id	sid	tid	token	lemma	pos
ejpam-6407	1	1	european	european	PROPN
ejpam-6407	1	2	journal	journal	PROPN
ejpam-6407	1	3	of	of	ADP
ejpam-6407	1	4	pure	pure	ADJ
ejpam-6407	1	5	and	and	CCONJ
ejpam-6407	1	6	applied	applied	ADJ
ejpam-6407	1	7	mathematics	mathematic	NOUN
ejpam-6407	1	8	2025	2025	NUM
ejpam-6407	1	9	,	,	PUNCT
ejpam-6407	1	10	vol	vol	NOUN
ejpam-6407	1	11	.	.	PROPN
ejpam-6407	1	12	18	18	NUM
ejpam-6407	1	13	,	,	PUNCT
ejpam-6407	1	14	issue	issue	NOUN
ejpam-6407	1	15	3	3	NUM
ejpam-6407	1	16	,	,	PUNCT
ejpam-6407	1	17	article	article	NOUN
ejpam-6407	1	18	number	number	NOUN
ejpam-6407	1	19	6407	6407	NUM
ejpam-6407	1	20	issn	issn	PROPN
ejpam-6407	1	21	1307	1307	NUM
ejpam-6407	1	22	-	-	SYM
ejpam-6407	1	23	5543	5543	NUM
ejpam-6407	1	24	–	–	PUNCT
ejpam-6407	1	25	ejpam.com	ejpam.com	X
ejpam-6407	1	26	published	publish	VERB
ejpam-6407	1	27	by	by	ADP
ejpam-6407	1	28	new	new	PROPN
ejpam-6407	1	29	york	york	PROPN
ejpam-6407	1	30	business	business	PROPN
ejpam-6407	1	31	global	global	ADJ
ejpam-6407	1	32	various	various	ADJ
ejpam-6407	1	33	types	type	NOUN
ejpam-6407	1	34	of	of	ADP
ejpam-6407	1	35	supra	supra	ADJ
ejpam-6407	1	36	ϵ-separation	ϵ-separation	NOUN
ejpam-6407	1	37	axioms	axiom	NOUN
ejpam-6407	1	38	and	and	CCONJ
ejpam-6407	1	39	relationships	relationship	NOUN
ejpam-6407	1	40	m.	m.	NOUN
ejpam-6407	1	41	aldawood	aldawood	PROPN
ejpam-6407	1	42	1	1	NUM
ejpam-6407	1	43	,	,	PUNCT
ejpam-6407	1	44	alaa	alaa	PROPN
ejpam-6407	1	45	m.	m.	PROPN
ejpam-6407	1	46	abd	abd	PROPN
ejpam-6407	1	47	el	el	PROPN
ejpam-6407	1	48	-	-	PUNCT
ejpam-6407	1	49	latif2	latif2	PROPN
ejpam-6407	1	50	,	,	PUNCT
ejpam-6407	1	51	khaled	khaled	ADJ
ejpam-6407	1	52	a.	a.	NOUN
ejpam-6407	1	53	aldwoah3	aldwoah3	PROPN
ejpam-6407	1	54	,	,	PUNCT
ejpam-6407	1	55	a.	a.	PROPN
ejpam-6407	1	56	a.	a.	PROPN
ejpam-6407	1	57	azzam1,4	azzam1,4	PROPN
ejpam-6407	1	58	,	,	PUNCT
ejpam-6407	1	59	abdelhalim	abdelhalim	PROPN
ejpam-6407	1	60	hasnaoui2,∗	hasnaoui2,∗	PROPN
ejpam-6407	1	61	,	,	PUNCT
ejpam-6407	1	62	m.	m.	NOUN
ejpam-6407	1	63	i.	i.	PROPN
ejpam-6407	1	64	elashiry2	elashiry2	PROPN
ejpam-6407	1	65	,	,	PUNCT
ejpam-6407	1	66	husham	husham	PROPN
ejpam-6407	1	67	m.	m.	PROPN
ejpam-6407	1	68	attaalfadeel2	attaalfadeel2	PROPN
ejpam-6407	1	69	,	,	PUNCT
ejpam-6407	1	70	enas	enas	PROPN
ejpam-6407	1	71	h.	h.	PROPN
ejpam-6407	1	72	elkordy1,5	elkordy1,5	PROPN
ejpam-6407	1	73	1	1	NUM
ejpam-6407	1	74	department	department	NOUN
ejpam-6407	1	75	of	of	ADP
ejpam-6407	1	76	mathematics	mathematic	NOUN
ejpam-6407	1	77	,	,	PUNCT
ejpam-6407	1	78	faculty	faculty	NOUN
ejpam-6407	1	79	of	of	ADP
ejpam-6407	1	80	science	science	NOUN
ejpam-6407	1	81	and	and	CCONJ
ejpam-6407	1	82	humanities	humanity	NOUN
ejpam-6407	1	83	,	,	PUNCT
ejpam-6407	1	84	prince	prince	PROPN
ejpam-6407	1	85	sattam	sattam	PROPN
ejpam-6407	1	86	bin	bin	PROPN
ejpam-6407	1	87	abdulaziz	abdulaziz	PROPN
ejpam-6407	1	88	university	university	PROPN
ejpam-6407	1	89	,	,	PUNCT
ejpam-6407	1	90	alkharj	alkharj	VERB
ejpam-6407	1	91	11942	11942	NUM
ejpam-6407	1	92	,	,	PUNCT
ejpam-6407	1	93	saudi	saudi	PROPN
ejpam-6407	1	94	arabia	arabia	PROPN
ejpam-6407	1	95	2	2	NUM
ejpam-6407	1	96	department	department	NOUN
ejpam-6407	1	97	of	of	ADP
ejpam-6407	1	98	mathematics	mathematic	NOUN
ejpam-6407	1	99	,	,	PUNCT
ejpam-6407	1	100	college	college	NOUN
ejpam-6407	1	101	of	of	ADP
ejpam-6407	1	102	science	science	NOUN
ejpam-6407	1	103	,	,	PUNCT
ejpam-6407	1	104	northern	northern	ADJ
ejpam-6407	1	105	border	border	NOUN
ejpam-6407	1	106	university	university	NOUN
ejpam-6407	1	107	,	,	PUNCT
ejpam-6407	1	108	arar	arar	NOUN
ejpam-6407	1	109	91431	91431	NUM
ejpam-6407	1	110	,	,	PUNCT
ejpam-6407	1	111	saudi	saudi	PROPN
ejpam-6407	1	112	arabia	arabia	PROPN
ejpam-6407	1	113	3	3	NUM
ejpam-6407	1	114	department	department	NOUN
ejpam-6407	1	115	of	of	ADP
ejpam-6407	1	116	mathematics	mathematic	NOUN
ejpam-6407	1	117	,	,	PUNCT
ejpam-6407	1	118	faculty	faculty	NOUN
ejpam-6407	1	119	of	of	ADP
ejpam-6407	1	120	science	science	NOUN
ejpam-6407	1	121	,	,	PUNCT
ejpam-6407	1	122	islamic	islamic	PROPN
ejpam-6407	1	123	university	university	PROPN
ejpam-6407	1	124	of	of	ADP
ejpam-6407	1	125	madinah	madinah	PROPN
ejpam-6407	1	126	,	,	PUNCT
ejpam-6407	1	127	medinah	medinah	PROPN
ejpam-6407	1	128	,	,	PUNCT
ejpam-6407	1	129	saudi	saudi	PROPN
ejpam-6407	1	130	arabia	arabia	PROPN
ejpam-6407	1	131	4	4	NUM
ejpam-6407	1	132	department	department	NOUN
ejpam-6407	1	133	of	of	ADP
ejpam-6407	1	134	mathematics	mathematic	NOUN
ejpam-6407	1	135	,	,	PUNCT
ejpam-6407	1	136	faculty	faculty	NOUN
ejpam-6407	1	137	of	of	ADP
ejpam-6407	1	138	science	science	NOUN
ejpam-6407	1	139	,	,	PUNCT
ejpam-6407	1	140	new	new	ADJ
ejpam-6407	1	141	valley	valley	NOUN
ejpam-6407	1	142	university	university	NOUN
ejpam-6407	1	143	,	,	PUNCT
ejpam-6407	1	144	elkharga	elkharga	NOUN
ejpam-6407	1	145	72511	72511	NUM
ejpam-6407	1	146	,	,	PUNCT
ejpam-6407	1	147	egypt	egypt	PROPN
ejpam-6407	1	148	5	5	NUM
ejpam-6407	1	149	mathematics	mathematic	NOUN
ejpam-6407	1	150	and	and	CCONJ
ejpam-6407	1	151	computer	computer	NOUN
ejpam-6407	1	152	science	science	PROPN
ejpam-6407	1	153	department	department	PROPN
ejpam-6407	1	154	,	,	PUNCT
ejpam-6407	1	155	faculty	faculty	NOUN
ejpam-6407	1	156	of	of	ADP
ejpam-6407	1	157	science	science	NOUN
ejpam-6407	1	158	,	,	PUNCT
ejpam-6407	1	159	beni	beni	ADJ
ejpam-6407	1	160	-	-	ADJ
ejpam-6407	1	161	suef	suef	ADJ
ejpam-6407	1	162	university	university	NOUN
ejpam-6407	1	163	,	,	PUNCT
ejpam-6407	1	164	beni	beni	ADJ
ejpam-6407	1	165	suef	suef	NOUN
ejpam-6407	1	166	,	,	PUNCT
ejpam-6407	1	167	egypt	egypt	PROPN
ejpam-6407	1	168	abstract	abstract	PROPN
ejpam-6407	1	169	.	.	PUNCT
ejpam-6407	2	1	this	this	DET
ejpam-6407	2	2	manuscript	manuscript	NOUN
ejpam-6407	2	3	presents	present	VERB
ejpam-6407	2	4	a	a	DET
ejpam-6407	2	5	new	new	ADJ
ejpam-6407	2	6	weaker	weak	ADJ
ejpam-6407	2	7	version	version	NOUN
ejpam-6407	2	8	of	of	ADP
ejpam-6407	2	9	supra	supra	PROPN
ejpam-6407	2	10	septarian	septarian	ADJ
ejpam-6407	2	11	axioms	axiom	NOUN
ejpam-6407	2	12	based	base	VERB
ejpam-6407	2	13	on	on	ADP
ejpam-6407	2	14	supra	supra	PROPN
ejpam-6407	2	15	ϵ-open	ϵ-open	PROPN
ejpam-6407	2	16	sets	set	NOUN
ejpam-6407	2	17	,	,	PUNCT
ejpam-6407	2	18	along	along	ADP
ejpam-6407	2	19	with	with	ADP
ejpam-6407	2	20	its	its	PRON
ejpam-6407	2	21	essential	essential	ADJ
ejpam-6407	2	22	features	feature	NOUN
ejpam-6407	2	23	,	,	PUNCT
ejpam-6407	2	24	which	which	PRON
ejpam-6407	2	25	are	be	AUX
ejpam-6407	2	26	called	call	VERB
ejpam-6407	2	27	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6407	2	28	-	-	PUNCT
ejpam-6407	2	29	space	space	NOUN
ejpam-6407	2	30	,	,	PUNCT
ejpam-6407	2	31	j	j	PROPN
ejpam-6407	2	32	=	=	SYM
ejpam-6407	2	33	0	0	NUM
ejpam-6407	2	34	,	,	PUNCT
ejpam-6407	2	35	1	1	NUM
ejpam-6407	2	36	,	,	PUNCT
ejpam-6407	2	37	2	2	NUM
ejpam-6407	2	38	,	,	PUNCT
ejpam-6407	2	39	in	in	ADP
ejpam-6407	2	40	the	the	DET
ejpam-6407	2	41	framework	framework	NOUN
ejpam-6407	2	42	of	of	ADP
ejpam-6407	2	43	supra	supra	PROPN
ejpam-6407	2	44	topological	topological	ADJ
ejpam-6407	2	45	spaces	space	NOUN
ejpam-6407	2	46	(	(	PUNCT
ejpam-6407	2	47	or	or	CCONJ
ejpam-6407	2	48	stss	stss	NOUN
ejpam-6407	2	49	)	)	PUNCT
ejpam-6407	2	50	.	.	PUNCT
ejpam-6407	3	1	we	we	PRON
ejpam-6407	3	2	give	give	VERB
ejpam-6407	3	3	comprehensive	comprehensive	ADJ
ejpam-6407	3	4	explanations	explanation	NOUN
ejpam-6407	3	5	of	of	ADP
ejpam-6407	3	6	each	each	DET
ejpam-6407	3	7	type	type	NOUN
ejpam-6407	3	8	of	of	ADP
ejpam-6407	3	9	them	they	PRON
ejpam-6407	3	10	,	,	PUNCT
ejpam-6407	3	11	backed	back	VERB
ejpam-6407	3	12	up	up	ADP
ejpam-6407	3	13	by	by	ADP
ejpam-6407	3	14	several	several	ADJ
ejpam-6407	3	15	examples	example	NOUN
ejpam-6407	3	16	and	and	CCONJ
ejpam-6407	3	17	counterexamples	counterexample	NOUN
ejpam-6407	3	18	that	that	PRON
ejpam-6407	3	19	highlight	highlight	VERB
ejpam-6407	3	20	the	the	DET
ejpam-6407	3	21	significance	significance	NOUN
ejpam-6407	3	22	of	of	ADP
ejpam-6407	3	23	our	our	PRON
ejpam-6407	3	24	original	original	ADJ
ejpam-6407	3	25	approaches	approach	NOUN
ejpam-6407	3	26	.	.	PUNCT
ejpam-6407	4	1	we	we	PRON
ejpam-6407	4	2	also	also	ADV
ejpam-6407	4	3	provide	provide	VERB
ejpam-6407	4	4	a	a	DET
ejpam-6407	4	5	diagram	diagram	NOUN
ejpam-6407	4	6	that	that	PRON
ejpam-6407	4	7	outlines	outline	VERB
ejpam-6407	4	8	these	these	DET
ejpam-6407	4	9	relationships	relationship	NOUN
ejpam-6407	4	10	.	.	PUNCT
ejpam-6407	5	1	additionally	additionally	ADV
ejpam-6407	5	2	,	,	PUNCT
ejpam-6407	5	3	we	we	PRON
ejpam-6407	5	4	present	present	VERB
ejpam-6407	5	5	the	the	DET
ejpam-6407	5	6	supra	supra	PROPN
ejpam-6407	5	7	ϵ-symmetric	ϵ-symmetric	ADJ
ejpam-6407	5	8	property	property	NOUN
ejpam-6407	5	9	and	and	CCONJ
ejpam-6407	5	10	supra	supra	ADJ
ejpam-6407	5	11	difference	difference	NOUN
ejpam-6407	5	12	property	property	NOUN
ejpam-6407	5	13	and	and	CCONJ
ejpam-6407	5	14	study	study	VERB
ejpam-6407	5	15	their	their	PRON
ejpam-6407	5	16	effects	effect	NOUN
ejpam-6407	5	17	on	on	ADP
ejpam-6407	5	18	these	these	DET
ejpam-6407	5	19	version	version	NOUN
ejpam-6407	5	20	of	of	ADP
ejpam-6407	5	21	supra-ϵ-septarian	supra-ϵ-septarian	ADJ
ejpam-6407	5	22	axioms	axiom	NOUN
ejpam-6407	5	23	.	.	PUNCT
ejpam-6407	6	1	in	in	ADP
ejpam-6407	6	2	especial	especial	NOUN
ejpam-6407	6	3	,	,	PUNCT
ejpam-6407	6	4	we	we	PRON
ejpam-6407	6	5	show	show	VERB
ejpam-6407	6	6	that	that	SCONJ
ejpam-6407	6	7	the	the	DET
ejpam-6407	6	8	two	two	NUM
ejpam-6407	6	9	concepts	concept	NOUN
ejpam-6407	6	10	of	of	ADP
ejpam-6407	6	11	supraϵ-t0	supraϵ-t0	NOUN
ejpam-6407	6	12	-	-	PUNCT
ejpam-6407	6	13	space	space	NOUN
ejpam-6407	6	14	and	and	CCONJ
ejpam-6407	6	15	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6407	6	16	-	-	PUNCT
ejpam-6407	6	17	space	space	NOUN
ejpam-6407	6	18	are	be	AUX
ejpam-6407	6	19	the	the	DET
ejpam-6407	6	20	same	same	ADJ
ejpam-6407	6	21	for	for	ADP
ejpam-6407	6	22	any	any	DET
ejpam-6407	6	23	sts	st	NOUN
ejpam-6407	6	24	that	that	PRON
ejpam-6407	6	25	fulfills	fulfill	VERB
ejpam-6407	6	26	supra	supra	PROPN
ejpam-6407	6	27	ϵ-symmetric	ϵ-symmetric	ADJ
ejpam-6407	6	28	property	property	NOUN
ejpam-6407	6	29	.	.	PUNCT
ejpam-6407	7	1	finally	finally	ADV
ejpam-6407	7	2	,	,	PUNCT
ejpam-6407	7	3	we	we	PRON
ejpam-6407	7	4	study	study	VERB
ejpam-6407	7	5	the	the	DET
ejpam-6407	7	6	supra	supra	PROPN
ejpam-6407	7	7	topological	topological	PROPN
ejpam-6407	7	8	and	and	CCONJ
ejpam-6407	7	9	supra	supra	ADJ
ejpam-6407	7	10	hereditary	hereditary	ADJ
ejpam-6407	7	11	properties	property	NOUN
ejpam-6407	7	12	for	for	ADP
ejpam-6407	7	13	each	each	PRON
ejpam-6407	7	14	of	of	ADP
ejpam-6407	7	15	the	the	DET
ejpam-6407	7	16	previously	previously	ADV
ejpam-6407	7	17	discussed	discuss	VERB
ejpam-6407	7	18	approaches	approach	NOUN
ejpam-6407	7	19	.	.	PUNCT
ejpam-6407	8	1	in	in	ADP
ejpam-6407	8	2	particular	particular	ADJ
ejpam-6407	8	3	,	,	PUNCT
ejpam-6407	8	4	we	we	PRON
ejpam-6407	8	5	show	show	VERB
ejpam-6407	8	6	that	that	SCONJ
ejpam-6407	8	7	the	the	DET
ejpam-6407	8	8	property	property	NOUN
ejpam-6407	8	9	of	of	ADP
ejpam-6407	8	10	being	be	AUX
ejpam-6407	8	11	a	a	DET
ejpam-6407	8	12	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6407	8	13	-	-	PUNCT
ejpam-6407	8	14	space	space	NOUN
ejpam-6407	8	15	,	,	PUNCT
ejpam-6407	8	16	where	where	SCONJ
ejpam-6407	8	17	j	j	PROPN
ejpam-6407	8	18	=	=	SYM
ejpam-6407	8	19	0	0	PROPN
ejpam-6407	8	20	,	,	PUNCT
ejpam-6407	8	21	1	1	NUM
ejpam-6407	8	22	,	,	PUNCT
ejpam-6407	8	23	2	2	NUM
ejpam-6407	8	24	,	,	PUNCT
ejpam-6407	8	25	is	be	AUX
ejpam-6407	8	26	a	a	DET
ejpam-6407	8	27	supra	supra	NOUN
ejpam-6407	8	28	-	-	PUNCT
ejpam-6407	8	29	hereditary	hereditary	ADJ
ejpam-6407	8	30	(	(	PUNCT
ejpam-6407	8	31	topological	topological	ADJ
ejpam-6407	8	32	)	)	PUNCT
ejpam-6407	8	33	property	property	NOUN
ejpam-6407	8	34	.	.	PUNCT
ejpam-6407	9	1	2020	2020	NUM
ejpam-6407	9	2	mathematics	mathematic	NOUN
ejpam-6407	9	3	subject	subject	NOUN
ejpam-6407	9	4	classifications	classification	NOUN
ejpam-6407	9	5	:	:	PUNCT
ejpam-6407	9	6	54a05	54a05	NUM
ejpam-6407	9	7	,	,	PUNCT
ejpam-6407	9	8	54c10	54c10	NUM
ejpam-6407	9	9	,	,	PUNCT
ejpam-6407	9	10	54d10	54d10	NUM
ejpam-6407	9	11	key	key	ADJ
ejpam-6407	9	12	words	word	NOUN
ejpam-6407	9	13	and	and	CCONJ
ejpam-6407	9	14	phrases	phrase	NOUN
ejpam-6407	9	15	:	:	PUNCT
ejpam-6407	9	16	supra	supra	ADJ
ejpam-6407	9	17	ϵ-separation	ϵ-separation	NOUN
ejpam-6407	9	18	axioms	axiom	NOUN
ejpam-6407	9	19	,	,	PUNCT
ejpam-6407	9	20	supra-ϵ-hausdorff	supra-ϵ-hausdorff	NOUN
ejpam-6407	9	21	-	-	PUNCT
ejpam-6407	9	22	space	space	NOUN
ejpam-6407	9	23	,	,	PUNCT
ejpam-6407	9	24	supra	supra	PROPN
ejpam-6407	9	25	ϵ-symmetric	ϵ-symmetric	ADJ
ejpam-6407	9	26	property	property	NOUN
ejpam-6407	9	27	∗corresponding	∗corresponde	VERB
ejpam-6407	9	28	author	author	NOUN
ejpam-6407	9	29	.	.	PUNCT
ejpam-6407	10	1	doi	doi	NOUN
ejpam-6407	10	2	:	:	PUNCT
ejpam-6407	10	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6407	https://doi.org/10.29020/nybg.ejpam.v18i3.6407	VERB
ejpam-6407	10	4	email	email	NOUN
ejpam-6407	10	5	addresses	address	NOUN
ejpam-6407	10	6	:	:	PUNCT
ejpam-6407	11	1	m.aldawood@psau.edu.sa	m.aldawood@psau.edu.sa	PROPN
ejpam-6407	11	2	(	(	PUNCT
ejpam-6407	11	3	m.	m.	NOUN
ejpam-6407	11	4	aldawood	aldawood	PROPN
ejpam-6407	11	5	)	)	PUNCT
ejpam-6407	11	6	,	,	PUNCT
ejpam-6407	11	7	alaa.ali@nbu.edu.sa	alaa.ali@nbu.edu.sa	PROPN
ejpam-6407	11	8	,	,	PUNCT
ejpam-6407	11	9	alaa−8560@yahoo.com	alaa−8560@yahoo.com	X
ejpam-6407	11	10	(	(	PUNCT
ejpam-6407	11	11	a.	a.	NOUN
ejpam-6407	11	12	m.	m.	PROPN
ejpam-6407	11	13	abd	abd	PROPN
ejpam-6407	11	14	el	el	PROPN
ejpam-6407	11	15	−	−	PROPN
ejpam-6407	11	16	latif	latif	PROPN
ejpam-6407	11	17	)	)	PUNCT
ejpam-6407	11	18	,	,	PUNCT
ejpam-6407	11	19	aldwoah@yahoo.com	aldwoah@yahoo.com	X
ejpam-6407	11	20	(	(	PUNCT
ejpam-6407	11	21	k.	k.	PROPN
ejpam-6407	11	22	a.	a.	PROPN
ejpam-6407	11	23	aldwoah	aldwoah	PROPN
ejpam-6407	11	24	)	)	PUNCT
ejpam-6407	11	25	,	,	PUNCT
ejpam-6407	11	26	aa.azzam@psau.edu.sa	aa.azzam@psau.edu.sa	PROPN
ejpam-6407	11	27	(	(	PUNCT
ejpam-6407	11	28	a.	a.	NOUN
ejpam-6407	11	29	a.	a.	PROPN
ejpam-6407	11	30	azzam	azzam	PROPN
ejpam-6407	11	31	)	)	PUNCT
ejpam-6407	11	32	,	,	PUNCT
ejpam-6407	11	33	abdllhalim.hasanawa@nbu.edu.sa	abdllhalim.hasanawa@nbu.edu.sa	PROPN
ejpam-6407	11	34	(	(	PUNCT
ejpam-6407	11	35	a.	a.	PROPN
ejpam-6407	11	36	hasnaoui	hasnaoui	PROPN
ejpam-6407	11	37	)	)	PUNCT
ejpam-6407	11	38	,	,	PUNCT
ejpam-6407	11	39	mustafa.elashiry@nbu.edu.sa	mustafa.elashiry@nbu.edu.sa	PROPN
ejpam-6407	11	40	(	(	PUNCT
ejpam-6407	11	41	m.	m.	NOUN
ejpam-6407	11	42	i.	i.	PROPN
ejpam-6407	11	43	elashiry	elashiry	PROPN
ejpam-6407	11	44	)	)	PUNCT
ejpam-6407	11	45	,	,	PUNCT
ejpam-6407	11	46	husham.alhassan@nbu.edu.sa	husham.alhassan@nbu.edu.sa	PROPN
ejpam-6407	11	47	(	(	PUNCT
ejpam-6407	11	48	h.	h.	PROPN
ejpam-6407	11	49	m.	m.	PROPN
ejpam-6407	11	50	attaalfadeel	attaalfadeel	PROPN
ejpam-6407	11	51	)	)	PUNCT
ejpam-6407	11	52	,	,	PUNCT
ejpam-6407	11	53	e.elkordy@psau.edu.sa	e.elkordy@psau.edu.sa	PROPN
ejpam-6407	11	54	(	(	PUNCT
ejpam-6407	11	55	e.	e.	PROPN
ejpam-6407	11	56	h.	h.	PROPN
ejpam-6407	11	57	elkordy	elkordy	PROPN
ejpam-6407	11	58	)	)	PUNCT
ejpam-6407	11	59	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6407	11	60	1	1	NUM
ejpam-6407	11	61	copyright	copyright	NOUN
ejpam-6407	11	62	:	:	PUNCT
ejpam-6407	11	63	©	©	PROPN
ejpam-6407	11	64	2025	2025	NUM
ejpam-6407	11	65	the	the	DET
ejpam-6407	11	66	author(s	author(s	NOUN
ejpam-6407	11	67	)	)	PUNCT
ejpam-6407	11	68	.	.	PUNCT
ejpam-6407	12	1	(	(	PUNCT
ejpam-6407	12	2	cc	cc	NOUN
ejpam-6407	12	3	by	by	ADP
ejpam-6407	12	4	-	-	PUNCT
ejpam-6407	12	5	nc	nc	PROPN
ejpam-6407	12	6	4.0	4.0	NUM
ejpam-6407	12	7	)	)	PUNCT
ejpam-6407	12	8	m.	m.	NOUN
ejpam-6407	12	9	aldawood	aldawood	NOUN
ejpam-6407	12	10	et	et	PROPN
ejpam-6407	12	11	al	al	PROPN
ejpam-6407	12	12	.	.	PUNCT
ejpam-6407	12	13	/	/	SYM
ejpam-6407	12	14	eur	eur	PROPN
ejpam-6407	12	15	.	.	PUNCT
ejpam-6407	13	1	j.	j.	PROPN
ejpam-6407	13	2	pure	pure	PROPN
ejpam-6407	13	3	appl	appl	PROPN
ejpam-6407	13	4	.	.	PROPN
ejpam-6407	13	5	math	math	PROPN
ejpam-6407	13	6	,	,	PUNCT
ejpam-6407	13	7	18	18	NUM
ejpam-6407	13	8	(	(	PUNCT
ejpam-6407	13	9	3	3	NUM
ejpam-6407	13	10	)	)	PUNCT
ejpam-6407	13	11	(	(	PUNCT
ejpam-6407	13	12	2025	2025	NUM
ejpam-6407	13	13	)	)	PUNCT
ejpam-6407	13	14	,	,	PUNCT
ejpam-6407	13	15	6407	6407	NUM
ejpam-6407	13	16	2	2	NUM
ejpam-6407	13	17	of	of	ADP
ejpam-6407	13	18	15	15	NUM
ejpam-6407	13	19	1	1	NUM
ejpam-6407	13	20	.	.	PUNCT
ejpam-6407	13	21	introduction	introduction	NOUN
ejpam-6407	13	22	the	the	DET
ejpam-6407	13	23	investigation	investigation	NOUN
ejpam-6407	13	24	of	of	ADP
ejpam-6407	13	25	different	different	ADJ
ejpam-6407	13	26	kinds	kind	NOUN
ejpam-6407	13	27	of	of	ADP
ejpam-6407	13	28	generalized	generalized	ADJ
ejpam-6407	13	29	open	open	ADJ
ejpam-6407	13	30	,	,	PUNCT
ejpam-6407	13	31	supra	supra	NOUN
ejpam-6407	13	32	open	open	ADJ
ejpam-6407	13	33	,	,	PUNCT
ejpam-6407	13	34	and	and	CCONJ
ejpam-6407	13	35	soft	soft	ADJ
ejpam-6407	13	36	open	open	ADJ
ejpam-6407	13	37	sets	set	NOUN
ejpam-6407	13	38	and	and	CCONJ
ejpam-6407	13	39	their	their	PRON
ejpam-6407	13	40	fundamental	fundamental	ADJ
ejpam-6407	13	41	features	feature	NOUN
ejpam-6407	13	42	has	have	AUX
ejpam-6407	13	43	played	play	VERB
ejpam-6407	13	44	a	a	DET
ejpam-6407	13	45	significant	significant	ADJ
ejpam-6407	13	46	role	role	NOUN
ejpam-6407	13	47	in	in	ADP
ejpam-6407	13	48	topological	topological	ADJ
ejpam-6407	13	49	,	,	PUNCT
ejpam-6407	13	50	supra	supra	PROPN
ejpam-6407	13	51	topological	topological	ADJ
ejpam-6407	13	52	,	,	PUNCT
ejpam-6407	13	53	and	and	CCONJ
ejpam-6407	13	54	soft	soft	ADJ
ejpam-6407	13	55	topological	topological	ADJ
ejpam-6407	13	56	research	research	NOUN
ejpam-6407	13	57	over	over	ADP
ejpam-6407	13	58	the	the	DET
ejpam-6407	13	59	past	past	ADJ
ejpam-6407	13	60	few	few	ADJ
ejpam-6407	13	61	decades	decade	NOUN
ejpam-6407	13	62	.	.	PUNCT
ejpam-6407	14	1	in	in	ADP
ejpam-6407	14	2	1963	1963	NUM
ejpam-6407	14	3	,	,	PUNCT
ejpam-6407	14	4	levine	levine	PROPN
ejpam-6407	14	5	[	[	X
ejpam-6407	14	6	1	1	NUM
ejpam-6407	14	7	]	]	PUNCT
ejpam-6407	14	8	first	first	ADV
ejpam-6407	14	9	proposed	propose	VERB
ejpam-6407	14	10	semi	semi	ADJ
ejpam-6407	14	11	-	-	ADJ
ejpam-6407	14	12	open	open	ADJ
ejpam-6407	14	13	sets	set	NOUN
ejpam-6407	14	14	(	(	PUNCT
ejpam-6407	14	15	continuity	continuity	NOUN
ejpam-6407	14	16	)	)	PUNCT
ejpam-6407	14	17	.	.	PUNCT
ejpam-6407	15	1	after	after	ADP
ejpam-6407	15	2	two	two	NUM
ejpam-6407	15	3	years	year	NOUN
ejpam-6407	15	4	,	,	PUNCT
ejpam-6407	15	5	njasta	njasta	NOUN
ejpam-6407	16	1	[	[	X
ejpam-6407	16	2	2	2	X
ejpam-6407	16	3	]	]	PUNCT
ejpam-6407	16	4	presented	present	VERB
ejpam-6407	16	5	the	the	DET
ejpam-6407	16	6	concept	concept	NOUN
ejpam-6407	16	7	of	of	ADP
ejpam-6407	16	8	α	α	NOUN
ejpam-6407	16	9	-	-	ADJ
ejpam-6407	16	10	open	open	ADJ
ejpam-6407	16	11	sets	set	NOUN
ejpam-6407	16	12	.	.	PUNCT
ejpam-6407	17	1	in	in	ADP
ejpam-6407	17	2	1982	1982	NUM
ejpam-6407	17	3	,	,	PUNCT
ejpam-6407	17	4	mashhour	mashhour	PROPN
ejpam-6407	17	5	et	et	PROPN
ejpam-6407	17	6	al	al	PROPN
ejpam-6407	17	7	.	.	PUNCT
ejpam-6407	18	1	[	[	X
ejpam-6407	18	2	3	3	NUM
ejpam-6407	18	3	]	]	PUNCT
ejpam-6407	18	4	provided	provide	VERB
ejpam-6407	18	5	the	the	DET
ejpam-6407	18	6	concept	concept	NOUN
ejpam-6407	18	7	of	of	ADP
ejpam-6407	18	8	pre	pre	ADJ
ejpam-6407	18	9	open	open	ADJ
ejpam-6407	18	10	sets	set	NOUN
ejpam-6407	18	11	(	(	PUNCT
ejpam-6407	18	12	pre	pre	X
ejpam-6407	18	13	continuity	continuity	NOUN
ejpam-6407	18	14	)	)	PUNCT
ejpam-6407	18	15	.	.	PUNCT
ejpam-6407	19	1	the	the	DET
ejpam-6407	19	2	notion	notion	NOUN
ejpam-6407	19	3	of	of	ADP
ejpam-6407	19	4	β	β	ADJ
ejpam-6407	19	5	-	-	ADJ
ejpam-6407	19	6	open	open	ADJ
ejpam-6407	19	7	sets	set	NOUN
ejpam-6407	19	8	(	(	PUNCT
ejpam-6407	19	9	β	β	NOUN
ejpam-6407	19	10	-	-	NOUN
ejpam-6407	19	11	continuity	continuity	NOUN
ejpam-6407	19	12	)	)	PUNCT
ejpam-6407	19	13	was	be	AUX
ejpam-6407	19	14	presented	present	VERB
ejpam-6407	19	15	by	by	ADP
ejpam-6407	19	16	abd	abd	PROPN
ejpam-6407	19	17	-	-	PUNCT
ejpam-6407	19	18	el	el	PROPN
ejpam-6407	19	19	-	-	PUNCT
ejpam-6407	19	20	monsef	monsef	ADJ
ejpam-6407	19	21	et	et	PROPN
ejpam-6407	19	22	al	al	PROPN
ejpam-6407	19	23	.	.	PUNCT
ejpam-6407	20	1	[	[	X
ejpam-6407	20	2	4	4	X
ejpam-6407	20	3	]	]	PUNCT
ejpam-6407	20	4	in	in	ADP
ejpam-6407	20	5	1983	1983	NUM
ejpam-6407	20	6	.	.	PUNCT
ejpam-6407	21	1	the	the	DET
ejpam-6407	21	2	definition	definition	NOUN
ejpam-6407	21	3	of	of	ADP
ejpam-6407	21	4	b	b	NOUN
ejpam-6407	21	5	-	-	PUNCT
ejpam-6407	21	6	open	open	ADJ
ejpam-6407	21	7	sets	set	NOUN
ejpam-6407	21	8	was	be	AUX
ejpam-6407	21	9	studied	study	VERB
ejpam-6407	21	10	in	in	ADP
ejpam-6407	21	11	detail	detail	NOUN
ejpam-6407	21	12	in	in	ADP
ejpam-6407	21	13	[	[	X
ejpam-6407	21	14	5	5	NUM
ejpam-6407	21	15	,	,	PUNCT
ejpam-6407	21	16	6	6	NUM
ejpam-6407	21	17	]	]	PUNCT
ejpam-6407	21	18	in	in	ADP
ejpam-6407	21	19	1966	1966	NUM
ejpam-6407	21	20	.	.	PUNCT
ejpam-6407	22	1	based	base	VERB
ejpam-6407	22	2	on	on	ADP
ejpam-6407	22	3	[	[	X
ejpam-6407	22	4	7	7	NUM
ejpam-6407	22	5	]	]	PUNCT
ejpam-6407	22	6	,	,	PUNCT
ejpam-6407	22	7	piotrowski	piotrowski	NOUN
ejpam-6407	22	8	[	[	X
ejpam-6407	22	9	8	8	NUM
ejpam-6407	22	10	]	]	PUNCT
ejpam-6407	22	11	presented	present	VERB
ejpam-6407	22	12	the	the	DET
ejpam-6407	22	13	notion	notion	NOUN
ejpam-6407	22	14	of	of	ADP
ejpam-6407	22	15	somewhat	somewhat	ADV
ejpam-6407	22	16	open	open	ADJ
ejpam-6407	22	17	sets	set	NOUN
ejpam-6407	22	18	(	(	PUNCT
ejpam-6407	22	19	continuity	continuity	NOUN
ejpam-6407	22	20	)	)	PUNCT
ejpam-6407	22	21	.	.	PUNCT
ejpam-6407	23	1	the	the	DET
ejpam-6407	23	2	approach	approach	NOUN
ejpam-6407	23	3	of	of	ADP
ejpam-6407	23	4	somewhere	somewhere	ADJ
ejpam-6407	23	5	dense	dense	ADJ
ejpam-6407	23	6	sets	set	NOUN
ejpam-6407	23	7	(	(	PUNCT
ejpam-6407	23	8	or	or	CCONJ
ejpam-6407	23	9	sd	sd	NOUN
ejpam-6407	23	10	-	-	PUNCT
ejpam-6407	23	11	sets	set	NOUN
ejpam-6407	23	12	)	)	PUNCT
ejpam-6407	23	13	was	be	AUX
ejpam-6407	23	14	proposed	propose	VERB
ejpam-6407	23	15	in	in	ADP
ejpam-6407	23	16	[	[	X
ejpam-6407	23	17	9	9	NUM
ejpam-6407	23	18	,	,	PUNCT
ejpam-6407	23	19	10	10	NUM
ejpam-6407	23	20	]	]	PUNCT
ejpam-6407	23	21	.	.	PUNCT
ejpam-6407	24	1	additional	additional	ADJ
ejpam-6407	24	2	facets	facet	NOUN
ejpam-6407	24	3	of	of	ADP
ejpam-6407	24	4	this	this	DET
ejpam-6407	24	5	idea	idea	NOUN
ejpam-6407	24	6	were	be	AUX
ejpam-6407	24	7	examined	examine	VERB
ejpam-6407	24	8	in	in	ADP
ejpam-6407	24	9	[	[	X
ejpam-6407	24	10	11	11	NUM
ejpam-6407	24	11	]	]	PUNCT
ejpam-6407	24	12	.	.	PUNCT
ejpam-6407	25	1	alqahtani	alqahtani	PROPN
ejpam-6407	25	2	introduced	introduce	VERB
ejpam-6407	25	3	the	the	DET
ejpam-6407	25	4	approach	approach	NOUN
ejpam-6407	25	5	of	of	ADP
ejpam-6407	25	6	f	f	NOUN
ejpam-6407	25	7	-	-	PUNCT
ejpam-6407	25	8	open	open	VERB
ejpam-6407	25	9	[	[	X
ejpam-6407	25	10	12	12	NUM
ejpam-6407	25	11	]	]	PUNCT
ejpam-6407	25	12	.	.	PUNCT
ejpam-6407	26	1	the	the	DET
ejpam-6407	26	2	n	n	CCONJ
ejpam-6407	26	3	-open	-open	PROPN
ejpam-6407	26	4	sets	set	NOUN
ejpam-6407	26	5	approach	approach	NOUN
ejpam-6407	26	6	was	be	AUX
ejpam-6407	26	7	presented	present	VERB
ejpam-6407	26	8	by	by	ADP
ejpam-6407	26	9	alqahtani	alqahtani	PROPN
ejpam-6407	26	10	and	and	CCONJ
ejpam-6407	26	11	abd	abd	PROPN
ejpam-6407	26	12	el	el	PROPN
ejpam-6407	26	13	-	-	PROPN
ejpam-6407	26	14	latif	latif	PROPN
ejpam-6407	26	15	[	[	X
ejpam-6407	26	16	13	13	NUM
ejpam-6407	26	17	]	]	PUNCT
ejpam-6407	26	18	in	in	ADP
ejpam-6407	26	19	2024	2024	NUM
ejpam-6407	26	20	,	,	PUNCT
ejpam-6407	26	21	and	and	CCONJ
ejpam-6407	26	22	it	it	PRON
ejpam-6407	26	23	is	be	AUX
ejpam-6407	26	24	generalized	generalize	VERB
ejpam-6407	26	25	almost	almost	ADV
ejpam-6407	26	26	all	all	PRON
ejpam-6407	26	27	of	of	ADP
ejpam-6407	26	28	the	the	DET
ejpam-6407	26	29	earlier	early	ADJ
ejpam-6407	26	30	concepts	concept	NOUN
ejpam-6407	26	31	.	.	PUNCT
ejpam-6407	27	1	alghamdi	alghamdi	NOUN
ejpam-6407	27	2	et	et	PROPN
ejpam-6407	27	3	al	al	PROPN
ejpam-6407	27	4	.	.	PROPN
ejpam-6407	27	5	provided	provide	VERB
ejpam-6407	27	6	new	new	ADJ
ejpam-6407	27	7	types	type	NOUN
ejpam-6407	27	8	of	of	ADP
ejpam-6407	27	9	operators	operator	NOUN
ejpam-6407	27	10	in	in	ADP
ejpam-6407	27	11	context	context	NOUN
ejpam-6407	27	12	of	of	ADP
ejpam-6407	27	13	primal	primal	ADJ
ejpam-6407	27	14	topological	topological	ADJ
ejpam-6407	27	15	spaces	space	NOUN
ejpam-6407	27	16	[	[	X
ejpam-6407	27	17	14	14	NUM
ejpam-6407	27	18	]	]	PUNCT
ejpam-6407	27	19	.	.	PUNCT
ejpam-6407	28	1	the	the	DET
ejpam-6407	28	2	concept	concept	NOUN
ejpam-6407	28	3	of	of	ADP
ejpam-6407	28	4	supra	supra	PROPN
ejpam-6407	28	5	open	open	ADJ
ejpam-6407	28	6	sets	set	NOUN
ejpam-6407	28	7	,	,	PUNCT
ejpam-6407	28	8	which	which	PRON
ejpam-6407	28	9	take	take	VERB
ejpam-6407	28	10	into	into	ADP
ejpam-6407	28	11	account	account	NOUN
ejpam-6407	28	12	the	the	DET
ejpam-6407	28	13	fundamental	fundamental	ADJ
ejpam-6407	28	14	components	component	NOUN
ejpam-6407	28	15	of	of	ADP
ejpam-6407	28	16	supra	supra	PROPN
ejpam-6407	28	17	topology	topology	NOUN
ejpam-6407	28	18	(	(	PUNCT
ejpam-6407	28	19	or	or	CCONJ
ejpam-6407	28	20	sts	st	NOUN
ejpam-6407	28	21	)	)	PUNCT
ejpam-6407	28	22	,	,	PUNCT
ejpam-6407	28	23	was	be	AUX
ejpam-6407	28	24	introduced	introduce	VERB
ejpam-6407	28	25	by	by	ADP
ejpam-6407	28	26	mashhour	mashhour	PROPN
ejpam-6407	28	27	et	et	PROPN
ejpam-6407	28	28	al	al	PROPN
ejpam-6407	28	29	.	.	PUNCT
ejpam-6407	29	1	[	[	X
ejpam-6407	29	2	15	15	NUM
ejpam-6407	29	3	]	]	PUNCT
ejpam-6407	29	4	.	.	PUNCT
ejpam-6407	30	1	among	among	ADP
ejpam-6407	30	2	the	the	DET
ejpam-6407	30	3	basic	basic	ADJ
ejpam-6407	30	4	topological	topological	ADJ
ejpam-6407	30	5	concepts	concept	NOUN
ejpam-6407	30	6	they	they	PRON
ejpam-6407	30	7	developed	develop	VERB
ejpam-6407	30	8	were	be	AUX
ejpam-6407	30	9	the	the	DET
ejpam-6407	30	10	separation	separation	NOUN
ejpam-6407	30	11	axioms	axiom	NOUN
ejpam-6407	30	12	,	,	PUNCT
ejpam-6407	30	13	continuity	continuity	NOUN
ejpam-6407	30	14	,	,	PUNCT
ejpam-6407	30	15	and	and	CCONJ
ejpam-6407	30	16	closure	closure	NOUN
ejpam-6407	30	17	(	(	PUNCT
ejpam-6407	30	18	interior	interior	ADJ
ejpam-6407	30	19	)	)	PUNCT
ejpam-6407	30	20	operators	operator	NOUN
ejpam-6407	30	21	.	.	PUNCT
ejpam-6407	31	1	along	along	ADP
ejpam-6407	31	2	with	with	ADP
ejpam-6407	31	3	their	their	PRON
ejpam-6407	31	4	key	key	ADJ
ejpam-6407	31	5	characteristics	characteristic	NOUN
ejpam-6407	31	6	,	,	PUNCT
ejpam-6407	31	7	the	the	DET
ejpam-6407	31	8	notions	notion	NOUN
ejpam-6407	31	9	of	of	ADP
ejpam-6407	31	10	supra	supra	PROPN
ejpam-6407	31	11	semi[16	semi[16	PROPN
ejpam-6407	31	12	]	]	PUNCT
ejpam-6407	31	13	(	(	PUNCT
ejpam-6407	31	14	r[17	r[17	PROPN
ejpam-6407	31	15	]	]	PUNCT
ejpam-6407	31	16	,	,	PUNCT
ejpam-6407	31	17	β[18	β[18	PROPN
ejpam-6407	31	18	]	]	PUNCT
ejpam-6407	31	19	,	,	PUNCT
ejpam-6407	31	20	b[19	b[19	PROPN
ejpam-6407	31	21	]	]	X
ejpam-6407	31	22	,	,	PUNCT
ejpam-6407	31	23	pre[20	pre[20	X
ejpam-6407	31	24	]	]	PUNCT
ejpam-6407	31	25	,	,	PUNCT
ejpam-6407	31	26	and	and	CCONJ
ejpam-6407	31	27	α	α	X
ejpam-6407	32	1	[	[	X
ejpam-6407	32	2	21	21	NUM
ejpam-6407	32	3	]	]	PUNCT
ejpam-6407	32	4	)	)	PUNCT
ejpam-6407	32	5	open	open	ADJ
ejpam-6407	32	6	sets	set	NOUN
ejpam-6407	32	7	have	have	AUX
ejpam-6407	32	8	been	be	AUX
ejpam-6407	32	9	presented	present	VERB
ejpam-6407	32	10	.	.	PUNCT
ejpam-6407	33	1	abd	abd	PROPN
ejpam-6407	33	2	el	el	PROPN
ejpam-6407	33	3	-	-	PROPN
ejpam-6407	33	4	latif	latif	PROPN
ejpam-6407	33	5	et	et	PROPN
ejpam-6407	33	6	al	al	PROPN
ejpam-6407	33	7	.	.	PUNCT
ejpam-6407	34	1	[	[	X
ejpam-6407	34	2	22	22	NUM
ejpam-6407	34	3	]	]	PUNCT
ejpam-6407	34	4	proposed	propose	VERB
ejpam-6407	34	5	the	the	DET
ejpam-6407	34	6	concept	concept	NOUN
ejpam-6407	34	7	of	of	ADP
ejpam-6407	34	8	supra	supra	PROPN
ejpam-6407	34	9	ϵ-open	ϵ-open	PROPN
ejpam-6407	34	10	sets	set	NOUN
ejpam-6407	34	11	in	in	ADP
ejpam-6407	34	12	stss	stss	NOUN
ejpam-6407	34	13	.	.	PUNCT
ejpam-6407	35	1	he	he	PRON
ejpam-6407	35	2	and	and	CCONJ
ejpam-6407	35	3	his	his	PRON
ejpam-6407	35	4	coauthors	coauthor	NOUN
ejpam-6407	35	5	[	[	X
ejpam-6407	35	6	23	23	NUM
ejpam-6407	35	7	]	]	PUNCT
ejpam-6407	35	8	used	use	VERB
ejpam-6407	35	9	this	this	DET
ejpam-6407	35	10	concept	concept	NOUN
ejpam-6407	35	11	to	to	PART
ejpam-6407	35	12	investigate	investigate	VERB
ejpam-6407	35	13	new	new	ADJ
ejpam-6407	35	14	forms	form	NOUN
ejpam-6407	35	15	of	of	ADP
ejpam-6407	35	16	supra	supra	ADJ
ejpam-6407	35	17	continuity	continuity	NOUN
ejpam-6407	35	18	.	.	PUNCT
ejpam-6407	36	1	the	the	DET
ejpam-6407	36	2	field	field	NOUN
ejpam-6407	36	3	of	of	ADP
ejpam-6407	36	4	broadly	broadly	ADV
ejpam-6407	36	5	applicable	applicable	ADJ
ejpam-6407	36	6	soft	soft	ADJ
ejpam-6407	36	7	open	open	ADJ
ejpam-6407	36	8	sets	set	NOUN
ejpam-6407	36	9	[	[	X
ejpam-6407	36	10	24	24	NUM
ejpam-6407	36	11	,	,	PUNCT
ejpam-6407	36	12	25	25	NUM
ejpam-6407	36	13	]	]	PUNCT
ejpam-6407	36	14	,	,	PUNCT
ejpam-6407	36	15	soft	soft	ADJ
ejpam-6407	36	16	semi	semi	ADJ
ejpam-6407	36	17	-	-	ADJ
ejpam-6407	36	18	open	open	ADJ
ejpam-6407	36	19	sets	set	NOUN
ejpam-6407	36	20	[	[	X
ejpam-6407	36	21	26	26	NUM
ejpam-6407	36	22	,	,	PUNCT
ejpam-6407	36	23	27	27	NUM
ejpam-6407	36	24	]	]	PUNCT
ejpam-6407	36	25	,	,	PUNCT
ejpam-6407	36	26	various	various	ADJ
ejpam-6407	36	27	kinds	kind	NOUN
ejpam-6407	36	28	of	of	ADP
ejpam-6407	36	29	soft	soft	ADJ
ejpam-6407	36	30	continuity	continuity	NOUN
ejpam-6407	36	31	[	[	X
ejpam-6407	36	32	28	28	NUM
ejpam-6407	36	33	,	,	PUNCT
ejpam-6407	36	34	29	29	NUM
ejpam-6407	36	35	]	]	PUNCT
ejpam-6407	36	36	,	,	PUNCT
ejpam-6407	36	37	soft	soft	ADJ
ejpam-6407	36	38	sd	sd	NOUN
ejpam-6407	36	39	-	-	PUNCT
ejpam-6407	36	40	sets	set	NOUN
ejpam-6407	36	41	[	[	X
ejpam-6407	36	42	30	30	NUM
ejpam-6407	36	43	,	,	PUNCT
ejpam-6407	36	44	31	31	NUM
ejpam-6407	36	45	]	]	PUNCT
ejpam-6407	36	46	,	,	PUNCT
ejpam-6407	36	47	and	and	CCONJ
ejpam-6407	36	48	nearly	nearly	ADV
ejpam-6407	36	49	soft	soft	ADJ
ejpam-6407	36	50	β	β	ADJ
ejpam-6407	36	51	-	-	ADJ
ejpam-6407	36	52	open	open	ADJ
ejpam-6407	36	53	sets	set	NOUN
ejpam-6407	36	54	[	[	X
ejpam-6407	36	55	32	32	NUM
ejpam-6407	36	56	]	]	PUNCT
ejpam-6407	36	57	has	have	AUX
ejpam-6407	36	58	produced	produce	VERB
ejpam-6407	36	59	a	a	DET
ejpam-6407	36	60	variety	variety	NOUN
ejpam-6407	36	61	of	of	ADP
ejpam-6407	36	62	soft	soft	ADJ
ejpam-6407	36	63	open	open	ADJ
ejpam-6407	36	64	sets	set	NOUN
ejpam-6407	36	65	and	and	CCONJ
ejpam-6407	36	66	soft	soft	ADJ
ejpam-6407	36	67	continuity	continuity	NOUN
ejpam-6407	36	68	.	.	PUNCT
ejpam-6407	37	1	more	more	ADJ
ejpam-6407	37	2	studies	study	NOUN
ejpam-6407	37	3	on	on	ADP
ejpam-6407	37	4	soft	soft	ADJ
ejpam-6407	37	5	continuity	continuity	NOUN
ejpam-6407	37	6	were	be	AUX
ejpam-6407	37	7	conducted	conduct	VERB
ejpam-6407	37	8	later	later	ADV
ejpam-6407	37	9	[	[	X
ejpam-6407	37	10	33	33	NUM
ejpam-6407	37	11	,	,	PUNCT
ejpam-6407	37	12	34	34	NUM
ejpam-6407	37	13	]	]	PUNCT
ejpam-6407	37	14	.	.	PUNCT
ejpam-6407	38	1	in	in	ADP
ejpam-6407	38	2	[	[	X
ejpam-6407	38	3	35	35	NUM
ejpam-6407	38	4	]	]	PUNCT
ejpam-6407	38	5	,	,	PUNCT
ejpam-6407	38	6	the	the	DET
ejpam-6407	38	7	idea	idea	NOUN
ejpam-6407	38	8	of	of	ADP
ejpam-6407	38	9	the	the	DET
ejpam-6407	38	10	soft	soft	ADJ
ejpam-6407	38	11	ideal	ideal	NOUN
ejpam-6407	38	12	was	be	AUX
ejpam-6407	38	13	first	first	ADV
ejpam-6407	38	14	introduced	introduce	VERB
ejpam-6407	38	15	.	.	PUNCT
ejpam-6407	39	1	after	after	ADP
ejpam-6407	39	2	thet	thet	NOUN
ejpam-6407	39	3	,	,	PUNCT
ejpam-6407	39	4	fatouh	fatouh	PROPN
ejpam-6407	39	5	et	et	PROPN
ejpam-6407	39	6	al	al	PROPN
ejpam-6407	39	7	.	.	PUNCT
ejpam-6407	40	1	[	[	X
ejpam-6407	40	2	36	36	NUM
ejpam-6407	40	3	]	]	PUNCT
ejpam-6407	40	4	used	use	VERB
ejpam-6407	40	5	soft	soft	ADJ
ejpam-6407	40	6	semi	semi	ADJ
ejpam-6407	40	7	-	-	ADJ
ejpam-6407	40	8	open	open	ADJ
ejpam-6407	40	9	sets	set	NOUN
ejpam-6407	40	10	to	to	PART
ejpam-6407	40	11	generalize	generalize	VERB
ejpam-6407	40	12	this	this	DET
ejpam-6407	40	13	idea	idea	NOUN
ejpam-6407	40	14	.	.	PUNCT
ejpam-6407	41	1	soft	soft	ADJ
ejpam-6407	41	2	compactness	compactness	NOUN
ejpam-6407	42	1	[	[	X
ejpam-6407	42	2	37	37	NUM
ejpam-6407	42	3	]	]	PUNCT
ejpam-6407	42	4	,	,	PUNCT
ejpam-6407	42	5	soft	soft	ADJ
ejpam-6407	42	6	connectedness	connectedness	NOUN
ejpam-6407	42	7	[	[	X
ejpam-6407	42	8	38	38	NUM
ejpam-6407	42	9	]	]	PUNCT
ejpam-6407	42	10	,	,	PUNCT
ejpam-6407	42	11	soft	soft	ADJ
ejpam-6407	42	12	generalized	generalized	ADJ
ejpam-6407	42	13	open	open	ADJ
ejpam-6407	42	14	sets	set	NOUN
ejpam-6407	42	15	[	[	X
ejpam-6407	42	16	39	39	NUM
ejpam-6407	42	17	]	]	PUNCT
ejpam-6407	42	18	,	,	PUNCT
ejpam-6407	42	19	soft	soft	ADJ
ejpam-6407	42	20	open	open	ADJ
ejpam-6407	42	21	sets	set	NOUN
ejpam-6407	42	22	via	via	ADP
ejpam-6407	42	23	soft	soft	ADJ
ejpam-6407	42	24	ideals	ideal	NOUN
ejpam-6407	42	25	[	[	X
ejpam-6407	42	26	40	40	NUM
ejpam-6407	42	27	,	,	PUNCT
ejpam-6407	42	28	41	41	NUM
ejpam-6407	42	29	]	]	PUNCT
ejpam-6407	42	30	,	,	PUNCT
ejpam-6407	42	31	soft	soft	ADJ
ejpam-6407	42	32	separation	separation	NOUN
ejpam-6407	42	33	axioms	axiom	NOUN
ejpam-6407	43	1	[	[	X
ejpam-6407	43	2	42	42	NUM
ejpam-6407	43	3	]	]	PUNCT
ejpam-6407	43	4	,	,	PUNCT
ejpam-6407	43	5	generalized	generalize	VERB
ejpam-6407	43	6	soft	soft	ADJ
ejpam-6407	43	7	rough	rough	ADJ
ejpam-6407	43	8	sets	set	NOUN
ejpam-6407	43	9	[	[	X
ejpam-6407	43	10	43	43	NUM
ejpam-6407	43	11	,	,	PUNCT
ejpam-6407	43	12	44	44	NUM
ejpam-6407	43	13	]	]	PUNCT
ejpam-6407	43	14	,	,	PUNCT
ejpam-6407	43	15	and	and	CCONJ
ejpam-6407	43	16	congruence	congruence	ADJ
ejpam-6407	43	17	representations	representation	NOUN
ejpam-6407	43	18	via	via	ADP
ejpam-6407	43	19	soft	soft	ADJ
ejpam-6407	43	20	ideals	ideal	NOUN
ejpam-6407	44	1	[	[	X
ejpam-6407	44	2	45	45	NUM
ejpam-6407	44	3	]	]	PUNCT
ejpam-6407	44	4	are	be	AUX
ejpam-6407	44	5	some	some	PRON
ejpam-6407	44	6	of	of	ADP
ejpam-6407	44	7	the	the	DET
ejpam-6407	44	8	topological	topological	ADJ
ejpam-6407	44	9	characteristics	characteristic	NOUN
ejpam-6407	44	10	that	that	SCONJ
ejpam-6407	44	11	this	this	DET
ejpam-6407	44	12	concept	concept	NOUN
ejpam-6407	44	13	is	be	AUX
ejpam-6407	44	14	then	then	ADV
ejpam-6407	44	15	used	use	VERB
ejpam-6407	44	16	to	to	PART
ejpam-6407	44	17	generalize	generalize	VERB
ejpam-6407	44	18	.	.	PUNCT
ejpam-6407	45	1	certain	certain	ADJ
ejpam-6407	45	2	applications	application	NOUN
ejpam-6407	45	3	of	of	ADP
ejpam-6407	45	4	soft	soft	ADJ
ejpam-6407	45	5	δ	δ	NOUN
ejpam-6407	45	6	-	-	PUNCT
ejpam-6407	45	7	closed	close	VERB
ejpam-6407	45	8	sets	set	NOUN
ejpam-6407	45	9	[	[	X
ejpam-6407	45	10	46	46	NUM
ejpam-6407	45	11	]	]	PUNCT
ejpam-6407	45	12	and	and	CCONJ
ejpam-6407	45	13	certain	certain	ADJ
ejpam-6407	45	14	lower	low	ADJ
ejpam-6407	45	15	soft	soft	ADJ
ejpam-6407	45	16	separation	separation	NOUN
ejpam-6407	45	17	axioms	axiom	NOUN
ejpam-6407	46	1	[	[	X
ejpam-6407	46	2	47	47	NUM
ejpam-6407	46	3	]	]	PUNCT
ejpam-6407	46	4	were	be	AUX
ejpam-6407	46	5	recently	recently	ADV
ejpam-6407	46	6	introduced	introduce	VERB
ejpam-6407	46	7	.	.	PUNCT
ejpam-6407	47	1	the	the	DET
ejpam-6407	47	2	definition	definition	NOUN
ejpam-6407	47	3	of	of	ADP
ejpam-6407	47	4	supra	supra	PROPN
ejpam-6407	47	5	soft	soft	ADJ
ejpam-6407	47	6	topological	topological	ADJ
ejpam-6407	47	7	space	space	NOUN
ejpam-6407	47	8	was	be	AUX
ejpam-6407	47	9	introduced	introduce	VERB
ejpam-6407	47	10	by	by	ADP
ejpam-6407	47	11	el	el	PROPN
ejpam-6407	47	12	-	-	PUNCT
ejpam-6407	47	13	sheikh	sheikh	PROPN
ejpam-6407	47	14	et	et	PROPN
ejpam-6407	47	15	al	al	PROPN
ejpam-6407	47	16	.	.	PUNCT
ejpam-6407	48	1	[	[	X
ejpam-6407	48	2	48	48	NUM
ejpam-6407	48	3	]	]	PUNCT
ejpam-6407	48	4	.	.	PUNCT
ejpam-6407	49	1	later	later	ADJ
ejpam-6407	49	2	research	research	NOUN
ejpam-6407	49	3	has	have	AUX
ejpam-6407	49	4	examined	examine	VERB
ejpam-6407	49	5	several	several	ADJ
ejpam-6407	49	6	kinds	kind	NOUN
ejpam-6407	49	7	of	of	ADP
ejpam-6407	49	8	generalized	generalized	ADJ
ejpam-6407	49	9	supra	supra	PROPN
ejpam-6407	49	10	soft	soft	ADJ
ejpam-6407	49	11	operators	operator	NOUN
ejpam-6407	49	12	using	use	VERB
ejpam-6407	49	13	supra	supra	PROPN
ejpam-6407	49	14	soft	soft	ADJ
ejpam-6407	49	15	-	-	PUNCT
ejpam-6407	49	16	b	b	NOUN
ejpam-6407	49	17	-	-	PUNCT
ejpam-6407	49	18	open	open	ADJ
ejpam-6407	49	19	sets	set	NOUN
ejpam-6407	49	20	[	[	X
ejpam-6407	49	21	49	49	NUM
ejpam-6407	49	22	]	]	PUNCT
ejpam-6407	49	23	,	,	PUNCT
ejpam-6407	49	24	supra	supra	PROPN
ejpam-6407	49	25	generalized	generalize	VERB
ejpam-6407	49	26	closed	close	VERB
ejpam-6407	49	27	soft	soft	ADJ
ejpam-6407	49	28	sets	set	NOUN
ejpam-6407	49	29	in	in	ADP
ejpam-6407	49	30	terms	term	NOUN
ejpam-6407	49	31	of	of	ADP
ejpam-6407	49	32	soft	soft	ADJ
ejpam-6407	49	33	ideals	ideal	NOUN
ejpam-6407	49	34	[	[	X
ejpam-6407	49	35	50	50	NUM
ejpam-6407	49	36	,	,	PUNCT
ejpam-6407	49	37	51	51	NUM
ejpam-6407	49	38	]	]	PUNCT
ejpam-6407	49	39	,	,	PUNCT
ejpam-6407	49	40	supra	supra	PROPN
ejpam-6407	49	41	soft	soft	ADJ
ejpam-6407	49	42	sw	sw	PROPN
ejpam-6407	49	43	-	-	PUNCT
ejpam-6407	49	44	open	open	ADJ
ejpam-6407	49	45	sets	set	NOUN
ejpam-6407	49	46	[	[	X
ejpam-6407	49	47	52	52	NUM
ejpam-6407	49	48	]	]	PUNCT
ejpam-6407	49	49	,	,	PUNCT
ejpam-6407	49	50	supra	supra	PROPN
ejpam-6407	49	51	soft	soft	ADJ
ejpam-6407	49	52	δi	δi	NOUN
ejpam-6407	49	53	-	-	PUNCT
ejpam-6407	49	54	open	open	ADJ
ejpam-6407	49	55	sets	set	NOUN
ejpam-6407	49	56	[	[	X
ejpam-6407	49	57	53	53	NUM
ejpam-6407	49	58	,	,	PUNCT
ejpam-6407	49	59	54	54	NUM
ejpam-6407	49	60	]	]	PUNCT
ejpam-6407	49	61	,	,	PUNCT
ejpam-6407	49	62	and	and	CCONJ
ejpam-6407	49	63	soft	soft	ADJ
