id	sid	tid	token	lemma	pos
ejpam-3544	1	1	european	european	PROPN
ejpam-3544	1	2	journal	journal	PROPN
ejpam-3544	1	3	of	of	ADP
ejpam-3544	1	4	pure	pure	ADJ
ejpam-3544	1	5	and	and	CCONJ
ejpam-3544	1	6	applied	apply	VERB
ejpam-3544	1	7	mathematics	mathematic	NOUN
ejpam-3544	1	8	vol	vol	NOUN
ejpam-3544	1	9	.	.	PROPN
ejpam-3544	2	1	12	12	NUM
ejpam-3544	2	2	,	,	PUNCT
ejpam-3544	2	3	no	no	INTJ
ejpam-3544	2	4	.	.	NOUN
ejpam-3544	2	5	4	4	NUM
ejpam-3544	2	6	,	,	PUNCT
ejpam-3544	2	7	2019	2019	NUM
ejpam-3544	2	8	,	,	PUNCT
ejpam-3544	2	9	1656	1656	NUM
ejpam-3544	2	10	-	-	SYM
ejpam-3544	2	11	1660	1660	NUM
ejpam-3544	2	12	issn	issn	PROPN
ejpam-3544	2	13	1307	1307	NUM
ejpam-3544	2	14	-	-	SYM
ejpam-3544	2	15	5543	5543	NUM
ejpam-3544	2	16	–	–	PUNCT
ejpam-3544	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3544	2	18	published	publish	VERB
ejpam-3544	2	19	by	by	ADP
ejpam-3544	2	20	new	new	PROPN
ejpam-3544	2	21	york	york	PROPN
ejpam-3544	2	22	business	business	PROPN
ejpam-3544	2	23	global	global	PROPN
ejpam-3544	2	24	a	a	DET
ejpam-3544	2	25	note	note	NOUN
ejpam-3544	2	26	on	on	ADP
ejpam-3544	2	27	“	"	PUNCT
ejpam-3544	2	28	on	on	ADP
ejpam-3544	2	29	β	β	ADJ
ejpam-3544	2	30	-	-	ADJ
ejpam-3544	2	31	open	open	ADJ
ejpam-3544	2	32	sets	set	NOUN
ejpam-3544	2	33	and	and	CCONJ
ejpam-3544	2	34	ideals	ideal	NOUN
ejpam-3544	2	35	in	in	ADP
ejpam-3544	2	36	topological	topological	ADJ
ejpam-3544	2	37	spaces”[european	spaces”[european	ADJ
ejpam-3544	2	38	journal	journal	NOUN
ejpam-3544	2	39	of	of	ADP
ejpam-3544	2	40	pure	pure	ADJ
ejpam-3544	2	41	and	and	CCONJ
ejpam-3544	2	42	applied	applied	ADJ
ejpam-3544	2	43	mathematics	mathematic	NOUN
ejpam-3544	2	44	6	6	NUM
ejpam-3544	2	45	(	(	PUNCT
ejpam-3544	2	46	2019	2019	NUM
ejpam-3544	2	47	)	)	PUNCT
ejpam-3544	3	1	893–903	893–903	NUM
ejpam-3544	3	2	]	]	X
ejpam-3544	3	3	mona	mona	PROPN
ejpam-3544	3	4	hosny1,2	hosny1,2	PROPN
ejpam-3544	3	5	1	1	NUM
ejpam-3544	3	6	department	department	NOUN
ejpam-3544	3	7	of	of	ADP
ejpam-3544	3	8	mathematics	mathematic	NOUN
ejpam-3544	3	9	,	,	PUNCT
ejpam-3544	3	10	faculty	faculty	NOUN
ejpam-3544	3	11	of	of	ADP
ejpam-3544	3	12	science	science	NOUN
ejpam-3544	3	13	for	for	ADP
ejpam-3544	3	14	girls	girl	NOUN
ejpam-3544	3	15	,	,	PUNCT
ejpam-3544	3	16	king	king	PROPN
ejpam-3544	3	17	khalid	khalid	PROPN
ejpam-3544	3	18	university	university	PROPN
ejpam-3544	3	19	,	,	PUNCT
ejpam-3544	3	20	abha	abha	NOUN
ejpam-3544	3	21	,	,	PUNCT
ejpam-3544	3	22	saudi	saudi	PROPN
ejpam-3544	3	23	arabia	arabia	PROPN
ejpam-3544	3	24	2	2	NUM
ejpam-3544	3	25	department	department	NOUN
ejpam-3544	3	26	of	of	ADP
ejpam-3544	3	27	mathematics	mathematic	NOUN
ejpam-3544	3	28	,	,	PUNCT
ejpam-3544	3	29	faculty	faculty	NOUN
ejpam-3544	3	30	of	of	ADP
ejpam-3544	3	31	education	education	NOUN
ejpam-3544	3	32	,	,	PUNCT
ejpam-3544	3	33	ain	ain	PROPN
ejpam-3544	3	34	shams	shams	PROPN
ejpam-3544	3	35	university	university	PROPN
ejpam-3544	3	36	,	,	PUNCT
ejpam-3544	3	37	cairo	cairo	PROPN
ejpam-3544	3	38	,	,	PUNCT
ejpam-3544	3	39	egypt	egypt	PROPN
ejpam-3544	3	40	abstract	abstract	PROPN
ejpam-3544	3	41	.	.	PUNCT
ejpam-3544	4	1	let	let	VERB
ejpam-3544	4	2	x	x	PRON
ejpam-3544	4	3	be	be	AUX
ejpam-3544	4	4	a	a	DET
ejpam-3544	4	5	non	non	ADJ
ejpam-3544	4	6	-	-	ADJ
ejpam-3544	4	7	empty	empty	ADJ
ejpam-3544	4	8	set	set	NOUN
ejpam-3544	4	9	.	.	PUNCT
ejpam-3544	5	1	i	i	PRON
ejpam-3544	5	2	6=	6=	PROPN
ejpam-3544	5	3	φ	φ	PROPN
ejpam-3544	5	4	,	,	PUNCT
ejpam-3544	5	5	i	i	PROPN
ejpam-3544	5	6	∈	∈	VERB
ejpam-3544	5	7	p	p	X
ejpam-3544	5	8	(	(	PUNCT
ejpam-3544	5	9	x	x	X
ejpam-3544	5	10	)	)	PUNCT
ejpam-3544	5	11	is	be	AUX
ejpam-3544	5	12	an	an	DET
ejpam-3544	5	13	ideal	ideal	NOUN
ejpam-3544	5	14	on	on	ADP
ejpam-3544	5	15	x	x	SYM
ejpam-3544	5	16	,	,	PUNCT
ejpam-3544	5	17	if	if	SCONJ
ejpam-3544	5	18	a	a	DET
ejpam-3544	5	19	∈	∈	X
ejpam-3544	5	20	i	i	PRON
ejpam-3544	5	21	and	and	CCONJ
ejpam-3544	5	22	b	b	X
ejpam-3544	5	23	∈	∈	PROPN
ejpam-3544	5	24	i	i	PRON
ejpam-3544	5	25	⇒	⇒	VERB
ejpam-3544	5	26	a	a	DET
ejpam-3544	5	27	∪	∪	X
ejpam-3544	5	28	b	b	NOUN
ejpam-3544	5	29	∈	∈	PROPN
ejpam-3544	5	30	i	i	PRON
ejpam-3544	5	31	&	&	CCONJ
ejpam-3544	5	32	a	a	DET
ejpam-3544	5	33	∈	∈	PROPN
ejpam-3544	5	34	i	i	PRON
ejpam-3544	5	35	and	and	CCONJ
ejpam-3544	5	36	b	b	X
ejpam-3544	6	1	⊆	⊆	NUM
ejpam-3544	6	2	a⇒	a⇒	PROPN
ejpam-3544	6	3	b	b	PROPN
ejpam-3544	6	4	∈	∈	PROPN
ejpam-3544	7	1	i	i	PRON
ejpam-3544	8	1	[	[	X
ejpam-3544	8	2	7	7	NUM
ejpam-3544	8	3	]	]	PUNCT
ejpam-3544	8	4	.	.	PUNCT
ejpam-3544	9	1	let	let	VERB
ejpam-3544	9	2	(	(	PUNCT
ejpam-3544	9	3	x	x	NOUN
ejpam-3544	9	4	,	,	PUNCT
ejpam-3544	9	5	τ	τ	X
ejpam-3544	9	6	)	)	PUNCT
ejpam-3544	9	7	be	be	VERB
ejpam-3544	9	8	a	a	DET
ejpam-3544	9	9	topological	topological	ADJ
ejpam-3544	9	10	space	space	NOUN
ejpam-3544	9	11	.	.	PUNCT
ejpam-3544	10	1	a	a	DET
ejpam-3544	10	2	⊆	⊆	NUM
ejpam-3544	10	3	x	x	NUM
ejpam-3544	10	4	is	be	AUX
ejpam-3544	10	5	called	call	VERB
ejpam-3544	10	6	β	β	VERB
ejpam-3544	10	7	-	-	ADJ
ejpam-3544	10	8	open	open	ADJ
ejpam-3544	10	9	,	,	PUNCT
ejpam-3544	10	10	if	if	SCONJ
ejpam-3544	10	11	a	a	DET
ejpam-3544	10	12	⊆	⊆	NUM
ejpam-3544	10	13	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-3544	10	14	)	)	PUNCT
ejpam-3544	10	15	)	)	PUNCT
ejpam-3544	10	16	)	)	PUNCT
ejpam-3544	11	1	[	[	X
ejpam-3544	11	2	1	1	NUM
ejpam-3544	11	3	]	]	PUNCT
ejpam-3544	11	4	.	.	PUNCT
ejpam-3544	12	1	let	let	VERB
ejpam-3544	12	2	(	(	PUNCT
ejpam-3544	12	3	x	x	X
ejpam-3544	12	4	,	,	PUNCT
ejpam-3544	12	5	τ	τ	PROPN
ejpam-3544	12	6	,	,	PUNCT
ejpam-3544	12	7	i	i	PRON
ejpam-3544	12	8	)	)	PUNCT
ejpam-3544	12	9	be	be	VERB
ejpam-3544	12	10	an	an	DET
ejpam-3544	12	11	ideal	ideal	ADJ
ejpam-3544	12	12	topological	topological	ADJ
ejpam-3544	12	13	space	space	NOUN
ejpam-3544	12	14	.	.	PUNCT
ejpam-3544	13	1	a	a	DET
ejpam-3544	13	2	⊆	⊆	NUM
ejpam-3544	13	3	x	x	AUX
ejpam-3544	13	4	is	be	AUX
ejpam-3544	13	5	called	call	VERB
ejpam-3544	13	6	βi	βi	ADJ
ejpam-3544	13	7	-	-	ADJ
ejpam-3544	13	8	open	open	ADJ
ejpam-3544	13	9	,	,	PUNCT
ejpam-3544	13	10	if	if	SCONJ
ejpam-3544	13	11	∃	∃	PROPN
ejpam-3544	13	12	u	u	PROPN
ejpam-3544	13	13	∈	∈	PROPN
ejpam-3544	13	14	τ	τ	X
ejpam-3544	13	15	such	such	ADJ
ejpam-3544	13	16	that	that	SCONJ
ejpam-3544	13	17	(	(	PUNCT
ejpam-3544	13	18	u	u	NOUN
ejpam-3544	13	19	−	−	PROPN
ejpam-3544	13	20	a	a	PRON
ejpam-3544	13	21	)	)	PUNCT
ejpam-3544	13	22	∈	∈	PROPN
ejpam-3544	13	23	i	i	PRON
ejpam-3544	13	24	and	and	CCONJ
ejpam-3544	13	25	(	(	PUNCT
ejpam-3544	13	26	a	a	DET
ejpam-3544	13	27	−	−	PROPN
ejpam-3544	13	28	cl(int(cl(u	cl(int(cl(u	NOUN
ejpam-3544	13	29	)	)	PUNCT
ejpam-3544	13	30	)	)	PUNCT
ejpam-3544	13	31	)	)	PUNCT
ejpam-3544	13	32	)	)	PUNCT
ejpam-3544	14	1	∈	∈	PROPN
ejpam-3544	14	2	i	i	PRON
ejpam-3544	15	1	[	[	X
ejpam-3544	15	2	4	4	NUM
ejpam-3544	15	3	]	]	PUNCT
ejpam-3544	15	4	.	.	PUNCT
ejpam-3544	16	1	this	this	DET
ejpam-3544	16	2	note	note	NOUN
ejpam-3544	16	3	shows	show	VERB
ejpam-3544	16	4	that	that	SCONJ
ejpam-3544	16	5	the	the	DET
ejpam-3544	16	6	main	main	ADJ
ejpam-3544	16	7	results	result	NOUN
ejpam-3544	16	8	of	of	ADP
ejpam-3544	16	9	the	the	DET
ejpam-3544	16	10	paper	paper	NOUN
ejpam-3544	16	11	[	[	X
ejpam-3544	16	12	4	4	X
ejpam-3544	16	13	]	]	X
ejpam-3544	16	14	[	[	X
ejpam-3544	16	15	european	european	ADJ
ejpam-3544	16	16	journal	journal	PROPN
ejpam-3544	16	17	of	of	ADP
ejpam-3544	16	18	pure	pure	ADJ
ejpam-3544	16	19	and	and	CCONJ
ejpam-3544	16	20	applied	applied	ADJ
ejpam-3544	16	21	mathematics	mathematic	NOUN
ejpam-3544	16	22	6	6	NUM
ejpam-3544	16	23	(	(	PUNCT
ejpam-3544	16	24	2019	2019	NUM
ejpam-3544	16	25	)	)	PUNCT
ejpam-3544	16	26	893–903	893–903	NUM
ejpam-3544	16	27	]	]	PUNCT
ejpam-3544	16	28	are	be	AUX
ejpam-3544	16	29	incorrect	incorrect	ADJ
ejpam-3544	16	30	in	in	ADP
ejpam-3544	16	31	general	general	ADJ
ejpam-3544	16	32	,	,	PUNCT
ejpam-3544	16	33	by	by	ADP
ejpam-3544	16	34	giving	give	VERB
ejpam-3544	16	35	counter	counter	ADJ
ejpam-3544	16	36	examples	example	NOUN
ejpam-3544	16	37	.	.	PUNCT
ejpam-3544	17	1	the	the	DET
ejpam-3544	17	2	correct	correct	ADJ
ejpam-3544	17	3	form	form	NOUN
ejpam-3544	17	4	of	of	ADP
ejpam-3544	17	5	the	the	DET
ejpam-3544	17	6	incorrect	incorrect	ADJ
ejpam-3544	17	7	results	result	NOUN
ejpam-3544	17	8	in	in	ADP
ejpam-3544	17	9	[	[	X
ejpam-3544	17	10	4	4	NUM
ejpam-3544	17	11	]	]	PUNCT
ejpam-3544	17	12	is	be	AUX
ejpam-3544	17	13	presented	present	VERB
ejpam-3544	17	14	.	.	PUNCT
ejpam-3544	18	1	2010	2010	NUM
ejpam-3544	18	2	mathematics	mathematic	NOUN
ejpam-3544	18	3	subject	subject	NOUN
ejpam-3544	18	4	classifications	classification	NOUN
ejpam-3544	18	5	:	:	PUNCT
ejpam-3544	18	6	54	54	NUM
ejpam-3544	18	7	-	-	PUNCT
ejpam-3544	18	8	xx	xx	NUM
ejpam-3544	18	9	key	key	ADJ
ejpam-3544	18	10	words	word	NOUN
ejpam-3544	18	11	and	and	CCONJ
ejpam-3544	18	12	phrases	phrase	NOUN
ejpam-3544	18	13	:	:	PUNCT
ejpam-3544	18	14	β	β	X
ejpam-3544	18	15	-	-	ADJ
ejpam-3544	18	16	open	open	ADJ
ejpam-3544	18	17	sets	set	NOUN
ejpam-3544	18	18	,	,	PUNCT
ejpam-3544	18	19	ideals	ideal	NOUN
ejpam-3544	18	20	,	,	PUNCT
ejpam-3544	18	21	βi	βi	NOUN
ejpam-3544	18	22	-	-	PUNCT
ejpam-3544	18	23	open	open	ADJ
ejpam-3544	18	24	sets	set	NOUN
ejpam-3544	18	25	.	.	PUNCT
ejpam-3544	19	1	1	1	X
ejpam-3544	19	2	.	.	X
ejpam-3544	19	3	introduction	introduction	NOUN
ejpam-3544	19	4	general	general	ADJ
ejpam-3544	19	5	topology	topology	NOUN
ejpam-3544	19	6	has	have	AUX
ejpam-3544	19	7	been	be	AUX
ejpam-3544	19	8	considered	consider	VERB
