id	sid	tid	token	lemma	pos
ejpam-5369	1	1	european	european	PROPN
ejpam-5369	1	2	journal	journal	PROPN
ejpam-5369	1	3	of	of	ADP
ejpam-5369	1	4	pure	pure	ADJ
ejpam-5369	1	5	and	and	CCONJ
ejpam-5369	1	6	applied	apply	VERB
ejpam-5369	1	7	mathematics	mathematic	NOUN
ejpam-5369	1	8	vol	vol	NOUN
ejpam-5369	1	9	.	.	PROPN
ejpam-5369	2	1	17	17	NUM
ejpam-5369	2	2	,	,	PUNCT
ejpam-5369	2	3	no	no	INTJ
ejpam-5369	2	4	.	.	NOUN
ejpam-5369	2	5	4	4	NUM
ejpam-5369	2	6	,	,	PUNCT
ejpam-5369	2	7	2024	2024	NUM
ejpam-5369	2	8	,	,	PUNCT
ejpam-5369	2	9	2800	2800	NUM
ejpam-5369	2	10	-	-	SYM
ejpam-5369	2	11	2811	2811	NUM
ejpam-5369	2	12	issn	issn	PROPN
ejpam-5369	2	13	1307	1307	NUM
ejpam-5369	2	14	-	-	SYM
ejpam-5369	2	15	5543	5543	NUM
ejpam-5369	2	16	–	–	PUNCT
ejpam-5369	2	17	ejpam.com	ejpam.com	X
ejpam-5369	2	18	published	publish	VERB
ejpam-5369	2	19	by	by	ADP
ejpam-5369	2	20	new	new	PROPN
ejpam-5369	2	21	york	york	PROPN
ejpam-5369	2	22	business	business	PROPN
ejpam-5369	2	23	global	global	PROPN
ejpam-5369	2	24	on	on	ADP
ejpam-5369	2	25	a	a	DET
ejpam-5369	2	26	new	new	ADJ
ejpam-5369	2	27	operator	operator	NOUN
ejpam-5369	2	28	based	base	VERB
ejpam-5369	2	29	on	on	ADP
ejpam-5369	2	30	a	a	DET
ejpam-5369	2	31	primal	primal	ADJ
ejpam-5369	2	32	and	and	CCONJ
ejpam-5369	2	33	its	its	PRON
ejpam-5369	2	34	associated	associated	ADJ
ejpam-5369	2	35	topology	topology	NOUN
ejpam-5369	2	36	pınar	pınar	NOUN
ejpam-5369	2	37	şaşmaz1	şaşmaz1	NOUN
ejpam-5369	2	38	,	,	PUNCT
ejpam-5369	2	39	murad	murad	NOUN
ejpam-5369	2	40	özkoç2,∗	özkoç2,∗	NOUN
ejpam-5369	2	41	1	1	NUM
ejpam-5369	2	42	muğla	muğla	NOUN
ejpam-5369	2	43	sıtkı	sıtkı	PROPN
ejpam-5369	2	44	koçman	koçman	PROPN
ejpam-5369	2	45	university	university	NOUN
ejpam-5369	2	46	,	,	PUNCT
ejpam-5369	2	47	graduate	graduate	NOUN
ejpam-5369	2	48	school	school	NOUN
ejpam-5369	2	49	of	of	ADP
ejpam-5369	2	50	natural	natural	ADJ
ejpam-5369	2	51	and	and	CCONJ
ejpam-5369	2	52	applied	applied	ADJ
ejpam-5369	2	53	sciences	science	NOUN
ejpam-5369	2	54	,	,	PUNCT
ejpam-5369	2	55	mathematics	mathematic	NOUN
ejpam-5369	2	56	,	,	PUNCT
ejpam-5369	2	57	48000	48000	NUM
ejpam-5369	2	58	menteşe	menteşe	NOUN
ejpam-5369	2	59	-	-	PUNCT
ejpam-5369	2	60	muğla	muğla	NOUN
ejpam-5369	2	61	,	,	PUNCT
ejpam-5369	2	62	turkey	turkey	NOUN
ejpam-5369	2	63	2	2	NUM
ejpam-5369	2	64	muğla	muğla	NOUN
ejpam-5369	2	65	sıtkı	sıtkı	ADJ
ejpam-5369	2	66	koçman	koçman	PROPN
ejpam-5369	2	67	university	university	NOUN
ejpam-5369	2	68	,	,	PUNCT
ejpam-5369	2	69	faculty	faculty	NOUN
ejpam-5369	2	70	of	of	ADP
ejpam-5369	2	71	science	science	NOUN
ejpam-5369	2	72	,	,	PUNCT
ejpam-5369	2	73	department	department	NOUN
ejpam-5369	2	74	of	of	ADP
ejpam-5369	2	75	mathematics	mathematic	NOUN
ejpam-5369	2	76	,	,	PUNCT
ejpam-5369	2	77	48000	48000	NUM
ejpam-5369	2	78	menteşe	menteşe	NOUN
ejpam-5369	2	79	-	-	PUNCT
ejpam-5369	2	80	muğla	muğla	NOUN
ejpam-5369	2	81	,	,	PUNCT
ejpam-5369	2	82	turkey	turkey	NOUN
ejpam-5369	2	83	abstract	abstract	NOUN
ejpam-5369	2	84	.	.	PUNCT
ejpam-5369	3	1	this	this	DET
ejpam-5369	3	2	paper	paper	NOUN
ejpam-5369	3	3	aims	aim	VERB
ejpam-5369	3	4	to	to	PART
ejpam-5369	3	5	introduce	introduce	VERB
ejpam-5369	3	6	and	and	CCONJ
ejpam-5369	3	7	study	study	VERB
ejpam-5369	3	8	two	two	NUM
ejpam-5369	3	9	new	new	ADJ
ejpam-5369	3	10	operators	operator	NOUN
ejpam-5369	3	11	(	(	PUNCT
ejpam-5369	3	12	.)⋄ω	.)⋄ω	PUNCT
ejpam-5369	3	13	and	and	CCONJ
ejpam-5369	3	14	cl⋄ω	cl⋄ω	PROPN
ejpam-5369	3	15	(	(	PUNCT
ejpam-5369	3	16	·	·	PUNCT
ejpam-5369	3	17	)	)	PUNCT
ejpam-5369	3	18	by	by	ADP
ejpam-5369	3	19	utilizing	utilize	VERB
ejpam-5369	3	20	the	the	DET
ejpam-5369	3	21	notion	notion	NOUN
ejpam-5369	3	22	of	of	ADP
ejpam-5369	3	23	primal	primal	ADJ
ejpam-5369	3	24	defined	define	VERB
ejpam-5369	3	25	by	by	ADP
ejpam-5369	3	26	acharjee	acharjee	NOUN
ejpam-5369	3	27	et	et	PROPN
ejpam-5369	3	28	al	al	PROPN
ejpam-5369	3	29	.	.	PUNCT
ejpam-5369	4	1	also	also	ADV
ejpam-5369	4	2	,	,	PUNCT
ejpam-5369	4	3	we	we	PRON
ejpam-5369	4	4	investigate	investigate	VERB
ejpam-5369	4	5	some	some	DET
ejpam-5369	4	6	fundamental	fundamental	ADJ
ejpam-5369	4	7	properties	property	NOUN
ejpam-5369	4	8	of	of	ADP
ejpam-5369	4	9	them	they	PRON
ejpam-5369	4	10	.	.	PUNCT
ejpam-5369	5	1	in	in	ADP
ejpam-5369	5	2	addition	addition	NOUN
ejpam-5369	5	3	,	,	PUNCT
ejpam-5369	5	4	we	we	PRON
ejpam-5369	5	5	showed	show	VERB
ejpam-5369	5	6	that	that	SCONJ
ejpam-5369	5	7	the	the	DET
ejpam-5369	5	8	operator	operator	NOUN
ejpam-5369	5	9	cl⋄ω	cl⋄ω	PROPN
ejpam-5369	5	10	(	(	PUNCT
ejpam-5369	5	11	.	.	PUNCT
ejpam-5369	5	12	)	)	PUNCT
ejpam-5369	5	13	satisfied	satisfy	VERB
ejpam-5369	5	14	the	the	DET
ejpam-5369	5	15	kuratowski	kuratowski	ADJ
ejpam-5369	5	16	closure	closure	NOUN
ejpam-5369	5	17	axioms	axiom	NOUN
ejpam-5369	5	18	.	.	PUNCT
ejpam-5369	6	1	therefore	therefore	ADV
ejpam-5369	6	2	,	,	PUNCT
ejpam-5369	6	3	we	we	PRON
ejpam-5369	6	4	obtain	obtain	VERB
ejpam-5369	6	5	a	a	DET
ejpam-5369	6	6	new	new	ADJ
ejpam-5369	6	7	topology	topology	NOUN
ejpam-5369	6	8	denoted	denote	VERB
ejpam-5369	6	9	by	by	ADP
ejpam-5369	6	10	τ⋄ω	τ⋄ω	NUM
ejpam-5369	6	11	,	,	PUNCT
ejpam-5369	6	12	which	which	PRON
ejpam-5369	6	13	is	be	AUX
ejpam-5369	6	14	finer	fine	ADJ
ejpam-5369	6	15	than	than	ADP
ejpam-5369	6	16	the	the	DET
ejpam-5369	6	17	original	original	ADJ
ejpam-5369	6	18	one	one	NUM
ejpam-5369	6	19	.	.	PUNCT
ejpam-5369	7	1	moreover	moreover	ADV
ejpam-5369	7	2	,	,	PUNCT
ejpam-5369	7	3	the	the	DET
ejpam-5369	7	4	topology	topology	NOUN
ejpam-5369	7	5	τ⋄ω	τ⋄ω	NUM
ejpam-5369	7	6	obtained	obtain	VERB
ejpam-5369	7	7	via	via	ADP
ejpam-5369	7	8	the	the	DET
ejpam-5369	7	9	operator	operator	NOUN
ejpam-5369	7	10	cl⋄ω	cl⋄ω	PROPN
ejpam-5369	7	11	(	(	PUNCT
ejpam-5369	7	12	·	·	PUNCT
ejpam-5369	7	13	)	)	PUNCT
ejpam-5369	7	14	is	be	AUX
ejpam-5369	7	15	finer	fine	ADJ
ejpam-5369	7	16	than	than	ADP
ejpam-5369	7	17	τω	τω	INTJ
ejpam-5369	7	18	,	,	PUNCT
ejpam-5369	7	19	where	where	SCONJ
ejpam-5369	7	20	τω	τω	PRON
ejpam-5369	7	21	is	be	AUX
ejpam-5369	7	22	the	the	DET
ejpam-5369	7	23	family	family	NOUN
ejpam-5369	7	24	of	of	ADP
ejpam-5369	7	25	all	all	DET
ejpam-5369	7	26	ω	ω	ADJ
ejpam-5369	7	27	-	-	ADJ
ejpam-5369	7	28	open	open	ADJ
ejpam-5369	7	29	subsets	subset	NOUN
ejpam-5369	7	30	of	of	ADP
ejpam-5369	7	31	a	a	DET
ejpam-5369	7	32	primal	primal	ADJ
ejpam-5369	7	33	topological	topological	ADJ
ejpam-5369	7	34	space	space	NOUN
ejpam-5369	7	35	(	(	PUNCT
ejpam-5369	7	36	x	x	X
ejpam-5369	7	37	,	,	PUNCT
ejpam-5369	7	38	τ	τ	PROPN
ejpam-5369	7	39	,	,	PUNCT
ejpam-5369	7	40	p	p	NOUN
ejpam-5369	7	41	)	)	PUNCT
ejpam-5369	7	42	.	.	PUNCT
ejpam-5369	8	1	furthermore	furthermore	ADV
ejpam-5369	8	2	,	,	PUNCT
ejpam-5369	8	3	we	we	PRON
ejpam-5369	8	4	not	not	PART
ejpam-5369	8	5	only	only	ADV
ejpam-5369	8	6	examine	examine	VERB
ejpam-5369	8	7	the	the	DET
ejpam-5369	8	8	fundamental	fundamental	ADJ
ejpam-5369	8	9	properties	property	NOUN
ejpam-5369	8	10	of	of	ADP
ejpam-5369	8	11	this	this	DET
ejpam-5369	8	12	class	class	NOUN
ejpam-5369	8	13	of	of	ADP
ejpam-5369	8	14	sets	set	NOUN
ejpam-5369	8	15	but	but	CCONJ
ejpam-5369	8	16	also	also	ADV
ejpam-5369	8	17	provide	provide	VERB
ejpam-5369	8	18	some	some	DET
ejpam-5369	8	19	counterexamples	counterexample	NOUN
ejpam-5369	8	20	.	.	PUNCT
ejpam-5369	9	1	2020	2020	NUM
ejpam-5369	9	2	mathematics	mathematic	NOUN
ejpam-5369	9	3	subject	subject	NOUN
ejpam-5369	9	4	classifications	classification	NOUN
ejpam-5369	9	5	:	:	PUNCT
ejpam-5369	9	6	54a05	54a05	NUM
ejpam-5369	9	7	,	,	PUNCT
ejpam-5369	9	8	54b99	54b99	NUM
ejpam-5369	9	9	,	,	PUNCT
ejpam-5369	9	10	94a60	94a60	PRON
ejpam-5369	9	11	key	key	ADJ
ejpam-5369	9	12	words	word	NOUN
ejpam-5369	9	13	and	and	CCONJ
