id	sid	tid	token	lemma	pos
ejpam-5969	1	1	european	european	PROPN
ejpam-5969	1	2	journal	journal	PROPN
ejpam-5969	1	3	of	of	ADP
ejpam-5969	1	4	pure	pure	ADJ
ejpam-5969	1	5	and	and	CCONJ
ejpam-5969	1	6	applied	applied	ADJ
ejpam-5969	1	7	mathematics	mathematic	NOUN
ejpam-5969	1	8	2025	2025	NUM
ejpam-5969	1	9	,	,	PUNCT
ejpam-5969	1	10	vol	vol	NOUN
ejpam-5969	1	11	.	.	PROPN
ejpam-5969	1	12	18	18	NUM
ejpam-5969	1	13	,	,	PUNCT
ejpam-5969	1	14	issue	issue	NOUN
ejpam-5969	1	15	2	2	NUM
ejpam-5969	1	16	,	,	PUNCT
ejpam-5969	1	17	article	article	NOUN
ejpam-5969	1	18	number	number	NOUN
ejpam-5969	1	19	5969	5969	NUM
ejpam-5969	1	20	issn	issn	PROPN
ejpam-5969	1	21	1307	1307	NUM
ejpam-5969	1	22	-	-	SYM
ejpam-5969	1	23	5543	5543	NUM
ejpam-5969	1	24	–	–	PUNCT
ejpam-5969	1	25	ejpam.com	ejpam.com	X
ejpam-5969	1	26	published	publish	VERB
ejpam-5969	1	27	by	by	ADP
ejpam-5969	1	28	new	new	PROPN
ejpam-5969	1	29	york	york	PROPN
ejpam-5969	1	30	business	business	PROPN
ejpam-5969	1	31	global	global	PROPN
ejpam-5969	1	32	supra	supra	PROPN
ejpam-5969	1	33	ϵ-open	ϵ-open	PROPN
ejpam-5969	1	34	sets	set	NOUN
ejpam-5969	1	35	:	:	PUNCT
ejpam-5969	1	36	features	feature	NOUN
ejpam-5969	1	37	,	,	PUNCT
ejpam-5969	1	38	operators	operator	NOUN
ejpam-5969	1	39	and	and	CCONJ
ejpam-5969	1	40	applications	application	NOUN
ejpam-5969	2	1	alaa	alaa	PROPN
ejpam-5969	2	2	m.	m.	PROPN
ejpam-5969	2	3	abd	abd	PROPN
ejpam-5969	2	4	el	el	PROPN
ejpam-5969	2	5	-	-	PROPN
ejpam-5969	2	6	latif1	latif1	PROPN
ejpam-5969	2	7	,	,	PUNCT
ejpam-5969	2	8	radwan	radwan	VERB
ejpam-5969	2	9	abu	abu	PROPN
ejpam-5969	2	10	-	-	PUNCT
ejpam-5969	2	11	gdairi2	gdairi2	PROPN
ejpam-5969	2	12	,	,	PUNCT
ejpam-5969	3	1	a.	a.	NOUN
ejpam-5969	3	2	a.	a.	NOUN
ejpam-5969	3	3	azzam3,4	azzam3,4	PROPN
ejpam-5969	3	4	,	,	PUNCT
ejpam-5969	3	5	husham	husham	PROPN
ejpam-5969	3	6	m.	m.	NOUN
ejpam-5969	3	7	attaalfadeel1,∗	attaalfadeel1,∗	PROPN
ejpam-5969	3	8	,	,	PUNCT
ejpam-5969	3	9	shaaban	shaaban	ADJ
ejpam-5969	3	10	m.	m.	NOUN
ejpam-5969	3	11	shaaban5	shaaban5	PROPN
ejpam-5969	3	12	,	,	PUNCT
ejpam-5969	3	13	m.	m.	NOUN
ejpam-5969	3	14	aldawood3	aldawood3	PROPN
ejpam-5969	3	15	,	,	PUNCT
ejpam-5969	3	16	khaled	khaled	PROPN
ejpam-5969	3	17	a.	a.	PROPN
ejpam-5969	3	18	aldwoah6	aldwoah6	PROPN
ejpam-5969	4	1	1	1	NUM
ejpam-5969	4	2	mathematics	mathematics	PROPN
ejpam-5969	4	3	department	department	NOUN
ejpam-5969	4	4	,	,	PUNCT
ejpam-5969	4	5	college	college	NOUN
ejpam-5969	4	6	of	of	ADP
ejpam-5969	4	7	science	science	NOUN
ejpam-5969	4	8	,	,	PUNCT
ejpam-5969	4	9	northern	northern	ADJ
ejpam-5969	4	10	border	border	NOUN
ejpam-5969	4	11	university	university	NOUN
ejpam-5969	4	12	,	,	PUNCT
ejpam-5969	4	13	arar	arar	NOUN
ejpam-5969	4	14	91431	91431	NUM
ejpam-5969	4	15	,	,	PUNCT
ejpam-5969	4	16	saudi	saudi	PROPN
ejpam-5969	4	17	arabia	arabia	PROPN
ejpam-5969	4	18	2	2	NUM
ejpam-5969	4	19	mathematics	mathematics	PROPN
ejpam-5969	4	20	department	department	NOUN
ejpam-5969	4	21	,	,	PUNCT
ejpam-5969	4	22	faculty	faculty	NOUN
ejpam-5969	4	23	of	of	ADP
ejpam-5969	4	24	science	science	NOUN
ejpam-5969	4	25	,	,	PUNCT
ejpam-5969	4	26	zarqa	zarqa	PROPN
ejpam-5969	4	27	university	university	PROPN
ejpam-5969	4	28	,	,	PUNCT
ejpam-5969	4	29	zarqa	zarqa	NOUN
ejpam-5969	4	30	13132	13132	NUM
ejpam-5969	4	31	,	,	PUNCT
ejpam-5969	4	32	jordan	jordan	PROPN
ejpam-5969	4	33	3	3	NUM
ejpam-5969	4	34	department	department	PROPN
ejpam-5969	4	35	of	of	ADP
ejpam-5969	4	36	mathematics	mathematic	NOUN
ejpam-5969	4	37	,	,	PUNCT
ejpam-5969	4	38	faculty	faculty	NOUN
ejpam-5969	4	39	of	of	ADP
ejpam-5969	4	40	science	science	NOUN
ejpam-5969	4	41	and	and	CCONJ
ejpam-5969	4	42	humanities	humanity	NOUN
ejpam-5969	4	43	,	,	PUNCT
ejpam-5969	4	44	prince	prince	PROPN
ejpam-5969	4	45	sattam	sattam	PROPN
ejpam-5969	4	46	bin	bin	PROPN
ejpam-5969	4	47	abdulaziz	abdulaziz	PROPN
ejpam-5969	4	48	university	university	PROPN
ejpam-5969	4	49	,	,	PUNCT
ejpam-5969	4	50	alkharj	alkharj	VERB
ejpam-5969	4	51	11942	11942	NUM
ejpam-5969	4	52	,	,	PUNCT
ejpam-5969	4	53	saudi	saudi	PROPN
ejpam-5969	4	54	arabia	arabia	PROPN
ejpam-5969	4	55	4	4	NUM
ejpam-5969	4	56	department	department	NOUN
ejpam-5969	4	57	of	of	ADP
ejpam-5969	4	58	mathematics	mathematic	NOUN
ejpam-5969	4	59	,	,	PUNCT
ejpam-5969	4	60	faculty	faculty	NOUN
ejpam-5969	4	61	of	of	ADP
ejpam-5969	4	62	science	science	NOUN
ejpam-5969	4	63	,	,	PUNCT
ejpam-5969	4	64	new	new	ADJ
ejpam-5969	4	65	valley	valley	NOUN
ejpam-5969	4	66	university	university	NOUN
ejpam-5969	4	67	,	,	PUNCT
ejpam-5969	4	68	elkharga	elkharga	NOUN
ejpam-5969	4	69	72511	72511	NUM
ejpam-5969	4	70	,	,	PUNCT
ejpam-5969	4	71	egypt	egypt	PROPN
ejpam-5969	4	72	5	5	NUM
ejpam-5969	4	73	center	center	NOUN
ejpam-5969	4	74	for	for	ADP
ejpam-5969	4	75	scientific	scientific	ADJ
ejpam-5969	4	76	research	research	NOUN
ejpam-5969	4	77	and	and	CCONJ
ejpam-5969	4	78	entrepreneurship	entrepreneurship	NOUN
ejpam-5969	4	79	,	,	PUNCT
ejpam-5969	4	80	northern	northern	ADJ
ejpam-5969	4	81	border	border	NOUN
ejpam-5969	4	82	university	university	NOUN
ejpam-5969	4	83	,	,	PUNCT
ejpam-5969	4	84	arar	arar	PROPN
ejpam-5969	4	85	73213	73213	NUM
ejpam-5969	4	86	,	,	PUNCT
ejpam-5969	4	87	saudi	saudi	PROPN
ejpam-5969	4	88	arabia	arabia	PROPN
ejpam-5969	4	89	6	6	NUM
ejpam-5969	4	90	department	department	NOUN
ejpam-5969	4	91	of	of	ADP
ejpam-5969	4	92	mathematics	mathematic	NOUN
ejpam-5969	4	93	,	,	PUNCT
ejpam-5969	4	94	faculty	faculty	NOUN
ejpam-5969	4	95	of	of	ADP
ejpam-5969	4	96	science	science	NOUN
ejpam-5969	4	97	,	,	PUNCT
ejpam-5969	4	98	islamic	islamic	PROPN
ejpam-5969	4	99	university	university	PROPN
ejpam-5969	4	100	of	of	ADP
ejpam-5969	4	101	madinah	madinah	PROPN
ejpam-5969	4	102	,	,	PUNCT
ejpam-5969	4	103	medinah	medinah	PROPN
ejpam-5969	4	104	,	,	PUNCT
ejpam-5969	4	105	saudi	saudi	PROPN
ejpam-5969	4	106	arabia	arabia	PROPN
ejpam-5969	4	107	abstract	abstract	NOUN
ejpam-5969	4	108	.	.	PUNCT
ejpam-5969	5	1	in	in	ADP
ejpam-5969	5	2	supra	supra	PROPN
ejpam-5969	5	3	topological	topological	ADJ
ejpam-5969	5	4	spaces	space	NOUN
ejpam-5969	5	5	,	,	PUNCT
ejpam-5969	5	6	we	we	PRON
ejpam-5969	5	7	provide	provide	VERB
ejpam-5969	5	8	supra	supra	PROPN
ejpam-5969	5	9	ϵ-open	ϵ-open	PROPN
ejpam-5969	5	10	sets	set	NOUN
ejpam-5969	5	11	,	,	PUNCT
ejpam-5969	5	12	an	an	DET
ejpam-5969	5	13	extremely	extremely	ADV
ejpam-5969	5	14	broad	broad	ADJ
ejpam-5969	5	15	class	class	NOUN
ejpam-5969	5	16	of	of	ADP
ejpam-5969	5	17	open	open	ADJ
ejpam-5969	5	18	sets	set	NOUN
ejpam-5969	5	19	.	.	PUNCT
ejpam-5969	6	1	we	we	PRON
ejpam-5969	6	2	demonstrate	demonstrate	VERB
ejpam-5969	6	3	that	that	SCONJ
ejpam-5969	6	4	,	,	PUNCT
ejpam-5969	6	5	the	the	DET
ejpam-5969	6	6	previously	previously	ADV
ejpam-5969	6	7	comparable	comparable	ADJ
ejpam-5969	6	8	concepts	concept	NOUN
ejpam-5969	6	9	of	of	ADP
ejpam-5969	6	10	supra	supra	PROPN
ejpam-5969	6	11	regular	regular	ADJ
ejpam-5969	6	12	(	(	PUNCT
ejpam-5969	6	13	respectively	respectively	ADV
ejpam-5969	6	14	,	,	PUNCT
ejpam-5969	6	15	α-	α-	X
ejpam-5969	6	16	,	,	PUNCT
ejpam-5969	6	17	semi-	semi-	ADJ
ejpam-5969	6	18	,	,	PUNCT
ejpam-5969	6	19	pre-	pre-	X
ejpam-5969	6	20	,	,	PUNCT
ejpam-5969	6	21	b-	b-	X
ejpam-5969	6	22	,	,	PUNCT
ejpam-5969	6	23	β-	β-	X
ejpam-5969	6	24	,	,	PUNCT
ejpam-5969	6	25	and	and	CCONJ
ejpam-5969	6	26	r-	r-	X
ejpam-5969	6	27	)	)	PUNCT
ejpam-5969	6	28	open	open	ADJ
ejpam-5969	6	29	sets	set	NOUN
ejpam-5969	6	30	are	be	AUX
ejpam-5969	6	31	contained	contain	VERB
ejpam-5969	6	32	in	in	ADP
ejpam-5969	6	33	this	this	DET
ejpam-5969	6	34	new	new	ADJ
ejpam-5969	6	35	category	category	NOUN
ejpam-5969	6	36	of	of	ADP
ejpam-5969	6	37	open	open	ADJ
ejpam-5969	6	38	sets	set	NOUN
ejpam-5969	6	39	.	.	PUNCT
ejpam-5969	7	1	to	to	PART
ejpam-5969	7	2	further	far	ADV
ejpam-5969	7	3	illustrate	illustrate	VERB
ejpam-5969	7	4	the	the	DET
ejpam-5969	7	5	key	key	ADJ
ejpam-5969	7	6	concepts	concept	NOUN
ejpam-5969	7	7	discussed	discuss	VERB
ejpam-5969	7	8	in	in	ADP
ejpam-5969	7	9	the	the	DET
ejpam-5969	7	10	study	study	NOUN
ejpam-5969	7	11	,	,	PUNCT
ejpam-5969	7	12	we	we	PRON
ejpam-5969	7	13	have	have	AUX
ejpam-5969	7	14	included	include	VERB
ejpam-5969	7	15	a	a	DET
ejpam-5969	7	16	geometric	geometric	ADJ
ejpam-5969	7	17	topological	topological	ADJ
ejpam-5969	7	18	diagram	diagram	NOUN
ejpam-5969	8	1	[	[	X
ejpam-5969	8	2	see	see	VERB
ejpam-5969	8	3	diagram	diagram	NOUN
ejpam-5969	8	4	1	1	NUM
ejpam-5969	8	5	]	]	PUNCT
ejpam-5969	8	6	.	.	PUNCT
ejpam-5969	9	1	also	also	ADV
ejpam-5969	9	2	,	,	PUNCT
ejpam-5969	9	3	we	we	PRON
ejpam-5969	9	4	outline	outline	VERB
ejpam-5969	9	5	this	this	DET
ejpam-5969	9	6	class	class	NOUN
ejpam-5969	9	7	’s	’s	PART
ejpam-5969	9	8	primary	primary	ADJ
ejpam-5969	9	9	characteristics	characteristic	NOUN
ejpam-5969	9	10	.	.	PUNCT
ejpam-5969	10	1	specifically	specifically	ADV
ejpam-5969	10	2	,	,	PUNCT
ejpam-5969	10	3	we	we	PRON
ejpam-5969	10	4	show	show	VERB
ejpam-5969	10	5	that	that	SCONJ
ejpam-5969	10	6	our	our	PRON
ejpam-5969	10	7	new	new	ADJ
ejpam-5969	10	8	category	category	NOUN
ejpam-5969	10	9	forms	form	VERB
ejpam-5969	10	10	a	a	DET
ejpam-5969	10	11	supra	supra	ADJ
ejpam-5969	10	12	topology	topology	NOUN
ejpam-5969	10	13	rather	rather	ADV
ejpam-5969	10	14	than	than	ADP
ejpam-5969	10	15	a	a	DET
ejpam-5969	10	16	topological	topological	ADJ
ejpam-5969	10	17	space	space	NOUN
ejpam-5969	10	18	.	.	PUNCT
ejpam-5969	11	1	utilizing	utilize	VERB
ejpam-5969	11	2	our	our	PRON
ejpam-5969	11	3	recently	recently	ADV
ejpam-5969	11	4	introduced	introduce	VERB
ejpam-5969	11	5	category	category	NOUN
ejpam-5969	11	6	of	of	ADP
ejpam-5969	11	7	supra	supra	PROPN
ejpam-5969	11	8	open	open	ADJ
ejpam-5969	11	9	sets	set	NOUN
ejpam-5969	11	10	,	,	PUNCT
ejpam-5969	11	11	we	we	PRON
ejpam-5969	11	12	define	define	VERB
ejpam-5969	11	13	new	new	ADJ
ejpam-5969	11	14	kinds	kind	NOUN
ejpam-5969	11	15	of	of	ADP
ejpam-5969	11	16	operators	operator	NOUN
ejpam-5969	11	17	called	call	VERB
ejpam-5969	11	18	supra	supra	PROPN
ejpam-5969	11	19	ϵ-interior	ϵ-interior	PROPN
ejpam-5969	11	20	(	(	PUNCT
ejpam-5969	11	21	closure	closure	NOUN
ejpam-5969	11	22	,	,	PUNCT
ejpam-5969	11	23	accumulation	accumulation	NOUN
ejpam-5969	11	24	,	,	PUNCT
ejpam-5969	11	25	exterior	exterior	ADJ
ejpam-5969	11	26	,	,	PUNCT
ejpam-5969	11	27	and	and	CCONJ
ejpam-5969	11	28	boundary	boundary	ADJ
ejpam-5969	11	29	,	,	PUNCT
ejpam-5969	11	30	respectively	respectively	ADV
ejpam-5969	11	31	)	)	PUNCT
ejpam-5969	11	32	.	.	PUNCT
ejpam-5969	12	1	moreover	moreover	ADV
ejpam-5969	12	2	,	,	PUNCT
ejpam-5969	12	3	we	we	PRON
ejpam-5969	12	4	highlight	highlight	VERB
ejpam-5969	12	5	the	the	DET
ejpam-5969	12	6	deviations	deviation	NOUN
ejpam-5969	12	7	between	between	ADP
ejpam-5969	12	8	these	these	DET
ejpam-5969	12	9	new	new	ADJ
ejpam-5969	12	10	operators	operator	NOUN
ejpam-5969	12	11	and	and	CCONJ
ejpam-5969	12	12	their	their	PRON
ejpam-5969	12	13	corresponding	correspond	VERB
ejpam-5969	12	14	operators	operator	NOUN
ejpam-5969	12	15	.	.	PUNCT
ejpam-5969	13	1	furthermore	furthermore	ADV
ejpam-5969	13	2	,	,	PUNCT
ejpam-5969	13	3	we	we	PRON
ejpam-5969	13	4	also	also	ADV
ejpam-5969	13	5	give	give	VERB
ejpam-5969	13	6	some	some	DET
ejpam-5969	13	7	key	key	ADJ
ejpam-5969	13	8	examples	example	NOUN
ejpam-5969	13	9	and	and	CCONJ
ejpam-5969	13	10	counterexamples	counterexample	NOUN
ejpam-5969	13	11	to	to	PART
ejpam-5969	13	12	illustrate	illustrate	VERB
ejpam-5969	13	13	the	the	DET
ejpam-5969	13	14	importance	importance	NOUN
ejpam-5969	13	15	of	of	ADP
ejpam-5969	13	16	our	our	PRON
ejpam-5969	13	17	new	new	ADJ
ejpam-5969	13	18	operators	operator	NOUN
ejpam-5969	13	19	.	.	PUNCT
ejpam-5969	14	1	in	in	ADP
ejpam-5969	14	2	addition	addition	NOUN
ejpam-5969	14	3	,	,	PUNCT
ejpam-5969	14	4	we	we	PRON
ejpam-5969	14	5	highlight	highlight	VERB
ejpam-5969	14	6	the	the	DET
ejpam-5969	14	7	advantages	advantage	NOUN
ejpam-5969	14	8	and	and	CCONJ
ejpam-5969	14	9	distinctions	distinction	NOUN
ejpam-5969	14	10	of	of	ADP
ejpam-5969	14	11	our	our	PRON
ejpam-5969	14	12	work	work	NOUN
ejpam-5969	14	13	in	in	ADP
ejpam-5969	14	14	comparison	comparison	NOUN
ejpam-5969	14	15	to	to	ADP
ejpam-5969	14	16	similar	similar	ADJ
ejpam-5969	14	17	studies	study	NOUN
ejpam-5969	14	18	in	in	ADP
ejpam-5969	14	19	the	the	DET
ejpam-5969	14	20	field	field	NOUN
ejpam-5969	14	21	.	.	PUNCT
ejpam-5969	15	1	2020	2020	NUM
ejpam-5969	15	2	mathematics	mathematic	NOUN
ejpam-5969	15	3	subject	subject	NOUN
ejpam-5969	15	4	classifications	classification	NOUN
ejpam-5969	15	5	:	:	PUNCT
ejpam-5969	15	6	54a05	54a05	NUM
ejpam-5969	15	7	,	,	PUNCT
ejpam-5969	15	8	54c10	54c10	NUM
ejpam-5969	15	9	,	,	PUNCT
ejpam-5969	15	10	54c08	54c08	NUM
ejpam-5969	15	11	.	.	PUNCT
ejpam-5969	16	1	key	key	ADJ
ejpam-5969	16	2	words	word	NOUN
ejpam-5969	16	3	and	and	CCONJ
ejpam-5969	16	4	phrases	phrase	NOUN
ejpam-5969	16	5	:	:	PUNCT
ejpam-5969	16	6	supra	supra	PROPN
ejpam-5969	16	7	ϵ-open	ϵ-open	PROPN
ejpam-5969	16	8	set	set	PROPN
ejpam-5969	16	9	;	;	PUNCT
ejpam-5969	16	10	supra	supra	PROPN
ejpam-5969	16	11	ϵ-interior	ϵ-interior	PROPN
ejpam-5969	16	12	operator	operator	NOUN
ejpam-5969	16	13	;	;	PUNCT
ejpam-5969	16	14	supra	supra	PROPN
ejpam-5969	16	15	ϵ-closure	ϵ-closure	PROPN
ejpam-5969	16	16	operator	operator	NOUN
ejpam-5969	16	17	;	;	PUNCT
ejpam-5969	16	18	partition	partition	NOUN
ejpam-5969	16	19	;	;	PUNCT
ejpam-5969	16	20	applications	application	NOUN
ejpam-5969	16	21	∗corresponding	∗corresponde	VERB
ejpam-5969	16	22	author	author	NOUN
ejpam-5969	16	23	.	.	PUNCT
ejpam-5969	17	1	doi	doi	PROPN
ejpam-5969	17	2	:	:	PUNCT
ejpam-5969	17	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5969	https://doi.org/10.29020/nybg.ejpam.v18i2.5969	PRON
ejpam-5969	17	4	email	email	NOUN
ejpam-5969	17	5	addresses	address	VERB
ejpam-5969	17	6	:	:	PUNCT
ejpam-5969	17	7	alaa.ali@nbu.edu.sa	alaa.ali@nbu.edu.sa	PROPN
ejpam-5969	17	8	(	(	PUNCT
ejpam-5969	17	9	a.	a.	NOUN
ejpam-5969	17	10	m.	m.	PROPN
ejpam-5969	17	11	abd	abd	PROPN
ejpam-5969	17	12	el	el	PROPN
ejpam-5969	17	13	-	-	PROPN
ejpam-5969	17	14	latif	latif	PROPN
ejpam-5969	17	15	)	)	PUNCT
ejpam-5969	17	16	,	,	PUNCT
ejpam-5969	17	17	rgdairi@zu.edu.jo	rgdairi@zu.edu.jo	PROPN
ejpam-5969	17	18	(	(	PUNCT
ejpam-5969	17	19	r.	r.	PROPN
ejpam-5969	17	20	abu	abu	PROPN
ejpam-5969	17	21	-	-	PUNCT
ejpam-5969	17	22	gdairi	gdairi	PROPN
ejpam-5969	17	23	)	)	PUNCT
ejpam-5969	17	24	,	,	PUNCT
ejpam-5969	17	25	aa.azzam@psau.edu.sa	aa.azzam@psau.edu.sa	PROPN
ejpam-5969	17	26	(	(	PUNCT
ejpam-5969	17	27	a.	a.	NOUN
ejpam-5969	17	28	a.	a.	PROPN
ejpam-5969	17	29	azzam	azzam	PROPN
ejpam-5969	17	30	)	)	PUNCT
ejpam-5969	17	31	,	,	PUNCT
ejpam-5969	17	32	husham.alhassan@nbu.edu.sa	husham.alhassan@nbu.edu.sa	PROPN
ejpam-5969	17	33	(	(	PUNCT
ejpam-5969	17	34	h.	h.	PROPN
ejpam-5969	17	35	m.	m.	PROPN
ejpam-5969	17	36	attaalfadeel),shabaan27@gmail.com	attaalfadeel),shabaan27@gmail.com	PROPN
ejpam-5969	17	37	(	(	PUNCT
ejpam-5969	17	38	s.	s.	PROPN
ejpam-5969	17	39	m.	m.	PROPN
ejpam-5969	17	40	shaaban	shaaban	PROPN
ejpam-5969	17	41	)	)	PUNCT
ejpam-5969	17	42	,	,	PUNCT
ejpam-5969	17	43	m.aldawood@psau.edu.sa	m.aldawood@psau.edu.sa	PROPN
ejpam-5969	17	44	(	(	PUNCT
ejpam-5969	17	45	m.	m.	NOUN
ejpam-5969	17	46	aldawood	aldawood	PROPN
ejpam-5969	17	47	)	)	PUNCT
ejpam-5969	17	48	,	,	PUNCT
ejpam-5969	17	49	aldwoah@yahoo.com	aldwoah@yahoo.com	X
ejpam-5969	17	50	(	(	PUNCT
ejpam-5969	17	51	k.	k.	PROPN
ejpam-5969	17	52	a.	a.	PROPN
ejpam-5969	17	53	aldwoah	aldwoah	PROPN
ejpam-5969	17	54	)	)	PUNCT
ejpam-5969	17	55	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5969	18	1	1	1	NUM
ejpam-5969	18	2	copyright	copyright	NOUN
ejpam-5969	18	3	:	:	PUNCT
ejpam-5969	18	4	©	©	PROPN
ejpam-5969	18	5	2025	2025	NUM
ejpam-5969	18	6	the	the	DET
ejpam-5969	18	7	author(s	author(s	NOUN
ejpam-5969	18	8	)	)	PUNCT
ejpam-5969	18	9	.	.	PUNCT
ejpam-5969	19	1	(	(	PUNCT
ejpam-5969	19	2	cc	cc	NOUN
ejpam-5969	19	3	by	by	ADP
ejpam-5969	19	4	-	-	PUNCT
ejpam-5969	19	5	nc	nc	PROPN
ejpam-5969	19	6	4.0	4.0	NUM
ejpam-5969	19	7	)	)	PUNCT
ejpam-5969	19	8	abd	abd	PROPN
ejpam-5969	19	9	el	el	PROPN
ejpam-5969	19	10	-	-	PROPN
ejpam-5969	19	11	latif	latif	PROPN
ejpam-5969	19	12	et	et	PROPN
ejpam-5969	19	13	al	al	PROPN
ejpam-5969	19	14	.	.	PUNCT
ejpam-5969	19	15	/	/	SYM
ejpam-5969	19	16	eur	eur	PROPN
ejpam-5969	19	17	.	.	PUNCT
ejpam-5969	20	1	j.	j.	PROPN
ejpam-5969	20	2	pure	pure	PROPN
ejpam-5969	20	3	appl	appl	PROPN
ejpam-5969	20	4	.	.	PROPN
ejpam-5969	20	5	math	math	PROPN
ejpam-5969	20	6	,	,	PUNCT
ejpam-5969	20	7	18	18	NUM
ejpam-5969	20	8	(	(	PUNCT
ejpam-5969	20	9	2	2	NUM
ejpam-5969	20	10	)	)	PUNCT
ejpam-5969	20	11	(	(	PUNCT
ejpam-5969	20	12	2025	2025	NUM
ejpam-5969	20	13	)	)	PUNCT
ejpam-5969	20	14	,	,	PUNCT
ejpam-5969	20	15	5969	5969	NUM
ejpam-5969	20	16	2	2	NUM
ejpam-5969	20	17	of	of	ADP
ejpam-5969	20	18	19	19	NUM
ejpam-5969	20	19	1	1	NUM
ejpam-5969	20	20	.	.	PUNCT
ejpam-5969	20	21	introduction	introduction	NOUN
ejpam-5969	20	22	in	in	ADP
ejpam-5969	20	23	the	the	DET
ejpam-5969	20	24	past	past	ADJ
ejpam-5969	20	25	few	few	ADJ
ejpam-5969	20	26	decades	decade	NOUN
ejpam-5969	20	27	,	,	PUNCT
ejpam-5969	20	28	a	a	DET
ejpam-5969	20	29	significant	significant	ADJ
ejpam-5969	20	30	focus	focus	NOUN
ejpam-5969	20	31	of	of	ADP
ejpam-5969	20	32	topological	topological	ADJ
ejpam-5969	20	33	,	,	PUNCT
ejpam-5969	20	34	supra	supra	PROPN
ejpam-5969	20	35	topological	topological	ADJ
ejpam-5969	20	36	,	,	PUNCT
ejpam-5969	20	37	and	and	CCONJ
ejpam-5969	20	38	soft	soft	ADJ
ejpam-5969	20	39	topological	topological	ADJ
ejpam-5969	20	40	research	research	NOUN
ejpam-5969	20	41	has	have	AUX
ejpam-5969	20	42	been	be	AUX
ejpam-5969	20	43	the	the	DET
ejpam-5969	20	44	examination	examination	NOUN
ejpam-5969	20	45	of	of	ADP
ejpam-5969	20	46	various	various	ADJ
ejpam-5969	20	47	generalized	generalized	ADJ
ejpam-5969	20	48	open	open	ADJ
ejpam-5969	20	49	,	,	PUNCT
ejpam-5969	20	50	supra	supra	NOUN
ejpam-5969	20	51	open	open	ADJ
ejpam-5969	20	52	,	,	PUNCT
ejpam-5969	20	53	and	and	CCONJ
ejpam-5969	20	54	soft	soft	ADJ
ejpam-5969	20	55	open	open	ADJ
ejpam-5969	20	56	set	set	VERB
ejpam-5969	20	57	types	type	NOUN
ejpam-5969	20	58	as	as	ADV
ejpam-5969	20	59	well	well	ADV
ejpam-5969	20	60	as	as	ADP
ejpam-5969	20	61	their	their	PRON
ejpam-5969	20	62	structural	structural	ADJ
ejpam-5969	20	63	characteristics	characteristic	NOUN
ejpam-5969	20	64	.	.	PUNCT
ejpam-5969	21	1	semi	semi	ADJ
ejpam-5969	21	2	-	-	ADJ
ejpam-5969	21	3	open	open	ADJ
ejpam-5969	21	4	sets	set	NOUN
ejpam-5969	21	5	,	,	PUNCT
ejpam-5969	21	6	and	and	CCONJ
ejpam-5969	21	7	semi	semi	ADJ
ejpam-5969	21	8	-	-	NOUN
ejpam-5969	21	9	continuity	continuity	NOUN
ejpam-5969	21	10	of	of	ADP
ejpam-5969	21	11	mappings	mapping	NOUN
ejpam-5969	21	12	were	be	AUX
ejpam-5969	21	13	first	first	ADV
ejpam-5969	21	14	proposed	propose	VERB
ejpam-5969	21	15	by	by	ADP
ejpam-5969	21	16	levine	levine	PROPN
ejpam-5969	21	17	[	[	X
ejpam-5969	21	18	1	1	NUM
ejpam-5969	21	19	]	]	PUNCT
ejpam-5969	21	20	in	in	ADP
ejpam-5969	21	21	1963	1963	NUM
ejpam-5969	21	22	.	.	PUNCT
ejpam-5969	22	1	njasta	njasta	NOUN
ejpam-5969	23	1	[	[	X
ejpam-5969	23	2	2	2	X
ejpam-5969	23	3	]	]	PUNCT
ejpam-5969	23	4	then	then	ADV
ejpam-5969	23	5	presented	present	VERB
ejpam-5969	23	6	his	his	PRON
ejpam-5969	23	7	approach	approach	NOUN
ejpam-5969	23	8	of	of	ADP
ejpam-5969	23	9	α	α	NOUN
ejpam-5969	23	10	-	-	ADJ
ejpam-5969	23	11	open	open	ADJ
ejpam-5969	23	12	sets	set	NOUN
ejpam-5969	23	13	in	in	ADP
ejpam-5969	23	14	1965	1965	NUM
ejpam-5969	23	15	.	.	PUNCT
ejpam-5969	24	1	mashhour	mashhour	INTJ
ejpam-5969	24	2	et	et	PROPN
ejpam-5969	24	3	al	al	PROPN
ejpam-5969	24	4	.	.	PUNCT
ejpam-5969	25	1	[	[	X
ejpam-5969	25	2	3	3	NUM
ejpam-5969	25	3	]	]	PUNCT
ejpam-5969	25	4	developed	develop	VERB
ejpam-5969	25	5	the	the	DET
ejpam-5969	25	6	notion	notion	NOUN
ejpam-5969	25	7	of	of	ADP
ejpam-5969	25	8	pre	pre	ADJ
ejpam-5969	25	9	-	-	ADJ
ejpam-5969	25	10	open	open	ADJ
ejpam-5969	25	11	set	set	NOUN
ejpam-5969	25	12	to	to	PART
ejpam-5969	25	13	analyze	analyze	VERB
ejpam-5969	25	14	the	the	DET
ejpam-5969	25	15	pre	pre	ADJ
ejpam-5969	25	16	-	-	ADJ
ejpam-5969	25	17	continuous	continuous	ADJ
ejpam-5969	25	18	mappings	mapping	NOUN
ejpam-5969	25	19	.	.	PUNCT
ejpam-5969	26	1	the	the	DET
ejpam-5969	26	2	notion	notion	NOUN
ejpam-5969	26	3	of	of	ADP
ejpam-5969	26	4	β	β	ADJ
ejpam-5969	26	5	-	-	ADJ
ejpam-5969	26	6	open	open	ADJ
ejpam-5969	26	7	sets	set	NOUN
ejpam-5969	26	8	was	be	AUX
ejpam-5969	26	9	proposed	propose	VERB
ejpam-5969	26	10	by	by	ADP
ejpam-5969	26	11	abd	abd	PROPN
ejpam-5969	26	12	-	-	PUNCT
ejpam-5969	26	13	el	el	PROPN
ejpam-5969	26	14	-	-	PUNCT
ejpam-5969	26	15	monsef	monsef	ADJ
ejpam-5969	26	16	et	et	PROPN
ejpam-5969	26	17	al	al	PROPN
ejpam-5969	26	18	.	.	PUNCT
ejpam-5969	27	1	[	[	X
ejpam-5969	27	2	4	4	X
ejpam-5969	27	3	]	]	PUNCT
ejpam-5969	27	4	in	in	ADP
ejpam-5969	27	5	1983	1983	NUM
ejpam-5969	27	6	as	as	ADP
ejpam-5969	27	7	a	a	DET
ejpam-5969	27	8	way	way	NOUN
ejpam-5969	27	9	to	to	PART
ejpam-5969	27	10	study	study	VERB
ejpam-5969	27	11	β	β	ADJ
ejpam-5969	27	12	-	-	ADJ
ejpam-5969	27	13	continuous	continuous	ADJ
ejpam-5969	27	14	mappings	mapping	NOUN
ejpam-5969	27	15	.	.	PUNCT
ejpam-5969	28	1	in	in	ADP
ejpam-5969	28	2	[	[	X
ejpam-5969	28	3	5	5	NUM
ejpam-5969	28	4	,	,	PUNCT
ejpam-5969	28	5	6	6	NUM
ejpam-5969	28	6	]	]	PUNCT
ejpam-5969	28	7	,	,	PUNCT
ejpam-5969	28	8	the	the	DET
ejpam-5969	28	9	notion	notion	NOUN
ejpam-5969	28	10	of	of	ADP
ejpam-5969	28	11	b	b	NOUN
ejpam-5969	28	12	-	-	PUNCT
ejpam-5969	28	13	open	open	ADJ
ejpam-5969	28	14	sets	set	NOUN
ejpam-5969	28	15	was	be	AUX
ejpam-5969	28	16	thoroughly	thoroughly	ADV
ejpam-5969	28	17	examined	examine	VERB
ejpam-5969	28	18	.	.	PUNCT
ejpam-5969	29	1	piotrowski	piotrowski	NOUN
ejpam-5969	30	1	[	[	X
ejpam-5969	30	2	7	7	X
ejpam-5969	30	3	]	]	PUNCT
ejpam-5969	30	4	defined	define	VERB
ejpam-5969	30	5	somewhat	somewhat	ADV
ejpam-5969	30	6	open	open	ADJ
ejpam-5969	30	7	sets	set	NOUN
ejpam-5969	30	8	to	to	PART
ejpam-5969	30	9	preseent	preseent	VERB
ejpam-5969	30	10	somewhat	somewhat	ADV
ejpam-5969	30	11	continuity	continuity	NOUN
ejpam-5969	30	12	as	as	SCONJ
ejpam-5969	30	13	stated	state	VERB
ejpam-5969	30	14	in	in	ADP
ejpam-5969	30	15	[	[	X
ejpam-5969	30	16	8	8	NUM
ejpam-5969	30	17	]	]	PUNCT
ejpam-5969	30	18	.	.	PUNCT
ejpam-5969	31	1	the	the	DET
ejpam-5969	31	2	notion	notion	NOUN
ejpam-5969	31	3	of	of	ADP
ejpam-5969	31	4	somewhere	somewhere	ADJ
ejpam-5969	31	5	dense	dense	ADJ
ejpam-5969	31	6	sets	set	NOUN
ejpam-5969	31	7	was	be	AUX
ejpam-5969	31	8	proposed	propose	VERB
ejpam-5969	31	9	in	in	ADP
ejpam-5969	31	10	[	[	X
ejpam-5969	31	11	9	9	NUM
ejpam-5969	31	12	,	,	PUNCT
ejpam-5969	31	13	10	10	NUM
ejpam-5969	31	14	]	]	PUNCT
ejpam-5969	31	15	.	.	PUNCT
ejpam-5969	32	1	additional	additional	ADJ
ejpam-5969	32	2	characteristics	characteristic	NOUN
ejpam-5969	32	3	of	of	ADP
ejpam-5969	32	4	this	this	DET
ejpam-5969	32	5	notion	notion	NOUN
ejpam-5969	32	6	were	be	AUX
ejpam-5969	32	7	examined	examine	VERB
ejpam-5969	32	8	in	in	ADP
ejpam-5969	32	9	[	[	X
ejpam-5969	32	10	11	11	NUM
ejpam-5969	32	11	]	]	PUNCT
ejpam-5969	32	12	.	.	PUNCT
ejpam-5969	33	1	recently	recently	ADV
ejpam-5969	33	2	,	,	PUNCT
ejpam-5969	33	3	alqahtani	alqahtani	PROPN
ejpam-5969	33	4	and	and	CCONJ
ejpam-5969	33	5	abd	abd	PROPN
ejpam-5969	33	6	el	el	PROPN
ejpam-5969	33	7	-	-	PROPN
ejpam-5969	33	8	latif	latif	PROPN
ejpam-5969	34	1	[	[	X
ejpam-5969	34	2	12	12	NUM
ejpam-5969	34	3	]	]	PUNCT
ejpam-5969	34	4	,	,	PUNCT
ejpam-5969	34	5	generalized	generalize	VERB
ejpam-5969	34	6	almost	almost	ADV
ejpam-5969	34	7	all	all	DET
ejpam-5969	34	8	the	the	DET
ejpam-5969	34	9	previous	previous	ADJ
ejpam-5969	34	10	notions	notion	NOUN
ejpam-5969	34	11	by	by	ADP
ejpam-5969	34	12	introducing	introduce	VERB
ejpam-5969	34	13	the	the	DET
ejpam-5969	34	14	approach	approach	NOUN
ejpam-5969	34	15	of	of	ADP
ejpam-5969	34	16	n	n	PRON
ejpam-5969	34	17	-open	-open	ADJ
ejpam-5969	34	18	sets	set	NOUN
ejpam-5969	34	19	,	,	PUNCT
ejpam-5969	34	20	in	in	ADP
ejpam-5969	34	21	2024	2024	NUM
ejpam-5969	34	22	.	.	PUNCT
ejpam-5969	35	1	mashhour	mashhour	PROPN
ejpam-5969	35	2	et	et	PROPN
ejpam-5969	35	3	al	al	PROPN
ejpam-5969	35	4	.	.	PUNCT
ejpam-5969	36	1	[	[	X
ejpam-5969	36	2	13	13	NUM
ejpam-5969	36	3	]	]	PUNCT
ejpam-5969	36	4	,	,	PUNCT
ejpam-5969	36	5	presented	present	VERB
ejpam-5969	36	6	the	the	DET
ejpam-5969	36	7	notion	notion	NOUN
ejpam-5969	36	8	of	of	ADP
ejpam-5969	36	9	supra	supra	PROPN
ejpam-5969	36	10	open	open	ADJ
ejpam-5969	36	11	sets	set	NOUN
ejpam-5969	36	12	which	which	PRON
ejpam-5969	36	13	consider	consider	VERB
ejpam-5969	36	14	the	the	DET
ejpam-5969	36	15	basic	basic	ADJ
ejpam-5969	36	16	building	building	NOUN
ejpam-5969	36	17	blocks	block	NOUN
ejpam-5969	36	18	of	of	ADP
ejpam-5969	36	19	supra	supra	ADJ
ejpam-5969	36	20	topology	topology	NOUN
ejpam-5969	36	21	(	(	PUNCT
ejpam-5969	36	22	(	(	PUNCT
ejpam-5969	36	23	abbreviated	abbreviate	VERB
ejpam-5969	36	24	,	,	PUNCT
ejpam-5969	36	25	sts	st	NOUN
ejpam-5969	36	26	)	)	PUNCT
ejpam-5969	36	27	)	)	PUNCT
ejpam-5969	36	28	.	.	PUNCT
ejpam-5969	37	1	they	they	PRON
ejpam-5969	37	2	expanded	expand	VERB
ejpam-5969	37	3	on	on	ADP
ejpam-5969	37	4	some	some	DET
ejpam-5969	37	5	basic	basic	ADJ
ejpam-5969	37	6	topological	topological	ADJ
ejpam-5969	37	7	concepts	concept	NOUN
ejpam-5969	37	8	,	,	PUNCT
ejpam-5969	37	9	including	include	VERB
ejpam-5969	37	10	the	the	DET
ejpam-5969	37	11	continuity	continuity	NOUN
ejpam-5969	37	12	and	and	CCONJ
ejpam-5969	37	13	separation	separation	NOUN
ejpam-5969	37	14	axioms	axiom	NOUN
ejpam-5969	37	15	,	,	PUNCT
ejpam-5969	37	16	as	as	ADV
ejpam-5969	37	17	well	well	ADV
ejpam-5969	37	18	as	as	ADP
ejpam-5969	37	19	interior	interior	ADJ
ejpam-5969	37	20	and	and	CCONJ
ejpam-5969	37	21	closure	closure	NOUN
ejpam-5969	37	22	operators	operator	NOUN
ejpam-5969	37	23	.	.	PUNCT
ejpam-5969	38	1	the	the	DET
ejpam-5969	38	2	notions	notion	NOUN
ejpam-5969	38	3	of	of	ADP
ejpam-5969	38	4	of	of	ADP
ejpam-5969	38	5	supra	supra	PROPN
ejpam-5969	38	6	α[14	α[14	PROPN
ejpam-5969	38	7	]	]	X
ejpam-5969	38	8	(	(	PUNCT
ejpam-5969	38	9	respectively	respectively	ADV
ejpam-5969	38	10	,	,	PUNCT
ejpam-5969	38	11	pre[15	pre[15	PROPN
ejpam-5969	38	12	]	]	X
ejpam-5969	38	13	,	,	PUNCT
ejpam-5969	38	14	b[16	b[16	PROPN
ejpam-5969	38	15	]	]	PUNCT
ejpam-5969	38	16	,	,	PUNCT
ejpam-5969	38	17	β[17	β[17	PROPN
ejpam-5969	38	18	]	]	X
ejpam-5969	38	19	,	,	PUNCT
ejpam-5969	38	20	r[18	r[18	PROPN
ejpam-5969	38	21	]	]	PUNCT
ejpam-5969	38	22	,	,	PUNCT
ejpam-5969	38	23	and	and	CCONJ
ejpam-5969	38	24	semi[19	semi[19	PROPN
ejpam-5969	38	25	]	]	PUNCT
ejpam-5969	38	26	)	)	PUNCT
ejpam-5969	38	27	open	open	ADJ
ejpam-5969	38	28	sets	set	NOUN
ejpam-5969	38	29	have	have	AUX
ejpam-5969	38	30	been	be	AUX
ejpam-5969	38	31	presented	present	VERB
ejpam-5969	38	32	and	and	CCONJ
ejpam-5969	38	33	their	their	PRON
ejpam-5969	38	34	primary	primary	ADJ
ejpam-5969	38	35	characteristics	characteristic	NOUN
ejpam-5969	38	36	have	have	AUX
ejpam-5969	38	37	been	be	AUX
ejpam-5969	38	38	presented	present	VERB
ejpam-5969	38	39	.	.	PUNCT
ejpam-5969	39	1	more	more	ADJ
ejpam-5969	39	2	operators	operator	NOUN
ejpam-5969	39	3	on	on	ADP
ejpam-5969	39	4	supra	supra	PROPN
ejpam-5969	39	5	topological	topological	ADJ
ejpam-5969	39	6	spaces	space	NOUN
ejpam-5969	39	7	[	[	X
ejpam-5969	39	8	20–22	20–22	NUM
ejpam-5969	39	9	]	]	X
ejpam-5969	39	10	have	have	AUX
ejpam-5969	39	11	been	be	AUX
ejpam-5969	39	12	introduced	introduce	VERB
ejpam-5969	39	13	.	.	PUNCT
ejpam-5969	40	1	in	in	ADP
ejpam-5969	40	2	the	the	DET
ejpam-5969	40	3	field	field	NOUN
ejpam-5969	40	4	of	of	ADP
ejpam-5969	40	5	generalized	generalized	ADJ
ejpam-5969	40	6	soft	soft	ADJ
ejpam-5969	40	7	open	open	ADJ
ejpam-5969	40	8	sets	set	NOUN
ejpam-5969	40	9	[	[	X
ejpam-5969	40	10	23	23	NUM
ejpam-5969	40	11	,	,	PUNCT
ejpam-5969	40	12	24	24	NUM
ejpam-5969	40	13	]	]	PUNCT
ejpam-5969	40	14	,	,	PUNCT
ejpam-5969	40	15	generalized	generalize	VERB
ejpam-5969	40	16	soft	soft	ADJ
ejpam-5969	40	17	continuity	continuity	NOUN
ejpam-5969	40	18	[	[	X
ejpam-5969	40	19	25	25	NUM
ejpam-5969	40	20	]	]	PUNCT
ejpam-5969	40	21	,	,	PUNCT
ejpam-5969	40	22	soft	soft	ADJ
ejpam-5969	40	23	semi	semi	ADJ
ejpam-5969	40	24	-	-	ADJ
ejpam-5969	40	25	open	open	ADJ
ejpam-5969	40	26	sets	set	NOUN
ejpam-5969	40	27	and	and	CCONJ
ejpam-5969	40	28	soft	soft	ADJ
ejpam-5969	40	29	semi	semi	ADJ
ejpam-5969	40	30	irresolute	irresolute	ADJ
ejpam-5969	40	31	soft	soft	ADJ
ejpam-5969	40	32	mappings	mapping	NOUN
ejpam-5969	40	33	[	[	X
ejpam-5969	40	34	26	26	NUM
ejpam-5969	40	35	,	,	PUNCT
ejpam-5969	40	36	27	27	NUM
ejpam-5969	40	37	]	]	PUNCT
ejpam-5969	40	38	,	,	PUNCT
ejpam-5969	40	39	various	various	ADJ
ejpam-5969	40	40	types	type	NOUN
ejpam-5969	40	41	of	of	ADP
ejpam-5969	40	42	soft	soft	ADJ
ejpam-5969	40	43	open	open	ADJ
ejpam-5969	40	44	sets	set	NOUN
ejpam-5969	40	45	and	and	CCONJ
ejpam-5969	40	46	continuity	continuity	NOUN
ejpam-5969	40	47	[	[	X
ejpam-5969	40	48	28	28	NUM
ejpam-5969	40	49	]	]	X
ejpam-5969	40	50	,	,	PUNCT
ejpam-5969	40	51	soft	soft	ADJ
ejpam-5969	40	52	somewhere	somewhere	ADV
ejpam-5969	40	53	dense	dense	ADJ
ejpam-5969	40	54	sets[29	sets[29	PROPN
ejpam-5969	40	55	]	]	X
ejpam-5969	40	56	,	,	PUNCT
ejpam-5969	40	57	and	and	CCONJ
ejpam-5969	40	58	nearly	nearly	ADV
ejpam-5969	40	59	soft	soft	ADJ
ejpam-5969	40	60	β	β	ADJ
ejpam-5969	40	61	-	-	ADJ
ejpam-5969	40	62	open	open	ADJ
ejpam-5969	40	63	sets	set	NOUN
ejpam-5969	40	64	[	[	X
ejpam-5969	40	65	30	30	NUM
ejpam-5969	40	66	]	]	PUNCT
ejpam-5969	40	67	,	,	PUNCT
ejpam-5969	40	68	have	have	AUX
ejpam-5969	40	69	been	be	AUX
ejpam-5969	40	70	provided	provide	VERB
ejpam-5969	40	71	.	.	PUNCT
ejpam-5969	41	1	subsequent	subsequent	ADJ
ejpam-5969	41	2	studies	study	NOUN
ejpam-5969	41	3	on	on	ADP
ejpam-5969	41	4	soft	soft	ADJ
ejpam-5969	41	5	continuity	continuity	NOUN
ejpam-5969	41	6	were	be	AUX
ejpam-5969	41	7	carried	carry	VERB
ejpam-5969	41	8	out	out	ADP
ejpam-5969	41	9	[	[	X
ejpam-5969	41	10	31	31	NUM
ejpam-5969	41	11	,	,	PUNCT
ejpam-5969	41	12	32	32	NUM
ejpam-5969	41	13	]	]	PUNCT
ejpam-5969	41	14	.	.	PUNCT
ejpam-5969	42	1	the	the	DET
ejpam-5969	42	2	concept	concept	NOUN
ejpam-5969	42	3	of	of	ADP
ejpam-5969	42	4	the	the	DET
ejpam-5969	42	5	soft	soft	ADJ
ejpam-5969	42	6	ideal	ideal	NOUN
ejpam-5969	42	7	was	be	AUX
ejpam-5969	42	8	initially	initially	ADV
ejpam-5969	42	9	presented	present	VERB
ejpam-5969	42	10	in	in	ADP
ejpam-5969	42	11	[	[	X
ejpam-5969	42	12	33	33	NUM
ejpam-5969	42	13	]	]	SYM
ejpam-5969	42	14	.	.	PUNCT
ejpam-5969	43	1	soft	soft	ADJ
ejpam-5969	43	2	compactness	compactness	NOUN
ejpam-5969	44	1	[	[	X
ejpam-5969	44	2	34	34	NUM
ejpam-5969	44	3	]	]	PUNCT
ejpam-5969	44	4	,	,	PUNCT
ejpam-5969	44	5	soft	soft	ADJ
ejpam-5969	44	6	connectedness	connectedness	NOUN
ejpam-5969	44	7	[	[	X
ejpam-5969	44	8	35	35	NUM
ejpam-5969	44	9	]	]	X
ejpam-5969	44	10	,	,	PUNCT
ejpam-5969	44	11	soft	soft	ADJ
ejpam-5969	44	12	generalized	generalized	ADJ
ejpam-5969	44	13	open	open	ADJ
ejpam-5969	44	14	sets	set	NOUN
ejpam-5969	44	15	[	[	X
ejpam-5969	44	16	36–38	36–38	NUM
ejpam-5969	44	17	]	]	PUNCT
ejpam-5969	44	18	,	,	PUNCT
ejpam-5969	44	19	generalized	generalize	VERB
ejpam-5969	44	20	(	(	PUNCT
ejpam-5969	44	21	fuzzy	fuzzy	ADJ
ejpam-5969	44	22	)	)	PUNCT
ejpam-5969	44	23	soft	soft	ADJ
ejpam-5969	44	24	rough	rough	ADJ
ejpam-5969	44	25	sets	set	NOUN
ejpam-5969	44	26	[	[	X
ejpam-5969	44	27	39	39	NUM
ejpam-5969	44	28	,	,	PUNCT
ejpam-5969	44	29	40	40	NUM
ejpam-5969	44	30	]	]	PUNCT
ejpam-5969	44	31	,	,	PUNCT
ejpam-5969	44	32	and	and	CCONJ
ejpam-5969	44	33	soft	soft	ADJ
ejpam-5969	44	34	separation	separation	NOUN
ejpam-5969	44	35	axioms	axiom	NOUN
ejpam-5969	44	36	[	[	X
ejpam-5969	44	37	41	41	NUM
ejpam-5969	44	38	]	]	PUNCT
ejpam-5969	44	39	are	be	AUX
ejpam-5969	44	40	just	just	ADV
ejpam-5969	44	41	a	a	DET
ejpam-5969	44	42	few	few	ADJ
ejpam-5969	44	43	of	of	ADP
ejpam-5969	44	44	the	the	DET
ejpam-5969	44	45	topological	topological	ADJ
ejpam-5969	44	46	properties	property	NOUN
ejpam-5969	44	47	that	that	PRON
ejpam-5969	44	48	are	be	AUX
ejpam-5969	44	49	generalized	generalize	VERB
ejpam-5969	44	50	using	use	VERB
ejpam-5969	44	51	this	this	DET
ejpam-5969	44	52	concept	concept	NOUN
ejpam-5969	44	53	.	.	PUNCT
ejpam-5969	45	1	el	el	ADJ
ejpam-5969	45	2	-	-	PUNCT
ejpam-5969	45	3	sheikh	sheikh	PROPN
ejpam-5969	45	4	et	et	PROPN
ejpam-5969	45	5	al	al	PROPN
ejpam-5969	45	6	.	.	PROPN
ejpam-5969	45	7	proposed	propose	VERB
ejpam-5969	45	8	the	the	DET
ejpam-5969	45	9	concept	concept	NOUN
ejpam-5969	45	10	of	of	ADP
ejpam-5969	45	11	supra	supra	PROPN
ejpam-5969	45	12	soft	soft	ADJ
ejpam-5969	45	13	topological	topological	ADJ
ejpam-5969	45	14	spaces	space	NOUN
ejpam-5969	46	1	[	[	X
ejpam-5969	46	2	42	42	NUM
ejpam-5969	46	3	]	]	PUNCT
ejpam-5969	46	4	.	.	PUNCT
ejpam-5969	47	1	additionally	additionally	ADV
ejpam-5969	47	2	,	,	PUNCT
ejpam-5969	47	3	they	they	PRON
ejpam-5969	47	4	presented	present	VERB
ejpam-5969	47	5	the	the	DET
ejpam-5969	47	6	notions	notion	NOUN
ejpam-5969	47	7	of	of	ADP
ejpam-5969	47	8	supra	supra	PROPN
ejpam-5969	47	9	soft	soft	ADJ
ejpam-5969	47	10	pre(respectively	pre(respectively	ADV
ejpam-5969	47	11	,	,	PUNCT
ejpam-5969	47	12	α	α	NOUN
ejpam-5969	47	13	,	,	PUNCT
ejpam-5969	47	14	semi	semi	ADV
ejpam-5969	47	15	,	,	PUNCT
ejpam-5969	47	16	β	β	X
ejpam-5969	47	17	,	,	PUNCT
ejpam-5969	47	18	and	and	CCONJ
ejpam-5969	47	19	γ-	γ-	NUM
ejpam-5969	47	20	)	)	PUNCT
ejpam-5969	47	21	open	open	ADJ
ejpam-5969	47	22	sets	set	NOUN
ejpam-5969	47	23	.	.	PUNCT
ejpam-5969	48	1	subsequent	subsequent	ADJ
ejpam-5969	48	2	research	research	NOUN
ejpam-5969	48	3	has	have	AUX
ejpam-5969	48	4	examined	examine	VERB
ejpam-5969	48	5	numerous	numerous	ADJ
ejpam-5969	48	6	generalized	generalized	ADJ
ejpam-5969	48	7	supra	supra	ADJ
ejpam-5969	48	8	soft	soft	ADJ
ejpam-5969	48	9	operators	operator	NOUN
ejpam-5969	48	10	through	through	ADP
ejpam-5969	48	11	supra	supra	PROPN
ejpam-5969	48	12	soft	soft	ADJ
ejpam-5969	48	13	-	-	PUNCT
ejpam-5969	48	14	b	b	NOUN
ejpam-5969	48	15	-	-	PUNCT
ejpam-5969	48	16	open	open	ADJ
ejpam-5969	48	17	sets	set	NOUN
ejpam-5969	48	18	[	[	X
ejpam-5969	48	19	43	43	NUM
ejpam-5969	48	20	]	]	PUNCT
ejpam-5969	48	21	,	,	PUNCT
ejpam-5969	48	22	supra	supra	PROPN
ejpam-5969	48	23	soft	soft	ADJ
ejpam-5969	48	24	-	-	PUNCT
ejpam-5969	48	25	δi	δi	NOUN
ejpam-5969	48	26	-	-	PUNCT
ejpam-5969	48	27	open	open	ADJ
ejpam-5969	48	28	sets	set	NOUN
ejpam-5969	48	29	[	[	X
ejpam-5969	48	30	44	44	NUM
ejpam-5969	48	31	,	,	PUNCT
ejpam-5969	48	32	45	45	NUM
ejpam-5969	48	33	]	]	PUNCT
ejpam-5969	48	34	,	,	PUNCT
ejpam-5969	48	35	supra	supra	PROPN
ejpam-5969	48	36	soft	soft	ADJ
ejpam-5969	48	37	somewhere	somewhere	ADV
ejpam-5969	48	38	dense	dense	ADJ
ejpam-5969	48	39	sets	set	NOUN
ejpam-5969	48	40	[	[	X
ejpam-5969	48	41	46	46	NUM
ejpam-5969	48	42	]	]	PUNCT
ejpam-5969	48	43	,	,	PUNCT
ejpam-5969	48	44	and	and	CCONJ
ejpam-5969	48	45	supra	supra	PROPN
ejpam-5969	48	46	soft	soft	ADJ
ejpam-5969	48	47	somewhat	somewhat	ADV
ejpam-5969	48	48	open	open	ADJ
ejpam-5969	48	49	sets	set	NOUN
ejpam-5969	48	50	[	[	X
ejpam-5969	48	51	47	47	NUM
ejpam-5969	48	52	]	]	PUNCT
ejpam-5969	48	53	.	.	PUNCT
ejpam-5969	49	1	we	we	PRON
ejpam-5969	49	2	aim	aim	VERB
ejpam-5969	49	3	in	in	ADP
ejpam-5969	49	4	this	this	DET
ejpam-5969	49	5	paper	paper	NOUN
ejpam-5969	49	6	to	to	PART
ejpam-5969	49	7	present	present	VERB
ejpam-5969	49	8	the	the	DET
ejpam-5969	49	9	approach	approach	NOUN
ejpam-5969	49	10	of	of	ADP
ejpam-5969	49	11	supra	supra	PROPN
ejpam-5969	49	12	ϵ-open	ϵ-open	PROPN
ejpam-5969	49	13	sets	set	NOUN
ejpam-5969	49	14	to	to	ADP
ejpam-5969	49	15	supra	supra	PROPN
ejpam-5969	49	16	topological	topological	ADJ
ejpam-5969	49	17	spaces	space	NOUN
ejpam-5969	49	18	.	.	PUNCT
ejpam-5969	50	1	also	also	ADV
ejpam-5969	50	2	,	,	PUNCT
ejpam-5969	50	3	we	we	PRON
ejpam-5969	50	4	go	go	VERB
ejpam-5969	50	5	over	over	ADP
ejpam-5969	50	6	the	the	DET
ejpam-5969	50	7	connections	connection	NOUN
ejpam-5969	50	8	between	between	ADP
ejpam-5969	50	9	our	our	PRON
ejpam-5969	50	10	novel	novel	ADJ
ejpam-5969	50	11	approach	approach	NOUN
ejpam-5969	50	12	and	and	CCONJ
ejpam-5969	50	13	the	the	DET
ejpam-5969	50	14	earlier	early	ADV
ejpam-5969	50	15	related	relate	VERB
ejpam-5969	50	16	studies	study	NOUN
ejpam-5969	50	17	.	.	PUNCT
ejpam-5969	51	1	in	in	ADP
ejpam-5969	51	2	order	order	NOUN
ejpam-5969	51	3	to	to	PART
ejpam-5969	51	4	properly	properly	ADV
ejpam-5969	51	5	demonstrate	demonstrate	VERB
ejpam-5969	51	6	the	the	DET
ejpam-5969	51	7	main	main	ADJ
ejpam-5969	51	8	ideas	idea	NOUN
ejpam-5969	51	9	covered	cover	VERB
ejpam-5969	51	10	in	in	ADP
ejpam-5969	51	11	the	the	DET
ejpam-5969	51	12	paper	paper	NOUN
ejpam-5969	51	13	,	,	PUNCT
ejpam-5969	51	14	we	we	PRON
ejpam-5969	51	15	have	have	AUX
ejpam-5969	51	16	included	include	VERB
ejpam-5969	51	17	a	a	DET
ejpam-5969	51	18	geometric	geometric	ADJ
ejpam-5969	51	19	topological	topological	ADJ
ejpam-5969	51	20	diagram	diagram	NOUN
ejpam-5969	51	21	[	[	X
ejpam-5969	51	22	see	see	VERB
ejpam-5969	51	23	diagram	diagram	NOUN
ejpam-5969	51	24	1	1	NUM
ejpam-5969	51	25	]	]	PUNCT
ejpam-5969	51	26	.	.	PUNCT
ejpam-5969	52	1	soregular(χ	soregular(χ	NOUN
ejpam-5969	52	2	)	)	PUNCT
ejpam-5969	52	3	−→so(χ	−→so(χ	ADJ
ejpam-5969	52	4	)	)	PUNCT
ejpam-5969	52	5	−→	−→	NOUN
ejpam-5969	52	6	sαo(χ	sαo(χ	VERB
ejpam-5969	52	7	)	)	PUNCT
ejpam-5969	52	8	−→	−→	NOUN
ejpam-5969	52	9	sso(χ	sso(χ	PROPN
ejpam-5969	52	10	)	)	PUNCT
ejpam-5969	52	11	−→	−→	NOUN
ejpam-5969	52	12	sβo(χ	sβo(χ	PROPN
ejpam-5969	52	13	)	)	PUNCT
ejpam-5969	52	14	−→	−→	NOUN
ejpam-5969	52	15	sro(χ	sro(χ	NOUN
ejpam-5969	52	16	)	)	PUNCT
ejpam-5969	52	17	↓	↓	NOUN
ejpam-5969	52	18	↓	↓	PROPN
ejpam-5969	52	19	↗	↗	PROPN
ejpam-5969	52	20	↓	↓	PROPN
ejpam-5969	52	21	spo(χ	spo(χ	PROPN
ejpam-5969	52	22	)	)	PUNCT
ejpam-5969	52	23	−→	−→	NOUN
ejpam-5969	52	24	sbo(χ	sbo(χ	NOUN
ejpam-5969	52	25	)	)	PUNCT
ejpam-5969	52	26	−→	−→	NOUN
