	j)−	PROPN
ejpam-4972	416	32	gψ	gψ	VERB
ejpam-4972	416	33	−	−	PROPN
ejpam-4972	416	34	closed	closed	ADJ
ejpam-4972	416	35	)	)	PUNCT
ejpam-4972	416	36	mapping	mapping	NOUN
ejpam-4972	416	37	.	.	PUNCT
ejpam-4972	417	1	thus	thus	ADV
ejpam-4972	417	2	all	all	DET
ejpam-4972	417	3	w	w	NOUN
ejpam-4972	417	4	is	be	AUX
ejpam-4972	417	5	fuzzy	fuzzy	ADJ
ejpam-4972	417	6	subgroup	subgroup	NOUN
ejpam-4972	417	7	of	of	ADP
ejpam-4972	417	8	y	y	PROPN
ejpam-4972	417	9	,	,	PUNCT
ejpam-4972	417	10	and	and	CCONJ
ejpam-4972	417	11	k	k	PROPN
ejpam-4972	417	12	∈	∈	PROPN
ejpam-4972	417	13	fδj	fδj	NOUN
ejpam-4972	417	14	(	(	PUNCT
ejpam-4972	417	15	resp	resp	NOUN
ejpam-4972	417	16	,	,	PUNCT
ejpam-4972	417	17	k	k	PROPN
ejpam-4972	417	18	∈	∈	PROPN
ejpam-4972	417	19	δj	δj	NOUN
ejpam-4972	417	20	)	)	PUNCT
ejpam-4972	417	21	including	include	VERB
ejpam-4972	417	22	t−1(w	t−1(w	NOUN
ejpam-4972	417	23	)	)	PUNCT
ejpam-4972	417	24	,	,	PUNCT
ejpam-4972	417	25	∃	∃	PROPN
ejpam-4972	417	26	w	w	PROPN
ejpam-4972	417	27	is	be	AUX
ejpam-4972	417	28	fuzzy	fuzzy	ADJ
ejpam-4972	417	29	(	(	PUNCT
ejpam-4972	417	30	i	i	PROPN
ejpam-4972	417	31	,	,	PUNCT
ejpam-4972	417	32	j)−	j)−	PROPN
ejpam-4972	417	33	gψ	gψ	VERB
ejpam-4972	417	34	−	−	PROPN
ejpam-4972	417	35	cld	cld	PROPN
ejpam-4972	417	36	(	(	PUNCT
ejpam-4972	417	37	resp	resp	NOUN
ejpam-4972	417	38	,	,	PUNCT
ejpam-4972	417	39	(	(	PUNCT
ejpam-4972	417	40	i	i	PROPN
ejpam-4972	417	41	,	,	PUNCT
ejpam-4972	417	42	j)−	j)−	PROPN
ejpam-4972	417	43	gψ	gψ	VERB
ejpam-4972	417	44	−	−	PROPN
ejpam-4972	417	45	open	open	ADJ
ejpam-4972	417	46	)	)	PUNCT
ejpam-4972	417	47	of	of	ADP
ejpam-4972	417	48	y	y	PRON
ejpam-4972	417	49	including	include	VERB
ejpam-4972	417	50	w	w	PROPN
ejpam-4972	417	51	as	as	ADP
ejpam-4972	417	52	t−1(w	t−1(w	NOUN
ejpam-4972	417	53	)	)	PUNCT
ejpam-4972	417	54	≤	≤	PUNCT
ejpam-4972	417	55	k.	k.	PROPN
ejpam-4972	417	56	proof	proof	PROPN
ejpam-4972	417	57	.	.	PUNCT
ejpam-4972	418	1	assume	assume	VERB
ejpam-4972	418	2	t	t	PROPN
ejpam-4972	418	3	is	be	AUX
ejpam-4972	418	4	(	(	PUNCT
ejpam-4972	418	5	i	i	PROPN
ejpam-4972	418	6	,	,	PUNCT
ejpam-4972	418	7	j)−	j)−	PROPN
ejpam-4972	418	8	gψ	gψ	VERB
ejpam-4972	418	9	−	−	PROPN
ejpam-4972	418	10	open	open	ADJ
ejpam-4972	418	11	,	,	PUNCT
ejpam-4972	418	12	k	k	PROPN
ejpam-4972	418	13	∈	∈	PROPN
ejpam-4972	418	14	fδj	fδj	NOUN
ejpam-4972	418	15	as	as	ADP
ejpam-4972	418	16	t−1(w	t−1(w	NOUN
ejpam-4972	418	17	)	)	PUNCT
ejpam-4972	418	18	≤	≤	PUNCT
ejpam-4972	419	1	k	k	X
ejpam-4972	419	2	,	,	PUNCT
ejpam-4972	419	3	as	as	ADP
ejpam-4972	419	4	w	w	PROPN
ejpam-4972	419	5	∈	∈	PROPN
ejpam-4972	419	6	iy	iy	PROPN
ejpam-4972	419	7	.	.	PUNCT
ejpam-4972	420	1	so	so	ADV
ejpam-4972	420	2	kc	kc	PROPN
ejpam-4972	420	3	≤	≤	PROPN
ejpam-4972	420	4	(	(	PUNCT
ejpam-4972	420	5	t−1(w	t−1(w	NOUN
ejpam-4972	420	6	)	)	PUNCT
ejpam-4972	420	7	)	)	PUNCT
ejpam-4972	421	1	c	c	X
ejpam-4972	422	1	=	=	PRON
ejpam-4972	422	2	t−1(w	t−1(w	NOUN
ejpam-4972	422	3	c	c	NOUN
ejpam-4972	422	4	)	)	PUNCT
ejpam-4972	422	5	.	.	PUNCT
ejpam-4972	423	1	since	since	SCONJ
ejpam-4972	423	2	t	t	PROPN
ejpam-4972	423	3	is	be	AUX
ejpam-4972	423	4	fuzzy	fuzzy	ADJ
ejpam-4972	423	5	(	(	PUNCT
ejpam-4972	423	6	i	i	NOUN
ejpam-4972	423	7	,	,	PUNCT
ejpam-4972	423	8	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	423	9	,	,	PUNCT
ejpam-4972	423	10	also	also	ADV
ejpam-4972	423	11	kc	kc	PROPN
ejpam-4972	423	12	is	be	AUX
ejpam-4972	423	13	fuzzy	fuzzy	ADJ
ejpam-4972	423	14	(	(	PUNCT
ejpam-4972	423	15	i	i	NOUN
ejpam-4972	423	16	,	,	PUNCT
ejpam-4972	423	17	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	423	18	group	group	NOUN
ejpam-4972	423	19	of	of	ADP
ejpam-4972	423	20	x	x	PROPN
ejpam-4972	423	21	,	,	PUNCT
ejpam-4972	423	22	hence	hence	ADV
ejpam-4972	423	23	t(kc	t(kc	NUM
ejpam-4972	423	24	)	)	PUNCT
ejpam-4972	423	25	is	be	AUX
ejpam-4972	423	26	fuzzy	fuzzy	ADJ
ejpam-4972	423	27	(	(	PUNCT
ejpam-4972	423	28	i	i	PROPN
ejpam-4972	423	29	,	,	PUNCT
ejpam-4972	423	30	j	j	PROPN
ejpam-4972	423	31	)	)	PUNCT
ejpam-4972	423	32	−	−	PROPN
ejpam-4972	423	33	gψ	gψ	VERB
ejpam-4972	423	34	−	−	PROPN
ejpam-4972	423	35	open	open	ADJ
ejpam-4972	423	36	of	of	ADP
ejpam-4972	423	37	y	y	PROPN
ejpam-4972	423	38	and	and	CCONJ
ejpam-4972	423	39	t(kc	t(kc	PROPN
ejpam-4972	423	40	)	)	PUNCT
ejpam-4972	423	41	≤	≤	NOUN
ejpam-4972	423	42	w	w	PROPN
ejpam-4972	423	43	c	c	NOUN
ejpam-4972	423	44	,	,	PUNCT
ejpam-4972	423	45	and	and	CCONJ
ejpam-4972	423	46	hence	hence	ADV
ejpam-4972	423	47	w	w	ADP
ejpam-4972	423	48	≤	≤	NOUN
ejpam-4972	423	49	(	(	PUNCT
ejpam-4972	423	50	t(kc))c	t(kc))c	VERB
ejpam-4972	423	51	if	if	SCONJ
ejpam-4972	423	52	we	we	PRON
ejpam-4972	423	53	chose	choose	VERB
ejpam-4972	423	54	w	w	NOUN
ejpam-4972	423	55	=	=	PUNCT
ejpam-4972	423	56	(	(	PUNCT
ejpam-4972	423	57	t(kc))c	t(kc))c	PROPN
ejpam-4972	423	58	,	,	PUNCT
ejpam-4972	423	59	thus	thus	ADV
ejpam-4972	423	60	∃w	∃w	PROPN
ejpam-4972	423	61	is	be	AUX
ejpam-4972	423	62	fuzzy	fuzzy	ADJ
ejpam-4972	423	63	(	(	PUNCT
ejpam-4972	423	64	i	i	PROPN
ejpam-4972	423	65	,	,	PUNCT
ejpam-4972	423	66	j	j	PROPN
ejpam-4972	423	67	)	)	PUNCT
ejpam-4972	423	68	−	−	PROPN
ejpam-4972	423	69	gψ	gψ	VERB
ejpam-4972	423	70	−	−	PROPN
ejpam-4972	423	71	cld	cld	NOUN
ejpam-4972	423	72	group	group	NOUN
ejpam-4972	423	73	of	of	ADP
ejpam-4972	423	74	y	y	PROPN
ejpam-4972	423	75	including	include	VERB
ejpam-4972	423	76	w	w	PROPN
ejpam-4972	423	77	as	as	ADP
ejpam-4972	423	78	t−1(w	t−1(w	NOUN
ejpam-4972	423	79	)	)	PUNCT
ejpam-4972	423	80	=	=	SYM
ejpam-4972	423	81	k.	k.	PROPN
ejpam-4972	423	82	theorem	theorem	PROPN
ejpam-4972	423	83	24	24	NUM
ejpam-4972	423	84	.	.	PUNCT
ejpam-4972	424	1	suppose	suppose	VERB
ejpam-4972	424	2	t	t	NOUN
ejpam-4972	424	3	:	:	PUNCT
ejpam-4972	424	4	(	(	PUNCT
ejpam-4972	424	5	x	x	X
ejpam-4972	424	6	,	,	PUNCT
ejpam-4972	424	7	δ1	δ1	NOUN
ejpam-4972	424	8	,	,	PUNCT
ejpam-4972	424	9	δ2	δ2	ADJ
ejpam-4972	424	10	)	)	PUNCT
ejpam-4972	424	11	→	→	SYM
ejpam-4972	424	12	(	(	PUNCT
ejpam-4972	424	13	y	y	PROPN
ejpam-4972	424	14	,	,	PUNCT
ejpam-4972	424	15	σ1	σ1	PROPN
ejpam-4972	424	16	,	,	PUNCT
ejpam-4972	424	17	σ2	σ2	PROPN
ejpam-4972	424	18	)	)	PUNCT
ejpam-4972	424	19	is	be	AUX
ejpam-4972	424	20	bijective	bijective	ADJ
ejpam-4972	424	21	mapping	mapping	NOUN
ejpam-4972	424	22	.	.	PUNCT
ejpam-4972	425	1	hence	hence	ADV
ejpam-4972	425	2	the	the	DET
ejpam-4972	425	3	next	next	ADJ
ejpam-4972	425	4	claims	claim	NOUN
ejpam-4972	425	5	are	be	AUX
ejpam-4972	425	6	equivalent	equivalent	ADJ
ejpam-4972	425	7	:	:	PUNCT
ejpam-4972	425	8	(	(	PUNCT
ejpam-4972	425	9	i	i	NOUN
ejpam-4972	425	10	)	)	PUNCT
ejpam-4972	425	11	t	t	PROPN
ejpam-4972	425	12	is	be	AUX
ejpam-4972	425	13	fuzzy	fuzzy	ADJ
ejpam-4972	425	14	(	(	PUNCT
ejpam-4972	425	15	i	i	PROPN
ejpam-4972	425	16	,	,	PUNCT
ejpam-4972	425	17	j)−	j)−	PROPN
ejpam-4972	425	18	gψ	gψ	VERB
ejpam-4972	425	19	−	−	DET
ejpam-4972	425	20	open	open	ADJ
ejpam-4972	425	21	mapping	mapping	NOUN
ejpam-4972	425	22	.	.	PUNCT
ejpam-4972	426	1	(	(	PUNCT
ejpam-4972	426	2	ii	ii	NOUN
ejpam-4972	426	3	)	)	PUNCT
ejpam-4972	426	4	t	t	PROPN
ejpam-4972	426	5	is	be	AUX
ejpam-4972	426	6	fuzzy	fuzzy	ADJ
ejpam-4972	426	7	(	(	PUNCT
ejpam-4972	426	8	i	i	PROPN
ejpam-4972	426	9	,	,	PUNCT
ejpam-4972	426	10	j)−	j)−	PROPN
ejpam-4972	426	11	gψ	gψ	VERB
ejpam-4972	426	12	−	−	PROPN
ejpam-4972	426	13	closed	closed	ADJ
ejpam-4972	426	14	mapping	mapping	NOUN
ejpam-4972	426	15	.	.	PUNCT
ejpam-4972	427	1	proof	proof	NOUN
ejpam-4972	427	2	.	.	PUNCT
ejpam-4972	428	1	a.	a.	NOUN
ejpam-4972	428	2	a.	a.	PROPN
ejpam-4972	428	3	alharbi	alharbi	PROPN
ejpam-4972	428	4	,	,	PUNCT
ejpam-4972	428	5	a.	a.	NOUN
ejpam-4972	428	6	kilicman	kilicman	PROPN
ejpam-4972	428	7	/	/	SYM
ejpam-4972	428	8	eur	eur	PROPN
ejpam-4972	428	9	.	.	PUNCT
ejpam-4972	429	1	j.	j.	PROPN
ejpam-4972	429	2	pure	pure	PROPN
ejpam-4972	429	3	appl	appl	PROPN
ejpam-4972	429	4	.	.	PROPN
ejpam-4972	429	5	math	math	PROPN
ejpam-4972	429	6	,	,	PUNCT
ejpam-4972	429	7	16	16	NUM
ejpam-4972	429	8	(	(	PUNCT
ejpam-4972	429	9	4	4	NUM
ejpam-4972	429	10	)	)	PUNCT
ejpam-4972	429	11	(	(	PUNCT
ejpam-4972	429	12	2023	2023	NUM
ejpam-4972	429	13	)	)	PUNCT
ejpam-4972	429	14	,	,	PUNCT
ejpam-4972	429	15	2613	2613	NUM
ejpam-4972	429	16	-	-	SYM
ejpam-4972	429	17	2631	2631	NUM
ejpam-4972	429	18	2627	2627	NUM
ejpam-4972	429	19	(	(	PUNCT
ejpam-4972	429	20	i	i	NOUN
ejpam-4972	429	21	)	)	PUNCT
ejpam-4972	429	22	→	→	SYM
ejpam-4972	429	23	(	(	PUNCT
ejpam-4972	429	24	ii	ii	NOUN
ejpam-4972	429	25	)	)	PUNCT
ejpam-4972	429	26	suppose	suppose	VERB
ejpam-4972	429	27	t	t	NOUN
ejpam-4972	429	28	is	be	AUX
ejpam-4972	429	29	(	(	PUNCT
ejpam-4972	429	30	i	i	PROPN
ejpam-4972	429	31	,	,	PUNCT
ejpam-4972	429	32	j)−	j)−	PROPN
ejpam-4972	429	33	gψ−	gψ−	PUNCT
ejpam-4972	429	34	open	open	ADJ
ejpam-4972	429	35	mapping	mapping	NOUN
ejpam-4972	429	36	,	,	PUNCT
ejpam-4972	429	37	k	k	X
ejpam-4972	429	38	is	be	AUX
ejpam-4972	429	39	(	(	PUNCT
ejpam-4972	429	40	i	i	NOUN
ejpam-4972	429	41	,	,	PUNCT
ejpam-4972	429	42	j)−	j)−	PROPN
ejpam-4972	429	43	gψ−	gψ−	PUNCT
ejpam-4972	429	44	cld	cld	PROPN
ejpam-4972	429	45	of	of	ADP
ejpam-4972	429	46	x.	x.	NOUN
ejpam-4972	429	47	thus	thus	ADV
ejpam-4972	429	48	kc	kc	PROPN
ejpam-4972	429	49	is	be	AUX
ejpam-4972	429	50	(	(	PUNCT
ejpam-4972	429	51	i	i	NOUN
ejpam-4972	429	52	,	,	PUNCT
ejpam-4972	429	53	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	429	54	of	of	ADP
ejpam-4972	429	55	x.	x.	NOUN
ejpam-4972	429	56	as	as	ADP
ejpam-4972	429	57	t	t	PROPN
ejpam-4972	429	58	is	be	AUX
ejpam-4972	429	59	(	(	PUNCT
ejpam-4972	429	60	i	i	NOUN
ejpam-4972	429	61	,	,	PUNCT
ejpam-4972	429	62	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	429	63	mapping	mapping	NOUN
ejpam-4972	429	64	,	,	PUNCT
ejpam-4972	429	65	so	so	ADV
ejpam-4972	429	66	t(kc	t(kc	NOUN
ejpam-4972	429	67	)	)	PUNCT
ejpam-4972	429	68	is	be	AUX
ejpam-4972	429	69	(	(	PUNCT
ejpam-4972	429	70	i	i	NOUN
ejpam-4972	429	71	,	,	PUNCT
ejpam-4972	429	72	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	429	73	of	of	ADP
ejpam-4972	429	74	y	y	PROPN
ejpam-4972	429	75	.	.	PUNCT
ejpam-4972	430	1	as	as	SCONJ
ejpam-4972	430	2	t	t	PROPN
ejpam-4972	430	3	is	be	AUX
ejpam-4972	430	4	bijective	bijective	ADJ
ejpam-4972	430	5	,	,	PUNCT
ejpam-4972	430	6	then	then	ADV
ejpam-4972	430	7	t(x	t(x	PROPN
ejpam-4972	430	8	)	)	PUNCT
ejpam-4972	431	1	=	=	SYM
ejpam-4972	431	2	y	y	PROPN
ejpam-4972	431	3	,	,	PUNCT
ejpam-4972	431	4	hence	hence	ADV
ejpam-4972	431	5	y	y	PROPN
ejpam-4972	431	6	−	−	PROPN
ejpam-4972	431	7	t(k	t(k	PROPN
ejpam-4972	431	8	)	)	PUNCT
ejpam-4972	431	9	=	=	PUNCT
ejpam-4972	432	1	(	(	PUNCT
ejpam-4972	432	2	t(k))c	t(k))c	NOUN
ejpam-4972	432	3	is	be	AUX
ejpam-4972	432	4	(	(	PUNCT
ejpam-4972	432	5	i	i	NOUN
ejpam-4972	432	6	,	,	PUNCT
ejpam-4972	432	7	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	432	8	of	of	ADP
ejpam-4972	432	9	y	y	PROPN
ejpam-4972	432	10	,	,	PUNCT
ejpam-4972	432	11	then	then	ADV
ejpam-4972	432	12	t(k	t(k	PROPN
ejpam-4972	432	13	)	)	PUNCT
ejpam-4972	433	1	is	be	AUX
ejpam-4972	433	2	(	(	PUNCT
ejpam-4972	433	3	i	i	PROPN
ejpam-4972	433	4	,	,	PUNCT
ejpam-4972	433	5	j)−	j)−	PROPN
