id	sid	tid	token	lemma	pos
ejpam-4625	1	1	european	european	PROPN
ejpam-4625	1	2	journal	journal	PROPN
ejpam-4625	1	3	of	of	ADP
ejpam-4625	1	4	pure	pure	ADJ
ejpam-4625	1	5	and	and	CCONJ
ejpam-4625	1	6	applied	apply	VERB
ejpam-4625	1	7	mathematics	mathematic	NOUN
ejpam-4625	1	8	vol	vol	NOUN
ejpam-4625	1	9	.	.	PUNCT
ejpam-4625	2	1	16	16	NUM
ejpam-4625	2	2	,	,	PUNCT
ejpam-4625	2	3	no	no	INTJ
ejpam-4625	2	4	.	.	NOUN
ejpam-4625	2	5	1	1	NUM
ejpam-4625	2	6	,	,	PUNCT
ejpam-4625	2	7	2023	2023	NUM
ejpam-4625	2	8	,	,	PUNCT
ejpam-4625	2	9	1	1	NUM
ejpam-4625	2	10	-	-	SYM
ejpam-4625	2	11	4	4	NUM
ejpam-4625	2	12	issn	issn	PROPN
ejpam-4625	2	13	1307	1307	NUM
ejpam-4625	2	14	-	-	SYM
ejpam-4625	2	15	5543	5543	NUM
ejpam-4625	2	16	–	–	PUNCT
ejpam-4625	2	17	ejpam.com	ejpam.com	X
ejpam-4625	2	18	published	publish	VERB
ejpam-4625	2	19	by	by	ADP
ejpam-4625	2	20	new	new	PROPN
ejpam-4625	2	21	york	york	PROPN
ejpam-4625	2	22	business	business	PROPN
ejpam-4625	2	23	global	global	PROPN
ejpam-4625	2	24	more	more	ADV
ejpam-4625	2	25	on	on	ADP
ejpam-4625	2	26	ideal	ideal	ADJ
ejpam-4625	2	27	rothberger	rothberger	NOUN
ejpam-4625	2	28	spaces	space	VERB
ejpam-4625	2	29	asli	asli	PROPN
ejpam-4625	2	30	guldurdek	guldurdek	PROPN
ejpam-4625	2	31	college	college	PROPN
ejpam-4625	2	32	of	of	ADP
ejpam-4625	2	33	engineering	engineering	NOUN
ejpam-4625	2	34	and	and	CCONJ
ejpam-4625	2	35	technology	technology	NOUN
ejpam-4625	2	36	,	,	PUNCT
ejpam-4625	2	37	american	american	PROPN
ejpam-4625	2	38	university	university	PROPN
ejpam-4625	2	39	of	of	ADP
ejpam-4625	2	40	the	the	DET
ejpam-4625	2	41	middle	middle	PROPN
ejpam-4625	2	42	east	east	PROPN
ejpam-4625	2	43	,	,	PUNCT
ejpam-4625	2	44	egaila	egaila	PROPN
ejpam-4625	2	45	,	,	PUNCT
ejpam-4625	2	46	54200	54200	NUM
ejpam-4625	2	47	,	,	PUNCT
ejpam-4625	2	48	kuwait	kuwait	PROPN
ejpam-4625	2	49	abstract	abstract	NOUN
ejpam-4625	2	50	.	.	PUNCT
ejpam-4625	3	1	the	the	DET
ejpam-4625	3	2	aim	aim	NOUN
ejpam-4625	3	3	of	of	ADP
ejpam-4625	3	4	this	this	DET
ejpam-4625	3	5	note	note	NOUN
ejpam-4625	3	6	is	be	AUX
ejpam-4625	3	7	to	to	PART
ejpam-4625	3	8	provide	provide	VERB
ejpam-4625	3	9	an	an	DET
ejpam-4625	3	10	answer	answer	NOUN
ejpam-4625	3	11	to	to	ADP
ejpam-4625	3	12	a	a	DET
ejpam-4625	3	13	question	question	NOUN
ejpam-4625	3	14	posted	post	VERB
ejpam-4625	3	15	in	in	ADP
ejpam-4625	3	16	a	a	DET
ejpam-4625	3	17	recent	recent	ADJ
ejpam-4625	3	18	paper	paper	NOUN
ejpam-4625	3	19	.	.	PUNCT
ejpam-4625	4	1	in	in	ADP
ejpam-4625	4	2	2018	2018	NUM
ejpam-4625	4	3	,	,	PUNCT
ejpam-4625	4	4	after	after	ADP
ejpam-4625	4	5	introducing	introduce	VERB
ejpam-4625	4	6	the	the	DET
ejpam-4625	4	7	notion	notion	NOUN
ejpam-4625	4	8	of	of	ADP
ejpam-4625	4	9	ideal	ideal	ADJ
ejpam-4625	4	10	rothberger	rothberger	NOUN
ejpam-4625	4	11	space	space	NOUN
ejpam-4625	4	12	,	,	PUNCT
ejpam-4625	4	13	author	author	NOUN
ejpam-4625	4	14	examines	examine	VERB
ejpam-4625	4	15	some	some	DET
ejpam-4625	4	16	properties	property	NOUN
ejpam-4625	4	17	of	of	ADP
ejpam-4625	4	18	these	these	DET
ejpam-4625	4	19	spaces	space	NOUN
ejpam-4625	4	20	.	.	PUNCT
ejpam-4625	5	1	also	also	ADV
ejpam-4625	5	2	there	there	PRON
ejpam-4625	5	3	has	have	AUX
ejpam-4625	5	4	been	be	AUX
ejpam-4625	5	5	a	a	DET
ejpam-4625	5	6	comparison	comparison	NOUN
ejpam-4625	5	7	of	of	ADP
ejpam-4625	5	8	the	the	DET
ejpam-4625	5	9	spaces	space	NOUN
ejpam-4625	5	10	(	(	PUNCT
ejpam-4625	5	11	x	x	X
ejpam-4625	5	12	,	,	PUNCT
ejpam-4625	5	13	τ	τ	PROPN
ejpam-4625	5	14	)	)	PUNCT
ejpam-4625	5	15	,	,	PUNCT
ejpam-4625	5	16	and	and	CCONJ
ejpam-4625	5	17	(	(	PUNCT
ejpam-4625	5	18	x	x	NOUN
ejpam-4625	5	19	,	,	PUNCT
ejpam-4625	5	20	τ∗	τ∗	NOUN
ejpam-4625	5	21	)	)	PUNCT
ejpam-4625	5	22	in	in	ADP
ejpam-4625	5	23	terms	term	NOUN
ejpam-4625	5	24	of	of	ADP
ejpam-4625	5	25	being	be	AUX
ejpam-4625	5	26	(	(	PUNCT
ejpam-4625	5	27	ideal)rothberger	ideal)rothberger	X
ejpam-4625	5	28	.	.	PUNCT
ejpam-4625	6	1	according	accord	VERB
ejpam-4625	6	2	to	to	ADP
ejpam-4625	6	3	this	this	PRON
ejpam-4625	6	4	,	,	PUNCT
ejpam-4625	6	5	it	it	PRON
ejpam-4625	6	6	is	be	AUX
ejpam-4625	6	7	shown	show	VERB
ejpam-4625	6	8	that	that	SCONJ
ejpam-4625	6	9	if	if	SCONJ
ejpam-4625	6	10	(	(	PUNCT
ejpam-4625	6	11	x	x	NOUN
ejpam-4625	6	12	,	,	PUNCT
ejpam-4625	6	13	τ∗	τ∗	ADJ
ejpam-4625	6	14	)	)	PUNCT
ejpam-4625	6	15	is	be	AUX
ejpam-4625	6	16	a	a	DET
ejpam-4625	6	17	rothberger	rothberger	NOUN
ejpam-4625	6	18	space	space	NOUN
ejpam-4625	6	19	,	,	PUNCT
ejpam-4625	6	20	then	then	ADV
ejpam-4625	6	21	(	(	PUNCT
ejpam-4625	6	22	x	x	X
ejpam-4625	6	23	,	,	PUNCT
ejpam-4625	6	24	τ	τ	X
ejpam-4625	6	25	)	)	PUNCT
ejpam-4625	6	26	is	be	AUX
ejpam-4625	6	27	also	also	ADV
ejpam-4625	6	28	rothberger	rothberger	NOUN
ejpam-4625	6	29	.	.	PUNCT
ejpam-4625	7	1	therefore	therefore	ADV
ejpam-4625	7	2	,	,	PUNCT
ejpam-4625	7	3	naturally	naturally	ADV
ejpam-4625	7	4	it	it	PRON
ejpam-4625	7	5	is	be	AUX
ejpam-4625	7	6	asked	ask	VERB
ejpam-4625	7	7	that	that	SCONJ
ejpam-4625	7	8	,	,	PUNCT
ejpam-4625	7	9	if	if	SCONJ
ejpam-4625	7	10	one	one	PRON
ejpam-4625	7	11	can	can	AUX
ejpam-4625	7	12	find	find	VERB
ejpam-4625	7	13	some	some	DET
ejpam-4625	7	14	extra	extra	ADJ
ejpam-4625	7	15	conditions	condition	NOUN
ejpam-4625	7	16	for	for	ADP
ejpam-4625	7	17	ideal	ideal	ADJ
ejpam-4625	7	18	i	i	PRON
ejpam-4625	7	19	,	,	PUNCT
ejpam-4625	7	20	then	then	ADV
ejpam-4625	7	21	the	the	DET
ejpam-4625	7	22	opposite	opposite	NOUN
ejpam-4625	7	23	also	also	ADV
ejpam-4625	7	24	holds	hold	VERB
ejpam-4625	7	25	.	.	PUNCT
ejpam-4625	8	1	thus	thus	ADV
ejpam-4625	8	2	,	,	PUNCT
ejpam-4625	8	3	for	for	ADP
ejpam-4625	8	4	which	which	PRON
ejpam-4625	8	5	ideal	ideal	NOUN
ejpam-4625	8	6	i	i	PRON
ejpam-4625	8	7	,	,	PUNCT
ejpam-4625	8	8	an	an	DET
ejpam-4625	8	9	i	i	NOUN
ejpam-4625	8	10	-	-	PUNCT
ejpam-4625	8	11	rothberger	rothberger	NOUN
ejpam-4625	8	12	space	space	NOUN
ejpam-4625	8	13	(	(	PUNCT
ejpam-4625	8	14	x	x	X
ejpam-4625	8	15	,	,	PUNCT
ejpam-4625	8	16	τ	τ	X
ejpam-4625	8	17	)	)	PUNCT
ejpam-4625	8	18	implies	imply	VERB
ejpam-4625	8	19	an	an	DET
ejpam-4625	8	20	i	i	NOUN
ejpam-4625	8	21	-	-	PUNCT
ejpam-4625	8	22	rothberger	rothberger	NOUN
ejpam-4625	8	23	space	space	NOUN
ejpam-4625	8	24	(	(	PUNCT
ejpam-4625	8	25	x	x	NOUN
ejpam-4625	8	26	,	,	PUNCT
ejpam-4625	8	27	τ∗	τ∗	NOUN
ejpam-4625	8	28	)	)	PUNCT
ejpam-4625	8	29	?	?	PUNCT
ejpam-4625	9	1	in	in	ADP
ejpam-4625	9	2	this	this	DET
ejpam-4625	9	3	work	work	NOUN
ejpam-4625	9	4	it	it	PRON
ejpam-4625	9	5	has	have	AUX
ejpam-4625	9	6	been	be	AUX
ejpam-4625	9	7	proved	prove	VERB
ejpam-4625	9	8	that	that	SCONJ
ejpam-4625	9	9	i	i	PRON
ejpam-4625	9	10	is	be	AUX
ejpam-4625	9	11	a	a	DET
ejpam-4625	9	12	σ	σ	NOUN
ejpam-4625	9	13	-	-	PUNCT
ejpam-4625	9	14	ideal	ideal	NOUN
ejpam-4625	9	15	,	,	PUNCT
ejpam-4625	9	16	and	and	CCONJ
ejpam-4625	9	17	τ	τ	PROPN
ejpam-4625	9	18	is	be	AUX
ejpam-4625	9	19	compatible	compatible	ADJ
ejpam-4625	9	20	with	with	ADP
ejpam-4625	9	21	i	i	PRON
ejpam-4625	9	22	,	,	PUNCT
ejpam-4625	9	23	which	which	PRON
ejpam-4625	9	24	provides	provide	VERB
ejpam-4625	9	25	the	the	DET
ejpam-4625	9	26	solution	solution	NOUN
ejpam-4625	9	27	.	.	PUNCT
ejpam-4625	10	1	2020	2020	NUM
ejpam-4625	10	2	mathematics	mathematic	NOUN
ejpam-4625	10	3	subject	subject	NOUN
ejpam-4625	10	4	classifications	classification	NOUN
ejpam-4625	10	5	:	:	PUNCT
ejpam-4625	10	6	54a05	54a05	NUM
ejpam-4625	10	7	,	,	PUNCT
ejpam-4625	10	8	54d20	54d20	NUM
ejpam-4625	10	9	key	key	ADJ
ejpam-4625	10	10	words	word	NOUN
ejpam-4625	10	11	and	and	CCONJ
ejpam-4625	10	12	phrases	phrase	NOUN
ejpam-4625	10	13	:	:	PUNCT
ejpam-4625	10	14	ideal	ideal	ADJ
ejpam-4625	10	15	topological	topological	ADJ
ejpam-4625	10	16	space	space	NOUN
ejpam-4625	10	17	,	,	PUNCT
ejpam-4625	10	18	ideal	ideal	ADJ
ejpam-4625	10	19	rothberger	rothberger	NOUN
ejpam-4625	10	20	space	space	NOUN
ejpam-4625	10	21	1	1	NUM
ejpam-4625	10	22	.	.	PUNCT
ejpam-4625	11	1	introduction	introduction	NOUN
ejpam-4625	11	2	and	and	CCONJ
