id	sid	tid	token	lemma	pos
ejpam-6408	1	1	european	european	PROPN
ejpam-6408	1	2	journal	journal	PROPN
ejpam-6408	1	3	of	of	ADP
ejpam-6408	1	4	pure	pure	ADJ
ejpam-6408	1	5	and	and	CCONJ
ejpam-6408	1	6	applied	applied	ADJ
ejpam-6408	1	7	mathematics	mathematic	NOUN
ejpam-6408	1	8	2025	2025	NUM
ejpam-6408	1	9	,	,	PUNCT
ejpam-6408	1	10	vol	vol	NOUN
ejpam-6408	1	11	.	.	PROPN
ejpam-6408	1	12	18	18	NUM
ejpam-6408	1	13	,	,	PUNCT
ejpam-6408	1	14	issue	issue	NOUN
ejpam-6408	1	15	3	3	NUM
ejpam-6408	1	16	,	,	PUNCT
ejpam-6408	1	17	article	article	NOUN
ejpam-6408	1	18	number	number	NOUN
ejpam-6408	1	19	6408	6408	NUM
ejpam-6408	1	20	issn	issn	PROPN
ejpam-6408	1	21	1307	1307	NUM
ejpam-6408	1	22	-	-	SYM
ejpam-6408	1	23	5543	5543	NUM
ejpam-6408	1	24	–	–	PUNCT
ejpam-6408	1	25	ejpam.com	ejpam.com	X
ejpam-6408	1	26	published	publish	VERB
ejpam-6408	1	27	by	by	ADP
ejpam-6408	1	28	new	new	PROPN
ejpam-6408	1	29	york	york	PROPN
ejpam-6408	1	30	business	business	PROPN
ejpam-6408	1	31	global	global	PROPN
ejpam-6408	1	32	supra	supra	PROPN
ejpam-6408	1	33	regularity	regularity	NOUN
ejpam-6408	1	34	and	and	CCONJ
ejpam-6408	1	35	supra	supra	ADJ
ejpam-6408	1	36	normality	normality	NOUN
ejpam-6408	1	37	inspired	inspire	VERB
ejpam-6408	1	38	by	by	ADP
ejpam-6408	1	39	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	1	40	sets	set	NOUN
ejpam-6408	1	41	m.	m.	NOUN
ejpam-6408	1	42	aldawood1	aldawood1	PROPN
ejpam-6408	1	43	,	,	PUNCT
ejpam-6408	1	44	alaa	alaa	PROPN
ejpam-6408	1	45	m.	m.	PROPN
ejpam-6408	1	46	abd	abd	PROPN
ejpam-6408	1	47	el	el	PROPN
ejpam-6408	1	48	-	-	PUNCT
ejpam-6408	1	49	latif2	latif2	PROPN
ejpam-6408	1	50	,	,	PUNCT
ejpam-6408	1	51	khaled	khaled	ADJ
ejpam-6408	1	52	a.	a.	NOUN
ejpam-6408	1	53	aldwoah3	aldwoah3	PROPN
ejpam-6408	1	54	,	,	PUNCT
ejpam-6408	2	1	a.	a.	PROPN
ejpam-6408	2	2	a.	a.	PROPN
ejpam-6408	2	3	azzam1,4	azzam1,4	PROPN
ejpam-6408	2	4	,	,	PUNCT
ejpam-6408	2	5	abdelhalim	abdelhalim	PROPN
ejpam-6408	2	6	hasnaoui2,∗	hasnaoui2,∗	PROPN
ejpam-6408	2	7	,	,	PUNCT
ejpam-6408	2	8	m.	m.	NOUN
ejpam-6408	2	9	i.	i.	PROPN
ejpam-6408	2	10	elashiry2	elashiry2	PROPN
ejpam-6408	2	11	,	,	PUNCT
ejpam-6408	2	12	enas	enas	PROPN
ejpam-6408	2	13	h.	h.	PROPN
ejpam-6408	2	14	elkordy1,5	elkordy1,5	PROPN
ejpam-6408	2	15	,	,	PUNCT
ejpam-6408	2	16	husham	husham	PROPN
ejpam-6408	2	17	m.	m.	NOUN
ejpam-6408	2	18	attaalfadeel2	attaalfadeel2	PROPN
ejpam-6408	2	19	1	1	NUM
ejpam-6408	2	20	department	department	NOUN
ejpam-6408	2	21	of	of	ADP
ejpam-6408	2	22	mathematics	mathematic	NOUN
ejpam-6408	2	23	,	,	PUNCT
ejpam-6408	2	24	faculty	faculty	NOUN
ejpam-6408	2	25	of	of	ADP
ejpam-6408	2	26	science	science	NOUN
ejpam-6408	2	27	and	and	CCONJ
ejpam-6408	2	28	humanities	humanity	NOUN
ejpam-6408	2	29	,	,	PUNCT
ejpam-6408	2	30	prince	prince	PROPN
ejpam-6408	2	31	sattam	sattam	PROPN
ejpam-6408	2	32	bin	bin	PROPN
ejpam-6408	2	33	abdulaziz	abdulaziz	PROPN
ejpam-6408	2	34	university	university	PROPN
ejpam-6408	2	35	,	,	PUNCT
ejpam-6408	2	36	alkharj	alkharj	VERB
ejpam-6408	2	37	11942	11942	NUM
ejpam-6408	2	38	,	,	PUNCT
ejpam-6408	2	39	saudi	saudi	PROPN
ejpam-6408	2	40	arabia	arabia	PROPN
ejpam-6408	2	41	2	2	NUM
ejpam-6408	2	42	department	department	NOUN
ejpam-6408	2	43	of	of	ADP
ejpam-6408	2	44	mathematics	mathematic	NOUN
ejpam-6408	2	45	,	,	PUNCT
ejpam-6408	2	46	college	college	NOUN
ejpam-6408	2	47	of	of	ADP
ejpam-6408	2	48	science	science	NOUN
ejpam-6408	2	49	,	,	PUNCT
ejpam-6408	2	50	northern	northern	ADJ
ejpam-6408	2	51	border	border	NOUN
ejpam-6408	2	52	university	university	NOUN
ejpam-6408	2	53	,	,	PUNCT
ejpam-6408	2	54	arar	arar	NOUN
ejpam-6408	2	55	91431	91431	NUM
ejpam-6408	2	56	,	,	PUNCT
ejpam-6408	2	57	saudi	saudi	PROPN
ejpam-6408	2	58	arabia	arabia	PROPN
ejpam-6408	2	59	3	3	NUM
ejpam-6408	2	60	department	department	NOUN
ejpam-6408	2	61	of	of	ADP
ejpam-6408	2	62	mathematics	mathematic	NOUN
ejpam-6408	2	63	,	,	PUNCT
ejpam-6408	2	64	faculty	faculty	NOUN
ejpam-6408	2	65	of	of	ADP
ejpam-6408	2	66	science	science	NOUN
ejpam-6408	2	67	,	,	PUNCT
ejpam-6408	2	68	islamic	islamic	PROPN
ejpam-6408	2	69	university	university	PROPN
ejpam-6408	2	70	of	of	ADP
ejpam-6408	2	71	madinah	madinah	PROPN
ejpam-6408	2	72	,	,	PUNCT
ejpam-6408	2	73	medinah	medinah	PROPN
ejpam-6408	2	74	,	,	PUNCT
ejpam-6408	2	75	saudi	saudi	PROPN
ejpam-6408	2	76	arabia	arabia	PROPN
ejpam-6408	2	77	4	4	NUM
ejpam-6408	2	78	department	department	NOUN
ejpam-6408	2	79	of	of	ADP
ejpam-6408	2	80	mathematics	mathematic	NOUN
ejpam-6408	2	81	,	,	PUNCT
ejpam-6408	2	82	faculty	faculty	NOUN
ejpam-6408	2	83	of	of	ADP
ejpam-6408	2	84	science	science	NOUN
ejpam-6408	2	85	,	,	PUNCT
ejpam-6408	2	86	new	new	ADJ
ejpam-6408	2	87	valley	valley	NOUN
ejpam-6408	2	88	university	university	NOUN
ejpam-6408	2	89	,	,	PUNCT
ejpam-6408	2	90	elkharga	elkharga	NOUN
ejpam-6408	2	91	72511	72511	NUM
ejpam-6408	2	92	,	,	PUNCT
ejpam-6408	2	93	egypt	egypt	PROPN
ejpam-6408	2	94	5	5	NUM
ejpam-6408	2	95	mathematics	mathematic	NOUN
ejpam-6408	2	96	and	and	CCONJ
ejpam-6408	2	97	computer	computer	NOUN
ejpam-6408	2	98	science	science	PROPN
ejpam-6408	2	99	department	department	PROPN
ejpam-6408	2	100	,	,	PUNCT
ejpam-6408	2	101	faculty	faculty	NOUN
ejpam-6408	2	102	of	of	ADP
ejpam-6408	2	103	science	science	NOUN
ejpam-6408	2	104	,	,	PUNCT
ejpam-6408	2	105	beni	beni	ADJ
ejpam-6408	2	106	-	-	ADJ
ejpam-6408	2	107	suef	suef	ADJ
ejpam-6408	2	108	university	university	NOUN
ejpam-6408	2	109	,	,	PUNCT
ejpam-6408	2	110	beni	beni	ADJ
ejpam-6408	2	111	suef	suef	NOUN
ejpam-6408	2	112	,	,	PUNCT
ejpam-6408	2	113	egypt	egypt	PROPN
ejpam-6408	2	114	abstract	abstract	PROPN
ejpam-6408	2	115	.	.	PUNCT
ejpam-6408	3	1	in	in	ADP
ejpam-6408	3	2	this	this	DET
ejpam-6408	3	3	article	article	NOUN
ejpam-6408	3	4	,	,	PUNCT
ejpam-6408	3	5	as	as	ADP
ejpam-6408	3	6	an	an	DET
ejpam-6408	3	7	extension	extension	NOUN
ejpam-6408	3	8	of	of	ADP
ejpam-6408	3	9	the	the	DET
ejpam-6408	3	10	concepts	concept	NOUN
ejpam-6408	3	11	of	of	ADP
ejpam-6408	3	12	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	3	13	-	-	PUNCT
ejpam-6408	3	14	space	space	NOUN
ejpam-6408	3	15	,	,	PUNCT
ejpam-6408	3	16	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6408	3	17	-	-	PUNCT
ejpam-6408	3	18	space	space	NOUN
ejpam-6408	3	19	,	,	PUNCT
ejpam-6408	3	20	and	and	CCONJ
ejpam-6408	3	21	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6408	3	22	-	-	NOUN
ejpam-6408	3	23	space	space	NOUN
ejpam-6408	3	24	,	,	PUNCT
ejpam-6408	3	25	we	we	PRON
ejpam-6408	3	26	present	present	VERB
ejpam-6408	3	27	the	the	DET
ejpam-6408	3	28	notion	notion	NOUN
ejpam-6408	3	29	of	of	ADP
ejpam-6408	3	30	supra-ϵ-completely	supra-ϵ-completely	ADV
ejpam-6408	3	31	space	space	NOUN
ejpam-6408	3	32	.	.	PUNCT
ejpam-6408	4	1	furthermore	furthermore	ADV
ejpam-6408	4	2	,	,	PUNCT
ejpam-6408	4	3	we	we	PRON
ejpam-6408	4	4	demonstrate	demonstrate	VERB
ejpam-6408	4	5	that	that	SCONJ
ejpam-6408	4	6	for	for	ADP
ejpam-6408	4	7	any	any	DET
ejpam-6408	4	8	sts	st	NOUN
ejpam-6408	4	9	(	(	PUNCT
ejpam-6408	4	10	γ	γ	X
ejpam-6408	4	11	,	,	PUNCT
ejpam-6408	4	12	θ	θ	PROPN
ejpam-6408	4	13	)	)	PUNCT
ejpam-6408	4	14	,	,	PUNCT
ejpam-6408	4	15	the	the	DET
ejpam-6408	4	16	concepts	concept	NOUN
ejpam-6408	4	17	of	of	ADP
ejpam-6408	4	18	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	4	19	-	-	PUNCT
ejpam-6408	4	20	space	space	NOUN
ejpam-6408	4	21	and	and	CCONJ
ejpam-6408	4	22	supra-ϵ-completely	supra-ϵ-completely	ADV
ejpam-6408	4	23	-	-	PUNCT
ejpam-6408	4	24	space	space	NOUN
ejpam-6408	4	25	are	be	AUX
ejpam-6408	4	26	the	the	DET
ejpam-6408	4	27	same	same	ADJ
ejpam-6408	4	28	if	if	SCONJ
ejpam-6408	4	29	|γ|	|γ|	PRON
ejpam-6408	4	30	⩽	⩽	NOUN
ejpam-6408	4	31	4	4	X
ejpam-6408	4	32	.	.	PUNCT
ejpam-6408	5	1	we	we	PRON
ejpam-6408	5	2	also	also	ADV
ejpam-6408	5	3	explore	explore	VERB
ejpam-6408	5	4	the	the	DET
ejpam-6408	5	5	behavior	behavior	NOUN
ejpam-6408	5	6	of	of	ADP
ejpam-6408	5	7	this	this	DET
ejpam-6408	5	8	notion	notion	NOUN
ejpam-6408	5	9	with	with	ADP
ejpam-6408	5	10	respect	respect	NOUN
ejpam-6408	5	11	to	to	ADP
ejpam-6408	5	12	specific	specific	ADJ
ejpam-6408	5	13	forms	form	NOUN
ejpam-6408	5	14	of	of	ADP
ejpam-6408	5	15	supra	supra	ADJ
ejpam-6408	5	16	functions	function	NOUN
ejpam-6408	5	17	.	.	PUNCT
ejpam-6408	6	1	we	we	PRON
ejpam-6408	6	2	demonstrate	demonstrate	VERB
ejpam-6408	6	3	that	that	SCONJ
ejpam-6408	6	4	,	,	PUNCT
ejpam-6408	6	5	under	under	ADP
ejpam-6408	6	6	a	a	DET
ejpam-6408	6	7	bijective	bijective	ADJ
ejpam-6408	6	8	supra	supra	PROPN
ejpam-6408	6	9	ϵ∗-open	ϵ∗-open	PROPN
ejpam-6408	6	10	function	function	NOUN
ejpam-6408	6	11	,	,	PUNCT
ejpam-6408	6	12	the	the	DET
ejpam-6408	6	13	image	image	NOUN
ejpam-6408	6	14	of	of	ADP
ejpam-6408	6	15	any	any	DET
ejpam-6408	6	16	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	6	17	1	1	NUM
ejpam-6408	6	18	2	2	NUM
ejpam-6408	6	19	-space	-space	NOUN
ejpam-6408	6	20	is	be	AUX
ejpam-6408	6	21	a	a	DET
ejpam-6408	6	22	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	6	23	1	1	NUM
ejpam-6408	6	24	2	2	NUM
ejpam-6408	6	25	.	.	PUNCT
ejpam-6408	7	1	additionally	additionally	ADV
ejpam-6408	7	2	,	,	PUNCT
ejpam-6408	7	3	we	we	PRON
ejpam-6408	7	4	demonstrate	demonstrate	VERB
ejpam-6408	7	5	that	that	SCONJ
ejpam-6408	7	6	every	every	DET
ejpam-6408	7	7	supra	supra	ADJ
ejpam-6408	7	8	subspace	subspace	NOUN
ejpam-6408	7	9	of	of	ADP
ejpam-6408	7	10	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	7	11	1	1	NUM
ejpam-6408	7	12	2	2	NUM
ejpam-6408	7	13	-space	-space	NOUN
ejpam-6408	7	14	is	be	AUX
ejpam-6408	7	15	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	7	16	1	1	NUM
ejpam-6408	7	17	2	2	NUM
ejpam-6408	7	18	.	.	PUNCT
ejpam-6408	8	1	moreover	moreover	ADV
ejpam-6408	8	2	,	,	PUNCT
ejpam-6408	8	3	four	four	NUM
ejpam-6408	8	4	new	new	ADJ
ejpam-6408	8	5	versions	version	NOUN
ejpam-6408	8	6	of	of	ADP
ejpam-6408	8	7	separation	separation	NOUN
ejpam-6408	8	8	axioms	axiom	NOUN
ejpam-6408	8	9	that	that	PRON
ejpam-6408	8	10	utilize	utilize	VERB
ejpam-6408	8	11	supra	supra	PROPN
ejpam-6408	8	12	ϵ-open	ϵ-open	PROPN
ejpam-6408	8	13	sets	set	NOUN
ejpam-6408	8	14	are	be	AUX
ejpam-6408	8	15	introduced	introduce	VERB
ejpam-6408	8	16	namely	namely	ADV
ejpam-6408	8	17	:	:	PUNCT
ejpam-6408	8	18	supra-ϵ-regular	supra-ϵ-regular	NOUN
ejpam-6408	8	19	-	-	PUNCT
ejpam-6408	8	20	space	space	NOUN
ejpam-6408	8	21	,	,	PUNCT
ejpam-6408	8	22	supra-ϵ-normal	supra-ϵ-normal	ADJ
ejpam-6408	8	23	-	-	PUNCT
ejpam-6408	8	24	space	space	NOUN
ejpam-6408	8	25	,	,	PUNCT
ejpam-6408	8	26	supra-ϵ-t3space	supra-ϵ-t3space	NOUN
ejpam-6408	8	27	,	,	PUNCT
ejpam-6408	8	28	and	and	CCONJ
ejpam-6408	8	29	supra-ϵ-t4	supra-ϵ-t4	NOUN
ejpam-6408	8	30	-	-	PUNCT
ejpam-6408	8	31	space	space	NOUN
ejpam-6408	8	32	.	.	PUNCT
ejpam-6408	9	1	we	we	PRON
ejpam-6408	9	2	also	also	ADV
ejpam-6408	9	3	give	give	VERB
ejpam-6408	9	4	a	a	DET
ejpam-6408	9	5	general	general	ADJ
ejpam-6408	9	6	illustration	illustration	NOUN
ejpam-6408	9	7	of	of	ADP
ejpam-6408	9	8	their	their	PRON
ejpam-6408	9	9	key	key	ADJ
ejpam-6408	9	10	traits	trait	NOUN
ejpam-6408	9	11	and	and	CCONJ
ejpam-6408	9	12	look	look	VERB
ejpam-6408	9	13	at	at	ADP
ejpam-6408	9	14	the	the	DET
ejpam-6408	9	15	prerequisites	prerequisite	NOUN
ejpam-6408	9	16	for	for	ADP
ejpam-6408	9	17	a	a	DET
ejpam-6408	9	18	number	number	NOUN
ejpam-6408	9	19	of	of	ADP
ejpam-6408	9	20	similar	similar	ADJ
ejpam-6408	9	21	links	link	NOUN
ejpam-6408	9	22	between	between	ADP
ejpam-6408	9	23	them	they	PRON
ejpam-6408	9	24	.	.	PUNCT
ejpam-6408	10	1	we	we	PRON
ejpam-6408	10	2	also	also	ADV
ejpam-6408	10	3	propose	propose	VERB
ejpam-6408	10	4	a	a	DET
ejpam-6408	10	5	figure	figure	NOUN
ejpam-6408	10	6	1	1	NUM
ejpam-6408	10	7	graphic	graphic	NOUN
ejpam-6408	10	8	that	that	PRON
ejpam-6408	10	9	shows	show	VERB
ejpam-6408	10	10	these	these	DET
ejpam-6408	10	11	linkages	linkage	NOUN
ejpam-6408	10	12	.	.	PUNCT
ejpam-6408	11	1	furthermore	furthermore	ADV
ejpam-6408	11	2	,	,	PUNCT
ejpam-6408	11	3	we	we	PRON
ejpam-6408	11	4	demonstrate	demonstrate	VERB
ejpam-6408	11	5	that	that	SCONJ
ejpam-6408	11	6	every	every	DET
ejpam-6408	11	7	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	11	8	-	-	NOUN
ejpam-6408	11	9	space	space	NOUN
ejpam-6408	11	10	(	(	PUNCT
ejpam-6408	11	11	γ	γ	X
ejpam-6408	11	12	,	,	PUNCT
ejpam-6408	11	13	θ	θ	NOUN
ejpam-6408	11	14	)	)	PUNCT
ejpam-6408	11	15	is	be	AUX
ejpam-6408	11	16	supra-ϵ-n	supra-ϵ-n	ADJ
ejpam-6408	11	17	space	space	NOUN
ejpam-6408	11	18	if	if	SCONJ
ejpam-6408	11	19	|γ|	|γ|	PRON
ejpam-6408	11	20	⩽	⩽	NOUN
ejpam-6408	11	21	4	4	X
ejpam-6408	11	22	.	.	PUNCT
ejpam-6408	12	1	this	this	PRON
ejpam-6408	12	2	implies	imply	VERB
ejpam-6408	12	3	that	that	SCONJ
ejpam-6408	12	4	the	the	DET
ejpam-6408	12	5	approaches	approach	NOUN
ejpam-6408	12	6	of	of	ADP
ejpam-6408	12	7	supra-ϵ-t3	supra-ϵ-t3	NOUN
ejpam-6408	12	8	-	-	PUNCT
ejpam-6408	12	9	space	space	NOUN
ejpam-6408	12	10	and	and	CCONJ
ejpam-6408	12	11	supra-ϵ-t4	supra-ϵ-t4	NOUN
ejpam-6408	12	12	-	-	PUNCT
ejpam-6408	12	13	space	space	NOUN
ejpam-6408	12	14	are	be	AUX
ejpam-6408	12	15	the	the	DET
ejpam-6408	12	16	same	same	ADJ
ejpam-6408	12	17	in	in	ADP
ejpam-6408	12	18	this	this	DET
ejpam-6408	12	19	case	case	NOUN
ejpam-6408	12	20	.	.	PUNCT
ejpam-6408	13	1	the	the	DET
ejpam-6408	13	2	necessary	necessary	ADJ
ejpam-6408	13	3	counterexamples	counterexample	NOUN
ejpam-6408	13	4	that	that	PRON
ejpam-6408	13	5	validate	validate	VERB
ejpam-6408	13	6	our	our	PRON
ejpam-6408	13	7	findings	finding	NOUN
ejpam-6408	13	8	are	be	AUX
ejpam-6408	13	9	finally	finally	ADV
ejpam-6408	13	10	presented	present	VERB
ejpam-6408	13	11	.	.	PUNCT
ejpam-6408	14	1	2020	2020	NUM
ejpam-6408	14	2	mathematics	mathematics	PROPN
ejpam-6408	14	3	subject	subject	NOUN
ejpam-6408	14	4	classifications	classification	NOUN
ejpam-6408	14	5	:	:	PUNCT
ejpam-6408	14	6	54a05	54a05	NUM
ejpam-6408	14	7	,	,	PUNCT
ejpam-6408	14	8	54c05	54c05	NUM
ejpam-6408	14	9	,	,	PUNCT
ejpam-6408	14	10	54c08	54c08	NUM
ejpam-6408	14	11	key	key	ADJ
ejpam-6408	14	12	words	word	NOUN
ejpam-6408	14	13	and	and	CCONJ
ejpam-6408	14	14	phrases	phrase	NOUN
ejpam-6408	14	15	:	:	PUNCT
ejpam-6408	14	16	supra-ϵ-completely	supra-ϵ-completely	ADV
ejpam-6408	14	17	space	space	NOUN
ejpam-6408	14	18	,	,	PUNCT
ejpam-6408	14	19	supra-ϵ-regularity	supra-ϵ-regularity	PROPN
ejpam-6408	14	20	,	,	PUNCT
ejpam-6408	14	21	supra-ϵ-normality	supra-ϵ-normality	PROPN
ejpam-6408	14	22	,	,	PUNCT
ejpam-6408	14	23	supra	supra	ADJ
ejpam-6408	14	24	hereditary	hereditary	ADJ
ejpam-6408	14	25	property	property	NOUN
ejpam-6408	14	26	∗corresponding	∗corresponde	VERB
ejpam-6408	14	27	author	author	NOUN
ejpam-6408	14	28	.	.	PUNCT
ejpam-6408	15	1	doi	doi	NOUN
ejpam-6408	15	2	:	:	PUNCT
ejpam-6408	15	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6408	https://doi.org/10.29020/nybg.ejpam.v18i3.6408	ADJ
ejpam-6408	15	4	email	email	NOUN
ejpam-6408	15	5	addresses	address	NOUN
ejpam-6408	15	6	:	:	PUNCT
ejpam-6408	15	7	m.aldawood@psau.edu.sa	m.aldawood@psau.edu.sa	PROPN
ejpam-6408	15	8	(	(	PUNCT
ejpam-6408	15	9	m.	m.	NOUN
ejpam-6408	15	10	aldawood	aldawood	PROPN
ejpam-6408	15	11	)	)	PUNCT
ejpam-6408	15	12	,	,	PUNCT
ejpam-6408	15	13	alaa.ali@nbu.edu.sa	alaa.ali@nbu.edu.sa	PROPN
ejpam-6408	15	14	,	,	PUNCT
ejpam-6408	15	15	alaa	alaa	PROPN
ejpam-6408	15	16	8560@yahoo.com	8560@yahoo.com	PROPN
ejpam-6408	15	17	(	(	PUNCT
ejpam-6408	15	18	a.	a.	PROPN
ejpam-6408	15	19	m.	m.	PROPN
ejpam-6408	15	20	abd	abd	PROPN
ejpam-6408	15	21	el	el	PROPN
ejpam-6408	15	22	-	-	PROPN
ejpam-6408	15	23	latif	latif	PROPN
ejpam-6408	15	24	)	)	PUNCT
ejpam-6408	15	25	,	,	PUNCT
ejpam-6408	15	26	aldwoah@yahoo.com	aldwoah@yahoo.com	X
ejpam-6408	15	27	(	(	PUNCT
ejpam-6408	15	28	k.	k.	PROPN
ejpam-6408	15	29	a.	a.	PROPN
ejpam-6408	15	30	aldwoah	aldwoah	PROPN
ejpam-6408	15	31	)	)	PUNCT
ejpam-6408	15	32	,	,	PUNCT
ejpam-6408	15	33	aa.azzam@psau.edu.sa	aa.azzam@psau.edu.sa	PROPN
ejpam-6408	15	34	(	(	PUNCT
ejpam-6408	15	35	a.	a.	NOUN
ejpam-6408	15	36	a.	a.	PROPN
ejpam-6408	15	37	azzam	azzam	PROPN
ejpam-6408	15	38	)	)	PUNCT
ejpam-6408	15	39	,	,	PUNCT
ejpam-6408	15	40	abdllhalim.hasanawa@nbu.edu.sa	abdllhalim.hasanawa@nbu.edu.sa	PROPN
ejpam-6408	15	41	(	(	PUNCT
ejpam-6408	15	42	a.	a.	PROPN
ejpam-6408	15	43	hasnaoui	hasnaoui	PROPN
ejpam-6408	15	44	)	)	PUNCT
ejpam-6408	15	45	,	,	PUNCT
ejpam-6408	15	46	mustafa.elashiry@nbu.edu.sa	mustafa.elashiry@nbu.edu.sa	PROPN
ejpam-6408	15	47	(	(	PUNCT
ejpam-6408	15	48	m.	m.	NOUN
ejpam-6408	15	49	i.	i.	PROPN
ejpam-6408	15	50	elashiry	elashiry	PROPN
ejpam-6408	15	51	)	)	PUNCT
ejpam-6408	15	52	,	,	PUNCT
ejpam-6408	15	53	e.elkordy@psau.edu.sa	e.elkordy@psau.edu.sa	PROPN
ejpam-6408	15	54	(	(	PUNCT
ejpam-6408	15	55	e.	e.	PROPN
ejpam-6408	15	56	h.	h.	PROPN
ejpam-6408	15	57	elkordy	elkordy	PROPN
ejpam-6408	15	58	)	)	PUNCT
ejpam-6408	15	59	,	,	PUNCT
ejpam-6408	15	60	husham.alhassan@nbu.edu.sa	husham.alhassan@nbu.edu.sa	PROPN
ejpam-6408	15	61	(	(	PUNCT
ejpam-6408	15	62	h.	h.	PROPN
ejpam-6408	15	63	m.	m.	PROPN
ejpam-6408	15	64	attaalfadeel	attaalfadeel	PROPN
ejpam-6408	15	65	)	)	PUNCT
ejpam-6408	15	66	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6408	15	67	1	1	NUM
ejpam-6408	15	68	copyright	copyright	NOUN
ejpam-6408	15	69	:	:	PUNCT
ejpam-6408	16	1	©	©	PROPN
ejpam-6408	16	2	2025	2025	NUM
ejpam-6408	16	3	the	the	DET
ejpam-6408	16	4	author(s	author(s	NOUN
ejpam-6408	16	5	)	)	PUNCT
ejpam-6408	16	6	.	.	PUNCT
ejpam-6408	17	1	(	(	PUNCT
ejpam-6408	17	2	cc	cc	NOUN
ejpam-6408	17	3	by	by	ADP
ejpam-6408	17	4	-	-	PUNCT
ejpam-6408	17	5	nc	nc	PROPN
ejpam-6408	17	6	4.0	4.0	NUM
ejpam-6408	17	7	)	)	PUNCT
ejpam-6408	17	8	m.	m.	NOUN
ejpam-6408	17	9	aldawood	aldawood	NOUN
ejpam-6408	17	10	et	et	PROPN
ejpam-6408	17	11	al	al	PROPN
ejpam-6408	17	12	.	.	PUNCT
ejpam-6408	17	13	/	/	SYM
ejpam-6408	17	14	eur	eur	PROPN
ejpam-6408	17	15	.	.	PUNCT
ejpam-6408	18	1	j.	j.	PROPN
ejpam-6408	18	2	pure	pure	PROPN
ejpam-6408	18	3	appl	appl	PROPN
ejpam-6408	18	4	.	.	PROPN
ejpam-6408	18	5	math	math	PROPN
ejpam-6408	18	6	,	,	PUNCT
ejpam-6408	18	7	18	18	NUM
ejpam-6408	18	8	(	(	PUNCT
ejpam-6408	18	9	3	3	NUM
ejpam-6408	18	10	)	)	PUNCT
ejpam-6408	18	11	(	(	PUNCT
ejpam-6408	18	12	2025	2025	NUM
ejpam-6408	18	13	)	)	PUNCT
ejpam-6408	18	14	,	,	PUNCT
ejpam-6408	18	15	6408	6408	NUM
ejpam-6408	18	16	2	2	NUM
ejpam-6408	18	17	of	of	ADP
ejpam-6408	18	18	16	16	NUM
ejpam-6408	18	19	1	1	NUM
ejpam-6408	18	20	.	.	PUNCT
ejpam-6408	19	1	introduction	introduction	NOUN
ejpam-6408	19	2	over	over	ADP
ejpam-6408	19	3	the	the	DET
ejpam-6408	19	4	past	past	ADJ
ejpam-6408	19	5	few	few	ADJ
ejpam-6408	19	6	decades	decade	NOUN
ejpam-6408	19	7	,	,	PUNCT
ejpam-6408	19	8	supra	supra	ADJ
ejpam-6408	19	9	topologies	topology	NOUN
ejpam-6408	19	10	,	,	PUNCT
ejpam-6408	19	11	topologies	topology	NOUN
ejpam-6408	19	12	,	,	PUNCT
ejpam-6408	19	13	fuzzy	fuzzy	ADJ
ejpam-6408	19	14	topologies	topology	NOUN
ejpam-6408	19	15	,	,	PUNCT
ejpam-6408	19	16	and	and	CCONJ
ejpam-6408	19	17	soft	soft	ADJ
ejpam-6408	19	18	topologies	topology	NOUN
ejpam-6408	19	19	research	research	NOUN
ejpam-6408	19	20	has	have	AUX
ejpam-6408	19	21	been	be	AUX
ejpam-6408	19	22	heavily	heavily	ADV
ejpam-6408	19	23	influenced	influence	VERB
ejpam-6408	19	24	by	by	ADP
ejpam-6408	19	25	the	the	DET
ejpam-6408	19	26	study	study	NOUN
ejpam-6408	19	27	of	of	ADP
ejpam-6408	19	28	many	many	ADJ
ejpam-6408	19	29	types	type	NOUN
ejpam-6408	19	30	of	of	ADP
ejpam-6408	19	31	generalized	generalized	ADJ
ejpam-6408	19	32	open	open	ADJ
ejpam-6408	19	33	,	,	PUNCT
ejpam-6408	19	34	supra	supra	NOUN
ejpam-6408	19	35	open	open	ADJ
ejpam-6408	19	36	,	,	PUNCT
ejpam-6408	19	37	and	and	CCONJ
ejpam-6408	19	38	soft	soft	ADJ
ejpam-6408	19	39	open	open	ADJ
ejpam-6408	19	40	sets	set	NOUN
ejpam-6408	19	41	as	as	ADV
ejpam-6408	19	42	well	well	ADV
ejpam-6408	19	43	as	as	ADP
ejpam-6408	19	44	their	their	PRON
ejpam-6408	19	45	basic	basic	ADJ
ejpam-6408	19	46	characteristics	characteristic	NOUN
ejpam-6408	19	47	.	.	PUNCT
ejpam-6408	20	1	semi	semi	ADJ
ejpam-6408	20	2	-	-	ADJ
ejpam-6408	20	3	open	open	ADJ
ejpam-6408	20	4	sets	set	NOUN
ejpam-6408	20	5	(	(	PUNCT
ejpam-6408	20	6	continuous	continuous	ADJ
ejpam-6408	20	7	maps	map	NOUN
ejpam-6408	20	8	)	)	PUNCT
ejpam-6408	20	9	were	be	AUX
ejpam-6408	20	10	initially	initially	ADV
ejpam-6408	20	11	proposed	propose	VERB
ejpam-6408	20	12	by	by	ADP
ejpam-6408	20	13	levine	levine	PROPN
ejpam-6408	20	14	[	[	X
ejpam-6408	20	15	1	1	NUM
ejpam-6408	20	16	]	]	PUNCT
ejpam-6408	20	17	in	in	ADP
ejpam-6408	20	18	1963	1963	NUM
ejpam-6408	20	19	.	.	PUNCT
ejpam-6408	21	1	njasta	njasta	NOUN
ejpam-6408	22	1	[	[	X
ejpam-6408	22	2	2	2	X
ejpam-6408	22	3	]	]	PUNCT
ejpam-6408	22	4	introduced	introduce	VERB
ejpam-6408	22	5	the	the	DET
ejpam-6408	22	6	idea	idea	NOUN
ejpam-6408	22	7	of	of	ADP
ejpam-6408	22	8	α	α	NOUN
ejpam-6408	22	9	-	-	ADJ
ejpam-6408	22	10	open	open	ADJ
ejpam-6408	22	11	sets	set	NOUN
ejpam-6408	22	12	two	two	NUM
ejpam-6408	22	13	years	year	NOUN
ejpam-6408	22	14	later	later	ADV
ejpam-6408	22	15	.	.	PUNCT
ejpam-6408	23	1	mashhour	mashhour	INTJ
ejpam-6408	23	2	et	et	PROPN
ejpam-6408	23	3	al	al	PROPN
ejpam-6408	23	4	.	.	PROPN
ejpam-6408	23	5	introduced	introduce	VERB
ejpam-6408	23	6	the	the	DET
ejpam-6408	23	7	idea	idea	NOUN
ejpam-6408	23	8	of	of	ADP
ejpam-6408	23	9	pre	pre	VERB
ejpam-6408	23	10	open	open	ADJ
ejpam-6408	23	11	sets	set	NOUN
ejpam-6408	23	12	(	(	PUNCT
ejpam-6408	23	13	pre	pre	X
ejpam-6408	23	14	continuous	continuous	ADJ
ejpam-6408	23	15	maps	map	NOUN
ejpam-6408	23	16	)	)	PUNCT
ejpam-6408	23	17	in	in	ADP
ejpam-6408	23	18	1982	1982	NUM
ejpam-6408	23	19	[	[	X
ejpam-6408	23	20	3	3	NUM
ejpam-6408	23	21	]	]	PUNCT
ejpam-6408	23	22	.	.	PUNCT
ejpam-6408	24	1	the	the	DET
ejpam-6408	24	2	notion	notion	NOUN
ejpam-6408	24	3	of	of	ADP
ejpam-6408	24	4	β	β	ADJ
ejpam-6408	24	5	-	-	ADJ
ejpam-6408	24	6	open	open	ADJ
ejpam-6408	24	7	sets	set	NOUN
ejpam-6408	24	8	(	(	PUNCT
ejpam-6408	24	9	β	β	X
ejpam-6408	24	10	-	-	ADJ
ejpam-6408	24	11	continuous	continuous	ADJ
ejpam-6408	24	12	maps	map	NOUN
ejpam-6408	24	13	)	)	PUNCT
ejpam-6408	24	14	was	be	AUX
ejpam-6408	24	15	first	first	ADV
ejpam-6408	24	16	presented	present	VERB
ejpam-6408	24	17	by	by	ADP
ejpam-6408	24	18	abd	abd	PROPN
ejpam-6408	24	19	-	-	PUNCT
ejpam-6408	24	20	el	el	PROPN
ejpam-6408	24	21	-	-	PUNCT
ejpam-6408	24	22	monsef	monsef	ADJ
ejpam-6408	24	23	et	et	PROPN
ejpam-6408	24	24	al	al	PROPN
ejpam-6408	24	25	.	.	PUNCT
ejpam-6408	25	1	[	[	X
ejpam-6408	25	2	4	4	X
ejpam-6408	25	3	]	]	PUNCT
ejpam-6408	25	4	in	in	ADP
ejpam-6408	25	5	1983	1983	NUM
ejpam-6408	25	6	.	.	PUNCT
ejpam-6408	26	1	in	in	ADP
ejpam-6408	26	2	1966	1966	NUM
ejpam-6408	26	3	,	,	PUNCT
ejpam-6408	26	4	the	the	DET
ejpam-6408	26	5	definition	definition	NOUN
ejpam-6408	26	6	of	of	ADP
ejpam-6408	26	7	b	b	NOUN
ejpam-6408	26	8	-	-	PUNCT
ejpam-6408	26	9	open	open	ADJ
ejpam-6408	26	10	sets	set	NOUN
ejpam-6408	26	11	was	be	AUX
ejpam-6408	26	12	investigated	investigate	VERB
ejpam-6408	26	13	in	in	ADP
ejpam-6408	26	14	detail	detail	NOUN
ejpam-6408	26	15	[	[	X
ejpam-6408	26	16	5	5	NUM
ejpam-6408	26	17	,	,	PUNCT
ejpam-6408	26	18	6	6	NUM
ejpam-6408	26	19	]	]	PUNCT
ejpam-6408	26	20	.	.	PUNCT
ejpam-6408	27	1	piotrowski	piotrowski	PROPN
ejpam-6408	28	1	[	[	X
ejpam-6408	28	2	7	7	X
ejpam-6408	28	3	]	]	PUNCT
ejpam-6408	28	4	presented	present	VERB
ejpam-6408	28	5	the	the	DET
ejpam-6408	28	6	notion	notion	NOUN
ejpam-6408	28	7	of	of	ADP
ejpam-6408	28	8	partially	partially	ADV
ejpam-6408	28	9	open	open	ADJ
ejpam-6408	28	10	sets	set	NOUN
ejpam-6408	28	11	(	(	PUNCT
ejpam-6408	28	12	continuous	continuous	ADJ
ejpam-6408	28	13	maps	map	NOUN
ejpam-6408	28	14	)	)	PUNCT
ejpam-6408	28	15	based	base	VERB
ejpam-6408	28	16	on	on	ADP
ejpam-6408	28	17	[	[	X
ejpam-6408	28	18	8	8	NUM
ejpam-6408	28	19	]	]	PUNCT
ejpam-6408	28	20	.	.	PUNCT
ejpam-6408	29	1	in	in	ADP
ejpam-6408	29	2	[	[	X
ejpam-6408	29	3	9	9	NUM
ejpam-6408	29	4	,	,	PUNCT
ejpam-6408	29	5	10	10	NUM
ejpam-6408	29	6	]	]	PUNCT
ejpam-6408	29	7	,	,	PUNCT
ejpam-6408	29	8	the	the	DET
ejpam-6408	29	9	approach	approach	NOUN
ejpam-6408	29	10	of	of	ADP
ejpam-6408	29	11	somewhere	somewhere	ADJ
ejpam-6408	29	12	dense	dense	ADJ
ejpam-6408	29	13	sets	set	NOUN
ejpam-6408	29	14	(	(	PUNCT
ejpam-6408	29	15	also	also	ADV
ejpam-6408	29	16	known	know	VERB
ejpam-6408	29	17	as	as	ADP
ejpam-6408	29	18	sd	sd	NOUN
ejpam-6408	29	19	-	-	PUNCT
ejpam-6408	29	20	sets	set	NOUN
ejpam-6408	29	21	)	)	PUNCT
ejpam-6408	29	22	was	be	AUX
ejpam-6408	29	23	proposed	propose	VERB
ejpam-6408	29	24	.	.	PUNCT
ejpam-6408	30	1	other	other	ADJ
ejpam-6408	30	2	aspects	aspect	NOUN
ejpam-6408	30	3	of	of	ADP
ejpam-6408	30	4	this	this	DET
ejpam-6408	30	5	concept	concept	NOUN
ejpam-6408	30	6	were	be	AUX
ejpam-6408	30	7	explored	explore	VERB
ejpam-6408	30	8	in	in	ADP
ejpam-6408	30	9	[	[	X
ejpam-6408	30	10	11	11	NUM
ejpam-6408	30	11	]	]	PUNCT
ejpam-6408	30	12	.	.	PUNCT
ejpam-6408	31	1	f	f	X
ejpam-6408	31	2	-	-	PUNCT
ejpam-6408	31	3	open	open	ADJ
ejpam-6408	31	4	was	be	AUX
ejpam-6408	31	5	first	first	ADV
ejpam-6408	31	6	introduced	introduce	VERB
ejpam-6408	31	7	by	by	ADP
ejpam-6408	31	8	alqahtani	alqahtani	PROPN
ejpam-6408	32	1	[	[	X
ejpam-6408	32	2	12	12	NUM
ejpam-6408	32	3	]	]	PUNCT
ejpam-6408	32	4	.	.	PUNCT
ejpam-6408	33	1	in	in	ADP
ejpam-6408	33	2	2024	2024	NUM
ejpam-6408	33	3	,	,	PUNCT
ejpam-6408	33	4	alqahtani	alqahtani	PROPN
ejpam-6408	33	5	et	et	PROPN
ejpam-6408	33	6	al	al	PROPN
ejpam-6408	33	7	.	.	PUNCT
ejpam-6408	34	1	[	[	X
ejpam-6408	34	2	13	13	NUM
ejpam-6408	34	3	]	]	PUNCT
ejpam-6408	34	4	presented	present	VERB
ejpam-6408	34	5	the	the	DET
ejpam-6408	34	6	n	n	CCONJ
ejpam-6408	34	7	-open	-open	PROPN
ejpam-6408	34	8	sets	set	NOUN
ejpam-6408	34	9	approach	approach	NOUN
ejpam-6408	34	10	,	,	PUNCT
ejpam-6408	34	11	which	which	PRON
ejpam-6408	34	12	generalizes	generalize	VERB
ejpam-6408	34	13	almost	almost	ADV
ejpam-6408	34	14	all	all	PRON
ejpam-6408	34	15	of	of	ADP
ejpam-6408	34	16	the	the	DET
ejpam-6408	34	17	earlier	early	ADJ
ejpam-6408	34	18	concepts	concept	NOUN
ejpam-6408	34	19	.	.	PUNCT
ejpam-6408	35	1	new	new	ADJ
ejpam-6408	35	2	kinds	kind	NOUN
ejpam-6408	35	3	of	of	ADP
ejpam-6408	35	4	operators	operator	NOUN
ejpam-6408	35	5	were	be	AUX
ejpam-6408	35	6	presented	present	VERB
ejpam-6408	35	7	by	by	ADP
ejpam-6408	35	8	alghamdi	alghamdi	PROPN
ejpam-6408	35	9	et	et	PROPN
ejpam-6408	35	10	al	al	PROPN
ejpam-6408	35	11	.	.	PROPN
ejpam-6408	36	1	in	in	ADP
ejpam-6408	36	2	the	the	DET
ejpam-6408	36	3	context	context	NOUN
ejpam-6408	36	4	of	of	ADP
ejpam-6408	36	5	primal	primal	ADJ
ejpam-6408	36	6	topological	topological	ADJ
ejpam-6408	36	7	spaces	space	NOUN
ejpam-6408	36	8	[	[	X
ejpam-6408	36	9	14	14	NUM
ejpam-6408	36	10	]	]	PUNCT
ejpam-6408	36	11	.	.	PUNCT
ejpam-6408	37	1	the	the	DET
ejpam-6408	37	2	concept	concept	NOUN
ejpam-6408	37	3	of	of	ADP
ejpam-6408	37	4	supra	supra	PROPN
ejpam-6408	37	5	open	open	ADJ
ejpam-6408	37	6	sets	set	NOUN
ejpam-6408	37	7	was	be	AUX
ejpam-6408	37	8	established	establish	VERB
ejpam-6408	37	9	by	by	ADP
ejpam-6408	37	10	mashhour	mashhour	PROPN
ejpam-6408	37	11	et	et	PROPN
ejpam-6408	37	12	al	al	PROPN
ejpam-6408	37	13	.	.	PUNCT
ejpam-6408	38	1	[	[	X
ejpam-6408	38	2	15	15	NUM
ejpam-6408	38	3	]	]	PUNCT
ejpam-6408	38	4	and	and	CCONJ
ejpam-6408	38	5	takes	take	VERB
ejpam-6408	38	6	into	into	ADP
ejpam-6408	38	7	account	account	NOUN
ejpam-6408	38	8	the	the	DET
ejpam-6408	38	9	fundamental	fundamental	ADJ
ejpam-6408	38	10	components	component	NOUN
ejpam-6408	38	11	of	of	ADP
ejpam-6408	38	12	supra	supra	PROPN
ejpam-6408	38	13	topology	topology	NOUN
ejpam-6408	38	14	(	(	PUNCT
ejpam-6408	38	15	or	or	CCONJ
ejpam-6408	38	16	sts	st	NOUN
ejpam-6408	38	17	)	)	PUNCT
ejpam-6408	38	18	.	.	PUNCT
ejpam-6408	39	1	they	they	PRON
ejpam-6408	39	2	created	create	VERB
ejpam-6408	39	3	fundamental	fundamental	ADJ
ejpam-6408	39	4	topological	topological	ADJ
ejpam-6408	39	5	concepts	concept	NOUN
ejpam-6408	39	6	like	like	ADP
ejpam-6408	39	7	as	as	ADP
ejpam-6408	39	8	continuity	continuity	NOUN
ejpam-6408	39	9	,	,	PUNCT
ejpam-6408	39	10	interior	interior	ADJ
ejpam-6408	39	11	(	(	PUNCT
ejpam-6408	39	12	closure	closure	NOUN
ejpam-6408	39	13	)	)	PUNCT
ejpam-6408	39	14	operators	operator	NOUN
ejpam-6408	39	15	,	,	PUNCT
ejpam-6408	39	16	and	and	CCONJ
ejpam-6408	39	17	separation	separation	NOUN
ejpam-6408	39	18	axioms	axiom	VERB
ejpam-6408	39	19	.	.	PUNCT
ejpam-6408	40	1	the	the	DET
ejpam-6408	40	2	concepts	concept	NOUN
ejpam-6408	40	3	of	of	ADP
ejpam-6408	40	4	supra	supra	PROPN
ejpam-6408	40	5	semi[16	semi[16	PROPN
ejpam-6408	40	6	]	]	PUNCT
ejpam-6408	40	7	(	(	PUNCT
ejpam-6408	40	8	r[17	r[17	PROPN
ejpam-6408	40	9	]	]	PUNCT
ejpam-6408	40	10	,	,	PUNCT
ejpam-6408	40	11	β[18	β[18	PROPN
ejpam-6408	40	12	]	]	PUNCT
ejpam-6408	40	13	,	,	PUNCT
ejpam-6408	40	14	b[19	b[19	PROPN
ejpam-6408	40	15	]	]	X
ejpam-6408	40	16	,	,	PUNCT
ejpam-6408	40	17	pre[20	pre[20	X
ejpam-6408	40	18	]	]	PUNCT
ejpam-6408	40	19	,	,	PUNCT
ejpam-6408	40	20	and	and	CCONJ
ejpam-6408	40	21	α[21	α[21	PROPN
ejpam-6408	40	22	]	]	PUNCT
ejpam-6408	40	23	)	)	PUNCT
ejpam-6408	40	24	open	open	ADJ
ejpam-6408	40	25	sets	set	NOUN
ejpam-6408	40	26	have	have	AUX
ejpam-6408	40	27	been	be	AUX
ejpam-6408	40	28	presented	present	VERB
ejpam-6408	40	29	as	as	ADV
ejpam-6408	40	30	well	well	ADV
ejpam-6408	40	31	as	as	ADP
ejpam-6408	40	32	their	their	PRON
ejpam-6408	40	33	key	key	ADJ
ejpam-6408	40	34	characteristics	characteristic	NOUN
ejpam-6408	40	35	.	.	PUNCT
ejpam-6408	41	1	a	a	DET
ejpam-6408	41	2	wide	wide	ADJ
ejpam-6408	41	3	range	range	NOUN
ejpam-6408	41	4	of	of	ADP
ejpam-6408	41	5	soft	soft	ADJ
ejpam-6408	41	6	continuity	continuity	NOUN
ejpam-6408	41	7	and	and	CCONJ
ejpam-6408	41	8	soft	soft	ADJ
ejpam-6408	41	9	open	open	ADJ
ejpam-6408	41	10	sets	set	NOUN
ejpam-6408	41	11	have	have	AUX
ejpam-6408	41	12	been	be	AUX
ejpam-6408	41	13	produced	produce	VERB
ejpam-6408	41	14	by	by	ADP
ejpam-6408	41	15	the	the	DET
ejpam-6408	41	16	fields	field	NOUN
ejpam-6408	41	17	of	of	ADP
ejpam-6408	41	18	broadly	broadly	ADV
ejpam-6408	41	19	applicable	applicable	ADJ
ejpam-6408	41	20	soft	soft	ADJ
ejpam-6408	41	21	open	open	ADJ
ejpam-6408	41	22	sets	set	NOUN
ejpam-6408	41	23	[	[	X
ejpam-6408	41	24	22	22	NUM
ejpam-6408	41	25	,	,	PUNCT
ejpam-6408	41	26	23	23	NUM
ejpam-6408	41	27	]	]	PUNCT
ejpam-6408	41	28	,	,	PUNCT
ejpam-6408	41	29	soft	soft	ADJ
ejpam-6408	41	30	semi	semi	ADJ
ejpam-6408	41	31	-	-	ADJ
ejpam-6408	41	32	open	open	ADJ
ejpam-6408	41	33	sets	set	NOUN
ejpam-6408	41	34	[	[	X
ejpam-6408	41	35	24	24	NUM
ejpam-6408	41	36	,	,	PUNCT
ejpam-6408	41	37	25	25	NUM
ejpam-6408	41	38	]	]	PUNCT
ejpam-6408	41	39	,	,	PUNCT
ejpam-6408	41	40	soft	soft	ADJ
ejpam-6408	41	41	sd	sd	NOUN
ejpam-6408	41	42	-	-	PUNCT
ejpam-6408	41	43	sets	set	NOUN
ejpam-6408	42	1	[	[	X
ejpam-6408	42	2	26	26	NUM
ejpam-6408	42	3	]	]	PUNCT
ejpam-6408	42	4	,	,	PUNCT
ejpam-6408	42	5	and	and	CCONJ
ejpam-6408	42	6	nearly	nearly	ADV
ejpam-6408	42	7	soft	soft	ADJ
ejpam-6408	42	8	β	β	ADJ
ejpam-6408	42	9	-	-	ADJ
ejpam-6408	42	10	open	open	ADJ
ejpam-6408	42	11	sets	set	NOUN
ejpam-6408	42	12	[	[	X
ejpam-6408	42	13	27	27	NUM
ejpam-6408	42	14	]	]	PUNCT
ejpam-6408	42	15	.	.	PUNCT
ejpam-6408	43	1	later	later	ADJ
ejpam-6408	43	2	research	research	NOUN
ejpam-6408	43	3	was	be	AUX
ejpam-6408	43	4	done	do	VERB
ejpam-6408	43	5	on	on	ADP
ejpam-6408	43	6	soft	soft	ADJ
ejpam-6408	43	7	continuity	continuity	NOUN
ejpam-6408	43	8	[	[	X
ejpam-6408	43	9	28	28	NUM
ejpam-6408	43	10	,	,	PUNCT
ejpam-6408	43	11	29	29	NUM
ejpam-6408	43	12	]	]	PUNCT
ejpam-6408	43	13	.	.	PUNCT
ejpam-6408	44	1	in	in	ADP
ejpam-6408	44	2	[	[	X
ejpam-6408	44	3	30	30	NUM
ejpam-6408	44	4	]	]	PUNCT
ejpam-6408	44	5	,	,	PUNCT
ejpam-6408	44	6	the	the	DET
ejpam-6408	44	7	concept	concept	NOUN
ejpam-6408	44	8	of	of	ADP
ejpam-6408	44	9	the	the	DET
ejpam-6408	44	10	soft	soft	ADJ
ejpam-6408	44	11	ideal	ideal	NOUN
ejpam-6408	44	12	initially	initially	ADV
ejpam-6408	44	13	appeared	appear	VERB
ejpam-6408	44	14	.	.	PUNCT
ejpam-6408	45	1	this	this	DET
ejpam-6408	45	2	concept	concept	NOUN
ejpam-6408	45	3	was	be	AUX
ejpam-6408	45	4	then	then	ADV
ejpam-6408	45	5	generalized	generalize	VERB
ejpam-6408	45	6	by	by	ADP
ejpam-6408	45	7	fatouh	fatouh	PROPN
ejpam-6408	45	8	et	et	PROPN
ejpam-6408	45	9	al	al	PROPN
ejpam-6408	45	10	.	.	PUNCT
ejpam-6408	46	1	[	[	X
ejpam-6408	46	2	31	31	NUM
ejpam-6408	46	3	]	]	PUNCT
ejpam-6408	46	4	using	use	VERB
ejpam-6408	46	5	soft	soft	ADJ
ejpam-6408	46	6	semi	semi	ADJ
ejpam-6408	46	7	-	-	ADJ
ejpam-6408	46	8	open	open	ADJ
ejpam-6408	46	9	sets	set	NOUN
ejpam-6408	46	10	.	.	PUNCT
ejpam-6408	47	1	this	this	DET
ejpam-6408	47	2	approcach	approcach	NOUN
ejpam-6408	47	3	is	be	AUX
ejpam-6408	47	4	then	then	ADV
ejpam-6408	47	5	used	use	VERB
ejpam-6408	47	6	to	to	PART
ejpam-6408	47	7	generalize	generalize	VERB
ejpam-6408	47	8	a	a	DET
ejpam-6408	47	9	number	number	NOUN
ejpam-6408	47	10	of	of	ADP
ejpam-6408	47	11	topological	topological	ADJ
ejpam-6408	47	12	features	feature	NOUN
ejpam-6408	47	13	,	,	PUNCT
ejpam-6408	47	14	including	include	VERB
ejpam-6408	47	15	soft	soft	ADJ
ejpam-6408	47	16	-	-	PUNCT
ejpam-6408	47	17	i	i	NOUN
ejpam-6408	47	18	-	-	PUNCT
ejpam-6408	47	19	open	open	ADJ
ejpam-6408	47	20	sets	set	NOUN
ejpam-6408	47	21	[	[	X
ejpam-6408	47	22	32	32	NUM
ejpam-6408	47	23	,	,	PUNCT
ejpam-6408	47	24	33	33	NUM
ejpam-6408	47	25	]	]	PUNCT
ejpam-6408	47	26	,	,	PUNCT
ejpam-6408	47	27	soft	soft	ADJ
ejpam-6408	47	28	open	open	ADJ
ejpam-6408	47	29	sets	set	NOUN
ejpam-6408	47	30	via	via	ADP
ejpam-6408	47	31	soft	soft	ADJ
ejpam-6408	47	32	ideals	ideal	NOUN
ejpam-6408	47	33	[	[	X
ejpam-6408	47	34	34	34	NUM
ejpam-6408	47	35	]	]	PUNCT
ejpam-6408	47	36	,	,	PUNCT
ejpam-6408	47	37	soft	soft	ADJ
ejpam-6408	47	38	compactness	compactness	NOUN
ejpam-6408	47	39	[	[	X
ejpam-6408	47	40	35	35	NUM
ejpam-6408	47	41	]	]	X
ejpam-6408	47	42	,	,	PUNCT
ejpam-6408	47	43	soft	soft	ADJ
ejpam-6408	47	44	ideals	ideal	NOUN
ejpam-6408	47	45	for	for	ADP
ejpam-6408	47	46	congruence	congruence	ADJ
ejpam-6408	47	47	representations	representation	NOUN
ejpam-6408	47	48	[	[	X
ejpam-6408	47	49	36	36	NUM
ejpam-6408	47	50	]	]	PUNCT
ejpam-6408	47	51	,	,	PUNCT
ejpam-6408	47	52	generalized	generalize	VERB
ejpam-6408	47	53	soft	soft	ADJ
ejpam-6408	47	54	rough	rough	ADJ
ejpam-6408	47	55	sets	set	NOUN
ejpam-6408	47	56	[	[	X
ejpam-6408	47	57	37	37	NUM
ejpam-6408	47	58	,	,	PUNCT
ejpam-6408	47	59	38	38	NUM
ejpam-6408	47	60	]	]	PUNCT
ejpam-6408	47	61	,	,	PUNCT
ejpam-6408	47	62	soft	soft	ADJ
ejpam-6408	47	63	separation	separation	NOUN
ejpam-6408	47	64	axioms	axiom	NOUN
ejpam-6408	48	1	[	[	X
ejpam-6408	48	2	39	39	NUM
ejpam-6408	48	3	]	]	PUNCT
ejpam-6408	48	4	,	,	PUNCT
ejpam-6408	48	5	and	and	CCONJ
ejpam-6408	48	6	soft	soft	ADJ
ejpam-6408	48	7	connectedness	connectedness	NOUN
ejpam-6408	49	1	[	[	X
ejpam-6408	49	2	40	40	NUM
ejpam-6408	49	3	]	]	PUNCT
ejpam-6408	49	4	.	.	PUNCT
ejpam-6408	50	1	recently	recently	ADV
ejpam-6408	50	2	,	,	PUNCT
ejpam-6408	50	3	several	several	ADJ
ejpam-6408	50	4	lower	low	ADJ
ejpam-6408	50	5	soft	soft	ADJ
ejpam-6408	50	6	separation	separation	NOUN
ejpam-6408	50	7	axioms	axiom	NOUN
ejpam-6408	50	8	[	[	X
ejpam-6408	50	9	41	41	NUM
ejpam-6408	50	10	]	]	PUNCT
ejpam-6408	50	11	and	and	CCONJ
ejpam-6408	50	12	certain	certain	ADJ
ejpam-6408	50	13	applications	application	NOUN
ejpam-6408	50	14	of	of	ADP
ejpam-6408	50	15	soft	soft	ADJ
ejpam-6408	50	16	δ	δ	NOUN
ejpam-6408	50	17	-	-	PUNCT
ejpam-6408	50	18	closed	close	VERB
ejpam-6408	50	19	sets	set	NOUN
ejpam-6408	50	20	[	[	X
ejpam-6408	50	21	42	42	NUM
ejpam-6408	50	22	]	]	PUNCT
ejpam-6408	50	23	were	be	AUX
ejpam-6408	50	24	presented	present	VERB
ejpam-6408	50	25	.	.	PUNCT
ejpam-6408	51	1	el	el	NOUN
ejpam-6408	51	2	-	-	PUNCT
ejpam-6408	51	3	sheikh	sheikh	PROPN
ejpam-6408	51	4	et	et	PROPN
ejpam-6408	51	5	al	al	PROPN
ejpam-6408	51	6	.	.	PUNCT
ejpam-6408	52	1	[	[	X
ejpam-6408	52	2	43	43	NUM
ejpam-6408	52	3	]	]	PUNCT
ejpam-6408	52	4	established	establish	VERB
ejpam-6408	52	5	the	the	DET
ejpam-6408	52	6	definition	definition	NOUN
ejpam-6408	52	7	of	of	ADP
ejpam-6408	52	8	supra	supra	PROPN
ejpam-6408	52	9	soft	soft	ADJ
ejpam-6408	52	10	topological	topological	ADJ
ejpam-6408	52	11	space	space	NOUN
ejpam-6408	52	12	.	.	PUNCT
ejpam-6408	53	1	a	a	DET
ejpam-6408	53	2	variety	variety	NOUN
ejpam-6408	53	3	of	of	ADP
ejpam-6408	53	4	supra	supra	PROPN
ejpam-6408	53	5	soft	soft	ADJ
ejpam-6408	53	6	operators	operator	NOUN
ejpam-6408	53	7	have	have	AUX
ejpam-6408	53	8	been	be	AUX
ejpam-6408	53	9	explored	explore	VERB
ejpam-6408	53	10	in	in	ADP
ejpam-6408	53	11	subsequent	subsequent	ADJ
ejpam-6408	53	12	studies	study	NOUN
ejpam-6408	53	13	in	in	ADP
ejpam-6408	53	14	terms	term	NOUN
ejpam-6408	53	15	of	of	ADP
ejpam-6408	53	16	supra	supra	ADJ
ejpam-6408	53	17	soft	soft	ADJ
ejpam-6408	53	18	-	-	PUNCT
ejpam-6408	53	19	bopen	bopen	NOUN
ejpam-6408	53	20	sets	set	NOUN
ejpam-6408	53	21	[	[	X
ejpam-6408	53	22	44	44	NUM
ejpam-6408	53	23	]	]	PUNCT
ejpam-6408	53	24	,	,	PUNCT
ejpam-6408	53	25	supra	supra	PROPN
ejpam-6408	53	26	(	(	PUNCT
ejpam-6408	53	27	strongly	strongly	ADV
ejpam-6408	53	28	)	)	PUNCT
ejpam-6408	53	29	generalized	generalize	VERB
ejpam-6408	53	30	closed	close	VERB
ejpam-6408	53	31	soft	soft	ADJ
ejpam-6408	53	32	sets	set	NOUN
ejpam-6408	53	33	via	via	ADP
ejpam-6408	53	34	soft	soft	ADJ
ejpam-6408	53	35	ideals	ideal	NOUN
ejpam-6408	53	36	[	[	X
ejpam-6408	53	37	45	45	NUM
ejpam-6408	53	38	,	,	PUNCT
ejpam-6408	53	39	46	46	NUM
ejpam-6408	53	40	]	]	PUNCT
ejpam-6408	53	41	,	,	PUNCT
ejpam-6408	53	42	supra	supra	PROPN
ejpam-6408	53	43	soft	soft	ADJ
ejpam-6408	53	44	sw	sw	PROPN
ejpam-6408	53	45	-	-	PUNCT
ejpam-6408	53	46	open	open	ADJ
ejpam-6408	53	47	sets	set	NOUN
ejpam-6408	53	48	[	[	X
ejpam-6408	53	49	47	47	NUM
ejpam-6408	53	50	]	]	PUNCT
ejpam-6408	53	51	,	,	PUNCT
ejpam-6408	53	52	supra	supra	PROPN
ejpam-6408	53	53	soft	soft	ADJ
ejpam-6408	53	54	δi	δi	NOUN
ejpam-6408	53	55	-	-	PUNCT
ejpam-6408	53	56	open	open	ADJ
ejpam-6408	53	57	sets	set	NOUN
ejpam-6408	53	58	[	[	X
ejpam-6408	53	59	48	48	NUM
ejpam-6408	53	60	,	,	PUNCT
ejpam-6408	53	61	49	49	NUM
ejpam-6408	53	62	]	]	PUNCT
ejpam-6408	53	63	,	,	PUNCT
ejpam-6408	53	64	and	and	CCONJ
ejpam-6408	53	65	soft	soft	ADJ
ejpam-6408	53	66	separation	separation	NOUN
ejpam-6408	53	67	axioms	axiom	NOUN
ejpam-6408	53	68	[	[	X
ejpam-6408	53	69	50	50	NUM
ejpam-6408	53	70	]	]	PUNCT
ejpam-6408	53	71	.	.	PUNCT
ejpam-6408	54	1	the	the	DET
ejpam-6408	54	2	concept	concept	NOUN
ejpam-6408	54	3	of	of	ADP
ejpam-6408	54	4	supra	supra	PROPN
ejpam-6408	54	5	soft	soft	ADJ
ejpam-6408	54	6	sd	sd	NOUN
ejpam-6408	54	7	-	-	PUNCT
ejpam-6408	54	8	sets	set	NOUN
ejpam-6408	54	9	[	[	X
ejpam-6408	54	10	51	51	NUM
ejpam-6408	54	11	,	,	PUNCT
ejpam-6408	54	12	52	52	NUM
ejpam-6408	54	13	]	]	PUNCT
ejpam-6408	54	14	was	be	AUX
ejpam-6408	54	15	recently	recently	ADV
ejpam-6408	54	16	exploited	exploit	VERB
ejpam-6408	54	17	by	by	ADP
ejpam-6408	54	18	abd	abd	PROPN
ejpam-6408	54	19	el	el	PROPN
ejpam-6408	54	20	-	-	PROPN
ejpam-6408	54	21	latif	latif	PROPN
ejpam-6408	54	22	et	et	PROPN
ejpam-6408	54	23	al	al	PROPN
ejpam-6408	54	24	.	.	PROPN
ejpam-6408	54	25	to	to	PART
ejpam-6408	54	26	introduce	introduce	VERB
ejpam-6408	54	27	new	new	ADJ
ejpam-6408	54	28	forms	form	NOUN
ejpam-6408	54	29	of	of	ADP
ejpam-6408	54	30	soft	soft	ADJ
ejpam-6408	54	31	connectedness	connectedness	NOUN