ejpam-4972	433	6	gψ	gψ	VERB
ejpam-4972	433	7	−	−	PROPN
ejpam-4972	433	8	cld	cld	NOUN
ejpam-4972	433	9	of	of	ADP
ejpam-4972	433	10	y	y	PROPN
ejpam-4972	433	11	.	.	PUNCT
ejpam-4972	434	1	so	so	ADV
ejpam-4972	434	2	,	,	PUNCT
ejpam-4972	434	3	t	t	PROPN
ejpam-4972	434	4	is	be	AUX
ejpam-4972	434	5	(	(	PUNCT
ejpam-4972	434	6	i	i	PROPN
ejpam-4972	434	7	,	,	PUNCT
ejpam-4972	434	8	j)−	j)−	PROPN
ejpam-4972	434	9	gψ	gψ	VERB
ejpam-4972	434	10	−	−	PROPN
ejpam-4972	434	11	closed	closed	ADJ
ejpam-4972	434	12	mapping	mapping	NOUN
ejpam-4972	434	13	.	.	PUNCT
ejpam-4972	435	1	(	(	PUNCT
ejpam-4972	435	2	ii	ii	NOUN
ejpam-4972	435	3	)	)	PUNCT
ejpam-4972	435	4	→	→	SYM
ejpam-4972	435	5	(	(	PUNCT
ejpam-4972	435	6	i	i	NOUN
ejpam-4972	435	7	)	)	PUNCT
ejpam-4972	435	8	suppose	suppose	VERB
ejpam-4972	435	9	t	t	PROPN
ejpam-4972	435	10	is	be	AUX
ejpam-4972	435	11	(	(	PUNCT
ejpam-4972	435	12	i	i	PROPN
ejpam-4972	435	13	,	,	PUNCT
ejpam-4972	435	14	j	j	PROPN
ejpam-4972	435	15	)	)	PUNCT
ejpam-4972	435	16	−	−	PROPN
ejpam-4972	435	17	gψ	gψ	VERB
ejpam-4972	435	18	−	−	PROPN
ejpam-4972	435	19	closed	closed	ADJ
ejpam-4972	435	20	mapping	mapping	NOUN
ejpam-4972	435	21	with	with	ADP
ejpam-4972	435	22	k	k	PROPN
ejpam-4972	435	23	is	be	AUX
ejpam-4972	435	24	(	(	PUNCT
ejpam-4972	435	25	i	i	PROPN
ejpam-4972	435	26	,	,	PUNCT
ejpam-4972	435	27	j	j	PROPN
ejpam-4972	435	28	)	)	PUNCT
ejpam-4972	435	29	−	−	PROPN
ejpam-4972	435	30	gψ	gψ	VERB
ejpam-4972	436	1	−	−	PROPN
ejpam-4972	436	2	open	open	ADJ
ejpam-4972	436	3	of	of	ADP
ejpam-4972	436	4	x.	x.	NOUN
ejpam-4972	436	5	thus	thus	ADV
ejpam-4972	436	6	kc	kc	PROPN
ejpam-4972	436	7	is	be	AUX
ejpam-4972	436	8	(	(	PUNCT
ejpam-4972	436	9	i	i	PROPN
ejpam-4972	436	10	,	,	PUNCT
ejpam-4972	436	11	j)−	j)−	PROPN
ejpam-4972	436	12	gψ	gψ	VERB
ejpam-4972	436	13	−	−	PROPN
ejpam-4972	436	14	cld	cld	NOUN
ejpam-4972	436	15	of	of	ADP
ejpam-4972	436	16	x.	x.	PROPN
ejpam-4972	436	17	as	as	ADP
ejpam-4972	436	18	t	t	PROPN
ejpam-4972	436	19	is	be	AUX
ejpam-4972	436	20	(	(	PUNCT
ejpam-4972	436	21	i	i	PROPN
ejpam-4972	436	22	,	,	PUNCT
ejpam-4972	436	23	j)−	j)−	PROPN
ejpam-4972	436	24	gψ	gψ	VERB
ejpam-4972	436	25	−	−	PROPN
ejpam-4972	436	26	closed	closed	ADJ
ejpam-4972	436	27	mapping	mapping	NOUN
ejpam-4972	436	28	,	,	PUNCT
ejpam-4972	436	29	so	so	ADV
ejpam-4972	436	30	t(kc	t(kc	NOUN
ejpam-4972	436	31	)	)	PUNCT
ejpam-4972	436	32	is	be	AUX
ejpam-4972	436	33	(	(	PUNCT
ejpam-4972	436	34	i	i	NOUN
ejpam-4972	436	35	,	,	PUNCT
ejpam-4972	436	36	j)−	j)−	PROPN
ejpam-4972	436	37	gψ−	gψ−	PUNCT
ejpam-4972	436	38	cld	cld	PROPN
ejpam-4972	436	39	of	of	ADP
ejpam-4972	436	40	y	y	PROPN
ejpam-4972	436	41	.	.	PUNCT
ejpam-4972	437	1	as	as	SCONJ
ejpam-4972	437	2	t	t	PROPN
ejpam-4972	437	3	is	be	AUX
ejpam-4972	437	4	bijective	bijective	ADJ
ejpam-4972	437	5	,	,	PUNCT
ejpam-4972	437	6	so	so	ADV
ejpam-4972	437	7	t(x	t(x	PROPN
ejpam-4972	437	8	)	)	PUNCT
ejpam-4972	438	1	=	=	SYM
ejpam-4972	438	2	y	y	PROPN
ejpam-4972	438	3	,	,	PUNCT
ejpam-4972	438	4	and	and	CCONJ
ejpam-4972	438	5	hence	hence	ADV
ejpam-4972	438	6	y	y	PROPN
ejpam-4972	438	7	−	−	PROPN
ejpam-4972	438	8	t(k	t(k	PROPN
ejpam-4972	438	9	)	)	PUNCT
ejpam-4972	438	10	=	=	PUNCT
ejpam-4972	439	1	(	(	PUNCT
ejpam-4972	439	2	t(k))c	t(k))c	NOUN
ejpam-4972	439	3	is	be	AUX
ejpam-4972	439	4	(	(	PUNCT
ejpam-4972	439	5	i	i	PROPN
ejpam-4972	439	6	,	,	PUNCT
ejpam-4972	439	7	j)−gψ−cld	j)−gψ−cld	PROPN
ejpam-4972	439	8	of	of	ADP
ejpam-4972	439	9	y	y	PROPN
ejpam-4972	439	10	,	,	PUNCT
ejpam-4972	439	11	then	then	ADV
ejpam-4972	439	12	t(k	t(k	PROPN
ejpam-4972	439	13	)	)	PUNCT
ejpam-4972	440	1	is	be	AUX
ejpam-4972	440	2	(	(	PUNCT
ejpam-4972	440	3	i	i	NOUN
ejpam-4972	440	4	,	,	PUNCT
ejpam-4972	440	5	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	440	6	of	of	ADP
ejpam-4972	440	7	y	y	PROPN
ejpam-4972	440	8	.	.	PUNCT
ejpam-4972	441	1	so	so	ADV
ejpam-4972	441	2	,	,	PUNCT
ejpam-4972	441	3	t	t	PROPN
ejpam-4972	441	4	is	be	AUX
ejpam-4972	441	5	(	(	PUNCT
ejpam-4972	441	6	i	i	NOUN
ejpam-4972	441	7	,	,	PUNCT
ejpam-4972	441	8	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	441	9	mapping	mapping	NOUN
ejpam-4972	441	10	.	.	PUNCT
ejpam-4972	442	1	theorem	theorem	VERB
ejpam-4972	442	2	25	25	NUM
ejpam-4972	442	3	.	.	PUNCT
ejpam-4972	443	1	suppose	suppose	VERB
ejpam-4972	443	2	t	t	NOUN
ejpam-4972	443	3	:	:	PUNCT
ejpam-4972	443	4	(	(	PUNCT
ejpam-4972	443	5	x	x	X
ejpam-4972	443	6	,	,	PUNCT
ejpam-4972	443	7	δ1	δ1	NOUN
ejpam-4972	443	8	,	,	PUNCT
ejpam-4972	443	9	δ2	δ2	ADJ
ejpam-4972	443	10	)	)	PUNCT
ejpam-4972	443	11	→	→	SYM
ejpam-4972	443	12	(	(	PUNCT
ejpam-4972	443	13	y	y	PROPN
ejpam-4972	443	14	,	,	PUNCT
ejpam-4972	443	15	σ1	σ1	PROPN
ejpam-4972	443	16	,	,	PUNCT
ejpam-4972	443	17	σ2	σ2	NOUN
ejpam-4972	443	18	)	)	PUNCT
ejpam-4972	443	19	is	be	AUX
ejpam-4972	443	20	fuzzy	fuzzy	ADJ
ejpam-4972	443	21	(	(	PUNCT
ejpam-4972	443	22	i	i	NOUN
ejpam-4972	443	23	,	,	PUNCT
ejpam-4972	443	24	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	443	25	(	(	PUNCT
ejpam-4972	443	26	resp	resp	NOUN
ejpam-4972	443	27	,	,	PUNCT
ejpam-4972	443	28	(	(	PUNCT
ejpam-4972	443	29	i	i	PROPN
ejpam-4972	443	30	,	,	PUNCT
ejpam-4972	443	31	j)−	j)−	PROPN
ejpam-4972	443	32	gψ−	gψ−	PUNCT
ejpam-4972	443	33	closed	closed	ADJ
ejpam-4972	443	34	)	)	PUNCT
ejpam-4972	443	35	mapping	mapping	NOUN
ejpam-4972	443	36	.	.	PUNCT
ejpam-4972	444	1	thus	thus	ADV
ejpam-4972	444	2	for	for	ADP
ejpam-4972	444	3	any	any	DET
ejpam-4972	444	4	r	r	NOUN
ejpam-4972	444	5	∈	∈	NOUN
ejpam-4972	444	6	ix	ix	ADV
ejpam-4972	444	7	,	,	PUNCT
ejpam-4972	444	8	t(δj	t(δj	PROPN
ejpam-4972	444	9	−ψ−	−ψ−	NOUN
ejpam-4972	444	10	int(r	int(r	PROPN
ejpam-4972	444	11	)	)	PUNCT
ejpam-4972	444	12	)	)	PUNCT
ejpam-4972	444	13	≤	≤	NOUN
ejpam-4972	444	14	(	(	PUNCT
ejpam-4972	444	15	i	i	NOUN
ejpam-4972	444	16	,	,	PUNCT
ejpam-4972	444	17	j)−	j)−	PROPN
ejpam-4972	444	18	gψ−	gψ−	PUNCT
ejpam-4972	444	19	int(t(r	int(t(r	ADJ
ejpam-4972	444	20	)	)	PUNCT
ejpam-4972	444	21	)	)	PUNCT
ejpam-4972	444	22	.	.	PUNCT
ejpam-4972	445	1	proof	proof	NOUN
ejpam-4972	445	2	.	.	PUNCT
ejpam-4972	446	1	suppose	suppose	VERB
ejpam-4972	446	2	t	t	PROPN
ejpam-4972	446	3	is	be	AUX
ejpam-4972	446	4	(	(	PUNCT
ejpam-4972	446	5	i	i	PROPN
ejpam-4972	446	6	,	,	PUNCT
ejpam-4972	446	7	j	j	PROPN
ejpam-4972	446	8	)	)	PUNCT
ejpam-4972	446	9	−	−	PROPN
ejpam-4972	446	10	gψ	gψ	VERB
ejpam-4972	446	11	−	−	DET
ejpam-4972	446	12	open	open	ADJ
ejpam-4972	446	13	mapping	mapping	NOUN
ejpam-4972	446	14	with	with	ADP
ejpam-4972	446	15	r	r	NOUN
ejpam-4972	446	16	is	be	AUX
ejpam-4972	446	17	subgroup	subgroup	NOUN
ejpam-4972	446	18	of	of	ADP
ejpam-4972	446	19	x.	x.	NOUN
ejpam-4972	446	20	since	since	SCONJ
ejpam-4972	446	21	t(δj	t(δj	PROPN
ejpam-4972	446	22	−	−	PROPN
ejpam-4972	446	23	ψ	ψ	NOUN
ejpam-4972	446	24	−	−	ADP
ejpam-4972	446	25	int(r	int(r	NOUN
ejpam-4972	446	26	)	)	PUNCT
ejpam-4972	446	27	)	)	PUNCT
ejpam-4972	446	28	≤	≤	NUM
ejpam-4972	446	29	t(r	t(r	PRON
ejpam-4972	446	30	)	)	PUNCT
ejpam-4972	446	31	and	and	CCONJ
ejpam-4972	446	32	δj	δj	ADP
ejpam-4972	446	33	−	−	PROPN
ejpam-4972	446	34	ψ	ψ	NOUN
ejpam-4972	446	35	−	−	ADP
ejpam-4972	446	36	int(r	int(r	NOUN
ejpam-4972	446	37	)	)	PUNCT
ejpam-4972	446	38	considers	consider	VERB
ejpam-4972	446	39	(	(	PUNCT
ejpam-4972	446	40	i	i	NOUN
ejpam-4972	446	41	,	,	PUNCT
ejpam-4972	446	42	j	j	PROPN
ejpam-4972	446	43	)	)	PUNCT
ejpam-4972	446	44	−	−	PROPN
ejpam-4972	446	45	gψ	gψ	VERB
ejpam-4972	446	46	−	−	DET
ejpam-4972	446	47	open	open	ADJ
ejpam-4972	446	48	group	group	NOUN
ejpam-4972	446	49	of	of	ADP
ejpam-4972	446	50	x.	x.	PROPN
ejpam-4972	446	51	then	then	ADV
ejpam-4972	446	52	t(δj	t(δj	PROPN
ejpam-4972	446	53	−	−	PROPN
ejpam-4972	446	54	ψ	ψ	NOUN
ejpam-4972	446	55	−	−	ADP
ejpam-4972	446	56	int(r	int(r	NOUN
ejpam-4972	446	57	)	)	PUNCT
ejpam-4972	446	58	)	)	PUNCT
ejpam-4972	446	59	≤	≤	NOUN
ejpam-4972	447	1	(	(	PUNCT
ejpam-4972	447	2	i	i	PRON
ejpam-4972	447	3	,	,	PUNCT
ejpam-4972	447	4	j)−	j)−	PROPN
ejpam-4972	447	5	gψ	gψ	VERB
ejpam-4972	447	6	−	−	NOUN
ejpam-4972	447	7	int(t(r	int(t(r	ADJ
ejpam-4972	447	8	)	)	PUNCT
ejpam-4972	447	9	)	)	PUNCT
ejpam-4972	447	10	.	.	PUNCT
ejpam-4972	448	1	6	6	X
ejpam-4972	448	2	.	.	X
ejpam-4972	448	3	fuzzy	fuzzy	ADJ
ejpam-4972	448	4	generalized	generalize	VERB
ejpam-4972	448	5	homomorphism	homomorphism	NOUN
ejpam-4972	448	6	mapping	mapping	NOUN
ejpam-4972	448	7	finally	finally	ADV
ejpam-4972	448	8	,	,	PUNCT
ejpam-4972	448	9	we	we	PRON
ejpam-4972	448	10	investigate	investigate	VERB
ejpam-4972	448	11	some	some	DET
ejpam-4972	448	12	theorems	theorem	NOUN
ejpam-4972	448	13	for	for	ADP
ejpam-4972	448	14	the	the	DET
ejpam-4972	448	15	fuzzy	fuzzy	ADJ
ejpam-4972	448	16	generalized	generalize	VERB
ejpam-4972	448	17	homomorphism	homomorphism	NOUN
ejpam-4972	448	18	and	and	CCONJ
ejpam-4972	448	19	we	we	PRON
ejpam-4972	448	20	denote	denote	VERB
ejpam-4972	448	21	by	by	ADP
ejpam-4972	448	22	gψ−homomorphism	gψ−homomorphism	NOUN
ejpam-4972	448	23	.	.	PUNCT
ejpam-4972	449	1	definition	definition	NOUN
ejpam-4972	449	2	12	12	NUM
ejpam-4972	449	3	.	.	PUNCT
ejpam-4972	450	1	suppose	suppose	VERB
ejpam-4972	450	2	t	t	NOUN
ejpam-4972	450	3	:	:	PUNCT
ejpam-4972	450	4	(	(	PUNCT
ejpam-4972	450	5	x	x	X
ejpam-4972	450	6	,	,	PUNCT
ejpam-4972	450	7	δ1	δ1	NOUN
ejpam-4972	450	8	,	,	PUNCT
ejpam-4972	450	9	δ2	δ2	ADJ
ejpam-4972	450	10	)	)	PUNCT
ejpam-4972	450	11	→	→	SYM
ejpam-4972	450	12	(	(	PUNCT
ejpam-4972	450	13	y	y	PROPN
ejpam-4972	450	14	,	,	PUNCT
ejpam-4972	450	15	σ1	σ1	PROPN
ejpam-4972	450	16	,	,	PUNCT
ejpam-4972	450	17	σ2	σ2	NOUN
ejpam-4972	450	18	)	)	PUNCT
ejpam-4972	450	19	.	.	PUNCT
ejpam-4972	451	1	hence	hence	ADV
ejpam-4972	451	2	t	t	PROPN
ejpam-4972	451	3	is	be	AUX
ejpam-4972	451	4	known	know	VERB
ejpam-4972	451	5	as	as	ADP
ejpam-4972	451	6	fuzzy	fuzzy	ADJ
ejpam-4972	451	7	gψ−homomorphism	gψ−homomorphism	NOUN
ejpam-4972	451	8	if	if	SCONJ
ejpam-4972	451	9	and	and	CCONJ
ejpam-4972	451	10	only	only	ADV
ejpam-4972	451	11	if	if	SCONJ
ejpam-4972	451	12	the	the	DET
ejpam-4972	451	13	claims	claim	NOUN
ejpam-4972	451	14	below	below	ADV
ejpam-4972	451	15	are	be	AUX
ejpam-4972	451	16	true	true	ADJ
ejpam-4972	451	17	:	:	PUNCT
ejpam-4972	451	18	(	(	PUNCT
ejpam-4972	451	19	1	1	X
ejpam-4972	451	20	)	)	PUNCT
ejpam-4972	451	21	t	t	PROPN
ejpam-4972	451	22	is	be	AUX
ejpam-4972	451	23	bijective	bijective	ADJ
ejpam-4972	451	24	.	.	PUNCT
ejpam-4972	452	1	(	(	PUNCT
ejpam-4972	452	2	2	2	X
ejpam-4972	452	3	)	)	PUNCT
ejpam-4972	452	4	t	t	NOUN
ejpam-4972	452	5	is	be	AUX
ejpam-4972	452	6	fuzzy	fuzzy	ADJ
ejpam-4972	452	7	(	(	PUNCT
ejpam-4972	452	8	i	i	PROPN
ejpam-4972	452	9	,	,	PUNCT
ejpam-4972	452	10	j)−	j)−	PROPN
ejpam-4972	452	11	gψ	gψ	VERB
ejpam-4972	452	12	−	−	PROPN
ejpam-4972	452	13	conts	cont	NOUN
ejpam-4972	452	14	.	.	PUNCT
ejpam-4972	453	1	(	(	PUNCT
ejpam-4972	453	2	3	3	X
ejpam-4972	453	3	)	)	PUNCT
ejpam-4972	453	4	t−1	t−1	NOUN
ejpam-4972	453	5	is	be	AUX
ejpam-4972	453	6	fuzzy	fuzzy	ADJ
ejpam-4972	453	7	(	(	PUNCT
ejpam-4972	453	8	i	i	PROPN
ejpam-4972	453	9	,	,	PUNCT
ejpam-4972	453	10	j)−	j)−	PROPN
ejpam-4972	453	11	gψ	gψ	VERB
ejpam-4972	453	12	−	−	PROPN
ejpam-4972	453	13	conts	cont	NOUN
