id	sid	tid	token	lemma	pos
ejpam-5848	1	1	european	european	PROPN
ejpam-5848	1	2	journal	journal	PROPN
ejpam-5848	1	3	of	of	ADP
ejpam-5848	1	4	pure	pure	ADJ
ejpam-5848	1	5	and	and	CCONJ
ejpam-5848	1	6	applied	applied	ADJ
ejpam-5848	1	7	mathematics	mathematic	NOUN
ejpam-5848	1	8	2025	2025	NUM
ejpam-5848	1	9	,	,	PUNCT
ejpam-5848	1	10	vol	vol	NOUN
ejpam-5848	1	11	.	.	PROPN
ejpam-5848	1	12	18	18	NUM
ejpam-5848	1	13	,	,	PUNCT
ejpam-5848	1	14	issue	issue	NOUN
ejpam-5848	1	15	1	1	NUM
ejpam-5848	1	16	,	,	PUNCT
ejpam-5848	1	17	article	article	NOUN
ejpam-5848	1	18	number	number	NOUN
ejpam-5848	1	19	5848	5848	NUM
ejpam-5848	1	20	issn	issn	PROPN
ejpam-5848	1	21	1307	1307	NUM
ejpam-5848	1	22	-	-	SYM
ejpam-5848	1	23	5543	5543	NUM
ejpam-5848	1	24	–	–	PUNCT
ejpam-5848	1	25	ejpam.com	ejpam.com	X
ejpam-5848	1	26	published	publish	VERB
ejpam-5848	1	27	by	by	ADP
ejpam-5848	1	28	new	new	PROPN
ejpam-5848	1	29	york	york	PROPN
ejpam-5848	1	30	business	business	PROPN
ejpam-5848	1	31	global	global	VERB
ejpam-5848	1	32	some	some	DET
ejpam-5848	1	33	new	new	ADJ
ejpam-5848	1	34	characterizations	characterization	NOUN
ejpam-5848	1	35	of	of	ADP
ejpam-5848	1	36	open	open	ADJ
ejpam-5848	1	37	and	and	CCONJ
ejpam-5848	1	38	closed	close	VERB
ejpam-5848	1	39	fuzzy	fuzzy	ADJ
ejpam-5848	1	40	mappings	mapping	NOUN
ejpam-5848	1	41	inspired	inspire	VERB
ejpam-5848	1	42	by	by	ADP
ejpam-5848	1	43	induced	induced	ADJ
ejpam-5848	1	44	mappings	mapping	NOUN
ejpam-5848	1	45	sandeep	sandeep	PROPN
ejpam-5848	1	46	kaur1	kaur1	PROPN
ejpam-5848	1	47	,	,	PUNCT
ejpam-5848	1	48	fathea	fathea	PROPN
ejpam-5848	1	49	m.	m.	PROPN
ejpam-5848	1	50	osman	osman	PROPN
ejpam-5848	1	51	birkea2,∗	birkea2,∗	PROPN
ejpam-5848	1	52	,	,	PUNCT
ejpam-5848	1	53	alkan	alkan	PROPN
ejpam-5848	1	54	özkan3	özkan3	PROPN
ejpam-5848	1	55	,	,	PUNCT
ejpam-5848	1	56	tareq	tareq	PROPN
ejpam-5848	1	57	m.	m.	PROPN
ejpam-5848	1	58	al	al	PROPN
ejpam-5848	1	59	-	-	PUNCT
ejpam-5848	1	60	shami4,5	shami4,5	PROPN
ejpam-5848	1	61	,	,	PUNCT
ejpam-5848	1	62	m.	m.	NOUN
ejpam-5848	1	63	omran6	omran6	NOUN
ejpam-5848	1	64	1	1	NUM
ejpam-5848	1	65	department	department	NOUN
ejpam-5848	1	66	of	of	ADP
ejpam-5848	1	67	mathematics	mathematic	NOUN
ejpam-5848	1	68	and	and	CCONJ
ejpam-5848	1	69	statistics	statistic	NOUN
ejpam-5848	1	70	,	,	PUNCT
ejpam-5848	1	71	central	central	ADJ
ejpam-5848	1	72	university	university	NOUN
ejpam-5848	1	73	of	of	ADP
ejpam-5848	1	74	punjab	punjab	PROPN
ejpam-5848	1	75	,	,	PUNCT
ejpam-5848	1	76	bathinda	bathinda	NOUN
ejpam-5848	1	77	,	,	PUNCT
ejpam-5848	1	78	india	india	PROPN
ejpam-5848	1	79	2	2	NUM
ejpam-5848	1	80	department	department	NOUN
ejpam-5848	1	81	of	of	ADP
ejpam-5848	1	82	mathematics	mathematic	NOUN
ejpam-5848	1	83	,	,	PUNCT
ejpam-5848	1	84	faculty	faculty	NOUN
ejpam-5848	1	85	of	of	ADP
ejpam-5848	1	86	science	science	NOUN
ejpam-5848	1	87	,	,	PUNCT
ejpam-5848	1	88	northern	northern	ADJ
ejpam-5848	1	89	border	border	NOUN
ejpam-5848	1	90	university	university	PROPN
ejpam-5848	1	91	,	,	PUNCT
ejpam-5848	1	92	arar	arar	PROPN
ejpam-5848	1	93	,	,	PUNCT
ejpam-5848	1	94	saudi	saudi	PROPN
ejpam-5848	1	95	arabia	arabia	PROPN
ejpam-5848	1	96	3	3	NUM
ejpam-5848	1	97	department	department	NOUN
ejpam-5848	1	98	of	of	ADP
ejpam-5848	1	99	mathematics	mathematic	NOUN
ejpam-5848	1	100	,	,	PUNCT
ejpam-5848	1	101	faculty	faculty	NOUN
ejpam-5848	1	102	of	of	ADP
ejpam-5848	1	103	arts	art	NOUN
ejpam-5848	1	104	and	and	CCONJ
ejpam-5848	1	105	sciences	science	NOUN
ejpam-5848	1	106	,	,	PUNCT
ejpam-5848	1	107	iğdır	iğdır	PROPN
ejpam-5848	1	108	university	university	NOUN
ejpam-5848	1	109	,	,	PUNCT
ejpam-5848	1	110	iğdır	iğdır	PROPN
ejpam-5848	1	111	,	,	PUNCT
ejpam-5848	1	112	turkey	turkey	PROPN
ejpam-5848	1	113	4	4	NUM
ejpam-5848	1	114	department	department	NOUN
ejpam-5848	1	115	of	of	ADP
ejpam-5848	1	116	mathematics	mathematic	NOUN
ejpam-5848	1	117	,	,	PUNCT
ejpam-5848	1	118	sana’a	sana’a	NOUN
ejpam-5848	1	119	university	university	NOUN
ejpam-5848	1	120	,	,	PUNCT
ejpam-5848	1	121	p.o.box	p.o.box	PROPN
ejpam-5848	1	122	1247	1247	NUM
ejpam-5848	1	123	sana’a	sana’a	NOUN
ejpam-5848	1	124	,	,	PUNCT
ejpam-5848	1	125	yemen	yemen	PROPN
ejpam-5848	1	126	5	5	NUM
ejpam-5848	1	127	jadara	jadara	PROPN
ejpam-5848	1	128	university	university	PROPN
ejpam-5848	1	129	research	research	NOUN
ejpam-5848	1	130	center	center	NOUN
ejpam-5848	1	131	,	,	PUNCT
ejpam-5848	1	132	jadara	jadara	PROPN
ejpam-5848	1	133	university	university	PROPN
ejpam-5848	1	134	,	,	PUNCT
ejpam-5848	1	135	irbid	irbid	PROPN
ejpam-5848	1	136	,	,	PUNCT
ejpam-5848	1	137	jordan	jordan	PROPN
ejpam-5848	1	138	6	6	NUM
ejpam-5848	1	139	department	department	PROPN
ejpam-5848	1	140	of	of	ADP
ejpam-5848	1	141	physics	physics	PROPN
ejpam-5848	1	142	and	and	CCONJ
ejpam-5848	1	143	engineering	engineering	NOUN
ejpam-5848	1	144	mathematics	mathematic	NOUN
ejpam-5848	1	145	,	,	PUNCT
ejpam-5848	1	146	faculty	faculty	NOUN
ejpam-5848	1	147	of	of	ADP
ejpam-5848	1	148	engineering	engineering	PROPN
ejpam-5848	1	149	,	,	PUNCT
ejpam-5848	1	150	tanta	tanta	PROPN
ejpam-5848	1	151	university	university	PROPN
ejpam-5848	1	152	,	,	PUNCT
ejpam-5848	1	153	egypt	egypt	PROPN
ejpam-5848	1	154	abstract	abstract	PROPN
ejpam-5848	1	155	.	.	PUNCT
ejpam-5848	2	1	in	in	ADP
ejpam-5848	2	2	this	this	DET
ejpam-5848	2	3	paper	paper	NOUN
ejpam-5848	2	4	,	,	PUNCT
ejpam-5848	2	5	we	we	PRON
ejpam-5848	2	6	use	use	VERB
ejpam-5848	2	7	the	the	DET
ejpam-5848	2	8	induced	induced	ADJ
ejpam-5848	2	9	mappings	mapping	NOUN
ejpam-5848	2	10	to	to	PART
ejpam-5848	2	11	obtain	obtain	VERB
ejpam-5848	2	12	some	some	DET
ejpam-5848	2	13	new	new	ADJ
ejpam-5848	2	14	characterizations	characterization	NOUN
ejpam-5848	2	15	of	of	ADP
ejpam-5848	2	16	open	open	ADJ
ejpam-5848	2	17	fuzzy	fuzzy	ADJ
ejpam-5848	2	18	mappings	mapping	NOUN
ejpam-5848	2	19	in	in	ADP
ejpam-5848	2	20	connection	connection	NOUN
ejpam-5848	2	21	with	with	ADP
ejpam-5848	2	22	closures	closure	NOUN
ejpam-5848	2	23	and	and	CCONJ
ejpam-5848	2	24	closed	close	VERB
ejpam-5848	2	25	fuzzy	fuzzy	ADJ
ejpam-5848	2	26	mappings	mapping	NOUN
ejpam-5848	2	27	in	in	ADP
ejpam-5848	2	28	connection	connection	NOUN
ejpam-5848	2	29	with	with	ADP
ejpam-5848	2	30	interiors	interior	NOUN
ejpam-5848	2	31	of	of	ADP
ejpam-5848	2	32	fuzzy	fuzzy	ADJ
ejpam-5848	2	33	sets	set	NOUN
ejpam-5848	2	34	.	.	PUNCT
ejpam-5848	3	1	we	we	PRON
ejpam-5848	3	2	also	also	ADV
ejpam-5848	3	3	investigate	investigate	VERB
ejpam-5848	3	4	another	another	DET
ejpam-5848	3	5	representation	representation	NOUN
ejpam-5848	3	6	of	of	ADP
ejpam-5848	3	7	open	open	ADJ
ejpam-5848	3	8	fuzzy	fuzzy	ADJ
ejpam-5848	3	9	and	and	CCONJ
ejpam-5848	3	10	closed	close	VERB
ejpam-5848	3	11	fuzzy	fuzzy	ADJ
ejpam-5848	3	12	mappings	mapping	NOUN
ejpam-5848	3	13	under	under	ADP
ejpam-5848	3	14	surjective	surjective	ADJ
ejpam-5848	3	15	mappings	mapping	NOUN
ejpam-5848	3	16	.	.	PUNCT
ejpam-5848	4	1	furthermore	furthermore	ADV
ejpam-5848	4	2	,	,	PUNCT
ejpam-5848	4	3	we	we	PRON
ejpam-5848	4	4	prove	prove	VERB
ejpam-5848	4	5	that	that	SCONJ
ejpam-5848	4	6	images	image	NOUN
ejpam-5848	4	7	of	of	ADP
ejpam-5848	4	8	saturated	saturate	VERB
ejpam-5848	4	9	fuzzy	fuzzy	ADJ
ejpam-5848	4	10	sets	set	NOUN
ejpam-5848	4	11	under	under	ADP
ejpam-5848	4	12	surjective	surjective	ADJ
ejpam-5848	4	13	open	open	ADJ
ejpam-5848	4	14	fuzzy	fuzzy	ADJ
ejpam-5848	4	15	and	and	CCONJ
ejpam-5848	4	16	closed	close	VERB
ejpam-5848	4	17	fuzzy	fuzzy	ADJ
ejpam-5848	4	18	mappings	mapping	NOUN
ejpam-5848	4	19	are	be	AUX
ejpam-5848	4	20	closed	close	VERB
ejpam-5848	4	21	fuzzy	fuzzy	ADJ
ejpam-5848	4	22	and	and	CCONJ
ejpam-5848	4	23	open	open	ADJ
ejpam-5848	4	24	fuzzy	fuzzy	ADJ
ejpam-5848	4	25	sets	set	NOUN
ejpam-5848	4	26	,	,	PUNCT
ejpam-5848	4	27	respectively	respectively	ADV
ejpam-5848	4	28	.	.	PUNCT
ejpam-5848	5	1	we	we	PRON
ejpam-5848	5	2	furnish	furnish	VERB
ejpam-5848	5	3	illustrative	illustrative	ADJ
ejpam-5848	5	4	examples	example	NOUN
ejpam-5848	5	5	to	to	PART
ejpam-5848	5	6	elucidate	elucidate	VERB
ejpam-5848	5	7	the	the	DET
ejpam-5848	5	8	displayed	display	VERB
ejpam-5848	5	9	results	result	NOUN
ejpam-5848	5	10	.	.	PUNCT
ejpam-5848	6	1	2020	2020	NUM
ejpam-5848	6	2	mathematics	mathematic	NOUN
ejpam-5848	6	3	subject	subject	NOUN
ejpam-5848	6	4	classifications	classification	NOUN
ejpam-5848	6	5	:	:	PUNCT
ejpam-5848	6	6	54a40	54a40	NUM
ejpam-5848	6	7	,	,	PUNCT
ejpam-5848	6	8	03e72	03e72	NUM
ejpam-5848	6	9	,	,	PUNCT
ejpam-5848	6	10	54c05	54c05	NUM
ejpam-5848	6	11	,	,	PUNCT
ejpam-5848	6	12	94d05	94d05	NUM
ejpam-5848	6	13	key	key	ADJ
ejpam-5848	6	14	words	word	NOUN
ejpam-5848	6	15	and	and	CCONJ
ejpam-5848	6	16	phrases	phrase	NOUN
ejpam-5848	6	17	:	:	PUNCT
ejpam-5848	6	18	fuzzy	fuzzy	ADJ
ejpam-5848	6	19	set	set	NOUN
ejpam-5848	6	20	,	,	PUNCT
ejpam-5848	6	21	fuzzy	fuzzy	ADJ
ejpam-5848	6	22	topological	topological	ADJ
ejpam-5848	6	23	space	space	NOUN
ejpam-5848	6	24	,	,	PUNCT
ejpam-5848	6	25	open	open	ADJ
ejpam-5848	6	26	fuzzy	fuzzy	ADJ
ejpam-5848	6	27	mapping	mapping	NOUN
ejpam-5848	6	28	,	,	PUNCT
ejpam-5848	6	29	closed	close	VERB
ejpam-5848	6	30	fuzzy	fuzzy	ADJ
ejpam-5848	6	31	mapping	mapping	NOUN
ejpam-5848	6	32	,	,	PUNCT
ejpam-5848	6	33	induced	induce	VERB
ejpam-5848	6	34	mapping	mapping	NOUN
ejpam-5848	6	35	1	1	NUM
ejpam-5848	6	36	.	.	PUNCT
ejpam-5848	6	37	introduction	introduction	NOUN
ejpam-5848	6	38	in	in	ADP
ejpam-5848	6	39	[	[	X
ejpam-5848	6	40	30	30	NUM
ejpam-5848	6	41	]	]	PUNCT
ejpam-5848	6	42	,	,	PUNCT
ejpam-5848	6	43	zadeh	zadeh	PROPN
ejpam-5848	6	44	initiated	initiate	VERB
ejpam-5848	6	45	the	the	DET
ejpam-5848	6	46	essential	essential	ADJ
ejpam-5848	6	47	principle	principle	NOUN
ejpam-5848	6	48	of	of	ADP
ejpam-5848	6	49	fuzzy	fuzzy	ADJ
ejpam-5848	6	50	units	unit	NOUN
ejpam-5848	6	51	and	and	CCONJ
ejpam-5848	6	52	set	set	VERB
ejpam-5848	6	53	up	up	ADP
ejpam-5848	6	54	the	the	DET
ejpam-5848	6	55	pillar	pillar	NOUN
ejpam-5848	6	56	of	of	ADP
ejpam-5848	6	57	fuzzy	fuzzy	ADJ
ejpam-5848	6	58	mathematics	mathematic	NOUN
ejpam-5848	6	59	.	.	PUNCT
ejpam-5848	7	1	this	this	DET
ejpam-5848	7	2	theory	theory	NOUN
ejpam-5848	7	3	has	have	VERB
ejpam-5848	7	4	extreme	extreme	ADJ
ejpam-5848	7	5	potential	potential	NOUN
ejpam-5848	7	6	for	for	ADP
ejpam-5848	7	7	packages	package	NOUN
ejpam-5848	7	8	in	in	ADP
ejpam-5848	7	9	various	various	ADJ
ejpam-5848	7	10	directions	direction	NOUN
ejpam-5848	7	11	[	[	X
ejpam-5848	7	12	24	24	NUM
ejpam-5848	7	13	,	,	PUNCT
ejpam-5848	7	14	25	25	NUM
ejpam-5848	7	15	]	]	PUNCT
ejpam-5848	7	16	.	.	PUNCT
ejpam-5848	8	1	after	after	ADP
ejpam-5848	8	2	introducing	introduce	VERB
ejpam-5848	8	3	the	the	DET
ejpam-5848	8	4	theory	theory	NOUN
ejpam-5848	8	5	of	of	ADP
ejpam-5848	8	6	fuzzy	fuzzy	ADJ
ejpam-5848	8	7	topological	topological	ADJ
ejpam-5848	8	8	spaces	space	NOUN
ejpam-5848	8	9	(	(	PUNCT
ejpam-5848	8	10	ftss	ftss	NOUN
ejpam-5848	8	11	,	,	PUNCT
ejpam-5848	8	12	in	in	ADP
ejpam-5848	8	13	short	short	ADJ
ejpam-5848	8	14	)	)	PUNCT
ejpam-5848	8	15	in	in	ADP
ejpam-5848	8	16	[	[	X
ejpam-5848	8	17	17	17	NUM
ejpam-5848	8	18	]	]	PUNCT
ejpam-5848	8	19	,	,	PUNCT
ejpam-5848	8	20	chang	chang	PROPN
ejpam-5848	8	21	introduced	introduce	VERB
ejpam-5848	8	22	the	the	DET
ejpam-5848	8	23	notion	notion	NOUN
ejpam-5848	8	24	of	of	ADP
ejpam-5848	8	25	fuzzy	fuzzy	ADJ
ejpam-5848	8	26	continuous	continuous	ADJ
ejpam-5848	8	27	mapping	mapping	NOUN
ejpam-5848	8	28	alongside	alongside	ADP
ejpam-5848	8	29	its	its	PRON
ejpam-5848	8	30	characterizations	characterization	NOUN
ejpam-5848	8	31	.	.	PUNCT
ejpam-5848	9	1	afterwards	afterwards	ADV
ejpam-5848	9	2	,	,	PUNCT
ejpam-5848	9	3	several	several	ADJ
ejpam-5848	9	4	authors	author	NOUN
ejpam-5848	9	5	worked	work	VERB
ejpam-5848	9	6	on	on	ADP
ejpam-5848	9	7	the	the	DET
ejpam-5848	9	8	fuzzification	fuzzification	NOUN
ejpam-5848	9	9	of	of	ADP
ejpam-5848	9	10	numerous	numerous	ADJ
ejpam-5848	9	11	classical	classical	ADJ
ejpam-5848	9	12	notions	notion	NOUN
ejpam-5848	9	13	related	relate	VERB
ejpam-5848	9	14	to	to	ADP
ejpam-5848	9	15	topology	topology	NOUN
ejpam-5848	9	16	[	[	X
ejpam-5848	9	17	1	1	NUM
ejpam-5848	9	18	,	,	PUNCT
ejpam-5848	9	19	2	2	NUM
ejpam-5848	9	20	,	,	PUNCT
ejpam-5848	9	21	14	14	NUM
ejpam-5848	9	22	,	,	PUNCT
ejpam-5848	9	23	15	15	NUM
ejpam-5848	9	24	,	,	PUNCT
ejpam-5848	9	25	26	26	NUM
ejpam-5848	9	26	]	]	PUNCT
ejpam-5848	9	27	and	and	CCONJ
ejpam-5848	9	28	its	its	PRON
ejpam-5848	9	29	generalizations	generalization	NOUN
ejpam-5848	9	30	[	[	X
ejpam-5848	9	31	11	11	NUM
ejpam-5848	9	32	,	,	PUNCT
ejpam-5848	9	33	27	27	NUM
ejpam-5848	9	34	,	,	PUNCT
ejpam-5848	9	35	28	28	NUM
ejpam-5848	9	36	]	]	PUNCT
ejpam-5848	9	37	.	.	PUNCT
ejpam-5848	10	1	interest	interest	NOUN
ejpam-5848	10	2	in	in	ADP
ejpam-5848	10	3	topological	topological	ADJ
ejpam-5848	10	4	studies	study	NOUN
ejpam-5848	10	5	and	and	CCONJ
ejpam-5848	10	6	their	their	PRON
ejpam-5848	10	7	practical	practical	ADJ
ejpam-5848	10	8	applications	application	NOUN
ejpam-5848	10	9	has	have	AUX
ejpam-5848	10	10	grown	grow	VERB
ejpam-5848	10	11	recently	recently	ADV
ejpam-5848	10	12	,	,	PUNCT
ejpam-5848	10	13	particularly	particularly	ADV
ejpam-5848	10	14	∗corresponding	∗corresponde	VERB
ejpam-5848	10	15	author	author	NOUN
ejpam-5848	10	16	.	.	PUNCT
ejpam-5848	11	1	doi	doi	NOUN
ejpam-5848	11	2	:	:	PUNCT
ejpam-5848	11	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5848	https://doi.org/10.29020/nybg.ejpam.v18i1.5848	NUM
ejpam-5848	11	4	email	email	NOUN
ejpam-5848	11	5	addresses	address	NOUN
ejpam-5848	11	6	:	:	PUNCT
ejpam-5848	11	7	sandybrar86@gmail.com	sandybrar86@gmail.com	NUM
ejpam-5848	11	8	(	(	PUNCT
ejpam-5848	11	9	s.	s.	PROPN
ejpam-5848	11	10	kaur	kaur	PROPN
ejpam-5848	11	11	)	)	PUNCT
ejpam-5848	11	12	,	,	PUNCT
ejpam-5848	11	13	fathia.birkia@nbu.edu.sa	fathia.birkia@nbu.edu.sa	PROPN
ejpam-5848	11	14	(	(	PUNCT
ejpam-5848	11	15	f.m.o	f.m.o	NOUN
ejpam-5848	11	16	.	.	PUNCT
ejpam-5848	11	17	birkea	birkea	PROPN
ejpam-5848	11	18	)	)	PUNCT
ejpam-5848	11	19	,	,	PUNCT
ejpam-5848	11	20	alkan.ozkan@igdir.edu.tr	alkan.ozkan@igdir.edu.tr	INTJ
ejpam-5848	11	21	(	(	PUNCT
ejpam-5848	11	22	a.	a.	NOUN
ejpam-5848	11	23	özkan	özkan	PROPN
ejpam-5848	11	24	)	)	PUNCT
ejpam-5848	11	25	,	,	PUNCT
ejpam-5848	11	26	tareqalshami83@gmail.com	tareqalshami83@gmail.com	X
ejpam-5848	11	27	(	(	PUNCT
ejpam-5848	11	28	t.m	t.m	PROPN
ejpam-5848	11	29	.	.	PROPN
ejpam-5848	11	30	al	al	PROPN
ejpam-5848	11	31	-	-	PUNCT
ejpam-5848	11	32	shami	shami	PROPN
ejpam-5848	11	33	)	)	PUNCT
ejpam-5848	11	34	,	,	PUNCT
ejpam-5848	11	35	manar.omran@f-eng.tanta.edu.eg	manar.omran@f-eng.tanta.edu.eg	X
ejpam-5848	11	36	(	(	PUNCT
ejpam-5848	11	37	m.	m.	NOUN
ejpam-5848	11	38	omran	omran	PROPN
ejpam-5848	11	39	)	)	PUNCT
ejpam-5848	11	40	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5848	12	1	1	1	NUM
ejpam-5848	12	2	copyright	copyright	NOUN
ejpam-5848	12	3	:	:	PUNCT
ejpam-5848	12	4	©	©	PROPN
ejpam-5848	12	5	2025	2025	NUM
ejpam-5848	12	6	the	the	DET
ejpam-5848	12	7	author(s	author(s	NOUN
ejpam-5848	12	8	)	)	PUNCT
ejpam-5848	12	9	.	.	PUNCT
ejpam-5848	13	1	(	(	PUNCT
ejpam-5848	13	2	cc	cc	NOUN
ejpam-5848	13	3	by	by	ADP
ejpam-5848	13	4	-	-	PUNCT
ejpam-5848	13	5	nc	nc	PROPN
ejpam-5848	13	6	4.0	4.0	NUM
ejpam-5848	13	7	)	)	PUNCT
ejpam-5848	13	8	s.	s.	PROPN
ejpam-5848	13	9	kaur	kaur	PROPN
ejpam-5848	13	10	et	et	PROPN
ejpam-5848	13	11	al	al	PROPN
ejpam-5848	13	12	.	.	PUNCT
ejpam-5848	13	13	/	/	SYM
ejpam-5848	13	14	eur	eur	PROPN
ejpam-5848	13	15	.	.	PUNCT
ejpam-5848	14	1	j.	j.	PROPN
ejpam-5848	14	2	pure	pure	PROPN
ejpam-5848	14	3	appl	appl	PROPN
ejpam-5848	14	4	.	.	PROPN
ejpam-5848	14	5	math	math	PROPN
ejpam-5848	14	6	,	,	PUNCT
ejpam-5848	14	7	18	18	NUM
ejpam-5848	14	8	(	(	PUNCT
ejpam-5848	14	9	1	1	NUM
ejpam-5848	14	10	)	)	PUNCT
ejpam-5848	14	11	(	(	PUNCT
ejpam-5848	14	12	2025	2025	NUM
ejpam-5848	14	13	)	)	PUNCT
ejpam-5848	14	14	,	,	PUNCT
ejpam-5848	14	15	5848	5848	NUM
ejpam-5848	14	16	2	2	NUM
ejpam-5848	14	17	of	of	ADP
ejpam-5848	14	18	11	11	NUM
ejpam-5848	14	19	after	after	ADP
ejpam-5848	14	20	realizing	realize	VERB
ejpam-5848	14	21	that	that	SCONJ
ejpam-5848	14	22	certain	certain	ADJ
ejpam-5848	14	23	abstract	abstract	ADJ
ejpam-5848	14	24	topological	topological	ADJ
ejpam-5848	14	25	concepts	concept	NOUN
ejpam-5848	14	26	can	can	AUX
ejpam-5848	14	27	be	be	AUX
ejpam-5848	14	28	applied	apply	VERB
ejpam-5848	14	29	to	to	PART
ejpam-5848	14	30	solve	solve	VERB
ejpam-5848	14	31	real	real	ADJ
ejpam-5848	14	32	-	-	PUNCT
ejpam-5848	14	33	life	life	NOUN
ejpam-5848	14	34	problems	problem	NOUN
ejpam-5848	14	35	.	.	PUNCT
ejpam-5848	15	1	for	for	ADP
ejpam-5848	15	2	example	example	NOUN
ejpam-5848	15	3	:	:	PUNCT
ejpam-5848	15	4	•	•	ADP
ejpam-5848	16	1	the	the	DET
ejpam-5848	16	2	studies	study	NOUN
ejpam-5848	16	3	in	in	ADP
ejpam-5848	16	4	[	[	X
ejpam-5848	16	5	7	7	NUM
ejpam-5848	16	6	,	,	PUNCT
ejpam-5848	16	7	10	10	NUM
ejpam-5848	16	8	,	,	PUNCT
ejpam-5848	16	9	19	19	NUM
ejpam-5848	16	10	]	]	PUNCT
ejpam-5848	16	11	utilized	utilize	VERB
ejpam-5848	16	12	certain	certain	ADJ
ejpam-5848	16	13	extended	extended	ADJ
ejpam-5848	16	14	forms	form	NOUN
ejpam-5848	16	15	of	of	ADP
ejpam-5848	16	16	open	open	ADJ
ejpam-5848	16	17	subsets	subset	NOUN
ejpam-5848	16	18	,	,	PUNCT
ejpam-5848	16	19	including	include	VERB
ejpam-5848	16	20	somewhat	somewhat	ADV
ejpam-5848	16	21	dense	dense	ADJ
ejpam-5848	16	22	,	,	PUNCT
ejpam-5848	16	23	somewhere	somewhere	ADV
ejpam-5848	16	24	dense	dense	ADJ
ejpam-5848	16	25	,	,	PUNCT
ejpam-5848	16	26	and	and	CCONJ
ejpam-5848	16	27	θβ	θβ	NOUN
ejpam-5848	16	28	-	-	PUNCT
ejpam-5848	16	29	open	open	ADJ
ejpam-5848	16	30	subsets	subset	NOUN
ejpam-5848	16	31	,	,	PUNCT
ejpam-5848	16	32	to	to	PART
ejpam-5848	16	33	analyze	analyze	VERB
ejpam-5848	16	34	information	information	NOUN
ejpam-5848	16	35	systems	system	NOUN
ejpam-5848	16	36	described	describe	VERB
ejpam-5848	16	37	by	by	ADP
ejpam-5848	16	38	rough	rough	ADJ
ejpam-5848	16	39	approximation	approximation	NOUN
ejpam-5848	16	40	operators	operator	NOUN
ejpam-5848	16	41	.	.	PUNCT
ejpam-5848	17	1	•	•	NUM
ejpam-5848	17	2	various	various	ADJ
ejpam-5848	17	3	separation	separation	NOUN
ejpam-5848	17	4	axioms	axiom	NOUN
ejpam-5848	17	5	were	be	AUX
ejpam-5848	17	6	examined	examine	VERB
ejpam-5848	17	7	and	and	CCONJ
ejpam-5848	17	8	applied	apply	VERB
ejpam-5848	17	9	in	in	ADP
ejpam-5848	17	10	[	[	X
ejpam-5848	17	11	8	8	NUM
ejpam-5848	17	12	,	,	PUNCT
ejpam-5848	17	13	9	9	NUM
ejpam-5848	17	14	,	,	PUNCT
ejpam-5848	17	15	18	18	NUM
ejpam-5848	17	16	]	]	PUNCT
ejpam-5848	17	17	to	to	PART
ejpam-5848	17	18	select	select	VERB
ejpam-5848	17	19	the	the	DET
ejpam-5848	17	20	optimal	optimal	ADJ
ejpam-5848	17	21	tourism	tourism	NOUN
ejpam-5848	17	22	program	program	NOUN
ejpam-5848	17	23	and	and	CCONJ
ejpam-5848	17	24	determine	determine	VERB
ejpam-5848	17	25	the	the	DET
ejpam-5848	17	26	appropriate	appropriate	ADJ
ejpam-5848	17	27	nutrition	nutrition	NOUN
ejpam-5848	17	28	system	system	NOUN
ejpam-5848	17	29	for	for	ADP
ejpam-5848	17	30	individuals	individual	NOUN
ejpam-5848	17	31	.	.	PUNCT
ejpam-5848	18	1	•	•	NUM
ejpam-5848	18	2	the	the	DET
ejpam-5848	18	3	concepts	concept	NOUN
ejpam-5848	18	4	of	of	ADP
ejpam-5848	18	5	compactness	compactness	NOUN
ejpam-5848	18	6	and	and	CCONJ
ejpam-5848	18	7	connectedness	connectedness	NOUN
ejpam-5848	18	8	were	be	AUX
ejpam-5848	18	9	exploited	exploit	VERB
ejpam-5848	18	10	in	in	ADP
ejpam-5848	18	11	[	[	X
ejpam-5848	18	12	6	6	NUM
ejpam-5848	18	13	,	,	PUNCT
ejpam-5848	18	14	13	13	NUM
ejpam-5848	18	15	]	]	PUNCT
ejpam-5848	18	16	for	for	ADP
ejpam-5848	18	17	optimal	optimal	ADJ
ejpam-5848	18	18	selection	selection	NOUN
ejpam-5848	18	19	and	and	CCONJ
ejpam-5848	18	20	to	to	PART
ejpam-5848	18	21	investigate	investigate	VERB
ejpam-5848	18	22	the	the	DET
ejpam-5848	18	23	fixed	fix	VERB
ejpam-5848	18	24	point	point	NOUN
ejpam-5848	18	25	theorem	theorem	VERB
ejpam-5848	18	26	.	.	PUNCT
ejpam-5848	19	1	in	in	ADP
ejpam-5848	19	2	1974	1974	NUM
ejpam-5848	19	3	,	,	PUNCT
ejpam-5848	19	4	wong	wong	PROPN
ejpam-5848	19	5	[	[	X
ejpam-5848	19	6	29	29	NUM
ejpam-5848	19	7	]	]	PUNCT
ejpam-5848	19	8	described	describe	VERB
ejpam-5848	19	9	open	open	ADJ
ejpam-5848	19	10	fuzzy	fuzzy	ADJ
ejpam-5848	19	11	and	and	CCONJ
ejpam-5848	19	12	closed	close	VERB
ejpam-5848	19	13	fuzzy	fuzzy	ADJ
ejpam-5848	19	14	mappings	mapping	NOUN
ejpam-5848	19	15	,	,	PUNCT
ejpam-5848	19	16	and	and	CCONJ
ejpam-5848	19	17	few	few	ADJ
ejpam-5848	19	18	characterizations	characterization	NOUN
ejpam-5848	19	19	of	of	ADP
ejpam-5848	19	20	those	those	DET
ejpam-5848	19	21	mappings	mapping	NOUN
ejpam-5848	19	22	were	be	AUX
ejpam-5848	19	23	observed	observe	VERB
ejpam-5848	19	24	in	in	ADP
ejpam-5848	19	25	[	[	X
ejpam-5848	19	26	22	22	NUM
ejpam-5848	19	27	]	]	PUNCT
ejpam-5848	19	28	,	,	PUNCT
ejpam-5848	19	29	whereas	whereas	SCONJ
ejpam-5848	19	30	,	,	PUNCT
ejpam-5848	19	31	in	in	ADP
ejpam-5848	19	32	1984	1984	NUM
ejpam-5848	19	33	[	[	X
ejpam-5848	19	34	23	23	NUM
ejpam-5848	19	35	]	]	PUNCT
ejpam-5848	19	36	,	,	PUNCT
ejpam-5848	19	37	a	a	DET
ejpam-5848	19	38	few	few	ADJ
ejpam-5848	19	39	additional	additional	ADJ
ejpam-5848	19	40	characterizations	characterization	NOUN
ejpam-5848	19	41	of	of	ADP
ejpam-5848	19	42	open	open	ADJ
ejpam-5848	19	43	fuzzy	fuzzy	ADJ
ejpam-5848	19	44	and	and	CCONJ
ejpam-5848	19	45	closed	close	VERB
ejpam-5848	19	46	fuzzy	fuzzy	ADJ
ejpam-5848	19	47	mappings	mapping	NOUN
ejpam-5848	19	48	were	be	AUX
ejpam-5848	19	49	investigated	investigate	VERB
ejpam-5848	19	50	.	.	PUNCT
ejpam-5848	20	1	open	open	ADJ
ejpam-5848	20	2	fuzzy	fuzzy	ADJ
ejpam-5848	20	3	mappings	mapping	NOUN
ejpam-5848	20	4	offer	offer	VERB
ejpam-5848	20	5	a	a	DET
ejpam-5848	20	6	logical	logical	ADJ
ejpam-5848	20	7	extension	extension	NOUN
ejpam-5848	20	8	for	for	ADP
ejpam-5848	20	9	addressing	address	VERB
ejpam-5848	20	10	uncertainties	uncertainty	NOUN
ejpam-5848	20	11	and	and	CCONJ
ejpam-5848	20	12	ambiguities	ambiguity	NOUN
ejpam-5848	20	13	inherent	inherent	ADJ
ejpam-5848	20	14	in	in	ADP
ejpam-5848	20	15	real	real	ADJ
ejpam-5848	20	16	-	-	PUNCT
ejpam-5848	20	17	world	world	NOUN
ejpam-5848	20	18	applications	application	NOUN
ejpam-5848	20	19	,	,	PUNCT
ejpam-5848	20	20	much	much	ADV
ejpam-5848	20	21	as	as	SCONJ
ejpam-5848	20	22	open	open	ADJ
ejpam-5848	20	23	mappings	mapping	NOUN
ejpam-5848	20	24	are	be	AUX
ejpam-5848	20	25	vital	vital	ADJ
ejpam-5848	20	26	in	in	ADP
ejpam-5848	20	27	classical	classical	ADJ
ejpam-5848	20	28	set	set	NOUN
ejpam-5848	20	29	theory	theory	NOUN
ejpam-5848	20	30	.	.	PUNCT
ejpam-5848	21	1	one	one	NUM
ejpam-5848	21	2	of	of	ADP
ejpam-5848	21	3	the	the	DET
ejpam-5848	21	4	key	key	ADJ
ejpam-5848	21	5	properties	property	NOUN
ejpam-5848	21	6	of	of	ADP
ejpam-5848	21	7	open	open	ADJ
ejpam-5848	21	8	fuzzy	fuzzy	ADJ
ejpam-5848	21	9	mappings	mapping	NOUN
ejpam-5848	21	10	is	be	AUX
ejpam-5848	21	11	that	that	SCONJ
ejpam-5848	21	12	they	they	PRON
ejpam-5848	21	13	preserve	preserve	VERB
ejpam-5848	21	14	the	the	DET
ejpam-5848	21	15	structure	structure	NOUN
ejpam-5848	21	16	of	of	ADP
ejpam-5848	21	17	open	open	ADJ
ejpam-5848	21	18	fuzzy	fuzzy	ADJ
ejpam-5848	21	19	sets	set	NOUN
ejpam-5848	21	20	.	.	PUNCT
ejpam-5848	22	1	open	open	ADJ
ejpam-5848	22	2	fuzzy	fuzzy	ADJ
ejpam-5848	22	3	mappings	mapping	NOUN
ejpam-5848	22	4	can	can	AUX
ejpam-5848	22	5	also	also	ADV
ejpam-5848	22	6	be	be	AUX
ejpam-5848	22	7	characterized	characterize	VERB
ejpam-5848	22	8	using	use	VERB
ejpam-5848	22	9	the	the	DET
ejpam-5848	22	10	fuzzy	fuzzy	ADJ
ejpam-5848	22	11	interior	interior	ADJ
ejpam-5848	22	12	operator	operator	NOUN
ejpam-5848	22	13	.	.	PUNCT
ejpam-5848	23	1	similarly	similarly	ADV
