id	sid	tid	token	lemma	pos
ejpam-6020	1	1	european	european	PROPN
ejpam-6020	1	2	journal	journal	PROPN
ejpam-6020	1	3	of	of	ADP
ejpam-6020	1	4	pure	pure	ADJ
ejpam-6020	1	5	and	and	CCONJ
ejpam-6020	1	6	applied	applied	ADJ
ejpam-6020	1	7	mathematics	mathematic	NOUN
ejpam-6020	1	8	2025	2025	NUM
ejpam-6020	1	9	,	,	PUNCT
ejpam-6020	1	10	vol	vol	NOUN
ejpam-6020	1	11	.	.	PROPN
ejpam-6020	1	12	18	18	NUM
ejpam-6020	1	13	,	,	PUNCT
ejpam-6020	1	14	issue	issue	NOUN
ejpam-6020	1	15	2	2	NUM
ejpam-6020	1	16	,	,	PUNCT
ejpam-6020	1	17	article	article	NOUN
ejpam-6020	1	18	number	number	NOUN
ejpam-6020	1	19	6020	6020	NUM
ejpam-6020	1	20	issn	issn	PROPN
ejpam-6020	1	21	1307	1307	NUM
ejpam-6020	1	22	-	-	SYM
ejpam-6020	1	23	5543	5543	NUM
ejpam-6020	1	24	–	–	PUNCT
ejpam-6020	1	25	ejpam.com	ejpam.com	X
ejpam-6020	1	26	published	publish	VERB
ejpam-6020	1	27	by	by	ADP
ejpam-6020	1	28	new	new	PROPN
ejpam-6020	1	29	york	york	PROPN
ejpam-6020	1	30	business	business	PROPN
ejpam-6020	1	31	global	global	ADJ
ejpam-6020	1	32	novel	novel	ADJ
ejpam-6020	1	33	types	type	NOUN
ejpam-6020	1	34	of	of	ADP
ejpam-6020	1	35	supra	supra	ADJ
ejpam-6020	1	36	functions	function	NOUN
ejpam-6020	1	37	inspired	inspire	VERB
ejpam-6020	1	38	by	by	ADP
ejpam-6020	1	39	supra	supra	PROPN
ejpam-6020	1	40	ϵ-open	ϵ-open	PROPN
ejpam-6020	1	41	sets	set	VERB
ejpam-6020	1	42	alaa	alaa	PROPN
ejpam-6020	1	43	m.	m.	PROPN
ejpam-6020	1	44	abd	abd	PROPN
ejpam-6020	1	45	el	el	PROPN
ejpam-6020	1	46	-	-	PROPN
ejpam-6020	1	47	latif1	latif1	PROPN
ejpam-6020	1	48	,	,	PUNCT
ejpam-6020	1	49	radwan	radwan	VERB
ejpam-6020	1	50	abu	abu	PROPN
ejpam-6020	1	51	-	-	PUNCT
ejpam-6020	1	52	gdairi2	gdairi2	PROPN
ejpam-6020	1	53	,	,	PUNCT
ejpam-6020	2	1	a.	a.	NOUN
ejpam-6020	2	2	a.	a.	NOUN
ejpam-6020	2	3	azzam3,4	azzam3,4	PROPN
ejpam-6020	2	4	,	,	PUNCT
ejpam-6020	2	5	f.	f.	PROPN
ejpam-6020	2	6	a.	a.	PROPN
ejpam-6020	2	7	gharib1,∗	gharib1,∗	PROPN
ejpam-6020	2	8	,	,	PUNCT
ejpam-6020	2	9	husham	husham	PROPN
ejpam-6020	2	10	m.	m.	NOUN
ejpam-6020	2	11	attaalfadeel1	attaalfadeel1	PROPN
ejpam-6020	2	12	,	,	PUNCT
ejpam-6020	2	13	walid	walid	PROPN
ejpam-6020	2	14	abdelfattah1	abdelfattah1	PROPN
ejpam-6020	2	15	,	,	PUNCT
ejpam-6020	2	16	shaaban	shaaban	ADJ
ejpam-6020	2	17	m.	m.	NOUN
ejpam-6020	2	18	shaaban5	shaaban5	PROPN
ejpam-6020	2	19	,	,	PUNCT
ejpam-6020	2	20	m.	m.	NOUN
ejpam-6020	2	21	aldawood3	aldawood3	PROPN
ejpam-6020	3	1	1	1	NUM
ejpam-6020	3	2	mathematics	mathematics	PROPN
ejpam-6020	3	3	department	department	NOUN
ejpam-6020	3	4	,	,	PUNCT
ejpam-6020	3	5	college	college	NOUN
ejpam-6020	3	6	of	of	ADP
ejpam-6020	3	7	science	science	NOUN
ejpam-6020	3	8	,	,	PUNCT
ejpam-6020	3	9	northern	northern	ADJ
ejpam-6020	3	10	border	border	NOUN
ejpam-6020	3	11	university	university	NOUN
ejpam-6020	3	12	,	,	PUNCT
ejpam-6020	3	13	arar	arar	NOUN
ejpam-6020	3	14	91431	91431	NUM
ejpam-6020	3	15	,	,	PUNCT
ejpam-6020	3	16	saudi	saudi	PROPN
ejpam-6020	3	17	arabia	arabia	PROPN
ejpam-6020	3	18	2	2	NUM
ejpam-6020	3	19	mathematics	mathematics	PROPN
ejpam-6020	3	20	department	department	NOUN
ejpam-6020	3	21	,	,	PUNCT
ejpam-6020	3	22	faculty	faculty	NOUN
ejpam-6020	3	23	of	of	ADP
ejpam-6020	3	24	science	science	NOUN
ejpam-6020	3	25	,	,	PUNCT
ejpam-6020	3	26	zarqa	zarqa	PROPN
ejpam-6020	3	27	university	university	PROPN
ejpam-6020	3	28	,	,	PUNCT
ejpam-6020	3	29	zarqa	zarqa	NOUN
ejpam-6020	3	30	13132	13132	NUM
ejpam-6020	3	31	,	,	PUNCT
ejpam-6020	3	32	jordan	jordan	PROPN
ejpam-6020	3	33	3	3	NUM
ejpam-6020	3	34	department	department	PROPN
ejpam-6020	3	35	of	of	ADP
ejpam-6020	3	36	mathematics	mathematic	NOUN
ejpam-6020	3	37	,	,	PUNCT
ejpam-6020	3	38	faculty	faculty	NOUN
ejpam-6020	3	39	of	of	ADP
ejpam-6020	3	40	science	science	NOUN
ejpam-6020	3	41	and	and	CCONJ
ejpam-6020	3	42	humanities	humanity	NOUN
ejpam-6020	3	43	,	,	PUNCT
ejpam-6020	3	44	prince	prince	PROPN
ejpam-6020	3	45	sattam	sattam	PROPN
ejpam-6020	3	46	bin	bin	PROPN
ejpam-6020	3	47	abdulaziz	abdulaziz	PROPN
ejpam-6020	3	48	university	university	PROPN
ejpam-6020	3	49	,	,	PUNCT
ejpam-6020	3	50	alkharj	alkharj	VERB
ejpam-6020	3	51	11942	11942	NUM
ejpam-6020	3	52	,	,	PUNCT
ejpam-6020	3	53	saudi	saudi	PROPN
ejpam-6020	3	54	arabia	arabia	PROPN
ejpam-6020	3	55	4	4	NUM
ejpam-6020	3	56	department	department	NOUN
ejpam-6020	3	57	of	of	ADP
ejpam-6020	3	58	mathematics	mathematic	NOUN
ejpam-6020	3	59	,	,	PUNCT
ejpam-6020	3	60	faculty	faculty	NOUN
ejpam-6020	3	61	of	of	ADP
ejpam-6020	3	62	science	science	NOUN
ejpam-6020	3	63	,	,	PUNCT
ejpam-6020	3	64	new	new	ADJ
ejpam-6020	3	65	valley	valley	NOUN
ejpam-6020	3	66	university	university	NOUN
ejpam-6020	3	67	,	,	PUNCT
ejpam-6020	3	68	elkharga	elkharga	NOUN
ejpam-6020	3	69	72511	72511	NUM
ejpam-6020	3	70	,	,	PUNCT
ejpam-6020	3	71	egypt	egypt	PROPN
ejpam-6020	3	72	5	5	NUM
ejpam-6020	3	73	center	center	NOUN
ejpam-6020	3	74	for	for	ADP
ejpam-6020	3	75	scientific	scientific	ADJ
ejpam-6020	3	76	research	research	NOUN
ejpam-6020	3	77	and	and	CCONJ
ejpam-6020	3	78	entrepreneurship	entrepreneurship	NOUN
ejpam-6020	3	79	,	,	PUNCT
ejpam-6020	3	80	northern	northern	ADJ
ejpam-6020	3	81	border	border	NOUN
ejpam-6020	3	82	university	university	NOUN
ejpam-6020	3	83	,	,	PUNCT
ejpam-6020	3	84	arar	arar	PROPN
ejpam-6020	3	85	73213	73213	NUM
ejpam-6020	3	86	,	,	PUNCT
ejpam-6020	3	87	saudi	saudi	PROPN
ejpam-6020	3	88	arabia	arabia	PROPN
ejpam-6020	3	89	abstract	abstract	NOUN
ejpam-6020	3	90	.	.	PUNCT
ejpam-6020	4	1	using	use	VERB
ejpam-6020	4	2	the	the	DET
ejpam-6020	4	3	concept	concept	NOUN
ejpam-6020	4	4	of	of	ADP
ejpam-6020	4	5	supra	supra	PROPN
ejpam-6020	4	6	ϵ-open	ϵ-open	PROPN
ejpam-6020	4	7	sets	set	NOUN
ejpam-6020	4	8	,	,	PUNCT
ejpam-6020	4	9	this	this	DET
ejpam-6020	4	10	manuscript	manuscript	NOUN
ejpam-6020	4	11	discusses	discuss	VERB
ejpam-6020	4	12	and	and	CCONJ
ejpam-6020	4	13	investigates	investigate	VERB
ejpam-6020	4	14	new	new	ADJ
ejpam-6020	4	15	forms	form	NOUN
ejpam-6020	4	16	of	of	ADP
ejpam-6020	4	17	supra	supra	ADJ
ejpam-6020	4	18	continuity	continuity	NOUN
ejpam-6020	4	19	.	.	PUNCT
ejpam-6020	5	1	more	more	ADV
ejpam-6020	5	2	specifically	specifically	ADV
ejpam-6020	5	3	,	,	PUNCT
ejpam-6020	5	4	we	we	PRON
ejpam-6020	5	5	introduce	introduce	VERB
ejpam-6020	5	6	the	the	DET
ejpam-6020	5	7	concept	concept	NOUN
ejpam-6020	5	8	of	of	ADP
ejpam-6020	5	9	supra	supra	PROPN
ejpam-6020	5	10	ϵ-continuous	ϵ-continuous	PROPN
ejpam-6020	5	11	functions	function	NOUN
ejpam-6020	5	12	,	,	PUNCT
ejpam-6020	5	13	which	which	PRON
ejpam-6020	5	14	built	build	VERB
ejpam-6020	5	15	upon	upon	SCONJ
ejpam-6020	5	16	the	the	DET
ejpam-6020	5	17	previous	previous	ADJ
ejpam-6020	5	18	types	type	NOUN
ejpam-6020	5	19	of	of	ADP
ejpam-6020	5	20	weaker	weak	ADJ
ejpam-6020	5	21	forms	form	NOUN
ejpam-6020	5	22	of	of	ADP
ejpam-6020	5	23	such	such	ADJ
ejpam-6020	5	24	notions	notion	NOUN
ejpam-6020	5	25	.	.	PUNCT
ejpam-6020	6	1	the	the	DET
ejpam-6020	6	2	relationships	relationship	NOUN
ejpam-6020	6	3	between	between	ADP
ejpam-6020	6	4	our	our	PRON
ejpam-6020	6	5	new	new	ADJ
ejpam-6020	6	6	class	class	NOUN
ejpam-6020	6	7	and	and	CCONJ
ejpam-6020	6	8	existing	exist	VERB
ejpam-6020	6	9	previous	previous	ADJ
ejpam-6020	6	10	supra	supra	ADJ
ejpam-6020	6	11	continuity	continuity	NOUN
ejpam-6020	6	12	notions	notion	NOUN
ejpam-6020	6	13	were	be	AUX
ejpam-6020	6	14	examined	examine	VERB
ejpam-6020	6	15	using	use	VERB
ejpam-6020	6	16	the	the	DET
ejpam-6020	6	17	diagram	diagram	NOUN
ejpam-6020	6	18	in	in	ADP
ejpam-6020	6	19	figure	figure	NOUN
ejpam-6020	6	20	1	1	NUM
ejpam-6020	6	21	.	.	PUNCT
ejpam-6020	7	1	furthermore	furthermore	ADV
ejpam-6020	7	2	,	,	PUNCT
ejpam-6020	7	3	the	the	DET
ejpam-6020	7	4	essential	essential	ADJ
ejpam-6020	7	5	features	feature	NOUN
ejpam-6020	7	6	of	of	ADP
ejpam-6020	7	7	this	this	DET
ejpam-6020	7	8	concept	concept	NOUN
ejpam-6020	7	9	are	be	AUX
ejpam-6020	7	10	analyzed	analyze	VERB
ejpam-6020	7	11	,	,	PUNCT
ejpam-6020	7	12	as	as	ADV
ejpam-6020	7	13	well	well	ADV
ejpam-6020	7	14	as	as	ADP
ejpam-6020	7	15	its	its	PRON
ejpam-6020	7	16	analogous	analogous	ADJ
ejpam-6020	7	17	circumstances	circumstance	NOUN
ejpam-6020	7	18	.	.	PUNCT
ejpam-6020	8	1	additionally	additionally	ADV
ejpam-6020	8	2	,	,	PUNCT
ejpam-6020	8	3	the	the	DET
ejpam-6020	8	4	notions	notion	NOUN
ejpam-6020	8	5	of	of	ADP
ejpam-6020	8	6	supra	supra	ADJ
ejpam-6020	8	7	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	8	8	functions	function	NOUN
ejpam-6020	8	9	and	and	CCONJ
ejpam-6020	8	10	supra	supra	ADJ
ejpam-6020	8	11	ϵ∗-cts	ϵ∗-ct	NOUN
ejpam-6020	8	12	functions	function	NOUN
ejpam-6020	8	13	were	be	AUX
ejpam-6020	8	14	introduced	introduce	VERB
ejpam-6020	8	15	.	.	PUNCT
ejpam-6020	9	1	moreover	moreover	ADV
ejpam-6020	9	2	,	,	PUNCT
ejpam-6020	9	3	we	we	PRON
ejpam-6020	9	4	prove	prove	VERB
ejpam-6020	9	5	that	that	SCONJ
ejpam-6020	9	6	the	the	DET
ejpam-6020	9	7	composition	composition	NOUN
ejpam-6020	9	8	of	of	ADP
ejpam-6020	9	9	supra	supra	ADJ
ejpam-6020	9	10	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	9	11	function	function	NOUN
ejpam-6020	9	12	and	and	CCONJ
ejpam-6020	9	13	supra	supra	ADJ
ejpam-6020	9	14	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	9	15	function	function	NOUN
ejpam-6020	9	16	(	(	PUNCT
ejpam-6020	9	17	respectively	respectively	ADV
ejpam-6020	9	18	,	,	PUNCT
ejpam-6020	9	19	supra	supra	ADJ
ejpam-6020	9	20	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	9	21	function	function	NOUN
ejpam-6020	9	22	and	and	CCONJ
ejpam-6020	9	23	cts	cts	PROPN
ejpam-6020	9	24	function	function	NOUN
ejpam-6020	9	25	is	be	AUX
ejpam-6020	9	26	supra	supra	ADJ
ejpam-6020	9	27	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	9	28	,	,	PUNCT
ejpam-6020	9	29	two	two	NUM
ejpam-6020	9	30	supra	supra	ADJ
ejpam-6020	9	31	ϵ-irresolute	ϵ-irresolute	NOUN
ejpam-6020	9	32	functions	function	NOUN
ejpam-6020	9	33	)	)	PUNCT
ejpam-6020	9	34	is	be	AUX
ejpam-6020	9	35	supra	supra	ADJ
ejpam-6020	9	36	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	9	37	(	(	PUNCT
ejpam-6020	9	38	respectively	respectively	ADV
ejpam-6020	9	39	,	,	PUNCT
ejpam-6020	9	40	supra	supra	ADJ
ejpam-6020	9	41	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	9	42	,	,	PUNCT
ejpam-6020	9	43	supra	supra	PROPN
ejpam-6020	9	44	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	9	45	)	)	PUNCT
ejpam-6020	9	46	.	.	PUNCT
ejpam-6020	10	1	also	also	ADV
ejpam-6020	10	2	,	,	PUNCT
ejpam-6020	10	3	we	we	PRON
ejpam-6020	10	4	provide	provide	VERB
ejpam-6020	10	5	three	three	NUM
ejpam-6020	10	6	new	new	ADJ
ejpam-6020	10	7	approaches	approach	NOUN
ejpam-6020	10	8	for	for	ADP
ejpam-6020	10	9	supra	supra	ADJ
ejpam-6020	10	10	functions	function	NOUN
ejpam-6020	10	11	named	name	VERB
ejpam-6020	10	12	supra	supra	PROPN
ejpam-6020	10	13	ϵ-open	ϵ-open	PROPN
ejpam-6020	10	14	functions	function	NOUN
ejpam-6020	10	15	,	,	PUNCT
ejpam-6020	10	16	supra	supra	ADJ
ejpam-6020	10	17	ϵ-closed	ϵ-close	VERB
ejpam-6020	10	18	functions	function	NOUN
ejpam-6020	10	19	,	,	PUNCT
ejpam-6020	10	20	and	and	CCONJ
ejpam-6020	10	21	supra	supra	PROPN
ejpam-6020	10	22	ϵ-homeomorphism	ϵ-homeomorphism	NOUN
ejpam-6020	10	23	functions	function	NOUN
ejpam-6020	10	24	.	.	PUNCT
ejpam-6020	11	1	we	we	PRON
ejpam-6020	11	2	conclude	conclude	VERB
ejpam-6020	11	3	with	with	ADP
ejpam-6020	11	4	a	a	DET
ejpam-6020	11	5	detailed	detailed	ADJ
ejpam-6020	11	6	discussion	discussion	NOUN
ejpam-6020	11	7	of	of	ADP
ejpam-6020	11	8	their	their	PRON
ejpam-6020	11	9	key	key	ADJ
ejpam-6020	11	10	characteristics	characteristic	NOUN
ejpam-6020	11	11	and	and	CCONJ
ejpam-6020	11	12	provide	provide	VERB
ejpam-6020	11	13	several	several	ADJ
ejpam-6020	11	14	essential	essential	ADJ
ejpam-6020	11	15	examples	example	NOUN
ejpam-6020	11	16	.	.	PUNCT
ejpam-6020	12	1	2020	2020	NUM
ejpam-6020	12	2	mathematics	mathematic	NOUN
ejpam-6020	12	3	subject	subject	NOUN
ejpam-6020	12	4	classifications	classification	NOUN
ejpam-6020	12	5	:	:	PUNCT
ejpam-6020	12	6	54a05	54a05	NUM
ejpam-6020	12	7	,	,	PUNCT
ejpam-6020	12	8	54c10	54c10	NUM
ejpam-6020	12	9	,	,	PUNCT
ejpam-6020	12	10	54c08	54c08	NUM
ejpam-6020	12	11	key	key	ADJ
ejpam-6020	12	12	words	word	NOUN
ejpam-6020	12	13	and	and	CCONJ
ejpam-6020	12	14	phrases	phrase	NOUN
ejpam-6020	12	15	:	:	PUNCT
ejpam-6020	12	16	supra	supra	PROPN
ejpam-6020	12	17	ϵ-open	ϵ-open	PROPN
ejpam-6020	12	18	set	set	PROPN
ejpam-6020	12	19	,	,	PUNCT
ejpam-6020	12	20	supra	supra	PROPN
ejpam-6020	12	21	ϵ-continuous	ϵ-continuous	PROPN
ejpam-6020	12	22	functions	function	NOUN
ejpam-6020	12	23	,	,	PUNCT
ejpam-6020	12	24	supra	supra	ADJ
ejpam-6020	12	25	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	12	26	functions	function	NOUN
ejpam-6020	12	27	,	,	PUNCT
ejpam-6020	12	28	supra	supra	PROPN
ejpam-6020	12	29	ϵ-homeomorphism	ϵ-homeomorphism	NOUN
ejpam-6020	12	30	functions	function	NOUN
ejpam-6020	12	31	∗corresponding	∗corresponde	VERB
ejpam-6020	12	32	author	author	NOUN
ejpam-6020	12	33	.	.	PUNCT
ejpam-6020	13	1	doi	doi	NOUN
ejpam-6020	13	2	:	:	PUNCT
ejpam-6020	13	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6020	https://doi.org/10.29020/nybg.ejpam.v18i2.6020	X
ejpam-6020	13	4	email	email	NOUN
ejpam-6020	13	5	addresses	address	NOUN
ejpam-6020	13	6	:	:	PUNCT
ejpam-6020	13	7	alaa.ali@nbu.edu.sa	alaa.ali@nbu.edu.sa	PROPN
ejpam-6020	13	8	(	(	PUNCT
ejpam-6020	13	9	a.	a.	NOUN
ejpam-6020	13	10	m.	m.	PROPN
ejpam-6020	13	11	abd	abd	PROPN
ejpam-6020	13	12	el	el	PROPN
ejpam-6020	13	13	-	-	PROPN
ejpam-6020	13	14	latif	latif	PROPN
ejpam-6020	13	15	)	)	PUNCT
ejpam-6020	13	16	,	,	PUNCT
ejpam-6020	13	17	rgdairi@zu.edu.jo	rgdairi@zu.edu.jo	PROPN
ejpam-6020	13	18	(	(	PUNCT
ejpam-6020	13	19	r.	r.	PROPN
ejpam-6020	13	20	abu	abu	PROPN
ejpam-6020	13	21	-	-	PUNCT
ejpam-6020	13	22	gdairi	gdairi	PROPN
ejpam-6020	13	23	)	)	PUNCT
ejpam-6020	13	24	,	,	PUNCT
ejpam-6020	13	25	aa.azzam@psau.edu.sa	aa.azzam@psau.edu.sa	PROPN
ejpam-6020	13	26	(	(	PUNCT
ejpam-6020	13	27	a.	a.	NOUN
ejpam-6020	13	28	a.	a.	PROPN
ejpam-6020	13	29	azzam	azzam	PROPN
ejpam-6020	13	30	)	)	PUNCT
ejpam-6020	13	31	,	,	PUNCT
ejpam-6020	13	32	fatouh.gharib@nbu.edu.sa	fatouh.gharib@nbu.edu.sa	PROPN
ejpam-6020	13	33	(	(	PUNCT
ejpam-6020	13	34	f.	f.	PROPN
ejpam-6020	13	35	a.	a.	PROPN
ejpam-6020	13	36	gharib	gharib	PROPN
ejpam-6020	13	37	)	)	PUNCT
ejpam-6020	13	38	,	,	PUNCT
ejpam-6020	13	39	husham.alhassan@nbu.edu.sa	husham.alhassan@nbu.edu.sa	PROPN
ejpam-6020	13	40	(	(	PUNCT
ejpam-6020	13	41	h.	h.	PROPN
ejpam-6020	13	42	m.	m.	PROPN
ejpam-6020	13	43	attaalfadeel	attaalfadeel	PROPN
ejpam-6020	13	44	)	)	PUNCT
ejpam-6020	13	45	,	,	PUNCT
ejpam-6020	13	46	walid.abdelfattah@nbu.edu.sa	walid.abdelfattah@nbu.edu.sa	PROPN
ejpam-6020	13	47	(	(	PUNCT
ejpam-6020	13	48	w.	w.	PROPN
ejpam-6020	13	49	abdelfattah	abdelfattah	PROPN
ejpam-6020	13	50	)	)	PUNCT
ejpam-6020	13	51	,	,	PUNCT
ejpam-6020	13	52	shabaan27@gmail.com	shabaan27@gmail.com	PROPN
ejpam-6020	13	53	(	(	PUNCT
ejpam-6020	13	54	s.	s.	PROPN
ejpam-6020	13	55	m.	m.	PROPN
ejpam-6020	13	56	shaaban	shaaban	PROPN
ejpam-6020	13	57	)	)	PUNCT
ejpam-6020	13	58	,	,	PUNCT
ejpam-6020	13	59	m.aldawood@psau.edu.sa	m.aldawood@psau.edu.sa	PROPN
ejpam-6020	13	60	(	(	PUNCT
ejpam-6020	13	61	m.	m.	NOUN
ejpam-6020	13	62	aldawood	aldawood	PROPN
ejpam-6020	13	63	)	)	PUNCT
ejpam-6020	13	64	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6020	14	1	1	1	NUM
ejpam-6020	14	2	copyright	copyright	NOUN
ejpam-6020	14	3	:	:	PUNCT
ejpam-6020	14	4	©	©	PROPN
ejpam-6020	14	5	2025	2025	NUM
ejpam-6020	14	6	the	the	DET
ejpam-6020	14	7	author(s	author(s	NOUN
ejpam-6020	14	8	)	)	PUNCT
ejpam-6020	14	9	.	.	PUNCT
ejpam-6020	15	1	(	(	PUNCT
ejpam-6020	15	2	cc	cc	NOUN
ejpam-6020	15	3	by	by	ADP
ejpam-6020	15	4	-	-	PUNCT
ejpam-6020	15	5	nc	nc	PROPN
ejpam-6020	15	6	4.0	4.0	NUM
ejpam-6020	15	7	)	)	PUNCT
ejpam-6020	15	8	a.	a.	NOUN
ejpam-6020	15	9	m.	m.	NOUN
ejpam-6020	15	10	abd	abd	PROPN
ejpam-6020	15	11	el	el	PROPN
ejpam-6020	15	12	-	-	PROPN
ejpam-6020	15	13	latif	latif	PROPN
ejpam-6020	15	14	et	et	PROPN
ejpam-6020	15	15	al	al	PROPN
ejpam-6020	15	16	.	.	PUNCT
ejpam-6020	15	17	/	/	SYM
ejpam-6020	15	18	eur	eur	PROPN
ejpam-6020	15	19	.	.	PUNCT
ejpam-6020	16	1	j.	j.	PROPN
ejpam-6020	16	2	pure	pure	PROPN
ejpam-6020	16	3	appl	appl	PROPN
ejpam-6020	16	4	.	.	PROPN
ejpam-6020	16	5	math	math	PROPN
ejpam-6020	16	6	,	,	PUNCT
ejpam-6020	16	7	18	18	NUM
ejpam-6020	16	8	(	(	PUNCT
ejpam-6020	16	9	2	2	NUM
ejpam-6020	16	10	)	)	PUNCT
ejpam-6020	16	11	(	(	PUNCT
ejpam-6020	16	12	2025	2025	NUM
ejpam-6020	16	13	)	)	PUNCT
ejpam-6020	16	14	,	,	PUNCT
ejpam-6020	16	15	6020	6020	NUM
ejpam-6020	16	16	2	2	NUM
ejpam-6020	16	17	of	of	ADP
ejpam-6020	16	18	17	17	NUM
ejpam-6020	16	19	1	1	NUM
ejpam-6020	16	20	.	.	PUNCT
ejpam-6020	16	21	introduction	introduction	NOUN
ejpam-6020	16	22	the	the	DET
ejpam-6020	16	23	study	study	NOUN
ejpam-6020	16	24	of	of	ADP
ejpam-6020	16	25	different	different	ADJ
ejpam-6020	16	26	types	type	NOUN
ejpam-6020	16	27	of	of	ADP
ejpam-6020	16	28	generalized	generalized	ADJ
ejpam-6020	16	29	continuous	continuous	ADJ
ejpam-6020	16	30	functions	function	NOUN
ejpam-6020	16	31	,	,	PUNCT
ejpam-6020	16	32	supra	supra	ADJ
ejpam-6020	16	33	continuous	continuous	ADJ
ejpam-6020	16	34	functions	function	NOUN
ejpam-6020	16	35	,	,	PUNCT
ejpam-6020	16	36	and	and	CCONJ
ejpam-6020	16	37	soft	soft	ADJ
ejpam-6020	16	38	continuous	continuous	ADJ
ejpam-6020	16	39	functions	function	NOUN
ejpam-6020	16	40	and	and	CCONJ
ejpam-6020	16	41	their	their	PRON
ejpam-6020	16	42	structural	structural	ADJ
ejpam-6020	16	43	properties	property	NOUN
ejpam-6020	16	44	has	have	AUX
ejpam-6020	16	45	been	be	AUX
ejpam-6020	16	46	a	a	DET
ejpam-6020	16	47	major	major	ADJ
ejpam-6020	16	48	area	area	NOUN
ejpam-6020	16	49	of	of	ADP
ejpam-6020	16	50	topological	topological	ADJ
ejpam-6020	16	51	,	,	PUNCT
ejpam-6020	16	52	supra	supra	PROPN
ejpam-6020	16	53	topological	topological	ADJ
ejpam-6020	16	54	,	,	PUNCT
ejpam-6020	16	55	and	and	CCONJ
ejpam-6020	16	56	soft	soft	ADJ
ejpam-6020	16	57	topological	topological	ADJ
ejpam-6020	16	58	research	research	NOUN
ejpam-6020	16	59	in	in	ADP
ejpam-6020	16	60	the	the	DET
ejpam-6020	16	61	last	last	ADJ
ejpam-6020	16	62	several	several	ADJ
ejpam-6020	16	63	decades	decade	NOUN
ejpam-6020	16	64	.	.	PUNCT
ejpam-6020	17	1	levine	levine	PROPN
ejpam-6020	17	2	[	[	X
ejpam-6020	17	3	1	1	X
ejpam-6020	17	4	]	]	PUNCT
ejpam-6020	17	5	initially	initially	ADV
ejpam-6020	17	6	introduced	introduce	VERB
ejpam-6020	17	7	semi	semi	ADJ
ejpam-6020	17	8	-	-	ADJ
ejpam-6020	17	9	open	open	ADJ
ejpam-6020	17	10	sets	set	NOUN
ejpam-6020	17	11	and	and	CCONJ
ejpam-6020	17	12	semi	semi	ADJ
ejpam-6020	17	13	-	-	NOUN
ejpam-6020	17	14	continuity	continuity	NOUN
ejpam-6020	17	15	of	of	ADP
ejpam-6020	17	16	functions	function	NOUN
ejpam-6020	17	17	in	in	ADP
ejpam-6020	17	18	1963	1963	NUM
ejpam-6020	17	19	.	.	PUNCT
ejpam-6020	18	1	then	then	ADV
ejpam-6020	18	2	,	,	PUNCT
ejpam-6020	18	3	in	in	ADP
ejpam-6020	18	4	1965	1965	NUM
ejpam-6020	18	5	,	,	PUNCT
ejpam-6020	18	6	njasta	njasta	NOUN
ejpam-6020	19	1	[	[	X
ejpam-6020	19	2	2	2	X
ejpam-6020	19	3	]	]	PUNCT
ejpam-6020	19	4	introduced	introduce	VERB
ejpam-6020	19	5	his	his	PRON
ejpam-6020	19	6	α	α	NOUN
ejpam-6020	19	7	-	-	ADJ
ejpam-6020	19	8	open	open	ADJ
ejpam-6020	19	9	sets	set	NOUN
ejpam-6020	19	10	approach	approach	NOUN
ejpam-6020	19	11	.	.	PUNCT
ejpam-6020	20	1	the	the	DET
ejpam-6020	20	2	concept	concept	NOUN
ejpam-6020	20	3	of	of	ADP
ejpam-6020	20	4	pre	pre	ADJ
ejpam-6020	20	5	-	-	ADJ
ejpam-6020	20	6	open	open	ADJ
ejpam-6020	20	7	set	set	NOUN
ejpam-6020	20	8	was	be	AUX
ejpam-6020	20	9	proposed	propose	VERB
ejpam-6020	20	10	by	by	ADP
ejpam-6020	20	11	mashhour	mashhour	PROPN
ejpam-6020	20	12	et	et	PROPN
ejpam-6020	20	13	al	al	PROPN
ejpam-6020	20	14	.	.	PUNCT
ejpam-6020	21	1	[	[	X
ejpam-6020	21	2	3	3	X
ejpam-6020	21	3	]	]	PUNCT
ejpam-6020	21	4	in	in	ADP
ejpam-6020	21	5	order	order	NOUN
ejpam-6020	21	6	to	to	PART
ejpam-6020	21	7	investigate	investigate	VERB
ejpam-6020	21	8	pre	pre	ADJ
ejpam-6020	21	9	-	-	ADJ
ejpam-6020	21	10	continuous	continuous	ADJ
ejpam-6020	21	11	functions	function	NOUN
ejpam-6020	21	12	.	.	PUNCT
ejpam-6020	22	1	abd	abd	PROPN
ejpam-6020	22	2	-	-	PUNCT
ejpam-6020	22	3	el	el	PROPN
ejpam-6020	22	4	-	-	PUNCT
ejpam-6020	22	5	monsef	monsef	ADJ
ejpam-6020	22	6	et	et	PROPN
ejpam-6020	22	7	al	al	PROPN
ejpam-6020	22	8	.	.	PUNCT
ejpam-6020	23	1	[	[	X
ejpam-6020	23	2	4	4	X
ejpam-6020	23	3	]	]	PUNCT
ejpam-6020	23	4	introduced	introduce	VERB
ejpam-6020	23	5	the	the	DET
ejpam-6020	23	6	concept	concept	NOUN
ejpam-6020	23	7	of	of	ADP
ejpam-6020	23	8	β	β	ADJ
ejpam-6020	23	9	-	-	ADJ
ejpam-6020	23	10	open	open	ADJ
ejpam-6020	23	11	sets	set	NOUN
ejpam-6020	23	12	in	in	ADP
ejpam-6020	23	13	1983	1983	NUM
ejpam-6020	23	14	as	as	ADP
ejpam-6020	23	15	a	a	DET
ejpam-6020	23	16	means	means	NOUN
ejpam-6020	23	17	of	of	ADP
ejpam-6020	23	18	studying	study	VERB
ejpam-6020	23	19	β	β	ADJ
ejpam-6020	23	20	-	-	ADJ
ejpam-6020	23	21	continuous	continuous	ADJ
ejpam-6020	23	22	functions	function	NOUN
ejpam-6020	23	23	.	.	PUNCT
ejpam-6020	24	1	the	the	DET
ejpam-6020	24	2	concept	concept	NOUN
ejpam-6020	24	3	of	of	ADP
ejpam-6020	24	4	b	b	NOUN
ejpam-6020	24	5	-	-	PUNCT
ejpam-6020	24	6	open	open	ADJ
ejpam-6020	24	7	sets	set	NOUN
ejpam-6020	24	8	was	be	AUX
ejpam-6020	24	9	studied	study	VERB
ejpam-6020	24	10	in	in	ADP
ejpam-6020	24	11	detail	detail	NOUN
ejpam-6020	24	12	in	in	ADP
ejpam-6020	24	13	[	[	X
ejpam-6020	24	14	5	5	NUM
ejpam-6020	24	15	,	,	PUNCT
ejpam-6020	24	16	6	6	NUM
ejpam-6020	24	17	]	]	PUNCT
ejpam-6020	24	18	.	.	PUNCT
ejpam-6020	25	1	according	accord	VERB
ejpam-6020	25	2	to	to	ADP
ejpam-6020	25	3	[	[	X
ejpam-6020	25	4	7	7	NUM
ejpam-6020	25	5	]	]	PUNCT
ejpam-6020	25	6	,	,	PUNCT
ejpam-6020	25	7	piotrowski	piotrowski	NOUN
ejpam-6020	25	8	[	[	X
ejpam-6020	25	9	8	8	NUM
ejpam-6020	25	10	]	]	PUNCT
ejpam-6020	25	11	defined	define	VERB
ejpam-6020	25	12	relatively	relatively	ADV
ejpam-6020	25	13	open	open	ADJ
ejpam-6020	25	14	sets	set	NOUN
ejpam-6020	25	15	to	to	PART
ejpam-6020	25	16	present	present	VERB
ejpam-6020	25	17	somewhat	somewhat	ADV
ejpam-6020	25	18	continuity	continuity	NOUN
ejpam-6020	25	19	.	.	PUNCT
ejpam-6020	26	1	in	in	ADP
ejpam-6020	26	2	[	[	X
ejpam-6020	26	3	9	9	NUM
ejpam-6020	26	4	,	,	PUNCT
ejpam-6020	26	5	10	10	NUM
ejpam-6020	26	6	]	]	PUNCT
ejpam-6020	26	7	,	,	PUNCT
ejpam-6020	26	8	the	the	DET
ejpam-6020	26	9	concept	concept	NOUN
ejpam-6020	26	10	of	of	ADP
ejpam-6020	26	11	somewhere	somewhere	ADJ
ejpam-6020	26	12	dense	dense	ADJ
ejpam-6020	26	13	sets	set	NOUN
ejpam-6020	26	14	was	be	AUX
ejpam-6020	26	15	presented	present	VERB
ejpam-6020	26	16	.	.	PUNCT
ejpam-6020	27	1	other	other	ADJ
ejpam-6020	27	2	aspects	aspect	NOUN
ejpam-6020	27	3	of	of	ADP
ejpam-6020	27	4	this	this	DET
ejpam-6020	27	5	concept	concept	NOUN
ejpam-6020	27	6	were	be	AUX
ejpam-6020	27	7	studied	study	VERB
ejpam-6020	27	8	in	in	ADP
ejpam-6020	27	9	[	[	X
ejpam-6020	27	10	11	11	NUM
ejpam-6020	27	11	]	]	PUNCT
ejpam-6020	27	12	.	.	PUNCT
ejpam-6020	28	1	in	in	ADP
ejpam-6020	28	2	2024	2024	NUM
ejpam-6020	28	3	,	,	PUNCT
ejpam-6020	28	4	alqahtani	alqahtani	PROPN
ejpam-6020	28	5	and	and	CCONJ
ejpam-6020	28	6	abd	abd	PROPN
ejpam-6020	28	7	el	el	PROPN
ejpam-6020	28	8	-	-	PROPN
ejpam-6020	28	9	latif	latif	PROPN
ejpam-6020	28	10	[	[	X
ejpam-6020	28	11	12	12	NUM
ejpam-6020	28	12	]	]	PUNCT
ejpam-6020	28	13	introduced	introduce	VERB
ejpam-6020	28	14	the	the	DET
ejpam-6020	28	15	n	n	CCONJ
ejpam-6020	28	16	-open	-open	NOUN
ejpam-6020	28	17	sets	set	NOUN
ejpam-6020	28	18	approach	approach	NOUN
ejpam-6020	28	19	,	,	PUNCT
ejpam-6020	28	20	which	which	PRON
ejpam-6020	28	21	generalized	generalize	VERB
ejpam-6020	28	22	nearly	nearly	ADV
ejpam-6020	28	23	all	all	PRON
ejpam-6020	28	24	of	of	ADP
ejpam-6020	28	25	the	the	DET
ejpam-6020	28	26	previously	previously	ADV
ejpam-6020	28	27	proposed	propose	VERB
ejpam-6020	28	28	concepts	concept	NOUN
ejpam-6020	28	29	.	.	PUNCT
ejpam-6020	29	1	the	the	DET
ejpam-6020	29	2	concept	concept	NOUN
ejpam-6020	29	3	of	of	ADP
ejpam-6020	29	4	supra	supra	PROPN
ejpam-6020	29	5	open	open	ADJ
ejpam-6020	29	6	sets	set	NOUN
ejpam-6020	29	7	,	,	PUNCT
ejpam-6020	29	8	which	which	PRON
ejpam-6020	29	9	take	take	VERB
ejpam-6020	29	10	into	into	ADP
ejpam-6020	29	11	account	account	NOUN
ejpam-6020	29	12	the	the	DET
ejpam-6020	29	13	fundamental	fundamental	ADJ
ejpam-6020	29	14	components	component	NOUN
ejpam-6020	29	15	of	of	ADP
ejpam-6020	29	16	supra	supra	PROPN
ejpam-6020	29	17	topology	topology	NOUN
ejpam-6020	29	18	(	(	PUNCT
ejpam-6020	29	19	abbreviated	abbreviate	VERB
ejpam-6020	29	20	,	,	PUNCT
ejpam-6020	29	21	sts	st	NOUN
ejpam-6020	29	22	)	)	PUNCT
ejpam-6020	29	23	,	,	PUNCT
ejpam-6020	29	24	was	be	AUX
ejpam-6020	29	25	introduced	introduce	VERB
ejpam-6020	29	26	by	by	ADP
ejpam-6020	29	27	mashhour	mashhour	PROPN
ejpam-6020	29	28	et	et	PROPN
ejpam-6020	29	29	al	al	PROPN
ejpam-6020	29	30	.	.	PUNCT
ejpam-6020	30	1	[	[	X
ejpam-6020	30	2	13	13	NUM
ejpam-6020	30	3	]	]	PUNCT
ejpam-6020	30	4	.	.	PUNCT
ejpam-6020	31	1	the	the	DET
ejpam-6020	31	2	continuity	continuity	NOUN
ejpam-6020	31	3	and	and	CCONJ
ejpam-6020	31	4	separation	separation	NOUN
ejpam-6020	31	5	axioms	axiom	NOUN
ejpam-6020	31	6	,	,	PUNCT
ejpam-6020	31	7	as	as	ADV
ejpam-6020	31	8	well	well	ADV
ejpam-6020	31	9	as	as	ADP
ejpam-6020	31	10	interior	interior	ADJ
ejpam-6020	31	11	and	and	CCONJ
ejpam-6020	31	12	closure	closure	NOUN
ejpam-6020	31	13	operators	operator	NOUN
ejpam-6020	31	14	,	,	PUNCT
ejpam-6020	31	15	were	be	AUX
ejpam-6020	31	16	among	among	ADP
ejpam-6020	31	17	the	the	DET
ejpam-6020	31	18	fundamental	fundamental	ADJ
ejpam-6020	31	19	topological	topological	ADJ
ejpam-6020	31	20	notions	notion	NOUN
ejpam-6020	31	21	they	they	PRON
ejpam-6020	31	22	elaborated	elaborate	VERB
ejpam-6020	31	23	on	on	ADP
ejpam-6020	31	24	.	.	PUNCT
ejpam-6020	32	1	the	the	DET
ejpam-6020	32	2	concepts	concept	NOUN
ejpam-6020	32	3	of	of	ADP
ejpam-6020	32	4	supra	supra	PROPN
ejpam-6020	32	5	α	α	PROPN
ejpam-6020	32	6	[	[	X
ejpam-6020	32	7	14	14	NUM
ejpam-6020	32	8	]	]	PUNCT
ejpam-6020	32	9	(	(	PUNCT
ejpam-6020	32	10	pre[15	pre[15	PROPN
ejpam-6020	32	11	]	]	X
ejpam-6020	32	12	,	,	PUNCT
ejpam-6020	32	13	b[16	b[16	PROPN
ejpam-6020	32	14	]	]	PUNCT
ejpam-6020	32	15	,	,	PUNCT
ejpam-6020	32	16	β[17	β[17	PROPN
ejpam-6020	32	17	]	]	X
ejpam-6020	32	18	,	,	PUNCT
ejpam-6020	32	19	r[18	r[18	PROPN
ejpam-6020	32	20	]	]	PUNCT
ejpam-6020	32	21	,	,	PUNCT
ejpam-6020	32	22	and	and	CCONJ
ejpam-6020	32	23	semi[19	semi[19	PROPN
ejpam-6020	32	24	]	]	PUNCT
ejpam-6020	32	25	)	)	PUNCT
ejpam-6020	32	26	open	open	ADJ
ejpam-6020	32	27	sets	set	NOUN
ejpam-6020	32	28	have	have	AUX
ejpam-6020	32	29	been	be	AUX
ejpam-6020	32	30	introduced	introduce	VERB
ejpam-6020	32	31	,	,	PUNCT
ejpam-6020	32	32	along	along	ADP
ejpam-6020	32	33	with	with	ADP
ejpam-6020	32	34	their	their	PRON
ejpam-6020	32	35	main	main	ADJ
ejpam-6020	32	36	features	feature	NOUN
ejpam-6020	32	37	.	.	PUNCT
ejpam-6020	33	1	several	several	ADJ
ejpam-6020	33	2	types	type	NOUN
ejpam-6020	33	3	of	of	ADP
ejpam-6020	33	4	soft	soft	ADJ
ejpam-6020	33	5	open	open	ADJ
ejpam-6020	33	6	sets	set	NOUN
ejpam-6020	33	7	and	and	CCONJ
ejpam-6020	33	8	soft	soft	ADJ
ejpam-6020	33	9	continuity	continuity	NOUN
ejpam-6020	33	10	have	have	AUX
ejpam-6020	33	11	been	be	AUX
ejpam-6020	33	12	provided	provide	VERB
ejpam-6020	33	13	in	in	ADP
ejpam-6020	33	14	the	the	DET
ejpam-6020	33	15	field	field	NOUN
ejpam-6020	33	16	of	of	ADP
ejpam-6020	33	17	generalized	generalized	ADJ
ejpam-6020	33	18	soft	soft	ADJ
ejpam-6020	33	19	open	open	ADJ
ejpam-6020	33	20	sets	set	NOUN
ejpam-6020	33	21	[	[	X
ejpam-6020	33	22	20	20	NUM
ejpam-6020	33	23	,	,	PUNCT
ejpam-6020	33	24	21	21	NUM
ejpam-6020	33	25	]	]	PUNCT
ejpam-6020	33	26	,	,	PUNCT
ejpam-6020	33	27	generalized	generalize	VERB
ejpam-6020	33	28	soft	soft	ADJ
ejpam-6020	33	29	continuity	continuity	NOUN
ejpam-6020	33	30	[	[	X
ejpam-6020	33	31	22	22	NUM
ejpam-6020	33	32	]	]	PUNCT
ejpam-6020	33	33	,	,	PUNCT
ejpam-6020	33	34	soft	soft	ADJ
ejpam-6020	33	35	semi	semi	ADJ
ejpam-6020	33	36	-	-	ADJ
ejpam-6020	33	37	open	open	ADJ
ejpam-6020	33	38	sets	set	NOUN
ejpam-6020	33	39	[	[	X
ejpam-6020	33	40	23	23	NUM
ejpam-6020	33	41	,	,	PUNCT
ejpam-6020	33	42	24	24	NUM
ejpam-6020	33	43	]	]	PUNCT
ejpam-6020	33	44	,	,	PUNCT
ejpam-6020	33	45	several	several	ADJ
ejpam-6020	33	46	types	type	NOUN
ejpam-6020	33	47	of	of	ADP
ejpam-6020	33	48	soft	soft	ADJ
ejpam-6020	33	49	continuity	continuity	NOUN
ejpam-6020	33	50	[	[	X
ejpam-6020	33	51	25	25	NUM
ejpam-6020	33	52	]	]	PUNCT
ejpam-6020	33	53	,	,	PUNCT
ejpam-6020	33	54	soft	soft	ADJ
ejpam-6020	33	55	somewhere	somewhere	ADV
ejpam-6020	33	56	dense	dense	ADJ
ejpam-6020	33	57	sets	set	NOUN
ejpam-6020	33	58	[	[	X
ejpam-6020	33	59	26	26	NUM
ejpam-6020	33	60	]	]	PUNCT
ejpam-6020	33	61	,	,	PUNCT
ejpam-6020	33	62	and	and	CCONJ
ejpam-6020	33	63	nearly	nearly	ADV
ejpam-6020	33	64	soft	soft	ADJ
ejpam-6020	33	65	β	β	ADJ
ejpam-6020	33	66	-	-	ADJ
ejpam-6020	33	67	open	open	ADJ
ejpam-6020	33	68	sets	set	NOUN
ejpam-6020	33	69	[	[	X
ejpam-6020	33	70	27	27	NUM
ejpam-6020	33	71	]	]	PUNCT
ejpam-6020	33	72	.	.	PUNCT
ejpam-6020	34	1	more	more	ADJ
ejpam-6020	34	2	research	research	NOUN
ejpam-6020	34	3	on	on	ADP
ejpam-6020	34	4	soft	soft	ADJ
ejpam-6020	34	5	continuity	continuity	NOUN
ejpam-6020	34	6	was	be	AUX
ejpam-6020	34	7	later	later	ADV
ejpam-6020	34	8	conducted	conduct	VERB
ejpam-6020	34	9	[	[	X
ejpam-6020	34	10	28	28	NUM
ejpam-6020	34	11	,	,	PUNCT
ejpam-6020	34	12	29	29	NUM
ejpam-6020	34	13	]	]	PUNCT
ejpam-6020	34	14	.	.	PUNCT
ejpam-6020	35	1	in	in	ADP
ejpam-6020	35	2	[	[	X
ejpam-6020	35	3	30	30	NUM
ejpam-6020	35	4	]	]	PUNCT
ejpam-6020	35	5	,	,	PUNCT
ejpam-6020	35	6	the	the	DET
ejpam-6020	35	7	notion	notion	NOUN
ejpam-6020	35	8	of	of	ADP
ejpam-6020	35	9	the	the	DET
ejpam-6020	35	10	soft	soft	ADJ
ejpam-6020	35	11	ideal	ideal	NOUN
ejpam-6020	35	12	was	be	AUX
ejpam-6020	35	13	first	first	ADV
ejpam-6020	35	14	introduced	introduce	VERB
ejpam-6020	35	15	.	.	PUNCT
ejpam-6020	36	1	later	later	ADV
ejpam-6020	36	2	,	,	PUNCT
ejpam-6020	36	3	fatouh	fatouh	PROPN
ejpam-6020	36	4	and	and	CCONJ
ejpam-6020	36	5	abd	abd	PROPN
ejpam-6020	36	6	el	el	PROPN
ejpam-6020	36	7	-	-	PROPN
ejpam-6020	36	8	latif	latif	PROPN
ejpam-6020	37	1	[	[	X
ejpam-6020	37	2	31	31	NUM
ejpam-6020	37	3	]	]	PUNCT
ejpam-6020	37	4	generalized	generalize	VERB
ejpam-6020	37	5	this	this	DET
ejpam-6020	37	6	notion	notion	NOUN
ejpam-6020	37	7	using	use	VERB
ejpam-6020	37	8	soft	soft	ADJ
ejpam-6020	37	9	semi	semi	ADJ
ejpam-6020	37	10	-	-	ADJ
ejpam-6020	37	11	open	open	ADJ
ejpam-6020	37	12	sets	set	NOUN
ejpam-6020	37	13	.	.	PUNCT
ejpam-6020	38	1	after	after	ADP
ejpam-6020	38	2	that	that	PRON
ejpam-6020	38	3	,	,	PUNCT
ejpam-6020	38	4	this	this	DET
ejpam-6020	38	5	concept	concept	NOUN
ejpam-6020	38	6	is	be	AUX
ejpam-6020	38	7	used	use	VERB
ejpam-6020	38	8	to	to	PART
ejpam-6020	38	9	generalize	generalize	VERB
ejpam-6020	38	10	several	several	ADJ
ejpam-6020	38	11	types	type	NOUN
ejpam-6020	38	12	of	of	ADP
ejpam-6020	38	13	topological	topological	ADJ
ejpam-6020	38	14	properties	property	NOUN
ejpam-6020	38	15	,	,	PUNCT
ejpam-6020	38	16	involving	involve	VERB
ejpam-6020	38	17	soft	soft	ADJ
ejpam-6020	38	18	compactness	compactness	NOUN
ejpam-6020	39	1	[	[	X
ejpam-6020	39	2	32	32	NUM
ejpam-6020	39	3	]	]	PUNCT
ejpam-6020	39	4	,	,	PUNCT
ejpam-6020	39	5	soft	soft	ADJ
ejpam-6020	39	6	connectedness	connectedness	NOUN
ejpam-6020	39	7	[	[	X
ejpam-6020	39	8	33	33	NUM
ejpam-6020	39	9	]	]	PUNCT
ejpam-6020	39	10	,	,	PUNCT
ejpam-6020	39	11	soft	soft	ADJ
ejpam-6020	39	12	generalized	generalized	ADJ
ejpam-6020	39	13	open	open	ADJ
ejpam-6020	39	14	sets	set	NOUN
ejpam-6020	39	15	[	[	X
ejpam-6020	39	16	34–36	34–36	NUM
ejpam-6020	39	17	]	]	X
ejpam-6020	39	18	,	,	PUNCT
ejpam-6020	39	19	soft	soft	ADJ
ejpam-6020	39	20	separation	separation	NOUN
ejpam-6020	39	21	axioms	axiom	NOUN
ejpam-6020	39	22	[	[	X
ejpam-6020	39	23	37	37	NUM
ejpam-6020	39	24	]	]	PUNCT
ejpam-6020	39	25	,	,	PUNCT
ejpam-6020	39	26	and	and	CCONJ
ejpam-6020	39	27	generalized	generalize	VERB
ejpam-6020	39	28	soft	soft	ADJ
ejpam-6020	39	29	rough	rough	ADJ
ejpam-6020	39	30	sets	set	NOUN
ejpam-6020	39	31	[	[	X
ejpam-6020	39	32	38	38	NUM
ejpam-6020	39	33	,	,	PUNCT
ejpam-6020	39	34	39	39	NUM
ejpam-6020	39	35	]	]	PUNCT
ejpam-6020	39	36	.	.	PUNCT
ejpam-6020	40	1	recently	recently	ADV
ejpam-6020	40	2	,	,	PUNCT
ejpam-6020	40	3	some	some	DET
ejpam-6020	40	4	lower	low	ADJ
ejpam-6020	40	5	soft	soft	ADJ
ejpam-6020	40	6	separation	separation	NOUN
ejpam-6020	40	7	axioms	axiom	NOUN
ejpam-6020	40	8	[	[	X
ejpam-6020	40	9	40	40	NUM
ejpam-6020	40	10	]	]	PUNCT
ejpam-6020	40	11	and	and	CCONJ
ejpam-6020	40	12	some	some	DET
ejpam-6020	40	13	applications	application	NOUN
ejpam-6020	40	14	of	of	ADP
ejpam-6020	40	15	soft	soft	ADJ
ejpam-6020	40	16	δ	δ	NOUN
ejpam-6020	40	17	-	-	PUNCT
ejpam-6020	40	18	closed	close	VERB
ejpam-6020	40	19	sets	set	NOUN
ejpam-6020	40	20	[	[	X
ejpam-6020	40	21	41	41	NUM
ejpam-6020	40	22	]	]	PUNCT
ejpam-6020	40	23	were	be	AUX
ejpam-6020	40	24	presented	present	VERB
ejpam-6020	40	25	.	.	PUNCT
ejpam-6020	41	1	the	the	DET
ejpam-6020	41	2	notion	notion	NOUN
ejpam-6020	41	3	of	of	ADP
ejpam-6020	41	4	supra	supra	PROPN
ejpam-6020	41	5	soft	soft	ADJ
ejpam-6020	41	6	topological	topological	ADJ
ejpam-6020	41	7	spaces	space	NOUN
ejpam-6020	41	8	(	(	PUNCT
ejpam-6020	41	9	ssts	sst	NOUN
ejpam-6020	41	10	)	)	PUNCT
ejpam-6020	41	11	was	be	AUX
ejpam-6020	41	12	put	put	VERB
ejpam-6020	41	13	forth	forth	ADV
ejpam-6020	41	14	by	by	ADP
ejpam-6020	41	15	el	el	PROPN
ejpam-6020	41	16	-	-	PUNCT
ejpam-6020	41	17	sheikh	sheikh	PROPN
ejpam-6020	41	18	et	et	PROPN
ejpam-6020	41	19	al	al	PROPN
ejpam-6020	41	20	.	.	PUNCT
ejpam-6020	42	1	[	[	X
ejpam-6020	42	2	42	42	NUM
ejpam-6020	42	3	]	]	PUNCT
ejpam-6020	42	4	.	.	PUNCT
ejpam-6020	43	1	additionally	additionally	ADV
ejpam-6020	43	2	,	,	PUNCT
ejpam-6020	43	3	the	the	DET
ejpam-6020	43	4	concepts	concept	NOUN
ejpam-6020	43	5	of	of	ADP
ejpam-6020	43	6	supra	supra	PROPN
ejpam-6020	43	7	soft	soft	ADJ
ejpam-6020	43	8	pre(respectively	pre(respectively	ADV
ejpam-6020	43	9	,	,	PUNCT
ejpam-6020	43	10	α-	α-	X
ejpam-6020	43	11	,	,	PUNCT
ejpam-6020	43	12	semi	semi	ADV
ejpam-6020	43	13	,	,	PUNCT
ejpam-6020	43	14	β	β	X
ejpam-6020	43	15	,	,	PUNCT
ejpam-6020	43	16	and	and	CCONJ
ejpam-6020	43	17	γ-	γ-	X
ejpam-6020	43	18	)	)	PUNCT
ejpam-6020	43	19	open	open	ADJ
ejpam-6020	43	20	sets	set	NOUN
ejpam-6020	43	21	were	be	AUX
ejpam-6020	43	22	presented	present	VERB
ejpam-6020	43	23	.	.	PUNCT
ejpam-6020	44	1	the	the	DET
ejpam-6020	44	2	approach	approach	NOUN
ejpam-6020	44	3	of	of	ADP
ejpam-6020	44	4	supra	supra	PROPN
ejpam-6020	44	5	ϵ-open	ϵ-open	PROPN
ejpam-6020	44	6	sets	set	NOUN
ejpam-6020	44	7	in	in	ADP
ejpam-6020	44	8	supra	supra	PROPN
ejpam-6020	44	9	topological	topological	ADJ
ejpam-6020	44	10	spaces	space	NOUN
ejpam-6020	44	11	(	(	PUNCT
ejpam-6020	44	12	stss	stss	NOUN
ejpam-6020	44	13	)	)	PUNCT
ejpam-6020	44	14	was	be	AUX
ejpam-6020	44	15	introduced	introduce	VERB
ejpam-6020	44	16	by	by	ADP
ejpam-6020	44	17	abd	abd	PROPN
ejpam-6020	44	18	el	el	PROPN
ejpam-6020	44	19	-	-	PROPN
ejpam-6020	44	20	latif	latif	PROPN
ejpam-6020	44	21	et	et	PROPN
ejpam-6020	44	22	al.[43	al.[43	PROPN
ejpam-6020	44	23	]	]	PUNCT
ejpam-6020	44	24	.	.	PUNCT
ejpam-6020	45	1	they	they	PRON
ejpam-6020	45	2	also	also	ADV
ejpam-6020	45	3	discussed	discuss	VERB
ejpam-6020	45	4	the	the	DET
ejpam-6020	45	5	relationships	relationship	NOUN
ejpam-6020	45	6	between	between	ADP
ejpam-6020	45	7	their	their	PRON
ejpam-6020	45	8	novel	novel	ADJ
ejpam-6020	45	9	approach	approach	NOUN
ejpam-6020	45	10	and	and	CCONJ
ejpam-6020	45	11	previous	previous	ADJ
ejpam-6020	45	12	relevant	relevant	ADJ
ejpam-6020	45	13	research	research	NOUN
ejpam-6020	45	14	.	.	PUNCT
ejpam-6020	46	1	additionally	additionally	ADV
ejpam-6020	46	2	,	,	PUNCT
ejpam-6020	46	3	they	they	PRON
ejpam-6020	46	4	supplied	supply	VERB
ejpam-6020	46	5	this	this	DET
ejpam-6020	46	6	new	new	ADJ
ejpam-6020	46	7	category	category	NOUN
ejpam-6020	46	8	’s	’s	PART
ejpam-6020	46	9	primary	primary	ADJ
ejpam-6020	46	10	characteristics	characteristic	NOUN
ejpam-6020	46	11	.	.	PUNCT
ejpam-6020	47	1	furthermore	furthermore	ADV
ejpam-6020	47	2	,	,	PUNCT
ejpam-6020	47	3	in	in	ADP
ejpam-6020	47	4	general	general	ADJ
ejpam-6020	47	5	,	,	PUNCT
ejpam-6020	47	6	the	the	DET
ejpam-6020	47	7	intersection	intersection	NOUN
ejpam-6020	47	8	of	of	ADP
ejpam-6020	47	9	finite	finite	ADJ
ejpam-6020	47	10	numbers	number	NOUN
ejpam-6020	47	11	of	of	ADP
ejpam-6020	47	12	supra	supra	PROPN
ejpam-6020	47	13	ϵ-open	ϵ-open	PROPN
ejpam-6020	47	14	sets	set	NOUN
ejpam-6020	47	15	is	be	AUX
ejpam-6020	47	16	not	not	PART
ejpam-6020	47	17	such	such	ADJ
ejpam-6020	47	18	.	.	PUNCT
ejpam-6020	48	1	they	they	PRON
ejpam-6020	48	2	then	then	ADV
ejpam-6020	48	3	used	use	VERB
ejpam-6020	48	4	their	their	PRON
ejpam-6020	48	5	previously	previously	ADV
ejpam-6020	48	6	defined	define	VERB
ejpam-6020	48	7	category	category	NOUN
ejpam-6020	48	8	of	of	ADP
ejpam-6020	48	9	supra	supra	PROPN
ejpam-6020	48	10	open	open	ADJ