ejpam-5369	9	14	phrases	phrase	NOUN
ejpam-5369	9	15	:	:	PUNCT
ejpam-5369	9	16	primal	primal	ADJ
ejpam-5369	9	17	,	,	PUNCT
ejpam-5369	9	18	primal	primal	ADJ
ejpam-5369	9	19	topological	topological	ADJ
ejpam-5369	9	20	space	space	NOUN
ejpam-5369	9	21	,	,	PUNCT
ejpam-5369	9	22	ω	ω	NOUN
ejpam-5369	9	23	-	-	NOUN
ejpam-5369	9	24	open	open	ADJ
ejpam-5369	9	25	,	,	PUNCT
ejpam-5369	9	26	the	the	DET
ejpam-5369	9	27	operator	operator	NOUN
ejpam-5369	9	28	(	(	PUNCT
ejpam-5369	9	29	·	·	PUNCT
ejpam-5369	9	30	)	)	PUNCT
ejpam-5369	9	31	⋄ω	⋄ω	NOUN
ejpam-5369	9	32	,	,	PUNCT
ejpam-5369	9	33	the	the	DET
ejpam-5369	9	34	operator	operator	NOUN
ejpam-5369	9	35	cl⋄ω	cl⋄ω	PROPN
ejpam-5369	9	36	,	,	PUNCT
ejpam-5369	9	37	the	the	DET
ejpam-5369	9	38	topology	topology	NOUN
ejpam-5369	9	39	τ⋄ω	τ⋄ω	NUM
ejpam-5369	9	40	1	1	X
ejpam-5369	9	41	.	.	X
ejpam-5369	9	42	introduction	introduction	NOUN
ejpam-5369	9	43	one	one	NUM
ejpam-5369	9	44	of	of	ADP
ejpam-5369	9	45	the	the	DET
ejpam-5369	9	46	most	most	ADV
ejpam-5369	9	47	popular	popular	ADJ
ejpam-5369	9	48	ways	way	NOUN
ejpam-5369	9	49	of	of	ADP
ejpam-5369	9	50	building	building	NOUN
ejpam-5369	9	51	topology	topology	NOUN
ejpam-5369	9	52	is	be	AUX
ejpam-5369	9	53	to	to	PART
ejpam-5369	9	54	add	add	VERB
ejpam-5369	9	55	another	another	DET
ejpam-5369	9	56	structures	structure	NOUN
ejpam-5369	9	57	such	such	ADJ
ejpam-5369	9	58	as	as	ADP
ejpam-5369	9	59	filter	filter	NOUN
ejpam-5369	9	60	[	[	X
ejpam-5369	9	61	16	16	NUM
ejpam-5369	9	62	]	]	PUNCT
ejpam-5369	9	63	,	,	PUNCT
ejpam-5369	9	64	ideal	ideal	ADJ
ejpam-5369	9	65	[	[	X
ejpam-5369	9	66	16	16	NUM
ejpam-5369	9	67	]	]	PUNCT
ejpam-5369	9	68	,	,	PUNCT
ejpam-5369	9	69	grill	grill	NOUN
ejpam-5369	10	1	[	[	X
ejpam-5369	10	2	12	12	NUM
ejpam-5369	10	3	]	]	PUNCT
ejpam-5369	10	4	,	,	PUNCT
ejpam-5369	10	5	and	and	CCONJ
ejpam-5369	10	6	primal	primal	ADJ
ejpam-5369	10	7	[	[	X
ejpam-5369	10	8	1	1	NUM
ejpam-5369	10	9	]	]	PUNCT
ejpam-5369	10	10	.	.	PUNCT
ejpam-5369	11	1	the	the	DET
ejpam-5369	11	2	concepts	concept	NOUN
ejpam-5369	11	3	of	of	ADP
ejpam-5369	11	4	filters	filter	NOUN
ejpam-5369	11	5	,	,	PUNCT
ejpam-5369	11	6	ideals	ideal	NOUN
ejpam-5369	11	7	,	,	PUNCT
ejpam-5369	11	8	and	and	CCONJ
ejpam-5369	11	9	grills	grill	NOUN
ejpam-5369	11	10	are	be	AUX
ejpam-5369	11	11	the	the	DET
ejpam-5369	11	12	structures	structure	NOUN
ejpam-5369	11	13	studied	study	VERB
ejpam-5369	11	14	for	for	ADP
ejpam-5369	11	15	many	many	ADJ
ejpam-5369	11	16	years	year	NOUN
ejpam-5369	11	17	and	and	CCONJ
ejpam-5369	11	18	among	among	ADP
ejpam-5369	11	19	the	the	DET
ejpam-5369	11	20	most	most	ADV
ejpam-5369	11	21	important	important	ADJ
ejpam-5369	11	22	concepts	concept	NOUN
ejpam-5369	11	23	of	of	ADP
ejpam-5369	11	24	topology	topology	NOUN
ejpam-5369	11	25	.	.	PUNCT
ejpam-5369	12	1	in	in	ADP
ejpam-5369	12	2	2014	2014	NUM
ejpam-5369	12	3	,	,	PUNCT
ejpam-5369	12	4	kuratowski	kuratowski	PROPN
ejpam-5369	12	5	introduced	introduce	VERB
ejpam-5369	12	6	the	the	DET
ejpam-5369	12	7	concept	concept	NOUN
ejpam-5369	12	8	of	of	ADP
ejpam-5369	12	9	ideal	ideal	NOUN
ejpam-5369	12	10	[	[	X
ejpam-5369	12	11	16	16	NUM
ejpam-5369	12	12	]	]	PUNCT
ejpam-5369	12	13	from	from	ADP
ejpam-5369	12	14	filter	filter	NOUN
ejpam-5369	12	15	[	[	X
ejpam-5369	12	16	16	16	NUM
ejpam-5369	12	17	]	]	PUNCT
ejpam-5369	12	18	.	.	PUNCT
ejpam-5369	13	1	the	the	DET
ejpam-5369	13	2	notion	notion	NOUN
ejpam-5369	13	3	of	of	ADP
ejpam-5369	13	4	ideal	ideal	NOUN
ejpam-5369	13	5	comes	come	VERB
ejpam-5369	13	6	across	across	ADP
ejpam-5369	13	7	as	as	ADP
ejpam-5369	13	8	the	the	DET
ejpam-5369	13	9	dual	dual	ADJ
ejpam-5369	13	10	structure	structure	NOUN
ejpam-5369	13	11	of	of	ADP
ejpam-5369	13	12	filter	filter	NOUN
ejpam-5369	13	13	.	.	PUNCT
ejpam-5369	14	1	the	the	DET
ejpam-5369	14	2	notion	notion	NOUN
ejpam-5369	14	3	of	of	ADP
ejpam-5369	14	4	grill	grill	NOUN
ejpam-5369	14	5	[	[	X
ejpam-5369	14	6	12	12	NUM
ejpam-5369	14	7	]	]	PUNCT
ejpam-5369	14	8	was	be	AUX
ejpam-5369	14	9	defined	define	VERB
ejpam-5369	14	10	and	and	CCONJ
ejpam-5369	14	11	studied	study	VERB
ejpam-5369	14	12	by	by	ADP
ejpam-5369	14	13	choquet	choquet	NOUN
ejpam-5369	14	14	in	in	ADP
ejpam-5369	14	15	1947	1947	NUM
ejpam-5369	14	16	;	;	PUNCT
ejpam-5369	14	17	for	for	ADP
ejpam-5369	14	18	more	more	ADJ
ejpam-5369	14	19	details	detail	NOUN
ejpam-5369	14	20	,	,	PUNCT
ejpam-5369	14	21	see	see	VERB
ejpam-5369	14	22	[	[	X
ejpam-5369	14	23	17	17	NUM
ejpam-5369	14	24	,	,	PUNCT
ejpam-5369	14	25	18	18	NUM
ejpam-5369	14	26	]	]	PUNCT
ejpam-5369	14	27	.	.	PUNCT
ejpam-5369	15	1	however	however	ADV
ejpam-5369	15	2	,	,	PUNCT
ejpam-5369	15	3	the	the	DET
ejpam-5369	15	4	dual	dual	ADJ
ejpam-5369	15	5	of	of	ADP
ejpam-5369	15	6	the	the	DET
ejpam-5369	15	7	notion	notion	NOUN
ejpam-5369	15	8	of	of	ADP
ejpam-5369	15	9	grill	grill	NOUN
ejpam-5369	15	10	has	have	AUX
ejpam-5369	15	11	not	not	PART
ejpam-5369	15	12	been	be	AUX
ejpam-5369	15	13	introduced	introduce	VERB
ejpam-5369	15	14	by	by	ADP
ejpam-5369	15	15	any	any	DET
ejpam-5369	15	16	authors	author	NOUN
ejpam-5369	15	17	until	until	ADP
ejpam-5369	15	18	2022	2022	NUM
ejpam-5369	15	19	.	.	PUNCT
ejpam-5369	16	1	in	in	ADP
ejpam-5369	16	2	2022	2022	NUM
ejpam-5369	16	3	,	,	PUNCT
ejpam-5369	16	4	the	the	DET
ejpam-5369	16	5	concept	concept	NOUN
ejpam-5369	16	6	of	of	ADP
ejpam-5369	16	7	primal	primal	ADJ
ejpam-5369	16	8	[	[	X
ejpam-5369	16	9	1	1	NUM
ejpam-5369	16	10	]	]	PUNCT
ejpam-5369	16	11	was	be	AUX
ejpam-5369	16	12	defined	define	VERB
ejpam-5369	16	13	and	and	CCONJ
ejpam-5369	16	14	studied	study	VERB
ejpam-5369	16	15	by	by	ADP
ejpam-5369	16	16	acharjee	acharjee	NOUN
ejpam-5369	16	17	et	et	PROPN
ejpam-5369	16	18	al	al	PROPN
ejpam-5369	16	19	.	.	PUNCT
ejpam-5369	17	1	they	they	PRON
ejpam-5369	17	2	introduced	introduce	VERB
ejpam-5369	17	3	primal	primal	ADJ
ejpam-5369	17	4	topological	topological	ADJ
ejpam-5369	17	5	spaces	space	NOUN
ejpam-5369	17	6	via	via	ADP
ejpam-5369	17	7	the	the	DET
ejpam-5369	17	8	notion	notion	NOUN
ejpam-5369	17	9	of	of	ADP
ejpam-5369	17	10	primal	primal	ADJ
ejpam-5369	17	11	.	.	PUNCT
ejpam-5369	18	1	the	the	DET
ejpam-5369	18	2	notion	notion	NOUN
ejpam-5369	18	3	of	of	ADP
ejpam-5369	18	4	primal	primal	ADJ
ejpam-5369	18	5	is	be	AUX
ejpam-5369	18	6	the	the	DET
ejpam-5369	18	7	dual	dual	ADJ
ejpam-5369	18	8	of	of	ADP
ejpam-5369	18	9	the	the	DET
ejpam-5369	18	10	notion	notion	NOUN
ejpam-5369	18	11	of	of	ADP
ejpam-5369	18	12	grill	grill	NOUN
ejpam-5369	18	13	.	.	PUNCT
ejpam-5369	19	1	this	this	DET
ejpam-5369	19	2	topic	topic	NOUN
ejpam-5369	19	3	has	have	AUX
ejpam-5369	19	4	won	win	VERB
ejpam-5369	19	5	its	its	PRON
ejpam-5369	19	6	importance	importance	NOUN
ejpam-5369	19	7	aspects	aspect	NOUN
ejpam-5369	19	8	of	of	ADP
ejpam-5369	19	9	interest	interest	NOUN
ejpam-5369	19	10	.	.	PUNCT
ejpam-5369	20	1	this	this	DET
ejpam-5369	20	2	concept	concept	NOUN
ejpam-5369	20	3	has	have	AUX
ejpam-5369	20	4	been	be	AUX
ejpam-5369	20	5	analysed	analyse	VERB
ejpam-5369	20	6	by	by	ADP
ejpam-5369	20	7	many	many	ADJ
ejpam-5369	20	8	authors	author	NOUN
ejpam-5369	20	9	in	in	ADP
ejpam-5369	20	10	a	a	DET
ejpam-5369	20	11	short	short	ADJ
ejpam-5369	20	12	period	period	NOUN
ejpam-5369	20	13	of	of	ADP
ejpam-5369	20	14	time	time	NOUN
ejpam-5369	20	15	;	;	PUNCT
ejpam-5369	20	16	for	for	ADP
ejpam-5369	20	17	more	more	ADJ
ejpam-5369	20	18	details	detail	NOUN
ejpam-5369	20	19	,	,	PUNCT
ejpam-5369	20	20	see	see	VERB
ejpam-5369	20	21	[	[	X
ejpam-5369	20	22	2–9	2–9	NUM
ejpam-5369	20	23	,	,	PUNCT
ejpam-5369	20	24	11	11	NUM
ejpam-5369	20	25	,	,	PUNCT
ejpam-5369	20	26	20	20	NUM
ejpam-5369	20	27	]	]	PUNCT
ejpam-5369	20	28	.	.	PUNCT
ejpam-5369	21	1	∗corresponding	∗corresponde	VERB