ejpam-5848	23	2	,	,	PUNCT
ejpam-5848	23	3	closed	close	VERB
ejpam-5848	23	4	fuzzy	fuzzy	ADJ
ejpam-5848	23	5	mappings	mapping	NOUN
ejpam-5848	23	6	also	also	ADV
ejpam-5848	23	7	play	play	VERB
ejpam-5848	23	8	a	a	DET
ejpam-5848	23	9	significant	significant	ADJ
ejpam-5848	23	10	role	role	NOUN
ejpam-5848	23	11	in	in	ADP
ejpam-5848	23	12	advancing	advance	VERB
ejpam-5848	23	13	our	our	PRON
ejpam-5848	23	14	understanding	understanding	NOUN
ejpam-5848	23	15	of	of	ADP
ejpam-5848	23	16	uncertainty	uncertainty	NOUN
ejpam-5848	23	17	modeling	model	VERB
ejpam-5848	23	18	and	and	CCONJ
ejpam-5848	23	19	reasoning	reasoning	NOUN
ejpam-5848	23	20	which	which	PRON
ejpam-5848	23	21	is	be	AUX
ejpam-5848	23	22	characterized	characterize	VERB
ejpam-5848	23	23	in	in	ADP
ejpam-5848	23	24	terms	term	NOUN
ejpam-5848	23	25	of	of	ADP
ejpam-5848	23	26	fuzzy	fuzzy	ADJ
ejpam-5848	23	27	closure	closure	NOUN
ejpam-5848	23	28	operator	operator	NOUN
ejpam-5848	23	29	.	.	PUNCT
ejpam-5848	24	1	our	our	PRON
ejpam-5848	24	2	motive	motive	NOUN
ejpam-5848	24	3	in	in	ADP
ejpam-5848	24	4	this	this	DET
ejpam-5848	24	5	study	study	NOUN
ejpam-5848	24	6	is	be	AUX
ejpam-5848	24	7	to	to	PART
ejpam-5848	24	8	find	find	VERB
ejpam-5848	24	9	more	more	ADJ
ejpam-5848	24	10	characterizations	characterization	NOUN
ejpam-5848	24	11	of	of	ADP
ejpam-5848	24	12	open	open	ADJ
ejpam-5848	24	13	fuzzy	fuzzy	ADJ
ejpam-5848	24	14	and	and	CCONJ
ejpam-5848	24	15	closed	close	VERB
ejpam-5848	24	16	fuzzy	fuzzy	ADJ
ejpam-5848	24	17	mappings	mapping	NOUN
ejpam-5848	24	18	in	in	ADP
ejpam-5848	24	19	terms	term	NOUN
ejpam-5848	24	20	of	of	ADP
ejpam-5848	24	21	fuzzy	fuzzy	ADJ
ejpam-5848	24	22	closure	closure	NOUN
ejpam-5848	24	23	operator	operator	NOUN
ejpam-5848	24	24	and	and	CCONJ
ejpam-5848	24	25	fuzzy	fuzzy	ADJ
ejpam-5848	24	26	interior	interior	ADJ
ejpam-5848	24	27	operator	operator	NOUN
ejpam-5848	24	28	,	,	PUNCT
ejpam-5848	24	29	respectively	respectively	ADV
ejpam-5848	24	30	.	.	PUNCT
ejpam-5848	25	1	for	for	ADP
ejpam-5848	25	2	this	this	PRON
ejpam-5848	25	3	,	,	PUNCT
ejpam-5848	25	4	we	we	PRON
ejpam-5848	25	5	make	make	VERB
ejpam-5848	25	6	use	use	NOUN
ejpam-5848	25	7	of	of	ADP
ejpam-5848	25	8	induced	induced	ADJ
ejpam-5848	25	9	mappings	mapping	NOUN
ejpam-5848	25	10	which	which	PRON
ejpam-5848	25	11	are	be	AUX
ejpam-5848	25	12	essential	essential	ADJ
ejpam-5848	25	13	in	in	ADP
ejpam-5848	25	14	the	the	DET
ejpam-5848	25	15	observation	observation	NOUN
ejpam-5848	25	16	of	of	ADP
ejpam-5848	25	17	many	many	ADJ
ejpam-5848	25	18	spaces	space	NOUN
ejpam-5848	25	19	in	in	ADP
ejpam-5848	25	20	topology	topology	NOUN
ejpam-5848	25	21	.	.	PUNCT
ejpam-5848	26	1	as	as	ADV
ejpam-5848	26	2	well	well	ADV
ejpam-5848	26	3	-	-	PUNCT
ejpam-5848	26	4	known	know	VERB
ejpam-5848	26	5	,	,	PUNCT
ejpam-5848	26	6	any	any	DET
ejpam-5848	26	7	type	type	NOUN
ejpam-5848	26	8	of	of	ADP
ejpam-5848	26	9	structure	structure	NOUN
ejpam-5848	26	10	or	or	CCONJ
ejpam-5848	26	11	application	application	NOUN
ejpam-5848	26	12	of	of	ADP
ejpam-5848	26	13	an	an	DET
ejpam-5848	26	14	operator	operator	NOUN
ejpam-5848	26	15	to	to	ADP
ejpam-5848	26	16	a	a	DET
ejpam-5848	26	17	mapping	mapping	NOUN
ejpam-5848	26	18	can	can	AUX
ejpam-5848	26	19	deliver	deliver	VERB
ejpam-5848	26	20	upward	upward	ADV
ejpam-5848	26	21	thrust	thrust	VERB
ejpam-5848	26	22	to	to	ADP
ejpam-5848	26	23	useful	useful	ADJ
ejpam-5848	26	24	induced	induced	ADJ
ejpam-5848	26	25	mappings	mapping	NOUN
ejpam-5848	26	26	.	.	PUNCT
ejpam-5848	27	1	in	in	ADP
ejpam-5848	27	2	view	view	NOUN
ejpam-5848	27	3	of	of	ADP
ejpam-5848	27	4	an	an	DET
ejpam-5848	27	5	induced	induce	VERB
ejpam-5848	27	6	mapping	mapping	NOUN
ejpam-5848	27	7	ψ	ψ	NOUN
ejpam-5848	27	8	#	#	NOUN
ejpam-5848	27	9	:	:	PUNCT
ejpam-5848	27	10	v	v	NOUN
ejpam-5848	27	11	→	→	SYM
ejpam-5848	27	12	w	w	NOUN
ejpam-5848	27	13	given	give	VERB
ejpam-5848	27	14	by	by	ADP
ejpam-5848	27	15	ψ#(u	ψ#(u	PROPN
ejpam-5848	27	16	)	)	PUNCT
ejpam-5848	27	17	=	=	PRON
ejpam-5848	27	18	{	{	PUNCT
ejpam-5848	27	19	w	w	NOUN
ejpam-5848	27	20	∈	∈	PROPN
ejpam-5848	27	21	w	w	PROPN
ejpam-5848	27	22	|ψ−1(w	|ψ−1(w	NOUN
ejpam-5848	27	23	)	)	PUNCT
ejpam-5848	27	24	⊆	⊆	NUM
ejpam-5848	27	25	u	u	NOUN
ejpam-5848	27	26	}	}	PUNCT
ejpam-5848	27	27	for	for	ADP
ejpam-5848	27	28	any	any	DET
ejpam-5848	27	29	subset	subset	NOUN
ejpam-5848	27	30	u	u	NOUN
ejpam-5848	27	31	of	of	ADP
ejpam-5848	27	32	v	v	NOUN
ejpam-5848	27	33	introduced	introduce	VERB
ejpam-5848	27	34	arkhangel’skii	arkhangel’skii	ADV
ejpam-5848	27	35	in	in	ADP
ejpam-5848	27	36	[	[	X
ejpam-5848	27	37	16	16	NUM
ejpam-5848	27	38	]	]	PUNCT
ejpam-5848	27	39	,	,	PUNCT
ejpam-5848	27	40	kaur	kaur	PROPN
ejpam-5848	27	41	and	and	CCONJ
ejpam-5848	27	42	goyal	goyal	PROPN
ejpam-5848	27	43	introduced	introduce	VERB
ejpam-5848	27	44	the	the	DET
ejpam-5848	27	45	#	#	SYM
ejpam-5848	27	46	-image	-image	NOUN
ejpam-5848	27	47	of	of	ADP
ejpam-5848	27	48	a	a	DET
ejpam-5848	27	49	fuzzy	fuzzy	ADJ
ejpam-5848	27	50	set	set	NOUN
ejpam-5848	27	51	(	(	PUNCT
ejpam-5848	27	52	f	f	PROPN
ejpam-5848	27	53	-set	-set	PROPN
ejpam-5848	27	54	,	,	PUNCT
ejpam-5848	27	55	in	in	ADP
ejpam-5848	27	56	short	short	ADJ
ejpam-5848	27	57	)	)	PUNCT
ejpam-5848	27	58	to	to	PART
ejpam-5848	27	59	define	define	VERB
ejpam-5848	27	60	a	a	DET
ejpam-5848	27	61	useful	useful	ADJ
ejpam-5848	27	62	induced	induced	ADJ
ejpam-5848	27	63	mapping	mapping	NOUN
ejpam-5848	27	64	ψ	ψ	NOUN
ejpam-5848	27	65	#	#	NOUN
ejpam-5848	27	66	in	in	ADP
ejpam-5848	27	67	[	[	X
ejpam-5848	27	68	21	21	NUM
ejpam-5848	27	69	]	]	PUNCT
ejpam-5848	27	70	together	together	ADV
ejpam-5848	27	71	with	with	ADP
ejpam-5848	27	72	its	its	PRON
ejpam-5848	27	73	properties	property	NOUN
ejpam-5848	27	74	.	.	PUNCT
ejpam-5848	28	1	with	with	ADP
ejpam-5848	28	2	this	this	DET
ejpam-5848	28	3	induced	induce	VERB
ejpam-5848	28	4	mapping	mapping	NOUN
ejpam-5848	28	5	ψ	ψ	NOUN
ejpam-5848	28	6	#	#	NUM
ejpam-5848	28	7	,	,	PUNCT
ejpam-5848	28	8	they	they	PRON
ejpam-5848	28	9	presented	present	VERB
ejpam-5848	28	10	a	a	DET
ejpam-5848	28	11	new	new	ADJ
ejpam-5848	28	12	sight	sight	NOUN
ejpam-5848	28	13	of	of	ADP
ejpam-5848	28	14	reading	read	VERB
ejpam-5848	28	15	bluecontinuous	bluecontinuous	ADJ
ejpam-5848	28	16	fuzzy	fuzzy	ADJ
ejpam-5848	28	17	mappings	mapping	NOUN
ejpam-5848	28	18	and	and	CCONJ
ejpam-5848	28	19	their	their	PRON
ejpam-5848	28	20	characterizations	characterization	NOUN
ejpam-5848	28	21	.	.	PUNCT
ejpam-5848	29	1	this	this	PRON
ejpam-5848	29	2	indicates	indicate	VERB
ejpam-5848	29	3	the	the	DET
ejpam-5848	29	4	possibility	possibility	NOUN
ejpam-5848	29	5	of	of	ADP
ejpam-5848	29	6	describing	describe	VERB
ejpam-5848	29	7	open	open	ADJ
ejpam-5848	29	8	fuzzy	fuzzy	ADJ
ejpam-5848	29	9	and	and	CCONJ
ejpam-5848	29	10	closed	close	VERB
ejpam-5848	29	11	fuzzy	fuzzy	ADJ
ejpam-5848	29	12	mappings	mapping	NOUN
ejpam-5848	29	13	in	in	ADP
ejpam-5848	29	14	connection	connection	NOUN
ejpam-5848	29	15	with	with	ADP
ejpam-5848	29	16	this	this	DET
ejpam-5848	29	17	induced	induce	VERB
ejpam-5848	29	18	mapping	mapping	NOUN
ejpam-5848	29	19	which	which	PRON
ejpam-5848	29	20	further	far	ADV
ejpam-5848	29	21	helps	help	VERB
ejpam-5848	29	22	us	we	PRON
ejpam-5848	29	23	to	to	PART
ejpam-5848	29	24	find	find	VERB
ejpam-5848	29	25	their	their	PRON
ejpam-5848	29	26	new	new	ADJ
ejpam-5848	29	27	representations	representation	NOUN
ejpam-5848	29	28	in	in	ADP
ejpam-5848	29	29	terms	term	NOUN
ejpam-5848	29	30	of	of	ADP
ejpam-5848	29	31	the	the	DET
ejpam-5848	29	32	fuzzy	fuzzy	ADJ
ejpam-5848	29	33	closure	closure	NOUN
ejpam-5848	29	34	operator	operator	NOUN
ejpam-5848	29	35	and	and	CCONJ
ejpam-5848	29	36	fuzzy	fuzzy	ADJ
ejpam-5848	29	37	interior	interior	ADJ
ejpam-5848	29	38	operator	operator	NOUN
ejpam-5848	29	39	,	,	PUNCT
ejpam-5848	29	40	respectively	respectively	ADV
ejpam-5848	29	41	.	.	PUNCT
ejpam-5848	30	1	to	to	PART
ejpam-5848	30	2	complete	complete	VERB
ejpam-5848	30	3	the	the	DET
ejpam-5848	30	4	literature	literature	NOUN
ejpam-5848	30	5	review	review	NOUN
ejpam-5848	30	6	presentation	presentation	NOUN
ejpam-5848	30	7	,	,	PUNCT
ejpam-5848	30	8	we	we	PRON
ejpam-5848	30	9	draw	draw	VERB
ejpam-5848	30	10	the	the	DET
ejpam-5848	30	11	readers	reader	NOUN
ejpam-5848	30	12	’	’	PART
ejpam-5848	30	13	attention	attention	NOUN
ejpam-5848	30	14	to	to	ADP
ejpam-5848	30	15	the	the	DET
ejpam-5848	30	16	fact	fact	NOUN
ejpam-5848	30	17	that	that	SCONJ
ejpam-5848	30	18	the	the	DET
ejpam-5848	30	19	proposed	propose	VERB
ejpam-5848	30	20	technique	technique	NOUN
ejpam-5848	30	21	of	of	ADP
ejpam-5848	30	22	describing	describe	VERB
ejpam-5848	30	23	mappings	mapping	NOUN
ejpam-5848	30	24	via	via	ADP
ejpam-5848	30	25	a	a	DET
ejpam-5848	30	26	soft	soft	ADJ
ejpam-5848	30	27	framework	framework	NOUN
ejpam-5848	30	28	was	be	AUX
ejpam-5848	30	29	studied	study	VERB
ejpam-5848	30	30	in	in	ADP
ejpam-5848	30	31	[	[	X
ejpam-5848	30	32	12	12	NUM
ejpam-5848	30	33	,	,	PUNCT
ejpam-5848	30	34	20	20	NUM
ejpam-5848	30	35	]	]	PUNCT
ejpam-5848	30	36	.	.	PUNCT
ejpam-5848	31	1	in	in	ADP
ejpam-5848	31	2	this	this	DET
ejpam-5848	31	3	study	study	NOUN
ejpam-5848	31	4	,	,	PUNCT
ejpam-5848	31	5	some	some	DET
ejpam-5848	31	6	new	new	ADJ
ejpam-5848	31	7	characterizations	characterization	NOUN
ejpam-5848	31	8	of	of	ADP
ejpam-5848	31	9	open	open	ADJ
ejpam-5848	31	10	fuzzy	fuzzy	ADJ
ejpam-5848	31	11	and	and	CCONJ
ejpam-5848	31	12	closed	close	VERB
ejpam-5848	31	13	fuzzy	fuzzy	ADJ
ejpam-5848	31	14	mappings	mapping	NOUN
ejpam-5848	31	15	and	and	CCONJ
ejpam-5848	31	16	the	the	DET
ejpam-5848	31	17	use	use	NOUN
ejpam-5848	31	18	of	of	ADP
ejpam-5848	31	19	induced	induce	VERB
ejpam-5848	31	20	mapping	mapping	NOUN
ejpam-5848	31	21	ψ	ψ	NOUN
ejpam-5848	31	22	#	#	NOUN
ejpam-5848	31	23	are	be	AUX
ejpam-5848	31	24	discussed	discuss	VERB
ejpam-5848	31	25	.	.	PUNCT
ejpam-5848	32	1	we	we	PRON
ejpam-5848	32	2	describe	describe	VERB
ejpam-5848	32	3	the	the	DET
ejpam-5848	32	4	open	open	ADJ
ejpam-5848	32	5	fuzzy	fuzzy	ADJ
ejpam-5848	32	6	mappings	mapping	NOUN
ejpam-5848	32	7	in	in	ADP
ejpam-5848	32	8	recognition	recognition	NOUN
ejpam-5848	32	9	of	of	ADP
ejpam-5848	32	10	induced	induced	ADJ
ejpam-5848	32	11	mapping	mapping	NOUN
ejpam-5848	32	12	of	of	ADP
ejpam-5848	32	13	closed	close	VERB
ejpam-5848	32	14	fuzzy	fuzzy	ADJ
ejpam-5848	32	15	sets	set	NOUN
ejpam-5848	32	16	rather	rather	ADV
ejpam-5848	32	17	than	than	ADP
ejpam-5848	32	18	already	already	ADV
ejpam-5848	32	19	proven	prove	VERB
ejpam-5848	32	20	results	result	NOUN
ejpam-5848	32	21	of	of	ADP
ejpam-5848	32	22	open	open	ADJ
ejpam-5848	32	23	fuzzy	fuzzy	ADJ
ejpam-5848	32	24	mappings	mapping	NOUN
ejpam-5848	32	25	in	in	ADP
ejpam-5848	32	26	regards	regard	NOUN
ejpam-5848	32	27	to	to	ADP
ejpam-5848	32	28	interiors	interior	NOUN
ejpam-5848	32	29	.	.	PUNCT
ejpam-5848	33	1	a	a	DET
ejpam-5848	33	2	few	few	ADJ
ejpam-5848	33	3	characterizations	characterization	NOUN
ejpam-5848	33	4	of	of	ADP
ejpam-5848	33	5	these	these	DET
ejpam-5848	33	6	mappings	mapping	NOUN
ejpam-5848	33	7	are	be	AUX
ejpam-5848	33	8	also	also	ADV
ejpam-5848	33	9	taken	take	VERB
ejpam-5848	33	10	into	into	ADP
ejpam-5848	33	11	consideration	consideration	NOUN
ejpam-5848	33	12	in	in	ADP
ejpam-5848	33	13	the	the	DET
ejpam-5848	33	14	use	use	NOUN
ejpam-5848	33	15	of	of	ADP
ejpam-5848	33	16	saturated	saturate	VERB
ejpam-5848	33	17	fuzzy	fuzzy	ADJ
ejpam-5848	33	18	sets	set	NOUN
ejpam-5848	33	19	.	.	PUNCT
ejpam-5848	34	1	s.	s.	PROPN
ejpam-5848	34	2	kaur	kaur	PROPN
ejpam-5848	34	3	et	et	PROPN
ejpam-5848	34	4	al	al	PROPN
ejpam-5848	34	5	.	.	PUNCT
ejpam-5848	34	6	/	/	SYM
ejpam-5848	34	7	eur	eur	PROPN
ejpam-5848	34	8	.	.	PUNCT
ejpam-5848	35	1	j.	j.	PROPN
ejpam-5848	35	2	pure	pure	PROPN
ejpam-5848	35	3	appl	appl	PROPN
ejpam-5848	35	4	.	.	PROPN
ejpam-5848	35	5	math	math	PROPN
ejpam-5848	35	6	,	,	PUNCT
ejpam-5848	35	7	18	18	NUM
ejpam-5848	35	8	(	(	PUNCT
ejpam-5848	35	9	1	1	NUM
ejpam-5848	35	10	)	)	PUNCT
ejpam-5848	35	11	(	(	PUNCT
ejpam-5848	35	12	2025	2025	NUM
ejpam-5848	35	13	)	)	PUNCT
ejpam-5848	35	14	,	,	PUNCT
ejpam-5848	35	15	5848	5848	NUM
ejpam-5848	35	16	3	3	NUM
ejpam-5848	35	17	of	of	ADP
ejpam-5848	35	18	11	11	NUM
ejpam-5848	35	19	2	2	NUM
ejpam-5848	35	20	.	.	PUNCT
ejpam-5848	35	21	preliminaries	preliminary	NOUN
ejpam-5848	35	22	throughout	throughout	ADP
ejpam-5848	35	23	this	this	DET
ejpam-5848	35	24	study	study	NOUN
ejpam-5848	35	25	,	,	PUNCT
ejpam-5848	35	26	v	v	NOUN
ejpam-5848	35	27	=	=	SYM
ejpam-5848	35	28	{	{	PUNCT
ejpam-5848	35	29	vi	vi	NOUN
ejpam-5848	35	30	:	:	PUNCT
ejpam-5848	36	1	i	i	PRON
ejpam-5848	36	2	∈	∈	PROPN
ejpam-5848	36	3	i	i	PRON
ejpam-5848	36	4	}	}	PUNCT
ejpam-5848	36	5	refers	refer	VERB
ejpam-5848	36	6	to	to	ADP
ejpam-5848	36	7	a	a	DET
ejpam-5848	36	8	space	space	NOUN
ejpam-5848	36	9	of	of	ADP
ejpam-5848	36	10	points	point	NOUN
ejpam-5848	36	11	and	and	CCONJ
ejpam-5848	36	12	a	a	DET
ejpam-5848	36	13	function	function	NOUN
ejpam-5848	36	14	µe	µe	ADP
ejpam-5848	36	15	is	be	AUX
ejpam-5848	36	16	the	the	DET
ejpam-5848	36	17	membership	membership	NOUN
ejpam-5848	36	18	function	function	NOUN
ejpam-5848	36	19	for	for	ADP
ejpam-5848	36	20	any	any	DET
ejpam-5848	36	21	f	f	PROPN
ejpam-5848	36	22	-set	-set	ADJ
ejpam-5848	36	23	e.	e.	PROPN
ejpam-5848	37	1	an	an	DET
ejpam-5848	37	2	f	f	PROPN
ejpam-5848	37	3	-set	-set	PROPN
ejpam-5848	37	4	a	a	PRON
ejpam-5848	37	5	in	in	ADP
ejpam-5848	37	6	v	v	NOUN
ejpam-5848	37	7	is	be	AUX
ejpam-5848	37	8	represented	represent	VERB
ejpam-5848	37	9	by	by	ADP
ejpam-5848	37	10	a	a	DET
ejpam-5848	37	11	membership	membership	NOUN
ejpam-5848	37	12	function	function	NOUN
ejpam-5848	37	13	µa	µa	ADV
ejpam-5848	37	14	from	from	ADP
ejpam-5848	37	15	v	v	NUM
ejpam-5848	37	16	to	to	ADP
ejpam-5848	37	17	[	[	X
ejpam-5848	37	18	0	0	NUM
ejpam-5848	37	19	,	,	PUNCT
ejpam-5848	37	20	1	1	NUM
ejpam-5848	37	21	]	]	PUNCT
ejpam-5848	37	22	that	that	PRON
ejpam-5848	37	23	associates	associate	VERB
ejpam-5848	37	24	every	every	DET
ejpam-5848	37	25	v	v	NOUN
ejpam-5848	37	26	in	in	ADP
ejpam-5848	37	27	v	v	NOUN
ejpam-5848	37	28	with	with	ADP
ejpam-5848	37	29	its	its	PRON
ejpam-5848	37	30	”	"	PUNCT
ejpam-5848	37	31	membership	membership	NOUN
ejpam-5848	37	32	grade	grade	NOUN
ejpam-5848	37	33	”	"	PUNCT
ejpam-5848	37	34	µa(v	µa(v	PUNCT
ejpam-5848	37	35	)	)	PUNCT
ejpam-5848	37	36	in	in	ADP
ejpam-5848	37	37	[	[	X
ejpam-5848	37	38	0	0	NUM
ejpam-5848	37	39	,	,	PUNCT
ejpam-5848	37	40	1	1	NUM
ejpam-5848	37	41	]	]	PUNCT
ejpam-5848	37	42	.	.	PUNCT
ejpam-5848	38	1	chang	chang	PROPN
ejpam-5848	38	2	has	have	AUX
ejpam-5848	38	3	discussed	discuss	VERB
ejpam-5848	38	4	some	some	DET
ejpam-5848	38	5	basic	basic	ADJ
ejpam-5848	38	6	definitions	definition	NOUN
ejpam-5848	38	7	and	and	CCONJ
ejpam-5848	38	8	related	related	ADJ
ejpam-5848	38	9	results	result	NOUN
ejpam-5848	38	10	of	of	ADP
ejpam-5848	38	11	the	the	DET
ejpam-5848	38	12	f	f	PROPN
ejpam-5848	38	13	-set	-set	PUNCT
ejpam-5848	38	14	theory	theory	NOUN
ejpam-5848	38	15	,	,	PUNCT
ejpam-5848	38	16	fuzzy	fuzzy	ADJ
ejpam-5848	38	17	topologies	topology	NOUN
ejpam-5848	38	18	,	,	PUNCT
ejpam-5848	38	19	and	and	CCONJ
ejpam-5848	38	20	fuzzy	fuzzy	ADJ
ejpam-5848	38	21	mappings	mapping	NOUN
ejpam-5848	38	22	in	in	ADP
ejpam-5848	38	23	[	[	X
ejpam-5848	38	24	17	17	NUM
ejpam-5848	38	25	]	]	PUNCT
ejpam-5848	38	26	.	.	PUNCT
ejpam-5848	39	1	therefore	therefore	ADV
ejpam-5848	39	2	,	,	PUNCT
ejpam-5848	39	3	we	we	PRON
ejpam-5848	39	4	recall	recall	VERB
ejpam-5848	39	5	some	some	DET
ejpam-5848	39	6	other	other	ADJ
ejpam-5848	39	7	useful	useful	ADJ
ejpam-5848	39	8	definitions	definition	NOUN
ejpam-5848	39	9	related	relate	VERB
ejpam-5848	39	10	to	to	ADP
ejpam-5848	39	11	induced	induce	VERB
ejpam-5848	39	12	mapping	mapping	NOUN
ejpam-5848	39	13	ψ	ψ	NOUN
ejpam-5848	39	14	#	#	NOUN
ejpam-5848	39	15	,	,	PUNCT
ejpam-5848	39	16	open	open	ADJ
ejpam-5848	39	17	fuzzy	fuzzy	ADJ
ejpam-5848	39	18	mapping	mapping	NOUN
ejpam-5848	39	19	,	,	PUNCT
ejpam-5848	39	20	and	and	CCONJ
ejpam-5848	39	21	closed	close	VERB
ejpam-5848	39	22	fuzzy	fuzzy	ADJ
ejpam-5848	39	23	mapping	mapping	NOUN
ejpam-5848	39	24	which	which	PRON
ejpam-5848	39	25	we	we	PRON
ejpam-5848	39	26	shall	shall	AUX
ejpam-5848	39	27	use	use	VERB
ejpam-5848	39	28	in	in	ADP
ejpam-5848	39	29	the	the	DET
ejpam-5848	39	30	results	result	NOUN
ejpam-5848	39	31	investigated	investigate	VERB
ejpam-5848	39	32	through	through	ADP
ejpam-5848	39	33	this	this	DET
ejpam-5848	39	34	content	content	NOUN
ejpam-5848	39	35	.	.	PUNCT
ejpam-5848	40	1	we	we	PRON
ejpam-5848	40	2	begin	begin	VERB
ejpam-5848	40	3	with	with	ADP
ejpam-5848	40	4	definitions	definition	NOUN
ejpam-5848	40	5	of	of	ADP
ejpam-5848	40	6	fts	fts	PROPN
ejpam-5848	40	7	,	,	PUNCT
ejpam-5848	40	8	interior	interior	NOUN
ejpam-5848	40	9	,	,	PUNCT
ejpam-5848	40	10	and	and	CCONJ
ejpam-5848	40	11	closure	closure	NOUN
ejpam-5848	40	12	of	of	ADP
ejpam-5848	40	13	an	an	DET
ejpam-5848	40	14	f	f	PROPN
ejpam-5848	40	15	-set	-set	PROPN
ejpam-5848	40	16	.	.	PUNCT
ejpam-5848	41	1	definition	definition	NOUN
ejpam-5848	41	2	1	1	NUM
ejpam-5848	41	3	.	.	PUNCT
ejpam-5848	42	1	[	[	X
ejpam-5848	42	2	17	17	NUM
ejpam-5848	42	3	]	]	PUNCT
ejpam-5848	42	4	a	a	DET
ejpam-5848	42	5	family	family	NOUN
ejpam-5848	42	6	t	t	NOUN
ejpam-5848	42	7	of	of	ADP
ejpam-5848	42	8	f	f	PROPN
ejpam-5848	42	9	-sets	-set	NOUN
ejpam-5848	42	10	in	in	ADP
ejpam-5848	42	11	v	v	NOUN
ejpam-5848	42	12	is	be	AUX
ejpam-5848	42	13	said	say	VERB
ejpam-5848	42	14	to	to	PART
ejpam-5848	42	15	be	be	AUX
ejpam-5848	42	16	a	a	DET
ejpam-5848	42	17	fuzzy	fuzzy	ADJ
ejpam-5848	42	18	topology	topology	NOUN
ejpam-5848	42	19	if	if	SCONJ
ejpam-5848	42	20	it	it	PRON
ejpam-5848	42	21	satisfies	satisfy	VERB
ejpam-5848	42	22	following	follow	VERB
ejpam-5848	42	23	conditions	condition	NOUN
ejpam-5848	42	24	:	:	PUNCT
ejpam-5848	42	25	(	(	PUNCT
ejpam-5848	42	26	a	a	X
ejpam-5848	42	27	)	)	PUNCT
ejpam-5848	42	28	ϕ	ϕ	NOUN
ejpam-5848	42	29	,	,	PUNCT
ejpam-5848	42	30	v	v	NOUN
ejpam-5848	42	31	∈	∈	PROPN
ejpam-5848	42	32	t	t	NOUN
ejpam-5848	42	33	.	.	PUNCT
ejpam-5848	43	1	(	(	PUNCT
ejpam-5848	43	2	b	b	X
ejpam-5848	43	3	)	)	PUNCT
ejpam-5848	43	4	if	if	SCONJ
ejpam-5848	43	5	a	a	DET
ejpam-5848	43	6	,	,	PUNCT
ejpam-5848	43	7	b	b	PROPN
ejpam-5848	43	8	∈	∈	PROPN
ejpam-5848	43	9	t	t	NOUN
ejpam-5848	43	10	,	,	PUNCT
ejpam-5848	43	11	then	then	ADV
ejpam-5848	43	12	a	a	DET
ejpam-5848	43	13	∩b	∩b	NOUN
ejpam-5848	43	14	∈	∈	PROPN
ejpam-5848	43	15	t	t	NOUN
ejpam-5848	43	16	.	.	PUNCT
ejpam-5848	44	1	(	(	PUNCT
ejpam-5848	44	2	c	c	X
ejpam-5848	44	3	)	)	PUNCT
ejpam-5848	44	4	if	if	SCONJ
ejpam-5848	44	5	ai	ai	VERB
ejpam-5848	44	6	∈	∈	PROPN
ejpam-5848	44	7	t	t	PROPN
ejpam-5848	44	8	for	for	ADP
ejpam-5848	44	9	each	each	DET
ejpam-5848	44	10	i	i	PRON
ejpam-5848	44	11	∈	∈	PROPN
ejpam-5848	45	1	i	i	PRON
ejpam-5848	45	2	,	,	PUNCT
ejpam-5848	45	3	then	then	ADV
ejpam-5848	45	4	∪ai	∪ai	PROPN
ejpam-5848	45	5	∈	∈	PROPN
ejpam-5848	45	6	t	t	PROPN
ejpam-5848	45	7	.	.	PUNCT
ejpam-5848	46	1	every	every	DET
ejpam-5848	46	2	member	member	NOUN
ejpam-5848	46	3	of	of	ADP
ejpam-5848	46	4	t	t	PROPN
ejpam-5848	46	5	is	be	AUX
ejpam-5848	46	6	called	call	VERB
ejpam-5848	46	7	a	a	DET
ejpam-5848	46	8	t	t	NOUN
ejpam-5848	46	9	-open	-open	PROPN
ejpam-5848	46	10	f	f	PROPN
ejpam-5848	46	11	-set	-set	X
ejpam-5848	46	12	and	and	CCONJ
ejpam-5848	46	13	the	the	DET
ejpam-5848	46	14	pair	pair	NOUN
ejpam-5848	46	15	(	(	PUNCT
ejpam-5848	46	16	v	v	NOUN
ejpam-5848	46	17	,	,	PUNCT
ejpam-5848	46	18	t	t	PROPN
ejpam-5848	46	19	)	)	PUNCT
ejpam-5848	46	20	is	be	AUX
ejpam-5848	46	21	known	know	VERB
ejpam-5848	46	22	as	as	ADP
ejpam-5848	46	23	fts	fts	PROPN
ejpam-5848	46	24	.	.	PROPN
ejpam-5848	46	25	also	also	ADV
ejpam-5848	46	26	an	an	DET
ejpam-5848	46	27	f	f	PROPN
ejpam-5848	46	28	-set	-set	PROPN
ejpam-5848	46	29	is	be	AUX
ejpam-5848	46	30	named	name	VERB
ejpam-5848	46	31	t	t	NOUN
ejpam-5848	46	32	-closed	-close	VERB
ejpam-5848	46	33	if	if	SCONJ
ejpam-5848	46	34	and	and	CCONJ
ejpam-5848	46	35	only	only	ADV
ejpam-5848	46	36	if	if	SCONJ
ejpam-5848	46	37	its	its	PRON
ejpam-5848	46	38	complement	complement	NOUN
ejpam-5848	46	39	is	be	AUX
ejpam-5848	46	40	a	a	DET
ejpam-5848	46	41	t	t	NOUN
ejpam-5848	46	42	-open	-open	PROPN
ejpam-5848	46	43	f	f	PROPN
ejpam-5848	46	44	-set	-set	ADJ
ejpam-5848	46	45	.	.	PUNCT
ejpam-5848	47	1	definition	definition	NOUN
ejpam-5848	47	2	2	2	NUM
ejpam-5848	47	3	.	.	PUNCT
ejpam-5848	48	1	[	[	X
ejpam-5848	48	2	26	26	NUM
ejpam-5848	48	3	]	]	X
ejpam-5848	48	4	let	let	ADJ
ejpam-5848	48	5	(	(	PUNCT
ejpam-5848	48	6	v	v	NOUN
ejpam-5848	48	7	,	,	PUNCT
ejpam-5848	48	8	t	t	PROPN
ejpam-5848	48	9	)	)	PUNCT
ejpam-5848	48	10	be	be	AUX
ejpam-5848	48	11	fts	fts	PROPN
ejpam-5848	48	12	and	and	CCONJ
ejpam-5848	48	13	m	m	AUX
ejpam-5848	48	14	be	be	AUX
ejpam-5848	48	15	any	any	DET
ejpam-5848	48	16	f	f	NOUN
ejpam-5848	48	17	-set	-set	PUNCT
ejpam-5848	48	18	in	in	ADP
ejpam-5848	48	19	v	v	NOUN
ejpam-5848	48	20	.	.	PUNCT
ejpam-5848	49	1	then	then	ADV
ejpam-5848	49	2	:	:	PUNCT
ejpam-5848	49	3	(	(	PUNCT
ejpam-5848	49	4	i	i	NOUN
ejpam-5848	49	5	)	)	PUNCT
ejpam-5848	49	6	interior	interior	NOUN
ejpam-5848	49	7	of	of	ADP
ejpam-5848	49	8	m	m	PROPN
ejpam-5848	49	9	is	be	AUX
ejpam-5848	49	10	described	describe	VERB
ejpam-5848	49	11	as	as	ADP
ejpam-5848	49	12	the	the	DET
ejpam-5848	49	13	union	union	NOUN
ejpam-5848	49	14	of	of	ADP
ejpam-5848	49	15	all	all	DET
ejpam-5848	49	16	t	t	NOUN
ejpam-5848	49	17	-open	-open	ADJ
ejpam-5848	49	18	f	f	PROPN
ejpam-5848	49	19	-sets	-set	NOUN
ejpam-5848	49	20	contained	contain	VERB
ejpam-5848	49	21	in	in	ADP
ejpam-5848	49	22	m	m	PROPN
ejpam-5848	49	23	,	,	PUNCT
ejpam-5848	49	24	indicated	indicate	VERB
ejpam-5848	49	25	by	by	ADP
ejpam-5848	49	26	ao	ao	PROPN
ejpam-5848	49	27	.	.	PUNCT
ejpam-5848	50	1	equivalently	equivalently	ADV
ejpam-5848	50	2	,	,	PUNCT
ejpam-5848	50	3	mo	mo	PROPN
ejpam-5848	50	4	is	be	AUX
ejpam-5848	50	5	the	the	DET
ejpam-5848	50	6	largest	large	ADJ
ejpam-5848	50	7	t	t	NOUN
ejpam-5848	50	8	-open	-open	PROPN
ejpam-5848	50	9	f	f	PROPN
ejpam-5848	50	10	-set	-set	VERB
ejpam-5848	50	11	contained	contain	VERB
ejpam-5848	50	12	in	in	ADP
ejpam-5848	50	13	m	m	PROPN
ejpam-5848	50	14	and	and	CCONJ
ejpam-5848	50	15	(	(	PUNCT
ejpam-5848	50	16	mo)o	mo)o	PROPN
ejpam-5848	50	17	=	=	SYM
ejpam-5848	50	18	mo	mo	PROPN
ejpam-5848	50	19	.	.	PROPN
ejpam-5848	50	20	(	(	PUNCT
ejpam-5848	50	21	ii	ii	NOUN
ejpam-5848	50	22	)	)	PUNCT
ejpam-5848	50	23	closure	closure	NOUN
ejpam-5848	50	24	of	of	ADP
ejpam-5848	50	25	m	m	PROPN
ejpam-5848	50	26	is	be	AUX
ejpam-5848	50	27	described	describe	VERB
ejpam-5848	50	28	as	as	ADP
ejpam-5848	50	29	the	the	DET
ejpam-5848	50	30	intersection	intersection	NOUN
ejpam-5848	50	31	of	of	ADP
ejpam-5848	50	32	all	all	DET
ejpam-5848	50	33	t	t	NOUN
ejpam-5848	50	34	-closed	-close	VERB
ejpam-5848	50	35	f	f	PROPN
ejpam-5848	50	36	-sets	-set	NOUN
ejpam-5848	50	37	containing	contain	VERB
ejpam-5848	50	38	m	m	PROPN
ejpam-5848	50	39	,	,	PUNCT
ejpam-5848	50	40	indicated	indicate	VERB
ejpam-5848	50	41	by	by	ADP
ejpam-5848	50	42	m	m	PROPN
ejpam-5848	50	43	.	.	PUNCT
ejpam-5848	51	1	clearly	clearly	ADV
ejpam-5848	51	2	,	,	PUNCT
ejpam-5848	51	3	m	m	VERB
ejpam-5848	51	4	is	be	AUX
ejpam-5848	51	5	the	the	DET
ejpam-5848	51	6	smallest	small	ADJ
ejpam-5848	51	7	t	t	NOUN
ejpam-5848	51	8	-closed	-close	VERB
ejpam-5848	51	9	f	f	PROPN
ejpam-5848	51	10	-set	-set	X
ejpam-5848	51	11	containing	contain	VERB
ejpam-5848	51	12	m	m	PROPN
ejpam-5848	51	13	and	and	CCONJ
ejpam-5848	51	14	m	m	PROPN
ejpam-5848	51	15	=	=	ADJ
ejpam-5848	51	16	m	m	PROPN
ejpam-5848	51	17	.	.	PUNCT
ejpam-5848	52	1	theorem	theorem	NOUN