ejpam-6407	49	64	separation	separation	NOUN
ejpam-6407	49	65	axioms	axiom	NOUN
ejpam-6407	49	66	[	[	X
ejpam-6407	49	67	55	55	NUM
ejpam-6407	49	68	]	]	PUNCT
ejpam-6407	49	69	.	.	PUNCT
ejpam-6407	50	1	recently	recently	ADV
ejpam-6407	50	2	,	,	PUNCT
ejpam-6407	50	3	abd	abd	PROPN
ejpam-6407	50	4	el	el	PROPN
ejpam-6407	50	5	-	-	PROPN
ejpam-6407	50	6	latif	latif	PROPN
ejpam-6407	50	7	et	et	PROPN
ejpam-6407	50	8	al	al	PROPN
ejpam-6407	50	9	.	.	PROPN
ejpam-6407	50	10	used	use	VERB
ejpam-6407	50	11	the	the	DET
ejpam-6407	50	12	notion	notion	NOUN
ejpam-6407	50	13	of	of	ADP
ejpam-6407	50	14	supra	supra	PROPN
ejpam-6407	50	15	soft	soft	ADJ
ejpam-6407	50	16	sd	sd	NOUN
ejpam-6407	50	17	-	-	PUNCT
ejpam-6407	50	18	sets	set	NOUN
ejpam-6407	50	19	[	[	X
ejpam-6407	50	20	56	56	NUM
ejpam-6407	50	21	,	,	PUNCT
ejpam-6407	50	22	57	57	NUM
ejpam-6407	50	23	]	]	PUNCT
ejpam-6407	50	24	to	to	PART
ejpam-6407	50	25	present	present	VERB
ejpam-6407	50	26	novel	novel	ADJ
ejpam-6407	50	27	kinds	kind	NOUN
ejpam-6407	50	28	of	of	ADP
ejpam-6407	50	29	soft	soft	ADJ
ejpam-6407	50	30	connectedness	connectedness	NOUN
ejpam-6407	50	31	[	[	X
ejpam-6407	50	32	58	58	NUM
ejpam-6407	50	33	]	]	PUNCT
ejpam-6407	50	34	and	and	CCONJ
ejpam-6407	50	35	several	several	ADJ
ejpam-6407	50	36	types	type	NOUN
ejpam-6407	50	37	of	of	ADP
ejpam-6407	50	38	compactness	compactness	NOUN
ejpam-6407	50	39	and	and	CCONJ
ejpam-6407	50	40	connectedness	connectedness	NOUN
ejpam-6407	50	41	[	[	X
ejpam-6407	50	42	59	59	NUM
ejpam-6407	50	43	,	,	PUNCT
ejpam-6407	50	44	60	60	NUM
ejpam-6407	50	45	]	]	PUNCT
ejpam-6407	50	46	.	.	PUNCT
ejpam-6407	51	1	alqahtani	alqahtani	PROPN
ejpam-6407	51	2	et	et	PROPN
ejpam-6407	51	3	al	al	PROPN
ejpam-6407	51	4	.	.	PROPN
ejpam-6407	51	5	presented	present	VERB
ejpam-6407	51	6	the	the	DET
ejpam-6407	51	7	notion	notion	NOUN
ejpam-6407	51	8	of	of	ADP
ejpam-6407	51	9	soft	soft	ADJ
ejpam-6407	51	10	nodec	nodec	ADJ
ejpam-6407	51	11	spaces	space	NOUN
ejpam-6407	52	1	[	[	X
ejpam-6407	52	2	61	61	NUM
ejpam-6407	52	3	,	,	PUNCT
ejpam-6407	52	4	62	62	NUM
ejpam-6407	52	5	]	]	PUNCT
ejpam-6407	52	6	.	.	PUNCT
ejpam-6407	53	1	our	our	PRON
ejpam-6407	53	2	aim	aim	NOUN
ejpam-6407	53	3	of	of	ADP
ejpam-6407	53	4	this	this	DET
ejpam-6407	53	5	work	work	NOUN
ejpam-6407	53	6	is	be	AUX
ejpam-6407	53	7	to	to	PART
ejpam-6407	53	8	provide	provide	VERB
ejpam-6407	53	9	new	new	ADJ
ejpam-6407	53	10	types	type	NOUN
ejpam-6407	53	11	of	of	ADP
ejpam-6407	53	12	generalized	generalized	ADJ
ejpam-6407	53	13	separation	separation	NOUN
ejpam-6407	53	14	axioms	axiom	NOUN
ejpam-6407	53	15	.	.	PUNCT
ejpam-6407	54	1	in	in	ADP
ejpam-6407	54	2	special	special	ADJ
ejpam-6407	54	3	,	,	PUNCT
ejpam-6407	54	4	we	we	PRON
ejpam-6407	54	5	present	present	VERB
ejpam-6407	54	6	three	three	NUM
ejpam-6407	54	7	new	new	ADJ
ejpam-6407	54	8	types	type	NOUN
ejpam-6407	54	9	of	of	ADP
ejpam-6407	54	10	separation	separation	NOUN
ejpam-6407	54	11	axioms	axiom	NOUN
ejpam-6407	54	12	inspired	inspire	VERB
ejpam-6407	54	13	by	by	ADP
ejpam-6407	54	14	supra	supra	PROPN
ejpam-6407	54	15	ϵ-open	ϵ-open	PROPN
ejpam-6407	54	16	sets	set	NOUN
ejpam-6407	54	17	named	name	VERB
ejpam-6407	54	18	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	54	19	-	-	NOUN
ejpam-6407	54	20	space	space	NOUN
ejpam-6407	54	21	,	,	PUNCT
ejpam-6407	54	22	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6407	54	23	-	-	PUNCT
ejpam-6407	54	24	space	space	NOUN
ejpam-6407	54	25	,	,	PUNCT
ejpam-6407	54	26	and	and	CCONJ
ejpam-6407	54	27	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6407	54	28	-	-	PUNCT
ejpam-6407	54	29	space	space	NOUN
ejpam-6407	54	30	.	.	PUNCT
ejpam-6407	55	1	we	we	PRON
ejpam-6407	55	2	give	give	VERB
ejpam-6407	55	3	in	in	ADP
ejpam-6407	55	4	-	-	PUNCT
ejpam-6407	55	5	depth	depth	NOUN
ejpam-6407	55	6	explanations	explanation	NOUN
ejpam-6407	55	7	of	of	ADP
ejpam-6407	55	8	each	each	PRON
ejpam-6407	55	9	of	of	ADP
ejpam-6407	55	10	them	they	PRON
ejpam-6407	55	11	,	,	PUNCT
ejpam-6407	55	12	backed	back	VERB
ejpam-6407	55	13	up	up	ADP
ejpam-6407	55	14	by	by	ADP
ejpam-6407	55	15	several	several	ADJ
ejpam-6407	55	16	examples	example	NOUN
ejpam-6407	55	17	and	and	CCONJ
ejpam-6407	55	18	counterexamples	counterexample	NOUN
ejpam-6407	55	19	that	that	PRON
ejpam-6407	55	20	highlight	highlight	VERB
ejpam-6407	55	21	the	the	DET
ejpam-6407	55	22	m.	m.	NOUN
ejpam-6407	55	23	aldawood	aldawood	NOUN
ejpam-6407	55	24	et	et	PROPN
ejpam-6407	55	25	al	al	PROPN
ejpam-6407	55	26	.	.	PUNCT
ejpam-6407	55	27	/	/	SYM
ejpam-6407	55	28	eur	eur	PROPN
ejpam-6407	55	29	.	.	PUNCT
ejpam-6407	56	1	j.	j.	PROPN
ejpam-6407	56	2	pure	pure	PROPN
ejpam-6407	56	3	appl	appl	PROPN
ejpam-6407	56	4	.	.	PROPN
ejpam-6407	56	5	math	math	PROPN
ejpam-6407	56	6	,	,	PUNCT
ejpam-6407	56	7	18	18	NUM
ejpam-6407	56	8	(	(	PUNCT
ejpam-6407	56	9	3	3	NUM
ejpam-6407	56	10	)	)	PUNCT
ejpam-6407	56	11	(	(	PUNCT
ejpam-6407	56	12	2025	2025	NUM
ejpam-6407	56	13	)	)	PUNCT
ejpam-6407	56	14	,	,	PUNCT
ejpam-6407	56	15	6407	6407	NUM
ejpam-6407	56	16	3	3	NUM
ejpam-6407	56	17	of	of	ADP
ejpam-6407	56	18	15	15	NUM
ejpam-6407	56	19	significance	significance	NOUN
ejpam-6407	56	20	of	of	ADP
ejpam-6407	56	21	our	our	PRON
ejpam-6407	56	22	original	original	ADJ
ejpam-6407	56	23	ideas	idea	NOUN
ejpam-6407	56	24	.	.	PUNCT
ejpam-6407	57	1	additionally	additionally	ADV
ejpam-6407	57	2	,	,	PUNCT
ejpam-6407	57	3	as	as	SCONJ
ejpam-6407	57	4	shown	show	VERB
ejpam-6407	57	5	in	in	ADP
ejpam-6407	57	6	figure	figure	NOUN
ejpam-6407	57	7	1	1	NUM
ejpam-6407	57	8	,	,	PUNCT
ejpam-6407	57	9	we	we	PRON
ejpam-6407	57	10	provide	provide	VERB
ejpam-6407	57	11	a	a	DET
ejpam-6407	57	12	diagram	diagram	NOUN
ejpam-6407	57	13	that	that	PRON
ejpam-6407	57	14	summarizes	summarize	VERB
ejpam-6407	57	15	their	their	PRON
ejpam-6407	57	16	links	link	NOUN
ejpam-6407	57	17	and	and	CCONJ
ejpam-6407	57	18	connections	connection	NOUN
ejpam-6407	57	19	to	to	ADP
ejpam-6407	57	20	earlier	early	ADJ
ejpam-6407	57	21	research	research	NOUN
ejpam-6407	57	22	.	.	PUNCT
ejpam-6407	58	1	supra	supra	ADJ
ejpam-6407	58	2	-	-	PUNCT
ejpam-6407	58	3	t2	t2	NOUN
ejpam-6407	58	4	-	-	PUNCT
ejpam-6407	58	5	space	space	NOUN
ejpam-6407	58	6	=	=	NOUN
ejpam-6407	58	7	⇒	⇒	NOUN
ejpam-6407	58	8	supra	supra	PROPN
ejpam-6407	58	9	-	-	PUNCT
ejpam-6407	58	10	t1	t1	NOUN
ejpam-6407	58	11	-	-	PUNCT
ejpam-6407	58	12	space	space	NOUN
ejpam-6407	58	13	=	=	NOUN
ejpam-6407	58	14	⇒	⇒	ADJ
ejpam-6407	58	15	supra	supra	PROPN
ejpam-6407	58	16	-	-	PUNCT
ejpam-6407	58	17	t0	t0	NOUN
ejpam-6407	58	18	-	-	PUNCT
ejpam-6407	58	19	space	space	NOUN
ejpam-6407	58	20	⇓	⇓	PROPN
ejpam-6407	58	21	⇓	⇓	PROPN
ejpam-6407	58	22	⇓	⇓	PROPN
ejpam-6407	58	23	supra-ϵ-t2	supra-ϵ-t2	NOUN
ejpam-6407	58	24	-	-	PUNCT
ejpam-6407	58	25	space	space	NOUN
ejpam-6407	58	26	=	=	NOUN
ejpam-6407	58	27	⇒	⇒	NOUN
ejpam-6407	58	28	supra-ϵ-t1	supra-ϵ-t1	PROPN
ejpam-6407	58	29	-	-	PUNCT
ejpam-6407	58	30	space	space	NOUN
ejpam-6407	58	31	=	=	NOUN
ejpam-6407	58	32	⇒	⇒	NOUN
ejpam-6407	58	33	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	58	34	-	-	PUNCT
ejpam-6407	58	35	space	space	NOUN
ejpam-6407	58	36	diagram	diagram	NOUN
ejpam-6407	58	37	1	1	NUM
ejpam-6407	58	38	.	.	PUNCT
ejpam-6407	59	1	the	the	DET
ejpam-6407	59	2	connections	connection	NOUN
ejpam-6407	59	3	among	among	ADP
ejpam-6407	59	4	various	various	ADJ
ejpam-6407	59	5	types	type	NOUN
ejpam-6407	59	6	of	of	ADP
ejpam-6407	59	7	separation	separation	NOUN
ejpam-6407	59	8	axioms	axiom	NOUN
ejpam-6407	59	9	in	in	ADP
ejpam-6407	59	10	the	the	DET
ejpam-6407	59	11	context	context	NOUN
ejpam-6407	59	12	of	of	ADP
ejpam-6407	59	13	stss	stss	NOUN
ejpam-6407	59	14	inspired	inspire	VERB
ejpam-6407	59	15	by	by	ADP
ejpam-6407	59	16	supra	supra	PROPN
ejpam-6407	59	17	ϵ-open	ϵ-open	PROPN
ejpam-6407	59	18	sets	set	NOUN
ejpam-6407	59	19	finally	finally	ADV
ejpam-6407	59	20	,	,	PUNCT
ejpam-6407	59	21	we	we	PRON
ejpam-6407	59	22	assess	assess	VERB
ejpam-6407	59	23	the	the	DET
ejpam-6407	59	24	supra	supra	PROPN
ejpam-6407	59	25	topological	topological	PROPN
ejpam-6407	59	26	and	and	CCONJ
ejpam-6407	59	27	supra	supra	ADJ
ejpam-6407	59	28	hereditary	hereditary	ADJ
ejpam-6407	59	29	properties	property	NOUN
ejpam-6407	59	30	for	for	ADP
ejpam-6407	59	31	each	each	PRON
ejpam-6407	59	32	of	of	ADP
ejpam-6407	59	33	the	the	DET
ejpam-6407	59	34	concepts	concept	NOUN
ejpam-6407	59	35	.	.	PUNCT
ejpam-6407	60	1	in	in	ADP
ejpam-6407	60	2	particular	particular	ADJ
ejpam-6407	60	3	,	,	PUNCT
ejpam-6407	60	4	we	we	PRON
ejpam-6407	60	5	show	show	VERB
ejpam-6407	60	6	that	that	SCONJ
ejpam-6407	60	7	the	the	DET
ejpam-6407	60	8	property	property	NOUN
ejpam-6407	60	9	of	of	ADP
ejpam-6407	60	10	being	be	AUX
ejpam-6407	60	11	a	a	DET
ejpam-6407	60	12	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6407	60	13	-	-	PUNCT
ejpam-6407	60	14	space	space	NOUN
ejpam-6407	60	15	,	,	PUNCT
ejpam-6407	60	16	where	where	SCONJ
ejpam-6407	60	17	j	j	PROPN
ejpam-6407	60	18	=	=	SYM
ejpam-6407	60	19	0	0	PROPN
ejpam-6407	60	20	,	,	PUNCT
ejpam-6407	60	21	1	1	NUM
ejpam-6407	60	22	,	,	PUNCT
ejpam-6407	60	23	2	2	NUM
ejpam-6407	60	24	,	,	PUNCT
ejpam-6407	60	25	is	be	AUX
ejpam-6407	60	26	a	a	DET
ejpam-6407	60	27	supra	supra	NOUN
ejpam-6407	60	28	-	-	PUNCT
ejpam-6407	60	29	hereditary	hereditary	ADJ
ejpam-6407	60	30	(	(	PUNCT
ejpam-6407	60	31	topological	topological	ADJ
ejpam-6407	60	32	)	)	PUNCT
ejpam-6407	60	33	property	property	NOUN
ejpam-6407	60	34	.	.	PUNCT
ejpam-6407	61	1	2	2	X
ejpam-6407	61	2	.	.	NUM
ejpam-6407	61	3	preliminaries	preliminary	NOUN
ejpam-6407	61	4	and	and	CCONJ
ejpam-6407	61	5	background	background	NOUN
ejpam-6407	61	6	definition	definition	NOUN
ejpam-6407	61	7	1	1	NUM
ejpam-6407	61	8	.	.	PUNCT
ejpam-6407	62	1	[	[	X
ejpam-6407	62	2	15	15	NUM
ejpam-6407	62	3	]	]	X
ejpam-6407	62	4	supra	supra	ADJ
ejpam-6407	62	5	topology	topology	NOUN
ejpam-6407	62	6	(	(	PUNCT
ejpam-6407	62	7	or	or	CCONJ
ejpam-6407	62	8	sts	st	NOUN
ejpam-6407	62	9	)	)	PUNCT
ejpam-6407	62	10	on	on	ADP
ejpam-6407	62	11	λ	λ	PROPN
ejpam-6407	62	12	is	be	AUX
ejpam-6407	62	13	the	the	DET
ejpam-6407	62	14	family	family	NOUN
ejpam-6407	62	15	ϑ	ϑ	PROPN
ejpam-6407	62	16	⊆	⊆	NUM
ejpam-6407	62	17	2λ	2λ	NOUN
ejpam-6407	62	18	which	which	PRON
ejpam-6407	62	19	contains	contain	VERB
ejpam-6407	62	20	λ	λ	NOUN
ejpam-6407	62	21	and	and	CCONJ
ejpam-6407	62	22	∅	∅	NOUN
ejpam-6407	62	23	and	and	CCONJ
ejpam-6407	62	24	closed	close	VERB
ejpam-6407	62	25	under	under	ADP
ejpam-6407	62	26	arbitrary	arbitrary	ADJ
ejpam-6407	62	27	union	union	NOUN
ejpam-6407	62	28	.	.	PUNCT
ejpam-6407	63	1	additionally	additionally	ADV
ejpam-6407	63	2	,	,	PUNCT
ejpam-6407	63	3	h	h	NOUN
ejpam-6407	63	4	and	and	CCONJ
ejpam-6407	63	5	hc	hc	PROPN
ejpam-6407	63	6	are	be	AUX
ejpam-6407	63	7	referred	refer	VERB
ejpam-6407	63	8	to	to	ADP
ejpam-6407	63	9	as	as	ADP
ejpam-6407	63	10	supra	supra	PROPN
ejpam-6407	63	11	open	open	ADJ
ejpam-6407	63	12	and	and	CCONJ
ejpam-6407	63	13	supra	supra	ADJ
ejpam-6407	63	14	closed	close	VERB
ejpam-6407	63	15	sets	set	NOUN
ejpam-6407	63	16	,	,	PUNCT
ejpam-6407	63	17	respectively	respectively	ADV
ejpam-6407	63	18	,	,	PUNCT
ejpam-6407	63	19	if	if	SCONJ
ejpam-6407	63	20	h	h	PROPN
ejpam-6407	63	21	∈	∈	PROPN
ejpam-6407	63	22	ϑ.	ϑ.	VERB
ejpam-6407	63	23	also	also	ADV
ejpam-6407	63	24	,	,	PUNCT
ejpam-6407	63	25	so(λ	so(λ	X
ejpam-6407	63	26	)	)	PUNCT
ejpam-6407	63	27	will	will	AUX
ejpam-6407	63	28	also	also	ADV
ejpam-6407	63	29	be	be	AUX
ejpam-6407	63	30	used	use	VERB
ejpam-6407	63	31	to	to	PART
ejpam-6407	63	32	indicate	indicate	VERB
ejpam-6407	63	33	the	the	DET
ejpam-6407	63	34	class	class	NOUN
ejpam-6407	63	35	of	of	ADP
ejpam-6407	63	36	all	all	DET
ejpam-6407	63	37	supra	supra	ADJ
ejpam-6407	63	38	open	open	ADJ
ejpam-6407	63	39	sets	set	NOUN
ejpam-6407	63	40	.	.	PUNCT
ejpam-6407	64	1	furthermore	furthermore	ADV
ejpam-6407	64	2	,	,	PUNCT
ejpam-6407	64	3	ϑ	ϑ	X
ejpam-6407	64	4	is	be	AUX
ejpam-6407	64	5	referred	refer	VERB
ejpam-6407	64	6	to	to	ADP
ejpam-6407	64	7	as	as	ADP
ejpam-6407	64	8	an	an	DET
ejpam-6407	64	9	associated	associate	VERB
ejpam-6407	64	10	sts	st	NOUN
ejpam-6407	64	11	with	with	ADP
ejpam-6407	64	12	σ	σ	PROPN
ejpam-6407	64	13	if	if	SCONJ
ejpam-6407	64	14	σ	σ	PROPN
ejpam-6407	64	15	⊂	⊂	PROPN
ejpam-6407	64	16	ϑ	ϑ	PROPN
ejpam-6407	64	17	for	for	ADP
ejpam-6407	64	18	a	a	DET
ejpam-6407	64	19	given	give	VERB
ejpam-6407	64	20	topology	topology	NOUN
ejpam-6407	64	21	σ	σ	PROPN
ejpam-6407	64	22	.	.	PUNCT
ejpam-6407	64	23	definition	definition	NOUN
ejpam-6407	64	24	2	2	NUM
ejpam-6407	64	25	.	.	PUNCT
ejpam-6407	65	1	[	[	X
ejpam-6407	65	2	15	15	NUM
ejpam-6407	65	3	]	]	PUNCT
ejpam-6407	65	4	the	the	DET
ejpam-6407	65	5	ints(h	ints(h	PROPN
ejpam-6407	65	6	)	)	PUNCT
ejpam-6407	65	7	(	(	PUNCT
ejpam-6407	65	8	cls(h	cls(h	NOUN
ejpam-6407	65	9	)	)	PUNCT
ejpam-6407	65	10	,	,	PUNCT
ejpam-6407	65	11	frs(h	frs(h	PROPN
ejpam-6407	65	12	)	)	PUNCT
ejpam-6407	65	13	)	)	PUNCT
ejpam-6407	65	14	will	will	AUX
ejpam-6407	65	15	indicate	indicate	VERB
ejpam-6407	65	16	the	the	DET
ejpam-6407	65	17	supra	supra	ADJ
ejpam-6407	65	18	interior	interior	NOUN
ejpam-6407	65	19	(	(	PUNCT
ejpam-6407	65	20	closure	closure	NOUN
ejpam-6407	65	21	,	,	PUNCT
ejpam-6407	65	22	boundary	boundary	NOUN
ejpam-6407	65	23	)	)	PUNCT
ejpam-6407	65	24	for	for	ADP
ejpam-6407	65	25	a	a	DET
ejpam-6407	65	26	subset	subset	ADJ
ejpam-6407	65	27	h	h	NOUN
ejpam-6407	65	28	of	of	ADP
ejpam-6407	65	29	an	an	DET
ejpam-6407	65	30	sts	st	NOUN
ejpam-6407	65	31	(	(	PUNCT
ejpam-6407	65	32	λ	λ	X
ejpam-6407	65	33	,	,	PUNCT
ejpam-6407	65	34	ϑ	ϑ	NOUN
ejpam-6407	65	35	)	)	PUNCT
ejpam-6407	65	36	,	,	PUNCT
ejpam-6407	65	37	where	where	SCONJ
ejpam-6407	65	38	ints(h	ints(h	ADP
ejpam-6407	65	39	)	)	PUNCT
ejpam-6407	65	40	=	=	SYM
ejpam-6407	65	41	∪{c	∪{c	PROPN
ejpam-6407	65	42	:	:	PUNCT
ejpam-6407	65	43	c	c	PROPN
ejpam-6407	65	44	∈	∈	PROPN
ejpam-6407	65	45	ϑ	ϑ	X
ejpam-6407	65	46	and	and	CCONJ
ejpam-6407	65	47	c	c	NOUN
ejpam-6407	65	48	⊆	⊆	NUM
ejpam-6407	65	49	h	h	NOUN
ejpam-6407	65	50	}	}	PUNCT
ejpam-6407	65	51	,	,	PUNCT
ejpam-6407	65	52	cls(h	cls(h	NOUN
ejpam-6407	65	53	)	)	PUNCT
ejpam-6407	66	1	=	=	SYM
ejpam-6407	66	2	∩{d	∩{d	NOUN
ejpam-6407	66	3	:	:	PUNCT
ejpam-6407	67	1	d	d	X
ejpam-6407	67	2	∈	∈	NOUN
ejpam-6407	67	3	ϑc	ϑc	NOUN
ejpam-6407	67	4	and	and	CCONJ
ejpam-6407	67	5	h	h	NOUN
ejpam-6407	67	6	⊆	⊆	NUM
ejpam-6407	67	7	d	d	NOUN
ejpam-6407	67	8	}	}	PUNCT
ejpam-6407	67	9	and	and	CCONJ
ejpam-6407	67	10	frs(h	frs(h	PROPN
ejpam-6407	67	11	)	)	PUNCT
ejpam-6407	67	12	=	=	SYM
ejpam-6407	67	13	cls(h)\ints(h	cls(h)\ints(h	PROPN
ejpam-6407	67	14	)	)	PUNCT
ejpam-6407	67	15	.	.	PUNCT
ejpam-6407	68	1	definition	definition	NOUN
ejpam-6407	68	2	3	3	NUM
ejpam-6407	68	3	.	.	PUNCT
ejpam-6407	69	1	[	[	X
ejpam-6407	69	2	17	17	NUM
ejpam-6407	69	3	]	]	PUNCT
ejpam-6407	69	4	let	let	VERB
ejpam-6407	69	5	e	e	PRON
ejpam-6407	69	6	be	be	AUX
ejpam-6407	69	7	a	a	DET
ejpam-6407	69	8	subset	subset	NOUN
ejpam-6407	69	9	of	of	ADP
ejpam-6407	69	10	an	an	DET
ejpam-6407	69	11	sts	st	NOUN
ejpam-6407	69	12	(	(	PUNCT
ejpam-6407	69	13	λ	λ	X
ejpam-6407	69	14	,	,	PUNCT
ejpam-6407	69	15	ϑ	ϑ	NOUN
ejpam-6407	69	16	)	)	PUNCT
ejpam-6407	69	17	.	.	PUNCT
ejpam-6407	70	1	if	if	SCONJ
ejpam-6407	70	2	ints(cls(e	ints(cls(e	NOUN
ejpam-6407	70	3	)	)	PUNCT
ejpam-6407	70	4	)	)	PUNCT
ejpam-6407	71	1	̸=	̸=	NOUN
ejpam-6407	71	2	∅	∅	NOUN
ejpam-6407	71	3	,	,	PUNCT
ejpam-6407	71	4	then	then	ADV
ejpam-6407	71	5	e	e	PROPN
ejpam-6407	71	6	∈	∈	PROPN
ejpam-6407	71	7	sro(λ	sro(λ	PROPN
ejpam-6407	71	8	)	)	PUNCT
ejpam-6407	71	9	.	.	PUNCT
ejpam-6407	72	1	also	also	ADV
ejpam-6407	72	2	,	,	PUNCT
ejpam-6407	72	3	if	if	SCONJ
ejpam-6407	72	4	ints(cls(e	ints(cls(e	NOUN
ejpam-6407	72	5	)	)	PUNCT
ejpam-6407	72	6	)	)	PUNCT
ejpam-6407	73	1	=	=	NOUN
ejpam-6407	73	2	∅	∅	NOUN
ejpam-6407	73	3	,	,	PUNCT
ejpam-6407	73	4	then	then	ADV
ejpam-6407	73	5	e	e	PROPN
ejpam-6407	73	6	∈	∈	PROPN
ejpam-6407	73	7	snd(λ	snd(λ	PROPN
ejpam-6407	73	8	)	)	PUNCT
ejpam-6407	73	9	.	.	PUNCT
ejpam-6407	74	1	definition	definition	NOUN
ejpam-6407	74	2	4	4	NUM
ejpam-6407	74	3	.	.	PUNCT
ejpam-6407	75	1	[	[	X
ejpam-6407	75	2	22	22	NUM
ejpam-6407	75	3	]	]	PUNCT
ejpam-6407	75	4	regarding	regard	VERB
ejpam-6407	75	5	the	the	DET
ejpam-6407	75	6	subset	subset	NOUN
ejpam-6407	75	7	s	s	NOUN
ejpam-6407	75	8	of	of	ADP
ejpam-6407	75	9	an	an	DET
ejpam-6407	75	10	sts	st	NOUN
ejpam-6407	75	11	(	(	PUNCT
ejpam-6407	75	12	λ	λ	X
ejpam-6407	75	13	,	,	PUNCT
ejpam-6407	75	14	ϑ	ϑ	NOUN
ejpam-6407	75	15	)	)	PUNCT
ejpam-6407	75	16	,	,	PUNCT
ejpam-6407	75	17	the	the	DET
ejpam-6407	75	18	family	family	NOUN
ejpam-6407	75	19	ϑs	ϑs	X
ejpam-6407	75	20	=	=	X
ejpam-6407	75	21	{	{	PUNCT
ejpam-6407	75	22	s	s	PROPN
ejpam-6407	75	23	∩	∩	ADJ
ejpam-6407	75	24	j	j	NOUN
ejpam-6407	75	25	:	:	PUNCT
ejpam-6407	75	26	j	j	PROPN
ejpam-6407	75	27	∈	∈	PROPN
ejpam-6407	75	28	ϑ	ϑ	PROPN
ejpam-6407	75	29	}	}	PUNCT
ejpam-6407	75	30	defines	define	VERB
ejpam-6407	75	31	an	an	DET
ejpam-6407	75	32	sts	st	NOUN
ejpam-6407	75	33	on	on	ADP
ejpam-6407	75	34	s	s	NOUN
ejpam-6407	75	35	,	,	PUNCT
ejpam-6407	75	36	which	which	PRON
ejpam-6407	75	37	is	be	AUX
ejpam-6407	75	38	referred	refer	VERB
ejpam-6407	75	39	to	to	ADP
ejpam-6407	75	40	as	as	ADP
ejpam-6407	75	41	a	a	DET
ejpam-6407	75	42	supra	supra	ADJ
ejpam-6407	75	43	subspace	subspace	NOUN
ejpam-6407	75	44	of	of	ADP
ejpam-6407	75	45	(	(	PUNCT
ejpam-6407	75	46	λ	λ	PROPN
ejpam-6407	75	47	,	,	PUNCT
ejpam-6407	75	48	ϑ	ϑ	NOUN
ejpam-6407	75	49	)	)	PUNCT
ejpam-6407	75	50	.	.	PUNCT
ejpam-6407	76	1	definition	definition	NOUN
ejpam-6407	76	2	5	5	NUM
ejpam-6407	76	3	.	.	PUNCT
ejpam-6407	77	1	[	[	X
ejpam-6407	77	2	22	22	NUM
ejpam-6407	77	3	]	]	PUNCT
ejpam-6407	77	4	a	a	DET
ejpam-6407	77	5	subset	subset	NOUN
ejpam-6407	77	6	e	e	NOUN
ejpam-6407	77	7	of	of	ADP
ejpam-6407	77	8	an	an	DET
ejpam-6407	77	9	sts	st	NOUN
ejpam-6407	77	10	(	(	PUNCT
ejpam-6407	77	11	λ	λ	X
ejpam-6407	77	12	,	,	PUNCT
ejpam-6407	77	13	ϑ	ϑ	NOUN
ejpam-6407	77	14	)	)	PUNCT
ejpam-6407	77	15	is	be	AUX
ejpam-6407	77	16	referred	refer	VERB
ejpam-6407	77	17	to	to	ADP
ejpam-6407	77	18	as	as	SCONJ
ejpam-6407	77	19	supra	supra	PROPN
ejpam-6407	77	20	ϵ-open	ϵ-open	PROPN
ejpam-6407	77	21	set	set	VERB
ejpam-6407	77	22	if	if	SCONJ
ejpam-6407	77	23	either	either	CCONJ
ejpam-6407	77	24	e	e	NOUN
ejpam-6407	77	25	=	=	NOUN
ejpam-6407	77	26	∅	∅	NOUN
ejpam-6407	77	27	or	or	CCONJ
ejpam-6407	77	28	e	e	NOUN
ejpam-6407	77	29	⊆	⊆	NUM
ejpam-6407	77	30	{	{	PUNCT
ejpam-6407	77	31	frs(e	frs(e	PROPN
ejpam-6407	77	32	)	)	PUNCT
ejpam-6407	77	33	∪	∪	ADP
ejpam-6407	77	34	ints(cls(e	ints(cls(e	NOUN
ejpam-6407	77	35	)	)	PUNCT
ejpam-6407	77	36	)	)	PUNCT
ejpam-6407	77	37	,	,	PUNCT
ejpam-6407	77	38	e	e	PROPN
ejpam-6407	77	39	∈	∈	PROPN
ejpam-6407	77	40	sro(λ	sro(λ	PROPN
ejpam-6407	77	41	)	)	PUNCT
ejpam-6407	77	42	,	,	PUNCT
ejpam-6407	77	43	frs(e	frs(e	PROPN
ejpam-6407	77	44	)	)	PUNCT
ejpam-6407	77	45	,	,	PUNCT
ejpam-6407	77	46	e	e	PROPN
ejpam-6407	77	47	∈	∈	PROPN
ejpam-6407	77	48	snd(λ	snd(λ	NOUN
ejpam-6407	77	49	)	)	PUNCT
ejpam-6407	77	50	and	and	CCONJ
ejpam-6407	77	51	frs(e	frs(e	NOUN
ejpam-6407	77	52	)	)	PUNCT
ejpam-6407	77	53	is	be	AUX
ejpam-6407	77	54	infinite	infinite	ADJ
ejpam-6407	77	55	.	.	PUNCT
ejpam-6407	78	1	additionally	additionally	ADV
ejpam-6407	78	2	,	,	PUNCT
ejpam-6407	78	3	ec	ec	PROPN
ejpam-6407	78	4	is	be	AUX
ejpam-6407	78	5	referred	refer	VERB
ejpam-6407	78	6	to	to	ADP
ejpam-6407	78	7	as	as	SCONJ
ejpam-6407	78	8	supra	supra	PROPN
ejpam-6407	78	9	ϵ-closed	ϵ-closed	PROPN
ejpam-6407	78	10	-	-	PUNCT
ejpam-6407	78	11	set	set	NOUN
ejpam-6407	78	12	.	.	PUNCT
ejpam-6407	79	1	furthermore	furthermore	ADV
ejpam-6407	79	2	,	,	PUNCT
ejpam-6407	79	3	all	all	DET
ejpam-6407	79	4	supra	supra	PROPN
ejpam-6407	79	5	ϵ-open	ϵ-open	PROPN
ejpam-6407	79	6	(	(	PUNCT
ejpam-6407	79	7	respectively	respectively	ADV
ejpam-6407	79	8	,	,	PUNCT
ejpam-6407	79	9	supra	supra	PROPN
ejpam-6407	79	10	ϵ-closed	ϵ-close	VERB
ejpam-6407	79	11	)	)	PUNCT
ejpam-6407	79	12	sets	set	NOUN
ejpam-6407	79	13	will	will	AUX
ejpam-6407	79	14	be	be	AUX
ejpam-6407	79	15	classified	classify	VERB
ejpam-6407	79	16	by	by	ADP
ejpam-6407	79	17	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	79	18	)	)	PUNCT
ejpam-6407	79	19	(	(	PUNCT
ejpam-6407	79	20	respectively	respectively	ADV
ejpam-6407	79	21	,	,	PUNCT
ejpam-6407	79	22	scϵ(λ	scϵ(λ	PROPN
ejpam-6407	79	23	)	)	PUNCT
ejpam-6407	79	24	)	)	PUNCT
ejpam-6407	79	25	.	.	PUNCT
ejpam-6407	80	1	definition	definition	NOUN
ejpam-6407	80	2	6	6	NUM
ejpam-6407	80	3	.	.	PUNCT
ejpam-6407	81	1	[	[	X
ejpam-6407	81	2	22	22	NUM
ejpam-6407	81	3	]	]	PUNCT
ejpam-6407	81	4	the	the	DET
ejpam-6407	81	5	intsϵ(s	intsϵ(s	PROPN
ejpam-6407	81	6	)	)	PUNCT
ejpam-6407	81	7	(	(	PUNCT
ejpam-6407	81	8	clsϵ(s	clsϵ(s	NOUN
ejpam-6407	81	9	)	)	PUNCT
ejpam-6407	81	10	)	)	PUNCT
ejpam-6407	81	11	will	will	AUX
ejpam-6407	81	12	indicate	indicate	VERB
ejpam-6407	81	13	the	the	DET
ejpam-6407	81	14	supra	supra	PROPN
ejpam-6407	81	15	ϵ-interior	ϵ-interior	PROPN
ejpam-6407	81	16	(	(	PUNCT
ejpam-6407	81	17	closure	closure	NOUN
ejpam-6407	81	18	)	)	PUNCT
ejpam-6407	81	19	of	of	ADP
ejpam-6407	81	20	s	s	PRON
ejpam-6407	81	21	for	for	ADP
ejpam-6407	81	22	a	a	DET
ejpam-6407	81	23	subset	subset	NOUN
ejpam-6407	81	24	s	s	NOUN
ejpam-6407	81	25	of	of	ADP
ejpam-6407	81	26	an	an	DET
ejpam-6407	81	27	sts	st	NOUN
ejpam-6407	81	28	(	(	PUNCT
ejpam-6407	81	29	λ	λ	X
ejpam-6407	81	30	,	,	PUNCT
ejpam-6407	81	31	ϑ	ϑ	NOUN
ejpam-6407	81	32	)	)	PUNCT
ejpam-6407	81	33	,	,	PUNCT
ejpam-6407	81	34	where	where	SCONJ
ejpam-6407	81	35	m.	m.	NOUN
ejpam-6407	81	36	aldawood	aldawood	VERB
ejpam-6407	81	37	et	et	PROPN
ejpam-6407	81	38	al	al	PROPN
ejpam-6407	81	39	.	.	PUNCT
ejpam-6407	81	40	/	/	SYM
ejpam-6407	81	41	eur	eur	PROPN
ejpam-6407	81	42	.	.	PUNCT
ejpam-6407	82	1	j.	j.	PROPN
ejpam-6407	82	2	pure	pure	PROPN
ejpam-6407	82	3	appl	appl	PROPN
ejpam-6407	82	4	.	.	PROPN
ejpam-6407	82	5	math	math	PROPN
ejpam-6407	82	6	,	,	PUNCT
ejpam-6407	82	7	18	18	NUM
ejpam-6407	82	8	(	(	PUNCT
ejpam-6407	82	9	3	3	NUM
ejpam-6407	82	10	)	)	PUNCT
ejpam-6407	82	11	(	(	PUNCT
ejpam-6407	82	12	2025	2025	NUM
ejpam-6407	82	13	)	)	PUNCT
ejpam-6407	82	14	,	,	PUNCT
ejpam-6407	82	15	6407	6407	NUM
ejpam-6407	82	16	4	4	NUM
ejpam-6407	82	17	of	of	ADP
ejpam-6407	82	18	15	15	NUM
ejpam-6407	82	19	intsϵ(s	intsϵ(s	NUM
ejpam-6407	82	20	)	)	PUNCT
ejpam-6407	82	21	=	=	PUNCT
ejpam-6407	83	1	∪{j	∪{j	X
ejpam-6407	83	2	:	:	PUNCT
ejpam-6407	83	3	j	j	PROPN
ejpam-6407	83	4	∈	∈	PROPN
ejpam-6407	83	5	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	83	6	)	)	PUNCT
ejpam-6407	83	7	and	and	CCONJ
ejpam-6407	83	8	j	j	PROPN
ejpam-6407	83	9	⊆	⊆	NUM
ejpam-6407	83	10	s	s	NOUN
ejpam-6407	83	11	}	}	PUNCT
ejpam-6407	83	12	and	and	CCONJ
ejpam-6407	83	13	clsϵ(s	clsϵ(	NOUN
ejpam-6407	83	14	)	)	PUNCT
ejpam-6407	83	15	=	=	VERB
ejpam-6407	84	1	∩{n	∩{n	INTJ
ejpam-6407	84	2	:	:	PUNCT
ejpam-6407	84	3	n	n	NOUN
ejpam-6407	84	4	∈	∈	PROPN
ejpam-6407	84	5	scϵ(λ	scϵ(λ	PROPN
ejpam-6407	84	6	)	)	PUNCT
ejpam-6407	84	7	and	and	CCONJ
ejpam-6407	84	8	s	s	VERB
ejpam-6407	84	9	⊆	⊆	NUM
ejpam-6407	84	10	n	n	CCONJ
ejpam-6407	84	11	}	}	PUNCT
ejpam-6407	84	12	theorem	theorem	VERB
ejpam-6407	84	13	1	1	NUM
ejpam-6407	84	14	.	.	PUNCT
ejpam-6407	85	1	[	[	X
ejpam-6407	85	2	22	22	NUM
ejpam-6407	85	3	]	]	PUNCT
ejpam-6407	85	4	if	if	SCONJ
ejpam-6407	85	5	we	we	PRON
ejpam-6407	85	6	consider	consider	VERB
ejpam-6407	85	7	a	a	DET
ejpam-6407	85	8	subset	subset	NOUN
ejpam-6407	85	9	t	t	NOUN
ejpam-6407	85	10	of	of	ADP
ejpam-6407	85	11	an	an	DET
ejpam-6407	85	12	sts	st	NOUN
ejpam-6407	85	13	(	(	PUNCT
ejpam-6407	85	14	λ	λ	X
ejpam-6407	85	15	,	,	PUNCT
ejpam-6407	85	16	ϑ	ϑ	NOUN
ejpam-6407	85	17	)	)	PUNCT
ejpam-6407	85	18	with	with	ADP
ejpam-6407	85	19	σ	σ	PROPN
ejpam-6407	85	20	⊂	⊂	PROPN
ejpam-6407	85	21	ϑ	ϑ	X
ejpam-6407	85	22	,	,	PUNCT
ejpam-6407	85	23	we	we	PRON
ejpam-6407	85	24	have	have	VERB
ejpam-6407	85	25	that	that	PRON
ejpam-6407	85	26	(	(	PUNCT
ejpam-6407	85	27	1	1	X
ejpam-6407	85	28	)	)	PUNCT
ejpam-6407	85	29	clsϵ(t	clsϵ(t	NOUN
ejpam-6407	85	30	c	c	NOUN
ejpam-6407	85	31	)	)	PUNCT
ejpam-6407	85	32	=	=	NOUN
ejpam-6407	86	1	[	[	X
ejpam-6407	86	2	intsϵ(t	intsϵ(t	NOUN
ejpam-6407	86	3	)	)	PUNCT
ejpam-6407	86	4	]	]	PUNCT
ejpam-6407	86	5	c.	c.	PROPN
ejpam-6407	86	6	(	(	PUNCT
ejpam-6407	86	7	2	2	X
ejpam-6407	86	8	)	)	PUNCT
ejpam-6407	86	9	intsϵ(t	intsϵ(t	NOUN
ejpam-6407	86	10	c	c	NOUN
ejpam-6407	86	11	)	)	PUNCT
ejpam-6407	86	12	=	=	NOUN
ejpam-6407	87	1	[	[	X
ejpam-6407	87	2	clsϵ(t	clsϵ(t	NOUN
ejpam-6407	87	3	)	)	PUNCT
ejpam-6407	87	4	]	]	PUNCT
ejpam-6407	87	5	c.	c.	PROPN
ejpam-6407	87	6	(	(	PUNCT
ejpam-6407	87	7	3	3	NUM
ejpam-6407	87	8	)	)	PUNCT
ejpam-6407	87	9	int(t	int(t	PROPN
ejpam-6407	87	10	)	)	PUNCT
ejpam-6407	87	11	⊆	⊆	NUM
ejpam-6407	87	12	ints(t	ints(t	NOUN
ejpam-6407	87	13	)	)	PUNCT
ejpam-6407	87	14	⊆	⊆	NUM
ejpam-6407	87	15	intsϵ(t	intsϵ(t	NOUN
ejpam-6407	87	16	)	)	PUNCT
ejpam-6407	87	17	,	,	PUNCT
ejpam-6407	87	18	where	where	SCONJ
ejpam-6407	87	19	int(t	int(t	PROPN
ejpam-6407	87	20	)	)	PUNCT
ejpam-6407	87	21	refers	refer	VERB
ejpam-6407	87	22	the	the	DET
ejpam-6407	87	23	interior	interior	NOUN
ejpam-6407	87	24	of	of	ADP
ejpam-6407	87	25	t	t	PROPN
ejpam-6407	87	26	w.r.t	w.r.t	PROPN
ejpam-6407	87	27	σ	σ	PROPN
ejpam-6407	87	28	.	.	PUNCT
ejpam-6407	88	1	(	(	PUNCT
ejpam-6407	88	2	4	4	X
ejpam-6407	88	3	)	)	PUNCT
ejpam-6407	88	4	clsϵ(t	clsϵ(t	NOUN
ejpam-6407	88	5	)	)	PUNCT
ejpam-6407	88	6	⊆	⊆	NUM
ejpam-6407	88	7	cls(t	cls(t	X
ejpam-6407	88	8	)	)	PUNCT
ejpam-6407	88	9	⊆	⊆	NUM
ejpam-6407	88	10	cl(t	cl(t	NOUN
ejpam-6407	88	11	)	)	PUNCT
ejpam-6407	88	12	,	,	PUNCT
ejpam-6407	88	13	where	where	SCONJ
ejpam-6407	88	14	cl(t	cl(t	X
ejpam-6407	88	15	)	)	PUNCT
ejpam-6407	88	16	refers	refer	VERB
ejpam-6407	88	17	the	the	DET
ejpam-6407	88	18	closure	closure	NOUN
ejpam-6407	88	19	of	of	ADP
ejpam-6407	88	20	t	t	PROPN
ejpam-6407	88	21	w.r.t	w.r.t	PROPN
ejpam-6407	88	22	σ	σ	PROPN
ejpam-6407	88	23	.	.	PUNCT
ejpam-6407	88	24	definition	definition	NOUN
ejpam-6407	88	25	7	7	NUM
ejpam-6407	88	26	.	.	PUNCT
ejpam-6407	89	1	[	[	X
ejpam-6407	89	2	22	22	NUM
ejpam-6407	89	3	]	]	PUNCT
ejpam-6407	89	4	let	let	VERB
ejpam-6407	89	5	t	t	NOUN
ejpam-6407	89	6	be	be	AUX
ejpam-6407	89	7	a	a	DET
ejpam-6407	89	8	subset	subset	NOUN
ejpam-6407	89	9	of	of	ADP
ejpam-6407	89	10	an	an	DET
ejpam-6407	89	11	sts	st	NOUN
ejpam-6407	89	12	(	(	PUNCT
ejpam-6407	89	13	λ	λ	X
ejpam-6407	89	14	,	,	PUNCT
ejpam-6407	89	15	ϑ	ϑ	NOUN
ejpam-6407	89	16	)	)	PUNCT
ejpam-6407	89	17	with	with	ADP
ejpam-6407	89	18	an	an	DET
ejpam-6407	89	19	arbitrary	arbitrary	ADJ
ejpam-6407	89	20	point	point	NOUN
ejpam-6407	89	21	s	s	VERB
ejpam-6407	89	22	∈	∈	PROPN
ejpam-6407	89	23	λ	λ	NOUN
ejpam-6407	89	24	.	.	PUNCT
ejpam-6407	90	1	if	if	SCONJ
ejpam-6407	90	2	each	each	DET
ejpam-6407	90	3	supra	supra	PROPN
ejpam-6407	90	4	ϵ-open	ϵ-open	PROPN
ejpam-6407	90	5	set	set	VERB
ejpam-6407	90	6	js	js	ADV
ejpam-6407	90	7	containing	contain	VERB
ejpam-6407	90	8	s	s	PART
ejpam-6407	90	9	,	,	PUNCT
ejpam-6407	90	10	we	we	PRON
ejpam-6407	90	11	have	have	VERB
ejpam-6407	90	12	that	that	PRON
ejpam-6407	90	13	[	[	X
ejpam-6407	90	14	t\{s	t\{s	X
ejpam-6407	90	15	}	}	PUNCT
ejpam-6407	90	16	]	]	PUNCT
ejpam-6407	90	17	∩	∩	PROPN
ejpam-6407	90	18	js	js	PROPN
ejpam-6407	90	19	̸=	̸=	PROPN
ejpam-6407	90	20	∅	∅	NOUN
ejpam-6407	90	21	,	,	PUNCT
ejpam-6407	90	22	then	then	ADV
ejpam-6407	90	23	s	s	VERB
ejpam-6407	90	24	is	be	AUX
ejpam-6407	90	25	referred	refer	VERB
ejpam-6407	90	26	to	to	ADP
ejpam-6407	90	27	as	as	ADP
ejpam-6407	90	28	a	a	DET
ejpam-6407	90	29	supra	supra	ADJ
ejpam-6407	90	30	ϵ-accumulation	ϵ-accumulation	NOUN
ejpam-6407	90	31	point	point	NOUN
ejpam-6407	90	32	of	of	ADP
ejpam-6407	90	33	t	t	PROPN
ejpam-6407	90	34	.	.	PUNCT
ejpam-6407	91	1	the	the	DET
ejpam-6407	91	2	notation	notation	NOUN
ejpam-6407	91	3	accϵ(t	accϵ(t	NOUN
ejpam-6407	91	4	)	)	PUNCT
ejpam-6407	91	5	will	will	AUX
ejpam-6407	91	6	represent	represent	VERB
ejpam-6407	91	7	the	the	DET
ejpam-6407	91	8	set	set	NOUN
ejpam-6407	91	9	of	of	ADP
ejpam-6407	91	10	all	all	DET
ejpam-6407	91	11	supra	supra	ADJ
ejpam-6407	91	12	ϵ-accumulation	ϵ-accumulation	PROPN
ejpam-6407	91	13	points	point	NOUN
ejpam-6407	91	14	of	of	ADP
ejpam-6407	91	15	t	t	PROPN
ejpam-6407	91	16	.	.	PUNCT
ejpam-6407	92	1	3	3	X
ejpam-6407	92	2	.	.	X
ejpam-6407	92	3	separation	separation	NOUN
ejpam-6407	92	4	axioms	axiom	NOUN
ejpam-6407	92	5	inspired	inspire	VERB
ejpam-6407	92	6	by	by	ADP
ejpam-6407	92	7	supra	supra	PROPN
ejpam-6407	92	8	ϵ-open	ϵ-open	PROPN
ejpam-6407	92	9	sets	set	NOUN
ejpam-6407	92	10	and	and	CCONJ
ejpam-6407	92	11	relationships	relationship	NOUN
ejpam-6407	92	12	in	in	ADP
ejpam-6407	92	13	this	this	DET
ejpam-6407	92	14	section	section	NOUN
ejpam-6407	92	15	,	,	PUNCT
ejpam-6407	92	16	we	we	PRON
ejpam-6407	92	17	present	present	VERB
ejpam-6407	92	18	three	three	NUM
ejpam-6407	92	19	new	new	ADJ
ejpam-6407	92	20	types	type	NOUN
ejpam-6407	92	21	of	of	ADP
ejpam-6407	92	22	separation	separation	NOUN
ejpam-6407	92	23	axioms	axiom	NOUN
ejpam-6407	92	24	inspired	inspire	VERB
ejpam-6407	92	25	by	by	ADP
ejpam-6407	92	26	supra	supra	PROPN
ejpam-6407	92	27	ϵ-open	ϵ-open	PROPN
ejpam-6407	92	28	sets	set	NOUN
ejpam-6407	92	29	named	name	VERB
ejpam-6407	92	30	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	92	31	-	-	NOUN
ejpam-6407	92	32	space	space	NOUN
ejpam-6407	92	33	,	,	PUNCT
ejpam-6407	92	34	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6407	92	35	-	-	PUNCT
ejpam-6407	92	36	space	space	NOUN
ejpam-6407	92	37	,	,	PUNCT
ejpam-6407	92	38	and	and	CCONJ
ejpam-6407	92	39	supra-ϵ-hausdorff	supra-ϵ-hausdorff	NOUN
ejpam-6407	92	40	-	-	PUNCT
ejpam-6407	92	41	space	space	NOUN
ejpam-6407	92	42	.	.	PUNCT
ejpam-6407	93	1	we	we	PRON
ejpam-6407	93	2	provide	provide	VERB
ejpam-6407	93	3	thorough	thorough	ADJ
ejpam-6407	93	4	descriptions	description	NOUN
ejpam-6407	93	5	of	of	ADP
ejpam-6407	93	6	each	each	PRON
ejpam-6407	93	7	of	of	ADP
ejpam-6407	93	8	them	they	PRON
ejpam-6407	93	9	.	.	PUNCT
ejpam-6407	94	1	specifically	specifically	ADV
ejpam-6407	94	2	,	,	PUNCT
ejpam-6407	94	3	we	we	PRON
ejpam-6407	94	4	explore	explore	VERB
ejpam-6407	94	5	sufficient	sufficient	ADJ
ejpam-6407	94	6	conditions	condition	NOUN
ejpam-6407	94	7	for	for	ADP
ejpam-6407	94	8	several	several	ADJ
ejpam-6407	94	9	analogous	analogous	ADJ
ejpam-6407	94	10	linkages	linkage	NOUN
ejpam-6407	94	11	between	between	ADP
ejpam-6407	94	12	them	they	PRON
ejpam-6407	94	13	and	and	CCONJ
ejpam-6407	94	14	generally	generally	ADV
ejpam-6407	94	15	illustrate	illustrate	VERB
ejpam-6407	94	16	their	their	PRON
ejpam-6407	94	17	key	key	ADJ
ejpam-6407	94	18	characteristics	characteristic	NOUN
ejpam-6407	94	19	.	.	PUNCT
ejpam-6407	95	1	moreover	moreover	ADV
ejpam-6407	95	2	,	,	PUNCT
ejpam-6407	95	3	we	we	PRON
ejpam-6407	95	4	propose	propose	VERB
ejpam-6407	95	5	a	a	DET
ejpam-6407	95	6	diagram	diagram	NOUN
ejpam-6407	96	1	[	[	X
ejpam-6407	96	2	see	see	VERB
ejpam-6407	96	3	diagram	diagram	NOUN
ejpam-6407	96	4	1	1	NUM
ejpam-6407	96	5	]	]	PUNCT
ejpam-6407	96	6	that	that	PRON
ejpam-6407	96	7	summarizes	summarize	VERB
ejpam-6407	96	8	their	their	PRON
ejpam-6407	96	9	relationships	relationship	NOUN
ejpam-6407	96	10	.	.	PUNCT
ejpam-6407	97	1	furthermore	furthermore	ADV
ejpam-6407	97	2	,	,	PUNCT
ejpam-6407	97	3	we	we	PRON
ejpam-6407	97	4	introduce	introduce	VERB
ejpam-6407	97	5	the	the	DET
ejpam-6407	97	6	supra	supra	PROPN
ejpam-6407	97	7	ϵ-symmetric	ϵ-symmetric	ADJ
ejpam-6407	97	8	property	property	NOUN
ejpam-6407	97	9	and	and	CCONJ
ejpam-6407	97	10	demonstrate	demonstrate	VERB
ejpam-6407	97	11	that	that	SCONJ
ejpam-6407	97	12	,	,	PUNCT
ejpam-6407	97	13	for	for	ADP
ejpam-6407	97	14	any	any	DET
ejpam-6407	97	15	sts	st	NOUN
ejpam-6407	97	16	that	that	PRON
ejpam-6407	97	17	satisfies	satisfy	VERB
ejpam-6407	97	18	it	it	PRON
ejpam-6407	97	19	,	,	PUNCT
ejpam-6407	97	20	the	the	DET
ejpam-6407	97	21	two	two	NUM
ejpam-6407	97	22	approaches	approach	NOUN
ejpam-6407	97	23	of	of	ADP
ejpam-6407	97	24	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	97	25	-	-	NOUN
ejpam-6407	97	26	space	space	NOUN
ejpam-6407	97	27	and	and	CCONJ
ejpam-6407	97	28	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6407	97	29	-	-	PUNCT
ejpam-6407	97	30	space	space	NOUN
ejpam-6407	97	31	are	be	AUX
ejpam-6407	97	32	identical	identical	ADJ
ejpam-6407	97	33	.	.	PUNCT
ejpam-6407	98	1	definition	definition	NOUN
ejpam-6407	98	2	8	8	NUM
ejpam-6407	98	3	.	.	PUNCT
ejpam-6407	99	1	an	an	DET
ejpam-6407	99	2	sts	st	NOUN
ejpam-6407	99	3	(	(	PUNCT
ejpam-6407	99	4	λ	λ	X
ejpam-6407	99	5	,	,	PUNCT
ejpam-6407	99	6	ϑ	ϑ	NOUN
ejpam-6407	99	7	)	)	PUNCT
ejpam-6407	99	8	is	be	AUX
ejpam-6407	99	9	said	say	VERB
ejpam-6407	99	10	to	to	PART
ejpam-6407	99	11	be	be	AUX
ejpam-6407	99	12	(	(	PUNCT
ejpam-6407	99	13	1	1	X
ejpam-6407	99	14	)	)	PUNCT
ejpam-6407	99	15	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	99	16	-	-	NOUN
ejpam-6407	99	17	space	space	NOUN
ejpam-6407	99	18	if	if	SCONJ
ejpam-6407	99	19	for	for	ADP
ejpam-6407	99	20	each	each	DET
ejpam-6407	99	21	two	two	NUM
ejpam-6407	99	22	distinct	distinct	ADJ
ejpam-6407	99	23	points	point	NOUN
ejpam-6407	99	24	there	there	PRON
ejpam-6407	99	25	is	be	VERB
ejpam-6407	99	26	a	a	DET
ejpam-6407	99	27	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	99	28	set	set	NOUN
ejpam-6407	99	29	including	include	VERB
ejpam-6407	99	30	one	one	NUM
ejpam-6407	99	31	but	but	CCONJ
ejpam-6407	99	32	excluding	exclude	VERB
ejpam-6407	99	33	the	the	DET
ejpam-6407	99	34	other	other	ADJ
ejpam-6407	99	35	.	.	PUNCT
ejpam-6407	100	1	(	(	PUNCT
ejpam-6407	100	2	2	2	X
ejpam-6407	100	3	)	)	PUNCT
ejpam-6407	100	4	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6407	100	5	-	-	PUNCT
ejpam-6407	100	6	space	space	NOUN
ejpam-6407	100	7	if	if	SCONJ
ejpam-6407	100	8	for	for	ADP
ejpam-6407	100	9	each	each	DET
ejpam-6407	100	10	two	two	NUM
ejpam-6407	100	11	distinct	distinct	ADJ
ejpam-6407	100	12	points	point	NOUN
ejpam-6407	100	13	ν1	ν1	NOUN
ejpam-6407	100	14	,	,	PUNCT
ejpam-6407	100	15	ν2	ν2	NOUN
ejpam-6407	100	16	∈	∈	PROPN
ejpam-6407	100	17	λ	λ	NOUN
ejpam-6407	100	18	,	,	PUNCT
ejpam-6407	100	19	then	then	ADV
ejpam-6407	100	20	there	there	PRON
ejpam-6407	100	21	are	be	VERB
ejpam-6407	100	22	two	two	NUM
ejpam-6407	100	23	supra-ϵopen	supra-ϵopen	ADJ
ejpam-6407	100	24	subsets	subset	NOUN
ejpam-6407	100	25	µ1	µ1	PROPN
ejpam-6407	100	26	and	and	CCONJ
ejpam-6407	100	27	µ2	µ2	PROPN
ejpam-6407	100	28	of	of	ADP
ejpam-6407	100	29	λ	λ	PROPN
ejpam-6407	100	30	,	,	PUNCT
ejpam-6407	100	31	such	such	ADJ
ejpam-6407	100	32	that	that	SCONJ
ejpam-6407	100	33	ν1	ν1	PROPN
ejpam-6407	100	34	∈	∈	PROPN
ejpam-6407	100	35	µ1	µ1	PROPN
ejpam-6407	100	36	,	,	PUNCT
ejpam-6407	100	37	ν2	ν2	NOUN
ejpam-6407	100	38	/∈	/∈	PUNCT
ejpam-6407	100	39	µ1	µ1	PROPN
ejpam-6407	100	40	,	,	PUNCT
ejpam-6407	100	41	and	and	CCONJ
ejpam-6407	100	42	ν1	ν1	NOUN
ejpam-6407	100	43	/∈	/∈	PUNCT
ejpam-6407	101	1	µ2	µ2	PROPN
ejpam-6407	101	2	,	,	PUNCT
ejpam-6407	101	3	ν2	ν2	NOUN
ejpam-6407	101	4	∈	∈	PROPN
ejpam-6407	101	5	µ2	µ2	NOUN
ejpam-6407	101	6	.	.	PUNCT
ejpam-6407	102	1	(	(	PUNCT
ejpam-6407	102	2	3	3	X
ejpam-6407	102	3	)	)	PUNCT
ejpam-6407	102	4	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6407	102	5	-	-	PUNCT
ejpam-6407	102	6	space	space	NOUN
ejpam-6407	102	7	”	"	PUNCT
ejpam-6407	102	8	supra-ϵ-hausdorff	supra-ϵ-hausdorff	PROPN
ejpam-6407	102	9	space	space	NOUN
ejpam-6407	102	10	”	"	PUNCT
ejpam-6407	102	11	if	if	SCONJ
ejpam-6407	102	12	for	for	ADP
ejpam-6407	102	13	each	each	DET
ejpam-6407	102	14	two	two	NUM
ejpam-6407	102	15	distinct	distinct	ADJ
ejpam-6407	102	16	points	point	NOUN
ejpam-6407	102	17	ν1	ν1	NOUN
ejpam-6407	102	18	,	,	PUNCT
ejpam-6407	102	19	ν2	ν2	NOUN
ejpam-6407	102	20	∈	∈	PROPN
ejpam-6407	102	21	λ	λ	NOUN
ejpam-6407	102	22	,	,	PUNCT
ejpam-6407	102	23	then	then	ADV
ejpam-6407	102	24	there	there	PRON
ejpam-6407	102	25	are	be	VERB
ejpam-6407	102	26	two	two	NUM
ejpam-6407	102	27	disjoint	disjoint	NOUN
ejpam-6407	102	28	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	102	29	subsets	subset	NOUN
ejpam-6407	102	30	µ1	µ1	PROPN
ejpam-6407	102	31	and	and	CCONJ
ejpam-6407	102	32	µ2	µ2	PROPN
ejpam-6407	102	33	of	of	ADP
ejpam-6407	102	34	λ	λ	PROPN
ejpam-6407	102	35	,	,	PUNCT
ejpam-6407	102	36	such	such	ADJ
ejpam-6407	102	37	that	that	SCONJ
ejpam-6407	102	38	ν1	ν1	PROPN
ejpam-6407	102	39	∈	∈	PROPN
ejpam-6407	102	40	µ1	µ1	NOUN
ejpam-6407	102	41	and	and	CCONJ
ejpam-6407	102	42	ν2	ν2	PROPN
ejpam-6407	102	43	∈	∈	PROPN
ejpam-6407	102	44	µ2	µ2	PROPN
ejpam-6407	102	45	.	.	PUNCT
ejpam-6407	102	46	theorem	theorem	PROPN
ejpam-6407	102	47	2	2	NUM
ejpam-6407	102	48	.	.	PUNCT
ejpam-6407	103	1	(	(	PUNCT
ejpam-6407	103	2	1	1	X
ejpam-6407	103	3	)	)	PUNCT
ejpam-6407	103	4	any	any	DET
ejpam-6407	103	5	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6407	103	6	-	-	PUNCT
ejpam-6407	103	7	space	space	NOUN
ejpam-6407	103	8	is	be	AUX
ejpam-6407	103	9	supra-ϵ-tj−1	supra-ϵ-tj−1	NOUN
ejpam-6407	103	10	,	,	PUNCT
ejpam-6407	103	11	j	j	NOUN
ejpam-6407	103	12	=	=	SYM
ejpam-6407	103	13	1	1	NUM
ejpam-6407	103	14	,	,	PUNCT
ejpam-6407	103	15	2	2	NUM
ejpam-6407	103	16	.	.	PUNCT
ejpam-6407	103	17	(	(	PUNCT
ejpam-6407	103	18	2	2	X
ejpam-6407	103	19	)	)	PUNCT
ejpam-6407	103	20	any	any	DET
ejpam-6407	103	21	supra	supra	NOUN
ejpam-6407	103	22	-	-	PUNCT
ejpam-6407	103	23	tj	tj	NOUN
ejpam-6407	103	24	-	-	PUNCT
ejpam-6407	103	25	space	space	NOUN
ejpam-6407	103	26	is	be	AUX
ejpam-6407	103	27	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6407	103	28	,	,	PUNCT
ejpam-6407	104	1	j	j	PROPN
ejpam-6407	104	2	=	=	SYM
ejpam-6407	104	3	1	1	NUM
ejpam-6407	104	4	,	,	PUNCT
ejpam-6407	104	5	2	2	NUM
ejpam-6407	104	6	.	.	PUNCT
ejpam-6407	104	7	proof	proof	NOUN
ejpam-6407	104	8	.	.	PUNCT
ejpam-6407	105	1	it	it	PRON
ejpam-6407	105	2	is	be	AUX