ejpam-3544	19	9	the	the	DET
ejpam-3544	19	10	entrance	entrance	NOUN
ejpam-3544	19	11	to	to	PART
ejpam-3544	19	12	understand	understand	VERB
ejpam-3544	19	13	topology	topology	NOUN
ejpam-3544	19	14	science	science	NOUN
ejpam-3544	19	15	,	,	PUNCT
ejpam-3544	19	16	moreover	moreover	ADV
ejpam-3544	19	17	the	the	DET
ejpam-3544	19	18	base	base	NOUN
ejpam-3544	19	19	of	of	ADP
ejpam-3544	19	20	general	general	ADJ
ejpam-3544	19	21	topology	topology	NOUN
ejpam-3544	19	22	is	be	AUX
ejpam-3544	19	23	the	the	DET
ejpam-3544	19	24	topological	topological	ADJ
ejpam-3544	19	25	space	space	NOUN
ejpam-3544	19	26	,	,	PUNCT
ejpam-3544	19	27	which	which	PRON
ejpam-3544	19	28	has	have	AUX
ejpam-3544	19	29	been	be	AUX
ejpam-3544	19	30	considered	consider	VERB
ejpam-3544	19	31	a	a	DET
ejpam-3544	19	32	representation	representation	NOUN
ejpam-3544	19	33	of	of	ADP
ejpam-3544	19	34	universal	universal	ADJ
ejpam-3544	19	35	space	space	NOUN
ejpam-3544	19	36	in	in	ADP
ejpam-3544	19	37	general	general	ADJ
ejpam-3544	19	38	,	,	PUNCT
ejpam-3544	19	39	and	and	CCONJ
ejpam-3544	19	40	geometric	geometric	ADJ
ejpam-3544	19	41	shape	shape	NOUN
ejpam-3544	19	42	in	in	ADP
ejpam-3544	19	43	special	special	ADJ
ejpam-3544	19	44	,	,	PUNCT
ejpam-3544	19	45	also	also	ADV
ejpam-3544	19	46	the	the	DET
ejpam-3544	19	47	mathematical	mathematical	ADJ
ejpam-3544	19	48	analysis	analysis	NOUN
ejpam-3544	19	49	concepts	concept	NOUN
ejpam-3544	19	50	.	.	PUNCT
ejpam-3544	20	1	the	the	DET
ejpam-3544	20	2	concept	concept	NOUN
ejpam-3544	20	3	of	of	ADP
ejpam-3544	20	4	topology	topology	NOUN
ejpam-3544	20	5	shows	show	VERB
ejpam-3544	20	6	up	up	ADP
ejpam-3544	20	7	naturally	naturally	ADV
ejpam-3544	20	8	in	in	ADP
ejpam-3544	20	9	almost	almost	ADV
ejpam-3544	20	10	every	every	PRON
ejpam-3544	20	11	branch	branch	NOUN
ejpam-3544	20	12	of	of	ADP
ejpam-3544	20	13	mathematics	mathematic	NOUN
ejpam-3544	20	14	[	[	X
ejpam-3544	20	15	8	8	NUM
ejpam-3544	20	16	,	,	PUNCT
ejpam-3544	20	17	14	14	NUM
ejpam-3544	20	18	,	,	PUNCT
ejpam-3544	20	19	17	17	NUM
ejpam-3544	20	20	,	,	PUNCT
ejpam-3544	20	21	18	18	NUM
ejpam-3544	20	22	]	]	PUNCT
ejpam-3544	20	23	.	.	PUNCT
ejpam-3544	21	1	this	this	PRON
ejpam-3544	21	2	has	have	AUX
ejpam-3544	21	3	made	make	VERB
ejpam-3544	21	4	topology	topology	NOUN
ejpam-3544	21	5	one	one	NUM
ejpam-3544	21	6	of	of	ADP
ejpam-3544	21	7	the	the	DET
ejpam-3544	21	8	great	great	ADJ
ejpam-3544	21	9	unifying	unifying	ADJ
ejpam-3544	21	10	ideas	idea	NOUN
ejpam-3544	21	11	of	of	ADP
ejpam-3544	21	12	mathematics	mathematic	NOUN
ejpam-3544	21	13	.	.	PUNCT
ejpam-3544	22	1	ordinary	ordinary	ADJ
ejpam-3544	22	2	topology	topology	NOUN
ejpam-3544	22	3	now	now	ADV
ejpam-3544	22	4	has	have	AUX
ejpam-3544	22	5	been	be	AUX
ejpam-3544	22	6	used	use	VERB
ejpam-3544	22	7	in	in	ADP
ejpam-3544	22	8	many	many	ADJ
ejpam-3544	22	9	subfields	subfield	NOUN
ejpam-3544	22	10	of	of	ADP
ejpam-3544	22	11	artificial	artificial	ADJ
ejpam-3544	22	12	intelligence	intelligence	NOUN
ejpam-3544	22	13	,	,	PUNCT
ejpam-3544	22	14	such	such	ADJ
ejpam-3544	22	15	as	as	ADP
ejpam-3544	22	16	knowledge	knowledge	NOUN
ejpam-3544	22	17	representation	representation	NOUN
ejpam-3544	22	18	,	,	PUNCT
ejpam-3544	22	19	spatial	spatial	ADJ
ejpam-3544	22	20	reasoning	reasoning	NOUN
ejpam-3544	22	21	etc	etc	X
ejpam-3544	22	22	.	.	PUNCT
ejpam-3544	23	1	the	the	DET
ejpam-3544	23	2	main	main	ADJ
ejpam-3544	23	3	component	component	NOUN
ejpam-3544	23	4	of	of	ADP
ejpam-3544	23	5	a	a	DET
ejpam-3544	23	6	topological	topological	ADJ
ejpam-3544	23	7	space	space	NOUN
ejpam-3544	23	8	is	be	AUX
ejpam-3544	23	9	the	the	DET
ejpam-3544	23	10	open	open	ADJ
ejpam-3544	23	11	sets	set	NOUN
ejpam-3544	23	12	,	,	PUNCT
ejpam-3544	23	13	and	and	CCONJ
ejpam-3544	23	14	overtime	overtime	NOUN
ejpam-3544	23	15	there	there	PRON
ejpam-3544	23	16	have	have	AUX
ejpam-3544	23	17	been	be	AUX
ejpam-3544	23	18	so	so	ADV
ejpam-3544	23	19	many	many	ADJ
ejpam-3544	23	20	generalizations	generalization	NOUN
ejpam-3544	23	21	of	of	ADP
ejpam-3544	23	22	it	it	PRON
ejpam-3544	23	23	.	.	PUNCT
ejpam-3544	24	1	stone	stone	NOUN
ejpam-3544	25	1	[	[	X
ejpam-3544	25	2	19	19	NUM
ejpam-3544	25	3	]	]	PUNCT
ejpam-3544	25	4	introduced	introduce	VERB
ejpam-3544	25	5	the	the	DET
ejpam-3544	25	6	concept	concept	NOUN
ejpam-3544	25	7	of	of	ADP
ejpam-3544	25	8	regular	regular	ADJ
ejpam-3544	25	9	open	open	ADJ
ejpam-3544	25	10	sets	set	NOUN
ejpam-3544	25	11	.	.	PUNCT
ejpam-3544	26	1	doi	doi	NOUN
ejpam-3544	26	2	:	:	PUNCT
ejpam-3544	26	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3544	https://doi.org/10.29020/nybg.ejpam.v12i4.3544	ADJ
ejpam-3544	26	4	email	email	NOUN
ejpam-3544	26	5	addresses	address	NOUN
ejpam-3544	26	6	:	:	PUNCT
ejpam-3544	26	7	monahosny@edu.asu.edu.eg	monahosny@edu.asu.edu.eg	NOUN
ejpam-3544	26	8	(	(	PUNCT
ejpam-3544	26	9	m.	m.	NOUN
ejpam-3544	26	10	hosny	hosny	PROPN
ejpam-3544	26	11	)	)	PUNCT
ejpam-3544	26	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3544	27	1	1656	1656	NUM
ejpam-3544	28	1	c	c	X
ejpam-3544	28	2	©	©	PROPN
ejpam-3544	28	3	2019	2019	NUM
ejpam-3544	28	4	ejpam	ejpam	NOUN
ejpam-3544	28	5	all	all	DET
ejpam-3544	28	6	rights	right	NOUN
ejpam-3544	28	7	reserved	reserve	VERB
ejpam-3544	28	8	.	.	PUNCT
ejpam-3544	29	1	m.	m.	PROPN
ejpam-3544	29	2	hosny	hosny	PROPN
ejpam-3544	29	3	/	/	SYM
ejpam-3544	29	4	eur	eur	PROPN
ejpam-3544	29	5	.	.	PUNCT
ejpam-3544	30	1	j.	j.	PROPN
ejpam-3544	30	2	pure	pure	PROPN
ejpam-3544	30	3	appl	appl	PROPN
ejpam-3544	30	4	.	.	PROPN
ejpam-3544	30	5	math	math	PROPN
ejpam-3544	30	6	,	,	PUNCT
ejpam-3544	30	7	12	12	NUM
ejpam-3544	30	8	(	(	PUNCT
ejpam-3544	30	9	4	4	NUM
ejpam-3544	30	10	)	)	PUNCT
ejpam-3544	30	11	(	(	PUNCT
ejpam-3544	30	12	2019	2019	NUM
ejpam-3544	30	13	)	)	PUNCT
ejpam-3544	30	14	,	,	PUNCT
ejpam-3544	30	15	1656	1656	NUM
ejpam-3544	30	16	-	-	SYM
ejpam-3544	30	17	1660	1660	NUM
ejpam-3544	30	18	1657	1657	NUM
ejpam-3544	30	19	the	the	DET
ejpam-3544	30	20	concept	concept	NOUN
ejpam-3544	30	21	of	of	ADP
ejpam-3544	30	22	semi	semi	ADJ
ejpam-3544	30	23	open	open	ADJ
ejpam-3544	30	24	sets	set	NOUN
ejpam-3544	30	25	was	be	AUX
ejpam-3544	30	26	presented	present	VERB
ejpam-3544	30	27	in	in	ADP
ejpam-3544	30	28	[	[	X
ejpam-3544	30	29	10	10	NUM
ejpam-3544	30	30	]	]	PUNCT
ejpam-3544	30	31	.	.	PUNCT
ejpam-3544	31	1	meantime	meantime	ADV
ejpam-3544	31	2	,	,	PUNCT
ejpam-3544	31	3	the	the	DET
ejpam-3544	31	4	concept	concept	NOUN
ejpam-3544	31	5	of	of	ADP
ejpam-3544	31	6	αopen	αopen	ADJ
ejpam-3544	31	7	sets	set	NOUN
ejpam-3544	31	8	was	be	AUX
ejpam-3544	31	9	proposed	propose	VERB
ejpam-3544	31	10	by	by	ADP
ejpam-3544	31	11	najastad	najastad	NOUN
ejpam-3544	31	12	[	[	X
ejpam-3544	31	13	15	15	NUM
ejpam-3544	31	14	]	]	PUNCT
ejpam-3544	31	15	.	.	PUNCT
ejpam-3544	32	1	mashhour	mashhour	INTJ
ejpam-3544	32	2	et	et	PROPN
ejpam-3544	32	3	al	al	PROPN
ejpam-3544	32	4	.	.	PUNCT
ejpam-3544	33	1	[	[	X
ejpam-3544	33	2	11	11	NUM
ejpam-3544	33	3	]	]	PUNCT
ejpam-3544	33	4	introduced	introduce	VERB
ejpam-3544	33	5	the	the	DET
ejpam-3544	33	6	concept	concept	NOUN
ejpam-3544	33	7	of	of	ADP
ejpam-3544	33	8	pre	pre	ADJ
ejpam-3544	33	9	-	-	ADJ
ejpam-3544	33	10	open	open	ADJ
ejpam-3544	33	11	sets	set	NOUN
ejpam-3544	33	12	.	.	PUNCT
ejpam-3544	34	1	in	in	ADP
ejpam-3544	34	2	1983	1983	NUM
ejpam-3544	34	3	,	,	PUNCT
ejpam-3544	34	4	abd	abd	PROPN
ejpam-3544	34	5	el	el	PROPN
ejpam-3544	34	6	-	-	PROPN
ejpam-3544	34	7	monsef	monsef	PROPN
ejpam-3544	34	8	et	et	PROPN
ejpam-3544	34	9	al	al	PROPN
ejpam-3544	34	10	.	.	PUNCT
ejpam-3544	35	1	[	[	X
ejpam-3544	35	2	1	1	X
ejpam-3544	35	3	]	]	PUNCT
ejpam-3544	35	4	discussed	discuss	VERB
ejpam-3544	35	5	the	the	DET
ejpam-3544	35	6	concept	concept	NOUN
ejpam-3544	35	7	of	of	ADP
ejpam-3544	35	8	β	β	ADJ
ejpam-3544	35	9	-	-	ADJ
ejpam-3544	35	10	open	open	ADJ
ejpam-3544	35	11	sets	set	NOUN
ejpam-3544	35	12	.	.	PUNCT
ejpam-3544	36	1	ideal	ideal	NOUN
ejpam-3544	36	2	is	be	AUX
ejpam-3544	36	3	a	a	DET
ejpam-3544	36	4	fundamental	fundamental	ADJ
ejpam-3544	36	5	concept	concept	NOUN
ejpam-3544	36	6	in	in	ADP
ejpam-3544	36	7	studying	study	VERB
ejpam-3544	36	8	the	the	DET
ejpam-3544	36	9	topological	topological	ADJ
ejpam-3544	36	10	problems	problem	NOUN
ejpam-3544	36	11	.	.	PUNCT
ejpam-3544	37	1	the	the	DET
ejpam-3544	37	2	notion	notion	NOUN
ejpam-3544	37	3	of	of	ADP
ejpam-3544	37	4	ideal	ideal	ADJ
ejpam-3544	37	5	topological	topological	ADJ
ejpam-3544	37	6	spaces	space	NOUN
ejpam-3544	37	7	was	be	AUX
ejpam-3544	37	8	first	first	ADV
ejpam-3544	37	9	studied	study	VERB
ejpam-3544	37	10	by	by	ADP
ejpam-3544	37	11	kuratowski	kuratowski	NOUN
ejpam-3544	37	12	[	[	X
ejpam-3544	37	13	9	9	NUM
ejpam-3544	37	14	]	]	PUNCT
ejpam-3544	37	15	and	and	CCONJ
ejpam-3544	37	16	vaidyanathaswamy	vaidyanathaswamy	NOUN
ejpam-3544	37	17	[	[	X
ejpam-3544	37	18	20	20	NUM
ejpam-3544	37	19	]	]	PUNCT
ejpam-3544	37	20	which	which	PRON
ejpam-3544	37	21	is	be	AUX
ejpam-3544	37	22	one	one	NUM
ejpam-3544	37	23	of	of	ADP
ejpam-3544	37	24	the	the	DET
ejpam-3544	37	25	important	important	ADJ
ejpam-3544	37	26	areas	area	NOUN
ejpam-3544	37	27	of	of	ADP
ejpam-3544	37	28	research	research	NOUN
ejpam-3544	37	29	in	in	ADP
ejpam-3544	37	30	the	the	DET
ejpam-3544	37	31	branch	branch	NOUN
ejpam-3544	37	32	of	of	ADP
ejpam-3544	37	33	mathematics	mathematic	NOUN
ejpam-3544	37	34	.	.	PUNCT
ejpam-3544	38	1	after	after	SCONJ
ejpam-3544	38	2	them	they	PRON
ejpam-3544	38	3	different	different	ADJ