ejpam-4625	11	3	preliminaries	preliminary	NOUN
ejpam-4625	11	4	extending	extend	VERB
ejpam-4625	11	5	topological	topological	ADJ
ejpam-4625	11	6	spaces	space	NOUN
ejpam-4625	11	7	by	by	ADP
ejpam-4625	11	8	adding	add	VERB
ejpam-4625	11	9	ideals	ideal	NOUN
ejpam-4625	11	10	,	,	PUNCT
ejpam-4625	11	11	has	have	AUX
ejpam-4625	11	12	been	be	AUX
ejpam-4625	11	13	done	do	VERB
ejpam-4625	11	14	since	since	SCONJ
ejpam-4625	11	15	vaidyanathaswamy	vaidyanathaswamy	NOUN
ejpam-4625	11	16	[	[	X
ejpam-4625	11	17	7	7	NUM
ejpam-4625	11	18	]	]	PUNCT
ejpam-4625	11	19	,	,	PUNCT
ejpam-4625	11	20	and	and	CCONJ
ejpam-4625	11	21	kuratowski	kuratowski	VERB
ejpam-4625	11	22	[	[	X
ejpam-4625	11	23	3	3	NUM
ejpam-4625	11	24	]	]	PUNCT
ejpam-4625	11	25	.	.	PUNCT
ejpam-4625	12	1	an	an	DET
ejpam-4625	12	2	ideal	ideal	NOUN
ejpam-4625	12	3	i	i	PRON
ejpam-4625	12	4	on	on	ADP
ejpam-4625	12	5	a	a	DET
ejpam-4625	12	6	set	set	NOUN
ejpam-4625	12	7	x	x	PUNCT
ejpam-4625	12	8	is	be	AUX
ejpam-4625	12	9	defined	define	VERB
ejpam-4625	12	10	to	to	PART
ejpam-4625	12	11	be	be	AUX
ejpam-4625	12	12	a	a	DET
ejpam-4625	12	13	nonempty	nonempty	ADJ
ejpam-4625	12	14	collection	collection	NOUN
ejpam-4625	12	15	of	of	ADP
ejpam-4625	12	16	subsets	subset	NOUN
ejpam-4625	12	17	of	of	ADP
ejpam-4625	12	18	x	x	PRON
ejpam-4625	12	19	,	,	PUNCT
ejpam-4625	12	20	which	which	PRON
ejpam-4625	12	21	is	be	AUX
ejpam-4625	12	22	closed	close	VERB
ejpam-4625	12	23	under	under	ADP
ejpam-4625	12	24	the	the	DET
ejpam-4625	12	25	subset	subset	NOUN
ejpam-4625	12	26	and	and	CCONJ
ejpam-4625	12	27	finite	finite	PROPN
ejpam-4625	12	28	union	union	NOUN
ejpam-4625	12	29	operations	operation	NOUN
ejpam-4625	12	30	.	.	PUNCT
ejpam-4625	13	1	a	a	DET
ejpam-4625	13	2	topological	topological	ADJ
ejpam-4625	13	3	space	space	NOUN
ejpam-4625	13	4	(	(	PUNCT
ejpam-4625	13	5	x	x	X
ejpam-4625	13	6	,	,	PUNCT
ejpam-4625	13	7	τ	τ	X
ejpam-4625	13	8	)	)	PUNCT
ejpam-4625	13	9	with	with	ADP
ejpam-4625	13	10	an	an	DET
ejpam-4625	13	11	ideal	ideal	NOUN
ejpam-4625	13	12	i	i	PRON
ejpam-4625	13	13	defined	define	VERB
ejpam-4625	13	14	on	on	ADP
ejpam-4625	13	15	x	x	VERB
ejpam-4625	13	16	is	be	AUX
ejpam-4625	13	17	donoted	donote	VERB
ejpam-4625	13	18	by	by	ADP
ejpam-4625	13	19	(	(	PUNCT
ejpam-4625	13	20	x	x	X
ejpam-4625	13	21	,	,	PUNCT
ejpam-4625	13	22	τ	τ	PROPN
ejpam-4625	13	23	,	,	PUNCT
ejpam-4625	13	24	i	i	PROPN
ejpam-4625	13	25	)	)	PUNCT
ejpam-4625	13	26	.	.	PUNCT
ejpam-4625	14	1	by	by	ADP
ejpam-4625	14	2	using	use	VERB
ejpam-4625	14	3	an	an	DET
ejpam-4625	14	4	ideal	ideal	NOUN
ejpam-4625	14	5	on	on	ADP
ejpam-4625	14	6	a	a	DET
ejpam-4625	14	7	topological	topological	ADJ
ejpam-4625	14	8	space	space	NOUN
ejpam-4625	14	9	,	,	PUNCT
ejpam-4625	14	10	a	a	DET
ejpam-4625	14	11	local	local	ADJ
ejpam-4625	14	12	function	function	NOUN
ejpam-4625	14	13	is	be	AUX
ejpam-4625	14	14	defined	define	VERB
ejpam-4625	14	15	in	in	ADP
ejpam-4625	14	16	[	[	X
ejpam-4625	14	17	3	3	NUM
ejpam-4625	14	18	]	]	PUNCT
ejpam-4625	14	19	as	as	SCONJ
ejpam-4625	14	20	follows	follow	VERB
ejpam-4625	14	21	:	:	PUNCT
ejpam-4625	14	22	definition	definition	NOUN
ejpam-4625	14	23	1	1	NUM
ejpam-4625	14	24	.	.	PUNCT
ejpam-4625	15	1	[	[	X
ejpam-4625	15	2	3	3	X
ejpam-4625	15	3	]	]	X
ejpam-4625	15	4	let	let	VERB
ejpam-4625	15	5	(	(	PUNCT
ejpam-4625	15	6	x	x	NOUN
ejpam-4625	15	7	,	,	PUNCT
ejpam-4625	15	8	τ	τ	X
ejpam-4625	15	9	)	)	PUNCT
ejpam-4625	15	10	be	be	VERB
ejpam-4625	15	11	a	a	DET
ejpam-4625	15	12	topological	topological	ADJ
ejpam-4625	15	13	space	space	NOUN
ejpam-4625	15	14	,	,	PUNCT
ejpam-4625	15	15	and	and	CCONJ
ejpam-4625	15	16	let	let	VERB
ejpam-4625	15	17	i	i	PRON
ejpam-4625	15	18	be	be	AUX
ejpam-4625	15	19	an	an	DET
ejpam-4625	15	20	ideal	ideal	NOUN
ejpam-4625	15	21	on	on	ADP
ejpam-4625	15	22	x.	x.	NOUN
ejpam-4625	15	23	then	then	ADV
ejpam-4625	15	24	the	the	DET
ejpam-4625	15	25	local	local	ADJ
ejpam-4625	15	26	function	function	NOUN
ejpam-4625	15	27	a∗(i	a∗(i	PROPN
ejpam-4625	15	28	,	,	PUNCT
ejpam-4625	15	29	τ	τ	X
ejpam-4625	15	30	)	)	PUNCT
ejpam-4625	15	31	of	of	ADP
ejpam-4625	15	32	a	a	DET
ejpam-4625	15	33	⊂	⊂	X
ejpam-4625	15	34	x	x	X
ejpam-4625	15	35	is	be	AUX
ejpam-4625	15	36	defined	define	VERB
ejpam-4625	15	37	as	as	ADP
ejpam-4625	15	38	:	:	PUNCT
ejpam-4625	15	39	a∗(i	a∗(i	PROPN
ejpam-4625	15	40	,	,	PUNCT
ejpam-4625	15	41	τ	τ	X
ejpam-4625	15	42	)	)	PUNCT
ejpam-4625	15	43	=	=	PRON
ejpam-4625	16	1	{	{	PUNCT
ejpam-4625	16	2	x	x	PUNCT
ejpam-4625	16	3	∈	∈	NOUN
ejpam-4625	16	4	x	x	PUNCT
ejpam-4625	16	5	|	|	ADV
ejpam-4625	16	6	a	a	DET
ejpam-4625	16	7	∩	∩	ADJ
ejpam-4625	16	8	u	u	NOUN
ejpam-4625	16	9	/∈	/∈	PUNCT
ejpam-4625	16	10	i	i	PRON
ejpam-4625	16	11	for	for	ADP
ejpam-4625	16	12	every	every	DET
ejpam-4625	16	13	u	u	PROPN
ejpam-4625	16	14	∈	∈	PROPN
ejpam-4625	16	15	τ(x	τ(x	NOUN
ejpam-4625	16	16	)	)	PUNCT
ejpam-4625	16	17	}	}	PUNCT
ejpam-4625	16	18	,	,	PUNCT
ejpam-4625	16	19	where	where	SCONJ
ejpam-4625	16	20	τ(x	τ(x	NOUN
ejpam-4625	16	21	)	)	PUNCT
ejpam-4625	16	22	=	=	PRON
ejpam-4625	16	23	{	{	PUNCT
ejpam-4625	16	24	u	u	X
ejpam-4625	16	25	∈	∈	PROPN
ejpam-4625	16	26	τ	τ	X
ejpam-4625	16	27	|	|	ADV
ejpam-4625	16	28	x	x	X
ejpam-4625	16	29	∈	∈	PROPN
ejpam-4625	16	30	u	u	NOUN
ejpam-4625	16	31	}	}	PUNCT
ejpam-4625	16	32	.	.	PUNCT
ejpam-4625	17	1	using	use	VERB
ejpam-4625	17	2	the	the	DET
ejpam-4625	17	3	notation	notation	NOUN
ejpam-4625	17	4	of	of	ADP
ejpam-4625	17	5	the	the	DET
ejpam-4625	17	6	previous	previous	ADJ
ejpam-4625	17	7	definition	definition	NOUN
ejpam-4625	17	8	,	,	PUNCT
ejpam-4625	17	9	it	it	PRON
ejpam-4625	17	10	can	can	AUX
ejpam-4625	17	11	easily	easily	ADV
ejpam-4625	17	12	be	be	AUX
ejpam-4625	17	13	seen	see	VERB
ejpam-4625	17	14	that	that	SCONJ
ejpam-4625	17	15	,	,	PUNCT
ejpam-4625	17	16	by	by	ADP
ejpam-4625	17	17	saying	say	VERB
ejpam-4625	17	18	,	,	PUNCT
ejpam-4625	17	19	for	for	ADP
ejpam-4625	17	20	every	every	DET
ejpam-4625	17	21	a	a	DET
ejpam-4625	17	22	⊂	⊂	PROPN
ejpam-4625	17	23	x	x	SYM
ejpam-4625	17	24	,	,	PUNCT
ejpam-4625	17	25	c∗(a	c∗(a	PROPN
ejpam-4625	17	26	)	)	PUNCT
ejpam-4625	17	27	=	=	PUNCT
ejpam-4625	17	28	a	a	DET
ejpam-4625	17	29	∪	∪	X
ejpam-4625	17	30	a∗(i	a∗(i	PROPN
ejpam-4625	17	31	,	,	PUNCT
ejpam-4625	17	32	τ	τ	PROPN
ejpam-4625	17	33	)	)	PUNCT
ejpam-4625	17	34	,	,	PUNCT
ejpam-4625	17	35	one	one	NUM
ejpam-4625	17	36	defines	define	VERB
ejpam-4625	17	37	a	a	DET
ejpam-4625	17	38	kuratowski	kuratowski	ADJ
ejpam-4625	17	39	closure	closure	NOUN
ejpam-4625	17	40	operator	operator	NOUN
ejpam-4625	18	1	c∗.this	c∗.this	PRON
ejpam-4625	18	2	closure	closure	NOUN
ejpam-4625	18	3	operator	operator	NOUN
ejpam-4625	18	4	induces	induce	VERB
ejpam-4625	18	5	a	a	DET
ejpam-4625	18	6	topology	topology	NOUN
ejpam-4625	18	7	on	on	ADP
ejpam-4625	18	8	x	x	PROPN
ejpam-4625	18	9	(	(	PUNCT
ejpam-4625	18	10	see	see	VERB
ejpam-4625	18	11	[	[	X
ejpam-4625	18	12	2	2	NUM
ejpam-4625	18	13	]	]	NUM
ejpam-4625	18	14	)	)	PUNCT
ejpam-4625	18	15	.	.	PUNCT
ejpam-4625	19	1	definition	definition	NOUN
ejpam-4625	19	2	2	2	NUM
ejpam-4625	19	3	.	.	PUNCT
ejpam-4625	20	1	for	for	ADP
ejpam-4625	20	2	an	an	DET
ejpam-4625	20	3	ideal	ideal	ADJ
ejpam-4625	20	4	i	i	PRON
ejpam-4625	20	5	of	of	ADP
ejpam-4625	20	6	subsets	subset	NOUN
ejpam-4625	20	7	of	of	ADP
ejpam-4625	20	8	a	a	DET
ejpam-4625	20	9	topological	topological	ADJ
ejpam-4625	20	10	space	space	NOUN
ejpam-4625	20	11	(	(	PUNCT
ejpam-4625	20	12	x	x	X
ejpam-4625	20	13	,	,	PUNCT
ejpam-4625	20	14	τ	τ	PROPN
ejpam-4625	20	15	)	)	PUNCT
ejpam-4625	20	16	,	,	PUNCT
ejpam-4625	20	17	the	the	DET
ejpam-4625	20	18	topology	topology	NOUN
ejpam-4625	20	19	on	on	ADV
ejpam-4625	20	20	x	x	PUNCT
ejpam-4625	20	21	induced	induce	VERB
ejpam-4625	20	22	by	by	ADP
ejpam-4625	20	23	the	the	DET
ejpam-4625	20	24	closure	closure	NOUN
ejpam-4625	20	25	operator	operator	NOUN
ejpam-4625	20	26	c∗	c∗	NOUN
ejpam-4625	20	27	is	be	AUX
ejpam-4625	20	28	denoted	denote	VERB
ejpam-4625	20	29	by	by	ADP
ejpam-4625	20	30	τ∗(i	τ∗(i	PROPN