ejpam-5369	21	2	author	author	NOUN
ejpam-5369	21	3	.	.	PUNCT
ejpam-5369	22	1	doi	doi	NOUN
ejpam-5369	22	2	:	:	PUNCT
ejpam-5369	22	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5369	https://doi.org/10.29020/nybg.ejpam.v17i4.5369	PROPN
ejpam-5369	22	4	email	email	NOUN
ejpam-5369	22	5	addresses	address	NOUN
ejpam-5369	22	6	:	:	PUNCT
ejpam-5369	22	7	pinarsasmaz@posta.mu.edu.tr	pinarsasmaz@posta.mu.edu.tr	PROPN
ejpam-5369	22	8	(	(	PUNCT
ejpam-5369	22	9	p.	p.	NOUN
ejpam-5369	22	10	şaşmaz	şaşmaz	PUNCT
ejpam-5369	22	11	)	)	PUNCT
ejpam-5369	22	12	,	,	PUNCT
ejpam-5369	22	13	murad.ozkoc@mu.edu.tr	murad.ozkoc@mu.edu.tr	PROPN
ejpam-5369	22	14	(	(	PUNCT
ejpam-5369	22	15	m.	m.	NOUN
ejpam-5369	22	16	özkoç	özkoç	PROPN
ejpam-5369	22	17	)	)	PUNCT
ejpam-5369	22	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5369	23	1	2800	2800	NUM
ejpam-5369	24	1	copyright	copyright	NOUN
ejpam-5369	24	2	:	:	PUNCT
ejpam-5369	24	3	©	©	PROPN
ejpam-5369	24	4	2024	2024	NUM
ejpam-5369	24	5	the	the	DET
ejpam-5369	24	6	author(s	author(s	NOUN
ejpam-5369	24	7	)	)	PUNCT
ejpam-5369	24	8	.	.	PUNCT
ejpam-5369	25	1	(	(	PUNCT
ejpam-5369	25	2	cc	cc	NOUN
ejpam-5369	25	3	by	by	ADP
ejpam-5369	25	4	-	-	PUNCT
ejpam-5369	25	5	nc	nc	PROPN
ejpam-5369	25	6	4.0	4.0	NUM
ejpam-5369	25	7	)	)	PUNCT
ejpam-5369	25	8	p.	p.	NOUN
ejpam-5369	25	9	şaşmaz	şaşmaz	NUM
ejpam-5369	25	10	,	,	PUNCT
ejpam-5369	25	11	m.	m.	NOUN
ejpam-5369	25	12	özkoç	özkoç	PROPN
ejpam-5369	25	13	/	/	SYM
ejpam-5369	25	14	eur	eur	PROPN
ejpam-5369	25	15	.	.	PUNCT
ejpam-5369	26	1	j.	j.	PROPN
ejpam-5369	26	2	pure	pure	PROPN
ejpam-5369	26	3	appl	appl	PROPN
ejpam-5369	26	4	.	.	PROPN
ejpam-5369	26	5	math	math	PROPN
ejpam-5369	26	6	,	,	PUNCT
ejpam-5369	26	7	17	17	NUM
ejpam-5369	26	8	(	(	PUNCT
ejpam-5369	26	9	4	4	NUM
ejpam-5369	26	10	)	)	PUNCT
ejpam-5369	26	11	(	(	PUNCT
ejpam-5369	26	12	2024	2024	NUM
ejpam-5369	26	13	)	)	PUNCT
ejpam-5369	26	14	,	,	PUNCT
ejpam-5369	26	15	2800	2800	NUM
ejpam-5369	26	16	-	-	SYM
ejpam-5369	26	17	2811	2811	NUM
ejpam-5369	26	18	2801	2801	NUM
ejpam-5369	26	19	undoubtedly	undoubtedly	ADV
ejpam-5369	26	20	,	,	PUNCT
ejpam-5369	26	21	another	another	DET
ejpam-5369	26	22	important	important	ADJ
ejpam-5369	26	23	concept	concept	NOUN
ejpam-5369	26	24	in	in	ADP
ejpam-5369	26	25	general	general	ADJ
ejpam-5369	26	26	topology	topology	NOUN
ejpam-5369	26	27	is	be	AUX
ejpam-5369	26	28	the	the	DET
ejpam-5369	26	29	types	type	NOUN
ejpam-5369	26	30	of	of	ADP
ejpam-5369	26	31	open	open	ADJ
ejpam-5369	26	32	sets	set	NOUN
ejpam-5369	26	33	.	.	PUNCT
ejpam-5369	27	1	some	some	PRON
ejpam-5369	27	2	of	of	ADP
ejpam-5369	27	3	these	these	DET
ejpam-5369	27	4	types	type	NOUN
ejpam-5369	27	5	of	of	ADP
ejpam-5369	27	6	sets	set	NOUN
ejpam-5369	27	7	are	be	AUX
ejpam-5369	27	8	regular	regular	ADJ
ejpam-5369	27	9	open	open	ADJ
ejpam-5369	27	10	sets	set	NOUN
ejpam-5369	27	11	[	[	X
ejpam-5369	27	12	22	22	NUM
ejpam-5369	27	13	]	]	PUNCT
ejpam-5369	27	14	,	,	PUNCT
ejpam-5369	27	15	δ	δ	PROPN
ejpam-5369	27	16	-	-	ADJ
ejpam-5369	27	17	open	open	ADJ
ejpam-5369	27	18	sets	set	NOUN
ejpam-5369	27	19	[	[	X
ejpam-5369	27	20	23	23	NUM
ejpam-5369	27	21	]	]	PUNCT
ejpam-5369	27	22	and	and	CCONJ
ejpam-5369	27	23	ω	ω	VERB
ejpam-5369	27	24	-	-	ADJ
ejpam-5369	27	25	open	open	ADJ
ejpam-5369	27	26	sets	set	NOUN
ejpam-5369	27	27	[	[	X
ejpam-5369	27	28	15	15	NUM
ejpam-5369	27	29	]	]	PUNCT
ejpam-5369	27	30	.	.	PUNCT
ejpam-5369	28	1	the	the	DET
ejpam-5369	28	2	notion	notion	NOUN
ejpam-5369	28	3	of	of	ADP
ejpam-5369	28	4	ω	ω	VERB
ejpam-5369	28	5	-	-	ADJ
ejpam-5369	28	6	open	open	ADJ
ejpam-5369	28	7	set	set	NOUN
ejpam-5369	28	8	comes	come	VERB
ejpam-5369	28	9	across	across	ADP
ejpam-5369	28	10	a	a	DET
ejpam-5369	28	11	weaker	weak	ADJ
ejpam-5369	28	12	concept	concept	NOUN
ejpam-5369	28	13	than	than	ADP
ejpam-5369	28	14	the	the	DET
ejpam-5369	28	15	concept	concept	NOUN
ejpam-5369	28	16	of	of	ADP
ejpam-5369	28	17	open	open	ADJ
ejpam-5369	28	18	set	set	NOUN
ejpam-5369	28	19	while	while	SCONJ
ejpam-5369	28	20	the	the	DET
ejpam-5369	28	21	notion	notion	NOUN
ejpam-5369	28	22	of	of	ADP
ejpam-5369	28	23	δ	δ	NOUN
ejpam-5369	28	24	-	-	ADJ
ejpam-5369	28	25	open	open	ADJ
ejpam-5369	28	26	set	set	NOUN
ejpam-5369	28	27	is	be	AUX
ejpam-5369	28	28	a	a	DET
ejpam-5369	28	29	stronger	strong	ADJ
ejpam-5369	28	30	concept	concept	NOUN
ejpam-5369	28	31	than	than	ADP
ejpam-5369	28	32	the	the	DET
ejpam-5369	28	33	concept	concept	NOUN
ejpam-5369	28	34	of	of	ADP
ejpam-5369	28	35	open	open	ADJ
ejpam-5369	28	36	set	set	NOUN
ejpam-5369	28	37	.	.	PUNCT
ejpam-5369	29	1	these	these	DET
ejpam-5369	29	2	types	type	NOUN
ejpam-5369	29	3	of	of	ADP
ejpam-5369	29	4	sets	set	NOUN
ejpam-5369	29	5	have	have	AUX
ejpam-5369	29	6	been	be	AUX
ejpam-5369	29	7	studied	study	VERB
ejpam-5369	29	8	by	by	ADP
ejpam-5369	29	9	many	many	ADJ
ejpam-5369	29	10	authors	author	NOUN
ejpam-5369	29	11	in	in	ADP
ejpam-5369	29	12	different	different	ADJ
ejpam-5369	29	13	directions	direction	NOUN
ejpam-5369	29	14	.	.	PUNCT
ejpam-5369	30	1	some	some	DET
ejpam-5369	30	2	other	other	ADJ
ejpam-5369	30	3	types	type	NOUN
ejpam-5369	30	4	of	of	ADP
ejpam-5369	30	5	sets	set	NOUN
ejpam-5369	30	6	such	such	ADJ
ejpam-5369	30	7	as	as	ADP
ejpam-5369	30	8	fuzzy	fuzzy	ADJ
ejpam-5369	30	9	sets	set	NOUN
ejpam-5369	30	10	,	,	PUNCT
ejpam-5369	30	11	soft	soft	ADJ
ejpam-5369	30	12	sets	set	NOUN
ejpam-5369	30	13	,	,	PUNCT
ejpam-5369	30	14	and	and	CCONJ
ejpam-5369	30	15	rough	rough	ADJ
ejpam-5369	30	16	sets	set	NOUN
ejpam-5369	30	17	play	play	VERB
ejpam-5369	30	18	an	an	DET
ejpam-5369	30	19	important	important	ADJ
ejpam-5369	30	20	role	role	NOUN
ejpam-5369	30	21	in	in	ADP
ejpam-5369	30	22	pure	pure	ADJ
ejpam-5369	30	23	and	and	CCONJ
ejpam-5369	30	24	applied	applied	ADJ
ejpam-5369	30	25	sciences	science	NOUN
ejpam-5369	30	26	.	.	PUNCT
ejpam-5369	31	1	the	the	DET
ejpam-5369	31	2	notion	notion	NOUN
ejpam-5369	31	3	of	of	ADP
ejpam-5369	31	4	fuzzy	fuzzy	ADJ
ejpam-5369	31	5	sets	set	NOUN
ejpam-5369	31	6	was	be	AUX
ejpam-5369	31	7	introduced	introduce	VERB
ejpam-5369	31	8	by	by	ADP
ejpam-5369	31	9	zadeh	zadeh	PROPN
ejpam-5369	32	1	[	[	X
ejpam-5369	32	2	24	24	NUM
ejpam-5369	32	3	]	]	PUNCT
ejpam-5369	32	4	and	and	CCONJ
ejpam-5369	32	5	studied	study	VERB
ejpam-5369	32	6	in	in	ADP
ejpam-5369	32	7	many	many	ADJ
ejpam-5369	32	8	directions	direction	NOUN
ejpam-5369	32	9	in	in	ADP
ejpam-5369	32	10	the	the	DET
ejpam-5369	32	11	recent	recent	ADJ
ejpam-5369	32	12	past	past	NOUN
ejpam-5369	32	13	.	.	PUNCT
ejpam-5369	33	1	after	after	ADP
ejpam-5369	33	2	then	then	ADV
ejpam-5369	33	3	,	,	PUNCT
ejpam-5369	33	4	the	the	DET
ejpam-5369	33	5	notion	notion	NOUN
ejpam-5369	33	6	of	of	ADP
ejpam-5369	33	7	soft	soft	ADJ
ejpam-5369	33	8	sets	set	NOUN
ejpam-5369	33	9	was	be	AUX
ejpam-5369	33	10	defined	define	VERB
ejpam-5369	33	11	by	by	ADP
ejpam-5369	33	12	molodtsov	molodtsov	NOUN
ejpam-5369	33	13	[	[	X
ejpam-5369	33	14	19	19	NUM
ejpam-5369	33	15	]	]	PUNCT
ejpam-5369	33	16	and	and	CCONJ
ejpam-5369	33	17	also	also	ADV
ejpam-5369	33	18	investigated	investigate	VERB
ejpam-5369	33	19	by	by	ADP
ejpam-5369	33	20	many	many	ADJ
ejpam-5369	33	21	authors	author	NOUN
ejpam-5369	33	22	in	in	ADP
ejpam-5369	33	23	many	many	ADJ
ejpam-5369	33	24	directions	direction	NOUN
ejpam-5369	33	25	;	;	PUNCT
ejpam-5369	33	26	for	for	ADP
ejpam-5369	33	27	more	more	ADJ
ejpam-5369	33	28	details	detail	NOUN
ejpam-5369	33	29	,	,	PUNCT
ejpam-5369	33	30	see	see	VERB
ejpam-5369	33	31	[	[	X
ejpam-5369	33	32	13	13	NUM
ejpam-5369	33	33	,	,	PUNCT
ejpam-5369	33	34	14	14	NUM
ejpam-5369	33	35	]	]	PUNCT
ejpam-5369	33	36	.	.	PUNCT
ejpam-5369	34	1	recently	recently	ADV
ejpam-5369	34	2	,	,	PUNCT
ejpam-5369	34	3	pawlak	pawlak	ADV