ejpam-3544	38	4	mathematicians	mathematician	NOUN
ejpam-3544	38	5	applied	apply	VERB
ejpam-3544	38	6	the	the	DET
ejpam-3544	38	7	concept	concept	NOUN
ejpam-3544	38	8	of	of	ADP
ejpam-3544	38	9	ideals	ideal	NOUN
ejpam-3544	38	10	in	in	ADP
ejpam-3544	38	11	topological	topological	ADJ
ejpam-3544	38	12	spaces	space	NOUN
ejpam-3544	38	13	(	(	PUNCT
ejpam-3544	38	14	see	see	VERB
ejpam-3544	38	15	:	:	PUNCT
ejpam-3544	38	16	[	[	X
ejpam-3544	38	17	3	3	NUM
ejpam-3544	38	18	,	,	PUNCT
ejpam-3544	38	19	5	5	NUM
ejpam-3544	38	20	–	–	PUNCT
ejpam-3544	38	21	7	7	NUM
ejpam-3544	38	22	,	,	PUNCT
ejpam-3544	38	23	13	13	NUM
ejpam-3544	38	24	]	]	NUM
ejpam-3544	38	25	)	)	PUNCT
ejpam-3544	38	26	.	.	PUNCT
ejpam-3544	39	1	the	the	DET
ejpam-3544	39	2	interest	interest	NOUN
ejpam-3544	39	3	in	in	ADP
ejpam-3544	39	4	the	the	DET
ejpam-3544	39	5	idealized	idealized	ADJ
ejpam-3544	39	6	version	version	NOUN
ejpam-3544	39	7	of	of	ADP
ejpam-3544	39	8	many	many	ADJ
ejpam-3544	39	9	general	general	ADJ
ejpam-3544	39	10	topological	topological	ADJ
ejpam-3544	39	11	properties	property	NOUN
ejpam-3544	39	12	has	have	AUX
ejpam-3544	39	13	grown	grow	VERB
ejpam-3544	39	14	drastically	drastically	ADV
ejpam-3544	39	15	in	in	ADP
ejpam-3544	39	16	the	the	DET
ejpam-3544	39	17	past	past	ADJ
ejpam-3544	39	18	20	20	NUM
ejpam-3544	39	19	years	year	NOUN
ejpam-3544	39	20	.	.	PUNCT
ejpam-3544	40	1	in	in	ADP
ejpam-3544	40	2	[	[	X
ejpam-3544	40	3	2	2	NUM
ejpam-3544	40	4	,	,	PUNCT
ejpam-3544	40	5	12	12	NUM
ejpam-3544	40	6	]	]	PUNCT
ejpam-3544	40	7	,	,	PUNCT
ejpam-3544	40	8	the	the	DET
ejpam-3544	40	9	concept	concept	NOUN
ejpam-3544	40	10	of	of	ADP
ejpam-3544	40	11	semi	semi	ADJ
ejpam-3544	40	12	-	-	ADJ
ejpam-3544	40	13	open	open	ADJ
ejpam-3544	40	14	sets	set	NOUN
ejpam-3544	40	15	with	with	ADP
ejpam-3544	40	16	respect	respect	NOUN
ejpam-3544	40	17	to	to	ADP
ejpam-3544	40	18	an	an	DET
ejpam-3544	40	19	ideal	ideal	NOUN
ejpam-3544	40	20	was	be	AUX
ejpam-3544	40	21	investigated	investigate	VERB
ejpam-3544	40	22	.	.	PUNCT
ejpam-3544	41	1	nasef	nasef	PROPN
ejpam-3544	41	2	et	et	PROPN
ejpam-3544	41	3	al	al	PROPN
ejpam-3544	41	4	.	.	PUNCT
ejpam-3544	42	1	[	[	X
ejpam-3544	42	2	16	16	NUM
ejpam-3544	42	3	]	]	PUNCT
ejpam-3544	42	4	presented	present	VERB
ejpam-3544	42	5	and	and	CCONJ
ejpam-3544	42	6	studied	study	VERB
ejpam-3544	42	7	the	the	DET
ejpam-3544	42	8	concept	concept	NOUN
ejpam-3544	42	9	of	of	ADP
ejpam-3544	42	10	α	α	NOUN
ejpam-3544	42	11	-	-	ADJ
ejpam-3544	42	12	open	open	ADJ
ejpam-3544	42	13	sets	set	NOUN
ejpam-3544	42	14	with	with	ADP
ejpam-3544	42	15	respect	respect	NOUN
ejpam-3544	42	16	to	to	ADP
ejpam-3544	42	17	an	an	DET
ejpam-3544	42	18	ideal	ideal	NOUN
ejpam-3544	42	19	.	.	PUNCT
ejpam-3544	43	1	recently	recently	ADV
ejpam-3544	43	2	,	,	PUNCT
ejpam-3544	43	3	in	in	ADP
ejpam-3544	43	4	[	[	PUNCT
ejpam-3544	43	5	4	4	NUM
ejpam-3544	43	6	]	]	PUNCT
ejpam-3544	43	7	,	,	PUNCT
ejpam-3544	43	8	the	the	DET
ejpam-3544	43	9	concept	concept	NOUN
ejpam-3544	43	10	of	of	ADP
ejpam-3544	43	11	β	β	ADJ
ejpam-3544	43	12	-	-	ADJ
ejpam-3544	43	13	open	open	ADJ
ejpam-3544	43	14	sets	set	NOUN
ejpam-3544	43	15	with	with	ADP
ejpam-3544	43	16	respect	respect	NOUN
ejpam-3544	43	17	to	to	ADP
ejpam-3544	43	18	an	an	DET
ejpam-3544	43	19	ideal	ideal	NOUN
ejpam-3544	43	20	(	(	PUNCT
ejpam-3544	43	21	βi	βi	NOUN
ejpam-3544	43	22	-	-	ADJ
ejpam-3544	43	23	open	open	ADJ
ejpam-3544	43	24	)	)	PUNCT
ejpam-3544	43	25	was	be	AUX
ejpam-3544	43	26	introduced	introduce	VERB
ejpam-3544	43	27	.	.	PUNCT
ejpam-3544	44	1	2	2	X
ejpam-3544	44	2	.	.	X
ejpam-3544	44	3	counter	counter	ADJ
ejpam-3544	44	4	examples	example	NOUN
ejpam-3544	44	5	in	in	ADP
ejpam-3544	44	6	this	this	DET
ejpam-3544	44	7	section	section	NOUN
ejpam-3544	44	8	,	,	PUNCT
ejpam-3544	44	9	i	i	PRON
ejpam-3544	44	10	point	point	VERB
ejpam-3544	44	11	out	out	ADP
ejpam-3544	44	12	where	where	SCONJ
ejpam-3544	44	13	the	the	DET
ejpam-3544	44	14	errors	error	NOUN
ejpam-3544	44	15	occur	occur	VERB
ejpam-3544	44	16	in	in	ADP
ejpam-3544	44	17	[	[	X
ejpam-3544	44	18	4	4	NUM
ejpam-3544	44	19	]	]	PUNCT
ejpam-3544	44	20	and	and	CCONJ
ejpam-3544	44	21	then	then	ADV
ejpam-3544	44	22	give	give	VERB
ejpam-3544	44	23	counter	counter	ADJ
ejpam-3544	44	24	examples	example	NOUN
ejpam-3544	44	25	to	to	PART
ejpam-3544	44	26	confirm	confirm	VERB
ejpam-3544	44	27	my	my	PRON
ejpam-3544	44	28	claim	claim	NOUN
ejpam-3544	44	29	.	.	PUNCT
ejpam-3544	45	1	eventually	eventually	ADV
ejpam-3544	45	2	,	,	PUNCT
ejpam-3544	45	3	the	the	DET
ejpam-3544	45	4	correct	correct	ADJ
ejpam-3544	45	5	form	form	NOUN
ejpam-3544	45	6	of	of	ADP
ejpam-3544	45	7	the	the	DET
ejpam-3544	45	8	incorrect	incorrect	ADJ
ejpam-3544	45	9	results	result	NOUN
ejpam-3544	45	10	is	be	AUX
ejpam-3544	45	11	introduced	introduce	VERB
ejpam-3544	45	12	.	.	PUNCT
ejpam-3544	46	1	in	in	ADP
ejpam-3544	46	2	[	[	X
ejpam-3544	46	3	[	[	X
ejpam-3544	46	4	4	4	NUM
ejpam-3544	46	5	]	]	PUNCT
ejpam-3544	46	6	,	,	PUNCT
ejpam-3544	46	7	lemma	lemma	PROPN
ejpam-3544	46	8	1	1	NUM
ejpam-3544	46	9	,	,	PUNCT
ejpam-3544	46	10	p.	p.	NOUN
ejpam-3544	46	11	895	895	NUM
ejpam-3544	46	12	]	]	PUNCT
ejpam-3544	46	13	,	,	PUNCT
ejpam-3544	46	14	the	the	DET
ejpam-3544	46	15	authors	author	NOUN
ejpam-3544	46	16	proved	prove	VERB
ejpam-3544	46	17	that	that	SCONJ
ejpam-3544	46	18	in	in	ADP
ejpam-3544	46	19	the	the	DET
ejpam-3544	46	20	topological	topological	ADJ
ejpam-3544	46	21	space	space	NOUN
ejpam-3544	46	22	(	(	PUNCT
ejpam-3544	46	23	x	x	X
ejpam-3544	46	24	,	,	PUNCT
ejpam-3544	46	25	τ	τ	PROPN
ejpam-3544	46	26	)	)	PUNCT
ejpam-3544	46	27	,	,	PUNCT
ejpam-3544	46	28	and	and	CCONJ
ejpam-3544	46	29	a	a	DET
ejpam-3544	46	30	⊆	⊆	NUM
ejpam-3544	46	31	x.	x.	NOUN
ejpam-3544	46	32	then	then	ADV
ejpam-3544	46	33	int(a	int(a	PROPN
ejpam-3544	46	34	)	)	PUNCT
ejpam-3544	46	35	=	=	SYM
ejpam-3544	46	36	int(cl(a	int(cl(a	PROPN
ejpam-3544	46	37	)	)	PUNCT
ejpam-3544	46	38	)	)	PUNCT
ejpam-3544	47	1	=	=	PUNCT
ejpam-3544	47	2	int(cl(int(a	int(cl(int(a	PROPN
ejpam-3544	47	3	)	)	PUNCT
ejpam-3544	47	4	)	)	PUNCT
ejpam-3544	47	5	)	)	PUNCT
ejpam-3544	47	6	.	.	PUNCT
ejpam-3544	48	1	the	the	DET
ejpam-3544	48	2	following	follow	VERB
ejpam-3544	48	3	examples	example	NOUN
ejpam-3544	48	4	show	show	VERB
ejpam-3544	48	5	that	that	SCONJ
ejpam-3544	48	6	[	[	X
ejpam-3544	48	7	lemma	lemma	PROPN
ejpam-3544	48	8	1	1	NUM
ejpam-3544	48	9	,	,	PUNCT
ejpam-3544	48	10	p.	p.	NOUN
ejpam-3544	48	11	895	895	NUM
ejpam-3544	48	12	]	]	PUNCT
ejpam-3544	48	13	is	be	AUX
ejpam-3544	48	14	not	not	PART
ejpam-3544	48	15	true	true	ADJ
ejpam-3544	48	16	in	in	ADP
ejpam-3544	48	17	general	general	ADJ
ejpam-3544	48	18	.	.	PUNCT
ejpam-3544	49	1	example	example	NOUN
ejpam-3544	49	2	2.1	2.1	NUM
ejpam-3544	49	3	.	.	PUNCT
ejpam-3544	50	1	let	let	VERB
ejpam-3544	50	2	x	x	PUNCT
ejpam-3544	50	3	=	=	PRON
ejpam-3544	50	4	{	{	PUNCT
ejpam-3544	50	5	1	1	NUM
ejpam-3544	50	6	,	,	PUNCT
ejpam-3544	50	7	2	2	NUM
ejpam-3544	50	8	,	,	PUNCT
ejpam-3544	50	9	3	3	NUM
ejpam-3544	50	10	,	,	PUNCT
ejpam-3544	50	11	4	4	NUM
ejpam-3544	50	12	}	}	PUNCT
ejpam-3544	50	13	and	and	CCONJ
ejpam-3544	50	14	τ	τ	PROPN
ejpam-3544	50	15	=	=	SYM
ejpam-3544	50	16	{	{	PUNCT
ejpam-3544	50	17	x	x	PROPN
ejpam-3544	50	18	,	,	PUNCT
ejpam-3544	50	19	φ	φ	NUM
ejpam-3544	50	20	,	,	PUNCT
ejpam-3544	50	21	{	{	PUNCT
ejpam-3544	50	22	1	1	NUM
ejpam-3544	50	23	}	}	PUNCT
ejpam-3544	50	24	,	,	PUNCT
ejpam-3544	50	25	{	{	PUNCT
ejpam-3544	50	26	1	1	NUM
ejpam-3544	50	27	,	,	PUNCT
ejpam-3544	50	28	2	2	NUM
ejpam-3544	50	29	}	}	PUNCT
ejpam-3544	50	30	,	,	PUNCT
ejpam-3544	50	31	{	{	PUNCT
ejpam-3544	50	32	1	1	NUM
ejpam-3544	50	33	,	,	PUNCT
ejpam-3544	50	34	3	3	NUM
ejpam-3544	50	35	}	}	PUNCT
ejpam-3544	50	36	,	,	PUNCT
ejpam-3544	50	37	{	{	PUNCT
ejpam-3544	50	38	1	1	NUM
ejpam-3544	50	39	,	,	PUNCT
ejpam-3544	50	40	2	2	NUM
ejpam-3544	50	41	,	,	PUNCT
ejpam-3544	50	42	3	3	NUM
ejpam-3544	50	43	}	}	PUNCT
ejpam-3544	50	44	}	}	PUNCT
ejpam-3544	50	45	.	.	PUNCT
ejpam-3544	51	1	take	take	VERB
ejpam-3544	51	2	a	a	DET
ejpam-3544	51	3	=	=	PUNCT
ejpam-3544	51	4	{	{	PUNCT
ejpam-3544	51	5	1	1	NUM
ejpam-3544	51	6	,	,	PUNCT
ejpam-3544	51	7	2	2	NUM
ejpam-3544	51	8	}	}	PUNCT
ejpam-3544	51	9	.	.	PUNCT
ejpam-3544	52	1	then	then	ADV
ejpam-3544	52	2	,	,	PUNCT
ejpam-3544	52	3	cl(a	cl(a	X
ejpam-3544	52	4	)	)	PUNCT
ejpam-3544	52	5	=	=	SYM
ejpam-3544	53	1	x	x	X
ejpam-3544	53	2	,	,	PUNCT
ejpam-3544	53	3	int(a	int(a	PROPN
ejpam-3544	53	4	)	)	PUNCT
ejpam-3544	53	5	=	=	SYM
ejpam-3544	53	6	a	a	PRON
ejpam-3544	53	7	,	,	PUNCT
ejpam-3544	53	8	int(cl(a	int(cl(a	PROPN
ejpam-3544	53	9	)	)	PUNCT
ejpam-3544	53	10	)	)	PUNCT
ejpam-3544	54	1	=	=	SYM
ejpam-3544	54	2	x	x	NOUN
ejpam-3544	54	3	,	,	PUNCT
ejpam-3544	54	4	cl(int(a	cl(int(a	PROPN
ejpam-3544	54	5	)	)	PUNCT
ejpam-3544	54	6	)	)	PUNCT
ejpam-3544	55	1	=	=	PUNCT
ejpam-3544	55	2	x	x	X
ejpam-3544	55	3	,	,	PUNCT
ejpam-3544	55	4	int(cl(int(a	int(cl(int(a	PROPN
ejpam-3544	55	5	)	)	PUNCT
ejpam-3544	55	6	)	)	PUNCT
ejpam-3544	55	7	)	)	PUNCT
ejpam-3544	56	1	=	=	PUNCT
ejpam-3544	56	2	x	x	NOUN
ejpam-3544	56	3	,	,	PUNCT
ejpam-3544	56	4	but	but	CCONJ
ejpam-3544	56	5	int(a	int(a	X
ejpam-3544	56	6	)	)	PUNCT
ejpam-3544	56	7	=	=	PUNCT
ejpam-3544	56	8	a	a	PRON
ejpam-3544	56	9	6=	6=	NUM
ejpam-3544	56	10	x	x	SYM
ejpam-3544	56	11	=	=	SYM
ejpam-3544	56	12	int(cl(a	int(cl(a	PROPN
ejpam-3544	56	13	)	)	PUNCT
ejpam-3544	56	14	)	)	PUNCT
ejpam-3544	56	15	and	and	CCONJ
ejpam-3544	56	16	int(a	int(a	PROPN
ejpam-3544	56	17	)	)	PUNCT
ejpam-3544	56	18	=	=	PUNCT