ejpam-4972	453	14	.	.	PUNCT
ejpam-4972	454	1	remark	remark	PROPN
ejpam-4972	454	2	9	9	NUM
ejpam-4972	454	3	.	.	PUNCT
ejpam-4972	455	1	suppose	suppose	VERB
ejpam-4972	455	2	t	t	NOUN
ejpam-4972	455	3	:	:	PUNCT
ejpam-4972	455	4	(	(	PUNCT
ejpam-4972	455	5	x	x	X
ejpam-4972	455	6	,	,	PUNCT
ejpam-4972	455	7	δ1	δ1	NOUN
ejpam-4972	455	8	,	,	PUNCT
ejpam-4972	455	9	δ2	δ2	ADJ
ejpam-4972	455	10	)	)	PUNCT
ejpam-4972	455	11	→	→	SYM
ejpam-4972	455	12	(	(	PUNCT
ejpam-4972	455	13	y	y	PROPN
ejpam-4972	455	14	,	,	PUNCT
ejpam-4972	455	15	σ1	σ1	PROPN
ejpam-4972	455	16	,	,	PUNCT
ejpam-4972	455	17	σ2	σ2	NOUN
ejpam-4972	455	18	)	)	PUNCT
ejpam-4972	455	19	,	,	PUNCT
ejpam-4972	455	20	g	g	NOUN
ejpam-4972	455	21	:	:	PUNCT
ejpam-4972	455	22	(	(	PUNCT
ejpam-4972	455	23	y	y	PROPN
ejpam-4972	455	24	,	,	PUNCT
ejpam-4972	455	25	σ1	σ1	PROPN
ejpam-4972	455	26	,	,	PUNCT
ejpam-4972	455	27	σ2	σ2	NOUN
ejpam-4972	455	28	)	)	PUNCT
ejpam-4972	455	29	→	→	SYM
ejpam-4972	455	30	(	(	PUNCT
ejpam-4972	455	31	z	z	NOUN
ejpam-4972	455	32	,	,	PUNCT
ejpam-4972	455	33	η1	η1	NOUN
ejpam-4972	455	34	,	,	PUNCT
ejpam-4972	455	35	η2	η2	PROPN
ejpam-4972	455	36	)	)	PUNCT
ejpam-4972	455	37	both	both	PRON
ejpam-4972	455	38	of	of	ADP
ejpam-4972	455	39	them	they	PRON
ejpam-4972	455	40	are	be	AUX
ejpam-4972	455	41	fuzzy	fuzzy	ADJ
ejpam-4972	455	42	gψ−homomorphism	gψ−homomorphism	NOUN
ejpam-4972	455	43	mapping	mapping	NOUN
ejpam-4972	455	44	.	.	PUNCT
ejpam-4972	456	1	then	then	ADV
ejpam-4972	456	2	g	g	NOUN
ejpam-4972	456	3	◦	◦	NOUN
ejpam-4972	456	4	t	t	NOUN
ejpam-4972	456	5	is	be	AUX
ejpam-4972	456	6	not	not	PART
ejpam-4972	456	7	fuzzy	fuzzy	ADJ
ejpam-4972	456	8	gψ−homomorphism	gψ−homomorphism	NOUN
ejpam-4972	456	9	because	because	SCONJ
ejpam-4972	456	10	g	g	PROPN
ejpam-4972	456	11	◦	◦	PROPN
ejpam-4972	456	12	t	t	PROPN
ejpam-4972	456	13	is	be	AUX
ejpam-4972	456	14	not	not	PART
ejpam-4972	456	15	fuzzy	fuzzy	ADJ
ejpam-4972	456	16	(	(	PUNCT
ejpam-4972	456	17	i	i	PROPN
ejpam-4972	456	18	,	,	PUNCT
ejpam-4972	456	19	j)−	j)−	PROPN
ejpam-4972	456	20	gψ	gψ	VERB
ejpam-4972	456	21	−	−	PROPN
ejpam-4972	456	22	conts	cont	NOUN
ejpam-4972	456	23	.	.	PUNCT
ejpam-4972	457	1	refer	refer	VERB
ejpam-4972	457	2	to	to	ADP
ejpam-4972	457	3	theorem	theorem	NOUN
ejpam-4972	457	4	6	6	NUM
ejpam-4972	457	5	.	.	PUNCT
ejpam-4972	457	6	theorem	theorem	NOUN
ejpam-4972	457	7	26	26	NUM
ejpam-4972	457	8	.	.	PUNCT
ejpam-4972	458	1	suppose	suppose	VERB
ejpam-4972	458	2	t	t	NOUN
ejpam-4972	458	3	:	:	PUNCT
ejpam-4972	458	4	(	(	PUNCT
ejpam-4972	458	5	x	x	X
ejpam-4972	458	6	,	,	PUNCT
ejpam-4972	458	7	δ1	δ1	NOUN
ejpam-4972	458	8	,	,	PUNCT
ejpam-4972	458	9	δ2	δ2	ADJ
ejpam-4972	458	10	)	)	PUNCT
ejpam-4972	458	11	→	→	SYM
ejpam-4972	458	12	(	(	PUNCT
ejpam-4972	458	13	y	y	PROPN
ejpam-4972	458	14	,	,	PUNCT
ejpam-4972	458	15	σ1	σ1	PROPN
ejpam-4972	458	16	,	,	PUNCT
ejpam-4972	458	17	σ2	σ2	NOUN
ejpam-4972	458	18	)	)	PUNCT
ejpam-4972	458	19	is	be	AUX
ejpam-4972	458	20	fuzzy	fuzzy	ADJ
ejpam-4972	458	21	gψ−homomorphism	gψ−homomorphism	NOUN
ejpam-4972	458	22	,	,	PUNCT
ejpam-4972	458	23	fuzzy	fuzzy	ADJ
ejpam-4972	458	24	(	(	PUNCT
ejpam-4972	458	25	i	i	NOUN
ejpam-4972	458	26	,	,	PUNCT
ejpam-4972	458	27	j)−gψ−irresolute	j)−gψ−irresolute	PROPN
ejpam-4972	458	28	mapping	mapping	NOUN
ejpam-4972	458	29	,	,	PUNCT
ejpam-4972	458	30	with	with	ADP
ejpam-4972	458	31	g	g	NOUN
ejpam-4972	458	32	:	:	PUNCT
ejpam-4972	458	33	(	(	PUNCT
ejpam-4972	458	34	y	y	PROPN
ejpam-4972	458	35	,	,	PUNCT
ejpam-4972	458	36	σ1	σ1	PROPN
ejpam-4972	458	37	,	,	PUNCT
ejpam-4972	458	38	σ2	σ2	NOUN
ejpam-4972	458	39	)	)	PUNCT
ejpam-4972	458	40	→	→	SYM
ejpam-4972	458	41	(	(	PUNCT
ejpam-4972	458	42	z	z	NOUN
ejpam-4972	458	43	,	,	PUNCT
ejpam-4972	458	44	η1	η1	NOUN
ejpam-4972	458	45	,	,	PUNCT
ejpam-4972	458	46	η2	η2	PROPN
ejpam-4972	458	47	)	)	PUNCT
ejpam-4972	458	48	is	be	AUX
ejpam-4972	458	49	fuzzy	fuzzy	ADJ
ejpam-4972	458	50	gψ−homomorphism	gψ−homomorphism	NOUN
ejpam-4972	458	51	mapping	mapping	NOUN
ejpam-4972	458	52	.	.	PUNCT
ejpam-4972	459	1	thus	thus	ADV
ejpam-4972	459	2	g	g	PROPN
ejpam-4972	459	3	◦	◦	PROPN
ejpam-4972	459	4	t	t	PROPN
ejpam-4972	459	5	is	be	AUX
ejpam-4972	459	6	fuzzy	fuzzy	ADJ
ejpam-4972	459	7	gψ−homomorphism	gψ−homomorphism	NOUN
ejpam-4972	459	8	.	.	PUNCT
ejpam-4972	460	1	proof	proof	NOUN
ejpam-4972	460	2	.	.	PUNCT
ejpam-4972	461	1	suppose	suppose	VERB
ejpam-4972	461	2	r	r	NOUN
ejpam-4972	461	3	∈	∈	PROPN
ejpam-4972	461	4	fηj	fηj	NOUN
ejpam-4972	461	5	.	.	PUNCT
ejpam-4972	462	1	hence	hence	ADV
ejpam-4972	462	2	g−1(r	g−1(r	NOUN
ejpam-4972	462	3	)	)	PUNCT
ejpam-4972	462	4	is	be	AUX
ejpam-4972	462	5	(	(	PUNCT
ejpam-4972	462	6	i	i	PROPN
ejpam-4972	462	7	,	,	PUNCT
ejpam-4972	462	8	j	j	PROPN
ejpam-4972	462	9	)	)	PUNCT
ejpam-4972	462	10	−	−	PROPN
ejpam-4972	462	11	gψ	gψ	VERB
ejpam-4972	462	12	−	−	PROPN
ejpam-4972	462	13	cld	cld	NOUN
ejpam-4972	462	14	of	of	ADP
ejpam-4972	462	15	y	y	PROPN
ejpam-4972	462	16	.	.	PUNCT
ejpam-4972	463	1	as	as	SCONJ
ejpam-4972	463	2	t	t	PROPN
ejpam-4972	463	3	is	be	AUX
ejpam-4972	463	4	fuzzy	fuzzy	ADJ
ejpam-4972	463	5	(	(	PUNCT
ejpam-4972	463	6	i	i	PROPN
ejpam-4972	463	7	,	,	PUNCT
ejpam-4972	463	8	j)−	j)−	PROPN
ejpam-4972	463	9	gψ	gψ	VERB
ejpam-4972	463	10	−	−	PROPN
ejpam-4972	463	11	irresolute	irresolute	ADJ
ejpam-4972	463	12	mapping	mapping	NOUN
ejpam-4972	463	13	,	,	PUNCT
ejpam-4972	463	14	then	then	ADV
ejpam-4972	463	15	t−1(g−1(r	t−1(g−1(r	NOUN
ejpam-4972	463	16	)	)	PUNCT
ejpam-4972	463	17	)	)	PUNCT
ejpam-4972	464	1	is	be	AUX
ejpam-4972	464	2	(	(	PUNCT
ejpam-4972	464	3	i	i	PROPN
ejpam-4972	464	4	,	,	PUNCT
ejpam-4972	464	5	j)−	j)−	PROPN
ejpam-4972	464	6	gψ	gψ	VERB
ejpam-4972	464	7	−	−	PROPN
ejpam-4972	464	8	cld	cld	NOUN
ejpam-4972	464	9	of	of	ADP
ejpam-4972	464	10	x.	x.	NOUN
ejpam-4972	465	1	so	so	ADV
ejpam-4972	465	2	(	(	PUNCT
ejpam-4972	465	3	g	g	NOUN
ejpam-4972	465	4	◦	◦	NOUN
ejpam-4972	465	5	t)(r	t)(r	NOUN
ejpam-4972	465	6	)	)	PUNCT
ejpam-4972	465	7	is	be	AUX
ejpam-4972	465	8	fuzzy	fuzzy	ADJ
ejpam-4972	465	9	(	(	PUNCT
ejpam-4972	465	10	i	i	PROPN
ejpam-4972	465	11	,	,	PUNCT
ejpam-4972	465	12	j)−	j)−	PROPN
ejpam-4972	465	13	gψ	gψ	VERB
ejpam-4972	465	14	−	−	PROPN
ejpam-4972	465	15	conts	cont	NOUN
ejpam-4972	465	16	.	.	PUNCT
ejpam-4972	466	1	assume	assume	VERB
ejpam-4972	466	2	r	r	NOUN
ejpam-4972	466	3	is	be	AUX
ejpam-4972	466	4	(	(	PUNCT
ejpam-4972	466	5	i	i	PROPN
ejpam-4972	466	6	,	,	PUNCT
ejpam-4972	466	7	j	j	PROPN
ejpam-4972	466	8	)	)	PUNCT
ejpam-4972	466	9	−	−	PROPN
ejpam-4972	466	10	gψ	gψ	VERB
ejpam-4972	466	11	−	−	PROPN
ejpam-4972	466	12	open	open	ADJ
ejpam-4972	466	13	of	of	ADP
ejpam-4972	466	14	x.	x.	NOUN
ejpam-4972	466	15	as	as	SCONJ
ejpam-4972	466	16	t−1	t−1	PROPN
ejpam-4972	466	17	is	be	AUX
ejpam-4972	466	18	(	(	PUNCT
ejpam-4972	466	19	i	i	PROPN
ejpam-4972	466	20	,	,	PUNCT
ejpam-4972	466	21	j	j	PROPN
ejpam-4972	466	22	)	)	PUNCT
ejpam-4972	466	23	−	−	PROPN
ejpam-4972	466	24	gψ	gψ	VERB
ejpam-4972	466	25	−	−	PROPN
ejpam-4972	466	26	conts	cont	NOUN
ejpam-4972	466	27	,	,	PUNCT
ejpam-4972	466	28	then	then	ADV
ejpam-4972	466	29	(	(	PUNCT
ejpam-4972	466	30	t−1)−1(r	t−1)−1(r	NOUN
ejpam-4972	466	31	)	)	PUNCT
ejpam-4972	466	32	=	=	SYM
ejpam-4972	466	33	t(r	t(r	X
ejpam-4972	466	34	)	)	PUNCT
ejpam-4972	466	35	∈	∈	NOUN
ejpam-4972	466	36	fσj	fσj	NOUN
ejpam-4972	466	37	,	,	PUNCT
ejpam-4972	466	38	and	and	CCONJ
ejpam-4972	466	39	hence	hence	ADV
ejpam-4972	466	40	t(r	t(r	ADV
ejpam-4972	466	41	)	)	PUNCT
ejpam-4972	466	42	is	be	AUX
ejpam-4972	466	43	(	(	PUNCT
ejpam-4972	466	44	i	i	PROPN
ejpam-4972	466	45	,	,	PUNCT
ejpam-4972	466	46	j)−	j)−	PROPN
ejpam-4972	466	47	gψ	gψ	VERB
ejpam-4972	466	48	−	−	PROPN
ejpam-4972	466	49	cld	cld	NOUN
ejpam-4972	466	50	of	of	ADP
ejpam-4972	466	51	y	y	PROPN
ejpam-4972	466	52	.	.	PUNCT
ejpam-4972	467	1	then	then	ADV
ejpam-4972	467	2	(	(	PUNCT
ejpam-4972	467	3	g−1)−1t(r	g−1)−1t(r	NUM
ejpam-4972	467	4	)	)	PUNCT
ejpam-4972	467	5	=	=	SYM
ejpam-4972	467	6	g(t(r	g(t(r	PROPN
ejpam-4972	467	7	)	)	PUNCT
ejpam-4972	467	8	)	)	PUNCT
ejpam-4972	468	1	∈	∈	PROPN
ejpam-4972	468	2	fηj	fηj	NOUN
ejpam-4972	468	3	,	,	PUNCT
ejpam-4972	468	4	a.	a.	NOUN
ejpam-4972	468	5	a.	a.	NOUN
ejpam-4972	468	6	alharbi	alharbi	PROPN
ejpam-4972	468	7	,	,	PUNCT
ejpam-4972	468	8	a.	a.	NOUN
ejpam-4972	468	9	kilicman	kilicman	PROPN
ejpam-4972	468	10	/	/	SYM
ejpam-4972	468	11	eur	eur	PROPN
ejpam-4972	468	12	.	.	PUNCT
ejpam-4972	469	1	j.	j.	PROPN
ejpam-4972	469	2	pure	pure	PROPN
ejpam-4972	469	3	appl	appl	PROPN
ejpam-4972	469	4	.	.	PROPN
ejpam-4972	469	5	math	math	PROPN
ejpam-4972	469	6	,	,	PUNCT
ejpam-4972	469	7	16	16	NUM
ejpam-4972	469	8	(	(	PUNCT
ejpam-4972	469	9	4	4	NUM
ejpam-4972	469	10	)	)	PUNCT
ejpam-4972	469	11	(	(	PUNCT
ejpam-4972	469	12	2023	2023	NUM
ejpam-4972	469	13	)	)	PUNCT
ejpam-4972	469	14	,	,	PUNCT
ejpam-4972	469	15	2613	2613	NUM
ejpam-4972	469	16	-	-	SYM
ejpam-4972	469	17	2631	2631	NUM
ejpam-4972	469	18	2628	2628	NUM
ejpam-4972	469	19	thus	thus	ADV
ejpam-4972	469	20	(	(	PUNCT
ejpam-4972	469	21	(	(	PUNCT
ejpam-4972	469	22	g	g	PROPN
ejpam-4972	469	23	◦	◦	PROPN
ejpam-4972	469	24	t)−1)−1(r	t)−1)−1(r	PROPN
ejpam-4972	469	25	)	)	PUNCT
ejpam-4972	470	1	=	=	PRON
ejpam-4972	470	2	(	(	PUNCT
ejpam-4972	470	3	g	g	NOUN
ejpam-4972	470	4	◦	◦	NOUN
ejpam-4972	470	5	t)(r	t)(r	NUM
ejpam-4972	470	6	)	)	PUNCT
ejpam-4972	470	7	=	=	SYM
ejpam-4972	470	8	g(t(r	g(t(r	PROPN
ejpam-4972	470	9	)	)	PUNCT
ejpam-4972	470	10	)	)	PUNCT
ejpam-4972	470	11	is	be	AUX
ejpam-4972	470	12	fuzzy	fuzzy	ADJ
ejpam-4972	470	13	closed	closed	ADJ
ejpam-4972	470	14	of	of	ADP
ejpam-4972	470	15	(	(	PUNCT
ejpam-4972	470	16	z	z	NOUN
ejpam-4972	470	17	,	,	PUNCT
ejpam-4972	470	18	ηj	ηj	NOUN
ejpam-4972	470	19	)	)	PUNCT
ejpam-4972	470	20	.	.	PUNCT
ejpam-4972	471	1	so	so	ADV
ejpam-4972	471	2	(	(	PUNCT
ejpam-4972	471	3	g	g	NOUN
ejpam-4972	471	4	◦	◦	NOUN
ejpam-4972	471	5	t)−1	t)−1	NOUN
ejpam-4972	471	6	is	be	AUX
ejpam-4972	471	7	tuzzy	tuzzy	ADJ
ejpam-4972	471	8	(	(	PUNCT
ejpam-4972	471	9	i	i	PROPN
ejpam-4972	471	10	,	,	PUNCT
ejpam-4972	471	11	j)−	j)−	PROPN
ejpam-4972	471	12	gψ	gψ	VERB
ejpam-4972	471	13	−	−	PROPN
ejpam-4972	471	14	conts	cont	NOUN
ejpam-4972	471	15	.	.	PUNCT
ejpam-4972	472	1	then	then	ADV
ejpam-4972	472	2	,	,	PUNCT
ejpam-4972	472	3	assume	assume	VERB
ejpam-4972	472	4	(	(	PUNCT
ejpam-4972	472	5	g	g	NOUN
ejpam-4972	472	6	◦	◦	NOUN
ejpam-4972	472	7	t)(r1	t)(r1	NOUN
ejpam-4972	472	8	)	)	PUNCT
ejpam-4972	472	9	=	=	SYM
ejpam-4972	473	1	(	(	PUNCT
ejpam-4972	473	2	g	g	PROPN
ejpam-4972	473	3	◦	◦	NOUN
ejpam-4972	473	4	t)(r2	t)(r2	NOUN
ejpam-4972	473	5	)	)	PUNCT
ejpam-4972	473	6	.	.	PUNCT
ejpam-4972	474	1	then	then	ADV
ejpam-4972	474	2	g(t(r1	g(t(r1	ADJ
ejpam-4972	474	3	)	)	PUNCT
ejpam-4972	474	4	)	)	PUNCT
ejpam-4972	475	1	=	=	SYM
ejpam-4972	475	2	g(t(r2	g(t(r2	NOUN
ejpam-4972	475	3	)	)	PUNCT
ejpam-4972	475	4	)	)	PUNCT
ejpam-4972	475	5	,	,	PUNCT
ejpam-4972	475	6	as	as	SCONJ
ejpam-4972	475	7	t	t	PROPN
ejpam-4972	475	8	is	be	AUX
ejpam-4972	475	9	injective	injective	ADJ
ejpam-4972	475	10	,	,	PUNCT
ejpam-4972	475	11	then	then	ADV
ejpam-4972	475	12	g(r1	g(r1	PROPN
ejpam-4972	475	13	)	)	PUNCT
ejpam-4972	476	1	=	=	NOUN