ejpam-5969	52	27	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	52	28	)	)	PUNCT
ejpam-5969	52	29	diagram	diagram	NOUN
ejpam-5969	52	30	1	1	NUM
ejpam-5969	52	31	.	.	PUNCT
ejpam-5969	53	1	the	the	DET
ejpam-5969	53	2	connections	connection	NOUN
ejpam-5969	53	3	between	between	ADP
ejpam-5969	53	4	the	the	DET
ejpam-5969	53	5	new	new	ADJ
ejpam-5969	53	6	category	category	NOUN
ejpam-5969	53	7	and	and	CCONJ
ejpam-5969	53	8	other	other	ADJ
ejpam-5969	53	9	preceding	precede	VERB
ejpam-5969	53	10	studies	study	NOUN
ejpam-5969	53	11	.	.	PUNCT
ejpam-5969	54	1	abd	abd	PROPN
ejpam-5969	54	2	el	el	PROPN
ejpam-5969	54	3	-	-	PROPN
ejpam-5969	54	4	latif	latif	PROPN
ejpam-5969	54	5	et	et	PROPN
ejpam-5969	54	6	al	al	PROPN
ejpam-5969	54	7	.	.	PUNCT
ejpam-5969	54	8	/	/	SYM
ejpam-5969	54	9	eur	eur	PROPN
ejpam-5969	54	10	.	.	PUNCT
ejpam-5969	55	1	j.	j.	PROPN
ejpam-5969	55	2	pure	pure	PROPN
ejpam-5969	55	3	appl	appl	PROPN
ejpam-5969	55	4	.	.	PROPN
ejpam-5969	55	5	math	math	PROPN
ejpam-5969	55	6	,	,	PUNCT
ejpam-5969	55	7	18	18	NUM
ejpam-5969	55	8	(	(	PUNCT
ejpam-5969	55	9	2	2	NUM
ejpam-5969	55	10	)	)	PUNCT
ejpam-5969	55	11	(	(	PUNCT
ejpam-5969	55	12	2025	2025	NUM
ejpam-5969	55	13	)	)	PUNCT
ejpam-5969	55	14	,	,	PUNCT
ejpam-5969	55	15	5969	5969	NUM
ejpam-5969	55	16	3	3	NUM
ejpam-5969	55	17	of	of	ADP
ejpam-5969	55	18	19	19	NUM
ejpam-5969	55	19	moreover	moreover	ADV
ejpam-5969	55	20	,	,	PUNCT
ejpam-5969	55	21	we	we	PRON
ejpam-5969	55	22	provide	provide	VERB
ejpam-5969	55	23	the	the	DET
ejpam-5969	55	24	main	main	ADJ
ejpam-5969	55	25	features	feature	NOUN
ejpam-5969	55	26	of	of	ADP
ejpam-5969	55	27	this	this	DET
ejpam-5969	55	28	new	new	ADJ
ejpam-5969	55	29	category	category	NOUN
ejpam-5969	55	30	.	.	PUNCT
ejpam-5969	56	1	in	in	ADP
ejpam-5969	56	2	particular	particular	ADJ
ejpam-5969	56	3	,	,	PUNCT
ejpam-5969	56	4	we	we	PRON
ejpam-5969	56	5	show	show	VERB
ejpam-5969	56	6	that	that	SCONJ
ejpam-5969	56	7	supra	supra	PROPN
ejpam-5969	56	8	ϵ-open	ϵ-open	PROPN
ejpam-5969	56	9	sets	set	NOUN
ejpam-5969	56	10	in	in	ADP
ejpam-5969	56	11	an	an	DET
ejpam-5969	56	12	sts	st	NOUN
ejpam-5969	56	13	and	and	CCONJ
ejpam-5969	56	14	their	their	PRON
ejpam-5969	56	15	subspaces	subspace	NOUN
ejpam-5969	56	16	generally	generally	ADV
ejpam-5969	56	17	do	do	AUX
ejpam-5969	56	18	not	not	PART
ejpam-5969	56	19	relate	relate	VERB
ejpam-5969	56	20	to	to	ADP
ejpam-5969	56	21	one	one	NUM
ejpam-5969	56	22	another	another	DET
ejpam-5969	56	23	.	.	PUNCT
ejpam-5969	57	1	in	in	ADP
ejpam-5969	57	2	addition	addition	NOUN
ejpam-5969	57	3	to	to	ADP
ejpam-5969	57	4	,	,	PUNCT
ejpam-5969	57	5	the	the	DET
ejpam-5969	57	6	intersection	intersection	NOUN
ejpam-5969	57	7	of	of	ADP
ejpam-5969	57	8	finite	finite	ADJ
ejpam-5969	57	9	numbers	number	NOUN
ejpam-5969	57	10	of	of	ADP
ejpam-5969	57	11	supra	supra	PROPN
ejpam-5969	57	12	ϵ-open	ϵ-open	PROPN
ejpam-5969	57	13	sets	set	NOUN
ejpam-5969	57	14	is	be	AUX
ejpam-5969	57	15	not	not	PART
ejpam-5969	57	16	supra	supra	NOUN
ejpam-5969	57	17	ϵ-open	ϵ-open	PROPN
ejpam-5969	57	18	,	,	PUNCT
ejpam-5969	57	19	generally	generally	ADV
ejpam-5969	57	20	.	.	PUNCT
ejpam-5969	58	1	after	after	ADP
ejpam-5969	58	2	that	that	PRON
ejpam-5969	58	3	,	,	PUNCT
ejpam-5969	58	4	we	we	PRON
ejpam-5969	58	5	investigate	investigate	VERB
ejpam-5969	58	6	new	new	ADJ
ejpam-5969	58	7	types	type	NOUN
ejpam-5969	58	8	of	of	ADP
ejpam-5969	58	9	operators	operator	NOUN
ejpam-5969	58	10	known	know	VERB
ejpam-5969	58	11	as	as	ADP
ejpam-5969	58	12	supra	supra	PROPN
ejpam-5969	58	13	ϵ-interior	ϵ-interior	PROPN
ejpam-5969	58	14	(	(	PUNCT
ejpam-5969	58	15	closure	closure	NOUN
ejpam-5969	58	16	,	,	PUNCT
ejpam-5969	58	17	accumulation	accumulation	NOUN
ejpam-5969	58	18	,	,	PUNCT
ejpam-5969	58	19	exterior	exterior	ADJ
ejpam-5969	58	20	,	,	PUNCT
ejpam-5969	58	21	and	and	CCONJ
ejpam-5969	58	22	boundary	boundary	ADJ
ejpam-5969	58	23	,	,	PUNCT
ejpam-5969	58	24	respectively	respectively	ADV
ejpam-5969	58	25	)	)	PUNCT
ejpam-5969	58	26	operator	operator	NOUN
ejpam-5969	58	27	using	use	VERB
ejpam-5969	58	28	our	our	PRON
ejpam-5969	58	29	recently	recently	ADV
ejpam-5969	58	30	established	establish	VERB
ejpam-5969	58	31	category	category	NOUN
ejpam-5969	58	32	of	of	ADP
ejpam-5969	58	33	supra	supra	PROPN
ejpam-5969	58	34	open	open	ADJ
ejpam-5969	58	35	sets	set	NOUN
ejpam-5969	58	36	.	.	PUNCT
ejpam-5969	59	1	in	in	ADP
ejpam-5969	59	2	order	order	NOUN
ejpam-5969	59	3	to	to	PART
ejpam-5969	59	4	demonstrate	demonstrate	VERB
ejpam-5969	59	5	the	the	DET
ejpam-5969	59	6	significance	significance	NOUN
ejpam-5969	59	7	of	of	ADP
ejpam-5969	59	8	our	our	PRON
ejpam-5969	59	9	new	new	ADJ
ejpam-5969	59	10	operators	operator	NOUN
ejpam-5969	59	11	,	,	PUNCT
ejpam-5969	59	12	we	we	PRON
ejpam-5969	59	13	also	also	ADV
ejpam-5969	59	14	provide	provide	VERB
ejpam-5969	59	15	some	some	DET
ejpam-5969	59	16	important	important	ADJ
ejpam-5969	59	17	examples	example	NOUN
ejpam-5969	59	18	and	and	CCONJ
ejpam-5969	59	19	counterexamples	counterexample	NOUN
ejpam-5969	59	20	.	.	PUNCT
ejpam-5969	60	1	2	2	X
ejpam-5969	60	2	.	.	NUM
ejpam-5969	60	3	preliminaries	preliminary	NOUN
ejpam-5969	60	4	and	and	CCONJ
ejpam-5969	60	5	background	background	NOUN
ejpam-5969	60	6	let	let	VERB
ejpam-5969	60	7	(	(	PUNCT
ejpam-5969	60	8	χ	χ	X
ejpam-5969	60	9	,	,	PUNCT
ejpam-5969	60	10	ν	ν	NOUN
ejpam-5969	60	11	)	)	PUNCT
ejpam-5969	60	12	be	be	VERB
ejpam-5969	60	13	an	an	DET
ejpam-5969	60	14	sts	st	NOUN
ejpam-5969	60	15	,	,	PUNCT
ejpam-5969	60	16	the	the	DET
ejpam-5969	60	17	categories	category	NOUN
ejpam-5969	60	18	of	of	ADP
ejpam-5969	60	19	supra	supra	PROPN
ejpam-5969	60	20	(	(	PUNCT
ejpam-5969	60	21	respectively	respectively	ADV
ejpam-5969	60	22	,	,	PUNCT
ejpam-5969	60	23	regular-	regular-	ADJ
ejpam-5969	60	24	,	,	PUNCT
ejpam-5969	60	25	pre-	pre-	X
ejpam-5969	60	26	,	,	PUNCT
ejpam-5969	60	27	semi	semi	ADV
ejpam-5969	60	28	,	,	PUNCT
ejpam-5969	60	29	β-	β-	PRON
ejpam-5969	60	30	,	,	PUNCT
ejpam-5969	60	31	α-	α-	X
ejpam-5969	60	32	,	,	PUNCT
ejpam-5969	60	33	b-	b-	X
ejpam-5969	60	34	,	,	PUNCT
ejpam-5969	60	35	and	and	CCONJ
ejpam-5969	60	36	r-	r-	X
ejpam-5969	60	37	)	)	PUNCT
ejpam-5969	60	38	open	open	ADJ
ejpam-5969	60	39	sets	set	NOUN
ejpam-5969	60	40	will	will	AUX
ejpam-5969	60	41	represented	represent	VERB
ejpam-5969	60	42	by	by	ADP
ejpam-5969	60	43	so(χ	so(χ	NOUN
ejpam-5969	60	44	)	)	PUNCT
ejpam-5969	60	45	(	(	PUNCT
ejpam-5969	60	46	respectively	respectively	ADV
ejpam-5969	60	47	,	,	PUNCT
ejpam-5969	60	48	soregular(χ	soregular(χ	NOUN
ejpam-5969	60	49	)	)	PUNCT
ejpam-5969	60	50	,	,	PUNCT
ejpam-5969	60	51	spo(χ	spo(χ	PROPN
ejpam-5969	60	52	)	)	PUNCT
ejpam-5969	60	53	,	,	PUNCT
ejpam-5969	60	54	sso(χ	sso(χ	PROPN
ejpam-5969	60	55	)	)	PUNCT
ejpam-5969	60	56	,	,	PUNCT
ejpam-5969	60	57	sβo(χ	sβo(χ	PROPN
ejpam-5969	60	58	)	)	PUNCT
ejpam-5969	60	59	,	,	PUNCT
ejpam-5969	60	60	sαo(χ	sαo(χ	PROPN
ejpam-5969	60	61	)	)	PUNCT
ejpam-5969	60	62	,	,	PUNCT
ejpam-5969	60	63	sbo(χ	sbo(χ	PROPN
ejpam-5969	60	64	)	)	PUNCT
ejpam-5969	60	65	,	,	PUNCT
ejpam-5969	60	66	and	and	CCONJ
ejpam-5969	60	67	sro(χ	sro(χ	PROPN
ejpam-5969	60	68	)	)	PUNCT
ejpam-5969	60	69	)	)	PUNCT
ejpam-5969	60	70	across	across	ADP
ejpam-5969	60	71	this	this	DET
ejpam-5969	60	72	paper	paper	NOUN
ejpam-5969	60	73	.	.	PUNCT
ejpam-5969	61	1	definition	definition	NOUN
ejpam-5969	61	2	1	1	NUM
ejpam-5969	61	3	.	.	PUNCT
ejpam-5969	62	1	[	[	X
ejpam-5969	62	2	13	13	NUM
ejpam-5969	62	3	]	]	PUNCT
ejpam-5969	62	4	the	the	DET
ejpam-5969	62	5	collection	collection	NOUN
ejpam-5969	62	6	ν	ν	VERB
ejpam-5969	62	7	⊆	⊆	NUM
ejpam-5969	62	8	p	p	NOUN
ejpam-5969	62	9	(	(	PUNCT
ejpam-5969	62	10	χ	χ	NOUN
ejpam-5969	62	11	)	)	PUNCT
ejpam-5969	62	12	is	be	AUX
ejpam-5969	62	13	called	call	VERB
ejpam-5969	62	14	supra	supra	ADJ
ejpam-5969	62	15	topology	topology	NOUN
ejpam-5969	62	16	(	(	PUNCT
ejpam-5969	62	17	or	or	CCONJ
ejpam-5969	62	18	sts	st	NOUN
ejpam-5969	62	19	)	)	PUNCT
ejpam-5969	62	20	on	on	ADP
ejpam-5969	62	21	χ	χ	PRON
ejpam-5969	62	22	if	if	SCONJ
ejpam-5969	62	23	ν	ν	NOUN
ejpam-5969	62	24	contains	contain	VERB
ejpam-5969	62	25	χ	χ	NOUN
ejpam-5969	62	26	and	and	CCONJ
ejpam-5969	62	27	∅	∅	NOUN
ejpam-5969	62	28	and	and	CCONJ
ejpam-5969	62	29	closed	close	VERB
ejpam-5969	62	30	under	under	ADP
ejpam-5969	62	31	arbitrary	arbitrary	ADJ
ejpam-5969	62	32	union	union	NOUN
ejpam-5969	62	33	.	.	PUNCT
ejpam-5969	63	1	also	also	ADV
ejpam-5969	63	2	,	,	PUNCT
ejpam-5969	63	3	if	if	SCONJ
ejpam-5969	63	4	g	g	PROPN
ejpam-5969	63	5	∈	∈	PROPN
ejpam-5969	63	6	ν	ν	NOUN
ejpam-5969	63	7	,	,	PUNCT
ejpam-5969	63	8	then	then	ADV
ejpam-5969	63	9	g	g	PROPN
ejpam-5969	63	10	is	be	AUX
ejpam-5969	63	11	called	call	VERB
ejpam-5969	63	12	supra	supra	PROPN
ejpam-5969	63	13	open	open	ADJ
ejpam-5969	63	14	set	set	NOUN
ejpam-5969	63	15	and	and	CCONJ
ejpam-5969	63	16	gc	gc	PROPN
ejpam-5969	63	17	is	be	AUX
ejpam-5969	63	18	called	call	VERB
ejpam-5969	63	19	supra	supra	PROPN
ejpam-5969	63	20	closed	close	VERB
ejpam-5969	63	21	set	set	NOUN
ejpam-5969	63	22	.	.	PUNCT
ejpam-5969	64	1	moreover	moreover	ADV
ejpam-5969	64	2	,	,	PUNCT
ejpam-5969	64	3	so(χ	so(χ	NOUN
ejpam-5969	64	4	)	)	PUNCT
ejpam-5969	64	5	will	will	AUX
ejpam-5969	64	6	denote	denote	VERB
ejpam-5969	64	7	the	the	DET
ejpam-5969	64	8	class	class	NOUN
ejpam-5969	64	9	of	of	ADP
ejpam-5969	64	10	all	all	DET
ejpam-5969	64	11	supra	supra	ADJ
ejpam-5969	64	12	open	open	ADJ
ejpam-5969	64	13	sets	set	NOUN
ejpam-5969	64	14	.	.	PUNCT
ejpam-5969	65	1	definition	definition	NOUN
ejpam-5969	65	2	2	2	NUM
ejpam-5969	65	3	.	.	PUNCT
ejpam-5969	66	1	[	[	X
ejpam-5969	66	2	13	13	NUM
ejpam-5969	66	3	]	]	PUNCT
ejpam-5969	66	4	for	for	ADP
ejpam-5969	66	5	the	the	DET
ejpam-5969	66	6	subset	subset	NOUN
ejpam-5969	66	7	k	k	PROPN
ejpam-5969	66	8	of	of	ADP
ejpam-5969	66	9	an	an	DET
ejpam-5969	66	10	sts	st	NOUN
ejpam-5969	66	11	(	(	PUNCT
ejpam-5969	66	12	χ	χ	NOUN
ejpam-5969	66	13	,	,	PUNCT
ejpam-5969	66	14	ν	ν	NOUN
ejpam-5969	66	15	)	)	PUNCT
ejpam-5969	66	16	,	,	PUNCT
ejpam-5969	66	17	the	the	DET
ejpam-5969	66	18	int(k	int(k	PROPN
ejpam-5969	66	19	)	)	PUNCT
ejpam-5969	66	20	or	or	CCONJ
ejpam-5969	66	21	k	k	NOUN
ejpam-5969	66	22	◦	◦	NOUN
ejpam-5969	66	23	(	(	PUNCT
ejpam-5969	66	24	respectively	respectively	ADV
ejpam-5969	66	25	,	,	PUNCT
ejpam-5969	66	26	cl(k	cl(k	NOUN
ejpam-5969	66	27	)	)	PUNCT
ejpam-5969	66	28	or	or	CCONJ
ejpam-5969	66	29	k	k	NOUN
ejpam-5969	66	30	,	,	PUNCT
ejpam-5969	66	31	and	and	CCONJ
ejpam-5969	66	32	b(k	b(k	PROPN
ejpam-5969	66	33	)	)	PUNCT
ejpam-5969	66	34	)	)	PUNCT
ejpam-5969	66	35	will	will	AUX
ejpam-5969	66	36	denote	denote	VERB
ejpam-5969	66	37	the	the	DET
ejpam-5969	66	38	supra	supra	ADJ
ejpam-5969	66	39	interior	interior	NOUN
ejpam-5969	66	40	(	(	PUNCT
ejpam-5969	66	41	respectively	respectively	ADV
ejpam-5969	66	42	,	,	PUNCT
ejpam-5969	66	43	closure	closure	NOUN
ejpam-5969	66	44	,	,	PUNCT
ejpam-5969	66	45	and	and	CCONJ
ejpam-5969	66	46	boundary	boundary	NOUN
ejpam-5969	66	47	)	)	PUNCT
ejpam-5969	66	48	of	of	ADP
ejpam-5969	66	49	k	k	NOUN
ejpam-5969	66	50	,	,	PUNCT
ejpam-5969	66	51	where	where	SCONJ
ejpam-5969	66	52	int(k	int(k	X
ejpam-5969	66	53	)	)	PUNCT
ejpam-5969	66	54	=	=	SYM
ejpam-5969	66	55	∪{g	∪{g	PROPN
ejpam-5969	66	56	:	:	PUNCT
ejpam-5969	66	57	g	g	PROPN
ejpam-5969	66	58	∈	∈	PROPN
ejpam-5969	66	59	ν	ν	NOUN
ejpam-5969	66	60	and	and	CCONJ
ejpam-5969	66	61	g	g	PROPN
ejpam-5969	66	62	⊆	⊆	NUM
ejpam-5969	66	63	k	k	NOUN
ejpam-5969	66	64	}	}	PUNCT
ejpam-5969	66	65	,	,	PUNCT
ejpam-5969	66	66	cl(k	cl(k	NOUN
ejpam-5969	66	67	)	)	PUNCT
ejpam-5969	67	1	=	=	VERB
ejpam-5969	67	2	∩{n	∩{n	INTJ
ejpam-5969	67	3	:	:	PUNCT
ejpam-5969	67	4	n	n	CCONJ
ejpam-5969	67	5	∈	∈	PROPN
ejpam-5969	67	6	νc	νc	NOUN
ejpam-5969	67	7	and	and	CCONJ
ejpam-5969	67	8	k	k	PROPN
ejpam-5969	67	9	⊆	⊆	PROPN
ejpam-5969	67	10	n	n	CCONJ
ejpam-5969	67	11	}	}	PUNCT
ejpam-5969	67	12	,	,	PUNCT
ejpam-5969	67	13	and	and	CCONJ
ejpam-5969	67	14	b(k	b(k	PROPN
ejpam-5969	67	15	)	)	PUNCT
ejpam-5969	67	16	=	=	SYM
ejpam-5969	67	17	cl(k)\int(k	cl(k)\int(k	PROPN
ejpam-5969	67	18	)	)	PUNCT
ejpam-5969	67	19	.	.	PUNCT
ejpam-5969	68	1	theorem	theorem	NOUN
ejpam-5969	68	2	1	1	NUM
ejpam-5969	68	3	.	.	PUNCT
ejpam-5969	69	1	[	[	X
ejpam-5969	69	2	13	13	NUM
ejpam-5969	69	3	]	]	PUNCT
ejpam-5969	69	4	regarding	regard	VERB
ejpam-5969	69	5	a	a	DET
ejpam-5969	69	6	subset	subset	ADJ
ejpam-5969	69	7	t	t	NOUN
ejpam-5969	69	8	of	of	ADP
ejpam-5969	69	9	an	an	DET
ejpam-5969	69	10	sts	st	NOUN
ejpam-5969	69	11	(	(	PUNCT
ejpam-5969	69	12	χ	χ	NOUN
ejpam-5969	69	13	,	,	PUNCT
ejpam-5969	69	14	ν	ν	NOUN
ejpam-5969	69	15	)	)	PUNCT
ejpam-5969	69	16	,	,	PUNCT
ejpam-5969	69	17	we	we	PRON
ejpam-5969	69	18	have	have	VERB
ejpam-5969	69	19	(	(	PUNCT
ejpam-5969	69	20	1	1	NUM
ejpam-5969	69	21	)	)	PUNCT
ejpam-5969	69	22	cl(t	cl(t	NOUN
ejpam-5969	69	23	c	c	X
ejpam-5969	69	24	)	)	PUNCT
ejpam-5969	69	25	=	=	PUNCT
ejpam-5969	70	1	[	[	X
ejpam-5969	70	2	int(t	int(t	PROPN
ejpam-5969	70	3	)	)	PUNCT
ejpam-5969	70	4	]	]	X
ejpam-5969	70	5	c.	c.	NOUN
ejpam-5969	70	6	(	(	PUNCT
ejpam-5969	70	7	2	2	NUM
ejpam-5969	70	8	)	)	PUNCT
ejpam-5969	70	9	int(t	int(t	PROPN
ejpam-5969	70	10	c	c	NOUN
ejpam-5969	70	11	)	)	PUNCT
ejpam-5969	70	12	=	=	NOUN
ejpam-5969	71	1	[	[	X
ejpam-5969	71	2	cl(t	cl(t	X
ejpam-5969	71	3	)	)	PUNCT
ejpam-5969	71	4	]	]	PUNCT
ejpam-5969	71	5	c.	c.	NOUN
ejpam-5969	71	6	definition	definition	NOUN
ejpam-5969	71	7	3	3	NUM
ejpam-5969	71	8	.	.	PUNCT
ejpam-5969	72	1	[	[	X
ejpam-5969	72	2	15–19	15–19	X
ejpam-5969	72	3	]	]	PUNCT
ejpam-5969	72	4	let	let	VERB
ejpam-5969	72	5	h	h	NOUN
ejpam-5969	72	6	be	be	AUX
ejpam-5969	72	7	a	a	DET
ejpam-5969	72	8	subset	subset	NOUN
ejpam-5969	72	9	of	of	ADP
ejpam-5969	72	10	an	an	DET
ejpam-5969	72	11	sts	st	NOUN
ejpam-5969	72	12	(	(	PUNCT
ejpam-5969	72	13	χ	χ	NOUN
ejpam-5969	72	14	,	,	PUNCT
ejpam-5969	72	15	ν	ν	NOUN
ejpam-5969	72	16	)	)	PUNCT
ejpam-5969	72	17	.	.	PUNCT
ejpam-5969	73	1	then	then	ADV
ejpam-5969	73	2	,	,	PUNCT
ejpam-5969	73	3	(	(	PUNCT
ejpam-5969	73	4	1	1	X
ejpam-5969	73	5	)	)	PUNCT
ejpam-5969	73	6	if	if	SCONJ
ejpam-5969	73	7	h	h	NOUN
ejpam-5969	73	8	=	=	SYM
ejpam-5969	73	9	int(cl(h	int(cl(h	PROPN
ejpam-5969	73	10	)	)	PUNCT
ejpam-5969	73	11	)	)	PUNCT
ejpam-5969	73	12	,	,	PUNCT
ejpam-5969	73	13	then	then	ADV
ejpam-5969	73	14	h	h	PROPN
ejpam-5969	73	15	∈	∈	PROPN
ejpam-5969	73	16	soregular(χ	soregular(χ	PROPN
ejpam-5969	73	17	)	)	PUNCT
ejpam-5969	73	18	.	.	PUNCT
ejpam-5969	74	1	(	(	PUNCT
ejpam-5969	74	2	2	2	X
ejpam-5969	74	3	)	)	PUNCT
ejpam-5969	74	4	if	if	SCONJ
ejpam-5969	74	5	h	h	NOUN
ejpam-5969	74	6	⊆	⊆	NUM
ejpam-5969	74	7	int(cl(h	int(cl(h	PROPN
ejpam-5969	74	8	)	)	PUNCT
ejpam-5969	74	9	)	)	PUNCT
ejpam-5969	74	10	,	,	PUNCT
ejpam-5969	74	11	then	then	ADV
ejpam-5969	74	12	h	h	PROPN
ejpam-5969	74	13	∈	∈	PROPN
ejpam-5969	74	14	spo(χ	spo(χ	PROPN
ejpam-5969	74	15	)	)	PUNCT
ejpam-5969	74	16	.	.	PUNCT
ejpam-5969	75	1	(	(	PUNCT
ejpam-5969	75	2	3	3	X
ejpam-5969	75	3	)	)	PUNCT
ejpam-5969	75	4	if	if	SCONJ
ejpam-5969	75	5	h	h	NOUN
ejpam-5969	75	6	⊆	⊆	NUM
ejpam-5969	75	7	cl(int(h	cl(int(h	NOUN
ejpam-5969	75	8	)	)	PUNCT
ejpam-5969	75	9	)	)	PUNCT
ejpam-5969	75	10	,	,	PUNCT
ejpam-5969	75	11	then	then	ADV
ejpam-5969	75	12	h	h	PROPN
ejpam-5969	75	13	∈	∈	PROPN
ejpam-5969	75	14	sso(χ	sso(χ	PROPN
ejpam-5969	75	15	)	)	PUNCT
ejpam-5969	75	16	.	.	PUNCT
ejpam-5969	76	1	(	(	PUNCT
ejpam-5969	76	2	4	4	X
ejpam-5969	76	3	)	)	PUNCT
ejpam-5969	76	4	if	if	SCONJ
ejpam-5969	76	5	h	h	NOUN
ejpam-5969	76	6	⊆	⊆	NUM
ejpam-5969	76	7	int(cl(int(h	int(cl(int(h	PROPN
ejpam-5969	76	8	)	)	PUNCT
ejpam-5969	76	9	)	)	PUNCT
ejpam-5969	76	10	)	)	PUNCT
ejpam-5969	76	11	,	,	PUNCT
ejpam-5969	76	12	then	then	ADV
ejpam-5969	76	13	h	h	PROPN
ejpam-5969	76	14	∈	∈	PROPN
ejpam-5969	76	15	sαo(χ	sαo(χ	VERB
ejpam-5969	76	16	)	)	PUNCT
ejpam-5969	76	17	.	.	PUNCT
ejpam-5969	77	1	(	(	PUNCT
ejpam-5969	77	2	5	5	X
ejpam-5969	77	3	)	)	PUNCT
ejpam-5969	77	4	if	if	SCONJ
ejpam-5969	77	5	h	h	NOUN
ejpam-5969	77	6	⊆	⊆	NUM
ejpam-5969	77	7	cl(int(cl(h	cl(int(cl(h	NOUN
ejpam-5969	77	8	)	)	PUNCT
ejpam-5969	77	9	)	)	PUNCT
ejpam-5969	77	10	)	)	PUNCT
ejpam-5969	77	11	,	,	PUNCT
ejpam-5969	77	12	then	then	ADV
ejpam-5969	77	13	h	h	PROPN
ejpam-5969	77	14	∈	∈	PROPN
ejpam-5969	77	15	sβo(χ	sβo(χ	PROPN
ejpam-5969	77	16	)	)	PUNCT
ejpam-5969	77	17	.	.	PUNCT
ejpam-5969	78	1	(	(	PUNCT
ejpam-5969	78	2	6	6	NUM
ejpam-5969	78	3	)	)	PUNCT
ejpam-5969	78	4	if	if	SCONJ
ejpam-5969	78	5	h	h	NOUN
ejpam-5969	78	6	⊆	⊆	NUM
ejpam-5969	78	7	cl(int(h))∪̃int(cl(h	cl(int(h))∪̃int(cl(h	NUM
ejpam-5969	78	8	)	)	PUNCT
ejpam-5969	78	9	)	)	PUNCT
ejpam-5969	78	10	,	,	PUNCT
ejpam-5969	78	11	then	then	ADV
ejpam-5969	78	12	h	h	PROPN
ejpam-5969	78	13	∈	∈	PROPN
ejpam-5969	78	14	sbo(χ	sbo(χ	PROPN
ejpam-5969	78	15	)	)	PUNCT
ejpam-5969	78	16	.	.	PUNCT
ejpam-5969	79	1	(	(	PUNCT
ejpam-5969	79	2	7	7	X
ejpam-5969	79	3	)	)	PUNCT
ejpam-5969	79	4	if	if	SCONJ
ejpam-5969	79	5	int(cl(h	int(cl(h	PROPN
ejpam-5969	79	6	)	)	PUNCT
ejpam-5969	79	7	)	)	PUNCT
ejpam-5969	80	1	̸=	̸=	NOUN
ejpam-5969	80	2	∅	∅	NOUN
ejpam-5969	80	3	,	,	PUNCT
ejpam-5969	80	4	then	then	ADV
ejpam-5969	80	5	h	h	NOUN
ejpam-5969	80	6	∈	∈	NOUN
ejpam-5969	80	7	sro(χ	sro(χ	PROPN
ejpam-5969	80	8	)	)	PUNCT
ejpam-5969	80	9	.	.	PUNCT
ejpam-5969	81	1	(	(	PUNCT
ejpam-5969	81	2	8)	8)	NUM
ejpam-5969	81	3	if	if	SCONJ
ejpam-5969	81	4	int(cl(h	int(cl(h	PROPN
ejpam-5969	81	5	)	)	PUNCT
ejpam-5969	81	6	)	)	PUNCT
ejpam-5969	82	1	=	=	NOUN
ejpam-5969	82	2	∅	∅	NOUN
ejpam-5969	82	3	,	,	PUNCT
ejpam-5969	82	4	then	then	ADV
ejpam-5969	82	5	h	h	PROPN
ejpam-5969	82	6	∈	∈	PROPN
ejpam-5969	82	7	snd(χ	snd(χ	PROPN
ejpam-5969	82	8	)	)	PUNCT
ejpam-5969	82	9	.	.	PUNCT
ejpam-5969	83	1	abd	abd	PROPN
ejpam-5969	83	2	el	el	PROPN
ejpam-5969	83	3	-	-	PROPN
ejpam-5969	83	4	latif	latif	PROPN
ejpam-5969	83	5	et	et	PROPN
ejpam-5969	83	6	al	al	PROPN
ejpam-5969	83	7	.	.	PUNCT
ejpam-5969	83	8	/	/	SYM
ejpam-5969	83	9	eur	eur	PROPN
ejpam-5969	83	10	.	.	PUNCT
ejpam-5969	84	1	j.	j.	PROPN
ejpam-5969	84	2	pure	pure	PROPN
ejpam-5969	84	3	appl	appl	PROPN
ejpam-5969	84	4	.	.	PROPN
ejpam-5969	84	5	math	math	PROPN
ejpam-5969	84	6	,	,	PUNCT
ejpam-5969	84	7	18	18	NUM
ejpam-5969	84	8	(	(	PUNCT
ejpam-5969	84	9	2	2	NUM
ejpam-5969	84	10	)	)	PUNCT
ejpam-5969	84	11	(	(	PUNCT
ejpam-5969	84	12	2025	2025	NUM
ejpam-5969	84	13	)	)	PUNCT
ejpam-5969	84	14	,	,	PUNCT
ejpam-5969	84	15	5969	5969	NUM
ejpam-5969	84	16	4	4	NUM
ejpam-5969	84	17	of	of	ADP
ejpam-5969	84	18	19	19	NUM
ejpam-5969	84	19	definition	definition	NOUN
ejpam-5969	84	20	4	4	NUM
ejpam-5969	84	21	.	.	PUNCT
ejpam-5969	85	1	for	for	ADP
ejpam-5969	85	2	the	the	DET
ejpam-5969	85	3	subset	subset	NOUN
ejpam-5969	85	4	k	k	PROPN
ejpam-5969	85	5	of	of	ADP
ejpam-5969	85	6	an	an	DET
ejpam-5969	85	7	sts	st	NOUN
ejpam-5969	85	8	(	(	PUNCT
ejpam-5969	85	9	χ	χ	NOUN
ejpam-5969	85	10	,	,	PUNCT
ejpam-5969	85	11	ν	ν	NOUN
ejpam-5969	85	12	)	)	PUNCT
ejpam-5969	85	13	,	,	PUNCT
ejpam-5969	85	14	the	the	DET
ejpam-5969	85	15	class	class	NOUN
ejpam-5969	85	16	νk	νk	NOUN
ejpam-5969	85	17	=	=	SYM
ejpam-5969	85	18	{	{	PUNCT
ejpam-5969	85	19	k	k	X
ejpam-5969	85	20	∩g	∩g	PROPN
ejpam-5969	85	21	:	:	PUNCT
ejpam-5969	85	22	g	g	PROPN
ejpam-5969	85	23	∈	∈	PROPN
ejpam-5969	85	24	ν	ν	PROPN
ejpam-5969	85	25	}	}	PUNCT
ejpam-5969	85	26	defines	define	VERB
ejpam-5969	85	27	an	an	DET
ejpam-5969	85	28	sts	st	NOUN
ejpam-5969	85	29	on	on	ADP
ejpam-5969	85	30	k	k	PROPN
ejpam-5969	85	31	,	,	PUNCT
ejpam-5969	85	32	and	and	CCONJ
ejpam-5969	85	33	it	it	PRON
ejpam-5969	85	34	is	be	AUX
ejpam-5969	85	35	called	call	VERB
ejpam-5969	85	36	a	a	DET
ejpam-5969	85	37	subspace	subspace	NOUN
ejpam-5969	85	38	of	of	ADP
ejpam-5969	85	39	(	(	PUNCT
ejpam-5969	85	40	χ	χ	NOUN
ejpam-5969	85	41	,	,	PUNCT
ejpam-5969	85	42	ν	ν	NOUN
ejpam-5969	85	43	)	)	PUNCT
ejpam-5969	85	44	.	.	PUNCT
ejpam-5969	86	1	3	3	X
ejpam-5969	86	2	.	.	X
ejpam-5969	86	3	supra	supra	PROPN
ejpam-5969	86	4	ϵ-open	ϵ-open	PROPN
ejpam-5969	86	5	sets	set	NOUN
ejpam-5969	86	6	and	and	CCONJ
ejpam-5969	86	7	relationships	relationship	NOUN
ejpam-5969	86	8	this	this	DET
ejpam-5969	86	9	part	part	NOUN
ejpam-5969	86	10	begins	begin	VERB
ejpam-5969	86	11	by	by	ADP
ejpam-5969	86	12	presenting	present	VERB
ejpam-5969	86	13	the	the	DET
ejpam-5969	86	14	definitions	definition	NOUN
ejpam-5969	86	15	of	of	ADP
ejpam-5969	86	16	supra	supra	PROPN
ejpam-5969	86	17	ϵ-open	ϵ-open	PROPN
ejpam-5969	86	18	and	and	CCONJ
ejpam-5969	86	19	supra	supra	ADJ
ejpam-5969	86	20	ϵ-closed	ϵ-close	VERB
ejpam-5969	86	21	sets	set	NOUN
ejpam-5969	86	22	and	and	CCONJ
ejpam-5969	86	23	the	the	DET
ejpam-5969	86	24	properties	property	NOUN
ejpam-5969	86	25	based	base	VERB
ejpam-5969	86	26	on	on	ADP
ejpam-5969	86	27	them	they	PRON
ejpam-5969	86	28	.	.	PUNCT
ejpam-5969	87	1	we	we	PRON
ejpam-5969	87	2	show	show	VERB
ejpam-5969	87	3	that	that	SCONJ
ejpam-5969	87	4	,	,	PUNCT
ejpam-5969	87	5	this	this	DET
ejpam-5969	87	6	new	new	ADJ
ejpam-5969	87	7	category	category	NOUN
ejpam-5969	87	8	of	of	ADP
ejpam-5969	87	9	supra	supra	PROPN
ejpam-5969	87	10	open	open	ADJ
ejpam-5969	87	11	sets	set	NOUN
ejpam-5969	87	12	includes	include	VERB
ejpam-5969	87	13	the	the	DET
ejpam-5969	87	14	previously	previously	ADV
ejpam-5969	87	15	comparable	comparable	ADJ
ejpam-5969	87	16	concepts	concept	NOUN
ejpam-5969	87	17	of	of	ADP
ejpam-5969	87	18	supra	supra	PROPN
ejpam-5969	87	19	regular	regular	PROPN
ejpam-5969	87	20	(	(	PUNCT
ejpam-5969	87	21	α-	α-	NUM
ejpam-5969	87	22	,	,	PUNCT
ejpam-5969	87	23	semi-	semi-	ADJ
ejpam-5969	87	24	,	,	PUNCT
ejpam-5969	87	25	pre-	pre-	X
ejpam-5969	87	26	,	,	PUNCT
ejpam-5969	87	27	b-	b-	X
ejpam-5969	87	28	,	,	PUNCT
ejpam-5969	87	29	β-	β-	X
ejpam-5969	87	30	,	,	PUNCT
ejpam-5969	87	31	and	and	CCONJ
ejpam-5969	87	32	r-	r-	X
ejpam-5969	87	33	)	)	PUNCT
ejpam-5969	87	34	open	open	ADJ
ejpam-5969	87	35	sets	set	NOUN
ejpam-5969	87	36	.	.	PUNCT
ejpam-5969	88	1	in	in	ADP
ejpam-5969	88	2	addition	addition	NOUN
ejpam-5969	88	3	,	,	PUNCT
ejpam-5969	88	4	we	we	PRON
ejpam-5969	88	5	have	have	AUX
ejpam-5969	88	6	included	include	VERB
ejpam-5969	88	7	a	a	DET
ejpam-5969	88	8	geometric	geometric	ADJ
ejpam-5969	88	9	topological	topological	ADJ
ejpam-5969	88	10	diagram	diagram	NOUN
ejpam-5969	88	11	[	[	X
ejpam-5969	88	12	see	see	VERB
ejpam-5969	88	13	diagram	diagram	NOUN
ejpam-5969	88	14	1	1	NUM
ejpam-5969	88	15	]	]	PUNCT
ejpam-5969	88	16	to	to	PART
ejpam-5969	88	17	further	far	ADV
ejpam-5969	88	18	demonstrate	demonstrate	VERB
ejpam-5969	88	19	the	the	DET
ejpam-5969	88	20	basic	basic	ADJ
ejpam-5969	88	21	concepts	concept	NOUN
ejpam-5969	88	22	covered	cover	VERB
ejpam-5969	88	23	in	in	ADP
ejpam-5969	88	24	the	the	DET
ejpam-5969	88	25	study	study	NOUN
ejpam-5969	88	26	.	.	PUNCT
ejpam-5969	89	1	moreover	moreover	ADV
ejpam-5969	89	2	,	,	PUNCT
ejpam-5969	89	3	we	we	PRON
ejpam-5969	89	4	discuss	discuss	VERB
ejpam-5969	89	5	the	the	DET
ejpam-5969	89	6	main	main	ADJ
ejpam-5969	89	7	features	feature	NOUN
ejpam-5969	89	8	of	of	ADP
ejpam-5969	89	9	this	this	DET
ejpam-5969	89	10	class	class	NOUN
ejpam-5969	89	11	.	.	PUNCT
ejpam-5969	90	1	in	in	ADP
ejpam-5969	90	2	particular	particular	ADJ
ejpam-5969	90	3	,	,	PUNCT
ejpam-5969	90	4	we	we	PRON
ejpam-5969	90	5	demonstrate	demonstrate	VERB
ejpam-5969	90	6	that	that	SCONJ
ejpam-5969	90	7	instead	instead	ADV
ejpam-5969	90	8	of	of	ADP
ejpam-5969	90	9	forming	form	VERB
ejpam-5969	90	10	a	a	DET
ejpam-5969	90	11	topological	topological	ADJ
ejpam-5969	90	12	space	space	NOUN
ejpam-5969	90	13	,	,	PUNCT
ejpam-5969	90	14	our	our	PRON
ejpam-5969	90	15	new	new	ADJ
ejpam-5969	90	16	category	category	NOUN
ejpam-5969	90	17	forms	form	VERB
ejpam-5969	90	18	a	a	DET
ejpam-5969	90	19	supra	supra	ADJ
ejpam-5969	90	20	topology	topology	NOUN
ejpam-5969	90	21	.	.	PUNCT
ejpam-5969	91	1	definition	definition	NOUN
ejpam-5969	91	2	5	5	NUM
ejpam-5969	91	3	.	.	PUNCT
ejpam-5969	92	1	let	let	VERB
ejpam-5969	92	2	h	h	PRON
ejpam-5969	92	3	be	be	AUX
ejpam-5969	92	4	a	a	DET
ejpam-5969	92	5	subset	subset	NOUN
ejpam-5969	92	6	of	of	ADP
ejpam-5969	92	7	an	an	DET
ejpam-5969	92	8	sts	st	NOUN
ejpam-5969	92	9	(	(	PUNCT
ejpam-5969	92	10	χ	χ	NOUN
ejpam-5969	92	11	,	,	PUNCT
ejpam-5969	92	12	ν	ν	NOUN
ejpam-5969	92	13	)	)	PUNCT
ejpam-5969	92	14	.	.	PUNCT
ejpam-5969	93	1	then	then	ADV
ejpam-5969	93	2	,	,	PUNCT
ejpam-5969	93	3	h	h	NOUN
ejpam-5969	93	4	is	be	AUX
ejpam-5969	93	5	called	call	VERB
ejpam-5969	93	6	supra	supra	PROPN
ejpam-5969	93	7	ϵ-open	ϵ-open	PROPN
ejpam-5969	93	8	set	set	VERB
ejpam-5969	93	9	if	if	SCONJ
ejpam-5969	93	10	either	either	PRON
ejpam-5969	93	11	h	h	NOUN
ejpam-5969	93	12	=	=	NOUN
ejpam-5969	93	13	∅	∅	NOUN
ejpam-5969	93	14	or	or	CCONJ
ejpam-5969	93	15	h	h	NOUN
ejpam-5969	93	16	⊆	⊆	NUM
ejpam-5969	93	17	{	{	PUNCT
ejpam-5969	93	18	b(h	b(h	PROPN
ejpam-5969	93	19	)	)	PUNCT
ejpam-5969	93	20	∪h	∪h	NUM
ejpam-5969	93	21	◦	◦	NOUN
ejpam-5969	93	22	,	,	PUNCT
ejpam-5969	93	23	h	h	NOUN
ejpam-5969	93	24	∈	∈	NOUN
ejpam-5969	93	25	sro(χ	sro(χ	PROPN
ejpam-5969	93	26	)	)	PUNCT
ejpam-5969	93	27	,	,	PUNCT
ejpam-5969	93	28	b(h	b(h	PROPN
ejpam-5969	93	29	)	)	PUNCT
ejpam-5969	93	30	,	,	PUNCT
ejpam-5969	93	31	h	h	NOUN
ejpam-5969	93	32	∈	∈	PROPN
ejpam-5969	93	33	snd(χ	snd(χ	PROPN
ejpam-5969	93	34	)	)	PUNCT
ejpam-5969	93	35	and	and	CCONJ
ejpam-5969	93	36	b(h	b(h	PROPN
ejpam-5969	93	37	)	)	PUNCT
ejpam-5969	93	38	is	be	AUX
ejpam-5969	93	39	infinite	infinite	ADJ
ejpam-5969	93	40	.	.	PUNCT
ejpam-5969	94	1	also	also	ADV
ejpam-5969	94	2	,	,	PUNCT
ejpam-5969	94	3	hc	hc	PROPN
ejpam-5969	94	4	is	be	AUX
ejpam-5969	94	5	called	call	VERB
ejpam-5969	94	6	supra	supra	ADJ
ejpam-5969	94	7	ϵ-closed	ϵ-close	VERB
ejpam-5969	94	8	-	-	PUNCT
ejpam-5969	94	9	set	set	NOUN
ejpam-5969	94	10	.	.	PUNCT
ejpam-5969	95	1	the	the	DET
ejpam-5969	95	2	category	category	NOUN
ejpam-5969	95	3	of	of	ADP
ejpam-5969	95	4	all	all	DET
ejpam-5969	95	5	supra	supra	PROPN
ejpam-5969	95	6	ϵ-open	ϵ-open	PROPN
ejpam-5969	95	7	(	(	PUNCT
ejpam-5969	95	8	closed	closed	ADJ
ejpam-5969	95	9	)	)	PUNCT
ejpam-5969	95	10	sets	set	NOUN
ejpam-5969	95	11	will	will	AUX
ejpam-5969	95	12	be	be	AUX
ejpam-5969	95	13	indicated	indicate	VERB
ejpam-5969	95	14	by	by	ADP
ejpam-5969	95	15	soϵ(χ	soϵ(χ	NOUN
ejpam-5969	95	16	)	)	PUNCT
ejpam-5969	95	17	(	(	PUNCT
ejpam-5969	95	18	scϵ(χ	scϵ(χ	NUM
ejpam-5969	95	19	)	)	PUNCT
ejpam-5969	95	20	)	)	PUNCT
ejpam-5969	95	21	.	.	PUNCT
ejpam-5969	96	1	proposition	proposition	NOUN
ejpam-5969	96	2	1	1	NUM
ejpam-5969	96	3	.	.	PUNCT
ejpam-5969	97	1	every	every	DET
ejpam-5969	97	2	singleton	singleton	NOUN
ejpam-5969	97	3	{	{	PUNCT
ejpam-5969	97	4	c	c	NOUN
ejpam-5969	97	5	}	}	PUNCT
ejpam-5969	97	6	subset	subset	NOUN
ejpam-5969	97	7	of	of	ADP
ejpam-5969	97	8	an	an	DET
ejpam-5969	97	9	sts	st	NOUN
ejpam-5969	97	10	(	(	PUNCT
ejpam-5969	97	11	χ	χ	NOUN
ejpam-5969	97	12	,	,	PUNCT
ejpam-5969	97	13	ν	ν	NOUN
ejpam-5969	97	14	)	)	PUNCT
ejpam-5969	97	15	is	be	AUX
ejpam-5969	97	16	either	either	CCONJ
ejpam-5969	97	17	supra	supra	PROPN
ejpam-5969	97	18	ϵ-open	ϵ-open	PROPN
ejpam-5969	97	19	or	or	CCONJ
ejpam-5969	97	20	supra	supra	ADJ
ejpam-5969	97	21	nowhere	nowhere	ADV
ejpam-5969	97	22	dense	dense	ADJ
ejpam-5969	97	23	.	.	PUNCT
ejpam-5969	98	1	proof	proof	NOUN
ejpam-5969	98	2	.	.	PUNCT
ejpam-5969	99	1	let	let	VERB
ejpam-5969	99	2	{	{	PUNCT
ejpam-5969	99	3	c	c	NOUN
ejpam-5969	99	4	}	}	PUNCT
ejpam-5969	99	5	⊈	⊈	PROPN
ejpam-5969	99	6	snd(χ	snd(χ	NUM
ejpam-5969	99	7	)	)	PUNCT
ejpam-5969	99	8	.	.	PUNCT
ejpam-5969	100	1	then	then	ADV
ejpam-5969	100	2	,	,	PUNCT
ejpam-5969	100	3	{	{	PUNCT
ejpam-5969	100	4	c	c	X
ejpam-5969	100	5	}	}	PUNCT
ejpam-5969	100	6	◦	◦	VERB
ejpam-5969	100	7	̸=	̸=	PROPN
ejpam-5969	100	8	∅̃	∅̃	NOUN
ejpam-5969	100	9	and	and	CCONJ
ejpam-5969	100	10	so	so	ADV
ejpam-5969	100	11	{	{	PUNCT
ejpam-5969	100	12	c	c	X
ejpam-5969	100	13	}	}	PUNCT
ejpam-5969	100	14	∈	∈	NOUN
ejpam-5969	100	15	sro(χ	sro(χ	NOUN
ejpam-5969	100	16	)	)	PUNCT
ejpam-5969	100	17	.	.	PUNCT
ejpam-5969	101	1	hence	hence	ADV
ejpam-5969	101	2	,	,	PUNCT
ejpam-5969	101	3	{	{	PUNCT
ejpam-5969	101	4	c	c	X
ejpam-5969	101	5	}	}	PUNCT
ejpam-5969	101	6	∈	∈	PROPN
ejpam-5969	101	7	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	101	8	)	)	PUNCT
ejpam-5969	101	9	.	.	PUNCT
ejpam-5969	102	1	on	on	ADP
ejpam-5969	102	2	the	the	DET
ejpam-5969	102	3	other	other	ADJ
ejpam-5969	102	4	way	way	NOUN
ejpam-5969	102	5	,	,	PUNCT
ejpam-5969	102	6	suppose	suppose	VERB
ejpam-5969	102	7	that	that	SCONJ
ejpam-5969	102	8	{	{	PUNCT
ejpam-5969	102	9	c	c	X
ejpam-5969	102	10	}	}	PUNCT
ejpam-5969	102	11	̸∈	̸∈	PROPN
ejpam-5969	102	12	soϵ(χ	soϵ(χ	X
ejpam-5969	102	13	)	)	PUNCT
ejpam-5969	102	14	,	,	PUNCT
ejpam-5969	102	15	then	then	ADV
ejpam-5969	102	16	{	{	PUNCT
ejpam-5969	102	17	c	c	X
ejpam-5969	102	18	}	}	PUNCT
ejpam-5969	102	19	⊈	⊈	PROPN
ejpam-5969	102	20	{	{	PUNCT
ejpam-5969	102	21	c	c	NOUN
ejpam-5969	102	22	}	}	PUNCT
ejpam-5969	102	23	◦	◦	VERB
ejpam-5969	102	24	∪b({c	∪b({c	NOUN
ejpam-5969	102	25	}	}	PUNCT
ejpam-5969	102	26	)	)	PUNCT
ejpam-5969	103	1	and	and	CCONJ
ejpam-5969	103	2	so	so	ADV
ejpam-5969	103	3	{	{	PUNCT
ejpam-5969	103	4	c	c	X
ejpam-5969	103	5	}	}	PUNCT
ejpam-5969	103	6	⊈	⊈	PROPN
ejpam-5969	103	7	{	{	PUNCT
ejpam-5969	103	8	c	c	NOUN
ejpam-5969	103	9	}	}	PUNCT
ejpam-5969	103	10	◦	◦	NOUN
ejpam-5969	103	11	.	.	PUNCT
ejpam-5969	104	1	therefore	therefore	ADV
ejpam-5969	104	2	,	,	PUNCT
ejpam-5969	104	3	{	{	PUNCT
ejpam-5969	104	4	c	c	X
ejpam-5969	104	5	}	}	PUNCT
ejpam-5969	104	6	∈	∈	PROPN
ejpam-5969	104	7	snd(χ	snd(χ	PROPN
ejpam-5969	104	8	)	)	PUNCT
ejpam-5969	104	9	.	.	PUNCT
ejpam-5969	105	1	remark	remark	PROPN
ejpam-5969	105	2	1	1	NUM
ejpam-5969	105	3	.	.	PUNCT
ejpam-5969	106	1	for	for	ADP
ejpam-5969	106	2	the	the	DET
ejpam-5969	106	3	subset	subset	NOUN
ejpam-5969	106	4	k	k	PROPN
ejpam-5969	106	5	of	of	ADP
ejpam-5969	106	6	an	an	DET
ejpam-5969	106	7	sts	st	NOUN
ejpam-5969	106	8	(	(	PUNCT
ejpam-5969	106	9	χ	χ	NOUN
ejpam-5969	106	10	,	,	PUNCT
ejpam-5969	106	11	ν	ν	NOUN
ejpam-5969	106	12	)	)	PUNCT
ejpam-5969	106	13	,	,	PUNCT
ejpam-5969	106	14	we	we	PRON
ejpam-5969	106	15	have	have	VERB
ejpam-5969	106	16	:	:	PUNCT
ejpam-5969	106	17	(	(	PUNCT
ejpam-5969	106	18	1	1	X
ejpam-5969	106	19	)	)	PUNCT
ejpam-5969	106	20	if	if	SCONJ
ejpam-5969	106	21	k	k	PROPN
ejpam-5969	106	22	is	be	AUX
ejpam-5969	106	23	a	a	DET
ejpam-5969	106	24	non	non	ADJ
ejpam-5969	106	25	-	-	ADJ
ejpam-5969	106	26	empty	empty	ADJ
ejpam-5969	106	27	finite	finite	NOUN
ejpam-5969	106	28	,	,	PUNCT
ejpam-5969	106	29	closed	closed	ADJ
ejpam-5969	106	30	and	and	CCONJ
ejpam-5969	106	31	nowhere	nowhere	ADV
ejpam-5969	106	32	dense	dense	ADJ
ejpam-5969	106	33	set	set	NOUN
ejpam-5969	106	34	,	,	PUNCT
ejpam-5969	106	35	then	then	ADV
ejpam-5969	106	36	k	k	PROPN
ejpam-5969	106	37	̸∈	̸∈	PROPN
ejpam-5969	106	38	soϵ(χ	soϵ(χ	X
ejpam-5969	106	39	)	)	PUNCT
ejpam-5969	106	40	.	.	PUNCT
ejpam-5969	107	1	(	(	PUNCT
ejpam-5969	107	2	2	2	X
ejpam-5969	107	3	)	)	PUNCT
ejpam-5969	107	4	if	if	SCONJ
ejpam-5969	107	5	k	k	PROPN
ejpam-5969	107	6	is	be	AUX
ejpam-5969	107	7	a	a	DET
ejpam-5969	107	8	infinite	infinite	ADJ
ejpam-5969	107	9	and	and	CCONJ
ejpam-5969	107	10	nowhere	nowhere	ADV
ejpam-5969	107	11	dense	dense	ADJ
ejpam-5969	107	12	set	set	NOUN
ejpam-5969	107	13	,	,	PUNCT
ejpam-5969	107	14	then	then	ADV
ejpam-5969	107	15	k	k	PROPN
ejpam-5969	107	16	∈	∈	PROPN
ejpam-5969	107	17	soϵ(χ	soϵ(χ	VERB
ejpam-5969	107	18	)	)	PUNCT
ejpam-5969	107	19	.	.	PUNCT
ejpam-5969	108	1	remark	remark	NOUN
ejpam-5969	108	2	2	2	NUM
ejpam-5969	108	3	.	.	PUNCT
ejpam-5969	109	1	as	as	SCONJ
ejpam-5969	109	2	the	the	DET
ejpam-5969	109	3	authors	author	NOUN
ejpam-5969	109	4	demonstrated	demonstrate	VERB
ejpam-5969	109	5	in	in	ADP
ejpam-5969	109	6	[	[	X
ejpam-5969	109	7	18	18	NUM
ejpam-5969	109	8	]	]	PUNCT
ejpam-5969	109	9	,	,	PUNCT
ejpam-5969	109	10	each	each	DET
ejpam-5969	109	11	supra	supra	PROPN
ejpam-5969	109	12	regular	regular	ADJ
ejpam-5969	109	13	(	(	PUNCT
ejpam-5969	109	14	respectively	respectively	ADV
ejpam-5969	109	15	,	,	PUNCT
ejpam-5969	109	16	α-	α-	X
ejpam-5969	109	17	,	,	PUNCT
ejpam-5969	109	18	semi-	semi-	ADJ
ejpam-5969	109	19	,	,	PUNCT
ejpam-5969	109	20	pre	pre	ADJ
ejpam-5969	109	21	-	-	PUNCT
ejpam-5969	109	22	,	,	PUNCT
ejpam-5969	109	23	b-	b-	X
ejpam-5969	109	24	,	,	PUNCT
ejpam-5969	109	25	and	and	CCONJ
ejpam-5969	109	26	β-	β-	NUM
ejpam-5969	109	27	)	)	PUNCT
ejpam-5969	109	28	open	open	ADJ
ejpam-5969	109	29	set	set	NOUN
ejpam-5969	109	30	is	be	AUX
ejpam-5969	109	31	a	a	DET
ejpam-5969	109	32	supra	supra	NOUN
ejpam-5969	109	33	-	-	PUNCT
ejpam-5969	109	34	r	r	NOUN
ejpam-5969	109	35	-	-	NOUN
ejpam-5969	109	36	open	open	ADJ
ejpam-5969	109	37	.	.	PUNCT
ejpam-5969	110	1	consequently	consequently	ADV
ejpam-5969	110	2	from	from	ADP
ejpam-5969	110	3	definition	definition	NOUN
ejpam-5969	110	4	5	5	NUM
ejpam-5969	110	5	,	,	PUNCT
ejpam-5969	110	6	the	the	DET
ejpam-5969	110	7	reader	reader	NOUN
ejpam-5969	110	8	can	can	AUX
ejpam-5969	110	9	notice	notice	VERB
ejpam-5969	110	10	that	that	SCONJ
ejpam-5969	110	11	,	,	PUNCT
ejpam-5969	110	12	they	they	PRON
ejpam-5969	110	13	are	be	AUX
ejpam-5969	110	14	all	all	ADV
ejpam-5969	110	15	supra	supra	PROPN
ejpam-5969	110	16	ϵ-open	ϵ-open	PROPN
ejpam-5969	110	17	.	.	PUNCT
ejpam-5969	111	1	the	the	DET
ejpam-5969	111	2	following	follow	VERB
ejpam-5969	111	3	counterexample	counterexample	NOUN
ejpam-5969	111	4	will	will	AUX
ejpam-5969	111	5	demonstrate	demonstrate	VERB
ejpam-5969	111	6	that	that	SCONJ
ejpam-5969	111	7	our	our	PRON
ejpam-5969	111	8	perspective	perspective	NOUN
ejpam-5969	111	9	on	on	ADP
ejpam-5969	111	10	the	the	DET
ejpam-5969	111	11	aforementioned	aforementioned	ADJ
ejpam-5969	111	12	remark	remark	NOUN
ejpam-5969	111	13	is	be	AUX
ejpam-5969	111	14	non	non	ADJ
ejpam-5969	111	15	-	-	ADJ
ejpam-5969	111	16	reversible	reversible	ADJ
ejpam-5969	111	17	,	,	PUNCT
ejpam-5969	111	18	generally	generally	ADV
ejpam-5969	111	19	.	.	PUNCT
ejpam-5969	112	1	example	example	NOUN
ejpam-5969	112	2	1	1	NUM
ejpam-5969	112	3	.	.	X
ejpam-5969	113	1	consider	consider	VERB
ejpam-5969	113	2	the	the	DET
ejpam-5969	113	3	supra	supra	PROPN
ejpam-5969	113	4	topology	topology	NOUN
ejpam-5969	113	5	ν	ν	NOUN
ejpam-5969	113	6	=	=	SYM
ejpam-5969	113	7	{	{	PUNCT
ejpam-5969	113	8	∅	∅	NOUN
ejpam-5969	113	9	,	,	PUNCT
ejpam-5969	113	10	t	t	PROPN
ejpam-5969	113	11	⊆	⊆	NUM
ejpam-5969	113	12	r	r	NOUN
ejpam-5969	113	13	:	:	PUNCT
ejpam-5969	113	14	−1	−1	NOUN
ejpam-5969	113	15	∈	∈	PROPN
ejpam-5969	113	16	t	t	NOUN
ejpam-5969	113	17	or	or	CCONJ
ejpam-5969	113	18	0	0	NUM
ejpam-5969	113	19	∈	∈	PROPN
ejpam-5969	113	20	t	t	PROPN
ejpam-5969	113	21	}	}	PUNCT
ejpam-5969	113	22	,	,	PUNCT
ejpam-5969	113	23	on	on	ADP
ejpam-5969	113	24	the	the	DET
ejpam-5969	113	25	set	set	NOUN
ejpam-5969	113	26	of	of	ADP
ejpam-5969	113	27	real	real	ADJ
ejpam-5969	113	28	numbers	number	NOUN
ejpam-5969	113	29	r.	r.	PROPN
ejpam-5969	113	30	regarding	regard	VERB
ejpam-5969	113	31	the	the	DET
ejpam-5969	113	32	set	set	NOUN
ejpam-5969	113	33	of	of	ADP
ejpam-5969	113	34	natural	natural	ADJ
ejpam-5969	113	35	numbers	number	NOUN
ejpam-5969	113	36	n	n	CCONJ
ejpam-5969	113	37	,	,	PUNCT
ejpam-5969	113	38	we	we	PRON
ejpam-5969	113	39	have	have	VERB
ejpam-5969	113	40	n	n	NUM
ejpam-5969	113	41	◦	◦	NOUN
ejpam-5969	113	42	=	=	SYM
ejpam-5969	113	43	n	n	CCONJ
ejpam-5969	113	44	◦	◦	NOUN
ejpam-5969	113	45	=	=	SYM
ejpam-5969	113	46	∅	∅	NOUN
ejpam-5969	113	47	,	,	PUNCT
ejpam-5969	113	48	and	and	CCONJ
ejpam-5969	113	49	hence	hence	ADV
ejpam-5969	113	50	n	n	DET
ejpam-5969	113	51	̸∈	̸∈	PROPN
ejpam-5969	113	52	sro(χ	sro(χ	PROPN
ejpam-5969	113	53	)	)	PUNCT
ejpam-5969	113	54	.	.	PUNCT
ejpam-5969	114	1	however	however	ADV
ejpam-5969	114	2	,	,	PUNCT
ejpam-5969	114	3	b(n	b(n	NOUN
ejpam-5969	114	4	)	)	PUNCT
ejpam-5969	114	5	=	=	SYM
ejpam-5969	115	1	n	n	PROPN
ejpam-5969	115	2	is	be	AUX
ejpam-5969	115	3	infinite	infinite	ADJ
ejpam-5969	115	4	.	.	PUNCT
ejpam-5969	116	1	hence	hence	ADV
ejpam-5969	116	2	,	,	PUNCT
ejpam-5969	116	3	n	n	PROPN
ejpam-5969	116	4	∈	∈	PROPN
ejpam-5969	116	5	soϵ(r	soϵ(r	PROPN
ejpam-5969	116	6	)	)	PUNCT
ejpam-5969	116	7	.	.	PUNCT
ejpam-5969	117	1	abd	abd	PROPN
ejpam-5969	117	2	el	el	PROPN
ejpam-5969	117	3	-	-	PROPN
ejpam-5969	117	4	latif	latif	PROPN
ejpam-5969	117	5	et	et	PROPN
ejpam-5969	117	6	al	al	PROPN
ejpam-5969	117	7	.	.	PUNCT
ejpam-5969	117	8	/	/	SYM
ejpam-5969	117	9	eur	eur	PROPN
ejpam-5969	117	10	.	.	PUNCT
ejpam-5969	118	1	j.	j.	PROPN
ejpam-5969	118	2	pure	pure	PROPN
ejpam-5969	118	3	appl	appl	PROPN
ejpam-5969	118	4	.	.	PROPN
ejpam-5969	118	5	math	math	PROPN
ejpam-5969	118	6	,	,	PUNCT
ejpam-5969	118	7	18	18	NUM
ejpam-5969	118	8	(	(	PUNCT
ejpam-5969	118	9	2	2	NUM
ejpam-5969	118	10	)	)	PUNCT
ejpam-5969	118	11	(	(	PUNCT
ejpam-5969	118	12	2025	2025	NUM
ejpam-5969	118	13	)	)	PUNCT
ejpam-5969	118	14	,	,	PUNCT
ejpam-5969	118	15	5969	5969	NUM
ejpam-5969	118	16	5	5	NUM
ejpam-5969	118	17	of	of	ADP
ejpam-5969	118	18	19	19	NUM
ejpam-5969	118	19	corollary	corollary	ADJ
ejpam-5969	118	20	1	1	NUM
ejpam-5969	118	21	.	.	PUNCT
ejpam-5969	119	1	the	the	DET
ejpam-5969	119	2	next	next	ADJ
ejpam-5969	119	3	implications	implication	NOUN
ejpam-5969	119	4	are	be	AUX
ejpam-5969	119	5	hold	hold	NOUN
ejpam-5969	119	6	for	for	ADP
ejpam-5969	119	7	an	an	DET
ejpam-5969	119	8	sts	st	NOUN
ejpam-5969	119	9	(	(	PUNCT
ejpam-5969	119	10	χ	χ	NOUN
ejpam-5969	119	11	,	,	PUNCT
ejpam-5969	119	12	ν	ν	NOUN
ejpam-5969	119	13	)	)	PUNCT
ejpam-5969	119	14	,	,	PUNCT
ejpam-5969	119	15	which	which	PRON
ejpam-5969	119	16	are	be	AUX
ejpam-5969	119	17	not	not	PART
ejpam-5969	119	18	reversible	reversible	ADJ
ejpam-5969	119	19	.	.	PUNCT
ejpam-5969	120	1	soregular(χ	soregular(χ	NOUN
ejpam-5969	120	2	)	)	PUNCT
ejpam-5969	120	3	−→so(χ	−→so(χ	ADJ
ejpam-5969	120	4	)	)	PUNCT
ejpam-5969	120	5	−→	−→	NOUN
ejpam-5969	120	6	sαo(χ	sαo(χ	VERB
ejpam-5969	120	7	)	)	PUNCT
ejpam-5969	120	8	−→	−→	NOUN
ejpam-5969	120	9	sso(χ	sso(χ	PROPN
ejpam-5969	120	10	)	)	PUNCT
ejpam-5969	120	11	−→	−→	NOUN
ejpam-5969	120	12	sβo(χ	sβo(χ	PROPN
ejpam-5969	120	13	)	)	PUNCT
ejpam-5969	120	14	−→	−→	NOUN