ejpam-6020	48	11	sets	set	NOUN
ejpam-6020	48	12	to	to	PART
ejpam-6020	48	13	study	study	VERB
ejpam-6020	48	14	new	new	ADJ
ejpam-6020	48	15	kinds	kind	NOUN
ejpam-6020	48	16	of	of	ADP
ejpam-6020	48	17	operators	operator	NOUN
ejpam-6020	48	18	called	call	VERB
ejpam-6020	48	19	supra	supra	PROPN
ejpam-6020	48	20	ϵ-interior	ϵ-interior	PROPN
ejpam-6020	48	21	(	(	PUNCT
ejpam-6020	48	22	closure	closure	NOUN
ejpam-6020	48	23	,	,	PUNCT
ejpam-6020	48	24	accumulation	accumulation	NOUN
ejpam-6020	48	25	,	,	PUNCT
ejpam-6020	48	26	exterior	exterior	ADJ
ejpam-6020	48	27	,	,	PUNCT
ejpam-6020	48	28	and	and	CCONJ
ejpam-6020	48	29	boundary	boundary	ADJ
ejpam-6020	48	30	,	,	PUNCT
ejpam-6020	48	31	respectively	respectively	ADV
ejpam-6020	48	32	)	)	PUNCT
ejpam-6020	48	33	.	.	PUNCT
ejpam-6020	49	1	several	several	ADJ
ejpam-6020	49	2	generalized	generalize	VERB
ejpam-6020	49	3	supra	supra	PROPN
ejpam-6020	49	4	soft	soft	ADJ
ejpam-6020	49	5	operators	operator	NOUN
ejpam-6020	49	6	have	have	AUX
ejpam-6020	49	7	been	be	AUX
ejpam-6020	49	8	studied	study	VERB
ejpam-6020	49	9	in	in	ADP
ejpam-6020	49	10	later	late	ADJ
ejpam-6020	49	11	studies	study	NOUN
ejpam-6020	49	12	using	use	VERB
ejpam-6020	49	13	supra	supra	PROPN
ejpam-6020	49	14	soft	soft	ADJ
ejpam-6020	49	15	-	-	PUNCT
ejpam-6020	49	16	b	b	NOUN
ejpam-6020	49	17	-	-	PUNCT
ejpam-6020	49	18	open	open	ADJ
ejpam-6020	49	19	sets	set	NOUN
ejpam-6020	49	20	[	[	X
ejpam-6020	49	21	44	44	NUM
ejpam-6020	49	22	]	]	PUNCT
ejpam-6020	49	23	,	,	PUNCT
ejpam-6020	49	24	supra	supra	PROPN
ejpam-6020	49	25	generalized	generalize	VERB
ejpam-6020	49	26	closed	close	VERB
ejpam-6020	49	27	soft	soft	ADJ
ejpam-6020	49	28	sets	set	NOUN
ejpam-6020	49	29	inspired	inspire	VERB
ejpam-6020	49	30	by	by	ADP
ejpam-6020	49	31	soft	soft	ADJ
ejpam-6020	49	32	ideals	ideal	NOUN
ejpam-6020	49	33	[	[	X
ejpam-6020	49	34	45	45	NUM
ejpam-6020	49	35	]	]	PUNCT
ejpam-6020	49	36	,	,	PUNCT
ejpam-6020	49	37	supra	supra	PROPN
ejpam-6020	49	38	soft	soft	ADJ
ejpam-6020	49	39	sw	sw	PROPN
ejpam-6020	49	40	-	-	PUNCT
ejpam-6020	49	41	open	open	ADJ
ejpam-6020	49	42	sets	set	NOUN
ejpam-6020	49	43	[	[	X
ejpam-6020	49	44	46	46	NUM
ejpam-6020	49	45	]	]	PUNCT
ejpam-6020	49	46	,	,	PUNCT
ejpam-6020	49	47	supra	supra	PROPN
ejpam-6020	49	48	soft	soft	ADJ
ejpam-6020	49	49	δi	δi	NOUN
ejpam-6020	49	50	-	-	PUNCT
ejpam-6020	49	51	open	open	ADJ
ejpam-6020	49	52	sets	set	NOUN
ejpam-6020	49	53	[	[	X
ejpam-6020	49	54	47	47	NUM
ejpam-6020	49	55	,	,	PUNCT
ejpam-6020	49	56	48	48	NUM
ejpam-6020	49	57	]	]	PUNCT
ejpam-6020	49	58	,	,	PUNCT
ejpam-6020	49	59	supra	supra	PROPN
ejpam-6020	49	60	soft	soft	ADJ
ejpam-6020	49	61	somewhere	somewhere	ADV
ejpam-6020	49	62	dense	dense	ADJ
ejpam-6020	49	63	sets	set	NOUN
ejpam-6020	49	64	[	[	X
ejpam-6020	49	65	49	49	NUM
ejpam-6020	49	66	]	]	PUNCT
ejpam-6020	49	67	,	,	PUNCT
ejpam-6020	49	68	and	and	CCONJ
ejpam-6020	49	69	separation	separation	NOUN
ejpam-6020	49	70	axioms	axiom	NOUN
ejpam-6020	49	71	via	via	ADP
ejpam-6020	49	72	supra	supra	PROPN
ejpam-6020	49	73	soft	soft	ADJ
ejpam-6020	49	74	topological	topological	ADJ
ejpam-6020	49	75	spaces	space	NOUN
ejpam-6020	49	76	[	[	X
ejpam-6020	49	77	50	50	NUM
ejpam-6020	49	78	]	]	PUNCT
ejpam-6020	49	79	.	.	PUNCT
ejpam-6020	50	1	a.	a.	PROPN
ejpam-6020	50	2	m.	m.	PROPN
ejpam-6020	50	3	abd	abd	PROPN
ejpam-6020	50	4	el	el	PROPN
ejpam-6020	50	5	-	-	PROPN
ejpam-6020	50	6	latif	latif	PROPN
ejpam-6020	50	7	et	et	PROPN
ejpam-6020	50	8	al	al	PROPN
ejpam-6020	50	9	.	.	PUNCT
ejpam-6020	50	10	/	/	SYM
ejpam-6020	50	11	eur	eur	PROPN
ejpam-6020	50	12	.	.	PUNCT
ejpam-6020	51	1	j.	j.	PROPN
ejpam-6020	51	2	pure	pure	PROPN
ejpam-6020	51	3	appl	appl	PROPN
ejpam-6020	51	4	.	.	PROPN
ejpam-6020	51	5	math	math	PROPN
ejpam-6020	51	6	,	,	PUNCT
ejpam-6020	51	7	18	18	NUM
ejpam-6020	51	8	(	(	PUNCT
ejpam-6020	51	9	2	2	NUM
ejpam-6020	51	10	)	)	PUNCT
ejpam-6020	51	11	(	(	PUNCT
ejpam-6020	51	12	2025	2025	NUM
ejpam-6020	51	13	)	)	PUNCT
ejpam-6020	51	14	,	,	PUNCT
ejpam-6020	51	15	6020	6020	NUM
ejpam-6020	51	16	3	3	NUM
ejpam-6020	51	17	of	of	ADP
ejpam-6020	51	18	17	17	NUM
ejpam-6020	52	1	we	we	PRON
ejpam-6020	52	2	continue	continue	VERB
ejpam-6020	52	3	studying	study	VERB
ejpam-6020	52	4	the	the	DET
ejpam-6020	52	5	features	feature	NOUN
ejpam-6020	52	6	of	of	ADP
ejpam-6020	52	7	supra	supra	PROPN
ejpam-6020	52	8	topological	topological	ADJ
ejpam-6020	52	9	spaces	space	NOUN
ejpam-6020	52	10	in	in	ADP
ejpam-6020	52	11	this	this	DET
ejpam-6020	52	12	paper	paper	NOUN
ejpam-6020	52	13	.	.	PUNCT
ejpam-6020	53	1	in	in	ADP
ejpam-6020	53	2	particular	particular	ADJ
ejpam-6020	53	3	,	,	PUNCT
ejpam-6020	53	4	we	we	PRON
ejpam-6020	53	5	present	present	VERB
ejpam-6020	53	6	and	and	CCONJ
ejpam-6020	53	7	discuss	discuss	VERB
ejpam-6020	53	8	novel	novel	ADJ
ejpam-6020	53	9	types	type	NOUN
ejpam-6020	53	10	of	of	ADP
ejpam-6020	53	11	supra	supra	ADJ
ejpam-6020	53	12	continuity	continuity	NOUN
ejpam-6020	53	13	.	.	PUNCT
ejpam-6020	54	1	building	build	VERB
ejpam-6020	54	2	on	on	ADP
ejpam-6020	54	3	the	the	DET
ejpam-6020	54	4	earlier	early	ADJ
ejpam-6020	54	5	types	type	NOUN
ejpam-6020	54	6	of	of	ADP
ejpam-6020	54	7	weaker	weak	ADJ
ejpam-6020	54	8	forms	form	NOUN
ejpam-6020	54	9	of	of	ADP
ejpam-6020	54	10	such	such	ADJ
ejpam-6020	54	11	conceptions	conception	NOUN
ejpam-6020	54	12	,	,	PUNCT
ejpam-6020	54	13	we	we	PRON
ejpam-6020	54	14	established	establish	VERB
ejpam-6020	54	15	the	the	DET
ejpam-6020	54	16	notion	notion	NOUN
ejpam-6020	54	17	of	of	ADP
ejpam-6020	54	18	supra	supra	PROPN
ejpam-6020	54	19	ϵ-continuous	ϵ-continuous	PROPN
ejpam-6020	54	20	functions	function	NOUN
ejpam-6020	54	21	.	.	PUNCT
ejpam-6020	55	1	figure	figure	VERB
ejpam-6020	55	2	1	1	NUM
ejpam-6020	55	3	’s	’s	PART
ejpam-6020	55	4	diagram	diagram	NOUN
ejpam-6020	55	5	was	be	AUX
ejpam-6020	55	6	used	use	VERB
ejpam-6020	55	7	to	to	PART
ejpam-6020	55	8	analyze	analyze	VERB
ejpam-6020	55	9	the	the	DET
ejpam-6020	55	10	connections	connection	NOUN
ejpam-6020	55	11	between	between	ADP
ejpam-6020	55	12	our	our	PRON
ejpam-6020	55	13	new	new	ADJ
ejpam-6020	55	14	class	class	NOUN
ejpam-6020	55	15	and	and	CCONJ
ejpam-6020	55	16	earlier	early	ADJ
ejpam-6020	55	17	supra	supra	ADJ
ejpam-6020	55	18	continuity	continuity	NOUN
ejpam-6020	55	19	concepts	concept	NOUN
ejpam-6020	55	20	.	.	PUNCT
ejpam-6020	56	1	figure	figure	VERB
ejpam-6020	56	2	1	1	NUM
ejpam-6020	56	3	:	:	PUNCT
ejpam-6020	56	4	the	the	DET
ejpam-6020	56	5	connections	connection	NOUN
ejpam-6020	56	6	between	between	ADP
ejpam-6020	56	7	supra-ϵ-cts	supra-ϵ-ct	NOUN
ejpam-6020	56	8	functions	function	NOUN
ejpam-6020	56	9	and	and	CCONJ
ejpam-6020	56	10	other	other	ADJ
ejpam-6020	56	11	preceding	precede	VERB
ejpam-6020	56	12	studies	study	NOUN
ejpam-6020	56	13	we	we	PRON
ejpam-6020	56	14	also	also	ADV
ejpam-6020	56	15	introduced	introduce	VERB
ejpam-6020	56	16	the	the	DET
ejpam-6020	56	17	concepts	concept	NOUN
ejpam-6020	56	18	of	of	ADP
ejpam-6020	56	19	supra	supra	ADJ
ejpam-6020	56	20	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	56	21	functions	function	NOUN
ejpam-6020	56	22	and	and	CCONJ
ejpam-6020	56	23	supra	supra	ADJ
ejpam-6020	56	24	ϵ∗-cts	ϵ∗-ct	NOUN
ejpam-6020	56	25	functions	function	NOUN
ejpam-6020	56	26	and	and	CCONJ
ejpam-6020	56	27	provide	provide	VERB
ejpam-6020	56	28	their	their	PRON
ejpam-6020	56	29	essential	essential	ADJ
ejpam-6020	56	30	features	feature	NOUN
ejpam-6020	56	31	in	in	ADP
ejpam-6020	56	32	detail	detail	NOUN
ejpam-6020	56	33	.	.	PUNCT
ejpam-6020	57	1	furthermore	furthermore	ADV
ejpam-6020	57	2	,	,	PUNCT
ejpam-6020	57	3	we	we	PRON
ejpam-6020	57	4	present	present	VERB
ejpam-6020	57	5	novel	novel	ADJ
ejpam-6020	57	6	approaches	approach	NOUN
ejpam-6020	57	7	for	for	ADP
ejpam-6020	57	8	supra	supra	ADJ
ejpam-6020	57	9	functions	function	NOUN
ejpam-6020	57	10	,	,	PUNCT
ejpam-6020	57	11	which	which	PRON
ejpam-6020	57	12	we	we	PRON
ejpam-6020	57	13	call	call	VERB
ejpam-6020	57	14	supra	supra	PROPN
ejpam-6020	57	15	ϵ-open	ϵ-open	PROPN
ejpam-6020	57	16	functions	function	NOUN
ejpam-6020	57	17	,	,	PUNCT
ejpam-6020	57	18	supra	supra	ADJ
ejpam-6020	57	19	ϵ-closed	ϵ-close	VERB
ejpam-6020	57	20	functions	function	NOUN
ejpam-6020	57	21	,	,	PUNCT
ejpam-6020	57	22	and	and	CCONJ
ejpam-6020	57	23	supra	supra	PROPN
ejpam-6020	57	24	ϵ-homeomorphism	ϵ-homeomorphism	NOUN
ejpam-6020	57	25	functions	function	NOUN
ejpam-6020	57	26	.	.	PUNCT
ejpam-6020	58	1	finally	finally	ADV
ejpam-6020	58	2	,	,	PUNCT
ejpam-6020	58	3	several	several	ADJ
ejpam-6020	58	4	essential	essential	ADJ
ejpam-6020	58	5	examples	example	NOUN
ejpam-6020	58	6	were	be	AUX
ejpam-6020	58	7	provided	provide	VERB
ejpam-6020	58	8	with	with	ADP
ejpam-6020	58	9	a	a	DET
ejpam-6020	58	10	detailed	detailed	ADJ
ejpam-6020	58	11	discussion	discussion	NOUN
ejpam-6020	58	12	of	of	ADP
ejpam-6020	58	13	their	their	PRON
ejpam-6020	58	14	key	key	ADJ
ejpam-6020	58	15	characteristics	characteristic	NOUN
ejpam-6020	58	16	.	.	PUNCT
ejpam-6020	59	1	2	2	X
ejpam-6020	59	2	.	.	NUM
ejpam-6020	59	3	preliminaries	preliminary	NOUN
ejpam-6020	59	4	and	and	CCONJ
ejpam-6020	59	5	background	background	NOUN
ejpam-6020	59	6	let	let	VERB
ejpam-6020	59	7	(	(	PUNCT
ejpam-6020	59	8	λ	λ	NOUN
ejpam-6020	59	9	,	,	PUNCT
ejpam-6020	59	10	ϑ	ϑ	NOUN
ejpam-6020	59	11	)	)	PUNCT
ejpam-6020	59	12	be	be	AUX
ejpam-6020	59	13	an	an	DET
ejpam-6020	59	14	sts	st	NOUN
ejpam-6020	59	15	,	,	PUNCT
ejpam-6020	59	16	the	the	DET
ejpam-6020	59	17	classes	class	NOUN
ejpam-6020	59	18	of	of	ADP
ejpam-6020	59	19	supra	supra	PROPN
ejpam-6020	59	20	(	(	PUNCT
ejpam-6020	59	21	respectively	respectively	ADV
ejpam-6020	59	22	,	,	PUNCT
ejpam-6020	59	23	regular-	regular-	ADJ
ejpam-6020	59	24	,	,	PUNCT
ejpam-6020	59	25	pre-	pre-	X
ejpam-6020	59	26	,	,	PUNCT
ejpam-6020	59	27	semi	semi	ADV
ejpam-6020	59	28	,	,	PUNCT
ejpam-6020	59	29	β-	β-	PRON
ejpam-6020	59	30	,	,	PUNCT
ejpam-6020	59	31	α-	α-	X
ejpam-6020	59	32	,	,	PUNCT
ejpam-6020	59	33	b-	b-	X
ejpam-6020	59	34	,	,	PUNCT
ejpam-6020	59	35	and	and	CCONJ
ejpam-6020	59	36	r-	r-	X
ejpam-6020	59	37	)	)	PUNCT
ejpam-6020	59	38	open	open	ADJ
ejpam-6020	59	39	sets	set	NOUN
ejpam-6020	59	40	will	will	AUX
ejpam-6020	59	41	represented	represent	VERB
ejpam-6020	59	42	by	by	ADP
ejpam-6020	59	43	so(λ	so(λ	PROPN
ejpam-6020	59	44	)	)	PUNCT
ejpam-6020	59	45	(	(	PUNCT
ejpam-6020	59	46	respectively	respectively	ADV
ejpam-6020	59	47	,	,	PUNCT
ejpam-6020	59	48	soregular(λ	soregular(λ	PROPN
ejpam-6020	59	49	)	)	PUNCT
ejpam-6020	59	50	,	,	PUNCT
ejpam-6020	59	51	spo(λ	spo(λ	PROPN
ejpam-6020	59	52	)	)	PUNCT
ejpam-6020	59	53	,	,	PUNCT
ejpam-6020	59	54	sso(λ	sso(λ	PROPN
ejpam-6020	59	55	)	)	PUNCT
ejpam-6020	59	56	,	,	PUNCT
ejpam-6020	59	57	sβo(λ	sβo(λ	PROPN
ejpam-6020	59	58	)	)	PUNCT
ejpam-6020	59	59	,	,	PUNCT
ejpam-6020	59	60	sαo(λ	sαo(λ	PROPN
ejpam-6020	59	61	)	)	PUNCT
ejpam-6020	59	62	,	,	PUNCT
ejpam-6020	59	63	sbo(λ	sbo(λ	PROPN
ejpam-6020	59	64	)	)	PUNCT
ejpam-6020	59	65	,	,	PUNCT
ejpam-6020	59	66	and	and	CCONJ
ejpam-6020	59	67	sro(λ	sro(λ	PROPN
ejpam-6020	59	68	)	)	PUNCT
ejpam-6020	59	69	)	)	PUNCT
ejpam-6020	59	70	.	.	PUNCT
ejpam-6020	60	1	also	also	ADV
ejpam-6020	60	2	,	,	PUNCT
ejpam-6020	60	3	the	the	DET
ejpam-6020	60	4	classes	class	NOUN
ejpam-6020	60	5	of	of	ADP
ejpam-6020	60	6	supra	supra	PROPN
ejpam-6020	60	7	(	(	PUNCT
ejpam-6020	60	8	respectively	respectively	ADV
ejpam-6020	60	9	,	,	PUNCT
ejpam-6020	60	10	regular	regular	ADJ
ejpam-6020	60	11	,	,	PUNCT
ejpam-6020	60	12	semi	semi	ADJ
ejpam-6020	60	13	,	,	PUNCT
ejpam-6020	60	14	pre-	pre-	X
ejpam-6020	60	15	,	,	PUNCT
ejpam-6020	60	16	β-	β-	X
ejpam-6020	60	17	,	,	PUNCT
ejpam-6020	60	18	b-	b-	X
ejpam-6020	60	19	,	,	PUNCT
ejpam-6020	60	20	α-	α-	X
ejpam-6020	60	21	,	,	PUNCT
ejpam-6020	60	22	and	and	CCONJ
ejpam-6020	60	23	r-	r-	NUM
ejpam-6020	60	24	)	)	PUNCT
ejpam-6020	60	25	continuous	continuous	ADJ
ejpam-6020	60	26	functions	function	NOUN
ejpam-6020	60	27	will	will	AUX
ejpam-6020	60	28	represented	represent	VERB
ejpam-6020	60	29	by	by	ADP
ejpam-6020	60	30	supra	supra	PROPN
ejpam-6020	60	31	(	(	PUNCT
ejpam-6020	60	32	respectively	respectively	ADV
ejpam-6020	60	33	,	,	PUNCT
ejpam-6020	60	34	regular-	regular-	INTJ
ejpam-6020	60	35	,	,	PUNCT
ejpam-6020	60	36	semi	semi	ADV
ejpam-6020	60	37	,	,	PUNCT
ejpam-6020	60	38	pre-	pre-	X
ejpam-6020	60	39	,	,	PUNCT
ejpam-6020	60	40	β-	β-	X
ejpam-6020	60	41	,	,	PUNCT
ejpam-6020	60	42	b-	b-	X
ejpam-6020	60	43	,	,	PUNCT
ejpam-6020	60	44	α-	α-	X
ejpam-6020	60	45	,	,	PUNCT
ejpam-6020	60	46	and	and	CCONJ
ejpam-6020	60	47	r-	r-	X
ejpam-6020	60	48	)	)	PUNCT
ejpam-6020	60	49	cts	cts	PROPN
ejpam-6020	60	50	,	,	PUNCT
ejpam-6020	60	51	through	through	ADP
ejpam-6020	60	52	this	this	DET
ejpam-6020	60	53	paper	paper	NOUN
ejpam-6020	60	54	.	.	PUNCT
ejpam-6020	61	1	definition	definition	NOUN
ejpam-6020	61	2	1	1	NUM
ejpam-6020	61	3	.	.	PUNCT
ejpam-6020	62	1	[	[	X
ejpam-6020	62	2	13	13	NUM
ejpam-6020	62	3	]	]	PUNCT
ejpam-6020	62	4	the	the	DET
ejpam-6020	62	5	collection	collection	NOUN
ejpam-6020	62	6	ϑ	ϑ	PROPN
ejpam-6020	62	7	⊆	⊆	NUM
ejpam-6020	62	8	p	p	PROPN
ejpam-6020	62	9	(	(	PUNCT
ejpam-6020	62	10	λ	λ	NOUN
ejpam-6020	62	11	)	)	PUNCT
ejpam-6020	62	12	is	be	AUX
ejpam-6020	62	13	called	call	VERB
ejpam-6020	62	14	supra	supra	ADJ
ejpam-6020	62	15	topology	topology	NOUN
ejpam-6020	62	16	(	(	PUNCT
ejpam-6020	62	17	or	or	CCONJ
ejpam-6020	62	18	sts	st	NOUN
ejpam-6020	62	19	)	)	PUNCT
ejpam-6020	62	20	on	on	ADP
ejpam-6020	62	21	λ	λ	PROPN
ejpam-6020	62	22	if	if	SCONJ
ejpam-6020	62	23	ϑ	ϑ	PROPN
ejpam-6020	62	24	contains	contain	VERB
ejpam-6020	62	25	λ	λ	NOUN
ejpam-6020	62	26	and	and	CCONJ
ejpam-6020	62	27	∅	∅	NOUN
ejpam-6020	62	28	and	and	CCONJ
ejpam-6020	62	29	closed	close	VERB
ejpam-6020	62	30	under	under	ADP
ejpam-6020	62	31	arbitrary	arbitrary	ADJ
ejpam-6020	62	32	union	union	NOUN
ejpam-6020	62	33	.	.	PUNCT
ejpam-6020	63	1	also	also	ADV
ejpam-6020	63	2	,	,	PUNCT
ejpam-6020	63	3	if	if	SCONJ
ejpam-6020	63	4	g	g	PROPN
ejpam-6020	63	5	∈	∈	PROPN
ejpam-6020	63	6	ϑ	ϑ	NOUN
ejpam-6020	63	7	,	,	PUNCT
ejpam-6020	63	8	then	then	ADV
ejpam-6020	63	9	g	g	PROPN
ejpam-6020	63	10	is	be	AUX
ejpam-6020	63	11	called	call	VERB
ejpam-6020	63	12	supra	supra	PROPN
ejpam-6020	63	13	open	open	ADJ
ejpam-6020	63	14	set	set	NOUN
ejpam-6020	63	15	and	and	CCONJ
ejpam-6020	63	16	gc	gc	PROPN
ejpam-6020	63	17	is	be	AUX
ejpam-6020	63	18	called	call	VERB
ejpam-6020	63	19	supra	supra	PROPN
ejpam-6020	63	20	closed	close	VERB
ejpam-6020	63	21	set	set	NOUN
ejpam-6020	63	22	.	.	PUNCT
ejpam-6020	64	1	moreover	moreover	ADV
ejpam-6020	64	2	,	,	PUNCT
ejpam-6020	64	3	if	if	SCONJ
ejpam-6020	64	4	ν	ν	PROPN
ejpam-6020	64	5	⊂	⊂	X
ejpam-6020	64	6	ϑ	ϑ	PROPN
ejpam-6020	64	7	for	for	ADP
ejpam-6020	64	8	a	a	DET
ejpam-6020	64	9	given	give	VERB
ejpam-6020	64	10	topology	topology	NOUN
ejpam-6020	64	11	ν	ν	NOUN
ejpam-6020	64	12	,	,	PUNCT
ejpam-6020	64	13	then	then	ADV
ejpam-6020	64	14	ϑ	ϑ	X
ejpam-6020	64	15	is	be	AUX
ejpam-6020	64	16	called	call	VERB
ejpam-6020	64	17	an	an	DET
ejpam-6020	64	18	associated	associate	VERB
ejpam-6020	64	19	sts	st	NOUN
ejpam-6020	64	20	with	with	ADP
ejpam-6020	64	21	ν	ν	PROPN
ejpam-6020	64	22	.	.	PUNCT
ejpam-6020	64	23	definition	definition	NOUN
ejpam-6020	64	24	2	2	NUM
ejpam-6020	64	25	.	.	PUNCT
ejpam-6020	65	1	[	[	X
ejpam-6020	65	2	13	13	NUM
ejpam-6020	65	3	]	]	PUNCT
ejpam-6020	65	4	regarding	regard	VERB
ejpam-6020	65	5	a	a	DET
ejpam-6020	65	6	subset	subset	NOUN
ejpam-6020	65	7	k	k	NOUN
ejpam-6020	65	8	of	of	ADP
ejpam-6020	65	9	an	an	DET
ejpam-6020	65	10	sts	st	NOUN
ejpam-6020	65	11	(	(	PUNCT
ejpam-6020	65	12	λ	λ	X
ejpam-6020	65	13	,	,	PUNCT
ejpam-6020	65	14	ϑ	ϑ	NOUN
ejpam-6020	65	15	)	)	PUNCT
ejpam-6020	65	16	,	,	PUNCT
ejpam-6020	65	17	the	the	DET
ejpam-6020	65	18	ints(k	ints(k	NOUN
ejpam-6020	65	19	)	)	PUNCT
ejpam-6020	65	20	or	or	CCONJ
ejpam-6020	65	21	k	k	X
ejpam-6020	65	22	◦	◦	NOUN
ejpam-6020	65	23	(	(	PUNCT
ejpam-6020	65	24	respectively	respectively	ADV
ejpam-6020	65	25	,	,	PUNCT
ejpam-6020	65	26	cls(k	cls(k	PROPN
ejpam-6020	65	27	)	)	PUNCT
ejpam-6020	65	28	or	or	CCONJ
ejpam-6020	65	29	k	k	NOUN
ejpam-6020	65	30	,	,	PUNCT
ejpam-6020	65	31	and	and	CCONJ
ejpam-6020	65	32	b(k	b(k	PROPN
ejpam-6020	65	33	)	)	PUNCT
ejpam-6020	65	34	)	)	PUNCT
ejpam-6020	65	35	will	will	AUX
ejpam-6020	65	36	refer	refer	VERB
ejpam-6020	65	37	to	to	ADP
ejpam-6020	65	38	the	the	DET
ejpam-6020	65	39	supra	supra	ADJ
ejpam-6020	65	40	interior	interior	PROPN
ejpam-6020	65	41	(	(	PUNCT
ejpam-6020	65	42	respectively	respectively	ADV
ejpam-6020	65	43	,	,	PUNCT
ejpam-6020	65	44	closure	closure	NOUN
ejpam-6020	65	45	,	,	PUNCT
ejpam-6020	65	46	and	and	CCONJ
ejpam-6020	65	47	boundary	boundary	NOUN
ejpam-6020	65	48	)	)	PUNCT
ejpam-6020	65	49	of	of	ADP
ejpam-6020	65	50	k	k	PROPN
ejpam-6020	65	51	,	,	PUNCT
ejpam-6020	65	52	where	where	SCONJ
ejpam-6020	65	53	ints(k	ints(k	NOUN
ejpam-6020	65	54	)	)	PUNCT
ejpam-6020	65	55	=	=	SYM
ejpam-6020	65	56	∪{g	∪{g	PROPN
ejpam-6020	65	57	:	:	PUNCT
ejpam-6020	65	58	g	g	PROPN
ejpam-6020	65	59	∈	∈	PROPN
ejpam-6020	65	60	ϑ	ϑ	X
ejpam-6020	65	61	and	and	CCONJ
ejpam-6020	65	62	g	g	PROPN
ejpam-6020	65	63	⊆	⊆	NUM
ejpam-6020	65	64	k	k	X
ejpam-6020	65	65	}	}	PUNCT
ejpam-6020	65	66	,	,	PUNCT
ejpam-6020	65	67	cls(k	cls(k	PROPN
ejpam-6020	65	68	)	)	PUNCT
ejpam-6020	66	1	=	=	VERB
ejpam-6020	66	2	∩{n	∩{n	INTJ
ejpam-6020	66	3	:	:	PUNCT
ejpam-6020	66	4	n	n	CCONJ
ejpam-6020	66	5	∈	∈	NOUN
ejpam-6020	66	6	ϑc	ϑc	NOUN
ejpam-6020	66	7	and	and	CCONJ
ejpam-6020	66	8	k	k	PROPN
ejpam-6020	66	9	⊆	⊆	NUM
ejpam-6020	66	10	n	n	CCONJ
ejpam-6020	66	11	}	}	PUNCT
ejpam-6020	66	12	,	,	PUNCT
ejpam-6020	66	13	and	and	CCONJ
ejpam-6020	66	14	b(k	b(k	PROPN
ejpam-6020	66	15	)	)	PUNCT
ejpam-6020	67	1	=	=	SYM
ejpam-6020	67	2	cls(k)\ints(k	cls(k)\ints(k	PROPN
ejpam-6020	67	3	)	)	PUNCT
ejpam-6020	67	4	.	.	PUNCT
ejpam-6020	68	1	theorem	theorem	NOUN
ejpam-6020	68	2	1	1	NUM
ejpam-6020	68	3	.	.	PUNCT
ejpam-6020	69	1	[	[	X
ejpam-6020	69	2	13	13	NUM
ejpam-6020	69	3	]	]	PUNCT
ejpam-6020	69	4	regarding	regard	VERB
ejpam-6020	69	5	a	a	DET
ejpam-6020	69	6	subset	subset	ADJ
ejpam-6020	69	7	t	t	NOUN
ejpam-6020	69	8	of	of	ADP
ejpam-6020	69	9	an	an	DET
ejpam-6020	69	10	sts	st	NOUN
ejpam-6020	69	11	(	(	PUNCT
ejpam-6020	69	12	λ	λ	X
ejpam-6020	69	13	,	,	PUNCT
ejpam-6020	69	14	ϑ	ϑ	NOUN
ejpam-6020	69	15	)	)	PUNCT
ejpam-6020	69	16	,	,	PUNCT
ejpam-6020	69	17	we	we	PRON
ejpam-6020	69	18	have	have	VERB
ejpam-6020	69	19	(	(	PUNCT
ejpam-6020	69	20	1	1	X
ejpam-6020	69	21	)	)	PUNCT
ejpam-6020	69	22	cls(t	cls(t	PROPN
ejpam-6020	69	23	c	c	NOUN
ejpam-6020	69	24	)	)	PUNCT
ejpam-6020	69	25	=	=	PUNCT
ejpam-6020	70	1	[	[	X
ejpam-6020	70	2	ints(t	ints(t	NOUN
ejpam-6020	70	3	)	)	PUNCT
ejpam-6020	70	4	]	]	PUNCT
ejpam-6020	71	1	c.	c.	PROPN
ejpam-6020	71	2	a.	a.	PROPN
ejpam-6020	71	3	m.	m.	PROPN
ejpam-6020	72	1	abd	abd	PROPN
ejpam-6020	73	1	el	el	PROPN
ejpam-6020	73	2	-	-	PROPN
ejpam-6020	73	3	latif	latif	PROPN
ejpam-6020	73	4	et	et	PROPN
ejpam-6020	73	5	al	al	PROPN
ejpam-6020	73	6	.	.	PUNCT
ejpam-6020	73	7	/	/	SYM
ejpam-6020	73	8	eur	eur	PROPN
ejpam-6020	73	9	.	.	PUNCT
ejpam-6020	74	1	j.	j.	PROPN
ejpam-6020	74	2	pure	pure	PROPN
ejpam-6020	74	3	appl	appl	PROPN
ejpam-6020	74	4	.	.	PROPN
ejpam-6020	74	5	math	math	PROPN
ejpam-6020	74	6	,	,	PUNCT
ejpam-6020	74	7	18	18	NUM
ejpam-6020	74	8	(	(	PUNCT
ejpam-6020	74	9	2	2	NUM
ejpam-6020	74	10	)	)	PUNCT
ejpam-6020	74	11	(	(	PUNCT
ejpam-6020	74	12	2025	2025	NUM
ejpam-6020	74	13	)	)	PUNCT
ejpam-6020	74	14	,	,	PUNCT
ejpam-6020	74	15	6020	6020	NUM
ejpam-6020	74	16	4	4	NUM
ejpam-6020	74	17	of	of	ADP
ejpam-6020	74	18	17	17	NUM
ejpam-6020	74	19	(	(	PUNCT
ejpam-6020	74	20	2	2	NUM
ejpam-6020	74	21	)	)	PUNCT
ejpam-6020	74	22	ints(t	ints(t	ADP
ejpam-6020	74	23	c	c	NOUN
ejpam-6020	74	24	)	)	PUNCT
ejpam-6020	74	25	=	=	PUNCT
ejpam-6020	75	1	[	[	X
ejpam-6020	75	2	cls(t	cls(t	INTJ
ejpam-6020	75	3	)	)	PUNCT
ejpam-6020	75	4	]	]	X
ejpam-6020	75	5	c.	c.	NOUN
ejpam-6020	75	6	definition	definition	NOUN
ejpam-6020	75	7	3	3	NUM
ejpam-6020	75	8	.	.	PUNCT
ejpam-6020	76	1	[	[	X
ejpam-6020	76	2	15–19	15–19	X
ejpam-6020	76	3	]	]	PUNCT
ejpam-6020	76	4	let	let	VERB
ejpam-6020	76	5	h	h	NOUN
ejpam-6020	76	6	be	be	AUX
ejpam-6020	76	7	a	a	DET
ejpam-6020	76	8	subset	subset	NOUN
ejpam-6020	76	9	of	of	ADP
ejpam-6020	76	10	an	an	DET
ejpam-6020	76	11	sts	st	NOUN
ejpam-6020	76	12	(	(	PUNCT
ejpam-6020	76	13	λ	λ	X
ejpam-6020	76	14	,	,	PUNCT
ejpam-6020	76	15	ϑ	ϑ	NOUN
ejpam-6020	76	16	)	)	PUNCT
ejpam-6020	76	17	.	.	PUNCT
ejpam-6020	77	1	then	then	ADV
ejpam-6020	77	2	,	,	PUNCT
ejpam-6020	77	3	(	(	PUNCT
ejpam-6020	77	4	1	1	X
ejpam-6020	77	5	)	)	PUNCT
ejpam-6020	77	6	if	if	SCONJ
ejpam-6020	77	7	h	h	NOUN
ejpam-6020	77	8	=	=	SYM
ejpam-6020	77	9	ints(cls(h	ints(cls(h	NOUN
ejpam-6020	77	10	)	)	PUNCT
ejpam-6020	77	11	)	)	PUNCT
ejpam-6020	77	12	,	,	PUNCT
ejpam-6020	77	13	then	then	ADV
ejpam-6020	77	14	h	h	PROPN
ejpam-6020	77	15	∈	∈	PROPN
ejpam-6020	77	16	soregular(λ	soregular(λ	PROPN
ejpam-6020	77	17	)	)	PUNCT
ejpam-6020	77	18	.	.	PUNCT
ejpam-6020	78	1	(	(	PUNCT
ejpam-6020	78	2	2	2	X
ejpam-6020	78	3	)	)	PUNCT
ejpam-6020	78	4	if	if	SCONJ
ejpam-6020	78	5	h	h	NOUN
ejpam-6020	78	6	⊆	⊆	NUM
ejpam-6020	78	7	ints(cls(h	ints(cls(h	NOUN
ejpam-6020	78	8	)	)	PUNCT
ejpam-6020	78	9	)	)	PUNCT
ejpam-6020	78	10	,	,	PUNCT
ejpam-6020	78	11	then	then	ADV
ejpam-6020	78	12	h	h	PROPN
ejpam-6020	78	13	∈	∈	PROPN
ejpam-6020	78	14	spo(λ	spo(λ	PROPN
ejpam-6020	78	15	)	)	PUNCT
ejpam-6020	78	16	.	.	PUNCT
ejpam-6020	79	1	(	(	PUNCT
ejpam-6020	79	2	3	3	X
ejpam-6020	79	3	)	)	PUNCT
ejpam-6020	79	4	if	if	SCONJ
ejpam-6020	79	5	h	h	NOUN
ejpam-6020	79	6	⊆	⊆	NUM
ejpam-6020	79	7	cls(ints(h	cls(ints(h	NOUN
ejpam-6020	79	8	)	)	PUNCT
ejpam-6020	79	9	)	)	PUNCT
ejpam-6020	79	10	,	,	PUNCT
ejpam-6020	79	11	then	then	ADV
ejpam-6020	79	12	h	h	PROPN
ejpam-6020	79	13	∈	∈	PROPN
ejpam-6020	79	14	sso(λ	sso(λ	PROPN
ejpam-6020	79	15	)	)	PUNCT
ejpam-6020	79	16	.	.	PUNCT
ejpam-6020	80	1	(	(	PUNCT
ejpam-6020	80	2	4	4	X
ejpam-6020	80	3	)	)	PUNCT
ejpam-6020	80	4	if	if	SCONJ
ejpam-6020	80	5	h	h	NOUN
ejpam-6020	80	6	⊆	⊆	NUM
ejpam-6020	80	7	ints(cls(ints(h	ints(cls(ints(h	PROPN
ejpam-6020	80	8	)	)	PUNCT
ejpam-6020	80	9	)	)	PUNCT
ejpam-6020	80	10	)	)	PUNCT
ejpam-6020	81	1	,	,	PUNCT
ejpam-6020	81	2	then	then	ADV
ejpam-6020	81	3	h	h	PROPN
ejpam-6020	81	4	∈	∈	PROPN
ejpam-6020	81	5	sαo(λ	sαo(λ	PROPN
ejpam-6020	81	6	)	)	PUNCT
ejpam-6020	81	7	.	.	PUNCT
ejpam-6020	82	1	(	(	PUNCT
ejpam-6020	82	2	5	5	X
ejpam-6020	82	3	)	)	PUNCT
ejpam-6020	82	4	if	if	SCONJ
ejpam-6020	82	5	h	h	NOUN
ejpam-6020	82	6	⊆	⊆	NUM
ejpam-6020	82	7	cls(ints(cls(h	cls(ints(cls(h	PROPN
ejpam-6020	82	8	)	)	PUNCT
ejpam-6020	82	9	)	)	PUNCT
ejpam-6020	82	10	)	)	PUNCT
ejpam-6020	82	11	,	,	PUNCT
ejpam-6020	82	12	then	then	ADV
ejpam-6020	82	13	h	h	PROPN
ejpam-6020	82	14	∈	∈	PROPN
ejpam-6020	82	15	sβo(λ	sβo(λ	PROPN
ejpam-6020	82	16	)	)	PUNCT
ejpam-6020	82	17	.	.	PUNCT
ejpam-6020	83	1	(	(	PUNCT
ejpam-6020	83	2	6	6	NUM
ejpam-6020	83	3	)	)	PUNCT
ejpam-6020	83	4	if	if	SCONJ
ejpam-6020	83	5	h	h	NOUN
ejpam-6020	83	6	⊆	⊆	NUM
ejpam-6020	83	7	cls(ints(h))∪̃ints(cls(h	cls(ints(h))∪̃ints(cls(h	NOUN
ejpam-6020	83	8	)	)	PUNCT
ejpam-6020	83	9	)	)	PUNCT
ejpam-6020	83	10	,	,	PUNCT
ejpam-6020	83	11	then	then	ADV
ejpam-6020	83	12	h	h	PROPN
ejpam-6020	83	13	∈	∈	PROPN
ejpam-6020	83	14	sbo(λ	sbo(λ	PROPN
ejpam-6020	83	15	)	)	PUNCT
ejpam-6020	83	16	.	.	PUNCT
ejpam-6020	84	1	(	(	PUNCT
ejpam-6020	84	2	7	7	X
ejpam-6020	84	3	)	)	PUNCT
ejpam-6020	84	4	if	if	SCONJ
ejpam-6020	84	5	ints(cls(h	ints(cls(h	NOUN
ejpam-6020	84	6	)	)	PUNCT
ejpam-6020	84	7	)	)	PUNCT
ejpam-6020	85	1	̸=	̸=	NOUN
ejpam-6020	85	2	∅	∅	NOUN
ejpam-6020	85	3	,	,	PUNCT
ejpam-6020	85	4	then	then	ADV
ejpam-6020	85	5	h	h	PROPN
ejpam-6020	85	6	∈	∈	PROPN
ejpam-6020	85	7	sro(λ	sro(λ	PROPN
ejpam-6020	85	8	)	)	PUNCT
ejpam-6020	85	9	.	.	PUNCT
ejpam-6020	86	1	(	(	PUNCT
ejpam-6020	86	2	8)	8)	NUM
ejpam-6020	86	3	if	if	SCONJ
ejpam-6020	86	4	ints(cls(h	ints(cls(h	NOUN
ejpam-6020	86	5	)	)	PUNCT
ejpam-6020	86	6	)	)	PUNCT
ejpam-6020	87	1	=	=	NOUN
ejpam-6020	87	2	∅	∅	NOUN
ejpam-6020	87	3	,	,	PUNCT
ejpam-6020	87	4	then	then	ADV
ejpam-6020	87	5	h	h	PROPN
ejpam-6020	87	6	∈	∈	PROPN
ejpam-6020	87	7	snd(λ	snd(λ	PROPN
ejpam-6020	87	8	)	)	PUNCT
ejpam-6020	87	9	.	.	PUNCT
ejpam-6020	88	1	definition	definition	NOUN
ejpam-6020	88	2	4	4	NUM
ejpam-6020	88	3	.	.	PUNCT
ejpam-6020	89	1	[	[	X
ejpam-6020	89	2	13	13	NUM
ejpam-6020	89	3	]	]	PUNCT
ejpam-6020	89	4	regarding	regard	VERB
ejpam-6020	89	5	the	the	DET
ejpam-6020	89	6	subset	subset	NOUN
ejpam-6020	89	7	k	k	PROPN
ejpam-6020	89	8	of	of	ADP
ejpam-6020	89	9	an	an	DET
ejpam-6020	89	10	sts	st	NOUN
ejpam-6020	89	11	(	(	PUNCT
ejpam-6020	89	12	λ	λ	X
ejpam-6020	89	13	,	,	PUNCT
ejpam-6020	89	14	ϑ	ϑ	NOUN
ejpam-6020	89	15	)	)	PUNCT
ejpam-6020	89	16	,	,	PUNCT
ejpam-6020	89	17	the	the	DET
ejpam-6020	89	18	class	class	NOUN
ejpam-6020	89	19	ϑk	ϑk	PROPN
ejpam-6020	89	20	=	=	PRON
ejpam-6020	89	21	{	{	PUNCT
ejpam-6020	89	22	k	k	X
ejpam-6020	89	23	∩g	∩g	PROPN
ejpam-6020	89	24	:	:	PUNCT
ejpam-6020	89	25	g	g	PROPN
ejpam-6020	89	26	∈	∈	PROPN
ejpam-6020	89	27	ϑ	ϑ	PART
ejpam-6020	89	28	}	}	PUNCT
ejpam-6020	89	29	defines	define	VERB
ejpam-6020	89	30	an	an	DET
ejpam-6020	89	31	sts	st	NOUN
ejpam-6020	89	32	on	on	ADP
ejpam-6020	89	33	k	k	PROPN
ejpam-6020	89	34	,	,	PUNCT
ejpam-6020	89	35	and	and	CCONJ
ejpam-6020	89	36	it	it	PRON
ejpam-6020	89	37	is	be	AUX
ejpam-6020	89	38	called	call	VERB
ejpam-6020	89	39	a	a	DET
ejpam-6020	89	40	subspace	subspace	NOUN
ejpam-6020	89	41	of	of	ADP
ejpam-6020	89	42	(	(	PUNCT
ejpam-6020	89	43	λ	λ	PROPN
ejpam-6020	89	44	,	,	PUNCT
ejpam-6020	89	45	ϑ	ϑ	NOUN
ejpam-6020	89	46	)	)	PUNCT
ejpam-6020	89	47	.	.	PUNCT
ejpam-6020	90	1	definition	definition	NOUN
ejpam-6020	90	2	5	5	NUM
ejpam-6020	90	3	.	.	PUNCT
ejpam-6020	91	1	[	[	X
ejpam-6020	91	2	43	43	NUM
ejpam-6020	91	3	]	]	PUNCT
ejpam-6020	91	4	let	let	VERB
ejpam-6020	91	5	h	h	PRON
ejpam-6020	91	6	be	be	AUX
ejpam-6020	91	7	a	a	DET
ejpam-6020	91	8	subset	subset	NOUN
ejpam-6020	91	9	of	of	ADP
ejpam-6020	91	10	an	an	DET
ejpam-6020	91	11	sts	st	NOUN
ejpam-6020	91	12	(	(	PUNCT
ejpam-6020	91	13	λ	λ	X
ejpam-6020	91	14	,	,	PUNCT
ejpam-6020	91	15	ϑ	ϑ	NOUN
ejpam-6020	91	16	)	)	PUNCT
ejpam-6020	91	17	.	.	PUNCT
ejpam-6020	92	1	then	then	ADV
ejpam-6020	92	2	,	,	PUNCT
ejpam-6020	92	3	h	h	NOUN
ejpam-6020	92	4	is	be	AUX
ejpam-6020	92	5	called	call	VERB
ejpam-6020	92	6	supra	supra	PROPN
ejpam-6020	92	7	ϵ-open	ϵ-open	PROPN
ejpam-6020	92	8	set	set	VERB
ejpam-6020	92	9	if	if	SCONJ
ejpam-6020	92	10	either	either	PRON
ejpam-6020	92	11	h	h	NOUN
ejpam-6020	92	12	=	=	NOUN
ejpam-6020	92	13	∅	∅	NOUN
ejpam-6020	92	14	or	or	CCONJ
ejpam-6020	92	15	h	h	NOUN
ejpam-6020	92	16	⊆	⊆	NUM
ejpam-6020	92	17	{	{	PUNCT
ejpam-6020	92	18	b(h	b(h	PROPN
ejpam-6020	92	19	)	)	PUNCT
ejpam-6020	92	20	∪h	∪h	NUM
ejpam-6020	92	21	◦	◦	NOUN
ejpam-6020	92	22	,	,	PUNCT
ejpam-6020	92	23	h	h	NOUN
ejpam-6020	92	24	∈	∈	PROPN
ejpam-6020	92	25	sro(λ	sro(λ	PROPN
ejpam-6020	92	26	)	)	PUNCT
ejpam-6020	92	27	,	,	PUNCT
ejpam-6020	92	28	b(h	b(h	PROPN
ejpam-6020	92	29	)	)	PUNCT
ejpam-6020	92	30	,	,	PUNCT
ejpam-6020	92	31	h	h	NOUN
ejpam-6020	92	32	∈	∈	PROPN
ejpam-6020	92	33	snd(λ	snd(λ	NOUN
ejpam-6020	92	34	)	)	PUNCT
ejpam-6020	92	35	and	and	CCONJ
ejpam-6020	92	36	b(h	b(h	NOUN
ejpam-6020	92	37	)	)	PUNCT
ejpam-6020	92	38	is	be	AUX
ejpam-6020	92	39	infinite	infinite	ADJ
ejpam-6020	92	40	.	.	PUNCT
ejpam-6020	93	1	also	also	ADV
ejpam-6020	93	2	,	,	PUNCT
ejpam-6020	93	3	hc	hc	PROPN
ejpam-6020	93	4	is	be	AUX
ejpam-6020	93	5	called	call	VERB
ejpam-6020	93	6	supra	supra	ADJ
ejpam-6020	93	7	ϵ-closed	ϵ-close	VERB
ejpam-6020	93	8	-	-	PUNCT
ejpam-6020	93	9	set	set	NOUN
ejpam-6020	93	10	.	.	PUNCT
ejpam-6020	94	1	the	the	DET
ejpam-6020	94	2	category	category	NOUN
ejpam-6020	94	3	of	of	ADP
ejpam-6020	94	4	all	all	DET
ejpam-6020	94	5	supra	supra	PROPN
ejpam-6020	94	6	ϵ-open	ϵ-open	PROPN
ejpam-6020	94	7	(	(	PUNCT
ejpam-6020	94	8	respectively	respectively	ADV
ejpam-6020	94	9	,	,	PUNCT
ejpam-6020	94	10	supra	supra	PROPN
ejpam-6020	94	11	ϵ-closed	ϵ-close	VERB
ejpam-6020	94	12	)	)	PUNCT
ejpam-6020	94	13	sets	set	NOUN
ejpam-6020	94	14	will	will	AUX
ejpam-6020	94	15	be	be	AUX
ejpam-6020	94	16	indicated	indicate	VERB
ejpam-6020	94	17	by	by	ADP
ejpam-6020	94	18	soϵ(λ	soϵ(λ	PROPN
ejpam-6020	94	19	)	)	PUNCT
ejpam-6020	94	20	(	(	PUNCT
ejpam-6020	94	21	respectively	respectively	ADV
ejpam-6020	94	22	,	,	PUNCT
ejpam-6020	94	23	scϵ(λ	scϵ(λ	PROPN
ejpam-6020	94	24	)	)	PUNCT
ejpam-6020	94	25	)	)	PUNCT
ejpam-6020	94	26	.	.	PUNCT
ejpam-6020	95	1	theorem	theorem	NOUN
ejpam-6020	95	2	2	2	NUM
ejpam-6020	95	3	.	.	PUNCT
ejpam-6020	96	1	[	[	X
ejpam-6020	96	2	43	43	NUM
ejpam-6020	96	3	]	]	PUNCT
ejpam-6020	96	4	every	every	DET
ejpam-6020	96	5	supra	supra	NOUN
ejpam-6020	96	6	(	(	PUNCT
ejpam-6020	96	7	respectively	respectively	ADV
ejpam-6020	96	8	,	,	PUNCT
ejpam-6020	96	9	α-	α-	X
ejpam-6020	96	10	,	,	PUNCT
ejpam-6020	96	11	semi-	semi-	ADJ
ejpam-6020	96	12	,	,	PUNCT
ejpam-6020	96	13	b-	b-	INTJ
ejpam-6020	96	14	,	,	PUNCT
ejpam-6020	96	15	regular	regular	ADJ
ejpam-6020	96	16	,	,	PUNCT
ejpam-6020	96	17	pre-	pre-	X
ejpam-6020	96	18	,	,	PUNCT
ejpam-6020	96	19	β-	β-	X
ejpam-6020	96	20	,	,	PUNCT
ejpam-6020	96	21	r-	r-	X
ejpam-6020	96	22	)	)	PUNCT
ejpam-6020	96	23	open	open	ADJ
ejpam-6020	96	24	set	set	NOUN
ejpam-6020	96	25	is	be	AUX
ejpam-6020	96	26	supra	supra	PROPN
ejpam-6020	96	27	ϵ-open	ϵ-open	PROPN
ejpam-6020	96	28	.	.	PUNCT
ejpam-6020	97	1	definition	definition	NOUN
ejpam-6020	97	2	6	6	NUM
ejpam-6020	97	3	.	.	PUNCT
ejpam-6020	98	1	[	[	X
ejpam-6020	98	2	43	43	NUM
ejpam-6020	98	3	]	]	PUNCT
ejpam-6020	98	4	for	for	ADP
ejpam-6020	98	5	the	the	DET
ejpam-6020	98	6	subset	subset	NOUN
ejpam-6020	98	7	k	k	PROPN
ejpam-6020	98	8	of	of	ADP
ejpam-6020	98	9	an	an	DET
ejpam-6020	98	10	sts	st	NOUN
ejpam-6020	98	11	(	(	PUNCT
ejpam-6020	98	12	λ	λ	X
ejpam-6020	98	13	,	,	PUNCT
ejpam-6020	98	14	ϑ	ϑ	NOUN
ejpam-6020	98	15	)	)	PUNCT
ejpam-6020	98	16	,	,	PUNCT
ejpam-6020	98	17	the	the	DET
ejpam-6020	98	18	intsϵ(k	intsϵ(k	NOUN
ejpam-6020	98	19	)	)	PUNCT
ejpam-6020	98	20	will	will	AUX
ejpam-6020	98	21	denote	denote	VERB
ejpam-6020	98	22	the	the	DET
ejpam-6020	98	23	supra	supra	ADJ
ejpam-6020	98	24	ϵ-interior	ϵ-interior	PROPN
ejpam-6020	98	25	of	of	ADP
ejpam-6020	98	26	k	k	NOUN
ejpam-6020	98	27	,	,	PUNCT
ejpam-6020	98	28	where	where	SCONJ
ejpam-6020	98	29	intsϵ(k	intsϵ(k	ADJ
ejpam-6020	98	30	)	)	PUNCT
ejpam-6020	98	31	=	=	SYM
ejpam-6020	98	32	∪{g	∪{g	PROPN
ejpam-6020	98	33	:	:	PUNCT
ejpam-6020	98	34	g	g	PROPN
ejpam-6020	98	35	∈	∈	PROPN
ejpam-6020	98	36	soϵ(λ	soϵ(λ	PROPN
ejpam-6020	98	37	)	)	PUNCT
ejpam-6020	98	38	and	and	CCONJ
ejpam-6020	98	39	g	g	PROPN
ejpam-6020	98	40	⊆	⊆	NUM
ejpam-6020	98	41	k	k	NOUN
ejpam-6020	98	42	}	}	PUNCT
ejpam-6020	98	43	.	.	PUNCT
ejpam-6020	99	1	theorem	theorem	NOUN
ejpam-6020	99	2	3	3	NUM
ejpam-6020	99	3	.	.	PUNCT
ejpam-6020	100	1	[	[	X
ejpam-6020	100	2	43	43	NUM
ejpam-6020	100	3	]	]	PUNCT
ejpam-6020	100	4	for	for	ADP
ejpam-6020	100	5	the	the	DET
ejpam-6020	100	6	supra	supra	PROPN
ejpam-6020	100	7	ϵ-interior	ϵ-interior	PROPN
ejpam-6020	100	8	operator	operator	NOUN
ejpam-6020	100	9	intsϵ	intsϵ	NOUN
ejpam-6020	100	10	:	:	PUNCT
ejpam-6020	101	1	p	p	X
ejpam-6020	101	2	(	(	PUNCT
ejpam-6020	101	3	λ	λ	NOUN
ejpam-6020	101	4	)	)	PUNCT
ejpam-6020	101	5	−→	−→	NOUN
ejpam-6020	101	6	p	p	X
ejpam-6020	101	7	(	(	PUNCT
ejpam-6020	101	8	λ	λ	NOUN
ejpam-6020	101	9	)	)	PUNCT
ejpam-6020	101	10	and	and	CCONJ
ejpam-6020	101	11	e	e	NOUN
ejpam-6020	101	12	∈	∈	PROPN
ejpam-6020	101	13	p	p	PROPN
ejpam-6020	101	14	(	(	PUNCT
ejpam-6020	101	15	λ	λ	NOUN
ejpam-6020	101	16	)	)	PUNCT
ejpam-6020	101	17	,	,	PUNCT
ejpam-6020	101	18	we	we	PRON
ejpam-6020	101	19	have	have	VERB
ejpam-6020	101	20	intsϵ(e	intsϵ(e	VERB
ejpam-6020	101	21	)	)	PUNCT
ejpam-6020	101	22	=	=	SYM
ejpam-6020	101	23			PUNCT
ejpam-6020	101	24	∅	∅	NOUN
ejpam-6020	101	25	,	,	PUNCT
ejpam-6020	101	26	e	e	PROPN
ejpam-6020	101	27	∈	∈	PROPN
ejpam-6020	101	28	snd(λ	snd(λ	NOUN
ejpam-6020	101	29	)	)	PUNCT
ejpam-6020	101	30	and	and	CCONJ
ejpam-6020	101	31	b(e	b(e	PROPN
ejpam-6020	101	32	)	)	PUNCT
ejpam-6020	101	33	is	be	AUX
ejpam-6020	101	34	finite	finite	ADJ
ejpam-6020	101	35	.	.	PUNCT
ejpam-6020	102	1	e	e	NOUN
ejpam-6020	102	2	∩	∩	NOUN
ejpam-6020	102	3	b(e	b(e	PROPN
ejpam-6020	102	4	)	)	PUNCT
ejpam-6020	102	5	,	,	PUNCT
ejpam-6020	102	6	e	e	PROPN
ejpam-6020	102	7	∈	∈	PROPN
ejpam-6020	102	8	snd(λ	snd(λ	NOUN
ejpam-6020	102	9	)	)	PUNCT
ejpam-6020	102	10	and	and	CCONJ
ejpam-6020	102	11	b(e	b(e	PROPN
ejpam-6020	102	12	)	)	PUNCT
ejpam-6020	102	13	is	be	AUX
ejpam-6020	102	14	infinite	infinite	ADJ
ejpam-6020	102	15	.	.	PUNCT
ejpam-6020	103	1	e	e	X
ejpam-6020	103	2	,	,	PUNCT
ejpam-6020	103	3	e	e	PROPN
ejpam-6020	103	4	∈	∈	PROPN
ejpam-6020	103	5	sro(λ	sro(λ	PROPN
ejpam-6020	103	6	)	)	PUNCT
ejpam-6020	103	7	.	.	PUNCT
ejpam-6020	104	1	definition	definition	NOUN
ejpam-6020	104	2	7	7	NUM
ejpam-6020	104	3	.	.	PUNCT
ejpam-6020	105	1	[	[	X
ejpam-6020	105	2	43	43	NUM
ejpam-6020	105	3	]	]	PUNCT
ejpam-6020	105	4	let	let	VERB
ejpam-6020	105	5	c	c	PROPN
ejpam-6020	105	6	∈	∈	PROPN
ejpam-6020	105	7	p	p	X
ejpam-6020	105	8	(	(	PUNCT
ejpam-6020	105	9	λ	λ	NOUN
ejpam-6020	105	10	)	)	PUNCT
ejpam-6020	105	11	be	be	VERB
ejpam-6020	105	12	a	a	DET
ejpam-6020	105	13	subset	subset	NOUN
ejpam-6020	105	14	of	of	ADP
ejpam-6020	105	15	an	an	DET
ejpam-6020	105	16	sts	st	NOUN
ejpam-6020	105	17	(	(	PUNCT
ejpam-6020	105	18	λ	λ	X
ejpam-6020	105	19	,	,	PUNCT
ejpam-6020	105	20	ϑ	ϑ	NOUN
ejpam-6020	105	21	)	)	PUNCT
ejpam-6020	105	22	,	,	PUNCT
ejpam-6020	105	23	then	then	ADV
ejpam-6020	105	24	clsϵ(c	clsϵ(c	ADJ
ejpam-6020	105	25	)	)	PUNCT
ejpam-6020	105	26	will	will	AUX
ejpam-6020	105	27	denote	denote	VERB
ejpam-6020	105	28	the	the	DET
ejpam-6020	105	29	supra	supra	ADJ
ejpam-6020	105	30	ϵ-closure	ϵ-closure	NOUN
ejpam-6020	105	31	of	of	ADP
ejpam-6020	105	32	c	c	NOUN
ejpam-6020	105	33	,	,	PUNCT
ejpam-6020	105	34	where	where	SCONJ
ejpam-6020	105	35	a.	a.	NOUN
ejpam-6020	105	36	m.	m.	PROPN
ejpam-6020	105	37	abd	abd	PROPN
ejpam-6020	105	38	el	el	PROPN
ejpam-6020	105	39	-	-	PROPN
ejpam-6020	105	40	latif	latif	PROPN
ejpam-6020	105	41	et	et	PROPN
ejpam-6020	105	42	al	al	PROPN
ejpam-6020	105	43	.	.	PUNCT
ejpam-6020	105	44	/	/	SYM
ejpam-6020	105	45	eur	eur	PROPN
ejpam-6020	105	46	.	.	PUNCT
ejpam-6020	106	1	j.	j.	PROPN
ejpam-6020	106	2	pure	pure	PROPN
ejpam-6020	106	3	appl	appl	PROPN
ejpam-6020	106	4	.	.	PROPN
ejpam-6020	106	5	math	math	PROPN
ejpam-6020	106	6	,	,	PUNCT
ejpam-6020	106	7	18	18	NUM
ejpam-6020	106	8	(	(	PUNCT
ejpam-6020	106	9	2	2	NUM
ejpam-6020	106	10	)	)	PUNCT
ejpam-6020	106	11	(	(	PUNCT
ejpam-6020	106	12	2025	2025	NUM
ejpam-6020	106	13	)	)	PUNCT
ejpam-6020	106	14	,	,	PUNCT
ejpam-6020	106	15	6020	6020	NUM
ejpam-6020	106	16	5	5	NUM
ejpam-6020	106	17	of	of	ADP
ejpam-6020	106	18	17	17	NUM
ejpam-6020	106	19	clsϵ(c	clsϵ(c	NOUN
ejpam-6020	106	20	)	)	PUNCT
ejpam-6020	106	21	=	=	VERB
ejpam-6020	107	1	∩{n	∩{n	INTJ
ejpam-6020	107	2	:	:	PUNCT
ejpam-6020	107	3	n	n	NOUN
ejpam-6020	107	4	∈	∈	PROPN
ejpam-6020	107	5	scϵ(λ	scϵ(λ	PROPN
ejpam-6020	107	6	)	)	PUNCT
ejpam-6020	107	7	and	and	CCONJ
ejpam-6020	107	8	c	c	NOUN
ejpam-6020	107	9	⊆	⊆	NUM
ejpam-6020	107	10	n	n	CCONJ
ejpam-6020	107	11	}	}	PUNCT
ejpam-6020	107	12	.	.	PUNCT
ejpam-6020	108	1	theorem	theorem	ADJ
ejpam-6020	108	2	4	4	NUM
ejpam-6020	108	3	.	.	PUNCT
ejpam-6020	109	1	[	[	X
ejpam-6020	109	2	43	43	NUM
ejpam-6020	109	3	]	]	PUNCT
ejpam-6020	109	4	for	for	ADP
ejpam-6020	109	5	the	the	DET
ejpam-6020	109	6	supra	supra	PROPN
ejpam-6020	109	7	ϵ-closure	ϵ-closure	PROPN
ejpam-6020	109	8	operator	operator	NOUN
ejpam-6020	109	9	clsϵ	clsϵ	NOUN
ejpam-6020	109	10	:	:	PUNCT
ejpam-6020	110	1	p	p	X
ejpam-6020	110	2	(	(	PUNCT
ejpam-6020	110	3	λ	λ	NOUN
ejpam-6020	110	4	)	)	PUNCT
ejpam-6020	110	5	−→	−→	NOUN
ejpam-6020	110	6	p	p	X
ejpam-6020	110	7	(	(	PUNCT
ejpam-6020	110	8	λ	λ	NOUN
ejpam-6020	110	9	)	)	PUNCT
ejpam-6020	110	10	and	and	CCONJ
ejpam-6020	110	11	e	e	NOUN
ejpam-6020	110	12	∈	∈	PROPN
ejpam-6020	110	13	p	p	PROPN
ejpam-6020	110	14	(	(	PUNCT
ejpam-6020	110	15	λ	λ	NOUN
ejpam-6020	110	16	)	)	PUNCT
ejpam-6020	110	17	,	,	PUNCT
ejpam-6020	110	18	we	we	PRON
ejpam-6020	110	19	have	have	AUX
ejpam-6020	110	20	clsϵ(e	clsϵ(e	VERB
ejpam-6020	110	21	)	)	PUNCT
ejpam-6020	110	22	=	=	PUNCT
ejpam-6020	110	23			PUNCT
ejpam-6020	110	24	λ	λ	PROPN
ejpam-6020	110	25	,	,	PUNCT
ejpam-6020	110	26	ec	ec	PROPN
ejpam-6020	110	27	∈	∈	PROPN
ejpam-6020	110	28	snd(λ	snd(λ	PROPN
ejpam-6020	110	29	)	)	PUNCT
ejpam-6020	110	30	and	and	CCONJ
ejpam-6020	110	31	b(ec	b(ec	NOUN
ejpam-6020	110	32	)	)	PUNCT
ejpam-6020	110	33	is	be	AUX
ejpam-6020	110	34	finite	finite	ADJ
ejpam-6020	110	35	.	.	PUNCT
ejpam-6020	111	1	e	e	X
ejpam-6020	111	2	,	,	PUNCT
ejpam-6020	111	3	ec	ec	PROPN
ejpam-6020	111	4	∈	∈	PROPN
ejpam-6020	111	5	snd(λ	snd(λ	PROPN
ejpam-6020	111	6	)	)	PUNCT
ejpam-6020	111	7	and	and	CCONJ
ejpam-6020	111	8	b(ec	b(ec	NOUN
ejpam-6020	111	9	)	)	PUNCT
ejpam-6020	111	10	is	be	AUX
ejpam-6020	111	11	infinite	infinite	ADJ
ejpam-6020	111	12	.	.	PUNCT
ejpam-6020	112	1	e	e	X
ejpam-6020	112	2	,	,	PUNCT
ejpam-6020	112	3	ec	ec	PROPN
ejpam-6020	112	4	∈	∈	PROPN