ejpam-6407	105	3	clear	clear	ADJ
ejpam-6407	105	4	from	from	ADP
ejpam-6407	105	5	definition	definition	NOUN
ejpam-6407	105	6	8	8	NUM
ejpam-6407	105	7	and	and	CCONJ
ejpam-6407	105	8	form	form	VERB
ejpam-6407	105	9	the	the	DET
ejpam-6407	105	10	fact	fact	NOUN
ejpam-6407	105	11	that	that	SCONJ
ejpam-6407	105	12	every	every	DET
ejpam-6407	105	13	supra	supra	PROPN
ejpam-6407	105	14	open	open	ADJ
ejpam-6407	105	15	set	set	NOUN
ejpam-6407	105	16	is	be	AUX
ejpam-6407	105	17	supra	supra	PROPN
ejpam-6407	105	18	ϵ-open	ϵ-open	PROPN
ejpam-6407	105	19	.	.	PUNCT
ejpam-6407	106	1	m.	m.	NOUN
ejpam-6407	106	2	aldawood	aldawood	PROPN
ejpam-6407	106	3	et	et	PROPN
ejpam-6407	106	4	al	al	PROPN
ejpam-6407	106	5	.	.	PUNCT
ejpam-6407	106	6	/	/	SYM
ejpam-6407	106	7	eur	eur	PROPN
ejpam-6407	106	8	.	.	PUNCT
ejpam-6407	107	1	j.	j.	PROPN
ejpam-6407	107	2	pure	pure	PROPN
ejpam-6407	107	3	appl	appl	PROPN
ejpam-6407	107	4	.	.	PROPN
ejpam-6407	107	5	math	math	PROPN
ejpam-6407	107	6	,	,	PUNCT
ejpam-6407	107	7	18	18	NUM
ejpam-6407	107	8	(	(	PUNCT
ejpam-6407	107	9	3	3	NUM
ejpam-6407	107	10	)	)	PUNCT
ejpam-6407	107	11	(	(	PUNCT
ejpam-6407	107	12	2025	2025	NUM
ejpam-6407	107	13	)	)	PUNCT
ejpam-6407	107	14	,	,	PUNCT
ejpam-6407	107	15	6407	6407	NUM
ejpam-6407	107	16	5	5	NUM
ejpam-6407	107	17	of	of	ADP
ejpam-6407	107	18	15	15	NUM
ejpam-6407	107	19	remark	remark	NOUN
ejpam-6407	107	20	1	1	NUM
ejpam-6407	107	21	.	.	PUNCT
ejpam-6407	108	1	the	the	DET
ejpam-6407	108	2	converse	converse	NOUN
ejpam-6407	108	3	of	of	ADP
ejpam-6407	108	4	theorem	theorem	ADJ
ejpam-6407	108	5	2	2	NUM
ejpam-6407	108	6	is	be	AUX
ejpam-6407	108	7	not	not	PART
ejpam-6407	108	8	hold	hold	NOUN
ejpam-6407	108	9	as	as	SCONJ
ejpam-6407	108	10	the	the	DET
ejpam-6407	108	11	upcoming	upcoming	ADJ
ejpam-6407	108	12	examples	example	NOUN
ejpam-6407	108	13	will	will	AUX
ejpam-6407	108	14	demonstrate	demonstrate	VERB
ejpam-6407	108	15	.	.	PUNCT
ejpam-6407	108	16	example	example	NOUN
ejpam-6407	109	1	1	1	NUM
ejpam-6407	109	2	.	.	PUNCT
ejpam-6407	109	3	(	(	PUNCT
ejpam-6407	109	4	1	1	X
ejpam-6407	109	5	)	)	PUNCT
ejpam-6407	109	6	let	let	VERB
ejpam-6407	109	7	ϑ	ϑ	X
ejpam-6407	109	8	=	=	X
ejpam-6407	109	9	{	{	PUNCT
ejpam-6407	109	10	λ	λ	PROPN
ejpam-6407	109	11	,	,	PUNCT
ejpam-6407	109	12	∅	∅	NOUN
ejpam-6407	109	13	,	,	PUNCT
ejpam-6407	109	14	{	{	PUNCT
ejpam-6407	109	15	b	b	NOUN
ejpam-6407	109	16	}	}	PUNCT
ejpam-6407	109	17	}	}	PUNCT
ejpam-6407	109	18	be	be	AUX
ejpam-6407	109	19	an	an	DET
ejpam-6407	109	20	sts	st	NOUN
ejpam-6407	109	21	on	on	ADP
ejpam-6407	109	22	λ	λ	X
ejpam-6407	109	23	=	=	PUNCT
ejpam-6407	109	24	{	{	PUNCT
ejpam-6407	109	25	v	v	NOUN
ejpam-6407	109	26	,	,	PUNCT
ejpam-6407	109	27	b	b	NOUN
ejpam-6407	109	28	,	,	PUNCT
ejpam-6407	109	29	n	n	CCONJ
ejpam-6407	109	30	}	}	PUNCT
ejpam-6407	109	31	.	.	PUNCT
ejpam-6407	110	1	then	then	ADV
ejpam-6407	110	2	we	we	PRON
ejpam-6407	110	3	have	have	VERB
ejpam-6407	110	4	that	that	PRON
ejpam-6407	110	5	soϵ(λ	soϵ(λ	NOUN
ejpam-6407	110	6	)	)	PUNCT
ejpam-6407	110	7	=	=	PRON
ejpam-6407	110	8	{	{	PUNCT
ejpam-6407	110	9	λ	λ	NOUN
ejpam-6407	110	10	,	,	PUNCT
ejpam-6407	110	11	∅	∅	NOUN
ejpam-6407	110	12	,	,	PUNCT
ejpam-6407	110	13	{	{	PUNCT
ejpam-6407	110	14	v	v	NOUN
ejpam-6407	110	15	,	,	PUNCT
ejpam-6407	110	16	b	b	NOUN
ejpam-6407	110	17	}	}	PUNCT
ejpam-6407	110	18	,	,	PUNCT
ejpam-6407	110	19	{	{	PUNCT
ejpam-6407	110	20	b	b	NOUN
ejpam-6407	110	21	,	,	PUNCT
ejpam-6407	110	22	n	n	CCONJ
ejpam-6407	110	23	}	}	PUNCT
ejpam-6407	110	24	,	,	PUNCT
ejpam-6407	110	25	{	{	PUNCT
ejpam-6407	110	26	b	b	X
ejpam-6407	110	27	}	}	PUNCT
ejpam-6407	110	28	}	}	PUNCT
ejpam-6407	110	29	.	.	PUNCT
ejpam-6407	111	1	it	it	PRON
ejpam-6407	111	2	easy	easy	ADJ
ejpam-6407	111	3	to	to	PART
ejpam-6407	111	4	check	check	VERB
ejpam-6407	111	5	that	that	PRON
ejpam-6407	111	6	,	,	PUNCT
ejpam-6407	111	7	λ	λ	PROPN
ejpam-6407	111	8	is	be	AUX
ejpam-6407	111	9	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	111	10	-	-	NOUN
ejpam-6407	111	11	space	space	NOUN
ejpam-6407	111	12	,	,	PUNCT
ejpam-6407	111	13	however	however	ADV
ejpam-6407	111	14	λ	λ	PROPN
ejpam-6407	111	15	is	be	AUX
ejpam-6407	111	16	not	not	PART
ejpam-6407	111	17	supra-ϵ-t1	supra-ϵ-t1	VERB
ejpam-6407	111	18	,	,	PUNCT
ejpam-6407	111	19	since	since	SCONJ
ejpam-6407	111	20	v	v	ADP
ejpam-6407	111	21	̸=	̸=	PROPN
ejpam-6407	111	22	n	n	CCONJ
ejpam-6407	111	23	∈	∈	PROPN
ejpam-6407	111	24	λ	λ	NOUN
ejpam-6407	111	25	,	,	PUNCT
ejpam-6407	111	26	however	however	ADV
ejpam-6407	111	27	there	there	PRON
ejpam-6407	111	28	are	be	VERB
ejpam-6407	111	29	not	not	PART
ejpam-6407	111	30	two	two	NUM
ejpam-6407	111	31	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	111	32	subsets	subset	NOUN
ejpam-6407	111	33	of	of	ADP
ejpam-6407	111	34	λ	λ	PROPN
ejpam-6407	111	35	separate	separate	VERB
ejpam-6407	111	36	them	they	PRON
ejpam-6407	111	37	.	.	PUNCT
ejpam-6407	112	1	(	(	PUNCT
ejpam-6407	112	2	2	2	X
ejpam-6407	112	3	)	)	PUNCT
ejpam-6407	112	4	let	let	VERB
ejpam-6407	112	5	ϑ	ϑ	X
ejpam-6407	112	6	=	=	X
ejpam-6407	112	7	{	{	PUNCT
ejpam-6407	112	8	λ	λ	PROPN
ejpam-6407	112	9	,	,	PUNCT
ejpam-6407	112	10	∅	∅	NOUN
ejpam-6407	112	11	,	,	PUNCT
ejpam-6407	112	12	{	{	PUNCT
ejpam-6407	112	13	a	a	DET
ejpam-6407	112	14	,	,	PUNCT
ejpam-6407	112	15	s	s	PART
ejpam-6407	112	16	}	}	PUNCT
ejpam-6407	112	17	,	,	PUNCT
ejpam-6407	112	18	{	{	PUNCT
ejpam-6407	112	19	a	a	PRON
ejpam-6407	112	20	,	,	PUNCT
ejpam-6407	112	21	s	s	NOUN
ejpam-6407	112	22	,	,	PUNCT
ejpam-6407	112	23	d	d	NOUN
ejpam-6407	112	24	}	}	PUNCT
ejpam-6407	112	25	,	,	PUNCT
ejpam-6407	112	26	{	{	PUNCT
ejpam-6407	112	27	a	a	DET
ejpam-6407	112	28	,	,	PUNCT
ejpam-6407	112	29	d	d	NOUN
ejpam-6407	112	30	}	}	PUNCT
ejpam-6407	112	31	,	,	PUNCT
ejpam-6407	112	32	{	{	PUNCT
ejpam-6407	112	33	s	s	X
ejpam-6407	112	34	,	,	PUNCT
ejpam-6407	112	35	d	d	NOUN
ejpam-6407	112	36	}	}	PUNCT
ejpam-6407	112	37	}	}	PUNCT
ejpam-6407	112	38	be	be	AUX
ejpam-6407	112	39	an	an	DET
ejpam-6407	112	40	sts	st	NOUN
ejpam-6407	112	41	on	on	ADP
ejpam-6407	112	42	λ	λ	X
ejpam-6407	112	43	=	=	PUNCT
ejpam-6407	112	44	{	{	PUNCT
ejpam-6407	112	45	a	a	X
ejpam-6407	112	46	,	,	PUNCT
ejpam-6407	112	47	s	s	NOUN
ejpam-6407	112	48	,	,	PUNCT
ejpam-6407	112	49	d	d	PROPN
ejpam-6407	112	50	,	,	PUNCT
ejpam-6407	112	51	f	f	NOUN
ejpam-6407	112	52	}	}	PUNCT
ejpam-6407	112	53	.	.	PUNCT
ejpam-6407	113	1	then	then	ADV
ejpam-6407	113	2	we	we	PRON
ejpam-6407	113	3	have	have	VERB
ejpam-6407	113	4	that	that	PRON
ejpam-6407	113	5	soϵ(λ	soϵ(λ	NOUN
ejpam-6407	113	6	)	)	PUNCT
ejpam-6407	113	7	=	=	PRON
ejpam-6407	113	8	{	{	PUNCT
ejpam-6407	113	9	λ	λ	NOUN
ejpam-6407	113	10	,	,	PUNCT
ejpam-6407	113	11	∅	∅	NOUN
ejpam-6407	113	12	,	,	PUNCT
ejpam-6407	113	13	{	{	PUNCT
ejpam-6407	113	14	a	a	PRON
ejpam-6407	113	15	,	,	PUNCT
ejpam-6407	113	16	s	s	PART
ejpam-6407	113	17	}	}	PUNCT
ejpam-6407	113	18	,	,	PUNCT
ejpam-6407	113	19	{	{	PUNCT
ejpam-6407	113	20	a	a	DET
ejpam-6407	113	21	,	,	PUNCT
ejpam-6407	113	22	d	d	NOUN
ejpam-6407	113	23	}	}	PUNCT
ejpam-6407	113	24	,	,	PUNCT
ejpam-6407	113	25	{	{	PUNCT
ejpam-6407	113	26	s	s	X
ejpam-6407	113	27	,	,	PUNCT
ejpam-6407	113	28	d	d	NOUN
ejpam-6407	113	29	}	}	PUNCT
ejpam-6407	113	30	,	,	PUNCT
ejpam-6407	113	31	{	{	PUNCT
ejpam-6407	113	32	a	a	PRON
ejpam-6407	113	33	,	,	PUNCT
ejpam-6407	113	34	s	s	NOUN
ejpam-6407	113	35	,	,	PUNCT
ejpam-6407	113	36	d	d	NOUN
ejpam-6407	113	37	}	}	PUNCT
ejpam-6407	113	38	,	,	PUNCT
ejpam-6407	113	39	{	{	PUNCT
ejpam-6407	113	40	a	a	PRON
ejpam-6407	113	41	,	,	PUNCT
ejpam-6407	113	42	s	s	PROPN
ejpam-6407	113	43	,	,	PUNCT
ejpam-6407	113	44	f	f	PROPN
ejpam-6407	113	45	}	}	PUNCT
ejpam-6407	113	46	,	,	PUNCT
ejpam-6407	113	47	{	{	PUNCT
ejpam-6407	113	48	a	a	DET
ejpam-6407	113	49	,	,	PUNCT
ejpam-6407	113	50	d	d	NOUN
ejpam-6407	113	51	,	,	PUNCT
ejpam-6407	113	52	f	f	PROPN
ejpam-6407	113	53	}	}	PUNCT
ejpam-6407	113	54	,	,	PUNCT
ejpam-6407	113	55	{	{	PUNCT
ejpam-6407	113	56	s	s	X
ejpam-6407	113	57	,	,	PUNCT
ejpam-6407	113	58	d	d	NOUN
ejpam-6407	113	59	,	,	PUNCT
ejpam-6407	113	60	f	f	NOUN
ejpam-6407	113	61	}	}	PUNCT
ejpam-6407	113	62	}	}	PUNCT
ejpam-6407	113	63	.	.	PUNCT
ejpam-6407	114	1	it	it	PRON
ejpam-6407	114	2	follows	follow	VERB
ejpam-6407	114	3	that	that	SCONJ
ejpam-6407	114	4	,	,	PUNCT
ejpam-6407	114	5	λ	λ	PROPN
ejpam-6407	114	6	is	be	AUX
ejpam-6407	114	7	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6407	114	8	-	-	PUNCT
ejpam-6407	114	9	space	space	NOUN
ejpam-6407	114	10	,	,	PUNCT
ejpam-6407	114	11	however	however	ADV
ejpam-6407	114	12	λ	λ	PROPN
ejpam-6407	114	13	is	be	AUX
ejpam-6407	114	14	not	not	PART
ejpam-6407	114	15	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6407	114	16	,	,	PUNCT
ejpam-6407	114	17	since	since	SCONJ
ejpam-6407	114	18	d	d	PROPN
ejpam-6407	114	19	̸=	̸=	PROPN
ejpam-6407	114	20	f	f	PROPN
ejpam-6407	114	21	∈	∈	PROPN
ejpam-6407	114	22	λ	λ	PROPN
ejpam-6407	114	23	,	,	PUNCT
ejpam-6407	114	24	however	however	ADV
ejpam-6407	114	25	there	there	PRON
ejpam-6407	114	26	are	be	VERB
ejpam-6407	114	27	not	not	PART
ejpam-6407	114	28	two	two	NUM
ejpam-6407	114	29	disjoint	disjoint	ADJ
ejpam-6407	114	30	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	114	31	subsets	subset	NOUN
ejpam-6407	114	32	of	of	ADP
ejpam-6407	114	33	λ	λ	PROPN
ejpam-6407	114	34	separates	separate	VERB
ejpam-6407	114	35	them	they	PRON
ejpam-6407	114	36	.	.	PUNCT
ejpam-6407	114	37	.	.	PUNCT
ejpam-6407	115	1	(	(	PUNCT
ejpam-6407	115	2	3	3	X
ejpam-6407	115	3	)	)	PUNCT
ejpam-6407	115	4	in	in	ADP
ejpam-6407	115	5	(	(	PUNCT
ejpam-6407	115	6	1	1	NUM
ejpam-6407	115	7	)	)	PUNCT
ejpam-6407	115	8	,	,	PUNCT
ejpam-6407	115	9	we	we	PRON
ejpam-6407	115	10	have	have	VERB
ejpam-6407	115	11	that	that	DET
ejpam-6407	115	12	λ	λ	PROPN
ejpam-6407	115	13	is	be	AUX
ejpam-6407	115	14	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	115	15	-	-	NOUN
ejpam-6407	115	16	space	space	NOUN
ejpam-6407	115	17	,	,	PUNCT
ejpam-6407	115	18	however	however	ADV
ejpam-6407	115	19	λ	λ	PROPN
ejpam-6407	115	20	is	be	AUX
ejpam-6407	115	21	not	not	PART
ejpam-6407	115	22	supra	supra	NOUN
ejpam-6407	115	23	-	-	PUNCT
ejpam-6407	115	24	t0	t0	NOUN
ejpam-6407	115	25	,	,	PUNCT
ejpam-6407	115	26	since	since	SCONJ
ejpam-6407	115	27	v	v	ADP
ejpam-6407	115	28	̸=	̸=	PROPN
ejpam-6407	115	29	n	n	CCONJ
ejpam-6407	115	30	∈	∈	PROPN
ejpam-6407	115	31	λ	λ	NOUN
ejpam-6407	115	32	,	,	PUNCT
ejpam-6407	115	33	however	however	ADV
ejpam-6407	115	34	there	there	PRON
ejpam-6407	115	35	are	be	VERB
ejpam-6407	115	36	not	not	PART
ejpam-6407	115	37	two	two	NUM
ejpam-6407	115	38	supra	supra	ADJ
ejpam-6407	115	39	open	open	ADJ
ejpam-6407	115	40	subsets	subset	NOUN
ejpam-6407	115	41	of	of	ADP
ejpam-6407	115	42	λ	λ	NOUN
ejpam-6407	115	43	separate	separate	VERB
ejpam-6407	115	44	them	they	PRON
ejpam-6407	115	45	.	.	PUNCT
ejpam-6407	116	1	(	(	PUNCT
ejpam-6407	116	2	4	4	X
ejpam-6407	116	3	)	)	PUNCT
ejpam-6407	116	4	let	let	VERB
ejpam-6407	116	5	ϑ	ϑ	X
ejpam-6407	116	6	=	=	X
ejpam-6407	116	7	{	{	PUNCT
ejpam-6407	116	8	λ	λ	PROPN
ejpam-6407	116	9	,	,	PUNCT
ejpam-6407	116	10	∅	∅	NOUN
ejpam-6407	116	11	,	,	PUNCT
ejpam-6407	116	12	{	{	PUNCT
ejpam-6407	116	13	a	a	DET
ejpam-6407	116	14	,	,	PUNCT
ejpam-6407	116	15	s	s	PART
ejpam-6407	116	16	}	}	PUNCT
ejpam-6407	116	17	,	,	PUNCT
ejpam-6407	116	18	{	{	PUNCT
ejpam-6407	116	19	d	d	X
ejpam-6407	116	20	,	,	PUNCT
ejpam-6407	116	21	f	f	NOUN
ejpam-6407	116	22	}	}	PUNCT
ejpam-6407	116	23	,	,	PUNCT
ejpam-6407	116	24	{	{	PUNCT
ejpam-6407	116	25	a	a	PRON
ejpam-6407	116	26	,	,	PUNCT
ejpam-6407	116	27	d	d	NOUN
ejpam-6407	116	28	}	}	PUNCT
ejpam-6407	116	29	,	,	PUNCT
ejpam-6407	116	30	{	{	PUNCT
ejpam-6407	116	31	s	s	X
ejpam-6407	116	32	,	,	PUNCT
ejpam-6407	116	33	f	f	PROPN
ejpam-6407	116	34	}	}	PUNCT
ejpam-6407	116	35	,	,	PUNCT
ejpam-6407	116	36	{	{	PUNCT
ejpam-6407	116	37	s	s	X
ejpam-6407	116	38	,	,	PUNCT
ejpam-6407	116	39	d	d	NOUN
ejpam-6407	116	40	}	}	PUNCT
ejpam-6407	116	41	,	,	PUNCT
ejpam-6407	116	42	{	{	PUNCT
ejpam-6407	116	43	a	a	PRON
ejpam-6407	116	44	,	,	PUNCT
ejpam-6407	116	45	s	s	NOUN
ejpam-6407	116	46	,	,	PUNCT
ejpam-6407	116	47	d	d	NOUN
ejpam-6407	116	48	}	}	PUNCT
ejpam-6407	116	49	,	,	PUNCT
ejpam-6407	116	50	{	{	PUNCT
ejpam-6407	116	51	a	a	PRON
ejpam-6407	116	52	,	,	PUNCT
ejpam-6407	116	53	s	s	PROPN
ejpam-6407	116	54	,	,	PUNCT
ejpam-6407	116	55	f	f	PROPN
ejpam-6407	116	56	}	}	PUNCT
ejpam-6407	116	57	,	,	PUNCT
ejpam-6407	116	58	{	{	PUNCT
ejpam-6407	116	59	a	a	PRON
ejpam-6407	116	60	,	,	PUNCT
ejpam-6407	116	61	d	d	NOUN
ejpam-6407	116	62	,	,	PUNCT
ejpam-6407	116	63	f	f	NOUN
ejpam-6407	116	64	}	}	PUNCT
ejpam-6407	116	65	}	}	PUNCT
ejpam-6407	116	66	be	be	AUX
ejpam-6407	116	67	an	an	DET
ejpam-6407	116	68	sts	st	NOUN
ejpam-6407	116	69	on	on	ADP
ejpam-6407	116	70	λ	λ	X
ejpam-6407	116	71	=	=	PUNCT
ejpam-6407	116	72	{	{	PUNCT
ejpam-6407	116	73	a	a	X
ejpam-6407	116	74	,	,	PUNCT
ejpam-6407	116	75	s	s	NOUN
ejpam-6407	116	76	,	,	PUNCT
ejpam-6407	116	77	d	d	PROPN
ejpam-6407	116	78	,	,	PUNCT
ejpam-6407	116	79	f	f	NOUN
ejpam-6407	116	80	}	}	PUNCT
ejpam-6407	116	81	.	.	PUNCT
ejpam-6407	117	1	then	then	ADV
ejpam-6407	117	2	we	we	PRON
ejpam-6407	117	3	have	have	VERB
ejpam-6407	117	4	that	that	DET
ejpam-6407	117	5	soϵ(λ	soϵ(λ	NOUN
ejpam-6407	117	6	)	)	PUNCT
ejpam-6407	117	7	=	=	PUNCT
ejpam-6407	118	1	ϑ.	ϑ.	NOUN
ejpam-6407	118	2	it	it	PRON
ejpam-6407	118	3	follows	follow	VERB
ejpam-6407	118	4	that	that	SCONJ
ejpam-6407	118	5	,	,	PUNCT
ejpam-6407	118	6	λ	λ	PROPN
ejpam-6407	118	7	is	be	AUX
ejpam-6407	118	8	supra-ϵ-t1space	supra-ϵ-t1space	NUM
ejpam-6407	118	9	,	,	PUNCT
ejpam-6407	118	10	however	however	ADV
ejpam-6407	118	11	λ	λ	PROPN
ejpam-6407	118	12	is	be	AUX
ejpam-6407	118	13	not	not	PART
ejpam-6407	118	14	supra	supra	NOUN
ejpam-6407	118	15	-	-	PUNCT
ejpam-6407	118	16	t1	t1	NOUN
ejpam-6407	118	17	,	,	PUNCT
ejpam-6407	118	18	since	since	SCONJ
ejpam-6407	118	19	{	{	PUNCT
ejpam-6407	118	20	a	a	PRON
ejpam-6407	118	21	}	}	PUNCT
ejpam-6407	118	22	̸∈	̸∈	PROPN
ejpam-6407	118	23	ϑc	ϑc	PROPN
ejpam-6407	118	24	.	.	PUNCT
ejpam-6407	119	1	proposition	proposition	NOUN
ejpam-6407	119	2	1	1	NUM
ejpam-6407	119	3	.	.	PUNCT
ejpam-6407	120	1	for	for	ADP
ejpam-6407	120	2	an	an	DET
ejpam-6407	120	3	sts	st	NOUN
ejpam-6407	120	4	(	(	PUNCT
ejpam-6407	120	5	λ	λ	X
ejpam-6407	120	6	,	,	PUNCT
ejpam-6407	120	7	ϑ	ϑ	NOUN
ejpam-6407	120	8	)	)	PUNCT
ejpam-6407	120	9	,	,	PUNCT
ejpam-6407	120	10	the	the	DET
ejpam-6407	120	11	following	follow	VERB
ejpam-6407	120	12	implications	implication	NOUN
ejpam-6407	120	13	are	be	AUX
ejpam-6407	120	14	held	hold	VERB
ejpam-6407	120	15	,	,	PUNCT
ejpam-6407	120	16	which	which	PRON
ejpam-6407	120	17	are	be	AUX
ejpam-6407	120	18	not	not	PART
ejpam-6407	120	19	reversible	reversible	ADJ
ejpam-6407	120	20	,	,	PUNCT
ejpam-6407	120	21	depending	depend	VERB
ejpam-6407	120	22	on	on	ADP
ejpam-6407	120	23	the	the	DET
ejpam-6407	120	24	previously	previously	ADV
ejpam-6407	120	25	mentioned	mention	VERB
ejpam-6407	120	26	results	result	NOUN
ejpam-6407	120	27	.	.	PUNCT
ejpam-6407	121	1	supra	supra	ADJ
ejpam-6407	121	2	-	-	PUNCT
ejpam-6407	121	3	t2	t2	NOUN
ejpam-6407	121	4	-	-	PUNCT
ejpam-6407	121	5	space	space	NOUN
ejpam-6407	121	6	=	=	NOUN
ejpam-6407	121	7	⇒	⇒	NOUN
ejpam-6407	121	8	supra	supra	PROPN
ejpam-6407	121	9	-	-	PUNCT
ejpam-6407	121	10	t1	t1	NOUN
ejpam-6407	121	11	-	-	PUNCT
ejpam-6407	121	12	space	space	NOUN
ejpam-6407	121	13	=	=	NOUN
ejpam-6407	121	14	⇒	⇒	ADJ
ejpam-6407	121	15	supra	supra	PROPN
ejpam-6407	121	16	-	-	PUNCT
ejpam-6407	121	17	t0	t0	NOUN
ejpam-6407	121	18	-	-	PUNCT
ejpam-6407	121	19	space	space	NOUN
ejpam-6407	121	20	⇓	⇓	PROPN
ejpam-6407	121	21	⇓	⇓	PROPN
ejpam-6407	121	22	⇓	⇓	PROPN
ejpam-6407	121	23	supra-ϵ-t2	supra-ϵ-t2	NOUN
ejpam-6407	121	24	-	-	PUNCT
ejpam-6407	121	25	space	space	NOUN
ejpam-6407	121	26	=	=	NOUN
ejpam-6407	121	27	⇒	⇒	NOUN
ejpam-6407	121	28	supra-ϵ-t1	supra-ϵ-t1	PROPN
ejpam-6407	121	29	-	-	PUNCT
ejpam-6407	121	30	space	space	NOUN
ejpam-6407	121	31	=	=	NOUN
ejpam-6407	121	32	⇒	⇒	NOUN
ejpam-6407	121	33	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	121	34	-	-	PUNCT
ejpam-6407	121	35	space	space	NOUN
ejpam-6407	121	36	diagram	diagram	NOUN
ejpam-6407	121	37	1	1	NUM
ejpam-6407	121	38	.	.	PUNCT
ejpam-6407	122	1	the	the	DET
ejpam-6407	122	2	connections	connection	NOUN
ejpam-6407	122	3	among	among	ADP
ejpam-6407	122	4	various	various	ADJ
ejpam-6407	122	5	types	type	NOUN
ejpam-6407	122	6	of	of	ADP
ejpam-6407	122	7	separation	separation	NOUN
ejpam-6407	122	8	axioms	axiom	NOUN
ejpam-6407	122	9	in	in	ADP
ejpam-6407	122	10	the	the	DET
ejpam-6407	122	11	context	context	NOUN
ejpam-6407	122	12	of	of	ADP
ejpam-6407	122	13	stss	stss	NOUN
ejpam-6407	122	14	inspired	inspire	VERB
ejpam-6407	122	15	by	by	ADP
ejpam-6407	122	16	supra	supra	PROPN
ejpam-6407	122	17	ϵ-open	ϵ-open	PROPN
ejpam-6407	122	18	sets	set	NOUN
ejpam-6407	122	19	theorem	theorem	VERB
ejpam-6407	122	20	3	3	NUM
ejpam-6407	122	21	.	.	PUNCT
ejpam-6407	123	1	any	any	DET
ejpam-6407	123	2	sts	st	NOUN
ejpam-6407	123	3	(	(	PUNCT
ejpam-6407	123	4	λ	λ	X
ejpam-6407	123	5	,	,	PUNCT
ejpam-6407	123	6	ϑ	ϑ	NOUN
ejpam-6407	123	7	)	)	PUNCT
ejpam-6407	123	8	is	be	AUX
ejpam-6407	123	9	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	123	10	-	-	NOUN
ejpam-6407	123	11	space	space	NOUN
ejpam-6407	123	12	.	.	PUNCT
ejpam-6407	124	1	proof	proof	NOUN
ejpam-6407	124	2	.	.	PUNCT
ejpam-6407	125	1	let	let	VERB
ejpam-6407	125	2	λ	λ	NOUN
ejpam-6407	125	3	be	be	AUX
ejpam-6407	125	4	an	an	DET
ejpam-6407	125	5	sts	st	NOUN
ejpam-6407	125	6	and	and	CCONJ
ejpam-6407	125	7	let	let	VERB
ejpam-6407	125	8	ν1	ν1	NOUN
ejpam-6407	125	9	̸=	̸=	PROPN
ejpam-6407	125	10	ν2	ν2	NOUN
ejpam-6407	125	11	in	in	ADP
ejpam-6407	125	12	λ	λ	PROPN
ejpam-6407	125	13	.	.	PUNCT
ejpam-6407	126	1	this	this	PRON
ejpam-6407	126	2	follows	follow	VERB
ejpam-6407	126	3	that	that	SCONJ
ejpam-6407	126	4	,	,	PUNCT
ejpam-6407	126	5	either	either	CCONJ
ejpam-6407	126	6	λ	λ	PROPN
ejpam-6407	126	7	\	\	PROPN
ejpam-6407	126	8	{	{	PUNCT
ejpam-6407	126	9	ν1	ν1	NOUN
ejpam-6407	126	10	}	}	PUNCT
ejpam-6407	126	11	∈	∈	PROPN
ejpam-6407	126	12	sro(λ	sro(λ	PROPN
ejpam-6407	126	13	)	)	PUNCT
ejpam-6407	126	14	or	or	CCONJ
ejpam-6407	126	15	λ	λ	PROPN
ejpam-6407	126	16	\	\	PROPN
ejpam-6407	126	17	{	{	PUNCT
ejpam-6407	126	18	ν1	ν1	NOUN
ejpam-6407	126	19	}	}	PUNCT
ejpam-6407	126	20	∈	∈	PROPN
ejpam-6407	126	21	snd(λ	snd(λ	NOUN
ejpam-6407	126	22	)	)	PUNCT
ejpam-6407	126	23	.	.	PUNCT
ejpam-6407	127	1	if	if	SCONJ
ejpam-6407	127	2	λ	λ	PROPN
ejpam-6407	127	3	\	\	PROPN
ejpam-6407	127	4	{	{	PUNCT
ejpam-6407	127	5	ν1	ν1	NOUN
ejpam-6407	127	6	}	}	PUNCT
ejpam-6407	127	7	∈	∈	PROPN
ejpam-6407	127	8	snd(λ	snd(λ	NOUN
ejpam-6407	127	9	)	)	PUNCT
ejpam-6407	127	10	,	,	PUNCT
ejpam-6407	127	11	then	then	ADV
ejpam-6407	127	12	λ	λ	X
ejpam-6407	127	13	\	\	PROPN
ejpam-6407	127	14	{	{	PUNCT
ejpam-6407	127	15	ν1	ν1	NOUN
ejpam-6407	127	16	}	}	PUNCT
ejpam-6407	127	17	=	=	SYM
ejpam-6407	127	18	̸	̸	NUM
ejpam-6407	127	19	λ	λ	PROPN
ejpam-6407	127	20	,	,	PUNCT
ejpam-6407	127	21	and	and	CCONJ
ejpam-6407	127	22	so	so	ADV
ejpam-6407	127	23	λ	λ	X
ejpam-6407	127	24	\	\	PROPN
ejpam-6407	127	25	{	{	PUNCT
ejpam-6407	127	26	ν1	ν1	NOUN
ejpam-6407	127	27	}	}	PUNCT
ejpam-6407	127	28	∈	∈	PROPN
ejpam-6407	127	29	ϑc	ϑc	NOUN
ejpam-6407	127	30	;	;	PUNCT
ejpam-6407	127	31	and	and	CCONJ
ejpam-6407	127	32	hence	hence	ADV
ejpam-6407	127	33	{	{	PUNCT
ejpam-6407	127	34	ν1	ν1	PROPN
ejpam-6407	127	35	}	}	PUNCT
ejpam-6407	127	36	∈	∈	PROPN
ejpam-6407	127	37	ϑ.	ϑ.	NOUN
ejpam-6407	127	38	therefore	therefore	ADV
ejpam-6407	127	39	,	,	PUNCT
ejpam-6407	127	40	{	{	PUNCT
ejpam-6407	127	41	ν1	ν1	NOUN
ejpam-6407	127	42	}	}	PUNCT
ejpam-6407	127	43	is	be	AUX
ejpam-6407	127	44	a	a	DET
ejpam-6407	127	45	supra	supra	PROPN
ejpam-6407	127	46	ϵ-open	ϵ-open	PROPN
ejpam-6407	127	47	set	set	PROPN
ejpam-6407	127	48	containing	contain	VERB
ejpam-6407	127	49	ν1	ν1	NOUN
ejpam-6407	127	50	,	,	PUNCT
ejpam-6407	127	51	but	but	CCONJ
ejpam-6407	127	52	not	not	PART
ejpam-6407	127	53	ν2	ν2	NOUN
ejpam-6407	127	54	.	.	PUNCT
ejpam-6407	128	1	in	in	ADP
ejpam-6407	128	2	addition	addition	NOUN
ejpam-6407	128	3	,	,	PUNCT
ejpam-6407	128	4	if	if	SCONJ
ejpam-6407	128	5	λ	λ	PROPN
ejpam-6407	128	6	\	\	PROPN
ejpam-6407	128	7	{	{	PUNCT
ejpam-6407	128	8	ν1	ν1	NOUN
ejpam-6407	128	9	}	}	PUNCT
ejpam-6407	128	10	∈	∈	PROPN
ejpam-6407	128	11	sro(λ	sro(λ	PROPN
ejpam-6407	128	12	)	)	PUNCT
ejpam-6407	128	13	,	,	PUNCT
ejpam-6407	128	14	then	then	ADV
ejpam-6407	128	15	λ	λ	X
ejpam-6407	128	16	\	\	PROPN
ejpam-6407	128	17	{	{	PUNCT
ejpam-6407	128	18	ν1	ν1	NOUN
ejpam-6407	128	19	}	}	PUNCT
ejpam-6407	128	20	⊆	⊆	NUM
ejpam-6407	128	21	λ	λ	X
ejpam-6407	128	22	\	\	NOUN
ejpam-6407	128	23	{	{	PUNCT
ejpam-6407	128	24	ν1	ν1	NOUN
ejpam-6407	128	25	}	}	PUNCT
ejpam-6407	128	26	◦	◦	NOUN
ejpam-6407	128	27	∪	∪	X
ejpam-6407	128	28	frs(λ	frs(λ	PROPN
ejpam-6407	128	29	\	\	PROPN
ejpam-6407	128	30	{	{	PUNCT
ejpam-6407	128	31	ν1	ν1	NOUN
ejpam-6407	128	32	}	}	PUNCT
ejpam-6407	128	33	)	)	PUNCT
ejpam-6407	128	34	=	=	PUNCT
ejpam-6407	128	35	λ	λ	X
ejpam-6407	128	36	\	\	PROPN
ejpam-6407	128	37	{	{	PUNCT
ejpam-6407	128	38	ν1	ν1	NOUN
ejpam-6407	128	39	}	}	PUNCT
ejpam-6407	128	40	is	be	AUX
ejpam-6407	128	41	a	a	DET
ejpam-6407	128	42	supra	supra	PROPN
ejpam-6407	128	43	ϵ-open	ϵ-open	PROPN
ejpam-6407	128	44	set	set	PROPN
ejpam-6407	128	45	containing	contain	VERB
ejpam-6407	128	46	ν2	ν2	NOUN
ejpam-6407	128	47	,	,	PUNCT
ejpam-6407	128	48	but	but	CCONJ
ejpam-6407	128	49	not	not	PART
ejpam-6407	128	50	ν1	ν1	NOUN
ejpam-6407	128	51	.	.	PUNCT
ejpam-6407	129	1	consequently	consequently	ADV
ejpam-6407	129	2	,	,	PUNCT
ejpam-6407	129	3	λ	λ	PROPN
ejpam-6407	129	4	is	be	AUX
ejpam-6407	129	5	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	129	6	-	-	NOUN
ejpam-6407	129	7	space	space	NOUN
ejpam-6407	129	8	.	.	PUNCT
ejpam-6407	130	1	lemma	lemma	PROPN
ejpam-6407	130	2	1	1	NUM
ejpam-6407	130	3	.	.	PUNCT
ejpam-6407	131	1	any	any	DET
ejpam-6407	131	2	infinite	infinite	ADJ
ejpam-6407	131	3	subset	subset	NOUN
ejpam-6407	131	4	of	of	ADP
ejpam-6407	131	5	an	an	DET
ejpam-6407	131	6	sts	st	NOUN
ejpam-6407	131	7	(	(	PUNCT
ejpam-6407	131	8	λ	λ	X
ejpam-6407	131	9	,	,	PUNCT
ejpam-6407	131	10	ϑ	ϑ	NOUN
ejpam-6407	131	11	)	)	PUNCT
ejpam-6407	131	12	is	be	AUX
ejpam-6407	131	13	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	131	14	.	.	PUNCT
ejpam-6407	132	1	proof	proof	NOUN
ejpam-6407	132	2	.	.	PUNCT
ejpam-6407	133	1	let	let	VERB
ejpam-6407	133	2	h	h	PRON
ejpam-6407	133	3	be	be	AUX
ejpam-6407	133	4	any	any	DET
ejpam-6407	133	5	infinite	infinite	ADJ
ejpam-6407	133	6	subset	subset	NOUN
ejpam-6407	133	7	of	of	ADP
ejpam-6407	133	8	an	an	DET
ejpam-6407	133	9	sts	st	NOUN
ejpam-6407	133	10	(	(	PUNCT
ejpam-6407	133	11	λ	λ	X
ejpam-6407	133	12	,	,	PUNCT
ejpam-6407	133	13	ϑ	ϑ	NOUN
ejpam-6407	133	14	)	)	PUNCT
ejpam-6407	133	15	.	.	PUNCT
ejpam-6407	134	1	then	then	ADV
ejpam-6407	134	2	,	,	PUNCT
ejpam-6407	134	3	h	h	NOUN
ejpam-6407	134	4	is	be	AUX
ejpam-6407	134	5	either	either	CCONJ
ejpam-6407	134	6	h	h	PROPN
ejpam-6407	134	7	∈	∈	PROPN
ejpam-6407	134	8	sro(λ	sro(λ	PROPN
ejpam-6407	134	9	)	)	PUNCT
ejpam-6407	134	10	or	or	CCONJ
ejpam-6407	134	11	h	h	NOUN
ejpam-6407	134	12	∈	∈	PROPN
ejpam-6407	134	13	snd(λ	snd(λ	NOUN
ejpam-6407	134	14	)	)	PUNCT
ejpam-6407	134	15	.	.	PUNCT
ejpam-6407	135	1	if	if	SCONJ
ejpam-6407	135	2	h	h	PROPN
ejpam-6407	135	3	∈	∈	PROPN
ejpam-6407	135	4	snd(λ	snd(λ	PROPN
ejpam-6407	135	5	)	)	PUNCT
ejpam-6407	135	6	,	,	PUNCT
ejpam-6407	135	7	then	then	ADV
ejpam-6407	135	8	h	h	PROPN
ejpam-6407	135	9	⊆	⊆	NUM
ejpam-6407	135	10	h	h	NOUN
ejpam-6407	135	11	◦	◦	NOUN
ejpam-6407	135	12	∪	∪	ADP
ejpam-6407	135	13	frs(h	frs(h	PROPN
ejpam-6407	135	14	)	)	PUNCT
ejpam-6407	135	15	=	=	SYM
ejpam-6407	135	16	frs(h	frs(h	PROPN
ejpam-6407	135	17	)	)	PUNCT
ejpam-6407	135	18	,	,	PUNCT
ejpam-6407	135	19	frs(h	frs(h	PROPN
ejpam-6407	135	20	)	)	PUNCT
ejpam-6407	135	21	is	be	AUX
ejpam-6407	135	22	infinite	infinite	ADJ
ejpam-6407	135	23	.	.	PUNCT
ejpam-6407	136	1	hence	hence	ADV
ejpam-6407	136	2	,	,	PUNCT
ejpam-6407	136	3	h	h	PROPN
ejpam-6407	136	4	∈	∈	PROPN
ejpam-6407	136	5	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	136	6	)	)	PUNCT
ejpam-6407	136	7	.	.	PUNCT
ejpam-6407	137	1	also	also	ADV
ejpam-6407	137	2	,	,	PUNCT
ejpam-6407	137	3	if	if	SCONJ
ejpam-6407	137	4	h	h	PROPN
ejpam-6407	137	5	∈	∈	PROPN
ejpam-6407	137	6	sro(λ	sro(λ	PROPN
ejpam-6407	137	7	)	)	PUNCT
ejpam-6407	137	8	,	,	PUNCT
ejpam-6407	137	9	then	then	ADV
ejpam-6407	137	10	h	h	PROPN
ejpam-6407	137	11	⊆	⊆	NUM
ejpam-6407	137	12	h	h	NOUN
ejpam-6407	137	13	◦	◦	NOUN
ejpam-6407	137	14	∪	∪	ADP
ejpam-6407	137	15	frs(h	frs(h	PROPN
ejpam-6407	137	16	)	)	PUNCT
ejpam-6407	137	17	=	=	SYM
ejpam-6407	137	18	h	h	NOUN
ejpam-6407	137	19	∈	∈	PROPN
ejpam-6407	137	20	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	137	21	)	)	PUNCT
ejpam-6407	137	22	.	.	PUNCT
ejpam-6407	138	1	theorem	theorem	ADJ
ejpam-6407	138	2	4	4	NUM
ejpam-6407	138	3	.	.	PUNCT
ejpam-6407	139	1	any	any	DET
ejpam-6407	139	2	supra	supra	NOUN
ejpam-6407	139	3	-	-	PUNCT
ejpam-6407	139	4	t1	t1	NOUN
ejpam-6407	139	5	-	-	PUNCT
ejpam-6407	139	6	space	space	NOUN
ejpam-6407	139	7	is	be	AUX
ejpam-6407	139	8	supra-ϵ-t2	supra-ϵ-t2	PROPN
ejpam-6407	139	9	.	.	PUNCT
ejpam-6407	140	1	m.	m.	PROPN
ejpam-6407	140	2	aldawood	aldawood	PROPN
ejpam-6407	140	3	et	et	PROPN
ejpam-6407	140	4	al	al	PROPN
ejpam-6407	140	5	.	.	PUNCT
ejpam-6407	140	6	/	/	SYM
ejpam-6407	140	7	eur	eur	PROPN
ejpam-6407	140	8	.	.	PUNCT
ejpam-6407	141	1	j.	j.	PROPN
ejpam-6407	141	2	pure	pure	PROPN
ejpam-6407	141	3	appl	appl	PROPN
ejpam-6407	141	4	.	.	PROPN
ejpam-6407	141	5	math	math	PROPN
ejpam-6407	141	6	,	,	PUNCT
ejpam-6407	141	7	18	18	NUM
ejpam-6407	141	8	(	(	PUNCT
ejpam-6407	141	9	3	3	NUM
ejpam-6407	141	10	)	)	PUNCT
ejpam-6407	141	11	(	(	PUNCT
ejpam-6407	141	12	2025	2025	NUM
ejpam-6407	141	13	)	)	PUNCT
ejpam-6407	141	14	,	,	PUNCT
ejpam-6407	141	15	6407	6407	NUM
ejpam-6407	141	16	6	6	NUM
ejpam-6407	141	17	of	of	ADP
ejpam-6407	141	18	15	15	NUM
ejpam-6407	141	19	proof	proof	NOUN
ejpam-6407	141	20	.	.	PUNCT
ejpam-6407	142	1	let	let	VERB
ejpam-6407	142	2	(	(	PUNCT
ejpam-6407	142	3	λ	λ	NOUN
ejpam-6407	142	4	,	,	PUNCT
ejpam-6407	142	5	ϑ	ϑ	NOUN
ejpam-6407	142	6	)	)	PUNCT
ejpam-6407	142	7	be	be	AUX
ejpam-6407	142	8	a	a	DET
ejpam-6407	142	9	supra	supra	NOUN
ejpam-6407	142	10	-	-	PUNCT
ejpam-6407	142	11	t1	t1	NOUN
ejpam-6407	142	12	-	-	PUNCT
ejpam-6407	142	13	space	space	NOUN
ejpam-6407	142	14	and	and	CCONJ
ejpam-6407	142	15	let	let	VERB
ejpam-6407	142	16	ν1	ν1	NOUN
ejpam-6407	142	17	̸=	̸=	PROPN
ejpam-6407	142	18	ν2	ν2	NOUN
ejpam-6407	142	19	in	in	ADP
ejpam-6407	143	1	v.	v.	ADV
ejpam-6407	144	1	if	if	SCONJ
ejpam-6407	144	2	λ	λ	PROPN
ejpam-6407	144	3	is	be	AUX
ejpam-6407	144	4	finite	finite	ADJ
ejpam-6407	144	5	,	,	PUNCT
ejpam-6407	144	6	then	then	ADV
ejpam-6407	144	7	λ	λ	PROPN
ejpam-6407	144	8	is	be	AUX
ejpam-6407	144	9	the	the	DET
ejpam-6407	144	10	discrete	discrete	ADJ
ejpam-6407	144	11	space	space	NOUN
ejpam-6407	144	12	,	,	PUNCT
ejpam-6407	144	13	hence	hence	ADV
ejpam-6407	144	14	λ	λ	PROPN
ejpam-6407	144	15	is	be	AUX
ejpam-6407	144	16	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6407	144	17	-	-	PUNCT
ejpam-6407	144	18	space	space	NOUN
ejpam-6407	144	19	.	.	PUNCT
ejpam-6407	145	1	now	now	ADV
ejpam-6407	145	2	,	,	PUNCT
ejpam-6407	145	3	assume	assume	VERB
ejpam-6407	145	4	that	that	SCONJ
ejpam-6407	145	5	λ	λ	PROPN
ejpam-6407	145	6	is	be	AUX
ejpam-6407	145	7	infinite	infinite	ADJ
ejpam-6407	145	8	.	.	PUNCT
ejpam-6407	146	1	then	then	ADV
ejpam-6407	146	2	,	,	PUNCT
ejpam-6407	146	3	there	there	PRON
ejpam-6407	146	4	exist	exist	VERB
ejpam-6407	146	5	two	two	NUM
ejpam-6407	146	6	infinite	infinite	ADJ
ejpam-6407	146	7	disjoint	disjoint	NOUN
ejpam-6407	146	8	k	k	PROPN
ejpam-6407	146	9	and	and	CCONJ
ejpam-6407	146	10	h	h	NOUN
ejpam-6407	146	11	subsets	subset	NOUN
ejpam-6407	146	12	of	of	ADP
ejpam-6407	146	13	λ	λ	PROPN
ejpam-6407	146	14	,	,	PUNCT
ejpam-6407	146	15	containing	contain	VERB
ejpam-6407	146	16	ν1	ν1	NOUN
ejpam-6407	146	17	and	and	CCONJ
ejpam-6407	146	18	ν2	ν2	NOUN
ejpam-6407	146	19	,	,	PUNCT
ejpam-6407	146	20	respectively	respectively	ADV
ejpam-6407	146	21	.	.	PUNCT
ejpam-6407	147	1	by	by	ADP
ejpam-6407	147	2	lemma	lemma	PROPN
ejpam-6407	147	3	1	1	NUM
ejpam-6407	147	4	,	,	PUNCT
ejpam-6407	147	5	k	k	PROPN
ejpam-6407	147	6	and	and	CCONJ
ejpam-6407	147	7	h	h	PROPN
ejpam-6407	147	8	are	be	AUX
ejpam-6407	147	9	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	147	10	sets	set	NOUN
ejpam-6407	147	11	.	.	PUNCT
ejpam-6407	148	1	therefore	therefore	ADV
ejpam-6407	148	2	,	,	PUNCT
ejpam-6407	148	3	λ	λ	PROPN
ejpam-6407	148	4	is	be	AUX
ejpam-6407	148	5	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6407	148	6	-	-	PUNCT
ejpam-6407	148	7	space	space	NOUN
ejpam-6407	148	8	.	.	PUNCT
ejpam-6407	149	1	corollary	corollary	ADJ
ejpam-6407	149	2	1	1	NUM
ejpam-6407	149	3	.	.	PUNCT
ejpam-6407	150	1	any	any	DET
ejpam-6407	150	2	infinite	infinite	ADJ
ejpam-6407	150	3	sts	st	NOUN
ejpam-6407	150	4	(	(	PUNCT
ejpam-6407	150	5	λ	λ	NOUN
ejpam-6407	150	6	,	,	PUNCT
ejpam-6407	150	7	ϑ	ϑ	NOUN
ejpam-6407	150	8	)	)	PUNCT
ejpam-6407	150	9	is	be	AUX
ejpam-6407	150	10	supra-ϵ-t2	supra-ϵ-t2	PROPN
ejpam-6407	150	11	.	.	PUNCT
ejpam-6407	151	1	proof	proof	NOUN
ejpam-6407	151	2	.	.	PUNCT
ejpam-6407	152	1	it	it	PRON
ejpam-6407	152	2	follows	follow	VERB
ejpam-6407	152	3	from	from	ADP
ejpam-6407	152	4	lemma	lemma	PROPN
ejpam-6407	152	5	1	1	NUM
ejpam-6407	152	6	.	.	PUNCT
ejpam-6407	152	7	definition	definition	NOUN
ejpam-6407	152	8	9	9	NUM
ejpam-6407	152	9	.	.	PUNCT
ejpam-6407	153	1	[	[	X
ejpam-6407	153	2	63	63	NUM
ejpam-6407	153	3	]	]	PUNCT
ejpam-6407	153	4	if	if	SCONJ
ejpam-6407	153	5	h	h	PROPN
ejpam-6407	153	6	∈	∈	PROPN
ejpam-6407	153	7	ψ	ψ	PROPN
ejpam-6407	153	8	implies	imply	VERB
ejpam-6407	153	9	that	that	SCONJ
ejpam-6407	153	10	h\{ν	h\{ν	NOUN
ejpam-6407	153	11	}	}	PUNCT
ejpam-6407	153	12	∈	∈	PROPN
ejpam-6407	153	13	ψ	ψ	NOUN
ejpam-6407	153	14	for	for	ADP
ejpam-6407	153	15	ν	ν	PROPN
ejpam-6407	153	16	∈	∈	PROPN
ejpam-6407	153	17	λ	λ	PROPN
ejpam-6407	153	18	,	,	PUNCT
ejpam-6407	153	19	then	then	ADV
ejpam-6407	153	20	a	a	DET
ejpam-6407	153	21	subfamily	subfamily	NOUN
ejpam-6407	153	22	ψ	ψ	ADP
ejpam-6407	153	23	⊆	⊆	NUM
ejpam-6407	153	24	2λ	2λ	NOUN
ejpam-6407	153	25	in	in	ADP
ejpam-6407	153	26	a	a	DET
ejpam-6407	153	27	nonempty	nonempty	ADV
ejpam-6407	153	28	set	set	VERB
ejpam-6407	153	29	λ	λ	NOUN
ejpam-6407	153	30	is	be	AUX
ejpam-6407	153	31	considered	consider	VERB
ejpam-6407	153	32	to	to	PART
ejpam-6407	153	33	have	have	VERB
ejpam-6407	153	34	the	the	DET
ejpam-6407	153	35	difference	difference	NOUN
ejpam-6407	153	36	property	property	NOUN
ejpam-6407	153	37	.	.	PUNCT
ejpam-6407	154	1	proposition	proposition	NOUN
ejpam-6407	154	2	2	2	NUM
ejpam-6407	154	3	.	.	PUNCT
ejpam-6407	155	1	any	any	DET
ejpam-6407	155	2	sts	st	NOUN
ejpam-6407	155	3	(	(	PUNCT
ejpam-6407	155	4	λ	λ	X
ejpam-6407	155	5	,	,	PUNCT
ejpam-6407	155	6	ϑ	ϑ	NOUN
ejpam-6407	155	7	)	)	PUNCT
ejpam-6407	155	8	has	have	VERB
ejpam-6407	155	9	the	the	DET
ejpam-6407	155	10	difference	difference	NOUN
ejpam-6407	155	11	property	property	NOUN
ejpam-6407	155	12	for	for	ADP
ejpam-6407	155	13	the	the	DET
ejpam-6407	155	14	category	category	NOUN
ejpam-6407	155	15	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	155	16	)	)	PUNCT
ejpam-6407	155	17	is	be	AUX
ejpam-6407	155	18	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6407	155	19	-	-	PUNCT
ejpam-6407	155	20	space	space	NOUN
ejpam-6407	155	21	.	.	PUNCT
ejpam-6407	156	1	proof	proof	NOUN
ejpam-6407	156	2	.	.	PUNCT
ejpam-6407	157	1	let	let	VERB
ejpam-6407	157	2	ν1	ν1	NOUN
ejpam-6407	157	3	̸=	̸=	PROPN
ejpam-6407	157	4	ν2	ν2	PROPN
ejpam-6407	157	5	∈	∈	PROPN
ejpam-6407	157	6	λ	λ	NOUN
ejpam-6407	157	7	.	.	PUNCT
ejpam-6407	158	1	given	give	VERB
ejpam-6407	158	2	the	the	DET
ejpam-6407	158	3	difference	difference	NOUN
ejpam-6407	158	4	property	property	NOUN
ejpam-6407	158	5	for	for	ADP
ejpam-6407	158	6	λ	λ	PROPN
ejpam-6407	158	7	∈	∈	PROPN
ejpam-6407	158	8	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	158	9	)	)	PUNCT
ejpam-6407	158	10	,	,	PUNCT
ejpam-6407	158	11	we	we	PRON
ejpam-6407	158	12	have	have	VERB
ejpam-6407	158	13	that	that	DET
ejpam-6407	158	14	λ\{ν1	λ\{ν1	NOUN
ejpam-6407	158	15	}	}	PUNCT
ejpam-6407	158	16	∈	∈	PROPN
ejpam-6407	158	17	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	158	18	)	)	PUNCT
ejpam-6407	158	19	and	and	CCONJ
ejpam-6407	158	20	λ\{ν2	λ\{ν2	PUNCT
ejpam-6407	158	21	}	}	PUNCT
ejpam-6407	158	22	∈	∈	PROPN
ejpam-6407	158	23	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	158	24	)	)	PUNCT
ejpam-6407	158	25	which	which	PRON
ejpam-6407	158	26	separate	separate	ADJ
ejpam-6407	158	27	ν1	ν1	NOUN
ejpam-6407	158	28	and	and	CCONJ
ejpam-6407	158	29	ν2	ν2	NOUN
ejpam-6407	158	30	.	.	PUNCT
ejpam-6407	159	1	consequently	consequently	ADV
ejpam-6407	159	2	,	,	PUNCT
ejpam-6407	159	3	λ	λ	PROPN
ejpam-6407	159	4	is	be	AUX
ejpam-6407	159	5	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6407	159	6	-	-	PUNCT
ejpam-6407	159	7	space	space	NOUN
ejpam-6407	159	8	.	.	PUNCT
ejpam-6407	160	1	theorem	theorem	NOUN
ejpam-6407	160	2	5	5	NUM
ejpam-6407	160	3	.	.	X
ejpam-6407	160	4	for	for	ADP
ejpam-6407	160	5	any	any	DET
ejpam-6407	160	6	sts	st	NOUN
ejpam-6407	160	7	(	(	PUNCT
ejpam-6407	160	8	λ	λ	X
ejpam-6407	160	9	,	,	PUNCT
ejpam-6407	160	10	ϑ	ϑ	NOUN
ejpam-6407	160	11	)	)	PUNCT
ejpam-6407	160	12	,	,	PUNCT
ejpam-6407	160	13	the	the	DET
ejpam-6407	160	14	following	follow	VERB
ejpam-6407	160	15	are	be	AUX
ejpam-6407	160	16	equivalent	equivalent	ADJ
ejpam-6407	160	17	:	:	PUNCT
ejpam-6407	160	18	(	(	PUNCT
ejpam-6407	160	19	1	1	X
ejpam-6407	160	20	)	)	PUNCT
ejpam-6407	160	21	λ	λ	NOUN
ejpam-6407	160	22	is	be	AUX
ejpam-6407	160	23	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	160	24	-	-	NOUN
ejpam-6407	160	25	space	space	NOUN
ejpam-6407	160	26	;	;	PUNCT
ejpam-6407	160	27	(	(	PUNCT
ejpam-6407	160	28	2	2	X
ejpam-6407	160	29	)	)	PUNCT
ejpam-6407	160	30	for	for	ADP
ejpam-6407	160	31	each	each	DET
ejpam-6407	160	32	ν1	ν1	NOUN
ejpam-6407	160	33	̸=	̸=	PROPN
ejpam-6407	160	34	ν2	ν2	NOUN
ejpam-6407	160	35	∈	∈	PROPN
ejpam-6407	160	36	λ	λ	NOUN
ejpam-6407	160	37	,	,	PUNCT
ejpam-6407	160	38	clsϵ({ν1	clsϵ({ν1	PROPN
ejpam-6407	160	39	}	}	PUNCT
ejpam-6407	160	40	)	)	PUNCT
ejpam-6407	161	1	̸=	̸=	PROPN
ejpam-6407	161	2	clsϵ({ν2	clsϵ({ν2	PROPN
ejpam-6407	161	3	}	}	PUNCT
ejpam-6407	161	4	)	)	PUNCT
ejpam-6407	161	5	;	;	PUNCT
ejpam-6407	161	6	(	(	PUNCT
ejpam-6407	161	7	3	3	X
ejpam-6407	161	8	)	)	PUNCT
ejpam-6407	161	9	for	for	ADP
ejpam-6407	161	10	each	each	DET
ejpam-6407	161	11	ν	ν	NOUN
ejpam-6407	161	12	∈	∈	PROPN
ejpam-6407	161	13	λ	λ	PROPN
ejpam-6407	161	14	,	,	PUNCT
ejpam-6407	161	15	accϵ({ν	accϵ({ν	PROPN
ejpam-6407	161	16	}	}	PUNCT
ejpam-6407	161	17	)	)	PUNCT
ejpam-6407	162	1	=	=	PUNCT
ejpam-6407	162	2	∪{g	∪{g	PROPN
ejpam-6407	162	3	:	:	PUNCT
ejpam-6407	162	4	g	g	PROPN
ejpam-6407	162	5	∈	∈	PROPN
ejpam-6407	162	6	scϵ(λ	scϵ(λ	PROPN
ejpam-6407	162	7	)	)	PUNCT
ejpam-6407	162	8	}	}	PUNCT
ejpam-6407	162	9	.	.	PUNCT
ejpam-6407	163	1	proof	proof	NOUN
ejpam-6407	163	2	.	.	PUNCT
ejpam-6407	164	1	(	(	PUNCT
ejpam-6407	164	2	1	1	X
ejpam-6407	164	3	)	)	PUNCT
ejpam-6407	164	4	⇒	⇒	NOUN
ejpam-6407	164	5	(	(	PUNCT
ejpam-6407	164	6	2	2	X
ejpam-6407	164	7	)	)	PUNCT
ejpam-6407	164	8	let	let	VERB
ejpam-6407	164	9	ν1	ν1	NOUN
ejpam-6407	164	10	̸=	̸=	PROPN
ejpam-6407	164	11	ν2	ν2	PROPN
ejpam-6407	164	12	∈	∈	PROPN
ejpam-6407	164	13	λ	λ	NOUN
ejpam-6407	164	14	.	.	PUNCT
ejpam-6407	165	1	given	give	VERB
ejpam-6407	165	2	(	(	PUNCT
ejpam-6407	165	3	1	1	NUM
ejpam-6407	165	4	)	)	PUNCT
ejpam-6407	165	5	,	,	PUNCT
ejpam-6407	165	6	there	there	PRON
ejpam-6407	165	7	is	be	VERB
ejpam-6407	165	8	a	a	DET
ejpam-6407	165	9	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	165	10	d	d	NOUN
ejpam-6407	165	11	set	set	NOUN
ejpam-6407	165	12	including	include	VERB
ejpam-6407	165	13	one	one	NUM
ejpam-6407	165	14	point	point	NOUN
ejpam-6407	165	15	(	(	PUNCT
ejpam-6407	165	16	say	say	INTJ
ejpam-6407	165	17	ν1	ν1	NOUN
ejpam-6407	165	18	)	)	PUNCT
ejpam-6407	165	19	but	but	CCONJ
ejpam-6407	165	20	excluding	exclude	VERB
ejpam-6407	165	21	the	the	DET
ejpam-6407	165	22	other	other	ADJ
ejpam-6407	165	23	.	.	PUNCT
ejpam-6407	166	1	this	this	PRON
ejpam-6407	166	2	follows	follow	VERB
ejpam-6407	166	3	that	that	SCONJ
ejpam-6407	166	4	,	,	PUNCT
ejpam-6407	166	5	ν1	ν1	NOUN
ejpam-6407	166	6	∈	∈	PROPN
ejpam-6407	166	7	d	d	PROPN
ejpam-6407	166	8	and	and	CCONJ
ejpam-6407	166	9	d∩{ν2	d∩{ν2	PROPN
ejpam-6407	166	10	}	}	PUNCT
ejpam-6407	166	11	=	=	PUNCT
ejpam-6407	166	12	∅.	∅.	VERB
ejpam-6407	166	13	hence	hence	ADV
ejpam-6407	166	14	,	,	PUNCT
ejpam-6407	166	15	ν1	ν1	NOUN
ejpam-6407	166	16	̸∈	̸∈	PROPN
ejpam-6407	166	17	clsϵ({ν2	clsϵ({ν2	PROPN
ejpam-6407	166	18	}	}	PUNCT
ejpam-6407	166	19	)	)	PUNCT
ejpam-6407	166	20	,	,	PUNCT
ejpam-6407	166	21	however	however	ADV
ejpam-6407	166	22	ν1	ν1	PROPN
ejpam-6407	166	23	∈	∈	PROPN
ejpam-6407	166	24	clsϵ({ν1	clsϵ({ν1	PROPN
ejpam-6407	166	25	}	}	PUNCT
ejpam-6407	166	26	)	)	PUNCT
ejpam-6407	166	27	.	.	PUNCT
ejpam-6407	167	1	thus	thus	ADV
ejpam-6407	167	2	,	,	PUNCT
ejpam-6407	167	3	clsϵ({ν1	clsϵ({ν1	PROPN
ejpam-6407	167	4	}	}	PUNCT
ejpam-6407	167	5	)	)	PUNCT
ejpam-6407	167	6	̸=	̸=	PROPN
ejpam-6407	167	7	clsϵ({ν2	clsϵ({ν2	PROPN
ejpam-6407	167	8	}	}	PUNCT
ejpam-6407	167	9	)	)	PUNCT
ejpam-6407	167	10	.	.	PUNCT
ejpam-6407	168	1	(	(	PUNCT
ejpam-6407	168	2	2	2	X
ejpam-6407	168	3	)	)	PUNCT
ejpam-6407	168	4	⇒	⇒	NOUN
ejpam-6407	168	5	(	(	PUNCT
ejpam-6407	168	6	3	3	X
ejpam-6407	168	7	)	)	PUNCT
ejpam-6407	168	8	let	let	VERB
ejpam-6407	168	9	ω	ω	NUM
ejpam-6407	168	10	∈	∈	PROPN
ejpam-6407	168	11	accϵ({ν	accϵ({ν	PROPN
ejpam-6407	168	12	}	}	PUNCT
ejpam-6407	168	13	)	)	PUNCT