ejpam-4972	476	2	g(r2	g(r2	NOUN
ejpam-4972	476	3	)	)	PUNCT
ejpam-4972	476	4	.	.	PUNCT
ejpam-4972	477	1	as	as	SCONJ
ejpam-4972	477	2	g	g	PROPN
ejpam-4972	477	3	is	be	AUX
ejpam-4972	477	4	injective	injective	ADJ
ejpam-4972	477	5	,	,	PUNCT
ejpam-4972	477	6	then	then	ADV
ejpam-4972	477	7	r1	r1	PROPN
ejpam-4972	477	8	=	=	SYM
ejpam-4972	477	9	r2	r2	PROPN
ejpam-4972	477	10	.	.	PUNCT
ejpam-4972	478	1	therefore	therefore	ADV
ejpam-4972	478	2	g	g	PROPN
ejpam-4972	478	3	◦	◦	PROPN
ejpam-4972	478	4	t	t	PROPN
ejpam-4972	478	5	is	be	AUX
ejpam-4972	478	6	injective	injective	ADJ
ejpam-4972	478	7	mapping	mapping	NOUN
ejpam-4972	478	8	.	.	PUNCT
ejpam-4972	479	1	also	also	ADV
ejpam-4972	479	2	,	,	PUNCT
ejpam-4972	479	3	assume	assume	VERB
ejpam-4972	479	4	c	c	PROPN
ejpam-4972	479	5	∈	∈	PROPN
ejpam-4972	479	6	z.	z.	PROPN
ejpam-4972	479	7	as	as	SCONJ
ejpam-4972	479	8	g	g	PROPN
ejpam-4972	479	9	is	be	AUX
ejpam-4972	479	10	surjective	surjective	ADJ
ejpam-4972	479	11	,	,	PUNCT
ejpam-4972	479	12	hence	hence	ADV
ejpam-4972	479	13	∃	∃	PROPN
ejpam-4972	479	14	b	b	PROPN
ejpam-4972	479	15	∈	∈	PROPN
ejpam-4972	479	16	y	y	PROPN
ejpam-4972	480	1	such	such	ADJ
ejpam-4972	480	2	that	that	SCONJ
ejpam-4972	480	3	g(b	g(b	NOUN
ejpam-4972	480	4	)	)	PUNCT
ejpam-4972	480	5	=	=	SYM
ejpam-4972	480	6	c.	c.	NOUN
ejpam-4972	480	7	as	as	SCONJ
ejpam-4972	480	8	t	t	PROPN
ejpam-4972	480	9	is	be	AUX
ejpam-4972	480	10	also	also	ADV
ejpam-4972	480	11	surjective	surjective	ADJ
ejpam-4972	480	12	,	,	PUNCT
ejpam-4972	480	13	hence	hence	ADV
ejpam-4972	480	14	for	for	ADP
ejpam-4972	480	15	any	any	DET
ejpam-4972	480	16	b	b	PROPN
ejpam-4972	480	17	∈	∈	PROPN
ejpam-4972	480	18	y	y	PROPN
ejpam-4972	480	19	∃	∃	PROPN
ejpam-4972	480	20	a	a	PROPN
ejpam-4972	480	21	∈	∈	PROPN
ejpam-4972	480	22	x	x	PUNCT
ejpam-4972	480	23	as	as	ADP
ejpam-4972	480	24	t(a	t(a	NOUN
ejpam-4972	480	25	)	)	PUNCT
ejpam-4972	481	1	=	=	SYM
ejpam-4972	481	2	b	b	NOUN
ejpam-4972	481	3	,	,	PUNCT
ejpam-4972	481	4	and	and	CCONJ
ejpam-4972	481	5	hence	hence	ADV
ejpam-4972	481	6	for	for	ADP
ejpam-4972	481	7	any	any	DET
ejpam-4972	481	8	c	c	PROPN
ejpam-4972	481	9	∈	∈	PROPN
ejpam-4972	481	10	z	z	PROPN
ejpam-4972	481	11	∃	∃	PROPN
ejpam-4972	481	12	a	a	PROPN
ejpam-4972	481	13	∈	∈	PROPN
ejpam-4972	481	14	x	x	PUNCT
ejpam-4972	481	15	such	such	ADJ
ejpam-4972	481	16	that	that	PRON
ejpam-4972	481	17	(	(	PUNCT
ejpam-4972	481	18	g	g	PROPN
ejpam-4972	481	19	◦	◦	NOUN
ejpam-4972	481	20	t)(a	t)(a	NUM
ejpam-4972	481	21	)	)	PUNCT
ejpam-4972	481	22	=	=	SYM
ejpam-4972	481	23	g(t(a	g(t(a	NOUN
ejpam-4972	481	24	)	)	PUNCT
ejpam-4972	481	25	)	)	PUNCT
ejpam-4972	482	1	=	=	PUNCT
ejpam-4972	482	2	g(b	g(b	X
ejpam-4972	482	3	)	)	PUNCT
ejpam-4972	482	4	=	=	SYM
ejpam-4972	482	5	c.	c.	NOUN
ejpam-4972	482	6	thus	thus	ADV
ejpam-4972	482	7	g	g	PROPN
ejpam-4972	482	8	◦	◦	PROPN
ejpam-4972	482	9	t	t	PROPN
ejpam-4972	482	10	is	be	AUX
ejpam-4972	482	11	surjection	surjection	NOUN
ejpam-4972	482	12	.	.	PUNCT
ejpam-4972	483	1	hence	hence	ADV
ejpam-4972	483	2	g	g	PROPN
ejpam-4972	483	3	◦	◦	PROPN
ejpam-4972	483	4	t	t	PROPN
ejpam-4972	483	5	is	be	AUX
ejpam-4972	483	6	bijective	bijective	ADJ
ejpam-4972	483	7	.	.	PUNCT
ejpam-4972	484	1	so	so	ADV
ejpam-4972	484	2	,	,	PUNCT
ejpam-4972	484	3	g	g	PROPN
ejpam-4972	484	4	◦	◦	PROPN
ejpam-4972	484	5	t	t	PROPN
ejpam-4972	484	6	is	be	AUX
ejpam-4972	484	7	fuzzy	fuzzy	ADJ
ejpam-4972	484	8	gψ−homomorphism	gψ−homomorphism	NOUN
ejpam-4972	484	9	.	.	PUNCT
ejpam-4972	485	1	corollary	corollary	ADJ
ejpam-4972	485	2	5	5	PROPN
ejpam-4972	485	3	.	.	PUNCT
ejpam-4972	485	4	suppose	suppose	VERB
ejpam-4972	485	5	t	t	NOUN
ejpam-4972	485	6	:	:	PUNCT
ejpam-4972	485	7	(	(	PUNCT
ejpam-4972	485	8	x	x	X
ejpam-4972	485	9	,	,	PUNCT
ejpam-4972	485	10	δ1	δ1	NOUN
ejpam-4972	485	11	,	,	PUNCT
ejpam-4972	485	12	δ2	δ2	ADJ
ejpam-4972	485	13	)	)	PUNCT
ejpam-4972	485	14	→	→	SYM
ejpam-4972	485	15	(	(	PUNCT
ejpam-4972	485	16	y	y	PROPN
ejpam-4972	485	17	,	,	PUNCT
ejpam-4972	485	18	σ1	σ1	PROPN
ejpam-4972	485	19	,	,	PUNCT
ejpam-4972	485	20	σ2	σ2	NOUN
ejpam-4972	485	21	)	)	PUNCT
ejpam-4972	485	22	is	be	AUX
ejpam-4972	485	23	fuzzy	fuzzy	ADJ
ejpam-4972	485	24	gψ−homomorphism	gψ−homomorphism	NOUN
ejpam-4972	485	25	,	,	PUNCT
ejpam-4972	485	26	(	(	PUNCT
ejpam-4972	485	27	i	i	PROPN
ejpam-4972	485	28	,	,	PUNCT
ejpam-4972	485	29	j	j	PROPN
ejpam-4972	485	30	)	)	PUNCT
ejpam-4972	485	31	−	−	PROPN
ejpam-4972	485	32	gψ	gψ	VERB
ejpam-4972	485	33	−	−	NOUN
ejpam-4972	485	34	strongly	strongly	ADV
ejpam-4972	485	35	conts	cont	NOUN
ejpam-4972	485	36	,	,	PUNCT
ejpam-4972	485	37	g	g	NOUN
ejpam-4972	485	38	:	:	PUNCT
ejpam-4972	485	39	(	(	PUNCT
ejpam-4972	485	40	y	y	PROPN
ejpam-4972	485	41	,	,	PUNCT
ejpam-4972	485	42	σ1	σ1	PROPN
ejpam-4972	485	43	,	,	PUNCT
ejpam-4972	485	44	σ2	σ2	NOUN
ejpam-4972	485	45	)	)	PUNCT
ejpam-4972	485	46	→	→	SYM
ejpam-4972	485	47	(	(	PUNCT
ejpam-4972	485	48	z	z	NOUN
ejpam-4972	485	49	,	,	PUNCT
ejpam-4972	485	50	η1	η1	NOUN
ejpam-4972	485	51	,	,	PUNCT
ejpam-4972	485	52	η2	η2	PROPN
ejpam-4972	485	53	)	)	PUNCT
ejpam-4972	485	54	is	be	AUX
ejpam-4972	485	55	gψ−homomorphism	gψ−homomorphism	NOUN
ejpam-4972	485	56	mapping	mapping	NOUN
ejpam-4972	485	57	.	.	PUNCT
ejpam-4972	486	1	then	then	ADV
ejpam-4972	486	2	g	g	PROPN
ejpam-4972	486	3	◦	◦	PROPN
ejpam-4972	486	4	t	t	PROPN
ejpam-4972	486	5	is	be	AUX
ejpam-4972	486	6	fuzzy	fuzzy	ADJ
ejpam-4972	486	7	gψ−homomorphism	gψ−homomorphism	NOUN
ejpam-4972	486	8	.	.	PUNCT
ejpam-4972	487	1	proof	proof	NOUN
ejpam-4972	487	2	.	.	PUNCT
ejpam-4972	488	1	since	since	SCONJ
ejpam-4972	488	2	t	t	PROPN
ejpam-4972	488	3	:	:	PUNCT
ejpam-4972	488	4	(	(	PUNCT
ejpam-4972	488	5	x	x	X
ejpam-4972	488	6	,	,	PUNCT
ejpam-4972	488	7	δ1	δ1	NOUN
ejpam-4972	488	8	,	,	PUNCT
ejpam-4972	488	9	δ2	δ2	ADJ
ejpam-4972	488	10	)	)	PUNCT
ejpam-4972	488	11	→	→	SYM
ejpam-4972	488	12	(	(	PUNCT
ejpam-4972	488	13	y	y	PROPN
ejpam-4972	488	14	,	,	PUNCT
ejpam-4972	488	15	σ1	σ1	PROPN
ejpam-4972	488	16	,	,	PUNCT
ejpam-4972	488	17	σ2	σ2	NOUN
ejpam-4972	488	18	)	)	PUNCT
ejpam-4972	488	19	is	be	AUX
ejpam-4972	488	20	fuzzy	fuzzy	ADJ
ejpam-4972	488	21	(	(	PUNCT
ejpam-4972	488	22	i	i	PROPN
ejpam-4972	488	23	,	,	PUNCT
ejpam-4972	488	24	j	j	PROPN
ejpam-4972	488	25	)	)	PUNCT
ejpam-4972	488	26	−	−	PROPN
ejpam-4972	488	27	gψ	gψ	VERB
ejpam-4972	488	28	−	−	NOUN
ejpam-4972	488	29	strongly	strongly	ADV
ejpam-4972	488	30	conts	cont	NOUN
ejpam-4972	488	31	,	,	PUNCT
ejpam-4972	488	32	so	so	ADV
ejpam-4972	488	33	by	by	ADP
ejpam-4972	488	34	theorem	theorem	NOUN
ejpam-4972	488	35	10	10	NUM
ejpam-4972	488	36	t	t	NOUN
ejpam-4972	488	37	is	be	AUX
ejpam-4972	488	38	fuzzy	fuzzy	ADJ
ejpam-4972	488	39	(	(	PUNCT
ejpam-4972	488	40	i	i	PROPN
ejpam-4972	488	41	,	,	PUNCT
ejpam-4972	488	42	j)−	j)−	PROPN
ejpam-4972	488	43	gψ	gψ	VERB
ejpam-4972	488	44	−	−	PROPN
ejpam-4972	488	45	irresolute	irresolute	ADJ
ejpam-4972	488	46	mapping	mapping	NOUN
ejpam-4972	488	47	,	,	PUNCT
ejpam-4972	488	48	and	and	CCONJ
ejpam-4972	488	49	hence	hence	ADV
ejpam-4972	488	50	by	by	ADP
ejpam-4972	488	51	theorem	theorem	NOUN
ejpam-4972	488	52	26	26	NUM
ejpam-4972	488	53	we	we	PRON
ejpam-4972	488	54	get	get	VERB
ejpam-4972	488	55	the	the	DET
ejpam-4972	488	56	desired	desire	VERB
ejpam-4972	488	57	.	.	PUNCT
ejpam-4972	489	1	theorem	theorem	ADJ
ejpam-4972	489	2	27	27	NUM
ejpam-4972	489	3	.	.	PUNCT
ejpam-4972	490	1	suppose	suppose	VERB
ejpam-4972	490	2	t	t	NOUN
ejpam-4972	490	3	:	:	PUNCT
ejpam-4972	490	4	(	(	PUNCT
ejpam-4972	490	5	x	x	X
ejpam-4972	490	6	,	,	PUNCT
ejpam-4972	490	7	δ1	δ1	NOUN
ejpam-4972	490	8	,	,	PUNCT
ejpam-4972	490	9	δ2	δ2	ADJ
ejpam-4972	490	10	)	)	PUNCT
ejpam-4972	490	11	→	→	SYM
ejpam-4972	490	12	(	(	PUNCT
ejpam-4972	490	13	y	y	PROPN
ejpam-4972	490	14	,	,	PUNCT
ejpam-4972	490	15	σ1	σ1	PROPN
ejpam-4972	490	16	,	,	PUNCT
ejpam-4972	490	17	σ2	σ2	PROPN
ejpam-4972	490	18	)	)	PUNCT
ejpam-4972	490	19	is	be	AUX
ejpam-4972	490	20	bijective	bijective	ADJ
ejpam-4972	490	21	function	function	NOUN
ejpam-4972	490	22	,	,	PUNCT
ejpam-4972	490	23	t−1	t−1	PROPN
ejpam-4972	490	24	is	be	AUX
ejpam-4972	490	25	(	(	PUNCT
ejpam-4972	490	26	i	i	PROPN
ejpam-4972	490	27	,	,	PUNCT
ejpam-4972	490	28	j)−gψ−	j)−gψ−	PROPN
ejpam-4972	490	29	conts	conts	PROPN
ejpam-4972	490	30	mapping	mapping	NOUN
ejpam-4972	490	31	.	.	PUNCT
ejpam-4972	491	1	then	then	ADV
ejpam-4972	491	2	t	t	PROPN
ejpam-4972	491	3	is	be	AUX
ejpam-4972	491	4	(	(	PUNCT
ejpam-4972	491	5	i	i	PROPN
ejpam-4972	491	6	,	,	PUNCT
ejpam-4972	491	7	j)−	j)−	PROPN
ejpam-4972	491	8	gψ	gψ	VERB
ejpam-4972	491	9	−	−	PROPN
ejpam-4972	491	10	open	open	ADJ
ejpam-4972	491	11	(	(	PUNCT
ejpam-4972	491	12	resp	resp	NOUN
ejpam-4972	491	13	,	,	PUNCT
ejpam-4972	491	14	(	(	PUNCT
ejpam-4972	491	15	i	i	PROPN
ejpam-4972	491	16	,	,	PUNCT
ejpam-4972	491	17	j)−	j)−	PROPN
ejpam-4972	491	18	gψ	gψ	VERB
ejpam-4972	491	19	−	−	PROPN
ejpam-4972	491	20	closed	closed	ADJ
ejpam-4972	491	21	)	)	PUNCT
ejpam-4972	491	22	mapping	mapping	NOUN
ejpam-4972	491	23	.	.	PUNCT
ejpam-4972	492	1	proof	proof	NOUN
ejpam-4972	492	2	.	.	PUNCT
ejpam-4972	493	1	assume	assume	VERB
ejpam-4972	493	2	t−1	t−1	PROPN
ejpam-4972	493	3	is	be	AUX
ejpam-4972	493	4	fuzzy	fuzzy	ADJ
ejpam-4972	493	5	(	(	PUNCT
ejpam-4972	493	6	i	i	PROPN
ejpam-4972	493	7	,	,	PUNCT
ejpam-4972	493	8	j	j	PROPN
ejpam-4972	493	9	)	)	PUNCT
ejpam-4972	493	10	−	−	PROPN
ejpam-4972	493	11	gψ	gψ	VERB
ejpam-4972	493	12	−	−	PROPN
ejpam-4972	493	13	conts	cont	NOUN
ejpam-4972	493	14	,	,	PUNCT
ejpam-4972	493	15	r	r	NOUN
ejpam-4972	493	16	is	be	AUX
ejpam-4972	493	17	fuzzy	fuzzy	ADJ
ejpam-4972	493	18	(	(	PUNCT
ejpam-4972	493	19	i	i	PROPN
ejpam-4972	493	20	,	,	PUNCT
ejpam-4972	493	21	j	j	PROPN
ejpam-4972	493	22	)	)	PUNCT
ejpam-4972	493	23	−	−	PROPN
ejpam-4972	493	24	gψ	gψ	VERB
ejpam-4972	493	25	−	−	PROPN
ejpam-4972	493	26	open	open	ADJ
ejpam-4972	493	27	of	of	ADP
ejpam-4972	493	28	x.	x.	NOUN
ejpam-4972	493	29	then	then	ADV
ejpam-4972	493	30	t−1(r	t−1(r	PROPN
ejpam-4972	493	31	)	)	PUNCT
ejpam-4972	493	32	∈	∈	PROPN
ejpam-4972	493	33	σj	σj	NOUN
ejpam-4972	493	34	,	,	PUNCT
ejpam-4972	493	35	hence	hence	ADV
ejpam-4972	493	36	t	t	PROPN
ejpam-4972	493	37	−1(r	−1(r	PROPN
ejpam-4972	493	38	)	)	PUNCT
ejpam-4972	493	39	is	be	AUX
ejpam-4972	493	40	fuzzy	fuzzy	ADJ
ejpam-4972	493	41	(	(	PUNCT
ejpam-4972	493	42	i	i	PROPN
ejpam-4972	493	43	,	,	PUNCT
ejpam-4972	493	44	j	j	PROPN
ejpam-4972	493	45	)	)	PUNCT
ejpam-4972	493	46	−	−	PROPN
ejpam-4972	493	47	gψ	gψ	VERB
ejpam-4972	493	48	−	−	PROPN
ejpam-4972	493	49	open	open	ADJ
ejpam-4972	493	50	of	of	ADP
ejpam-4972	493	51	y	y	PROPN
ejpam-4972	493	52	.	.	PUNCT
ejpam-4972	494	1	as	as	SCONJ
ejpam-4972	494	2	t	t	PROPN
ejpam-4972	494	3	is	be	AUX
ejpam-4972	494	4	bijection	bijection	ADJ
ejpam-4972	494	5	,	,	PUNCT
ejpam-4972	494	6	then	then	ADV
ejpam-4972	494	7	(	(	PUNCT
ejpam-4972	494	8	t−1)−1(r	t−1)−1(r	NOUN
ejpam-4972	494	9	)	)	PUNCT
ejpam-4972	494	10	=	=	SYM
ejpam-4972	494	11	t(r	t(r	NOUN
ejpam-4972	494	12	)	)	PUNCT
ejpam-4972	494	13	.	.	PUNCT
ejpam-4972	495	1	so	so	ADV
ejpam-4972	495	2	t(r	t(r	ADV
ejpam-4972	495	3	)	)	PUNCT
ejpam-4972	495	4	is	be	AUX
ejpam-4972	495	5	fuzzy	fuzzy	ADJ