ejpam-6020	112	5	sro(λ	sro(λ	PROPN
ejpam-6020	112	6	)	)	PUNCT
ejpam-6020	112	7	.	.	PUNCT
ejpam-6020	113	1	theorem	theorem	VERB
ejpam-6020	113	2	5	5	NUM
ejpam-6020	113	3	.	.	PUNCT
ejpam-6020	114	1	[	[	X
ejpam-6020	114	2	43	43	NUM
ejpam-6020	114	3	]	]	PUNCT
ejpam-6020	114	4	regarding	regard	VERB
ejpam-6020	114	5	a	a	DET
ejpam-6020	114	6	subset	subset	ADJ
ejpam-6020	114	7	t	t	NOUN
ejpam-6020	114	8	of	of	ADP
ejpam-6020	114	9	an	an	DET
ejpam-6020	114	10	sts	st	NOUN
ejpam-6020	114	11	(	(	PUNCT
ejpam-6020	114	12	λ	λ	X
ejpam-6020	114	13	,	,	PUNCT
ejpam-6020	114	14	ϑ	ϑ	NOUN
ejpam-6020	114	15	)	)	PUNCT
ejpam-6020	114	16	,	,	PUNCT
ejpam-6020	114	17	we	we	PRON
ejpam-6020	114	18	have	have	VERB
ejpam-6020	114	19	(	(	PUNCT
ejpam-6020	114	20	1	1	X
ejpam-6020	114	21	)	)	PUNCT
ejpam-6020	114	22	clsϵ(t	clsϵ(t	NOUN
ejpam-6020	114	23	c	c	NOUN
ejpam-6020	114	24	)	)	PUNCT
ejpam-6020	114	25	=	=	NOUN
ejpam-6020	115	1	[	[	X
ejpam-6020	115	2	intsϵ(t	intsϵ(t	NOUN
ejpam-6020	115	3	)	)	PUNCT
ejpam-6020	115	4	]	]	PUNCT
ejpam-6020	115	5	c.	c.	PROPN
ejpam-6020	115	6	(	(	PUNCT
ejpam-6020	115	7	2	2	X
ejpam-6020	115	8	)	)	PUNCT
ejpam-6020	115	9	intsϵ(t	intsϵ(t	NOUN
ejpam-6020	115	10	c	c	NOUN
ejpam-6020	115	11	)	)	PUNCT
ejpam-6020	115	12	=	=	NOUN
ejpam-6020	116	1	[	[	X
ejpam-6020	116	2	clsϵ(t	clsϵ(t	NOUN
ejpam-6020	116	3	)	)	PUNCT
ejpam-6020	116	4	]	]	PUNCT
ejpam-6020	116	5	c.	c.	PROPN
ejpam-6020	116	6	(	(	PUNCT
ejpam-6020	116	7	3	3	NUM
ejpam-6020	116	8	)	)	PUNCT
ejpam-6020	116	9	int(t	int(t	PROPN
ejpam-6020	116	10	)	)	PUNCT
ejpam-6020	116	11	⊆	⊆	NUM
ejpam-6020	116	12	ints(t	ints(t	NOUN
ejpam-6020	116	13	)	)	PUNCT
ejpam-6020	116	14	⊆	⊆	NUM
ejpam-6020	116	15	intsϵ(t	intsϵ(t	NOUN
ejpam-6020	116	16	)	)	PUNCT
ejpam-6020	116	17	.	.	PUNCT
ejpam-6020	117	1	(	(	PUNCT
ejpam-6020	117	2	4	4	X
ejpam-6020	117	3	)	)	PUNCT
ejpam-6020	117	4	clsϵ(t	clsϵ(t	NOUN
ejpam-6020	117	5	)	)	PUNCT
ejpam-6020	117	6	⊆	⊆	NUM
ejpam-6020	117	7	cls(t	cls(t	X
ejpam-6020	117	8	)	)	PUNCT
ejpam-6020	117	9	⊆	⊆	NUM
ejpam-6020	117	10	cl(t	cl(t	NOUN
ejpam-6020	117	11	)	)	PUNCT
ejpam-6020	117	12	.	.	PUNCT
ejpam-6020	118	1	definition	definition	NOUN
ejpam-6020	118	2	8	8	NUM
ejpam-6020	118	3	.	.	PUNCT
ejpam-6020	119	1	[	[	X
ejpam-6020	119	2	43	43	NUM
ejpam-6020	119	3	]	]	PUNCT
ejpam-6020	119	4	given	give	VERB
ejpam-6020	119	5	a	a	DET
ejpam-6020	119	6	subset	subset	NOUN
ejpam-6020	119	7	t	t	NOUN
ejpam-6020	119	8	of	of	ADP
ejpam-6020	119	9	an	an	DET
ejpam-6020	119	10	sts	st	NOUN
ejpam-6020	119	11	(	(	PUNCT
ejpam-6020	119	12	λ	λ	X
ejpam-6020	119	13	,	,	PUNCT
ejpam-6020	119	14	ϑ	ϑ	NOUN
ejpam-6020	119	15	)	)	PUNCT
ejpam-6020	119	16	with	with	ADP
ejpam-6020	119	17	arbitrary	arbitrary	ADJ
ejpam-6020	119	18	point	point	NOUN
ejpam-6020	119	19	s	s	VERB
ejpam-6020	119	20	∈	∈	PROPN
ejpam-6020	119	21	λ	λ	PROPN
ejpam-6020	119	22	.	.	PUNCT
ejpam-6020	120	1	then	then	ADV
ejpam-6020	120	2	,	,	PUNCT
ejpam-6020	120	3	s	s	AUX
ejpam-6020	120	4	called	call	VERB
ejpam-6020	120	5	a	a	DET
ejpam-6020	120	6	supra	supra	ADJ
ejpam-6020	120	7	ϵ-accumulation	ϵ-accumulation	PROPN
ejpam-6020	120	8	point	point	NOUN
ejpam-6020	120	9	of	of	ADP
ejpam-6020	120	10	t	t	PROPN
ejpam-6020	120	11	if	if	SCONJ
ejpam-6020	120	12	all	all	DET
ejpam-6020	120	13	each	each	DET
ejpam-6020	120	14	supra	supra	PROPN
ejpam-6020	120	15	ϵ-open	ϵ-open	PROPN
ejpam-6020	120	16	set	set	PROPN
ejpam-6020	121	1	gs	gs	INTJ
ejpam-6020	121	2	,	,	PUNCT
ejpam-6020	121	3	we	we	PRON
ejpam-6020	121	4	have	have	VERB
ejpam-6020	121	5	[	[	X
ejpam-6020	121	6	t\{s	t\{s	X
ejpam-6020	121	7	}	}	PUNCT
ejpam-6020	121	8	]	]	PUNCT
ejpam-6020	121	9	∩g	∩g	PROPN
ejpam-6020	122	1	̸=	̸=	PROPN
ejpam-6020	122	2	∅.	∅.	ADP
ejpam-6020	122	3	the	the	DET
ejpam-6020	122	4	set	set	NOUN
ejpam-6020	122	5	of	of	ADP
ejpam-6020	122	6	all	all	DET
ejpam-6020	122	7	supra	supra	ADJ
ejpam-6020	122	8	ϵ-accumulation	ϵ-accumulation	PROPN
ejpam-6020	122	9	points	point	NOUN
ejpam-6020	122	10	of	of	ADP
ejpam-6020	122	11	t	t	PROPN
ejpam-6020	122	12	will	will	AUX
ejpam-6020	122	13	denoted	denote	VERB
ejpam-6020	122	14	by	by	ADP
ejpam-6020	122	15	accϵ(t	accϵ(t	NOUN
ejpam-6020	122	16	)	)	PUNCT
ejpam-6020	122	17	.	.	PUNCT
ejpam-6020	123	1	definition	definition	NOUN
ejpam-6020	123	2	9	9	NUM
ejpam-6020	123	3	.	.	PUNCT
ejpam-6020	124	1	[	[	X
ejpam-6020	124	2	43	43	NUM
ejpam-6020	124	3	]	]	X
ejpam-6020	124	4	if	if	SCONJ
ejpam-6020	124	5	s	s	X
ejpam-6020	124	6	∈	∈	PROPN
ejpam-6020	124	7	[	[	X
ejpam-6020	124	8	clsϵ(z)\intsϵ(z	clsϵ(z)\intsϵ(z	X
ejpam-6020	124	9	)	)	PUNCT
ejpam-6020	124	10	]	]	PUNCT
ejpam-6020	124	11	for	for	ADP
ejpam-6020	124	12	an	an	DET
ejpam-6020	124	13	arbitrary	arbitrary	ADJ
ejpam-6020	124	14	point	point	NOUN
ejpam-6020	124	15	s	s	PART
ejpam-6020	124	16	and	and	CCONJ
ejpam-6020	124	17	oft	oft	ADV
ejpam-6020	124	18	subset	subset	VERB
ejpam-6020	124	19	z	z	PROPN
ejpam-6020	124	20	of	of	ADP
ejpam-6020	124	21	an	an	DET
ejpam-6020	124	22	sts	st	NOUN
ejpam-6020	124	23	(	(	PUNCT
ejpam-6020	124	24	λ	λ	X
ejpam-6020	124	25	,	,	PUNCT
ejpam-6020	124	26	ϑ	ϑ	NOUN
ejpam-6020	124	27	)	)	PUNCT
ejpam-6020	124	28	,	,	PUNCT
ejpam-6020	124	29	then	then	ADV
ejpam-6020	124	30	s	s	VERB
ejpam-6020	124	31	is	be	AUX
ejpam-6020	124	32	called	call	VERB
ejpam-6020	124	33	a	a	DET
ejpam-6020	124	34	supra-ϵ-boundary	supra-ϵ-boundary	ADJ
ejpam-6020	124	35	point	point	NOUN
ejpam-6020	124	36	of	of	ADP
ejpam-6020	124	37	z.	z.	PROPN
ejpam-6020	124	38	the	the	DET
ejpam-6020	124	39	supra-ϵ-boundary	supra-ϵ-boundary	ADJ
ejpam-6020	124	40	set	set	NOUN
ejpam-6020	124	41	of	of	ADP
ejpam-6020	124	42	(	(	PUNCT
ejpam-6020	124	43	z	z	NOUN
ejpam-6020	124	44	)	)	PUNCT
ejpam-6020	124	45	is	be	AUX
ejpam-6020	124	46	the	the	DET
ejpam-6020	124	47	set	set	NOUN
ejpam-6020	124	48	of	of	ADP
ejpam-6020	124	49	all	all	DET
ejpam-6020	124	50	upper	upper	ADJ
ejpam-6020	124	51	-	-	PUNCT
ejpam-6020	124	52	so	so	ADV
ejpam-6020	124	53	-	-	PUNCT
ejpam-6020	124	54	boundary	boundary	ADJ
ejpam-6020	124	55	points	point	NOUN
ejpam-6020	124	56	of	of	ADP
ejpam-6020	124	57	z	z	NOUN
ejpam-6020	124	58	,	,	PUNCT
ejpam-6020	124	59	and	and	CCONJ
ejpam-6020	124	60	it	it	PRON
ejpam-6020	124	61	is	be	AUX
ejpam-6020	124	62	represented	represent	VERB
ejpam-6020	124	63	by	by	ADP
ejpam-6020	124	64	bϵ(z	bϵ(z	NOUN
ejpam-6020	124	65	)	)	PUNCT
ejpam-6020	124	66	.	.	PUNCT
ejpam-6020	125	1	also	also	ADV
ejpam-6020	125	2	,	,	PUNCT
ejpam-6020	125	3	the	the	DET
ejpam-6020	125	4	upper	upper	ADJ
ejpam-6020	125	5	-	-	PUNCT
ejpam-6020	125	6	so	so	ADV
ejpam-6020	125	7	-	-	PUNCT
ejpam-6020	125	8	exterior	exterior	NOUN
ejpam-6020	125	9	of	of	ADP
ejpam-6020	125	10	z	z	NOUN
ejpam-6020	125	11	is	be	AUX
ejpam-6020	125	12	also	also	ADV
ejpam-6020	125	13	represented	represent	VERB
ejpam-6020	125	14	by	by	ADP
ejpam-6020	125	15	extϵ(z	extϵ(z	PROPN
ejpam-6020	125	16	)	)	PUNCT
ejpam-6020	125	17	,	,	PUNCT
ejpam-6020	125	18	where	where	SCONJ
ejpam-6020	125	19	extϵ(z	extϵ(z	NOUN
ejpam-6020	125	20	)	)	PUNCT
ejpam-6020	125	21	=	=	PUNCT
ejpam-6020	126	1	intsϵ(z	intsϵ(z	NOUN
ejpam-6020	126	2	c	c	NOUN
ejpam-6020	126	3	)	)	PUNCT
ejpam-6020	126	4	.	.	PUNCT
ejpam-6020	127	1	3	3	X
ejpam-6020	127	2	.	.	X
ejpam-6020	127	3	new	new	ADJ
ejpam-6020	127	4	types	type	NOUN
ejpam-6020	127	5	of	of	ADP
ejpam-6020	127	6	supra	supra	ADJ
ejpam-6020	127	7	continuous	continuous	ADJ
ejpam-6020	127	8	functions	function	NOUN
ejpam-6020	127	9	based	base	VERB
ejpam-6020	127	10	on	on	ADP
ejpam-6020	127	11	supra	supra	PROPN
ejpam-6020	127	12	ϵ-open	ϵ-open	PROPN
ejpam-6020	127	13	sets	set	VERB
ejpam-6020	127	14	this	this	DET
ejpam-6020	127	15	section	section	NOUN
ejpam-6020	127	16	refers	refer	VERB
ejpam-6020	127	17	to	to	ADP
ejpam-6020	127	18	supra	supra	ADJ
ejpam-6020	127	19	continuity	continuity	NOUN
ejpam-6020	127	20	using	use	VERB
ejpam-6020	127	21	the	the	DET
ejpam-6020	127	22	concept	concept	NOUN
ejpam-6020	127	23	of	of	ADP
ejpam-6020	127	24	supra	supra	PROPN
ejpam-6020	127	25	ϵ-open	ϵ-open	PROPN
ejpam-6020	127	26	sets	set	NOUN
ejpam-6020	127	27	.	.	PUNCT
ejpam-6020	128	1	to	to	PART
ejpam-6020	128	2	be	be	AUX
ejpam-6020	128	3	more	more	ADV
ejpam-6020	128	4	precise	precise	ADJ
ejpam-6020	128	5	,	,	PUNCT
ejpam-6020	128	6	we	we	PRON
ejpam-6020	128	7	expanded	expand	VERB
ejpam-6020	128	8	on	on	ADP
ejpam-6020	128	9	the	the	DET
ejpam-6020	128	10	earlier	early	ADJ
ejpam-6020	128	11	kinds	kind	NOUN
ejpam-6020	128	12	of	of	ADP
ejpam-6020	128	13	weaker	weak	ADJ
ejpam-6020	128	14	forms	form	NOUN
ejpam-6020	128	15	of	of	ADP
ejpam-6020	128	16	such	such	ADJ
ejpam-6020	128	17	conceptions	conception	NOUN
ejpam-6020	128	18	by	by	ADP
ejpam-6020	128	19	introducing	introduce	VERB
ejpam-6020	128	20	the	the	DET
ejpam-6020	128	21	concept	concept	NOUN
ejpam-6020	128	22	of	of	ADP
ejpam-6020	128	23	supra	supra	PROPN
ejpam-6020	128	24	ϵ-continuous	ϵ-continuous	PROPN
ejpam-6020	128	25	functions	function	NOUN
ejpam-6020	128	26	.	.	PUNCT
ejpam-6020	129	1	figure	figure	NOUN
ejpam-6020	129	2	1	1	NUM
ejpam-6020	129	3	,	,	PUNCT
ejpam-6020	129	4	shows	show	VERB
ejpam-6020	129	5	a	a	DET
ejpam-6020	129	6	diagram	diagram	NOUN
ejpam-6020	129	7	that	that	PRON
ejpam-6020	129	8	was	be	AUX
ejpam-6020	129	9	used	use	VERB
ejpam-6020	129	10	to	to	PART
ejpam-6020	129	11	examine	examine	VERB
ejpam-6020	129	12	the	the	DET
ejpam-6020	129	13	connections	connection	NOUN
ejpam-6020	129	14	between	between	ADP
ejpam-6020	129	15	our	our	PRON
ejpam-6020	129	16	new	new	ADJ
ejpam-6020	129	17	class	class	NOUN
ejpam-6020	129	18	and	and	CCONJ
ejpam-6020	129	19	other	other	ADJ
ejpam-6020	129	20	earlier	early	ADJ
ejpam-6020	129	21	supra	supra	ADJ
ejpam-6020	129	22	continuity	continuity	NOUN
ejpam-6020	129	23	concepts	concept	NOUN
ejpam-6020	129	24	.	.	PUNCT
ejpam-6020	130	1	additionally	additionally	ADV
ejpam-6020	130	2	,	,	PUNCT
ejpam-6020	130	3	the	the	DET
ejpam-6020	130	4	fundamental	fundamental	ADJ
ejpam-6020	130	5	characteristics	characteristic	NOUN
ejpam-6020	130	6	of	of	ADP
ejpam-6020	130	7	this	this	DET
ejpam-6020	130	8	notion	notion	NOUN
ejpam-6020	130	9	are	be	AUX
ejpam-6020	130	10	examined	examine	VERB
ejpam-6020	130	11	,	,	PUNCT
ejpam-6020	130	12	along	along	ADP
ejpam-6020	130	13	with	with	ADP
ejpam-6020	130	14	its	its	PRON
ejpam-6020	130	15	comparable	comparable	ADJ
ejpam-6020	130	16	conditions	condition	NOUN
ejpam-6020	130	17	.	.	PUNCT
ejpam-6020	131	1	furthermore	furthermore	ADV
ejpam-6020	131	2	,	,	PUNCT
ejpam-6020	131	3	we	we	PRON
ejpam-6020	131	4	presented	present	VERB
ejpam-6020	131	5	the	the	DET
ejpam-6020	131	6	concepts	concept	NOUN
ejpam-6020	131	7	of	of	ADP
ejpam-6020	131	8	supra	supra	ADJ
ejpam-6020	131	9	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	131	10	functions	function	NOUN
ejpam-6020	131	11	and	and	CCONJ
ejpam-6020	131	12	supra	supra	ADJ
ejpam-6020	131	13	ϵ∗-cts	ϵ∗-ct	NOUN
ejpam-6020	131	14	functions	function	NOUN
ejpam-6020	131	15	.	.	PUNCT
ejpam-6020	132	1	in	in	ADP
ejpam-6020	132	2	addition	addition	NOUN
ejpam-6020	132	3	,	,	PUNCT
ejpam-6020	132	4	we	we	PRON
ejpam-6020	132	5	prove	prove	VERB
ejpam-6020	132	6	that	that	SCONJ
ejpam-6020	132	7	the	the	DET
ejpam-6020	132	8	composition	composition	NOUN
ejpam-6020	132	9	of	of	ADP
ejpam-6020	132	10	supra	supra	ADJ
ejpam-6020	132	11	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	132	12	function	function	NOUN
ejpam-6020	132	13	and	and	CCONJ
ejpam-6020	132	14	supra	supra	ADJ
ejpam-6020	132	15	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	132	16	function	function	NOUN
ejpam-6020	132	17	(	(	PUNCT
ejpam-6020	132	18	respectively	respectively	ADV
ejpam-6020	132	19	,	,	PUNCT
ejpam-6020	132	20	supra	supra	ADJ
ejpam-6020	132	21	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	132	22	function	function	NOUN
ejpam-6020	132	23	and	and	CCONJ
ejpam-6020	132	24	cts	cts	PROPN
ejpam-6020	132	25	function	function	NOUN
ejpam-6020	132	26	is	be	AUX
ejpam-6020	132	27	supra	supra	ADJ
ejpam-6020	132	28	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	132	29	,	,	PUNCT
ejpam-6020	132	30	two	two	NUM
ejpam-6020	132	31	supra	supra	ADJ
ejpam-6020	132	32	ϵ-irresolute	ϵ-irresolute	NOUN
ejpam-6020	132	33	functions	function	NOUN
ejpam-6020	132	34	)	)	PUNCT
ejpam-6020	132	35	is	be	AUX
ejpam-6020	132	36	supra	supra	ADJ
ejpam-6020	132	37	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	132	38	(	(	PUNCT
ejpam-6020	132	39	respectively	respectively	ADV
ejpam-6020	132	40	,	,	PUNCT
ejpam-6020	132	41	supra	supra	ADJ
ejpam-6020	132	42	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	132	43	,	,	PUNCT
ejpam-6020	132	44	supra	supra	PROPN
ejpam-6020	132	45	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	132	46	)	)	PUNCT
ejpam-6020	132	47	.	.	PUNCT
ejpam-6020	133	1	finally	finally	ADV
ejpam-6020	133	2	,	,	PUNCT
ejpam-6020	133	3	several	several	ADJ
ejpam-6020	133	4	essential	essential	ADJ
ejpam-6020	133	5	examples	example	NOUN
ejpam-6020	133	6	are	be	AUX
ejpam-6020	133	7	provided	provide	VERB
ejpam-6020	133	8	.	.	PUNCT
ejpam-6020	134	1	definition	definition	NOUN
ejpam-6020	134	2	10	10	NUM
ejpam-6020	134	3	.	.	PUNCT
ejpam-6020	135	1	a	a	DET
ejpam-6020	135	2	function	function	NOUN
ejpam-6020	135	3	πϵ	πϵ	X
ejpam-6020	135	4	:	:	PUNCT
ejpam-6020	135	5	(	(	PUNCT
ejpam-6020	135	6	λ1	λ1	ADJ
ejpam-6020	135	7	,	,	PUNCT
ejpam-6020	135	8	ν1	ν1	NOUN
ejpam-6020	135	9	)	)	PUNCT
ejpam-6020	135	10	→	→	SYM
ejpam-6020	135	11	(	(	PUNCT
ejpam-6020	135	12	λ2	λ2	NOUN
ejpam-6020	135	13	,	,	PUNCT
ejpam-6020	135	14	ν2	ν2	NOUN
ejpam-6020	135	15	)	)	PUNCT
ejpam-6020	135	16	with	with	ADP
ejpam-6020	135	17	ϑ1	ϑ1	NOUN
ejpam-6020	135	18	as	as	ADP
ejpam-6020	135	19	an	an	DET
ejpam-6020	135	20	associated	associate	VERB
ejpam-6020	135	21	sts	st	NOUN
ejpam-6020	135	22	with	with	ADP
ejpam-6020	135	23	ν1	ν1	NOUN
ejpam-6020	135	24	is	be	AUX
ejpam-6020	135	25	said	say	VERB
ejpam-6020	135	26	to	to	PART
ejpam-6020	135	27	be	be	AUX
ejpam-6020	135	28	a	a	DET
ejpam-6020	135	29	supra	supra	ADJ
ejpam-6020	135	30	ϵ-continuous	ϵ-continuous	ADJ
ejpam-6020	135	31	(	(	PUNCT
ejpam-6020	135	32	abbreviate	abbreviate	NOUN
ejpam-6020	135	33	:	:	PUNCT
ejpam-6020	135	34	supra	supra	ADJ
ejpam-6020	135	35	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	135	36	)	)	PUNCT
ejpam-6020	136	1	if	if	SCONJ
ejpam-6020	136	2	π−1	π−1	PROPN
ejpam-6020	136	3	ϵ	ϵ	X
ejpam-6020	136	4	(	(	PUNCT
ejpam-6020	136	5	g	g	NOUN
ejpam-6020	136	6	)	)	PUNCT
ejpam-6020	136	7	∈	∈	PROPN
ejpam-6020	136	8	soϵ(λ1	soϵ(λ1	NOUN
ejpam-6020	136	9	)	)	PUNCT
ejpam-6020	136	10	for	for	ADP
ejpam-6020	136	11	each	each	DET
ejpam-6020	136	12	g	g	PROPN
ejpam-6020	136	13	∈	∈	PROPN
ejpam-6020	136	14	ν2	ν2	NOUN
ejpam-6020	136	15	.	.	PUNCT
ejpam-6020	136	16	a.	a.	PROPN
ejpam-6020	136	17	m.	m.	PROPN
ejpam-6020	136	18	abd	abd	PROPN
ejpam-6020	136	19	el	el	PROPN
ejpam-6020	136	20	-	-	PROPN
ejpam-6020	136	21	latif	latif	PROPN
ejpam-6020	136	22	et	et	PROPN
ejpam-6020	136	23	al	al	PROPN
ejpam-6020	136	24	.	.	PUNCT
ejpam-6020	136	25	/	/	SYM
ejpam-6020	136	26	eur	eur	PROPN
ejpam-6020	136	27	.	.	PUNCT
ejpam-6020	137	1	j.	j.	PROPN
ejpam-6020	137	2	pure	pure	PROPN
ejpam-6020	137	3	appl	appl	PROPN
ejpam-6020	137	4	.	.	PROPN
ejpam-6020	137	5	math	math	PROPN
ejpam-6020	137	6	,	,	PUNCT
ejpam-6020	137	7	18	18	NUM
ejpam-6020	137	8	(	(	PUNCT
ejpam-6020	137	9	2	2	NUM
ejpam-6020	137	10	)	)	PUNCT
ejpam-6020	137	11	(	(	PUNCT
ejpam-6020	137	12	2025	2025	NUM
ejpam-6020	137	13	)	)	PUNCT
ejpam-6020	137	14	,	,	PUNCT
ejpam-6020	137	15	6020	6020	NUM
ejpam-6020	137	16	6	6	NUM
ejpam-6020	137	17	of	of	ADP
ejpam-6020	137	18	17	17	NUM
ejpam-6020	137	19	theorem	theorem	NOUN
ejpam-6020	137	20	6	6	NUM
ejpam-6020	137	21	.	.	PUNCT
ejpam-6020	138	1	every	every	DET
ejpam-6020	138	2	supra	supra	NOUN
ejpam-6020	138	3	(	(	PUNCT
ejpam-6020	138	4	respectively	respectively	ADV
ejpam-6020	138	5	,	,	PUNCT
ejpam-6020	138	6	semi-	semi-	ADJ
ejpam-6020	138	7	,	,	PUNCT
ejpam-6020	138	8	α-	α-	X
ejpam-6020	138	9	,	,	PUNCT
ejpam-6020	138	10	b-	b-	X
ejpam-6020	138	11	,	,	PUNCT
ejpam-6020	138	12	pre	pre	ADJ
ejpam-6020	138	13	,	,	PUNCT
ejpam-6020	138	14	regular	regular	ADJ
ejpam-6020	138	15	,	,	PUNCT
ejpam-6020	138	16	β-	β-	X
ejpam-6020	138	17	,	,	PUNCT
ejpam-6020	138	18	and	and	CCONJ
ejpam-6020	138	19	r-	r-	X
ejpam-6020	138	20	)	)	PUNCT
ejpam-6020	138	21	cts	cts	PROPN
ejpam-6020	138	22	function	function	NOUN
ejpam-6020	138	23	is	be	AUX
ejpam-6020	138	24	supra	supra	ADJ
ejpam-6020	138	25	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	138	26	.	.	PUNCT
ejpam-6020	139	1	proof	proof	NOUN
ejpam-6020	139	2	.	.	PUNCT
ejpam-6020	140	1	it	it	PRON
ejpam-6020	140	2	is	be	AUX
ejpam-6020	140	3	inferred	infer	VERB
ejpam-6020	140	4	from	from	ADP
ejpam-6020	140	5	theorem	theorem	ADJ
ejpam-6020	140	6	2	2	NUM
ejpam-6020	140	7	.	.	NOUN
ejpam-6020	140	8	remark	remark	NOUN
ejpam-6020	140	9	1	1	NUM
ejpam-6020	140	10	.	.	PUNCT
ejpam-6020	141	1	in	in	ADP
ejpam-6020	141	2	general	general	ADJ
ejpam-6020	141	3	,	,	PUNCT
ejpam-6020	141	4	the	the	DET
ejpam-6020	141	5	following	follow	VERB
ejpam-6020	141	6	example	example	NOUN
ejpam-6020	141	7	demonstrates	demonstrate	VERB
ejpam-6020	141	8	that	that	SCONJ
ejpam-6020	141	9	the	the	DET
ejpam-6020	141	10	contrary	contrary	NOUN
ejpam-6020	141	11	of	of	ADP
ejpam-6020	141	12	theorem	theorem	NOUN
ejpam-6020	141	13	6	6	NUM
ejpam-6020	141	14	is	be	AUX
ejpam-6020	141	15	not	not	PART
ejpam-6020	141	16	valid	valid	ADJ
ejpam-6020	141	17	.	.	PUNCT
ejpam-6020	142	1	example	example	NOUN
ejpam-6020	143	1	1	1	NUM
ejpam-6020	143	2	.	.	X
ejpam-6020	143	3	consider	consider	VERB
ejpam-6020	143	4	the	the	DET
ejpam-6020	143	5	two	two	NUM
ejpam-6020	143	6	topologies	topology	NOUN
ejpam-6020	143	7	ν1	ν1	NOUN
ejpam-6020	143	8	=	=	SYM
ejpam-6020	143	9	{	{	PUNCT
ejpam-6020	143	10	∅	∅	NOUN
ejpam-6020	143	11	,	,	PUNCT
ejpam-6020	143	12	a	a	DET
ejpam-6020	143	13	⊆	⊆	NUM
ejpam-6020	143	14	r	r	NOUN
ejpam-6020	143	15	:	:	PUNCT
ejpam-6020	143	16	−1	−1	NOUN
ejpam-6020	143	17	∈	∈	PROPN
ejpam-6020	143	18	a	a	PRON
ejpam-6020	143	19	}	}	PUNCT
ejpam-6020	143	20	,	,	PUNCT
ejpam-6020	143	21	ν2	ν2	NOUN
ejpam-6020	143	22	=	=	SYM
ejpam-6020	143	23	{	{	PUNCT
ejpam-6020	143	24	∅,r	∅,r	PROPN
ejpam-6020	143	25	,	,	PUNCT
ejpam-6020	143	26	n	n	CCONJ
ejpam-6020	143	27	}	}	PUNCT
ejpam-6020	143	28	and	and	CCONJ
ejpam-6020	143	29	λ	λ	X
ejpam-6020	143	30	=	=	SYM
ejpam-6020	143	31	{	{	PUNCT
ejpam-6020	143	32	∅	∅	NOUN
ejpam-6020	143	33	,	,	PUNCT
ejpam-6020	143	34	t	t	PROPN
ejpam-6020	143	35	⊆	⊆	NUM
ejpam-6020	143	36	r	r	NOUN
ejpam-6020	143	37	:	:	PUNCT
ejpam-6020	143	38	−1	−1	NOUN
ejpam-6020	143	39	∈	∈	PROPN
ejpam-6020	143	40	t	t	NOUN
ejpam-6020	143	41	or	or	CCONJ
ejpam-6020	143	42	0	0	NUM
ejpam-6020	143	43	∈	∈	PROPN
ejpam-6020	143	44	t	t	PROPN
ejpam-6020	143	45	}	}	PUNCT
ejpam-6020	143	46	be	be	AUX
ejpam-6020	143	47	an	an	DET
ejpam-6020	143	48	associated	associate	VERB
ejpam-6020	143	49	sts	st	NOUN
ejpam-6020	143	50	with	with	ADP
ejpam-6020	143	51	ν1	ν1	NOUN
ejpam-6020	143	52	on	on	ADP
ejpam-6020	143	53	the	the	DET
ejpam-6020	143	54	set	set	NOUN
ejpam-6020	143	55	of	of	ADP
ejpam-6020	143	56	real	real	ADJ
ejpam-6020	143	57	numbers	number	NOUN
ejpam-6020	143	58	r.	r.	X
ejpam-6020	143	59	consider	consider	VERB
ejpam-6020	143	60	the	the	DET
ejpam-6020	143	61	identity	identity	NOUN
ejpam-6020	143	62	function	function	NOUN
ejpam-6020	143	63	πϵ	πϵ	X
ejpam-6020	143	64	:	:	PUNCT
ejpam-6020	143	65	(	(	PUNCT
ejpam-6020	143	66	r	r	NOUN
ejpam-6020	143	67	,	,	PUNCT
ejpam-6020	143	68	ν1	ν1	NOUN
ejpam-6020	143	69	)	)	PUNCT
ejpam-6020	143	70	→	→	SYM
ejpam-6020	143	71	(	(	PUNCT
ejpam-6020	143	72	r	r	NOUN
ejpam-6020	143	73	,	,	PUNCT
ejpam-6020	143	74	ν2	ν2	NOUN
ejpam-6020	143	75	)	)	PUNCT
ejpam-6020	143	76	.	.	PUNCT
ejpam-6020	144	1	regarding	regard	VERB
ejpam-6020	144	2	the	the	DET
ejpam-6020	144	3	set	set	NOUN
ejpam-6020	144	4	of	of	ADP
ejpam-6020	144	5	natural	natural	ADJ
ejpam-6020	144	6	numbers	number	NOUN
ejpam-6020	144	7	n	n	CCONJ
ejpam-6020	144	8	,	,	PUNCT
ejpam-6020	144	9	we	we	PRON
ejpam-6020	144	10	have	have	VERB
ejpam-6020	144	11	π−1	π−1	PROPN
ejpam-6020	144	12	ϵ	ϵ	X
ejpam-6020	144	13	(	(	PUNCT
ejpam-6020	144	14	n	n	CCONJ
ejpam-6020	144	15	)	)	PUNCT
ejpam-6020	144	16	=	=	PRON
ejpam-6020	145	1	n	n	X
ejpam-6020	145	2	is	be	AUX
ejpam-6020	145	3	a	a	DET
ejpam-6020	145	4	supra	supra	PROPN
ejpam-6020	145	5	ϵ-open	ϵ-open	PROPN
ejpam-6020	145	6	subset	subset	NOUN
ejpam-6020	145	7	of	of	ADP
ejpam-6020	145	8	r	r	NOUN
ejpam-6020	145	9	,	,	PUNCT
ejpam-6020	145	10	but	but	CCONJ
ejpam-6020	145	11	it	it	PRON
ejpam-6020	145	12	is	be	AUX
ejpam-6020	145	13	not	not	PART
ejpam-6020	145	14	supra	supra	ADJ
ejpam-6020	145	15	r	r	NOUN
ejpam-6020	145	16	-	-	NOUN
ejpam-6020	145	17	open	open	ADJ
ejpam-6020	145	18	.	.	PUNCT
ejpam-6020	146	1	hence	hence	ADV
ejpam-6020	146	2	,	,	PUNCT
ejpam-6020	146	3	πϵ	πϵ	INTJ
ejpam-6020	146	4	is	be	AUX
ejpam-6020	146	5	supra	supra	ADJ
ejpam-6020	146	6	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	146	7	,	,	PUNCT
ejpam-6020	146	8	but	but	CCONJ
ejpam-6020	146	9	it	it	PRON
ejpam-6020	146	10	is	be	AUX
ejpam-6020	146	11	not	not	PART
ejpam-6020	146	12	supra	supra	ADJ
ejpam-6020	146	13	r	r	PROPN
ejpam-6020	146	14	-	-	PUNCT
ejpam-6020	146	15	cts	cts	PROPN
ejpam-6020	146	16	.	.	PUNCT
ejpam-6020	147	1	theorem	theorem	NOUN
ejpam-6020	147	2	7	7	NUM
ejpam-6020	147	3	.	.	PUNCT
ejpam-6020	148	1	let	let	VERB
ejpam-6020	148	2	πϵ	πϵ	INTJ
ejpam-6020	148	3	:	:	PUNCT
ejpam-6020	148	4	(	(	PUNCT
ejpam-6020	148	5	λ1	λ1	ADJ
ejpam-6020	148	6	,	,	PUNCT
ejpam-6020	148	7	ν1	ν1	NOUN
ejpam-6020	148	8	)	)	PUNCT
ejpam-6020	148	9	→	→	SYM
ejpam-6020	148	10	(	(	PUNCT
ejpam-6020	148	11	λ2	λ2	NOUN
ejpam-6020	148	12	,	,	PUNCT
ejpam-6020	148	13	ν2	ν2	NOUN
ejpam-6020	148	14	)	)	PUNCT
ejpam-6020	148	15	be	be	VERB
ejpam-6020	148	16	a	a	DET
ejpam-6020	148	17	function	function	NOUN
ejpam-6020	148	18	with	with	ADP
ejpam-6020	148	19	ϑ1	ϑ1	PROPN
ejpam-6020	148	20	as	as	ADP
ejpam-6020	148	21	an	an	DET
ejpam-6020	148	22	associated	associate	VERB
ejpam-6020	148	23	sts	st	NOUN
ejpam-6020	148	24	with	with	ADP
ejpam-6020	148	25	ν1	ν1	NOUN
ejpam-6020	148	26	,	,	PUNCT
ejpam-6020	148	27	then	then	ADV
ejpam-6020	148	28	the	the	DET
ejpam-6020	148	29	next	next	ADJ
ejpam-6020	148	30	assertions	assertion	NOUN
ejpam-6020	148	31	are	be	AUX
ejpam-6020	148	32	equivalent	equivalent	ADJ
ejpam-6020	148	33	:	:	PUNCT
ejpam-6020	148	34	(	(	PUNCT
ejpam-6020	148	35	1	1	X
ejpam-6020	148	36	)	)	PUNCT
ejpam-6020	148	37	πϵ	πϵ	X
ejpam-6020	148	38	is	be	AUX
ejpam-6020	148	39	supra	supra	ADJ
ejpam-6020	148	40	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	148	41	.	.	PUNCT
ejpam-6020	149	1	(	(	PUNCT
ejpam-6020	149	2	2	2	X
ejpam-6020	149	3	)	)	PUNCT
ejpam-6020	149	4	for	for	ADP
ejpam-6020	149	5	each	each	DET
ejpam-6020	149	6	z	z	PROPN
ejpam-6020	149	7	∈	∈	PROPN
ejpam-6020	149	8	νc2	νc2	PROPN
ejpam-6020	149	9	,	,	PUNCT
ejpam-6020	149	10	π	π	PROPN
ejpam-6020	149	11	−1	−1	NOUN
ejpam-6020	149	12	ϵ	ϵ	X
ejpam-6020	149	13	(	(	PUNCT
ejpam-6020	149	14	z	z	NOUN
ejpam-6020	149	15	)	)	PUNCT
ejpam-6020	149	16	∈	∈	PROPN
ejpam-6020	149	17	scϵ(λ1	scϵ(λ1	PROPN
ejpam-6020	149	18	)	)	PUNCT
ejpam-6020	149	19	.	.	PUNCT
ejpam-6020	150	1	(	(	PUNCT
ejpam-6020	150	2	3	3	X
ejpam-6020	150	3	)	)	PUNCT
ejpam-6020	150	4	clsϵ(π	clsϵ(π	NOUN
ejpam-6020	150	5	−1	−1	NOUN
ejpam-6020	150	6	ϵ	ϵ	X
ejpam-6020	150	7	(	(	PUNCT
ejpam-6020	150	8	z	z	NOUN
ejpam-6020	150	9	)	)	PUNCT
ejpam-6020	150	10	)	)	PUNCT
ejpam-6020	151	1	⊆	⊆	NUM
ejpam-6020	151	2	π−1	π−1	PROPN
ejpam-6020	151	3	ϵ	ϵ	X
ejpam-6020	151	4	(	(	PUNCT
ejpam-6020	151	5	cl(z	cl(z	NOUN
ejpam-6020	151	6	)	)	PUNCT
ejpam-6020	151	7	)	)	PUNCT
ejpam-6020	151	8	∀	∀	X
ejpam-6020	152	1	z	z	NOUN
ejpam-6020	152	2	⊆	⊆	NUM
ejpam-6020	152	3	λ2	λ2	NOUN
ejpam-6020	152	4	.	.	PUNCT
ejpam-6020	153	1	(	(	PUNCT
ejpam-6020	153	2	4	4	X
ejpam-6020	153	3	)	)	PUNCT
ejpam-6020	153	4	πϵ(cl	πϵ(cl	NOUN
ejpam-6020	153	5	s	s	PART
ejpam-6020	153	6	ϵ(y	ϵ(y	PROPN
ejpam-6020	153	7	)	)	PUNCT
ejpam-6020	153	8	)	)	PUNCT
ejpam-6020	154	1	⊆	⊆	NUM
ejpam-6020	154	2	cl(πϵ(y	cl(πϵ(y	NOUN
ejpam-6020	154	3	)	)	PUNCT
ejpam-6020	154	4	)	)	PUNCT
ejpam-6020	154	5	∀	∀	X
ejpam-6020	155	1	y	y	PROPN
ejpam-6020	155	2	⊆	⊆	NUM
ejpam-6020	155	3	λ1	λ1	PROPN
ejpam-6020	155	4	.	.	PUNCT
ejpam-6020	156	1	(	(	PUNCT
ejpam-6020	156	2	5	5	NUM
ejpam-6020	156	3	)	)	PUNCT
ejpam-6020	156	4	π−1	π−1	PROPN
ejpam-6020	156	5	ϵ	ϵ	X
ejpam-6020	156	6	(	(	PUNCT
ejpam-6020	156	7	int(z	int(z	PROPN
ejpam-6020	156	8	)	)	PUNCT
ejpam-6020	156	9	)	)	PUNCT
ejpam-6020	157	1	⊆	⊆	NUM
ejpam-6020	157	2	intsϵ(π	intsϵ(π	PROPN
ejpam-6020	157	3	−1	−1	NOUN
ejpam-6020	157	4	ϵ	ϵ	X
ejpam-6020	157	5	(	(	PUNCT
ejpam-6020	157	6	z	z	NOUN
ejpam-6020	157	7	)	)	PUNCT
ejpam-6020	157	8	)	)	PUNCT
ejpam-6020	157	9	∀	∀	X
ejpam-6020	158	1	z	z	NOUN
ejpam-6020	158	2	⊆	⊆	NUM
ejpam-6020	158	3	λ2	λ2	NOUN
ejpam-6020	158	4	.	.	PUNCT
ejpam-6020	159	1	proof	proof	NOUN
ejpam-6020	159	2	.	.	PUNCT
ejpam-6020	160	1	(	(	PUNCT
ejpam-6020	160	2	1	1	X
ejpam-6020	160	3	)	)	PUNCT
ejpam-6020	160	4	⇒	⇒	NOUN
ejpam-6020	160	5	(	(	PUNCT
ejpam-6020	160	6	2	2	X
ejpam-6020	160	7	)	)	PUNCT
ejpam-6020	160	8	let	let	VERB
ejpam-6020	160	9	z	z	NOUN
ejpam-6020	160	10	∈	∈	PROPN
ejpam-6020	160	11	νc2	νc2	PROPN
ejpam-6020	160	12	,	,	PUNCT
ejpam-6020	160	13	then	then	ADV
ejpam-6020	160	14	z	z	NOUN
ejpam-6020	160	15	c	c	PROPN
ejpam-6020	160	16	∈	∈	PROPN
ejpam-6020	160	17	ν2	ν2	NOUN
ejpam-6020	160	18	.	.	PUNCT
ejpam-6020	161	1	given	give	VERB
ejpam-6020	161	2	(	(	PUNCT
ejpam-6020	161	3	1	1	NUM
ejpam-6020	161	4	)	)	PUNCT
ejpam-6020	161	5	,	,	PUNCT
ejpam-6020	161	6	π−1	π−1	PROPN
ejpam-6020	161	7	ϵ	ϵ	X
ejpam-6020	161	8	(	(	PUNCT
ejpam-6020	161	9	zc	zc	INTJ
ejpam-6020	161	10	)	)	PUNCT
ejpam-6020	161	11	=	=	PUNCT
ejpam-6020	162	1	[	[	X
ejpam-6020	162	2	π−1	π−1	NOUN
ejpam-6020	162	3	ϵ	ϵ	X
ejpam-6020	162	4	(	(	PUNCT
ejpam-6020	162	5	z)]c	z)]c	PROPN
ejpam-6020	162	6	∈	∈	PROPN
ejpam-6020	162	7	soϵ(λ1	soϵ(λ1	NOUN
ejpam-6020	162	8	)	)	PUNCT
ejpam-6020	162	9	.	.	PUNCT
ejpam-6020	163	1	hence	hence	ADV
ejpam-6020	163	2	,	,	PUNCT
ejpam-6020	163	3	π−1	π−1	PROPN
ejpam-6020	163	4	ϵ	ϵ	X
ejpam-6020	163	5	(	(	PUNCT
ejpam-6020	163	6	z	z	NOUN
ejpam-6020	163	7	)	)	PUNCT
ejpam-6020	163	8	∈	∈	PROPN
ejpam-6020	163	9	scϵ(λ1	scϵ(λ1	PROPN
ejpam-6020	163	10	)	)	PUNCT
ejpam-6020	163	11	.	.	PUNCT
ejpam-6020	164	1	(	(	PUNCT
ejpam-6020	164	2	2	2	X
ejpam-6020	164	3	)	)	PUNCT
ejpam-6020	164	4	⇒	⇒	NOUN
ejpam-6020	164	5	(	(	PUNCT
ejpam-6020	164	6	3	3	X
ejpam-6020	164	7	)	)	PUNCT
ejpam-6020	164	8	let	let	VERB
ejpam-6020	164	9	z	z	NOUN
ejpam-6020	164	10	⊆	⊆	NUM
ejpam-6020	164	11	λ2	λ2	NOUN
ejpam-6020	164	12	.	.	PUNCT
ejpam-6020	165	1	since	since	SCONJ
ejpam-6020	165	2	cl(z	cl(z	NOUN
ejpam-6020	165	3	)	)	PUNCT
ejpam-6020	165	4	∈	∈	NOUN
ejpam-6020	165	5	νc2	νc2	NOUN
ejpam-6020	165	6	and	and	CCONJ
ejpam-6020	165	7	given	give	VERB
ejpam-6020	165	8	(	(	PUNCT
ejpam-6020	165	9	2	2	NUM
ejpam-6020	165	10	)	)	PUNCT
ejpam-6020	165	11	,	,	PUNCT
ejpam-6020	165	12	π−1	π−1	PROPN
ejpam-6020	165	13	ϵ	ϵ	X
ejpam-6020	165	14	(	(	PUNCT
ejpam-6020	165	15	z	z	NOUN
ejpam-6020	165	16	)	)	PUNCT
ejpam-6020	165	17	∈	∈	PROPN
ejpam-6020	165	18	scϵ(λ1	scϵ(λ1	PROPN
ejpam-6020	165	19	)	)	PUNCT
ejpam-6020	165	20	,	,	PUNCT
ejpam-6020	165	21	which	which	PRON
ejpam-6020	165	22	implies	imply	VERB
ejpam-6020	165	23	clsϵ(π	clsϵ(π	PROPN
ejpam-6020	165	24	−1	−1	NOUN
ejpam-6020	165	25	ϵ	ϵ	PROPN
ejpam-6020	165	26	(	(	PUNCT
ejpam-6020	165	27	z	z	NOUN
ejpam-6020	165	28	)	)	PUNCT
ejpam-6020	165	29	)	)	PUNCT
ejpam-6020	166	1	⊆	⊆	NUM
ejpam-6020	166	2	clsϵ(π	clsϵ(π	NUM
ejpam-6020	166	3	−1	−1	NOUN
ejpam-6020	166	4	ϵ	ϵ	X
ejpam-6020	166	5	(	(	PUNCT
ejpam-6020	166	6	cl(z	cl(z	NOUN
ejpam-6020	166	7	)	)	PUNCT
ejpam-6020	166	8	)	)	PUNCT
ejpam-6020	166	9	)	)	PUNCT
ejpam-6020	167	1	=	=	PUNCT
ejpam-6020	167	2	π−1	π−1	PROPN
ejpam-6020	167	3	ϵ	ϵ	X
ejpam-6020	167	4	(	(	PUNCT
ejpam-6020	167	5	cl(z	cl(z	NOUN
ejpam-6020	167	6	)	)	PUNCT
ejpam-6020	167	7	)	)	PUNCT
ejpam-6020	167	8	.	.	PUNCT
ejpam-6020	168	1	consequently	consequently	ADV
ejpam-6020	168	2	,	,	PUNCT
ejpam-6020	168	3	the	the	DET
ejpam-6020	168	4	proof	proof	NOUN
ejpam-6020	168	5	is	be	AUX
ejpam-6020	168	6	acquired	acquire	VERB
ejpam-6020	168	7	.	.	PUNCT
ejpam-6020	169	1	(	(	PUNCT
ejpam-6020	169	2	3	3	X
ejpam-6020	169	3	)	)	PUNCT
ejpam-6020	169	4	⇒	⇒	NOUN
ejpam-6020	169	5	(	(	PUNCT
ejpam-6020	169	6	4	4	NUM
ejpam-6020	169	7	)	)	PUNCT
ejpam-6020	169	8	regarding	regard	VERB
ejpam-6020	169	9	πϵ(y	πϵ(y	NUM
ejpam-6020	169	10	)	)	PUNCT
ejpam-6020	169	11	⊆	⊆	NUM
ejpam-6020	169	12	λ2	λ2	NOUN
ejpam-6020	169	13	for	for	ADP
ejpam-6020	169	14	a	a	DET
ejpam-6020	169	15	subset	subset	NOUN
ejpam-6020	169	16	y	y	PROPN
ejpam-6020	169	17	⊆	⊆	NUM
ejpam-6020	169	18	λ1	λ1	PROPN
ejpam-6020	169	19	,	,	PUNCT
ejpam-6020	169	20	we	we	PRON
ejpam-6020	169	21	have	have	VERB
ejpam-6020	169	22	y	y	PROPN
ejpam-6020	169	23	⊆	⊆	NUM
ejpam-6020	169	24	π−1	π−1	PROPN
ejpam-6020	169	25	ϵ	ϵ	X
ejpam-6020	169	26	(	(	PUNCT
ejpam-6020	169	27	πϵ(y	πϵ(y	NOUN
ejpam-6020	169	28	)	)	PUNCT
ejpam-6020	169	29	)	)	PUNCT
ejpam-6020	169	30	.	.	PUNCT
ejpam-6020	170	1	given	give	VERB
ejpam-6020	170	2	(	(	PUNCT
ejpam-6020	170	3	3	3	NUM
ejpam-6020	170	4	)	)	PUNCT
ejpam-6020	170	5	,	,	PUNCT
ejpam-6020	170	6	we	we	PRON
ejpam-6020	170	7	obtain	obtain	VERB
ejpam-6020	170	8	clsϵ(π	clsϵ(π	PROPN
ejpam-6020	170	9	−1	−1	NOUN
ejpam-6020	170	10	ϵ	ϵ	PROPN
ejpam-6020	170	11	(	(	PUNCT
ejpam-6020	170	12	πϵ(y	πϵ(y	NOUN
ejpam-6020	170	13	)	)	PUNCT
ejpam-6020	170	14	)	)	PUNCT
ejpam-6020	170	15	)	)	PUNCT
ejpam-6020	171	1	⊆	⊆	NUM
ejpam-6020	171	2	π−1	π−1	PROPN
ejpam-6020	171	3	ϵ	ϵ	X
ejpam-6020	171	4	(	(	PUNCT
ejpam-6020	171	5	cl(πϵ(y	cl(πϵ(y	PROPN
ejpam-6020	171	6	)	)	PUNCT
ejpam-6020	171	7	)	)	PUNCT
ejpam-6020	171	8	)	)	PUNCT
ejpam-6020	171	9	.	.	PUNCT
ejpam-6020	172	1	hence	hence	ADV
ejpam-6020	172	2	,	,	PUNCT
ejpam-6020	172	3	πϵ[cl	πϵ[cl	PROPN
ejpam-6020	172	4	s	s	PART
ejpam-6020	172	5	ϵ(π	ϵ(π	PROPN
ejpam-6020	172	6	−1	−1	NOUN
ejpam-6020	172	7	ϵ	ϵ	X
ejpam-6020	172	8	(	(	PUNCT
ejpam-6020	172	9	πϵ(y	πϵ(y	NOUN
ejpam-6020	172	10	)	)	PUNCT
ejpam-6020	172	11	)	)	PUNCT
ejpam-6020	172	12	)	)	PUNCT
ejpam-6020	172	13	]	]	PUNCT
ejpam-6020	173	1	⊆	⊆	NUM
ejpam-6020	173	2	πϵ[π	πϵ[π	NOUN
ejpam-6020	173	3	−1	−1	NOUN
ejpam-6020	173	4	ϵ	ϵ	X
ejpam-6020	173	5	(	(	PUNCT
ejpam-6020	173	6	cl(πϵ(y	cl(πϵ(y	PROPN
ejpam-6020	173	7	)	)	PUNCT
ejpam-6020	173	8	)	)	PUNCT
ejpam-6020	173	9	)	)	PUNCT
ejpam-6020	173	10	]	]	PUNCT
ejpam-6020	174	1	⊆	⊆	NUM
ejpam-6020	174	2	cl(πϵ(y	cl(πϵ(y	NOUN
ejpam-6020	174	3	)	)	PUNCT
ejpam-6020	174	4	)	)	PUNCT
ejpam-6020	174	5	.	.	PUNCT
ejpam-6020	175	1	therefore	therefore	ADV
ejpam-6020	175	2	,	,	PUNCT
ejpam-6020	175	3	πϵ(cl	πϵ(cl	PROPN
ejpam-6020	175	4	s	s	PART
ejpam-6020	175	5	ϵ(y	ϵ(y	PROPN
ejpam-6020	175	6	)	)	PUNCT
ejpam-6020	175	7	)	)	PUNCT
ejpam-6020	176	1	⊆	⊆	NUM
ejpam-6020	176	2	cl(πϵ(y	cl(πϵ(y	NOUN
ejpam-6020	176	3	)	)	PUNCT
ejpam-6020	176	4	)	)	PUNCT
ejpam-6020	176	5	.	.	PUNCT
ejpam-6020	177	1	a.	a.	PROPN
ejpam-6020	177	2	m.	m.	PROPN
ejpam-6020	177	3	abd	abd	PROPN
ejpam-6020	177	4	el	el	PROPN
ejpam-6020	177	5	-	-	PROPN
ejpam-6020	177	6	latif	latif	PROPN
ejpam-6020	177	7	et	et	PROPN
ejpam-6020	177	8	al	al	PROPN
ejpam-6020	177	9	.	.	PUNCT
ejpam-6020	177	10	/	/	SYM
ejpam-6020	177	11	eur	eur	PROPN
ejpam-6020	177	12	.	.	PUNCT
ejpam-6020	178	1	j.	j.	PROPN
ejpam-6020	178	2	pure	pure	PROPN
ejpam-6020	178	3	appl	appl	PROPN
ejpam-6020	178	4	.	.	PROPN
ejpam-6020	178	5	math	math	PROPN
ejpam-6020	178	6	,	,	PUNCT
ejpam-6020	178	7	18	18	NUM
ejpam-6020	178	8	(	(	PUNCT
ejpam-6020	178	9	2	2	NUM
ejpam-6020	178	10	)	)	PUNCT
ejpam-6020	178	11	(	(	PUNCT
ejpam-6020	178	12	2025	2025	NUM
ejpam-6020	178	13	)	)	PUNCT
ejpam-6020	178	14	,	,	PUNCT
ejpam-6020	178	15	6020	6020	NUM
ejpam-6020	178	16	7	7	NUM
ejpam-6020	178	17	of	of	ADP
ejpam-6020	178	18	17	17	NUM
ejpam-6020	178	19	(	(	PUNCT
ejpam-6020	178	20	4	4	NUM
ejpam-6020	178	21	)	)	PUNCT
ejpam-6020	178	22	⇒	⇒	NOUN
ejpam-6020	178	23	(	(	PUNCT
ejpam-6020	178	24	5	5	NUM
ejpam-6020	178	25	)	)	PUNCT
ejpam-6020	178	26	regarding	regard	VERB
ejpam-6020	178	27	π−1	π−1	PROPN
ejpam-6020	178	28	ϵ	ϵ	PROPN
ejpam-6020	178	29	(	(	PUNCT
ejpam-6020	178	30	zc	zc	INTJ
ejpam-6020	178	31	)	)	PUNCT
ejpam-6020	178	32	⊆	⊆	NUM
ejpam-6020	178	33	λ1	λ1	PROPN
ejpam-6020	178	34	for	for	ADP
ejpam-6020	178	35	a	a	DET
ejpam-6020	178	36	subset	subset	NOUN
ejpam-6020	178	37	zc	zc	NOUN
ejpam-6020	178	38	⊆	⊆	NUM
ejpam-6020	178	39	λ2	λ2	NOUN
ejpam-6020	178	40	,	,	PUNCT
ejpam-6020	178	41	and	and	CCONJ
ejpam-6020	178	42	by	by	ADP
ejpam-6020	178	43	utilizing	utilize	VERB
ejpam-6020	178	44	(	(	PUNCT
ejpam-6020	178	45	4	4	NUM
ejpam-6020	178	46	)	)	PUNCT
ejpam-6020	178	47	,	,	PUNCT
ejpam-6020	178	48	we	we	PRON
ejpam-6020	178	49	obtain	obtain	VERB
ejpam-6020	178	50	that	that	PRON
ejpam-6020	178	51	πϵ[cl	πϵ[cl	PROPN
ejpam-6020	178	52	s	s	PART
ejpam-6020	178	53	ϵ	ϵ	X
ejpam-6020	179	1	[	[	X
ejpam-6020	179	2	π	π	X
ejpam-6020	179	3	−1	−1	NOUN
ejpam-6020	179	4	ϵ	ϵ	X
ejpam-6020	179	5	(	(	PUNCT
ejpam-6020	179	6	zc	zc	NOUN
ejpam-6020	179	7	)	)	PUNCT
ejpam-6020	179	8	]	]	PUNCT
ejpam-6020	179	9	]	]	X
ejpam-6020	179	10	⊆	⊆	NUM
ejpam-6020	179	11	cl(πϵ[π	cl(πϵ[π	NUM
ejpam-6020	179	12	−1	−1	NOUN
ejpam-6020	179	13	ϵ	ϵ	X
ejpam-6020	179	14	(	(	PUNCT
ejpam-6020	179	15	zc	zc	NOUN
ejpam-6020	179	16	)	)	PUNCT
ejpam-6020	179	17	]	]	PUNCT
ejpam-6020	179	18	)	)	PUNCT
ejpam-6020	179	19	⊆	⊆	NUM
ejpam-6020	179	20	cl(zc	cl(zc	NOUN
ejpam-6020	179	21	)	)	PUNCT
ejpam-6020	179	22	=	=	PUNCT
ejpam-6020	180	1	[	[	X
ejpam-6020	180	2	int(z)]c	int(z)]c	X
ejpam-6020	180	3	,	,	PUNCT
ejpam-6020	180	4	from	from	ADP
ejpam-6020	180	5	theorem	theorem	NOUN
ejpam-6020	180	6	5	5	NUM
ejpam-6020	180	7	.	.	PUNCT
ejpam-6020	180	8	hence	hence	ADV
ejpam-6020	180	9	,	,	PUNCT
ejpam-6020	180	10	π−1	π−1	PROPN
ejpam-6020	180	11	ϵ	ϵ	X
ejpam-6020	181	1	[	[	X
ejpam-6020	181	2	πϵ(cl	πϵ(cl	X
ejpam-6020	181	3	s	s	X
ejpam-6020	181	4	ϵ	ϵ	X
ejpam-6020	182	1	[	[	X
ejpam-6020	182	2	π	π	X
ejpam-6020	182	3	−1	−1	NOUN
ejpam-6020	182	4	ϵ	ϵ	X
ejpam-6020	182	5	(	(	PUNCT
ejpam-6020	182	6	zc	zc	NOUN
ejpam-6020	182	7	)	)	PUNCT
ejpam-6020	182	8	]	]	PUNCT
ejpam-6020	182	9	)	)	PUNCT
ejpam-6020	182	10	]	]	PUNCT
ejpam-6020	183	1	⊆	⊆	NUM
ejpam-6020	183	2	π−1	π−1	PROPN
ejpam-6020	183	3	ϵ	ϵ	X
ejpam-6020	184	1	[	[	X
ejpam-6020	184	2	[	[	X
ejpam-6020	184	3	int(z)]c	int(z)]c	X
ejpam-6020	184	4	]	]	X
ejpam-6020	184	5	=	=	PUNCT
ejpam-6020	185	1	[	[	X
ejpam-6020	185	2	π−1	π−1	PROPN
ejpam-6020	185	3	ϵ	ϵ	X
ejpam-6020	185	4	(	(	PUNCT
ejpam-6020	185	5	int(z))]c	int(z))]c	NOUN
ejpam-6020	185	6	.	.	PUNCT
ejpam-6020	185	7	therefore	therefore	ADV
ejpam-6020	185	8	,	,	PUNCT
ejpam-6020	185	9	clsϵ	clsϵ	NOUN
ejpam-6020	185	10	[	[	X
ejpam-6020	185	11	(	(	PUNCT
ejpam-6020	185	12	π	π	NOUN
ejpam-6020	185	13	−1	−1	NOUN
ejpam-6020	185	14	ϵ	ϵ	X
ejpam-6020	185	15	(	(	PUNCT
ejpam-6020	185	16	z))]c	z))]c	NUM
ejpam-6020	185	17	⊆	⊆	NUM
ejpam-6020	185	18	[	[	X
ejpam-6020	185	19	π−1	π−1	PROPN
ejpam-6020	185	20	ϵ	ϵ	X
ejpam-6020	185	21	(	(	PUNCT
ejpam-6020	185	22	int(z))]c	int(z))]c	NOUN
ejpam-6020	185	23	.	.	PUNCT
ejpam-6020	186	1	thus	thus	ADV
ejpam-6020	186	2	,	,	PUNCT
ejpam-6020	186	3	π−1	π−1	PROPN
ejpam-6020	186	4	ϵ	ϵ	X
ejpam-6020	186	5	(	(	PUNCT
ejpam-6020	186	6	int(z	int(z	PROPN
ejpam-6020	186	7	)	)	PUNCT
ejpam-6020	186	8	)	)	PUNCT
ejpam-6020	187	1	⊆	⊆	NUM
ejpam-6020	188	1	[	[	X
ejpam-6020	188	2	clsϵ	clsϵ	NOUN
ejpam-6020	188	3	[	[	X
ejpam-6020	188	4	(	(	PUNCT
ejpam-6020	188	5	π	π	NOUN
ejpam-6020	188	6	−1	−1	NOUN
ejpam-6020	188	7	ϵ	ϵ	X
ejpam-6020	188	8	(	(	PUNCT
ejpam-6020	188	9	z))]c]c	z))]c]c	NOUN
ejpam-6020	188	10	=	=	SYM
ejpam-6020	188	11	intsϵ(π	intsϵ(π	PROPN
ejpam-6020	188	12	−1	−1	NOUN
ejpam-6020	188	13	ϵ	ϵ	X
ejpam-6020	188	14	(	(	PUNCT
ejpam-6020	188	15	z	z	NOUN
ejpam-6020	188	16	)	)	PUNCT
ejpam-6020	188	17	)	)	PUNCT
ejpam-6020	188	18	.	.	PUNCT
ejpam-6020	189	1	(	(	PUNCT
ejpam-6020	189	2	5	5	X
ejpam-6020	189	3	)	)	PUNCT
ejpam-6020	189	4	⇒	⇒	NOUN
ejpam-6020	189	5	(	(	PUNCT
ejpam-6020	189	6	1	1	NUM
ejpam-6020	189	7	)	)	PUNCT
ejpam-6020	189	8	regarding	regard	VERB
ejpam-6020	189	9	z	z	NOUN
ejpam-6020	189	10	=	=	SYM
ejpam-6020	189	11	int(z	int(z	PROPN
ejpam-6020	189	12	)	)	PUNCT
ejpam-6020	189	13	for	for	ADP
ejpam-6020	189	14	a	a	DET
ejpam-6020	189	15	supra	supra	PROPN
ejpam-6020	189	16	open	open	NOUN
ejpam-6020	189	17	set	set	VERB
ejpam-6020	189	18	z.	z.	PROPN
ejpam-6020	189	19	given	give	VERB
ejpam-6020	189	20	(	(	PUNCT
ejpam-6020	189	21	5	5	NUM
ejpam-6020	189	22	)	)	PUNCT
ejpam-6020	189	23	,	,	PUNCT
ejpam-6020	189	24	π−1	π−1	PROPN
ejpam-6020	189	25	ϵ	ϵ	X
ejpam-6020	189	26	(	(	PUNCT
ejpam-6020	189	27	z	z	NOUN
ejpam-6020	189	28	)	)	PUNCT
ejpam-6020	189	29	⊆	⊆	PROPN
ejpam-6020	189	30	intsϵ(π	intsϵ(π	PROPN
ejpam-6020	189	31	−1	−1	NOUN
ejpam-6020	189	32	ϵ	ϵ	X
ejpam-6020	189	33	(	(	PUNCT
ejpam-6020	189	34	z	z	NOUN
ejpam-6020	189	35	)	)	PUNCT
ejpam-6020	189	36	)	)	PUNCT
ejpam-6020	189	37	.	.	PUNCT
ejpam-6020	190	1	however	however	ADV
ejpam-6020	190	2	,	,	PUNCT
ejpam-6020	190	3	intsϵ(π	intsϵ(π	PROPN
ejpam-6020	190	4	−1	−1	NOUN
ejpam-6020	190	5	ϵ	ϵ	X
ejpam-6020	190	6	(	(	PUNCT
ejpam-6020	190	7	z	z	NOUN
ejpam-6020	190	8	)	)	PUNCT
ejpam-6020	190	9	)	)	PUNCT
ejpam-6020	191	1	⊆	⊆	NUM