ejpam-3544	56	19	a	a	PRON
ejpam-3544	56	20	6=	6=	NUM
ejpam-3544	56	21	x	x	SYM
ejpam-3544	56	22	=	=	SYM
ejpam-3544	56	23	int(cl(int(a	int(cl(int(a	PROPN
ejpam-3544	56	24	)	)	PUNCT
ejpam-3544	56	25	)	)	PUNCT
ejpam-3544	56	26	)	)	PUNCT
ejpam-3544	56	27	.	.	PUNCT
ejpam-3544	57	1	example	example	NOUN
ejpam-3544	58	1	2.2	2.2	NUM
ejpam-3544	58	2	.	.	PUNCT
ejpam-3544	59	1	let	let	VERB
ejpam-3544	59	2	x	x	PUNCT
ejpam-3544	59	3	=	=	PRON
ejpam-3544	59	4	{	{	PUNCT
ejpam-3544	59	5	1	1	NUM
ejpam-3544	59	6	,	,	PUNCT
ejpam-3544	59	7	2	2	NUM
ejpam-3544	59	8	,	,	PUNCT
ejpam-3544	59	9	3	3	NUM
ejpam-3544	59	10	,	,	PUNCT
ejpam-3544	59	11	4	4	NUM
ejpam-3544	59	12	}	}	PUNCT
ejpam-3544	59	13	and	and	CCONJ
ejpam-3544	59	14	τ	τ	PROPN
ejpam-3544	59	15	=	=	SYM
ejpam-3544	59	16	{	{	PUNCT
ejpam-3544	59	17	x	x	PROPN
ejpam-3544	59	18	,	,	PUNCT
ejpam-3544	59	19	φ	φ	NUM
ejpam-3544	59	20	,	,	PUNCT
ejpam-3544	59	21	{	{	PUNCT
ejpam-3544	59	22	1	1	NUM
ejpam-3544	59	23	}	}	PUNCT
ejpam-3544	59	24	,	,	PUNCT
ejpam-3544	59	25	{	{	PUNCT
ejpam-3544	59	26	2	2	NUM
ejpam-3544	59	27	}	}	PUNCT
ejpam-3544	59	28	,	,	PUNCT
ejpam-3544	59	29	{	{	PUNCT
ejpam-3544	59	30	1	1	NUM
ejpam-3544	59	31	,	,	PUNCT
ejpam-3544	59	32	2	2	NUM
ejpam-3544	59	33	}	}	PUNCT
ejpam-3544	59	34	,	,	PUNCT
ejpam-3544	59	35	{	{	PUNCT
ejpam-3544	59	36	3	3	NUM
ejpam-3544	59	37	,	,	PUNCT
ejpam-3544	59	38	4	4	NUM
ejpam-3544	59	39	}	}	PUNCT
ejpam-3544	59	40	,	,	PUNCT
ejpam-3544	59	41	{	{	PUNCT
ejpam-3544	59	42	1	1	NUM
ejpam-3544	59	43	,	,	PUNCT
ejpam-3544	59	44	3	3	NUM
ejpam-3544	59	45	,	,	PUNCT
ejpam-3544	59	46	4	4	NUM
ejpam-3544	59	47	}	}	PUNCT
ejpam-3544	59	48	,	,	PUNCT
ejpam-3544	59	49	{	{	PUNCT
ejpam-3544	59	50	2	2	NUM
ejpam-3544	59	51	,	,	PUNCT
ejpam-3544	59	52	3	3	NUM
ejpam-3544	59	53	,	,	PUNCT
ejpam-3544	59	54	4	4	NUM
ejpam-3544	59	55	}	}	PUNCT
ejpam-3544	59	56	}	}	PUNCT
ejpam-3544	59	57	.	.	PUNCT
ejpam-3544	60	1	take	take	VERB
ejpam-3544	60	2	a	a	PRON
ejpam-3544	60	3	=	=	PUNCT
ejpam-3544	60	4	{	{	PUNCT
ejpam-3544	60	5	1	1	NUM
ejpam-3544	60	6	,	,	PUNCT
ejpam-3544	60	7	2	2	NUM
ejpam-3544	60	8	,	,	PUNCT
ejpam-3544	60	9	3	3	NUM
ejpam-3544	60	10	}	}	PUNCT
ejpam-3544	60	11	.	.	PUNCT
ejpam-3544	61	1	then	then	ADV
ejpam-3544	61	2	,	,	PUNCT
ejpam-3544	61	3	cl(a	cl(a	X
ejpam-3544	61	4	)	)	PUNCT
ejpam-3544	61	5	=	=	SYM
ejpam-3544	62	1	x	x	X
ejpam-3544	62	2	,	,	PUNCT
ejpam-3544	62	3	int(a	int(a	PROPN
ejpam-3544	62	4	)	)	PUNCT
ejpam-3544	62	5	=	=	SYM
ejpam-3544	62	6	{	{	PUNCT
ejpam-3544	62	7	1	1	NUM
ejpam-3544	62	8	,	,	PUNCT
ejpam-3544	62	9	2	2	NUM
ejpam-3544	62	10	}	}	PUNCT
ejpam-3544	62	11	,	,	PUNCT
ejpam-3544	62	12	int(cl(a	int(cl(a	PROPN
ejpam-3544	62	13	)	)	PUNCT
ejpam-3544	62	14	)	)	PUNCT
ejpam-3544	63	1	=	=	SYM
ejpam-3544	63	2	x	x	NOUN
ejpam-3544	63	3	,	,	PUNCT
ejpam-3544	63	4	cl(int(a	cl(int(a	PROPN
ejpam-3544	63	5	)	)	PUNCT
ejpam-3544	63	6	)	)	PUNCT
ejpam-3544	64	1	=	=	PRON
ejpam-3544	64	2	{	{	PUNCT
ejpam-3544	64	3	1	1	NUM
ejpam-3544	64	4	,	,	PUNCT
ejpam-3544	64	5	2	2	NUM
ejpam-3544	64	6	}	}	PUNCT
ejpam-3544	64	7	,	,	PUNCT
ejpam-3544	64	8	int(cl(int(a	int(cl(int(a	PROPN
ejpam-3544	64	9	)	)	PUNCT
ejpam-3544	64	10	)	)	PUNCT
ejpam-3544	64	11	)	)	PUNCT
ejpam-3544	65	1	=	=	PRON
ejpam-3544	65	2	{	{	PUNCT
ejpam-3544	65	3	1	1	NUM
ejpam-3544	65	4	,	,	PUNCT
ejpam-3544	65	5	2	2	NUM
ejpam-3544	65	6	}	}	PUNCT
ejpam-3544	65	7	,	,	PUNCT
ejpam-3544	65	8	but	but	CCONJ
ejpam-3544	65	9	int(cl(a	int(cl(a	PROPN
ejpam-3544	65	10	)	)	PUNCT
ejpam-3544	65	11	)	)	PUNCT
ejpam-3544	66	1	=	=	PUNCT
ejpam-3544	66	2	x	x	SYM
ejpam-3544	66	3	6=	6=	X
ejpam-3544	66	4	{	{	PUNCT
ejpam-3544	66	5	1	1	NUM
ejpam-3544	66	6	,	,	PUNCT
ejpam-3544	66	7	2	2	NUM
ejpam-3544	66	8	}	}	PUNCT
ejpam-3544	66	9	=	=	SYM
ejpam-3544	66	10	int(cl(int(a	int(cl(int(a	PROPN
ejpam-3544	66	11	)	)	PUNCT
ejpam-3544	66	12	)	)	PUNCT
ejpam-3544	66	13	)	)	PUNCT
ejpam-3544	66	14	.	.	PUNCT
ejpam-3544	67	1	in	in	ADP
ejpam-3544	67	2	[	[	X
ejpam-3544	67	3	[	[	X
ejpam-3544	67	4	4	4	NUM
ejpam-3544	67	5	]	]	PUNCT
ejpam-3544	67	6	,	,	PUNCT
ejpam-3544	67	7	lemma	lemma	PROPN
ejpam-3544	67	8	2	2	NUM
ejpam-3544	67	9	,	,	PUNCT
ejpam-3544	67	10	p.	p.	NOUN
ejpam-3544	67	11	895	895	NUM
ejpam-3544	67	12	]	]	PUNCT
ejpam-3544	67	13	,	,	PUNCT
ejpam-3544	67	14	the	the	DET
ejpam-3544	67	15	authors	author	NOUN
ejpam-3544	67	16	proved	prove	VERB
ejpam-3544	67	17	that	that	SCONJ
ejpam-3544	67	18	in	in	ADP
ejpam-3544	67	19	an	an	DET
ejpam-3544	67	20	ideal	ideal	ADJ
ejpam-3544	67	21	topological	topological	ADJ
ejpam-3544	67	22	space	space	NOUN
ejpam-3544	67	23	(	(	PUNCT
ejpam-3544	67	24	x	x	X
ejpam-3544	67	25	,	,	PUNCT
ejpam-3544	67	26	τ	τ	PROPN
ejpam-3544	67	27	,	,	PUNCT
ejpam-3544	67	28	i	i	PROPN
ejpam-3544	67	29	)	)	PUNCT
ejpam-3544	67	30	.	.	PUNCT
ejpam-3544	68	1	a	a	DET
ejpam-3544	68	2	subset	subset	NOUN
ejpam-3544	68	3	a	a	PRON
ejpam-3544	68	4	of	of	ADP
ejpam-3544	68	5	x	x	NOUN
ejpam-3544	68	6	is	be	AUX
ejpam-3544	68	7	β	β	X
ejpam-3544	68	8	-	-	ADJ
ejpam-3544	68	9	open	open	ADJ
ejpam-3544	68	10	if	if	SCONJ
ejpam-3544	68	11	and	and	CCONJ
ejpam-3544	68	12	only	only	ADV
ejpam-3544	68	13	if	if	SCONJ
ejpam-3544	68	14	there	there	PRON
ejpam-3544	68	15	exists	exist	VERB
ejpam-3544	68	16	an	an	DET
ejpam-3544	68	17	open	open	ADJ
ejpam-3544	68	18	set	set	NOUN
ejpam-3544	68	19	u	u	PRON
ejpam-3544	68	20	such	such	ADJ
ejpam-3544	68	21	that	that	SCONJ
ejpam-3544	68	22	u	u	PROPN
ejpam-3544	68	23	⊆	⊆	NUM
ejpam-3544	68	24	a	a	DET
ejpam-3544	68	25	⊆	⊆	NUM
ejpam-3544	68	26	cl(int(cl(u	cl(int(cl(u	NOUN
ejpam-3544	68	27	)	)	PUNCT
ejpam-3544	68	28	)	)	PUNCT
ejpam-3544	68	29	)	)	PUNCT
ejpam-3544	68	30	.	.	PUNCT
ejpam-3544	69	1	the	the	DET
ejpam-3544	69	2	following	follow	VERB
ejpam-3544	69	3	example	example	NOUN
ejpam-3544	69	4	shows	show	VERB
ejpam-3544	69	5	that	that	SCONJ
ejpam-3544	69	6	the	the	DET
ejpam-3544	69	7	necessary	necessary	ADJ
ejpam-3544	69	8	condition	condition	NOUN
ejpam-3544	69	9	(	(	PUNCT
ejpam-3544	69	10	a	a	PRON
ejpam-3544	69	11	is	be	AUX
ejpam-3544	69	12	β	β	NOUN
ejpam-3544	69	13	-	-	ADJ
ejpam-3544	69	14	open	open	ADJ
ejpam-3544	69	15	,	,	PUNCT
ejpam-3544	69	16	then	then	ADV
ejpam-3544	69	17	there	there	PRON
ejpam-3544	69	18	exists	exist	VERB
ejpam-3544	69	19	an	an	DET
ejpam-3544	69	20	open	open	ADJ
ejpam-3544	69	21	set	set	NOUN
ejpam-3544	69	22	u	u	PRON
ejpam-3544	69	23	such	such	ADJ
ejpam-3544	69	24	that	that	SCONJ
ejpam-3544	69	25	u	u	PROPN
ejpam-3544	69	26	⊆	⊆	NUM
ejpam-3544	69	27	a	a	DET
ejpam-3544	69	28	⊆	⊆	NUM
ejpam-3544	69	29	cl(int(cl(u	cl(int(cl(u	NOUN
ejpam-3544	69	30	)	)	PUNCT
ejpam-3544	69	31	)	)	PUNCT
ejpam-3544	69	32	)	)	PUNCT
ejpam-3544	69	33	)	)	PUNCT
ejpam-3544	70	1	in	in	ADP
ejpam-3544	70	2	[	[	X
ejpam-3544	70	3	lemma	lemma	PROPN
ejpam-3544	70	4	2	2	NUM
ejpam-3544	70	5	,	,	PUNCT
ejpam-3544	70	6	p.	p.	NOUN
ejpam-3544	70	7	895	895	NUM
ejpam-3544	70	8	]	]	PUNCT
ejpam-3544	70	9	is	be	AUX
ejpam-3544	70	10	not	not	PART
ejpam-3544	70	11	true	true	ADJ
ejpam-3544	70	12	in	in	ADP
ejpam-3544	70	13	general	general	ADJ
ejpam-3544	70	14	.	.	PUNCT
ejpam-3544	71	1	example	example	NOUN
ejpam-3544	71	2	2.3	2.3	NUM
ejpam-3544	71	3	.	.	PUNCT
ejpam-3544	72	1	let	let	VERB
ejpam-3544	72	2	x	x	PUNCT
ejpam-3544	72	3	=	=	PRON
ejpam-3544	72	4	{	{	PUNCT
ejpam-3544	72	5	1	1	NUM
ejpam-3544	72	6	,	,	PUNCT
ejpam-3544	72	7	2	2	NUM
ejpam-3544	72	8	,	,	PUNCT
ejpam-3544	72	9	3	3	NUM
ejpam-3544	72	10	,	,	PUNCT
ejpam-3544	72	11	4	4	NUM
ejpam-3544	72	12	}	}	PUNCT
ejpam-3544	72	13	and	and	CCONJ
ejpam-3544	72	14	τ	τ	PROPN
ejpam-3544	72	15	=	=	SYM
ejpam-3544	72	16	{	{	PUNCT
ejpam-3544	72	17	x	x	PROPN
ejpam-3544	72	18	,	,	PUNCT
ejpam-3544	72	19	φ	φ	NUM
ejpam-3544	72	20	,	,	PUNCT
ejpam-3544	72	21	{	{	PUNCT
ejpam-3544	72	22	1	1	NUM
ejpam-3544	72	23	,	,	PUNCT
ejpam-3544	72	24	2	2	NUM
ejpam-3544	72	25	,	,	PUNCT
ejpam-3544	72	26	3	3	NUM
ejpam-3544	72	27	}	}	PUNCT
ejpam-3544	72	28	}	}	PUNCT
ejpam-3544	72	29	.	.	PUNCT
ejpam-3544	73	1	take	take	VERB
ejpam-3544	73	2	a	a	DET
ejpam-3544	73	3	=	=	X
ejpam-3544	73	4	{	{	PUNCT
ejpam-3544	73	5	3	3	NUM
ejpam-3544	73	6	}	}	PUNCT
ejpam-3544	73	7	.	.	PUNCT
ejpam-3544	74	1	then	then	ADV
ejpam-3544	74	2	,	,	PUNCT
ejpam-3544	74	3	a	a	PRON
ejpam-3544	74	4	is	be	AUX
ejpam-3544	74	5	β	β	NOUN
ejpam-3544	74	6	-	-	ADJ
ejpam-3544	74	7	open	open	ADJ
ejpam-3544	74	8	,	,	PUNCT
ejpam-3544	74	9	but	but	CCONJ
ejpam-3544	74	10	6	6	NUM
ejpam-3544	74	11	∃	∃	NOUN
ejpam-3544	74	12	u	u	PROPN
ejpam-3544	74	13	∈	∈	PROPN
ejpam-3544	74	14	τ	τ	X
ejpam-3544	74	15	such	such	ADJ
ejpam-3544	74	16	that	that	SCONJ
ejpam-3544	74	17	u	u	PROPN
ejpam-3544	74	18	⊆	⊆	NUM
ejpam-3544	74	19	a	a	DET
ejpam-3544	74	20	⊆	⊆	NUM
ejpam-3544	74	21	cl(int(cl(u	cl(int(cl(u	NOUN
ejpam-3544	74	22	)	)	PUNCT
ejpam-3544	74	23	)	)	PUNCT
ejpam-3544	74	24	)	)	PUNCT
ejpam-3544	74	25	.	.	PUNCT
ejpam-3544	75	1	m.	m.	PROPN
ejpam-3544	75	2	hosny	hosny	PROPN
ejpam-3544	75	3	/	/	SYM
ejpam-3544	75	4	eur	eur	PROPN
ejpam-3544	75	5	.	.	PUNCT
ejpam-3544	76	1	j.	j.	PROPN
ejpam-3544	76	2	pure	pure	PROPN
ejpam-3544	76	3	appl	appl	PROPN
ejpam-3544	76	4	.	.	PROPN
ejpam-3544	76	5	math	math	PROPN
ejpam-3544	76	6	,	,	PUNCT
ejpam-3544	76	7	12	12	NUM
ejpam-3544	76	8	(	(	PUNCT
ejpam-3544	76	9	4	4	NUM
ejpam-3544	76	10	)	)	PUNCT
ejpam-3544	76	11	(	(	PUNCT
ejpam-3544	76	12	2019	2019	NUM
ejpam-3544	76	13	)	)	PUNCT
ejpam-3544	76	14	,	,	PUNCT
ejpam-3544	76	15	1656	1656	NUM
ejpam-3544	76	16	-	-	SYM
ejpam-3544	76	17	1660	1660	NUM
ejpam-3544	76	18	1658	1658	NUM
ejpam-3544	76	19	it	it	PRON