ejpam-6407	168	14	,	,	PUNCT
ejpam-6407	168	15	then	then	ADV
ejpam-6407	168	16	ω	ω	NUM
ejpam-6407	168	17	̸=	̸=	PROPN
ejpam-6407	168	18	ν	ν	NOUN
ejpam-6407	168	19	and	and	CCONJ
ejpam-6407	168	20	ω	ω	NUM
ejpam-6407	168	21	∈	∈	PROPN
ejpam-6407	168	22	accϵ({ν	accϵ({ν	PROPN
ejpam-6407	168	23	}	}	PUNCT
ejpam-6407	168	24	)	)	PUNCT
ejpam-6407	168	25	∪	∪	ADP
ejpam-6407	168	26	{	{	PUNCT
ejpam-6407	168	27	ν	ν	NOUN
ejpam-6407	168	28	}	}	PUNCT
ejpam-6407	168	29	=	=	SYM
ejpam-6407	168	30	clsϵ({ν	clsϵ({ν	PROPN
ejpam-6407	168	31	}	}	PUNCT
ejpam-6407	168	32	)	)	PUNCT
ejpam-6407	168	33	.	.	PUNCT
ejpam-6407	169	1	hence	hence	ADV
ejpam-6407	169	2	,	,	PUNCT
ejpam-6407	169	3	ω	ω	PROPN
ejpam-6407	169	4	∈	∈	PROPN
ejpam-6407	169	5	clsϵ{ω	clsϵ{ω	PROPN
ejpam-6407	169	6	}	}	PUNCT
ejpam-6407	169	7	⊆	⊆	NUM
ejpam-6407	169	8	clsϵ({ν	clsϵ({ν	PROPN
ejpam-6407	169	9	}	}	PUNCT
ejpam-6407	169	10	)	)	PUNCT
ejpam-6407	169	11	=	=	SYM
ejpam-6407	169	12	accϵ({ν	accϵ({ν	PROPN
ejpam-6407	169	13	}	}	PUNCT
ejpam-6407	169	14	)	)	PUNCT
ejpam-6407	169	15	∪	∪	ADP
ejpam-6407	169	16	{	{	PUNCT
ejpam-6407	169	17	ν	ν	NOUN
ejpam-6407	169	18	}	}	PUNCT
ejpam-6407	169	19	.	.	PUNCT
ejpam-6407	170	1	since	since	SCONJ
ejpam-6407	170	2	ω	ω	PROPN
ejpam-6407	170	3	̸∈	̸∈	PROPN
ejpam-6407	170	4	{	{	PUNCT
ejpam-6407	170	5	ν	ν	NOUN
ejpam-6407	170	6	}	}	PUNCT
ejpam-6407	170	7	,	,	PUNCT
ejpam-6407	170	8	ω	ω	PROPN
ejpam-6407	170	9	∈	∈	PROPN
ejpam-6407	170	10	accϵ({ν	accϵ({ν	PROPN
ejpam-6407	170	11	}	}	PUNCT
ejpam-6407	170	12	)	)	PUNCT
ejpam-6407	170	13	.	.	PUNCT
ejpam-6407	171	1	therefore	therefore	ADV
ejpam-6407	171	2	,	,	PUNCT
ejpam-6407	171	3	ω	ω	PROPN
ejpam-6407	171	4	∈	∈	PROPN
ejpam-6407	171	5	clsϵ{ω	clsϵ{ω	PROPN
ejpam-6407	171	6	}	}	PUNCT
ejpam-6407	171	7	⊆	⊆	NUM
ejpam-6407	171	8	accϵ({ν	accϵ({ν	PROPN
ejpam-6407	171	9	}	}	PUNCT
ejpam-6407	171	10	)	)	PUNCT
ejpam-6407	171	11	,	,	PUNCT
ejpam-6407	171	12	and	and	CCONJ
ejpam-6407	171	13	consequently	consequently	ADV
ejpam-6407	171	14	accϵ({ν	accϵ({ν	PROPN
ejpam-6407	171	15	}	}	PUNCT
ejpam-6407	171	16	)	)	PUNCT
ejpam-6407	171	17	=	=	SYM
ejpam-6407	171	18	∪{clsϵ{ω	∪{clsϵ{ω	NUM
ejpam-6407	171	19	}	}	PUNCT
ejpam-6407	171	20	:	:	PUNCT
ejpam-6407	171	21	ω	ω	PROPN
ejpam-6407	171	22	∈	∈	PROPN
ejpam-6407	171	23	accϵ({ν	accϵ({ν	PROPN
ejpam-6407	171	24	}	}	PUNCT
ejpam-6407	171	25	)	)	PUNCT
ejpam-6407	171	26	}	}	PUNCT
ejpam-6407	171	27	.	.	PUNCT
ejpam-6407	172	1	(	(	PUNCT
ejpam-6407	172	2	3	3	X
ejpam-6407	172	3	)	)	PUNCT
ejpam-6407	172	4	⇒	⇒	NOUN
ejpam-6407	172	5	(	(	PUNCT
ejpam-6407	172	6	1	1	X
ejpam-6407	172	7	)	)	PUNCT
ejpam-6407	172	8	let	let	VERB
ejpam-6407	172	9	ν1	ν1	NOUN
ejpam-6407	172	10	̸=	̸=	PROPN
ejpam-6407	172	11	ν2	ν2	NOUN
ejpam-6407	172	12	∈	∈	PROPN
ejpam-6407	172	13	λ	λ	NOUN
ejpam-6407	172	14	.	.	PUNCT
ejpam-6407	173	1	then	then	ADV
ejpam-6407	173	2	,	,	PUNCT
ejpam-6407	173	3	either	either	CCONJ
ejpam-6407	173	4	ν2	ν2	NOUN
ejpam-6407	173	5	∈	∈	NOUN
ejpam-6407	173	6	accϵ({ν1	accϵ({ν1	PROPN
ejpam-6407	173	7	}	}	PUNCT
ejpam-6407	173	8	)	)	PUNCT
ejpam-6407	173	9	or	or	CCONJ
ejpam-6407	173	10	ν2	ν2	NOUN
ejpam-6407	173	11	̸∈	̸∈	PROPN
ejpam-6407	173	12	accϵ({ν1	accϵ({ν1	PROPN
ejpam-6407	173	13	}	}	PUNCT
ejpam-6407	173	14	)	)	PUNCT
ejpam-6407	173	15	.	.	PUNCT
ejpam-6407	174	1	if	if	SCONJ
ejpam-6407	174	2	ν2	ν2	NOUN
ejpam-6407	174	3	∈	∈	NOUN
ejpam-6407	174	4	accϵ({ν1	accϵ({ν1	PROPN
ejpam-6407	174	5	}	}	PUNCT
ejpam-6407	174	6	)	)	PUNCT
ejpam-6407	174	7	,	,	PUNCT
ejpam-6407	174	8	then	then	ADV
ejpam-6407	174	9	there	there	PRON
ejpam-6407	174	10	is	be	VERB
ejpam-6407	174	11	h	h	PRON
ejpam-6407	174	12	∈	∈	PROPN
ejpam-6407	174	13	scϵ(λ	scϵ(λ	PROPN
ejpam-6407	174	14	)	)	PUNCT
ejpam-6407	175	1	such	such	ADJ
ejpam-6407	175	2	that	that	SCONJ
ejpam-6407	175	3	ν2	ν2	NOUN
ejpam-6407	175	4	∈	∈	PROPN
ejpam-6407	175	5	h	h	NOUN
ejpam-6407	175	6	⊆	⊆	NOUN
ejpam-6407	175	7	accϵ({ν1	accϵ({ν1	PROPN
ejpam-6407	175	8	}	}	PUNCT
ejpam-6407	175	9	)	)	PUNCT
ejpam-6407	175	10	.	.	PUNCT
ejpam-6407	176	1	since	since	SCONJ
ejpam-6407	176	2	ν1	ν1	PROPN
ejpam-6407	176	3	̸∈	̸∈	PROPN
ejpam-6407	176	4	accϵ({ν1	accϵ({ν1	PROPN
ejpam-6407	176	5	}	}	PUNCT
ejpam-6407	176	6	,	,	PUNCT
ejpam-6407	176	7	ν1	ν1	NOUN
ejpam-6407	176	8	̸∈	̸∈	PROPN
ejpam-6407	176	9	h	h	NOUN
ejpam-6407	176	10	,	,	PUNCT
ejpam-6407	176	11	and	and	CCONJ
ejpam-6407	176	12	so	so	ADV
ejpam-6407	176	13	ν1	ν1	PROPN
ejpam-6407	176	14	∈	∈	PROPN
ejpam-6407	176	15	hc	hc	PROPN
ejpam-6407	176	16	and	and	CCONJ
ejpam-6407	176	17	ν2	ν2	PROPN
ejpam-6407	176	18	̸∈	̸∈	PROPN
ejpam-6407	176	19	hc	hc	PROPN
ejpam-6407	176	20	,	,	PUNCT
ejpam-6407	176	21	hc	hc	PROPN
ejpam-6407	176	22	∈	∈	PROPN
ejpam-6407	176	23	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	176	24	)	)	PUNCT
ejpam-6407	176	25	.	.	PUNCT
ejpam-6407	177	1	thus	thus	ADV
ejpam-6407	177	2	,	,	PUNCT
ejpam-6407	177	3	λ	λ	PROPN
ejpam-6407	177	4	is	be	AUX
ejpam-6407	177	5	supra-ϵt0	supra-ϵt0	NOUN
ejpam-6407	177	6	-	-	PUNCT
ejpam-6407	177	7	space	space	NOUN
ejpam-6407	177	8	.	.	PUNCT
ejpam-6407	178	1	additionally	additionally	ADV
ejpam-6407	178	2	,	,	PUNCT
ejpam-6407	178	3	if	if	SCONJ
ejpam-6407	178	4	ν2	ν2	ADP
ejpam-6407	178	5	̸∈	̸∈	PROPN
ejpam-6407	178	6	accϵ({ν1	accϵ({ν1	PROPN
ejpam-6407	178	7	}	}	PUNCT
ejpam-6407	178	8	)	)	PUNCT
ejpam-6407	178	9	,	,	PUNCT
ejpam-6407	178	10	then	then	ADV
ejpam-6407	178	11	there	there	PRON
ejpam-6407	178	12	is	be	VERB
ejpam-6407	178	13	k	k	PROPN
ejpam-6407	178	14	∈	∈	PROPN
ejpam-6407	178	15	scϵ(λ	scϵ(λ	PROPN
ejpam-6407	178	16	)	)	PUNCT
ejpam-6407	178	17	such	such	ADJ
ejpam-6407	178	18	that	that	SCONJ
ejpam-6407	178	19	ν2	ν2	NOUN
ejpam-6407	178	20	∈	∈	PROPN
ejpam-6407	178	21	k	k	PROPN
ejpam-6407	178	22	and	and	CCONJ
ejpam-6407	178	23	ν1	ν1	PROPN
ejpam-6407	178	24	̸∈	̸∈	PROPN
ejpam-6407	178	25	k.	k.	PROPN
ejpam-6407	178	26	thus	thus	ADV
ejpam-6407	178	27	,	,	PUNCT
ejpam-6407	178	28	λ	λ	PROPN
ejpam-6407	178	29	is	be	AUX
ejpam-6407	178	30	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	178	31	-	-	NOUN
ejpam-6407	178	32	space	space	NOUN
ejpam-6407	178	33	.	.	PUNCT
ejpam-6407	179	1	definition	definition	NOUN
ejpam-6407	179	2	10	10	NUM
ejpam-6407	179	3	.	.	PUNCT
ejpam-6407	180	1	a	a	DET
ejpam-6407	180	2	subset	subset	NOUN
ejpam-6407	180	3	s	s	NOUN
ejpam-6407	180	4	of	of	ADP
ejpam-6407	180	5	an	an	DET
ejpam-6407	180	6	sts	st	NOUN
ejpam-6407	180	7	(	(	PUNCT
ejpam-6407	180	8	λ	λ	X
ejpam-6407	180	9	,	,	PUNCT
ejpam-6407	180	10	ϑ	ϑ	NOUN
ejpam-6407	180	11	)	)	PUNCT
ejpam-6407	180	12	is	be	AUX
ejpam-6407	180	13	called	call	VERB
ejpam-6407	180	14	supra	supra	PROPN
ejpam-6407	180	15	ϵ-dense	ϵ-dense	NOUN
ejpam-6407	180	16	if	if	SCONJ
ejpam-6407	180	17	clsϵ(s	clsϵ(	NOUN
ejpam-6407	180	18	)	)	PUNCT
ejpam-6407	180	19	=	=	SYM
ejpam-6407	180	20	λ	λ	PROPN
ejpam-6407	180	21	.	.	NOUN
ejpam-6407	180	22	corollary	corollary	ADJ
ejpam-6407	180	23	2	2	NUM
ejpam-6407	180	24	.	.	PUNCT
ejpam-6407	181	1	if	if	SCONJ
ejpam-6407	181	2	(	(	PUNCT
ejpam-6407	181	3	λ	λ	NOUN
ejpam-6407	181	4	,	,	PUNCT
ejpam-6407	181	5	ϑ	ϑ	NOUN
ejpam-6407	181	6	)	)	PUNCT
ejpam-6407	181	7	is	be	AUX
ejpam-6407	181	8	a	a	DET
ejpam-6407	181	9	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	181	10	-	-	NOUN
ejpam-6407	181	11	space	space	NOUN
ejpam-6407	181	12	,	,	PUNCT
ejpam-6407	181	13	then	then	ADV
ejpam-6407	181	14	there	there	PRON
ejpam-6407	181	15	is	be	VERB
ejpam-6407	181	16	at	at	ADP
ejpam-6407	181	17	most	most	ADJ
ejpam-6407	181	18	a	a	DET
ejpam-6407	181	19	supra	supra	PROPN
ejpam-6407	181	20	ϵ-dense	ϵ-dense	PROPN
ejpam-6407	181	21	singleton	singleton	PROPN
ejpam-6407	181	22	set	set	VERB
ejpam-6407	181	23	in	in	ADP
ejpam-6407	181	24	λ	λ	PROPN
ejpam-6407	181	25	.	.	PROPN
ejpam-6407	181	26	m.	m.	PROPN
ejpam-6407	181	27	aldawood	aldawood	PROPN
ejpam-6407	182	1	et	et	PROPN
ejpam-6407	182	2	al	al	PROPN
ejpam-6407	182	3	.	.	PUNCT
ejpam-6407	182	4	/	/	SYM
ejpam-6407	182	5	eur	eur	PROPN
ejpam-6407	182	6	.	.	PUNCT
ejpam-6407	183	1	j.	j.	PROPN
ejpam-6407	183	2	pure	pure	PROPN
ejpam-6407	183	3	appl	appl	PROPN
ejpam-6407	183	4	.	.	PROPN
ejpam-6407	183	5	math	math	PROPN
ejpam-6407	183	6	,	,	PUNCT
ejpam-6407	183	7	18	18	NUM
ejpam-6407	183	8	(	(	PUNCT
ejpam-6407	183	9	3	3	NUM
ejpam-6407	183	10	)	)	PUNCT
ejpam-6407	183	11	(	(	PUNCT
ejpam-6407	183	12	2025	2025	NUM
ejpam-6407	183	13	)	)	PUNCT
ejpam-6407	183	14	,	,	PUNCT
ejpam-6407	183	15	6407	6407	NUM
ejpam-6407	183	16	7	7	NUM
ejpam-6407	183	17	of	of	ADP
ejpam-6407	183	18	15	15	NUM
ejpam-6407	183	19	proof	proof	NOUN
ejpam-6407	183	20	.	.	PUNCT
ejpam-6407	184	1	it	it	PRON
ejpam-6407	184	2	is	be	AUX
ejpam-6407	184	3	follows	follow	VERB
ejpam-6407	184	4	from	from	ADP
ejpam-6407	184	5	theorem	theorem	ADJ
ejpam-6407	184	6	5	5	NUM
ejpam-6407	184	7	.	.	PUNCT
ejpam-6407	184	8	theorem	theorem	VERB
ejpam-6407	184	9	6	6	NUM
ejpam-6407	184	10	.	.	PUNCT
ejpam-6407	184	11	for	for	ADP
ejpam-6407	184	12	any	any	DET
ejpam-6407	184	13	sts	st	NOUN
ejpam-6407	184	14	(	(	PUNCT
ejpam-6407	184	15	λ	λ	X
ejpam-6407	184	16	,	,	PUNCT
ejpam-6407	184	17	ϑ	ϑ	NOUN
ejpam-6407	184	18	)	)	PUNCT
ejpam-6407	184	19	,	,	PUNCT
ejpam-6407	184	20	the	the	DET
ejpam-6407	184	21	following	follow	VERB
ejpam-6407	184	22	are	be	AUX
ejpam-6407	184	23	equivalent	equivalent	ADJ
ejpam-6407	184	24	:	:	PUNCT
ejpam-6407	184	25	(	(	PUNCT
ejpam-6407	184	26	1	1	X
ejpam-6407	184	27	)	)	PUNCT
ejpam-6407	184	28	λ	λ	NOUN
ejpam-6407	184	29	is	be	AUX
ejpam-6407	184	30	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6407	184	31	-	-	PUNCT
ejpam-6407	184	32	space	space	NOUN
ejpam-6407	184	33	;	;	PUNCT
ejpam-6407	184	34	(	(	PUNCT
ejpam-6407	184	35	2	2	X
ejpam-6407	184	36	)	)	PUNCT
ejpam-6407	184	37	for	for	ADP
ejpam-6407	184	38	each	each	DET
ejpam-6407	184	39	ν	ν	NOUN
ejpam-6407	184	40	∈	∈	PROPN
ejpam-6407	184	41	λ	λ	PROPN
ejpam-6407	184	42	,	,	PUNCT
ejpam-6407	184	43	{	{	PUNCT
ejpam-6407	184	44	ν	ν	NOUN
ejpam-6407	184	45	}	}	PUNCT
ejpam-6407	184	46	∈	∈	PROPN
ejpam-6407	184	47	scϵ(λ	scϵ(λ	PROPN
ejpam-6407	184	48	)	)	PUNCT
ejpam-6407	184	49	;	;	PUNCT
ejpam-6407	184	50	(	(	PUNCT
ejpam-6407	184	51	3	3	X
ejpam-6407	184	52	)	)	PUNCT
ejpam-6407	184	53	∩{h	∩{h	PROPN
ejpam-6407	184	54	:	:	PUNCT
ejpam-6407	184	55	h	h	PROPN
ejpam-6407	184	56	∈	∈	PROPN
ejpam-6407	184	57	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	184	58	)	)	PUNCT
ejpam-6407	184	59	and	and	CCONJ
ejpam-6407	184	60	c	c	NOUN
ejpam-6407	184	61	⊆	⊆	NUM
ejpam-6407	184	62	h	h	NOUN
ejpam-6407	184	63	}	}	PUNCT
ejpam-6407	184	64	=	=	SYM
ejpam-6407	184	65	c	c	NOUN
ejpam-6407	184	66	;	;	PUNCT
ejpam-6407	184	67	(	(	PUNCT
ejpam-6407	184	68	4	4	X
ejpam-6407	184	69	)	)	PUNCT
ejpam-6407	184	70	for	for	ADP
ejpam-6407	184	71	each	each	DET
ejpam-6407	184	72	ν	ν	NOUN
ejpam-6407	184	73	∈	∈	PROPN
ejpam-6407	184	74	λ	λ	PROPN
ejpam-6407	184	75	,	,	PUNCT
ejpam-6407	184	76	accϵ({ν	accϵ({ν	PROPN
ejpam-6407	184	77	}	}	PUNCT
ejpam-6407	184	78	)	)	PUNCT
ejpam-6407	185	1	=	=	PUNCT
ejpam-6407	185	2	∅.	∅.	NOUN
ejpam-6407	185	3	proof	proof	NOUN
ejpam-6407	185	4	.	.	PUNCT
ejpam-6407	186	1	(	(	PUNCT
ejpam-6407	186	2	1	1	X
ejpam-6407	186	3	)	)	PUNCT
ejpam-6407	186	4	⇒	⇒	NOUN
ejpam-6407	186	5	(	(	PUNCT
ejpam-6407	186	6	2	2	X
ejpam-6407	186	7	)	)	PUNCT
ejpam-6407	186	8	let	let	VERB
ejpam-6407	186	9	ν	ν	PRON
ejpam-6407	186	10	∈	∈	PROPN
ejpam-6407	186	11	λ	λ	PROPN
ejpam-6407	186	12	.	.	PUNCT
ejpam-6407	187	1	we	we	PRON
ejpam-6407	187	2	prove	prove	VERB
ejpam-6407	187	3	that	that	SCONJ
ejpam-6407	187	4	{	{	PUNCT
ejpam-6407	187	5	ν}c	ν}c	PROPN
ejpam-6407	187	6	∈	∈	PROPN
ejpam-6407	187	7	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	187	8	)	)	PUNCT
ejpam-6407	187	9	,	,	PUNCT
ejpam-6407	187	10	so	so	ADV
ejpam-6407	187	11	let	let	VERB
ejpam-6407	187	12	ω	ω	NUM
ejpam-6407	187	13	∈	∈	PROPN
ejpam-6407	187	14	{	{	PUNCT
ejpam-6407	187	15	ν}c	ν}c	NOUN
ejpam-6407	187	16	.	.	PUNCT
ejpam-6407	188	1	then	then	ADV
ejpam-6407	188	2	,	,	PUNCT
ejpam-6407	188	3	ω	ω	PROPN
ejpam-6407	188	4	̸=	̸=	PROPN
ejpam-6407	188	5	ν	ν	NOUN
ejpam-6407	188	6	.	.	PUNCT
ejpam-6407	188	7	given	give	VERB
ejpam-6407	188	8	(	(	PUNCT
ejpam-6407	188	9	1	1	NUM
ejpam-6407	188	10	)	)	PUNCT
ejpam-6407	188	11	,	,	PUNCT
ejpam-6407	188	12	there	there	PRON
ejpam-6407	188	13	is	be	VERB
ejpam-6407	188	14	hω	hω	ADP
ejpam-6407	188	15	∈	∈	PROPN
ejpam-6407	188	16	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	188	17	)	)	PUNCT
ejpam-6407	188	18	such	such	ADJ
ejpam-6407	188	19	that	that	SCONJ
ejpam-6407	188	20	ω	ω	PROPN
ejpam-6407	188	21	∈	∈	PROPN
ejpam-6407	188	22	hω	hω	ADP
ejpam-6407	188	23	and	and	CCONJ
ejpam-6407	188	24	ν	ν	X
ejpam-6407	188	25	̸∈	̸∈	PROPN
ejpam-6407	188	26	hω	hω	PROPN
ejpam-6407	188	27	.	.	PUNCT
ejpam-6407	189	1	hence	hence	ADV
ejpam-6407	189	2	,	,	PUNCT
ejpam-6407	189	3	ω	ω	PROPN
ejpam-6407	189	4	∈	∈	ADJ
ejpam-6407	189	5	hω	hω	ADP
ejpam-6407	189	6	⊆	⊆	NUM
ejpam-6407	189	7	{	{	PUNCT
ejpam-6407	189	8	ν}c	ν}c	NOUN
ejpam-6407	189	9	,	,	PUNCT
ejpam-6407	189	10	and	and	CCONJ
ejpam-6407	189	11	consequently	consequently	ADV
ejpam-6407	189	12	{	{	PUNCT
ejpam-6407	189	13	ν}c	ν}c	PROPN
ejpam-6407	189	14	∈	∈	PROPN
ejpam-6407	189	15	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	189	16	)	)	PUNCT
ejpam-6407	189	17	.	.	PUNCT
ejpam-6407	190	1	therefore	therefore	ADV
ejpam-6407	190	2	,	,	PUNCT
ejpam-6407	190	3	we	we	PRON
ejpam-6407	190	4	get	get	VERB
ejpam-6407	190	5	the	the	DET
ejpam-6407	190	6	desired	desire	VERB
ejpam-6407	190	7	outcome	outcome	NOUN
ejpam-6407	190	8	.	.	PUNCT
ejpam-6407	191	1	(	(	PUNCT
ejpam-6407	191	2	2	2	X
ejpam-6407	191	3	)	)	PUNCT
ejpam-6407	191	4	⇒	⇒	NOUN
ejpam-6407	191	5	(	(	PUNCT
ejpam-6407	191	6	3	3	X
ejpam-6407	191	7	)	)	PUNCT
ejpam-6407	191	8	let	let	VERB
ejpam-6407	191	9	k	k	PROPN
ejpam-6407	191	10	⊆	⊆	NUM
ejpam-6407	191	11	λ	λ	NOUN
ejpam-6407	191	12	.	.	PROPN
ejpam-6407	192	1	given	give	VERB
ejpam-6407	192	2	(	(	PUNCT
ejpam-6407	192	3	2	2	NUM
ejpam-6407	192	4	)	)	PUNCT
ejpam-6407	192	5	,	,	PUNCT
ejpam-6407	192	6	for	for	ADP
ejpam-6407	192	7	all	all	DET
ejpam-6407	192	8	ν	ν	NOUN
ejpam-6407	192	9	∈	∈	NOUN
ejpam-6407	192	10	kc	kc	NOUN
ejpam-6407	192	11	we	we	PRON
ejpam-6407	192	12	have	have	VERB
ejpam-6407	192	13	that	that	PRON
ejpam-6407	192	14	{	{	PUNCT
ejpam-6407	192	15	ν	ν	NOUN
ejpam-6407	192	16	}	}	PUNCT
ejpam-6407	192	17	∈	∈	PROPN
ejpam-6407	192	18	scϵ(λ	scϵ(λ	PROPN
ejpam-6407	192	19	)	)	PUNCT
ejpam-6407	192	20	.	.	PUNCT
ejpam-6407	193	1	then	then	ADV
ejpam-6407	193	2	,	,	PUNCT
ejpam-6407	193	3	{	{	PUNCT
ejpam-6407	193	4	ν}c	ν}c	PROPN
ejpam-6407	193	5	∈	∈	PROPN
ejpam-6407	193	6	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	193	7	)	)	PUNCT
ejpam-6407	193	8	.	.	PUNCT
ejpam-6407	194	1	hence	hence	ADV
ejpam-6407	194	2	,	,	PUNCT
ejpam-6407	194	3	k	k	PROPN
ejpam-6407	194	4	⊆	⊆	NUM
ejpam-6407	194	5	{	{	PUNCT
ejpam-6407	194	6	h	h	NOUN
ejpam-6407	194	7	:	:	PUNCT
ejpam-6407	194	8	h	h	PROPN
ejpam-6407	194	9	∈	∈	PROPN
ejpam-6407	194	10	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	194	11	)	)	PUNCT
ejpam-6407	194	12	and	and	CCONJ
ejpam-6407	194	13	k	k	PROPN
ejpam-6407	194	14	⊆	⊆	NUM
ejpam-6407	194	15	h	h	NOUN
ejpam-6407	194	16	}	}	PUNCT
ejpam-6407	194	17	⊆	⊆	NUM
ejpam-6407	194	18	{	{	PUNCT
ejpam-6407	194	19	{	{	PUNCT
ejpam-6407	194	20	ν}c	ν}c	NOUN
ejpam-6407	194	21	:	:	PUNCT
ejpam-6407	194	22	ν	ν	PROPN
ejpam-6407	194	23	∈	∈	PROPN
ejpam-6407	194	24	kc	kc	PROPN
ejpam-6407	194	25	}	}	PUNCT
ejpam-6407	194	26	⊆	⊆	NUM
ejpam-6407	194	27	k.	k.	PROPN
ejpam-6407	194	28	therefore	therefore	ADV
ejpam-6407	194	29	,	,	PUNCT
ejpam-6407	194	30	k	k	PROPN
ejpam-6407	194	31	=	=	PRON
ejpam-6407	194	32	{	{	PUNCT
ejpam-6407	194	33	h	h	NOUN
ejpam-6407	194	34	:	:	PUNCT
ejpam-6407	194	35	h	h	PROPN
ejpam-6407	194	36	∈	∈	PROPN
ejpam-6407	194	37	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	194	38	)	)	PUNCT
ejpam-6407	194	39	and	and	CCONJ
ejpam-6407	194	40	k	k	PROPN
ejpam-6407	194	41	⊆	⊆	NUM
ejpam-6407	194	42	h	h	NOUN
ejpam-6407	194	43	}	}	PUNCT
ejpam-6407	194	44	.	.	PUNCT
ejpam-6407	195	1	(	(	PUNCT
ejpam-6407	195	2	3	3	X
ejpam-6407	195	3	)	)	PUNCT
ejpam-6407	195	4	⇒	⇒	NOUN
ejpam-6407	195	5	(	(	PUNCT
ejpam-6407	195	6	4	4	X
ejpam-6407	195	7	)	)	PUNCT
ejpam-6407	195	8	assume	assume	VERB
ejpam-6407	195	9	the	the	DET
ejpam-6407	195	10	contrary	contrary	NOUN
ejpam-6407	195	11	that	that	SCONJ
ejpam-6407	195	12	accϵ({ν	accϵ({ν	PROPN
ejpam-6407	195	13	}	}	PUNCT
ejpam-6407	195	14	)	)	PUNCT
ejpam-6407	195	15	̸=	̸=	NOUN
ejpam-6407	195	16	∅	∅	NOUN
ejpam-6407	195	17	for	for	ADP
ejpam-6407	195	18	some	some	DET
ejpam-6407	195	19	ν	ν	NOUN
ejpam-6407	195	20	∈	∈	PROPN
ejpam-6407	195	21	λ	λ	PROPN
ejpam-6407	195	22	,	,	PUNCT
ejpam-6407	195	23	then	then	ADV
ejpam-6407	195	24	there	there	PRON
ejpam-6407	195	25	is	be	VERB
ejpam-6407	195	26	ω	ω	NUM
ejpam-6407	195	27	̸=	̸=	PROPN
ejpam-6407	195	28	ν	ν	NOUN
ejpam-6407	195	29	such	such	ADJ
ejpam-6407	195	30	that	that	SCONJ
ejpam-6407	195	31	ω	ω	PROPN
ejpam-6407	195	32	∈	∈	PROPN
ejpam-6407	195	33	accϵ({ν	accϵ({ν	PROPN
ejpam-6407	195	34	}	}	PUNCT
ejpam-6407	195	35	)	)	PUNCT
ejpam-6407	195	36	.	.	PUNCT
ejpam-6407	196	1	hence	hence	ADV
ejpam-6407	196	2	,	,	PUNCT
ejpam-6407	196	3	for	for	SCONJ
ejpam-6407	196	4	every	every	DET
ejpam-6407	196	5	supra	supra	PROPN
ejpam-6407	196	6	ϵ-open	ϵ-open	PROPN
ejpam-6407	196	7	set	set	PROPN
ejpam-6407	196	8	gω	gω	PROPN
ejpam-6407	196	9	containing	contain	VERB
ejpam-6407	196	10	ω	ω	PROPN
ejpam-6407	196	11	we	we	PRON
ejpam-6407	196	12	have	have	VERB
ejpam-6407	196	13	that	that	PRON
ejpam-6407	196	14	[	[	X
ejpam-6407	196	15	gω\{ω	gω\{ω	X
ejpam-6407	196	16	}	}	PUNCT
ejpam-6407	196	17	]	]	PUNCT
ejpam-6407	196	18	∩	∩	NOUN
ejpam-6407	196	19	{	{	PUNCT
ejpam-6407	196	20	ν	ν	NOUN
ejpam-6407	196	21	}	}	PUNCT
ejpam-6407	196	22	=	=	NOUN
ejpam-6407	196	23	̸	̸	ADJ
ejpam-6407	196	24	∅	∅	NOUN
ejpam-6407	196	25	and	and	CCONJ
ejpam-6407	196	26	so	so	ADV
ejpam-6407	196	27	ν	ν	ADP
ejpam-6407	196	28	∈	∈	NOUN
ejpam-6407	196	29	gω\{ω	gω\{ω	NUM
ejpam-6407	196	30	}	}	PUNCT
ejpam-6407	196	31	.	.	PUNCT
ejpam-6407	197	1	this	this	PRON
ejpam-6407	197	2	means	mean	VERB
ejpam-6407	197	3	that	that	SCONJ
ejpam-6407	197	4	,	,	PUNCT
ejpam-6407	197	5	every	every	DET
ejpam-6407	197	6	supra	supra	PROPN
ejpam-6407	197	7	ϵ-open	ϵ-open	PROPN
ejpam-6407	197	8	set	set	PROPN
ejpam-6407	197	9	gω	gω	PROPN
ejpam-6407	197	10	containing	contain	VERB
ejpam-6407	197	11	ω	ω	PROPN
ejpam-6407	197	12	also	also	ADV
ejpam-6407	197	13	contains	contain	VERB
ejpam-6407	197	14	ν	ν	X
ejpam-6407	197	15	.	.	PUNCT
ejpam-6407	197	16	therefore	therefore	ADV
ejpam-6407	197	17	,	,	PUNCT
ejpam-6407	197	18	∩{gω	∩{gω	VERB
ejpam-6407	197	19	:	:	PUNCT
ejpam-6407	197	20	gω	gω	PROPN
ejpam-6407	197	21	∈	∈	PROPN
ejpam-6407	197	22	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	197	23	)	)	PUNCT
ejpam-6407	197	24	and	and	CCONJ
ejpam-6407	197	25	{	{	PUNCT
ejpam-6407	197	26	ω	ω	NOUN
ejpam-6407	197	27	}	}	PUNCT
ejpam-6407	197	28	⊆	⊆	NUM
ejpam-6407	197	29	gω	gω	PROPN
ejpam-6407	197	30	}	}	PUNCT
ejpam-6407	197	31	̸=	̸=	PROPN
ejpam-6407	197	32	{	{	PUNCT
ejpam-6407	197	33	ω	ω	NOUN
ejpam-6407	197	34	}	}	PUNCT
ejpam-6407	197	35	,	,	PUNCT
ejpam-6407	197	36	which	which	PRON
ejpam-6407	197	37	contradicts	contradict	VERB
ejpam-6407	197	38	(	(	PUNCT
ejpam-6407	197	39	3	3	NUM
ejpam-6407	197	40	)	)	PUNCT
ejpam-6407	197	41	.	.	PUNCT
ejpam-6407	198	1	thus	thus	ADV
ejpam-6407	198	2	,	,	PUNCT
ejpam-6407	198	3	for	for	ADP
ejpam-6407	198	4	each	each	DET
ejpam-6407	198	5	ν	ν	NOUN
ejpam-6407	198	6	∈	∈	PROPN
ejpam-6407	198	7	λ	λ	PROPN
ejpam-6407	198	8	,	,	PUNCT
ejpam-6407	198	9	accϵ({ν	accϵ({ν	PROPN
ejpam-6407	198	10	}	}	PUNCT
ejpam-6407	198	11	)	)	PUNCT
ejpam-6407	198	12	=	=	SYM
ejpam-6407	198	13	∅.	∅.	X
ejpam-6407	198	14	(	(	PUNCT
ejpam-6407	198	15	4	4	NUM
ejpam-6407	198	16	)	)	PUNCT
ejpam-6407	198	17	⇒	⇒	NOUN
ejpam-6407	198	18	(	(	PUNCT
ejpam-6407	198	19	1	1	X
ejpam-6407	198	20	)	)	PUNCT
ejpam-6407	198	21	let	let	VERB
ejpam-6407	198	22	ν1	ν1	NOUN
ejpam-6407	198	23	̸=	̸=	PROPN
ejpam-6407	198	24	ν2	ν2	PROPN
ejpam-6407	198	25	∈	∈	PROPN
ejpam-6407	198	26	λ	λ	PROPN
ejpam-6407	198	27	.	.	PUNCT
ejpam-6407	199	1	given	give	VERB
ejpam-6407	199	2	(	(	PUNCT
ejpam-6407	199	3	4	4	NUM
ejpam-6407	199	4	)	)	PUNCT
ejpam-6407	199	5	,	,	PUNCT
ejpam-6407	199	6	accϵ({ν1	accϵ({ν1	PROPN
ejpam-6407	199	7	}	}	PUNCT
ejpam-6407	199	8	)	)	PUNCT
ejpam-6407	200	1	=	=	NOUN
ejpam-6407	200	2	∅	∅	NOUN
ejpam-6407	200	3	and	and	CCONJ
ejpam-6407	200	4	accϵ({ν2	accϵ({ν2	PROPN
ejpam-6407	200	5	}	}	PUNCT
ejpam-6407	200	6	)	)	PUNCT
ejpam-6407	201	1	=	=	NOUN
ejpam-6407	201	2	∅	∅	NOUN
ejpam-6407	201	3	which	which	PRON
ejpam-6407	201	4	follows	follow	VERB
ejpam-6407	201	5	clϵ({ν1	clϵ({ν1	NOUN
ejpam-6407	201	6	}	}	PUNCT
ejpam-6407	201	7	)	)	PUNCT
ejpam-6407	202	1	=	=	PRON
ejpam-6407	202	2	{	{	PUNCT
ejpam-6407	202	3	ν1	ν1	NOUN
ejpam-6407	202	4	}	}	PUNCT
ejpam-6407	202	5	∪	∪	ADP
ejpam-6407	202	6	accϵ({ν1	accϵ({ν1	ADP
ejpam-6407	202	7	}	}	PUNCT
ejpam-6407	202	8	)	)	PUNCT
ejpam-6407	202	9	=	=	PRON
ejpam-6407	202	10	{	{	PUNCT
ejpam-6407	202	11	ν1	ν1	NOUN
ejpam-6407	202	12	}	}	PUNCT
ejpam-6407	202	13	and	and	CCONJ
ejpam-6407	202	14	clϵ({ν2	clϵ({ν2	NUM
ejpam-6407	202	15	}	}	PUNCT
ejpam-6407	202	16	)	)	PUNCT
ejpam-6407	203	1	=	=	PRON
ejpam-6407	203	2	{	{	PUNCT
ejpam-6407	203	3	ν2	ν2	NOUN
ejpam-6407	203	4	}	}	PUNCT
ejpam-6407	203	5	∪	∪	NOUN
ejpam-6407	203	6	accϵ({ν2	accϵ({ν2	PROPN
ejpam-6407	203	7	}	}	PUNCT
ejpam-6407	203	8	)	)	PUNCT
ejpam-6407	203	9	=	=	PRON
ejpam-6407	203	10	{	{	PUNCT
ejpam-6407	203	11	ν2	ν2	NOUN
ejpam-6407	203	12	}	}	PUNCT
ejpam-6407	203	13	.	.	PUNCT
ejpam-6407	204	1	hence	hence	ADV
ejpam-6407	204	2	,	,	PUNCT
ejpam-6407	204	3	{	{	PUNCT
ejpam-6407	204	4	ν1}c	ν1}c	NOUN
ejpam-6407	204	5	and	and	CCONJ
ejpam-6407	204	6	{	{	PUNCT
ejpam-6407	204	7	ν2}c	ν2}c	NOUN
ejpam-6407	204	8	∈	∈	PROPN
ejpam-6407	204	9	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	204	10	)	)	PUNCT
ejpam-6407	204	11	which	which	PRON
ejpam-6407	204	12	separate	separate	ADJ
ejpam-6407	204	13	ν1	ν1	NOUN
ejpam-6407	204	14	and	and	CCONJ
ejpam-6407	204	15	ν2	ν2	NOUN
ejpam-6407	204	16	.	.	PUNCT
ejpam-6407	205	1	consequently	consequently	ADV
ejpam-6407	205	2	,	,	PUNCT
ejpam-6407	205	3	λ	λ	PROPN
ejpam-6407	205	4	is	be	AUX
ejpam-6407	205	5	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6407	205	6	-	-	PUNCT
ejpam-6407	205	7	space	space	NOUN
ejpam-6407	205	8	.	.	PUNCT
ejpam-6407	206	1	definition	definition	NOUN
ejpam-6407	206	2	11	11	NUM
ejpam-6407	206	3	.	.	PUNCT
ejpam-6407	207	1	the	the	DET
ejpam-6407	207	2	space	space	NOUN
ejpam-6407	207	3	(	(	PUNCT
ejpam-6407	207	4	λ	λ	NOUN
ejpam-6407	207	5	,	,	PUNCT
ejpam-6407	207	6	ϑ	ϑ	NOUN
ejpam-6407	207	7	)	)	PUNCT
ejpam-6407	207	8	is	be	AUX
ejpam-6407	207	9	referred	refer	VERB
ejpam-6407	207	10	to	to	ADP
ejpam-6407	207	11	as	as	ADP
ejpam-6407	207	12	supra	supra	PROPN
ejpam-6407	207	13	ϵ-symmetric	ϵ-symmetric	PROPN
ejpam-6407	207	14	if	if	SCONJ
ejpam-6407	207	15	ν1	ν1	NOUN
ejpam-6407	207	16	∈	∈	PROPN
ejpam-6407	207	17	clϵ({ν2	clϵ({ν2	NOUN
ejpam-6407	207	18	}	}	PUNCT
ejpam-6407	207	19	)	)	PUNCT
ejpam-6407	207	20	demonstrates	demonstrate	VERB
ejpam-6407	207	21	that	that	SCONJ
ejpam-6407	207	22	ν2	ν2	NOUN
ejpam-6407	207	23	∈	∈	PROPN
ejpam-6407	207	24	clϵ({ν1	clϵ({ν1	NOUN
ejpam-6407	207	25	}	}	PUNCT
ejpam-6407	207	26	)	)	PUNCT
ejpam-6407	207	27	for	for	ADP
ejpam-6407	207	28	ν1	ν1	NOUN
ejpam-6407	207	29	̸=	̸=	PROPN
ejpam-6407	207	30	ν2	ν2	NOUN
ejpam-6407	207	31	∈	∈	PROPN
ejpam-6407	207	32	λ	λ	PROPN
ejpam-6407	207	33	.	.	PUNCT
ejpam-6407	207	34	theorem	theorem	VERB
ejpam-6407	207	35	7	7	NUM
ejpam-6407	207	36	.	.	PUNCT
ejpam-6407	208	1	every	every	DET
ejpam-6407	208	2	supra	supra	PROPN
ejpam-6407	208	3	ϵ-symmetric	ϵ-symmetric	PROPN
ejpam-6407	208	4	and	and	CCONJ
ejpam-6407	208	5	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	208	6	-	-	NOUN
ejpam-6407	208	7	space	space	NOUN
ejpam-6407	208	8	(	(	PUNCT
ejpam-6407	208	9	λ	λ	NOUN
ejpam-6407	208	10	,	,	PUNCT
ejpam-6407	208	11	ϑ	ϑ	NOUN
ejpam-6407	208	12	)	)	PUNCT
ejpam-6407	208	13	is	be	AUX
ejpam-6407	208	14	supra-ϵ-t1	supra-ϵ-t1	VERB
ejpam-6407	208	15	.	.	PUNCT
ejpam-6407	209	1	proof	proof	NOUN
ejpam-6407	209	2	.	.	PUNCT
ejpam-6407	210	1	let	let	VERB
ejpam-6407	210	2	ν1	ν1	NOUN
ejpam-6407	210	3	̸=	̸=	PROPN
ejpam-6407	210	4	ν2	ν2	NOUN
ejpam-6407	210	5	∈	∈	PROPN
ejpam-6407	210	6	λ	λ	NOUN
ejpam-6407	210	7	.	.	PUNCT
ejpam-6407	211	1	since	since	SCONJ
ejpam-6407	211	2	λ	λ	PROPN
ejpam-6407	211	3	is	be	AUX
ejpam-6407	211	4	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	211	5	-	-	NOUN
ejpam-6407	211	6	space	space	NOUN
ejpam-6407	211	7	,	,	PUNCT
ejpam-6407	211	8	there	there	PRON
ejpam-6407	211	9	is	be	VERB
ejpam-6407	211	10	a	a	DET
ejpam-6407	211	11	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	211	12	set	set	VERB
ejpam-6407	211	13	h	h	NOUN
ejpam-6407	211	14	including	include	VERB
ejpam-6407	211	15	one	one	NUM
ejpam-6407	211	16	point	point	NOUN
ejpam-6407	211	17	(	(	PUNCT
ejpam-6407	211	18	say	say	INTJ
ejpam-6407	211	19	ν1	ν1	NOUN
ejpam-6407	211	20	)	)	PUNCT
ejpam-6407	211	21	but	but	CCONJ
ejpam-6407	211	22	excluding	exclude	VERB
ejpam-6407	211	23	the	the	DET
ejpam-6407	211	24	other	other	ADJ
ejpam-6407	211	25	and	and	CCONJ
ejpam-6407	211	26	so	so	ADV
ejpam-6407	211	27	ν1	ν1	PROPN
ejpam-6407	211	28	̸∈	̸∈	PROPN
ejpam-6407	211	29	clϵ({ν2	clϵ({ν2	PROPN
ejpam-6407	211	30	}	}	PUNCT
ejpam-6407	211	31	)	)	PUNCT
ejpam-6407	211	32	.	.	PUNCT
ejpam-6407	212	1	given	give	VERB
ejpam-6407	212	2	λ	λ	PROPN
ejpam-6407	212	3	is	be	AUX
ejpam-6407	212	4	supra	supra	PROPN
ejpam-6407	212	5	ϵ-symmetric	ϵ-symmetric	PROPN
ejpam-6407	212	6	,	,	PUNCT
ejpam-6407	212	7	ν2	ν2	PROPN
ejpam-6407	212	8	̸∈	̸∈	PROPN
ejpam-6407	212	9	clϵ({ν1	clϵ({ν1	PROPN
ejpam-6407	212	10	}	}	PUNCT
ejpam-6407	212	11	)	)	PUNCT
ejpam-6407	212	12	.	.	PUNCT
ejpam-6407	213	1	therefore	therefore	ADV
ejpam-6407	213	2	,	,	PUNCT
ejpam-6407	213	3	[	[	X
ejpam-6407	213	4	clϵ({ν1})]c	clϵ({ν1})]c	X
ejpam-6407	213	5	and	and	CCONJ
ejpam-6407	213	6	[	[	X
ejpam-6407	213	7	clϵ({ν2})]c	clϵ({ν2})]c	NOUN
ejpam-6407	213	8	are	be	AUX
ejpam-6407	213	9	two	two	NUM
ejpam-6407	213	10	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	213	11	sets	set	NOUN
ejpam-6407	213	12	which	which	PRON
ejpam-6407	213	13	separate	separate	ADJ
ejpam-6407	213	14	ν1	ν1	NOUN
ejpam-6407	213	15	and	and	CCONJ
ejpam-6407	213	16	ν2	ν2	NOUN
ejpam-6407	213	17	.	.	PUNCT
ejpam-6407	214	1	thus	thus	ADV
ejpam-6407	214	2	,	,	PUNCT
ejpam-6407	214	3	λ	λ	PROPN
ejpam-6407	214	4	is	be	AUX
ejpam-6407	214	5	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6407	214	6	-	-	PUNCT
ejpam-6407	214	7	space	space	NOUN
ejpam-6407	214	8	.	.	PUNCT
ejpam-6407	215	1	corollary	corollary	ADJ
ejpam-6407	215	2	3	3	NUM
ejpam-6407	215	3	.	.	PUNCT
ejpam-6407	216	1	every	every	DET
ejpam-6407	216	2	supra	supra	PROPN
ejpam-6407	216	3	ϵ-symmetric	ϵ-symmetric	ADJ
ejpam-6407	216	4	space	space	NOUN
ejpam-6407	216	5	is	be	AUX
ejpam-6407	216	6	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	216	7	-	-	NOUN
ejpam-6407	216	8	space	space	NOUN
ejpam-6407	216	9	if	if	SCONJ
ejpam-6407	216	10	and	and	CCONJ
ejpam-6407	216	11	only	only	ADV
ejpam-6407	216	12	if	if	SCONJ
ejpam-6407	216	13	it	it	PRON
ejpam-6407	216	14	is	be	AUX
ejpam-6407	216	15	supraϵ-t1	supraϵ-t1	NOUN
ejpam-6407	216	16	.	.	PUNCT
ejpam-6407	216	17	m.	m.	NOUN
ejpam-6407	216	18	aldawood	aldawood	PROPN
ejpam-6407	216	19	et	et	PROPN
ejpam-6407	216	20	al	al	PROPN
ejpam-6407	216	21	.	.	PUNCT
ejpam-6407	216	22	/	/	SYM
ejpam-6407	216	23	eur	eur	PROPN
ejpam-6407	216	24	.	.	PUNCT
ejpam-6407	217	1	j.	j.	PROPN
ejpam-6407	217	2	pure	pure	PROPN
ejpam-6407	217	3	appl	appl	PROPN
ejpam-6407	217	4	.	.	PROPN
ejpam-6407	217	5	math	math	PROPN
ejpam-6407	217	6	,	,	PUNCT
ejpam-6407	217	7	18	18	NUM
ejpam-6407	217	8	(	(	PUNCT
ejpam-6407	217	9	3	3	NUM
ejpam-6407	217	10	)	)	PUNCT
ejpam-6407	217	11	(	(	PUNCT
ejpam-6407	217	12	2025	2025	NUM
ejpam-6407	217	13	)	)	PUNCT
ejpam-6407	217	14	,	,	PUNCT
ejpam-6407	217	15	6407	6407	NUM
ejpam-6407	217	16	8	8	NUM
ejpam-6407	217	17	of	of	ADP
ejpam-6407	217	18	15	15	NUM
ejpam-6407	217	19	proof	proof	NOUN
ejpam-6407	217	20	.	.	PUNCT
ejpam-6407	218	1	it	it	PRON
ejpam-6407	218	2	is	be	AUX
ejpam-6407	218	3	direct	direct	ADJ
ejpam-6407	218	4	from	from	ADP
ejpam-6407	218	5	theorem	theorem	ADJ
ejpam-6407	218	6	2	2	NUM
ejpam-6407	218	7	and	and	CCONJ
ejpam-6407	218	8	theorem	theorem	VERB
ejpam-6407	218	9	7	7	NUM
ejpam-6407	218	10	.	.	PUNCT
ejpam-6407	218	11	theorem	theorem	NOUN
ejpam-6407	218	12	8	8	NUM
ejpam-6407	218	13	.	.	PUNCT
ejpam-6407	219	1	for	for	ADP
ejpam-6407	219	2	any	any	DET
ejpam-6407	219	3	sts	st	NOUN
ejpam-6407	219	4	(	(	PUNCT
ejpam-6407	219	5	λ	λ	X
ejpam-6407	219	6	,	,	PUNCT
ejpam-6407	219	7	ϑ	ϑ	NOUN
ejpam-6407	219	8	)	)	PUNCT
ejpam-6407	219	9	,	,	PUNCT
ejpam-6407	219	10	the	the	DET
ejpam-6407	219	11	following	follow	VERB
ejpam-6407	219	12	are	be	AUX
ejpam-6407	219	13	equivalent	equivalent	ADJ
ejpam-6407	219	14	:	:	PUNCT
ejpam-6407	219	15	(	(	PUNCT
ejpam-6407	219	16	1	1	X
ejpam-6407	219	17	)	)	PUNCT
ejpam-6407	219	18	λ	λ	NOUN
ejpam-6407	219	19	is	be	AUX
ejpam-6407	219	20	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6407	219	21	-	-	PUNCT
ejpam-6407	219	22	space	space	NOUN
ejpam-6407	219	23	;	;	PUNCT
ejpam-6407	219	24	(	(	PUNCT
ejpam-6407	219	25	2	2	X
ejpam-6407	219	26	)	)	PUNCT
ejpam-6407	219	27	ψ	ψ	NOUN
ejpam-6407	219	28	=	=	SYM
ejpam-6407	219	29	{	{	PUNCT
ejpam-6407	219	30	(	(	PUNCT
ejpam-6407	219	31	ν	ν	NOUN
ejpam-6407	219	32	,	,	PUNCT
ejpam-6407	219	33	ν	ν	NOUN
ejpam-6407	219	34	)	)	PUNCT
ejpam-6407	219	35	:	:	PUNCT
ejpam-6407	219	36	ν	ν	PROPN
ejpam-6407	219	37	∈	∈	PROPN
ejpam-6407	219	38	λ	λ	PROPN
ejpam-6407	219	39	}	}	PUNCT
ejpam-6407	219	40	is	be	AUX
ejpam-6407	219	41	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6407	219	42	subset	subset	NOUN
ejpam-6407	219	43	of	of	ADP
ejpam-6407	219	44	λ×	λ×	PROPN
ejpam-6407	219	45	λ	λ	PROPN
ejpam-6407	219	46	;	;	PUNCT
ejpam-6407	219	47	(	(	PUNCT
ejpam-6407	219	48	3	3	X
ejpam-6407	219	49	)	)	PUNCT
ejpam-6407	219	50	∩{hν	∩{hν	NOUN
ejpam-6407	219	51	:	:	PUNCT
ejpam-6407	219	52	hν	hν	VERB
ejpam-6407	219	53	∈	∈	PROPN
ejpam-6407	219	54	scϵ(λ	scϵ(λ	PROPN
ejpam-6407	219	55	)	)	PUNCT
ejpam-6407	219	56	}	}	PUNCT
ejpam-6407	220	1	=	=	SYM
ejpam-6407	220	2	{	{	PUNCT
ejpam-6407	220	3	ν	ν	NOUN
ejpam-6407	220	4	}	}	PUNCT
ejpam-6407	220	5	,	,	PUNCT
ejpam-6407	220	6	for	for	ADP
ejpam-6407	220	7	each	each	DET
ejpam-6407	220	8	ν	ν	X
ejpam-6407	220	9	∈	∈	PROPN
ejpam-6407	220	10	λ	λ	PROPN
ejpam-6407	220	11	.	.	PUNCT
ejpam-6407	220	12	proof	proof	NOUN
ejpam-6407	220	13	.	.	PUNCT
ejpam-6407	221	1	(	(	PUNCT
ejpam-6407	221	2	1	1	X
ejpam-6407	221	3	)	)	PUNCT
ejpam-6407	221	4	⇒	⇒	NOUN
ejpam-6407	221	5	(	(	PUNCT
ejpam-6407	221	6	2	2	X
ejpam-6407	221	7	)	)	PUNCT
ejpam-6407	221	8	let	let	NOUN
ejpam-6407	221	9	(	(	PUNCT
ejpam-6407	221	10	ν1	ν1	NOUN
ejpam-6407	221	11	,	,	PUNCT
ejpam-6407	221	12	ν2	ν2	NOUN
ejpam-6407	221	13	)	)	PUNCT
ejpam-6407	221	14	∈	∈	NOUN
ejpam-6407	222	1	λ×	λ×	X
ejpam-6407	222	2	λ\ψ	λ\ψ	NOUN
ejpam-6407	222	3	,	,	PUNCT
ejpam-6407	222	4	then	then	ADV
ejpam-6407	222	5	ν1	ν1	VERB
ejpam-6407	222	6	̸=	̸=	PROPN
ejpam-6407	222	7	ν2	ν2	NOUN
ejpam-6407	222	8	.	.	PUNCT
ejpam-6407	223	1	given	give	VERB
ejpam-6407	223	2	(	(	PUNCT
ejpam-6407	223	3	1	1	NUM
ejpam-6407	223	4	)	)	PUNCT
ejpam-6407	223	5	,	,	PUNCT
ejpam-6407	223	6	there	there	PRON
ejpam-6407	223	7	are	be	VERB
ejpam-6407	223	8	two	two	NUM
ejpam-6407	223	9	disjoint	disjoint	ADJ
ejpam-6407	223	10	supraϵ-open	supraϵ-open	ADJ
ejpam-6407	223	11	subsets	subset	NOUN
ejpam-6407	223	12	µ1	µ1	PROPN
ejpam-6407	223	13	and	and	CCONJ
ejpam-6407	223	14	µ2	µ2	PROPN
ejpam-6407	223	15	of	of	ADP
ejpam-6407	223	16	λ	λ	PROPN
ejpam-6407	223	17	,	,	PUNCT
ejpam-6407	223	18	such	such	ADJ
ejpam-6407	223	19	that	that	SCONJ
ejpam-6407	223	20	ν1	ν1	PROPN
ejpam-6407	223	21	∈	∈	PROPN
ejpam-6407	223	22	µ1	µ1	NOUN
ejpam-6407	223	23	and	and	CCONJ
ejpam-6407	223	24	ν2	ν2	NOUN
ejpam-6407	223	25	∈	∈	PROPN
ejpam-6407	223	26	µ2	µ2	NOUN
ejpam-6407	223	27	.	.	PUNCT
ejpam-6407	224	1	hence	hence	ADV
ejpam-6407	224	2	,	,	PUNCT
ejpam-6407	224	3	(	(	PUNCT
ejpam-6407	224	4	ν1	ν1	NOUN
ejpam-6407	224	5	,	,	PUNCT
ejpam-6407	224	6	ν2	ν2	NOUN
ejpam-6407	224	7	)	)	PUNCT
ejpam-6407	224	8	∈	∈	PROPN
ejpam-6407	224	9	µ1	µ1	PROPN
ejpam-6407	224	10	×	×	NOUN
ejpam-6407	224	11	µ1	µ1	NOUN
ejpam-6407	224	12	⊆	⊆	NUM
ejpam-6407	224	13	λ	λ	SYM
ejpam-6407	224	14	×	×	NOUN
ejpam-6407	224	15	λ\ψ	λ\ψ	NOUN
ejpam-6407	224	16	,	,	PUNCT
ejpam-6407	224	17	and	and	CCONJ
ejpam-6407	224	18	thus	thus	ADV
ejpam-6407	224	19	λ	λ	X
ejpam-6407	224	20	×	×	NOUN
ejpam-6407	224	21	λ\ψ	λ\ψ	NOUN
ejpam-6407	224	22	is	be	AUX
ejpam-6407	224	23	a	a	DET
ejpam-6407	224	24	supra	supra	ADJ
ejpam-6407	224	25	supra-ϵ-neighborhood	supra-ϵ-neighborhood	NOUN
ejpam-6407	224	26	for	for	ADP
ejpam-6407	224	27	each	each	PRON
ejpam-6407	224	28	of	of	ADP
ejpam-6407	224	29	its	its	PRON
ejpam-6407	224	30	points	point	NOUN
ejpam-6407	224	31	.	.	PUNCT
ejpam-6407	225	1	therefore	therefore	ADV
ejpam-6407	225	2	,	,	PUNCT
ejpam-6407	225	3	ψ	ψ	X
ejpam-6407	225	4	is	be	AUX
ejpam-6407	225	5	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6407	225	6	subset	subset	NOUN
ejpam-6407	225	7	of	of	ADP
ejpam-6407	225	8	λ×	λ×	PROPN
ejpam-6407	225	9	λ	λ	PROPN
ejpam-6407	225	10	.	.	PROPN
ejpam-6407	225	11	(	(	PUNCT
ejpam-6407	225	12	2	2	X
ejpam-6407	225	13	)	)	PUNCT
ejpam-6407	225	14	⇒	⇒	NOUN
ejpam-6407	225	15	(	(	PUNCT
ejpam-6407	225	16	1	1	X
ejpam-6407	225	17	)	)	PUNCT
ejpam-6407	225	18	assume	assume	VERB
ejpam-6407	225	19	that	that	SCONJ
ejpam-6407	225	20	ψ	ψ	X
ejpam-6407	225	21	=	=	X
ejpam-6407	225	22	{	{	PUNCT
ejpam-6407	225	23	(	(	PUNCT
ejpam-6407	225	24	ν	ν	NOUN
ejpam-6407	225	25	,	,	PUNCT
ejpam-6407	225	26	ν	ν	NOUN
ejpam-6407	225	27	)	)	PUNCT
ejpam-6407	225	28	:	:	PUNCT
ejpam-6407	225	29	ν	ν	PROPN
ejpam-6407	225	30	∈	∈	PROPN
ejpam-6407	225	31	λ	λ	PROPN
ejpam-6407	225	32	}	}	PUNCT
ejpam-6407	225	33	is	be	AUX
ejpam-6407	225	34	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6407	225	35	subset	subset	NOUN
ejpam-6407	225	36	of	of	ADP
ejpam-6407	225	37	λ	λ	PROPN
ejpam-6407	225	38	×	×	NOUN
ejpam-6407	225	39	λ	λ	NOUN
ejpam-6407	225	40	and	and	CCONJ
ejpam-6407	225	41	ν1	ν1	NOUN
ejpam-6407	225	42	̸=	̸=	PROPN
ejpam-6407	225	43	ν2	ν2	NOUN
ejpam-6407	225	44	∈	∈	PROPN
ejpam-6407	225	45	λ	λ	NOUN
ejpam-6407	225	46	,	,	PUNCT
ejpam-6407	225	47	then	then	ADV
ejpam-6407	225	48	λ	λ	X
ejpam-6407	225	49	×	×	NOUN
ejpam-6407	225	50	λ\ψ	λ\ψ	NOUN
ejpam-6407	225	51	is	be	AUX
ejpam-6407	225	52	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	225	53	set	set	VERB
ejpam-6407	225	54	including	include	VERB
ejpam-6407	225	55	(	(	PUNCT
ejpam-6407	225	56	ν1	ν1	NOUN
ejpam-6407	225	57	,	,	PUNCT
ejpam-6407	225	58	ν2	ν2	NOUN
ejpam-6407	225	59	)	)	PUNCT
ejpam-6407	225	60	.	.	PUNCT
ejpam-6407	226	1	hence	hence	ADV
ejpam-6407	226	2	,	,	PUNCT
ejpam-6407	226	3	there	there	PRON
ejpam-6407	226	4	are	be	VERB
ejpam-6407	226	5	a	a	DET
ejpam-6407	226	6	,	,	PUNCT
ejpam-6407	226	7	b	b	PROPN
ejpam-6407	226	8	∈	∈	PROPN
ejpam-6407	226	9	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	226	10	)	)	PUNCT
ejpam-6407	226	11	such	such	ADJ
ejpam-6407	226	12	that	that	SCONJ
ejpam-6407	226	13	(	(	PUNCT
ejpam-6407	226	14	ν1	ν1	NOUN
ejpam-6407	226	15	,	,	PUNCT
ejpam-6407	226	16	ν2	ν2	NOUN
ejpam-6407	226	17	)	)	PUNCT
ejpam-6407	226	18	∈	∈	NOUN
ejpam-6407	226	19	a	a	DET
ejpam-6407	226	20	×	×	NOUN
ejpam-6407	226	21	b	b	PROPN
ejpam-6407	226	22	⊆	⊆	NUM
ejpam-6407	226	23	λ	λ	SYM
ejpam-6407	226	24	×	×	NOUN
ejpam-6407	226	25	λ\ψ	λ\ψ	NOUN
ejpam-6407	226	26	.	.	PUNCT
ejpam-6407	227	1	therefore	therefore	ADV
ejpam-6407	227	2	,	,	PUNCT
ejpam-6407	227	3	a	a	DET
ejpam-6407	227	4	,	,	PUNCT
ejpam-6407	227	5	b	b	PROPN
ejpam-6407	227	6	∈	∈	PROPN
ejpam-6407	227	7	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	227	8	)	)	PUNCT
ejpam-6407	227	9	separate	separate	ADJ
ejpam-6407	227	10	ν1	ν1	NOUN
ejpam-6407	227	11	and	and	CCONJ
ejpam-6407	227	12	ν2	ν2	NOUN
ejpam-6407	227	13	with	with	ADP
ejpam-6407	227	14	a	a	DET
ejpam-6407	227	15	∩b	∩b	NOUN
ejpam-6407	227	16	=	=	X
ejpam-6407	227	17	∅.	∅.	VERB
ejpam-6407	227	18	thus	thus	ADV
ejpam-6407	227	19	,	,	PUNCT
ejpam-6407	227	20	λ	λ	PROPN
ejpam-6407	227	21	is	be	AUX
ejpam-6407	227	22	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6407	227	23	-	-	PUNCT
ejpam-6407	227	24	space	space	NOUN
ejpam-6407	227	25	.	.	PUNCT
ejpam-6407	228	1	(	(	PUNCT
ejpam-6407	228	2	1	1	X
ejpam-6407	228	3	)	)	PUNCT
ejpam-6407	228	4	⇒	⇒	NOUN
ejpam-6407	228	5	(	(	PUNCT
ejpam-6407	228	6	3	3	X
ejpam-6407	228	7	)	)	PUNCT
ejpam-6407	228	8	let	let	VERB
ejpam-6407	228	9	λ	λ	NOUN
ejpam-6407	228	10	be	be	AUX
ejpam-6407	228	11	a	a	DET
ejpam-6407	228	12	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6407	228	13	-	-	PUNCT
ejpam-6407	228	14	space	space	NOUN
ejpam-6407	228	15	.	.	PUNCT
ejpam-6407	229	1	then	then	ADV
ejpam-6407	229	2	,	,	PUNCT
ejpam-6407	229	3	for	for	ADP
ejpam-6407	229	4	any	any	DET
ejpam-6407	229	5	ν1	ν1	NOUN
ejpam-6407	229	6	̸=	̸=	PROPN
ejpam-6407	229	7	ν2	ν2	NOUN
ejpam-6407	229	8	∈	∈	PROPN
ejpam-6407	229	9	λ	λ	NOUN
ejpam-6407	229	10	,	,	PUNCT
ejpam-6407	229	11	there	there	PRON
ejpam-6407	229	12	are	be	VERB
ejpam-6407	229	13	two	two	NUM
ejpam-6407	229	14	disjoint	disjoint	NOUN
ejpam-6407	229	15	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	229	16	subsets	subset	NOUN
ejpam-6407	229	17	µ1	µ1	PROPN
ejpam-6407	229	18	and	and	CCONJ
ejpam-6407	229	19	µ2	µ2	PROPN
ejpam-6407	229	20	of	of	ADP
ejpam-6407	229	21	λ	λ	PROPN
ejpam-6407	229	22	,	,	PUNCT
ejpam-6407	229	23	such	such	ADJ
ejpam-6407	229	24	that	that	SCONJ
ejpam-6407	229	25	ν1	ν1	PROPN
ejpam-6407	229	26	∈	∈	PROPN
ejpam-6407	229	27	µ1	µ1	NOUN
ejpam-6407	229	28	and	and	CCONJ
ejpam-6407	229	29	ν2	ν2	PROPN
ejpam-6407	229	30	∈	∈	PROPN