ejpam-5848	52	2	1	1	NUM
ejpam-5848	52	3	.	.	PUNCT
ejpam-5848	53	1	[	[	X
ejpam-5848	53	2	26	26	NUM
ejpam-5848	53	3	]	]	PUNCT
ejpam-5848	53	4	in	in	ADP
ejpam-5848	53	5	any	any	DET
ejpam-5848	53	6	fts	fts	PROPN
ejpam-5848	53	7	(	(	PUNCT
ejpam-5848	53	8	v	v	NOUN
ejpam-5848	53	9	,	,	PUNCT
ejpam-5848	53	10	t	t	PROPN
ejpam-5848	53	11	)	)	PUNCT
ejpam-5848	53	12	,	,	PUNCT
ejpam-5848	53	13	(	(	PUNCT
ejpam-5848	53	14	e)c	e)c	X
ejpam-5848	53	15	=	=	SYM
ejpam-5848	53	16	(	(	PUNCT
ejpam-5848	53	17	ec)o	ec)o	PROPN
ejpam-5848	53	18	and	and	CCONJ
ejpam-5848	53	19	so	so	ADV
ejpam-5848	53	20	ec	ec	PROPN
ejpam-5848	53	21	=	=	SYM
ejpam-5848	53	22	(	(	PUNCT
ejpam-5848	53	23	eo)c	eo)c	NOUN
ejpam-5848	53	24	,	,	PUNCT
ejpam-5848	53	25	for	for	ADP
ejpam-5848	53	26	any	any	DET
ejpam-5848	53	27	fuzzy	fuzzy	ADJ
ejpam-5848	53	28	subset	subset	NOUN
ejpam-5848	53	29	e	e	NOUN
ejpam-5848	53	30	of	of	ADP
ejpam-5848	53	31	v	v	NOUN
ejpam-5848	53	32	.	.	PUNCT
ejpam-5848	54	1	definition	definition	NOUN
ejpam-5848	54	2	3	3	NUM
ejpam-5848	54	3	.	.	PUNCT
ejpam-5848	55	1	[	[	X
ejpam-5848	55	2	17	17	NUM
ejpam-5848	55	3	]	]	PUNCT
ejpam-5848	55	4	let	let	VERB
ejpam-5848	55	5	ψ	ψ	X
ejpam-5848	55	6	:	:	PUNCT
ejpam-5848	55	7	v	v	AUX
ejpam-5848	55	8	−→	−→	NOUN
ejpam-5848	55	9	w	w	NOUN
ejpam-5848	55	10	be	be	AUX
ejpam-5848	55	11	a	a	DET
ejpam-5848	55	12	mapping	mapping	NOUN
ejpam-5848	55	13	.	.	PUNCT
ejpam-5848	56	1	then	then	ADV
ejpam-5848	56	2	,	,	PUNCT
ejpam-5848	56	3	for	for	ADP
ejpam-5848	56	4	f	f	PROPN
ejpam-5848	56	5	-subsets	-subsets	PROPN
ejpam-5848	56	6	h	h	NOUN
ejpam-5848	56	7	of	of	ADP
ejpam-5848	56	8	v	v	NOUN
ejpam-5848	56	9	and	and	CCONJ
ejpam-5848	56	10	g	g	NOUN
ejpam-5848	56	11	of	of	ADP
ejpam-5848	56	12	w	w	PROPN
ejpam-5848	56	13	,	,	PUNCT
ejpam-5848	56	14	we	we	PRON
ejpam-5848	56	15	have	have	AUX
ejpam-5848	56	16	:	:	PUNCT
ejpam-5848	56	17	(	(	PUNCT
ejpam-5848	56	18	a	a	X
ejpam-5848	56	19	)	)	PUNCT
ejpam-5848	56	20	ψ(h	ψ(h	NOUN
ejpam-5848	56	21	)	)	PUNCT
ejpam-5848	56	22	is	be	AUX
ejpam-5848	56	23	an	an	DET
ejpam-5848	56	24	f	f	PROPN
ejpam-5848	56	25	-subset	-subset	PROPN
ejpam-5848	56	26	ofw	ofw	NOUN
ejpam-5848	56	27	given	give	VERB
ejpam-5848	56	28	as	as	ADP
ejpam-5848	56	29	ψ(h)(w	ψ(h)(w	NOUN
ejpam-5848	56	30	)	)	PUNCT
ejpam-5848	56	31	=	=	SYM
ejpam-5848	56	32	sup{h(u	sup{h(u	PROPN
ejpam-5848	56	33	)	)	PUNCT
ejpam-5848	56	34	:	:	PUNCT
ejpam-5848	56	35	u	u	PROPN
ejpam-5848	56	36	∈	∈	PROPN
ejpam-5848	56	37	ψ−1(w	ψ−1(w	NOUN
ejpam-5848	56	38	)	)	PUNCT
ejpam-5848	56	39	}	}	PUNCT
ejpam-5848	56	40	if	if	SCONJ
ejpam-5848	56	41	ψ−1(w	ψ−1(w	NOUN
ejpam-5848	56	42	)	)	PUNCT
ejpam-5848	56	43	̸=	̸=	PROPN
ejpam-5848	56	44	∅	∅	NOUN
ejpam-5848	56	45	and	and	CCONJ
ejpam-5848	56	46	ψ(h)(w	ψ(h)(w	NOUN
ejpam-5848	56	47	)	)	PUNCT
ejpam-5848	57	1	=	=	SYM
ejpam-5848	57	2	0	0	PUNCT
ejpam-5848	58	1	if	if	SCONJ
ejpam-5848	58	2	ψ−1(w	ψ−1(w	NOUN
ejpam-5848	58	3	)	)	PUNCT
ejpam-5848	58	4	=	=	PUNCT
ejpam-5848	58	5	∅.	∅.	X
ejpam-5848	58	6	(	(	PUNCT
ejpam-5848	58	7	b	b	NOUN
ejpam-5848	58	8	)	)	PUNCT
ejpam-5848	58	9	ψ−1(g	ψ−1(g	PROPN
ejpam-5848	58	10	)	)	PUNCT
ejpam-5848	58	11	is	be	AUX
ejpam-5848	58	12	an	an	DET
ejpam-5848	58	13	f	f	PROPN
ejpam-5848	58	14	-subset	-subset	PROPN
ejpam-5848	58	15	of	of	ADP
ejpam-5848	58	16	u	u	PRON
ejpam-5848	58	17	given	give	VERB
ejpam-5848	58	18	as	as	ADP
ejpam-5848	58	19	ψ−1(g)(u	ψ−1(g)(u	ADJ
ejpam-5848	58	20	)	)	PUNCT
ejpam-5848	58	21	=	=	SYM
ejpam-5848	58	22	g(ψ(u	g(ψ(u	NOUN
ejpam-5848	58	23	)	)	PUNCT
ejpam-5848	58	24	)	)	PUNCT
ejpam-5848	58	25	for	for	ADP
ejpam-5848	58	26	every	every	DET
ejpam-5848	58	27	u	u	PROPN
ejpam-5848	58	28	∈	∈	PROPN
ejpam-5848	58	29	u	u	NOUN
ejpam-5848	58	30	.	.	PUNCT
ejpam-5848	59	1	theorem	theorem	NOUN
ejpam-5848	59	2	2	2	NUM
ejpam-5848	59	3	.	.	PUNCT
ejpam-5848	60	1	[	[	X
ejpam-5848	60	2	17	17	NUM
ejpam-5848	60	3	]	]	PUNCT
ejpam-5848	60	4	let	let	VERB
ejpam-5848	60	5	ψ	ψ	PART
ejpam-5848	60	6	be	be	AUX
ejpam-5848	60	7	a	a	DET
ejpam-5848	60	8	mapping	mapping	NOUN
ejpam-5848	60	9	from	from	ADP
ejpam-5848	60	10	a	a	DET
ejpam-5848	60	11	set	set	NOUN
ejpam-5848	60	12	v	v	NOUN
ejpam-5848	60	13	into	into	ADP
ejpam-5848	60	14	a	a	DET
ejpam-5848	60	15	setw	setw	NOUN
ejpam-5848	60	16	.	.	PUNCT
ejpam-5848	61	1	then	then	ADV
ejpam-5848	61	2	for	for	ADP
ejpam-5848	61	3	every	every	DET
ejpam-5848	61	4	f	f	PROPN
ejpam-5848	61	5	-subsets	-subsets	PROPN
ejpam-5848	61	6	m	m	VERB
ejpam-5848	61	7	and	and	CCONJ
ejpam-5848	61	8	n	n	PROPN
ejpam-5848	61	9	of	of	ADP
ejpam-5848	61	10	v	v	NOUN
ejpam-5848	61	11	and	and	CCONJ
ejpam-5848	61	12	f	f	PROPN
ejpam-5848	61	13	-subsets	-subsets	PROPN
ejpam-5848	61	14	k	k	PROPN
ejpam-5848	61	15	and	and	CCONJ
ejpam-5848	61	16	l	l	PROPN
ejpam-5848	61	17	of	of	ADP
ejpam-5848	61	18	w	w	ADV
ejpam-5848	61	19	we	we	PRON
ejpam-5848	61	20	have	have	VERB
ejpam-5848	61	21	:	:	PUNCT
ejpam-5848	61	22	s.	s.	PROPN
ejpam-5848	61	23	kaur	kaur	PROPN
ejpam-5848	61	24	et	et	PROPN
ejpam-5848	61	25	al	al	PROPN
ejpam-5848	61	26	.	.	PUNCT
ejpam-5848	61	27	/	/	SYM
ejpam-5848	61	28	eur	eur	PROPN
ejpam-5848	61	29	.	.	PUNCT
ejpam-5848	62	1	j.	j.	PROPN
ejpam-5848	62	2	pure	pure	PROPN
ejpam-5848	62	3	appl	appl	PROPN
ejpam-5848	62	4	.	.	PROPN
ejpam-5848	62	5	math	math	PROPN
ejpam-5848	62	6	,	,	PUNCT
ejpam-5848	62	7	18	18	NUM
ejpam-5848	62	8	(	(	PUNCT
ejpam-5848	62	9	1	1	NUM
ejpam-5848	62	10	)	)	PUNCT
ejpam-5848	62	11	(	(	PUNCT
ejpam-5848	62	12	2025	2025	NUM
ejpam-5848	62	13	)	)	PUNCT
ejpam-5848	62	14	,	,	PUNCT
ejpam-5848	62	15	5848	5848	NUM
ejpam-5848	62	16	4	4	NUM
ejpam-5848	62	17	of	of	ADP
ejpam-5848	62	18	11	11	NUM
ejpam-5848	62	19	(	(	PUNCT
ejpam-5848	62	20	i	i	NOUN
ejpam-5848	62	21	)	)	PUNCT
ejpam-5848	62	22	ψ(m	ψ(m	PROPN
ejpam-5848	62	23	)	)	PUNCT
ejpam-5848	62	24	⊆	⊆	NUM
ejpam-5848	62	25	ψ(n	ψ(n	NOUN
ejpam-5848	62	26	)	)	PUNCT
ejpam-5848	62	27	if	if	SCONJ
ejpam-5848	62	28	m	m	PROPN
ejpam-5848	62	29	⊆	⊆	NUM
ejpam-5848	62	30	n	n	NOUN
ejpam-5848	62	31	.	.	PUNCT
ejpam-5848	63	1	(	(	PUNCT
ejpam-5848	63	2	ii	ii	NOUN
ejpam-5848	63	3	)	)	PUNCT
ejpam-5848	63	4	ψ−1(k	ψ−1(k	NOUN
ejpam-5848	63	5	)	)	PUNCT
ejpam-5848	63	6	⊆	⊆	NUM
ejpam-5848	63	7	ψ−1(l	ψ−1(l	NOUN
ejpam-5848	63	8	)	)	PUNCT
ejpam-5848	64	1	if	if	SCONJ
ejpam-5848	64	2	k	k	PROPN
ejpam-5848	64	3	⊆	⊆	NUM
ejpam-5848	64	4	l.	l.	PROPN
ejpam-5848	64	5	(	(	PUNCT
ejpam-5848	64	6	iii	iii	PROPN
ejpam-5848	64	7	)	)	PUNCT
ejpam-5848	64	8	m	m	PROPN
ejpam-5848	64	9	⊆	⊆	NUM
ejpam-5848	64	10	ψ−1(ψ(m	ψ−1(ψ(m	NOUN
ejpam-5848	64	11	)	)	PUNCT
ejpam-5848	64	12	)	)	PUNCT
ejpam-5848	64	13	,	,	PUNCT
ejpam-5848	64	14	equality	equality	NOUN
ejpam-5848	64	15	holds	hold	VERB
ejpam-5848	64	16	if	if	SCONJ
ejpam-5848	64	17	ψ	ψ	NOUN
ejpam-5848	64	18	is	be	AUX
ejpam-5848	64	19	one	one	NUM
ejpam-5848	64	20	-	-	PUNCT
ejpam-5848	64	21	one	one	NUM
ejpam-5848	64	22	.	.	PUNCT
ejpam-5848	65	1	(	(	PUNCT
ejpam-5848	65	2	iv	iv	X
ejpam-5848	65	3	)	)	PUNCT
ejpam-5848	65	4	ψ(ψ−1(k	ψ(ψ−1(k	NOUN
ejpam-5848	65	5	)	)	PUNCT
ejpam-5848	65	6	)	)	PUNCT
ejpam-5848	66	1	⊆	⊆	NUM
ejpam-5848	66	2	k	k	NOUN
ejpam-5848	66	3	,	,	PUNCT
ejpam-5848	66	4	equality	equality	NOUN
ejpam-5848	66	5	holds	hold	VERB
ejpam-5848	66	6	if	if	SCONJ
ejpam-5848	66	7	ψ	ψ	NOUN
ejpam-5848	66	8	is	be	AUX
ejpam-5848	66	9	onto	onto	ADP
ejpam-5848	66	10	.	.	PUNCT
ejpam-5848	67	1	(	(	PUNCT
ejpam-5848	67	2	v	v	NOUN
ejpam-5848	67	3	)	)	PUNCT
ejpam-5848	67	4	ψ−1(kc	ψ−1(kc	PUNCT
ejpam-5848	67	5	)	)	PUNCT
ejpam-5848	68	1	=	=	SYM
ejpam-5848	68	2	(	(	PUNCT
ejpam-5848	68	3	ψ−1(k))c	ψ−1(k))c	PROPN
ejpam-5848	68	4	.	.	PUNCT
ejpam-5848	69	1	(	(	PUNCT
ejpam-5848	69	2	vi	vi	NOUN
ejpam-5848	69	3	)	)	PUNCT
ejpam-5848	69	4	(	(	PUNCT
ejpam-5848	69	5	ψ(m))c	ψ(m))c	PROPN
ejpam-5848	69	6	⊆	⊆	NUM
ejpam-5848	69	7	ψ(m	ψ(m	PROPN
ejpam-5848	69	8	c	c	NOUN
ejpam-5848	69	9	)	)	PUNCT
ejpam-5848	69	10	.	.	PUNCT
ejpam-5848	70	1	definition	definition	NOUN
ejpam-5848	70	2	4	4	NUM
ejpam-5848	70	3	.	.	PUNCT
ejpam-5848	71	1	[	[	X
ejpam-5848	71	2	29	29	NUM
ejpam-5848	71	3	]	]	PUNCT
ejpam-5848	71	4	let	let	VERB
ejpam-5848	71	5	ψ	ψ	PART
ejpam-5848	71	6	be	be	AUX
ejpam-5848	71	7	a	a	DET
ejpam-5848	71	8	mapping	mapping	NOUN
ejpam-5848	71	9	from	from	ADP
ejpam-5848	71	10	an	an	DET
ejpam-5848	71	11	fts	fts	PROPN
ejpam-5848	71	12	(	(	PUNCT
ejpam-5848	71	13	v	v	NOUN
ejpam-5848	71	14	,	,	PUNCT
ejpam-5848	71	15	t	t	PROPN
ejpam-5848	71	16	1	1	NUM
ejpam-5848	71	17	)	)	PUNCT
ejpam-5848	71	18	to	to	ADP
ejpam-5848	71	19	an	an	DET
ejpam-5848	71	20	fts	fts	PROPN
ejpam-5848	71	21	(	(	PUNCT
ejpam-5848	71	22	w	w	PROPN
ejpam-5848	71	23	,	,	PUNCT
ejpam-5848	71	24	t	t	NOUN
ejpam-5848	71	25	2	2	NUM
ejpam-5848	71	26	)	)	PUNCT
ejpam-5848	71	27	.	.	PUNCT
ejpam-5848	72	1	then	then	ADV
ejpam-5848	72	2	,	,	PUNCT
ejpam-5848	72	3	ψ	ψ	X
ejpam-5848	72	4	is	be	AUX
ejpam-5848	72	5	named	name	VERB
ejpam-5848	72	6	an	an	DET
ejpam-5848	72	7	open	open	ADJ
ejpam-5848	72	8	fuzzy	fuzzy	ADJ
ejpam-5848	72	9	(	(	PUNCT
ejpam-5848	72	10	resp	resp	NOUN
ejpam-5848	72	11	.	.	PROPN
ejpam-5848	72	12	,	,	PUNCT
ejpam-5848	72	13	a	a	DET
ejpam-5848	72	14	closed	close	VERB
ejpam-5848	72	15	fuzzy	fuzzy	ADJ
ejpam-5848	72	16	)	)	PUNCT
ejpam-5848	72	17	mapping	mapping	NOUN
ejpam-5848	72	18	if	if	SCONJ
ejpam-5848	72	19	and	and	CCONJ
ejpam-5848	72	20	only	only	ADV
ejpam-5848	72	21	if	if	SCONJ
ejpam-5848	72	22	ψ(b	ψ(b	PROPN
ejpam-5848	72	23	)	)	PUNCT
ejpam-5848	72	24	is	be	AUX
ejpam-5848	72	25	an	an	DET
ejpam-5848	72	26	open	open	ADJ
ejpam-5848	72	27	(	(	PUNCT
ejpam-5848	72	28	resp	resp	NOUN
ejpam-5848	72	29	.	.	PROPN
ejpam-5848	72	30	,	,	PUNCT
ejpam-5848	72	31	a	a	DET
ejpam-5848	72	32	closed	closed	ADJ
ejpam-5848	72	33	)	)	PUNCT
ejpam-5848	72	34	f	f	NOUN
ejpam-5848	72	35	-set	-set	PUNCT
ejpam-5848	72	36	in	in	ADP
ejpam-5848	72	37	(	(	PUNCT
ejpam-5848	72	38	w	w	PROPN
ejpam-5848	72	39	,	,	PUNCT
ejpam-5848	72	40	t	t	NOUN
ejpam-5848	72	41	2	2	NUM
ejpam-5848	72	42	)	)	PUNCT
ejpam-5848	72	43	,	,	PUNCT
ejpam-5848	72	44	for	for	SCONJ
ejpam-5848	72	45	every	every	DET
ejpam-5848	72	46	open	open	ADJ
ejpam-5848	72	47	(	(	PUNCT
ejpam-5848	72	48	resp	resp	NOUN
ejpam-5848	72	49	.	.	PROPN
ejpam-5848	72	50	,	,	PUNCT
ejpam-5848	72	51	closed	close	VERB
ejpam-5848	72	52	)	)	PUNCT
ejpam-5848	72	53	f	f	PROPN
ejpam-5848	72	54	-set	-set	PUNCT
ejpam-5848	72	55	b	b	X
ejpam-5848	72	56	in	in	ADP
ejpam-5848	72	57	(	(	PUNCT
ejpam-5848	72	58	v	v	NOUN
ejpam-5848	72	59	,	,	PUNCT
ejpam-5848	72	60	t	t	PROPN
ejpam-5848	72	61	1	1	NUM
ejpam-5848	72	62	)	)	PUNCT
ejpam-5848	72	63	.	.	PUNCT
ejpam-5848	73	1	theorem	theorem	NOUN
ejpam-5848	73	2	3	3	NUM
ejpam-5848	73	3	.	.	PUNCT
ejpam-5848	74	1	[	[	X
ejpam-5848	74	2	23	23	NUM
ejpam-5848	74	3	]	]	PUNCT
ejpam-5848	74	4	let	let	VERB
ejpam-5848	74	5	ψ	ψ	PART
ejpam-5848	74	6	be	be	AUX
ejpam-5848	74	7	a	a	DET
ejpam-5848	74	8	mapping	mapping	NOUN
ejpam-5848	74	9	from	from	ADP
ejpam-5848	74	10	an	an	DET
ejpam-5848	74	11	fts	fts	PROPN
ejpam-5848	74	12	(	(	PUNCT
ejpam-5848	74	13	v	v	NOUN
ejpam-5848	74	14	,	,	PUNCT
ejpam-5848	74	15	t	t	PROPN
ejpam-5848	74	16	1	1	NUM
ejpam-5848	74	17	)	)	PUNCT
ejpam-5848	74	18	to	to	ADP
ejpam-5848	74	19	an	an	DET
ejpam-5848	74	20	fts	fts	PROPN
ejpam-5848	74	21	(	(	PUNCT
ejpam-5848	74	22	w	w	PROPN
ejpam-5848	74	23	,	,	PUNCT
ejpam-5848	74	24	t	t	NOUN
ejpam-5848	74	25	2	2	NUM
ejpam-5848	74	26	)	)	PUNCT
ejpam-5848	74	27	.	.	PUNCT
ejpam-5848	75	1	then	then	ADV
ejpam-5848	75	2	,	,	PUNCT
ejpam-5848	75	3	for	for	ADP
ejpam-5848	75	4	any	any	DET
ejpam-5848	75	5	f	f	PROPN
ejpam-5848	75	6	-sets	-set	NOUN
ejpam-5848	75	7	m	m	VERB
ejpam-5848	75	8	in	in	ADP
ejpam-5848	75	9	v	v	NOUN
ejpam-5848	75	10	and	and	CCONJ
ejpam-5848	75	11	n	n	CCONJ
ejpam-5848	75	12	in	in	ADP
ejpam-5848	75	13	w	w	PROPN
ejpam-5848	75	14	,	,	PUNCT
ejpam-5848	75	15	the	the	DET
ejpam-5848	75	16	following	follow	VERB
ejpam-5848	75	17	statements	statement	NOUN
ejpam-5848	75	18	are	be	AUX
ejpam-5848	75	19	equivalent	equivalent	ADJ
ejpam-5848	75	20	.	.	PUNCT
ejpam-5848	76	1	(	(	PUNCT
ejpam-5848	76	2	1	1	X
ejpam-5848	76	3	)	)	PUNCT
ejpam-5848	76	4	ψ	ψ	NOUN
ejpam-5848	76	5	is	be	AUX
ejpam-5848	76	6	open	open	ADJ
ejpam-5848	76	7	fuzzy	fuzzy	ADJ
ejpam-5848	76	8	mapping	mapping	NOUN
ejpam-5848	76	9	.	.	PUNCT
ejpam-5848	77	1	(	(	PUNCT
ejpam-5848	77	2	2	2	X
ejpam-5848	77	3	)	)	PUNCT
ejpam-5848	77	4	ψ(m	ψ(m	NOUN
ejpam-5848	77	5	◦	◦	NOUN
ejpam-5848	77	6	)	)	PUNCT
ejpam-5848	77	7	⊆	⊆	NUM
ejpam-5848	77	8	(	(	PUNCT
ejpam-5848	77	9	ψ(m))	ψ(m))	NOUN
ejpam-5848	77	10	◦	◦	NOUN
ejpam-5848	77	11	.	.	PUNCT
ejpam-5848	78	1	(	(	PUNCT
ejpam-5848	78	2	3	3	X
ejpam-5848	78	3	)	)	PUNCT
ejpam-5848	78	4	ψ−1(n	ψ−1(n	NOUN
ejpam-5848	78	5	)	)	PUNCT
ejpam-5848	78	6	⊆	⊆	NUM
ejpam-5848	78	7	ψ−1(n	ψ−1(n	NOUN
ejpam-5848	78	8	)	)	PUNCT
ejpam-5848	78	9	.	.	PUNCT
ejpam-5848	79	1	(	(	PUNCT
ejpam-5848	79	2	4	4	X
ejpam-5848	79	3	)	)	PUNCT
ejpam-5848	79	4	(	(	PUNCT
ejpam-5848	79	5	ψ−1(n	ψ−1(n	NOUN
ejpam-5848	79	6	)	)	PUNCT
ejpam-5848	79	7	)	)	PUNCT
ejpam-5848	80	1	◦	◦	VERB
ejpam-5848	80	2	⊆	⊆	NUM
ejpam-5848	80	3	ψ−1(n	ψ−1(n	NOUN
ejpam-5848	80	4	◦	◦	NOUN
ejpam-5848	80	5	)	)	PUNCT
ejpam-5848	80	6	.	.	PUNCT
ejpam-5848	81	1	theorem	theorem	ADJ
ejpam-5848	81	2	4	4	NUM
ejpam-5848	81	3	.	.	PUNCT
ejpam-5848	82	1	[	[	X
ejpam-5848	82	2	22	22	NUM
ejpam-5848	82	3	]	]	PUNCT
ejpam-5848	82	4	let	let	VERB
ejpam-5848	82	5	ψ	ψ	PART
ejpam-5848	82	6	be	be	AUX
ejpam-5848	82	7	a	a	DET
ejpam-5848	82	8	mapping	mapping	NOUN
ejpam-5848	82	9	from	from	ADP
ejpam-5848	82	10	an	an	DET
ejpam-5848	82	11	fts	fts	PROPN
ejpam-5848	82	12	(	(	PUNCT
ejpam-5848	82	13	v	v	NOUN
ejpam-5848	82	14	,	,	PUNCT
ejpam-5848	82	15	t	t	PROPN
ejpam-5848	82	16	1	1	NUM
ejpam-5848	82	17	)	)	PUNCT
ejpam-5848	82	18	to	to	ADP
ejpam-5848	82	19	an	an	DET
ejpam-5848	82	20	fts	fts	PROPN
ejpam-5848	82	21	(	(	PUNCT
ejpam-5848	82	22	w	w	PROPN
ejpam-5848	82	23	,	,	PUNCT
ejpam-5848	82	24	t	t	NOUN
ejpam-5848	82	25	2	2	NUM
ejpam-5848	82	26	)	)	PUNCT
ejpam-5848	82	27	.	.	PUNCT
ejpam-5848	83	1	then	then	ADV
ejpam-5848	83	2	,	,	PUNCT
ejpam-5848	83	3	ψ	ψ	X
ejpam-5848	83	4	is	be	AUX
ejpam-5848	83	5	a	a	DET
ejpam-5848	83	6	closed	closed	ADJ
ejpam-5848	83	7	fuzzy	fuzzy	ADJ
ejpam-5848	83	8	mapping	mapping	NOUN
ejpam-5848	83	9	iff	iff	PROPN
ejpam-5848	83	10	ψ(m	ψ(m	NOUN
ejpam-5848	83	11	)	)	PUNCT
ejpam-5848	83	12	⊆	⊆	NUM
ejpam-5848	83	13	ψ(m	ψ(m	NOUN
ejpam-5848	83	14	)	)	PUNCT
ejpam-5848	83	15	for	for	ADP
ejpam-5848	83	16	every	every	DET
ejpam-5848	83	17	f	f	PROPN
ejpam-5848	83	18	-set	-set	NOUN
ejpam-5848	83	19	m	m	VERB
ejpam-5848	83	20	in	in	ADP
ejpam-5848	83	21	v	v	PROPN
ejpam-5848	83	22	.	.	PUNCT
ejpam-5848	84	1	kaur	kaur	PROPN
ejpam-5848	84	2	and	and	CCONJ
ejpam-5848	84	3	goyal	goyal	PROPN
ejpam-5848	84	4	introduced	introduce	VERB
ejpam-5848	84	5	the	the	DET
ejpam-5848	84	6	#	#	NOUN
ejpam-5848	84	7	image	image	NOUN
ejpam-5848	84	8	of	of	ADP
ejpam-5848	84	9	an	an	DET
ejpam-5848	84	10	f	f	NOUN
ejpam-5848	84	11	-set	-set	PUNCT
ejpam-5848	84	12	in	in	ADP
ejpam-5848	84	13	[	[	X
ejpam-5848	84	14	21	21	NUM
ejpam-5848	84	15	]	]	PUNCT
ejpam-5848	84	16	to	to	PART
ejpam-5848	84	17	define	define	VERB
ejpam-5848	84	18	an	an	DET
ejpam-5848	84	19	induced	induced	ADJ
ejpam-5848	84	20	mapping	mapping	NOUN
ejpam-5848	84	21	ψ	ψ	NOUN
ejpam-5848	84	22	#	#	NOUN
ejpam-5848	84	23	:	:	PUNCT
ejpam-5848	84	24	gz(v	gz(v	X
ejpam-5848	84	25	)	)	PUNCT
ejpam-5848	84	26	→	→	SYM
ejpam-5848	84	27	gz(w	gz(w	NUM
ejpam-5848	84	28	)	)	PUNCT
ejpam-5848	84	29	associated	associate	VERB
ejpam-5848	84	30	to	to	ADP
ejpam-5848	84	31	any	any	DET
ejpam-5848	84	32	mapping	mapping	NOUN
ejpam-5848	84	33	ψ	ψ	X
ejpam-5848	84	34	:	:	PUNCT
ejpam-5848	84	35	v	v	X
ejpam-5848	84	36	→	→	SYM
ejpam-5848	84	37	w	w	ADP
ejpam-5848	84	38	where	where	SCONJ
ejpam-5848	84	39	v	v	NOUN
ejpam-5848	84	40	and	and	CCONJ
ejpam-5848	84	41	w	w	NOUN
ejpam-5848	84	42	are	be	AUX
ejpam-5848	84	43	crisp	crisp	ADJ
ejpam-5848	84	44	sets	set	NOUN
ejpam-5848	84	45	and	and	CCONJ
ejpam-5848	84	46	gz(v	gz(v	PUNCT
ejpam-5848	84	47	)	)	PUNCT
ejpam-5848	84	48	and	and	CCONJ
ejpam-5848	84	49	gz(w	gz(w	NUM
ejpam-5848	84	50	)	)	PUNCT
ejpam-5848	84	51	are	be	AUX
ejpam-5848	84	52	the	the	DET
ejpam-5848	84	53	collections	collection	NOUN
ejpam-5848	84	54	of	of	ADP
ejpam-5848	84	55	all	all	DET
ejpam-5848	84	56	fuzzy	fuzzy	ADJ
ejpam-5848	84	57	subsets	subset	NOUN
ejpam-5848	84	58	of	of	ADP
ejpam-5848	84	59	v	v	NOUN
ejpam-5848	84	60	and	and	CCONJ
ejpam-5848	84	61	w	w	NOUN
ejpam-5848	84	62	,	,	PUNCT
ejpam-5848	84	63	respectively	respectively	ADV
ejpam-5848	84	64	.	.	PUNCT
ejpam-5848	85	1	definition	definition	NOUN
ejpam-5848	85	2	5	5	NUM
ejpam-5848	85	3	.	.	PUNCT
ejpam-5848	86	1	[	[	X
ejpam-5848	86	2	21	21	NUM
ejpam-5848	86	3	]	]	PUNCT
ejpam-5848	86	4	the	the	DET
ejpam-5848	86	5	#	#	NOUN
ejpam-5848	86	6	image	image	NOUN
ejpam-5848	86	7	of	of	ADP
ejpam-5848	86	8	an	an	DET
ejpam-5848	86	9	f	f	X
ejpam-5848	86	10	-set	-set	NOUN
ejpam-5848	86	11	m	m	VERB
ejpam-5848	86	12	in	in	ADP
ejpam-5848	86	13	v	v	NOUN
ejpam-5848	86	14	with	with	ADP
ejpam-5848	86	15	membership	membership	NOUN
ejpam-5848	86	16	function	function	NOUN
ejpam-5848	86	17	µm	µm	ADP
ejpam-5848	86	18	(	(	PUNCT
ejpam-5848	86	19	v	v	NOUN
ejpam-5848	86	20	)	)	PUNCT
ejpam-5848	86	21	,	,	PUNCT
ejpam-5848	86	22	written	write	VERB
ejpam-5848	86	23	as	as	ADP
ejpam-5848	86	24	ψ#(m	ψ#(m	PROPN
ejpam-5848	86	25	)	)	PUNCT
ejpam-5848	86	26	,	,	PUNCT
ejpam-5848	86	27	is	be	AUX
ejpam-5848	86	28	an	an	DET
ejpam-5848	86	29	f	f	NOUN
ejpam-5848	86	30	-set	-set	PUNCT
ejpam-5848	86	31	in	in	ADP
ejpam-5848	86	32	w	w	NOUN
ejpam-5848	86	33	with	with	ADP
ejpam-5848	86	34	a	a	DET
ejpam-5848	86	35	membership	membership	NOUN
ejpam-5848	86	36	function	function	NOUN
ejpam-5848	86	37	defined	define	VERB
ejpam-5848	86	38	as	as	ADP
ejpam-5848	86	39	µψ#(m)(w	µψ#(m)(w	NOUN
ejpam-5848	86	40	)	)	PUNCT
ejpam-5848	86	41	=	=	SYM
ejpam-5848	86	42	{	{	PUNCT
ejpam-5848	86	43	infz∈ψ−1(w	infz∈ψ−1(w	NOUN
ejpam-5848	86	44	)	)	PUNCT
ejpam-5848	86	45	µm	µm	ADP
ejpam-5848	86	46	(	(	PUNCT
ejpam-5848	86	47	z	z	NOUN
ejpam-5848	86	48	)	)	PUNCT
ejpam-5848	86	49	if	if	SCONJ
ejpam-5848	86	50	ψ−1(w	ψ−1(w	NOUN
ejpam-5848	86	51	)	)	PUNCT
ejpam-5848	86	52	̸=	̸=	PROPN
ejpam-5848	86	53	∅	∅	NOUN
ejpam-5848	86	54	1	1	NUM
ejpam-5848	86	55	otherwise	otherwise	ADV
ejpam-5848	86	56	definition	definition	NOUN
ejpam-5848	86	57	6	6	NUM
ejpam-5848	86	58	.	.	PUNCT
ejpam-5848	87	1	[	[	X
ejpam-5848	87	2	21	21	NUM
ejpam-5848	87	3	]	]	X
ejpam-5848	87	4	an	an	DET
ejpam-5848	87	5	f	f	X
ejpam-5848	87	6	-set	-set	NOUN
ejpam-5848	87	7	m	m	NOUN
ejpam-5848	87	8	#	#	NOUN
ejpam-5848	87	9	in	in	ADP
ejpam-5848	87	10	v	v	NUM
ejpam-5848	87	11	is	be	AUX
ejpam-5848	87	12	defined	define	VERB
ejpam-5848	87	13	as	as	ADP
ejpam-5848	87	14	m	m	NOUN
ejpam-5848	87	15	#	#	NOUN
ejpam-5848	87	16	=	=	SYM
ejpam-5848	87	17	ψ−1(ψ#(m	ψ−1(ψ#(m	PROPN
ejpam-5848	87	18	)	)	PUNCT
ejpam-5848	87	19	)	)	PUNCT
ejpam-5848	87	20	with	with	ADP
ejpam-5848	87	21	membership	membership	NOUN
ejpam-5848	87	22	mapping	mapping	NOUN
ejpam-5848	87	23	as	as	ADP
ejpam-5848	87	24	µm#(v	µm#(v	NOUN
ejpam-5848	87	25	)	)	PUNCT
ejpam-5848	87	26	=	=	SYM
ejpam-5848	88	1	µψ−1(ψ#(m))(v	µψ−1(ψ#(m))(v	X
ejpam-5848	88	2	)	)	PUNCT
ejpam-5848	88	3	=	=	SYM
ejpam-5848	88	4	µψ#(m)(ψ(v	µψ#(m)(ψ(v	NOUN
ejpam-5848	88	5	)	)	PUNCT
ejpam-5848	88	6	)	)	PUNCT
ejpam-5848	88	7	few	few	ADJ
ejpam-5848	88	8	properties	property	NOUN
ejpam-5848	88	9	of	of	ADP
ejpam-5848	88	10	ψ	ψ	NOUN
ejpam-5848	88	11	#	#	NOUN
ejpam-5848	88	12	mapping	mapping	NOUN
ejpam-5848	88	13	are	be	AUX
ejpam-5848	88	14	given	give	VERB
ejpam-5848	88	15	by	by	ADP
ejpam-5848	88	16	the	the	DET
ejpam-5848	88	17	lemma	lemma	PROPN
ejpam-5848	88	18	below	below	ADV
ejpam-5848	88	19	.	.	PUNCT
ejpam-5848	89	1	lemma	lemma	PROPN
ejpam-5848	89	2	1	1	NUM
ejpam-5848	89	3	.	.	PUNCT
ejpam-5848	90	1	[	[	X
ejpam-5848	90	2	21	21	NUM
ejpam-5848	90	3	]	]	X
ejpam-5848	90	4	let	let	VERB
ejpam-5848	90	5	ψ	ψ	NOUN
ejpam-5848	90	6	:	:	PUNCT
ejpam-5848	90	7	v	v	X
ejpam-5848	90	8	→	→	SYM
ejpam-5848	90	9	w	w	X
ejpam-5848	90	10	be	be	AUX
ejpam-5848	90	11	any	any	DET
ejpam-5848	90	12	mapping	mapping	NOUN
ejpam-5848	90	13	and	and	CCONJ
ejpam-5848	90	14	m	m	PROPN
ejpam-5848	90	15	,	,	PUNCT
ejpam-5848	90	16	n	n	PRON
ejpam-5848	90	17	be	be	VERB
ejpam-5848	90	18	fuzzy	fuzzy	ADJ
ejpam-5848	90	19	subsets	subset	NOUN
ejpam-5848	90	20	of	of	ADP
ejpam-5848	90	21	v	v	NOUN
ejpam-5848	90	22	and	and	CCONJ
ejpam-5848	90	23	u	u	NOUN
ejpam-5848	90	24	be	be	VERB
ejpam-5848	90	25	a	a	DET
ejpam-5848	90	26	fuzzy	fuzzy	ADJ
ejpam-5848	90	27	subset	subset	NOUN
ejpam-5848	90	28	of	of	ADP
ejpam-5848	90	29	w	w	PROPN
ejpam-5848	90	30	.	.	PUNCT
ejpam-5848	91	1	then	then	ADV
ejpam-5848	91	2	:	:	PUNCT
ejpam-5848	92	1	s.	s.	PROPN
ejpam-5848	92	2	kaur	kaur	PROPN
ejpam-5848	92	3	et	et	PROPN
ejpam-5848	92	4	al	al	PROPN
ejpam-5848	92	5	.	.	PUNCT
ejpam-5848	92	6	/	/	SYM
ejpam-5848	92	7	eur	eur	PROPN
ejpam-5848	92	8	.	.	PUNCT
ejpam-5848	93	1	j.	j.	PROPN
ejpam-5848	93	2	pure	pure	PROPN
ejpam-5848	93	3	appl	appl	PROPN
ejpam-5848	93	4	.	.	PROPN
ejpam-5848	93	5	math	math	PROPN
ejpam-5848	93	6	,	,	PUNCT
ejpam-5848	93	7	18	18	NUM
ejpam-5848	93	8	(	(	PUNCT
ejpam-5848	93	9	1	1	NUM
ejpam-5848	93	10	)	)	PUNCT
ejpam-5848	93	11	(	(	PUNCT
ejpam-5848	93	12	2025	2025	NUM
ejpam-5848	93	13	)	)	PUNCT
ejpam-5848	93	14	,	,	PUNCT
ejpam-5848	93	15	5848	5848	NUM
ejpam-5848	93	16	5	5	NUM
ejpam-5848	93	17	of	of	ADP
ejpam-5848	93	18	11	11	NUM
ejpam-5848	93	19	(	(	PUNCT
ejpam-5848	93	20	a	a	NOUN
ejpam-5848	93	21	)	)	PUNCT
ejpam-5848	93	22	(	(	PUNCT
ejpam-5848	93	23	ψ#(m	ψ#(m	PROPN
ejpam-5848	93	24	)	)	PUNCT
ejpam-5848	93	25	)	)	PUNCT
ejpam-5848	94	1	⊆	⊆	NUM
ejpam-5848	94	2	(	(	PUNCT
ejpam-5848	94	3	ψ#(n	ψ#(n	PROPN
ejpam-5848	94	4	)	)	PUNCT
ejpam-5848	94	5	)	)	PUNCT
ejpam-5848	95	1	if	if	SCONJ
ejpam-5848	95	2	m	m	PROPN
ejpam-5848	95	3	⊆	⊆	NUM
ejpam-5848	95	4	n	n	NOUN
ejpam-5848	95	5	.	.	PUNCT
ejpam-5848	96	1	(	(	PUNCT
ejpam-5848	96	2	b	b	NOUN
ejpam-5848	96	3	)	)	PUNCT
ejpam-5848	96	4	ψ−1(ψ#(m	ψ−1(ψ#(m	NOUN
ejpam-5848	96	5	)	)	PUNCT
ejpam-5848	96	6	)	)	PUNCT
ejpam-5848	97	1	⊆m	⊆m	NOUN
ejpam-5848	97	2	i.e.	i.e.	X
ejpam-5848	97	3	m	m	NOUN
ejpam-5848	97	4	#	#	NOUN
ejpam-5848	97	5	⊆m	⊆m	NOUN
ejpam-5848	97	6	.	.	PUNCT
ejpam-5848	98	1	(	(	PUNCT
ejpam-5848	98	2	c	c	X
ejpam-5848	98	3	)	)	PUNCT
ejpam-5848	98	4	u	u	NOUN
ejpam-5848	98	5	⊆	⊆	NUM
ejpam-5848	98	6	ψ#(ψ−1(u	ψ#(ψ−1(u	NOUN
ejpam-5848	98	7	)	)	PUNCT
ejpam-5848	98	8	)	)	PUNCT
ejpam-5848	98	9	and	and	CCONJ
ejpam-5848	98	10	equality	equality	NOUN
ejpam-5848	98	11	holds	hold	VERB
ejpam-5848	98	12	if	if	SCONJ
ejpam-5848	98	13	ψ	ψ	NOUN
ejpam-5848	98	14	is	be	AUX
ejpam-5848	98	15	onto	onto	ADP
ejpam-5848	98	16	.	.	PUNCT
ejpam-5848	99	1	(	(	PUNCT
ejpam-5848	99	2	d	d	X
ejpam-5848	99	3	)	)	PUNCT
ejpam-5848	99	4	ψ(m	ψ(m	NOUN
ejpam-5848	99	5	#	#	NOUN
ejpam-5848	99	6	)	)	PUNCT
ejpam-5848	99	7	=	=	SYM
ejpam-5848	99	8	ψ#(m	ψ#(m	PROPN
ejpam-5848	99	9	)	)	PUNCT
ejpam-5848	99	10	∩	∩	NOUN
ejpam-5848	99	11	ψ(v	ψ(v	PROPN
ejpam-5848	99	12	)	)	PUNCT
ejpam-5848	99	13	.	.	PUNCT
ejpam-5848	100	1	(	(	PUNCT
ejpam-5848	100	2	e	e	X
ejpam-5848	100	3	)	)	PUNCT
ejpam-5848	100	4	ψ#(m	ψ#(m	PROPN
ejpam-5848	100	5	∩n	∩n	PROPN
ejpam-5848	100	6	)	)	PUNCT
ejpam-5848	101	1	=	=	PUNCT
ejpam-5848	101	2	ψ#(m	ψ#(m	PROPN
ejpam-5848	101	3	)	)	PUNCT
ejpam-5848	101	4	∩	∩	PROPN
ejpam-5848	101	5	ψ#(n	ψ#(n	PROPN
ejpam-5848	101	6	)	)	PUNCT
ejpam-5848	101	7	.	.	PUNCT
ejpam-5848	102	1	(	(	PUNCT
ejpam-5848	102	2	f	f	X
ejpam-5848	102	3	)	)	PUNCT
ejpam-5848	102	4	ψ#(ψ	ψ#(ψ	PROPN
ejpam-5848	102	5	)	)	PUNCT
ejpam-5848	102	6	=	=	PUNCT
ejpam-5848	102	7	(	(	PUNCT
ejpam-5848	102	8	ψ(v	ψ(v	PROPN
ejpam-5848	102	9	)	)	PUNCT