ejpam-4625	20	31	,	,	PUNCT
ejpam-4625	20	32	τ	τ	PROPN
ejpam-4625	20	33	)	)	PUNCT
ejpam-4625	20	34	or	or	CCONJ
ejpam-4625	20	35	for	for	ADP
ejpam-4625	20	36	simplicity	simplicity	NOUN
ejpam-4625	20	37	,	,	PUNCT
ejpam-4625	20	38	τ∗	τ∗	X
ejpam-4625	20	39	if	if	SCONJ
ejpam-4625	20	40	this	this	PRON
ejpam-4625	20	41	does	do	AUX
ejpam-4625	20	42	not	not	PART
ejpam-4625	20	43	lead	lead	VERB
ejpam-4625	20	44	to	to	ADP
ejpam-4625	20	45	misunderstanding	misunderstanding	NOUN
ejpam-4625	20	46	.	.	PUNCT
ejpam-4625	21	1	doi	doi	NOUN
ejpam-4625	21	2	:	:	PUNCT
ejpam-4625	21	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4625	https://doi.org/10.29020/nybg.ejpam.v16i1.4625	VERB
ejpam-4625	21	4	email	email	NOUN
ejpam-4625	21	5	address	address	NOUN
ejpam-4625	21	6	:	:	PUNCT
ejpam-4625	21	7	asli.guldurdek@aum.edu.kw	asli.guldurdek@aum.edu.kw	NUM
ejpam-4625	21	8	(	(	PUNCT
ejpam-4625	21	9	a.	a.	NOUN
ejpam-4625	21	10	guldurdek	guldurdek	PROPN
ejpam-4625	21	11	)	)	PUNCT
ejpam-4625	21	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4625	21	13	1	1	NUM
ejpam-4625	21	14	©	©	PROPN
ejpam-4625	21	15	2023	2023	NUM
ejpam-4625	21	16	ejpam	ejpam	NOUN
ejpam-4625	21	17	all	all	DET
ejpam-4625	21	18	rights	right	NOUN
ejpam-4625	21	19	reserved	reserve	VERB
ejpam-4625	21	20	.	.	PUNCT
ejpam-4625	22	1	a.	a.	PROPN
ejpam-4625	22	2	guldurdek	guldurdek	PROPN
ejpam-4625	22	3	/	/	SYM
ejpam-4625	22	4	eur	eur	PROPN
ejpam-4625	22	5	.	.	PUNCT
ejpam-4625	23	1	j.	j.	PROPN
ejpam-4625	23	2	pure	pure	PROPN
ejpam-4625	23	3	appl	appl	PROPN
ejpam-4625	23	4	.	.	PROPN
ejpam-4625	23	5	math	math	PROPN
ejpam-4625	23	6	,	,	PUNCT
ejpam-4625	23	7	16	16	NUM
ejpam-4625	23	8	(	(	PUNCT
ejpam-4625	23	9	1	1	NUM
ejpam-4625	23	10	)	)	PUNCT
ejpam-4625	23	11	(	(	PUNCT
ejpam-4625	23	12	2023	2023	NUM
ejpam-4625	23	13	)	)	PUNCT
ejpam-4625	23	14	,	,	PUNCT
ejpam-4625	23	15	1	1	NUM
ejpam-4625	23	16	-	-	SYM
ejpam-4625	23	17	4	4	NUM
ejpam-4625	23	18	2	2	NUM
ejpam-4625	23	19	on	on	ADP
ejpam-4625	23	20	the	the	DET
ejpam-4625	23	21	other	other	ADJ
ejpam-4625	23	22	hand	hand	NOUN
ejpam-4625	23	23	,	,	PUNCT
ejpam-4625	23	24	examining	examine	VERB
ejpam-4625	23	25	the	the	DET
ejpam-4625	23	26	covering	covering	NOUN
ejpam-4625	23	27	properties	property	NOUN
ejpam-4625	23	28	of	of	ADP
ejpam-4625	23	29	topological	topological	ADJ
ejpam-4625	23	30	spaces	space	NOUN
ejpam-4625	23	31	is	be	AUX
ejpam-4625	23	32	also	also	ADV
ejpam-4625	23	33	an	an	DET
ejpam-4625	23	34	attractive	attractive	ADJ
ejpam-4625	23	35	area	area	NOUN
ejpam-4625	23	36	for	for	ADP
ejpam-4625	23	37	topologists	topologist	NOUN
ejpam-4625	23	38	.	.	PUNCT
ejpam-4625	24	1	one	one	NUM
ejpam-4625	24	2	of	of	ADP
ejpam-4625	24	3	these	these	DET
ejpam-4625	24	4	covering	cover	VERB
ejpam-4625	24	5	properties	property	NOUN
ejpam-4625	24	6	,	,	PUNCT
ejpam-4625	24	7	which	which	PRON
ejpam-4625	24	8	is	be	AUX
ejpam-4625	24	9	introduced	introduce	VERB
ejpam-4625	24	10	in	in	ADP
ejpam-4625	24	11	[	[	X
ejpam-4625	24	12	5	5	NUM
ejpam-4625	24	13	]	]	PUNCT
ejpam-4625	24	14	,	,	PUNCT
ejpam-4625	24	15	[	[	X
ejpam-4625	24	16	6	6	NUM
ejpam-4625	24	17	]	]	PUNCT
ejpam-4625	24	18	,	,	PUNCT
ejpam-4625	24	19	is	be	AUX
ejpam-4625	24	20	being	be	AUX
ejpam-4625	24	21	a	a	DET
ejpam-4625	24	22	rothberger	rothberger	NOUN
ejpam-4625	24	23	space	space	NOUN
ejpam-4625	24	24	.	.	PUNCT
ejpam-4625	25	1	definition	definition	NOUN
ejpam-4625	25	2	3	3	NUM
ejpam-4625	25	3	.	.	PUNCT
ejpam-4625	26	1	[	[	X
ejpam-4625	26	2	5	5	NUM
ejpam-4625	26	3	]	]	PUNCT
ejpam-4625	26	4	,	,	PUNCT
ejpam-4625	26	5	[	[	X
ejpam-4625	26	6	6	6	NUM
ejpam-4625	26	7	]	]	PUNCT
ejpam-4625	26	8	a	a	DET
ejpam-4625	26	9	space	space	NOUN
ejpam-4625	26	10	x	x	PUNCT
ejpam-4625	26	11	is	be	AUX
ejpam-4625	26	12	rothberger	rothberger	NOUN
ejpam-4625	26	13	if	if	SCONJ
ejpam-4625	26	14	for	for	ADP
ejpam-4625	26	15	every	every	DET
ejpam-4625	26	16	sequence	sequence	NOUN
ejpam-4625	26	17	{	{	PUNCT
ejpam-4625	26	18	un	un	PROPN
ejpam-4625	26	19	|	|	ADV
ejpam-4625	26	20	n	n	CCONJ
ejpam-4625	26	21	∈	∈	PROPN
ejpam-4625	26	22	n	n	CCONJ
ejpam-4625	26	23	}	}	PUNCT
ejpam-4625	26	24	of	of	ADP
ejpam-4625	26	25	open	open	ADJ
ejpam-4625	26	26	covers	cover	NOUN
ejpam-4625	26	27	of	of	ADP
ejpam-4625	26	28	x	x	SYM
ejpam-4625	26	29	there	there	PRON
ejpam-4625	26	30	exists	exist	VERB
ejpam-4625	26	31	a	a	DET
ejpam-4625	26	32	sequence	sequence	NOUN
ejpam-4625	26	33	{	{	PUNCT
ejpam-4625	26	34	un	un	PROPN
ejpam-4625	26	35	|	|	ADV
ejpam-4625	26	36	n	n	CCONJ
ejpam-4625	26	37	∈	∈	PROPN
ejpam-4625	26	38	n	n	CCONJ
ejpam-4625	26	39	}	}	PUNCT
ejpam-4625	26	40	such	such	ADJ
ejpam-4625	26	41	that	that	SCONJ
ejpam-4625	26	42	un	un	PROPN
ejpam-4625	26	43	∈	∈	PROPN
ejpam-4625	26	44	un	un	PROPN
ejpam-4625	26	45	for	for	ADP
ejpam-4625	26	46	every	every	DET
ejpam-4625	26	47	n	n	PRON
ejpam-4625	26	48	∈	∈	PROPN
ejpam-4625	26	49	n	n	CCONJ
ejpam-4625	26	50	,	,	PUNCT
ejpam-4625	26	51	and	and	CCONJ
ejpam-4625	26	52	x	x	X
ejpam-4625	26	53	=	=	SYM
ejpam-4625	26	54	⋃	⋃	NOUN
ejpam-4625	26	55	n∈n	n∈n	NOUN
ejpam-4625	26	56	un	un	NOUN
ejpam-4625	26	57	.	.	PUNCT
ejpam-4625	27	1	so	so	ADV
ejpam-4625	27	2	,	,	PUNCT
ejpam-4625	27	3	in	in	ADP
ejpam-4625	27	4	[	[	X
ejpam-4625	27	5	1	1	X
ejpam-4625	27	6	]	]	PUNCT
ejpam-4625	27	7	the	the	DET
ejpam-4625	27	8	notions	notion	NOUN
ejpam-4625	27	9	of	of	ADP
ejpam-4625	27	10	ideal	ideal	ADJ
ejpam-4625	27	11	topological	topological	ADJ
ejpam-4625	27	12	space	space	NOUN
ejpam-4625	27	13	and	and	CCONJ
ejpam-4625	27	14	rothberger	rothberger	NOUN
ejpam-4625	27	15	space	space	NOUN
ejpam-4625	27	16	were	be	AUX
ejpam-4625	27	17	brought	bring	VERB
ejpam-4625	27	18	together	together	ADV
ejpam-4625	27	19	,	,	PUNCT
ejpam-4625	27	20	and	and	CCONJ
ejpam-4625	27	21	resulted	result	VERB
ejpam-4625	27	22	in	in	ADP
ejpam-4625	27	23	ideal	ideal	ADJ
ejpam-4625	27	24	rothberger(i	rothberger(i	NOUN
ejpam-4625	27	25	-	-	PUNCT
ejpam-4625	27	26	rothberger	rothberger	NOUN
ejpam-4625	27	27	)	)	PUNCT
ejpam-4625	27	28	spaces	space	NOUN
ejpam-4625	27	29	.	.	PUNCT
ejpam-4625	28	1	definition	definition	NOUN
ejpam-4625	28	2	4	4	NUM
ejpam-4625	28	3	.	.	PUNCT
ejpam-4625	29	1	[	[	X
ejpam-4625	29	2	1	1	X
ejpam-4625	29	3	]	]	X
ejpam-4625	29	4	let	let	VERB
ejpam-4625	29	5	(	(	PUNCT
ejpam-4625	29	6	x	x	NOUN
ejpam-4625	29	7	,	,	PUNCT
ejpam-4625	29	8	τ	τ	PROPN
ejpam-4625	29	9	,	,	PUNCT
ejpam-4625	29	10	i	i	PRON
ejpam-4625	29	11	)	)	PUNCT
ejpam-4625	29	12	be	be	VERB
ejpam-4625	29	13	an	an	DET
ejpam-4625	29	14	ideal	ideal	ADJ
ejpam-4625	29	15	topological	topological	ADJ
ejpam-4625	29	16	space	space	NOUN
ejpam-4625	29	17	.	.	PUNCT
ejpam-4625	30	1	(	(	PUNCT
ejpam-4625	30	2	x	x	X
ejpam-4625	30	3	,	,	PUNCT
ejpam-4625	30	4	τ	τ	X
ejpam-4625	30	5	)	)	PUNCT
ejpam-4625	30	6	is	be	AUX
ejpam-4625	30	7	said	say	VERB
ejpam-4625	30	8	to	to	PART
ejpam-4625	30	9	be	be	AUX
ejpam-4625	30	10	irothberger	irothberger	NOUN
ejpam-4625	30	11	or	or	CCONJ
ejpam-4625	30	12	rothberger	rothberger	NOUN
ejpam-4625	30	13	with	with	ADP
ejpam-4625	30	14	respect	respect	NOUN
ejpam-4625	30	15	to	to	ADP
ejpam-4625	30	16	i	i	PRON
ejpam-4625	30	17	,	,	PUNCT
ejpam-4625	30	18	if	if	SCONJ
ejpam-4625	30	19	for	for	ADP
ejpam-4625	30	20	every	every	DET
ejpam-4625	30	21	sequence	sequence	NOUN
ejpam-4625	30	22	{	{	PUNCT
ejpam-4625	30	23	un	un	PROPN
ejpam-4625	30	24	|	|	ADV
ejpam-4625	30	25	n	n	CCONJ
ejpam-4625	30	26	∈	∈	PROPN
ejpam-4625	30	27	n	n	CCONJ
ejpam-4625	30	28	}	}	PUNCT
ejpam-4625	30	29	of	of	ADP
ejpam-4625	30	30	open	open	ADJ
ejpam-4625	30	31	covers	cover	NOUN
ejpam-4625	30	32	of	of	ADP
ejpam-4625	30	33	x	x	SYM
ejpam-4625	30	34	there	there	PRON
ejpam-4625	30	35	exists	exist	VERB
ejpam-4625	30	36	a	a	DET
ejpam-4625	30	37	sequence	sequence	NOUN
ejpam-4625	30	38	{	{	PUNCT
ejpam-4625	30	39	un	un	PROPN
ejpam-4625	30	40	|	|	ADV
ejpam-4625	30	41	n	n	CCONJ
ejpam-4625	30	42	∈	∈	PROPN
ejpam-4625	30	43	n	n	CCONJ
ejpam-4625	30	44	}	}	PUNCT
ejpam-4625	30	45	such	such	ADJ