ejpam-4972	495	6	(	(	PUNCT
ejpam-4972	495	7	i	i	NOUN
ejpam-4972	495	8	,	,	PUNCT
ejpam-4972	495	9	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	495	10	of	of	ADP
ejpam-4972	495	11	y	y	PROPN
ejpam-4972	495	12	.	.	PUNCT
ejpam-4972	496	1	so	so	ADV
ejpam-4972	496	2	,	,	PUNCT
ejpam-4972	496	3	t	t	PROPN
ejpam-4972	496	4	is	be	AUX
ejpam-4972	496	5	fuzzy	fuzzy	ADJ
ejpam-4972	496	6	(	(	PUNCT
ejpam-4972	496	7	i	i	NOUN
ejpam-4972	496	8	,	,	PUNCT
ejpam-4972	496	9	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	496	10	mapping	mapping	NOUN
ejpam-4972	496	11	.	.	PUNCT
ejpam-4972	497	1	corollary	corollary	ADJ
ejpam-4972	497	2	6	6	NUM
ejpam-4972	497	3	.	.	PUNCT
ejpam-4972	497	4	suppose	suppose	VERB
ejpam-4972	497	5	t	t	NOUN
ejpam-4972	497	6	:	:	PUNCT
ejpam-4972	497	7	(	(	PUNCT
ejpam-4972	497	8	x	x	X
ejpam-4972	497	9	,	,	PUNCT
ejpam-4972	497	10	δ1	δ1	NOUN
ejpam-4972	497	11	,	,	PUNCT
ejpam-4972	497	12	δ2	δ2	ADJ
ejpam-4972	497	13	)	)	PUNCT
ejpam-4972	497	14	→	→	SYM
ejpam-4972	497	15	(	(	PUNCT
ejpam-4972	497	16	y	y	PROPN
ejpam-4972	497	17	,	,	PUNCT
ejpam-4972	497	18	σ1	σ1	PROPN
ejpam-4972	497	19	,	,	PUNCT
ejpam-4972	497	20	σ2	σ2	PROPN
ejpam-4972	497	21	)	)	PUNCT
ejpam-4972	497	22	is	be	AUX
ejpam-4972	497	23	bijective	bijective	ADJ
ejpam-4972	497	24	function	function	NOUN
ejpam-4972	497	25	,	,	PUNCT
ejpam-4972	497	26	gψ−homomorphism	gψ−homomorphism	NOUN
ejpam-4972	497	27	.	.	PUNCT
ejpam-4972	498	1	then	then	ADV
ejpam-4972	498	2	t	t	PROPN
ejpam-4972	498	3	is	be	AUX
ejpam-4972	498	4	(	(	PUNCT
ejpam-4972	498	5	i	i	PROPN
ejpam-4972	498	6	,	,	PUNCT
ejpam-4972	498	7	j)−	j)−	PROPN
ejpam-4972	498	8	gψ	gψ	VERB
ejpam-4972	498	9	−	−	PROPN
ejpam-4972	498	10	open	open	ADJ
ejpam-4972	498	11	(	(	PUNCT
ejpam-4972	498	12	resp	resp	NOUN
ejpam-4972	498	13	,	,	PUNCT
ejpam-4972	498	14	(	(	PUNCT
ejpam-4972	498	15	i	i	PROPN
ejpam-4972	498	16	,	,	PUNCT
ejpam-4972	498	17	j)−	j)−	PROPN
ejpam-4972	498	18	gψ	gψ	VERB
ejpam-4972	498	19	−	−	PROPN
ejpam-4972	498	20	closed	closed	ADJ
ejpam-4972	498	21	)	)	PUNCT
ejpam-4972	498	22	mapping	mapping	NOUN
ejpam-4972	498	23	.	.	PUNCT
ejpam-4972	499	1	proof	proof	NOUN
ejpam-4972	499	2	.	.	PUNCT
ejpam-4972	500	1	assume	assume	VERB
ejpam-4972	500	2	t	t	PROPN
ejpam-4972	500	3	is	be	AUX
ejpam-4972	500	4	fuzzy	fuzzy	ADJ
ejpam-4972	500	5	gψ−homomorphism	gψ−homomorphism	NOUN
ejpam-4972	500	6	.	.	PUNCT
ejpam-4972	501	1	then	then	ADV
ejpam-4972	501	2	by	by	ADP
ejpam-4972	501	3	definition	definition	NOUN
ejpam-4972	501	4	12	12	NUM
ejpam-4972	501	5	we	we	PRON
ejpam-4972	501	6	find	find	VERB
ejpam-4972	501	7	t−1	t−1	PROPN
ejpam-4972	501	8	is	be	AUX
ejpam-4972	501	9	(	(	PUNCT
ejpam-4972	501	10	i	i	PROPN
ejpam-4972	501	11	,	,	PUNCT
ejpam-4972	501	12	j)−	j)−	PROPN
ejpam-4972	501	13	gψ	gψ	VERB
ejpam-4972	501	14	−	−	PROPN
ejpam-4972	501	15	conts	cont	NOUN
ejpam-4972	501	16	mapping	mapping	NOUN
ejpam-4972	501	17	,	,	PUNCT
ejpam-4972	501	18	hence	hence	ADV
ejpam-4972	501	19	by	by	ADP
ejpam-4972	501	20	theorem	theorem	ADJ
ejpam-4972	501	21	27	27	NUM
ejpam-4972	501	22	achieved	achieve	VERB
ejpam-4972	501	23	what	what	PRON
ejpam-4972	501	24	we	we	PRON
ejpam-4972	501	25	want	want	VERB
ejpam-4972	501	26	to	to	PART
ejpam-4972	501	27	be	be	AUX
ejpam-4972	501	28	proved	prove	VERB
ejpam-4972	501	29	.	.	PUNCT
ejpam-4972	502	1	in	in	ADP
ejpam-4972	502	2	the	the	DET
ejpam-4972	502	3	following	follow	VERB
ejpam-4972	502	4	table	table	NOUN
ejpam-4972	502	5	,	,	PUNCT
ejpam-4972	502	6	we	we	PRON
ejpam-4972	502	7	summarize	summarize	VERB
ejpam-4972	502	8	the	the	DET
ejpam-4972	502	9	composition	composition	NOUN
ejpam-4972	502	10	process	process	NOUN
ejpam-4972	502	11	among	among	ADP
ejpam-4972	502	12	all	all	DET
ejpam-4972	502	13	types	type	NOUN
ejpam-4972	502	14	of	of	ADP
ejpam-4972	502	15	functions	function	NOUN
ejpam-4972	502	16	:	:	PUNCT
ejpam-4972	502	17	(	(	PUNCT
ejpam-4972	502	18	i	i	NOUN
ejpam-4972	502	19	,	,	PUNCT
ejpam-4972	502	20	j)−gψ−conts	j)−gψ−cont	NOUN
ejpam-4972	502	21	,	,	PUNCT
ejpam-4972	502	22	(	(	PUNCT
ejpam-4972	502	23	i	i	PROPN
ejpam-4972	502	24	,	,	PUNCT
ejpam-4972	502	25	j)−gψ−stronglyconts	j)−gψ−stronglyconts	PROPN
ejpam-4972	502	26	,	,	PUNCT
ejpam-4972	502	27	(	(	PUNCT
ejpam-4972	502	28	i	i	X
ejpam-4972	502	29	,	,	PUNCT
ejpam-4972	502	30	j)−gψ−irresolute	j)−gψ−irresolute	PROPN
ejpam-4972	502	31	,	,	PUNCT
ejpam-4972	502	32	(	(	PUNCT
ejpam-4972	502	33	i	i	NOUN
ejpam-4972	502	34	,	,	PUNCT
ejpam-4972	502	35	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	502	36	,	,	PUNCT
ejpam-4972	502	37	δj	δj	ADJ
ejpam-4972	502	38	−ψ−	−ψ−	NOUN
ejpam-4972	502	39	conts	cont	NOUN
ejpam-4972	502	40	,	,	PUNCT
ejpam-4972	502	41	δj	δj	ADP
ejpam-4972	502	42	−	−	PROPN
ejpam-4972	502	43	open	open	ADJ
ejpam-4972	502	44	,	,	PUNCT
ejpam-4972	502	45	σj	σj	VERB
ejpam-4972	502	46	−	−	PROPN
ejpam-4972	502	47	conts	cont	NOUN
ejpam-4972	502	48	,	,	PUNCT
ejpam-4972	502	49	and	and	CCONJ
ejpam-4972	502	50	σj	σj	VERB
ejpam-4972	502	51	−	−	PROPN
ejpam-4972	502	52	open	open	ADJ
ejpam-4972	502	53	,	,	PUNCT
ejpam-4972	502	54	where	where	SCONJ
ejpam-4972	502	55	zero	zero	NUM
ejpam-4972	502	56	indicates	indicate	VERB
ejpam-4972	502	57	that	that	SCONJ
ejpam-4972	502	58	there	there	PRON
ejpam-4972	502	59	is	be	VERB
ejpam-4972	502	60	no	no	DET
ejpam-4972	502	61	result	result	NOUN
ejpam-4972	502	62	of	of	ADP
ejpam-4972	502	63	the	the	DET
ejpam-4972	502	64	outcome	outcome	NOUN
ejpam-4972	502	65	while	while	SCONJ
ejpam-4972	502	66	1	1	NUM
ejpam-4972	502	67	indicates	indicate	VERB
ejpam-4972	502	68	that	that	SCONJ
ejpam-4972	502	69	the	the	DET
ejpam-4972	502	70	composition	composition	NOUN
ejpam-4972	502	71	process	process	NOUN
ejpam-4972	502	72	is	be	AUX
ejpam-4972	502	73	possible	possible	ADJ
ejpam-4972	502	74	and	and	CCONJ
ejpam-4972	502	75	has	have	VERB
ejpam-4972	502	76	a	a	DET
ejpam-4972	502	77	result	result	NOUN
ejpam-4972	502	78	.	.	PUNCT
ejpam-4972	503	1	a.	a.	NOUN
ejpam-4972	503	2	a.	a.	PROPN
ejpam-4972	503	3	alharbi	alharbi	PROPN
ejpam-4972	503	4	,	,	PUNCT
ejpam-4972	503	5	a.	a.	NOUN
ejpam-4972	503	6	kilicman	kilicman	PROPN
ejpam-4972	503	7	/	/	SYM
ejpam-4972	503	8	eur	eur	PROPN
ejpam-4972	503	9	.	.	PUNCT
ejpam-4972	504	1	j.	j.	PROPN
ejpam-4972	504	2	pure	pure	PROPN
ejpam-4972	504	3	appl	appl	PROPN
ejpam-4972	504	4	.	.	PROPN
ejpam-4972	504	5	math	math	PROPN
ejpam-4972	504	6	,	,	PUNCT
ejpam-4972	504	7	16	16	NUM
ejpam-4972	504	8	(	(	PUNCT
ejpam-4972	504	9	4	4	NUM
ejpam-4972	504	10	)	)	PUNCT
ejpam-4972	504	11	(	(	PUNCT
ejpam-4972	504	12	2023	2023	NUM
ejpam-4972	504	13	)	)	PUNCT
ejpam-4972	504	14	,	,	PUNCT
ejpam-4972	504	15	2613	2613	NUM
ejpam-4972	504	16	-	-	SYM
ejpam-4972	504	17	2631	2631	NUM
ejpam-4972	504	18	2629	2629	NUM
ejpam-4972	504	19	remark	remark	NOUN
ejpam-4972	504	20	10	10	NUM
ejpam-4972	504	21	.	.	PUNCT
ejpam-4972	505	1	(	(	PUNCT
ejpam-4972	505	2	1	1	X
ejpam-4972	505	3	)	)	PUNCT
ejpam-4972	505	4	to	to	PART
ejpam-4972	505	5	clarify	clarify	VERB
ejpam-4972	505	6	further	far	ADV
ejpam-4972	505	7	,	,	PUNCT
ejpam-4972	505	8	for	for	ADP
ejpam-4972	505	9	example	example	NOUN
ejpam-4972	505	10	,	,	PUNCT
ejpam-4972	505	11	if	if	SCONJ
ejpam-4972	505	12	g	g	PROPN
ejpam-4972	505	13	is	be	AUX
ejpam-4972	505	14	(	(	PUNCT
ejpam-4972	505	15	i	i	NOUN
ejpam-4972	505	16	,	,	PUNCT
ejpam-4972	505	17	j)−gψ−open	j)−gψ−open	PROPN
ejpam-4972	505	18	and	and	CCONJ
ejpam-4972	505	19	t	t	PROPN
ejpam-4972	505	20	is	be	AUX
ejpam-4972	505	21	(	(	PUNCT
ejpam-4972	505	22	i	i	PROPN
ejpam-4972	505	23	,	,	PUNCT
ejpam-4972	505	24	j)−	j)−	PROPN
ejpam-4972	505	25	gψ	gψ	VERB
ejpam-4972	505	26	−	−	PROPN
ejpam-4972	505	27	irresolute	irresolute	ADJ
ejpam-4972	505	28	,	,	PUNCT
ejpam-4972	505	29	we	we	PRON
ejpam-4972	505	30	notice	notice	VERB
ejpam-4972	505	31	from	from	ADP
ejpam-4972	505	32	the	the	DET
ejpam-4972	505	33	table	table	NOUN
ejpam-4972	505	34	that	that	SCONJ
ejpam-4972	505	35	the	the	DET
ejpam-4972	505	36	result	result	NOUN
ejpam-4972	505	37	of	of	ADP
ejpam-4972	505	38	the	the	DET
ejpam-4972	505	39	composition	composition	NOUN
ejpam-4972	505	40	process	process	NOUN
ejpam-4972	505	41	is	be	AUX
ejpam-4972	505	42	equal	equal	ADJ
ejpam-4972	505	43	to	to	ADP
ejpam-4972	505	44	0	0	NUM
ejpam-4972	505	45	because	because	SCONJ
ejpam-4972	505	46	of	of	ADP
ejpam-4972	505	47	the	the	DET
ejpam-4972	505	48	difference	difference	NOUN
ejpam-4972	505	49	in	in	ADP
ejpam-4972	505	50	the	the	DET
ejpam-4972	505	51	effect	effect	NOUN
ejpam-4972	505	52	of	of	ADP
ejpam-4972	505	53	domains	domain	NOUN
ejpam-4972	505	54	,	,	PUNCT
ejpam-4972	505	55	as	as	SCONJ
ejpam-4972	505	56	t	t	PROPN
ejpam-4972	505	57	is	be	AUX
ejpam-4972	505	58	moved	move	VERB
ejpam-4972	505	59	from	from	ADP
ejpam-4972	505	60	y	y	PROPN
ejpam-4972	505	61	to	to	ADP
ejpam-4972	505	62	x	x	PRON
ejpam-4972	505	63	,	,	PUNCT
ejpam-4972	505	64	but	but	CCONJ
ejpam-4972	505	65	g	g	NOUN
ejpam-4972	505	66	is	be	AUX
ejpam-4972	505	67	moved	move	VERB
ejpam-4972	505	68	from	from	ADP
ejpam-4972	505	69	y	y	PROPN
ejpam-4972	505	70	to	to	ADP
ejpam-4972	505	71	z	z	PROPN
ejpam-4972	505	72	,	,	PUNCT
ejpam-4972	505	73	there	there	PRON
ejpam-4972	505	74	is	be	VERB
ejpam-4972	505	75	no	no	DET
ejpam-4972	505	76	connection	connection	NOUN
ejpam-4972	505	77	between	between	ADP
ejpam-4972	505	78	x	x	PROPN
ejpam-4972	505	79	and	and	CCONJ
ejpam-4972	505	80	z	z	NOUN
ejpam-4972	505	81	,	,	PUNCT
ejpam-4972	505	82	so	so	ADV
ejpam-4972	505	83	the	the	DET
ejpam-4972	505	84	result	result	NOUN
ejpam-4972	505	85	equals	equal	VERB
ejpam-4972	505	86	0	0	NUM
ejpam-4972	505	87	,	,	PUNCT
ejpam-4972	505	88	while	while	SCONJ
ejpam-4972	505	89	we	we	PRON
ejpam-4972	505	90	find	find	VERB
ejpam-4972	505	91	that	that	SCONJ
ejpam-4972	505	92	if	if	SCONJ
ejpam-4972	505	93	g	g	PROPN
ejpam-4972	505	94	,	,	PUNCT
ejpam-4972	505	95	t	t	PROPN
ejpam-4972	505	96	are	be	AUX
ejpam-4972	505	97	(	(	PUNCT
ejpam-4972	505	98	i	i	PROPN
ejpam-4972	505	99	,	,	PUNCT
ejpam-4972	505	100	j)−	j)−	PROPN
ejpam-4972	505	101	gψ	gψ	VERB
ejpam-4972	505	102	−	−	PROPN
ejpam-4972	505	103	irresolute	irresolute	ADJ
ejpam-4972	505	104	,	,	PUNCT
ejpam-4972	505	105	thus	thus	ADV
ejpam-4972	505	106	g	g	ADP
ejpam-4972	505	107	◦	◦	NOUN
ejpam-4972	505	108	t	t	X
ejpam-4972	505	109	=	=	SYM
ejpam-4972	505	110	1	1	NUM
ejpam-4972	505	111	,	,	PUNCT
ejpam-4972	505	112	because	because	SCONJ
ejpam-4972	505	113	g	g	PROPN
ejpam-4972	505	114	◦	◦	PROPN
ejpam-4972	505	115	t	t	PROPN
ejpam-4972	505	116	has	have	VERB
ejpam-4972	505	117	a	a	DET
ejpam-4972	505	118	result	result	NOUN
ejpam-4972	505	119	and	and	CCONJ
ejpam-4972	505	120	its	its	PRON
ejpam-4972	505	121	(	(	PUNCT
ejpam-4972	505	122	i	i	PROPN
ejpam-4972	505	123	,	,	PUNCT
ejpam-4972	505	124	j)−	j)−	PROPN
ejpam-4972	505	125	gψ	gψ	VERB
ejpam-4972	505	126	−	−	PROPN
ejpam-4972	505	127	irresolute	irresolute	ADJ
ejpam-4972	505	128	too	too	ADV
ejpam-4972	505	129	,	,	PUNCT
ejpam-4972	505	130	see	see	VERB
ejpam-4972	505	131	theorem	theorem	VERB
ejpam-4972	505	132	16	16	NUM
ejpam-4972	505	133	.	.	PUNCT
ejpam-4972	506	1	(	(	PUNCT
ejpam-4972	506	2	2	2	X
ejpam-4972	506	3	)	)	PUNCT
ejpam-4972	506	4	we	we	PRON
ejpam-4972	506	5	would	would	AUX