ejpam-5969	120	15	sro(χ	sro(χ	NOUN
ejpam-5969	120	16	)	)	PUNCT
ejpam-5969	120	17	↓	↓	NOUN
ejpam-5969	120	18	↓	↓	PROPN
ejpam-5969	120	19	↗	↗	PROPN
ejpam-5969	120	20	↓	↓	PROPN
ejpam-5969	120	21	spo(χ	spo(χ	PROPN
ejpam-5969	120	22	)	)	PUNCT
ejpam-5969	120	23	−→	−→	NOUN
ejpam-5969	120	24	sbo(χ	sbo(χ	NOUN
ejpam-5969	120	25	)	)	PUNCT
ejpam-5969	120	26	−→	−→	NOUN
ejpam-5969	120	27	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	120	28	)	)	PUNCT
ejpam-5969	120	29	diagram	diagram	NOUN
ejpam-5969	120	30	1	1	NUM
ejpam-5969	120	31	.	.	PUNCT
ejpam-5969	121	1	the	the	DET
ejpam-5969	121	2	connections	connection	NOUN
ejpam-5969	121	3	between	between	ADP
ejpam-5969	121	4	the	the	DET
ejpam-5969	121	5	new	new	ADJ
ejpam-5969	121	6	category	category	NOUN
ejpam-5969	121	7	and	and	CCONJ
ejpam-5969	121	8	other	other	ADJ
ejpam-5969	121	9	preceding	precede	VERB
ejpam-5969	121	10	studies	study	NOUN
ejpam-5969	121	11	.	.	PUNCT
ejpam-5969	122	1	supra	supra	PROPN
ejpam-5969	122	2	ϵ-open	ϵ-open	PROPN
ejpam-5969	122	3	sets	set	NOUN
ejpam-5969	122	4	in	in	ADP
ejpam-5969	122	5	an	an	DET
ejpam-5969	122	6	sts	st	NOUN
ejpam-5969	122	7	(	(	PUNCT
ejpam-5969	122	8	χ	χ	NOUN
ejpam-5969	122	9	,	,	PUNCT
ejpam-5969	122	10	ν	ν	NOUN
ejpam-5969	122	11	)	)	PUNCT
ejpam-5969	122	12	and	and	CCONJ
ejpam-5969	122	13	their	their	PRON
ejpam-5969	122	14	subspaces	subspace	NOUN
ejpam-5969	122	15	generally	generally	ADV
ejpam-5969	122	16	do	do	AUX
ejpam-5969	122	17	not	not	PART
ejpam-5969	122	18	relate	relate	VERB
ejpam-5969	122	19	to	to	ADP
ejpam-5969	122	20	one	one	NUM
ejpam-5969	122	21	another	another	DET
ejpam-5969	122	22	,	,	PUNCT
ejpam-5969	122	23	as	as	SCONJ
ejpam-5969	122	24	shown	show	VERB
ejpam-5969	122	25	in	in	ADP
ejpam-5969	122	26	the	the	DET
ejpam-5969	122	27	upcoming	upcoming	ADJ
ejpam-5969	122	28	example	example	NOUN
ejpam-5969	122	29	.	.	PUNCT
ejpam-5969	123	1	example	example	NOUN
ejpam-5969	124	1	2	2	NUM
ejpam-5969	124	2	.	.	PUNCT
ejpam-5969	124	3	let	let	VERB
ejpam-5969	124	4	ν	ν	NOUN
ejpam-5969	124	5	=	=	PRON
ejpam-5969	124	6	{	{	PUNCT
ejpam-5969	124	7	χ	χ	NOUN
ejpam-5969	124	8	,	,	PUNCT
ejpam-5969	124	9	∅	∅	NOUN
ejpam-5969	124	10	,	,	PUNCT
ejpam-5969	124	11	{	{	PUNCT
ejpam-5969	124	12	i	i	NOUN
ejpam-5969	124	13	,	,	PUNCT
ejpam-5969	124	14	l	l	NOUN
ejpam-5969	124	15	}	}	PUNCT
ejpam-5969	124	16	,	,	PUNCT
ejpam-5969	124	17	{	{	PUNCT
ejpam-5969	124	18	i	i	PROPN
ejpam-5969	124	19	,	,	PUNCT
ejpam-5969	124	20	j	j	PROPN
ejpam-5969	124	21	,	,	PUNCT
ejpam-5969	124	22	k	k	PROPN
ejpam-5969	124	23	}	}	PUNCT
ejpam-5969	124	24	,	,	PUNCT
ejpam-5969	124	25	{	{	PUNCT
ejpam-5969	124	26	i	i	PROPN
ejpam-5969	124	27	,	,	PUNCT
ejpam-5969	124	28	j	j	PROPN
ejpam-5969	124	29	,	,	PUNCT
ejpam-5969	124	30	l	l	NOUN
ejpam-5969	124	31	}	}	PUNCT
ejpam-5969	124	32	}	}	PUNCT
ejpam-5969	124	33	be	be	AUX
ejpam-5969	124	34	an	an	DET
ejpam-5969	124	35	sts	st	NOUN
ejpam-5969	124	36	on	on	ADP
ejpam-5969	124	37	χ	χ	X
ejpam-5969	124	38	=	=	PUNCT
ejpam-5969	124	39	{	{	PUNCT
ejpam-5969	124	40	i	i	PROPN
ejpam-5969	124	41	,	,	PUNCT
ejpam-5969	124	42	j	j	PROPN
ejpam-5969	124	43	,	,	PUNCT
ejpam-5969	124	44	k	k	PROPN
ejpam-5969	124	45	,	,	PUNCT
ejpam-5969	124	46	l	l	NOUN
ejpam-5969	124	47	}	}	PUNCT
ejpam-5969	124	48	.	.	PUNCT
ejpam-5969	125	1	regarding	regard	VERB
ejpam-5969	125	2	the	the	DET
ejpam-5969	125	3	set	set	NOUN
ejpam-5969	125	4	w	w	NOUN
ejpam-5969	125	5	=	=	SYM
ejpam-5969	125	6	{	{	PUNCT
ejpam-5969	125	7	k	k	NOUN
ejpam-5969	125	8	,	,	PUNCT
ejpam-5969	125	9	l	l	NOUN
ejpam-5969	125	10	}	}	PUNCT
ejpam-5969	125	11	,	,	PUNCT
ejpam-5969	125	12	we	we	PRON
ejpam-5969	125	13	have	have	VERB
ejpam-5969	125	14	νw	νw	NOUN
ejpam-5969	125	15	=	=	SYM
ejpam-5969	125	16	{	{	PUNCT
ejpam-5969	125	17	w	w	NOUN
ejpam-5969	125	18	,	,	PUNCT
ejpam-5969	125	19	∅	∅	NOUN
ejpam-5969	125	20	,	,	PUNCT
ejpam-5969	125	21	{	{	PUNCT
ejpam-5969	125	22	k	k	NOUN
ejpam-5969	125	23	}	}	PUNCT
ejpam-5969	125	24	,	,	PUNCT
ejpam-5969	125	25	{	{	PUNCT
ejpam-5969	125	26	l	l	NOUN
ejpam-5969	125	27	}	}	PUNCT
ejpam-5969	125	28	}	}	PUNCT
ejpam-5969	125	29	.	.	PUNCT
ejpam-5969	126	1	the	the	DET
ejpam-5969	126	2	set	set	NOUN
ejpam-5969	126	3	{	{	PUNCT
ejpam-5969	126	4	k	k	NOUN
ejpam-5969	126	5	}	}	PUNCT
ejpam-5969	126	6	is	be	AUX
ejpam-5969	126	7	supra	supra	PROPN
ejpam-5969	126	8	ϵ-open	ϵ-open	PROPN
ejpam-5969	126	9	in	in	ADP
ejpam-5969	126	10	(	(	PUNCT
ejpam-5969	126	11	w	w	PROPN
ejpam-5969	126	12	,	,	PUNCT
ejpam-5969	126	13	νw	νw	PROPN
ejpam-5969	126	14	)	)	PUNCT
ejpam-5969	126	15	whereas	whereas	SCONJ
ejpam-5969	126	16	{	{	PUNCT
ejpam-5969	126	17	k	k	NOUN
ejpam-5969	126	18	}	}	PUNCT
ejpam-5969	126	19	is	be	AUX
ejpam-5969	126	20	not	not	PART
ejpam-5969	126	21	supra	supra	NOUN
ejpam-5969	126	22	ϵ-open	ϵ-open	VERB
ejpam-5969	126	23	in	in	ADP
ejpam-5969	126	24	(	(	PUNCT
ejpam-5969	126	25	χ	χ	NOUN
ejpam-5969	126	26	,	,	PUNCT
ejpam-5969	126	27	ν	ν	NOUN
ejpam-5969	126	28	)	)	PUNCT
ejpam-5969	126	29	.	.	PUNCT
ejpam-5969	127	1	definition	definition	NOUN
ejpam-5969	127	2	6	6	NUM
ejpam-5969	127	3	.	.	PUNCT
ejpam-5969	128	1	for	for	ADP
ejpam-5969	128	2	the	the	DET
ejpam-5969	128	3	subset	subset	NOUN
ejpam-5969	128	4	k	k	PROPN
ejpam-5969	128	5	of	of	ADP
ejpam-5969	128	6	an	an	DET
ejpam-5969	128	7	sts	st	NOUN
ejpam-5969	128	8	(	(	PUNCT
ejpam-5969	128	9	χ	χ	NOUN
ejpam-5969	128	10	,	,	PUNCT
ejpam-5969	128	11	ν	ν	NOUN
ejpam-5969	128	12	)	)	PUNCT
ejpam-5969	128	13	,	,	PUNCT
ejpam-5969	128	14	the	the	DET
ejpam-5969	128	15	class	class	NOUN
ejpam-5969	128	16	νk	νk	NOUN
ejpam-5969	128	17	=	=	SYM
ejpam-5969	128	18	{	{	PUNCT
ejpam-5969	128	19	k	k	X
ejpam-5969	128	20	∩g	∩g	PROPN
ejpam-5969	128	21	:	:	PUNCT
ejpam-5969	128	22	g	g	PROPN
ejpam-5969	128	23	∈	∈	PROPN
ejpam-5969	128	24	soϵ(χ	soϵ(χ	X
ejpam-5969	128	25	)	)	PUNCT
ejpam-5969	128	26	}	}	PUNCT
ejpam-5969	128	27	defines	define	VERB
ejpam-5969	128	28	an	an	DET
ejpam-5969	128	29	sts	st	NOUN
ejpam-5969	128	30	on	on	ADP
ejpam-5969	128	31	k	k	PROPN
ejpam-5969	128	32	,	,	PUNCT
ejpam-5969	128	33	and	and	CCONJ
ejpam-5969	128	34	it	it	PRON
ejpam-5969	128	35	is	be	AUX
ejpam-5969	128	36	called	call	VERB
ejpam-5969	128	37	an	an	DET
ejpam-5969	128	38	ϵ-subspace	ϵ-subspace	NOUN
ejpam-5969	128	39	of	of	ADP
ejpam-5969	128	40	(	(	PUNCT
ejpam-5969	128	41	χ	χ	NOUN
ejpam-5969	128	42	,	,	PUNCT
ejpam-5969	128	43	ν	ν	NOUN
ejpam-5969	128	44	)	)	PUNCT
ejpam-5969	128	45	.	.	PUNCT
ejpam-5969	129	1	proposition	proposition	NOUN
ejpam-5969	129	2	2	2	NUM
ejpam-5969	129	3	.	.	PUNCT
ejpam-5969	130	1	let	let	AUX
ejpam-5969	130	2	(	(	PUNCT
ejpam-5969	130	3	w	w	PROPN
ejpam-5969	130	4	,	,	PUNCT
ejpam-5969	130	5	νw	νw	PROPN
ejpam-5969	130	6	)	)	PUNCT
ejpam-5969	130	7	be	be	AUX
ejpam-5969	130	8	an	an	DET
ejpam-5969	130	9	ϵ-subspace	ϵ-subspace	NOUN
ejpam-5969	130	10	of	of	ADP
ejpam-5969	130	11	an	an	DET
ejpam-5969	130	12	sts	st	NOUN
ejpam-5969	130	13	(	(	PUNCT
ejpam-5969	130	14	χ	χ	NOUN
ejpam-5969	130	15	,	,	PUNCT
ejpam-5969	130	16	ν	ν	NOUN
ejpam-5969	130	17	)	)	PUNCT
ejpam-5969	130	18	and	and	CCONJ
ejpam-5969	130	19	f	f	PROPN
ejpam-5969	130	20	be	be	AUX
ejpam-5969	130	21	a	a	DET
ejpam-5969	130	22	subset	subset	NOUN
ejpam-5969	130	23	of	of	ADP
ejpam-5969	130	24	χ	χ	NOUN
ejpam-5969	130	25	.	.	PUNCT
ejpam-5969	131	1	then	then	ADV
ejpam-5969	131	2	,	,	PUNCT
ejpam-5969	131	3	f	f	PROPN
ejpam-5969	131	4	∈	∈	PROPN
ejpam-5969	131	5	scϵ(w	scϵ(w	PROPN
ejpam-5969	131	6	)	)	PUNCT
ejpam-5969	131	7	if	if	SCONJ
ejpam-5969	131	8	and	and	CCONJ
ejpam-5969	131	9	only	only	ADV
ejpam-5969	131	10	if	if	SCONJ
ejpam-5969	131	11	there	there	PRON
ejpam-5969	131	12	is	be	VERB
ejpam-5969	131	13	b	b	NOUN
ejpam-5969	131	14	∈	∈	NOUN
ejpam-5969	131	15	scϵ(χ	scϵ(χ	X
ejpam-5969	131	16	)	)	PUNCT
ejpam-5969	131	17	such	such	ADJ
ejpam-5969	131	18	that	that	SCONJ
ejpam-5969	131	19	f	f	PROPN
ejpam-5969	132	1	=	=	NOUN
ejpam-5969	132	2	w	w	NOUN
ejpam-5969	132	3	∩b	∩b	NOUN
ejpam-5969	132	4	.	.	PUNCT
ejpam-5969	133	1	proof	proof	NOUN
ejpam-5969	133	2	.	.	PUNCT
ejpam-5969	134	1	obvious	obvious	ADJ
ejpam-5969	134	2	.	.	PUNCT
ejpam-5969	135	1	theorem	theorem	NOUN
ejpam-5969	135	2	2	2	NUM
ejpam-5969	135	3	.	.	PUNCT
ejpam-5969	136	1	if	if	SCONJ
ejpam-5969	136	2	y	y	PROPN
ejpam-5969	136	3	∈	∈	PROPN
ejpam-5969	136	4	sbo(χ	sbo(χ	PROPN
ejpam-5969	136	5	)	)	PUNCT
ejpam-5969	136	6	such	such	ADJ
ejpam-5969	136	7	that	that	SCONJ
ejpam-5969	136	8	int(y	int(y	PROPN
ejpam-5969	136	9	)	)	PUNCT
ejpam-5969	136	10	=	=	NOUN
ejpam-5969	136	11	∅	∅	NOUN
ejpam-5969	136	12	,	,	PUNCT
ejpam-5969	136	13	for	for	ADP
ejpam-5969	136	14	a	a	DET
ejpam-5969	136	15	proper	proper	ADJ
ejpam-5969	136	16	subset	subset	NOUN
ejpam-5969	136	17	y	y	PROPN
ejpam-5969	136	18	of	of	ADP
ejpam-5969	136	19	an	an	DET
ejpam-5969	136	20	sts	st	NOUN
ejpam-5969	136	21	(	(	PUNCT
ejpam-5969	136	22	χ	χ	NOUN
ejpam-5969	136	23	,	,	PUNCT
ejpam-5969	136	24	ν	ν	NOUN
ejpam-5969	136	25	)	)	PUNCT
ejpam-5969	136	26	,	,	PUNCT
ejpam-5969	136	27	then	then	ADV
ejpam-5969	136	28	both	both	PRON
ejpam-5969	136	29	of	of	ADP
ejpam-5969	136	30	y	y	PROPN
ejpam-5969	136	31	and	and	CCONJ
ejpam-5969	136	32	y	y	PROPN
ejpam-5969	136	33	c	c	PROPN
ejpam-5969	136	34	are	be	AUX
ejpam-5969	136	35	supra	supra	PROPN
ejpam-5969	136	36	ϵ-open	ϵ-open	PROPN
ejpam-5969	136	37	.	.	PUNCT
ejpam-5969	137	1	proof	proof	NOUN
ejpam-5969	137	2	.	.	PUNCT
ejpam-5969	138	1	let	let	VERB
ejpam-5969	138	2	y	y	PROPN
ejpam-5969	138	3	∈	∈	PROPN
ejpam-5969	138	4	sbo(χ	sbo(χ	PROPN
ejpam-5969	138	5	)	)	PUNCT
ejpam-5969	138	6	,	,	PUNCT
ejpam-5969	138	7	then	then	ADV
ejpam-5969	138	8	y	y	PROPN
ejpam-5969	138	9	⊆	⊆	NUM
ejpam-5969	138	10	cl(int(y	cl(int(y	NOUN
ejpam-5969	138	11	)	)	PUNCT
ejpam-5969	138	12	)	)	PUNCT
ejpam-5969	138	13	∪̃int(cl(y	∪̃int(cl(y	NOUN
ejpam-5969	138	14	)	)	PUNCT
ejpam-5969	138	15	)	)	PUNCT
ejpam-5969	138	16	.	.	PUNCT
ejpam-5969	139	1	since	since	SCONJ
ejpam-5969	139	2	int(y	int(y	PROPN
ejpam-5969	139	3	)	)	PUNCT
ejpam-5969	139	4	=	=	NOUN
ejpam-5969	139	5	∅	∅	NOUN
ejpam-5969	139	6	,	,	PUNCT
ejpam-5969	139	7	y	y	PROPN
ejpam-5969	139	8	⊆	⊆	NUM
ejpam-5969	139	9	int(cl(y	int(cl(y	PROPN
ejpam-5969	139	10	)	)	PUNCT
ejpam-5969	139	11	)	)	PUNCT
ejpam-5969	139	12	.	.	PUNCT
ejpam-5969	140	1	hence	hence	ADV
ejpam-5969	140	2	,	,	PUNCT
ejpam-5969	140	3	y	y	PROPN
ejpam-5969	140	4	∈	∈	PROPN
ejpam-5969	140	5	sro(χ	sro(χ	PROPN
ejpam-5969	140	6	)	)	PUNCT
ejpam-5969	140	7	.	.	PUNCT
ejpam-5969	141	1	given	give	VERB
ejpam-5969	141	2	remark	remark	NOUN
ejpam-5969	141	3	2	2	NUM
ejpam-5969	141	4	,	,	PUNCT
ejpam-5969	141	5	y	y	PROPN
ejpam-5969	141	6	∈	∈	PROPN
ejpam-5969	141	7	soϵ(χ	soϵ(χ	VERB
ejpam-5969	141	8	)	)	PUNCT
ejpam-5969	141	9	.	.	PUNCT
ejpam-5969	142	1	furthermore	furthermore	ADV
ejpam-5969	142	2	,	,	PUNCT
ejpam-5969	142	3	we	we	PRON
ejpam-5969	142	4	have	have	VERB
ejpam-5969	142	5	[	[	X
ejpam-5969	142	6	int(y	int(y	PROPN
ejpam-5969	142	7	)	)	PUNCT
ejpam-5969	142	8	]	]	X
ejpam-5969	142	9	c	c	X
ejpam-5969	142	10	=	=	SYM
ejpam-5969	142	11	cl(gc	cl(gc	PROPN
ejpam-5969	142	12	)	)	PUNCT
ejpam-5969	143	1	=	=	NOUN
ejpam-5969	143	2	∅c	∅c	NOUN
ejpam-5969	143	3	=	=	PUNCT
ejpam-5969	143	4	χ	χ	X
ejpam-5969	143	5	.	.	PUNCT
ejpam-5969	144	1	this	this	PRON
ejpam-5969	144	2	implies	imply	VERB
ejpam-5969	144	3	,	,	PUNCT
ejpam-5969	144	4	int(cl(gc	int(cl(gc	NOUN
ejpam-5969	144	5	)	)	PUNCT
ejpam-5969	144	6	)	)	PUNCT
ejpam-5969	145	1	=	=	SYM
ejpam-5969	145	2	int(χ	int(χ	PROPN
ejpam-5969	145	3	)	)	PUNCT
ejpam-5969	145	4	=	=	PUNCT
ejpam-5969	145	5	χ	χ	DET
ejpam-5969	145	6	̸=	̸=	PROPN
ejpam-5969	145	7	∅	∅	NOUN
ejpam-5969	145	8	and	and	CCONJ
ejpam-5969	145	9	so	so	ADV
ejpam-5969	145	10	gc	gc	PROPN
ejpam-5969	145	11	∈	∈	PROPN
ejpam-5969	145	12	sro(χ	sro(χ	PROPN
ejpam-5969	145	13	)	)	PUNCT
ejpam-5969	145	14	.	.	PUNCT
ejpam-5969	146	1	thus	thus	ADV
ejpam-5969	146	2	,	,	PUNCT
ejpam-5969	146	3	gc	gc	PROPN
ejpam-5969	146	4	∈	∈	PROPN
ejpam-5969	146	5	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	146	6	)	)	PUNCT
ejpam-5969	146	7	.	.	PUNCT
ejpam-5969	147	1	proposition	proposition	NOUN
ejpam-5969	147	2	3	3	NUM
ejpam-5969	147	3	.	.	PUNCT
ejpam-5969	148	1	each	each	DET
ejpam-5969	148	2	supra	supra	PROPN
ejpam-5969	148	3	neighbourhood	neighbourhood	NOUN
ejpam-5969	148	4	of	of	ADP
ejpam-5969	148	5	any	any	DET
ejpam-5969	148	6	point	point	NOUN
ejpam-5969	148	7	in	in	ADP
ejpam-5969	148	8	an	an	DET
ejpam-5969	148	9	sts	st	NOUN
ejpam-5969	148	10	(	(	PUNCT
ejpam-5969	148	11	χ	χ	NOUN
ejpam-5969	148	12	,	,	PUNCT
ejpam-5969	148	13	ν	ν	NOUN
ejpam-5969	148	14	)	)	PUNCT
ejpam-5969	148	15	is	be	AUX
ejpam-5969	148	16	supra	supra	PROPN
ejpam-5969	148	17	ϵ-open	ϵ-open	PROPN
ejpam-5969	148	18	.	.	PUNCT
ejpam-5969	149	1	proof	proof	NOUN
ejpam-5969	149	2	.	.	PUNCT
ejpam-5969	150	1	suppose	suppose	VERB
ejpam-5969	150	2	that	that	SCONJ
ejpam-5969	150	3	s	s	VERB
ejpam-5969	150	4	is	be	AUX
ejpam-5969	150	5	a	a	DET
ejpam-5969	150	6	supra	supra	ADJ
ejpam-5969	150	7	neighbourhood	neighbourhood	NOUN
ejpam-5969	150	8	for	for	ADP
ejpam-5969	150	9	x	x	PROPN
ejpam-5969	150	10	∈	∈	PROPN
ejpam-5969	150	11	χ	χ	NOUN
ejpam-5969	150	12	.	.	PUNCT
ejpam-5969	151	1	then	then	ADV
ejpam-5969	151	2	,	,	PUNCT
ejpam-5969	151	3	∃	∃	PROPN
ejpam-5969	151	4	g	g	PROPN
ejpam-5969	151	5	∈	∈	PROPN
ejpam-5969	151	6	ν	ν	NOUN
ejpam-5969	151	7	such	such	ADJ
ejpam-5969	151	8	that	that	SCONJ
ejpam-5969	151	9	x	x	SYM
ejpam-5969	151	10	∈	∈	NOUN
ejpam-5969	151	11	g	g	PROPN
ejpam-5969	151	12	⊆	⊆	NUM
ejpam-5969	151	13	s.	s.	PROPN
ejpam-5969	151	14	hence	hence	ADV
ejpam-5969	151	15	,	,	PUNCT
ejpam-5969	151	16	g	g	PROPN
ejpam-5969	151	17	⊆	⊆	NUM
ejpam-5969	151	18	cl(g	cl(g	NOUN
ejpam-5969	151	19	)	)	PUNCT
ejpam-5969	151	20	⊆	⊆	NUM
ejpam-5969	151	21	cl(s	cl(	NOUN
ejpam-5969	151	22	)	)	PUNCT
ejpam-5969	151	23	and	and	CCONJ
ejpam-5969	151	24	so	so	ADV
ejpam-5969	151	25	s	s	X
ejpam-5969	151	26	∈	∈	NOUN
ejpam-5969	151	27	sro(χ	sro(χ	PROPN
ejpam-5969	151	28	)	)	PUNCT
ejpam-5969	151	29	.	.	PUNCT
ejpam-5969	152	1	therefore	therefore	ADV
ejpam-5969	152	2	,	,	PUNCT
ejpam-5969	152	3	s	s	VERB
ejpam-5969	152	4	⊆	⊆	NUM
ejpam-5969	152	5	s	s	NOUN
ejpam-5969	152	6	◦	◦	NOUN
ejpam-5969	152	7	∪	∪	ADJ
ejpam-5969	152	8	b(s	b(	NOUN
ejpam-5969	152	9	)	)	PUNCT
ejpam-5969	152	10	=	=	SYM
ejpam-5969	152	11	cl(s	cl(s	NOUN
ejpam-5969	152	12	)	)	PUNCT
ejpam-5969	152	13	.	.	PUNCT
ejpam-5969	153	1	thus	thus	ADV
ejpam-5969	153	2	,	,	PUNCT
ejpam-5969	153	3	s	s	VERB
ejpam-5969	153	4	∈	∈	NOUN
ejpam-5969	153	5	soϵ(χ	soϵ(χ	NOUN
ejpam-5969	153	6	)	)	PUNCT
ejpam-5969	153	7	.	.	PUNCT
ejpam-5969	154	1	remark	remark	PROPN
ejpam-5969	154	2	3	3	NUM
ejpam-5969	154	3	.	.	PUNCT
ejpam-5969	155	1	generally	generally	ADV
ejpam-5969	155	2	,	,	PUNCT
ejpam-5969	155	3	the	the	DET
ejpam-5969	155	4	converse	converse	NOUN
ejpam-5969	155	5	of	of	ADP
ejpam-5969	155	6	proposition	proposition	NOUN
ejpam-5969	155	7	3	3	NUM
ejpam-5969	155	8	is	be	AUX
ejpam-5969	155	9	untrue	untrue	ADJ
ejpam-5969	155	10	.	.	PUNCT
ejpam-5969	156	1	let	let	VERB
ejpam-5969	156	2	ν	ν	X
ejpam-5969	156	3	=	=	PRON
ejpam-5969	156	4	{	{	PUNCT
ejpam-5969	156	5	χ	χ	NOUN
ejpam-5969	156	6	,	,	PUNCT
ejpam-5969	156	7	∅	∅	NOUN
ejpam-5969	156	8	,	,	PUNCT
ejpam-5969	156	9	{	{	PUNCT
ejpam-5969	156	10	1	1	NUM
ejpam-5969	156	11	,	,	PUNCT
ejpam-5969	156	12	2	2	NUM
ejpam-5969	156	13	}	}	PUNCT
ejpam-5969	156	14	,	,	PUNCT
ejpam-5969	156	15	{	{	PUNCT
ejpam-5969	156	16	1	1	NUM
ejpam-5969	156	17	,	,	PUNCT
ejpam-5969	156	18	3	3	NUM
ejpam-5969	156	19	,	,	PUNCT
ejpam-5969	156	20	4	4	NUM
ejpam-5969	156	21	}	}	PUNCT
ejpam-5969	156	22	}	}	PUNCT
ejpam-5969	156	23	be	be	AUX
ejpam-5969	156	24	an	an	DET
ejpam-5969	156	25	sts	st	NOUN
ejpam-5969	156	26	on	on	ADP
ejpam-5969	156	27	χ	χ	X
ejpam-5969	156	28	=	=	PUNCT
ejpam-5969	156	29	{	{	PUNCT
ejpam-5969	156	30	1	1	NUM
ejpam-5969	156	31	,	,	PUNCT
ejpam-5969	156	32	2	2	NUM
ejpam-5969	156	33	,	,	PUNCT
ejpam-5969	156	34	3	3	NUM
ejpam-5969	156	35	,	,	PUNCT
ejpam-5969	156	36	4	4	NUM
ejpam-5969	156	37	}	}	PUNCT
ejpam-5969	156	38	.	.	PUNCT
ejpam-5969	157	1	then	then	ADV
ejpam-5969	157	2	,	,	PUNCT
ejpam-5969	157	3	{	{	PUNCT
ejpam-5969	157	4	1	1	NUM
ejpam-5969	157	5	}	}	PUNCT
ejpam-5969	157	6	∈	∈	PROPN
ejpam-5969	157	7	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	157	8	)	)	PUNCT
ejpam-5969	157	9	,	,	PUNCT
ejpam-5969	157	10	however	however	ADV
ejpam-5969	157	11	{	{	PUNCT
ejpam-5969	157	12	1	1	X
ejpam-5969	157	13	}	}	PUNCT
ejpam-5969	157	14	is	be	AUX
ejpam-5969	157	15	not	not	PART
ejpam-5969	157	16	supra	supra	ADJ
ejpam-5969	157	17	neighbourhood	neighbourhood	NOUN
ejpam-5969	157	18	for	for	ADP
ejpam-5969	157	19	any	any	DET
ejpam-5969	157	20	point	point	NOUN
ejpam-5969	157	21	in	in	ADP
ejpam-5969	157	22	χ	χ	PROPN
ejpam-5969	157	23	.	.	PUNCT
ejpam-5969	158	1	theorem	theorem	NOUN
ejpam-5969	158	2	3	3	NUM
ejpam-5969	158	3	.	.	PUNCT
ejpam-5969	159	1	(	(	PUNCT
ejpam-5969	159	2	1	1	X
ejpam-5969	159	3	)	)	PUNCT
ejpam-5969	159	4	if	if	SCONJ
ejpam-5969	159	5	ψ	ψ	VERB
ejpam-5969	159	6	=	=	SYM
ejpam-5969	159	7	{	{	PUNCT
ejpam-5969	159	8	hȷ	hȷ	NOUN
ejpam-5969	159	9	,	,	PUNCT
ejpam-5969	159	10	ȷ	ȷ	PROPN
ejpam-5969	159	11	∈	∈	PROPN
ejpam-5969	159	12	π	π	PROPN
ejpam-5969	159	13	}	}	PUNCT
ejpam-5969	159	14	⊆	⊆	NUM
ejpam-5969	159	15	soϵ(χ	soϵ(χ	NUM
ejpam-5969	159	16	)	)	PUNCT
ejpam-5969	159	17	,	,	PUNCT
ejpam-5969	159	18	then	then	ADV
ejpam-5969	159	19	⋃	⋃	PUNCT
ejpam-5969	159	20	ȷ∈πhȷ	ȷ∈πhȷ	PROPN
ejpam-5969	159	21	∈	∈	PROPN
ejpam-5969	159	22	soϵ(χ	soϵ(χ	NOUN
ejpam-5969	159	23	)	)	PUNCT
ejpam-5969	159	24	.	.	PUNCT
ejpam-5969	160	1	(	(	PUNCT
ejpam-5969	160	2	2	2	X
ejpam-5969	160	3	)	)	PUNCT
ejpam-5969	160	4	if	if	SCONJ
ejpam-5969	160	5	ψ	ψ	X
ejpam-5969	160	6	=	=	SYM
ejpam-5969	160	7	{	{	PUNCT
ejpam-5969	160	8	hȷ	hȷ	NOUN
ejpam-5969	160	9	,	,	PUNCT
ejpam-5969	160	10	ȷ	ȷ	PROPN
ejpam-5969	160	11	∈	∈	PROPN
ejpam-5969	160	12	π	π	PROPN
ejpam-5969	160	13	}	}	PUNCT
ejpam-5969	160	14	⊆	⊆	NUM
ejpam-5969	160	15	scϵ(χ	scϵ(χ	NUM
ejpam-5969	160	16	)	)	PUNCT
ejpam-5969	160	17	)	)	PUNCT
ejpam-5969	160	18	,	,	PUNCT
ejpam-5969	160	19	then	then	ADV
ejpam-5969	160	20	⋂̃	⋂̃	X
ejpam-5969	160	21	ȷ∈πhȷ	ȷ∈πhȷ	PROPN
ejpam-5969	160	22	∈	∈	PROPN
ejpam-5969	160	23	scϵ(χ	scϵ(χ	NUM
ejpam-5969	160	24	)	)	PUNCT
ejpam-5969	160	25	.	.	PUNCT
ejpam-5969	161	1	abd	abd	PROPN
ejpam-5969	161	2	el	el	PROPN
ejpam-5969	161	3	-	-	PROPN
ejpam-5969	161	4	latif	latif	PROPN
ejpam-5969	161	5	et	et	PROPN
ejpam-5969	161	6	al	al	PROPN
ejpam-5969	161	7	.	.	PUNCT
ejpam-5969	161	8	/	/	SYM
ejpam-5969	161	9	eur	eur	PROPN
ejpam-5969	161	10	.	.	PUNCT
ejpam-5969	162	1	j.	j.	PROPN
ejpam-5969	162	2	pure	pure	PROPN
ejpam-5969	162	3	appl	appl	PROPN
ejpam-5969	162	4	.	.	PROPN
ejpam-5969	162	5	math	math	PROPN
ejpam-5969	162	6	,	,	PUNCT
ejpam-5969	162	7	18	18	NUM
ejpam-5969	162	8	(	(	PUNCT
ejpam-5969	162	9	2	2	NUM
ejpam-5969	162	10	)	)	PUNCT
ejpam-5969	162	11	(	(	PUNCT
ejpam-5969	162	12	2025	2025	NUM
ejpam-5969	162	13	)	)	PUNCT
ejpam-5969	162	14	,	,	PUNCT
ejpam-5969	162	15	5969	5969	NUM
ejpam-5969	162	16	6	6	NUM
ejpam-5969	162	17	of	of	ADP
ejpam-5969	162	18	19	19	NUM
ejpam-5969	162	19	proof	proof	NOUN
ejpam-5969	162	20	.	.	PUNCT
ejpam-5969	163	1	(	(	PUNCT
ejpam-5969	163	2	1	1	X
ejpam-5969	163	3	)	)	PUNCT
ejpam-5969	163	4	let	let	VERB
ejpam-5969	163	5	ψ	ψ	X
ejpam-5969	163	6	=	=	PUNCT
ejpam-5969	163	7	{	{	PUNCT
ejpam-5969	163	8	hȷ	hȷ	NOUN
ejpam-5969	163	9	,	,	PUNCT
ejpam-5969	163	10	ȷ	ȷ	PROPN
ejpam-5969	163	11	∈	∈	PROPN
ejpam-5969	163	12	π	π	PROPN
ejpam-5969	163	13	}	}	PUNCT
ejpam-5969	163	14	⊆	⊆	NUM
ejpam-5969	163	15	soϵ(χ	soϵ(χ	NUM
ejpam-5969	163	16	)	)	PUNCT
ejpam-5969	163	17	.	.	PUNCT
ejpam-5969	164	1	if	if	SCONJ
ejpam-5969	164	2	for	for	ADP
ejpam-5969	164	3	all	all	DET
ejpam-5969	164	4	ȷ	ȷ	NOUN
ejpam-5969	164	5	∈	∈	PROPN
ejpam-5969	164	6	π	π	PROPN
ejpam-5969	164	7	,	,	PUNCT
ejpam-5969	164	8	hȷ	hȷ	NOUN
ejpam-5969	164	9	=	=	NOUN
ejpam-5969	164	10	∅	∅	NOUN
ejpam-5969	164	11	,	,	PUNCT
ejpam-5969	164	12	then	then	ADV
ejpam-5969	164	13	we	we	PRON
ejpam-5969	164	14	get	get	VERB
ejpam-5969	164	15	our	our	PRON
ejpam-5969	164	16	result	result	NOUN
ejpam-5969	164	17	.	.	PUNCT
ejpam-5969	165	1	now	now	ADV
ejpam-5969	165	2	,	,	PUNCT
ejpam-5969	165	3	if	if	SCONJ
ejpam-5969	165	4	some	some	DET
ejpam-5969	165	5	members	member	NOUN
ejpam-5969	165	6	of	of	ADP
ejpam-5969	165	7	ψ	ψ	NOUN
ejpam-5969	165	8	are	be	AUX
ejpam-5969	165	9	non	non	ADJ
ejpam-5969	165	10	-	-	ADJ
ejpam-5969	165	11	empty	empty	ADJ
ejpam-5969	165	12	,	,	PUNCT
ejpam-5969	165	13	then	then	ADV
ejpam-5969	165	14	we	we	PRON
ejpam-5969	165	15	have	have	VERB
ejpam-5969	165	16	to	to	PART
ejpam-5969	165	17	cases	case	NOUN
ejpam-5969	165	18	.	.	PUNCT
ejpam-5969	166	1	case	case	NOUN
ejpam-5969	166	2	(	(	PUNCT
ejpam-5969	166	3	1	1	NUM
ejpam-5969	166	4	):	):	PUNCT
ejpam-5969	166	5	if	if	SCONJ
ejpam-5969	166	6	⋃	⋃	PUNCT
ejpam-5969	166	7	ȷ∈πhȷ	ȷ∈πhȷ	PROPN
ejpam-5969	166	8	∈	∈	PROPN
ejpam-5969	166	9	snd(χ	snd(χ	PROPN
ejpam-5969	166	10	)	)	PUNCT
ejpam-5969	166	11	,	,	PUNCT
ejpam-5969	166	12	then	then	ADV
ejpam-5969	166	13	⋃	⋃	PUNCT
ejpam-5969	166	14	ȷ∈πhȷ	ȷ∈πhȷ	PROPN
ejpam-5969	166	15	◦	◦	NOUN
ejpam-5969	166	16	⊆	⊆	NUM
ejpam-5969	166	17	⋃	⋃	NOUN
ejpam-5969	166	18	ȷ∈πhȷ	ȷ∈πhȷ	NOUN
ejpam-5969	166	19	◦	◦	NOUN
ejpam-5969	166	20	=	=	PUNCT
ejpam-5969	166	21	∅.	∅.	ADP
ejpam-5969	166	22	this	this	DET
ejpam-5969	166	23	means	mean	NOUN
ejpam-5969	166	24	,	,	PUNCT
ejpam-5969	166	25	hȷ	hȷ	PROPN
ejpam-5969	166	26	∈	∈	PROPN
ejpam-5969	166	27	snd(χ	snd(χ	PROPN
ejpam-5969	166	28	)	)	PUNCT
ejpam-5969	166	29	for	for	ADP
ejpam-5969	166	30	each	each	DET
ejpam-5969	166	31	ȷ	ȷ	NOUN
ejpam-5969	166	32	∈	∈	PROPN
ejpam-5969	166	33	π	π	PROPN
ejpam-5969	166	34	,	,	PUNCT
ejpam-5969	166	35	which	which	PRON
ejpam-5969	166	36	follows	follow	VERB
ejpam-5969	166	37	b(hȷ	b(hȷ	PROPN
ejpam-5969	166	38	)	)	PUNCT
ejpam-5969	166	39	is	be	AUX
ejpam-5969	166	40	infinite	infinite	ADJ
ejpam-5969	166	41	for	for	ADP
ejpam-5969	166	42	all	all	DET
ejpam-5969	166	43	ȷ	ȷ	NOUN
ejpam-5969	166	44	∈	∈	NOUN
ejpam-5969	166	45	π	π	NOUN
ejpam-5969	166	46	and	and	CCONJ
ejpam-5969	166	47	hence	hence	ADV
ejpam-5969	166	48	b	b	X
ejpam-5969	166	49	(	(	PUNCT
ejpam-5969	166	50	⋃	⋃	PROPN
ejpam-5969	166	51	ȷ∈πhȷ	ȷ∈πhȷ	PROPN
ejpam-5969	166	52	)	)	PUNCT
ejpam-5969	166	53	=	=	SYM
ejpam-5969	166	54	⋃	⋃	PROPN
ejpam-5969	166	55	ȷ∈π	ȷ∈π	NOUN
ejpam-5969	166	56	b(hȷ	b(hȷ	NOUN
ejpam-5969	166	57	)	)	PUNCT
ejpam-5969	166	58	is	be	AUX
ejpam-5969	166	59	infinite	infinite	ADJ
ejpam-5969	166	60	.	.	PUNCT
ejpam-5969	167	1	therefore	therefore	ADV
ejpam-5969	167	2	,	,	PUNCT
ejpam-5969	167	3	we	we	PRON
ejpam-5969	167	4	get	get	VERB
ejpam-5969	167	5	our	our	PRON
ejpam-5969	167	6	result	result	NOUN
ejpam-5969	167	7	.	.	PUNCT
ejpam-5969	168	1	case	case	NOUN
ejpam-5969	168	2	(	(	PUNCT
ejpam-5969	168	3	2	2	NUM
ejpam-5969	168	4	):	):	PUNCT
ejpam-5969	168	5	if	if	SCONJ
ejpam-5969	168	6	(	(	PUNCT
ejpam-5969	168	7	⋃	⋃	PUNCT
ejpam-5969	168	8	ȷ∈πhȷ	ȷ∈πhȷ	PROPN
ejpam-5969	168	9	∈	∈	NOUN
ejpam-5969	168	10	sro(χ	sro(χ	PROPN
ejpam-5969	168	11	)	)	PUNCT
ejpam-5969	168	12	,	,	PUNCT
ejpam-5969	168	13	then	then	ADV
ejpam-5969	168	14	(	(	PUNCT
ejpam-5969	168	15	⋃	⋃	PROPN
ejpam-5969	168	16	ȷ∈πhȷ	ȷ∈πhȷ	PROPN
ejpam-5969	168	17	◦	◦	NOUN
ejpam-5969	168	18	)	)	PUNCT
ejpam-5969	168	19	̸=	̸=	PROPN
ejpam-5969	168	20	∅.	∅.	PRON
ejpam-5969	168	21	hence	hence	ADV
ejpam-5969	168	22	,	,	PUNCT
ejpam-5969	168	23	⋃	⋃	SCONJ
ejpam-5969	168	24	ȷ∈πhȷ	ȷ∈πhȷ	PROPN
ejpam-5969	168	25	⊆	⊆	NUM
ejpam-5969	168	26	(	(	PUNCT
ejpam-5969	168	27	⋃	⋃	PROPN
ejpam-5969	168	28	ȷ∈πhȷ	ȷ∈πhȷ	PROPN
ejpam-5969	168	29	◦	◦	NOUN
ejpam-5969	168	30	)	)	PUNCT
ejpam-5969	168	31	∪	∪	ADP
ejpam-5969	168	32	b	b	PROPN
ejpam-5969	168	33	(	(	PUNCT
ejpam-5969	168	34	⋃	⋃	PROPN
ejpam-5969	168	35	ȷ∈πhȷ	ȷ∈πhȷ	PROPN
ejpam-5969	168	36	)	)	PUNCT
ejpam-5969	168	37	=	=	PRON
ejpam-5969	168	38	(	(	PUNCT
ejpam-5969	168	39	⋃	⋃	PROPN
ejpam-5969	168	40	ȷ∈πhȷ	ȷ∈πhȷ	PROPN
ejpam-5969	168	41	)	)	PUNCT
ejpam-5969	168	42	.	.	PUNCT
ejpam-5969	169	1	therefore	therefore	ADV
ejpam-5969	169	2	,	,	PUNCT
ejpam-5969	169	3	⋃	⋃	PROPN
ejpam-5969	169	4	ȷ∈πhȷ	ȷ∈πhȷ	PROPN
ejpam-5969	169	5	∈	∈	PROPN
ejpam-5969	169	6	soϵ(χ	soϵ(χ	NOUN
ejpam-5969	169	7	)	)	PUNCT
ejpam-5969	169	8	.	.	PUNCT
ejpam-5969	170	1	(	(	PUNCT
ejpam-5969	170	2	2	2	X
ejpam-5969	170	3	)	)	PUNCT
ejpam-5969	170	4	by	by	ADP
ejpam-5969	170	5	a	a	DET
ejpam-5969	170	6	similar	similar	ADJ
ejpam-5969	170	7	way	way	NOUN
ejpam-5969	170	8	to	to	ADP
ejpam-5969	170	9	(	(	PUNCT
ejpam-5969	170	10	1	1	NUM
ejpam-5969	170	11	)	)	PUNCT
ejpam-5969	170	12	.	.	PUNCT
ejpam-5969	170	13	remark	remark	PROPN
ejpam-5969	170	14	4	4	NUM
ejpam-5969	170	15	.	.	PUNCT
ejpam-5969	171	1	the	the	DET
ejpam-5969	171	2	next	next	ADJ
ejpam-5969	171	3	example	example	NOUN
ejpam-5969	171	4	shall	shall	AUX
ejpam-5969	171	5	prove	prove	VERB
ejpam-5969	171	6	that	that	SCONJ
ejpam-5969	171	7	:	:	PUNCT
ejpam-5969	171	8	(	(	PUNCT
ejpam-5969	171	9	1	1	X
ejpam-5969	171	10	)	)	PUNCT
ejpam-5969	171	11	the	the	DET
ejpam-5969	171	12	intersection	intersection	NOUN
ejpam-5969	171	13	of	of	ADP
ejpam-5969	171	14	finite	finite	ADJ
ejpam-5969	171	15	numbers	number	NOUN
ejpam-5969	171	16	of	of	ADP
ejpam-5969	171	17	supra	supra	PROPN
ejpam-5969	171	18	ϵ-open	ϵ-open	PROPN
ejpam-5969	171	19	sets	set	NOUN
ejpam-5969	171	20	is	be	AUX
ejpam-5969	171	21	not	not	PART
ejpam-5969	171	22	supra	supra	NOUN
ejpam-5969	171	23	ϵ-open	ϵ-open	PROPN
ejpam-5969	171	24	,	,	PUNCT
ejpam-5969	171	25	generally	generally	ADV
ejpam-5969	171	26	.	.	PUNCT
ejpam-5969	172	1	(	(	PUNCT
ejpam-5969	172	2	2	2	X
ejpam-5969	172	3	)	)	PUNCT
ejpam-5969	172	4	the	the	DET
ejpam-5969	172	5	union	union	NOUN
ejpam-5969	172	6	of	of	ADP
ejpam-5969	172	7	finite	finite	ADJ
ejpam-5969	172	8	numbers	number	NOUN
ejpam-5969	172	9	of	of	ADP
ejpam-5969	172	10	supra	supra	ADJ
ejpam-5969	172	11	ϵ-closed	ϵ-close	VERB
ejpam-5969	172	12	sets	set	NOUN
ejpam-5969	172	13	is	be	AUX
ejpam-5969	172	14	not	not	PART
ejpam-5969	172	15	supra	supra	NOUN
ejpam-5969	172	16	ϵ-closed	ϵ-close	VERB
ejpam-5969	172	17	,	,	PUNCT
ejpam-5969	172	18	generally	generally	ADV
ejpam-5969	172	19	.	.	PUNCT
ejpam-5969	173	1	example	example	NOUN
ejpam-5969	174	1	3	3	X
ejpam-5969	174	2	.	.	PUNCT
ejpam-5969	174	3	let	let	VERB
ejpam-5969	174	4	ν	ν	X
ejpam-5969	174	5	=	=	PRON
ejpam-5969	174	6	{	{	PUNCT
ejpam-5969	174	7	χ	χ	NOUN
ejpam-5969	174	8	,	,	PUNCT
ejpam-5969	174	9	∅	∅	NOUN
ejpam-5969	174	10	,	,	PUNCT
ejpam-5969	174	11	{	{	PUNCT
ejpam-5969	174	12	200	200	NUM
ejpam-5969	174	13	,	,	PUNCT
ejpam-5969	174	14	300	300	NUM
ejpam-5969	174	15	}	}	PUNCT
ejpam-5969	174	16	,	,	PUNCT
ejpam-5969	174	17	{	{	PUNCT
ejpam-5969	174	18	100	100	NUM
ejpam-5969	174	19	,	,	PUNCT
ejpam-5969	174	20	300	300	NUM
ejpam-5969	174	21	}	}	PUNCT
ejpam-5969	174	22	}	}	PUNCT
ejpam-5969	174	23	be	be	AUX
ejpam-5969	174	24	an	an	DET
ejpam-5969	174	25	sts	st	NOUN
ejpam-5969	174	26	on	on	ADP
ejpam-5969	174	27	χ	χ	X
ejpam-5969	174	28	=	=	PUNCT
ejpam-5969	174	29	{	{	PUNCT
ejpam-5969	174	30	100	100	NUM
ejpam-5969	174	31	,	,	PUNCT
ejpam-5969	174	32	200	200	NUM
ejpam-5969	174	33	,	,	PUNCT
ejpam-5969	174	34	300	300	NUM
ejpam-5969	174	35	}	}	PUNCT
ejpam-5969	174	36	.	.	PUNCT
ejpam-5969	175	1	then	then	ADV
ejpam-5969	175	2	,	,	PUNCT
ejpam-5969	175	3	a	a	PRON
ejpam-5969	175	4	=	=	X
ejpam-5969	175	5	{	{	PUNCT
ejpam-5969	175	6	100	100	NUM
ejpam-5969	175	7	,	,	PUNCT
ejpam-5969	175	8	300	300	NUM
ejpam-5969	175	9	}	}	PUNCT
ejpam-5969	175	10	and	and	CCONJ
ejpam-5969	175	11	b	b	X
ejpam-5969	175	12	=	=	PUNCT
ejpam-5969	175	13	{	{	PUNCT
ejpam-5969	175	14	100	100	NUM
ejpam-5969	175	15	,	,	PUNCT
ejpam-5969	175	16	200	200	NUM
ejpam-5969	175	17	}	}	PUNCT
ejpam-5969	175	18	are	be	AUX
ejpam-5969	175	19	supra	supra	PROPN
ejpam-5969	175	20	ϵ-open	ϵ-open	PROPN
ejpam-5969	175	21	sets	set	NOUN
ejpam-5969	175	22	,	,	PUNCT
ejpam-5969	175	23	however	however	ADV
ejpam-5969	175	24	a	a	DET
ejpam-5969	175	25	∩b	∩b	NOUN
ejpam-5969	175	26	=	=	SYM
ejpam-5969	175	27	{	{	PUNCT
ejpam-5969	175	28	100	100	NUM
ejpam-5969	175	29	}	}	PUNCT
ejpam-5969	175	30	is	be	AUX
ejpam-5969	175	31	not	not	PART
ejpam-5969	175	32	supra	supra	NOUN
ejpam-5969	175	33	ϵ-open	ϵ-open	PROPN
ejpam-5969	175	34	.	.	PUNCT
ejpam-5969	176	1	also	also	ADV
ejpam-5969	176	2	,	,	PUNCT
ejpam-5969	176	3	c	c	X
ejpam-5969	176	4	=	=	PUNCT
ejpam-5969	176	5	{	{	PUNCT
ejpam-5969	176	6	200	200	NUM
ejpam-5969	176	7	}	}	PUNCT
ejpam-5969	176	8	and	and	CCONJ
ejpam-5969	176	9	d	d	NOUN
ejpam-5969	176	10	=	=	SYM
ejpam-5969	176	11	{	{	PUNCT
ejpam-5969	176	12	300	300	NUM
ejpam-5969	176	13	}	}	PUNCT
ejpam-5969	176	14	are	be	AUX
ejpam-5969	176	15	supra	supra	ADJ
ejpam-5969	176	16	ϵ-closed	ϵ-close	VERB
ejpam-5969	176	17	sets	set	NOUN
ejpam-5969	176	18	,	,	PUNCT
ejpam-5969	176	19	however	however	ADV
ejpam-5969	176	20	c	c	NOUN
ejpam-5969	176	21	∪d	∪d	PUNCT
ejpam-5969	176	22	=	=	PUNCT
ejpam-5969	176	23	{	{	PUNCT
ejpam-5969	176	24	200	200	NUM
ejpam-5969	176	25	,	,	PUNCT
ejpam-5969	176	26	300	300	NUM
ejpam-5969	176	27	}	}	PUNCT
ejpam-5969	176	28	is	be	AUX
ejpam-5969	176	29	not	not	PART
ejpam-5969	176	30	supra	supra	ADJ
ejpam-5969	176	31	ϵ-closed	ϵ-close	VERB
ejpam-5969	176	32	.	.	PUNCT
ejpam-5969	177	1	remark	remark	NOUN
ejpam-5969	177	2	5	5	NUM
ejpam-5969	177	3	.	.	PUNCT
ejpam-5969	178	1	it	it	PRON
ejpam-5969	178	2	is	be	AUX
ejpam-5969	178	3	evident	evident	ADJ
ejpam-5969	178	4	from	from	ADP
ejpam-5969	178	5	theorem	theorem	ADJ
ejpam-5969	178	6	3	3	NUM
ejpam-5969	178	7	and	and	CCONJ
ejpam-5969	178	8	remark	remark	NOUN
ejpam-5969	178	9	4	4	NUM
ejpam-5969	178	10	that	that	SCONJ
ejpam-5969	178	11	our	our	PRON
ejpam-5969	178	12	new	new	ADJ
ejpam-5969	178	13	category	category	NOUN
ejpam-5969	178	14	does	do	AUX
ejpam-5969	178	15	not	not	PART
ejpam-5969	178	16	form	form	VERB
ejpam-5969	178	17	a	a	DET
ejpam-5969	178	18	topological	topological	ADJ
ejpam-5969	178	19	space	space	NOUN
ejpam-5969	178	20	and	and	CCONJ
ejpam-5969	178	21	instead	instead	ADV
ejpam-5969	178	22	forms	form	VERB
ejpam-5969	178	23	a	a	DET
ejpam-5969	178	24	supra	supra	ADJ
ejpam-5969	178	25	topology	topology	NOUN
ejpam-5969	178	26	.	.	PUNCT
ejpam-5969	179	1	4	4	X
ejpam-5969	179	2	.	.	X
ejpam-5969	179	3	applications	application	NOUN
ejpam-5969	179	4	of	of	ADP
ejpam-5969	179	5	supra	supra	PROPN
ejpam-5969	179	6	ϵ-open	ϵ-open	PROPN
ejpam-5969	179	7	for	for	ADP
ejpam-5969	179	8	new	new	ADJ
ejpam-5969	179	9	supra	supra	PROPN
ejpam-5969	179	10	operators	operator	NOUN
ejpam-5969	179	11	the	the	DET
ejpam-5969	179	12	objective	objective	NOUN
ejpam-5969	179	13	of	of	ADP
ejpam-5969	179	14	this	this	DET
ejpam-5969	179	15	section	section	NOUN
ejpam-5969	179	16	,	,	PUNCT
ejpam-5969	179	17	is	be	AUX
ejpam-5969	179	18	to	to	PART
ejpam-5969	179	19	outline	outline	VERB
ejpam-5969	179	20	novel	novel	ADJ
ejpam-5969	179	21	kinds	kind	NOUN
ejpam-5969	179	22	of	of	ADP
ejpam-5969	179	23	operators	operator	NOUN
ejpam-5969	179	24	,	,	PUNCT
ejpam-5969	179	25	called	call	VERB
ejpam-5969	179	26	supra	supra	PROPN
ejpam-5969	179	27	ϵinterior	ϵinterior	PROPN
ejpam-5969	179	28	(	(	PUNCT
ejpam-5969	179	29	respectively	respectively	ADV
ejpam-5969	179	30	,	,	PUNCT
ejpam-5969	179	31	closure	closure	NOUN
ejpam-5969	179	32	,	,	PUNCT
ejpam-5969	179	33	accumulation	accumulation	NOUN
ejpam-5969	179	34	,	,	PUNCT
ejpam-5969	179	35	exterior	exterior	ADJ
ejpam-5969	179	36	,	,	PUNCT
ejpam-5969	179	37	and	and	CCONJ
ejpam-5969	179	38	boundary	boundary	ADJ
ejpam-5969	179	39	)	)	PUNCT
ejpam-5969	179	40	operator	operator	NOUN
ejpam-5969	179	41	,	,	PUNCT
ejpam-5969	179	42	using	use	VERB
ejpam-5969	179	43	our	our	PRON
ejpam-5969	179	44	new	new	ADJ
ejpam-5969	179	45	category	category	NOUN
ejpam-5969	179	46	of	of	ADP
ejpam-5969	179	47	supra	supra	PROPN
ejpam-5969	179	48	open	open	ADJ
ejpam-5969	179	49	sets	set	NOUN
ejpam-5969	179	50	.	.	PUNCT
ejpam-5969	180	1	the	the	DET
ejpam-5969	180	2	primary	primary	ADJ
ejpam-5969	180	3	characteristics	characteristic	NOUN
ejpam-5969	180	4	of	of	ADP
ejpam-5969	180	5	every	every	DET
ejpam-5969	180	6	operator	operator	NOUN
ejpam-5969	180	7	are	be	AUX
ejpam-5969	180	8	listed	list	VERB
ejpam-5969	180	9	.	.	PUNCT
ejpam-5969	181	1	we	we	PRON
ejpam-5969	181	2	also	also	ADV
ejpam-5969	181	3	give	give	VERB
ejpam-5969	181	4	the	the	DET
ejpam-5969	181	5	distinctions	distinction	NOUN
ejpam-5969	181	6	between	between	ADP
ejpam-5969	181	7	these	these	DET
ejpam-5969	181	8	new	new	ADJ
ejpam-5969	181	9	operators	operator	NOUN
ejpam-5969	181	10	and	and	CCONJ
ejpam-5969	181	11	the	the	DET
ejpam-5969	181	12	operators	operator	NOUN
ejpam-5969	181	13	that	that	PRON
ejpam-5969	181	14	correspond	correspond	VERB
ejpam-5969	181	15	to	to	ADP
ejpam-5969	181	16	them	they	PRON
ejpam-5969	181	17	.	.	PUNCT
ejpam-5969	182	1	furthermore	furthermore	ADV
ejpam-5969	182	2	,	,	PUNCT
ejpam-5969	182	3	in	in	ADP
ejpam-5969	182	4	order	order	NOUN
ejpam-5969	182	5	to	to	PART
ejpam-5969	182	6	demonstrate	demonstrate	VERB
ejpam-5969	182	7	the	the	DET
ejpam-5969	182	8	significance	significance	NOUN
ejpam-5969	182	9	of	of	ADP
ejpam-5969	182	10	our	our	PRON
ejpam-5969	182	11	new	new	ADJ
ejpam-5969	182	12	operators	operator	NOUN
ejpam-5969	182	13	,	,	PUNCT
ejpam-5969	182	14	we	we	PRON
ejpam-5969	182	15	provide	provide	VERB
ejpam-5969	182	16	several	several	ADJ
ejpam-5969	182	17	essential	essential	ADJ
ejpam-5969	182	18	examples	example	NOUN
ejpam-5969	182	19	and	and	CCONJ
ejpam-5969	182	20	counterexamples	counterexample	NOUN
ejpam-5969	182	21	.	.	PUNCT
ejpam-5969	183	1	abd	abd	PROPN
ejpam-5969	183	2	el	el	PROPN
ejpam-5969	183	3	-	-	PROPN
ejpam-5969	183	4	latif	latif	PROPN
ejpam-5969	183	5	et	et	PROPN
ejpam-5969	183	6	al	al	PROPN
ejpam-5969	183	7	.	.	PUNCT
ejpam-5969	183	8	/	/	SYM
ejpam-5969	183	9	eur	eur	PROPN
ejpam-5969	183	10	.	.	PUNCT
ejpam-5969	184	1	j.	j.	PROPN
ejpam-5969	184	2	pure	pure	PROPN
ejpam-5969	184	3	appl	appl	PROPN
ejpam-5969	184	4	.	.	PROPN
ejpam-5969	184	5	math	math	PROPN
ejpam-5969	184	6	,	,	PUNCT
ejpam-5969	184	7	18	18	NUM
ejpam-5969	184	8	(	(	PUNCT
ejpam-5969	184	9	2	2	NUM
ejpam-5969	184	10	)	)	PUNCT
ejpam-5969	184	11	(	(	PUNCT
ejpam-5969	184	12	2025	2025	NUM
ejpam-5969	184	13	)	)	PUNCT
ejpam-5969	184	14	,	,	PUNCT
ejpam-5969	184	15	5969	5969	NUM
ejpam-5969	184	16	7	7	NUM
ejpam-5969	184	17	of	of	ADP
ejpam-5969	184	18	19	19	NUM
ejpam-5969	184	19	definition	definition	NOUN
ejpam-5969	184	20	7	7	NUM
ejpam-5969	184	21	.	.	X
ejpam-5969	185	1	for	for	ADP
ejpam-5969	185	2	the	the	DET
ejpam-5969	185	3	subset	subset	NOUN
ejpam-5969	185	4	k	k	PROPN
ejpam-5969	185	5	of	of	ADP
ejpam-5969	185	6	an	an	DET
ejpam-5969	185	7	sts	st	NOUN
ejpam-5969	185	8	(	(	PUNCT
ejpam-5969	185	9	χ	χ	NOUN
ejpam-5969	185	10	,	,	PUNCT
ejpam-5969	185	11	ν	ν	NOUN
ejpam-5969	185	12	)	)	PUNCT
ejpam-5969	185	13	,	,	PUNCT
ejpam-5969	185	14	the	the	DET
ejpam-5969	185	15	intϵ(k	intϵ(k	NOUN
ejpam-5969	185	16	)	)	PUNCT
ejpam-5969	185	17	will	will	AUX
ejpam-5969	185	18	denote	denote	VERB
ejpam-5969	185	19	the	the	DET
ejpam-5969	185	20	supra	supra	ADJ
ejpam-5969	185	21	ϵ-interior	ϵ-interior	PROPN
ejpam-5969	185	22	of	of	ADP
ejpam-5969	185	23	k	k	NOUN
ejpam-5969	185	24	,	,	PUNCT
ejpam-5969	185	25	where	where	SCONJ
ejpam-5969	185	26	intϵ(k	intϵ(k	X
ejpam-5969	185	27	)	)	PUNCT
ejpam-5969	185	28	=	=	SYM
ejpam-5969	185	29	∪{g	∪{g	PROPN
ejpam-5969	185	30	:	:	PUNCT
ejpam-5969	185	31	g	g	PROPN
ejpam-5969	185	32	∈	∈	PROPN
ejpam-5969	185	33	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	185	34	)	)	PUNCT
ejpam-5969	185	35	and	and	CCONJ
ejpam-5969	185	36	g	g	PROPN
ejpam-5969	185	37	⊆	⊆	NUM
ejpam-5969	185	38	k	k	NOUN
ejpam-5969	185	39	}	}	PUNCT
ejpam-5969	185	40	.	.	PUNCT
ejpam-5969	186	1	the	the	DET
ejpam-5969	186	2	proof	proof	NOUN
ejpam-5969	186	3	of	of	ADP
ejpam-5969	186	4	the	the	DET
ejpam-5969	186	5	next	next	ADJ
ejpam-5969	186	6	lemma	lemma	PROPN
ejpam-5969	186	7	is	be	AUX
ejpam-5969	186	8	obvious	obvious	ADJ
ejpam-5969	186	9	from	from	ADP
ejpam-5969	186	10	definition	definition	NOUN
ejpam-5969	186	11	7	7	NUM
ejpam-5969	186	12	,	,	PUNCT
ejpam-5969	186	13	so	so	SCONJ
ejpam-5969	186	14	it	it	PRON
ejpam-5969	186	15	is	be	AUX
ejpam-5969	186	16	omitted	omit	VERB
ejpam-5969	186	17	.	.	PUNCT
ejpam-5969	187	1	lemma	lemma	PROPN
ejpam-5969	187	2	1	1	NUM
ejpam-5969	187	3	.	.	PUNCT
ejpam-5969	188	1	for	for	ADP
ejpam-5969	188	2	the	the	DET
ejpam-5969	188	3	subsets	subset	NOUN
ejpam-5969	188	4	k	k	PROPN
ejpam-5969	188	5	and	and	CCONJ
ejpam-5969	188	6	i	i	PRON
ejpam-5969	188	7	of	of	ADP
ejpam-5969	188	8	an	an	DET
ejpam-5969	188	9	sts	st	NOUN
ejpam-5969	188	10	(	(	PUNCT
ejpam-5969	188	11	χ	χ	NOUN
ejpam-5969	188	12	,	,	PUNCT
ejpam-5969	188	13	ν	ν	NOUN
ejpam-5969	188	14	)	)	PUNCT
ejpam-5969	188	15	,	,	PUNCT
ejpam-5969	188	16	we	we	PRON
ejpam-5969	188	17	have	have	VERB
ejpam-5969	188	18	the	the	DET
ejpam-5969	188	19	following	following	NOUN
ejpam-5969	188	20	:	:	PUNCT
ejpam-5969	188	21	(	(	PUNCT
ejpam-5969	188	22	1	1	X
ejpam-5969	188	23	)	)	PUNCT
ejpam-5969	188	24	u	u	NOUN
ejpam-5969	188	25	∈	∈	PROPN
ejpam-5969	188	26	intϵ(k	intϵ(k	PROPN
ejpam-5969	188	27	)	)	PUNCT
ejpam-5969	188	28	⇔	⇔	NOUN
ejpam-5969	188	29	if	if	SCONJ
ejpam-5969	188	30	there	there	PRON
ejpam-5969	188	31	is	be	VERB
ejpam-5969	188	32	i	i	PRON
ejpam-5969	188	33	∈	∈	PROPN
ejpam-5969	188	34	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	188	35	)	)	PUNCT
ejpam-5969	188	36	such	such	ADJ
ejpam-5969	188	37	that	that	SCONJ
ejpam-5969	188	38	u	u	PROPN
ejpam-5969	188	39	∈	∈	PROPN
ejpam-5969	188	40	i	i	PROPN
ejpam-5969	188	41	⊆	⊆	NUM
ejpam-5969	188	42	k.	k.	NOUN
ejpam-5969	188	43	(	(	PUNCT
ejpam-5969	188	44	2	2	NUM
ejpam-5969	188	45	)	)	PUNCT
ejpam-5969	188	46	k	k	PROPN
ejpam-5969	188	47	∈	∈	PROPN
ejpam-5969	188	48	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	188	49	)	)	PUNCT
ejpam-5969	188	50	⇔	⇔	X
ejpam-5969	188	51	intϵ(k	intϵ(k	PROPN
ejpam-5969	188	52	)	)	PUNCT
ejpam-5969	189	1	=	=	SYM
ejpam-5969	189	2	k	k	PROPN
ejpam-5969	189	3	.	.	PUNCT
ejpam-5969	190	1	theorem	theorem	ADJ
ejpam-5969	190	2	4	4	NUM
ejpam-5969	190	3	.	.	X
ejpam-5969	191	1	for	for	SCONJ