ejpam-4625	30	46	that	that	SCONJ
ejpam-4625	30	47	un	un	PROPN
ejpam-4625	30	48	∈	∈	PROPN
ejpam-4625	30	49	un	un	PROPN
ejpam-4625	30	50	for	for	ADP
ejpam-4625	30	51	every	every	DET
ejpam-4625	30	52	n	n	PRON
ejpam-4625	30	53	∈	∈	PROPN
ejpam-4625	30	54	n	n	CCONJ
ejpam-4625	30	55	,	,	PUNCT
ejpam-4625	30	56	and	and	CCONJ
ejpam-4625	30	57	x	x	X
ejpam-4625	30	58	\	\	PROPN
ejpam-4625	30	59	⋃	⋃	PUNCT
ejpam-4625	30	60	n∈n	n∈n	NOUN
ejpam-4625	30	61	un	un	PROPN
ejpam-4625	30	62	∈	∈	PROPN
ejpam-4625	30	63	i.	i.	PROPN
ejpam-4625	30	64	in	in	ADP
ejpam-4625	30	65	[	[	X
ejpam-4625	30	66	1	1	NUM
ejpam-4625	30	67	]	]	PUNCT
ejpam-4625	30	68	besides	besides	SCONJ
ejpam-4625	30	69	exploring	explore	VERB
ejpam-4625	30	70	properties	property	NOUN
ejpam-4625	30	71	,	,	PUNCT
ejpam-4625	30	72	and	and	CCONJ
ejpam-4625	30	73	weak	weak	ADJ
ejpam-4625	30	74	forms	form	NOUN
ejpam-4625	30	75	of	of	ADP
ejpam-4625	30	76	i	i	PROPN
ejpam-4625	30	77	-	-	PUNCT
ejpam-4625	30	78	rothberger	rothberger	NOUN
ejpam-4625	30	79	spaces	space	VERB
ejpam-4625	30	80	,	,	PUNCT
ejpam-4625	30	81	a	a	DET
ejpam-4625	30	82	theorem	theorem	NOUN
ejpam-4625	30	83	about	about	ADP
ejpam-4625	30	84	the	the	DET
ejpam-4625	30	85	transition	transition	NOUN
ejpam-4625	30	86	between	between	ADP
ejpam-4625	30	87	(	(	PUNCT
ejpam-4625	30	88	x	x	NOUN
ejpam-4625	30	89	,	,	PUNCT
ejpam-4625	30	90	τ	τ	PROPN
ejpam-4625	30	91	)	)	PUNCT
ejpam-4625	30	92	,	,	PUNCT
ejpam-4625	30	93	and	and	CCONJ
ejpam-4625	30	94	(	(	PUNCT
ejpam-4625	30	95	x	x	NOUN
ejpam-4625	30	96	,	,	PUNCT
ejpam-4625	30	97	τ∗	τ∗	NOUN
ejpam-4625	30	98	)	)	PUNCT
ejpam-4625	30	99	is	be	AUX
ejpam-4625	30	100	given	give	VERB
ejpam-4625	30	101	as	as	ADP
ejpam-4625	30	102	following	follow	VERB
ejpam-4625	30	103	:	:	PUNCT
ejpam-4625	30	104	theorem	theorem	NOUN
ejpam-4625	30	105	1	1	X
ejpam-4625	30	106	.	.	PUNCT
ejpam-4625	31	1	let	let	AUX
ejpam-4625	31	2	(	(	PUNCT
ejpam-4625	31	3	x	x	NOUN
ejpam-4625	31	4	,	,	PUNCT
ejpam-4625	31	5	τ	τ	X
ejpam-4625	31	6	)	)	PUNCT
ejpam-4625	31	7	be	be	VERB
ejpam-4625	31	8	a	a	DET
ejpam-4625	31	9	topological	topological	ADJ
ejpam-4625	31	10	space	space	NOUN
ejpam-4625	31	11	,	,	PUNCT
ejpam-4625	31	12	i	i	PRON
ejpam-4625	31	13	be	be	VERB
ejpam-4625	31	14	an	an	DET
ejpam-4625	31	15	ideal	ideal	NOUN
ejpam-4625	31	16	on	on	ADP
ejpam-4625	31	17	x	x	NOUN
ejpam-4625	31	18	,	,	PUNCT
ejpam-4625	31	19	and	and	CCONJ
ejpam-4625	31	20	(	(	PUNCT
ejpam-4625	31	21	x	x	NOUN
ejpam-4625	31	22	,	,	PUNCT
ejpam-4625	31	23	τ∗	τ∗	ADJ
ejpam-4625	31	24	)	)	PUNCT
ejpam-4625	31	25	be	be	VERB
ejpam-4625	31	26	a	a	DET
ejpam-4625	31	27	rothberger	rothberger	NOUN
ejpam-4625	31	28	space	space	NOUN
ejpam-4625	31	29	.	.	PUNCT
ejpam-4625	32	1	then	then	ADV
ejpam-4625	32	2	(	(	PUNCT
ejpam-4625	32	3	x	x	X
ejpam-4625	32	4	,	,	PUNCT
ejpam-4625	32	5	τ	τ	X
ejpam-4625	32	6	)	)	PUNCT
ejpam-4625	32	7	is	be	AUX
ejpam-4625	32	8	also	also	ADV
ejpam-4625	32	9	rothberger	rothberger	NOUN
ejpam-4625	32	10	,	,	PUNCT
ejpam-4625	32	11	and	and	CCONJ
ejpam-4625	32	12	since	since	SCONJ
ejpam-4625	32	13	every	every	DET
ejpam-4625	32	14	rothberger	rothberger	NOUN
ejpam-4625	32	15	space	space	NOUN
ejpam-4625	32	16	is	be	AUX
ejpam-4625	32	17	shown	show	VERB
ejpam-4625	32	18	to	to	PART
ejpam-4625	32	19	be	be	AUX
ejpam-4625	32	20	i	i	NOUN
ejpam-4625	32	21	-	-	NOUN
ejpam-4625	32	22	rothberger	rothberger	PROPN
ejpam-4625	32	23	,	,	PUNCT
ejpam-4625	32	24	therefore	therefore	ADV
ejpam-4625	32	25	(	(	PUNCT
ejpam-4625	32	26	x	x	X
ejpam-4625	32	27	,	,	PUNCT
ejpam-4625	32	28	τ	τ	X
ejpam-4625	32	29	)	)	PUNCT
ejpam-4625	32	30	is	be	AUX
ejpam-4625	32	31	indeed	indeed	ADV
ejpam-4625	32	32	an	an	DET
ejpam-4625	32	33	i	i	NOUN
ejpam-4625	32	34	-	-	PUNCT
ejpam-4625	32	35	rothberger	rothberger	NOUN
ejpam-4625	32	36	space	space	NOUN
ejpam-4625	32	37	.	.	PUNCT
ejpam-4625	33	1	note	note	VERB
ejpam-4625	33	2	that	that	SCONJ
ejpam-4625	33	3	,	,	PUNCT
ejpam-4625	33	4	the	the	DET
ejpam-4625	33	5	proof	proof	NOUN
ejpam-4625	33	6	is	be	AUX
ejpam-4625	33	7	clear	clear	ADJ
ejpam-4625	33	8	via	via	ADP
ejpam-4625	33	9	the	the	DET
ejpam-4625	33	10	fact	fact	NOUN
ejpam-4625	33	11	that	that	SCONJ
ejpam-4625	33	12	τ	τ	PROPN
ejpam-4625	33	13	⊂	⊂	PROPN
ejpam-4625	33	14	τ∗.	τ∗.	AUX
ejpam-4625	33	15	following	follow	VERB
ejpam-4625	33	16	the	the	DET
ejpam-4625	33	17	previous	previous	ADJ
ejpam-4625	33	18	theorem	theorem	NOUN
ejpam-4625	33	19	,	,	PUNCT
ejpam-4625	33	20	an	an	DET
ejpam-4625	33	21	example	example	NOUN
ejpam-4625	33	22	which	which	PRON
ejpam-4625	33	23	shows	show	VERB
ejpam-4625	33	24	that	that	SCONJ
ejpam-4625	33	25	being	be	AUX
ejpam-4625	33	26	i	i	NOUN
ejpam-4625	33	27	-	-	NOUN
ejpam-4625	33	28	rothberger	rothberger	NOUN
ejpam-4625	33	29	for	for	ADP
ejpam-4625	33	30	(	(	PUNCT
ejpam-4625	33	31	x	x	NOUN
ejpam-4625	33	32	,	,	PUNCT
ejpam-4625	33	33	τ	τ	X
ejpam-4625	33	34	)	)	PUNCT
ejpam-4625	33	35	does	do	AUX
ejpam-4625	33	36	not	not	PART
ejpam-4625	33	37	imply	imply	VERB
ejpam-4625	33	38	being	be	AUX
ejpam-4625	33	39	rothberger	rothberger	NOUN
ejpam-4625	33	40	for	for	ADP
ejpam-4625	33	41	(	(	PUNCT
ejpam-4625	33	42	x	x	NOUN
ejpam-4625	33	43	,	,	PUNCT
ejpam-4625	33	44	τ∗	τ∗	NOUN
ejpam-4625	33	45	)	)	PUNCT
ejpam-4625	33	46	.	.	PUNCT
ejpam-4625	34	1	example	example	NOUN
ejpam-4625	35	1	1	1	NUM
ejpam-4625	35	2	.	.	PUNCT
ejpam-4625	36	1	[	[	X
ejpam-4625	36	2	1	1	X
ejpam-4625	36	3	]	]	PUNCT
ejpam-4625	36	4	let	let	VERB
ejpam-4625	36	5	x	x	PRON
ejpam-4625	36	6	be	be	AUX
ejpam-4625	36	7	the	the	DET
ejpam-4625	36	8	set	set	NOUN
ejpam-4625	36	9	of	of	ADP
ejpam-4625	36	10	real	real	ADJ
ejpam-4625	36	11	numbers	number	NOUN
ejpam-4625	36	12	r	r	NOUN
ejpam-4625	36	13	,	,	PUNCT
ejpam-4625	36	14	the	the	DET
ejpam-4625	36	15	topology	topology	NOUN
ejpam-4625	36	16	τ	τ	PROPN
ejpam-4625	36	17	be	be	AUX
ejpam-4625	36	18	the	the	DET
ejpam-4625	36	19	usual	usual	ADJ
ejpam-4625	36	20	topology	topology	NOUN
ejpam-4625	36	21	of	of	ADP
ejpam-4625	36	22	r	r	NOUN
ejpam-4625	36	23	,	,	PUNCT
ejpam-4625	36	24	and	and	CCONJ
ejpam-4625	36	25	the	the	DET
ejpam-4625	36	26	ideal	ideal	NOUN
ejpam-4625	36	27	i	i	PRON
ejpam-4625	36	28	be	be	VERB
ejpam-4625	36	29	the	the	DET
ejpam-4625	36	30	power	power	NOUN
ejpam-4625	36	31	set	set	VERB
ejpam-4625	36	32	p(r	p(r	PROPN
ejpam-4625	36	33	)	)	PUNCT
ejpam-4625	36	34	.	.	PUNCT
ejpam-4625	37	1	it	it	PRON
ejpam-4625	37	2	is	be	AUX
ejpam-4625	37	3	clear	clear	ADJ
ejpam-4625	37	4	that	that	SCONJ
ejpam-4625	37	5	,	,	PUNCT
ejpam-4625	37	6	(	(	PUNCT
ejpam-4625	37	7	r	r	NOUN
ejpam-4625	37	8	,	,	PUNCT
ejpam-4625	37	9	τ	τ	X
ejpam-4625	37	10	)	)	PUNCT
ejpam-4625	37	11	is	be	AUX
ejpam-4625	37	12	p(r)-rothberger	p(r)-rothberger	PROPN
ejpam-4625	37	13	.	.	PUNCT
ejpam-4625	38	1	on	on	ADP
ejpam-4625	38	2	the	the	DET
ejpam-4625	38	3	other	other	ADJ
ejpam-4625	38	4	hand	hand	NOUN
ejpam-4625	38	5	τ∗	τ∗	NOUN
ejpam-4625	38	6	on	on	ADP
ejpam-4625	38	7	r	r	NOUN
ejpam-4625	38	8	is	be	AUX
ejpam-4625	38	9	the	the	DET
ejpam-4625	38	10	discrete	discrete	ADJ
ejpam-4625	38	11	topology	topology	NOUN
ejpam-4625	38	12	,	,	PUNCT
ejpam-4625	38	13	which	which	PRON
ejpam-4625	38	14	does	do	AUX
ejpam-4625	38	15	not	not	PART
ejpam-4625	38	16	qualify	qualify	VERB
ejpam-4625	38	17	as	as	ADP
ejpam-4625	38	18	lindelöf	lindelöf	NOUN
ejpam-4625	38	19	,	,	PUNCT
ejpam-4625	38	20	therefore	therefore	ADV
ejpam-4625	38	21	,	,	PUNCT
ejpam-4625	38	22	it	it	PRON
ejpam-4625	38	23	is	be	AUX
ejpam-4625	38	24	not	not	PART
ejpam-4625	38	25	rothberger	rothberger	NOUN
ejpam-4625	38	26	.	.	PUNCT
ejpam-4625	39	1	based	base	VERB
ejpam-4625	39	2	on	on	ADP
ejpam-4625	39	3	these	these	PRON
ejpam-4625	39	4	,	,	PUNCT
ejpam-4625	39	5	a	a	DET
ejpam-4625	39	6	question	question	NOUN
ejpam-4625	39	7	is	be	AUX
ejpam-4625	39	8	posted	post	VERB
ejpam-4625	39	9	in	in	ADP
ejpam-4625	39	10	[	[	X
ejpam-4625	39	11	1	1	NUM
ejpam-4625	39	12	]	]	PUNCT
ejpam-4625	39	13	.	.	PUNCT
ejpam-4625	40	1	[	[	X
ejpam-4625	40	2	1	1	X