ejpam-5369	34	4	introduced	introduce	VERB
ejpam-5369	34	5	and	and	CCONJ
ejpam-5369	34	6	studied	study	VERB
ejpam-5369	34	7	the	the	DET
ejpam-5369	34	8	concept	concept	NOUN
ejpam-5369	34	9	of	of	ADP
ejpam-5369	34	10	rough	rough	ADJ
ejpam-5369	34	11	set	set	NOUN
ejpam-5369	34	12	in	in	ADP
ejpam-5369	34	13	[	[	X
ejpam-5369	34	14	21	21	NUM
ejpam-5369	34	15	]	]	PUNCT
ejpam-5369	34	16	.	.	PUNCT
ejpam-5369	35	1	the	the	DET
ejpam-5369	35	2	concepts	concept	NOUN
ejpam-5369	35	3	of	of	ADP
ejpam-5369	35	4	fuzzy	fuzzy	ADJ
ejpam-5369	35	5	sets	set	NOUN
ejpam-5369	35	6	,	,	PUNCT
ejpam-5369	35	7	soft	soft	ADJ
ejpam-5369	35	8	sets	set	NOUN
ejpam-5369	35	9	,	,	PUNCT
ejpam-5369	35	10	and	and	CCONJ
ejpam-5369	35	11	rough	rough	ADJ
ejpam-5369	35	12	sets	set	NOUN
ejpam-5369	35	13	have	have	VERB
ejpam-5369	35	14	many	many	ADJ
ejpam-5369	35	15	applications	application	NOUN
ejpam-5369	35	16	in	in	ADP
ejpam-5369	35	17	the	the	DET
ejpam-5369	35	18	literature	literature	NOUN
ejpam-5369	35	19	.	.	PUNCT
ejpam-5369	36	1	these	these	DET
ejpam-5369	36	2	kind	kind	NOUN
ejpam-5369	36	3	of	of	ADP
ejpam-5369	36	4	sets	set	NOUN
ejpam-5369	36	5	are	be	AUX
ejpam-5369	36	6	very	very	ADV
ejpam-5369	36	7	important	important	ADJ
ejpam-5369	36	8	in	in	ADP
ejpam-5369	36	9	terms	term	NOUN
ejpam-5369	36	10	of	of	ADP
ejpam-5369	36	11	having	have	VERB
ejpam-5369	36	12	applications	application	NOUN
ejpam-5369	36	13	.	.	PUNCT
ejpam-5369	37	1	fuzzy	fuzzy	ADJ
ejpam-5369	37	2	sets	set	NOUN
ejpam-5369	37	3	,	,	PUNCT
ejpam-5369	37	4	soft	soft	ADJ
ejpam-5369	37	5	sets	set	NOUN
ejpam-5369	37	6	and	and	CCONJ
ejpam-5369	37	7	especially	especially	ADV
ejpam-5369	37	8	the	the	DET
ejpam-5369	37	9	concept	concept	NOUN
ejpam-5369	37	10	of	of	ADP
ejpam-5369	37	11	rough	rough	ADJ
ejpam-5369	37	12	sets	set	NOUN
ejpam-5369	37	13	are	be	AUX
ejpam-5369	37	14	still	still	ADV
ejpam-5369	37	15	intensively	intensively	ADV
ejpam-5369	37	16	studied	study	VERB
ejpam-5369	37	17	in	in	ADP
ejpam-5369	37	18	the	the	DET
ejpam-5369	37	19	literature	literature	NOUN
ejpam-5369	37	20	.	.	PUNCT
ejpam-5369	38	1	also	also	ADV
ejpam-5369	38	2	,	,	PUNCT
ejpam-5369	38	3	these	these	DET
ejpam-5369	38	4	kind	kind	NOUN
ejpam-5369	38	5	of	of	ADP
ejpam-5369	38	6	sets	set	NOUN
ejpam-5369	38	7	has	have	AUX
ejpam-5369	38	8	been	be	AUX
ejpam-5369	38	9	considered	consider	VERB
ejpam-5369	38	10	with	with	ADP
ejpam-5369	38	11	different	different	ADJ
ejpam-5369	38	12	structures	structure	NOUN
ejpam-5369	38	13	such	such	ADJ
ejpam-5369	38	14	as	as	ADP
ejpam-5369	38	15	filter	filter	NOUN
ejpam-5369	38	16	,	,	PUNCT
ejpam-5369	38	17	ideal	ideal	ADJ
ejpam-5369	38	18	,	,	PUNCT
ejpam-5369	38	19	grill	grill	ADJ
ejpam-5369	38	20	,	,	PUNCT
ejpam-5369	38	21	and	and	CCONJ
ejpam-5369	38	22	primal	primal	ADJ
ejpam-5369	38	23	as	as	ADV
ejpam-5369	38	24	well	well	ADV
ejpam-5369	38	25	.	.	PUNCT
ejpam-5369	39	1	in	in	ADP
ejpam-5369	39	2	this	this	DET
ejpam-5369	39	3	study	study	NOUN
ejpam-5369	39	4	,	,	PUNCT
ejpam-5369	39	5	we	we	PRON
ejpam-5369	39	6	will	will	AUX
ejpam-5369	39	7	define	define	VERB
ejpam-5369	39	8	the	the	DET
ejpam-5369	39	9	operator	operator	NOUN
ejpam-5369	39	10	cl⋄ω	cl⋄ω	PROPN
ejpam-5369	39	11	with	with	ADP
ejpam-5369	39	12	the	the	DET
ejpam-5369	39	13	help	help	NOUN
ejpam-5369	39	14	of	of	ADP
ejpam-5369	39	15	the	the	DET
ejpam-5369	39	16	definition	definition	NOUN
ejpam-5369	39	17	of	of	ADP
ejpam-5369	39	18	primal	primal	ADJ
ejpam-5369	39	19	topological	topological	ADJ
ejpam-5369	39	20	space	space	NOUN
ejpam-5369	39	21	given	give	VERB
ejpam-5369	39	22	by	by	ADP
ejpam-5369	39	23	acharjee	acharjee	NOUN
ejpam-5369	39	24	et	et	PROPN
ejpam-5369	39	25	al	al	PROPN
ejpam-5369	39	26	.	.	PUNCT
ejpam-5369	40	1	[	[	X
ejpam-5369	40	2	1	1	X
ejpam-5369	40	3	]	]	PUNCT
ejpam-5369	40	4	in	in	ADP
ejpam-5369	40	5	2022	2022	NUM
ejpam-5369	40	6	and	and	CCONJ
ejpam-5369	40	7	the	the	DET
ejpam-5369	40	8	operator	operator	NOUN
ejpam-5369	40	9	clω	clω	PROPN
ejpam-5369	40	10	or	or	CCONJ
ejpam-5369	40	11	ω	ω	NOUN
ejpam-5369	40	12	-	-	NOUN
ejpam-5369	40	13	cl	cl	NOUN
ejpam-5369	40	14	[	[	X
ejpam-5369	40	15	15	15	NUM
ejpam-5369	40	16	]	]	PUNCT
ejpam-5369	40	17	given	give	VERB
ejpam-5369	40	18	by	by	ADP
ejpam-5369	40	19	hdeib	hdeib	PROPN
ejpam-5369	40	20	in	in	ADP
ejpam-5369	40	21	1982	1982	NUM
ejpam-5369	40	22	.	.	PUNCT
ejpam-5369	41	1	accordingly	accordingly	ADV
ejpam-5369	41	2	,	,	PUNCT
ejpam-5369	41	3	we	we	PRON
ejpam-5369	41	4	will	will	AUX
ejpam-5369	41	5	introduce	introduce	VERB
ejpam-5369	41	6	the	the	DET
ejpam-5369	41	7	topology	topology	NOUN
ejpam-5369	41	8	τ⋄ω	τ⋄ω	PUNCT
ejpam-5369	41	9	and	and	CCONJ
ejpam-5369	41	10	examine	examine	VERB
ejpam-5369	41	11	some	some	DET
ejpam-5369	41	12	important	important	ADJ
ejpam-5369	41	13	set	set	VERB
ejpam-5369	41	14	theoretical	theoretical	ADJ
ejpam-5369	41	15	properties	property	NOUN
ejpam-5369	41	16	.	.	PUNCT
ejpam-5369	42	1	we	we	PRON
ejpam-5369	42	2	also	also	ADV
ejpam-5369	42	3	examined	examine	VERB
ejpam-5369	42	4	the	the	DET
ejpam-5369	42	5	relationship	relationship	NOUN
ejpam-5369	42	6	between	between	ADP
ejpam-5369	42	7	the	the	DET
ejpam-5369	42	8	definitions	definition	NOUN
ejpam-5369	42	9	given	give	VERB
ejpam-5369	42	10	before	before	ADV
ejpam-5369	42	11	and	and	CCONJ
ejpam-5369	42	12	gave	give	VERB
ejpam-5369	42	13	examples	example	NOUN
ejpam-5369	42	14	to	to	ADP
ejpam-5369	42	15	the	the	DET
ejpam-5369	42	16	contrary	contrary	NOUN
ejpam-5369	42	17	.	.	PUNCT
ejpam-5369	43	1	in	in	ADP
ejpam-5369	43	2	addition	addition	NOUN
ejpam-5369	43	3	,	,	PUNCT
ejpam-5369	43	4	we	we	PRON
ejpam-5369	43	5	showed	show	VERB
ejpam-5369	43	6	that	that	SCONJ
ejpam-5369	43	7	the	the	DET
ejpam-5369	43	8	operator	operator	NOUN
ejpam-5369	43	9	cl⋄ω	cl⋄ω	PROPN
ejpam-5369	43	10	is	be	AUX
ejpam-5369	43	11	a	a	DET
ejpam-5369	43	12	kuratowski	kuratowski	ADJ
ejpam-5369	43	13	closure	closure	NOUN
ejpam-5369	43	14	operator	operator	NOUN
ejpam-5369	43	15	.	.	PUNCT
ejpam-5369	44	1	we	we	PRON
ejpam-5369	44	2	also	also	ADV
ejpam-5369	44	3	showed	show	VERB
ejpam-5369	44	4	that	that	SCONJ
ejpam-5369	44	5	the	the	DET
ejpam-5369	44	6	topology	topology	NOUN
ejpam-5369	44	7	τ⋄ω	τ⋄ω	PUNCT
ejpam-5369	44	8	,	,	PUNCT
ejpam-5369	44	9	given	give	VERB
ejpam-5369	44	10	with	with	ADP
ejpam-5369	44	11	the	the	DET
ejpam-5369	44	12	help	help	NOUN
ejpam-5369	44	13	of	of	ADP
ejpam-5369	44	14	the	the	DET
ejpam-5369	44	15	operator	operator	NOUN
ejpam-5369	44	16	cl⋄ω	cl⋄ω	PROPN
ejpam-5369	44	17	,	,	PUNCT
ejpam-5369	44	18	is	be	AUX
ejpam-5369	44	19	finer	fine	ADJ
ejpam-5369	44	20	than	than	ADP
ejpam-5369	44	21	both	both	DET
ejpam-5369	44	22	τ	τ	PROPN
ejpam-5369	44	23	and	and	CCONJ
ejpam-5369	44	24	τω	τω	INTJ
ejpam-5369	44	25	.	.	PUNCT
ejpam-5369	45	1	some	some	DET
ejpam-5369	45	2	examples	example	NOUN
ejpam-5369	45	3	related	relate	VERB
ejpam-5369	45	4	to	to	ADP
ejpam-5369	45	5	the	the	DET
ejpam-5369	45	6	notions	notion	NOUN
ejpam-5369	45	7	were	be	AUX
ejpam-5369	45	8	given	give	VERB
ejpam-5369	45	9	.	.	PUNCT
ejpam-5369	46	1	2	2	X
ejpam-5369	46	2	.	.	NUM
ejpam-5369	46	3	preliminaries	preliminary	NOUN
ejpam-5369	46	4	throughout	throughout	ADP
ejpam-5369	46	5	this	this	DET
ejpam-5369	46	6	present	present	ADJ
ejpam-5369	46	7	paper	paper	NOUN
ejpam-5369	46	8	,	,	PUNCT
ejpam-5369	46	9	x	x	PUNCT
ejpam-5369	46	10	and	and	CCONJ
ejpam-5369	46	11	y	y	PROPN
ejpam-5369	46	12	represent	represent	VERB
ejpam-5369	46	13	topological	topological	ADJ
ejpam-5369	46	14	spaces	space	NOUN
ejpam-5369	46	15	.	.	PUNCT
ejpam-5369	47	1	for	for	ADP
ejpam-5369	47	2	a	a	DET
ejpam-5369	47	3	subset	subset	NOUN
ejpam-5369	47	4	a	a	PRON
ejpam-5369	47	5	of	of	ADP
ejpam-5369	47	6	a	a	DET
ejpam-5369	47	7	space	space	NOUN