ejpam-5969	191	2	the	the	DET
ejpam-5969	191	3	supra	supra	PROPN
ejpam-5969	191	4	ϵ-interior	ϵ-interior	PROPN
ejpam-5969	191	5	operator	operator	NOUN
ejpam-5969	191	6	intϵ	intϵ	VERB
ejpam-5969	191	7	:	:	PUNCT
ejpam-5969	191	8	p	p	X
ejpam-5969	191	9	(	(	PUNCT
ejpam-5969	191	10	χ	χ	X
ejpam-5969	191	11	)	)	PUNCT
ejpam-5969	191	12	−→	−→	NOUN
ejpam-5969	191	13	p	p	X
ejpam-5969	191	14	(	(	PUNCT
ejpam-5969	191	15	χ	χ	NOUN
ejpam-5969	191	16	)	)	PUNCT
ejpam-5969	191	17	and	and	CCONJ
ejpam-5969	191	18	e	e	X
ejpam-5969	191	19	∈	∈	PROPN
ejpam-5969	191	20	p	p	X
ejpam-5969	191	21	(	(	PUNCT
ejpam-5969	191	22	χ	χ	NOUN
ejpam-5969	191	23	)	)	PUNCT
ejpam-5969	191	24	,	,	PUNCT
ejpam-5969	191	25	we	we	PRON
ejpam-5969	191	26	have	have	AUX
ejpam-5969	191	27	intϵ(e	intϵ(e	VERB
ejpam-5969	191	28	)	)	PUNCT
ejpam-5969	191	29	=	=	SYM
ejpam-5969	191	30			PUNCT
ejpam-5969	191	31	∅	∅	NOUN
ejpam-5969	191	32	,	,	PUNCT
ejpam-5969	191	33	e	e	PROPN
ejpam-5969	191	34	∈	∈	PROPN
ejpam-5969	191	35	snd(χ	snd(χ	PROPN
ejpam-5969	191	36	)	)	PUNCT
ejpam-5969	191	37	and	and	CCONJ
ejpam-5969	191	38	b(e	b(e	PROPN
ejpam-5969	191	39	)	)	PUNCT
ejpam-5969	191	40	is	be	AUX
ejpam-5969	191	41	finite	finite	ADJ
ejpam-5969	191	42	.	.	PUNCT
ejpam-5969	192	1	e	e	NOUN
ejpam-5969	192	2	∩	∩	NOUN
ejpam-5969	192	3	b(e	b(e	PROPN
ejpam-5969	192	4	)	)	PUNCT
ejpam-5969	192	5	,	,	PUNCT
ejpam-5969	192	6	e	e	PROPN
ejpam-5969	192	7	∈	∈	PROPN
ejpam-5969	192	8	snd(χ	snd(χ	PROPN
ejpam-5969	192	9	)	)	PUNCT
ejpam-5969	192	10	and	and	CCONJ
ejpam-5969	192	11	b(e	b(e	PROPN
ejpam-5969	192	12	)	)	PUNCT
ejpam-5969	192	13	is	be	AUX
ejpam-5969	192	14	infinite	infinite	ADJ
ejpam-5969	192	15	.	.	PUNCT
ejpam-5969	193	1	e	e	X
ejpam-5969	193	2	,	,	PUNCT
ejpam-5969	193	3	e	e	X
ejpam-5969	193	4	∈	∈	PROPN
ejpam-5969	193	5	sro(χ	sro(χ	PROPN
ejpam-5969	193	6	)	)	PUNCT
ejpam-5969	193	7	.	.	PUNCT
ejpam-5969	194	1	proof	proof	NOUN
ejpam-5969	194	2	.	.	PUNCT
ejpam-5969	195	1	assume	assume	VERB
ejpam-5969	195	2	contrary	contrary	ADJ
ejpam-5969	195	3	that	that	SCONJ
ejpam-5969	195	4	,	,	PUNCT
ejpam-5969	195	5	s	s	VERB
ejpam-5969	195	6	∈	∈	PROPN
ejpam-5969	195	7	e	e	NOUN
ejpam-5969	195	8	,	,	PUNCT
ejpam-5969	195	9	where	where	SCONJ
ejpam-5969	195	10	as	as	ADP
ejpam-5969	195	11	e	e	PROPN
ejpam-5969	195	12	∈	∈	PROPN
ejpam-5969	195	13	snd(χ	snd(χ	PROPN
ejpam-5969	195	14	)	)	PUNCT
ejpam-5969	195	15	and	and	CCONJ
ejpam-5969	195	16	b(e	b(e	PROPN
ejpam-5969	195	17	)	)	PUNCT
ejpam-5969	195	18	is	be	AUX
ejpam-5969	195	19	finite	finite	PROPN
ejpam-5969	195	20	.	.	PUNCT
ejpam-5969	196	1	given	give	VERB
ejpam-5969	196	2	lemma	lemma	PROPN
ejpam-5969	196	3	1	1	NUM
ejpam-5969	196	4	(	(	PUNCT
ejpam-5969	196	5	1	1	NUM
ejpam-5969	196	6	)	)	PUNCT
ejpam-5969	196	7	,	,	PUNCT
ejpam-5969	196	8	there	there	PRON
ejpam-5969	196	9	is	be	VERB
ejpam-5969	196	10	i	i	PRON
ejpam-5969	196	11	∈	∈	PROPN
ejpam-5969	196	12	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	196	13	)	)	PUNCT
ejpam-5969	196	14	such	such	ADJ
ejpam-5969	196	15	that	that	PRON
ejpam-5969	196	16	s	s	VERB
ejpam-5969	196	17	∈	∈	PROPN
ejpam-5969	196	18	i	i	PROPN
ejpam-5969	196	19	⊆	⊆	NUM
ejpam-5969	196	20	e.	e.	PROPN
ejpam-5969	196	21	since	since	SCONJ
ejpam-5969	196	22	e	e	PROPN
ejpam-5969	196	23	∈	∈	PROPN
ejpam-5969	196	24	snd(χ	snd(χ	PROPN
ejpam-5969	196	25	)	)	PUNCT
ejpam-5969	196	26	,	,	PUNCT
ejpam-5969	196	27	i	i	PRON
ejpam-5969	196	28	∈	∈	PROPN
ejpam-5969	196	29	snd(χ	snd(χ	PROPN
ejpam-5969	196	30	)	)	PUNCT
ejpam-5969	196	31	and	and	CCONJ
ejpam-5969	196	32	so	so	ADV
ejpam-5969	196	33	s	s	X
ejpam-5969	196	34	∈	∈	PROPN
ejpam-5969	196	35	b(i	b(i	NOUN
ejpam-5969	196	36	)	)	PUNCT
ejpam-5969	196	37	⊆	⊆	NUM
ejpam-5969	196	38	b(e	b(e	PROPN
ejpam-5969	196	39	)	)	PUNCT
ejpam-5969	196	40	.	.	PUNCT
ejpam-5969	197	1	given	give	VERB
ejpam-5969	197	2	i	i	PRON
ejpam-5969	197	3	∈	∈	PROPN
ejpam-5969	197	4	soϵ(χ	soϵ(χ	NOUN
ejpam-5969	197	5	)	)	PUNCT
ejpam-5969	197	6	,	,	PUNCT
ejpam-5969	197	7	b(i	b(i	NUM
ejpam-5969	197	8	)	)	PUNCT
ejpam-5969	197	9	is	be	AUX
ejpam-5969	197	10	infinite	infinite	ADJ
ejpam-5969	197	11	,	,	PUNCT
ejpam-5969	197	12	then	then	ADV
ejpam-5969	197	13	b(e	b(e	PROPN
ejpam-5969	197	14	)	)	PUNCT
ejpam-5969	197	15	is	be	AUX
ejpam-5969	197	16	also	also	ADV
ejpam-5969	197	17	infinite	infinite	ADJ
ejpam-5969	197	18	,	,	PUNCT
ejpam-5969	197	19	which	which	PRON
ejpam-5969	197	20	contradicts	contradict	VERB
ejpam-5969	197	21	our	our	PRON
ejpam-5969	197	22	assumption	assumption	NOUN
ejpam-5969	197	23	.	.	PUNCT
ejpam-5969	198	1	hence	hence	ADV
ejpam-5969	198	2	,	,	PUNCT
ejpam-5969	198	3	intϵ(e	intϵ(e	PROPN
ejpam-5969	198	4	)	)	PUNCT
ejpam-5969	198	5	=	=	NOUN
ejpam-5969	198	6	∅.	∅.	ADP
ejpam-5969	198	7	now	now	ADV
ejpam-5969	198	8	,	,	PUNCT
ejpam-5969	198	9	assume	assume	VERB
ejpam-5969	198	10	contrary	contrary	ADJ
ejpam-5969	198	11	that	that	SCONJ
ejpam-5969	198	12	s	s	VERB
ejpam-5969	198	13	∈	∈	ADJ
ejpam-5969	198	14	e	e	NOUN
ejpam-5969	198	15	,	,	PUNCT
ejpam-5969	198	16	where	where	SCONJ
ejpam-5969	198	17	as	as	ADP
ejpam-5969	198	18	e	e	PROPN
ejpam-5969	198	19	∈	∈	PROPN
ejpam-5969	198	20	snd(χ	snd(χ	PROPN
ejpam-5969	198	21	)	)	PUNCT
ejpam-5969	198	22	and	and	CCONJ
ejpam-5969	198	23	b(e	b(e	PROPN
ejpam-5969	198	24	)	)	PUNCT
ejpam-5969	198	25	is	be	AUX
ejpam-5969	198	26	infinite	infinite	ADJ
ejpam-5969	198	27	.	.	PUNCT
ejpam-5969	199	1	by	by	ADP
ejpam-5969	199	2	the	the	DET
ejpam-5969	199	3	same	same	ADJ
ejpam-5969	199	4	technique	technique	NOUN
ejpam-5969	199	5	,	,	PUNCT
ejpam-5969	199	6	we	we	PRON
ejpam-5969	199	7	can	can	AUX
ejpam-5969	199	8	get	get	VERB
ejpam-5969	199	9	intϵ(e	intϵ(e	NOUN
ejpam-5969	199	10	)	)	PUNCT
ejpam-5969	199	11	⊆	⊆	NUM
ejpam-5969	199	12	e	e	NOUN
ejpam-5969	199	13	∩	∩	NOUN
ejpam-5969	199	14	b(e	b(e	VERB
ejpam-5969	199	15	)	)	PUNCT
ejpam-5969	199	16	(	(	PUNCT
ejpam-5969	199	17	1	1	X
ejpam-5969	199	18	)	)	PUNCT
ejpam-5969	199	19	on	on	ADP
ejpam-5969	199	20	the	the	DET
ejpam-5969	199	21	other	other	ADJ
ejpam-5969	199	22	way	way	NOUN
ejpam-5969	199	23	,	,	PUNCT
ejpam-5969	199	24	assume	assume	VERB
ejpam-5969	199	25	that	that	SCONJ
ejpam-5969	199	26	s	s	VERB
ejpam-5969	199	27	∈	∈	PROPN
ejpam-5969	199	28	e	e	NOUN
ejpam-5969	199	29	∩	∩	NOUN
ejpam-5969	199	30	b(e	b(e	VERB
ejpam-5969	199	31	)	)	PUNCT
ejpam-5969	199	32	.	.	PUNCT
ejpam-5969	200	1	since	since	SCONJ
ejpam-5969	200	2	e	e	PROPN
ejpam-5969	200	3	∈	∈	PROPN
ejpam-5969	200	4	snd(χ	snd(χ	PROPN
ejpam-5969	200	5	)	)	PUNCT
ejpam-5969	200	6	and	and	CCONJ
ejpam-5969	200	7	b(e	b(e	PROPN
ejpam-5969	200	8	)	)	PUNCT
ejpam-5969	200	9	is	be	AUX
ejpam-5969	200	10	infinite	infinite	ADJ
ejpam-5969	200	11	,	,	PUNCT
ejpam-5969	200	12	e	e	PROPN
ejpam-5969	200	13	∈	∈	PROPN
ejpam-5969	200	14	soϵ(χ	soϵ(χ	NOUN
ejpam-5969	200	15	)	)	PUNCT
ejpam-5969	200	16	,	,	PUNCT
ejpam-5969	200	17	given	give	VERB
ejpam-5969	200	18	definition	definition	NOUN
ejpam-5969	200	19	7	7	NUM
ejpam-5969	200	20	.	.	PUNCT
ejpam-5969	201	1	by	by	ADP
ejpam-5969	201	2	lemma	lemma	PROPN
ejpam-5969	201	3	1	1	NUM
ejpam-5969	201	4	(	(	PUNCT
ejpam-5969	201	5	2	2	NUM
ejpam-5969	201	6	)	)	PUNCT
ejpam-5969	201	7	,	,	PUNCT
ejpam-5969	201	8	s	s	VERB
ejpam-5969	201	9	∈	∈	PROPN
ejpam-5969	201	10	e	e	NOUN
ejpam-5969	201	11	=	=	SYM
ejpam-5969	201	12	intϵ(e	intϵ(e	PROPN
ejpam-5969	201	13	)	)	PUNCT
ejpam-5969	201	14	.	.	PUNCT
ejpam-5969	202	1	hence	hence	ADV
ejpam-5969	202	2	,	,	PUNCT
ejpam-5969	202	3	e	e	X
ejpam-5969	202	4	∩	∩	NOUN
ejpam-5969	202	5	b(e	b(e	VERB
ejpam-5969	202	6	)	)	PUNCT
ejpam-5969	202	7	⊆	⊆	NUM
ejpam-5969	202	8	intϵ(e	intϵ(e	PROPN
ejpam-5969	202	9	)	)	PUNCT
ejpam-5969	202	10	(	(	PUNCT
ejpam-5969	202	11	2	2	NUM
ejpam-5969	202	12	)	)	PUNCT
ejpam-5969	202	13	from	from	ADP
ejpam-5969	202	14	eqs	eqs	X
ejpam-5969	202	15	(	(	PUNCT
ejpam-5969	202	16	1	1	NUM
ejpam-5969	202	17	)	)	PUNCT
ejpam-5969	202	18	and	and	CCONJ
ejpam-5969	202	19	(	(	PUNCT
ejpam-5969	202	20	2	2	NUM
ejpam-5969	202	21	)	)	PUNCT
ejpam-5969	202	22	,	,	PUNCT
ejpam-5969	202	23	intϵ(e	intϵ(e	PROPN
ejpam-5969	202	24	)	)	PUNCT
ejpam-5969	202	25	=	=	SYM
ejpam-5969	202	26	e	e	NOUN
ejpam-5969	202	27	∩	∩	NOUN
ejpam-5969	202	28	b(e	b(e	VERB
ejpam-5969	202	29	)	)	PUNCT
ejpam-5969	202	30	.	.	PUNCT
ejpam-5969	203	1	finally	finally	ADV
ejpam-5969	203	2	,	,	PUNCT
ejpam-5969	203	3	if	if	SCONJ
ejpam-5969	203	4	e	e	PROPN
ejpam-5969	203	5	∈	∈	NOUN
ejpam-5969	203	6	sro(χ	sro(χ	PROPN
ejpam-5969	203	7	)	)	PUNCT
ejpam-5969	203	8	,	,	PUNCT
ejpam-5969	203	9	given	give	VERB
ejpam-5969	203	10	definition	definition	NOUN
ejpam-5969	203	11	7	7	NUM
ejpam-5969	203	12	and	and	CCONJ
ejpam-5969	203	13	lemma	lemma	PROPN
ejpam-5969	203	14	1	1	NUM
ejpam-5969	203	15	(	(	PUNCT
ejpam-5969	203	16	2	2	NUM
ejpam-5969	203	17	)	)	PUNCT
ejpam-5969	203	18	,	,	PUNCT
ejpam-5969	203	19	intϵ(e	intϵ(e	PROPN
ejpam-5969	203	20	)	)	PUNCT
ejpam-5969	203	21	=	=	SYM
ejpam-5969	203	22	e.	e.	PROPN
ejpam-5969	203	23	in	in	ADP
ejpam-5969	203	24	the	the	DET
ejpam-5969	203	25	example	example	NOUN
ejpam-5969	203	26	that	that	PRON
ejpam-5969	203	27	follows	follow	VERB
ejpam-5969	203	28	,	,	PUNCT
ejpam-5969	203	29	we	we	PRON
ejpam-5969	203	30	illustrate	illustrate	VERB
ejpam-5969	203	31	the	the	DET
ejpam-5969	203	32	previously	previously	ADV
ejpam-5969	203	33	mentioned	mention	VERB
ejpam-5969	203	34	theorem	theorem	VERB
ejpam-5969	203	35	.	.	PROPN
ejpam-5969	203	36	example	example	NOUN
ejpam-5969	203	37	4	4	NUM
ejpam-5969	203	38	.	.	PUNCT
ejpam-5969	203	39	consider	consider	VERB
ejpam-5969	203	40	the	the	DET
ejpam-5969	203	41	sets	set	NOUN
ejpam-5969	203	42	b	b	NOUN
ejpam-5969	203	43	=	=	SYM
ejpam-5969	203	44	{	{	PUNCT
ejpam-5969	203	45	0	0	NUM
ejpam-5969	203	46	,	,	PUNCT
ejpam-5969	203	47	1	1	NUM
ejpam-5969	203	48	,	,	PUNCT
ejpam-5969	203	49	2	2	NUM
ejpam-5969	203	50	}	}	PUNCT
ejpam-5969	203	51	,	,	PUNCT
ejpam-5969	203	52	c	c	X
ejpam-5969	203	53	=	=	SYM
ejpam-5969	203	54	{	{	PUNCT
ejpam-5969	203	55	2	2	NUM
ejpam-5969	203	56	,	,	PUNCT
ejpam-5969	203	57	3	3	NUM
ejpam-5969	203	58	,	,	PUNCT
ejpam-5969	203	59	4	4	NUM
ejpam-5969	203	60	,	,	PUNCT
ejpam-5969	203	61	5	5	NUM
ejpam-5969	203	62	}	}	PUNCT
ejpam-5969	203	63	and	and	CCONJ
ejpam-5969	203	64	the	the	DET
ejpam-5969	203	65	natural	natural	ADJ
ejpam-5969	203	66	number	number	NOUN
ejpam-5969	203	67	set	set	VERB
ejpam-5969	203	68	n	n	CCONJ
ejpam-5969	203	69	,	,	PUNCT
ejpam-5969	203	70	in	in	ADP
ejpam-5969	203	71	example	example	NOUN
ejpam-5969	203	72	1	1	NUM
ejpam-5969	203	73	,	,	PUNCT
ejpam-5969	203	74	we	we	PRON
ejpam-5969	203	75	have	have	VERB
ejpam-5969	203	76	(	(	PUNCT
ejpam-5969	203	77	1	1	X
ejpam-5969	203	78	)	)	PUNCT
ejpam-5969	203	79	n	n	PRON
ejpam-5969	203	80	∈	∈	PROPN
ejpam-5969	203	81	snd(χ	snd(χ	PROPN
ejpam-5969	203	82	)	)	PUNCT
ejpam-5969	203	83	and	and	CCONJ
ejpam-5969	203	84	b(n	b(n	NOUN
ejpam-5969	203	85	)	)	PUNCT
ejpam-5969	203	86	is	be	AUX
ejpam-5969	203	87	infinite	infinite	ADJ
ejpam-5969	203	88	,	,	PUNCT
ejpam-5969	203	89	and	and	CCONJ
ejpam-5969	203	90	hence	hence	ADV
ejpam-5969	203	91	intϵ(n	intϵ(n	NUM
ejpam-5969	203	92	)	)	PUNCT
ejpam-5969	203	93	=	=	SYM
ejpam-5969	203	94	n	n	NOUN
ejpam-5969	203	95	∩	∩	ADJ
ejpam-5969	203	96	b(n	b(n	NOUN
ejpam-5969	203	97	)	)	PUNCT
ejpam-5969	203	98	=	=	SYM
ejpam-5969	203	99	n.	n.	NOUN
ejpam-5969	203	100	(	(	PUNCT
ejpam-5969	203	101	2	2	NUM
ejpam-5969	203	102	)	)	PUNCT
ejpam-5969	203	103	b	b	NOUN
ejpam-5969	203	104	∈	∈	NOUN
ejpam-5969	203	105	sro(χ	sro(χ	NOUN
ejpam-5969	203	106	)	)	PUNCT
ejpam-5969	203	107	,	,	PUNCT
ejpam-5969	203	108	and	and	CCONJ
ejpam-5969	203	109	so	so	ADV
ejpam-5969	203	110	intϵ(b	intϵ(b	PROPN
ejpam-5969	203	111	)	)	PUNCT
ejpam-5969	203	112	=	=	SYM
ejpam-5969	203	113	b.	b.	PROPN
ejpam-5969	203	114	(	(	PUNCT
ejpam-5969	203	115	3	3	NUM
ejpam-5969	203	116	)	)	PUNCT
ejpam-5969	203	117	c	c	NOUN
ejpam-5969	203	118	∈	∈	PROPN
ejpam-5969	203	119	snd(χ	snd(χ	PROPN
ejpam-5969	203	120	)	)	PUNCT
ejpam-5969	203	121	and	and	CCONJ
ejpam-5969	203	122	b(c	b(c	NOUN
ejpam-5969	203	123	)	)	PUNCT
ejpam-5969	203	124	is	be	AUX
ejpam-5969	203	125	finite	finite	ADJ
ejpam-5969	203	126	,	,	PUNCT
ejpam-5969	203	127	and	and	CCONJ
ejpam-5969	203	128	then	then	ADV
ejpam-5969	203	129	intϵ(c	intϵ(c	ADJ
ejpam-5969	203	130	)	)	PUNCT
ejpam-5969	203	131	=	=	PUNCT
ejpam-5969	203	132	∅.	∅.	NOUN
ejpam-5969	203	133	theorem	theorem	ADJ
ejpam-5969	203	134	5	5	NUM
ejpam-5969	203	135	.	.	PUNCT
ejpam-5969	203	136	for	for	ADP
ejpam-5969	203	137	the	the	DET
ejpam-5969	203	138	subsets	subset	NOUN
ejpam-5969	203	139	k	k	PROPN
ejpam-5969	203	140	and	and	CCONJ
ejpam-5969	203	141	i	i	PRON
ejpam-5969	203	142	of	of	ADP
ejpam-5969	203	143	an	an	DET
ejpam-5969	203	144	sts	st	NOUN
ejpam-5969	203	145	(	(	PUNCT
ejpam-5969	203	146	χ	χ	NOUN
ejpam-5969	203	147	,	,	PUNCT
ejpam-5969	203	148	ν	ν	NOUN
ejpam-5969	203	149	)	)	PUNCT
ejpam-5969	203	150	,	,	PUNCT
ejpam-5969	203	151	we	we	PRON
ejpam-5969	203	152	have	have	VERB
ejpam-5969	203	153	the	the	DET
ejpam-5969	203	154	following	following	NOUN
ejpam-5969	203	155	:	:	PUNCT
ejpam-5969	203	156	(	(	PUNCT
ejpam-5969	203	157	1	1	X
ejpam-5969	203	158	)	)	PUNCT
ejpam-5969	203	159	if	if	SCONJ
ejpam-5969	203	160	k	k	PROPN
ejpam-5969	203	161	⊆	⊆	NUM
ejpam-5969	203	162	i	i	PRON
ejpam-5969	203	163	,	,	PUNCT
ejpam-5969	203	164	then	then	ADV
ejpam-5969	203	165	intϵ(k	intϵ(k	PROPN
ejpam-5969	203	166	)	)	PUNCT
ejpam-5969	203	167	⊆	⊆	NUM
ejpam-5969	203	168	intϵ(i	intϵ(i	NUM
ejpam-5969	203	169	)	)	PUNCT
ejpam-5969	203	170	.	.	PUNCT
ejpam-5969	204	1	abd	abd	PROPN
ejpam-5969	204	2	el	el	PROPN
ejpam-5969	204	3	-	-	PROPN
ejpam-5969	204	4	latif	latif	PROPN
ejpam-5969	204	5	et	et	PROPN
ejpam-5969	204	6	al	al	PROPN
ejpam-5969	204	7	.	.	PUNCT
ejpam-5969	204	8	/	/	SYM
ejpam-5969	204	9	eur	eur	PROPN
ejpam-5969	204	10	.	.	PUNCT
ejpam-5969	205	1	j.	j.	PROPN
ejpam-5969	205	2	pure	pure	PROPN
ejpam-5969	205	3	appl	appl	PROPN
ejpam-5969	205	4	.	.	PROPN
ejpam-5969	205	5	math	math	PROPN
ejpam-5969	205	6	,	,	PUNCT
ejpam-5969	205	7	18	18	NUM
ejpam-5969	205	8	(	(	PUNCT
ejpam-5969	205	9	2	2	NUM
ejpam-5969	205	10	)	)	PUNCT
ejpam-5969	205	11	(	(	PUNCT
ejpam-5969	205	12	2025	2025	NUM
ejpam-5969	205	13	)	)	PUNCT
ejpam-5969	205	14	,	,	PUNCT
ejpam-5969	205	15	5969	5969	NUM
ejpam-5969	205	16	8	8	NUM
ejpam-5969	205	17	of	of	ADP
ejpam-5969	205	18	19	19	NUM
ejpam-5969	205	19	(	(	PUNCT
ejpam-5969	205	20	2	2	NUM
ejpam-5969	205	21	)	)	PUNCT
ejpam-5969	205	22	int(k	int(k	PROPN
ejpam-5969	205	23	)	)	PUNCT
ejpam-5969	205	24	⊆	⊆	NUM
ejpam-5969	205	25	intϵ(k	intϵ(k	NOUN
ejpam-5969	205	26	)	)	PUNCT
ejpam-5969	205	27	.	.	PUNCT
ejpam-5969	206	1	proof	proof	NOUN
ejpam-5969	206	2	.	.	PUNCT
ejpam-5969	207	1	(	(	PUNCT
ejpam-5969	207	2	1	1	X
ejpam-5969	207	3	)	)	PUNCT
ejpam-5969	207	4	suppose	suppose	VERB
ejpam-5969	207	5	that	that	SCONJ
ejpam-5969	207	6	u	u	PROPN
ejpam-5969	207	7	∈	∈	PROPN
ejpam-5969	207	8	intϵ(k	intϵ(k	PROPN
ejpam-5969	207	9	)	)	PUNCT
ejpam-5969	207	10	.	.	PUNCT
ejpam-5969	208	1	given	give	VERB
ejpam-5969	208	2	theorem	theorem	VERB
ejpam-5969	208	3	4	4	NUM
ejpam-5969	208	4	,	,	PUNCT
ejpam-5969	208	5	eitherk	eitherk	NOUN
ejpam-5969	208	6	∈	∈	PROPN
ejpam-5969	208	7	snd(χ	snd(χ	PROPN
ejpam-5969	208	8	)	)	PUNCT
ejpam-5969	208	9	and	and	CCONJ
ejpam-5969	208	10	b(k	b(k	PROPN
ejpam-5969	208	11	)	)	PUNCT
ejpam-5969	208	12	is	be	AUX
ejpam-5969	208	13	infinite	infinite	ADJ
ejpam-5969	208	14	or	or	CCONJ
ejpam-5969	208	15	k	k	PROPN
ejpam-5969	208	16	∈	∈	PROPN
ejpam-5969	208	17	sro(χ	sro(χ	PROPN
ejpam-5969	208	18	)	)	PUNCT
ejpam-5969	208	19	,	,	PUNCT
ejpam-5969	208	20	and	and	CCONJ
ejpam-5969	208	21	in	in	ADP
ejpam-5969	208	22	both	both	DET
ejpam-5969	208	23	situations	situation	NOUN
ejpam-5969	208	24	,	,	PUNCT
ejpam-5969	208	25	results	result	NOUN
ejpam-5969	208	26	in	in	ADP
ejpam-5969	208	27	intϵ(k	intϵ(k	NUM
ejpam-5969	208	28	)	)	PUNCT
ejpam-5969	208	29	=	=	SYM
ejpam-5969	208	30	k.	k.	PROPN
ejpam-5969	209	1	hence	hence	ADV
ejpam-5969	209	2	,	,	PUNCT
ejpam-5969	209	3	u	u	PROPN
ejpam-5969	209	4	∈	∈	PROPN
ejpam-5969	209	5	intϵ(i	intϵ(i	NOUN
ejpam-5969	209	6	)	)	PUNCT
ejpam-5969	209	7	,	,	PUNCT
ejpam-5969	209	8	and	and	CCONJ
ejpam-5969	209	9	therefore	therefore	ADV
ejpam-5969	209	10	intϵ(k	intϵ(k	ADJ
ejpam-5969	209	11	)	)	PUNCT
ejpam-5969	209	12	⊆	⊆	NUM
ejpam-5969	209	13	intϵ(i	intϵ(i	NUM
ejpam-5969	209	14	)	)	PUNCT
ejpam-5969	209	15	.	.	PUNCT
ejpam-5969	210	1	(	(	PUNCT
ejpam-5969	210	2	2	2	X
ejpam-5969	210	3	)	)	PUNCT
ejpam-5969	210	4	suppose	suppose	VERB
ejpam-5969	210	5	that	that	SCONJ
ejpam-5969	210	6	u	u	PROPN
ejpam-5969	210	7	∈	∈	PROPN
ejpam-5969	210	8	int(k	int(k	PROPN
ejpam-5969	210	9	)	)	PUNCT
ejpam-5969	210	10	,	,	PUNCT
ejpam-5969	210	11	then	then	ADV
ejpam-5969	210	12	there	there	PRON
ejpam-5969	210	13	exists	exist	VERB
ejpam-5969	210	14	g	g	PROPN
ejpam-5969	210	15	∈	∈	PROPN
ejpam-5969	210	16	ν	ν	NOUN
ejpam-5969	210	17	such	such	ADJ
ejpam-5969	210	18	that	that	SCONJ
ejpam-5969	210	19	u	u	PROPN
ejpam-5969	210	20	∈	∈	PROPN
ejpam-5969	210	21	g	g	PROPN
ejpam-5969	210	22	⊆	⊆	NUM
ejpam-5969	210	23	k.	k.	NOUN
ejpam-5969	210	24	given	give	VERB
ejpam-5969	210	25	(	(	PUNCT
ejpam-5969	210	26	1	1	NUM
ejpam-5969	210	27	)	)	PUNCT
ejpam-5969	210	28	,	,	PUNCT
ejpam-5969	210	29	g	g	PROPN
ejpam-5969	210	30	∈	∈	PROPN
ejpam-5969	210	31	soϵ(χ	soϵ(χ	VERB
ejpam-5969	210	32	)	)	PUNCT
ejpam-5969	210	33	and	and	CCONJ
ejpam-5969	210	34	u	u	PROPN
ejpam-5969	210	35	∈	∈	PROPN
ejpam-5969	210	36	intϵ(g	intϵ(g	PROPN
ejpam-5969	210	37	)	)	PUNCT
ejpam-5969	211	1	=	=	PROPN
ejpam-5969	211	2	g	g	PROPN
ejpam-5969	211	3	⊆	⊆	NUM
ejpam-5969	211	4	intϵ(k	intϵ(k	NOUN
ejpam-5969	211	5	)	)	PUNCT
ejpam-5969	211	6	.	.	PUNCT
ejpam-5969	212	1	thus	thus	ADV
ejpam-5969	212	2	,	,	PUNCT
ejpam-5969	212	3	u	u	PROPN
ejpam-5969	212	4	∈	∈	NOUN
ejpam-5969	212	5	intϵ(k	intϵ(k	PROPN
ejpam-5969	212	6	)	)	PUNCT
ejpam-5969	212	7	.	.	PUNCT
ejpam-5969	213	1	theorem	theorem	ADJ
ejpam-5969	213	2	6	6	NUM
ejpam-5969	213	3	.	.	PUNCT
ejpam-5969	214	1	let	let	AUX
ejpam-5969	214	2	(	(	PUNCT
ejpam-5969	214	3	χ	χ	X
ejpam-5969	214	4	,	,	PUNCT
ejpam-5969	214	5	ν	ν	NOUN
ejpam-5969	214	6	)	)	PUNCT
ejpam-5969	214	7	be	be	AUX
ejpam-5969	214	8	an	an	DET
ejpam-5969	214	9	sts	st	NOUN
ejpam-5969	214	10	and	and	CCONJ
ejpam-5969	214	11	v	v	NOUN
ejpam-5969	214	12	,	,	PUNCT
ejpam-5969	214	13	u	u	NOUN
ejpam-5969	214	14	∈	∈	PROPN
ejpam-5969	214	15	p	p	X
ejpam-5969	214	16	(	(	PUNCT
ejpam-5969	214	17	χ	χ	NOUN
ejpam-5969	214	18	)	)	PUNCT
ejpam-5969	214	19	.	.	PUNCT
ejpam-5969	215	1	then	then	ADV
ejpam-5969	215	2	,	,	PUNCT
ejpam-5969	215	3	(	(	PUNCT
ejpam-5969	215	4	1	1	X
ejpam-5969	215	5	)	)	PUNCT
ejpam-5969	215	6	intϵ(χ	intϵ(χ	NOUN
ejpam-5969	215	7	)	)	PUNCT
ejpam-5969	215	8	=	=	SYM
ejpam-5969	215	9	χ	χ	NOUN
ejpam-5969	215	10	and	and	CCONJ
ejpam-5969	215	11	intϵ(∅	intϵ(∅	NOUN
ejpam-5969	215	12	)	)	PUNCT
ejpam-5969	215	13	=	=	PUNCT
ejpam-5969	215	14	∅.	∅.	X
ejpam-5969	215	15	(	(	PUNCT
ejpam-5969	215	16	2	2	X
ejpam-5969	215	17	)	)	PUNCT
ejpam-5969	215	18	intϵ(v	intϵ(v	NOUN
ejpam-5969	215	19	)	)	PUNCT
ejpam-5969	216	1	⊆	⊆	NUM
ejpam-5969	216	2	(	(	PUNCT
ejpam-5969	216	3	v	v	NOUN
ejpam-5969	216	4	)	)	PUNCT
ejpam-5969	216	5	.	.	PUNCT
ejpam-5969	217	1	(	(	PUNCT
ejpam-5969	217	2	3	3	X
ejpam-5969	217	3	)	)	PUNCT
ejpam-5969	217	4	intϵ(intϵ(v	intϵ(intϵ(v	NOUN
ejpam-5969	217	5	)	)	PUNCT
ejpam-5969	217	6	)	)	PUNCT
ejpam-5969	218	1	=	=	PUNCT
ejpam-5969	218	2	intϵ(v	intϵ(v	X
ejpam-5969	218	3	)	)	PUNCT
ejpam-5969	218	4	.	.	PUNCT
ejpam-5969	219	1	(	(	PUNCT
ejpam-5969	219	2	4	4	X
ejpam-5969	219	3	)	)	PUNCT
ejpam-5969	219	4	intϵ[v	intϵ[v	NOUN
ejpam-5969	219	5	∩	∩	ADJ
ejpam-5969	219	6	u	u	NOUN
ejpam-5969	219	7	]	]	PUNCT
ejpam-5969	219	8	⊆	⊆	NUM
ejpam-5969	219	9	intϵ(v	intϵ(v	NOUN
ejpam-5969	219	10	)	)	PUNCT
ejpam-5969	219	11	∩	∩	PROPN
ejpam-5969	219	12	intϵ(u	intϵ(u	NOUN
ejpam-5969	219	13	)	)	PUNCT
ejpam-5969	219	14	.	.	PUNCT
ejpam-5969	220	1	(	(	PUNCT
ejpam-5969	220	2	5	5	X
ejpam-5969	220	3	)	)	PUNCT
ejpam-5969	220	4	intϵ(v	intϵ(v	NOUN
ejpam-5969	220	5	)	)	PUNCT
ejpam-5969	220	6	∪	∪	PROPN
ejpam-5969	220	7	intϵ(u	intϵ(u	NOUN
ejpam-5969	220	8	)	)	PUNCT
ejpam-5969	220	9	⊆	⊆	NUM
ejpam-5969	220	10	intϵ[v	intϵ[v	NOUN
ejpam-5969	220	11	∪	∪	NOUN
ejpam-5969	220	12	u	u	NOUN
ejpam-5969	220	13	]	]	PUNCT
ejpam-5969	220	14	.	.	PUNCT
ejpam-5969	221	1	proof	proof	NOUN
ejpam-5969	221	2	.	.	PUNCT
ejpam-5969	222	1	follows	follow	VERB
ejpam-5969	222	2	from	from	ADP
ejpam-5969	222	3	definition	definition	NOUN
ejpam-5969	222	4	7	7	NUM
ejpam-5969	222	5	.	.	PUNCT
ejpam-5969	222	6	remark	remark	PROPN
ejpam-5969	222	7	6	6	NUM
ejpam-5969	222	8	.	.	PUNCT
ejpam-5969	223	1	the	the	DET
ejpam-5969	223	2	equality	equality	NOUN
ejpam-5969	223	3	of	of	ADP
ejpam-5969	223	4	theorem	theorem	ADJ
ejpam-5969	223	5	5	5	NUM
ejpam-5969	223	6	and	and	CCONJ
ejpam-5969	223	7	theorem	theorem	VERB
ejpam-5969	223	8	6	6	NUM
ejpam-5969	223	9	parts	part	NOUN
ejpam-5969	223	10	(	(	PUNCT
ejpam-5969	223	11	2	2	NUM
ejpam-5969	223	12	)	)	PUNCT
ejpam-5969	223	13	,	,	PUNCT
ejpam-5969	223	14	(	(	PUNCT
ejpam-5969	223	15	4	4	NUM
ejpam-5969	223	16	)	)	PUNCT
ejpam-5969	223	17	and	and	CCONJ
ejpam-5969	223	18	(	(	PUNCT
ejpam-5969	223	19	5	5	X
ejpam-5969	223	20	)	)	PUNCT
ejpam-5969	223	21	are	be	AUX
ejpam-5969	223	22	not	not	PART
ejpam-5969	223	23	satisfied	satisfied	ADJ
ejpam-5969	223	24	as	as	SCONJ
ejpam-5969	223	25	shall	shall	AUX
ejpam-5969	223	26	shown	show	VERB
ejpam-5969	223	27	in	in	ADP
ejpam-5969	223	28	the	the	DET
ejpam-5969	223	29	provided	provide	VERB
ejpam-5969	223	30	counterexamples	counterexample	NOUN
ejpam-5969	223	31	.	.	PUNCT
ejpam-5969	224	1	examples	example	NOUN
ejpam-5969	224	2	1	1	NUM
ejpam-5969	224	3	.	.	PUNCT
ejpam-5969	224	4	consider	consider	VERB
ejpam-5969	224	5	the	the	DET
ejpam-5969	224	6	sets	set	NOUN
ejpam-5969	224	7	b	b	NOUN
ejpam-5969	224	8	=	=	SYM
ejpam-5969	224	9	{	{	PUNCT
ejpam-5969	224	10	0	0	NUM
ejpam-5969	224	11	,	,	PUNCT
ejpam-5969	224	12	1	1	NUM
ejpam-5969	224	13	,	,	PUNCT
ejpam-5969	224	14	2	2	NUM
ejpam-5969	224	15	,	,	PUNCT
ejpam-5969	224	16	3	3	NUM
ejpam-5969	224	17	}	}	PUNCT
ejpam-5969	224	18	,	,	PUNCT
ejpam-5969	224	19	c	c	X
ejpam-5969	224	20	=	=	SYM
ejpam-5969	224	21	{	{	PUNCT
ejpam-5969	224	22	2	2	NUM
ejpam-5969	224	23	,	,	PUNCT
ejpam-5969	224	24	3	3	NUM
ejpam-5969	224	25	,	,	PUNCT
ejpam-5969	224	26	4	4	NUM
ejpam-5969	224	27	,	,	PUNCT
ejpam-5969	224	28	6	6	NUM
ejpam-5969	224	29	}	}	PUNCT
ejpam-5969	224	30	,	,	PUNCT
ejpam-5969	224	31	d	d	NOUN
ejpam-5969	224	32	=	=	PRON
ejpam-5969	224	33	{	{	PUNCT
ejpam-5969	224	34	−1	−1	NOUN
ejpam-5969	224	35	,	,	PUNCT
ejpam-5969	224	36	2	2	NUM
ejpam-5969	224	37	,	,	PUNCT
ejpam-5969	224	38	4	4	NUM
ejpam-5969	224	39	,	,	PUNCT
ejpam-5969	224	40	5	5	NUM
ejpam-5969	224	41	}	}	PUNCT
ejpam-5969	224	42	and	and	CCONJ
ejpam-5969	224	43	the	the	DET
ejpam-5969	224	44	natural	natural	ADJ
ejpam-5969	224	45	number	number	NOUN
ejpam-5969	224	46	set	set	VERB
ejpam-5969	224	47	n	n	CCONJ
ejpam-5969	224	48	,	,	PUNCT
ejpam-5969	224	49	in	in	ADP
ejpam-5969	224	50	example	example	NOUN
ejpam-5969	224	51	1	1	NUM
ejpam-5969	224	52	,	,	PUNCT
ejpam-5969	224	53	we	we	PRON
ejpam-5969	224	54	have	have	VERB
ejpam-5969	224	55	:	:	PUNCT
ejpam-5969	224	56	(	(	PUNCT
ejpam-5969	224	57	1	1	X
ejpam-5969	224	58	)	)	PUNCT
ejpam-5969	224	59	intϵ(c	intϵ(c	NOUN
ejpam-5969	224	60	)	)	PUNCT
ejpam-5969	224	61	=	=	PUNCT
ejpam-5969	225	1	∅	∅	NOUN
ejpam-5969	225	2	⊆	⊆	NUM
ejpam-5969	225	3	intϵ(b	intϵ(b	PROPN
ejpam-5969	225	4	)	)	PUNCT
ejpam-5969	225	5	=	=	SYM
ejpam-5969	225	6	b	b	X
ejpam-5969	225	7	,	,	PUNCT
ejpam-5969	226	1	however	however	ADV
ejpam-5969	226	2	c	c	PROPN
ejpam-5969	226	3	⊈	⊈	PROPN
ejpam-5969	226	4	b.	b.	PROPN
ejpam-5969	226	5	(	(	PUNCT
ejpam-5969	226	6	2	2	X
ejpam-5969	226	7	)	)	PUNCT
ejpam-5969	226	8	intϵ(n	intϵ(n	PROPN
ejpam-5969	226	9	)	)	PUNCT
ejpam-5969	226	10	=	=	SYM
ejpam-5969	226	11	n	n	PRON
ejpam-5969	226	12	⊈	⊈	NUM
ejpam-5969	226	13	int(n	int(n	NOUN
ejpam-5969	226	14	)	)	PUNCT
ejpam-5969	227	1	=	=	PUNCT
ejpam-5969	227	2	∅.	∅.	X
ejpam-5969	227	3	(	(	PUNCT
ejpam-5969	227	4	3	3	NUM
ejpam-5969	227	5	)	)	PUNCT
ejpam-5969	227	6	c	c	NOUN
ejpam-5969	227	7	⊈	⊈	PROPN
ejpam-5969	228	1	intϵ(c	intϵ(c	NOUN
ejpam-5969	228	2	)	)	PUNCT
ejpam-5969	228	3	=	=	PUNCT
ejpam-5969	228	4	∅.	∅.	X
ejpam-5969	228	5	(	(	PUNCT
ejpam-5969	228	6	4	4	NUM
ejpam-5969	228	7	)	)	PUNCT
ejpam-5969	228	8	intϵ(b	intϵ(b	PROPN
ejpam-5969	228	9	)	)	PUNCT
ejpam-5969	228	10	∩	∩	ADJ
ejpam-5969	228	11	intϵ(d	intϵ(d	NOUN
ejpam-5969	228	12	)	)	PUNCT
ejpam-5969	228	13	=	=	NOUN
ejpam-5969	228	14	{	{	PUNCT
ejpam-5969	228	15	2	2	NUM
ejpam-5969	228	16	}	}	PUNCT
ejpam-5969	228	17	⊈	⊈	PROPN
ejpam-5969	228	18	intϵ[b	intϵ[b	NOUN
ejpam-5969	228	19	∩d	∩d	NOUN
ejpam-5969	228	20	]	]	X
ejpam-5969	228	21	=	=	PUNCT
ejpam-5969	228	22	intϵ({2	intϵ({2	NOUN
ejpam-5969	228	23	}	}	PUNCT
ejpam-5969	228	24	)	)	PUNCT
ejpam-5969	228	25	=	=	PUNCT
ejpam-5969	228	26	∅.	∅.	X
ejpam-5969	228	27	(	(	PUNCT
ejpam-5969	228	28	5	5	NUM
ejpam-5969	228	29	)	)	PUNCT
ejpam-5969	228	30	intϵ(b∪c	intϵ(b∪c	PROPN
ejpam-5969	228	31	)	)	PUNCT
ejpam-5969	228	32	=	=	SYM
ejpam-5969	228	33	intϵ({0	intϵ({0	NOUN
ejpam-5969	228	34	,	,	PUNCT
ejpam-5969	228	35	1	1	NUM
ejpam-5969	228	36	,	,	PUNCT
ejpam-5969	228	37	2	2	NUM
ejpam-5969	228	38	,	,	PUNCT
ejpam-5969	228	39	3	3	NUM
ejpam-5969	228	40	,	,	PUNCT
ejpam-5969	228	41	4	4	NUM
ejpam-5969	228	42	,	,	PUNCT
ejpam-5969	228	43	6	6	NUM
ejpam-5969	228	44	}	}	PUNCT
ejpam-5969	228	45	)	)	PUNCT
ejpam-5969	228	46	=	=	SYM
ejpam-5969	228	47	{	{	PUNCT
ejpam-5969	228	48	0	0	NUM
ejpam-5969	228	49	,	,	PUNCT
ejpam-5969	228	50	1	1	NUM
ejpam-5969	228	51	,	,	PUNCT
ejpam-5969	228	52	2	2	NUM
ejpam-5969	228	53	,	,	PUNCT
ejpam-5969	228	54	3	3	NUM
ejpam-5969	228	55	,	,	PUNCT
ejpam-5969	228	56	4	4	NUM
ejpam-5969	228	57	,	,	PUNCT
ejpam-5969	228	58	6	6	NUM
ejpam-5969	228	59	}	}	PUNCT
ejpam-5969	228	60	⊈	⊈	PROPN
ejpam-5969	228	61	intϵ(b)∪intϵ(c	intϵ(b)∪intϵ(c	NOUN
ejpam-5969	228	62	)	)	PUNCT
ejpam-5969	228	63	=	=	PUNCT
ejpam-5969	228	64	{	{	PUNCT
ejpam-5969	228	65	0	0	NUM
ejpam-5969	228	66	,	,	PUNCT
ejpam-5969	228	67	1	1	NUM
ejpam-5969	228	68	,	,	PUNCT
ejpam-5969	228	69	2	2	NUM
ejpam-5969	228	70	,	,	PUNCT
ejpam-5969	228	71	3	3	NUM
ejpam-5969	228	72	}	}	PUNCT
ejpam-5969	228	73	.	.	PUNCT
ejpam-5969	229	1	definition	definition	NOUN
ejpam-5969	229	2	8	8	NUM
ejpam-5969	229	3	.	.	PUNCT
ejpam-5969	230	1	let	let	VERB
ejpam-5969	230	2	c	c	NOUN
ejpam-5969	230	3	∈	∈	PROPN
ejpam-5969	230	4	p	p	X
ejpam-5969	230	5	(	(	PUNCT
ejpam-5969	230	6	χ	χ	X
ejpam-5969	230	7	)	)	PUNCT
ejpam-5969	230	8	be	be	AUX
ejpam-5969	230	9	a	a	DET
ejpam-5969	230	10	subset	subset	NOUN
ejpam-5969	230	11	of	of	ADP
ejpam-5969	230	12	an	an	DET
ejpam-5969	230	13	sts	st	NOUN
ejpam-5969	230	14	(	(	PUNCT
ejpam-5969	230	15	χ	χ	NOUN
ejpam-5969	230	16	,	,	PUNCT
ejpam-5969	230	17	ν	ν	NOUN
ejpam-5969	230	18	)	)	PUNCT
ejpam-5969	230	19	,	,	PUNCT
ejpam-5969	230	20	then	then	ADV
ejpam-5969	230	21	clϵ(c	clϵ(c	PROPN
ejpam-5969	230	22	)	)	PUNCT
ejpam-5969	230	23	will	will	AUX
ejpam-5969	230	24	denote	denote	VERB
ejpam-5969	230	25	the	the	DET
ejpam-5969	230	26	supra	supra	ADJ
ejpam-5969	230	27	ϵ-closure	ϵ-closure	NOUN
ejpam-5969	230	28	of	of	ADP
ejpam-5969	230	29	c	c	NOUN
ejpam-5969	230	30	,	,	PUNCT
ejpam-5969	230	31	where	where	SCONJ
ejpam-5969	230	32	clϵ(c	clϵ(c	NOUN
ejpam-5969	230	33	)	)	PUNCT
ejpam-5969	231	1	=	=	VERB
ejpam-5969	231	2	∩{n	∩{n	INTJ
ejpam-5969	231	3	:	:	PUNCT
ejpam-5969	231	4	n	n	NOUN
ejpam-5969	231	5	∈	∈	NOUN
ejpam-5969	231	6	scϵ(χ	scϵ(χ	NUM
ejpam-5969	231	7	)	)	PUNCT
ejpam-5969	231	8	and	and	CCONJ
ejpam-5969	231	9	c	c	NOUN
ejpam-5969	231	10	⊆	⊆	NUM
ejpam-5969	231	11	n	n	CCONJ
ejpam-5969	231	12	}	}	PUNCT
ejpam-5969	231	13	.	.	PUNCT
ejpam-5969	232	1	theorem	theorem	ADJ
ejpam-5969	232	2	7	7	NUM
ejpam-5969	232	3	.	.	PUNCT
ejpam-5969	232	4	given	give	VERB
ejpam-5969	232	5	a	a	DET
ejpam-5969	232	6	subset	subset	NOUN
ejpam-5969	232	7	j	j	NOUN
ejpam-5969	232	8	of	of	ADP
ejpam-5969	232	9	an	an	DET
ejpam-5969	232	10	sts	st	NOUN
ejpam-5969	232	11	(	(	PUNCT
ejpam-5969	232	12	χ	χ	NOUN
ejpam-5969	232	13	,	,	PUNCT
ejpam-5969	232	14	ν	ν	NOUN
ejpam-5969	232	15	)	)	PUNCT
ejpam-5969	232	16	,	,	PUNCT
ejpam-5969	232	17	then	then	ADV
ejpam-5969	232	18	j	j	PROPN
ejpam-5969	232	19	has	have	VERB
ejpam-5969	232	20	the	the	DET
ejpam-5969	232	21	following	follow	VERB
ejpam-5969	232	22	characteristics	characteristic	NOUN
ejpam-5969	232	23	:	:	PUNCT
ejpam-5969	232	24	abd	abd	PROPN
ejpam-5969	232	25	el	el	PROPN
ejpam-5969	232	26	-	-	PROPN
ejpam-5969	232	27	latif	latif	PROPN
ejpam-5969	232	28	et	et	PROPN
ejpam-5969	232	29	al	al	PROPN
ejpam-5969	232	30	.	.	PUNCT
ejpam-5969	232	31	/	/	SYM
ejpam-5969	232	32	eur	eur	PROPN
ejpam-5969	232	33	.	.	PUNCT
ejpam-5969	233	1	j.	j.	PROPN
ejpam-5969	233	2	pure	pure	PROPN
ejpam-5969	233	3	appl	appl	PROPN
ejpam-5969	233	4	.	.	PROPN
ejpam-5969	233	5	math	math	PROPN
ejpam-5969	233	6	,	,	PUNCT
ejpam-5969	233	7	18	18	NUM
ejpam-5969	233	8	(	(	PUNCT
ejpam-5969	233	9	2	2	NUM
ejpam-5969	233	10	)	)	PUNCT
ejpam-5969	233	11	(	(	PUNCT
ejpam-5969	233	12	2025	2025	NUM
ejpam-5969	233	13	)	)	PUNCT
ejpam-5969	233	14	,	,	PUNCT
ejpam-5969	233	15	5969	5969	NUM
ejpam-5969	233	16	9	9	NUM
ejpam-5969	233	17	of	of	ADP
ejpam-5969	233	18	19	19	NUM
ejpam-5969	233	19	(	(	PUNCT
ejpam-5969	233	20	1	1	NUM
ejpam-5969	233	21	)	)	PUNCT
ejpam-5969	233	22	clϵ(j	clϵ(j	NOUN
ejpam-5969	233	23	)	)	PUNCT
ejpam-5969	233	24	=	=	SYM
ejpam-5969	234	1	j	j	PROPN
ejpam-5969	234	2	⇔	⇔	PROPN
ejpam-5969	234	3	j	j	PROPN
ejpam-5969	234	4	∈	∈	PROPN
ejpam-5969	234	5	scϵ(χ	scϵ(χ	NUM
ejpam-5969	234	6	)	)	PUNCT
ejpam-5969	234	7	)	)	PUNCT
ejpam-5969	234	8	.	.	PUNCT
ejpam-5969	235	1	(	(	PUNCT
ejpam-5969	235	2	2	2	X
ejpam-5969	235	3	)	)	PUNCT
ejpam-5969	235	4	u	u	PROPN
ejpam-5969	235	5	∈	∈	PROPN
ejpam-5969	235	6	clϵ(j	clϵ(j	PROPN
ejpam-5969	235	7	)	)	PUNCT
ejpam-5969	235	8	⇔	⇔	PROPN
ejpam-5969	235	9	j	j	PROPN
ejpam-5969	235	10	∩g	∩g	PROPN
ejpam-5969	235	11	̸=	̸=	PROPN
ejpam-5969	235	12	∅	∅	NOUN
ejpam-5969	235	13	for	for	ADP
ejpam-5969	235	14	each	each	DET
ejpam-5969	235	15	gu	gu	NOUN
ejpam-5969	235	16	∈	∈	PROPN
ejpam-5969	235	17	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	235	18	)	)	PUNCT
ejpam-5969	235	19	.	.	PUNCT
ejpam-5969	236	1	(	(	PUNCT
ejpam-5969	236	2	3	3	X
ejpam-5969	236	3	)	)	PUNCT
ejpam-5969	236	4	clϵ(j	clϵ(j	NOUN
ejpam-5969	236	5	)	)	PUNCT
ejpam-5969	236	6	⊆	⊆	NUM
ejpam-5969	236	7	cl(j	cl(j	NOUN
ejpam-5969	236	8	)	)	PUNCT
ejpam-5969	236	9	.	.	PUNCT
ejpam-5969	237	1	proof	proof	NOUN
ejpam-5969	237	2	.	.	PUNCT
ejpam-5969	238	1	(	(	PUNCT
ejpam-5969	238	2	1	1	X
ejpam-5969	238	3	)	)	PUNCT
ejpam-5969	238	4	follows	follow	VERB
ejpam-5969	238	5	from	from	ADP
ejpam-5969	238	6	definition	definition	NOUN
ejpam-5969	238	7	8	8	NUM
ejpam-5969	238	8	.	.	PUNCT
ejpam-5969	239	1	(	(	PUNCT
ejpam-5969	239	2	2	2	NUM
ejpam-5969	239	3	)	)	PUNCT
ejpam-5969	239	4	”	"	PUNCT
ejpam-5969	239	5	necessity	necessity	NOUN
ejpam-5969	239	6	”	"	PUNCT
ejpam-5969	239	7	assume	assume	VERB
ejpam-5969	239	8	that	that	SCONJ
ejpam-5969	239	9	there	there	PRON
ejpam-5969	239	10	is	be	VERB
ejpam-5969	239	11	gu	gu	PRON
ejpam-5969	239	12	∈	∈	PROPN
ejpam-5969	239	13	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	239	14	)	)	PUNCT
ejpam-5969	239	15	such	such	ADJ
ejpam-5969	239	16	that	that	SCONJ
ejpam-5969	239	17	j	j	PROPN
ejpam-5969	239	18	∩	∩	PROPN
ejpam-5969	239	19	g	g	NOUN
ejpam-5969	239	20	=	=	NOUN
ejpam-5969	239	21	∅	∅	NOUN
ejpam-5969	239	22	,	,	PUNCT
ejpam-5969	239	23	whereas	whereas	SCONJ
ejpam-5969	239	24	u	u	PROPN
ejpam-5969	239	25	∈	∈	PROPN
ejpam-5969	239	26	clϵ(j	clϵ(j	PROPN
ejpam-5969	239	27	)	)	PUNCT
ejpam-5969	239	28	.	.	PUNCT
ejpam-5969	240	1	then	then	ADV
ejpam-5969	240	2	,	,	PUNCT
ejpam-5969	240	3	j	j	PROPN
ejpam-5969	240	4	⊆	⊆	NUM
ejpam-5969	240	5	gc	gc	AUX
ejpam-5969	240	6	.	.	PROPN
ejpam-5969	240	7	given	give	VERB
ejpam-5969	240	8	(	(	PUNCT
ejpam-5969	240	9	1	1	NUM
ejpam-5969	240	10	)	)	PUNCT
ejpam-5969	240	11	,	,	PUNCT
ejpam-5969	240	12	clϵ(j	clϵ(j	PROPN
ejpam-5969	240	13	)	)	PUNCT
ejpam-5969	240	14	⊆	⊆	NUM
ejpam-5969	240	15	gc	gc	PROPN
ejpam-5969	240	16	and	and	CCONJ
ejpam-5969	240	17	u	u	PROPN
ejpam-5969	240	18	̸∈	̸∈	PROPN
ejpam-5969	240	19	gc	gc	PROPN
ejpam-5969	240	20	.	.	PROPN
ejpam-5969	241	1	therefore	therefore	ADV
ejpam-5969	241	2	,	,	PUNCT
ejpam-5969	241	3	u	u	PROPN
ejpam-5969	241	4	̸∈	̸∈	PROPN
ejpam-5969	241	5	clϵ(j	clϵ(j	PROPN
ejpam-5969	241	6	)	)	PUNCT
ejpam-5969	241	7	,	,	PUNCT
ejpam-5969	241	8	which	which	PRON
ejpam-5969	241	9	is	be	AUX
ejpam-5969	241	10	a	a	DET
ejpam-5969	241	11	contradiction	contradiction	NOUN
ejpam-5969	241	12	.	.	PUNCT
ejpam-5969	242	1	”	"	PUNCT
ejpam-5969	242	2	sufficient	sufficient	ADJ
ejpam-5969	242	3	”	"	PUNCT
ejpam-5969	242	4	assume	assume	VERB
ejpam-5969	242	5	contrary	contrary	ADJ
ejpam-5969	242	6	that	that	SCONJ
ejpam-5969	242	7	,	,	PUNCT
ejpam-5969	242	8	u	u	PROPN
ejpam-5969	242	9	̸∈	̸∈	PROPN
ejpam-5969	242	10	clϵ(j	clϵ(j	PROPN
ejpam-5969	242	11	)	)	PUNCT
ejpam-5969	242	12	,	,	PUNCT
ejpam-5969	242	13	then	then	ADV
ejpam-5969	242	14	there	there	PRON
ejpam-5969	242	15	is	be	VERB
ejpam-5969	242	16	v	v	ADP
ejpam-5969	242	17	∈	∈	NOUN
ejpam-5969	242	18	scϵ(χ	scϵ(χ	X
ejpam-5969	242	19	)	)	PUNCT
ejpam-5969	243	1	such	such	ADJ
ejpam-5969	243	2	that	that	SCONJ
ejpam-5969	243	3	u	u	PROPN
ejpam-5969	243	4	̸∈	̸∈	PROPN
ejpam-5969	243	5	v	v	PROPN
ejpam-5969	243	6	and	and	CCONJ
ejpam-5969	243	7	j	j	PROPN
ejpam-5969	243	8	⊆	⊆	NUM
ejpam-5969	243	9	v	v	NOUN
ejpam-5969	243	10	,	,	PUNCT
ejpam-5969	243	11	and	and	CCONJ
ejpam-5969	243	12	so	so	ADV
ejpam-5969	243	13	u	u	PROPN
ejpam-5969	243	14	∈	∈	PROPN
ejpam-5969	243	15	v	v	ADP
ejpam-5969	243	16	c	c	NOUN
ejpam-5969	243	17	and	and	CCONJ
ejpam-5969	243	18	v	v	NOUN
ejpam-5969	243	19	c	c	NOUN
ejpam-5969	243	20	∩	∩	PROPN
ejpam-5969	243	21	j	j	PROPN
ejpam-5969	243	22	=	=	SYM
ejpam-5969	243	23	∅	∅	NOUN
ejpam-5969	243	24	,	,	PUNCT
ejpam-5969	243	25	where	where	SCONJ
ejpam-5969	243	26	v	v	NOUN
ejpam-5969	243	27	c	c	PROPN
ejpam-5969	243	28	∈	∈	PROPN
ejpam-5969	243	29	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	243	30	)	)	PUNCT
ejpam-5969	243	31	,	,	PUNCT
ejpam-5969	243	32	which	which	PRON
ejpam-5969	243	33	is	be	AUX
ejpam-5969	243	34	a	a	DET
ejpam-5969	243	35	contradiction	contradiction	NOUN
ejpam-5969	243	36	.	.	PUNCT
ejpam-5969	244	1	(	(	PUNCT
ejpam-5969	244	2	3	3	X
ejpam-5969	244	3	)	)	PUNCT
ejpam-5969	244	4	assume	assume	VERB
ejpam-5969	244	5	that	that	SCONJ
ejpam-5969	244	6	u	u	PROPN
ejpam-5969	244	7	̸∈	̸∈	PROPN
ejpam-5969	244	8	cl(j	cl(j	NOUN
ejpam-5969	244	9	)	)	PUNCT
ejpam-5969	244	10	.	.	PUNCT
ejpam-5969	245	1	then	then	ADV
ejpam-5969	245	2	,	,	PUNCT
ejpam-5969	245	3	j	j	PROPN
ejpam-5969	245	4	∩	∩	PROPN
ejpam-5969	245	5	g	g	NOUN
ejpam-5969	245	6	=	=	NOUN
ejpam-5969	245	7	∅	∅	NOUN
ejpam-5969	245	8	,	,	PUNCT
ejpam-5969	245	9	for	for	ADP
ejpam-5969	245	10	some	some	DET
ejpam-5969	245	11	gu	gu	NOUN
ejpam-5969	245	12	∈	∈	PROPN
ejpam-5969	245	13	ν	ν	NOUN
ejpam-5969	245	14	.	.	PUNCT
ejpam-5969	245	15	hence	hence	ADV
ejpam-5969	245	16	,	,	PUNCT
ejpam-5969	245	17	j	j	PROPN
ejpam-5969	245	18	∩	∩	PROPN
ejpam-5969	245	19	g	g	NOUN
ejpam-5969	245	20	=	=	NOUN
ejpam-5969	245	21	∅	∅	NOUN
ejpam-5969	245	22	,	,	PUNCT
ejpam-5969	245	23	for	for	ADP
ejpam-5969	245	24	some	some	DET
ejpam-5969	245	25	gu	gu	NOUN
ejpam-5969	245	26	∈	∈	PROPN
ejpam-5969	245	27	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	245	28	)	)	PUNCT
ejpam-5969	245	29	.	.	PUNCT
ejpam-5969	246	1	given	give	VERB
ejpam-5969	246	2	(	(	PUNCT
ejpam-5969	246	3	2	2	NUM
ejpam-5969	246	4	)	)	PUNCT
ejpam-5969	246	5	,	,	PUNCT
ejpam-5969	246	6	u	u	PROPN
ejpam-5969	246	7	̸∈	̸∈	PROPN
ejpam-5969	246	8	clϵ(j	clϵ(j	PROPN
ejpam-5969	246	9	)	)	PUNCT
ejpam-5969	246	10	.	.	PUNCT
ejpam-5969	247	1	theorem	theorem	VERB
ejpam-5969	247	2	8	8	NUM
ejpam-5969	247	3	.	.	PUNCT
ejpam-5969	248	1	for	for	ADP
ejpam-5969	248	2	the	the	DET
ejpam-5969	248	3	supra	supra	PROPN
ejpam-5969	248	4	ϵ-closure	ϵ-closure	PROPN
ejpam-5969	248	5	operator	operator	NOUN
ejpam-5969	248	6	clϵ	clϵ	VERB
ejpam-5969	248	7	:	:	PUNCT
ejpam-5969	248	8	p	p	X
ejpam-5969	248	9	(	(	PUNCT
ejpam-5969	248	10	χ	χ	X
ejpam-5969	248	11	)	)	PUNCT
ejpam-5969	248	12	−→	−→	NOUN
ejpam-5969	248	13	p	p	X
ejpam-5969	248	14	(	(	PUNCT
ejpam-5969	248	15	χ	χ	NOUN
ejpam-5969	248	16	)	)	PUNCT
ejpam-5969	248	17	and	and	CCONJ
ejpam-5969	248	18	e	e	X
ejpam-5969	248	19	∈	∈	PROPN
ejpam-5969	248	20	p	p	X
ejpam-5969	248	21	(	(	PUNCT
ejpam-5969	248	22	χ	χ	NOUN
ejpam-5969	248	23	)	)	PUNCT
ejpam-5969	248	24	,	,	PUNCT
ejpam-5969	248	25	we	we	PRON
ejpam-5969	248	26	have	have	VERB
ejpam-5969	248	27	clϵ(e	clϵ(e	PROPN
ejpam-5969	248	28	)	)	PUNCT
ejpam-5969	248	29	=	=	PUNCT
ejpam-5969	248	30			PUNCT
ejpam-5969	248	31	χ	χ	NOUN
ejpam-5969	248	32	,	,	PUNCT
ejpam-5969	248	33	ec	ec	PROPN
ejpam-5969	248	34	∈	∈	PROPN
ejpam-5969	248	35	snd(χ	snd(χ	PROPN
ejpam-5969	248	36	)	)	PUNCT
ejpam-5969	248	37	and	and	CCONJ
ejpam-5969	248	38	b(ec	b(ec	PROPN
ejpam-5969	248	39	)	)	PUNCT
ejpam-5969	248	40	is	be	AUX
ejpam-5969	248	41	finite	finite	ADJ
ejpam-5969	248	42	.	.	PUNCT
ejpam-5969	249	1	e	e	X
ejpam-5969	249	2	,	,	PUNCT
ejpam-5969	249	3	ec	ec	PROPN
ejpam-5969	249	4	∈	∈	PROPN
ejpam-5969	249	5	snd(χ	snd(χ	PROPN
ejpam-5969	249	6	)	)	PUNCT
ejpam-5969	249	7	and	and	CCONJ
ejpam-5969	249	8	b(ec	b(ec	PROPN
ejpam-5969	249	9	)	)	PUNCT
ejpam-5969	249	10	is	be	AUX
ejpam-5969	249	11	infinite	infinite	ADJ
ejpam-5969	249	12	.	.	PUNCT
ejpam-5969	250	1	e	e	X
ejpam-5969	250	2	,	,	PUNCT
ejpam-5969	250	3	ec	ec	PROPN
ejpam-5969	250	4	∈	∈	PROPN
ejpam-5969	250	5	sro(χ	sro(χ	PROPN
ejpam-5969	250	6	)	)	PUNCT
ejpam-5969	250	7	.	.	PUNCT
ejpam-5969	251	1	proof	proof	NOUN
ejpam-5969	251	2	.	.	PUNCT
ejpam-5969	252	1	much	much	ADV
ejpam-5969	252	2	like	like	ADP
ejpam-5969	252	3	the	the	DET
ejpam-5969	252	4	proof	proof	NOUN
ejpam-5969	252	5	of	of	ADP
ejpam-5969	252	6	theorem	theorem	ADJ
ejpam-5969	252	7	4	4	NUM
ejpam-5969	252	8	.	.	X