ejpam-4972	506	6	like	like	VERB
ejpam-4972	506	7	to	to	PART
ejpam-4972	506	8	note	note	VERB
ejpam-4972	506	9	that	that	SCONJ
ejpam-4972	506	10	the	the	DET
ejpam-4972	506	11	composition	composition	NOUN
ejpam-4972	506	12	process	process	NOUN
ejpam-4972	506	13	collecting	collect	VERB
ejpam-4972	506	14	t	t	PROPN
ejpam-4972	506	15	,	,	PUNCT
ejpam-4972	506	16	g	g	PROPN
ejpam-4972	506	17	is	be	AUX
ejpam-4972	506	18	not	not	PART
ejpam-4972	506	19	equal	equal	ADJ
ejpam-4972	506	20	to	to	ADP
ejpam-4972	506	21	the	the	DET
ejpam-4972	506	22	process	process	NOUN
ejpam-4972	506	23	of	of	ADP
ejpam-4972	506	24	collecting	collect	VERB
ejpam-4972	506	25	g	g	NOUN
ejpam-4972	506	26	,	,	PUNCT
ejpam-4972	506	27	t.	t.	X
ejpam-4972	506	28	i.e.	i.e.	X
ejpam-4972	506	29	g	g	PROPN
ejpam-4972	506	30	◦	◦	NOUN
ejpam-4972	506	31	t	t	PROPN
ejpam-4972	506	32	̸=	̸=	PROPN
ejpam-4972	506	33	t	t	PROPN
ejpam-4972	506	34	◦	◦	NOUN
ejpam-4972	506	35	g.	g.	PROPN
ejpam-4972	506	36	(	(	PUNCT
ejpam-4972	506	37	3	3	X
ejpam-4972	506	38	)	)	PUNCT
ejpam-4972	506	39	a	a	DET
ejpam-4972	506	40	detailed	detailed	ADJ
ejpam-4972	506	41	explanation	explanation	NOUN
ejpam-4972	506	42	of	of	ADP
ejpam-4972	506	43	the	the	DET
ejpam-4972	506	44	resultant	resultant	NOUN
ejpam-4972	506	45	of	of	ADP
ejpam-4972	506	46	the	the	DET
ejpam-4972	506	47	composition	composition	NOUN
ejpam-4972	506	48	,	,	PUNCT
ejpam-4972	506	49	t	t	NOUN
ejpam-4972	506	50	if	if	SCONJ
ejpam-4972	506	51	δj	δj	VERB
ejpam-4972	506	52	−	−	PROPN
ejpam-4972	506	53	open	open	ADJ
ejpam-4972	506	54	and	and	CCONJ
ejpam-4972	506	55	g	g	NOUN
ejpam-4972	506	56	if	if	SCONJ
ejpam-4972	506	57	(	(	PUNCT
ejpam-4972	506	58	i	i	NOUN
ejpam-4972	506	59	,	,	PUNCT
ejpam-4972	506	60	j)−	j)−	PROPN
ejpam-4972	506	61	gψ	gψ	VERB
ejpam-4972	506	62	−	−	PROPN
ejpam-4972	506	63	open	open	ADJ
ejpam-4972	506	64	.	.	PUNCT
ejpam-4972	507	1	the	the	DET
ejpam-4972	507	2	reslut	reslut	NOUN
ejpam-4972	507	3	g	g	PROPN
ejpam-4972	507	4	◦	◦	NOUN
ejpam-4972	507	5	t	t	PROPN
ejpam-4972	507	6	=	=	SYM
ejpam-4972	507	7	0	0	NUM
ejpam-4972	507	8	,	,	PUNCT
ejpam-4972	507	9	but	but	CCONJ
ejpam-4972	507	10	(	(	PUNCT
ejpam-4972	507	11	g	g	NOUN
ejpam-4972	507	12	◦	◦	NOUN
ejpam-4972	507	13	t)(k	t)(k	NOUN
ejpam-4972	507	14	)	)	PUNCT
ejpam-4972	507	15	is	be	AUX
ejpam-4972	507	16	(	(	PUNCT
ejpam-4972	507	17	i	i	PROPN
ejpam-4972	507	18	,	,	PUNCT
ejpam-4972	507	19	j)−	j)−	PROPN
ejpam-4972	507	20	gψ	gψ	VERB
ejpam-4972	507	21	−	−	DET
ejpam-4972	507	22	open	open	ADJ
ejpam-4972	507	23	group	group	NOUN
ejpam-4972	507	24	of	of	ADP
ejpam-4972	507	25	z	z	PROPN
ejpam-4972	507	26	,	,	PUNCT
ejpam-4972	507	27	when	when	SCONJ
ejpam-4972	507	28	k	k	PROPN
ejpam-4972	507	29	is	be	AUX
ejpam-4972	507	30	open	open	ADJ
ejpam-4972	507	31	group	group	NOUN
ejpam-4972	507	32	of	of	ADP
ejpam-4972	507	33	x.	x.	PROPN
ejpam-4972	507	34	7	7	NUM
ejpam-4972	507	35	.	.	PUNCT
ejpam-4972	507	36	conclusion	conclusion	NOUN
ejpam-4972	507	37	in	in	ADP
ejpam-4972	507	38	this	this	DET
ejpam-4972	507	39	research	research	NOUN
ejpam-4972	507	40	,	,	PUNCT
ejpam-4972	507	41	we	we	PRON
ejpam-4972	507	42	have	have	AUX
ejpam-4972	507	43	delved	delve	VERB
ejpam-4972	507	44	into	into	ADP
ejpam-4972	507	45	the	the	DET
ejpam-4972	507	46	structures	structure	NOUN
ejpam-4972	507	47	of	of	ADP
ejpam-4972	507	48	various	various	ADJ
ejpam-4972	507	49	functions	function	NOUN
ejpam-4972	507	50	within	within	ADP
ejpam-4972	507	51	generalized	generalized	ADJ
ejpam-4972	507	52	closed	closed	ADJ
ejpam-4972	507	53	groups	group	NOUN
ejpam-4972	507	54	in	in	ADP
ejpam-4972	507	55	the	the	DET
ejpam-4972	507	56	context	context	NOUN
ejpam-4972	507	57	of	of	ADP
ejpam-4972	507	58	bitopological	bitopological	ADJ
ejpam-4972	507	59	fuzzy	fuzzy	ADJ
ejpam-4972	507	60	spaces	space	NOUN
ejpam-4972	507	61	.	.	PUNCT
ejpam-4972	508	1	additionally	additionally	ADV
ejpam-4972	508	2	,	,	PUNCT
ejpam-4972	508	3	we	we	PRON
ejpam-4972	508	4	have	have	AUX
ejpam-4972	508	5	explored	explore	VERB
ejpam-4972	508	6	the	the	DET
ejpam-4972	508	7	interconnections	interconnection	NOUN
ejpam-4972	508	8	among	among	ADP
ejpam-4972	508	9	these	these	DET
ejpam-4972	508	10	functions	function	NOUN
ejpam-4972	508	11	.	.	PUNCT
ejpam-4972	509	1	subsequently	subsequently	ADV
ejpam-4972	509	2	,	,	PUNCT
ejpam-4972	509	3	we	we	PRON
ejpam-4972	509	4	have	have	AUX
ejpam-4972	509	5	scrutinized	scrutinize	VERB
ejpam-4972	509	6	fundamental	fundamental	ADJ
ejpam-4972	509	7	theorems	theorem	NOUN
ejpam-4972	509	8	and	and	CCONJ
ejpam-4972	509	9	distinctive	distinctive	ADJ
ejpam-4972	509	10	characteristics	characteristic	NOUN
ejpam-4972	509	11	associated	associate	VERB
ejpam-4972	509	12	with	with	ADP
ejpam-4972	509	13	these	these	DET
ejpam-4972	509	14	concepts	concept	NOUN
ejpam-4972	509	15	.	.	PUNCT
ejpam-4972	510	1	through	through	ADP
ejpam-4972	510	2	this	this	DET
ejpam-4972	510	3	in	in	ADP
ejpam-4972	510	4	-	-	PUNCT
ejpam-4972	510	5	depth	depth	NOUN
ejpam-4972	510	6	analysis	analysis	NOUN
ejpam-4972	510	7	,	,	PUNCT
ejpam-4972	510	8	we	we	PRON
ejpam-4972	510	9	contribute	contribute	VERB
ejpam-4972	510	10	to	to	ADP
ejpam-4972	510	11	a	a	DET
ejpam-4972	510	12	better	well	ADJ
ejpam-4972	510	13	comprehension	comprehension	NOUN
ejpam-4972	510	14	of	of	ADP
ejpam-4972	510	15	these	these	DET
ejpam-4972	510	16	key	key	ADJ
ejpam-4972	510	17	ideas	idea	NOUN
ejpam-4972	510	18	in	in	ADP
ejpam-4972	510	19	the	the	DET
ejpam-4972	510	20	references	reference	NOUN
ejpam-4972	510	21	2630	2630	NUM
ejpam-4972	510	22	context	context	NOUN
ejpam-4972	510	23	of	of	ADP
ejpam-4972	510	24	fuzzy	fuzzy	ADJ
ejpam-4972	510	25	bitopological	bitopological	ADJ
ejpam-4972	510	26	spaces	space	NOUN
ejpam-4972	510	27	.	.	PUNCT
ejpam-4972	511	1	this	this	DET
ejpam-4972	511	2	work	work	NOUN
ejpam-4972	511	3	also	also	ADV
ejpam-4972	511	4	opens	open	VERB
ejpam-4972	511	5	up	up	ADP
ejpam-4972	511	6	new	new	ADJ
ejpam-4972	511	7	horizons	horizon	NOUN
ejpam-4972	511	8	for	for	ADP
ejpam-4972	511	9	the	the	DET
ejpam-4972	511	10	future	future	ADJ
ejpam-4972	511	11	study	study	NOUN
ejpam-4972	511	12	of	of	ADP
ejpam-4972	511	13	these	these	DET
ejpam-4972	511	14	functions	function	NOUN
ejpam-4972	511	15	in	in	ADP
ejpam-4972	511	16	other	other	ADJ
ejpam-4972	511	17	fields	field	NOUN
ejpam-4972	511	18	such	such	ADJ
ejpam-4972	511	19	as	as	ADP
ejpam-4972	511	20	fuzzy	fuzzy	ADJ
ejpam-4972	511	21	sets	set	NOUN
ejpam-4972	511	22	like	like	ADP
ejpam-4972	511	23	gamma	gamma	NOUN
ejpam-4972	511	24	,	,	PUNCT
ejpam-4972	511	25	theta	theta	NOUN
ejpam-4972	511	26	,	,	PUNCT
ejpam-4972	511	27	or	or	CCONJ
ejpam-4972	511	28	regular	regular	ADJ
ejpam-4972	511	29	set	set	NOUN
ejpam-4972	511	30	,	,	PUNCT
ejpam-4972	511	31	also	also	ADV
ejpam-4972	511	32	for	for	ADP
ejpam-4972	511	33	more	more	ADJ
ejpam-4972	511	34	than	than	ADP
ejpam-4972	511	35	two	two	NUM
ejpam-4972	511	36	topologies	topology	NOUN
ejpam-4972	511	37	.	.	PUNCT
ejpam-4972	512	1	acknowledgements	acknowledgement	NOUN
ejpam-4972	512	2	the	the	DET
ejpam-4972	512	3	authors	author	NOUN
ejpam-4972	512	4	gratefully	gratefully	ADV
ejpam-4972	512	5	acknowledge	acknowledge	VERB
ejpam-4972	512	6	the	the	DET
ejpam-4972	512	7	constructive	constructive	ADJ
ejpam-4972	512	8	comments	comment	NOUN
ejpam-4972	512	9	from	from	ADP
ejpam-4972	512	10	anonymous	anonymous	ADJ
ejpam-4972	512	11	referees	referee	NOUN
ejpam-4972	512	12	that	that	PRON
ejpam-4972	512	13	improved	improve	VERB
ejpam-4972	512	14	the	the	DET
ejpam-4972	512	15	current	current	ADJ
ejpam-4972	512	16	version	version	NOUN
ejpam-4972	512	17	of	of	ADP
ejpam-4972	512	18	manuscript	manuscript	NOUN
ejpam-4972	512	19	.	.	PUNCT
ejpam-4972	513	1	references	reference	NOUN
ejpam-4972	513	2	[	[	X
ejpam-4972	513	3	1	1	NUM
ejpam-4972	513	4	]	]	X
ejpam-4972	513	5	abd	abd	PROPN
ejpam-4972	513	6	el	el	PROPN
ejpam-4972	513	7	-	-	PUNCT
ejpam-4972	513	8	monsef	monsef	ADJ
ejpam-4972	513	9	,	,	PUNCT
ejpam-4972	513	10	m.	m.	NOUN
ejpam-4972	513	11	e	e	PROPN
ejpam-4972	513	12	,	,	PUNCT
ejpam-4972	513	13	el	el	PROPN
ejpam-4972	513	14	-	-	NOUN
ejpam-4972	513	15	gayar	gayar	NOUN
ejpam-4972	513	16	,	,	PUNCT
ejpam-4972	513	17	m.	m.	NOUN
ejpam-4972	513	18	a	a	PRON
ejpam-4972	513	19	,	,	PUNCT
ejpam-4972	513	20	and	and	CCONJ
ejpam-4972	513	21	aqeel	aqeel	PROPN
ejpam-4972	513	22	,	,	PUNCT
ejpam-4972	513	23	r.	r.	PROPN
ejpam-4972	513	24	m.	m.	PROPN
ejpam-4972	513	25	a	a	DET
ejpam-4972	513	26	comparison	comparison	NOUN
ejpam-4972	513	27	of	of	ADP
ejpam-4972	513	28	three	three	NUM
ejpam-4972	513	29	types	type	NOUN
ejpam-4972	513	30	of	of	ADP
ejpam-4972	513	31	rough	rough	ADJ
ejpam-4972	513	32	fuzzy	fuzzy	ADJ
ejpam-4972	513	33	sets	set	NOUN
ejpam-4972	513	34	based	base	VERB
ejpam-4972	513	35	on	on	ADP
ejpam-4972	513	36	two	two	NUM
ejpam-4972	513	37	universal	universal	ADJ
ejpam-4972	513	38	sets	set	NOUN
ejpam-4972	513	39	.	.	PUNCT
ejpam-4972	514	1	international	international	ADJ
ejpam-4972	514	2	journal	journal	NOUN
ejpam-4972	514	3	of	of	ADP
ejpam-4972	514	4	machine	machine	NOUN
ejpam-4972	514	5	learning	learning	NOUN
ejpam-4972	514	6	and	and	CCONJ
ejpam-4972	514	7	cybernetics	cybernetic	NOUN
ejpam-4972	514	8	,	,	PUNCT
ejpam-4972	514	9	(	(	PUNCT
ejpam-4972	514	10	2017	2017	NUM
ejpam-4972	514	11	)	)	PUNCT
ejpam-4972	514	12	,	,	PUNCT
ejpam-4972	514	13	vol	vol	NOUN
ejpam-4972	514	14	8	8	NUM
ejpam-4972	514	15	.	.	PUNCT
ejpam-4972	515	1	pp.343–353	pp.343–353	NOUN
ejpam-4972	515	2	.	.	PUNCT
ejpam-4972	516	1	[	[	X
ejpam-4972	516	2	2	2	NUM
ejpam-4972	516	3	]	]	X
ejpam-4972	516	4	abu	abu	PROPN
ejpam-4972	516	5	-	-	PUNCT
ejpam-4972	516	6	gdairi	gdairi	PROPN
ejpam-4972	516	7	,	,	PUNCT
ejpam-4972	516	8	r.	r.	PROPN
ejpam-4972	516	9	,	,	PUNCT
ejpam-4972	516	10	nasef	nasef	PROPN
ejpam-4972	516	11	,	,	PUNCT
ejpam-4972	516	12	a.	a.	NOUN
ejpam-4972	516	13	a.	a.	PROPN
ejpam-4972	516	14	,	,	PUNCT
ejpam-4972	516	15	el	el	PROPN
ejpam-4972	516	16	-	-	PUNCT
ejpam-4972	516	17	gayar	gayar	NOUN
ejpam-4972	516	18	,	,	PUNCT
ejpam-4972	516	19	m.	m.	NOUN
ejpam-4972	516	20	a.	a.	PROPN
ejpam-4972	516	21	,	,	PUNCT
ejpam-4972	516	22	and	and	CCONJ
ejpam-4972	516	23	el	el	PROPN
ejpam-4972	516	24	-	-	ADJ
ejpam-4972	516	25	bably	bably	ADV
ejpam-4972	516	26	,	,	PUNCT
ejpam-4972	516	27	m.	m.	NOUN
ejpam-4972	516	28	k.	k.	PROPN
ejpam-4972	516	29	on	on	ADP
ejpam-4972	516	30	fuzzy	fuzzy	ADJ
ejpam-4972	516	31	point	point	NOUN
ejpam-4972	516	32	applications	application	NOUN
ejpam-4972	516	33	of	of	ADP
ejpam-4972	516	34	fuzzy	fuzzy	ADJ
ejpam-4972	516	35	topological	topological	ADJ
ejpam-4972	516	36	spaces	space	NOUN
ejpam-4972	516	37	.	.	PUNCT
ejpam-4972	517	1	international	international	ADJ
ejpam-4972	517	2	journal	journal	NOUN
ejpam-4972	517	3	of	of	ADP
ejpam-4972	517	4	fuzzy	fuzzy	ADJ
ejpam-4972	517	5	logic	logic	NOUN
ejpam-4972	517	6	and	and	CCONJ
ejpam-4972	517	7	intelligent	intelligent	ADJ
ejpam-4972	517	8	systems	system	NOUN
ejpam-4972	517	9	,	,	PUNCT
ejpam-4972	517	10	(	(	PUNCT
ejpam-4972	517	11	2023	2023	NUM
ejpam-4972	517	12	)	)	PUNCT
ejpam-4972	517	13	,	,	PUNCT
ejpam-4972	517	14	vol	vol	NOUN
ejpam-4972	517	15	23(2	23(2	NOUN