ejpam-6020	191	2	π−1	π−1	PROPN
ejpam-6020	191	3	ϵ	ϵ	X
ejpam-6020	191	4	(	(	PUNCT
ejpam-6020	191	5	z	z	NOUN
ejpam-6020	191	6	)	)	PUNCT
ejpam-6020	191	7	.	.	PUNCT
ejpam-6020	192	1	therefore	therefore	ADV
ejpam-6020	192	2	,	,	PUNCT
ejpam-6020	192	3	intsϵ(π	intsϵ(π	PROPN
ejpam-6020	192	4	−1	−1	NOUN
ejpam-6020	192	5	ϵ	ϵ	X
ejpam-6020	192	6	(	(	PUNCT
ejpam-6020	192	7	z	z	NOUN
ejpam-6020	192	8	)	)	PUNCT
ejpam-6020	192	9	)	)	PUNCT
ejpam-6020	193	1	=	=	PUNCT
ejpam-6020	193	2	π−1	π−1	PROPN
ejpam-6020	193	3	ϵ	ϵ	X
ejpam-6020	193	4	(	(	PUNCT
ejpam-6020	193	5	z	z	NOUN
ejpam-6020	193	6	)	)	PUNCT
ejpam-6020	193	7	∈	∈	PROPN
ejpam-6020	193	8	soϵ(λ1	soϵ(λ1	NOUN
ejpam-6020	193	9	)	)	PUNCT
ejpam-6020	193	10	.	.	PUNCT
ejpam-6020	194	1	thus	thus	ADV
ejpam-6020	194	2	,	,	PUNCT
ejpam-6020	194	3	πϵ	πϵ	INTJ
ejpam-6020	194	4	is	be	AUX
ejpam-6020	194	5	a	a	DET
ejpam-6020	194	6	supra	supra	ADJ
ejpam-6020	194	7	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	194	8	.	.	PUNCT
ejpam-6020	195	1	definition	definition	NOUN
ejpam-6020	195	2	11	11	NUM
ejpam-6020	195	3	.	.	PUNCT
ejpam-6020	196	1	a	a	DET
ejpam-6020	196	2	function	function	NOUN
ejpam-6020	196	3	πϵ	πϵ	X
ejpam-6020	196	4	:	:	PUNCT
ejpam-6020	196	5	(	(	PUNCT
ejpam-6020	196	6	λ1	λ1	ADJ
ejpam-6020	196	7	,	,	PUNCT
ejpam-6020	196	8	ν1	ν1	NOUN
ejpam-6020	196	9	)	)	PUNCT
ejpam-6020	196	10	→	→	SYM
ejpam-6020	196	11	(	(	PUNCT
ejpam-6020	196	12	λ2	λ2	NOUN
ejpam-6020	196	13	,	,	PUNCT
ejpam-6020	196	14	ν2	ν2	NOUN
ejpam-6020	196	15	)	)	PUNCT
ejpam-6020	196	16	with	with	ADP
ejpam-6020	196	17	ϑ1	ϑ1	NOUN
ejpam-6020	196	18	,	,	PUNCT
ejpam-6020	196	19	ϑ2	ϑ2	PROPN
ejpam-6020	196	20	associated	associate	VERB
ejpam-6020	196	21	stss	stss	NOUN
ejpam-6020	196	22	with	with	ADP
ejpam-6020	196	23	ν1	ν1	NOUN
ejpam-6020	196	24	,	,	PUNCT
ejpam-6020	196	25	ν2	ν2	NOUN
ejpam-6020	196	26	,	,	PUNCT
ejpam-6020	196	27	respectively	respectively	ADV
ejpam-6020	196	28	,	,	PUNCT
ejpam-6020	196	29	is	be	AUX
ejpam-6020	196	30	said	say	VERB
ejpam-6020	196	31	to	to	PART
ejpam-6020	196	32	be	be	AUX
ejpam-6020	196	33	supra	supra	ADJ
ejpam-6020	196	34	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	196	35	(	(	PUNCT
ejpam-6020	196	36	supra	supra	ADJ
ejpam-6020	196	37	ϵ∗-cts	ϵ∗-ct	NOUN
ejpam-6020	196	38	)	)	PUNCT
ejpam-6020	197	1	if	if	SCONJ
ejpam-6020	197	2	π−1	π−1	PROPN
ejpam-6020	197	3	ϵ	ϵ	X
ejpam-6020	197	4	(	(	PUNCT
ejpam-6020	197	5	d	d	NOUN
ejpam-6020	197	6	)	)	PUNCT
ejpam-6020	197	7	∈	∈	PROPN
ejpam-6020	197	8	soϵ(λ1	soϵ(λ1	NOUN
ejpam-6020	197	9	)	)	PUNCT
ejpam-6020	197	10	for	for	ADP
ejpam-6020	197	11	each	each	DET
ejpam-6020	197	12	d	d	PROPN
ejpam-6020	197	13	∈	∈	PROPN
ejpam-6020	197	14	soϵ(λ2	soϵ(λ2	PROPN
ejpam-6020	197	15	)	)	PUNCT
ejpam-6020	197	16	(	(	PUNCT
ejpam-6020	197	17	d	d	PROPN
ejpam-6020	197	18	∈	∈	PROPN
ejpam-6020	197	19	ϑ2	ϑ2	PROPN
ejpam-6020	197	20	)	)	PUNCT
ejpam-6020	197	21	.	.	PUNCT
ejpam-6020	198	1	theorem	theorem	ADJ
ejpam-6020	198	2	8	8	NUM
ejpam-6020	198	3	.	.	PUNCT
ejpam-6020	199	1	(	(	PUNCT
ejpam-6020	199	2	1	1	X
ejpam-6020	199	3	)	)	PUNCT
ejpam-6020	199	4	every	every	DET
ejpam-6020	199	5	supra	supra	ADJ
ejpam-6020	199	6	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	199	7	function	function	NOUN
ejpam-6020	199	8	is	be	AUX
ejpam-6020	199	9	supra	supra	ADJ
ejpam-6020	199	10	ϵ∗-cts	ϵ∗-ct	NOUN
ejpam-6020	199	11	.	.	PUNCT
ejpam-6020	200	1	(	(	PUNCT
ejpam-6020	200	2	2	2	X
ejpam-6020	200	3	)	)	PUNCT
ejpam-6020	200	4	every	every	DET
ejpam-6020	200	5	supra	supra	ADJ
ejpam-6020	200	6	ϵ∗-cts	ϵ∗-ct	NOUN
ejpam-6020	200	7	function	function	NOUN
ejpam-6020	200	8	is	be	AUX
ejpam-6020	200	9	supra	supra	ADJ
ejpam-6020	200	10	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	200	11	.	.	PUNCT
ejpam-6020	201	1	proof	proof	NOUN
ejpam-6020	201	2	.	.	PUNCT
ejpam-6020	202	1	it	it	PRON
ejpam-6020	202	2	is	be	AUX
ejpam-6020	202	3	immediately	immediately	ADV
ejpam-6020	202	4	obvious	obvious	ADJ
ejpam-6020	202	5	from	from	ADP
ejpam-6020	202	6	theorem	theorem	ADJ
ejpam-6020	202	7	2	2	NUM
ejpam-6020	202	8	.	.	NOUN
ejpam-6020	202	9	remark	remark	NOUN
ejpam-6020	202	10	2	2	NUM
ejpam-6020	202	11	.	.	PUNCT
ejpam-6020	203	1	the	the	DET
ejpam-6020	203	2	following	follow	VERB
ejpam-6020	203	3	examples	example	NOUN
ejpam-6020	203	4	demonstrate	demonstrate	VERB
ejpam-6020	203	5	that	that	SCONJ
ejpam-6020	203	6	the	the	DET
ejpam-6020	203	7	contrary	contrary	NOUN
ejpam-6020	203	8	of	of	ADP
ejpam-6020	203	9	theorem	theorem	ADJ
ejpam-6020	203	10	8	8	NUM
ejpam-6020	203	11	is	be	AUX
ejpam-6020	203	12	generally	generally	ADV
ejpam-6020	203	13	untrue	untrue	ADJ
ejpam-6020	203	14	.	.	PUNCT
ejpam-6020	204	1	examples	example	NOUN
ejpam-6020	204	2	1	1	NUM
ejpam-6020	204	3	.	.	PUNCT
ejpam-6020	205	1	(	(	PUNCT
ejpam-6020	205	2	1	1	X
ejpam-6020	205	3	)	)	PUNCT
ejpam-6020	205	4	consider	consider	VERB
ejpam-6020	205	5	the	the	DET
ejpam-6020	205	6	two	two	NUM
ejpam-6020	205	7	topologies	topology	NOUN
ejpam-6020	205	8	ν1	ν1	NOUN
ejpam-6020	205	9	=	=	SYM
ejpam-6020	205	10	{	{	PUNCT
ejpam-6020	205	11	∅	∅	NOUN
ejpam-6020	205	12	,	,	PUNCT
ejpam-6020	205	13	a	a	DET
ejpam-6020	205	14	⊆	⊆	NUM
ejpam-6020	205	15	r	r	NOUN
ejpam-6020	205	16	:	:	PUNCT
ejpam-6020	205	17	−2	−2	PROPN
ejpam-6020	205	18	∈	∈	PROPN
ejpam-6020	205	19	a	a	X
ejpam-6020	205	20	}	}	PUNCT
ejpam-6020	205	21	,	,	PUNCT
ejpam-6020	205	22	ν2	ν2	NOUN
ejpam-6020	205	23	=	=	SYM
ejpam-6020	205	24	{	{	PUNCT
ejpam-6020	205	25	∅,r	∅,r	PROPN
ejpam-6020	205	26	,	,	PUNCT
ejpam-6020	205	27	n	n	CCONJ
ejpam-6020	205	28	}	}	PUNCT
ejpam-6020	205	29	}	}	PUNCT
ejpam-6020	205	30	on	on	ADP
ejpam-6020	205	31	the	the	DET
ejpam-6020	205	32	set	set	NOUN
ejpam-6020	205	33	of	of	ADP
ejpam-6020	205	34	real	real	ADJ
ejpam-6020	205	35	numbers	number	NOUN
ejpam-6020	205	36	r.	r.	X
ejpam-6020	205	37	let	let	VERB
ejpam-6020	205	38	ϑ1	ϑ1	NOUN
ejpam-6020	205	39	=	=	SYM
ejpam-6020	205	40	{	{	PUNCT
ejpam-6020	205	41	∅	∅	NOUN
ejpam-6020	205	42	,	,	PUNCT
ejpam-6020	205	43	t	t	PROPN
ejpam-6020	205	44	⊆	⊆	NUM
ejpam-6020	205	45	r	r	NOUN
ejpam-6020	205	46	:	:	PUNCT
ejpam-6020	205	47	−2	−2	PROPN
ejpam-6020	205	48	∈	∈	PROPN
ejpam-6020	205	49	t	t	PROPN
ejpam-6020	205	50	or	or	CCONJ
ejpam-6020	205	51	0	0	NUM
ejpam-6020	205	52	∈	∈	PROPN
ejpam-6020	205	53	t	t	PROPN
ejpam-6020	205	54	}	}	PUNCT
ejpam-6020	205	55	and	and	CCONJ
ejpam-6020	205	56	ϑ2	ϑ2	PROPN
ejpam-6020	205	57	=	=	SYM
ejpam-6020	205	58	{	{	PUNCT
ejpam-6020	205	59	∅,r	∅,r	PROPN
ejpam-6020	205	60	,	,	PUNCT
ejpam-6020	205	61	n	n	CCONJ
ejpam-6020	205	62	,	,	PUNCT
ejpam-6020	205	63	{	{	PUNCT
ejpam-6020	205	64	0	0	NUM
ejpam-6020	205	65	,	,	PUNCT
ejpam-6020	205	66	1	1	NUM
ejpam-6020	205	67	}	}	PUNCT
ejpam-6020	205	68	,	,	PUNCT
ejpam-6020	205	69	{	{	PUNCT
ejpam-6020	205	70	0	0	NUM
ejpam-6020	205	71	,	,	PUNCT
ejpam-6020	205	72	2	2	NUM
ejpam-6020	205	73	}	}	PUNCT
ejpam-6020	205	74	,	,	PUNCT
ejpam-6020	205	75	{	{	PUNCT
ejpam-6020	205	76	0	0	NUM
ejpam-6020	205	77	,	,	PUNCT
ejpam-6020	205	78	1	1	NUM
ejpam-6020	205	79	,	,	PUNCT
ejpam-6020	205	80	2	2	NUM
ejpam-6020	205	81	}	}	PUNCT
ejpam-6020	205	82	}	}	PUNCT
ejpam-6020	205	83	be	be	AUX
ejpam-6020	205	84	associated	associate	VERB
ejpam-6020	205	85	stss	stss	NOUN
ejpam-6020	205	86	with	with	ADP
ejpam-6020	205	87	ν1	ν1	NOUN
ejpam-6020	205	88	and	and	CCONJ
ejpam-6020	205	89	ν1	ν1	NOUN
ejpam-6020	205	90	,	,	PUNCT
ejpam-6020	205	91	respectively	respectively	ADV
ejpam-6020	205	92	,	,	PUNCT
ejpam-6020	205	93	and	and	CCONJ
ejpam-6020	205	94	let	let	VERB
ejpam-6020	205	95	πϵ	πϵ	X
ejpam-6020	205	96	:	:	PUNCT
ejpam-6020	205	97	(	(	PUNCT
ejpam-6020	205	98	r	r	NOUN
ejpam-6020	205	99	,	,	PUNCT
ejpam-6020	205	100	ν1	ν1	NOUN
ejpam-6020	205	101	)	)	PUNCT
ejpam-6020	205	102	→	→	SYM
ejpam-6020	205	103	(	(	PUNCT
ejpam-6020	205	104	r	r	NOUN
ejpam-6020	205	105	,	,	PUNCT
ejpam-6020	205	106	ν2	ν2	NOUN
ejpam-6020	205	107	)	)	PUNCT
ejpam-6020	205	108	be	be	VERB
ejpam-6020	205	109	the	the	DET
ejpam-6020	205	110	identity	identity	NOUN
ejpam-6020	205	111	function	function	NOUN
ejpam-6020	205	112	.	.	PUNCT
ejpam-6020	206	1	then	then	ADV
ejpam-6020	206	2	,	,	PUNCT
ejpam-6020	206	3	we	we	PRON
ejpam-6020	206	4	have	have	VERB
ejpam-6020	206	5	π−1	π−1	PROPN
ejpam-6020	206	6	ϵ	ϵ	X
ejpam-6020	206	7	(	(	PUNCT
ejpam-6020	206	8	d	d	NOUN
ejpam-6020	206	9	)	)	PUNCT
ejpam-6020	206	10	∈	∈	PROPN
ejpam-6020	206	11	soϵ(r	soϵ(r	PROPN
ejpam-6020	206	12	)	)	PUNCT
ejpam-6020	206	13	for	for	ADP
ejpam-6020	206	14	each	each	DET
ejpam-6020	206	15	d	d	PROPN
ejpam-6020	206	16	∈	∈	PROPN
ejpam-6020	206	17	ϑ2	ϑ2	NOUN
ejpam-6020	206	18	,	,	PUNCT
ejpam-6020	206	19	and	and	CCONJ
ejpam-6020	206	20	hence	hence	ADV
ejpam-6020	206	21	πϵ	πϵ	INTJ
ejpam-6020	206	22	is	be	VERB
ejpam-6020	206	23	supra	supra	PROPN
ejpam-6020	206	24	ϵ	ϵ	PROPN
ejpam-6020	206	25	∗-cts	∗-ct	VERB
ejpam-6020	206	26	.	.	PUNCT
ejpam-6020	207	1	however	however	ADV
ejpam-6020	207	2	,	,	PUNCT
ejpam-6020	207	3	πϵ	πϵ	PRON
ejpam-6020	207	4	is	be	AUX
ejpam-6020	207	5	not	not	PART
ejpam-6020	207	6	supra	supra	ADJ
ejpam-6020	207	7	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	207	8	,	,	PUNCT
ejpam-6020	207	9	since	since	SCONJ
ejpam-6020	207	10	{	{	PUNCT
ejpam-6020	207	11	−3,−4	−3,−4	NOUN
ejpam-6020	207	12	}	}	PUNCT
ejpam-6020	207	13	is	be	AUX
ejpam-6020	207	14	supra	supra	PROPN
ejpam-6020	207	15	ϵ-open	ϵ-open	PROPN
ejpam-6020	207	16	set	set	VERB
ejpam-6020	207	17	over	over	ADP
ejpam-6020	207	18	ϑ2	ϑ2	NOUN
ejpam-6020	207	19	,	,	PUNCT
ejpam-6020	207	20	but	but	CCONJ
ejpam-6020	207	21	π	π	PROPN
ejpam-6020	207	22	−1	−1	NOUN
ejpam-6020	207	23	ϵ	ϵ	X
ejpam-6020	207	24	(	(	PUNCT
ejpam-6020	207	25	{	{	PUNCT
ejpam-6020	207	26	−3,−4	−3,−4	NOUN
ejpam-6020	207	27	}	}	PUNCT
ejpam-6020	207	28	)	)	PUNCT
ejpam-6020	208	1	=	=	SYM
ejpam-6020	208	2	{	{	PUNCT
ejpam-6020	208	3	−3,−4	−3,−4	NOUN
ejpam-6020	208	4	}	}	PUNCT
ejpam-6020	208	5	is	be	AUX
ejpam-6020	208	6	not	not	PART
ejpam-6020	208	7	supra	supra	NOUN
ejpam-6020	208	8	ϵ-open	ϵ-open	VERB
ejpam-6020	208	9	over	over	ADP
ejpam-6020	208	10	ϑ1	ϑ1	PROPN
ejpam-6020	208	11	.	.	PUNCT
ejpam-6020	209	1	therefore	therefore	ADV
ejpam-6020	209	2	,	,	PUNCT
ejpam-6020	209	3	πϵ	πϵ	INTJ
ejpam-6020	209	4	is	be	AUX
ejpam-6020	209	5	supra	supra	ADJ
ejpam-6020	209	6	ϵ∗-cts	ϵ∗-ct	NOUN
ejpam-6020	209	7	,	,	PUNCT
ejpam-6020	209	8	but	but	CCONJ
ejpam-6020	209	9	it	it	PRON
ejpam-6020	209	10	is	be	AUX
ejpam-6020	209	11	not	not	PART
ejpam-6020	209	12	supra	supra	ADJ
ejpam-6020	209	13	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	209	14	.	.	PUNCT
ejpam-6020	210	1	a.	a.	PROPN
ejpam-6020	210	2	m.	m.	PROPN
ejpam-6020	210	3	abd	abd	PROPN
ejpam-6020	210	4	el	el	PROPN
ejpam-6020	210	5	-	-	PROPN
ejpam-6020	210	6	latif	latif	PROPN
ejpam-6020	210	7	et	et	PROPN
ejpam-6020	210	8	al	al	PROPN
ejpam-6020	210	9	.	.	PUNCT
ejpam-6020	210	10	/	/	SYM
ejpam-6020	210	11	eur	eur	PROPN
ejpam-6020	210	12	.	.	PUNCT
ejpam-6020	211	1	j.	j.	PROPN
ejpam-6020	211	2	pure	pure	PROPN
ejpam-6020	211	3	appl	appl	PROPN
ejpam-6020	211	4	.	.	PROPN
ejpam-6020	211	5	math	math	PROPN
ejpam-6020	211	6	,	,	PUNCT
ejpam-6020	211	7	18	18	NUM
ejpam-6020	211	8	(	(	PUNCT
ejpam-6020	211	9	2	2	NUM
ejpam-6020	211	10	)	)	PUNCT
ejpam-6020	211	11	(	(	PUNCT
ejpam-6020	211	12	2025	2025	NUM
ejpam-6020	211	13	)	)	PUNCT
ejpam-6020	211	14	,	,	PUNCT
ejpam-6020	211	15	6020	6020	NUM
ejpam-6020	211	16	8	8	NUM
ejpam-6020	211	17	of	of	ADP
ejpam-6020	211	18	17	17	NUM
ejpam-6020	211	19	(	(	PUNCT
ejpam-6020	211	20	2	2	NUM
ejpam-6020	211	21	)	)	PUNCT
ejpam-6020	211	22	consider	consider	VERB
ejpam-6020	211	23	the	the	DET
ejpam-6020	211	24	two	two	NUM
ejpam-6020	211	25	topologies	topology	NOUN
ejpam-6020	211	26	ν1	ν1	NOUN
ejpam-6020	211	27	=	=	SYM
ejpam-6020	211	28	{	{	PUNCT
ejpam-6020	211	29	λ1	λ1	ADJ
ejpam-6020	211	30	,	,	PUNCT
ejpam-6020	211	31	∅	∅	NOUN
ejpam-6020	211	32	,	,	PUNCT
ejpam-6020	211	33	{	{	PUNCT
ejpam-6020	211	34	1	1	NUM
ejpam-6020	211	35	}	}	PUNCT
ejpam-6020	211	36	,	,	PUNCT
ejpam-6020	211	37	{	{	PUNCT
ejpam-6020	211	38	1	1	NUM
ejpam-6020	211	39	,	,	PUNCT
ejpam-6020	211	40	2	2	NUM
ejpam-6020	211	41	}	}	PUNCT
ejpam-6020	211	42	}	}	PUNCT
ejpam-6020	211	43	,	,	PUNCT
ejpam-6020	211	44	ν2	ν2	NOUN
ejpam-6020	211	45	=	=	SYM
ejpam-6020	211	46	{	{	PUNCT
ejpam-6020	211	47	λ2	λ2	NOUN
ejpam-6020	211	48	,	,	PUNCT
ejpam-6020	211	49	∅	∅	NOUN
ejpam-6020	211	50	,	,	PUNCT
ejpam-6020	211	51	{	{	PUNCT
ejpam-6020	211	52	y	y	NOUN
ejpam-6020	211	53	,	,	PUNCT
ejpam-6020	211	54	z	z	NOUN
ejpam-6020	211	55	}	}	PUNCT
ejpam-6020	211	56	}	}	PUNCT
ejpam-6020	211	57	on	on	ADP
ejpam-6020	211	58	λ1	λ1	PROPN
ejpam-6020	211	59	=	=	SYM
ejpam-6020	211	60	{	{	PUNCT
ejpam-6020	211	61	1	1	NUM
ejpam-6020	211	62	,	,	PUNCT
ejpam-6020	211	63	2	2	NUM
ejpam-6020	211	64	,	,	PUNCT
ejpam-6020	211	65	3	3	NUM
ejpam-6020	211	66	}	}	PUNCT
ejpam-6020	211	67	and	and	CCONJ
ejpam-6020	211	68	λ2	λ2	NOUN
ejpam-6020	211	69	=	=	SYM
ejpam-6020	211	70	{	{	PUNCT
ejpam-6020	211	71	x	x	NOUN
ejpam-6020	211	72	,	,	PUNCT
ejpam-6020	211	73	y	y	PROPN
ejpam-6020	211	74	,	,	PUNCT
ejpam-6020	211	75	z	z	NOUN
ejpam-6020	211	76	}	}	PUNCT
ejpam-6020	211	77	,	,	PUNCT
ejpam-6020	211	78	respectively	respectively	ADV
ejpam-6020	211	79	.	.	PUNCT
ejpam-6020	212	1	let	let	VERB
ejpam-6020	212	2	ϑ1	ϑ1	NOUN
ejpam-6020	212	3	=	=	SYM
ejpam-6020	212	4	{	{	PUNCT
ejpam-6020	212	5	λ1	λ1	ADJ
ejpam-6020	212	6	,	,	PUNCT
ejpam-6020	212	7	∅	∅	NOUN
ejpam-6020	212	8	,	,	PUNCT
ejpam-6020	212	9	{	{	PUNCT
ejpam-6020	212	10	1	1	NUM
ejpam-6020	212	11	}	}	PUNCT
ejpam-6020	212	12	,	,	PUNCT
ejpam-6020	212	13	{	{	PUNCT
ejpam-6020	212	14	1	1	NUM
ejpam-6020	212	15	,	,	PUNCT
ejpam-6020	212	16	2	2	NUM
ejpam-6020	212	17	}	}	PUNCT
ejpam-6020	212	18	,	,	PUNCT
ejpam-6020	212	19	{	{	PUNCT
ejpam-6020	212	20	2	2	NUM
ejpam-6020	212	21	,	,	PUNCT
ejpam-6020	212	22	3	3	NUM
ejpam-6020	212	23	}	}	PUNCT
ejpam-6020	212	24	}	}	PUNCT
ejpam-6020	212	25	and	and	CCONJ
ejpam-6020	212	26	ϑ2	ϑ2	PROPN
ejpam-6020	212	27	=	=	SYM
ejpam-6020	212	28	{	{	PUNCT
ejpam-6020	212	29	λ2	λ2	NOUN
ejpam-6020	212	30	,	,	PUNCT
ejpam-6020	212	31	∅	∅	NOUN
ejpam-6020	212	32	,	,	PUNCT
ejpam-6020	212	33	{	{	PUNCT
ejpam-6020	212	34	z	z	NOUN
ejpam-6020	212	35	}	}	PUNCT
ejpam-6020	212	36	,	,	PUNCT
ejpam-6020	212	37	{	{	PUNCT
ejpam-6020	212	38	y	y	NOUN
ejpam-6020	212	39	,	,	PUNCT
ejpam-6020	212	40	z	z	NOUN
ejpam-6020	212	41	}	}	PUNCT
ejpam-6020	212	42	,	,	PUNCT
ejpam-6020	212	43	{	{	PUNCT
ejpam-6020	212	44	x	x	NOUN
ejpam-6020	212	45	,	,	PUNCT
ejpam-6020	212	46	y	y	NOUN
ejpam-6020	212	47	}	}	PUNCT
ejpam-6020	212	48	}	}	PUNCT
ejpam-6020	212	49	be	be	AUX
ejpam-6020	212	50	associated	associate	VERB
ejpam-6020	212	51	stss	stss	NOUN
ejpam-6020	212	52	with	with	ADP
ejpam-6020	212	53	ν1	ν1	NOUN
ejpam-6020	212	54	and	and	CCONJ
ejpam-6020	212	55	ν1	ν1	NOUN
ejpam-6020	212	56	,	,	PUNCT
ejpam-6020	212	57	respectively	respectively	ADV
ejpam-6020	212	58	,	,	PUNCT
ejpam-6020	212	59	and	and	CCONJ
ejpam-6020	212	60	let	let	VERB
ejpam-6020	212	61	πϵ	πϵ	X
ejpam-6020	212	62	:	:	PUNCT
ejpam-6020	212	63	(	(	PUNCT
ejpam-6020	212	64	λ1	λ1	ADJ
ejpam-6020	212	65	,	,	PUNCT
ejpam-6020	212	66	ν1	ν1	NOUN
ejpam-6020	212	67	)	)	PUNCT
ejpam-6020	212	68	→	→	SYM
ejpam-6020	212	69	(	(	PUNCT
ejpam-6020	212	70	λ2	λ2	NOUN
ejpam-6020	212	71	,	,	PUNCT
ejpam-6020	212	72	ν2	ν2	NOUN
ejpam-6020	212	73	)	)	PUNCT
ejpam-6020	212	74	be	be	VERB
ejpam-6020	212	75	a	a	DET
ejpam-6020	212	76	function	function	NOUN
ejpam-6020	212	77	defined	define	VERB
ejpam-6020	212	78	as	as	SCONJ
ejpam-6020	212	79	follows	follow	VERB
ejpam-6020	212	80	:	:	PUNCT
ejpam-6020	212	81	πϵ({1	πϵ({1	X
ejpam-6020	212	82	}	}	PUNCT
ejpam-6020	212	83	)	)	PUNCT
ejpam-6020	213	1	=	=	PRON
ejpam-6020	213	2	{	{	PUNCT
ejpam-6020	213	3	y	y	NOUN
ejpam-6020	213	4	}	}	PUNCT
ejpam-6020	213	5	,	,	PUNCT
ejpam-6020	213	6	πϵ({2	πϵ({2	NOUN
ejpam-6020	213	7	}	}	PUNCT
ejpam-6020	213	8	)	)	PUNCT
ejpam-6020	214	1	=	=	PRON
ejpam-6020	214	2	{	{	PUNCT
ejpam-6020	214	3	x	x	NOUN
ejpam-6020	214	4	}	}	PUNCT
ejpam-6020	214	5	,	,	PUNCT
ejpam-6020	214	6	and	and	CCONJ
ejpam-6020	214	7	πϵ({3	πϵ({3	VERB
ejpam-6020	214	8	}	}	PUNCT
ejpam-6020	214	9	)	)	PUNCT
ejpam-6020	215	1	=	=	PRON
ejpam-6020	215	2	{	{	PUNCT
ejpam-6020	215	3	z	z	NOUN
ejpam-6020	215	4	}	}	PUNCT
ejpam-6020	215	5	.	.	PUNCT
ejpam-6020	216	1	then	then	ADV
ejpam-6020	216	2	,	,	PUNCT
ejpam-6020	216	3	we	we	PRON
ejpam-6020	216	4	have	have	VERB
ejpam-6020	216	5	π−1	π−1	PROPN
ejpam-6020	216	6	ϵ	ϵ	X
ejpam-6020	216	7	(	(	PUNCT
ejpam-6020	216	8	d	d	NOUN
ejpam-6020	216	9	)	)	PUNCT
ejpam-6020	216	10	∈	∈	PROPN
ejpam-6020	216	11	soϵ(r	soϵ(r	PROPN
ejpam-6020	216	12	)	)	PUNCT
ejpam-6020	216	13	for	for	ADP
ejpam-6020	216	14	each	each	DET
ejpam-6020	216	15	d	d	PROPN
ejpam-6020	216	16	∈	∈	PROPN
ejpam-6020	216	17	ν2	ν2	NOUN
ejpam-6020	216	18	,	,	PUNCT
ejpam-6020	216	19	and	and	CCONJ
ejpam-6020	216	20	hence	hence	ADV
ejpam-6020	216	21	πϵ	πϵ	INTJ
ejpam-6020	216	22	is	be	VERB
ejpam-6020	216	23	supra	supra	ADJ
ejpam-6020	216	24	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	216	25	.	.	PUNCT
ejpam-6020	217	1	however	however	ADV
ejpam-6020	217	2	,	,	PUNCT
ejpam-6020	217	3	πϵ	πϵ	PRON
ejpam-6020	217	4	is	be	AUX
ejpam-6020	217	5	not	not	PART
ejpam-6020	217	6	supra	supra	ADJ
ejpam-6020	217	7	ϵ∗-cts	ϵ∗-ct	NOUN
ejpam-6020	217	8	,	,	PUNCT
ejpam-6020	217	9	since	since	SCONJ
ejpam-6020	217	10	{	{	PUNCT
ejpam-6020	217	11	z	z	NOUN
ejpam-6020	217	12	}	}	PUNCT
ejpam-6020	217	13	∈	∈	PROPN
ejpam-6020	217	14	ϑ2	ϑ2	NOUN
ejpam-6020	217	15	,	,	PUNCT
ejpam-6020	217	16	but	but	CCONJ
ejpam-6020	217	17	π	π	PROPN
ejpam-6020	217	18	−1	−1	NOUN
ejpam-6020	217	19	ϵ	ϵ	X
ejpam-6020	217	20	(	(	PUNCT
ejpam-6020	217	21	{	{	PUNCT
ejpam-6020	217	22	z	z	NOUN
ejpam-6020	217	23	}	}	PUNCT
ejpam-6020	217	24	)	)	PUNCT
ejpam-6020	218	1	=	=	PRON
ejpam-6020	218	2	{	{	PUNCT
ejpam-6020	218	3	3	3	NUM
ejpam-6020	218	4	}	}	PUNCT
ejpam-6020	218	5	̸∈	̸∈	PROPN
ejpam-6020	218	6	soϵ(λ1	soϵ(λ1	PROPN
ejpam-6020	218	7	)	)	PUNCT
ejpam-6020	218	8	.	.	PUNCT
ejpam-6020	219	1	therefore	therefore	ADV
ejpam-6020	219	2	,	,	PUNCT
ejpam-6020	219	3	πϵ	πϵ	INTJ
ejpam-6020	219	4	is	be	AUX
ejpam-6020	219	5	supra	supra	ADJ
ejpam-6020	219	6	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	219	7	,	,	PUNCT
ejpam-6020	219	8	but	but	CCONJ
ejpam-6020	219	9	it	it	PRON
ejpam-6020	219	10	is	be	AUX
ejpam-6020	219	11	not	not	PART
ejpam-6020	219	12	supra	supra	ADJ
ejpam-6020	219	13	ϵ∗-cts	ϵ∗-ct	NOUN
ejpam-6020	219	14	.	.	PUNCT
ejpam-6020	220	1	corollary	corollary	ADJ
ejpam-6020	220	2	1	1	NUM
ejpam-6020	220	3	.	.	PUNCT
ejpam-6020	221	1	it	it	PRON
ejpam-6020	221	2	follows	follow	VERB
ejpam-6020	221	3	from	from	ADP
ejpam-6020	221	4	theorem	theorem	ADJ
ejpam-6020	221	5	6	6	NUM
ejpam-6020	221	6	,	,	PUNCT
ejpam-6020	221	7	theorem	theorem	VERB
ejpam-6020	221	8	8	8	NUM
ejpam-6020	221	9	and	and	CCONJ
ejpam-6020	221	10	[	[	X
ejpam-6020	221	11	18	18	NUM
ejpam-6020	221	12	,	,	PUNCT
ejpam-6020	221	13	reamrk	reamrk	NOUN
ejpam-6020	221	14	2	2	NUM
ejpam-6020	221	15	]	]	PUNCT
ejpam-6020	221	16	that	that	SCONJ
ejpam-6020	221	17	we	we	PRON
ejpam-6020	221	18	have	have	VERB
ejpam-6020	221	19	the	the	DET
ejpam-6020	221	20	following	follow	VERB
ejpam-6020	221	21	implications	implication	NOUN
ejpam-6020	221	22	for	for	ADP
ejpam-6020	221	23	an	an	DET
ejpam-6020	221	24	sts	st	NOUN
ejpam-6020	221	25	(	(	PUNCT
ejpam-6020	221	26	λ	λ	NOUN
ejpam-6020	221	27	,	,	PUNCT
ejpam-6020	221	28	ν	ν	NOUN
ejpam-6020	221	29	)	)	PUNCT
ejpam-6020	221	30	,	,	PUNCT
ejpam-6020	221	31	which	which	PRON
ejpam-6020	221	32	are	be	AUX
ejpam-6020	221	33	not	not	PART
ejpam-6020	221	34	reversible	reversible	ADJ
ejpam-6020	221	35	.	.	PUNCT
ejpam-6020	222	1	figure	figure	NOUN
ejpam-6020	222	2	1	1	NUM
ejpam-6020	222	3	:	:	PUNCT
ejpam-6020	222	4	the	the	DET
ejpam-6020	222	5	connections	connection	NOUN
ejpam-6020	222	6	between	between	ADP
ejpam-6020	222	7	supra-ϵ-cts	supra-ϵ-ct	NOUN
ejpam-6020	222	8	functions	function	NOUN
ejpam-6020	222	9	and	and	CCONJ
ejpam-6020	222	10	other	other	ADJ
ejpam-6020	222	11	preceding	precede	VERB
ejpam-6020	222	12	studies	study	NOUN
ejpam-6020	222	13	the	the	DET
ejpam-6020	222	14	proofs	proof	NOUN
ejpam-6020	222	15	for	for	ADP
ejpam-6020	222	16	the	the	DET
ejpam-6020	222	17	next	next	ADJ
ejpam-6020	222	18	two	two	NUM
ejpam-6020	222	19	theorems	theorem	NOUN
ejpam-6020	222	20	are	be	AUX
ejpam-6020	222	21	eliminated	eliminate	VERB
ejpam-6020	222	22	since	since	SCONJ
ejpam-6020	222	23	they	they	PRON
ejpam-6020	222	24	could	could	AUX
ejpam-6020	222	25	be	be	AUX
ejpam-6020	222	26	demonstrated	demonstrate	VERB
ejpam-6020	222	27	similarly	similarly	ADV
ejpam-6020	222	28	to	to	PART
ejpam-6020	222	29	theorem	theorem	VERB
ejpam-6020	222	30	7	7	NUM
ejpam-6020	222	31	.	.	PUNCT
ejpam-6020	222	32	theorem	theorem	NOUN
ejpam-6020	222	33	9	9	NUM
ejpam-6020	222	34	.	.	PUNCT
ejpam-6020	223	1	let	let	VERB
ejpam-6020	223	2	πϵ	πϵ	INTJ
ejpam-6020	223	3	:	:	PUNCT
ejpam-6020	223	4	(	(	PUNCT
ejpam-6020	223	5	λ1	λ1	ADJ
ejpam-6020	223	6	,	,	PUNCT
ejpam-6020	223	7	ν1	ν1	NOUN
ejpam-6020	223	8	)	)	PUNCT
ejpam-6020	223	9	→	→	SYM
ejpam-6020	223	10	(	(	PUNCT
ejpam-6020	223	11	λ2	λ2	NOUN
ejpam-6020	223	12	,	,	PUNCT
ejpam-6020	223	13	ν2	ν2	NOUN
ejpam-6020	223	14	)	)	PUNCT
ejpam-6020	223	15	be	be	VERB
ejpam-6020	223	16	a	a	DET
ejpam-6020	223	17	function	function	NOUN
ejpam-6020	223	18	with	with	ADP
ejpam-6020	223	19	ϑ1	ϑ1	NOUN
ejpam-6020	223	20	and	and	CCONJ
ejpam-6020	223	21	ϑ2	ϑ2	PROPN
ejpam-6020	223	22	as	as	ADP
ejpam-6020	223	23	associated	associated	ADJ
ejpam-6020	223	24	stss	stss	NOUN
ejpam-6020	223	25	with	with	ADP
ejpam-6020	223	26	ν1	ν1	NOUN
ejpam-6020	223	27	and	and	CCONJ
ejpam-6020	223	28	ν1	ν1	NOUN
ejpam-6020	223	29	,	,	PUNCT
ejpam-6020	223	30	respectively	respectively	ADV
ejpam-6020	223	31	,	,	PUNCT
ejpam-6020	223	32	then	then	ADV
ejpam-6020	223	33	the	the	DET
ejpam-6020	223	34	next	next	ADJ
ejpam-6020	223	35	assertions	assertion	NOUN
ejpam-6020	223	36	are	be	AUX
ejpam-6020	223	37	equivalent	equivalent	ADJ
ejpam-6020	223	38	:	:	PUNCT
ejpam-6020	223	39	(	(	PUNCT
ejpam-6020	223	40	1	1	X
ejpam-6020	223	41	)	)	PUNCT
ejpam-6020	223	42	πϵ	πϵ	X
ejpam-6020	223	43	is	be	AUX
ejpam-6020	223	44	supra	supra	ADJ
ejpam-6020	223	45	ϵ∗-cts	ϵ∗-ct	NOUN
ejpam-6020	223	46	.	.	PUNCT
ejpam-6020	224	1	(	(	PUNCT
ejpam-6020	224	2	2	2	X
ejpam-6020	224	3	)	)	PUNCT
ejpam-6020	224	4	for	for	ADP
ejpam-6020	224	5	each	each	DET
ejpam-6020	224	6	z	z	PROPN
ejpam-6020	224	7	∈	∈	PROPN
ejpam-6020	224	8	ϑc2	ϑc2	NOUN
ejpam-6020	224	9	,	,	PUNCT
ejpam-6020	224	10	π	π	PROPN
ejpam-6020	224	11	−1	−1	NOUN
ejpam-6020	224	12	ϵ	ϵ	X
ejpam-6020	224	13	(	(	PUNCT
ejpam-6020	224	14	z	z	NOUN
ejpam-6020	224	15	)	)	PUNCT
ejpam-6020	224	16	∈	∈	PROPN
ejpam-6020	224	17	scϵ(λ1	scϵ(λ1	PROPN
ejpam-6020	224	18	)	)	PUNCT
ejpam-6020	224	19	.	.	PUNCT
ejpam-6020	225	1	(	(	PUNCT
ejpam-6020	225	2	3	3	X
ejpam-6020	225	3	)	)	PUNCT
ejpam-6020	225	4	clsϵ(π	clsϵ(π	NOUN
ejpam-6020	225	5	−1	−1	NOUN
ejpam-6020	225	6	ϵ	ϵ	X
ejpam-6020	225	7	(	(	PUNCT
ejpam-6020	225	8	z	z	NOUN
ejpam-6020	225	9	)	)	PUNCT
ejpam-6020	225	10	)	)	PUNCT
ejpam-6020	226	1	⊆	⊆	NUM
ejpam-6020	226	2	π−1	π−1	PROPN
ejpam-6020	226	3	ϵ	ϵ	X
ejpam-6020	226	4	(	(	PUNCT
ejpam-6020	226	5	cls(z	cls(z	NOUN
ejpam-6020	226	6	)	)	PUNCT
ejpam-6020	226	7	)	)	PUNCT
ejpam-6020	226	8	∀	∀	X
ejpam-6020	227	1	z	z	NOUN
ejpam-6020	228	1	⊆	⊆	NUM
ejpam-6020	228	2	λ2	λ2	NOUN
ejpam-6020	228	3	.	.	PUNCT
ejpam-6020	229	1	(	(	PUNCT
ejpam-6020	229	2	4	4	X
ejpam-6020	229	3	)	)	PUNCT
ejpam-6020	229	4	πϵ(cl	πϵ(cl	NOUN
ejpam-6020	229	5	s	s	PART
ejpam-6020	229	6	ϵ(y	ϵ(y	PROPN
ejpam-6020	229	7	)	)	PUNCT
ejpam-6020	229	8	)	)	PUNCT
ejpam-6020	230	1	⊆	⊆	NUM
ejpam-6020	230	2	clsϵ(πϵ(y	clsϵ(πϵ(y	NOUN
ejpam-6020	230	3	)	)	PUNCT
ejpam-6020	230	4	)	)	PUNCT
ejpam-6020	230	5	∀	∀	X
ejpam-6020	231	1	y	y	PROPN
ejpam-6020	231	2	⊆	⊆	NUM
ejpam-6020	231	3	λ1	λ1	PROPN
ejpam-6020	231	4	.	.	PUNCT
ejpam-6020	232	1	(	(	PUNCT
ejpam-6020	232	2	5	5	NUM
ejpam-6020	232	3	)	)	PUNCT
ejpam-6020	232	4	π−1	π−1	PROPN
ejpam-6020	232	5	ϵ	ϵ	X
ejpam-6020	232	6	(	(	PUNCT
ejpam-6020	232	7	intsϵ(z	intsϵ(z	NOUN
ejpam-6020	232	8	)	)	PUNCT
ejpam-6020	232	9	)	)	PUNCT
ejpam-6020	233	1	⊆	⊆	NUM
ejpam-6020	233	2	intsϵ(π	intsϵ(π	PROPN
ejpam-6020	233	3	−1	−1	NOUN
ejpam-6020	233	4	ϵ	ϵ	X
ejpam-6020	233	5	(	(	PUNCT
ejpam-6020	233	6	z	z	NOUN
ejpam-6020	233	7	)	)	PUNCT
ejpam-6020	233	8	)	)	PUNCT
ejpam-6020	233	9	∀	∀	X
ejpam-6020	234	1	z	z	NOUN
ejpam-6020	234	2	⊆	⊆	NUM
ejpam-6020	234	3	λ2	λ2	NOUN
ejpam-6020	234	4	.	.	PUNCT
ejpam-6020	235	1	theorem	theorem	NOUN
ejpam-6020	235	2	10	10	NUM
ejpam-6020	235	3	.	.	PUNCT
ejpam-6020	236	1	let	let	AUX
ejpam-6020	236	2	πϵ	πϵ	INTJ
ejpam-6020	236	3	:	:	PUNCT
ejpam-6020	236	4	(	(	PUNCT
ejpam-6020	236	5	λ1	λ1	ADJ
ejpam-6020	236	6	,	,	PUNCT
ejpam-6020	236	7	ν1	ν1	NOUN
ejpam-6020	236	8	)	)	PUNCT
ejpam-6020	236	9	→	→	SYM
ejpam-6020	236	10	(	(	PUNCT
ejpam-6020	236	11	λ2	λ2	NOUN
ejpam-6020	236	12	,	,	PUNCT
ejpam-6020	236	13	ν2	ν2	NOUN
ejpam-6020	236	14	)	)	PUNCT
ejpam-6020	236	15	be	be	VERB
ejpam-6020	236	16	a	a	DET
ejpam-6020	236	17	function	function	NOUN
ejpam-6020	236	18	with	with	ADP
ejpam-6020	236	19	ϑ1	ϑ1	NOUN
ejpam-6020	236	20	and	and	CCONJ
ejpam-6020	236	21	ϑ2	ϑ2	PROPN
ejpam-6020	236	22	as	as	ADP
ejpam-6020	236	23	associated	associated	ADJ
ejpam-6020	236	24	stss	stss	NOUN
ejpam-6020	236	25	with	with	ADP
ejpam-6020	236	26	ν1	ν1	NOUN
ejpam-6020	236	27	and	and	CCONJ
ejpam-6020	236	28	ν1	ν1	NOUN
ejpam-6020	236	29	,	,	PUNCT
ejpam-6020	236	30	respectively	respectively	ADV
ejpam-6020	236	31	,	,	PUNCT
ejpam-6020	236	32	then	then	ADV
ejpam-6020	236	33	the	the	DET
ejpam-6020	236	34	next	next	ADJ
ejpam-6020	236	35	assertions	assertion	NOUN
ejpam-6020	236	36	are	be	AUX
ejpam-6020	236	37	equivalent	equivalent	ADJ
ejpam-6020	236	38	:	:	PUNCT
ejpam-6020	236	39	(	(	PUNCT
ejpam-6020	236	40	1	1	X
ejpam-6020	236	41	)	)	PUNCT
ejpam-6020	236	42	πϵ	πϵ	X
ejpam-6020	236	43	is	be	AUX
ejpam-6020	236	44	supra	supra	ADJ
ejpam-6020	236	45	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	236	46	.	.	PUNCT
ejpam-6020	237	1	(	(	PUNCT
ejpam-6020	237	2	2	2	X
ejpam-6020	237	3	)	)	PUNCT
ejpam-6020	237	4	for	for	ADP
ejpam-6020	237	5	each	each	DET
ejpam-6020	237	6	z	z	PROPN
ejpam-6020	237	7	∈	∈	PROPN
ejpam-6020	237	8	scϵ(λ2	scϵ(λ2	NOUN
ejpam-6020	237	9	)	)	PUNCT
ejpam-6020	237	10	,	,	PUNCT
ejpam-6020	238	1	π	π	PROPN
ejpam-6020	238	2	−1	−1	NOUN
ejpam-6020	238	3	ϵ	ϵ	X
ejpam-6020	238	4	(	(	PUNCT
ejpam-6020	238	5	z	z	NOUN
ejpam-6020	238	6	)	)	PUNCT
ejpam-6020	238	7	∈	∈	PROPN
ejpam-6020	238	8	scϵ(λ1	scϵ(λ1	PROPN
ejpam-6020	238	9	)	)	PUNCT
ejpam-6020	238	10	.	.	PUNCT
ejpam-6020	239	1	(	(	PUNCT
ejpam-6020	239	2	3	3	X
ejpam-6020	239	3	)	)	PUNCT
ejpam-6020	239	4	clsϵ(π	clsϵ(π	NOUN
ejpam-6020	239	5	−1	−1	NOUN
ejpam-6020	239	6	ϵ	ϵ	X
ejpam-6020	239	7	(	(	PUNCT
ejpam-6020	239	8	z	z	NOUN
ejpam-6020	239	9	)	)	PUNCT
ejpam-6020	239	10	)	)	PUNCT
ejpam-6020	240	1	⊆	⊆	NUM
ejpam-6020	240	2	π−1	π−1	PROPN
ejpam-6020	240	3	ϵ	ϵ	X
ejpam-6020	240	4	(	(	PUNCT
ejpam-6020	240	5	clsϵ(z	clsϵ(z	NOUN
ejpam-6020	240	6	)	)	PUNCT
ejpam-6020	240	7	)	)	PUNCT
ejpam-6020	240	8	∀	∀	X
ejpam-6020	241	1	z	z	NOUN
ejpam-6020	241	2	⊆	⊆	NUM
ejpam-6020	241	3	λ2	λ2	NOUN
ejpam-6020	241	4	.	.	PUNCT
ejpam-6020	242	1	(	(	PUNCT
ejpam-6020	242	2	4	4	X
ejpam-6020	242	3	)	)	PUNCT
ejpam-6020	242	4	πϵ(cl	πϵ(cl	NOUN
ejpam-6020	242	5	s	s	PART
ejpam-6020	242	6	ϵ(y	ϵ(y	PROPN
ejpam-6020	242	7	)	)	PUNCT
ejpam-6020	242	8	)	)	PUNCT
ejpam-6020	243	1	⊆	⊆	NUM
ejpam-6020	243	2	clsϵ(πϵ(y	clsϵ(πϵ(y	NOUN
ejpam-6020	243	3	)	)	PUNCT
ejpam-6020	243	4	)	)	PUNCT
ejpam-6020	243	5	∀	∀	X
ejpam-6020	244	1	y	y	PROPN
ejpam-6020	244	2	⊆	⊆	NUM
ejpam-6020	244	3	λ1	λ1	PROPN
ejpam-6020	244	4	.	.	PUNCT
ejpam-6020	244	5	a.	a.	PROPN
ejpam-6020	244	6	m.	m.	PROPN
ejpam-6020	245	1	abd	abd	PROPN
ejpam-6020	246	1	el	el	PROPN
ejpam-6020	246	2	-	-	PROPN
ejpam-6020	246	3	latif	latif	PROPN
ejpam-6020	246	4	et	et	PROPN
ejpam-6020	246	5	al	al	PROPN
ejpam-6020	246	6	.	.	PUNCT
ejpam-6020	246	7	/	/	SYM
ejpam-6020	246	8	eur	eur	PROPN
ejpam-6020	246	9	.	.	PUNCT
ejpam-6020	247	1	j.	j.	PROPN
ejpam-6020	247	2	pure	pure	PROPN
ejpam-6020	247	3	appl	appl	PROPN
ejpam-6020	247	4	.	.	PROPN
ejpam-6020	247	5	math	math	PROPN
ejpam-6020	247	6	,	,	PUNCT
ejpam-6020	247	7	18	18	NUM
ejpam-6020	247	8	(	(	PUNCT
ejpam-6020	247	9	2	2	NUM
ejpam-6020	247	10	)	)	PUNCT
ejpam-6020	247	11	(	(	PUNCT
ejpam-6020	247	12	2025	2025	NUM
ejpam-6020	247	13	)	)	PUNCT
ejpam-6020	247	14	,	,	PUNCT
ejpam-6020	247	15	6020	6020	NUM
ejpam-6020	247	16	9	9	NUM
ejpam-6020	247	17	of	of	ADP
ejpam-6020	247	18	17	17	NUM
ejpam-6020	247	19	(	(	PUNCT
ejpam-6020	247	20	5	5	NUM
ejpam-6020	247	21	)	)	PUNCT
ejpam-6020	247	22	π−1	π−1	PROPN
ejpam-6020	247	23	ϵ	ϵ	X
ejpam-6020	247	24	(	(	PUNCT
ejpam-6020	247	25	intsϵ(z	intsϵ(z	NOUN
ejpam-6020	247	26	)	)	PUNCT
ejpam-6020	247	27	)	)	PUNCT
ejpam-6020	248	1	⊆	⊆	NUM
ejpam-6020	248	2	intsϵ(π	intsϵ(π	PROPN
ejpam-6020	248	3	−1	−1	NOUN
ejpam-6020	248	4	ϵ	ϵ	X
ejpam-6020	248	5	(	(	PUNCT
ejpam-6020	248	6	z	z	NOUN
ejpam-6020	248	7	)	)	PUNCT
ejpam-6020	248	8	)	)	PUNCT
ejpam-6020	248	9	∀	∀	X
ejpam-6020	249	1	z	z	NOUN
ejpam-6020	249	2	⊆	⊆	NUM
ejpam-6020	249	3	λ2	λ2	NOUN
ejpam-6020	249	4	.	.	PUNCT
ejpam-6020	250	1	theorem	theorem	NOUN
ejpam-6020	250	2	11	11	NUM
ejpam-6020	250	3	.	.	PUNCT
ejpam-6020	251	1	let	let	AUX
ejpam-6020	251	2	πϵ	πϵ	INTJ
ejpam-6020	251	3	:	:	PUNCT
ejpam-6020	251	4	(	(	PUNCT
ejpam-6020	251	5	λ1	λ1	ADJ
ejpam-6020	251	6	,	,	PUNCT
ejpam-6020	251	7	ν1	ν1	NOUN
ejpam-6020	251	8	)	)	PUNCT
ejpam-6020	251	9	→	→	SYM
ejpam-6020	251	10	(	(	PUNCT
ejpam-6020	251	11	λ2	λ2	NOUN
ejpam-6020	251	12	,	,	PUNCT
ejpam-6020	251	13	ν2	ν2	NOUN
ejpam-6020	251	14	)	)	PUNCT
ejpam-6020	251	15	be	be	VERB
ejpam-6020	251	16	a	a	DET
ejpam-6020	251	17	supra	supra	ADJ
ejpam-6020	251	18	ϵ-irresolute	ϵ-irresolute	NOUN
ejpam-6020	251	19	with	with	ADP
ejpam-6020	251	20	ϑ1	ϑ1	NOUN
ejpam-6020	251	21	,	,	PUNCT
ejpam-6020	251	22	ϑ2	ϑ2	PROPN
ejpam-6020	251	23	associated	associate	VERB
ejpam-6020	251	24	stss	stss	NOUN
ejpam-6020	251	25	with	with	ADP
ejpam-6020	251	26	ν1	ν1	NOUN
ejpam-6020	251	27	,	,	PUNCT
ejpam-6020	251	28	ν2	ν2	NOUN
ejpam-6020	251	29	,	,	PUNCT
ejpam-6020	251	30	respectively	respectively	ADV
ejpam-6020	251	31	,	,	PUNCT
ejpam-6020	251	32	and	and	CCONJ
ejpam-6020	251	33	ψϵ	ψϵ	VERB
ejpam-6020	251	34	:	:	PUNCT
ejpam-6020	251	35	(	(	PUNCT
ejpam-6020	251	36	λ2	λ2	NOUN
ejpam-6020	251	37	,	,	PUNCT
ejpam-6020	251	38	ν2	ν2	NOUN
ejpam-6020	251	39	)	)	PUNCT
ejpam-6020	251	40	→	→	SYM
ejpam-6020	251	41	(	(	PUNCT
ejpam-6020	251	42	λ3	λ3	PROPN
ejpam-6020	251	43	,	,	PUNCT
ejpam-6020	251	44	ν3	ν3	NOUN
ejpam-6020	251	45	)	)	PUNCT
ejpam-6020	251	46	be	be	AUX
ejpam-6020	251	47	a	a	DET
ejpam-6020	251	48	supra	supra	ADJ
ejpam-6020	251	49	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	251	50	with	with	ADP
ejpam-6020	251	51	ϑ3	ϑ3	NOUN
ejpam-6020	251	52	as	as	ADP
ejpam-6020	251	53	an	an	DET
ejpam-6020	251	54	associated	associate	VERB
ejpam-6020	251	55	sts	st	NOUN
ejpam-6020	251	56	with	with	ADP
ejpam-6020	251	57	ν3	ν3	NOUN
ejpam-6020	251	58	,	,	PUNCT
ejpam-6020	251	59	then	then	ADV
ejpam-6020	251	60	the	the	DET
ejpam-6020	251	61	composition	composition	NOUN
ejpam-6020	251	62	ψϵ	ψϵ	ADP
ejpam-6020	251	63	◦	◦	NOUN
ejpam-6020	251	64	πϵ	πϵ	ADP
ejpam-6020	251	65	:	:	PUNCT
ejpam-6020	251	66	(	(	PUNCT
ejpam-6020	251	67	λ1	λ1	ADJ
ejpam-6020	251	68	,	,	PUNCT
ejpam-6020	251	69	ν1	ν1	NOUN
ejpam-6020	251	70	)	)	PUNCT
ejpam-6020	251	71	→	→	SYM
ejpam-6020	251	72	(	(	PUNCT
ejpam-6020	251	73	λ3	λ3	PROPN
ejpam-6020	251	74	,	,	PUNCT
ejpam-6020	251	75	ν3	ν3	NOUN
ejpam-6020	251	76	)	)	PUNCT
ejpam-6020	251	77	is	be	AUX
ejpam-6020	251	78	supra	supra	ADJ
ejpam-6020	251	79	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	251	80	.	.	PUNCT
ejpam-6020	252	1	proof	proof	NOUN
ejpam-6020	252	2	.	.	PUNCT
ejpam-6020	253	1	let	let	VERB
ejpam-6020	253	2	e	e	PROPN
ejpam-6020	253	3	∈	∈	PROPN
ejpam-6020	253	4	ϑ3	ϑ3	NOUN
ejpam-6020	253	5	.	.	PUNCT
ejpam-6020	254	1	since	since	SCONJ
ejpam-6020	254	2	ψϵ	ψϵ	PROPN
ejpam-6020	254	3	is	be	AUX
ejpam-6020	254	4	supra	supra	ADJ
ejpam-6020	254	5	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	254	6	,	,	PUNCT
ejpam-6020	254	7	ψ−1	ψ−1	PROPN
ejpam-6020	254	8	ϵ	ϵ	X
ejpam-6020	254	9	(	(	PUNCT
ejpam-6020	254	10	e	e	NOUN
ejpam-6020	254	11	)	)	PUNCT
ejpam-6020	254	12	∈	∈	PROPN
ejpam-6020	254	13	soϵ(λ2	soϵ(λ2	PROPN
ejpam-6020	254	14	)	)	PUNCT
ejpam-6020	254	15	.	.	PUNCT
ejpam-6020	255	1	given	give	VERB
ejpam-6020	255	2	πϵ	πϵ	ADP
ejpam-6020	255	3	is	be	AUX
ejpam-6020	255	4	supra	supra	PROPN
ejpam-6020	255	5	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	255	6	,	,	PUNCT
ejpam-6020	255	7	then	then	ADV
ejpam-6020	255	8	[	[	X
ejpam-6020	255	9	ψϵ	ψϵ	ADP
ejpam-6020	255	10	◦	◦	NOUN
ejpam-6020	255	11	πϵ]−1(e	πϵ]−1(e	PROPN
ejpam-6020	255	12	)	)	PUNCT
ejpam-6020	256	1	=	=	SYM
ejpam-6020	257	1	π−1	π−1	PROPN
ejpam-6020	257	2	ϵ	ϵ	X
ejpam-6020	258	1	[	[	X
ejpam-6020	258	2	ψ−1	ψ−1	PROPN
ejpam-6020	258	3	ϵ	ϵ	X
ejpam-6020	258	4	(	(	PUNCT
ejpam-6020	258	5	e	e	NOUN
ejpam-6020	258	6	)	)	PUNCT
ejpam-6020	258	7	]	]	PUNCT
ejpam-6020	259	1	∈	∈	PROPN
ejpam-6020	259	2	soϵ(λ1	soϵ(λ1	NOUN
ejpam-6020	259	3	)	)	PUNCT
ejpam-6020	259	4	.	.	PUNCT
ejpam-6020	260	1	hence	hence	ADV
ejpam-6020	260	2	,	,	PUNCT
ejpam-6020	260	3	ψϵ	ψϵ	ADP
ejpam-6020	260	4	◦	◦	NOUN
ejpam-6020	260	5	πϵ	πϵ	ADP
ejpam-6020	260	6	is	be	AUX
ejpam-6020	260	7	supra	supra	ADJ
ejpam-6020	260	8	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	260	9	.	.	PUNCT
ejpam-6020	261	1	the	the	DET
ejpam-6020	261	2	proof	proof	NOUN
ejpam-6020	261	3	of	of	ADP
ejpam-6020	261	4	the	the	DET
ejpam-6020	261	5	upcoming	upcoming	ADJ
ejpam-6020	261	6	two	two	NUM
ejpam-6020	261	7	corollaries	corollary	NOUN
ejpam-6020	261	8	is	be	AUX
ejpam-6020	261	9	straightforward	straightforward	ADJ
ejpam-6020	261	10	from	from	ADP
ejpam-6020	261	11	theorem	theorem	ADJ
ejpam-6020	261	12	11	11	NUM
ejpam-6020	261	13	.	.	PUNCT
ejpam-6020	261	14	corollary	corollary	ADJ
ejpam-6020	261	15	2	2	NUM
ejpam-6020	261	16	.	.	PUNCT
ejpam-6020	262	1	the	the	DET
ejpam-6020	262	2	composition	composition	NOUN
ejpam-6020	262	3	of	of	ADP
ejpam-6020	262	4	supra	supra	ADJ
ejpam-6020	262	5	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	262	6	function	function	NOUN
ejpam-6020	262	7	and	and	CCONJ
ejpam-6020	262	8	cts	cts	PROPN
ejpam-6020	262	9	function	function	NOUN
ejpam-6020	262	10	is	be	AUX
ejpam-6020	262	11	supra	supra	ADJ
ejpam-6020	262	12	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	262	13	.	.	PUNCT
ejpam-6020	263	1	corollary	corollary	ADJ
ejpam-6020	263	2	3	3	NUM
ejpam-6020	263	3	.	.	PUNCT
ejpam-6020	264	1	the	the	DET
ejpam-6020	264	2	composition	composition	NOUN
ejpam-6020	264	3	of	of	ADP
ejpam-6020	264	4	two	two	NUM
ejpam-6020	264	5	supra	supra	ADJ
ejpam-6020	264	6	ϵ-irresolute	ϵ-irresolute	NOUN
ejpam-6020	264	7	functions	function	NOUN
ejpam-6020	264	8	is	be	AUX
ejpam-6020	264	9	also	also	ADV
ejpam-6020	264	10	supra	supra	PROPN
ejpam-6020	264	11	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	264	12	.	.	PUNCT
ejpam-6020	265	1	theorem	theorem	VERB
ejpam-6020	265	2	12	12	NUM
ejpam-6020	265	3	.	.	PUNCT
ejpam-6020	266	1	a	a	DET
ejpam-6020	266	2	function	function	NOUN
ejpam-6020	266	3	πϵ	πϵ	X
ejpam-6020	266	4	:	:	PUNCT
ejpam-6020	266	5	(	(	PUNCT
ejpam-6020	266	6	λ1	λ1	ADJ
ejpam-6020	266	7	,	,	PUNCT
ejpam-6020	266	8	ν1	ν1	NOUN
ejpam-6020	266	9	)	)	PUNCT
ejpam-6020	266	10	→	→	SYM
ejpam-6020	266	11	(	(	PUNCT
ejpam-6020	266	12	λ2	λ2	NOUN
ejpam-6020	266	13	,	,	PUNCT
ejpam-6020	266	14	ν2	ν2	NOUN
ejpam-6020	266	15	)	)	PUNCT
ejpam-6020	266	16	with	with	ADP
ejpam-6020	266	17	with	with	ADP
ejpam-6020	266	18	ϑ1	ϑ1	NOUN
ejpam-6020	266	19	,	,	PUNCT
ejpam-6020	266	20	ϑ2	ϑ2	PROPN
ejpam-6020	266	21	associated	associate	VERB
ejpam-6020	266	22	stss	stss	NOUN
ejpam-6020	266	23	with	with	ADP
ejpam-6020	266	24	ν1	ν1	NOUN
ejpam-6020	266	25	,	,	PUNCT
ejpam-6020	266	26	ν2	ν2	NOUN
ejpam-6020	266	27	,	,	PUNCT
ejpam-6020	266	28	respectively	respectively	ADV
ejpam-6020	266	29	,	,	PUNCT
ejpam-6020	266	30	is	be	AUX
ejpam-6020	266	31	supra	supra	ADJ
ejpam-6020	266	32	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	266	33	if	if	SCONJ
ejpam-6020	266	34	cls(π−1	cls(π−1	PROPN
ejpam-6020	266	35	ϵ	ϵ	X
ejpam-6020	266	36	(	(	PUNCT
ejpam-6020	266	37	w	w	NOUN
ejpam-6020	266	38	)	)	PUNCT
ejpam-6020	266	39	)	)	PUNCT
ejpam-6020	267	1	⊆	⊆	NUM
ejpam-6020	267	2	π−1	π−1	PROPN
ejpam-6020	267	3	ϵ	ϵ	X
ejpam-6020	267	4	(	(	PUNCT
ejpam-6020	267	5	clsϵ(w	clsϵ(w	PROPN
ejpam-6020	267	6	)	)	PUNCT
ejpam-6020	267	7	)	)	PUNCT
ejpam-6020	267	8	∀w	∀w	X
ejpam-6020	268	1	⊆	⊆	NUM
ejpam-6020	268	2	λ2	λ2	NOUN
ejpam-6020	268	3	.	.	PUNCT
ejpam-6020	269	1	proof	proof	NOUN
ejpam-6020	269	2	.	.	PUNCT
ejpam-6020	270	1	assume	assume	VERB
ejpam-6020	270	2	that	that	SCONJ
ejpam-6020	270	3	w	w	ADP
ejpam-6020	270	4	⊆	⊆	NUM
ejpam-6020	270	5	λ2	λ2	NOUN
ejpam-6020	270	6	.	.	PUNCT
ejpam-6020	271	1	for	for	ADP
ejpam-6020	271	2	π−1	π−1	PROPN
ejpam-6020	271	3	ϵ	ϵ	PROPN
ejpam-6020	271	4	(	(	PUNCT
ejpam-6020	271	5	w	w	PROPN
ejpam-6020	271	6	)	)	PUNCT
ejpam-6020	271	7	,	,	PUNCT
ejpam-6020	271	8	taking	take	VERB
ejpam-6020	271	9	into	into	ADP
ejpam-6020	271	10	account	account	NOUN