ejpam-4625	40	3	]	]	X
ejpam-4625	40	4	what	what	DET
ejpam-4625	40	5	extra	extra	ADJ
ejpam-4625	40	6	conditions	condition	NOUN
ejpam-4625	40	7	the	the	DET
ejpam-4625	40	8	ideal	ideal	NOUN
ejpam-4625	40	9	i	i	PRON
ejpam-4625	40	10	might	might	AUX
ejpam-4625	40	11	have	have	VERB
ejpam-4625	40	12	,	,	PUNCT
ejpam-4625	40	13	in	in	ADP
ejpam-4625	40	14	order	order	NOUN
ejpam-4625	40	15	to	to	PART
ejpam-4625	40	16	provide	provide	VERB
ejpam-4625	40	17	the	the	DET
ejpam-4625	40	18	converse	converse	NOUN
ejpam-4625	40	19	of	of	ADP
ejpam-4625	40	20	the	the	DET
ejpam-4625	40	21	previous	previous	ADJ
ejpam-4625	40	22	theorem	theorem	NOUN
ejpam-4625	40	23	?	?	PUNCT
ejpam-4625	41	1	in	in	ADP
ejpam-4625	41	2	this	this	DET
ejpam-4625	41	3	paper	paper	NOUN
ejpam-4625	41	4	,	,	PUNCT
ejpam-4625	41	5	the	the	DET
ejpam-4625	41	6	condition	condition	NOUN
ejpam-4625	41	7	for	for	ADP
ejpam-4625	41	8	the	the	DET
ejpam-4625	41	9	ideal	ideal	NOUN
ejpam-4625	41	10	i	i	PRON
ejpam-4625	41	11	is	be	AUX
ejpam-4625	41	12	provided	provide	VERB
ejpam-4625	41	13	.	.	PUNCT
ejpam-4625	42	1	2	2	X
ejpam-4625	42	2	.	.	X
ejpam-4625	42	3	main	main	ADJ
ejpam-4625	42	4	result	result	NOUN
ejpam-4625	42	5	given	give	VERB
ejpam-4625	42	6	a	a	DET
ejpam-4625	42	7	topology	topology	NOUN
ejpam-4625	42	8	τ	τ	NOUN
ejpam-4625	42	9	on	on	ADP
ejpam-4625	42	10	a	a	DET
ejpam-4625	42	11	set	set	NOUN
ejpam-4625	42	12	x	x	PUNCT
ejpam-4625	42	13	and	and	CCONJ
ejpam-4625	42	14	an	an	DET
ejpam-4625	42	15	ideal	ideal	ADJ
ejpam-4625	42	16	i	i	PRON
ejpam-4625	42	17	of	of	ADP
ejpam-4625	42	18	subsets	subset	NOUN
ejpam-4625	42	19	of	of	ADP
ejpam-4625	42	20	x	x	NOUN
ejpam-4625	42	21	,	,	PUNCT
ejpam-4625	42	22	such	such	ADJ
ejpam-4625	42	23	that	that	SCONJ
ejpam-4625	42	24	i	i	PRON
ejpam-4625	42	25	is	be	AUX
ejpam-4625	42	26	compatible	compatible	ADJ
ejpam-4625	42	27	with	with	ADP
ejpam-4625	42	28	τ	τ	PROPN
ejpam-4625	42	29	,	,	PUNCT
ejpam-4625	42	30	τ∗	τ∗	PROPN
ejpam-4625	42	31	denotes	denote	VERB
ejpam-4625	42	32	the	the	DET
ejpam-4625	42	33	topology	topology	NOUN
ejpam-4625	42	34	on	on	ADP
ejpam-4625	42	35	x	x	PUNCT
ejpam-4625	42	36	consisting	consist	VERB
ejpam-4625	42	37	of	of	ADP
ejpam-4625	42	38	all	all	DET
ejpam-4625	42	39	sets	set	NOUN
ejpam-4625	42	40	of	of	ADP
ejpam-4625	42	41	the	the	DET
ejpam-4625	42	42	form	form	NOUN
ejpam-4625	42	43	u	u	NOUN
ejpam-4625	42	44	\a	\a	VERB
ejpam-4625	42	45	where	where	SCONJ
ejpam-4625	42	46	u	u	PROPN
ejpam-4625	42	47	∈	∈	PROPN
ejpam-4625	42	48	τ	τ	X
ejpam-4625	42	49	and	and	CCONJ
ejpam-4625	42	50	a	a	DET
ejpam-4625	42	51	∈	∈	PROPN
ejpam-4625	42	52	i.	i.	NOUN
ejpam-4625	42	53	in	in	ADP
ejpam-4625	42	54	2018	2018	NUM
ejpam-4625	42	55	,	,	PUNCT
ejpam-4625	42	56	the	the	DET
ejpam-4625	42	57	notion	notion	NOUN
ejpam-4625	42	58	of	of	ADP
ejpam-4625	42	59	an	an	DET
ejpam-4625	42	60	i	i	PROPN
ejpam-4625	42	61	-	-	PUNCT
ejpam-4625	42	62	rothberger	rothberger	NOUN
ejpam-4625	42	63	space	space	NOUN
ejpam-4625	42	64	was	be	AUX
ejpam-4625	42	65	introduced	introduce	VERB
ejpam-4625	42	66	.	.	PUNCT
ejpam-4625	43	1	it	it	PRON
ejpam-4625	43	2	is	be	AUX
ejpam-4625	43	3	known	know	VERB
ejpam-4625	43	4	that	that	SCONJ
ejpam-4625	43	5	if	if	SCONJ
ejpam-4625	43	6	(	(	PUNCT
ejpam-4625	43	7	x	x	NOUN
ejpam-4625	43	8	,	,	PUNCT
ejpam-4625	43	9	τ∗	τ∗	ADJ
ejpam-4625	43	10	)	)	PUNCT
ejpam-4625	43	11	is	be	AUX
ejpam-4625	43	12	a	a	DET
ejpam-4625	43	13	rothberger	rothberger	NOUN
ejpam-4625	43	14	space	space	NOUN
ejpam-4625	43	15	,	,	PUNCT
ejpam-4625	43	16	so	so	ADV
ejpam-4625	43	17	is	be	AUX
ejpam-4625	43	18	(	(	PUNCT
ejpam-4625	43	19	x	x	NOUN
ejpam-4625	43	20	,	,	PUNCT
ejpam-4625	43	21	τ	τ	PROPN
ejpam-4625	43	22	)	)	PUNCT
ejpam-4625	43	23	.	.	PUNCT
ejpam-4625	44	1	however	however	ADV
ejpam-4625	44	2	,	,	PUNCT
ejpam-4625	44	3	a	a	DET
ejpam-4625	44	4	satisfactory	satisfactory	ADJ
ejpam-4625	44	5	answer	answer	NOUN
ejpam-4625	44	6	to	to	ADP
ejpam-4625	44	7	the	the	DET
ejpam-4625	44	8	a.	a.	NOUN
ejpam-4625	44	9	guldurdek	guldurdek	PROPN
ejpam-4625	44	10	/	/	SYM
ejpam-4625	44	11	eur	eur	PROPN
ejpam-4625	44	12	.	.	PUNCT
ejpam-4625	45	1	j.	j.	PROPN
ejpam-4625	45	2	pure	pure	PROPN
ejpam-4625	45	3	appl	appl	PROPN
ejpam-4625	45	4	.	.	PROPN
ejpam-4625	45	5	math	math	PROPN
ejpam-4625	45	6	,	,	PUNCT
ejpam-4625	45	7	16	16	NUM
ejpam-4625	45	8	(	(	PUNCT
ejpam-4625	45	9	1	1	NUM
ejpam-4625	45	10	)	)	PUNCT
ejpam-4625	45	11	(	(	PUNCT
ejpam-4625	45	12	2023	2023	NUM
ejpam-4625	45	13	)	)	PUNCT
ejpam-4625	45	14	,	,	PUNCT
ejpam-4625	45	15	1	1	NUM
ejpam-4625	45	16	-	-	SYM
ejpam-4625	45	17	4	4	NUM
ejpam-4625	45	18	3	3	NUM
ejpam-4625	45	19	question	question	NOUN
ejpam-4625	45	20	under	under	ADP
ejpam-4625	45	21	which	which	PRON
ejpam-4625	45	22	conditions	condition	NOUN
ejpam-4625	45	23	on	on	ADP
ejpam-4625	45	24	i	i	PRON
ejpam-4625	45	25	the	the	DET
ejpam-4625	45	26	reverse	reverse	ADJ
ejpam-4625	45	27	implication	implication	NOUN
ejpam-4625	45	28	also	also	ADV
ejpam-4625	45	29	holds	hold	VERB
ejpam-4625	45	30	is	be	AUX
ejpam-4625	45	31	still	still	ADV
ejpam-4625	45	32	unknown	unknown	ADJ
ejpam-4625	45	33	.	.	PUNCT
ejpam-4625	46	1	the	the	DET
ejpam-4625	46	2	main	main	ADJ
ejpam-4625	46	3	theorem	theorem	NOUN
ejpam-4625	46	4	of	of	ADP
ejpam-4625	46	5	the	the	DET
ejpam-4625	46	6	article	article	NOUN
ejpam-4625	46	7	asserts	assert	VERB
ejpam-4625	46	8	that	that	SCONJ
ejpam-4625	46	9	it	it	PRON
ejpam-4625	46	10	holds	hold	VERB
ejpam-4625	46	11	if	if	SCONJ
ejpam-4625	46	12	i	i	PRON
ejpam-4625	46	13	is	be	AUX
ejpam-4625	46	14	a	a	DET
ejpam-4625	46	15	σ	σ	NOUN
ejpam-4625	46	16	-	-	PUNCT
ejpam-4625	46	17	ideal	ideal	NOUN
ejpam-4625	46	18	of	of	ADP
ejpam-4625	46	19	subsets	subset	NOUN
ejpam-4625	46	20	of	of	ADP
ejpam-4625	46	21	x	x	SYM
ejpam-4625	46	22	such	such	ADJ
ejpam-4625	46	23	that	that	SCONJ
ejpam-4625	46	24	i	i	PRON
ejpam-4625	46	25	is	be	AUX
ejpam-4625	46	26	compatible	compatible	ADJ
ejpam-4625	46	27	with	with	ADP
ejpam-4625	46	28	a	a	DET
ejpam-4625	46	29	topology	topology	NOUN
ejpam-4625	46	30	τ	τ	X
ejpam-4625	46	31	on	on	ADP
ejpam-4625	46	32	x	x	PRON
ejpam-4625	46	33	,	,	PUNCT
ejpam-4625	46	34	and	and	CCONJ
ejpam-4625	46	35	the	the	DET
ejpam-4625	46	36	space	space	NOUN
ejpam-4625	46	37	(	(	PUNCT
ejpam-4625	46	38	x	x	X
ejpam-4625	46	39	,	,	PUNCT
ejpam-4625	46	40	τ	τ	X
ejpam-4625	46	41	)	)	PUNCT
ejpam-4625	46	42	is	be	AUX
ejpam-4625	46	43	i	i	NOUN
ejpam-4625	46	44	-	-	NOUN
ejpam-4625	46	45	rothberger	rothberger	NOUN
ejpam-4625	46	46	,	,	PUNCT
ejpam-4625	46	47	so	so	ADV
ejpam-4625	46	48	is	be	AUX
ejpam-4625	46	49	(	(	PUNCT
ejpam-4625	46	50	x	x	NOUN
ejpam-4625	46	51	,	,	PUNCT
ejpam-4625	46	52	τ∗	τ∗	NOUN
ejpam-4625	46	53	)	)	PUNCT
ejpam-4625	46	54	.	.	PUNCT
ejpam-4625	47	1	this	this	PRON
ejpam-4625	47	2	gives	give	VERB
ejpam-4625	47	3	a	a	DET
ejpam-4625	47	4	partial	partial	ADJ
ejpam-4625	47	5	answer	answer	NOUN
ejpam-4625	47	6	to	to	ADP
ejpam-4625	47	7	the	the	DET
ejpam-4625	47	8	above	above	ADV
ejpam-4625	47	9	-	-	PUNCT
ejpam-4625	47	10	mentioned	mention	VERB
ejpam-4625	47	11	question	question	NOUN
ejpam-4625	47	12	.	.	PUNCT
ejpam-4625	48	1	before	before	ADP
ejpam-4625	48	2	providing	provide	VERB
ejpam-4625	48	3	this	this	DET
ejpam-4625	48	4	condition	condition	NOUN
ejpam-4625	48	5	,	,	PUNCT
ejpam-4625	48	6	some	some	DET
ejpam-4625	48	7	basic	basic	ADJ
ejpam-4625	48	8	definitions	definition	NOUN
ejpam-4625	48	9	,	,	PUNCT
ejpam-4625	48	10	and	and	CCONJ
ejpam-4625	48	11	theorems	theorem	NOUN
ejpam-4625	48	12	to	to	PART
ejpam-4625	48	13	be	be	AUX
ejpam-4625	48	14	used	use	VERB
ejpam-4625	48	15	are	be	AUX
ejpam-4625	48	16	included	include	VERB
ejpam-4625	48	17	:	:	PUNCT
ejpam-4625	48	18	definition	definition	NOUN
ejpam-4625	48	19	5	5	NUM
ejpam-4625	48	20	.	.	PUNCT
ejpam-4625	49	1	[	[	X
ejpam-4625	49	2	2	2	X
ejpam-4625	49	3	]	]	PUNCT
ejpam-4625	49	4	an	an	DET
ejpam-4625	49	5	ideal	ideal	NOUN
ejpam-4625	49	6	i	i	PRON
ejpam-4625	49	7	is	be	AUX
ejpam-4625	49	8	said	say	VERB