ejpam-5369	47	8	x	x	NOUN
ejpam-5369	47	9	,	,	PUNCT
ejpam-5369	47	10	cl(a	cl(a	NUM
ejpam-5369	47	11	)	)	PUNCT
ejpam-5369	47	12	and	and	CCONJ
ejpam-5369	47	13	int(a	int(a	PROPN
ejpam-5369	47	14	)	)	PUNCT
ejpam-5369	47	15	denote	denote	VERB
ejpam-5369	47	16	the	the	DET
ejpam-5369	47	17	closure	closure	NOUN
ejpam-5369	47	18	of	of	ADP
ejpam-5369	47	19	a	a	PRON
ejpam-5369	47	20	and	and	CCONJ
ejpam-5369	47	21	the	the	DET
ejpam-5369	47	22	interior	interior	NOUN
ejpam-5369	47	23	of	of	ADP
ejpam-5369	47	24	a	a	PRON
ejpam-5369	47	25	,	,	PUNCT
ejpam-5369	47	26	respectively	respectively	ADV
ejpam-5369	47	27	.	.	PUNCT
ejpam-5369	48	1	the	the	DET
ejpam-5369	48	2	family	family	NOUN
ejpam-5369	48	3	of	of	ADP
ejpam-5369	48	4	all	all	DET
ejpam-5369	48	5	closed	closed	ADJ
ejpam-5369	48	6	(	(	PUNCT
ejpam-5369	48	7	resp	resp	NOUN
ejpam-5369	48	8	.	.	PUNCT
ejpam-5369	49	1	open	open	ADJ
ejpam-5369	49	2	)	)	PUNCT
ejpam-5369	49	3	sets	set	NOUN
ejpam-5369	49	4	of	of	ADP
ejpam-5369	49	5	x	x	SYM
ejpam-5369	49	6	is	be	AUX
ejpam-5369	49	7	denoted	denote	VERB
ejpam-5369	49	8	c(x	c(x	NOUN
ejpam-5369	49	9	)	)	PUNCT
ejpam-5369	49	10	(	(	PUNCT
ejpam-5369	49	11	resp	resp	NOUN
ejpam-5369	49	12	.	.	PUNCT
ejpam-5369	50	1	o(x	o(x	ADJ
ejpam-5369	50	2	)	)	PUNCT
ejpam-5369	50	3	or	or	CCONJ
ejpam-5369	50	4	τ	τ	PROPN
ejpam-5369	50	5	)	)	PUNCT
ejpam-5369	50	6	and	and	CCONJ
ejpam-5369	50	7	the	the	DET
ejpam-5369	50	8	family	family	NOUN
ejpam-5369	50	9	of	of	ADP
ejpam-5369	50	10	all	all	DET
ejpam-5369	50	11	closed	closed	ADJ
ejpam-5369	50	12	(	(	PUNCT
ejpam-5369	50	13	resp	resp	NOUN
ejpam-5369	50	14	.	.	PUNCT
ejpam-5369	51	1	open	open	ADJ
ejpam-5369	51	2	)	)	PUNCT
ejpam-5369	51	3	sets	set	NOUN
ejpam-5369	51	4	of	of	ADP
ejpam-5369	51	5	x	x	PUNCT
ejpam-5369	51	6	containing	contain	VERB
ejpam-5369	51	7	a	a	DET
ejpam-5369	51	8	point	point	NOUN
ejpam-5369	51	9	x	x	PUNCT
ejpam-5369	51	10	of	of	ADP
ejpam-5369	51	11	x	x	PRON
ejpam-5369	51	12	is	be	AUX
ejpam-5369	51	13	denoted	denote	VERB
ejpam-5369	51	14	by	by	ADP
ejpam-5369	51	15	c(x	c(x	NOUN
ejpam-5369	51	16	,	,	PUNCT
ejpam-5369	51	17	x	x	NOUN
ejpam-5369	51	18	)	)	PUNCT
ejpam-5369	51	19	(	(	PUNCT
ejpam-5369	51	20	resp	resp	NOUN
ejpam-5369	51	21	.	.	PUNCT
ejpam-5369	52	1	o(x	o(x	ADJ
ejpam-5369	52	2	,	,	PUNCT
ejpam-5369	52	3	x	x	NOUN
ejpam-5369	52	4	)	)	PUNCT
ejpam-5369	52	5	or	or	CCONJ
ejpam-5369	52	6	τ(x	τ(x	NOUN
ejpam-5369	52	7	)	)	PUNCT
ejpam-5369	52	8	)	)	PUNCT
ejpam-5369	52	9	.	.	PUNCT
ejpam-5369	53	1	now	now	ADV
ejpam-5369	53	2	,	,	PUNCT
ejpam-5369	53	3	we	we	PRON
ejpam-5369	53	4	recall	recall	VERB
ejpam-5369	53	5	some	some	PRON
ejpam-5369	53	6	of	of	ADP
ejpam-5369	53	7	the	the	DET
ejpam-5369	53	8	definitions	definition	NOUN
ejpam-5369	53	9	in	in	ADP
ejpam-5369	53	10	the	the	DET
ejpam-5369	53	11	literature	literature	NOUN
ejpam-5369	53	12	and	and	CCONJ
ejpam-5369	53	13	used	use	VERB
ejpam-5369	53	14	in	in	ADP
ejpam-5369	53	15	this	this	DET
ejpam-5369	53	16	study	study	NOUN
ejpam-5369	53	17	.	.	PUNCT
ejpam-5369	54	1	definition	definition	NOUN
ejpam-5369	54	2	1	1	NUM
ejpam-5369	54	3	.	.	PUNCT
ejpam-5369	55	1	let	let	VERB
ejpam-5369	55	2	a	a	DET
ejpam-5369	55	3	be	be	AUX
ejpam-5369	55	4	a	a	DET
ejpam-5369	55	5	subset	subset	NOUN
ejpam-5369	55	6	of	of	ADP
ejpam-5369	55	7	a	a	DET
ejpam-5369	55	8	space	space	NOUN
ejpam-5369	55	9	x.	x.	NOUN
ejpam-5369	55	10	a	a	PRON
ejpam-5369	55	11	is	be	AUX
ejpam-5369	55	12	said	say	VERB
ejpam-5369	55	13	to	to	PART
ejpam-5369	55	14	be	be	AUX
ejpam-5369	55	15	ω	ω	NOUN
ejpam-5369	55	16	-	-	ADJ
ejpam-5369	55	17	open	open	ADJ
ejpam-5369	55	18	[	[	X
ejpam-5369	55	19	10	10	NUM
ejpam-5369	55	20	]	]	X
ejpam-5369	55	21	if	if	SCONJ
ejpam-5369	55	22	for	for	ADP
ejpam-5369	55	23	every	every	DET
ejpam-5369	55	24	x	x	PROPN
ejpam-5369	55	25	∈	∈	PROPN
ejpam-5369	55	26	a	a	PRON
ejpam-5369	55	27	,	,	PUNCT
ejpam-5369	55	28	there	there	PRON
ejpam-5369	55	29	exists	exist	VERB
ejpam-5369	55	30	an	an	DET
ejpam-5369	55	31	open	open	ADJ
ejpam-5369	55	32	set	set	NOUN
ejpam-5369	55	33	u	u	NOUN
ejpam-5369	55	34	containing	contain	VERB
ejpam-5369	55	35	x	x	PUNCT
ejpam-5369	55	36	such	such	ADJ
ejpam-5369	55	37	that	that	SCONJ
ejpam-5369	55	38	u	u	NOUN
ejpam-5369	55	39	\a	\a	ADJ
ejpam-5369	55	40	is	be	AUX
ejpam-5369	55	41	countable	countable	ADJ
ejpam-5369	55	42	.	.	PUNCT
ejpam-5369	56	1	the	the	DET
ejpam-5369	56	2	complement	complement	NOUN
ejpam-5369	56	3	of	of	ADP
ejpam-5369	56	4	an	an	DET
ejpam-5369	56	5	ω	ω	ADV
ejpam-5369	56	6	-	-	ADJ
ejpam-5369	56	7	open	open	ADJ
ejpam-5369	56	8	set	set	NOUN
ejpam-5369	56	9	is	be	AUX
ejpam-5369	56	10	called	call	VERB
ejpam-5369	56	11	an	an	DET
ejpam-5369	56	12	ω	ω	NOUN
ejpam-5369	56	13	-	-	PUNCT
ejpam-5369	56	14	closed	closed	ADJ
ejpam-5369	56	15	.	.	PUNCT
ejpam-5369	57	1	the	the	DET
ejpam-5369	57	2	family	family	NOUN
ejpam-5369	57	3	of	of	ADP
ejpam-5369	57	4	all	all	DET
ejpam-5369	57	5	ω	ω	NOUN
ejpam-5369	57	6	-	-	ADJ
ejpam-5369	57	7	open	open	ADJ
ejpam-5369	57	8	(	(	PUNCT
ejpam-5369	57	9	resp	resp	NOUN
ejpam-5369	57	10	.	.	PUNCT
ejpam-5369	58	1	ω	ω	VERB
ejpam-5369	58	2	-	-	VERB
ejpam-5369	58	3	closed	closed	ADJ
ejpam-5369	58	4	)	)	PUNCT
ejpam-5369	58	5	sets	set	NOUN
ejpam-5369	58	6	of	of	ADP
ejpam-5369	58	7	x	x	PUNCT
ejpam-5369	58	8	will	will	AUX
ejpam-5369	58	9	be	be	AUX
ejpam-5369	58	10	denoted	denote	VERB
ejpam-5369	58	11	by	by	ADP
ejpam-5369	58	12	ωo(x	ωo(x	NUM
ejpam-5369	58	13	)	)	PUNCT
ejpam-5369	58	14	or	or	CCONJ
ejpam-5369	58	15	τω	τω	DET
ejpam-5369	58	16	(	(	PUNCT
ejpam-5369	58	17	resp	resp	PROPN
ejpam-5369	58	18	.	.	PUNCT
ejpam-5369	58	19	ωc(x	ωc(x	NOUN
ejpam-5369	58	20	)	)	PUNCT
ejpam-5369	58	21	)	)	PUNCT
ejpam-5369	58	22	.	.	PUNCT
ejpam-5369	59	1	the	the	DET
ejpam-5369	59	2	family	family	NOUN
ejpam-5369	59	3	of	of	ADP
ejpam-5369	59	4	all	all	DET
ejpam-5369	59	5	ω	ω	NOUN
ejpam-5369	59	6	-	-	ADJ
ejpam-5369	59	7	open	open	ADJ
ejpam-5369	59	8	(	(	PUNCT
ejpam-5369	59	9	resp	resp	NOUN
ejpam-5369	59	10	.	.	PUNCT
ejpam-5369	60	1	ω	ω	VERB
ejpam-5369	60	2	-	-	VERB
ejpam-5369	60	3	closed	closed	ADJ
ejpam-5369	60	4	)	)	PUNCT
ejpam-5369	60	5	sets	set	NOUN
ejpam-5369	60	6	of	of	ADP
ejpam-5369	60	7	x	x	PUNCT
ejpam-5369	60	8	containing	contain	VERB
ejpam-5369	60	9	a	a	DET
ejpam-5369	60	10	point	point	NOUN
ejpam-5369	60	11	x	x	PUNCT
ejpam-5369	60	12	of	of	ADP
ejpam-5369	60	13	x	x	PRON
ejpam-5369	60	14	will	will	AUX
ejpam-5369	60	15	be	be	AUX
ejpam-5369	60	16	denoted	denote	VERB
ejpam-5369	60	17	by	by	ADP
ejpam-5369	60	18	ωo(x	ωo(x	PROPN
ejpam-5369	60	19	,	,	PUNCT
ejpam-5369	60	20	x	x	X
ejpam-5369	60	21	)	)	PUNCT
ejpam-5369	60	22	(	(	PUNCT
ejpam-5369	60	23	resp	resp	NOUN
ejpam-5369	60	24	.	.	PUNCT
ejpam-5369	60	25	ωc(x	ωc(x	NOUN
ejpam-5369	60	26	,	,	PUNCT
ejpam-5369	60	27	x	x	NOUN
ejpam-5369	60	28	)	)	PUNCT
ejpam-5369	60	29	)	)	PUNCT
ejpam-5369	60	30	.	.	PUNCT
ejpam-5369	61	1	the	the	DET
ejpam-5369	61	2	intersection	intersection	NOUN
ejpam-5369	61	3	of	of	ADP
ejpam-5369	61	4	all	all	DET
ejpam-5369	61	5	ω	ω	ADJ
ejpam-5369	61	6	-	-	ADJ
ejpam-5369	61	7	closed	closed	ADJ
ejpam-5369	61	8	sets	set	NOUN
ejpam-5369	61	9	containing	contain	VERB
ejpam-5369	61	10	a	a	PRON
ejpam-5369	61	11	is	be	AUX
ejpam-5369	61	12	called	call	VERB
ejpam-5369	61	13	the	the	DET
ejpam-5369	61	14	ω	ω	NOUN
ejpam-5369	61	15	-	-	NOUN
ejpam-5369	61	16	closure	closure	NOUN
ejpam-5369	61	17	of	of	ADP
ejpam-5369	61	18	a	a	PRON
ejpam-5369	61	19	and	and	CCONJ
ejpam-5369	61	20	is	be	AUX
ejpam-5369	61	21	denoted	denote	VERB
ejpam-5369	61	22	by	by	ADP
ejpam-5369	61	23	clω(a	clω(a	PROPN
ejpam-5369	61	24	)	)	PUNCT
ejpam-5369	61	25	or	or	CCONJ
ejpam-5369	61	26	ω	ω	NOUN
ejpam-5369	61	27	-	-	PUNCT
ejpam-5369	61	28	cl(a	cl(a	NUM