ejpam-6020	271	11	the	the	DET
ejpam-6020	271	12	specified	specified	ADJ
ejpam-6020	271	13	condition	condition	NOUN
ejpam-6020	271	14	and	and	CCONJ
ejpam-6020	271	15	theorem	theorem	VERB
ejpam-6020	271	16	5	5	NUM
ejpam-6020	271	17	(	(	PUNCT
ejpam-6020	271	18	4	4	NUM
ejpam-6020	271	19	)	)	PUNCT
ejpam-6020	271	20	,	,	PUNCT
ejpam-6020	271	21	we	we	PRON
ejpam-6020	271	22	get	get	VERB
ejpam-6020	271	23	clsϵ(π	clsϵ(π	NOUN
ejpam-6020	271	24	−1	−1	NOUN
ejpam-6020	271	25	ϵ	ϵ	PROPN
ejpam-6020	271	26	(	(	PUNCT
ejpam-6020	271	27	w	w	NOUN
ejpam-6020	271	28	)	)	PUNCT
ejpam-6020	271	29	)	)	PUNCT
ejpam-6020	272	1	⊆	⊆	NUM
ejpam-6020	272	2	cls(π−1	cls(π−1	NOUN
ejpam-6020	272	3	ϵ	ϵ	X
ejpam-6020	272	4	(	(	PUNCT
ejpam-6020	272	5	w	w	NOUN
ejpam-6020	272	6	)	)	PUNCT
ejpam-6020	272	7	)	)	PUNCT
ejpam-6020	273	1	⊆	⊆	NUM
ejpam-6020	273	2	π−1	π−1	PROPN
ejpam-6020	273	3	ϵ	ϵ	X
ejpam-6020	273	4	(	(	PUNCT
ejpam-6020	273	5	clsϵ(w	clsϵ(w	PROPN
ejpam-6020	273	6	)	)	PUNCT
ejpam-6020	273	7	)	)	PUNCT
ejpam-6020	273	8	.	.	PUNCT
ejpam-6020	274	1	given	give	VERB
ejpam-6020	274	2	theorem	theorem	VERB
ejpam-6020	274	3	10	10	NUM
ejpam-6020	274	4	(	(	PUNCT
ejpam-6020	274	5	3	3	NUM
ejpam-6020	274	6	)	)	PUNCT
ejpam-6020	274	7	,	,	PUNCT
ejpam-6020	274	8	πϵ	πϵ	X
ejpam-6020	274	9	is	be	AUX
ejpam-6020	274	10	supra	supra	PROPN
ejpam-6020	274	11	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	274	12	.	.	PUNCT
ejpam-6020	275	1	theorem	theorem	VERB
ejpam-6020	275	2	13	13	NUM
ejpam-6020	275	3	.	.	PUNCT
ejpam-6020	276	1	a	a	DET
ejpam-6020	276	2	function	function	NOUN
ejpam-6020	276	3	πϵ	πϵ	X
ejpam-6020	276	4	:	:	PUNCT
ejpam-6020	276	5	(	(	PUNCT
ejpam-6020	276	6	λ1	λ1	ADJ
ejpam-6020	276	7	,	,	PUNCT
ejpam-6020	276	8	ν1	ν1	NOUN
ejpam-6020	276	9	)	)	PUNCT
ejpam-6020	276	10	→	→	SYM
ejpam-6020	276	11	(	(	PUNCT
ejpam-6020	276	12	λ2	λ2	NOUN
ejpam-6020	276	13	,	,	PUNCT
ejpam-6020	276	14	ν2	ν2	NOUN
ejpam-6020	276	15	)	)	PUNCT
ejpam-6020	276	16	with	with	ADP
ejpam-6020	276	17	ϑ1	ϑ1	NOUN
ejpam-6020	276	18	,	,	PUNCT
ejpam-6020	276	19	ϑ2	ϑ2	PROPN
ejpam-6020	276	20	associated	associate	VERB
ejpam-6020	276	21	stss	stss	NOUN
ejpam-6020	276	22	with	with	ADP
ejpam-6020	276	23	ν1	ν1	NOUN
ejpam-6020	276	24	,	,	PUNCT
ejpam-6020	276	25	ν2	ν2	NOUN
ejpam-6020	276	26	,	,	PUNCT
ejpam-6020	276	27	respectively	respectively	ADV
ejpam-6020	276	28	,	,	PUNCT
ejpam-6020	276	29	is	be	AUX
ejpam-6020	276	30	supra	supra	ADJ
ejpam-6020	276	31	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	276	32	in	in	ADP
ejpam-6020	276	33	the	the	DET
ejpam-6020	276	34	event	event	NOUN
ejpam-6020	276	35	that	that	SCONJ
ejpam-6020	276	36	one	one	NUM
ejpam-6020	276	37	of	of	ADP
ejpam-6020	276	38	the	the	DET
ejpam-6020	276	39	subsequent	subsequent	ADJ
ejpam-6020	276	40	conditions	condition	NOUN
ejpam-6020	276	41	is	be	AUX
ejpam-6020	276	42	fulfilled	fulfil	VERB
ejpam-6020	276	43	:	:	PUNCT
ejpam-6020	276	44	(	(	PUNCT
ejpam-6020	276	45	1	1	NUM
ejpam-6020	276	46	)	)	PUNCT
ejpam-6020	276	47	πϵ(cl(y	πϵ(cl(y	NOUN
ejpam-6020	276	48	)	)	PUNCT
ejpam-6020	276	49	)	)	PUNCT
ejpam-6020	277	1	⊆	⊆	NUM
ejpam-6020	277	2	clsϵ(πϵ(y	clsϵ(πϵ(y	NOUN
ejpam-6020	277	3	)	)	PUNCT
ejpam-6020	277	4	)	)	PUNCT
ejpam-6020	277	5	∀	∀	X
ejpam-6020	278	1	y	y	PROPN
ejpam-6020	278	2	⊆	⊆	NUM
ejpam-6020	278	3	λ1	λ1	PROPN
ejpam-6020	278	4	.	.	PUNCT
ejpam-6020	279	1	(	(	PUNCT
ejpam-6020	279	2	2	2	X
ejpam-6020	279	3	)	)	PUNCT
ejpam-6020	279	4	cl(π−1	cl(π−1	NOUN
ejpam-6020	279	5	ϵ	ϵ	PROPN
ejpam-6020	279	6	(	(	PUNCT
ejpam-6020	279	7	z	z	NOUN
ejpam-6020	279	8	)	)	PUNCT
ejpam-6020	279	9	)	)	PUNCT
ejpam-6020	280	1	⊆	⊆	NUM
ejpam-6020	280	2	π−1	π−1	PROPN
ejpam-6020	280	3	ϵ	ϵ	X
ejpam-6020	280	4	(	(	PUNCT
ejpam-6020	280	5	clsϵ(z	clsϵ(z	NOUN
ejpam-6020	280	6	)	)	PUNCT
ejpam-6020	280	7	)	)	PUNCT
ejpam-6020	280	8	∀	∀	X
ejpam-6020	281	1	z	z	NOUN
ejpam-6020	281	2	⊆	⊆	NUM
ejpam-6020	281	3	λ2	λ2	NOUN
ejpam-6020	281	4	.	.	PUNCT
ejpam-6020	282	1	(	(	PUNCT
ejpam-6020	282	2	3	3	X
ejpam-6020	282	3	)	)	PUNCT
ejpam-6020	282	4	π−1	π−1	PROPN
ejpam-6020	282	5	ϵ	ϵ	X
ejpam-6020	282	6	(	(	PUNCT
ejpam-6020	282	7	intsϵ(z	intsϵ(z	NOUN
ejpam-6020	282	8	)	)	PUNCT
ejpam-6020	282	9	)	)	PUNCT
ejpam-6020	283	1	⊆	⊆	NUM
ejpam-6020	283	2	int(π−1	int(π−1	NOUN
ejpam-6020	283	3	ϵ	ϵ	X
ejpam-6020	283	4	(	(	PUNCT
ejpam-6020	283	5	z	z	NOUN
ejpam-6020	283	6	)	)	PUNCT
ejpam-6020	283	7	)	)	PUNCT
ejpam-6020	283	8	∀	∀	X
ejpam-6020	284	1	z	z	NOUN
ejpam-6020	284	2	⊆	⊆	NUM
ejpam-6020	284	3	λ2	λ2	NOUN
ejpam-6020	284	4	.	.	PUNCT
ejpam-6020	285	1	proof	proof	NOUN
ejpam-6020	285	2	.	.	PUNCT
ejpam-6020	286	1	if	if	SCONJ
ejpam-6020	286	2	the	the	DET
ejpam-6020	286	3	first	first	ADJ
ejpam-6020	286	4	condition	condition	NOUN
ejpam-6020	286	5	is	be	AUX
ejpam-6020	286	6	fulfilled	fulfil	VERB
ejpam-6020	286	7	,	,	PUNCT
ejpam-6020	286	8	then	then	ADV
ejpam-6020	286	9	πϵ(cl(y	πϵ(cl(y	NOUN
ejpam-6020	286	10	)	)	PUNCT
ejpam-6020	286	11	)	)	PUNCT
ejpam-6020	287	1	⊆	⊆	NUM
ejpam-6020	287	2	clsϵ(πϵ(y	clsϵ(πϵ(y	NOUN
ejpam-6020	287	3	)	)	PUNCT
ejpam-6020	287	4	)	)	PUNCT
ejpam-6020	287	5	∀	∀	X
ejpam-6020	288	1	y	y	PROPN
ejpam-6020	288	2	⊆	⊆	NUM
ejpam-6020	288	3	λ1	λ1	PROPN
ejpam-6020	288	4	.	.	PUNCT
ejpam-6020	289	1	since	since	SCONJ
ejpam-6020	289	2	clsϵ(y	clsϵ(y	PROPN
ejpam-6020	289	3	,	,	PUNCT
ejpam-6020	289	4	θ	θ	NOUN
ejpam-6020	289	5	)	)	PUNCT
ejpam-6020	289	6	⊆	⊆	NUM
ejpam-6020	289	7	cl(y	cl(y	NOUN
ejpam-6020	289	8	,	,	PUNCT
ejpam-6020	289	9	θ	θ	NOUN
ejpam-6020	289	10	)	)	PUNCT
ejpam-6020	289	11	from	from	ADP
ejpam-6020	289	12	theorem	theorem	ADJ
ejpam-6020	289	13	5	5	NUM
ejpam-6020	289	14	(	(	PUNCT
ejpam-6020	289	15	4	4	NUM
ejpam-6020	289	16	)	)	PUNCT
ejpam-6020	289	17	,	,	PUNCT
ejpam-6020	289	18	πϵ(cl	πϵ(cl	PROPN
ejpam-6020	289	19	s	s	PART
ejpam-6020	289	20	ϵ(y	ϵ(y	PROPN
ejpam-6020	289	21	)	)	PUNCT
ejpam-6020	289	22	)	)	PUNCT
ejpam-6020	290	1	⊆	⊆	NUM
ejpam-6020	290	2	πϵ(cl(y	πϵ(cl(y	NOUN
ejpam-6020	290	3	)	)	PUNCT
ejpam-6020	290	4	)	)	PUNCT
ejpam-6020	291	1	⊆	⊆	NUM
ejpam-6020	291	2	clsϵ(πϵ(y	clsϵ(πϵ(y	NOUN
ejpam-6020	291	3	)	)	PUNCT
ejpam-6020	291	4	)	)	PUNCT
ejpam-6020	292	1	⊆	⊆	NUM
ejpam-6020	292	2	cl(πϵ(y	cl(πϵ(y	NOUN
ejpam-6020	292	3	)	)	PUNCT
ejpam-6020	292	4	)	)	PUNCT
ejpam-6020	292	5	.	.	PUNCT
ejpam-6020	293	1	therefore	therefore	ADV
ejpam-6020	293	2	,	,	PUNCT
ejpam-6020	293	3	πϵ	πϵ	INTJ
ejpam-6020	293	4	is	be	AUX
ejpam-6020	293	5	supra	supra	ADJ
ejpam-6020	293	6	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	293	7	according	accord	VERB
ejpam-6020	293	8	to	to	ADP
ejpam-6020	293	9	theorem	theorem	ADJ
ejpam-6020	293	10	7	7	NUM
ejpam-6020	293	11	(	(	PUNCT
ejpam-6020	293	12	4	4	NUM
ejpam-6020	293	13	)	)	PUNCT
ejpam-6020	293	14	.	.	PUNCT
ejpam-6020	294	1	if	if	SCONJ
ejpam-6020	294	2	the	the	DET
ejpam-6020	294	3	second	second	ADJ
ejpam-6020	294	4	condition	condition	NOUN
ejpam-6020	294	5	is	be	AUX
ejpam-6020	294	6	fulfilled	fulfil	VERB
ejpam-6020	294	7	,	,	PUNCT
ejpam-6020	294	8	then	then	ADV
ejpam-6020	294	9	∀	∀	X
ejpam-6020	294	10	z	z	NOUN
ejpam-6020	294	11	⊆	⊆	NUM
ejpam-6020	294	12	λ2	λ2	NOUN
ejpam-6020	294	13	,	,	PUNCT
ejpam-6020	294	14	then	then	ADV
ejpam-6020	294	15	clsϵ(π	clsϵ(π	NOUN
ejpam-6020	294	16	−1	−1	NOUN
ejpam-6020	294	17	ϵ	ϵ	X
ejpam-6020	294	18	(	(	PUNCT
ejpam-6020	294	19	z	z	NOUN
ejpam-6020	294	20	)	)	PUNCT
ejpam-6020	294	21	)	)	PUNCT
ejpam-6020	295	1	⊆	⊆	NUM
ejpam-6020	295	2	cl(π−1	cl(π−1	PROPN
ejpam-6020	295	3	ϵ	ϵ	X
ejpam-6020	295	4	(	(	PUNCT
ejpam-6020	295	5	z	z	NOUN
ejpam-6020	295	6	)	)	PUNCT
ejpam-6020	295	7	)	)	PUNCT
ejpam-6020	296	1	⊆	⊆	NUM
ejpam-6020	296	2	π−1	π−1	PROPN
ejpam-6020	296	3	ϵ	ϵ	X
ejpam-6020	296	4	(	(	PUNCT
ejpam-6020	296	5	clsϵ(z	clsϵ(z	NOUN
ejpam-6020	296	6	)	)	PUNCT
ejpam-6020	296	7	)	)	PUNCT
ejpam-6020	297	1	⊆	⊆	NUM
ejpam-6020	297	2	π−1	π−1	PROPN
ejpam-6020	297	3	ϵ	ϵ	X
ejpam-6020	297	4	(	(	PUNCT
ejpam-6020	297	5	cl(z	cl(z	NOUN
ejpam-6020	297	6	)	)	PUNCT
ejpam-6020	297	7	)	)	PUNCT
ejpam-6020	297	8	,	,	PUNCT
ejpam-6020	297	9	given	give	VERB
ejpam-6020	297	10	theorem	theorem	VERB
ejpam-6020	297	11	5	5	NUM
ejpam-6020	297	12	(	(	PUNCT
ejpam-6020	297	13	4	4	NUM
ejpam-6020	297	14	)	)	PUNCT
ejpam-6020	297	15	.	.	PUNCT
ejpam-6020	298	1	this	this	PRON
ejpam-6020	298	2	implies	imply	VERB
ejpam-6020	298	3	,	,	PUNCT
ejpam-6020	298	4	clsϵ(π	clsϵ(π	NOUN
ejpam-6020	298	5	−1	−1	NOUN
ejpam-6020	298	6	ϵ	ϵ	X
ejpam-6020	298	7	(	(	PUNCT
ejpam-6020	298	8	z	z	NOUN
ejpam-6020	298	9	)	)	PUNCT
ejpam-6020	298	10	)	)	PUNCT
ejpam-6020	299	1	⊆	⊆	NUM
ejpam-6020	299	2	π−1	π−1	PROPN
ejpam-6020	299	3	ϵ	ϵ	X
ejpam-6020	299	4	(	(	PUNCT
ejpam-6020	299	5	cl(z	cl(z	NOUN
ejpam-6020	299	6	)	)	PUNCT
ejpam-6020	299	7	)	)	PUNCT
ejpam-6020	299	8	∀	∀	X
ejpam-6020	300	1	z	z	NOUN
ejpam-6020	300	2	⊆	⊆	NUM
ejpam-6020	300	3	λ2	λ2	NOUN
ejpam-6020	300	4	,	,	PUNCT
ejpam-6020	300	5	and	and	CCONJ
ejpam-6020	300	6	therefore	therefore	ADV
ejpam-6020	300	7	therefore	therefore	ADV
ejpam-6020	300	8	,	,	PUNCT
ejpam-6020	300	9	πϵ	πϵ	INTJ
ejpam-6020	300	10	is	be	AUX
ejpam-6020	300	11	supra	supra	ADJ
ejpam-6020	300	12	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	300	13	according	accord	VERB
ejpam-6020	300	14	to	to	ADP
ejpam-6020	300	15	theorem	theorem	ADJ
ejpam-6020	300	16	7	7	NUM
ejpam-6020	300	17	(	(	PUNCT
ejpam-6020	300	18	3	3	NUM
ejpam-6020	300	19	)	)	PUNCT
ejpam-6020	300	20	.	.	PUNCT
ejpam-6020	301	1	if	if	SCONJ
ejpam-6020	301	2	the	the	DET
ejpam-6020	301	3	third	third	ADJ
ejpam-6020	301	4	condition	condition	NOUN
ejpam-6020	301	5	is	be	AUX
ejpam-6020	301	6	fulfilled	fulfil	VERB
ejpam-6020	301	7	,	,	PUNCT
ejpam-6020	301	8	and	and	CCONJ
ejpam-6020	301	9	given	give	VERB
ejpam-6020	301	10	theorem	theorem	VERB
ejpam-6020	301	11	5	5	NUM
ejpam-6020	301	12	(	(	PUNCT
ejpam-6020	301	13	3	3	NUM
ejpam-6020	301	14	)	)	PUNCT
ejpam-6020	302	1	π−1	π−1	PROPN
ejpam-6020	302	2	ϵ	ϵ	X
ejpam-6020	302	3	(	(	PUNCT
ejpam-6020	302	4	int(z	int(z	PROPN
ejpam-6020	302	5	)	)	PUNCT
ejpam-6020	302	6	)	)	PUNCT
ejpam-6020	303	1	⊆	⊆	NUM
ejpam-6020	303	2	π−1	π−1	PROPN
ejpam-6020	303	3	ϵ	ϵ	X
ejpam-6020	303	4	(	(	PUNCT
ejpam-6020	303	5	intsϵ(z	intsϵ(z	NOUN
ejpam-6020	303	6	)	)	PUNCT
ejpam-6020	303	7	)	)	PUNCT
ejpam-6020	304	1	⊆	⊆	NUM
ejpam-6020	304	2	int(π−1	int(π−1	NOUN
ejpam-6020	304	3	ϵ	ϵ	X
ejpam-6020	304	4	(	(	PUNCT
ejpam-6020	304	5	z	z	NOUN
ejpam-6020	304	6	)	)	PUNCT
ejpam-6020	304	7	)	)	PUNCT
ejpam-6020	305	1	⊆	⊆	NUM
ejpam-6020	305	2	intsϵ(π	intsϵ(π	PROPN
ejpam-6020	305	3	−1	−1	NOUN
ejpam-6020	305	4	ϵ	ϵ	X
ejpam-6020	305	5	(	(	PUNCT
ejpam-6020	305	6	z	z	NOUN
ejpam-6020	305	7	)	)	PUNCT
ejpam-6020	305	8	)	)	PUNCT
ejpam-6020	305	9	∀	∀	X
ejpam-6020	305	10	z	z	NOUN
ejpam-6020	305	11	⊆	⊆	NUM
ejpam-6020	305	12	λ2	λ2	NOUN
ejpam-6020	305	13	.	.	PUNCT
ejpam-6020	306	1	hence	hence	ADV
ejpam-6020	306	2	,	,	PUNCT
ejpam-6020	306	3	π−1	π−1	PROPN
ejpam-6020	306	4	ϵ	ϵ	X
ejpam-6020	306	5	(	(	PUNCT
ejpam-6020	306	6	int(z	int(z	PROPN
ejpam-6020	306	7	)	)	PUNCT
ejpam-6020	306	8	)	)	PUNCT
ejpam-6020	307	1	⊆	⊆	NUM
ejpam-6020	307	2	intsϵ(π	intsϵ(π	PROPN
ejpam-6020	307	3	−1	−1	NOUN
ejpam-6020	307	4	ϵ	ϵ	X
ejpam-6020	307	5	(	(	PUNCT
ejpam-6020	307	6	z	z	NOUN
ejpam-6020	307	7	)	)	PUNCT
ejpam-6020	307	8	)	)	PUNCT
ejpam-6020	307	9	∀	∀	X
ejpam-6020	308	1	z	z	NOUN
ejpam-6020	308	2	⊆	⊆	NUM
ejpam-6020	308	3	λ2	λ2	NOUN
ejpam-6020	308	4	.	.	PUNCT
ejpam-6020	309	1	hence	hence	ADV
ejpam-6020	309	2	,	,	PUNCT
ejpam-6020	309	3	πϵ	πϵ	INTJ
ejpam-6020	309	4	is	be	AUX
ejpam-6020	309	5	supra	supra	ADJ
ejpam-6020	309	6	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	309	7	according	accord	VERB
ejpam-6020	309	8	to	to	ADP
ejpam-6020	309	9	theorem	theorem	ADJ
ejpam-6020	309	10	7	7	NUM
ejpam-6020	309	11	(	(	PUNCT
ejpam-6020	309	12	5	5	NUM
ejpam-6020	309	13	)	)	PUNCT
ejpam-6020	309	14	.	.	PUNCT
ejpam-6020	310	1	a.	a.	PROPN
ejpam-6020	310	2	m.	m.	PROPN
ejpam-6020	310	3	abd	abd	PROPN
ejpam-6020	310	4	el	el	PROPN
ejpam-6020	310	5	-	-	PROPN
ejpam-6020	310	6	latif	latif	PROPN
ejpam-6020	310	7	et	et	PROPN
ejpam-6020	310	8	al	al	PROPN
ejpam-6020	310	9	.	.	PUNCT
ejpam-6020	310	10	/	/	SYM
ejpam-6020	310	11	eur	eur	PROPN
ejpam-6020	310	12	.	.	PUNCT
ejpam-6020	311	1	j.	j.	PROPN
ejpam-6020	311	2	pure	pure	PROPN
ejpam-6020	311	3	appl	appl	PROPN
ejpam-6020	311	4	.	.	PROPN
ejpam-6020	311	5	math	math	PROPN
ejpam-6020	311	6	,	,	PUNCT
ejpam-6020	311	7	18	18	NUM
ejpam-6020	311	8	(	(	PUNCT
ejpam-6020	311	9	2	2	NUM
ejpam-6020	311	10	)	)	PUNCT
ejpam-6020	311	11	(	(	PUNCT
ejpam-6020	311	12	2025	2025	NUM
ejpam-6020	311	13	)	)	PUNCT
ejpam-6020	311	14	,	,	PUNCT
ejpam-6020	311	15	6020	6020	NUM
ejpam-6020	311	16	10	10	NUM
ejpam-6020	311	17	of	of	ADP
ejpam-6020	311	18	17	17	NUM
ejpam-6020	311	19	the	the	DET
ejpam-6020	311	20	proofs	proof	NOUN
ejpam-6020	311	21	for	for	ADP
ejpam-6020	311	22	the	the	DET
ejpam-6020	311	23	next	next	ADJ
ejpam-6020	311	24	two	two	NUM
ejpam-6020	311	25	theorems	theorem	NOUN
ejpam-6020	311	26	are	be	AUX
ejpam-6020	311	27	eliminated	eliminate	VERB
ejpam-6020	311	28	since	since	SCONJ
ejpam-6020	311	29	they	they	PRON
ejpam-6020	311	30	could	could	AUX
ejpam-6020	311	31	be	be	AUX
ejpam-6020	311	32	demonstrated	demonstrate	VERB
ejpam-6020	311	33	similarly	similarly	ADV
ejpam-6020	311	34	to	to	PART
ejpam-6020	311	35	theorem	theorem	VERB
ejpam-6020	311	36	13	13	NUM
ejpam-6020	311	37	.	.	PUNCT
ejpam-6020	312	1	theorem	theorem	VERB
ejpam-6020	312	2	14	14	NUM
ejpam-6020	312	3	.	.	PUNCT
ejpam-6020	313	1	a	a	DET
ejpam-6020	313	2	function	function	NOUN
ejpam-6020	313	3	πϵ	πϵ	X
ejpam-6020	313	4	:	:	PUNCT
ejpam-6020	313	5	(	(	PUNCT
ejpam-6020	313	6	λ1	λ1	ADJ
ejpam-6020	313	7	,	,	PUNCT
ejpam-6020	313	8	ν1	ν1	NOUN
ejpam-6020	313	9	)	)	PUNCT
ejpam-6020	313	10	→	→	SYM
ejpam-6020	313	11	(	(	PUNCT
ejpam-6020	313	12	λ2	λ2	NOUN
ejpam-6020	313	13	,	,	PUNCT
ejpam-6020	313	14	ν2	ν2	NOUN
ejpam-6020	313	15	)	)	PUNCT
ejpam-6020	313	16	with	with	ADP
ejpam-6020	313	17	ϑ1	ϑ1	NOUN
ejpam-6020	313	18	,	,	PUNCT
ejpam-6020	313	19	ϑ2	ϑ2	PROPN
ejpam-6020	313	20	associated	associate	VERB
ejpam-6020	313	21	stss	stss	NOUN
ejpam-6020	313	22	with	with	ADP
ejpam-6020	313	23	ν1	ν1	NOUN
ejpam-6020	313	24	,	,	PUNCT
ejpam-6020	313	25	ν2	ν2	NOUN
ejpam-6020	313	26	,	,	PUNCT
ejpam-6020	313	27	respectively	respectively	ADV
ejpam-6020	313	28	,	,	PUNCT
ejpam-6020	313	29	is	be	AUX
ejpam-6020	313	30	supra	supra	ADJ
ejpam-6020	313	31	ϵ∗-cts	ϵ∗-ct	NOUN
ejpam-6020	313	32	in	in	ADP
ejpam-6020	313	33	the	the	DET
ejpam-6020	313	34	event	event	NOUN
ejpam-6020	313	35	that	that	SCONJ
ejpam-6020	313	36	one	one	NUM
ejpam-6020	313	37	of	of	ADP
ejpam-6020	313	38	the	the	DET
ejpam-6020	313	39	subsequent	subsequent	ADJ
ejpam-6020	313	40	conditions	condition	NOUN
ejpam-6020	313	41	is	be	AUX
ejpam-6020	313	42	fulfilled	fulfil	VERB
ejpam-6020	313	43	:	:	PUNCT
ejpam-6020	313	44	(	(	PUNCT
ejpam-6020	313	45	1	1	X
ejpam-6020	313	46	)	)	PUNCT
ejpam-6020	313	47	πϵ(cl	πϵ(cl	NOUN
ejpam-6020	313	48	s(y	s(y	PROPN
ejpam-6020	313	49	)	)	PUNCT
ejpam-6020	313	50	)	)	PUNCT
ejpam-6020	314	1	⊆	⊆	NUM
ejpam-6020	314	2	clsϵ(πϵ(y	clsϵ(πϵ(y	NOUN
ejpam-6020	314	3	)	)	PUNCT
ejpam-6020	314	4	)	)	PUNCT
ejpam-6020	314	5	∀	∀	X
ejpam-6020	315	1	y	y	PROPN
ejpam-6020	315	2	⊆	⊆	NUM
ejpam-6020	315	3	λ1	λ1	PROPN
ejpam-6020	315	4	.	.	PUNCT
ejpam-6020	316	1	(	(	PUNCT
ejpam-6020	316	2	2	2	NUM
ejpam-6020	316	3	)	)	PUNCT
ejpam-6020	316	4	cls(π−1	cls(π−1	PROPN
ejpam-6020	317	1	ϵ	ϵ	X
ejpam-6020	317	2	(	(	PUNCT
ejpam-6020	317	3	z	z	NOUN
ejpam-6020	317	4	)	)	PUNCT
ejpam-6020	317	5	)	)	PUNCT
ejpam-6020	318	1	⊆	⊆	NUM
ejpam-6020	318	2	π−1	π−1	PROPN
ejpam-6020	318	3	ϵ	ϵ	X
ejpam-6020	318	4	(	(	PUNCT
ejpam-6020	318	5	clsϵ(z	clsϵ(z	NOUN
ejpam-6020	318	6	)	)	PUNCT
ejpam-6020	318	7	)	)	PUNCT
ejpam-6020	318	8	∀	∀	X
ejpam-6020	319	1	z	z	NOUN
ejpam-6020	319	2	⊆	⊆	NUM
ejpam-6020	319	3	λ2	λ2	NOUN
ejpam-6020	319	4	.	.	PUNCT
ejpam-6020	320	1	(	(	PUNCT
ejpam-6020	320	2	3	3	X
ejpam-6020	320	3	)	)	PUNCT
ejpam-6020	320	4	π−1	π−1	PROPN
ejpam-6020	320	5	ϵ	ϵ	X
ejpam-6020	320	6	(	(	PUNCT
ejpam-6020	320	7	intsϵ(z	intsϵ(z	NOUN
ejpam-6020	320	8	)	)	PUNCT
ejpam-6020	320	9	)	)	PUNCT
ejpam-6020	321	1	⊆	⊆	NUM
ejpam-6020	321	2	ints(π−1	ints(π−1	NOUN
ejpam-6020	321	3	ϵ	ϵ	X
ejpam-6020	321	4	(	(	PUNCT
ejpam-6020	321	5	z	z	NOUN
ejpam-6020	321	6	)	)	PUNCT
ejpam-6020	321	7	)	)	PUNCT
ejpam-6020	321	8	∀	∀	X
ejpam-6020	321	9	z	z	NOUN
ejpam-6020	321	10	⊆	⊆	NUM
ejpam-6020	321	11	λ2	λ2	NOUN
ejpam-6020	321	12	.	.	PUNCT
ejpam-6020	321	13	theorem	theorem	VERB
ejpam-6020	321	14	15	15	NUM
ejpam-6020	321	15	.	.	PUNCT
ejpam-6020	322	1	a	a	DET
ejpam-6020	322	2	function	function	NOUN
ejpam-6020	322	3	πϵ	πϵ	X
ejpam-6020	322	4	:	:	PUNCT
ejpam-6020	322	5	(	(	PUNCT
ejpam-6020	322	6	λ1	λ1	ADJ
ejpam-6020	322	7	,	,	PUNCT
ejpam-6020	322	8	ν1	ν1	NOUN
ejpam-6020	322	9	)	)	PUNCT
ejpam-6020	322	10	→	→	SYM
ejpam-6020	322	11	(	(	PUNCT
ejpam-6020	322	12	λ2	λ2	NOUN
ejpam-6020	322	13	,	,	PUNCT
ejpam-6020	322	14	ν2	ν2	NOUN
ejpam-6020	322	15	)	)	PUNCT
ejpam-6020	322	16	with	with	ADP
ejpam-6020	322	17	ϑ1	ϑ1	NOUN
ejpam-6020	322	18	,	,	PUNCT
ejpam-6020	322	19	ϑ2	ϑ2	PROPN
ejpam-6020	322	20	associated	associate	VERB
ejpam-6020	322	21	stss	stss	NOUN
ejpam-6020	322	22	with	with	ADP
ejpam-6020	322	23	ν1	ν1	NOUN
ejpam-6020	322	24	,	,	PUNCT
ejpam-6020	322	25	ν2	ν2	NOUN
ejpam-6020	322	26	,	,	PUNCT
ejpam-6020	322	27	respectively	respectively	ADV
ejpam-6020	322	28	,	,	PUNCT
ejpam-6020	322	29	is	be	AUX
ejpam-6020	322	30	supra	supra	ADJ
ejpam-6020	322	31	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	322	32	in	in	ADP
ejpam-6020	322	33	the	the	DET
ejpam-6020	322	34	event	event	NOUN
ejpam-6020	322	35	that	that	SCONJ
ejpam-6020	322	36	one	one	NUM
ejpam-6020	322	37	of	of	ADP
ejpam-6020	322	38	the	the	DET
ejpam-6020	322	39	subsequent	subsequent	ADJ
ejpam-6020	322	40	conditions	condition	NOUN
ejpam-6020	322	41	is	be	AUX
ejpam-6020	322	42	fulfilled	fulfil	VERB
ejpam-6020	322	43	:	:	PUNCT
ejpam-6020	322	44	(	(	PUNCT
ejpam-6020	322	45	1	1	X
ejpam-6020	322	46	)	)	PUNCT
ejpam-6020	322	47	πϵ(cl	πϵ(cl	NOUN
ejpam-6020	322	48	s	s	PART
ejpam-6020	322	49	ϵ(y	ϵ(y	PROPN
ejpam-6020	322	50	)	)	PUNCT
ejpam-6020	322	51	)	)	PUNCT
ejpam-6020	323	1	⊆	⊆	NUM
ejpam-6020	323	2	clsϵ(πϵ(y	clsϵ(πϵ(y	NOUN
ejpam-6020	323	3	)	)	PUNCT
ejpam-6020	323	4	)	)	PUNCT
ejpam-6020	323	5	∀	∀	X
ejpam-6020	324	1	y	y	PROPN
ejpam-6020	324	2	⊆	⊆	NUM
ejpam-6020	324	3	λ1	λ1	PROPN
ejpam-6020	324	4	.	.	PUNCT
ejpam-6020	325	1	(	(	PUNCT
ejpam-6020	325	2	2	2	X
ejpam-6020	325	3	)	)	PUNCT
ejpam-6020	325	4	clsϵ(π	clsϵ(π	NOUN
ejpam-6020	325	5	−1	−1	NOUN
ejpam-6020	325	6	ϵ	ϵ	X
ejpam-6020	325	7	(	(	PUNCT
ejpam-6020	325	8	z	z	NOUN
ejpam-6020	325	9	)	)	PUNCT
ejpam-6020	325	10	)	)	PUNCT
ejpam-6020	326	1	⊆	⊆	NUM
ejpam-6020	326	2	π−1	π−1	PROPN
ejpam-6020	326	3	ϵ	ϵ	X
ejpam-6020	326	4	(	(	PUNCT
ejpam-6020	326	5	clsϵ(z	clsϵ(z	NOUN
ejpam-6020	326	6	)	)	PUNCT
ejpam-6020	326	7	)	)	PUNCT
ejpam-6020	326	8	∀	∀	X
ejpam-6020	327	1	z	z	NOUN
ejpam-6020	327	2	⊆	⊆	NUM
ejpam-6020	327	3	λ2	λ2	NOUN
ejpam-6020	327	4	.	.	PUNCT
ejpam-6020	328	1	(	(	PUNCT
ejpam-6020	328	2	3	3	X
ejpam-6020	328	3	)	)	PUNCT
ejpam-6020	328	4	π−1	π−1	PROPN
ejpam-6020	328	5	ϵ	ϵ	X
ejpam-6020	328	6	(	(	PUNCT
ejpam-6020	328	7	intsϵ(z	intsϵ(z	NOUN
ejpam-6020	328	8	)	)	PUNCT
ejpam-6020	328	9	)	)	PUNCT
ejpam-6020	329	1	⊆	⊆	NUM
ejpam-6020	329	2	intsϵ(π	intsϵ(π	PROPN
ejpam-6020	329	3	−1	−1	NOUN
ejpam-6020	329	4	ϵ	ϵ	X
ejpam-6020	329	5	(	(	PUNCT
ejpam-6020	329	6	z	z	NOUN
ejpam-6020	329	7	)	)	PUNCT
ejpam-6020	329	8	)	)	PUNCT
ejpam-6020	329	9	∀	∀	X
ejpam-6020	329	10	z	z	NOUN
ejpam-6020	329	11	⊆	⊆	NUM
ejpam-6020	329	12	λ2	λ2	NOUN
ejpam-6020	329	13	.	.	PUNCT
ejpam-6020	330	1	4	4	NUM
ejpam-6020	330	2	.	.	X
ejpam-6020	330	3	supra	supra	PROPN
ejpam-6020	330	4	ϵ-homeomorphism	ϵ-homeomorphism	NOUN
ejpam-6020	330	5	functions	function	NOUN
ejpam-6020	330	6	we	we	PRON
ejpam-6020	330	7	present	present	VERB
ejpam-6020	330	8	new	new	ADJ
ejpam-6020	330	9	approaches	approach	NOUN
ejpam-6020	330	10	for	for	ADP
ejpam-6020	330	11	supra	supra	ADJ
ejpam-6020	330	12	functions	function	NOUN
ejpam-6020	330	13	in	in	ADP
ejpam-6020	330	14	this	this	DET
ejpam-6020	330	15	section	section	NOUN
ejpam-6020	330	16	,	,	PUNCT
ejpam-6020	330	17	which	which	PRON
ejpam-6020	330	18	we	we	PRON
ejpam-6020	330	19	call	call	VERB
ejpam-6020	330	20	supra	supra	PROPN
ejpam-6020	330	21	ϵ-open	ϵ-open	PROPN
ejpam-6020	330	22	functions	function	NOUN
ejpam-6020	330	23	,	,	PUNCT
ejpam-6020	330	24	supra	supra	ADJ
ejpam-6020	330	25	ϵ-closed	ϵ-close	VERB
ejpam-6020	330	26	functions	function	NOUN
ejpam-6020	330	27	,	,	PUNCT
ejpam-6020	330	28	and	and	CCONJ
ejpam-6020	330	29	supra	supra	PROPN
ejpam-6020	330	30	ϵ-homeomorphism	ϵ-homeomorphism	NOUN
ejpam-6020	330	31	functions	function	NOUN
ejpam-6020	330	32	.	.	PUNCT
ejpam-6020	331	1	furthermore	furthermore	ADV
ejpam-6020	331	2	,	,	PUNCT
ejpam-6020	331	3	we	we	PRON
ejpam-6020	331	4	show	show	VERB
ejpam-6020	331	5	their	their	PRON
ejpam-6020	331	6	corresponding	correspond	VERB
ejpam-6020	331	7	properties	property	NOUN
ejpam-6020	331	8	in	in	ADP
ejpam-6020	331	9	a	a	DET
ejpam-6020	331	10	transparent	transparent	ADJ
ejpam-6020	331	11	way	way	NOUN
ejpam-6020	331	12	.	.	PUNCT
ejpam-6020	332	1	moreover	moreover	ADV
ejpam-6020	332	2	,	,	PUNCT
ejpam-6020	332	3	for	for	ADP
ejpam-6020	332	4	every	every	DET
ejpam-6020	332	5	notion	notion	NOUN
ejpam-6020	332	6	,	,	PUNCT
ejpam-6020	332	7	we	we	PRON
ejpam-6020	332	8	give	give	VERB
ejpam-6020	332	9	the	the	DET
ejpam-6020	332	10	analogous	analogous	ADJ
ejpam-6020	332	11	conditions	condition	NOUN
ejpam-6020	332	12	that	that	PRON
ejpam-6020	332	13	are	be	AUX
ejpam-6020	332	14	required	require	VERB
ejpam-6020	332	15	.	.	PUNCT
ejpam-6020	333	1	definition	definition	NOUN
ejpam-6020	333	2	12	12	NUM
ejpam-6020	333	3	.	.	PUNCT
ejpam-6020	334	1	a	a	DET
ejpam-6020	334	2	function	function	NOUN
ejpam-6020	334	3	πϵ	πϵ	X
ejpam-6020	334	4	:	:	PUNCT
ejpam-6020	334	5	(	(	PUNCT
ejpam-6020	334	6	λ1	λ1	ADJ
ejpam-6020	334	7	,	,	PUNCT
ejpam-6020	334	8	ν1	ν1	NOUN
ejpam-6020	334	9	)	)	PUNCT
ejpam-6020	334	10	→	→	SYM
ejpam-6020	334	11	(	(	PUNCT
ejpam-6020	334	12	λ2	λ2	NOUN
ejpam-6020	334	13	,	,	PUNCT
ejpam-6020	334	14	ν2	ν2	NOUN
ejpam-6020	334	15	)	)	PUNCT
ejpam-6020	334	16	with	with	ADP
ejpam-6020	334	17	ϑ2	ϑ2	PROPN
ejpam-6020	334	18	as	as	ADP
ejpam-6020	334	19	an	an	DET
ejpam-6020	334	20	associated	associate	VERB
ejpam-6020	334	21	sts	st	NOUN
ejpam-6020	334	22	with	with	ADP
ejpam-6020	334	23	ν2	ν2	NOUN
ejpam-6020	334	24	is	be	AUX
ejpam-6020	334	25	said	say	VERB
ejpam-6020	334	26	to	to	PART
ejpam-6020	334	27	be	be	AUX
ejpam-6020	334	28	:	:	PUNCT
ejpam-6020	334	29	(	(	PUNCT
ejpam-6020	334	30	1	1	X
ejpam-6020	334	31	)	)	PUNCT
ejpam-6020	334	32	supra	supra	NOUN
ejpam-6020	334	33	ϵ-open	ϵ-open	PROPN
ejpam-6020	334	34	if	if	SCONJ
ejpam-6020	334	35	πϵ(u	πϵ(u	NOUN
ejpam-6020	334	36	)	)	PUNCT
ejpam-6020	334	37	∈	∈	PROPN
ejpam-6020	334	38	soϵ(λ2	soϵ(λ2	PROPN
ejpam-6020	334	39	)	)	PUNCT
ejpam-6020	334	40	for	for	ADP
ejpam-6020	334	41	each	each	DET
ejpam-6020	334	42	u	u	PROPN
ejpam-6020	334	43	∈	∈	PROPN
ejpam-6020	334	44	ν1	ν1	NOUN
ejpam-6020	334	45	.	.	PUNCT
ejpam-6020	335	1	(	(	PUNCT
ejpam-6020	335	2	2	2	X
ejpam-6020	335	3	)	)	PUNCT
ejpam-6020	335	4	supra	supra	NOUN
ejpam-6020	335	5	ϵ-closed	ϵ-close	VERB
ejpam-6020	335	6	if	if	SCONJ
ejpam-6020	335	7	πϵ(c	πϵ(c	ADJ
ejpam-6020	335	8	)	)	PUNCT
ejpam-6020	335	9	∈	∈	PROPN
ejpam-6020	335	10	scϵ(λ2	scϵ(λ2	NOUN
ejpam-6020	335	11	)	)	PUNCT
ejpam-6020	335	12	for	for	ADP
ejpam-6020	335	13	each	each	DET
ejpam-6020	335	14	c	c	PROPN
ejpam-6020	335	15	∈	∈	PROPN
ejpam-6020	335	16	νc1	νc1	NOUN
ejpam-6020	335	17	.	.	PUNCT
ejpam-6020	336	1	theorem	theorem	VERB
ejpam-6020	336	2	16	16	NUM
ejpam-6020	336	3	.	.	PUNCT
ejpam-6020	337	1	let	let	VERB
ejpam-6020	337	2	πϵ	πϵ	INTJ
ejpam-6020	337	3	:	:	PUNCT
ejpam-6020	337	4	(	(	PUNCT
ejpam-6020	337	5	λ1	λ1	ADJ
ejpam-6020	337	6	,	,	PUNCT
ejpam-6020	337	7	ν1	ν1	NOUN
ejpam-6020	337	8	)	)	PUNCT
ejpam-6020	337	9	→	→	SYM
ejpam-6020	337	10	(	(	PUNCT
ejpam-6020	337	11	λ2	λ2	NOUN
ejpam-6020	337	12	,	,	PUNCT
ejpam-6020	337	13	ν2	ν2	NOUN
ejpam-6020	337	14	)	)	PUNCT
ejpam-6020	337	15	be	be	VERB
ejpam-6020	337	16	a	a	DET
ejpam-6020	337	17	function	function	NOUN
ejpam-6020	337	18	with	with	ADP
ejpam-6020	337	19	ϑ2	ϑ2	PROPN
ejpam-6020	337	20	as	as	ADP
ejpam-6020	337	21	an	an	DET
ejpam-6020	337	22	associated	associate	VERB
ejpam-6020	337	23	sts	st	NOUN
ejpam-6020	337	24	with	with	ADP
ejpam-6020	337	25	ν2	ν2	NOUN
ejpam-6020	337	26	and	and	CCONJ
ejpam-6020	337	27	y	y	PROPN
ejpam-6020	337	28	⊆	⊆	NUM
ejpam-6020	337	29	λ1	λ1	PROPN
ejpam-6020	337	30	,	,	PUNCT
ejpam-6020	337	31	then	then	ADV
ejpam-6020	337	32	πϵ	πϵ	INTJ
ejpam-6020	337	33	is	be	AUX
ejpam-6020	337	34	supra	supra	PROPN
ejpam-6020	337	35	ϵ-open	ϵ-open	PROPN
ejpam-6020	338	1	if	if	SCONJ
ejpam-6020	338	2	and	and	CCONJ
ejpam-6020	338	3	only	only	ADV
ejpam-6020	338	4	if	if	SCONJ
ejpam-6020	338	5	πϵ(int(u	πϵ(int(u	NOUN
ejpam-6020	338	6	)	)	PUNCT
ejpam-6020	338	7	)	)	PUNCT
ejpam-6020	339	1	⊆	⊆	NUM
ejpam-6020	339	2	intsϵ	intsϵ	NOUN
ejpam-6020	339	3	[	[	X
ejpam-6020	339	4	πϵ(u	πϵ(u	PROPN
ejpam-6020	339	5	)	)	PUNCT
ejpam-6020	339	6	]	]	PUNCT
ejpam-6020	339	7	∀	∀	PUNCT
ejpam-6020	339	8	u	u	NOUN
ejpam-6020	339	9	⊆	⊆	NUM
ejpam-6020	339	10	λ1	λ1	ADJ
ejpam-6020	339	11	.	.	PUNCT
ejpam-6020	340	1	proof	proof	NOUN
ejpam-6020	340	2	.	.	PUNCT
ejpam-6020	341	1	“	"	PUNCT
ejpam-6020	341	2	⇒	⇒	NOUN
ejpam-6020	341	3	”	"	PUNCT
ejpam-6020	341	4	let	let	VERB
ejpam-6020	341	5	πϵ	πϵ	PART
ejpam-6020	341	6	be	be	AUX
ejpam-6020	341	7	a	a	DET
ejpam-6020	341	8	supra	supra	ADJ
ejpam-6020	341	9	ϵ-open	ϵ-open	PROPN
ejpam-6020	341	10	function	function	NOUN
ejpam-6020	341	11	and	and	CCONJ
ejpam-6020	341	12	u	u	NOUN
ejpam-6020	341	13	⊆	⊆	NUM
ejpam-6020	341	14	λ1	λ1	PROPN
ejpam-6020	341	15	.	.	PUNCT
ejpam-6020	342	1	since	since	SCONJ
ejpam-6020	342	2	int(u	int(u	PROPN
ejpam-6020	342	3	)	)	PUNCT
ejpam-6020	342	4	⊆	⊆	NUM
ejpam-6020	342	5	u	u	NOUN
ejpam-6020	342	6	,	,	PUNCT
ejpam-6020	342	7	πϵ(int(u	πϵ(int(u	ADV
ejpam-6020	342	8	)	)	PUNCT
ejpam-6020	342	9	)	)	PUNCT
ejpam-6020	342	10	⊆	⊆	NUM
ejpam-6020	342	11	πϵ((u	πϵ((u	NOUN
ejpam-6020	342	12	)	)	PUNCT
ejpam-6020	342	13	)	)	PUNCT
ejpam-6020	342	14	,	,	PUNCT
ejpam-6020	342	15	which	which	PRON
ejpam-6020	342	16	implies	imply	VERB
ejpam-6020	342	17	πϵ(int(u	πϵ(int(u	ADV
ejpam-6020	342	18	)	)	PUNCT
ejpam-6020	342	19	)	)	PUNCT
ejpam-6020	343	1	=	=	PRON
ejpam-6020	343	2	intsϵ	intsϵ	NOUN
ejpam-6020	343	3	[	[	X
ejpam-6020	343	4	πϵ(int(u	πϵ(int(u	ADV
ejpam-6020	343	5	)	)	PUNCT
ejpam-6020	343	6	)	)	PUNCT
ejpam-6020	343	7	]	]	PUNCT
ejpam-6020	344	1	⊆	⊆	NUM
ejpam-6020	344	2	intsϵ	intsϵ	NOUN
ejpam-6020	344	3	[	[	X
ejpam-6020	344	4	πϵ((u	πϵ((u	NOUN
ejpam-6020	344	5	)	)	PUNCT
ejpam-6020	344	6	)	)	PUNCT
ejpam-6020	344	7	]	]	PUNCT
ejpam-6020	344	8	.	.	PUNCT
ejpam-6020	345	1	“	"	PUNCT
ejpam-6020	345	2	⇐	⇐	ADJ
ejpam-6020	345	3	”	"	PUNCT
ejpam-6020	345	4	assume	assume	VERB
ejpam-6020	345	5	that	that	SCONJ
ejpam-6020	345	6	u	u	PROPN
ejpam-6020	345	7	∈	∈	PROPN
ejpam-6020	345	8	ν1	ν1	NOUN
ejpam-6020	345	9	.	.	PUNCT
ejpam-6020	346	1	based	base	VERB
ejpam-6020	346	2	on	on	ADP
ejpam-6020	346	3	the	the	DET
ejpam-6020	346	4	presumption	presumption	NOUN
ejpam-6020	346	5	,	,	PUNCT
ejpam-6020	346	6	πϵ(u	πϵ(u	PROPN
ejpam-6020	346	7	)	)	PUNCT
ejpam-6020	346	8	=	=	SYM
ejpam-6020	346	9	πϵ(int(u	πϵ(int(u	X
ejpam-6020	346	10	)	)	PUNCT
ejpam-6020	346	11	)	)	PUNCT
ejpam-6020	347	1	⊆	⊆	NUM
ejpam-6020	347	2	intsϵ	intsϵ	NOUN
ejpam-6020	347	3	[	[	X
ejpam-6020	347	4	πϵ(u	πϵ(u	NOUN
ejpam-6020	347	5	)	)	PUNCT
ejpam-6020	347	6	]	]	PUNCT
ejpam-6020	347	7	.	.	PUNCT
ejpam-6020	348	1	a.	a.	PROPN
ejpam-6020	348	2	m.	m.	PROPN
ejpam-6020	348	3	abd	abd	PROPN
ejpam-6020	348	4	el	el	PROPN
ejpam-6020	348	5	-	-	PROPN
ejpam-6020	348	6	latif	latif	PROPN
ejpam-6020	348	7	et	et	PROPN
ejpam-6020	348	8	al	al	PROPN
ejpam-6020	348	9	.	.	PUNCT
ejpam-6020	348	10	/	/	SYM
ejpam-6020	348	11	eur	eur	PROPN
ejpam-6020	348	12	.	.	PUNCT
ejpam-6020	349	1	j.	j.	PROPN
ejpam-6020	349	2	pure	pure	PROPN
ejpam-6020	349	3	appl	appl	PROPN
ejpam-6020	349	4	.	.	PROPN
ejpam-6020	349	5	math	math	PROPN
ejpam-6020	349	6	,	,	PUNCT
ejpam-6020	349	7	18	18	NUM
ejpam-6020	349	8	(	(	PUNCT
ejpam-6020	349	9	2	2	NUM
ejpam-6020	349	10	)	)	PUNCT
ejpam-6020	349	11	(	(	PUNCT
ejpam-6020	349	12	2025	2025	NUM
ejpam-6020	349	13	)	)	PUNCT
ejpam-6020	349	14	,	,	PUNCT
ejpam-6020	349	15	6020	6020	NUM
ejpam-6020	349	16	11	11	NUM
ejpam-6020	349	17	of	of	ADP
ejpam-6020	349	18	17	17	NUM
ejpam-6020	349	19	but	but	CCONJ
ejpam-6020	349	20	,	,	PUNCT
ejpam-6020	349	21	we	we	PRON
ejpam-6020	349	22	have	have	VERB
ejpam-6020	349	23	intsϵ	intsϵ	NOUN
ejpam-6020	349	24	[	[	X
ejpam-6020	349	25	πϵ(u	πϵ(u	PROPN
ejpam-6020	349	26	)	)	PUNCT
ejpam-6020	349	27	]	]	PUNCT
ejpam-6020	350	1	⊆	⊆	NUM
ejpam-6020	350	2	πϵ(u	πϵ(u	NUM
ejpam-6020	350	3	)	)	PUNCT
ejpam-6020	350	4	.	.	PUNCT
ejpam-6020	351	1	hence	hence	ADV
ejpam-6020	351	2	,	,	PUNCT
ejpam-6020	351	3	intsϵ	intsϵ	VERB
ejpam-6020	351	4	[	[	X
ejpam-6020	351	5	πϵ(u	πϵ(u	NOUN
ejpam-6020	351	6	)	)	PUNCT
ejpam-6020	351	7	]	]	PUNCT
ejpam-6020	352	1	=	=	PUNCT
ejpam-6020	352	2	πϵ(u	πϵ(u	PROPN
ejpam-6020	352	3	)	)	PUNCT
ejpam-6020	352	4	.	.	PUNCT
ejpam-6020	353	1	therefore	therefore	ADV
ejpam-6020	353	2	,	,	PUNCT
ejpam-6020	353	3	πϵ(u	πϵ(u	ADV
ejpam-6020	353	4	)	)	PUNCT
ejpam-6020	353	5	∈	∈	PROPN
ejpam-6020	353	6	soϵ(λ2	soϵ(λ2	PROPN
ejpam-6020	353	7	)	)	PUNCT
ejpam-6020	353	8	,	,	PUNCT
ejpam-6020	353	9	and	and	CCONJ
ejpam-6020	353	10	thus	thus	ADV
ejpam-6020	353	11	πϵ	πϵ	PRON
ejpam-6020	353	12	is	be	VERB
ejpam-6020	353	13	a	a	DET
ejpam-6020	353	14	supra	supra	ADJ
ejpam-6020	353	15	ϵ-open	ϵ-open	PROPN
ejpam-6020	353	16	function	function	PROPN
ejpam-6020	353	17	.	.	PUNCT
ejpam-6020	354	1	theorem	theorem	VERB
ejpam-6020	354	2	17	17	NUM
ejpam-6020	354	3	.	.	PUNCT
ejpam-6020	355	1	let	let	AUX
ejpam-6020	355	2	πϵ	πϵ	INTJ
ejpam-6020	355	3	:	:	PUNCT
ejpam-6020	355	4	(	(	PUNCT
ejpam-6020	355	5	λ1	λ1	ADJ
ejpam-6020	355	6	,	,	PUNCT
ejpam-6020	355	7	ν1	ν1	NOUN
ejpam-6020	355	8	)	)	PUNCT
ejpam-6020	355	9	→	→	SYM
ejpam-6020	355	10	(	(	PUNCT
ejpam-6020	355	11	λ2	λ2	NOUN
ejpam-6020	355	12	,	,	PUNCT
ejpam-6020	355	13	ν2	ν2	NOUN
ejpam-6020	355	14	)	)	PUNCT
ejpam-6020	355	15	be	be	VERB
ejpam-6020	355	16	a	a	DET
ejpam-6020	355	17	function	function	NOUN
ejpam-6020	355	18	with	with	ADP
ejpam-6020	355	19	ϑ2	ϑ2	PROPN
ejpam-6020	355	20	as	as	ADP
ejpam-6020	355	21	an	an	DET
ejpam-6020	355	22	associated	associate	VERB
ejpam-6020	355	23	sts	st	NOUN
ejpam-6020	355	24	with	with	ADP
ejpam-6020	355	25	ν2	ν2	NOUN
ejpam-6020	355	26	and	and	CCONJ
ejpam-6020	355	27	y	y	PROPN
ejpam-6020	355	28	⊆	⊆	NUM
ejpam-6020	355	29	λ1	λ1	PROPN
ejpam-6020	355	30	,	,	PUNCT
ejpam-6020	355	31	then	then	ADV
ejpam-6020	355	32	πϵ	πϵ	INTJ
ejpam-6020	355	33	is	be	AUX
ejpam-6020	355	34	supra	supra	PROPN
ejpam-6020	355	35	ϵ-closed	ϵ-close	VERB
ejpam-6020	355	36	if	if	SCONJ
ejpam-6020	355	37	and	and	CCONJ
ejpam-6020	355	38	only	only	ADV
ejpam-6020	355	39	if	if	SCONJ
ejpam-6020	355	40	clsϵ	clsϵ	NOUN
ejpam-6020	355	41	[	[	X
ejpam-6020	355	42	πϵ(h	πϵ(h	NOUN
ejpam-6020	355	43	)	)	PUNCT
ejpam-6020	355	44	]	]	PUNCT
ejpam-6020	355	45	⊆	⊆	NUM
ejpam-6020	355	46	πϵ(cl(h	πϵ(cl(h	NUM
ejpam-6020	355	47	)	)	PUNCT
ejpam-6020	355	48	)	)	PUNCT
ejpam-6020	355	49	.	.	PUNCT
ejpam-6020	356	1	proof	proof	NOUN
ejpam-6020	356	2	.	.	PUNCT
ejpam-6020	356	3	”	"	PUNCT
ejpam-6020	356	4	⇒	⇒	NOUN
ejpam-6020	356	5	”	"	PUNCT
ejpam-6020	356	6	assume	assume	VERB
ejpam-6020	356	7	that	that	SCONJ
ejpam-6020	356	8	πϵ	πϵ	INTJ
ejpam-6020	356	9	is	be	AUX
ejpam-6020	356	10	supra	supra	ADJ
ejpam-6020	356	11	ϵ-closed	ϵ-close	VERB
ejpam-6020	356	12	function	function	NOUN
ejpam-6020	356	13	and	and	CCONJ
ejpam-6020	356	14	h	h	NOUN
ejpam-6020	356	15	⊆	⊆	NUM
ejpam-6020	356	16	λ1	λ1	PROPN
ejpam-6020	356	17	.	.	PUNCT
ejpam-6020	357	1	since	since	SCONJ
ejpam-6020	357	2	πϵ(h	πϵ(h	NOUN
ejpam-6020	357	3	)	)	PUNCT
ejpam-6020	357	4	⊆	⊆	NUM
ejpam-6020	357	5	πϵ(cl(h	πϵ(cl(h	NOUN
ejpam-6020	357	6	)	)	PUNCT
ejpam-6020	357	7	)	)	PUNCT
ejpam-6020	358	1	,	,	PUNCT
ejpam-6020	358	2	clsϵ	clsϵ	NOUN
ejpam-6020	358	3	[	[	X
ejpam-6020	358	4	πϵ(h	πϵ(h	NOUN
ejpam-6020	358	5	)	)	PUNCT
ejpam-6020	358	6	]	]	PUNCT
ejpam-6020	359	1	⊆	⊆	NUM
ejpam-6020	359	2	clsϵ	clsϵ	NOUN
ejpam-6020	359	3	[	[	X
ejpam-6020	359	4	πϵ(cl(h	πϵ(cl(h	PROPN
ejpam-6020	359	5	)	)	PUNCT
ejpam-6020	359	6	)	)	PUNCT
ejpam-6020	359	7	]	]	PUNCT
ejpam-6020	359	8	=	=	PUNCT
ejpam-6020	359	9	πϵ(cl(h	πϵ(cl(h	X
ejpam-6020	359	10	)	)	PUNCT
ejpam-6020	359	11	)	)	PUNCT
ejpam-6020	359	12	,	,	PUNCT
ejpam-6020	359	13	given	give	VERB
ejpam-6020	359	14	πϵ	πϵ	ADP
ejpam-6020	359	15	is	be	AUX
ejpam-6020	359	16	supra	supra	ADJ
ejpam-6020	359	17	ϵ-closed	ϵ-close	VERB
ejpam-6020	359	18	function	function	NOUN
ejpam-6020	359	19	.	.	PUNCT
ejpam-6020	360	1	“	"	PUNCT
ejpam-6020	360	2	⇐	⇐	INTJ
ejpam-6020	360	3	”	"	PUNCT
ejpam-6020	360	4	let	let	VERB
ejpam-6020	360	5	h	h	PROPN
ejpam-6020	360	6	∈	∈	PROPN
ejpam-6020	360	7	νc1	νc1	PROPN
ejpam-6020	360	8	.	.	PUNCT
ejpam-6020	361	1	based	base	VERB
ejpam-6020	361	2	on	on	ADP
ejpam-6020	361	3	the	the	DET
ejpam-6020	361	4	presumption	presumption	NOUN
ejpam-6020	361	5	,	,	PUNCT
ejpam-6020	361	6	πϵ(h	πϵ(h	PUNCT
ejpam-6020	361	7	)	)	PUNCT
ejpam-6020	361	8	⊆	⊆	NUM
ejpam-6020	361	9	clsϵ	clsϵ	NOUN
ejpam-6020	361	10	[	[	X
ejpam-6020	361	11	πϵ(h	πϵ(h	NOUN
ejpam-6020	361	12	)	)	PUNCT
ejpam-6020	361	13	]	]	PUNCT
ejpam-6020	361	14	⊆	⊆	NUM
ejpam-6020	361	15	πϵ(cl(h	πϵ(cl(h	NUM
ejpam-6020	361	16	)	)	PUNCT
ejpam-6020	361	17	)	)	PUNCT
ejpam-6020	361	18	=	=	SYM
ejpam-6020	361	19	πϵ(h	πϵ(h	X
ejpam-6020	361	20	)	)	PUNCT
ejpam-6020	361	21	.	.	PUNCT
ejpam-6020	362	1	hence	hence	ADV
ejpam-6020	362	2	,	,	PUNCT
ejpam-6020	362	3	clsϵ	clsϵ	NOUN
ejpam-6020	362	4	[	[	X
ejpam-6020	362	5	πϵ(h	πϵ(h	NOUN
ejpam-6020	362	6	)	)	PUNCT
ejpam-6020	362	7	]	]	PUNCT
ejpam-6020	363	1	=	=	PUNCT
ejpam-6020	363	2	πϵ(h	πϵ(h	X
ejpam-6020	363	3	)	)	PUNCT
ejpam-6020	363	4	.	.	PUNCT
ejpam-6020	364	1	therefore	therefore	ADV
ejpam-6020	364	2	,	,	PUNCT
ejpam-6020	364	3	πϵ(h	πϵ(h	PUNCT
ejpam-6020	364	4	)	)	PUNCT
ejpam-6020	364	5	∈	∈	PROPN
ejpam-6020	364	6	sc(λ2)θ2	sc(λ2)θ2	PROPN
ejpam-6020	364	7	,	,	PUNCT
ejpam-6020	364	8	and	and	CCONJ
ejpam-6020	364	9	hence	hence	ADV
ejpam-6020	364	10	πϵ	πϵ	INTJ
ejpam-6020	364	11	is	be	VERB
ejpam-6020	364	12	a	a	DET
ejpam-6020	364	13	supra	supra	ADJ
ejpam-6020	364	14	ϵ-closed	ϵ-close	VERB
ejpam-6020	364	15	function	function	NOUN
ejpam-6020	364	16	.	.	PUNCT
ejpam-6020	365	1	theorem	theorem	VERB
ejpam-6020	365	2	18	18	NUM
ejpam-6020	365	3	.	.	PUNCT
ejpam-6020	366	1	let	let	AUX
ejpam-6020	366	2	πϵ	πϵ	INTJ
ejpam-6020	366	3	:	:	PUNCT
ejpam-6020	366	4	(	(	PUNCT
ejpam-6020	366	5	λ1	λ1	ADJ
ejpam-6020	366	6	,	,	PUNCT
ejpam-6020	366	7	ν1	ν1	NOUN
ejpam-6020	366	8	)	)	PUNCT
ejpam-6020	366	9	→	→	SYM
ejpam-6020	366	10	(	(	PUNCT
ejpam-6020	366	11	λ2	λ2	NOUN
ejpam-6020	366	12	,	,	PUNCT
ejpam-6020	366	13	ν2	ν2	NOUN
ejpam-6020	366	14	)	)	PUNCT
ejpam-6020	366	15	be	be	VERB
ejpam-6020	366	16	a	a	DET
ejpam-6020	366	17	bijective	bijective	ADJ
ejpam-6020	366	18	function	function	NOUN
ejpam-6020	366	19	with	with	ADP
ejpam-6020	366	20	ϑ2	ϑ2	PROPN
ejpam-6020	366	21	as	as	ADP
ejpam-6020	366	22	an	an	DET
ejpam-6020	366	23	associated	associate	VERB
ejpam-6020	366	24	sts	st	NOUN
ejpam-6020	366	25	with	with	ADP
ejpam-6020	366	26	ν2	ν2	NOUN
ejpam-6020	366	27	,	,	PUNCT
ejpam-6020	366	28	then	then	ADV
ejpam-6020	366	29	πϵ	πϵ	INTJ
ejpam-6020	366	30	is	be	AUX
ejpam-6020	366	31	supra	supra	PROPN
ejpam-6020	366	32	ϵ-open	ϵ-open	PROPN
ejpam-6020	366	33	function	function	PROPN
ejpam-6020	366	34	if	if	SCONJ
ejpam-6020	366	35	and	and	CCONJ
ejpam-6020	366	36	only	only	ADV
ejpam-6020	366	37	if	if	SCONJ
ejpam-6020	366	38	it	it	PRON
ejpam-6020	366	39	is	be	AUX
ejpam-6020	366	40	supra	supra	PROPN
ejpam-6020	366	41	ϵ-closed	ϵ-close	VERB
ejpam-6020	366	42	.	.	PUNCT
ejpam-6020	367	1	proof	proof	NOUN
ejpam-6020	367	2	.	.	PUNCT
ejpam-6020	368	1	“	"	PUNCT
ejpam-6020	368	2	⇒	⇒	NOUN
ejpam-6020	368	3	”	"	PUNCT
ejpam-6020	368	4	let	let	VERB
ejpam-6020	368	5	r	r	NOUN
ejpam-6020	368	6	∈	∈	PROPN
ejpam-6020	368	7	νc1	νc1	NOUN
ejpam-6020	368	8	,	,	PUNCT
ejpam-6020	368	9	then	then	ADV
ejpam-6020	368	10	r	r	NOUN
ejpam-6020	368	11	c	c	PROPN
ejpam-6020	368	12	∈	∈	PROPN
ejpam-6020	368	13	ν1	ν1	NOUN
ejpam-6020	368	14	.	.	PUNCT
ejpam-6020	369	1	since	since	SCONJ
ejpam-6020	369	2	πϵ	πϵ	INTJ
ejpam-6020	369	3	is	be	AUX
ejpam-6020	369	4	supra	supra	PROPN
ejpam-6020	369	5	bijective	bijective	ADJ
ejpam-6020	369	6	ϵ-open	ϵ-open	PROPN
ejpam-6020	369	7	function	function	PROPN
ejpam-6020	369	8	,	,	PUNCT
ejpam-6020	369	9	[	[	X
ejpam-6020	369	10	πϵ(r	πϵ(r	NOUN
ejpam-6020	369	11	)	)	PUNCT
ejpam-6020	369	12	]	]	PUNCT
ejpam-6020	370	1	c	c	X
ejpam-6020	370	2	=	=	SYM
ejpam-6020	370	3	πϵ(r	πϵ(r	NUM
ejpam-6020	370	4	c	c	X
ejpam-6020	370	5	)	)	PUNCT
ejpam-6020	370	6	∈	∈	PROPN
ejpam-6020	370	7	soϵ(λ1	soϵ(λ1	NOUN
ejpam-6020	370	8	)	)	PUNCT
ejpam-6020	370	9	.	.	PUNCT
ejpam-6020	371	1	it	it	PRON
ejpam-6020	371	2	follows	follow	VERB
ejpam-6020	371	3	that	that	SCONJ
ejpam-6020	371	4	,	,	PUNCT
ejpam-6020	371	5	πϵ(r	πϵ(r	NUM
ejpam-6020	371	6	)	)	PUNCT
ejpam-6020	371	7	∈	∈	PROPN