ejpam-4625	49	9	to	to	PART
ejpam-4625	49	10	be	be	AUX
ejpam-4625	49	11	a	a	DET
ejpam-4625	49	12	σ	σ	NOUN
ejpam-4625	49	13	-	-	PUNCT
ejpam-4625	49	14	ideal	ideal	NOUN
ejpam-4625	49	15	if	if	SCONJ
ejpam-4625	49	16	it	it	PRON
ejpam-4625	49	17	is	be	AUX
ejpam-4625	49	18	countably	countably	ADV
ejpam-4625	49	19	additive	additive	ADJ
ejpam-4625	49	20	,	,	PUNCT
ejpam-4625	49	21	that	that	ADV
ejpam-4625	49	22	is	is	ADV
ejpam-4625	49	23	,	,	PUNCT
ejpam-4625	49	24	if	if	SCONJ
ejpam-4625	49	25	in	in	ADP
ejpam-4625	49	26	∈	∈	PROPN
ejpam-4625	49	27	i	i	PRON
ejpam-4625	49	28	,	,	PUNCT
ejpam-4625	49	29	for	for	ADP
ejpam-4625	49	30	each	each	DET
ejpam-4625	49	31	n	n	PRON
ejpam-4625	49	32	∈	∈	PROPN
ejpam-4625	49	33	n	n	CCONJ
ejpam-4625	49	34	,	,	PUNCT
ejpam-4625	49	35	then	then	ADV
ejpam-4625	49	36	⋃	⋃	PROPN
ejpam-4625	49	37	{	{	PUNCT
ejpam-4625	49	38	in|n	in|n	NOUN
ejpam-4625	49	39	∈	∈	PROPN
ejpam-4625	49	40	n	n	CCONJ
ejpam-4625	49	41	}	}	PUNCT
ejpam-4625	49	42	∈	∈	PROPN
ejpam-4625	49	43	i.	i.	NOUN
ejpam-4625	49	44	definition	definition	NOUN
ejpam-4625	49	45	6	6	NUM
ejpam-4625	49	46	.	.	PUNCT
ejpam-4625	50	1	[	[	X
ejpam-4625	50	2	4	4	X
ejpam-4625	50	3	]	]	X
ejpam-4625	50	4	let	let	VERB
ejpam-4625	50	5	(	(	PUNCT
ejpam-4625	50	6	x	x	NOUN
ejpam-4625	50	7	,	,	PUNCT
ejpam-4625	50	8	τ	τ	X
ejpam-4625	50	9	)	)	PUNCT
ejpam-4625	50	10	be	be	VERB
ejpam-4625	50	11	a	a	DET
ejpam-4625	50	12	topological	topological	ADJ
ejpam-4625	50	13	space	space	NOUN
ejpam-4625	50	14	with	with	ADP
ejpam-4625	50	15	an	an	DET
ejpam-4625	50	16	ideal	ideal	ADJ
ejpam-4625	50	17	i.	i.	NOUN
ejpam-4625	50	18	the	the	DET
ejpam-4625	50	19	topology	topology	NOUN
ejpam-4625	50	20	τ	τ	PROPN
ejpam-4625	50	21	is	be	AUX
ejpam-4625	50	22	indicated	indicate	VERB
ejpam-4625	50	23	as	as	ADP
ejpam-4625	50	24	compatible	compatible	ADJ
ejpam-4625	50	25	with	with	ADP
ejpam-4625	50	26	the	the	DET
ejpam-4625	50	27	ideal	ideal	NOUN
ejpam-4625	50	28	i	i	PRON
ejpam-4625	50	29	,	,	PUNCT
ejpam-4625	50	30	which	which	PRON
ejpam-4625	50	31	is	be	AUX
ejpam-4625	50	32	denoted	denote	VERB
ejpam-4625	50	33	by	by	ADP
ejpam-4625	50	34	τ	τ	PROPN
ejpam-4625	50	35	∼	∼	NOUN
ejpam-4625	50	36	i	i	PRON
ejpam-4625	50	37	,	,	PUNCT
ejpam-4625	50	38	if	if	SCONJ
ejpam-4625	50	39	the	the	DET
ejpam-4625	50	40	following	follow	VERB
ejpam-4625	50	41	holds	hold	VERB
ejpam-4625	50	42	for	for	SCONJ
ejpam-4625	50	43	every	every	DET
ejpam-4625	50	44	a	a	DET
ejpam-4625	50	45	⊂	⊂	PROPN
ejpam-4625	50	46	x	x	NOUN
ejpam-4625	50	47	:	:	PUNCT
ejpam-4625	50	48	if	if	SCONJ
ejpam-4625	50	49	for	for	ADP
ejpam-4625	50	50	every	every	DET
ejpam-4625	50	51	x	x	PROPN
ejpam-4625	50	52	∈	∈	PROPN
ejpam-4625	50	53	a	a	PRON
ejpam-4625	50	54	,	,	PUNCT
ejpam-4625	50	55	there	there	PRON
ejpam-4625	50	56	exists	exist	VERB
ejpam-4625	50	57	a	a	DET
ejpam-4625	50	58	set	set	NOUN
ejpam-4625	50	59	u	u	PROPN
ejpam-4625	50	60	∈	∈	NOUN
ejpam-4625	50	61	τ(x	τ(x	NOUN
ejpam-4625	50	62	)	)	PUNCT
ejpam-4625	50	63	such	such	ADJ
ejpam-4625	50	64	that	that	SCONJ
ejpam-4625	50	65	u	u	NOUN
ejpam-4625	50	66	∩a	∩a	PROPN
ejpam-4625	50	67	∈	∈	PROPN
ejpam-4625	51	1	i	i	PRON
ejpam-4625	51	2	,	,	PUNCT
ejpam-4625	51	3	then	then	ADV
ejpam-4625	51	4	a	a	DET
ejpam-4625	51	5	∈	∈	PROPN
ejpam-4625	51	6	i.	i.	NOUN
ejpam-4625	51	7	theorem	theorem	VERB
ejpam-4625	51	8	2	2	NUM
ejpam-4625	51	9	.	.	PUNCT
ejpam-4625	52	1	[	[	X
ejpam-4625	52	2	4	4	X
ejpam-4625	52	3	]	]	X
ejpam-4625	52	4	let	let	VERB
ejpam-4625	52	5	(	(	PUNCT
ejpam-4625	52	6	x	x	NOUN
ejpam-4625	52	7	,	,	PUNCT
ejpam-4625	52	8	τ	τ	X
ejpam-4625	52	9	)	)	PUNCT
ejpam-4625	52	10	be	be	VERB
ejpam-4625	52	11	a	a	DET
ejpam-4625	52	12	topological	topological	ADJ
ejpam-4625	52	13	space	space	NOUN
ejpam-4625	52	14	,	,	PUNCT
ejpam-4625	52	15	i	i	PRON
ejpam-4625	52	16	be	be	VERB
ejpam-4625	52	17	an	an	DET
ejpam-4625	52	18	ideal	ideal	NOUN
ejpam-4625	52	19	on	on	ADP
ejpam-4625	52	20	x	x	NOUN
ejpam-4625	52	21	,	,	PUNCT
ejpam-4625	52	22	and	and	CCONJ
ejpam-4625	52	23	τ	τ	PROPN
ejpam-4625	52	24	be	be	AUX
ejpam-4625	52	25	compatible	compatible	ADJ
ejpam-4625	52	26	with	with	ADP
ejpam-4625	52	27	i.	i.	PROPN
ejpam-4625	52	28	a	a	DET
ejpam-4625	52	29	set	set	NOUN
ejpam-4625	52	30	is	be	AUX
ejpam-4625	52	31	closed	close	VERB
ejpam-4625	52	32	in	in	ADP
ejpam-4625	52	33	τ∗	τ∗	NOUN
ejpam-4625	52	34	if	if	SCONJ
ejpam-4625	52	35	and	and	CCONJ
ejpam-4625	52	36	only	only	ADV
ejpam-4625	52	37	if	if	SCONJ
ejpam-4625	52	38	it	it	PRON
ejpam-4625	52	39	is	be	AUX
ejpam-4625	52	40	the	the	DET
ejpam-4625	52	41	union	union	NOUN
ejpam-4625	52	42	of	of	ADP
ejpam-4625	52	43	a	a	DET
ejpam-4625	52	44	set	set	NOUN
ejpam-4625	52	45	which	which	PRON
ejpam-4625	52	46	is	be	AUX
ejpam-4625	52	47	closed	close	VERB
ejpam-4625	52	48	with	with	ADP
ejpam-4625	52	49	respect	respect	NOUN
ejpam-4625	52	50	to	to	ADP
ejpam-4625	52	51	τ	τ	PROPN
ejpam-4625	52	52	and	and	CCONJ
ejpam-4625	52	53	a	a	DET
ejpam-4625	52	54	set	set	NOUN
ejpam-4625	52	55	from	from	ADP
ejpam-4625	52	56	the	the	DET
ejpam-4625	52	57	ideal	ideal	ADJ
ejpam-4625	52	58	i.	i.	PROPN
ejpam-4625	52	59	corollary	corollary	PROPN
ejpam-4625	52	60	1	1	NUM
ejpam-4625	52	61	.	.	PUNCT
ejpam-4625	53	1	[	[	X
ejpam-4625	53	2	2	2	NUM
ejpam-4625	53	3	]	]	X
ejpam-4625	53	4	let	let	VERB
ejpam-4625	53	5	(	(	PUNCT
ejpam-4625	53	6	x	x	NOUN
ejpam-4625	53	7	,	,	PUNCT
ejpam-4625	53	8	τ	τ	X
ejpam-4625	53	9	)	)	PUNCT
ejpam-4625	53	10	be	be	VERB
ejpam-4625	53	11	a	a	DET
ejpam-4625	53	12	topological	topological	ADJ
ejpam-4625	53	13	space	space	NOUN
ejpam-4625	54	1	and	and	CCONJ
ejpam-4625	54	2	i	i	PRON
ejpam-4625	54	3	be	be	VERB
ejpam-4625	54	4	an	an	DET
ejpam-4625	54	5	ideal	ideal	NOUN
ejpam-4625	54	6	on	on	ADP
ejpam-4625	54	7	x	x	X
ejpam-4625	54	8	,	,	PUNCT
ejpam-4625	54	9	with	with	ADP
ejpam-4625	54	10	τ	τ	PROPN
ejpam-4625	54	11	∼	∼	NOUN
ejpam-4625	54	12	i.	i.	NOUN
ejpam-4625	54	13	based	base	VERB
ejpam-4625	54	14	on	on	ADP
ejpam-4625	54	15	the	the	DET
ejpam-4625	54	16	previous	previous	ADJ
ejpam-4625	54	17	theorem	theorem	NOUN
ejpam-4625	54	18	it	it	PRON
ejpam-4625	54	19	is	be	AUX
ejpam-4625	54	20	known	know	VERB
ejpam-4625	54	21	that	that	SCONJ
ejpam-4625	54	22	every	every	DET
ejpam-4625	54	23	closed	close	VERB
ejpam-4625	54	24	set	set	NOUN
ejpam-4625	54	25	k	k	NOUN
ejpam-4625	54	26	can	can	AUX
ejpam-4625	54	27	be	be	AUX
ejpam-4625	54	28	written	write	VERB
ejpam-4625	54	29	as	as	ADP
ejpam-4625	54	30	k	k	PROPN
ejpam-4625	54	31	=	=	PROPN
ejpam-4625	54	32	f	f	PROPN
ejpam-4625	54	33	∪	∪	VERB
ejpam-4625	54	34	i	i	PRON
ejpam-4625	54	35	,	,	PUNCT
ejpam-4625	54	36	where	where	SCONJ
ejpam-4625	54	37	f	f	PROPN
ejpam-4625	54	38	is	be	AUX
ejpam-4625	54	39	closed	close	VERB
ejpam-4625	54	40	with	with	ADP
ejpam-4625	54	41	respect	respect	NOUN
ejpam-4625	54	42	to	to	ADP
ejpam-4625	54	43	τ	τ	PROPN
ejpam-4625	54	44	,	,	PUNCT
ejpam-4625	54	45	and	and	CCONJ
ejpam-4625	54	46	i	i	PROPN
ejpam-4625	54	47	∈	∈	PROPN
ejpam-4625	54	48	i.	i.	NOUN
ejpam-4625	54	49	then	then	ADV
ejpam-4625	54	50	every	every	DET
ejpam-4625	54	51	τ∗-open	τ∗-open	PUNCT
ejpam-4625	54	52	set	set	NOUN
ejpam-4625	54	53	u	u	NOUN
ejpam-4625	54	54	will	will	AUX
ejpam-4625	54	55	be	be	AUX
ejpam-4625	54	56	the	the	DET
ejpam-4625	54	57	complement	complement	NOUN
ejpam-4625	54	58	of	of	ADP
ejpam-4625	54	59	the	the	DET
ejpam-4625	54	60	sets	set	NOUN
ejpam-4625	54	61	of	of	ADP
ejpam-4625	54	62	this	this	DET
ejpam-4625	54	63	type	type	NOUN
ejpam-4625	54	64	and	and	CCONJ
ejpam-4625	54	65	hence	hence	ADV
ejpam-4625	54	66	will	will	AUX
ejpam-4625	54	67	have	have	VERB
ejpam-4625	54	68	the	the	DET
ejpam-4625	54	69	form	form	NOUN
ejpam-4625	54	70	:	:	PUNCT
ejpam-4625	54	71	u	u	NOUN
ejpam-4625	54	72	=	=	PROPN
ejpam-4625	54	73	g	g	PROPN
ejpam-4625	54	74	\	\	PROPN
ejpam-4625	55	1	i	i	PRON
ejpam-4625	55	2	,	,	PUNCT
ejpam-4625	55	3	where	where	SCONJ
ejpam-4625	55	4	g	g	PROPN
ejpam-4625	55	5	∈	∈	PROPN
ejpam-4625	55	6	τ	τ	X
ejpam-4625	55	7	,	,	PUNCT