ejpam-6407	229	31	µ2	µ2	NOUN
ejpam-6407	229	32	.	.	PUNCT
ejpam-6407	230	1	this	this	PRON
ejpam-6407	230	2	implies	imply	VERB
ejpam-6407	230	3	that	that	SCONJ
ejpam-6407	230	4	ν1	ν1	PROPN
ejpam-6407	230	5	∈	∈	PROPN
ejpam-6407	230	6	clϵ(µ1	clϵ(µ1	NOUN
ejpam-6407	230	7	)	)	PUNCT
ejpam-6407	230	8	⊆	⊆	NUM
ejpam-6407	230	9	µc2	µc2	PROPN
ejpam-6407	230	10	,	,	PUNCT
ejpam-6407	230	11	µ	µ	NOUN
ejpam-6407	230	12	c	c	NOUN
ejpam-6407	230	13	2	2	NUM
ejpam-6407	230	14	∈	∈	NOUN
ejpam-6407	230	15	scϵ(λ	scϵ(λ	NOUN
ejpam-6407	230	16	)	)	PUNCT
ejpam-6407	230	17	which	which	PRON
ejpam-6407	230	18	containing	contain	VERB
ejpam-6407	230	19	ν1	ν1	NOUN
ejpam-6407	230	20	but	but	CCONJ
ejpam-6407	230	21	not	not	PART
ejpam-6407	230	22	ν2	ν2	NOUN
ejpam-6407	230	23	.	.	PUNCT
ejpam-6407	231	1	hence	hence	ADV
ejpam-6407	231	2	,	,	PUNCT
ejpam-6407	231	3	∩{µc2	∩{µc2	PROPN
ejpam-6407	231	4	:	:	PUNCT
ejpam-6407	231	5	ν1	ν1	PROPN
ejpam-6407	231	6	∈	∈	PROPN
ejpam-6407	231	7	µc2	µc2	PROPN
ejpam-6407	231	8	∈	∈	PROPN
ejpam-6407	231	9	scϵ(λ	scϵ(λ	PROPN
ejpam-6407	231	10	)	)	PUNCT
ejpam-6407	231	11	}	}	PUNCT
ejpam-6407	232	1	=	=	SYM
ejpam-6407	232	2	{	{	PUNCT
ejpam-6407	232	3	ν1	ν1	NOUN
ejpam-6407	232	4	}	}	PUNCT
ejpam-6407	232	5	.	.	PUNCT
ejpam-6407	233	1	(	(	PUNCT
ejpam-6407	233	2	3	3	X
ejpam-6407	233	3	)	)	PUNCT
ejpam-6407	233	4	⇒	⇒	NOUN
ejpam-6407	233	5	(	(	PUNCT
ejpam-6407	233	6	1	1	X
ejpam-6407	233	7	)	)	PUNCT
ejpam-6407	233	8	let	let	VERB
ejpam-6407	233	9	ν1	ν1	NOUN
ejpam-6407	233	10	̸=	̸=	PROPN
ejpam-6407	233	11	ν2	ν2	PROPN
ejpam-6407	233	12	∈	∈	PROPN
ejpam-6407	233	13	λ	λ	NOUN
ejpam-6407	233	14	.	.	PUNCT
ejpam-6407	234	1	given	give	VERB
ejpam-6407	234	2	(	(	PUNCT
ejpam-6407	234	3	3	3	NUM
ejpam-6407	234	4	)	)	PUNCT
ejpam-6407	234	5	,	,	PUNCT
ejpam-6407	234	6	∩{hν1	∩{hν1	PROPN
ejpam-6407	234	7	:	:	PUNCT
ejpam-6407	234	8	hν1	hν1	NOUN
ejpam-6407	234	9	∈	∈	PROPN
ejpam-6407	234	10	scϵ(λ	scϵ(λ	NOUN
ejpam-6407	234	11	)	)	PUNCT
ejpam-6407	234	12	}	}	PUNCT
ejpam-6407	235	1	=	=	SYM
ejpam-6407	235	2	{	{	PUNCT
ejpam-6407	235	3	ν1	ν1	NOUN
ejpam-6407	235	4	}	}	PUNCT
ejpam-6407	235	5	.	.	PUNCT
ejpam-6407	236	1	this	this	PRON
ejpam-6407	236	2	means	mean	VERB
ejpam-6407	236	3	that	that	SCONJ
ejpam-6407	236	4	,	,	PUNCT
ejpam-6407	236	5	there	there	PRON
ejpam-6407	236	6	is	be	VERB
ejpam-6407	236	7	hν1	hν1	NOUN
ejpam-6407	236	8	∈	∈	PROPN
ejpam-6407	236	9	scϵ(λ	scϵ(λ	PROPN
ejpam-6407	236	10	)	)	PUNCT
ejpam-6407	236	11	including	include	VERB
ejpam-6407	236	12	ν1	ν1	NOUN
ejpam-6407	236	13	but	but	CCONJ
ejpam-6407	236	14	not	not	PART
ejpam-6407	236	15	ν2	ν2	NOUN
ejpam-6407	236	16	.	.	PUNCT
ejpam-6407	237	1	hence	hence	ADV
ejpam-6407	237	2	,	,	PUNCT
ejpam-6407	237	3	there	there	PRON
ejpam-6407	237	4	is	be	VERB
ejpam-6407	237	5	oν1	oν1	PROPN
ejpam-6407	237	6	∈	∈	PROPN
ejpam-6407	237	7	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	237	8	)	)	PUNCT
ejpam-6407	237	9	such	such	ADJ
ejpam-6407	237	10	that	that	DET
ejpam-6407	237	11	ν1	ν1	NOUN
ejpam-6407	237	12	∈	∈	PROPN
ejpam-6407	237	13	clϵ(oν1	clϵ(oν1	NOUN
ejpam-6407	237	14	)	)	PUNCT
ejpam-6407	237	15	⊆	⊆	NUM
ejpam-6407	237	16	hν1	hν1	NOUN
ejpam-6407	237	17	,	,	PUNCT
ejpam-6407	237	18	and	and	CCONJ
ejpam-6407	237	19	consequently	consequently	ADV
ejpam-6407	237	20	oν1	oν1	NOUN
ejpam-6407	237	21	,	,	PUNCT
ejpam-6407	237	22	[	[	X
ejpam-6407	237	23	clϵ(oν1	clϵ(oν1	NOUN
ejpam-6407	237	24	)	)	PUNCT
ejpam-6407	237	25	]	]	PUNCT
ejpam-6407	237	26	c	c	PROPN
ejpam-6407	237	27	∈	∈	PROPN
ejpam-6407	237	28	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	237	29	)	)	PUNCT
ejpam-6407	237	30	separate	separate	ADJ
ejpam-6407	237	31	ν1	ν1	NOUN
ejpam-6407	237	32	and	and	CCONJ
ejpam-6407	237	33	ν2	ν2	NOUN
ejpam-6407	237	34	with	with	ADP
ejpam-6407	237	35	[	[	X
ejpam-6407	237	36	clϵ(oν1	clϵ(oν1	NOUN
ejpam-6407	237	37	)	)	PUNCT
ejpam-6407	237	38	]	]	PUNCT
ejpam-6407	238	1	c	c	NOUN
ejpam-6407	238	2	∩oν1	∩oν1	NOUN
ejpam-6407	238	3	=	=	SYM
ejpam-6407	238	4	∅.	∅.	VERB
ejpam-6407	238	5	therefore	therefore	ADV
ejpam-6407	238	6	,	,	PUNCT
ejpam-6407	238	7	λ	λ	PROPN
ejpam-6407	238	8	is	be	AUX
ejpam-6407	238	9	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6407	238	10	-	-	PUNCT
ejpam-6407	238	11	space	space	NOUN
ejpam-6407	238	12	.	.	PUNCT
ejpam-6407	239	1	4	4	X
ejpam-6407	239	2	.	.	X
ejpam-6407	239	3	more	more	ADJ
ejpam-6407	239	4	features	feature	NOUN
ejpam-6407	239	5	of	of	ADP
ejpam-6407	239	6	supra	supra	ADJ
ejpam-6407	239	7	ϵ-separation	ϵ-separation	NOUN
ejpam-6407	239	8	axioms	axiom	NOUN
ejpam-6407	239	9	herein	herein	NOUN
ejpam-6407	239	10	,	,	PUNCT
ejpam-6407	239	11	we	we	PRON
ejpam-6407	239	12	study	study	VERB
ejpam-6407	239	13	the	the	DET
ejpam-6407	239	14	supra	supra	ADJ
ejpam-6407	239	15	hereditary	hereditary	ADJ
ejpam-6407	239	16	property	property	NOUN
ejpam-6407	239	17	and	and	CCONJ
ejpam-6407	239	18	supra	supra	PROPN
ejpam-6407	239	19	topological	topological	ADJ
ejpam-6407	239	20	property	property	NOUN
ejpam-6407	239	21	for	for	ADP
ejpam-6407	239	22	each	each	DET
ejpam-6407	239	23	aforementioned	aforementioned	ADJ
ejpam-6407	239	24	notion	notion	NOUN
ejpam-6407	239	25	.	.	PUNCT
ejpam-6407	240	1	in	in	ADP
ejpam-6407	240	2	special	special	ADJ
ejpam-6407	240	3	,	,	PUNCT
ejpam-6407	240	4	we	we	PRON
ejpam-6407	240	5	show	show	VERB
ejpam-6407	240	6	that	that	SCONJ
ejpam-6407	240	7	he	he	PRON
ejpam-6407	240	8	property	property	NOUN
ejpam-6407	240	9	of	of	ADP
ejpam-6407	240	10	being	be	AUX
ejpam-6407	240	11	a	a	DET
ejpam-6407	240	12	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6407	240	13	-	-	PUNCT
ejpam-6407	240	14	space	space	NOUN
ejpam-6407	240	15	,	,	PUNCT
ejpam-6407	240	16	j	j	PROPN
ejpam-6407	240	17	=	=	SYM
ejpam-6407	240	18	0	0	NUM
ejpam-6407	240	19	,	,	PUNCT
ejpam-6407	240	20	1	1	NUM
ejpam-6407	240	21	,	,	PUNCT
ejpam-6407	240	22	2	2	NUM
ejpam-6407	240	23	,	,	PUNCT
ejpam-6407	240	24	is	be	AUX
ejpam-6407	240	25	a	a	DET
ejpam-6407	240	26	supra	supra	ADJ
ejpam-6407	240	27	hereditary	hereditary	ADJ
ejpam-6407	240	28	property	property	NOUN
ejpam-6407	240	29	.	.	PUNCT
ejpam-6407	241	1	moreover	moreover	ADV
ejpam-6407	241	2	,	,	PUNCT
ejpam-6407	241	3	we	we	PRON
ejpam-6407	241	4	show	show	VERB
ejpam-6407	241	5	that	that	SCONJ
ejpam-6407	241	6	he	he	PRON
ejpam-6407	241	7	property	property	NOUN
ejpam-6407	241	8	of	of	ADP
ejpam-6407	241	9	being	be	AUX
ejpam-6407	241	10	a	a	DET
ejpam-6407	241	11	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6407	241	12	-	-	PUNCT
ejpam-6407	241	13	space	space	NOUN
ejpam-6407	241	14	,	,	PUNCT
ejpam-6407	241	15	j	j	PROPN
ejpam-6407	241	16	=	=	SYM
ejpam-6407	241	17	0	0	NUM
ejpam-6407	241	18	,	,	PUNCT
ejpam-6407	241	19	1	1	NUM
ejpam-6407	241	20	,	,	PUNCT
ejpam-6407	241	21	2	2	NUM
ejpam-6407	241	22	,	,	PUNCT
ejpam-6407	241	23	is	be	AUX
ejpam-6407	241	24	a	a	DET
ejpam-6407	241	25	supra	supra	ADJ
ejpam-6407	241	26	topological	topological	ADJ
ejpam-6407	241	27	property	property	NOUN
ejpam-6407	241	28	under	under	ADP
ejpam-6407	241	29	special	special	ADJ
ejpam-6407	241	30	types	type	NOUN
ejpam-6407	241	31	of	of	ADP
ejpam-6407	241	32	supra-ϵfunctions	supra-ϵfunction	NOUN
ejpam-6407	241	33	.	.	PUNCT
ejpam-6407	242	1	definition	definition	NOUN
ejpam-6407	242	2	12	12	NUM
ejpam-6407	242	3	.	.	PUNCT
ejpam-6407	243	1	for	for	ADP
ejpam-6407	243	2	the	the	DET
ejpam-6407	243	3	subset	subset	ADJ
ejpam-6407	243	4	l	l	NOUN
ejpam-6407	243	5	of	of	ADP
ejpam-6407	243	6	an	an	DET
ejpam-6407	243	7	sts	st	NOUN
ejpam-6407	243	8	(	(	PUNCT
ejpam-6407	243	9	λ	λ	NOUN
ejpam-6407	243	10	,	,	PUNCT
ejpam-6407	243	11	ν	ν	NOUN
ejpam-6407	243	12	)	)	PUNCT
ejpam-6407	243	13	,	,	PUNCT
ejpam-6407	243	14	the	the	DET
ejpam-6407	243	15	class	class	NOUN
ejpam-6407	243	16	νl	νl	NOUN
ejpam-6407	243	17	=	=	SYM
ejpam-6407	243	18	{	{	PUNCT
ejpam-6407	243	19	l	l	NOUN
ejpam-6407	243	20	∩o	∩o	NOUN
ejpam-6407	243	21	:	:	PUNCT
ejpam-6407	243	22	o	o	PROPN
ejpam-6407	243	23	∈	∈	PROPN
ejpam-6407	243	24	soϵ(λ	soϵ(λ	PROPN
ejpam-6407	243	25	)	)	PUNCT
ejpam-6407	243	26	}	}	PUNCT
ejpam-6407	243	27	defines	define	VERB
ejpam-6407	243	28	an	an	DET
ejpam-6407	243	29	sts	st	NOUN
ejpam-6407	243	30	on	on	ADP
ejpam-6407	243	31	l	l	NOUN
ejpam-6407	243	32	,	,	PUNCT
ejpam-6407	243	33	and	and	CCONJ
ejpam-6407	243	34	it	it	PRON
ejpam-6407	243	35	is	be	AUX
ejpam-6407	243	36	called	call	VERB
ejpam-6407	243	37	a	a	DET
ejpam-6407	243	38	supra-ϵ-subspace	supra-ϵ-subspace	PROPN
ejpam-6407	243	39	of	of	ADP
ejpam-6407	243	40	(	(	PUNCT
ejpam-6407	243	41	λ	λ	PROPN
ejpam-6407	243	42	,	,	PUNCT
ejpam-6407	243	43	ν	ν	NOUN
ejpam-6407	243	44	)	)	PUNCT
ejpam-6407	243	45	.	.	PUNCT
ejpam-6407	244	1	m.	m.	NOUN
ejpam-6407	244	2	aldawood	aldawood	PROPN
ejpam-6407	244	3	et	et	PROPN
ejpam-6407	244	4	al	al	PROPN
ejpam-6407	244	5	.	.	PUNCT
ejpam-6407	244	6	/	/	SYM
ejpam-6407	244	7	eur	eur	PROPN
ejpam-6407	244	8	.	.	PUNCT
ejpam-6407	245	1	j.	j.	PROPN
ejpam-6407	245	2	pure	pure	PROPN
ejpam-6407	245	3	appl	appl	PROPN
ejpam-6407	245	4	.	.	PROPN
ejpam-6407	245	5	math	math	PROPN
ejpam-6407	245	6	,	,	PUNCT
ejpam-6407	245	7	18	18	NUM
ejpam-6407	245	8	(	(	PUNCT
ejpam-6407	245	9	3	3	NUM
ejpam-6407	245	10	)	)	PUNCT
ejpam-6407	245	11	(	(	PUNCT
ejpam-6407	245	12	2025	2025	NUM
ejpam-6407	245	13	)	)	PUNCT
ejpam-6407	245	14	,	,	PUNCT
ejpam-6407	245	15	6407	6407	NUM
ejpam-6407	245	16	9	9	NUM
ejpam-6407	245	17	of	of	ADP
ejpam-6407	245	18	15	15	NUM
ejpam-6407	245	19	since	since	SCONJ
ejpam-6407	245	20	definition	definition	NOUN
ejpam-6407	245	21	12	12	NUM
ejpam-6407	245	22	provides	provide	VERB
ejpam-6407	245	23	a	a	DET
ejpam-6407	245	24	clear	clear	ADJ
ejpam-6407	245	25	evidence	evidence	NOUN
ejpam-6407	245	26	for	for	ADP
ejpam-6407	245	27	the	the	DET
ejpam-6407	245	28	next	next	ADJ
ejpam-6407	245	29	two	two	NUM
ejpam-6407	245	30	propositions	proposition	NOUN
ejpam-6407	245	31	,	,	PUNCT
ejpam-6407	245	32	their	their	PRON
ejpam-6407	245	33	proofs	proof	NOUN
ejpam-6407	245	34	are	be	AUX
ejpam-6407	245	35	excluded	exclude	VERB
ejpam-6407	245	36	.	.	PUNCT
ejpam-6407	246	1	proposition	proposition	NOUN
ejpam-6407	246	2	3	3	NUM
ejpam-6407	246	3	.	.	PUNCT
ejpam-6407	247	1	let	let	VERB
ejpam-6407	247	2	(	(	PUNCT
ejpam-6407	247	3	u	u	NOUN
ejpam-6407	247	4	,	,	PUNCT
ejpam-6407	247	5	νu	νu	PROPN
ejpam-6407	247	6	)	)	PUNCT
ejpam-6407	247	7	be	be	AUX
ejpam-6407	247	8	an	an	DET
ejpam-6407	247	9	supra	supra	ADJ
ejpam-6407	247	10	ϵ-subspace	ϵ-subspace	NOUN
ejpam-6407	247	11	of	of	ADP
ejpam-6407	247	12	an	an	DET
ejpam-6407	247	13	sts	st	NOUN
ejpam-6407	247	14	(	(	PUNCT
ejpam-6407	247	15	λ	λ	NOUN
ejpam-6407	247	16	,	,	PUNCT
ejpam-6407	247	17	ν	ν	NOUN
ejpam-6407	247	18	)	)	PUNCT
ejpam-6407	247	19	and	and	CCONJ
ejpam-6407	247	20	v	v	AUX
ejpam-6407	247	21	be	be	AUX
ejpam-6407	247	22	a	a	DET
ejpam-6407	247	23	subset	subset	NOUN
ejpam-6407	247	24	of	of	ADP
ejpam-6407	247	25	λ	λ	PROPN
ejpam-6407	247	26	.	.	PUNCT
ejpam-6407	248	1	then	then	ADV
ejpam-6407	248	2	,	,	PUNCT
ejpam-6407	248	3	(	(	PUNCT
ejpam-6407	248	4	clϵ(v	clϵ(v	PROPN
ejpam-6407	248	5	)	)	PUNCT
ejpam-6407	248	6	)	)	PUNCT
ejpam-6407	249	1	νu	νu	PROPN
ejpam-6407	250	1	=	=	SYM
ejpam-6407	250	2	u	u	PROPN
ejpam-6407	250	3	∩	∩	ADJ
ejpam-6407	250	4	clϵ(v	clϵ(v	NOUN
ejpam-6407	250	5	)	)	PUNCT
ejpam-6407	250	6	.	.	PUNCT
ejpam-6407	251	1	proposition	proposition	NOUN
ejpam-6407	251	2	4	4	NUM
ejpam-6407	251	3	.	.	PUNCT
ejpam-6407	252	1	let	let	VERB
ejpam-6407	252	2	(	(	PUNCT
ejpam-6407	252	3	u	u	NOUN
ejpam-6407	252	4	,	,	PUNCT
ejpam-6407	252	5	νu	νu	PROPN
ejpam-6407	252	6	)	)	PUNCT
ejpam-6407	252	7	be	be	AUX
ejpam-6407	252	8	an	an	DET
ejpam-6407	252	9	supra	supra	ADJ
ejpam-6407	252	10	ϵ-subspace	ϵ-subspace	NOUN
ejpam-6407	252	11	of	of	ADP
ejpam-6407	252	12	an	an	DET
ejpam-6407	252	13	sts	st	NOUN
ejpam-6407	252	14	(	(	PUNCT
ejpam-6407	252	15	λ	λ	NOUN
ejpam-6407	252	16	,	,	PUNCT
ejpam-6407	252	17	ν	ν	NOUN
ejpam-6407	252	18	)	)	PUNCT
ejpam-6407	252	19	and	and	CCONJ
ejpam-6407	252	20	v	v	AUX
ejpam-6407	252	21	be	be	AUX
ejpam-6407	252	22	a	a	DET
ejpam-6407	252	23	subset	subset	NOUN
ejpam-6407	252	24	of	of	ADP
ejpam-6407	252	25	λ	λ	PROPN
ejpam-6407	252	26	.	.	PUNCT
ejpam-6407	253	1	then	then	ADV
ejpam-6407	253	2	,	,	PUNCT
ejpam-6407	253	3	v	v	NOUN
ejpam-6407	253	4	∈	∈	PROPN
ejpam-6407	253	5	scϵ(u	scϵ(u	PROPN
ejpam-6407	253	6	)	)	PUNCT
ejpam-6407	254	1	if	if	SCONJ
ejpam-6407	254	2	and	and	CCONJ
ejpam-6407	254	3	only	only	ADV
ejpam-6407	254	4	if	if	SCONJ
ejpam-6407	254	5	there	there	PRON
ejpam-6407	254	6	is	be	VERB
ejpam-6407	254	7	n	n	DET
ejpam-6407	254	8	∈	∈	PROPN
ejpam-6407	254	9	scϵ(λ	scϵ(λ	PROPN
ejpam-6407	254	10	)	)	PUNCT
ejpam-6407	254	11	such	such	ADJ
ejpam-6407	254	12	that	that	DET
ejpam-6407	254	13	v	v	NOUN
ejpam-6407	254	14	=	=	SYM
ejpam-6407	254	15	u	u	NOUN
ejpam-6407	254	16	∩n	∩n	NOUN
ejpam-6407	254	17	.	.	PUNCT
ejpam-6407	255	1	theorem	theorem	VERB
ejpam-6407	255	2	9	9	NUM
ejpam-6407	255	3	.	.	PUNCT
ejpam-6407	256	1	every	every	DET
ejpam-6407	256	2	supra-ϵ-subspace	supra-ϵ-subspace	PROPN
ejpam-6407	256	3	of	of	ADP
ejpam-6407	256	4	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6407	256	5	-	-	PUNCT
ejpam-6407	256	6	space	space	NOUN
ejpam-6407	256	7	is	be	AUX
ejpam-6407	256	8	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6407	256	9	,	,	PUNCT
ejpam-6407	256	10	j	j	PROPN
ejpam-6407	256	11	=	=	SYM
ejpam-6407	256	12	0	0	NUM
ejpam-6407	256	13	,	,	PUNCT
ejpam-6407	256	14	1	1	NUM
ejpam-6407	256	15	,	,	PUNCT
ejpam-6407	256	16	2	2	NUM
ejpam-6407	256	17	.	.	PUNCT
ejpam-6407	256	18	proof	proof	NOUN
ejpam-6407	256	19	.	.	PUNCT
ejpam-6407	257	1	the	the	DET
ejpam-6407	257	2	other	other	ADJ
ejpam-6407	257	3	cases	case	NOUN
ejpam-6407	257	4	are	be	AUX
ejpam-6407	257	5	evidently	evidently	ADV
ejpam-6407	257	6	contained	contain	VERB
ejpam-6407	257	7	in	in	ADP
ejpam-6407	257	8	the	the	DET
ejpam-6407	257	9	case	case	NOUN
ejpam-6407	257	10	of	of	ADP
ejpam-6407	257	11	j	j	PROPN
ejpam-6407	257	12	=	=	SYM
ejpam-6407	257	13	2	2	PROPN
ejpam-6407	257	14	,	,	PUNCT
ejpam-6407	257	15	which	which	PRON
ejpam-6407	257	16	we	we	PRON
ejpam-6407	257	17	prove	prove	VERB
ejpam-6407	257	18	.	.	PUNCT
ejpam-6407	258	1	assume	assume	VERB
ejpam-6407	258	2	that	that	SCONJ
ejpam-6407	258	3	(	(	PUNCT
ejpam-6407	258	4	χ	χ	X
ejpam-6407	258	5	,	,	PUNCT
ejpam-6407	258	6	ϑχ	ϑχ	NOUN
ejpam-6407	258	7	)	)	PUNCT
ejpam-6407	258	8	is	be	AUX
ejpam-6407	258	9	a	a	DET
ejpam-6407	258	10	supra	supra	ADJ
ejpam-6407	258	11	subspace	subspace	NOUN
ejpam-6407	258	12	of	of	ADP
ejpam-6407	258	13	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6407	258	14	-	-	PUNCT
ejpam-6407	258	15	space	space	NOUN
ejpam-6407	258	16	(	(	PUNCT
ejpam-6407	258	17	λ	λ	NOUN
ejpam-6407	258	18	,	,	PUNCT
ejpam-6407	258	19	ϑ	ϑ	NOUN
ejpam-6407	258	20	)	)	PUNCT
ejpam-6407	258	21	and	and	CCONJ
ejpam-6407	258	22	ν1	ν1	NOUN
ejpam-6407	258	23	̸=	̸=	PROPN
ejpam-6407	258	24	ν2	ν2	NOUN
ejpam-6407	258	25	∈	∈	NOUN
ejpam-6407	258	26	χ	χ	ADP
ejpam-6407	258	27	⊆	⊆	NUM
ejpam-6407	258	28	λ	λ	NOUN
ejpam-6407	258	29	.	.	PROPN
ejpam-6407	258	30	given	give	VERB
ejpam-6407	258	31	λ	λ	PROPN
ejpam-6407	258	32	is	be	AUX
ejpam-6407	258	33	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6407	258	34	,	,	PUNCT
ejpam-6407	258	35	then	then	ADV
ejpam-6407	258	36	there	there	PRON
ejpam-6407	258	37	are	be	VERB
ejpam-6407	258	38	two	two	NUM
ejpam-6407	258	39	disjoint	disjoint	NOUN
ejpam-6407	258	40	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	258	41	subsets	subset	NOUN
ejpam-6407	258	42	µ1	µ1	PROPN
ejpam-6407	258	43	and	and	CCONJ
ejpam-6407	258	44	µ2	µ2	PROPN
ejpam-6407	258	45	of	of	ADP
ejpam-6407	258	46	λ	λ	PROPN
ejpam-6407	258	47	,	,	PUNCT
ejpam-6407	259	1	such	such	ADJ
ejpam-6407	259	2	that	that	SCONJ
ejpam-6407	259	3	ν1	ν1	PROPN
ejpam-6407	259	4	∈	∈	PROPN
ejpam-6407	259	5	µ1	µ1	NOUN
ejpam-6407	259	6	and	and	CCONJ
ejpam-6407	259	7	ν2	ν2	NOUN
ejpam-6407	259	8	∈	∈	PROPN
ejpam-6407	259	9	µ2	µ2	NOUN
ejpam-6407	260	1	.	.	PUNCT
ejpam-6407	261	1	hence	hence	ADV
ejpam-6407	261	2	,	,	PUNCT
ejpam-6407	261	3	ν1	ν1	NOUN
ejpam-6407	261	4	∈	∈	PROPN
ejpam-6407	261	5	µ1	µ1	PROPN
ejpam-6407	261	6	∩	∩	ADJ
ejpam-6407	261	7	χ	χ	NOUN
ejpam-6407	261	8	and	and	CCONJ
ejpam-6407	261	9	ν2	ν2	PROPN
ejpam-6407	261	10	∈	∈	PROPN
ejpam-6407	261	11	µ2	µ2	NOUN
ejpam-6407	261	12	∩	∩	NOUN
ejpam-6407	261	13	χ	χ	VERB
ejpam-6407	261	14	such	such	ADJ
ejpam-6407	261	15	that	that	SCONJ
ejpam-6407	261	16	[	[	X
ejpam-6407	261	17	µ1	µ1	NOUN
ejpam-6407	261	18	∩	∩	ADJ
ejpam-6407	261	19	χ	χ	NOUN
ejpam-6407	261	20	]	]	X
ejpam-6407	261	21	∩	∩	NOUN
ejpam-6407	261	22	[	[	X
ejpam-6407	261	23	µ2	µ2	NOUN
ejpam-6407	261	24	∩	∩	NOUN
ejpam-6407	261	25	χ	χ	X
ejpam-6407	261	26	]	]	PUNCT
ejpam-6407	261	27	=	=	SYM
ejpam-6407	261	28	χ	χ	NOUN
ejpam-6407	261	29	∩	∩	X
ejpam-6407	261	30	[	[	X
ejpam-6407	261	31	µ1	µ1	NOUN
ejpam-6407	261	32	∩	∩	NOUN
ejpam-6407	261	33	µ1	µ1	NOUN
ejpam-6407	261	34	]	]	PUNCT
ejpam-6407	261	35	=	=	SYM
ejpam-6407	261	36	χ	χ	NOUN
ejpam-6407	261	37	∩	∩	ADJ
ejpam-6407	261	38	∅	∅	NOUN
ejpam-6407	261	39	=	=	SYM
ejpam-6407	261	40	∅	∅	NOUN
ejpam-6407	261	41	and	and	CCONJ
ejpam-6407	261	42	µ1	µ1	PROPN
ejpam-6407	261	43	∩	∩	ADJ
ejpam-6407	261	44	χ	χ	NOUN
ejpam-6407	261	45	,	,	PUNCT
ejpam-6407	261	46	µ2	µ2	PROPN
ejpam-6407	261	47	∩	∩	ADJ
ejpam-6407	261	48	χ	χ	ADP
ejpam-6407	261	49	∈	∈	PROPN
ejpam-6407	261	50	ϑχ	ϑχ	NOUN
ejpam-6407	261	51	.	.	PUNCT
ejpam-6407	262	1	therefore	therefore	ADV
ejpam-6407	262	2	,	,	PUNCT
ejpam-6407	262	3	χ	χ	X
ejpam-6407	262	4	is	be	AUX
ejpam-6407	262	5	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6407	262	6	-	-	PUNCT
ejpam-6407	262	7	space	space	NOUN
ejpam-6407	262	8	.	.	PUNCT
ejpam-6407	263	1	definition	definition	NOUN
ejpam-6407	263	2	13	13	NUM
ejpam-6407	263	3	.	.	PUNCT
ejpam-6407	264	1	a	a	DET
ejpam-6407	264	2	function	function	NOUN
ejpam-6407	264	3	λϵ	λϵ	VERB
ejpam-6407	264	4	:	:	PUNCT
ejpam-6407	264	5	(	(	PUNCT
ejpam-6407	264	6	λ1	λ1	ADJ
ejpam-6407	264	7	,	,	PUNCT
ejpam-6407	264	8	σ1	σ1	PROPN
ejpam-6407	264	9	)	)	PUNCT
ejpam-6407	264	10	→	→	SYM
ejpam-6407	264	11	(	(	PUNCT
ejpam-6407	264	12	λ2	λ2	PROPN
ejpam-6407	264	13	,	,	PUNCT
ejpam-6407	264	14	σ2	σ2	NOUN
ejpam-6407	264	15	)	)	PUNCT
ejpam-6407	264	16	with	with	ADP
ejpam-6407	264	17	ϑ1	ϑ1	PROPN
ejpam-6407	264	18	as	as	ADP
ejpam-6407	264	19	an	an	DET
ejpam-6407	264	20	associated	associate	VERB
ejpam-6407	264	21	sts	st	NOUN
ejpam-6407	264	22	with	with	ADP
ejpam-6407	264	23	σ1	σ1	PROPN
ejpam-6407	264	24	is	be	AUX
ejpam-6407	264	25	said	say	VERB
ejpam-6407	264	26	to	to	PART
ejpam-6407	264	27	be	be	AUX
ejpam-6407	264	28	a	a	DET
ejpam-6407	264	29	supra	supra	ADJ
ejpam-6407	264	30	ϵ-continuous	ϵ-continuous	ADJ
ejpam-6407	264	31	(	(	PUNCT
ejpam-6407	264	32	abbreviate	abbreviate	NOUN
ejpam-6407	264	33	:	:	PUNCT
ejpam-6407	264	34	supra	supra	ADJ
ejpam-6407	264	35	ϵ-cts	ϵ-ct	NOUN
ejpam-6407	264	36	)	)	PUNCT
ejpam-6407	265	1	if	if	SCONJ
ejpam-6407	265	2	λ−1	λ−1	PROPN
ejpam-6407	265	3	ϵ	ϵ	X
ejpam-6407	265	4	(	(	PUNCT
ejpam-6407	265	5	g	g	NOUN
ejpam-6407	265	6	)	)	PUNCT
ejpam-6407	265	7	∈	∈	PROPN
ejpam-6407	265	8	soϵ(λ1	soϵ(λ1	NOUN
ejpam-6407	265	9	)	)	PUNCT
ejpam-6407	265	10	for	for	ADP
ejpam-6407	265	11	each	each	DET
ejpam-6407	265	12	g	g	PROPN
ejpam-6407	265	13	∈	∈	PROPN
ejpam-6407	265	14	σ2	σ2	PROPN
ejpam-6407	265	15	.	.	PUNCT
ejpam-6407	266	1	theorem	theorem	VERB
ejpam-6407	266	2	10	10	NUM
ejpam-6407	266	3	.	.	PUNCT
ejpam-6407	267	1	if	if	SCONJ
ejpam-6407	267	2	λϵ	λϵ	X
ejpam-6407	267	3	:	:	PUNCT
ejpam-6407	267	4	(	(	PUNCT
ejpam-6407	267	5	λ1	λ1	ADJ
ejpam-6407	267	6	,	,	PUNCT
ejpam-6407	267	7	σ1	σ1	PROPN
ejpam-6407	267	8	)	)	PUNCT
ejpam-6407	267	9	→	→	SYM
ejpam-6407	267	10	(	(	PUNCT
ejpam-6407	267	11	λ2	λ2	PROPN
ejpam-6407	267	12	,	,	PUNCT
ejpam-6407	267	13	σ2	σ2	PROPN
ejpam-6407	267	14	)	)	PUNCT
ejpam-6407	267	15	is	be	AUX
ejpam-6407	267	16	an	an	DET
ejpam-6407	267	17	injective	injective	ADJ
ejpam-6407	267	18	supra	supra	NOUN
ejpam-6407	267	19	ϵ-cts	ϵ-ct	NOUN
ejpam-6407	267	20	function	function	NOUN
ejpam-6407	267	21	with	with	ADP
ejpam-6407	267	22	ϑ1	ϑ1	PROPN
ejpam-6407	267	23	as	as	ADP
ejpam-6407	267	24	an	an	DET
ejpam-6407	267	25	associated	associate	VERB
ejpam-6407	267	26	sts	st	NOUN
ejpam-6407	267	27	with	with	ADP
ejpam-6407	267	28	σ1	σ1	PROPN
ejpam-6407	267	29	such	such	ADJ
ejpam-6407	267	30	that	that	SCONJ
ejpam-6407	267	31	(	(	PUNCT
ejpam-6407	267	32	λ2	λ2	PROPN
ejpam-6407	267	33	,	,	PUNCT
ejpam-6407	267	34	σ2	σ2	PROPN
ejpam-6407	267	35	)	)	PUNCT
ejpam-6407	267	36	is	be	AUX
ejpam-6407	267	37	tj	tj	NOUN
ejpam-6407	267	38	-	-	NOUN
ejpam-6407	267	39	space	space	NOUN
ejpam-6407	267	40	,	,	PUNCT
ejpam-6407	267	41	then	then	ADV
ejpam-6407	267	42	(	(	PUNCT
ejpam-6407	267	43	λ1	λ1	ADJ
ejpam-6407	267	44	,	,	PUNCT
ejpam-6407	267	45	ϑ1	ϑ1	PROPN
ejpam-6407	267	46	)	)	PUNCT
ejpam-6407	267	47	is	be	AUX
ejpam-6407	267	48	a	a	DET
ejpam-6407	267	49	supra-ϵtj	supra-ϵtj	NOUN
ejpam-6407	267	50	,	,	PUNCT
ejpam-6407	267	51	j	j	PROPN
ejpam-6407	267	52	=	=	SYM
ejpam-6407	267	53	0	0	NUM
ejpam-6407	267	54	,	,	PUNCT
ejpam-6407	267	55	1	1	NUM
ejpam-6407	267	56	,	,	PUNCT
ejpam-6407	267	57	2	2	NUM
ejpam-6407	267	58	.	.	PUNCT
ejpam-6407	268	1	proof	proof	NOUN
ejpam-6407	268	2	.	.	PUNCT
ejpam-6407	269	1	the	the	DET
ejpam-6407	269	2	other	other	ADJ
ejpam-6407	269	3	cases	case	NOUN
ejpam-6407	269	4	are	be	AUX
ejpam-6407	269	5	evidently	evidently	ADV
ejpam-6407	269	6	contained	contain	VERB
ejpam-6407	269	7	in	in	ADP
ejpam-6407	269	8	the	the	DET
ejpam-6407	269	9	case	case	NOUN
ejpam-6407	269	10	of	of	ADP
ejpam-6407	269	11	j	j	PROPN
ejpam-6407	269	12	=	=	SYM
ejpam-6407	269	13	2	2	PROPN
ejpam-6407	269	14	,	,	PUNCT
ejpam-6407	269	15	which	which	PRON
ejpam-6407	269	16	we	we	PRON
ejpam-6407	269	17	prove	prove	VERB
ejpam-6407	269	18	.	.	PUNCT
ejpam-6407	270	1	let	let	VERB
ejpam-6407	270	2	ν1	ν1	NOUN
ejpam-6407	270	3	̸=	̸=	PROPN
ejpam-6407	270	4	ν2	ν2	PROPN
ejpam-6407	270	5	∈	∈	PROPN
ejpam-6407	270	6	λ1	λ1	PROPN
ejpam-6407	270	7	.	.	PUNCT
ejpam-6407	271	1	since	since	SCONJ
ejpam-6407	271	2	λϵ	λϵ	PROPN
ejpam-6407	271	3	is	be	AUX
ejpam-6407	271	4	injective	injective	ADJ
ejpam-6407	271	5	,	,	PUNCT
ejpam-6407	271	6	there	there	PRON
ejpam-6407	271	7	are	be	VERB
ejpam-6407	271	8	ζ1	ζ1	PROPN
ejpam-6407	271	9	̸=	̸=	PROPN
ejpam-6407	271	10	ζ2	ζ2	NOUN
ejpam-6407	271	11	∈	∈	NOUN
ejpam-6407	271	12	λ2	λ2	NOUN
ejpam-6407	271	13	such	such	ADJ
ejpam-6407	271	14	that	that	PRON
ejpam-6407	271	15	λϵ(ν1	λϵ(ν1	NOUN
ejpam-6407	271	16	)	)	PUNCT
ejpam-6407	271	17	=	=	SYM
ejpam-6407	271	18	ζ1	ζ1	NOUN
ejpam-6407	271	19	and	and	CCONJ
ejpam-6407	271	20	λϵ(ν2	λϵ(ν2	NUM
ejpam-6407	271	21	)	)	PUNCT
ejpam-6407	271	22	=	=	VERB
ejpam-6407	271	23	ζ2	ζ2	NOUN
ejpam-6407	271	24	.	.	PUNCT
ejpam-6407	272	1	since	since	SCONJ
ejpam-6407	272	2	(	(	PUNCT
ejpam-6407	272	3	λ2	λ2	PROPN
ejpam-6407	272	4	,	,	PUNCT
ejpam-6407	272	5	σ2	σ2	NOUN
ejpam-6407	272	6	)	)	PUNCT
ejpam-6407	272	7	is	be	AUX
ejpam-6407	272	8	t2	t2	NOUN
ejpam-6407	272	9	-	-	PUNCT
ejpam-6407	272	10	space	space	NOUN
ejpam-6407	272	11	,	,	PUNCT
ejpam-6407	272	12	there	there	PRON
ejpam-6407	272	13	are	be	VERB
ejpam-6407	272	14	two	two	NUM
ejpam-6407	272	15	disjoint	disjoint	ADJ
ejpam-6407	272	16	open	open	ADJ
ejpam-6407	272	17	subsets	subset	NOUN
ejpam-6407	272	18	µ1	µ1	PROPN
ejpam-6407	272	19	and	and	CCONJ
ejpam-6407	272	20	µ2	µ2	PROPN
ejpam-6407	272	21	of	of	ADP
ejpam-6407	272	22	λ2	λ2	NOUN
ejpam-6407	272	23	,	,	PUNCT
ejpam-6407	272	24	such	such	ADJ
ejpam-6407	272	25	that	that	SCONJ
ejpam-6407	272	26	ζ1	ζ1	PROPN
ejpam-6407	272	27	∈	∈	PROPN
ejpam-6407	272	28	µ1	µ1	PROPN
ejpam-6407	272	29	and	and	CCONJ
ejpam-6407	272	30	ζ2	ζ2	NOUN
ejpam-6407	272	31	∈	∈	PROPN
ejpam-6407	272	32	µ2	µ2	NOUN
ejpam-6407	272	33	.	.	PUNCT
ejpam-6407	273	1	given	give	VERB
ejpam-6407	273	2	λϵ	λϵ	PROPN
ejpam-6407	273	3	is	be	AUX
ejpam-6407	273	4	supra	supra	ADJ
ejpam-6407	273	5	ϵ-cts	ϵ-ct	NOUN
ejpam-6407	273	6	,	,	PUNCT
ejpam-6407	273	7	λ	λ	X
ejpam-6407	273	8	−1	−1	NOUN
ejpam-6407	273	9	ϵ	ϵ	X
ejpam-6407	273	10	(	(	PUNCT
ejpam-6407	273	11	µ1	µ1	PROPN
ejpam-6407	273	12	)	)	PUNCT
ejpam-6407	273	13	and	and	CCONJ
ejpam-6407	273	14	λ−1	λ−1	PROPN
ejpam-6407	273	15	ϵ	ϵ	X
ejpam-6407	273	16	(	(	PUNCT
ejpam-6407	273	17	µ2	µ2	PROPN
ejpam-6407	273	18	)	)	PUNCT
ejpam-6407	273	19	are	be	AUX
ejpam-6407	273	20	two	two	NUM
ejpam-6407	273	21	disjoint	disjoint	ADJ
ejpam-6407	273	22	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	273	23	subsets	subset	NOUN
ejpam-6407	273	24	of	of	ADP
ejpam-6407	273	25	λ1	λ1	ADJ
ejpam-6407	273	26	containing	contain	VERB
ejpam-6407	273	27	ν1	ν1	NOUN
ejpam-6407	273	28	,	,	PUNCT
ejpam-6407	273	29	ν2	ν2	NOUN
ejpam-6407	273	30	,	,	PUNCT
ejpam-6407	273	31	respectively	respectively	ADV
ejpam-6407	273	32	.	.	PUNCT
ejpam-6407	274	1	therefore	therefore	ADV
ejpam-6407	274	2	,	,	PUNCT
ejpam-6407	274	3	(	(	PUNCT
ejpam-6407	274	4	λ1	λ1	ADJ
ejpam-6407	274	5	,	,	PUNCT
ejpam-6407	274	6	ϑ1	ϑ1	PROPN
ejpam-6407	274	7	)	)	PUNCT
ejpam-6407	274	8	is	be	AUX
ejpam-6407	274	9	supra-ϵ-t2	supra-ϵ-t2	PROPN
ejpam-6407	274	10	.	.	PUNCT
ejpam-6407	275	1	definition	definition	NOUN
ejpam-6407	275	2	14	14	NUM
ejpam-6407	275	3	.	.	PUNCT
ejpam-6407	276	1	a	a	DET
ejpam-6407	276	2	function	function	NOUN
ejpam-6407	276	3	λϵ	λϵ	VERB
ejpam-6407	276	4	:	:	PUNCT
ejpam-6407	276	5	(	(	PUNCT
ejpam-6407	276	6	σ1	σ1	PROPN
ejpam-6407	276	7	,	,	PUNCT
ejpam-6407	276	8	ν1	ν1	NOUN
ejpam-6407	276	9	)	)	PUNCT
ejpam-6407	276	10	→	→	SYM
ejpam-6407	276	11	(	(	PUNCT
ejpam-6407	276	12	σ2	σ2	NOUN
ejpam-6407	276	13	,	,	PUNCT
ejpam-6407	276	14	ν2	ν2	NOUN
ejpam-6407	276	15	)	)	PUNCT
ejpam-6407	276	16	with	with	ADP
ejpam-6407	276	17	ϑ1	ϑ1	NOUN
ejpam-6407	276	18	,	,	PUNCT
ejpam-6407	276	19	ϑ2	ϑ2	PROPN
ejpam-6407	276	20	associated	associate	VERB
ejpam-6407	276	21	stss	stss	NOUN
ejpam-6407	276	22	with	with	ADP
ejpam-6407	276	23	σ1	σ1	PROPN
ejpam-6407	276	24	,	,	PUNCT
ejpam-6407	276	25	σ2	σ2	PROPN
ejpam-6407	276	26	,	,	PUNCT
ejpam-6407	276	27	respectively	respectively	ADV
ejpam-6407	276	28	,	,	PUNCT
ejpam-6407	276	29	is	be	AUX
ejpam-6407	276	30	said	say	VERB
ejpam-6407	276	31	to	to	PART
ejpam-6407	276	32	be	be	AUX
ejpam-6407	276	33	supra	supra	ADJ
ejpam-6407	276	34	ϵ-irresolute	ϵ-irresolute	VERB
ejpam-6407	276	35	if	if	SCONJ
ejpam-6407	276	36	λ−1	λ−1	PROPN
ejpam-6407	276	37	ϵ	ϵ	X
ejpam-6407	276	38	(	(	PUNCT
ejpam-6407	276	39	d	d	NOUN
ejpam-6407	276	40	)	)	PUNCT
ejpam-6407	276	41	∈	∈	PROPN
ejpam-6407	276	42	soϵ(λ1	soϵ(λ1	NOUN
ejpam-6407	276	43	)	)	PUNCT
ejpam-6407	276	44	for	for	ADP
ejpam-6407	276	45	each	each	DET
ejpam-6407	276	46	d	d	PROPN
ejpam-6407	276	47	∈	∈	PROPN
ejpam-6407	276	48	soϵ(λ2	soϵ(λ2	PROPN
ejpam-6407	276	49	)	)	PUNCT
ejpam-6407	276	50	.	.	PUNCT
ejpam-6407	277	1	proposition	proposition	NOUN
ejpam-6407	277	2	5	5	NUM
ejpam-6407	277	3	.	.	PUNCT
ejpam-6407	278	1	if	if	SCONJ
ejpam-6407	278	2	λϵ	λϵ	X
ejpam-6407	278	3	:	:	PUNCT
ejpam-6407	278	4	(	(	PUNCT
ejpam-6407	278	5	λ1	λ1	ADJ
ejpam-6407	278	6	,	,	PUNCT
ejpam-6407	278	7	σ1	σ1	PROPN
ejpam-6407	278	8	)	)	PUNCT
ejpam-6407	278	9	→	→	SYM
ejpam-6407	278	10	(	(	PUNCT
ejpam-6407	278	11	λ2	λ2	PROPN
ejpam-6407	278	12	,	,	PUNCT
ejpam-6407	278	13	σ2	σ2	PROPN
ejpam-6407	278	14	)	)	PUNCT
ejpam-6407	278	15	is	be	AUX
ejpam-6407	278	16	an	an	DET
ejpam-6407	278	17	injective	injective	ADJ
ejpam-6407	278	18	supra	supra	NOUN
ejpam-6407	278	19	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6407	278	20	function	function	NOUN
ejpam-6407	278	21	with	with	ADP
ejpam-6407	278	22	ϑ1	ϑ1	NOUN
ejpam-6407	278	23	,	,	PUNCT
ejpam-6407	278	24	ϑ2	ϑ2	PROPN
ejpam-6407	278	25	associated	associate	VERB
ejpam-6407	278	26	stss	stss	NOUN
ejpam-6407	278	27	with	with	ADP
ejpam-6407	278	28	σ1	σ1	PROPN
ejpam-6407	278	29	,	,	PUNCT
ejpam-6407	278	30	σ2	σ2	NOUN
ejpam-6407	278	31	respectively	respectively	ADV
ejpam-6407	278	32	,	,	PUNCT
ejpam-6407	278	33	such	such	ADJ
ejpam-6407	278	34	that	that	SCONJ
ejpam-6407	278	35	(	(	PUNCT
ejpam-6407	278	36	λ2	λ2	PROPN
ejpam-6407	278	37	,	,	PUNCT
ejpam-6407	278	38	σ2	σ2	NOUN
ejpam-6407	278	39	)	)	PUNCT
ejpam-6407	278	40	is	be	AUX
ejpam-6407	278	41	supra-ϵ-tj	supra-ϵ-tj	NOUN
ejpam-6407	278	42	-	-	NOUN
ejpam-6407	278	43	space	space	NOUN
ejpam-6407	278	44	,	,	PUNCT
ejpam-6407	278	45	then	then	ADV
ejpam-6407	279	1	(	(	PUNCT
ejpam-6407	279	2	λ1	λ1	ADJ
ejpam-6407	279	3	,	,	PUNCT
ejpam-6407	279	4	ϑ1	ϑ1	PROPN
ejpam-6407	279	5	)	)	PUNCT
ejpam-6407	279	6	is	be	AUX
ejpam-6407	279	7	a	a	DET
ejpam-6407	279	8	supra-ϵ-tj	supra-ϵ-tj	NOUN
ejpam-6407	279	9	,	,	PUNCT
ejpam-6407	279	10	j	j	PROPN
ejpam-6407	279	11	=	=	SYM
ejpam-6407	279	12	0	0	NUM
ejpam-6407	279	13	,	,	PUNCT
ejpam-6407	279	14	1	1	NUM
ejpam-6407	279	15	,	,	PUNCT
ejpam-6407	279	16	2	2	NUM
ejpam-6407	279	17	.	.	PUNCT
ejpam-6407	280	1	proof	proof	NOUN
ejpam-6407	280	2	.	.	PUNCT
ejpam-6407	281	1	the	the	DET
ejpam-6407	281	2	other	other	ADJ
ejpam-6407	281	3	cases	case	NOUN
ejpam-6407	281	4	are	be	AUX
ejpam-6407	281	5	evidently	evidently	ADV
ejpam-6407	281	6	contained	contain	VERB
ejpam-6407	281	7	in	in	ADP
ejpam-6407	281	8	the	the	DET
ejpam-6407	281	9	case	case	NOUN
ejpam-6407	281	10	of	of	ADP
ejpam-6407	281	11	j	j	PROPN
ejpam-6407	281	12	=	=	SYM
ejpam-6407	281	13	2	2	PROPN
ejpam-6407	281	14	,	,	PUNCT
ejpam-6407	281	15	which	which	PRON
ejpam-6407	281	16	we	we	PRON
ejpam-6407	281	17	prove	prove	VERB
ejpam-6407	281	18	.	.	PUNCT
ejpam-6407	282	1	let	let	VERB
ejpam-6407	282	2	ν1	ν1	NOUN
ejpam-6407	282	3	̸=	̸=	PROPN
ejpam-6407	282	4	ν2	ν2	PROPN
ejpam-6407	282	5	∈	∈	PROPN
ejpam-6407	282	6	λ1	λ1	PROPN
ejpam-6407	282	7	.	.	PUNCT
ejpam-6407	283	1	since	since	SCONJ
ejpam-6407	283	2	λϵ	λϵ	PROPN
ejpam-6407	283	3	is	be	AUX
ejpam-6407	283	4	injective	injective	ADJ
ejpam-6407	283	5	,	,	PUNCT
ejpam-6407	283	6	there	there	PRON
ejpam-6407	283	7	are	be	VERB
ejpam-6407	283	8	ζ1	ζ1	PROPN
ejpam-6407	283	9	̸=	̸=	PROPN
ejpam-6407	283	10	ζ2	ζ2	NOUN
ejpam-6407	283	11	∈	∈	NOUN
ejpam-6407	283	12	λ2	λ2	NOUN
ejpam-6407	283	13	such	such	ADJ
ejpam-6407	283	14	that	that	PRON
ejpam-6407	283	15	λϵ(ν1	λϵ(ν1	NOUN
ejpam-6407	283	16	)	)	PUNCT
ejpam-6407	283	17	=	=	SYM
ejpam-6407	283	18	ζ1	ζ1	NOUN
ejpam-6407	283	19	and	and	CCONJ
ejpam-6407	283	20	λϵ(ν2	λϵ(ν2	NUM
ejpam-6407	283	21	)	)	PUNCT
ejpam-6407	283	22	=	=	VERB
ejpam-6407	283	23	ζ2	ζ2	NOUN
ejpam-6407	283	24	.	.	PUNCT
ejpam-6407	284	1	since	since	SCONJ
ejpam-6407	284	2	(	(	PUNCT
ejpam-6407	284	3	λ2	λ2	PROPN
ejpam-6407	284	4	,	,	PUNCT
ejpam-6407	284	5	σ2	σ2	PROPN
ejpam-6407	284	6	)	)	PUNCT
ejpam-6407	284	7	is	be	AUX
ejpam-6407	284	8	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6407	284	9	,	,	PUNCT
ejpam-6407	284	10	there	there	PRON
ejpam-6407	284	11	are	be	VERB
ejpam-6407	284	12	two	two	NUM
ejpam-6407	284	13	disjoint	disjoint	NOUN
ejpam-6407	284	14	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	284	15	subsets	subset	NOUN
ejpam-6407	284	16	µ1	µ1	PROPN
ejpam-6407	284	17	and	and	CCONJ
ejpam-6407	284	18	µ2	µ2	PROPN
ejpam-6407	284	19	of	of	ADP
ejpam-6407	284	20	λ2	λ2	NOUN
ejpam-6407	284	21	,	,	PUNCT
ejpam-6407	284	22	such	such	ADJ
ejpam-6407	284	23	that	that	SCONJ
ejpam-6407	284	24	ζ1	ζ1	PROPN
ejpam-6407	284	25	∈	∈	PROPN
ejpam-6407	284	26	µ1	µ1	PROPN
ejpam-6407	284	27	and	and	CCONJ
ejpam-6407	284	28	ζ2	ζ2	NOUN
ejpam-6407	284	29	∈	∈	PROPN
ejpam-6407	284	30	µ2	µ2	NOUN
ejpam-6407	284	31	.	.	PUNCT
ejpam-6407	285	1	given	give	VERB
ejpam-6407	285	2	λϵ	λϵ	PROPN
ejpam-6407	285	3	is	be	AUX
ejpam-6407	285	4	supra	supra	ADJ
ejpam-6407	285	5	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6407	285	6	,	,	PUNCT
ejpam-6407	285	7	λ−1	λ−1	PROPN
ejpam-6407	285	8	ϵ	ϵ	X
ejpam-6407	285	9	(	(	PUNCT
ejpam-6407	285	10	µ1	µ1	PROPN
ejpam-6407	285	11	)	)	PUNCT
ejpam-6407	285	12	and	and	CCONJ
ejpam-6407	286	1	λ−1	λ−1	PROPN
ejpam-6407	286	2	ϵ	ϵ	X
ejpam-6407	286	3	(	(	PUNCT
ejpam-6407	286	4	µ2	µ2	PROPN
ejpam-6407	286	5	)	)	PUNCT
ejpam-6407	286	6	are	be	AUX
ejpam-6407	286	7	two	two	NUM
ejpam-6407	286	8	disjoint	disjoint	ADJ
ejpam-6407	286	9	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	286	10	subsets	subset	NOUN
ejpam-6407	286	11	of	of	ADP
ejpam-6407	286	12	λ1	λ1	ADJ
ejpam-6407	286	13	containing	contain	VERB
ejpam-6407	286	14	ν1	ν1	NOUN
ejpam-6407	286	15	,	,	PUNCT
ejpam-6407	286	16	ν2	ν2	NOUN
ejpam-6407	286	17	,	,	PUNCT
ejpam-6407	286	18	respectively	respectively	ADV
ejpam-6407	286	19	.	.	PUNCT
ejpam-6407	287	1	therefore	therefore	ADV
ejpam-6407	287	2	,	,	PUNCT
ejpam-6407	287	3	(	(	PUNCT
ejpam-6407	287	4	λ1	λ1	ADJ
ejpam-6407	287	5	,	,	PUNCT
ejpam-6407	287	6	ϑ1	ϑ1	PROPN
ejpam-6407	287	7	)	)	PUNCT
ejpam-6407	287	8	is	be	AUX
ejpam-6407	287	9	supra-ϵ-t2	supra-ϵ-t2	PROPN
ejpam-6407	287	10	.	.	PUNCT
ejpam-6407	288	1	m.	m.	PROPN
ejpam-6407	288	2	aldawood	aldawood	PROPN
ejpam-6407	288	3	et	et	PROPN
ejpam-6407	288	4	al	al	PROPN
ejpam-6407	288	5	.	.	PUNCT
ejpam-6407	288	6	/	/	SYM
ejpam-6407	288	7	eur	eur	PROPN
ejpam-6407	288	8	.	.	PUNCT
ejpam-6407	289	1	j.	j.	PROPN
ejpam-6407	289	2	pure	pure	PROPN
ejpam-6407	289	3	appl	appl	PROPN
ejpam-6407	289	4	.	.	PROPN
ejpam-6407	289	5	math	math	PROPN
ejpam-6407	289	6	,	,	PUNCT
ejpam-6407	289	7	18	18	NUM
ejpam-6407	289	8	(	(	PUNCT
ejpam-6407	289	9	3	3	NUM
ejpam-6407	289	10	)	)	PUNCT
ejpam-6407	289	11	(	(	PUNCT
ejpam-6407	289	12	2025	2025	NUM
ejpam-6407	289	13	)	)	PUNCT
ejpam-6407	289	14	,	,	PUNCT
ejpam-6407	289	15	6407	6407	NUM
ejpam-6407	289	16	10	10	NUM
ejpam-6407	289	17	of	of	ADP
ejpam-6407	289	18	15	15	NUM
ejpam-6407	289	19	definition	definition	NOUN
ejpam-6407	289	20	15	15	NUM
ejpam-6407	289	21	.	.	PUNCT
ejpam-6407	290	1	a	a	DET
ejpam-6407	290	2	function	function	NOUN
ejpam-6407	290	3	λϵ	λϵ	VERB
ejpam-6407	290	4	:	:	PUNCT
ejpam-6407	290	5	(	(	PUNCT
ejpam-6407	290	6	λ1	λ1	ADJ
ejpam-6407	290	7	,	,	PUNCT
ejpam-6407	290	8	σ1	σ1	PROPN
ejpam-6407	290	9	)	)	PUNCT
ejpam-6407	290	10	→	→	SYM
ejpam-6407	290	11	(	(	PUNCT
ejpam-6407	290	12	λ2	λ2	PROPN
ejpam-6407	290	13	,	,	PUNCT
ejpam-6407	290	14	σ2	σ2	NOUN
ejpam-6407	290	15	)	)	PUNCT
ejpam-6407	290	16	with	with	ADP
ejpam-6407	290	17	ϑ1	ϑ1	NOUN
ejpam-6407	290	18	,	,	PUNCT
ejpam-6407	290	19	ϑ2	ϑ2	PROPN
ejpam-6407	290	20	associated	associate	VERB
ejpam-6407	290	21	stss	stss	NOUN
ejpam-6407	290	22	with	with	ADP
ejpam-6407	290	23	σ1	σ1	PROPN
ejpam-6407	290	24	,	,	PUNCT
ejpam-6407	290	25	σ2	σ2	NOUN
ejpam-6407	290	26	respectively	respectively	ADV
ejpam-6407	290	27	,	,	PUNCT
ejpam-6407	290	28	is	be	AUX
ejpam-6407	290	29	said	say	VERB
ejpam-6407	290	30	to	to	PART
ejpam-6407	290	31	be	be	AUX
ejpam-6407	290	32	supra	supra	PROPN
ejpam-6407	290	33	ϵ	ϵ	X
ejpam-6407	290	34	(	(	PUNCT
ejpam-6407	290	35	ϵ∗)-open	ϵ∗)-open	INTJ
ejpam-6407	290	36	if	if	SCONJ
ejpam-6407	290	37	λϵ(u	λϵ(u	NOUN
ejpam-6407	290	38	)	)	PUNCT
ejpam-6407	290	39	∈	∈	PROPN
ejpam-6407	290	40	soϵ(λ2	soϵ(λ2	PROPN
ejpam-6407	290	41	)	)	PUNCT
ejpam-6407	290	42	for	for	ADP
ejpam-6407	290	43	each	each	DET
ejpam-6407	290	44	u	u	PROPN
ejpam-6407	290	45	∈	∈	PROPN
ejpam-6407	290	46	σ1	σ1	PROPN
ejpam-6407	290	47	(	(	PUNCT
ejpam-6407	290	48	u	u	NOUN
ejpam-6407	290	49	∈	∈	PROPN
ejpam-6407	290	50	soϵ(λ1	soϵ(λ1	PROPN
ejpam-6407	290	51	)	)	PUNCT
ejpam-6407	290	52	)	)	PUNCT
ejpam-6407	290	53	.	.	PUNCT
ejpam-6407	291	1	theorem	theorem	NOUN
ejpam-6407	291	2	11	11	NUM
ejpam-6407	291	3	.	.	PUNCT
ejpam-6407	292	1	let	let	AUX
ejpam-6407	292	2	λϵ	λϵ	VERB
ejpam-6407	292	3	:	:	PUNCT
ejpam-6407	292	4	(	(	PUNCT
ejpam-6407	292	5	λ1	λ1	ADJ
ejpam-6407	292	6	,	,	PUNCT
ejpam-6407	292	7	σ1	σ1	PROPN
ejpam-6407	292	8	)	)	PUNCT
ejpam-6407	292	9	→	→	SYM
ejpam-6407	292	10	(	(	PUNCT
ejpam-6407	292	11	λ2	λ2	PROPN
ejpam-6407	292	12	,	,	PUNCT
ejpam-6407	292	13	σ2	σ2	PROPN
ejpam-6407	292	14	)	)	PUNCT
ejpam-6407	292	15	be	be	VERB
ejpam-6407	292	16	a	a	DET
ejpam-6407	292	17	function	function	NOUN
ejpam-6407	292	18	with	with	ADP
ejpam-6407	292	19	ϑ2	ϑ2	PROPN
ejpam-6407	292	20	as	as	ADP
ejpam-6407	292	21	an	an	DET
ejpam-6407	292	22	associated	associate	VERB
ejpam-6407	292	23	sts	st	NOUN
ejpam-6407	292	24	with	with	ADP
ejpam-6407	292	25	σ2	σ2	PROPN
ejpam-6407	292	26	and	and	CCONJ
ejpam-6407	292	27	α	α	NOUN
ejpam-6407	292	28	⊆	⊆	NUM
ejpam-6407	292	29	λ1	λ1	PROPN
ejpam-6407	292	30	,	,	PUNCT
ejpam-6407	292	31	then	then	ADV
ejpam-6407	292	32	λϵ	λϵ	VERB
ejpam-6407	292	33	is	be	AUX
ejpam-6407	292	34	supra	supra	PROPN
ejpam-6407	292	35	ϵ-open	ϵ-open	PROPN
ejpam-6407	293	1	if	if	SCONJ
ejpam-6407	293	2	and	and	CCONJ
ejpam-6407	293	3	only	only	ADV
ejpam-6407	293	4	if	if	SCONJ
ejpam-6407	293	5	λϵ(int(α	λϵ(int(α	NOUN
ejpam-6407	293	6	)	)	PUNCT
ejpam-6407	293	7	)	)	PUNCT
ejpam-6407	294	1	⊆	⊆	NUM
ejpam-6407	294	2	intsϵ	intsϵ	NOUN
ejpam-6407	294	3	[	[	X
ejpam-6407	294	4	λϵ(α	λϵ(α	NOUN
ejpam-6407	294	5	)	)	PUNCT
ejpam-6407	294	6	]	]	PUNCT
ejpam-6407	294	7	∀	∀	PUNCT
ejpam-6407	294	8	α	α	PRON
ejpam-6407	294	9	⊆	⊆	NUM
ejpam-6407	294	10	λ1	λ1	ADJ
ejpam-6407	294	11	.	.	PUNCT
ejpam-6407	295	1	proof	proof	NOUN
ejpam-6407	295	2	.	.	PUNCT
ejpam-6407	296	1	“	"	PUNCT
ejpam-6407	296	2	⇒	⇒	NOUN
ejpam-6407	296	3	”	"	PUNCT
ejpam-6407	296	4	let	let	VERB
ejpam-6407	296	5	λϵ	λϵ	PRON
ejpam-6407	296	6	be	be	AUX
ejpam-6407	296	7	a	a	DET
ejpam-6407	296	8	supra	supra	PROPN
ejpam-6407	296	9	ϵ-open	ϵ-open	PROPN
ejpam-6407	296	10	function	function	NOUN
ejpam-6407	296	11	and	and	CCONJ
ejpam-6407	296	12	α	α	NOUN
ejpam-6407	296	13	⊆	⊆	NUM
ejpam-6407	296	14	λ1	λ1	PROPN
ejpam-6407	296	15	.	.	PUNCT
ejpam-6407	297	1	since	since	SCONJ
ejpam-6407	297	2	int(α	int(α	NUM
ejpam-6407	297	3	)	)	PUNCT
ejpam-6407	297	4	⊆	⊆	NUM
ejpam-6407	297	5	α	α	NOUN
ejpam-6407	297	6	,	,	PUNCT
ejpam-6407	297	7	λϵ(int(α	λϵ(int(α	NOUN
ejpam-6407	297	8	)	)	PUNCT
ejpam-6407	297	9	)	)	PUNCT
ejpam-6407	297	10	⊆	⊆	NUM
ejpam-6407	297	11	λϵ((α	λϵ((α	PROPN
ejpam-6407	297	12	)	)	PUNCT
ejpam-6407	297	13	)	)	PUNCT
ejpam-6407	297	14	,	,	PUNCT
ejpam-6407	297	15	which	which	PRON
ejpam-6407	297	16	leads	lead	VERB
ejpam-6407	297	17	to	to	ADP
ejpam-6407	297	18	λϵ(int(α	λϵ(int(α	NOUN