ejpam-6020	371	8	soϵ(λ2	soϵ(λ2	PROPN
ejpam-6020	371	9	)	)	PUNCT
ejpam-6020	371	10	.	.	PUNCT
ejpam-6020	372	1	therefore	therefore	ADV
ejpam-6020	372	2	,	,	PUNCT
ejpam-6020	372	3	πϵ	πϵ	X
ejpam-6020	372	4	is	be	AUX
ejpam-6020	372	5	a	a	DET
ejpam-6020	372	6	supra	supra	ADJ
ejpam-6020	372	7	ϵ-closed	ϵ-close	VERB
ejpam-6020	372	8	function	function	NOUN
ejpam-6020	372	9	.	.	PUNCT
ejpam-6020	373	1	“	"	PUNCT
ejpam-6020	373	2	⇐	⇐	INTJ
ejpam-6020	373	3	”	"	PUNCT
ejpam-6020	373	4	it	it	PRON
ejpam-6020	373	5	is	be	AUX
ejpam-6020	373	6	followed	follow	VERB
ejpam-6020	373	7	by	by	ADP
ejpam-6020	373	8	a	a	DET
ejpam-6020	373	9	comparable	comparable	ADJ
ejpam-6020	373	10	argument	argument	NOUN
ejpam-6020	373	11	.	.	PUNCT
ejpam-6020	374	1	proposition	proposition	NOUN
ejpam-6020	374	2	1	1	NUM
ejpam-6020	374	3	.	.	PUNCT
ejpam-6020	375	1	let	let	AUX
ejpam-6020	375	2	πϵ	πϵ	INTJ
ejpam-6020	375	3	:	:	PUNCT
ejpam-6020	375	4	(	(	PUNCT
ejpam-6020	375	5	λ1	λ1	ADJ
ejpam-6020	375	6	,	,	PUNCT
ejpam-6020	375	7	ν1	ν1	NOUN
ejpam-6020	375	8	)	)	PUNCT
ejpam-6020	375	9	→	→	SYM
ejpam-6020	375	10	(	(	PUNCT
ejpam-6020	375	11	λ2	λ2	NOUN
ejpam-6020	375	12	,	,	PUNCT
ejpam-6020	375	13	ν2	ν2	NOUN
ejpam-6020	375	14	)	)	PUNCT
ejpam-6020	375	15	be	be	VERB
ejpam-6020	375	16	a	a	DET
ejpam-6020	375	17	bijective	bijective	ADJ
ejpam-6020	375	18	function	function	NOUN
ejpam-6020	375	19	with	with	ADP
ejpam-6020	375	20	ϑ2	ϑ2	PROPN
ejpam-6020	375	21	as	as	ADP
ejpam-6020	375	22	an	an	DET
ejpam-6020	375	23	associated	associate	VERB
ejpam-6020	375	24	sts	st	NOUN
ejpam-6020	375	25	with	with	ADP
ejpam-6020	375	26	ν2	ν2	NOUN
ejpam-6020	375	27	,	,	PUNCT
ejpam-6020	375	28	then	then	ADV
ejpam-6020	375	29	the	the	DET
ejpam-6020	375	30	next	next	ADJ
ejpam-6020	375	31	assertions	assertion	NOUN
ejpam-6020	375	32	are	be	AUX
ejpam-6020	375	33	equivalent	equivalent	ADJ
ejpam-6020	375	34	:	:	PUNCT
ejpam-6020	375	35	(	(	PUNCT
ejpam-6020	375	36	1	1	X
ejpam-6020	375	37	)	)	PUNCT
ejpam-6020	375	38	πϵ	πϵ	PRON
ejpam-6020	375	39	is	be	AUX
ejpam-6020	375	40	a	a	DET
ejpam-6020	375	41	supra	supra	ADJ
ejpam-6020	375	42	ϵ-open	ϵ-open	PROPN
ejpam-6020	375	43	function	function	PROPN
ejpam-6020	375	44	.	.	PUNCT
ejpam-6020	376	1	(	(	PUNCT
ejpam-6020	376	2	2	2	X
ejpam-6020	376	3	)	)	PUNCT
ejpam-6020	376	4	πϵ	πϵ	PRON
ejpam-6020	376	5	is	be	AUX
ejpam-6020	376	6	a	a	DET
ejpam-6020	376	7	supra	supra	ADJ
ejpam-6020	376	8	ϵ-closed	ϵ-close	VERB
ejpam-6020	376	9	function	function	NOUN
ejpam-6020	376	10	.	.	PUNCT
ejpam-6020	377	1	a.	a.	PROPN
ejpam-6020	377	2	m.	m.	PROPN
ejpam-6020	377	3	abd	abd	PROPN
ejpam-6020	377	4	el	el	PROPN
ejpam-6020	377	5	-	-	PROPN
ejpam-6020	377	6	latif	latif	PROPN
ejpam-6020	377	7	et	et	PROPN
ejpam-6020	377	8	al	al	PROPN
ejpam-6020	377	9	.	.	PUNCT
ejpam-6020	377	10	/	/	SYM
ejpam-6020	377	11	eur	eur	PROPN
ejpam-6020	377	12	.	.	PUNCT
ejpam-6020	378	1	j.	j.	PROPN
ejpam-6020	378	2	pure	pure	PROPN
ejpam-6020	378	3	appl	appl	PROPN
ejpam-6020	378	4	.	.	PROPN
ejpam-6020	378	5	math	math	PROPN
ejpam-6020	378	6	,	,	PUNCT
ejpam-6020	378	7	18	18	NUM
ejpam-6020	378	8	(	(	PUNCT
ejpam-6020	378	9	2	2	NUM
ejpam-6020	378	10	)	)	PUNCT
ejpam-6020	378	11	(	(	PUNCT
ejpam-6020	378	12	2025	2025	NUM
ejpam-6020	378	13	)	)	PUNCT
ejpam-6020	378	14	,	,	PUNCT
ejpam-6020	378	15	6020	6020	NUM
ejpam-6020	378	16	12	12	NUM
ejpam-6020	378	17	of	of	ADP
ejpam-6020	378	18	17	17	NUM
ejpam-6020	378	19	(	(	PUNCT
ejpam-6020	378	20	3	3	NUM
ejpam-6020	378	21	)	)	PUNCT
ejpam-6020	378	22	π−1	π−1	PROPN
ejpam-6020	379	1	ϵ	ϵ	PROPN
ejpam-6020	379	2	is	be	AUX
ejpam-6020	379	3	a	a	DET
ejpam-6020	379	4	supra	supra	ADJ
ejpam-6020	379	5	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	379	6	function	function	NOUN
ejpam-6020	379	7	.	.	PUNCT
ejpam-6020	380	1	proof	proof	NOUN
ejpam-6020	380	2	.	.	PUNCT
ejpam-6020	381	1	(	(	PUNCT
ejpam-6020	381	2	1	1	X
ejpam-6020	381	3	)	)	PUNCT
ejpam-6020	381	4	⇒	⇒	NOUN
ejpam-6020	381	5	(	(	PUNCT
ejpam-6020	381	6	2	2	X
ejpam-6020	381	7	)	)	PUNCT
ejpam-6020	381	8	direct	direct	ADJ
ejpam-6020	381	9	from	from	ADP
ejpam-6020	381	10	theorem	theorem	ADJ
ejpam-6020	381	11	18	18	NUM
ejpam-6020	381	12	.	.	PUNCT
ejpam-6020	382	1	(	(	PUNCT
ejpam-6020	382	2	2	2	X
ejpam-6020	382	3	)	)	PUNCT
ejpam-6020	382	4	⇒	⇒	NOUN
ejpam-6020	382	5	(	(	PUNCT
ejpam-6020	382	6	3	3	X
ejpam-6020	382	7	)	)	PUNCT
ejpam-6020	382	8	let	let	VERB
ejpam-6020	382	9	z	z	NOUN
ejpam-6020	382	10	∈	∈	PROPN
ejpam-6020	382	11	νc1	νc1	NOUN
ejpam-6020	382	12	.	.	PUNCT
ejpam-6020	383	1	since	since	SCONJ
ejpam-6020	383	2	πϵ	πϵ	INTJ
ejpam-6020	383	3	is	be	AUX
ejpam-6020	383	4	supra	supra	PROPN
ejpam-6020	383	5	bijective	bijective	ADJ
ejpam-6020	383	6	function	function	NOUN
ejpam-6020	383	7	and	and	CCONJ
ejpam-6020	383	8	given	give	VERB
ejpam-6020	383	9	(	(	PUNCT
ejpam-6020	383	10	2	2	NUM
ejpam-6020	383	11	)	)	PUNCT
ejpam-6020	383	12	,	,	PUNCT
ejpam-6020	383	13	(	(	PUNCT
ejpam-6020	383	14	π−1	π−1	PROPN
ejpam-6020	383	15	ϵ	ϵ	NOUN
ejpam-6020	383	16	)	)	PUNCT
ejpam-6020	383	17	−1(z	−1(z	PROPN
ejpam-6020	383	18	)	)	PUNCT
ejpam-6020	383	19	=	=	SYM
ejpam-6020	383	20	πϵ(z	πϵ(z	PRON
ejpam-6020	383	21	)	)	PUNCT
ejpam-6020	383	22	∈	∈	PROPN
ejpam-6020	383	23	scϵ(λ2	scϵ(λ2	NOUN
ejpam-6020	383	24	)	)	PUNCT
ejpam-6020	383	25	.	.	PUNCT
ejpam-6020	384	1	hence	hence	ADV
ejpam-6020	384	2	,	,	PUNCT
ejpam-6020	384	3	π−1	π−1	PROPN
ejpam-6020	384	4	ϵ	ϵ	PROPN
ejpam-6020	384	5	is	be	AUX
ejpam-6020	384	6	a	a	DET
ejpam-6020	384	7	supra	supra	ADJ
ejpam-6020	384	8	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	384	9	function	function	NOUN
ejpam-6020	384	10	.	.	PUNCT
ejpam-6020	385	1	(	(	PUNCT
ejpam-6020	385	2	3	3	X
ejpam-6020	385	3	)	)	PUNCT
ejpam-6020	385	4	⇒	⇒	NOUN
ejpam-6020	385	5	(	(	PUNCT
ejpam-6020	385	6	1	1	X
ejpam-6020	385	7	)	)	PUNCT
ejpam-6020	385	8	let	let	VERB
ejpam-6020	385	9	s	s	PRON
ejpam-6020	385	10	∈	∈	PROPN
ejpam-6020	385	11	ν1	ν1	NOUN
ejpam-6020	385	12	.	.	PUNCT
ejpam-6020	386	1	then	then	ADV
ejpam-6020	386	2	,	,	PUNCT
ejpam-6020	386	3	πϵ(s	πϵ(s	NUM
ejpam-6020	386	4	)	)	PUNCT
ejpam-6020	387	1	=	=	SYM
ejpam-6020	388	1	(	(	PUNCT
ejpam-6020	388	2	π−1	π−1	PROPN
ejpam-6020	388	3	ϵ	ϵ	NOUN
ejpam-6020	388	4	)	)	PUNCT
ejpam-6020	388	5	−1(s	−1(	NOUN
ejpam-6020	388	6	)	)	PUNCT
ejpam-6020	388	7	∈	∈	PROPN
ejpam-6020	388	8	soϵ(λ2	soϵ(λ2	PROPN
ejpam-6020	388	9	)	)	PUNCT
ejpam-6020	388	10	,	,	PUNCT
ejpam-6020	388	11	given	give	VERB
ejpam-6020	388	12	(	(	PUNCT
ejpam-6020	388	13	3	3	NUM
ejpam-6020	388	14	)	)	PUNCT
ejpam-6020	388	15	.	.	PUNCT
ejpam-6020	389	1	therefore	therefore	ADV
ejpam-6020	389	2	,	,	PUNCT
ejpam-6020	389	3	πϵ	πϵ	X
ejpam-6020	389	4	is	be	AUX
ejpam-6020	389	5	a	a	DET
ejpam-6020	389	6	supra	supra	ADJ
ejpam-6020	389	7	ϵ-open	ϵ-open	PROPN
ejpam-6020	389	8	function	function	PROPN
ejpam-6020	389	9	.	.	PUNCT
ejpam-6020	390	1	theorem	theorem	NOUN
ejpam-6020	390	2	19	19	NUM
ejpam-6020	390	3	.	.	PUNCT
ejpam-6020	391	1	let	let	VERB
ejpam-6020	391	2	πϵ	πϵ	INTJ
ejpam-6020	391	3	:	:	PUNCT
ejpam-6020	391	4	(	(	PUNCT
ejpam-6020	391	5	λ1	λ1	ADJ
ejpam-6020	391	6	,	,	PUNCT
ejpam-6020	391	7	ν1	ν1	NOUN
ejpam-6020	391	8	)	)	PUNCT
ejpam-6020	391	9	→	→	SYM
ejpam-6020	391	10	(	(	PUNCT
ejpam-6020	391	11	λ2	λ2	NOUN
ejpam-6020	391	12	,	,	PUNCT
ejpam-6020	391	13	ν2	ν2	NOUN
ejpam-6020	391	14	)	)	PUNCT
ejpam-6020	391	15	and	and	CCONJ
ejpam-6020	391	16	ψϵ	ψϵ	VERB
ejpam-6020	391	17	:	:	PUNCT
ejpam-6020	391	18	(	(	PUNCT
ejpam-6020	391	19	λ2	λ2	NOUN
ejpam-6020	391	20	,	,	PUNCT
ejpam-6020	391	21	ν2	ν2	NOUN
ejpam-6020	391	22	)	)	PUNCT
ejpam-6020	391	23	→	→	SYM
ejpam-6020	391	24	(	(	PUNCT
ejpam-6020	391	25	λ3	λ3	PROPN
ejpam-6020	391	26	,	,	PUNCT
ejpam-6020	391	27	ν3	ν3	NOUN
ejpam-6020	391	28	)	)	PUNCT
ejpam-6020	391	29	be	be	VERB
ejpam-6020	391	30	two	two	NUM
ejpam-6020	391	31	functions	function	NOUN
ejpam-6020	391	32	with	with	ADP
ejpam-6020	391	33	ϑ1	ϑ1	NOUN
ejpam-6020	391	34	,	,	PUNCT
ejpam-6020	391	35	ϑ2	ϑ2	PROPN
ejpam-6020	391	36	,	,	PUNCT
ejpam-6020	391	37	ϑ3	ϑ3	NOUN
ejpam-6020	391	38	associated	associate	VERB
ejpam-6020	391	39	stss	stss	NOUN
ejpam-6020	391	40	with	with	ADP
ejpam-6020	391	41	ν1	ν1	NOUN
ejpam-6020	391	42	,	,	PUNCT
ejpam-6020	391	43	ν2	ν2	NOUN
ejpam-6020	391	44	,	,	PUNCT
ejpam-6020	391	45	ν3	ν3	NOUN
ejpam-6020	391	46	,	,	PUNCT
ejpam-6020	391	47	respectively	respectively	ADV
ejpam-6020	391	48	.	.	PUNCT
ejpam-6020	392	1	then	then	ADV
ejpam-6020	392	2	(	(	PUNCT
ejpam-6020	392	3	1	1	X
ejpam-6020	392	4	)	)	PUNCT
ejpam-6020	392	5	if	if	SCONJ
ejpam-6020	392	6	ψϵ	ψϵ	ADP
ejpam-6020	392	7	◦	◦	NOUN
ejpam-6020	392	8	πϵ	πϵ	ADP
ejpam-6020	392	9	is	be	AUX
ejpam-6020	392	10	a	a	DET
ejpam-6020	392	11	supra	supra	ADJ
ejpam-6020	392	12	ϵ-open	ϵ-open	PROPN
ejpam-6020	392	13	function	function	NOUN
ejpam-6020	392	14	and	and	CCONJ
ejpam-6020	392	15	πϵ	πϵ	INTJ
ejpam-6020	392	16	is	be	AUX
ejpam-6020	392	17	a	a	DET
ejpam-6020	392	18	surjective	surjective	ADJ
ejpam-6020	392	19	cts	cts	NOUN
ejpam-6020	392	20	function	function	NOUN
ejpam-6020	392	21	,	,	PUNCT
ejpam-6020	392	22	then	then	ADV
ejpam-6020	392	23	ψϵ	ψϵ	PROPN
ejpam-6020	392	24	is	be	AUX
ejpam-6020	392	25	a	a	DET
ejpam-6020	392	26	supra	supra	ADJ
ejpam-6020	392	27	ϵ-open	ϵ-open	PROPN
ejpam-6020	392	28	function	function	PROPN
ejpam-6020	392	29	.	.	PUNCT
ejpam-6020	393	1	(	(	PUNCT
ejpam-6020	393	2	2	2	X
ejpam-6020	393	3	)	)	PUNCT
ejpam-6020	393	4	if	if	SCONJ
ejpam-6020	393	5	ψϵ	ψϵ	ADP
ejpam-6020	393	6	◦	◦	NOUN
ejpam-6020	393	7	πϵ	πϵ	ADP
ejpam-6020	393	8	is	be	AUX
ejpam-6020	393	9	an	an	DET
ejpam-6020	393	10	open	open	ADJ
ejpam-6020	393	11	function	function	NOUN
ejpam-6020	393	12	and	and	CCONJ
ejpam-6020	393	13	ψϵ	ψϵ	NOUN
ejpam-6020	393	14	is	be	AUX
ejpam-6020	393	15	an	an	DET
ejpam-6020	393	16	injective	injective	ADJ
ejpam-6020	393	17	supra	supra	NOUN
ejpam-6020	393	18	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	393	19	function	function	NOUN
ejpam-6020	393	20	,	,	PUNCT
ejpam-6020	393	21	then	then	ADV
ejpam-6020	393	22	πϵ	πϵ	INTJ
ejpam-6020	393	23	is	be	AUX
ejpam-6020	393	24	a	a	DET
ejpam-6020	393	25	supra	supra	ADJ
ejpam-6020	393	26	ϵ-open	ϵ-open	PROPN
ejpam-6020	393	27	function	function	PROPN
ejpam-6020	393	28	.	.	PUNCT
ejpam-6020	394	1	(	(	PUNCT
ejpam-6020	394	2	3	3	X
ejpam-6020	394	3	)	)	PUNCT
ejpam-6020	394	4	if	if	SCONJ
ejpam-6020	394	5	ψϵ	ψϵ	ADP
ejpam-6020	394	6	◦	◦	NOUN
ejpam-6020	394	7	πϵ	πϵ	ADP
ejpam-6020	394	8	is	be	AUX
ejpam-6020	394	9	a	a	DET
ejpam-6020	394	10	supra	supra	ADJ
ejpam-6020	394	11	open	open	ADJ
ejpam-6020	394	12	function	function	NOUN
ejpam-6020	394	13	and	and	CCONJ
ejpam-6020	394	14	ψϵ	ψϵ	NOUN
ejpam-6020	394	15	is	be	AUX
ejpam-6020	394	16	an	an	DET
ejpam-6020	394	17	injective	injective	ADJ
ejpam-6020	394	18	supra	supra	ADJ
ejpam-6020	394	19	ϵ∗-cts	ϵ∗-ct	NOUN
ejpam-6020	394	20	function	function	NOUN
ejpam-6020	394	21	,	,	PUNCT
ejpam-6020	394	22	then	then	ADV
ejpam-6020	394	23	πϵ	πϵ	INTJ
ejpam-6020	394	24	is	be	AUX
ejpam-6020	394	25	a	a	DET
ejpam-6020	394	26	supra	supra	ADJ
ejpam-6020	394	27	ϵ-open	ϵ-open	PROPN
ejpam-6020	394	28	function	function	PROPN
ejpam-6020	394	29	.	.	PUNCT
ejpam-6020	395	1	(	(	PUNCT
ejpam-6020	395	2	4	4	X
ejpam-6020	395	3	)	)	PUNCT
ejpam-6020	395	4	if	if	SCONJ
ejpam-6020	395	5	ψϵ	ψϵ	ADP
ejpam-6020	395	6	◦	◦	NOUN
ejpam-6020	395	7	πϵ	πϵ	ADP
ejpam-6020	395	8	is	be	AUX
ejpam-6020	395	9	a	a	DET
ejpam-6020	395	10	supra	supra	NOUN
ejpam-6020	395	11	ϵ-open	ϵ-open	PROPN
ejpam-6020	395	12	and	and	CCONJ
ejpam-6020	395	13	ψϵ	ψϵ	PROPN
ejpam-6020	395	14	is	be	AUX
ejpam-6020	395	15	an	an	DET
ejpam-6020	395	16	injective	injective	ADJ
ejpam-6020	395	17	supra	supra	ADJ
ejpam-6020	395	18	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	395	19	function	function	NOUN
ejpam-6020	395	20	,	,	PUNCT
ejpam-6020	395	21	then	then	ADV
ejpam-6020	395	22	πϵ	πϵ	INTJ
ejpam-6020	395	23	is	be	AUX
ejpam-6020	395	24	a	a	DET
ejpam-6020	395	25	supra	supra	ADJ
ejpam-6020	395	26	ϵ-open	ϵ-open	PROPN
ejpam-6020	395	27	function	function	NOUN
ejpam-6020	395	28	.	.	PUNCT
ejpam-6020	396	1	proof	proof	NOUN
ejpam-6020	396	2	.	.	PUNCT
ejpam-6020	397	1	(	(	PUNCT
ejpam-6020	397	2	1	1	X
ejpam-6020	397	3	)	)	PUNCT
ejpam-6020	397	4	let	let	VERB
ejpam-6020	397	5	f	f	PROPN
ejpam-6020	397	6	∈	∈	PROPN
ejpam-6020	397	7	ν2	ν2	NOUN
ejpam-6020	397	8	.	.	PUNCT
ejpam-6020	398	1	since	since	SCONJ
ejpam-6020	398	2	πϵ	πϵ	INTJ
ejpam-6020	398	3	is	be	VERB
ejpam-6020	398	4	a	a	DET
ejpam-6020	398	5	cts	cts	NUM
ejpam-6020	398	6	function	function	NOUN
ejpam-6020	398	7	,	,	PUNCT
ejpam-6020	398	8	π−1	π−1	PROPN
ejpam-6020	398	9	ϵ	ϵ	X
ejpam-6020	398	10	(	(	PUNCT
ejpam-6020	398	11	f	f	PROPN
ejpam-6020	398	12	)	)	PUNCT
ejpam-6020	398	13	∈	∈	PROPN
ejpam-6020	398	14	ν1	ν1	NOUN
ejpam-6020	398	15	.	.	PUNCT
ejpam-6020	399	1	given	give	VERB
ejpam-6020	399	2	ψϵ	ψϵ	ADP
ejpam-6020	399	3	◦	◦	NOUN
ejpam-6020	399	4	πϵ	πϵ	SCONJ
ejpam-6020	399	5	is	be	AUX
ejpam-6020	399	6	a	a	DET
ejpam-6020	399	7	supra	supra	ADJ
ejpam-6020	399	8	ϵ-open	ϵ-open	PROPN
ejpam-6020	399	9	function	function	NOUN
ejpam-6020	399	10	and	and	CCONJ
ejpam-6020	399	11	πϵ	πϵ	INTJ
ejpam-6020	399	12	is	be	AUX
ejpam-6020	399	13	a	a	DET
ejpam-6020	399	14	surjective	surjective	ADJ
ejpam-6020	399	15	function	function	NOUN
ejpam-6020	399	16	,	,	PUNCT
ejpam-6020	399	17	then	then	ADV
ejpam-6020	399	18	(	(	PUNCT
ejpam-6020	399	19	ψϵ	ψϵ	ADP
ejpam-6020	399	20	◦	◦	NOUN
ejpam-6020	400	1	πϵ)[π−1	πϵ)[π−1	NOUN
ejpam-6020	400	2	ϵ	ϵ	X
ejpam-6020	400	3	(	(	PUNCT
ejpam-6020	400	4	f	f	PROPN
ejpam-6020	400	5	)	)	PUNCT
ejpam-6020	400	6	]	]	PUNCT
ejpam-6020	401	1	=	=	PUNCT
ejpam-6020	401	2	ψϵ[πϵ(π	ψϵ[πϵ(π	PUNCT
ejpam-6020	401	3	−1	−1	NOUN
ejpam-6020	401	4	ϵ	ϵ	PROPN
ejpam-6020	401	5	(	(	PUNCT
ejpam-6020	401	6	f	f	PROPN
ejpam-6020	401	7	)	)	PUNCT
ejpam-6020	401	8	)	)	PUNCT
ejpam-6020	401	9	]	]	PUNCT
ejpam-6020	401	10	=	=	SYM
ejpam-6020	401	11	ψϵ(f	ψϵ(f	PRON
ejpam-6020	401	12	)	)	PUNCT
ejpam-6020	401	13	∈	∈	PROPN
ejpam-6020	401	14	soϵ(λ3	soϵ(λ3	NOUN
ejpam-6020	401	15	)	)	PUNCT
ejpam-6020	401	16	.	.	PUNCT
ejpam-6020	402	1	therefore	therefore	ADV
ejpam-6020	402	2	,	,	PUNCT
ejpam-6020	402	3	ψϵ	ψϵ	PROPN
ejpam-6020	402	4	is	be	AUX
ejpam-6020	402	5	a	a	DET
ejpam-6020	402	6	supra	supra	ADJ
ejpam-6020	402	7	ϵ-open	ϵ-open	PROPN
ejpam-6020	402	8	function	function	PROPN
ejpam-6020	402	9	.	.	PUNCT
ejpam-6020	403	1	(	(	PUNCT
ejpam-6020	403	2	2	2	X
ejpam-6020	403	3	)	)	PUNCT
ejpam-6020	403	4	let	let	VERB
ejpam-6020	403	5	f	f	PROPN
ejpam-6020	403	6	∈	∈	PROPN
ejpam-6020	403	7	ν1	ν1	NOUN
ejpam-6020	403	8	.	.	PUNCT
ejpam-6020	404	1	since	since	SCONJ
ejpam-6020	404	2	ψϵ	ψϵ	ADP
ejpam-6020	404	3	◦	◦	NOUN
ejpam-6020	404	4	πϵ	πϵ	ADV
ejpam-6020	404	5	is	be	AUX
ejpam-6020	404	6	an	an	DET
ejpam-6020	404	7	open	open	ADJ
ejpam-6020	404	8	function	function	NOUN
ejpam-6020	404	9	,	,	PUNCT
ejpam-6020	404	10	(	(	PUNCT
ejpam-6020	404	11	ψϵ	ψϵ	ADP
ejpam-6020	404	12	◦	◦	NOUN
ejpam-6020	404	13	πϵ)(f	πϵ)(f	NOUN
ejpam-6020	404	14	)	)	PUNCT
ejpam-6020	405	1	∈	∈	PROPN
ejpam-6020	405	2	ν3	ν3	NOUN
ejpam-6020	405	3	.	.	PUNCT
ejpam-6020	406	1	given	give	VERB
ejpam-6020	406	2	ψϵ	ψϵ	PROPN
ejpam-6020	406	3	is	be	AUX
ejpam-6020	406	4	an	an	DET
ejpam-6020	406	5	injective	injective	ADJ
ejpam-6020	406	6	supra	supra	NOUN
ejpam-6020	406	7	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	406	8	function	function	NOUN
ejpam-6020	406	9	,	,	PUNCT
ejpam-6020	406	10	then	then	ADV
ejpam-6020	406	11	ψ−1	ψ−1	PROPN
ejpam-6020	407	1	ϵ	ϵ	X
ejpam-6020	408	1	[	[	X
ejpam-6020	408	2	ψϵ	ψϵ	ADP
ejpam-6020	408	3	◦	◦	NOUN
ejpam-6020	408	4	πϵ(f	πϵ(f	PUNCT
ejpam-6020	408	5	)	)	PUNCT
ejpam-6020	408	6	]	]	PUNCT
ejpam-6020	409	1	=	=	PUNCT
ejpam-6020	409	2	(	(	PUNCT
ejpam-6020	409	3	ψ−1	ψ−1	PROPN
ejpam-6020	409	4	ϵ	ϵ	PART
ejpam-6020	409	5	◦	◦	NOUN
ejpam-6020	409	6	ψϵ)(πϵ(f	ψϵ)(πϵ(f	NUM
ejpam-6020	409	7	)	)	PUNCT
ejpam-6020	409	8	)	)	PUNCT
ejpam-6020	410	1	=	=	SYM
ejpam-6020	410	2	πϵ(f	πϵ(f	SYM
ejpam-6020	410	3	)	)	PUNCT
ejpam-6020	410	4	∈	∈	PROPN
ejpam-6020	410	5	soϵ(λ2	soϵ(λ2	PROPN
ejpam-6020	410	6	)	)	PUNCT
ejpam-6020	410	7	.	.	PUNCT
ejpam-6020	411	1	therefore	therefore	ADV
ejpam-6020	411	2	,	,	PUNCT
ejpam-6020	411	3	πϵ	πϵ	X
ejpam-6020	411	4	is	be	AUX
ejpam-6020	411	5	a	a	DET
ejpam-6020	411	6	supra	supra	PROPN
ejpam-6020	411	7	ϵ-open	ϵ-open	PROPN
ejpam-6020	411	8	function.function	function.function	PROPN
ejpam-6020	411	9	.	.	PUNCT
ejpam-6020	412	1	(	(	PUNCT
ejpam-6020	412	2	3	3	X
ejpam-6020	412	3	)	)	PUNCT
ejpam-6020	412	4	let	let	VERB
ejpam-6020	412	5	f	f	PROPN
ejpam-6020	412	6	∈	∈	PROPN
ejpam-6020	412	7	ν1	ν1	NOUN
ejpam-6020	412	8	.	.	PUNCT
ejpam-6020	413	1	since	since	SCONJ
ejpam-6020	413	2	ψϵ	ψϵ	ADP
ejpam-6020	413	3	◦	◦	NOUN
ejpam-6020	413	4	πϵ	πϵ	ADP
ejpam-6020	413	5	is	be	AUX
ejpam-6020	413	6	a	a	DET
ejpam-6020	413	7	supra	supra	ADJ
ejpam-6020	413	8	open	open	ADJ
ejpam-6020	413	9	function	function	NOUN
ejpam-6020	413	10	,	,	PUNCT
ejpam-6020	413	11	(	(	PUNCT
ejpam-6020	413	12	ψϵ	ψϵ	ADP
ejpam-6020	413	13	◦	◦	NOUN
ejpam-6020	413	14	πϵ)(f	πϵ)(f	PROPN
ejpam-6020	413	15	)	)	PUNCT
ejpam-6020	414	1	∈	∈	PROPN
ejpam-6020	414	2	ϑ3	ϑ3	NOUN
ejpam-6020	414	3	.	.	PUNCT
ejpam-6020	415	1	given	give	VERB
ejpam-6020	415	2	ψϵ	ψϵ	PROPN
ejpam-6020	415	3	is	be	AUX
ejpam-6020	415	4	an	an	DET
ejpam-6020	415	5	injective	injective	ADJ
ejpam-6020	415	6	supra	supra	ADJ
ejpam-6020	415	7	ϵ∗-cts	ϵ∗-ct	NOUN
ejpam-6020	415	8	function	function	NOUN
ejpam-6020	415	9	,	,	PUNCT
ejpam-6020	415	10	then	then	ADV
ejpam-6020	415	11	ψ−1	ψ−1	PROPN
ejpam-6020	416	1	ϵ	ϵ	X
ejpam-6020	417	1	[	[	X
ejpam-6020	417	2	ψϵ	ψϵ	ADP
ejpam-6020	417	3	◦	◦	NOUN
ejpam-6020	417	4	πϵ(f	πϵ(f	PUNCT
ejpam-6020	417	5	)	)	PUNCT
ejpam-6020	417	6	]	]	PUNCT
ejpam-6020	418	1	=	=	PUNCT
ejpam-6020	418	2	(	(	PUNCT
ejpam-6020	418	3	ψ−1	ψ−1	PROPN
ejpam-6020	418	4	ϵ	ϵ	PART
ejpam-6020	418	5	◦	◦	NOUN
ejpam-6020	418	6	ψϵ)(πϵ(f	ψϵ)(πϵ(f	NUM
ejpam-6020	418	7	)	)	PUNCT
ejpam-6020	418	8	)	)	PUNCT
ejpam-6020	419	1	=	=	SYM
ejpam-6020	419	2	πϵ(f	πϵ(f	SYM
ejpam-6020	419	3	)	)	PUNCT
ejpam-6020	419	4	∈	∈	PROPN
ejpam-6020	419	5	soϵ(λ2	soϵ(λ2	PROPN
ejpam-6020	419	6	)	)	PUNCT
ejpam-6020	419	7	.	.	PUNCT
ejpam-6020	420	1	therefore	therefore	ADV
ejpam-6020	420	2	,	,	PUNCT
ejpam-6020	420	3	πϵ	πϵ	X
ejpam-6020	420	4	is	be	AUX
ejpam-6020	420	5	a	a	DET
ejpam-6020	420	6	supra	supra	ADJ
ejpam-6020	420	7	ϵ-open	ϵ-open	PROPN
ejpam-6020	420	8	function	function	PROPN
ejpam-6020	420	9	.	.	PUNCT
ejpam-6020	421	1	(	(	PUNCT
ejpam-6020	421	2	4	4	X
ejpam-6020	421	3	)	)	PUNCT
ejpam-6020	421	4	let	let	VERB
ejpam-6020	421	5	f	f	PROPN
ejpam-6020	421	6	∈	∈	PROPN
ejpam-6020	421	7	ν1	ν1	NOUN
ejpam-6020	421	8	.	.	PUNCT
ejpam-6020	422	1	since	since	SCONJ
ejpam-6020	422	2	ψϵ	ψϵ	ADP
ejpam-6020	422	3	◦	◦	NOUN
ejpam-6020	422	4	πϵ	πϵ	ADV
ejpam-6020	422	5	is	be	AUX
ejpam-6020	422	6	a	a	DET
ejpam-6020	422	7	supra	supra	PROPN
ejpam-6020	422	8	ϵ-open	ϵ-open	PROPN
ejpam-6020	422	9	function	function	PROPN
ejpam-6020	422	10	,	,	PUNCT
ejpam-6020	422	11	(	(	PUNCT
ejpam-6020	422	12	ψϵ	ψϵ	ADP
ejpam-6020	422	13	◦	◦	NOUN
ejpam-6020	422	14	πϵ)(f	πϵ)(f	NOUN
ejpam-6020	422	15	)	)	PUNCT
ejpam-6020	423	1	∈	∈	PROPN
ejpam-6020	423	2	soϵ(λ3	soϵ(λ3	NOUN
ejpam-6020	423	3	)	)	PUNCT
ejpam-6020	423	4	.	.	PUNCT
ejpam-6020	424	1	given	give	VERB
ejpam-6020	424	2	ψϵ	ψϵ	PROPN
ejpam-6020	424	3	is	be	AUX
ejpam-6020	424	4	an	an	DET
ejpam-6020	424	5	injective	injective	ADJ
ejpam-6020	424	6	supra	supra	ADJ
ejpam-6020	424	7	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	424	8	function	function	NOUN
ejpam-6020	424	9	,	,	PUNCT
ejpam-6020	424	10	then	then	ADV
ejpam-6020	424	11	ψ−1	ψ−1	PROPN
ejpam-6020	424	12	ϵ	ϵ	X
ejpam-6020	425	1	[	[	X
ejpam-6020	425	2	ψϵ	ψϵ	ADP
ejpam-6020	425	3	◦	◦	NOUN
ejpam-6020	425	4	πϵ(f	πϵ(f	PUNCT
ejpam-6020	425	5	)	)	PUNCT
ejpam-6020	425	6	]	]	PUNCT
ejpam-6020	426	1	=	=	PUNCT
ejpam-6020	426	2	(	(	PUNCT
ejpam-6020	426	3	ψ−1	ψ−1	PROPN
ejpam-6020	426	4	ϵ	ϵ	X
ejpam-6020	426	5	◦	◦	NOUN
ejpam-6020	426	6	ψϵ)(πϵ(f	ψϵ)(πϵ(f	PUNCT
ejpam-6020	426	7	)	)	PUNCT
ejpam-6020	426	8	)	)	PUNCT
ejpam-6020	427	1	=	=	SYM
ejpam-6020	427	2	πϵ(f	πϵ(f	SYM
ejpam-6020	427	3	)	)	PUNCT
ejpam-6020	427	4	∈	∈	PROPN
ejpam-6020	427	5	soϵ(λ2	soϵ(λ2	PROPN
ejpam-6020	427	6	)	)	PUNCT
ejpam-6020	427	7	.	.	PUNCT
ejpam-6020	428	1	therefore	therefore	ADV
ejpam-6020	428	2	,	,	PUNCT
ejpam-6020	428	3	πϵ	πϵ	X
ejpam-6020	428	4	is	be	AUX
ejpam-6020	428	5	a	a	DET
ejpam-6020	428	6	supra	supra	ADJ
ejpam-6020	428	7	ϵ-open	ϵ-open	PROPN
ejpam-6020	428	8	function	function	PROPN
ejpam-6020	428	9	.	.	PUNCT
ejpam-6020	429	1	definition	definition	NOUN
ejpam-6020	429	2	13	13	NUM
ejpam-6020	429	3	.	.	PUNCT
ejpam-6020	430	1	a	a	DET
ejpam-6020	430	2	bijective	bijective	ADJ
ejpam-6020	430	3	function	function	NOUN
ejpam-6020	430	4	πϵ	πϵ	ADP
ejpam-6020	430	5	:	:	PUNCT
ejpam-6020	430	6	(	(	PUNCT
ejpam-6020	430	7	λ1	λ1	ADJ
ejpam-6020	430	8	,	,	PUNCT
ejpam-6020	430	9	ν1	ν1	NOUN
ejpam-6020	430	10	)	)	PUNCT
ejpam-6020	430	11	→	→	SYM
ejpam-6020	430	12	(	(	PUNCT
ejpam-6020	430	13	λ2	λ2	NOUN
ejpam-6020	430	14	,	,	PUNCT
ejpam-6020	430	15	ν2	ν2	NOUN
ejpam-6020	430	16	)	)	PUNCT
ejpam-6020	430	17	with	with	ADP
ejpam-6020	430	18	ϑ1	ϑ1	NOUN
ejpam-6020	430	19	,	,	PUNCT
ejpam-6020	430	20	ϑ2	ϑ2	PROPN
ejpam-6020	430	21	associated	associate	VERB
ejpam-6020	430	22	stss	stss	NOUN
ejpam-6020	430	23	with	with	ADP
ejpam-6020	430	24	ν1	ν1	NOUN
ejpam-6020	430	25	,	,	PUNCT
ejpam-6020	430	26	ν2	ν2	NOUN
ejpam-6020	430	27	,	,	PUNCT
ejpam-6020	430	28	respectively	respectively	ADV
ejpam-6020	430	29	,	,	PUNCT
ejpam-6020	430	30	is	be	AUX
ejpam-6020	430	31	said	say	VERB
ejpam-6020	430	32	to	to	PART
ejpam-6020	430	33	be	be	AUX
ejpam-6020	430	34	supra	supra	ADJ
ejpam-6020	430	35	ϵ-homeomorphism	ϵ-homeomorphism	NOUN
ejpam-6020	430	36	if	if	SCONJ
ejpam-6020	430	37	it	it	PRON
ejpam-6020	430	38	is	be	AUX
ejpam-6020	430	39	supra	supra	ADJ
ejpam-6020	430	40	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	430	41	and	and	CCONJ
ejpam-6020	430	42	supra	supra	PROPN
ejpam-6020	430	43	ϵ-open	ϵ-open	PROPN
ejpam-6020	430	44	.	.	PUNCT
ejpam-6020	431	1	a.	a.	PROPN
ejpam-6020	431	2	m.	m.	PROPN
ejpam-6020	431	3	abd	abd	PROPN
ejpam-6020	431	4	el	el	PROPN
ejpam-6020	431	5	-	-	PROPN
ejpam-6020	431	6	latif	latif	PROPN
ejpam-6020	431	7	et	et	PROPN
ejpam-6020	431	8	al	al	PROPN
ejpam-6020	431	9	.	.	PUNCT
ejpam-6020	431	10	/	/	SYM
ejpam-6020	431	11	eur	eur	PROPN
ejpam-6020	431	12	.	.	PUNCT
ejpam-6020	432	1	j.	j.	PROPN
ejpam-6020	432	2	pure	pure	PROPN
ejpam-6020	432	3	appl	appl	PROPN
ejpam-6020	432	4	.	.	PROPN
ejpam-6020	432	5	math	math	PROPN
ejpam-6020	432	6	,	,	PUNCT
ejpam-6020	432	7	18	18	NUM
ejpam-6020	432	8	(	(	PUNCT
ejpam-6020	432	9	2	2	NUM
ejpam-6020	432	10	)	)	PUNCT
ejpam-6020	432	11	(	(	PUNCT
ejpam-6020	432	12	2025	2025	NUM
ejpam-6020	432	13	)	)	PUNCT
ejpam-6020	432	14	,	,	PUNCT
ejpam-6020	432	15	6020	6020	NUM
ejpam-6020	432	16	13	13	NUM
ejpam-6020	432	17	of	of	ADP
ejpam-6020	432	18	17	17	NUM
ejpam-6020	432	19	theorem	theorem	NOUN
ejpam-6020	432	20	20	20	NUM
ejpam-6020	432	21	.	.	PUNCT
ejpam-6020	433	1	for	for	ADP
ejpam-6020	433	2	a	a	DET
ejpam-6020	433	3	bijective	bijective	ADJ
ejpam-6020	433	4	supra	supra	NOUN
ejpam-6020	433	5	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	433	6	function	function	VERB
ejpam-6020	433	7	πϵ	πϵ	X
ejpam-6020	433	8	:	:	PUNCT
ejpam-6020	433	9	(	(	PUNCT
ejpam-6020	433	10	λ1	λ1	ADJ
ejpam-6020	433	11	,	,	PUNCT
ejpam-6020	433	12	ν1	ν1	NOUN
ejpam-6020	433	13	)	)	PUNCT
ejpam-6020	433	14	→	→	SYM
ejpam-6020	433	15	(	(	PUNCT
ejpam-6020	433	16	λ2	λ2	NOUN
ejpam-6020	433	17	,	,	PUNCT
ejpam-6020	433	18	ν2	ν2	NOUN
ejpam-6020	433	19	)	)	PUNCT
ejpam-6020	433	20	with	with	ADP
ejpam-6020	433	21	ϑ1	ϑ1	NOUN
ejpam-6020	433	22	,	,	PUNCT
ejpam-6020	433	23	ϑ2	ϑ2	PROPN
ejpam-6020	433	24	associated	associate	VERB
ejpam-6020	433	25	stss	stss	NOUN
ejpam-6020	433	26	with	with	ADP
ejpam-6020	433	27	ν1	ν1	NOUN
ejpam-6020	433	28	,	,	PUNCT
ejpam-6020	433	29	ν2	ν2	NOUN
ejpam-6020	433	30	,	,	PUNCT
ejpam-6020	433	31	respectively	respectively	ADV
ejpam-6020	433	32	.	.	PUNCT
ejpam-6020	434	1	the	the	DET
ejpam-6020	434	2	statements	statement	NOUN
ejpam-6020	434	3	that	that	PRON
ejpam-6020	434	4	follow	follow	VERB
ejpam-6020	434	5	are	be	AUX
ejpam-6020	434	6	interchangeable	interchangeable	ADJ
ejpam-6020	434	7	:	:	PUNCT
ejpam-6020	434	8	(	(	PUNCT
ejpam-6020	434	9	1	1	X
ejpam-6020	434	10	)	)	PUNCT
ejpam-6020	434	11	πϵ	πϵ	X
ejpam-6020	434	12	is	be	AUX
ejpam-6020	434	13	supra	supra	ADJ
ejpam-6020	434	14	ϵ-homeomorphism	ϵ-homeomorphism	NOUN
ejpam-6020	434	15	.	.	PUNCT
ejpam-6020	435	1	(	(	PUNCT
ejpam-6020	435	2	2	2	X
ejpam-6020	435	3	)	)	PUNCT
ejpam-6020	435	4	ψ−1	ψ−1	PROPN
ejpam-6020	435	5	sd	sd	NOUN
ejpam-6020	435	6	is	be	AUX
ejpam-6020	435	7	supra	supra	ADJ
ejpam-6020	435	8	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	435	9	.	.	PUNCT
ejpam-6020	436	1	(	(	PUNCT
ejpam-6020	436	2	3	3	X
ejpam-6020	436	3	)	)	PUNCT
ejpam-6020	436	4	πϵ	πϵ	X
ejpam-6020	436	5	is	be	AUX
ejpam-6020	436	6	supra	supra	PROPN
ejpam-6020	436	7	ϵ-closed	ϵ-close	VERB
ejpam-6020	436	8	.	.	PUNCT
ejpam-6020	437	1	proof	proof	NOUN
ejpam-6020	437	2	.	.	PUNCT
ejpam-6020	438	1	it	it	PRON
ejpam-6020	438	2	is	be	AUX
ejpam-6020	438	3	instantly	instantly	ADV
ejpam-6020	438	4	evident	evident	ADJ
ejpam-6020	438	5	from	from	ADP
ejpam-6020	438	6	definition	definition	NOUN
ejpam-6020	438	7	13	13	NUM
ejpam-6020	438	8	and	and	CCONJ
ejpam-6020	438	9	theorem	theorem	VERB
ejpam-6020	438	10	18	18	NUM
ejpam-6020	438	11	.	.	PUNCT
ejpam-6020	438	12	theorem	theorem	NOUN
ejpam-6020	438	13	21	21	NUM
ejpam-6020	438	14	.	.	PUNCT
ejpam-6020	439	1	a	a	DET
ejpam-6020	439	2	bijective	bijective	ADJ
ejpam-6020	439	3	function	function	NOUN
ejpam-6020	439	4	πϵ	πϵ	ADP
ejpam-6020	439	5	:	:	PUNCT
ejpam-6020	439	6	(	(	PUNCT
ejpam-6020	439	7	λ1	λ1	ADJ
ejpam-6020	439	8	,	,	PUNCT
ejpam-6020	439	9	ν1	ν1	NOUN
ejpam-6020	439	10	)	)	PUNCT
ejpam-6020	439	11	→	→	SYM
ejpam-6020	439	12	(	(	PUNCT
ejpam-6020	439	13	λ2	λ2	NOUN
ejpam-6020	439	14	,	,	PUNCT
ejpam-6020	439	15	ν2	ν2	NOUN
ejpam-6020	439	16	)	)	PUNCT
ejpam-6020	439	17	with	with	ADP
ejpam-6020	439	18	ν1	ν1	NOUN
ejpam-6020	439	19	,	,	PUNCT
ejpam-6020	439	20	ν2	ν2	NOUN
ejpam-6020	439	21	associated	associate	VERB
ejpam-6020	439	22	stss	stss	NOUN
ejpam-6020	439	23	with	with	ADP
ejpam-6020	439	24	ϑ1	ϑ1	PROPN
ejpam-6020	439	25	,	,	PUNCT
ejpam-6020	439	26	ϑ2	ϑ2	PROPN
ejpam-6020	439	27	,	,	PUNCT
ejpam-6020	439	28	respectively	respectively	ADV
ejpam-6020	439	29	,	,	PUNCT
ejpam-6020	439	30	is	be	AUX
ejpam-6020	439	31	an	an	DET
ejpam-6020	439	32	supra	supra	ADJ
ejpam-6020	439	33	ϵ-homeomorphism	ϵ-homeomorphism	NOUN
ejpam-6020	439	34	in	in	ADP
ejpam-6020	439	35	the	the	DET
ejpam-6020	439	36	event	event	NOUN
ejpam-6020	439	37	that	that	SCONJ
ejpam-6020	439	38	one	one	NUM
ejpam-6020	439	39	of	of	ADP
ejpam-6020	439	40	the	the	DET
ejpam-6020	439	41	subsequent	subsequent	ADJ
ejpam-6020	439	42	conditions	condition	NOUN
ejpam-6020	439	43	is	be	AUX
ejpam-6020	439	44	fulfilled	fulfil	VERB
ejpam-6020	439	45	:	:	PUNCT
ejpam-6020	439	46	(	(	PUNCT
ejpam-6020	439	47	1	1	X
ejpam-6020	439	48	)	)	PUNCT
ejpam-6020	439	49	πϵ(cl	πϵ(cl	NOUN
ejpam-6020	439	50	s	s	PART
ejpam-6020	439	51	ϵ(h	ϵ(h	NOUN
ejpam-6020	439	52	)	)	PUNCT
ejpam-6020	439	53	)	)	PUNCT
ejpam-6020	440	1	⊆	⊆	NUM
ejpam-6020	440	2	cl(πϵ(h	cl(πϵ(h	NOUN
ejpam-6020	440	3	)	)	PUNCT
ejpam-6020	440	4	)	)	PUNCT
ejpam-6020	440	5	and	and	CCONJ
ejpam-6020	440	6	clsϵ(πϵ(h	clsϵ(πϵ(h	NOUN
ejpam-6020	440	7	)	)	PUNCT
ejpam-6020	440	8	)	)	PUNCT
ejpam-6020	441	1	⊆	⊆	NUM
ejpam-6020	441	2	πϵ(cl(h	πϵ(cl(h	NOUN
ejpam-6020	441	3	)	)	PUNCT
ejpam-6020	441	4	)	)	PUNCT
ejpam-6020	441	5	,	,	PUNCT
ejpam-6020	441	6	∀	∀	X
ejpam-6020	441	7	(	(	PUNCT
ejpam-6020	441	8	h	h	NOUN
ejpam-6020	441	9	)	)	PUNCT
ejpam-6020	441	10	⊆	⊆	NUM
ejpam-6020	441	11	λ1	λ1	NOUN
ejpam-6020	441	12	.	.	PUNCT
ejpam-6020	442	1	(	(	PUNCT
ejpam-6020	442	2	2	2	NUM
ejpam-6020	442	3	)	)	PUNCT
ejpam-6020	442	4	πϵ(int(h	πϵ(int(h	ADJ
ejpam-6020	442	5	)	)	PUNCT
ejpam-6020	442	6	)	)	PUNCT
ejpam-6020	443	1	⊆	⊆	NUM
ejpam-6020	443	2	intsϵ(πϵ(h	intsϵ(πϵ(h	NOUN
ejpam-6020	443	3	)	)	PUNCT
ejpam-6020	443	4	)	)	PUNCT
ejpam-6020	443	5	,	,	PUNCT
ejpam-6020	443	6	∀	∀	X
ejpam-6020	443	7	(	(	PUNCT
ejpam-6020	443	8	h	h	NOUN
ejpam-6020	443	9	)	)	PUNCT
ejpam-6020	444	1	⊆	⊆	NUM
ejpam-6020	444	2	λ1	λ1	ADJ
ejpam-6020	444	3	and	and	CCONJ
ejpam-6020	444	4	ψ−1	ψ−1	PROPN
ejpam-6020	444	5	sd	sd	PROPN
ejpam-6020	444	6	(	(	PUNCT
ejpam-6020	444	7	int(h	int(h	NOUN
ejpam-6020	444	8	)	)	PUNCT
ejpam-6020	444	9	)	)	PUNCT
ejpam-6020	445	1	⊆	⊆	NUM
ejpam-6020	445	2	intsϵ(ψ	intsϵ(ψ	NOUN
ejpam-6020	445	3	−1	−1	NOUN
ejpam-6020	445	4	sd	sd	ADP
ejpam-6020	445	5	(	(	PUNCT
ejpam-6020	445	6	z	z	PROPN
ejpam-6020	445	7	,	,	PUNCT
ejpam-6020	445	8	θ2	θ2	PROPN
ejpam-6020	445	9	)	)	PUNCT
ejpam-6020	445	10	)	)	PUNCT
ejpam-6020	445	11	,	,	PUNCT
ejpam-6020	445	12	∀	∀	NUM
ejpam-6020	445	13	h	h	NOUN
ejpam-6020	445	14	⊆	⊆	NUM
ejpam-6020	445	15	λ2	λ2	NOUN
ejpam-6020	445	16	.	.	PUNCT
ejpam-6020	446	1	proof	proof	NOUN
ejpam-6020	446	2	.	.	PUNCT
ejpam-6020	447	1	if	if	SCONJ
ejpam-6020	447	2	the	the	DET
ejpam-6020	447	3	first	first	ADJ
ejpam-6020	447	4	condition	condition	NOUN
ejpam-6020	447	5	is	be	AUX
ejpam-6020	447	6	fulfilled	fulfil	VERB
ejpam-6020	447	7	,	,	PUNCT
ejpam-6020	447	8	then	then	ADV
ejpam-6020	447	9	πϵ(cl	πϵ(cl	PROPN
ejpam-6020	447	10	s	s	PART
ejpam-6020	447	11	ϵ(h	ϵ(h	NOUN
ejpam-6020	447	12	)	)	PUNCT
ejpam-6020	447	13	)	)	PUNCT
ejpam-6020	448	1	⊆	⊆	NUM
ejpam-6020	448	2	cl(πϵ(h	cl(πϵ(h	NOUN
ejpam-6020	448	3	)	)	PUNCT
ejpam-6020	448	4	)	)	PUNCT
ejpam-6020	448	5	,	,	PUNCT
ejpam-6020	448	6	implies	imply	VERB
ejpam-6020	448	7	πϵ	πϵ	ADP
ejpam-6020	448	8	is	be	AUX
ejpam-6020	448	9	supra	supra	ADJ
ejpam-6020	448	10	ϵcts	ϵct	NOUN
ejpam-6020	448	11	,	,	PUNCT
ejpam-6020	448	12	given	give	VERB
ejpam-6020	448	13	theorem	theorem	VERB
ejpam-6020	448	14	7	7	NUM
ejpam-6020	448	15	(	(	PUNCT
ejpam-6020	448	16	4	4	NUM
ejpam-6020	448	17	)	)	PUNCT
ejpam-6020	448	18	.	.	PUNCT
ejpam-6020	449	1	moreover	moreover	ADV
ejpam-6020	449	2	,	,	PUNCT
ejpam-6020	449	3	clsϵ(πϵ(h	clsϵ(πϵ(h	NOUN
ejpam-6020	449	4	)	)	PUNCT
ejpam-6020	449	5	)	)	PUNCT
ejpam-6020	450	1	⊆	⊆	NUM
ejpam-6020	450	2	πϵ(cl(h	πϵ(cl(h	NOUN
ejpam-6020	450	3	)	)	PUNCT
ejpam-6020	450	4	)	)	PUNCT
ejpam-6020	450	5	,	,	PUNCT
ejpam-6020	450	6	implies	imply	VERB
ejpam-6020	450	7	πϵ	πϵ	ADP
ejpam-6020	450	8	is	be	AUX
ejpam-6020	450	9	supra	supra	PROPN
ejpam-6020	450	10	ϵ-closed	ϵ-close	VERB
ejpam-6020	450	11	,	,	PUNCT
ejpam-6020	450	12	given	give	VERB
ejpam-6020	450	13	proposition	proposition	NOUN
ejpam-6020	450	14	17	17	NUM
ejpam-6020	450	15	.	.	PUNCT
ejpam-6020	451	1	consequently	consequently	ADV
ejpam-6020	451	2	,	,	PUNCT
ejpam-6020	451	3	πϵ	πϵ	INTJ
ejpam-6020	451	4	is	be	AUX
ejpam-6020	451	5	supra	supra	ADJ
ejpam-6020	451	6	ϵ-homeomorphism	ϵ-homeomorphism	NOUN
ejpam-6020	451	7	,	,	PUNCT
ejpam-6020	451	8	in	in	ADP
ejpam-6020	451	9	line	line	NOUN
ejpam-6020	451	10	with	with	ADP
ejpam-6020	451	11	theorem	theorem	NOUN
ejpam-6020	451	12	20	20	NUM
ejpam-6020	451	13	.	.	PUNCT
ejpam-6020	452	1	if	if	SCONJ
ejpam-6020	452	2	the	the	DET
ejpam-6020	452	3	first	first	ADJ
ejpam-6020	452	4	condition	condition	NOUN
ejpam-6020	452	5	is	be	AUX
ejpam-6020	452	6	fulfilled	fulfil	VERB
ejpam-6020	452	7	,	,	PUNCT
ejpam-6020	452	8	then	then	ADV
ejpam-6020	452	9	by	by	ADP
ejpam-6020	452	10	a	a	DET
ejpam-6020	452	11	similar	similar	ADJ
ejpam-6020	452	12	way	way	NOUN
ejpam-6020	452	13	πϵ	πϵ	ADP
ejpam-6020	452	14	is	be	AUX
ejpam-6020	452	15	supra	supra	ADJ
ejpam-6020	452	16	ϵ-homeomorphism	ϵ-homeomorphism	NOUN
ejpam-6020	452	17	,	,	PUNCT
ejpam-6020	452	18	in	in	ADP
ejpam-6020	452	19	line	line	NOUN
ejpam-6020	452	20	with	with	ADP
ejpam-6020	452	21	definition	definition	NOUN
ejpam-6020	452	22	13	13	NUM
ejpam-6020	452	23	,	,	PUNCT
ejpam-6020	452	24	theorem	theorem	VERB
ejpam-6020	452	25	7	7	NUM
ejpam-6020	452	26	(	(	PUNCT
ejpam-6020	452	27	5	5	NUM
ejpam-6020	452	28	)	)	PUNCT
ejpam-6020	452	29	and	and	CCONJ
ejpam-6020	452	30	theorem	theorem	VERB
ejpam-6020	452	31	16	16	NUM
ejpam-6020	452	32	.	.	PUNCT
ejpam-6020	453	1	5	5	NUM
ejpam-6020	453	2	.	.	X
ejpam-6020	453	3	conclusion	conclusion	PROPN
ejpam-6020	453	4	abd	abd	PROPN
ejpam-6020	453	5	el	el	PROPN
ejpam-6020	453	6	-	-	PROPN
ejpam-6020	453	7	latif	latif	PROPN
ejpam-6020	453	8	et	et	PROPN
ejpam-6020	453	9	al	al	PROPN
ejpam-6020	453	10	.	.	PROPN
ejpam-6020	453	11	introduced	introduce	VERB
ejpam-6020	453	12	the	the	DET
ejpam-6020	453	13	utilization	utilization	NOUN
ejpam-6020	453	14	of	of	ADP
ejpam-6020	453	15	supra	supra	PROPN
ejpam-6020	453	16	ϵ-open	ϵ-open	PROPN
ejpam-6020	453	17	sets	set	NOUN
ejpam-6020	453	18	to	to	ADP
ejpam-6020	453	19	supra	supra	PROPN
ejpam-6020	453	20	topological	topological	ADJ
ejpam-6020	453	21	spaces[43	spaces[43	PROPN
ejpam-6020	453	22	]	]	PUNCT
ejpam-6020	453	23	.	.	PUNCT
ejpam-6020	454	1	then	then	ADV
ejpam-6020	454	2	,	,	PUNCT
ejpam-6020	454	3	using	use	VERB
ejpam-6020	454	4	their	their	PRON
ejpam-6020	454	5	previously	previously	ADV
ejpam-6020	454	6	established	establish	VERB
ejpam-6020	454	7	category	category	NOUN
ejpam-6020	454	8	of	of	ADP
ejpam-6020	454	9	supra	supra	PROPN
ejpam-6020	454	10	open	open	ADJ
ejpam-6020	454	11	sets	set	NOUN
ejpam-6020	454	12	,	,	PUNCT
ejpam-6020	454	13	they	they	PRON
ejpam-6020	454	14	investigated	investigate	VERB
ejpam-6020	454	15	new	new	ADJ
ejpam-6020	454	16	types	type	NOUN
ejpam-6020	454	17	of	of	ADP
ejpam-6020	454	18	operators	operator	NOUN
ejpam-6020	454	19	known	know	VERB
ejpam-6020	454	20	as	as	ADP
ejpam-6020	454	21	supra	supra	PROPN
ejpam-6020	454	22	ϵ-interior	ϵ-interior	PROPN
ejpam-6020	454	23	(	(	PUNCT
ejpam-6020	454	24	closure	closure	NOUN
ejpam-6020	454	25	,	,	PUNCT
ejpam-6020	454	26	accumulation	accumulation	NOUN
ejpam-6020	454	27	,	,	PUNCT
ejpam-6020	454	28	exterior	exterior	ADJ
ejpam-6020	454	29	,	,	PUNCT
ejpam-6020	454	30	and	and	CCONJ
ejpam-6020	454	31	boundary	boundary	ADJ
ejpam-6020	454	32	,	,	PUNCT
ejpam-6020	454	33	respectively	respectively	ADV
ejpam-6020	454	34	)	)	PUNCT
ejpam-6020	454	35	.	.	PUNCT
ejpam-6020	455	1	we	we	PRON
ejpam-6020	455	2	introduce	introduce	VERB
ejpam-6020	455	3	and	and	CCONJ
ejpam-6020	455	4	explore	explore	VERB
ejpam-6020	455	5	new	new	ADJ
ejpam-6020	455	6	forms	form	NOUN
ejpam-6020	455	7	of	of	ADP
ejpam-6020	455	8	supra	supra	ADJ
ejpam-6020	455	9	continuity	continuity	NOUN
ejpam-6020	455	10	in	in	ADP
ejpam-6020	455	11	this	this	DET
ejpam-6020	455	12	work	work	NOUN
ejpam-6020	455	13	.	.	PUNCT
ejpam-6020	456	1	the	the	DET
ejpam-6020	456	2	concept	concept	NOUN
ejpam-6020	456	3	of	of	ADP
ejpam-6020	456	4	supra	supra	PROPN
ejpam-6020	456	5	ϵ-continuous	ϵ-continuous	ADJ
ejpam-6020	456	6	functions	function	NOUN
ejpam-6020	456	7	was	be	AUX
ejpam-6020	456	8	developed	develop	VERB
ejpam-6020	456	9	by	by	ADP
ejpam-6020	456	10	us	we	PRON
ejpam-6020	456	11	,	,	PUNCT
ejpam-6020	456	12	building	build	VERB
ejpam-6020	456	13	on	on	ADP
ejpam-6020	456	14	the	the	DET
ejpam-6020	456	15	previous	previous	ADJ
ejpam-6020	456	16	sorts	sort	NOUN
ejpam-6020	456	17	of	of	ADP
ejpam-6020	456	18	weaker	weak	ADJ
ejpam-6020	456	19	forms	form	NOUN
ejpam-6020	456	20	of	of	ADP
ejpam-6020	456	21	such	such	ADJ
ejpam-6020	456	22	conceptions	conception	NOUN
ejpam-6020	456	23	.	.	PUNCT
ejpam-6020	457	1	moreover	moreover	ADV
ejpam-6020	457	2	,	,	PUNCT
ejpam-6020	457	3	we	we	PRON
ejpam-6020	457	4	provide	provide	VERB
ejpam-6020	457	5	a	a	DET
ejpam-6020	457	6	diagram	diagram	NOUN
ejpam-6020	457	7	to	to	PART
ejpam-6020	457	8	analyze	analyze	VERB
ejpam-6020	457	9	the	the	DET
ejpam-6020	457	10	connections	connection	NOUN
ejpam-6020	457	11	between	between	ADP
ejpam-6020	457	12	our	our	PRON
ejpam-6020	457	13	new	new	ADJ
ejpam-6020	457	14	class	class	NOUN
ejpam-6020	457	15	and	and	CCONJ
ejpam-6020	457	16	earlier	early	ADJ
ejpam-6020	457	17	supra	supra	ADJ
ejpam-6020	457	18	continuity	continuity	NOUN
ejpam-6020	457	19	concepts	concept	NOUN
ejpam-6020	457	20	.	.	PUNCT
ejpam-6020	458	1	additionally	additionally	ADV
ejpam-6020	458	2	,	,	PUNCT
ejpam-6020	458	3	we	we	PRON
ejpam-6020	458	4	presented	present	VERB
ejpam-6020	458	5	the	the	DET
ejpam-6020	458	6	notions	notion	NOUN
ejpam-6020	458	7	of	of	ADP
ejpam-6020	458	8	supra	supra	ADJ
ejpam-6020	458	9	ϵ-irresolute	ϵ-irresolute	PROPN
ejpam-6020	458	10	functions	function	NOUN
ejpam-6020	458	11	and	and	CCONJ
ejpam-6020	458	12	supra	supra	ADJ
ejpam-6020	458	13	ϵ-cts	ϵ-ct	NOUN
ejpam-6020	458	14	functions	function	NOUN
ejpam-6020	458	15	and	and	CCONJ
ejpam-6020	458	16	thoroughly	thoroughly	ADV
ejpam-6020	458	17	described	describe	VERB
ejpam-6020	458	18	their	their	PRON
ejpam-6020	458	19	key	key	ADJ
ejpam-6020	458	20	characteristics	characteristic	NOUN
ejpam-6020	458	21	.	.	PUNCT
ejpam-6020	459	1	furthermore	furthermore	ADV
ejpam-6020	459	2	,	,	PUNCT
ejpam-6020	459	3	we	we	PRON
ejpam-6020	459	4	propose	propose	VERB
ejpam-6020	459	5	novel	novel	ADJ
ejpam-6020	459	6	approaches	approach	NOUN
ejpam-6020	459	7	for	for	ADP
ejpam-6020	459	8	supra	supra	ADJ
ejpam-6020	459	9	functions	function	NOUN
ejpam-6020	459	10	,	,	PUNCT
ejpam-6020	459	11	which	which	PRON
ejpam-6020	459	12	we	we	PRON
ejpam-6020	459	13	refer	refer	VERB