ejpam-3544	76	20	should	should	AUX
ejpam-3544	76	21	be	be	AUX
ejpam-3544	76	22	noted	note	VERB
ejpam-3544	76	23	that	that	SCONJ
ejpam-3544	76	24	,	,	PUNCT
ejpam-3544	76	25	in	in	ADP
ejpam-3544	76	26	the	the	DET
ejpam-3544	76	27	head	head	NOUN
ejpam-3544	76	28	of	of	ADP
ejpam-3544	76	29	[	[	X
ejpam-3544	76	30	lemma	lemma	PROPN
ejpam-3544	76	31	2	2	NUM
ejpam-3544	76	32	,	,	PUNCT
ejpam-3544	76	33	p.	p.	NOUN
ejpam-3544	76	34	895	895	NUM
ejpam-3544	76	35	]	]	PUNCT
ejpam-3544	76	36	the	the	DET
ejpam-3544	76	37	authors	author	NOUN
ejpam-3544	76	38	supposed	suppose	VERB
ejpam-3544	76	39	that	that	SCONJ
ejpam-3544	76	40	“	"	PUNCT
ejpam-3544	76	41	(	(	PUNCT
ejpam-3544	76	42	x	x	X
ejpam-3544	76	43	,	,	PUNCT
ejpam-3544	76	44	τ	τ	PROPN
ejpam-3544	76	45	,	,	PUNCT
ejpam-3544	76	46	i	i	NOUN
ejpam-3544	76	47	)	)	PUNCT
ejpam-3544	76	48	”	"	PUNCT
ejpam-3544	76	49	is	be	AUX
ejpam-3544	76	50	an	an	DET
ejpam-3544	76	51	ideal	ideal	ADJ
ejpam-3544	76	52	topological	topological	ADJ
ejpam-3544	76	53	space	space	NOUN
ejpam-3544	76	54	,	,	PUNCT
ejpam-3544	76	55	but	but	CCONJ
ejpam-3544	76	56	they	they	PRON
ejpam-3544	76	57	did	do	AUX
ejpam-3544	76	58	n’t	not	PART
ejpam-3544	76	59	use	use	VERB
ejpam-3544	76	60	it	it	PRON
ejpam-3544	76	61	in	in	ADP
ejpam-3544	76	62	the	the	DET
ejpam-3544	76	63	proof	proof	NOUN
ejpam-3544	76	64	as	as	SCONJ
ejpam-3544	76	65	this	this	DET
ejpam-3544	76	66	lemma	lemma	PROPN
ejpam-3544	76	67	studied	study	VERB
ejpam-3544	76	68	only	only	ADV
ejpam-3544	76	69	the	the	DET
ejpam-3544	76	70	properties	property	NOUN
ejpam-3544	76	71	of	of	ADP
ejpam-3544	76	72	β	β	ADJ
ejpam-3544	76	73	-	-	ADJ
ejpam-3544	76	74	open	open	ADJ
ejpam-3544	76	75	sets	set	NOUN
ejpam-3544	76	76	.	.	PUNCT
ejpam-3544	77	1	so	so	ADV
ejpam-3544	77	2	,	,	PUNCT
ejpam-3544	77	3	it	it	PRON
ejpam-3544	77	4	must	must	AUX
ejpam-3544	77	5	be	be	AUX
ejpam-3544	77	6	replaced	replace	VERB
ejpam-3544	77	7	by	by	ADP
ejpam-3544	77	8	“	"	PUNCT
ejpam-3544	77	9	(	(	PUNCT
ejpam-3544	77	10	x	x	NOUN
ejpam-3544	77	11	,	,	PUNCT
ejpam-3544	77	12	τ	τ	PROPN
ejpam-3544	77	13	)	)	PUNCT
ejpam-3544	77	14	”	"	PUNCT
ejpam-3544	77	15	is	be	AUX
ejpam-3544	77	16	a	a	DET
ejpam-3544	77	17	topological	topological	ADJ
ejpam-3544	77	18	space	space	NOUN
ejpam-3544	77	19	and	and	CCONJ
ejpam-3544	77	20	the	the	DET
ejpam-3544	77	21	correct	correct	ADJ
ejpam-3544	77	22	form	form	NOUN
ejpam-3544	77	23	of	of	ADP
ejpam-3544	77	24	this	this	DET
ejpam-3544	77	25	lemma	lemma	PROPN
ejpam-3544	77	26	is	be	AUX
ejpam-3544	77	27	:	:	PUNCT
ejpam-3544	77	28	lemma	lemma	PROPN
ejpam-3544	77	29	2.1	2.1	NUM
ejpam-3544	77	30	.	.	PUNCT
ejpam-3544	78	1	let	let	VERB
ejpam-3544	78	2	(	(	PUNCT
ejpam-3544	78	3	x	x	NOUN
ejpam-3544	78	4	,	,	PUNCT
ejpam-3544	78	5	τ	τ	X
ejpam-3544	78	6	)	)	PUNCT
ejpam-3544	78	7	be	be	VERB
ejpam-3544	78	8	a	a	DET
ejpam-3544	78	9	topological	topological	ADJ
ejpam-3544	78	10	space	space	NOUN
ejpam-3544	78	11	and	and	CCONJ
ejpam-3544	78	12	a	a	DET
ejpam-3544	78	13	⊆	⊆	NUM
ejpam-3544	78	14	x.	x.	NOUN
ejpam-3544	78	15	if	if	SCONJ
ejpam-3544	78	16	there	there	PRON
ejpam-3544	78	17	exists	exist	VERB
ejpam-3544	78	18	an	an	DET
ejpam-3544	78	19	open	open	ADJ
ejpam-3544	78	20	set	set	NOUN
ejpam-3544	78	21	u	u	PRON
ejpam-3544	78	22	such	such	ADJ
ejpam-3544	78	23	that	that	SCONJ
ejpam-3544	78	24	u	u	PROPN
ejpam-3544	78	25	⊆	⊆	NUM
ejpam-3544	78	26	a	a	DET
ejpam-3544	78	27	⊆	⊆	NUM
ejpam-3544	78	28	cl(int(cl(u	cl(int(cl(u	NOUN
ejpam-3544	78	29	)	)	PUNCT
ejpam-3544	78	30	)	)	PUNCT
ejpam-3544	78	31	)	)	PUNCT
ejpam-3544	78	32	,	,	PUNCT
ejpam-3544	78	33	then	then	ADV
ejpam-3544	78	34	a	a	PRON
ejpam-3544	78	35	is	be	AUX
ejpam-3544	78	36	β	β	NOUN
ejpam-3544	78	37	-	-	ADJ
ejpam-3544	78	38	open	open	ADJ
ejpam-3544	78	39	set	set	NOUN
ejpam-3544	78	40	.	.	PUNCT
ejpam-3544	79	1	in	in	ADP
ejpam-3544	79	2	[	[	X
ejpam-3544	79	3	[	[	X
ejpam-3544	79	4	4	4	NUM
ejpam-3544	79	5	]	]	PUNCT
ejpam-3544	79	6	,	,	PUNCT
ejpam-3544	79	7	lemma	lemma	PROPN
ejpam-3544	79	8	3	3	NUM
ejpam-3544	79	9	,	,	PUNCT
ejpam-3544	79	10	p.	p.	NOUN
ejpam-3544	79	11	895	895	NUM
ejpam-3544	79	12	]	]	PUNCT
ejpam-3544	79	13	,	,	PUNCT
ejpam-3544	79	14	the	the	DET
ejpam-3544	79	15	authors	author	NOUN
ejpam-3544	79	16	proved	prove	VERB
ejpam-3544	79	17	in	in	ADP
ejpam-3544	79	18	part	part	NOUN
ejpam-3544	79	19	(	(	PUNCT
ejpam-3544	79	20	iii	iii	NOUN
ejpam-3544	79	21	)	)	PUNCT
ejpam-3544	79	22	that	that	SCONJ
ejpam-3544	79	23	in	in	ADP
ejpam-3544	79	24	an	an	DET
ejpam-3544	79	25	ideal	ideal	ADJ
ejpam-3544	79	26	topological	topological	ADJ
ejpam-3544	79	27	space	space	NOUN
ejpam-3544	79	28	(	(	PUNCT
ejpam-3544	79	29	x	x	X
ejpam-3544	79	30	,	,	PUNCT
ejpam-3544	79	31	τ	τ	PROPN
ejpam-3544	79	32	,	,	PUNCT
ejpam-3544	79	33	i	i	PROPN
ejpam-3544	79	34	)	)	PUNCT
ejpam-3544	79	35	.	.	PUNCT
ejpam-3544	80	1	if	if	SCONJ
ejpam-3544	80	2	a	a	PRON
ejpam-3544	80	3	is	be	AUX
ejpam-3544	80	4	β	β	NOUN
ejpam-3544	80	5	-	-	ADJ
ejpam-3544	80	6	open	open	ADJ
ejpam-3544	80	7	,	,	PUNCT
ejpam-3544	80	8	then	then	ADV
ejpam-3544	80	9	a	a	PRON
ejpam-3544	80	10	is	be	AUX
ejpam-3544	80	11	βi	βi	NOUN
ejpam-3544	80	12	-	-	ADJ
ejpam-3544	80	13	open	open	ADJ
ejpam-3544	80	14	.	.	PUNCT
ejpam-3544	81	1	in	in	ADP
ejpam-3544	81	2	example	example	NOUN
ejpam-3544	81	3	2.3	2.3	NUM
ejpam-3544	81	4	,	,	PUNCT
ejpam-3544	81	5	put	put	VERB
ejpam-3544	81	6	i	i	PRON
ejpam-3544	81	7	=	=	PUNCT
ejpam-3544	81	8	{	{	PUNCT
ejpam-3544	81	9	φ	φ	PROPN
ejpam-3544	81	10	,	,	PUNCT
ejpam-3544	81	11	{	{	PUNCT
ejpam-3544	81	12	3	3	NUM
ejpam-3544	81	13	}	}	PUNCT
ejpam-3544	81	14	}	}	PUNCT
ejpam-3544	81	15	.	.	PUNCT
ejpam-3544	82	1	then	then	ADV
ejpam-3544	82	2	it	it	PRON
ejpam-3544	82	3	shows	show	VERB
ejpam-3544	82	4	part	part	NOUN
ejpam-3544	82	5	(	(	PUNCT
ejpam-3544	82	6	iii	iii	NOUN
ejpam-3544	82	7	)	)	PUNCT
ejpam-3544	82	8	in	in	ADP
ejpam-3544	82	9	[	[	X
ejpam-3544	82	10	lemma	lemma	PROPN
ejpam-3544	82	11	3	3	NUM
ejpam-3544	82	12	,	,	PUNCT
ejpam-3544	82	13	p.	p.	NOUN
ejpam-3544	82	14	895	895	NUM
ejpam-3544	82	15	]	]	PUNCT
ejpam-3544	82	16	is	be	AUX
ejpam-3544	82	17	not	not	PART
ejpam-3544	82	18	true	true	ADJ
ejpam-3544	82	19	in	in	ADP
ejpam-3544	82	20	general	general	ADJ
ejpam-3544	82	21	.	.	PUNCT
ejpam-3544	83	1	take	take	VERB
ejpam-3544	83	2	a	a	DET
ejpam-3544	83	3	=	=	X
ejpam-3544	83	4	{	{	PUNCT
ejpam-3544	83	5	1	1	NUM
ejpam-3544	83	6	}	}	PUNCT
ejpam-3544	83	7	.	.	PUNCT
ejpam-3544	84	1	then	then	ADV
ejpam-3544	84	2	,	,	PUNCT
ejpam-3544	84	3	a	a	PRON
ejpam-3544	84	4	is	be	AUX
ejpam-3544	84	5	β	β	NOUN
ejpam-3544	84	6	-	-	ADJ
ejpam-3544	84	7	open	open	ADJ
ejpam-3544	84	8	,	,	PUNCT
ejpam-3544	84	9	but	but	CCONJ
ejpam-3544	84	10	a	a	PRON
ejpam-3544	84	11	is	be	AUX
ejpam-3544	84	12	not	not	PART
ejpam-3544	84	13	βi	βi	ADJ
ejpam-3544	84	14	-	-	NOUN
ejpam-3544	84	15	open	open	ADJ
ejpam-3544	84	16	.	.	PUNCT
ejpam-3544	85	1	in	in	ADP
ejpam-3544	85	2	[	[	X
ejpam-3544	85	3	[	[	X
ejpam-3544	85	4	4	4	NUM
ejpam-3544	85	5	]	]	PUNCT
ejpam-3544	85	6	,	,	PUNCT
ejpam-3544	85	7	lemma	lemma	PROPN
ejpam-3544	85	8	4	4	NUM
ejpam-3544	85	9	,	,	PUNCT
ejpam-3544	85	10	p.	p.	NOUN
ejpam-3544	85	11	896	896	NUM
ejpam-3544	85	12	]	]	PUNCT
ejpam-3544	85	13	,	,	PUNCT
ejpam-3544	85	14	the	the	DET
ejpam-3544	85	15	authors	author	NOUN
ejpam-3544	85	16	proved	prove	VERB
ejpam-3544	85	17	that	that	SCONJ
ejpam-3544	85	18	in	in	ADP
ejpam-3544	85	19	an	an	DET
ejpam-3544	85	20	ideal	ideal	ADJ
ejpam-3544	85	21	topological	topological	ADJ
ejpam-3544	85	22	space	space	NOUN
ejpam-3544	85	23	(	(	PUNCT
ejpam-3544	85	24	x	x	X
ejpam-3544	85	25	,	,	PUNCT
ejpam-3544	85	26	τ	τ	PROPN
ejpam-3544	85	27	,	,	PUNCT
ejpam-3544	85	28	i	i	PROPN
ejpam-3544	85	29	)	)	PUNCT
ejpam-3544	85	30	.	.	PUNCT
ejpam-3544	86	1	if	if	SCONJ
ejpam-3544	86	2	i	i	PRON
ejpam-3544	86	3	is	be	AUX
ejpam-3544	86	4	not	not	PART
ejpam-3544	86	5	countably	countably	ADV
ejpam-3544	86	6	additive	additive	ADJ
ejpam-3544	86	7	,	,	PUNCT
ejpam-3544	86	8	then	then	ADV
ejpam-3544	86	9	the	the	DET
ejpam-3544	86	10	following	following	ADJ
ejpam-3544	86	11	statements	statement	NOUN
ejpam-3544	86	12	are	be	AUX
ejpam-3544	86	13	equivalent	equivalent	ADJ
ejpam-3544	86	14	.	.	PUNCT
ejpam-3544	87	1	(	(	PUNCT
ejpam-3544	87	2	i	i	NOUN
ejpam-3544	87	3	)	)	PUNCT
ejpam-3544	87	4	if	if	SCONJ
ejpam-3544	87	5	i	i	PRON
ejpam-3544	87	6	=	=	X
ejpam-3544	87	7	{	{	PUNCT
ejpam-3544	87	8	φ	φ	NOUN
ejpam-3544	87	9	}	}	PUNCT
ejpam-3544	87	10	.	.	PUNCT
ejpam-3544	88	1	(	(	PUNCT
ejpam-3544	88	2	ii	ii	NOUN
ejpam-3544	88	3	)	)	PUNCT
ejpam-3544	88	4	a	a	PRON
ejpam-3544	88	5	is	be	AUX
ejpam-3544	88	6	a	a	DET
ejpam-3544	88	7	β	β	NOUN
ejpam-3544	88	8	-	-	ADJ
ejpam-3544	88	9	open	open	ADJ
ejpam-3544	88	10	set	set	NOUN
ejpam-3544	88	11	if	if	SCONJ
ejpam-3544	88	12	and	and	CCONJ
ejpam-3544	88	13	only	only	ADV
ejpam-3544	88	14	if	if	SCONJ
ejpam-3544	88	15	a	a	PRON
ejpam-3544	88	16	is	be	AUX
ejpam-3544	88	17	a	a	DET
ejpam-3544	88	18	βi	βi	ADV
ejpam-3544	88	19	-	-	PUNCT
ejpam-3544	88	20	open	open	ADJ
ejpam-3544	88	21	set	set	NOUN
ejpam-3544	88	22	.	.	PUNCT
ejpam-3544	89	1	1	1	X
ejpam-3544	89	2	.	.	X
ejpam-3544	89	3	in	in	ADP
ejpam-3544	89	4	example	example	NOUN
ejpam-3544	89	5	2.3	2.3	NUM
ejpam-3544	89	6	,	,	PUNCT
ejpam-3544	89	7	i	i	PRON
ejpam-3544	89	8	=	=	PUNCT
ejpam-3544	89	9	{	{	PUNCT
ejpam-3544	89	10	φ	φ	NOUN
ejpam-3544	89	11	}	}	PUNCT
ejpam-3544	89	12	.	.	PUNCT
ejpam-3544	90	1	then	then	ADV
ejpam-3544	90	2	it	it	PRON
ejpam-3544	90	3	shows	show	VERB