ejpam-5969	252	9	abd	abd	PROPN
ejpam-5969	252	10	el	el	PROPN
ejpam-5969	252	11	-	-	PROPN
ejpam-5969	252	12	latif	latif	PROPN
ejpam-5969	252	13	et	et	PROPN
ejpam-5969	252	14	al	al	PROPN
ejpam-5969	252	15	.	.	PUNCT
ejpam-5969	252	16	/	/	SYM
ejpam-5969	252	17	eur	eur	PROPN
ejpam-5969	252	18	.	.	PUNCT
ejpam-5969	253	1	j.	j.	PROPN
ejpam-5969	253	2	pure	pure	PROPN
ejpam-5969	253	3	appl	appl	PROPN
ejpam-5969	253	4	.	.	PROPN
ejpam-5969	253	5	math	math	PROPN
ejpam-5969	253	6	,	,	PUNCT
ejpam-5969	253	7	18	18	NUM
ejpam-5969	253	8	(	(	PUNCT
ejpam-5969	253	9	2	2	NUM
ejpam-5969	253	10	)	)	PUNCT
ejpam-5969	253	11	(	(	PUNCT
ejpam-5969	253	12	2025	2025	NUM
ejpam-5969	253	13	)	)	PUNCT
ejpam-5969	253	14	,	,	PUNCT
ejpam-5969	253	15	5969	5969	NUM
ejpam-5969	253	16	10	10	NUM
ejpam-5969	253	17	of	of	ADP
ejpam-5969	253	18	19	19	NUM
ejpam-5969	253	19	the	the	DET
ejpam-5969	253	20	relationship	relationship	NOUN
ejpam-5969	253	21	between	between	ADP
ejpam-5969	253	22	the	the	DET
ejpam-5969	253	23	supra	supra	PROPN
ejpam-5969	253	24	ϵ-closure	ϵ-closure	NOUN
ejpam-5969	253	25	operator	operator	NOUN
ejpam-5969	253	26	and	and	CCONJ
ejpam-5969	253	27	the	the	DET
ejpam-5969	253	28	supra	supra	PROPN
ejpam-5969	253	29	ϵ-closure	ϵ-closure	PROPN
ejpam-5969	253	30	operator	operator	NOUN
ejpam-5969	253	31	is	be	AUX
ejpam-5969	253	32	examined	examine	VERB
ejpam-5969	253	33	in	in	ADP
ejpam-5969	253	34	the	the	DET
ejpam-5969	253	35	forthcoming	forthcoming	ADJ
ejpam-5969	253	36	theorem	theorem	NOUN
ejpam-5969	253	37	.	.	PUNCT
ejpam-5969	253	38	theorem	theorem	NOUN
ejpam-5969	253	39	9	9	NUM
ejpam-5969	253	40	.	.	PUNCT
ejpam-5969	253	41	regarding	regard	VERB
ejpam-5969	253	42	a	a	DET
ejpam-5969	253	43	subset	subset	ADJ
ejpam-5969	253	44	t	t	NOUN
ejpam-5969	253	45	of	of	ADP
ejpam-5969	253	46	an	an	DET
ejpam-5969	253	47	sts	st	NOUN
ejpam-5969	253	48	(	(	PUNCT
ejpam-5969	253	49	χ	χ	NOUN
ejpam-5969	253	50	,	,	PUNCT
ejpam-5969	253	51	ν	ν	NOUN
ejpam-5969	253	52	)	)	PUNCT
ejpam-5969	253	53	,	,	PUNCT
ejpam-5969	253	54	we	we	PRON
ejpam-5969	253	55	have	have	VERB
ejpam-5969	253	56	(	(	PUNCT
ejpam-5969	253	57	1	1	X
ejpam-5969	253	58	)	)	PUNCT
ejpam-5969	253	59	clϵ(t	clϵ(t	PROPN
ejpam-5969	253	60	c	c	NOUN
ejpam-5969	253	61	)	)	PUNCT
ejpam-5969	253	62	=	=	PUNCT
ejpam-5969	254	1	[	[	X
ejpam-5969	254	2	intϵ(t	intϵ(t	NOUN
ejpam-5969	254	3	)	)	PUNCT
ejpam-5969	254	4	]	]	PUNCT
ejpam-5969	255	1	c.	c.	PROPN
ejpam-5969	255	2	(	(	PUNCT
ejpam-5969	255	3	2	2	X
ejpam-5969	255	4	)	)	PUNCT
ejpam-5969	255	5	intϵ(t	intϵ(t	NOUN
ejpam-5969	255	6	c	c	NOUN
ejpam-5969	255	7	)	)	PUNCT
ejpam-5969	255	8	=	=	PUNCT
ejpam-5969	256	1	[	[	X
ejpam-5969	256	2	clϵ(t	clϵ(t	NOUN
ejpam-5969	256	3	)	)	PUNCT
ejpam-5969	256	4	]	]	PUNCT
ejpam-5969	257	1	c.	c.	PROPN
ejpam-5969	257	2	proof	proof	NOUN
ejpam-5969	257	3	.	.	PUNCT
ejpam-5969	258	1	(	(	PUNCT
ejpam-5969	258	2	1	1	X
ejpam-5969	258	3	)	)	PUNCT
ejpam-5969	258	4	suppose	suppose	VERB
ejpam-5969	258	5	that	that	SCONJ
ejpam-5969	258	6	u	u	PRON
ejpam-5969	258	7	̸∈	̸∈	PROPN
ejpam-5969	258	8	[	[	X
ejpam-5969	258	9	intϵ(t	intϵ(t	NOUN
ejpam-5969	258	10	)	)	PUNCT
ejpam-5969	258	11	]	]	PUNCT
ejpam-5969	258	12	c.	c.	PROPN
ejpam-5969	258	13	then	then	ADV
ejpam-5969	258	14	,	,	PUNCT
ejpam-5969	258	15	u	u	PROPN
ejpam-5969	258	16	∈	∈	PROPN
ejpam-5969	258	17	intϵ(t	intϵ(t	NOUN
ejpam-5969	258	18	)	)	PUNCT
ejpam-5969	258	19	.	.	PUNCT
ejpam-5969	259	1	this	this	PRON
ejpam-5969	259	2	implies	imply	VERB
ejpam-5969	259	3	that	that	SCONJ
ejpam-5969	259	4	,	,	PUNCT
ejpam-5969	259	5	∃	∃	PROPN
ejpam-5969	259	6	g	g	PROPN
ejpam-5969	259	7	∈	∈	PROPN
ejpam-5969	259	8	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	259	9	)	)	PUNCT
ejpam-5969	259	10	such	such	ADJ
ejpam-5969	259	11	that	that	SCONJ
ejpam-5969	259	12	u	u	PROPN
ejpam-5969	259	13	∈	∈	PROPN
ejpam-5969	259	14	g	g	PROPN
ejpam-5969	259	15	⊆	⊆	NUM
ejpam-5969	259	16	t	t	NOUN
ejpam-5969	259	17	,	,	PUNCT
ejpam-5969	259	18	given	give	VERB
ejpam-5969	259	19	lemma	lemma	PROPN
ejpam-5969	259	20	1	1	NUM
ejpam-5969	259	21	,	,	PUNCT
ejpam-5969	259	22	which	which	PRON
ejpam-5969	259	23	follows	follow	VERB
ejpam-5969	259	24	t	t	PROPN
ejpam-5969	259	25	c	c	NOUN
ejpam-5969	259	26	∩g	∩g	NOUN
ejpam-5969	260	1	=	=	PUNCT
ejpam-5969	260	2	∅.	∅.	VERB
ejpam-5969	260	3	hence	hence	ADV
ejpam-5969	260	4	,	,	PUNCT
ejpam-5969	260	5	u	u	PROPN
ejpam-5969	260	6	̸∈	̸∈	PROPN
ejpam-5969	260	7	clϵ(t	clϵ(t	PROPN
ejpam-5969	260	8	c	c	PROPN
ejpam-5969	260	9	)	)	PUNCT
ejpam-5969	260	10	from	from	ADP
ejpam-5969	260	11	theorem	theorem	ADJ
ejpam-5969	260	12	7	7	NUM
ejpam-5969	260	13	(	(	PUNCT
ejpam-5969	260	14	2	2	NUM
ejpam-5969	260	15	)	)	PUNCT
ejpam-5969	260	16	.	.	PUNCT
ejpam-5969	261	1	thus	thus	ADV
ejpam-5969	261	2	,	,	PUNCT
ejpam-5969	261	3	clϵ(t	clϵ(t	PROPN
ejpam-5969	261	4	c	c	NOUN
ejpam-5969	261	5	)	)	PUNCT
ejpam-5969	261	6	⊆	⊆	NUM
ejpam-5969	262	1	[	[	X
ejpam-5969	262	2	intϵ(t	intϵ(t	NOUN
ejpam-5969	262	3	)	)	PUNCT
ejpam-5969	262	4	]	]	PUNCT
ejpam-5969	263	1	c	c	X
ejpam-5969	263	2	(	(	PUNCT
ejpam-5969	263	3	3	3	NUM
ejpam-5969	263	4	)	)	PUNCT
ejpam-5969	263	5	now	now	ADV
ejpam-5969	263	6	,	,	PUNCT
ejpam-5969	263	7	assume	assume	VERB
ejpam-5969	263	8	that	that	SCONJ
ejpam-5969	263	9	u	u	PROPN
ejpam-5969	263	10	̸∈	̸∈	PROPN
ejpam-5969	263	11	clϵ(t	clϵ(t	PROPN
ejpam-5969	263	12	c	c	PROPN
ejpam-5969	263	13	)	)	PUNCT
ejpam-5969	263	14	.	.	PUNCT
ejpam-5969	264	1	given	give	VERB
ejpam-5969	264	2	theorem	theorem	VERB
ejpam-5969	264	3	7	7	NUM
ejpam-5969	264	4	(	(	PUNCT
ejpam-5969	264	5	2	2	NUM
ejpam-5969	264	6	)	)	PUNCT
ejpam-5969	264	7	,	,	PUNCT
ejpam-5969	264	8	there	there	PRON
ejpam-5969	264	9	is	be	VERB
ejpam-5969	264	10	gu	gu	PRON
ejpam-5969	264	11	∈	∈	PROPN
ejpam-5969	264	12	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	264	13	)	)	PUNCT
ejpam-5969	264	14	such	such	ADJ
ejpam-5969	264	15	that	that	SCONJ
ejpam-5969	264	16	t	t	NOUN
ejpam-5969	264	17	c	c	NOUN
ejpam-5969	264	18	∩g	∩g	NOUN
ejpam-5969	265	1	=	=	PUNCT
ejpam-5969	266	1	∅	∅	NOUN
ejpam-5969	266	2	that	that	PRON
ejpam-5969	266	3	means	mean	VERB
ejpam-5969	266	4	,	,	PUNCT
ejpam-5969	266	5	u	u	PROPN
ejpam-5969	266	6	∈	∈	PROPN
ejpam-5969	266	7	g	g	PROPN
ejpam-5969	266	8	⊆	⊆	NUM
ejpam-5969	266	9	t	t	NOUN
ejpam-5969	266	10	given	give	VERB
ejpam-5969	266	11	lemma	lemma	PROPN
ejpam-5969	266	12	1	1	NUM
ejpam-5969	266	13	,	,	PUNCT
ejpam-5969	266	14	u	u	PROPN
ejpam-5969	266	15	∈	∈	PROPN
ejpam-5969	266	16	intϵ(t	intϵ(t	NOUN
ejpam-5969	266	17	)	)	PUNCT
ejpam-5969	266	18	,	,	PUNCT
ejpam-5969	266	19	and	and	CCONJ
ejpam-5969	266	20	so	so	ADV
ejpam-5969	266	21	u	u	X
ejpam-5969	266	22	̸∈	̸∈	PROPN
ejpam-5969	266	23	[	[	X
ejpam-5969	266	24	intϵ(t	intϵ(t	NOUN
ejpam-5969	266	25	)	)	PUNCT
ejpam-5969	266	26	]	]	PUNCT
ejpam-5969	267	1	c	c	X
ejpam-5969	267	2	therefore	therefore	ADV
ejpam-5969	267	3	,	,	PUNCT
ejpam-5969	267	4	[	[	X
ejpam-5969	267	5	intϵ(t	intϵ(t	NOUN
ejpam-5969	267	6	)	)	PUNCT
ejpam-5969	267	7	]	]	PUNCT
ejpam-5969	267	8	c	c	PROPN
ejpam-5969	267	9	⊆	⊆	NUM
ejpam-5969	267	10	clϵ(t	clϵ(t	PROPN
ejpam-5969	267	11	c	c	NOUN
ejpam-5969	267	12	)	)	PUNCT
ejpam-5969	267	13	(	(	PUNCT
ejpam-5969	267	14	4	4	NUM
ejpam-5969	267	15	)	)	PUNCT
ejpam-5969	267	16	from	from	ADP
ejpam-5969	267	17	eqs	eqs	X
ejpam-5969	267	18	(	(	PUNCT
ejpam-5969	267	19	3	3	NUM
ejpam-5969	267	20	)	)	PUNCT
ejpam-5969	267	21	and	and	CCONJ
ejpam-5969	267	22	(	(	PUNCT
ejpam-5969	267	23	4	4	NUM
ejpam-5969	267	24	)	)	PUNCT
ejpam-5969	267	25	,	,	PUNCT
ejpam-5969	267	26	clϵ(t	clϵ(t	PROPN
ejpam-5969	267	27	c	c	NOUN
ejpam-5969	267	28	)	)	PUNCT
ejpam-5969	267	29	=	=	PUNCT
ejpam-5969	268	1	[	[	X
ejpam-5969	268	2	intϵ(t	intϵ(t	NOUN
ejpam-5969	268	3	)	)	PUNCT
ejpam-5969	268	4	]	]	PUNCT
ejpam-5969	269	1	c.	c.	PROPN
ejpam-5969	269	2	(	(	PUNCT
ejpam-5969	269	3	2	2	NUM
ejpam-5969	269	4	)	)	PUNCT
ejpam-5969	269	5	through	through	ADP
ejpam-5969	269	6	a	a	DET
ejpam-5969	269	7	method	method	NOUN
ejpam-5969	269	8	akin	akin	ADJ
ejpam-5969	269	9	to	to	ADP
ejpam-5969	269	10	(	(	PUNCT
ejpam-5969	269	11	1	1	NUM
ejpam-5969	269	12	)	)	PUNCT
ejpam-5969	269	13	.	.	PUNCT
ejpam-5969	270	1	proposition	proposition	NOUN
ejpam-5969	270	2	4	4	NUM
ejpam-5969	270	3	.	.	PUNCT
ejpam-5969	271	1	regarding	regard	VERB
ejpam-5969	271	2	subsets	subsets	PROPN
ejpam-5969	271	3	j	j	PROPN
ejpam-5969	271	4	and	and	CCONJ
ejpam-5969	271	5	i	i	PRON
ejpam-5969	271	6	of	of	ADP
ejpam-5969	271	7	an	an	DET
ejpam-5969	271	8	sts	st	NOUN
ejpam-5969	271	9	(	(	PUNCT
ejpam-5969	271	10	χ	χ	NOUN
ejpam-5969	271	11	,	,	PUNCT
ejpam-5969	271	12	ν	ν	NOUN
ejpam-5969	271	13	)	)	PUNCT
ejpam-5969	271	14	.	.	PUNCT
ejpam-5969	272	1	then	then	ADV
ejpam-5969	272	2	,	,	PUNCT
ejpam-5969	272	3	abd	abd	PROPN
ejpam-5969	272	4	el	el	PROPN
ejpam-5969	272	5	-	-	PROPN
ejpam-5969	272	6	latif	latif	PROPN
ejpam-5969	272	7	et	et	PROPN
ejpam-5969	272	8	al	al	PROPN
ejpam-5969	272	9	.	.	PUNCT
ejpam-5969	272	10	/	/	SYM
ejpam-5969	272	11	eur	eur	PROPN
ejpam-5969	272	12	.	.	PUNCT
ejpam-5969	273	1	j.	j.	PROPN
ejpam-5969	273	2	pure	pure	PROPN
ejpam-5969	273	3	appl	appl	PROPN
ejpam-5969	273	4	.	.	PROPN
ejpam-5969	273	5	math	math	PROPN
ejpam-5969	273	6	,	,	PUNCT
ejpam-5969	273	7	18	18	NUM
ejpam-5969	273	8	(	(	PUNCT
ejpam-5969	273	9	2	2	NUM
ejpam-5969	273	10	)	)	PUNCT
ejpam-5969	273	11	(	(	PUNCT
ejpam-5969	273	12	2025	2025	NUM
ejpam-5969	273	13	)	)	PUNCT
ejpam-5969	273	14	,	,	PUNCT
ejpam-5969	273	15	5969	5969	NUM
ejpam-5969	273	16	11	11	NUM
ejpam-5969	273	17	of	of	ADP
ejpam-5969	273	18	19	19	NUM
ejpam-5969	273	19	(	(	PUNCT
ejpam-5969	273	20	1	1	NUM
ejpam-5969	273	21	)	)	PUNCT
ejpam-5969	273	22	clϵ(∅	clϵ(∅	NOUN
ejpam-5969	273	23	)	)	PUNCT
ejpam-5969	273	24	=	=	SYM
ejpam-5969	273	25	∅	∅	NOUN
ejpam-5969	273	26	and	and	CCONJ
ejpam-5969	273	27	clϵ(χ	clϵ(χ	NOUN
ejpam-5969	273	28	)	)	PUNCT
ejpam-5969	273	29	=	=	SYM
ejpam-5969	274	1	χ	χ	X
ejpam-5969	274	2	.	.	PUNCT
ejpam-5969	275	1	(	(	PUNCT
ejpam-5969	275	2	2	2	X
ejpam-5969	275	3	)	)	PUNCT
ejpam-5969	275	4	j	j	NOUN
ejpam-5969	275	5	⊆	⊆	NUM
ejpam-5969	275	6	clϵ(j	clϵ(j	PROPN
ejpam-5969	275	7	)	)	PUNCT
ejpam-5969	275	8	.	.	PUNCT
ejpam-5969	276	1	(	(	PUNCT
ejpam-5969	276	2	3	3	X
ejpam-5969	276	3	)	)	PUNCT
ejpam-5969	276	4	clϵ(clϵ(j	clϵ(clϵ(j	NOUN
ejpam-5969	276	5	)	)	PUNCT
ejpam-5969	276	6	)	)	PUNCT
ejpam-5969	277	1	=	=	PUNCT
ejpam-5969	277	2	clϵ(j	clϵ(j	PROPN
ejpam-5969	277	3	)	)	PUNCT
ejpam-5969	277	4	.	.	PUNCT
ejpam-5969	278	1	(	(	PUNCT
ejpam-5969	278	2	4	4	X
ejpam-5969	278	3	)	)	PUNCT
ejpam-5969	278	4	if	if	SCONJ
ejpam-5969	278	5	j	j	PROPN
ejpam-5969	278	6	⊆	⊆	NUM
ejpam-5969	278	7	(	(	PUNCT
ejpam-5969	278	8	i	i	NOUN
ejpam-5969	278	9	)	)	PUNCT
ejpam-5969	278	10	,	,	PUNCT
ejpam-5969	278	11	then	then	ADV
ejpam-5969	278	12	clϵ(j	clϵ(j	PROPN
ejpam-5969	278	13	)	)	PUNCT
ejpam-5969	278	14	⊆	⊆	NUM
ejpam-5969	278	15	clϵ(i	clϵ(i	NOUN
ejpam-5969	278	16	)	)	PUNCT
ejpam-5969	278	17	.	.	PUNCT
ejpam-5969	279	1	(	(	PUNCT
ejpam-5969	279	2	5	5	X
ejpam-5969	279	3	)	)	PUNCT
ejpam-5969	279	4	clϵ(j	clϵ(j	NOUN
ejpam-5969	279	5	∩	∩	X
ejpam-5969	279	6	i	i	NOUN
ejpam-5969	279	7	)	)	PUNCT
ejpam-5969	279	8	⊆	⊆	NUM
ejpam-5969	279	9	clϵ(j	clϵ(j	PROPN
ejpam-5969	279	10	)	)	PUNCT
ejpam-5969	279	11	∩	∩	NOUN
ejpam-5969	279	12	clϵ(i	clϵ(i	NOUN
ejpam-5969	279	13	)	)	PUNCT
ejpam-5969	279	14	.	.	PUNCT
ejpam-5969	280	1	(	(	PUNCT
ejpam-5969	280	2	6	6	X
ejpam-5969	280	3	)	)	PUNCT
ejpam-5969	280	4	clϵ(j	clϵ(j	PROPN
ejpam-5969	280	5	)	)	PUNCT
ejpam-5969	280	6	∪	∪	ADP
ejpam-5969	280	7	clϵ(i	clϵ(i	NOUN
ejpam-5969	280	8	)	)	PUNCT
ejpam-5969	281	1	⊆	⊆	NUM
ejpam-5969	281	2	clϵ(j	clϵ(j	PROPN
ejpam-5969	281	3	∪	∪	PROPN
ejpam-5969	281	4	i	i	PROPN
ejpam-5969	281	5	)	)	PUNCT
ejpam-5969	281	6	.	.	PUNCT
ejpam-5969	282	1	proof	proof	NOUN
ejpam-5969	282	2	.	.	PUNCT
ejpam-5969	283	1	straightforward	straightforward	ADJ
ejpam-5969	283	2	.	.	PUNCT
ejpam-5969	284	1	remark	remark	PROPN
ejpam-5969	284	2	7	7	NUM
ejpam-5969	284	3	.	.	PUNCT
ejpam-5969	285	1	the	the	DET
ejpam-5969	285	2	inclusions	inclusion	NOUN
ejpam-5969	285	3	of	of	ADP
ejpam-5969	285	4	part	part	NOUN
ejpam-5969	285	5	(	(	PUNCT
ejpam-5969	285	6	3	3	NUM
ejpam-5969	285	7	)	)	PUNCT
ejpam-5969	285	8	in	in	ADP
ejpam-5969	285	9	theorem	theorem	ADJ
ejpam-5969	285	10	7	7	NUM
ejpam-5969	285	11	and	and	CCONJ
ejpam-5969	285	12	parts	part	NOUN
ejpam-5969	285	13	(	(	PUNCT
ejpam-5969	285	14	2	2	NUM
ejpam-5969	285	15	)	)	PUNCT
ejpam-5969	285	16	,	,	PUNCT
ejpam-5969	285	17	(	(	PUNCT
ejpam-5969	285	18	4	4	NUM
ejpam-5969	285	19	)	)	PUNCT
ejpam-5969	285	20	,	,	PUNCT
ejpam-5969	285	21	(	(	PUNCT
ejpam-5969	285	22	5	5	NUM
ejpam-5969	285	23	)	)	PUNCT
ejpam-5969	285	24	and	and	CCONJ
ejpam-5969	285	25	(	(	PUNCT
ejpam-5969	285	26	6	6	NUM
ejpam-5969	285	27	)	)	PUNCT
ejpam-5969	285	28	in	in	ADP
ejpam-5969	285	29	proposition	proposition	NOUN
ejpam-5969	285	30	4	4	NUM
ejpam-5969	285	31	are	be	AUX
ejpam-5969	285	32	proper	proper	ADJ
ejpam-5969	285	33	as	as	SCONJ
ejpam-5969	285	34	the	the	DET
ejpam-5969	285	35	upcoming	upcoming	ADJ
ejpam-5969	285	36	examples	example	NOUN
ejpam-5969	285	37	will	will	AUX
ejpam-5969	285	38	demonstrate	demonstrate	VERB
ejpam-5969	285	39	.	.	PUNCT
ejpam-5969	286	1	examples	example	NOUN
ejpam-5969	286	2	2	2	X
ejpam-5969	286	3	.	.	PUNCT
ejpam-5969	287	1	let	let	VERB
ejpam-5969	287	2	ν	ν	NOUN
ejpam-5969	287	3	=	=	PRON
ejpam-5969	287	4	{	{	PUNCT
ejpam-5969	287	5	χ	χ	NOUN
ejpam-5969	287	6	,	,	PUNCT
ejpam-5969	287	7	∅	∅	NOUN
ejpam-5969	287	8	,	,	PUNCT
ejpam-5969	287	9	{	{	PUNCT
ejpam-5969	287	10	2	2	NUM
ejpam-5969	287	11	,	,	PUNCT
ejpam-5969	287	12	3	3	NUM
ejpam-5969	287	13	}	}	PUNCT
ejpam-5969	287	14	,	,	PUNCT
ejpam-5969	287	15	{	{	PUNCT
ejpam-5969	287	16	1	1	NUM
ejpam-5969	287	17	,	,	PUNCT
ejpam-5969	287	18	3	3	NUM
ejpam-5969	287	19	}	}	PUNCT
ejpam-5969	287	20	}	}	PUNCT
ejpam-5969	287	21	be	be	AUX
ejpam-5969	287	22	an	an	DET
ejpam-5969	287	23	sts	st	NOUN
ejpam-5969	287	24	on	on	ADP
ejpam-5969	287	25	χ	χ	X
ejpam-5969	287	26	=	=	PUNCT
ejpam-5969	287	27	{	{	PUNCT
ejpam-5969	287	28	1	1	NUM
ejpam-5969	287	29	,	,	PUNCT
ejpam-5969	287	30	2	2	NUM
ejpam-5969	287	31	,	,	PUNCT
ejpam-5969	287	32	3	3	NUM
ejpam-5969	287	33	}	}	PUNCT
ejpam-5969	287	34	.	.	PUNCT
ejpam-5969	288	1	consider	consider	VERB
ejpam-5969	288	2	the	the	DET
ejpam-5969	288	3	sets	set	NOUN
ejpam-5969	288	4	a	a	PRON
ejpam-5969	288	5	=	=	SYM
ejpam-5969	288	6	{	{	PUNCT
ejpam-5969	288	7	1	1	NUM
ejpam-5969	288	8	,	,	PUNCT
ejpam-5969	288	9	3	3	NUM
ejpam-5969	288	10	}	}	PUNCT
ejpam-5969	288	11	,	,	PUNCT
ejpam-5969	288	12	c	c	X
ejpam-5969	288	13	=	=	PUNCT
ejpam-5969	288	14	{	{	PUNCT
ejpam-5969	288	15	2	2	NUM
ejpam-5969	288	16	}	}	PUNCT
ejpam-5969	288	17	,	,	PUNCT
ejpam-5969	288	18	d	d	PROPN
ejpam-5969	288	19	=	=	PUNCT
ejpam-5969	288	20	{	{	PUNCT
ejpam-5969	288	21	3	3	NUM
ejpam-5969	288	22	}	}	PUNCT
ejpam-5969	288	23	and	and	CCONJ
ejpam-5969	288	24	e	e	NOUN
ejpam-5969	288	25	=	=	PUNCT
ejpam-5969	288	26	{	{	PUNCT
ejpam-5969	288	27	2	2	NUM
ejpam-5969	288	28	,	,	PUNCT
ejpam-5969	288	29	3	3	NUM
ejpam-5969	288	30	}	}	PUNCT
ejpam-5969	288	31	.	.	PUNCT
ejpam-5969	289	1	we	we	PRON
ejpam-5969	289	2	have	have	VERB
ejpam-5969	289	3	(	(	PUNCT
ejpam-5969	289	4	1	1	NUM
ejpam-5969	289	5	)	)	PUNCT
ejpam-5969	289	6	cl(d	cl(d	NUM
ejpam-5969	289	7	)	)	PUNCT
ejpam-5969	290	1	=	=	PUNCT
ejpam-5969	290	2	χ	χ	PRON
ejpam-5969	290	3	⊈	⊈	PROPN
ejpam-5969	290	4	clϵ(d	clϵ(d	PROPN
ejpam-5969	290	5	)	)	PUNCT
ejpam-5969	290	6	=	=	SYM
ejpam-5969	290	7	d.	d.	NOUN
ejpam-5969	290	8	(	(	PUNCT
ejpam-5969	290	9	2	2	NUM
ejpam-5969	290	10	)	)	PUNCT
ejpam-5969	290	11	clϵ(e	clϵ(e	PROPN
ejpam-5969	290	12	)	)	PUNCT
ejpam-5969	290	13	=	=	PUNCT
ejpam-5969	291	1	χ	χ	PRON
ejpam-5969	291	2	⊈	⊈	PROPN
ejpam-5969	291	3	e.	e.	PROPN
ejpam-5969	291	4	(	(	PUNCT
ejpam-5969	291	5	3	3	NUM
ejpam-5969	291	6	)	)	PUNCT
ejpam-5969	291	7	e	e	X
ejpam-5969	291	8	⊈	⊈	PROPN
ejpam-5969	291	9	a	a	DET
ejpam-5969	291	10	whereas	whereas	NOUN
ejpam-5969	291	11	clϵ(e	clϵ(e	PROPN
ejpam-5969	291	12	)	)	PUNCT
ejpam-5969	291	13	=	=	PUNCT
ejpam-5969	291	14	χ	χ	PRON
ejpam-5969	291	15	⊆	⊆	NUM
ejpam-5969	291	16	clϵ(a	clϵ(a	NOUN
ejpam-5969	291	17	)	)	PUNCT
ejpam-5969	291	18	=	=	SYM
ejpam-5969	292	1	χ	χ	X
ejpam-5969	292	2	.	.	PUNCT
ejpam-5969	293	1	(	(	PUNCT
ejpam-5969	293	2	4	4	X
ejpam-5969	293	3	)	)	PUNCT
ejpam-5969	293	4	clϵ(a	clϵ(a	NOUN
ejpam-5969	293	5	)	)	PUNCT
ejpam-5969	293	6	∩	∩	NOUN
ejpam-5969	293	7	clϵ(e	clϵ(e	X
ejpam-5969	293	8	)	)	PUNCT
ejpam-5969	293	9	=	=	PUNCT
ejpam-5969	294	1	χ	χ	DET
ejpam-5969	294	2	⊈	⊈	PROPN
ejpam-5969	294	3	clϵ[a	clϵ[a	NOUN
ejpam-5969	294	4	∩	∩	NOUN
ejpam-5969	294	5	e	e	X
ejpam-5969	294	6	]	]	X
ejpam-5969	294	7	=	=	SYM
ejpam-5969	294	8	clϵ(d	clϵ(d	PROPN
ejpam-5969	294	9	)	)	PUNCT
ejpam-5969	294	10	=	=	SYM
ejpam-5969	294	11	d.	d.	NOUN
ejpam-5969	294	12	(	(	PUNCT
ejpam-5969	294	13	5	5	NUM
ejpam-5969	294	14	)	)	PUNCT
ejpam-5969	294	15	clϵ(c	clϵ(c	PROPN
ejpam-5969	294	16	∪d	∪d	NUM
ejpam-5969	294	17	)	)	PUNCT
ejpam-5969	294	18	=	=	SYM
ejpam-5969	294	19	clϵ(e	clϵ(e	PROPN
ejpam-5969	294	20	)	)	PUNCT
ejpam-5969	294	21	=	=	PUNCT
ejpam-5969	294	22	χ	χ	PRON
ejpam-5969	294	23	⊈	⊈	PROPN
ejpam-5969	294	24	clϵ(c	clϵ(c	PROPN
ejpam-5969	294	25	)	)	PUNCT
ejpam-5969	294	26	∪	∪	X
ejpam-5969	294	27	clϵ(d	clϵ(d	PROPN
ejpam-5969	294	28	)	)	PUNCT
ejpam-5969	294	29	=	=	SYM
ejpam-5969	294	30	e.	e.	PROPN
ejpam-5969	294	31	definition	definition	NOUN
ejpam-5969	294	32	9	9	NUM
ejpam-5969	294	33	.	.	PUNCT
ejpam-5969	294	34	given	give	VERB
ejpam-5969	294	35	a	a	DET
ejpam-5969	294	36	subset	subset	NOUN
ejpam-5969	294	37	t	t	NOUN
ejpam-5969	294	38	of	of	ADP
ejpam-5969	294	39	an	an	DET
ejpam-5969	294	40	sts	st	NOUN
ejpam-5969	294	41	(	(	PUNCT
ejpam-5969	294	42	χ	χ	NOUN
ejpam-5969	294	43	,	,	PUNCT
ejpam-5969	294	44	ν	ν	NOUN
ejpam-5969	294	45	)	)	PUNCT
ejpam-5969	294	46	with	with	ADP
ejpam-5969	294	47	arbitrary	arbitrary	ADJ
ejpam-5969	294	48	point	point	NOUN
ejpam-5969	294	49	s	s	VERB
ejpam-5969	294	50	∈	∈	NOUN
ejpam-5969	294	51	χ	χ	NOUN
ejpam-5969	294	52	.	.	PUNCT
ejpam-5969	295	1	then	then	ADV
ejpam-5969	295	2	,	,	PUNCT
ejpam-5969	295	3	s	s	AUX
ejpam-5969	295	4	called	call	VERB
ejpam-5969	295	5	a	a	DET
ejpam-5969	295	6	supra	supra	ADJ
ejpam-5969	295	7	ϵ-accumulation	ϵ-accumulation	PROPN
ejpam-5969	295	8	point	point	NOUN
ejpam-5969	295	9	of	of	ADP
ejpam-5969	295	10	t	t	PROPN
ejpam-5969	295	11	if	if	SCONJ
ejpam-5969	295	12	each	each	DET
ejpam-5969	295	13	supra	supra	PROPN
ejpam-5969	295	14	ϵ-open	ϵ-open	PROPN
ejpam-5969	295	15	set	set	PROPN
ejpam-5969	296	1	gs	gs	INTJ
ejpam-5969	296	2	,	,	PUNCT
ejpam-5969	296	3	we	we	PRON
ejpam-5969	296	4	have	have	VERB
ejpam-5969	296	5	[	[	X
ejpam-5969	296	6	t\{s	t\{s	X
ejpam-5969	296	7	}	}	PUNCT
ejpam-5969	296	8	]	]	PUNCT
ejpam-5969	296	9	∩g	∩g	PROPN
ejpam-5969	297	1	̸=	̸=	PROPN
ejpam-5969	297	2	∅.	∅.	ADP
ejpam-5969	297	3	the	the	DET
ejpam-5969	297	4	set	set	NOUN
ejpam-5969	297	5	of	of	ADP
ejpam-5969	297	6	all	all	DET
ejpam-5969	297	7	supra	supra	ADJ
ejpam-5969	297	8	ϵ-accumulation	ϵ-accumulation	PROPN
ejpam-5969	297	9	points	point	NOUN
ejpam-5969	297	10	of	of	ADP
ejpam-5969	297	11	t	t	PROPN
ejpam-5969	297	12	will	will	AUX
ejpam-5969	297	13	denoted	denote	VERB
ejpam-5969	297	14	by	by	ADP
ejpam-5969	297	15	accϵ(t	accϵ(t	NOUN
ejpam-5969	297	16	)	)	PUNCT
ejpam-5969	297	17	.	.	PUNCT
ejpam-5969	298	1	theorem	theorem	ADJ
ejpam-5969	298	2	10	10	NUM
ejpam-5969	298	3	.	.	PUNCT
ejpam-5969	299	1	let	let	VERB
ejpam-5969	299	2	(	(	PUNCT
ejpam-5969	299	3	χ	χ	X
ejpam-5969	299	4	,	,	PUNCT
ejpam-5969	299	5	ν	ν	NOUN
ejpam-5969	299	6	)	)	PUNCT
ejpam-5969	299	7	be	be	VERB
ejpam-5969	299	8	an	an	DET
ejpam-5969	299	9	sts	st	NOUN
ejpam-5969	299	10	and	and	CCONJ
ejpam-5969	299	11	t	t	NOUN
ejpam-5969	299	12	∈	∈	PROPN
ejpam-5969	300	1	p	p	X
ejpam-5969	300	2	(	(	PUNCT
ejpam-5969	300	3	χ	χ	NOUN
ejpam-5969	300	4	)	)	PUNCT
ejpam-5969	300	5	.	.	PUNCT
ejpam-5969	301	1	then	then	ADV
ejpam-5969	301	2	,	,	PUNCT
ejpam-5969	301	3	(	(	PUNCT
ejpam-5969	301	4	1	1	X
ejpam-5969	301	5	)	)	PUNCT
ejpam-5969	301	6	accϵ(t	accϵ(t	NOUN
ejpam-5969	301	7	)	)	PUNCT
ejpam-5969	301	8	⊆	⊆	NUM
ejpam-5969	301	9	acc(t	acc(t	PROPN
ejpam-5969	301	10	)	)	PUNCT
ejpam-5969	301	11	.	.	PUNCT
ejpam-5969	302	1	(	(	PUNCT
ejpam-5969	302	2	2	2	X
ejpam-5969	302	3	)	)	PUNCT
ejpam-5969	302	4	accϵ(t	accϵ(t	NOUN
ejpam-5969	302	5	)	)	PUNCT
ejpam-5969	302	6	⊆	⊆	NUM
ejpam-5969	302	7	t	t	PROPN
ejpam-5969	302	8	⇔	⇔	PROPN
ejpam-5969	302	9	t	t	PROPN
ejpam-5969	302	10	is	be	AUX
ejpam-5969	302	11	a	a	DET
ejpam-5969	302	12	proper	proper	ADJ
ejpam-5969	302	13	supra	supra	NOUN
ejpam-5969	302	14	ϵ-closed	ϵ-close	VERB
ejpam-5969	302	15	set	set	NOUN
ejpam-5969	302	16	.	.	PUNCT
ejpam-5969	303	1	proof	proof	NOUN
ejpam-5969	303	2	.	.	PUNCT
ejpam-5969	304	1	(	(	PUNCT
ejpam-5969	304	2	1	1	X
ejpam-5969	304	3	)	)	PUNCT
ejpam-5969	304	4	let	let	VERB
ejpam-5969	304	5	’s	’s	NOUN
ejpam-5969	304	6	pretend	pretend	VERB
ejpam-5969	304	7	that	that	SCONJ
ejpam-5969	304	8	s	s	VERB
ejpam-5969	304	9	̸∈	̸∈	PROPN
ejpam-5969	304	10	acc(t	acc(t	PROPN
ejpam-5969	304	11	)	)	PUNCT
ejpam-5969	304	12	,	,	PUNCT
ejpam-5969	304	13	then	then	ADV
ejpam-5969	304	14	∃	∃	PROPN
ejpam-5969	304	15	gs	gs	PROPN
ejpam-5969	304	16	∈	∈	PROPN
ejpam-5969	304	17	ν	ν	NOUN
ejpam-5969	304	18	such	such	ADJ
ejpam-5969	304	19	that	that	SCONJ
ejpam-5969	304	20	[	[	X
ejpam-5969	304	21	t\{s	t\{s	NOUN
ejpam-5969	304	22	}	}	PUNCT
ejpam-5969	304	23	]	]	PUNCT
ejpam-5969	305	1	∩	∩	PROPN
ejpam-5969	305	2	g	g	NOUN
ejpam-5969	305	3	=	=	PUNCT
ejpam-5969	305	4	∅.	∅.	NOUN
ejpam-5969	305	5	then	then	ADV
ejpam-5969	305	6	,	,	PUNCT
ejpam-5969	305	7	gs	gs	PROPN
ejpam-5969	305	8	∈	∈	PROPN
ejpam-5969	305	9	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	305	10	)	)	PUNCT
ejpam-5969	306	1	such	such	ADJ
ejpam-5969	306	2	that	that	SCONJ
ejpam-5969	306	3	[	[	X
ejpam-5969	306	4	t\{s	t\{s	X
ejpam-5969	306	5	}	}	PUNCT
ejpam-5969	306	6	]	]	PUNCT
ejpam-5969	306	7	∩g	∩g	PROPN
ejpam-5969	306	8	=	=	PUNCT
ejpam-5969	306	9	∅.	∅.	VERB
ejpam-5969	306	10	hence	hence	ADV
ejpam-5969	306	11	,	,	PUNCT
ejpam-5969	306	12	s	s	VERB
ejpam-5969	306	13	̸∈	̸∈	PROPN
ejpam-5969	306	14	accϵ(t	accϵ(t	PROPN
ejpam-5969	306	15	)	)	PUNCT
ejpam-5969	306	16	.	.	PUNCT
ejpam-5969	307	1	abd	abd	PROPN
ejpam-5969	307	2	el	el	PROPN
ejpam-5969	307	3	-	-	PROPN
ejpam-5969	307	4	latif	latif	PROPN
ejpam-5969	307	5	et	et	PROPN
ejpam-5969	307	6	al	al	PROPN
ejpam-5969	307	7	.	.	PUNCT
ejpam-5969	307	8	/	/	SYM
ejpam-5969	307	9	eur	eur	PROPN
ejpam-5969	307	10	.	.	PUNCT
ejpam-5969	308	1	j.	j.	PROPN
ejpam-5969	308	2	pure	pure	PROPN
ejpam-5969	308	3	appl	appl	PROPN
ejpam-5969	308	4	.	.	PROPN
ejpam-5969	308	5	math	math	PROPN
ejpam-5969	308	6	,	,	PUNCT
ejpam-5969	308	7	18	18	NUM
ejpam-5969	308	8	(	(	PUNCT
ejpam-5969	308	9	2	2	NUM
ejpam-5969	308	10	)	)	PUNCT
ejpam-5969	308	11	(	(	PUNCT
ejpam-5969	308	12	2025	2025	NUM
ejpam-5969	308	13	)	)	PUNCT
ejpam-5969	308	14	,	,	PUNCT
ejpam-5969	308	15	5969	5969	NUM
ejpam-5969	308	16	12	12	NUM
ejpam-5969	308	17	of	of	ADP
ejpam-5969	308	18	19	19	NUM
ejpam-5969	308	19	(	(	PUNCT
ejpam-5969	308	20	2	2	NUM
ejpam-5969	308	21	)	)	PUNCT
ejpam-5969	308	22	(	(	PUNCT
ejpam-5969	308	23	⇒	⇒	NOUN
ejpam-5969	308	24	)	)	PUNCT
ejpam-5969	308	25	pretend	pretend	VERB
ejpam-5969	308	26	that	that	SCONJ
ejpam-5969	308	27	s	s	VERB
ejpam-5969	308	28	̸∈	̸∈	PROPN
ejpam-5969	308	29	t	t	PROPN
ejpam-5969	308	30	for	for	ADP
ejpam-5969	308	31	a	a	DET
ejpam-5969	308	32	proper	proper	ADJ
ejpam-5969	308	33	subset	subset	NOUN
ejpam-5969	308	34	t	t	NOUN
ejpam-5969	308	35	.	.	PUNCT
ejpam-5969	309	1	considering	consider	VERB
ejpam-5969	309	2	the	the	DET
ejpam-5969	309	3	condition	condition	NOUN
ejpam-5969	309	4	,	,	PUNCT
ejpam-5969	309	5	s	s	PART
ejpam-5969	309	6	̸∈	̸∈	PROPN
ejpam-5969	309	7	accϵ(t	accϵ(t	NOUN
ejpam-5969	309	8	)	)	PUNCT
ejpam-5969	310	1	and	and	CCONJ
ejpam-5969	310	2	so	so	ADV
ejpam-5969	310	3	there	there	PRON
ejpam-5969	310	4	is	be	VERB
ejpam-5969	310	5	gs	gs	PRON
ejpam-5969	310	6	∈	∈	PROPN
ejpam-5969	310	7	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	310	8	)	)	PUNCT
ejpam-5969	310	9	such	such	ADJ
ejpam-5969	310	10	that	that	SCONJ
ejpam-5969	311	1	[	[	X
ejpam-5969	311	2	gs\{s	gs\{s	NUM
ejpam-5969	311	3	}	}	PUNCT
ejpam-5969	311	4	]	]	PUNCT
ejpam-5969	311	5	∩	∩	PROPN
ejpam-5969	311	6	t	t	NOUN
ejpam-5969	311	7	=	=	PUNCT
ejpam-5969	311	8	∅.	∅.	NOUN
ejpam-5969	311	9	since	since	SCONJ
ejpam-5969	311	10	s	s	PROPN
ejpam-5969	311	11	̸∈	̸∈	PROPN
ejpam-5969	311	12	t	t	PROPN
ejpam-5969	311	13	,	,	PUNCT
ejpam-5969	311	14	gs	gs	PROPN
ejpam-5969	311	15	∩	∩	NOUN
ejpam-5969	311	16	t	t	NOUN
ejpam-5969	311	17	=	=	SYM
ejpam-5969	311	18	∅	∅	NOUN
ejpam-5969	311	19	and	and	CCONJ
ejpam-5969	311	20	so	so	ADV
ejpam-5969	311	21	s	s	X
ejpam-5969	311	22	̸∈	̸∈	PROPN
ejpam-5969	311	23	clϵ(t	clϵ(t	PROPN
ejpam-5969	311	24	)	)	PUNCT
ejpam-5969	311	25	.	.	PUNCT
ejpam-5969	312	1	hence	hence	ADV
ejpam-5969	312	2	,	,	PUNCT
ejpam-5969	312	3	clϵ(t	clϵ(t	PROPN
ejpam-5969	312	4	)	)	PUNCT
ejpam-5969	312	5	⊆	⊆	NUM
ejpam-5969	312	6	t	t	NOUN
ejpam-5969	312	7	.	.	PUNCT
ejpam-5969	313	1	nevertheless	nevertheless	ADV
ejpam-5969	313	2	,	,	PUNCT
ejpam-5969	313	3	we	we	PRON
ejpam-5969	313	4	have	have	VERB
ejpam-5969	313	5	t	t	PROPN
ejpam-5969	313	6	⊆	⊆	NUM
ejpam-5969	313	7	clϵ(t	clϵ(t	NOUN
ejpam-5969	313	8	)	)	PUNCT
ejpam-5969	313	9	.	.	PUNCT
ejpam-5969	314	1	therefore	therefore	ADV
ejpam-5969	314	2	,	,	PUNCT
ejpam-5969	314	3	t	t	PROPN
ejpam-5969	314	4	=	=	SYM
ejpam-5969	314	5	clϵ(t	clϵ(t	PROPN
ejpam-5969	314	6	)	)	PUNCT
ejpam-5969	314	7	.	.	PUNCT
ejpam-5969	315	1	thus	thus	ADV
ejpam-5969	315	2	,	,	PUNCT
ejpam-5969	315	3	t	t	PROPN
ejpam-5969	315	4	is	be	AUX
ejpam-5969	315	5	a	a	DET
ejpam-5969	315	6	proper	proper	ADJ
ejpam-5969	315	7	supra	supra	NOUN
ejpam-5969	315	8	ϵ-closed	ϵ-close	VERB
ejpam-5969	315	9	set	set	NOUN
ejpam-5969	315	10	.	.	PUNCT
ejpam-5969	316	1	(	(	PUNCT
ejpam-5969	316	2	⇐	⇐	NOUN
ejpam-5969	316	3	)	)	PUNCT
ejpam-5969	316	4	let	let	VERB
ejpam-5969	316	5	s	s	PRON
ejpam-5969	316	6	̸∈	̸∈	PROPN
ejpam-5969	316	7	t	t	PROPN
ejpam-5969	316	8	for	for	ADP
ejpam-5969	316	9	a	a	DET
ejpam-5969	316	10	proper	proper	ADJ
ejpam-5969	316	11	supra	supra	NOUN
ejpam-5969	316	12	ϵ-closed	ϵ-close	VERB
ejpam-5969	316	13	set	set	VERB
ejpam-5969	316	14	t	t	NOUN
ejpam-5969	316	15	and	and	CCONJ
ejpam-5969	316	16	then	then	ADV
ejpam-5969	316	17	s	s	VERB
ejpam-5969	316	18	∈	∈	PROPN
ejpam-5969	316	19	t	t	X
ejpam-5969	316	20	c	c	PROPN
ejpam-5969	316	21	for	for	ADP
ejpam-5969	316	22	t	t	PROPN
ejpam-5969	316	23	c	c	PROPN
ejpam-5969	316	24	∈	∈	PROPN
ejpam-5969	316	25	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	316	26	)	)	PUNCT
ejpam-5969	316	27	.	.	PUNCT
ejpam-5969	317	1	since	since	SCONJ
ejpam-5969	317	2	t	t	NOUN
ejpam-5969	317	3	∩	∩	PROPN
ejpam-5969	317	4	[	[	X
ejpam-5969	317	5	t	t	X
ejpam-5969	317	6	c\{s	c\{s	PROPN
ejpam-5969	317	7	}	}	PUNCT
ejpam-5969	317	8	]	]	PUNCT
ejpam-5969	317	9	=	=	PUNCT
ejpam-5969	317	10	∅	∅	NOUN
ejpam-5969	317	11	for	for	ADP
ejpam-5969	317	12	t	t	PROPN
ejpam-5969	317	13	c	c	PROPN
ejpam-5969	317	14	∈	∈	PROPN
ejpam-5969	317	15	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	317	16	)	)	PUNCT
ejpam-5969	317	17	,	,	PUNCT
ejpam-5969	317	18	s	s	PART
ejpam-5969	317	19	̸∈	̸∈	PROPN
ejpam-5969	317	20	accϵ(t	accϵ(t	PROPN
ejpam-5969	317	21	)	)	PUNCT
ejpam-5969	317	22	.	.	PUNCT
ejpam-5969	318	1	therefore	therefore	ADV
ejpam-5969	318	2	,	,	PUNCT
ejpam-5969	318	3	accϵ(t	accϵ(t	INTJ
ejpam-5969	318	4	)	)	PUNCT
ejpam-5969	318	5	⊆	⊆	NUM
ejpam-5969	318	6	t	t	NOUN
ejpam-5969	318	7	.	.	PUNCT
ejpam-5969	319	1	proposition	proposition	NOUN
ejpam-5969	319	2	5	5	NUM
ejpam-5969	319	3	.	.	PUNCT
ejpam-5969	320	1	let	let	VERB
ejpam-5969	320	2	(	(	PUNCT
ejpam-5969	320	3	χ	χ	X
ejpam-5969	320	4	,	,	PUNCT
ejpam-5969	320	5	ν	ν	NOUN
ejpam-5969	320	6	)	)	PUNCT
ejpam-5969	320	7	be	be	VERB
ejpam-5969	320	8	an	an	DET
ejpam-5969	320	9	sts	st	NOUN
ejpam-5969	320	10	and	and	CCONJ
ejpam-5969	320	11	t	t	NOUN
ejpam-5969	320	12	,	,	PUNCT
ejpam-5969	320	13	h	h	NOUN
ejpam-5969	320	14	∈	∈	PROPN
ejpam-5969	320	15	p	p	X
ejpam-5969	320	16	(	(	PUNCT
ejpam-5969	320	17	χ	χ	NOUN
ejpam-5969	320	18	)	)	PUNCT
ejpam-5969	320	19	,	,	PUNCT
ejpam-5969	320	20	then	then	ADV
ejpam-5969	320	21	(	(	PUNCT
ejpam-5969	320	22	1	1	X
ejpam-5969	320	23	)	)	PUNCT
ejpam-5969	320	24	if	if	SCONJ
ejpam-5969	320	25	t	t	PROPN
ejpam-5969	320	26	⊆	⊆	NUM
ejpam-5969	320	27	h	h	NOUN
ejpam-5969	320	28	,	,	PUNCT
ejpam-5969	320	29	then	then	ADV
ejpam-5969	320	30	accϵ(t	accϵ(t	ADV
ejpam-5969	320	31	)	)	PUNCT
ejpam-5969	320	32	⊆	⊆	NUM
ejpam-5969	320	33	accϵ(h	accϵ(h	NOUN
ejpam-5969	320	34	)	)	PUNCT
ejpam-5969	320	35	.	.	PUNCT
ejpam-5969	321	1	(	(	PUNCT
ejpam-5969	321	2	2	2	X
ejpam-5969	321	3	)	)	PUNCT
ejpam-5969	321	4	accϵ[t	accϵ[t	ADV
ejpam-5969	321	5	∩h	∩h	NOUN
ejpam-5969	321	6	]	]	PUNCT
ejpam-5969	321	7	⊆	⊆	NUM
ejpam-5969	321	8	accϵ(t	accϵ(t	NOUN
ejpam-5969	321	9	)	)	PUNCT
ejpam-5969	321	10	∩	∩	ADJ
ejpam-5969	321	11	accϵ(h	accϵ(h	NOUN
ejpam-5969	321	12	)	)	PUNCT
ejpam-5969	321	13	.	.	PUNCT
ejpam-5969	322	1	(	(	PUNCT
ejpam-5969	322	2	3	3	X
ejpam-5969	322	3	)	)	PUNCT
ejpam-5969	322	4	accϵ(t	accϵ(t	NOUN
ejpam-5969	322	5	)	)	PUNCT
ejpam-5969	322	6	∪	∪	PROPN
ejpam-5969	322	7	accϵ(h	accϵ(h	PROPN
ejpam-5969	322	8	)	)	PUNCT
ejpam-5969	322	9	⊆	⊆	NUM
ejpam-5969	322	10	accϵ[t	accϵ[t	ADV
ejpam-5969	322	11	∪h	∪h	NUM
ejpam-5969	322	12	]	]	PUNCT
ejpam-5969	322	13	.	.	PUNCT
ejpam-5969	323	1	proof	proof	NOUN
ejpam-5969	323	2	.	.	PUNCT
ejpam-5969	324	1	follows	follow	VERB
ejpam-5969	324	2	from	from	ADP
ejpam-5969	324	3	definition	definition	NOUN
ejpam-5969	324	4	9	9	NUM
ejpam-5969	324	5	and	and	CCONJ
ejpam-5969	324	6	theorem	theorem	VERB
ejpam-5969	324	7	10	10	NUM
ejpam-5969	324	8	.	.	PUNCT
ejpam-5969	325	1	remark	remark	PROPN
ejpam-5969	325	2	8	8	NUM
ejpam-5969	325	3	.	.	PUNCT
ejpam-5969	326	1	in	in	ADP
ejpam-5969	326	2	proposition	proposition	NOUN
ejpam-5969	326	3	5	5	NUM
ejpam-5969	326	4	,	,	PUNCT
ejpam-5969	326	5	the	the	DET
ejpam-5969	326	6	reverse	reverse	ADJ
ejpam-5969	326	7	inclusions	inclusion	NOUN
ejpam-5969	326	8	are	be	AUX
ejpam-5969	326	9	n’t	not	PART
ejpam-5969	326	10	hold	hold	NOUN
ejpam-5969	326	11	in	in	ADP
ejpam-5969	326	12	general	general	ADJ
ejpam-5969	326	13	,	,	PUNCT
ejpam-5969	326	14	as	as	SCONJ
ejpam-5969	326	15	demonstrated	demonstrate	VERB
ejpam-5969	326	16	by	by	ADP
ejpam-5969	326	17	the	the	DET
ejpam-5969	326	18	upcoming	upcoming	ADJ
ejpam-5969	326	19	examples	example	NOUN
ejpam-5969	326	20	.	.	PUNCT
ejpam-5969	327	1	examples	example	NOUN
ejpam-5969	327	2	3	3	NUM
ejpam-5969	327	3	.	.	PUNCT
ejpam-5969	328	1	in	in	ADP
ejpam-5969	328	2	examples	example	NOUN
ejpam-5969	328	3	2	2	NUM
ejpam-5969	328	4	,	,	PUNCT
ejpam-5969	328	5	consider	consider	VERB
ejpam-5969	328	6	the	the	DET
ejpam-5969	328	7	sets	set	NOUN
ejpam-5969	328	8	a	a	DET
ejpam-5969	328	9	=	=	SYM
ejpam-5969	328	10	{	{	PUNCT
ejpam-5969	328	11	1	1	NUM
ejpam-5969	328	12	,	,	PUNCT
ejpam-5969	328	13	3	3	NUM
ejpam-5969	328	14	}	}	PUNCT
ejpam-5969	328	15	and	and	CCONJ
ejpam-5969	328	16	b	b	X
ejpam-5969	328	17	=	=	SYM
ejpam-5969	328	18	{	{	PUNCT
ejpam-5969	328	19	1	1	NUM
ejpam-5969	328	20	,	,	PUNCT
ejpam-5969	328	21	2	2	NUM
ejpam-5969	328	22	}	}	PUNCT
ejpam-5969	328	23	.	.	PUNCT
ejpam-5969	329	1	we	we	PRON
ejpam-5969	329	2	have	have	VERB
ejpam-5969	329	3	(	(	PUNCT
ejpam-5969	329	4	1	1	X
ejpam-5969	329	5	)	)	PUNCT
ejpam-5969	329	6	accϵ(b	accϵ(b	NOUN
ejpam-5969	329	7	)	)	PUNCT
ejpam-5969	329	8	=	=	PUNCT
ejpam-5969	329	9	{	{	PUNCT
ejpam-5969	329	10	3	3	NUM
ejpam-5969	329	11	}	}	SYM
ejpam-5969	329	12	⊆	⊆	NUM
ejpam-5969	329	13	accϵ(a	accϵ(a	NOUN
ejpam-5969	329	14	)	)	PUNCT
ejpam-5969	329	15	=	=	PUNCT
ejpam-5969	329	16	{	{	PUNCT
ejpam-5969	329	17	2	2	NUM
ejpam-5969	329	18	,	,	PUNCT
ejpam-5969	329	19	3	3	NUM
ejpam-5969	329	20	}	}	PUNCT
ejpam-5969	329	21	,	,	PUNCT
ejpam-5969	329	22	whereas	whereas	SCONJ
ejpam-5969	329	23	b	b	X
ejpam-5969	329	24	⊈	⊈	PROPN
ejpam-5969	329	25	a.	a.	NOUN
ejpam-5969	329	26	(	(	PUNCT
ejpam-5969	329	27	2	2	X
ejpam-5969	329	28	)	)	PUNCT
ejpam-5969	329	29	accϵ(a	accϵ(a	NOUN
ejpam-5969	329	30	)	)	PUNCT
ejpam-5969	329	31	∩	∩	ADJ
ejpam-5969	329	32	accϵ(b	accϵ(b	PROPN
ejpam-5969	329	33	)	)	PUNCT
ejpam-5969	329	34	=	=	PUNCT
ejpam-5969	329	35	{	{	PUNCT
ejpam-5969	329	36	3	3	NUM
ejpam-5969	329	37	}	}	PUNCT
ejpam-5969	329	38	⊈	⊈	PROPN
ejpam-5969	329	39	accϵ[a	accϵ[a	NOUN
ejpam-5969	329	40	∩b	∩b	NOUN
ejpam-5969	329	41	]	]	X
ejpam-5969	329	42	=	=	SYM
ejpam-5969	329	43	∅.	∅.	X
ejpam-5969	329	44	(	(	PUNCT
ejpam-5969	329	45	3	3	NUM
ejpam-5969	329	46	)	)	PUNCT
ejpam-5969	329	47	accϵ[a	accϵ[a	NOUN
ejpam-5969	329	48	∪b	∪b	NOUN
ejpam-5969	329	49	]	]	PUNCT
ejpam-5969	329	50	=	=	SYM
ejpam-5969	329	51	χ	χ	PRON
ejpam-5969	329	52	⊈	⊈	NUM
ejpam-5969	329	53	accϵ(a	accϵ(a	NOUN
ejpam-5969	329	54	)	)	PUNCT
ejpam-5969	329	55	∪	∪	ADP
ejpam-5969	329	56	accϵ(b	accϵ(b	PROPN
ejpam-5969	329	57	)	)	PUNCT
ejpam-5969	329	58	=	=	PUNCT
ejpam-5969	329	59	{	{	PUNCT
ejpam-5969	329	60	2	2	NUM
ejpam-5969	329	61	,	,	PUNCT
ejpam-5969	329	62	3	3	NUM
ejpam-5969	329	63	}	}	PUNCT
ejpam-5969	329	64	.	.	PUNCT
ejpam-5969	330	1	lemma	lemma	PROPN
ejpam-5969	330	2	2	2	NUM
ejpam-5969	330	3	.	.	PUNCT
ejpam-5969	331	1	given	give	VERB
ejpam-5969	331	2	a	a	DET
ejpam-5969	331	3	subset	subset	NOUN
ejpam-5969	331	4	t	t	NOUN
ejpam-5969	331	5	of	of	ADP
ejpam-5969	331	6	an	an	DET
ejpam-5969	331	7	sts	st	NOUN
ejpam-5969	331	8	(	(	PUNCT
ejpam-5969	331	9	χ	χ	NOUN
ejpam-5969	331	10	,	,	PUNCT
ejpam-5969	331	11	ν	ν	NOUN
ejpam-5969	331	12	)	)	PUNCT
ejpam-5969	331	13	with	with	ADP
ejpam-5969	331	14	arbitrary	arbitrary	ADJ
ejpam-5969	331	15	point	point	NOUN
ejpam-5969	331	16	x	x	SYM
ejpam-5969	331	17	∈	∈	NOUN
ejpam-5969	331	18	χ	χ	NOUN
ejpam-5969	331	19	.	.	PUNCT
ejpam-5969	332	1	then	then	ADV
ejpam-5969	332	2	,	,	PUNCT
ejpam-5969	332	3	x	x	PUNCT
ejpam-5969	332	4	∈	∈	NOUN
ejpam-5969	332	5	accϵ(t	accϵ(t	NOUN
ejpam-5969	332	6	)	)	PUNCT
ejpam-5969	332	7	if	if	SCONJ
ejpam-5969	332	8	and	and	CCONJ
ejpam-5969	332	9	only	only	ADV
ejpam-5969	332	10	if	if	SCONJ
ejpam-5969	332	11	x	x	PROPN
ejpam-5969	332	12	∈	∈	PROPN
ejpam-5969	332	13	accϵ(t\{x	accϵ(t\{x	X
ejpam-5969	332	14	}	}	PUNCT
ejpam-5969	332	15	)	)	PUNCT
ejpam-5969	332	16	.	.	PUNCT
ejpam-5969	333	1	proof	proof	NOUN
ejpam-5969	333	2	.	.	PUNCT
ejpam-5969	334	1	follows	follow	VERB
ejpam-5969	334	2	from	from	ADP
ejpam-5969	334	3	lemma	lemma	PROPN
ejpam-5969	334	4	5	5	NUM
ejpam-5969	334	5	.	.	PUNCT
ejpam-5969	334	6	theorem	theorem	VERB
ejpam-5969	334	7	11	11	NUM
ejpam-5969	334	8	.	.	PUNCT
ejpam-5969	335	1	for	for	ADP
ejpam-5969	335	2	any	any	DET
ejpam-5969	335	3	subset	subset	NOUN
ejpam-5969	335	4	z	z	NOUN
ejpam-5969	335	5	of	of	ADP
ejpam-5969	335	6	an	an	DET
ejpam-5969	335	7	sts	st	NOUN
ejpam-5969	335	8	(	(	PUNCT
ejpam-5969	335	9	χ	χ	NOUN
ejpam-5969	335	10	,	,	PUNCT
ejpam-5969	335	11	ν	ν	NOUN
ejpam-5969	335	12	)	)	PUNCT
ejpam-5969	335	13	.	.	PUNCT
ejpam-5969	336	1	(	(	PUNCT
ejpam-5969	336	2	1	1	X
ejpam-5969	336	3	)	)	PUNCT
ejpam-5969	336	4	z	z	NOUN
ejpam-5969	336	5	∈	∈	NOUN
ejpam-5969	336	6	scϵ(χ	scϵ(χ	NUM
ejpam-5969	336	7	)	)	PUNCT
ejpam-5969	336	8	)	)	PUNCT
ejpam-5969	337	1	if	if	SCONJ
ejpam-5969	337	2	and	and	CCONJ
ejpam-5969	337	3	only	only	ADV
ejpam-5969	337	4	if	if	SCONJ
ejpam-5969	337	5	accϵ(z	accϵ(z	NOUN
ejpam-5969	337	6	)	)	PUNCT
ejpam-5969	337	7	⊆	⊆	NUM
ejpam-5969	337	8	z.	z.	X
ejpam-5969	337	9	(	(	PUNCT
ejpam-5969	337	10	2	2	NUM
ejpam-5969	337	11	)	)	PUNCT
ejpam-5969	337	12	z	z	NOUN
ejpam-5969	337	13	∪	∪	ADP
ejpam-5969	337	14	accϵ(z	accϵ(z	NOUN
ejpam-5969	337	15	)	)	PUNCT
ejpam-5969	337	16	∈	∈	PROPN
ejpam-5969	337	17	scϵ(χ	scϵ(χ	NUM
ejpam-5969	337	18	)	)	PUNCT
ejpam-5969	337	19	.	.	PUNCT
ejpam-5969	338	1	proof	proof	NOUN
ejpam-5969	338	2	.	.	PUNCT
ejpam-5969	339	1	(	(	PUNCT
ejpam-5969	339	2	1	1	X
ejpam-5969	339	3	)	)	PUNCT
ejpam-5969	339	4	assume	assume	VERB
ejpam-5969	339	5	that	that	SCONJ
ejpam-5969	339	6	z	z	NOUN
ejpam-5969	339	7	is	be	AUX
ejpam-5969	339	8	a	a	DET
ejpam-5969	339	9	supra	supra	NOUN
ejpam-5969	339	10	ϵ-closed	ϵ-close	VERB
ejpam-5969	339	11	set	set	NOUN
ejpam-5969	339	12	and	and	CCONJ
ejpam-5969	339	13	z	z	PROPN
ejpam-5969	339	14	̸∈	̸∈	PROPN
ejpam-5969	339	15	z.	z.	PROPN
ejpam-5969	339	16	then	then	ADV
ejpam-5969	339	17	,	,	PUNCT
ejpam-5969	339	18	zc	zc	X
ejpam-5969	339	19	is	be	AUX
ejpam-5969	339	20	a	a	DET
ejpam-5969	339	21	supra	supra	PROPN
ejpam-5969	339	22	ϵ-open	ϵ-open	PROPN
ejpam-5969	339	23	set	set	VERB
ejpam-5969	339	24	with	with	ADP
ejpam-5969	339	25	z	z	PROPN
ejpam-5969	339	26	∈	∈	PROPN
ejpam-5969	339	27	zc	zc	NOUN
ejpam-5969	339	28	,	,	PUNCT
ejpam-5969	339	29	and	and	CCONJ
ejpam-5969	340	1	hence	hence	ADV
ejpam-5969	340	2	[	[	X
ejpam-5969	340	3	z\{z	z\{z	NOUN
ejpam-5969	340	4	}	}	PUNCT
ejpam-5969	340	5	]	]	PUNCT
ejpam-5969	340	6	∩	∩	ADJ
ejpam-5969	340	7	zc	zc	X
ejpam-5969	340	8	=	=	PUNCT
ejpam-5969	340	9	∅.	∅.	VERB
ejpam-5969	340	10	therefore	therefore	ADV
ejpam-5969	340	11	,	,	PUNCT
ejpam-5969	340	12	z	z	PROPN
ejpam-5969	340	13	̸∈	̸∈	PROPN
ejpam-5969	340	14	accϵ(z	accϵ(z	PROPN
ejpam-5969	340	15	)	)	PUNCT
ejpam-5969	340	16	,	,	PUNCT
ejpam-5969	340	17	and	and	CCONJ
ejpam-5969	340	18	thus	thus	ADV
ejpam-5969	340	19	accϵ(z	accϵ(z	ADJ
ejpam-5969	340	20	)	)	PUNCT
ejpam-5969	340	21	⊆	⊆	NUM
ejpam-5969	340	22	z.	z.	PROPN
ejpam-5969	340	23	presently	presently	ADV
ejpam-5969	340	24	,	,	PUNCT
ejpam-5969	340	25	we	we	PRON
ejpam-5969	340	26	prove	prove	VERB
ejpam-5969	340	27	that	that	SCONJ
ejpam-5969	340	28	z	z	NOUN
ejpam-5969	340	29	∈	∈	NOUN
ejpam-5969	340	30	scϵ(χ	scϵ(χ	NUM
ejpam-5969	340	31	)	)	PUNCT
ejpam-5969	340	32	)	)	PUNCT
ejpam-5969	340	33	which	which	PRON
ejpam-5969	340	34	sufficient	sufficient	ADJ
ejpam-5969	340	35	to	to	PART
ejpam-5969	340	36	prove	prove	VERB
ejpam-5969	340	37	that	that	SCONJ
ejpam-5969	340	38	zc	zc	PROPN
ejpam-5969	340	39	∈	∈	PROPN
ejpam-5969	340	40	soϵ(χ	soϵ(χ	NOUN
ejpam-5969	340	41	)	)	PUNCT
ejpam-5969	340	42	)	)	PUNCT
ejpam-5969	340	43	.	.	PUNCT
ejpam-5969	341	1	so	so	ADV