ejpam-6408	55	1	[	[	X
ejpam-6408	55	2	53	53	NUM
ejpam-6408	55	3	]	]	PUNCT
ejpam-6408	55	4	and	and	CCONJ
ejpam-6408	55	5	several	several	ADJ
ejpam-6408	55	6	forms	form	NOUN
ejpam-6408	55	7	of	of	ADP
ejpam-6408	55	8	compactness	compactness	NOUN
ejpam-6408	55	9	[	[	X
ejpam-6408	55	10	54	54	NUM
ejpam-6408	55	11	,	,	PUNCT
ejpam-6408	55	12	55	55	NUM
ejpam-6408	55	13	]	]	PUNCT
ejpam-6408	55	14	.	.	PUNCT
ejpam-6408	56	1	soft	soft	ADJ
ejpam-6408	56	2	nodec	nodec	PROPN
ejpam-6408	56	3	spaces	space	NOUN
ejpam-6408	56	4	were	be	AUX
ejpam-6408	56	5	given	give	VERB
ejpam-6408	56	6	by	by	ADP
ejpam-6408	56	7	alqahtani	alqahtani	PROPN
ejpam-6408	56	8	et	et	PROPN
ejpam-6408	56	9	al	al	PROPN
ejpam-6408	56	10	.	.	PUNCT
ejpam-6408	57	1	[	[	X
ejpam-6408	57	2	56	56	NUM
ejpam-6408	57	3	,	,	PUNCT
ejpam-6408	57	4	57	57	NUM
ejpam-6408	57	5	]	]	PUNCT
ejpam-6408	57	6	.	.	PUNCT
ejpam-6408	58	1	in	in	ADP
ejpam-6408	58	2	stss	stss	NOUN
ejpam-6408	58	3	,	,	PUNCT
ejpam-6408	58	4	abd	abd	PROPN
ejpam-6408	58	5	el	el	PROPN
ejpam-6408	58	6	-	-	PROPN
ejpam-6408	58	7	latif	latif	PROPN
ejpam-6408	58	8	et	et	PROPN
ejpam-6408	58	9	al	al	PROPN
ejpam-6408	58	10	.	.	PROPN
ejpam-6408	58	11	established	establish	VERB
ejpam-6408	58	12	the	the	DET
ejpam-6408	58	13	concept	concept	NOUN
ejpam-6408	58	14	of	of	ADP
ejpam-6408	58	15	supra	supra	PROPN
ejpam-6408	58	16	ϵ-open	ϵ-open	PROPN
ejpam-6408	58	17	sets	set	NOUN
ejpam-6408	58	18	[	[	X
ejpam-6408	58	19	58	58	NUM
ejpam-6408	58	20	]	]	PUNCT
ejpam-6408	58	21	.	.	PUNCT
ejpam-6408	59	1	they	they	PRON
ejpam-6408	59	2	also	also	ADV
ejpam-6408	59	3	provided	provide	VERB
ejpam-6408	59	4	many	many	ADJ
ejpam-6408	59	5	kinds	kind	NOUN
ejpam-6408	59	6	of	of	ADP
ejpam-6408	59	7	operators	operator	NOUN
ejpam-6408	59	8	,	,	PUNCT
ejpam-6408	59	9	named	name	VERB
ejpam-6408	59	10	supra	supra	ADJ
ejpam-6408	59	11	ϵ-closure	ϵ-closure	PROPN
ejpam-6408	59	12	(	(	PUNCT
ejpam-6408	59	13	boundary	boundary	ADJ
ejpam-6408	59	14	,	,	PUNCT
ejpam-6408	59	15	exterior	exterior	ADJ
ejpam-6408	59	16	,	,	PUNCT
ejpam-6408	59	17	accumulation	accumulation	NOUN
ejpam-6408	59	18	,	,	PUNCT
ejpam-6408	59	19	and	and	CCONJ
ejpam-6408	59	20	interior	interior	NOUN
ejpam-6408	59	21	,	,	PUNCT
ejpam-6408	59	22	respectively	respectively	ADV
ejpam-6408	59	23	)	)	PUNCT
ejpam-6408	59	24	.	.	PUNCT
ejpam-6408	60	1	using	use	VERB
ejpam-6408	60	2	this	this	DET
ejpam-6408	60	3	notion	notion	NOUN
ejpam-6408	60	4	,	,	PUNCT
ejpam-6408	60	5	he	he	PRON
ejpam-6408	60	6	and	and	CCONJ
ejpam-6408	60	7	his	his	PRON
ejpam-6408	60	8	colleagues	colleague	NOUN
ejpam-6408	60	9	[	[	X
ejpam-6408	60	10	59	59	NUM
ejpam-6408	60	11	]	]	PUNCT
ejpam-6408	60	12	explored	explore	VERB
ejpam-6408	60	13	novel	novel	ADJ
ejpam-6408	60	14	types	type	NOUN
ejpam-6408	60	15	of	of	ADP
ejpam-6408	60	16	supra	supra	ADJ
ejpam-6408	60	17	maps	map	NOUN
ejpam-6408	60	18	,	,	PUNCT
ejpam-6408	60	19	named	name	VERB
ejpam-6408	60	20	supra	supra	PROPN
ejpam-6408	60	21	ϵ	ϵ	PROPN
ejpam-6408	60	22	(	(	PUNCT
ejpam-6408	60	23	ϵ∗)-continuous	ϵ∗)-continuous	ADJ
ejpam-6408	60	24	maps	map	NOUN
ejpam-6408	60	25	,	,	PUNCT
ejpam-6408	60	26	supra	supra	ADJ
ejpam-6408	60	27	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6408	60	28	maps	map	NOUN
ejpam-6408	60	29	,	,	PUNCT
ejpam-6408	60	30	supra	supra	PROPN
ejpam-6408	60	31	ϵ-open	ϵ-open	PROPN
ejpam-6408	60	32	(	(	PUNCT
ejpam-6408	60	33	closed	closed	ADJ
ejpam-6408	60	34	)	)	PUNCT
ejpam-6408	60	35	maps	map	NOUN
ejpam-6408	60	36	,	,	PUNCT
ejpam-6408	60	37	and	and	CCONJ
ejpam-6408	60	38	supra	supra	PROPN
ejpam-6408	60	39	ϵ-homeomorphism	ϵ-homeomorphism	NOUN
ejpam-6408	60	40	maps	map	NOUN
ejpam-6408	60	41	.	.	PUNCT
ejpam-6408	61	1	in	in	ADP
ejpam-6408	61	2	[	[	X
ejpam-6408	61	3	60	60	NUM
ejpam-6408	61	4	]	]	PUNCT
ejpam-6408	61	5	,	,	PUNCT
ejpam-6408	61	6	in	in	ADP
ejpam-6408	61	7	the	the	DET
ejpam-6408	61	8	framem	framem	PROPN
ejpam-6408	61	9	.	.	PUNCT
ejpam-6408	62	1	aldawood	aldawood	VERB
ejpam-6408	62	2	et	et	PROPN
ejpam-6408	62	3	al	al	PROPN
ejpam-6408	62	4	.	.	PUNCT
ejpam-6408	62	5	/	/	SYM
ejpam-6408	62	6	eur	eur	PROPN
ejpam-6408	62	7	.	.	PUNCT
ejpam-6408	63	1	j.	j.	PROPN
ejpam-6408	63	2	pure	pure	PROPN
ejpam-6408	63	3	appl	appl	PROPN
ejpam-6408	63	4	.	.	PROPN
ejpam-6408	63	5	math	math	PROPN
ejpam-6408	63	6	,	,	PUNCT
ejpam-6408	63	7	18	18	NUM
ejpam-6408	63	8	(	(	PUNCT
ejpam-6408	63	9	3	3	NUM
ejpam-6408	63	10	)	)	PUNCT
ejpam-6408	63	11	(	(	PUNCT
ejpam-6408	63	12	2025	2025	NUM
ejpam-6408	63	13	)	)	PUNCT
ejpam-6408	63	14	,	,	PUNCT
ejpam-6408	63	15	6408	6408	NUM
ejpam-6408	63	16	3	3	NUM
ejpam-6408	63	17	of	of	ADP
ejpam-6408	63	18	16	16	NUM
ejpam-6408	63	19	work	work	NOUN
ejpam-6408	63	20	of	of	ADP
ejpam-6408	63	21	stss	stss	NOUN
ejpam-6408	64	1	,	,	PUNCT
ejpam-6408	64	2	the	the	DET
ejpam-6408	64	3	authors	author	NOUN
ejpam-6408	64	4	introduced	introduce	VERB
ejpam-6408	64	5	new	new	ADJ
ejpam-6408	64	6	weaker	weak	ADJ
ejpam-6408	64	7	version	version	NOUN
ejpam-6408	64	8	of	of	ADP
ejpam-6408	64	9	the	the	DET
ejpam-6408	64	10	supra	supra	PROPN
ejpam-6408	64	11	septarian	septarian	ADJ
ejpam-6408	64	12	axioms	axiom	NOUN
ejpam-6408	64	13	based	base	VERB
ejpam-6408	64	14	on	on	ADP
ejpam-6408	64	15	supra	supra	PROPN
ejpam-6408	64	16	ϵ-open	ϵ-open	PROPN
ejpam-6408	64	17	sets	set	NOUN
ejpam-6408	64	18	,	,	PUNCT
ejpam-6408	64	19	along	along	ADP
ejpam-6408	64	20	with	with	ADP
ejpam-6408	64	21	its	its	PRON
ejpam-6408	64	22	key	key	ADJ
ejpam-6408	64	23	characteristics	characteristic	NOUN
ejpam-6408	64	24	,	,	PUNCT
ejpam-6408	64	25	which	which	PRON
ejpam-6408	64	26	are	be	AUX
ejpam-6408	64	27	referred	refer	VERB
ejpam-6408	64	28	to	to	ADP
ejpam-6408	64	29	as	as	ADP
ejpam-6408	64	30	supra-ϵ-tj	supra-ϵ-tj	NOUN
ejpam-6408	64	31	-	-	PUNCT
ejpam-6408	64	32	space	space	NOUN
ejpam-6408	64	33	,	,	PUNCT
ejpam-6408	64	34	j	j	PROPN
ejpam-6408	64	35	=	=	SYM
ejpam-6408	64	36	0	0	NUM
ejpam-6408	64	37	,	,	PUNCT
ejpam-6408	64	38	1	1	NUM
ejpam-6408	64	39	,	,	PUNCT
ejpam-6408	64	40	2	2	NUM
ejpam-6408	64	41	.	.	PUNCT
ejpam-6408	65	1	this	this	DET
ejpam-6408	65	2	manuscript	manuscript	NOUN
ejpam-6408	65	3	is	be	AUX
ejpam-6408	65	4	structured	structure	VERB
ejpam-6408	65	5	as	as	SCONJ
ejpam-6408	65	6	follows	follow	VERB
ejpam-6408	65	7	:	:	PUNCT
ejpam-6408	65	8	we	we	PRON
ejpam-6408	65	9	give	give	VERB
ejpam-6408	65	10	the	the	DET
ejpam-6408	65	11	definitions	definition	NOUN
ejpam-6408	65	12	and	and	CCONJ
ejpam-6408	65	13	findings	finding	NOUN
ejpam-6408	65	14	that	that	PRON
ejpam-6408	65	15	are	be	AUX
ejpam-6408	65	16	required	require	VERB
ejpam-6408	65	17	for	for	ADP
ejpam-6408	65	18	the	the	DET
ejpam-6408	65	19	sequel	sequel	NOUN
ejpam-6408	65	20	in	in	ADP
ejpam-6408	65	21	preliminaries	preliminary	NOUN
ejpam-6408	65	22	.	.	PUNCT
ejpam-6408	66	1	in	in	ADP
ejpam-6408	66	2	section	section	NOUN
ejpam-6408	66	3	3	3	NUM
ejpam-6408	66	4	,	,	PUNCT
ejpam-6408	66	5	we	we	PRON
ejpam-6408	66	6	present	present	VERB
ejpam-6408	66	7	the	the	DET
ejpam-6408	66	8	notion	notion	NOUN
ejpam-6408	66	9	of	of	ADP
ejpam-6408	66	10	supra-ϵ-completely	supra-ϵ-completely	ADV
ejpam-6408	66	11	space	space	NOUN
ejpam-6408	66	12	as	as	ADP
ejpam-6408	66	13	an	an	DET
ejpam-6408	66	14	extension	extension	NOUN
ejpam-6408	66	15	of	of	ADP
ejpam-6408	66	16	the	the	DET
ejpam-6408	66	17	notions	notion	NOUN
ejpam-6408	66	18	of	of	ADP
ejpam-6408	66	19	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	66	20	-	-	PUNCT
ejpam-6408	66	21	space	space	NOUN
ejpam-6408	66	22	,	,	PUNCT
ejpam-6408	66	23	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6408	66	24	-	-	PUNCT
ejpam-6408	66	25	space	space	NOUN
ejpam-6408	66	26	,	,	PUNCT
ejpam-6408	66	27	and	and	CCONJ
ejpam-6408	66	28	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6408	66	29	-	-	NOUN
ejpam-6408	66	30	space	space	NOUN
ejpam-6408	66	31	.	.	PUNCT
ejpam-6408	67	1	we	we	PRON
ejpam-6408	67	2	also	also	ADV
ejpam-6408	67	3	investigate	investigate	VERB
ejpam-6408	67	4	how	how	SCONJ
ejpam-6408	67	5	this	this	DET
ejpam-6408	67	6	concept	concept	NOUN
ejpam-6408	67	7	behaves	behave	VERB
ejpam-6408	67	8	in	in	ADP
ejpam-6408	67	9	relation	relation	NOUN
ejpam-6408	67	10	to	to	ADP
ejpam-6408	67	11	particular	particular	ADJ
ejpam-6408	67	12	supra	supra	NOUN
ejpam-6408	67	13	function	function	NOUN
ejpam-6408	67	14	forms	form	NOUN
ejpam-6408	67	15	.	.	PUNCT
ejpam-6408	68	1	in	in	ADP
ejpam-6408	68	2	section	section	NOUN
ejpam-6408	68	3	4	4	NUM
ejpam-6408	68	4	,	,	PUNCT
ejpam-6408	68	5	four	four	NUM
ejpam-6408	68	6	new	new	ADJ
ejpam-6408	68	7	categories	category	NOUN
ejpam-6408	68	8	of	of	ADP
ejpam-6408	68	9	separation	separation	NOUN
ejpam-6408	68	10	axioms	axiom	NOUN
ejpam-6408	68	11	are	be	AUX
ejpam-6408	68	12	presented	present	VERB
ejpam-6408	68	13	that	that	PRON
ejpam-6408	68	14	utilize	utilize	VERB
ejpam-6408	68	15	the	the	DET
ejpam-6408	68	16	employing	employing	NOUN
ejpam-6408	68	17	of	of	ADP
ejpam-6408	68	18	supra	supra	PROPN
ejpam-6408	68	19	ϵ-open	ϵ-open	PROPN
ejpam-6408	68	20	sets	set	NOUN
ejpam-6408	68	21	named	name	VERB
ejpam-6408	68	22	:	:	PUNCT
ejpam-6408	68	23	supra-ϵ-regular	supra-ϵ-regular	NOUN
ejpam-6408	68	24	-	-	PUNCT
ejpam-6408	68	25	space	space	NOUN
ejpam-6408	68	26	,	,	PUNCT
ejpam-6408	68	27	supra-ϵ-normal	supra-ϵ-normal	ADJ
ejpam-6408	68	28	-	-	NOUN
ejpam-6408	68	29	space	space	NOUN
ejpam-6408	68	30	,	,	PUNCT
ejpam-6408	68	31	supraϵ-t3	supraϵ-t3	NOUN
ejpam-6408	68	32	-	-	PUNCT
ejpam-6408	68	33	space	space	NOUN
ejpam-6408	68	34	,	,	PUNCT
ejpam-6408	68	35	and	and	CCONJ
ejpam-6408	68	36	supra-ϵ-t4	supra-ϵ-t4	NOUN
ejpam-6408	68	37	-	-	PUNCT
ejpam-6408	68	38	space	space	NOUN
ejpam-6408	68	39	.	.	PUNCT
ejpam-6408	69	1	we	we	PRON
ejpam-6408	69	2	also	also	ADV
ejpam-6408	69	3	present	present	VERB
ejpam-6408	69	4	an	an	DET
ejpam-6408	69	5	overview	overview	NOUN
ejpam-6408	69	6	of	of	ADP
ejpam-6408	69	7	their	their	PRON
ejpam-6408	69	8	key	key	ADJ
ejpam-6408	69	9	characteristics	characteristic	NOUN
ejpam-6408	69	10	and	and	CCONJ
ejpam-6408	69	11	look	look	VERB
ejpam-6408	69	12	at	at	ADP
ejpam-6408	69	13	the	the	DET
ejpam-6408	69	14	prerequisites	prerequisite	NOUN
ejpam-6408	69	15	for	for	ADP
ejpam-6408	69	16	a	a	DET
ejpam-6408	69	17	number	number	NOUN
ejpam-6408	69	18	of	of	ADP
ejpam-6408	69	19	similar	similar	ADJ
ejpam-6408	69	20	relationships	relationship	NOUN
ejpam-6408	69	21	between	between	ADP
ejpam-6408	69	22	them	they	PRON
ejpam-6408	69	23	.	.	PUNCT
ejpam-6408	70	1	we	we	PRON
ejpam-6408	70	2	also	also	ADV
ejpam-6408	70	3	propose	propose	VERB
ejpam-6408	70	4	a	a	DET
ejpam-6408	70	5	figure	figure	NOUN
ejpam-6408	70	6	1	1	NUM
ejpam-6408	70	7	that	that	PRON
ejpam-6408	70	8	shows	show	VERB
ejpam-6408	70	9	these	these	DET
ejpam-6408	70	10	linkages	linkage	NOUN
ejpam-6408	70	11	.	.	PUNCT
ejpam-6408	71	1	supra-ϵ-t4	supra-ϵ-t4	NOUN
ejpam-6408	71	2	-	-	PUNCT
ejpam-6408	71	3	space	space	NOUN
ejpam-6408	71	4	=	=	NOUN
ejpam-6408	71	5	⇒	⇒	NOUN
ejpam-6408	71	6	supra-ϵ-t3	supra-ϵ-t3	NOUN
ejpam-6408	71	7	-	-	PUNCT
ejpam-6408	71	8	space	space	NOUN
ejpam-6408	71	9	=	=	NOUN
ejpam-6408	71	10	⇒	⇒	NOUN
ejpam-6408	71	11	supra-ϵ-t2	supra-ϵ-t2	NOUN
ejpam-6408	71	12	1	1	NUM
ejpam-6408	71	13	2	2	NUM
ejpam-6408	71	14	-space	-space	NOUN
ejpam-6408	71	15	=	=	NOUN
ejpam-6408	71	16	⇒	⇒	NOUN
ejpam-6408	71	17	supra-ϵ-t2	supra-ϵ-t2	NOUN
ejpam-6408	71	18	-	-	PUNCT
ejpam-6408	71	19	space	space	NOUN
ejpam-6408	71	20	⇓	⇓	PROPN
ejpam-6408	71	21	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6408	71	22	-	-	PUNCT
ejpam-6408	71	23	space	space	NOUN
ejpam-6408	71	24	⇐	⇐	NOUN
ejpam-6408	71	25	=	=	NOUN
ejpam-6408	71	26	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6408	71	27	-	-	PUNCT
ejpam-6408	71	28	space	space	NOUN
ejpam-6408	71	29	.	.	PUNCT
ejpam-6408	72	1	figure	figure	NOUN
ejpam-6408	72	2	1	1	NUM
ejpam-6408	72	3	.	.	PUNCT
ejpam-6408	73	1	the	the	DET
ejpam-6408	73	2	relationships	relationship	NOUN
ejpam-6408	73	3	between	between	ADP
ejpam-6408	73	4	different	different	ADJ
ejpam-6408	73	5	kinds	kind	NOUN
ejpam-6408	73	6	of	of	ADP
ejpam-6408	73	7	separation	separation	NOUN
ejpam-6408	73	8	axioms	axiom	NOUN
ejpam-6408	73	9	in	in	ADP
ejpam-6408	73	10	the	the	DET
ejpam-6408	73	11	context	context	NOUN
ejpam-6408	73	12	of	of	ADP
ejpam-6408	73	13	stss	stss	NOUN
ejpam-6408	73	14	which	which	PRON
ejpam-6408	73	15	are	be	AUX
ejpam-6408	73	16	motivated	motivate	VERB
ejpam-6408	73	17	by	by	ADP
ejpam-6408	73	18	supra	supra	PROPN
ejpam-6408	73	19	ϵ-open	ϵ-open	PROPN
ejpam-6408	73	20	sets	set	NOUN
ejpam-6408	73	21	furthermore	furthermore	ADV
ejpam-6408	73	22	,	,	PUNCT
ejpam-6408	73	23	the	the	DET
ejpam-6408	73	24	necessary	necessary	ADJ
ejpam-6408	73	25	counterexamples	counterexample	NOUN
ejpam-6408	73	26	that	that	PRON
ejpam-6408	73	27	validate	validate	VERB
ejpam-6408	73	28	our	our	PRON
ejpam-6408	73	29	findings	finding	NOUN
ejpam-6408	73	30	are	be	AUX
ejpam-6408	73	31	finally	finally	ADV
ejpam-6408	73	32	presented	present	VERB
ejpam-6408	73	33	.	.	PUNCT
ejpam-6408	74	1	in	in	ADP
ejpam-6408	74	2	conclusion	conclusion	NOUN
ejpam-6408	74	3	and	and	CCONJ
ejpam-6408	74	4	future	future	ADJ
ejpam-6408	74	5	works	work	NOUN
ejpam-6408	74	6	section	section	NOUN
ejpam-6408	74	7	,	,	PUNCT
ejpam-6408	74	8	we	we	PRON
ejpam-6408	74	9	present	present	VERB
ejpam-6408	74	10	an	an	DET
ejpam-6408	74	11	analytical	analytical	ADJ
ejpam-6408	74	12	explanation	explanation	NOUN
ejpam-6408	74	13	of	of	ADP
ejpam-6408	74	14	the	the	DET
ejpam-6408	74	15	concepts	concept	NOUN
ejpam-6408	74	16	and	and	CCONJ
ejpam-6408	74	17	conclusions	conclusion	NOUN
ejpam-6408	74	18	discussed	discuss	VERB
ejpam-6408	74	19	in	in	ADP
ejpam-6408	74	20	this	this	DET
ejpam-6408	74	21	paper	paper	NOUN
ejpam-6408	74	22	,	,	PUNCT
ejpam-6408	74	23	along	along	ADP
ejpam-6408	74	24	with	with	ADP
ejpam-6408	74	25	a	a	DET
ejpam-6408	74	26	plan	plan	NOUN
ejpam-6408	74	27	for	for	ADP
ejpam-6408	74	28	next	next	ADJ
ejpam-6408	74	29	research	research	NOUN
ejpam-6408	74	30	based	base	VERB
ejpam-6408	74	31	on	on	ADP
ejpam-6408	74	32	this	this	DET
ejpam-6408	74	33	study	study	NOUN
ejpam-6408	74	34	.	.	PUNCT
ejpam-6408	75	1	2	2	X
ejpam-6408	75	2	.	.	X
ejpam-6408	75	3	preliminaries	preliminary	NOUN
ejpam-6408	75	4	definition	definition	NOUN
ejpam-6408	75	5	1	1	NUM
ejpam-6408	75	6	.	.	PUNCT
ejpam-6408	76	1	[	[	X
ejpam-6408	76	2	15	15	NUM
ejpam-6408	76	3	]	]	X
ejpam-6408	76	4	supra	supra	ADJ
ejpam-6408	76	5	topology	topology	NOUN
ejpam-6408	76	6	(	(	PUNCT
ejpam-6408	76	7	or	or	CCONJ
ejpam-6408	76	8	sts	st	NOUN
ejpam-6408	76	9	)	)	PUNCT
ejpam-6408	76	10	on	on	ADP
ejpam-6408	76	11	γ	γ	X
ejpam-6408	76	12	is	be	AUX
ejpam-6408	76	13	the	the	DET
ejpam-6408	76	14	family	family	NOUN
ejpam-6408	76	15	θ	θ	NOUN
ejpam-6408	76	16	⊆	⊆	NUM
ejpam-6408	76	17	2γ	2γ	NOUN
ejpam-6408	76	18	which	which	PRON
ejpam-6408	76	19	contains	contain	VERB
ejpam-6408	76	20	γ	γ	NOUN
ejpam-6408	76	21	and	and	CCONJ
ejpam-6408	76	22	∅	∅	NOUN
ejpam-6408	76	23	and	and	CCONJ
ejpam-6408	76	24	closed	close	VERB
ejpam-6408	76	25	under	under	ADP
ejpam-6408	76	26	arbitrary	arbitrary	ADJ
ejpam-6408	76	27	union	union	NOUN
ejpam-6408	76	28	.	.	PUNCT
ejpam-6408	77	1	additionally	additionally	ADV
ejpam-6408	77	2	,	,	PUNCT
ejpam-6408	77	3	h	h	NOUN
ejpam-6408	77	4	and	and	CCONJ
ejpam-6408	77	5	hc	hc	PROPN
ejpam-6408	77	6	are	be	AUX
ejpam-6408	77	7	referred	refer	VERB
ejpam-6408	77	8	to	to	ADP
ejpam-6408	77	9	as	as	ADP
ejpam-6408	77	10	supra	supra	PROPN
ejpam-6408	77	11	open	open	ADJ
ejpam-6408	77	12	and	and	CCONJ
ejpam-6408	77	13	supra	supra	ADJ
ejpam-6408	77	14	closed	close	VERB
ejpam-6408	77	15	sets	set	NOUN
ejpam-6408	77	16	,	,	PUNCT
ejpam-6408	77	17	respectively	respectively	ADV
ejpam-6408	77	18	,	,	PUNCT
ejpam-6408	77	19	if	if	SCONJ
ejpam-6408	77	20	h	h	PRON
ejpam-6408	77	21	∈	∈	PROPN
ejpam-6408	77	22	θ	θ	PROPN
ejpam-6408	77	23	.	.	PUNCT
ejpam-6408	78	1	moreover	moreover	ADV
ejpam-6408	78	2	,	,	PUNCT
ejpam-6408	78	3	all	all	DET
ejpam-6408	78	4	supra	supra	ADJ
ejpam-6408	78	5	open	open	ADJ
ejpam-6408	78	6	sets	set	NOUN
ejpam-6408	78	7	will	will	AUX
ejpam-6408	78	8	additionally	additionally	ADV
ejpam-6408	78	9	have	have	VERB
ejpam-6408	78	10	their	their	PRON
ejpam-6408	78	11	class	class	NOUN
ejpam-6408	78	12	indicated	indicate	VERB
ejpam-6408	78	13	by	by	ADP
ejpam-6408	78	14	so(γ	so(γ	NOUN
ejpam-6408	78	15	)	)	PUNCT
ejpam-6408	78	16	.	.	PUNCT
ejpam-6408	79	1	additionally	additionally	ADV
ejpam-6408	79	2	,	,	PUNCT
ejpam-6408	79	3	θ	θ	PROPN
ejpam-6408	79	4	is	be	AUX
ejpam-6408	79	5	referred	refer	VERB
ejpam-6408	79	6	to	to	PART
ejpam-6408	79	7	be	be	AUX
ejpam-6408	79	8	an	an	DET
ejpam-6408	79	9	associated	associate	VERB
ejpam-6408	79	10	sts	st	NOUN
ejpam-6408	79	11	with	with	ADP
ejpam-6408	79	12	σ	σ	NOUN
ejpam-6408	79	13	for	for	ADP
ejpam-6408	79	14	a	a	DET
ejpam-6408	79	15	particular	particular	ADJ
ejpam-6408	79	16	topology	topology	NOUN
ejpam-6408	79	17	σ	σ	NOUN
ejpam-6408	79	18	if	if	SCONJ
ejpam-6408	79	19	σ	σ	PROPN
ejpam-6408	79	20	⊂	⊂	PROPN
ejpam-6408	79	21	θ	θ	PROPN
ejpam-6408	79	22	.	.	PUNCT
ejpam-6408	79	23	definition	definition	NOUN
ejpam-6408	79	24	2	2	NUM
ejpam-6408	79	25	.	.	PUNCT
ejpam-6408	80	1	[	[	X
ejpam-6408	80	2	15	15	NUM
ejpam-6408	80	3	]	]	X
ejpam-6408	80	4	the	the	DET
ejpam-6408	80	5	ints(w	ints(w	NOUN
ejpam-6408	80	6	)	)	PUNCT
ejpam-6408	80	7	(	(	PUNCT
ejpam-6408	80	8	cls(w	cls(w	PROPN
ejpam-6408	80	9	)	)	PUNCT
ejpam-6408	80	10	,	,	PUNCT
ejpam-6408	80	11	frs(w	frs(w	PROPN
ejpam-6408	80	12	)	)	PUNCT
ejpam-6408	80	13	)	)	PUNCT
ejpam-6408	80	14	will	will	AUX
ejpam-6408	80	15	indicate	indicate	VERB
ejpam-6408	80	16	the	the	DET
ejpam-6408	80	17	supra	supra	ADJ
ejpam-6408	80	18	interior	interior	NOUN
ejpam-6408	80	19	(	(	PUNCT
ejpam-6408	80	20	closure	closure	NOUN
ejpam-6408	80	21	,	,	PUNCT
ejpam-6408	80	22	boundary	boundary	NOUN
ejpam-6408	80	23	)	)	PUNCT
ejpam-6408	80	24	for	for	ADP
ejpam-6408	80	25	a	a	DET
ejpam-6408	80	26	subset	subset	NOUN
ejpam-6408	80	27	w	w	NOUN
ejpam-6408	80	28	of	of	ADP
ejpam-6408	80	29	an	an	DET
ejpam-6408	80	30	sts	st	NOUN
ejpam-6408	80	31	(	(	PUNCT
ejpam-6408	80	32	γ	γ	X
ejpam-6408	80	33	,	,	PUNCT
ejpam-6408	80	34	θ	θ	NOUN
ejpam-6408	80	35	)	)	PUNCT
ejpam-6408	80	36	,	,	PUNCT
ejpam-6408	80	37	where	where	SCONJ
ejpam-6408	80	38	ints(w	ints(w	VERB
ejpam-6408	80	39	)	)	PUNCT
ejpam-6408	80	40	=	=	SYM
ejpam-6408	81	1	∪{q	∪{q	NOUN
ejpam-6408	81	2	:	:	PUNCT
ejpam-6408	81	3	q	q	NOUN
ejpam-6408	81	4	∈	∈	PROPN
ejpam-6408	81	5	θ	θ	PROPN
ejpam-6408	81	6	and	and	CCONJ
ejpam-6408	81	7	q	q	NOUN
ejpam-6408	82	1	⊆	⊆	NUM
ejpam-6408	82	2	w	w	NOUN
ejpam-6408	82	3	}	}	PUNCT
ejpam-6408	82	4	,	,	PUNCT
ejpam-6408	82	5	cls(w	cls(w	PROPN
ejpam-6408	82	6	)	)	PUNCT
ejpam-6408	83	1	=	=	VERB
ejpam-6408	83	2	∩{p	∩{p	NOUN
ejpam-6408	83	3	:	:	PUNCT
ejpam-6408	83	4	p	p	X
ejpam-6408	83	5	∈	∈	NOUN
ejpam-6408	83	6	θc	θc	NOUN
ejpam-6408	83	7	and	and	CCONJ
ejpam-6408	83	8	w	w	ADP
ejpam-6408	83	9	⊆	⊆	NUM
ejpam-6408	83	10	p	p	NOUN
ejpam-6408	83	11	}	}	PUNCT
ejpam-6408	83	12	and	and	CCONJ
ejpam-6408	83	13	frs(w	frs(w	VERB
ejpam-6408	83	14	)	)	PUNCT
ejpam-6408	84	1	=	=	SYM
ejpam-6408	84	2	cls(w	cls(w	NOUN
ejpam-6408	84	3	)	)	PUNCT
ejpam-6408	84	4	\ints(w	\ints(w	NOUN
ejpam-6408	84	5	)	)	PUNCT
ejpam-6408	84	6	.	.	PUNCT
ejpam-6408	85	1	definition	definition	NOUN
ejpam-6408	85	2	3	3	NUM
ejpam-6408	85	3	.	.	PUNCT
ejpam-6408	86	1	[	[	X
ejpam-6408	86	2	17	17	NUM
ejpam-6408	86	3	]	]	PUNCT
ejpam-6408	86	4	let	let	VERB
ejpam-6408	86	5	p	p	PRON
ejpam-6408	86	6	be	be	AUX
ejpam-6408	86	7	a	a	DET
ejpam-6408	86	8	subset	subset	NOUN
ejpam-6408	86	9	of	of	ADP
ejpam-6408	86	10	an	an	DET
ejpam-6408	86	11	sts	st	NOUN
ejpam-6408	86	12	(	(	PUNCT
ejpam-6408	86	13	γ	γ	X
ejpam-6408	86	14	,	,	PUNCT
ejpam-6408	86	15	θ	θ	NOUN
ejpam-6408	86	16	)	)	PUNCT
ejpam-6408	86	17	.	.	PUNCT
ejpam-6408	87	1	if	if	SCONJ
ejpam-6408	87	2	ints(cls(p	ints(cls(p	NOUN
ejpam-6408	87	3	)	)	PUNCT
ejpam-6408	87	4	)	)	PUNCT
ejpam-6408	88	1	̸=	̸=	NOUN
ejpam-6408	88	2	∅	∅	NOUN
ejpam-6408	88	3	,	,	PUNCT
ejpam-6408	88	4	then	then	ADV
ejpam-6408	88	5	p	p	PROPN
ejpam-6408	88	6	∈	∈	PROPN
ejpam-6408	88	7	sro(γ	sro(γ	NOUN
ejpam-6408	88	8	)	)	PUNCT
ejpam-6408	88	9	.	.	PUNCT
ejpam-6408	89	1	also	also	ADV
ejpam-6408	89	2	,	,	PUNCT
ejpam-6408	89	3	if	if	SCONJ
ejpam-6408	89	4	ints(cls(p	ints(cls(p	NOUN
ejpam-6408	89	5	)	)	PUNCT
ejpam-6408	89	6	)	)	PUNCT
ejpam-6408	90	1	=	=	NOUN
ejpam-6408	90	2	∅	∅	NOUN
ejpam-6408	90	3	,	,	PUNCT
ejpam-6408	90	4	then	then	ADV
ejpam-6408	90	5	p	p	PROPN
ejpam-6408	90	6	∈	∈	PROPN
ejpam-6408	90	7	snd(γ	snd(γ	NOUN
ejpam-6408	90	8	)	)	PUNCT
ejpam-6408	90	9	.	.	PUNCT
ejpam-6408	91	1	definition	definition	NOUN
ejpam-6408	91	2	4	4	NUM
ejpam-6408	91	3	.	.	PUNCT
ejpam-6408	92	1	[	[	X
ejpam-6408	92	2	58	58	NUM
ejpam-6408	92	3	]	]	PUNCT
ejpam-6408	92	4	regarding	regard	VERB
ejpam-6408	92	5	the	the	DET
ejpam-6408	92	6	subset	subset	NOUN
ejpam-6408	92	7	z	z	NOUN
ejpam-6408	92	8	of	of	ADP
ejpam-6408	92	9	an	an	DET
ejpam-6408	92	10	sts	st	NOUN
ejpam-6408	92	11	(	(	PUNCT
ejpam-6408	92	12	γ	γ	X
ejpam-6408	92	13	,	,	PUNCT
ejpam-6408	92	14	θ	θ	PROPN
ejpam-6408	92	15	)	)	PUNCT
ejpam-6408	92	16	,	,	PUNCT
ejpam-6408	92	17	the	the	DET
ejpam-6408	92	18	class	class	NOUN
ejpam-6408	92	19	m.	m.	NOUN
ejpam-6408	92	20	aldawood	aldawood	NOUN
ejpam-6408	92	21	et	et	PROPN
ejpam-6408	92	22	al	al	PROPN
ejpam-6408	92	23	.	.	PUNCT
ejpam-6408	92	24	/	/	SYM
ejpam-6408	92	25	eur	eur	PROPN
ejpam-6408	92	26	.	.	PUNCT
ejpam-6408	93	1	j.	j.	PROPN
ejpam-6408	93	2	pure	pure	PROPN
ejpam-6408	93	3	appl	appl	PROPN
ejpam-6408	93	4	.	.	PROPN
ejpam-6408	93	5	math	math	PROPN
ejpam-6408	93	6	,	,	PUNCT
ejpam-6408	93	7	18	18	NUM
ejpam-6408	93	8	(	(	PUNCT
ejpam-6408	93	9	3	3	NUM
ejpam-6408	93	10	)	)	PUNCT
ejpam-6408	93	11	(	(	PUNCT
ejpam-6408	93	12	2025	2025	NUM
ejpam-6408	93	13	)	)	PUNCT
ejpam-6408	93	14	,	,	PUNCT
ejpam-6408	93	15	6408	6408	NUM
ejpam-6408	93	16	4	4	NUM
ejpam-6408	93	17	of	of	ADP
ejpam-6408	93	18	16	16	NUM
ejpam-6408	93	19	θz	θz	NOUN
ejpam-6408	93	20	=	=	PUNCT
ejpam-6408	93	21	{	{	PUNCT
ejpam-6408	93	22	z	z	NOUN
ejpam-6408	93	23	∩g	∩g	NOUN
ejpam-6408	93	24	:	:	PUNCT
ejpam-6408	93	25	g	g	PROPN
ejpam-6408	93	26	∈	∈	PROPN
ejpam-6408	93	27	θ	θ	PROPN
ejpam-6408	93	28	}	}	PUNCT
ejpam-6408	93	29	defines	define	VERB
ejpam-6408	93	30	an	an	DET
ejpam-6408	93	31	sts	st	NOUN
ejpam-6408	93	32	on	on	ADP
ejpam-6408	93	33	z	z	PROPN
ejpam-6408	93	34	,	,	PUNCT
ejpam-6408	93	35	also	also	ADV
ejpam-6408	93	36	known	know	VERB
ejpam-6408	93	37	as	as	ADP
ejpam-6408	93	38	a	a	DET
ejpam-6408	93	39	supra	supra	ADJ
ejpam-6408	93	40	subspace	subspace	NOUN
ejpam-6408	93	41	of	of	ADP
ejpam-6408	93	42	(	(	PUNCT
ejpam-6408	93	43	γ	γ	X
ejpam-6408	93	44	,	,	PUNCT
ejpam-6408	93	45	θ	θ	NOUN
ejpam-6408	93	46	)	)	PUNCT
ejpam-6408	93	47	.	.	PUNCT
ejpam-6408	94	1	definition	definition	NOUN
ejpam-6408	94	2	5	5	NUM
ejpam-6408	94	3	.	.	PUNCT
ejpam-6408	95	1	[	[	X
ejpam-6408	95	2	58	58	NUM
ejpam-6408	95	3	]	]	PUNCT
ejpam-6408	95	4	a	a	DET
ejpam-6408	95	5	subset	subset	NOUN
ejpam-6408	95	6	w	w	NOUN
ejpam-6408	95	7	of	of	ADP
ejpam-6408	95	8	an	an	DET
ejpam-6408	95	9	sts	st	NOUN
ejpam-6408	95	10	(	(	PUNCT
ejpam-6408	95	11	γ	γ	X
ejpam-6408	95	12	,	,	PUNCT
ejpam-6408	95	13	θ	θ	NOUN
ejpam-6408	95	14	)	)	PUNCT
ejpam-6408	95	15	is	be	AUX
ejpam-6408	95	16	referred	refer	VERB
ejpam-6408	95	17	to	to	ADP
ejpam-6408	95	18	as	as	SCONJ
ejpam-6408	95	19	supra	supra	PROPN
ejpam-6408	95	20	ϵ-open	ϵ-open	PROPN
ejpam-6408	95	21	set	set	VERB
ejpam-6408	95	22	if	if	SCONJ
ejpam-6408	95	23	either	either	CCONJ
ejpam-6408	95	24	w	w	NOUN
ejpam-6408	95	25	=	=	PUNCT
ejpam-6408	95	26	∅	∅	NOUN
ejpam-6408	95	27	or	or	CCONJ
ejpam-6408	95	28	w	w	NOUN
ejpam-6408	95	29	⊆	⊆	NUM
ejpam-6408	95	30	{	{	PUNCT
ejpam-6408	95	31	frs(w	frs(w	NOUN
ejpam-6408	95	32	)	)	PUNCT
ejpam-6408	95	33	∪	∪	ADP
ejpam-6408	95	34	ints(cls(w	ints(cls(w	NOUN
ejpam-6408	95	35	)	)	PUNCT
ejpam-6408	95	36	)	)	PUNCT
ejpam-6408	95	37	,	,	PUNCT
ejpam-6408	95	38	w	w	PROPN
ejpam-6408	95	39	∈	∈	PROPN
ejpam-6408	95	40	sro(γ	sro(γ	NOUN
ejpam-6408	95	41	)	)	PUNCT
ejpam-6408	95	42	,	,	PUNCT
ejpam-6408	95	43	frs(w	frs(w	PROPN
ejpam-6408	95	44	)	)	PUNCT
ejpam-6408	95	45	,	,	PUNCT
ejpam-6408	95	46	w	w	PROPN
ejpam-6408	95	47	∈	∈	PROPN
ejpam-6408	95	48	snd(γ	snd(γ	NOUN
ejpam-6408	95	49	)	)	PUNCT
ejpam-6408	95	50	and	and	CCONJ
ejpam-6408	95	51	frs(w	frs(w	VERB
ejpam-6408	95	52	)	)	PUNCT
ejpam-6408	95	53	is	be	AUX
ejpam-6408	95	54	infinite	infinite	ADJ
ejpam-6408	95	55	.	.	PUNCT
ejpam-6408	96	1	furthermore	furthermore	ADV
ejpam-6408	96	2	,	,	PUNCT
ejpam-6408	96	3	w	w	PROPN
ejpam-6408	96	4	c	c	PROPN
ejpam-6408	96	5	is	be	AUX
ejpam-6408	96	6	called	call	VERB
ejpam-6408	96	7	supra	supra	ADJ
ejpam-6408	96	8	ϵ-closed	ϵ-close	VERB
ejpam-6408	96	9	-	-	PUNCT
ejpam-6408	96	10	set	set	NOUN
ejpam-6408	96	11	.	.	PUNCT
ejpam-6408	97	1	additionally	additionally	ADV
ejpam-6408	97	2	,	,	PUNCT
ejpam-6408	97	3	soϵ(γ	soϵ(γ	PROPN
ejpam-6408	97	4	)	)	PUNCT
ejpam-6408	97	5	(	(	PUNCT
ejpam-6408	97	6	scϵ(γ	scϵ(γ	PROPN
ejpam-6408	97	7	)	)	PUNCT
ejpam-6408	97	8	)	)	PUNCT
ejpam-6408	97	9	will	will	AUX
ejpam-6408	97	10	be	be	AUX
ejpam-6408	97	11	used	use	VERB
ejpam-6408	97	12	to	to	PART
ejpam-6408	97	13	classify	classify	VERB
ejpam-6408	97	14	all	all	DET
ejpam-6408	97	15	supra	supra	PROPN
ejpam-6408	97	16	ϵ-open	ϵ-open	PROPN
ejpam-6408	97	17	(	(	PUNCT
ejpam-6408	97	18	supra	supra	PROPN
ejpam-6408	97	19	ϵ-closed	ϵ-close	VERB
ejpam-6408	97	20	)	)	PUNCT
ejpam-6408	97	21	sets	set	NOUN
ejpam-6408	97	22	.	.	PUNCT
ejpam-6408	98	1	definition	definition	NOUN
ejpam-6408	98	2	6	6	NUM
ejpam-6408	98	3	.	.	PUNCT
ejpam-6408	99	1	[	[	X
ejpam-6408	99	2	58	58	NUM
ejpam-6408	99	3	]	]	PUNCT
ejpam-6408	99	4	for	for	ADP
ejpam-6408	99	5	a	a	DET
ejpam-6408	99	6	subset	subset	NOUN
ejpam-6408	99	7	w	w	NOUN
ejpam-6408	99	8	of	of	ADP
ejpam-6408	99	9	an	an	DET
ejpam-6408	99	10	sts	st	NOUN
ejpam-6408	99	11	(	(	PUNCT
ejpam-6408	99	12	γ	γ	X
ejpam-6408	99	13	,	,	PUNCT
ejpam-6408	99	14	θ	θ	PROPN
ejpam-6408	99	15	)	)	PUNCT
ejpam-6408	99	16	,	,	PUNCT
ejpam-6408	99	17	the	the	DET
ejpam-6408	99	18	supra	supra	PROPN
ejpam-6408	99	19	ϵ-interior	ϵ-interior	PROPN
ejpam-6408	99	20	(	(	PUNCT
ejpam-6408	99	21	closure	closure	NOUN
ejpam-6408	99	22	)	)	PUNCT
ejpam-6408	99	23	of	of	ADP
ejpam-6408	99	24	w	w	PROPN
ejpam-6408	99	25	will	will	AUX
ejpam-6408	99	26	be	be	AUX
ejpam-6408	99	27	indicated	indicate	VERB
ejpam-6408	99	28	by	by	ADP
ejpam-6408	99	29	the	the	DET
ejpam-6408	99	30	intsϵ(w	intsϵ(w	NOUN
ejpam-6408	99	31	)	)	PUNCT
ejpam-6408	99	32	(	(	PUNCT
ejpam-6408	99	33	clsϵ(w	clsϵ(w	NOUN
ejpam-6408	99	34	)	)	PUNCT
ejpam-6408	99	35	)	)	PUNCT
ejpam-6408	99	36	,	,	PUNCT
ejpam-6408	99	37	where	where	SCONJ
ejpam-6408	99	38	intsϵ(w	intsϵ(w	NOUN
ejpam-6408	99	39	)	)	PUNCT
ejpam-6408	99	40	=	=	SYM
ejpam-6408	100	1	∪{q	∪{q	NOUN
ejpam-6408	100	2	:	:	PUNCT
ejpam-6408	100	3	q	q	NOUN
ejpam-6408	100	4	∈	∈	PROPN
ejpam-6408	100	5	soϵ(γ	soϵ(γ	PROPN
ejpam-6408	100	6	)	)	PUNCT
ejpam-6408	100	7	and	and	CCONJ
ejpam-6408	100	8	q	q	NOUN
ejpam-6408	100	9	⊆	⊆	NUM
ejpam-6408	100	10	w	w	NOUN
ejpam-6408	100	11	}	}	PUNCT
ejpam-6408	100	12	and	and	CCONJ
ejpam-6408	100	13	clsϵ(w	clsϵ(w	NUM
ejpam-6408	100	14	)	)	PUNCT
ejpam-6408	101	1	=	=	SYM
ejpam-6408	101	2	∩{r	∩{r	NOUN
ejpam-6408	101	3	:	:	PUNCT
ejpam-6408	101	4	r	r	NOUN
ejpam-6408	101	5	∈	∈	NOUN
ejpam-6408	101	6	scϵ(γ	scϵ(γ	PROPN
ejpam-6408	101	7	)	)	PUNCT
ejpam-6408	101	8	and	and	CCONJ
ejpam-6408	101	9	w	w	ADP
ejpam-6408	101	10	⊆	⊆	NUM
ejpam-6408	101	11	r	r	NOUN
ejpam-6408	101	12	}	}	PUNCT
ejpam-6408	101	13	theorem	theorem	NOUN
ejpam-6408	101	14	1	1	NUM
ejpam-6408	101	15	.	.	PUNCT
ejpam-6408	102	1	[	[	X
ejpam-6408	102	2	58	58	NUM
ejpam-6408	102	3	]	]	PUNCT
ejpam-6408	102	4	if	if	SCONJ
ejpam-6408	102	5	we	we	PRON
ejpam-6408	102	6	consider	consider	VERB
ejpam-6408	102	7	a	a	DET
ejpam-6408	102	8	subset	subset	NOUN
ejpam-6408	102	9	s	s	NOUN
ejpam-6408	102	10	of	of	ADP
ejpam-6408	102	11	an	an	DET
ejpam-6408	102	12	sts	st	NOUN
ejpam-6408	102	13	(	(	PUNCT
ejpam-6408	102	14	γ	γ	X
ejpam-6408	102	15	,	,	PUNCT
ejpam-6408	102	16	θ	θ	PROPN
ejpam-6408	102	17	)	)	PUNCT
ejpam-6408	102	18	with	with	ADP
ejpam-6408	102	19	σ	σ	PROPN
ejpam-6408	102	20	⊂	⊂	PROPN
ejpam-6408	102	21	θ	θ	PROPN
ejpam-6408	102	22	,	,	PUNCT
ejpam-6408	102	23	then	then	ADV
ejpam-6408	102	24	we	we	PRON
ejpam-6408	102	25	obtain	obtain	VERB
ejpam-6408	102	26	that	that	SCONJ
ejpam-6408	102	27	(	(	PUNCT
ejpam-6408	102	28	1	1	X
ejpam-6408	102	29	)	)	PUNCT
ejpam-6408	102	30	clsϵ(s	clsϵ(	NOUN
ejpam-6408	102	31	c	c	NOUN
ejpam-6408	102	32	)	)	PUNCT
ejpam-6408	102	33	=	=	NOUN
ejpam-6408	103	1	[	[	X
ejpam-6408	103	2	intsϵ(s	intsϵ(s	NOUN
ejpam-6408	103	3	)	)	PUNCT
ejpam-6408	103	4	]	]	PUNCT
ejpam-6408	103	5	c.	c.	NOUN
ejpam-6408	103	6	(	(	PUNCT
ejpam-6408	103	7	2	2	X
ejpam-6408	103	8	)	)	PUNCT
ejpam-6408	103	9	intsϵ(s	intsϵ(	NOUN
ejpam-6408	103	10	c	c	NOUN
ejpam-6408	103	11	)	)	PUNCT
ejpam-6408	104	1	=	=	PUNCT
ejpam-6408	105	1	[	[	X
ejpam-6408	105	2	clsϵ(s	clsϵ(s	NOUN
ejpam-6408	105	3	)	)	PUNCT
ejpam-6408	105	4	]	]	PUNCT
ejpam-6408	106	1	c.	c.	NOUN
ejpam-6408	106	2	(	(	PUNCT
ejpam-6408	106	3	3	3	X
ejpam-6408	106	4	)	)	PUNCT
ejpam-6408	106	5	int(s	int(s	PROPN
ejpam-6408	106	6	)	)	PUNCT
ejpam-6408	106	7	⊆	⊆	NUM
ejpam-6408	106	8	ints(s	ints(s	NOUN
ejpam-6408	106	9	)	)	PUNCT
ejpam-6408	106	10	⊆	⊆	NUM
ejpam-6408	106	11	intsϵ(s	intsϵ(s	PROPN
ejpam-6408	106	12	)	)	PUNCT
ejpam-6408	106	13	,	,	PUNCT
ejpam-6408	106	14	where	where	SCONJ
ejpam-6408	106	15	int(s	int(s	PROPN
ejpam-6408	106	16	)	)	PUNCT
ejpam-6408	106	17	denotes	denote	VERB
ejpam-6408	106	18	the	the	DET
ejpam-6408	106	19	interior	interior	NOUN
ejpam-6408	106	20	of	of	ADP
ejpam-6408	106	21	s	s	NOUN
ejpam-6408	106	22	with	with	ADP
ejpam-6408	106	23	respect	respect	NOUN
ejpam-6408	106	24	to	to	ADP
ejpam-6408	106	25	σ	σ	PROPN
ejpam-6408	106	26	.	.	PUNCT
ejpam-6408	107	1	(	(	PUNCT
ejpam-6408	107	2	4	4	X
ejpam-6408	107	3	)	)	PUNCT
ejpam-6408	107	4	clsϵ(s	clsϵ(	NOUN
ejpam-6408	107	5	)	)	PUNCT
ejpam-6408	107	6	⊆	⊆	NUM
ejpam-6408	107	7	cls(s	cls(s	PROPN
ejpam-6408	107	8	)	)	PUNCT
ejpam-6408	107	9	⊆	⊆	NUM
ejpam-6408	107	10	cl(s	cl(	NOUN
ejpam-6408	107	11	)	)	PUNCT
ejpam-6408	107	12	,	,	PUNCT
ejpam-6408	107	13	where	where	SCONJ
ejpam-6408	107	14	cl(s	cl(	NOUN
ejpam-6408	107	15	)	)	PUNCT
ejpam-6408	107	16	denotes	denote	VERB
ejpam-6408	107	17	the	the	DET
ejpam-6408	107	18	closure	closure	NOUN
ejpam-6408	107	19	of	of	ADP
ejpam-6408	107	20	s	s	NOUN
ejpam-6408	107	21	with	with	ADP
ejpam-6408	107	22	respect	respect	NOUN
ejpam-6408	107	23	to	to	ADP
ejpam-6408	107	24	σ	σ	PROPN
ejpam-6408	107	25	.	.	PUNCT
ejpam-6408	108	1	definition	definition	NOUN
ejpam-6408	108	2	7	7	NUM
ejpam-6408	108	3	.	.	PUNCT
ejpam-6408	109	1	[	[	X
ejpam-6408	109	2	58	58	NUM
ejpam-6408	109	3	]	]	PUNCT
ejpam-6408	109	4	let	let	VERB
ejpam-6408	109	5	w	w	PART
ejpam-6408	109	6	be	be	AUX
ejpam-6408	109	7	a	a	DET
ejpam-6408	109	8	subset	subset	NOUN
ejpam-6408	109	9	of	of	ADP
ejpam-6408	109	10	an	an	DET
ejpam-6408	109	11	sts	st	NOUN
ejpam-6408	109	12	(	(	PUNCT
ejpam-6408	109	13	γ	γ	X
ejpam-6408	109	14	,	,	PUNCT
ejpam-6408	109	15	θ	θ	PROPN
ejpam-6408	109	16	)	)	PUNCT
ejpam-6408	109	17	with	with	ADP
ejpam-6408	109	18	an	an	DET
ejpam-6408	109	19	arbitrary	arbitrary	ADJ
ejpam-6408	109	20	point	point	NOUN
ejpam-6408	109	21	s	s	PART
ejpam-6408	109	22	∈	∈	PROPN
ejpam-6408	109	23	γ	γ	X
ejpam-6408	109	24	.	.	PUNCT
ejpam-6408	110	1	if	if	SCONJ
ejpam-6408	110	2	each	each	DET
ejpam-6408	110	3	supra	supra	PROPN
ejpam-6408	110	4	ϵ-open	ϵ-open	PROPN
ejpam-6408	110	5	set	set	VERB
ejpam-6408	110	6	gs	g	NOUN
ejpam-6408	110	7	containing	contain	VERB
ejpam-6408	110	8	s	s	NOUN
ejpam-6408	110	9	,	,	PUNCT
ejpam-6408	110	10	we	we	PRON
ejpam-6408	110	11	obtain	obtain	VERB
ejpam-6408	110	12	that	that	PRON
ejpam-6408	110	13	[	[	X
ejpam-6408	110	14	w\{s	w\{s	ADV
ejpam-6408	110	15	}	}	PUNCT
ejpam-6408	110	16	]	]	PUNCT
ejpam-6408	111	1	∩gs	∩gs	PROPN
ejpam-6408	111	2	̸=	̸=	PROPN
ejpam-6408	111	3	∅	∅	NOUN
ejpam-6408	111	4	,	,	PUNCT
ejpam-6408	111	5	consequently	consequently	ADV
ejpam-6408	111	6	,	,	PUNCT
ejpam-6408	111	7	s	s	VERB
ejpam-6408	111	8	is	be	AUX
ejpam-6408	111	9	called	call	VERB
ejpam-6408	111	10	a	a	DET
ejpam-6408	111	11	supra	supra	ADJ
ejpam-6408	111	12	ϵ-accumulation	ϵ-accumulation	PROPN
ejpam-6408	111	13	point	point	NOUN
ejpam-6408	111	14	of	of	ADP
ejpam-6408	111	15	w	w	PROPN
ejpam-6408	111	16	.	.	PUNCT
ejpam-6408	112	1	also	also	ADV
ejpam-6408	112	2	,	,	PUNCT
ejpam-6408	112	3	the	the	DET
ejpam-6408	112	4	set	set	NOUN
ejpam-6408	112	5	of	of	ADP
ejpam-6408	112	6	all	all	DET
ejpam-6408	112	7	supra	supra	ADJ
ejpam-6408	112	8	ϵ-accumulation	ϵ-accumulation	PROPN
ejpam-6408	112	9	points	point	NOUN
ejpam-6408	112	10	of	of	ADP
ejpam-6408	112	11	w	w	NOUN
ejpam-6408	112	12	shall	shall	AUX
ejpam-6408	112	13	be	be	AUX
ejpam-6408	112	14	represented	represent	VERB
ejpam-6408	112	15	by	by	ADP
ejpam-6408	112	16	the	the	DET
ejpam-6408	112	17	notation	notation	NOUN
ejpam-6408	112	18	accϵ(w	accϵ(w	PROPN
ejpam-6408	112	19	)	)	PUNCT
ejpam-6408	112	20	.	.	PUNCT
ejpam-6408	113	1	definition	definition	NOUN
ejpam-6408	113	2	8	8	NUM
ejpam-6408	113	3	.	.	PUNCT
ejpam-6408	114	1	[	[	X
ejpam-6408	114	2	60	60	NUM
ejpam-6408	114	3	]	]	X
ejpam-6408	114	4	an	an	DET
ejpam-6408	114	5	sts	st	NOUN
ejpam-6408	114	6	(	(	PUNCT
ejpam-6408	114	7	γ	γ	X
ejpam-6408	114	8	,	,	PUNCT
ejpam-6408	114	9	θ	θ	NOUN
ejpam-6408	114	10	)	)	PUNCT
ejpam-6408	114	11	is	be	AUX
ejpam-6408	114	12	said	say	VERB
ejpam-6408	114	13	to	to	PART
ejpam-6408	114	14	be	be	AUX
ejpam-6408	114	15	(	(	PUNCT
ejpam-6408	114	16	1	1	X
ejpam-6408	114	17	)	)	PUNCT
ejpam-6408	114	18	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6408	114	19	-	-	NOUN
ejpam-6408	114	20	space	space	NOUN
ejpam-6408	114	21	if	if	SCONJ
ejpam-6408	114	22	for	for	ADP
ejpam-6408	114	23	each	each	DET
ejpam-6408	114	24	distinct	distinct	ADJ
ejpam-6408	114	25	points	point	NOUN
ejpam-6408	114	26	there	there	PRON
ejpam-6408	114	27	is	be	VERB
ejpam-6408	114	28	a	a	DET
ejpam-6408	114	29	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	114	30	set	set	NOUN
ejpam-6408	114	31	including	include	VERB
ejpam-6408	114	32	one	one	NUM
ejpam-6408	114	33	but	but	CCONJ
ejpam-6408	114	34	excluding	exclude	VERB
ejpam-6408	114	35	the	the	DET
ejpam-6408	114	36	other	other	ADJ
ejpam-6408	114	37	.	.	PUNCT
ejpam-6408	115	1	(	(	PUNCT
ejpam-6408	115	2	2	2	X
ejpam-6408	115	3	)	)	PUNCT
ejpam-6408	115	4	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6408	115	5	-	-	PUNCT
ejpam-6408	115	6	space	space	NOUN
ejpam-6408	115	7	if	if	SCONJ
ejpam-6408	115	8	for	for	ADP
ejpam-6408	115	9	each	each	DET
ejpam-6408	115	10	distinct	distinct	ADJ
ejpam-6408	115	11	points	point	NOUN
ejpam-6408	115	12	ϑ1	ϑ1	NOUN
ejpam-6408	115	13	,	,	PUNCT
ejpam-6408	115	14	ϑ2	ϑ2	PROPN
ejpam-6408	115	15	∈	∈	PROPN
ejpam-6408	115	16	γ	γ	PROPN
ejpam-6408	115	17	,	,	PUNCT
ejpam-6408	115	18	then	then	ADV
ejpam-6408	115	19	there	there	PRON
ejpam-6408	115	20	are	be	VERB
ejpam-6408	115	21	two	two	NUM
ejpam-6408	115	22	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	115	23	subsets	subset	NOUN
ejpam-6408	115	24	ν1	ν1	NOUN
ejpam-6408	115	25	and	and	CCONJ
ejpam-6408	115	26	ν2	ν2	NOUN
ejpam-6408	115	27	of	of	ADP
ejpam-6408	115	28	γ	γ	NOUN
ejpam-6408	115	29	,	,	PUNCT
ejpam-6408	115	30	such	such	ADJ
ejpam-6408	115	31	that	that	DET
ejpam-6408	115	32	ϑ1	ϑ1	PROPN
ejpam-6408	115	33	∈	∈	PROPN
ejpam-6408	115	34	ν1	ν1	NOUN
ejpam-6408	115	35	,	,	PUNCT
ejpam-6408	115	36	ϑ2	ϑ2	PROPN
ejpam-6408	115	37	/∈	/∈	PUNCT
ejpam-6408	115	38	ν1	ν1	NOUN
ejpam-6408	115	39	,	,	PUNCT
ejpam-6408	115	40	and	and	CCONJ
ejpam-6408	115	41	ϑ1	ϑ1	NOUN
ejpam-6408	115	42	/∈	/∈	PUNCT
ejpam-6408	115	43	ν2	ν2	NOUN
ejpam-6408	115	44	,	,	PUNCT
ejpam-6408	115	45	ϑ2	ϑ2	PROPN
ejpam-6408	115	46	∈	∈	PROPN
ejpam-6408	115	47	ν2	ν2	NOUN
ejpam-6408	115	48	.	.	PUNCT
ejpam-6408	116	1	(	(	PUNCT
ejpam-6408	116	2	3	3	X
ejpam-6408	116	3	)	)	PUNCT
ejpam-6408	116	4	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	116	5	-	-	PUNCT
ejpam-6408	116	6	space	space	NOUN
ejpam-6408	116	7	”	"	PUNCT
ejpam-6408	116	8	supra-ϵ-hausdorff	supra-ϵ-hausdorff	PROPN
ejpam-6408	116	9	space	space	NOUN
ejpam-6408	116	10	”	"	PUNCT
ejpam-6408	116	11	if	if	SCONJ
ejpam-6408	116	12	for	for	ADP
ejpam-6408	116	13	each	each	DET
ejpam-6408	116	14	distinct	distinct	ADJ
ejpam-6408	116	15	points	point	NOUN
ejpam-6408	116	16	ϑ1	ϑ1	NOUN
ejpam-6408	116	17	,	,	PUNCT
ejpam-6408	116	18	ϑ2	ϑ2	PROPN
ejpam-6408	116	19	∈	∈	PROPN
ejpam-6408	116	20	γ	γ	PROPN
ejpam-6408	116	21	,	,	PUNCT
ejpam-6408	116	22	then	then	ADV
ejpam-6408	116	23	there	there	PRON
ejpam-6408	116	24	are	be	VERB
ejpam-6408	116	25	two	two	NUM
ejpam-6408	116	26	disjoint	disjoint	ADJ
ejpam-6408	116	27	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	116	28	subsets	subset	NOUN
ejpam-6408	116	29	ν1	ν1	NOUN
ejpam-6408	116	30	and	and	CCONJ
ejpam-6408	116	31	ν2	ν2	NOUN
ejpam-6408	116	32	of	of	ADP
ejpam-6408	116	33	γ	γ	NOUN
ejpam-6408	116	34	,	,	PUNCT
ejpam-6408	116	35	such	such	ADJ
ejpam-6408	116	36	that	that	DET
ejpam-6408	116	37	ϑ1	ϑ1	PROPN
ejpam-6408	116	38	∈	∈	PROPN
ejpam-6408	116	39	ν1	ν1	NOUN
ejpam-6408	116	40	and	and	CCONJ
ejpam-6408	116	41	ϑ2	ϑ2	PROPN
ejpam-6408	116	42	∈	∈	PROPN
ejpam-6408	116	43	ν2	ν2	NOUN
ejpam-6408	116	44	.	.	PUNCT
ejpam-6408	117	1	definition	definition	NOUN
ejpam-6408	117	2	9	9	NUM
ejpam-6408	117	3	.	.	PUNCT
ejpam-6408	118	1	[	[	X
ejpam-6408	118	2	60	60	NUM
ejpam-6408	118	3	]	]	PUNCT
ejpam-6408	118	4	for	for	ADP
ejpam-6408	118	5	the	the	DET
ejpam-6408	118	6	subset	subset	ADJ
ejpam-6408	118	7	l	l	NOUN
ejpam-6408	118	8	of	of	ADP
ejpam-6408	118	9	an	an	DET
ejpam-6408	118	10	sts	st	NOUN
ejpam-6408	118	11	(	(	PUNCT
ejpam-6408	118	12	γ	γ	X
ejpam-6408	118	13	,	,	PUNCT
ejpam-6408	118	14	ϑ	ϑ	NOUN
ejpam-6408	118	15	)	)	PUNCT
ejpam-6408	118	16	,	,	PUNCT
ejpam-6408	118	17	the	the	DET
ejpam-6408	118	18	class	class	NOUN
ejpam-6408	118	19	m.	m.	NOUN
ejpam-6408	118	20	aldawood	aldawood	NOUN
ejpam-6408	118	21	et	et	PROPN
ejpam-6408	118	22	al	al	PROPN
ejpam-6408	118	23	.	.	PUNCT
ejpam-6408	118	24	/	/	SYM
ejpam-6408	118	25	eur	eur	PROPN
ejpam-6408	118	26	.	.	PUNCT
ejpam-6408	119	1	j.	j.	PROPN
ejpam-6408	119	2	pure	pure	PROPN
ejpam-6408	119	3	appl	appl	PROPN
ejpam-6408	119	4	.	.	PROPN
ejpam-6408	119	5	math	math	PROPN
ejpam-6408	119	6	,	,	PUNCT
ejpam-6408	119	7	18	18	NUM
ejpam-6408	119	8	(	(	PUNCT
ejpam-6408	119	9	3	3	NUM
ejpam-6408	119	10	)	)	PUNCT
ejpam-6408	119	11	(	(	PUNCT
ejpam-6408	119	12	2025	2025	NUM
ejpam-6408	119	13	)	)	PUNCT
ejpam-6408	119	14	,	,	PUNCT
ejpam-6408	119	15	6408	6408	NUM
ejpam-6408	119	16	5	5	NUM
ejpam-6408	119	17	of	of	ADP
ejpam-6408	119	18	16	16	NUM
ejpam-6408	119	19	ϑl	ϑl	NOUN
ejpam-6408	119	20	=	=	PUNCT
ejpam-6408	119	21	{	{	PUNCT
ejpam-6408	119	22	l	l	NOUN
ejpam-6408	119	23	∩o	∩o	NOUN
ejpam-6408	119	24	:	:	PUNCT
ejpam-6408	120	1	o	o	X
ejpam-6408	120	2	∈	∈	PROPN
ejpam-6408	120	3	soϵ(γ	soϵ(γ	PROPN
ejpam-6408	120	4	)	)	PUNCT
ejpam-6408	120	5	}	}	PUNCT
ejpam-6408	120	6	defines	define	VERB
ejpam-6408	120	7	an	an	DET
ejpam-6408	120	8	sts	st	NOUN
ejpam-6408	120	9	on	on	ADP
ejpam-6408	120	10	l	l	NOUN
ejpam-6408	120	11	,	,	PUNCT
ejpam-6408	120	12	and	and	CCONJ
ejpam-6408	120	13	it	it	PRON
ejpam-6408	120	14	is	be	AUX