ejpam-6407	297	19	)	)	PUNCT
ejpam-6407	297	20	)	)	PUNCT
ejpam-6407	297	21	=	=	PRON
ejpam-6407	297	22	intsϵ	intsϵ	NOUN
ejpam-6407	297	23	[	[	X
ejpam-6407	297	24	λϵ(int(α	λϵ(int(α	NOUN
ejpam-6407	297	25	)	)	PUNCT
ejpam-6407	297	26	)	)	PUNCT
ejpam-6407	297	27	]	]	PUNCT
ejpam-6407	298	1	⊆	⊆	NUM
ejpam-6407	298	2	intsϵ	intsϵ	NOUN
ejpam-6407	298	3	[	[	X
ejpam-6407	298	4	λϵ((α	λϵ((α	PROPN
ejpam-6407	298	5	)	)	PUNCT
ejpam-6407	298	6	)	)	PUNCT
ejpam-6407	298	7	]	]	PUNCT
ejpam-6407	298	8	,	,	PUNCT
ejpam-6407	298	9	given	give	VERB
ejpam-6407	298	10	λϵ	λϵ	PROPN
ejpam-6407	298	11	is	be	AUX
ejpam-6407	298	12	supra	supra	PROPN
ejpam-6407	298	13	ϵ-open	ϵ-open	PROPN
ejpam-6407	298	14	.	.	PUNCT
ejpam-6407	299	1	“	"	PUNCT
ejpam-6407	299	2	⇐	⇐	INTJ
ejpam-6407	299	3	”	"	PUNCT
ejpam-6407	299	4	suppose	suppose	VERB
ejpam-6407	299	5	that	that	SCONJ
ejpam-6407	299	6	α	α	PROPN
ejpam-6407	299	7	∈	∈	PROPN
ejpam-6407	299	8	σ1	σ1	PROPN
ejpam-6407	299	9	.	.	PUNCT
ejpam-6407	300	1	considering	consider	VERB
ejpam-6407	300	2	the	the	DET
ejpam-6407	300	3	condition	condition	NOUN
ejpam-6407	300	4	,	,	PUNCT
ejpam-6407	300	5	λϵ(α	λϵ(α	NOUN
ejpam-6407	300	6	)	)	PUNCT
ejpam-6407	300	7	=	=	SYM
ejpam-6407	300	8	λϵ(int(α	λϵ(int(α	NOUN
ejpam-6407	300	9	)	)	PUNCT
ejpam-6407	300	10	)	)	PUNCT
ejpam-6407	301	1	⊆	⊆	NUM
ejpam-6407	301	2	intsϵ	intsϵ	NOUN
ejpam-6407	301	3	[	[	X
ejpam-6407	301	4	λϵ(α	λϵ(α	NOUN
ejpam-6407	301	5	)	)	PUNCT
ejpam-6407	301	6	]	]	PUNCT
ejpam-6407	301	7	.	.	PUNCT
ejpam-6407	302	1	however	however	ADV
ejpam-6407	302	2	,	,	PUNCT
ejpam-6407	302	3	we	we	PRON
ejpam-6407	302	4	have	have	VERB
ejpam-6407	302	5	that	that	DET
ejpam-6407	302	6	intsϵ	intsϵ	NOUN
ejpam-6407	302	7	[	[	X
ejpam-6407	302	8	λϵ(α	λϵ(α	NOUN
ejpam-6407	302	9	)	)	PUNCT
ejpam-6407	302	10	]	]	PUNCT
ejpam-6407	303	1	⊆	⊆	NUM
ejpam-6407	303	2	λϵ(α	λϵ(α	NOUN
ejpam-6407	303	3	)	)	PUNCT
ejpam-6407	303	4	.	.	PUNCT
ejpam-6407	304	1	hence	hence	ADV
ejpam-6407	304	2	,	,	PUNCT
ejpam-6407	304	3	intsϵ	intsϵ	VERB
ejpam-6407	304	4	[	[	X
ejpam-6407	304	5	λϵ(α	λϵ(α	NOUN
ejpam-6407	304	6	)	)	PUNCT
ejpam-6407	304	7	]	]	PUNCT
ejpam-6407	305	1	=	=	SYM
ejpam-6407	305	2	λϵ(α	λϵ(α	NOUN
ejpam-6407	305	3	)	)	PUNCT
ejpam-6407	305	4	.	.	PUNCT
ejpam-6407	306	1	therefore	therefore	ADV
ejpam-6407	306	2	,	,	PUNCT
ejpam-6407	306	3	λϵ(α	λϵ(α	X
ejpam-6407	306	4	)	)	PUNCT
ejpam-6407	306	5	∈	∈	PROPN
ejpam-6407	306	6	soϵ(λ2	soϵ(λ2	PROPN
ejpam-6407	306	7	)	)	PUNCT
ejpam-6407	306	8	,	,	PUNCT
ejpam-6407	306	9	and	and	CCONJ
ejpam-6407	306	10	consequently	consequently	ADV
ejpam-6407	306	11	λϵ	λϵ	X
ejpam-6407	306	12	is	be	AUX
ejpam-6407	306	13	a	a	DET
ejpam-6407	306	14	supra	supra	ADJ
ejpam-6407	306	15	ϵ-open	ϵ-open	PROPN
ejpam-6407	306	16	function	function	NOUN
ejpam-6407	306	17	.	.	PUNCT
ejpam-6407	307	1	proposition	proposition	NOUN
ejpam-6407	307	2	6	6	NUM
ejpam-6407	307	3	.	.	PUNCT
ejpam-6407	308	1	let	let	AUX
ejpam-6407	308	2	λϵ	λϵ	VERB
ejpam-6407	308	3	:	:	PUNCT
ejpam-6407	308	4	(	(	PUNCT
ejpam-6407	308	5	λ1	λ1	ADJ
ejpam-6407	308	6	,	,	PUNCT
ejpam-6407	308	7	σ1	σ1	PROPN
ejpam-6407	308	8	)	)	PUNCT
ejpam-6407	308	9	→	→	SYM
ejpam-6407	308	10	(	(	PUNCT
ejpam-6407	308	11	λ2	λ2	PROPN
ejpam-6407	308	12	,	,	PUNCT
ejpam-6407	308	13	σ2	σ2	PROPN
ejpam-6407	308	14	)	)	PUNCT
ejpam-6407	308	15	be	be	VERB
ejpam-6407	308	16	a	a	DET
ejpam-6407	308	17	function	function	NOUN
ejpam-6407	308	18	with	with	ADP
ejpam-6407	308	19	ϑ1	ϑ1	NOUN
ejpam-6407	308	20	,	,	PUNCT
ejpam-6407	308	21	ϑ2	ϑ2	PROPN
ejpam-6407	308	22	associated	associate	VERB
ejpam-6407	308	23	stss	stss	NOUN
ejpam-6407	308	24	with	with	ADP
ejpam-6407	308	25	σ1	σ1	PROPN
ejpam-6407	308	26	,	,	PUNCT
ejpam-6407	308	27	σ2	σ2	NOUN
ejpam-6407	308	28	respectively	respectively	ADV
ejpam-6407	308	29	,	,	PUNCT
ejpam-6407	308	30	and	and	CCONJ
ejpam-6407	308	31	α	α	PRON
ejpam-6407	308	32	⊆	⊆	NUM
ejpam-6407	308	33	λ1	λ1	PROPN
ejpam-6407	308	34	,	,	PUNCT
ejpam-6407	308	35	then	then	ADV
ejpam-6407	308	36	λϵ	λϵ	VERB
ejpam-6407	308	37	is	be	AUX
ejpam-6407	308	38	supra	supra	PROPN
ejpam-6407	308	39	ϵ∗-open	ϵ∗-open	PROPN
ejpam-6407	308	40	if	if	SCONJ
ejpam-6407	308	41	and	and	CCONJ
ejpam-6407	308	42	only	only	ADV
ejpam-6407	308	43	if	if	SCONJ
ejpam-6407	308	44	λϵ(int	λϵ(int	NUM
ejpam-6407	308	45	s	s	PART
ejpam-6407	308	46	ϵ(α	ϵ(α	NOUN
ejpam-6407	308	47	)	)	PUNCT
ejpam-6407	308	48	)	)	PUNCT
ejpam-6407	309	1	⊆	⊆	NUM
ejpam-6407	309	2	intsϵ	intsϵ	NOUN
ejpam-6407	309	3	[	[	X
ejpam-6407	309	4	λϵ(α	λϵ(α	NOUN
ejpam-6407	309	5	)	)	PUNCT
ejpam-6407	309	6	]	]	PUNCT
ejpam-6407	309	7	∀	∀	PUNCT
ejpam-6407	309	8	α	α	PRON
ejpam-6407	309	9	⊆	⊆	NUM
ejpam-6407	309	10	λ1	λ1	ADJ
ejpam-6407	309	11	.	.	PUNCT
ejpam-6407	310	1	proof	proof	NOUN
ejpam-6407	310	2	.	.	PUNCT
ejpam-6407	311	1	it	it	PRON
ejpam-6407	311	2	is	be	AUX
ejpam-6407	311	3	similar	similar	ADJ
ejpam-6407	311	4	to	to	ADP
ejpam-6407	311	5	the	the	DET
ejpam-6407	311	6	proof	proof	NOUN
ejpam-6407	311	7	of	of	ADP
ejpam-6407	311	8	theorem	theorem	ADJ
ejpam-6407	311	9	11	11	NUM
ejpam-6407	311	10	.	.	PUNCT
ejpam-6407	312	1	theorem	theorem	NOUN
ejpam-6407	312	2	12	12	NUM
ejpam-6407	312	3	.	.	PUNCT
ejpam-6407	313	1	the	the	DET
ejpam-6407	313	2	image	image	NOUN
ejpam-6407	313	3	of	of	ADP
ejpam-6407	313	4	each	each	DET
ejpam-6407	313	5	tj	tj	NOUN
ejpam-6407	313	6	-	-	NOUN
ejpam-6407	313	7	space	space	NOUN
ejpam-6407	313	8	is	be	AUX
ejpam-6407	313	9	a	a	DET
ejpam-6407	313	10	supra-ϵ-tj	supra-ϵ-tj	NOUN
ejpam-6407	313	11	under	under	ADP
ejpam-6407	313	12	a	a	DET
ejpam-6407	313	13	bijective	bijective	ADJ
ejpam-6407	313	14	supra	supra	PROPN
ejpam-6407	313	15	ϵ-open	ϵ-open	PROPN
ejpam-6407	313	16	function	function	PROPN
ejpam-6407	313	17	,	,	PUNCT
ejpam-6407	313	18	j	j	PROPN
ejpam-6407	313	19	=	=	SYM
ejpam-6407	313	20	0	0	NUM
ejpam-6407	313	21	,	,	PUNCT
ejpam-6407	313	22	1	1	NUM
ejpam-6407	313	23	,	,	PUNCT
ejpam-6407	313	24	2	2	NUM
ejpam-6407	313	25	.	.	PUNCT
ejpam-6407	314	1	proof	proof	NOUN
ejpam-6407	314	2	.	.	PUNCT
ejpam-6407	315	1	the	the	DET
ejpam-6407	315	2	other	other	ADJ
ejpam-6407	315	3	cases	case	NOUN
ejpam-6407	315	4	are	be	AUX
ejpam-6407	315	5	evidently	evidently	ADV
ejpam-6407	315	6	contained	contain	VERB
ejpam-6407	315	7	in	in	ADP
ejpam-6407	315	8	the	the	DET
ejpam-6407	315	9	case	case	NOUN
ejpam-6407	315	10	of	of	ADP
ejpam-6407	315	11	j	j	PROPN
ejpam-6407	315	12	=	=	SYM
ejpam-6407	315	13	2	2	PROPN
ejpam-6407	315	14	,	,	PUNCT
ejpam-6407	315	15	which	which	PRON
ejpam-6407	315	16	we	we	PRON
ejpam-6407	315	17	prove	prove	VERB
ejpam-6407	315	18	.	.	PUNCT
ejpam-6407	316	1	let	let	VERB
ejpam-6407	316	2	λϵ	λϵ	X
ejpam-6407	316	3	:	:	PUNCT
ejpam-6407	316	4	(	(	PUNCT
ejpam-6407	316	5	λ1	λ1	ADJ
ejpam-6407	316	6	,	,	PUNCT
ejpam-6407	316	7	σ1	σ1	PROPN
ejpam-6407	316	8	)	)	PUNCT
ejpam-6407	316	9	→	→	SYM
ejpam-6407	316	10	(	(	PUNCT
ejpam-6407	316	11	λ2	λ2	PROPN
ejpam-6407	316	12	,	,	PUNCT
ejpam-6407	316	13	σ2	σ2	NOUN
ejpam-6407	316	14	)	)	PUNCT
ejpam-6407	316	15	with	with	ADP
ejpam-6407	316	16	ϑ1	ϑ1	NOUN
ejpam-6407	316	17	,	,	PUNCT
ejpam-6407	316	18	ϑ2	ϑ2	PROPN
ejpam-6407	316	19	associated	associate	VERB
ejpam-6407	316	20	stss	stss	NOUN
ejpam-6407	316	21	with	with	ADP
ejpam-6407	316	22	σ1	σ1	PROPN
ejpam-6407	316	23	,	,	PUNCT
ejpam-6407	316	24	σ2	σ2	NOUN
ejpam-6407	316	25	respectively	respectively	ADV
ejpam-6407	316	26	,	,	PUNCT
ejpam-6407	316	27	be	be	AUX
ejpam-6407	316	28	a	a	DET
ejpam-6407	316	29	bijective	bijective	ADJ
ejpam-6407	316	30	supra	supra	NOUN
ejpam-6407	316	31	ϵ-open	ϵ-open	PROPN
ejpam-6407	316	32	function	function	NOUN
ejpam-6407	316	33	such	such	ADJ
ejpam-6407	316	34	that	that	SCONJ
ejpam-6407	316	35	(	(	PUNCT
ejpam-6407	316	36	λ1	λ1	ADJ
ejpam-6407	316	37	,	,	PUNCT
ejpam-6407	316	38	ϑ1	ϑ1	PROPN
ejpam-6407	316	39	)	)	PUNCT
ejpam-6407	316	40	is	be	AUX
ejpam-6407	316	41	t2	t2	NOUN
ejpam-6407	316	42	-	-	PUNCT
ejpam-6407	316	43	space	space	NOUN
ejpam-6407	316	44	.	.	PUNCT
ejpam-6407	317	1	let	let	VERB
ejpam-6407	317	2	θ1	θ1	PROPN
ejpam-6407	317	3	̸=	̸=	PROPN
ejpam-6407	317	4	θ2	θ2	ADP
ejpam-6407	317	5	∈	∈	PROPN
ejpam-6407	317	6	λ2	λ2	PROPN
ejpam-6407	317	7	.	.	PUNCT
ejpam-6407	318	1	since	since	SCONJ
ejpam-6407	318	2	λϵ	λϵ	PROPN
ejpam-6407	318	3	is	be	AUX
ejpam-6407	318	4	bijective	bijective	ADJ
ejpam-6407	318	5	,	,	PUNCT
ejpam-6407	318	6	there	there	PRON
ejpam-6407	318	7	are	be	VERB
ejpam-6407	318	8	ξ1	ξ1	PROPN
ejpam-6407	318	9	̸=	̸=	PROPN
ejpam-6407	318	10	ξ2	ξ2	NOUN
ejpam-6407	318	11	∈	∈	PROPN
ejpam-6407	318	12	λ1	λ1	PROPN
ejpam-6407	318	13	such	such	ADJ
ejpam-6407	318	14	that	that	DET
ejpam-6407	318	15	λϵ(ξ1	λϵ(ξ1	X
ejpam-6407	318	16	)	)	PUNCT
ejpam-6407	318	17	=	=	NOUN
ejpam-6407	318	18	θ1	θ1	NOUN
ejpam-6407	318	19	and	and	CCONJ
ejpam-6407	318	20	λϵ(ξ2	λϵ(ξ2	NOUN
ejpam-6407	318	21	)	)	PUNCT
ejpam-6407	318	22	=	=	SYM
ejpam-6407	318	23	θ2	θ2	PROPN
ejpam-6407	318	24	.	.	PUNCT
ejpam-6407	319	1	since	since	SCONJ
ejpam-6407	319	2	(	(	PUNCT
ejpam-6407	319	3	λ1	λ1	ADJ
ejpam-6407	319	4	,	,	PUNCT
ejpam-6407	319	5	σ1	σ1	PROPN
ejpam-6407	319	6	)	)	PUNCT
ejpam-6407	319	7	is	be	AUX
ejpam-6407	319	8	t2	t2	NOUN
ejpam-6407	319	9	-	-	PUNCT
ejpam-6407	319	10	space	space	NOUN
ejpam-6407	319	11	,	,	PUNCT
ejpam-6407	319	12	there	there	PRON
ejpam-6407	319	13	are	be	VERB
ejpam-6407	319	14	two	two	NUM
ejpam-6407	319	15	disjoint	disjoint	ADJ
ejpam-6407	319	16	open	open	ADJ
ejpam-6407	319	17	subsets	subset	NOUN
ejpam-6407	319	18	ρ1	ρ1	NOUN
ejpam-6407	319	19	and	and	CCONJ
ejpam-6407	319	20	ρ2	ρ2	NOUN
ejpam-6407	319	21	of	of	ADP
ejpam-6407	319	22	λ2	λ2	NOUN
ejpam-6407	319	23	,	,	PUNCT
ejpam-6407	319	24	such	such	ADJ
ejpam-6407	319	25	that	that	SCONJ
ejpam-6407	319	26	ξ1	ξ1	PROPN
ejpam-6407	319	27	∈	∈	PROPN
ejpam-6407	319	28	ρ1	ρ1	NOUN
ejpam-6407	319	29	and	and	CCONJ
ejpam-6407	319	30	ξ2	ξ2	NOUN
ejpam-6407	319	31	∈	∈	PROPN
ejpam-6407	319	32	ρ2	ρ2	NOUN
ejpam-6407	319	33	.	.	PUNCT
ejpam-6407	320	1	given	give	VERB
ejpam-6407	320	2	λϵ	λϵ	PROPN
ejpam-6407	320	3	is	be	AUX
ejpam-6407	320	4	supra	supra	PROPN
ejpam-6407	320	5	ϵ-open	ϵ-open	PROPN
ejpam-6407	320	6	,	,	PUNCT
ejpam-6407	320	7	λϵ(ρ1	λϵ(ρ1	PROPN
ejpam-6407	320	8	)	)	PUNCT
ejpam-6407	320	9	and	and	CCONJ
ejpam-6407	320	10	λϵ(ρ2	λϵ(ρ2	NUM
ejpam-6407	320	11	)	)	PUNCT
ejpam-6407	320	12	are	be	AUX
ejpam-6407	320	13	two	two	NUM
ejpam-6407	320	14	disjoint	disjoint	ADJ
ejpam-6407	320	15	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6407	320	16	subsets	subset	NOUN
ejpam-6407	320	17	of	of	ADP
ejpam-6407	320	18	λ2	λ2	NOUN
ejpam-6407	320	19	containing	contain	VERB
ejpam-6407	320	20	θ1	θ1	NOUN
ejpam-6407	320	21	,	,	PUNCT
ejpam-6407	320	22	θ2	θ2	PROPN
ejpam-6407	320	23	,	,	PUNCT
ejpam-6407	320	24	respectively	respectively	ADV
ejpam-6407	320	25	.	.	PUNCT
ejpam-6407	321	1	therefore	therefore	ADV
ejpam-6407	321	2	,	,	PUNCT
ejpam-6407	321	3	(	(	PUNCT
ejpam-6407	321	4	λ2	λ2	NOUN
ejpam-6407	321	5	,	,	PUNCT
ejpam-6407	321	6	ϑ2	ϑ2	PROPN
ejpam-6407	321	7	)	)	PUNCT
ejpam-6407	321	8	is	be	AUX
ejpam-6407	321	9	supra-ϵ-t2	supra-ϵ-t2	PROPN
ejpam-6407	321	10	.	.	PUNCT
ejpam-6407	322	1	corollary	corollary	ADJ
ejpam-6407	322	2	4	4	NUM
ejpam-6407	322	3	.	.	PUNCT
ejpam-6407	323	1	the	the	DET
ejpam-6407	323	2	image	image	NOUN
ejpam-6407	323	3	of	of	ADP
ejpam-6407	323	4	each	each	DET
ejpam-6407	323	5	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6407	323	6	-	-	PUNCT
ejpam-6407	323	7	space	space	NOUN
ejpam-6407	323	8	is	be	AUX
ejpam-6407	323	9	a	a	DET
ejpam-6407	323	10	supra-ϵ-tj	supra-ϵ-tj	NOUN
ejpam-6407	323	11	under	under	ADP
ejpam-6407	323	12	a	a	DET
ejpam-6407	323	13	bijective	bijective	ADJ
ejpam-6407	323	14	supra	supra	NOUN
ejpam-6407	323	15	ϵ∗-open	ϵ∗-open	PROPN
ejpam-6407	323	16	function	function	NOUN
ejpam-6407	323	17	,	,	PUNCT
ejpam-6407	323	18	j	j	PROPN
ejpam-6407	323	19	=	=	SYM
ejpam-6407	323	20	0	0	NUM
ejpam-6407	323	21	,	,	PUNCT
ejpam-6407	323	22	1	1	NUM
ejpam-6407	323	23	,	,	PUNCT
ejpam-6407	323	24	2	2	NUM
ejpam-6407	323	25	.	.	PUNCT
ejpam-6407	324	1	m.	m.	NOUN
ejpam-6407	324	2	aldawood	aldawood	PROPN
ejpam-6407	324	3	et	et	PROPN
ejpam-6407	324	4	al	al	PROPN
ejpam-6407	324	5	.	.	PUNCT
ejpam-6407	324	6	/	/	SYM
ejpam-6407	324	7	eur	eur	PROPN
ejpam-6407	324	8	.	.	PUNCT
ejpam-6407	325	1	j.	j.	PROPN
ejpam-6407	325	2	pure	pure	PROPN
ejpam-6407	325	3	appl	appl	PROPN
ejpam-6407	325	4	.	.	PROPN
ejpam-6407	325	5	math	math	PROPN
ejpam-6407	325	6	,	,	PUNCT
ejpam-6407	325	7	18	18	NUM
ejpam-6407	325	8	(	(	PUNCT
ejpam-6407	325	9	3	3	NUM
ejpam-6407	325	10	)	)	PUNCT
ejpam-6407	325	11	(	(	PUNCT
ejpam-6407	325	12	2025	2025	NUM
ejpam-6407	325	13	)	)	PUNCT
ejpam-6407	325	14	,	,	PUNCT
ejpam-6407	325	15	6407	6407	NUM
ejpam-6407	325	16	11	11	NUM
ejpam-6407	325	17	of	of	ADP
ejpam-6407	325	18	15	15	NUM
ejpam-6407	325	19	proof	proof	NOUN
ejpam-6407	325	20	.	.	PUNCT
ejpam-6407	326	1	it	it	PRON
ejpam-6407	326	2	is	be	AUX
ejpam-6407	326	3	deduced	deduce	VERB
ejpam-6407	326	4	using	use	VERB
ejpam-6407	326	5	a	a	DET
ejpam-6407	326	6	similar	similar	ADJ
ejpam-6407	326	7	procedure	procedure	NOUN
ejpam-6407	326	8	to	to	ADP
ejpam-6407	326	9	that	that	PRON
ejpam-6407	326	10	of	of	ADP
ejpam-6407	326	11	theorem	theorem	NOUN
ejpam-6407	326	12	12	12	NUM
ejpam-6407	326	13	.	.	PUNCT
ejpam-6407	327	1	definition	definition	NOUN
ejpam-6407	327	2	16	16	NUM
ejpam-6407	327	3	.	.	PUNCT
ejpam-6407	328	1	a	a	DET
ejpam-6407	328	2	function	function	NOUN
ejpam-6407	328	3	λϵ	λϵ	VERB
ejpam-6407	328	4	:	:	PUNCT
ejpam-6407	328	5	(	(	PUNCT
ejpam-6407	328	6	λ1	λ1	ADJ
ejpam-6407	328	7	,	,	PUNCT
ejpam-6407	328	8	σ1	σ1	PROPN
ejpam-6407	328	9	)	)	PUNCT
ejpam-6407	328	10	→	→	SYM
ejpam-6407	328	11	(	(	PUNCT
ejpam-6407	328	12	λ2	λ2	PROPN
ejpam-6407	328	13	,	,	PUNCT
ejpam-6407	328	14	σ2	σ2	NOUN
ejpam-6407	328	15	)	)	PUNCT
ejpam-6407	328	16	with	with	ADP
ejpam-6407	328	17	ϑ1	ϑ1	NOUN
ejpam-6407	328	18	,	,	PUNCT
ejpam-6407	328	19	ϑ2	ϑ2	PROPN
ejpam-6407	328	20	associated	associate	VERB
ejpam-6407	328	21	stss	stss	NOUN
ejpam-6407	328	22	with	with	ADP
ejpam-6407	328	23	σ1	σ1	PROPN
ejpam-6407	328	24	,	,	PUNCT
ejpam-6407	328	25	σ2	σ2	NOUN
ejpam-6407	328	26	respectively	respectively	ADV
ejpam-6407	328	27	,	,	PUNCT
ejpam-6407	328	28	is	be	AUX
ejpam-6407	328	29	said	say	VERB
ejpam-6407	328	30	to	to	PART
ejpam-6407	328	31	be	be	AUX
ejpam-6407	328	32	supra-ϵ∗-homeomorphism	supra-ϵ∗-homeomorphism	NOUN
ejpam-6407	328	33	if	if	SCONJ
ejpam-6407	328	34	it	it	PRON
ejpam-6407	328	35	is	be	AUX
ejpam-6407	328	36	bijective	bijective	ADJ
ejpam-6407	328	37	supra	supra	PROPN
ejpam-6407	328	38	ϵ∗-open	ϵ∗-open	PROPN
ejpam-6407	328	39	and	and	CCONJ
ejpam-6407	328	40	supra	supra	ADJ
ejpam-6407	328	41	ϵ∗-cts	ϵ∗-ct	NOUN
ejpam-6407	328	42	lemma	lemma	PROPN
ejpam-6407	329	1	2	2	X
ejpam-6407	329	2	.	.	PUNCT
ejpam-6407	330	1	if	if	SCONJ
ejpam-6407	330	2	λϵ	λϵ	X
ejpam-6407	330	3	:	:	PUNCT
ejpam-6407	330	4	(	(	PUNCT
ejpam-6407	330	5	λ1	λ1	ADJ
ejpam-6407	330	6	,	,	PUNCT
ejpam-6407	330	7	σ1	σ1	PROPN
ejpam-6407	330	8	)	)	PUNCT
ejpam-6407	330	9	→	→	SYM
ejpam-6407	330	10	(	(	PUNCT
ejpam-6407	330	11	λ2	λ2	PROPN
ejpam-6407	330	12	,	,	PUNCT
ejpam-6407	330	13	σ2	σ2	PROPN
ejpam-6407	330	14	)	)	PUNCT
ejpam-6407	330	15	is	be	AUX
ejpam-6407	330	16	supra-ϵ∗-homeomorphism	supra-ϵ∗-homeomorphism	NOUN
ejpam-6407	330	17	function	function	NOUN
ejpam-6407	330	18	with	with	ADP
ejpam-6407	330	19	ϑ1	ϑ1	PROPN
ejpam-6407	330	20	,	,	PUNCT
ejpam-6407	330	21	ϑ2	ϑ2	PROPN
ejpam-6407	330	22	associated	associate	VERB
ejpam-6407	330	23	stss	stss	NOUN
ejpam-6407	330	24	with	with	ADP
ejpam-6407	330	25	σ1	σ1	PROPN
ejpam-6407	330	26	,	,	PUNCT
ejpam-6407	330	27	σ2	σ2	NOUN
ejpam-6407	330	28	respectively	respectively	ADV
ejpam-6407	330	29	,	,	PUNCT
ejpam-6407	330	30	then	then	ADV
ejpam-6407	330	31	(	(	PUNCT
ejpam-6407	330	32	λ2	λ2	PROPN
ejpam-6407	330	33	,	,	PUNCT
ejpam-6407	330	34	σ2	σ2	NOUN
ejpam-6407	330	35	)	)	PUNCT
ejpam-6407	330	36	is	be	AUX
ejpam-6407	330	37	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6407	330	38	-	-	PUNCT
ejpam-6407	330	39	space	space	NOUN
ejpam-6407	330	40	if	if	SCONJ
ejpam-6407	330	41	and	and	CCONJ
ejpam-6407	330	42	only	only	ADV
ejpam-6407	330	43	if	if	SCONJ
ejpam-6407	330	44	(	(	PUNCT
ejpam-6407	330	45	λ1	λ1	ADJ
ejpam-6407	330	46	,	,	PUNCT
ejpam-6407	330	47	ϑ1	ϑ1	PROPN
ejpam-6407	330	48	)	)	PUNCT
ejpam-6407	330	49	is	be	AUX
ejpam-6407	330	50	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6407	330	51	,	,	PUNCT
ejpam-6407	331	1	j	j	PROPN
ejpam-6407	331	2	=	=	SYM
ejpam-6407	331	3	0	0	NUM
ejpam-6407	331	4	,	,	PUNCT
ejpam-6407	331	5	1	1	NUM
ejpam-6407	331	6	,	,	PUNCT
ejpam-6407	331	7	2	2	NUM
ejpam-6407	331	8	.	.	PUNCT
ejpam-6407	331	9	proof	proof	NOUN
ejpam-6407	331	10	.	.	PUNCT
ejpam-6407	332	1	it	it	PRON
ejpam-6407	332	2	is	be	AUX
ejpam-6407	332	3	follows	follow	VERB
ejpam-6407	332	4	from	from	ADP
ejpam-6407	332	5	proposition	proposition	NOUN
ejpam-6407	332	6	5	5	NUM
ejpam-6407	332	7	and	and	CCONJ
ejpam-6407	332	8	corollary	corollary	ADJ
ejpam-6407	332	9	4	4	NUM
ejpam-6407	332	10	.	.	NOUN
ejpam-6407	332	11	5	5	NUM
ejpam-6407	332	12	.	.	X
ejpam-6407	332	13	conclusion	conclusion	NOUN
ejpam-6407	332	14	a	a	DET
ejpam-6407	332	15	new	new	ADJ
ejpam-6407	332	16	weaker	weak	ADJ
ejpam-6407	332	17	version	version	NOUN
ejpam-6407	332	18	of	of	ADP
ejpam-6407	332	19	supra	supra	PROPN
ejpam-6407	332	20	septarian	septarian	ADJ
ejpam-6407	332	21	axioms	axiom	NOUN
ejpam-6407	332	22	based	base	VERB
ejpam-6407	332	23	on	on	ADP
ejpam-6407	332	24	supra	supra	PROPN
ejpam-6407	332	25	ϵ-open	ϵ-open	PROPN
ejpam-6407	332	26	sets	set	NOUN
ejpam-6407	332	27	is	be	AUX
ejpam-6407	332	28	presented	present	VERB
ejpam-6407	332	29	in	in	ADP
ejpam-6407	332	30	this	this	DET
ejpam-6407	332	31	manuscript	manuscript	NOUN
ejpam-6407	332	32	,	,	PUNCT
ejpam-6407	332	33	along	along	ADP
ejpam-6407	332	34	with	with	ADP
ejpam-6407	332	35	its	its	PRON
ejpam-6407	332	36	key	key	ADJ
ejpam-6407	332	37	characteristics	characteristic	NOUN
ejpam-6407	332	38	named	name	VERB
ejpam-6407	332	39	supra-ϵ-tj	supra-ϵ-tj	NOUN
ejpam-6407	332	40	-	-	PUNCT
ejpam-6407	332	41	space	space	NOUN
ejpam-6407	332	42	,	,	PUNCT
ejpam-6407	332	43	j	j	PROPN
ejpam-6407	332	44	=	=	SYM
ejpam-6407	332	45	0	0	NUM
ejpam-6407	332	46	,	,	PUNCT
ejpam-6407	332	47	1	1	NUM
ejpam-6407	332	48	,	,	PUNCT
ejpam-6407	332	49	2	2	NUM
ejpam-6407	332	50	.	.	X
ejpam-6407	333	1	in	in	ADP
ejpam-6407	333	2	detail	detail	NOUN
ejpam-6407	333	3	,	,	PUNCT
ejpam-6407	333	4	we	we	PRON
ejpam-6407	333	5	present	present	VERB
ejpam-6407	333	6	three	three	NUM
ejpam-6407	333	7	new	new	ADJ
ejpam-6407	333	8	types	type	NOUN
ejpam-6407	333	9	of	of	ADP
ejpam-6407	333	10	separation	separation	NOUN
ejpam-6407	333	11	axioms	axiom	NOUN
ejpam-6407	333	12	inspired	inspire	VERB
ejpam-6407	333	13	by	by	ADP
ejpam-6407	333	14	supra	supra	PROPN
ejpam-6407	333	15	ϵ-open	ϵ-open	PROPN
ejpam-6407	333	16	sets	set	NOUN
ejpam-6407	333	17	named	name	VERB
ejpam-6407	333	18	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	333	19	-	-	NOUN
ejpam-6407	333	20	space	space	NOUN
ejpam-6407	333	21	,	,	PUNCT
ejpam-6407	333	22	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6407	333	23	-	-	PUNCT
ejpam-6407	333	24	space	space	NOUN
ejpam-6407	333	25	,	,	PUNCT
ejpam-6407	333	26	and	and	CCONJ
ejpam-6407	333	27	supra-ϵ-hausdorff	supra-ϵ-hausdorff	NOUN
ejpam-6407	333	28	-	-	PUNCT
ejpam-6407	333	29	space	space	NOUN
ejpam-6407	333	30	.	.	PUNCT
ejpam-6407	334	1	we	we	PRON
ejpam-6407	334	2	provide	provide	VERB
ejpam-6407	334	3	thorough	thorough	ADJ
ejpam-6407	334	4	descriptions	description	NOUN
ejpam-6407	334	5	of	of	ADP
ejpam-6407	334	6	each	each	PRON
ejpam-6407	334	7	of	of	ADP
ejpam-6407	334	8	them	they	PRON
ejpam-6407	334	9	supported	support	VERB
ejpam-6407	334	10	with	with	ADP
ejpam-6407	334	11	several	several	ADJ
ejpam-6407	334	12	examples	example	NOUN
ejpam-6407	334	13	and	and	CCONJ
ejpam-6407	334	14	counterexamples	counterexample	NOUN
ejpam-6407	334	15	that	that	PRON
ejpam-6407	334	16	demonstrate	demonstrate	VERB
ejpam-6407	334	17	the	the	DET
ejpam-6407	334	18	importance	importance	NOUN
ejpam-6407	334	19	of	of	ADP
ejpam-6407	334	20	our	our	PRON
ejpam-6407	334	21	novel	novel	ADJ
ejpam-6407	334	22	concepts	concept	NOUN
ejpam-6407	334	23	.	.	PUNCT
ejpam-6407	335	1	specifically	specifically	ADV
ejpam-6407	335	2	,	,	PUNCT
ejpam-6407	335	3	we	we	PRON
ejpam-6407	335	4	explore	explore	VERB
ejpam-6407	335	5	sufficient	sufficient	ADJ
ejpam-6407	335	6	conditions	condition	NOUN
ejpam-6407	335	7	for	for	ADP
ejpam-6407	335	8	several	several	ADJ
ejpam-6407	335	9	analogous	analogous	ADJ
ejpam-6407	335	10	linkages	linkage	NOUN
ejpam-6407	335	11	between	between	ADP
ejpam-6407	335	12	them	they	PRON
ejpam-6407	335	13	and	and	CCONJ
ejpam-6407	335	14	generally	generally	ADV
ejpam-6407	335	15	illustrate	illustrate	VERB
ejpam-6407	335	16	their	their	PRON
ejpam-6407	335	17	key	key	ADJ
ejpam-6407	335	18	characteristics	characteristic	NOUN
ejpam-6407	335	19	.	.	PUNCT
ejpam-6407	336	1	furthermore	furthermore	ADV
ejpam-6407	336	2	,	,	PUNCT
ejpam-6407	336	3	we	we	PRON
ejpam-6407	336	4	propose	propose	VERB
ejpam-6407	336	5	a	a	DET
ejpam-6407	336	6	diagram	diagram	NOUN
ejpam-6407	336	7	that	that	PRON
ejpam-6407	336	8	encapsulates	encapsulate	VERB
ejpam-6407	336	9	their	their	PRON
ejpam-6407	336	10	connections	connection	NOUN
ejpam-6407	336	11	[	[	X
ejpam-6407	336	12	see	see	INTJ
ejpam-6407	336	13	figure	figure	NOUN
ejpam-6407	336	14	1	1	NUM
ejpam-6407	336	15	]	]	PUNCT
ejpam-6407	336	16	.	.	PUNCT
ejpam-6407	337	1	additionally	additionally	ADV
ejpam-6407	337	2	,	,	PUNCT
ejpam-6407	337	3	we	we	PRON
ejpam-6407	337	4	present	present	VERB
ejpam-6407	337	5	the	the	DET
ejpam-6407	337	6	supra	supra	PROPN
ejpam-6407	337	7	ϵ-symmetric	ϵ-symmetric	ADJ
ejpam-6407	337	8	property	property	NOUN
ejpam-6407	337	9	and	and	CCONJ
ejpam-6407	337	10	show	show	VERB
ejpam-6407	337	11	that	that	SCONJ
ejpam-6407	337	12	the	the	DET
ejpam-6407	337	13	two	two	NUM
ejpam-6407	337	14	notions	notion	NOUN
ejpam-6407	337	15	of	of	ADP
ejpam-6407	337	16	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6407	337	17	-	-	NOUN
ejpam-6407	337	18	space	space	NOUN
ejpam-6407	337	19	and	and	CCONJ
ejpam-6407	337	20	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6407	337	21	-	-	PUNCT
ejpam-6407	337	22	space	space	NOUN
ejpam-6407	337	23	are	be	AUX
ejpam-6407	337	24	the	the	DET
ejpam-6407	337	25	same	same	ADJ
ejpam-6407	337	26	for	for	ADP
ejpam-6407	337	27	any	any	DET
ejpam-6407	337	28	sts	st	NOUN
ejpam-6407	337	29	that	that	PRON
ejpam-6407	337	30	fulfills	fulfill	VERB
ejpam-6407	337	31	it	it	PRON
ejpam-6407	337	32	.	.	PUNCT
ejpam-6407	338	1	finally	finally	ADV
ejpam-6407	338	2	,	,	PUNCT
ejpam-6407	338	3	for	for	ADP
ejpam-6407	338	4	each	each	PRON
ejpam-6407	338	5	of	of	ADP
ejpam-6407	338	6	the	the	DET
ejpam-6407	338	7	previously	previously	ADV
ejpam-6407	338	8	described	describe	VERB
ejpam-6407	338	9	concepts	concept	NOUN
ejpam-6407	338	10	,	,	PUNCT
ejpam-6407	338	11	we	we	PRON
ejpam-6407	338	12	examine	examine	VERB
ejpam-6407	338	13	the	the	DET
ejpam-6407	338	14	supra	supra	PROPN
ejpam-6407	338	15	topological	topological	PROPN
ejpam-6407	338	16	and	and	CCONJ
ejpam-6407	338	17	supra	supra	ADJ
ejpam-6407	338	18	hereditary	hereditary	ADJ
ejpam-6407	338	19	properties	property	NOUN
ejpam-6407	338	20	.	.	PUNCT
ejpam-6407	339	1	specifically	specifically	ADV
ejpam-6407	339	2	,	,	PUNCT
ejpam-6407	339	3	we	we	PRON
ejpam-6407	339	4	demonstrate	demonstrate	VERB
ejpam-6407	339	5	that	that	SCONJ
ejpam-6407	339	6	the	the	DET
ejpam-6407	339	7	property	property	NOUN
ejpam-6407	339	8	of	of	ADP
ejpam-6407	339	9	being	be	AUX
ejpam-6407	339	10	a	a	DET
ejpam-6407	339	11	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6407	339	12	-	-	PUNCT
ejpam-6407	339	13	space	space	NOUN
ejpam-6407	339	14	,	,	PUNCT
ejpam-6407	339	15	where	where	SCONJ
ejpam-6407	339	16	j	j	PROPN
ejpam-6407	339	17	=	=	SYM
ejpam-6407	339	18	0	0	PROPN
ejpam-6407	339	19	,	,	PUNCT
ejpam-6407	339	20	1	1	NUM
ejpam-6407	339	21	,	,	PUNCT
ejpam-6407	339	22	2	2	NUM
ejpam-6407	339	23	,	,	PUNCT
ejpam-6407	339	24	is	be	AUX
ejpam-6407	339	25	a	a	DET
ejpam-6407	339	26	supra	supra	NOUN
ejpam-6407	339	27	-	-	PUNCT
ejpam-6407	339	28	hereditary	hereditary	ADJ
ejpam-6407	339	29	(	(	PUNCT
ejpam-6407	339	30	topological	topological	ADJ
ejpam-6407	339	31	)	)	PUNCT
ejpam-6407	339	32	property	property	NOUN
ejpam-6407	339	33	.	.	PUNCT
ejpam-6407	340	1	from	from	ADP
ejpam-6407	340	2	the	the	DET
ejpam-6407	340	3	specific	specific	ADJ
ejpam-6407	340	4	approaches	approach	NOUN
ejpam-6407	340	5	described	describe	VERB
ejpam-6407	340	6	in	in	ADP
ejpam-6407	340	7	this	this	DET
ejpam-6407	340	8	paper	paper	NOUN
ejpam-6407	340	9	,	,	PUNCT
ejpam-6407	340	10	additional	additional	ADJ
ejpam-6407	340	11	research	research	NOUN
ejpam-6407	340	12	on	on	ADP
ejpam-6407	340	13	the	the	DET
ejpam-6407	340	14	theoretical	theoretical	ADJ
ejpam-6407	340	15	aspects	aspect	NOUN
ejpam-6407	340	16	of	of	ADP
ejpam-6407	340	17	these	these	DET
ejpam-6407	340	18	generalized	generalize	VERB
ejpam-6407	340	19	concepts	concept	NOUN
ejpam-6407	340	20	could	could	AUX
ejpam-6407	340	21	be	be	AUX
ejpam-6407	340	22	carried	carry	VERB
ejpam-6407	340	23	out	out	ADP
ejpam-6407	340	24	by	by	ADP
ejpam-6407	340	25	looking	look	VERB
ejpam-6407	340	26	at	at	ADP
ejpam-6407	340	27	the	the	DET
ejpam-6407	340	28	following	follow	VERB
ejpam-6407	340	29	subjects	subject	NOUN
ejpam-6407	340	30	:	:	PUNCT
ejpam-6407	340	31	•	•	NUM
ejpam-6407	340	32	introducing	introduce	VERB
ejpam-6407	340	33	more	more	ADJ
ejpam-6407	340	34	types	type	NOUN
ejpam-6407	340	35	of	of	ADP
ejpam-6407	340	36	septarian	septarian	ADJ
ejpam-6407	340	37	axioms	axiom	NOUN
ejpam-6407	340	38	based	base	VERB
ejpam-6407	340	39	on	on	ADP
ejpam-6407	340	40	supra	supra	PROPN
ejpam-6407	340	41	ϵ-open	ϵ-open	PROPN
ejpam-6407	340	42	sets	set	NOUN
ejpam-6407	340	43	,	,	PUNCT
ejpam-6407	340	44	like	like	ADP
ejpam-6407	340	45	supraϵ-completely	supraϵ-completely	ADV
ejpam-6407	340	46	space	space	NOUN
ejpam-6407	340	47	,	,	PUNCT
ejpam-6407	340	48	supra-ϵ-regular	supra-ϵ-regular	NOUN
ejpam-6407	340	49	-	-	PUNCT
ejpam-6407	340	50	space	space	NOUN
ejpam-6407	340	51	,	,	PUNCT
ejpam-6407	340	52	supra-ϵ-completely	supra-ϵ-completely	ADV
ejpam-6407	340	53	regular	regular	ADJ
ejpam-6407	340	54	space	space	NOUN
ejpam-6407	340	55	,	,	PUNCT
ejpam-6407	340	56	supraϵ-normal	supraϵ-normal	ADJ
ejpam-6407	340	57	-	-	PUNCT
ejpam-6407	340	58	space	space	NOUN
ejpam-6407	340	59	,	,	PUNCT
ejpam-6407	340	60	supra-ϵ-t3	supra-ϵ-t3	NOUN
ejpam-6407	340	61	-	-	PUNCT
ejpam-6407	340	62	space	space	NOUN
ejpam-6407	340	63	,	,	PUNCT
ejpam-6407	340	64	and	and	CCONJ
ejpam-6407	340	65	supra-ϵ-t4	supra-ϵ-t4	NOUN
ejpam-6407	340	66	-	-	PUNCT
ejpam-6407	340	67	space	space	NOUN
ejpam-6407	340	68	.	.	PUNCT
ejpam-6407	341	1	•	•	NUM
ejpam-6407	341	2	considering	consider	VERB
ejpam-6407	341	3	whether	whether	SCONJ
ejpam-6407	341	4	information	information	NOUN
ejpam-6407	341	5	systems	system	NOUN
ejpam-6407	341	6	can	can	AUX
ejpam-6407	341	7	benefit	benefit	VERB
ejpam-6407	341	8	from	from	ADP
ejpam-6407	341	9	the	the	DET
ejpam-6407	341	10	use	use	NOUN
ejpam-6407	341	11	of	of	ADP
ejpam-6407	341	12	these	these	DET
ejpam-6407	341	13	kinds	kind	NOUN
ejpam-6407	341	14	of	of	ADP
ejpam-6407	341	15	separation	separation	NOUN
ejpam-6407	341	16	axioms	axiom	NOUN
ejpam-6407	341	17	.	.	PUNCT
ejpam-6407	342	1	•	•	NUM
ejpam-6407	342	2	introducing	introduce	VERB
ejpam-6407	342	3	theses	thesis	NOUN
ejpam-6407	342	4	concepts	concept	NOUN
ejpam-6407	342	5	to	to	ADP
ejpam-6407	342	6	fuzzy	fuzzy	ADJ
ejpam-6407	342	7	supra	supra	PROPN
ejpam-6407	342	8	soft	soft	ADJ
ejpam-6407	342	9	topological	topological	ADJ
ejpam-6407	342	10	spaces	space	NOUN
ejpam-6407	342	11	[	[	X
ejpam-6407	342	12	64	64	NUM
ejpam-6407	342	13	,	,	PUNCT
ejpam-6407	342	14	65	65	NUM
ejpam-6407	342	15	]	]	PUNCT
ejpam-6407	342	16	.	.	PUNCT
ejpam-6407	343	1	•	•	NUM
ejpam-6407	343	2	applying	apply	VERB
ejpam-6407	343	3	our	our	PRON
ejpam-6407	343	4	new	new	ADJ
ejpam-6407	343	5	notions	notion	NOUN
ejpam-6407	343	6	to	to	ADP
ejpam-6407	343	7	rough	rough	ADJ
ejpam-6407	343	8	approximations	approximation	NOUN
ejpam-6407	343	9	based	base	VERB
ejpam-6407	343	10	on	on	ADP
ejpam-6407	343	11	relations	relation	NOUN
ejpam-6407	343	12	with	with	ADP
ejpam-6407	343	13	decision	decision	NOUN
ejpam-6407	343	14	making	make	VERB
ejpam-6407	343	15	applications	application	NOUN
ejpam-6407	343	16	[	[	X
ejpam-6407	343	17	66	66	NUM
ejpam-6407	343	18	]	]	PUNCT
ejpam-6407	343	19	.	.	PUNCT
ejpam-6407	344	1	conflicts	conflict	NOUN
ejpam-6407	344	2	of	of	ADP
ejpam-6407	344	3	interest	interest	NOUN
ejpam-6407	344	4	in	in	ADP
ejpam-6407	344	5	relation	relation	NOUN
ejpam-6407	344	6	to	to	ADP
ejpam-6407	344	7	the	the	DET
ejpam-6407	344	8	publication	publication	NOUN
ejpam-6407	344	9	of	of	ADP
ejpam-6407	344	10	this	this	DET
ejpam-6407	344	11	work	work	NOUN
ejpam-6407	344	12	,	,	PUNCT
ejpam-6407	344	13	the	the	DET
ejpam-6407	344	14	authors	author	NOUN
ejpam-6407	344	15	declare	declare	VERB
ejpam-6407	344	16	that	that	SCONJ
ejpam-6407	344	17	they	they	PRON
ejpam-6407	344	18	have	have	VERB
ejpam-6407	344	19	no	no	DET
ejpam-6407	344	20	competing	compete	VERB
ejpam-6407	344	21	interests	interest	NOUN
ejpam-6407	344	22	.	.	PUNCT
ejpam-6407	345	1	m.	m.	NOUN
ejpam-6407	345	2	aldawood	aldawood	PROPN
ejpam-6407	345	3	et	et	PROPN
ejpam-6407	345	4	al	al	PROPN
ejpam-6407	345	5	.	.	PUNCT
ejpam-6407	345	6	/	/	SYM
ejpam-6407	345	7	eur	eur	PROPN
ejpam-6407	345	8	.	.	PUNCT
ejpam-6407	346	1	j.	j.	PROPN
ejpam-6407	346	2	pure	pure	PROPN
ejpam-6407	346	3	appl	appl	PROPN
ejpam-6407	346	4	.	.	PROPN
ejpam-6407	346	5	math	math	PROPN
ejpam-6407	346	6	,	,	PUNCT
ejpam-6407	346	7	18	18	NUM
ejpam-6407	346	8	(	(	PUNCT
ejpam-6407	346	9	3	3	NUM
ejpam-6407	346	10	)	)	PUNCT
ejpam-6407	346	11	(	(	PUNCT
ejpam-6407	346	12	2025	2025	NUM
ejpam-6407	346	13	)	)	PUNCT
ejpam-6407	346	14	,	,	PUNCT
ejpam-6407	346	15	6407	6407	NUM
ejpam-6407	346	16	12	12	NUM
ejpam-6407	346	17	of	of	ADP
ejpam-6407	346	18	15	15	NUM
ejpam-6407	346	19	author	author	NOUN
ejpam-6407	346	20	contributions	contribution	NOUN
ejpam-6407	346	21	each	each	DET
ejpam-6407	346	22	author	author	NOUN
ejpam-6407	346	23	’s	’s	PART
ejpam-6407	346	24	contribution	contribution	NOUN
ejpam-6407	346	25	was	be	AUX
ejpam-6407	346	26	equal	equal	ADJ
ejpam-6407	346	27	.	.	PUNCT
ejpam-6407	347	1	acknowledgements	acknowledgement	NOUN
ejpam-6407	347	2	the	the	DET
ejpam-6407	347	3	authors	author	NOUN
ejpam-6407	347	4	extend	extend	VERB
ejpam-6407	347	5	their	their	PRON
ejpam-6407	347	6	appreciation	appreciation	NOUN
ejpam-6407	347	7	to	to	ADP
ejpam-6407	347	8	the	the	DET
ejpam-6407	347	9	deanship	deanship	NOUN
ejpam-6407	347	10	of	of	ADP
ejpam-6407	347	11	scientific	scientific	ADJ
ejpam-6407	347	12	research	research	NOUN
ejpam-6407	347	13	at	at	ADP
ejpam-6407	347	14	northern	northern	ADJ
ejpam-6407	347	15	border	border	NOUN
ejpam-6407	347	16	university	university	PROPN
ejpam-6407	347	17	,	,	PUNCT
ejpam-6407	347	18	arar	arar	PROPN
ejpam-6407	347	19	,	,	PUNCT
ejpam-6407	347	20	ksa	ksa	PROPN
ejpam-6407	347	21	for	for	ADP
ejpam-6407	347	22	funding	fund	VERB
ejpam-6407	347	23	this	this	DET
ejpam-6407	347	24	research	research	NOUN
ejpam-6407	347	25	work	work	NOUN
ejpam-6407	347	26	through	through	ADP
ejpam-6407	347	27	the	the	DET
ejpam-6407	347	28	project	project	NOUN
ejpam-6407	347	29	number	number	NOUN
ejpam-6407	347	30	”	"	PUNCT
ejpam-6407	347	31	nbu	nbu	NOUN
ejpam-6407	347	32	-	-	PUNCT
ejpam-6407	347	33	ffr-2025	ffr-2025	NOUN
ejpam-6407	347	34	-	-	PUNCT
ejpam-6407	347	35	2941	2941	NUM
ejpam-6407	347	36	-	-	SYM
ejpam-6407	347	37	02	02	NUM
ejpam-6407	347	38	”	"	PUNCT
ejpam-6407	347	39	.	.	PUNCT
ejpam-6407	348	1	also	also	ADV
ejpam-6407	348	2	,	,	PUNCT
ejpam-6407	348	3	this	this	DET
ejpam-6407	348	4	study	study	NOUN
ejpam-6407	348	5	is	be	AUX
ejpam-6407	348	6	supported	support	VERB
ejpam-6407	348	7	via	via	ADP
ejpam-6407	348	8	funding	funding	NOUN
ejpam-6407	348	9	from	from	ADP
ejpam-6407	348	10	prince	prince	PROPN
ejpam-6407	348	11	sattam	sattam	PROPN
ejpam-6407	348	12	bin	bin	PROPN
ejpam-6407	348	13	abdulaziz	abdulaziz	PROPN
ejpam-6407	348	14	university	university	PROPN
ejpam-6407	348	15	project	project	NOUN
ejpam-6407	348	16	number	number	NOUN
ejpam-6407	348	17	(	(	PUNCT
ejpam-6407	348	18	psau/2025	psau/2025	NOUN
ejpam-6407	348	19	/	/	SYM
ejpam-6407	348	20	r/1446	r/1446	PROPN
ejpam-6407	348	21	)	)	PUNCT
ejpam-6407	348	22	.	.	PUNCT
ejpam-6407	349	1	references	reference	NOUN
ejpam-6407	349	2	[	[	X
ejpam-6407	349	3	1	1	NUM
ejpam-6407	349	4	]	]	X
ejpam-6407	349	5	n.	n.	PROPN
ejpam-6407	349	6	levine	levine	PROPN
ejpam-6407	349	7	.	.	PUNCT
ejpam-6407	350	1	semi	semi	ADJ
ejpam-6407	350	2	-	-	ADJ
ejpam-6407	350	3	open	open	ADJ
ejpam-6407	350	4	sets	set	NOUN
ejpam-6407	350	5	and	and	CCONJ
ejpam-6407	350	6	semi	semi	ADJ
ejpam-6407	350	7	-	-	NOUN
ejpam-6407	350	8	continuity	continuity	NOUN
ejpam-6407	350	9	in	in	ADP
ejpam-6407	350	10	topological	topological	ADJ
ejpam-6407	350	11	spaces	space	NOUN
ejpam-6407	350	12	.	.	PUNCT
ejpam-6407	351	1	american	american	PROPN
ejpam-6407	351	2	mathematical	mathematical	PROPN
ejpam-6407	351	3	monthly	monthly	ADV
ejpam-6407	351	4	,	,	PUNCT
ejpam-6407	351	5	70(1):36–41	70(1):36–41	NUM
ejpam-6407	351	6	,	,	PUNCT
ejpam-6407	351	7	1963	1963	NUM
ejpam-6407	351	8	.	.	PUNCT
ejpam-6407	352	1	[	[	X
ejpam-6407	352	2	2	2	NUM
ejpam-6407	352	3	]	]	X
ejpam-6407	352	4	o.	o.	PROPN
ejpam-6407	352	5	njastad	njastad	PROPN
ejpam-6407	352	6	.	.	PUNCT
ejpam-6407	353	1	on	on	ADP
ejpam-6407	353	2	some	some	DET
ejpam-6407	353	3	classes	class	NOUN
ejpam-6407	353	4	of	of	ADP
ejpam-6407	353	5	nearly	nearly	ADV
ejpam-6407	353	6	open	open	ADJ
ejpam-6407	353	7	sets	set	NOUN
ejpam-6407	353	8	.	.	PUNCT
ejpam-6407	354	1	pacific	pacific	PROPN
ejpam-6407	354	2	journal	journal	PROPN
ejpam-6407	354	3	of	of	ADP
ejpam-6407	354	4	mathematics	mathematic	NOUN
ejpam-6407	354	5	,	,	PUNCT
ejpam-6407	354	6	15(3):961–970	15(3):961–970	PROPN
ejpam-6407	354	7	,	,	PUNCT
ejpam-6407	354	8	1965	1965	NUM
ejpam-6407	354	9	.	.	PUNCT
ejpam-6407	355	1	[	[	X
ejpam-6407	355	2	3	3	X
ejpam-6407	355	3	]	]	PUNCT
ejpam-6407	355	4	a.	a.	NOUN
ejpam-6407	355	5	mashhour	mashhour	PROPN
ejpam-6407	355	6	,	,	PUNCT
ejpam-6407	355	7	m.	m.	PROPN
ejpam-6407	355	8	abd	abd	PROPN
ejpam-6407	355	9	el	el	PROPN
ejpam-6407	355	10	-	-	PROPN
ejpam-6407	355	11	monsef	monsef	ADJ
ejpam-6407	355	12	,	,	PUNCT
ejpam-6407	355	13	and	and	CCONJ
ejpam-6407	355	14	s.	s.	PROPN
ejpam-6407	355	15	el	el	PROPN
ejpam-6407	355	16	-	-	PROPN
ejpam-6407	355	17	deeb	deeb	PROPN
ejpam-6407	355	18	.	.	PUNCT
ejpam-6407	356	1	on	on	ADP
ejpam-6407	356	2	precontinuous	precontinuous	ADJ
ejpam-6407	356	3	and	and	CCONJ
ejpam-6407	356	4	weak	weak	ADJ
ejpam-6407	356	5	precontinuous	precontinuous	ADJ
ejpam-6407	356	6	mappings	mapping	NOUN
ejpam-6407	356	7	.	.	PUNCT
ejpam-6407	357	1	proceedings	proceeding	NOUN
ejpam-6407	357	2	of	of	ADP
ejpam-6407	357	3	the	the	DET
ejpam-6407	357	4	mathematical	mathematical	ADJ
ejpam-6407	357	5	and	and	CCONJ
ejpam-6407	357	6	physical	physical	ADJ
ejpam-6407	357	7	society	society	NOUN
ejpam-6407	357	8	,	,	PUNCT
ejpam-6407	357	9	53:47–53	53:47–53	NUM
ejpam-6407	357	10	,	,	PUNCT
ejpam-6407	357	11	1982	1982	NUM
ejpam-6407	357	12	.	.	PUNCT
ejpam-6407	358	1	[	[	X
ejpam-6407	358	2	4	4	X
ejpam-6407	358	3	]	]	PUNCT
ejpam-6407	358	4	m.	m.	NOUN
ejpam-6407	358	5	abd	abd	PROPN
ejpam-6407	358	6	el	el	PROPN
ejpam-6407	358	7	-	-	PROPN
ejpam-6407	358	8	monsef	monsef	PROPN
ejpam-6407	358	9	,	,	PUNCT
ejpam-6407	358	10	s.	s.	PROPN
ejpam-6407	358	11	el	el	PROPN
ejpam-6407	358	12	-	-	PROPN
ejpam-6407	358	13	deeb	deeb	PROPN
ejpam-6407	358	14	,	,	PUNCT
ejpam-6407	358	15	and	and	CCONJ
ejpam-6407	358	16	r.	r.	PROPN
ejpam-6407	358	17	mahmoud	mahmoud	PROPN
ejpam-6407	358	18	.	.	PUNCT
ejpam-6407	359	1	β	β	X
ejpam-6407	359	2	-	-	ADJ
ejpam-6407	359	3	open	open	ADJ
ejpam-6407	359	4	sets	set	NOUN
ejpam-6407	359	5	and	and	CCONJ
ejpam-6407	359	6	β	β	ADJ
ejpam-6407	359	7	-	-	ADJ
ejpam-6407	359	8	continuous	continuous	ADJ
ejpam-6407	359	9	mappings	mapping	NOUN
ejpam-6407	359	10	.	.	PUNCT
ejpam-6407	360	1	bulletin	bulletin	NOUN
ejpam-6407	360	2	of	of	ADP
ejpam-6407	360	3	the	the	DET
ejpam-6407	360	4	faculty	faculty	NOUN
ejpam-6407	360	5	of	of	ADP
ejpam-6407	360	6	science	science	NOUN
ejpam-6407	360	7	,	,	PUNCT
ejpam-6407	360	8	assiut	assiut	NOUN
ejpam-6407	360	9	university	university	NOUN
ejpam-6407	360	10	,	,	PUNCT
ejpam-6407	360	11	12(1):77–90	12(1):77–90	NUM
ejpam-6407	360	12	,	,	PUNCT
ejpam-6407	360	13	1983	1983	NUM
ejpam-6407	360	14	.	.	PUNCT
ejpam-6407	361	1	[	[	X
ejpam-6407	361	2	5	5	X
ejpam-6407	361	3	]	]	PUNCT
ejpam-6407	361	4	d.	d.	PROPN
ejpam-6407	361	5	andrijevic	andrijevic	VERB
ejpam-6407	361	6	.	.	PUNCT
ejpam-6407	362	1	on	on	ADP
ejpam-6407	362	2	b	b	X
ejpam-6407	362	3	-	-	PUNCT
ejpam-6407	362	4	open	open	ADJ
ejpam-6407	362	5	sets	set	NOUN
ejpam-6407	362	6	.	.	PUNCT
ejpam-6407	363	1	matematicki	matematicki	NOUN
ejpam-6407	363	2	vesnik	vesnik	PROPN
ejpam-6407	363	3	,	,	PUNCT
ejpam-6407	363	4	48:59–64	48:59–64	PROPN
ejpam-6407	363	5	,	,	PUNCT
ejpam-6407	363	6	1996	1996	NUM
ejpam-6407	363	7	.	.	PUNCT
ejpam-6407	364	1	[	[	X
ejpam-6407	364	2	6	6	NUM
ejpam-6407	364	3	]	]	PUNCT
ejpam-6407	364	4	j.	j.	PROPN
ejpam-6407	364	5	dontchev	dontchev	PROPN
ejpam-6407	364	6	and	and	CCONJ
ejpam-6407	364	7	m.	m.	PROPN
ejpam-6407	364	8	przemski	przemski	PROPN
ejpam-6407	364	9	.	.	PUNCT
ejpam-6407	365	1	on	on	ADP
ejpam-6407	365	2	the	the	DET
ejpam-6407	365	3	various	various	ADJ
ejpam-6407	365	4	decompositions	decomposition	NOUN
ejpam-6407	365	5	of	of	ADP
ejpam-6407	365	6	continuous	continuous	ADJ
ejpam-6407	365	7	and	and	CCONJ
ejpam-6407	365	8	some	some	DET
ejpam-6407	365	9	weakly	weakly	ADJ