ejpam-5369	61	29	)	)	PUNCT
ejpam-5369	61	30	.	.	PUNCT
ejpam-5369	62	1	definition	definition	NOUN
ejpam-5369	62	2	2	2	NUM
ejpam-5369	62	3	.	.	PUNCT
ejpam-5369	63	1	let	let	VERB
ejpam-5369	63	2	x	x	PRON
ejpam-5369	63	3	be	be	AUX
ejpam-5369	63	4	a	a	DET
ejpam-5369	63	5	non	non	ADJ
ejpam-5369	63	6	-	-	ADJ
ejpam-5369	63	7	empty	empty	ADJ
ejpam-5369	63	8	set	set	NOUN
ejpam-5369	63	9	.	.	PUNCT
ejpam-5369	64	1	a	a	DET
ejpam-5369	64	2	collection	collection	NOUN
ejpam-5369	64	3	p	p	NOUN
ejpam-5369	64	4	⊆	⊆	NUM
ejpam-5369	64	5	2x	2x	NUM
ejpam-5369	64	6	is	be	AUX
ejpam-5369	64	7	called	call	VERB
ejpam-5369	64	8	a	a	DET
ejpam-5369	64	9	primal	primal	NOUN
ejpam-5369	64	10	on	on	ADP
ejpam-5369	64	11	x	x	PUNCT
ejpam-5369	64	12	[	[	X
ejpam-5369	64	13	1	1	X
ejpam-5369	64	14	]	]	PUNCT
ejpam-5369	64	15	if	if	SCONJ
ejpam-5369	64	16	it	it	PRON
ejpam-5369	64	17	satisfies	satisfy	VERB
ejpam-5369	64	18	the	the	DET
ejpam-5369	64	19	following	follow	VERB
ejpam-5369	64	20	conditions	condition	NOUN
ejpam-5369	64	21	:	:	PUNCT
ejpam-5369	64	22	p.	p.	NOUN
ejpam-5369	64	23	şaşmaz	şaşmaz	NUM
ejpam-5369	64	24	,	,	PUNCT
ejpam-5369	64	25	m.	m.	NOUN
ejpam-5369	64	26	özkoç	özkoç	PROPN
ejpam-5369	64	27	/	/	SYM
ejpam-5369	64	28	eur	eur	PROPN
ejpam-5369	64	29	.	.	PUNCT
ejpam-5369	65	1	j.	j.	PROPN
ejpam-5369	65	2	pure	pure	PROPN
ejpam-5369	65	3	appl	appl	PROPN
ejpam-5369	65	4	.	.	PROPN
ejpam-5369	65	5	math	math	PROPN
ejpam-5369	65	6	,	,	PUNCT
ejpam-5369	65	7	17	17	NUM
ejpam-5369	65	8	(	(	PUNCT
ejpam-5369	65	9	4	4	NUM
ejpam-5369	65	10	)	)	PUNCT
ejpam-5369	65	11	(	(	PUNCT
ejpam-5369	65	12	2024	2024	NUM
ejpam-5369	65	13	)	)	PUNCT
ejpam-5369	65	14	,	,	PUNCT
ejpam-5369	65	15	2800	2800	NUM
ejpam-5369	65	16	-	-	SYM
ejpam-5369	65	17	2811	2811	NUM
ejpam-5369	65	18	2802	2802	NUM
ejpam-5369	65	19	(	(	PUNCT
ejpam-5369	65	20	a	a	NOUN
ejpam-5369	65	21	)	)	PUNCT
ejpam-5369	65	22	x	x	SYM
ejpam-5369	65	23	/∈	/∈	PUNCT
ejpam-5369	66	1	p	p	X
ejpam-5369	66	2	,	,	PUNCT
ejpam-5369	66	3	(	(	PUNCT
ejpam-5369	66	4	b	b	X
ejpam-5369	66	5	)	)	PUNCT
ejpam-5369	66	6	if	if	SCONJ
ejpam-5369	66	7	a	a	DET
ejpam-5369	66	8	∈	∈	PROPN
ejpam-5369	66	9	p	p	NOUN
ejpam-5369	66	10	and	and	CCONJ
ejpam-5369	66	11	b	b	NOUN
ejpam-5369	66	12	⊆	⊆	NUM
ejpam-5369	66	13	a	a	PRON
ejpam-5369	66	14	,	,	PUNCT
ejpam-5369	66	15	then	then	ADV
ejpam-5369	66	16	b	b	PROPN
ejpam-5369	66	17	∈	∈	PROPN
ejpam-5369	66	18	p	p	X
ejpam-5369	66	19	,	,	PUNCT
ejpam-5369	66	20	(	(	PUNCT
ejpam-5369	66	21	c	c	X
ejpam-5369	66	22	)	)	PUNCT
ejpam-5369	66	23	if	if	SCONJ
ejpam-5369	66	24	a	a	DET
ejpam-5369	66	25	∩b	∩b	NOUN
ejpam-5369	66	26	∈	∈	X
ejpam-5369	66	27	p	p	NOUN
ejpam-5369	66	28	,	,	PUNCT
ejpam-5369	66	29	then	then	ADV
ejpam-5369	66	30	a	a	DET
ejpam-5369	66	31	∈	∈	PROPN
ejpam-5369	66	32	p	p	NOUN
ejpam-5369	66	33	or	or	CCONJ
ejpam-5369	66	34	b	b	PROPN
ejpam-5369	66	35	∈	∈	PROPN
ejpam-5369	66	36	p.	p.	NOUN
ejpam-5369	66	37	definition	definition	NOUN
ejpam-5369	66	38	3	3	X
ejpam-5369	66	39	.	.	PUNCT
ejpam-5369	67	1	[	[	X
ejpam-5369	67	2	1	1	X
ejpam-5369	67	3	]	]	PUNCT
ejpam-5369	67	4	a	a	DET
ejpam-5369	67	5	topological	topological	ADJ
ejpam-5369	67	6	space	space	NOUN
ejpam-5369	67	7	(	(	PUNCT
ejpam-5369	67	8	x	x	X
ejpam-5369	67	9	,	,	PUNCT
ejpam-5369	67	10	τ	τ	X
ejpam-5369	67	11	)	)	PUNCT
ejpam-5369	67	12	with	with	ADP
ejpam-5369	67	13	a	a	DET
ejpam-5369	67	14	primal	primal	ADJ
ejpam-5369	67	15	p	p	NOUN
ejpam-5369	67	16	on	on	ADP
ejpam-5369	67	17	x	x	SYM
ejpam-5369	67	18	is	be	AUX
ejpam-5369	67	19	called	call	VERB
ejpam-5369	67	20	a	a	DET
ejpam-5369	67	21	primal	primal	ADJ
ejpam-5369	67	22	topological	topological	ADJ
ejpam-5369	67	23	space	space	NOUN
ejpam-5369	67	24	and	and	CCONJ
ejpam-5369	67	25	denoted	denote	VERB
ejpam-5369	67	26	by	by	ADP
ejpam-5369	67	27	(	(	PUNCT
ejpam-5369	67	28	x	x	NOUN
ejpam-5369	67	29	,	,	PUNCT
ejpam-5369	67	30	τ	τ	PROPN
ejpam-5369	67	31	,	,	PUNCT
ejpam-5369	67	32	p	p	NOUN
ejpam-5369	67	33	)	)	PUNCT
ejpam-5369	67	34	.	.	PUNCT
ejpam-5369	68	1	definition	definition	NOUN
ejpam-5369	68	2	4	4	NUM
ejpam-5369	68	3	.	.	PUNCT
ejpam-5369	69	1	[	[	X
ejpam-5369	69	2	1	1	X
ejpam-5369	69	3	]	]	X
ejpam-5369	69	4	let	let	VERB
ejpam-5369	69	5	(	(	PUNCT
ejpam-5369	69	6	x	x	NOUN
ejpam-5369	69	7	,	,	PUNCT
ejpam-5369	69	8	τ	τ	PROPN
ejpam-5369	69	9	,	,	PUNCT
ejpam-5369	69	10	p	p	NOUN
ejpam-5369	69	11	)	)	PUNCT
ejpam-5369	69	12	be	be	AUX
ejpam-5369	69	13	a	a	DET
ejpam-5369	69	14	primal	primal	ADJ
ejpam-5369	69	15	topological	topological	ADJ
ejpam-5369	69	16	space	space	NOUN
ejpam-5369	69	17	.	.	PUNCT
ejpam-5369	70	1	we	we	PRON
ejpam-5369	70	2	consider	consider	VERB
ejpam-5369	70	3	a	a	DET
ejpam-5369	70	4	map	map	NOUN
ejpam-5369	70	5	(	(	PUNCT
ejpam-5369	70	6	·	·	PUNCT
ejpam-5369	70	7	)	)	PUNCT
ejpam-5369	70	8	⋄	⋄	NOUN
ejpam-5369	70	9	:	:	PUNCT
ejpam-5369	70	10	2x	2x	NUM
ejpam-5369	70	11	→	→	SYM
ejpam-5369	70	12	2x	2x	NUM
ejpam-5369	70	13	as	as	ADP
ejpam-5369	70	14	a⋄(x	a⋄(x	PROPN
ejpam-5369	70	15	,	,	PUNCT
ejpam-5369	70	16	τ	τ	PROPN
ejpam-5369	70	17	,	,	PUNCT
ejpam-5369	70	18	p	p	NOUN
ejpam-5369	70	19	)	)	PUNCT
ejpam-5369	70	20	=	=	SYM
ejpam-5369	70	21	{	{	PUNCT
ejpam-5369	70	22	x	x	PUNCT
ejpam-5369	70	23	∈	∈	PROPN
ejpam-5369	70	24	x	x	X
ejpam-5369	70	25	:	:	PUNCT
ejpam-5369	70	26	(	(	PUNCT
ejpam-5369	70	27	∀u	∀u	NOUN
ejpam-5369	70	28	∈	∈	PROPN
ejpam-5369	70	29	o(x	o(x	PROPN
ejpam-5369	70	30	,	,	PUNCT
ejpam-5369	70	31	x))(ac	x))(ac	PROPN
ejpam-5369	70	32	∪	∪	VERB
ejpam-5369	70	33	u	u	NOUN
ejpam-5369	70	34	c	c	PROPN
ejpam-5369	70	35	∈	∈	PROPN
ejpam-5369	70	36	p	p	NOUN
ejpam-5369	70	37	)	)	PUNCT
ejpam-5369	70	38	}	}	PUNCT
ejpam-5369	70	39	for	for	ADP
ejpam-5369	70	40	any	any	DET
ejpam-5369	70	41	subset	subset	NOUN
ejpam-5369	70	42	a	a	PRON
ejpam-5369	70	43	of	of	ADP
ejpam-5369	70	44	x.	x.	NOUN
ejpam-5369	70	45	we	we	PRON
ejpam-5369	70	46	can	can	AUX
ejpam-5369	70	47	also	also	ADV
ejpam-5369	70	48	write	write	VERB
ejpam-5369	70	49	a⋄	a⋄	NOUN
ejpam-5369	70	50	as	as	ADP
ejpam-5369	70	51	a⋄(x	a⋄(x	PROPN
ejpam-5369	70	52	,	,	PUNCT
ejpam-5369	70	53	τ	τ	PROPN
ejpam-5369	70	54	,	,	PUNCT
ejpam-5369	70	55	p	p	NOUN
ejpam-5369	70	56	)	)	PUNCT
ejpam-5369	70	57	to	to	PART
ejpam-5369	70	58	specify	specify	VERB
ejpam-5369	70	59	the	the	DET
ejpam-5369	70	60	primal	primal	NOUN
ejpam-5369	70	61	as	as	ADP
ejpam-5369	70	62	per	per	ADP
ejpam-5369	70	63	our	our	PRON
ejpam-5369	70	64	requirements	requirement	NOUN
ejpam-5369	70	65	.	.	PUNCT
ejpam-5369	71	1	definition	definition	NOUN
ejpam-5369	71	2	5	5	NUM
ejpam-5369	71	3	.	.	PUNCT
ejpam-5369	72	1	[	[	X
ejpam-5369	72	2	1	1	X
ejpam-5369	72	3	]	]	X
ejpam-5369	72	4	let	let	VERB
ejpam-5369	72	5	(	(	PUNCT
ejpam-5369	72	6	x	x	NOUN
ejpam-5369	72	7	,	,	PUNCT
ejpam-5369	72	8	τ	τ	PROPN
ejpam-5369	72	9	,	,	PUNCT
ejpam-5369	72	10	p	p	NOUN
ejpam-5369	72	11	)	)	PUNCT
ejpam-5369	72	12	be	be	AUX
ejpam-5369	72	13	a	a	DET
ejpam-5369	72	14	primal	primal	ADJ
ejpam-5369	72	15	topological	topological	ADJ
ejpam-5369	72	16	space	space	NOUN
ejpam-5369	72	17	.	.	PUNCT
ejpam-5369	73	1	we	we	PRON
ejpam-5369	73	2	consider	consider	VERB
ejpam-5369	73	3	a	a	DET
ejpam-5369	73	4	map	map	NOUN
ejpam-5369	73	5	cl⋄	cl⋄	NOUN
ejpam-5369	73	6	:	:	PUNCT
ejpam-5369	73	7	2x	2x	NUM
ejpam-5369	73	8	→	→	SYM
ejpam-5369	73	9	2x	2x	NUM
ejpam-5369	73	10	as	as	ADP
ejpam-5369	73	11	cl⋄(a	cl⋄(a	PUNCT
ejpam-5369	73	12	)	)	PUNCT
ejpam-5369	73	13	=	=	PUNCT
ejpam-5369	73	14	a	a	DET
ejpam-5369	73	15	∪a⋄	∪a⋄	NOUN
ejpam-5369	73	16	,	,	PUNCT
ejpam-5369	73	17	where	where	SCONJ
ejpam-5369	73	18	a	a	PRON
ejpam-5369	73	19	is	be	AUX
ejpam-5369	73	20	any	any	DET
ejpam-5369	73	21	subset	subset	NOUN
ejpam-5369	73	22	of	of	ADP
ejpam-5369	73	23	x.	x.	NOUN
ejpam-5369	73	24	definition	definition	NOUN