ejpam-5848	102	10	)	)	PUNCT
ejpam-5848	103	1	c	c	NOUN
ejpam-5848	103	2	and	and	CCONJ
ejpam-5848	103	3	ψ#(v	ψ#(v	NOUN
ejpam-5848	103	4	)	)	PUNCT
ejpam-5848	104	1	=	=	NOUN
ejpam-5848	104	2	w	w	NOUN
ejpam-5848	104	3	.	.	PUNCT
ejpam-5848	105	1	(	(	PUNCT
ejpam-5848	105	2	g	g	NOUN
ejpam-5848	105	3	)	)	PUNCT
ejpam-5848	105	4	ψ(m	ψ(m	NOUN
ejpam-5848	105	5	#	#	NOUN
ejpam-5848	105	6	)	)	PUNCT
ejpam-5848	105	7	=	=	SYM
ejpam-5848	105	8	ψ#(m	ψ#(m	PROPN
ejpam-5848	105	9	)	)	PUNCT
ejpam-5848	105	10	∩	∩	NOUN
ejpam-5848	105	11	ψ(m	ψ(m	NOUN
ejpam-5848	105	12	)	)	PUNCT
ejpam-5848	105	13	.	.	PUNCT
ejpam-5848	106	1	(	(	PUNCT
ejpam-5848	106	2	h	h	NOUN
ejpam-5848	106	3	)	)	PUNCT
ejpam-5848	106	4	ψ#(ψ−1(ψ#(m	ψ#(ψ−1(ψ#(m	NOUN
ejpam-5848	106	5	)	)	PUNCT
ejpam-5848	106	6	)	)	PUNCT
ejpam-5848	106	7	)	)	PUNCT
ejpam-5848	107	1	=	=	PUNCT
ejpam-5848	107	2	ψ#(m	ψ#(m	NOUN
ejpam-5848	107	3	#	#	NOUN
ejpam-5848	107	4	)	)	PUNCT
ejpam-5848	107	5	=	=	PUNCT
ejpam-5848	107	6	ψ#(m	ψ#(m	PROPN
ejpam-5848	107	7	)	)	PUNCT
ejpam-5848	107	8	.	.	PUNCT
ejpam-5848	108	1	(	(	PUNCT
ejpam-5848	108	2	i	i	NOUN
ejpam-5848	108	3	)	)	PUNCT
ejpam-5848	108	4	ψ−1(ψ#(ψ−1(u	ψ−1(ψ#(ψ−1(u	NOUN
ejpam-5848	108	5	)	)	PUNCT
ejpam-5848	108	6	)	)	PUNCT
ejpam-5848	108	7	)	)	PUNCT
ejpam-5848	109	1	=	=	SYM
ejpam-5848	109	2	ψ−1(u	ψ−1(u	PROPN
ejpam-5848	109	3	)	)	PUNCT
ejpam-5848	109	4	.	.	PUNCT
ejpam-5848	110	1	3	3	X
ejpam-5848	110	2	.	.	X
ejpam-5848	110	3	characterizations	characterization	NOUN
ejpam-5848	110	4	of	of	ADP
ejpam-5848	110	5	open	open	ADJ
ejpam-5848	110	6	fuzzy	fuzzy	ADJ
ejpam-5848	110	7	mappings	mapping	NOUN
ejpam-5848	110	8	in	in	ADP
ejpam-5848	110	9	this	this	DET
ejpam-5848	110	10	section	section	NOUN
ejpam-5848	110	11	,	,	PUNCT
ejpam-5848	110	12	we	we	PRON
ejpam-5848	110	13	study	study	VERB
ejpam-5848	110	14	some	some	DET
ejpam-5848	110	15	new	new	ADJ
ejpam-5848	110	16	representations	representation	NOUN
ejpam-5848	110	17	of	of	ADP
ejpam-5848	110	18	open	open	ADJ
ejpam-5848	110	19	fuzzy	fuzzy	ADJ
ejpam-5848	110	20	mappings	mapping	NOUN
ejpam-5848	110	21	which	which	PRON
ejpam-5848	110	22	provides	provide	VERB
ejpam-5848	110	23	valuable	valuable	ADJ
ejpam-5848	110	24	insights	insight	NOUN
ejpam-5848	110	25	into	into	ADP
ejpam-5848	110	26	the	the	DET
ejpam-5848	110	27	properties	property	NOUN
ejpam-5848	110	28	and	and	CCONJ
ejpam-5848	110	29	behavior	behavior	NOUN
ejpam-5848	110	30	of	of	ADP
ejpam-5848	110	31	these	these	DET
ejpam-5848	110	32	mappings	mapping	NOUN
ejpam-5848	110	33	.	.	PUNCT
ejpam-5848	111	1	we	we	PRON
ejpam-5848	111	2	begin	begin	VERB
ejpam-5848	111	3	with	with	ADP
ejpam-5848	111	4	a	a	DET
ejpam-5848	111	5	characterization	characterization	NOUN
ejpam-5848	111	6	of	of	ADP
ejpam-5848	111	7	the	the	DET
ejpam-5848	111	8	open	open	ADJ
ejpam-5848	111	9	fuzzy	fuzzy	ADJ
ejpam-5848	111	10	mapping	mapping	NOUN
ejpam-5848	111	11	using	use	VERB
ejpam-5848	111	12	induced	induce	VERB
ejpam-5848	111	13	mapping	mapping	NOUN
ejpam-5848	111	14	ψ	ψ	NOUN
ejpam-5848	111	15	#	#	NOUN
ejpam-5848	111	16	for	for	ADP
ejpam-5848	111	17	which	which	PRON
ejpam-5848	111	18	we	we	PRON
ejpam-5848	111	19	make	make	VERB
ejpam-5848	111	20	use	use	NOUN
ejpam-5848	111	21	of	of	ADP
ejpam-5848	111	22	the	the	DET
ejpam-5848	111	23	following	follow	VERB
ejpam-5848	111	24	lemma	lemma	PROPN
ejpam-5848	111	25	on	on	ADP
ejpam-5848	111	26	the	the	DET
ejpam-5848	111	27	properties	property	NOUN
ejpam-5848	111	28	of	of	ADP
ejpam-5848	111	29	the	the	DET
ejpam-5848	111	30	#	#	SYM
ejpam-5848	111	31	-image	-image	NOUN
ejpam-5848	111	32	of	of	ADP
ejpam-5848	111	33	an	an	DET
ejpam-5848	111	34	f	f	X
ejpam-5848	111	35	-set	-set	NOUN
ejpam-5848	111	36	m	m	VERB
ejpam-5848	111	37	in	in	ADP
ejpam-5848	111	38	v	v	NUM
ejpam-5848	111	39	.	.	PUNCT
ejpam-5848	112	1	lemma	lemma	PROPN
ejpam-5848	112	2	2	2	NUM
ejpam-5848	112	3	.	.	PUNCT
ejpam-5848	113	1	[	[	X
ejpam-5848	113	2	21	21	NUM
ejpam-5848	113	3	]	]	X
ejpam-5848	113	4	let	let	VERB
ejpam-5848	113	5	ψ	ψ	X
ejpam-5848	113	6	:	:	PUNCT
ejpam-5848	113	7	v	v	PART
ejpam-5848	113	8	→w	→w	PUNCT
ejpam-5848	113	9	be	be	AUX
ejpam-5848	113	10	any	any	DET
ejpam-5848	113	11	mapping	mapping	NOUN
ejpam-5848	113	12	,	,	PUNCT
ejpam-5848	113	13	m	m	VERB
ejpam-5848	113	14	and	and	CCONJ
ejpam-5848	113	15	u	u	PRON
ejpam-5848	113	16	be	be	VERB
ejpam-5848	113	17	any	any	DET
ejpam-5848	113	18	fuzzy	fuzzy	ADJ
ejpam-5848	113	19	subsets	subset	NOUN
ejpam-5848	113	20	of	of	ADP
ejpam-5848	113	21	v	v	NOUN
ejpam-5848	113	22	and	and	CCONJ
ejpam-5848	113	23	w	w	NOUN
ejpam-5848	113	24	,	,	PUNCT
ejpam-5848	113	25	respectively	respectively	ADV
ejpam-5848	113	26	.	.	PUNCT
ejpam-5848	114	1	then	then	ADV
ejpam-5848	114	2	:	:	PUNCT
ejpam-5848	114	3	(	(	PUNCT
ejpam-5848	114	4	a	a	X
ejpam-5848	114	5	)	)	PUNCT
ejpam-5848	114	6	ψ−1(u	ψ−1(u	PROPN
ejpam-5848	114	7	)	)	PUNCT
ejpam-5848	114	8	⊆m	⊆m	NOUN
ejpam-5848	114	9	iff	iff	PROPN
ejpam-5848	114	10	u	u	PROPN
ejpam-5848	114	11	⊆	⊆	NUM
ejpam-5848	114	12	ψ#(m	ψ#(m	PROPN
ejpam-5848	114	13	)	)	PUNCT
ejpam-5848	114	14	.	.	PUNCT
ejpam-5848	115	1	(	(	PUNCT
ejpam-5848	115	2	b	b	X
ejpam-5848	115	3	)	)	PUNCT
ejpam-5848	115	4	ψ#(m	ψ#(m	PROPN
ejpam-5848	115	5	c	c	NOUN
ejpam-5848	115	6	)	)	PUNCT
ejpam-5848	116	1	=	=	SYM
ejpam-5848	116	2	(	(	PUNCT
ejpam-5848	116	3	ψ(m))c	ψ(m))c	PROPN
ejpam-5848	116	4	and	and	CCONJ
ejpam-5848	116	5	so	so	ADV
ejpam-5848	116	6	ψ#(m	ψ#(m	PROPN
ejpam-5848	116	7	)	)	PUNCT
ejpam-5848	116	8	=	=	PUNCT
ejpam-5848	116	9	(	(	PUNCT
ejpam-5848	116	10	ψ(m	ψ(m	PROPN
ejpam-5848	116	11	c))c	c))c	NOUN
ejpam-5848	116	12	and	and	CCONJ
ejpam-5848	116	13	ψ(m	ψ(m	PROPN
ejpam-5848	116	14	)	)	PUNCT
ejpam-5848	116	15	=	=	SYM
ejpam-5848	116	16	(	(	PUNCT
ejpam-5848	116	17	ψ#(m	ψ#(m	PROPN
ejpam-5848	116	18	c))c	c))c	PROPN
ejpam-5848	116	19	.	.	PUNCT
ejpam-5848	117	1	theorem	theorem	VERB
ejpam-5848	117	2	5	5	NUM
ejpam-5848	117	3	.	.	PUNCT
ejpam-5848	118	1	let	let	VERB
ejpam-5848	118	2	ψ	ψ	NOUN
ejpam-5848	118	3	:	:	PUNCT
ejpam-5848	118	4	v	v	X
ejpam-5848	118	5	→	→	SYM
ejpam-5848	118	6	w	w	ADP
ejpam-5848	118	7	where	where	SCONJ
ejpam-5848	118	8	v	v	NOUN
ejpam-5848	118	9	,	,	PUNCT
ejpam-5848	118	10	w	w	PROPN
ejpam-5848	118	11	be	be	AUX
ejpam-5848	118	12	spaces	space	NOUN
ejpam-5848	118	13	of	of	ADP
ejpam-5848	118	14	points	point	NOUN
ejpam-5848	118	15	.	.	PUNCT
ejpam-5848	119	1	then	then	ADV
ejpam-5848	119	2	,	,	PUNCT
ejpam-5848	119	3	ψ	ψ	X
ejpam-5848	119	4	is	be	AUX
ejpam-5848	119	5	an	an	DET
ejpam-5848	119	6	open	open	ADJ
ejpam-5848	119	7	fuzzy	fuzzy	ADJ
ejpam-5848	119	8	mapping	mapping	NOUN
ejpam-5848	119	9	if	if	SCONJ
ejpam-5848	119	10	and	and	CCONJ
ejpam-5848	119	11	only	only	ADV
ejpam-5848	119	12	if	if	SCONJ
ejpam-5848	119	13	ψ#(m	ψ#(m	PROPN
ejpam-5848	119	14	)	)	PUNCT
ejpam-5848	119	15	⊆	⊆	NUM
ejpam-5848	119	16	ψ#(m	ψ#(m	PROPN
ejpam-5848	119	17	)	)	PUNCT
ejpam-5848	119	18	for	for	ADP
ejpam-5848	119	19	every	every	DET
ejpam-5848	119	20	subset	subset	NOUN
ejpam-5848	119	21	m	m	NOUN
ejpam-5848	119	22	of	of	ADP
ejpam-5848	119	23	v.	v.	ADP
ejpam-5848	119	24	proof	proof	NOUN
ejpam-5848	119	25	.	.	PUNCT
ejpam-5848	120	1	let	let	VERB
ejpam-5848	120	2	ψ	ψ	PART
ejpam-5848	120	3	be	be	AUX
ejpam-5848	120	4	an	an	DET
ejpam-5848	120	5	open	open	ADJ
ejpam-5848	120	6	fuzzy	fuzzy	ADJ
ejpam-5848	120	7	mapping	mapping	NOUN
ejpam-5848	120	8	and	and	CCONJ
ejpam-5848	120	9	m	m	AUX
ejpam-5848	120	10	be	be	AUX
ejpam-5848	120	11	a	a	DET
ejpam-5848	120	12	subset	subset	NOUN
ejpam-5848	120	13	of	of	ADP
ejpam-5848	120	14	v	v	NOUN
ejpam-5848	120	15	.	.	PUNCT
ejpam-5848	121	1	by	by	ADP
ejpam-5848	121	2	lemma	lemma	PROPN
ejpam-5848	121	3	2	2	NUM
ejpam-5848	121	4	and	and	CCONJ
ejpam-5848	121	5	theorem	theorem	VERB
ejpam-5848	121	6	1	1	NUM
ejpam-5848	121	7	,	,	PUNCT
ejpam-5848	121	8	we	we	PRON
ejpam-5848	121	9	get	get	VERB
ejpam-5848	121	10	ψ#(m	ψ#(m	PROPN
ejpam-5848	121	11	)	)	PUNCT
ejpam-5848	122	1	=	=	PUNCT
ejpam-5848	122	2	(	(	PUNCT
ejpam-5848	122	3	ψ(m	ψ(m	PROPN
ejpam-5848	122	4	c)c	c)c	PUNCT
ejpam-5848	122	5	and	and	CCONJ
ejpam-5848	122	6	(	(	PUNCT
ejpam-5848	122	7	ψ(m	ψ(m	PROPN
ejpam-5848	122	8	c))c	c))c	NOUN
ejpam-5848	122	9	=	=	PUNCT
ejpam-5848	122	10	(	(	PUNCT
ejpam-5848	122	11	(	(	PUNCT
ejpam-5848	122	12	ψ(m	ψ(m	PROPN
ejpam-5848	122	13	c))	c))	PROPN
ejpam-5848	122	14	◦	◦	NOUN
ejpam-5848	122	15	)c	)c	PUNCT
ejpam-5848	122	16	since	since	SCONJ
ejpam-5848	122	17	ψ	ψ	NOUN
ejpam-5848	122	18	is	be	AUX
ejpam-5848	122	19	an	an	DET
ejpam-5848	122	20	open	open	ADJ
ejpam-5848	122	21	fuzzy	fuzzy	ADJ
ejpam-5848	122	22	mapping	mapping	NOUN
ejpam-5848	122	23	,	,	PUNCT
ejpam-5848	122	24	then	then	ADV
ejpam-5848	122	25	by	by	ADP
ejpam-5848	122	26	theorem	theorem	NOUN
ejpam-5848	122	27	3	3	NUM
ejpam-5848	122	28	(	(	PUNCT
ejpam-5848	122	29	2	2	NUM
ejpam-5848	122	30	)	)	PUNCT
ejpam-5848	122	31	,	,	PUNCT
ejpam-5848	122	32	(	(	PUNCT
ejpam-5848	122	33	(	(	PUNCT
ejpam-5848	122	34	ψ(m	ψ(m	PROPN
ejpam-5848	122	35	c))	c))	PROPN
ejpam-5848	122	36	◦	◦	NOUN
ejpam-5848	122	37	)c	)c	PUNCT
ejpam-5848	122	38	⊆	⊆	NUM
ejpam-5848	122	39	(	(	PUNCT
ejpam-5848	122	40	ψ((m	ψ((m	X
ejpam-5848	122	41	c)	c)	X
ejpam-5848	122	42	◦	◦	NOUN
ejpam-5848	122	43	)c	)c	PROPN
ejpam-5848	122	44	.	.	PUNCT
ejpam-5848	123	1	therefore	therefore	ADV
ejpam-5848	123	2	,	,	PUNCT
ejpam-5848	123	3	ψ#(m	ψ#(m	PROPN
ejpam-5848	123	4	)	)	PUNCT
ejpam-5848	123	5	⊆	⊆	NUM
ejpam-5848	123	6	(	(	PUNCT
ejpam-5848	123	7	ψ((m	ψ((m	X
ejpam-5848	123	8	c)	c)	X
ejpam-5848	123	9	◦	◦	NOUN
ejpam-5848	123	10	))c	))c	SYM
ejpam-5848	123	11	=	=	SYM
ejpam-5848	123	12	(	(	PUNCT
ejpam-5848	123	13	(	(	PUNCT
ejpam-5848	123	14	ψ(m)c))c	ψ(m)c))c	X
ejpam-5848	123	15	.	.	PUNCT
ejpam-5848	123	16	again	again	ADV
ejpam-5848	123	17	,	,	PUNCT
ejpam-5848	123	18	by	by	ADP
ejpam-5848	123	19	lemma	lemma	PROPN
ejpam-5848	123	20	2	2	NUM
ejpam-5848	123	21	(	(	PUNCT
ejpam-5848	123	22	b	b	NOUN
ejpam-5848	123	23	)	)	PUNCT
ejpam-5848	123	24	,	,	PUNCT
ejpam-5848	123	25	(	(	PUNCT
ejpam-5848	123	26	ψ(m)c)c	ψ(m)c)c	X
ejpam-5848	123	27	=	=	PUNCT
ejpam-5848	123	28	ψ#(m	ψ#(m	PROPN
ejpam-5848	123	29	)	)	PUNCT
ejpam-5848	123	30	.	.	PUNCT
ejpam-5848	124	1	hence	hence	ADV
ejpam-5848	124	2	,	,	PUNCT
ejpam-5848	124	3	ψ#(m	ψ#(m	PROPN
ejpam-5848	124	4	)	)	PUNCT
ejpam-5848	124	5	⊆	⊆	NUM
ejpam-5848	124	6	ψ#(m	ψ#(m	PROPN
ejpam-5848	124	7	)	)	PUNCT
ejpam-5848	124	8	.	.	PUNCT
ejpam-5848	125	1	s.	s.	PROPN
ejpam-5848	125	2	kaur	kaur	PROPN
ejpam-5848	125	3	et	et	PROPN
ejpam-5848	125	4	al	al	PROPN
ejpam-5848	125	5	.	.	PUNCT
ejpam-5848	125	6	/	/	SYM
ejpam-5848	125	7	eur	eur	PROPN
ejpam-5848	125	8	.	.	PUNCT
ejpam-5848	126	1	j.	j.	PROPN
ejpam-5848	126	2	pure	pure	PROPN
ejpam-5848	126	3	appl	appl	PROPN
ejpam-5848	126	4	.	.	PROPN
ejpam-5848	126	5	math	math	PROPN
ejpam-5848	126	6	,	,	PUNCT
ejpam-5848	126	7	18	18	NUM
ejpam-5848	126	8	(	(	PUNCT
ejpam-5848	126	9	1	1	NUM
ejpam-5848	126	10	)	)	PUNCT
ejpam-5848	126	11	(	(	PUNCT
ejpam-5848	126	12	2025	2025	NUM
ejpam-5848	126	13	)	)	PUNCT
ejpam-5848	126	14	,	,	PUNCT
ejpam-5848	126	15	5848	5848	NUM
ejpam-5848	126	16	6	6	NUM
ejpam-5848	126	17	of	of	ADP
ejpam-5848	126	18	11	11	NUM
ejpam-5848	126	19	conversely	conversely	ADV
ejpam-5848	126	20	,	,	PUNCT
ejpam-5848	126	21	let	let	VERB
ejpam-5848	126	22	g	g	PRON
ejpam-5848	126	23	be	be	AUX
ejpam-5848	126	24	any	any	DET
ejpam-5848	126	25	open	open	ADJ
ejpam-5848	126	26	fuzzy	fuzzy	ADJ
ejpam-5848	126	27	subset	subset	NOUN
ejpam-5848	126	28	of	of	ADP
ejpam-5848	126	29	v	v	NOUN
ejpam-5848	126	30	.	.	PUNCT
ejpam-5848	127	1	then	then	ADV
ejpam-5848	127	2	by	by	ADP
ejpam-5848	127	3	assumption	assumption	NOUN
ejpam-5848	127	4	,	,	PUNCT
ejpam-5848	127	5	ψ#(gc	ψ#(gc	PROPN
ejpam-5848	127	6	)	)	PUNCT
ejpam-5848	127	7	⊆	⊆	NUM
ejpam-5848	127	8	ψ#(gc	ψ#(gc	NOUN
ejpam-5848	127	9	)	)	PUNCT
ejpam-5848	127	10	we	we	PRON
ejpam-5848	127	11	obtain	obtain	VERB
ejpam-5848	127	12	ψ#(gc	ψ#(gc	PROPN
ejpam-5848	127	13	)	)	PUNCT
ejpam-5848	128	1	⊆	⊆	NUM
ejpam-5848	128	2	ψ#(gc	ψ#(gc	NOUN
ejpam-5848	128	3	)	)	PUNCT
ejpam-5848	128	4	since	since	SCONJ
ejpam-5848	128	5	gc	gc	PROPN
ejpam-5848	128	6	is	be	AUX
ejpam-5848	128	7	a	a	DET
ejpam-5848	128	8	closed	closed	ADJ
ejpam-5848	128	9	fuzzy	fuzzy	ADJ
ejpam-5848	128	10	subset	subset	NOUN
ejpam-5848	128	11	of	of	ADP
ejpam-5848	128	12	v	v	NOUN
ejpam-5848	128	13	.	.	PUNCT
ejpam-5848	129	1	this	this	DET
ejpam-5848	129	2	further	far	ADV
ejpam-5848	129	3	implies	imply	VERB
ejpam-5848	129	4	that	that	SCONJ
ejpam-5848	129	5	ψ#(gc	ψ#(gc	PROPN
ejpam-5848	129	6	)	)	PUNCT
ejpam-5848	129	7	is	be	AUX
ejpam-5848	129	8	a	a	DET
ejpam-5848	129	9	closed	closed	ADJ
ejpam-5848	129	10	fuzzy	fuzzy	ADJ
ejpam-5848	129	11	subset	subset	NOUN
ejpam-5848	129	12	of	of	ADP
ejpam-5848	129	13	w	w	PROPN
ejpam-5848	129	14	and	and	CCONJ
ejpam-5848	129	15	hence	hence	ADV
ejpam-5848	129	16	,	,	PUNCT
ejpam-5848	129	17	(	(	PUNCT
ejpam-5848	129	18	ψ#(gc))c	ψ#(gc))c	VERB
ejpam-5848	129	19	is	be	AUX
ejpam-5848	129	20	an	an	DET
ejpam-5848	129	21	open	open	ADJ
ejpam-5848	129	22	fuzzy	fuzzy	ADJ
ejpam-5848	129	23	set	set	NOUN
ejpam-5848	129	24	.	.	PUNCT
ejpam-5848	130	1	therefore	therefore	ADV
ejpam-5848	130	2	,	,	PUNCT
ejpam-5848	130	3	by	by	ADP
ejpam-5848	130	4	lemma	lemma	PROPN
ejpam-5848	130	5	2	2	NUM
ejpam-5848	130	6	(	(	PUNCT
ejpam-5848	130	7	b	b	NOUN
ejpam-5848	130	8	)	)	PUNCT
ejpam-5848	130	9	,	,	PUNCT
ejpam-5848	130	10	(	(	PUNCT
ejpam-5848	130	11	ψ#(gc))c	ψ#(gc))c	VERB
ejpam-5848	130	12	=	=	SYM
ejpam-5848	130	13	ψ(g	ψ(g	PROPN
ejpam-5848	130	14	)	)	PUNCT
ejpam-5848	130	15	is	be	AUX
ejpam-5848	130	16	an	an	DET
ejpam-5848	130	17	open	open	ADJ
ejpam-5848	130	18	fuzzy	fuzzy	ADJ
ejpam-5848	130	19	subset	subset	NOUN
ejpam-5848	130	20	of	of	ADP
ejpam-5848	130	21	w	w	PROPN
ejpam-5848	130	22	.	.	PUNCT
ejpam-5848	131	1	hence	hence	ADV
ejpam-5848	131	2	,	,	PUNCT
ejpam-5848	131	3	ψ	ψ	X
ejpam-5848	131	4	is	be	AUX
ejpam-5848	131	5	an	an	DET
ejpam-5848	131	6	open	open	ADJ
ejpam-5848	131	7	fuzzy	fuzzy	ADJ
ejpam-5848	131	8	mapping	mapping	NOUN
ejpam-5848	131	9	.	.	PUNCT
ejpam-5848	132	1	in	in	ADP
ejpam-5848	132	2	the	the	DET
ejpam-5848	132	3	next	next	ADJ
ejpam-5848	132	4	theorem	theorem	NOUN
ejpam-5848	132	5	,	,	PUNCT
ejpam-5848	132	6	we	we	PRON
ejpam-5848	132	7	discuss	discuss	VERB
ejpam-5848	132	8	another	another	DET
ejpam-5848	132	9	characterization	characterization	NOUN
ejpam-5848	132	10	of	of	ADP
ejpam-5848	132	11	the	the	DET
ejpam-5848	132	12	open	open	ADJ
ejpam-5848	132	13	fuzzy	fuzzy	ADJ
ejpam-5848	132	14	mapping	mapping	NOUN
ejpam-5848	132	15	in	in	ADP
ejpam-5848	132	16	terms	term	NOUN
ejpam-5848	132	17	of	of	ADP
ejpam-5848	132	18	closed	closed	ADJ
ejpam-5848	132	19	fuzzy	fuzzy	ADJ
ejpam-5848	132	20	subsets	subset	NOUN
ejpam-5848	132	21	.	.	PUNCT
ejpam-5848	133	1	theorem	theorem	NOUN
ejpam-5848	133	2	6	6	NUM
ejpam-5848	133	3	.	.	PUNCT
ejpam-5848	134	1	let	let	VERB
ejpam-5848	134	2	ψ	ψ	PART
ejpam-5848	134	3	be	be	AUX
ejpam-5848	134	4	a	a	DET
ejpam-5848	134	5	mapping	mapping	NOUN
ejpam-5848	134	6	from	from	ADP
ejpam-5848	134	7	v	v	NUM
ejpam-5848	134	8	to	to	ADP
ejpam-5848	134	9	w	w	PROPN
ejpam-5848	134	10	.	.	PUNCT
ejpam-5848	135	1	then	then	ADV
ejpam-5848	135	2	,	,	PUNCT
ejpam-5848	135	3	ψ	ψ	X
ejpam-5848	135	4	is	be	AUX
ejpam-5848	135	5	an	an	DET
ejpam-5848	135	6	open	open	ADJ
ejpam-5848	135	7	fuzzy	fuzzy	ADJ
ejpam-5848	135	8	mapping	mapping	NOUN
ejpam-5848	135	9	if	if	SCONJ
ejpam-5848	135	10	and	and	CCONJ
ejpam-5848	135	11	only	only	ADV
ejpam-5848	135	12	if	if	SCONJ
ejpam-5848	135	13	for	for	ADP
ejpam-5848	135	14	each	each	DET
ejpam-5848	135	15	closed	close	VERB
ejpam-5848	135	16	fuzzy	fuzzy	ADJ
ejpam-5848	135	17	subset	subset	VERB
ejpam-5848	135	18	g	g	NOUN
ejpam-5848	135	19	of	of	ADP
ejpam-5848	135	20	v	v	NOUN
ejpam-5848	135	21	,	,	PUNCT
ejpam-5848	135	22	ψ#(g	ψ#(g	PROPN
ejpam-5848	135	23	)	)	PUNCT
ejpam-5848	135	24	is	be	AUX
ejpam-5848	135	25	a	a	DET
ejpam-5848	135	26	closed	closed	ADJ
ejpam-5848	135	27	fuzzy	fuzzy	ADJ
ejpam-5848	135	28	subset	subset	NOUN
ejpam-5848	135	29	of	of	ADP
ejpam-5848	135	30	w	w	PROPN
ejpam-5848	135	31	.	.	PUNCT
ejpam-5848	136	1	proof	proof	NOUN
ejpam-5848	136	2	.	.	PUNCT
ejpam-5848	137	1	the	the	DET
ejpam-5848	137	2	necessity	necessity	NOUN
ejpam-5848	137	3	of	of	ADP
ejpam-5848	137	4	the	the	DET
ejpam-5848	137	5	condition	condition	NOUN
ejpam-5848	137	6	follows	follow	VERB
ejpam-5848	137	7	from	from	ADP
ejpam-5848	137	8	theorem	theorem	ADJ
ejpam-5848	137	9	5	5	NUM
ejpam-5848	137	10	.	.	PUNCT
ejpam-5848	137	11	conversely	conversely	ADV
ejpam-5848	137	12	,	,	PUNCT
ejpam-5848	137	13	let	let	VERB
ejpam-5848	137	14	o	o	NOUN
ejpam-5848	137	15	be	be	AUX
ejpam-5848	137	16	an	an	DET
ejpam-5848	137	17	open	open	ADJ
ejpam-5848	137	18	fuzzy	fuzzy	ADJ
ejpam-5848	137	19	subset	subset	NOUN
ejpam-5848	137	20	of	of	ADP
ejpam-5848	137	21	v	v	NOUN
ejpam-5848	137	22	.	.	PUNCT
ejpam-5848	138	1	then	then	ADV
ejpam-5848	138	2	by	by	ADP
ejpam-5848	138	3	assumption	assumption	NOUN
ejpam-5848	138	4	,	,	PUNCT
ejpam-5848	138	5	ψ#(oc	ψ#(oc	PROPN
ejpam-5848	138	6	)	)	PUNCT
ejpam-5848	138	7	is	be	AUX
ejpam-5848	138	8	a	a	DET
ejpam-5848	138	9	closed	closed	ADJ
ejpam-5848	138	10	fuzzy	fuzzy	ADJ
ejpam-5848	138	11	set	set	VERB
ejpam-5848	138	12	in	in	ADP
ejpam-5848	138	13	w	w	PROPN
ejpam-5848	138	14	.	.	PUNCT
ejpam-5848	139	1	but	but	CCONJ
ejpam-5848	139	2	by	by	ADP
ejpam-5848	139	3	lemma	lemma	PROPN
ejpam-5848	139	4	2	2	NUM
ejpam-5848	139	5	(	(	PUNCT
ejpam-5848	139	6	b	b	NOUN
ejpam-5848	139	7	)	)	PUNCT
ejpam-5848	139	8	,	,	PUNCT
ejpam-5848	139	9	ψ#(oc	ψ#(oc	NOUN
ejpam-5848	139	10	)	)	PUNCT
ejpam-5848	139	11	=	=	SYM
ejpam-5848	139	12	ψ(o)c	ψ(o)c	PROPN
ejpam-5848	139	13	.	.	PUNCT
ejpam-5848	140	1	therefore	therefore	ADV
ejpam-5848	140	2	,	,	PUNCT
ejpam-5848	140	3	ψ(o)c	ψ(o)c	PROPN
ejpam-5848	140	4	is	be	AUX
ejpam-5848	140	5	a	a	DET
ejpam-5848	140	6	closed	closed	ADJ
ejpam-5848	140	7	fuzzy	fuzzy	ADJ
ejpam-5848	140	8	set	set	VERB
ejpam-5848	140	9	in	in	ADP
ejpam-5848	140	10	w	w	PROPN
ejpam-5848	140	11	,	,	PUNCT
ejpam-5848	140	12	and	and	CCONJ
ejpam-5848	140	13	hence	hence	ADV
ejpam-5848	140	14	,	,	PUNCT
ejpam-5848	140	15	ψ(o	ψ(o	PROPN
ejpam-5848	140	16	)	)	PUNCT
ejpam-5848	140	17	is	be	AUX
ejpam-5848	140	18	an	an	DET
ejpam-5848	140	19	open	open	ADJ
ejpam-5848	140	20	fuzzy	fuzzy	ADJ
ejpam-5848	140	21	set	set	NOUN
ejpam-5848	140	22	in	in	ADP
ejpam-5848	140	23	w	w	PROPN
ejpam-5848	140	24	,	,	PUNCT
ejpam-5848	140	25	which	which	PRON
ejpam-5848	140	26	proves	prove	VERB
ejpam-5848	140	27	ψ	ψ	NOUN
ejpam-5848	140	28	is	be	AUX
ejpam-5848	140	29	an	an	DET
ejpam-5848	140	30	open	open	ADJ
ejpam-5848	140	31	fuzzy	fuzzy	ADJ
ejpam-5848	140	32	mapping	mapping	NOUN
ejpam-5848	140	33	.	.	PUNCT
ejpam-5848	141	1	blueas	bluea	NOUN
ejpam-5848	141	2	an	an	DET
ejpam-5848	141	3	instance	instance	NOUN
ejpam-5848	141	4	of	of	ADP
ejpam-5848	141	5	the	the	DET
ejpam-5848	141	6	above	above	ADJ
ejpam-5848	141	7	theorem	theorem	NOUN
ejpam-5848	141	8	,	,	PUNCT
ejpam-5848	141	9	we	we	PRON
ejpam-5848	141	10	have	have	VERB
ejpam-5848	141	11	the	the	DET
ejpam-5848	141	12	following	following	ADJ
ejpam-5848	141	13	example	example	NOUN
ejpam-5848	141	14	which	which	PRON
ejpam-5848	141	15	shows	show	VERB
ejpam-5848	141	16	that	that	SCONJ
ejpam-5848	141	17	if	if	SCONJ
ejpam-5848	141	18	for	for	ADP
ejpam-5848	141	19	any	any	DET
ejpam-5848	141	20	closed	closed	ADJ
ejpam-5848	141	21	fuzzy	fuzzy	ADJ
ejpam-5848	141	22	subset	subset	VERB
ejpam-5848	141	23	g	g	NOUN
ejpam-5848	141	24	of	of	ADP
ejpam-5848	141	25	v	v	NOUN
ejpam-5848	141	26	,	,	PUNCT
ejpam-5848	141	27	ψ#(g	ψ#(g	PROPN
ejpam-5848	141	28	)	)	PUNCT
ejpam-5848	141	29	is	be	AUX
ejpam-5848	141	30	not	not	PART
ejpam-5848	141	31	a	a	DET
ejpam-5848	141	32	closed	closed	ADJ
ejpam-5848	141	33	fuzzy	fuzzy	ADJ
ejpam-5848	141	34	subset	subset	NOUN
ejpam-5848	141	35	of	of	ADP
ejpam-5848	141	36	w	w	PROPN
ejpam-5848	141	37	then	then	ADV
ejpam-5848	141	38	ψ	ψ	X
ejpam-5848	141	39	is	be	AUX
ejpam-5848	141	40	not	not	PART
ejpam-5848	141	41	an	an	DET
ejpam-5848	141	42	open	open	ADJ
ejpam-5848	141	43	fuzzy	fuzzy	ADJ
ejpam-5848	141	44	mapping	mapping	NOUN
ejpam-5848	141	45	.	.	PUNCT
ejpam-5848	142	1	example	example	NOUN
ejpam-5848	143	1	1	1	NUM
ejpam-5848	143	2	.	.	PUNCT
ejpam-5848	143	3	let	let	VERB
ejpam-5848	143	4	v	v	NOUN
ejpam-5848	143	5	=	=	PUNCT
ejpam-5848	144	1	[	[	X
ejpam-5848	144	2	0	0	NUM
ejpam-5848	144	3	,	,	PUNCT
ejpam-5848	144	4	1	1	NUM
ejpam-5848	144	5	]	]	PUNCT
ejpam-5848	144	6	,	,	PUNCT
ejpam-5848	144	7	consider	consider	VERB
ejpam-5848	144	8	the	the	DET
ejpam-5848	144	9	f	f	PROPN
ejpam-5848	144	10	-sets	-set	NOUN
ejpam-5848	144	11	m	m	PROPN
ejpam-5848	144	12	,	,	PUNCT
ejpam-5848	144	13	n	n	CCONJ
ejpam-5848	144	14	,	,	PUNCT
ejpam-5848	144	15	p	p	NOUN
ejpam-5848	144	16	with	with	ADP
ejpam-5848	144	17	membership	membership	NOUN
ejpam-5848	144	18	functions	function	NOUN
ejpam-5848	144	19	given	give	VERB
ejpam-5848	144	20	by	by	ADP
ejpam-5848	144	21	µm	µm	ADP
ejpam-5848	144	22	(	(	PUNCT
ejpam-5848	144	23	v	v	NOUN
ejpam-5848	144	24	)	)	PUNCT
ejpam-5848	144	25	=	=	SYM
ejpam-5848	144	26	{	{	PUNCT
ejpam-5848	144	27	2v	2v	PROPN
ejpam-5848	144	28	if	if	SCONJ
ejpam-5848	144	29	0	0	NUM
ejpam-5848	144	30	≤	≤	NUM
ejpam-5848	144	31	v	v	ADP
ejpam-5848	144	32	≤	≤	NUM
ejpam-5848	144	33	1/2	1/2	NUM
ejpam-5848	144	34	1/2	1/2	NUM
ejpam-5848	144	35	if	if	SCONJ
ejpam-5848	144	36	1/2	1/2	NUM
ejpam-5848	144	37	<	<	X
ejpam-5848	144	38	v	v	ADJ
ejpam-5848	144	39	≤	≤	NUM
ejpam-5848	144	40	1	1	NUM
ejpam-5848	144	41	µn	µn	NOUN
ejpam-5848	144	42	(	(	PUNCT
ejpam-5848	144	43	v	v	NOUN
ejpam-5848	144	44	)	)	PUNCT
ejpam-5848	144	45	=	=	PUNCT
ejpam-5848	145	1			NUM
ejpam-5848	145	2	1/2	1/2	NUM
ejpam-5848	145	3	if	if	SCONJ
ejpam-5848	145	4	0	0	NUM
ejpam-5848	145	5	≤	≤	NUM
ejpam-5848	145	6	v	v	ADP
ejpam-5848	145	7	<	<	X
ejpam-5848	145	8	1/4	1/4	NUM
ejpam-5848	145	9	2v	2v	NUM
ejpam-5848	145	10	if	if	SCONJ
ejpam-5848	145	11	1/4	1/4	NUM
ejpam-5848	145	12	≤	≤	NOUN
ejpam-5848	145	13	v	v	ADJ
ejpam-5848	145	14	≤	≤	NUM
ejpam-5848	145	15	1/2	1/2	NUM
ejpam-5848	145	16	0	0	NUM
ejpam-5848	146	1	if	if	SCONJ
ejpam-5848	146	2	1/2	1/2	NUM
ejpam-5848	146	3	<	<	X
ejpam-5848	146	4	v	v	NOUN
ejpam-5848	146	5	≤	≤	NUM
ejpam-5848	146	6	1	1	NUM
ejpam-5848	146	7	µp	µp	NOUN
ejpam-5848	146	8	(	(	PUNCT
ejpam-5848	146	9	v	v	NOUN
ejpam-5848	146	10	)	)	PUNCT
ejpam-5848	146	11	=	=	NOUN
ejpam-5848	146	12	{	{	PUNCT
ejpam-5848	146	13	1	1	NUM
ejpam-5848	146	14	if	if	SCONJ
ejpam-5848	146	15	0	0	NUM
ejpam-5848	146	16	≤	≤	NUM
ejpam-5848	146	17	v	v	ADP
ejpam-5848	146	18	≤	≤	NUM
ejpam-5848	146	19	1/2	1/2	NUM
ejpam-5848	146	20	0	0	NUM
ejpam-5848	147	1	if	if	SCONJ
ejpam-5848	147	2	1/2	1/2	NUM
ejpam-5848	147	3	<	<	X
ejpam-5848	147	4	v	v	NOUN
ejpam-5848	147	5	≤	≤	NUM
ejpam-5848	147	6	1	1	NUM
ejpam-5848	147	7	let	let	VERB
ejpam-5848	147	8	t1	t1	NOUN
ejpam-5848	147	9	=	=	PUNCT
ejpam-5848	147	10	{	{	PUNCT
ejpam-5848	147	11	∅	∅	NOUN
ejpam-5848	147	12	,	,	PUNCT
ejpam-5848	147	13	v	v	NOUN
ejpam-5848	147	14	,	,	PUNCT
ejpam-5848	147	15	m	m	VERB
ejpam-5848	147	16	}	}	PUNCT
ejpam-5848	147	17	be	be	AUX
ejpam-5848	147	18	a	a	DET
ejpam-5848	147	19	fuzzy	fuzzy	ADJ
ejpam-5848	147	20	topology	topology	NOUN
ejpam-5848	147	21	on	on	ADP
ejpam-5848	147	22	v	v	NOUN
ejpam-5848	147	23	and	and	CCONJ
ejpam-5848	147	24	ψ	ψ	X
ejpam-5848	147	25	:	:	PUNCT
ejpam-5848	147	26	(	(	PUNCT
ejpam-5848	147	27	v	v	NOUN
ejpam-5848	147	28	,	,	PUNCT
ejpam-5848	147	29	t1	t1	NOUN
ejpam-5848	147	30	)	)	PUNCT
ejpam-5848	147	31	→	→	SYM
ejpam-5848	147	32	v	v	X
ejpam-5848	147	33	(	(	PUNCT
ejpam-5848	147	34	t1	t1	NOUN
ejpam-5848	147	35	)	)	PUNCT
ejpam-5848	147	36	be	be	AUX
ejpam-5848	147	37	a	a	DET
ejpam-5848	147	38	fuzzy	fuzzy	ADJ