ejpam-6408	120	15	called	call	VERB
ejpam-6408	120	16	an	an	DET
ejpam-6408	120	17	supra	supra	PROPN
ejpam-6408	120	18	ϵ-subspace	ϵ-subspace	PROPN
ejpam-6408	120	19	of	of	ADP
ejpam-6408	120	20	(	(	PUNCT
ejpam-6408	120	21	γ	γ	X
ejpam-6408	120	22	,	,	PUNCT
ejpam-6408	120	23	ϑ	ϑ	NOUN
ejpam-6408	120	24	)	)	PUNCT
ejpam-6408	120	25	.	.	PUNCT
ejpam-6408	121	1	definition	definition	NOUN
ejpam-6408	121	2	10	10	NUM
ejpam-6408	121	3	.	.	PUNCT
ejpam-6408	122	1	[	[	X
ejpam-6408	122	2	60	60	NUM
ejpam-6408	122	3	]	]	PUNCT
ejpam-6408	122	4	a	a	DET
ejpam-6408	122	5	function	function	NOUN
ejpam-6408	122	6	γϵ	γϵ	NOUN
ejpam-6408	122	7	:	:	PUNCT
ejpam-6408	122	8	(	(	PUNCT
ejpam-6408	122	9	γ1	γ1	NOUN
ejpam-6408	122	10	,	,	PUNCT
ejpam-6408	122	11	ϑ1	ϑ1	PROPN
ejpam-6408	122	12	)	)	PUNCT
ejpam-6408	122	13	→	→	SYM
ejpam-6408	122	14	(	(	PUNCT
ejpam-6408	122	15	γ2	γ2	ADJ
ejpam-6408	122	16	,	,	PUNCT
ejpam-6408	122	17	ϑ2	ϑ2	PROPN
ejpam-6408	122	18	)	)	PUNCT
ejpam-6408	122	19	with	with	ADP
ejpam-6408	122	20	θ1	θ1	NOUN
ejpam-6408	122	21	,	,	PUNCT
ejpam-6408	122	22	θ2	θ2	PROPN
ejpam-6408	122	23	associated	associate	VERB
ejpam-6408	122	24	stss	stss	NOUN
ejpam-6408	122	25	with	with	ADP
ejpam-6408	122	26	ϑ1	ϑ1	PROPN
ejpam-6408	122	27	,	,	PUNCT
ejpam-6408	122	28	ϑ2	ϑ2	PROPN
ejpam-6408	122	29	,	,	PUNCT
ejpam-6408	122	30	respectively	respectively	ADV
ejpam-6408	122	31	,	,	PUNCT
ejpam-6408	122	32	is	be	AUX
ejpam-6408	122	33	said	say	VERB
ejpam-6408	122	34	to	to	PART
ejpam-6408	122	35	be	be	AUX
ejpam-6408	122	36	:	:	PUNCT
ejpam-6408	122	37	(	(	PUNCT
ejpam-6408	122	38	1	1	X
ejpam-6408	122	39	)	)	PUNCT
ejpam-6408	122	40	supra	supra	NOUN
ejpam-6408	122	41	ϵ-continuous	ϵ-continuous	PROPN
ejpam-6408	122	42	(	(	PUNCT
ejpam-6408	122	43	abbreviate	abbreviate	NOUN
ejpam-6408	122	44	:	:	PUNCT
ejpam-6408	122	45	supra	supra	ADJ
ejpam-6408	122	46	ϵ-cts	ϵ-ct	NOUN
ejpam-6408	122	47	)	)	PUNCT
ejpam-6408	122	48	if	if	SCONJ
ejpam-6408	122	49	γ−1	γ−1	PROPN
ejpam-6408	122	50	ϵ	ϵ	X
ejpam-6408	122	51	(	(	PUNCT
ejpam-6408	122	52	g	g	NOUN
ejpam-6408	122	53	)	)	PUNCT
ejpam-6408	122	54	∈	∈	PROPN
ejpam-6408	122	55	soϵ(γ1	soϵ(γ1	NOUN
ejpam-6408	122	56	)	)	PUNCT
ejpam-6408	122	57	for	for	ADP
ejpam-6408	122	58	each	each	DET
ejpam-6408	122	59	g	g	PROPN
ejpam-6408	122	60	∈	∈	PROPN
ejpam-6408	122	61	ϑ2	ϑ2	PROPN
ejpam-6408	122	62	.	.	PUNCT
ejpam-6408	123	1	(	(	PUNCT
ejpam-6408	123	2	2	2	X
ejpam-6408	123	3	)	)	PUNCT
ejpam-6408	123	4	supra	supra	NOUN
ejpam-6408	123	5	ϵ-irresolute	ϵ-irresolute	NOUN
ejpam-6408	123	6	if	if	SCONJ
ejpam-6408	123	7	γ−1	γ−1	PROPN
ejpam-6408	123	8	ϵ	ϵ	X
ejpam-6408	123	9	(	(	PUNCT
ejpam-6408	123	10	d	d	NOUN
ejpam-6408	123	11	)	)	PUNCT
ejpam-6408	123	12	∈	∈	PROPN
ejpam-6408	123	13	soϵ(γ1	soϵ(γ1	NOUN
ejpam-6408	123	14	)	)	PUNCT
ejpam-6408	123	15	for	for	ADP
ejpam-6408	123	16	each	each	DET
ejpam-6408	123	17	d	d	PROPN
ejpam-6408	123	18	∈	∈	PROPN
ejpam-6408	123	19	soϵ(γ2	soϵ(γ2	PROPN
ejpam-6408	123	20	)	)	PUNCT
ejpam-6408	123	21	.	.	PUNCT
ejpam-6408	124	1	(	(	PUNCT
ejpam-6408	124	2	3	3	X
ejpam-6408	124	3	)	)	PUNCT
ejpam-6408	124	4	supra	supra	NOUN
ejpam-6408	124	5	ϵ	ϵ	X
ejpam-6408	124	6	(	(	PUNCT
ejpam-6408	124	7	ϵ∗)-open	ϵ∗)-open	VERB
ejpam-6408	124	8	if	if	SCONJ
ejpam-6408	124	9	γϵ(u	γϵ(u	NUM
ejpam-6408	124	10	)	)	PUNCT
ejpam-6408	124	11	∈	∈	PROPN
ejpam-6408	124	12	soϵ(γ2	soϵ(γ2	NOUN
ejpam-6408	124	13	)	)	PUNCT
ejpam-6408	124	14	for	for	ADP
ejpam-6408	124	15	each	each	DET
ejpam-6408	124	16	u	u	PROPN
ejpam-6408	124	17	∈	∈	PROPN
ejpam-6408	124	18	θ1	θ1	NOUN
ejpam-6408	124	19	(	(	PUNCT
ejpam-6408	124	20	u	u	NOUN
ejpam-6408	124	21	∈	∈	PROPN
ejpam-6408	124	22	soϵ(γ1	soϵ(γ1	NOUN
ejpam-6408	124	23	)	)	PUNCT
ejpam-6408	124	24	)	)	PUNCT
ejpam-6408	124	25	.	.	PUNCT
ejpam-6408	125	1	(	(	PUNCT
ejpam-6408	125	2	4	4	X
ejpam-6408	125	3	)	)	PUNCT
ejpam-6408	125	4	supra-ϵ∗-homeomorphism	supra-ϵ∗-homeomorphism	NOUN
ejpam-6408	125	5	if	if	SCONJ
ejpam-6408	125	6	it	it	PRON
ejpam-6408	125	7	is	be	AUX
ejpam-6408	125	8	bijective	bijective	ADJ
ejpam-6408	125	9	supra	supra	PROPN
ejpam-6408	125	10	ϵ∗-open	ϵ∗-open	PROPN
ejpam-6408	125	11	and	and	CCONJ
ejpam-6408	125	12	supra	supra	ADJ
ejpam-6408	125	13	ϵ∗-cts	ϵ∗-ct	NOUN
ejpam-6408	125	14	.	.	PUNCT
ejpam-6408	126	1	3	3	X
ejpam-6408	126	2	.	.	X
ejpam-6408	126	3	supra	supra	PROPN
ejpam-6408	126	4	ϵ-completely	ϵ-completely	ADJ
ejpam-6408	126	5	spaces	space	NOUN
ejpam-6408	126	6	in	in	ADP
ejpam-6408	126	7	this	this	DET
ejpam-6408	126	8	section	section	NOUN
ejpam-6408	126	9	,	,	PUNCT
ejpam-6408	126	10	we	we	PRON
ejpam-6408	126	11	provide	provide	VERB
ejpam-6408	126	12	the	the	DET
ejpam-6408	126	13	notion	notion	NOUN
ejpam-6408	126	14	of	of	ADP
ejpam-6408	126	15	supra-ϵ-completely	supra-ϵ-completely	ADV
ejpam-6408	126	16	space	space	NOUN
ejpam-6408	126	17	as	as	ADP
ejpam-6408	126	18	a	a	DET
ejpam-6408	126	19	generalization	generalization	NOUN
ejpam-6408	126	20	to	to	ADP
ejpam-6408	126	21	the	the	DET
ejpam-6408	126	22	approaches	approach	NOUN
ejpam-6408	126	23	of	of	ADP
ejpam-6408	126	24	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	126	25	-	-	PUNCT
ejpam-6408	126	26	space	space	NOUN
ejpam-6408	126	27	,	,	PUNCT
ejpam-6408	126	28	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6408	126	29	-	-	PUNCT
ejpam-6408	126	30	space	space	NOUN
ejpam-6408	126	31	,	,	PUNCT
ejpam-6408	126	32	and	and	CCONJ
ejpam-6408	126	33	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6408	126	34	-	-	NOUN
ejpam-6408	126	35	space	space	NOUN
ejpam-6408	126	36	.	.	PUNCT
ejpam-6408	127	1	additionally	additionally	ADV
ejpam-6408	127	2	,	,	PUNCT
ejpam-6408	127	3	we	we	PRON
ejpam-6408	127	4	prove	prove	VERB
ejpam-6408	127	5	that	that	SCONJ
ejpam-6408	127	6	the	the	DET
ejpam-6408	127	7	notions	notion	NOUN
ejpam-6408	127	8	of	of	ADP
ejpam-6408	127	9	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	127	10	-	-	PUNCT
ejpam-6408	127	11	space	space	NOUN
ejpam-6408	127	12	supra-ϵ-completely	supra-ϵ-completely	ADV
ejpam-6408	127	13	-	-	PUNCT
ejpam-6408	127	14	space	space	NOUN
ejpam-6408	127	15	are	be	AUX
ejpam-6408	127	16	identical	identical	ADJ
ejpam-6408	127	17	for	for	ADP
ejpam-6408	127	18	any	any	DET
ejpam-6408	127	19	sts	st	NOUN
ejpam-6408	127	20	(	(	PUNCT
ejpam-6408	127	21	γ	γ	X
ejpam-6408	127	22	,	,	PUNCT
ejpam-6408	127	23	θ	θ	NOUN
ejpam-6408	127	24	)	)	PUNCT
ejpam-6408	127	25	,	,	PUNCT
ejpam-6408	127	26	if	if	SCONJ
ejpam-6408	127	27	|γ|	|γ|	PROPN
ejpam-6408	127	28	⩽	⩽	NOUN
ejpam-6408	127	29	4	4	X
ejpam-6408	127	30	.	.	PUNCT
ejpam-6408	128	1	furthermore	furthermore	ADV
ejpam-6408	128	2	,	,	PUNCT
ejpam-6408	128	3	we	we	PRON
ejpam-6408	128	4	investigate	investigate	VERB
ejpam-6408	128	5	this	this	DET
ejpam-6408	128	6	concept	concept	NOUN
ejpam-6408	128	7	’s	’s	PART
ejpam-6408	128	8	behavior	behavior	NOUN
ejpam-6408	128	9	in	in	ADP
ejpam-6408	128	10	relation	relation	NOUN
ejpam-6408	128	11	to	to	ADP
ejpam-6408	128	12	particular	particular	ADJ
ejpam-6408	128	13	supra	supra	NOUN
ejpam-6408	128	14	function	function	NOUN
ejpam-6408	128	15	types	type	NOUN
ejpam-6408	128	16	.	.	PUNCT
ejpam-6408	129	1	in	in	ADP
ejpam-6408	129	2	special	special	ADJ
ejpam-6408	129	3	,	,	PUNCT
ejpam-6408	129	4	we	we	PRON
ejpam-6408	129	5	show	show	VERB
ejpam-6408	129	6	that	that	SCONJ
ejpam-6408	129	7	the	the	DET
ejpam-6408	129	8	image	image	NOUN
ejpam-6408	129	9	of	of	ADP
ejpam-6408	129	10	each	each	DET
ejpam-6408	129	11	supra-ϵt2	supra-ϵt2	NUM
ejpam-6408	129	12	1	1	NUM
ejpam-6408	129	13	2	2	NUM
ejpam-6408	129	14	-space	-space	NOUN
ejpam-6408	129	15	is	be	AUX
ejpam-6408	129	16	a	a	DET
ejpam-6408	129	17	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	129	18	1	1	NUM
ejpam-6408	129	19	2	2	NUM
ejpam-6408	129	20	under	under	ADP
ejpam-6408	129	21	a	a	DET
ejpam-6408	129	22	bijective	bijective	ADJ
ejpam-6408	129	23	supra	supra	NOUN
ejpam-6408	129	24	ϵ∗-open	ϵ∗-open	PROPN
ejpam-6408	129	25	function	function	NOUN
ejpam-6408	129	26	.	.	PUNCT
ejpam-6408	130	1	finally	finally	ADV
ejpam-6408	130	2	,	,	PUNCT
ejpam-6408	130	3	we	we	PRON
ejpam-6408	130	4	prove	prove	VERB
ejpam-6408	130	5	that	that	SCONJ
ejpam-6408	130	6	every	every	DET
ejpam-6408	130	7	supra	supra	ADJ
ejpam-6408	130	8	subspace	subspace	NOUN
ejpam-6408	130	9	of	of	ADP
ejpam-6408	130	10	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	130	11	1	1	NUM
ejpam-6408	130	12	2	2	NUM
ejpam-6408	130	13	-space	-space	NOUN
ejpam-6408	130	14	is	be	AUX
ejpam-6408	130	15	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	130	16	1	1	NUM
ejpam-6408	130	17	2	2	NUM
ejpam-6408	130	18	.	.	PUNCT
ejpam-6408	131	1	definition	definition	NOUN
ejpam-6408	131	2	11	11	NUM
ejpam-6408	131	3	.	.	PUNCT
ejpam-6408	132	1	an	an	DET
ejpam-6408	132	2	sts	st	NOUN
ejpam-6408	132	3	(	(	PUNCT
ejpam-6408	132	4	γ	γ	X
ejpam-6408	132	5	,	,	PUNCT
ejpam-6408	132	6	θ	θ	NOUN
ejpam-6408	132	7	)	)	PUNCT
ejpam-6408	132	8	is	be	AUX
ejpam-6408	132	9	said	say	VERB
ejpam-6408	132	10	to	to	PART
ejpam-6408	132	11	be	be	AUX
ejpam-6408	132	12	supra-ϵ-t2	supra-ϵ-t2	NOUN
ejpam-6408	132	13	1	1	NUM
ejpam-6408	132	14	2	2	NUM
ejpam-6408	132	15	-space	-space	NOUN
ejpam-6408	132	16	”	"	PUNCT
ejpam-6408	132	17	supra-ϵ-completely	supra-ϵ-completely	ADV
ejpam-6408	132	18	space	space	NOUN
ejpam-6408	132	19	”	"	PUNCT
ejpam-6408	132	20	if	if	SCONJ
ejpam-6408	132	21	for	for	ADP
ejpam-6408	132	22	each	each	DET
ejpam-6408	132	23	distinct	distinct	ADJ
ejpam-6408	132	24	points	point	NOUN
ejpam-6408	132	25	ϑ1	ϑ1	NOUN
ejpam-6408	132	26	,	,	PUNCT
ejpam-6408	132	27	ϑ2	ϑ2	PROPN
ejpam-6408	132	28	∈	∈	PROPN
ejpam-6408	132	29	γ	γ	PROPN
ejpam-6408	132	30	,	,	PUNCT
ejpam-6408	132	31	then	then	ADV
ejpam-6408	132	32	there	there	PRON
ejpam-6408	132	33	are	be	VERB
ejpam-6408	132	34	two	two	NUM
ejpam-6408	132	35	disjoint	disjoint	ADJ
ejpam-6408	132	36	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	132	37	subsets	subset	NOUN
ejpam-6408	132	38	ν1	ν1	NOUN
ejpam-6408	132	39	and	and	CCONJ
ejpam-6408	132	40	ν2	ν2	NOUN
ejpam-6408	132	41	of	of	ADP
ejpam-6408	132	42	γ	γ	NOUN
ejpam-6408	132	43	,	,	PUNCT
ejpam-6408	132	44	such	such	ADJ
ejpam-6408	132	45	that	that	DET
ejpam-6408	132	46	ϑ1	ϑ1	PROPN
ejpam-6408	132	47	∈	∈	PROPN
ejpam-6408	132	48	ν1	ν1	NOUN
ejpam-6408	132	49	,	,	PUNCT
ejpam-6408	132	50	ϑ2	ϑ2	PROPN
ejpam-6408	132	51	∈	∈	PROPN
ejpam-6408	132	52	ν2	ν2	NOUN
ejpam-6408	132	53	and	and	CCONJ
ejpam-6408	132	54	clsϵ(ν1	clsϵ(ν1	NOUN
ejpam-6408	132	55	)	)	PUNCT
ejpam-6408	132	56	∩	∩	ADJ
ejpam-6408	132	57	clsϵ(ν2	clsϵ(ν2	NOUN
ejpam-6408	132	58	)	)	PUNCT
ejpam-6408	132	59	=	=	PUNCT
ejpam-6408	132	60	∅.	∅.	NOUN
ejpam-6408	132	61	theorem	theorem	NOUN
ejpam-6408	132	62	2	2	NUM
ejpam-6408	132	63	.	.	PUNCT
ejpam-6408	133	1	any	any	DET
ejpam-6408	133	2	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	133	3	1	1	NUM
ejpam-6408	133	4	2	2	NUM
ejpam-6408	133	5	-space	-space	NOUN
ejpam-6408	133	6	is	be	AUX
ejpam-6408	133	7	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	133	8	.	.	PUNCT
ejpam-6408	134	1	proof	proof	NOUN
ejpam-6408	134	2	.	.	PUNCT
ejpam-6408	135	1	follows	follow	VERB
ejpam-6408	135	2	from	from	ADP
ejpam-6408	135	3	definition	definition	NOUN
ejpam-6408	135	4	11	11	NUM
ejpam-6408	135	5	.	.	PUNCT
ejpam-6408	136	1	remark	remark	NOUN
ejpam-6408	136	2	1	1	NUM
ejpam-6408	136	3	.	.	PUNCT
ejpam-6408	137	1	the	the	DET
ejpam-6408	137	2	converse	converse	NOUN
ejpam-6408	137	3	of	of	ADP
ejpam-6408	137	4	theorem	theorem	ADJ
ejpam-6408	137	5	2	2	NUM
ejpam-6408	137	6	is	be	AUX
ejpam-6408	137	7	not	not	PART
ejpam-6408	137	8	hold	hold	NOUN
ejpam-6408	137	9	as	as	SCONJ
ejpam-6408	137	10	the	the	DET
ejpam-6408	137	11	upcoming	upcoming	ADJ
ejpam-6408	137	12	example	example	NOUN
ejpam-6408	137	13	will	will	AUX
ejpam-6408	137	14	demonstrate	demonstrate	VERB
ejpam-6408	137	15	.	.	PUNCT
ejpam-6408	137	16	example	example	NOUN
ejpam-6408	138	1	1	1	NUM
ejpam-6408	138	2	.	.	PUNCT
ejpam-6408	138	3	let	let	VERB
ejpam-6408	138	4	θ	θ	NOUN
ejpam-6408	138	5	=	=	PUNCT
ejpam-6408	138	6	{	{	PUNCT
ejpam-6408	138	7	γ	γ	X
ejpam-6408	138	8	,	,	PUNCT
ejpam-6408	138	9	∅	∅	NOUN
ejpam-6408	138	10	,	,	PUNCT
ejpam-6408	138	11	{	{	PUNCT
ejpam-6408	138	12	2	2	NUM
ejpam-6408	138	13	,	,	PUNCT
ejpam-6408	138	14	4	4	NUM
ejpam-6408	138	15	}	}	PUNCT
ejpam-6408	138	16	,	,	PUNCT
ejpam-6408	138	17	{	{	PUNCT
ejpam-6408	138	18	1	1	NUM
ejpam-6408	138	19	,	,	PUNCT
ejpam-6408	138	20	3	3	NUM
ejpam-6408	138	21	}	}	PUNCT
ejpam-6408	138	22	,	,	PUNCT
ejpam-6408	138	23	{	{	PUNCT
ejpam-6408	138	24	2	2	NUM
ejpam-6408	138	25	,	,	PUNCT
ejpam-6408	138	26	3	3	NUM
ejpam-6408	138	27	,	,	PUNCT
ejpam-6408	138	28	4	4	NUM
ejpam-6408	138	29	}	}	PUNCT
ejpam-6408	138	30	,	,	PUNCT
ejpam-6408	138	31	{	{	PUNCT
ejpam-6408	138	32	1	1	NUM
ejpam-6408	138	33	,	,	PUNCT
ejpam-6408	138	34	2	2	NUM
ejpam-6408	138	35	,	,	PUNCT
ejpam-6408	138	36	4	4	NUM
ejpam-6408	138	37	}	}	PUNCT
ejpam-6408	138	38	,	,	PUNCT
ejpam-6408	138	39	{	{	PUNCT
ejpam-6408	138	40	1	1	NUM
ejpam-6408	138	41	,	,	PUNCT
ejpam-6408	138	42	2	2	NUM
ejpam-6408	138	43	,	,	PUNCT
ejpam-6408	138	44	3	3	NUM
ejpam-6408	138	45	}	}	PUNCT
ejpam-6408	138	46	,	,	PUNCT
ejpam-6408	138	47	{	{	PUNCT
ejpam-6408	138	48	3	3	NUM
ejpam-6408	138	49	,	,	PUNCT
ejpam-6408	138	50	4	4	NUM
ejpam-6408	138	51	}	}	PUNCT
ejpam-6408	138	52	,	,	PUNCT
ejpam-6408	138	53	{	{	PUNCT
ejpam-6408	138	54	1	1	NUM
ejpam-6408	138	55	,	,	PUNCT
ejpam-6408	138	56	3	3	NUM
ejpam-6408	138	57	,	,	PUNCT
ejpam-6408	138	58	4	4	NUM
ejpam-6408	138	59	}	}	PUNCT
ejpam-6408	138	60	,	,	PUNCT
ejpam-6408	138	61	{	{	PUNCT
ejpam-6408	138	62	1	1	NUM
ejpam-6408	138	63	,	,	PUNCT
ejpam-6408	138	64	4	4	NUM
ejpam-6408	138	65	}	}	PUNCT
ejpam-6408	138	66	,	,	PUNCT
ejpam-6408	138	67	{	{	PUNCT
ejpam-6408	138	68	1	1	NUM
ejpam-6408	138	69	,	,	PUNCT
ejpam-6408	138	70	2	2	NUM
ejpam-6408	138	71	,	,	PUNCT
ejpam-6408	138	72	5	5	NUM
ejpam-6408	138	73	}	}	PUNCT
ejpam-6408	138	74	,	,	PUNCT
ejpam-6408	138	75	{	{	PUNCT
ejpam-6408	138	76	3	3	NUM
ejpam-6408	138	77	,	,	PUNCT
ejpam-6408	138	78	4	4	NUM
ejpam-6408	138	79	,	,	PUNCT
ejpam-6408	138	80	5	5	NUM
ejpam-6408	138	81	}	}	PUNCT
ejpam-6408	138	82	,	,	PUNCT
ejpam-6408	138	83	{	{	PUNCT
ejpam-6408	138	84	2	2	NUM
ejpam-6408	138	85	,	,	PUNCT
ejpam-6408	138	86	3	3	NUM
ejpam-6408	138	87	,	,	PUNCT
ejpam-6408	138	88	4	4	NUM
ejpam-6408	138	89	,	,	PUNCT
ejpam-6408	138	90	5	5	NUM
ejpam-6408	138	91	}	}	PUNCT
ejpam-6408	138	92	,	,	PUNCT
ejpam-6408	138	93	{	{	PUNCT
ejpam-6408	138	94	1	1	NUM
ejpam-6408	138	95	,	,	PUNCT
ejpam-6408	138	96	3	3	NUM
ejpam-6408	138	97	,	,	PUNCT
ejpam-6408	138	98	4	4	NUM
ejpam-6408	138	99	,	,	PUNCT
ejpam-6408	138	100	5	5	NUM
ejpam-6408	138	101	}	}	PUNCT
ejpam-6408	138	102	,	,	PUNCT
ejpam-6408	138	103	{	{	PUNCT
ejpam-6408	138	104	1	1	NUM
ejpam-6408	138	105	,	,	PUNCT
ejpam-6408	138	106	2	2	NUM
ejpam-6408	138	107	,	,	PUNCT
ejpam-6408	138	108	4	4	NUM
ejpam-6408	138	109	,	,	PUNCT
ejpam-6408	138	110	5	5	NUM
ejpam-6408	138	111	}	}	PUNCT
ejpam-6408	138	112	,	,	PUNCT
ejpam-6408	138	113	{	{	PUNCT
ejpam-6408	138	114	1	1	NUM
ejpam-6408	138	115	,	,	PUNCT
ejpam-6408	138	116	2	2	NUM
ejpam-6408	138	117	}	}	PUNCT
ejpam-6408	138	118	,	,	PUNCT
ejpam-6408	138	119	{	{	PUNCT
ejpam-6408	138	120	1	1	NUM
ejpam-6408	138	121	,	,	PUNCT
ejpam-6408	138	122	2	2	NUM
ejpam-6408	138	123	,	,	PUNCT
ejpam-6408	138	124	3	3	NUM
ejpam-6408	138	125	,	,	PUNCT
ejpam-6408	138	126	5	5	NUM
ejpam-6408	138	127	}	}	PUNCT
ejpam-6408	138	128	,	,	PUNCT
ejpam-6408	138	129	{	{	PUNCT
ejpam-6408	138	130	1	1	NUM
ejpam-6408	138	131	,	,	PUNCT
ejpam-6408	138	132	2	2	NUM
ejpam-6408	138	133	,	,	PUNCT
ejpam-6408	138	134	3	3	NUM
ejpam-6408	138	135	,	,	PUNCT
ejpam-6408	138	136	4	4	NUM
ejpam-6408	138	137	}	}	PUNCT
ejpam-6408	138	138	,	,	PUNCT
ejpam-6408	138	139	{	{	PUNCT
ejpam-6408	138	140	2	2	NUM
ejpam-6408	138	141	,	,	PUNCT
ejpam-6408	138	142	3	3	NUM
ejpam-6408	138	143	}	}	PUNCT
ejpam-6408	138	144	}	}	PUNCT
ejpam-6408	138	145	be	be	AUX
ejpam-6408	138	146	an	an	DET
ejpam-6408	138	147	sts	st	NOUN
ejpam-6408	138	148	on	on	ADP
ejpam-6408	138	149	γ	γ	X
ejpam-6408	138	150	=	=	SYM
ejpam-6408	138	151	{	{	PUNCT
ejpam-6408	138	152	1	1	NUM
ejpam-6408	138	153	,	,	PUNCT
ejpam-6408	138	154	2	2	NUM
ejpam-6408	138	155	,	,	PUNCT
ejpam-6408	138	156	3	3	NUM
ejpam-6408	138	157	,	,	PUNCT
ejpam-6408	138	158	4	4	NUM
ejpam-6408	138	159	,	,	PUNCT
ejpam-6408	138	160	5	5	NUM
ejpam-6408	138	161	}	}	PUNCT
ejpam-6408	138	162	.	.	PUNCT
ejpam-6408	139	1	regarding	regard	VERB
ejpam-6408	139	2	1	1	NUM
ejpam-6408	139	3	̸=	̸=	PROPN
ejpam-6408	139	4	2	2	NUM
ejpam-6408	139	5	∈	∈	PROPN
ejpam-6408	139	6	γ	γ	NOUN
ejpam-6408	139	7	,	,	PUNCT
ejpam-6408	139	8	then	then	ADV
ejpam-6408	139	9	there	there	PRON
ejpam-6408	139	10	are	be	VERB
ejpam-6408	139	11	not	not	PART
ejpam-6408	139	12	two	two	NUM
ejpam-6408	139	13	disjoint	disjoint	ADJ
ejpam-6408	139	14	supra-ϵopen	supra-ϵopen	ADJ
ejpam-6408	139	15	subsets	subset	NOUN
ejpam-6408	139	16	ν1	ν1	NOUN
ejpam-6408	139	17	and	and	CCONJ
ejpam-6408	139	18	ν2	ν2	NOUN
ejpam-6408	139	19	of	of	ADP
ejpam-6408	139	20	γ	γ	NOUN
ejpam-6408	139	21	,	,	PUNCT
ejpam-6408	139	22	such	such	ADJ
ejpam-6408	139	23	that	that	SCONJ
ejpam-6408	139	24	1	1	NUM
ejpam-6408	139	25	∈	∈	NOUN
ejpam-6408	139	26	ν1	ν1	NOUN
ejpam-6408	139	27	,	,	PUNCT
ejpam-6408	139	28	2	2	NUM
ejpam-6408	139	29	∈	∈	NOUN
ejpam-6408	139	30	ν2	ν2	NOUN
ejpam-6408	139	31	and	and	CCONJ
ejpam-6408	139	32	clsϵ(ν1	clsϵ(ν1	NOUN
ejpam-6408	139	33	)	)	PUNCT
ejpam-6408	139	34	∩	∩	ADJ
ejpam-6408	139	35	clsϵ(ν2	clsϵ(ν2	NOUN
ejpam-6408	139	36	)	)	PUNCT
ejpam-6408	139	37	=	=	PUNCT
ejpam-6408	139	38	∅.	∅.	VERB
ejpam-6408	139	39	hence	hence	ADV
ejpam-6408	139	40	,	,	PUNCT
ejpam-6408	139	41	γ	γ	X
ejpam-6408	139	42	is	be	AUX
ejpam-6408	139	43	not	not	PART
ejpam-6408	139	44	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	139	45	1	1	NUM
ejpam-6408	139	46	2	2	NUM
ejpam-6408	139	47	.	.	PUNCT
ejpam-6408	140	1	also	also	ADV
ejpam-6408	140	2	,	,	PUNCT
ejpam-6408	140	3	it	it	PRON
ejpam-6408	140	4	is	be	AUX
ejpam-6408	140	5	easy	easy	ADJ
ejpam-6408	140	6	to	to	PART
ejpam-6408	140	7	check	check	VERB
ejpam-6408	140	8	that	that	SCONJ
ejpam-6408	140	9	γ	γ	PROPN
ejpam-6408	140	10	is	be	AUX
ejpam-6408	140	11	supra-ϵ-t2	supra-ϵ-t2	PROPN
ejpam-6408	140	12	.	.	PUNCT
ejpam-6408	141	1	theorem	theorem	NOUN
ejpam-6408	141	2	3	3	NUM
ejpam-6408	141	3	.	.	X
ejpam-6408	141	4	for	for	ADP
ejpam-6408	141	5	any	any	DET
ejpam-6408	141	6	sts	st	NOUN
ejpam-6408	141	7	(	(	PUNCT
ejpam-6408	141	8	γ	γ	X
ejpam-6408	141	9	,	,	PUNCT
ejpam-6408	141	10	θ	θ	NOUN
ejpam-6408	141	11	)	)	PUNCT
ejpam-6408	141	12	,	,	PUNCT
ejpam-6408	141	13	if	if	SCONJ
ejpam-6408	141	14	|γ|	|γ|	PROPN
ejpam-6408	141	15	⩽	⩽	NOUN
ejpam-6408	141	16	4	4	NUM
ejpam-6408	141	17	,	,	PUNCT
ejpam-6408	141	18	then	then	ADV
ejpam-6408	141	19	the	the	DET
ejpam-6408	141	20	approaches	approach	NOUN
ejpam-6408	141	21	of	of	ADP
ejpam-6408	141	22	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	141	23	1	1	NUM
ejpam-6408	141	24	2	2	NUM
ejpam-6408	141	25	-space	-space	NOUN
ejpam-6408	141	26	and	and	CCONJ
ejpam-6408	141	27	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	141	28	-	-	PUNCT
ejpam-6408	141	29	space	space	NOUN
ejpam-6408	141	30	are	be	AUX
ejpam-6408	141	31	identical	identical	ADJ
ejpam-6408	141	32	.	.	PUNCT
ejpam-6408	142	1	m.	m.	NOUN
ejpam-6408	142	2	aldawood	aldawood	PROPN
ejpam-6408	142	3	et	et	PROPN
ejpam-6408	142	4	al	al	PROPN
ejpam-6408	142	5	.	.	PUNCT
ejpam-6408	142	6	/	/	SYM
ejpam-6408	142	7	eur	eur	PROPN
ejpam-6408	142	8	.	.	PUNCT
ejpam-6408	143	1	j.	j.	PROPN
ejpam-6408	143	2	pure	pure	PROPN
ejpam-6408	143	3	appl	appl	PROPN
ejpam-6408	143	4	.	.	PROPN
ejpam-6408	143	5	math	math	PROPN
ejpam-6408	143	6	,	,	PUNCT
ejpam-6408	143	7	18	18	NUM
ejpam-6408	143	8	(	(	PUNCT
ejpam-6408	143	9	3	3	NUM
ejpam-6408	143	10	)	)	PUNCT
ejpam-6408	143	11	(	(	PUNCT
ejpam-6408	143	12	2025	2025	NUM
ejpam-6408	143	13	)	)	PUNCT
ejpam-6408	143	14	,	,	PUNCT
ejpam-6408	143	15	6408	6408	NUM
ejpam-6408	143	16	6	6	NUM
ejpam-6408	143	17	of	of	ADP
ejpam-6408	143	18	16	16	NUM
ejpam-6408	143	19	proof	proof	NOUN
ejpam-6408	143	20	.	.	PUNCT
ejpam-6408	144	1	given	give	VERB
ejpam-6408	144	2	theorem	theorem	NOUN
ejpam-6408	144	3	2	2	NUM
ejpam-6408	144	4	,	,	PUNCT
ejpam-6408	144	5	we	we	PRON
ejpam-6408	144	6	have	have	VERB
ejpam-6408	144	7	that	that	SCONJ
ejpam-6408	144	8	every	every	DET
ejpam-6408	144	9	supra	supra	NOUN
ejpam-6408	144	10	-	-	PUNCT
ejpam-6408	144	11	t2	t2	NOUN
ejpam-6408	144	12	1	1	NUM
ejpam-6408	144	13	2	2	NUM
ejpam-6408	144	14	-space	-space	NOUN
ejpam-6408	144	15	is	be	AUX
ejpam-6408	144	16	supra-ϵ-t2	supra-ϵ-t2	PROPN
ejpam-6408	144	17	.	.	PUNCT
ejpam-6408	145	1	now	now	ADV
ejpam-6408	145	2	,	,	PUNCT
ejpam-6408	145	3	let	let	VERB
ejpam-6408	145	4	(	(	PUNCT
ejpam-6408	145	5	γ	γ	X
ejpam-6408	145	6	,	,	PUNCT
ejpam-6408	145	7	θ	θ	NOUN
ejpam-6408	145	8	)	)	PUNCT
ejpam-6408	145	9	be	be	VERB
ejpam-6408	145	10	a	a	DET
ejpam-6408	145	11	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	145	12	-	-	PUNCT
ejpam-6408	145	13	space	space	NOUN
ejpam-6408	145	14	and	and	CCONJ
ejpam-6408	145	15	ϑ1	ϑ1	NOUN
ejpam-6408	145	16	̸=	̸=	PROPN
ejpam-6408	145	17	ϑ2	ϑ2	PROPN
ejpam-6408	145	18	∈	∈	PROPN
ejpam-6408	145	19	γ	γ	PROPN
ejpam-6408	145	20	.	.	PUNCT
ejpam-6408	146	1	then	then	ADV
ejpam-6408	146	2	,	,	PUNCT
ejpam-6408	146	3	there	there	PRON
ejpam-6408	146	4	are	be	VERB
ejpam-6408	146	5	two	two	NUM
ejpam-6408	146	6	disjoint	disjoint	ADJ
ejpam-6408	146	7	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	146	8	subsets	subset	NOUN
ejpam-6408	146	9	ν1	ν1	NOUN
ejpam-6408	146	10	and	and	CCONJ
ejpam-6408	146	11	ν2	ν2	NOUN
ejpam-6408	146	12	of	of	ADP
ejpam-6408	146	13	γ	γ	X
ejpam-6408	146	14	containing	contain	VERB
ejpam-6408	146	15	ϑ1	ϑ1	NOUN
ejpam-6408	146	16	and	and	CCONJ
ejpam-6408	146	17	ϑ2	ϑ2	PROPN
ejpam-6408	146	18	,	,	PUNCT
ejpam-6408	146	19	respectively	respectively	ADV
ejpam-6408	146	20	.	.	PUNCT
ejpam-6408	147	1	this	this	PRON
ejpam-6408	147	2	implies	imply	VERB
ejpam-6408	147	3	that	that	SCONJ
ejpam-6408	147	4	,	,	PUNCT
ejpam-6408	147	5	clsϵ(ν1	clsϵ(ν1	VERB
ejpam-6408	147	6	)	)	PUNCT
ejpam-6408	147	7	⊆	⊆	NUM
ejpam-6408	147	8	νc2	νc2	ADJ
ejpam-6408	147	9	and	and	CCONJ
ejpam-6408	147	10	clsϵ(ν2	clsϵ(ν2	NOUN
ejpam-6408	147	11	)	)	PUNCT
ejpam-6408	147	12	⊆	⊆	NUM
ejpam-6408	147	13	νc1	νc1	NOUN
ejpam-6408	147	14	(	(	PUNCT
ejpam-6408	147	15	1	1	NUM
ejpam-6408	147	16	)	)	PUNCT
ejpam-6408	147	17	now	now	ADV
ejpam-6408	147	18	,	,	PUNCT
ejpam-6408	147	19	we	we	PRON
ejpam-6408	147	20	have	have	VERB
ejpam-6408	147	21	two	two	NUM
ejpam-6408	147	22	cases	case	NOUN
ejpam-6408	147	23	:	:	PUNCT
ejpam-6408	147	24	case	case	NOUN
ejpam-6408	147	25	(	(	PUNCT
ejpam-6408	147	26	1	1	NUM
ejpam-6408	147	27	)	)	PUNCT
ejpam-6408	147	28	,	,	PUNCT
ejpam-6408	147	29	|ν1|	|ν1|	NOUN
ejpam-6408	147	30	=	=	SYM
ejpam-6408	147	31	1	1	NUM
ejpam-6408	147	32	or	or	CCONJ
ejpam-6408	147	33	|ν1|	|ν1|	NUM
ejpam-6408	147	34	=	=	SYM
ejpam-6408	147	35	3	3	NUM
ejpam-6408	147	36	,	,	PUNCT
ejpam-6408	147	37	then	then	ADV
ejpam-6408	147	38	ν1	ν1	NOUN
ejpam-6408	147	39	is	be	AUX
ejpam-6408	147	40	both	both	PRON
ejpam-6408	147	41	supra-ϵ-open	supra-ϵ-open	VERB
ejpam-6408	147	42	and	and	CCONJ
ejpam-6408	147	43	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	147	44	,	,	PUNCT
ejpam-6408	147	45	which	which	PRON
ejpam-6408	147	46	implies	imply	VERB
ejpam-6408	147	47	that	that	SCONJ
ejpam-6408	147	48	clsϵ(ν1	clsϵ(ν1	NOUN
ejpam-6408	147	49	)	)	PUNCT
ejpam-6408	147	50	∩	∩	ADJ
ejpam-6408	147	51	clsϵ(ν2	clsϵ(ν2	NOUN
ejpam-6408	147	52	)	)	PUNCT
ejpam-6408	147	53	=	=	NOUN
ejpam-6408	147	54	∅	∅	NOUN
ejpam-6408	147	55	,	,	PUNCT
ejpam-6408	147	56	given	give	VERB
ejpam-6408	147	57	equation	equation	NOUN
ejpam-6408	147	58	1	1	NUM
ejpam-6408	147	59	.	.	PUNCT
ejpam-6408	148	1	case	case	NOUN
ejpam-6408	148	2	(	(	PUNCT
ejpam-6408	148	3	2	2	NUM
ejpam-6408	148	4	)	)	PUNCT
ejpam-6408	148	5	,	,	PUNCT
ejpam-6408	148	6	|ν1|	|ν1|	NOUN
ejpam-6408	148	7	=	=	SYM
ejpam-6408	148	8	2	2	NUM
ejpam-6408	148	9	,	,	PUNCT
ejpam-6408	148	10	then	then	ADV
ejpam-6408	148	11	either	either	CCONJ
ejpam-6408	148	12	|ν2|	|ν2|	NOUN
ejpam-6408	148	13	=	=	SYM
ejpam-6408	148	14	2	2	NUM
ejpam-6408	148	15	or	or	CCONJ
ejpam-6408	148	16	|ν2|	|ν2|	NOUN
ejpam-6408	148	17	=	=	NOUN
ejpam-6408	148	18	1	1	X
ejpam-6408	148	19	.	.	PUNCT
ejpam-6408	149	1	if	if	SCONJ
ejpam-6408	149	2	|ν2|	|ν2|	NOUN
ejpam-6408	149	3	=	=	SYM
ejpam-6408	149	4	2	2	NUM
ejpam-6408	149	5	,	,	PUNCT
ejpam-6408	149	6	then	then	ADV
ejpam-6408	149	7	both	both	DET
ejpam-6408	149	8	ν1	ν1	NOUN
ejpam-6408	149	9	and	and	CCONJ
ejpam-6408	149	10	ν2	ν2	NOUN
ejpam-6408	149	11	are	be	AUX
ejpam-6408	149	12	both	both	PRON
ejpam-6408	149	13	supra-ϵ-open	supra-ϵ-open	VERB
ejpam-6408	149	14	and	and	CCONJ
ejpam-6408	149	15	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	149	16	,	,	PUNCT
ejpam-6408	149	17	and	and	CCONJ
ejpam-6408	149	18	hence	hence	ADV
ejpam-6408	149	19	clsϵ(ν1	clsϵ(ν1	VERB
ejpam-6408	149	20	)	)	PUNCT
ejpam-6408	149	21	∩	∩	ADJ
ejpam-6408	149	22	clsϵ(ν2	clsϵ(ν2	NOUN
ejpam-6408	149	23	)	)	PUNCT
ejpam-6408	150	1	=	=	PUNCT
ejpam-6408	150	2	∅.	∅.	NOUN
ejpam-6408	150	3	if	if	SCONJ
ejpam-6408	150	4	|ν2|	|ν2|	NOUN
ejpam-6408	150	5	=	=	SYM
ejpam-6408	150	6	1	1	NUM
ejpam-6408	150	7	,	,	PUNCT
ejpam-6408	150	8	then	then	ADV
ejpam-6408	150	9	ν2	ν2	NOUN
ejpam-6408	150	10	is	be	AUX
ejpam-6408	150	11	both	both	PRON
ejpam-6408	150	12	supra-ϵ-open	supra-ϵ-open	VERB
ejpam-6408	150	13	and	and	CCONJ
ejpam-6408	150	14	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	150	15	,	,	PUNCT
ejpam-6408	150	16	and	and	CCONJ
ejpam-6408	150	17	thus	thus	ADV
ejpam-6408	150	18	clsϵ(ν1)∩	clsϵ(ν1)∩	PROPN
ejpam-6408	150	19	clsϵ(ν2	clsϵ(ν2	NOUN
ejpam-6408	150	20	)	)	PUNCT
ejpam-6408	151	1	=	=	PUNCT
ejpam-6408	151	2	∅.	∅.	VERB
ejpam-6408	151	3	therefore	therefore	ADV
ejpam-6408	151	4	,	,	PUNCT
ejpam-6408	151	5	γ	γ	X
ejpam-6408	151	6	is	be	AUX
ejpam-6408	151	7	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	151	8	1	1	NUM
ejpam-6408	151	9	2	2	NUM
ejpam-6408	151	10	.	.	PUNCT
ejpam-6408	152	1	definition	definition	NOUN
ejpam-6408	152	2	12	12	NUM
ejpam-6408	152	3	.	.	PUNCT
ejpam-6408	153	1	a	a	DET
ejpam-6408	153	2	function	function	NOUN
ejpam-6408	153	3	γϵ	γϵ	NOUN
ejpam-6408	153	4	:	:	PUNCT
ejpam-6408	153	5	(	(	PUNCT
ejpam-6408	153	6	γ1	γ1	PROPN
ejpam-6408	153	7	,	,	PUNCT
ejpam-6408	153	8	σ1	σ1	PROPN
ejpam-6408	153	9	)	)	PUNCT
ejpam-6408	153	10	→	→	SYM
ejpam-6408	153	11	(	(	PUNCT
ejpam-6408	153	12	γ2	γ2	ADJ
ejpam-6408	153	13	,	,	PUNCT
ejpam-6408	153	14	σ2	σ2	PROPN
ejpam-6408	153	15	)	)	PUNCT
ejpam-6408	153	16	with	with	ADP
ejpam-6408	153	17	θ1	θ1	NOUN
ejpam-6408	153	18	,	,	PUNCT
ejpam-6408	153	19	θ2	θ2	PROPN
ejpam-6408	153	20	associated	associate	VERB
ejpam-6408	153	21	stss	stss	NOUN
ejpam-6408	153	22	with	with	ADP
ejpam-6408	153	23	σ1	σ1	PROPN
ejpam-6408	153	24	,	,	PUNCT
ejpam-6408	153	25	σ2	σ2	NOUN
ejpam-6408	153	26	respectively	respectively	ADV
ejpam-6408	153	27	,	,	PUNCT
ejpam-6408	153	28	is	be	AUX
ejpam-6408	153	29	said	say	VERB
ejpam-6408	153	30	to	to	PART
ejpam-6408	153	31	be	be	AUX
ejpam-6408	153	32	supra	supra	PROPN
ejpam-6408	153	33	ϵ	ϵ	PROPN
ejpam-6408	153	34	(	(	PUNCT
ejpam-6408	153	35	ϵ∗)-closed	ϵ∗)-close	VERB
ejpam-6408	153	36	if	if	SCONJ
ejpam-6408	153	37	γϵ(u	γϵ(u	NUM
ejpam-6408	153	38	)	)	PUNCT
ejpam-6408	153	39	∈	∈	PROPN
ejpam-6408	153	40	scϵ(γ2	scϵ(γ2	NOUN
ejpam-6408	153	41	)	)	PUNCT
ejpam-6408	153	42	for	for	ADP
ejpam-6408	153	43	each	each	DET
ejpam-6408	153	44	u	u	PROPN
ejpam-6408	153	45	∈	∈	PROPN
ejpam-6408	153	46	θc1	θc1	NOUN
ejpam-6408	153	47	(	(	PUNCT
ejpam-6408	153	48	u	u	NOUN
ejpam-6408	153	49	∈	∈	PROPN
ejpam-6408	153	50	scϵ(γ1	scϵ(γ1	NOUN
ejpam-6408	153	51	)	)	PUNCT
ejpam-6408	153	52	)	)	PUNCT
ejpam-6408	153	53	.	.	PUNCT
ejpam-6408	154	1	theorem	theorem	ADJ
ejpam-6408	154	2	4	4	NUM
ejpam-6408	154	3	.	.	PUNCT
ejpam-6408	155	1	let	let	VERB
ejpam-6408	155	2	γϵ	γϵ	VERB
ejpam-6408	155	3	:	:	PUNCT
ejpam-6408	155	4	(	(	PUNCT
ejpam-6408	155	5	γ1	γ1	PROPN
ejpam-6408	155	6	,	,	PUNCT
ejpam-6408	155	7	σ1	σ1	PROPN
ejpam-6408	155	8	)	)	PUNCT
ejpam-6408	155	9	→	→	SYM
ejpam-6408	155	10	(	(	PUNCT
ejpam-6408	155	11	γ2	γ2	ADJ
ejpam-6408	155	12	,	,	PUNCT
ejpam-6408	155	13	σ2	σ2	PROPN
ejpam-6408	155	14	)	)	PUNCT
ejpam-6408	155	15	be	be	AUX
ejpam-6408	155	16	a	a	DET
ejpam-6408	155	17	function	function	NOUN
ejpam-6408	155	18	with	with	ADP
ejpam-6408	155	19	θ1	θ1	NOUN
ejpam-6408	155	20	,	,	PUNCT
ejpam-6408	155	21	θ2	θ2	PROPN
ejpam-6408	155	22	associated	associate	VERB
ejpam-6408	155	23	stss	stss	NOUN
ejpam-6408	155	24	with	with	ADP
ejpam-6408	155	25	σ1	σ1	PROPN
ejpam-6408	155	26	,	,	PUNCT
ejpam-6408	155	27	σ2	σ2	NOUN
ejpam-6408	155	28	respectively	respectively	ADV
ejpam-6408	155	29	,	,	PUNCT
ejpam-6408	155	30	and	and	CCONJ
ejpam-6408	155	31	β	β	NOUN
ejpam-6408	155	32	⊆	⊆	NUM
ejpam-6408	155	33	γ1	γ1	NOUN
ejpam-6408	155	34	,	,	PUNCT
ejpam-6408	155	35	then	then	ADV
ejpam-6408	155	36	γϵ	γϵ	PROPN
ejpam-6408	155	37	is	be	AUX
ejpam-6408	155	38	supra	supra	NOUN
ejpam-6408	155	39	ϵ-closed	ϵ-close	VERB
ejpam-6408	155	40	if	if	SCONJ
ejpam-6408	155	41	and	and	CCONJ
ejpam-6408	155	42	only	only	ADV
ejpam-6408	155	43	if	if	SCONJ
ejpam-6408	155	44	clsϵ	clsϵ	PROPN
ejpam-6408	155	45	[	[	X
ejpam-6408	155	46	γϵ(β	γϵ(β	NUM
ejpam-6408	155	47	)	)	PUNCT
ejpam-6408	155	48	]	]	PUNCT
ejpam-6408	155	49	⊆	⊆	NUM
ejpam-6408	155	50	γϵ(cl	γϵ(cl	PROPN
ejpam-6408	155	51	s(β	s(β	PROPN
ejpam-6408	155	52	)	)	PUNCT
ejpam-6408	155	53	)	)	PUNCT
ejpam-6408	155	54	.	.	PUNCT
ejpam-6408	156	1	proof	proof	NOUN
ejpam-6408	156	2	.	.	PUNCT
ejpam-6408	156	3	”	"	PUNCT
ejpam-6408	156	4	⇒	⇒	NOUN
ejpam-6408	156	5	”	"	PUNCT
ejpam-6408	156	6	let	let	VERB
ejpam-6408	156	7	us	we	PRON
ejpam-6408	156	8	suppose	suppose	VERB
ejpam-6408	156	9	that	that	SCONJ
ejpam-6408	156	10	γϵ	γϵ	PROPN
ejpam-6408	156	11	be	be	AUX
ejpam-6408	156	12	a	a	DET
ejpam-6408	156	13	supra	supra	ADJ
ejpam-6408	156	14	ϵ-closed	ϵ-close	VERB
ejpam-6408	156	15	function	function	NOUN
ejpam-6408	156	16	and	and	CCONJ
ejpam-6408	156	17	β	β	NOUN
ejpam-6408	156	18	⊆	⊆	NUM
ejpam-6408	156	19	γ1	γ1	NOUN
ejpam-6408	156	20	.	.	PUNCT
ejpam-6408	157	1	since	since	SCONJ
ejpam-6408	157	2	γϵ(β	γϵ(β	NUM
ejpam-6408	157	3	)	)	PUNCT
ejpam-6408	157	4	⊆	⊆	NUM
ejpam-6408	157	5	γϵ(cl	γϵ(cl	PROPN
ejpam-6408	157	6	s(β	s(β	PROPN
ejpam-6408	157	7	)	)	PUNCT
ejpam-6408	157	8	)	)	PUNCT
ejpam-6408	157	9	,	,	PUNCT
ejpam-6408	157	10	clsϵ	clsϵ	NOUN
ejpam-6408	157	11	[	[	X
ejpam-6408	157	12	γϵ(β	γϵ(β	NUM
ejpam-6408	157	13	)	)	PUNCT
ejpam-6408	157	14	]	]	PUNCT
ejpam-6408	158	1	⊆	⊆	NUM
ejpam-6408	158	2	clsϵ	clsϵ	NOUN
ejpam-6408	158	3	[	[	X
ejpam-6408	158	4	γϵ(cl	γϵ(cl	PROPN
ejpam-6408	158	5	s(β	s(β	PROPN
ejpam-6408	158	6	)	)	PUNCT
ejpam-6408	158	7	)	)	PUNCT
ejpam-6408	158	8	]	]	PUNCT
ejpam-6408	158	9	=	=	SYM
ejpam-6408	158	10	γϵ(cl	γϵ(cl	PROPN
ejpam-6408	158	11	s(β	s(β	PROPN
ejpam-6408	158	12	)	)	PUNCT
ejpam-6408	158	13	)	)	PUNCT
ejpam-6408	158	14	,	,	PUNCT
ejpam-6408	158	15	given	give	VERB
ejpam-6408	158	16	γϵ	γϵ	PROPN
ejpam-6408	158	17	is	be	AUX
ejpam-6408	158	18	supra	supra	ADJ
ejpam-6408	158	19	ϵ-closed	ϵ-close	VERB
ejpam-6408	158	20	function	function	NOUN
ejpam-6408	158	21	.	.	PUNCT
ejpam-6408	159	1	“	"	PUNCT
ejpam-6408	159	2	⇐	⇐	INTJ
ejpam-6408	159	3	”	"	PUNCT
ejpam-6408	159	4	let	let	VERB
ejpam-6408	159	5	β	β	X
ejpam-6408	159	6	∈	∈	PROPN
ejpam-6408	159	7	θc1	θc1	PROPN
ejpam-6408	159	8	.	.	PUNCT
ejpam-6408	160	1	considering	consider	VERB
ejpam-6408	160	2	the	the	DET
ejpam-6408	160	3	assumption	assumption	NOUN
ejpam-6408	160	4	,	,	PUNCT
ejpam-6408	160	5	γϵ(β	γϵ(β	PRON
ejpam-6408	160	6	)	)	PUNCT
ejpam-6408	160	7	⊆	⊆	NUM
ejpam-6408	160	8	clsϵ	clsϵ	NOUN
ejpam-6408	160	9	[	[	X
ejpam-6408	160	10	γϵ(β	γϵ(β	NUM
ejpam-6408	160	11	)	)	PUNCT
ejpam-6408	160	12	]	]	PUNCT
ejpam-6408	160	13	⊆	⊆	NUM
ejpam-6408	160	14	γϵ(cl	γϵ(cl	PROPN
ejpam-6408	160	15	s(β	s(β	PROPN
ejpam-6408	160	16	)	)	PUNCT
ejpam-6408	160	17	)	)	PUNCT
ejpam-6408	161	1	=	=	SYM
ejpam-6408	161	2	γϵ(β	γϵ(β	PROPN
ejpam-6408	161	3	)	)	PUNCT
ejpam-6408	161	4	.	.	PUNCT
ejpam-6408	162	1	hence	hence	ADV
ejpam-6408	162	2	,	,	PUNCT
ejpam-6408	162	3	clsϵ	clsϵ	PROPN
ejpam-6408	162	4	[	[	X
ejpam-6408	162	5	γϵ(β	γϵ(β	X
ejpam-6408	162	6	)	)	PUNCT
ejpam-6408	162	7	]	]	PUNCT
ejpam-6408	163	1	=	=	SYM
ejpam-6408	163	2	γϵ(β	γϵ(β	PROPN
ejpam-6408	163	3	)	)	PUNCT
ejpam-6408	163	4	.	.	PUNCT
ejpam-6408	164	1	therefore	therefore	ADV
ejpam-6408	164	2	,	,	PUNCT
ejpam-6408	164	3	γϵ(β	γϵ(β	PRON
ejpam-6408	164	4	)	)	PUNCT
ejpam-6408	164	5	∈	∈	PROPN
ejpam-6408	164	6	scϵ(γ2	scϵ(γ2	NOUN
ejpam-6408	164	7	)	)	PUNCT
ejpam-6408	164	8	,	,	PUNCT
ejpam-6408	164	9	and	and	CCONJ
ejpam-6408	164	10	hence	hence	ADV
ejpam-6408	164	11	γϵ	γϵ	PROPN
ejpam-6408	164	12	is	be	AUX
ejpam-6408	164	13	a	a	DET
ejpam-6408	164	14	supra	supra	ADJ
ejpam-6408	164	15	ϵ-closed	ϵ-close	VERB
ejpam-6408	164	16	function	function	NOUN
ejpam-6408	164	17	.	.	PUNCT
ejpam-6408	165	1	proposition	proposition	NOUN
ejpam-6408	165	2	1	1	NUM
ejpam-6408	165	3	.	.	PUNCT
ejpam-6408	166	1	let	let	VERB
ejpam-6408	166	2	γϵ	γϵ	VERB
ejpam-6408	166	3	:	:	PUNCT
ejpam-6408	166	4	(	(	PUNCT
ejpam-6408	166	5	γ1	γ1	PROPN
ejpam-6408	166	6	,	,	PUNCT
ejpam-6408	166	7	σ1	σ1	PROPN
ejpam-6408	166	8	)	)	PUNCT
ejpam-6408	166	9	→	→	SYM
ejpam-6408	166	10	(	(	PUNCT
ejpam-6408	166	11	γ2	γ2	ADJ
ejpam-6408	166	12	,	,	PUNCT
ejpam-6408	166	13	σ2	σ2	PROPN
ejpam-6408	166	14	)	)	PUNCT
ejpam-6408	166	15	be	be	AUX
ejpam-6408	166	16	a	a	DET
ejpam-6408	166	17	function	function	NOUN
ejpam-6408	166	18	with	with	ADP
ejpam-6408	166	19	θ1	θ1	NOUN
ejpam-6408	166	20	,	,	PUNCT
ejpam-6408	166	21	θ2	θ2	PROPN
ejpam-6408	166	22	associated	associate	VERB
ejpam-6408	166	23	stss	stss	NOUN
ejpam-6408	166	24	with	with	ADP
ejpam-6408	166	25	σ1	σ1	PROPN
ejpam-6408	166	26	,	,	PUNCT
ejpam-6408	166	27	σ2	σ2	NOUN
ejpam-6408	166	28	respectively	respectively	ADV
ejpam-6408	166	29	,	,	PUNCT
ejpam-6408	166	30	and	and	CCONJ
ejpam-6408	166	31	β	β	NOUN
ejpam-6408	166	32	⊆	⊆	NUM
ejpam-6408	166	33	γ1	γ1	NOUN
ejpam-6408	166	34	,	,	PUNCT
ejpam-6408	166	35	then	then	ADV
ejpam-6408	166	36	γϵ	γϵ	PROPN
ejpam-6408	166	37	is	be	AUX
ejpam-6408	166	38	supra	supra	NOUN
ejpam-6408	166	39	ϵ∗-closed	ϵ∗-close	VERB
ejpam-6408	166	40	if	if	SCONJ
ejpam-6408	166	41	and	and	CCONJ
ejpam-6408	166	42	only	only	ADV
ejpam-6408	166	43	if	if	SCONJ
ejpam-6408	166	44	clsϵ	clsϵ	PROPN
ejpam-6408	166	45	[	[	X
ejpam-6408	166	46	γϵ(β	γϵ(β	NUM
ejpam-6408	166	47	)	)	PUNCT
ejpam-6408	166	48	]	]	PUNCT
ejpam-6408	167	1	⊆	⊆	NUM
ejpam-6408	167	2	γϵ(cl	γϵ(cl	PROPN
ejpam-6408	167	3	s	s	PART
ejpam-6408	167	4	ϵ(β	ϵ(β	PROPN
ejpam-6408	167	5	)	)	PUNCT
ejpam-6408	167	6	)	)	PUNCT
ejpam-6408	167	7	.	.	PUNCT
ejpam-6408	168	1	proof	proof	NOUN
ejpam-6408	168	2	.	.	PUNCT
ejpam-6408	169	1	by	by	ADP
ejpam-6408	169	2	a	a	DET
ejpam-6408	169	3	similar	similar	ADJ
ejpam-6408	169	4	manner	manner	NOUN
ejpam-6408	169	5	to	to	ADP
ejpam-6408	169	6	the	the	DET
ejpam-6408	169	7	proof	proof	NOUN
ejpam-6408	169	8	of	of	ADP
ejpam-6408	169	9	theorem	theorem	ADJ
ejpam-6408	169	10	4	4	NUM
ejpam-6408	169	11	.	.	PUNCT
ejpam-6408	169	12	theorem	theorem	NOUN
ejpam-6408	169	13	5	5	NUM
ejpam-6408	169	14	.	.	PUNCT
ejpam-6408	170	1	let	let	VERB
ejpam-6408	170	2	γϵ	γϵ	VERB
ejpam-6408	170	3	:	:	PUNCT
ejpam-6408	170	4	(	(	PUNCT
ejpam-6408	170	5	γ1	γ1	PROPN
ejpam-6408	170	6	,	,	PUNCT
ejpam-6408	170	7	σ1	σ1	PROPN
ejpam-6408	170	8	)	)	PUNCT
ejpam-6408	170	9	→	→	SYM
ejpam-6408	170	10	(	(	PUNCT
ejpam-6408	170	11	γ2	γ2	ADJ
ejpam-6408	170	12	,	,	PUNCT
ejpam-6408	170	13	σ2	σ2	PROPN
ejpam-6408	170	14	)	)	PUNCT
ejpam-6408	170	15	be	be	VERB
ejpam-6408	170	16	a	a	DET
ejpam-6408	170	17	bijective	bijective	ADJ
ejpam-6408	170	18	function	function	NOUN
ejpam-6408	170	19	with	with	ADP
ejpam-6408	170	20	θ1	θ1	NOUN
ejpam-6408	170	21	,	,	PUNCT
ejpam-6408	170	22	θ2	θ2	PROPN
ejpam-6408	170	23	associated	associate	VERB
ejpam-6408	170	24	stss	stss	NOUN
ejpam-6408	170	25	with	with	ADP
ejpam-6408	170	26	σ1	σ1	PROPN
ejpam-6408	170	27	,	,	PUNCT
ejpam-6408	170	28	σ2	σ2	NOUN
ejpam-6408	170	29	respectively	respectively	ADV
ejpam-6408	170	30	,	,	PUNCT
ejpam-6408	170	31	then	then	ADV
ejpam-6408	170	32	γϵ	γϵ	PROPN
ejpam-6408	170	33	is	be	AUX
ejpam-6408	170	34	supra	supra	PROPN
ejpam-6408	170	35	ϵ-open	ϵ-open	PROPN
ejpam-6408	170	36	function	function	PROPN
ejpam-6408	170	37	if	if	SCONJ
ejpam-6408	170	38	and	and	CCONJ
ejpam-6408	170	39	only	only	ADV
ejpam-6408	170	40	if	if	SCONJ
ejpam-6408	170	41	it	it	PRON
ejpam-6408	170	42	is	be	AUX
ejpam-6408	170	43	supra	supra	PROPN
ejpam-6408	170	44	ϵ-closed	ϵ-close	VERB
ejpam-6408	170	45	.	.	PUNCT
ejpam-6408	171	1	m.	m.	NOUN
ejpam-6408	171	2	aldawood	aldawood	PROPN
ejpam-6408	171	3	et	et	PROPN
ejpam-6408	171	4	al	al	PROPN
ejpam-6408	171	5	.	.	PUNCT
ejpam-6408	171	6	/	/	SYM
ejpam-6408	171	7	eur	eur	PROPN
ejpam-6408	171	8	.	.	PUNCT
ejpam-6408	172	1	j.	j.	PROPN
ejpam-6408	172	2	pure	pure	PROPN
ejpam-6408	172	3	appl	appl	PROPN
ejpam-6408	172	4	.	.	PROPN
ejpam-6408	172	5	math	math	PROPN
ejpam-6408	172	6	,	,	PUNCT
ejpam-6408	172	7	18	18	NUM
ejpam-6408	172	8	(	(	PUNCT
ejpam-6408	172	9	3	3	NUM
ejpam-6408	172	10	)	)	PUNCT
ejpam-6408	172	11	(	(	PUNCT
ejpam-6408	172	12	2025	2025	NUM
ejpam-6408	172	13	)	)	PUNCT
ejpam-6408	172	14	,	,	PUNCT
ejpam-6408	172	15	6408	6408	NUM
ejpam-6408	172	16	7	7	NUM
ejpam-6408	172	17	of	of	ADP
ejpam-6408	172	18	16	16	NUM
ejpam-6408	172	19	proof	proof	NOUN
ejpam-6408	172	20	.	.	PUNCT
ejpam-6408	173	1	“	"	PUNCT
ejpam-6408	173	2	⇒	⇒	NOUN
ejpam-6408	173	3	”	"	PUNCT
ejpam-6408	173	4	let	let	VERB
ejpam-6408	173	5	w	w	PROPN
ejpam-6408	173	6	∈	∈	PROPN
ejpam-6408	173	7	θc1	θc1	PROPN
ejpam-6408	173	8	,	,	PUNCT
ejpam-6408	173	9	then	then	ADV
ejpam-6408	173	10	w	w	PROPN
ejpam-6408	173	11	c	c	PROPN
ejpam-6408	173	12	∈	∈	PROPN
ejpam-6408	173	13	θ1	θ1	NOUN
ejpam-6408	173	14	.	.	PUNCT
ejpam-6408	174	1	since	since	SCONJ
ejpam-6408	174	2	γϵ	γϵ	PROPN
ejpam-6408	174	3	is	be	AUX
ejpam-6408	174	4	supra	supra	PROPN
ejpam-6408	174	5	bijective	bijective	ADJ
ejpam-6408	174	6	ϵ-open	ϵ-open	PROPN
ejpam-6408	174	7	function	function	NOUN
ejpam-6408	174	8	,	,	PUNCT
ejpam-6408	174	9	[	[	X
ejpam-6408	174	10	γϵ(w	γϵ(w	X
ejpam-6408	174	11	)	)	PUNCT
ejpam-6408	174	12	]	]	X
ejpam-6408	174	13	c	c	X
ejpam-6408	174	14	=	=	SYM
ejpam-6408	174	15	γϵ(w	γϵ(w	SYM
ejpam-6408	174	16	c	c	X
ejpam-6408	174	17	)	)	PUNCT
ejpam-6408	174	18	∈	∈	PROPN
ejpam-6408	174	19	soϵ(γ1	soϵ(γ1	NOUN
ejpam-6408	174	20	)	)	PUNCT
ejpam-6408	174	21	.	.	PUNCT
ejpam-6408	175	1	this	this	PRON
ejpam-6408	175	2	implies	imply	VERB
ejpam-6408	175	3	that	that	SCONJ
ejpam-6408	175	4	,	,	PUNCT
ejpam-6408	175	5	γϵ(w	γϵ(w	PRON
ejpam-6408	175	6	)	)	PUNCT
ejpam-6408	175	7	∈	∈	PROPN
ejpam-6408	175	8	soϵ(γ2	soϵ(γ2	NOUN
ejpam-6408	175	9	)	)	PUNCT
ejpam-6408	175	10	.	.	PUNCT
ejpam-6408	176	1	thus	thus	ADV
ejpam-6408	176	2	,	,	PUNCT
ejpam-6408	176	3	γϵ	γϵ	PROPN
ejpam-6408	176	4	is	be	AUX
ejpam-6408	176	5	a	a	DET
ejpam-6408	176	6	supra	supra	ADJ
ejpam-6408	176	7	ϵ-closed	ϵ-close	VERB
ejpam-6408	176	8	function	function	NOUN
ejpam-6408	176	9	.	.	PUNCT
ejpam-6408	177	1	“	"	PUNCT
ejpam-6408	177	2	⇐	⇐	INTJ
ejpam-6408	177	3	”	"	PUNCT
ejpam-6408	177	4	it	it	PRON
ejpam-6408	177	5	is	be	AUX
ejpam-6408	177	6	preceded	precede	VERB
ejpam-6408	177	7	by	by	ADP
ejpam-6408	177	8	a	a	DET
ejpam-6408	177	9	similar	similar	ADJ
ejpam-6408	177	10	assertion	assertion	NOUN