ejpam-6020	459	14	to	to	ADP
ejpam-6020	459	15	as	as	ADP
ejpam-6020	459	16	supra	supra	PROPN
ejpam-6020	459	17	ϵ-open	ϵ-open	PROPN
ejpam-6020	459	18	functions	function	NOUN
ejpam-6020	459	19	,	,	PUNCT
ejpam-6020	459	20	supra	supra	ADJ
ejpam-6020	459	21	ϵ-closed	ϵ-close	VERB
ejpam-6020	459	22	functions	function	NOUN
ejpam-6020	459	23	,	,	PUNCT
ejpam-6020	459	24	and	and	CCONJ
ejpam-6020	459	25	supra	supra	PROPN
ejpam-6020	459	26	ϵ-homeomorphism	ϵ-homeomorphism	NOUN
ejpam-6020	459	27	functions	function	NOUN
ejpam-6020	459	28	.	.	PUNCT
ejpam-6020	460	1	we	we	PRON
ejpam-6020	460	2	also	also	ADV
ejpam-6020	460	3	discuss	discuss	VERB
ejpam-6020	460	4	the	the	DET
ejpam-6020	460	5	main	main	ADJ
ejpam-6020	460	6	features	feature	NOUN
ejpam-6020	460	7	of	of	ADP
ejpam-6020	460	8	each	each	DET
ejpam-6020	460	9	notions	notion	NOUN
ejpam-6020	460	10	.	.	PUNCT
ejpam-6020	461	1	from	from	ADP
ejpam-6020	461	2	the	the	DET
ejpam-6020	461	3	particular	particular	ADJ
ejpam-6020	461	4	methods	method	NOUN
ejpam-6020	461	5	described	describe	VERB
ejpam-6020	461	6	in	in	ADP
ejpam-6020	461	7	this	this	DET
ejpam-6020	461	8	article	article	NOUN
ejpam-6020	461	9	,	,	PUNCT
ejpam-6020	461	10	additional	additional	ADJ
ejpam-6020	461	11	research	research	NOUN
ejpam-6020	461	12	on	on	ADP
ejpam-6020	461	13	the	the	DET
ejpam-6020	461	14	theoretical	theoretical	ADJ
ejpam-6020	461	15	elements	element	NOUN
ejpam-6020	461	16	of	of	ADP
ejpam-6020	461	17	these	these	DET
ejpam-6020	461	18	generalized	generalize	VERB
ejpam-6020	461	19	concepts	concept	NOUN
ejpam-6020	461	20	could	could	AUX
ejpam-6020	461	21	be	be	AUX
ejpam-6020	461	22	carried	carry	VERB
ejpam-6020	461	23	out	out	ADP
ejpam-6020	461	24	by	by	ADP
ejpam-6020	461	25	looking	look	VERB
ejpam-6020	461	26	at	at	ADP
ejpam-6020	461	27	the	the	DET
ejpam-6020	461	28	following	follow	VERB
ejpam-6020	461	29	subjects	subject	NOUN
ejpam-6020	461	30	:	:	PUNCT
ejpam-6020	461	31	utilizing	utilize	VERB
ejpam-6020	461	32	these	these	DET
ejpam-6020	461	33	methods	method	NOUN
ejpam-6020	461	34	in	in	ADP
ejpam-6020	461	35	supra	supra	PROPN
ejpam-6020	461	36	soft	soft	ADJ
ejpam-6020	461	37	ideal	ideal	ADJ
ejpam-6020	461	38	topological	topological	ADJ
ejpam-6020	461	39	spaces	space	NOUN
ejpam-6020	461	40	[	[	X
ejpam-6020	461	41	30	30	NUM
ejpam-6020	461	42	]	]	PUNCT
ejpam-6020	461	43	.	.	PUNCT
ejpam-6020	462	1	in	in	ADP
ejpam-6020	462	2	addition	addition	NOUN
ejpam-6020	462	3	,	,	PUNCT
ejpam-6020	462	4	we	we	PRON
ejpam-6020	462	5	investigate	investigate	VERB
ejpam-6020	462	6	certain	certain	ADJ
ejpam-6020	462	7	topological	topological	ADJ
ejpam-6020	462	8	characteristics	characteristic	NOUN
ejpam-6020	462	9	,	,	PUNCT
ejpam-6020	462	10	such	such	ADJ
ejpam-6020	462	11	as	as	ADP
ejpam-6020	462	12	supra	supra	NOUN
ejpam-6020	462	13	(	(	PUNCT
ejpam-6020	462	14	connectedness	connectedness	NOUN
ejpam-6020	462	15	,	,	PUNCT
ejpam-6020	462	16	separation	separation	NOUN
ejpam-6020	462	17	axioms	axiom	NOUN
ejpam-6020	462	18	,	,	PUNCT
ejpam-6020	462	19	and	and	CCONJ
ejpam-6020	462	20	compactness	compactness	NOUN
ejpam-6020	462	21	)	)	PUNCT
ejpam-6020	462	22	,	,	PUNCT
ejpam-6020	462	23	that	that	PRON
ejpam-6020	462	24	are	be	AUX
ejpam-6020	462	25	motivated	motivate	VERB
ejpam-6020	462	26	by	by	ADP
ejpam-6020	462	27	specific	specific	ADJ
ejpam-6020	462	28	approaches	approach	NOUN
ejpam-6020	462	29	discussed	discuss	VERB
ejpam-6020	462	30	in	in	ADP
ejpam-6020	462	31	this	this	DET
ejpam-6020	462	32	work	work	NOUN
ejpam-6020	462	33	.	.	PUNCT
ejpam-6020	463	1	a.	a.	PROPN
ejpam-6020	463	2	m.	m.	PROPN
ejpam-6020	463	3	abd	abd	PROPN
ejpam-6020	463	4	el	el	PROPN
ejpam-6020	463	5	-	-	PROPN
ejpam-6020	463	6	latif	latif	PROPN
ejpam-6020	463	7	et	et	PROPN
ejpam-6020	463	8	al	al	PROPN
ejpam-6020	463	9	.	.	PUNCT
ejpam-6020	463	10	/	/	SYM
ejpam-6020	463	11	eur	eur	PROPN
ejpam-6020	463	12	.	.	PUNCT
ejpam-6020	464	1	j.	j.	PROPN
ejpam-6020	464	2	pure	pure	PROPN
ejpam-6020	464	3	appl	appl	PROPN
ejpam-6020	464	4	.	.	PROPN
ejpam-6020	464	5	math	math	PROPN
ejpam-6020	464	6	,	,	PUNCT
ejpam-6020	464	7	18	18	NUM
ejpam-6020	464	8	(	(	PUNCT
ejpam-6020	464	9	2	2	NUM
ejpam-6020	464	10	)	)	PUNCT
ejpam-6020	464	11	(	(	PUNCT
ejpam-6020	464	12	2025	2025	NUM
ejpam-6020	464	13	)	)	PUNCT
ejpam-6020	464	14	,	,	PUNCT
ejpam-6020	464	15	6020	6020	NUM
ejpam-6020	464	16	14	14	NUM
ejpam-6020	464	17	of	of	ADP
ejpam-6020	464	18	17	17	NUM
ejpam-6020	464	19	acknowledgements	acknowledgement	NOUN
ejpam-6020	464	20	the	the	DET
ejpam-6020	464	21	authors	author	NOUN
ejpam-6020	464	22	extend	extend	VERB
ejpam-6020	464	23	their	their	PRON
ejpam-6020	464	24	appreciation	appreciation	NOUN
ejpam-6020	464	25	to	to	ADP
ejpam-6020	464	26	the	the	DET
ejpam-6020	464	27	deanship	deanship	NOUN
ejpam-6020	464	28	of	of	ADP
ejpam-6020	464	29	scientific	scientific	ADJ
ejpam-6020	464	30	research	research	NOUN
ejpam-6020	464	31	at	at	ADP
ejpam-6020	464	32	northern	northern	ADJ
ejpam-6020	464	33	border	border	NOUN
ejpam-6020	464	34	university	university	PROPN
ejpam-6020	464	35	,	,	PUNCT
ejpam-6020	464	36	arar	arar	PROPN
ejpam-6020	464	37	,	,	PUNCT
ejpam-6020	464	38	ksa	ksa	PROPN
ejpam-6020	464	39	for	for	ADP
ejpam-6020	464	40	funding	fund	VERB
ejpam-6020	464	41	this	this	DET
ejpam-6020	464	42	research	research	NOUN
ejpam-6020	464	43	work	work	NOUN
ejpam-6020	464	44	through	through	ADP
ejpam-6020	464	45	the	the	DET
ejpam-6020	464	46	project	project	NOUN
ejpam-6020	464	47	number	number	NOUN
ejpam-6020	464	48	”	"	PUNCT
ejpam-6020	464	49	nbu	nbu	NOUN
ejpam-6020	464	50	-	-	PUNCT
ejpam-6020	464	51	ffr-2025	ffr-2025	NOUN
ejpam-6020	464	52	-	-	PUNCT
ejpam-6020	464	53	1687	1687	NUM
ejpam-6020	464	54	-	-	SYM
ejpam-6020	464	55	01	01	NUM
ejpam-6020	464	56	”	"	PUNCT
ejpam-6020	464	57	.	.	PUNCT
ejpam-6020	465	1	also	also	ADV
ejpam-6020	465	2	,	,	PUNCT
ejpam-6020	465	3	this	this	DET
ejpam-6020	465	4	study	study	NOUN
ejpam-6020	465	5	is	be	AUX
ejpam-6020	465	6	supported	support	VERB
ejpam-6020	465	7	via	via	ADP
ejpam-6020	465	8	funding	funding	NOUN
ejpam-6020	465	9	from	from	ADP
ejpam-6020	465	10	prince	prince	PROPN
ejpam-6020	465	11	sattam	sattam	PROPN
ejpam-6020	465	12	bin	bin	PROPN
ejpam-6020	465	13	abdulaziz	abdulaziz	PROPN
ejpam-6020	465	14	university	university	PROPN
ejpam-6020	465	15	project	project	NOUN
ejpam-6020	465	16	number	number	NOUN
ejpam-6020	465	17	(	(	PUNCT
ejpam-6020	465	18	psau/2025	psau/2025	NOUN
ejpam-6020	465	19	/	/	SYM
ejpam-6020	465	20	r/1446	r/1446	PROPN
ejpam-6020	465	21	)	)	PUNCT
ejpam-6020	465	22	and	and	CCONJ
ejpam-6020	465	23	this	this	DET
ejpam-6020	465	24	research	research	NOUN
ejpam-6020	465	25	is	be	AUX
ejpam-6020	465	26	funded	fund	VERB
ejpam-6020	465	27	by	by	ADP
ejpam-6020	465	28	zarqa	zarqa	PROPN
ejpam-6020	465	29	university	university	PROPN
ejpam-6020	465	30	jordan	jordan	PROPN
ejpam-6020	465	31	.	.	PUNCT
ejpam-6020	466	1	author	author	NOUN
ejpam-6020	466	2	contributions	contribution	NOUN
ejpam-6020	466	3	alaa	alaa	PROPN
ejpam-6020	466	4	m.	m.	PROPN
ejpam-6020	466	5	abd	abd	PROPN
ejpam-6020	466	6	el	el	PROPN
ejpam-6020	466	7	-	-	PROPN
ejpam-6020	466	8	latif	latif	PROPN
ejpam-6020	466	9	:	:	PUNCT
ejpam-6020	466	10	conceptualization	conceptualization	NOUN
ejpam-6020	466	11	,	,	PUNCT
ejpam-6020	466	12	methodology	methodology	NOUN
ejpam-6020	466	13	,	,	PUNCT
ejpam-6020	466	14	formal	formal	ADJ
ejpam-6020	466	15	analysis	analysis	NOUN
ejpam-6020	466	16	,	,	PUNCT
ejpam-6020	466	17	investigation	investigation	NOUN
ejpam-6020	466	18	,	,	PUNCT
ejpam-6020	466	19	writing	writing	NOUN
ejpam-6020	466	20	,	,	PUNCT
ejpam-6020	466	21	original	original	ADJ
ejpam-6020	466	22	draft	draft	NOUN
ejpam-6020	466	23	preparation	preparation	NOUN
ejpam-6020	466	24	,	,	PUNCT
ejpam-6020	466	25	review	review	NOUN
ejpam-6020	466	26	and	and	CCONJ
ejpam-6020	466	27	editing	editing	NOUN
ejpam-6020	466	28	,	,	PUNCT
ejpam-6020	466	29	funding	funding	NOUN
ejpam-6020	466	30	acquisition	acquisition	NOUN
ejpam-6020	466	31	radwan	radwan	VERB
ejpam-6020	466	32	abu	abu	PROPN
ejpam-6020	466	33	-	-	PUNCT
ejpam-6020	466	34	gdairi	gdairi	PROPN
ejpam-6020	466	35	:	:	PUNCT
ejpam-6020	466	36	methodology	methodology	NOUN
ejpam-6020	466	37	,	,	PUNCT
ejpam-6020	466	38	formal	formal	ADJ
ejpam-6020	466	39	analysis	analysis	NOUN
ejpam-6020	466	40	,	,	PUNCT
ejpam-6020	466	41	investigation	investigation	NOUN
ejpam-6020	466	42	,	,	PUNCT
ejpam-6020	466	43	writing	writing	NOUN
ejpam-6020	466	44	,	,	PUNCT
ejpam-6020	466	45	original	original	ADJ
ejpam-6020	466	46	,	,	PUNCT
ejpam-6020	466	47	review	review	NOUN
ejpam-6020	466	48	and	and	CCONJ
ejpam-6020	466	49	editing	editing	NOUN
ejpam-6020	466	50	,	,	PUNCT
ejpam-6020	466	51	funding	funding	NOUN
ejpam-6020	466	52	acquisition	acquisition	NOUN
ejpam-6020	466	53	a.	a.	NOUN
ejpam-6020	466	54	a.	a.	PROPN
ejpam-6020	466	55	azzam	azzam	PROPN
ejpam-6020	466	56	:	:	PUNCT
ejpam-6020	466	57	conceptualization	conceptualization	NOUN
ejpam-6020	466	58	,	,	PUNCT
ejpam-6020	466	59	formal	formal	ADJ
ejpam-6020	466	60	analysis	analysis	NOUN
ejpam-6020	466	61	,	,	PUNCT
ejpam-6020	466	62	investigation	investigation	NOUN
ejpam-6020	466	63	,	,	PUNCT
ejpam-6020	466	64	original	original	ADJ
ejpam-6020	466	65	draft	draft	NOUN
ejpam-6020	466	66	preparation	preparation	NOUN
ejpam-6020	466	67	,	,	PUNCT
ejpam-6020	466	68	review	review	NOUN
ejpam-6020	466	69	and	and	CCONJ
ejpam-6020	466	70	editing	editing	NOUN
ejpam-6020	466	71	,	,	PUNCT
ejpam-6020	466	72	funding	funding	NOUN
ejpam-6020	466	73	acquisition	acquisition	NOUN
ejpam-6020	466	74	f.	f.	PROPN
ejpam-6020	466	75	a.	a.	PROPN
ejpam-6020	466	76	gharib	gharib	PROPN
ejpam-6020	466	77	:	:	PUNCT
ejpam-6020	466	78	conceptualization	conceptualization	NOUN
ejpam-6020	466	79	,	,	PUNCT
ejpam-6020	466	80	methodology	methodology	NOUN
ejpam-6020	466	81	,	,	PUNCT
ejpam-6020	466	82	investigation	investigation	NOUN
ejpam-6020	466	83	,	,	PUNCT
ejpam-6020	466	84	writing	writing	NOUN
ejpam-6020	466	85	,	,	PUNCT
ejpam-6020	466	86	original	original	ADJ
ejpam-6020	466	87	draft	draft	NOUN
ejpam-6020	466	88	preparation	preparation	NOUN
ejpam-6020	466	89	,	,	PUNCT
ejpam-6020	466	90	review	review	NOUN
ejpam-6020	466	91	and	and	CCONJ
ejpam-6020	466	92	editing	edit	VERB
ejpam-6020	466	93	husham	husham	PROPN
ejpam-6020	466	94	m.	m.	NOUN
ejpam-6020	466	95	attaalfadeel	attaalfadeel	PROPN
ejpam-6020	466	96	:	:	PUNCT
ejpam-6020	466	97	conceptualization	conceptualization	NOUN
ejpam-6020	466	98	,	,	PUNCT
ejpam-6020	466	99	methodology	methodology	NOUN
ejpam-6020	466	100	,	,	PUNCT
ejpam-6020	466	101	investigation	investigation	NOUN
ejpam-6020	466	102	,	,	PUNCT
ejpam-6020	466	103	writing	writing	NOUN
ejpam-6020	466	104	,	,	PUNCT
ejpam-6020	466	105	original	original	ADJ
ejpam-6020	466	106	draft	draft	NOUN
ejpam-6020	466	107	preparation	preparation	NOUN
ejpam-6020	466	108	,	,	PUNCT
ejpam-6020	466	109	review	review	NOUN
ejpam-6020	466	110	and	and	CCONJ
ejpam-6020	466	111	editing	edit	VERB
ejpam-6020	466	112	walid	walid	PROPN
ejpam-6020	466	113	abdelfattah	abdelfattah	PROPN
ejpam-6020	466	114	:	:	PUNCT
ejpam-6020	466	115	conceptualization	conceptualization	NOUN
ejpam-6020	466	116	,	,	PUNCT
ejpam-6020	466	117	methodology	methodology	NOUN
ejpam-6020	466	118	,	,	PUNCT
ejpam-6020	466	119	investigation	investigation	NOUN
ejpam-6020	466	120	,	,	PUNCT
ejpam-6020	466	121	writing	writing	NOUN
ejpam-6020	466	122	,	,	PUNCT
ejpam-6020	466	123	original	original	ADJ
ejpam-6020	466	124	draft	draft	NOUN
ejpam-6020	466	125	preparation	preparation	NOUN
ejpam-6020	466	126	,	,	PUNCT
ejpam-6020	466	127	review	review	NOUN
ejpam-6020	466	128	and	and	CCONJ
ejpam-6020	466	129	editing	edit	VERB
ejpam-6020	466	130	shaaban	shaaban	ADJ
ejpam-6020	466	131	m.	m.	NOUN
ejpam-6020	466	132	shaaban	shaaban	NOUN
ejpam-6020	466	133	:	:	PUNCT
ejpam-6020	466	134	conceptualization	conceptualization	NOUN
ejpam-6020	466	135	,	,	PUNCT
ejpam-6020	466	136	methodology	methodology	NOUN
ejpam-6020	466	137	,	,	PUNCT
ejpam-6020	466	138	investigation	investigation	NOUN
ejpam-6020	466	139	,	,	PUNCT
ejpam-6020	466	140	writing	writing	NOUN
ejpam-6020	466	141	,	,	PUNCT
ejpam-6020	466	142	original	original	ADJ
ejpam-6020	466	143	draft	draft	NOUN
ejpam-6020	466	144	preparation	preparation	NOUN
ejpam-6020	466	145	,	,	PUNCT
ejpam-6020	466	146	review	review	NOUN
ejpam-6020	466	147	and	and	CCONJ
ejpam-6020	466	148	editing	edit	VERB
ejpam-6020	466	149	m.	m.	NOUN
ejpam-6020	466	150	aldawood	aldawood	PROPN
ejpam-6020	466	151	:	:	PUNCT
ejpam-6020	466	152	conceptualization	conceptualization	NOUN
ejpam-6020	466	153	,	,	PUNCT
ejpam-6020	466	154	formal	formal	ADJ
ejpam-6020	466	155	analysis	analysis	NOUN
ejpam-6020	466	156	,	,	PUNCT
ejpam-6020	466	157	investigation	investigation	NOUN
ejpam-6020	466	158	,	,	PUNCT
ejpam-6020	466	159	original	original	ADJ
ejpam-6020	466	160	draft	draft	NOUN
ejpam-6020	466	161	preparation	preparation	NOUN
ejpam-6020	466	162	,	,	PUNCT
ejpam-6020	466	163	review	review	NOUN
ejpam-6020	466	164	and	and	CCONJ
ejpam-6020	466	165	editing	editing	NOUN
ejpam-6020	466	166	,	,	PUNCT
ejpam-6020	466	167	funding	funding	NOUN
ejpam-6020	466	168	acquisition	acquisition	NOUN
ejpam-6020	466	169	references	reference	NOUN
ejpam-6020	466	170	[	[	X
ejpam-6020	466	171	1	1	NUM
ejpam-6020	466	172	]	]	X
ejpam-6020	466	173	n.	n.	PROPN
ejpam-6020	466	174	levine	levine	PROPN
ejpam-6020	466	175	.	.	PUNCT
ejpam-6020	467	1	semi	semi	ADJ
ejpam-6020	467	2	-	-	ADJ
ejpam-6020	467	3	open	open	ADJ
ejpam-6020	467	4	sets	set	NOUN
ejpam-6020	467	5	and	and	CCONJ
ejpam-6020	467	6	semi	semi	ADJ
ejpam-6020	467	7	-	-	NOUN
ejpam-6020	467	8	continuity	continuity	NOUN
ejpam-6020	467	9	in	in	ADP
ejpam-6020	467	10	topological	topological	ADJ
ejpam-6020	467	11	spaces	space	NOUN
ejpam-6020	467	12	.	.	PUNCT
ejpam-6020	468	1	american	american	PROPN
ejpam-6020	468	2	mathematical	mathematical	PROPN
ejpam-6020	468	3	monthly	monthly	ADV
ejpam-6020	468	4	,	,	PUNCT
ejpam-6020	468	5	70(1):36–41	70(1):36–41	NUM
ejpam-6020	468	6	,	,	PUNCT
ejpam-6020	468	7	1963	1963	NUM
ejpam-6020	468	8	.	.	PUNCT
ejpam-6020	469	1	[	[	X
ejpam-6020	469	2	2	2	NUM
ejpam-6020	469	3	]	]	X
ejpam-6020	469	4	o.	o.	PROPN
ejpam-6020	469	5	njastad	njastad	PROPN
ejpam-6020	469	6	.	.	PUNCT
ejpam-6020	470	1	on	on	ADP
ejpam-6020	470	2	some	some	DET
ejpam-6020	470	3	classes	class	NOUN
ejpam-6020	470	4	of	of	ADP
ejpam-6020	470	5	nearly	nearly	ADV
ejpam-6020	470	6	open	open	ADJ
ejpam-6020	470	7	sets	set	NOUN
ejpam-6020	470	8	.	.	PUNCT
ejpam-6020	471	1	pacific	pacific	PROPN
ejpam-6020	471	2	journal	journal	PROPN
ejpam-6020	471	3	of	of	ADP
ejpam-6020	471	4	mathematics	mathematic	NOUN
ejpam-6020	471	5	,	,	PUNCT
ejpam-6020	471	6	15(3):961–970	15(3):961–970	PROPN
ejpam-6020	471	7	,	,	PUNCT
ejpam-6020	471	8	1965	1965	NUM
ejpam-6020	471	9	.	.	PUNCT
ejpam-6020	472	1	[	[	X
ejpam-6020	472	2	3	3	X
ejpam-6020	472	3	]	]	PUNCT
ejpam-6020	472	4	a.	a.	NOUN
ejpam-6020	472	5	mashhour	mashhour	PROPN
ejpam-6020	472	6	,	,	PUNCT
ejpam-6020	472	7	m.	m.	PROPN
ejpam-6020	472	8	abd	abd	PROPN
ejpam-6020	472	9	el	el	PROPN
ejpam-6020	472	10	-	-	PROPN
ejpam-6020	472	11	monsef	monsef	ADJ
ejpam-6020	472	12	,	,	PUNCT
ejpam-6020	472	13	and	and	CCONJ
ejpam-6020	472	14	s.	s.	PROPN
ejpam-6020	472	15	el	el	PROPN
ejpam-6020	472	16	-	-	PROPN
ejpam-6020	472	17	deeb	deeb	PROPN
ejpam-6020	472	18	.	.	PUNCT
ejpam-6020	473	1	on	on	ADP
ejpam-6020	473	2	precontinuous	precontinuous	ADJ
ejpam-6020	473	3	and	and	CCONJ
ejpam-6020	473	4	weak	weak	ADJ
ejpam-6020	473	5	precontinuous	precontinuous	ADJ
ejpam-6020	473	6	mappings	mapping	NOUN
ejpam-6020	473	7	.	.	PUNCT
ejpam-6020	474	1	proceedings	proceeding	NOUN
ejpam-6020	474	2	of	of	ADP
ejpam-6020	474	3	the	the	DET
ejpam-6020	474	4	mathematical	mathematical	ADJ
ejpam-6020	474	5	and	and	CCONJ
ejpam-6020	474	6	physical	physical	ADJ
ejpam-6020	474	7	society	society	NOUN
ejpam-6020	474	8	,	,	PUNCT
ejpam-6020	474	9	53:47–53	53:47–53	NUM
ejpam-6020	474	10	,	,	PUNCT
ejpam-6020	474	11	1982	1982	NUM
ejpam-6020	474	12	.	.	PUNCT
ejpam-6020	475	1	[	[	X
ejpam-6020	475	2	4	4	X
ejpam-6020	475	3	]	]	PUNCT
ejpam-6020	475	4	m.	m.	NOUN
ejpam-6020	475	5	abd	abd	PROPN
ejpam-6020	475	6	el	el	PROPN
ejpam-6020	475	7	-	-	PROPN
ejpam-6020	475	8	monsef	monsef	PROPN
ejpam-6020	475	9	,	,	PUNCT
ejpam-6020	475	10	s.	s.	PROPN
ejpam-6020	475	11	el	el	PROPN
ejpam-6020	475	12	-	-	PROPN
ejpam-6020	475	13	deeb	deeb	PROPN
ejpam-6020	475	14	,	,	PUNCT
ejpam-6020	475	15	and	and	CCONJ
ejpam-6020	475	16	r.	r.	PROPN
ejpam-6020	475	17	mahmoud	mahmoud	PROPN
ejpam-6020	475	18	.	.	PUNCT
ejpam-6020	476	1	β	β	X
ejpam-6020	476	2	-	-	ADJ
ejpam-6020	476	3	open	open	ADJ
ejpam-6020	476	4	sets	set	NOUN
ejpam-6020	476	5	and	and	CCONJ
ejpam-6020	476	6	β	β	ADJ
ejpam-6020	476	7	-	-	ADJ
ejpam-6020	476	8	continuous	continuous	ADJ
ejpam-6020	476	9	mappings	mapping	NOUN
ejpam-6020	476	10	.	.	PUNCT
ejpam-6020	477	1	bulletin	bulletin	NOUN
ejpam-6020	477	2	of	of	ADP
ejpam-6020	477	3	the	the	DET
ejpam-6020	477	4	faculty	faculty	NOUN
ejpam-6020	477	5	of	of	ADP
ejpam-6020	477	6	science	science	NOUN
ejpam-6020	477	7	,	,	PUNCT
ejpam-6020	477	8	assiut	assiut	NOUN
ejpam-6020	477	9	university	university	NOUN
ejpam-6020	477	10	,	,	PUNCT
ejpam-6020	477	11	12(1):77–90	12(1):77–90	NUM
ejpam-6020	477	12	,	,	PUNCT
ejpam-6020	477	13	1983	1983	NUM
ejpam-6020	477	14	.	.	PUNCT
ejpam-6020	478	1	[	[	X
ejpam-6020	478	2	5	5	X
ejpam-6020	478	3	]	]	PUNCT
ejpam-6020	478	4	d.	d.	PROPN
ejpam-6020	478	5	andrijević.	andrijević.	PROPN
ejpam-6020	478	6	on	on	ADP
ejpam-6020	478	7	b	b	X
ejpam-6020	478	8	-	-	PUNCT
ejpam-6020	478	9	open	open	ADJ
ejpam-6020	478	10	sets	set	NOUN
ejpam-6020	478	11	.	.	PUNCT
ejpam-6020	479	1	matematički	matematički	PROPN
ejpam-6020	479	2	vesnik	vesnik	PROPN
ejpam-6020	479	3	,	,	PUNCT
ejpam-6020	479	4	48:59–64	48:59–64	PROPN
ejpam-6020	479	5	,	,	PUNCT
ejpam-6020	479	6	1996	1996	NUM
ejpam-6020	479	7	.	.	PUNCT
ejpam-6020	480	1	[	[	X
ejpam-6020	480	2	6	6	NUM
ejpam-6020	480	3	]	]	PUNCT
ejpam-6020	480	4	j.	j.	PROPN
ejpam-6020	480	5	dontchev	dontchev	PROPN
ejpam-6020	480	6	and	and	CCONJ
ejpam-6020	480	7	m.	m.	PROPN
ejpam-6020	480	8	przemski	przemski	PROPN
ejpam-6020	480	9	.	.	PUNCT
ejpam-6020	481	1	on	on	ADP
ejpam-6020	481	2	the	the	DET
ejpam-6020	481	3	various	various	ADJ
ejpam-6020	481	4	decompositions	decomposition	NOUN
ejpam-6020	481	5	of	of	ADP
ejpam-6020	481	6	continuous	continuous	ADJ
ejpam-6020	481	7	and	and	CCONJ
ejpam-6020	481	8	some	some	DET
ejpam-6020	481	9	weakly	weakly	ADJ
ejpam-6020	481	10	continuous	continuous	ADJ
ejpam-6020	481	11	functions	function	NOUN
ejpam-6020	481	12	.	.	PUNCT
ejpam-6020	482	1	acta	acta	PROPN
ejpam-6020	482	2	mathematica	mathematica	PROPN
ejpam-6020	482	3	hungarica	hungarica	PROPN
ejpam-6020	482	4	,	,	PUNCT
ejpam-6020	482	5	71(1–2):109–120	71(1–2):109–120	NUM
ejpam-6020	482	6	,	,	PUNCT
ejpam-6020	482	7	1996	1996	NUM
ejpam-6020	482	8	.	.	PUNCT
ejpam-6020	483	1	a.	a.	PROPN
ejpam-6020	483	2	m.	m.	PROPN
ejpam-6020	483	3	abd	abd	PROPN
ejpam-6020	483	4	el	el	PROPN
ejpam-6020	483	5	-	-	PROPN
ejpam-6020	483	6	latif	latif	PROPN
ejpam-6020	483	7	et	et	PROPN
ejpam-6020	483	8	al	al	PROPN
ejpam-6020	483	9	.	.	PUNCT
ejpam-6020	483	10	/	/	SYM
ejpam-6020	483	11	eur	eur	PROPN
ejpam-6020	483	12	.	.	PUNCT
ejpam-6020	484	1	j.	j.	PROPN
ejpam-6020	484	2	pure	pure	PROPN
ejpam-6020	484	3	appl	appl	PROPN
ejpam-6020	484	4	.	.	PROPN
ejpam-6020	484	5	math	math	PROPN
ejpam-6020	484	6	,	,	PUNCT
ejpam-6020	484	7	18	18	NUM
ejpam-6020	484	8	(	(	PUNCT
ejpam-6020	484	9	2	2	NUM
ejpam-6020	484	10	)	)	PUNCT
ejpam-6020	484	11	(	(	PUNCT
ejpam-6020	484	12	2025	2025	NUM
ejpam-6020	484	13	)	)	PUNCT
ejpam-6020	484	14	,	,	PUNCT
ejpam-6020	484	15	6020	6020	NUM
ejpam-6020	484	16	15	15	NUM
ejpam-6020	484	17	of	of	ADP
ejpam-6020	484	18	17	17	NUM
ejpam-6020	484	19	[	[	SYM
ejpam-6020	484	20	7	7	NUM
ejpam-6020	484	21	]	]	PUNCT
ejpam-6020	484	22	k.	k.	PROPN
ejpam-6020	484	23	r.	r.	PROPN
ejpam-6020	484	24	gentry	gentry	PROPN
ejpam-6020	484	25	and	and	CCONJ
ejpam-6020	484	26	h.	h.	PROPN
ejpam-6020	484	27	b.	b.	PROPN
ejpam-6020	484	28	hoyle	hoyle	PROPN
ejpam-6020	484	29	.	.	PUNCT
ejpam-6020	485	1	somewhat	somewhat	ADV
ejpam-6020	485	2	continuous	continuous	ADJ
ejpam-6020	485	3	functions	function	NOUN
ejpam-6020	485	4	.	.	PUNCT
ejpam-6020	486	1	czechoslovak	czechoslovak	ADJ
ejpam-6020	486	2	mathematical	mathematical	PROPN
ejpam-6020	486	3	journal	journal	PROPN
ejpam-6020	486	4	,	,	PUNCT
ejpam-6020	486	5	21:5–12	21:5–12	NUM
ejpam-6020	486	6	,	,	PUNCT
ejpam-6020	486	7	1971	1971	NUM
ejpam-6020	486	8	.	.	PUNCT
ejpam-6020	487	1	[	[	X
ejpam-6020	487	2	8	8	NUM
ejpam-6020	487	3	]	]	PUNCT
ejpam-6020	487	4	z.	z.	PROPN
ejpam-6020	487	5	piotrowski	piotrowski	PROPN
ejpam-6020	487	6	.	.	PUNCT
ejpam-6020	488	1	a	a	DET
ejpam-6020	488	2	survey	survey	NOUN
ejpam-6020	488	3	of	of	ADP
ejpam-6020	488	4	results	result	NOUN
ejpam-6020	488	5	concerning	concern	VERB
ejpam-6020	488	6	generalized	generalized	ADJ
ejpam-6020	488	7	continuity	continuity	NOUN
ejpam-6020	488	8	on	on	ADP
ejpam-6020	488	9	topological	topological	ADJ
ejpam-6020	488	10	spaces	space	NOUN
ejpam-6020	488	11	.	.	PUNCT
ejpam-6020	489	1	acta	acta	PROPN
ejpam-6020	489	2	mathematica	mathematica	PROPN
ejpam-6020	489	3	universitatis	universitatis	PROPN
ejpam-6020	489	4	comenianae	comenianae	PROPN
ejpam-6020	489	5	,	,	PUNCT
ejpam-6020	489	6	52:91–110	52:91–110	NUM
ejpam-6020	489	7	,	,	PUNCT
ejpam-6020	489	8	1987	1987	NUM
ejpam-6020	489	9	.	.	PUNCT
ejpam-6020	490	1	[	[	X
ejpam-6020	490	2	9	9	NUM
ejpam-6020	490	3	]	]	X
ejpam-6020	490	4	o.	o.	PROPN
ejpam-6020	490	5	njastad	njastad	PROPN
ejpam-6020	490	6	.	.	PUNCT
ejpam-6020	491	1	on	on	ADP
ejpam-6020	491	2	some	some	DET
ejpam-6020	491	3	classes	class	NOUN
ejpam-6020	491	4	of	of	ADP
ejpam-6020	491	5	nearly	nearly	ADV
ejpam-6020	491	6	open	open	ADJ
ejpam-6020	491	7	sets	set	NOUN
ejpam-6020	491	8	.	.	PUNCT
ejpam-6020	492	1	pacific	pacific	PROPN
ejpam-6020	492	2	journal	journal	PROPN
ejpam-6020	492	3	of	of	ADP
ejpam-6020	492	4	mathematics	mathematic	NOUN
ejpam-6020	492	5	,	,	PUNCT
ejpam-6020	492	6	15:961–970	15:961–970	PROPN
ejpam-6020	492	7	,	,	PUNCT
ejpam-6020	492	8	1965	1965	NUM
ejpam-6020	492	9	.	.	PUNCT
ejpam-6020	493	1	[	[	X
ejpam-6020	493	2	10	10	NUM
ejpam-6020	493	3	]	]	X
ejpam-6020	493	4	c.	c.	PROPN
ejpam-6020	493	5	c.	c.	PROPN
ejpam-6020	493	6	pugh	pugh	PROPN
ejpam-6020	493	7	.	.	PUNCT
ejpam-6020	494	1	real	real	ADJ
ejpam-6020	494	2	mathematical	mathematical	ADJ
ejpam-6020	494	3	analysis	analysis	NOUN
ejpam-6020	494	4	.	.	PUNCT
ejpam-6020	495	1	springer	springer	NOUN
ejpam-6020	495	2	science	science	NOUN
ejpam-6020	495	3	and	and	CCONJ
ejpam-6020	495	4	business	business	NOUN
ejpam-6020	495	5	media	medium	NOUN
ejpam-6020	495	6	,	,	PUNCT
ejpam-6020	495	7	2003	2003	NUM
ejpam-6020	495	8	.	.	PUNCT
ejpam-6020	496	1	[	[	X
ejpam-6020	496	2	11	11	NUM
ejpam-6020	496	3	]	]	PUNCT
ejpam-6020	496	4	t.	t.	PROPN
ejpam-6020	496	5	m.	m.	PROPN
ejpam-6020	496	6	al	al	PROPN
ejpam-6020	496	7	-	-	PUNCT
ejpam-6020	496	8	shami	shami	PROPN
ejpam-6020	496	9	.	.	PUNCT
ejpam-6020	497	1	somewhere	somewhere	ADV
ejpam-6020	497	2	dense	dense	ADJ
ejpam-6020	497	3	sets	set	NOUN
ejpam-6020	497	4	and	and	CCONJ
ejpam-6020	497	5	st1	st1	PROPN
ejpam-6020	497	6	spaces	space	NOUN
ejpam-6020	497	7	.	.	PUNCT
ejpam-6020	498	1	punjab	punjab	PROPN
ejpam-6020	498	2	university	university	PROPN
ejpam-6020	498	3	journal	journal	NOUN
ejpam-6020	498	4	of	of	ADP
ejpam-6020	498	5	mathematics	mathematic	NOUN
ejpam-6020	498	6	,	,	PUNCT
ejpam-6020	498	7	49(2):101–111	49(2):101–111	PROPN
ejpam-6020	498	8	,	,	PUNCT
ejpam-6020	498	9	2017	2017	NUM
ejpam-6020	498	10	.	.	PUNCT
ejpam-6020	499	1	[	[	X
ejpam-6020	499	2	12	12	NUM
ejpam-6020	499	3	]	]	PUNCT
ejpam-6020	499	4	m.	m.	NOUN
ejpam-6020	499	5	h.	h.	PROPN
ejpam-6020	499	6	alqahtani	alqahtani	PROPN
ejpam-6020	499	7	and	and	CCONJ
ejpam-6020	499	8	a.	a.	NOUN
ejpam-6020	499	9	m.	m.	PROPN
ejpam-6020	499	10	abd	abd	PROPN
ejpam-6020	499	11	el	el	PROPN
ejpam-6020	499	12	-	-	PROPN
ejpam-6020	499	13	latif	latif	PROPN
ejpam-6020	499	14	.	.	PUNCT
ejpam-6020	500	1	separation	separation	NOUN
ejpam-6020	500	2	axioms	axiom	NOUN
ejpam-6020	500	3	via	via	ADP
ejpam-6020	500	4	novel	novel	ADJ
ejpam-6020	500	5	operators	operator	NOUN
ejpam-6020	500	6	in	in	ADP
ejpam-6020	500	7	the	the	DET
ejpam-6020	500	8	frame	frame	NOUN
ejpam-6020	500	9	of	of	ADP
ejpam-6020	500	10	topological	topological	ADJ
ejpam-6020	500	11	spaces	space	NOUN
ejpam-6020	500	12	and	and	CCONJ
ejpam-6020	500	13	applications	application	NOUN
ejpam-6020	500	14	.	.	PUNCT
ejpam-6020	501	1	aims	aim	VERB
ejpam-6020	501	2	mathematics	mathematic	NOUN
ejpam-6020	501	3	,	,	PUNCT
ejpam-6020	501	4	9(6):14213–14227	9(6):14213–14227	NUM
ejpam-6020	501	5	,	,	PUNCT
ejpam-6020	501	6	2024	2024	NUM
ejpam-6020	501	7	.	.	PUNCT
ejpam-6020	502	1	[	[	X
ejpam-6020	502	2	13	13	NUM
ejpam-6020	502	3	]	]	PUNCT
ejpam-6020	502	4	a.	a.	NOUN
ejpam-6020	502	5	s.	s.	PROPN
ejpam-6020	502	6	mashhour	mashhour	PROPN
ejpam-6020	502	7	,	,	PUNCT
ejpam-6020	502	8	a.	a.	PROPN
ejpam-6020	502	9	a.	a.	PROPN
ejpam-6020	502	10	allam	allam	PROPN
ejpam-6020	502	11	,	,	PUNCT
ejpam-6020	502	12	f.	f.	PROPN
ejpam-6020	502	13	s.	s.	PROPN
ejpam-6020	502	14	mahmoud	mahmoud	PROPN
ejpam-6020	502	15	,	,	PUNCT
ejpam-6020	502	16	and	and	CCONJ
ejpam-6020	502	17	f.	f.	PROPN
ejpam-6020	502	18	h.	h.	PROPN
ejpam-6020	502	19	kheder	kheder	PROPN
ejpam-6020	502	20	.	.	PUNCT
ejpam-6020	503	1	on	on	ADP
ejpam-6020	503	2	supra	supra	PROPN
ejpam-6020	503	3	topological	topological	ADJ
ejpam-6020	503	4	spaces	space	NOUN
ejpam-6020	503	5	.	.	PUNCT
ejpam-6020	504	1	indian	indian	ADJ
ejpam-6020	504	2	journal	journal	PROPN
ejpam-6020	504	3	of	of	ADP
ejpam-6020	504	4	pure	pure	ADJ
ejpam-6020	504	5	and	and	CCONJ
ejpam-6020	504	6	applied	applied	ADJ
ejpam-6020	504	7	mathematics	mathematic	NOUN
ejpam-6020	504	8	,	,	PUNCT
ejpam-6020	504	9	pages	page	NOUN
ejpam-6020	504	10	502–510	502–510	NUM
ejpam-6020	504	11	,	,	PUNCT
ejpam-6020	504	12	1983	1983	NUM
ejpam-6020	504	13	.	.	PUNCT
ejpam-6020	505	1	[	[	X
ejpam-6020	505	2	14	14	NUM
ejpam-6020	505	3	]	]	X
ejpam-6020	505	4	r.	r.	PROPN
ejpam-6020	505	5	devi	devi	PROPN
ejpam-6020	505	6	,	,	PUNCT
ejpam-6020	505	7	s.	s.	PROPN
ejpam-6020	505	8	sampathkumar	sampathkumar	PROPN
ejpam-6020	505	9	,	,	PUNCT
ejpam-6020	505	10	and	and	CCONJ
ejpam-6020	505	11	m.	m.	PROPN
ejpam-6020	505	12	caldas	caldas	PROPN
ejpam-6020	505	13	.	.	PUNCT
ejpam-6020	506	1	on	on	ADP
ejpam-6020	506	2	α	α	NOUN
ejpam-6020	506	3	-	-	ADJ
ejpam-6020	506	4	open	open	ADJ
ejpam-6020	506	5	sets	set	NOUN
ejpam-6020	506	6	and	and	CCONJ
ejpam-6020	506	7	sa	sa	NOUN
ejpam-6020	506	8	-	-	ADJ
ejpam-6020	506	9	continuous	continuous	ADJ
ejpam-6020	506	10	maps	map	NOUN
ejpam-6020	506	11	.	.	PUNCT
ejpam-6020	507	1	general	general	ADJ
ejpam-6020	507	2	mathematics	mathematics	PROPN
ejpam-6020	507	3	,	,	PUNCT
ejpam-6020	507	4	16:77–84	16:77–84	NOUN
ejpam-6020	507	5	,	,	PUNCT
ejpam-6020	507	6	2008	2008	NUM
ejpam-6020	507	7	.	.	PUNCT
ejpam-6020	508	1	[	[	X
ejpam-6020	508	2	15	15	NUM
ejpam-6020	508	3	]	]	X
ejpam-6020	508	4	o.	o.	PROPN
ejpam-6020	508	5	r.	r.	PROPN
ejpam-6020	508	6	sayed	say	VERB
ejpam-6020	508	7	.	.	PUNCT
ejpam-6020	509	1	supra	supra	PROPN
ejpam-6020	509	2	pre	pre	ADJ
ejpam-6020	509	3	-	-	ADJ
ejpam-6020	509	4	open	open	ADJ
ejpam-6020	509	5	sets	set	NOUN
ejpam-6020	509	6	and	and	CCONJ
ejpam-6020	509	7	supra	supra	NOUN
ejpam-6020	509	8	pre	pre	ADJ
ejpam-6020	509	9	-	-	ADJ
ejpam-6020	509	10	continuous	continuous	ADJ
ejpam-6020	509	11	on	on	ADP
ejpam-6020	509	12	topological	topological	ADJ
ejpam-6020	509	13	spaces	space	NOUN
ejpam-6020	509	14	.	.	PUNCT
ejpam-6020	510	1	series	series	PROPN
ejpam-6020	510	2	mathematics	mathematics	PROPN
ejpam-6020	510	3	and	and	CCONJ
ejpam-6020	510	4	informatics	informatic	NOUN
ejpam-6020	510	5	,	,	PUNCT
ejpam-6020	510	6	20:79–88	20:79–88	NUM
ejpam-6020	510	7	,	,	PUNCT
ejpam-6020	510	8	2010	2010	NUM
ejpam-6020	510	9	.	.	PUNCT
ejpam-6020	511	1	[	[	X
ejpam-6020	511	2	16	16	NUM
ejpam-6020	511	3	]	]	X
ejpam-6020	511	4	o.	o.	PROPN
ejpam-6020	511	5	r.	r.	PROPN
ejpam-6020	511	6	sayed	sayed	PROPN
ejpam-6020	511	7	and	and	CCONJ
ejpam-6020	511	8	t.	t.	PROPN
ejpam-6020	511	9	noiri	noiri	PROPN
ejpam-6020	511	10	.	.	PUNCT
ejpam-6020	512	1	on	on	ADP
ejpam-6020	512	2	supra	supra	PROPN
ejpam-6020	512	3	b	b	PROPN
ejpam-6020	512	4	-	-	PUNCT
ejpam-6020	512	5	open	open	ADJ
ejpam-6020	512	6	sets	set	NOUN
ejpam-6020	512	7	and	and	CCONJ
ejpam-6020	512	8	supra	supra	PROPN
ejpam-6020	512	9	b	b	NOUN
ejpam-6020	512	10	-	-	PUNCT
ejpam-6020	512	11	continuity	continuity	NOUN
ejpam-6020	512	12	on	on	ADP
ejpam-6020	512	13	topological	topological	ADJ
ejpam-6020	512	14	spaces	space	NOUN
ejpam-6020	512	15	.	.	PUNCT
ejpam-6020	513	1	european	european	ADJ
ejpam-6020	513	2	journal	journal	PROPN
ejpam-6020	513	3	of	of	ADP
ejpam-6020	513	4	pure	pure	ADJ
ejpam-6020	513	5	and	and	CCONJ
ejpam-6020	513	6	applied	applied	ADJ
ejpam-6020	513	7	mathematics	mathematic	NOUN
ejpam-6020	513	8	,	,	PUNCT
ejpam-6020	513	9	3:295–302	3:295–302	NUM
ejpam-6020	513	10	,	,	PUNCT
ejpam-6020	513	11	2010	2010	NUM
ejpam-6020	513	12	.	.	PUNCT
ejpam-6020	514	1	[	[	X
ejpam-6020	514	2	17	17	NUM
ejpam-6020	514	3	]	]	PUNCT
ejpam-6020	514	4	s.	s.	PROPN
ejpam-6020	514	5	jafari	jafari	PROPN
ejpam-6020	514	6	and	and	CCONJ
ejpam-6020	514	7	s.	s.	PROPN
ejpam-6020	514	8	tahiliani	tahiliani	PROPN
ejpam-6020	514	9	.	.	PUNCT
ejpam-6020	515	1	supra	supra	PROPN
ejpam-6020	515	2	β	β	X
ejpam-6020	515	3	-	-	ADJ
ejpam-6020	515	4	open	open	ADJ
ejpam-6020	515	5	sets	set	NOUN
ejpam-6020	515	6	and	and	CCONJ
ejpam-6020	515	7	supra	supra	ADJ
ejpam-6020	515	8	β	β	NOUN
ejpam-6020	515	9	-	-	NOUN
ejpam-6020	515	10	continuity	continuity	NOUN
ejpam-6020	515	11	on	on	ADP
ejpam-6020	515	12	topological	topological	ADJ
ejpam-6020	515	13	spaces	space	NOUN
ejpam-6020	515	14	.	.	PUNCT
ejpam-6020	516	1	annales	annales	PROPN
ejpam-6020	516	2	universitatis	universitatis	PROPN
ejpam-6020	516	3	scientiarum	scientiarum	PROPN
ejpam-6020	516	4	budapestinensis	budapestinensis	PROPN
ejpam-6020	516	5	de	de	PROPN
ejpam-6020	516	6	rolando	rolando	PROPN
ejpam-6020	516	7	eötvös	eötvös	PROPN
ejpam-6020	516	8	nominatae	nominatae	NOUN
ejpam-6020	516	9	,	,	PUNCT
ejpam-6020	516	10	56:1–9	56:1–9	NUM
ejpam-6020	516	11	,	,	PUNCT
ejpam-6020	516	12	2013	2013	NUM
ejpam-6020	516	13	.	.	PUNCT
ejpam-6020	517	1	[	[	X
ejpam-6020	517	2	18	18	NUM
ejpam-6020	517	3	]	]	PUNCT
ejpam-6020	517	4	m.	m.	PROPN
ejpam-6020	517	5	e.	e.	PROPN
ejpam-6020	517	6	el	el	PROPN
ejpam-6020	517	7	-	-	PROPN
ejpam-6020	517	8	shafei	shafei	PROPN
ejpam-6020	517	9	,	,	PUNCT
ejpam-6020	517	10	m.	m.	NOUN
ejpam-6020	517	11	abo	abo	NOUN
ejpam-6020	517	12	-	-	PUNCT
ejpam-6020	517	13	elhamayel	elhamayel	NOUN
ejpam-6020	517	14	,	,	PUNCT
ejpam-6020	517	15	and	and	CCONJ
ejpam-6020	517	16	t.	t.	PROPN
ejpam-6020	517	17	m.	m.	PROPN
ejpam-6020	517	18	al	al	PROPN
ejpam-6020	517	19	-	-	PUNCT
ejpam-6020	517	20	shami	shami	PROPN
ejpam-6020	517	21	.	.	PUNCT
ejpam-6020	518	1	on	on	ADP
ejpam-6020	518	2	supra	supra	PROPN
ejpam-6020	518	3	r	r	NOUN
ejpam-6020	518	4	-	-	PUNCT
ejpam-6020	518	5	open	open	ADJ
ejpam-6020	518	6	sets	set	NOUN
ejpam-6020	518	7	and	and	CCONJ
ejpam-6020	518	8	some	some	DET
ejpam-6020	518	9	applications	application	NOUN
ejpam-6020	518	10	on	on	ADP
ejpam-6020	518	11	topological	topological	ADJ
ejpam-6020	518	12	spaces	space	NOUN
ejpam-6020	518	13	.	.	PUNCT
ejpam-6020	519	1	journal	journal	NOUN
ejpam-6020	519	2	of	of	ADP
ejpam-6020	519	3	progressive	progressive	ADJ
ejpam-6020	519	4	research	research	NOUN
ejpam-6020	519	5	in	in	ADP
ejpam-6020	519	6	mathematics	mathematic	NOUN
ejpam-6020	519	7	,	,	PUNCT
ejpam-6020	519	8	8:1237–1248	8:1237–1248	NUM
ejpam-6020	519	9	,	,	PUNCT
ejpam-6020	519	10	2016	2016	NUM
ejpam-6020	519	11	.	.	PUNCT
ejpam-6020	520	1	[	[	X
ejpam-6020	520	2	19	19	NUM
ejpam-6020	520	3	]	]	X
ejpam-6020	520	4	t.	t.	PROPN
ejpam-6020	520	5	m.	m.	PROPN
ejpam-6020	520	6	al	al	PROPN
ejpam-6020	520	7	-	-	PUNCT
ejpam-6020	520	8	shami	shami	PROPN
ejpam-6020	520	9	.	.	PUNCT
ejpam-6020	521	1	on	on	ADP
ejpam-6020	521	2	supra	supra	PROPN
ejpam-6020	521	3	semi	semi	ADV
ejpam-6020	521	4	open	open	ADJ
ejpam-6020	521	5	sets	set	NOUN
ejpam-6020	521	6	and	and	CCONJ
ejpam-6020	521	7	some	some	DET
ejpam-6020	521	8	applications	application	NOUN
ejpam-6020	521	9	on	on	ADP
ejpam-6020	521	10	topological	topological	ADJ
ejpam-6020	521	11	spaces	space	NOUN
ejpam-6020	521	12	.	.	PUNCT
ejpam-6020	522	1	journal	journal	NOUN
ejpam-6020	522	2	of	of	ADP
ejpam-6020	522	3	advanced	advanced	ADJ
ejpam-6020	522	4	studies	study	NOUN
ejpam-6020	522	5	in	in	ADP
ejpam-6020	522	6	topology	topology	NOUN
ejpam-6020	522	7	,	,	PUNCT
ejpam-6020	522	8	8(2):144–153	8(2):144–153	NOUN
ejpam-6020	522	9	,	,	PUNCT
ejpam-6020	522	10	2017	2017	NUM
ejpam-6020	522	11	.	.	PUNCT
ejpam-6020	523	1	[	[	X
ejpam-6020	523	2	20	20	NUM
ejpam-6020	523	3	]	]	PUNCT
ejpam-6020	523	4	m.	m.	NOUN
ejpam-6020	523	5	shabir	shabir	PROPN
ejpam-6020	523	6	and	and	CCONJ
ejpam-6020	523	7	m.	m.	PROPN
ejpam-6020	523	8	naz	naz	PROPN
ejpam-6020	523	9	.	.	PUNCT
ejpam-6020	524	1	on	on	ADP
ejpam-6020	524	2	soft	soft	ADJ
ejpam-6020	524	3	topological	topological	ADJ
ejpam-6020	524	4	spaces	space	NOUN
ejpam-6020	524	5	.	.	PUNCT
ejpam-6020	525	1	computers	computer	NOUN
ejpam-6020	525	2	and	and	CCONJ
ejpam-6020	525	3	mathematics	mathematic	NOUN
ejpam-6020	525	4	with	with	ADP
ejpam-6020	525	5	applications	application	NOUN
ejpam-6020	525	6	,	,	PUNCT
ejpam-6020	525	7	61:1786–1799	61:1786–1799	NUM
ejpam-6020	525	8	,	,	PUNCT
ejpam-6020	525	9	2011	2011	NUM
ejpam-6020	525	10	.	.	PUNCT
ejpam-6020	526	1	[	[	X
ejpam-6020	526	2	21	21	NUM
ejpam-6020	526	3	]	]	PUNCT
ejpam-6020	526	4	zanyar	zanyar	PROPN
ejpam-6020	526	5	a.	a.	NOUN
ejpam-6020	526	6	ameen	ameen	PROPN
ejpam-6020	526	7	and	and	CCONJ
ejpam-6020	526	8	s.	s.	PROPN
ejpam-6020	526	9	al	al	PROPN
ejpam-6020	526	10	ghour	ghour	PROPN
ejpam-6020	526	11	.	.	PUNCT
ejpam-6020	527	1	cluster	cluster	NOUN
ejpam-6020	527	2	soft	soft	ADJ
ejpam-6020	527	3	sets	set	NOUN
ejpam-6020	527	4	and	and	CCONJ
ejpam-6020	527	5	cluster	cluster	NOUN
ejpam-6020	527	6	soft	soft	ADJ
ejpam-6020	527	7	topologies	topology	NOUN
ejpam-6020	527	8	.	.	PUNCT
ejpam-6020	528	1	computational	computational	ADJ
ejpam-6020	528	2	and	and	CCONJ
ejpam-6020	528	3	applied	applied	ADJ
ejpam-6020	528	4	mathematics	mathematic	NOUN
ejpam-6020	528	5	,	,	PUNCT
ejpam-6020	528	6	42:337	42:337	NUM
ejpam-6020	528	7	,	,	PUNCT
ejpam-6020	528	8	2023	2023	NUM
ejpam-6020	528	9	.	.	PUNCT
ejpam-6020	529	1	[	[	X
ejpam-6020	529	2	22	22	NUM
ejpam-6020	529	3	]	]	PUNCT
ejpam-6020	529	4	s.	s.	PROPN
ejpam-6020	529	5	a.	a.	PROPN
ejpam-6020	529	6	el	el	PROPN
ejpam-6020	529	7	-	-	PUNCT
ejpam-6020	529	8	sheikh	sheikh	PROPN
ejpam-6020	529	9	and	and	CCONJ
ejpam-6020	529	10	a.	a.	NOUN
ejpam-6020	529	11	m.	m.	PROPN
ejpam-6020	529	12	el	el	PROPN
ejpam-6020	529	13	-	-	PROPN
ejpam-6020	529	14	latif	latif	PROPN
ejpam-6020	529	15	.	.	PUNCT
ejpam-6020	530	1	characterization	characterization	NOUN
ejpam-6020	530	2	of	of	ADP
ejpam-6020	530	3	b	b	NOUN
ejpam-6020	530	4	-	-	PUNCT
ejpam-6020	530	5	open	open	ADJ
ejpam-6020	530	6	soft	soft	ADJ
ejpam-6020	530	7	sets	set	NOUN
ejpam-6020	530	8	in	in	ADP
ejpam-6020	530	9	soft	soft	ADJ
ejpam-6020	530	10	topological	topological	ADJ
ejpam-6020	530	11	spaces	space	NOUN
ejpam-6020	530	12	.	.	PUNCT
ejpam-6020	531	1	journal	journal	NOUN
ejpam-6020	531	2	of	of	ADP
ejpam-6020	531	3	new	new	ADJ
ejpam-6020	531	4	theory	theory	NOUN
ejpam-6020	531	5	,	,	PUNCT
ejpam-6020	531	6	2:8–18	2:8–18	NUM
ejpam-6020	531	7	,	,	PUNCT
ejpam-6020	531	8	2015	2015	NUM
ejpam-6020	531	9	.	.	PUNCT
ejpam-6020	532	1	[	[	X
ejpam-6020	532	2	23	23	NUM
ejpam-6020	532	3	]	]	PUNCT
ejpam-6020	532	4	a.	a.	NOUN
ejpam-6020	532	5	kandil	kandil	PROPN
ejpam-6020	532	6	,	,	PUNCT
ejpam-6020	532	7	o.	o.	PROPN
ejpam-6020	532	8	a.	a.	PROPN
ejpam-6020	532	9	e.	e.	PROPN
ejpam-6020	532	10	tantawy	tantawy	PROPN
ejpam-6020	532	11	,	,	PUNCT
ejpam-6020	532	12	s.	s.	PROPN
ejpam-6020	532	13	a.	a.	PROPN
ejpam-6020	532	14	el	el	PROPN
ejpam-6020	532	15	-	-	PUNCT
ejpam-6020	532	16	sheikh	sheikh	NOUN
ejpam-6020	532	17	,	,	PUNCT
ejpam-6020	532	18	and	and	CCONJ
ejpam-6020	532	19	a.	a.	NOUN
ejpam-6020	532	20	m.	m.	PROPN
ejpam-6020	532	21	abd	abd	PROPN
ejpam-6020	532	22	el	el	PROPN
ejpam-6020	532	23	-	-	PROPN
ejpam-6020	532	24	latif	latif	PROPN
ejpam-6020	532	25	.	.	PUNCT
ejpam-6020	533	1	soft	soft	ADJ
ejpam-6020	533	2	semi	semi	ADJ
ejpam-6020	533	3	separation	separation	NOUN
ejpam-6020	533	4	axioms	axiom	NOUN
ejpam-6020	533	5	and	and	CCONJ
ejpam-6020	533	6	irresolute	irresolute	ADJ
ejpam-6020	533	7	soft	soft	ADJ
ejpam-6020	533	8	functions	function	NOUN
ejpam-6020	533	9	.	.	PUNCT
ejpam-6020	534	1	annals	annal	NOUN
ejpam-6020	534	2	of	of	ADP
ejpam-6020	534	3	fuzzy	fuzzy	ADJ
ejpam-6020	534	4	mathematics	mathematic	NOUN
ejpam-6020	534	5	and	and	CCONJ
ejpam-6020	534	6	informatics	informatic	NOUN
ejpam-6020	534	7	,	,	PUNCT
ejpam-6020	534	8	8(2):305–318	8(2):305–318	NUM
ejpam-6020	534	9	,	,	PUNCT
ejpam-6020	534	10	2014	2014	NUM