ejpam-5848	147	39	mapping	mapping	NOUN
ejpam-5848	147	40	defined	define	VERB
ejpam-5848	147	41	by	by	ADP
ejpam-5848	147	42	ψ(v	ψ(v	PROPN
ejpam-5848	147	43	)	)	PUNCT
ejpam-5848	148	1	=	=	PRON
ejpam-5848	148	2	{	{	PUNCT
ejpam-5848	148	3	v	v	NOUN
ejpam-5848	148	4	if	if	SCONJ
ejpam-5848	148	5	0	0	NUM
ejpam-5848	148	6	≤	≤	NUM
ejpam-5848	149	1	v	v	PRON
ejpam-5848	149	2	≤	≤	NUM
ejpam-5848	149	3	1/2	1/2	NUM
ejpam-5848	149	4	1−	1−	NUM
ejpam-5848	149	5	v	v	NOUN
ejpam-5848	149	6	if	if	SCONJ
ejpam-5848	149	7	1/2	1/2	NUM
ejpam-5848	149	8	<	<	X
ejpam-5848	149	9	v	v	NOUN
ejpam-5848	149	10	≤	≤	NUM
ejpam-5848	149	11	1	1	NUM
ejpam-5848	149	12	clearly	clearly	ADV
ejpam-5848	149	13	,	,	PUNCT
ejpam-5848	149	14	ψ(m	ψ(m	NOUN
ejpam-5848	149	15	)	)	PUNCT
ejpam-5848	149	16	=	=	SYM
ejpam-5848	149	17	n	n	NOUN
ejpam-5848	149	18	and	and	CCONJ
ejpam-5848	149	19	ψ(v	ψ(v	PROPN
ejpam-5848	149	20	)	)	PUNCT
ejpam-5848	150	1	=	=	PUNCT
ejpam-5848	150	2	p	p	NOUN
ejpam-5848	150	3	.	.	PUNCT
ejpam-5848	151	1	since	since	SCONJ
ejpam-5848	151	2	m	m	PROPN
ejpam-5848	151	3	and	and	CCONJ
ejpam-5848	151	4	v	v	NOUN
ejpam-5848	151	5	are	be	AUX
ejpam-5848	151	6	open	open	ADJ
ejpam-5848	151	7	fuzzy	fuzzy	ADJ
ejpam-5848	151	8	subsets	subset	NOUN
ejpam-5848	151	9	of	of	ADP
ejpam-5848	151	10	v	v	NOUN
ejpam-5848	151	11	but	but	CCONJ
ejpam-5848	151	12	their	their	PRON
ejpam-5848	151	13	fuzzy	fuzzy	ADJ
ejpam-5848	151	14	images	image	NOUN
ejpam-5848	151	15	,	,	PUNCT
ejpam-5848	151	16	n	n	NOUN
ejpam-5848	151	17	and	and	CCONJ
ejpam-5848	151	18	p	p	NOUN
ejpam-5848	151	19	are	be	AUX
ejpam-5848	151	20	not	not	PART
ejpam-5848	151	21	open	open	ADJ
ejpam-5848	151	22	fuzzy	fuzzy	ADJ
ejpam-5848	151	23	subsets	subset	NOUN
ejpam-5848	151	24	of	of	ADP
ejpam-5848	151	25	v	v	NOUN
ejpam-5848	151	26	,	,	PUNCT
ejpam-5848	151	27	ψ	ψ	X
ejpam-5848	151	28	is	be	AUX
ejpam-5848	151	29	not	not	PART
ejpam-5848	151	30	an	an	DET
ejpam-5848	151	31	open	open	ADJ
ejpam-5848	151	32	fuzzy	fuzzy	ADJ
ejpam-5848	151	33	mapping	mapping	NOUN
ejpam-5848	151	34	.	.	PUNCT
ejpam-5848	152	1	on	on	ADP
ejpam-5848	152	2	the	the	DET
ejpam-5848	152	3	other	other	ADJ
ejpam-5848	152	4	hand	hand	NOUN
ejpam-5848	152	5	,	,	PUNCT
ejpam-5848	152	6	let	let	VERB
ejpam-5848	152	7	q	q	PART
ejpam-5848	152	8	be	be	AUX
ejpam-5848	152	9	a	a	DET
ejpam-5848	152	10	closed	closed	ADJ
ejpam-5848	152	11	fuzzy	fuzzy	ADJ
ejpam-5848	152	12	set	set	NOUN
ejpam-5848	152	13	in	in	ADP
ejpam-5848	152	14	(	(	PUNCT
ejpam-5848	152	15	v	v	NOUN
ejpam-5848	152	16	,	,	PUNCT
ejpam-5848	152	17	t1	t1	NOUN
ejpam-5848	152	18	)	)	PUNCT
ejpam-5848	152	19	defined	define	VERB
ejpam-5848	152	20	by	by	ADP
ejpam-5848	152	21	a	a	DET
ejpam-5848	152	22	membership	membership	NOUN
ejpam-5848	152	23	function	function	NOUN
ejpam-5848	152	24	µq(v	µq(v	PUNCT
ejpam-5848	152	25	)	)	PUNCT
ejpam-5848	152	26	=	=	PRON
ejpam-5848	152	27	{	{	PUNCT
ejpam-5848	152	28	1−	1−	NUM
ejpam-5848	152	29	2v	2v	NUM
ejpam-5848	152	30	if	if	SCONJ
ejpam-5848	152	31	0	0	NUM
ejpam-5848	152	32	≤	≤	NUM
ejpam-5848	152	33	v	v	ADP
ejpam-5848	152	34	≤	≤	NUM
ejpam-5848	152	35	1/2	1/2	NUM
ejpam-5848	152	36	1/2	1/2	NUM
ejpam-5848	152	37	if	if	SCONJ
ejpam-5848	152	38	1/2	1/2	NUM
ejpam-5848	152	39	<	<	X
ejpam-5848	152	40	v	v	NOUN
ejpam-5848	152	41	≤	≤	NUM
ejpam-5848	152	42	1	1	NUM
ejpam-5848	152	43	s.	s.	PROPN
ejpam-5848	152	44	kaur	kaur	PROPN
ejpam-5848	152	45	et	et	PROPN
ejpam-5848	152	46	al	al	PROPN
ejpam-5848	152	47	.	.	PUNCT
ejpam-5848	152	48	/	/	SYM
ejpam-5848	152	49	eur	eur	PROPN
ejpam-5848	152	50	.	.	PUNCT
ejpam-5848	153	1	j.	j.	PROPN
ejpam-5848	153	2	pure	pure	PROPN
ejpam-5848	153	3	appl	appl	PROPN
ejpam-5848	153	4	.	.	PROPN
ejpam-5848	153	5	math	math	PROPN
ejpam-5848	153	6	,	,	PUNCT
ejpam-5848	153	7	18	18	NUM
ejpam-5848	153	8	(	(	PUNCT
ejpam-5848	153	9	1	1	NUM
ejpam-5848	153	10	)	)	PUNCT
ejpam-5848	153	11	(	(	PUNCT
ejpam-5848	153	12	2025	2025	NUM
ejpam-5848	153	13	)	)	PUNCT
ejpam-5848	153	14	,	,	PUNCT
ejpam-5848	153	15	5848	5848	NUM
ejpam-5848	153	16	7	7	NUM
ejpam-5848	153	17	of	of	ADP
ejpam-5848	153	18	11	11	NUM
ejpam-5848	153	19	then	then	ADV
ejpam-5848	153	20	#	#	SYM
ejpam-5848	153	21	-image	-image	NOUN
ejpam-5848	153	22	of	of	ADP
ejpam-5848	153	23	q	q	NOUN
ejpam-5848	153	24	,	,	PUNCT
ejpam-5848	153	25	ψ#(q	ψ#(q	ADJ
ejpam-5848	153	26	)	)	PUNCT
ejpam-5848	153	27	will	will	AUX
ejpam-5848	153	28	be	be	AUX
ejpam-5848	153	29	an	an	DET
ejpam-5848	153	30	f	f	NOUN
ejpam-5848	153	31	-set	-set	VERB
ejpam-5848	153	32	defined	define	VERB
ejpam-5848	153	33	by	by	ADP
ejpam-5848	153	34	the	the	DET
ejpam-5848	153	35	membership	membership	NOUN
ejpam-5848	153	36	function	function	NOUN
ejpam-5848	153	37	µq(v	µq(v	PUNCT
ejpam-5848	153	38	)	)	PUNCT
ejpam-5848	153	39	=	=	PRON
ejpam-5848	153	40	{	{	PUNCT
ejpam-5848	153	41	1−	1−	NUM
ejpam-5848	153	42	2v	2v	NUM
ejpam-5848	153	43	if	if	SCONJ
ejpam-5848	153	44	0	0	NUM
ejpam-5848	153	45	≤	≤	NUM
ejpam-5848	153	46	v	v	PRON
ejpam-5848	153	47	≤	≤	NUM
ejpam-5848	153	48	1/2	1/2	NUM
ejpam-5848	153	49	1−	1−	NUM
ejpam-5848	153	50	v	v	NOUN
ejpam-5848	153	51	if	if	SCONJ
ejpam-5848	153	52	1/2	1/2	NUM
ejpam-5848	153	53	<	<	X
ejpam-5848	153	54	v	v	NOUN
ejpam-5848	153	55	≤	≤	NUM
ejpam-5848	153	56	1	1	NUM
ejpam-5848	153	57	which	which	PRON
ejpam-5848	153	58	is	be	AUX
ejpam-5848	153	59	not	not	PART
ejpam-5848	153	60	a	a	DET
ejpam-5848	153	61	closed	closed	ADJ
ejpam-5848	153	62	fuzzy	fuzzy	ADJ
ejpam-5848	153	63	subset	subset	NOUN
ejpam-5848	153	64	of	of	ADP
ejpam-5848	153	65	v	v	NOUN
ejpam-5848	153	66	.	.	PUNCT
ejpam-5848	154	1	the	the	DET
ejpam-5848	154	2	following	follow	VERB
ejpam-5848	154	3	theorem	theorem	NOUN
ejpam-5848	154	4	gives	give	VERB
ejpam-5848	154	5	another	another	DET
ejpam-5848	154	6	characterization	characterization	NOUN
ejpam-5848	154	7	of	of	ADP
ejpam-5848	154	8	open	open	ADJ
ejpam-5848	154	9	fuzzy	fuzzy	ADJ
ejpam-5848	154	10	mappings	mapping	NOUN
ejpam-5848	154	11	for	for	ADP
ejpam-5848	154	12	a	a	DET
ejpam-5848	154	13	surjective	surjective	ADJ
ejpam-5848	154	14	mapping	mapping	NOUN
ejpam-5848	154	15	ψ	ψ	NOUN
ejpam-5848	154	16	:	:	PUNCT
ejpam-5848	154	17	v	v	ADP
ejpam-5848	154	18	→w	→w	NUM
ejpam-5848	154	19	in	in	ADP
ejpam-5848	154	20	connection	connection	NOUN
ejpam-5848	154	21	with	with	ADP
ejpam-5848	154	22	the	the	DET
ejpam-5848	154	23	closed	close	VERB
ejpam-5848	154	24	fuzzy	fuzzy	ADJ
ejpam-5848	154	25	subsets	subset	NOUN
ejpam-5848	154	26	of	of	ADP
ejpam-5848	154	27	v	v	NOUN
ejpam-5848	154	28	.	.	PUNCT
ejpam-5848	155	1	theorem	theorem	ADJ
ejpam-5848	155	2	7	7	NUM
ejpam-5848	155	3	.	.	PUNCT
ejpam-5848	156	1	let	let	VERB
ejpam-5848	156	2	ψ	ψ	X
ejpam-5848	156	3	:	:	PUNCT
ejpam-5848	156	4	v	v	PART
ejpam-5848	156	5	→w	→w	PUNCT
ejpam-5848	156	6	be	be	AUX
ejpam-5848	156	7	a	a	DET
ejpam-5848	156	8	surjective	surjective	ADJ
ejpam-5848	156	9	mapping	mapping	NOUN
ejpam-5848	156	10	.	.	PUNCT
ejpam-5848	157	1	then	then	ADV
ejpam-5848	157	2	ψ	ψ	X
ejpam-5848	157	3	is	be	AUX
ejpam-5848	157	4	an	an	DET
ejpam-5848	157	5	open	open	ADJ
ejpam-5848	157	6	fuzzy	fuzzy	ADJ
ejpam-5848	157	7	mapping	mapping	NOUN
ejpam-5848	157	8	if	if	SCONJ
ejpam-5848	157	9	and	and	CCONJ
ejpam-5848	157	10	only	only	ADV
ejpam-5848	157	11	if	if	SCONJ
ejpam-5848	157	12	for	for	ADP
ejpam-5848	157	13	every	every	DET
ejpam-5848	157	14	closed	close	VERB
ejpam-5848	157	15	fuzzy	fuzzy	ADJ
ejpam-5848	157	16	subset	subset	VERB
ejpam-5848	157	17	g	g	NOUN
ejpam-5848	157	18	of	of	ADP
ejpam-5848	157	19	v	v	NOUN
ejpam-5848	157	20	,	,	PUNCT
ejpam-5848	157	21	ψ(g	ψ(g	PROPN
ejpam-5848	157	22	#	#	NOUN
ejpam-5848	157	23	)	)	PUNCT
ejpam-5848	157	24	is	be	AUX
ejpam-5848	157	25	a	a	DET
ejpam-5848	157	26	closed	closed	ADJ
ejpam-5848	157	27	fuzzy	fuzzy	ADJ
ejpam-5848	157	28	set	set	VERB
ejpam-5848	157	29	in	in	ADP
ejpam-5848	157	30	w	w	PROPN
ejpam-5848	157	31	.	.	PUNCT
ejpam-5848	158	1	proof	proof	NOUN
ejpam-5848	158	2	.	.	PUNCT
ejpam-5848	159	1	assume	assume	VERB
ejpam-5848	159	2	ψ(g	ψ(g	NOUN
ejpam-5848	159	3	#	#	NOUN
ejpam-5848	159	4	)	)	PUNCT
ejpam-5848	159	5	is	be	AUX
ejpam-5848	159	6	a	a	DET
ejpam-5848	159	7	closed	closed	ADJ
ejpam-5848	159	8	fuzzy	fuzzy	ADJ
ejpam-5848	159	9	subset	subset	NOUN
ejpam-5848	159	10	of	of	ADP
ejpam-5848	159	11	w	w	NOUN
ejpam-5848	159	12	for	for	ADP
ejpam-5848	159	13	every	every	DET
ejpam-5848	159	14	closed	close	VERB
ejpam-5848	159	15	fuzzy	fuzzy	ADJ
ejpam-5848	159	16	subset	subset	VERB
ejpam-5848	159	17	g	g	NOUN
ejpam-5848	159	18	of	of	ADP
ejpam-5848	159	19	v	v	NOUN
ejpam-5848	159	20	.	.	PUNCT
ejpam-5848	160	1	now	now	ADV
ejpam-5848	160	2	,	,	PUNCT
ejpam-5848	160	3	since	since	SCONJ
ejpam-5848	160	4	ψ	ψ	NOUN
ejpam-5848	160	5	is	be	AUX
ejpam-5848	160	6	surjective	surjective	ADJ
ejpam-5848	160	7	mapping	mapping	NOUN
ejpam-5848	160	8	,	,	PUNCT
ejpam-5848	160	9	ψ−1(v	ψ−1(v	NOUN
ejpam-5848	160	10	)	)	PUNCT
ejpam-5848	160	11	̸=	̸=	NOUN
ejpam-5848	160	12	∅	∅	NOUN
ejpam-5848	160	13	for	for	ADP
ejpam-5848	160	14	every	every	DET
ejpam-5848	160	15	v	v	NOUN
ejpam-5848	160	16	∈	∈	NOUN
ejpam-5848	160	17	v	v	ADP
ejpam-5848	160	18	then	then	ADV
ejpam-5848	160	19	,	,	PUNCT
ejpam-5848	160	20	µψ(g#)(v	µψ(g#)(v	X
ejpam-5848	160	21	)	)	PUNCT
ejpam-5848	160	22	=	=	SYM
ejpam-5848	160	23	supz∈ψ−1(v	supz∈ψ−1(v	NOUN
ejpam-5848	160	24	)	)	PUNCT
ejpam-5848	160	25	µg#(z	µg#(z	VERB
ejpam-5848	160	26	)	)	PUNCT
ejpam-5848	160	27	=	=	SYM
ejpam-5848	160	28	supz∈ψ−1(v	supz∈ψ−1(v	NOUN
ejpam-5848	160	29	)	)	PUNCT
ejpam-5848	160	30	µψ−1(ψ#(g))(z	µψ−1(ψ#(g))(z	PUNCT
ejpam-5848	160	31	)	)	PUNCT
ejpam-5848	160	32	=	=	SYM
ejpam-5848	160	33	supz∈ψ−1(v	supz∈ψ−1(v	NOUN
ejpam-5848	160	34	)	)	PUNCT
ejpam-5848	160	35	µψ#(g)(ψ(z	µψ#(g)(ψ(z	NOUN
ejpam-5848	160	36	)	)	PUNCT
ejpam-5848	160	37	)	)	PUNCT
ejpam-5848	161	1	=	=	SYM
ejpam-5848	161	2	µψ#(g)(v	µψ#(g)(v	NOUN
ejpam-5848	161	3	)	)	PUNCT
ejpam-5848	161	4	which	which	PRON
ejpam-5848	161	5	gives	give	VERB
ejpam-5848	161	6	ψ#(g	ψ#(g	PROPN
ejpam-5848	161	7	)	)	PUNCT
ejpam-5848	161	8	is	be	AUX
ejpam-5848	161	9	a	a	DET
ejpam-5848	161	10	closed	closed	ADJ
ejpam-5848	161	11	fuzzy	fuzzy	ADJ
ejpam-5848	161	12	subset	subset	NOUN
ejpam-5848	161	13	of	of	ADP
ejpam-5848	161	14	w	w	PROPN
ejpam-5848	161	15	.	.	PUNCT
ejpam-5848	162	1	hence	hence	ADV
ejpam-5848	162	2	,	,	PUNCT
ejpam-5848	162	3	by	by	ADP
ejpam-5848	162	4	theorem	theorem	NOUN
ejpam-5848	162	5	6	6	NUM
ejpam-5848	162	6	,	,	PUNCT
ejpam-5848	162	7	ψ	ψ	NOUN
ejpam-5848	162	8	is	be	AUX
ejpam-5848	162	9	an	an	DET
ejpam-5848	162	10	open	open	ADJ
ejpam-5848	162	11	fuzzy	fuzzy	ADJ
ejpam-5848	162	12	mapping	mapping	NOUN
ejpam-5848	162	13	.	.	PUNCT
ejpam-5848	163	1	the	the	DET
ejpam-5848	163	2	converse	converse	NOUN
ejpam-5848	163	3	part	part	NOUN
ejpam-5848	163	4	is	be	AUX
ejpam-5848	163	5	obvious	obvious	ADJ
ejpam-5848	163	6	by	by	ADP
ejpam-5848	163	7	using	use	VERB
ejpam-5848	163	8	the	the	DET
ejpam-5848	163	9	same	same	ADJ
ejpam-5848	163	10	argument	argument	NOUN
ejpam-5848	163	11	that	that	PRON
ejpam-5848	163	12	ψ(e	ψ(e	VERB
ejpam-5848	163	13	#	#	NOUN
ejpam-5848	163	14	)	)	PUNCT
ejpam-5848	163	15	=	=	SYM
ejpam-5848	163	16	ψ#(e	ψ#(e	PROPN
ejpam-5848	163	17	)	)	PUNCT
ejpam-5848	163	18	and	and	CCONJ
ejpam-5848	163	19	theorem	theorem	VERB
ejpam-5848	163	20	6	6	NUM
ejpam-5848	163	21	.	.	PUNCT
ejpam-5848	163	22	in	in	ADP
ejpam-5848	163	23	the	the	DET
ejpam-5848	163	24	final	final	ADJ
ejpam-5848	163	25	result	result	NOUN
ejpam-5848	163	26	about	about	ADP
ejpam-5848	163	27	open	open	ADJ
ejpam-5848	163	28	fuzzy	fuzzy	ADJ
ejpam-5848	163	29	mappings	mapping	NOUN
ejpam-5848	163	30	,	,	PUNCT
ejpam-5848	163	31	we	we	PRON
ejpam-5848	163	32	see	see	VERB
ejpam-5848	163	33	that	that	SCONJ
ejpam-5848	163	34	images	image	NOUN
ejpam-5848	163	35	of	of	ADP
ejpam-5848	163	36	saturated	saturate	VERB
ejpam-5848	163	37	closed	close	VERB
ejpam-5848	163	38	fuzzy	fuzzy	ADJ
ejpam-5848	163	39	sets	set	NOUN
ejpam-5848	163	40	under	under	ADP
ejpam-5848	163	41	surjective	surjective	ADJ
ejpam-5848	163	42	open	open	ADJ
ejpam-5848	163	43	fuzzy	fuzzy	ADJ
ejpam-5848	163	44	mappings	mapping	NOUN
ejpam-5848	163	45	are	be	AUX
ejpam-5848	163	46	closed	close	VERB
ejpam-5848	163	47	fuzzy	fuzzy	ADJ
ejpam-5848	163	48	sets	set	NOUN
ejpam-5848	163	49	.	.	PUNCT
ejpam-5848	164	1	firstly	firstly	ADV
ejpam-5848	164	2	,	,	PUNCT
ejpam-5848	164	3	we	we	PRON
ejpam-5848	164	4	recall	recall	VERB
ejpam-5848	164	5	the	the	DET
ejpam-5848	164	6	definition	definition	NOUN
ejpam-5848	164	7	of	of	ADP
ejpam-5848	164	8	a	a	DET
ejpam-5848	164	9	saturated	saturate	VERB
ejpam-5848	164	10	fuzzy	fuzzy	ADJ
ejpam-5848	164	11	set	set	NOUN
ejpam-5848	164	12	and	and	CCONJ
ejpam-5848	164	13	a	a	DET
ejpam-5848	164	14	remark	remark	NOUN
ejpam-5848	164	15	to	to	PART
ejpam-5848	164	16	use	use	VERB
ejpam-5848	164	17	in	in	ADP
ejpam-5848	164	18	the	the	DET
ejpam-5848	164	19	final	final	ADJ
ejpam-5848	164	20	corollary	corollary	NOUN
ejpam-5848	164	21	.	.	PUNCT
ejpam-5848	165	1	definition	definition	NOUN
ejpam-5848	165	2	7	7	NUM
ejpam-5848	165	3	.	.	PUNCT
ejpam-5848	166	1	[	[	X
ejpam-5848	166	2	21	21	NUM
ejpam-5848	166	3	]	]	X
ejpam-5848	166	4	a	a	DET
ejpam-5848	166	5	fuzzy	fuzzy	ADJ
ejpam-5848	166	6	subset	subset	NOUN
ejpam-5848	166	7	m	m	NOUN
ejpam-5848	166	8	of	of	ADP
ejpam-5848	166	9	v	v	NOUN
ejpam-5848	166	10	is	be	AUX
ejpam-5848	166	11	said	say	VERB
ejpam-5848	166	12	to	to	PART
ejpam-5848	166	13	be	be	AUX
ejpam-5848	166	14	a	a	DET
ejpam-5848	166	15	saturated	saturate	VERB
ejpam-5848	166	16	fuzzy	fuzzy	ADJ
ejpam-5848	166	17	subset	subset	NOUN
ejpam-5848	166	18	of	of	ADP
ejpam-5848	166	19	v	v	NOUN
ejpam-5848	166	20	if	if	SCONJ
ejpam-5848	166	21	m	m	NOUN
ejpam-5848	166	22	=	=	SYM
ejpam-5848	166	23	ψ−1(u	ψ−1(u	PROPN
ejpam-5848	166	24	)	)	PUNCT
ejpam-5848	166	25	for	for	ADP
ejpam-5848	166	26	a	a	DET
ejpam-5848	166	27	fuzzy	fuzzy	ADJ
ejpam-5848	166	28	subset	subset	NOUN
ejpam-5848	166	29	u	u	NOUN
ejpam-5848	166	30	of	of	ADP
ejpam-5848	166	31	w	w	NOUN
ejpam-5848	166	32	i.e.	i.e.	X
ejpam-5848	166	33	µm	µm	X
ejpam-5848	166	34	(	(	PUNCT
ejpam-5848	166	35	v	v	NOUN
ejpam-5848	166	36	)	)	PUNCT
ejpam-5848	166	37	=	=	PUNCT
ejpam-5848	166	38	µψ−1(u)(v	µψ−1(u)(v	X
ejpam-5848	166	39	)	)	PUNCT
ejpam-5848	166	40	for	for	ADP
ejpam-5848	166	41	each	each	DET
ejpam-5848	166	42	v	v	NUM
ejpam-5848	166	43	∈	∈	PROPN
ejpam-5848	166	44	v	v	NOUN
ejpam-5848	166	45	.	.	PUNCT
ejpam-5848	167	1	remark	remark	PROPN
ejpam-5848	167	2	1	1	NUM
ejpam-5848	167	3	.	.	PUNCT
ejpam-5848	168	1	for	for	ADP
ejpam-5848	168	2	any	any	DET
ejpam-5848	168	3	mapping	mapping	NOUN
ejpam-5848	168	4	ψ	ψ	X
ejpam-5848	168	5	:	:	PUNCT
ejpam-5848	168	6	v	v	X
ejpam-5848	168	7	→	→	SYM
ejpam-5848	168	8	w	w	PROPN
ejpam-5848	168	9	,	,	PUNCT
ejpam-5848	168	10	m	m	NOUN
ejpam-5848	168	11	#	#	NOUN
ejpam-5848	168	12	is	be	AUX
ejpam-5848	168	13	saturated	saturate	VERB
ejpam-5848	168	14	fuzzy	fuzzy	ADJ
ejpam-5848	168	15	for	for	SCONJ
ejpam-5848	168	16	each	each	DET
ejpam-5848	168	17	fuzzy	fuzzy	ADJ
ejpam-5848	168	18	subset	subset	NOUN
ejpam-5848	168	19	m	m	NOUN
ejpam-5848	168	20	of	of	ADP
ejpam-5848	168	21	v	v	NOUN
ejpam-5848	168	22	,	,	PUNCT
ejpam-5848	168	23	since	since	SCONJ
ejpam-5848	168	24	,	,	PUNCT
ejpam-5848	168	25	ψ−1(ψ(m	ψ−1(ψ(m	ADV
ejpam-5848	168	26	#	#	NUM
ejpam-5848	168	27	)	)	PUNCT
ejpam-5848	168	28	)	)	PUNCT
ejpam-5848	169	1	=	=	SYM
ejpam-5848	169	2	ψ−1(ψ(ψ−1(ψ#(m	ψ−1(ψ(ψ−1(ψ#(m	NOUN
ejpam-5848	169	3	)	)	PUNCT
ejpam-5848	169	4	)	)	PUNCT
ejpam-5848	169	5	)	)	PUNCT
ejpam-5848	169	6	)	)	PUNCT
ejpam-5848	170	1	=	=	SYM
ejpam-5848	170	2	ψ−1(ψ#(m	ψ−1(ψ#(m	PROPN
ejpam-5848	170	3	)	)	PUNCT
ejpam-5848	170	4	)	)	PUNCT
ejpam-5848	171	1	=	=	NOUN
ejpam-5848	171	2	m	m	NOUN
ejpam-5848	171	3	#	#	X
ejpam-5848	171	4	.	.	PUNCT
ejpam-5848	172	1	theorem	theorem	ADJ
ejpam-5848	172	2	8	8	NUM
ejpam-5848	172	3	.	.	PUNCT
ejpam-5848	173	1	let	let	VERB
ejpam-5848	173	2	ψ	ψ	NOUN
ejpam-5848	173	3	:	:	PUNCT
ejpam-5848	173	4	v	v	X
ejpam-5848	173	5	→	→	SYM
ejpam-5848	173	6	w	w	X
ejpam-5848	173	7	be	be	AUX
ejpam-5848	173	8	an	an	DET
ejpam-5848	173	9	open	open	ADJ
ejpam-5848	173	10	fuzzy	fuzzy	ADJ
ejpam-5848	173	11	and	and	CCONJ
ejpam-5848	173	12	surjective	surjective	ADJ
ejpam-5848	173	13	mapping	mapping	NOUN
ejpam-5848	173	14	.	.	PUNCT
ejpam-5848	174	1	then	then	ADV
ejpam-5848	174	2	ψ(m	ψ(m	NOUN
ejpam-5848	174	3	)	)	PUNCT
ejpam-5848	174	4	is	be	AUX
ejpam-5848	174	5	a	a	DET
ejpam-5848	174	6	closed	closed	ADJ
ejpam-5848	174	7	fuzzy	fuzzy	ADJ
ejpam-5848	174	8	set	set	VERB
ejpam-5848	174	9	in	in	ADP
ejpam-5848	174	10	w	w	NOUN
ejpam-5848	174	11	for	for	ADP
ejpam-5848	174	12	every	every	DET
ejpam-5848	174	13	saturated	saturate	VERB
ejpam-5848	174	14	closed	close	VERB
ejpam-5848	174	15	fuzzy	fuzzy	ADJ
ejpam-5848	174	16	subset	subset	NOUN
ejpam-5848	174	17	m	m	NOUN
ejpam-5848	174	18	of	of	ADP
ejpam-5848	174	19	v	v	NOUN
ejpam-5848	174	20	.	.	PUNCT
ejpam-5848	175	1	particularly	particularly	ADV
ejpam-5848	175	2	,	,	PUNCT
ejpam-5848	175	3	for	for	ADP
ejpam-5848	175	4	any	any	DET
ejpam-5848	175	5	f	f	NOUN
ejpam-5848	175	6	-set	-set	PUNCT
ejpam-5848	175	7	n	n	NOUN
ejpam-5848	175	8	,	,	PUNCT
ejpam-5848	175	9	if	if	SCONJ
ejpam-5848	175	10	n	n	CCONJ
ejpam-5848	175	11	#	#	NOUN
ejpam-5848	175	12	is	be	AUX
ejpam-5848	175	13	a	a	DET
ejpam-5848	175	14	closed	closed	ADJ
ejpam-5848	175	15	fuzzy	fuzzy	ADJ
ejpam-5848	175	16	set	set	NOUN
ejpam-5848	175	17	in	in	ADP
ejpam-5848	175	18	v	v	NOUN
ejpam-5848	175	19	,	,	PUNCT
ejpam-5848	175	20	then	then	ADV
ejpam-5848	175	21	ψ(n	ψ(n	PROPN
ejpam-5848	175	22	#	#	NOUN
ejpam-5848	175	23	)	)	PUNCT
ejpam-5848	175	24	is	be	AUX
ejpam-5848	175	25	a	a	DET
ejpam-5848	175	26	closed	closed	ADJ
ejpam-5848	175	27	fuzzy	fuzzy	ADJ
ejpam-5848	175	28	set	set	VERB
ejpam-5848	175	29	in	in	ADP
ejpam-5848	175	30	w	w	PROPN
ejpam-5848	175	31	.	.	PUNCT
ejpam-5848	176	1	proof	proof	NOUN
ejpam-5848	176	2	.	.	PUNCT
ejpam-5848	177	1	let	let	VERB
ejpam-5848	177	2	ψ	ψ	X
ejpam-5848	177	3	:	:	PUNCT
ejpam-5848	177	4	v	v	PART
ejpam-5848	177	5	→w	→w	PUNCT
ejpam-5848	177	6	be	be	AUX
ejpam-5848	177	7	an	an	DET
ejpam-5848	177	8	open	open	ADJ
ejpam-5848	177	9	fuzzy	fuzzy	ADJ
ejpam-5848	177	10	and	and	CCONJ
ejpam-5848	177	11	surjective	surjective	ADJ
ejpam-5848	177	12	mapping	mapping	NOUN
ejpam-5848	177	13	andm	andm	NOUN
ejpam-5848	177	14	be	be	AUX
ejpam-5848	177	15	a	a	DET
ejpam-5848	177	16	saturated	saturate	VERB
ejpam-5848	177	17	closed	close	VERB
ejpam-5848	177	18	fuzzy	fuzzy	ADJ
ejpam-5848	177	19	subset	subset	NOUN
ejpam-5848	177	20	of	of	ADP
ejpam-5848	177	21	v	v	NOUN
ejpam-5848	177	22	.	.	PUNCT
ejpam-5848	178	1	then	then	ADV
ejpam-5848	178	2	,	,	PUNCT
ejpam-5848	178	3	by	by	ADP
ejpam-5848	178	4	theorem	theorem	NOUN
ejpam-5848	178	5	7	7	NUM
ejpam-5848	178	6	,	,	PUNCT
ejpam-5848	178	7	ψ(m	ψ(m	NOUN
ejpam-5848	178	8	#	#	NOUN
ejpam-5848	178	9	)	)	PUNCT
ejpam-5848	178	10	is	be	AUX
ejpam-5848	178	11	a	a	DET
ejpam-5848	178	12	closed	closed	ADJ
ejpam-5848	178	13	fuzzy	fuzzy	ADJ
ejpam-5848	178	14	in	in	ADP
ejpam-5848	178	15	w	w	PROPN
ejpam-5848	178	16	.	.	PUNCT
ejpam-5848	179	1	now	now	ADV
ejpam-5848	179	2	,	,	PUNCT
ejpam-5848	179	3	since	since	SCONJ
ejpam-5848	179	4	m	m	PROPN
ejpam-5848	179	5	is	be	AUX
ejpam-5848	179	6	a	a	DET
ejpam-5848	179	7	saturated	saturate	VERB
ejpam-5848	179	8	fuzzy	fuzzy	ADJ
ejpam-5848	179	9	set	set	NOUN
ejpam-5848	179	10	,	,	PUNCT
ejpam-5848	179	11	we	we	PRON
ejpam-5848	179	12	have	have	VERB
ejpam-5848	179	13	,	,	PUNCT
ejpam-5848	179	14	µm#(u	µm#(u	NOUN
ejpam-5848	179	15	)	)	PUNCT
ejpam-5848	179	16	=	=	SYM
ejpam-5848	179	17	µψ−1(ψ#(m))(u	µψ−1(ψ#(m))(u	X
ejpam-5848	179	18	)	)	PUNCT
ejpam-5848	179	19	=	=	SYM
ejpam-5848	179	20	µψ#(m)(ψ(u	µψ#(m)(ψ(u	PROPN
ejpam-5848	179	21	)	)	PUNCT
ejpam-5848	179	22	)	)	PUNCT
ejpam-5848	180	1	=	=	SYM
ejpam-5848	180	2	infz∈ψ−1(ψ(u	infz∈ψ−1(ψ(u	PROPN
ejpam-5848	180	3	)	)	PUNCT
ejpam-5848	180	4	)	)	PUNCT
ejpam-5848	181	1	µm	µm	ADP
ejpam-5848	181	2	(	(	PUNCT
ejpam-5848	181	3	z	z	NOUN
ejpam-5848	181	4	)	)	PUNCT
ejpam-5848	181	5	=	=	SYM
ejpam-5848	181	6	µm	µm	X
ejpam-5848	181	7	(	(	PUNCT
ejpam-5848	181	8	u	u	NOUN
ejpam-5848	181	9	)	)	PUNCT
ejpam-5848	181	10	which	which	PRON
ejpam-5848	181	11	gives	give	VERB
ejpam-5848	181	12	m	m	PRON
ejpam-5848	181	13	#	#	NOUN
ejpam-5848	181	14	=	=	PRON
ejpam-5848	181	15	m	m	PROPN
ejpam-5848	181	16	,	,	PUNCT
ejpam-5848	181	17	and	and	CCONJ
ejpam-5848	181	18	which	which	PRON
ejpam-5848	181	19	further	far	ADV
ejpam-5848	181	20	implies	imply	VERB
ejpam-5848	181	21	ψ(m	ψ(m	NOUN
ejpam-5848	181	22	#	#	NOUN
ejpam-5848	181	23	)	)	PUNCT
ejpam-5848	181	24	=	=	SYM
ejpam-5848	181	25	ψ(m	ψ(m	PROPN
ejpam-5848	181	26	)	)	PUNCT
ejpam-5848	181	27	is	be	AUX
ejpam-5848	181	28	a	a	DET
ejpam-5848	181	29	closed	closed	ADJ
ejpam-5848	181	30	fuzzy	fuzzy	ADJ
ejpam-5848	181	31	in	in	ADP
ejpam-5848	181	32	w	w	PROPN
ejpam-5848	181	33	.	.	PUNCT
ejpam-5848	182	1	hence	hence	ADV
ejpam-5848	182	2	,	,	PUNCT
ejpam-5848	182	3	we	we	PRON
ejpam-5848	182	4	prove	prove	VERB
ejpam-5848	182	5	the	the	DET
ejpam-5848	182	6	desired	desire	VERB
ejpam-5848	182	7	result	result	NOUN
ejpam-5848	182	8	.	.	PUNCT
ejpam-5848	183	1	from	from	ADP
ejpam-5848	183	2	the	the	DET
ejpam-5848	183	3	above	above	ADJ
ejpam-5848	183	4	theorem	theorem	NOUN
ejpam-5848	183	5	,	,	PUNCT
ejpam-5848	183	6	we	we	PRON
ejpam-5848	183	7	get	get	VERB
ejpam-5848	183	8	the	the	DET
ejpam-5848	183	9	following	follow	VERB
ejpam-5848	183	10	corollary	corollary	NOUN
ejpam-5848	183	11	.	.	PUNCT
ejpam-5848	184	1	corollary	corollary	ADJ
ejpam-5848	184	2	1	1	NUM
ejpam-5848	184	3	.	.	PUNCT
ejpam-5848	185	1	let	let	VERB
ejpam-5848	185	2	ψ	ψ	NOUN
ejpam-5848	185	3	:	:	PUNCT
ejpam-5848	185	4	v	v	X
ejpam-5848	185	5	→	→	SYM
ejpam-5848	185	6	w	w	X
ejpam-5848	185	7	be	be	AUX
ejpam-5848	185	8	an	an	DET
ejpam-5848	185	9	open	open	ADJ
ejpam-5848	185	10	fuzzy	fuzzy	ADJ
ejpam-5848	185	11	and	and	CCONJ
ejpam-5848	185	12	surjective	surjective	ADJ
ejpam-5848	185	13	mapping	mapping	NOUN
ejpam-5848	185	14	.	.	PUNCT
ejpam-5848	186	1	then	then	ADV
ejpam-5848	186	2	,	,	PUNCT
ejpam-5848	186	3	for	for	ADP
ejpam-5848	186	4	any	any	DET
ejpam-5848	186	5	f	f	NOUN
ejpam-5848	186	6	-set	-set	PUNCT
ejpam-5848	186	7	n	n	NOUN
ejpam-5848	186	8	,	,	PUNCT
ejpam-5848	186	9	if	if	SCONJ
ejpam-5848	186	10	n	n	CCONJ
ejpam-5848	186	11	#	#	NOUN
ejpam-5848	186	12	is	be	AUX
ejpam-5848	186	13	a	a	DET
ejpam-5848	186	14	closed	closed	ADJ
ejpam-5848	186	15	fuzzy	fuzzy	ADJ
ejpam-5848	186	16	set	set	NOUN
ejpam-5848	186	17	in	in	ADP
ejpam-5848	186	18	v	v	NOUN
ejpam-5848	186	19	,	,	PUNCT
ejpam-5848	186	20	then	then	ADV
ejpam-5848	186	21	ψ(n	ψ(n	PROPN
ejpam-5848	186	22	#	#	NOUN
ejpam-5848	186	23	)	)	PUNCT
ejpam-5848	186	24	is	be	AUX
ejpam-5848	186	25	a	a	DET
ejpam-5848	186	26	closed	closed	ADJ
ejpam-5848	186	27	fuzzy	fuzzy	ADJ
ejpam-5848	186	28	set	set	VERB
ejpam-5848	186	29	in	in	ADP
ejpam-5848	186	30	w	w	PROPN
ejpam-5848	186	31	.	.	PUNCT
ejpam-5848	187	1	s.	s.	PROPN
ejpam-5848	187	2	kaur	kaur	PROPN
ejpam-5848	187	3	et	et	PROPN
ejpam-5848	187	4	al	al	PROPN
ejpam-5848	187	5	.	.	PUNCT
ejpam-5848	187	6	/	/	SYM
ejpam-5848	187	7	eur	eur	PROPN
ejpam-5848	187	8	.	.	PUNCT
ejpam-5848	188	1	j.	j.	PROPN
ejpam-5848	188	2	pure	pure	PROPN
ejpam-5848	188	3	appl	appl	PROPN
ejpam-5848	188	4	.	.	PROPN
ejpam-5848	188	5	math	math	PROPN
ejpam-5848	188	6	,	,	PUNCT
ejpam-5848	188	7	18	18	NUM
ejpam-5848	188	8	(	(	PUNCT
ejpam-5848	188	9	1	1	NUM
ejpam-5848	188	10	)	)	PUNCT
ejpam-5848	188	11	(	(	PUNCT
ejpam-5848	188	12	2025	2025	NUM
ejpam-5848	188	13	)	)	PUNCT
ejpam-5848	188	14	,	,	PUNCT
ejpam-5848	188	15	5848	5848	NUM
ejpam-5848	188	16	8	8	NUM
ejpam-5848	188	17	of	of	ADP
ejpam-5848	188	18	11	11	NUM
ejpam-5848	188	19	4	4	NUM