ejpam-3544	90	4	for	for	ADP
ejpam-3544	90	5	[	[	X
ejpam-3544	90	6	(	(	PUNCT
ejpam-3544	90	7	i	i	NOUN
ejpam-3544	90	8	)	)	PUNCT
ejpam-3544	90	9	→	→	SYM
ejpam-3544	90	10	(	(	PUNCT
ejpam-3544	90	11	ii	ii	NOUN
ejpam-3544	90	12	)	)	PUNCT
ejpam-3544	90	13	]	]	PUNCT
ejpam-3544	90	14	in	in	ADP
ejpam-3544	90	15	[	[	X
ejpam-3544	90	16	lemma	lemma	PROPN
ejpam-3544	90	17	4	4	NUM
ejpam-3544	90	18	,	,	PUNCT
ejpam-3544	90	19	p.	p.	NOUN
ejpam-3544	90	20	896	896	NUM
ejpam-3544	90	21	]	]	PUNCT
ejpam-3544	90	22	is	be	AUX
ejpam-3544	90	23	not	not	PART
ejpam-3544	90	24	true	true	ADJ
ejpam-3544	90	25	in	in	ADP
ejpam-3544	90	26	general	general	ADJ
ejpam-3544	90	27	.	.	PUNCT
ejpam-3544	91	1	take	take	VERB
ejpam-3544	91	2	a	a	DET
ejpam-3544	91	3	=	=	X
ejpam-3544	91	4	{	{	PUNCT
ejpam-3544	91	5	3	3	NUM
ejpam-3544	91	6	}	}	PUNCT
ejpam-3544	91	7	.	.	PUNCT
ejpam-3544	92	1	then	then	ADV
ejpam-3544	92	2	,	,	PUNCT
ejpam-3544	92	3	a	a	PRON
ejpam-3544	92	4	is	be	AUX
ejpam-3544	92	5	β	β	NOUN
ejpam-3544	92	6	-	-	ADJ
ejpam-3544	92	7	open	open	ADJ
ejpam-3544	92	8	,	,	PUNCT
ejpam-3544	92	9	but	but	CCONJ
ejpam-3544	92	10	a	a	PRON
ejpam-3544	92	11	is	be	AUX
ejpam-3544	92	12	not	not	PART
ejpam-3544	92	13	βi	βi	ADJ
ejpam-3544	92	14	-	-	NOUN
ejpam-3544	92	15	open	open	ADJ
ejpam-3544	92	16	.	.	PUNCT
ejpam-3544	93	1	2	2	X
ejpam-3544	93	2	.	.	X
ejpam-3544	93	3	the	the	DET
ejpam-3544	93	4	following	follow	VERB
ejpam-3544	93	5	example	example	NOUN
ejpam-3544	93	6	shows	show	VERB
ejpam-3544	93	7	that	that	SCONJ
ejpam-3544	93	8	for	for	ADP
ejpam-3544	93	9	[	[	X
ejpam-3544	93	10	(	(	PUNCT
ejpam-3544	93	11	ii)→	ii)→	NOUN
ejpam-3544	93	12	(	(	PUNCT
ejpam-3544	93	13	i	i	NOUN
ejpam-3544	93	14	)	)	PUNCT
ejpam-3544	93	15	]	]	PUNCT
ejpam-3544	93	16	in	in	ADP
ejpam-3544	93	17	[	[	X
ejpam-3544	93	18	lemma	lemma	PROPN
ejpam-3544	93	19	4	4	NUM
ejpam-3544	93	20	,	,	PUNCT
ejpam-3544	93	21	p.	p.	NOUN
ejpam-3544	93	22	896	896	NUM
ejpam-3544	93	23	]	]	PUNCT
ejpam-3544	93	24	is	be	AUX
ejpam-3544	93	25	not	not	PART
ejpam-3544	93	26	true	true	ADJ
ejpam-3544	93	27	in	in	ADP
ejpam-3544	93	28	general	general	ADJ
ejpam-3544	93	29	.	.	PUNCT
ejpam-3544	93	30	example	example	NOUN
ejpam-3544	94	1	2.4	2.4	NUM
ejpam-3544	94	2	.	.	PUNCT
ejpam-3544	95	1	let	let	VERB
ejpam-3544	95	2	x	x	PUNCT
ejpam-3544	95	3	=	=	PRON
ejpam-3544	95	4	{	{	PUNCT
ejpam-3544	95	5	1	1	NUM
ejpam-3544	95	6	,	,	PUNCT
ejpam-3544	95	7	2	2	NUM
ejpam-3544	95	8	,	,	PUNCT
ejpam-3544	95	9	3	3	NUM
ejpam-3544	95	10	,	,	PUNCT
ejpam-3544	95	11	4	4	NUM
ejpam-3544	95	12	}	}	PUNCT
ejpam-3544	95	13	,	,	PUNCT
ejpam-3544	95	14	i	i	PRON
ejpam-3544	95	15	=	=	NOUN
ejpam-3544	95	16	p	p	X
ejpam-3544	95	17	(	(	PUNCT
ejpam-3544	95	18	x	x	NOUN
ejpam-3544	95	19	)	)	PUNCT
ejpam-3544	95	20	and	and	CCONJ
ejpam-3544	95	21	τ	τ	X
ejpam-3544	95	22	=	=	SYM
ejpam-3544	95	23	{	{	PUNCT
ejpam-3544	95	24	x	x	PROPN
ejpam-3544	95	25	,	,	PUNCT
ejpam-3544	95	26	φ	φ	NUM
ejpam-3544	95	27	}	}	PUNCT
ejpam-3544	95	28	.	.	PUNCT
ejpam-3544	96	1	then	then	ADV
ejpam-3544	96	2	,	,	PUNCT
ejpam-3544	96	3	the	the	DET
ejpam-3544	96	4	family	family	NOUN
ejpam-3544	96	5	of	of	ADP
ejpam-3544	96	6	all	all	DET
ejpam-3544	96	7	β	β	ADJ
ejpam-3544	96	8	-	-	ADJ
ejpam-3544	96	9	open	open	ADJ
ejpam-3544	96	10	sets	set	NOUN
ejpam-3544	96	11	is	be	AUX
ejpam-3544	96	12	p	p	NOUN
ejpam-3544	96	13	(	(	PUNCT
ejpam-3544	96	14	x	x	X
ejpam-3544	96	15	)	)	PUNCT
ejpam-3544	96	16	which	which	PRON
ejpam-3544	96	17	is	be	AUX
ejpam-3544	96	18	precisely	precisely	ADV
ejpam-3544	96	19	the	the	DET
ejpam-3544	96	20	family	family	NOUN
ejpam-3544	96	21	of	of	ADP
ejpam-3544	96	22	all	all	DET
ejpam-3544	96	23	βi	βi	ADJ
ejpam-3544	96	24	-	-	PUNCT
ejpam-3544	96	25	open	open	ADJ
ejpam-3544	96	26	sets	set	NOUN
ejpam-3544	96	27	,	,	PUNCT
ejpam-3544	96	28	but	but	CCONJ
ejpam-3544	96	29	i	i	PRON
ejpam-3544	96	30	6=	6=	PROPN
ejpam-3544	96	31	{	{	PUNCT
ejpam-3544	96	32	φ	φ	NOUN
ejpam-3544	96	33	}	}	PUNCT
ejpam-3544	96	34	.	.	PUNCT
ejpam-3544	97	1	the	the	DET
ejpam-3544	97	2	following	follow	VERB
ejpam-3544	97	3	lemma	lemma	PROPN
ejpam-3544	97	4	is	be	AUX
ejpam-3544	97	5	the	the	DET
ejpam-3544	97	6	correct	correct	ADJ
ejpam-3544	97	7	form	form	NOUN
ejpam-3544	97	8	of	of	ADP
ejpam-3544	97	9	[	[	X
ejpam-3544	97	10	lemma	lemma	PROPN
ejpam-3544	97	11	4	4	NUM
ejpam-3544	97	12	,	,	PUNCT
ejpam-3544	97	13	p.	p.	NOUN
ejpam-3544	97	14	896	896	NUM
ejpam-3544	97	15	]	]	PUNCT
ejpam-3544	97	16	.	.	PUNCT
ejpam-3544	98	1	lemma	lemma	PROPN
ejpam-3544	98	2	2.2	2.2	NUM
ejpam-3544	98	3	.	.	PUNCT
ejpam-3544	99	1	let	let	VERB
ejpam-3544	99	2	(	(	PUNCT
ejpam-3544	99	3	x	x	X
ejpam-3544	99	4	,	,	PUNCT
ejpam-3544	99	5	τ	τ	PROPN
ejpam-3544	99	6	,	,	PUNCT
ejpam-3544	99	7	i	i	PRON
ejpam-3544	99	8	)	)	PUNCT
ejpam-3544	99	9	be	be	VERB
ejpam-3544	99	10	an	an	DET
ejpam-3544	99	11	ideal	ideal	ADJ
ejpam-3544	99	12	topological	topological	ADJ
ejpam-3544	99	13	space	space	NOUN
ejpam-3544	99	14	and	and	CCONJ
ejpam-3544	99	15	a	a	DET
ejpam-3544	99	16	⊆	⊆	NUM
ejpam-3544	99	17	x.	x.	NOUN
ejpam-3544	99	18	if	if	SCONJ
ejpam-3544	99	19	i	i	PRON
ejpam-3544	99	20	=	=	SYM
ejpam-3544	99	21	{	{	PUNCT
ejpam-3544	99	22	φ	φ	NOUN
ejpam-3544	99	23	}	}	PUNCT
ejpam-3544	99	24	and	and	CCONJ
ejpam-3544	99	25	a	a	PRON
ejpam-3544	99	26	is	be	AUX
ejpam-3544	99	27	a	a	DET
ejpam-3544	99	28	βi	βi	ADV
ejpam-3544	99	29	-	-	PUNCT
ejpam-3544	99	30	open	open	ADJ
ejpam-3544	99	31	set	set	NOUN
ejpam-3544	99	32	,	,	PUNCT
ejpam-3544	99	33	then	then	ADV
ejpam-3544	99	34	a	a	PRON
ejpam-3544	99	35	is	be	AUX
ejpam-3544	99	36	a	a	DET
ejpam-3544	99	37	β	β	NOUN
ejpam-3544	99	38	-	-	ADJ
ejpam-3544	99	39	open	open	ADJ
ejpam-3544	99	40	set	set	NOUN
ejpam-3544	99	41	.	.	PUNCT
ejpam-3544	100	1	it	it	PRON
ejpam-3544	100	2	should	should	AUX
ejpam-3544	100	3	be	be	AUX
ejpam-3544	100	4	noted	note	VERB
ejpam-3544	100	5	that	that	SCONJ
ejpam-3544	100	6	,	,	PUNCT
ejpam-3544	100	7	i	i	PRON
ejpam-3544	100	8	can	can	AUX
ejpam-3544	100	9	add	add	VERB
ejpam-3544	100	10	examples	example	NOUN
ejpam-3544	100	11	in	in	ADP
ejpam-3544	100	12	the	the	DET
ejpam-3544	100	13	same	same	ADJ
ejpam-3544	100	14	manner	manner	NOUN
ejpam-3544	100	15	,	,	PUNCT
ejpam-3544	100	16	to	to	PART
ejpam-3544	100	17	show	show	VERB
ejpam-3544	100	18	that	that	SCONJ
ejpam-3544	100	19	[	[	X
ejpam-3544	100	20	theorem	theorem	ADJ
ejpam-3544	100	21	1	1	NUM
ejpam-3544	100	22	,	,	PUNCT
ejpam-3544	100	23	p.	p.	NOUN
ejpam-3544	100	24	896	896	NUM
ejpam-3544	100	25	]	]	PUNCT
ejpam-3544	100	26	,	,	PUNCT
ejpam-3544	100	27	[	[	X
ejpam-3544	100	28	theorem	theorem	ADJ
ejpam-3544	100	29	8	8	NUM
ejpam-3544	100	30	for	for	ADP
ejpam-3544	100	31	part	part	NOUN
ejpam-3544	100	32	(	(	PUNCT
ejpam-3544	100	33	ii	ii	NOUN
ejpam-3544	100	34	)	)	PUNCT
ejpam-3544	100	35	,	,	PUNCT
ejpam-3544	100	36	claim	claim	VERB
ejpam-3544	100	37	1	1	NUM
ejpam-3544	100	38	,	,	PUNCT
ejpam-3544	100	39	claim	claim	VERB
ejpam-3544	100	40	2	2	NUM
ejpam-3544	100	41	p.	p.	NOUN
ejpam-3544	100	42	899	899	NUM
ejpam-3544	100	43	]	]	PUNCT
ejpam-3544	100	44	and	and	CCONJ
ejpam-3544	100	45	[	[	AUX
ejpam-3544	100	46	theorem	theorem	ADJ
ejpam-3544	100	47	9	9	NUM
ejpam-3544	100	48	,	,	PUNCT
ejpam-3544	100	49	p.	p.	NOUN
ejpam-3544	100	50	900	900	NUM
ejpam-3544	100	51	]	]	PUNCT
ejpam-3544	100	52	,	,	PUNCT
ejpam-3544	100	53	are	be	AUX
ejpam-3544	100	54	also	also	ADV
ejpam-3544	100	55	not	not	PART
ejpam-3544	100	56	true	true	ADJ
ejpam-3544	100	57	in	in	ADP
ejpam-3544	100	58	general	general	ADJ
ejpam-3544	100	59	.	.	PUNCT
ejpam-3544	101	1	acknowledgements	acknowledgement	VERB
ejpam-3544	101	2	the	the	DET
ejpam-3544	101	3	author	author	NOUN
ejpam-3544	101	4	would	would	AUX
ejpam-3544	101	5	like	like	VERB
ejpam-3544	101	6	to	to	PART
ejpam-3544	101	7	express	express	VERB
ejpam-3544	101	8	her	her	PRON
ejpam-3544	101	9	sincere	sincere	ADJ
ejpam-3544	101	10	thanks	thank	NOUN
ejpam-3544	101	11	and	and	CCONJ
ejpam-3544	101	12	gratitude	gratitude	NOUN
ejpam-3544	101	13	to	to	ADP
ejpam-3544	101	14	king	king	PROPN
ejpam-3544	101	15	khalid	khalid	PROPN
ejpam-3544	101	16	university	university	PROPN
ejpam-3544	101	17	,	,	PUNCT
ejpam-3544	101	18	saudi	saudi	PROPN
ejpam-3544	101	19	arabia	arabia	PROPN
ejpam-3544	101	20	for	for	ADP
ejpam-3544	101	21	providing	provide	VERB
ejpam-3544	101	22	administrative	administrative	ADJ
ejpam-3544	101	23	and	and	CCONJ
ejpam-3544	101	24	technical	technical	ADJ
ejpam-3544	101	25	support	support	NOUN
ejpam-3544	101	26	.	.	PUNCT
ejpam-3544	102	1	references	reference	NOUN
ejpam-3544	102	2	1659	1659	NUM
ejpam-3544	102	3	references	reference	NOUN
ejpam-3544	102	4	[	[	X
ejpam-3544	102	5	1	1	NUM
ejpam-3544	102	6	]	]	PUNCT
ejpam-3544	102	7	m.	m.	NOUN
ejpam-3544	102	8	e.	e.	PROPN
ejpam-3544	102	9	abd	abd	PROPN
ejpam-3544	102	10	el	el	PROPN
ejpam-3544	102	11	-	-	PROPN
ejpam-3544	102	12	monsef	monsef	PROPN
ejpam-3544	102	13	,	,	PUNCT
ejpam-3544	102	14	s.	s.	PROPN
ejpam-3544	102	15	n.	n.	PROPN
ejpam-3544	102	16	el	el	PROPN
ejpam-3544	102	17	-	-	PROPN
ejpam-3544	102	18	deeb	deeb	PROPN
ejpam-3544	102	19	,	,	PUNCT
ejpam-3544	102	20	r.	r.	PROPN
ejpam-3544	102	21	a.	a.	PROPN
ejpam-3544	102	22	mahmoud	mahmoud	PROPN
ejpam-3544	102	23	,	,	PUNCT
ejpam-3544	102	24	β	β	ADJ
ejpam-3544	102	25	-	-	ADJ
ejpam-3544	102	26	open	open	ADJ
ejpam-3544	102	27	sets	set	NOUN
ejpam-3544	102	28	and	and	CCONJ
ejpam-3544	102	29	β	β	ADJ
ejpam-3544	102	30	-	-	ADJ
ejpam-3544	102	31	continuous	continuous	ADJ
ejpam-3544	102	32	mappings	mapping	NOUN