ejpam-6408	177	11	.	.	PUNCT
ejpam-6408	178	1	corollary	corollary	ADJ
ejpam-6408	178	2	1	1	NUM
ejpam-6408	178	3	.	.	PUNCT
ejpam-6408	179	1	let	let	VERB
ejpam-6408	179	2	γϵ	γϵ	VERB
ejpam-6408	179	3	:	:	PUNCT
ejpam-6408	179	4	(	(	PUNCT
ejpam-6408	179	5	γ1	γ1	PROPN
ejpam-6408	179	6	,	,	PUNCT
ejpam-6408	179	7	σ1	σ1	PROPN
ejpam-6408	179	8	)	)	PUNCT
ejpam-6408	179	9	→	→	SYM
ejpam-6408	179	10	(	(	PUNCT
ejpam-6408	179	11	γ2	γ2	ADJ
ejpam-6408	179	12	,	,	PUNCT
ejpam-6408	179	13	σ2	σ2	PROPN
ejpam-6408	179	14	)	)	PUNCT
ejpam-6408	179	15	be	be	VERB
ejpam-6408	179	16	a	a	DET
ejpam-6408	179	17	bijective	bijective	ADJ
ejpam-6408	179	18	function	function	NOUN
ejpam-6408	179	19	with	with	ADP
ejpam-6408	179	20	θ1	θ1	NOUN
ejpam-6408	179	21	,	,	PUNCT
ejpam-6408	179	22	θ2	θ2	PROPN
ejpam-6408	179	23	associated	associate	VERB
ejpam-6408	179	24	stss	stss	NOUN
ejpam-6408	179	25	with	with	ADP
ejpam-6408	179	26	σ1	σ1	PROPN
ejpam-6408	179	27	,	,	PUNCT
ejpam-6408	179	28	σ2	σ2	NOUN
ejpam-6408	179	29	respectively	respectively	ADV
ejpam-6408	179	30	,	,	PUNCT
ejpam-6408	179	31	then	then	ADV
ejpam-6408	179	32	γϵ	γϵ	PROPN
ejpam-6408	179	33	is	be	AUX
ejpam-6408	179	34	supra	supra	ADJ
ejpam-6408	179	35	ϵ∗-open	ϵ∗-open	PROPN
ejpam-6408	179	36	function	function	NOUN
ejpam-6408	179	37	if	if	SCONJ
ejpam-6408	179	38	and	and	CCONJ
ejpam-6408	179	39	only	only	ADV
ejpam-6408	179	40	if	if	SCONJ
ejpam-6408	179	41	it	it	PRON
ejpam-6408	179	42	is	be	AUX
ejpam-6408	179	43	supra	supra	NOUN
ejpam-6408	179	44	ϵ∗-closed	ϵ∗-close	VERB
ejpam-6408	179	45	.	.	PUNCT
ejpam-6408	180	1	proof	proof	NOUN
ejpam-6408	180	2	.	.	PUNCT
ejpam-6408	181	1	direct	direct	ADJ
ejpam-6408	181	2	from	from	ADP
ejpam-6408	181	3	theorem	theorem	ADJ
ejpam-6408	181	4	5	5	NUM
ejpam-6408	181	5	.	.	PUNCT
ejpam-6408	181	6	theorem	theorem	NOUN
ejpam-6408	181	7	6	6	NUM
ejpam-6408	181	8	.	.	PUNCT
ejpam-6408	182	1	the	the	DET
ejpam-6408	182	2	image	image	NOUN
ejpam-6408	182	3	of	of	ADP
ejpam-6408	182	4	each	each	DET
ejpam-6408	182	5	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	182	6	1	1	NUM
ejpam-6408	182	7	2	2	NUM
ejpam-6408	182	8	-space	-space	NOUN
ejpam-6408	182	9	is	be	AUX
ejpam-6408	182	10	a	a	DET
ejpam-6408	182	11	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	182	12	1	1	NUM
ejpam-6408	182	13	2	2	NUM
ejpam-6408	182	14	under	under	ADP
ejpam-6408	182	15	a	a	DET
ejpam-6408	182	16	bijective	bijective	ADJ
ejpam-6408	182	17	supra	supra	NOUN
ejpam-6408	182	18	ϵ∗-open	ϵ∗-open	PROPN
ejpam-6408	182	19	function	function	NOUN
ejpam-6408	182	20	.	.	PUNCT
ejpam-6408	183	1	proof	proof	NOUN
ejpam-6408	183	2	.	.	PUNCT
ejpam-6408	184	1	let	let	VERB
ejpam-6408	184	2	γϵ	γϵ	VERB
ejpam-6408	184	3	:	:	PUNCT
ejpam-6408	184	4	(	(	PUNCT
ejpam-6408	184	5	γ1	γ1	PROPN
ejpam-6408	184	6	,	,	PUNCT
ejpam-6408	184	7	σ1	σ1	PROPN
ejpam-6408	184	8	)	)	PUNCT
ejpam-6408	184	9	→	→	SYM
ejpam-6408	184	10	(	(	PUNCT
ejpam-6408	184	11	γ2	γ2	ADJ
ejpam-6408	184	12	,	,	PUNCT
ejpam-6408	184	13	σ2	σ2	PROPN
ejpam-6408	184	14	)	)	PUNCT
ejpam-6408	184	15	with	with	ADP
ejpam-6408	184	16	θ1	θ1	NOUN
ejpam-6408	184	17	,	,	PUNCT
ejpam-6408	184	18	θ2	θ2	PROPN
ejpam-6408	184	19	associated	associate	VERB
ejpam-6408	184	20	stss	stss	NOUN
ejpam-6408	184	21	with	with	ADP
ejpam-6408	184	22	σ1	σ1	PROPN
ejpam-6408	184	23	,	,	PUNCT
ejpam-6408	184	24	σ2	σ2	NOUN
ejpam-6408	184	25	respectively	respectively	ADV
ejpam-6408	184	26	,	,	PUNCT
ejpam-6408	184	27	be	be	AUX
ejpam-6408	184	28	a	a	DET
ejpam-6408	184	29	bijective	bijective	ADJ
ejpam-6408	184	30	supra	supra	NOUN
ejpam-6408	184	31	ϵ∗-open	ϵ∗-open	PROPN
ejpam-6408	184	32	function	function	NOUN
ejpam-6408	184	33	such	such	ADJ
ejpam-6408	184	34	that	that	SCONJ
ejpam-6408	184	35	(	(	PUNCT
ejpam-6408	184	36	γ1	γ1	NOUN
ejpam-6408	184	37	,	,	PUNCT
ejpam-6408	184	38	θ1	θ1	NOUN
ejpam-6408	184	39	)	)	PUNCT
ejpam-6408	184	40	is	be	AUX
ejpam-6408	184	41	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	184	42	1	1	NUM
ejpam-6408	184	43	2	2	NUM
ejpam-6408	184	44	.	.	PUNCT
ejpam-6408	185	1	let	let	VERB
ejpam-6408	185	2	α1	α1	PROPN
ejpam-6408	185	3	̸=	̸=	PROPN
ejpam-6408	185	4	α2	α2	PROPN
ejpam-6408	185	5	∈	∈	PROPN
ejpam-6408	185	6	γ2	γ2	NOUN
ejpam-6408	185	7	.	.	PUNCT
ejpam-6408	186	1	since	since	SCONJ
ejpam-6408	186	2	γϵ	γϵ	PROPN
ejpam-6408	186	3	is	be	AUX
ejpam-6408	186	4	bijective	bijective	ADJ
ejpam-6408	186	5	,	,	PUNCT
ejpam-6408	186	6	there	there	PRON
ejpam-6408	186	7	are	be	VERB
ejpam-6408	186	8	ξ1	ξ1	PROPN
ejpam-6408	186	9	̸=	̸=	PROPN
ejpam-6408	186	10	ξ2	ξ2	PROPN
ejpam-6408	186	11	∈	∈	PROPN
ejpam-6408	186	12	γ1	γ1	NOUN
ejpam-6408	186	13	such	such	ADJ
ejpam-6408	186	14	that	that	SCONJ
ejpam-6408	186	15	γ−1	γ−1	PROPN
ejpam-6408	186	16	ϵ	ϵ	X
ejpam-6408	186	17	(	(	PUNCT
ejpam-6408	186	18	α1	α1	PROPN
ejpam-6408	186	19	)	)	PUNCT
ejpam-6408	186	20	=	=	SYM
ejpam-6408	186	21	ξ1	ξ1	NOUN
ejpam-6408	186	22	and	and	CCONJ
ejpam-6408	186	23	γ−1	γ−1	PROPN
ejpam-6408	186	24	ϵ	ϵ	X
ejpam-6408	186	25	(	(	PUNCT
ejpam-6408	186	26	α2	α2	PROPN
ejpam-6408	186	27	)	)	PUNCT
ejpam-6408	186	28	=	=	SYM
ejpam-6408	186	29	ξ2	ξ2	NOUN
ejpam-6408	186	30	.	.	PUNCT
ejpam-6408	187	1	since	since	SCONJ
ejpam-6408	187	2	(	(	PUNCT
ejpam-6408	187	3	γ1	γ1	PROPN
ejpam-6408	187	4	,	,	PUNCT
ejpam-6408	187	5	σ1	σ1	PROPN
ejpam-6408	187	6	)	)	PUNCT
ejpam-6408	187	7	is	be	AUX
ejpam-6408	187	8	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	187	9	1	1	NUM
ejpam-6408	187	10	2	2	NUM
ejpam-6408	187	11	,	,	PUNCT
ejpam-6408	187	12	there	there	PRON
ejpam-6408	187	13	are	be	VERB
ejpam-6408	187	14	two	two	NUM
ejpam-6408	187	15	disjoint	disjoint	NOUN
ejpam-6408	187	16	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	187	17	subsets	subset	NOUN
ejpam-6408	187	18	ρ1	ρ1	NOUN
ejpam-6408	187	19	and	and	CCONJ
ejpam-6408	187	20	ρ2	ρ2	NOUN
ejpam-6408	187	21	of	of	ADP
ejpam-6408	187	22	γ1	γ1	NOUN
ejpam-6408	187	23	,	,	PUNCT
ejpam-6408	187	24	such	such	ADJ
ejpam-6408	187	25	that	that	SCONJ
ejpam-6408	187	26	ξ1	ξ1	PROPN
ejpam-6408	187	27	∈	∈	PROPN
ejpam-6408	187	28	ρ1	ρ1	NOUN
ejpam-6408	187	29	,	,	PUNCT
ejpam-6408	187	30	ξ2	ξ2	NOUN
ejpam-6408	187	31	∈	∈	PROPN
ejpam-6408	187	32	ρ2	ρ2	PROPN
ejpam-6408	187	33	and	and	CCONJ
ejpam-6408	187	34	clsϵ(ρ1	clsϵ(ρ1	NOUN
ejpam-6408	187	35	)	)	PUNCT
ejpam-6408	187	36	∩	∩	NOUN
ejpam-6408	187	37	clsϵ(ρ2	clsϵ(ρ2	ADJ
ejpam-6408	187	38	)	)	PUNCT
ejpam-6408	187	39	=	=	PUNCT
ejpam-6408	187	40	∅.	∅.	NOUN
ejpam-6408	187	41	since	since	SCONJ
ejpam-6408	187	42	γϵ	γϵ	PROPN
ejpam-6408	187	43	is	be	AUX
ejpam-6408	187	44	supra	supra	PROPN
ejpam-6408	187	45	ϵ∗-open	ϵ∗-open	PROPN
ejpam-6408	187	46	,	,	PUNCT
ejpam-6408	187	47	γϵ(ρ1	γϵ(ρ1	PROPN
ejpam-6408	187	48	)	)	PUNCT
ejpam-6408	187	49	and	and	CCONJ
ejpam-6408	187	50	γϵ(ρ2	γϵ(ρ2	X
ejpam-6408	187	51	)	)	PUNCT
ejpam-6408	187	52	are	be	AUX
ejpam-6408	187	53	two	two	NUM
ejpam-6408	187	54	disjoint	disjoint	ADJ
ejpam-6408	187	55	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	187	56	subsets	subset	NOUN
ejpam-6408	187	57	of	of	ADP
ejpam-6408	187	58	γ2	γ2	NOUN
ejpam-6408	187	59	containing	contain	VERB
ejpam-6408	187	60	α1	α1	PROPN
ejpam-6408	187	61	,	,	PUNCT
ejpam-6408	187	62	α2	α2	ADJ
ejpam-6408	187	63	,	,	PUNCT
ejpam-6408	187	64	respectively	respectively	ADV
ejpam-6408	187	65	,	,	PUNCT
ejpam-6408	187	66	such	such	ADJ
ejpam-6408	187	67	that	that	SCONJ
ejpam-6408	187	68	γϵ(cl	γϵ(cl	PROPN
ejpam-6408	187	69	s	s	PROPN
ejpam-6408	187	70	ϵ(ρ1	ϵ(ρ1	PROPN
ejpam-6408	187	71	)	)	PUNCT
ejpam-6408	187	72	)	)	PUNCT
ejpam-6408	187	73	∩	∩	PROPN
ejpam-6408	187	74	γϵ(cl	γϵ(cl	PROPN
ejpam-6408	187	75	s	s	PART
ejpam-6408	187	76	ϵ(ρ2	ϵ(ρ2	PROPN
ejpam-6408	187	77	)	)	PUNCT
ejpam-6408	187	78	)	)	PUNCT
ejpam-6408	188	1	=	=	PUNCT
ejpam-6408	188	2	∅.	∅.	VERB
ejpam-6408	188	3	given	give	VERB
ejpam-6408	188	4	corollary	corollary	ADJ
ejpam-6408	188	5	1	1	NUM
ejpam-6408	188	6	,	,	PUNCT
ejpam-6408	188	7	γϵ	γϵ	PROPN
ejpam-6408	188	8	is	be	AUX
ejpam-6408	188	9	supra	supra	PROPN
ejpam-6408	188	10	ϵ∗closed	ϵ∗closed	ADJ
ejpam-6408	188	11	.	.	PUNCT
ejpam-6408	189	1	according	accord	VERB
ejpam-6408	189	2	to	to	ADP
ejpam-6408	189	3	proposition	proposition	NOUN
ejpam-6408	189	4	1	1	NUM
ejpam-6408	189	5	,	,	PUNCT
ejpam-6408	189	6	clsϵ	clsϵ	NOUN
ejpam-6408	189	7	[	[	X
ejpam-6408	189	8	γϵ(ρ1	γϵ(ρ1	NOUN
ejpam-6408	189	9	)	)	PUNCT
ejpam-6408	189	10	]	]	PUNCT
ejpam-6408	190	1	⊆	⊆	NUM
ejpam-6408	190	2	γϵ(cl	γϵ(cl	PROPN
ejpam-6408	190	3	s	s	PART
ejpam-6408	190	4	ϵ(ρ1	ϵ(ρ1	PROPN
ejpam-6408	190	5	)	)	PUNCT
ejpam-6408	190	6	)	)	PUNCT
ejpam-6408	190	7	and	and	CCONJ
ejpam-6408	190	8	clsϵ	clsϵ	NOUN
ejpam-6408	190	9	[	[	X
ejpam-6408	190	10	γϵ(ρ2	γϵ(ρ2	X
ejpam-6408	190	11	)	)	PUNCT
ejpam-6408	190	12	]	]	PUNCT
ejpam-6408	190	13	⊆	⊆	NUM
ejpam-6408	190	14	γϵ(cl	γϵ(cl	PROPN
ejpam-6408	190	15	s	s	PART
ejpam-6408	190	16	ϵ(ρ2	ϵ(ρ2	PROPN
ejpam-6408	190	17	)	)	PUNCT
ejpam-6408	190	18	)	)	PUNCT
ejpam-6408	190	19	and	and	CCONJ
ejpam-6408	190	20	consequently	consequently	ADV
ejpam-6408	190	21	clsϵ(γϵ(ρ1	clsϵ(γϵ(ρ1	NOUN
ejpam-6408	190	22	)	)	PUNCT
ejpam-6408	190	23	)	)	PUNCT
ejpam-6408	190	24	∩	∩	NOUN
ejpam-6408	190	25	clsϵ(γϵ(ρ2	clsϵ(γϵ(ρ2	NOUN
ejpam-6408	190	26	)	)	PUNCT
ejpam-6408	190	27	)	)	PUNCT
ejpam-6408	191	1	=	=	PUNCT
ejpam-6408	191	2	∅.	∅.	VERB
ejpam-6408	191	3	therefore	therefore	ADV
ejpam-6408	191	4	,	,	PUNCT
ejpam-6408	191	5	(	(	PUNCT
ejpam-6408	191	6	γ2	γ2	PROPN
ejpam-6408	191	7	,	,	PUNCT
ejpam-6408	191	8	θ2	θ2	PROPN
ejpam-6408	191	9	)	)	PUNCT
ejpam-6408	191	10	is	be	AUX
ejpam-6408	191	11	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	191	12	1	1	NUM
ejpam-6408	191	13	2	2	NUM
ejpam-6408	191	14	.	.	PUNCT
ejpam-6408	192	1	the	the	DET
ejpam-6408	192	2	proof	proof	NOUN
ejpam-6408	192	3	of	of	ADP
ejpam-6408	192	4	the	the	DET
ejpam-6408	192	5	following	follow	VERB
ejpam-6408	192	6	corollary	corollary	NOUN
ejpam-6408	192	7	is	be	AUX
ejpam-6408	192	8	obvious	obvious	ADJ
ejpam-6408	192	9	from	from	ADP
ejpam-6408	192	10	theorem	theorem	ADJ
ejpam-6408	192	11	6	6	NUM
ejpam-6408	192	12	.	.	PUNCT
ejpam-6408	192	13	corollary	corollary	ADJ
ejpam-6408	192	14	2	2	NUM
ejpam-6408	192	15	.	.	PUNCT
ejpam-6408	193	1	the	the	DET
ejpam-6408	193	2	property	property	NOUN
ejpam-6408	193	3	of	of	ADP
ejpam-6408	193	4	being	be	AUX
ejpam-6408	193	5	a	a	DET
ejpam-6408	193	6	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	193	7	1	1	NUM
ejpam-6408	193	8	2	2	NUM
ejpam-6408	193	9	-space	-space	NOUN
ejpam-6408	193	10	is	be	AUX
ejpam-6408	193	11	a	a	DET
ejpam-6408	193	12	supra	supra	ADJ
ejpam-6408	193	13	hereditary	hereditary	ADJ
ejpam-6408	193	14	property	property	NOUN
ejpam-6408	193	15	.	.	PUNCT
ejpam-6408	194	1	proposition	proposition	NOUN
ejpam-6408	194	2	2	2	NUM
ejpam-6408	194	3	.	.	PUNCT
ejpam-6408	195	1	let	let	VERB
ejpam-6408	195	2	(	(	PUNCT
ejpam-6408	195	3	u	u	NOUN
ejpam-6408	195	4	,	,	PUNCT
ejpam-6408	195	5	ϑu	ϑu	NOUN
ejpam-6408	195	6	)	)	PUNCT
ejpam-6408	195	7	be	be	AUX
ejpam-6408	195	8	an	an	DET
ejpam-6408	195	9	supra	supra	ADJ
ejpam-6408	195	10	ϵ-subspace	ϵ-subspace	NOUN
ejpam-6408	195	11	of	of	ADP
ejpam-6408	195	12	an	an	DET
ejpam-6408	195	13	sts	st	NOUN
ejpam-6408	195	14	(	(	PUNCT
ejpam-6408	195	15	γ	γ	X
ejpam-6408	195	16	,	,	PUNCT
ejpam-6408	195	17	ϑ	ϑ	NOUN
ejpam-6408	195	18	)	)	PUNCT
ejpam-6408	195	19	and	and	CCONJ
ejpam-6408	195	20	v	v	AUX
ejpam-6408	195	21	be	be	AUX
ejpam-6408	195	22	a	a	DET
ejpam-6408	195	23	subset	subset	NOUN
ejpam-6408	195	24	of	of	ADP
ejpam-6408	195	25	γ	γ	PROPN
ejpam-6408	195	26	.	.	PROPN
ejpam-6408	196	1	then	then	ADV
ejpam-6408	196	2	,	,	PUNCT
ejpam-6408	196	3	(	(	PUNCT
ejpam-6408	196	4	clϵ(v	clϵ(v	NOUN
ejpam-6408	196	5	)	)	PUNCT
ejpam-6408	196	6	)	)	PUNCT
ejpam-6408	196	7	ϑu	ϑu	NOUN
ejpam-6408	196	8	=	=	SYM
ejpam-6408	196	9	u	u	NOUN
ejpam-6408	196	10	∩	∩	ADJ
ejpam-6408	196	11	clϵ(v	clϵ(v	NOUN
ejpam-6408	196	12	)	)	PUNCT
ejpam-6408	196	13	theorem	theorem	VERB
ejpam-6408	196	14	7	7	NUM
ejpam-6408	196	15	.	.	PUNCT
ejpam-6408	197	1	every	every	DET
ejpam-6408	197	2	supra	supra	PROPN
ejpam-6408	197	3	subspace	subspace	NOUN
ejpam-6408	197	4	of	of	ADP
ejpam-6408	197	5	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	197	6	1	1	NUM
ejpam-6408	197	7	2	2	NUM
ejpam-6408	197	8	-space	-space	NOUN
ejpam-6408	197	9	is	be	AUX
ejpam-6408	197	10	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	197	11	1	1	NUM
ejpam-6408	197	12	2	2	NUM
ejpam-6408	197	13	.	.	PUNCT
ejpam-6408	198	1	proof	proof	NOUN
ejpam-6408	198	2	.	.	PUNCT
ejpam-6408	199	1	suppose	suppose	VERB
ejpam-6408	199	2	that	that	SCONJ
ejpam-6408	199	3	(	(	PUNCT
ejpam-6408	199	4	χ	χ	X
ejpam-6408	199	5	,	,	PUNCT
ejpam-6408	199	6	θχ	θχ	NOUN
ejpam-6408	199	7	)	)	PUNCT
ejpam-6408	199	8	is	be	AUX
ejpam-6408	199	9	a	a	DET
ejpam-6408	199	10	supra	supra	ADJ
ejpam-6408	199	11	subspace	subspace	NOUN
ejpam-6408	199	12	of	of	ADP
ejpam-6408	199	13	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	199	14	1	1	NUM
ejpam-6408	199	15	2	2	NUM
ejpam-6408	199	16	-space	-space	NOUN
ejpam-6408	199	17	(	(	PUNCT
ejpam-6408	199	18	γ	γ	X
ejpam-6408	199	19	,	,	PUNCT
ejpam-6408	199	20	θ	θ	NOUN
ejpam-6408	199	21	)	)	PUNCT
ejpam-6408	199	22	and	and	CCONJ
ejpam-6408	199	23	ϑ1	ϑ1	PROPN
ejpam-6408	199	24	̸=	̸=	PROPN
ejpam-6408	199	25	ϑ2	ϑ2	PROPN
ejpam-6408	199	26	∈	∈	PROPN
ejpam-6408	199	27	χ	χ	ADP
ejpam-6408	199	28	⊆	⊆	NUM
ejpam-6408	199	29	γ	γ	X
ejpam-6408	199	30	.	.	PUNCT
ejpam-6408	199	31	given	give	VERB
ejpam-6408	199	32	γ	γ	PROPN
ejpam-6408	199	33	is	be	AUX
ejpam-6408	199	34	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	199	35	1	1	NUM
ejpam-6408	199	36	2	2	NUM
ejpam-6408	199	37	,	,	PUNCT
ejpam-6408	199	38	then	then	ADV
ejpam-6408	199	39	there	there	PRON
ejpam-6408	199	40	are	be	VERB
ejpam-6408	199	41	two	two	NUM
ejpam-6408	199	42	disjoint	disjoint	ADJ
ejpam-6408	199	43	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	199	44	subsets	subset	NOUN
ejpam-6408	199	45	ν1	ν1	NOUN
ejpam-6408	199	46	and	and	CCONJ
ejpam-6408	199	47	ν2	ν2	NOUN
ejpam-6408	199	48	of	of	ADP
ejpam-6408	199	49	γ	γ	NOUN
ejpam-6408	199	50	,	,	PUNCT
ejpam-6408	199	51	such	such	ADJ
ejpam-6408	199	52	that	that	DET
ejpam-6408	199	53	ϑ1	ϑ1	PROPN
ejpam-6408	199	54	∈	∈	PROPN
ejpam-6408	199	55	ν1	ν1	NOUN
ejpam-6408	199	56	and	and	CCONJ
ejpam-6408	199	57	ϑ2	ϑ2	PROPN
ejpam-6408	199	58	∈	∈	PROPN
ejpam-6408	199	59	ν2	ν2	NOUN
ejpam-6408	199	60	and	and	CCONJ
ejpam-6408	199	61	clsϵ(ν1)∩	clsϵ(ν1)∩	NOUN
ejpam-6408	199	62	clsϵ(ν2	clsϵ(ν2	NOUN
ejpam-6408	199	63	)	)	PUNCT
ejpam-6408	200	1	=	=	PUNCT
ejpam-6408	200	2	∅.	∅.	VERB
ejpam-6408	200	3	given	give	VERB
ejpam-6408	200	4	proposition	proposition	NOUN
ejpam-6408	200	5	2	2	NUM
ejpam-6408	200	6	,	,	PUNCT
ejpam-6408	200	7	(	(	PUNCT
ejpam-6408	200	8	clϵ(s))θχ	clϵ(s))θχ	X
ejpam-6408	200	9	=	=	SYM
ejpam-6408	200	10	χ	χ	NOUN
ejpam-6408	200	11	∩	∩	NOUN
ejpam-6408	200	12	(	(	PUNCT
ejpam-6408	200	13	clϵ(s	clϵ(s	NOUN
ejpam-6408	200	14	)	)	PUNCT
ejpam-6408	200	15	)	)	PUNCT
ejpam-6408	200	16	=	=	SYM
ejpam-6408	201	1	χ	χ	PRON
ejpam-6408	201	2	∩	∩	NOUN
ejpam-6408	201	3	(	(	PUNCT
ejpam-6408	201	4	clϵ(ν1	clϵ(ν1	PROPN
ejpam-6408	201	5	∩	∩	ADJ
ejpam-6408	201	6	χ	χ	X
ejpam-6408	201	7	)	)	PUNCT
ejpam-6408	201	8	)	)	PUNCT
ejpam-6408	202	1	⊆	⊆	NUM
ejpam-6408	202	2	χ	χ	DET
ejpam-6408	202	3	∩	∩	NOUN
ejpam-6408	202	4	clsϵ(ν1	clsϵ(ν1	NOUN
ejpam-6408	202	5	)	)	PUNCT
ejpam-6408	202	6	and	and	CCONJ
ejpam-6408	202	7	(	(	PUNCT
ejpam-6408	202	8	clϵ(t	clϵ(t	PROPN
ejpam-6408	202	9	)	)	PUNCT
ejpam-6408	202	10	)	)	PUNCT
ejpam-6408	202	11	θχ	θχ	NOUN
ejpam-6408	202	12	=	=	SYM
ejpam-6408	202	13	χ	χ	NOUN
ejpam-6408	202	14	∩	∩	NOUN
ejpam-6408	202	15	(	(	PUNCT
ejpam-6408	202	16	clϵ(t	clϵ(t	NOUN
ejpam-6408	202	17	)	)	PUNCT
ejpam-6408	202	18	)	)	PUNCT
ejpam-6408	203	1	=	=	SYM
ejpam-6408	204	1	χ	χ	PRON
ejpam-6408	204	2	∩	∩	NOUN
ejpam-6408	204	3	(	(	PUNCT
ejpam-6408	204	4	clϵ(ν1	clϵ(ν1	PROPN
ejpam-6408	204	5	∩	∩	ADJ
ejpam-6408	204	6	χ	χ	X
ejpam-6408	204	7	)	)	PUNCT
ejpam-6408	204	8	)	)	PUNCT
ejpam-6408	205	1	⊆	⊆	NUM
ejpam-6408	205	2	χ	χ	DET
ejpam-6408	205	3	∩	∩	ADJ
ejpam-6408	205	4	clsϵ(ν2	clsϵ(ν2	NOUN
ejpam-6408	205	5	)	)	PUNCT
ejpam-6408	205	6	.	.	PUNCT
ejpam-6408	206	1	hence	hence	ADV
ejpam-6408	206	2	,	,	PUNCT
ejpam-6408	206	3	ϑ1	ϑ1	PROPN
ejpam-6408	206	4	∈	∈	PROPN
ejpam-6408	206	5	s	s	PART
ejpam-6408	206	6	=	=	NOUN
ejpam-6408	206	7	ν1	ν1	NOUN
ejpam-6408	206	8	∩	∩	X
ejpam-6408	206	9	χ	χ	NOUN
ejpam-6408	206	10	and	and	CCONJ
ejpam-6408	206	11	ϑ2	ϑ2	PROPN
ejpam-6408	206	12	∈	∈	PROPN
ejpam-6408	206	13	t	t	NOUN
ejpam-6408	206	14	=	=	SYM
ejpam-6408	206	15	ν2	ν2	PROPN
ejpam-6408	206	16	∩	∩	NOUN
ejpam-6408	206	17	χ	χ	PRON
ejpam-6408	206	18	such	such	ADJ
ejpam-6408	206	19	that	that	SCONJ
ejpam-6408	206	20	(	(	PUNCT
ejpam-6408	206	21	clϵ(s))θχ	clϵ(s))θχ	NOUN
ejpam-6408	206	22	∩	∩	NOUN
ejpam-6408	206	23	(	(	PUNCT
ejpam-6408	206	24	clϵ(t	clϵ(t	PROPN
ejpam-6408	206	25	)	)	PUNCT
ejpam-6408	206	26	)	)	PUNCT
ejpam-6408	206	27	θχ	θχ	NOUN
ejpam-6408	206	28	=	=	PUNCT
ejpam-6408	206	29	∅.	∅.	VERB
ejpam-6408	206	30	therefore	therefore	ADV
ejpam-6408	206	31	,	,	PUNCT
ejpam-6408	206	32	χ	χ	X
ejpam-6408	206	33	is	be	AUX
ejpam-6408	206	34	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	206	35	1	1	NUM
ejpam-6408	206	36	2	2	NUM
ejpam-6408	206	37	-space	-space	NOUN
ejpam-6408	206	38	.	.	PUNCT
ejpam-6408	207	1	m.	m.	NOUN
ejpam-6408	207	2	aldawood	aldawood	PROPN
ejpam-6408	207	3	et	et	PROPN
ejpam-6408	207	4	al	al	PROPN
ejpam-6408	207	5	.	.	PUNCT
ejpam-6408	207	6	/	/	SYM
ejpam-6408	207	7	eur	eur	PROPN
ejpam-6408	207	8	.	.	PUNCT
ejpam-6408	208	1	j.	j.	PROPN
ejpam-6408	208	2	pure	pure	PROPN
ejpam-6408	208	3	appl	appl	PROPN
ejpam-6408	208	4	.	.	PROPN
ejpam-6408	208	5	math	math	PROPN
ejpam-6408	208	6	,	,	PUNCT
ejpam-6408	208	7	18	18	NUM
ejpam-6408	208	8	(	(	PUNCT
ejpam-6408	208	9	3	3	NUM
ejpam-6408	208	10	)	)	PUNCT
ejpam-6408	208	11	(	(	PUNCT
ejpam-6408	208	12	2025	2025	NUM
ejpam-6408	208	13	)	)	PUNCT
ejpam-6408	208	14	,	,	PUNCT
ejpam-6408	208	15	6408	6408	NUM
ejpam-6408	208	16	8	8	NUM
ejpam-6408	208	17	of	of	ADP
ejpam-6408	208	18	16	16	NUM
ejpam-6408	208	19	4	4	NUM
ejpam-6408	208	20	.	.	PUNCT
ejpam-6408	208	21	supra	supra	PROPN
ejpam-6408	208	22	ϵ-regularity	ϵ-regularity	PROPN
ejpam-6408	208	23	and	and	CCONJ
ejpam-6408	208	24	supra	supra	PROPN
ejpam-6408	208	25	ϵ-normality	ϵ-normality	NOUN
ejpam-6408	208	26	in	in	ADP
ejpam-6408	208	27	this	this	DET
ejpam-6408	208	28	section	section	NOUN
ejpam-6408	208	29	,	,	PUNCT
ejpam-6408	208	30	we	we	PRON
ejpam-6408	208	31	introduce	introduce	VERB
ejpam-6408	208	32	four	four	NUM
ejpam-6408	208	33	new	new	ADJ
ejpam-6408	208	34	kinds	kind	NOUN
ejpam-6408	208	35	of	of	ADP
ejpam-6408	208	36	separation	separation	NOUN
ejpam-6408	208	37	axioms	axiom	NOUN
ejpam-6408	208	38	based	base	VERB
ejpam-6408	208	39	on	on	ADP
ejpam-6408	208	40	supra	supra	PROPN
ejpam-6408	208	41	ϵ-open	ϵ-open	PROPN
ejpam-6408	208	42	sets	set	NOUN
ejpam-6408	208	43	named	name	VERB
ejpam-6408	208	44	supra-ϵ-regular	supra-ϵ-regular	NOUN
ejpam-6408	208	45	-	-	PUNCT
ejpam-6408	208	46	space	space	NOUN
ejpam-6408	208	47	,	,	PUNCT
ejpam-6408	208	48	supra-ϵ-normal	supra-ϵ-normal	ADJ
ejpam-6408	208	49	-	-	NOUN
ejpam-6408	208	50	space	space	NOUN
ejpam-6408	208	51	,	,	PUNCT
ejpam-6408	208	52	supra-ϵ-t3	supra-ϵ-t3	NOUN
ejpam-6408	208	53	-	-	PUNCT
ejpam-6408	208	54	space	space	NOUN
ejpam-6408	208	55	,	,	PUNCT
ejpam-6408	208	56	and	and	CCONJ
ejpam-6408	208	57	supra-ϵ-t4space	supra-ϵ-t4space	NOUN
ejpam-6408	208	58	.	.	PUNCT
ejpam-6408	209	1	we	we	PRON
ejpam-6408	209	2	provide	provide	VERB
ejpam-6408	209	3	thorough	thorough	ADJ
ejpam-6408	209	4	descriptions	description	NOUN
ejpam-6408	209	5	of	of	ADP
ejpam-6408	209	6	each	each	PRON
ejpam-6408	209	7	of	of	ADP
ejpam-6408	209	8	them	they	PRON
ejpam-6408	209	9	.	.	PUNCT
ejpam-6408	210	1	in	in	ADP
ejpam-6408	210	2	particular	particular	ADJ
ejpam-6408	210	3	,	,	PUNCT
ejpam-6408	210	4	we	we	PRON
ejpam-6408	210	5	examine	examine	VERB
ejpam-6408	210	6	necessary	necessary	ADJ
ejpam-6408	210	7	conditions	condition	NOUN
ejpam-6408	210	8	for	for	ADP
ejpam-6408	210	9	several	several	ADJ
ejpam-6408	210	10	comparable	comparable	ADJ
ejpam-6408	210	11	connections	connection	NOUN
ejpam-6408	210	12	between	between	ADP
ejpam-6408	210	13	them	they	PRON
ejpam-6408	210	14	and	and	CCONJ
ejpam-6408	210	15	provide	provide	VERB
ejpam-6408	210	16	a	a	DET
ejpam-6408	210	17	general	general	ADJ
ejpam-6408	210	18	illustration	illustration	NOUN
ejpam-6408	210	19	of	of	ADP
ejpam-6408	210	20	their	their	PRON
ejpam-6408	210	21	salient	salient	NOUN
ejpam-6408	210	22	features	feature	NOUN
ejpam-6408	210	23	.	.	PUNCT
ejpam-6408	211	1	we	we	PRON
ejpam-6408	211	2	also	also	ADV
ejpam-6408	211	3	suggest	suggest	VERB
ejpam-6408	211	4	a	a	DET
ejpam-6408	211	5	diagram	diagram	NOUN
ejpam-6408	211	6	that	that	PRON
ejpam-6408	211	7	outlines	outline	VERB
ejpam-6408	211	8	these	these	DET
ejpam-6408	211	9	relationships	relationship	NOUN
ejpam-6408	211	10	[	[	X
ejpam-6408	211	11	see	see	VERB
ejpam-6408	211	12	figure	figure	NOUN
ejpam-6408	211	13	1	1	NUM
ejpam-6408	211	14	]	]	PUNCT
ejpam-6408	211	15	.	.	PUNCT
ejpam-6408	212	1	moreover	moreover	ADV
ejpam-6408	212	2	,	,	PUNCT
ejpam-6408	212	3	we	we	PRON
ejpam-6408	212	4	show	show	VERB
ejpam-6408	212	5	prove	prove	VERB
ejpam-6408	212	6	that	that	SCONJ
ejpam-6408	212	7	every	every	DET
ejpam-6408	212	8	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	212	9	-	-	NOUN
ejpam-6408	212	10	space	space	NOUN
ejpam-6408	212	11	(	(	PUNCT
ejpam-6408	212	12	γ	γ	X
ejpam-6408	212	13	,	,	PUNCT
ejpam-6408	212	14	θ	θ	NOUN
ejpam-6408	212	15	)	)	PUNCT
ejpam-6408	212	16	is	be	AUX
ejpam-6408	212	17	supra-ϵ-n	supra-ϵ-n	ADJ
ejpam-6408	212	18	-space	-space	NOUN
ejpam-6408	212	19	,	,	PUNCT
ejpam-6408	212	20	if	if	SCONJ
ejpam-6408	212	21	|γ|	|γ|	PROPN
ejpam-6408	212	22	⩽	⩽	NOUN
ejpam-6408	212	23	4	4	NUM
ejpam-6408	212	24	,	,	PUNCT
ejpam-6408	212	25	which	which	PRON
ejpam-6408	212	26	implies	imply	VERB
ejpam-6408	212	27	that	that	SCONJ
ejpam-6408	212	28	the	the	DET
ejpam-6408	212	29	two	two	NUM
ejpam-6408	212	30	approaches	approach	NOUN
ejpam-6408	212	31	of	of	ADP
ejpam-6408	212	32	supra-ϵ-t3	supra-ϵ-t3	NOUN
ejpam-6408	212	33	-	-	PUNCT
ejpam-6408	212	34	space	space	NOUN
ejpam-6408	212	35	and	and	CCONJ
ejpam-6408	212	36	supra-ϵ-t4	supra-ϵ-t4	PROPN
ejpam-6408	212	37	-	-	PUNCT
ejpam-6408	212	38	space	space	NOUN
ejpam-6408	212	39	are	be	AUX
ejpam-6408	212	40	identical	identical	ADJ
ejpam-6408	212	41	.	.	PUNCT
ejpam-6408	213	1	finally	finally	ADV
ejpam-6408	213	2	,	,	PUNCT
ejpam-6408	213	3	we	we	PRON
ejpam-6408	213	4	provide	provide	VERB
ejpam-6408	213	5	the	the	DET
ejpam-6408	213	6	required	require	VERB
ejpam-6408	213	7	counterexamples	counterexample	NOUN
ejpam-6408	213	8	which	which	PRON
ejpam-6408	213	9	confirm	confirm	VERB
ejpam-6408	213	10	our	our	PRON
ejpam-6408	213	11	study	study	NOUN
ejpam-6408	213	12	.	.	PUNCT
ejpam-6408	214	1	definition	definition	NOUN
ejpam-6408	214	2	13	13	NUM
ejpam-6408	214	3	.	.	PUNCT
ejpam-6408	215	1	an	an	DET
ejpam-6408	215	2	sts	st	NOUN
ejpam-6408	215	3	(	(	PUNCT
ejpam-6408	215	4	γ	γ	X
ejpam-6408	215	5	,	,	PUNCT
ejpam-6408	215	6	θ	θ	NOUN
ejpam-6408	215	7	)	)	PUNCT
ejpam-6408	215	8	is	be	AUX
ejpam-6408	215	9	said	say	VERB
ejpam-6408	215	10	to	to	PART
ejpam-6408	215	11	be	be	AUX
ejpam-6408	215	12	(	(	PUNCT
ejpam-6408	215	13	1	1	X
ejpam-6408	215	14	)	)	PUNCT
ejpam-6408	215	15	supra-ϵ-regular	supra-ϵ-regular	NOUN
ejpam-6408	215	16	-	-	PUNCT
ejpam-6408	215	17	space	space	NOUN
ejpam-6408	215	18	(	(	PUNCT
ejpam-6408	215	19	or	or	CCONJ
ejpam-6408	215	20	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	215	21	-	-	NOUN
ejpam-6408	215	22	space	space	NOUN
ejpam-6408	215	23	)	)	PUNCT
ejpam-6408	215	24	if	if	SCONJ
ejpam-6408	215	25	for	for	ADP
ejpam-6408	215	26	each	each	DET
ejpam-6408	215	27	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	215	28	set	set	VERB
ejpam-6408	215	29	h	h	NOUN
ejpam-6408	215	30	with	with	ADP
ejpam-6408	215	31	ϑ	ϑ	X
ejpam-6408	215	32	̸∈	̸∈	PROPN
ejpam-6408	215	33	h	h	NOUN
ejpam-6408	215	34	,	,	PUNCT
ejpam-6408	215	35	there	there	PRON
ejpam-6408	215	36	are	be	VERB
ejpam-6408	215	37	two	two	NUM
ejpam-6408	215	38	disjoint	disjoint	ADJ
ejpam-6408	215	39	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	215	40	subsets	subset	NOUN
ejpam-6408	215	41	ν1	ν1	NOUN
ejpam-6408	215	42	and	and	CCONJ
ejpam-6408	215	43	ν2	ν2	NOUN
ejpam-6408	215	44	of	of	ADP
ejpam-6408	215	45	γ	γ	NOUN
ejpam-6408	215	46	,	,	PUNCT
ejpam-6408	215	47	such	such	ADJ
ejpam-6408	215	48	that	that	SCONJ
ejpam-6408	215	49	ϑ	ϑ	PROPN
ejpam-6408	215	50	∈	∈	PROPN
ejpam-6408	215	51	ν1	ν1	NOUN
ejpam-6408	215	52	and	and	CCONJ
ejpam-6408	215	53	h	h	NOUN
ejpam-6408	215	54	⊆	⊆	NUM
ejpam-6408	215	55	ν2	ν2	NOUN
ejpam-6408	215	56	.	.	PUNCT
ejpam-6408	216	1	(	(	PUNCT
ejpam-6408	216	2	2	2	X
ejpam-6408	216	3	)	)	PUNCT
ejpam-6408	216	4	supra-ϵ-normal	supra-ϵ-normal	ADJ
ejpam-6408	216	5	-	-	PUNCT
ejpam-6408	216	6	space	space	NOUN
ejpam-6408	216	7	(	(	PUNCT
ejpam-6408	216	8	or	or	CCONJ
ejpam-6408	216	9	supra-ϵ-n	supra-ϵ-n	ADJ
ejpam-6408	216	10	-space	-space	NOUN
ejpam-6408	216	11	)	)	PUNCT
ejpam-6408	216	12	if	if	SCONJ
ejpam-6408	216	13	for	for	ADP
ejpam-6408	216	14	each	each	DET
ejpam-6408	216	15	two	two	NUM
ejpam-6408	216	16	disjoint	disjoint	NOUN
ejpam-6408	216	17	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	216	18	sets	set	NOUN
ejpam-6408	216	19	h	h	NOUN
ejpam-6408	216	20	,	,	PUNCT
ejpam-6408	216	21	k	k	NOUN
ejpam-6408	216	22	,	,	PUNCT
ejpam-6408	216	23	there	there	PRON
ejpam-6408	216	24	are	be	VERB
ejpam-6408	216	25	two	two	NUM
ejpam-6408	216	26	disjoint	disjoint	ADJ
ejpam-6408	216	27	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	216	28	subsets	subset	NOUN
ejpam-6408	216	29	ν1	ν1	NOUN
ejpam-6408	216	30	and	and	CCONJ
ejpam-6408	216	31	ν2	ν2	NOUN
ejpam-6408	216	32	of	of	ADP
ejpam-6408	216	33	γ	γ	NOUN
ejpam-6408	216	34	,	,	PUNCT
ejpam-6408	216	35	such	such	ADJ
ejpam-6408	216	36	that	that	SCONJ
ejpam-6408	216	37	h	h	NOUN
ejpam-6408	216	38	⊆	⊆	NUM
ejpam-6408	216	39	ν1	ν1	NOUN
ejpam-6408	216	40	and	and	CCONJ
ejpam-6408	216	41	k	k	NOUN
ejpam-6408	216	42	⊆	⊆	NUM
ejpam-6408	216	43	ν2	ν2	NOUN
ejpam-6408	216	44	.	.	PUNCT
ejpam-6408	217	1	(	(	PUNCT
ejpam-6408	217	2	3	3	X
ejpam-6408	217	3	)	)	PUNCT
ejpam-6408	217	4	supra-ϵ-t3	supra-ϵ-t3	NOUN
ejpam-6408	217	5	-	-	PUNCT
ejpam-6408	217	6	space	space	NOUN
ejpam-6408	217	7	,	,	PUNCT
ejpam-6408	217	8	if	if	SCONJ
ejpam-6408	217	9	it	it	PRON
ejpam-6408	217	10	is	be	AUX
ejpam-6408	217	11	both	both	PRON
ejpam-6408	217	12	supra-ϵ-r	supra-ϵ-r	ADJ
ejpam-6408	217	13	-	-	NOUN
ejpam-6408	217	14	space	space	NOUN
ejpam-6408	217	15	and	and	CCONJ
ejpam-6408	217	16	supra-ϵ-t1	supra-ϵ-t1	PROPN
ejpam-6408	217	17	.	.	PUNCT
ejpam-6408	218	1	(	(	PUNCT
ejpam-6408	218	2	4	4	X
ejpam-6408	218	3	)	)	PUNCT
ejpam-6408	218	4	supra-ϵ-t4	supra-ϵ-t4	NOUN
ejpam-6408	218	5	-	-	PUNCT
ejpam-6408	218	6	space	space	NOUN
ejpam-6408	218	7	,	,	PUNCT
ejpam-6408	218	8	if	if	SCONJ
ejpam-6408	218	9	it	it	PRON
ejpam-6408	218	10	is	be	AUX
ejpam-6408	218	11	both	both	DET
ejpam-6408	218	12	supra-ϵ-n	supra-ϵ-n	ADJ
ejpam-6408	218	13	-	-	PUNCT
ejpam-6408	218	14	space	space	NOUN
ejpam-6408	218	15	and	and	CCONJ
ejpam-6408	218	16	supra-ϵ-t1	supra-ϵ-t1	PROPN
ejpam-6408	218	17	.	.	PUNCT
ejpam-6408	219	1	theorem	theorem	VERB
ejpam-6408	219	2	8	8	NUM
ejpam-6408	219	3	.	.	PUNCT
ejpam-6408	220	1	the	the	DET
ejpam-6408	220	2	following	follow	VERB
ejpam-6408	220	3	are	be	AUX
ejpam-6408	220	4	equivalent	equivalent	ADJ
ejpam-6408	220	5	for	for	ADP
ejpam-6408	220	6	any	any	DET
ejpam-6408	220	7	sts	st	NOUN
ejpam-6408	220	8	(	(	PUNCT
ejpam-6408	220	9	γ	γ	X
ejpam-6408	220	10	,	,	PUNCT
ejpam-6408	220	11	θ	θ	PROPN
ejpam-6408	220	12	):	):	PUNCT
ejpam-6408	220	13	(	(	PUNCT
ejpam-6408	220	14	1	1	X
ejpam-6408	220	15	)	)	PUNCT
ejpam-6408	220	16	γ	γ	X
ejpam-6408	220	17	is	be	AUX
ejpam-6408	220	18	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	220	19	-	-	NOUN
ejpam-6408	220	20	space	space	NOUN
ejpam-6408	220	21	;	;	PUNCT
ejpam-6408	220	22	(	(	PUNCT
ejpam-6408	220	23	2	2	X
ejpam-6408	220	24	)	)	PUNCT
ejpam-6408	220	25	for	for	SCONJ
ejpam-6408	220	26	every	every	DET
ejpam-6408	220	27	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	220	28	subset	subset	VERB
ejpam-6408	220	29	ν	ν	NOUN
ejpam-6408	220	30	of	of	ADP
ejpam-6408	220	31	γ	γ	PROPN
ejpam-6408	220	32	continuing	continue	VERB
ejpam-6408	220	33	ϑ	ϑ	NOUN
ejpam-6408	220	34	,	,	PUNCT
ejpam-6408	220	35	there	there	PRON
ejpam-6408	220	36	is	be	VERB
ejpam-6408	220	37	a	a	DET
ejpam-6408	220	38	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	220	39	subset	subset	VERB
ejpam-6408	220	40	η	η	PROPN
ejpam-6408	220	41	of	of	ADP
ejpam-6408	220	42	γ	γ	PROPN
ejpam-6408	220	43	,	,	PUNCT
ejpam-6408	220	44	such	such	ADJ
ejpam-6408	220	45	that	that	SCONJ
ejpam-6408	220	46	ϑ	ϑ	PROPN
ejpam-6408	220	47	∈	∈	PROPN
ejpam-6408	220	48	η	η	PROPN
ejpam-6408	220	49	⊆	⊆	NUM
ejpam-6408	220	50	clϵ(η	clϵ(η	PROPN
ejpam-6408	220	51	)	)	PUNCT
ejpam-6408	220	52	⊆	⊆	NUM
ejpam-6408	220	53	ν	ν	NOUN
ejpam-6408	220	54	;	;	PUNCT
ejpam-6408	220	55	(	(	PUNCT
ejpam-6408	220	56	3	3	X
ejpam-6408	220	57	)	)	PUNCT
ejpam-6408	220	58	for	for	ADP
ejpam-6408	220	59	every	every	DET
ejpam-6408	220	60	ν	ν	X
ejpam-6408	220	61	∈	∈	PROPN
ejpam-6408	220	62	soϵ(γ	soϵ(γ	NOUN
ejpam-6408	220	63	)	)	PUNCT
ejpam-6408	220	64	can	can	AUX
ejpam-6408	220	65	be	be	AUX
ejpam-6408	220	66	expressed	express	VERB
ejpam-6408	220	67	by	by	ADP
ejpam-6408	220	68	ν	ν	NOUN
ejpam-6408	220	69	=	=	SYM
ejpam-6408	220	70	∪{η	∪{η	PROPN
ejpam-6408	220	71	:	:	PUNCT
ejpam-6408	220	72	η	η	PROPN
ejpam-6408	220	73	∈	∈	PROPN
ejpam-6408	220	74	soϵ(γ	soϵ(γ	PROPN
ejpam-6408	220	75	)	)	PUNCT
ejpam-6408	220	76	and	and	CCONJ
ejpam-6408	220	77	clϵ(η	clϵ(η	PROPN
ejpam-6408	220	78	)	)	PUNCT
ejpam-6408	220	79	⊆	⊆	NUM
ejpam-6408	220	80	ν	ν	NOUN
ejpam-6408	220	81	}	}	PUNCT
ejpam-6408	220	82	.	.	PUNCT
ejpam-6408	221	1	proof	proof	NOUN
ejpam-6408	221	2	.	.	PUNCT
ejpam-6408	222	1	(	(	PUNCT
ejpam-6408	222	2	1	1	X
ejpam-6408	222	3	)	)	PUNCT
ejpam-6408	222	4	⇒	⇒	NOUN
ejpam-6408	222	5	(	(	PUNCT
ejpam-6408	222	6	2	2	X
ejpam-6408	222	7	)	)	PUNCT
ejpam-6408	222	8	let	let	VERB
ejpam-6408	222	9	ν	ν	NOUN
ejpam-6408	222	10	be	be	AUX
ejpam-6408	222	11	a	a	DET
ejpam-6408	222	12	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	222	13	subset	subset	NOUN
ejpam-6408	222	14	of	of	ADP
ejpam-6408	222	15	γ	γ	PROPN
ejpam-6408	222	16	continuing	continue	VERB
ejpam-6408	222	17	ϑ	ϑ	NOUN
ejpam-6408	222	18	,	,	PUNCT
ejpam-6408	222	19	then	then	ADV
ejpam-6408	222	20	νc	νc	X
ejpam-6408	222	21	is	be	AUX
ejpam-6408	222	22	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	222	23	subset	subset	NOUN
ejpam-6408	222	24	of	of	ADP
ejpam-6408	222	25	γ	γ	PROPN
ejpam-6408	222	26	with	with	ADP
ejpam-6408	222	27	ϑ	ϑ	X
ejpam-6408	222	28	̸∈	̸∈	PROPN
ejpam-6408	222	29	νc	νc	PROPN
ejpam-6408	222	30	.	.	PROPN
ejpam-6408	223	1	given	give	VERB
ejpam-6408	223	2	(	(	PUNCT
ejpam-6408	223	3	1	1	NUM
ejpam-6408	223	4	)	)	PUNCT
ejpam-6408	223	5	,	,	PUNCT
ejpam-6408	223	6	there	there	PRON
ejpam-6408	223	7	are	be	VERB
ejpam-6408	223	8	two	two	NUM
ejpam-6408	223	9	disjoint	disjoint	NOUN
ejpam-6408	223	10	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	223	11	subsets	subset	NOUN
ejpam-6408	223	12	η1	η1	NOUN
ejpam-6408	223	13	and	and	CCONJ
ejpam-6408	223	14	η2	η2	PROPN
ejpam-6408	223	15	of	of	ADP
ejpam-6408	223	16	γ	γ	PROPN
ejpam-6408	223	17	,	,	PUNCT
ejpam-6408	223	18	such	such	ADJ
ejpam-6408	223	19	that	that	SCONJ
ejpam-6408	223	20	ϑ	ϑ	PROPN
ejpam-6408	223	21	∈	∈	NOUN
ejpam-6408	223	22	η1	η1	NOUN
ejpam-6408	223	23	and	and	CCONJ
ejpam-6408	223	24	νc	νc	ADP
ejpam-6408	223	25	⊆	⊆	NUM
ejpam-6408	223	26	η2	η2	NOUN
ejpam-6408	223	27	.	.	PUNCT
ejpam-6408	224	1	hence	hence	ADV
ejpam-6408	224	2	,	,	PUNCT
ejpam-6408	224	3	ϑ	ϑ	X
ejpam-6408	224	4	∈	∈	NOUN
ejpam-6408	224	5	η1	η1	NOUN
ejpam-6408	224	6	⊆	⊆	NUM
ejpam-6408	224	7	ηc2	ηc2	PRON
ejpam-6408	224	8	⊆	⊆	NUM
ejpam-6408	224	9	ν	ν	NOUN
ejpam-6408	224	10	.	.	PUNCT
ejpam-6408	225	1	therefore	therefore	ADV
ejpam-6408	225	2	,	,	PUNCT
ejpam-6408	225	3	ϑ	ϑ	X
ejpam-6408	225	4	∈	∈	NOUN
ejpam-6408	225	5	η1	η1	NOUN
ejpam-6408	225	6	⊆	⊆	NUM
ejpam-6408	225	7	clϵ(η1	clϵ(η1	NOUN
ejpam-6408	225	8	)	)	PUNCT
ejpam-6408	225	9	⊆	⊆	NUM
ejpam-6408	225	10	ν	ν	X
ejpam-6408	225	11	.	.	PUNCT
ejpam-6408	226	1	(	(	PUNCT
ejpam-6408	226	2	2	2	X
ejpam-6408	226	3	)	)	PUNCT
ejpam-6408	226	4	⇒	⇒	NOUN
ejpam-6408	226	5	(	(	PUNCT
ejpam-6408	226	6	3	3	X
ejpam-6408	226	7	)	)	PUNCT
ejpam-6408	226	8	let	let	VERB
ejpam-6408	226	9	ν	ν	X
ejpam-6408	226	10	∈	∈	PROPN
ejpam-6408	226	11	soϵ(γ	soϵ(γ	PROPN
ejpam-6408	226	12	)	)	PUNCT
ejpam-6408	226	13	.	.	PUNCT
ejpam-6408	227	1	applying	apply	VERB
ejpam-6408	227	2	(	(	PUNCT
ejpam-6408	227	3	2	2	NUM
ejpam-6408	227	4	)	)	PUNCT
ejpam-6408	227	5	,	,	PUNCT
ejpam-6408	227	6	for	for	ADP
ejpam-6408	227	7	each	each	DET
ejpam-6408	227	8	ϑ	ϑ	X
ejpam-6408	227	9	∈	∈	PROPN
ejpam-6408	227	10	ν	ν	NOUN
ejpam-6408	227	11	,	,	PUNCT
ejpam-6408	227	12	there	there	PRON
ejpam-6408	227	13	is	be	VERB
ejpam-6408	227	14	a	a	DET
ejpam-6408	227	15	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	227	16	subset	subset	VERB
ejpam-6408	227	17	η	η	PROPN
ejpam-6408	227	18	of	of	ADP
ejpam-6408	227	19	γ	γ	PROPN
ejpam-6408	227	20	,	,	PUNCT
ejpam-6408	228	1	such	such	ADJ
ejpam-6408	228	2	that	that	SCONJ
ejpam-6408	228	3	ϑ	ϑ	PROPN
ejpam-6408	228	4	∈	∈	PROPN
ejpam-6408	228	5	η	η	PROPN
ejpam-6408	228	6	⊆	⊆	NUM
ejpam-6408	228	7	clϵ(η	clϵ(η	PROPN
ejpam-6408	228	8	)	)	PUNCT
ejpam-6408	228	9	⊆	⊆	NUM
ejpam-6408	228	10	ν	ν	NOUN
ejpam-6408	228	11	.	.	PUNCT
ejpam-6408	229	1	hence	hence	ADV
ejpam-6408	229	2	,	,	PUNCT
ejpam-6408	229	3	∪{η	∪{η	PROPN
ejpam-6408	229	4	:	:	PUNCT
ejpam-6408	229	5	η	η	PROPN
ejpam-6408	229	6	∈	∈	PROPN
ejpam-6408	229	7	soϵ(γ	soϵ(γ	PROPN
ejpam-6408	229	8	)	)	PUNCT
ejpam-6408	229	9	and	and	CCONJ
ejpam-6408	229	10	clϵ(η	clϵ(η	PROPN
ejpam-6408	229	11	)	)	PUNCT
ejpam-6408	229	12	⊆	⊆	NUM
ejpam-6408	229	13	ν	ν	X
ejpam-6408	229	14	}	}	PUNCT
ejpam-6408	229	15	=	=	SYM
ejpam-6408	229	16	ν	ν	X
ejpam-6408	229	17	.	.	PUNCT
ejpam-6408	229	18	(	(	PUNCT
ejpam-6408	229	19	3	3	X
ejpam-6408	229	20	)	)	PUNCT
ejpam-6408	229	21	⇒	⇒	NOUN
ejpam-6408	229	22	(	(	PUNCT
ejpam-6408	229	23	1	1	X
ejpam-6408	229	24	)	)	PUNCT
ejpam-6408	229	25	let	let	VERB
ejpam-6408	229	26	k	k	PRON
ejpam-6408	229	27	be	be	AUX
ejpam-6408	229	28	a	a	DET
ejpam-6408	229	29	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	229	30	set	set	NOUN
ejpam-6408	229	31	with	with	ADP
ejpam-6408	229	32	ϑ	ϑ	PROPN
ejpam-6408	229	33	̸∈	̸∈	PROPN
ejpam-6408	229	34	k	k	PROPN
ejpam-6408	229	35	,	,	PUNCT
ejpam-6408	229	36	then	then	ADV
ejpam-6408	229	37	kc	kc	PROPN
ejpam-6408	229	38	∈	∈	PROPN
ejpam-6408	229	39	soϵ(γ	soϵ(γ	PROPN
ejpam-6408	229	40	)	)	PUNCT
ejpam-6408	229	41	with	with	ADP
ejpam-6408	229	42	ϑ	ϑ	PROPN
ejpam-6408	229	43	∈	∈	PROPN
ejpam-6408	229	44	kc	kc	PROPN
ejpam-6408	229	45	.	.	PUNCT
ejpam-6408	230	1	given	give	VERB
ejpam-6408	230	2	(	(	PUNCT
ejpam-6408	230	3	3	3	NUM
ejpam-6408	230	4	)	)	PUNCT
ejpam-6408	230	5	,	,	PUNCT
ejpam-6408	230	6	kc	kc	PROPN
ejpam-6408	230	7	=	=	SYM
ejpam-6408	230	8	∪{η	∪{η	PROPN
ejpam-6408	230	9	:	:	PUNCT
ejpam-6408	230	10	η	η	PROPN
ejpam-6408	230	11	∈	∈	PROPN
ejpam-6408	230	12	soϵ(γ	soϵ(γ	PROPN
ejpam-6408	230	13	)	)	PUNCT
ejpam-6408	230	14	and	and	CCONJ
ejpam-6408	230	15	clϵ(η	clϵ(η	PROPN
ejpam-6408	230	16	)	)	PUNCT
ejpam-6408	230	17	⊆	⊆	NUM
ejpam-6408	230	18	kc	kc	PROPN
ejpam-6408	230	19	}	}	PUNCT
ejpam-6408	230	20	.	.	PUNCT
ejpam-6408	231	1	since	since	SCONJ
ejpam-6408	231	2	ϑ	ϑ	PROPN
ejpam-6408	231	3	∈	∈	PROPN
ejpam-6408	231	4	kc	kc	PROPN
ejpam-6408	231	5	,	,	PUNCT
ejpam-6408	231	6	there	there	PRON
ejpam-6408	231	7	is	be	VERB
ejpam-6408	231	8	gϑ	gϑ	ADP
ejpam-6408	231	9	∈	∈	PROPN
ejpam-6408	231	10	soϵ(γ	soϵ(γ	NOUN
ejpam-6408	231	11	)	)	PUNCT
ejpam-6408	231	12	including	include	VERB
ejpam-6408	231	13	ϑ	ϑ	PROPN
ejpam-6408	231	14	such	such	ADJ
ejpam-6408	231	15	that	that	DET
ejpam-6408	231	16	clϵ(gϑ	clϵ(gϑ	NOUN
ejpam-6408	231	17	)	)	PUNCT
ejpam-6408	231	18	⊆	⊆	NUM
ejpam-6408	231	19	kc	kc	PROPN
ejpam-6408	231	20	.	.	PUNCT
ejpam-6408	232	1	thus	thus	ADV
ejpam-6408	232	2	,	,	PUNCT
ejpam-6408	232	3	k	k	PROPN
ejpam-6408	232	4	⊆	⊆	NUM
ejpam-6408	232	5	[	[	X
ejpam-6408	232	6	clϵ(gϑ	clϵ(gϑ	X
ejpam-6408	232	7	)	)	PUNCT
ejpam-6408	232	8	]	]	PUNCT
ejpam-6408	232	9	c	c	X
ejpam-6408	232	10	∈	∈	PROPN
ejpam-6408	232	11	soϵ(γ	soϵ(γ	PROPN
ejpam-6408	232	12	)	)	PUNCT
ejpam-6408	232	13	,	,	PUNCT
ejpam-6408	232	14	ϑ	ϑ	X
ejpam-6408	232	15	∈	∈	X
ejpam-6408	232	16	gϑ	gϑ	X
ejpam-6408	232	17	and	and	CCONJ
ejpam-6408	232	18	[	[	X
ejpam-6408	232	19	clϵ(gϑ	clϵ(gϑ	X
ejpam-6408	232	20	)	)	PUNCT
ejpam-6408	232	21	]	]	PUNCT
ejpam-6408	233	1	c	c	NOUN
ejpam-6408	233	2	∩gϑ	∩gϑ	ADJ
ejpam-6408	233	3	=	=	X
ejpam-6408	233	4	∅.	∅.	VERB
ejpam-6408	233	5	therefore	therefore	ADV
ejpam-6408	233	6	,	,	PUNCT
ejpam-6408	233	7	γ	γ	X
ejpam-6408	233	8	is	be	AUX
ejpam-6408	233	9	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	233	10	-	-	NOUN
ejpam-6408	233	11	space	space	NOUN
ejpam-6408	233	12	.	.	PUNCT
ejpam-6408	234	1	m.	m.	NOUN
ejpam-6408	234	2	aldawood	aldawood	PROPN
ejpam-6408	234	3	et	et	PROPN
ejpam-6408	234	4	al	al	PROPN
ejpam-6408	234	5	.	.	PUNCT
ejpam-6408	234	6	/	/	SYM
ejpam-6408	234	7	eur	eur	PROPN
ejpam-6408	234	8	.	.	PUNCT
ejpam-6408	235	1	j.	j.	PROPN
ejpam-6408	235	2	pure	pure	PROPN
ejpam-6408	235	3	appl	appl	PROPN
ejpam-6408	235	4	.	.	PROPN
ejpam-6408	235	5	math	math	PROPN
ejpam-6408	235	6	,	,	PUNCT
ejpam-6408	235	7	18	18	NUM
ejpam-6408	235	8	(	(	PUNCT
ejpam-6408	235	9	3	3	NUM
ejpam-6408	235	10	)	)	PUNCT
ejpam-6408	235	11	(	(	PUNCT
ejpam-6408	235	12	2025	2025	NUM
ejpam-6408	235	13	)	)	PUNCT
ejpam-6408	235	14	,	,	PUNCT
ejpam-6408	235	15	6408	6408	NUM
ejpam-6408	235	16	9	9	NUM
ejpam-6408	235	17	of	of	ADP
ejpam-6408	235	18	16	16	NUM
ejpam-6408	235	19	theorem	theorem	NOUN
ejpam-6408	235	20	9	9	NUM
ejpam-6408	235	21	.	.	PUNCT
ejpam-6408	236	1	[	[	X
ejpam-6408	236	2	60	60	NUM
ejpam-6408	236	3	]	]	X
ejpam-6408	236	4	the	the	DET
ejpam-6408	236	5	following	follow	VERB
ejpam-6408	236	6	are	be	AUX
ejpam-6408	236	7	equivalent	equivalent	ADJ
ejpam-6408	236	8	for	for	ADP
ejpam-6408	236	9	any	any	DET
ejpam-6408	236	10	sts	st	NOUN
ejpam-6408	236	11	(	(	PUNCT
ejpam-6408	236	12	γ	γ	X
ejpam-6408	236	13	,	,	PUNCT
ejpam-6408	236	14	θ	θ	PROPN
ejpam-6408	236	15	):	):	PUNCT
ejpam-6408	236	16	(	(	PUNCT
ejpam-6408	236	17	1	1	X
ejpam-6408	236	18	)	)	PUNCT
ejpam-6408	236	19	γ	γ	PROPN
ejpam-6408	236	20	is	be	AUX
ejpam-6408	236	21	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6408	236	22	-	-	NOUN
ejpam-6408	236	23	space	space	NOUN
ejpam-6408	236	24	;	;	PUNCT
ejpam-6408	236	25	(	(	PUNCT
ejpam-6408	236	26	2	2	X
ejpam-6408	236	27	)	)	PUNCT
ejpam-6408	236	28	for	for	ADP
ejpam-6408	236	29	each	each	DET
ejpam-6408	236	30	ϑ1	ϑ1	NOUN
ejpam-6408	236	31	̸=	̸=	PROPN
ejpam-6408	236	32	ϑ2	ϑ2	PROPN
ejpam-6408	236	33	∈	∈	PROPN
ejpam-6408	236	34	γ	γ	PROPN
ejpam-6408	236	35	,	,	PUNCT
ejpam-6408	236	36	clsϵ({ϑ1	clsϵ({ϑ1	PROPN
ejpam-6408	236	37	}	}	PUNCT
ejpam-6408	236	38	)	)	PUNCT
ejpam-6408	237	1	̸=	̸=	PROPN
ejpam-6408	237	2	clsϵ({ϑ2	clsϵ({ϑ2	PROPN
ejpam-6408	237	3	}	}	PUNCT
ejpam-6408	237	4	)	)	PUNCT
ejpam-6408	237	5	;	;	PUNCT