ejpam-6407	365	10	continuous	continuous	ADJ
ejpam-6407	365	11	functions	function	NOUN
ejpam-6407	365	12	.	.	PUNCT
ejpam-6407	366	1	acta	acta	PROPN
ejpam-6407	366	2	mathematica	mathematica	PROPN
ejpam-6407	366	3	hungarica	hungarica	PROPN
ejpam-6407	366	4	,	,	PUNCT
ejpam-6407	366	5	71(1	71(1	NOUN
ejpam-6407	366	6	-	-	SYM
ejpam-6407	366	7	2):109–120	2):109–120	NUM
ejpam-6407	366	8	,	,	PUNCT
ejpam-6407	366	9	1996	1996	NUM
ejpam-6407	366	10	.	.	PUNCT
ejpam-6407	367	1	[	[	X
ejpam-6407	367	2	7	7	X
ejpam-6407	367	3	]	]	PUNCT
ejpam-6407	367	4	k.	k.	PROPN
ejpam-6407	367	5	r.	r.	PROPN
ejpam-6407	367	6	gentry	gentry	PROPN
ejpam-6407	367	7	and	and	CCONJ
ejpam-6407	367	8	h.	h.	PROPN
ejpam-6407	367	9	b.	b.	PROPN
ejpam-6407	367	10	hoyle	hoyle	PROPN
ejpam-6407	367	11	,	,	PUNCT
ejpam-6407	367	12	iii	iii	X
ejpam-6407	367	13	.	.	PUNCT
ejpam-6407	367	14	somewhat	somewhat	ADV
ejpam-6407	367	15	continuous	continuous	ADJ
ejpam-6407	367	16	functions	function	NOUN
ejpam-6407	367	17	.	.	PUNCT
ejpam-6407	368	1	czechoslovak	czechoslovak	ADJ
ejpam-6407	368	2	mathematical	mathematical	PROPN
ejpam-6407	368	3	journal	journal	PROPN
ejpam-6407	368	4	,	,	PUNCT
ejpam-6407	368	5	21:5–12	21:5–12	NUM
ejpam-6407	368	6	,	,	PUNCT
ejpam-6407	368	7	1971	1971	NUM
ejpam-6407	368	8	.	.	PUNCT
ejpam-6407	369	1	[	[	X
ejpam-6407	369	2	8	8	NUM
ejpam-6407	369	3	]	]	PUNCT
ejpam-6407	369	4	z.	z.	PROPN
ejpam-6407	369	5	piotrowski	piotrowski	PROPN
ejpam-6407	369	6	.	.	PUNCT
ejpam-6407	370	1	a	a	DET
ejpam-6407	370	2	survey	survey	NOUN
ejpam-6407	370	3	of	of	ADP
ejpam-6407	370	4	results	result	NOUN
ejpam-6407	370	5	concerning	concern	VERB
ejpam-6407	370	6	generalized	generalized	ADJ
ejpam-6407	370	7	continuity	continuity	NOUN
ejpam-6407	370	8	on	on	ADP
ejpam-6407	370	9	topological	topological	ADJ
ejpam-6407	370	10	spaces	space	NOUN
ejpam-6407	370	11	.	.	PUNCT
ejpam-6407	371	1	acta	acta	PROPN
ejpam-6407	371	2	mathematica	mathematica	PROPN
ejpam-6407	371	3	universitatis	universitatis	PROPN
ejpam-6407	371	4	comenianae	comenianae	PROPN
ejpam-6407	371	5	,	,	PUNCT
ejpam-6407	371	6	52:91–110	52:91–110	NUM
ejpam-6407	371	7	,	,	PUNCT
ejpam-6407	371	8	1987	1987	NUM
ejpam-6407	371	9	.	.	PUNCT
ejpam-6407	372	1	[	[	X
ejpam-6407	372	2	9	9	NUM
ejpam-6407	372	3	]	]	X
ejpam-6407	372	4	o.	o.	PROPN
ejpam-6407	372	5	njastad	njastad	PROPN
ejpam-6407	372	6	.	.	PUNCT
ejpam-6407	373	1	on	on	ADP
ejpam-6407	373	2	some	some	DET
ejpam-6407	373	3	classes	class	NOUN
ejpam-6407	373	4	of	of	ADP
ejpam-6407	373	5	nearly	nearly	ADV
ejpam-6407	373	6	open	open	ADJ
ejpam-6407	373	7	sets	set	NOUN
ejpam-6407	373	8	.	.	PUNCT
ejpam-6407	374	1	pacific	pacific	PROPN
ejpam-6407	374	2	journal	journal	PROPN
ejpam-6407	374	3	of	of	ADP
ejpam-6407	374	4	mathematics	mathematic	NOUN
ejpam-6407	374	5	,	,	PUNCT
ejpam-6407	374	6	15:961–970	15:961–970	PROPN
ejpam-6407	374	7	,	,	PUNCT
ejpam-6407	374	8	1965	1965	NUM
ejpam-6407	374	9	.	.	PUNCT
ejpam-6407	375	1	[	[	X
ejpam-6407	375	2	10	10	NUM
ejpam-6407	375	3	]	]	X
ejpam-6407	375	4	c.	c.	PROPN
ejpam-6407	375	5	c.	c.	PROPN
ejpam-6407	375	6	pugh	pugh	PROPN
ejpam-6407	375	7	.	.	PUNCT
ejpam-6407	376	1	real	real	ADJ
ejpam-6407	376	2	mathematical	mathematical	ADJ
ejpam-6407	376	3	analysis	analysis	NOUN
ejpam-6407	376	4	.	.	PUNCT
ejpam-6407	377	1	springer	springer	NOUN
ejpam-6407	377	2	science	science	NOUN
ejpam-6407	377	3	and	and	CCONJ
ejpam-6407	377	4	business	business	NOUN
ejpam-6407	377	5	media	medium	NOUN
ejpam-6407	377	6	,	,	PUNCT
ejpam-6407	377	7	2003	2003	NUM
ejpam-6407	377	8	.	.	PUNCT
ejpam-6407	378	1	[	[	X
ejpam-6407	378	2	11	11	NUM
ejpam-6407	378	3	]	]	PUNCT
ejpam-6407	378	4	t.	t.	PROPN
ejpam-6407	378	5	m.	m.	PROPN
ejpam-6407	378	6	al	al	PROPN
ejpam-6407	378	7	-	-	PUNCT
ejpam-6407	378	8	shami	shami	PROPN
ejpam-6407	378	9	.	.	PUNCT
ejpam-6407	379	1	somewhere	somewhere	ADV
ejpam-6407	379	2	dense	dense	ADJ
ejpam-6407	379	3	sets	set	NOUN
ejpam-6407	379	4	and	and	CCONJ
ejpam-6407	379	5	st1	st1	PROPN
ejpam-6407	379	6	spaces	space	NOUN
ejpam-6407	379	7	.	.	PUNCT
ejpam-6407	380	1	punjab	punjab	PROPN
ejpam-6407	380	2	university	university	PROPN
ejpam-6407	380	3	journal	journal	NOUN
ejpam-6407	380	4	of	of	ADP
ejpam-6407	380	5	mathematics	mathematic	NOUN
ejpam-6407	380	6	,	,	PUNCT
ejpam-6407	380	7	49(2):101–111	49(2):101–111	PROPN
ejpam-6407	380	8	,	,	PUNCT
ejpam-6407	380	9	2017	2017	NUM
ejpam-6407	380	10	.	.	PUNCT
ejpam-6407	381	1	[	[	X
ejpam-6407	381	2	12	12	NUM
ejpam-6407	381	3	]	]	PUNCT
ejpam-6407	381	4	m.	m.	NOUN
ejpam-6407	381	5	h.	h.	PROPN
ejpam-6407	381	6	alqahtani	alqahtani	PROPN
ejpam-6407	381	7	.	.	PUNCT
ejpam-6407	382	1	f	f	X
ejpam-6407	382	2	-	-	PUNCT
ejpam-6407	382	3	open	open	ADJ
ejpam-6407	382	4	and	and	CCONJ
ejpam-6407	382	5	f	f	X
ejpam-6407	382	6	-	-	PUNCT
ejpam-6407	382	7	closed	close	VERB
ejpam-6407	382	8	sets	set	NOUN
ejpam-6407	382	9	in	in	ADP
ejpam-6407	382	10	topological	topological	ADJ
ejpam-6407	382	11	spaces	space	NOUN
ejpam-6407	382	12	.	.	PUNCT
ejpam-6407	383	1	european	european	ADJ
ejpam-6407	383	2	journal	journal	PROPN
ejpam-6407	383	3	of	of	ADP
ejpam-6407	383	4	pure	pure	ADJ
ejpam-6407	383	5	and	and	CCONJ
ejpam-6407	383	6	applied	applied	ADJ
ejpam-6407	383	7	mathematics	mathematic	NOUN
ejpam-6407	383	8	,	,	PUNCT
ejpam-6407	383	9	16:819–832	16:819–832	NUM
ejpam-6407	383	10	,	,	PUNCT
ejpam-6407	383	11	2023	2023	NUM
ejpam-6407	383	12	.	.	PUNCT
ejpam-6407	384	1	[	[	X
ejpam-6407	384	2	13	13	NUM
ejpam-6407	384	3	]	]	PUNCT
ejpam-6407	384	4	m.	m.	NOUN
ejpam-6407	384	5	h.	h.	PROPN
ejpam-6407	384	6	alqahtani	alqahtani	PROPN
ejpam-6407	384	7	and	and	CCONJ
ejpam-6407	384	8	a.	a.	NOUN
ejpam-6407	384	9	m.	m.	PROPN
ejpam-6407	384	10	abd	abd	PROPN
ejpam-6407	384	11	el	el	PROPN
ejpam-6407	384	12	-	-	PROPN
ejpam-6407	384	13	latif	latif	PROPN
ejpam-6407	384	14	.	.	PUNCT
ejpam-6407	385	1	separation	separation	NOUN
ejpam-6407	385	2	axioms	axiom	NOUN
ejpam-6407	385	3	via	via	ADP
ejpam-6407	385	4	novel	novel	ADJ
ejpam-6407	385	5	operators	operator	NOUN
ejpam-6407	385	6	in	in	ADP
ejpam-6407	385	7	the	the	DET
ejpam-6407	385	8	frame	frame	NOUN
ejpam-6407	385	9	of	of	ADP
ejpam-6407	385	10	topological	topological	ADJ
ejpam-6407	385	11	spaces	space	NOUN
ejpam-6407	385	12	and	and	CCONJ
ejpam-6407	385	13	applications	application	NOUN
ejpam-6407	385	14	.	.	PUNCT
ejpam-6407	386	1	aims	aim	VERB
ejpam-6407	386	2	mathematics	mathematic	NOUN
ejpam-6407	386	3	,	,	PUNCT
ejpam-6407	386	4	9(6):14213–14227	9(6):14213–14227	NUM
ejpam-6407	386	5	,	,	PUNCT
ejpam-6407	386	6	2024	2024	NUM
ejpam-6407	386	7	.	.	PUNCT
ejpam-6407	387	1	[	[	X
ejpam-6407	387	2	14	14	NUM
ejpam-6407	387	3	]	]	X
ejpam-6407	387	4	o.	o.	NOUN
ejpam-6407	387	5	alghamdi	alghamdi	NOUN
ejpam-6407	387	6	,	,	PUNCT
ejpam-6407	387	7	ahmad	ahmad	PROPN
ejpam-6407	387	8	al	al	PROPN
ejpam-6407	387	9	-	-	PUNCT
ejpam-6407	387	10	omari	omari	PROPN
ejpam-6407	387	11	,	,	PUNCT
ejpam-6407	387	12	and	and	CCONJ
ejpam-6407	387	13	m.	m.	PROPN
ejpam-6407	387	14	h.	h.	PROPN
ejpam-6407	387	15	alqahtani	alqahtani	PROPN
ejpam-6407	387	16	.	.	PUNCT
ejpam-6407	388	1	novel	novel	ADJ
ejpam-6407	388	2	operators	operator	NOUN
ejpam-6407	388	3	in	in	ADP
ejpam-6407	388	4	the	the	DET
ejpam-6407	388	5	frame	frame	NOUN
ejpam-6407	388	6	of	of	ADP
ejpam-6407	388	7	primal	primal	ADJ
ejpam-6407	388	8	topological	topological	ADJ
ejpam-6407	388	9	spaces	space	NOUN
ejpam-6407	388	10	.	.	PUNCT
ejpam-6407	389	1	aims	aim	VERB
ejpam-6407	389	2	mathematics	mathematic	NOUN
ejpam-6407	389	3	,	,	PUNCT
ejpam-6407	389	4	9(9):25792–25808	9(9):25792–25808	NUM
ejpam-6407	389	5	,	,	PUNCT
ejpam-6407	389	6	2024	2024	NUM
ejpam-6407	389	7	.	.	PUNCT
ejpam-6407	390	1	[	[	X
ejpam-6407	390	2	15	15	NUM
ejpam-6407	390	3	]	]	X
ejpam-6407	390	4	a.	a.	NOUN
ejpam-6407	390	5	s.	s.	PROPN
ejpam-6407	390	6	mashhour	mashhour	PROPN
ejpam-6407	390	7	,	,	PUNCT
ejpam-6407	390	8	a.	a.	PROPN
ejpam-6407	390	9	a.	a.	PROPN
ejpam-6407	390	10	allam	allam	PROPN
ejpam-6407	390	11	,	,	PUNCT
ejpam-6407	390	12	f.	f.	PROPN
ejpam-6407	390	13	s.	s.	PROPN
ejpam-6407	390	14	mahmoud	mahmoud	PROPN
ejpam-6407	390	15	,	,	PUNCT
ejpam-6407	390	16	and	and	CCONJ
ejpam-6407	390	17	f.	f.	PROPN
ejpam-6407	390	18	h.	h.	PROPN
ejpam-6407	390	19	kheder	kheder	PROPN
ejpam-6407	390	20	.	.	PUNCT
ejpam-6407	391	1	on	on	ADP
ejpam-6407	391	2	supra	supra	PROPN
ejpam-6407	391	3	topological	topological	ADJ
ejpam-6407	391	4	spaces	space	NOUN
ejpam-6407	391	5	.	.	PUNCT
ejpam-6407	392	1	indian	indian	ADJ
ejpam-6407	392	2	journal	journal	PROPN
ejpam-6407	392	3	of	of	ADP
ejpam-6407	392	4	pure	pure	ADJ
ejpam-6407	392	5	and	and	CCONJ
ejpam-6407	392	6	applied	applied	ADJ
ejpam-6407	392	7	mathematics	mathematic	NOUN
ejpam-6407	392	8	,	,	PUNCT
ejpam-6407	392	9	pages	page	NOUN
ejpam-6407	392	10	502–510	502–510	NUM
ejpam-6407	392	11	,	,	PUNCT
ejpam-6407	392	12	1983	1983	NUM
ejpam-6407	392	13	.	.	PUNCT
ejpam-6407	393	1	m.	m.	NOUN
ejpam-6407	393	2	aldawood	aldawood	PROPN
ejpam-6407	393	3	et	et	PROPN
ejpam-6407	393	4	al	al	PROPN
ejpam-6407	393	5	.	.	PUNCT
ejpam-6407	393	6	/	/	SYM
ejpam-6407	393	7	eur	eur	PROPN
ejpam-6407	393	8	.	.	PUNCT
ejpam-6407	394	1	j.	j.	PROPN
ejpam-6407	394	2	pure	pure	PROPN
ejpam-6407	394	3	appl	appl	PROPN
ejpam-6407	394	4	.	.	PROPN
ejpam-6407	394	5	math	math	PROPN
ejpam-6407	394	6	,	,	PUNCT
ejpam-6407	394	7	18	18	NUM
ejpam-6407	394	8	(	(	PUNCT
ejpam-6407	394	9	3	3	NUM
ejpam-6407	394	10	)	)	PUNCT
ejpam-6407	394	11	(	(	PUNCT
ejpam-6407	394	12	2025	2025	NUM
ejpam-6407	394	13	)	)	PUNCT
ejpam-6407	394	14	,	,	PUNCT
ejpam-6407	394	15	6407	6407	NUM
ejpam-6407	394	16	13	13	NUM
ejpam-6407	394	17	of	of	ADP
ejpam-6407	394	18	15	15	NUM
ejpam-6407	395	1	[	[	X
ejpam-6407	395	2	16	16	NUM
ejpam-6407	395	3	]	]	PUNCT
ejpam-6407	395	4	t.	t.	PROPN
ejpam-6407	395	5	al	al	PROPN
ejpam-6407	395	6	-	-	PUNCT
ejpam-6407	395	7	shami	shami	PROPN
ejpam-6407	395	8	.	.	PUNCT
ejpam-6407	396	1	on	on	ADP
ejpam-6407	396	2	supra	supra	PROPN
ejpam-6407	396	3	semi	semi	ADV
ejpam-6407	396	4	open	open	ADJ
ejpam-6407	396	5	sets	set	NOUN
ejpam-6407	396	6	and	and	CCONJ
ejpam-6407	396	7	some	some	DET
ejpam-6407	396	8	applications	application	NOUN
ejpam-6407	396	9	on	on	ADP
ejpam-6407	396	10	topological	topological	ADJ
ejpam-6407	396	11	spaces	space	NOUN
ejpam-6407	396	12	.	.	PUNCT
ejpam-6407	397	1	journal	journal	NOUN
ejpam-6407	397	2	of	of	ADP
ejpam-6407	397	3	advanced	advanced	ADJ
ejpam-6407	397	4	studies	study	NOUN
ejpam-6407	397	5	in	in	ADP
ejpam-6407	397	6	topology	topology	NOUN
ejpam-6407	397	7	,	,	PUNCT
ejpam-6407	397	8	8(2):144–153	8(2):144–153	NOUN
ejpam-6407	397	9	,	,	PUNCT
ejpam-6407	397	10	2017	2017	NUM
ejpam-6407	397	11	.	.	PUNCT
ejpam-6407	398	1	[	[	X
ejpam-6407	398	2	17	17	NUM
ejpam-6407	398	3	]	]	PUNCT
ejpam-6407	398	4	m.	m.	PROPN
ejpam-6407	398	5	e.	e.	PROPN
ejpam-6407	398	6	el	el	PROPN
ejpam-6407	398	7	-	-	PROPN
ejpam-6407	398	8	shafei	shafei	PROPN
ejpam-6407	398	9	,	,	PUNCT
ejpam-6407	398	10	m.	m.	NOUN
ejpam-6407	398	11	abo	abo	NOUN
ejpam-6407	398	12	-	-	PUNCT
ejpam-6407	398	13	elhamayel	elhamayel	NOUN
ejpam-6407	398	14	,	,	PUNCT
ejpam-6407	398	15	and	and	CCONJ
ejpam-6407	398	16	t.	t.	PROPN
ejpam-6407	398	17	m.	m.	PROPN
ejpam-6407	398	18	al	al	PROPN
ejpam-6407	398	19	-	-	PUNCT
ejpam-6407	398	20	shami	shami	PROPN
ejpam-6407	398	21	.	.	PUNCT
ejpam-6407	399	1	on	on	ADP
ejpam-6407	399	2	supra	supra	PROPN
ejpam-6407	399	3	r	r	NOUN
ejpam-6407	399	4	-	-	PUNCT
ejpam-6407	399	5	open	open	ADJ
ejpam-6407	399	6	sets	set	NOUN
ejpam-6407	399	7	and	and	CCONJ
ejpam-6407	399	8	some	some	DET
ejpam-6407	399	9	applications	application	NOUN
ejpam-6407	399	10	on	on	ADP
ejpam-6407	399	11	topological	topological	ADJ
ejpam-6407	399	12	spaces	space	NOUN
ejpam-6407	399	13	.	.	PUNCT
ejpam-6407	400	1	journal	journal	NOUN
ejpam-6407	400	2	of	of	ADP
ejpam-6407	400	3	progressive	progressive	ADJ
ejpam-6407	400	4	research	research	NOUN
ejpam-6407	400	5	in	in	ADP
ejpam-6407	400	6	mathematics	mathematic	NOUN
ejpam-6407	400	7	,	,	PUNCT
ejpam-6407	400	8	8:1237–1248	8:1237–1248	NUM
ejpam-6407	400	9	,	,	PUNCT
ejpam-6407	400	10	2016	2016	NUM
ejpam-6407	400	11	.	.	PUNCT
ejpam-6407	401	1	[	[	X
ejpam-6407	401	2	18	18	NUM
ejpam-6407	401	3	]	]	X
ejpam-6407	401	4	s.	s.	PROPN
ejpam-6407	401	5	jafari	jafari	PROPN
ejpam-6407	401	6	and	and	CCONJ
ejpam-6407	401	7	s.	s.	PROPN
ejpam-6407	401	8	tahiliani	tahiliani	PROPN
ejpam-6407	401	9	.	.	PUNCT
ejpam-6407	402	1	supra	supra	PROPN
ejpam-6407	402	2	β	β	X
ejpam-6407	402	3	-	-	ADJ
ejpam-6407	402	4	open	open	ADJ
ejpam-6407	402	5	sets	set	NOUN
ejpam-6407	402	6	and	and	CCONJ
ejpam-6407	402	7	supra	supra	ADJ
ejpam-6407	402	8	β	β	NOUN
ejpam-6407	402	9	-	-	NOUN
ejpam-6407	402	10	continuity	continuity	NOUN
ejpam-6407	402	11	on	on	ADP
ejpam-6407	402	12	topological	topological	ADJ
ejpam-6407	402	13	spaces	space	NOUN
ejpam-6407	402	14	.	.	PUNCT
ejpam-6407	403	1	annales	annales	PROPN
ejpam-6407	403	2	universitatis	universitatis	PROPN
ejpam-6407	403	3	scientiarum	scientiarum	PROPN
ejpam-6407	403	4	budapestinensis	budapestinensis	PROPN
ejpam-6407	403	5	,	,	PUNCT
ejpam-6407	403	6	56:1–9	56:1–9	NUM
ejpam-6407	403	7	,	,	PUNCT
ejpam-6407	403	8	2013	2013	NUM
ejpam-6407	403	9	.	.	PUNCT
ejpam-6407	404	1	[	[	X
ejpam-6407	404	2	19	19	NUM
ejpam-6407	404	3	]	]	X
ejpam-6407	404	4	o.	o.	PROPN
ejpam-6407	404	5	r.	r.	PROPN
ejpam-6407	404	6	sayed	sayed	PROPN
ejpam-6407	404	7	and	and	CCONJ
ejpam-6407	404	8	t.	t.	PROPN
ejpam-6407	404	9	noiri	noiri	PROPN
ejpam-6407	404	10	.	.	PUNCT
ejpam-6407	405	1	on	on	ADP
ejpam-6407	405	2	supra	supra	PROPN
ejpam-6407	405	3	b	b	PROPN
ejpam-6407	405	4	-	-	PUNCT
ejpam-6407	405	5	open	open	ADJ
ejpam-6407	405	6	sets	set	NOUN
ejpam-6407	405	7	and	and	CCONJ
ejpam-6407	405	8	supra	supra	PROPN
ejpam-6407	405	9	b	b	NOUN
ejpam-6407	405	10	-	-	PUNCT
ejpam-6407	405	11	continuity	continuity	NOUN
ejpam-6407	405	12	on	on	ADP
ejpam-6407	405	13	topological	topological	ADJ
ejpam-6407	405	14	spaces	space	NOUN
ejpam-6407	405	15	.	.	PUNCT
ejpam-6407	406	1	european	european	ADJ
ejpam-6407	406	2	journal	journal	PROPN
ejpam-6407	406	3	of	of	ADP
ejpam-6407	406	4	pure	pure	ADJ
ejpam-6407	406	5	and	and	CCONJ
ejpam-6407	406	6	applied	applied	ADJ
ejpam-6407	406	7	mathematics	mathematic	NOUN
ejpam-6407	406	8	,	,	PUNCT
ejpam-6407	406	9	3:295–302	3:295–302	NUM
ejpam-6407	406	10	,	,	PUNCT
ejpam-6407	406	11	2010	2010	NUM
ejpam-6407	406	12	.	.	PUNCT
ejpam-6407	407	1	[	[	X
ejpam-6407	407	2	20	20	NUM
ejpam-6407	407	3	]	]	X
ejpam-6407	407	4	o.	o.	PROPN
ejpam-6407	407	5	r.	r.	PROPN
ejpam-6407	407	6	sayed	say	VERB
ejpam-6407	407	7	.	.	PUNCT
ejpam-6407	408	1	supra	supra	PROPN
ejpam-6407	408	2	pre	pre	ADJ
ejpam-6407	408	3	-	-	ADJ
ejpam-6407	408	4	open	open	ADJ
ejpam-6407	408	5	sets	set	NOUN
ejpam-6407	408	6	and	and	CCONJ
ejpam-6407	408	7	supra	supra	NOUN
ejpam-6407	408	8	pre	pre	ADJ
ejpam-6407	408	9	-	-	ADJ
ejpam-6407	408	10	continuous	continuous	ADJ
ejpam-6407	408	11	on	on	ADP
ejpam-6407	408	12	topological	topological	ADJ
ejpam-6407	408	13	spaces	space	NOUN
ejpam-6407	408	14	.	.	PUNCT
ejpam-6407	409	1	series	series	PROPN
ejpam-6407	409	2	mathematics	mathematics	PROPN
ejpam-6407	409	3	and	and	CCONJ
ejpam-6407	409	4	information	information	NOUN
ejpam-6407	409	5	,	,	PUNCT
ejpam-6407	409	6	20:79–88	20:79–88	NUM
ejpam-6407	409	7	,	,	PUNCT
ejpam-6407	409	8	2010	2010	NUM
ejpam-6407	409	9	.	.	PUNCT
ejpam-6407	410	1	[	[	X
ejpam-6407	410	2	21	21	NUM
ejpam-6407	410	3	]	]	X
ejpam-6407	410	4	r.	r.	PROPN
ejpam-6407	410	5	devi	devi	PROPN
ejpam-6407	410	6	,	,	PUNCT
ejpam-6407	410	7	s.	s.	PROPN
ejpam-6407	410	8	sampathkumar	sampathkumar	PROPN
ejpam-6407	410	9	,	,	PUNCT
ejpam-6407	410	10	and	and	CCONJ
ejpam-6407	410	11	m.	m.	PROPN
ejpam-6407	410	12	caldas	caldas	PROPN
ejpam-6407	410	13	.	.	PUNCT
ejpam-6407	411	1	on	on	ADP
ejpam-6407	411	2	α	α	NOUN
ejpam-6407	411	3	-	-	ADJ
ejpam-6407	411	4	open	open	ADJ
ejpam-6407	411	5	sets	set	NOUN
ejpam-6407	411	6	and	and	CCONJ
ejpam-6407	411	7	sa	sa	NOUN
ejpam-6407	411	8	-	-	ADJ
ejpam-6407	411	9	continuous	continuous	ADJ
ejpam-6407	411	10	maps	map	NOUN
ejpam-6407	411	11	.	.	PUNCT
ejpam-6407	412	1	general	general	ADJ
ejpam-6407	412	2	mathematics	mathematics	PROPN
ejpam-6407	412	3	,	,	PUNCT
ejpam-6407	412	4	16:77–84	16:77–84	NOUN
ejpam-6407	412	5	,	,	PUNCT
ejpam-6407	412	6	2008	2008	NUM
ejpam-6407	412	7	.	.	PUNCT
ejpam-6407	413	1	[	[	X
ejpam-6407	413	2	22	22	NUM
ejpam-6407	413	3	]	]	PUNCT
ejpam-6407	413	4	a.	a.	NOUN
ejpam-6407	413	5	m.	m.	PROPN
ejpam-6407	413	6	abd	abd	PROPN
ejpam-6407	414	1	el	el	PROPN
ejpam-6407	414	2	-	-	PROPN
ejpam-6407	414	3	latif	latif	PROPN
ejpam-6407	414	4	,	,	PUNCT
ejpam-6407	414	5	radwan	radwan	VERB
ejpam-6407	414	6	abu	abu	PROPN
ejpam-6407	414	7	-	-	PUNCT
ejpam-6407	414	8	gdairi	gdairi	PROPN
ejpam-6407	414	9	,	,	PUNCT
ejpam-6407	415	1	a.	a.	PROPN
ejpam-6407	415	2	a.	a.	PROPN
ejpam-6407	415	3	azzam	azzam	PROPN
ejpam-6407	415	4	,	,	PUNCT
ejpam-6407	415	5	husham	husham	PROPN
ejpam-6407	415	6	m.	m.	PROPN
ejpam-6407	415	7	attaalfadeel	attaalfadeel	PROPN
ejpam-6407	415	8	,	,	PUNCT
ejpam-6407	415	9	shaaban	shaaban	ADJ
ejpam-6407	415	10	m.	m.	NOUN
ejpam-6407	415	11	shaaban	shaaban	PROPN
ejpam-6407	415	12	,	,	PUNCT
ejpam-6407	415	13	m.	m.	NOUN
ejpam-6407	415	14	aldawood	aldawood	PROPN
ejpam-6407	415	15	,	,	PUNCT
ejpam-6407	415	16	and	and	CCONJ
ejpam-6407	415	17	khaled	khaled	PROPN
ejpam-6407	415	18	a.	a.	PROPN
ejpam-6407	415	19	aldwoah	aldwoah	PROPN
ejpam-6407	415	20	.	.	PUNCT
ejpam-6407	416	1	supra	supra	PROPN
ejpam-6407	416	2	ϵ-open	ϵ-open	PROPN
ejpam-6407	416	3	sets	set	NOUN
ejpam-6407	416	4	:	:	PUNCT
ejpam-6407	416	5	features	feature	NOUN
ejpam-6407	416	6	,	,	PUNCT
ejpam-6407	416	7	operators	operator	NOUN
ejpam-6407	416	8	and	and	CCONJ
ejpam-6407	416	9	applications	application	NOUN
ejpam-6407	416	10	.	.	PUNCT
ejpam-6407	417	1	european	european	ADJ
ejpam-6407	417	2	journal	journal	PROPN
ejpam-6407	417	3	of	of	ADP
ejpam-6407	417	4	pure	pure	ADJ
ejpam-6407	417	5	and	and	CCONJ
ejpam-6407	417	6	applied	applied	ADJ
ejpam-6407	417	7	mathematics	mathematic	NOUN
ejpam-6407	417	8	,	,	PUNCT
ejpam-6407	417	9	18(2):5969	18(2):5969	NUM
ejpam-6407	417	10	,	,	PUNCT
ejpam-6407	417	11	2025	2025	NUM
ejpam-6407	417	12	.	.	PUNCT
ejpam-6407	418	1	[	[	X
ejpam-6407	418	2	23	23	NUM
ejpam-6407	418	3	]	]	PUNCT
ejpam-6407	418	4	a.	a.	NOUN
ejpam-6407	418	5	m.	m.	PROPN
ejpam-6407	418	6	abd	abd	PROPN
ejpam-6407	418	7	el	el	PROPN
ejpam-6407	418	8	-	-	PROPN
ejpam-6407	418	9	latif	latif	PROPN
ejpam-6407	418	10	,	,	PUNCT
ejpam-6407	418	11	radwan	radwan	VERB
ejpam-6407	418	12	abu	abu	PROPN
ejpam-6407	418	13	-	-	PUNCT
ejpam-6407	418	14	gdairi	gdairi	PROPN
ejpam-6407	418	15	,	,	PUNCT
ejpam-6407	418	16	abd	abd	PROPN
ejpam-6407	418	17	elfattah	elfattah	PROPN
ejpam-6407	418	18	azzam	azzam	PROPN
ejpam-6407	418	19	,	,	PUNCT
ejpam-6407	418	20	fatouh	fatouh	PROPN
ejpam-6407	418	21	gharib	gharib	PROPN
ejpam-6407	418	22	,	,	PUNCT
ejpam-6407	418	23	husham	husham	PROPN
ejpam-6407	418	24	mohammed	mohammed	PROPN
ejpam-6407	418	25	alhassan	alhassan	PROPN
ejpam-6407	418	26	attaalfadeel	attaalfadeel	PROPN
ejpam-6407	418	27	,	,	PUNCT
ejpam-6407	418	28	walid	walid	PROPN
ejpam-6407	418	29	abdelfattah	abdelfattah	PROPN
ejpam-6407	418	30	,	,	PUNCT
ejpam-6407	418	31	shaaban	shaaban	ADJ
ejpam-6407	418	32	m.	m.	NOUN
ejpam-6407	418	33	shaaban	shaaban	PROPN
ejpam-6407	418	34	,	,	PUNCT
ejpam-6407	418	35	and	and	CCONJ
ejpam-6407	418	36	m.	m.	PROPN
ejpam-6407	418	37	aldawood	aldawood	PROPN
ejpam-6407	418	38	.	.	PUNCT
ejpam-6407	419	1	novel	novel	ADJ
ejpam-6407	419	2	types	type	NOUN
ejpam-6407	419	3	of	of	ADP
ejpam-6407	419	4	supra	supra	ADJ
ejpam-6407	419	5	functions	function	NOUN
ejpam-6407	419	6	inspired	inspire	VERB
ejpam-6407	419	7	by	by	ADP
ejpam-6407	419	8	supra	supra	PROPN
ejpam-6407	419	9	ϵ-open	ϵ-open	PROPN
ejpam-6407	419	10	sets	set	NOUN
ejpam-6407	419	11	.	.	PUNCT
ejpam-6407	420	1	european	european	ADJ
ejpam-6407	420	2	journal	journal	PROPN
ejpam-6407	420	3	of	of	ADP
ejpam-6407	420	4	pure	pure	ADJ
ejpam-6407	420	5	and	and	CCONJ
ejpam-6407	420	6	applied	applied	ADJ
ejpam-6407	420	7	mathematics	mathematic	NOUN
ejpam-6407	420	8	,	,	PUNCT
ejpam-6407	420	9	18(2):6020	18(2):6020	NUM
ejpam-6407	420	10	,	,	PUNCT
ejpam-6407	420	11	2025	2025	NUM
ejpam-6407	420	12	.	.	PUNCT
ejpam-6407	421	1	[	[	X
ejpam-6407	421	2	24	24	NUM
ejpam-6407	421	3	]	]	PUNCT
ejpam-6407	421	4	m.	m.	NOUN
ejpam-6407	421	5	shabir	shabir	PROPN
ejpam-6407	421	6	and	and	CCONJ
ejpam-6407	421	7	m.	m.	PROPN
ejpam-6407	421	8	naz	naz	PROPN
ejpam-6407	421	9	.	.	PUNCT
ejpam-6407	422	1	on	on	ADP
ejpam-6407	422	2	soft	soft	ADJ
ejpam-6407	422	3	topological	topological	ADJ
ejpam-6407	422	4	spaces	space	NOUN
ejpam-6407	422	5	.	.	PUNCT
ejpam-6407	423	1	computers	computer	NOUN
ejpam-6407	423	2	and	and	CCONJ
ejpam-6407	423	3	mathematics	mathematic	NOUN
ejpam-6407	423	4	with	with	ADP
ejpam-6407	423	5	applications	application	NOUN
ejpam-6407	423	6	,	,	PUNCT
ejpam-6407	423	7	61:1786–1799	61:1786–1799	NUM
ejpam-6407	423	8	,	,	PUNCT
ejpam-6407	423	9	2011	2011	NUM
ejpam-6407	423	10	.	.	PUNCT
ejpam-6407	424	1	[	[	X
ejpam-6407	424	2	25	25	NUM
ejpam-6407	424	3	]	]	PUNCT
ejpam-6407	424	4	zanyar	zanyar	PROPN
ejpam-6407	424	5	a.	a.	NOUN
ejpam-6407	424	6	ameen	ameen	PROPN
ejpam-6407	424	7	and	and	CCONJ
ejpam-6407	424	8	s.	s.	PROPN
ejpam-6407	424	9	al	al	PROPN
ejpam-6407	424	10	ghour	ghour	PROPN
ejpam-6407	424	11	.	.	PUNCT
ejpam-6407	425	1	cluster	cluster	NOUN
ejpam-6407	425	2	soft	soft	ADJ
ejpam-6407	425	3	sets	set	NOUN
ejpam-6407	425	4	and	and	CCONJ
ejpam-6407	425	5	cluster	cluster	NOUN
ejpam-6407	425	6	soft	soft	ADJ
ejpam-6407	425	7	topologies	topology	NOUN
ejpam-6407	425	8	.	.	PUNCT
ejpam-6407	426	1	computational	computational	ADJ
ejpam-6407	426	2	and	and	CCONJ
ejpam-6407	426	3	applied	applied	ADJ
ejpam-6407	426	4	mathematics	mathematic	NOUN
ejpam-6407	426	5	,	,	PUNCT
ejpam-6407	426	6	42:337	42:337	NUM
ejpam-6407	426	7	,	,	PUNCT
ejpam-6407	426	8	2023	2023	NUM
ejpam-6407	426	9	.	.	PUNCT
ejpam-6407	427	1	[	[	X
ejpam-6407	427	2	26	26	NUM
ejpam-6407	427	3	]	]	PUNCT
ejpam-6407	427	4	a.	a.	NOUN
ejpam-6407	427	5	kandil	kandil	PROPN
ejpam-6407	427	6	,	,	PUNCT
ejpam-6407	427	7	o.	o.	PROPN
ejpam-6407	427	8	a.	a.	PROPN
ejpam-6407	427	9	e.	e.	PROPN
ejpam-6407	427	10	tantawy	tantawy	PROPN
ejpam-6407	427	11	,	,	PUNCT
ejpam-6407	427	12	s.	s.	PROPN
ejpam-6407	427	13	a.	a.	PROPN
ejpam-6407	427	14	el	el	PROPN
ejpam-6407	427	15	-	-	PUNCT
ejpam-6407	427	16	sheikh	sheikh	NOUN
ejpam-6407	427	17	,	,	PUNCT
ejpam-6407	427	18	and	and	CCONJ
ejpam-6407	427	19	a.	a.	NOUN
ejpam-6407	427	20	m.	m.	PROPN
ejpam-6407	427	21	abd	abd	PROPN
ejpam-6407	427	22	el	el	PROPN
ejpam-6407	427	23	-	-	PROPN
ejpam-6407	427	24	latif	latif	PROPN
ejpam-6407	427	25	.	.	PUNCT
ejpam-6407	428	1	soft	soft	ADJ
ejpam-6407	428	2	semi	semi	ADJ
ejpam-6407	428	3	separation	separation	NOUN
ejpam-6407	428	4	axioms	axiom	NOUN
ejpam-6407	428	5	and	and	CCONJ
ejpam-6407	428	6	irresolute	irresolute	ADJ
ejpam-6407	428	7	soft	soft	ADJ
ejpam-6407	428	8	functions	function	NOUN
ejpam-6407	428	9	.	.	PUNCT
ejpam-6407	429	1	annals	annal	NOUN
ejpam-6407	429	2	of	of	ADP
ejpam-6407	429	3	fuzzy	fuzzy	ADJ
ejpam-6407	429	4	mathematics	mathematic	NOUN
ejpam-6407	429	5	and	and	CCONJ
ejpam-6407	429	6	informatics	informatic	NOUN
ejpam-6407	429	7	,	,	PUNCT
ejpam-6407	429	8	8(2):305–318	8(2):305–318	NUM
ejpam-6407	429	9	,	,	PUNCT
ejpam-6407	429	10	2014	2014	NUM
ejpam-6407	429	11	.	.	PUNCT
ejpam-6407	430	1	[	[	X
ejpam-6407	430	2	27	27	NUM
ejpam-6407	430	3	]	]	X
ejpam-6407	430	4	tareq	tareq	PROPN
ejpam-6407	430	5	m.	m.	PROPN
ejpam-6407	430	6	al	al	PROPN
ejpam-6407	430	7	-	-	PUNCT
ejpam-6407	430	8	shami	shami	PROPN
ejpam-6407	430	9	,	,	PUNCT
ejpam-6407	430	10	abdelwaheb	abdelwaheb	PROPN
ejpam-6407	430	11	mhemdi	mhemdi	PROPN
ejpam-6407	430	12	,	,	PUNCT
ejpam-6407	430	13	and	and	CCONJ
ejpam-6407	430	14	radwan	radwan	VERB
ejpam-6407	430	15	abu	abu	PROPN
ejpam-6407	430	16	-	-	PUNCT
ejpam-6407	430	17	gdairi	gdairi	PROPN
ejpam-6407	430	18	.	.	PUNCT
ejpam-6407	431	1	a	a	DET
ejpam-6407	431	2	novel	novel	ADJ
ejpam-6407	431	3	framework	framework	NOUN
ejpam-6407	431	4	for	for	ADP
ejpam-6407	431	5	generalizations	generalization	NOUN
ejpam-6407	431	6	of	of	ADP
ejpam-6407	431	7	soft	soft	ADJ
ejpam-6407	431	8	open	open	ADJ
ejpam-6407	431	9	sets	set	NOUN
ejpam-6407	431	10	and	and	CCONJ
ejpam-6407	431	11	its	its	PRON
ejpam-6407	431	12	applications	application	NOUN
ejpam-6407	431	13	via	via	ADP
ejpam-6407	431	14	soft	soft	ADJ
ejpam-6407	431	15	topologies	topology	NOUN
ejpam-6407	431	16	.	.	PUNCT
ejpam-6407	432	1	mathematics	mathematic	NOUN
ejpam-6407	432	2	,	,	PUNCT
ejpam-6407	432	3	11(4):840	11(4):840	NOUN
ejpam-6407	432	4	,	,	PUNCT
ejpam-6407	432	5	2023	2023	NUM
ejpam-6407	432	6	.	.	PUNCT
ejpam-6407	433	1	[	[	X
ejpam-6407	433	2	28	28	NUM
ejpam-6407	433	3	]	]	X
ejpam-6407	433	4	a.	a.	NOUN
ejpam-6407	433	5	kandil	kandil	PROPN
ejpam-6407	433	6	,	,	PUNCT
ejpam-6407	433	7	o.	o.	PROPN
ejpam-6407	433	8	a.	a.	PROPN
ejpam-6407	433	9	e.	e.	PROPN
ejpam-6407	433	10	tantawy	tantawy	PROPN
ejpam-6407	433	11	,	,	PUNCT
ejpam-6407	433	12	s.	s.	PROPN
ejpam-6407	433	13	a.	a.	PROPN
ejpam-6407	433	14	el	el	PROPN
ejpam-6407	433	15	-	-	PUNCT
ejpam-6407	433	16	sheikh	sheikh	NOUN
ejpam-6407	433	17	,	,	PUNCT
ejpam-6407	433	18	and	and	CCONJ
ejpam-6407	433	19	a.	a.	NOUN
ejpam-6407	433	20	m.	m.	PROPN
ejpam-6407	433	21	abd	abd	PROPN
ejpam-6407	433	22	el	el	PROPN
ejpam-6407	433	23	-	-	PROPN
ejpam-6407	433	24	latif	latif	PROPN
ejpam-6407	433	25	.	.	PUNCT
ejpam-6407	434	1	γ	γ	PROPN
ejpam-6407	434	2	-	-	PUNCT
ejpam-6407	434	3	operation	operation	NOUN
ejpam-6407	434	4	and	and	CCONJ
ejpam-6407	434	5	decompositions	decomposition	NOUN
ejpam-6407	434	6	of	of	ADP
ejpam-6407	434	7	some	some	DET
ejpam-6407	434	8	forms	form	NOUN
ejpam-6407	434	9	of	of	ADP
ejpam-6407	434	10	soft	soft	ADJ
ejpam-6407	434	11	continuity	continuity	NOUN
ejpam-6407	434	12	in	in	ADP
ejpam-6407	434	13	soft	soft	ADJ
ejpam-6407	434	14	topological	topological	ADJ
ejpam-6407	434	15	spaces	space	NOUN
ejpam-6407	434	16	.	.	PUNCT
ejpam-6407	435	1	annals	annal	NOUN
ejpam-6407	435	2	of	of	ADP
ejpam-6407	435	3	fuzzy	fuzzy	ADJ
ejpam-6407	435	4	mathematics	mathematic	NOUN
ejpam-6407	435	5	and	and	CCONJ
ejpam-6407	435	6	informatics	informatic	NOUN
ejpam-6407	435	7	,	,	PUNCT
ejpam-6407	435	8	7(2):181–196	7(2):181–196	NUM
ejpam-6407	435	9	,	,	PUNCT
ejpam-6407	435	10	2014	2014	NUM
ejpam-6407	435	11	.	.	PUNCT
ejpam-6407	436	1	[	[	X
ejpam-6407	436	2	29	29	NUM
ejpam-6407	436	3	]	]	PUNCT
ejpam-6407	436	4	s.	s.	PROPN
ejpam-6407	436	5	a.	a.	PROPN
ejpam-6407	436	6	el	el	PROPN
ejpam-6407	436	7	-	-	PUNCT
ejpam-6407	436	8	sheikh	sheikh	PROPN
ejpam-6407	436	9	and	and	CCONJ
ejpam-6407	436	10	a.	a.	NOUN
ejpam-6407	436	11	m.	m.	NOUN
ejpam-6407	436	12	abd	abd	PROPN
ejpam-6407	436	13	el	el	PROPN
ejpam-6407	436	14	-	-	PROPN
ejpam-6407	436	15	latif	latif	PROPN
ejpam-6407	436	16	.	.	PUNCT
ejpam-6407	437	1	characterization	characterization	NOUN
ejpam-6407	437	2	of	of	ADP
ejpam-6407	437	3	b	b	NOUN
ejpam-6407	437	4	-	-	PUNCT
ejpam-6407	437	5	open	open	ADJ
ejpam-6407	437	6	soft	soft	ADJ
ejpam-6407	437	7	sets	set	NOUN
ejpam-6407	437	8	in	in	ADP
ejpam-6407	437	9	soft	soft	ADJ
ejpam-6407	437	10	topological	topological	ADJ
ejpam-6407	437	11	spaces	space	NOUN
ejpam-6407	437	12	.	.	PUNCT
ejpam-6407	438	1	journal	journal	NOUN
ejpam-6407	438	2	of	of	ADP
ejpam-6407	438	3	new	new	ADJ
ejpam-6407	438	4	theory	theory	NOUN
ejpam-6407	438	5	,	,	PUNCT
ejpam-6407	438	6	2:8–18	2:8–18	NUM
ejpam-6407	438	7	,	,	PUNCT
ejpam-6407	438	8	2015	2015	NUM
ejpam-6407	438	9	.	.	PUNCT
ejpam-6407	439	1	[	[	X
ejpam-6407	439	2	30	30	NUM
ejpam-6407	439	3	]	]	PUNCT
ejpam-6407	439	4	t.	t.	PROPN
ejpam-6407	439	5	m.	m.	PROPN
ejpam-6407	439	6	al	al	PROPN
ejpam-6407	439	7	-	-	PUNCT
ejpam-6407	439	8	shami	shami	PROPN
ejpam-6407	439	9	.	.	PUNCT
ejpam-6407	440	1	soft	soft	ADJ
ejpam-6407	440	2	somewhere	somewhere	ADV
ejpam-6407	440	3	dense	dense	ADJ
ejpam-6407	440	4	sets	set	NOUN
ejpam-6407	440	5	on	on	ADP
ejpam-6407	440	6	soft	soft	ADJ
ejpam-6407	440	7	topological	topological	ADJ
ejpam-6407	440	8	spaces	space	NOUN
ejpam-6407	440	9	.	.	PUNCT
ejpam-6407	441	1	communications	communication	NOUN
ejpam-6407	441	2	of	of	ADP
ejpam-6407	441	3	the	the	DET
ejpam-6407	441	4	korean	korean	ADJ
ejpam-6407	441	5	mathematical	mathematical	ADJ
ejpam-6407	441	6	society	society	NOUN
ejpam-6407	441	7	,	,	PUNCT
ejpam-6407	441	8	33(2):1341–1356	33(2):1341–1356	NUM
ejpam-6407	441	9	,	,	PUNCT
ejpam-6407	441	10	2018	2018	NUM
ejpam-6407	441	11	.	.	PUNCT
ejpam-6407	442	1	[	[	X
ejpam-6407	442	2	31	31	NUM
ejpam-6407	442	3	]	]	PUNCT
ejpam-6407	442	4	a.	a.	NOUN
ejpam-6407	442	5	m.	m.	PROPN
ejpam-6407	442	6	abd	abd	PROPN
ejpam-6407	442	7	el	el	PROPN
ejpam-6407	442	8	-	-	PROPN
ejpam-6407	442	9	latif	latif	PROPN
ejpam-6407	442	10	,	,	PUNCT
ejpam-6407	442	11	a.	a.	PROPN
ejpam-6407	442	12	a.	a.	PROPN
ejpam-6407	442	13	azzam	azzam	PROPN
ejpam-6407	442	14	,	,	PUNCT
ejpam-6407	442	15	r.	r.	PROPN
ejpam-6407	442	16	abu	abu	PROPN
ejpam-6407	442	17	-	-	PUNCT
ejpam-6407	442	18	gdairi	gdairi	PROPN
ejpam-6407	442	19	,	,	PUNCT
ejpam-6407	442	20	m.	m.	NOUN
ejpam-6407	442	21	h.	h.	PROPN
ejpam-6407	442	22	alqahtani	alqahtani	PROPN
ejpam-6407	442	23	,	,	PUNCT
ejpam-6407	442	24	and	and	CCONJ
ejpam-6407	442	25	g.	g.	PROPN
ejpam-6407	442	26	m.	m.	PROPN
ejpam-6407	442	27	abdelhamed	abdelhame	VERB
ejpam-6407	442	28	.	.	PUNCT
ejpam-6407	443	1	applications	application	NOUN
ejpam-6407	443	2	on	on	ADP
ejpam-6407	443	3	soft	soft	ADJ
ejpam-6407	443	4	somewhere	somewhere	ADV
ejpam-6407	443	5	dense	dense	ADJ
ejpam-6407	443	6	sets	set	NOUN
ejpam-6407	443	7	.	.	PUNCT
ejpam-6407	444	1	journal	journal	NOUN
ejpam-6407	444	2	of	of	ADP
ejpam-6407	444	3	interdisciplinary	interdisciplinary	ADJ
ejpam-6407	444	4	mathematics	mathematic	NOUN
ejpam-6407	444	5	,	,	PUNCT
ejpam-6407	444	6	27:1679–1699	27:1679–1699	NUM
ejpam-6407	444	7	,	,	PUNCT
ejpam-6407	444	8	2024	2024	NUM
ejpam-6407	444	9	.	.	PUNCT
ejpam-6407	445	1	[	[	X
ejpam-6407	445	2	32	32	NUM
ejpam-6407	445	3	]	]	PUNCT
ejpam-6407	445	4	radwan	radwan	VERB
ejpam-6407	445	5	abu	abu	PROPN
ejpam-6407	445	6	-	-	PUNCT
ejpam-6407	445	7	gdairi	gdairi	PROPN
ejpam-6407	445	8	,	,	PUNCT
ejpam-6407	445	9	a.	a.	PROPN
ejpam-6407	445	10	a.	a.	PROPN
ejpam-6407	445	11	azzam	azzam	PROPN
ejpam-6407	445	12	,	,	PUNCT
ejpam-6407	445	13	and	and	CCONJ
ejpam-6407	445	14	ibrahim	ibrahim	PROPN
ejpam-6407	445	15	noaman	noaman	PROPN
ejpam-6407	445	16	.	.	PUNCT
ejpam-6407	446	1	nearly	nearly	ADV
ejpam-6407	446	2	soft	soft	ADJ
ejpam-6407	446	3	β	β	ADJ
ejpam-6407	446	4	-	-	ADJ
ejpam-6407	446	5	open	open	ADJ
ejpam-6407	446	6	sets	set	NOUN
ejpam-6407	446	7	via	via	ADP
ejpam-6407	446	8	soft	soft	ADJ
ejpam-6407	446	9	ditopological	ditopological	ADJ
ejpam-6407	446	10	spaces	space	NOUN
ejpam-6407	446	11	.	.	PUNCT
ejpam-6407	447	1	european	european	ADJ
ejpam-6407	447	2	journal	journal	PROPN
ejpam-6407	447	3	of	of	ADP
ejpam-6407	447	4	pure	pure	ADJ
ejpam-6407	447	5	and	and	CCONJ
ejpam-6407	447	6	applied	applied	ADJ
ejpam-6407	447	7	mathematics	mathematic	NOUN
ejpam-6407	447	8	,	,	PUNCT
ejpam-6407	447	9	m.	m.	NOUN
ejpam-6407	447	10	aldawood	aldawood	PROPN
ejpam-6407	447	11	et	et	PROPN
ejpam-6407	447	12	al	al	PROPN
ejpam-6407	447	13	.	.	PUNCT
ejpam-6407	447	14	/	/	SYM
ejpam-6407	447	15	eur	eur	PROPN
ejpam-6407	447	16	.	.	PUNCT
ejpam-6407	448	1	j.	j.	PROPN
ejpam-6407	448	2	pure	pure	PROPN
ejpam-6407	448	3	appl	appl	PROPN
ejpam-6407	448	4	.	.	PROPN
ejpam-6407	448	5	math	math	PROPN
ejpam-6407	448	6	,	,	PUNCT
ejpam-6407	448	7	18	18	NUM
ejpam-6407	448	8	(	(	PUNCT
ejpam-6407	448	9	3	3	NUM
ejpam-6407	448	10	)	)	PUNCT
ejpam-6407	448	11	(	(	PUNCT
ejpam-6407	448	12	2025	2025	NUM
ejpam-6407	448	13	)	)	PUNCT
ejpam-6407	448	14	,	,	PUNCT
ejpam-6407	448	15	6407	6407	NUM
ejpam-6407	448	16	14	14	NUM
ejpam-6407	448	17	of	of	ADP
ejpam-6407	448	18	15	15	NUM
ejpam-6407	448	19	15(1):126–134	15(1):126–134	NUM
ejpam-6407	448	20	,	,	PUNCT
ejpam-6407	448	21	2022	2022	NUM
ejpam-6407	448	22	.	.	PUNCT
ejpam-6407	449	1	[	[	X
ejpam-6407	449	2	33	33	NUM
ejpam-6407	449	3	]	]	PUNCT
ejpam-6407	449	4	s.	s.	PROPN
ejpam-6407	449	5	al	al	PROPN
ejpam-6407	449	6	ghour	ghour	PROPN
ejpam-6407	449	7	.	.	PUNCT
ejpam-6407	450	1	soft	soft	ADJ
ejpam-6407	450	2	ω	ω	NOUN
ejpam-6407	450	3	-	-	PUNCT
ejpam-6407	450	4	continuity	continuity	NOUN
ejpam-6407	450	5	and	and	CCONJ
ejpam-6407	450	6	soft	soft	ADJ
ejpam-6407	450	7	ωs	ω	NOUN
ejpam-6407	450	8	-	-	NOUN
ejpam-6407	450	9	continuity	continuity	NOUN
ejpam-6407	450	10	in	in	ADP
ejpam-6407	450	11	soft	soft	ADJ
ejpam-6407	450	12	topological	topological	ADJ
ejpam-6407	450	13	spaces	space	NOUN
ejpam-6407	450	14	.	.	PUNCT
ejpam-6407	451	1	international	international	ADJ
ejpam-6407	451	2	journal	journal	NOUN
ejpam-6407	451	3	of	of	ADP
ejpam-6407	451	4	fuzzy	fuzzy	ADJ
ejpam-6407	451	5	logic	logic	NOUN
ejpam-6407	451	6	and	and	CCONJ
ejpam-6407	451	7	intelligent	intelligent	ADJ
ejpam-6407	451	8	systems	system	NOUN
ejpam-6407	451	9	,	,	PUNCT
ejpam-6407	451	10	22(2):183–192	22(2):183–192	NOUN
ejpam-6407	451	11	,	,	PUNCT
ejpam-6407	451	12	2022	2022	NUM
ejpam-6407	451	13	.	.	PUNCT
ejpam-6407	452	1	[	[	X
ejpam-6407	452	2	34	34	NUM
ejpam-6407	452	3	]	]	PUNCT
ejpam-6407	452	4	s.	s.	PROPN
ejpam-6407	452	5	al	al	PROPN
ejpam-6407	452	6	ghour	ghour	PROPN
ejpam-6407	452	7	and	and	CCONJ
ejpam-6407	452	8	b.	b.	PROPN
ejpam-6407	452	9	irshidat	irshidat	PROPN
ejpam-6407	452	10	.	.	PUNCT
ejpam-6407	453	1	on	on	ADP
ejpam-6407	453	2	θω	θω	ADP
ejpam-6407	453	3	continuity	continuity	NOUN
ejpam-6407	453	4	.	.	PUNCT
ejpam-6407	454	1	heliyon	heliyon	NOUN
ejpam-6407	454	2	,	,	PUNCT
ejpam-6407	454	3	6(2):e03349	6(2):e03349	NUM
ejpam-6407	454	4	,	,	PUNCT
ejpam-6407	454	5	2020	2020	NUM
ejpam-6407	454	6	.	.	PUNCT
ejpam-6407	455	1	[	[	X
ejpam-6407	455	2	35	35	NUM
ejpam-6407	455	3	]	]	PUNCT
ejpam-6407	455	4	a.	a.	NOUN
ejpam-6407	455	5	kandil	kandil	PROPN
ejpam-6407	455	6	,	,	PUNCT
ejpam-6407	455	7	o.	o.	PROPN
ejpam-6407	455	8	a.	a.	PROPN
ejpam-6407	455	9	e.	e.	PROPN
ejpam-6407	455	10	tantawy	tantawy	PROPN
ejpam-6407	455	11	,	,	PUNCT
ejpam-6407	455	12	s.	s.	PROPN
ejpam-6407	455	13	a.	a.	PROPN
ejpam-6407	455	14	el	el	PROPN
ejpam-6407	455	15	-	-	PUNCT
ejpam-6407	455	16	sheikh	sheikh	NOUN
ejpam-6407	455	17	,	,	PUNCT
ejpam-6407	455	18	and	and	CCONJ
ejpam-6407	455	19	a.	a.	NOUN
ejpam-6407	455	20	m.	m.	PROPN
ejpam-6407	455	21	abd	abd	PROPN
ejpam-6407	455	22	el	el	PROPN
ejpam-6407	455	23	-	-	PROPN
ejpam-6407	455	24	latif	latif	PROPN
ejpam-6407	455	25	.	.	PUNCT
ejpam-6407	456	1	soft	soft	ADJ
ejpam-6407	456	2	ideal	ideal	ADJ
ejpam-6407	456	3	theory	theory	NOUN
ejpam-6407	456	4	,	,	PUNCT
ejpam-6407	456	5	soft	soft	ADJ
ejpam-6407	456	6	local	local	ADJ
ejpam-6407	456	7	function	function	NOUN
ejpam-6407	456	8	and	and	CCONJ
ejpam-6407	456	9	generated	generate	VERB
ejpam-6407	456	10	soft	soft	ADJ
ejpam-6407	456	11	topological	topological	ADJ
ejpam-6407	456	12	spaces	space	NOUN
ejpam-6407	456	13	.	.	PUNCT
ejpam-6407	457	1	applied	apply	VERB
ejpam-6407	457	2	mathematics	mathematic	NOUN
ejpam-6407	457	3	and	and	CCONJ
ejpam-6407	457	4	information	information	NOUN
ejpam-6407	457	5	sciences	science	NOUN
ejpam-6407	457	6	,	,	PUNCT
ejpam-6407	457	7	8(4):1595–1603	8(4):1595–1603	NOUN
ejpam-6407	457	8	,	,	PUNCT
ejpam-6407	457	9	2014	2014	NUM
ejpam-6407	457	10	.	.	PUNCT
ejpam-6407	458	1	[	[	X
ejpam-6407	458	2	36	36	NUM
ejpam-6407	458	3	]	]	X
ejpam-6407	458	4	f.	f.	PROPN
ejpam-6407	458	5	gharib	gharib	PROPN
ejpam-6407	458	6	and	and	CCONJ
ejpam-6407	458	7	a.	a.	NOUN
ejpam-6407	458	8	m.	m.	PROPN
ejpam-6407	458	9	abd	abd	PROPN
ejpam-6407	458	10	el	el	PROPN
ejpam-6407	458	11	-	-	PROPN
ejpam-6407	458	12	latif	latif	PROPN
ejpam-6407	458	13	.	.	PUNCT
ejpam-6407	459	1	soft	soft	ADJ
ejpam-6407	459	2	semi	semi	ADJ
ejpam-6407	459	3	local	local	ADJ
ejpam-6407	459	4	functions	function	NOUN
ejpam-6407	459	5	in	in	ADP
ejpam-6407	459	6	soft	soft	ADJ
ejpam-6407	459	7	ideal	ideal	ADJ
ejpam-6407	459	8	topological	topological	ADJ
ejpam-6407	459	9	spaces	space	NOUN
ejpam-6407	459	10	.	.	PUNCT
ejpam-6407	460	1	european	european	ADJ
ejpam-6407	460	2	journal	journal	PROPN
ejpam-6407	460	3	of	of	ADP
ejpam-6407	460	4	pure	pure	ADJ
ejpam-6407	460	5	and	and	CCONJ
ejpam-6407	460	6	applied	applied	ADJ
ejpam-6407	460	7	mathematics	mathematic	NOUN
ejpam-6407	460	8	,	,	PUNCT
ejpam-6407	460	9	12(3):857–869	12(3):857–869	NUM
ejpam-6407	460	10	,	,	PUNCT
ejpam-6407	460	11	2019	2019	NUM
ejpam-6407	460	12	.	.	PUNCT
ejpam-6407	461	1	[	[	X
ejpam-6407	461	2	37	37	NUM
ejpam-6407	461	3	]	]	PUNCT
ejpam-6407	461	4	a.	a.	NOUN
ejpam-6407	461	5	kandil	kandil	PROPN
ejpam-6407	461	6	,	,	PUNCT
ejpam-6407	461	7	o.	o.	PROPN
ejpam-6407	461	8	a.	a.	PROPN
ejpam-6407	461	9	e.	e.	PROPN
ejpam-6407	461	10	tantawy	tantawy	PROPN
ejpam-6407	461	11	,	,	PUNCT
ejpam-6407	461	12	s.	s.	PROPN
ejpam-6407	461	13	a.	a.	PROPN
ejpam-6407	461	14	el	el	PROPN
ejpam-6407	461	15	-	-	PUNCT
ejpam-6407	461	16	sheikh	sheikh	NOUN
ejpam-6407	461	17	,	,	PUNCT
ejpam-6407	461	18	and	and	CCONJ
ejpam-6407	461	19	a.	a.	NOUN
ejpam-6407	461	20	m.	m.	PROPN
ejpam-6407	461	21	abd	abd	PROPN
ejpam-6407	461	22	el	el	PROPN
ejpam-6407	461	23	-	-	PROPN
ejpam-6407	461	24	latif	latif	PROPN
ejpam-6407	461	25	.	.	PUNCT
ejpam-6407	462	1	soft	soft	ADJ
ejpam-6407	462	2	semi	semi	ADJ
ejpam-6407	462	3	compactness	compactness	NOUN
ejpam-6407	462	4	via	via	ADP
ejpam-6407	462	5	soft	soft	ADJ
ejpam-6407	462	6	ideals	ideal	NOUN
ejpam-6407	462	7	.	.	PUNCT
ejpam-6407	463	1	applied	apply	VERB
ejpam-6407	463	2	mathematics	mathematic	NOUN
ejpam-6407	463	3	and	and	CCONJ
ejpam-6407	463	4	information	information	NOUN
ejpam-6407	463	5	sciences	science	NOUN
ejpam-6407	463	6	,	,	PUNCT
ejpam-6407	463	7	8(5):2297	8(5):2297	NUM
ejpam-6407	463	8	–	–	PUNCT