ejpam-3544	102	33	,	,	PUNCT
ejpam-3544	102	34	bull	bull	PROPN
ejpam-3544	102	35	fac	fac	PROPN
ejpam-3544	102	36	sci	sci	PROPN
ejpam-3544	102	37	assiut	assiut	PROPN
ejpam-3544	102	38	univ	univ	PROPN
ejpam-3544	102	39	12	12	NUM
ejpam-3544	102	40	(	(	PUNCT
ejpam-3544	102	41	1983	1983	NUM
ejpam-3544	102	42	)	)	PUNCT
ejpam-3544	102	43	77–90	77–90	NUM
ejpam-3544	102	44	.	.	PUNCT
ejpam-3544	103	1	[	[	X
ejpam-3544	103	2	2	2	NUM
ejpam-3544	103	3	]	]	X
ejpam-3544	103	4	m.e	m.e	PROPN
ejpam-3544	103	5	.	.	PROPN
ejpam-3544	103	6	abd	abd	PROPN
ejpam-3544	103	7	el	el	PROPN
ejpam-3544	103	8	-	-	PROPN
ejpam-3544	103	9	monsef	monsef	ADJ
ejpam-3544	103	10	,	,	PUNCT
ejpam-3544	103	11	a.a	a.a	PROPN
ejpam-3544	103	12	.	.	PROPN
ejpam-3544	103	13	nasef	nasef	PROPN
ejpam-3544	103	14	,	,	PUNCT
ejpam-3544	103	15	a.e	a.e	PROPN
ejpam-3544	103	16	.	.	PROPN
ejpam-3544	103	17	radwan	radwan	PROPN
ejpam-3544	103	18	,	,	PUNCT
ejpam-3544	103	19	f.a	f.a	PROPN
ejpam-3544	103	20	.	.	PROPN
ejpam-3544	103	21	ibrahem	ibrahem	PROPN
ejpam-3544	103	22	,	,	PUNCT
ejpam-3544	103	23	r.b	r.b	PROPN
ejpam-3544	103	24	.	.	PROPN
ejpam-3544	103	25	esmaeel	esmaeel	PROPN
ejpam-3544	103	26	,	,	PUNCT
ejpam-3544	103	27	some	some	DET
ejpam-3544	103	28	properties	property	NOUN
ejpam-3544	103	29	of	of	ADP
ejpam-3544	103	30	semi	semi	ADJ
ejpam-3544	103	31	-	-	ADJ
ejpam-3544	103	32	open	open	ADJ
ejpam-3544	103	33	sets	set	NOUN
ejpam-3544	103	34	with	with	ADP
ejpam-3544	103	35	respect	respect	NOUN
ejpam-3544	103	36	to	to	ADP
ejpam-3544	103	37	an	an	DET
ejpam-3544	103	38	ideal	ideal	NOUN
ejpam-3544	103	39	,	,	PUNCT
ejpam-3544	103	40	(	(	PUNCT
ejpam-3544	103	41	submitted	submit	VERB
ejpam-3544	103	42	)	)	PUNCT
ejpam-3544	103	43	.	.	PUNCT
ejpam-3544	104	1	[	[	X
ejpam-3544	104	2	3	3	X
ejpam-3544	104	3	]	]	X
ejpam-3544	104	4	f.g	f.g	NOUN
ejpam-3544	104	5	.	.	PUNCT
ejpam-3544	104	6	arenas	arenas	PROPN
ejpam-3544	104	7	,	,	PUNCT
ejpam-3544	104	8	j.	j.	PROPN
ejpam-3544	104	9	dontchev	dontchev	PROPN
ejpam-3544	104	10	,	,	PUNCT
ejpam-3544	104	11	m.l	m.l	PROPN
ejpam-3544	104	12	.	.	PROPN
ejpam-3544	104	13	puertas	puertas	PROPN
ejpam-3544	104	14	,	,	PUNCT
ejpam-3544	104	15	idealization	idealization	NOUN
ejpam-3544	104	16	of	of	ADP
ejpam-3544	104	17	some	some	DET
ejpam-3544	104	18	weak	weak	ADJ
ejpam-3544	104	19	separation	separation	NOUN
ejpam-3544	104	20	axioms	axiom	NOUN
ejpam-3544	104	21	,	,	PUNCT
ejpam-3544	104	22	acta	acta	PROPN
ejpam-3544	104	23	math	math	PROPN
ejpam-3544	104	24	.	.	PUNCT
ejpam-3544	105	1	hungar	hungar	NOUN
ejpam-3544	105	2	.	.	PUNCT
ejpam-3544	106	1	89	89	NUM
ejpam-3544	106	2	(	(	PUNCT
ejpam-3544	106	3	2000	2000	NUM
ejpam-3544	106	4	)	)	PUNCT
ejpam-3544	106	5	47–53	47–53	NOUN
ejpam-3544	106	6	.	.	PUNCT
ejpam-3544	107	1	[	[	X
ejpam-3544	107	2	4	4	X
ejpam-3544	107	3	]	]	X
ejpam-3544	107	4	glaisa	glaisa	VERB
ejpam-3544	107	5	t.	t.	PROPN
ejpam-3544	107	6	catalan	catalan	PROPN
ejpam-3544	107	7	,	,	PUNCT
ejpam-3544	107	8	roberto	roberto	PROPN
ejpam-3544	107	9	n.	n.	PROPN
ejpam-3544	107	10	padua	padua	PROPN
ejpam-3544	107	11	,	,	PUNCT
ejpam-3544	107	12	michael	michael	PROPN
ejpam-3544	107	13	p.	p.	PROPN
ejpam-3544	107	14	baldado	baldado	PROPN
ejpam-3544	108	1	jr	jr	PROPN
ejpam-3544	108	2	,	,	PUNCT
ejpam-3544	108	3	on	on	ADP
ejpam-3544	108	4	β	β	ADJ
ejpam-3544	108	5	-	-	ADJ
ejpam-3544	108	6	open	open	ADJ
ejpam-3544	108	7	sets	set	NOUN
ejpam-3544	108	8	and	and	CCONJ
ejpam-3544	108	9	ideals	ideal	NOUN
ejpam-3544	108	10	in	in	ADP
ejpam-3544	108	11	topological	topological	ADJ
ejpam-3544	108	12	spaces	space	NOUN
ejpam-3544	108	13	,	,	PUNCT
ejpam-3544	108	14	european	european	PROPN
ejpam-3544	108	15	journal	journal	PROPN
ejpam-3544	108	16	of	of	ADP
ejpam-3544	108	17	pure	pure	ADJ
ejpam-3544	108	18	and	and	CCONJ
ejpam-3544	108	19	applied	applied	ADJ
ejpam-3544	108	20	mathematics	mathematic	NOUN
ejpam-3544	108	21	6	6	NUM
ejpam-3544	108	22	(	(	PUNCT
ejpam-3544	108	23	2019	2019	NUM
ejpam-3544	108	24	)	)	PUNCT
ejpam-3544	109	1	893–903	893–903	NUM
ejpam-3544	109	2	.	.	PUNCT
ejpam-3544	110	1	[	[	X
ejpam-3544	110	2	5	5	X
ejpam-3544	110	3	]	]	PUNCT
ejpam-3544	110	4	e.	e.	PROPN
ejpam-3544	110	5	ekici	ekici	PROPN
ejpam-3544	110	6	,	,	PUNCT
ejpam-3544	110	7	t.	t.	PROPN
ejpam-3544	110	8	noiri	noiri	PROPN
ejpam-3544	110	9	,	,	PUNCT
ejpam-3544	110	10	∗-extremally	∗-extremally	ADV
ejpam-3544	110	11	disconnected	disconnect	VERB
ejpam-3544	110	12	ideal	ideal	ADJ
ejpam-3544	110	13	topological	topological	ADJ
ejpam-3544	110	14	spaces	space	NOUN
ejpam-3544	110	15	,	,	PUNCT
ejpam-3544	110	16	acta	acta	PROPN
ejpam-3544	110	17	math	math	PROPN
ejpam-3544	110	18	.	.	PUNCT
ejpam-3544	111	1	hungar	hungar	NOUN
ejpam-3544	111	2	.	.	PUNCT
ejpam-3544	112	1	122	122	NUM
ejpam-3544	112	2	(	(	PUNCT
ejpam-3544	112	3	2009	2009	NUM
ejpam-3544	112	4	)	)	PUNCT
ejpam-3544	112	5	81–90	81–90	NUM
ejpam-3544	112	6	.	.	PUNCT
ejpam-3544	113	1	[	[	X
ejpam-3544	113	2	6	6	NUM
ejpam-3544	113	3	]	]	PUNCT
ejpam-3544	113	4	e.	e.	PROPN
ejpam-3544	113	5	hatir	hatir	PROPN
ejpam-3544	113	6	,	,	PUNCT
ejpam-3544	113	7	t.	t.	PROPN
ejpam-3544	113	8	noiri	noiri	PROPN
ejpam-3544	113	9	,	,	PUNCT
ejpam-3544	113	10	on	on	ADP
ejpam-3544	113	11	semi	semi	ADJ
ejpam-3544	113	12	-	-	ADJ
ejpam-3544	113	13	i	i	PRON
ejpam-3544	113	14	-	-	PUNCT
ejpam-3544	113	15	open	open	ADJ
ejpam-3544	113	16	set	set	NOUN
ejpam-3544	113	17	and	and	CCONJ
ejpam-3544	113	18	semi	semi	ADJ
ejpam-3544	113	19	-	-	ADJ
ejpam-3544	113	20	i	i	ADJ
ejpam-3544	113	21	-	-	PUNCT
ejpam-3544	113	22	continuous	continuous	ADJ
ejpam-3544	113	23	functions	function	NOUN
ejpam-3544	113	24	,	,	PUNCT
ejpam-3544	113	25	acta	acta	PROPN
ejpam-3544	113	26	math	math	PROPN
ejpam-3544	113	27	.	.	PUNCT
ejpam-3544	114	1	hungar	hungar	NOUN
ejpam-3544	114	2	.	.	PUNCT
ejpam-3544	115	1	107	107	NUM
ejpam-3544	115	2	(	(	PUNCT
ejpam-3544	115	3	2005	2005	NUM
ejpam-3544	115	4	)	)	PUNCT
ejpam-3544	115	5	345–353	345–353	NUM
ejpam-3544	115	6	.	.	PUNCT
ejpam-3544	116	1	[	[	X
ejpam-3544	116	2	7	7	X
ejpam-3544	116	3	]	]	X
ejpam-3544	116	4	d.	d.	PROPN
ejpam-3544	116	5	jankovic	jankovic	PROPN
ejpam-3544	116	6	,	,	PUNCT
ejpam-3544	116	7	t.r	t.r	PROPN
ejpam-3544	116	8	.	.	PROPN
ejpam-3544	116	9	hamlet	hamlet	PROPN
ejpam-3544	116	10	,	,	PUNCT
ejpam-3544	116	11	new	new	ADJ
ejpam-3544	116	12	topologies	topology	NOUN
ejpam-3544	116	13	from	from	ADP
ejpam-3544	116	14	old	old	ADJ
ejpam-3544	116	15	via	via	ADP
ejpam-3544	116	16	ideals	ideal	NOUN
ejpam-3544	116	17	,	,	PUNCT
ejpam-3544	116	18	amer	amer	PROPN
ejpam-3544	116	19	.	.	PROPN
ejpam-3544	116	20	math	math	PROPN
ejpam-3544	116	21	.	.	PUNCT
ejpam-3544	117	1	monthly	monthly	ADJ
ejpam-3544	117	2	97	97	NUM
ejpam-3544	117	3	(	(	PUNCT
ejpam-3544	117	4	1990	1990	NUM
ejpam-3544	117	5	)	)	PUNCT
ejpam-3544	117	6	295−310	295−310	X
ejpam-3544	117	7	.	.	PUNCT
ejpam-3544	118	1	[	[	X
ejpam-3544	118	2	8	8	X
ejpam-3544	118	3	]	]	PUNCT
ejpam-3544	118	4	j.	j.	PROPN
ejpam-3544	118	5	jarvinen	jarvinen	PROPN
ejpam-3544	118	6	,	,	PUNCT
ejpam-3544	118	7	j.	j.	PROPN
ejpam-3544	118	8	kortelainen	kortelainen	PROPN
ejpam-3544	118	9	,	,	PUNCT
ejpam-3544	118	10	a	a	DET
ejpam-3544	118	11	unifying	unifying	ADJ
ejpam-3544	118	12	study	study	NOUN
ejpam-3544	118	13	between	between	ADP
ejpam-3544	118	14	model	model	NOUN
ejpam-3544	118	15	-	-	PUNCT
ejpam-3544	118	16	like	like	ADJ
ejpam-3544	118	17	operators	operator	NOUN
ejpam-3544	118	18	,	,	PUNCT
ejpam-3544	118	19	topologies	topology	NOUN
ejpam-3544	118	20	,	,	PUNCT
ejpam-3544	118	21	and	and	CCONJ
ejpam-3544	118	22	fuzzy	fuzzy	ADJ
ejpam-3544	118	23	sets	set	NOUN
ejpam-3544	118	24	,	,	PUNCT
ejpam-3544	118	25	fuzzy	fuzzy	ADJ
ejpam-3544	118	26	sets	set	NOUN
ejpam-3544	118	27	and	and	CCONJ
ejpam-3544	118	28	systems	system	NOUN
ejpam-3544	118	29	158	158	NUM
ejpam-3544	118	30	(	(	PUNCT
ejpam-3544	118	31	2007	2007	NUM
ejpam-3544	118	32	)	)	PUNCT
ejpam-3544	118	33	1217–1225	1217–1225	NUM
ejpam-3544	118	34	.	.	PUNCT
ejpam-3544	119	1	[	[	X
ejpam-3544	119	2	9	9	NUM
ejpam-3544	119	3	]	]	PUNCT
ejpam-3544	119	4	k.	k.	PROPN
ejpam-3544	119	5	kuratowski	kuratowski	PROPN
ejpam-3544	119	6	,	,	PUNCT
ejpam-3544	119	7	topology	topology	NOUN
ejpam-3544	119	8	vol	vol	NOUN
ejpam-3544	119	9	.	.	PUNCT
ejpam-3544	120	1	i	i	PRON
ejpam-3544	120	2	,	,	PUNCT
ejpam-3544	120	3	academic	academic	ADJ
ejpam-3544	120	4	press	press	NOUN
ejpam-3544	120	5	,	,	PUNCT
ejpam-3544	120	6	new	new	PROPN
ejpam-3544	120	7	york	york	PROPN
ejpam-3544	120	8	,	,	PUNCT
ejpam-3544	120	9	1966	1966	NUM
ejpam-3544	120	10	.	.	PUNCT
ejpam-3544	121	1	[	[	X
ejpam-3544	121	2	10	10	NUM
ejpam-3544	121	3	]	]	X
ejpam-3544	121	4	n.	n.	PROPN
ejpam-3544	121	5	levine	levine	PROPN
ejpam-3544	121	6	,	,	PUNCT
ejpam-3544	121	7	semi	semi	ADV
ejpam-3544	121	8	open	open	ADJ
ejpam-3544	121	9	sets	set	NOUN
ejpam-3544	121	10	and	and	CCONJ
ejpam-3544	121	11	semi	semi	ADV
ejpam-3544	121	12	continuous	continuous	ADJ
ejpam-3544	121	13	mappings	mapping	NOUN
ejpam-3544	121	14	in	in	ADP
ejpam-3544	121	15	topological	topological	ADJ
ejpam-3544	121	16	spaces	space	NOUN
ejpam-3544	121	17	,	,	PUNCT
ejpam-3544	121	18	amr	amr	PROPN
ejpam-3544	121	19	math	math	NOUN
ejpam-3544	121	20	monthly	monthly	ADJ
ejpam-3544	121	21	70	70	NUM
ejpam-3544	121	22	(	(	PUNCT
ejpam-3544	121	23	1963	1963	NUM
ejpam-3544	121	24	)	)	PUNCT
ejpam-3544	121	25	36–41	36–41	NUM
ejpam-3544	121	26	.	.	PUNCT
ejpam-3544	122	1	[	[	X
ejpam-3544	122	2	11	11	NUM
ejpam-3544	122	3	]	]	X
ejpam-3544	122	4	a.s	a.s	PROPN