ejpam-5969	341	2	,	,	PUNCT
ejpam-5969	341	3	let	let	VERB
ejpam-5969	341	4	z	z	PROPN
ejpam-5969	341	5	∈	∈	PROPN
ejpam-5969	341	6	zc	zc	X
ejpam-5969	341	7	.	.	PUNCT
ejpam-5969	342	1	then	then	ADV
ejpam-5969	342	2	,	,	PUNCT
ejpam-5969	342	3	z	z	PROPN
ejpam-5969	342	4	̸∈	̸∈	PROPN
ejpam-5969	342	5	z.	z.	PROPN
ejpam-5969	342	6	given	give	VERB
ejpam-5969	342	7	the	the	DET
ejpam-5969	342	8	condition	condition	NOUN
ejpam-5969	342	9	,	,	PUNCT
ejpam-5969	342	10	z	z	PROPN
ejpam-5969	342	11	̸∈	̸∈	PROPN
ejpam-5969	342	12	accϵ(z	accϵ(z	PROPN
ejpam-5969	342	13	)	)	PUNCT
ejpam-5969	342	14	,	,	PUNCT
ejpam-5969	342	15	and	and	CCONJ
ejpam-5969	342	16	hence	hence	ADV
ejpam-5969	342	17	[	[	X
ejpam-5969	342	18	z\{z}]∩	z\{z}]∩	NOUN
ejpam-5969	342	19	gz	gz	NOUN
ejpam-5969	342	20	̸=	̸=	PROPN
ejpam-5969	342	21	∅	∅	NOUN
ejpam-5969	342	22	,	,	PUNCT
ejpam-5969	342	23	for	for	ADP
ejpam-5969	342	24	some	some	DET
ejpam-5969	342	25	supra	supra	PROPN
ejpam-5969	342	26	ϵ-open	ϵ-open	PROPN
ejpam-5969	342	27	set	set	PROPN
ejpam-5969	342	28	gz	gz	PROPN
ejpam-5969	342	29	.	.	PUNCT
ejpam-5969	343	1	since	since	SCONJ
ejpam-5969	343	2	z	z	PROPN
ejpam-5969	343	3	̸∈	̸∈	PROPN
ejpam-5969	343	4	z	z	PROPN
ejpam-5969	343	5	,	,	PUNCT
ejpam-5969	343	6	z	z	PROPN
ejpam-5969	343	7	∩gz	∩gz	NOUN
ejpam-5969	343	8	̸=	̸=	PROPN
ejpam-5969	343	9	∅	∅	NOUN
ejpam-5969	343	10	and	and	CCONJ
ejpam-5969	343	11	thus	thus	ADV
ejpam-5969	343	12	gz	gz	VERB
ejpam-5969	343	13	⊆	⊆	NUM
ejpam-5969	343	14	zc	zc	NOUN
ejpam-5969	343	15	.	.	PUNCT
ejpam-5969	344	1	therefore	therefore	ADV
ejpam-5969	344	2	,	,	PUNCT
ejpam-5969	344	3	zc	zc	PROPN
ejpam-5969	344	4	∈	∈	PROPN
ejpam-5969	344	5	soϵ(χ	soϵ(χ	NOUN
ejpam-5969	344	6	)	)	PUNCT
ejpam-5969	344	7	)	)	PUNCT
ejpam-5969	344	8	,	,	PUNCT
ejpam-5969	344	9	and	and	CCONJ
ejpam-5969	344	10	consequently	consequently	ADV
ejpam-5969	344	11	z	z	X
ejpam-5969	344	12	∈	∈	NOUN
ejpam-5969	344	13	scϵ(χ	scϵ(χ	NUM
ejpam-5969	344	14	)	)	PUNCT
ejpam-5969	344	15	)	)	PUNCT
ejpam-5969	344	16	.	.	PUNCT
ejpam-5969	345	1	(	(	PUNCT
ejpam-5969	345	2	2	2	X
ejpam-5969	345	3	)	)	PUNCT
ejpam-5969	345	4	suppose	suppose	VERB
ejpam-5969	345	5	that	that	SCONJ
ejpam-5969	345	6	s	s	VERB
ejpam-5969	345	7	̸∈	̸∈	PROPN
ejpam-5969	345	8	z	z	PROPN
ejpam-5969	345	9	∪	∪	ADP
ejpam-5969	345	10	accϵ(z	accϵ(z	NOUN
ejpam-5969	345	11	)	)	PUNCT
ejpam-5969	345	12	and	and	CCONJ
ejpam-5969	345	13	so	so	ADV
ejpam-5969	345	14	s	s	X
ejpam-5969	345	15	̸∈	̸∈	PROPN
ejpam-5969	345	16	z	z	PROPN
ejpam-5969	345	17	and	and	CCONJ
ejpam-5969	345	18	s	s	PROPN
ejpam-5969	345	19	̸∈	̸∈	PROPN
ejpam-5969	345	20	accϵ(z	accϵ(z	PROPN
ejpam-5969	345	21	)	)	PUNCT
ejpam-5969	345	22	.	.	PUNCT
ejpam-5969	346	1	hence	hence	ADV
ejpam-5969	346	2	,	,	PUNCT
ejpam-5969	346	3	there	there	PRON
ejpam-5969	346	4	is	be	VERB
ejpam-5969	346	5	gs	gs	PRON
ejpam-5969	346	6	∈	∈	PROPN
ejpam-5969	346	7	soϵ(χ	soϵ(χ	PROPN
ejpam-5969	346	8	)	)	PUNCT
ejpam-5969	346	9	such	such	ADJ
ejpam-5969	346	10	that	that	SCONJ
ejpam-5969	346	11	abd	abd	PROPN
ejpam-5969	346	12	el	el	PROPN
ejpam-5969	346	13	-	-	PROPN
ejpam-5969	346	14	latif	latif	PROPN
ejpam-5969	346	15	et	et	PROPN
ejpam-5969	346	16	al	al	PROPN
ejpam-5969	346	17	.	.	PUNCT
ejpam-5969	346	18	/	/	SYM
ejpam-5969	346	19	eur	eur	PROPN
ejpam-5969	346	20	.	.	PUNCT
ejpam-5969	347	1	j.	j.	PROPN
ejpam-5969	347	2	pure	pure	PROPN
ejpam-5969	347	3	appl	appl	PROPN
ejpam-5969	347	4	.	.	PROPN
ejpam-5969	347	5	math	math	PROPN
ejpam-5969	347	6	,	,	PUNCT
ejpam-5969	347	7	18	18	NUM
ejpam-5969	347	8	(	(	PUNCT
ejpam-5969	347	9	2	2	NUM
ejpam-5969	347	10	)	)	PUNCT
ejpam-5969	347	11	(	(	PUNCT
ejpam-5969	347	12	2025	2025	NUM
ejpam-5969	347	13	)	)	PUNCT
ejpam-5969	347	14	,	,	PUNCT
ejpam-5969	347	15	5969	5969	NUM
ejpam-5969	347	16	13	13	NUM
ejpam-5969	347	17	of	of	ADP
ejpam-5969	347	18	19	19	NUM
ejpam-5969	347	19	[	[	NOUN
ejpam-5969	347	20	z\{s	z\{s	NUM
ejpam-5969	347	21	}	}	PUNCT
ejpam-5969	347	22	]	]	PUNCT
ejpam-5969	347	23	∩gs	∩gs	PROPN
ejpam-5969	347	24	=	=	NOUN
ejpam-5969	347	25	∅	∅	NOUN
ejpam-5969	347	26	and	and	CCONJ
ejpam-5969	347	27	then	then	ADV
ejpam-5969	347	28	s	s	VERB
ejpam-5969	347	29	̸∈	̸∈	PROPN
ejpam-5969	347	30	clϵ(z	clϵ(z	PROPN
ejpam-5969	347	31	)	)	PUNCT
ejpam-5969	347	32	.	.	PUNCT
ejpam-5969	348	1	hence	hence	ADV
ejpam-5969	348	2	,	,	PUNCT
ejpam-5969	348	3	clϵ(z	clϵ(z	PROPN
ejpam-5969	348	4	)	)	PUNCT
ejpam-5969	348	5	⊆	⊆	NUM
ejpam-5969	348	6	z	z	NOUN
ejpam-5969	348	7	∪	∪	ADP
ejpam-5969	348	8	accϵ(z	accϵ(z	NOUN
ejpam-5969	348	9	)	)	PUNCT
ejpam-5969	348	10	(	(	PUNCT
ejpam-5969	348	11	5	5	X
ejpam-5969	348	12	)	)	PUNCT
ejpam-5969	348	13	now	now	ADV
ejpam-5969	348	14	,	,	PUNCT
ejpam-5969	348	15	suppose	suppose	VERB
ejpam-5969	348	16	that	that	SCONJ
ejpam-5969	348	17	s	s	VERB
ejpam-5969	348	18	̸∈	̸∈	PROPN
ejpam-5969	348	19	clϵ(z	clϵ(z	PROPN
ejpam-5969	348	20	)	)	PUNCT
ejpam-5969	348	21	.	.	PUNCT
ejpam-5969	349	1	given	give	VERB
ejpam-5969	349	2	theorem	theorem	VERB
ejpam-5969	349	3	7	7	NUM
ejpam-5969	349	4	(	(	PUNCT
ejpam-5969	349	5	2	2	NUM
ejpam-5969	349	6	)	)	PUNCT
ejpam-5969	349	7	,	,	PUNCT
ejpam-5969	349	8	nu	nu	PROPN
ejpam-5969	349	9	∩	∩	PROPN
ejpam-5969	349	10	z	z	PROPN
ejpam-5969	349	11	̸=	̸=	PROPN
ejpam-5969	349	12	∅	∅	NOUN
ejpam-5969	349	13	for	for	ADP
ejpam-5969	349	14	some	some	DET
ejpam-5969	349	15	nu	nu	PROPN
ejpam-5969	349	16	∈	∈	PROPN
ejpam-5969	349	17	soϵ(χ	soϵ(χ	NOUN
ejpam-5969	349	18	)	)	PUNCT
ejpam-5969	349	19	.	.	PUNCT
ejpam-5969	350	1	since	since	SCONJ
ejpam-5969	350	2	,	,	PUNCT
ejpam-5969	350	3	z	z	NOUN
ejpam-5969	350	4	⊆	⊆	NUM
ejpam-5969	350	5	clϵ(z	clϵ(z	NOUN
ejpam-5969	350	6	)	)	PUNCT
ejpam-5969	350	7	,	,	PUNCT
ejpam-5969	350	8	s	s	PROPN
ejpam-5969	350	9	̸∈	̸∈	PROPN
ejpam-5969	350	10	z	z	PROPN
ejpam-5969	350	11	and	and	CCONJ
ejpam-5969	350	12	hence	hence	ADV
ejpam-5969	350	13	[	[	X
ejpam-5969	350	14	z\{s}]∩nu	z\{s}]∩nu	PROPN
ejpam-5969	350	15	=	=	PUNCT
ejpam-5969	350	16	∅.	∅.	ADP
ejpam-5969	350	17	hence	hence	ADV
ejpam-5969	350	18	,	,	PUNCT
ejpam-5969	350	19	s	s	PROPN
ejpam-5969	350	20	̸∈	̸∈	PROPN
ejpam-5969	350	21	accϵ(z	accϵ(z	PROPN
ejpam-5969	350	22	)	)	PUNCT
ejpam-5969	350	23	.	.	PUNCT
ejpam-5969	351	1	therefore	therefore	ADV
ejpam-5969	351	2	,	,	PUNCT
ejpam-5969	351	3	z	z	NOUN
ejpam-5969	351	4	∪	∪	ADP
ejpam-5969	351	5	accϵ(z	accϵ(z	NOUN
ejpam-5969	351	6	)	)	PUNCT
ejpam-5969	351	7	⊆	⊆	NUM
ejpam-5969	351	8	clϵ(z	clϵ(z	NOUN
ejpam-5969	351	9	)	)	PUNCT
ejpam-5969	351	10	(	(	PUNCT
ejpam-5969	351	11	6	6	NUM
ejpam-5969	351	12	)	)	PUNCT
ejpam-5969	351	13	according	accord	VERB
ejpam-5969	351	14	to	to	ADP
ejpam-5969	351	15	eqs	eqs	X
ejpam-5969	351	16	5	5	NUM
ejpam-5969	351	17	and	and	CCONJ
ejpam-5969	351	18	6	6	NUM
ejpam-5969	351	19	,	,	PUNCT
ejpam-5969	351	20	z∪accϵ(z	z∪accϵ(z	NUM
ejpam-5969	351	21	)	)	PUNCT
ejpam-5969	351	22	=	=	SYM
ejpam-5969	351	23	clϵ(z	clϵ(z	PROPN
ejpam-5969	351	24	)	)	PUNCT
ejpam-5969	351	25	.	.	PUNCT
ejpam-5969	352	1	given	give	VERB
ejpam-5969	352	2	theorem	theorem	VERB
ejpam-5969	352	3	7	7	NUM
ejpam-5969	352	4	(	(	PUNCT
ejpam-5969	352	5	1	1	NUM
ejpam-5969	352	6	)	)	PUNCT
ejpam-5969	352	7	,	,	PUNCT
ejpam-5969	352	8	z∪accϵ(z	z∪accϵ(z	NUM
ejpam-5969	352	9	)	)	PUNCT
ejpam-5969	352	10	∈	∈	PROPN
ejpam-5969	352	11	scϵ(χ	scϵ(χ	NUM
ejpam-5969	352	12	)	)	PUNCT
ejpam-5969	352	13	.	.	PUNCT
ejpam-5969	353	1	corollary	corollary	ADJ
ejpam-5969	353	2	2	2	NUM
ejpam-5969	353	3	.	.	PUNCT
ejpam-5969	353	4	given	give	VERB
ejpam-5969	353	5	a	a	DET
ejpam-5969	353	6	subset	subset	NOUN
ejpam-5969	353	7	z	z	NOUN
ejpam-5969	353	8	of	of	ADP
ejpam-5969	353	9	an	an	DET
ejpam-5969	353	10	sts	st	NOUN
ejpam-5969	353	11	(	(	PUNCT
ejpam-5969	353	12	χ	χ	NOUN
ejpam-5969	353	13	,	,	PUNCT
ejpam-5969	353	14	ν	ν	NOUN
ejpam-5969	353	15	)	)	PUNCT
ejpam-5969	353	16	.	.	PUNCT
ejpam-5969	354	1	then	then	ADV
ejpam-5969	354	2	,	,	PUNCT
ejpam-5969	354	3	clϵ(z	clϵ(z	PROPN
ejpam-5969	354	4	)	)	PUNCT
ejpam-5969	354	5	=	=	SYM
ejpam-5969	355	1	z	z	NOUN
ejpam-5969	355	2	∪	∪	ADP
ejpam-5969	355	3	accϵ(z	accϵ(z	NOUN
ejpam-5969	355	4	)	)	PUNCT
ejpam-5969	355	5	.	.	PUNCT
ejpam-5969	356	1	proof	proof	NOUN
ejpam-5969	356	2	.	.	PUNCT
ejpam-5969	357	1	it	it	PRON
ejpam-5969	357	2	is	be	AUX
ejpam-5969	357	3	derived	derive	VERB
ejpam-5969	357	4	from	from	ADP
ejpam-5969	357	5	theorem	theorem	ADJ
ejpam-5969	357	6	11	11	NUM
ejpam-5969	357	7	.	.	PUNCT
ejpam-5969	358	1	definition	definition	NOUN
ejpam-5969	358	2	10	10	NUM
ejpam-5969	358	3	.	.	PUNCT
ejpam-5969	359	1	if	if	SCONJ
ejpam-5969	359	2	s	s	X
ejpam-5969	359	3	∈	∈	PROPN
ejpam-5969	360	1	[	[	X
ejpam-5969	360	2	clϵ(z)\intϵ(z	clϵ(z)\intϵ(z	NOUN
ejpam-5969	360	3	)	)	PUNCT
ejpam-5969	360	4	]	]	PUNCT
ejpam-5969	360	5	for	for	ADP
ejpam-5969	360	6	an	an	DET
ejpam-5969	360	7	arbitrary	arbitrary	ADJ
ejpam-5969	360	8	point	point	NOUN
ejpam-5969	360	9	s	s	PART
ejpam-5969	360	10	and	and	CCONJ
ejpam-5969	360	11	subset	subset	VERB
ejpam-5969	360	12	z	z	NOUN
ejpam-5969	360	13	of	of	ADP
ejpam-5969	360	14	an	an	DET
ejpam-5969	360	15	sts	st	NOUN
ejpam-5969	360	16	(	(	PUNCT
ejpam-5969	360	17	χ	χ	NOUN
ejpam-5969	360	18	,	,	PUNCT
ejpam-5969	360	19	ν	ν	NOUN
ejpam-5969	360	20	)	)	PUNCT
ejpam-5969	360	21	,	,	PUNCT
ejpam-5969	360	22	then	then	ADV
ejpam-5969	360	23	s	s	VERB
ejpam-5969	360	24	is	be	AUX
ejpam-5969	360	25	called	call	VERB
ejpam-5969	360	26	a	a	DET
ejpam-5969	360	27	supra-ϵ-boundary	supra-ϵ-boundary	ADJ
ejpam-5969	360	28	point	point	NOUN
ejpam-5969	360	29	of	of	ADP
ejpam-5969	360	30	z.	z.	PROPN
ejpam-5969	360	31	the	the	DET
ejpam-5969	360	32	supra-ϵ-boundary	supra-ϵ-boundary	ADJ
ejpam-5969	360	33	set	set	NOUN
ejpam-5969	360	34	of	of	ADP
ejpam-5969	360	35	z	z	PROPN
ejpam-5969	360	36	is	be	AUX
ejpam-5969	360	37	the	the	DET
ejpam-5969	360	38	set	set	NOUN
ejpam-5969	360	39	of	of	ADP
ejpam-5969	360	40	all	all	DET
ejpam-5969	360	41	upper	upper	ADJ
ejpam-5969	360	42	-	-	PUNCT
ejpam-5969	360	43	so	so	ADV
ejpam-5969	360	44	-	-	PUNCT
ejpam-5969	360	45	boundary	boundary	ADJ
ejpam-5969	360	46	points	point	NOUN
ejpam-5969	360	47	of	of	ADP
ejpam-5969	360	48	z	z	NOUN
ejpam-5969	360	49	,	,	PUNCT
ejpam-5969	360	50	and	and	CCONJ
ejpam-5969	360	51	it	it	PRON
ejpam-5969	360	52	is	be	AUX
ejpam-5969	360	53	represented	represent	VERB
ejpam-5969	360	54	by	by	ADP
ejpam-5969	360	55	bϵ(z	bϵ(z	NOUN
ejpam-5969	360	56	)	)	PUNCT
ejpam-5969	360	57	.	.	PUNCT
ejpam-5969	361	1	also	also	ADV
ejpam-5969	361	2	,	,	PUNCT
ejpam-5969	361	3	the	the	DET
ejpam-5969	361	4	supra-ϵ-exterior	supra-ϵ-exterior	PROPN
ejpam-5969	361	5	of	of	ADP
ejpam-5969	361	6	z	z	PROPN
ejpam-5969	361	7	is	be	AUX
ejpam-5969	361	8	also	also	ADV
ejpam-5969	361	9	represented	represent	VERB
ejpam-5969	361	10	by	by	ADP
ejpam-5969	361	11	extϵ(z	extϵ(z	PROPN
ejpam-5969	361	12	)	)	PUNCT
ejpam-5969	361	13	,	,	PUNCT
ejpam-5969	361	14	where	where	SCONJ
ejpam-5969	361	15	extϵ(z	extϵ(z	NOUN
ejpam-5969	361	16	)	)	PUNCT
ejpam-5969	361	17	=	=	PUNCT
ejpam-5969	361	18	intϵ(z	intϵ(z	ADP
ejpam-5969	361	19	c	c	NOUN
ejpam-5969	361	20	)	)	PUNCT
ejpam-5969	361	21	.	.	PUNCT
ejpam-5969	362	1	theorem	theorem	NOUN
ejpam-5969	362	2	12	12	NUM
ejpam-5969	362	3	.	.	PUNCT
ejpam-5969	363	1	regarding	regard	VERB
ejpam-5969	363	2	a	a	DET
ejpam-5969	363	3	subset	subset	NOUN
ejpam-5969	363	4	j	j	PROPN
ejpam-5969	363	5	of	of	ADP
ejpam-5969	363	6	an	an	DET
ejpam-5969	363	7	sts	st	NOUN
ejpam-5969	363	8	(	(	PUNCT
ejpam-5969	363	9	χ	χ	NOUN
ejpam-5969	363	10	,	,	PUNCT
ejpam-5969	363	11	ν	ν	NOUN
ejpam-5969	363	12	)	)	PUNCT
ejpam-5969	363	13	,	,	PUNCT
ejpam-5969	363	14	we	we	PRON
ejpam-5969	363	15	have	have	VERB
ejpam-5969	363	16	(	(	PUNCT
ejpam-5969	363	17	1	1	NUM
ejpam-5969	363	18	)	)	PUNCT
ejpam-5969	363	19	bϵ(j	bϵ(j	NOUN
ejpam-5969	363	20	)	)	PUNCT
ejpam-5969	363	21	=	=	SYM
ejpam-5969	363	22	clϵ(j	clϵ(j	PROPN
ejpam-5969	363	23	)	)	PUNCT
ejpam-5969	363	24	∩	∩	NOUN
ejpam-5969	364	1	[	[	X
ejpam-5969	364	2	intϵ(j	intϵ(j	NOUN
ejpam-5969	364	3	)	)	PUNCT
ejpam-5969	364	4	]	]	PUNCT
ejpam-5969	365	1	c	c	NOUN
ejpam-5969	365	2	=	=	SYM
ejpam-5969	365	3	clϵ(j	clϵ(j	PROPN
ejpam-5969	365	4	)	)	PUNCT
ejpam-5969	365	5	∩	∩	NOUN
ejpam-5969	365	6	clϵ(jc	clϵ(jc	X
ejpam-5969	365	7	)	)	PUNCT
ejpam-5969	365	8	=	=	PUNCT
ejpam-5969	366	1	[	[	X
ejpam-5969	366	2	intϵ(j)∪̃extϵ(j)]c	intϵ(j)∪̃extϵ(j)]c	NOUN
ejpam-5969	366	3	.	.	PUNCT
ejpam-5969	367	1	(	(	PUNCT
ejpam-5969	367	2	2	2	NUM
ejpam-5969	367	3	)	)	PUNCT
ejpam-5969	367	4	bϵ(j	bϵ(j	NOUN
ejpam-5969	367	5	)	)	PUNCT
ejpam-5969	368	1	=	=	PUNCT
ejpam-5969	368	2	bϵ(j	bϵ(j	NUM
ejpam-5969	368	3	c	c	NOUN
ejpam-5969	368	4	)	)	PUNCT
ejpam-5969	368	5	.	.	PUNCT
ejpam-5969	369	1	proof	proof	NOUN
ejpam-5969	369	2	.	.	PUNCT
ejpam-5969	370	1	(	(	PUNCT
ejpam-5969	370	2	1	1	X
ejpam-5969	370	3	)	)	PUNCT
ejpam-5969	370	4	[	[	X
ejpam-5969	370	5	intϵ(j)∪̃extϵ(j)]c	intϵ(j)∪̃extϵ(j)]c	NOUN
ejpam-5969	370	6	=	=	PUNCT
ejpam-5969	371	1	[	[	X
ejpam-5969	371	2	intϵ(j	intϵ(j	NOUN
ejpam-5969	371	3	)	)	PUNCT
ejpam-5969	371	4	]	]	PUNCT
ejpam-5969	372	1	c	c	NOUN
ejpam-5969	372	2	∩	∩	X
ejpam-5969	372	3	[	[	X
ejpam-5969	372	4	intϵ(j	intϵ(j	NUM
ejpam-5969	372	5	c)]c	c)]c	NOUN
ejpam-5969	372	6	=	=	SYM
ejpam-5969	372	7	clϵ(j	clϵ(j	PROPN
ejpam-5969	372	8	)	)	PUNCT
ejpam-5969	372	9	∩	∩	NOUN
ejpam-5969	372	10	[	[	X
ejpam-5969	372	11	intϵ(j	intϵ(j	NOUN
ejpam-5969	372	12	)	)	PUNCT
ejpam-5969	372	13	]	]	PUNCT
ejpam-5969	373	1	c	c	NOUN
ejpam-5969	373	2	from	from	ADP
ejpam-5969	373	3	theorem	theorem	ADJ
ejpam-5969	373	4	9	9	NUM
ejpam-5969	373	5	(	(	PUNCT
ejpam-5969	373	6	1	1	NUM
ejpam-5969	373	7	)	)	PUNCT
ejpam-5969	373	8	=	=	SYM
ejpam-5969	373	9	clϵ(j	clϵ(j	PROPN
ejpam-5969	373	10	)	)	PUNCT
ejpam-5969	373	11	∩	∩	NOUN
ejpam-5969	373	12	clϵ(jc	clϵ(jc	X
ejpam-5969	373	13	)	)	PUNCT
ejpam-5969	373	14	=	=	SYM
ejpam-5969	373	15	clϵ(j)\intϵ(j	clϵ(j)\intϵ(j	NOUN
ejpam-5969	373	16	)	)	PUNCT
ejpam-5969	373	17	=	=	PUNCT
ejpam-5969	373	18	bϵ(j	bϵ(j	NOUN
ejpam-5969	373	19	)	)	PUNCT
ejpam-5969	373	20	.	.	PUNCT
ejpam-5969	374	1	(	(	PUNCT
ejpam-5969	374	2	2	2	X
ejpam-5969	374	3	)	)	PUNCT
ejpam-5969	374	4	bϵ(j	bϵ(j	NOUN
ejpam-5969	374	5	c	c	NOUN
ejpam-5969	374	6	)	)	PUNCT
ejpam-5969	374	7	=	=	PUNCT
ejpam-5969	374	8	clϵ(j	clϵ(j	PROPN
ejpam-5969	374	9	c	c	NOUN
ejpam-5969	374	10	)	)	PUNCT
ejpam-5969	374	11	∩	∩	NOUN
ejpam-5969	375	1	[	[	X
ejpam-5969	375	2	intϵ(j	intϵ(j	NOUN
ejpam-5969	375	3	c)]c	c)]c	NOUN
ejpam-5969	375	4	=	=	PUNCT
ejpam-5969	376	1	[	[	X
ejpam-5969	376	2	intϵ(j	intϵ(j	NOUN
ejpam-5969	376	3	)	)	PUNCT
ejpam-5969	376	4	]	]	PUNCT
ejpam-5969	377	1	c	c	PROPN
ejpam-5969	377	2	∩	∩	X
ejpam-5969	377	3	clϵ(j	clϵ(j	PROPN
ejpam-5969	377	4	)	)	PUNCT
ejpam-5969	377	5	=	=	SYM
ejpam-5969	377	6	bϵ(j	bϵ(j	NOUN
ejpam-5969	377	7	)	)	PUNCT
ejpam-5969	377	8	.	.	PUNCT
ejpam-5969	378	1	theorem	theorem	VERB
ejpam-5969	378	2	13	13	NUM
ejpam-5969	378	3	.	.	PUNCT
ejpam-5969	379	1	regarding	regard	VERB
ejpam-5969	379	2	a	a	DET
ejpam-5969	379	3	subset	subset	NOUN
ejpam-5969	379	4	j	j	PROPN
ejpam-5969	379	5	of	of	ADP
ejpam-5969	379	6	an	an	DET
ejpam-5969	379	7	sts	st	NOUN
ejpam-5969	379	8	(	(	PUNCT
ejpam-5969	379	9	χ	χ	NOUN
ejpam-5969	379	10	,	,	PUNCT
ejpam-5969	379	11	ν	ν	NOUN
ejpam-5969	379	12	)	)	PUNCT
ejpam-5969	379	13	,	,	PUNCT
ejpam-5969	379	14	we	we	PRON
ejpam-5969	379	15	have	have	VERB
ejpam-5969	379	16	(	(	PUNCT
ejpam-5969	379	17	1	1	X
ejpam-5969	379	18	)	)	PUNCT
ejpam-5969	379	19	clϵ(j	clϵ(j	PROPN
ejpam-5969	379	20	)	)	PUNCT
ejpam-5969	379	21	=	=	SYM
ejpam-5969	379	22	intϵ(j)∪̃bϵ(j	intϵ(j)∪̃bϵ(j	PROPN
ejpam-5969	379	23	)	)	PUNCT
ejpam-5969	379	24	.	.	PUNCT
ejpam-5969	380	1	(	(	PUNCT
ejpam-5969	380	2	2	2	X
ejpam-5969	380	3	)	)	PUNCT
ejpam-5969	380	4	clϵ(j	clϵ(j	PROPN
ejpam-5969	380	5	)	)	PUNCT
ejpam-5969	380	6	=	=	SYM
ejpam-5969	380	7	j∪̃bϵ(j	j∪̃bϵ(j	PROPN
ejpam-5969	380	8	)	)	PUNCT
ejpam-5969	380	9	.	.	PUNCT
ejpam-5969	381	1	(	(	PUNCT
ejpam-5969	381	2	3	3	X
ejpam-5969	381	3	)	)	PUNCT
ejpam-5969	381	4	intϵ(j	intϵ(j	NOUN
ejpam-5969	381	5	)	)	PUNCT
ejpam-5969	381	6	=	=	SYM
ejpam-5969	381	7	j\bϵ(j	j\bϵ(j	NOUN
ejpam-5969	381	8	)	)	PUNCT
ejpam-5969	381	9	.	.	PUNCT
ejpam-5969	382	1	proof	proof	NOUN
ejpam-5969	382	2	.	.	PUNCT
ejpam-5969	383	1	abd	abd	PROPN
ejpam-5969	383	2	el	el	PROPN
ejpam-5969	383	3	-	-	PROPN
ejpam-5969	383	4	latif	latif	PROPN
ejpam-5969	383	5	et	et	PROPN
ejpam-5969	383	6	al	al	PROPN
ejpam-5969	383	7	.	.	PUNCT
ejpam-5969	383	8	/	/	SYM
ejpam-5969	383	9	eur	eur	PROPN
ejpam-5969	383	10	.	.	PUNCT
ejpam-5969	384	1	j.	j.	PROPN
ejpam-5969	384	2	pure	pure	PROPN
ejpam-5969	384	3	appl	appl	PROPN
ejpam-5969	384	4	.	.	PROPN
ejpam-5969	384	5	math	math	PROPN
ejpam-5969	384	6	,	,	PUNCT
ejpam-5969	384	7	18	18	NUM
ejpam-5969	384	8	(	(	PUNCT
ejpam-5969	384	9	2	2	NUM
ejpam-5969	384	10	)	)	PUNCT
ejpam-5969	384	11	(	(	PUNCT
ejpam-5969	384	12	2025	2025	NUM
ejpam-5969	384	13	)	)	PUNCT
ejpam-5969	384	14	,	,	PUNCT
ejpam-5969	384	15	5969	5969	NUM
ejpam-5969	384	16	14	14	NUM
ejpam-5969	384	17	of	of	ADP
ejpam-5969	384	18	19	19	NUM
ejpam-5969	384	19	(	(	PUNCT
ejpam-5969	384	20	1	1	NUM
ejpam-5969	384	21	)	)	PUNCT
ejpam-5969	384	22	intϵ(j)∪̃bϵ(j	intϵ(j)∪̃bϵ(j	NUM
ejpam-5969	384	23	)	)	PUNCT
ejpam-5969	384	24	=	=	SYM
ejpam-5969	384	25	intϵ(j)∪̃[clϵ(j	intϵ(j)∪̃[clϵ(j	NOUN
ejpam-5969	384	26	)	)	PUNCT
ejpam-5969	384	27	∩	∩	NOUN
ejpam-5969	385	1	[	[	X
ejpam-5969	385	2	intϵ(j	intϵ(j	NOUN
ejpam-5969	385	3	)	)	PUNCT
ejpam-5969	385	4	]	]	PUNCT
ejpam-5969	386	1	c	c	X
ejpam-5969	386	2	]	]	PUNCT
ejpam-5969	386	3	from	from	ADP
ejpam-5969	386	4	theorem	theorem	ADJ
ejpam-5969	386	5	12	12	NUM
ejpam-5969	386	6	(	(	PUNCT
ejpam-5969	386	7	1	1	NUM
ejpam-5969	386	8	)	)	PUNCT
ejpam-5969	386	9	=	=	NOUN
ejpam-5969	387	1	[	[	X
ejpam-5969	387	2	intϵ(j)∪̃clϵ(j	intϵ(j)∪̃clϵ(j	NOUN
ejpam-5969	387	3	)	)	PUNCT
ejpam-5969	387	4	]	]	PUNCT
ejpam-5969	387	5	∩	∩	NOUN
ejpam-5969	387	6	[	[	X
ejpam-5969	387	7	intϵ(j)∪̃[intϵ(j)]c	intϵ(j)∪̃[intϵ(j)]c	X
ejpam-5969	387	8	]	]	X
ejpam-5969	387	9	=	=	SYM
ejpam-5969	387	10	clϵ(j	clϵ(j	PROPN
ejpam-5969	387	11	)	)	PUNCT
ejpam-5969	387	12	∩	∩	NOUN
ejpam-5969	387	13	χ	χ	X
ejpam-5969	387	14	=	=	PUNCT
ejpam-5969	387	15	clϵ(j	clϵ(j	PROPN
ejpam-5969	387	16	)	)	PUNCT
ejpam-5969	387	17	.	.	PUNCT
ejpam-5969	388	1	(	(	PUNCT
ejpam-5969	388	2	2	2	X
ejpam-5969	388	3	)	)	PUNCT
ejpam-5969	388	4	by	by	ADP
ejpam-5969	388	5	a	a	DET
ejpam-5969	388	6	similar	similar	ADJ
ejpam-5969	388	7	way	way	NOUN
ejpam-5969	388	8	to	to	ADP
ejpam-5969	388	9	(	(	PUNCT
ejpam-5969	388	10	1	1	NUM
ejpam-5969	388	11	)	)	PUNCT
ejpam-5969	388	12	.	.	PUNCT
ejpam-5969	389	1	(	(	PUNCT
ejpam-5969	389	2	3	3	X
ejpam-5969	389	3	)	)	PUNCT
ejpam-5969	389	4	j\bϵ(j	j\bϵ(j	NOUN
ejpam-5969	389	5	)	)	PUNCT
ejpam-5969	390	1	=	=	SYM
ejpam-5969	390	2	j	j	PROPN
ejpam-5969	390	3	∩	∩	NOUN
ejpam-5969	390	4	[	[	X
ejpam-5969	390	5	clϵ(j	clϵ(j	NOUN
ejpam-5969	390	6	)	)	PUNCT
ejpam-5969	390	7	∩	∩	NOUN
ejpam-5969	390	8	[	[	X
ejpam-5969	390	9	intϵ(j	intϵ(j	NOUN
ejpam-5969	390	10	)	)	PUNCT
ejpam-5969	390	11	]	]	PUNCT
ejpam-5969	390	12	c]c	c]c	NOUN
ejpam-5969	390	13	=	=	SYM
ejpam-5969	390	14	j	j	PROPN
ejpam-5969	390	15	∩	∩	NOUN
ejpam-5969	390	16	[	[	X
ejpam-5969	390	17	[	[	X
ejpam-5969	390	18	clϵ(j	clϵ(j	NOUN
ejpam-5969	390	19	)	)	PUNCT
ejpam-5969	390	20	]	]	X
ejpam-5969	390	21	c∪̃[intϵ(j	c∪̃[intϵ(j	PROPN
ejpam-5969	390	22	)	)	PUNCT
ejpam-5969	390	23	]	]	X
ejpam-5969	390	24	]	]	PUNCT
ejpam-5969	390	25	=	=	PUNCT
ejpam-5969	391	1	[	[	X
ejpam-5969	391	2	j	j	X
ejpam-5969	391	3	∩	∩	NOUN
ejpam-5969	391	4	[	[	X
ejpam-5969	391	5	clϵ(j	clϵ(j	NOUN
ejpam-5969	391	6	)	)	PUNCT
ejpam-5969	391	7	]	]	PUNCT
ejpam-5969	391	8	c]∪̃[j	c]∪̃[j	NOUN
ejpam-5969	391	9	∩	∩	ADJ
ejpam-5969	391	10	intϵ(j	intϵ(j	NOUN
ejpam-5969	391	11	)	)	PUNCT
ejpam-5969	391	12	]	]	PUNCT
ejpam-5969	391	13	=	=	PUNCT
ejpam-5969	391	14	∅∪̃intϵ(j	∅∪̃intϵ(j	NOUN
ejpam-5969	391	15	)	)	PUNCT
ejpam-5969	391	16	=	=	SYM
ejpam-5969	391	17	intϵ(j	intϵ(j	NOUN
ejpam-5969	391	18	)	)	PUNCT
ejpam-5969	391	19	.	.	PUNCT
ejpam-5969	392	1	proposition	proposition	NOUN
ejpam-5969	392	2	6	6	NUM
ejpam-5969	392	3	.	.	PUNCT
ejpam-5969	393	1	regarding	regard	VERB
ejpam-5969	393	2	a	a	DET
ejpam-5969	393	3	subset	subset	NOUN
ejpam-5969	393	4	j	j	PROPN
ejpam-5969	393	5	of	of	ADP
ejpam-5969	393	6	an	an	DET
ejpam-5969	393	7	sts	st	NOUN
ejpam-5969	393	8	(	(	PUNCT
ejpam-5969	393	9	χ	χ	NOUN
ejpam-5969	393	10	,	,	PUNCT
ejpam-5969	393	11	ν	ν	NOUN
ejpam-5969	393	12	)	)	PUNCT
ejpam-5969	393	13	,	,	PUNCT
ejpam-5969	393	14	the	the	DET
ejpam-5969	393	15	class	class	NOUN
ejpam-5969	393	16	{	{	PUNCT
ejpam-5969	393	17	bϵ(j	bϵ(j	NOUN
ejpam-5969	393	18	)	)	PUNCT
ejpam-5969	393	19	,	,	PUNCT
ejpam-5969	393	20	intϵ(j	intϵ(j	NOUN
ejpam-5969	393	21	)	)	PUNCT
ejpam-5969	393	22	,	,	PUNCT
ejpam-5969	393	23	extϵ(j	extϵ(j	NOUN
ejpam-5969	393	24	)	)	PUNCT
ejpam-5969	393	25	}	}	PUNCT
ejpam-5969	393	26	forms	form	VERB
ejpam-5969	393	27	a	a	DET
ejpam-5969	393	28	partition	partition	NOUN
ejpam-5969	393	29	for	for	ADP
ejpam-5969	393	30	χ	χ	NOUN
ejpam-5969	393	31	.	.	PUNCT
ejpam-5969	394	1	proof	proof	NOUN
ejpam-5969	394	2	.	.	PUNCT
ejpam-5969	395	1	bϵ(j	bϵ(j	NUM
ejpam-5969	395	2	)	)	PUNCT
ejpam-5969	395	3	∪	∪	ADP
ejpam-5969	395	4	intϵ(j	intϵ(j	NOUN
ejpam-5969	395	5	)	)	PUNCT
ejpam-5969	395	6	∪	∪	ADP
ejpam-5969	395	7	extϵ(j	extϵ(j	NOUN
ejpam-5969	395	8	)	)	PUNCT
ejpam-5969	395	9	=	=	PUNCT
ejpam-5969	396	1	[	[	X
ejpam-5969	396	2	clϵ(j	clϵ(j	NOUN
ejpam-5969	396	3	)	)	PUNCT
ejpam-5969	396	4	∩	∩	NOUN
ejpam-5969	397	1	[	[	X
ejpam-5969	397	2	intϵ(j	intϵ(j	NOUN
ejpam-5969	397	3	)	)	PUNCT
ejpam-5969	397	4	]	]	PUNCT
ejpam-5969	398	1	c	c	X
ejpam-5969	398	2	]	]	X
ejpam-5969	398	3	∪	∪	ADP
ejpam-5969	398	4	intϵ(j	intϵ(j	NOUN
ejpam-5969	398	5	)	)	PUNCT
ejpam-5969	398	6	∪	∪	ADP
ejpam-5969	398	7	[	[	X
ejpam-5969	398	8	clϵ(j	clϵ(j	NOUN
ejpam-5969	398	9	)	)	PUNCT
ejpam-5969	398	10	]	]	PUNCT
ejpam-5969	399	1	c	c	NOUN
ejpam-5969	399	2	=	=	SYM
ejpam-5969	399	3	χ	χ	X
ejpam-5969	399	4	.	.	PUNCT
ejpam-5969	400	1	moreover	moreover	ADV
ejpam-5969	400	2	,	,	PUNCT
ejpam-5969	400	3	bϵ(j	bϵ(j	NUM
ejpam-5969	400	4	)	)	PUNCT
ejpam-5969	400	5	∩	∩	ADJ
ejpam-5969	400	6	intϵ(j	intϵ(j	NOUN
ejpam-5969	400	7	)	)	PUNCT
ejpam-5969	400	8	∩	∩	ADJ
ejpam-5969	400	9	extϵ(j	extϵ(j	NOUN
ejpam-5969	400	10	)	)	PUNCT
ejpam-5969	400	11	=	=	PUNCT
ejpam-5969	401	1	[	[	X
ejpam-5969	401	2	clϵ(j	clϵ(j	NOUN
ejpam-5969	401	3	)	)	PUNCT
ejpam-5969	401	4	∩	∩	NOUN
ejpam-5969	402	1	[	[	X
ejpam-5969	402	2	intϵ(j	intϵ(j	NOUN
ejpam-5969	402	3	)	)	PUNCT
ejpam-5969	402	4	]	]	PUNCT
ejpam-5969	403	1	c	c	X
ejpam-5969	403	2	]	]	X
ejpam-5969	403	3	∩	∩	ADJ
ejpam-5969	403	4	intϵ(j	intϵ(j	NOUN
ejpam-5969	403	5	)	)	PUNCT
ejpam-5969	403	6	∩	∩	NOUN
ejpam-5969	403	7	[	[	X
ejpam-5969	403	8	clϵ(j	clϵ(j	NOUN
ejpam-5969	403	9	)	)	PUNCT
ejpam-5969	403	10	]	]	PUNCT
ejpam-5969	404	1	c	c	X
ejpam-5969	404	2	=	=	PUNCT
ejpam-5969	404	3	∅.	∅.	NOUN
ejpam-5969	404	4	proposition	proposition	NOUN
ejpam-5969	404	5	7	7	NUM
ejpam-5969	404	6	.	.	PUNCT
ejpam-5969	404	7	regarding	regard	VERB
ejpam-5969	404	8	subsets	subset	NOUN
ejpam-5969	404	9	t	t	PROPN
ejpam-5969	404	10	and	and	CCONJ
ejpam-5969	404	11	j	j	PROPN
ejpam-5969	404	12	of	of	ADP
ejpam-5969	404	13	an	an	DET
ejpam-5969	404	14	sts	st	NOUN
ejpam-5969	404	15	(	(	PUNCT
ejpam-5969	404	16	χ	χ	NOUN
ejpam-5969	404	17	,	,	PUNCT
ejpam-5969	404	18	ν	ν	NOUN
ejpam-5969	404	19	)	)	PUNCT
ejpam-5969	404	20	,	,	PUNCT
ejpam-5969	404	21	we	we	PRON
ejpam-5969	404	22	have	have	VERB
ejpam-5969	404	23	(	(	PUNCT
ejpam-5969	404	24	1	1	NUM
ejpam-5969	404	25	)	)	PUNCT
ejpam-5969	404	26	bϵ[intϵ(t	bϵ[intϵ(t	NOUN
ejpam-5969	404	27	)	)	PUNCT
ejpam-5969	404	28	]	]	PUNCT
ejpam-5969	405	1	⊆	⊆	NUM
ejpam-5969	405	2	bϵ(t	bϵ(t	NOUN
ejpam-5969	405	3	)	)	PUNCT
ejpam-5969	405	4	.	.	PUNCT
ejpam-5969	406	1	(	(	PUNCT
ejpam-5969	406	2	2	2	X
ejpam-5969	406	3	)	)	PUNCT
ejpam-5969	406	4	bϵ[clϵ(t	bϵ[clϵ(t	PROPN
ejpam-5969	406	5	)	)	PUNCT
ejpam-5969	406	6	]	]	PUNCT
ejpam-5969	407	1	⊆	⊆	NUM
ejpam-5969	407	2	bϵ(t	bϵ(t	NOUN
ejpam-5969	407	3	)	)	PUNCT
ejpam-5969	407	4	.	.	PUNCT
ejpam-5969	408	1	(	(	PUNCT
ejpam-5969	408	2	3	3	X
ejpam-5969	408	3	)	)	PUNCT
ejpam-5969	408	4	bϵ[t	bϵ[t	PROPN
ejpam-5969	408	5	∪	∪	ADP
ejpam-5969	408	6	j	j	PROPN
ejpam-5969	408	7	]	]	PUNCT
ejpam-5969	408	8	⊆	⊆	NUM
ejpam-5969	408	9	bϵ(t	bϵ(t	NOUN
ejpam-5969	408	10	)	)	PUNCT
ejpam-5969	408	11	∪	∪	ADP
ejpam-5969	408	12	bϵ(j	bϵ(j	NUM
ejpam-5969	408	13	)	)	PUNCT
ejpam-5969	408	14	.	.	PUNCT
ejpam-5969	409	1	(	(	PUNCT
ejpam-5969	409	2	4	4	X
ejpam-5969	409	3	)	)	PUNCT
ejpam-5969	409	4	bϵ[t	bϵ[t	PROPN
ejpam-5969	409	5	∩	∩	NOUN
ejpam-5969	409	6	j	j	X
ejpam-5969	409	7	]	]	PUNCT
ejpam-5969	409	8	⊆	⊆	NUM
ejpam-5969	409	9	bϵ(t	bϵ(t	NOUN
ejpam-5969	409	10	)	)	PUNCT
ejpam-5969	409	11	∪	∪	ADP
ejpam-5969	409	12	bϵ(j	bϵ(j	NUM
ejpam-5969	409	13	)	)	PUNCT
ejpam-5969	409	14	.	.	PUNCT
ejpam-5969	410	1	proof	proof	NOUN
ejpam-5969	410	2	.	.	PUNCT
ejpam-5969	411	1	(	(	PUNCT
ejpam-5969	411	2	1	1	X
ejpam-5969	411	3	)	)	PUNCT
ejpam-5969	411	4	bϵ[intϵ(t	bϵ[intϵ(t	NOUN
ejpam-5969	411	5	)	)	PUNCT
ejpam-5969	411	6	]	]	PUNCT
ejpam-5969	412	1	=	=	SYM
ejpam-5969	412	2	clϵ(intϵ(t	clϵ(intϵ(t	NOUN
ejpam-5969	412	3	)	)	PUNCT
ejpam-5969	412	4	)	)	PUNCT
ejpam-5969	413	1	∩	∩	NOUN
ejpam-5969	413	2	[	[	X
ejpam-5969	413	3	intϵ(intϵ(t	intϵ(intϵ(t	NOUN
ejpam-5969	413	4	)	)	PUNCT
ejpam-5969	413	5	)	)	PUNCT
ejpam-5969	413	6	]	]	PUNCT
ejpam-5969	414	1	c	c	X
ejpam-5969	414	2	⊆	⊆	NUM
ejpam-5969	414	3	clϵ(t	clϵ(t	NOUN
ejpam-5969	414	4	)	)	PUNCT
ejpam-5969	414	5	∩	∩	NOUN
ejpam-5969	415	1	[	[	X
ejpam-5969	415	2	intϵ(t	intϵ(t	NOUN
ejpam-5969	415	3	)	)	PUNCT
ejpam-5969	415	4	]	]	PUNCT
ejpam-5969	416	1	c	c	NOUN
ejpam-5969	416	2	=	=	PUNCT
ejpam-5969	416	3	bϵ(t	bϵ(t	NOUN
ejpam-5969	416	4	)	)	PUNCT
ejpam-5969	416	5	.	.	PUNCT
ejpam-5969	417	1	(	(	PUNCT
ejpam-5969	417	2	2	2	X
ejpam-5969	417	3	)	)	PUNCT
ejpam-5969	417	4	bϵ[clϵ(t	bϵ[clϵ(t	PROPN
ejpam-5969	417	5	)	)	PUNCT
ejpam-5969	417	6	]	]	PUNCT
ejpam-5969	418	1	=	=	SYM
ejpam-5969	418	2	clϵ(clϵ(t	clϵ(clϵ(t	X
ejpam-5969	418	3	)	)	PUNCT
ejpam-5969	418	4	)	)	PUNCT
ejpam-5969	419	1	∩	∩	NOUN
ejpam-5969	419	2	[	[	X
ejpam-5969	419	3	intϵ(clϵ(t	intϵ(clϵ(t	NOUN
ejpam-5969	419	4	)	)	PUNCT
ejpam-5969	419	5	)	)	PUNCT
ejpam-5969	419	6	]	]	PUNCT
ejpam-5969	420	1	c	c	X
ejpam-5969	420	2	=	=	SYM
ejpam-5969	420	3	clϵ(t	clϵ(t	PROPN
ejpam-5969	420	4	)	)	PUNCT
ejpam-5969	420	5	∩	∩	NOUN
ejpam-5969	420	6	clϵ[clϵ(t	clϵ[clϵ(t	NOUN
ejpam-5969	420	7	)	)	PUNCT
ejpam-5969	420	8	]	]	PUNCT
ejpam-5969	420	9	c	c	X
ejpam-5969	420	10	⊆	⊆	NUM
ejpam-5969	420	11	clϵ(t	clϵ(t	NOUN
ejpam-5969	420	12	)	)	PUNCT
ejpam-5969	420	13	∩	∩	NOUN
ejpam-5969	420	14	[	[	X
ejpam-5969	420	15	intϵ(t	intϵ(t	NOUN
ejpam-5969	420	16	)	)	PUNCT
ejpam-5969	420	17	]	]	PUNCT
ejpam-5969	421	1	c	c	NOUN
ejpam-5969	421	2	=	=	PUNCT
ejpam-5969	421	3	bϵ(t	bϵ(t	NOUN
ejpam-5969	421	4	)	)	PUNCT
ejpam-5969	421	5	.	.	PUNCT
ejpam-5969	422	1	(	(	PUNCT
ejpam-5969	422	2	3)-(4	3)-(4	NUM
ejpam-5969	422	3	)	)	PUNCT
ejpam-5969	422	4	follows	follow	VERB
ejpam-5969	422	5	from	from	ADP
ejpam-5969	422	6	theorem	theorem	ADJ
ejpam-5969	422	7	12	12	NUM
ejpam-5969	422	8	.	.	PUNCT
ejpam-5969	422	9	remark	remark	NOUN
ejpam-5969	422	10	9	9	NUM
ejpam-5969	422	11	.	.	PUNCT
ejpam-5969	423	1	the	the	DET
ejpam-5969	423	2	inclusions	inclusion	NOUN
ejpam-5969	423	3	of	of	ADP
ejpam-5969	423	4	proposition	proposition	NOUN
ejpam-5969	423	5	7	7	NUM
ejpam-5969	423	6	are	be	AUX
ejpam-5969	423	7	proper	proper	ADJ
ejpam-5969	423	8	as	as	SCONJ
ejpam-5969	423	9	shown	show	VERB
ejpam-5969	423	10	in	in	ADP
ejpam-5969	423	11	the	the	DET
ejpam-5969	423	12	next	next	ADJ
ejpam-5969	423	13	example	example	NOUN
ejpam-5969	423	14	.	.	PUNCT
ejpam-5969	424	1	example	example	NOUN
ejpam-5969	424	2	5	5	NUM
ejpam-5969	424	3	.	.	PUNCT
ejpam-5969	425	1	regarding	regard	VERB
ejpam-5969	425	2	the	the	DET
ejpam-5969	425	3	sets	set	NOUN
ejpam-5969	425	4	a	a	PRON
ejpam-5969	425	5	=	=	SYM
ejpam-5969	425	6	{	{	PUNCT
ejpam-5969	425	7	1	1	NUM
ejpam-5969	425	8	,	,	PUNCT
ejpam-5969	425	9	3	3	NUM
ejpam-5969	425	10	}	}	PUNCT
ejpam-5969	425	11	,	,	PUNCT
ejpam-5969	425	12	c	c	X
ejpam-5969	425	13	=	=	PUNCT
ejpam-5969	425	14	{	{	PUNCT
ejpam-5969	425	15	2	2	NUM
ejpam-5969	425	16	}	}	PUNCT
ejpam-5969	425	17	,	,	PUNCT
ejpam-5969	425	18	d	d	PROPN
ejpam-5969	425	19	=	=	PUNCT
ejpam-5969	425	20	{	{	PUNCT
ejpam-5969	425	21	3	3	NUM
ejpam-5969	425	22	}	}	PUNCT
ejpam-5969	425	23	and	and	CCONJ
ejpam-5969	425	24	e	e	NOUN
ejpam-5969	425	25	=	=	PUNCT
ejpam-5969	425	26	{	{	PUNCT
ejpam-5969	425	27	2	2	NUM
ejpam-5969	425	28	,	,	PUNCT
ejpam-5969	425	29	3	3	NUM
ejpam-5969	425	30	}	}	PUNCT
ejpam-5969	425	31	,	,	PUNCT
ejpam-5969	425	32	in	in	ADP
ejpam-5969	425	33	example	example	NOUN
ejpam-5969	425	34	2	2	NUM
ejpam-5969	425	35	,	,	PUNCT
ejpam-5969	425	36	we	we	PRON
ejpam-5969	425	37	have	have	VERB
ejpam-5969	425	38	:	:	PUNCT
ejpam-5969	425	39	(	(	PUNCT
ejpam-5969	425	40	1	1	X
ejpam-5969	425	41	)	)	PUNCT
ejpam-5969	425	42	bϵ(c	bϵ(c	NUM
ejpam-5969	425	43	)	)	PUNCT
ejpam-5969	425	44	=	=	SYM
ejpam-5969	426	1	c	c	NOUN
ejpam-5969	426	2	⊈	⊈	PUNCT
ejpam-5969	427	1	bϵ[intϵ(c	bϵ[intϵ(c	ADJ
ejpam-5969	427	2	)	)	PUNCT
ejpam-5969	427	3	]	]	PUNCT
ejpam-5969	428	1	=	=	PUNCT
ejpam-5969	428	2	bϵ(∅	bϵ(∅	PROPN
ejpam-5969	428	3	)	)	PUNCT
ejpam-5969	428	4	=	=	PUNCT
ejpam-5969	428	5	∅.	∅.	X
ejpam-5969	428	6	(	(	PUNCT
ejpam-5969	428	7	2	2	NUM
ejpam-5969	428	8	)	)	PUNCT
ejpam-5969	428	9	bϵ(e	bϵ(e	NUM
ejpam-5969	428	10	)	)	PUNCT
ejpam-5969	429	1	=	=	SYM
ejpam-5969	429	2	χ\{2	χ\{2	PROPN
ejpam-5969	429	3	,	,	PUNCT
ejpam-5969	429	4	3	3	NUM
ejpam-5969	429	5	}	}	PUNCT
ejpam-5969	429	6	=	=	SYM
ejpam-5969	429	7	{	{	PUNCT
ejpam-5969	429	8	1	1	NUM
ejpam-5969	429	9	}	}	PUNCT
ejpam-5969	429	10	⊈	⊈	PROPN
ejpam-5969	429	11	bϵ[clϵ(e	bϵ[clϵ(e	PROPN
ejpam-5969	429	12	)	)	PUNCT
ejpam-5969	429	13	]	]	PUNCT
ejpam-5969	429	14	=	=	PUNCT
ejpam-5969	429	15	bϵ(χ	bϵ(χ	X
ejpam-5969	429	16	)	)	PUNCT
ejpam-5969	429	17	=	=	PUNCT
ejpam-5969	429	18	∅.	∅.	X
ejpam-5969	429	19	(	(	PUNCT
ejpam-5969	429	20	3	3	NUM
ejpam-5969	429	21	)	)	PUNCT
ejpam-5969	429	22	bϵ(a	bϵ(a	NOUN
ejpam-5969	429	23	)	)	PUNCT
ejpam-5969	429	24	∪	∪	ADP
ejpam-5969	429	25	bϵ(e	bϵ(e	NOUN
ejpam-5969	429	26	)	)	PUNCT
ejpam-5969	429	27	=	=	SYM
ejpam-5969	429	28	{	{	PUNCT
ejpam-5969	429	29	1	1	NUM
ejpam-5969	429	30	,	,	PUNCT
ejpam-5969	429	31	2	2	NUM
ejpam-5969	429	32	}	}	PUNCT
ejpam-5969	429	33	∪	∪	ADJ
ejpam-5969	429	34	{	{	PUNCT
ejpam-5969	429	35	2	2	NUM
ejpam-5969	429	36	}	}	PUNCT
ejpam-5969	429	37	=	=	NOUN
ejpam-5969	429	38	{	{	PUNCT
ejpam-5969	429	39	1	1	NUM
ejpam-5969	429	40	,	,	PUNCT
ejpam-5969	429	41	2	2	NUM
ejpam-5969	429	42	}	}	PUNCT
ejpam-5969	429	43	⊈	⊈	PROPN
ejpam-5969	429	44	bϵ[a	bϵ[a	NOUN
ejpam-5969	429	45	∪	∪	VERB
ejpam-5969	429	46	e	e	NOUN
ejpam-5969	429	47	]	]	X
ejpam-5969	429	48	=	=	SYM
ejpam-5969	429	49	bϵ(χ	bϵ(χ	X
ejpam-5969	429	50	)	)	PUNCT
ejpam-5969	429	51	=	=	PUNCT
ejpam-5969	429	52	∅.	∅.	PROPN
ejpam-5969	429	53	abd	abd	PROPN
ejpam-5969	429	54	el	el	PROPN
ejpam-5969	429	55	-	-	PROPN
ejpam-5969	429	56	latif	latif	PROPN
ejpam-5969	429	57	et	et	PROPN
ejpam-5969	429	58	al	al	PROPN
ejpam-5969	429	59	.	.	PUNCT
ejpam-5969	429	60	/	/	SYM
ejpam-5969	429	61	eur	eur	PROPN
ejpam-5969	429	62	.	.	PUNCT
ejpam-5969	430	1	j.	j.	PROPN
ejpam-5969	430	2	pure	pure	PROPN
ejpam-5969	430	3	appl	appl	PROPN
ejpam-5969	430	4	.	.	PROPN
ejpam-5969	430	5	math	math	PROPN
ejpam-5969	430	6	,	,	PUNCT
ejpam-5969	430	7	18	18	NUM
ejpam-5969	430	8	(	(	PUNCT
ejpam-5969	430	9	2	2	NUM
ejpam-5969	430	10	)	)	PUNCT
ejpam-5969	430	11	(	(	PUNCT
ejpam-5969	430	12	2025	2025	NUM
ejpam-5969	430	13	)	)	PUNCT
ejpam-5969	430	14	,	,	PUNCT
ejpam-5969	430	15	5969	5969	NUM
ejpam-5969	430	16	15	15	NUM
ejpam-5969	430	17	of	of	ADP
ejpam-5969	430	18	19	19	NUM
ejpam-5969	430	19	(	(	PUNCT
ejpam-5969	430	20	4	4	NUM
ejpam-5969	430	21	)	)	PUNCT
ejpam-5969	430	22	bϵ(a	bϵ(a	NUM
ejpam-5969	430	23	)	)	PUNCT
ejpam-5969	430	24	∪	∪	ADP
ejpam-5969	430	25	bϵ(e	bϵ(e	NOUN
ejpam-5969	430	26	)	)	PUNCT
ejpam-5969	430	27	=	=	SYM
ejpam-5969	430	28	{	{	PUNCT
ejpam-5969	430	29	1	1	NUM
ejpam-5969	430	30	,	,	PUNCT
ejpam-5969	430	31	2	2	NUM
ejpam-5969	430	32	}	}	PUNCT
ejpam-5969	430	33	⊈	⊈	PROPN
ejpam-5969	431	1	bϵ[a	bϵ[a	NOUN
ejpam-5969	431	2	∩	∩	X
ejpam-5969	431	3	e	e	NOUN
ejpam-5969	431	4	]	]	X
ejpam-5969	431	5	=	=	SYM
ejpam-5969	431	6	bϵ({3	bϵ({3	PROPN
ejpam-5969	431	7	}	}	PUNCT
ejpam-5969	431	8	)	)	PUNCT
ejpam-5969	431	9	=	=	PUNCT
ejpam-5969	431	10	∅.	∅.	NOUN
ejpam-5969	431	11	proposition	proposition	NOUN
ejpam-5969	431	12	8	8	NUM
ejpam-5969	431	13	.	.	PUNCT
ejpam-5969	432	1	the	the	DET
ejpam-5969	432	2	following	follow	VERB
ejpam-5969	432	3	holds	hold	VERB
ejpam-5969	432	4	for	for	ADP
ejpam-5969	432	5	a	a	DET
ejpam-5969	432	6	subset	subset	ADJ
ejpam-5969	432	7	h	h	NOUN
ejpam-5969	432	8	of	of	ADP
ejpam-5969	432	9	an	an	DET
ejpam-5969	432	10	sts	st	NOUN
ejpam-5969	432	11	(	(	PUNCT
ejpam-5969	432	12	χ	χ	NOUN
ejpam-5969	432	13	,	,	PUNCT
ejpam-5969	432	14	ν	ν	NOUN
ejpam-5969	432	15	):	):	PUNCT
ejpam-5969	432	16	(	(	PUNCT
ejpam-5969	432	17	1	1	NUM
ejpam-5969	432	18	)	)	PUNCT
ejpam-5969	432	19	bϵ(h	bϵ(h	NOUN
ejpam-5969	432	20	)	)	PUNCT
ejpam-5969	432	21	∩h	∩h	NOUN
ejpam-5969	433	1	=	=	PUNCT
ejpam-5969	434	1	∅	∅	NOUN
ejpam-5969	435	1	if	if	SCONJ
ejpam-5969	436	1	and	and	CCONJ
ejpam-5969	436	2	only	only	ADV
ejpam-5969	436	3	if	if	SCONJ
ejpam-5969	436	4	h	h	PROPN
ejpam-5969	436	5	∈	∈	PROPN
ejpam-5969	436	6	soϵ(χ	soϵ(χ	VERB
ejpam-5969	436	7	)	)	PUNCT
ejpam-5969	436	8	.	.	PUNCT
ejpam-5969	437	1	(	(	PUNCT
ejpam-5969	437	2	2	2	NUM
ejpam-5969	437	3	)	)	PUNCT
ejpam-5969	437	4	bϵ(h	bϵ(h	NOUN
ejpam-5969	437	5	)	)	PUNCT
ejpam-5969	437	6	⊆	⊆	NUM
ejpam-5969	437	7	h	h	NOUN
ejpam-5969	437	8	if	if	SCONJ
ejpam-5969	437	9	and	and	CCONJ
ejpam-5969	437	10	only	only	ADV
ejpam-5969	437	11	if	if	SCONJ
ejpam-5969	437	12	h	h	NOUN
ejpam-5969	437	13	is	be	AUX
ejpam-5969	437	14	a	a	DET
ejpam-5969	437	15	supra	supra	NOUN
ejpam-5969	437	16	ϵ-closed	ϵ-close	VERB
ejpam-5969	437	17	set	set	NOUN
ejpam-5969	437	18	.	.	PUNCT
ejpam-5969	438	1	(	(	PUNCT
ejpam-5969	438	2	3	3	NUM
ejpam-5969	438	3	)	)	PUNCT
ejpam-5969	438	4	bϵ(h	bϵ(h	NOUN
ejpam-5969	438	5	)	)	PUNCT
ejpam-5969	439	1	=	=	PUNCT
ejpam-5969	439	2	∅	∅	NOUN
ejpam-5969	439	3	if	if	SCONJ
ejpam-5969	439	4	and	and	CCONJ
ejpam-5969	439	5	only	only	ADV
ejpam-5969	439	6	if	if	SCONJ
ejpam-5969	439	7	h	h	NOUN
ejpam-5969	439	8	is	be	AUX
ejpam-5969	439	9	both	both	PRON
ejpam-5969	439	10	supra	supra	PROPN
ejpam-5969	439	11	ϵ-closed	ϵ-close	VERB
ejpam-5969	439	12	and	and	CCONJ
ejpam-5969	439	13	supra	supra	PROPN
ejpam-5969	439	14	ϵ-open	ϵ-open	PROPN
ejpam-5969	439	15	set	set	PROPN
ejpam-5969	439	16	.	.	PUNCT
ejpam-5969	440	1	proof	proof	NOUN
ejpam-5969	440	2	.	.	PUNCT
ejpam-5969	441	1	(	(	PUNCT
ejpam-5969	441	2	1	1	X
ejpam-5969	441	3	)	)	PUNCT
ejpam-5969	441	4	“	"	PUNCT
ejpam-5969	441	5	⇒	⇒	NOUN
ejpam-5969	441	6	”	"	PUNCT
ejpam-5969	441	7	let	let	VERB
ejpam-5969	441	8	bϵ(h	bϵ(h	NOUN
ejpam-5969	441	9	)	)	PUNCT
ejpam-5969	441	10	∩	∩	NOUN
ejpam-5969	441	11	(	(	PUNCT
ejpam-5969	441	12	h	h	NOUN
ejpam-5969	441	13	)	)	PUNCT
ejpam-5969	441	14	=	=	NOUN
ejpam-5969	441	15	∅	∅	NOUN
ejpam-5969	441	16	,	,	PUNCT
ejpam-5969	441	17	then	then	ADV
ejpam-5969	441	18	[	[	X
ejpam-5969	441	19	clϵ(h	clϵ(h	NOUN
ejpam-5969	441	20	)	)	PUNCT
ejpam-5969	441	21	∩	∩	NOUN
ejpam-5969	442	1	[	[	X
ejpam-5969	442	2	intϵ(h)]c	intϵ(h)]c	NOUN
ejpam-5969	442	3	]	]	X
ejpam-5969	442	4	∩	∩	NOUN
ejpam-5969	442	5	(	(	PUNCT
ejpam-5969	442	6	h	h	NOUN
ejpam-5969	442	7	)	)	PUNCT
ejpam-5969	442	8	=	=	NOUN
ejpam-5969	443	1	[	[	X
ejpam-5969	443	2	intϵ(h)]c	intϵ(h)]c	X
ejpam-5969	443	3	∩h	∩h	NOUN
ejpam-5969	443	4	=	=	PUNCT
ejpam-5969	443	5	∅.	∅.	ADP
ejpam-5969	443	6	hence	hence	ADV
ejpam-5969	443	7	,	,	PUNCT
ejpam-5969	443	8	h	h	NOUN
ejpam-5969	443	9	⊆	⊆	NUM
ejpam-5969	443	10	intϵ(h	intϵ(h	NOUN
ejpam-5969	443	11	)	)	PUNCT
ejpam-5969	443	12	.	.	PUNCT
ejpam-5969	444	1	but	but	CCONJ
ejpam-5969	444	2	,	,	PUNCT
ejpam-5969	444	3	we	we	PRON
ejpam-5969	444	4	have	have	VERB
ejpam-5969	444	5	intϵ(h	intϵ(h	NOUN
ejpam-5969	444	6	)	)	PUNCT
ejpam-5969	444	7	⊆	⊆	NUM
ejpam-5969	444	8	h.	h.	PROPN
ejpam-5969	444	9	thus	thus	ADV
ejpam-5969	444	10	,	,	PUNCT
ejpam-5969	444	11	intϵ(h	intϵ(h	ADP
ejpam-5969	444	12	)	)	PUNCT
ejpam-5969	445	1	=	=	SYM
ejpam-5969	445	2	h	h	NOUN
ejpam-5969	446	1	and	and	CCONJ
ejpam-5969	446	2	so	so	ADV
ejpam-5969	446	3	h	h	PROPN
ejpam-5969	446	4	∈	∈	PROPN
ejpam-5969	446	5	soϵ(χ	soϵ(χ	X
ejpam-5969	446	6	)	)	PUNCT
ejpam-5969	446	7	,	,	PUNCT
ejpam-5969	446	8	given	give	VERB
ejpam-5969	446	9	proposition	proposition	NOUN
ejpam-5969	446	10	1	1	NUM
ejpam-5969	446	11	.	.	PUNCT
ejpam-5969	447	1	“	"	PUNCT
ejpam-5969	447	2	⇐	⇐	ADJ
ejpam-5969	447	3	”	"	PUNCT
ejpam-5969	447	4	obvious	obvious	ADJ
ejpam-5969	447	5	.	.	PUNCT
ejpam-5969	448	1	(	(	PUNCT
ejpam-5969	448	2	2	2	X
ejpam-5969	448	3	)	)	PUNCT
ejpam-5969	448	4	clear	clear	ADJ
ejpam-5969	448	5	.	.	PUNCT
ejpam-5969	449	1	(	(	PUNCT
ejpam-5969	449	2	3	3	X
ejpam-5969	449	3	)	)	PUNCT
ejpam-5969	449	4	“	"	PUNCT
ejpam-5969	449	5	⇒	⇒	NOUN
ejpam-5969	449	6	”	"	PUNCT
ejpam-5969	449	7	assume	assume	VERB
ejpam-5969	449	8	that	that	SCONJ
ejpam-5969	449	9	bϵ(h	bϵ(h	NOUN
ejpam-5969	449	10	)	)	PUNCT
ejpam-5969	449	11	=	=	SYM
ejpam-5969	449	12	∅	∅	NOUN
ejpam-5969	449	13	,	,	PUNCT
ejpam-5969	449	14	then	then	ADV
ejpam-5969	449	15	clϵ(h)∩[intϵ(h)]c	clϵ(h)∩[intϵ(h)]c	NOUN
ejpam-5969	449	16	=	=	PUNCT
ejpam-5969	449	17	∅.	∅.	VERB
ejpam-5969	449	18	hence	hence	ADV
ejpam-5969	449	19	,	,	PUNCT
ejpam-5969	449	20	clϵ(h	clϵ(h	PROPN
ejpam-5969	449	21	)	)	PUNCT
ejpam-5969	449	22	⊆	⊆	NUM
ejpam-5969	449	23	intϵ(h	intϵ(h	NOUN
ejpam-5969	449	24	)	)	PUNCT
ejpam-5969	449	25	.	.	PUNCT
ejpam-5969	450	1	however	however	ADV
ejpam-5969	450	2	,	,	PUNCT
ejpam-5969	450	3	we	we	PRON
ejpam-5969	450	4	have	have	VERB
ejpam-5969	450	5	that	that	DET
ejpam-5969	450	6	intϵ(h	intϵ(h	NOUN
ejpam-5969	450	7	)	)	PUNCT
ejpam-5969	450	8	⊆	⊆	NUM
ejpam-5969	450	9	clϵ(h	clϵ(h	PROPN
ejpam-5969	450	10	)	)	PUNCT
ejpam-5969	450	11	.	.	PUNCT
ejpam-5969	451	1	thus	thus	ADV
ejpam-5969	451	2	,	,	PUNCT