ejpam-6020	534	11	.	.	PUNCT
ejpam-6020	535	1	[	[	X
ejpam-6020	535	2	24	24	NUM
ejpam-6020	535	3	]	]	X
ejpam-6020	535	4	tareq	tareq	PROPN
ejpam-6020	535	5	m.	m.	PROPN
ejpam-6020	535	6	al	al	PROPN
ejpam-6020	535	7	-	-	PUNCT
ejpam-6020	535	8	shami	shami	PROPN
ejpam-6020	535	9	,	,	PUNCT
ejpam-6020	535	10	abdelwaheb	abdelwaheb	PROPN
ejpam-6020	535	11	mhemdi	mhemdi	PROPN
ejpam-6020	535	12	,	,	PUNCT
ejpam-6020	535	13	and	and	CCONJ
ejpam-6020	535	14	radwan	radwan	VERB
ejpam-6020	535	15	abu	abu	PROPN
ejpam-6020	535	16	-	-	PUNCT
ejpam-6020	535	17	gdairi	gdairi	PROPN
ejpam-6020	535	18	.	.	PUNCT
ejpam-6020	536	1	a	a	DET
ejpam-6020	536	2	novel	novel	ADJ
ejpam-6020	536	3	framework	framework	NOUN
ejpam-6020	536	4	for	for	ADP
ejpam-6020	536	5	generalizations	generalization	NOUN
ejpam-6020	536	6	of	of	ADP
ejpam-6020	536	7	soft	soft	ADJ
ejpam-6020	536	8	open	open	ADJ
ejpam-6020	536	9	sets	set	NOUN
ejpam-6020	536	10	and	and	CCONJ
ejpam-6020	536	11	its	its	PRON
ejpam-6020	536	12	applications	application	NOUN
ejpam-6020	536	13	via	via	ADP
ejpam-6020	536	14	soft	soft	ADJ
ejpam-6020	536	15	topologies	topology	NOUN
ejpam-6020	536	16	.	.	PUNCT
ejpam-6020	537	1	mathematics	mathematic	NOUN
ejpam-6020	537	2	,	,	PUNCT
ejpam-6020	537	3	11(4):840	11(4):840	NOUN
ejpam-6020	537	4	,	,	PUNCT
ejpam-6020	537	5	2023	2023	NUM
ejpam-6020	537	6	.	.	PUNCT
ejpam-6020	538	1	[	[	X
ejpam-6020	538	2	25	25	NUM
ejpam-6020	538	3	]	]	PUNCT
ejpam-6020	538	4	a.	a.	NOUN
ejpam-6020	538	5	kandil	kandil	PROPN
ejpam-6020	538	6	,	,	PUNCT
ejpam-6020	538	7	o.	o.	PROPN
ejpam-6020	538	8	a.	a.	PROPN
ejpam-6020	538	9	e.	e.	PROPN
ejpam-6020	538	10	tantawy	tantawy	PROPN
ejpam-6020	538	11	,	,	PUNCT
ejpam-6020	538	12	s.	s.	PROPN
ejpam-6020	538	13	a.	a.	PROPN
ejpam-6020	538	14	el	el	PROPN
ejpam-6020	538	15	-	-	PUNCT
ejpam-6020	538	16	sheikh	sheikh	NOUN
ejpam-6020	538	17	,	,	PUNCT
ejpam-6020	538	18	and	and	CCONJ
ejpam-6020	538	19	a.	a.	NOUN
ejpam-6020	538	20	m.	m.	PROPN
ejpam-6020	538	21	abd	abd	PROPN
ejpam-6020	538	22	el	el	PROPN
ejpam-6020	538	23	-	-	PROPN
ejpam-6020	538	24	latif	latif	PROPN
ejpam-6020	538	25	.	.	PUNCT
ejpam-6020	539	1	γ	γ	PROPN
ejpam-6020	539	2	-	-	PUNCT
ejpam-6020	539	3	operation	operation	NOUN
ejpam-6020	539	4	a.	a.	NOUN
ejpam-6020	539	5	m.	m.	PROPN
ejpam-6020	539	6	abd	abd	PROPN
ejpam-6020	539	7	el	el	PROPN
ejpam-6020	539	8	-	-	PROPN
ejpam-6020	539	9	latif	latif	PROPN
ejpam-6020	539	10	et	et	PROPN
ejpam-6020	539	11	al	al	PROPN
ejpam-6020	539	12	.	.	PUNCT
ejpam-6020	539	13	/	/	SYM
ejpam-6020	539	14	eur	eur	PROPN
ejpam-6020	539	15	.	.	PUNCT
ejpam-6020	540	1	j.	j.	PROPN
ejpam-6020	540	2	pure	pure	PROPN
ejpam-6020	540	3	appl	appl	PROPN
ejpam-6020	540	4	.	.	PROPN
ejpam-6020	540	5	math	math	PROPN
ejpam-6020	540	6	,	,	PUNCT
ejpam-6020	540	7	18	18	NUM
ejpam-6020	540	8	(	(	PUNCT
ejpam-6020	540	9	2	2	NUM
ejpam-6020	540	10	)	)	PUNCT
ejpam-6020	540	11	(	(	PUNCT
ejpam-6020	540	12	2025	2025	NUM
ejpam-6020	540	13	)	)	PUNCT
ejpam-6020	540	14	,	,	PUNCT
ejpam-6020	540	15	6020	6020	NUM
ejpam-6020	540	16	16	16	NUM
ejpam-6020	540	17	of	of	ADP
ejpam-6020	540	18	17	17	NUM
ejpam-6020	540	19	and	and	CCONJ
ejpam-6020	540	20	decompositions	decomposition	NOUN
ejpam-6020	540	21	of	of	ADP
ejpam-6020	540	22	some	some	DET
ejpam-6020	540	23	forms	form	NOUN
ejpam-6020	540	24	of	of	ADP
ejpam-6020	540	25	soft	soft	ADJ
ejpam-6020	540	26	continuity	continuity	NOUN
ejpam-6020	540	27	in	in	ADP
ejpam-6020	540	28	soft	soft	ADJ
ejpam-6020	540	29	topological	topological	ADJ
ejpam-6020	540	30	spaces	space	NOUN
ejpam-6020	540	31	.	.	PUNCT
ejpam-6020	541	1	annals	annal	NOUN
ejpam-6020	541	2	of	of	ADP
ejpam-6020	541	3	fuzzy	fuzzy	ADJ
ejpam-6020	541	4	mathematics	mathematic	NOUN
ejpam-6020	541	5	and	and	CCONJ
ejpam-6020	541	6	informatics	informatic	NOUN
ejpam-6020	541	7	,	,	PUNCT
ejpam-6020	541	8	7(2):181–196	7(2):181–196	NUM
ejpam-6020	541	9	,	,	PUNCT
ejpam-6020	541	10	2014	2014	NUM
ejpam-6020	541	11	.	.	PUNCT
ejpam-6020	542	1	[	[	X
ejpam-6020	542	2	26	26	NUM
ejpam-6020	542	3	]	]	X
ejpam-6020	542	4	tareq	tareq	PROPN
ejpam-6020	542	5	m.	m.	PROPN
ejpam-6020	542	6	al	al	PROPN
ejpam-6020	542	7	-	-	PUNCT
ejpam-6020	542	8	shami	shami	PROPN
ejpam-6020	542	9	.	.	PUNCT
ejpam-6020	543	1	soft	soft	ADJ
ejpam-6020	543	2	somewhere	somewhere	ADV
ejpam-6020	543	3	dense	dense	ADJ
ejpam-6020	543	4	sets	set	NOUN
ejpam-6020	543	5	on	on	ADP
ejpam-6020	543	6	soft	soft	ADJ
ejpam-6020	543	7	topological	topological	ADJ
ejpam-6020	543	8	spaces	space	NOUN
ejpam-6020	543	9	.	.	PUNCT
ejpam-6020	544	1	communications	communication	NOUN
ejpam-6020	544	2	of	of	ADP
ejpam-6020	544	3	the	the	DET
ejpam-6020	544	4	korean	korean	ADJ
ejpam-6020	544	5	mathematical	mathematical	ADJ
ejpam-6020	544	6	society	society	NOUN
ejpam-6020	544	7	,	,	PUNCT
ejpam-6020	544	8	33(2):1341–1356	33(2):1341–1356	NUM
ejpam-6020	544	9	,	,	PUNCT
ejpam-6020	544	10	2018	2018	NUM
ejpam-6020	544	11	.	.	PUNCT
ejpam-6020	545	1	[	[	X
ejpam-6020	545	2	27	27	NUM
ejpam-6020	545	3	]	]	PUNCT
ejpam-6020	545	4	radwan	radwan	VERB
ejpam-6020	545	5	abu	abu	PROPN
ejpam-6020	545	6	-	-	PUNCT
ejpam-6020	545	7	gdairi	gdairi	PROPN
ejpam-6020	545	8	,	,	PUNCT
ejpam-6020	545	9	a.	a.	PROPN
ejpam-6020	545	10	a.	a.	PROPN
ejpam-6020	545	11	azzam	azzam	PROPN
ejpam-6020	545	12	,	,	PUNCT
ejpam-6020	545	13	and	and	CCONJ
ejpam-6020	545	14	ibrahim	ibrahim	PROPN
ejpam-6020	545	15	noaman	noaman	PROPN
ejpam-6020	545	16	.	.	PUNCT
ejpam-6020	546	1	nearly	nearly	ADV
ejpam-6020	546	2	soft	soft	ADJ
ejpam-6020	546	3	β	β	ADJ
ejpam-6020	546	4	-	-	ADJ
ejpam-6020	546	5	open	open	ADJ
ejpam-6020	546	6	sets	set	NOUN
ejpam-6020	546	7	via	via	ADP
ejpam-6020	546	8	soft	soft	ADJ
ejpam-6020	546	9	ditopological	ditopological	ADJ
ejpam-6020	546	10	spaces	space	NOUN
ejpam-6020	546	11	.	.	PUNCT
ejpam-6020	547	1	european	european	ADJ
ejpam-6020	547	2	journal	journal	PROPN
ejpam-6020	547	3	of	of	ADP
ejpam-6020	547	4	pure	pure	ADJ
ejpam-6020	547	5	and	and	CCONJ
ejpam-6020	547	6	applied	applied	ADJ
ejpam-6020	547	7	mathematics	mathematic	NOUN
ejpam-6020	547	8	,	,	PUNCT
ejpam-6020	547	9	15(1):126–134	15(1):126–134	PROPN
ejpam-6020	547	10	,	,	PUNCT
ejpam-6020	547	11	2022	2022	NUM
ejpam-6020	547	12	.	.	PUNCT
ejpam-6020	548	1	[	[	X
ejpam-6020	548	2	28	28	NUM
ejpam-6020	548	3	]	]	X
ejpam-6020	548	4	s.	s.	PROPN
ejpam-6020	548	5	al	al	PROPN
ejpam-6020	548	6	ghour	ghour	PROPN
ejpam-6020	548	7	.	.	PUNCT
ejpam-6020	549	1	soft	soft	ADJ
ejpam-6020	549	2	ω	ω	NOUN
ejpam-6020	549	3	-	-	PUNCT
ejpam-6020	549	4	continuity	continuity	NOUN
ejpam-6020	549	5	and	and	CCONJ
ejpam-6020	549	6	soft	soft	ADJ
ejpam-6020	549	7	ωs	ω	NOUN
ejpam-6020	549	8	-	-	NOUN
ejpam-6020	549	9	continuity	continuity	NOUN
ejpam-6020	549	10	in	in	ADP
ejpam-6020	549	11	soft	soft	ADJ
ejpam-6020	549	12	topological	topological	ADJ
ejpam-6020	549	13	spaces	space	NOUN
ejpam-6020	549	14	.	.	PUNCT
ejpam-6020	550	1	international	international	ADJ
ejpam-6020	550	2	journal	journal	NOUN
ejpam-6020	550	3	of	of	ADP
ejpam-6020	550	4	fuzzy	fuzzy	ADJ
ejpam-6020	550	5	logic	logic	NOUN
ejpam-6020	550	6	and	and	CCONJ
ejpam-6020	550	7	intelligent	intelligent	ADJ
ejpam-6020	550	8	systems	system	NOUN
ejpam-6020	550	9	,	,	PUNCT
ejpam-6020	550	10	22(2):183–192	22(2):183–192	NOUN
ejpam-6020	550	11	,	,	PUNCT
ejpam-6020	550	12	2022	2022	NUM
ejpam-6020	550	13	.	.	PUNCT
ejpam-6020	551	1	[	[	X
ejpam-6020	551	2	29	29	NUM
ejpam-6020	551	3	]	]	PUNCT
ejpam-6020	551	4	s.	s.	PROPN
ejpam-6020	551	5	al	al	PROPN
ejpam-6020	551	6	ghour	ghour	PROPN
ejpam-6020	551	7	and	and	CCONJ
ejpam-6020	551	8	b.	b.	PROPN
ejpam-6020	551	9	irshidat	irshidat	PROPN
ejpam-6020	551	10	.	.	PUNCT
ejpam-6020	552	1	on	on	ADP
ejpam-6020	552	2	θω	θω	ADP
ejpam-6020	552	3	continuity	continuity	NOUN
ejpam-6020	552	4	.	.	PUNCT
ejpam-6020	553	1	heliyon	heliyon	NOUN
ejpam-6020	553	2	,	,	PUNCT
ejpam-6020	553	3	6(2):e03349	6(2):e03349	NUM
ejpam-6020	553	4	,	,	PUNCT
ejpam-6020	553	5	2020	2020	NUM
ejpam-6020	553	6	.	.	PUNCT
ejpam-6020	554	1	[	[	X
ejpam-6020	554	2	30	30	NUM
ejpam-6020	554	3	]	]	X
ejpam-6020	554	4	a.	a.	NOUN
ejpam-6020	554	5	kandil	kandil	PROPN
ejpam-6020	554	6	,	,	PUNCT
ejpam-6020	554	7	o.	o.	PROPN
ejpam-6020	554	8	a.	a.	PROPN
ejpam-6020	554	9	e.	e.	PROPN
ejpam-6020	554	10	tantawy	tantawy	PROPN
ejpam-6020	554	11	,	,	PUNCT
ejpam-6020	554	12	s.	s.	PROPN
ejpam-6020	554	13	a.	a.	PROPN
ejpam-6020	554	14	el	el	PROPN
ejpam-6020	554	15	-	-	PUNCT
ejpam-6020	554	16	sheikh	sheikh	NOUN
ejpam-6020	554	17	,	,	PUNCT
ejpam-6020	554	18	and	and	CCONJ
ejpam-6020	554	19	a.	a.	NOUN
ejpam-6020	554	20	m.	m.	PROPN
ejpam-6020	554	21	abd	abd	PROPN
ejpam-6020	554	22	el	el	PROPN
ejpam-6020	554	23	-	-	PROPN
ejpam-6020	554	24	latif	latif	PROPN
ejpam-6020	554	25	.	.	PUNCT
ejpam-6020	555	1	soft	soft	ADJ
ejpam-6020	555	2	ideal	ideal	ADJ
ejpam-6020	555	3	theory	theory	NOUN
ejpam-6020	555	4	,	,	PUNCT
ejpam-6020	555	5	soft	soft	ADJ
ejpam-6020	555	6	local	local	ADJ
ejpam-6020	555	7	function	function	NOUN
ejpam-6020	555	8	and	and	CCONJ
ejpam-6020	555	9	generated	generate	VERB
ejpam-6020	555	10	soft	soft	ADJ
ejpam-6020	555	11	topological	topological	ADJ
ejpam-6020	555	12	spaces	space	NOUN
ejpam-6020	555	13	.	.	PUNCT
ejpam-6020	556	1	applied	apply	VERB
ejpam-6020	556	2	mathematics	mathematic	NOUN
ejpam-6020	556	3	and	and	CCONJ
ejpam-6020	556	4	information	information	NOUN
ejpam-6020	556	5	sciences	science	NOUN
ejpam-6020	556	6	,	,	PUNCT
ejpam-6020	556	7	8(4):1595–1603	8(4):1595–1603	NOUN
ejpam-6020	556	8	,	,	PUNCT
ejpam-6020	556	9	2014	2014	NUM
ejpam-6020	556	10	.	.	PUNCT
ejpam-6020	557	1	[	[	X
ejpam-6020	557	2	31	31	NUM
ejpam-6020	557	3	]	]	X
ejpam-6020	557	4	f.	f.	PROPN
ejpam-6020	557	5	gharib	gharib	PROPN
ejpam-6020	557	6	and	and	CCONJ
ejpam-6020	557	7	a.	a.	NOUN
ejpam-6020	557	8	m.	m.	PROPN
ejpam-6020	557	9	abd	abd	PROPN
ejpam-6020	557	10	el	el	PROPN
ejpam-6020	557	11	-	-	PROPN
ejpam-6020	557	12	latif	latif	PROPN
ejpam-6020	557	13	.	.	PUNCT
ejpam-6020	558	1	soft	soft	ADJ
ejpam-6020	558	2	semi	semi	ADJ
ejpam-6020	558	3	local	local	ADJ
ejpam-6020	558	4	functions	function	NOUN
ejpam-6020	558	5	in	in	ADP
ejpam-6020	558	6	soft	soft	ADJ
ejpam-6020	558	7	ideal	ideal	ADJ
ejpam-6020	558	8	topological	topological	ADJ
ejpam-6020	558	9	spaces	space	NOUN
ejpam-6020	558	10	.	.	PUNCT
ejpam-6020	559	1	european	european	ADJ
ejpam-6020	559	2	journal	journal	PROPN
ejpam-6020	559	3	of	of	ADP
ejpam-6020	559	4	pure	pure	ADJ
ejpam-6020	559	5	and	and	CCONJ
ejpam-6020	559	6	applied	applied	ADJ
ejpam-6020	559	7	mathematics	mathematic	NOUN
ejpam-6020	559	8	,	,	PUNCT
ejpam-6020	559	9	12(3):857–869	12(3):857–869	NUM
ejpam-6020	559	10	,	,	PUNCT
ejpam-6020	559	11	2019	2019	NUM
ejpam-6020	559	12	.	.	PUNCT
ejpam-6020	560	1	[	[	X
ejpam-6020	560	2	32	32	NUM
ejpam-6020	560	3	]	]	PUNCT
ejpam-6020	560	4	a.	a.	NOUN
ejpam-6020	560	5	kandil	kandil	PROPN
ejpam-6020	560	6	,	,	PUNCT
ejpam-6020	560	7	o.	o.	PROPN
ejpam-6020	560	8	a.	a.	PROPN
ejpam-6020	560	9	e.	e.	PROPN
ejpam-6020	560	10	tantawy	tantawy	PROPN
ejpam-6020	560	11	,	,	PUNCT
ejpam-6020	560	12	s.	s.	PROPN
ejpam-6020	560	13	a.	a.	PROPN
ejpam-6020	560	14	el	el	PROPN
ejpam-6020	560	15	-	-	PUNCT
ejpam-6020	560	16	sheikh	sheikh	NOUN
ejpam-6020	560	17	,	,	PUNCT
ejpam-6020	560	18	and	and	CCONJ
ejpam-6020	560	19	a.	a.	NOUN
ejpam-6020	560	20	m.	m.	PROPN
ejpam-6020	560	21	abd	abd	PROPN
ejpam-6020	560	22	el	el	PROPN
ejpam-6020	560	23	-	-	PROPN
ejpam-6020	560	24	latif	latif	PROPN
ejpam-6020	560	25	.	.	PUNCT
ejpam-6020	561	1	soft	soft	ADJ
ejpam-6020	561	2	semi	semi	ADJ
ejpam-6020	561	3	compactness	compactness	NOUN
ejpam-6020	561	4	via	via	ADP
ejpam-6020	561	5	soft	soft	ADJ
ejpam-6020	561	6	ideals	ideal	NOUN
ejpam-6020	561	7	.	.	PUNCT
ejpam-6020	562	1	applied	apply	VERB
ejpam-6020	562	2	mathematics	mathematic	NOUN
ejpam-6020	562	3	and	and	CCONJ
ejpam-6020	562	4	information	information	NOUN
ejpam-6020	562	5	sciences	science	NOUN
ejpam-6020	562	6	,	,	PUNCT
ejpam-6020	562	7	8(5):2297	8(5):2297	NUM
ejpam-6020	562	8	–	–	PUNCT
ejpam-6020	562	9	2306	2306	NUM
ejpam-6020	562	10	,	,	PUNCT
ejpam-6020	562	11	2014	2014	NUM
ejpam-6020	562	12	.	.	PUNCT
ejpam-6020	563	1	[	[	X
ejpam-6020	563	2	33	33	NUM
ejpam-6020	563	3	]	]	PUNCT
ejpam-6020	563	4	a.	a.	NOUN
ejpam-6020	563	5	kandil	kandil	PROPN
ejpam-6020	563	6	,	,	PUNCT
ejpam-6020	563	7	o.	o.	PROPN
ejpam-6020	563	8	a.	a.	PROPN
ejpam-6020	563	9	e.	e.	PROPN
ejpam-6020	563	10	tantawy	tantawy	PROPN
ejpam-6020	563	11	,	,	PUNCT
ejpam-6020	563	12	s.	s.	PROPN
ejpam-6020	563	13	a.	a.	PROPN
ejpam-6020	563	14	el	el	PROPN
ejpam-6020	563	15	-	-	PUNCT
ejpam-6020	563	16	sheikh	sheikh	NOUN
ejpam-6020	563	17	,	,	PUNCT
ejpam-6020	563	18	and	and	CCONJ
ejpam-6020	563	19	a.	a.	NOUN
ejpam-6020	563	20	m.	m.	PROPN
ejpam-6020	563	21	abd	abd	PROPN
ejpam-6020	563	22	el	el	PROPN
ejpam-6020	563	23	-	-	PROPN
ejpam-6020	563	24	latif	latif	PROPN
ejpam-6020	563	25	.	.	PUNCT
ejpam-6020	564	1	soft	soft	ADJ
ejpam-6020	564	2	connectedness	connectedness	NOUN
ejpam-6020	564	3	via	via	ADP
ejpam-6020	564	4	soft	soft	ADJ
ejpam-6020	564	5	ideals	ideal	NOUN
ejpam-6020	564	6	.	.	PUNCT
ejpam-6020	565	1	journal	journal	NOUN
ejpam-6020	565	2	of	of	ADP
ejpam-6020	565	3	new	new	ADJ
ejpam-6020	565	4	results	result	NOUN
ejpam-6020	565	5	in	in	ADP
ejpam-6020	565	6	science	science	NOUN
ejpam-6020	565	7	,	,	PUNCT
ejpam-6020	565	8	4:90–108	4:90–108	NUM
ejpam-6020	565	9	,	,	PUNCT
ejpam-6020	565	10	2014	2014	NUM
ejpam-6020	565	11	.	.	PUNCT
ejpam-6020	566	1	[	[	X
ejpam-6020	566	2	34	34	NUM
ejpam-6020	566	3	]	]	PUNCT
ejpam-6020	566	4	m.	m.	NOUN
ejpam-6020	566	5	akdag	akdag	PROPN
ejpam-6020	566	6	and	and	CCONJ
ejpam-6020	566	7	f.	f.	PROPN
ejpam-6020	566	8	erol	erol	PROPN
ejpam-6020	566	9	.	.	PUNCT
ejpam-6020	567	1	soft	soft	ADJ
ejpam-6020	567	2	i	i	NOUN
ejpam-6020	567	3	-	-	PUNCT
ejpam-6020	567	4	sets	set	NOUN
ejpam-6020	567	5	and	and	CCONJ
ejpam-6020	567	6	soft	soft	ADJ
ejpam-6020	567	7	i	i	NOUN
ejpam-6020	567	8	-	-	PUNCT
ejpam-6020	567	9	continuity	continuity	NOUN
ejpam-6020	567	10	of	of	ADP
ejpam-6020	567	11	functions	function	NOUN
ejpam-6020	567	12	.	.	PUNCT
ejpam-6020	568	1	gazi	gazi	PROPN
ejpam-6020	568	2	university	university	PROPN
ejpam-6020	568	3	journal	journal	PROPN
ejpam-6020	568	4	of	of	ADP
ejpam-6020	568	5	science	science	NOUN
ejpam-6020	568	6	,	,	PUNCT
ejpam-6020	568	7	27:923–932	27:923–932	NUM
ejpam-6020	568	8	,	,	PUNCT
ejpam-6020	568	9	2014	2014	NUM
ejpam-6020	568	10	.	.	PUNCT
ejpam-6020	569	1	[	[	X
ejpam-6020	569	2	35	35	NUM
ejpam-6020	569	3	]	]	PUNCT
ejpam-6020	569	4	a.	a.	NOUN
ejpam-6020	569	5	kandil	kandil	PROPN
ejpam-6020	569	6	,	,	PUNCT
ejpam-6020	569	7	o.	o.	PROPN
ejpam-6020	569	8	a.	a.	PROPN
ejpam-6020	569	9	e.	e.	PROPN
ejpam-6020	569	10	tantawy	tantawy	PROPN
ejpam-6020	569	11	,	,	PUNCT
ejpam-6020	569	12	s.	s.	PROPN
ejpam-6020	569	13	a.	a.	PROPN
ejpam-6020	569	14	el	el	PROPN
ejpam-6020	569	15	-	-	PUNCT
ejpam-6020	569	16	sheikh	sheikh	NOUN
ejpam-6020	569	17	,	,	PUNCT
ejpam-6020	569	18	and	and	CCONJ
ejpam-6020	569	19	a.	a.	NOUN
ejpam-6020	569	20	m.	m.	PROPN
ejpam-6020	569	21	abd	abd	PROPN
ejpam-6020	569	22	el	el	PROPN
ejpam-6020	569	23	-	-	PROPN
ejpam-6020	569	24	latif	latif	PROPN
ejpam-6020	569	25	.	.	PUNCT
ejpam-6020	570	1	γ	γ	PROPN
ejpam-6020	570	2	-	-	PUNCT
ejpam-6020	570	3	operation	operation	NOUN
ejpam-6020	570	4	and	and	CCONJ
ejpam-6020	570	5	decompositions	decomposition	NOUN
ejpam-6020	570	6	of	of	ADP
ejpam-6020	570	7	some	some	DET
ejpam-6020	570	8	forms	form	NOUN
ejpam-6020	570	9	of	of	ADP
ejpam-6020	570	10	soft	soft	ADJ
ejpam-6020	570	11	continuity	continuity	NOUN
ejpam-6020	570	12	of	of	ADP
ejpam-6020	570	13	soft	soft	ADJ
ejpam-6020	570	14	topological	topological	ADJ
ejpam-6020	570	15	spaces	space	NOUN
ejpam-6020	570	16	via	via	ADP
ejpam-6020	570	17	soft	soft	ADJ
ejpam-6020	570	18	ideal	ideal	NOUN
ejpam-6020	570	19	.	.	PUNCT
ejpam-6020	571	1	annals	annal	NOUN
ejpam-6020	571	2	of	of	ADP
ejpam-6020	571	3	fuzzy	fuzzy	ADJ
ejpam-6020	571	4	mathematics	mathematic	NOUN
ejpam-6020	571	5	and	and	CCONJ
ejpam-6020	571	6	informatics	informatic	NOUN
ejpam-6020	571	7	,	,	PUNCT
ejpam-6020	571	8	9(3):385–402	9(3):385–402	NUM
ejpam-6020	571	9	,	,	PUNCT
ejpam-6020	571	10	2015	2015	NUM
ejpam-6020	571	11	.	.	PUNCT
ejpam-6020	572	1	[	[	X
ejpam-6020	572	2	36	36	NUM
ejpam-6020	572	3	]	]	PUNCT
ejpam-6020	572	4	a.	a.	NOUN
ejpam-6020	572	5	a.	a.	PROPN
ejpam-6020	572	6	nasef	nasef	PROPN
ejpam-6020	572	7	,	,	PUNCT
ejpam-6020	572	8	m.	m.	NOUN
ejpam-6020	572	9	parimala	parimala	PROPN
ejpam-6020	572	10	,	,	PUNCT
ejpam-6020	572	11	r.	r.	PROPN
ejpam-6020	572	12	jeevitha	jeevitha	PROPN
ejpam-6020	572	13	,	,	PUNCT
ejpam-6020	572	14	and	and	CCONJ
ejpam-6020	572	15	m.	m.	PROPN
ejpam-6020	572	16	k.	k.	PROPN
ejpam-6020	573	1	el	el	PROPN
ejpam-6020	573	2	-	-	PUNCT
ejpam-6020	573	3	sayed	say	VERB
ejpam-6020	573	4	.	.	PUNCT
ejpam-6020	574	1	soft	soft	ADJ
ejpam-6020	574	2	ideal	ideal	ADJ
ejpam-6020	574	3	theory	theory	NOUN
ejpam-6020	574	4	and	and	CCONJ
ejpam-6020	574	5	applications	application	NOUN
ejpam-6020	574	6	.	.	PUNCT
ejpam-6020	575	1	international	international	ADJ
ejpam-6020	575	2	journal	journal	PROPN
ejpam-6020	575	3	of	of	ADP
ejpam-6020	575	4	nonlinear	nonlinear	ADJ
ejpam-6020	575	5	analysis	analysis	NOUN
ejpam-6020	575	6	and	and	CCONJ
ejpam-6020	575	7	applications	application	NOUN
ejpam-6020	575	8	,	,	PUNCT
ejpam-6020	575	9	13(2):1335	13(2):1335	NUM
ejpam-6020	575	10	–	–	PUNCT
ejpam-6020	575	11	1342	1342	NUM
ejpam-6020	575	12	,	,	PUNCT
ejpam-6020	575	13	2022	2022	NUM
ejpam-6020	575	14	.	.	PUNCT
ejpam-6020	576	1	[	[	X
ejpam-6020	576	2	37	37	NUM
ejpam-6020	576	3	]	]	PUNCT
ejpam-6020	576	4	a.	a.	NOUN
ejpam-6020	576	5	kandil	kandil	PROPN
ejpam-6020	576	6	,	,	PUNCT
ejpam-6020	576	7	o.	o.	PROPN
ejpam-6020	576	8	a.	a.	PROPN
ejpam-6020	576	9	e.	e.	PROPN
ejpam-6020	576	10	tantawy	tantawy	PROPN
ejpam-6020	576	11	,	,	PUNCT
ejpam-6020	576	12	s.	s.	PROPN
ejpam-6020	576	13	a.	a.	PROPN
ejpam-6020	576	14	el	el	PROPN
ejpam-6020	576	15	-	-	PUNCT
ejpam-6020	576	16	sheikh	sheikh	NOUN
ejpam-6020	576	17	,	,	PUNCT
ejpam-6020	576	18	and	and	CCONJ
ejpam-6020	576	19	a.	a.	NOUN
ejpam-6020	576	20	m.	m.	PROPN
ejpam-6020	576	21	abd	abd	PROPN
ejpam-6020	576	22	el	el	PROPN
ejpam-6020	576	23	-	-	PROPN
ejpam-6020	576	24	latif	latif	PROPN
ejpam-6020	576	25	.	.	PUNCT
ejpam-6020	577	1	soft	soft	ADJ
ejpam-6020	577	2	semi	semi	ADJ
ejpam-6020	577	3	(	(	PUNCT
ejpam-6020	577	4	quasi	quasi	ADJ
ejpam-6020	577	5	)	)	PUNCT
ejpam-6020	577	6	hausdorff	hausdorff	NOUN
ejpam-6020	577	7	spaces	space	NOUN
ejpam-6020	577	8	via	via	ADP
ejpam-6020	577	9	soft	soft	ADJ
ejpam-6020	577	10	ideals	ideal	NOUN
ejpam-6020	577	11	.	.	PUNCT
ejpam-6020	578	1	south	south	ADJ
ejpam-6020	578	2	asian	asian	PROPN
ejpam-6020	578	3	journal	journal	PROPN
ejpam-6020	578	4	of	of	ADP
ejpam-6020	578	5	mathematics	mathematic	NOUN
ejpam-6020	578	6	,	,	PUNCT
ejpam-6020	578	7	4(6):265–284	4(6):265–284	NUM
ejpam-6020	578	8	,	,	PUNCT
ejpam-6020	578	9	2014	2014	NUM
ejpam-6020	578	10	.	.	PUNCT
ejpam-6020	579	1	[	[	X
ejpam-6020	579	2	38	38	NUM
ejpam-6020	579	3	]	]	PUNCT
ejpam-6020	579	4	a.	a.	NOUN
ejpam-6020	579	5	m.	m.	PROPN
ejpam-6020	579	6	abd	abd	PROPN
ejpam-6020	579	7	el	el	PROPN
ejpam-6020	579	8	-	-	PROPN
ejpam-6020	579	9	latif	latif	PROPN
ejpam-6020	579	10	.	.	PUNCT
ejpam-6020	580	1	generalized	generalize	VERB
ejpam-6020	580	2	soft	soft	ADJ
ejpam-6020	580	3	rough	rough	ADJ
ejpam-6020	580	4	sets	set	NOUN
ejpam-6020	580	5	and	and	CCONJ
ejpam-6020	580	6	generated	generate	VERB
ejpam-6020	580	7	soft	soft	ADJ
ejpam-6020	580	8	ideal	ideal	NOUN
ejpam-6020	580	9	rough	rough	ADJ
ejpam-6020	580	10	topological	topological	ADJ
ejpam-6020	580	11	spaces	space	NOUN
ejpam-6020	580	12	.	.	PUNCT
ejpam-6020	581	1	journal	journal	NOUN
ejpam-6020	581	2	of	of	ADP
ejpam-6020	581	3	intelligent	intelligent	ADJ
ejpam-6020	581	4	and	and	CCONJ
ejpam-6020	581	5	fuzzy	fuzzy	ADJ
ejpam-6020	581	6	systems	system	NOUN
ejpam-6020	581	7	,	,	PUNCT
ejpam-6020	581	8	34:517–524	34:517–524	PROPN
ejpam-6020	581	9	,	,	PUNCT
ejpam-6020	581	10	2018	2018	NUM
ejpam-6020	581	11	.	.	PUNCT
ejpam-6020	582	1	[	[	X
ejpam-6020	582	2	39	39	NUM
ejpam-6020	582	3	]	]	PUNCT
ejpam-6020	582	4	a.	a.	NOUN
ejpam-6020	582	5	m.	m.	PROPN
ejpam-6020	582	6	abd	abd	PROPN
ejpam-6020	582	7	el	el	PROPN
ejpam-6020	582	8	-	-	PROPN
ejpam-6020	582	9	latif	latif	PROPN
ejpam-6020	582	10	.	.	PUNCT
ejpam-6020	583	1	new	new	ADJ
ejpam-6020	583	2	generalized	generalize	VERB
ejpam-6020	583	3	fuzzy	fuzzy	ADJ
ejpam-6020	583	4	soft	soft	ADJ
ejpam-6020	583	5	rough	rough	ADJ
ejpam-6020	583	6	approximations	approximation	NOUN
ejpam-6020	583	7	applied	apply	VERB
ejpam-6020	583	8	to	to	ADP
ejpam-6020	583	9	fuzzy	fuzzy	ADJ
ejpam-6020	583	10	topological	topological	ADJ
ejpam-6020	583	11	spaces	space	NOUN
ejpam-6020	583	12	.	.	PUNCT
ejpam-6020	584	1	journal	journal	NOUN
ejpam-6020	584	2	of	of	ADP
ejpam-6020	584	3	intelligent	intelligent	ADJ
ejpam-6020	584	4	and	and	CCONJ
ejpam-6020	584	5	fuzzy	fuzzy	ADJ
ejpam-6020	584	6	systems	system	NOUN
ejpam-6020	584	7	,	,	PUNCT
ejpam-6020	584	8	35:2123–2136	35:2123–2136	NUM
ejpam-6020	584	9	,	,	PUNCT
ejpam-6020	584	10	2018	2018	NUM
ejpam-6020	584	11	.	.	PUNCT
ejpam-6020	585	1	[	[	X
ejpam-6020	585	2	40	40	NUM
ejpam-6020	585	3	]	]	PUNCT
ejpam-6020	586	1	s.	s.	PROPN
ejpam-6020	586	2	saleh	saleh	PROPN
ejpam-6020	586	3	and	and	CCONJ
ejpam-6020	586	4	k.	k.	PROPN
ejpam-6020	586	5	hur	hur	PROPN
ejpam-6020	586	6	.	.	PROPN
ejpam-6020	587	1	on	on	ADP
ejpam-6020	587	2	some	some	DET
ejpam-6020	587	3	lower	low	ADJ
ejpam-6020	587	4	soft	soft	ADJ
ejpam-6020	587	5	separation	separation	NOUN
ejpam-6020	587	6	axioms	axiom	NOUN
ejpam-6020	587	7	.	.	PUNCT
ejpam-6020	588	1	annals	annal	NOUN
ejpam-6020	588	2	of	of	ADP
ejpam-6020	588	3	fuzzy	fuzzy	ADJ
ejpam-6020	588	4	mathematics	mathematic	NOUN
ejpam-6020	588	5	and	and	CCONJ
ejpam-6020	588	6	informatics	informatic	NOUN
ejpam-6020	588	7	,	,	PUNCT
ejpam-6020	588	8	19(1):61–72	19(1):61–72	NUM
ejpam-6020	588	9	,	,	PUNCT
ejpam-6020	588	10	2020	2020	NUM
ejpam-6020	588	11	.	.	PUNCT
ejpam-6020	589	1	[	[	X
ejpam-6020	589	2	41	41	NUM
ejpam-6020	589	3	]	]	X
ejpam-6020	589	4	s.	s.	PROPN
ejpam-6020	589	5	saleh	saleh	PROPN
ejpam-6020	589	6	,	,	PUNCT
ejpam-6020	589	7	laith	laith	PROPN
ejpam-6020	589	8	r.	r.	PROPN
ejpam-6020	589	9	flaih	flaih	PROPN
ejpam-6020	589	10	,	,	PUNCT
ejpam-6020	589	11	and	and	CCONJ
ejpam-6020	589	12	khaled	khaled	PROPN
ejpam-6020	589	13	f.	f.	PROPN
ejpam-6020	589	14	jasim	jasim	PROPN
ejpam-6020	589	15	.	.	PUNCT
ejpam-6020	590	1	some	some	DET
ejpam-6020	590	2	applications	application	NOUN
ejpam-6020	590	3	of	of	ADP
ejpam-6020	590	4	soft	soft	ADJ
ejpam-6020	590	5	δ	δ	NOUN
ejpam-6020	590	6	-	-	PUNCT
ejpam-6020	590	7	closed	close	VERB
ejpam-6020	590	8	sets	set	NOUN
ejpam-6020	590	9	in	in	ADP
ejpam-6020	590	10	soft	soft	ADJ
ejpam-6020	590	11	closure	closure	NOUN
ejpam-6020	590	12	spaces	space	NOUN
ejpam-6020	590	13	.	.	PUNCT
ejpam-6020	591	1	communications	communication	NOUN
ejpam-6020	591	2	in	in	ADP
ejpam-6020	591	3	mathematics	mathematic	NOUN
ejpam-6020	591	4	and	and	CCONJ
ejpam-6020	591	5	applications	application	NOUN
ejpam-6020	591	6	,	,	PUNCT
ejpam-6020	591	7	14(2):481	14(2):481	NUM
ejpam-6020	591	8	–	–	PUNCT
ejpam-6020	591	9	492	492	NUM
ejpam-6020	591	10	,	,	PUNCT
ejpam-6020	591	11	2023	2023	NUM
ejpam-6020	591	12	.	.	PUNCT
ejpam-6020	592	1	[	[	X
ejpam-6020	592	2	42	42	NUM
ejpam-6020	592	3	]	]	PUNCT
ejpam-6020	592	4	s.	s.	PROPN
ejpam-6020	592	5	a.	a.	PROPN
ejpam-6020	592	6	el	el	PROPN
ejpam-6020	592	7	-	-	PUNCT
ejpam-6020	592	8	sheikh	sheikh	PROPN
ejpam-6020	592	9	and	and	CCONJ
ejpam-6020	592	10	a.	a.	NOUN
ejpam-6020	592	11	m.	m.	NOUN
ejpam-6020	592	12	abd	abd	PROPN
ejpam-6020	592	13	el	el	PROPN
ejpam-6020	592	14	-	-	PROPN
ejpam-6020	592	15	latif	latif	PROPN
ejpam-6020	592	16	.	.	PUNCT
ejpam-6020	593	1	decompositions	decomposition	NOUN
ejpam-6020	593	2	of	of	ADP
ejpam-6020	593	3	some	some	DET
ejpam-6020	593	4	types	type	NOUN
ejpam-6020	593	5	of	of	ADP
ejpam-6020	593	6	supra	supra	ADJ
ejpam-6020	593	7	soft	soft	ADJ
ejpam-6020	593	8	sets	set	NOUN
ejpam-6020	593	9	and	and	CCONJ
ejpam-6020	593	10	soft	soft	ADJ
ejpam-6020	593	11	continuity	continuity	NOUN
ejpam-6020	593	12	.	.	PUNCT
ejpam-6020	594	1	international	international	ADJ
ejpam-6020	594	2	journal	journal	PROPN
ejpam-6020	594	3	of	of	ADP
ejpam-6020	594	4	mathematical	mathematical	ADJ
ejpam-6020	594	5	trends	trend	NOUN
ejpam-6020	594	6	and	and	CCONJ
ejpam-6020	594	7	technology	technology	NOUN
ejpam-6020	594	8	,	,	PUNCT
ejpam-6020	594	9	9(1):37–56	9(1):37–56	NUM
ejpam-6020	594	10	,	,	PUNCT
ejpam-6020	594	11	2014	2014	NUM
ejpam-6020	594	12	.	.	PUNCT
ejpam-6020	595	1	a.	a.	PROPN
ejpam-6020	595	2	m.	m.	PROPN
ejpam-6020	595	3	abd	abd	PROPN
ejpam-6020	595	4	el	el	PROPN
ejpam-6020	595	5	-	-	PROPN
ejpam-6020	595	6	latif	latif	PROPN
ejpam-6020	595	7	et	et	PROPN
ejpam-6020	595	8	al	al	PROPN
ejpam-6020	595	9	.	.	PUNCT
ejpam-6020	595	10	/	/	SYM
ejpam-6020	595	11	eur	eur	PROPN
ejpam-6020	595	12	.	.	PUNCT
ejpam-6020	596	1	j.	j.	PROPN
ejpam-6020	596	2	pure	pure	PROPN
ejpam-6020	596	3	appl	appl	PROPN
ejpam-6020	596	4	.	.	PROPN
ejpam-6020	596	5	math	math	PROPN
ejpam-6020	596	6	,	,	PUNCT
ejpam-6020	596	7	18	18	NUM
ejpam-6020	596	8	(	(	PUNCT
ejpam-6020	596	9	2	2	NUM
ejpam-6020	596	10	)	)	PUNCT
ejpam-6020	596	11	(	(	PUNCT
ejpam-6020	596	12	2025	2025	NUM
ejpam-6020	596	13	)	)	PUNCT
ejpam-6020	596	14	,	,	PUNCT
ejpam-6020	596	15	6020	6020	NUM
ejpam-6020	596	16	17	17	NUM
ejpam-6020	596	17	of	of	ADP
ejpam-6020	596	18	17	17	NUM
ejpam-6020	596	19	[	[	SYM
ejpam-6020	596	20	43	43	NUM
ejpam-6020	596	21	]	]	PUNCT
ejpam-6020	596	22	a.	a.	NOUN
ejpam-6020	596	23	m.	m.	PROPN
ejpam-6020	596	24	abd	abd	PROPN
ejpam-6020	597	1	el	el	PROPN
ejpam-6020	597	2	-	-	PROPN
ejpam-6020	597	3	latif	latif	PROPN
ejpam-6020	597	4	,	,	PUNCT
ejpam-6020	597	5	radwan	radwan	VERB
ejpam-6020	597	6	abu	abu	PROPN
ejpam-6020	597	7	-	-	PUNCT
ejpam-6020	597	8	gdairi	gdairi	PROPN
ejpam-6020	597	9	,	,	PUNCT
ejpam-6020	598	1	a.	a.	PROPN
ejpam-6020	598	2	a.	a.	PROPN
ejpam-6020	598	3	azzam	azzam	PROPN
ejpam-6020	598	4	,	,	PUNCT
ejpam-6020	598	5	husham	husham	PROPN
ejpam-6020	598	6	m.	m.	PROPN
ejpam-6020	598	7	attaalfadeel	attaalfadeel	PROPN
ejpam-6020	598	8	,	,	PUNCT
ejpam-6020	598	9	shaaban	shaaban	ADJ
ejpam-6020	598	10	m.	m.	NOUN
ejpam-6020	598	11	shaaban	shaaban	PROPN
ejpam-6020	598	12	,	,	PUNCT
ejpam-6020	598	13	m.	m.	NOUN
ejpam-6020	598	14	aldawood	aldawood	PROPN
ejpam-6020	598	15	,	,	PUNCT
ejpam-6020	598	16	and	and	CCONJ
ejpam-6020	598	17	khaled	khaled	PROPN
ejpam-6020	598	18	a.	a.	PROPN
ejpam-6020	598	19	aldwoah	aldwoah	PROPN
ejpam-6020	598	20	.	.	PUNCT
ejpam-6020	599	1	supra	supra	PROPN
ejpam-6020	599	2	ϵ-open	ϵ-open	PROPN
ejpam-6020	599	3	sets	set	NOUN
ejpam-6020	599	4	:	:	PUNCT
ejpam-6020	599	5	features	feature	NOUN
ejpam-6020	599	6	,	,	PUNCT
ejpam-6020	599	7	operators	operator	NOUN
ejpam-6020	599	8	and	and	CCONJ
ejpam-6020	599	9	applications	application	NOUN
ejpam-6020	599	10	.	.	PUNCT
ejpam-6020	600	1	european	european	ADJ
ejpam-6020	600	2	journal	journal	PROPN
ejpam-6020	600	3	of	of	ADP
ejpam-6020	600	4	pure	pure	ADJ
ejpam-6020	600	5	and	and	CCONJ
ejpam-6020	600	6	applied	applied	ADJ
ejpam-6020	600	7	mathematics	mathematic	NOUN
ejpam-6020	600	8	,	,	PUNCT
ejpam-6020	600	9	18(2):5969	18(2):5969	NUM
ejpam-6020	600	10	,	,	PUNCT
ejpam-6020	600	11	2025	2025	NUM
ejpam-6020	600	12	.	.	PUNCT
ejpam-6020	601	1	[	[	X
ejpam-6020	601	2	44	44	NUM
ejpam-6020	601	3	]	]	PUNCT
ejpam-6020	601	4	a.	a.	NOUN
ejpam-6020	601	5	m.	m.	PROPN
ejpam-6020	601	6	abd	abd	PROPN
ejpam-6020	601	7	el	el	PROPN
ejpam-6020	601	8	-	-	PROPN
ejpam-6020	601	9	latif	latif	PROPN
ejpam-6020	601	10	and	and	CCONJ
ejpam-6020	601	11	s.	s.	PROPN
ejpam-6020	601	12	karataş.	karataş.	PROPN
ejpam-6020	602	1	supra	supra	PROPN
ejpam-6020	602	2	b	b	PROPN
ejpam-6020	602	3	-	-	PUNCT
ejpam-6020	602	4	open	open	ADJ
ejpam-6020	602	5	soft	soft	ADJ
ejpam-6020	602	6	sets	set	NOUN
ejpam-6020	602	7	and	and	CCONJ
ejpam-6020	602	8	supra	supra	PROPN
ejpam-6020	602	9	b	b	NOUN
ejpam-6020	602	10	-	-	PUNCT
ejpam-6020	602	11	soft	soft	ADJ
ejpam-6020	602	12	continuity	continuity	NOUN
ejpam-6020	602	13	on	on	ADP
ejpam-6020	602	14	soft	soft	ADJ
ejpam-6020	602	15	topological	topological	ADJ
ejpam-6020	602	16	spaces	space	NOUN
ejpam-6020	602	17	.	.	PUNCT
ejpam-6020	603	1	journal	journal	NOUN
ejpam-6020	603	2	of	of	ADP
ejpam-6020	603	3	mathematical	mathematical	ADJ
ejpam-6020	603	4	and	and	CCONJ
ejpam-6020	603	5	computational	computational	ADJ
ejpam-6020	603	6	applications	application	NOUN
ejpam-6020	603	7	research	research	NOUN
ejpam-6020	603	8	,	,	PUNCT
ejpam-6020	603	9	5(1):1–18	5(1):1–18	NUM
ejpam-6020	603	10	,	,	PUNCT
ejpam-6020	603	11	2015	2015	NUM
ejpam-6020	603	12	.	.	PUNCT
ejpam-6020	604	1	[	[	X
ejpam-6020	604	2	45	45	NUM
ejpam-6020	604	3	]	]	PUNCT
ejpam-6020	604	4	a.	a.	NOUN
ejpam-6020	604	5	kandil	kandil	PROPN
ejpam-6020	604	6	,	,	PUNCT
ejpam-6020	604	7	o.	o.	PROPN
ejpam-6020	604	8	a.	a.	PROPN
ejpam-6020	604	9	e.	e.	PROPN
ejpam-6020	604	10	tantawy	tantawy	PROPN
ejpam-6020	604	11	,	,	PUNCT
ejpam-6020	604	12	s.	s.	PROPN
ejpam-6020	604	13	a.	a.	PROPN
ejpam-6020	604	14	el	el	PROPN
ejpam-6020	604	15	-	-	PUNCT
ejpam-6020	604	16	sheikh	sheikh	NOUN
ejpam-6020	604	17	,	,	PUNCT
ejpam-6020	604	18	and	and	CCONJ
ejpam-6020	604	19	a.	a.	NOUN
ejpam-6020	604	20	m.	m.	PROPN
ejpam-6020	604	21	abd	abd	PROPN
ejpam-6020	604	22	el	el	PROPN
ejpam-6020	604	23	-	-	PROPN
ejpam-6020	604	24	latif	latif	PROPN
ejpam-6020	604	25	.	.	PUNCT
ejpam-6020	605	1	supra	supra	PROPN
ejpam-6020	605	2	generalized	generalize	VERB
ejpam-6020	605	3	closed	close	VERB
ejpam-6020	605	4	soft	soft	ADJ
ejpam-6020	605	5	sets	set	NOUN
ejpam-6020	605	6	with	with	ADP
ejpam-6020	605	7	respect	respect	NOUN
ejpam-6020	605	8	to	to	ADP
ejpam-6020	605	9	a	a	DET
ejpam-6020	605	10	soft	soft	ADJ
ejpam-6020	605	11	ideal	ideal	NOUN
ejpam-6020	605	12	in	in	ADP
ejpam-6020	605	13	supra	supra	PROPN
ejpam-6020	605	14	soft	soft	ADJ
ejpam-6020	605	15	topological	topological	ADJ
ejpam-6020	605	16	spaces	space	NOUN
ejpam-6020	605	17	.	.	PUNCT
ejpam-6020	606	1	applied	apply	VERB
ejpam-6020	606	2	mathematics	mathematic	NOUN
ejpam-6020	606	3	and	and	CCONJ
ejpam-6020	606	4	information	information	NOUN
ejpam-6020	606	5	sciences	science	NOUN
ejpam-6020	606	6	,	,	PUNCT
ejpam-6020	606	7	8(4):1731–1740	8(4):1731–1740	PROPN
ejpam-6020	606	8	,	,	PUNCT
ejpam-6020	606	9	2014	2014	NUM
ejpam-6020	606	10	.	.	PUNCT
ejpam-6020	607	1	[	[	X
ejpam-6020	607	2	46	46	NUM
ejpam-6020	607	3	]	]	PUNCT
ejpam-6020	607	4	a.	a.	NOUN
ejpam-6020	607	5	m.	m.	PROPN
ejpam-6020	607	6	abd	abd	PROPN
ejpam-6020	607	7	el	el	PROPN
ejpam-6020	607	8	-	-	PROPN
ejpam-6020	607	9	latif	latif	PROPN
ejpam-6020	607	10	,	,	PUNCT
ejpam-6020	607	11	radwan	radwan	VERB
ejpam-6020	607	12	abu	abu	PROPN
ejpam-6020	607	13	-	-	PUNCT
ejpam-6020	607	14	gdairi	gdairi	PROPN
ejpam-6020	607	15	,	,	PUNCT
ejpam-6020	607	16	a.	a.	PROPN
ejpam-6020	607	17	a.	a.	PROPN
ejpam-6020	607	18	azzam	azzam	PROPN
ejpam-6020	607	19	,	,	PUNCT
ejpam-6020	607	20	f.	f.	PROPN
ejpam-6020	607	21	a.	a.	PROPN
ejpam-6020	607	22	gharib	gharib	PROPN
ejpam-6020	607	23	,	,	PUNCT
ejpam-6020	607	24	and	and	CCONJ
ejpam-6020	607	25	khaled	khaled	PROPN
ejpam-6020	607	26	a.	a.	PROPN
ejpam-6020	607	27	aldwoah	aldwoah	PROPN
ejpam-6020	607	28	.	.	PUNCT
ejpam-6020	608	1	supra	supra	PROPN
ejpam-6020	608	2	soft	soft	ADJ
ejpam-6020	608	3	somewhat	somewhat	ADV
ejpam-6020	608	4	open	open	ADJ
ejpam-6020	608	5	sets	set	NOUN
ejpam-6020	608	6	:	:	PUNCT
ejpam-6020	608	7	characterizations	characterization	NOUN
ejpam-6020	608	8	and	and	CCONJ
ejpam-6020	608	9	continuity	continuity	NOUN
ejpam-6020	608	10	.	.	PUNCT
ejpam-6020	609	1	european	european	ADJ
ejpam-6020	609	2	journal	journal	PROPN
ejpam-6020	609	3	of	of	ADP
ejpam-6020	609	4	pure	pure	ADJ
ejpam-6020	609	5	and	and	CCONJ
ejpam-6020	609	6	applied	applied	ADJ
ejpam-6020	609	7	mathematics	mathematic	NOUN
ejpam-6020	609	8	,	,	PUNCT
ejpam-6020	609	9	18(2):5863	18(2):5863	NUM
ejpam-6020	609	10	,	,	PUNCT
ejpam-6020	609	11	2025	2025	NUM
ejpam-6020	609	12	.	.	PUNCT
ejpam-6020	610	1	[	[	X
ejpam-6020	610	2	47	47	NUM
ejpam-6020	610	3	]	]	PUNCT
ejpam-6020	610	4	a.	a.	NOUN
ejpam-6020	610	5	m.	m.	PROPN
ejpam-6020	610	6	abd	abd	PROPN
ejpam-6020	610	7	el	el	PROPN
ejpam-6020	610	8	-	-	PROPN
ejpam-6020	610	9	latif	latif	PROPN
ejpam-6020	610	10	and	and	CCONJ
ejpam-6020	610	11	mesfer	mesfer	VERB
ejpam-6020	610	12	h.	h.	PROPN
ejpam-6020	610	13	alqahtani	alqahtani	PROPN
ejpam-6020	610	14	.	.	PUNCT
ejpam-6020	611	1	new	new	ADJ
ejpam-6020	611	2	soft	soft	ADJ
ejpam-6020	611	3	operators	operator	NOUN
ejpam-6020	611	4	related	relate	VERB
ejpam-6020	611	5	to	to	ADP
ejpam-6020	611	6	supra	supra	PROPN
ejpam-6020	611	7	soft	soft	ADJ
ejpam-6020	611	8	δi	δi	NOUN
ejpam-6020	611	9	-	-	PUNCT
ejpam-6020	611	10	open	open	ADJ
ejpam-6020	611	11	sets	set	NOUN
ejpam-6020	611	12	and	and	CCONJ
ejpam-6020	611	13	applications	application	NOUN
ejpam-6020	611	14	.	.	PUNCT
ejpam-6020	612	1	aims	aim	VERB
ejpam-6020	612	2	mathematics	mathematic	NOUN
ejpam-6020	612	3	,	,	PUNCT
ejpam-6020	612	4	9(2):3076–3096	9(2):3076–3096	NUM
ejpam-6020	612	5	,	,	PUNCT
ejpam-6020	612	6	2024	2024	NUM
ejpam-6020	612	7	.	.	PUNCT
ejpam-6020	613	1	[	[	X
ejpam-6020	613	2	48	48	NUM
ejpam-6020	613	3	]	]	PUNCT
ejpam-6020	613	4	a.	a.	NOUN
ejpam-6020	613	5	m.	m.	PROPN
ejpam-6020	613	6	abd	abd	PROPN
ejpam-6020	613	7	el	el	PROPN
ejpam-6020	613	8	-	-	PROPN
ejpam-6020	613	9	latif	latif	PROPN
ejpam-6020	613	10	,	,	PUNCT
ejpam-6020	613	11	mesfer	mesfer	VERB
ejpam-6020	613	12	h.	h.	PROPN
ejpam-6020	613	13	alqahtani	alqahtani	PROPN
ejpam-6020	613	14	,	,	PUNCT
ejpam-6020	613	15	and	and	CCONJ
ejpam-6020	613	16	f.	f.	PROPN
ejpam-6020	613	17	a.	a.	PROPN
ejpam-6020	613	18	gharib	gharib	PROPN
ejpam-6020	613	19	.	.	PUNCT
ejpam-6020	614	1	strictly	strictly	ADV
ejpam-6020	614	2	wider	wide	ADJ
ejpam-6020	614	3	class	class	NOUN
ejpam-6020	614	4	of	of	ADP
ejpam-6020	614	5	soft	soft	ADJ
ejpam-6020	614	6	sets	set	NOUN
ejpam-6020	614	7	via	via	ADP
ejpam-6020	614	8	supra	supra	PROPN
ejpam-6020	614	9	soft	soft	PROPN
ejpam-6020	614	10	δ	δ	PROPN
ejpam-6020	614	11	-	-	PUNCT
ejpam-6020	614	12	closure	closure	NOUN
ejpam-6020	614	13	operator	operator	NOUN
ejpam-6020	614	14	.	.	PUNCT
ejpam-6020	615	1	international	international	ADJ
ejpam-6020	615	2	journal	journal	NOUN
ejpam-6020	615	3	of	of	ADP
ejpam-6020	615	4	analysis	analysis	NOUN
ejpam-6020	615	5	and	and	CCONJ
ejpam-6020	615	6	applications	application	NOUN
ejpam-6020	615	7	,	,	PUNCT
ejpam-6020	615	8	22:47	22:47	NUM
ejpam-6020	615	9	,	,	PUNCT
ejpam-6020	615	10	2024	2024	NUM
ejpam-6020	615	11	.	.	PUNCT
ejpam-6020	616	1	[	[	X
ejpam-6020	616	2	49	49	NUM
ejpam-6020	616	3	]	]	PUNCT
ejpam-6020	616	4	a.	a.	NOUN
ejpam-6020	616	5	m.	m.	PROPN
ejpam-6020	616	6	abd	abd	PROPN
ejpam-6020	616	7	el	el	PROPN
ejpam-6020	616	8	-	-	PROPN
ejpam-6020	616	9	latif	latif	PROPN
ejpam-6020	616	10	.	.	PUNCT
ejpam-6020	617	1	novel	novel	ADJ
ejpam-6020	617	2	types	type	NOUN
ejpam-6020	617	3	of	of	ADP
ejpam-6020	617	4	supra	supra	ADJ
ejpam-6020	617	5	soft	soft	ADJ
ejpam-6020	617	6	operators	operator	NOUN
ejpam-6020	617	7	via	via	ADP
ejpam-6020	617	8	supra	supra	PROPN
ejpam-6020	617	9	soft	soft	ADJ
ejpam-6020	617	10	sd	sd	NOUN
ejpam-6020	617	11	-	-	PUNCT
ejpam-6020	617	12	sets	set	NOUN
ejpam-6020	617	13	and	and	CCONJ
ejpam-6020	617	14	applications	application	NOUN
ejpam-6020	617	15	.	.	PUNCT
ejpam-6020	618	1	aims	aim	VERB
ejpam-6020	618	2	mathematics	mathematic	NOUN
ejpam-6020	618	3	,	,	PUNCT
ejpam-6020	618	4	9(3):6586–6602	9(3):6586–6602	PROPN
ejpam-6020	618	5	,	,	PUNCT
ejpam-6020	618	6	2024	2024	NUM
ejpam-6020	618	7	.	.	PUNCT
ejpam-6020	619	1	[	[	X
ejpam-6020	619	2	50	50	NUM
ejpam-6020	619	3	]	]	PUNCT
ejpam-6020	619	4	s.	s.	PROPN
ejpam-6020	619	5	saleh	saleh	PROPN
ejpam-6020	619	6	,	,	PUNCT
ejpam-6020	619	7	t.	t.	PROPN
ejpam-6020	619	8	al	al	PROPN
ejpam-6020	619	9	-	-	PUNCT
ejpam-6020	619	10	shami	shami	PROPN
ejpam-6020	619	11	,	,	PUNCT
ejpam-6020	619	12	laith	laith	PROPN
ejpam-6020	619	13	r.	r.	PROPN
ejpam-6020	619	14	flaih	flaih	PROPN
ejpam-6020	619	15	,	,	PUNCT
ejpam-6020	619	16	murad	murad	NOUN
ejpam-6020	619	17	arar	arar	NOUN
ejpam-6020	619	18	,	,	PUNCT
ejpam-6020	619	19	and	and	CCONJ
ejpam-6020	619	20	radwan	radwan	VERB
ejpam-6020	619	21	abu	abu	PROPN
ejpam-6020	619	22	-	-	PUNCT
ejpam-6020	619	23	gdairi	gdairi	PROPN
ejpam-6020	619	24	.	.	PUNCT
ejpam-6020	620	1	riseparation	riseparation	NOUN
ejpam-6020	620	2	axioms	axiom	NOUN
ejpam-6020	620	3	via	via	ADP
ejpam-6020	620	4	supra	supra	PROPN
ejpam-6020	620	5	soft	soft	ADJ
ejpam-6020	620	6	topological	topological	ADJ
ejpam-6020	620	7	spaces	space	NOUN
ejpam-6020	620	8	.	.	PUNCT
ejpam-6020	621	1	journal	journal	NOUN
ejpam-6020	621	2	of	of	ADP
ejpam-6020	621	3	mathematical	mathematical	ADJ
ejpam-6020	621	4	and	and	CCONJ
ejpam-6020	621	5	computer	computer	NOUN
ejpam-6020	621	6	science	science	NOUN
ejpam-6020	621	7	,	,	PUNCT
ejpam-6020	621	8	32:263–274	32:263–274	NUM
ejpam-6020	621	9	,	,	PUNCT
ejpam-6020	621	10	2024	2024	NUM
ejpam-6020	621	11	.	.	PUNCT