ejpam-6408	237	6	(	(	PUNCT
ejpam-6408	237	7	3	3	X
ejpam-6408	237	8	)	)	PUNCT
ejpam-6408	237	9	for	for	ADP
ejpam-6408	237	10	each	each	DET
ejpam-6408	237	11	ϑ	ϑ	PRON
ejpam-6408	237	12	∈	∈	PROPN
ejpam-6408	237	13	γ	γ	X
ejpam-6408	237	14	,	,	PUNCT
ejpam-6408	237	15	accϵ({ϑ	accϵ({ϑ	NUM
ejpam-6408	237	16	}	}	PUNCT
ejpam-6408	237	17	)	)	PUNCT
ejpam-6408	238	1	=	=	PUNCT
ejpam-6408	238	2	∪{g	∪{g	PROPN
ejpam-6408	238	3	:	:	PUNCT
ejpam-6408	238	4	g	g	PROPN
ejpam-6408	238	5	∈	∈	PROPN
ejpam-6408	238	6	scϵ(γ	scϵ(γ	PROPN
ejpam-6408	238	7	)	)	PUNCT
ejpam-6408	238	8	}	}	PUNCT
ejpam-6408	238	9	.	.	PUNCT
ejpam-6408	239	1	theorem	theorem	ADJ
ejpam-6408	239	2	10	10	NUM
ejpam-6408	239	3	.	.	PUNCT
ejpam-6408	240	1	[	[	X
ejpam-6408	240	2	60	60	NUM
ejpam-6408	240	3	]	]	SYM
ejpam-6408	240	4	(	(	PUNCT
ejpam-6408	240	5	1	1	X
ejpam-6408	240	6	)	)	PUNCT
ejpam-6408	240	7	any	any	DET
ejpam-6408	240	8	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6408	240	9	-	-	PUNCT
ejpam-6408	240	10	space	space	NOUN
ejpam-6408	240	11	is	be	AUX
ejpam-6408	240	12	supra-ϵ-tj−1	supra-ϵ-tj−1	NOUN
ejpam-6408	240	13	,	,	PUNCT
ejpam-6408	240	14	j	j	NOUN
ejpam-6408	240	15	=	=	SYM
ejpam-6408	240	16	1	1	NUM
ejpam-6408	240	17	,	,	PUNCT
ejpam-6408	240	18	2	2	NUM
ejpam-6408	240	19	.	.	PUNCT
ejpam-6408	240	20	(	(	PUNCT
ejpam-6408	240	21	2	2	X
ejpam-6408	240	22	)	)	PUNCT
ejpam-6408	240	23	any	any	DET
ejpam-6408	240	24	supra	supra	NOUN
ejpam-6408	240	25	-	-	PUNCT
ejpam-6408	240	26	tj	tj	NOUN
ejpam-6408	240	27	-	-	PUNCT
ejpam-6408	240	28	space	space	NOUN
ejpam-6408	240	29	is	be	AUX
ejpam-6408	240	30	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6408	240	31	,	,	PUNCT
ejpam-6408	240	32	j	j	PROPN
ejpam-6408	241	1	=	=	SYM
ejpam-6408	241	2	1	1	NUM
ejpam-6408	241	3	,	,	PUNCT
ejpam-6408	241	4	2	2	NUM
ejpam-6408	241	5	.	.	X
ejpam-6408	241	6	theorem	theorem	NOUN
ejpam-6408	241	7	11	11	NUM
ejpam-6408	241	8	.	.	PUNCT
ejpam-6408	242	1	[	[	X
ejpam-6408	242	2	60	60	NUM
ejpam-6408	242	3	]	]	PUNCT
ejpam-6408	242	4	for	for	ADP
ejpam-6408	242	5	any	any	DET
ejpam-6408	242	6	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	242	7	-	-	NOUN
ejpam-6408	242	8	space	space	NOUN
ejpam-6408	242	9	(	(	PUNCT
ejpam-6408	242	10	γ	γ	X
ejpam-6408	242	11	,	,	PUNCT
ejpam-6408	242	12	θ	θ	PROPN
ejpam-6408	242	13	)	)	PUNCT
ejpam-6408	242	14	,	,	PUNCT
ejpam-6408	242	15	the	the	DET
ejpam-6408	242	16	following	follow	VERB
ejpam-6408	242	17	are	be	AUX
ejpam-6408	242	18	equivalent	equivalent	ADJ
ejpam-6408	242	19	:	:	PUNCT
ejpam-6408	242	20	(	(	PUNCT
ejpam-6408	242	21	1	1	X
ejpam-6408	242	22	)	)	PUNCT
ejpam-6408	242	23	γ	γ	PROPN
ejpam-6408	242	24	is	be	AUX
ejpam-6408	242	25	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6408	242	26	-	-	NOUN
ejpam-6408	242	27	space	space	NOUN
ejpam-6408	242	28	;	;	PUNCT
ejpam-6408	242	29	(	(	PUNCT
ejpam-6408	242	30	2	2	X
ejpam-6408	242	31	)	)	PUNCT
ejpam-6408	242	32	γ	γ	X
ejpam-6408	242	33	is	be	AUX
ejpam-6408	242	34	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	242	35	-	-	PUNCT
ejpam-6408	242	36	space	space	NOUN
ejpam-6408	242	37	;	;	PUNCT
ejpam-6408	242	38	(	(	PUNCT
ejpam-6408	242	39	3	3	X
ejpam-6408	242	40	)	)	PUNCT
ejpam-6408	242	41	γ	γ	PROPN
ejpam-6408	242	42	is	be	AUX
ejpam-6408	242	43	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6408	242	44	-	-	PUNCT
ejpam-6408	242	45	space	space	NOUN
ejpam-6408	242	46	.	.	PUNCT
ejpam-6408	243	1	proof	proof	NOUN
ejpam-6408	243	2	.	.	PUNCT
ejpam-6408	244	1	(	(	PUNCT
ejpam-6408	244	2	1	1	X
ejpam-6408	244	3	)	)	PUNCT
ejpam-6408	244	4	⇒	⇒	NOUN
ejpam-6408	244	5	(	(	PUNCT
ejpam-6408	244	6	2	2	X
ejpam-6408	244	7	)	)	PUNCT
ejpam-6408	244	8	let	let	VERB
ejpam-6408	244	9	ϑ1	ϑ1	NOUN
ejpam-6408	244	10	̸=	̸=	PROPN
ejpam-6408	244	11	ϑ2	ϑ2	PROPN
ejpam-6408	244	12	∈	∈	PROPN
ejpam-6408	244	13	γ	γ	PROPN
ejpam-6408	244	14	.	.	PROPN
ejpam-6408	244	15	since	since	SCONJ
ejpam-6408	244	16	γ	γ	X
ejpam-6408	244	17	is	be	AUX
ejpam-6408	244	18	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	244	19	-	-	NOUN
ejpam-6408	244	20	space	space	NOUN
ejpam-6408	244	21	,	,	PUNCT
ejpam-6408	244	22	clsϵ({ϑ1	clsϵ({ϑ1	PROPN
ejpam-6408	244	23	}	}	PUNCT
ejpam-6408	244	24	)	)	PUNCT
ejpam-6408	244	25	̸=	̸=	PROPN
ejpam-6408	244	26	clsϵ({ϑ2	clsϵ({ϑ2	PROPN
ejpam-6408	244	27	}	}	PUNCT
ejpam-6408	244	28	)	)	PUNCT
ejpam-6408	244	29	according	accord	VERB
ejpam-6408	244	30	to	to	ADP
ejpam-6408	244	31	theorem	theorem	ADJ
ejpam-6408	244	32	9	9	NUM
ejpam-6408	244	33	.	.	PUNCT
ejpam-6408	245	1	hence	hence	ADV
ejpam-6408	245	2	,	,	PUNCT
ejpam-6408	245	3	either	either	CCONJ
ejpam-6408	245	4	ϑ2	ϑ2	PROPN
ejpam-6408	245	5	̸∈	̸∈	PROPN
ejpam-6408	245	6	clsϵ({ϑ1	clsϵ({ϑ1	PROPN
ejpam-6408	245	7	}	}	PUNCT
ejpam-6408	245	8	)	)	PUNCT
ejpam-6408	245	9	or	or	CCONJ
ejpam-6408	245	10	ϑ1	ϑ1	PROPN
ejpam-6408	245	11	̸∈	̸∈	PROPN
ejpam-6408	245	12	clsϵ({ϑ2	clsϵ({ϑ2	PROPN
ejpam-6408	245	13	}	}	PUNCT
ejpam-6408	245	14	)	)	PUNCT
ejpam-6408	245	15	.	.	PUNCT
ejpam-6408	246	1	considering	consider	VERB
ejpam-6408	246	2	ϑ2	ϑ2	PROPN
ejpam-6408	246	3	̸∈	̸∈	PROPN
ejpam-6408	246	4	clsϵ({ϑ1	clsϵ({ϑ1	PROPN
ejpam-6408	246	5	}	}	PUNCT
ejpam-6408	246	6	)	)	PUNCT
ejpam-6408	246	7	and	and	CCONJ
ejpam-6408	246	8	by	by	ADP
ejpam-6408	246	9	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	246	10	-	-	ADJ
ejpam-6408	246	11	spaceness	spaceness	ADJ
ejpam-6408	246	12	,	,	PUNCT
ejpam-6408	246	13	there	there	PRON
ejpam-6408	246	14	are	be	VERB
ejpam-6408	246	15	two	two	NUM
ejpam-6408	246	16	disjoint	disjoint	ADJ
ejpam-6408	246	17	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	246	18	subsets	subset	NOUN
ejpam-6408	246	19	ν1	ν1	NOUN
ejpam-6408	246	20	and	and	CCONJ
ejpam-6408	246	21	ν2	ν2	NOUN
ejpam-6408	246	22	of	of	ADP
ejpam-6408	246	23	γ	γ	X
ejpam-6408	246	24	,	,	PUNCT
ejpam-6408	246	25	containing	contain	VERB
ejpam-6408	246	26	ϑ2	ϑ2	NOUN
ejpam-6408	246	27	and	and	CCONJ
ejpam-6408	246	28	clsϵ({ϑ1	clsϵ({ϑ1	PROPN
ejpam-6408	246	29	,	,	PUNCT
ejpam-6408	246	30	repetitively	repetitively	ADV
ejpam-6408	246	31	.	.	PUNCT
ejpam-6408	247	1	therefore	therefore	ADV
ejpam-6408	247	2	,	,	PUNCT
ejpam-6408	247	3	γ	γ	X
ejpam-6408	247	4	is	be	AUX
ejpam-6408	247	5	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	247	6	-	-	PUNCT
ejpam-6408	247	7	space	space	NOUN
ejpam-6408	247	8	.	.	PUNCT
ejpam-6408	248	1	(	(	PUNCT
ejpam-6408	248	2	2	2	X
ejpam-6408	248	3	)	)	PUNCT
ejpam-6408	248	4	⇒	⇒	NOUN
ejpam-6408	248	5	(	(	PUNCT
ejpam-6408	248	6	3	3	NUM
ejpam-6408	248	7	)	)	PUNCT
ejpam-6408	248	8	and	and	CCONJ
ejpam-6408	248	9	(	(	PUNCT
ejpam-6408	248	10	3	3	X
ejpam-6408	248	11	)	)	PUNCT
ejpam-6408	248	12	⇒	⇒	NOUN
ejpam-6408	248	13	(	(	PUNCT
ejpam-6408	248	14	1	1	X
ejpam-6408	248	15	)	)	PUNCT
ejpam-6408	248	16	follows	follow	VERB
ejpam-6408	248	17	from	from	ADP
ejpam-6408	248	18	theorem	theorem	ADJ
ejpam-6408	248	19	10	10	NUM
ejpam-6408	248	20	(	(	PUNCT
ejpam-6408	248	21	1	1	NUM
ejpam-6408	248	22	)	)	PUNCT
ejpam-6408	248	23	.	.	PUNCT
ejpam-6408	249	1	theorem	theorem	NOUN
ejpam-6408	249	2	12	12	NUM
ejpam-6408	249	3	.	.	PUNCT
ejpam-6408	250	1	the	the	DET
ejpam-6408	250	2	following	follow	VERB
ejpam-6408	250	3	are	be	AUX
ejpam-6408	250	4	equivalent	equivalent	ADJ
ejpam-6408	250	5	for	for	ADP
ejpam-6408	250	6	any	any	DET
ejpam-6408	250	7	sts	st	NOUN
ejpam-6408	250	8	(	(	PUNCT
ejpam-6408	250	9	γ	γ	X
ejpam-6408	250	10	,	,	PUNCT
ejpam-6408	250	11	θ	θ	PROPN
ejpam-6408	250	12	):	):	PUNCT
ejpam-6408	250	13	(	(	PUNCT
ejpam-6408	250	14	1	1	X
ejpam-6408	250	15	)	)	PUNCT
ejpam-6408	250	16	γ	γ	PROPN
ejpam-6408	250	17	is	be	AUX
ejpam-6408	250	18	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6408	250	19	-	-	PUNCT
ejpam-6408	250	20	space	space	NOUN
ejpam-6408	250	21	;	;	PUNCT
ejpam-6408	250	22	(	(	PUNCT
ejpam-6408	250	23	2	2	X
ejpam-6408	250	24	)	)	PUNCT
ejpam-6408	250	25	for	for	ADP
ejpam-6408	250	26	each	each	DET
ejpam-6408	250	27	ϑ	ϑ	PRON
ejpam-6408	250	28	∈	∈	PROPN
ejpam-6408	250	29	γ	γ	X
ejpam-6408	250	30	,	,	PUNCT
ejpam-6408	250	31	{	{	PUNCT
ejpam-6408	250	32	ϑ	ϑ	NOUN
ejpam-6408	250	33	}	}	PUNCT
ejpam-6408	250	34	∈	∈	NOUN
ejpam-6408	250	35	scϵ(γ	scϵ(γ	PROPN
ejpam-6408	250	36	)	)	PUNCT
ejpam-6408	250	37	;	;	PUNCT
ejpam-6408	250	38	(	(	PUNCT
ejpam-6408	250	39	3	3	X
ejpam-6408	250	40	)	)	PUNCT
ejpam-6408	250	41	∩{h	∩{h	PROPN
ejpam-6408	250	42	:	:	PUNCT
ejpam-6408	250	43	h	h	PROPN
ejpam-6408	250	44	∈	∈	PROPN
ejpam-6408	250	45	soϵ(γ	soϵ(γ	PROPN
ejpam-6408	250	46	)	)	PUNCT
ejpam-6408	250	47	and	and	CCONJ
ejpam-6408	250	48	c	c	NOUN
ejpam-6408	250	49	⊆	⊆	NUM
ejpam-6408	250	50	h	h	NOUN
ejpam-6408	250	51	}	}	PUNCT
ejpam-6408	250	52	=	=	SYM
ejpam-6408	250	53	c	c	NOUN
ejpam-6408	250	54	;	;	PUNCT
ejpam-6408	250	55	(	(	PUNCT
ejpam-6408	250	56	4	4	X
ejpam-6408	250	57	)	)	PUNCT
ejpam-6408	250	58	for	for	ADP
ejpam-6408	250	59	each	each	DET
ejpam-6408	250	60	ϑ	ϑ	PRON
ejpam-6408	250	61	∈	∈	PROPN
ejpam-6408	250	62	γ	γ	X
ejpam-6408	250	63	,	,	PUNCT
ejpam-6408	250	64	accϵ({ϑ	accϵ({ϑ	NUM
ejpam-6408	250	65	}	}	PUNCT
ejpam-6408	250	66	)	)	PUNCT
ejpam-6408	250	67	=	=	PUNCT
ejpam-6408	250	68	∅.	∅.	NOUN
ejpam-6408	250	69	theorem	theorem	VERB
ejpam-6408	250	70	13	13	NUM
ejpam-6408	250	71	.	.	PUNCT
ejpam-6408	251	1	any	any	DET
ejpam-6408	251	2	supra-ϵ-t3	supra-ϵ-t3	NOUN
ejpam-6408	251	3	-	-	PUNCT
ejpam-6408	251	4	space	space	NOUN
ejpam-6408	251	5	is	be	AUX
ejpam-6408	251	6	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	251	7	1	1	NUM
ejpam-6408	251	8	2	2	NUM
ejpam-6408	251	9	.	.	PUNCT
ejpam-6408	252	1	proof	proof	NOUN
ejpam-6408	252	2	.	.	PUNCT
ejpam-6408	253	1	let	let	VERB
ejpam-6408	253	2	(	(	PUNCT
ejpam-6408	253	3	γ	γ	X
ejpam-6408	253	4	,	,	PUNCT
ejpam-6408	253	5	θ	θ	NOUN
ejpam-6408	253	6	)	)	PUNCT
ejpam-6408	253	7	be	be	AUX
ejpam-6408	253	8	a	a	DET
ejpam-6408	253	9	supra-ϵ-t3	supra-ϵ-t3	NOUN
ejpam-6408	253	10	-	-	PUNCT
ejpam-6408	253	11	space	space	NOUN
ejpam-6408	253	12	and	and	CCONJ
ejpam-6408	253	13	ϑ1	ϑ1	NOUN
ejpam-6408	253	14	̸=	̸=	PROPN
ejpam-6408	253	15	ϑ2	ϑ2	PROPN
ejpam-6408	253	16	∈	∈	PROPN
ejpam-6408	253	17	γ	γ	PROPN
ejpam-6408	253	18	.	.	PUNCT
ejpam-6408	253	19	given	give	VERB
ejpam-6408	253	20	theorem	theorem	NOUN
ejpam-6408	253	21	12	12	NUM
ejpam-6408	253	22	,	,	PUNCT
ejpam-6408	253	23	{	{	PUNCT
ejpam-6408	253	24	ϑ1	ϑ1	NOUN
ejpam-6408	253	25	}	}	PUNCT
ejpam-6408	253	26	,	,	PUNCT
ejpam-6408	253	27	{	{	PUNCT
ejpam-6408	253	28	ϑ2	ϑ2	NOUN
ejpam-6408	253	29	}	}	PUNCT
ejpam-6408	253	30	∈	∈	PROPN
ejpam-6408	253	31	scϵ(γ	scϵ(γ	NOUN
ejpam-6408	253	32	)	)	PUNCT
ejpam-6408	253	33	with	with	ADP
ejpam-6408	253	34	ϑ2	ϑ2	PROPN
ejpam-6408	253	35	̸∈	̸∈	PROPN
ejpam-6408	253	36	{	{	PUNCT
ejpam-6408	253	37	ϑ1	ϑ1	PROPN
ejpam-6408	253	38	}	}	PUNCT
ejpam-6408	253	39	and	and	CCONJ
ejpam-6408	253	40	ϑ1	ϑ1	PROPN
ejpam-6408	253	41	̸∈	̸∈	PROPN
ejpam-6408	253	42	{	{	PUNCT
ejpam-6408	253	43	ϑ2	ϑ2	PROPN
ejpam-6408	253	44	}	}	PUNCT
ejpam-6408	253	45	.	.	PUNCT
ejpam-6408	254	1	since	since	SCONJ
ejpam-6408	254	2	γ	γ	X
ejpam-6408	254	3	is	be	AUX
ejpam-6408	254	4	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	254	5	-	-	NOUN
ejpam-6408	254	6	space	space	NOUN
ejpam-6408	254	7	,	,	PUNCT
ejpam-6408	254	8	there	there	PRON
ejpam-6408	254	9	are	be	VERB
ejpam-6408	254	10	two	two	NUM
ejpam-6408	254	11	disjoint	disjoint	ADJ
ejpam-6408	254	12	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	254	13	subsets	subset	NOUN
ejpam-6408	254	14	ν1	ν1	NOUN
ejpam-6408	254	15	and	and	CCONJ
ejpam-6408	254	16	ν2	ν2	NOUN
ejpam-6408	254	17	of	of	ADP
ejpam-6408	254	18	γ	γ	X
ejpam-6408	254	19	containing	contain	VERB
ejpam-6408	254	20	ϑ1	ϑ1	NOUN
ejpam-6408	254	21	and	and	CCONJ
ejpam-6408	254	22	ϑ2	ϑ2	PROPN
ejpam-6408	254	23	,	,	PUNCT
ejpam-6408	254	24	respectively	respectively	ADV
ejpam-6408	254	25	.	.	PUNCT
ejpam-6408	255	1	hence	hence	ADV
ejpam-6408	255	2	,	,	PUNCT
ejpam-6408	255	3	there	there	PRON
ejpam-6408	255	4	are	be	VERB
ejpam-6408	255	5	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	255	6	subsets	subset	NOUN
ejpam-6408	255	7	η1	η1	NOUN
ejpam-6408	255	8	,	,	PUNCT
ejpam-6408	255	9	η2	η2	PROPN
ejpam-6408	255	10	of	of	ADP
ejpam-6408	255	11	γ	γ	PROPN
ejpam-6408	255	12	,	,	PUNCT
ejpam-6408	255	13	such	such	ADJ
ejpam-6408	255	14	that	that	DET
ejpam-6408	255	15	ϑ1	ϑ1	PROPN
ejpam-6408	255	16	∈	∈	PROPN
ejpam-6408	255	17	η1	η1	NOUN
ejpam-6408	255	18	⊆	⊆	NUM
ejpam-6408	255	19	clϵ(η1	clϵ(η1	NOUN
ejpam-6408	255	20	)	)	PUNCT
ejpam-6408	255	21	⊆	⊆	NUM
ejpam-6408	255	22	ν1	ν1	NOUN
ejpam-6408	255	23	and	and	CCONJ
ejpam-6408	255	24	ϑ2	ϑ2	PROPN
ejpam-6408	255	25	∈	∈	PROPN
ejpam-6408	255	26	η2	η2	VERB
ejpam-6408	255	27	⊆	⊆	NUM
ejpam-6408	255	28	clϵ(η2	clϵ(η2	NOUN
ejpam-6408	255	29	)	)	PUNCT
ejpam-6408	255	30	⊆	⊆	NUM
ejpam-6408	255	31	ν2	ν2	NOUN
ejpam-6408	255	32	according	accord	VERB
ejpam-6408	255	33	to	to	ADP
ejpam-6408	255	34	theorem	theorem	NOUN
ejpam-6408	255	35	8	8	NUM
ejpam-6408	255	36	.	.	PUNCT
ejpam-6408	256	1	since	since	SCONJ
ejpam-6408	256	2	ν1	ν1	NOUN
ejpam-6408	256	3	and	and	CCONJ
ejpam-6408	256	4	ν2	ν2	NOUN
ejpam-6408	256	5	are	be	AUX
ejpam-6408	256	6	disjoint	disjoint	ADJ
ejpam-6408	256	7	,	,	PUNCT
ejpam-6408	256	8	clϵ(η1	clϵ(η1	PROPN
ejpam-6408	256	9	)	)	PUNCT
ejpam-6408	256	10	and	and	CCONJ
ejpam-6408	256	11	clϵ(η2	clϵ(η2	NOUN
ejpam-6408	256	12	)	)	PUNCT
ejpam-6408	256	13	are	be	AUX
ejpam-6408	256	14	disjoint	disjoint	ADJ
ejpam-6408	256	15	.	.	PUNCT
ejpam-6408	257	1	therefore	therefore	ADV
ejpam-6408	257	2	,	,	PUNCT
ejpam-6408	257	3	γ	γ	X
ejpam-6408	257	4	is	be	AUX
ejpam-6408	257	5	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	257	6	1	1	NUM
ejpam-6408	257	7	2	2	NUM
ejpam-6408	257	8	.	.	PUNCT
ejpam-6408	258	1	m.	m.	NOUN
ejpam-6408	258	2	aldawood	aldawood	PROPN
ejpam-6408	258	3	et	et	PROPN
ejpam-6408	258	4	al	al	PROPN
ejpam-6408	258	5	.	.	PUNCT
ejpam-6408	258	6	/	/	SYM
ejpam-6408	258	7	eur	eur	PROPN
ejpam-6408	258	8	.	.	PUNCT
ejpam-6408	259	1	j.	j.	PROPN
ejpam-6408	259	2	pure	pure	PROPN
ejpam-6408	259	3	appl	appl	PROPN
ejpam-6408	259	4	.	.	PROPN
ejpam-6408	259	5	math	math	PROPN
ejpam-6408	259	6	,	,	PUNCT
ejpam-6408	259	7	18	18	NUM
ejpam-6408	259	8	(	(	PUNCT
ejpam-6408	259	9	3	3	NUM
ejpam-6408	259	10	)	)	PUNCT
ejpam-6408	259	11	(	(	PUNCT
ejpam-6408	259	12	2025	2025	NUM
ejpam-6408	259	13	)	)	PUNCT
ejpam-6408	259	14	,	,	PUNCT
ejpam-6408	259	15	6408	6408	NUM
ejpam-6408	259	16	10	10	NUM
ejpam-6408	259	17	of	of	ADP
ejpam-6408	259	18	16	16	NUM
ejpam-6408	259	19	remark	remark	NOUN
ejpam-6408	259	20	2	2	NUM
ejpam-6408	259	21	.	.	PUNCT
ejpam-6408	260	1	the	the	DET
ejpam-6408	260	2	converse	converse	NOUN
ejpam-6408	260	3	of	of	ADP
ejpam-6408	260	4	theorem	theorem	NOUN
ejpam-6408	260	5	13	13	NUM
ejpam-6408	260	6	is	be	AUX
ejpam-6408	260	7	not	not	PART
ejpam-6408	260	8	hold	hold	NOUN
ejpam-6408	260	9	as	as	SCONJ
ejpam-6408	260	10	the	the	DET
ejpam-6408	260	11	upcoming	upcoming	ADJ
ejpam-6408	260	12	example	example	NOUN
ejpam-6408	260	13	will	will	AUX
ejpam-6408	260	14	demonstrate	demonstrate	VERB
ejpam-6408	260	15	.	.	PUNCT
ejpam-6408	260	16	example	example	NOUN
ejpam-6408	261	1	2	2	NUM
ejpam-6408	261	2	.	.	PUNCT
ejpam-6408	261	3	let	let	VERB
ejpam-6408	261	4	θ	θ	NOUN
ejpam-6408	261	5	=	=	PUNCT
ejpam-6408	261	6	{	{	PUNCT
ejpam-6408	261	7	γ	γ	X
ejpam-6408	261	8	,	,	PUNCT
ejpam-6408	261	9	∅	∅	NOUN
ejpam-6408	261	10	,	,	PUNCT
ejpam-6408	261	11	{	{	PUNCT
ejpam-6408	261	12	5	5	NUM
ejpam-6408	261	13	,	,	PUNCT
ejpam-6408	261	14	6	6	NUM
ejpam-6408	261	15	}	}	PUNCT
ejpam-6408	261	16	,	,	PUNCT
ejpam-6408	261	17	{	{	PUNCT
ejpam-6408	261	18	7	7	NUM
ejpam-6408	261	19	,	,	PUNCT
ejpam-6408	261	20	8	8	NUM
ejpam-6408	261	21	}	}	PUNCT
ejpam-6408	261	22	,	,	PUNCT
ejpam-6408	261	23	{	{	PUNCT
ejpam-6408	261	24	5	5	NUM
ejpam-6408	261	25	,	,	PUNCT
ejpam-6408	261	26	7	7	NUM
ejpam-6408	261	27	}	}	PUNCT
ejpam-6408	261	28	,	,	PUNCT
ejpam-6408	261	29	{	{	PUNCT
ejpam-6408	261	30	6	6	NUM
ejpam-6408	261	31	,	,	PUNCT
ejpam-6408	261	32	8	8	NUM
ejpam-6408	261	33	}	}	PUNCT
ejpam-6408	261	34	,	,	PUNCT
ejpam-6408	261	35	{	{	PUNCT
ejpam-6408	261	36	6	6	NUM
ejpam-6408	261	37	,	,	PUNCT
ejpam-6408	261	38	7	7	NUM
ejpam-6408	261	39	}	}	PUNCT
ejpam-6408	261	40	,	,	PUNCT
ejpam-6408	261	41	{	{	PUNCT
ejpam-6408	261	42	5	5	NUM
ejpam-6408	261	43	,	,	PUNCT
ejpam-6408	261	44	6	6	NUM
ejpam-6408	261	45	,	,	PUNCT
ejpam-6408	261	46	7	7	NUM
ejpam-6408	261	47	}	}	PUNCT
ejpam-6408	261	48	,	,	PUNCT
ejpam-6408	261	49	{	{	PUNCT
ejpam-6408	261	50	5	5	NUM
ejpam-6408	261	51	,	,	PUNCT
ejpam-6408	261	52	6	6	NUM
ejpam-6408	261	53	,	,	PUNCT
ejpam-6408	261	54	8	8	NUM
ejpam-6408	261	55	}	}	PUNCT
ejpam-6408	261	56	,	,	PUNCT
ejpam-6408	261	57	{	{	PUNCT
ejpam-6408	261	58	5	5	NUM
ejpam-6408	261	59	,	,	PUNCT
ejpam-6408	261	60	7	7	NUM
ejpam-6408	261	61	,	,	PUNCT
ejpam-6408	261	62	8	8	NUM
ejpam-6408	261	63	}	}	PUNCT
ejpam-6408	261	64	,	,	PUNCT
ejpam-6408	261	65	{	{	PUNCT
ejpam-6408	261	66	6	6	NUM
ejpam-6408	261	67	,	,	PUNCT
ejpam-6408	261	68	7	7	NUM
ejpam-6408	261	69	,	,	PUNCT
ejpam-6408	261	70	8	8	NUM
ejpam-6408	261	71	}	}	PUNCT
ejpam-6408	261	72	,	,	PUNCT
ejpam-6408	261	73	}	}	PUNCT
ejpam-6408	261	74	be	be	AUX
ejpam-6408	261	75	an	an	DET
ejpam-6408	261	76	sts	st	NOUN
ejpam-6408	261	77	on	on	ADP
ejpam-6408	261	78	γ	γ	X
ejpam-6408	261	79	=	=	SYM
ejpam-6408	261	80	{	{	PUNCT
ejpam-6408	261	81	5	5	NUM
ejpam-6408	261	82	,	,	PUNCT
ejpam-6408	261	83	6	6	NUM
ejpam-6408	261	84	,	,	PUNCT
ejpam-6408	261	85	7	7	NUM
ejpam-6408	261	86	,	,	PUNCT
ejpam-6408	261	87	8	8	NUM
ejpam-6408	261	88	}	}	PUNCT
ejpam-6408	261	89	.	.	PUNCT
ejpam-6408	262	1	regarding	regard	VERB
ejpam-6408	262	2	{	{	PUNCT
ejpam-6408	262	3	5	5	NUM
ejpam-6408	262	4	,	,	PUNCT
ejpam-6408	262	5	8	8	NUM
ejpam-6408	262	6	}	}	PUNCT
ejpam-6408	262	7	∈	∈	NOUN
ejpam-6408	262	8	scϵ(γ	scϵ(γ	NOUN
ejpam-6408	262	9	)	)	PUNCT
ejpam-6408	262	10	with	with	ADP
ejpam-6408	262	11	6	6	NUM
ejpam-6408	262	12	̸∈	̸∈	PROPN
ejpam-6408	262	13	{	{	PUNCT
ejpam-6408	262	14	5	5	NUM
ejpam-6408	262	15	,	,	PUNCT
ejpam-6408	262	16	8	8	NUM
ejpam-6408	262	17	}	}	PUNCT
ejpam-6408	262	18	,	,	PUNCT
ejpam-6408	262	19	however	however	ADV
ejpam-6408	262	20	here	here	ADV
ejpam-6408	262	21	are	be	AUX
ejpam-6408	262	22	not	not	PART
ejpam-6408	262	23	two	two	NUM
ejpam-6408	262	24	disjoint	disjoint	NOUN
ejpam-6408	262	25	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	262	26	subsets	subset	NOUN
ejpam-6408	262	27	γ	γ	X
ejpam-6408	262	28	separate	separate	VERB
ejpam-6408	262	29	6	6	NUM
ejpam-6408	262	30	and	and	CCONJ
ejpam-6408	262	31	{	{	PUNCT
ejpam-6408	262	32	5	5	NUM
ejpam-6408	262	33	,	,	PUNCT
ejpam-6408	262	34	8	8	NUM
ejpam-6408	262	35	}	}	PUNCT
ejpam-6408	262	36	.	.	PUNCT
ejpam-6408	263	1	hence	hence	ADV
ejpam-6408	263	2	,	,	PUNCT
ejpam-6408	263	3	γ	γ	X
ejpam-6408	263	4	is	be	AUX
ejpam-6408	263	5	not	not	PART
ejpam-6408	263	6	supra-ϵ-r	supra-ϵ-r	ADJ
ejpam-6408	263	7	-	-	NOUN
ejpam-6408	263	8	space	space	NOUN
ejpam-6408	263	9	,	,	PUNCT
ejpam-6408	263	10	which	which	PRON
ejpam-6408	263	11	implies	imply	VERB
ejpam-6408	263	12	that	that	SCONJ
ejpam-6408	263	13	it	it	PRON
ejpam-6408	263	14	is	be	AUX
ejpam-6408	263	15	not	not	PART
ejpam-6408	263	16	supra-ϵ-t3	supra-ϵ-t3	VERB
ejpam-6408	263	17	.	.	PUNCT
ejpam-6408	264	1	also	also	ADV
ejpam-6408	264	2	,	,	PUNCT
ejpam-6408	264	3	it	it	PRON
ejpam-6408	264	4	is	be	AUX
ejpam-6408	264	5	easy	easy	ADJ
ejpam-6408	264	6	to	to	PART
ejpam-6408	264	7	check	check	VERB
ejpam-6408	264	8	that	that	SCONJ
ejpam-6408	264	9	γ	γ	PROPN
ejpam-6408	264	10	is	be	AUX
ejpam-6408	264	11	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	264	12	1	1	NUM
ejpam-6408	264	13	2	2	NUM
ejpam-6408	264	14	.	.	PUNCT
ejpam-6408	265	1	theorem	theorem	VERB
ejpam-6408	265	2	14	14	NUM
ejpam-6408	265	3	.	.	PUNCT
ejpam-6408	266	1	the	the	DET
ejpam-6408	266	2	following	follow	VERB
ejpam-6408	266	3	are	be	AUX
ejpam-6408	266	4	equivalent	equivalent	ADJ
ejpam-6408	266	5	for	for	ADP
ejpam-6408	266	6	any	any	DET
ejpam-6408	266	7	sts	st	NOUN
ejpam-6408	266	8	(	(	PUNCT
ejpam-6408	266	9	γ	γ	X
ejpam-6408	266	10	,	,	PUNCT
ejpam-6408	266	11	θ	θ	PROPN
ejpam-6408	266	12	):	):	PUNCT
ejpam-6408	266	13	(	(	PUNCT
ejpam-6408	266	14	1	1	X
ejpam-6408	266	15	)	)	PUNCT
ejpam-6408	266	16	γ	γ	NOUN
ejpam-6408	266	17	is	be	AUX
ejpam-6408	266	18	supra-ϵ-n	supra-ϵ-n	ADJ
ejpam-6408	266	19	-space	-space	NOUN
ejpam-6408	266	20	;	;	PUNCT
ejpam-6408	266	21	(	(	PUNCT
ejpam-6408	266	22	2	2	X
ejpam-6408	266	23	)	)	PUNCT
ejpam-6408	266	24	for	for	ADP
ejpam-6408	266	25	every	every	DET
ejpam-6408	266	26	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	266	27	subset	subset	NOUN
ejpam-6408	266	28	ν	ν	NOUN
ejpam-6408	266	29	of	of	ADP
ejpam-6408	266	30	γ	γ	NOUN
ejpam-6408	266	31	and	and	CCONJ
ejpam-6408	266	32	for	for	ADP
ejpam-6408	266	33	every	every	DET
ejpam-6408	266	34	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	266	35	superset	superset	NOUN
ejpam-6408	266	36	ω	ω	PROPN
ejpam-6408	266	37	of	of	ADP
ejpam-6408	266	38	ν	ν	NOUN
ejpam-6408	266	39	,	,	PUNCT
ejpam-6408	266	40	there	there	PRON
ejpam-6408	266	41	is	be	VERB
ejpam-6408	266	42	a	a	DET
ejpam-6408	266	43	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	266	44	subset	subset	NOUN
ejpam-6408	266	45	ρ1	ρ1	NOUN
ejpam-6408	266	46	of	of	ADP
ejpam-6408	266	47	γ	γ	PROPN
ejpam-6408	266	48	,	,	PUNCT
ejpam-6408	266	49	such	such	ADJ
ejpam-6408	266	50	that	that	SCONJ
ejpam-6408	266	51	ν	ν	NOUN
ejpam-6408	266	52	⊆	⊆	NUM
ejpam-6408	266	53	ρ1	ρ1	NOUN
ejpam-6408	266	54	⊆	⊆	NUM
ejpam-6408	266	55	clϵ(ρ1	clϵ(ρ1	NOUN
ejpam-6408	266	56	)	)	PUNCT
ejpam-6408	266	57	⊆	⊆	NUM
ejpam-6408	266	58	ω	ω	NUM
ejpam-6408	266	59	;	;	PUNCT
ejpam-6408	266	60	(	(	PUNCT
ejpam-6408	266	61	3	3	X
ejpam-6408	266	62	)	)	PUNCT
ejpam-6408	266	63	for	for	ADP
ejpam-6408	266	64	every	every	DET
ejpam-6408	266	65	ω1	ω1	PROPN
ejpam-6408	266	66	and	and	CCONJ
ejpam-6408	266	67	ω2	ω2	ADJ
ejpam-6408	266	68	∈	∈	PROPN
ejpam-6408	266	69	soϵ(γ	soϵ(γ	PROPN
ejpam-6408	266	70	)	)	PUNCT
ejpam-6408	266	71	such	such	ADJ
ejpam-6408	267	1	that	that	SCONJ
ejpam-6408	267	2	γ	γ	PROPN
ejpam-6408	267	3	=	=	SYM
ejpam-6408	267	4	ω1	ω1	PROPN
ejpam-6408	267	5	∪	∪	X
ejpam-6408	267	6	ω2	ω2	NOUN
ejpam-6408	267	7	,	,	PUNCT
ejpam-6408	267	8	there	there	PRON
ejpam-6408	267	9	are	be	VERB
ejpam-6408	267	10	two	two	NUM
ejpam-6408	267	11	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	267	12	subsets	subset	NOUN
ejpam-6408	267	13	ν1	ν1	NOUN
ejpam-6408	267	14	and	and	CCONJ
ejpam-6408	267	15	ν2	ν2	NOUN
ejpam-6408	267	16	of	of	ADP
ejpam-6408	267	17	γ	γ	NOUN
ejpam-6408	267	18	,	,	PUNCT
ejpam-6408	267	19	such	such	ADJ
ejpam-6408	267	20	that	that	SCONJ
ejpam-6408	267	21	ω1	ω1	PROPN
ejpam-6408	267	22	⊆	⊆	NUM
ejpam-6408	267	23	ν1	ν1	NOUN
ejpam-6408	267	24	,	,	PUNCT
ejpam-6408	267	25	ω2	ω2	ADJ
ejpam-6408	267	26	⊆	⊆	NUM
ejpam-6408	267	27	ν2	ν2	NOUN
ejpam-6408	267	28	and	and	CCONJ
ejpam-6408	267	29	γ	γ	NOUN
ejpam-6408	267	30	=	=	SYM
ejpam-6408	267	31	ν1	ν1	NOUN
ejpam-6408	267	32	∪	∪	VERB
ejpam-6408	267	33	ν2	ν2	NOUN
ejpam-6408	267	34	.	.	PUNCT
ejpam-6408	268	1	proof	proof	NOUN
ejpam-6408	268	2	.	.	PUNCT
ejpam-6408	269	1	(	(	PUNCT
ejpam-6408	269	2	1	1	X
ejpam-6408	269	3	)	)	PUNCT
ejpam-6408	269	4	⇒	⇒	NOUN
ejpam-6408	269	5	(	(	PUNCT
ejpam-6408	269	6	2	2	X
ejpam-6408	269	7	)	)	PUNCT
ejpam-6408	269	8	let	let	VERB
ejpam-6408	269	9	ν	ν	NOUN
ejpam-6408	269	10	be	be	AUX
ejpam-6408	269	11	a	a	DET
ejpam-6408	269	12	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	269	13	subset	subset	NOUN
ejpam-6408	269	14	of	of	ADP
ejpam-6408	269	15	γ	γ	PROPN
ejpam-6408	269	16	and	and	CCONJ
ejpam-6408	269	17	ω	ω	NUM
ejpam-6408	269	18	∈	∈	PROPN
ejpam-6408	269	19	soϵ(γ	soϵ(γ	PROPN
ejpam-6408	269	20	)	)	PUNCT
ejpam-6408	269	21	such	such	ADJ
ejpam-6408	269	22	that	that	SCONJ
ejpam-6408	269	23	ν	ν	PROPN
ejpam-6408	269	24	⊆	⊆	NUM
ejpam-6408	269	25	ω	ω	NUM
ejpam-6408	269	26	,	,	PUNCT
ejpam-6408	269	27	then	then	ADV
ejpam-6408	269	28	ν	ν	PROPN
ejpam-6408	269	29	and	and	CCONJ
ejpam-6408	269	30	ωc	ωc	X
ejpam-6408	269	31	are	be	AUX
ejpam-6408	269	32	two	two	NUM
ejpam-6408	269	33	disjoint	disjoint	ADJ
ejpam-6408	269	34	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	269	35	sets	set	NOUN
ejpam-6408	269	36	.	.	PUNCT
ejpam-6408	270	1	given	give	VERB
ejpam-6408	270	2	(	(	PUNCT
ejpam-6408	270	3	1	1	NUM
ejpam-6408	270	4	)	)	PUNCT
ejpam-6408	270	5	,	,	PUNCT
ejpam-6408	270	6	there	there	PRON
ejpam-6408	270	7	are	be	VERB
ejpam-6408	270	8	two	two	NUM
ejpam-6408	270	9	disjoint	disjoint	NOUN
ejpam-6408	270	10	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	270	11	subsets	subset	NOUN
ejpam-6408	270	12	ρ1	ρ1	NOUN
ejpam-6408	270	13	and	and	CCONJ
ejpam-6408	270	14	ρ2	ρ2	NOUN
ejpam-6408	270	15	of	of	ADP
ejpam-6408	270	16	γ	γ	NOUN
ejpam-6408	270	17	,	,	PUNCT
ejpam-6408	270	18	such	such	ADJ
ejpam-6408	270	19	that	that	SCONJ
ejpam-6408	270	20	ν	ν	NOUN
ejpam-6408	270	21	⊆	⊆	NUM
ejpam-6408	270	22	ρ1	ρ1	NOUN
ejpam-6408	270	23	and	and	CCONJ
ejpam-6408	270	24	ωc	ωc	PROPN
ejpam-6408	270	25	⊆	⊆	NUM
ejpam-6408	270	26	ρ2	ρ2	NOUN
ejpam-6408	270	27	.	.	PUNCT
ejpam-6408	271	1	therefore	therefore	ADV
ejpam-6408	271	2	,	,	PUNCT
ejpam-6408	271	3	ν	ν	NOUN
ejpam-6408	271	4	⊆	⊆	NUM
ejpam-6408	271	5	ρ1	ρ1	NOUN
ejpam-6408	271	6	⊆	⊆	NUM
ejpam-6408	271	7	clϵ(ρ	clϵ(ρ	NOUN
ejpam-6408	271	8	c	c	NOUN
ejpam-6408	271	9	2	2	NUM
ejpam-6408	271	10	)	)	PUNCT
ejpam-6408	271	11	=	=	PUNCT
ejpam-6408	271	12	ρc2	ρc2	NOUN
ejpam-6408	271	13	⊆	⊆	NUM
ejpam-6408	271	14	ω	ω	NOUN
ejpam-6408	271	15	.	.	PUNCT
ejpam-6408	272	1	thus	thus	ADV
ejpam-6408	272	2	,	,	PUNCT
ejpam-6408	272	3	ν	ν	NOUN
ejpam-6408	272	4	⊆	⊆	NUM
ejpam-6408	272	5	ρ1	ρ1	NOUN
ejpam-6408	272	6	⊆	⊆	NUM
ejpam-6408	272	7	clϵ(ρ1	clϵ(ρ1	NOUN
ejpam-6408	272	8	)	)	PUNCT
ejpam-6408	272	9	⊆	⊆	NUM
ejpam-6408	272	10	ω	ω	NOUN
ejpam-6408	272	11	.	.	PUNCT
ejpam-6408	273	1	(	(	PUNCT
ejpam-6408	273	2	2	2	X
ejpam-6408	273	3	)	)	PUNCT
ejpam-6408	273	4	⇒	⇒	NOUN
ejpam-6408	273	5	(	(	PUNCT
ejpam-6408	273	6	3	3	X
ejpam-6408	273	7	)	)	PUNCT
ejpam-6408	273	8	let	let	VERB
ejpam-6408	273	9	ω1	ω1	PROPN
ejpam-6408	273	10	and	and	CCONJ
ejpam-6408	273	11	ω2	ω2	ADJ
ejpam-6408	273	12	∈	∈	PROPN
ejpam-6408	273	13	soϵ(γ	soϵ(γ	PROPN
ejpam-6408	273	14	)	)	PUNCT
ejpam-6408	273	15	such	such	ADJ
ejpam-6408	273	16	that	that	SCONJ
ejpam-6408	273	17	γ	γ	PROPN
ejpam-6408	273	18	=	=	SYM
ejpam-6408	273	19	ω1	ω1	PROPN
ejpam-6408	273	20	∪	∪	X
ejpam-6408	273	21	ω2	ω2	PROPN
ejpam-6408	273	22	.	.	PUNCT
ejpam-6408	274	1	then	then	ADV
ejpam-6408	274	2	,	,	PUNCT
ejpam-6408	274	3	νc1	νc1	PROPN
ejpam-6408	274	4	is	be	AUX
ejpam-6408	274	5	a	a	DET
ejpam-6408	274	6	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	274	7	subset	subset	NOUN
ejpam-6408	274	8	of	of	ADP
ejpam-6408	274	9	ν2	ν2	NOUN
ejpam-6408	274	10	.	.	PUNCT
ejpam-6408	275	1	given	give	VERB
ejpam-6408	275	2	(	(	PUNCT
ejpam-6408	275	3	2	2	NUM
ejpam-6408	275	4	)	)	PUNCT
ejpam-6408	275	5	,	,	PUNCT
ejpam-6408	275	6	there	there	PRON
ejpam-6408	275	7	is	be	VERB
ejpam-6408	275	8	a	a	DET
ejpam-6408	275	9	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	275	10	subset	subset	NOUN
ejpam-6408	275	11	ρ1	ρ1	NOUN
ejpam-6408	275	12	of	of	ADP
ejpam-6408	275	13	γ	γ	PROPN
ejpam-6408	275	14	,	,	PUNCT
ejpam-6408	275	15	such	such	ADJ
ejpam-6408	275	16	that	that	DET
ejpam-6408	275	17	νc1	νc1	NOUN
ejpam-6408	275	18	⊆	⊆	NUM
ejpam-6408	275	19	ρ1	ρ1	NOUN
ejpam-6408	275	20	⊆	⊆	NUM
ejpam-6408	275	21	clϵ(ρ1	clϵ(ρ1	PROPN
ejpam-6408	275	22	)	)	PUNCT
ejpam-6408	275	23	⊆	⊆	NUM
ejpam-6408	275	24	ν2	ν2	NOUN
ejpam-6408	275	25	.	.	PUNCT
ejpam-6408	276	1	therefore	therefore	ADV
ejpam-6408	276	2	,	,	PUNCT
ejpam-6408	276	3	ρc1	ρc1	ADJ
ejpam-6408	276	4	⊆	⊆	NUM
ejpam-6408	276	5	ν1	ν1	NOUN
ejpam-6408	276	6	and	and	CCONJ
ejpam-6408	276	7	clϵ(ρ1	clϵ(ρ1	PROPN
ejpam-6408	276	8	)	)	PUNCT
ejpam-6408	276	9	⊆	⊆	NUM
ejpam-6408	276	10	ν2	ν2	NOUN
ejpam-6408	276	11	in	in	ADP
ejpam-6408	276	12	which	which	PRON
ejpam-6408	276	13	ρc1	ρc1	PROPN
ejpam-6408	276	14	and	and	CCONJ
ejpam-6408	276	15	clϵ(ρ1	clϵ(ρ1	PROPN
ejpam-6408	276	16	)	)	PUNCT
ejpam-6408	276	17	∈	∈	PROPN
ejpam-6408	276	18	scϵ(γ	scϵ(γ	PROPN
ejpam-6408	276	19	)	)	PUNCT
ejpam-6408	276	20	with	with	ADP
ejpam-6408	276	21	ρc1	ρc1	NOUN
ejpam-6408	276	22	∪	∪	ADJ
ejpam-6408	276	23	clϵ(ρ1	clϵ(ρ1	PROPN
ejpam-6408	276	24	)	)	PUNCT
ejpam-6408	276	25	=	=	SYM
ejpam-6408	277	1	γ	γ	X
ejpam-6408	277	2	.	.	PROPN
ejpam-6408	277	3	(	(	PUNCT
ejpam-6408	277	4	3	3	X
ejpam-6408	277	5	)	)	PUNCT
ejpam-6408	277	6	⇒	⇒	NOUN
ejpam-6408	277	7	(	(	PUNCT
ejpam-6408	277	8	1	1	X
ejpam-6408	277	9	)	)	PUNCT
ejpam-6408	277	10	let	let	VERB
ejpam-6408	277	11	ν1	ν1	NOUN
ejpam-6408	277	12	and	and	CCONJ
ejpam-6408	277	13	ν2	ν2	NOUN
ejpam-6408	277	14	are	be	AUX
ejpam-6408	277	15	disjoint	disjoint	ADV
ejpam-6408	277	16	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	277	17	sets	set	NOUN
ejpam-6408	277	18	,	,	PUNCT
ejpam-6408	277	19	then	then	ADV
ejpam-6408	277	20	νc1	νc1	VERB
ejpam-6408	277	21	and	and	CCONJ
ejpam-6408	277	22	νc2	νc2	NOUN
ejpam-6408	277	23	are	be	AUX
ejpam-6408	277	24	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	277	25	sets	set	NOUN
ejpam-6408	277	26	in	in	ADP
ejpam-6408	277	27	which	which	PRON
ejpam-6408	277	28	γ	γ	X
ejpam-6408	277	29	=	=	SYM
ejpam-6408	277	30	νc1∪νc2	νc1∪νc2	PROPN
ejpam-6408	277	31	.	.	PUNCT
ejpam-6408	278	1	given	give	VERB
ejpam-6408	278	2	(	(	PUNCT
ejpam-6408	278	3	3	3	NUM
ejpam-6408	278	4	)	)	PUNCT
ejpam-6408	278	5	,	,	PUNCT
ejpam-6408	278	6	there	there	PRON
ejpam-6408	278	7	are	be	VERB
ejpam-6408	278	8	two	two	NUM
ejpam-6408	278	9	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	278	10	subsets	subset	NOUN
ejpam-6408	278	11	δ1	δ1	NOUN
ejpam-6408	278	12	and	and	CCONJ
ejpam-6408	278	13	δ2	δ2	VERB
ejpam-6408	278	14	of	of	ADP
ejpam-6408	278	15	γ	γ	NOUN
ejpam-6408	278	16	,	,	PUNCT
ejpam-6408	278	17	such	such	ADJ
ejpam-6408	278	18	that	that	DET
ejpam-6408	278	19	δ1	δ1	NOUN
ejpam-6408	278	20	⊆	⊆	NUM
ejpam-6408	278	21	νc1	νc1	NOUN
ejpam-6408	278	22	,	,	PUNCT
ejpam-6408	278	23	δ2	δ2	VERB
ejpam-6408	278	24	⊆	⊆	NUM
ejpam-6408	278	25	νc2	νc2	ADJ
ejpam-6408	278	26	and	and	CCONJ
ejpam-6408	278	27	γ	γ	NOUN
ejpam-6408	278	28	=	=	SYM
ejpam-6408	278	29	δ1	δ1	NOUN
ejpam-6408	278	30	∪	∪	NOUN
ejpam-6408	278	31	δ2	δ2	PROPN
ejpam-6408	278	32	.	.	PUNCT
ejpam-6408	279	1	thus	thus	ADV
ejpam-6408	279	2	,	,	PUNCT
ejpam-6408	279	3	δ	δ	PROPN
ejpam-6408	279	4	c	c	NOUN
ejpam-6408	279	5	1	1	NUM
ejpam-6408	279	6	and	and	CCONJ
ejpam-6408	279	7	δc2	δc2	PROPN
ejpam-6408	279	8	∈	∈	PROPN
ejpam-6408	279	9	soϵ(γ	soϵ(γ	PROPN
ejpam-6408	279	10	)	)	PUNCT
ejpam-6408	279	11	containing	contain	VERB
ejpam-6408	279	12	ν1	ν1	NOUN
ejpam-6408	279	13	,	,	PUNCT
ejpam-6408	279	14	ν2	ν2	NOUN
ejpam-6408	279	15	,	,	PUNCT
ejpam-6408	279	16	respectively	respectively	ADV
ejpam-6408	279	17	in	in	ADP
ejpam-6408	279	18	which	which	PRON
ejpam-6408	279	19	δc1	δc1	NOUN
ejpam-6408	279	20	∩	∩	ADJ
ejpam-6408	279	21	δc2	δc2	NOUN
ejpam-6408	279	22	=	=	X
ejpam-6408	279	23	∅.	∅.	NOUN
ejpam-6408	279	24	therefore	therefore	ADV
ejpam-6408	279	25	,	,	PUNCT
ejpam-6408	279	26	γ	γ	X
ejpam-6408	279	27	is	be	AUX
ejpam-6408	279	28	supra-ϵ-n	supra-ϵ-n	ADJ
ejpam-6408	279	29	-space	-space	NOUN
ejpam-6408	279	30	.	.	PUNCT
ejpam-6408	280	1	theorem	theorem	NOUN
ejpam-6408	280	2	15	15	NUM
ejpam-6408	280	3	.	.	PUNCT
ejpam-6408	281	1	any	any	DET
ejpam-6408	281	2	supra-ϵ-tj	supra-ϵ-tj	ADJ
ejpam-6408	281	3	-	-	PUNCT
ejpam-6408	281	4	space	space	NOUN
ejpam-6408	281	5	is	be	AUX
ejpam-6408	281	6	supra-ϵ-tj−1	supra-ϵ-tj−1	NOUN
ejpam-6408	281	7	,	,	PUNCT
ejpam-6408	281	8	j	j	PROPN
ejpam-6408	281	9	=	=	SYM
ejpam-6408	281	10	3	3	NUM
ejpam-6408	281	11	,	,	PUNCT
ejpam-6408	281	12	4	4	NUM
ejpam-6408	281	13	.	.	PUNCT
ejpam-6408	282	1	proof	proof	NOUN
ejpam-6408	282	2	.	.	PUNCT
ejpam-6408	283	1	we	we	PRON
ejpam-6408	283	2	prove	prove	VERB
ejpam-6408	283	3	the	the	DET
ejpam-6408	283	4	case	case	NOUN
ejpam-6408	283	5	when	when	SCONJ
ejpam-6408	283	6	j	j	PROPN
ejpam-6408	283	7	=	=	SYM
ejpam-6408	283	8	4	4	NUM
ejpam-6408	283	9	,	,	PUNCT
ejpam-6408	283	10	the	the	DET
ejpam-6408	283	11	other	other	ADJ
ejpam-6408	283	12	case	case	NOUN
ejpam-6408	283	13	by	by	ADP
ejpam-6408	283	14	a	a	DET
ejpam-6408	283	15	similar	similar	ADJ
ejpam-6408	283	16	manner	manner	NOUN
ejpam-6408	283	17	.	.	PUNCT
ejpam-6408	284	1	let	let	VERB
ejpam-6408	284	2	(	(	PUNCT
ejpam-6408	284	3	γ	γ	X
ejpam-6408	284	4	,	,	PUNCT
ejpam-6408	284	5	θ	θ	NOUN
ejpam-6408	284	6	)	)	PUNCT
ejpam-6408	284	7	be	be	VERB
ejpam-6408	284	8	a	a	DET
ejpam-6408	284	9	supra-ϵ-t4	supra-ϵ-t4	NOUN
ejpam-6408	284	10	-	-	PUNCT
ejpam-6408	284	11	space	space	NOUN
ejpam-6408	284	12	,	,	PUNCT
ejpam-6408	284	13	then	then	ADV
ejpam-6408	284	14	it	it	PRON
ejpam-6408	284	15	is	be	AUX
ejpam-6408	284	16	both	both	DET
ejpam-6408	284	17	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6408	284	18	-	-	PUNCT
ejpam-6408	284	19	space	space	NOUN
ejpam-6408	284	20	and	and	CCONJ
ejpam-6408	284	21	supra-ϵ-n	supra-ϵ-n	ADJ
ejpam-6408	284	22	-space	-space	NOUN
ejpam-6408	284	23	.	.	PUNCT
ejpam-6408	285	1	now	now	ADV
ejpam-6408	285	2	,	,	PUNCT
ejpam-6408	285	3	we	we	PRON
ejpam-6408	285	4	want	want	VERB
ejpam-6408	285	5	to	to	PART
ejpam-6408	285	6	prove	prove	VERB
ejpam-6408	285	7	that	that	SCONJ
ejpam-6408	285	8	γ	γ	PROPN
ejpam-6408	285	9	is	be	AUX
ejpam-6408	285	10	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	285	11	-	-	NOUN
ejpam-6408	285	12	space	space	NOUN
ejpam-6408	285	13	.	.	PUNCT
ejpam-6408	286	1	so	so	ADV
ejpam-6408	286	2	,	,	PUNCT
ejpam-6408	286	3	let	let	VERB
ejpam-6408	286	4	h	h	PRON
ejpam-6408	286	5	be	be	AUX
ejpam-6408	286	6	a	a	DET
ejpam-6408	286	7	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	286	8	set	set	NOUN
ejpam-6408	286	9	with	with	ADP
ejpam-6408	286	10	ϑ	ϑ	X
ejpam-6408	286	11	̸∈	̸∈	PROPN
ejpam-6408	286	12	h.	h.	PROPN
ejpam-6408	286	13	given	give	VERB
ejpam-6408	286	14	theorem	theorem	PROPN
ejpam-6408	286	15	12	12	NUM
ejpam-6408	286	16	,	,	PUNCT
ejpam-6408	286	17	{	{	PUNCT
ejpam-6408	286	18	ϑ	ϑ	AUX
ejpam-6408	286	19	}	}	PUNCT
ejpam-6408	286	20	is	be	AUX
ejpam-6408	286	21	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	286	22	.	.	PUNCT
ejpam-6408	287	1	hence	hence	ADV
ejpam-6408	287	2	,	,	PUNCT
ejpam-6408	287	3	h	h	NOUN
ejpam-6408	287	4	and	and	CCONJ
ejpam-6408	287	5	{	{	PUNCT
ejpam-6408	287	6	ϑ	ϑ	X
ejpam-6408	287	7	}	}	PUNCT
ejpam-6408	287	8	are	be	AUX
ejpam-6408	287	9	disjoint	disjoint	ADJ
ejpam-6408	287	10	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	287	11	sets	set	NOUN
ejpam-6408	287	12	.	.	PUNCT
ejpam-6408	288	1	by	by	ADP
ejpam-6408	288	2	supra-ϵ-t4	supra-ϵ-t4	PROPN
ejpam-6408	288	3	-	-	PUNCT
ejpam-6408	288	4	spaceness	spaceness	ADJ
ejpam-6408	288	5	,	,	PUNCT
ejpam-6408	288	6	there	there	PRON
ejpam-6408	288	7	are	be	VERB
ejpam-6408	288	8	two	two	NUM
ejpam-6408	288	9	disjoint	disjoint	ADJ
ejpam-6408	288	10	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	288	11	subsets	subset	NOUN
ejpam-6408	288	12	ν1	ν1	NOUN
ejpam-6408	288	13	and	and	CCONJ
ejpam-6408	288	14	ν2	ν2	NOUN
ejpam-6408	288	15	of	of	ADP
ejpam-6408	288	16	γ	γ	NOUN
ejpam-6408	288	17	,	,	PUNCT
ejpam-6408	288	18	such	such	ADJ
ejpam-6408	288	19	that	that	SCONJ
ejpam-6408	288	20	{	{	PUNCT
ejpam-6408	288	21	ϑ	ϑ	NOUN
ejpam-6408	288	22	}	}	PUNCT
ejpam-6408	288	23	⊆	⊆	NUM
ejpam-6408	288	24	ν1	ν1	NOUN
ejpam-6408	288	25	and	and	CCONJ
ejpam-6408	288	26	h	h	NOUN
ejpam-6408	288	27	⊆	⊆	NUM
ejpam-6408	288	28	ν2	ν2	NOUN
ejpam-6408	288	29	.	.	PUNCT
ejpam-6408	289	1	therefore	therefore	ADV
ejpam-6408	289	2	,	,	PUNCT
ejpam-6408	289	3	ϑ	ϑ	PROPN
ejpam-6408	289	4	∈	∈	NOUN
ejpam-6408	289	5	ν1	ν1	NOUN
ejpam-6408	289	6	and	and	CCONJ
ejpam-6408	289	7	h	h	NOUN
ejpam-6408	289	8	⊆	⊆	NUM
ejpam-6408	289	9	ν2	ν2	NOUN
ejpam-6408	289	10	.	.	PUNCT
ejpam-6408	290	1	thus	thus	ADV
ejpam-6408	290	2	,	,	PUNCT
ejpam-6408	290	3	γ	γ	X
ejpam-6408	290	4	is	be	AUX
ejpam-6408	290	5	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	290	6	-	-	NOUN
ejpam-6408	290	7	space	space	NOUN
ejpam-6408	290	8	,	,	PUNCT
ejpam-6408	290	9	and	and	CCONJ
ejpam-6408	290	10	so	so	ADV
ejpam-6408	290	11	it	it	PRON
ejpam-6408	290	12	is	be	AUX
ejpam-6408	290	13	(	(	PUNCT
ejpam-6408	290	14	γ	γ	X
ejpam-6408	290	15	,	,	PUNCT
ejpam-6408	290	16	θ	θ	NOUN
ejpam-6408	290	17	)	)	PUNCT
ejpam-6408	290	18	be	be	AUX
ejpam-6408	290	19	a	a	DET
ejpam-6408	290	20	supra-ϵ-t3	supra-ϵ-t3	NOUN
ejpam-6408	290	21	-	-	PUNCT
ejpam-6408	290	22	space	space	NOUN
ejpam-6408	290	23	.	.	PUNCT
ejpam-6408	291	1	remark	remark	PROPN
ejpam-6408	291	2	3	3	NUM
ejpam-6408	291	3	.	.	PUNCT
ejpam-6408	292	1	the	the	DET
ejpam-6408	292	2	converse	converse	NOUN
ejpam-6408	292	3	of	of	ADP
ejpam-6408	292	4	theorem	theorem	NOUN
ejpam-6408	292	5	15	15	NUM
ejpam-6408	292	6	is	be	AUX
ejpam-6408	292	7	not	not	PART
ejpam-6408	292	8	hold	hold	NOUN
ejpam-6408	292	9	as	as	SCONJ
ejpam-6408	292	10	the	the	DET
ejpam-6408	292	11	upcoming	upcoming	ADJ
ejpam-6408	292	12	examples	example	NOUN
ejpam-6408	292	13	will	will	AUX
ejpam-6408	292	14	demonstrate	demonstrate	VERB
ejpam-6408	292	15	.	.	PUNCT
ejpam-6408	293	1	m.	m.	NOUN
ejpam-6408	293	2	aldawood	aldawood	PROPN
ejpam-6408	293	3	et	et	PROPN
ejpam-6408	293	4	al	al	PROPN
ejpam-6408	293	5	.	.	PUNCT
ejpam-6408	293	6	/	/	SYM
ejpam-6408	293	7	eur	eur	PROPN
ejpam-6408	293	8	.	.	PUNCT
ejpam-6408	294	1	j.	j.	PROPN
ejpam-6408	294	2	pure	pure	PROPN
ejpam-6408	294	3	appl	appl	PROPN
ejpam-6408	294	4	.	.	PROPN
ejpam-6408	294	5	math	math	PROPN
ejpam-6408	294	6	,	,	PUNCT
ejpam-6408	294	7	18	18	NUM
ejpam-6408	294	8	(	(	PUNCT
ejpam-6408	294	9	3	3	NUM
ejpam-6408	294	10	)	)	PUNCT
ejpam-6408	294	11	(	(	PUNCT
ejpam-6408	294	12	2025	2025	NUM
ejpam-6408	294	13	)	)	PUNCT
ejpam-6408	294	14	,	,	PUNCT
ejpam-6408	294	15	6408	6408	NUM
ejpam-6408	294	16	11	11	NUM
ejpam-6408	294	17	of	of	ADP
ejpam-6408	294	18	16	16	NUM
ejpam-6408	294	19	examples	example	NOUN
ejpam-6408	294	20	1	1	NUM
ejpam-6408	294	21	.	.	PUNCT
ejpam-6408	295	1	(	(	PUNCT
ejpam-6408	295	2	1	1	X
ejpam-6408	295	3	)	)	PUNCT
ejpam-6408	295	4	let	let	VERB
ejpam-6408	295	5	θ	θ	NOUN
ejpam-6408	295	6	=	=	PUNCT
ejpam-6408	295	7	{	{	PUNCT
ejpam-6408	295	8	γ	γ	X
ejpam-6408	295	9	,	,	PUNCT
ejpam-6408	295	10	∅	∅	NOUN
ejpam-6408	295	11	,	,	PUNCT
ejpam-6408	295	12	{	{	PUNCT
ejpam-6408	295	13	e	e	NOUN
ejpam-6408	295	14	,	,	PUNCT
ejpam-6408	295	15	r	r	NOUN
ejpam-6408	295	16	}	}	PUNCT
ejpam-6408	295	17	,	,	PUNCT
ejpam-6408	295	18	{	{	PUNCT
ejpam-6408	295	19	t	t	PROPN
ejpam-6408	295	20	,	,	PUNCT
ejpam-6408	295	21	y	y	PROPN
ejpam-6408	295	22	}	}	PUNCT
ejpam-6408	295	23	,	,	PUNCT
ejpam-6408	295	24	{	{	PUNCT
ejpam-6408	295	25	e	e	NOUN
ejpam-6408	295	26	,	,	PUNCT
ejpam-6408	295	27	t	t	PROPN
ejpam-6408	295	28	}	}	PUNCT
ejpam-6408	295	29	,	,	PUNCT
ejpam-6408	295	30	{	{	PUNCT
ejpam-6408	295	31	r	r	NOUN
ejpam-6408	295	32	,	,	PUNCT
ejpam-6408	295	33	y	y	NOUN
ejpam-6408	295	34	}	}	PUNCT
ejpam-6408	295	35	,	,	PUNCT
ejpam-6408	295	36	{	{	PUNCT
ejpam-6408	295	37	r	r	NOUN
ejpam-6408	295	38	,	,	PUNCT
ejpam-6408	295	39	t	t	PROPN
ejpam-6408	295	40	}	}	PUNCT
ejpam-6408	295	41	,	,	PUNCT
ejpam-6408	295	42	{	{	PUNCT
ejpam-6408	295	43	e	e	NOUN
ejpam-6408	295	44	,	,	PUNCT
ejpam-6408	295	45	r	r	NOUN
ejpam-6408	295	46	,	,	PUNCT
ejpam-6408	295	47	t	t	PROPN
ejpam-6408	295	48	}	}	PUNCT
ejpam-6408	295	49	,	,	PUNCT
ejpam-6408	295	50	{	{	PUNCT
ejpam-6408	295	51	e	e	NOUN
ejpam-6408	295	52	,	,	PUNCT
ejpam-6408	295	53	r	r	NOUN
ejpam-6408	295	54	,	,	PUNCT