ejpam-3544	122	5	.	.	PROPN
ejpam-3544	122	6	mashhour	mashhour	PROPN
ejpam-3544	122	7	,	,	PUNCT
ejpam-3544	122	8	m.e	m.e	PROPN
ejpam-3544	122	9	.	.	PROPN
ejpam-3544	122	10	abd	abd	PROPN
ejpam-3544	122	11	el	el	PROPN
ejpam-3544	122	12	-	-	PROPN
ejpam-3544	122	13	monsef	monsef	ADJ
ejpam-3544	122	14	,	,	PUNCT
ejpam-3544	122	15	s.n	s.n	PROPN
ejpam-3544	122	16	.	.	PROPN
ejpam-3544	122	17	el	el	PROPN
ejpam-3544	122	18	-	-	PUNCT
ejpam-3544	122	19	deeb	deeb	PROPN
ejpam-3544	122	20	,	,	PUNCT
ejpam-3544	122	21	on	on	ADP
ejpam-3544	122	22	pre	pre	ADJ
ejpam-3544	122	23	-	-	ADJ
ejpam-3544	122	24	continuous	continuous	ADJ
ejpam-3544	122	25	and	and	CCONJ
ejpam-3544	122	26	3	3	NUM
ejpam-3544	122	27	weak	weak	ADJ
ejpam-3544	122	28	pre	pre	ADJ
ejpam-3544	122	29	-	-	ADJ
ejpam-3544	122	30	continuous	continuous	ADJ
ejpam-3544	122	31	mappings	mapping	NOUN
ejpam-3544	122	32	,	,	PUNCT
ejpam-3544	122	33	proc	proc	NOUN
ejpam-3544	122	34	math	math	NOUN
ejpam-3544	122	35	and	and	CCONJ
ejpam-3544	122	36	phys	phy	NOUN
ejpam-3544	122	37	soc	soc	NOUN
ejpam-3544	122	38	egypt	egypt	PROPN
ejpam-3544	122	39	53	53	NUM
ejpam-3544	122	40	(	(	PUNCT
ejpam-3544	122	41	1982	1982	NUM
ejpam-3544	122	42	)	)	PUNCT
ejpam-3544	122	43	47–53	47–53	NOUN
ejpam-3544	122	44	.	.	PUNCT
ejpam-3544	123	1	[	[	X
ejpam-3544	123	2	12	12	NUM
ejpam-3544	123	3	]	]	X
ejpam-3544	123	4	f.i	f.i	PROPN
ejpam-3544	123	5	.	.	PROPN
ejpam-3544	123	6	michael	michael	PROPN
ejpam-3544	123	7	,	,	PUNCT
ejpam-3544	123	8	on	on	ADP
ejpam-3544	123	9	the	the	DET
ejpam-3544	123	10	semi	semi	ADJ
ejpam-3544	123	11	-	-	ADJ
ejpam-3544	123	12	open	open	ADJ
ejpam-3544	123	13	sets	set	NOUN
ejpam-3544	123	14	with	with	ADP
ejpam-3544	123	15	respect	respect	NOUN
ejpam-3544	123	16	to	to	ADP
ejpam-3544	123	17	an	an	DET
ejpam-3544	123	18	ideal	ideal	ADJ
ejpam-3544	123	19	,	,	PUNCT
ejpam-3544	123	20	european	european	ADJ
ejpam-3544	123	21	journal	journal	PROPN
ejpam-3544	123	22	of	of	ADP
ejpam-3544	123	23	pure	pure	ADJ
ejpam-3544	123	24	and	and	CCONJ
ejpam-3544	123	25	applied	applied	ADJ
ejpam-3544	123	26	mathematics	mathematic	NOUN
ejpam-3544	123	27	6	6	NUM
ejpam-3544	123	28	(	(	PUNCT
ejpam-3544	123	29	2013	2013	NUM
ejpam-3544	123	30	)	)	PUNCT
ejpam-3544	123	31	53–58	53–58	NUM
ejpam-3544	123	32	.	.	PUNCT
ejpam-3544	124	1	[	[	X
ejpam-3544	124	2	13	13	NUM
ejpam-3544	124	3	]	]	X
ejpam-3544	124	4	m.n	m.n	PROPN
ejpam-3544	124	5	.	.	PROPN
ejpam-3544	124	6	mukherjee	mukherjee	PROPN
ejpam-3544	124	7	,	,	PUNCT
ejpam-3544	124	8	b.	b.	PROPN
ejpam-3544	124	9	roy	roy	PROPN
ejpam-3544	124	10	,	,	PUNCT
ejpam-3544	124	11	r.	r.	PROPN
ejpam-3544	124	12	sen	sen	PROPN
ejpam-3544	124	13	,	,	PUNCT
ejpam-3544	124	14	on	on	ADP
ejpam-3544	124	15	extension	extension	NOUN
ejpam-3544	124	16	of	of	ADP
ejpam-3544	124	17	topological	topological	ADJ
ejpam-3544	124	18	spaces	space	NOUN
ejpam-3544	124	19	in	in	ADP
ejpam-3544	124	20	terms	term	NOUN
ejpam-3544	124	21	of	of	ADP
ejpam-3544	124	22	ideals	ideal	NOUN
ejpam-3544	124	23	,	,	PUNCT
ejpam-3544	124	24	topology	topology	NOUN
ejpam-3544	124	25	appl	appl	NOUN
ejpam-3544	124	26	.	.	PUNCT
ejpam-3544	125	1	154	154	NUM
ejpam-3544	125	2	(	(	PUNCT
ejpam-3544	125	3	2007	2007	NUM
ejpam-3544	125	4	)	)	PUNCT
ejpam-3544	125	5	3167–3172	3167–3172	NUM
ejpam-3544	125	6	.	.	PUNCT
ejpam-3544	126	1	[	[	X
ejpam-3544	126	2	14	14	NUM
ejpam-3544	126	3	]	]	X
ejpam-3544	126	4	j.	j.	PROPN
ejpam-3544	126	5	r.	r.	PROPN
ejpam-3544	126	6	munkers	munkers	PROPN
ejpam-3544	126	7	,	,	PUNCT
ejpam-3544	126	8	topology	topology	NOUN
ejpam-3544	126	9	:	:	PUNCT
ejpam-3544	126	10	a	a	DET
ejpam-3544	126	11	first	first	ADJ
ejpam-3544	126	12	course	course	NOUN
ejpam-3544	126	13	.	.	PUNCT
ejpam-3544	127	1	new	new	PROPN
ejpam-3544	127	2	jersey	jersey	PROPN
ejpam-3544	127	3	:	:	PUNCT
ejpam-3544	127	4	prentice	prentice	PROPN
ejpam-3544	127	5	hall	hall	PROPN
ejpam-3544	127	6	inc	inc	PROPN
ejpam-3544	127	7	,	,	PUNCT
ejpam-3544	127	8	englewood	englewood	PROPN
ejpam-3544	127	9	cliffs	cliff	NOUN
ejpam-3544	127	10	,	,	PUNCT
ejpam-3544	127	11	1975	1975	NUM
ejpam-3544	127	12	.	.	PUNCT
ejpam-3544	128	1	[	[	X
ejpam-3544	128	2	15	15	NUM
ejpam-3544	128	3	]	]	X
ejpam-3544	128	4	o.	o.	PROPN
ejpam-3544	128	5	najastad	najastad	PROPN
ejpam-3544	128	6	,	,	PUNCT
ejpam-3544	128	7	on	on	ADP
ejpam-3544	128	8	some	some	DET
ejpam-3544	128	9	classes	class	NOUN
ejpam-3544	128	10	of	of	ADP
ejpam-3544	128	11	nearly	nearly	ADV
ejpam-3544	128	12	open	open	ADJ
ejpam-3544	128	13	sets	set	NOUN
ejpam-3544	128	14	,	,	PUNCT
ejpam-3544	128	15	pacific	pacific	PROPN
ejpam-3544	128	16	j	j	PROPN
ejpam-3544	128	17	math	math	PROPN
ejpam-3544	128	18	15	15	NUM
ejpam-3544	128	19	(	(	PUNCT
ejpam-3544	128	20	1965	1965	NUM
ejpam-3544	128	21	)	)	PUNCT
ejpam-3544	128	22	961–970	961–970	NUM
ejpam-3544	128	23	.	.	PUNCT
ejpam-3544	129	1	[	[	X
ejpam-3544	129	2	16	16	NUM
ejpam-3544	129	3	]	]	X
ejpam-3544	129	4	a.a	a.a	PROPN
ejpam-3544	129	5	.	.	PROPN
ejpam-3544	129	6	nasef	nasef	PROPN
ejpam-3544	129	7	,	,	PUNCT
ejpam-3544	129	8	a.e	a.e	PROPN
ejpam-3544	129	9	.	.	PROPN
ejpam-3544	129	10	radwan	radwan	PROPN
ejpam-3544	129	11	,	,	PUNCT
ejpam-3544	129	12	r.b	r.b	PROPN
ejpam-3544	129	13	.	.	PROPN
ejpam-3544	129	14	esmaeel	esmaeel	PROPN
ejpam-3544	129	15	,	,	PUNCT
ejpam-3544	129	16	some	some	DET
ejpam-3544	129	17	properties	property	NOUN
ejpam-3544	129	18	of	of	ADP
ejpam-3544	129	19	α	α	NOUN
ejpam-3544	129	20	-	-	ADJ
ejpam-3544	129	21	open	open	ADJ
ejpam-3544	129	22	sets	set	NOUN
ejpam-3544	129	23	with	with	ADP
ejpam-3544	129	24	respect	respect	NOUN
ejpam-3544	129	25	to	to	ADP
ejpam-3544	129	26	an	an	DET
ejpam-3544	129	27	ideal	ideal	ADJ
ejpam-3544	129	28	,	,	PUNCT
ejpam-3544	129	29	int	int	NOUN
ejpam-3544	129	30	journal	journal	NOUN
ejpam-3544	129	31	of	of	ADP
ejpam-3544	129	32	pure	pure	ADJ
ejpam-3544	129	33	and	and	CCONJ
ejpam-3544	129	34	applied	applied	ADJ
ejpam-3544	129	35	mathematics	mathematic	NOUN
ejpam-3544	129	36	102	102	NUM
ejpam-3544	129	37	(	(	PUNCT
ejpam-3544	129	38	2015	2015	NUM
ejpam-3544	129	39	)	)	PUNCT
ejpam-3544	129	40	613–630	613–630	NUM
ejpam-3544	129	41	.	.	PUNCT
ejpam-3544	130	1	references	reference	NOUN
ejpam-3544	130	2	1660	1660	NUM
ejpam-3544	130	3	[	[	X
ejpam-3544	130	4	17	17	NUM
ejpam-3544	130	5	]	]	X
ejpam-3544	130	6	l.	l.	PROPN
ejpam-3544	130	7	polkowski	polkowski	PROPN
ejpam-3544	130	8	,	,	PUNCT
ejpam-3544	130	9	rough	rough	ADJ
ejpam-3544	130	10	sets	set	NOUN
ejpam-3544	130	11	:	:	PUNCT
ejpam-3544	130	12	mathematical	mathematical	ADJ
ejpam-3544	130	13	foundations	foundation	NOUN
ejpam-3544	130	14	,	,	PUNCT
ejpam-3544	130	15	physica	physica	NOUN
ejpam-3544	130	16	-	-	PUNCT
ejpam-3544	130	17	verlag	verlag	PROPN
ejpam-3544	130	18	,	,	PUNCT
ejpam-3544	130	19	heidelberg	heidelberg	PROPN
ejpam-3544	130	20	,	,	PUNCT
ejpam-3544	130	21	2002	2002	NUM
ejpam-3544	130	22	.	.	PUNCT
ejpam-3544	131	1	[	[	X
ejpam-3544	131	2	18	18	NUM
ejpam-3544	131	3	]	]	X
ejpam-3544	131	4	d.	d.	PROPN
ejpam-3544	131	5	scott	scott	PROPN
ejpam-3544	131	6	,	,	PUNCT
ejpam-3544	131	7	domains	domain	NOUN
ejpam-3544	131	8	for	for	ADP
ejpam-3544	131	9	denotational	denotational	ADJ
ejpam-3544	131	10	semantics	semantic	NOUN
ejpam-3544	131	11	,	,	PUNCT
ejpam-3544	131	12	lecture	lecture	NOUN
ejpam-3544	131	13	notes	note	NOUN
ejpam-3544	131	14	on	on	ADP
ejpam-3544	131	15	computer	computer	NOUN
ejpam-3544	131	16	science	science	NOUN
ejpam-3544	131	17	140	140	NUM
ejpam-3544	131	18	(	(	PUNCT
ejpam-3544	131	19	1982	1982	NUM
ejpam-3544	131	20	)	)	PUNCT
ejpam-3544	132	1	577–613	577–613	NUM
ejpam-3544	132	2	.	.	PUNCT
ejpam-3544	133	1	[	[	X
ejpam-3544	133	2	19	19	NUM
ejpam-3544	133	3	]	]	X
ejpam-3544	133	4	m.h	m.h	PROPN
ejpam-3544	133	5	.	.	PROPN
ejpam-3544	133	6	stone	stone	PROPN
ejpam-3544	133	7	,	,	PUNCT
ejpam-3544	133	8	applications	application	NOUN
ejpam-3544	133	9	of	of	ADP
ejpam-3544	133	10	the	the	DET
ejpam-3544	133	11	theory	theory	NOUN
ejpam-3544	133	12	of	of	ADP
ejpam-3544	133	13	boolean	boolean	ADJ
ejpam-3544	133	14	rings	ring	NOUN
ejpam-3544	133	15	to	to	ADP
ejpam-3544	133	16	general	general	ADJ
ejpam-3544	133	17	topology	topology	NOUN
ejpam-3544	133	18	,	,	PUNCT
ejpam-3544	133	19	trans	trans	PROPN
ejpam-3544	133	20	.	.	PROPN
ejpam-3544	133	21	amer	amer	PROPN
ejpam-3544	133	22	.	.	PUNCT
ejpam-3544	133	23	math	math	PROPN
ejpam-3544	133	24	.	.	PUNCT
ejpam-3544	134	1	soc	soc	PROPN
ejpam-3544	134	2	.	.	PUNCT
ejpam-3544	135	1	41	41	NUM
ejpam-3544	135	2	(	(	PUNCT
ejpam-3544	135	3	1937	1937	NUM
ejpam-3544	135	4	)	)	PUNCT
ejpam-3544	136	1	375–481	375–481	NUM
ejpam-3544	136	2	.	.	PUNCT
ejpam-3544	137	1	[	[	X
ejpam-3544	137	2	20	20	NUM
ejpam-3544	137	3	]	]	PUNCT
ejpam-3544	137	4	r.	r.	PROPN
ejpam-3544	137	5	vaidynathaswamy	vaidynathaswamy	PROPN
ejpam-3544	137	6	,	,	PUNCT
ejpam-3544	137	7	the	the	DET
ejpam-3544	137	8	localization	localization	NOUN
ejpam-3544	137	9	theory	theory	NOUN
ejpam-3544	137	10	in	in	ADP
ejpam-3544	137	11	set	set	NOUN
ejpam-3544	137	12	topology	topology	NOUN
ejpam-3544	137	13	,	,	PUNCT
ejpam-3544	137	14	proc	proc	NOUN
ejpam-3544	137	15	.	.	PUNCT
ejpam-3544	138	1	ind	ind	PROPN
ejpam-3544	138	2	.	.	PUNCT
ejpam-3544	139	1	acad	acad	PROPN
ejpam-3544	139	2	.	.	PROPN
ejpam-3544	139	3	of	of	ADP
ejpam-3544	139	4	sci	sci	PROPN
ejpam-3544	139	5	.	.	PROPN
ejpam-3544	139	6	20	20	NUM
ejpam-3544	139	7	(	(	PUNCT
ejpam-3544	139	8	1945	1945	NUM
ejpam-3544	139	9	)	)	PUNCT
ejpam-3544	139	10	515–61	515–61	X
ejpam-3544	139	11	.	.	PUNCT