ejpam-5848	188	20	.	.	PUNCT
ejpam-5848	189	1	characterizations	characterization	NOUN
ejpam-5848	189	2	of	of	ADP
ejpam-5848	189	3	closed	close	VERB
ejpam-5848	189	4	fuzzy	fuzzy	ADJ
ejpam-5848	189	5	mappings	mapping	NOUN
ejpam-5848	189	6	in	in	ADP
ejpam-5848	189	7	this	this	DET
ejpam-5848	189	8	section	section	NOUN
ejpam-5848	189	9	,	,	PUNCT
ejpam-5848	189	10	we	we	PRON
ejpam-5848	189	11	discuss	discuss	VERB
ejpam-5848	189	12	some	some	DET
ejpam-5848	189	13	new	new	ADJ
ejpam-5848	189	14	characterizations	characterization	NOUN
ejpam-5848	189	15	of	of	ADP
ejpam-5848	189	16	closed	close	VERB
ejpam-5848	189	17	fuzzy	fuzzy	ADJ
ejpam-5848	189	18	mappings	mapping	NOUN
ejpam-5848	189	19	.	.	PUNCT
ejpam-5848	190	1	the	the	DET
ejpam-5848	190	2	following	follow	VERB
ejpam-5848	190	3	theorem	theorem	NOUN
ejpam-5848	190	4	shows	show	VERB
ejpam-5848	190	5	how	how	SCONJ
ejpam-5848	190	6	induced	induced	ADJ
ejpam-5848	190	7	mapping	mapping	NOUN
ejpam-5848	190	8	ψ	ψ	NOUN
ejpam-5848	190	9	#	#	NOUN
ejpam-5848	190	10	enables	enable	VERB
ejpam-5848	190	11	us	we	PRON
ejpam-5848	190	12	to	to	PART
ejpam-5848	190	13	find	find	VERB
ejpam-5848	190	14	a	a	DET
ejpam-5848	190	15	characterization	characterization	NOUN
ejpam-5848	190	16	of	of	ADP
ejpam-5848	190	17	the	the	DET
ejpam-5848	190	18	closed	close	VERB
ejpam-5848	190	19	fuzzy	fuzzy	ADJ
ejpam-5848	190	20	mapping	mapping	NOUN
ejpam-5848	190	21	in	in	ADP
ejpam-5848	190	22	terms	term	NOUN
ejpam-5848	190	23	of	of	ADP
ejpam-5848	190	24	the	the	DET
ejpam-5848	190	25	interior	interior	ADJ
ejpam-5848	190	26	operator	operator	NOUN
ejpam-5848	190	27	rather	rather	ADV
ejpam-5848	190	28	than	than	ADP
ejpam-5848	190	29	the	the	DET
ejpam-5848	190	30	closure	closure	NOUN
ejpam-5848	190	31	operator	operator	NOUN
ejpam-5848	190	32	.	.	PUNCT
ejpam-5848	191	1	theorem	theorem	VERB
ejpam-5848	191	2	9	9	NUM
ejpam-5848	191	3	.	.	PUNCT
ejpam-5848	192	1	let	let	VERB
ejpam-5848	192	2	ψ	ψ	PART
ejpam-5848	192	3	be	be	AUX
ejpam-5848	192	4	a	a	DET
ejpam-5848	192	5	mapping	mapping	NOUN
ejpam-5848	192	6	from	from	ADP
ejpam-5848	192	7	v	v	NUM
ejpam-5848	192	8	to	to	ADP
ejpam-5848	192	9	w	w	PROPN
ejpam-5848	192	10	.	.	PUNCT
ejpam-5848	193	1	then	then	ADV
ejpam-5848	193	2	,	,	PUNCT
ejpam-5848	193	3	ψ	ψ	X
ejpam-5848	193	4	is	be	AUX
ejpam-5848	193	5	a	a	DET
ejpam-5848	193	6	closed	closed	ADJ
ejpam-5848	193	7	fuzzy	fuzzy	ADJ
ejpam-5848	193	8	mapping	mapping	NOUN
ejpam-5848	193	9	if	if	SCONJ
ejpam-5848	193	10	and	and	CCONJ
ejpam-5848	193	11	only	only	ADV
ejpam-5848	193	12	if	if	SCONJ
ejpam-5848	193	13	for	for	ADP
ejpam-5848	193	14	each	each	DET
ejpam-5848	193	15	subset	subset	NOUN
ejpam-5848	193	16	b	b	PROPN
ejpam-5848	193	17	of	of	ADP
ejpam-5848	193	18	v	v	NUM
ejpam-5848	193	19	,	,	PUNCT
ejpam-5848	193	20	ψ#(b	ψ#(b	PROPN
ejpam-5848	193	21	◦	◦	NOUN
ejpam-5848	193	22	)	)	PUNCT
ejpam-5848	193	23	⊆	⊆	NUM
ejpam-5848	193	24	(	(	PUNCT
ejpam-5848	193	25	ψ#(b))	ψ#(b))	NOUN
ejpam-5848	193	26	◦	◦	NOUN
ejpam-5848	193	27	.	.	PUNCT
ejpam-5848	194	1	proof	proof	NOUN
ejpam-5848	194	2	.	.	PUNCT
ejpam-5848	195	1	let	let	VERB
ejpam-5848	195	2	ψ	ψ	PART
ejpam-5848	195	3	be	be	AUX
ejpam-5848	195	4	a	a	DET
ejpam-5848	195	5	closed	closed	ADJ
ejpam-5848	195	6	fuzzy	fuzzy	ADJ
ejpam-5848	195	7	mapping	mapping	NOUN
ejpam-5848	195	8	and	and	CCONJ
ejpam-5848	195	9	b	b	NOUN
ejpam-5848	195	10	be	be	AUX
ejpam-5848	195	11	a	a	DET
ejpam-5848	195	12	subset	subset	NOUN
ejpam-5848	195	13	of	of	ADP
ejpam-5848	195	14	v	v	NOUN
ejpam-5848	195	15	.	.	PUNCT
ejpam-5848	196	1	by	by	ADP
ejpam-5848	196	2	lemma	lemma	PROPN
ejpam-5848	196	3	2	2	NUM
ejpam-5848	196	4	(	(	PUNCT
ejpam-5848	196	5	b	b	NOUN
ejpam-5848	196	6	)	)	PUNCT
ejpam-5848	196	7	and	and	CCONJ
ejpam-5848	196	8	theorem	theorem	VERB
ejpam-5848	196	9	1	1	NUM
ejpam-5848	196	10	,	,	PUNCT
ejpam-5848	196	11	we	we	PRON
ejpam-5848	196	12	get	get	VERB
ejpam-5848	196	13	ψ#(b	ψ#(b	PROPN
ejpam-5848	196	14	◦	◦	NOUN
ejpam-5848	196	15	)	)	PUNCT
ejpam-5848	196	16	=	=	SYM
ejpam-5848	196	17	(	(	PUNCT
ejpam-5848	196	18	ψ((b	ψ((b	NOUN
ejpam-5848	196	19	◦	◦	NOUN
ejpam-5848	196	20	)c))c	)c))c	PROPN
ejpam-5848	196	21	,	,	PUNCT
ejpam-5848	196	22	and	and	CCONJ
ejpam-5848	196	23	(	(	PUNCT
ejpam-5848	196	24	ψ((b	ψ((b	NOUN
ejpam-5848	196	25	◦	◦	NOUN
ejpam-5848	196	26	)c))c	)c))c	PUNCT
ejpam-5848	196	27	=	=	SYM
ejpam-5848	197	1	ψ((bc))c	ψ((bc))c	ADJ
ejpam-5848	197	2	since	since	SCONJ
ejpam-5848	197	3	ψ	ψ	NOUN
ejpam-5848	197	4	is	be	AUX
ejpam-5848	197	5	a	a	DET
ejpam-5848	197	6	closed	closed	ADJ
ejpam-5848	197	7	fuzzy	fuzzy	ADJ
ejpam-5848	197	8	mapping	mapping	NOUN
ejpam-5848	197	9	,	,	PUNCT
ejpam-5848	197	10	then	then	ADV
ejpam-5848	197	11	by	by	ADP
ejpam-5848	197	12	theorem	theorem	NOUN
ejpam-5848	197	13	4	4	NUM
ejpam-5848	197	14	,	,	PUNCT
ejpam-5848	197	15	ψ(bc)c	ψ(bc)c	PROPN
ejpam-5848	197	16	⊆	⊆	NUM
ejpam-5848	197	17	ψ(bc	ψ(bc	NUM
ejpam-5848	197	18	)	)	PUNCT
ejpam-5848	197	19	c	c	NOUN
ejpam-5848	197	20	.	.	PUNCT
ejpam-5848	198	1	but	but	CCONJ
ejpam-5848	198	2	ψ(bc	ψ(bc	NUM
ejpam-5848	198	3	)	)	PUNCT
ejpam-5848	199	1	c	c	NOUN
ejpam-5848	200	1	=	=	PUNCT
ejpam-5848	200	2	ψ#(b)c	ψ#(b)c	NOUN
ejpam-5848	200	3	c	c	NOUN
ejpam-5848	200	4	,	,	PUNCT
ejpam-5848	200	5	since	since	SCONJ
ejpam-5848	200	6	lemma	lemma	PROPN
ejpam-5848	200	7	2	2	NUM
ejpam-5848	200	8	(	(	PUNCT
ejpam-5848	200	9	b	b	NOUN
ejpam-5848	200	10	)	)	PUNCT
ejpam-5848	200	11	holds	hold	NOUN
ejpam-5848	200	12	.	.	PUNCT
ejpam-5848	201	1	this	this	PRON
ejpam-5848	201	2	implies	imply	VERB
ejpam-5848	201	3	that	that	SCONJ
ejpam-5848	201	4	ψ#(b	ψ#(b	PROPN
ejpam-5848	201	5	◦	◦	NOUN
ejpam-5848	201	6	)	)	PUNCT
ejpam-5848	201	7	⊆	⊆	NUM
ejpam-5848	201	8	ψ#(b)c	ψ#(b)c	NOUN
ejpam-5848	201	9	c	c	NOUN
ejpam-5848	201	10	=	=	SYM
ejpam-5848	201	11	(	(	PUNCT
ejpam-5848	201	12	ψ#(b))	ψ#(b))	NOUN
ejpam-5848	201	13	◦	◦	NOUN
ejpam-5848	201	14	.	.	PUNCT
ejpam-5848	202	1	hence	hence	ADV
ejpam-5848	202	2	,	,	PUNCT
ejpam-5848	202	3	ψ#(b	ψ#(b	PROPN
ejpam-5848	202	4	◦	◦	NOUN
ejpam-5848	202	5	)	)	PUNCT
ejpam-5848	202	6	⊆	⊆	NUM
ejpam-5848	202	7	(	(	PUNCT
ejpam-5848	202	8	ψ#(b))	ψ#(b))	NOUN
ejpam-5848	202	9	◦	◦	NOUN
ejpam-5848	202	10	.	.	PUNCT
ejpam-5848	202	11	conversely	conversely	ADV
ejpam-5848	202	12	,	,	PUNCT
ejpam-5848	202	13	let	let	VERB
ejpam-5848	202	14	g	g	NOUN
ejpam-5848	202	15	be	be	AUX
ejpam-5848	202	16	closed	close	VERB
ejpam-5848	202	17	fuzzy	fuzzy	ADJ
ejpam-5848	202	18	subset	subset	NOUN
ejpam-5848	202	19	of	of	ADP
ejpam-5848	202	20	v	v	NOUN
ejpam-5848	202	21	.	.	PUNCT
ejpam-5848	203	1	then	then	ADV
ejpam-5848	203	2	,	,	PUNCT
ejpam-5848	203	3	by	by	ADP
ejpam-5848	203	4	assumption	assumption	NOUN
ejpam-5848	203	5	,	,	PUNCT
ejpam-5848	203	6	ψ#((gc	ψ#((gc	NOUN
ejpam-5848	203	7	)	)	PUNCT
ejpam-5848	203	8	◦	◦	NOUN
ejpam-5848	203	9	)	)	PUNCT
ejpam-5848	203	10	⊆	⊆	NUM
ejpam-5848	203	11	(	(	PUNCT
ejpam-5848	203	12	ψ#(gc	ψ#(gc	PROPN
ejpam-5848	203	13	)	)	PUNCT
ejpam-5848	203	14	)	)	PUNCT
ejpam-5848	203	15	◦	◦	NOUN
ejpam-5848	203	16	which	which	PRON
ejpam-5848	203	17	implies	imply	VERB
ejpam-5848	203	18	ψ#(gc	ψ#(gc	PROPN
ejpam-5848	203	19	)	)	PUNCT
ejpam-5848	204	1	⊆	⊆	NUM
ejpam-5848	204	2	(	(	PUNCT
ejpam-5848	204	3	ψ#(gc))	ψ#(gc))	NOUN
ejpam-5848	204	4	◦	◦	NOUN
ejpam-5848	204	5	.	.	PUNCT
ejpam-5848	205	1	since	since	SCONJ
ejpam-5848	205	2	gc	gc	PROPN
ejpam-5848	205	3	is	be	AUX
ejpam-5848	205	4	an	an	DET
ejpam-5848	205	5	open	open	ADJ
ejpam-5848	205	6	fuzzy	fuzzy	ADJ
ejpam-5848	205	7	subset	subset	NOUN
ejpam-5848	205	8	of	of	ADP
ejpam-5848	205	9	v	v	NOUN
ejpam-5848	205	10	,	,	PUNCT
ejpam-5848	205	11	then	then	ADV
ejpam-5848	205	12	ψ#(gc	ψ#(gc	PROPN
ejpam-5848	205	13	)	)	PUNCT
ejpam-5848	205	14	is	be	AUX
ejpam-5848	205	15	an	an	DET
ejpam-5848	205	16	open	open	ADJ
ejpam-5848	205	17	fuzzy	fuzzy	ADJ
ejpam-5848	205	18	subset	subset	NOUN
ejpam-5848	205	19	of	of	ADP
ejpam-5848	205	20	w	w	PROPN
ejpam-5848	205	21	,	,	PUNCT
ejpam-5848	205	22	and	and	CCONJ
ejpam-5848	205	23	hence	hence	ADV
ejpam-5848	205	24	,	,	PUNCT
ejpam-5848	205	25	(	(	PUNCT
ejpam-5848	205	26	ψ#(gc))c	ψ#(gc))c	VERB
ejpam-5848	205	27	is	be	AUX
ejpam-5848	205	28	a	a	DET
ejpam-5848	205	29	closed	closed	ADJ
ejpam-5848	205	30	fuzzy	fuzzy	ADJ
ejpam-5848	205	31	mapping	mapping	NOUN
ejpam-5848	205	32	.	.	PUNCT
ejpam-5848	206	1	therefore	therefore	ADV
ejpam-5848	206	2	,	,	PUNCT
ejpam-5848	206	3	by	by	ADP
ejpam-5848	206	4	lemma	lemma	PROPN
ejpam-5848	206	5	2	2	NUM
ejpam-5848	206	6	(	(	PUNCT
ejpam-5848	206	7	b	b	NOUN
ejpam-5848	206	8	)	)	PUNCT
ejpam-5848	206	9	,	,	PUNCT
ejpam-5848	206	10	(	(	PUNCT
ejpam-5848	206	11	ψ#(gc))c	ψ#(gc))c	VERB
ejpam-5848	206	12	=	=	SYM
ejpam-5848	206	13	ψ(g	ψ(g	PROPN
ejpam-5848	206	14	)	)	PUNCT
ejpam-5848	206	15	is	be	AUX
ejpam-5848	206	16	a	a	DET
ejpam-5848	206	17	closed	closed	ADJ
ejpam-5848	206	18	fuzzy	fuzzy	ADJ
ejpam-5848	206	19	subset	subset	NOUN
ejpam-5848	206	20	of	of	ADP
ejpam-5848	206	21	w	w	PROPN
ejpam-5848	206	22	.	.	PUNCT
ejpam-5848	207	1	hence	hence	ADV
ejpam-5848	207	2	,	,	PUNCT
ejpam-5848	207	3	ψ	ψ	X
ejpam-5848	207	4	is	be	AUX
ejpam-5848	207	5	a	a	DET
ejpam-5848	207	6	closed	closed	ADJ
ejpam-5848	207	7	fuzzy	fuzzy	ADJ
ejpam-5848	207	8	mapping	mapping	NOUN
ejpam-5848	207	9	.	.	PUNCT
ejpam-5848	208	1	the	the	DET
ejpam-5848	208	2	following	follow	VERB
ejpam-5848	208	3	theorem	theorem	NOUN
ejpam-5848	208	4	gives	give	VERB
ejpam-5848	208	5	another	another	DET
ejpam-5848	208	6	representation	representation	NOUN
ejpam-5848	208	7	of	of	ADP
ejpam-5848	208	8	a	a	DET
ejpam-5848	208	9	closed	closed	ADJ
ejpam-5848	208	10	fuzzy	fuzzy	ADJ
ejpam-5848	208	11	mapping	mapping	NOUN
ejpam-5848	208	12	in	in	ADP
ejpam-5848	208	13	terms	term	NOUN
ejpam-5848	208	14	of	of	ADP
ejpam-5848	208	15	open	open	ADJ
ejpam-5848	208	16	fuzzy	fuzzy	ADJ
ejpam-5848	208	17	subsets	subset	NOUN
ejpam-5848	208	18	.	.	PUNCT
ejpam-5848	209	1	theorem	theorem	ADJ
ejpam-5848	209	2	10	10	NUM
ejpam-5848	209	3	.	.	PUNCT
ejpam-5848	210	1	let	let	VERB
ejpam-5848	210	2	ψ	ψ	PART
ejpam-5848	210	3	be	be	AUX
ejpam-5848	210	4	any	any	DET
ejpam-5848	210	5	mapping	mapping	NOUN
ejpam-5848	210	6	from	from	ADP
ejpam-5848	210	7	v	v	NUM
ejpam-5848	210	8	to	to	ADP
ejpam-5848	210	9	w	w	PROPN
ejpam-5848	210	10	.	.	PUNCT
ejpam-5848	211	1	then	then	ADV
ejpam-5848	211	2	ψ	ψ	X
ejpam-5848	211	3	is	be	AUX
ejpam-5848	211	4	a	a	DET
ejpam-5848	211	5	closed	closed	ADJ
ejpam-5848	211	6	fuzzy	fuzzy	ADJ
ejpam-5848	211	7	mapping	mapping	NOUN
ejpam-5848	211	8	if	if	SCONJ
ejpam-5848	211	9	and	and	CCONJ
ejpam-5848	211	10	only	only	ADV
ejpam-5848	211	11	if	if	SCONJ
ejpam-5848	211	12	for	for	ADP
ejpam-5848	211	13	every	every	DET
ejpam-5848	211	14	open	open	ADJ
ejpam-5848	211	15	fuzzy	fuzzy	ADJ
ejpam-5848	211	16	subset	subset	NOUN
ejpam-5848	211	17	o	o	NOUN
ejpam-5848	211	18	of	of	ADP
ejpam-5848	211	19	v	v	NOUN
ejpam-5848	211	20	,	,	PUNCT
ejpam-5848	211	21	ψ#(o	ψ#(o	PROPN
ejpam-5848	211	22	)	)	PUNCT
ejpam-5848	211	23	is	be	AUX
ejpam-5848	211	24	an	an	DET
ejpam-5848	211	25	open	open	ADJ
ejpam-5848	211	26	fuzzy	fuzzy	ADJ
ejpam-5848	211	27	set	set	VERB
ejpam-5848	211	28	in	in	ADP
ejpam-5848	211	29	w	w	PROPN
ejpam-5848	211	30	.	.	PUNCT
ejpam-5848	212	1	proof	proof	NOUN
ejpam-5848	212	2	.	.	PUNCT
ejpam-5848	213	1	the	the	DET
ejpam-5848	213	2	necessity	necessity	NOUN
ejpam-5848	213	3	of	of	ADP
ejpam-5848	213	4	the	the	DET
ejpam-5848	213	5	condition	condition	NOUN
ejpam-5848	213	6	follows	follow	VERB
ejpam-5848	213	7	from	from	ADP
ejpam-5848	213	8	theorem	theorem	ADJ
ejpam-5848	213	9	9	9	NUM
ejpam-5848	213	10	.	.	PUNCT
ejpam-5848	214	1	conversely	conversely	ADV
ejpam-5848	214	2	,	,	PUNCT
ejpam-5848	214	3	let	let	VERB
ejpam-5848	214	4	g	g	PRON
ejpam-5848	214	5	be	be	AUX
ejpam-5848	214	6	a	a	DET
ejpam-5848	214	7	closed	closed	ADJ
ejpam-5848	214	8	fuzzy	fuzzy	ADJ
ejpam-5848	214	9	subset	subset	NOUN
ejpam-5848	214	10	of	of	ADP
ejpam-5848	214	11	v	v	NOUN
ejpam-5848	214	12	.	.	PUNCT
ejpam-5848	215	1	then	then	ADV
ejpam-5848	215	2	,	,	PUNCT
ejpam-5848	215	3	by	by	ADP
ejpam-5848	215	4	assumption	assumption	NOUN
ejpam-5848	215	5	,	,	PUNCT
ejpam-5848	215	6	ψ#(gc	ψ#(gc	PROPN
ejpam-5848	215	7	)	)	PUNCT
ejpam-5848	215	8	is	be	AUX
ejpam-5848	215	9	an	an	DET
ejpam-5848	215	10	open	open	ADJ
ejpam-5848	215	11	fuzzy	fuzzy	ADJ
ejpam-5848	215	12	set	set	NOUN
ejpam-5848	215	13	in	in	ADP
ejpam-5848	215	14	w	w	PROPN
ejpam-5848	215	15	.	.	PUNCT
ejpam-5848	216	1	but	but	CCONJ
ejpam-5848	216	2	we	we	PRON
ejpam-5848	216	3	get	get	VERB
ejpam-5848	216	4	by	by	ADP
ejpam-5848	216	5	lemma	lemma	PROPN
ejpam-5848	216	6	2	2	NUM
ejpam-5848	216	7	(	(	PUNCT
ejpam-5848	216	8	b	b	NOUN
ejpam-5848	216	9	)	)	PUNCT
ejpam-5848	216	10	that	that	PRON
ejpam-5848	216	11	ψ#(gc	ψ#(gc	NOUN
ejpam-5848	216	12	)	)	PUNCT
ejpam-5848	217	1	=	=	SYM
ejpam-5848	217	2	ψ(g)c	ψ(g)c	PROPN
ejpam-5848	217	3	,	,	PUNCT
ejpam-5848	217	4	which	which	PRON
ejpam-5848	217	5	implies	imply	VERB
ejpam-5848	217	6	ψ(g)c	ψ(g)c	PROPN
ejpam-5848	217	7	is	be	AUX
ejpam-5848	217	8	an	an	DET
ejpam-5848	217	9	open	open	ADJ
ejpam-5848	217	10	fuzzy	fuzzy	ADJ
ejpam-5848	217	11	set	set	NOUN
ejpam-5848	217	12	in	in	ADP
ejpam-5848	217	13	w	w	PROPN
ejpam-5848	217	14	.	.	PUNCT
ejpam-5848	218	1	therefore	therefore	ADV
ejpam-5848	218	2	,	,	PUNCT
ejpam-5848	218	3	ψ(g	ψ(g	PROPN
ejpam-5848	218	4	)	)	PUNCT
ejpam-5848	218	5	is	be	AUX
ejpam-5848	218	6	a	a	DET
ejpam-5848	218	7	closed	closed	ADJ
ejpam-5848	218	8	fuzzy	fuzzy	ADJ
ejpam-5848	218	9	set	set	VERB
ejpam-5848	218	10	in	in	ADP
ejpam-5848	218	11	w	w	PROPN
ejpam-5848	218	12	.	.	PUNCT
ejpam-5848	219	1	hence	hence	ADV
ejpam-5848	219	2	,	,	PUNCT
ejpam-5848	219	3	ψ	ψ	X
ejpam-5848	219	4	is	be	AUX
ejpam-5848	219	5	a	a	DET
ejpam-5848	219	6	closed	closed	ADJ
ejpam-5848	219	7	fuzzy	fuzzy	ADJ
ejpam-5848	219	8	mapping	mapping	NOUN
ejpam-5848	219	9	.	.	PUNCT
ejpam-5848	220	1	the	the	DET
ejpam-5848	220	2	following	follow	VERB
ejpam-5848	220	3	example	example	NOUN
ejpam-5848	220	4	illustrates	illustrate	VERB
ejpam-5848	220	5	the	the	DET
ejpam-5848	220	6	above	above	ADJ
ejpam-5848	220	7	theorem	theorem	NOUN
ejpam-5848	220	8	.	.	PUNCT
ejpam-5848	221	1	s.	s.	PROPN
ejpam-5848	221	2	kaur	kaur	PROPN
ejpam-5848	221	3	et	et	PROPN
ejpam-5848	221	4	al	al	PROPN
ejpam-5848	221	5	.	.	PUNCT
ejpam-5848	221	6	/	/	SYM
ejpam-5848	221	7	eur	eur	PROPN
ejpam-5848	221	8	.	.	PUNCT
ejpam-5848	222	1	j.	j.	PROPN
ejpam-5848	222	2	pure	pure	PROPN
ejpam-5848	222	3	appl	appl	PROPN
ejpam-5848	222	4	.	.	PROPN
ejpam-5848	222	5	math	math	PROPN
ejpam-5848	222	6	,	,	PUNCT
ejpam-5848	222	7	18	18	NUM
ejpam-5848	222	8	(	(	PUNCT
ejpam-5848	222	9	1	1	NUM
ejpam-5848	222	10	)	)	PUNCT
ejpam-5848	222	11	(	(	PUNCT
ejpam-5848	222	12	2025	2025	NUM
ejpam-5848	222	13	)	)	PUNCT
ejpam-5848	222	14	,	,	PUNCT
ejpam-5848	222	15	5848	5848	NUM
ejpam-5848	222	16	9	9	NUM
ejpam-5848	222	17	of	of	ADP
ejpam-5848	222	18	11	11	NUM
ejpam-5848	222	19	example	example	NOUN
ejpam-5848	222	20	2	2	NUM
ejpam-5848	222	21	.	.	X
ejpam-5848	222	22	assume	assume	VERB
ejpam-5848	222	23	v	v	NOUN
ejpam-5848	222	24	=	=	SYM
ejpam-5848	222	25	{	{	PUNCT
ejpam-5848	222	26	v1	v1	NOUN
ejpam-5848	222	27	,	,	PUNCT
ejpam-5848	222	28	v2	v2	NOUN
ejpam-5848	222	29	}	}	PUNCT
ejpam-5848	222	30	and	and	CCONJ
ejpam-5848	222	31	w	w	NOUN
ejpam-5848	222	32	=	=	SYM
ejpam-5848	222	33	{	{	PUNCT
ejpam-5848	222	34	w1	w1	NOUN
ejpam-5848	222	35	,	,	PUNCT
ejpam-5848	222	36	w2	w2	NOUN
ejpam-5848	222	37	}	}	PUNCT
ejpam-5848	222	38	,	,	PUNCT
ejpam-5848	222	39	consider	consider	VERB
ejpam-5848	222	40	f	f	PRON
ejpam-5848	222	41	-sets	-set	NOUN
ejpam-5848	222	42	m	m	VERB
ejpam-5848	222	43	and	and	CCONJ
ejpam-5848	222	44	n	n	PROPN
ejpam-5848	222	45	as	as	ADP
ejpam-5848	222	46	m	m	PROPN
ejpam-5848	222	47	=	=	PRON
ejpam-5848	222	48	{	{	PUNCT
ejpam-5848	222	49	<	<	X
ejpam-5848	222	50	v1	v1	NOUN
ejpam-5848	222	51	,	,	PUNCT
ejpam-5848	222	52	0.6	0.6	NUM
ejpam-5848	222	53	>	>	PUNCT
ejpam-5848	222	54	,	,	PUNCT
ejpam-5848	222	55	<	<	X
ejpam-5848	222	56	v2	v2	PROPN
ejpam-5848	222	57	,	,	PUNCT
ejpam-5848	222	58	0.7	0.7	NUM
ejpam-5848	222	59	>	>	PUNCT
ejpam-5848	222	60	}	}	PUNCT
ejpam-5848	222	61	and	and	CCONJ
ejpam-5848	222	62	n	n	CCONJ
ejpam-5848	222	63	=	=	PRON
ejpam-5848	222	64	{	{	PUNCT
ejpam-5848	222	65	<	<	X
ejpam-5848	222	66	w1	w1	NOUN
ejpam-5848	222	67	,	,	PUNCT
ejpam-5848	222	68	0.6	0.6	NUM
ejpam-5848	222	69	>	>	PUNCT
ejpam-5848	222	70	,	,	PUNCT
ejpam-5848	222	71	<	<	X
ejpam-5848	222	72	w2	w2	NOUN
ejpam-5848	222	73	,	,	PUNCT
ejpam-5848	222	74	0.5	0.5	NUM
ejpam-5848	222	75	>	>	PUNCT
ejpam-5848	222	76	}	}	PUNCT
ejpam-5848	222	77	.	.	PUNCT
ejpam-5848	223	1	then	then	ADV
ejpam-5848	223	2	t1	t1	NOUN
ejpam-5848	223	3	=	=	PUNCT
ejpam-5848	223	4	{	{	PUNCT
ejpam-5848	223	5	∅,m	∅,m	NOUN
ejpam-5848	223	6	,	,	PUNCT
ejpam-5848	223	7	v	v	NOUN
ejpam-5848	223	8	}	}	PUNCT
ejpam-5848	223	9	and	and	CCONJ
ejpam-5848	223	10	t2	t2	PROPN
ejpam-5848	223	11	=	=	SYM
ejpam-5848	223	12	{	{	PUNCT
ejpam-5848	223	13	∅	∅	NOUN
ejpam-5848	223	14	,	,	PUNCT
ejpam-5848	223	15	n	n	CCONJ
ejpam-5848	223	16	,	,	PUNCT
ejpam-5848	223	17	w	w	NOUN
ejpam-5848	223	18	}	}	PUNCT
ejpam-5848	223	19	be	be	AUX
ejpam-5848	223	20	fuzzy	fuzzy	ADJ
ejpam-5848	223	21	topologies	topology	NOUN
ejpam-5848	223	22	on	on	ADP
ejpam-5848	223	23	v	v	NOUN
ejpam-5848	223	24	and	and	CCONJ
ejpam-5848	223	25	w	w	NOUN
ejpam-5848	223	26	,	,	PUNCT
ejpam-5848	223	27	respectively	respectively	ADV
ejpam-5848	223	28	.	.	PUNCT
ejpam-5848	224	1	we	we	PRON
ejpam-5848	224	2	define	define	VERB
ejpam-5848	224	3	a	a	DET
ejpam-5848	224	4	fuzzy	fuzzy	ADJ
ejpam-5848	224	5	mapping	mapping	NOUN
ejpam-5848	224	6	ψ	ψ	X
ejpam-5848	224	7	:	:	PUNCT
ejpam-5848	224	8	(	(	PUNCT
ejpam-5848	224	9	v	v	NOUN
ejpam-5848	224	10	,	,	PUNCT
ejpam-5848	224	11	t1	t1	NOUN
ejpam-5848	224	12	)	)	PUNCT
ejpam-5848	224	13	→	→	SYM
ejpam-5848	224	14	(	(	PUNCT
ejpam-5848	224	15	w	w	PROPN
ejpam-5848	224	16	,	,	PUNCT
ejpam-5848	224	17	t2	t2	NOUN
ejpam-5848	224	18	)	)	PUNCT
ejpam-5848	224	19	as	as	SCONJ
ejpam-5848	224	20	follows	follow	VERB
ejpam-5848	224	21	ψ(v1	ψ(v1	NOUN
ejpam-5848	224	22	)	)	PUNCT
ejpam-5848	224	23	=	=	SYM
ejpam-5848	224	24	w1	w1	NOUN
ejpam-5848	224	25	,	,	PUNCT
ejpam-5848	224	26	ψ(v2	ψ(v2	NOUN
ejpam-5848	224	27	)	)	PUNCT
ejpam-5848	224	28	=	=	SYM
ejpam-5848	224	29	w2	w2	NOUN
ejpam-5848	224	30	.	.	PUNCT
ejpam-5848	225	1	one	one	PRON
ejpam-5848	225	2	can	can	AUX
ejpam-5848	225	3	check	check	VERB
ejpam-5848	225	4	that	that	PRON
ejpam-5848	225	5	ψ	ψ	NOUN
ejpam-5848	225	6	is	be	AUX
ejpam-5848	225	7	not	not	PART
ejpam-5848	225	8	a	a	DET
ejpam-5848	225	9	closed	closed	ADJ
ejpam-5848	225	10	fuzzy	fuzzy	ADJ
ejpam-5848	225	11	mapping	mapping	NOUN
ejpam-5848	225	12	.	.	PUNCT
ejpam-5848	226	1	on	on	ADP
ejpam-5848	226	2	the	the	DET
ejpam-5848	226	3	other	other	ADJ
ejpam-5848	226	4	hand	hand	NOUN
ejpam-5848	226	5	,	,	PUNCT
ejpam-5848	226	6	let	let	VERB
ejpam-5848	226	7	m	m	PRON
ejpam-5848	226	8	be	be	AUX
ejpam-5848	226	9	an	an	DET
ejpam-5848	226	10	open	open	ADJ
ejpam-5848	226	11	fuzzy	fuzzy	ADJ
ejpam-5848	226	12	set	set	NOUN
ejpam-5848	226	13	in	in	ADP
ejpam-5848	226	14	v	v	NOUN
ejpam-5848	226	15	.	.	PUNCT
ejpam-5848	227	1	then	then	ADV
ejpam-5848	227	2	,	,	PUNCT
ejpam-5848	227	3	ψ#(m	ψ#(m	PROPN
ejpam-5848	227	4	)	)	PUNCT
ejpam-5848	227	5	=	=	PRON
ejpam-5848	228	1	{	{	PUNCT
ejpam-5848	228	2	<	<	X
ejpam-5848	228	3	w1	w1	NOUN
ejpam-5848	228	4	,	,	PUNCT
ejpam-5848	228	5	0.6	0.6	NUM
ejpam-5848	228	6	>	>	PUNCT
ejpam-5848	228	7	,	,	PUNCT
ejpam-5848	228	8	<	<	X
ejpam-5848	228	9	w2	w2	NOUN
ejpam-5848	228	10	,	,	PUNCT
ejpam-5848	228	11	0.7	0.7	NUM
ejpam-5848	228	12	>	>	PUNCT
ejpam-5848	228	13	}	}	PUNCT
ejpam-5848	228	14	is	be	AUX
ejpam-5848	228	15	not	not	PART
ejpam-5848	228	16	an	an	DET
ejpam-5848	228	17	open	open	ADJ
ejpam-5848	228	18	fuzzy	fuzzy	ADJ
ejpam-5848	228	19	set	set	NOUN
ejpam-5848	228	20	in	in	ADP
ejpam-5848	228	21	w	w	PROPN
ejpam-5848	228	22	.	.	PUNCT
ejpam-5848	229	1	in	in	ADP
ejpam-5848	229	2	the	the	DET
ejpam-5848	229	3	next	next	ADJ
ejpam-5848	229	4	theorem	theorem	NOUN
ejpam-5848	229	5	,	,	PUNCT
ejpam-5848	229	6	we	we	PRON
ejpam-5848	229	7	discuss	discuss	VERB
ejpam-5848	229	8	another	another	DET
ejpam-5848	229	9	representation	representation	NOUN
ejpam-5848	229	10	of	of	ADP
ejpam-5848	229	11	a	a	DET
ejpam-5848	229	12	closed	closed	ADJ
ejpam-5848	229	13	fuzzy	fuzzy	ADJ
ejpam-5848	229	14	mapping	mapping	NOUN
ejpam-5848	229	15	when	when	SCONJ
ejpam-5848	229	16	a	a	DET
ejpam-5848	229	17	mapping	mapping	NOUN
ejpam-5848	229	18	is	be	AUX
ejpam-5848	229	19	surjective	surjective	ADJ
ejpam-5848	229	20	.	.	PUNCT
ejpam-5848	230	1	theorem	theorem	NOUN
ejpam-5848	230	2	11	11	NUM
ejpam-5848	230	3	.	.	PUNCT
ejpam-5848	231	1	let	let	VERB
ejpam-5848	231	2	ψ	ψ	X
ejpam-5848	231	3	:	:	PUNCT
ejpam-5848	231	4	v	v	PART
ejpam-5848	231	5	→w	→w	PUNCT
ejpam-5848	231	6	be	be	AUX
ejpam-5848	231	7	a	a	DET
ejpam-5848	231	8	surjective	surjective	ADJ
ejpam-5848	231	9	mapping	mapping	NOUN
ejpam-5848	231	10	.	.	PUNCT
ejpam-5848	232	1	then	then	ADV
ejpam-5848	232	2	ψ	ψ	X
ejpam-5848	232	3	is	be	AUX
ejpam-5848	232	4	a	a	DET
ejpam-5848	232	5	closed	closed	ADJ
ejpam-5848	232	6	fuzzy	fuzzy	ADJ
ejpam-5848	232	7	mapping	mapping	NOUN
ejpam-5848	232	8	if	if	SCONJ
ejpam-5848	232	9	and	and	CCONJ
ejpam-5848	232	10	only	only	ADV
ejpam-5848	232	11	if	if	SCONJ
ejpam-5848	232	12	for	for	ADP
ejpam-5848	232	13	each	each	DET
ejpam-5848	232	14	open	open	ADJ
ejpam-5848	232	15	fuzzy	fuzzy	ADJ
ejpam-5848	232	16	subset	subset	NOUN
ejpam-5848	232	17	o	o	NOUN
ejpam-5848	232	18	of	of	ADP
ejpam-5848	232	19	w	w	PROPN
ejpam-5848	232	20	,	,	PUNCT
ejpam-5848	232	21	ψ(o	ψ(o	PROPN
ejpam-5848	232	22	#	#	NOUN
ejpam-5848	232	23	)	)	PUNCT
ejpam-5848	232	24	is	be	AUX
ejpam-5848	232	25	an	an	DET
ejpam-5848	232	26	open	open	ADJ
ejpam-5848	232	27	fuzzy	fuzzy	ADJ
ejpam-5848	232	28	set	set	VERB
ejpam-5848	232	29	in	in	ADP
ejpam-5848	232	30	w	w	PROPN
ejpam-5848	232	31	.	.	PUNCT
ejpam-5848	233	1	proof	proof	NOUN
ejpam-5848	233	2	.	.	PUNCT
ejpam-5848	234	1	the	the	DET
ejpam-5848	234	2	proof	proof	NOUN
ejpam-5848	234	3	is	be	AUX
ejpam-5848	234	4	similar	similar	ADJ
ejpam-5848	234	5	to	to	ADP
ejpam-5848	234	6	that	that	PRON
ejpam-5848	234	7	of	of	ADP
ejpam-5848	234	8	theorem	theorem	NOUN
ejpam-5848	234	9	7	7	NUM
ejpam-5848	234	10	.	.	PUNCT
ejpam-5848	234	11	in	in	ADP
ejpam-5848	234	12	the	the	DET
ejpam-5848	234	13	final	final	ADJ
ejpam-5848	234	14	result	result	NOUN
ejpam-5848	234	15	about	about	ADP
ejpam-5848	234	16	closed	close	VERB
ejpam-5848	234	17	fuzzy	fuzzy	ADJ
ejpam-5848	234	18	mappings	mapping	NOUN
ejpam-5848	234	19	,	,	PUNCT
ejpam-5848	234	20	we	we	PRON
ejpam-5848	234	21	see	see	VERB
ejpam-5848	234	22	that	that	DET
ejpam-5848	234	23	image	image	NOUN
ejpam-5848	234	24	of	of	ADP
ejpam-5848	234	25	saturated	saturate	VERB
ejpam-5848	234	26	open	open	ADJ
ejpam-5848	234	27	fuzzy	fuzzy	ADJ
ejpam-5848	234	28	sets	set	NOUN
ejpam-5848	234	29	under	under	ADP
ejpam-5848	234	30	the	the	DET
ejpam-5848	234	31	surjective	surjective	ADJ
ejpam-5848	234	32	closed	closed	ADJ
ejpam-5848	234	33	fuzzy	fuzzy	ADJ
ejpam-5848	234	34	mapping	mapping	NOUN
ejpam-5848	234	35	is	be	AUX
ejpam-5848	234	36	an	an	DET
ejpam-5848	234	37	open	open	ADJ
ejpam-5848	234	38	fuzzy	fuzzy	ADJ
ejpam-5848	234	39	set	set	NOUN
ejpam-5848	234	40	.	.	PUNCT
ejpam-5848	235	1	theorem	theorem	PROPN
ejpam-5848	235	2	12	12	NUM
ejpam-5848	235	3	.	.	PUNCT
ejpam-5848	236	1	let	let	VERB
ejpam-5848	236	2	ψ	ψ	NOUN
ejpam-5848	236	3	:	:	PUNCT
ejpam-5848	236	4	v	v	X
ejpam-5848	236	5	→	→	SYM
ejpam-5848	236	6	w	w	X
ejpam-5848	236	7	be	be	AUX
ejpam-5848	236	8	a	a	DET
ejpam-5848	236	9	surjective	surjective	ADJ
ejpam-5848	236	10	closed	closed	ADJ