ejpam-4625	55	8	and	and	CCONJ
ejpam-4625	55	9	i	i	PRON
ejpam-4625	55	10	∈	∈	PROPN
ejpam-4625	55	11	i.	i.	NOUN
ejpam-4625	55	12	finally	finally	ADV
ejpam-4625	55	13	,	,	PUNCT
ejpam-4625	55	14	the	the	DET
ejpam-4625	55	15	answer	answer	NOUN
ejpam-4625	55	16	to	to	ADP
ejpam-4625	55	17	the	the	DET
ejpam-4625	55	18	question	question	NOUN
ejpam-4625	55	19	that	that	PRON
ejpam-4625	55	20	was	be	AUX
ejpam-4625	55	21	posted	post	VERB
ejpam-4625	55	22	:	:	PUNCT
ejpam-4625	55	23	theorem	theorem	NOUN
ejpam-4625	55	24	3	3	X
ejpam-4625	55	25	.	.	PUNCT
ejpam-4625	56	1	let	let	AUX
ejpam-4625	56	2	(	(	PUNCT
ejpam-4625	56	3	x	x	NOUN
ejpam-4625	56	4	,	,	PUNCT
ejpam-4625	56	5	τ	τ	X
ejpam-4625	56	6	)	)	PUNCT
ejpam-4625	56	7	be	be	VERB
ejpam-4625	56	8	a	a	DET
ejpam-4625	56	9	topological	topological	ADJ
ejpam-4625	56	10	space	space	NOUN
ejpam-4625	56	11	,	,	PUNCT
ejpam-4625	56	12	i	i	PRON
ejpam-4625	56	13	be	be	VERB
ejpam-4625	56	14	a	a	DET
ejpam-4625	56	15	σ	σ	NOUN
ejpam-4625	56	16	-	-	PUNCT
ejpam-4625	56	17	ideal	ideal	NOUN
ejpam-4625	56	18	on	on	ADP
ejpam-4625	56	19	x	x	NOUN
ejpam-4625	56	20	,	,	PUNCT
ejpam-4625	56	21	and	and	CCONJ
ejpam-4625	56	22	τ	τ	PROPN
ejpam-4625	56	23	∼	∼	NOUN
ejpam-4625	56	24	i.	i.	NOUN
ejpam-4625	56	25	if	if	SCONJ
ejpam-4625	56	26	(	(	PUNCT
ejpam-4625	56	27	x	x	X
ejpam-4625	56	28	,	,	PUNCT
ejpam-4625	56	29	τ	τ	X
ejpam-4625	56	30	)	)	PUNCT
ejpam-4625	56	31	is	be	AUX
ejpam-4625	56	32	i	i	NOUN
ejpam-4625	56	33	-	-	PUNCT
ejpam-4625	56	34	rothberger	rothberger	NOUN
ejpam-4625	56	35	,	,	PUNCT
ejpam-4625	56	36	then	then	ADV
ejpam-4625	56	37	(	(	PUNCT
ejpam-4625	56	38	x	x	NOUN
ejpam-4625	56	39	,	,	PUNCT
ejpam-4625	56	40	τ∗	τ∗	ADJ
ejpam-4625	56	41	)	)	PUNCT
ejpam-4625	57	1	is	be	AUX
ejpam-4625	57	2	also	also	ADV
ejpam-4625	57	3	an	an	DET
ejpam-4625	57	4	i	i	NOUN
ejpam-4625	57	5	-	-	PUNCT
ejpam-4625	57	6	rothberger	rothberger	NOUN
ejpam-4625	57	7	space	space	NOUN
ejpam-4625	57	8	.	.	PUNCT
ejpam-4625	58	1	proof	proof	NOUN
ejpam-4625	58	2	.	.	PUNCT
ejpam-4625	59	1	let	let	VERB
ejpam-4625	59	2	{	{	PUNCT
ejpam-4625	59	3	un	un	VERB
ejpam-4625	59	4	|	|	ADV
ejpam-4625	59	5	n	n	CCONJ
ejpam-4625	59	6	∈	∈	PROPN
ejpam-4625	59	7	n	n	CCONJ
ejpam-4625	59	8	}	}	PUNCT
ejpam-4625	59	9	be	be	AUX
ejpam-4625	59	10	a	a	DET
ejpam-4625	59	11	sequence	sequence	NOUN
ejpam-4625	59	12	of	of	ADP
ejpam-4625	59	13	open	open	ADJ
ejpam-4625	59	14	covers	cover	NOUN
ejpam-4625	59	15	of	of	ADP
ejpam-4625	59	16	x	x	PUNCT
ejpam-4625	59	17	with	with	ADP
ejpam-4625	59	18	respect	respect	NOUN
ejpam-4625	59	19	to	to	ADP
ejpam-4625	59	20	topology	topology	NOUN
ejpam-4625	59	21	τ∗.	τ∗.	VERB
ejpam-4625	59	22	so	so	ADV
ejpam-4625	59	23	;	;	PUNCT
ejpam-4625	59	24	un	un	PROPN
ejpam-4625	59	25	=	=	PRON
ejpam-4625	59	26	{	{	PUNCT
ejpam-4625	59	27	uα	uα	PROPN
ejpam-4625	59	28	n	n	CCONJ
ejpam-4625	59	29	|	|	ADV
ejpam-4625	59	30	α	α	PROPN
ejpam-4625	59	31	∈	∈	PROPN
ejpam-4625	59	32	∆n	∆n	PROPN
ejpam-4625	59	33	}	}	PUNCT
ejpam-4625	59	34	;	;	PUNCT
ejpam-4625	59	35	for	for	ADP
ejpam-4625	59	36	every	every	DET
ejpam-4625	59	37	n	n	PRON
ejpam-4625	59	38	∈	∈	PROPN
ejpam-4625	59	39	n	n	CCONJ
ejpam-4625	59	40	,	,	PUNCT
ejpam-4625	59	41	and	and	CCONJ
ejpam-4625	59	42	uα	uα	PROPN
ejpam-4625	59	43	n	n	PRON
ejpam-4625	59	44	∈	∈	NOUN
ejpam-4625	59	45	τ∗.	τ∗.	X
ejpam-4625	59	46	by	by	ADP
ejpam-4625	59	47	compatibility	compatibility	NOUN
ejpam-4625	59	48	:	:	PUNCT
ejpam-4625	59	49	uα	uα	PROPN
ejpam-4625	59	50	n	n	NOUN
ejpam-4625	59	51	=	=	PUNCT
ejpam-4625	59	52	gα	gα	ADP
ejpam-4625	59	53	n	n	PRON
ejpam-4625	59	54	\	\	PROPN
ejpam-4625	59	55	iαn	iαn	PROPN
ejpam-4625	59	56	,	,	PUNCT
ejpam-4625	59	57	where	where	SCONJ
ejpam-4625	59	58	gα	gα	ADP
ejpam-4625	59	59	n	n	PRON
ejpam-4625	59	60	∈	∈	PROPN
ejpam-4625	59	61	τ	τ	X
ejpam-4625	59	62	,	,	PUNCT
ejpam-4625	59	63	and	and	CCONJ
ejpam-4625	59	64	iαn	iαn	PROPN
ejpam-4625	59	65	∈	∈	PROPN
ejpam-4625	59	66	i.	i.	NOUN
ejpam-4625	59	67	clearly	clearly	ADV
ejpam-4625	59	68	gn	gn	PROPN
ejpam-4625	60	1	=	=	PUNCT
ejpam-4625	60	2	{	{	PUNCT
ejpam-4625	60	3	gα	gα	NOUN
ejpam-4625	60	4	n	n	PRON
ejpam-4625	61	1	|	|	ADV
ejpam-4625	61	2	α	α	PRON
ejpam-4625	61	3	∈	∈	PROPN
ejpam-4625	61	4	∆n	∆n	PROPN
ejpam-4625	61	5	}	}	PUNCT
ejpam-4625	61	6	is	be	AUX
ejpam-4625	61	7	an	an	DET
ejpam-4625	61	8	open	open	ADJ
ejpam-4625	61	9	cover	cover	NOUN
ejpam-4625	61	10	of	of	ADP
ejpam-4625	61	11	x	x	X
ejpam-4625	61	12	,	,	PUNCT
ejpam-4625	61	13	with	with	ADP
ejpam-4625	61	14	respect	respect	NOUN
ejpam-4625	61	15	to	to	ADP
ejpam-4625	61	16	topology	topology	NOUN
ejpam-4625	61	17	τ	τ	NOUN
ejpam-4625	61	18	,	,	PUNCT
ejpam-4625	61	19	and	and	CCONJ
ejpam-4625	61	20	so	so	ADV
ejpam-4625	61	21	{	{	PUNCT
ejpam-4625	61	22	gn	gn	INTJ
ejpam-4625	61	23	|	|	ADV
ejpam-4625	61	24	n	n	CCONJ
ejpam-4625	61	25	∈	∈	PROPN
ejpam-4625	61	26	n	n	CCONJ
ejpam-4625	61	27	}	}	PUNCT
ejpam-4625	61	28	is	be	AUX
ejpam-4625	61	29	a	a	DET
ejpam-4625	61	30	sequence	sequence	NOUN
ejpam-4625	61	31	of	of	ADP
ejpam-4625	61	32	open	open	ADJ
ejpam-4625	61	33	covers	cover	NOUN
ejpam-4625	61	34	.	.	PUNCT
ejpam-4625	62	1	since	since	SCONJ
ejpam-4625	62	2	(	(	PUNCT
ejpam-4625	62	3	x	x	X
ejpam-4625	62	4	,	,	PUNCT
ejpam-4625	62	5	τ	τ	X
ejpam-4625	62	6	)	)	PUNCT
ejpam-4625	62	7	is	be	AUX
ejpam-4625	62	8	i	i	NOUN
ejpam-4625	62	9	-	-	PUNCT
ejpam-4625	62	10	rothberger	rothberger	NOUN
ejpam-4625	62	11	,	,	PUNCT
ejpam-4625	62	12	there	there	PRON
ejpam-4625	62	13	exists	exist	VERB
ejpam-4625	62	14	a	a	DET
ejpam-4625	62	15	sequence	sequence	NOUN
ejpam-4625	62	16	{	{	PUNCT
ejpam-4625	62	17	αn	αn	INTJ
ejpam-4625	62	18	|	|	ADV
ejpam-4625	62	19	n	n	CCONJ
ejpam-4625	62	20	∈	∈	PROPN
ejpam-4625	62	21	n	n	CCONJ
ejpam-4625	62	22	}	}	PUNCT
ejpam-4625	62	23	such	such	ADJ
ejpam-4625	62	24	that	that	SCONJ
ejpam-4625	62	25	,	,	PUNCT
ejpam-4625	62	26	for	for	ADP
ejpam-4625	62	27	every	every	DET
ejpam-4625	62	28	n	n	PRON
ejpam-4625	62	29	∈	∈	PROPN
ejpam-4625	62	30	n	n	CCONJ
ejpam-4625	62	31	,	,	PUNCT
ejpam-4625	62	32	αn	αn	NOUN
ejpam-4625	62	33	∈	∈	PROPN
ejpam-4625	62	34	∆n	∆n	PROPN
ejpam-4625	62	35	,	,	PUNCT
ejpam-4625	62	36	and	and	CCONJ
ejpam-4625	62	37	j	j	PROPN
ejpam-4625	62	38	=	=	SYM
ejpam-4625	62	39	x	x	SYM
ejpam-4625	62	40	\	\	PROPN
ejpam-4625	62	41	∞⋃	∞⋃	PROPN
ejpam-4625	62	42	n=1	n=1	PUNCT
ejpam-4625	62	43	gαn	gαn	PROPN
ejpam-4625	62	44	n	n	CCONJ
ejpam-4625	62	45	∈	∈	PROPN
ejpam-4625	62	46	i.	i.	NOUN
ejpam-4625	62	47	on	on	ADP
ejpam-4625	62	48	the	the	DET
ejpam-4625	62	49	other	other	ADJ
ejpam-4625	62	50	hand	hand	NOUN
ejpam-4625	62	51	,	,	PUNCT
ejpam-4625	62	52	since	since	SCONJ
ejpam-4625	62	53	i	i	PRON
ejpam-4625	62	54	is	be	AUX
ejpam-4625	62	55	a	a	DET
ejpam-4625	62	56	σ	σ	NOUN
ejpam-4625	62	57	-	-	PUNCT
ejpam-4625	62	58	ideal	ideal	NOUN
ejpam-4625	62	59	,	,	PUNCT
ejpam-4625	62	60	it	it	PRON
ejpam-4625	62	61	is	be	AUX
ejpam-4625	62	62	accepted	accept	VERB
ejpam-4625	62	63	that	that	SCONJ
ejpam-4625	62	64	k	k	PROPN
ejpam-4625	62	65	=	=	SYM
ejpam-4625	62	66	∞⋃	∞⋃	PROPN
ejpam-4625	62	67	n=1	n=1	PROPN
ejpam-4625	62	68	iαn	iαn	PROPN
ejpam-4625	62	69	n	n	PROPN
ejpam-4625	62	70	∈	∈	PROPN
ejpam-4625	62	71	i.	i.	NOUN
ejpam-4625	63	1	so	so	ADV
ejpam-4625	63	2	;	;	PUNCT
ejpam-4625	63	3	j	j	PROPN
ejpam-4625	63	4	∪k	∪k	PROPN
ejpam-4625	63	5	=	=	SYM
ejpam-4625	63	6	(	(	PUNCT
ejpam-4625	63	7	x	x	SYM
ejpam-4625	63	8	\	\	PROPN
ejpam-4625	63	9	∞⋃	∞⋃	PROPN
ejpam-4625	63	10	n=1	n=1	PUNCT
ejpam-4625	63	11	gαn	gαn	PROPN
ejpam-4625	63	12	n	n	ADV
ejpam-4625	63	13	)	)	PUNCT
ejpam-4625	63	14	∪	∪	PROPN
ejpam-4625	63	15	(	(	PUNCT
ejpam-4625	63	16	∞⋃	∞⋃	PROPN
ejpam-4625	63	17	n=1	n=1	PROPN
ejpam-4625	63	18	iαn	iαn	PROPN
ejpam-4625	63	19	n	n	CCONJ
ejpam-4625	63	20	)	)	PUNCT
ejpam-4625	63	21	∈	∈	PROPN
ejpam-4625	63	22	i.	i.	NOUN
ejpam-4625	63	23	and	and	CCONJ
ejpam-4625	63	24	clearly	clearly	ADV
ejpam-4625	63	25	;	;	PUNCT
ejpam-4625	63	26	references	reference	NOUN
ejpam-4625	63	27	4	4	NUM
ejpam-4625	63	28	x	x	SYM
ejpam-4625	63	29	\	\	PROPN