ejpam-5369	73	25	6	6	NUM
ejpam-5369	73	26	.	.	PUNCT
ejpam-5369	74	1	[	[	X
ejpam-5369	74	2	1	1	X
ejpam-5369	74	3	]	]	X
ejpam-5369	74	4	let	let	VERB
ejpam-5369	74	5	(	(	PUNCT
ejpam-5369	74	6	x	x	NOUN
ejpam-5369	74	7	,	,	PUNCT
ejpam-5369	74	8	τ	τ	PROPN
ejpam-5369	74	9	,	,	PUNCT
ejpam-5369	74	10	p	p	NOUN
ejpam-5369	74	11	)	)	PUNCT
ejpam-5369	74	12	be	be	AUX
ejpam-5369	74	13	a	a	DET
ejpam-5369	74	14	primal	primal	ADJ
ejpam-5369	74	15	topological	topological	ADJ
ejpam-5369	74	16	space	space	NOUN
ejpam-5369	74	17	.	.	PUNCT
ejpam-5369	75	1	then	then	ADV
ejpam-5369	75	2	,	,	PUNCT
ejpam-5369	75	3	the	the	DET
ejpam-5369	75	4	family	family	NOUN
ejpam-5369	75	5	τ⋄	τ⋄	NOUN
ejpam-5369	75	6	=	=	PUNCT
ejpam-5369	75	7	{	{	PUNCT
ejpam-5369	75	8	a	a	DET
ejpam-5369	75	9	⊆	⊆	NUM
ejpam-5369	75	10	x|cl⋄(ac	x|cl⋄(ac	PRON
ejpam-5369	75	11	)	)	PUNCT
ejpam-5369	75	12	=	=	SYM
ejpam-5369	75	13	ac	ac	PROPN
ejpam-5369	75	14	}	}	PUNCT
ejpam-5369	75	15	is	be	AUX
ejpam-5369	75	16	a	a	DET
ejpam-5369	75	17	topology	topology	NOUN
ejpam-5369	75	18	on	on	ADP
ejpam-5369	75	19	x	x	PUNCT
ejpam-5369	75	20	induced	induce	VERB
ejpam-5369	75	21	by	by	ADP
ejpam-5369	75	22	topology	topology	NOUN
ejpam-5369	75	23	τ	τ	PROPN
ejpam-5369	75	24	and	and	CCONJ
ejpam-5369	75	25	primal	primal	ADJ
ejpam-5369	75	26	p.	p.	NOUN
ejpam-5369	75	27	3	3	NUM
ejpam-5369	75	28	.	.	PUNCT
ejpam-5369	76	1	the	the	DET
ejpam-5369	76	2	operator	operator	NOUN
ejpam-5369	76	3	(	(	PUNCT
ejpam-5369	76	4	.)⋄ω	.)⋄ω	NOUN
ejpam-5369	76	5	and	and	CCONJ
ejpam-5369	76	6	its	its	PRON
ejpam-5369	76	7	basic	basic	ADJ
ejpam-5369	76	8	properties	property	NOUN
ejpam-5369	76	9	definition	definition	NOUN
ejpam-5369	76	10	7	7	NUM
ejpam-5369	76	11	.	.	PUNCT
ejpam-5369	77	1	let	let	VERB
ejpam-5369	77	2	(	(	PUNCT
ejpam-5369	77	3	x	x	X
ejpam-5369	77	4	,	,	PUNCT
ejpam-5369	77	5	τ	τ	PROPN
ejpam-5369	77	6	,	,	PUNCT
ejpam-5369	77	7	p	p	NOUN
ejpam-5369	77	8	)	)	PUNCT
ejpam-5369	77	9	be	be	AUX
ejpam-5369	77	10	a	a	DET
ejpam-5369	77	11	primal	primal	ADJ
ejpam-5369	77	12	topological	topological	ADJ
ejpam-5369	77	13	space	space	NOUN
ejpam-5369	77	14	.	.	PUNCT
ejpam-5369	78	1	we	we	PRON
ejpam-5369	78	2	consider	consider	VERB
ejpam-5369	78	3	a	a	DET
ejpam-5369	78	4	map	map	NOUN
ejpam-5369	78	5	(	(	PUNCT
ejpam-5369	78	6	·	·	PUNCT
ejpam-5369	78	7	)	)	PUNCT
ejpam-5369	78	8	⋄ω	⋄ω	NUM
ejpam-5369	78	9	:	:	PUNCT
ejpam-5369	78	10	2x	2x	NUM
ejpam-5369	78	11	→	→	SYM
ejpam-5369	78	12	2x	2x	NUM
ejpam-5369	78	13	as	as	ADP
ejpam-5369	78	14	a⋄	a⋄	NOUN
ejpam-5369	78	15	ω(x	ω(x	NOUN
ejpam-5369	78	16	,	,	PUNCT
ejpam-5369	78	17	τ	τ	X
ejpam-5369	78	18	,	,	PUNCT
ejpam-5369	78	19	p	p	NOUN
ejpam-5369	78	20	)	)	PUNCT
ejpam-5369	78	21	=	=	SYM
ejpam-5369	78	22	{	{	PUNCT
ejpam-5369	78	23	x	x	PUNCT
ejpam-5369	78	24	∈	∈	PROPN
ejpam-5369	78	25	x	x	X
ejpam-5369	78	26	:	:	PUNCT
ejpam-5369	78	27	(	(	PUNCT
ejpam-5369	78	28	∀u	∀u	NOUN
ejpam-5369	78	29	∈	∈	NOUN
ejpam-5369	78	30	ωo(x	ωo(x	NUM
ejpam-5369	78	31	,	,	PUNCT
ejpam-5369	78	32	x))(ac	x))(ac	PROPN
ejpam-5369	78	33	∪	∪	VERB
ejpam-5369	78	34	u	u	NOUN
ejpam-5369	78	35	c	c	PROPN
ejpam-5369	78	36	∈	∈	PROPN
ejpam-5369	78	37	p	p	NOUN
ejpam-5369	78	38	)	)	PUNCT
ejpam-5369	78	39	}	}	PUNCT
ejpam-5369	78	40	for	for	ADP
ejpam-5369	78	41	any	any	DET
ejpam-5369	78	42	subset	subset	NOUN
ejpam-5369	78	43	a	a	PRON
ejpam-5369	78	44	of	of	ADP
ejpam-5369	78	45	x.	x.	NOUN
ejpam-5369	78	46	we	we	PRON
ejpam-5369	78	47	can	can	AUX
ejpam-5369	78	48	also	also	ADV
ejpam-5369	78	49	write	write	VERB
ejpam-5369	78	50	a⋄	a⋄	ADJ
ejpam-5369	78	51	ω	ω	NOUN
ejpam-5369	78	52	as	as	ADP
ejpam-5369	78	53	a⋄	a⋄	NOUN
ejpam-5369	78	54	ω(x	ω(x	NOUN
ejpam-5369	78	55	,	,	PUNCT
ejpam-5369	78	56	τ	τ	X
ejpam-5369	78	57	,	,	PUNCT
ejpam-5369	78	58	p	p	NOUN
ejpam-5369	78	59	)	)	PUNCT
ejpam-5369	78	60	to	to	PART
ejpam-5369	78	61	specify	specify	VERB
ejpam-5369	78	62	the	the	DET
ejpam-5369	78	63	primal	primal	NOUN
ejpam-5369	78	64	and	and	CCONJ
ejpam-5369	78	65	the	the	DET
ejpam-5369	78	66	topology	topology	NOUN
ejpam-5369	78	67	if	if	SCONJ
ejpam-5369	78	68	necessary	necessary	ADJ
ejpam-5369	78	69	.	.	PUNCT
ejpam-5369	79	1	corollary	corollary	ADJ
ejpam-5369	79	2	1	1	NUM
ejpam-5369	79	3	.	.	PUNCT
ejpam-5369	80	1	let	let	VERB
ejpam-5369	80	2	(	(	PUNCT
ejpam-5369	80	3	x	x	X
ejpam-5369	80	4	,	,	PUNCT
ejpam-5369	80	5	τ	τ	PROPN
ejpam-5369	80	6	,	,	PUNCT
ejpam-5369	80	7	p	p	NOUN
ejpam-5369	80	8	)	)	PUNCT
ejpam-5369	80	9	be	be	AUX
ejpam-5369	80	10	a	a	DET
ejpam-5369	80	11	primal	primal	ADJ
ejpam-5369	80	12	topological	topological	ADJ
ejpam-5369	80	13	space	space	NOUN
ejpam-5369	80	14	and	and	CCONJ
ejpam-5369	80	15	a	a	DET
ejpam-5369	80	16	⊆	⊆	NUM
ejpam-5369	80	17	x.	x.	NOUN
ejpam-5369	80	18	then	then	ADV
ejpam-5369	80	19	,	,	PUNCT
ejpam-5369	80	20	a⋄	a⋄	PROPN
ejpam-5369	80	21	ω	ω	NOUN
ejpam-5369	80	22	⊆	⊆	NUM
ejpam-5369	80	23	a⋄.	a⋄.	ADJ
ejpam-5369	80	24	remark	remark	NOUN
ejpam-5369	80	25	1	1	NUM
ejpam-5369	80	26	.	.	PUNCT
ejpam-5369	81	1	let	let	VERB
ejpam-5369	81	2	(	(	PUNCT
ejpam-5369	81	3	x	x	X
ejpam-5369	81	4	,	,	PUNCT
ejpam-5369	81	5	τ	τ	PROPN
ejpam-5369	81	6	,	,	PUNCT
ejpam-5369	81	7	p	p	NOUN
ejpam-5369	81	8	)	)	PUNCT
ejpam-5369	81	9	be	be	AUX
ejpam-5369	81	10	a	a	DET
ejpam-5369	81	11	primal	primal	ADJ
ejpam-5369	81	12	topological	topological	ADJ
ejpam-5369	81	13	space	space	NOUN
ejpam-5369	81	14	and	and	CCONJ
ejpam-5369	81	15	a	a	DET
ejpam-5369	81	16	⊆	⊆	NUM
ejpam-5369	81	17	x.	x.	NOUN
ejpam-5369	81	18	there	there	PRON
ejpam-5369	81	19	is	be	VERB
ejpam-5369	81	20	no	no	DET
ejpam-5369	81	21	relationship	relationship	NOUN
ejpam-5369	81	22	between	between	ADP
ejpam-5369	81	23	a⋄	a⋄	NOUN
ejpam-5369	81	24	ω	ω	PROPN
ejpam-5369	81	25	and	and	CCONJ
ejpam-5369	81	26	a	a	PRON
ejpam-5369	81	27	as	as	SCONJ
ejpam-5369	81	28	shown	show	VERB
ejpam-5369	81	29	by	by	ADP
ejpam-5369	81	30	the	the	DET
ejpam-5369	81	31	following	follow	VERB
ejpam-5369	81	32	examples	example	NOUN
ejpam-5369	81	33	.	.	PUNCT
ejpam-5369	82	1	example	example	NOUN
ejpam-5369	83	1	1	1	NUM
ejpam-5369	83	2	.	.	PUNCT
ejpam-5369	83	3	let	let	VERB
ejpam-5369	83	4	x	x	PUNCT
ejpam-5369	83	5	=	=	PRON
ejpam-5369	83	6	{	{	PUNCT
ejpam-5369	83	7	1	1	NUM
ejpam-5369	83	8	,	,	PUNCT
ejpam-5369	83	9	2	2	NUM
ejpam-5369	83	10	,	,	PUNCT
ejpam-5369	83	11	3	3	NUM
ejpam-5369	83	12	}	}	PUNCT
ejpam-5369	83	13	with	with	ADP
ejpam-5369	83	14	the	the	DET
ejpam-5369	83	15	topology	topology	NOUN
ejpam-5369	83	16	τ	τ	X
ejpam-5369	83	17	=	=	PUNCT
ejpam-5369	83	18	{	{	PUNCT
ejpam-5369	83	19	∅	∅	NOUN
ejpam-5369	83	20	,	,	PUNCT
ejpam-5369	83	21	x	x	NOUN
ejpam-5369	83	22	}	}	PUNCT
ejpam-5369	83	23	.	.	PUNCT
ejpam-5369	84	1	we	we	PRON
ejpam-5369	84	2	consider	consider	VERB
ejpam-5369	84	3	the	the	DET
ejpam-5369	84	4	primal	primal	ADJ
ejpam-5369	84	5	p	p	X
ejpam-5369	84	6	=	=	X
ejpam-5369	84	7	{	{	PUNCT
ejpam-5369	84	8	∅	∅	NOUN
ejpam-5369	84	9	,	,	PUNCT
ejpam-5369	84	10	{	{	PUNCT
ejpam-5369	84	11	1	1	NUM
ejpam-5369	84	12	}	}	PUNCT
ejpam-5369	84	13	,	,	PUNCT
ejpam-5369	84	14	{	{	PUNCT
ejpam-5369	84	15	2	2	NUM
ejpam-5369	84	16	}	}	PUNCT
ejpam-5369	84	17	,	,	PUNCT
ejpam-5369	84	18	{	{	PUNCT
ejpam-5369	84	19	1	1	NUM
ejpam-5369	84	20	,	,	PUNCT
ejpam-5369	84	21	2	2	NUM
ejpam-5369	84	22	}	}	PUNCT
ejpam-5369	84	23	}	}	PUNCT
ejpam-5369	84	24	on	on	ADP
ejpam-5369	84	25	x.	x.	NOUN
ejpam-5369	84	26	now	now	ADV
ejpam-5369	84	27	,	,	PUNCT
ejpam-5369	84	28	if	if	SCONJ
ejpam-5369	84	29	a	a	PRON
ejpam-5369	84	30	=	=	X
ejpam-5369	84	31	{	{	PUNCT
ejpam-5369	84	32	1	1	NUM
ejpam-5369	84	33	}	}	PUNCT
ejpam-5369	84	34	,	,	PUNCT
ejpam-5369	84	35	then	then	ADV
ejpam-5369	84	36	a	a	DET
ejpam-5369	84	37	=	=	X
ejpam-5369	84	38	{	{	PUNCT
ejpam-5369	84	39	1	1	NUM