ejpam-4972	517	16	)	)	PUNCT
ejpam-4972	517	17	,	,	PUNCT
ejpam-4972	517	18	pp	pp	ADP
ejpam-4972	517	19	.	.	PUNCT
ejpam-4972	518	1	162–172	162–172	NUM
ejpam-4972	518	2	.	.	PUNCT
ejpam-4972	519	1	[	[	X
ejpam-4972	519	2	3	3	NUM
ejpam-4972	519	3	]	]	X
ejpam-4972	519	4	alharbi	alharbi	NOUN
ejpam-4972	519	5	.	.	PUNCT
ejpam-4972	520	1	a	a	PRON
ejpam-4972	520	2	and	and	CCONJ
ejpam-4972	520	3	kilicman	kilicman	NOUN
ejpam-4972	520	4	.	.	PUNCT
ejpam-4972	521	1	a	a	DET
ejpam-4972	521	2	,	,	PUNCT
ejpam-4972	521	3	note	note	NOUN
ejpam-4972	521	4	on	on	ADP
ejpam-4972	521	5	generalized	generalized	ADJ
ejpam-4972	521	6	neighborhoods	neighborhood	NOUN
ejpam-4972	521	7	structures	structure	NOUN
ejpam-4972	521	8	in	in	ADP
ejpam-4972	521	9	fuzzy	fuzzy	ADJ
ejpam-4972	521	10	bitopological	bitopological	ADJ
ejpam-4972	521	11	spaces	space	NOUN
ejpam-4972	521	12	.	.	PUNCT
ejpam-4972	522	1	european	european	ADJ
ejpam-4972	522	2	journal	journal	PROPN
ejpam-4972	522	3	of	of	ADP
ejpam-4972	522	4	pure	pure	ADJ
ejpam-4972	522	5	and	and	CCONJ
ejpam-4972	522	6	applied	applied	ADJ
ejpam-4972	522	7	mathematics	mathematic	NOUN
ejpam-4972	522	8	,	,	PUNCT
ejpam-4972	522	9	(	(	PUNCT
ejpam-4972	522	10	2023	2023	NUM
ejpam-4972	522	11	)	)	PUNCT
ejpam-4972	522	12	,	,	PUNCT
ejpam-4972	522	13	pp	pp	ADJ
ejpam-4972	522	14	.	.	PUNCT
ejpam-4972	523	1	1980–1990	1980–1990	NUM
ejpam-4972	523	2	.	.	PUNCT
ejpam-4972	524	1	[	[	X
ejpam-4972	524	2	4	4	NUM
ejpam-4972	524	3	]	]	PUNCT
ejpam-4972	524	4	a.	a.	NOUN
ejpam-4972	524	5	kandil	kandil	PROPN
ejpam-4972	524	6	,	,	PUNCT
ejpam-4972	524	7	biproximities	biproximitie	NOUN
ejpam-4972	524	8	and	and	CCONJ
ejpam-4972	524	9	fuzzy	fuzzy	ADJ
ejpam-4972	524	10	bitopological	bitopological	ADJ
ejpam-4972	524	11	spaces	space	NOUN
ejpam-4972	524	12	.	.	PUNCT
ejpam-4972	525	1	simon	simon	PROPN
ejpam-4972	525	2	stevin	stevin	PROPN
ejpam-4972	525	3	,	,	PUNCT
ejpam-4972	525	4	(	(	PUNCT
ejpam-4972	525	5	1989	1989	NUM
ejpam-4972	525	6	)	)	PUNCT
ejpam-4972	525	7	,	,	PUNCT
ejpam-4972	525	8	pp	pp	PROPN
ejpam-4972	525	9	.	.	PUNCT
ejpam-4972	526	1	45	45	NUM
ejpam-4972	526	2	-	-	SYM
ejpam-4972	526	3	66	66	NUM
ejpam-4972	526	4	.	.	PUNCT
ejpam-4972	527	1	[	[	X
ejpam-4972	527	2	5	5	NUM
ejpam-4972	527	3	]	]	PUNCT
ejpam-4972	527	4	a.	a.	NOUN
ejpam-4972	527	5	mashhour	mashhour	PROPN
ejpam-4972	527	6	,	,	PUNCT
ejpam-4972	527	7	a.	a.	PROPN
ejpam-4972	527	8	allam	allam	PROPN
ejpam-4972	527	9	and	and	CCONJ
ejpam-4972	527	10	a.	a.	NOUN
ejpam-4972	527	11	zahran	zahran	PROPN
ejpam-4972	527	12	,	,	PUNCT
ejpam-4972	527	13	fuzzy	fuzzy	ADJ
ejpam-4972	527	14	g−continuous	g−continuous	ADJ
ejpam-4972	527	15	and	and	CCONJ
ejpam-4972	527	16	fuzzy	fuzzy	ADJ
ejpam-4972	527	17	g−open	g−open	NOUN
ejpam-4972	527	18	mapping	mapping	NOUN
ejpam-4972	527	19	.	.	PUNCT
ejpam-4972	528	1	bulletin	bulletin	NOUN
ejpam-4972	528	2	.	.	PUNCT
ejpam-4972	529	1	assiut	assiut	PROPN
ejpam-4972	529	2	university	university	PROPN
ejpam-4972	529	3	,	,	PUNCT
ejpam-4972	529	4	(	(	PUNCT
ejpam-4972	529	5	1985	1985	NUM
ejpam-4972	529	6	)	)	PUNCT
ejpam-4972	529	7	,	,	PUNCT
ejpam-4972	529	8	pp	pp	ADP
ejpam-4972	529	9	.	.	PUNCT
ejpam-4972	530	1	93–106	93–106	NUM
ejpam-4972	530	2	.	.	PUNCT
ejpam-4972	531	1	[	[	X
ejpam-4972	531	2	6	6	NUM
ejpam-4972	531	3	]	]	PUNCT
ejpam-4972	531	4	a.	a.	NOUN
ejpam-4972	531	5	pushpalatha	pushpalatha	PROPN
ejpam-4972	531	6	and	and	CCONJ
ejpam-4972	531	7	s.	s.	PROPN
ejpam-4972	531	8	eswaran	eswaran	PROPN
ejpam-4972	531	9	,	,	PUNCT
ejpam-4972	531	10	strong	strong	ADJ
ejpam-4972	531	11	forms	form	NOUN
ejpam-4972	531	12	of	of	ADP
ejpam-4972	531	13	δ∗−generalized	δ∗−generalize	VERB
ejpam-4972	531	14	continuous	continuous	ADJ
ejpam-4972	531	15	map	map	NOUN
ejpam-4972	531	16	in	in	ADP
ejpam-4972	531	17	topological	topological	ADJ
ejpam-4972	531	18	spaces	space	NOUN
ejpam-4972	531	19	.	.	PUNCT
ejpam-4972	532	1	wce	wce	X
ejpam-4972	532	2	,	,	PUNCT
ejpam-4972	532	3	(	(	PUNCT
ejpam-4972	532	4	2010	2010	NUM
ejpam-4972	532	5	)	)	PUNCT
ejpam-4972	532	6	,	,	PUNCT
ejpam-4972	532	7	pp	pp	ADP
ejpam-4972	532	8	.	.	PUNCT
ejpam-4972	533	1	815–822	815–822	NUM
ejpam-4972	533	2	.	.	PUNCT
ejpam-4972	534	1	[	[	X
ejpam-4972	534	2	7	7	X
ejpam-4972	534	3	]	]	X
ejpam-4972	534	4	b.	b.	PROPN
ejpam-4972	534	5	ahmad	ahmad	PROPN
ejpam-4972	534	6	and	and	CCONJ
ejpam-4972	534	7	athar	athar	PROPN
ejpam-4972	534	8	kharal	kharal	ADJ
ejpam-4972	534	9	,	,	PUNCT
ejpam-4972	534	10	fuzzy	fuzzy	ADJ
ejpam-4972	534	11	sets	set	NOUN
ejpam-4972	534	12	,	,	PUNCT
ejpam-4972	534	13	fuzzy	fuzzy	ADJ
ejpam-4972	534	14	s	s	NOUN
ejpam-4972	534	15	-	-	PUNCT
ejpam-4972	534	16	open	open	ADJ
ejpam-4972	534	17	and	and	CCONJ
ejpam-4972	534	18	s	s	NOUN
ejpam-4972	534	19	-	-	PUNCT
ejpam-4972	534	20	closed	closed	ADJ
ejpam-4972	534	21	mappings	mapping	NOUN
ejpam-4972	534	22	.	.	PUNCT
ejpam-4972	535	1	hindawi	hindawi	ADJ
ejpam-4972	535	2	publishing	publishing	NOUN
ejpam-4972	535	3	corporation	corporation	NOUN
ejpam-4972	535	4	,	,	PUNCT
ejpam-4972	535	5	(	(	PUNCT
ejpam-4972	535	6	2009	2009	NUM
ejpam-4972	535	7	)	)	PUNCT
ejpam-4972	535	8	,	,	PUNCT
ejpam-4972	535	9	pp	pp	ADJ
ejpam-4972	535	10	.	.	PUNCT
ejpam-4972	536	1	5	5	X
ejpam-4972	536	2	.	.	PUNCT
ejpam-4972	537	1	[	[	X
ejpam-4972	537	2	8	8	NUM
ejpam-4972	537	3	]	]	X
ejpam-4972	537	4	c.	c.	PROPN
ejpam-4972	537	5	chang	chang	PROPN
ejpam-4972	537	6	,	,	PUNCT
ejpam-4972	537	7	fuzzy	fuzzy	ADJ
ejpam-4972	537	8	topological	topological	ADJ
ejpam-4972	537	9	spaces	space	NOUN
ejpam-4972	537	10	.	.	PUNCT
ejpam-4972	538	1	j.	j.	PROPN
ejpam-4972	538	2	math	math	PROPN
ejpam-4972	538	3	.	.	PUNCT
ejpam-4972	539	1	anal	anal	ADJ
ejpam-4972	539	2	appl	appl	PROPN
ejpam-4972	539	3	,	,	PUNCT
ejpam-4972	539	4	(	(	PUNCT
ejpam-4972	539	5	1968	1968	NUM
ejpam-4972	539	6	)	)	PUNCT
ejpam-4972	539	7	,	,	PUNCT
ejpam-4972	539	8	pp	pp	ADP
ejpam-4972	539	9	.	.	PUNCT
ejpam-4972	540	1	182–190	182–190	NUM
ejpam-4972	540	2	.	.	PUNCT
ejpam-4972	541	1	[	[	X
ejpam-4972	541	2	9	9	NUM
ejpam-4972	541	3	]	]	PUNCT
ejpam-4972	541	4	c.	c.	PROPN
ejpam-4972	541	5	k.	k.	PROPN
ejpam-4972	541	6	wong	wong	PROPN
ejpam-4972	541	7	,	,	PUNCT
ejpam-4972	541	8	fuzzy	fuzzy	ADJ
ejpam-4972	541	9	points	point	NOUN
ejpam-4972	541	10	and	and	CCONJ
ejpam-4972	541	11	local	local	ADJ
ejpam-4972	541	12	properties	property	NOUN
ejpam-4972	541	13	of	of	ADP
ejpam-4972	541	14	fuzzy	fuzzy	ADJ
ejpam-4972	541	15	topology	topology	NOUN
ejpam-4972	541	16	,	,	PUNCT
ejpam-4972	541	17	journal	journal	NOUN
ejpam-4972	541	18	ofmathematical	ofmathematical	ADJ
ejpam-4972	541	19	analysis	analysis	NOUN
ejpam-4972	541	20	and	and	CCONJ
ejpam-4972	541	21	applications	application	NOUN
ejpam-4972	541	22	,	,	PUNCT
ejpam-4972	541	23	(	(	PUNCT
ejpam-4972	541	24	1974	1974	NUM
ejpam-4972	541	25	)	)	PUNCT
ejpam-4972	541	26	,	,	PUNCT
ejpam-4972	541	27	pp.316	pp.316	PROPN
ejpam-4972	541	28	-	-	SYM
ejpam-4972	541	29	328	328	NUM
ejpam-4972	541	30	.	.	PUNCT
ejpam-4972	542	1	[	[	X
ejpam-4972	542	2	10	10	NUM
ejpam-4972	542	3	]	]	X
ejpam-4972	542	4	e.	e.	PROPN
ejpam-4972	542	5	ekici	ekici	PROPN
ejpam-4972	542	6	,	,	PUNCT
ejpam-4972	542	7	on	on	ADP
ejpam-4972	542	8	some	some	DET
ejpam-4972	542	9	types	type	NOUN
ejpam-4972	542	10	of	of	ADP
ejpam-4972	542	11	continuous	continuous	ADJ
ejpam-4972	542	12	fuzzy	fuzzy	ADJ
ejpam-4972	542	13	functions	function	NOUN
ejpam-4972	542	14	.	.	PUNCT
ejpam-4972	543	1	applied	apply	VERB
ejpam-4972	543	2	mathematics	mathematic	NOUN
ejpam-4972	543	3	,	,	PUNCT
ejpam-4972	543	4	(	(	PUNCT
ejpam-4972	543	5	2004	2004	NUM
ejpam-4972	543	6	)	)	PUNCT
ejpam-4972	543	7	,	,	PUNCT
ejpam-4972	543	8	pp	pp	ADP
ejpam-4972	543	9	.	.	PUNCT
ejpam-4972	544	1	21–25	21–25	X
ejpam-4972	544	2	.	.	PUNCT
ejpam-4972	545	1	[	[	X
ejpam-4972	545	2	11	11	NUM
ejpam-4972	545	3	]	]	X
ejpam-4972	545	4	g.	g.	PROPN
ejpam-4972	545	5	balasubramanian	balasubramanian	PROPN
ejpam-4972	545	6	and	and	CCONJ
ejpam-4972	545	7	p.	p.	PROPN
ejpam-4972	545	8	sundaram	sundaram	PROPN
ejpam-4972	545	9	,	,	PUNCT
ejpam-4972	545	10	on	on	ADP
ejpam-4972	545	11	some	some	DET
ejpam-4972	545	12	generalizations	generalization	NOUN
ejpam-4972	545	13	of	of	ADP
ejpam-4972	545	14	fuzzy	fuzzy	ADJ
ejpam-4972	545	15	continuous	continuous	ADJ
ejpam-4972	545	16	functions	function	NOUN
ejpam-4972	545	17	.	.	PUNCT
ejpam-4972	546	1	fuzzy	fuzzy	ADJ
ejpam-4972	546	2	sets	set	NOUN
ejpam-4972	546	3	and	and	CCONJ
ejpam-4972	546	4	systems	system	NOUN
ejpam-4972	546	5	,	,	PUNCT
ejpam-4972	546	6	(	(	PUNCT
ejpam-4972	546	7	1997	1997	NUM
ejpam-4972	546	8	)	)	PUNCT
ejpam-4972	546	9	,	,	PUNCT
ejpam-4972	546	10	pp	pp	ADP
ejpam-4972	546	11	.	.	PUNCT
ejpam-4972	547	1	93–100	93–100	X
ejpam-4972	547	2	.	.	PUNCT
ejpam-4972	548	1	references	reference	NOUN
ejpam-4972	548	2	2631	2631	NUM
ejpam-4972	549	1	[	[	X
ejpam-4972	549	2	12	12	NUM
ejpam-4972	549	3	]	]	PUNCT
ejpam-4972	549	4	govindappa	govindappa	NOUN
ejpam-4972	549	5	.	.	PUNCT
ejpam-4972	550	1	n	n	CCONJ
ejpam-4972	550	2	,	,	PUNCT
ejpam-4972	550	3	g.h	g.h	PROPN
ejpam-4972	550	4	and	and	CCONJ
ejpam-4972	550	5	md	md	PROPN
ejpam-4972	550	6	.	.	PUNCT
ejpam-4972	551	1	hanif	hanif	PROPN
ejpam-4972	551	2	,	,	PUNCT
ejpam-4972	551	3	θ−generalized	θ−generalized	ADJ
ejpam-4972	551	4	semi	semi	ADJ
ejpam-4972	551	5	-	-	ADJ
ejpam-4972	551	6	open	open	ADJ
ejpam-4972	551	7	and	and	CCONJ
ejpam-4972	551	8	θ−generalized	θ−generalized	ADJ
ejpam-4972	551	9	semi	semi	ADJ
ejpam-4972	551	10	-	-	ADJ
ejpam-4972	551	11	closed	closed	ADJ
ejpam-4972	551	12	functions	function	NOUN
ejpam-4972	551	13	.	.	PUNCT
ejpam-4972	552	1	proyecciones	proyecciones	PROPN
ejpam-4972	552	2	journal	journal	PROPN
ejpam-4972	552	3	of	of	ADP
ejpam-4972	552	4	math	math	NOUN
ejpam-4972	552	5	,	,	PUNCT
ejpam-4972	552	6	(	(	PUNCT
ejpam-4972	552	7	2009	2009	NUM
ejpam-4972	552	8	)	)	PUNCT
ejpam-4972	552	9	,	,	PUNCT
ejpam-4972	552	10	pp	pp	ADP
ejpam-4972	552	11	.	.	PUNCT
ejpam-4972	553	1	111–123	111–123	NUM
ejpam-4972	553	2	.	.	PUNCT
ejpam-4972	554	1	[	[	X
ejpam-4972	554	2	13	13	NUM
ejpam-4972	554	3	]	]	PUNCT
ejpam-4972	554	4	hakeem	hakeem	PROPN
ejpam-4972	554	5	a.	a.	PROPN
ejpam-4972	554	6	othman	othman	PROPN
ejpam-4972	554	7	and	and	CCONJ
ejpam-4972	554	8	s.	s.	PROPN
ejpam-4972	554	9	latha	latha	PROPN
ejpam-4972	554	10	,	,	PUNCT
ejpam-4972	554	11	new	new	ADJ
ejpam-4972	554	12	results	result	NOUN
ejpam-4972	554	13	of	of	ADP
ejpam-4972	554	14	fuzzy	fuzzy	ADJ
ejpam-4972	554	15	alpha	alpha	NOUN
ejpam-4972	554	16	-	-	PUNCT
ejpam-4972	554	17	open	open	ADJ
ejpam-4972	554	18	sets	set	VERB
ejpam-4972	554	19	fuzzy	fuzzy	ADJ
ejpam-4972	554	20	alpha	alpha	ADJ
ejpam-4972	554	21	-	-	PUNCT
ejpam-4972	554	22	continuous	continuous	ADJ
ejpam-4972	554	23	mappings	mapping	NOUN
ejpam-4972	554	24	.	.	PUNCT
ejpam-4972	555	1	int	int	NOUN
ejpam-4972	555	2	.	.	PUNCT
ejpam-4972	556	1	j.	j.	PROPN
ejpam-4972	556	2	contemp	contemp	PROPN
ejpam-4972	556	3	.	.	PUNCT
ejpam-4972	557	1	math	math	NOUN
ejpam-4972	557	2	.	.	PUNCT
ejpam-4972	558	1	sciences	science	NOUN
ejpam-4972	558	2	,	,	PUNCT
ejpam-4972	558	3	(	(	PUNCT
ejpam-4972	558	4	2009	2009	NUM
ejpam-4972	558	5	)	)	PUNCT
ejpam-4972	558	6	,	,	PUNCT