ejpam-4625	63	30	∞⋃	∞⋃	PROPN
ejpam-4625	63	31	n=1	n=1	PROPN
ejpam-4625	63	32	uαn	uαn	PROPN
ejpam-4625	63	33	n	n	PROPN
ejpam-4625	63	34	⊆	⊆	NUM
ejpam-4625	63	35	(	(	PUNCT
ejpam-4625	63	36	x	x	SYM
ejpam-4625	63	37	\	\	PROPN
ejpam-4625	63	38	∞⋃	∞⋃	PROPN
ejpam-4625	63	39	n=1	n=1	PUNCT
ejpam-4625	63	40	gαn	gαn	PROPN
ejpam-4625	63	41	n	n	ADV
ejpam-4625	63	42	)	)	PUNCT
ejpam-4625	63	43	∪	∪	PROPN
ejpam-4625	63	44	(	(	PUNCT
ejpam-4625	63	45	∞⋃	∞⋃	PROPN
ejpam-4625	63	46	n=1	n=1	PROPN
ejpam-4625	63	47	iαn	iαn	PROPN
ejpam-4625	63	48	n	n	PROPN
ejpam-4625	63	49	)	)	PUNCT
ejpam-4625	63	50	.	.	PUNCT
ejpam-4625	64	1	finally	finally	ADV
ejpam-4625	64	2	;	;	PUNCT
ejpam-4625	64	3	x	x	SYM
ejpam-4625	64	4	\	\	PROPN
ejpam-4625	64	5	∞⋃	∞⋃	PROPN
ejpam-4625	64	6	n=1	n=1	PROPN
ejpam-4625	64	7	uαn	uαn	PROPN
ejpam-4625	64	8	n	n	PROPN
ejpam-4625	64	9	∈	∈	PROPN
ejpam-4625	65	1	i	i	PRON
ejpam-4625	65	2	,	,	PUNCT
ejpam-4625	65	3	so	so	CCONJ
ejpam-4625	65	4	(	(	PUNCT
ejpam-4625	65	5	x	x	NOUN
ejpam-4625	65	6	,	,	PUNCT
ejpam-4625	65	7	τ∗	τ∗	ADJ
ejpam-4625	65	8	)	)	PUNCT
ejpam-4625	65	9	is	be	AUX
ejpam-4625	65	10	an	an	DET
ejpam-4625	65	11	i	i	NOUN
ejpam-4625	65	12	-	-	PUNCT
ejpam-4625	65	13	rothberger	rothberger	NOUN
ejpam-4625	65	14	space	space	NOUN
ejpam-4625	65	15	.	.	PUNCT
ejpam-4625	66	1	3	3	X
ejpam-4625	66	2	.	.	X
ejpam-4625	66	3	conclusions	conclusion	NOUN
ejpam-4625	66	4	in	in	ADP
ejpam-4625	66	5	this	this	DET
ejpam-4625	66	6	work	work	NOUN
ejpam-4625	66	7	,	,	PUNCT
ejpam-4625	66	8	a	a	DET
ejpam-4625	66	9	question	question	NOUN
ejpam-4625	66	10	posted	post	VERB
ejpam-4625	66	11	in	in	ADP
ejpam-4625	66	12	[	[	X
ejpam-4625	66	13	1	1	X
ejpam-4625	66	14	]	]	PUNCT
ejpam-4625	66	15	is	be	AUX
ejpam-4625	66	16	partially	partially	ADV
ejpam-4625	66	17	answered	answer	VERB
ejpam-4625	66	18	.	.	PUNCT
ejpam-4625	67	1	so	so	ADV
ejpam-4625	67	2	,	,	PUNCT
ejpam-4625	67	3	one	one	PRON
ejpam-4625	67	4	may	may	AUX
ejpam-4625	67	5	still	still	ADV
ejpam-4625	67	6	search	search	VERB
ejpam-4625	67	7	for	for	ADP
ejpam-4625	67	8	a	a	DET
ejpam-4625	67	9	weaker	weak	ADJ
ejpam-4625	67	10	condition	condition	NOUN
ejpam-4625	67	11	for	for	ADP
ejpam-4625	67	12	a	a	DET
ejpam-4625	67	13	possible	possible	ADJ
ejpam-4625	67	14	future	future	ADJ
ejpam-4625	67	15	work	work	NOUN
ejpam-4625	67	16	.	.	PUNCT
ejpam-4625	68	1	acknowledgements	acknowledgement	VERB
ejpam-4625	68	2	the	the	DET
ejpam-4625	68	3	author	author	NOUN
ejpam-4625	68	4	would	would	AUX
ejpam-4625	68	5	like	like	VERB
ejpam-4625	68	6	to	to	PART
ejpam-4625	68	7	thank	thank	VERB
ejpam-4625	68	8	the	the	DET
ejpam-4625	68	9	anonymous	anonymous	ADJ
ejpam-4625	68	10	referee	referee	NOUN
ejpam-4625	68	11	for	for	ADP
ejpam-4625	68	12	their	their	PRON
ejpam-4625	68	13	useful	useful	ADJ
ejpam-4625	68	14	comments	comment	NOUN
ejpam-4625	68	15	.	.	PUNCT
ejpam-4625	69	1	references	reference	NOUN
ejpam-4625	69	2	[	[	X
ejpam-4625	69	3	1	1	NUM
ejpam-4625	69	4	]	]	PUNCT
ejpam-4625	69	5	a.	a.	NOUN
ejpam-4625	69	6	güldürdek	güldürdek	PROPN
ejpam-4625	69	7	.	.	PUNCT
ejpam-4625	70	1	ideal	ideal	ADJ
ejpam-4625	70	2	rothberger	rothberger	NOUN
ejpam-4625	70	3	spaces	space	VERB
ejpam-4625	70	4	.	.	PUNCT
ejpam-4625	71	1	hacettepe	hacettepe	PROPN
ejpam-4625	71	2	journal	journal	PROPN
ejpam-4625	71	3	of	of	ADP
ejpam-4625	71	4	mathematics	mathematic	NOUN
ejpam-4625	71	5	and	and	CCONJ
ejpam-4625	71	6	statistics	statistic	NOUN
ejpam-4625	71	7	,	,	PUNCT
ejpam-4625	71	8	47:69–75	47:69–75	PROPN
ejpam-4625	71	9	,	,	PUNCT
ejpam-4625	71	10	2018	2018	NUM
ejpam-4625	71	11	.	.	PUNCT
ejpam-4625	72	1	[	[	X
ejpam-4625	72	2	2	2	NUM
ejpam-4625	72	3	]	]	X
ejpam-4625	72	4	d.	d.	PROPN
ejpam-4625	72	5	janković	janković	PROPN
ejpam-4625	72	6	and	and	CCONJ
ejpam-4625	72	7	t.r	t.r	PROPN
ejpam-4625	72	8	.	.	PROPN
ejpam-4625	72	9	hamlett	hamlett	PROPN
ejpam-4625	72	10	.	.	PUNCT
ejpam-4625	73	1	new	new	ADJ
ejpam-4625	73	2	topologies	topology	NOUN
ejpam-4625	73	3	from	from	ADP
ejpam-4625	73	4	old	old	ADJ
ejpam-4625	73	5	via	via	ADP
ejpam-4625	73	6	ideals	ideal	NOUN
ejpam-4625	73	7	.	.	PUNCT
ejpam-4625	74	1	the	the	DET
ejpam-4625	74	2	american	american	PROPN
ejpam-4625	74	3	mathematical	mathematical	PROPN
ejpam-4625	74	4	monthly	monthly	PROPN
ejpam-4625	74	5	,	,	PUNCT
ejpam-4625	74	6	97(4):295–310	97(4):295–310	PROPN
ejpam-4625	74	7	,	,	PUNCT
ejpam-4625	74	8	1990	1990	NUM
ejpam-4625	74	9	.	.	PUNCT
ejpam-4625	75	1	[	[	X
ejpam-4625	75	2	3	3	X
ejpam-4625	75	3	]	]	PUNCT
ejpam-4625	75	4	k.	k.	PROPN
ejpam-4625	75	5	kuratowski	kuratowski	PROPN
ejpam-4625	75	6	.	.	PUNCT
ejpam-4625	76	1	topology	topology	PROPN
ejpam-4625	76	2	.	.	PUNCT
ejpam-4625	77	1	academic	academic	ADJ
ejpam-4625	77	2	press	press	NOUN
ejpam-4625	77	3	,	,	PUNCT
ejpam-4625	77	4	new	new	PROPN
ejpam-4625	77	5	york	york	PROPN
ejpam-4625	77	6	,	,	PUNCT
ejpam-4625	77	7	ny	ny	PROPN
ejpam-4625	77	8	,	,	PUNCT
ejpam-4625	77	9	1966	1966	NUM
ejpam-4625	77	10	.	.	PUNCT
ejpam-4625	78	1	[	[	X
ejpam-4625	78	2	4	4	X
ejpam-4625	78	3	]	]	X
ejpam-4625	78	4	o.	o.	PROPN
ejpam-4625	78	5	njastad	njastad	PROPN
ejpam-4625	78	6	.	.	PUNCT
ejpam-4625	79	1	remarks	remark	NOUN
ejpam-4625	79	2	on	on	ADP
ejpam-4625	79	3	topologies	topology	NOUN
ejpam-4625	79	4	defined	define	VERB
ejpam-4625	79	5	by	by	ADP
ejpam-4625	79	6	local	local	ADJ
ejpam-4625	79	7	properties	property	NOUN
ejpam-4625	79	8	.	.	PUNCT
ejpam-4625	80	1	avh	avh	PROPN
ejpam-4625	80	2	.	.	PUNCT
ejpam-4625	81	1	norske	norske	PROPN
ejpam-4625	81	2	vid.-akad	vid.-akad	PROPN
ejpam-4625	81	3	.	.	PUNCT
ejpam-4625	82	1	oslo	oslo	PROPN
ejpam-4625	83	1	i	i	PRON
ejpam-4625	83	2	(	(	PUNCT
ejpam-4625	83	3	n.s	n.s	PROPN
ejpam-4625	83	4	.	.	PROPN
ejpam-4625	83	5	)	)	PUNCT
ejpam-4625	83	6	,	,	PUNCT
ejpam-4625	83	7	8:1–16	8:1–16	NUM
ejpam-4625	83	8	,	,	PUNCT
ejpam-4625	83	9	1966	1966	NUM
ejpam-4625	83	10	.	.	PUNCT
ejpam-4625	84	1	[	[	X
ejpam-4625	84	2	5	5	X
ejpam-4625	84	3	]	]	PUNCT
ejpam-4625	84	4	f.	f.	PROPN
ejpam-4625	84	5	rothberger	rothberger	PROPN
ejpam-4625	84	6	.	.	PUNCT
ejpam-4625	85	1	eine	eine	PROPN
ejpam-4625	85	2	verschärfung	verschärfung	PROPN
ejpam-4625	85	3	der	der	PROPN
ejpam-4625	85	4	eigenschalft	eigenschalft	PROPN
ejpam-4625	85	5	.	.	PUNCT
ejpam-4625	86	1	fund	fund	PROPN
ejpam-4625	86	2	.	.	PUNCT
ejpam-4625	87	1	math	math	NOUN
ejpam-4625	87	2	.	.	PUNCT
ejpam-4625	88	1	,	,	PUNCT
ejpam-4625	88	2	3:50–55	3:50–55	NUM
ejpam-4625	88	3	,	,	PUNCT
ejpam-4625	88	4	1938	1938	NUM
ejpam-4625	88	5	.	.	PUNCT
ejpam-4625	89	1	[	[	X
ejpam-4625	89	2	6	6	NUM
ejpam-4625	89	3	]	]	PUNCT
ejpam-4625	89	4	m.	m.	NOUN
ejpam-4625	89	5	scheepers	scheeper	NOUN
ejpam-4625	89	6	.	.	PUNCT
ejpam-4625	90	1	combinatorics	combinatoric	NOUN
ejpam-4625	90	2	of	of	ADP
ejpam-4625	90	3	open	open	ADJ
ejpam-4625	90	4	covers(i	covers(i	NOUN
ejpam-4625	90	5	):	):	PUNCT
ejpam-4625	90	6	ramsey	ramsey	PROPN
ejpam-4625	90	7	theory	theory	NOUN
ejpam-4625	90	8	.	.	PUNCT
ejpam-4625	91	1	topology	topology	NOUN
ejpam-4625	91	2	appl	appl	PROPN
ejpam-4625	91	3	.	.	PROPN
ejpam-4625	91	4	,	,	PUNCT
ejpam-4625	91	5	69:31	69:31	NUM
ejpam-4625	91	6	–	–	PUNCT
ejpam-4625	91	7	62	62	NUM
ejpam-4625	91	8	,	,	PUNCT
ejpam-4625	91	9	1996	1996	NUM
ejpam-4625	91	10	.	.	PUNCT
ejpam-4625	92	1	[	[	X
ejpam-4625	92	2	7	7	X
ejpam-4625	92	3	]	]	X
ejpam-4625	92	4	r.	r.	NOUN
ejpam-4625	92	5	vaidyanathaswamy	vaidyanathaswamy	PROPN
ejpam-4625	92	6	.	.	PUNCT
ejpam-4625	93	1	the	the	DET
ejpam-4625	93	2	localisation	localisation	NOUN
ejpam-4625	93	3	theory	theory	NOUN
ejpam-4625	93	4	in	in	ADP
ejpam-4625	93	5	the	the	DET
ejpam-4625	93	6	set	set	NOUN
ejpam-4625	93	7	topology	topology	NOUN
ejpam-4625	93	8	.	.	PUNCT
ejpam-4625	94	1	proc.indian	proc.indian	ADJ
ejpam-4625	94	2	acad	acad	NOUN
ejpam-4625	94	3	.	.	PUNCT
ejpam-4625	95	1	sci	sci	PROPN
ejpam-4625	95	2	.	.	PROPN
ejpam-4625	95	3	,	,	PUNCT
ejpam-4625	95	4	20:51–61	20:51–61	NUM
ejpam-4625	95	5	,	,	PUNCT
ejpam-4625	95	6	1945	1945	NUM
ejpam-4625	95	7	.	.	PUNCT