ejpam-5848	236	11	fuzzy	fuzzy	ADJ
ejpam-5848	236	12	mapping	mapping	NOUN
ejpam-5848	236	13	.	.	PUNCT
ejpam-5848	237	1	then	then	ADV
ejpam-5848	237	2	ψ(o	ψ(o	PROPN
ejpam-5848	237	3	)	)	PUNCT
ejpam-5848	237	4	is	be	AUX
ejpam-5848	237	5	an	an	DET
ejpam-5848	237	6	open	open	ADJ
ejpam-5848	237	7	fuzzy	fuzzy	ADJ
ejpam-5848	237	8	set	set	VERB
ejpam-5848	237	9	in	in	ADP
ejpam-5848	237	10	w	w	NOUN
ejpam-5848	237	11	for	for	ADP
ejpam-5848	237	12	every	every	DET
ejpam-5848	237	13	saturated	saturate	VERB
ejpam-5848	237	14	open	open	ADJ
ejpam-5848	237	15	fuzzy	fuzzy	ADJ
ejpam-5848	237	16	subset	subset	NOUN
ejpam-5848	237	17	o	o	NOUN
ejpam-5848	237	18	in	in	ADP
ejpam-5848	237	19	v	v	NOUN
ejpam-5848	237	20	.	.	PUNCT
ejpam-5848	238	1	proof	proof	NOUN
ejpam-5848	238	2	.	.	PUNCT
ejpam-5848	239	1	the	the	DET
ejpam-5848	239	2	proof	proof	NOUN
ejpam-5848	239	3	is	be	AUX
ejpam-5848	239	4	similar	similar	ADJ
ejpam-5848	239	5	to	to	ADP
ejpam-5848	239	6	the	the	DET
ejpam-5848	239	7	above	above	ADJ
ejpam-5848	239	8	theorem	theorem	ADJ
ejpam-5848	239	9	8	8	NUM
ejpam-5848	239	10	.	.	PUNCT
ejpam-5848	239	11	corollary	corollary	ADJ
ejpam-5848	239	12	2	2	NUM
ejpam-5848	239	13	.	.	PUNCT
ejpam-5848	240	1	let	let	VERB
ejpam-5848	240	2	ψ	ψ	NOUN
ejpam-5848	240	3	:	:	PUNCT
ejpam-5848	240	4	v	v	X
ejpam-5848	240	5	→	→	SYM
ejpam-5848	240	6	w	w	X
ejpam-5848	240	7	be	be	AUX
ejpam-5848	240	8	an	an	DET
ejpam-5848	240	9	closed	closed	ADJ
ejpam-5848	240	10	fuzzy	fuzzy	ADJ
ejpam-5848	240	11	mapping	mapping	NOUN
ejpam-5848	240	12	and	and	CCONJ
ejpam-5848	240	13	surjective	surjective	ADJ
ejpam-5848	240	14	.	.	PUNCT
ejpam-5848	241	1	then	then	ADV
ejpam-5848	241	2	,	,	PUNCT
ejpam-5848	241	3	for	for	ADP
ejpam-5848	241	4	any	any	DET
ejpam-5848	241	5	open	open	ADJ
ejpam-5848	241	6	fuzzy	fuzzy	ADJ
ejpam-5848	241	7	subset	subset	NOUN
ejpam-5848	242	1	b	b	NOUN
ejpam-5848	242	2	#	#	NOUN
ejpam-5848	242	3	of	of	ADP
ejpam-5848	242	4	v	v	NUM
ejpam-5848	242	5	,	,	PUNCT
ejpam-5848	242	6	we	we	PRON
ejpam-5848	242	7	have	have	VERB
ejpam-5848	242	8	ψ(b	ψ(b	NOUN
ejpam-5848	242	9	#	#	NOUN
ejpam-5848	242	10	)	)	PUNCT
ejpam-5848	242	11	is	be	AUX
ejpam-5848	242	12	an	an	DET
ejpam-5848	242	13	open	open	ADJ
ejpam-5848	242	14	fuzzy	fuzzy	ADJ
ejpam-5848	242	15	set	set	NOUN
ejpam-5848	242	16	in	in	ADP
ejpam-5848	242	17	w	w	PROPN
ejpam-5848	242	18	.	.	PROPN
ejpam-5848	243	1	5	5	X
ejpam-5848	243	2	.	.	X
ejpam-5848	243	3	conclusion	conclusion	NOUN
ejpam-5848	243	4	applications	application	NOUN
ejpam-5848	243	5	of	of	ADP
ejpam-5848	243	6	operators	operator	NOUN
ejpam-5848	243	7	which	which	PRON
ejpam-5848	243	8	are	be	AUX
ejpam-5848	243	9	either	either	PRON
ejpam-5848	243	10	obtained	obtain	VERB
ejpam-5848	243	11	from	from	ADP
ejpam-5848	243	12	a	a	DET
ejpam-5848	243	13	prior	prior	ADJ
ejpam-5848	243	14	structure	structure	NOUN
ejpam-5848	243	15	or	or	CCONJ
ejpam-5848	243	16	an	an	DET
ejpam-5848	243	17	operator	operator	NOUN
ejpam-5848	243	18	acting	act	VERB
ejpam-5848	243	19	on	on	ADP
ejpam-5848	243	20	a	a	DET
ejpam-5848	243	21	given	give	VERB
ejpam-5848	243	22	mapping	mapping	NOUN
ejpam-5848	243	23	,	,	PUNCT
ejpam-5848	243	24	induce	induce	VERB
ejpam-5848	243	25	useful	useful	ADJ
ejpam-5848	243	26	mappings	mapping	NOUN
ejpam-5848	243	27	which	which	PRON
ejpam-5848	243	28	enable	enable	VERB
ejpam-5848	243	29	us	we	PRON
ejpam-5848	243	30	to	to	PART
ejpam-5848	243	31	study	study	VERB
ejpam-5848	243	32	the	the	DET
ejpam-5848	243	33	important	important	ADJ
ejpam-5848	243	34	topological	topological	ADJ
ejpam-5848	243	35	concepts	concept	NOUN
ejpam-5848	243	36	or	or	CCONJ
ejpam-5848	243	37	enable	enable	VERB
ejpam-5848	243	38	us	we	PRON
ejpam-5848	243	39	to	to	PART
ejpam-5848	243	40	give	give	VERB
ejpam-5848	243	41	a	a	DET
ejpam-5848	243	42	new	new	ADJ
ejpam-5848	243	43	characterization	characterization	NOUN
ejpam-5848	243	44	of	of	ADP
ejpam-5848	243	45	such	such	ADJ
ejpam-5848	243	46	important	important	ADJ
ejpam-5848	243	47	concepts	concept	NOUN
ejpam-5848	243	48	as	as	ADP
ejpam-5848	243	49	continuity	continuity	NOUN
ejpam-5848	243	50	,	,	PUNCT
ejpam-5848	243	51	open	open	ADJ
ejpam-5848	243	52	and	and	CCONJ
ejpam-5848	243	53	closed	closed	ADJ
ejpam-5848	243	54	mappings	mapping	NOUN
ejpam-5848	243	55	.	.	PUNCT
ejpam-5848	244	1	in	in	ADP
ejpam-5848	244	2	view	view	NOUN
ejpam-5848	244	3	of	of	ADP
ejpam-5848	244	4	the	the	DET
ejpam-5848	244	5	research	research	NOUN
ejpam-5848	244	6	done	do	VERB
ejpam-5848	244	7	on	on	ADP
ejpam-5848	244	8	f	f	PROPN
ejpam-5848	244	9	-set	-set	PUNCT
ejpam-5848	244	10	theory	theory	NOUN
ejpam-5848	244	11	,	,	PUNCT
ejpam-5848	244	12	much	much	ADJ
ejpam-5848	244	13	needs	need	VERB
ejpam-5848	244	14	to	to	PART
ejpam-5848	244	15	be	be	AUX
ejpam-5848	244	16	investigated	investigate	VERB
ejpam-5848	244	17	in	in	ADP
ejpam-5848	244	18	the	the	DET
ejpam-5848	244	19	application	application	NOUN
ejpam-5848	244	20	of	of	ADP
ejpam-5848	244	21	mappings	mapping	NOUN
ejpam-5848	244	22	induced	induce	VERB
ejpam-5848	244	23	by	by	ADP
ejpam-5848	244	24	operators	operator	NOUN
ejpam-5848	244	25	defined	define	VERB
ejpam-5848	244	26	by	by	ADP
ejpam-5848	244	27	f	f	PROPN
ejpam-5848	244	28	-sets	-set	NOUN
ejpam-5848	244	29	.	.	PUNCT
ejpam-5848	245	1	in	in	ADP
ejpam-5848	245	2	this	this	DET
ejpam-5848	245	3	paper	paper	NOUN
ejpam-5848	245	4	,	,	PUNCT
ejpam-5848	245	5	we	we	PRON
ejpam-5848	245	6	have	have	AUX
ejpam-5848	245	7	established	establish	VERB
ejpam-5848	245	8	new	new	ADJ
ejpam-5848	245	9	characterizations	characterization	NOUN
ejpam-5848	245	10	of	of	ADP
ejpam-5848	245	11	open	open	ADJ
ejpam-5848	245	12	and	and	CCONJ
ejpam-5848	245	13	closed	close	VERB
ejpam-5848	245	14	fuzzy	fuzzy	ADJ
ejpam-5848	245	15	mappings	mapping	NOUN
ejpam-5848	245	16	in	in	ADP
ejpam-5848	245	17	connection	connection	NOUN
ejpam-5848	245	18	with	with	ADP
ejpam-5848	245	19	induced	induced	ADJ
ejpam-5848	245	20	fuzzy	fuzzy	ADJ
ejpam-5848	245	21	mapping	mapping	NOUN
ejpam-5848	245	22	rather	rather	ADV
ejpam-5848	245	23	than	than	ADP
ejpam-5848	245	24	the	the	DET
ejpam-5848	245	25	well	well	ADV
ejpam-5848	245	26	-	-	PUNCT
ejpam-5848	245	27	known	know	VERB
ejpam-5848	245	28	results	result	NOUN
ejpam-5848	245	29	of	of	ADP
ejpam-5848	245	30	open	open	ADJ
ejpam-5848	245	31	fuzzy	fuzzy	ADJ
ejpam-5848	245	32	mappings	mapping	NOUN
ejpam-5848	245	33	in	in	ADP
ejpam-5848	245	34	terms	term	NOUN
ejpam-5848	245	35	of	of	ADP
ejpam-5848	245	36	interiors	interior	NOUN
ejpam-5848	245	37	and	and	CCONJ
ejpam-5848	245	38	closed	close	VERB
ejpam-5848	245	39	fuzzy	fuzzy	ADJ
ejpam-5848	245	40	mapping	mapping	NOUN
ejpam-5848	245	41	in	in	ADP
ejpam-5848	245	42	terms	term	NOUN
ejpam-5848	245	43	of	of	ADP
ejpam-5848	245	44	closures	closure	NOUN
ejpam-5848	245	45	.	.	PUNCT
ejpam-5848	246	1	the	the	DET
ejpam-5848	246	2	significat	significat	NOUN
ejpam-5848	246	3	of	of	ADP
ejpam-5848	246	4	these	these	DET
ejpam-5848	246	5	characterizations	characterization	NOUN
ejpam-5848	246	6	is	be	AUX
ejpam-5848	246	7	that	that	SCONJ
ejpam-5848	246	8	it	it	PRON
ejpam-5848	246	9	leads	lead	VERB
ejpam-5848	246	10	to	to	ADP
ejpam-5848	246	11	the	the	DET
ejpam-5848	246	12	growth	growth	NOUN
ejpam-5848	246	13	of	of	ADP
ejpam-5848	246	14	the	the	DET
ejpam-5848	246	15	theoretical	theoretical	ADJ
ejpam-5848	246	16	study	study	NOUN
ejpam-5848	246	17	of	of	ADP
ejpam-5848	246	18	ftss	ftss	NOUN
ejpam-5848	246	19	and	and	CCONJ
ejpam-5848	246	20	offers	offer	VERB
ejpam-5848	246	21	various	various	ADJ
ejpam-5848	246	22	descriptions	description	NOUN
ejpam-5848	246	23	for	for	ADP
ejpam-5848	246	24	fuzzy	fuzzy	ADJ
ejpam-5848	246	25	mappings	mapping	NOUN
ejpam-5848	246	26	.	.	PUNCT
ejpam-5848	247	1	our	our	PRON
ejpam-5848	247	2	next	next	ADJ
ejpam-5848	247	3	target	target	NOUN
ejpam-5848	247	4	will	will	AUX
ejpam-5848	247	5	be	be	AUX
ejpam-5848	247	6	to	to	PART
ejpam-5848	247	7	study	study	VERB
ejpam-5848	247	8	the	the	DET
ejpam-5848	247	9	concepts	concept	NOUN
ejpam-5848	247	10	of	of	ADP
ejpam-5848	247	11	invertedly	invertedly	ADV
ejpam-5848	247	12	open	open	ADJ
ejpam-5848	247	13	fuzzy	fuzzy	ADJ
ejpam-5848	247	14	mappings	mapping	NOUN
ejpam-5848	247	15	and	and	CCONJ
ejpam-5848	247	16	invertedly	invertedly	ADV
ejpam-5848	247	17	closed	close	VERB
ejpam-5848	247	18	fuzzy	fuzzy	ADJ
ejpam-5848	247	19	mappings	mapping	NOUN
ejpam-5848	247	20	by	by	ADP
ejpam-5848	247	21	using	use	VERB
ejpam-5848	247	22	this	this	DET
ejpam-5848	247	23	induced	induced	ADJ
ejpam-5848	247	24	mapping	mapping	NOUN
ejpam-5848	247	25	.	.	PUNCT
ejpam-5848	248	1	also	also	ADV
ejpam-5848	248	2	,	,	PUNCT
ejpam-5848	248	3	we	we	PRON
ejpam-5848	248	4	look	look	VERB
ejpam-5848	248	5	at	at	ADP
ejpam-5848	248	6	the	the	DET
ejpam-5848	248	7	validity	validity	NOUN
ejpam-5848	248	8	of	of	ADP
ejpam-5848	248	9	the	the	DET
ejpam-5848	248	10	results	result	NOUN
ejpam-5848	248	11	introduced	introduce	VERB
ejpam-5848	248	12	herein	herein	NOUN
ejpam-5848	248	13	via	via	ADP
ejpam-5848	248	14	some	some	DET
ejpam-5848	248	15	generalizations	generalization	NOUN
ejpam-5848	248	16	of	of	ADP
ejpam-5848	248	17	fuzzy	fuzzy	ADJ
ejpam-5848	248	18	topology	topology	NOUN
ejpam-5848	248	19	,	,	PUNCT
ejpam-5848	248	20	such	such	ADJ
ejpam-5848	248	21	as	as	ADP
ejpam-5848	248	22	infra	infra	NOUN
ejpam-5848	248	23	fuzzy	fuzzy	ADJ
ejpam-5848	248	24	(	(	PUNCT
ejpam-5848	248	25	soft	soft	ADJ
ejpam-5848	248	26	)	)	PUNCT
ejpam-5848	248	27	topology	topology	NOUN
ejpam-5848	249	1	[	[	X
ejpam-5848	249	2	3	3	X
ejpam-5848	249	3	]	]	PUNCT
ejpam-5848	249	4	and	and	CCONJ
ejpam-5848	249	5	supra	supra	ADJ
ejpam-5848	249	6	fuzzy	fuzzy	ADJ
ejpam-5848	249	7	(	(	PUNCT
ejpam-5848	249	8	soft	soft	ADJ
ejpam-5848	249	9	)	)	PUNCT
ejpam-5848	249	10	topology	topology	NOUN
ejpam-5848	250	1	[	[	X
ejpam-5848	250	2	4	4	NUM
ejpam-5848	250	3	,	,	PUNCT
ejpam-5848	250	4	5	5	NUM
ejpam-5848	250	5	]	]	PUNCT
ejpam-5848	250	6	.	.	PUNCT
ejpam-5848	251	1	s.	s.	PROPN
ejpam-5848	251	2	kaur	kaur	PROPN
ejpam-5848	251	3	et	et	PROPN
ejpam-5848	251	4	al	al	PROPN
ejpam-5848	251	5	.	.	PUNCT
ejpam-5848	251	6	/	/	SYM
ejpam-5848	251	7	eur	eur	PROPN
ejpam-5848	251	8	.	.	PUNCT
ejpam-5848	252	1	j.	j.	PROPN
ejpam-5848	252	2	pure	pure	PROPN
ejpam-5848	252	3	appl	appl	PROPN
ejpam-5848	252	4	.	.	PROPN
ejpam-5848	252	5	math	math	PROPN
ejpam-5848	252	6	,	,	PUNCT
ejpam-5848	252	7	18	18	NUM
ejpam-5848	252	8	(	(	PUNCT
ejpam-5848	252	9	1	1	NUM
ejpam-5848	252	10	)	)	PUNCT
ejpam-5848	252	11	(	(	PUNCT
ejpam-5848	252	12	2025	2025	NUM
ejpam-5848	252	13	)	)	PUNCT
ejpam-5848	252	14	,	,	PUNCT
ejpam-5848	252	15	5848	5848	NUM
ejpam-5848	252	16	10	10	NUM
ejpam-5848	252	17	of	of	ADP
ejpam-5848	252	18	11	11	NUM
ejpam-5848	252	19	acknowledgments	acknowledgment	NOUN
ejpam-5848	252	20	the	the	DET
ejpam-5848	252	21	authors	author	NOUN
ejpam-5848	252	22	extend	extend	VERB
ejpam-5848	252	23	their	their	PRON
ejpam-5848	252	24	appreciation	appreciation	NOUN
ejpam-5848	252	25	to	to	ADP
ejpam-5848	252	26	the	the	DET
ejpam-5848	252	27	deanship	deanship	NOUN
ejpam-5848	252	28	of	of	ADP
ejpam-5848	252	29	scientific	scientific	ADJ
ejpam-5848	252	30	research	research	NOUN
ejpam-5848	252	31	at	at	ADP
ejpam-5848	252	32	northern	northern	ADJ
ejpam-5848	252	33	border	border	NOUN
ejpam-5848	252	34	university	university	PROPN
ejpam-5848	252	35	,	,	PUNCT
ejpam-5848	252	36	arar	arar	PROPN
ejpam-5848	252	37	,	,	PUNCT
ejpam-5848	252	38	ksa	ksa	PROPN
ejpam-5848	252	39	for	for	ADP
ejpam-5848	252	40	funding	fund	VERB
ejpam-5848	252	41	this	this	DET
ejpam-5848	252	42	research	research	NOUN
ejpam-5848	252	43	work	work	NOUN
ejpam-5848	252	44	through	through	ADP
ejpam-5848	252	45	the	the	DET
ejpam-5848	252	46	project	project	NOUN
ejpam-5848	252	47	number	number	NOUN
ejpam-5848	252	48	“	"	PUNCT
ejpam-5848	252	49	nbu	nbu	NOUN
ejpam-5848	252	50	-	-	PUNCT
ejpam-5848	252	51	ffr-2025	ffr-2025	NOUN
ejpam-5848	252	52	-	-	PUNCT
ejpam-5848	252	53	1166	1166	NUM
ejpam-5848	252	54	-	-	PUNCT
ejpam-5848	252	55	01	01	NUM
ejpam-5848	252	56	”	"	PUNCT
ejpam-5848	252	57	conflict	conflict	NOUN
ejpam-5848	252	58	of	of	ADP
ejpam-5848	252	59	interest	interest	NOUN
ejpam-5848	252	60	the	the	DET
ejpam-5848	252	61	authors	author	NOUN
ejpam-5848	252	62	declare	declare	VERB
ejpam-5848	252	63	that	that	SCONJ
ejpam-5848	252	64	there	there	PRON
ejpam-5848	252	65	is	be	VERB
ejpam-5848	252	66	no	no	DET
ejpam-5848	252	67	conflict	conflict	NOUN
ejpam-5848	252	68	of	of	ADP
ejpam-5848	252	69	interest	interest	NOUN
ejpam-5848	252	70	regarding	regard	VERB
ejpam-5848	252	71	the	the	DET
ejpam-5848	252	72	publication	publication	NOUN
ejpam-5848	252	73	of	of	ADP
ejpam-5848	252	74	this	this	DET
ejpam-5848	252	75	paper	paper	NOUN
ejpam-5848	252	76	.	.	PUNCT
ejpam-5848	253	1	references	reference	NOUN
ejpam-5848	253	2	[	[	X
ejpam-5848	253	3	1	1	NUM
ejpam-5848	253	4	]	]	X
ejpam-5848	253	5	w.f	w.f	PROPN
ejpam-5848	253	6	.	.	PUNCT
ejpam-5848	253	7	al	al	PROPN
ejpam-5848	253	8	-	-	PUNCT
ejpam-5848	253	9	omeri	omeri	NOUN
ejpam-5848	253	10	.	.	PUNCT
ejpam-5848	254	1	on	on	ADP
ejpam-5848	254	2	mixed	mixed	ADJ
ejpam-5848	254	3	b	b	NOUN
ejpam-5848	254	4	-	-	PUNCT
ejpam-5848	254	5	fuzzy	fuzzy	ADJ
ejpam-5848	254	6	topological	topological	ADJ
ejpam-5848	254	7	spaces	space	NOUN
ejpam-5848	254	8	.	.	PUNCT
ejpam-5848	255	1	international	international	ADJ
ejpam-5848	255	2	journal	journal	NOUN
ejpam-5848	255	3	of	of	ADP
ejpam-5848	255	4	fuzzy	fuzzy	ADJ
ejpam-5848	255	5	logic	logic	NOUN
ejpam-5848	255	6	and	and	CCONJ
ejpam-5848	255	7	intelligent	intelligent	ADJ
ejpam-5848	255	8	systems	system	NOUN
ejpam-5848	255	9	,	,	PUNCT
ejpam-5848	255	10	20(3):242–246	20(3):242–246	NUM
ejpam-5848	255	11	,	,	PUNCT
ejpam-5848	255	12	2020	2020	NUM
ejpam-5848	255	13	.	.	PUNCT
ejpam-5848	256	1	[	[	X
ejpam-5848	256	2	2	2	NUM
ejpam-5848	256	3	]	]	X
ejpam-5848	256	4	w.f	w.f	PROPN
ejpam-5848	256	5	.	.	PUNCT
ejpam-5848	256	6	al	al	PROPN
ejpam-5848	256	7	-	-	PUNCT
ejpam-5848	256	8	omeri	omeri	ADJ
ejpam-5848	256	9	,	,	PUNCT
ejpam-5848	256	10	o.h	o.h	PROPN
ejpam-5848	256	11	.	.	PROPN
ejpam-5848	256	12	khalil	khalil	PROPN
ejpam-5848	256	13	,	,	PUNCT
ejpam-5848	256	14	and	and	CCONJ
ejpam-5848	256	15	a.	a.	NOUN
ejpam-5848	256	16	ghareeb	ghareeb	PROPN
ejpam-5848	256	17	.	.	PUNCT
ejpam-5848	256	18	degree	degree	NOUN
ejpam-5848	256	19	of	of	ADP
ejpam-5848	256	20	(	(	PUNCT
ejpam-5848	256	21	l	l	NOUN
ejpam-5848	256	22	,	,	PUNCT
ejpam-5848	256	23	m)-fuzzy	m)-fuzzy	VERB
ejpam-5848	256	24	semiprecontinuous	semiprecontinuous	ADJ
ejpam-5848	256	25	and	and	CCONJ
ejpam-5848	256	26	(	(	PUNCT
ejpam-5848	256	27	l	l	NOUN
ejpam-5848	256	28	,	,	PUNCT
ejpam-5848	256	29	m)-fuzzy	m)-fuzzy	VERB
ejpam-5848	256	30	semi	semi	ADJ
ejpam-5848	256	31	-	-	ADJ
ejpam-5848	256	32	preirresolute	preirresolute	ADJ
ejpam-5848	256	33	functions	function	NOUN
ejpam-5848	256	34	.	.	PUNCT
ejpam-5848	257	1	demonstratio	demonstratio	PROPN
ejpam-5848	257	2	mathematica	mathematica	PROPN
ejpam-5848	257	3	,	,	PUNCT
ejpam-5848	257	4	51(1):182–197	51(1):182–197	PROPN
ejpam-5848	257	5	,	,	PUNCT
ejpam-5848	257	6	2018	2018	NUM
ejpam-5848	257	7	.	.	PUNCT
ejpam-5848	258	1	[	[	X
ejpam-5848	258	2	3	3	X
ejpam-5848	258	3	]	]	PUNCT
ejpam-5848	258	4	t.	t.	PROPN
ejpam-5848	258	5	m.	m.	PROPN
ejpam-5848	258	6	al	al	PROPN
ejpam-5848	258	7	-	-	PUNCT
ejpam-5848	258	8	shami	shami	PROPN
ejpam-5848	258	9	.	.	PUNCT
ejpam-5848	259	1	new	new	ADJ
ejpam-5848	259	2	soft	soft	ADJ
ejpam-5848	259	3	structure	structure	NOUN
ejpam-5848	259	4	:	:	PUNCT
ejpam-5848	259	5	infra	infra	NOUN
ejpam-5848	259	6	soft	soft	ADJ
ejpam-5848	259	7	topological	topological	ADJ
ejpam-5848	259	8	spaces	space	NOUN
ejpam-5848	259	9	.	.	PUNCT
ejpam-5848	260	1	mathematical	mathematical	ADJ
ejpam-5848	260	2	problems	problem	NOUN
ejpam-5848	260	3	in	in	ADP
ejpam-5848	260	4	engineering	engineering	NOUN
ejpam-5848	260	5	,	,	PUNCT
ejpam-5848	260	6	2021	2021	NUM
ejpam-5848	260	7	:	:	PUNCT
ejpam-5848	260	8	article	article	NOUN
ejpam-5848	260	9	i	i	PROPN
ejpam-5848	260	10	d	d	PROPN
ejpam-5848	260	11	3361604	3361604	NUM
ejpam-5848	260	12	,	,	PUNCT
ejpam-5848	260	13	12	12	NUM
ejpam-5848	260	14	pages	page	NOUN
ejpam-5848	260	15	,	,	PUNCT
ejpam-5848	260	16	2021	2021	NUM
ejpam-5848	260	17	.	.	PUNCT
ejpam-5848	261	1	[	[	X
ejpam-5848	261	2	4	4	X
ejpam-5848	261	3	]	]	PUNCT
ejpam-5848	261	4	t.	t.	PROPN
ejpam-5848	261	5	m.	m.	PROPN
ejpam-5848	261	6	al	al	PROPN
ejpam-5848	261	7	-	-	PUNCT
ejpam-5848	261	8	shami	shami	PROPN
ejpam-5848	261	9	and	and	CCONJ
ejpam-5848	261	10	m.	m.	PROPN
ejpam-5848	261	11	e.	e.	PROPN
ejpam-5848	261	12	el	el	PROPN
ejpam-5848	261	13	-	-	PROPN
ejpam-5848	261	14	shafei	shafei	PROPN
ejpam-5848	261	15	.	.	PUNCT
ejpam-5848	262	1	on	on	ADP
ejpam-5848	262	2	supra	supra	PROPN
ejpam-5848	262	3	soft	soft	ADJ
ejpam-5848	262	4	topological	topological	ADJ
ejpam-5848	262	5	ordered	order	VERB
ejpam-5848	262	6	spaces	space	NOUN
ejpam-5848	262	7	.	.	PUNCT
ejpam-5848	263	1	arab	arab	PROPN
ejpam-5848	263	2	journal	journal	PROPN
ejpam-5848	263	3	of	of	ADP
ejpam-5848	263	4	basic	basic	ADJ
ejpam-5848	263	5	and	and	CCONJ
ejpam-5848	263	6	applied	applied	ADJ
ejpam-5848	263	7	sciences	science	NOUN
ejpam-5848	263	8	,	,	PUNCT
ejpam-5848	263	9	26(1):433–445	26(1):433–445	NOUN
ejpam-5848	263	10	,	,	PUNCT
ejpam-5848	263	11	2019	2019	NUM
ejpam-5848	263	12	.	.	PUNCT
ejpam-5848	264	1	[	[	X
ejpam-5848	264	2	5	5	X
ejpam-5848	264	3	]	]	PUNCT
ejpam-5848	264	4	t.	t.	PROPN
ejpam-5848	264	5	m.	m.	PROPN
ejpam-5848	264	6	al	al	PROPN
ejpam-5848	264	7	-	-	PUNCT
ejpam-5848	264	8	shami	shami	PROPN
ejpam-5848	264	9	and	and	CCONJ
ejpam-5848	264	10	m.	m.	PROPN
ejpam-5848	264	11	e.	e.	PROPN
ejpam-5848	264	12	el	el	PROPN
ejpam-5848	264	13	-	-	PROPN
ejpam-5848	264	14	shafei	shafei	PROPN
ejpam-5848	264	15	.	.	PUNCT
ejpam-5848	265	1	two	two	NUM
ejpam-5848	265	2	types	type	NOUN
ejpam-5848	265	3	of	of	ADP
ejpam-5848	265	4	separation	separation	NOUN
ejpam-5848	265	5	axioms	axiom	NOUN
ejpam-5848	265	6	on	on	ADP
ejpam-5848	265	7	supra	supra	ADJ
ejpam-5848	265	8	soft	soft	ADJ
ejpam-5848	265	9	separation	separation	NOUN
ejpam-5848	265	10	spaces	space	NOUN
ejpam-5848	265	11	.	.	PUNCT
ejpam-5848	266	1	demonstratio	demonstratio	PROPN
ejpam-5848	266	2	mathematica	mathematica	PROPN
ejpam-5848	266	3	,	,	PUNCT
ejpam-5848	266	4	52(1):147–165	52(1):147–165	PROPN
ejpam-5848	266	5	,	,	PUNCT
ejpam-5848	266	6	2019	2019	NUM
ejpam-5848	266	7	.	.	PUNCT
ejpam-5848	267	1	[	[	X
ejpam-5848	267	2	6	6	NUM
ejpam-5848	267	3	]	]	X
ejpam-5848	267	4	t.m	t.m	PROPN
ejpam-5848	267	5	.	.	PROPN
ejpam-5848	267	6	al	al	PROPN
ejpam-5848	267	7	-	-	PUNCT
ejpam-5848	267	8	shami	shami	PROPN
ejpam-5848	267	9	.	.	PUNCT
ejpam-5848	268	1	compactness	compactness	NOUN
ejpam-5848	268	2	on	on	ADP
ejpam-5848	268	3	soft	soft	ADJ
ejpam-5848	268	4	topological	topological	ADJ
ejpam-5848	268	5	ordered	order	VERB
ejpam-5848	268	6	spaces	space	NOUN
ejpam-5848	268	7	and	and	CCONJ
ejpam-5848	268	8	its	its	PRON
ejpam-5848	268	9	application	application	NOUN
ejpam-5848	268	10	on	on	ADP
ejpam-5848	268	11	the	the	DET
ejpam-5848	268	12	information	information	NOUN
ejpam-5848	268	13	system	system	NOUN
ejpam-5848	268	14	.	.	PUNCT
ejpam-5848	269	1	journal	journal	NOUN
ejpam-5848	269	2	of	of	ADP
ejpam-5848	269	3	mathematics	mathematic	NOUN
ejpam-5848	269	4	,	,	PUNCT
ejpam-5848	269	5	2021:12	2021:12	NUM
ejpam-5848	269	6	,	,	PUNCT
ejpam-5848	269	7	2021	2021	NUM
ejpam-5848	269	8	.	.	PUNCT
ejpam-5848	270	1	[	[	X
ejpam-5848	270	2	7	7	X
ejpam-5848	270	3	]	]	X
ejpam-5848	270	4	t.m	t.m	PROPN
ejpam-5848	270	5	.	.	PROPN
ejpam-5848	270	6	al	al	PROPN
ejpam-5848	270	7	-	-	PUNCT
ejpam-5848	270	8	shami	shami	PROPN
ejpam-5848	270	9	.	.	PUNCT
ejpam-5848	271	1	improvement	improvement	NOUN
ejpam-5848	271	2	of	of	ADP
ejpam-5848	271	3	the	the	DET
ejpam-5848	271	4	approximations	approximation	NOUN
ejpam-5848	271	5	and	and	CCONJ
ejpam-5848	271	6	accuracy	accuracy	NOUN
ejpam-5848	271	7	measure	measure	NOUN
ejpam-5848	271	8	of	of	ADP
ejpam-5848	271	9	a	a	DET
ejpam-5848	271	10	rough	rough	ADJ
ejpam-5848	271	11	set	set	NOUN
ejpam-5848	271	12	using	use	VERB
ejpam-5848	271	13	somewhere	somewhere	ADV
ejpam-5848	271	14	dense	dense	ADJ
ejpam-5848	271	15	sets	set	NOUN
ejpam-5848	271	16	.	.	PUNCT
ejpam-5848	272	1	soft	soft	ADJ
ejpam-5848	272	2	computing	computing	NOUN
ejpam-5848	272	3	,	,	PUNCT
ejpam-5848	272	4	25(23):14449–14460	25(23):14449–14460	NUM
ejpam-5848	272	5	,	,	PUNCT
ejpam-5848	272	6	2021	2021	NUM
ejpam-5848	272	7	.	.	PUNCT
ejpam-5848	273	1	[	[	X
ejpam-5848	273	2	8	8	NUM
ejpam-5848	273	3	]	]	X
ejpam-5848	273	4	t.m	t.m	PROPN
ejpam-5848	273	5	.	.	PROPN
ejpam-5848	273	6	al	al	PROPN
ejpam-5848	273	7	-	-	PUNCT
ejpam-5848	273	8	shami	shami	PROPN
ejpam-5848	273	9	.	.	PUNCT
ejpam-5848	274	1	on	on	ADP
ejpam-5848	274	2	soft	soft	ADJ
ejpam-5848	274	3	separation	separation	NOUN
ejpam-5848	274	4	axioms	axiom	NOUN
ejpam-5848	274	5	and	and	CCONJ
ejpam-5848	274	6	their	their	PRON
ejpam-5848	274	7	applications	application	NOUN
ejpam-5848	274	8	on	on	ADP
ejpam-5848	274	9	decision	decision	NOUN
ejpam-5848	274	10	-	-	PUNCT
ejpam-5848	274	11	making	make	VERB
ejpam-5848	274	12	problem	problem	NOUN
ejpam-5848	274	13	.	.	PUNCT
ejpam-5848	275	1	mathematical	mathematical	ADJ
ejpam-5848	275	2	problems	problem	NOUN
ejpam-5848	275	3	in	in	ADP
ejpam-5848	275	4	engineering	engineering	NOUN
ejpam-5848	275	5	,	,	PUNCT
ejpam-5848	275	6	2021:12	2021:12	NUM
ejpam-5848	275	7	,	,	PUNCT
ejpam-5848	275	8	2021	2021	NUM
ejpam-5848	275	9	.	.	PUNCT
ejpam-5848	276	1	[	[	X
ejpam-5848	276	2	9	9	NUM
ejpam-5848	276	3	]	]	X
ejpam-5848	276	4	t.m	t.m	PROPN
ejpam-5848	276	5	.	.	PROPN
ejpam-5848	276	6	al	al	PROPN
ejpam-5848	276	7	-	-	PUNCT
ejpam-5848	276	8	shami	shami	PROPN
ejpam-5848	276	9	.	.	PUNCT
ejpam-5848	277	1	soft	soft	ADJ
ejpam-5848	277	2	somewhat	somewhat	ADV
ejpam-5848	277	3	open	open	ADJ
ejpam-5848	277	4	sets	set	NOUN
ejpam-5848	277	5	:	:	PUNCT
ejpam-5848	277	6	soft	soft	ADJ
ejpam-5848	277	7	separation	separation	NOUN
ejpam-5848	277	8	axioms	axiom	NOUN
ejpam-5848	277	9	and	and	CCONJ
ejpam-5848	277	10	medical	medical	ADJ
ejpam-5848	277	11	application	application	NOUN
ejpam-5848	277	12	to	to	ADP
ejpam-5848	277	13	nutrition	nutrition	NOUN
ejpam-5848	277	14	.	.	PUNCT
ejpam-5848	278	1	computational	computational	ADJ
ejpam-5848	278	2	and	and	CCONJ
ejpam-5848	278	3	applied	applied	ADJ
ejpam-5848	278	4	mathematics	mathematic	NOUN
ejpam-5848	278	5	,	,	PUNCT
ejpam-5848	278	6	41	41	NUM
ejpam-5848	278	7	,	,	PUNCT
ejpam-5848	278	8	2022	2022	NUM
ejpam-5848	278	9	.	.	PUNCT
ejpam-5848	279	1	[	[	X
ejpam-5848	279	2	10	10	NUM
ejpam-5848	279	3	]	]	X
ejpam-5848	279	4	t.m	t.m	PROPN
ejpam-5848	279	5	.	.	PROPN
ejpam-5848	279	6	al	al	PROPN
ejpam-5848	279	7	-	-	PUNCT
ejpam-5848	279	8	shami	shami	PROPN
ejpam-5848	279	9	.	.	PUNCT
ejpam-5848	280	1	topological	topological	ADJ
ejpam-5848	280	2	approach	approach	NOUN
ejpam-5848	280	3	to	to	PART
ejpam-5848	280	4	generate	generate	VERB
ejpam-5848	280	5	new	new	ADJ
ejpam-5848	280	6	rough	rough	ADJ
ejpam-5848	280	7	set	set	NOUN
ejpam-5848	280	8	models	model	NOUN
ejpam-5848	280	9	.	.	PUNCT
ejpam-5848	281	1	complex	complex	ADJ
ejpam-5848	281	2	&	&	CCONJ
ejpam-5848	281	3	intelligent	intelligent	ADJ
ejpam-5848	281	4	systems	system	NOUN
ejpam-5848	281	5	,	,	PUNCT
ejpam-5848	281	6	8:4101–4113	8:4101–4113	NUM
ejpam-5848	281	7	,	,	PUNCT
ejpam-5848	281	8	2022	2022	NUM
ejpam-5848	281	9	.	.	PUNCT
ejpam-5848	282	1	[	[	X
ejpam-5848	282	2	11	11	NUM
ejpam-5848	282	3	]	]	X
ejpam-5848	282	4	t.m	t.m	PROPN
ejpam-5848	282	5	.	.	PROPN
ejpam-5848	282	6	al	al	PROPN
ejpam-5848	282	7	-	-	PUNCT
ejpam-5848	282	8	shami	shami	PROPN