ejpam-4972	558	7	pp	pp	ADJ
ejpam-4972	558	8	.	.	PUNCT
ejpam-4972	558	9	1415	1415	NUM
ejpam-4972	558	10	–	–	PUNCT
ejpam-4972	558	11	1422	1422	NUM
ejpam-4972	558	12	.	.	PUNCT
ejpam-4972	559	1	[	[	X
ejpam-4972	559	2	14	14	NUM
ejpam-4972	559	3	]	]	X
ejpam-4972	559	4	l.	l.	PROPN
ejpam-4972	559	5	zadeh	zadeh	PROPN
ejpam-4972	559	6	,	,	PUNCT
ejpam-4972	559	7	fuzzy	fuzzy	ADJ
ejpam-4972	559	8	sets	set	NOUN
ejpam-4972	559	9	,	,	PUNCT
ejpam-4972	559	10	information	information	NOUN
ejpam-4972	559	11	and	and	CCONJ
ejpam-4972	559	12	control	control	NOUN
ejpam-4972	559	13	,	,	PUNCT
ejpam-4972	559	14	(	(	PUNCT
ejpam-4972	559	15	1965	1965	NUM
ejpam-4972	559	16	)	)	PUNCT
ejpam-4972	559	17	,	,	PUNCT
ejpam-4972	559	18	pp	pp	ADJ
ejpam-4972	559	19	.	.	PUNCT
ejpam-4972	560	1	338–353	338–353	NUM
ejpam-4972	560	2	.	.	PUNCT
ejpam-4972	561	1	[	[	X
ejpam-4972	561	2	15	15	NUM
ejpam-4972	561	3	]	]	X
ejpam-4972	561	4	m.	m.	NOUN
ejpam-4972	561	5	caldas	caldas	PROPN
ejpam-4972	561	6	,	,	PUNCT
ejpam-4972	561	7	g.	g.	PROPN
ejpam-4972	561	8	navalagi	navalagi	PROPN
ejpam-4972	561	9	and	and	CCONJ
ejpam-4972	561	10	r.	r.	PROPN
ejpam-4972	561	11	saraf	saraf	PROPN
ejpam-4972	561	12	,	,	PUNCT
ejpam-4972	561	13	on	on	ADP
ejpam-4972	561	14	some	some	DET
ejpam-4972	561	15	functions	function	NOUN
ejpam-4972	561	16	concerning	concern	VERB
ejpam-4972	561	17	fuzzy	fuzzy	ADJ
ejpam-4972	561	18	pg	pg	ADJ
ejpam-4972	561	19	-	-	PUNCT
ejpam-4972	561	20	closed	close	VERB
ejpam-4972	561	21	sets	set	NOUN
ejpam-4972	561	22	.	.	PUNCT
ejpam-4972	562	1	proyecciones	proyeccione	NOUN
ejpam-4972	562	2	,	,	PUNCT
ejpam-4972	562	3	(	(	PUNCT
ejpam-4972	562	4	2006	2006	NUM
ejpam-4972	562	5	)	)	PUNCT
ejpam-4972	562	6	,	,	PUNCT
ejpam-4972	562	7	pp	pp	ADP
ejpam-4972	562	8	.	.	PUNCT
ejpam-4972	563	1	261–270	261–270	NUM
ejpam-4972	563	2	.	.	PUNCT
ejpam-4972	564	1	[	[	X
ejpam-4972	564	2	16	16	NUM
ejpam-4972	564	3	]	]	PUNCT
ejpam-4972	564	4	m.	m.	NOUN
ejpam-4972	564	5	el	el	PROPN
ejpam-4972	564	6	-	-	PUNCT
ejpam-4972	564	7	shafei	shafei	PROPN
ejpam-4972	564	8	,	,	PUNCT
ejpam-4972	564	9	some	some	DET
ejpam-4972	564	10	applications	application	NOUN
ejpam-4972	564	11	of	of	ADP
ejpam-4972	564	12	generalized	generalized	ADJ
ejpam-4972	564	13	closed	closed	ADJ
ejpam-4972	564	14	sets	set	NOUN
ejpam-4972	564	15	in	in	ADP
ejpam-4972	564	16	fuzzy	fuzzy	ADJ
ejpam-4972	564	17	topological	topological	ADJ
ejpam-4972	564	18	space	space	NOUN
ejpam-4972	564	19	.	.	PUNCT
ejpam-4972	565	1	kyngpook	kyngpook	NOUN
ejpam-4972	565	2	math	math	NOUN
ejpam-4972	565	3	,	,	PUNCT
ejpam-4972	565	4	(	(	PUNCT
ejpam-4972	565	5	2005	2005	NUM
ejpam-4972	565	6	)	)	PUNCT
ejpam-4972	565	7	,	,	PUNCT
ejpam-4972	565	8	pp	pp	ADJ
ejpam-4972	565	9	.	.	PUNCT
ejpam-4972	566	1	13–19	13–19	NUM
ejpam-4972	566	2	.	.	PUNCT
ejpam-4972	567	1	[	[	X
ejpam-4972	567	2	17	17	NUM
ejpam-4972	567	3	]	]	PUNCT
ejpam-4972	567	4	m.	m.	NOUN
ejpam-4972	567	5	el	el	PROPN
ejpam-4972	567	6	-	-	PROPN
ejpam-4972	567	7	shafei	shafei	PROPN
ejpam-4972	567	8	and	and	CCONJ
ejpam-4972	567	9	a.	a.	NOUN
ejpam-4972	567	10	zakari	zakari	PROPN
ejpam-4972	567	11	,	,	PUNCT
ejpam-4972	567	12	semi	semi	ADV
ejpam-4972	567	13	generalized	generalized	ADJ
ejpam-4972	567	14	continuous	continuous	ADJ
ejpam-4972	567	15	mappings	mapping	NOUN
ejpam-4972	567	16	in	in	ADP
ejpam-4972	567	17	fuzzy	fuzzy	ADJ
ejpam-4972	567	18	topological	topological	ADJ
ejpam-4972	567	19	spaces	space	NOUN
ejpam-4972	567	20	.	.	PUNCT
ejpam-4972	568	1	journal	journal	NOUN
ejpam-4972	568	2	of	of	ADP
ejpam-4972	568	3	the	the	DET
ejpam-4972	568	4	egyptian	egyptian	PROPN
ejpam-4972	568	5	mathematical	mathematical	PROPN
ejpam-4972	568	6	society	society	NOUN
ejpam-4972	568	7	,	,	PUNCT
ejpam-4972	568	8	(	(	PUNCT
ejpam-4972	568	9	2007	2007	NUM
ejpam-4972	568	10	)	)	PUNCT
ejpam-4972	568	11	,	,	PUNCT
ejpam-4972	568	12	pp	pp	ADP
ejpam-4972	568	13	.	.	PUNCT
ejpam-4972	569	1	57–67	57–67	NUM
ejpam-4972	569	2	.	.	PUNCT
ejpam-4972	570	1	[	[	X
ejpam-4972	570	2	18	18	NUM
ejpam-4972	570	3	]	]	X
ejpam-4972	570	4	n.	n.	PROPN
ejpam-4972	570	5	nakajima	nakajima	PROPN
ejpam-4972	570	6	,	,	PUNCT
ejpam-4972	570	7	generalized	generalize	VERB
ejpam-4972	570	8	fuzzy	fuzzy	ADJ
ejpam-4972	570	9	sets	set	NOUN
ejpam-4972	570	10	.	.	PUNCT
ejpam-4972	571	1	fuzzy	fuzzy	ADJ
ejpam-4972	571	2	sets	set	NOUN
ejpam-4972	571	3	and	and	CCONJ
ejpam-4972	571	4	systems	system	NOUN
ejpam-4972	571	5	,	,	PUNCT
ejpam-4972	571	6	(	(	PUNCT
ejpam-4972	571	7	1989	1989	NUM
ejpam-4972	571	8	)	)	PUNCT
ejpam-4972	571	9	,	,	PUNCT
ejpam-4972	571	10	pp	pp	ADP
ejpam-4972	571	11	.	.	PUNCT
ejpam-4972	572	1	307–314	307–314	NUM
ejpam-4972	572	2	.	.	PUNCT
ejpam-4972	573	1	[	[	X
ejpam-4972	573	2	19	19	NUM
ejpam-4972	573	3	]	]	X
ejpam-4972	573	4	n.	n.	PROPN
ejpam-4972	573	5	palaniappan	palaniappan	PROPN
ejpam-4972	573	6	,	,	PUNCT
ejpam-4972	573	7	fuzzy	fuzzy	ADJ
ejpam-4972	573	8	topology	topology	NOUN
ejpam-4972	573	9	.	.	PUNCT
ejpam-4972	574	1	alpha	alpha	PROPN
ejpam-4972	574	2	science	science	PROPN
ejpam-4972	574	3	international	international	PROPN
ejpam-4972	574	4	ltd	ltd	PROPN
ejpam-4972	574	5	,	,	PUNCT
ejpam-4972	574	6	(	(	PUNCT
ejpam-4972	574	7	2002	2002	NUM
ejpam-4972	574	8	)	)	PUNCT
ejpam-4972	574	9	,	,	PUNCT
ejpam-4972	575	1	pp	pp	ADJ
ejpam-4972	575	2	.	.	PUNCT
ejpam-4972	576	1	1	1	NUM
ejpam-4972	576	2	–	–	PUNCT
ejpam-4972	576	3	177	177	NUM
ejpam-4972	576	4	.	.	PUNCT
ejpam-4972	577	1	[	[	X
ejpam-4972	577	2	20	20	NUM
ejpam-4972	577	3	]	]	PUNCT
ejpam-4972	577	4	s.	s.	PROPN
ejpam-4972	577	5	h.	h.	PROPN
ejpam-4972	577	6	cho	cho	PROPN
ejpam-4972	577	7	and	and	CCONJ
ejpam-4972	577	8	j.	j.	PROPN
ejpam-4972	577	9	k.	k.	PROPN
ejpam-4972	577	10	park	park	PROPN
ejpam-4972	577	11	,	,	PUNCT
ejpam-4972	577	12	a	a	DET
ejpam-4972	577	13	note	note	NOUN
ejpam-4972	577	14	on	on	ADP
ejpam-4972	577	15	fuzzy	fuzzy	ADJ
ejpam-4972	577	16	semi	semi	ADJ
ejpam-4972	577	17	-	-	ADJ
ejpam-4972	577	18	irresolute	irresolute	ADJ
ejpam-4972	577	19	and	and	CCONJ
ejpam-4972	577	20	strongly	strongly	ADV
ejpam-4972	577	21	irresolute	irresolute	ADJ
ejpam-4972	577	22	functions	function	NOUN
ejpam-4972	577	23	.	.	PUNCT
ejpam-4972	578	1	commun	commun	PROPN
ejpam-4972	578	2	korean	korean	PROPN
ejpam-4972	578	3	math	math	PROPN
ejpam-4972	578	4	,	,	PUNCT
ejpam-4972	578	5	(	(	PUNCT
ejpam-4972	578	6	2003	2003	NUM
ejpam-4972	578	7	)	)	PUNCT
ejpam-4972	578	8	,	,	PUNCT
ejpam-4972	578	9	pp	pp	ADP
ejpam-4972	578	10	.	.	PUNCT
ejpam-4972	579	1	355–366	355–366	NUM
ejpam-4972	579	2	.	.	PUNCT
ejpam-4972	580	1	[	[	X
ejpam-4972	580	2	21	21	NUM
ejpam-4972	580	3	]	]	SYM
ejpam-4972	580	4	sadanand	sadanand	PROPN
ejpam-4972	580	5	.	.	PROPN
ejpam-4972	580	6	potil	potil	PROPN
ejpam-4972	580	7	,	,	PUNCT
ejpam-4972	580	8	on	on	ADP
ejpam-4972	580	9	∗µ−closed	∗µ−closed	ADJ
ejpam-4972	580	10	fuzzy	fuzzy	ADJ
ejpam-4972	580	11	sets	set	NOUN
ejpam-4972	580	12	,	,	PUNCT
ejpam-4972	580	13	fuzzy	fuzzy	ADJ
ejpam-4972	580	14	∗µ−closed	∗µ−closed	ADJ
ejpam-4972	580	15	maps	map	NOUN
ejpam-4972	580	16	,	,	PUNCT
ejpam-4972	580	17	fuzzy	fuzzy	ADJ
ejpam-4972	580	18	∗µ−irresolute	∗µ−irresolute	NOUN
ejpam-4972	580	19	maps	map	NOUN
ejpam-4972	580	20	and	and	CCONJ
ejpam-4972	580	21	∗µ−homeomorphism	∗µ−homeomorphism	NOUN
ejpam-4972	580	22	mappings	mapping	NOUN
ejpam-4972	580	23	in	in	ADP
ejpam-4972	580	24	fuzzy	fuzzy	ADJ
ejpam-4972	580	25	topological	topological	ADJ
ejpam-4972	580	26	spaces	space	NOUN
ejpam-4972	580	27	.	.	PUNCT
ejpam-4972	581	1	conference	conference	NOUN
ejpam-4972	581	2	on	on	ADP
ejpam-4972	581	3	mathematics	mathematic	NOUN
ejpam-4972	581	4	,	,	PUNCT
ejpam-4972	581	5	statistics	statistic	NOUN
ejpam-4972	581	6	and	and	CCONJ
ejpam-4972	581	7	its	its	PRON
ejpam-4972	581	8	application	application	NOUN
ejpam-4972	581	9	,	,	PUNCT
ejpam-4972	581	10	(	(	PUNCT
ejpam-4972	581	11	2010	2010	NUM
ejpam-4972	581	12	)	)	PUNCT
ejpam-4972	581	13	,	,	PUNCT
ejpam-4972	581	14	pp	pp	ADP
ejpam-4972	581	15	.	.	PUNCT
ejpam-4972	582	1	201–213	201–213	NUM
ejpam-4972	582	2	.	.	PUNCT
ejpam-4972	583	1	[	[	X
ejpam-4972	583	2	22	22	NUM
ejpam-4972	583	3	]	]	PUNCT
ejpam-4972	583	4	v.	v.	CCONJ
ejpam-4972	583	5	chandrasekar	chandrasekar	PROPN
ejpam-4972	583	6	,	,	PUNCT
ejpam-4972	583	7	g.	g.	PROPN
ejpam-4972	583	8	balasubramanian	balasubramanian	PROPN
ejpam-4972	583	9	and	and	CCONJ
ejpam-4972	583	10	g.	g.	PROPN
ejpam-4972	583	11	thangaraj	thangaraj	PROPN
ejpam-4972	583	12	,	,	PUNCT
ejpam-4972	583	13	somewhat	somewhat	ADV
ejpam-4972	583	14	fuzzy	fuzzy	ADJ
ejpam-4972	583	15	pre	pre	ADJ
ejpam-4972	583	16	α−irresolute	α−irresolute	NOUN
ejpam-4972	583	17	functions	function	NOUN
ejpam-4972	583	18	.	.	PUNCT
ejpam-4972	584	1	advances	advance	NOUN
ejpam-4972	584	2	in	in	ADP
ejpam-4972	584	3	fuzzy	fuzzy	ADJ
ejpam-4972	584	4	mathematics	mathematic	NOUN
ejpam-4972	584	5	,	,	PUNCT
ejpam-4972	584	6	(	(	PUNCT
ejpam-4972	584	7	2008	2008	NUM
ejpam-4972	584	8	)	)	PUNCT
ejpam-4972	584	9	,	,	PUNCT
ejpam-4972	584	10	pp	pp	ADP
ejpam-4972	584	11	11–18	11–18	NUM
ejpam-4972	584	12	.	.	PUNCT
ejpam-4972	585	1	[	[	X
ejpam-4972	585	2	23	23	NUM
ejpam-4972	585	3	]	]	X
ejpam-4972	585	4	y.	y.	NOUN
ejpam-4972	585	5	beceren	beceren	PROPN
ejpam-4972	585	6	and	and	CCONJ
ejpam-4972	585	7	t.	t.	PROPN
ejpam-4972	585	8	noiri	noiri	PROPN
ejpam-4972	585	9	,	,	PUNCT
ejpam-4972	585	10	some	some	DET
ejpam-4972	585	11	functions	function	NOUN
ejpam-4972	585	12	defined	define	VERB
ejpam-4972	585	13	by	by	ADP
ejpam-4972	585	14	semi	semi	ADJ
ejpam-4972	585	15	-	-	ADJ
ejpam-4972	585	16	open	open	ADJ
ejpam-4972	585	17	and	and	CCONJ
ejpam-4972	585	18	β−open	β−open	PUNCT
ejpam-4972	585	19	sets	set	NOUN
ejpam-4972	585	20	.	.	PUNCT
ejpam-4972	586	1	science	science	NOUN
ejpam-4972	586	2	direct	direct	PROPN
ejpam-4972	586	3	,	,	PUNCT
ejpam-4972	586	4	(	(	PUNCT
ejpam-4972	586	5	2008	2008	NUM
ejpam-4972	586	6	)	)	PUNCT
ejpam-4972	586	7	,	,	PUNCT
ejpam-4972	586	8	pp	pp	PROPN
ejpam-4972	586	9	.	.	PUNCT
ejpam-4972	586	10	1225–1231	1225–1231	NUM
ejpam-4972	586	11	.	.	PUNCT
ejpam-4972	587	1	[	[	X
ejpam-4972	587	2	24	24	NUM
ejpam-4972	587	3	]	]	PUNCT
ejpam-4972	587	4	zahran	zahran	NOUN
ejpam-4972	587	5	,	,	PUNCT
ejpam-4972	587	6	a.	a.	NOUN
ejpam-4972	587	7	m	m	PROPN
ejpam-4972	587	8	and	and	CCONJ
ejpam-4972	587	9	el	el	PROPN
ejpam-4972	587	10	-	-	PUNCT
ejpam-4972	587	11	maghrabi	maghrabi	PROPN
ejpam-4972	587	12	,	,	PUNCT
ejpam-4972	587	13	a.	a.	PROPN
ejpam-4972	587	14	i.	i.	PROPN
ejpam-4972	587	15	generalized	generalize	VERB
ejpam-4972	587	16	-	-	PUNCT
ejpam-4972	587	17	operations	operation	NOUN
ejpam-4972	587	18	on	on	ADP
ejpam-4972	587	19	fuzzy	fuzzy	ADJ
ejpam-4972	587	20	topological	topological	ADJ
ejpam-4972	587	21	spaces	space	NOUN
ejpam-4972	587	22	.	.	PUNCT
ejpam-4972	588	1	abstract	abstract	ADJ
ejpam-4972	588	2	and	and	CCONJ
ejpam-4972	588	3	applied	apply	VERB
ejpam-4972	588	4	analysis	analysis	NOUN
ejpam-4972	588	5	,	,	PUNCT
ejpam-4972	588	6	(	(	PUNCT
ejpam-4972	588	7	2011	2011	NUM
ejpam-4972	588	8	)	)	PUNCT
ejpam-4972	588	9	,	,	PUNCT
ejpam-4972	588	10	pp	pp	PROPN
ejpam-4972	588	11	.	.	PUNCT
ejpam-4972	589	1	1–12	1–12	NOUN
ejpam-4972	589	2	.	.	PUNCT