ejpam-6407	463	9	2306	2306	NUM
ejpam-6407	463	10	,	,	PUNCT
ejpam-6407	463	11	2014	2014	NUM
ejpam-6407	463	12	.	.	PUNCT
ejpam-6407	464	1	[	[	X
ejpam-6407	464	2	38	38	NUM
ejpam-6407	464	3	]	]	PUNCT
ejpam-6407	464	4	a.	a.	NOUN
ejpam-6407	464	5	kandil	kandil	PROPN
ejpam-6407	464	6	,	,	PUNCT
ejpam-6407	464	7	o.	o.	PROPN
ejpam-6407	464	8	a.	a.	PROPN
ejpam-6407	464	9	e.	e.	PROPN
ejpam-6407	464	10	tantawy	tantawy	PROPN
ejpam-6407	464	11	,	,	PUNCT
ejpam-6407	464	12	s.	s.	PROPN
ejpam-6407	464	13	a.	a.	PROPN
ejpam-6407	464	14	el	el	PROPN
ejpam-6407	464	15	-	-	PUNCT
ejpam-6407	464	16	sheikh	sheikh	NOUN
ejpam-6407	464	17	,	,	PUNCT
ejpam-6407	464	18	and	and	CCONJ
ejpam-6407	464	19	a.	a.	NOUN
ejpam-6407	464	20	m.	m.	PROPN
ejpam-6407	464	21	abd	abd	PROPN
ejpam-6407	464	22	el	el	PROPN
ejpam-6407	464	23	-	-	PROPN
ejpam-6407	464	24	latif	latif	PROPN
ejpam-6407	464	25	.	.	PUNCT
ejpam-6407	465	1	soft	soft	ADJ
ejpam-6407	465	2	connectedness	connectedness	NOUN
ejpam-6407	465	3	via	via	ADP
ejpam-6407	465	4	soft	soft	ADJ
ejpam-6407	465	5	ideals	ideal	NOUN
ejpam-6407	465	6	.	.	PUNCT
ejpam-6407	466	1	journal	journal	NOUN
ejpam-6407	466	2	of	of	ADP
ejpam-6407	466	3	new	new	ADJ
ejpam-6407	466	4	results	result	NOUN
ejpam-6407	466	5	in	in	ADP
ejpam-6407	466	6	science	science	NOUN
ejpam-6407	466	7	,	,	PUNCT
ejpam-6407	466	8	4:90–108	4:90–108	NUM
ejpam-6407	466	9	,	,	PUNCT
ejpam-6407	466	10	2014	2014	NUM
ejpam-6407	466	11	.	.	PUNCT
ejpam-6407	467	1	[	[	X
ejpam-6407	467	2	39	39	NUM
ejpam-6407	467	3	]	]	PUNCT
ejpam-6407	467	4	a.	a.	NOUN
ejpam-6407	467	5	kandil	kandil	PROPN
ejpam-6407	467	6	,	,	PUNCT
ejpam-6407	467	7	o.	o.	PROPN
ejpam-6407	467	8	a.	a.	PROPN
ejpam-6407	467	9	e.	e.	PROPN
ejpam-6407	467	10	tantawy	tantawy	PROPN
ejpam-6407	467	11	,	,	PUNCT
ejpam-6407	467	12	s.	s.	PROPN
ejpam-6407	467	13	a.	a.	PROPN
ejpam-6407	467	14	el	el	PROPN
ejpam-6407	467	15	-	-	PUNCT
ejpam-6407	467	16	sheikh	sheikh	NOUN
ejpam-6407	467	17	,	,	PUNCT
ejpam-6407	467	18	and	and	CCONJ
ejpam-6407	467	19	a.	a.	NOUN
ejpam-6407	467	20	m.	m.	PROPN
ejpam-6407	467	21	abd	abd	PROPN
ejpam-6407	467	22	el	el	PROPN
ejpam-6407	467	23	-	-	PROPN
ejpam-6407	467	24	latif	latif	PROPN
ejpam-6407	467	25	.	.	PUNCT
ejpam-6407	468	1	γ	γ	PROPN
ejpam-6407	468	2	-	-	PUNCT
ejpam-6407	468	3	operation	operation	NOUN
ejpam-6407	468	4	and	and	CCONJ
ejpam-6407	468	5	decompositions	decomposition	NOUN
ejpam-6407	468	6	of	of	ADP
ejpam-6407	468	7	some	some	DET
ejpam-6407	468	8	forms	form	NOUN
ejpam-6407	468	9	of	of	ADP
ejpam-6407	468	10	soft	soft	ADJ
ejpam-6407	468	11	continuity	continuity	NOUN
ejpam-6407	468	12	of	of	ADP
ejpam-6407	468	13	soft	soft	ADJ
ejpam-6407	468	14	topological	topological	ADJ
ejpam-6407	468	15	spaces	space	NOUN
ejpam-6407	468	16	via	via	ADP
ejpam-6407	468	17	soft	soft	ADJ
ejpam-6407	468	18	ideal	ideal	NOUN
ejpam-6407	468	19	.	.	PUNCT
ejpam-6407	469	1	annals	annal	NOUN
ejpam-6407	469	2	of	of	ADP
ejpam-6407	469	3	fuzzy	fuzzy	ADJ
ejpam-6407	469	4	mathematics	mathematic	NOUN
ejpam-6407	469	5	and	and	CCONJ
ejpam-6407	469	6	informatics	informatic	NOUN
ejpam-6407	469	7	,	,	PUNCT
ejpam-6407	469	8	9(3):385–402	9(3):385–402	NUM
ejpam-6407	469	9	,	,	PUNCT
ejpam-6407	469	10	2015	2015	NUM
ejpam-6407	469	11	.	.	PUNCT
ejpam-6407	470	1	[	[	X
ejpam-6407	470	2	40	40	NUM
ejpam-6407	470	3	]	]	PUNCT
ejpam-6407	470	4	m.	m.	NOUN
ejpam-6407	470	5	akdag	akdag	PROPN
ejpam-6407	470	6	and	and	CCONJ
ejpam-6407	470	7	f.	f.	PROPN
ejpam-6407	470	8	erol	erol	PROPN
ejpam-6407	470	9	.	.	PUNCT
ejpam-6407	471	1	soft	soft	ADJ
ejpam-6407	471	2	i	i	NOUN
ejpam-6407	471	3	-	-	PUNCT
ejpam-6407	471	4	sets	set	NOUN
ejpam-6407	471	5	and	and	CCONJ
ejpam-6407	471	6	soft	soft	ADJ
ejpam-6407	471	7	i	i	NOUN
ejpam-6407	471	8	-	-	PUNCT
ejpam-6407	471	9	continuity	continuity	NOUN
ejpam-6407	471	10	of	of	ADP
ejpam-6407	471	11	functions	function	NOUN
ejpam-6407	471	12	.	.	PUNCT
ejpam-6407	472	1	gazi	gazi	PROPN
ejpam-6407	472	2	university	university	PROPN
ejpam-6407	472	3	journal	journal	PROPN
ejpam-6407	472	4	of	of	ADP
ejpam-6407	472	5	science	science	NOUN
ejpam-6407	472	6	,	,	PUNCT
ejpam-6407	472	7	27:923–932	27:923–932	NUM
ejpam-6407	472	8	,	,	PUNCT
ejpam-6407	472	9	2014	2014	NUM
ejpam-6407	472	10	.	.	PUNCT
ejpam-6407	473	1	[	[	X
ejpam-6407	473	2	41	41	NUM
ejpam-6407	473	3	]	]	PUNCT
ejpam-6407	473	4	a.	a.	NOUN
ejpam-6407	473	5	a.	a.	NOUN
ejpam-6407	473	6	nasef	nasef	PROPN
ejpam-6407	473	7	,	,	PUNCT
ejpam-6407	473	8	m.	m.	NOUN
ejpam-6407	473	9	parimala	parimala	PROPN
ejpam-6407	473	10	,	,	PUNCT
ejpam-6407	473	11	r.	r.	PROPN
ejpam-6407	473	12	jeevitha	jeevitha	PROPN
ejpam-6407	473	13	,	,	PUNCT
ejpam-6407	473	14	and	and	CCONJ
ejpam-6407	473	15	m.	m.	PROPN
ejpam-6407	473	16	k.	k.	PROPN
ejpam-6407	474	1	el	el	PROPN
ejpam-6407	474	2	-	-	PUNCT
ejpam-6407	474	3	sayed	say	VERB
ejpam-6407	474	4	.	.	PUNCT
ejpam-6407	475	1	soft	soft	ADJ
ejpam-6407	475	2	ideal	ideal	ADJ
ejpam-6407	475	3	theory	theory	NOUN
ejpam-6407	475	4	and	and	CCONJ
ejpam-6407	475	5	applications	application	NOUN
ejpam-6407	475	6	.	.	PUNCT
ejpam-6407	476	1	international	international	ADJ
ejpam-6407	476	2	journal	journal	PROPN
ejpam-6407	476	3	of	of	ADP
ejpam-6407	476	4	nonlinear	nonlinear	ADJ
ejpam-6407	476	5	analysis	analysis	NOUN
ejpam-6407	476	6	and	and	CCONJ
ejpam-6407	476	7	applications	application	NOUN
ejpam-6407	476	8	,	,	PUNCT
ejpam-6407	476	9	13(2):1335	13(2):1335	NUM
ejpam-6407	476	10	–	–	PUNCT
ejpam-6407	476	11	1342	1342	NUM
ejpam-6407	476	12	,	,	PUNCT
ejpam-6407	476	13	2022	2022	NUM
ejpam-6407	476	14	.	.	PUNCT
ejpam-6407	477	1	[	[	X
ejpam-6407	477	2	42	42	NUM
ejpam-6407	477	3	]	]	PUNCT
ejpam-6407	477	4	a.	a.	NOUN
ejpam-6407	477	5	kandil	kandil	PROPN
ejpam-6407	477	6	,	,	PUNCT
ejpam-6407	477	7	o.	o.	PROPN
ejpam-6407	477	8	a.	a.	PROPN
ejpam-6407	477	9	e.	e.	PROPN
ejpam-6407	477	10	tantawy	tantawy	PROPN
ejpam-6407	477	11	,	,	PUNCT
ejpam-6407	477	12	s.	s.	PROPN
ejpam-6407	477	13	a.	a.	PROPN
ejpam-6407	477	14	el	el	PROPN
ejpam-6407	477	15	-	-	PUNCT
ejpam-6407	477	16	sheikh	sheikh	NOUN
ejpam-6407	477	17	,	,	PUNCT
ejpam-6407	477	18	and	and	CCONJ
ejpam-6407	477	19	a.	a.	NOUN
ejpam-6407	477	20	m.	m.	PROPN
ejpam-6407	477	21	abd	abd	PROPN
ejpam-6407	477	22	el	el	PROPN
ejpam-6407	477	23	-	-	PROPN
ejpam-6407	477	24	latif	latif	PROPN
ejpam-6407	477	25	.	.	PUNCT
ejpam-6407	478	1	soft	soft	ADJ
ejpam-6407	478	2	semi	semi	ADJ
ejpam-6407	478	3	(	(	PUNCT
ejpam-6407	478	4	quasi	quasi	ADJ
ejpam-6407	478	5	)	)	PUNCT
ejpam-6407	478	6	hausdorff	hausdorff	NOUN
ejpam-6407	478	7	spaces	space	NOUN
ejpam-6407	478	8	via	via	ADP
ejpam-6407	478	9	soft	soft	ADJ
ejpam-6407	478	10	ideals	ideal	NOUN
ejpam-6407	478	11	.	.	PUNCT
ejpam-6407	479	1	south	south	ADJ
ejpam-6407	479	2	asian	asian	PROPN
ejpam-6407	479	3	journal	journal	PROPN
ejpam-6407	479	4	of	of	ADP
ejpam-6407	479	5	mathematics	mathematic	NOUN
ejpam-6407	479	6	,	,	PUNCT
ejpam-6407	479	7	4(6):265–284	4(6):265–284	NUM
ejpam-6407	479	8	,	,	PUNCT
ejpam-6407	479	9	2014	2014	NUM
ejpam-6407	479	10	.	.	PUNCT
ejpam-6407	480	1	[	[	X
ejpam-6407	480	2	43	43	NUM
ejpam-6407	480	3	]	]	PUNCT
ejpam-6407	480	4	a.	a.	NOUN
ejpam-6407	480	5	m.	m.	PROPN
ejpam-6407	480	6	abd	abd	PROPN
ejpam-6407	480	7	el	el	PROPN
ejpam-6407	480	8	-	-	PROPN
ejpam-6407	480	9	latif	latif	PROPN
ejpam-6407	480	10	.	.	PUNCT
ejpam-6407	481	1	generalized	generalize	VERB
ejpam-6407	481	2	soft	soft	ADJ
ejpam-6407	481	3	rough	rough	ADJ
ejpam-6407	481	4	sets	set	NOUN
ejpam-6407	481	5	and	and	CCONJ
ejpam-6407	481	6	generated	generate	VERB
ejpam-6407	481	7	soft	soft	ADJ
ejpam-6407	481	8	ideal	ideal	NOUN
ejpam-6407	481	9	rough	rough	ADJ
ejpam-6407	481	10	topological	topological	ADJ
ejpam-6407	481	11	spaces	space	NOUN
ejpam-6407	481	12	.	.	PUNCT
ejpam-6407	482	1	journal	journal	NOUN
ejpam-6407	482	2	of	of	ADP
ejpam-6407	482	3	intelligent	intelligent	ADJ
ejpam-6407	482	4	and	and	CCONJ
ejpam-6407	482	5	fuzzy	fuzzy	ADJ
ejpam-6407	482	6	systems	system	NOUN
ejpam-6407	482	7	,	,	PUNCT
ejpam-6407	482	8	34:517–524	34:517–524	PROPN
ejpam-6407	482	9	,	,	PUNCT
ejpam-6407	482	10	2018	2018	NUM
ejpam-6407	482	11	.	.	PUNCT
ejpam-6407	483	1	[	[	X
ejpam-6407	483	2	44	44	NUM
ejpam-6407	483	3	]	]	PUNCT
ejpam-6407	483	4	a.	a.	NOUN
ejpam-6407	483	5	m.	m.	PROPN
ejpam-6407	483	6	abd	abd	PROPN
ejpam-6407	483	7	el	el	PROPN
ejpam-6407	483	8	-	-	PROPN
ejpam-6407	483	9	latif	latif	PROPN
ejpam-6407	483	10	.	.	PUNCT
ejpam-6407	484	1	new	new	ADJ
ejpam-6407	484	2	generalized	generalize	VERB
ejpam-6407	484	3	fuzzy	fuzzy	ADJ
ejpam-6407	484	4	soft	soft	ADJ
ejpam-6407	484	5	rough	rough	ADJ
ejpam-6407	484	6	approximations	approximation	NOUN
ejpam-6407	484	7	applied	apply	VERB
ejpam-6407	484	8	to	to	ADP
ejpam-6407	484	9	fuzzy	fuzzy	ADJ
ejpam-6407	484	10	topological	topological	ADJ
ejpam-6407	484	11	spaces	space	NOUN
ejpam-6407	484	12	.	.	PUNCT
ejpam-6407	485	1	journal	journal	NOUN
ejpam-6407	485	2	of	of	ADP
ejpam-6407	485	3	intelligent	intelligent	ADJ
ejpam-6407	485	4	and	and	CCONJ
ejpam-6407	485	5	fuzzy	fuzzy	ADJ
ejpam-6407	485	6	systems	system	NOUN
ejpam-6407	485	7	,	,	PUNCT
ejpam-6407	485	8	35:2123–2136	35:2123–2136	NUM
ejpam-6407	485	9	,	,	PUNCT
ejpam-6407	485	10	2018	2018	NUM
ejpam-6407	485	11	.	.	PUNCT
ejpam-6407	486	1	[	[	X
ejpam-6407	486	2	45	45	NUM
ejpam-6407	486	3	]	]	SYM
ejpam-6407	486	4	mesfer	mesfer	NOUN
ejpam-6407	486	5	h.	h.	PROPN
ejpam-6407	486	6	alqahtani	alqahtani	PROPN
ejpam-6407	486	7	and	and	CCONJ
ejpam-6407	486	8	zanyar	zanyar	PROPN
ejpam-6407	486	9	a.	a.	NOUN
ejpam-6407	486	10	ameen	ameen	PROPN
ejpam-6407	486	11	.	.	PUNCT
ejpam-6407	487	1	congruence	congruence	PROPN
ejpam-6407	487	2	representations	representation	NOUN
ejpam-6407	487	3	via	via	ADP
ejpam-6407	487	4	soft	soft	ADJ
ejpam-6407	487	5	ideals	ideal	NOUN
ejpam-6407	487	6	in	in	ADP
ejpam-6407	487	7	soft	soft	ADJ
ejpam-6407	487	8	topological	topological	ADJ
ejpam-6407	487	9	spaces	space	NOUN
ejpam-6407	487	10	.	.	PUNCT
ejpam-6407	488	1	axioms	axiom	NOUN
ejpam-6407	488	2	,	,	PUNCT
ejpam-6407	488	3	12:1015	12:1015	NUM
ejpam-6407	488	4	,	,	PUNCT
ejpam-6407	488	5	2023	2023	NUM
ejpam-6407	488	6	.	.	PUNCT
ejpam-6407	489	1	[	[	X
ejpam-6407	489	2	46	46	NUM
ejpam-6407	489	3	]	]	PUNCT
ejpam-6407	489	4	s.	s.	PROPN
ejpam-6407	489	5	saleh	saleh	PROPN
ejpam-6407	489	6	,	,	PUNCT
ejpam-6407	489	7	laith	laith	PROPN
ejpam-6407	489	8	r.	r.	PROPN
ejpam-6407	489	9	flaih	flaih	PROPN
ejpam-6407	489	10	,	,	PUNCT
ejpam-6407	489	11	and	and	CCONJ
ejpam-6407	489	12	khaled	khaled	PROPN
ejpam-6407	489	13	f.	f.	PROPN
ejpam-6407	489	14	jasim	jasim	PROPN
ejpam-6407	489	15	.	.	PUNCT
ejpam-6407	490	1	some	some	DET
ejpam-6407	490	2	applications	application	NOUN
ejpam-6407	490	3	of	of	ADP
ejpam-6407	490	4	soft	soft	ADJ
ejpam-6407	490	5	δ	δ	NOUN
ejpam-6407	490	6	-	-	PUNCT
ejpam-6407	490	7	closed	close	VERB
ejpam-6407	490	8	sets	set	NOUN
ejpam-6407	490	9	in	in	ADP
ejpam-6407	490	10	soft	soft	ADJ
ejpam-6407	490	11	closure	closure	NOUN
ejpam-6407	490	12	spaces	space	NOUN
ejpam-6407	490	13	.	.	PUNCT
ejpam-6407	491	1	communications	communication	NOUN
ejpam-6407	491	2	in	in	ADP
ejpam-6407	491	3	mathematics	mathematic	NOUN
ejpam-6407	491	4	and	and	CCONJ
ejpam-6407	491	5	applications	application	NOUN
ejpam-6407	491	6	,	,	PUNCT
ejpam-6407	491	7	14(2):481	14(2):481	NUM
ejpam-6407	491	8	–	–	PUNCT
ejpam-6407	491	9	492	492	NUM
ejpam-6407	491	10	,	,	PUNCT
ejpam-6407	491	11	2023	2023	NUM
ejpam-6407	491	12	.	.	PUNCT
ejpam-6407	492	1	[	[	X
ejpam-6407	492	2	47	47	NUM
ejpam-6407	492	3	]	]	PUNCT
ejpam-6407	492	4	s.	s.	PROPN
ejpam-6407	492	5	saleh	saleh	PROPN
ejpam-6407	492	6	and	and	CCONJ
ejpam-6407	492	7	k.	k.	PROPN
ejpam-6407	492	8	hur	hur	PROPN
ejpam-6407	492	9	.	.	PROPN
ejpam-6407	493	1	on	on	ADP
ejpam-6407	493	2	some	some	DET
ejpam-6407	493	3	lower	low	ADJ
ejpam-6407	493	4	soft	soft	ADJ
ejpam-6407	493	5	separation	separation	NOUN
ejpam-6407	493	6	axioms	axiom	NOUN
ejpam-6407	493	7	.	.	PUNCT
ejpam-6407	494	1	annals	annal	NOUN
ejpam-6407	494	2	of	of	ADP
ejpam-6407	494	3	fuzzy	fuzzy	ADJ
ejpam-6407	494	4	mathematics	mathematic	NOUN
ejpam-6407	494	5	and	and	CCONJ
ejpam-6407	494	6	informatics	informatic	NOUN
ejpam-6407	494	7	,	,	PUNCT
ejpam-6407	494	8	19(1):61–72	19(1):61–72	NUM
ejpam-6407	494	9	,	,	PUNCT
ejpam-6407	494	10	2020	2020	NUM
ejpam-6407	494	11	.	.	PUNCT
ejpam-6407	495	1	[	[	X
ejpam-6407	495	2	48	48	NUM
ejpam-6407	495	3	]	]	PUNCT
ejpam-6407	495	4	s.	s.	PROPN
ejpam-6407	495	5	a.	a.	PROPN
ejpam-6407	495	6	el	el	PROPN
ejpam-6407	495	7	-	-	PUNCT
ejpam-6407	495	8	sheikh	sheikh	PROPN
ejpam-6407	495	9	and	and	CCONJ
ejpam-6407	495	10	a.	a.	NOUN
ejpam-6407	495	11	m.	m.	NOUN
ejpam-6407	495	12	abd	abd	PROPN
ejpam-6407	495	13	el	el	PROPN
ejpam-6407	495	14	-	-	PROPN
ejpam-6407	495	15	latif	latif	PROPN
ejpam-6407	495	16	.	.	PUNCT
ejpam-6407	496	1	decompositions	decomposition	NOUN
ejpam-6407	496	2	of	of	ADP
ejpam-6407	496	3	some	some	DET
ejpam-6407	496	4	types	type	NOUN
ejpam-6407	496	5	of	of	ADP
ejpam-6407	496	6	supra	supra	ADJ
ejpam-6407	496	7	soft	soft	ADJ
ejpam-6407	496	8	sets	set	NOUN
ejpam-6407	496	9	and	and	CCONJ
ejpam-6407	496	10	soft	soft	ADJ
ejpam-6407	496	11	continuity	continuity	NOUN
ejpam-6407	496	12	.	.	PUNCT
ejpam-6407	497	1	international	international	ADJ
ejpam-6407	497	2	journal	journal	PROPN
ejpam-6407	497	3	of	of	ADP
ejpam-6407	497	4	mathematical	mathematical	ADJ
ejpam-6407	497	5	trends	trend	NOUN
ejpam-6407	497	6	and	and	CCONJ
ejpam-6407	497	7	technology	technology	NOUN
ejpam-6407	497	8	,	,	PUNCT
ejpam-6407	497	9	9(1):37–56	9(1):37–56	NUM
ejpam-6407	497	10	,	,	PUNCT
ejpam-6407	497	11	2014	2014	NUM
ejpam-6407	497	12	.	.	PUNCT
ejpam-6407	498	1	[	[	X
ejpam-6407	498	2	49	49	NUM
ejpam-6407	498	3	]	]	PUNCT
ejpam-6407	498	4	a.	a.	NOUN
ejpam-6407	498	5	m.	m.	PROPN
ejpam-6407	498	6	abd	abd	PROPN
ejpam-6407	498	7	el	el	PROPN
ejpam-6407	498	8	-	-	PROPN
ejpam-6407	498	9	latif	latif	PROPN
ejpam-6407	498	10	and	and	CCONJ
ejpam-6407	498	11	s.	s.	PROPN
ejpam-6407	498	12	karataş.	karataş.	PROPN
ejpam-6407	499	1	supra	supra	PROPN
ejpam-6407	499	2	b	b	PROPN
ejpam-6407	499	3	-	-	PUNCT
ejpam-6407	499	4	open	open	ADJ
ejpam-6407	499	5	soft	soft	ADJ
ejpam-6407	499	6	sets	set	NOUN
ejpam-6407	499	7	and	and	CCONJ
ejpam-6407	499	8	supra	supra	PROPN
ejpam-6407	499	9	b	b	NOUN
ejpam-6407	499	10	-	-	PUNCT
ejpam-6407	499	11	soft	soft	ADJ
ejpam-6407	499	12	continuity	continuity	NOUN
ejpam-6407	499	13	on	on	ADP
ejpam-6407	499	14	soft	soft	ADJ
ejpam-6407	499	15	topological	topological	ADJ
ejpam-6407	499	16	spaces	space	NOUN
ejpam-6407	499	17	.	.	PUNCT
ejpam-6407	500	1	journal	journal	NOUN
ejpam-6407	500	2	of	of	ADP
ejpam-6407	500	3	mathematics	mathematics	PROPN
ejpam-6407	500	4	and	and	CCONJ
ejpam-6407	500	5	computer	computer	NOUN
ejpam-6407	500	6	applications	application	NOUN
ejpam-6407	500	7	research	research	NOUN
ejpam-6407	500	8	,	,	PUNCT
ejpam-6407	500	9	5(1):1–18	5(1):1–18	NUM
ejpam-6407	500	10	,	,	PUNCT
ejpam-6407	500	11	2015	2015	NUM
ejpam-6407	500	12	.	.	PUNCT
ejpam-6407	501	1	[	[	X
ejpam-6407	501	2	50	50	NUM
ejpam-6407	501	3	]	]	PUNCT
ejpam-6407	501	4	a.	a.	NOUN
ejpam-6407	501	5	m.	m.	PROPN
ejpam-6407	501	6	abd	abd	PROPN
ejpam-6407	501	7	el	el	PROPN
ejpam-6407	501	8	-	-	PROPN
ejpam-6407	501	9	latif	latif	PROPN
ejpam-6407	501	10	.	.	PUNCT
ejpam-6407	502	1	soft	soft	ADJ
ejpam-6407	502	2	supra	supra	PROPN
ejpam-6407	502	3	strongly	strongly	ADV
ejpam-6407	502	4	generalized	generalize	VERB
ejpam-6407	502	5	closed	closed	ADJ
ejpam-6407	502	6	sets	set	NOUN
ejpam-6407	502	7	.	.	PUNCT
ejpam-6407	503	1	journal	journal	NOUN
ejpam-6407	503	2	of	of	ADP
ejpam-6407	503	3	intelligent	intelligent	ADJ
ejpam-6407	503	4	m.	m.	NOUN
ejpam-6407	503	5	aldawood	aldawood	NOUN
ejpam-6407	503	6	et	et	PROPN
ejpam-6407	503	7	al	al	PROPN
ejpam-6407	503	8	.	.	PUNCT
ejpam-6407	503	9	/	/	SYM
ejpam-6407	503	10	eur	eur	PROPN
ejpam-6407	503	11	.	.	PUNCT
ejpam-6407	504	1	j.	j.	PROPN
ejpam-6407	504	2	pure	pure	PROPN
ejpam-6407	504	3	appl	appl	PROPN
ejpam-6407	504	4	.	.	PROPN
ejpam-6407	504	5	math	math	PROPN
ejpam-6407	504	6	,	,	PUNCT
ejpam-6407	504	7	18	18	NUM
ejpam-6407	504	8	(	(	PUNCT
ejpam-6407	504	9	3	3	NUM
ejpam-6407	504	10	)	)	PUNCT
ejpam-6407	504	11	(	(	PUNCT
ejpam-6407	504	12	2025	2025	NUM
ejpam-6407	504	13	)	)	PUNCT
ejpam-6407	504	14	,	,	PUNCT
ejpam-6407	504	15	6407	6407	NUM
ejpam-6407	504	16	15	15	NUM
ejpam-6407	504	17	of	of	ADP
ejpam-6407	504	18	15	15	NUM
ejpam-6407	504	19	and	and	CCONJ
ejpam-6407	504	20	fuzzy	fuzzy	ADJ
ejpam-6407	504	21	systems	system	NOUN
ejpam-6407	504	22	,	,	PUNCT
ejpam-6407	504	23	31(3):1311–1317	31(3):1311–1317	NUM
ejpam-6407	504	24	,	,	PUNCT
ejpam-6407	504	25	2016	2016	NUM
ejpam-6407	504	26	.	.	PUNCT
ejpam-6407	505	1	[	[	X
ejpam-6407	505	2	51	51	NUM
ejpam-6407	505	3	]	]	PUNCT
ejpam-6407	505	4	a.	a.	NOUN
ejpam-6407	505	5	kandil	kandil	PROPN
ejpam-6407	505	6	,	,	PUNCT
ejpam-6407	505	7	o.	o.	PROPN
ejpam-6407	505	8	a.	a.	PROPN
ejpam-6407	505	9	e.	e.	PROPN
ejpam-6407	505	10	tantawy	tantawy	PROPN
ejpam-6407	505	11	,	,	PUNCT
ejpam-6407	505	12	s.	s.	PROPN
ejpam-6407	505	13	a.	a.	PROPN
ejpam-6407	505	14	el	el	PROPN
ejpam-6407	505	15	-	-	PUNCT
ejpam-6407	505	16	sheikh	sheikh	NOUN
ejpam-6407	505	17	,	,	PUNCT
ejpam-6407	505	18	and	and	CCONJ
ejpam-6407	505	19	a.	a.	NOUN
ejpam-6407	505	20	m.	m.	PROPN
ejpam-6407	505	21	abd	abd	PROPN
ejpam-6407	505	22	el	el	PROPN
ejpam-6407	505	23	-	-	PROPN
ejpam-6407	505	24	latif	latif	PROPN
ejpam-6407	505	25	.	.	PUNCT
ejpam-6407	506	1	supra	supra	PROPN
ejpam-6407	506	2	generalized	generalize	VERB
ejpam-6407	506	3	closed	close	VERB
ejpam-6407	506	4	soft	soft	ADJ
ejpam-6407	506	5	sets	set	NOUN
ejpam-6407	506	6	with	with	ADP
ejpam-6407	506	7	respect	respect	NOUN
ejpam-6407	506	8	to	to	ADP
ejpam-6407	506	9	an	an	DET
ejpam-6407	506	10	soft	soft	ADJ
ejpam-6407	506	11	ideal	ideal	NOUN
ejpam-6407	506	12	in	in	ADP
ejpam-6407	506	13	supra	supra	PROPN
ejpam-6407	506	14	soft	soft	ADJ
ejpam-6407	506	15	topological	topological	ADJ
ejpam-6407	506	16	spaces	space	NOUN
ejpam-6407	506	17	.	.	PUNCT
ejpam-6407	507	1	applied	apply	VERB
ejpam-6407	507	2	mathematics	mathematic	NOUN
ejpam-6407	507	3	and	and	CCONJ
ejpam-6407	507	4	information	information	NOUN
ejpam-6407	507	5	sciences	science	NOUN
ejpam-6407	507	6	,	,	PUNCT
ejpam-6407	507	7	8(4):1731–1740	8(4):1731–1740	PROPN
ejpam-6407	507	8	,	,	PUNCT
ejpam-6407	507	9	2014	2014	NUM
ejpam-6407	507	10	.	.	PUNCT
ejpam-6407	508	1	[	[	X
ejpam-6407	508	2	52	52	NUM
ejpam-6407	508	3	]	]	PUNCT
ejpam-6407	508	4	a.	a.	NOUN
ejpam-6407	508	5	m.	m.	PROPN
ejpam-6407	508	6	abd	abd	PROPN
ejpam-6407	508	7	el	el	PROPN
ejpam-6407	508	8	-	-	PROPN
ejpam-6407	508	9	latif	latif	PROPN
ejpam-6407	508	10	,	,	PUNCT
ejpam-6407	508	11	radwan	radwan	VERB
ejpam-6407	508	12	abu	abu	PROPN
ejpam-6407	508	13	-	-	PUNCT
ejpam-6407	508	14	gdairi	gdairi	PROPN
ejpam-6407	508	15	,	,	PUNCT
ejpam-6407	508	16	a.	a.	PROPN
ejpam-6407	508	17	a.	a.	PROPN
ejpam-6407	508	18	azzam	azzam	PROPN
ejpam-6407	508	19	,	,	PUNCT
ejpam-6407	508	20	f.	f.	PROPN
ejpam-6407	508	21	a.	a.	PROPN
ejpam-6407	508	22	gharib	gharib	PROPN
ejpam-6407	508	23	,	,	PUNCT
ejpam-6407	508	24	and	and	CCONJ
ejpam-6407	508	25	khaled	khaled	PROPN
ejpam-6407	508	26	a.	a.	PROPN
ejpam-6407	508	27	aldwoah	aldwoah	PROPN
ejpam-6407	508	28	.	.	PUNCT
ejpam-6407	509	1	supra	supra	PROPN
ejpam-6407	509	2	soft	soft	ADJ
ejpam-6407	509	3	somewhat	somewhat	ADV
ejpam-6407	509	4	open	open	ADJ
ejpam-6407	509	5	sets	set	NOUN
ejpam-6407	509	6	:	:	PUNCT
ejpam-6407	509	7	characterizations	characterization	NOUN
ejpam-6407	509	8	and	and	CCONJ
ejpam-6407	509	9	continuity	continuity	NOUN
ejpam-6407	509	10	.	.	PUNCT
ejpam-6407	510	1	european	european	ADJ
ejpam-6407	510	2	journal	journal	PROPN
ejpam-6407	510	3	of	of	ADP
ejpam-6407	510	4	pure	pure	ADJ
ejpam-6407	510	5	and	and	CCONJ
ejpam-6407	510	6	applied	applied	ADJ
ejpam-6407	510	7	mathematics	mathematic	NOUN
ejpam-6407	510	8	,	,	PUNCT
ejpam-6407	510	9	18(1):5863	18(1):5863	NUM
ejpam-6407	510	10	,	,	PUNCT
ejpam-6407	510	11	2025	2025	NUM
ejpam-6407	510	12	.	.	PUNCT
ejpam-6407	511	1	[	[	X
ejpam-6407	511	2	53	53	NUM
ejpam-6407	511	3	]	]	PUNCT
ejpam-6407	511	4	a.	a.	NOUN
ejpam-6407	511	5	m.	m.	PROPN
ejpam-6407	511	6	abd	abd	PROPN
ejpam-6407	511	7	el	el	PROPN
ejpam-6407	511	8	-	-	PROPN
ejpam-6407	511	9	latif	latif	PROPN
ejpam-6407	511	10	and	and	CCONJ
ejpam-6407	511	11	mesfer	mesfer	VERB
ejpam-6407	511	12	h.	h.	PROPN
ejpam-6407	511	13	alqahtani	alqahtani	PROPN
ejpam-6407	511	14	.	.	PUNCT
ejpam-6407	512	1	new	new	ADJ
ejpam-6407	512	2	soft	soft	ADJ
ejpam-6407	512	3	operators	operator	NOUN
ejpam-6407	512	4	related	relate	VERB
ejpam-6407	512	5	to	to	ADP
ejpam-6407	512	6	supra	supra	PROPN
ejpam-6407	512	7	soft	soft	ADJ
ejpam-6407	512	8	δi	δi	NOUN
ejpam-6407	512	9	-	-	PUNCT
ejpam-6407	512	10	open	open	ADJ
ejpam-6407	512	11	sets	set	NOUN
ejpam-6407	512	12	and	and	CCONJ
ejpam-6407	512	13	applications	application	NOUN
ejpam-6407	512	14	.	.	PUNCT
ejpam-6407	513	1	aims	aim	VERB
ejpam-6407	513	2	mathematics	mathematic	NOUN
ejpam-6407	513	3	,	,	PUNCT
ejpam-6407	513	4	9(2):3076–3096	9(2):3076–3096	NUM
ejpam-6407	513	5	,	,	PUNCT
ejpam-6407	513	6	2024	2024	NUM
ejpam-6407	513	7	.	.	PUNCT
ejpam-6407	514	1	[	[	X
ejpam-6407	514	2	54	54	NUM
ejpam-6407	514	3	]	]	PUNCT
ejpam-6407	514	4	alaa	alaa	PROPN
ejpam-6407	514	5	m.	m.	PROPN
ejpam-6407	514	6	abd	abd	PROPN
ejpam-6407	514	7	el	el	PROPN
ejpam-6407	514	8	-	-	PROPN
ejpam-6407	514	9	latif	latif	PROPN
ejpam-6407	514	10	,	,	PUNCT
ejpam-6407	514	11	mesfer	mesfer	VERB
ejpam-6407	514	12	h.	h.	PROPN
ejpam-6407	514	13	alqahtani	alqahtani	PROPN
ejpam-6407	514	14	,	,	PUNCT
ejpam-6407	514	15	and	and	CCONJ
ejpam-6407	514	16	f.	f.	PROPN
ejpam-6407	514	17	a.	a.	PROPN
ejpam-6407	514	18	gharib	gharib	PROPN
ejpam-6407	514	19	.	.	PUNCT
ejpam-6407	515	1	strictly	strictly	ADV
ejpam-6407	515	2	wider	wide	ADJ
ejpam-6407	515	3	class	class	NOUN
ejpam-6407	515	4	of	of	ADP
ejpam-6407	515	5	soft	soft	ADJ
ejpam-6407	515	6	sets	set	NOUN
ejpam-6407	515	7	via	via	ADP
ejpam-6407	515	8	supra	supra	PROPN
ejpam-6407	515	9	soft	soft	PROPN
ejpam-6407	515	10	δ	δ	PROPN
ejpam-6407	515	11	-	-	PUNCT
ejpam-6407	515	12	closure	closure	NOUN
ejpam-6407	515	13	operator	operator	NOUN
ejpam-6407	515	14	.	.	PUNCT
ejpam-6407	516	1	international	international	ADJ
ejpam-6407	516	2	journal	journal	NOUN
ejpam-6407	516	3	of	of	ADP
ejpam-6407	516	4	analysis	analysis	NOUN
ejpam-6407	516	5	and	and	CCONJ
ejpam-6407	516	6	applications	application	NOUN
ejpam-6407	516	7	,	,	PUNCT
ejpam-6407	516	8	22:47	22:47	NUM
ejpam-6407	516	9	,	,	PUNCT
ejpam-6407	516	10	2024	2024	NUM
ejpam-6407	516	11	.	.	PUNCT
ejpam-6407	517	1	[	[	X
ejpam-6407	517	2	55	55	NUM
ejpam-6407	517	3	]	]	PUNCT
ejpam-6407	517	4	s.	s.	PROPN
ejpam-6407	517	5	saleh	saleh	PROPN
ejpam-6407	517	6	,	,	PUNCT
ejpam-6407	517	7	t.	t.	PROPN
ejpam-6407	517	8	al	al	PROPN
ejpam-6407	517	9	-	-	PUNCT
ejpam-6407	517	10	shami	shami	PROPN
ejpam-6407	517	11	,	,	PUNCT
ejpam-6407	517	12	laith	laith	PROPN
ejpam-6407	517	13	r.	r.	PROPN
ejpam-6407	517	14	flaiha	flaiha	PROPN
ejpam-6407	517	15	,	,	PUNCT
ejpam-6407	517	16	murad	murad	NOUN
ejpam-6407	517	17	arar	arar	NOUN
ejpam-6407	517	18	,	,	PUNCT
ejpam-6407	517	19	and	and	CCONJ
ejpam-6407	517	20	radwan	radwan	VERB
ejpam-6407	517	21	abu	abu	PROPN
ejpam-6407	517	22	-	-	PUNCT
ejpam-6407	517	23	gdairi	gdairi	PROPN
ejpam-6407	517	24	.	.	PUNCT
ejpam-6407	518	1	riseparation	riseparation	NOUN
ejpam-6407	518	2	axioms	axiom	NOUN
ejpam-6407	518	3	via	via	ADP
ejpam-6407	518	4	supra	supra	PROPN
ejpam-6407	518	5	soft	soft	ADJ
ejpam-6407	518	6	topological	topological	ADJ
ejpam-6407	518	7	spaces	space	NOUN
ejpam-6407	518	8	.	.	PUNCT
ejpam-6407	519	1	journal	journal	NOUN
ejpam-6407	519	2	of	of	ADP
ejpam-6407	519	3	mathematics	mathematic	NOUN
ejpam-6407	519	4	and	and	CCONJ
ejpam-6407	519	5	computer	computer	NOUN
ejpam-6407	519	6	science	science	NOUN
ejpam-6407	519	7	,	,	PUNCT
ejpam-6407	519	8	32:263–274	32:263–274	NUM
ejpam-6407	519	9	,	,	PUNCT
ejpam-6407	519	10	2024	2024	NUM
ejpam-6407	519	11	.	.	PUNCT
ejpam-6407	520	1	[	[	X
ejpam-6407	520	2	56	56	NUM
ejpam-6407	520	3	]	]	PUNCT
ejpam-6407	520	4	a.	a.	NOUN
ejpam-6407	520	5	m.	m.	PROPN
ejpam-6407	520	6	abd	abd	PROPN
ejpam-6407	520	7	el	el	PROPN
ejpam-6407	520	8	-	-	PROPN
ejpam-6407	520	9	latif	latif	PROPN
ejpam-6407	520	10	.	.	PUNCT
ejpam-6407	521	1	novel	novel	ADJ
ejpam-6407	521	2	types	type	NOUN
ejpam-6407	521	3	of	of	ADP
ejpam-6407	521	4	supra	supra	ADJ
ejpam-6407	521	5	soft	soft	ADJ
ejpam-6407	521	6	operators	operator	NOUN
ejpam-6407	521	7	via	via	ADP
ejpam-6407	521	8	supra	supra	PROPN
ejpam-6407	521	9	soft	soft	ADJ
ejpam-6407	521	10	sd	sd	NOUN
ejpam-6407	521	11	-	-	PUNCT
ejpam-6407	521	12	sets	set	NOUN
ejpam-6407	521	13	and	and	CCONJ
ejpam-6407	521	14	applications	application	NOUN
ejpam-6407	521	15	.	.	PUNCT
ejpam-6407	522	1	aims	aim	VERB
ejpam-6407	522	2	mathematics	mathematic	NOUN
ejpam-6407	522	3	,	,	PUNCT
ejpam-6407	522	4	9(3):6586–6602	9(3):6586–6602	PROPN
ejpam-6407	522	5	,	,	PUNCT
ejpam-6407	522	6	2024	2024	NUM
ejpam-6407	522	7	.	.	PUNCT
ejpam-6407	523	1	[	[	X
ejpam-6407	523	2	57	57	NUM
ejpam-6407	523	3	]	]	PUNCT
ejpam-6407	523	4	a.	a.	NOUN
ejpam-6407	523	5	m.	m.	PROPN
ejpam-6407	523	6	abd	abd	PROPN
ejpam-6407	523	7	el	el	PROPN
ejpam-6407	523	8	-	-	PROPN
ejpam-6407	523	9	latif	latif	PROPN
ejpam-6407	523	10	and	and	CCONJ
ejpam-6407	523	11	m.	m.	PROPN
ejpam-6407	523	12	h.	h.	PROPN
ejpam-6407	523	13	alqahtani	alqahtani	PROPN
ejpam-6407	523	14	.	.	PUNCT
ejpam-6407	524	1	novel	novel	ADJ
ejpam-6407	524	2	categories	category	NOUN
ejpam-6407	524	3	of	of	ADP
ejpam-6407	524	4	supra	supra	ADJ
ejpam-6407	524	5	soft	soft	ADJ
ejpam-6407	524	6	continuous	continuous	ADJ
ejpam-6407	524	7	maps	map	NOUN
ejpam-6407	524	8	via	via	ADP
ejpam-6407	524	9	new	new	ADJ
ejpam-6407	524	10	soft	soft	ADJ
ejpam-6407	524	11	operators	operator	NOUN
ejpam-6407	524	12	.	.	PUNCT
ejpam-6407	525	1	aims	aim	VERB
ejpam-6407	525	2	mathematics	mathematic	NOUN
ejpam-6407	525	3	,	,	PUNCT
ejpam-6407	525	4	9:7449–7470	9:7449–7470	NUM
ejpam-6407	525	5	,	,	PUNCT
ejpam-6407	525	6	2024	2024	NUM
ejpam-6407	525	7	.	.	PUNCT
ejpam-6407	526	1	[	[	X
ejpam-6407	526	2	58	58	NUM
ejpam-6407	526	3	]	]	PUNCT
ejpam-6407	526	4	a.	a.	NOUN
ejpam-6407	526	5	m.	m.	PROPN
ejpam-6407	526	6	abd	abd	PROPN
ejpam-6407	526	7	el	el	PROPN
ejpam-6407	526	8	-	-	PROPN
ejpam-6407	526	9	latif	latif	PROPN
ejpam-6407	526	10	,	,	PUNCT
ejpam-6407	526	11	a.	a.	PROPN
ejpam-6407	526	12	a.	a.	PROPN
ejpam-6407	526	13	azzam	azzam	PROPN
ejpam-6407	526	14	,	,	PUNCT
ejpam-6407	526	15	radwan	radwan	VERB
ejpam-6407	526	16	abu	abu	PROPN
ejpam-6407	526	17	-	-	PUNCT
ejpam-6407	526	18	gdairi	gdairi	PROPN
ejpam-6407	526	19	,	,	PUNCT
ejpam-6407	526	20	m.	m.	NOUN
ejpam-6407	526	21	aldawood	aldawood	PROPN
ejpam-6407	526	22	,	,	PUNCT
ejpam-6407	526	23	and	and	CCONJ
ejpam-6407	526	24	mesfer	mesfer	VERB
ejpam-6407	526	25	h.	h.	PROPN
ejpam-6407	526	26	alqahtani	alqahtani	PROPN
ejpam-6407	526	27	.	.	PUNCT
ejpam-6407	527	1	new	new	ADJ
ejpam-6407	527	2	versions	version	NOUN
ejpam-6407	527	3	of	of	ADP
ejpam-6407	527	4	maps	map	NOUN
ejpam-6407	527	5	and	and	CCONJ
ejpam-6407	527	6	connected	connected	ADJ
ejpam-6407	527	7	spaces	space	NOUN
ejpam-6407	527	8	via	via	ADP
ejpam-6407	527	9	supra	supra	PROPN
ejpam-6407	527	10	soft	soft	ADJ
ejpam-6407	527	11	sd	sd	NOUN
ejpam-6407	527	12	-	-	PUNCT
ejpam-6407	527	13	operators	operator	NOUN
ejpam-6407	527	14	.	.	PUNCT
ejpam-6407	528	1	plos	plos	PROPN
ejpam-6407	528	2	one	one	NUM
ejpam-6407	528	3	,	,	PUNCT
ejpam-6407	528	4	19(10):e0304042	19(10):e0304042	NUM
ejpam-6407	528	5	,	,	PUNCT
ejpam-6407	528	6	2024	2024	NUM
ejpam-6407	528	7	.	.	PUNCT
ejpam-6407	529	1	[	[	X
ejpam-6407	529	2	59	59	NUM
ejpam-6407	529	3	]	]	PUNCT
ejpam-6407	529	4	a.	a.	NOUN
ejpam-6407	529	5	m.	m.	PROPN
ejpam-6407	529	6	abd	abd	PROPN
ejpam-6407	529	7	el	el	PROPN
ejpam-6407	529	8	-	-	PROPN
ejpam-6407	529	9	latif	latif	PROPN
ejpam-6407	529	10	,	,	PUNCT
ejpam-6407	529	11	radwan	radwan	VERB
ejpam-6407	529	12	abu	abu	PROPN
ejpam-6407	529	13	gdairi	gdairi	PROPN
ejpam-6407	529	14	,	,	PUNCT
ejpam-6407	529	15	a.	a.	PROPN
ejpam-6407	529	16	a.	a.	PROPN
ejpam-6407	529	17	azzam	azzam	PROPN
ejpam-6407	529	18	,	,	PUNCT
ejpam-6407	529	19	khaled	khaled	PROPN
ejpam-6407	529	20	a.	a.	PROPN
ejpam-6407	529	21	aldwoah	aldwoah	PROPN
ejpam-6407	529	22	,	,	PUNCT
ejpam-6407	529	23	m.	m.	NOUN
ejpam-6407	529	24	aldawood	aldawood	PROPN
ejpam-6407	529	25	,	,	PUNCT
ejpam-6407	529	26	and	and	CCONJ
ejpam-6407	529	27	shaaban	shaaban	ADJ
ejpam-6407	529	28	m.	m.	NOUN
ejpam-6407	529	29	shaaban	shaaban	PROPN
ejpam-6407	529	30	.	.	PUNCT
ejpam-6407	530	1	applications	application	NOUN
ejpam-6407	530	2	of	of	ADP
ejpam-6407	530	3	the	the	DET
ejpam-6407	530	4	supra	supra	PROPN
ejpam-6407	530	5	soft	soft	ADJ
ejpam-6407	530	6	sd	sd	NOUN
ejpam-6407	530	7	-	-	PUNCT
ejpam-6407	530	8	closure	closure	NOUN
ejpam-6407	530	9	operator	operator	NOUN
ejpam-6407	530	10	to	to	ADP
ejpam-6407	530	11	soft	soft	ADJ
ejpam-6407	530	12	connectedness	connectedness	NOUN
ejpam-6407	530	13	and	and	CCONJ
ejpam-6407	530	14	compactness	compactness	NOUN
ejpam-6407	530	15	.	.	PUNCT
ejpam-6407	531	1	european	european	ADJ
ejpam-6407	531	2	journal	journal	PROPN
ejpam-6407	531	3	of	of	ADP
ejpam-6407	531	4	pure	pure	ADJ
ejpam-6407	531	5	and	and	CCONJ
ejpam-6407	531	6	applied	applied	ADJ
ejpam-6407	531	7	mathematics	mathematic	NOUN
ejpam-6407	531	8	,	,	PUNCT
ejpam-6407	531	9	18(2):5896	18(2):5896	NUM
ejpam-6407	531	10	,	,	PUNCT
ejpam-6407	531	11	2025	2025	NUM
ejpam-6407	531	12	.	.	PUNCT
ejpam-6407	532	1	[	[	X
ejpam-6407	532	2	60	60	NUM
ejpam-6407	532	3	]	]	PUNCT
ejpam-6407	532	4	a.	a.	NOUN
ejpam-6407	532	5	m.	m.	PROPN
ejpam-6407	532	6	abd	abd	PROPN
ejpam-6407	532	7	el	el	PROPN
ejpam-6407	532	8	-	-	PROPN
ejpam-6407	532	9	latif	latif	PROPN
ejpam-6407	532	10	.	.	PUNCT
ejpam-6407	533	1	specific	specific	ADJ
ejpam-6407	533	2	types	type	NOUN
ejpam-6407	533	3	of	of	ADP
ejpam-6407	533	4	lindelofness	lindelofness	NOUN
ejpam-6407	533	5	and	and	CCONJ
ejpam-6407	533	6	compactness	compactness	NOUN
ejpam-6407	533	7	based	base	VERB
ejpam-6407	533	8	on	on	ADP
ejpam-6407	533	9	novel	novel	ADJ
ejpam-6407	533	10	supra	supra	ADJ
ejpam-6407	533	11	soft	soft	ADJ
ejpam-6407	533	12	operator	operator	NOUN
ejpam-6407	533	13	.	.	PUNCT
ejpam-6407	534	1	aims	aim	VERB
ejpam-6407	534	2	mathematics	mathematic	NOUN
ejpam-6407	534	3	,	,	PUNCT
ejpam-6407	534	4	10(4):8144–8164	10(4):8144–8164	NUM
ejpam-6407	534	5	,	,	PUNCT
ejpam-6407	534	6	2025	2025	NUM
ejpam-6407	534	7	.	.	PUNCT
ejpam-6407	535	1	[	[	X
ejpam-6407	535	2	61	61	NUM
ejpam-6407	535	3	]	]	PUNCT
ejpam-6407	535	4	mesfer	mesfer	NOUN
ejpam-6407	535	5	h.	h.	PROPN
ejpam-6407	535	6	alqahtani	alqahtani	PROPN
ejpam-6407	535	7	and	and	CCONJ
ejpam-6407	535	8	zanyar	zanyar	PROPN
ejpam-6407	535	9	a.	a.	NOUN
ejpam-6407	535	10	ameen	ameen	PROPN
ejpam-6407	535	11	.	.	PUNCT
ejpam-6407	536	1	soft	soft	ADJ
ejpam-6407	536	2	nodec	nodec	ADJ
ejpam-6407	536	3	spaces	space	NOUN
ejpam-6407	536	4	.	.	PUNCT
ejpam-6407	537	1	aims	aim	VERB
ejpam-6407	537	2	mathematics	mathematic	NOUN
ejpam-6407	537	3	,	,	PUNCT
ejpam-6407	537	4	9(2):3289–3302	9(2):3289–3302	PROPN
ejpam-6407	537	5	,	,	PUNCT
ejpam-6407	537	6	2024	2024	NUM
ejpam-6407	537	7	.	.	PUNCT
ejpam-6407	538	1	[	[	X
ejpam-6407	538	2	62	62	NUM
ejpam-6407	538	3	]	]	PUNCT
ejpam-6407	538	4	m.	m.	NOUN
ejpam-6407	538	5	h.	h.	PROPN
ejpam-6407	538	6	alqahtani	alqahtani	PROPN
ejpam-6407	538	7	,	,	PUNCT
ejpam-6407	538	8	o.	o.	PROPN
ejpam-6407	538	9	f.	f.	PROPN
ejpam-6407	538	10	alghamdi	alghamdi	PROPN
ejpam-6407	538	11	,	,	PUNCT
ejpam-6407	538	12	and	and	CCONJ
ejpam-6407	538	13	z.	z.	PROPN
ejpam-6407	538	14	a.	a.	PROPN
ejpam-6407	538	15	ameen	ameen	PROPN
ejpam-6407	538	16	.	.	PUNCT
ejpam-6407	539	1	nodecness	nodecness	NOUN
ejpam-6407	539	2	of	of	ADP
ejpam-6407	539	3	soft	soft	ADJ
ejpam-6407	539	4	generalized	generalized	ADJ
ejpam-6407	539	5	topological	topological	ADJ
ejpam-6407	539	6	spaces	space	NOUN
ejpam-6407	539	7	.	.	PUNCT
ejpam-6407	540	1	international	international	ADJ
ejpam-6407	540	2	journal	journal	NOUN
ejpam-6407	540	3	of	of	ADP
ejpam-6407	540	4	analysis	analysis	NOUN
ejpam-6407	540	5	and	and	CCONJ
ejpam-6407	540	6	applications	application	NOUN
ejpam-6407	540	7	,	,	PUNCT
ejpam-6407	540	8	22:149	22:149	NUM
ejpam-6407	540	9	,	,	PUNCT
ejpam-6407	540	10	2024	2024	NUM
ejpam-6407	540	11	.	.	PUNCT
ejpam-6407	541	1	[	[	X
ejpam-6407	541	2	63	63	NUM
ejpam-6407	541	3	]	]	PUNCT
ejpam-6407	541	4	t.	t.	PROPN
ejpam-6407	541	5	m.	m.	PROPN
ejpam-6407	541	6	al	al	PROPN
ejpam-6407	541	7	-	-	PUNCT
ejpam-6407	541	8	shami	shami	PROPN
ejpam-6407	541	9	,	,	PUNCT
ejpam-6407	541	10	e.	e.	PROPN
ejpam-6407	541	11	a.	a.	PROPN
ejpam-6407	541	12	abo	abo	PROPN
ejpam-6407	541	13	-	-	PUNCT
ejpam-6407	541	14	tabl	tabl	NOUN
ejpam-6407	541	15	,	,	PUNCT
ejpam-6407	541	16	b.	b.	PROPN
ejpam-6407	541	17	a.	a.	PROPN
ejpam-6407	541	18	asaad	asaad	PROPN
ejpam-6407	541	19	,	,	PUNCT
ejpam-6407	541	20	and	and	CCONJ
ejpam-6407	541	21	m.	m.	NOUN
ejpam-6407	541	22	a.	a.	NOUN
ejpam-6407	541	23	arahet	arahet	PROPN
ejpam-6407	541	24	.	.	PUNCT
ejpam-6407	542	1	limit	limit	NOUN
ejpam-6407	542	2	points	point	NOUN
ejpam-6407	542	3	and	and	CCONJ
ejpam-6407	542	4	separation	separation	NOUN
ejpam-6407	542	5	axioms	axiom	NOUN
ejpam-6407	542	6	with	with	ADP
ejpam-6407	542	7	respect	respect	NOUN
ejpam-6407	542	8	to	to	ADP
ejpam-6407	542	9	supra	supra	PROPN
ejpam-6407	542	10	semi	semi	ADJ
ejpam-6407	542	11	-	-	ADJ
ejpam-6407	542	12	open	open	ADJ
ejpam-6407	542	13	sets	set	NOUN
ejpam-6407	542	14	.	.	PUNCT
ejpam-6407	543	1	european	european	ADJ
ejpam-6407	543	2	journal	journal	PROPN
ejpam-6407	543	3	of	of	ADP
ejpam-6407	543	4	pure	pure	ADJ
ejpam-6407	543	5	and	and	CCONJ
ejpam-6407	543	6	applied	applied	ADJ
ejpam-6407	543	7	mathematics	mathematic	NOUN
ejpam-6407	543	8	,	,	PUNCT
ejpam-6407	543	9	13(3):427–443	13(3):427–443	PROPN
ejpam-6407	543	10	,	,	PUNCT
ejpam-6407	543	11	2020	2020	NUM
ejpam-6407	543	12	.	.	PUNCT
ejpam-6407	544	1	[	[	X
ejpam-6407	544	2	64	64	NUM
ejpam-6407	544	3	]	]	PUNCT
ejpam-6407	544	4	a.	a.	NOUN
ejpam-6407	544	5	m.	m.	PROPN
ejpam-6407	544	6	abd	abd	PROPN
ejpam-6407	544	7	el	el	PROPN
ejpam-6407	544	8	-	-	PROPN
ejpam-6407	544	9	latif	latif	PROPN
ejpam-6407	544	10	.	.	PUNCT
ejpam-6407	545	1	some	some	DET
ejpam-6407	545	2	properties	property	NOUN
ejpam-6407	545	3	of	of	ADP
ejpam-6407	545	4	fuzzy	fuzzy	ADJ
ejpam-6407	545	5	supra	supra	PROPN
ejpam-6407	545	6	soft	soft	ADJ
ejpam-6407	545	7	topological	topological	ADJ
ejpam-6407	545	8	spaces	space	NOUN
ejpam-6407	545	9	.	.	PUNCT
ejpam-6407	546	1	european	european	ADJ
ejpam-6407	546	2	journal	journal	PROPN
ejpam-6407	546	3	of	of	ADP
ejpam-6407	546	4	pure	pure	ADJ
ejpam-6407	546	5	and	and	CCONJ
ejpam-6407	546	6	applied	applied	ADJ
ejpam-6407	546	7	mathematics	mathematic	NOUN
ejpam-6407	546	8	,	,	PUNCT
ejpam-6407	546	9	12(3):999–1017	12(3):999–1017	NUM
ejpam-6407	546	10	,	,	PUNCT
ejpam-6407	546	11	2019	2019	NUM
ejpam-6407	546	12	.	.	PUNCT
ejpam-6407	547	1	[	[	X
ejpam-6407	547	2	65	65	NUM
ejpam-6407	547	3	]	]	X
ejpam-6407	547	4	a.	a.	NOUN
ejpam-6407	547	5	m.	m.	PROPN
ejpam-6407	547	6	abd	abd	PROPN
ejpam-6407	547	7	el	el	PROPN
ejpam-6407	547	8	-	-	PROPN
ejpam-6407	547	9	latif	latif	PROPN
ejpam-6407	547	10	.	.	PUNCT
ejpam-6407	548	1	results	result	NOUN
ejpam-6407	548	2	on	on	ADP
ejpam-6407	548	3	fuzzy	fuzzy	ADJ
ejpam-6407	548	4	supra	supra	PROPN
ejpam-6407	548	5	soft	soft	ADJ
ejpam-6407	548	6	topological	topological	ADJ
ejpam-6407	548	7	spaces	space	NOUN
ejpam-6407	548	8	.	.	PUNCT
ejpam-6407	549	1	journal	journal	NOUN
ejpam-6407	549	2	of	of	ADP
ejpam-6407	549	3	interdisciplinary	interdisciplinary	ADJ
ejpam-6407	549	4	mathematics	mathematic	NOUN
ejpam-6407	549	5	,	,	PUNCT
ejpam-6407	549	6	22(8):1311–1323	22(8):1311–1323	NUM
ejpam-6407	549	7	,	,	PUNCT
ejpam-6407	549	8	2019	2019	NUM
ejpam-6407	549	9	.	.	PUNCT
ejpam-6407	550	1	[	[	X
ejpam-6407	550	2	66	66	NUM
ejpam-6407	550	3	]	]	PUNCT
ejpam-6407	550	4	rani	rani	PROPN
ejpam-6407	550	5	sumaira	sumaira	PROPN
ejpam-6407	550	6	kanwal	kanwal	PROPN
ejpam-6407	550	7	,	,	PUNCT
ejpam-6407	550	8	saqib	saqib	NOUN
ejpam-6407	550	9	mazher	mazher	NOUN
ejpam-6407	550	10	qurashi	qurashi	NOUN
ejpam-6407	550	11	,	,	PUNCT
ejpam-6407	550	12	rizwan	rizwan	PROPN
ejpam-6407	550	13	gul	gul	PROPN
ejpam-6407	550	14	,	,	PUNCT
ejpam-6407	550	15	alaa	alaa	PROPN
ejpam-6407	550	16	m.	m.	PROPN
ejpam-6407	550	17	abd	abd	PROPN
ejpam-6407	550	18	el	el	PROPN
ejpam-6407	550	19	-	-	PROPN
ejpam-6407	550	20	latif	latif	PROPN
ejpam-6407	550	21	,	,	PUNCT
ejpam-6407	550	22	tareq	tareq	PROPN
ejpam-6407	550	23	m.	m.	PROPN
ejpam-6407	550	24	al	al	PROPN
ejpam-6407	550	25	-	-	PUNCT
ejpam-6407	550	26	shami	shami	PROPN
ejpam-6407	550	27	,	,	PUNCT
ejpam-6407	550	28	and	and	CCONJ
ejpam-6407	550	29	faiza	faiza	PROPN
ejpam-6407	550	30	tufail	tufail	PROPN
ejpam-6407	550	31	.	.	PUNCT
ejpam-6407	551	1	new	new	ADJ
ejpam-6407	551	2	insights	insight	NOUN
ejpam-6407	551	3	into	into	ADP
ejpam-6407	551	4	rough	rough	ADJ
ejpam-6407	551	5	approximations	approximation	NOUN
ejpam-6407	551	6	of	of	ADP
ejpam-6407	551	7	a	a	DET
ejpam-6407	551	8	fuzzy	fuzzy	ADJ
ejpam-6407	551	9	set	set	NOUN
ejpam-6407	551	10	inspired	inspire	VERB
ejpam-6407	551	11	by	by	ADP
ejpam-6407	551	12	soft	soft	ADJ
ejpam-6407	551	13	relations	relation	NOUN
ejpam-6407	551	14	with	with	ADP
ejpam-6407	551	15	decision	decision	NOUN
ejpam-6407	551	16	making	make	VERB
ejpam-6407	551	17	applications	application	NOUN
ejpam-6407	551	18	.	.	PUNCT
ejpam-6407	552	1	aims	aim	VERB
ejpam-6407	552	2	mathematics	mathematic	NOUN
ejpam-6407	552	3	,	,	PUNCT
ejpam-6407	552	4	10(4):9637–9673	10(4):9637–9673	NUM
ejpam-6407	552	5	,	,	PUNCT
ejpam-6407	552	6	2025	2025	NUM
ejpam-6407	552	7	.	.	PUNCT