ejpam-5969	451	3	intϵ(h	intϵ(h	ADP
ejpam-5969	451	4	)	)	PUNCT
ejpam-5969	451	5	=	=	SYM
ejpam-5969	451	6	clϵ(h	clϵ(h	PROPN
ejpam-5969	451	7	)	)	PUNCT
ejpam-5969	451	8	.	.	PUNCT
ejpam-5969	452	1	therefore	therefore	ADV
ejpam-5969	452	2	,	,	PUNCT
ejpam-5969	452	3	h	h	NOUN
ejpam-5969	452	4	is	be	AUX
ejpam-5969	452	5	both	both	PRON
ejpam-5969	452	6	supra	supra	PROPN
ejpam-5969	452	7	ϵ-closed	ϵ-close	VERB
ejpam-5969	452	8	and	and	CCONJ
ejpam-5969	452	9	supra	supra	PROPN
ejpam-5969	452	10	ϵ-open	ϵ-open	PROPN
ejpam-5969	452	11	set	set	PROPN
ejpam-5969	452	12	,	,	PUNCT
ejpam-5969	452	13	given	give	VERB
ejpam-5969	452	14	theorem	theorem	VERB
ejpam-5969	452	15	6	6	NUM
ejpam-5969	452	16	(	(	PUNCT
ejpam-5969	452	17	2	2	NUM
ejpam-5969	452	18	)	)	PUNCT
ejpam-5969	452	19	and	and	CCONJ
ejpam-5969	452	20	proposition	proposition	NOUN
ejpam-5969	452	21	4	4	NUM
ejpam-5969	452	22	(	(	PUNCT
ejpam-5969	452	23	2	2	NUM
ejpam-5969	452	24	)	)	PUNCT
ejpam-5969	452	25	.	.	PUNCT
ejpam-5969	453	1	“	"	PUNCT
ejpam-5969	453	2	⇐	⇐	ADJ
ejpam-5969	453	3	”	"	PUNCT
ejpam-5969	453	4	obvious	obvious	ADJ
ejpam-5969	453	5	theorem	theorem	NOUN
ejpam-5969	453	6	14	14	NUM
ejpam-5969	453	7	.	.	PUNCT
ejpam-5969	453	8	bϵ(h	bϵ(h	NOUN
ejpam-5969	453	9	)	)	PUNCT
ejpam-5969	453	10	∈	∈	PROPN
ejpam-5969	453	11	scϵ(χ	scϵ(χ	PROPN
ejpam-5969	453	12	)	)	PUNCT
ejpam-5969	453	13	for	for	ADP
ejpam-5969	453	14	a	a	DET
ejpam-5969	453	15	subset	subset	ADJ
ejpam-5969	453	16	h	h	NOUN
ejpam-5969	453	17	of	of	ADP
ejpam-5969	453	18	an	an	DET
ejpam-5969	453	19	sts	st	NOUN
ejpam-5969	453	20	(	(	PUNCT
ejpam-5969	453	21	χ	χ	NOUN
ejpam-5969	453	22	,	,	PUNCT
ejpam-5969	453	23	ν	ν	NOUN
ejpam-5969	453	24	)	)	PUNCT
ejpam-5969	453	25	.	.	PUNCT
ejpam-5969	454	1	proof	proof	NOUN
ejpam-5969	454	2	.	.	PUNCT
ejpam-5969	455	1	if	if	SCONJ
ejpam-5969	455	2	either	either	PRON
ejpam-5969	455	3	clϵ(h	clϵ(h	PROPN
ejpam-5969	455	4	)	)	PUNCT
ejpam-5969	455	5	=	=	SYM
ejpam-5969	455	6	χ	χ	NOUN
ejpam-5969	455	7	or	or	CCONJ
ejpam-5969	455	8	clϵ(h	clϵ(h	PROPN
ejpam-5969	455	9	c	c	NOUN
ejpam-5969	455	10	)	)	PUNCT
ejpam-5969	456	1	=	=	SYM
ejpam-5969	456	2	χ	χ	NOUN
ejpam-5969	456	3	,	,	PUNCT
ejpam-5969	456	4	given	give	VERB
ejpam-5969	456	5	theorem	theorem	VERB
ejpam-5969	456	6	12	12	NUM
ejpam-5969	456	7	(	(	PUNCT
ejpam-5969	456	8	1	1	NUM
ejpam-5969	456	9	)	)	PUNCT
ejpam-5969	456	10	,	,	PUNCT
ejpam-5969	456	11	we	we	PRON
ejpam-5969	456	12	get	get	VERB
ejpam-5969	456	13	the	the	DET
ejpam-5969	456	14	our	our	PRON
ejpam-5969	456	15	proof	proof	NOUN
ejpam-5969	456	16	.	.	PUNCT
ejpam-5969	457	1	if	if	SCONJ
ejpam-5969	457	2	clϵ(h	clϵ(h	PROPN
ejpam-5969	457	3	)	)	PUNCT
ejpam-5969	457	4	̸=	̸=	PROPN
ejpam-5969	457	5	χ	χ	NOUN
ejpam-5969	457	6	and	and	CCONJ
ejpam-5969	457	7	clϵ(h	clϵ(h	PROPN
ejpam-5969	457	8	c	c	X
ejpam-5969	457	9	)	)	PUNCT
ejpam-5969	457	10	̸=	̸=	PROPN
ejpam-5969	457	11	χ	χ	NOUN
ejpam-5969	457	12	,	,	PUNCT
ejpam-5969	457	13	given	give	VERB
ejpam-5969	457	14	theorem	theorem	VERB
ejpam-5969	457	15	3	3	NUM
ejpam-5969	457	16	(	(	PUNCT
ejpam-5969	457	17	2	2	NUM
ejpam-5969	457	18	)	)	PUNCT
ejpam-5969	457	19	,	,	PUNCT
ejpam-5969	457	20	bϵ(h	bϵ(h	NOUN
ejpam-5969	457	21	)	)	PUNCT
ejpam-5969	457	22	=	=	SYM
ejpam-5969	457	23	clϵ(h	clϵ(h	ADJ
ejpam-5969	457	24	)	)	PUNCT
ejpam-5969	457	25	∩	∩	ADJ
ejpam-5969	457	26	clϵ(hc	clϵ(hc	NOUN
ejpam-5969	457	27	)	)	PUNCT
ejpam-5969	457	28	∈	∈	PROPN
ejpam-5969	457	29	scϵ(χ	scϵ(χ	NUM
ejpam-5969	457	30	)	)	PUNCT
ejpam-5969	457	31	.	.	PUNCT
ejpam-5969	458	1	5	5	X
ejpam-5969	458	2	.	.	X
ejpam-5969	458	3	conclusion	conclusion	NOUN
ejpam-5969	458	4	in	in	ADP
ejpam-5969	458	5	this	this	DET
ejpam-5969	458	6	project	project	NOUN
ejpam-5969	458	7	,	,	PUNCT
ejpam-5969	458	8	we	we	PRON
ejpam-5969	458	9	introduce	introduce	VERB
ejpam-5969	458	10	a	a	DET
ejpam-5969	458	11	novel	novel	NOUN
ejpam-5969	458	12	weaker	weak	ADJ
ejpam-5969	458	13	form	form	NOUN
ejpam-5969	458	14	of	of	ADP
ejpam-5969	458	15	supra	supra	ADJ
ejpam-5969	458	16	open	open	ADJ
ejpam-5969	458	17	sets	set	NOUN
ejpam-5969	458	18	,	,	PUNCT
ejpam-5969	458	19	named	name	VERB
ejpam-5969	458	20	supra	supra	PROPN
ejpam-5969	458	21	ϵopen	ϵopen	NOUN
ejpam-5969	458	22	sets	set	NOUN
ejpam-5969	458	23	and	and	CCONJ
ejpam-5969	458	24	provide	provide	VERB
ejpam-5969	458	25	its	its	PRON
ejpam-5969	458	26	essential	essential	ADJ
ejpam-5969	458	27	features	feature	NOUN
ejpam-5969	458	28	.	.	PUNCT
ejpam-5969	459	1	the	the	DET
ejpam-5969	459	2	notions	notion	NOUN
ejpam-5969	459	3	of	of	ADP
ejpam-5969	459	4	supra	supra	PROPN
ejpam-5969	459	5	regular	regular	PROPN
ejpam-5969	459	6	(	(	PUNCT
ejpam-5969	459	7	α-	α-	X
ejpam-5969	459	8	,	,	PUNCT
ejpam-5969	459	9	semi-	semi-	ADJ
ejpam-5969	459	10	,	,	PUNCT
ejpam-5969	459	11	pre-	pre-	X
ejpam-5969	459	12	,	,	PUNCT
ejpam-5969	459	13	b-	b-	X
ejpam-5969	459	14	,	,	PUNCT
ejpam-5969	459	15	β-	β-	X
ejpam-5969	459	16	,	,	PUNCT
ejpam-5969	459	17	and	and	CCONJ
ejpam-5969	459	18	r-	r-	X
ejpam-5969	459	19	)	)	PUNCT
ejpam-5969	459	20	open	open	ADJ
ejpam-5969	459	21	sets	set	NOUN
ejpam-5969	459	22	,	,	PUNCT
ejpam-5969	459	23	which	which	PRON
ejpam-5969	459	24	were	be	AUX
ejpam-5969	459	25	previously	previously	ADV
ejpam-5969	459	26	similar	similar	ADJ
ejpam-5969	459	27	,	,	PUNCT
ejpam-5969	459	28	are	be	AUX
ejpam-5969	459	29	shown	show	VERB
ejpam-5969	459	30	to	to	PART
ejpam-5969	459	31	be	be	AUX
ejpam-5969	459	32	included	include	VERB
ejpam-5969	459	33	in	in	ADP
ejpam-5969	459	34	this	this	DET
ejpam-5969	459	35	new	new	ADJ
ejpam-5969	459	36	supra	supra	PROPN
ejpam-5969	459	37	open	open	ADJ
ejpam-5969	459	38	set	set	VERB
ejpam-5969	459	39	category	category	NOUN
ejpam-5969	459	40	.	.	PUNCT
ejpam-5969	460	1	moreover	moreover	ADV
ejpam-5969	460	2	,	,	PUNCT
ejpam-5969	460	3	we	we	PRON
ejpam-5969	460	4	provide	provide	VERB
ejpam-5969	460	5	new	new	ADJ
ejpam-5969	460	6	types	type	NOUN
ejpam-5969	460	7	of	of	ADP
ejpam-5969	460	8	operators	operator	NOUN
ejpam-5969	460	9	named	name	VERB
ejpam-5969	460	10	supra	supra	PROPN
ejpam-5969	460	11	ϵ-interior	ϵ-interior	PROPN
ejpam-5969	460	12	(	(	PUNCT
ejpam-5969	460	13	closure	closure	NOUN
ejpam-5969	460	14	,	,	PUNCT
ejpam-5969	460	15	accumulation	accumulation	NOUN
ejpam-5969	460	16	,	,	PUNCT
ejpam-5969	460	17	exterior	exterior	ADJ
ejpam-5969	460	18	,	,	PUNCT
ejpam-5969	460	19	and	and	CCONJ
ejpam-5969	460	20	boundary	boundary	ADJ
ejpam-5969	460	21	,	,	PUNCT
ejpam-5969	460	22	respectively	respectively	ADV
ejpam-5969	460	23	)	)	PUNCT
ejpam-5969	460	24	using	use	VERB
ejpam-5969	460	25	our	our	PRON
ejpam-5969	460	26	recently	recently	ADV
ejpam-5969	460	27	established	establish	VERB
ejpam-5969	460	28	category	category	NOUN
ejpam-5969	460	29	of	of	ADP
ejpam-5969	460	30	supra	supra	PROPN
ejpam-5969	460	31	open	open	ADJ
ejpam-5969	460	32	sets	set	NOUN
ejpam-5969	460	33	.	.	PUNCT
ejpam-5969	461	1	we	we	PRON
ejpam-5969	461	2	also	also	ADV
ejpam-5969	461	3	describe	describe	VERB
ejpam-5969	461	4	the	the	DET
ejpam-5969	461	5	differences	difference	NOUN
ejpam-5969	461	6	between	between	ADP
ejpam-5969	461	7	these	these	DET
ejpam-5969	461	8	new	new	ADJ
ejpam-5969	461	9	operators	operator	NOUN
ejpam-5969	461	10	and	and	CCONJ
ejpam-5969	461	11	their	their	PRON
ejpam-5969	461	12	corresponding	correspond	VERB
ejpam-5969	461	13	operators	operator	NOUN
ejpam-5969	461	14	.	.	PUNCT
ejpam-5969	462	1	moreover	moreover	ADV
ejpam-5969	462	2	,	,	PUNCT
ejpam-5969	462	3	we	we	PRON
ejpam-5969	462	4	prove	prove	VERB
ejpam-5969	462	5	that	that	SCONJ
ejpam-5969	462	6	supra	supra	PROPN
ejpam-5969	462	7	ϵ-interior	ϵ-interior	PROPN
ejpam-5969	462	8	abd	abd	PROPN
ejpam-5969	462	9	el	el	PROPN
ejpam-5969	462	10	-	-	PROPN
ejpam-5969	462	11	latif	latif	PROPN
ejpam-5969	462	12	et	et	PROPN
ejpam-5969	462	13	al	al	PROPN
ejpam-5969	462	14	.	.	PUNCT
ejpam-5969	462	15	/	/	SYM
ejpam-5969	462	16	eur	eur	PROPN
ejpam-5969	462	17	.	.	PUNCT
ejpam-5969	463	1	j.	j.	PROPN
ejpam-5969	463	2	pure	pure	PROPN
ejpam-5969	463	3	appl	appl	PROPN
ejpam-5969	463	4	.	.	PROPN
ejpam-5969	463	5	math	math	PROPN
ejpam-5969	463	6	,	,	PUNCT
ejpam-5969	463	7	18	18	NUM
ejpam-5969	463	8	(	(	PUNCT
ejpam-5969	463	9	2	2	NUM
ejpam-5969	463	10	)	)	PUNCT
ejpam-5969	463	11	(	(	PUNCT
ejpam-5969	463	12	2025	2025	NUM
ejpam-5969	463	13	)	)	PUNCT
ejpam-5969	463	14	,	,	PUNCT
ejpam-5969	463	15	5969	5969	NUM
ejpam-5969	463	16	16	16	NUM
ejpam-5969	463	17	of	of	ADP
ejpam-5969	463	18	19	19	NUM
ejpam-5969	463	19	operator	operator	NOUN
ejpam-5969	463	20	,	,	PUNCT
ejpam-5969	463	21	supra	supra	NOUN
ejpam-5969	463	22	ϵ-boundary	ϵ-boundary	ADJ
ejpam-5969	463	23	operator	operator	NOUN
ejpam-5969	463	24	and	and	CCONJ
ejpam-5969	463	25	supra	supra	ADJ
ejpam-5969	463	26	ϵ-exterior	ϵ-exterior	PROPN
ejpam-5969	463	27	operator	operator	NOUN
ejpam-5969	463	28	form	form	VERB
ejpam-5969	463	29	a	a	DET
ejpam-5969	463	30	partition	partition	NOUN
ejpam-5969	463	31	for	for	ADP
ejpam-5969	463	32	χ	χ	NOUN
ejpam-5969	463	33	.	.	PUNCT
ejpam-5969	464	1	finally	finally	ADV
ejpam-5969	464	2	,	,	PUNCT
ejpam-5969	464	3	we	we	PRON
ejpam-5969	464	4	complement	complement	VERB
ejpam-5969	464	5	our	our	PRON
ejpam-5969	464	6	investigations	investigation	NOUN
ejpam-5969	464	7	with	with	ADP
ejpam-5969	464	8	many	many	ADJ
ejpam-5969	464	9	examples	example	NOUN
ejpam-5969	464	10	and	and	CCONJ
ejpam-5969	464	11	counterexamples	counterexample	NOUN
ejpam-5969	464	12	that	that	PRON
ejpam-5969	464	13	highlight	highlight	VERB
ejpam-5969	464	14	the	the	DET
ejpam-5969	464	15	significance	significance	NOUN
ejpam-5969	464	16	of	of	ADP
ejpam-5969	464	17	our	our	PRON
ejpam-5969	464	18	innovative	innovative	ADJ
ejpam-5969	464	19	operators	operator	NOUN
ejpam-5969	464	20	.	.	PUNCT
ejpam-5969	465	1	further	further	ADJ
ejpam-5969	465	2	research	research	NOUN
ejpam-5969	465	3	on	on	ADP
ejpam-5969	465	4	the	the	DET
ejpam-5969	465	5	theoretical	theoretical	ADJ
ejpam-5969	465	6	aspects	aspect	NOUN
ejpam-5969	465	7	of	of	ADP
ejpam-5969	465	8	these	these	DET
ejpam-5969	465	9	generalized	generalize	VERB
ejpam-5969	465	10	concepts	concept	NOUN
ejpam-5969	465	11	might	might	AUX
ejpam-5969	465	12	be	be	AUX
ejpam-5969	465	13	conducted	conduct	VERB
ejpam-5969	465	14	from	from	ADP
ejpam-5969	465	15	the	the	DET
ejpam-5969	465	16	specific	specific	ADJ
ejpam-5969	465	17	approaches	approach	NOUN
ejpam-5969	465	18	presented	present	VERB
ejpam-5969	465	19	in	in	ADP
ejpam-5969	465	20	this	this	DET
ejpam-5969	465	21	work	work	NOUN
ejpam-5969	465	22	by	by	ADP
ejpam-5969	465	23	examining	examine	VERB
ejpam-5969	465	24	the	the	DET
ejpam-5969	465	25	following	follow	VERB
ejpam-5969	465	26	topics	topic	NOUN
ejpam-5969	465	27	:	:	PUNCT
ejpam-5969	465	28	•	•	NUM
ejpam-5969	465	29	study	study	VERB
ejpam-5969	465	30	some	some	DET
ejpam-5969	465	31	topological	topological	ADJ
ejpam-5969	465	32	properties	property	NOUN
ejpam-5969	465	33	inspired	inspire	VERB
ejpam-5969	465	34	by	by	ADP
ejpam-5969	465	35	the	the	DET
ejpam-5969	465	36	specific	specific	ADJ
ejpam-5969	465	37	approaches	approach	NOUN
ejpam-5969	465	38	presented	present	VERB
ejpam-5969	465	39	in	in	ADP
ejpam-5969	465	40	this	this	DET
ejpam-5969	465	41	work	work	NOUN
ejpam-5969	465	42	,	,	PUNCT
ejpam-5969	465	43	like	like	ADP
ejpam-5969	465	44	supra	supra	ADJ
ejpam-5969	465	45	continuity	continuity	NOUN
ejpam-5969	465	46	(	(	PUNCT
ejpam-5969	465	47	separation	separation	NOUN
ejpam-5969	465	48	axioms	axiom	NOUN
ejpam-5969	465	49	,	,	PUNCT
ejpam-5969	465	50	connectedness	connectedness	NOUN
ejpam-5969	465	51	,	,	PUNCT
ejpam-5969	465	52	and	and	CCONJ
ejpam-5969	465	53	compactness	compactness	NOUN
ejpam-5969	465	54	)	)	PUNCT
ejpam-5969	465	55	.	.	PUNCT
ejpam-5969	466	1	•	•	NUM
ejpam-5969	466	2	examine	examine	VERB
ejpam-5969	466	3	whether	whether	SCONJ
ejpam-5969	466	4	these	these	DET
ejpam-5969	466	5	notions	notion	NOUN
ejpam-5969	466	6	,	,	PUNCT
ejpam-5969	466	7	in	in	ADP
ejpam-5969	466	8	particular	particular	ADJ
ejpam-5969	466	9	the	the	DET
ejpam-5969	466	10	separation	separation	NOUN
ejpam-5969	466	11	axiom	axiom	NOUN
ejpam-5969	466	12	,	,	PUNCT
ejpam-5969	466	13	may	may	AUX
ejpam-5969	466	14	be	be	AUX
ejpam-5969	466	15	applied	apply	VERB
ejpam-5969	466	16	to	to	ADP
ejpam-5969	466	17	information	information	NOUN
ejpam-5969	466	18	systems	system	NOUN
ejpam-5969	466	19	.	.	PUNCT
ejpam-5969	467	1	•	•	NUM
ejpam-5969	467	2	apply	apply	VERB
ejpam-5969	467	3	these	these	DET
ejpam-5969	467	4	approaches	approach	NOUN
ejpam-5969	467	5	to	to	ADP
ejpam-5969	467	6	soft	soft	ADJ
ejpam-5969	467	7	ideal	ideal	ADJ
ejpam-5969	467	8	topological	topological	ADJ
ejpam-5969	467	9	spaces	space	NOUN
ejpam-5969	467	10	[	[	X
ejpam-5969	467	11	33	33	NUM
ejpam-5969	467	12	,	,	PUNCT
ejpam-5969	467	13	48	48	NUM
ejpam-5969	467	14	,	,	PUNCT
ejpam-5969	467	15	49	49	NUM
ejpam-5969	467	16	]	]	PUNCT
ejpam-5969	467	17	,	,	PUNCT
ejpam-5969	467	18	and	and	CCONJ
ejpam-5969	467	19	supra	supra	PROPN
ejpam-5969	467	20	soft	soft	ADJ
ejpam-5969	467	21	topological	topological	ADJ
ejpam-5969	467	22	spaces	space	NOUN
ejpam-5969	467	23	[	[	X
ejpam-5969	467	24	42	42	NUM
ejpam-5969	467	25	]	]	PUNCT
ejpam-5969	467	26	.	.	PUNCT
ejpam-5969	468	1	acknowledgements	acknowledgement	NOUN
ejpam-5969	468	2	the	the	DET
ejpam-5969	468	3	authors	author	NOUN
ejpam-5969	468	4	extend	extend	VERB
ejpam-5969	468	5	their	their	PRON
ejpam-5969	468	6	appreciation	appreciation	NOUN
ejpam-5969	468	7	to	to	ADP
ejpam-5969	468	8	the	the	DET
ejpam-5969	468	9	deanship	deanship	NOUN
ejpam-5969	468	10	of	of	ADP
ejpam-5969	468	11	scientific	scientific	ADJ
ejpam-5969	468	12	research	research	NOUN
ejpam-5969	468	13	at	at	ADP
ejpam-5969	468	14	northern	northern	ADJ
ejpam-5969	468	15	border	border	NOUN
ejpam-5969	468	16	university	university	PROPN
ejpam-5969	468	17	,	,	PUNCT
ejpam-5969	468	18	arar	arar	PROPN
ejpam-5969	468	19	,	,	PUNCT
ejpam-5969	468	20	ksa	ksa	PROPN
ejpam-5969	468	21	for	for	ADP
ejpam-5969	468	22	funding	fund	VERB
ejpam-5969	468	23	this	this	DET
ejpam-5969	468	24	research	research	NOUN
ejpam-5969	468	25	work	work	NOUN
ejpam-5969	468	26	through	through	ADP
ejpam-5969	468	27	the	the	DET
ejpam-5969	468	28	project	project	NOUN
ejpam-5969	468	29	number	number	NOUN
ejpam-5969	468	30	”	"	PUNCT
ejpam-5969	468	31	nbu	nbu	NOUN
ejpam-5969	468	32	-	-	PUNCT
ejpam-5969	468	33	ffr-2025	ffr-2025	NOUN
ejpam-5969	468	34	-	-	PUNCT
ejpam-5969	468	35	1153	1153	NUM
ejpam-5969	468	36	-	-	SYM
ejpam-5969	468	37	01	01	NUM
ejpam-5969	468	38	”	"	PUNCT
ejpam-5969	468	39	.	.	PUNCT
ejpam-5969	469	1	also	also	ADV
ejpam-5969	469	2	,	,	PUNCT
ejpam-5969	469	3	this	this	DET
ejpam-5969	469	4	study	study	NOUN
ejpam-5969	469	5	is	be	AUX
ejpam-5969	469	6	supported	support	VERB
ejpam-5969	469	7	via	via	ADP
ejpam-5969	469	8	funding	funding	NOUN
ejpam-5969	469	9	from	from	ADP
ejpam-5969	469	10	prince	prince	PROPN
ejpam-5969	469	11	sattam	sattam	PROPN
ejpam-5969	469	12	bin	bin	PROPN
ejpam-5969	469	13	abdulaziz	abdulaziz	PROPN
ejpam-5969	469	14	university	university	PROPN
ejpam-5969	469	15	project	project	NOUN
ejpam-5969	469	16	number	number	NOUN
ejpam-5969	469	17	(	(	PUNCT
ejpam-5969	469	18	psau/2025	psau/2025	NOUN
ejpam-5969	469	19	/	/	SYM
ejpam-5969	469	20	r/1446	r/1446	PROPN
ejpam-5969	469	21	)	)	PUNCT
ejpam-5969	469	22	and	and	CCONJ
ejpam-5969	469	23	this	this	DET
ejpam-5969	469	24	research	research	NOUN
ejpam-5969	469	25	is	be	AUX
ejpam-5969	469	26	funded	fund	VERB
ejpam-5969	469	27	by	by	ADP
ejpam-5969	469	28	zarqa	zarqa	PROPN
ejpam-5969	469	29	university	university	PROPN
ejpam-5969	469	30	jordan	jordan	PROPN
ejpam-5969	469	31	.	.	PUNCT
ejpam-5969	470	1	conflict	conflict	NOUN
ejpam-5969	470	2	of	of	ADP
ejpam-5969	470	3	interest	interest	NOUN
ejpam-5969	470	4	there	there	PRON
ejpam-5969	470	5	are	be	VERB
ejpam-5969	470	6	no	no	DET
ejpam-5969	470	7	conflicts	conflict	NOUN
ejpam-5969	470	8	of	of	ADP
ejpam-5969	470	9	interest	interest	NOUN
ejpam-5969	470	10	disclosed	disclose	VERB
ejpam-5969	470	11	by	by	ADP
ejpam-5969	470	12	the	the	DET
ejpam-5969	470	13	authors	author	NOUN
ejpam-5969	470	14	.	.	PUNCT
ejpam-5969	471	1	references	reference	NOUN
ejpam-5969	471	2	[	[	X
ejpam-5969	471	3	1	1	NUM
ejpam-5969	471	4	]	]	X
ejpam-5969	471	5	n.	n.	PROPN
ejpam-5969	471	6	levine	levine	PROPN
ejpam-5969	471	7	.	.	PUNCT
ejpam-5969	472	1	semi	semi	ADJ
ejpam-5969	472	2	-	-	ADJ
ejpam-5969	472	3	open	open	ADJ
ejpam-5969	472	4	sets	set	NOUN
ejpam-5969	472	5	and	and	CCONJ
ejpam-5969	472	6	semi	semi	ADJ
ejpam-5969	472	7	-	-	NOUN
ejpam-5969	472	8	continuity	continuity	NOUN
ejpam-5969	472	9	in	in	ADP
ejpam-5969	472	10	topological	topological	ADJ
ejpam-5969	472	11	spaces	space	NOUN
ejpam-5969	472	12	.	.	PUNCT
ejpam-5969	473	1	american	american	PROPN
ejpam-5969	473	2	mathematical	mathematical	PROPN
ejpam-5969	473	3	monthly	monthly	ADV
ejpam-5969	473	4	,	,	PUNCT
ejpam-5969	473	5	70(1):36–41	70(1):36–41	NUM
ejpam-5969	473	6	,	,	PUNCT
ejpam-5969	473	7	1963	1963	NUM
ejpam-5969	473	8	.	.	PUNCT
ejpam-5969	474	1	[	[	X
ejpam-5969	474	2	2	2	NUM
ejpam-5969	474	3	]	]	X
ejpam-5969	474	4	o.	o.	PROPN
ejpam-5969	474	5	njastad	njastad	PROPN
ejpam-5969	474	6	.	.	PUNCT
ejpam-5969	475	1	on	on	ADP
ejpam-5969	475	2	some	some	DET
ejpam-5969	475	3	classes	class	NOUN
ejpam-5969	475	4	of	of	ADP
ejpam-5969	475	5	nearly	nearly	ADV
ejpam-5969	475	6	open	open	ADJ
ejpam-5969	475	7	sets	set	NOUN
ejpam-5969	475	8	.	.	PUNCT
ejpam-5969	476	1	pacific	pacific	PROPN
ejpam-5969	476	2	journal	journal	PROPN
ejpam-5969	476	3	of	of	ADP
ejpam-5969	476	4	mathematics	mathematic	NOUN
ejpam-5969	476	5	,	,	PUNCT
ejpam-5969	476	6	15(3):961–970	15(3):961–970	PROPN
ejpam-5969	476	7	,	,	PUNCT
ejpam-5969	476	8	1965	1965	NUM
ejpam-5969	476	9	.	.	PUNCT
ejpam-5969	477	1	[	[	X
ejpam-5969	477	2	3	3	X
ejpam-5969	477	3	]	]	PUNCT
ejpam-5969	477	4	a.	a.	NOUN
ejpam-5969	477	5	mashhour	mashhour	PROPN
ejpam-5969	477	6	,	,	PUNCT
ejpam-5969	477	7	m.	m.	PROPN
ejpam-5969	477	8	abd	abd	PROPN
ejpam-5969	477	9	el	el	PROPN
ejpam-5969	477	10	-	-	PROPN
ejpam-5969	477	11	monsef	monsef	ADJ
ejpam-5969	477	12	,	,	PUNCT
ejpam-5969	477	13	and	and	CCONJ
ejpam-5969	477	14	s.	s.	PROPN
ejpam-5969	477	15	el	el	PROPN
ejpam-5969	477	16	-	-	PROPN
ejpam-5969	477	17	deeb	deeb	PROPN
ejpam-5969	477	18	.	.	PUNCT
ejpam-5969	478	1	on	on	ADP
ejpam-5969	478	2	precontinuous	precontinuous	ADJ
ejpam-5969	478	3	and	and	CCONJ
ejpam-5969	478	4	weak	weak	ADJ
ejpam-5969	478	5	precontinuous	precontinuous	ADJ
ejpam-5969	478	6	mappings	mapping	NOUN
ejpam-5969	478	7	.	.	PUNCT
ejpam-5969	479	1	proceedings	proceeding	NOUN
ejpam-5969	479	2	of	of	ADP
ejpam-5969	479	3	the	the	DET
ejpam-5969	479	4	mathematical	mathematical	ADJ
ejpam-5969	479	5	and	and	CCONJ
ejpam-5969	479	6	physical	physical	ADJ
ejpam-5969	479	7	society	society	NOUN
ejpam-5969	479	8	,	,	PUNCT
ejpam-5969	479	9	53:47–53	53:47–53	NUM
ejpam-5969	479	10	,	,	PUNCT
ejpam-5969	479	11	1982	1982	NUM
ejpam-5969	479	12	.	.	PUNCT
ejpam-5969	480	1	[	[	X
ejpam-5969	480	2	4	4	X
ejpam-5969	480	3	]	]	PUNCT
ejpam-5969	480	4	m.	m.	NOUN
ejpam-5969	480	5	abd	abd	PROPN
ejpam-5969	480	6	el	el	PROPN
ejpam-5969	480	7	-	-	PROPN
ejpam-5969	480	8	monsef	monsef	PROPN
ejpam-5969	480	9	,	,	PUNCT
ejpam-5969	480	10	s.	s.	PROPN
ejpam-5969	480	11	el	el	PROPN
ejpam-5969	480	12	-	-	PROPN
ejpam-5969	480	13	deeb	deeb	PROPN
ejpam-5969	480	14	,	,	PUNCT
ejpam-5969	480	15	and	and	CCONJ
ejpam-5969	480	16	r.	r.	PROPN
ejpam-5969	480	17	mahmoud	mahmoud	PROPN
ejpam-5969	480	18	.	.	PUNCT
ejpam-5969	481	1	β	β	X
ejpam-5969	481	2	-	-	ADJ
ejpam-5969	481	3	open	open	ADJ
ejpam-5969	481	4	sets	set	NOUN
ejpam-5969	481	5	and	and	CCONJ
ejpam-5969	481	6	β	β	ADJ
ejpam-5969	481	7	-	-	ADJ
ejpam-5969	481	8	continuous	continuous	ADJ
ejpam-5969	481	9	mappings	mapping	NOUN
ejpam-5969	481	10	.	.	PUNCT
ejpam-5969	482	1	bulletin	bulletin	NOUN
ejpam-5969	482	2	of	of	ADP
ejpam-5969	482	3	the	the	DET
ejpam-5969	482	4	faculty	faculty	NOUN
ejpam-5969	482	5	of	of	ADP
ejpam-5969	482	6	science	science	NOUN
ejpam-5969	482	7	,	,	PUNCT
ejpam-5969	482	8	assiut	assiut	NOUN
ejpam-5969	482	9	university	university	NOUN
ejpam-5969	482	10	,	,	PUNCT
ejpam-5969	482	11	12(1):77–90	12(1):77–90	NUM
ejpam-5969	482	12	,	,	PUNCT
ejpam-5969	482	13	1983	1983	NUM
ejpam-5969	482	14	.	.	PUNCT
ejpam-5969	483	1	[	[	X
ejpam-5969	483	2	5	5	X
ejpam-5969	483	3	]	]	PUNCT
ejpam-5969	483	4	d.	d.	PROPN
ejpam-5969	483	5	andrijević.	andrijević.	PROPN
ejpam-5969	483	6	on	on	ADP
ejpam-5969	483	7	b	b	X
ejpam-5969	483	8	-	-	PUNCT
ejpam-5969	483	9	open	open	ADJ
ejpam-5969	483	10	sets	set	NOUN
ejpam-5969	483	11	.	.	PUNCT
ejpam-5969	484	1	matematički	matematički	PROPN
ejpam-5969	484	2	vesnik	vesnik	PROPN
ejpam-5969	484	3	,	,	PUNCT
ejpam-5969	484	4	48:59–64	48:59–64	PROPN
ejpam-5969	484	5	,	,	PUNCT
ejpam-5969	484	6	1996	1996	NUM
ejpam-5969	484	7	.	.	PUNCT
ejpam-5969	485	1	[	[	X
ejpam-5969	485	2	6	6	NUM
ejpam-5969	485	3	]	]	PUNCT
ejpam-5969	485	4	j.	j.	PROPN
ejpam-5969	485	5	dontchev	dontchev	PROPN
ejpam-5969	485	6	and	and	CCONJ
ejpam-5969	485	7	m.	m.	PROPN
ejpam-5969	485	8	przemski	przemski	PROPN
ejpam-5969	485	9	.	.	PUNCT
ejpam-5969	486	1	on	on	ADP
ejpam-5969	486	2	the	the	DET
ejpam-5969	486	3	various	various	ADJ
ejpam-5969	486	4	decompositions	decomposition	NOUN
ejpam-5969	486	5	of	of	ADP
ejpam-5969	486	6	continuous	continuous	ADJ
ejpam-5969	486	7	and	and	CCONJ
ejpam-5969	486	8	some	some	DET
ejpam-5969	486	9	weakly	weakly	ADJ
ejpam-5969	486	10	continuous	continuous	ADJ
ejpam-5969	486	11	functions	function	NOUN
ejpam-5969	486	12	.	.	PUNCT
ejpam-5969	487	1	acta	acta	PROPN
ejpam-5969	487	2	mathematica	mathematica	PROPN
ejpam-5969	487	3	hungarica	hungarica	PROPN
ejpam-5969	487	4	,	,	PUNCT
ejpam-5969	487	5	71(1–2):109–120	71(1–2):109–120	NUM
ejpam-5969	487	6	,	,	PUNCT
ejpam-5969	487	7	1996	1996	NUM
ejpam-5969	487	8	.	.	PUNCT
ejpam-5969	488	1	[	[	X
ejpam-5969	488	2	7	7	X
ejpam-5969	488	3	]	]	PUNCT
ejpam-5969	488	4	z.	z.	PROPN
ejpam-5969	488	5	piotrowski	piotrowski	PROPN
ejpam-5969	488	6	.	.	PUNCT
ejpam-5969	489	1	a	a	DET
ejpam-5969	489	2	survey	survey	NOUN
ejpam-5969	489	3	of	of	ADP
ejpam-5969	489	4	results	result	NOUN
ejpam-5969	489	5	concerning	concern	VERB
ejpam-5969	489	6	generalized	generalized	ADJ
ejpam-5969	489	7	continuity	continuity	NOUN
ejpam-5969	489	8	on	on	ADP
ejpam-5969	489	9	topological	topological	ADJ
ejpam-5969	489	10	spaces	space	NOUN
ejpam-5969	489	11	.	.	PUNCT
ejpam-5969	490	1	acta	acta	PROPN
ejpam-5969	490	2	mathematica	mathematica	PROPN
ejpam-5969	490	3	universitatis	universitatis	PROPN
ejpam-5969	490	4	comenianae	comenianae	PROPN
ejpam-5969	490	5	,	,	PUNCT
ejpam-5969	490	6	52:91–110	52:91–110	NUM
ejpam-5969	490	7	,	,	PUNCT
ejpam-5969	490	8	1987	1987	NUM
ejpam-5969	490	9	.	.	PUNCT
ejpam-5969	491	1	abd	abd	PROPN
ejpam-5969	491	2	el	el	PROPN
ejpam-5969	491	3	-	-	PROPN
ejpam-5969	491	4	latif	latif	PROPN
ejpam-5969	491	5	et	et	PROPN
ejpam-5969	491	6	al	al	PROPN
ejpam-5969	491	7	.	.	PUNCT
ejpam-5969	491	8	/	/	SYM
ejpam-5969	491	9	eur	eur	PROPN
ejpam-5969	491	10	.	.	PUNCT
ejpam-5969	492	1	j.	j.	PROPN
ejpam-5969	492	2	pure	pure	PROPN
ejpam-5969	492	3	appl	appl	PROPN
ejpam-5969	492	4	.	.	PROPN
ejpam-5969	492	5	math	math	PROPN
ejpam-5969	492	6	,	,	PUNCT
ejpam-5969	492	7	18	18	NUM
ejpam-5969	492	8	(	(	PUNCT
ejpam-5969	492	9	2	2	NUM
ejpam-5969	492	10	)	)	PUNCT
ejpam-5969	492	11	(	(	PUNCT
ejpam-5969	492	12	2025	2025	NUM
ejpam-5969	492	13	)	)	PUNCT
ejpam-5969	492	14	,	,	PUNCT
ejpam-5969	492	15	5969	5969	NUM
ejpam-5969	492	16	17	17	NUM
ejpam-5969	492	17	of	of	ADP
ejpam-5969	492	18	19	19	NUM
ejpam-5969	493	1	[	[	SYM
ejpam-5969	493	2	8	8	NUM
ejpam-5969	493	3	]	]	PUNCT
ejpam-5969	493	4	k.	k.	PROPN
ejpam-5969	493	5	r.	r.	PROPN
ejpam-5969	493	6	gentry	gentry	PROPN
ejpam-5969	493	7	and	and	CCONJ
ejpam-5969	493	8	h.	h.	PROPN
ejpam-5969	493	9	b.	b.	PROPN
ejpam-5969	493	10	hoyle	hoyle	PROPN
ejpam-5969	493	11	.	.	PUNCT
ejpam-5969	494	1	somewhat	somewhat	ADV
ejpam-5969	494	2	continuous	continuous	ADJ
ejpam-5969	494	3	functions	function	NOUN
ejpam-5969	494	4	.	.	PUNCT
ejpam-5969	495	1	czechoslovak	czechoslovak	ADJ
ejpam-5969	495	2	mathematical	mathematical	PROPN
ejpam-5969	495	3	journal	journal	PROPN
ejpam-5969	495	4	,	,	PUNCT
ejpam-5969	495	5	21:5–12	21:5–12	NUM
ejpam-5969	495	6	,	,	PUNCT
ejpam-5969	495	7	1971	1971	NUM
ejpam-5969	495	8	.	.	PUNCT
ejpam-5969	496	1	[	[	X
ejpam-5969	496	2	9	9	NUM
ejpam-5969	496	3	]	]	X
ejpam-5969	496	4	o.	o.	PROPN
ejpam-5969	496	5	njastad	njastad	PROPN
ejpam-5969	496	6	.	.	PUNCT
ejpam-5969	497	1	on	on	ADP
ejpam-5969	497	2	some	some	DET
ejpam-5969	497	3	classes	class	NOUN
ejpam-5969	497	4	of	of	ADP
ejpam-5969	497	5	nearly	nearly	ADV
ejpam-5969	497	6	open	open	ADJ
ejpam-5969	497	7	sets	set	NOUN
ejpam-5969	497	8	.	.	PUNCT
ejpam-5969	498	1	pacific	pacific	PROPN
ejpam-5969	498	2	journal	journal	PROPN
ejpam-5969	498	3	of	of	ADP
ejpam-5969	498	4	mathematics	mathematic	NOUN
ejpam-5969	498	5	,	,	PUNCT
ejpam-5969	498	6	15:961–970	15:961–970	PROPN
ejpam-5969	498	7	,	,	PUNCT
ejpam-5969	498	8	1965	1965	NUM
ejpam-5969	498	9	.	.	PUNCT
ejpam-5969	499	1	[	[	X
ejpam-5969	499	2	10	10	NUM
ejpam-5969	499	3	]	]	X
ejpam-5969	499	4	c.	c.	PROPN
ejpam-5969	499	5	c.	c.	PROPN
ejpam-5969	499	6	pugh	pugh	PROPN
ejpam-5969	499	7	.	.	PUNCT
ejpam-5969	500	1	real	real	ADJ
ejpam-5969	500	2	mathematical	mathematical	ADJ
ejpam-5969	500	3	analysis	analysis	NOUN
ejpam-5969	500	4	.	.	PUNCT
ejpam-5969	501	1	springer	springer	NOUN
ejpam-5969	501	2	science	science	NOUN
ejpam-5969	501	3	and	and	CCONJ
ejpam-5969	501	4	business	business	NOUN
ejpam-5969	501	5	media	medium	NOUN
ejpam-5969	501	6	,	,	PUNCT
ejpam-5969	501	7	2003	2003	NUM
ejpam-5969	501	8	.	.	PUNCT
ejpam-5969	502	1	[	[	X
ejpam-5969	502	2	11	11	NUM
ejpam-5969	502	3	]	]	PUNCT
ejpam-5969	502	4	t.	t.	PROPN
ejpam-5969	502	5	m.	m.	PROPN
ejpam-5969	502	6	al	al	PROPN
ejpam-5969	502	7	-	-	PUNCT
ejpam-5969	502	8	shami	shami	PROPN
ejpam-5969	502	9	.	.	PUNCT
ejpam-5969	503	1	somewhere	somewhere	ADV
ejpam-5969	503	2	dense	dense	ADJ
ejpam-5969	503	3	sets	set	NOUN
ejpam-5969	503	4	and	and	CCONJ
ejpam-5969	503	5	st1	st1	PROPN
ejpam-5969	503	6	spaces	space	NOUN
ejpam-5969	503	7	.	.	PUNCT
ejpam-5969	504	1	punjab	punjab	PROPN
ejpam-5969	504	2	university	university	PROPN
ejpam-5969	504	3	journal	journal	NOUN
ejpam-5969	504	4	of	of	ADP
ejpam-5969	504	5	mathematics	mathematic	NOUN
ejpam-5969	504	6	,	,	PUNCT
ejpam-5969	504	7	49(2):101–111	49(2):101–111	PROPN
ejpam-5969	504	8	,	,	PUNCT
ejpam-5969	504	9	2017	2017	NUM
ejpam-5969	504	10	.	.	PUNCT
ejpam-5969	505	1	[	[	X
ejpam-5969	505	2	12	12	NUM
ejpam-5969	505	3	]	]	PUNCT
ejpam-5969	505	4	m.	m.	NOUN
ejpam-5969	505	5	h.	h.	PROPN
ejpam-5969	505	6	alqahtani	alqahtani	PROPN
ejpam-5969	505	7	and	and	CCONJ
ejpam-5969	505	8	a.	a.	NOUN
ejpam-5969	505	9	m.	m.	PROPN
ejpam-5969	505	10	abd	abd	PROPN
ejpam-5969	505	11	el	el	PROPN
ejpam-5969	505	12	-	-	PROPN
ejpam-5969	505	13	latif	latif	PROPN
ejpam-5969	505	14	.	.	PUNCT
ejpam-5969	506	1	separation	separation	NOUN
ejpam-5969	506	2	axioms	axiom	NOUN
ejpam-5969	506	3	via	via	ADP
ejpam-5969	506	4	novel	novel	ADJ
ejpam-5969	506	5	operators	operator	NOUN
ejpam-5969	506	6	in	in	ADP
ejpam-5969	506	7	the	the	DET
ejpam-5969	506	8	frame	frame	NOUN
ejpam-5969	506	9	of	of	ADP
ejpam-5969	506	10	topological	topological	ADJ
ejpam-5969	506	11	spaces	space	NOUN
ejpam-5969	506	12	and	and	CCONJ
ejpam-5969	506	13	applications	application	NOUN
ejpam-5969	506	14	.	.	PUNCT
ejpam-5969	507	1	aims	aim	VERB
ejpam-5969	507	2	mathematics	mathematic	NOUN
ejpam-5969	507	3	,	,	PUNCT
ejpam-5969	507	4	9(6):14213–14227	9(6):14213–14227	NUM
ejpam-5969	507	5	,	,	PUNCT
ejpam-5969	507	6	2024	2024	NUM
ejpam-5969	507	7	.	.	PUNCT
ejpam-5969	508	1	[	[	X
ejpam-5969	508	2	13	13	NUM
ejpam-5969	508	3	]	]	PUNCT
ejpam-5969	508	4	a.	a.	NOUN
ejpam-5969	508	5	s.	s.	PROPN
ejpam-5969	508	6	mashhour	mashhour	PROPN
ejpam-5969	508	7	,	,	PUNCT
ejpam-5969	508	8	a.	a.	PROPN
ejpam-5969	508	9	a.	a.	PROPN
ejpam-5969	508	10	allam	allam	PROPN
ejpam-5969	508	11	,	,	PUNCT
ejpam-5969	508	12	f.	f.	PROPN
ejpam-5969	508	13	s.	s.	PROPN
ejpam-5969	508	14	mahmoud	mahmoud	PROPN
ejpam-5969	508	15	,	,	PUNCT
ejpam-5969	508	16	and	and	CCONJ
ejpam-5969	508	17	f.	f.	PROPN
ejpam-5969	508	18	h.	h.	PROPN
ejpam-5969	508	19	kheder	kheder	PROPN
ejpam-5969	508	20	.	.	PUNCT
ejpam-5969	509	1	on	on	ADP
ejpam-5969	509	2	supra	supra	PROPN
ejpam-5969	509	3	topological	topological	ADJ
ejpam-5969	509	4	spaces	space	NOUN
ejpam-5969	509	5	.	.	PUNCT
ejpam-5969	510	1	indian	indian	ADJ
ejpam-5969	510	2	journal	journal	PROPN
ejpam-5969	510	3	of	of	ADP
ejpam-5969	510	4	pure	pure	ADJ
ejpam-5969	510	5	and	and	CCONJ
ejpam-5969	510	6	applied	applied	ADJ
ejpam-5969	510	7	mathematics	mathematic	NOUN
ejpam-5969	510	8	,	,	PUNCT
ejpam-5969	510	9	pages	page	NOUN
ejpam-5969	510	10	502–510	502–510	NUM
ejpam-5969	510	11	,	,	PUNCT
ejpam-5969	510	12	1983	1983	NUM
ejpam-5969	510	13	.	.	PUNCT
ejpam-5969	511	1	[	[	X
ejpam-5969	511	2	14	14	NUM
ejpam-5969	511	3	]	]	X
ejpam-5969	511	4	r.	r.	PROPN
ejpam-5969	511	5	devi	devi	PROPN
ejpam-5969	511	6	,	,	PUNCT
ejpam-5969	511	7	s.	s.	PROPN
ejpam-5969	511	8	sampathkumar	sampathkumar	PROPN
ejpam-5969	511	9	,	,	PUNCT
ejpam-5969	511	10	and	and	CCONJ
ejpam-5969	511	11	m.	m.	PROPN
ejpam-5969	511	12	caldas	caldas	PROPN
ejpam-5969	511	13	.	.	PUNCT
ejpam-5969	512	1	on	on	ADP
ejpam-5969	512	2	α	α	NOUN
ejpam-5969	512	3	-	-	ADJ
ejpam-5969	512	4	open	open	ADJ
ejpam-5969	512	5	sets	set	NOUN
ejpam-5969	512	6	and	and	CCONJ
ejpam-5969	512	7	sa	sa	NOUN
ejpam-5969	512	8	-	-	ADJ
ejpam-5969	512	9	continuous	continuous	ADJ
ejpam-5969	512	10	maps	map	NOUN
ejpam-5969	512	11	.	.	PUNCT
ejpam-5969	513	1	general	general	ADJ
ejpam-5969	513	2	mathematics	mathematics	PROPN
ejpam-5969	513	3	,	,	PUNCT
ejpam-5969	513	4	16:77–84	16:77–84	NOUN
ejpam-5969	513	5	,	,	PUNCT
ejpam-5969	513	6	2008	2008	NUM
ejpam-5969	513	7	.	.	PUNCT
ejpam-5969	514	1	[	[	X
ejpam-5969	514	2	15	15	NUM
ejpam-5969	514	3	]	]	X
ejpam-5969	514	4	o.	o.	PROPN
ejpam-5969	514	5	r.	r.	PROPN
ejpam-5969	514	6	sayed	say	VERB
ejpam-5969	514	7	.	.	PUNCT
ejpam-5969	515	1	supra	supra	PROPN
ejpam-5969	515	2	pre	pre	ADJ
ejpam-5969	515	3	-	-	ADJ
ejpam-5969	515	4	open	open	ADJ
ejpam-5969	515	5	sets	set	NOUN
ejpam-5969	515	6	and	and	CCONJ
ejpam-5969	515	7	supra	supra	NOUN
ejpam-5969	515	8	pre	pre	ADJ
ejpam-5969	515	9	-	-	ADJ
ejpam-5969	515	10	continuous	continuous	ADJ
ejpam-5969	515	11	on	on	ADP
ejpam-5969	515	12	topological	topological	ADJ
ejpam-5969	515	13	spaces	space	NOUN
ejpam-5969	515	14	.	.	PUNCT
ejpam-5969	516	1	series	series	PROPN
ejpam-5969	516	2	mathematics	mathematics	PROPN
ejpam-5969	516	3	and	and	CCONJ
ejpam-5969	516	4	informatics	informatic	NOUN
ejpam-5969	516	5	,	,	PUNCT
ejpam-5969	516	6	20:79–88	20:79–88	NUM
ejpam-5969	516	7	,	,	PUNCT
ejpam-5969	516	8	2010	2010	NUM
ejpam-5969	516	9	.	.	PUNCT
ejpam-5969	517	1	[	[	X
ejpam-5969	517	2	16	16	NUM
ejpam-5969	517	3	]	]	X
ejpam-5969	517	4	o.	o.	PROPN
ejpam-5969	517	5	r.	r.	PROPN
ejpam-5969	517	6	sayed	sayed	PROPN
ejpam-5969	517	7	and	and	CCONJ
ejpam-5969	517	8	t.	t.	PROPN
ejpam-5969	517	9	noiri	noiri	PROPN
ejpam-5969	517	10	.	.	PUNCT
ejpam-5969	518	1	on	on	ADP
ejpam-5969	518	2	supra	supra	PROPN
ejpam-5969	518	3	b	b	PROPN
ejpam-5969	518	4	-	-	PUNCT
ejpam-5969	518	5	open	open	ADJ
ejpam-5969	518	6	sets	set	NOUN
ejpam-5969	518	7	and	and	CCONJ
ejpam-5969	518	8	supra	supra	PROPN
ejpam-5969	518	9	b	b	NOUN
ejpam-5969	518	10	-	-	PUNCT
ejpam-5969	518	11	continuity	continuity	NOUN
ejpam-5969	518	12	on	on	ADP
ejpam-5969	518	13	topological	topological	ADJ
ejpam-5969	518	14	spaces	space	NOUN
ejpam-5969	518	15	.	.	PUNCT
ejpam-5969	519	1	european	european	ADJ
ejpam-5969	519	2	journal	journal	PROPN
ejpam-5969	519	3	of	of	ADP
ejpam-5969	519	4	pure	pure	ADJ
ejpam-5969	519	5	and	and	CCONJ
ejpam-5969	519	6	applied	applied	ADJ
ejpam-5969	519	7	mathematics	mathematic	NOUN
ejpam-5969	519	8	,	,	PUNCT
ejpam-5969	519	9	3:295–302	3:295–302	NUM
ejpam-5969	519	10	,	,	PUNCT
ejpam-5969	519	11	2010	2010	NUM
ejpam-5969	519	12	.	.	PUNCT
ejpam-5969	520	1	[	[	X
ejpam-5969	520	2	17	17	NUM
ejpam-5969	520	3	]	]	PUNCT
ejpam-5969	520	4	s.	s.	PROPN
ejpam-5969	520	5	jafari	jafari	PROPN
ejpam-5969	520	6	and	and	CCONJ
ejpam-5969	520	7	s.	s.	PROPN
ejpam-5969	520	8	tahiliani	tahiliani	PROPN
ejpam-5969	520	9	.	.	PUNCT
ejpam-5969	521	1	supra	supra	PROPN
ejpam-5969	521	2	β	β	X
ejpam-5969	521	3	-	-	ADJ
ejpam-5969	521	4	open	open	ADJ
ejpam-5969	521	5	sets	set	NOUN
ejpam-5969	521	6	and	and	CCONJ
ejpam-5969	521	7	supra	supra	ADJ
ejpam-5969	521	8	β	β	NOUN
ejpam-5969	521	9	-	-	NOUN
ejpam-5969	521	10	continuity	continuity	NOUN
ejpam-5969	521	11	on	on	ADP
ejpam-5969	521	12	topological	topological	ADJ
ejpam-5969	521	13	spaces	space	NOUN
ejpam-5969	521	14	.	.	PUNCT
ejpam-5969	522	1	annales	annales	PROPN
ejpam-5969	522	2	universitatis	universitatis	PROPN
ejpam-5969	522	3	scientiarum	scientiarum	PROPN
ejpam-5969	522	4	budapestinensis	budapestinensis	PROPN
ejpam-5969	522	5	de	de	PROPN
ejpam-5969	522	6	rolando	rolando	PROPN
ejpam-5969	522	7	eötvös	eötvös	PROPN
ejpam-5969	522	8	nominatae	nominatae	NOUN
ejpam-5969	522	9	,	,	PUNCT
ejpam-5969	522	10	56:1–9	56:1–9	NUM
ejpam-5969	522	11	,	,	PUNCT
ejpam-5969	522	12	2013	2013	NUM
ejpam-5969	522	13	.	.	PUNCT
ejpam-5969	523	1	[	[	X
ejpam-5969	523	2	18	18	NUM
ejpam-5969	523	3	]	]	PUNCT
ejpam-5969	523	4	m.	m.	PROPN
ejpam-5969	523	5	e.	e.	PROPN
ejpam-5969	523	6	el	el	PROPN
ejpam-5969	523	7	-	-	PROPN
ejpam-5969	523	8	shafei	shafei	PROPN
ejpam-5969	523	9	,	,	PUNCT
ejpam-5969	523	10	m.	m.	NOUN
ejpam-5969	523	11	abo	abo	NOUN
ejpam-5969	523	12	-	-	PUNCT
ejpam-5969	523	13	elhamayel	elhamayel	NOUN
ejpam-5969	523	14	,	,	PUNCT
ejpam-5969	523	15	and	and	CCONJ
ejpam-5969	523	16	t.	t.	PROPN
ejpam-5969	523	17	m.	m.	PROPN
ejpam-5969	523	18	al	al	PROPN
ejpam-5969	523	19	-	-	PUNCT
ejpam-5969	523	20	shami	shami	PROPN
ejpam-5969	523	21	.	.	PUNCT
ejpam-5969	524	1	on	on	ADP
ejpam-5969	524	2	supra	supra	PROPN
ejpam-5969	524	3	r	r	NOUN
ejpam-5969	524	4	-	-	PUNCT
ejpam-5969	524	5	open	open	ADJ
ejpam-5969	524	6	sets	set	NOUN
ejpam-5969	524	7	and	and	CCONJ
ejpam-5969	524	8	some	some	DET
ejpam-5969	524	9	applications	application	NOUN
ejpam-5969	524	10	on	on	ADP
ejpam-5969	524	11	topological	topological	ADJ
ejpam-5969	524	12	spaces	space	NOUN
ejpam-5969	524	13	.	.	PUNCT
ejpam-5969	525	1	journal	journal	NOUN
ejpam-5969	525	2	of	of	ADP
ejpam-5969	525	3	progressive	progressive	ADJ
ejpam-5969	525	4	research	research	NOUN
ejpam-5969	525	5	in	in	ADP
ejpam-5969	525	6	mathematics	mathematic	NOUN
ejpam-5969	525	7	,	,	PUNCT
ejpam-5969	525	8	8:1237–1248	8:1237–1248	NUM
ejpam-5969	525	9	,	,	PUNCT
ejpam-5969	525	10	2016	2016	NUM
ejpam-5969	525	11	.	.	PUNCT
ejpam-5969	526	1	[	[	X
ejpam-5969	526	2	19	19	NUM
ejpam-5969	526	3	]	]	X
ejpam-5969	526	4	t.	t.	PROPN
ejpam-5969	526	5	m.	m.	PROPN
ejpam-5969	526	6	al	al	PROPN
ejpam-5969	526	7	-	-	PUNCT
ejpam-5969	526	8	shami	shami	PROPN
ejpam-5969	526	9	.	.	PUNCT
ejpam-5969	527	1	on	on	ADP
ejpam-5969	527	2	supra	supra	PROPN
ejpam-5969	527	3	semi	semi	ADV
ejpam-5969	527	4	open	open	ADJ
ejpam-5969	527	5	sets	set	NOUN
ejpam-5969	527	6	and	and	CCONJ
ejpam-5969	527	7	some	some	DET
ejpam-5969	527	8	applications	application	NOUN
ejpam-5969	527	9	on	on	ADP
ejpam-5969	527	10	topological	topological	ADJ
ejpam-5969	527	11	spaces	space	NOUN
ejpam-5969	527	12	.	.	PUNCT
ejpam-5969	528	1	journal	journal	NOUN
ejpam-5969	528	2	of	of	ADP
ejpam-5969	528	3	advanced	advanced	ADJ
ejpam-5969	528	4	studies	study	NOUN
ejpam-5969	528	5	in	in	ADP
ejpam-5969	528	6	topology	topology	NOUN
ejpam-5969	528	7	,	,	PUNCT
ejpam-5969	528	8	8(2):144–153	8(2):144–153	NOUN
ejpam-5969	528	9	,	,	PUNCT
ejpam-5969	528	10	2017	2017	NUM
ejpam-5969	528	11	.	.	PUNCT
ejpam-5969	529	1	[	[	X
ejpam-5969	529	2	20	20	NUM
ejpam-5969	529	3	]	]	PUNCT
ejpam-5969	529	4	b.	b.	PROPN
ejpam-5969	529	5	a.	a.	PROPN
ejpam-5969	529	6	asaad	asaad	PROPN
ejpam-5969	529	7	,	,	PUNCT
ejpam-5969	529	8	tareq	tareq	PROPN
ejpam-5969	529	9	m.	m.	PROPN
ejpam-5969	529	10	al	al	PROPN
ejpam-5969	529	11	-	-	PUNCT
ejpam-5969	529	12	shami	shami	PROPN
ejpam-5969	529	13	,	,	PUNCT
ejpam-5969	529	14	and	and	CCONJ
ejpam-5969	529	15	el	el	PROPN
ejpam-5969	529	16	-	-	PUNCT
ejpam-5969	529	17	sayed	say	VERB
ejpam-5969	529	18	a.	a.	PROPN
ejpam-5969	529	19	abo	abo	NOUN
ejpam-5969	529	20	-	-	PUNCT
ejpam-5969	529	21	tabl	tabl	NOUN
ejpam-5969	529	22	.	.	PUNCT
ejpam-5969	530	1	applications	application	NOUN
ejpam-5969	530	2	of	of	ADP
ejpam-5969	530	3	some	some	DET
ejpam-5969	530	4	operators	operator	NOUN
ejpam-5969	530	5	on	on	ADP
ejpam-5969	530	6	supra	supra	PROPN
ejpam-5969	530	7	topological	topological	ADJ
ejpam-5969	530	8	spaces	space	NOUN
ejpam-5969	530	9	.	.	PUNCT
ejpam-5969	531	1	demonstratio	demonstratio	PROPN
ejpam-5969	531	2	mathematica	mathematica	PROPN
ejpam-5969	531	3	,	,	PUNCT
ejpam-5969	531	4	53(1):292–308	53(1):292–308	PROPN
ejpam-5969	531	5	,	,	PUNCT
ejpam-5969	531	6	2020	2020	NUM
ejpam-5969	531	7	.	.	PUNCT
ejpam-5969	532	1	[	[	X
ejpam-5969	532	2	21	21	NUM
ejpam-5969	532	3	]	]	X
ejpam-5969	532	4	t.	t.	PROPN
ejpam-5969	532	5	m.	m.	PROPN
ejpam-5969	532	6	al	al	PROPN
ejpam-5969	532	7	-	-	PUNCT
ejpam-5969	532	8	shami	shami	PROPN
ejpam-5969	532	9	,	,	PUNCT
ejpam-5969	532	10	e.	e.	PROPN
ejpam-5969	532	11	a.	a.	PROPN
ejpam-5969	532	12	abo	abo	PROPN
ejpam-5969	532	13	-	-	PUNCT
ejpam-5969	532	14	tabl	tabl	NOUN
ejpam-5969	532	15	,	,	PUNCT
ejpam-5969	532	16	and	and	CCONJ
ejpam-5969	532	17	b.	b.	PROPN
ejpam-5969	532	18	a.	a.	PROPN
ejpam-5969	532	19	asaad	asaad	PROPN
ejpam-5969	532	20	.	.	PUNCT
ejpam-5969	533	1	investigation	investigation	NOUN
ejpam-5969	533	2	of	of	ADP
ejpam-5969	533	3	limit	limit	NOUN
ejpam-5969	533	4	points	point	NOUN
ejpam-5969	533	5	and	and	CCONJ
ejpam-5969	533	6	separation	separation	NOUN
ejpam-5969	533	7	axioms	axiom	NOUN
ejpam-5969	533	8	using	use	VERB
ejpam-5969	533	9	supra	supra	PROPN
ejpam-5969	533	10	β	β	NOUN
ejpam-5969	533	11	-	-	ADJ