ejpam-6408	295	55	y	y	PROPN
ejpam-6408	295	56	}	}	PUNCT
ejpam-6408	295	57	,	,	PUNCT
ejpam-6408	295	58	{	{	PUNCT
ejpam-6408	295	59	e	e	NOUN
ejpam-6408	295	60	,	,	PUNCT
ejpam-6408	295	61	t	t	PROPN
ejpam-6408	295	62	,	,	PUNCT
ejpam-6408	295	63	y	y	PROPN
ejpam-6408	295	64	}	}	PUNCT
ejpam-6408	295	65	,	,	PUNCT
ejpam-6408	295	66	{	{	PUNCT
ejpam-6408	295	67	r	r	NOUN
ejpam-6408	295	68	,	,	PUNCT
ejpam-6408	295	69	t	t	PROPN
ejpam-6408	295	70	,	,	PUNCT
ejpam-6408	295	71	y	y	NOUN
ejpam-6408	295	72	}	}	PUNCT
ejpam-6408	295	73	}	}	PUNCT
ejpam-6408	295	74	be	be	AUX
ejpam-6408	295	75	an	an	DET
ejpam-6408	295	76	sts	st	NOUN
ejpam-6408	295	77	on	on	ADP
ejpam-6408	295	78	γ	γ	X
ejpam-6408	295	79	=	=	SYM
ejpam-6408	295	80	{	{	PUNCT
ejpam-6408	295	81	e	e	NOUN
ejpam-6408	295	82	,	,	PUNCT
ejpam-6408	295	83	r	r	NOUN
ejpam-6408	295	84	,	,	PUNCT
ejpam-6408	295	85	t	t	PROPN
ejpam-6408	295	86	,	,	PUNCT
ejpam-6408	295	87	y	y	PROPN
ejpam-6408	295	88	}	}	PUNCT
ejpam-6408	295	89	.	.	PUNCT
ejpam-6408	296	1	then	then	ADV
ejpam-6408	296	2	we	we	PRON
ejpam-6408	296	3	have	have	VERB
ejpam-6408	296	4	that	that	PRON
ejpam-6408	296	5	soϵ(γ	soϵ(γ	NOUN
ejpam-6408	296	6	)	)	PUNCT
ejpam-6408	296	7	=	=	SYM
ejpam-6408	296	8	θ	θ	X
ejpam-6408	296	9	.	.	PUNCT
ejpam-6408	297	1	it	it	PRON
ejpam-6408	297	2	follows	follow	VERB
ejpam-6408	297	3	that	that	SCONJ
ejpam-6408	297	4	,	,	PUNCT
ejpam-6408	297	5	γ	γ	X
ejpam-6408	297	6	is	be	AUX
ejpam-6408	297	7	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	297	8	-	-	PUNCT
ejpam-6408	297	9	space	space	NOUN
ejpam-6408	297	10	,	,	PUNCT
ejpam-6408	297	11	and	and	CCONJ
ejpam-6408	297	12	so	so	ADV
ejpam-6408	297	13	it	it	PRON
ejpam-6408	297	14	is	be	AUX
ejpam-6408	297	15	both	both	DET
ejpam-6408	297	16	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6408	297	17	-	-	PUNCT
ejpam-6408	297	18	space	space	NOUN
ejpam-6408	297	19	and	and	CCONJ
ejpam-6408	297	20	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6408	297	21	-	-	NOUN
ejpam-6408	297	22	space	space	NOUN
ejpam-6408	297	23	.	.	PUNCT
ejpam-6408	298	1	moreover	moreover	ADV
ejpam-6408	298	2	,	,	PUNCT
ejpam-6408	298	3	regarding	regard	VERB
ejpam-6408	298	4	{	{	PUNCT
ejpam-6408	298	5	e	e	NOUN
ejpam-6408	298	6	,	,	PUNCT
ejpam-6408	298	7	y	y	PROPN
ejpam-6408	298	8	}	}	PUNCT
ejpam-6408	298	9	∈	∈	NOUN
ejpam-6408	298	10	scϵ(γ	scϵ(γ	NOUN
ejpam-6408	298	11	)	)	PUNCT
ejpam-6408	298	12	with	with	ADP
ejpam-6408	298	13	r	r	PROPN
ejpam-6408	298	14	̸∈	̸∈	PROPN
ejpam-6408	298	15	{	{	PUNCT
ejpam-6408	298	16	e	e	PROPN
ejpam-6408	298	17	,	,	PUNCT
ejpam-6408	298	18	y	y	PROPN
ejpam-6408	298	19	}	}	PUNCT
ejpam-6408	298	20	,	,	PUNCT
ejpam-6408	298	21	however	however	ADV
ejpam-6408	298	22	there	there	PRON
ejpam-6408	298	23	are	be	VERB
ejpam-6408	298	24	not	not	PART
ejpam-6408	298	25	two	two	NUM
ejpam-6408	298	26	disjoint	disjoint	ADJ
ejpam-6408	298	27	supraϵ-open	supraϵ-open	ADJ
ejpam-6408	298	28	subsets	subset	NOUN
ejpam-6408	298	29	γ	γ	X
ejpam-6408	298	30	separate	separate	ADJ
ejpam-6408	298	31	r	r	NOUN
ejpam-6408	298	32	and	and	CCONJ
ejpam-6408	298	33	{	{	PUNCT
ejpam-6408	298	34	e	e	NOUN
ejpam-6408	298	35	,	,	PUNCT
ejpam-6408	298	36	y	y	NOUN
ejpam-6408	298	37	}	}	PUNCT
ejpam-6408	298	38	.	.	PUNCT
ejpam-6408	299	1	hence	hence	ADV
ejpam-6408	299	2	,	,	PUNCT
ejpam-6408	299	3	γ	γ	X
ejpam-6408	299	4	is	be	AUX
ejpam-6408	299	5	not	not	PART
ejpam-6408	299	6	supra-ϵ-r	supra-ϵ-r	ADJ
ejpam-6408	299	7	-	-	NOUN
ejpam-6408	299	8	space	space	NOUN
ejpam-6408	299	9	,	,	PUNCT
ejpam-6408	299	10	and	and	CCONJ
ejpam-6408	299	11	so	so	ADV
ejpam-6408	299	12	it	it	PRON
ejpam-6408	299	13	is	be	AUX
ejpam-6408	299	14	not	not	PART
ejpam-6408	299	15	supra-ϵ-t3	supra-ϵ-t3	NOUN
ejpam-6408	299	16	-	-	NOUN
ejpam-6408	299	17	space	space	NOUN
ejpam-6408	299	18	.	.	PUNCT
ejpam-6408	300	1	(	(	PUNCT
ejpam-6408	300	2	2	2	X
ejpam-6408	300	3	)	)	PUNCT
ejpam-6408	300	4	let	let	VERB
ejpam-6408	300	5	θ	θ	NOUN
ejpam-6408	300	6	=	=	PUNCT
ejpam-6408	300	7	{	{	PUNCT
ejpam-6408	300	8	∅,w	∅,w	ADV
ejpam-6408	300	9	⊆	⊆	NUM
ejpam-6408	300	10	n	n	NUM
ejpam-6408	300	11	:	:	PUNCT
ejpam-6408	300	12	1	1	NUM
ejpam-6408	300	13	∈	∈	NOUN
ejpam-6408	300	14	w	w	NOUN
ejpam-6408	300	15	or	or	CCONJ
ejpam-6408	300	16	1	1	NUM
ejpam-6408	300	17	̸∈	̸∈	PROPN
ejpam-6408	300	18	w	w	PROPN
ejpam-6408	300	19	and	and	CCONJ
ejpam-6408	300	20	w	w	PROPN
ejpam-6408	300	21	c	c	PROPN
ejpam-6408	300	22	is	be	AUX
ejpam-6408	300	23	finite	finite	ADJ
ejpam-6408	300	24	}	}	PUNCT
ejpam-6408	300	25	be	be	VERB
ejpam-6408	300	26	a	a	DET
ejpam-6408	300	27	supra	supra	ADJ
ejpam-6408	300	28	topology	topology	NOUN
ejpam-6408	300	29	in	in	ADP
ejpam-6408	300	30	n	n	NOUN
ejpam-6408	300	31	=	=	PUNCT
ejpam-6408	300	32	{	{	PUNCT
ejpam-6408	300	33	1	1	NUM
ejpam-6408	300	34	,	,	PUNCT
ejpam-6408	300	35	2	2	NUM
ejpam-6408	300	36	,	,	PUNCT
ejpam-6408	300	37	3	3	NUM
ejpam-6408	300	38	,	,	PUNCT
ejpam-6408	300	39	4	4	NUM
ejpam-6408	300	40	,	,	PUNCT
ejpam-6408	300	41	5	5	NUM
ejpam-6408	300	42	,	,	PUNCT
ejpam-6408	300	43	.......	.......	PUNCT
ejpam-6408	300	44	}	}	PUNCT
ejpam-6408	300	45	.	.	PUNCT
ejpam-6408	301	1	it	it	PRON
ejpam-6408	301	2	i	i	PRON
ejpam-6408	301	3	clear	clear	VERB
ejpam-6408	301	4	that	that	SCONJ
ejpam-6408	301	5	γ	γ	PROPN
ejpam-6408	301	6	is	be	AUX
ejpam-6408	301	7	both	both	DET
ejpam-6408	301	8	supra-ϵ-t1	supra-ϵ-t1	NOUN
ejpam-6408	301	9	-	-	PUNCT
ejpam-6408	301	10	space	space	NOUN
ejpam-6408	301	11	and	and	CCONJ
ejpam-6408	301	12	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	301	13	-	-	NOUN
ejpam-6408	301	14	space	space	NOUN
ejpam-6408	301	15	,	,	PUNCT
ejpam-6408	301	16	and	and	CCONJ
ejpam-6408	301	17	then	then	ADV
ejpam-6408	301	18	it	it	PRON
ejpam-6408	301	19	is	be	AUX
ejpam-6408	301	20	supra-ϵ-t3	supra-ϵ-t3	NOUN
ejpam-6408	301	21	-	-	NOUN
ejpam-6408	301	22	space	space	NOUN
ejpam-6408	301	23	.	.	PUNCT
ejpam-6408	302	1	however	however	ADV
ejpam-6408	302	2	,	,	PUNCT
ejpam-6408	302	3	regarding	regard	VERB
ejpam-6408	302	4	the	the	DET
ejpam-6408	302	5	sets	set	NOUN
ejpam-6408	302	6	a	a	PRON
ejpam-6408	302	7	=	=	SYM
ejpam-6408	302	8	{	{	PUNCT
ejpam-6408	302	9	n	n	NOUN
ejpam-6408	302	10	∈	∈	PROPN
ejpam-6408	302	11	n	n	NOUN
ejpam-6408	302	12	:	:	PUNCT
ejpam-6408	302	13	n	n	PRON
ejpam-6408	302	14	is	be	AUX
ejpam-6408	302	15	even	even	ADV
ejpam-6408	302	16	}	}	PUNCT
ejpam-6408	302	17	and	and	CCONJ
ejpam-6408	302	18	b	b	X
ejpam-6408	302	19	=	=	SYM
ejpam-6408	302	20	{	{	PUNCT
ejpam-6408	302	21	n	n	NOUN
ejpam-6408	302	22	∈	∈	PROPN
ejpam-6408	302	23	n	n	NOUN
ejpam-6408	302	24	:	:	PUNCT
ejpam-6408	302	25	n	n	CCONJ
ejpam-6408	302	26	⩾	⩾	PROPN
ejpam-6408	302	27	5	5	NUM
ejpam-6408	302	28	and	and	CCONJ
ejpam-6408	302	29	n	n	PRON
ejpam-6408	302	30	is	be	AUX
ejpam-6408	302	31	odd	odd	ADJ
ejpam-6408	302	32	}	}	PUNCT
ejpam-6408	302	33	.	.	PUNCT
ejpam-6408	303	1	we	we	PRON
ejpam-6408	303	2	have	have	VERB
ejpam-6408	303	3	a	a	PRON
ejpam-6408	303	4	and	and	CCONJ
ejpam-6408	303	5	b	b	NOUN
ejpam-6408	303	6	are	be	AUX
ejpam-6408	303	7	disjoint	disjoint	ADJ
ejpam-6408	303	8	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	303	9	subsets	subset	NOUN
ejpam-6408	303	10	of	of	ADP
ejpam-6408	303	11	n	n	CCONJ
ejpam-6408	303	12	,	,	PUNCT
ejpam-6408	303	13	however	however	ADV
ejpam-6408	303	14	there	there	PRON
ejpam-6408	303	15	are	be	VERB
ejpam-6408	303	16	not	not	PART
ejpam-6408	303	17	two	two	NUM
ejpam-6408	303	18	disjoint	disjoint	ADJ
ejpam-6408	303	19	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	303	20	subsets	subset	NOUN
ejpam-6408	303	21	of	of	ADP
ejpam-6408	303	22	γ	γ	NOUN
ejpam-6408	303	23	containing	contain	VERB
ejpam-6408	303	24	them	they	PRON
ejpam-6408	303	25	.	.	PUNCT
ejpam-6408	304	1	therefore	therefore	ADV
ejpam-6408	304	2	,	,	PUNCT
ejpam-6408	304	3	γ	γ	X
ejpam-6408	304	4	is	be	AUX
ejpam-6408	304	5	not	not	PART
ejpam-6408	304	6	supra-ϵ-n	supra-ϵ-n	ADJ
ejpam-6408	304	7	-space	-space	NOUN
ejpam-6408	304	8	and	and	CCONJ
ejpam-6408	304	9	thus	thus	ADV
ejpam-6408	304	10	γ	γ	X
ejpam-6408	304	11	is	be	AUX
ejpam-6408	304	12	not	not	PART
ejpam-6408	304	13	supra-ϵ-t4	supra-ϵ-t4	NOUN
ejpam-6408	304	14	-	-	PUNCT
ejpam-6408	304	15	space	space	NOUN
ejpam-6408	304	16	.	.	PUNCT
ejpam-6408	305	1	proposition	proposition	NOUN
ejpam-6408	305	2	3	3	NUM
ejpam-6408	305	3	.	.	PUNCT
ejpam-6408	305	4	based	base	VERB
ejpam-6408	305	5	on	on	ADP
ejpam-6408	305	6	the	the	DET
ejpam-6408	305	7	aforementioned	aforementioned	ADJ
ejpam-6408	305	8	conclusions	conclusion	NOUN
ejpam-6408	305	9	,	,	PUNCT
ejpam-6408	305	10	the	the	DET
ejpam-6408	305	11	following	follow	VERB
ejpam-6408	305	12	irreversible	irreversible	ADJ
ejpam-6408	305	13	implications	implication	NOUN
ejpam-6408	305	14	are	be	AUX
ejpam-6408	305	15	held	hold	VERB
ejpam-6408	305	16	for	for	ADP
ejpam-6408	305	17	an	an	DET
ejpam-6408	305	18	sts	st	NOUN
ejpam-6408	305	19	(	(	PUNCT
ejpam-6408	305	20	γ	γ	X
ejpam-6408	305	21	,	,	PUNCT
ejpam-6408	305	22	θ	θ	NOUN
ejpam-6408	305	23	)	)	PUNCT
ejpam-6408	305	24	.	.	PUNCT
ejpam-6408	306	1	supra-ϵ-t4	supra-ϵ-t4	NOUN
ejpam-6408	306	2	-	-	PUNCT
ejpam-6408	306	3	space	space	NOUN
ejpam-6408	306	4	=	=	SYM
ejpam-6408	306	5	⇒supra-ϵ-t3	⇒supra-ϵ-t3	NOUN
ejpam-6408	306	6	-	-	PUNCT
ejpam-6408	306	7	space	space	NOUN
ejpam-6408	306	8	=	=	NOUN
ejpam-6408	306	9	⇒	⇒	NOUN
ejpam-6408	306	10	supra-ϵ-t2	supra-ϵ-t2	NOUN
ejpam-6408	306	11	1	1	NUM
ejpam-6408	306	12	2	2	NUM
ejpam-6408	306	13	-space	-space	NOUN
ejpam-6408	306	14	=	=	NOUN
ejpam-6408	306	15	⇒	⇒	NOUN
ejpam-6408	306	16	supra-ϵ-t2	supra-ϵ-t2	NOUN
ejpam-6408	306	17	-	-	PUNCT
ejpam-6408	306	18	space	space	NOUN
ejpam-6408	306	19	⇓	⇓	PROPN
ejpam-6408	306	20	supra-ϵ-t0	supra-ϵ-t0	NOUN
ejpam-6408	306	21	-	-	PUNCT
ejpam-6408	306	22	space	space	NOUN
ejpam-6408	306	23	⇐	⇐	NOUN
ejpam-6408	306	24	=	=	NOUN
ejpam-6408	306	25	supra-ϵ-t1	supra-ϵ-t1	VERB
ejpam-6408	306	26	-	-	PUNCT
ejpam-6408	306	27	space	space	NOUN
ejpam-6408	306	28	figure	figure	NOUN
ejpam-6408	306	29	1	1	NUM
ejpam-6408	306	30	.	.	PUNCT
ejpam-6408	307	1	the	the	DET
ejpam-6408	307	2	relationships	relationship	NOUN
ejpam-6408	307	3	between	between	ADP
ejpam-6408	307	4	different	different	ADJ
ejpam-6408	307	5	kinds	kind	NOUN
ejpam-6408	307	6	of	of	ADP
ejpam-6408	307	7	separation	separation	NOUN
ejpam-6408	307	8	axioms	axiom	NOUN
ejpam-6408	307	9	in	in	ADP
ejpam-6408	307	10	the	the	DET
ejpam-6408	307	11	context	context	NOUN
ejpam-6408	307	12	of	of	ADP
ejpam-6408	307	13	stss	stss	NOUN
ejpam-6408	307	14	which	which	PRON
ejpam-6408	307	15	are	be	AUX
ejpam-6408	307	16	motivated	motivate	VERB
ejpam-6408	307	17	by	by	ADP
ejpam-6408	307	18	supra	supra	PROPN
ejpam-6408	307	19	ϵ-open	ϵ-open	PROPN
ejpam-6408	307	20	sets	set	NOUN
ejpam-6408	307	21	proof	proof	NOUN
ejpam-6408	307	22	.	.	PUNCT
ejpam-6408	308	1	it	it	PRON
ejpam-6408	308	2	is	be	AUX
ejpam-6408	308	3	follow	follow	VERB
ejpam-6408	308	4	from	from	ADP
ejpam-6408	308	5	[	[	X
ejpam-6408	308	6	[	[	X
ejpam-6408	308	7	60	60	NUM
ejpam-6408	308	8	]	]	PUNCT
ejpam-6408	308	9	,	,	PUNCT
ejpam-6408	308	10	proposition	proposition	NOUN
ejpam-6408	308	11	1	1	NUM
ejpam-6408	308	12	]	]	PUNCT
ejpam-6408	308	13	and	and	CCONJ
ejpam-6408	308	14	theorems	theorem	NOUN
ejpam-6408	308	15	13	13	NUM
ejpam-6408	308	16	and	and	CCONJ
ejpam-6408	308	17	15	15	NUM
ejpam-6408	308	18	.	.	PUNCT
ejpam-6408	309	1	proposition	proposition	NOUN
ejpam-6408	309	2	4	4	NUM
ejpam-6408	309	3	.	.	PUNCT
ejpam-6408	310	1	[	[	X
ejpam-6408	310	2	58	58	NUM
ejpam-6408	310	3	]	]	PUNCT
ejpam-6408	310	4	let	let	VERB
ejpam-6408	310	5	(	(	PUNCT
ejpam-6408	310	6	y	y	NOUN
ejpam-6408	310	7	,	,	PUNCT
ejpam-6408	310	8	θy	θy	AUX
ejpam-6408	310	9	)	)	PUNCT
ejpam-6408	310	10	be	be	AUX
ejpam-6408	310	11	an	an	DET
ejpam-6408	310	12	supra	supra	ADJ
ejpam-6408	310	13	ϵ-subspace	ϵ-subspace	NOUN
ejpam-6408	310	14	of	of	ADP
ejpam-6408	310	15	an	an	DET
ejpam-6408	310	16	sts	st	NOUN
ejpam-6408	310	17	(	(	PUNCT
ejpam-6408	310	18	γ	γ	X
ejpam-6408	310	19	,	,	PUNCT
ejpam-6408	310	20	θ	θ	NOUN
ejpam-6408	310	21	)	)	PUNCT
ejpam-6408	310	22	and	and	CCONJ
ejpam-6408	310	23	w	w	AUX
ejpam-6408	310	24	be	be	AUX
ejpam-6408	310	25	a	a	DET
ejpam-6408	310	26	subset	subset	NOUN
ejpam-6408	310	27	of	of	ADP
ejpam-6408	310	28	γ	γ	PROPN
ejpam-6408	310	29	.	.	PROPN
ejpam-6408	311	1	then	then	ADV
ejpam-6408	311	2	,	,	PUNCT
ejpam-6408	311	3	w	w	PROPN
ejpam-6408	311	4	∈	∈	PROPN
ejpam-6408	311	5	scϵ(y	scϵ(y	PROPN
ejpam-6408	311	6	)	)	PUNCT
ejpam-6408	312	1	if	if	SCONJ
ejpam-6408	312	2	and	and	CCONJ
ejpam-6408	312	3	only	only	ADV
ejpam-6408	312	4	if	if	SCONJ
ejpam-6408	312	5	there	there	PRON
ejpam-6408	312	6	is	be	VERB
ejpam-6408	312	7	g	g	PROPN
ejpam-6408	312	8	∈	∈	PROPN
ejpam-6408	312	9	scϵ(γ	scϵ(γ	NUM
ejpam-6408	312	10	)	)	PUNCT
ejpam-6408	312	11	such	such	ADJ
ejpam-6408	312	12	that	that	PRON
ejpam-6408	312	13	w	w	PROPN
ejpam-6408	312	14	=	=	VERB
ejpam-6408	312	15	y	y	PROPN
ejpam-6408	312	16	∩g	∩g	PROPN
ejpam-6408	312	17	.	.	PUNCT
ejpam-6408	313	1	theorem	theorem	VERB
ejpam-6408	313	2	16	16	NUM
ejpam-6408	313	3	.	.	PUNCT
ejpam-6408	314	1	every	every	DET
ejpam-6408	314	2	supra	supra	PROPN
ejpam-6408	314	3	subspace	subspace	NOUN
ejpam-6408	314	4	of	of	ADP
ejpam-6408	314	5	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	314	6	-	-	NOUN
ejpam-6408	314	7	space	space	NOUN
ejpam-6408	314	8	is	be	AUX
ejpam-6408	314	9	supra-ϵ-r	supra-ϵ-r	X
ejpam-6408	314	10	.	.	PUNCT
ejpam-6408	315	1	proof	proof	NOUN
ejpam-6408	315	2	.	.	PUNCT
ejpam-6408	316	1	assume	assume	VERB
ejpam-6408	316	2	that	that	SCONJ
ejpam-6408	316	3	(	(	PUNCT
ejpam-6408	316	4	χ	χ	X
ejpam-6408	316	5	,	,	PUNCT
ejpam-6408	316	6	θχ	θχ	NOUN
ejpam-6408	316	7	)	)	PUNCT
ejpam-6408	316	8	is	be	AUX
ejpam-6408	316	9	a	a	DET
ejpam-6408	316	10	supra	supra	ADJ
ejpam-6408	316	11	subspace	subspace	NOUN
ejpam-6408	316	12	of	of	ADP
ejpam-6408	316	13	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	316	14	-	-	NOUN
ejpam-6408	316	15	space	space	NOUN
ejpam-6408	316	16	(	(	PUNCT
ejpam-6408	316	17	γ	γ	X
ejpam-6408	316	18	,	,	PUNCT
ejpam-6408	316	19	θ	θ	NOUN
ejpam-6408	316	20	)	)	PUNCT
ejpam-6408	316	21	and	and	CCONJ
ejpam-6408	316	22	h	h	NOUN
ejpam-6408	316	23	is	be	AUX
ejpam-6408	316	24	a	a	DET
ejpam-6408	316	25	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	316	26	subset	subset	NOUN
ejpam-6408	316	27	of	of	ADP
ejpam-6408	316	28	χ	χ	PRON
ejpam-6408	316	29	with	with	ADP
ejpam-6408	316	30	ϑ	ϑ	X
ejpam-6408	316	31	̸∈	̸∈	PROPN
ejpam-6408	316	32	h.	h.	PROPN
ejpam-6408	316	33	given	give	VERB
ejpam-6408	316	34	proposition	proposition	NOUN
ejpam-6408	316	35	4	4	NUM
ejpam-6408	316	36	,	,	PUNCT
ejpam-6408	316	37	there	there	PRON
ejpam-6408	316	38	is	be	VERB
ejpam-6408	316	39	n	n	DET
ejpam-6408	316	40	∈	∈	NOUN
ejpam-6408	316	41	scϵ(γ	scϵ(γ	NUM
ejpam-6408	316	42	)	)	PUNCT
ejpam-6408	316	43	such	such	ADJ
ejpam-6408	316	44	that	that	SCONJ
ejpam-6408	316	45	h	h	NOUN
ejpam-6408	316	46	=	=	NOUN
ejpam-6408	316	47	χ	χ	DET
ejpam-6408	316	48	∩n	∩n	NOUN
ejpam-6408	316	49	,	,	PUNCT
ejpam-6408	316	50	and	and	CCONJ
ejpam-6408	316	51	then	then	ADV
ejpam-6408	316	52	ϑ	ϑ	X
ejpam-6408	316	53	̸∈	̸∈	PROPN
ejpam-6408	316	54	n	n	X
ejpam-6408	316	55	.	.	PUNCT
ejpam-6408	317	1	since	since	SCONJ
ejpam-6408	317	2	(	(	PUNCT
ejpam-6408	317	3	γ	γ	X
ejpam-6408	317	4	,	,	PUNCT
ejpam-6408	317	5	θ	θ	NOUN
ejpam-6408	317	6	)	)	PUNCT
ejpam-6408	317	7	is	be	AUX
ejpam-6408	317	8	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	317	9	-	-	NOUN
ejpam-6408	317	10	space	space	NOUN
ejpam-6408	317	11	,	,	PUNCT
ejpam-6408	317	12	there	there	PRON
ejpam-6408	317	13	are	be	VERB
ejpam-6408	317	14	two	two	NUM
ejpam-6408	317	15	disjoint	disjoint	ADJ
ejpam-6408	317	16	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	317	17	subsets	subset	NOUN
ejpam-6408	317	18	ν1	ν1	NOUN
ejpam-6408	317	19	and	and	CCONJ
ejpam-6408	317	20	ν2	ν2	NOUN
ejpam-6408	317	21	of	of	ADP
ejpam-6408	317	22	γ	γ	NOUN
ejpam-6408	317	23	,	,	PUNCT
ejpam-6408	317	24	such	such	ADJ
ejpam-6408	317	25	that	that	SCONJ
ejpam-6408	317	26	ϑ	ϑ	PROPN
ejpam-6408	317	27	∈	∈	NOUN
ejpam-6408	317	28	ν1	ν1	NOUN
ejpam-6408	317	29	and	and	CCONJ
ejpam-6408	317	30	n	n	CCONJ
ejpam-6408	317	31	⊆	⊆	NUM
ejpam-6408	317	32	ν2	ν2	NOUN
ejpam-6408	317	33	.	.	PUNCT
ejpam-6408	318	1	hence	hence	ADV
ejpam-6408	318	2	,	,	PUNCT
ejpam-6408	318	3	χ	χ	PRON
ejpam-6408	318	4	∩	∩	ADJ
ejpam-6408	318	5	ν1	ν1	NOUN
ejpam-6408	318	6	and	and	CCONJ
ejpam-6408	318	7	χ	χ	NOUN
ejpam-6408	318	8	∩	∩	ADJ
ejpam-6408	318	9	ν2	ν2	NOUN
ejpam-6408	318	10	are	be	AUX
ejpam-6408	318	11	two	two	NUM
ejpam-6408	318	12	disjoint	disjoint	NOUN
ejpam-6408	318	13	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	318	14	subsets	subset	NOUN
ejpam-6408	318	15	of	of	ADP
ejpam-6408	318	16	χ	χ	PRON
ejpam-6408	318	17	which	which	PRON
ejpam-6408	318	18	containing	contain	VERB
ejpam-6408	318	19	ϑ	ϑ	PROPN
ejpam-6408	318	20	and	and	CCONJ
ejpam-6408	318	21	h	h	NOUN
ejpam-6408	318	22	,	,	PUNCT
ejpam-6408	318	23	respectively	respectively	ADV
ejpam-6408	318	24	.	.	PUNCT
ejpam-6408	319	1	therefore	therefore	ADV
ejpam-6408	319	2	,	,	PUNCT
ejpam-6408	319	3	(	(	PUNCT
ejpam-6408	319	4	χ	χ	X
ejpam-6408	319	5	,	,	PUNCT
ejpam-6408	319	6	θχ	θχ	NOUN
ejpam-6408	319	7	)	)	PUNCT
ejpam-6408	319	8	is	be	AUX
ejpam-6408	319	9	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	319	10	-	-	NOUN
ejpam-6408	319	11	space	space	NOUN
ejpam-6408	319	12	.	.	PUNCT
ejpam-6408	320	1	corollary	corollary	ADJ
ejpam-6408	320	2	3	3	NUM
ejpam-6408	320	3	.	.	PUNCT
ejpam-6408	321	1	every	every	DET
ejpam-6408	321	2	supra	supra	PROPN
ejpam-6408	321	3	subspace	subspace	NOUN
ejpam-6408	321	4	of	of	ADP
ejpam-6408	321	5	supra-ϵ-t3	supra-ϵ-t3	NOUN
ejpam-6408	321	6	-	-	PUNCT
ejpam-6408	321	7	space	space	NOUN
ejpam-6408	321	8	is	be	AUX
ejpam-6408	321	9	supra-ϵ-t3	supra-ϵ-t3	NOUN
ejpam-6408	321	10	.	.	PUNCT
ejpam-6408	322	1	proof	proof	NOUN
ejpam-6408	322	2	.	.	PUNCT
ejpam-6408	323	1	it	it	PRON
ejpam-6408	323	2	is	be	AUX
ejpam-6408	323	3	derived	derive	VERB
ejpam-6408	323	4	from	from	ADP
ejpam-6408	323	5	theorem	theorem	ADJ
ejpam-6408	323	6	10	10	NUM
ejpam-6408	323	7	and	and	CCONJ
ejpam-6408	323	8	theorem	theorem	VERB
ejpam-6408	323	9	16	16	NUM
ejpam-6408	323	10	.	.	PUNCT
ejpam-6408	324	1	theorem	theorem	VERB
ejpam-6408	324	2	17	17	NUM
ejpam-6408	324	3	.	.	PUNCT
ejpam-6408	325	1	for	for	ADP
ejpam-6408	325	2	any	any	DET
ejpam-6408	325	3	sts	st	NOUN
ejpam-6408	325	4	(	(	PUNCT
ejpam-6408	325	5	γ	γ	X
ejpam-6408	325	6	,	,	PUNCT
ejpam-6408	325	7	θ	θ	NOUN
ejpam-6408	325	8	)	)	PUNCT
ejpam-6408	325	9	,	,	PUNCT
ejpam-6408	325	10	if	if	SCONJ
ejpam-6408	325	11	|γ|	|γ|	PROPN
ejpam-6408	325	12	⩽	⩽	NOUN
ejpam-6408	325	13	4	4	NUM
ejpam-6408	325	14	,	,	PUNCT
ejpam-6408	325	15	then	then	ADV
ejpam-6408	325	16	every	every	DET
ejpam-6408	325	17	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	325	18	-	-	NOUN
ejpam-6408	325	19	space	space	NOUN
ejpam-6408	325	20	is	be	AUX
ejpam-6408	325	21	supra-ϵ-n	supra-ϵ-n	ADJ
ejpam-6408	325	22	space	space	NOUN
ejpam-6408	325	23	.	.	PUNCT
ejpam-6408	326	1	m.	m.	NOUN
ejpam-6408	326	2	aldawood	aldawood	PROPN
ejpam-6408	326	3	et	et	PROPN
ejpam-6408	326	4	al	al	PROPN
ejpam-6408	326	5	.	.	PUNCT
ejpam-6408	326	6	/	/	SYM
ejpam-6408	326	7	eur	eur	PROPN
ejpam-6408	326	8	.	.	PUNCT
ejpam-6408	327	1	j.	j.	PROPN
ejpam-6408	327	2	pure	pure	PROPN
ejpam-6408	327	3	appl	appl	PROPN
ejpam-6408	327	4	.	.	PROPN
ejpam-6408	327	5	math	math	PROPN
ejpam-6408	327	6	,	,	PUNCT
ejpam-6408	327	7	18	18	NUM
ejpam-6408	327	8	(	(	PUNCT
ejpam-6408	327	9	3	3	NUM
ejpam-6408	327	10	)	)	PUNCT
ejpam-6408	327	11	(	(	PUNCT
ejpam-6408	327	12	2025	2025	NUM
ejpam-6408	327	13	)	)	PUNCT
ejpam-6408	327	14	,	,	PUNCT
ejpam-6408	327	15	6408	6408	NUM
ejpam-6408	327	16	12	12	NUM
ejpam-6408	327	17	of	of	ADP
ejpam-6408	327	18	16	16	NUM
ejpam-6408	327	19	proof	proof	NOUN
ejpam-6408	327	20	.	.	PUNCT
ejpam-6408	328	1	let	let	VERB
ejpam-6408	328	2	h	h	NOUN
ejpam-6408	328	3	,	,	PUNCT
ejpam-6408	328	4	k	k	PROPN
ejpam-6408	328	5	be	be	AUX
ejpam-6408	328	6	two	two	NUM
ejpam-6408	328	7	disjoint	disjoint	ADJ
ejpam-6408	328	8	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	328	9	subsets	subset	NOUN
ejpam-6408	328	10	of	of	ADP
ejpam-6408	328	11	a	a	DET
ejpam-6408	328	12	supra-ϵ-r	supra-ϵ-r	ADJ
ejpam-6408	328	13	-	-	NOUN
ejpam-6408	328	14	space	space	NOUN
ejpam-6408	328	15	(	(	PUNCT
ejpam-6408	328	16	γ	γ	X
ejpam-6408	328	17	,	,	PUNCT
ejpam-6408	328	18	θ	θ	NOUN
ejpam-6408	328	19	)	)	PUNCT
ejpam-6408	328	20	.	.	PUNCT
ejpam-6408	329	1	then	then	ADV
ejpam-6408	329	2	,	,	PUNCT
ejpam-6408	329	3	we	we	PRON
ejpam-6408	329	4	have	have	VERB
ejpam-6408	329	5	five	five	NUM
ejpam-6408	329	6	cases	case	NOUN
ejpam-6408	329	7	:	:	PUNCT
ejpam-6408	329	8	case	case	NOUN
ejpam-6408	329	9	(	(	PUNCT
ejpam-6408	329	10	1	1	NUM
ejpam-6408	329	11	)	)	PUNCT
ejpam-6408	329	12	,	,	PUNCT
ejpam-6408	329	13	|k|	|k|	NOUN
ejpam-6408	329	14	=	=	SYM
ejpam-6408	329	15	4	4	NUM
ejpam-6408	329	16	,	,	PUNCT
ejpam-6408	329	17	then	then	ADV
ejpam-6408	329	18	k	k	PROPN
ejpam-6408	329	19	=	=	PUNCT
ejpam-6408	329	20	γ	γ	X
ejpam-6408	329	21	and	and	CCONJ
ejpam-6408	329	22	h	h	NOUN
ejpam-6408	329	23	=	=	NOUN
ejpam-6408	329	24	∅.	∅.	PRON
ejpam-6408	329	25	hence	hence	ADV
ejpam-6408	329	26	,	,	PUNCT
ejpam-6408	329	27	we	we	PRON
ejpam-6408	329	28	get	get	VERB
ejpam-6408	329	29	our	our	PRON
ejpam-6408	329	30	result	result	NOUN
ejpam-6408	329	31	.	.	PUNCT
ejpam-6408	330	1	case	case	NOUN
ejpam-6408	330	2	(	(	PUNCT
ejpam-6408	330	3	2	2	NUM
ejpam-6408	330	4	)	)	PUNCT
ejpam-6408	330	5	,	,	PUNCT
ejpam-6408	330	6	|k|	|k|	NOUN
ejpam-6408	330	7	=	=	SYM
ejpam-6408	330	8	3	3	NUM
ejpam-6408	330	9	,	,	PUNCT
ejpam-6408	330	10	then	then	ADV
ejpam-6408	330	11	|h|	|h|	PROPN
ejpam-6408	330	12	=	=	SYM
ejpam-6408	330	13	1	1	NUM
ejpam-6408	330	14	,	,	PUNCT
ejpam-6408	330	15	and	and	CCONJ
ejpam-6408	330	16	so	so	ADV
ejpam-6408	330	17	kc	kc	PROPN
ejpam-6408	330	18	=	=	PUNCT
ejpam-6408	330	19	h	h	PROPN
ejpam-6408	330	20	and	and	CCONJ
ejpam-6408	330	21	hc	hc	PROPN
ejpam-6408	330	22	=	=	PROPN
ejpam-6408	330	23	k.	k.	PROPN
ejpam-6408	331	1	hence	hence	ADV
ejpam-6408	331	2	,	,	PUNCT
ejpam-6408	331	3	we	we	PRON
ejpam-6408	331	4	get	get	VERB
ejpam-6408	331	5	our	our	PRON
ejpam-6408	331	6	result	result	NOUN
ejpam-6408	331	7	.	.	PUNCT
ejpam-6408	332	1	case	case	NOUN
ejpam-6408	332	2	(	(	PUNCT
ejpam-6408	332	3	3	3	NUM
ejpam-6408	332	4	)	)	PUNCT
ejpam-6408	332	5	,	,	PUNCT
ejpam-6408	332	6	|k|	|k|	NOUN
ejpam-6408	332	7	=	=	SYM
ejpam-6408	332	8	2	2	NUM
ejpam-6408	332	9	,	,	PUNCT
ejpam-6408	332	10	then	then	ADV
ejpam-6408	332	11	either	either	CCONJ
ejpam-6408	332	12	|h|	|h|	PROPN
ejpam-6408	332	13	=	=	SYM
ejpam-6408	332	14	1	1	NUM
ejpam-6408	332	15	or	or	CCONJ
ejpam-6408	332	16	|h|	|h|	PROPN
ejpam-6408	332	17	=	=	SYM
ejpam-6408	332	18	2	2	X
ejpam-6408	332	19	.	.	X
ejpam-6408	333	1	if	if	SCONJ
ejpam-6408	333	2	|h|	|h|	PRON
ejpam-6408	333	3	=	=	SYM
ejpam-6408	333	4	2	2	NUM
ejpam-6408	333	5	,	,	PUNCT
ejpam-6408	333	6	then	then	ADV
ejpam-6408	333	7	both	both	DET
ejpam-6408	333	8	h	h	NOUN
ejpam-6408	333	9	,	,	PUNCT
ejpam-6408	333	10	k	k	PROPN
ejpam-6408	333	11	are	be	AUX
ejpam-6408	333	12	disjoint	disjoint	ADJ
ejpam-6408	333	13	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	333	14	sets	set	NOUN
ejpam-6408	333	15	.	.	PUNCT
ejpam-6408	334	1	hence	hence	ADV
ejpam-6408	334	2	,	,	PUNCT
ejpam-6408	334	3	we	we	PRON
ejpam-6408	334	4	get	get	VERB
ejpam-6408	334	5	our	our	PRON
ejpam-6408	334	6	result	result	NOUN
ejpam-6408	334	7	.	.	PUNCT
ejpam-6408	335	1	if	if	SCONJ
ejpam-6408	335	2	|h|	|h|	PRON
ejpam-6408	335	3	=	=	SYM
ejpam-6408	335	4	1	1	NUM
ejpam-6408	335	5	,	,	PUNCT
ejpam-6408	335	6	then	then	ADV
ejpam-6408	335	7	h	h	PROPN
ejpam-6408	335	8	is	be	AUX
ejpam-6408	335	9	singleton	singleton	PROPN
ejpam-6408	335	10	say	say	VERB
ejpam-6408	335	11	h	h	NOUN
ejpam-6408	336	1	=	=	PRON
ejpam-6408	336	2	{	{	PUNCT
ejpam-6408	336	3	a	a	NOUN
ejpam-6408	336	4	}	}	PUNCT
ejpam-6408	336	5	and	and	CCONJ
ejpam-6408	336	6	so	so	ADV
ejpam-6408	336	7	a	a	DET
ejpam-6408	336	8	̸∈	̸∈	PROPN
ejpam-6408	336	9	k.	k.	PROPN
ejpam-6408	336	10	since	since	SCONJ
ejpam-6408	336	11	γ	γ	PROPN
ejpam-6408	336	12	is	be	AUX
ejpam-6408	336	13	supra-ϵ-r	supra-ϵ-r	NOUN
ejpam-6408	336	14	-	-	NOUN
ejpam-6408	336	15	space	space	NOUN
ejpam-6408	336	16	,	,	PUNCT
ejpam-6408	336	17	there	there	PRON
ejpam-6408	336	18	are	be	VERB
ejpam-6408	336	19	two	two	NUM
ejpam-6408	336	20	disjoint	disjoint	ADJ
ejpam-6408	336	21	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	336	22	subsets	subset	NOUN
ejpam-6408	336	23	ν1	ν1	NOUN
ejpam-6408	336	24	and	and	CCONJ
ejpam-6408	336	25	ν2	ν2	NOUN
ejpam-6408	336	26	of	of	ADP
ejpam-6408	336	27	γ	γ	X
ejpam-6408	336	28	,	,	PUNCT
ejpam-6408	336	29	containing	contain	VERB
ejpam-6408	336	30	h	h	NOUN
ejpam-6408	336	31	,	,	PUNCT
ejpam-6408	336	32	k	k	NOUN
ejpam-6408	336	33	,	,	PUNCT
ejpam-6408	336	34	respectively	respectively	ADV
ejpam-6408	336	35	.	.	PUNCT
ejpam-6408	337	1	hence	hence	ADV
ejpam-6408	337	2	,	,	PUNCT
ejpam-6408	337	3	we	we	PRON
ejpam-6408	337	4	get	get	VERB
ejpam-6408	337	5	our	our	PRON
ejpam-6408	337	6	result	result	NOUN
ejpam-6408	337	7	.	.	PUNCT
ejpam-6408	338	1	case	case	NOUN
ejpam-6408	338	2	(	(	PUNCT
ejpam-6408	338	3	4	4	NUM
ejpam-6408	338	4	)	)	PUNCT
ejpam-6408	338	5	,	,	PUNCT
ejpam-6408	338	6	|k|	|k|	NOUN
ejpam-6408	338	7	=	=	SYM
ejpam-6408	338	8	1	1	NUM
ejpam-6408	338	9	,	,	PUNCT
ejpam-6408	338	10	then	then	ADV
ejpam-6408	338	11	k	k	PROPN
ejpam-6408	338	12	is	be	AUX
ejpam-6408	338	13	singleton	singleton	PROPN
ejpam-6408	338	14	say	say	VERB
ejpam-6408	338	15	k	k	PROPN
ejpam-6408	338	16	=	=	X
ejpam-6408	338	17	{	{	PUNCT
ejpam-6408	338	18	s	s	NOUN
ejpam-6408	338	19	}	}	PUNCT
ejpam-6408	338	20	and	and	CCONJ
ejpam-6408	338	21	so	so	ADV
ejpam-6408	338	22	s	s	PROPN
ejpam-6408	338	23	̸∈	̸∈	PROPN
ejpam-6408	338	24	h.	h.	PROPN
ejpam-6408	338	25	since	since	SCONJ
ejpam-6408	338	26	γ	γ	PROPN
ejpam-6408	338	27	is	be	AUX
ejpam-6408	338	28	supraϵ-r	supraϵ-r	NOUN
ejpam-6408	338	29	-	-	NOUN
ejpam-6408	338	30	space	space	NOUN
ejpam-6408	338	31	,	,	PUNCT
ejpam-6408	338	32	there	there	PRON
ejpam-6408	338	33	are	be	VERB
ejpam-6408	338	34	two	two	NUM
ejpam-6408	338	35	disjoint	disjoint	ADJ
ejpam-6408	338	36	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	338	37	subsets	subset	NOUN
ejpam-6408	338	38	ν1	ν1	NOUN
ejpam-6408	338	39	and	and	CCONJ
ejpam-6408	338	40	ν2	ν2	NOUN
ejpam-6408	338	41	of	of	ADP
ejpam-6408	338	42	γ	γ	X
ejpam-6408	338	43	,	,	PUNCT
ejpam-6408	338	44	containing	contain	VERB
ejpam-6408	338	45	h	h	NOUN
ejpam-6408	338	46	,	,	PUNCT
ejpam-6408	338	47	k	k	NOUN
ejpam-6408	338	48	,	,	PUNCT
ejpam-6408	338	49	respectively	respectively	ADV
ejpam-6408	338	50	.	.	PUNCT
ejpam-6408	339	1	hence	hence	ADV
ejpam-6408	339	2	,	,	PUNCT
ejpam-6408	339	3	we	we	PRON
ejpam-6408	339	4	get	get	VERB
ejpam-6408	339	5	our	our	PRON
ejpam-6408	339	6	result	result	NOUN
ejpam-6408	339	7	.	.	PUNCT
ejpam-6408	340	1	case	case	NOUN
ejpam-6408	340	2	(	(	PUNCT
ejpam-6408	340	3	5	5	NUM
ejpam-6408	340	4	)	)	PUNCT
ejpam-6408	340	5	,	,	PUNCT
ejpam-6408	340	6	k	k	NOUN
ejpam-6408	340	7	=	=	PUNCT
ejpam-6408	340	8	∅	∅	NOUN
ejpam-6408	340	9	,	,	PUNCT
ejpam-6408	340	10	then	then	ADV
ejpam-6408	340	11	h	h	NOUN
ejpam-6408	341	1	=	=	SYM
ejpam-6408	341	2	γ	γ	X
ejpam-6408	341	3	.	.	PROPN
ejpam-6408	341	4	hence	hence	ADV
ejpam-6408	341	5	,	,	PUNCT
ejpam-6408	341	6	we	we	PRON
ejpam-6408	341	7	get	get	VERB
ejpam-6408	341	8	our	our	PRON
ejpam-6408	341	9	result	result	NOUN
ejpam-6408	341	10	.	.	PUNCT
ejpam-6408	342	1	consequently	consequently	ADV
ejpam-6408	342	2	,	,	PUNCT
ejpam-6408	342	3	γ	γ	X
ejpam-6408	342	4	is	be	AUX
ejpam-6408	342	5	supra-ϵ-n	supra-ϵ-n	ADJ
ejpam-6408	342	6	-space	-space	NOUN
ejpam-6408	342	7	.	.	PUNCT
ejpam-6408	343	1	corollary	corollary	ADJ
ejpam-6408	343	2	4	4	NUM
ejpam-6408	343	3	.	.	PUNCT
ejpam-6408	344	1	for	for	ADP
ejpam-6408	344	2	any	any	DET
ejpam-6408	344	3	sts	st	NOUN
ejpam-6408	344	4	(	(	PUNCT
ejpam-6408	344	5	γ	γ	X
ejpam-6408	344	6	,	,	PUNCT
ejpam-6408	344	7	θ	θ	NOUN
ejpam-6408	344	8	)	)	PUNCT
ejpam-6408	344	9	,	,	PUNCT
ejpam-6408	344	10	if	if	SCONJ
ejpam-6408	344	11	|γ|	|γ|	PROPN
ejpam-6408	344	12	⩽	⩽	NOUN
ejpam-6408	344	13	4	4	NUM
ejpam-6408	344	14	,	,	PUNCT
ejpam-6408	344	15	then	then	ADV
ejpam-6408	344	16	then	then	ADV
ejpam-6408	344	17	the	the	DET
ejpam-6408	344	18	two	two	NUM
ejpam-6408	344	19	approaches	approach	NOUN
ejpam-6408	344	20	of	of	ADP
ejpam-6408	344	21	supra-ϵ-t3space	supra-ϵ-t3space	NOUN
ejpam-6408	344	22	and	and	CCONJ
ejpam-6408	344	23	supra-ϵ-t4	supra-ϵ-t4	NOUN
ejpam-6408	344	24	-	-	PUNCT
ejpam-6408	344	25	space	space	NOUN
ejpam-6408	344	26	are	be	AUX
ejpam-6408	344	27	identical	identical	ADJ
ejpam-6408	344	28	.	.	PUNCT
ejpam-6408	345	1	proof	proof	NOUN
ejpam-6408	345	2	.	.	PUNCT
ejpam-6408	346	1	follows	follow	VERB
ejpam-6408	346	2	from	from	ADP
ejpam-6408	346	3	theorem	theorem	ADJ
ejpam-6408	346	4	17	17	NUM
ejpam-6408	346	5	.	.	PUNCT
ejpam-6408	347	1	remark	remark	PROPN
ejpam-6408	347	2	4	4	NUM
ejpam-6408	347	3	.	.	PUNCT
ejpam-6408	348	1	if	if	SCONJ
ejpam-6408	348	2	|γ|	|γ|	PROPN
ejpam-6408	348	3	>	>	ADP
ejpam-6408	348	4	4	4	NUM
ejpam-6408	348	5	in	in	ADP
ejpam-6408	348	6	theorem	theorem	NOUN
ejpam-6408	348	7	17	17	NUM
ejpam-6408	348	8	,	,	PUNCT
ejpam-6408	348	9	then	then	ADV
ejpam-6408	348	10	the	the	DET
ejpam-6408	348	11	result	result	NOUN
ejpam-6408	348	12	will	will	AUX
ejpam-6408	348	13	not	not	PART
ejpam-6408	348	14	be	be	AUX
ejpam-6408	348	15	achieved	achieve	VERB
ejpam-6408	348	16	,	,	PUNCT
ejpam-6408	348	17	as	as	SCONJ
ejpam-6408	348	18	demonstrated	demonstrate	VERB
ejpam-6408	348	19	in	in	ADP
ejpam-6408	348	20	the	the	DET
ejpam-6408	348	21	following	follow	VERB
ejpam-6408	348	22	example	example	NOUN
ejpam-6408	348	23	.	.	PUNCT
ejpam-6408	349	1	example	example	NOUN
ejpam-6408	350	1	3	3	X
ejpam-6408	350	2	.	.	PUNCT
ejpam-6408	350	3	let	let	VERB
ejpam-6408	350	4	θ	θ	PROPN
ejpam-6408	350	5	=	=	SYM
ejpam-6408	350	6	2γ\{{3	2γ\{{3	PROPN
ejpam-6408	350	7	,	,	PUNCT
ejpam-6408	350	8	4	4	NUM
ejpam-6408	350	9	}	}	PUNCT
ejpam-6408	350	10	,	,	PUNCT
ejpam-6408	350	11	{	{	PUNCT
ejpam-6408	350	12	1	1	NUM
ejpam-6408	350	13	,	,	PUNCT
ejpam-6408	350	14	2	2	NUM
ejpam-6408	350	15	}	}	PUNCT
ejpam-6408	350	16	,	,	PUNCT
ejpam-6408	350	17	{	{	PUNCT
ejpam-6408	350	18	1	1	NUM
ejpam-6408	350	19	}	}	PUNCT
ejpam-6408	350	20	,	,	PUNCT
ejpam-6408	350	21	{	{	PUNCT
ejpam-6408	350	22	3	3	NUM
ejpam-6408	350	23	}	}	PUNCT
ejpam-6408	350	24	}	}	PUNCT
ejpam-6408	350	25	be	be	AUX
ejpam-6408	350	26	an	an	DET
ejpam-6408	350	27	sts	st	NOUN
ejpam-6408	350	28	on	on	ADP
ejpam-6408	350	29	γ	γ	X
ejpam-6408	350	30	=	=	SYM
ejpam-6408	350	31	{	{	PUNCT
ejpam-6408	350	32	1	1	NUM
ejpam-6408	350	33	,	,	PUNCT
ejpam-6408	350	34	2	2	NUM
ejpam-6408	350	35	,	,	PUNCT
ejpam-6408	350	36	3	3	NUM
ejpam-6408	350	37	,	,	PUNCT
ejpam-6408	350	38	4	4	NUM
ejpam-6408	350	39	,	,	PUNCT
ejpam-6408	350	40	5	5	NUM
ejpam-6408	350	41	}	}	PUNCT
ejpam-6408	350	42	.	.	PUNCT
ejpam-6408	351	1	regarding	regard	VERB
ejpam-6408	351	2	the	the	DET
ejpam-6408	351	3	two	two	NUM
ejpam-6408	351	4	disjoint	disjoint	ADJ
ejpam-6408	351	5	supra-ϵ-closed	supra-ϵ-close	VERB
ejpam-6408	351	6	subsets	subset	NOUN
ejpam-6408	351	7	{	{	PUNCT
ejpam-6408	351	8	1	1	NUM
ejpam-6408	351	9	,	,	PUNCT
ejpam-6408	351	10	2	2	NUM
ejpam-6408	351	11	}	}	PUNCT
ejpam-6408	351	12	and	and	CCONJ
ejpam-6408	351	13	{	{	PUNCT
ejpam-6408	351	14	3	3	NUM
ejpam-6408	351	15	,	,	PUNCT
ejpam-6408	351	16	4	4	NUM
ejpam-6408	351	17	}	}	PUNCT
ejpam-6408	351	18	of	of	ADP
ejpam-6408	351	19	γ	γ	NOUN
ejpam-6408	351	20	,	,	PUNCT
ejpam-6408	351	21	then	then	ADV
ejpam-6408	351	22	there	there	PRON
ejpam-6408	351	23	are	be	VERB
ejpam-6408	351	24	not	not	PART
ejpam-6408	351	25	two	two	NUM
ejpam-6408	351	26	disjoint	disjoint	ADJ
ejpam-6408	351	27	supra-ϵ-open	supra-ϵ-open	NOUN
ejpam-6408	351	28	subsets	subset	NOUN
ejpam-6408	351	29	ν1	ν1	NOUN
ejpam-6408	351	30	and	and	CCONJ
ejpam-6408	351	31	ν2	ν2	NOUN
ejpam-6408	351	32	of	of	ADP
ejpam-6408	351	33	γ	γ	PROPN
ejpam-6408	351	34	,	,	PUNCT
ejpam-6408	351	35	containing	contain	VERB
ejpam-6408	351	36	them	they	PRON
ejpam-6408	351	37	,	,	PUNCT
ejpam-6408	351	38	respectively	respectively	ADV
ejpam-6408	351	39	.	.	PUNCT
ejpam-6408	352	1	hence	hence	ADV
ejpam-6408	352	2	,	,	PUNCT
ejpam-6408	352	3	γ	γ	X
ejpam-6408	352	4	is	be	AUX
ejpam-6408	352	5	not	not	PART
ejpam-6408	352	6	supra-ϵ-n	supra-ϵ-n	ADJ
ejpam-6408	352	7	-space	-space	NOUN
ejpam-6408	352	8	.	.	PUNCT
ejpam-6408	353	1	also	also	ADV
ejpam-6408	353	2	,	,	PUNCT
ejpam-6408	353	3	it	it	PRON
ejpam-6408	353	4	is	be	AUX
ejpam-6408	353	5	easy	easy	ADJ
ejpam-6408	353	6	to	to	PART
ejpam-6408	353	7	check	check	VERB
ejpam-6408	353	8	that	that	SCONJ
ejpam-6408	353	9	γ	γ	PROPN
ejpam-6408	353	10	is	be	AUX
ejpam-6408	353	11	supra-ϵ-r	supra-ϵ-r	X
ejpam-6408	353	12	.	.	PUNCT
ejpam-6408	353	13	5	5	NUM
ejpam-6408	353	14	.	.	X
ejpam-6408	353	15	conclusion	conclusion	NOUN
ejpam-6408	353	16	and	and	CCONJ
ejpam-6408	353	17	future	future	ADJ
ejpam-6408	353	18	works	work	NOUN
ejpam-6408	353	19	in	in	ADP
ejpam-6408	353	20	this	this	DET
ejpam-6408	353	21	article	article	NOUN
ejpam-6408	353	22	,	,	PUNCT
ejpam-6408	353	23	we	we	PRON
ejpam-6408	353	24	provide	provide	VERB
ejpam-6408	353	25	new	new	ADJ
ejpam-6408	353	26	versions	version	NOUN
ejpam-6408	353	27	of	of	ADP
ejpam-6408	353	28	supra	supra	ADJ
ejpam-6408	353	29	septation	septation	NOUN
ejpam-6408	353	30	axioms	axiom	NOUN
ejpam-6408	353	31	inspired	inspire	VERB
ejpam-6408	353	32	by	by	ADP
ejpam-6408	353	33	supra-ϵopen	supra-ϵopen	ADJ
ejpam-6408	353	34	sets	set	NOUN
ejpam-6408	353	35	.	.	PUNCT
ejpam-6408	354	1	to	to	PART
ejpam-6408	354	2	name	name	VERB
ejpam-6408	354	3	a	a	DET
ejpam-6408	354	4	few	few	ADJ
ejpam-6408	354	5	:	:	PUNCT
ejpam-6408	354	6	supra-ϵ-t2	supra-ϵ-t2	ADJ
ejpam-6408	354	7	1	1	NUM
ejpam-6408	354	8	2	2	NUM
ejpam-6408	354	9	-space	-space	NOUN
ejpam-6408	354	10	,	,	PUNCT
ejpam-6408	354	11	supra-ϵ-regular	supra-ϵ-regular	NOUN
ejpam-6408	354	12	-	-	PUNCT
ejpam-6408	354	13	space	space	NOUN
ejpam-6408	354	14	,	,	PUNCT
ejpam-6408	354	15	supra-ϵ-normal	supra-ϵ-normal	ADJ
ejpam-6408	354	16	-	-	NOUN
ejpam-6408	354	17	space	space	NOUN
ejpam-6408	354	18	,	,	PUNCT
ejpam-6408	354	19	supra-ϵ-t3	supra-ϵ-t3	NOUN
ejpam-6408	354	20	-	-	PUNCT
ejpam-6408	354	21	space	space	NOUN
ejpam-6408	354	22	,	,	PUNCT
ejpam-6408	354	23	and	and	CCONJ
ejpam-6408	354	24	supra-ϵ-t4	supra-ϵ-t4	NOUN
ejpam-6408	354	25	-	-	PUNCT
ejpam-6408	354	26	space	space	NOUN
ejpam-6408	354	27	.	.	PUNCT
ejpam-6408	355	1	the	the	DET
ejpam-6408	355	2	behavior	behavior	NOUN
ejpam-6408	355	3	of	of	ADP
ejpam-6408	355	4	these	these	DET
ejpam-6408	355	5	concepts	concept	NOUN
ejpam-6408	355	6	with	with	ADP
ejpam-6408	355	7	regard	regard	NOUN
ejpam-6408	355	8	to	to	ADP
ejpam-6408	355	9	particular	particular	ADJ
ejpam-6408	355	10	types	type	NOUN
ejpam-6408	355	11	of	of	ADP
ejpam-6408	355	12	supra	supra	ADJ
ejpam-6408	355	13	functions	function	NOUN
ejpam-6408	355	14	is	be	AUX
ejpam-6408	355	15	also	also	ADV
ejpam-6408	355	16	examined	examine	VERB
ejpam-6408	355	17	.	.	PUNCT
ejpam-6408	356	1	we	we	PRON
ejpam-6408	356	2	also	also	ADV
ejpam-6408	356	3	give	give	VERB
ejpam-6408	356	4	a	a	DET
ejpam-6408	356	5	general	general	ADJ
ejpam-6408	356	6	illustration	illustration	NOUN
ejpam-6408	356	7	of	of	ADP
ejpam-6408	356	8	their	their	PRON
ejpam-6408	356	9	key	key	ADJ
ejpam-6408	356	10	traits	trait	NOUN
ejpam-6408	356	11	and	and	CCONJ
ejpam-6408	356	12	look	look	VERB
ejpam-6408	356	13	at	at	ADP
ejpam-6408	356	14	the	the	DET
ejpam-6408	356	15	prerequisites	prerequisite	NOUN
ejpam-6408	356	16	for	for	ADP
ejpam-6408	356	17	a	a	DET
ejpam-6408	356	18	number	number	NOUN
ejpam-6408	356	19	of	of	ADP
ejpam-6408	356	20	similar	similar	ADJ
ejpam-6408	356	21	links	link	NOUN
ejpam-6408	356	22	between	between	ADP
ejpam-6408	356	23	them	they	PRON
ejpam-6408	356	24	.	.	PUNCT
ejpam-6408	357	1	finally	finally	ADV
ejpam-6408	357	2	,	,	PUNCT
ejpam-6408	357	3	the	the	DET
ejpam-6408	357	4	required	require	VERB
ejpam-6408	357	5	counterexamples	counterexample	NOUN
ejpam-6408	357	6	that	that	PRON
ejpam-6408	357	7	support	support	VERB
ejpam-6408	357	8	our	our	PRON
ejpam-6408	357	9	conclusions	conclusion	NOUN
ejpam-6408	357	10	are	be	AUX
ejpam-6408	357	11	provided	provide	VERB
ejpam-6408	357	12	.	.	PUNCT
ejpam-6408	358	1	the	the	DET
ejpam-6408	358	2	following	follow	VERB
ejpam-6408	358	3	topics	topic	NOUN
ejpam-6408	358	4	could	could	AUX
ejpam-6408	358	5	be	be	AUX
ejpam-6408	358	6	examined	examine	VERB
ejpam-6408	358	7	in	in	ADP
ejpam-6408	358	8	further	further	ADJ
ejpam-6408	358	9	research	research	NOUN
ejpam-6408	358	10	on	on	ADP
ejpam-6408	358	11	the	the	DET
ejpam-6408	358	12	theoretical	theoretical	ADJ
ejpam-6408	358	13	aspects	aspect	NOUN
ejpam-6408	358	14	of	of	ADP
ejpam-6408	358	15	these	these	DET
ejpam-6408	358	16	generalized	generalized	ADJ
ejpam-6408	358	17	notions	notion	NOUN
ejpam-6408	358	18	based	base	VERB
ejpam-6408	358	19	on	on	ADP
ejpam-6408	358	20	the	the	DET
ejpam-6408	358	21	particular	particular	ADJ
ejpam-6408	358	22	methodologies	methodology	NOUN
ejpam-6408	358	23	discussed	discuss	VERB
ejpam-6408	358	24	in	in	ADP
ejpam-6408	358	25	this	this	DET
ejpam-6408	358	26	paper	paper	NOUN
ejpam-6408	358	27	:	:	PUNCT
ejpam-6408	358	28	introducing	introduce	VERB
ejpam-6408	358	29	more	more	ADJ
ejpam-6408	358	30	investigation	investigation	NOUN
ejpam-6408	358	31	of	of	ADP
ejpam-6408	358	32	septarian	septarian	ADJ
ejpam-6408	358	33	axioms	axioms	ADJ
ejpam-6408	358	34	term	term	NOUN
ejpam-6408	358	35	in	in	ADP
ejpam-6408	358	36	supra	supra	PROPN
ejpam-6408	358	37	ϵ-open	ϵ-open	PROPN
ejpam-6408	358	38	sets	set	NOUN
ejpam-6408	358	39	by	by	ADP
ejpam-6408	358	40	using	use	VERB
ejpam-6408	358	41	the	the	DET
ejpam-6408	358	42	ideal	ideal	ADJ
ejpam-6408	358	43	notions	notion	NOUN
ejpam-6408	358	44	.	.	PUNCT
ejpam-6408	359	1	also	also	ADV
ejpam-6408	359	2	,	,	PUNCT
ejpam-6408	359	3	presenting	present	VERB
ejpam-6408	359	4	these	these	DET
ejpam-6408	359	5	notion	notion	NOUN
ejpam-6408	359	6	to	to	ADP
ejpam-6408	359	7	soft	soft	ADJ
ejpam-6408	359	8	topological	topological	ADJ
ejpam-6408	359	9	spaces	space	NOUN
ejpam-6408	359	10	[	[	X
ejpam-6408	359	11	22	22	NUM
ejpam-6408	359	12	]	]	PUNCT
ejpam-6408	359	13	.	.	PUNCT
ejpam-6408	360	1	moreover	moreover	ADV
ejpam-6408	360	2	,	,	PUNCT
ejpam-6408	360	3	using	use	VERB
ejpam-6408	360	4	fuzzy	fuzzy	ADJ
ejpam-6408	360	5	supra	supra	PROPN
ejpam-6408	360	6	soft	soft	ADJ
ejpam-6408	360	7	topological	topological	ADJ
ejpam-6408	360	8	spaces	space	NOUN
ejpam-6408	360	9	to	to	PART
ejpam-6408	360	10	generalize	generalize	VERB
ejpam-6408	360	11	these	these	DET
ejpam-6408	360	12	notions	notion	NOUN
ejpam-6408	360	13	[	[	X
ejpam-6408	360	14	61	61	NUM
ejpam-6408	360	15	,	,	PUNCT
ejpam-6408	360	16	62	62	NUM
ejpam-6408	360	17	]	]	PUNCT
ejpam-6408	360	18	.	.	PUNCT
ejpam-6408	361	1	conflicts	conflict	NOUN
ejpam-6408	361	2	of	of	ADP
ejpam-6408	361	3	interest	interest	NOUN
ejpam-6408	361	4	the	the	DET
ejpam-6408	361	5	authors	author	NOUN
ejpam-6408	361	6	of	of	ADP
ejpam-6408	361	7	this	this	DET
ejpam-6408	361	8	work	work	NOUN
ejpam-6408	361	9	state	state	NOUN
ejpam-6408	361	10	that	that	SCONJ
ejpam-6408	361	11	they	they	PRON
ejpam-6408	361	12	have	have	VERB