ejpam-5848	282	9	,	,	PUNCT
ejpam-5848	282	10	h.z	h.z	PROPN
ejpam-5848	282	11	.	.	PROPN
ejpam-5848	282	12	ibrahim	ibrahim	PROPN
ejpam-5848	282	13	,	,	PUNCT
ejpam-5848	282	14	a.	a.	NOUN
ejpam-5848	282	15	mhemdi	mhemdi	PROPN
ejpam-5848	282	16	,	,	PUNCT
ejpam-5848	282	17	and	and	CCONJ
ejpam-5848	282	18	radwan	radwan	VERB
ejpam-5848	282	19	abu	abu	PROPN
ejpam-5848	282	20	-	-	PUNCT
ejpam-5848	282	21	gdairi	gdairi	PROPN
ejpam-5848	282	22	.	.	PUNCT
ejpam-5848	283	1	nth	nth	PROPN
ejpam-5848	283	2	power	power	NOUN
ejpam-5848	283	3	root	root	NOUN
ejpam-5848	283	4	fuzzy	fuzzy	ADJ
ejpam-5848	283	5	sets	set	NOUN
ejpam-5848	283	6	and	and	CCONJ
ejpam-5848	283	7	its	its	PRON
ejpam-5848	283	8	topology	topology	NOUN
ejpam-5848	283	9	.	.	PUNCT
ejpam-5848	284	1	international	international	ADJ
ejpam-5848	284	2	journal	journal	PROPN
ejpam-5848	284	3	of	of	ADP
ejpam-5848	284	4	fuzzy	fuzzy	ADJ
ejpam-5848	284	5	logic	logic	NOUN
ejpam-5848	284	6	and	and	CCONJ
ejpam-5848	284	7	intelligent	intelligent	ADJ
ejpam-5848	284	8	systems	system	NOUN
ejpam-5848	284	9	,	,	PUNCT
ejpam-5848	284	10	22(4):350–365	22(4):350–365	NOUN
ejpam-5848	284	11	,	,	PUNCT
ejpam-5848	284	12	2022	2022	NUM
ejpam-5848	284	13	.	.	PUNCT
ejpam-5848	285	1	[	[	X
ejpam-5848	285	2	12	12	NUM
ejpam-5848	285	3	]	]	X
ejpam-5848	285	4	t.m	t.m	PROPN
ejpam-5848	285	5	.	.	PROPN
ejpam-5848	285	6	al	al	PROPN
ejpam-5848	285	7	-	-	PUNCT
ejpam-5848	285	8	shami	shami	PROPN
ejpam-5848	285	9	,	,	PUNCT
ejpam-5848	285	10	s.	s.	PROPN
ejpam-5848	285	11	kaur	kaur	PROPN
ejpam-5848	285	12	,	,	PUNCT
ejpam-5848	285	13	a.	a.	PROPN
ejpam-5848	285	14	özkan	özkan	PROPN
ejpam-5848	285	15	,	,	PUNCT
ejpam-5848	285	16	m.	m.	PROPN
ejpam-5848	285	17	hosny	hosny	PROPN
ejpam-5848	285	18	,	,	PUNCT
ejpam-5848	285	19	and	and	CCONJ
ejpam-5848	285	20	a.	a.	NOUN
ejpam-5848	285	21	mhemdi	mhemdi	PROPN
ejpam-5848	285	22	.	.	PUNCT
ejpam-5848	286	1	some	some	DET
ejpam-5848	286	2	characterizations	characterization	NOUN
ejpam-5848	286	3	of	of	ADP
ejpam-5848	286	4	soft	soft	ADJ
ejpam-5848	286	5	continuous	continuous	ADJ
ejpam-5848	286	6	mappings	mapping	NOUN
ejpam-5848	286	7	using	use	VERB
ejpam-5848	286	8	soft	soft	ADJ
ejpam-5848	286	9	graphs	graph	NOUN
ejpam-5848	286	10	.	.	PUNCT
ejpam-5848	287	1	filomat	filomat	NOUN
ejpam-5848	287	2	,	,	PUNCT
ejpam-5848	287	3	38(22):7823–7830	38(22):7823–7830	NUM
ejpam-5848	287	4	,	,	PUNCT
ejpam-5848	287	5	2024	2024	NUM
ejpam-5848	287	6	.	.	PUNCT
ejpam-5848	288	1	[	[	X
ejpam-5848	288	2	13	13	NUM
ejpam-5848	288	3	]	]	X
ejpam-5848	288	4	t.m	t.m	PROPN
ejpam-5848	288	5	.	.	PROPN
ejpam-5848	288	6	al	al	PROPN
ejpam-5848	288	7	-	-	PUNCT
ejpam-5848	288	8	shami	shami	PROPN
ejpam-5848	288	9	,	,	PUNCT
ejpam-5848	288	10	a.	a.	NOUN
ejpam-5848	288	11	rawshdeh	rawshdeh	PROPN
ejpam-5848	288	12	,	,	PUNCT
ejpam-5848	288	13	h.	h.	PROPN
ejpam-5848	288	14	al	al	PROPN
ejpam-5848	288	15	-	-	PUNCT
ejpam-5848	288	16	jarrah	jarrah	PROPN
ejpam-5848	288	17	,	,	PUNCT
ejpam-5848	288	18	and	and	CCONJ
ejpam-5848	288	19	a.	a.	NOUN
ejpam-5848	288	20	mhemdi	mhemdi	PROPN
ejpam-5848	288	21	.	.	PUNCT
ejpam-5848	289	1	connectedness	connectedness	NOUN
ejpam-5848	289	2	and	and	CCONJ
ejpam-5848	289	3	covering	cover	VERB
ejpam-5848	289	4	properties	property	NOUN
ejpam-5848	289	5	via	via	ADP
ejpam-5848	289	6	infra	infra	NOUN
ejpam-5848	289	7	topologies	topology	NOUN
ejpam-5848	289	8	with	with	ADP
ejpam-5848	289	9	application	application	NOUN
ejpam-5848	289	10	to	to	ADP
ejpam-5848	289	11	fixed	fix	VERB
ejpam-5848	289	12	point	point	NOUN
ejpam-5848	289	13	theorem	theorem	VERB
ejpam-5848	289	14	.	.	PUNCT
ejpam-5848	290	1	aims	aim	VERB
ejpam-5848	290	2	mathematics	mathematic	NOUN
ejpam-5848	290	3	,	,	PUNCT
ejpam-5848	290	4	8(4):8928–8948	8(4):8928–8948	PROPN
ejpam-5848	290	5	,	,	PUNCT
ejpam-5848	290	6	2023	2023	NUM
ejpam-5848	290	7	.	.	PUNCT
ejpam-5848	291	1	s.	s.	PROPN
ejpam-5848	291	2	kaur	kaur	PROPN
ejpam-5848	291	3	et	et	PROPN
ejpam-5848	291	4	al	al	PROPN
ejpam-5848	291	5	.	.	PUNCT
ejpam-5848	291	6	/	/	SYM
ejpam-5848	291	7	eur	eur	PROPN
ejpam-5848	291	8	.	.	PUNCT
ejpam-5848	292	1	j.	j.	PROPN
ejpam-5848	292	2	pure	pure	PROPN
ejpam-5848	292	3	appl	appl	PROPN
ejpam-5848	292	4	.	.	PROPN
ejpam-5848	292	5	math	math	PROPN
ejpam-5848	292	6	,	,	PUNCT
ejpam-5848	292	7	18	18	NUM
ejpam-5848	292	8	(	(	PUNCT
ejpam-5848	292	9	1	1	NUM
ejpam-5848	292	10	)	)	PUNCT
ejpam-5848	292	11	(	(	PUNCT
ejpam-5848	292	12	2025	2025	NUM
ejpam-5848	292	13	)	)	PUNCT
ejpam-5848	292	14	,	,	PUNCT
ejpam-5848	292	15	5848	5848	NUM
ejpam-5848	292	16	11	11	NUM
ejpam-5848	292	17	of	of	ADP
ejpam-5848	292	18	11	11	NUM
ejpam-5848	292	19	[	[	SYM
ejpam-5848	292	20	14	14	NUM
ejpam-5848	292	21	]	]	PUNCT
ejpam-5848	292	22	m.	m.	NOUN
ejpam-5848	292	23	alimohammady	alimohammady	PROPN
ejpam-5848	292	24	,	,	PUNCT
ejpam-5848	292	25	e.	e.	PROPN
ejpam-5848	292	26	ekici	ekici	PROPN
ejpam-5848	292	27	,	,	PUNCT
ejpam-5848	292	28	s.	s.	PROPN
ejpam-5848	292	29	jafari	jafari	PROPN
ejpam-5848	292	30	,	,	PUNCT
ejpam-5848	292	31	and	and	CCONJ
ejpam-5848	292	32	m.	m.	NOUN
ejpam-5848	292	33	roohi	roohi	PROPN
ejpam-5848	292	34	.	.	PUNCT
ejpam-5848	293	1	on	on	ADP
ejpam-5848	293	2	fuzzy	fuzzy	ADJ
ejpam-5848	293	3	upper	upper	ADJ
ejpam-5848	293	4	and	and	CCONJ
ejpam-5848	293	5	lower	low	ADJ
ejpam-5848	293	6	contra	contra	ADJ
ejpam-5848	293	7	-	-	ADJ
ejpam-5848	293	8	continuous	continuous	ADJ
ejpam-5848	293	9	multifunctions	multifunction	NOUN
ejpam-5848	293	10	.	.	PUNCT
ejpam-5848	294	1	iranian	iranian	ADJ
ejpam-5848	294	2	journal	journal	PROPN
ejpam-5848	294	3	of	of	ADP
ejpam-5848	294	4	fuzzy	fuzzy	ADJ
ejpam-5848	294	5	systems	system	NOUN
ejpam-5848	294	6	,	,	PUNCT
ejpam-5848	294	7	8(3):149–158	8(3):149–158	NUM
ejpam-5848	294	8	,	,	PUNCT
ejpam-5848	294	9	2011	2011	NUM
ejpam-5848	294	10	.	.	PUNCT
ejpam-5848	295	1	[	[	X
ejpam-5848	295	2	15	15	NUM
ejpam-5848	295	3	]	]	X
ejpam-5848	295	4	z.a	z.a	PROPN
ejpam-5848	295	5	.	.	PROPN
ejpam-5848	295	6	ameen	ameen	PROPN
ejpam-5848	295	7	,	,	PUNCT
ejpam-5848	295	8	r.a	r.a	PROPN
ejpam-5848	295	9	.	.	PROPN
ejpam-5848	295	10	mohammed	mohammed	PROPN
ejpam-5848	295	11	,	,	PUNCT
ejpam-5848	295	12	t.m	t.m	PROPN
ejpam-5848	295	13	.	.	PROPN
ejpam-5848	295	14	al	al	PROPN
ejpam-5848	295	15	-	-	PUNCT
ejpam-5848	295	16	shami	shami	PROPN
ejpam-5848	295	17	,	,	PUNCT
ejpam-5848	295	18	and	and	CCONJ
ejpam-5848	295	19	b.a	b.a	PROPN
ejpam-5848	295	20	.	.	PROPN
ejpam-5848	295	21	asaad	asaad	PROPN
ejpam-5848	295	22	.	.	PUNCT
ejpam-5848	296	1	novel	novel	ADJ
ejpam-5848	296	2	fuzzy	fuzzy	ADJ
ejpam-5848	296	3	topologies	topology	NOUN
ejpam-5848	296	4	formed	form	VERB
ejpam-5848	296	5	by	by	ADP
ejpam-5848	296	6	fuzzy	fuzzy	ADJ
ejpam-5848	296	7	primal	primal	ADJ
ejpam-5848	296	8	frameworks	framework	NOUN
ejpam-5848	296	9	.	.	PUNCT
ejpam-5848	297	1	journal	journal	NOUN
ejpam-5848	297	2	of	of	ADP
ejpam-5848	297	3	intelligent	intelligent	ADJ
ejpam-5848	297	4	&	&	CCONJ
ejpam-5848	297	5	fuzzy	fuzzy	ADJ
ejpam-5848	297	6	systems	system	NOUN
ejpam-5848	297	7	,	,	PUNCT
ejpam-5848	297	8	2024	2024	NUM
ejpam-5848	297	9	.	.	PUNCT
ejpam-5848	298	1	[	[	X
ejpam-5848	298	2	16	16	NUM
ejpam-5848	298	3	]	]	X
ejpam-5848	298	4	a.v	a.v	PROPN
ejpam-5848	298	5	.	.	PROPN
ejpam-5848	299	1	arkhangel’skii	arkhangel’skii	PROPN
ejpam-5848	299	2	and	and	CCONJ
ejpam-5848	299	3	v.i	v.i	PROPN
ejpam-5848	299	4	.	.	PROPN
ejpam-5848	299	5	ponomarev	ponomarev	PROPN
ejpam-5848	299	6	.	.	PUNCT
ejpam-5848	300	1	fundamentals	fundamental	NOUN
ejpam-5848	300	2	of	of	ADP
ejpam-5848	300	3	general	general	ADJ
ejpam-5848	300	4	topology	topology	NOUN
ejpam-5848	300	5	:	:	PUNCT
ejpam-5848	300	6	problems	problem	NOUN
ejpam-5848	300	7	and	and	CCONJ
ejpam-5848	300	8	exercises	exercise	NOUN
ejpam-5848	300	9	.	.	PUNCT
ejpam-5848	301	1	mathematics	mathematic	NOUN
ejpam-5848	301	2	and	and	CCONJ
ejpam-5848	301	3	its	its	PRON
ejpam-5848	301	4	applications	application	NOUN
ejpam-5848	301	5	.	.	PUNCT
ejpam-5848	302	1	hindustan	hindustan	PROPN
ejpam-5848	302	2	publishing	publishing	PROPN
ejpam-5848	302	3	corporation	corporation	PROPN
ejpam-5848	302	4	,	,	PUNCT
ejpam-5848	302	5	new	new	PROPN
ejpam-5848	302	6	delhi	delhi	PROPN
ejpam-5848	302	7	,	,	PUNCT
ejpam-5848	302	8	india	india	PROPN
ejpam-5848	302	9	,	,	PUNCT
ejpam-5848	302	10	1984	1984	NUM
ejpam-5848	302	11	.	.	PUNCT
ejpam-5848	303	1	[	[	X
ejpam-5848	303	2	17	17	NUM
ejpam-5848	303	3	]	]	X
ejpam-5848	303	4	c.l	c.l	PROPN
ejpam-5848	303	5	.	.	PROPN
ejpam-5848	303	6	chang	chang	PROPN
ejpam-5848	303	7	.	.	PUNCT
ejpam-5848	304	1	fuzzy	fuzzy	ADJ
ejpam-5848	304	2	topological	topological	ADJ
ejpam-5848	304	3	spaces	space	NOUN
ejpam-5848	304	4	.	.	PUNCT
ejpam-5848	305	1	journal	journal	PROPN
ejpam-5848	305	2	of	of	ADP
ejpam-5848	305	3	mathematical	mathematical	ADJ
ejpam-5848	305	4	analysis	analysis	NOUN
ejpam-5848	305	5	and	and	CCONJ
ejpam-5848	305	6	applications	application	NOUN
ejpam-5848	305	7	,	,	PUNCT
ejpam-5848	305	8	24:182–190	24:182–190	NUM
ejpam-5848	305	9	,	,	PUNCT
ejpam-5848	305	10	1968	1968	NUM
ejpam-5848	305	11	.	.	PUNCT
ejpam-5848	306	1	[	[	X
ejpam-5848	306	2	18	18	NUM
ejpam-5848	306	3	]	]	X
ejpam-5848	306	4	s.	s.	PROPN
ejpam-5848	306	5	demiralp	demiralp	PROPN
ejpam-5848	306	6	,	,	PUNCT
ejpam-5848	306	7	t.m	t.m	PROPN
ejpam-5848	306	8	.	.	PROPN
ejpam-5848	306	9	al	al	PROPN
ejpam-5848	306	10	-	-	PUNCT
ejpam-5848	306	11	shami	shami	PROPN
ejpam-5848	306	12	,	,	PUNCT
ejpam-5848	306	13	a.m.	a.m.	PROPN
ejpam-5848	307	1	abd	abd	PROPN
ejpam-5848	307	2	el	el	PROPN
ejpam-5848	307	3	-	-	PROPN
ejpam-5848	307	4	latif	latif	PROPN
ejpam-5848	307	5	,	,	PUNCT
ejpam-5848	307	6	and	and	CCONJ
ejpam-5848	307	7	f.a	f.a	PROPN
ejpam-5848	307	8	.	.	PROPN
ejpam-5848	308	1	abu	abu	PROPN
ejpam-5848	308	2	shaheen	shaheen	PROPN
ejpam-5848	308	3	.	.	PUNCT
ejpam-5848	309	1	topologically	topologically	ADV
ejpam-5848	309	2	indistinguishable	indistinguishable	ADJ
ejpam-5848	309	3	relations	relation	NOUN
ejpam-5848	309	4	and	and	CCONJ
ejpam-5848	309	5	separation	separation	NOUN
ejpam-5848	309	6	axioms	axiom	NOUN
ejpam-5848	309	7	.	.	PUNCT
ejpam-5848	310	1	aims	aim	VERB
ejpam-5848	310	2	mathematics	mathematic	NOUN
ejpam-5848	310	3	,	,	PUNCT
ejpam-5848	310	4	9(6):15701	9(6):15701	NUM
ejpam-5848	310	5	–	–	PUNCT
ejpam-5848	310	6	15723	15723	NUM
ejpam-5848	310	7	,	,	PUNCT
ejpam-5848	310	8	2024	2024	NUM
ejpam-5848	310	9	.	.	PUNCT
ejpam-5848	311	1	[	[	X
ejpam-5848	311	2	19	19	NUM
ejpam-5848	311	3	]	]	PUNCT
ejpam-5848	311	4	m.	m.	NOUN
ejpam-5848	311	5	hosny	hosny	PROPN
ejpam-5848	311	6	and	and	CCONJ
ejpam-5848	311	7	t.m	t.m	PROPN
ejpam-5848	311	8	.	.	PROPN
ejpam-5848	311	9	al	al	PROPN
ejpam-5848	311	10	-	-	PUNCT
ejpam-5848	311	11	shami	shami	PROPN
ejpam-5848	311	12	.	.	PUNCT
ejpam-5848	312	1	employing	employ	VERB
ejpam-5848	312	2	a	a	DET
ejpam-5848	312	3	generalization	generalization	NOUN
ejpam-5848	312	4	of	of	ADP
ejpam-5848	312	5	open	open	ADJ
ejpam-5848	312	6	sets	set	NOUN
ejpam-5848	312	7	defined	define	VERB
ejpam-5848	312	8	by	by	ADP
ejpam-5848	312	9	ideals	ideal	NOUN
ejpam-5848	312	10	to	to	PART
ejpam-5848	312	11	initiate	initiate	VERB
ejpam-5848	312	12	novel	novel	ADJ
ejpam-5848	312	13	rough	rough	ADJ
ejpam-5848	312	14	approximation	approximation	NOUN
ejpam-5848	312	15	spaces	space	NOUN
ejpam-5848	312	16	with	with	ADP
ejpam-5848	312	17	a	a	DET
ejpam-5848	312	18	chemical	chemical	NOUN
ejpam-5848	312	19	application	application	NOUN
ejpam-5848	312	20	.	.	PUNCT
ejpam-5848	313	1	european	european	ADJ
ejpam-5848	313	2	journal	journal	PROPN
ejpam-5848	313	3	of	of	ADP
ejpam-5848	313	4	pure	pure	ADJ
ejpam-5848	313	5	and	and	CCONJ
ejpam-5848	313	6	applied	applied	ADJ
ejpam-5848	313	7	mathematics	mathematic	NOUN
ejpam-5848	313	8	,	,	PUNCT
ejpam-5848	313	9	17(4):3436–3463	17(4):3436–3463	NUM
ejpam-5848	313	10	,	,	PUNCT
ejpam-5848	313	11	2024	2024	NUM
ejpam-5848	313	12	.	.	PUNCT
ejpam-5848	314	1	[	[	X
ejpam-5848	314	2	20	20	NUM
ejpam-5848	314	3	]	]	PUNCT
ejpam-5848	314	4	s.	s.	PROPN
ejpam-5848	314	5	kaur	kaur	PROPN
ejpam-5848	314	6	,	,	PUNCT
ejpam-5848	314	7	t.m	t.m	PROPN
ejpam-5848	314	8	.	.	PROPN
ejpam-5848	314	9	al	al	PROPN
ejpam-5848	314	10	-	-	PUNCT
ejpam-5848	314	11	shami	shami	PROPN
ejpam-5848	314	12	,	,	PUNCT
ejpam-5848	314	13	a.	a.	NOUN
ejpam-5848	314	14	ozkan	ozkan	PROPN
ejpam-5848	314	15	,	,	PUNCT
ejpam-5848	314	16	and	and	CCONJ
ejpam-5848	314	17	m.	m.	PROPN
ejpam-5848	314	18	hosny	hosny	PROPN
ejpam-5848	314	19	.	.	PUNCT
ejpam-5848	315	1	a	a	DET
ejpam-5848	315	2	new	new	ADJ
ejpam-5848	315	3	approach	approach	NOUN
ejpam-5848	315	4	to	to	ADP
ejpam-5848	315	5	soft	soft	ADJ
ejpam-5848	315	6	continuity	continuity	NOUN
ejpam-5848	315	7	.	.	PUNCT
ejpam-5848	316	1	mathematics	mathematic	NOUN
ejpam-5848	316	2	,	,	PUNCT
ejpam-5848	316	3	11:3164	11:3164	NUM
ejpam-5848	316	4	,	,	PUNCT
ejpam-5848	316	5	2023	2023	NUM
ejpam-5848	316	6	.	.	PUNCT
ejpam-5848	317	1	[	[	X
ejpam-5848	317	2	21	21	NUM
ejpam-5848	317	3	]	]	X
ejpam-5848	317	4	s.	s.	PROPN
ejpam-5848	317	5	kaur	kaur	PROPN
ejpam-5848	317	6	and	and	CCONJ
ejpam-5848	317	7	n.	n.	PROPN
ejpam-5848	317	8	goyal	goyal	PROPN
ejpam-5848	317	9	.	.	PUNCT
ejpam-5848	318	1	on	on	ADP
ejpam-5848	318	2	induced	induced	ADJ
ejpam-5848	318	3	map	map	NOUN
ejpam-5848	318	4	ψ	ψ	NOUN
ejpam-5848	318	5	#	#	NOUN
ejpam-5848	318	6	in	in	ADP
ejpam-5848	318	7	fuzzy	fuzzy	ADJ
ejpam-5848	318	8	set	set	NOUN
ejpam-5848	318	9	theory	theory	NOUN
ejpam-5848	318	10	and	and	CCONJ
ejpam-5848	318	11	its	its	PRON
ejpam-5848	318	12	applications	application	NOUN
ejpam-5848	318	13	,	,	PUNCT
ejpam-5848	318	14	n.d	n.d	PROPN
ejpam-5848	318	15	.	.	PUNCT
ejpam-5848	319	1	[	[	X
ejpam-5848	319	2	22	22	NUM
ejpam-5848	319	3	]	]	X
ejpam-5848	319	4	s.r	s.r	PROPN
ejpam-5848	319	5	.	.	PROPN
ejpam-5848	319	6	malghan	malghan	PROPN
ejpam-5848	319	7	and	and	CCONJ
ejpam-5848	319	8	s.s	s.s	PROPN
ejpam-5848	319	9	.	.	PROPN
ejpam-5848	319	10	benchalli	benchalli	PROPN
ejpam-5848	319	11	.	.	PUNCT
ejpam-5848	320	1	on	on	ADP
ejpam-5848	320	2	fuzzy	fuzzy	ADJ
ejpam-5848	320	3	topological	topological	ADJ
ejpam-5848	320	4	spaces	space	NOUN
ejpam-5848	320	5	.	.	PUNCT
ejpam-5848	321	1	glassnik	glassnik	PROPN
ejpam-5848	321	2	mathematicki	mathematicki	PROPN
ejpam-5848	321	3	,	,	PUNCT
ejpam-5848	321	4	16(36):313–325	16(36):313–325	NUM
ejpam-5848	321	5	,	,	PUNCT
ejpam-5848	321	6	1981	1981	NUM
ejpam-5848	321	7	.	.	PUNCT
ejpam-5848	322	1	[	[	X
ejpam-5848	322	2	23	23	NUM
ejpam-5848	322	3	]	]	X
ejpam-5848	322	4	s.r	s.r	PROPN
ejpam-5848	322	5	.	.	PROPN
ejpam-5848	322	6	malghan	malghan	PROPN
ejpam-5848	322	7	and	and	CCONJ
ejpam-5848	322	8	s.s	s.s	PROPN
ejpam-5848	322	9	.	.	PROPN
ejpam-5848	322	10	benchalli	benchalli	PROPN
ejpam-5848	322	11	.	.	PUNCT
ejpam-5848	323	1	open	open	ADJ
ejpam-5848	323	2	maps	map	NOUN
ejpam-5848	323	3	,	,	PUNCT
ejpam-5848	323	4	closed	closed	ADJ
ejpam-5848	323	5	maps	map	NOUN
ejpam-5848	323	6	and	and	CCONJ
ejpam-5848	323	7	local	local	ADJ
ejpam-5848	323	8	compactness	compactness	NOUN
ejpam-5848	323	9	in	in	ADP
ejpam-5848	323	10	fuzzy	fuzzy	ADJ
ejpam-5848	323	11	topological	topological	ADJ
ejpam-5848	323	12	spaces	space	NOUN
ejpam-5848	323	13	.	.	PUNCT
ejpam-5848	324	1	journal	journal	PROPN
ejpam-5848	324	2	of	of	ADP
ejpam-5848	324	3	mathematical	mathematical	ADJ
ejpam-5848	324	4	analysis	analysis	NOUN
ejpam-5848	324	5	and	and	CCONJ
ejpam-5848	324	6	applications	application	NOUN
ejpam-5848	324	7	,	,	PUNCT
ejpam-5848	324	8	99:338	99:338	NUM
ejpam-5848	324	9	–	–	PUNCT
ejpam-5848	324	10	349	349	NUM
ejpam-5848	324	11	,	,	PUNCT
ejpam-5848	324	12	1984	1984	NUM
ejpam-5848	324	13	.	.	PUNCT
ejpam-5848	325	1	[	[	X
ejpam-5848	325	2	24	24	NUM
ejpam-5848	325	3	]	]	X
ejpam-5848	325	4	n.	n.	PROPN
ejpam-5848	325	5	malik	malik	PROPN
ejpam-5848	325	6	,	,	PUNCT
ejpam-5848	325	7	m.	m.	NOUN
ejpam-5848	325	8	shabir	shabir	PROPN
ejpam-5848	325	9	,	,	PUNCT
ejpam-5848	325	10	t.	t.	PROPN
ejpam-5848	325	11	m.	m.	PROPN
ejpam-5848	325	12	al	al	PROPN
ejpam-5848	325	13	-	-	PUNCT
ejpam-5848	325	14	shami	shami	PROPN
ejpam-5848	325	15	,	,	PUNCT
ejpam-5848	325	16	r.	r.	PROPN
ejpam-5848	325	17	gul	gul	PROPN
ejpam-5848	325	18	,	,	PUNCT
ejpam-5848	325	19	and	and	CCONJ
ejpam-5848	325	20	m.	m.	NOUN
ejpam-5848	325	21	arar	arar	PROPN
ejpam-5848	325	22	.	.	PUNCT
ejpam-5848	326	1	a	a	DET
ejpam-5848	326	2	novel	novel	ADJ
ejpam-5848	326	3	decision	decision	NOUN
ejpam-5848	326	4	-	-	PUNCT
ejpam-5848	326	5	making	make	VERB
ejpam-5848	326	6	technique	technique	NOUN
ejpam-5848	326	7	based	base	VERB
ejpam-5848	326	8	on	on	ADP
ejpam-5848	326	9	t	t	PROPN
ejpam-5848	326	10	-	-	PUNCT
ejpam-5848	326	11	rough	rough	ADJ
ejpam-5848	326	12	bipolar	bipolar	ADJ
ejpam-5848	326	13	fuzzy	fuzzy	ADJ
ejpam-5848	326	14	sets	set	NOUN
ejpam-5848	326	15	.	.	PUNCT
ejpam-5848	327	1	journal	journal	NOUN
ejpam-5848	327	2	of	of	ADP
ejpam-5848	327	3	mathematics	mathematic	NOUN
ejpam-5848	327	4	and	and	CCONJ
ejpam-5848	327	5	computer	computer	NOUN
ejpam-5848	327	6	science	science	NOUN
ejpam-5848	327	7	,	,	PUNCT
ejpam-5848	327	8	33(3):275–289	33(3):275–289	PROPN
ejpam-5848	327	9	,	,	PUNCT
ejpam-5848	327	10	2024	2024	NUM
ejpam-5848	327	11	.	.	PUNCT
ejpam-5848	328	1	[	[	X
ejpam-5848	328	2	25	25	NUM
ejpam-5848	328	3	]	]	X
ejpam-5848	328	4	n.	n.	PROPN
ejpam-5848	328	5	malik	malik	PROPN
ejpam-5848	328	6	,	,	PUNCT
ejpam-5848	328	7	m.	m.	NOUN
ejpam-5848	328	8	shabir	shabir	PROPN
ejpam-5848	328	9	,	,	PUNCT
ejpam-5848	328	10	t.	t.	PROPN
ejpam-5848	328	11	m.	m.	PROPN
ejpam-5848	328	12	al	al	PROPN
ejpam-5848	328	13	-	-	PUNCT
ejpam-5848	328	14	shami	shami	PROPN
ejpam-5848	328	15	,	,	PUNCT
ejpam-5848	328	16	r.	r.	PROPN
ejpam-5848	328	17	gul	gul	PROPN
ejpam-5848	328	18	,	,	PUNCT
ejpam-5848	328	19	m.	m.	NOUN
ejpam-5848	328	20	arar	arar	PROPN
ejpam-5848	328	21	,	,	PUNCT
ejpam-5848	328	22	and	and	CCONJ
ejpam-5848	328	23	m.	m.	PROPN
ejpam-5848	328	24	hosny	hosny	PROPN
ejpam-5848	328	25	.	.	PUNCT
ejpam-5848	329	1	rough	rough	ADJ
ejpam-5848	329	2	bipolar	bipolar	ADJ
ejpam-5848	329	3	fuzzy	fuzzy	ADJ
ejpam-5848	329	4	ideals	ideal	NOUN
ejpam-5848	329	5	in	in	ADP
ejpam-5848	329	6	semigroups	semigroup	NOUN
ejpam-5848	329	7	.	.	PUNCT
ejpam-5848	330	1	complex	complex	ADJ
ejpam-5848	330	2	&	&	CCONJ
ejpam-5848	330	3	intelligent	intelligent	ADJ
ejpam-5848	330	4	systems	system	NOUN
ejpam-5848	330	5	,	,	PUNCT
ejpam-5848	330	6	9(6):7197–7212	9(6):7197–7212	PROPN
ejpam-5848	330	7	,	,	PUNCT
ejpam-5848	330	8	2023	2023	NUM
ejpam-5848	330	9	.	.	PUNCT
ejpam-5848	331	1	[	[	X
ejpam-5848	331	2	26	26	NUM
ejpam-5848	331	3	]	]	X
ejpam-5848	331	4	p.	p.	PROPN
ejpam-5848	331	5	pao	pao	PROPN
ejpam-5848	331	6	-	-	PROPN
ejpam-5848	331	7	ming	ming	PROPN
ejpam-5848	331	8	and	and	CCONJ
ejpam-5848	331	9	ying	ying	PROPN
ejpam-5848	331	10	-	-	PUNCT
ejpam-5848	331	11	ming	ming	PROPN
ejpam-5848	331	12	liu	liu	PROPN
ejpam-5848	331	13	.	.	PUNCT
ejpam-5848	331	14	fuzzy	fuzzy	ADJ
ejpam-5848	331	15	topology	topology	PROPN
ejpam-5848	331	16	i.	i.	PROPN
ejpam-5848	331	17	neighborhood	neighborhood	PROPN
ejpam-5848	331	18	structure	structure	NOUN
ejpam-5848	331	19	of	of	ADP
ejpam-5848	331	20	a	a	DET
ejpam-5848	331	21	fuzzy	fuzzy	ADJ
ejpam-5848	331	22	point	point	NOUN
ejpam-5848	331	23	and	and	CCONJ
ejpam-5848	331	24	moore	moore	PROPN
ejpam-5848	331	25	-	-	PUNCT
ejpam-5848	331	26	smith	smith	PROPN
ejpam-5848	331	27	convergence	convergence	NOUN
ejpam-5848	331	28	.	.	PUNCT
ejpam-5848	332	1	journal	journal	PROPN
ejpam-5848	332	2	of	of	ADP
ejpam-5848	332	3	mathematical	mathematical	ADJ
ejpam-5848	332	4	analysis	analysis	NOUN
ejpam-5848	332	5	and	and	CCONJ
ejpam-5848	332	6	applications	application	NOUN
ejpam-5848	332	7	,	,	PUNCT
ejpam-5848	332	8	76:571–599	76:571–599	NUM
ejpam-5848	332	9	,	,	PUNCT
ejpam-5848	332	10	1980	1980	NUM
ejpam-5848	332	11	.	.	PUNCT
ejpam-5848	333	1	[	[	X
ejpam-5848	333	2	27	27	NUM
ejpam-5848	333	3	]	]	X
ejpam-5848	333	4	s.	s.	PROPN
ejpam-5848	333	5	saleh	saleh	PROPN
ejpam-5848	333	6	,	,	PUNCT
ejpam-5848	333	7	r.	r.	PROPN
ejpam-5848	333	8	abu	abu	PROPN
ejpam-5848	333	9	-	-	PUNCT
ejpam-5848	333	10	gdairi	gdairi	PROPN
ejpam-5848	333	11	,	,	PUNCT
ejpam-5848	333	12	t.m	t.m	PROPN
ejpam-5848	333	13	.	.	PROPN
ejpam-5848	333	14	al	al	PROPN
ejpam-5848	333	15	-	-	PUNCT
ejpam-5848	333	16	shami	shami	PROPN
ejpam-5848	333	17	,	,	PUNCT
ejpam-5848	333	18	and	and	CCONJ
ejpam-5848	333	19	mohammed	mohammed	PROPN
ejpam-5848	333	20	s.	s.	PROPN
ejpam-5848	333	21	abdo	abdo	PROPN
ejpam-5848	333	22	.	.	PUNCT
ejpam-5848	334	1	on	on	ADP
ejpam-5848	334	2	categorical	categorical	ADJ
ejpam-5848	334	3	property	property	NOUN
ejpam-5848	334	4	of	of	ADP
ejpam-5848	334	5	fuzzy	fuzzy	ADJ
ejpam-5848	334	6	soft	soft	ADJ
ejpam-5848	334	7	topological	topological	ADJ
ejpam-5848	334	8	spaces	space	NOUN
ejpam-5848	334	9	.	.	PUNCT
ejpam-5848	335	1	applied	apply	VERB
ejpam-5848	335	2	mathematics	mathematics	PROPN
ejpam-5848	335	3	&	&	CCONJ
ejpam-5848	335	4	information	information	NOUN
ejpam-5848	335	5	sciences	sciences	PROPN
ejpam-5848	335	6	,	,	PUNCT
ejpam-5848	335	7	16(4):635–641	16(4):635–641	PROPN
ejpam-5848	335	8	,	,	PUNCT
ejpam-5848	335	9	2022	2022	NUM
ejpam-5848	335	10	.	.	PUNCT
ejpam-5848	336	1	[	[	X
ejpam-5848	336	2	28	28	NUM
ejpam-5848	336	3	]	]	X
ejpam-5848	336	4	s.	s.	PROPN
ejpam-5848	336	5	saleh	saleh	PROPN
ejpam-5848	336	6	,	,	PUNCT
ejpam-5848	336	7	t.m	t.m	PROPN
ejpam-5848	336	8	.	.	PROPN
ejpam-5848	336	9	al	al	PROPN
ejpam-5848	336	10	-	-	PUNCT
ejpam-5848	336	11	shami	shami	PROPN
ejpam-5848	336	12	,	,	PUNCT
ejpam-5848	336	13	and	and	CCONJ
ejpam-5848	336	14	a.	a.	NOUN
ejpam-5848	336	15	mhemdi	mhemdi	PROPN
ejpam-5848	336	16	.	.	PUNCT
ejpam-5848	337	1	on	on	ADP
ejpam-5848	337	2	some	some	DET
ejpam-5848	337	3	new	new	ADJ
ejpam-5848	337	4	types	type	NOUN
ejpam-5848	337	5	of	of	ADP
ejpam-5848	337	6	fuzzy	fuzzy	ADJ
ejpam-5848	337	7	soft	soft	ADJ
ejpam-5848	337	8	compact	compact	ADJ
ejpam-5848	337	9	spaces	space	NOUN
ejpam-5848	337	10	.	.	PUNCT
ejpam-5848	338	1	journal	journal	NOUN
ejpam-5848	338	2	of	of	ADP
ejpam-5848	338	3	mathematics	mathematic	NOUN
ejpam-5848	338	4	,	,	PUNCT
ejpam-5848	338	5	2023:8	2023:8	NUM
ejpam-5848	338	6	,	,	PUNCT
ejpam-5848	338	7	2023	2023	NUM
ejpam-5848	338	8	.	.	PUNCT
ejpam-5848	339	1	[	[	X
ejpam-5848	339	2	29	29	NUM
ejpam-5848	339	3	]	]	X
ejpam-5848	339	4	c.k	c.k	PROPN
ejpam-5848	339	5	.	.	PROPN
ejpam-5848	339	6	wong	wong	PROPN
ejpam-5848	339	7	.	.	PROPN
ejpam-5848	340	1	fuzzy	fuzzy	ADJ
ejpam-5848	340	2	points	point	NOUN
ejpam-5848	340	3	and	and	CCONJ
ejpam-5848	340	4	local	local	ADJ
ejpam-5848	340	5	properties	property	NOUN
ejpam-5848	340	6	of	of	ADP
ejpam-5848	340	7	fuzzy	fuzzy	ADJ
ejpam-5848	340	8	topology	topology	NOUN
ejpam-5848	340	9	.	.	PUNCT
ejpam-5848	341	1	journal	journal	PROPN
ejpam-5848	341	2	of	of	ADP
ejpam-5848	341	3	mathematical	mathematical	ADJ
ejpam-5848	341	4	analysis	analysis	NOUN
ejpam-5848	341	5	and	and	CCONJ
ejpam-5848	341	6	applications	application	NOUN
ejpam-5848	341	7	,	,	PUNCT
ejpam-5848	341	8	46:316–328	46:316–328	PROPN
ejpam-5848	341	9	,	,	PUNCT
ejpam-5848	341	10	1974	1974	NUM
ejpam-5848	341	11	.	.	PUNCT
ejpam-5848	342	1	[	[	X
ejpam-5848	342	2	30	30	NUM
ejpam-5848	342	3	]	]	X
ejpam-5848	342	4	l.a	l.a	PROPN
ejpam-5848	342	5	.	.	PROPN
ejpam-5848	342	6	zadeh	zadeh	PROPN
ejpam-5848	342	7	.	.	PUNCT
ejpam-5848	342	8	fuzzy	fuzzy	ADJ
ejpam-5848	342	9	sets	set	NOUN
ejpam-5848	342	10	.	.	PUNCT
ejpam-5848	343	1	information	information	NOUN
ejpam-5848	343	2	and	and	CCONJ
ejpam-5848	343	3	computation	computation	NOUN
ejpam-5848	343	4	,	,	PUNCT
ejpam-5848	343	5	8:338–353	8:338–353	NUM
ejpam-5848	343	6	,	,	PUNCT
ejpam-5848	343	7	1965	1965	NUM
ejpam-5848	343	8	.	.	PUNCT