ejpam-5969	533	12	open	open	ADJ
ejpam-5969	533	13	sets	set	NOUN
ejpam-5969	533	14	.	.	PUNCT
ejpam-5969	534	1	missouri	missouri	PROPN
ejpam-5969	534	2	journal	journal	PROPN
ejpam-5969	534	3	of	of	ADP
ejpam-5969	534	4	mathematical	mathematical	ADJ
ejpam-5969	534	5	sciences	science	NOUN
ejpam-5969	534	6	,	,	PUNCT
ejpam-5969	534	7	32(2):171–187	32(2):171–187	PROPN
ejpam-5969	534	8	,	,	PUNCT
ejpam-5969	534	9	2020	2020	NUM
ejpam-5969	534	10	.	.	PUNCT
ejpam-5969	535	1	[	[	X
ejpam-5969	535	2	22	22	NUM
ejpam-5969	535	3	]	]	PUNCT
ejpam-5969	535	4	t.	t.	PROPN
ejpam-5969	535	5	m.	m.	PROPN
ejpam-5969	535	6	al	al	PROPN
ejpam-5969	535	7	-	-	PUNCT
ejpam-5969	535	8	shami	shami	PROPN
ejpam-5969	535	9	,	,	PUNCT
ejpam-5969	535	10	e.	e.	PROPN
ejpam-5969	535	11	a.	a.	PROPN
ejpam-5969	535	12	abo	abo	PROPN
ejpam-5969	535	13	-	-	PUNCT
ejpam-5969	535	14	tabl	tabl	NOUN
ejpam-5969	535	15	,	,	PUNCT
ejpam-5969	535	16	b.	b.	PROPN
ejpam-5969	535	17	a.	a.	PROPN
ejpam-5969	535	18	asaad	asaad	PROPN
ejpam-5969	535	19	,	,	PUNCT
ejpam-5969	535	20	and	and	CCONJ
ejpam-5969	535	21	m.	m.	NOUN
ejpam-5969	535	22	a.	a.	NOUN
ejpam-5969	535	23	arahet	arahet	PROPN
ejpam-5969	535	24	.	.	PUNCT
ejpam-5969	536	1	limit	limit	NOUN
ejpam-5969	536	2	points	point	NOUN
ejpam-5969	536	3	and	and	CCONJ
ejpam-5969	536	4	separation	separation	NOUN
ejpam-5969	536	5	axioms	axiom	NOUN
ejpam-5969	536	6	with	with	ADP
ejpam-5969	536	7	respect	respect	NOUN
ejpam-5969	536	8	to	to	ADP
ejpam-5969	536	9	supra	supra	PROPN
ejpam-5969	536	10	semi	semi	ADJ
ejpam-5969	536	11	-	-	ADJ
ejpam-5969	536	12	open	open	ADJ
ejpam-5969	536	13	sets	set	NOUN
ejpam-5969	536	14	.	.	PUNCT
ejpam-5969	537	1	european	european	ADJ
ejpam-5969	537	2	journal	journal	PROPN
ejpam-5969	537	3	of	of	ADP
ejpam-5969	537	4	pure	pure	ADJ
ejpam-5969	537	5	and	and	CCONJ
ejpam-5969	537	6	applied	applied	ADJ
ejpam-5969	537	7	mathematics	mathematic	NOUN
ejpam-5969	537	8	,	,	PUNCT
ejpam-5969	537	9	13(3):427–443	13(3):427–443	PROPN
ejpam-5969	537	10	,	,	PUNCT
ejpam-5969	537	11	2020	2020	NUM
ejpam-5969	537	12	.	.	PUNCT
ejpam-5969	538	1	[	[	X
ejpam-5969	538	2	23	23	NUM
ejpam-5969	538	3	]	]	PUNCT
ejpam-5969	538	4	m.	m.	NOUN
ejpam-5969	538	5	shabir	shabir	PROPN
ejpam-5969	538	6	and	and	CCONJ
ejpam-5969	538	7	m.	m.	PROPN
ejpam-5969	538	8	naz	naz	PROPN
ejpam-5969	538	9	.	.	PUNCT
ejpam-5969	539	1	on	on	ADP
ejpam-5969	539	2	soft	soft	ADJ
ejpam-5969	539	3	topological	topological	ADJ
ejpam-5969	539	4	spaces	space	NOUN
ejpam-5969	539	5	.	.	PUNCT
ejpam-5969	540	1	computers	computer	NOUN
ejpam-5969	540	2	and	and	CCONJ
ejpam-5969	540	3	mathematics	mathematic	NOUN
ejpam-5969	540	4	with	with	ADP
ejpam-5969	540	5	applications	application	NOUN
ejpam-5969	540	6	,	,	PUNCT
ejpam-5969	540	7	61:1786–1799	61:1786–1799	NUM
ejpam-5969	540	8	,	,	PUNCT
ejpam-5969	540	9	2011	2011	NUM
ejpam-5969	540	10	.	.	PUNCT
ejpam-5969	541	1	[	[	X
ejpam-5969	541	2	24	24	NUM
ejpam-5969	541	3	]	]	PUNCT
ejpam-5969	541	4	zanyar	zanyar	PROPN
ejpam-5969	541	5	a.	a.	NOUN
ejpam-5969	541	6	ameen	ameen	PROPN
ejpam-5969	541	7	and	and	CCONJ
ejpam-5969	541	8	s.	s.	PROPN
ejpam-5969	541	9	al	al	PROPN
ejpam-5969	541	10	ghour	ghour	PROPN
ejpam-5969	541	11	.	.	PUNCT
ejpam-5969	542	1	cluster	cluster	NOUN
ejpam-5969	542	2	soft	soft	ADJ
ejpam-5969	542	3	sets	set	NOUN
ejpam-5969	542	4	and	and	CCONJ
ejpam-5969	542	5	cluster	cluster	NOUN
ejpam-5969	542	6	soft	soft	ADJ
ejpam-5969	542	7	topologies	topology	NOUN
ejpam-5969	542	8	.	.	PUNCT
ejpam-5969	543	1	computational	computational	ADJ
ejpam-5969	543	2	and	and	CCONJ
ejpam-5969	543	3	applied	applied	ADJ
ejpam-5969	543	4	mathematics	mathematic	NOUN
ejpam-5969	543	5	,	,	PUNCT
ejpam-5969	543	6	42:337	42:337	NUM
ejpam-5969	543	7	,	,	PUNCT
ejpam-5969	543	8	2023	2023	NUM
ejpam-5969	543	9	.	.	PUNCT
ejpam-5969	544	1	[	[	X
ejpam-5969	544	2	25	25	NUM
ejpam-5969	544	3	]	]	PUNCT
ejpam-5969	544	4	s.	s.	PROPN
ejpam-5969	544	5	a.	a.	PROPN
ejpam-5969	544	6	el	el	PROPN
ejpam-5969	544	7	-	-	PUNCT
ejpam-5969	544	8	sheikh	sheikh	PROPN
ejpam-5969	544	9	and	and	CCONJ
ejpam-5969	544	10	a.	a.	NOUN
ejpam-5969	544	11	m.	m.	PROPN
ejpam-5969	544	12	el	el	PROPN
ejpam-5969	544	13	-	-	PROPN
ejpam-5969	544	14	latif	latif	PROPN
ejpam-5969	544	15	.	.	PUNCT
ejpam-5969	545	1	characterization	characterization	NOUN
ejpam-5969	545	2	of	of	ADP
ejpam-5969	545	3	b	b	NOUN
ejpam-5969	545	4	-	-	PUNCT
ejpam-5969	545	5	open	open	ADJ
ejpam-5969	545	6	soft	soft	ADJ
ejpam-5969	545	7	sets	set	NOUN
ejpam-5969	545	8	in	in	ADP
ejpam-5969	545	9	soft	soft	ADJ
ejpam-5969	545	10	topological	topological	ADJ
ejpam-5969	545	11	spaces	space	NOUN
ejpam-5969	545	12	.	.	PUNCT
ejpam-5969	546	1	journal	journal	NOUN
ejpam-5969	546	2	of	of	ADP
ejpam-5969	546	3	new	new	ADJ
ejpam-5969	546	4	theory	theory	NOUN
ejpam-5969	546	5	,	,	PUNCT
ejpam-5969	546	6	2:8–18	2:8–18	NUM
ejpam-5969	546	7	,	,	PUNCT
ejpam-5969	546	8	2015	2015	NUM
ejpam-5969	546	9	.	.	PUNCT
ejpam-5969	547	1	[	[	X
ejpam-5969	547	2	26	26	NUM
ejpam-5969	547	3	]	]	PUNCT
ejpam-5969	547	4	a.	a.	NOUN
ejpam-5969	547	5	kandil	kandil	PROPN
ejpam-5969	547	6	,	,	PUNCT
ejpam-5969	547	7	o.	o.	PROPN
ejpam-5969	547	8	a.	a.	PROPN
ejpam-5969	547	9	e.	e.	PROPN
ejpam-5969	547	10	tantawy	tantawy	PROPN
ejpam-5969	547	11	,	,	PUNCT
ejpam-5969	547	12	s.	s.	PROPN
ejpam-5969	547	13	a.	a.	PROPN
ejpam-5969	547	14	el	el	PROPN
ejpam-5969	547	15	-	-	PUNCT
ejpam-5969	547	16	sheikh	sheikh	NOUN
ejpam-5969	547	17	,	,	PUNCT
ejpam-5969	547	18	and	and	CCONJ
ejpam-5969	547	19	a.	a.	NOUN
ejpam-5969	547	20	m.	m.	PROPN
ejpam-5969	547	21	abd	abd	PROPN
ejpam-5969	547	22	el	el	PROPN
ejpam-5969	547	23	-	-	PROPN
ejpam-5969	547	24	latif	latif	PROPN
ejpam-5969	547	25	.	.	PUNCT
ejpam-5969	548	1	soft	soft	ADJ
ejpam-5969	548	2	semi	semi	ADJ
ejpam-5969	548	3	separation	separation	NOUN
ejpam-5969	548	4	axioms	axiom	NOUN
ejpam-5969	548	5	and	and	CCONJ
ejpam-5969	548	6	irresolute	irresolute	ADJ
ejpam-5969	548	7	soft	soft	ADJ
ejpam-5969	548	8	functions	function	NOUN
ejpam-5969	548	9	.	.	PUNCT
ejpam-5969	549	1	annals	annal	NOUN
ejpam-5969	549	2	of	of	ADP
ejpam-5969	549	3	fuzzy	fuzzy	ADJ
ejpam-5969	549	4	mathematics	mathematic	NOUN
ejpam-5969	549	5	and	and	CCONJ
ejpam-5969	549	6	abd	abd	PROPN
ejpam-5969	549	7	el	el	PROPN
ejpam-5969	549	8	-	-	PROPN
ejpam-5969	549	9	latif	latif	PROPN
ejpam-5969	549	10	et	et	PROPN
ejpam-5969	549	11	al	al	PROPN
ejpam-5969	549	12	.	.	PUNCT
ejpam-5969	549	13	/	/	SYM
ejpam-5969	549	14	eur	eur	PROPN
ejpam-5969	549	15	.	.	PUNCT
ejpam-5969	550	1	j.	j.	PROPN
ejpam-5969	550	2	pure	pure	PROPN
ejpam-5969	550	3	appl	appl	PROPN
ejpam-5969	550	4	.	.	PROPN
ejpam-5969	550	5	math	math	PROPN
ejpam-5969	550	6	,	,	PUNCT
ejpam-5969	550	7	18	18	NUM
ejpam-5969	550	8	(	(	PUNCT
ejpam-5969	550	9	2	2	NUM
ejpam-5969	550	10	)	)	PUNCT
ejpam-5969	550	11	(	(	PUNCT
ejpam-5969	550	12	2025	2025	NUM
ejpam-5969	550	13	)	)	PUNCT
ejpam-5969	550	14	,	,	PUNCT
ejpam-5969	550	15	5969	5969	NUM
ejpam-5969	550	16	18	18	NUM
ejpam-5969	550	17	of	of	ADP
ejpam-5969	550	18	19	19	NUM
ejpam-5969	550	19	informatics	informatic	NOUN
ejpam-5969	550	20	,	,	PUNCT
ejpam-5969	550	21	8(2):305–318	8(2):305–318	NUM
ejpam-5969	550	22	,	,	PUNCT
ejpam-5969	550	23	2014	2014	NUM
ejpam-5969	550	24	.	.	PUNCT
ejpam-5969	551	1	[	[	X
ejpam-5969	551	2	27	27	NUM
ejpam-5969	551	3	]	]	X
ejpam-5969	551	4	tareq	tareq	PROPN
ejpam-5969	551	5	m.	m.	PROPN
ejpam-5969	551	6	al	al	PROPN
ejpam-5969	551	7	-	-	PUNCT
ejpam-5969	551	8	shami	shami	PROPN
ejpam-5969	551	9	,	,	PUNCT
ejpam-5969	551	10	abdelwaheb	abdelwaheb	PROPN
ejpam-5969	551	11	mhemdi	mhemdi	PROPN
ejpam-5969	551	12	,	,	PUNCT
ejpam-5969	551	13	and	and	CCONJ
ejpam-5969	551	14	radwan	radwan	VERB
ejpam-5969	551	15	abu	abu	PROPN
ejpam-5969	551	16	-	-	PUNCT
ejpam-5969	551	17	gdairi	gdairi	PROPN
ejpam-5969	551	18	.	.	PUNCT
ejpam-5969	552	1	a	a	DET
ejpam-5969	552	2	novel	novel	ADJ
ejpam-5969	552	3	framework	framework	NOUN
ejpam-5969	552	4	for	for	ADP
ejpam-5969	552	5	generalizations	generalization	NOUN
ejpam-5969	552	6	of	of	ADP
ejpam-5969	552	7	soft	soft	ADJ
ejpam-5969	552	8	open	open	ADJ
ejpam-5969	552	9	sets	set	NOUN
ejpam-5969	552	10	and	and	CCONJ
ejpam-5969	552	11	its	its	PRON
ejpam-5969	552	12	applications	application	NOUN
ejpam-5969	552	13	via	via	ADP
ejpam-5969	552	14	soft	soft	ADJ
ejpam-5969	552	15	topologies	topology	NOUN
ejpam-5969	552	16	.	.	PUNCT
ejpam-5969	553	1	mathematics	mathematic	NOUN
ejpam-5969	553	2	,	,	PUNCT
ejpam-5969	553	3	11(4):840	11(4):840	NOUN
ejpam-5969	553	4	,	,	PUNCT
ejpam-5969	553	5	2023	2023	NUM
ejpam-5969	553	6	.	.	PUNCT
ejpam-5969	554	1	[	[	X
ejpam-5969	554	2	28	28	NUM
ejpam-5969	554	3	]	]	X
ejpam-5969	554	4	a.	a.	NOUN
ejpam-5969	554	5	kandil	kandil	PROPN
ejpam-5969	554	6	,	,	PUNCT
ejpam-5969	554	7	o.	o.	PROPN
ejpam-5969	554	8	a.	a.	PROPN
ejpam-5969	554	9	e.	e.	PROPN
ejpam-5969	554	10	tantawy	tantawy	PROPN
ejpam-5969	554	11	,	,	PUNCT
ejpam-5969	554	12	s.	s.	PROPN
ejpam-5969	554	13	a.	a.	PROPN
ejpam-5969	554	14	el	el	PROPN
ejpam-5969	554	15	-	-	PUNCT
ejpam-5969	554	16	sheikh	sheikh	NOUN
ejpam-5969	554	17	,	,	PUNCT
ejpam-5969	554	18	and	and	CCONJ
ejpam-5969	554	19	a.	a.	NOUN
ejpam-5969	554	20	m.	m.	PROPN
ejpam-5969	554	21	abd	abd	PROPN
ejpam-5969	554	22	el	el	PROPN
ejpam-5969	554	23	-	-	PROPN
ejpam-5969	554	24	latif	latif	PROPN
ejpam-5969	554	25	.	.	PUNCT
ejpam-5969	555	1	γ	γ	PROPN
ejpam-5969	555	2	-	-	PUNCT
ejpam-5969	555	3	operation	operation	NOUN
ejpam-5969	555	4	and	and	CCONJ
ejpam-5969	555	5	decompositions	decomposition	NOUN
ejpam-5969	555	6	of	of	ADP
ejpam-5969	555	7	some	some	DET
ejpam-5969	555	8	forms	form	NOUN
ejpam-5969	555	9	of	of	ADP
ejpam-5969	555	10	soft	soft	ADJ
ejpam-5969	555	11	continuity	continuity	NOUN
ejpam-5969	555	12	in	in	ADP
ejpam-5969	555	13	soft	soft	ADJ
ejpam-5969	555	14	topological	topological	ADJ
ejpam-5969	555	15	spaces	space	NOUN
ejpam-5969	555	16	.	.	PUNCT
ejpam-5969	556	1	annals	annal	NOUN
ejpam-5969	556	2	of	of	ADP
ejpam-5969	556	3	fuzzy	fuzzy	ADJ
ejpam-5969	556	4	mathematics	mathematic	NOUN
ejpam-5969	556	5	and	and	CCONJ
ejpam-5969	556	6	informatics	informatic	NOUN
ejpam-5969	556	7	,	,	PUNCT
ejpam-5969	556	8	7(2):181–196	7(2):181–196	NUM
ejpam-5969	556	9	,	,	PUNCT
ejpam-5969	556	10	2014	2014	NUM
ejpam-5969	556	11	.	.	PUNCT
ejpam-5969	557	1	[	[	X
ejpam-5969	557	2	29	29	NUM
ejpam-5969	557	3	]	]	X
ejpam-5969	557	4	tareq	tareq	PROPN
ejpam-5969	557	5	m.	m.	PROPN
ejpam-5969	557	6	al	al	PROPN
ejpam-5969	557	7	-	-	PUNCT
ejpam-5969	557	8	shami	shami	PROPN
ejpam-5969	557	9	.	.	PUNCT
ejpam-5969	558	1	soft	soft	ADJ
ejpam-5969	558	2	somewhere	somewhere	ADV
ejpam-5969	558	3	dense	dense	ADJ
ejpam-5969	558	4	sets	set	NOUN
ejpam-5969	558	5	on	on	ADP
ejpam-5969	558	6	soft	soft	ADJ
ejpam-5969	558	7	topological	topological	ADJ
ejpam-5969	558	8	spaces	space	NOUN
ejpam-5969	558	9	.	.	PUNCT
ejpam-5969	559	1	communications	communication	NOUN
ejpam-5969	559	2	of	of	ADP
ejpam-5969	559	3	the	the	DET
ejpam-5969	559	4	korean	korean	ADJ
ejpam-5969	559	5	mathematical	mathematical	ADJ
ejpam-5969	559	6	society	society	NOUN
ejpam-5969	559	7	,	,	PUNCT
ejpam-5969	559	8	33(2):1341–1356	33(2):1341–1356	NUM
ejpam-5969	559	9	,	,	PUNCT
ejpam-5969	559	10	2018	2018	NUM
ejpam-5969	559	11	.	.	PUNCT
ejpam-5969	560	1	[	[	X
ejpam-5969	560	2	30	30	NUM
ejpam-5969	560	3	]	]	PUNCT
ejpam-5969	560	4	radwan	radwan	VERB
ejpam-5969	560	5	abu	abu	PROPN
ejpam-5969	560	6	-	-	PUNCT
ejpam-5969	560	7	gdairi	gdairi	PROPN
ejpam-5969	560	8	,	,	PUNCT
ejpam-5969	560	9	a.	a.	PROPN
ejpam-5969	560	10	a.	a.	PROPN
ejpam-5969	560	11	azzam	azzam	PROPN
ejpam-5969	560	12	,	,	PUNCT
ejpam-5969	560	13	and	and	CCONJ
ejpam-5969	560	14	ibrahim	ibrahim	PROPN
ejpam-5969	560	15	noaman	noaman	PROPN
ejpam-5969	560	16	.	.	PUNCT
ejpam-5969	561	1	nearly	nearly	ADV
ejpam-5969	561	2	soft	soft	ADJ
ejpam-5969	561	3	β	β	ADJ
ejpam-5969	561	4	-	-	ADJ
ejpam-5969	561	5	open	open	ADJ
ejpam-5969	561	6	sets	set	NOUN
ejpam-5969	561	7	via	via	ADP
ejpam-5969	561	8	soft	soft	ADJ
ejpam-5969	561	9	ditopological	ditopological	ADJ
ejpam-5969	561	10	spaces	space	NOUN
ejpam-5969	561	11	.	.	PUNCT
ejpam-5969	562	1	european	european	ADJ
ejpam-5969	562	2	journal	journal	PROPN
ejpam-5969	562	3	of	of	ADP
ejpam-5969	562	4	pure	pure	ADJ
ejpam-5969	562	5	and	and	CCONJ
ejpam-5969	562	6	applied	applied	ADJ
ejpam-5969	562	7	mathematics	mathematic	NOUN
ejpam-5969	562	8	,	,	PUNCT
ejpam-5969	562	9	15(1):126–134	15(1):126–134	PROPN
ejpam-5969	562	10	,	,	PUNCT
ejpam-5969	562	11	2022	2022	NUM
ejpam-5969	562	12	.	.	PUNCT
ejpam-5969	563	1	[	[	X
ejpam-5969	563	2	31	31	NUM
ejpam-5969	563	3	]	]	PUNCT
ejpam-5969	563	4	s.	s.	PROPN
ejpam-5969	563	5	al	al	PROPN
ejpam-5969	563	6	ghour	ghour	PROPN
ejpam-5969	563	7	.	.	PUNCT
ejpam-5969	564	1	soft	soft	ADJ
ejpam-5969	564	2	ω	ω	NOUN
ejpam-5969	564	3	-	-	PUNCT
ejpam-5969	564	4	continuity	continuity	NOUN
ejpam-5969	564	5	and	and	CCONJ
ejpam-5969	564	6	soft	soft	ADJ
ejpam-5969	564	7	ωs	ω	NOUN
ejpam-5969	564	8	-	-	NOUN
ejpam-5969	564	9	continuity	continuity	NOUN
ejpam-5969	564	10	in	in	ADP
ejpam-5969	564	11	soft	soft	ADJ
ejpam-5969	564	12	topological	topological	ADJ
ejpam-5969	564	13	spaces	space	NOUN
ejpam-5969	564	14	.	.	PUNCT
ejpam-5969	565	1	international	international	ADJ
ejpam-5969	565	2	journal	journal	NOUN
ejpam-5969	565	3	of	of	ADP
ejpam-5969	565	4	fuzzy	fuzzy	ADJ
ejpam-5969	565	5	logic	logic	NOUN
ejpam-5969	565	6	and	and	CCONJ
ejpam-5969	565	7	intelligent	intelligent	ADJ
ejpam-5969	565	8	systems	system	NOUN
ejpam-5969	565	9	,	,	PUNCT
ejpam-5969	565	10	22(2):183–192	22(2):183–192	NOUN
ejpam-5969	565	11	,	,	PUNCT
ejpam-5969	565	12	2022	2022	NUM
ejpam-5969	565	13	.	.	PUNCT
ejpam-5969	566	1	[	[	X
ejpam-5969	566	2	32	32	NUM
ejpam-5969	566	3	]	]	PUNCT
ejpam-5969	566	4	s.	s.	PROPN
ejpam-5969	566	5	al	al	PROPN
ejpam-5969	566	6	ghour	ghour	PROPN
ejpam-5969	566	7	and	and	CCONJ
ejpam-5969	566	8	b.	b.	PROPN
ejpam-5969	566	9	irshidat	irshidat	PROPN
ejpam-5969	566	10	.	.	PUNCT
ejpam-5969	567	1	on	on	ADP
ejpam-5969	567	2	θω	θω	ADP
ejpam-5969	567	3	continuity	continuity	NOUN
ejpam-5969	567	4	.	.	PUNCT
ejpam-5969	568	1	heliyon	heliyon	NOUN
ejpam-5969	568	2	,	,	PUNCT
ejpam-5969	568	3	6(2):e03349	6(2):e03349	NUM
ejpam-5969	568	4	,	,	PUNCT
ejpam-5969	568	5	2020	2020	NUM
ejpam-5969	568	6	.	.	PUNCT
ejpam-5969	569	1	[	[	X
ejpam-5969	569	2	33	33	NUM
ejpam-5969	569	3	]	]	PUNCT
ejpam-5969	569	4	a.	a.	NOUN
ejpam-5969	569	5	kandil	kandil	PROPN
ejpam-5969	569	6	,	,	PUNCT
ejpam-5969	569	7	o.	o.	PROPN
ejpam-5969	569	8	a.	a.	PROPN
ejpam-5969	569	9	e.	e.	PROPN
ejpam-5969	569	10	tantawy	tantawy	PROPN
ejpam-5969	569	11	,	,	PUNCT
ejpam-5969	569	12	s.	s.	PROPN
ejpam-5969	569	13	a.	a.	PROPN
ejpam-5969	569	14	el	el	PROPN
ejpam-5969	569	15	-	-	PUNCT
ejpam-5969	569	16	sheikh	sheikh	NOUN
ejpam-5969	569	17	,	,	PUNCT
ejpam-5969	569	18	and	and	CCONJ
ejpam-5969	569	19	a.	a.	NOUN
ejpam-5969	569	20	m.	m.	PROPN
ejpam-5969	569	21	abd	abd	PROPN
ejpam-5969	569	22	el	el	PROPN
ejpam-5969	569	23	-	-	PROPN
ejpam-5969	569	24	latif	latif	PROPN
ejpam-5969	569	25	.	.	PUNCT
ejpam-5969	570	1	soft	soft	ADJ
ejpam-5969	570	2	ideal	ideal	ADJ
ejpam-5969	570	3	theory	theory	NOUN
ejpam-5969	570	4	,	,	PUNCT
ejpam-5969	570	5	soft	soft	ADJ
ejpam-5969	570	6	local	local	ADJ
ejpam-5969	570	7	function	function	NOUN
ejpam-5969	570	8	and	and	CCONJ
ejpam-5969	570	9	generated	generate	VERB
ejpam-5969	570	10	soft	soft	ADJ
ejpam-5969	570	11	topological	topological	ADJ
ejpam-5969	570	12	spaces	space	NOUN
ejpam-5969	570	13	.	.	PUNCT
ejpam-5969	571	1	applied	apply	VERB
ejpam-5969	571	2	mathematics	mathematic	NOUN
ejpam-5969	571	3	and	and	CCONJ
ejpam-5969	571	4	information	information	NOUN
ejpam-5969	571	5	sciences	science	NOUN
ejpam-5969	571	6	,	,	PUNCT
ejpam-5969	571	7	8(4):1595–1603	8(4):1595–1603	NOUN
ejpam-5969	571	8	,	,	PUNCT
ejpam-5969	571	9	2014	2014	NUM
ejpam-5969	571	10	.	.	PUNCT
ejpam-5969	572	1	[	[	X
ejpam-5969	572	2	34	34	NUM
ejpam-5969	572	3	]	]	X
ejpam-5969	572	4	a.	a.	NOUN
ejpam-5969	572	5	kandil	kandil	PROPN
ejpam-5969	572	6	,	,	PUNCT
ejpam-5969	572	7	o.	o.	PROPN
ejpam-5969	572	8	a.	a.	PROPN
ejpam-5969	572	9	e.	e.	PROPN
ejpam-5969	572	10	tantawy	tantawy	PROPN
ejpam-5969	572	11	,	,	PUNCT
ejpam-5969	572	12	s.	s.	PROPN
ejpam-5969	572	13	a.	a.	PROPN
ejpam-5969	572	14	el	el	PROPN
ejpam-5969	572	15	-	-	PUNCT
ejpam-5969	572	16	sheikh	sheikh	NOUN
ejpam-5969	572	17	,	,	PUNCT
ejpam-5969	572	18	and	and	CCONJ
ejpam-5969	572	19	a.	a.	NOUN
ejpam-5969	572	20	m.	m.	PROPN
ejpam-5969	572	21	abd	abd	PROPN
ejpam-5969	572	22	el	el	PROPN
ejpam-5969	572	23	-	-	PROPN
ejpam-5969	572	24	latif	latif	PROPN
ejpam-5969	572	25	.	.	PUNCT
ejpam-5969	573	1	soft	soft	ADJ
ejpam-5969	573	2	semi	semi	ADJ
ejpam-5969	573	3	compactness	compactness	NOUN
ejpam-5969	573	4	via	via	ADP
ejpam-5969	573	5	soft	soft	ADJ
ejpam-5969	573	6	ideals	ideal	NOUN
ejpam-5969	573	7	.	.	PUNCT
ejpam-5969	574	1	applied	apply	VERB
ejpam-5969	574	2	mathematics	mathematic	NOUN
ejpam-5969	574	3	and	and	CCONJ
ejpam-5969	574	4	information	information	NOUN
ejpam-5969	574	5	sciences	science	NOUN
ejpam-5969	574	6	,	,	PUNCT
ejpam-5969	574	7	8(5):2297	8(5):2297	NUM
ejpam-5969	574	8	–	–	PUNCT
ejpam-5969	574	9	2306	2306	NUM
ejpam-5969	574	10	,	,	PUNCT
ejpam-5969	574	11	2014	2014	NUM
ejpam-5969	574	12	.	.	PUNCT
ejpam-5969	575	1	[	[	X
ejpam-5969	575	2	35	35	NUM
ejpam-5969	575	3	]	]	PUNCT
ejpam-5969	575	4	a.	a.	NOUN
ejpam-5969	575	5	kandil	kandil	PROPN
ejpam-5969	575	6	,	,	PUNCT
ejpam-5969	575	7	o.	o.	PROPN
ejpam-5969	575	8	a.	a.	PROPN
ejpam-5969	575	9	e.	e.	PROPN
ejpam-5969	575	10	tantawy	tantawy	PROPN
ejpam-5969	575	11	,	,	PUNCT
ejpam-5969	575	12	s.	s.	PROPN
ejpam-5969	575	13	a.	a.	PROPN
ejpam-5969	575	14	el	el	PROPN
ejpam-5969	575	15	-	-	PUNCT
ejpam-5969	575	16	sheikh	sheikh	NOUN
ejpam-5969	575	17	,	,	PUNCT
ejpam-5969	575	18	and	and	CCONJ
ejpam-5969	575	19	a.	a.	NOUN
ejpam-5969	575	20	m.	m.	PROPN
ejpam-5969	575	21	abd	abd	PROPN
ejpam-5969	575	22	el	el	PROPN
ejpam-5969	575	23	-	-	PROPN
ejpam-5969	575	24	latif	latif	PROPN
ejpam-5969	575	25	.	.	PUNCT
ejpam-5969	576	1	soft	soft	ADJ
ejpam-5969	576	2	connectedness	connectedness	NOUN
ejpam-5969	576	3	via	via	ADP
ejpam-5969	576	4	soft	soft	ADJ
ejpam-5969	576	5	ideals	ideal	NOUN
ejpam-5969	576	6	.	.	PUNCT
ejpam-5969	577	1	journal	journal	NOUN
ejpam-5969	577	2	of	of	ADP
ejpam-5969	577	3	new	new	ADJ
ejpam-5969	577	4	results	result	NOUN
ejpam-5969	577	5	in	in	ADP
ejpam-5969	577	6	science	science	NOUN
ejpam-5969	577	7	,	,	PUNCT
ejpam-5969	577	8	4:90–108	4:90–108	NUM
ejpam-5969	577	9	,	,	PUNCT
ejpam-5969	577	10	2014	2014	NUM
ejpam-5969	577	11	.	.	PUNCT
ejpam-5969	578	1	[	[	X
ejpam-5969	578	2	36	36	NUM
ejpam-5969	578	3	]	]	PUNCT
ejpam-5969	578	4	m.	m.	NOUN
ejpam-5969	578	5	akdag	akdag	PROPN
ejpam-5969	578	6	and	and	CCONJ
ejpam-5969	578	7	f.	f.	PROPN
ejpam-5969	578	8	erol	erol	PROPN
ejpam-5969	578	9	.	.	PUNCT
ejpam-5969	579	1	soft	soft	ADJ
ejpam-5969	579	2	i	i	NOUN
ejpam-5969	579	3	-	-	PUNCT
ejpam-5969	579	4	sets	set	NOUN
ejpam-5969	579	5	and	and	CCONJ
ejpam-5969	579	6	soft	soft	ADJ
ejpam-5969	579	7	i	i	NOUN
ejpam-5969	579	8	-	-	PUNCT
ejpam-5969	579	9	continuity	continuity	NOUN
ejpam-5969	579	10	of	of	ADP
ejpam-5969	579	11	functions	function	NOUN
ejpam-5969	579	12	.	.	PUNCT
ejpam-5969	580	1	gazi	gazi	PROPN
ejpam-5969	580	2	university	university	PROPN
ejpam-5969	580	3	journal	journal	PROPN
ejpam-5969	580	4	of	of	ADP
ejpam-5969	580	5	science	science	NOUN
ejpam-5969	580	6	,	,	PUNCT
ejpam-5969	580	7	27:923–932	27:923–932	NUM
ejpam-5969	580	8	,	,	PUNCT
ejpam-5969	580	9	2014	2014	NUM
ejpam-5969	580	10	.	.	PUNCT
ejpam-5969	581	1	[	[	X
ejpam-5969	581	2	37	37	NUM
ejpam-5969	581	3	]	]	PUNCT
ejpam-5969	581	4	a.	a.	NOUN
ejpam-5969	581	5	kandil	kandil	PROPN
ejpam-5969	581	6	,	,	PUNCT
ejpam-5969	581	7	o.	o.	PROPN
ejpam-5969	581	8	a.	a.	PROPN
ejpam-5969	581	9	e.	e.	PROPN
ejpam-5969	581	10	tantawy	tantawy	PROPN
ejpam-5969	581	11	,	,	PUNCT
ejpam-5969	581	12	s.	s.	PROPN
ejpam-5969	581	13	a.	a.	PROPN
ejpam-5969	581	14	el	el	PROPN
ejpam-5969	581	15	-	-	PUNCT
ejpam-5969	581	16	sheikh	sheikh	NOUN
ejpam-5969	581	17	,	,	PUNCT
ejpam-5969	581	18	and	and	CCONJ
ejpam-5969	581	19	a.	a.	NOUN
ejpam-5969	581	20	m.	m.	PROPN
ejpam-5969	581	21	abd	abd	PROPN
ejpam-5969	581	22	el	el	PROPN
ejpam-5969	581	23	-	-	PROPN
ejpam-5969	581	24	latif	latif	PROPN
ejpam-5969	581	25	.	.	PUNCT
ejpam-5969	582	1	γ	γ	PROPN
ejpam-5969	582	2	-	-	PUNCT
ejpam-5969	582	3	operation	operation	NOUN
ejpam-5969	582	4	and	and	CCONJ
ejpam-5969	582	5	decompositions	decomposition	NOUN
ejpam-5969	582	6	of	of	ADP
ejpam-5969	582	7	some	some	DET
ejpam-5969	582	8	forms	form	NOUN
ejpam-5969	582	9	of	of	ADP
ejpam-5969	582	10	soft	soft	ADJ
ejpam-5969	582	11	continuity	continuity	NOUN
ejpam-5969	582	12	of	of	ADP
ejpam-5969	582	13	soft	soft	ADJ
ejpam-5969	582	14	topological	topological	ADJ
ejpam-5969	582	15	spaces	space	NOUN
ejpam-5969	582	16	via	via	ADP
ejpam-5969	582	17	soft	soft	ADJ
ejpam-5969	582	18	ideal	ideal	NOUN
ejpam-5969	582	19	.	.	PUNCT
ejpam-5969	583	1	annals	annal	NOUN
ejpam-5969	583	2	of	of	ADP
ejpam-5969	583	3	fuzzy	fuzzy	ADJ
ejpam-5969	583	4	mathematics	mathematic	NOUN
ejpam-5969	583	5	and	and	CCONJ
ejpam-5969	583	6	informatics	informatic	NOUN
ejpam-5969	583	7	,	,	PUNCT
ejpam-5969	583	8	9(3):385–402	9(3):385–402	NUM
ejpam-5969	583	9	,	,	PUNCT
ejpam-5969	583	10	2014	2014	NUM
ejpam-5969	583	11	.	.	PUNCT
ejpam-5969	584	1	[	[	X
ejpam-5969	584	2	38	38	NUM
ejpam-5969	584	3	]	]	PUNCT
ejpam-5969	584	4	a.	a.	NOUN
ejpam-5969	584	5	a.	a.	NOUN
ejpam-5969	584	6	nasef	nasef	PROPN
ejpam-5969	584	7	,	,	PUNCT
ejpam-5969	584	8	m.	m.	NOUN
ejpam-5969	584	9	parimala	parimala	PROPN
ejpam-5969	584	10	,	,	PUNCT
ejpam-5969	584	11	r.	r.	PROPN
ejpam-5969	584	12	jeevitha	jeevitha	PROPN
ejpam-5969	584	13	,	,	PUNCT
ejpam-5969	584	14	and	and	CCONJ
ejpam-5969	584	15	m.	m.	PROPN
ejpam-5969	584	16	k.	k.	PROPN
ejpam-5969	585	1	el	el	PROPN
ejpam-5969	585	2	-	-	PUNCT
ejpam-5969	585	3	sayed	say	VERB
ejpam-5969	585	4	.	.	PUNCT
ejpam-5969	586	1	soft	soft	ADJ
ejpam-5969	586	2	ideal	ideal	ADJ
ejpam-5969	586	3	theory	theory	NOUN
ejpam-5969	586	4	and	and	CCONJ
ejpam-5969	586	5	applications	application	NOUN
ejpam-5969	586	6	.	.	PUNCT
ejpam-5969	587	1	international	international	ADJ
ejpam-5969	587	2	journal	journal	PROPN
ejpam-5969	587	3	of	of	ADP
ejpam-5969	587	4	nonlinear	nonlinear	ADJ
ejpam-5969	587	5	analysis	analysis	NOUN
ejpam-5969	587	6	and	and	CCONJ
ejpam-5969	587	7	applications	application	NOUN
ejpam-5969	587	8	,	,	PUNCT
ejpam-5969	587	9	13(2):1335	13(2):1335	NUM
ejpam-5969	587	10	–	–	PUNCT
ejpam-5969	587	11	1342	1342	NUM
ejpam-5969	587	12	,	,	PUNCT
ejpam-5969	587	13	2022	2022	NUM
ejpam-5969	587	14	.	.	PUNCT
ejpam-5969	588	1	[	[	X
ejpam-5969	588	2	39	39	NUM
ejpam-5969	588	3	]	]	PUNCT
ejpam-5969	588	4	a.	a.	NOUN
ejpam-5969	588	5	m.	m.	PROPN
ejpam-5969	588	6	abd	abd	PROPN
ejpam-5969	588	7	el	el	PROPN
ejpam-5969	588	8	-	-	PROPN
ejpam-5969	588	9	latif	latif	PROPN
ejpam-5969	588	10	.	.	PUNCT
ejpam-5969	589	1	generalized	generalize	VERB
ejpam-5969	589	2	soft	soft	ADJ
ejpam-5969	589	3	rough	rough	ADJ
ejpam-5969	589	4	sets	set	NOUN
ejpam-5969	589	5	and	and	CCONJ
ejpam-5969	589	6	generated	generate	VERB
ejpam-5969	589	7	soft	soft	ADJ
ejpam-5969	589	8	ideal	ideal	NOUN
ejpam-5969	589	9	rough	rough	ADJ
ejpam-5969	589	10	topological	topological	ADJ
ejpam-5969	589	11	spaces	space	NOUN
ejpam-5969	589	12	.	.	PUNCT
ejpam-5969	590	1	journal	journal	NOUN
ejpam-5969	590	2	of	of	ADP
ejpam-5969	590	3	intelligent	intelligent	ADJ
ejpam-5969	590	4	and	and	CCONJ
ejpam-5969	590	5	fuzzy	fuzzy	ADJ
ejpam-5969	590	6	systems	system	NOUN
ejpam-5969	590	7	,	,	PUNCT
ejpam-5969	590	8	34:517–524	34:517–524	PROPN
ejpam-5969	590	9	,	,	PUNCT
ejpam-5969	590	10	2018	2018	NUM
ejpam-5969	590	11	.	.	PUNCT
ejpam-5969	591	1	[	[	X
ejpam-5969	591	2	40	40	NUM
ejpam-5969	591	3	]	]	PUNCT
ejpam-5969	591	4	a.	a.	NOUN
ejpam-5969	591	5	m.	m.	PROPN
ejpam-5969	591	6	abd	abd	PROPN
ejpam-5969	591	7	el	el	PROPN
ejpam-5969	591	8	-	-	PROPN
ejpam-5969	591	9	latif	latif	PROPN
ejpam-5969	591	10	.	.	PUNCT
ejpam-5969	592	1	new	new	ADJ
ejpam-5969	592	2	generalized	generalize	VERB
ejpam-5969	592	3	fuzzy	fuzzy	ADJ
ejpam-5969	592	4	soft	soft	ADJ
ejpam-5969	592	5	rough	rough	ADJ
ejpam-5969	592	6	approximations	approximation	NOUN
ejpam-5969	592	7	applied	apply	VERB
ejpam-5969	592	8	to	to	ADP
ejpam-5969	592	9	fuzzy	fuzzy	ADJ
ejpam-5969	592	10	topological	topological	ADJ
ejpam-5969	592	11	spaces	space	NOUN
ejpam-5969	592	12	.	.	PUNCT
ejpam-5969	593	1	journal	journal	NOUN
ejpam-5969	593	2	of	of	ADP
ejpam-5969	593	3	intelligent	intelligent	ADJ
ejpam-5969	593	4	and	and	CCONJ
ejpam-5969	593	5	fuzzy	fuzzy	ADJ
ejpam-5969	593	6	systems	system	NOUN
ejpam-5969	593	7	,	,	PUNCT
ejpam-5969	593	8	35:2123–2136	35:2123–2136	NUM
ejpam-5969	593	9	,	,	PUNCT
ejpam-5969	593	10	2018	2018	NUM
ejpam-5969	593	11	.	.	PUNCT
ejpam-5969	594	1	[	[	X
ejpam-5969	594	2	41	41	NUM
ejpam-5969	594	3	]	]	PUNCT
ejpam-5969	594	4	a.	a.	NOUN
ejpam-5969	594	5	kandil	kandil	PROPN
ejpam-5969	594	6	,	,	PUNCT
ejpam-5969	594	7	o.	o.	PROPN
ejpam-5969	594	8	a.	a.	PROPN
ejpam-5969	594	9	e.	e.	PROPN
ejpam-5969	594	10	tantawy	tantawy	PROPN
ejpam-5969	594	11	,	,	PUNCT
ejpam-5969	594	12	s.	s.	PROPN
ejpam-5969	594	13	a.	a.	PROPN
ejpam-5969	594	14	el	el	PROPN
ejpam-5969	594	15	-	-	PUNCT
ejpam-5969	594	16	sheikh	sheikh	NOUN
ejpam-5969	594	17	,	,	PUNCT
ejpam-5969	594	18	and	and	CCONJ
ejpam-5969	594	19	a.	a.	NOUN
ejpam-5969	594	20	m.	m.	PROPN
ejpam-5969	594	21	abd	abd	PROPN
ejpam-5969	594	22	el	el	PROPN
ejpam-5969	594	23	-	-	PROPN
ejpam-5969	594	24	latif	latif	PROPN
ejpam-5969	594	25	.	.	PUNCT
ejpam-5969	595	1	soft	soft	ADJ
ejpam-5969	595	2	semi	semi	ADJ
ejpam-5969	595	3	(	(	PUNCT
ejpam-5969	595	4	quasi	quasi	ADJ
ejpam-5969	595	5	)	)	PUNCT
ejpam-5969	595	6	hausdorff	hausdorff	NOUN
ejpam-5969	595	7	spaces	space	NOUN
ejpam-5969	595	8	via	via	ADP
ejpam-5969	595	9	soft	soft	ADJ
ejpam-5969	595	10	ideals	ideal	NOUN
ejpam-5969	595	11	.	.	PUNCT
ejpam-5969	596	1	south	south	ADJ
ejpam-5969	596	2	asian	asian	PROPN
ejpam-5969	596	3	journal	journal	PROPN
ejpam-5969	596	4	of	of	ADP
ejpam-5969	596	5	mathematics	mathematic	NOUN
ejpam-5969	596	6	,	,	PUNCT
ejpam-5969	596	7	4(6):265–284	4(6):265–284	NUM
ejpam-5969	596	8	,	,	PUNCT
ejpam-5969	596	9	2014	2014	NUM
ejpam-5969	596	10	.	.	PUNCT
ejpam-5969	597	1	[	[	X
ejpam-5969	597	2	42	42	NUM
ejpam-5969	597	3	]	]	PUNCT
ejpam-5969	597	4	s.	s.	PROPN
ejpam-5969	597	5	a.	a.	PROPN
ejpam-5969	597	6	el	el	PROPN
ejpam-5969	597	7	-	-	PUNCT
ejpam-5969	597	8	sheikh	sheikh	PROPN
ejpam-5969	597	9	and	and	CCONJ
ejpam-5969	597	10	a.	a.	NOUN
ejpam-5969	597	11	m.	m.	NOUN
ejpam-5969	597	12	abd	abd	PROPN
ejpam-5969	597	13	el	el	PROPN
ejpam-5969	597	14	-	-	PROPN
ejpam-5969	597	15	latif	latif	PROPN
ejpam-5969	597	16	.	.	PUNCT
ejpam-5969	598	1	decompositions	decomposition	NOUN
ejpam-5969	598	2	of	of	ADP
ejpam-5969	598	3	some	some	DET
ejpam-5969	598	4	types	type	NOUN
ejpam-5969	598	5	of	of	ADP
ejpam-5969	598	6	supra	supra	ADJ
ejpam-5969	598	7	soft	soft	ADJ
ejpam-5969	598	8	sets	set	NOUN
ejpam-5969	598	9	and	and	CCONJ
ejpam-5969	598	10	soft	soft	ADJ
ejpam-5969	598	11	continuity	continuity	NOUN
ejpam-5969	598	12	.	.	PUNCT
ejpam-5969	599	1	international	international	ADJ
ejpam-5969	599	2	journal	journal	PROPN
ejpam-5969	599	3	of	of	ADP
ejpam-5969	599	4	mathematical	mathematical	ADJ
ejpam-5969	599	5	trends	trend	NOUN
ejpam-5969	599	6	and	and	CCONJ
ejpam-5969	599	7	technology	technology	NOUN
ejpam-5969	599	8	,	,	PUNCT
ejpam-5969	599	9	9(1):37–56	9(1):37–56	NUM
ejpam-5969	599	10	,	,	PUNCT
ejpam-5969	599	11	2014	2014	NUM
ejpam-5969	599	12	.	.	PUNCT
ejpam-5969	600	1	[	[	X
ejpam-5969	600	2	43	43	NUM
ejpam-5969	600	3	]	]	PUNCT
ejpam-5969	600	4	a.	a.	NOUN
ejpam-5969	600	5	m.	m.	PROPN
ejpam-5969	600	6	abd	abd	PROPN
ejpam-5969	600	7	el	el	PROPN
ejpam-5969	600	8	-	-	PROPN
ejpam-5969	600	9	latif	latif	PROPN
ejpam-5969	600	10	and	and	CCONJ
ejpam-5969	600	11	s.	s.	PROPN
ejpam-5969	600	12	karataş.	karataş.	PROPN
ejpam-5969	601	1	supra	supra	PROPN
ejpam-5969	601	2	b	b	PROPN
ejpam-5969	601	3	-	-	PUNCT
ejpam-5969	601	4	open	open	ADJ
ejpam-5969	601	5	soft	soft	ADJ
ejpam-5969	601	6	sets	set	NOUN
ejpam-5969	601	7	and	and	CCONJ
ejpam-5969	601	8	supra	supra	PROPN
ejpam-5969	601	9	b	b	NOUN
ejpam-5969	601	10	-	-	PUNCT
ejpam-5969	601	11	soft	soft	ADJ
ejpam-5969	601	12	continuity	continuity	NOUN
ejpam-5969	601	13	on	on	ADP
ejpam-5969	601	14	soft	soft	ADJ
ejpam-5969	601	15	topological	topological	ADJ
ejpam-5969	601	16	spaces	space	NOUN
ejpam-5969	601	17	.	.	PUNCT
ejpam-5969	602	1	journal	journal	NOUN
ejpam-5969	602	2	of	of	ADP
ejpam-5969	602	3	mathematical	mathematical	ADJ
ejpam-5969	602	4	and	and	CCONJ
ejpam-5969	602	5	computational	computational	ADJ
ejpam-5969	602	6	applications	application	NOUN
ejpam-5969	602	7	abd	abd	PROPN
ejpam-5969	602	8	el	el	PROPN
ejpam-5969	602	9	-	-	PROPN
ejpam-5969	602	10	latif	latif	PROPN
ejpam-5969	602	11	et	et	PROPN
ejpam-5969	602	12	al	al	PROPN
ejpam-5969	602	13	.	.	PUNCT
ejpam-5969	602	14	/	/	SYM
ejpam-5969	602	15	eur	eur	PROPN
ejpam-5969	602	16	.	.	PUNCT
ejpam-5969	603	1	j.	j.	PROPN
ejpam-5969	603	2	pure	pure	PROPN
ejpam-5969	603	3	appl	appl	PROPN
ejpam-5969	603	4	.	.	PROPN
ejpam-5969	603	5	math	math	PROPN
ejpam-5969	603	6	,	,	PUNCT
ejpam-5969	603	7	18	18	NUM
ejpam-5969	603	8	(	(	PUNCT
ejpam-5969	603	9	2	2	NUM
ejpam-5969	603	10	)	)	PUNCT
ejpam-5969	603	11	(	(	PUNCT
ejpam-5969	603	12	2025	2025	NUM
ejpam-5969	603	13	)	)	PUNCT
ejpam-5969	603	14	,	,	PUNCT
ejpam-5969	603	15	5969	5969	NUM
ejpam-5969	603	16	19	19	NUM
ejpam-5969	603	17	of	of	ADP
ejpam-5969	603	18	19	19	NUM
ejpam-5969	603	19	research	research	NOUN
ejpam-5969	603	20	,	,	PUNCT
ejpam-5969	603	21	5(1):1–18	5(1):1–18	NUM
ejpam-5969	603	22	,	,	PUNCT
ejpam-5969	603	23	2015	2015	NUM
ejpam-5969	603	24	.	.	PUNCT
ejpam-5969	604	1	[	[	X
ejpam-5969	604	2	44	44	NUM
ejpam-5969	604	3	]	]	PUNCT
ejpam-5969	604	4	a.	a.	NOUN
ejpam-5969	604	5	m.	m.	PROPN
ejpam-5969	604	6	abd	abd	PROPN
ejpam-5969	604	7	el	el	PROPN
ejpam-5969	604	8	-	-	PROPN
ejpam-5969	604	9	latif	latif	PROPN
ejpam-5969	604	10	and	and	CCONJ
ejpam-5969	604	11	mesfer	mesfer	VERB
ejpam-5969	604	12	h.	h.	PROPN
ejpam-5969	604	13	alqahtani	alqahtani	PROPN
ejpam-5969	604	14	.	.	PUNCT
ejpam-5969	605	1	new	new	ADJ
ejpam-5969	605	2	soft	soft	ADJ
ejpam-5969	605	3	operators	operator	NOUN
ejpam-5969	605	4	related	relate	VERB
ejpam-5969	605	5	to	to	ADP
ejpam-5969	605	6	supra	supra	PROPN
ejpam-5969	605	7	soft	soft	ADJ
ejpam-5969	605	8	δi	δi	NOUN
ejpam-5969	605	9	-	-	PUNCT
ejpam-5969	605	10	open	open	ADJ
ejpam-5969	605	11	sets	set	NOUN
ejpam-5969	605	12	and	and	CCONJ
ejpam-5969	605	13	applications	application	NOUN
ejpam-5969	605	14	.	.	PUNCT
ejpam-5969	606	1	aims	aim	VERB
ejpam-5969	606	2	mathematics	mathematic	NOUN
ejpam-5969	606	3	,	,	PUNCT
ejpam-5969	606	4	9(2):3076–3096	9(2):3076–3096	NUM
ejpam-5969	606	5	,	,	PUNCT
ejpam-5969	606	6	2024	2024	NUM
ejpam-5969	606	7	.	.	PUNCT
ejpam-5969	607	1	[	[	X
ejpam-5969	607	2	45	45	NUM
ejpam-5969	607	3	]	]	X
ejpam-5969	607	4	alaa	alaa	PROPN
ejpam-5969	607	5	m.	m.	PROPN
ejpam-5969	607	6	abd	abd	PROPN
ejpam-5969	607	7	el	el	PROPN
ejpam-5969	607	8	-	-	PROPN
ejpam-5969	607	9	latif	latif	PROPN
ejpam-5969	607	10	,	,	PUNCT
ejpam-5969	607	11	mesfer	mesfer	VERB
ejpam-5969	607	12	h.	h.	PROPN
ejpam-5969	607	13	alqahtani	alqahtani	PROPN
ejpam-5969	607	14	,	,	PUNCT
ejpam-5969	607	15	and	and	CCONJ
ejpam-5969	607	16	f.	f.	PROPN
ejpam-5969	607	17	a.	a.	PROPN
ejpam-5969	607	18	gharib	gharib	PROPN
ejpam-5969	607	19	.	.	PUNCT
ejpam-5969	608	1	strictly	strictly	ADV
ejpam-5969	608	2	wider	wide	ADJ
ejpam-5969	608	3	class	class	NOUN
ejpam-5969	608	4	of	of	ADP
ejpam-5969	608	5	soft	soft	ADJ
ejpam-5969	608	6	sets	set	NOUN
ejpam-5969	608	7	via	via	ADP
ejpam-5969	608	8	supra	supra	PROPN
ejpam-5969	608	9	soft	soft	PROPN
ejpam-5969	608	10	δ	δ	PROPN
ejpam-5969	608	11	-	-	PUNCT
ejpam-5969	608	12	closure	closure	NOUN
ejpam-5969	608	13	operator	operator	NOUN
ejpam-5969	608	14	.	.	PUNCT
ejpam-5969	609	1	international	international	ADJ
ejpam-5969	609	2	journal	journal	NOUN
ejpam-5969	609	3	of	of	ADP
ejpam-5969	609	4	analysis	analysis	NOUN
ejpam-5969	609	5	and	and	CCONJ
ejpam-5969	609	6	applications	application	NOUN
ejpam-5969	609	7	,	,	PUNCT
ejpam-5969	609	8	22:47	22:47	NUM
ejpam-5969	609	9	,	,	PUNCT
ejpam-5969	609	10	2024	2024	NUM
ejpam-5969	609	11	.	.	PUNCT
ejpam-5969	610	1	[	[	X
ejpam-5969	610	2	46	46	NUM
ejpam-5969	610	3	]	]	PUNCT
ejpam-5969	610	4	a.	a.	NOUN
ejpam-5969	610	5	m.	m.	PROPN
ejpam-5969	610	6	abd	abd	PROPN
ejpam-5969	610	7	el	el	PROPN
ejpam-5969	610	8	-	-	PROPN
ejpam-5969	610	9	latif	latif	PROPN
ejpam-5969	610	10	.	.	PUNCT
ejpam-5969	611	1	novel	novel	ADJ
ejpam-5969	611	2	types	type	NOUN
ejpam-5969	611	3	of	of	ADP
ejpam-5969	611	4	supra	supra	ADJ
ejpam-5969	611	5	soft	soft	ADJ
ejpam-5969	611	6	operators	operator	NOUN
ejpam-5969	611	7	via	via	ADP
ejpam-5969	611	8	supra	supra	PROPN
ejpam-5969	611	9	soft	soft	ADJ
ejpam-5969	611	10	sd	sd	NOUN
ejpam-5969	611	11	-	-	PUNCT
ejpam-5969	611	12	sets	set	NOUN
ejpam-5969	611	13	and	and	CCONJ
ejpam-5969	611	14	applications	application	NOUN
ejpam-5969	611	15	.	.	PUNCT
ejpam-5969	612	1	aims	aim	VERB
ejpam-5969	612	2	mathematics	mathematic	NOUN
ejpam-5969	612	3	,	,	PUNCT
ejpam-5969	612	4	9(3):6586–6602	9(3):6586–6602	PROPN
ejpam-5969	612	5	,	,	PUNCT
ejpam-5969	612	6	2024	2024	NUM
ejpam-5969	612	7	.	.	PUNCT
ejpam-5969	613	1	[	[	X
ejpam-5969	613	2	47	47	NUM
ejpam-5969	613	3	]	]	PUNCT
ejpam-5969	613	4	a.	a.	NOUN
ejpam-5969	613	5	m.	m.	PROPN
ejpam-5969	613	6	abd	abd	PROPN
ejpam-5969	613	7	el	el	PROPN
ejpam-5969	613	8	-	-	PROPN
ejpam-5969	613	9	latif	latif	PROPN
ejpam-5969	613	10	,	,	PUNCT
ejpam-5969	613	11	radwan	radwan	VERB
ejpam-5969	613	12	abu	abu	PROPN
ejpam-5969	613	13	-	-	PUNCT
ejpam-5969	613	14	gdairi	gdairi	PROPN
ejpam-5969	613	15	,	,	PUNCT
ejpam-5969	613	16	a.	a.	PROPN
ejpam-5969	613	17	a.	a.	PROPN
ejpam-5969	613	18	azzam	azzam	PROPN
ejpam-5969	613	19	,	,	PUNCT
ejpam-5969	613	20	f.	f.	PROPN
ejpam-5969	613	21	a.	a.	PROPN
ejpam-5969	613	22	gharib	gharib	PROPN
ejpam-5969	613	23	,	,	PUNCT
ejpam-5969	613	24	and	and	CCONJ
ejpam-5969	613	25	khaled	khaled	PROPN
ejpam-5969	613	26	a.	a.	PROPN
ejpam-5969	613	27	aldwoah	aldwoah	PROPN
ejpam-5969	613	28	.	.	PUNCT
ejpam-5969	614	1	supra	supra	PROPN
ejpam-5969	614	2	soft	soft	ADJ
ejpam-5969	614	3	somewhat	somewhat	ADV
ejpam-5969	614	4	open	open	ADJ
ejpam-5969	614	5	sets	set	NOUN
ejpam-5969	614	6	:	:	PUNCT
ejpam-5969	614	7	characterizations	characterization	NOUN
ejpam-5969	614	8	and	and	CCONJ
ejpam-5969	614	9	continuity	continuity	NOUN
ejpam-5969	614	10	.	.	PUNCT
ejpam-5969	615	1	european	european	ADJ
ejpam-5969	615	2	journal	journal	PROPN
ejpam-5969	615	3	of	of	ADP
ejpam-5969	615	4	pure	pure	ADJ
ejpam-5969	615	5	and	and	CCONJ
ejpam-5969	615	6	applied	applied	ADJ
ejpam-5969	615	7	mathematics	mathematic	NOUN
ejpam-5969	615	8	,	,	PUNCT
ejpam-5969	615	9	18(2):5863	18(2):5863	NUM
ejpam-5969	615	10	,	,	PUNCT
ejpam-5969	615	11	2025	2025	NUM
ejpam-5969	615	12	.	.	PUNCT
ejpam-5969	616	1	[	[	X
ejpam-5969	616	2	48	48	NUM
ejpam-5969	616	3	]	]	PUNCT
ejpam-5969	616	4	a.	a.	NOUN
ejpam-5969	616	5	kandil	kandil	PROPN
ejpam-5969	616	6	,	,	PUNCT
ejpam-5969	616	7	o.	o.	PROPN
ejpam-5969	616	8	a.	a.	PROPN
ejpam-5969	616	9	e.	e.	PROPN
ejpam-5969	616	10	tantawy	tantawy	PROPN
ejpam-5969	616	11	,	,	PUNCT
ejpam-5969	616	12	s.	s.	PROPN
ejpam-5969	616	13	a.	a.	PROPN
ejpam-5969	616	14	el	el	PROPN
ejpam-5969	616	15	-	-	PUNCT
ejpam-5969	616	16	sheikh	sheikh	NOUN
ejpam-5969	616	17	,	,	PUNCT
ejpam-5969	616	18	and	and	CCONJ
ejpam-5969	616	19	a.	a.	NOUN
ejpam-5969	616	20	m.	m.	PROPN
ejpam-5969	616	21	abd	abd	PROPN
ejpam-5969	616	22	el	el	PROPN
ejpam-5969	616	23	-	-	PROPN
ejpam-5969	616	24	latif	latif	PROPN
ejpam-5969	616	25	.	.	PUNCT
ejpam-5969	617	1	supra	supra	PROPN
ejpam-5969	617	2	generalized	generalize	VERB
ejpam-5969	617	3	closed	close	VERB
ejpam-5969	617	4	soft	soft	ADJ
ejpam-5969	617	5	sets	set	NOUN
ejpam-5969	617	6	with	with	ADP
ejpam-5969	617	7	respect	respect	NOUN
ejpam-5969	617	8	to	to	ADP
ejpam-5969	617	9	a	a	DET
ejpam-5969	617	10	soft	soft	ADJ
ejpam-5969	617	11	ideal	ideal	NOUN
ejpam-5969	617	12	in	in	ADP
ejpam-5969	617	13	supra	supra	PROPN
ejpam-5969	617	14	soft	soft	ADJ
ejpam-5969	617	15	topological	topological	ADJ
ejpam-5969	617	16	spaces	space	NOUN
ejpam-5969	617	17	.	.	PUNCT
ejpam-5969	618	1	applied	apply	VERB
ejpam-5969	618	2	mathematics	mathematic	NOUN
ejpam-5969	618	3	and	and	CCONJ
ejpam-5969	618	4	information	information	NOUN
ejpam-5969	618	5	sciences	science	NOUN
ejpam-5969	618	6	,	,	PUNCT
ejpam-5969	618	7	8(4):1731–1740	8(4):1731–1740	PROPN
ejpam-5969	618	8	,	,	PUNCT
ejpam-5969	618	9	2014	2014	NUM
ejpam-5969	618	10	.	.	PUNCT
ejpam-5969	619	1	[	[	X
ejpam-5969	619	2	49	49	NUM
ejpam-5969	619	3	]	]	X
ejpam-5969	619	4	f.	f.	PROPN
ejpam-5969	619	5	gharib	gharib	PROPN
ejpam-5969	619	6	and	and	CCONJ
ejpam-5969	619	7	a.	a.	NOUN
ejpam-5969	619	8	m.	m.	PROPN
ejpam-5969	619	9	abd	abd	PROPN
ejpam-5969	619	10	el	el	PROPN
ejpam-5969	619	11	-	-	PROPN
ejpam-5969	619	12	latif	latif	PROPN
ejpam-5969	619	13	.	.	PUNCT
ejpam-5969	620	1	soft	soft	ADJ
ejpam-5969	620	2	semi	semi	ADJ
ejpam-5969	620	3	local	local	ADJ
ejpam-5969	620	4	functions	function	NOUN
ejpam-5969	620	5	in	in	ADP
ejpam-5969	620	6	soft	soft	ADJ
ejpam-5969	620	7	ideal	ideal	ADJ
ejpam-5969	620	8	topological	topological	ADJ
ejpam-5969	620	9	spaces	space	NOUN
ejpam-5969	620	10	.	.	PUNCT
ejpam-5969	621	1	european	european	ADJ
ejpam-5969	621	2	journal	journal	PROPN
ejpam-5969	621	3	of	of	ADP
ejpam-5969	621	4	pure	pure	ADJ
ejpam-5969	621	5	and	and	CCONJ
ejpam-5969	621	6	applied	applied	ADJ
ejpam-5969	621	7	mathematics	mathematic	NOUN
ejpam-5969	621	8	,	,	PUNCT
ejpam-5969	621	9	12(3):857–869	12(3):857–869	NUM
ejpam-5969	621	10	,	,	PUNCT
ejpam-5969	621	11	2019	2019	NUM
ejpam-5969	621	12	.	.	PUNCT