ejpam-6408	361	13	no	no	DET
ejpam-6408	361	14	conflicting	conflict	VERB
ejpam-6408	361	15	interests	interest	NOUN
ejpam-6408	361	16	with	with	ADP
ejpam-6408	361	17	regard	regard	NOUN
ejpam-6408	361	18	to	to	ADP
ejpam-6408	361	19	its	its	PRON
ejpam-6408	361	20	publication	publication	NOUN
ejpam-6408	361	21	.	.	PUNCT
ejpam-6408	362	1	m.	m.	NOUN
ejpam-6408	362	2	aldawood	aldawood	PROPN
ejpam-6408	362	3	et	et	PROPN
ejpam-6408	362	4	al	al	PROPN
ejpam-6408	362	5	.	.	PUNCT
ejpam-6408	362	6	/	/	SYM
ejpam-6408	362	7	eur	eur	PROPN
ejpam-6408	362	8	.	.	PUNCT
ejpam-6408	363	1	j.	j.	PROPN
ejpam-6408	363	2	pure	pure	PROPN
ejpam-6408	363	3	appl	appl	PROPN
ejpam-6408	363	4	.	.	PROPN
ejpam-6408	363	5	math	math	PROPN
ejpam-6408	363	6	,	,	PUNCT
ejpam-6408	363	7	18	18	NUM
ejpam-6408	363	8	(	(	PUNCT
ejpam-6408	363	9	3	3	NUM
ejpam-6408	363	10	)	)	PUNCT
ejpam-6408	363	11	(	(	PUNCT
ejpam-6408	363	12	2025	2025	NUM
ejpam-6408	363	13	)	)	PUNCT
ejpam-6408	363	14	,	,	PUNCT
ejpam-6408	363	15	6408	6408	NUM
ejpam-6408	363	16	13	13	NUM
ejpam-6408	363	17	of	of	ADP
ejpam-6408	363	18	16	16	NUM
ejpam-6408	363	19	authors	author	NOUN
ejpam-6408	363	20	contributions	contribution	NOUN
ejpam-6408	363	21	all	all	DET
ejpam-6408	363	22	authors	author	NOUN
ejpam-6408	363	23	made	make	VERB
ejpam-6408	363	24	equal	equal	ADJ
ejpam-6408	363	25	contributions	contribution	NOUN
ejpam-6408	363	26	.	.	PUNCT
ejpam-6408	364	1	acknowledgements	acknowledgement	NOUN
ejpam-6408	364	2	the	the	DET
ejpam-6408	364	3	authors	author	NOUN
ejpam-6408	364	4	extend	extend	VERB
ejpam-6408	364	5	their	their	PRON
ejpam-6408	364	6	appreciation	appreciation	NOUN
ejpam-6408	364	7	to	to	ADP
ejpam-6408	364	8	the	the	DET
ejpam-6408	364	9	deanship	deanship	NOUN
ejpam-6408	364	10	of	of	ADP
ejpam-6408	364	11	scientific	scientific	ADJ
ejpam-6408	364	12	research	research	NOUN
ejpam-6408	364	13	at	at	ADP
ejpam-6408	364	14	northern	northern	ADJ
ejpam-6408	364	15	border	border	NOUN
ejpam-6408	364	16	university	university	PROPN
ejpam-6408	364	17	,	,	PUNCT
ejpam-6408	364	18	arar	arar	PROPN
ejpam-6408	364	19	,	,	PUNCT
ejpam-6408	364	20	ksa	ksa	PROPN
ejpam-6408	364	21	for	for	ADP
ejpam-6408	364	22	funding	fund	VERB
ejpam-6408	364	23	this	this	DET
ejpam-6408	364	24	research	research	NOUN
ejpam-6408	364	25	work	work	NOUN
ejpam-6408	364	26	through	through	ADP
ejpam-6408	364	27	the	the	DET
ejpam-6408	364	28	project	project	NOUN
ejpam-6408	364	29	number	number	NOUN
ejpam-6408	364	30	”	"	PUNCT
ejpam-6408	364	31	nbu	nbu	NOUN
ejpam-6408	364	32	-	-	PUNCT
ejpam-6408	364	33	ffr-2025	ffr-2025	NOUN
ejpam-6408	364	34	-	-	PUNCT
ejpam-6408	364	35	2941	2941	NUM
ejpam-6408	364	36	-	-	SYM
ejpam-6408	364	37	01	01	NUM
ejpam-6408	364	38	”	"	PUNCT
ejpam-6408	364	39	.	.	PUNCT
ejpam-6408	365	1	also	also	ADV
ejpam-6408	365	2	,	,	PUNCT
ejpam-6408	365	3	this	this	DET
ejpam-6408	365	4	study	study	NOUN
ejpam-6408	365	5	is	be	AUX
ejpam-6408	365	6	supported	support	VERB
ejpam-6408	365	7	via	via	ADP
ejpam-6408	365	8	funding	funding	NOUN
ejpam-6408	365	9	from	from	ADP
ejpam-6408	365	10	prince	prince	PROPN
ejpam-6408	365	11	sattam	sattam	PROPN
ejpam-6408	365	12	bin	bin	PROPN
ejpam-6408	365	13	abdulaziz	abdulaziz	PROPN
ejpam-6408	365	14	university	university	PROPN
ejpam-6408	365	15	project	project	NOUN
ejpam-6408	365	16	number	number	NOUN
ejpam-6408	365	17	(	(	PUNCT
ejpam-6408	365	18	psau/2025	psau/2025	NOUN
ejpam-6408	365	19	/	/	SYM
ejpam-6408	365	20	r/1446	r/1446	PROPN
ejpam-6408	365	21	)	)	PUNCT
ejpam-6408	365	22	.	.	PUNCT
ejpam-6408	366	1	references	reference	NOUN
ejpam-6408	366	2	[	[	X
ejpam-6408	366	3	1	1	NUM
ejpam-6408	366	4	]	]	X
ejpam-6408	366	5	n.	n.	PROPN
ejpam-6408	366	6	levine	levine	PROPN
ejpam-6408	366	7	.	.	PUNCT
ejpam-6408	367	1	semi	semi	ADJ
ejpam-6408	367	2	-	-	ADJ
ejpam-6408	367	3	open	open	ADJ
ejpam-6408	367	4	sets	set	NOUN
ejpam-6408	367	5	and	and	CCONJ
ejpam-6408	367	6	semi	semi	ADJ
ejpam-6408	367	7	-	-	NOUN
ejpam-6408	367	8	continuity	continuity	NOUN
ejpam-6408	367	9	in	in	ADP
ejpam-6408	367	10	topological	topological	ADJ
ejpam-6408	367	11	spaces	space	NOUN
ejpam-6408	367	12	.	.	PUNCT
ejpam-6408	368	1	american	american	PROPN
ejpam-6408	368	2	mathematical	mathematical	PROPN
ejpam-6408	368	3	monthly	monthly	ADV
ejpam-6408	368	4	,	,	PUNCT
ejpam-6408	368	5	70(1):36–41	70(1):36–41	NUM
ejpam-6408	368	6	,	,	PUNCT
ejpam-6408	368	7	1963	1963	NUM
ejpam-6408	368	8	.	.	PUNCT
ejpam-6408	369	1	[	[	X
ejpam-6408	369	2	2	2	NUM
ejpam-6408	369	3	]	]	X
ejpam-6408	369	4	o.	o.	PROPN
ejpam-6408	369	5	njastad	njastad	PROPN
ejpam-6408	369	6	.	.	PUNCT
ejpam-6408	370	1	on	on	ADP
ejpam-6408	370	2	some	some	DET
ejpam-6408	370	3	classes	class	NOUN
ejpam-6408	370	4	of	of	ADP
ejpam-6408	370	5	nearly	nearly	ADV
ejpam-6408	370	6	open	open	ADJ
ejpam-6408	370	7	sets	set	NOUN
ejpam-6408	370	8	.	.	PUNCT
ejpam-6408	371	1	pacific	pacific	PROPN
ejpam-6408	371	2	journal	journal	PROPN
ejpam-6408	371	3	of	of	ADP
ejpam-6408	371	4	mathematics	mathematic	NOUN
ejpam-6408	371	5	,	,	PUNCT
ejpam-6408	371	6	15(3):961–970	15(3):961–970	PROPN
ejpam-6408	371	7	,	,	PUNCT
ejpam-6408	371	8	1965	1965	NUM
ejpam-6408	371	9	.	.	PUNCT
ejpam-6408	372	1	[	[	X
ejpam-6408	372	2	3	3	X
ejpam-6408	372	3	]	]	PUNCT
ejpam-6408	372	4	a.	a.	NOUN
ejpam-6408	372	5	mashhour	mashhour	PROPN
ejpam-6408	372	6	,	,	PUNCT
ejpam-6408	372	7	m.	m.	PROPN
ejpam-6408	372	8	abd	abd	PROPN
ejpam-6408	372	9	el	el	PROPN
ejpam-6408	372	10	-	-	PROPN
ejpam-6408	372	11	monsef	monsef	ADJ
ejpam-6408	372	12	,	,	PUNCT
ejpam-6408	372	13	and	and	CCONJ
ejpam-6408	372	14	s.	s.	PROPN
ejpam-6408	372	15	el	el	PROPN
ejpam-6408	372	16	-	-	PROPN
ejpam-6408	372	17	deeb	deeb	PROPN
ejpam-6408	372	18	.	.	PUNCT
ejpam-6408	373	1	on	on	ADP
ejpam-6408	373	2	precontinuous	precontinuous	ADJ
ejpam-6408	373	3	and	and	CCONJ
ejpam-6408	373	4	weak	weak	ADJ
ejpam-6408	373	5	precontinuous	precontinuous	ADJ
ejpam-6408	373	6	mappings	mapping	NOUN
ejpam-6408	373	7	.	.	PUNCT
ejpam-6408	374	1	proceedings	proceeding	NOUN
ejpam-6408	374	2	of	of	ADP
ejpam-6408	374	3	the	the	DET
ejpam-6408	374	4	mathematical	mathematical	ADJ
ejpam-6408	374	5	and	and	CCONJ
ejpam-6408	374	6	physical	physical	ADJ
ejpam-6408	374	7	society	society	NOUN
ejpam-6408	374	8	,	,	PUNCT
ejpam-6408	374	9	53:47–53	53:47–53	NUM
ejpam-6408	374	10	,	,	PUNCT
ejpam-6408	374	11	1982	1982	NUM
ejpam-6408	374	12	.	.	PUNCT
ejpam-6408	375	1	[	[	X
ejpam-6408	375	2	4	4	X
ejpam-6408	375	3	]	]	PUNCT
ejpam-6408	375	4	m.	m.	NOUN
ejpam-6408	375	5	abd	abd	PROPN
ejpam-6408	375	6	el	el	PROPN
ejpam-6408	375	7	-	-	PROPN
ejpam-6408	375	8	monsef	monsef	PROPN
ejpam-6408	375	9	,	,	PUNCT
ejpam-6408	375	10	s.	s.	PROPN
ejpam-6408	375	11	el	el	PROPN
ejpam-6408	375	12	-	-	PROPN
ejpam-6408	375	13	deeb	deeb	PROPN
ejpam-6408	375	14	,	,	PUNCT
ejpam-6408	375	15	and	and	CCONJ
ejpam-6408	375	16	r.	r.	PROPN
ejpam-6408	375	17	mahmoud	mahmoud	PROPN
ejpam-6408	375	18	.	.	PUNCT
ejpam-6408	376	1	β	β	X
ejpam-6408	376	2	-	-	ADJ
ejpam-6408	376	3	open	open	ADJ
ejpam-6408	376	4	sets	set	NOUN
ejpam-6408	376	5	and	and	CCONJ
ejpam-6408	376	6	β	β	ADJ
ejpam-6408	376	7	-	-	ADJ
ejpam-6408	376	8	continuous	continuous	ADJ
ejpam-6408	376	9	mappings	mapping	NOUN
ejpam-6408	376	10	.	.	PUNCT
ejpam-6408	377	1	bulletin	bulletin	NOUN
ejpam-6408	377	2	of	of	ADP
ejpam-6408	377	3	the	the	DET
ejpam-6408	377	4	faculty	faculty	NOUN
ejpam-6408	377	5	of	of	ADP
ejpam-6408	377	6	science	science	NOUN
ejpam-6408	377	7	,	,	PUNCT
ejpam-6408	377	8	assiut	assiut	NOUN
ejpam-6408	377	9	university	university	NOUN
ejpam-6408	377	10	,	,	PUNCT
ejpam-6408	377	11	12(1):77–90	12(1):77–90	NUM
ejpam-6408	377	12	,	,	PUNCT
ejpam-6408	377	13	1983	1983	NUM
ejpam-6408	377	14	.	.	PUNCT
ejpam-6408	378	1	[	[	X
ejpam-6408	378	2	5	5	X
ejpam-6408	378	3	]	]	PUNCT
ejpam-6408	378	4	d.	d.	PROPN
ejpam-6408	378	5	andrijevic	andrijevic	VERB
ejpam-6408	378	6	.	.	PUNCT
ejpam-6408	379	1	on	on	ADP
ejpam-6408	379	2	b	b	X
ejpam-6408	379	3	-	-	PUNCT
ejpam-6408	379	4	open	open	ADJ
ejpam-6408	379	5	sets	set	NOUN
ejpam-6408	379	6	.	.	PUNCT
ejpam-6408	380	1	matematicki	matematicki	NOUN
ejpam-6408	380	2	vesnik	vesnik	PROPN
ejpam-6408	380	3	,	,	PUNCT
ejpam-6408	380	4	48:59–64	48:59–64	PROPN
ejpam-6408	380	5	,	,	PUNCT
ejpam-6408	380	6	1996	1996	NUM
ejpam-6408	380	7	.	.	PUNCT
ejpam-6408	381	1	[	[	X
ejpam-6408	381	2	6	6	NUM
ejpam-6408	381	3	]	]	PUNCT
ejpam-6408	381	4	j.	j.	PROPN
ejpam-6408	381	5	dontchev	dontchev	PROPN
ejpam-6408	381	6	and	and	CCONJ
ejpam-6408	381	7	m.	m.	PROPN
ejpam-6408	381	8	przemski	przemski	PROPN
ejpam-6408	381	9	.	.	PUNCT
ejpam-6408	382	1	on	on	ADP
ejpam-6408	382	2	the	the	DET
ejpam-6408	382	3	various	various	ADJ
ejpam-6408	382	4	decompositions	decomposition	NOUN
ejpam-6408	382	5	of	of	ADP
ejpam-6408	382	6	continuous	continuous	ADJ
ejpam-6408	382	7	and	and	CCONJ
ejpam-6408	382	8	some	some	DET
ejpam-6408	382	9	weakly	weakly	ADJ
ejpam-6408	382	10	continuous	continuous	ADJ
ejpam-6408	382	11	functions	function	NOUN
ejpam-6408	382	12	.	.	PUNCT
ejpam-6408	383	1	acta	acta	PROPN
ejpam-6408	383	2	mathematica	mathematica	PROPN
ejpam-6408	383	3	hungarica	hungarica	PROPN
ejpam-6408	383	4	,	,	PUNCT
ejpam-6408	383	5	71(1	71(1	NOUN
ejpam-6408	383	6	-	-	SYM
ejpam-6408	383	7	2):109–120	2):109–120	NUM
ejpam-6408	383	8	,	,	PUNCT
ejpam-6408	383	9	1996	1996	NUM
ejpam-6408	383	10	.	.	PUNCT
ejpam-6408	384	1	[	[	X
ejpam-6408	384	2	7	7	X
ejpam-6408	384	3	]	]	PUNCT
ejpam-6408	384	4	z.	z.	PROPN
ejpam-6408	384	5	piotrowski	piotrowski	PROPN
ejpam-6408	384	6	.	.	PUNCT
ejpam-6408	385	1	a	a	DET
ejpam-6408	385	2	survey	survey	NOUN
ejpam-6408	385	3	of	of	ADP
ejpam-6408	385	4	results	result	NOUN
ejpam-6408	385	5	concerning	concern	VERB
ejpam-6408	385	6	generalized	generalized	ADJ
ejpam-6408	385	7	continuity	continuity	NOUN
ejpam-6408	385	8	on	on	ADP
ejpam-6408	385	9	topological	topological	ADJ
ejpam-6408	385	10	spaces	space	NOUN
ejpam-6408	385	11	.	.	PUNCT
ejpam-6408	386	1	acta	acta	PROPN
ejpam-6408	386	2	mathematica	mathematica	PROPN
ejpam-6408	386	3	universitatis	universitatis	PROPN
ejpam-6408	386	4	comenianae	comenianae	PROPN
ejpam-6408	386	5	,	,	PUNCT
ejpam-6408	386	6	52:91–110	52:91–110	NUM
ejpam-6408	386	7	,	,	PUNCT
ejpam-6408	386	8	1987	1987	NUM
ejpam-6408	386	9	.	.	PUNCT
ejpam-6408	387	1	[	[	X
ejpam-6408	387	2	8	8	NUM
ejpam-6408	387	3	]	]	PUNCT
ejpam-6408	387	4	k.	k.	PROPN
ejpam-6408	387	5	r.	r.	PROPN
ejpam-6408	387	6	gentry	gentry	PROPN
ejpam-6408	387	7	and	and	CCONJ
ejpam-6408	387	8	h.	h.	PROPN
ejpam-6408	387	9	b.	b.	PROPN
ejpam-6408	387	10	hoyle	hoyle	PROPN
ejpam-6408	387	11	,	,	PUNCT
ejpam-6408	387	12	iii	iii	X
ejpam-6408	387	13	.	.	PUNCT
ejpam-6408	387	14	somewhat	somewhat	ADV
ejpam-6408	387	15	continuous	continuous	ADJ
ejpam-6408	387	16	functions	function	NOUN
ejpam-6408	387	17	.	.	PUNCT
ejpam-6408	388	1	czechoslovak	czechoslovak	ADJ
ejpam-6408	388	2	mathematical	mathematical	PROPN
ejpam-6408	388	3	journal	journal	PROPN
ejpam-6408	388	4	,	,	PUNCT
ejpam-6408	388	5	21:5–12	21:5–12	NUM
ejpam-6408	388	6	,	,	PUNCT
ejpam-6408	388	7	1971	1971	NUM
ejpam-6408	388	8	.	.	PUNCT
ejpam-6408	389	1	[	[	X
ejpam-6408	389	2	9	9	NUM
ejpam-6408	389	3	]	]	X
ejpam-6408	389	4	o.	o.	PROPN
ejpam-6408	389	5	njastad	njastad	PROPN
ejpam-6408	389	6	.	.	PUNCT
ejpam-6408	390	1	on	on	ADP
ejpam-6408	390	2	some	some	DET
ejpam-6408	390	3	classes	class	NOUN
ejpam-6408	390	4	of	of	ADP
ejpam-6408	390	5	nearly	nearly	ADV
ejpam-6408	390	6	open	open	ADJ
ejpam-6408	390	7	sets	set	NOUN
ejpam-6408	390	8	.	.	PUNCT
ejpam-6408	391	1	pacific	pacific	PROPN
ejpam-6408	391	2	journal	journal	PROPN
ejpam-6408	391	3	of	of	ADP
ejpam-6408	391	4	mathematics	mathematic	NOUN
ejpam-6408	391	5	,	,	PUNCT
ejpam-6408	391	6	15:961–970	15:961–970	PROPN
ejpam-6408	391	7	,	,	PUNCT
ejpam-6408	391	8	1965	1965	NUM
ejpam-6408	391	9	.	.	PUNCT
ejpam-6408	392	1	[	[	X
ejpam-6408	392	2	10	10	NUM
ejpam-6408	392	3	]	]	X
ejpam-6408	392	4	c.	c.	PROPN
ejpam-6408	392	5	c.	c.	PROPN
ejpam-6408	392	6	pugh	pugh	PROPN
ejpam-6408	392	7	.	.	PUNCT
ejpam-6408	393	1	real	real	ADJ
ejpam-6408	393	2	mathematical	mathematical	ADJ
ejpam-6408	393	3	analysis	analysis	NOUN
ejpam-6408	393	4	.	.	PUNCT
ejpam-6408	394	1	springer	springer	NOUN
ejpam-6408	394	2	science	science	NOUN
ejpam-6408	394	3	and	and	CCONJ
ejpam-6408	394	4	business	business	NOUN
ejpam-6408	394	5	media	medium	NOUN
ejpam-6408	394	6	,	,	PUNCT
ejpam-6408	394	7	2003	2003	NUM
ejpam-6408	394	8	.	.	PUNCT
ejpam-6408	395	1	[	[	X
ejpam-6408	395	2	11	11	NUM
ejpam-6408	395	3	]	]	PUNCT
ejpam-6408	395	4	t.	t.	PROPN
ejpam-6408	395	5	m.	m.	PROPN
ejpam-6408	395	6	al	al	PROPN
ejpam-6408	395	7	-	-	PUNCT
ejpam-6408	395	8	shami	shami	PROPN
ejpam-6408	395	9	.	.	PUNCT
ejpam-6408	396	1	somewhere	somewhere	ADV
ejpam-6408	396	2	dense	dense	ADJ
ejpam-6408	396	3	sets	set	NOUN
ejpam-6408	396	4	and	and	CCONJ
ejpam-6408	396	5	st1	st1	PROPN
ejpam-6408	396	6	spaces	space	NOUN
ejpam-6408	396	7	.	.	PUNCT
ejpam-6408	397	1	punjab	punjab	PROPN
ejpam-6408	397	2	university	university	PROPN
ejpam-6408	397	3	journal	journal	NOUN
ejpam-6408	397	4	of	of	ADP
ejpam-6408	397	5	mathematics	mathematic	NOUN
ejpam-6408	397	6	,	,	PUNCT
ejpam-6408	397	7	49(2):101–111	49(2):101–111	PROPN
ejpam-6408	397	8	,	,	PUNCT
ejpam-6408	397	9	2017	2017	NUM
ejpam-6408	397	10	.	.	PUNCT
ejpam-6408	398	1	[	[	X
ejpam-6408	398	2	12	12	NUM
ejpam-6408	398	3	]	]	PUNCT
ejpam-6408	398	4	m.	m.	NOUN
ejpam-6408	398	5	h.	h.	PROPN
ejpam-6408	398	6	alqahtani	alqahtani	PROPN
ejpam-6408	398	7	.	.	PUNCT
ejpam-6408	399	1	f	f	X
ejpam-6408	399	2	-	-	PUNCT
ejpam-6408	399	3	open	open	ADJ
ejpam-6408	399	4	and	and	CCONJ
ejpam-6408	399	5	f	f	X
ejpam-6408	399	6	-	-	PUNCT
ejpam-6408	399	7	closed	close	VERB
ejpam-6408	399	8	sets	set	NOUN
ejpam-6408	399	9	in	in	ADP
ejpam-6408	399	10	topological	topological	ADJ
ejpam-6408	399	11	spaces	space	NOUN
ejpam-6408	399	12	.	.	PUNCT
ejpam-6408	400	1	european	european	ADJ
ejpam-6408	400	2	journal	journal	PROPN
ejpam-6408	400	3	of	of	ADP
ejpam-6408	400	4	pure	pure	ADJ
ejpam-6408	400	5	and	and	CCONJ
ejpam-6408	400	6	applied	applied	ADJ
ejpam-6408	400	7	mathematics	mathematic	NOUN
ejpam-6408	400	8	,	,	PUNCT
ejpam-6408	400	9	16:819–832	16:819–832	NUM
ejpam-6408	400	10	,	,	PUNCT
ejpam-6408	400	11	2023	2023	NUM
ejpam-6408	400	12	.	.	PUNCT
ejpam-6408	401	1	[	[	X
ejpam-6408	401	2	13	13	NUM
ejpam-6408	401	3	]	]	PUNCT
ejpam-6408	401	4	m.	m.	NOUN
ejpam-6408	401	5	h.	h.	PROPN
ejpam-6408	401	6	alqahtani	alqahtani	PROPN
ejpam-6408	401	7	and	and	CCONJ
ejpam-6408	401	8	a.	a.	NOUN
ejpam-6408	401	9	m.	m.	PROPN
ejpam-6408	401	10	abd	abd	PROPN
ejpam-6408	401	11	el	el	PROPN
ejpam-6408	401	12	-	-	PROPN
ejpam-6408	401	13	latif	latif	PROPN
ejpam-6408	401	14	.	.	PUNCT
ejpam-6408	402	1	separation	separation	NOUN
ejpam-6408	402	2	axioms	axiom	NOUN
ejpam-6408	402	3	via	via	ADP
ejpam-6408	402	4	novel	novel	ADJ
ejpam-6408	402	5	operators	operator	NOUN
ejpam-6408	402	6	in	in	ADP
ejpam-6408	402	7	the	the	DET
ejpam-6408	402	8	frame	frame	NOUN
ejpam-6408	402	9	of	of	ADP
ejpam-6408	402	10	topological	topological	ADJ
ejpam-6408	402	11	spaces	space	NOUN
ejpam-6408	402	12	and	and	CCONJ
ejpam-6408	402	13	applications	application	NOUN
ejpam-6408	402	14	.	.	PUNCT
ejpam-6408	403	1	aims	aim	VERB
ejpam-6408	403	2	mathematics	mathematic	NOUN
ejpam-6408	403	3	,	,	PUNCT
ejpam-6408	403	4	9(6):14213–14227	9(6):14213–14227	NUM
ejpam-6408	403	5	,	,	PUNCT
ejpam-6408	403	6	2024	2024	NUM
ejpam-6408	403	7	.	.	PUNCT
ejpam-6408	404	1	[	[	X
ejpam-6408	404	2	14	14	NUM
ejpam-6408	404	3	]	]	X
ejpam-6408	404	4	o.	o.	NOUN
ejpam-6408	404	5	alghamdi	alghamdi	NOUN
ejpam-6408	404	6	,	,	PUNCT
ejpam-6408	404	7	ahmad	ahmad	PROPN
ejpam-6408	404	8	al	al	PROPN
ejpam-6408	404	9	-	-	PUNCT
ejpam-6408	404	10	omari	omari	PROPN
ejpam-6408	404	11	,	,	PUNCT
ejpam-6408	404	12	and	and	CCONJ
ejpam-6408	404	13	m.	m.	PROPN
ejpam-6408	404	14	h.	h.	PROPN
ejpam-6408	404	15	alqahtani	alqahtani	PROPN
ejpam-6408	404	16	.	.	PUNCT
ejpam-6408	405	1	novel	novel	ADJ
ejpam-6408	405	2	operators	operator	NOUN
ejpam-6408	405	3	in	in	ADP
ejpam-6408	405	4	the	the	DET
ejpam-6408	405	5	frame	frame	NOUN
ejpam-6408	405	6	of	of	ADP
ejpam-6408	405	7	primal	primal	ADJ
ejpam-6408	405	8	topological	topological	ADJ
ejpam-6408	405	9	spaces	space	NOUN
ejpam-6408	405	10	.	.	PUNCT
ejpam-6408	406	1	aims	aim	VERB
ejpam-6408	406	2	mathematics	mathematic	NOUN
ejpam-6408	406	3	,	,	PUNCT
ejpam-6408	406	4	9(9):25792–25808	9(9):25792–25808	NUM
ejpam-6408	406	5	,	,	PUNCT
ejpam-6408	406	6	2024	2024	NUM
ejpam-6408	406	7	.	.	PUNCT
ejpam-6408	407	1	[	[	X
ejpam-6408	407	2	15	15	NUM
ejpam-6408	407	3	]	]	X
ejpam-6408	407	4	a.	a.	NOUN
ejpam-6408	407	5	s.	s.	PROPN
ejpam-6408	407	6	mashhour	mashhour	PROPN
ejpam-6408	407	7	,	,	PUNCT
ejpam-6408	407	8	a.	a.	PROPN
ejpam-6408	407	9	a.	a.	PROPN
ejpam-6408	407	10	allam	allam	PROPN
ejpam-6408	407	11	,	,	PUNCT
ejpam-6408	407	12	f.	f.	PROPN
ejpam-6408	407	13	s.	s.	PROPN
ejpam-6408	407	14	mahmoud	mahmoud	PROPN
ejpam-6408	407	15	,	,	PUNCT
ejpam-6408	407	16	and	and	CCONJ
ejpam-6408	407	17	f.	f.	PROPN
ejpam-6408	407	18	h.	h.	PROPN
ejpam-6408	407	19	kheder	kheder	PROPN
ejpam-6408	407	20	.	.	PUNCT
ejpam-6408	408	1	on	on	ADP
ejpam-6408	408	2	supra	supra	PROPN
ejpam-6408	408	3	topological	topological	ADJ
ejpam-6408	408	4	spaces	space	NOUN
ejpam-6408	408	5	.	.	PUNCT
ejpam-6408	409	1	indian	indian	ADJ
ejpam-6408	409	2	journal	journal	PROPN
ejpam-6408	409	3	of	of	ADP
ejpam-6408	409	4	pure	pure	ADJ
ejpam-6408	409	5	and	and	CCONJ
ejpam-6408	409	6	applied	applied	ADJ
ejpam-6408	409	7	mathematics	mathematic	NOUN
ejpam-6408	409	8	,	,	PUNCT
ejpam-6408	409	9	pages	page	NOUN
ejpam-6408	409	10	502–510	502–510	NUM
ejpam-6408	409	11	,	,	PUNCT
ejpam-6408	409	12	1983	1983	NUM
ejpam-6408	409	13	.	.	PUNCT
ejpam-6408	410	1	m.	m.	NOUN
ejpam-6408	410	2	aldawood	aldawood	PROPN
ejpam-6408	410	3	et	et	PROPN
ejpam-6408	410	4	al	al	PROPN
ejpam-6408	410	5	.	.	PUNCT
ejpam-6408	410	6	/	/	SYM
ejpam-6408	410	7	eur	eur	PROPN
ejpam-6408	410	8	.	.	PUNCT
ejpam-6408	411	1	j.	j.	PROPN
ejpam-6408	411	2	pure	pure	PROPN
ejpam-6408	411	3	appl	appl	PROPN
ejpam-6408	411	4	.	.	PROPN
ejpam-6408	411	5	math	math	PROPN
ejpam-6408	411	6	,	,	PUNCT
ejpam-6408	411	7	18	18	NUM
ejpam-6408	411	8	(	(	PUNCT
ejpam-6408	411	9	3	3	NUM
ejpam-6408	411	10	)	)	PUNCT
ejpam-6408	411	11	(	(	PUNCT
ejpam-6408	411	12	2025	2025	NUM
ejpam-6408	411	13	)	)	PUNCT
ejpam-6408	411	14	,	,	PUNCT
ejpam-6408	411	15	6408	6408	NUM
ejpam-6408	411	16	14	14	NUM
ejpam-6408	411	17	of	of	ADP
ejpam-6408	411	18	16	16	NUM
ejpam-6408	412	1	[	[	X
ejpam-6408	412	2	16	16	NUM
ejpam-6408	412	3	]	]	PUNCT
ejpam-6408	412	4	t.	t.	PROPN
ejpam-6408	412	5	al	al	PROPN
ejpam-6408	412	6	-	-	PUNCT
ejpam-6408	412	7	shami	shami	PROPN
ejpam-6408	412	8	.	.	PUNCT
ejpam-6408	413	1	on	on	ADP
ejpam-6408	413	2	supra	supra	PROPN
ejpam-6408	413	3	semi	semi	ADV
ejpam-6408	413	4	open	open	ADJ
ejpam-6408	413	5	sets	set	NOUN
ejpam-6408	413	6	and	and	CCONJ
ejpam-6408	413	7	some	some	DET
ejpam-6408	413	8	applications	application	NOUN
ejpam-6408	413	9	on	on	ADP
ejpam-6408	413	10	topological	topological	ADJ
ejpam-6408	413	11	spaces	space	NOUN
ejpam-6408	413	12	.	.	PUNCT
ejpam-6408	414	1	journal	journal	NOUN
ejpam-6408	414	2	of	of	ADP
ejpam-6408	414	3	advanced	advanced	ADJ
ejpam-6408	414	4	studies	study	NOUN
ejpam-6408	414	5	in	in	ADP
ejpam-6408	414	6	topology	topology	NOUN
ejpam-6408	414	7	,	,	PUNCT
ejpam-6408	414	8	8(2):144–153	8(2):144–153	NOUN
ejpam-6408	414	9	,	,	PUNCT
ejpam-6408	414	10	2017	2017	NUM
ejpam-6408	414	11	.	.	PUNCT
ejpam-6408	415	1	[	[	X
ejpam-6408	415	2	17	17	NUM
ejpam-6408	415	3	]	]	PUNCT
ejpam-6408	415	4	m.	m.	PROPN
ejpam-6408	415	5	e.	e.	PROPN
ejpam-6408	415	6	el	el	PROPN
ejpam-6408	415	7	-	-	PROPN
ejpam-6408	415	8	shafei	shafei	PROPN
ejpam-6408	415	9	,	,	PUNCT
ejpam-6408	415	10	m.	m.	NOUN
ejpam-6408	415	11	abo	abo	NOUN
ejpam-6408	415	12	-	-	PUNCT
ejpam-6408	415	13	elhamayel	elhamayel	NOUN
ejpam-6408	415	14	,	,	PUNCT
ejpam-6408	415	15	and	and	CCONJ
ejpam-6408	415	16	t.	t.	PROPN
ejpam-6408	415	17	m.	m.	PROPN
ejpam-6408	415	18	al	al	PROPN
ejpam-6408	415	19	-	-	PUNCT
ejpam-6408	415	20	shami	shami	PROPN
ejpam-6408	415	21	.	.	PUNCT
ejpam-6408	416	1	on	on	ADP
ejpam-6408	416	2	supra	supra	PROPN
ejpam-6408	416	3	r	r	NOUN
ejpam-6408	416	4	-	-	PUNCT
ejpam-6408	416	5	open	open	ADJ
ejpam-6408	416	6	sets	set	NOUN
ejpam-6408	416	7	and	and	CCONJ
ejpam-6408	416	8	some	some	DET
ejpam-6408	416	9	applications	application	NOUN
ejpam-6408	416	10	on	on	ADP
ejpam-6408	416	11	topological	topological	ADJ
ejpam-6408	416	12	spaces	space	NOUN
ejpam-6408	416	13	.	.	PUNCT
ejpam-6408	417	1	journal	journal	NOUN
ejpam-6408	417	2	of	of	ADP
ejpam-6408	417	3	progressive	progressive	ADJ
ejpam-6408	417	4	research	research	NOUN
ejpam-6408	417	5	in	in	ADP
ejpam-6408	417	6	mathematics	mathematic	NOUN
ejpam-6408	417	7	,	,	PUNCT
ejpam-6408	417	8	8:1237–1248	8:1237–1248	NUM
ejpam-6408	417	9	,	,	PUNCT
ejpam-6408	417	10	2016	2016	NUM
ejpam-6408	417	11	.	.	PUNCT
ejpam-6408	418	1	[	[	X
ejpam-6408	418	2	18	18	NUM
ejpam-6408	418	3	]	]	X
ejpam-6408	418	4	s.	s.	PROPN
ejpam-6408	418	5	jafari	jafari	PROPN
ejpam-6408	418	6	and	and	CCONJ
ejpam-6408	418	7	s.	s.	PROPN
ejpam-6408	418	8	tahiliani	tahiliani	PROPN
ejpam-6408	418	9	.	.	PUNCT
ejpam-6408	419	1	supra	supra	PROPN
ejpam-6408	419	2	β	β	X
ejpam-6408	419	3	-	-	ADJ
ejpam-6408	419	4	open	open	ADJ
ejpam-6408	419	5	sets	set	NOUN
ejpam-6408	419	6	and	and	CCONJ
ejpam-6408	419	7	supra	supra	ADJ
ejpam-6408	419	8	β	β	NOUN
ejpam-6408	419	9	-	-	NOUN
ejpam-6408	419	10	continuity	continuity	NOUN
ejpam-6408	419	11	on	on	ADP
ejpam-6408	419	12	topological	topological	ADJ
ejpam-6408	419	13	spaces	space	NOUN
ejpam-6408	419	14	.	.	PUNCT
ejpam-6408	420	1	annales	annales	PROPN
ejpam-6408	420	2	universitatis	universitatis	PROPN
ejpam-6408	420	3	scientiarum	scientiarum	PROPN
ejpam-6408	420	4	budapestinensis	budapestinensis	PROPN
ejpam-6408	420	5	,	,	PUNCT
ejpam-6408	420	6	56:1–9	56:1–9	NUM
ejpam-6408	420	7	,	,	PUNCT
ejpam-6408	420	8	2013	2013	NUM
ejpam-6408	420	9	.	.	PUNCT
ejpam-6408	421	1	[	[	X
ejpam-6408	421	2	19	19	NUM
ejpam-6408	421	3	]	]	X
ejpam-6408	421	4	o.	o.	PROPN
ejpam-6408	421	5	r.	r.	PROPN
ejpam-6408	421	6	sayed	sayed	PROPN
ejpam-6408	421	7	and	and	CCONJ
ejpam-6408	421	8	t.	t.	PROPN
ejpam-6408	421	9	noiri	noiri	PROPN
ejpam-6408	421	10	.	.	PUNCT
ejpam-6408	422	1	on	on	ADP
ejpam-6408	422	2	supra	supra	PROPN
ejpam-6408	422	3	b	b	PROPN
ejpam-6408	422	4	-	-	PUNCT
ejpam-6408	422	5	open	open	ADJ
ejpam-6408	422	6	sets	set	NOUN
ejpam-6408	422	7	and	and	CCONJ
ejpam-6408	422	8	supra	supra	PROPN
ejpam-6408	422	9	b	b	NOUN
ejpam-6408	422	10	-	-	PUNCT
ejpam-6408	422	11	continuity	continuity	NOUN
ejpam-6408	422	12	on	on	ADP
ejpam-6408	422	13	topological	topological	ADJ
ejpam-6408	422	14	spaces	space	NOUN
ejpam-6408	422	15	.	.	PUNCT
ejpam-6408	423	1	european	european	ADJ
ejpam-6408	423	2	journal	journal	PROPN
ejpam-6408	423	3	of	of	ADP
ejpam-6408	423	4	pure	pure	ADJ
ejpam-6408	423	5	and	and	CCONJ
ejpam-6408	423	6	applied	applied	ADJ
ejpam-6408	423	7	mathematics	mathematic	NOUN
ejpam-6408	423	8	,	,	PUNCT
ejpam-6408	423	9	3:295–302	3:295–302	NUM
ejpam-6408	423	10	,	,	PUNCT
ejpam-6408	423	11	2010	2010	NUM
ejpam-6408	423	12	.	.	PUNCT
ejpam-6408	424	1	[	[	X
ejpam-6408	424	2	20	20	NUM
ejpam-6408	424	3	]	]	X
ejpam-6408	424	4	o.	o.	PROPN
ejpam-6408	424	5	r.	r.	PROPN
ejpam-6408	424	6	sayed	say	VERB
ejpam-6408	424	7	.	.	PUNCT
ejpam-6408	425	1	supra	supra	PROPN
ejpam-6408	425	2	pre	pre	ADJ
ejpam-6408	425	3	-	-	ADJ
ejpam-6408	425	4	open	open	ADJ
ejpam-6408	425	5	sets	set	NOUN
ejpam-6408	425	6	and	and	CCONJ
ejpam-6408	425	7	supra	supra	NOUN
ejpam-6408	425	8	pre	pre	ADJ
ejpam-6408	425	9	-	-	ADJ
ejpam-6408	425	10	continuous	continuous	ADJ
ejpam-6408	425	11	on	on	ADP
ejpam-6408	425	12	topological	topological	ADJ
ejpam-6408	425	13	spaces	space	NOUN
ejpam-6408	425	14	.	.	PUNCT
ejpam-6408	426	1	series	series	PROPN
ejpam-6408	426	2	mathematics	mathematics	PROPN
ejpam-6408	426	3	and	and	CCONJ
ejpam-6408	426	4	information	information	NOUN
ejpam-6408	426	5	,	,	PUNCT
ejpam-6408	426	6	20:79–88	20:79–88	NUM
ejpam-6408	426	7	,	,	PUNCT
ejpam-6408	426	8	2010	2010	NUM
ejpam-6408	426	9	.	.	PUNCT
ejpam-6408	427	1	[	[	X
ejpam-6408	427	2	21	21	NUM
ejpam-6408	427	3	]	]	X
ejpam-6408	427	4	r.	r.	PROPN
ejpam-6408	427	5	devi	devi	PROPN
ejpam-6408	427	6	,	,	PUNCT
ejpam-6408	427	7	s.	s.	PROPN
ejpam-6408	427	8	sampathkumar	sampathkumar	PROPN
ejpam-6408	427	9	,	,	PUNCT
ejpam-6408	427	10	and	and	CCONJ
ejpam-6408	427	11	m.	m.	PROPN
ejpam-6408	427	12	caldas	caldas	PROPN
ejpam-6408	427	13	.	.	PUNCT
ejpam-6408	428	1	on	on	ADP
ejpam-6408	428	2	α	α	NOUN
ejpam-6408	428	3	-	-	ADJ
ejpam-6408	428	4	open	open	ADJ
ejpam-6408	428	5	sets	set	NOUN
ejpam-6408	428	6	and	and	CCONJ
ejpam-6408	428	7	sa	sa	NOUN
ejpam-6408	428	8	-	-	ADJ
ejpam-6408	428	9	continuous	continuous	ADJ
ejpam-6408	428	10	maps	map	NOUN
ejpam-6408	428	11	.	.	PUNCT
ejpam-6408	429	1	general	general	ADJ
ejpam-6408	429	2	mathematics	mathematics	PROPN
ejpam-6408	429	3	,	,	PUNCT
ejpam-6408	429	4	16:77–84	16:77–84	NOUN
ejpam-6408	429	5	,	,	PUNCT
ejpam-6408	429	6	2008	2008	NUM
ejpam-6408	429	7	.	.	PUNCT
ejpam-6408	430	1	[	[	X
ejpam-6408	430	2	22	22	NUM
ejpam-6408	430	3	]	]	PUNCT
ejpam-6408	430	4	m.	m.	NOUN
ejpam-6408	430	5	shabir	shabir	PROPN
ejpam-6408	430	6	and	and	CCONJ
ejpam-6408	430	7	m.	m.	PROPN
ejpam-6408	430	8	naz	naz	PROPN
ejpam-6408	430	9	.	.	PUNCT
ejpam-6408	431	1	on	on	ADP
ejpam-6408	431	2	soft	soft	ADJ
ejpam-6408	431	3	topological	topological	ADJ
ejpam-6408	431	4	spaces	space	NOUN
ejpam-6408	431	5	.	.	PUNCT
ejpam-6408	432	1	computers	computer	NOUN
ejpam-6408	432	2	and	and	CCONJ
ejpam-6408	432	3	mathematics	mathematic	NOUN
ejpam-6408	432	4	with	with	ADP
ejpam-6408	432	5	applications	application	NOUN
ejpam-6408	432	6	,	,	PUNCT
ejpam-6408	432	7	61:1786–1799	61:1786–1799	NUM
ejpam-6408	432	8	,	,	PUNCT
ejpam-6408	432	9	2011	2011	NUM
ejpam-6408	432	10	.	.	PUNCT
ejpam-6408	433	1	[	[	X
ejpam-6408	433	2	23	23	NUM
ejpam-6408	433	3	]	]	PUNCT
ejpam-6408	433	4	zanyar	zanyar	PROPN
ejpam-6408	433	5	a.	a.	NOUN
ejpam-6408	433	6	ameen	ameen	PROPN
ejpam-6408	433	7	and	and	CCONJ
ejpam-6408	433	8	s.	s.	PROPN
ejpam-6408	433	9	al	al	PROPN
ejpam-6408	433	10	ghour	ghour	PROPN
ejpam-6408	433	11	.	.	PUNCT
ejpam-6408	434	1	cluster	cluster	NOUN
ejpam-6408	434	2	soft	soft	ADJ
ejpam-6408	434	3	sets	set	NOUN
ejpam-6408	434	4	and	and	CCONJ
ejpam-6408	434	5	cluster	cluster	NOUN
ejpam-6408	434	6	soft	soft	ADJ
ejpam-6408	434	7	topologies	topology	NOUN
ejpam-6408	434	8	.	.	PUNCT
ejpam-6408	435	1	computational	computational	ADJ
ejpam-6408	435	2	and	and	CCONJ
ejpam-6408	435	3	applied	applied	ADJ
ejpam-6408	435	4	mathematics	mathematic	NOUN
ejpam-6408	435	5	,	,	PUNCT
ejpam-6408	435	6	42:337	42:337	NUM
ejpam-6408	435	7	,	,	PUNCT
ejpam-6408	435	8	2023	2023	NUM
ejpam-6408	435	9	.	.	PUNCT
ejpam-6408	436	1	[	[	X
ejpam-6408	436	2	24	24	NUM
ejpam-6408	436	3	]	]	PUNCT
ejpam-6408	436	4	a.	a.	NOUN
ejpam-6408	436	5	kandil	kandil	PROPN
ejpam-6408	436	6	,	,	PUNCT
ejpam-6408	436	7	o.	o.	PROPN
ejpam-6408	436	8	a.	a.	PROPN
ejpam-6408	436	9	e.	e.	PROPN
ejpam-6408	436	10	tantawy	tantawy	PROPN
ejpam-6408	436	11	,	,	PUNCT
ejpam-6408	436	12	s.	s.	PROPN
ejpam-6408	436	13	a.	a.	PROPN
ejpam-6408	436	14	el	el	PROPN
ejpam-6408	436	15	-	-	PUNCT
ejpam-6408	436	16	sheikh	sheikh	NOUN
ejpam-6408	436	17	,	,	PUNCT
ejpam-6408	436	18	and	and	CCONJ
ejpam-6408	436	19	a.	a.	NOUN
ejpam-6408	436	20	m.	m.	PROPN
ejpam-6408	436	21	abd	abd	PROPN
ejpam-6408	436	22	el	el	PROPN
ejpam-6408	436	23	-	-	PROPN
ejpam-6408	436	24	latif	latif	PROPN
ejpam-6408	436	25	.	.	PUNCT
ejpam-6408	437	1	soft	soft	ADJ
ejpam-6408	437	2	semi	semi	ADJ
ejpam-6408	437	3	separation	separation	NOUN
ejpam-6408	437	4	axioms	axiom	NOUN
ejpam-6408	437	5	and	and	CCONJ
ejpam-6408	437	6	irresolute	irresolute	ADJ
ejpam-6408	437	7	soft	soft	ADJ
ejpam-6408	437	8	functions	function	NOUN
ejpam-6408	437	9	.	.	PUNCT
ejpam-6408	438	1	annals	annal	NOUN
ejpam-6408	438	2	of	of	ADP
ejpam-6408	438	3	fuzzy	fuzzy	ADJ
ejpam-6408	438	4	mathematics	mathematic	NOUN
ejpam-6408	438	5	and	and	CCONJ
ejpam-6408	438	6	informatics	informatic	NOUN
ejpam-6408	438	7	,	,	PUNCT
ejpam-6408	438	8	8(2):305–318	8(2):305–318	NUM
ejpam-6408	438	9	,	,	PUNCT
ejpam-6408	438	10	2014	2014	NUM
ejpam-6408	438	11	.	.	PUNCT
ejpam-6408	439	1	[	[	X
ejpam-6408	439	2	25	25	NUM
ejpam-6408	439	3	]	]	X
ejpam-6408	439	4	tareq	tareq	PROPN
ejpam-6408	439	5	m.	m.	PROPN
ejpam-6408	439	6	al	al	PROPN
ejpam-6408	439	7	-	-	PUNCT
ejpam-6408	439	8	shami	shami	PROPN
ejpam-6408	439	9	,	,	PUNCT
ejpam-6408	439	10	abdelwaheb	abdelwaheb	PROPN
ejpam-6408	439	11	mhemdi	mhemdi	PROPN
ejpam-6408	439	12	,	,	PUNCT
ejpam-6408	439	13	and	and	CCONJ
ejpam-6408	439	14	radwan	radwan	VERB
ejpam-6408	439	15	abu	abu	PROPN
ejpam-6408	439	16	-	-	PUNCT
ejpam-6408	439	17	gdairi	gdairi	PROPN
ejpam-6408	439	18	.	.	PUNCT
ejpam-6408	440	1	a	a	DET
ejpam-6408	440	2	novel	novel	ADJ
ejpam-6408	440	3	framework	framework	NOUN
ejpam-6408	440	4	for	for	ADP
ejpam-6408	440	5	generalizations	generalization	NOUN
ejpam-6408	440	6	of	of	ADP
ejpam-6408	440	7	soft	soft	ADJ
ejpam-6408	440	8	open	open	ADJ
ejpam-6408	440	9	sets	set	NOUN
ejpam-6408	440	10	and	and	CCONJ
ejpam-6408	440	11	its	its	PRON
ejpam-6408	440	12	applications	application	NOUN
ejpam-6408	440	13	via	via	ADP
ejpam-6408	440	14	soft	soft	ADJ
ejpam-6408	440	15	topologies	topology	NOUN
ejpam-6408	440	16	.	.	PUNCT
ejpam-6408	441	1	mathematics	mathematic	NOUN
ejpam-6408	441	2	,	,	PUNCT
ejpam-6408	441	3	11(4):840	11(4):840	NOUN
ejpam-6408	441	4	,	,	PUNCT
ejpam-6408	441	5	2023	2023	NUM
ejpam-6408	441	6	.	.	PUNCT
ejpam-6408	442	1	[	[	X
ejpam-6408	442	2	26	26	NUM
ejpam-6408	442	3	]	]	PUNCT
ejpam-6408	442	4	t.	t.	PROPN
ejpam-6408	442	5	m.	m.	PROPN
ejpam-6408	442	6	al	al	PROPN
ejpam-6408	442	7	-	-	PUNCT
ejpam-6408	442	8	shami	shami	PROPN
ejpam-6408	442	9	.	.	PUNCT
ejpam-6408	443	1	soft	soft	ADJ
ejpam-6408	443	2	somewhere	somewhere	ADV
ejpam-6408	443	3	dense	dense	ADJ
ejpam-6408	443	4	sets	set	NOUN
ejpam-6408	443	5	on	on	ADP
ejpam-6408	443	6	soft	soft	ADJ
ejpam-6408	443	7	topological	topological	ADJ
ejpam-6408	443	8	spaces	space	NOUN
ejpam-6408	443	9	.	.	PUNCT
ejpam-6408	444	1	communications	communication	NOUN
ejpam-6408	444	2	of	of	ADP
ejpam-6408	444	3	the	the	DET
ejpam-6408	444	4	korean	korean	ADJ
ejpam-6408	444	5	mathematical	mathematical	ADJ
ejpam-6408	444	6	society	society	NOUN
ejpam-6408	444	7	,	,	PUNCT
ejpam-6408	444	8	33(2):1341–1356	33(2):1341–1356	NUM
ejpam-6408	444	9	,	,	PUNCT
ejpam-6408	444	10	2018	2018	NUM
ejpam-6408	444	11	.	.	PUNCT
ejpam-6408	445	1	[	[	X
ejpam-6408	445	2	27	27	NUM
ejpam-6408	445	3	]	]	PUNCT
ejpam-6408	445	4	radwan	radwan	VERB
ejpam-6408	445	5	abu	abu	PROPN
ejpam-6408	445	6	-	-	PUNCT
ejpam-6408	445	7	gdairi	gdairi	PROPN
ejpam-6408	445	8	,	,	PUNCT
ejpam-6408	445	9	a.	a.	PROPN
ejpam-6408	445	10	a.	a.	PROPN
ejpam-6408	445	11	azzam	azzam	PROPN
ejpam-6408	445	12	,	,	PUNCT
ejpam-6408	445	13	and	and	CCONJ
ejpam-6408	445	14	ibrahim	ibrahim	PROPN
ejpam-6408	445	15	noaman	noaman	PROPN
ejpam-6408	445	16	.	.	PUNCT
ejpam-6408	446	1	nearly	nearly	ADV
ejpam-6408	446	2	soft	soft	ADJ
ejpam-6408	446	3	β	β	ADJ
ejpam-6408	446	4	-	-	ADJ
ejpam-6408	446	5	open	open	ADJ
ejpam-6408	446	6	sets	set	NOUN
ejpam-6408	446	7	via	via	ADP
ejpam-6408	446	8	soft	soft	ADJ
ejpam-6408	446	9	ditopological	ditopological	ADJ
ejpam-6408	446	10	spaces	space	NOUN
ejpam-6408	446	11	.	.	PUNCT
ejpam-6408	447	1	european	european	ADJ
ejpam-6408	447	2	journal	journal	PROPN
ejpam-6408	447	3	of	of	ADP
ejpam-6408	447	4	pure	pure	ADJ
ejpam-6408	447	5	and	and	CCONJ
ejpam-6408	447	6	applied	applied	ADJ
ejpam-6408	447	7	mathematics	mathematic	NOUN
ejpam-6408	447	8	,	,	PUNCT
ejpam-6408	447	9	15(1):126–134	15(1):126–134	PROPN
ejpam-6408	447	10	,	,	PUNCT
ejpam-6408	447	11	2022	2022	NUM
ejpam-6408	447	12	.	.	PUNCT
ejpam-6408	448	1	[	[	X
ejpam-6408	448	2	28	28	NUM
ejpam-6408	448	3	]	]	X
ejpam-6408	448	4	s.	s.	PROPN
ejpam-6408	448	5	al	al	PROPN
ejpam-6408	448	6	ghour	ghour	PROPN
ejpam-6408	448	7	.	.	PUNCT
ejpam-6408	449	1	soft	soft	ADJ
ejpam-6408	449	2	ω	ω	NOUN
ejpam-6408	449	3	-	-	PUNCT
ejpam-6408	449	4	continuity	continuity	NOUN
ejpam-6408	449	5	and	and	CCONJ
ejpam-6408	449	6	soft	soft	ADJ
ejpam-6408	449	7	ωs	ω	NOUN
ejpam-6408	449	8	-	-	NOUN
ejpam-6408	449	9	continuity	continuity	NOUN
ejpam-6408	449	10	in	in	ADP
ejpam-6408	449	11	soft	soft	ADJ
ejpam-6408	449	12	topological	topological	ADJ
ejpam-6408	449	13	spaces	space	NOUN
ejpam-6408	449	14	.	.	PUNCT
ejpam-6408	450	1	international	international	ADJ
ejpam-6408	450	2	journal	journal	NOUN
ejpam-6408	450	3	of	of	ADP
ejpam-6408	450	4	fuzzy	fuzzy	ADJ
ejpam-6408	450	5	logic	logic	NOUN
ejpam-6408	450	6	and	and	CCONJ
ejpam-6408	450	7	intelligent	intelligent	ADJ
ejpam-6408	450	8	systems	system	NOUN
ejpam-6408	450	9	,	,	PUNCT
ejpam-6408	450	10	22(2):183–192	22(2):183–192	NOUN
ejpam-6408	450	11	,	,	PUNCT
ejpam-6408	450	12	2022	2022	NUM
ejpam-6408	450	13	.	.	PUNCT
ejpam-6408	451	1	[	[	X
ejpam-6408	451	2	29	29	NUM
ejpam-6408	451	3	]	]	PUNCT
ejpam-6408	451	4	s.	s.	PROPN
ejpam-6408	451	5	al	al	PROPN
ejpam-6408	451	6	ghour	ghour	PROPN
ejpam-6408	451	7	and	and	CCONJ
ejpam-6408	451	8	b.	b.	PROPN
ejpam-6408	451	9	irshidat	irshidat	PROPN
ejpam-6408	451	10	.	.	PUNCT
ejpam-6408	452	1	on	on	ADP
ejpam-6408	452	2	θω	θω	ADP
ejpam-6408	452	3	continuity	continuity	NOUN
ejpam-6408	452	4	.	.	PUNCT
ejpam-6408	453	1	heliyon	heliyon	NOUN
ejpam-6408	453	2	,	,	PUNCT
ejpam-6408	453	3	6(2):e03349	6(2):e03349	NUM
ejpam-6408	453	4	,	,	PUNCT
ejpam-6408	453	5	2020	2020	NUM
ejpam-6408	453	6	.	.	PUNCT
ejpam-6408	454	1	[	[	X
ejpam-6408	454	2	30	30	NUM
ejpam-6408	454	3	]	]	X
ejpam-6408	454	4	a.	a.	NOUN
ejpam-6408	454	5	kandil	kandil	PROPN
ejpam-6408	454	6	,	,	PUNCT
ejpam-6408	454	7	o.	o.	PROPN
ejpam-6408	454	8	a.	a.	PROPN
ejpam-6408	454	9	e.	e.	PROPN
ejpam-6408	454	10	tantawy	tantawy	PROPN
ejpam-6408	454	11	,	,	PUNCT
ejpam-6408	454	12	s.	s.	PROPN
ejpam-6408	454	13	a.	a.	PROPN
ejpam-6408	454	14	el	el	PROPN
ejpam-6408	454	15	-	-	PUNCT
ejpam-6408	454	16	sheikh	sheikh	NOUN
ejpam-6408	454	17	,	,	PUNCT
ejpam-6408	454	18	and	and	CCONJ
ejpam-6408	454	19	a.	a.	NOUN
ejpam-6408	454	20	m.	m.	PROPN
ejpam-6408	454	21	abd	abd	PROPN
ejpam-6408	454	22	el	el	PROPN
ejpam-6408	454	23	-	-	PROPN
ejpam-6408	454	24	latif	latif	PROPN
ejpam-6408	454	25	.	.	PUNCT
ejpam-6408	455	1	soft	soft	ADJ
ejpam-6408	455	2	ideal	ideal	ADJ
ejpam-6408	455	3	theory	theory	NOUN
ejpam-6408	455	4	,	,	PUNCT
ejpam-6408	455	5	soft	soft	ADJ
ejpam-6408	455	6	local	local	ADJ
ejpam-6408	455	7	function	function	NOUN
ejpam-6408	455	8	and	and	CCONJ
ejpam-6408	455	9	generated	generate	VERB
ejpam-6408	455	10	soft	soft	ADJ
ejpam-6408	455	11	topological	topological	ADJ
ejpam-6408	455	12	spaces	space	NOUN
ejpam-6408	455	13	.	.	PUNCT
ejpam-6408	456	1	applied	apply	VERB
ejpam-6408	456	2	mathematics	mathematic	NOUN
ejpam-6408	456	3	and	and	CCONJ
ejpam-6408	456	4	information	information	NOUN
ejpam-6408	456	5	sciences	science	NOUN
ejpam-6408	456	6	,	,	PUNCT
ejpam-6408	456	7	8(4):1595–1603	8(4):1595–1603	NOUN
ejpam-6408	456	8	,	,	PUNCT
ejpam-6408	456	9	2014	2014	NUM
ejpam-6408	456	10	.	.	PUNCT
ejpam-6408	457	1	[	[	X
ejpam-6408	457	2	31	31	NUM
ejpam-6408	457	3	]	]	X
ejpam-6408	457	4	f.	f.	PROPN
ejpam-6408	457	5	gharib	gharib	PROPN
ejpam-6408	457	6	and	and	CCONJ
ejpam-6408	457	7	a.	a.	NOUN
ejpam-6408	457	8	m.	m.	PROPN
ejpam-6408	457	9	abd	abd	PROPN
ejpam-6408	457	10	el	el	PROPN
ejpam-6408	457	11	-	-	PROPN
ejpam-6408	457	12	latif	latif	PROPN
ejpam-6408	457	13	.	.	PUNCT
ejpam-6408	458	1	soft	soft	ADJ
ejpam-6408	458	2	semi	semi	ADJ
ejpam-6408	458	3	local	local	ADJ
ejpam-6408	458	4	functions	function	NOUN
ejpam-6408	458	5	in	in	ADP
ejpam-6408	458	6	soft	soft	ADJ
ejpam-6408	458	7	ideal	ideal	ADJ
ejpam-6408	458	8	topological	topological	ADJ
ejpam-6408	458	9	spaces	space	NOUN
ejpam-6408	458	10	.	.	PUNCT
ejpam-6408	459	1	european	european	ADJ
ejpam-6408	459	2	journal	journal	PROPN
ejpam-6408	459	3	of	of	ADP
ejpam-6408	459	4	pure	pure	ADJ
ejpam-6408	459	5	and	and	CCONJ
ejpam-6408	459	6	applied	applied	ADJ
ejpam-6408	459	7	mathematics	mathematic	NOUN
ejpam-6408	459	8	,	,	PUNCT
ejpam-6408	459	9	12(3):857–869	12(3):857–869	NUM
ejpam-6408	459	10	,	,	PUNCT
ejpam-6408	459	11	2019	2019	NUM
ejpam-6408	459	12	.	.	PUNCT
ejpam-6408	460	1	[	[	X
ejpam-6408	460	2	32	32	NUM
ejpam-6408	460	3	]	]	PUNCT
ejpam-6408	460	4	m.	m.	NOUN
ejpam-6408	460	5	akdag	akdag	PROPN
ejpam-6408	460	6	and	and	CCONJ
ejpam-6408	460	7	f.	f.	PROPN
ejpam-6408	460	8	erol	erol	PROPN
ejpam-6408	460	9	.	.	PUNCT
ejpam-6408	461	1	soft	soft	ADJ
ejpam-6408	461	2	i	i	NOUN
ejpam-6408	461	3	-	-	PUNCT
ejpam-6408	461	4	sets	set	NOUN
ejpam-6408	461	5	and	and	CCONJ
ejpam-6408	461	6	soft	soft	ADJ
ejpam-6408	461	7	i	i	NOUN
ejpam-6408	461	8	-	-	PUNCT
ejpam-6408	461	9	continuity	continuity	NOUN
ejpam-6408	461	10	of	of	ADP
ejpam-6408	461	11	functions	function	NOUN
ejpam-6408	461	12	.	.	PUNCT
ejpam-6408	462	1	gazi	gazi	PROPN
ejpam-6408	462	2	university	university	PROPN
ejpam-6408	462	3	journal	journal	PROPN
ejpam-6408	462	4	of	of	ADP
ejpam-6408	462	5	science	science	NOUN
ejpam-6408	462	6	,	,	PUNCT
ejpam-6408	462	7	27:923–932	27:923–932	NUM
ejpam-6408	462	8	,	,	PUNCT
ejpam-6408	462	9	2014	2014	NUM
ejpam-6408	462	10	.	.	PUNCT
ejpam-6408	463	1	[	[	X
ejpam-6408	463	2	33	33	NUM
ejpam-6408	463	3	]	]	PUNCT
ejpam-6408	463	4	a.	a.	NOUN
ejpam-6408	463	5	a.	a.	PROPN
ejpam-6408	463	6	nasef	nasef	PROPN
ejpam-6408	463	7	,	,	PUNCT
ejpam-6408	463	8	m.	m.	NOUN
ejpam-6408	463	9	parimala	parimala	PROPN
ejpam-6408	463	10	,	,	PUNCT
ejpam-6408	463	11	r.	r.	PROPN
ejpam-6408	463	12	jeevitha	jeevitha	PROPN
ejpam-6408	463	13	,	,	PUNCT
ejpam-6408	463	14	and	and	CCONJ
ejpam-6408	463	15	m.	m.	PROPN
ejpam-6408	463	16	k.	k.	PROPN
ejpam-6408	464	1	el	el	PROPN
ejpam-6408	464	2	-	-	PUNCT
ejpam-6408	464	3	sayed	say	VERB
ejpam-6408	464	4	.	.	PUNCT
ejpam-6408	465	1	soft	soft	ADJ
ejpam-6408	465	2	ideal	ideal	ADJ
ejpam-6408	465	3	theory	theory	NOUN
ejpam-6408	465	4	and	and	CCONJ
ejpam-6408	465	5	applications	application	NOUN
ejpam-6408	465	6	.	.	PUNCT
ejpam-6408	466	1	international	international	ADJ
ejpam-6408	466	2	journal	journal	PROPN
ejpam-6408	466	3	of	of	ADP
ejpam-6408	466	4	nonlinear	nonlinear	ADJ
ejpam-6408	466	5	analysis	analysis	NOUN
ejpam-6408	466	6	and	and	CCONJ
ejpam-6408	466	7	applications	application	NOUN
ejpam-6408	466	8	,	,	PUNCT
ejpam-6408	466	9	13(2):1335	13(2):1335	NUM
ejpam-6408	466	10	–	–	PUNCT
ejpam-6408	466	11	1342	1342	NUM
ejpam-6408	466	12	,	,	PUNCT
ejpam-6408	466	13	2022	2022	NUM
ejpam-6408	466	14	.	.	PUNCT
ejpam-6408	467	1	[	[	X
ejpam-6408	467	2	34	34	NUM
ejpam-6408	467	3	]	]	PUNCT
ejpam-6408	467	4	a.	a.	NOUN
ejpam-6408	467	5	kandil	kandil	PROPN
ejpam-6408	467	6	,	,	PUNCT
ejpam-6408	467	7	o.	o.	PROPN
ejpam-6408	467	8	a.	a.	PROPN
ejpam-6408	467	9	e.	e.	PROPN
ejpam-6408	467	10	tantawy	tantawy	PROPN
ejpam-6408	467	11	,	,	PUNCT
ejpam-6408	467	12	s.	s.	PROPN
ejpam-6408	467	13	a.	a.	PROPN
ejpam-6408	467	14	el	el	PROPN
ejpam-6408	467	15	-	-	PUNCT
ejpam-6408	467	16	sheikh	sheikh	NOUN
ejpam-6408	467	17	,	,	PUNCT
ejpam-6408	467	18	and	and	CCONJ
ejpam-6408	467	19	a.	a.	NOUN
ejpam-6408	467	20	m.	m.	PROPN
ejpam-6408	467	21	abd	abd	PROPN
ejpam-6408	467	22	el	el	PROPN
ejpam-6408	467	23	-	-	PROPN
ejpam-6408	467	24	latif	latif	PROPN
ejpam-6408	467	25	.	.	PUNCT
ejpam-6408	468	1	γ	γ	PROPN
ejpam-6408	468	2	-	-	PUNCT
ejpam-6408	468	3	operation	operation	NOUN
ejpam-6408	468	4	and	and	CCONJ
ejpam-6408	468	5	decompositions	decomposition	NOUN
ejpam-6408	468	6	of	of	ADP
ejpam-6408	468	7	some	some	DET
ejpam-6408	468	8	forms	form	NOUN
ejpam-6408	468	9	of	of	ADP
ejpam-6408	468	10	soft	soft	ADJ
ejpam-6408	468	11	continuity	continuity	NOUN
ejpam-6408	468	12	of	of	ADP
ejpam-6408	468	13	soft	soft	ADJ
ejpam-6408	468	14	topological	topological	ADJ
ejpam-6408	468	15	spaces	space	NOUN
ejpam-6408	468	16	via	via	ADP
ejpam-6408	468	17	soft	soft	ADJ
ejpam-6408	468	18	m.	m.	NOUN
ejpam-6408	468	19	aldawood	aldawood	NOUN
ejpam-6408	468	20	et	et	PROPN
ejpam-6408	468	21	al	al	PROPN
ejpam-6408	468	22	.	.	PUNCT
ejpam-6408	468	23	/	/	SYM
ejpam-6408	468	24	eur	eur	PROPN
ejpam-6408	468	25	.	.	PUNCT
ejpam-6408	469	1	j.	j.	PROPN
ejpam-6408	469	2	pure	pure	PROPN
ejpam-6408	469	3	appl	appl	PROPN
ejpam-6408	469	4	.	.	PROPN
ejpam-6408	469	5	math	math	PROPN
ejpam-6408	469	6	,	,	PUNCT
ejpam-6408	469	7	18	18	NUM
ejpam-6408	469	8	(	(	PUNCT
ejpam-6408	469	9	3	3	NUM
ejpam-6408	469	10	)	)	PUNCT
ejpam-6408	469	11	(	(	PUNCT
ejpam-6408	469	12	2025	2025	NUM
ejpam-6408	469	13	)	)	PUNCT
ejpam-6408	469	14	,	,	PUNCT
ejpam-6408	469	15	6408	6408	NUM
ejpam-6408	469	16	15	15	NUM
ejpam-6408	469	17	of	of	ADP
ejpam-6408	469	18	16	16	NUM
ejpam-6408	469	19	ideal	ideal	ADJ
ejpam-6408	469	20	.	.	PUNCT
ejpam-6408	470	1	annals	annal	NOUN
ejpam-6408	470	2	of	of	ADP
ejpam-6408	470	3	fuzzy	fuzzy	ADJ
ejpam-6408	470	4	mathematics	mathematic	NOUN
ejpam-6408	470	5	and	and	CCONJ
ejpam-6408	470	6	informatics	informatic	NOUN
ejpam-6408	470	7	,	,	PUNCT
ejpam-6408	470	8	9(3):385–402	9(3):385–402	NUM
ejpam-6408	470	9	,	,	PUNCT
ejpam-6408	470	10	2015	2015	NUM
ejpam-6408	470	11	.	.	PUNCT
ejpam-6408	471	1	[	[	X
ejpam-6408	471	2	35	35	NUM
ejpam-6408	471	3	]	]	PUNCT
ejpam-6408	471	4	a.	a.	NOUN
ejpam-6408	471	5	kandil	kandil	PROPN
ejpam-6408	471	6	,	,	PUNCT
ejpam-6408	471	7	o.	o.	PROPN
ejpam-6408	471	8	a.	a.	PROPN
ejpam-6408	471	9	e.	e.	PROPN
ejpam-6408	471	10	tantawy	tantawy	PROPN
ejpam-6408	471	11	,	,	PUNCT
ejpam-6408	471	12	s.	s.	PROPN
ejpam-6408	471	13	a.	a.	PROPN
ejpam-6408	471	14	el	el	PROPN
ejpam-6408	471	15	-	-	PUNCT
ejpam-6408	471	16	sheikh	sheikh	NOUN
ejpam-6408	471	17	,	,	PUNCT
ejpam-6408	471	18	and	and	CCONJ
ejpam-6408	471	19	a.	a.	NOUN
ejpam-6408	471	20	m.	m.	PROPN
ejpam-6408	471	21	abd	abd	PROPN
ejpam-6408	471	22	el	el	PROPN
ejpam-6408	471	23	-	-	PROPN
ejpam-6408	471	24	latif	latif	PROPN
ejpam-6408	471	25	.	.	PUNCT
ejpam-6408	472	1	soft	soft	ADJ
ejpam-6408	472	2	semi	semi	ADJ
ejpam-6408	472	3	compactness	compactness	NOUN
ejpam-6408	472	4	via	via	ADP
ejpam-6408	472	5	soft	soft	ADJ
ejpam-6408	472	6	ideals	ideal	NOUN
ejpam-6408	472	7	.	.	PUNCT
ejpam-6408	473	1	applied	apply	VERB
ejpam-6408	473	2	mathematics	mathematic	NOUN
ejpam-6408	473	3	and	and	CCONJ
ejpam-6408	473	4	information	information	NOUN
ejpam-6408	473	5	sciences	science	NOUN
ejpam-6408	473	6	,	,	PUNCT
ejpam-6408	473	7	8(5):2297	8(5):2297	NUM
ejpam-6408	473	8	–	–	PUNCT
ejpam-6408	473	9	2306	2306	NUM
ejpam-6408	473	10	,	,	PUNCT
ejpam-6408	473	11	2014	2014	NUM
ejpam-6408	473	12	.	.	PUNCT
ejpam-6408	474	1	[	[	X
ejpam-6408	474	2	36	36	NUM
ejpam-6408	474	3	]	]	PUNCT
ejpam-6408	474	4	z.	z.	PROPN
ejpam-6408	474	5	a.	a.	NOUN
ejpam-6408	474	6	ameen	ameen	PROPN
ejpam-6408	474	7	and	and	CCONJ
ejpam-6408	474	8	m.	m.	PROPN
ejpam-6408	474	9	h.	h.	PROPN
ejpam-6408	474	10	alqahtani	alqahtani	PROPN
ejpam-6408	474	11	.	.	PUNCT
ejpam-6408	475	1	congruence	congruence	PROPN
ejpam-6408	475	2	representations	representation	NOUN
ejpam-6408	475	3	via	via	ADP
ejpam-6408	475	4	soft	soft	ADJ
ejpam-6408	475	5	ideals	ideal	NOUN
ejpam-6408	475	6	in	in	ADP
ejpam-6408	475	7	soft	soft	ADJ
ejpam-6408	475	8	topological	topological	ADJ
ejpam-6408	475	9	spaces	space	NOUN
ejpam-6408	475	10	.	.	PUNCT
ejpam-6408	476	1	axioms	axiom	NOUN
ejpam-6408	476	2	,	,	PUNCT
ejpam-6408	476	3	12:1015	12:1015	NUM
ejpam-6408	476	4	,	,	PUNCT
ejpam-6408	476	5	2023	2023	NUM
ejpam-6408	476	6	.	.	PUNCT
ejpam-6408	477	1	[	[	X
ejpam-6408	477	2	37	37	NUM
ejpam-6408	477	3	]	]	PUNCT
ejpam-6408	477	4	a.	a.	NOUN
ejpam-6408	477	5	m.	m.	PROPN
ejpam-6408	477	6	abd	abd	PROPN
ejpam-6408	477	7	el	el	PROPN
ejpam-6408	477	8	-	-	PROPN
ejpam-6408	477	9	latif	latif	PROPN
ejpam-6408	477	10	.	.	PUNCT
ejpam-6408	478	1	generalized	generalize	VERB
ejpam-6408	478	2	soft	soft	ADJ
ejpam-6408	478	3	rough	rough	ADJ
ejpam-6408	478	4	sets	set	NOUN
ejpam-6408	478	5	and	and	CCONJ
ejpam-6408	478	6	generated	generate	VERB
ejpam-6408	478	7	soft	soft	ADJ
ejpam-6408	478	8	ideal	ideal	NOUN
ejpam-6408	478	9	rough	rough	ADJ
ejpam-6408	478	10	topological	topological	ADJ
ejpam-6408	478	11	spaces	space	NOUN
ejpam-6408	478	12	.	.	PUNCT
ejpam-6408	479	1	journal	journal	NOUN
ejpam-6408	479	2	of	of	ADP
ejpam-6408	479	3	intelligent	intelligent	ADJ
ejpam-6408	479	4	and	and	CCONJ
ejpam-6408	479	5	fuzzy	fuzzy	ADJ
ejpam-6408	479	6	systems	system	NOUN
ejpam-6408	479	7	,	,	PUNCT
ejpam-6408	479	8	34:517–524	34:517–524	PROPN
ejpam-6408	479	9	,	,	PUNCT
ejpam-6408	479	10	2018	2018	NUM
ejpam-6408	479	11	.	.	PUNCT
ejpam-6408	480	1	[	[	X
ejpam-6408	480	2	38	38	NUM
ejpam-6408	480	3	]	]	PUNCT
ejpam-6408	480	4	a.	a.	NOUN
ejpam-6408	480	5	m.	m.	PROPN
ejpam-6408	480	6	abd	abd	PROPN
ejpam-6408	480	7	el	el	PROPN
ejpam-6408	480	8	-	-	PROPN
ejpam-6408	480	9	latif	latif	PROPN
ejpam-6408	480	10	.	.	PUNCT
ejpam-6408	481	1	new	new	ADJ
ejpam-6408	481	2	generalized	generalize	VERB
ejpam-6408	481	3	fuzzy	fuzzy	ADJ
ejpam-6408	481	4	soft	soft	ADJ
ejpam-6408	481	5	rough	rough	ADJ
ejpam-6408	481	6	approximations	approximation	NOUN
ejpam-6408	481	7	applied	apply	VERB
ejpam-6408	481	8	to	to	ADP
ejpam-6408	481	9	fuzzy	fuzzy	ADJ
ejpam-6408	481	10	topological	topological	ADJ
ejpam-6408	481	11	spaces	space	NOUN
ejpam-6408	481	12	.	.	PUNCT
ejpam-6408	482	1	journal	journal	NOUN
ejpam-6408	482	2	of	of	ADP
ejpam-6408	482	3	intelligent	intelligent	ADJ
ejpam-6408	482	4	and	and	CCONJ
ejpam-6408	482	5	fuzzy	fuzzy	ADJ
ejpam-6408	482	6	systems	system	NOUN
ejpam-6408	482	7	,	,	PUNCT
ejpam-6408	482	8	35:2123–2136	35:2123–2136	NUM
ejpam-6408	482	9	,	,	PUNCT
ejpam-6408	482	10	2018	2018	NUM
ejpam-6408	482	11	.	.	PUNCT
ejpam-6408	483	1	[	[	X
ejpam-6408	483	2	39	39	NUM
ejpam-6408	483	3	]	]	PUNCT
ejpam-6408	483	4	a.	a.	NOUN
ejpam-6408	483	5	kandil	kandil	PROPN
ejpam-6408	483	6	,	,	PUNCT
ejpam-6408	483	7	o.	o.	PROPN
ejpam-6408	483	8	a.	a.	PROPN
ejpam-6408	483	9	e.	e.	PROPN
ejpam-6408	483	10	tantawy	tantawy	PROPN
ejpam-6408	483	11	,	,	PUNCT
ejpam-6408	483	12	s.	s.	PROPN
ejpam-6408	483	13	a.	a.	PROPN
ejpam-6408	483	14	el	el	PROPN
ejpam-6408	483	15	-	-	PUNCT
ejpam-6408	483	16	sheikh	sheikh	NOUN
ejpam-6408	483	17	,	,	PUNCT
ejpam-6408	483	18	and	and	CCONJ
ejpam-6408	483	19	a.	a.	NOUN
ejpam-6408	483	20	m.	m.	PROPN
ejpam-6408	483	21	abd	abd	PROPN
ejpam-6408	483	22	el	el	PROPN
ejpam-6408	483	23	-	-	PROPN
ejpam-6408	483	24	latif	latif	PROPN
ejpam-6408	483	25	.	.	PUNCT
ejpam-6408	484	1	soft	soft	ADJ
ejpam-6408	484	2	semi	semi	ADJ
ejpam-6408	484	3	(	(	PUNCT
ejpam-6408	484	4	quasi	quasi	ADJ
ejpam-6408	484	5	)	)	PUNCT
ejpam-6408	484	6	hausdorff	hausdorff	NOUN
ejpam-6408	484	7	spaces	space	NOUN
ejpam-6408	484	8	via	via	ADP
ejpam-6408	484	9	soft	soft	ADJ
ejpam-6408	484	10	ideals	ideal	NOUN
ejpam-6408	484	11	.	.	PUNCT
ejpam-6408	485	1	south	south	ADJ
ejpam-6408	485	2	asian	asian	PROPN
ejpam-6408	485	3	journal	journal	PROPN
ejpam-6408	485	4	of	of	ADP
ejpam-6408	485	5	mathematics	mathematic	NOUN
ejpam-6408	485	6	,	,	PUNCT
ejpam-6408	485	7	4(6):265–284	4(6):265–284	NUM
ejpam-6408	485	8	,	,	PUNCT
ejpam-6408	485	9	2014	2014	NUM
ejpam-6408	485	10	.	.	PUNCT
ejpam-6408	486	1	[	[	X
ejpam-6408	486	2	40	40	NUM
ejpam-6408	486	3	]	]	PUNCT
ejpam-6408	486	4	a.	a.	NOUN
ejpam-6408	486	5	kandil	kandil	PROPN
ejpam-6408	486	6	,	,	PUNCT
ejpam-6408	486	7	o.	o.	PROPN
ejpam-6408	486	8	a.	a.	PROPN
ejpam-6408	486	9	e.	e.	PROPN
ejpam-6408	486	10	tantawy	tantawy	PROPN
ejpam-6408	486	11	,	,	PUNCT
ejpam-6408	486	12	s.	s.	PROPN
ejpam-6408	486	13	a.	a.	PROPN
ejpam-6408	486	14	el	el	PROPN
ejpam-6408	486	15	-	-	PUNCT
ejpam-6408	486	16	sheikh	sheikh	NOUN
ejpam-6408	486	17	,	,	PUNCT
ejpam-6408	486	18	and	and	CCONJ
ejpam-6408	486	19	a.	a.	NOUN
ejpam-6408	486	20	m.	m.	PROPN
ejpam-6408	486	21	abd	abd	PROPN
ejpam-6408	486	22	el	el	PROPN
ejpam-6408	486	23	-	-	PROPN
ejpam-6408	486	24	latif	latif	PROPN
ejpam-6408	486	25	.	.	PUNCT
ejpam-6408	487	1	soft	soft	ADJ
ejpam-6408	487	2	connectedness	connectedness	NOUN
ejpam-6408	487	3	via	via	ADP
ejpam-6408	487	4	soft	soft	ADJ
ejpam-6408	487	5	ideals	ideal	NOUN
ejpam-6408	487	6	.	.	PUNCT
ejpam-6408	488	1	journal	journal	NOUN
ejpam-6408	488	2	of	of	ADP
ejpam-6408	488	3	new	new	ADJ
ejpam-6408	488	4	results	result	NOUN
ejpam-6408	488	5	in	in	ADP
ejpam-6408	488	6	science	science	NOUN
ejpam-6408	488	7	,	,	PUNCT
ejpam-6408	488	8	4:90–108	4:90–108	NUM
ejpam-6408	488	9	,	,	PUNCT
ejpam-6408	488	10	2014	2014	NUM
ejpam-6408	488	11	.	.	PUNCT
ejpam-6408	489	1	[	[	X
ejpam-6408	489	2	41	41	NUM
ejpam-6408	489	3	]	]	X
ejpam-6408	489	4	s.	s.	PROPN
ejpam-6408	489	5	saleh	saleh	PROPN
ejpam-6408	489	6	and	and	CCONJ
ejpam-6408	489	7	k.	k.	PROPN
ejpam-6408	489	8	hur	hur	PROPN
ejpam-6408	489	9	.	.	PROPN
ejpam-6408	490	1	on	on	ADP
ejpam-6408	490	2	some	some	DET
ejpam-6408	490	3	lower	low	ADJ
ejpam-6408	490	4	soft	soft	ADJ
ejpam-6408	490	5	separation	separation	NOUN
ejpam-6408	490	6	axioms	axiom	NOUN
ejpam-6408	490	7	.	.	PUNCT
ejpam-6408	491	1	annals	annal	NOUN
ejpam-6408	491	2	of	of	ADP
ejpam-6408	491	3	fuzzy	fuzzy	ADJ
ejpam-6408	491	4	mathematics	mathematic	NOUN
ejpam-6408	491	5	and	and	CCONJ
ejpam-6408	491	6	informatics	informatic	NOUN
ejpam-6408	491	7	,	,	PUNCT
ejpam-6408	491	8	19(1):61–72	19(1):61–72	NUM
ejpam-6408	491	9	,	,	PUNCT
ejpam-6408	491	10	2020	2020	NUM
ejpam-6408	491	11	.	.	PUNCT
ejpam-6408	492	1	[	[	X
ejpam-6408	492	2	42	42	NUM
ejpam-6408	492	3	]	]	PUNCT
ejpam-6408	492	4	s.	s.	PROPN
ejpam-6408	492	5	saleh	saleh	PROPN
ejpam-6408	492	6	,	,	PUNCT
ejpam-6408	492	7	laith	laith	PROPN
ejpam-6408	492	8	r.	r.	PROPN
ejpam-6408	492	9	flaih	flaih	PROPN
ejpam-6408	492	10	,	,	PUNCT
ejpam-6408	492	11	and	and	CCONJ
ejpam-6408	492	12	khaled	khaled	PROPN
ejpam-6408	492	13	f.	f.	PROPN
ejpam-6408	492	14	jasim	jasim	PROPN
ejpam-6408	492	15	.	.	PUNCT
ejpam-6408	493	1	some	some	DET
ejpam-6408	493	2	applications	application	NOUN
ejpam-6408	493	3	of	of	ADP
ejpam-6408	493	4	soft	soft	ADJ
ejpam-6408	493	5	δ	δ	NOUN
ejpam-6408	493	6	-	-	PUNCT
ejpam-6408	493	7	closed	close	VERB
ejpam-6408	493	8	sets	set	NOUN
ejpam-6408	493	9	in	in	ADP
ejpam-6408	493	10	soft	soft	ADJ
ejpam-6408	493	11	closure	closure	NOUN
ejpam-6408	493	12	spaces	space	NOUN
ejpam-6408	493	13	.	.	PUNCT
ejpam-6408	494	1	communications	communication	NOUN
ejpam-6408	494	2	in	in	ADP
ejpam-6408	494	3	mathematics	mathematic	NOUN
ejpam-6408	494	4	and	and	CCONJ
ejpam-6408	494	5	applications	application	NOUN
ejpam-6408	494	6	,	,	PUNCT
ejpam-6408	494	7	14(2):481	14(2):481	NUM
ejpam-6408	494	8	–	–	PUNCT
ejpam-6408	494	9	492	492	NUM
ejpam-6408	494	10	,	,	PUNCT
ejpam-6408	494	11	2023	2023	NUM
ejpam-6408	494	12	.	.	PUNCT
ejpam-6408	495	1	[	[	X
ejpam-6408	495	2	43	43	NUM
ejpam-6408	495	3	]	]	PUNCT
ejpam-6408	495	4	s.	s.	PROPN
ejpam-6408	495	5	a.	a.	PROPN
ejpam-6408	495	6	el	el	PROPN
ejpam-6408	495	7	-	-	PUNCT
ejpam-6408	495	8	sheikh	sheikh	PROPN
ejpam-6408	495	9	and	and	CCONJ
ejpam-6408	495	10	a.	a.	NOUN
ejpam-6408	495	11	m.	m.	NOUN
ejpam-6408	495	12	abd	abd	PROPN
ejpam-6408	495	13	el	el	PROPN
ejpam-6408	495	14	-	-	PROPN
ejpam-6408	495	15	latif	latif	PROPN
ejpam-6408	495	16	.	.	PUNCT
ejpam-6408	496	1	decompositions	decomposition	NOUN
ejpam-6408	496	2	of	of	ADP
ejpam-6408	496	3	some	some	DET
ejpam-6408	496	4	types	type	NOUN
ejpam-6408	496	5	of	of	ADP
ejpam-6408	496	6	supra	supra	ADJ
ejpam-6408	496	7	soft	soft	ADJ
ejpam-6408	496	8	sets	set	NOUN
ejpam-6408	496	9	and	and	CCONJ
ejpam-6408	496	10	soft	soft	ADJ
ejpam-6408	496	11	continuity	continuity	NOUN
ejpam-6408	496	12	.	.	PUNCT
ejpam-6408	497	1	international	international	ADJ
ejpam-6408	497	2	journal	journal	PROPN
ejpam-6408	497	3	of	of	ADP
ejpam-6408	497	4	mathematical	mathematical	ADJ
ejpam-6408	497	5	trends	trend	NOUN
ejpam-6408	497	6	and	and	CCONJ
ejpam-6408	497	7	technology	technology	NOUN
ejpam-6408	497	8	,	,	PUNCT
ejpam-6408	497	9	9(1):37–56	9(1):37–56	NUM
ejpam-6408	497	10	,	,	PUNCT
ejpam-6408	497	11	2014	2014	NUM
ejpam-6408	497	12	.	.	PUNCT
ejpam-6408	498	1	[	[	X
ejpam-6408	498	2	44	44	NUM
ejpam-6408	498	3	]	]	PUNCT
ejpam-6408	498	4	a.	a.	NOUN
ejpam-6408	498	5	m.	m.	PROPN
ejpam-6408	498	6	abd	abd	PROPN
ejpam-6408	498	7	el	el	PROPN
ejpam-6408	498	8	-	-	PROPN
ejpam-6408	498	9	latif	latif	PROPN
ejpam-6408	498	10	and	and	CCONJ
ejpam-6408	498	11	s.	s.	PROPN
ejpam-6408	498	12	karataş.	karataş.	PROPN
ejpam-6408	499	1	supra	supra	PROPN
ejpam-6408	499	2	b	b	PROPN
ejpam-6408	499	3	-	-	PUNCT
ejpam-6408	499	4	open	open	ADJ
ejpam-6408	499	5	soft	soft	ADJ
ejpam-6408	499	6	sets	set	NOUN
ejpam-6408	499	7	and	and	CCONJ
ejpam-6408	499	8	supra	supra	PROPN
ejpam-6408	499	9	b	b	NOUN
ejpam-6408	499	10	-	-	PUNCT
ejpam-6408	499	11	soft	soft	ADJ
ejpam-6408	499	12	continuity	continuity	NOUN
ejpam-6408	499	13	on	on	ADP
ejpam-6408	499	14	soft	soft	ADJ
ejpam-6408	499	15	topological	topological	ADJ
ejpam-6408	499	16	spaces	space	NOUN
ejpam-6408	499	17	.	.	PUNCT
ejpam-6408	500	1	journal	journal	NOUN
ejpam-6408	500	2	of	of	ADP
ejpam-6408	500	3	mathematics	mathematics	PROPN
ejpam-6408	500	4	and	and	CCONJ
ejpam-6408	500	5	computer	computer	NOUN
ejpam-6408	500	6	applications	application	NOUN
ejpam-6408	500	7	research	research	NOUN
ejpam-6408	500	8	,	,	PUNCT
ejpam-6408	500	9	5(1):1–18	5(1):1–18	NUM
ejpam-6408	500	10	,	,	PUNCT
ejpam-6408	500	11	2015	2015	NUM
ejpam-6408	500	12	.	.	PUNCT
ejpam-6408	501	1	[	[	X
ejpam-6408	501	2	45	45	NUM
ejpam-6408	501	3	]	]	PUNCT
ejpam-6408	501	4	a.	a.	NOUN
ejpam-6408	501	5	m.	m.	PROPN
ejpam-6408	501	6	abd	abd	PROPN
ejpam-6408	501	7	el	el	PROPN
ejpam-6408	501	8	-	-	PROPN
ejpam-6408	501	9	latif	latif	PROPN
ejpam-6408	501	10	.	.	PUNCT
ejpam-6408	502	1	soft	soft	ADJ
ejpam-6408	502	2	supra	supra	PROPN
ejpam-6408	502	3	strongly	strongly	ADV
ejpam-6408	502	4	generalized	generalize	VERB
ejpam-6408	502	5	closed	closed	ADJ
ejpam-6408	502	6	sets	set	NOUN
ejpam-6408	502	7	.	.	PUNCT
ejpam-6408	503	1	journal	journal	NOUN
ejpam-6408	503	2	of	of	ADP
ejpam-6408	503	3	intelligent	intelligent	ADJ
ejpam-6408	503	4	and	and	CCONJ
ejpam-6408	503	5	fuzzy	fuzzy	ADJ
ejpam-6408	503	6	systems	system	NOUN
ejpam-6408	503	7	,	,	PUNCT
ejpam-6408	503	8	31(3):1311–1317	31(3):1311–1317	NUM
ejpam-6408	503	9	,	,	PUNCT
ejpam-6408	503	10	2016	2016	NUM
ejpam-6408	503	11	.	.	PUNCT
ejpam-6408	504	1	[	[	X
ejpam-6408	504	2	46	46	NUM
ejpam-6408	504	3	]	]	X
ejpam-6408	504	4	a.	a.	NOUN
ejpam-6408	504	5	kandil	kandil	PROPN
ejpam-6408	504	6	,	,	PUNCT
ejpam-6408	504	7	o.	o.	PROPN
ejpam-6408	504	8	a.	a.	PROPN
ejpam-6408	504	9	e.	e.	PROPN
ejpam-6408	504	10	tantawy	tantawy	PROPN
ejpam-6408	504	11	,	,	PUNCT
ejpam-6408	504	12	s.	s.	PROPN
ejpam-6408	504	13	a.	a.	PROPN
ejpam-6408	504	14	el	el	PROPN
ejpam-6408	504	15	-	-	PUNCT
ejpam-6408	504	16	sheikh	sheikh	NOUN
ejpam-6408	504	17	,	,	PUNCT
ejpam-6408	504	18	and	and	CCONJ
ejpam-6408	504	19	a.	a.	NOUN
ejpam-6408	504	20	m.	m.	PROPN
ejpam-6408	504	21	abd	abd	PROPN
ejpam-6408	504	22	el	el	PROPN
ejpam-6408	504	23	-	-	PROPN
ejpam-6408	504	24	latif	latif	PROPN
ejpam-6408	504	25	.	.	PUNCT
ejpam-6408	505	1	supra	supra	PROPN
ejpam-6408	505	2	generalized	generalize	VERB
ejpam-6408	505	3	closed	close	VERB
ejpam-6408	505	4	soft	soft	ADJ
ejpam-6408	505	5	sets	set	NOUN
ejpam-6408	505	6	with	with	ADP
ejpam-6408	505	7	respect	respect	NOUN
ejpam-6408	505	8	to	to	ADP
ejpam-6408	505	9	an	an	DET
ejpam-6408	505	10	soft	soft	ADJ
ejpam-6408	505	11	ideal	ideal	NOUN
ejpam-6408	505	12	in	in	ADP
ejpam-6408	505	13	supra	supra	PROPN
ejpam-6408	505	14	soft	soft	ADJ
ejpam-6408	505	15	topological	topological	ADJ
ejpam-6408	505	16	spaces	space	NOUN
ejpam-6408	505	17	.	.	PUNCT
ejpam-6408	506	1	applied	apply	VERB
ejpam-6408	506	2	mathematics	mathematic	NOUN
ejpam-6408	506	3	and	and	CCONJ
ejpam-6408	506	4	information	information	NOUN
ejpam-6408	506	5	sciences	science	NOUN
ejpam-6408	506	6	,	,	PUNCT
ejpam-6408	506	7	8(4):1731–1740	8(4):1731–1740	PROPN
ejpam-6408	506	8	,	,	PUNCT
ejpam-6408	506	9	2014	2014	NUM
ejpam-6408	506	10	.	.	PUNCT
ejpam-6408	507	1	[	[	X
ejpam-6408	507	2	47	47	NUM
ejpam-6408	507	3	]	]	PUNCT
ejpam-6408	507	4	a.	a.	NOUN
ejpam-6408	507	5	m.	m.	PROPN
ejpam-6408	507	6	abd	abd	PROPN
ejpam-6408	507	7	el	el	PROPN
ejpam-6408	507	8	-	-	PROPN
ejpam-6408	507	9	latif	latif	PROPN
ejpam-6408	507	10	,	,	PUNCT
ejpam-6408	507	11	radwan	radwan	VERB
ejpam-6408	507	12	abu	abu	PROPN
ejpam-6408	507	13	-	-	PUNCT
ejpam-6408	507	14	gdairi	gdairi	PROPN
ejpam-6408	507	15	,	,	PUNCT
ejpam-6408	507	16	a.	a.	PROPN
ejpam-6408	507	17	a.	a.	PROPN
ejpam-6408	507	18	azzam	azzam	PROPN
ejpam-6408	507	19	,	,	PUNCT
ejpam-6408	507	20	f.	f.	PROPN
ejpam-6408	507	21	a.	a.	PROPN
ejpam-6408	507	22	gharib	gharib	PROPN
ejpam-6408	507	23	,	,	PUNCT
ejpam-6408	507	24	and	and	CCONJ
ejpam-6408	507	25	khaled	khaled	PROPN
ejpam-6408	507	26	a.	a.	PROPN
ejpam-6408	507	27	aldwoah	aldwoah	PROPN
ejpam-6408	507	28	.	.	PUNCT
ejpam-6408	508	1	supra	supra	PROPN
ejpam-6408	508	2	soft	soft	ADJ
ejpam-6408	508	3	somewhat	somewhat	ADV
ejpam-6408	508	4	open	open	ADJ
ejpam-6408	508	5	sets	set	NOUN
ejpam-6408	508	6	:	:	PUNCT
ejpam-6408	508	7	characterizations	characterization	NOUN
ejpam-6408	508	8	and	and	CCONJ
ejpam-6408	508	9	continuity	continuity	NOUN
ejpam-6408	508	10	.	.	PUNCT
ejpam-6408	509	1	european	european	ADJ
ejpam-6408	509	2	journal	journal	PROPN
ejpam-6408	509	3	of	of	ADP
ejpam-6408	509	4	pure	pure	ADJ
ejpam-6408	509	5	and	and	CCONJ
ejpam-6408	509	6	applied	applied	ADJ
ejpam-6408	509	7	mathematics	mathematic	NOUN
ejpam-6408	509	8	,	,	PUNCT
ejpam-6408	509	9	18(1):5863	18(1):5863	NUM
ejpam-6408	509	10	,	,	PUNCT
ejpam-6408	509	11	2025	2025	NUM
ejpam-6408	509	12	.	.	PUNCT
ejpam-6408	510	1	[	[	X
ejpam-6408	510	2	48	48	NUM
ejpam-6408	510	3	]	]	PUNCT
ejpam-6408	510	4	a.	a.	NOUN
ejpam-6408	510	5	m.	m.	PROPN
ejpam-6408	510	6	abd	abd	PROPN
ejpam-6408	510	7	el	el	PROPN
ejpam-6408	510	8	-	-	PROPN
ejpam-6408	510	9	latif	latif	PROPN
ejpam-6408	510	10	and	and	CCONJ
ejpam-6408	510	11	m.	m.	PROPN
ejpam-6408	510	12	h.	h.	PROPN
ejpam-6408	510	13	alqahtani	alqahtani	PROPN
ejpam-6408	510	14	.	.	PUNCT
ejpam-6408	511	1	new	new	ADJ
ejpam-6408	511	2	soft	soft	ADJ
ejpam-6408	511	3	operators	operator	NOUN
ejpam-6408	511	4	related	relate	VERB
ejpam-6408	511	5	to	to	ADP
ejpam-6408	511	6	supra	supra	PROPN
ejpam-6408	511	7	soft	soft	ADJ
ejpam-6408	511	8	δi	δi	NOUN
ejpam-6408	511	9	-	-	PUNCT
ejpam-6408	511	10	open	open	ADJ
ejpam-6408	511	11	sets	set	NOUN
ejpam-6408	511	12	and	and	CCONJ
ejpam-6408	511	13	applications	application	NOUN
ejpam-6408	511	14	.	.	PUNCT
ejpam-6408	512	1	aims	aim	VERB
ejpam-6408	512	2	mathematics	mathematic	NOUN
ejpam-6408	512	3	,	,	PUNCT
ejpam-6408	512	4	9(2):3076–3096	9(2):3076–3096	NUM
ejpam-6408	512	5	,	,	PUNCT
ejpam-6408	512	6	2024	2024	NUM
ejpam-6408	512	7	.	.	PUNCT
ejpam-6408	513	1	[	[	X
ejpam-6408	513	2	49	49	NUM
ejpam-6408	513	3	]	]	PUNCT
ejpam-6408	513	4	a.	a.	NOUN
ejpam-6408	513	5	m.	m.	PROPN
ejpam-6408	513	6	abd	abd	PROPN
ejpam-6408	513	7	el	el	PROPN
ejpam-6408	513	8	-	-	PROPN
ejpam-6408	513	9	latif	latif	PROPN
ejpam-6408	513	10	,	,	PUNCT
ejpam-6408	513	11	m.	m.	PROPN
ejpam-6408	513	12	h.	h.	PROPN
ejpam-6408	513	13	alqahtani	alqahtani	PROPN
ejpam-6408	513	14	,	,	PUNCT
ejpam-6408	513	15	and	and	CCONJ
ejpam-6408	513	16	f.	f.	PROPN
ejpam-6408	513	17	a.	a.	PROPN
ejpam-6408	513	18	gharib	gharib	PROPN
ejpam-6408	513	19	.	.	PUNCT
ejpam-6408	514	1	strictly	strictly	ADV
ejpam-6408	514	2	wider	wide	ADJ
ejpam-6408	514	3	class	class	NOUN
ejpam-6408	514	4	of	of	ADP
ejpam-6408	514	5	soft	soft	ADJ
ejpam-6408	514	6	sets	set	NOUN
ejpam-6408	514	7	via	via	ADP
ejpam-6408	514	8	supra	supra	PROPN
ejpam-6408	514	9	soft	soft	PROPN
ejpam-6408	514	10	δ	δ	PROPN
ejpam-6408	514	11	-	-	PUNCT
ejpam-6408	514	12	closure	closure	NOUN
ejpam-6408	514	13	operator	operator	NOUN
ejpam-6408	514	14	.	.	PUNCT
ejpam-6408	515	1	international	international	ADJ
ejpam-6408	515	2	journal	journal	NOUN
ejpam-6408	515	3	of	of	ADP
ejpam-6408	515	4	analysis	analysis	NOUN
ejpam-6408	515	5	and	and	CCONJ
ejpam-6408	515	6	applications	application	NOUN
ejpam-6408	515	7	,	,	PUNCT
ejpam-6408	515	8	22:47	22:47	NUM
ejpam-6408	515	9	,	,	PUNCT
ejpam-6408	515	10	2024	2024	NUM
ejpam-6408	515	11	.	.	PUNCT
ejpam-6408	516	1	[	[	X
ejpam-6408	516	2	50	50	NUM
ejpam-6408	516	3	]	]	PUNCT
ejpam-6408	516	4	s.	s.	PROPN
ejpam-6408	516	5	saleh	saleh	PROPN
ejpam-6408	516	6	,	,	PUNCT
ejpam-6408	516	7	t.	t.	PROPN
ejpam-6408	516	8	al	al	PROPN
ejpam-6408	516	9	-	-	PUNCT
ejpam-6408	516	10	shami	shami	PROPN
ejpam-6408	516	11	,	,	PUNCT
ejpam-6408	516	12	laith	laith	PROPN
ejpam-6408	516	13	r.	r.	PROPN
ejpam-6408	516	14	flaih	flaih	PROPN
ejpam-6408	516	15	,	,	PUNCT
ejpam-6408	516	16	murad	murad	NOUN
ejpam-6408	516	17	arar	arar	NOUN
ejpam-6408	516	18	,	,	PUNCT
ejpam-6408	516	19	and	and	CCONJ
ejpam-6408	516	20	radwan	radwan	VERB
ejpam-6408	516	21	abu	abu	PROPN
ejpam-6408	516	22	-	-	PUNCT
ejpam-6408	516	23	gdairi	gdairi	PROPN
ejpam-6408	516	24	.	.	PUNCT
ejpam-6408	517	1	riseparation	riseparation	NOUN
ejpam-6408	517	2	axioms	axiom	NOUN
ejpam-6408	517	3	via	via	ADP
ejpam-6408	517	4	supra	supra	PROPN
ejpam-6408	517	5	soft	soft	ADJ
ejpam-6408	517	6	topological	topological	ADJ
ejpam-6408	517	7	spaces	space	NOUN
ejpam-6408	517	8	.	.	PUNCT
ejpam-6408	518	1	journal	journal	NOUN
ejpam-6408	518	2	of	of	ADP
ejpam-6408	518	3	mathematics	mathematic	NOUN
ejpam-6408	518	4	and	and	CCONJ
ejpam-6408	518	5	computer	computer	NOUN
ejpam-6408	518	6	science	science	NOUN
ejpam-6408	518	7	,	,	PUNCT
ejpam-6408	518	8	32:263–274	32:263–274	NUM
ejpam-6408	518	9	,	,	PUNCT
ejpam-6408	518	10	2024	2024	NUM
ejpam-6408	518	11	.	.	PUNCT
ejpam-6408	519	1	[	[	X
ejpam-6408	519	2	51	51	NUM
ejpam-6408	519	3	]	]	PUNCT
ejpam-6408	519	4	a.	a.	NOUN
ejpam-6408	519	5	m.	m.	PROPN
ejpam-6408	519	6	abd	abd	PROPN
ejpam-6408	519	7	el	el	PROPN
ejpam-6408	519	8	-	-	PROPN
ejpam-6408	519	9	latif	latif	PROPN
ejpam-6408	519	10	.	.	PUNCT
ejpam-6408	520	1	novel	novel	ADJ
ejpam-6408	520	2	types	type	NOUN
ejpam-6408	520	3	of	of	ADP
ejpam-6408	520	4	supra	supra	ADJ
ejpam-6408	520	5	soft	soft	ADJ
ejpam-6408	520	6	operators	operator	NOUN
ejpam-6408	520	7	via	via	ADP
ejpam-6408	520	8	supra	supra	PROPN
ejpam-6408	520	9	soft	soft	ADJ
ejpam-6408	520	10	sd	sd	NOUN
ejpam-6408	520	11	-	-	PUNCT
ejpam-6408	520	12	sets	set	NOUN
ejpam-6408	520	13	and	and	CCONJ
ejpam-6408	520	14	m.	m.	NOUN
ejpam-6408	520	15	aldawood	aldawood	PROPN
ejpam-6408	520	16	et	et	PROPN
ejpam-6408	520	17	al	al	PROPN
ejpam-6408	520	18	.	.	PUNCT
ejpam-6408	520	19	/	/	SYM
ejpam-6408	520	20	eur	eur	PROPN
ejpam-6408	520	21	.	.	PUNCT
ejpam-6408	521	1	j.	j.	PROPN
ejpam-6408	521	2	pure	pure	PROPN
ejpam-6408	521	3	appl	appl	PROPN
ejpam-6408	521	4	.	.	PROPN
ejpam-6408	521	5	math	math	PROPN
ejpam-6408	521	6	,	,	PUNCT
ejpam-6408	521	7	18	18	NUM
ejpam-6408	521	8	(	(	PUNCT
ejpam-6408	521	9	3	3	NUM
ejpam-6408	521	10	)	)	PUNCT
ejpam-6408	521	11	(	(	PUNCT
ejpam-6408	521	12	2025	2025	NUM
ejpam-6408	521	13	)	)	PUNCT
ejpam-6408	521	14	,	,	PUNCT
ejpam-6408	521	15	6408	6408	NUM
ejpam-6408	521	16	16	16	NUM
ejpam-6408	521	17	of	of	ADP
ejpam-6408	521	18	16	16	NUM
ejpam-6408	521	19	applications	application	NOUN
ejpam-6408	521	20	.	.	PUNCT
ejpam-6408	522	1	aims	aim	VERB
ejpam-6408	522	2	mathematics	mathematic	NOUN
ejpam-6408	522	3	,	,	PUNCT
ejpam-6408	522	4	9(3):6586–6602	9(3):6586–6602	PROPN
ejpam-6408	522	5	,	,	PUNCT
ejpam-6408	522	6	2024	2024	NUM
ejpam-6408	522	7	.	.	PUNCT
ejpam-6408	523	1	[	[	X
ejpam-6408	523	2	52	52	NUM
ejpam-6408	523	3	]	]	PUNCT
ejpam-6408	523	4	a.	a.	NOUN
ejpam-6408	523	5	m.	m.	PROPN
ejpam-6408	523	6	abd	abd	PROPN
ejpam-6408	523	7	el	el	PROPN
ejpam-6408	523	8	-	-	PROPN
ejpam-6408	523	9	latif	latif	PROPN
ejpam-6408	523	10	and	and	CCONJ
ejpam-6408	523	11	m.	m.	PROPN
ejpam-6408	523	12	h.	h.	PROPN
ejpam-6408	523	13	alqahtani	alqahtani	PROPN
ejpam-6408	523	14	.	.	PUNCT
ejpam-6408	524	1	novel	novel	ADJ
ejpam-6408	524	2	categories	category	NOUN
ejpam-6408	524	3	of	of	ADP
ejpam-6408	524	4	supra	supra	ADJ
ejpam-6408	524	5	soft	soft	ADJ
ejpam-6408	524	6	continuous	continuous	ADJ
ejpam-6408	524	7	maps	map	NOUN
ejpam-6408	524	8	via	via	ADP
ejpam-6408	524	9	new	new	ADJ
ejpam-6408	524	10	soft	soft	ADJ
ejpam-6408	524	11	operators	operator	NOUN
ejpam-6408	524	12	.	.	PUNCT
ejpam-6408	525	1	aims	aim	VERB
ejpam-6408	525	2	mathematics	mathematic	NOUN
ejpam-6408	525	3	,	,	PUNCT
ejpam-6408	525	4	9:7449–7470	9:7449–7470	NUM
ejpam-6408	525	5	,	,	PUNCT
ejpam-6408	525	6	2024	2024	NUM
ejpam-6408	525	7	.	.	PUNCT
ejpam-6408	526	1	[	[	X
ejpam-6408	526	2	53	53	NUM
ejpam-6408	526	3	]	]	PUNCT
ejpam-6408	526	4	a.	a.	NOUN
ejpam-6408	526	5	m.	m.	PROPN
ejpam-6408	526	6	abd	abd	PROPN
ejpam-6408	526	7	el	el	PROPN
ejpam-6408	526	8	-	-	PROPN
ejpam-6408	526	9	latif	latif	PROPN
ejpam-6408	526	10	,	,	PUNCT
ejpam-6408	526	11	a.	a.	PROPN
ejpam-6408	526	12	a.	a.	PROPN
ejpam-6408	526	13	azzam	azzam	PROPN
ejpam-6408	526	14	,	,	PUNCT
ejpam-6408	526	15	radwan	radwan	VERB
ejpam-6408	526	16	abu	abu	PROPN
ejpam-6408	526	17	-	-	PUNCT
ejpam-6408	526	18	gdairi	gdairi	PROPN
ejpam-6408	526	19	,	,	PUNCT
ejpam-6408	526	20	m.	m.	NOUN
ejpam-6408	526	21	aldawood	aldawood	PROPN
ejpam-6408	526	22	,	,	PUNCT
ejpam-6408	526	23	and	and	CCONJ
ejpam-6408	526	24	m.	m.	PROPN
ejpam-6408	526	25	h.	h.	PROPN
ejpam-6408	526	26	alqahtani	alqahtani	PROPN
ejpam-6408	526	27	.	.	PUNCT
ejpam-6408	527	1	new	new	ADJ
ejpam-6408	527	2	versions	version	NOUN
ejpam-6408	527	3	of	of	ADP
ejpam-6408	527	4	maps	map	NOUN
ejpam-6408	527	5	and	and	CCONJ
ejpam-6408	527	6	connected	connected	ADJ
ejpam-6408	527	7	spaces	space	NOUN
ejpam-6408	527	8	via	via	ADP
ejpam-6408	527	9	supra	supra	PROPN
ejpam-6408	527	10	soft	soft	ADJ
ejpam-6408	527	11	sd	sd	NOUN
ejpam-6408	527	12	-	-	PUNCT
ejpam-6408	527	13	operators	operator	NOUN
ejpam-6408	527	14	.	.	PUNCT
ejpam-6408	528	1	plos	plos	PROPN
ejpam-6408	528	2	one	one	NUM
ejpam-6408	528	3	,	,	PUNCT
ejpam-6408	528	4	19(10):e0304042	19(10):e0304042	NUM
ejpam-6408	528	5	,	,	PUNCT
ejpam-6408	528	6	2024	2024	NUM
ejpam-6408	528	7	.	.	PUNCT
ejpam-6408	529	1	[	[	X
ejpam-6408	529	2	54	54	NUM
ejpam-6408	529	3	]	]	PUNCT
ejpam-6408	529	4	a.	a.	NOUN
ejpam-6408	529	5	m.	m.	PROPN
ejpam-6408	529	6	abd	abd	PROPN
ejpam-6408	529	7	el	el	PROPN
ejpam-6408	529	8	-	-	PROPN
ejpam-6408	529	9	latif	latif	PROPN
ejpam-6408	529	10	,	,	PUNCT
ejpam-6408	529	11	radwan	radwan	VERB
ejpam-6408	529	12	abu	abu	PROPN
ejpam-6408	529	13	-	-	PUNCT
ejpam-6408	529	14	gdairi	gdairi	PROPN
ejpam-6408	529	15	,	,	PUNCT
ejpam-6408	529	16	a.	a.	PROPN
ejpam-6408	529	17	a.	a.	PROPN
ejpam-6408	529	18	azzam	azzam	PROPN
ejpam-6408	529	19	,	,	PUNCT
ejpam-6408	529	20	khaled	khaled	PROPN
ejpam-6408	529	21	a.	a.	PROPN
ejpam-6408	529	22	aldwoah	aldwoah	PROPN
ejpam-6408	529	23	,	,	PUNCT
ejpam-6408	529	24	m.	m.	NOUN
ejpam-6408	529	25	aldawood	aldawood	PROPN
ejpam-6408	529	26	,	,	PUNCT
ejpam-6408	529	27	and	and	CCONJ
ejpam-6408	529	28	shaaban	shaaban	ADJ
ejpam-6408	529	29	m.	m.	NOUN
ejpam-6408	529	30	shaaban	shaaban	PROPN
ejpam-6408	529	31	.	.	PUNCT
ejpam-6408	530	1	applications	application	NOUN
ejpam-6408	530	2	of	of	ADP
ejpam-6408	530	3	the	the	DET
ejpam-6408	530	4	supra	supra	PROPN
ejpam-6408	530	5	soft	soft	ADJ
ejpam-6408	530	6	sd	sd	NOUN
ejpam-6408	530	7	-	-	PUNCT
ejpam-6408	530	8	closure	closure	NOUN
ejpam-6408	530	9	operator	operator	NOUN
ejpam-6408	530	10	to	to	ADP
ejpam-6408	530	11	soft	soft	ADJ
ejpam-6408	530	12	connectedness	connectedness	NOUN
ejpam-6408	530	13	and	and	CCONJ
ejpam-6408	530	14	compactness	compactness	NOUN
ejpam-6408	530	15	.	.	PUNCT
ejpam-6408	531	1	european	european	ADJ
ejpam-6408	531	2	journal	journal	PROPN
ejpam-6408	531	3	of	of	ADP
ejpam-6408	531	4	pure	pure	ADJ
ejpam-6408	531	5	and	and	CCONJ
ejpam-6408	531	6	applied	applied	ADJ
ejpam-6408	531	7	mathematics	mathematic	NOUN
ejpam-6408	531	8	,	,	PUNCT
ejpam-6408	531	9	18(2):5896	18(2):5896	NUM
ejpam-6408	531	10	,	,	PUNCT
ejpam-6408	531	11	2025	2025	NUM
ejpam-6408	531	12	.	.	PUNCT
ejpam-6408	532	1	[	[	X
ejpam-6408	532	2	55	55	NUM
ejpam-6408	532	3	]	]	PUNCT
ejpam-6408	532	4	a.	a.	NOUN
ejpam-6408	532	5	m.	m.	PROPN
ejpam-6408	532	6	abd	abd	PROPN
ejpam-6408	532	7	el	el	PROPN
ejpam-6408	532	8	-	-	PROPN
ejpam-6408	532	9	latif	latif	PROPN
ejpam-6408	532	10	.	.	PUNCT
ejpam-6408	533	1	specific	specific	ADJ
ejpam-6408	533	2	types	type	NOUN
ejpam-6408	533	3	of	of	ADP
ejpam-6408	533	4	lindelofness	lindelofness	NOUN
ejpam-6408	533	5	and	and	CCONJ
ejpam-6408	533	6	compactness	compactness	NOUN
ejpam-6408	533	7	based	base	VERB
ejpam-6408	533	8	on	on	ADP
ejpam-6408	533	9	novel	novel	ADJ
ejpam-6408	533	10	supra	supra	ADJ
ejpam-6408	533	11	soft	soft	ADJ
ejpam-6408	533	12	operator	operator	NOUN
ejpam-6408	533	13	.	.	PUNCT
ejpam-6408	534	1	aims	aim	VERB
ejpam-6408	534	2	mathematics	mathematic	NOUN
ejpam-6408	534	3	,	,	PUNCT
ejpam-6408	534	4	10(4):8144–8164	10(4):8144–8164	NUM
ejpam-6408	534	5	,	,	PUNCT
ejpam-6408	534	6	2025	2025	NUM
ejpam-6408	534	7	.	.	PUNCT
ejpam-6408	535	1	[	[	X
ejpam-6408	535	2	56	56	NUM
ejpam-6408	535	3	]	]	PUNCT
ejpam-6408	535	4	m.	m.	NOUN
ejpam-6408	535	5	h.	h.	PROPN
ejpam-6408	535	6	alqahtani	alqahtani	PROPN
ejpam-6408	535	7	and	and	CCONJ
ejpam-6408	535	8	zanyar	zanyar	PROPN
ejpam-6408	535	9	a.	a.	NOUN
ejpam-6408	535	10	ameen	ameen	PROPN
ejpam-6408	535	11	.	.	PUNCT
ejpam-6408	536	1	soft	soft	ADJ
ejpam-6408	536	2	nodec	nodec	ADJ
ejpam-6408	536	3	spaces	space	NOUN
ejpam-6408	536	4	.	.	PUNCT
ejpam-6408	537	1	aims	aim	VERB
ejpam-6408	537	2	mathematics	mathematic	NOUN
ejpam-6408	537	3	,	,	PUNCT
ejpam-6408	537	4	9(2):3289–3302	9(2):3289–3302	PROPN
ejpam-6408	537	5	,	,	PUNCT
ejpam-6408	537	6	2024	2024	NUM
ejpam-6408	537	7	.	.	PUNCT
ejpam-6408	538	1	[	[	X
ejpam-6408	538	2	57	57	NUM
ejpam-6408	538	3	]	]	PUNCT
ejpam-6408	538	4	m.	m.	NOUN
ejpam-6408	538	5	h.	h.	PROPN
ejpam-6408	538	6	alqahtani	alqahtani	PROPN
ejpam-6408	538	7	,	,	PUNCT
ejpam-6408	538	8	o.	o.	PROPN
ejpam-6408	538	9	f.	f.	PROPN
ejpam-6408	538	10	alghamdi	alghamdi	PROPN
ejpam-6408	538	11	,	,	PUNCT
ejpam-6408	538	12	and	and	CCONJ
ejpam-6408	538	13	z.	z.	PROPN
ejpam-6408	538	14	a.	a.	PROPN
ejpam-6408	538	15	ameen	ameen	PROPN
ejpam-6408	538	16	.	.	PUNCT
ejpam-6408	539	1	nodecness	nodecness	NOUN
ejpam-6408	539	2	of	of	ADP
ejpam-6408	539	3	soft	soft	ADJ
ejpam-6408	539	4	generalized	generalized	ADJ
ejpam-6408	539	5	topological	topological	ADJ
ejpam-6408	539	6	spaces	space	NOUN
ejpam-6408	539	7	.	.	PUNCT
ejpam-6408	540	1	international	international	ADJ
ejpam-6408	540	2	journal	journal	NOUN
ejpam-6408	540	3	of	of	ADP
ejpam-6408	540	4	analysis	analysis	NOUN
ejpam-6408	540	5	and	and	CCONJ
ejpam-6408	540	6	applications	application	NOUN
ejpam-6408	540	7	,	,	PUNCT
ejpam-6408	540	8	22:149	22:149	NUM
ejpam-6408	540	9	,	,	PUNCT
ejpam-6408	540	10	2024	2024	NUM
ejpam-6408	540	11	.	.	PUNCT
ejpam-6408	541	1	[	[	X
ejpam-6408	541	2	58	58	NUM
ejpam-6408	541	3	]	]	PUNCT
ejpam-6408	541	4	a.	a.	NOUN
ejpam-6408	541	5	m.	m.	PROPN
ejpam-6408	541	6	abd	abd	PROPN
ejpam-6408	541	7	el	el	PROPN
ejpam-6408	541	8	-	-	PROPN
ejpam-6408	541	9	latif	latif	PROPN
ejpam-6408	541	10	,	,	PUNCT
ejpam-6408	541	11	radwan	radwan	VERB
ejpam-6408	541	12	abu	abu	PROPN
ejpam-6408	541	13	-	-	PUNCT
ejpam-6408	541	14	gdairi	gdairi	PROPN
ejpam-6408	541	15	,	,	PUNCT
ejpam-6408	541	16	a.	a.	PROPN
ejpam-6408	541	17	a.	a.	PROPN
ejpam-6408	541	18	azzam	azzam	PROPN
ejpam-6408	541	19	,	,	PUNCT
ejpam-6408	541	20	husham	husham	PROPN
ejpam-6408	541	21	m.	m.	PROPN
ejpam-6408	541	22	attaalfadeel	attaalfadeel	PROPN
ejpam-6408	541	23	,	,	PUNCT
ejpam-6408	541	24	shaaban	shaaban	ADJ
ejpam-6408	541	25	m.	m.	NOUN
ejpam-6408	541	26	shaaban	shaaban	PROPN
ejpam-6408	541	27	,	,	PUNCT
ejpam-6408	541	28	m.	m.	NOUN
ejpam-6408	541	29	aldawood	aldawood	PROPN
ejpam-6408	541	30	,	,	PUNCT
ejpam-6408	541	31	and	and	CCONJ
ejpam-6408	541	32	khaled	khaled	PROPN
ejpam-6408	541	33	a.	a.	PROPN
ejpam-6408	541	34	aldwoah	aldwoah	PROPN
ejpam-6408	541	35	.	.	PUNCT
ejpam-6408	542	1	supra	supra	PROPN
ejpam-6408	542	2	ϵ-open	ϵ-open	PROPN
ejpam-6408	542	3	sets	set	NOUN
ejpam-6408	542	4	:	:	PUNCT
ejpam-6408	542	5	features	feature	NOUN
ejpam-6408	542	6	,	,	PUNCT
ejpam-6408	542	7	operators	operator	NOUN
ejpam-6408	542	8	and	and	CCONJ
ejpam-6408	542	9	applications	application	NOUN
ejpam-6408	542	10	.	.	PUNCT
ejpam-6408	543	1	european	european	ADJ
ejpam-6408	543	2	journal	journal	PROPN
ejpam-6408	543	3	of	of	ADP
ejpam-6408	543	4	pure	pure	ADJ
ejpam-6408	543	5	and	and	CCONJ
ejpam-6408	543	6	applied	applied	ADJ
ejpam-6408	543	7	mathematics	mathematic	NOUN
ejpam-6408	543	8	,	,	PUNCT
ejpam-6408	543	9	18(2):5969	18(2):5969	NUM
ejpam-6408	543	10	,	,	PUNCT
ejpam-6408	543	11	2025	2025	NUM
ejpam-6408	543	12	.	.	PUNCT
ejpam-6408	544	1	[	[	X
ejpam-6408	544	2	59	59	NUM
ejpam-6408	544	3	]	]	PUNCT
ejpam-6408	544	4	a.	a.	NOUN
ejpam-6408	544	5	m.	m.	PROPN
ejpam-6408	544	6	abd	abd	PROPN
ejpam-6408	544	7	el	el	PROPN
ejpam-6408	544	8	-	-	PROPN
ejpam-6408	544	9	latif	latif	PROPN
ejpam-6408	544	10	,	,	PUNCT
ejpam-6408	544	11	radwan	radwan	VERB
ejpam-6408	544	12	abu	abu	PROPN
ejpam-6408	544	13	-	-	PUNCT
ejpam-6408	544	14	gdairi	gdairi	PROPN
ejpam-6408	544	15	,	,	PUNCT
ejpam-6408	544	16	abd	abd	PROPN
ejpam-6408	544	17	elfattah	elfattah	PROPN
ejpam-6408	544	18	azzam	azzam	PROPN
ejpam-6408	544	19	,	,	PUNCT
ejpam-6408	544	20	fatouh	fatouh	PROPN
ejpam-6408	544	21	gharib	gharib	PROPN
ejpam-6408	544	22	,	,	PUNCT
ejpam-6408	544	23	husham	husham	PROPN
ejpam-6408	544	24	mohammed	mohammed	PROPN
ejpam-6408	544	25	alhassan	alhassan	PROPN
ejpam-6408	544	26	attaalfadeel	attaalfadeel	PROPN
ejpam-6408	544	27	,	,	PUNCT
ejpam-6408	544	28	walid	walid	PROPN
ejpam-6408	544	29	abdelfattah	abdelfattah	PROPN
ejpam-6408	544	30	,	,	PUNCT
ejpam-6408	544	31	shaaban	shaaban	ADJ
ejpam-6408	544	32	m.	m.	NOUN
ejpam-6408	544	33	shaaban	shaaban	PROPN
ejpam-6408	544	34	,	,	PUNCT
ejpam-6408	544	35	and	and	CCONJ
ejpam-6408	544	36	m.	m.	PROPN
ejpam-6408	544	37	aldawood	aldawood	PROPN
ejpam-6408	544	38	.	.	PUNCT
ejpam-6408	545	1	novel	novel	ADJ
ejpam-6408	545	2	types	type	NOUN
ejpam-6408	545	3	of	of	ADP
ejpam-6408	545	4	supra	supra	ADJ
ejpam-6408	545	5	functions	function	NOUN
ejpam-6408	545	6	inspired	inspire	VERB
ejpam-6408	545	7	by	by	ADP
ejpam-6408	545	8	supra	supra	PROPN
ejpam-6408	545	9	ϵ-open	ϵ-open	PROPN
ejpam-6408	545	10	sets	set	NOUN
ejpam-6408	545	11	.	.	PUNCT
ejpam-6408	546	1	european	european	ADJ
ejpam-6408	546	2	journal	journal	PROPN
ejpam-6408	546	3	of	of	ADP
ejpam-6408	546	4	pure	pure	ADJ
ejpam-6408	546	5	and	and	CCONJ
ejpam-6408	546	6	applied	applied	ADJ
ejpam-6408	546	7	mathematics	mathematic	NOUN
ejpam-6408	546	8	,	,	PUNCT
ejpam-6408	546	9	18(2):6020	18(2):6020	NUM
ejpam-6408	546	10	,	,	PUNCT
ejpam-6408	546	11	2025	2025	NUM
ejpam-6408	546	12	.	.	PUNCT
ejpam-6408	547	1	[	[	X
ejpam-6408	547	2	60	60	NUM
ejpam-6408	547	3	]	]	PUNCT
ejpam-6408	547	4	m.	m.	NOUN
ejpam-6408	547	5	aldawood	aldawood	PROPN
ejpam-6408	547	6	,	,	PUNCT
ejpam-6408	547	7	a.	a.	NOUN
ejpam-6408	547	8	m.	m.	PROPN
ejpam-6408	547	9	abd	abd	PROPN
ejpam-6408	547	10	el	el	PROPN
ejpam-6408	547	11	-	-	PROPN
ejpam-6408	547	12	latif	latif	PROPN
ejpam-6408	547	13	,	,	PUNCT
ejpam-6408	547	14	radwan	radwan	VERB
ejpam-6408	547	15	abu	abu	PROPN
ejpam-6408	547	16	-	-	PUNCT
ejpam-6408	547	17	gdairi	gdairi	PROPN
ejpam-6408	547	18	,	,	PUNCT
ejpam-6408	547	19	a.	a.	PROPN
ejpam-6408	547	20	a.	a.	PROPN
ejpam-6408	547	21	azzam	azzam	PROPN
ejpam-6408	547	22	,	,	PUNCT
ejpam-6408	547	23	abdelhalim	abdelhalim	PROPN
ejpam-6408	547	24	hasnaoui	hasnaoui	PROPN
ejpam-6408	547	25	,	,	PUNCT
ejpam-6408	547	26	m.	m.	NOUN
ejpam-6408	547	27	i.	i.	PROPN
ejpam-6408	547	28	elashiry	elashiry	PROPN
ejpam-6408	547	29	,	,	PUNCT
ejpam-6408	547	30	husham	husham	PROPN
ejpam-6408	547	31	m.	m.	PROPN
ejpam-6408	547	32	attaalfadeel	attaalfadeel	PROPN
ejpam-6408	547	33	,	,	PUNCT
ejpam-6408	547	34	and	and	CCONJ
ejpam-6408	547	35	enas	enas	PROPN
ejpam-6408	547	36	h.	h.	PROPN
ejpam-6408	547	37	elkordy	elkordy	PROPN
ejpam-6408	547	38	.	.	PUNCT
ejpam-6408	548	1	various	various	ADJ
ejpam-6408	548	2	types	type	NOUN
ejpam-6408	548	3	of	of	ADP
ejpam-6408	548	4	supra	supra	ADJ
ejpam-6408	548	5	ϵ-separation	ϵ-separation	NOUN
ejpam-6408	548	6	axioms	axiom	NOUN
ejpam-6408	548	7	and	and	CCONJ
ejpam-6408	548	8	relationships	relationship	NOUN
ejpam-6408	548	9	.	.	PUNCT
ejpam-6408	549	1	european	european	ADJ
ejpam-6408	549	2	journal	journal	PROPN
ejpam-6408	549	3	of	of	ADP
ejpam-6408	549	4	pure	pure	ADJ
ejpam-6408	549	5	and	and	CCONJ
ejpam-6408	549	6	applied	applied	ADJ
ejpam-6408	549	7	mathematics	mathematic	NOUN
ejpam-6408	549	8	,	,	PUNCT
ejpam-6408	549	9	18(3):6407	18(3):6407	NUM
ejpam-6408	549	10	,	,	PUNCT
ejpam-6408	549	11	2025	2025	NUM
ejpam-6408	549	12	.	.	PUNCT
ejpam-6408	550	1	[	[	X
ejpam-6408	550	2	61	61	NUM
ejpam-6408	550	3	]	]	PUNCT
ejpam-6408	550	4	a.	a.	NOUN
ejpam-6408	550	5	m.	m.	PROPN
ejpam-6408	550	6	abd	abd	PROPN
ejpam-6408	550	7	el	el	PROPN
ejpam-6408	550	8	-	-	PROPN
ejpam-6408	550	9	latif	latif	PROPN
ejpam-6408	550	10	.	.	PUNCT
ejpam-6408	551	1	some	some	DET
ejpam-6408	551	2	properties	property	NOUN
ejpam-6408	551	3	of	of	ADP
ejpam-6408	551	4	fuzzy	fuzzy	ADJ
ejpam-6408	551	5	supra	supra	PROPN
ejpam-6408	551	6	soft	soft	ADJ
ejpam-6408	551	7	topological	topological	ADJ
ejpam-6408	551	8	spaces	space	NOUN
ejpam-6408	551	9	.	.	PUNCT
ejpam-6408	552	1	european	european	ADJ
ejpam-6408	552	2	journal	journal	PROPN
ejpam-6408	552	3	of	of	ADP
ejpam-6408	552	4	pure	pure	ADJ
ejpam-6408	552	5	and	and	CCONJ
ejpam-6408	552	6	applied	applied	ADJ
ejpam-6408	552	7	mathematics	mathematic	NOUN
ejpam-6408	552	8	,	,	PUNCT
ejpam-6408	552	9	12(3):999–1017	12(3):999–1017	NUM
ejpam-6408	552	10	,	,	PUNCT
ejpam-6408	552	11	2019	2019	NUM
ejpam-6408	552	12	.	.	PUNCT
ejpam-6408	553	1	[	[	X
ejpam-6408	553	2	62	62	NUM
ejpam-6408	553	3	]	]	PUNCT
ejpam-6408	553	4	a.	a.	NOUN
ejpam-6408	553	5	m.	m.	PROPN
ejpam-6408	553	6	abd	abd	PROPN
ejpam-6408	553	7	el	el	PROPN
ejpam-6408	553	8	-	-	PROPN
ejpam-6408	553	9	latif	latif	PROPN
ejpam-6408	553	10	.	.	PUNCT
ejpam-6408	554	1	results	result	NOUN
ejpam-6408	554	2	on	on	ADP
ejpam-6408	554	3	fuzzy	fuzzy	ADJ
ejpam-6408	554	4	supra	supra	PROPN
ejpam-6408	554	5	soft	soft	ADJ
ejpam-6408	554	6	topological	topological	ADJ
ejpam-6408	554	7	spaces	space	NOUN
ejpam-6408	554	8	.	.	PUNCT
ejpam-6408	555	1	journal	journal	NOUN
ejpam-6408	555	2	of	of	ADP
ejpam-6408	555	3	interdisciplinary	interdisciplinary	ADJ
ejpam-6408	555	4	mathematics	mathematic	NOUN
ejpam-6408	555	5	,	,	PUNCT
ejpam-6408	555	6	22(8):1311–1323	22(8):1311–1323	NUM
ejpam-6408	555	7	,	,	PUNCT
ejpam-6408	555	8	2019	2019	NUM
ejpam-6408	555	9	.	.	PUNCT