ejpam-5369	84	40	}	}	PUNCT
ejpam-5369	84	41	⊈	⊈	PROPN
ejpam-5369	84	42	∅	∅	NOUN
ejpam-5369	84	43	=	=	SYM
ejpam-5369	84	44	a⋄	a⋄	PROPN
ejpam-5369	84	45	ω	ω	PROPN
ejpam-5369	84	46	.	.	PUNCT
ejpam-5369	84	47	example	example	NOUN
ejpam-5369	85	1	2	2	NUM
ejpam-5369	85	2	.	.	X
ejpam-5369	86	1	let	let	AUX
ejpam-5369	86	2	(	(	PUNCT
ejpam-5369	86	3	r	r	NOUN
ejpam-5369	86	4	,	,	PUNCT
ejpam-5369	86	5	τ	τ	X
ejpam-5369	86	6	)	)	PUNCT
ejpam-5369	86	7	be	be	AUX
ejpam-5369	86	8	indiscrete	indiscrete	ADJ
ejpam-5369	86	9	topological	topological	ADJ
ejpam-5369	86	10	space	space	NOUN
ejpam-5369	86	11	.	.	PUNCT
ejpam-5369	87	1	consider	consider	VERB
ejpam-5369	87	2	the	the	DET
ejpam-5369	87	3	primal	primal	ADJ
ejpam-5369	87	4	p	p	X
ejpam-5369	87	5	=	=	X
ejpam-5369	87	6	2r	2r	NUM
ejpam-5369	87	7	\{r	\{r	NOUN
ejpam-5369	87	8	}	}	PUNCT
ejpam-5369	87	9	.	.	PUNCT
ejpam-5369	88	1	for	for	ADP
ejpam-5369	88	2	the	the	DET
ejpam-5369	88	3	subset	subset	NOUN
ejpam-5369	88	4	a	a	X
ejpam-5369	88	5	=	=	X
ejpam-5369	88	6	[	[	X
ejpam-5369	88	7	0,∞	0,∞	NOUN
ejpam-5369	88	8	)	)	PUNCT
ejpam-5369	88	9	,	,	PUNCT
ejpam-5369	88	10	we	we	PRON
ejpam-5369	88	11	have	have	VERB
ejpam-5369	88	12	−1	−1	NOUN
ejpam-5369	88	13	∈	∈	NOUN
ejpam-5369	88	14	a⋄	a⋄	NOUN
ejpam-5369	88	15	ω	ω	NOUN
ejpam-5369	88	16	but	but	CCONJ
ejpam-5369	88	17	−1	−1	NOUN
ejpam-5369	88	18	/∈	/∈	PUNCT
ejpam-5369	89	1	a.	a.	NOUN
ejpam-5369	89	2	therefore	therefore	ADV
ejpam-5369	89	3	,	,	PUNCT
ejpam-5369	89	4	a⋄	a⋄	PROPN
ejpam-5369	89	5	ω	ω	NUM
ejpam-5369	89	6	⊈	⊈	PROPN
ejpam-5369	89	7	a.	a.	NOUN
ejpam-5369	89	8	theorem	theorem	NOUN
ejpam-5369	89	9	1	1	X
ejpam-5369	89	10	.	.	PUNCT
ejpam-5369	90	1	let	let	VERB
ejpam-5369	90	2	(	(	PUNCT
ejpam-5369	90	3	x	x	X
ejpam-5369	90	4	,	,	PUNCT
ejpam-5369	90	5	τ	τ	PROPN
ejpam-5369	90	6	,	,	PUNCT
ejpam-5369	90	7	p	p	NOUN
ejpam-5369	90	8	)	)	PUNCT
ejpam-5369	90	9	be	be	AUX
ejpam-5369	90	10	a	a	DET
ejpam-5369	90	11	primal	primal	ADJ
ejpam-5369	90	12	topological	topological	ADJ
ejpam-5369	90	13	space	space	NOUN
ejpam-5369	90	14	and	and	CCONJ
ejpam-5369	90	15	a	a	DET
ejpam-5369	90	16	⊆	⊆	NUM
ejpam-5369	90	17	x.	x.	NOUN
ejpam-5369	90	18	if	if	SCONJ
ejpam-5369	90	19	a	a	PRON
ejpam-5369	90	20	is	be	AUX
ejpam-5369	90	21	ω	ω	NOUN
ejpam-5369	90	22	-	-	ADJ
ejpam-5369	90	23	closed	closed	ADJ
ejpam-5369	90	24	,	,	PUNCT
ejpam-5369	90	25	then	then	ADV
ejpam-5369	90	26	a⋄	a⋄	PROPN
ejpam-5369	90	27	ω	ω	NOUN
ejpam-5369	90	28	⊆	⊆	NUM
ejpam-5369	90	29	a.	a.	NOUN
ejpam-5369	90	30	proof	proof	NOUN
ejpam-5369	90	31	.	.	PUNCT
ejpam-5369	91	1	let	let	VERB
ejpam-5369	91	2	a	a	DET
ejpam-5369	91	3	∈	∈	NOUN
ejpam-5369	91	4	ωc(x	ωc(x	NOUN
ejpam-5369	91	5	)	)	PUNCT
ejpam-5369	91	6	and	and	CCONJ
ejpam-5369	91	7	x	x	PUNCT
ejpam-5369	91	8	∈	∈	PROPN
ejpam-5369	91	9	a⋄	a⋄	PROPN
ejpam-5369	91	10	ω	ω	PROPN
ejpam-5369	91	11	.	.	PUNCT
ejpam-5369	91	12	suppose	suppose	VERB
ejpam-5369	91	13	that	that	SCONJ
ejpam-5369	91	14	x	x	SYM
ejpam-5369	91	15	/∈	/∈	PUNCT
ejpam-5369	91	16	a.	a.	NOUN
ejpam-5369	91	17	x	x	PUNCT
ejpam-5369	91	18	∈	∈	PROPN
ejpam-5369	91	19	a⋄	a⋄	NOUN
ejpam-5369	91	20	ω	ω	NOUN
ejpam-5369	91	21	⇒	⇒	NOUN
ejpam-5369	91	22	(	(	PUNCT
ejpam-5369	91	23	∀u	∀u	NOUN
ejpam-5369	91	24	∈	∈	NOUN
ejpam-5369	91	25	ωo(x	ωo(x	NUM
ejpam-5369	91	26	,	,	PUNCT
ejpam-5369	91	27	x))(ac	x))(ac	PROPN
ejpam-5369	91	28	∪	∪	VERB
ejpam-5369	91	29	u	u	PROPN
ejpam-5369	91	30	c	c	PROPN
ejpam-5369	91	31	∈	∈	PROPN
ejpam-5369	91	32	p	p	X
ejpam-5369	91	33	)	)	PUNCT
ejpam-5369	92	1	x	x	SYM
ejpam-5369	92	2	/∈	/∈	PUNCT
ejpam-5369	93	1	a	a	DET
ejpam-5369	93	2	∈	∈	PROPN
ejpam-5369	93	3	ωc(x	ωc(x	NOUN
ejpam-5369	93	4	)	)	PUNCT
ejpam-5369	93	5	⇒	⇒	NOUN
ejpam-5369	93	6	ac	ac	PROPN
ejpam-5369	93	7	∈	∈	PROPN
ejpam-5369	93	8	ωo(x	ωo(x	NUM
ejpam-5369	93	9	,	,	PUNCT
ejpam-5369	93	10	x	x	NOUN
ejpam-5369	93	11	)	)	PUNCT
ejpam-5369	93	12	}	}	PUNCT
ejpam-5369	93	13	⇒	⇒	VERB
ejpam-5369	93	14	ac	ac	PROPN
ejpam-5369	93	15	∪	∪	ADV
ejpam-5369	93	16	(	(	PUNCT
ejpam-5369	93	17	ac)c	ac)c	PROPN
ejpam-5369	93	18	=	=	SYM
ejpam-5369	93	19	ac	ac	ADJ
ejpam-5369	93	20	∪a	∪a	NUM
ejpam-5369	93	21	=	=	PUNCT
ejpam-5369	93	22	x	x	SYM
ejpam-5369	93	23	∈	∈	PROPN
ejpam-5369	94	1	p	p	NOUN
ejpam-5369	94	2	this	this	PRON
ejpam-5369	94	3	is	be	AUX
ejpam-5369	94	4	a	a	DET
ejpam-5369	94	5	contradiction	contradiction	NOUN
ejpam-5369	94	6	because	because	SCONJ
ejpam-5369	94	7	any	any	DET
ejpam-5369	94	8	primal	primal	NOUN
ejpam-5369	94	9	does	do	AUX
ejpam-5369	94	10	not	not	PART
ejpam-5369	94	11	involve	involve	VERB
ejpam-5369	94	12	the	the	DET
ejpam-5369	94	13	set	set	NOUN
ejpam-5369	94	14	x.	x.	NOUN
ejpam-5369	94	15	p.	p.	PROPN
ejpam-5369	94	16	şaşmaz	şaşmaz	NUM
ejpam-5369	94	17	,	,	PUNCT
ejpam-5369	94	18	m.	m.	NOUN
ejpam-5369	94	19	özkoç	özkoç	PROPN
ejpam-5369	94	20	/	/	SYM
ejpam-5369	94	21	eur	eur	PROPN
ejpam-5369	94	22	.	.	PUNCT
ejpam-5369	95	1	j.	j.	PROPN
ejpam-5369	95	2	pure	pure	PROPN
ejpam-5369	95	3	appl	appl	PROPN
ejpam-5369	95	4	.	.	PROPN
ejpam-5369	95	5	math	math	PROPN
ejpam-5369	95	6	,	,	PUNCT
ejpam-5369	95	7	17	17	NUM
ejpam-5369	95	8	(	(	PUNCT
ejpam-5369	95	9	4	4	NUM
ejpam-5369	95	10	)	)	PUNCT
ejpam-5369	95	11	(	(	PUNCT
ejpam-5369	95	12	2024	2024	NUM
ejpam-5369	95	13	)	)	PUNCT
ejpam-5369	95	14	,	,	PUNCT
ejpam-5369	95	15	2800	2800	NUM
ejpam-5369	95	16	-	-	SYM
ejpam-5369	95	17	2811	2811	NUM
ejpam-5369	95	18	2803	2803	NUM
ejpam-5369	95	19	theorem	theorem	VERB
ejpam-5369	95	20	2	2	NUM
ejpam-5369	95	21	.	.	X
ejpam-5369	96	1	let	let	VERB
ejpam-5369	96	2	(	(	PUNCT
ejpam-5369	96	3	x	x	X
ejpam-5369	96	4	,	,	PUNCT
ejpam-5369	96	5	τ	τ	PROPN
ejpam-5369	96	6	,	,	PUNCT
ejpam-5369	96	7	p	p	NOUN
ejpam-5369	96	8	)	)	PUNCT
ejpam-5369	96	9	be	be	AUX
ejpam-5369	96	10	a	a	DET
ejpam-5369	96	11	primal	primal	ADJ
ejpam-5369	96	12	topological	topological	ADJ
ejpam-5369	96	13	space	space	NOUN
ejpam-5369	96	14	.	.	PUNCT
ejpam-5369	97	1	then	then	ADV
ejpam-5369	97	2	,	,	PUNCT
ejpam-5369	97	3	the	the	DET
ejpam-5369	97	4	following	follow	VERB
ejpam-5369	97	5	statements	statement	NOUN
ejpam-5369	97	6	hold	hold	VERB
ejpam-5369	97	7	for	for	ADP
ejpam-5369	97	8	any	any	DET
ejpam-5369	97	9	two	two	NUM
ejpam-5369	97	10	subsets	subset	NOUN
ejpam-5369	97	11	a	a	PRON
ejpam-5369	97	12	and	and	CCONJ
ejpam-5369	97	13	b	b	NOUN
ejpam-5369	97	14	of	of	ADP
ejpam-5369	97	15	x.	x.	NOUN
ejpam-5369	97	16	(	(	PUNCT
ejpam-5369	97	17	a	a	X
ejpam-5369	97	18	)	)	PUNCT
ejpam-5369	97	19	∅⋄ω	∅⋄ω	PROPN
ejpam-5369	97	20	=	=	SYM
ejpam-5369	97	21	∅	∅	NOUN
ejpam-5369	97	22	,	,	PUNCT
ejpam-5369	97	23	(	(	PUNCT
ejpam-5369	97	24	b	b	NOUN
ejpam-5369	97	25	)	)	PUNCT
ejpam-5369	97	26	a⋄	a⋄	PROPN
ejpam-5369	97	27	ω	ω	PROPN
ejpam-5369	97	28	∈	∈	PROPN
ejpam-5369	97	29	ωc(x	ωc(x	NOUN
ejpam-5369	97	30	)	)	PUNCT
ejpam-5369	97	31	,	,	PUNCT
ejpam-5369	97	32	(	(	PUNCT
ejpam-5369	97	33	c	c	X
ejpam-5369	97	34	)	)	PUNCT
ejpam-5369	97	35	(	(	PUNCT
ejpam-5369	97	36	a⋄	a⋄	PROPN
ejpam-5369	97	37	ω	ω	NUM
ejpam-5369	97	38	)	)	PUNCT
ejpam-5369	98	1	⋄	⋄	PROPN
ejpam-5369	98	2	ω	ω	NUM
ejpam-5369	98	3	⊆	⊆	NUM
ejpam-5369	98	4	a⋄	a⋄	PROPN
ejpam-5369	98	5	ω	ω	NUM
ejpam-5369	98	6	,	,	PUNCT
ejpam-5369	98	7	(	(	PUNCT
ejpam-5369	98	8	d	d	X
ejpam-5369	98	9	)	)	PUNCT
ejpam-5369	98	10	if	if	SCONJ
ejpam-5369	98	11	a	a	DET
ejpam-5369	98	12	⊆	⊆	NUM
ejpam-5369	98	13	b	b	NOUN
ejpam-5369	98	14	,	,	PUNCT
ejpam-5369	98	15	then	then	ADV
ejpam-5369	98	16	a⋄	a⋄	PROPN
ejpam-5369	98	17	ω	ω	NOUN
ejpam-5369	98	18	⊆	⊆	NUM
ejpam-5369	98	19	b⋄	b⋄	PROPN
ejpam-5369	98	20	ω	ω	NUM
ejpam-5369	98	21	,	,	PUNCT
ejpam-5369	98	22	(	(	PUNCT
ejpam-5369	98	23	e	e	NOUN
ejpam-5369	98	24	)	)	PUNCT
ejpam-5369	98	25	a⋄	a⋄	PROPN
ejpam-5369	98	26	ω	ω	PROPN
ejpam-5369	98	27	∪b⋄	∪b⋄	NOUN
ejpam-5369	98	28	ω	ω	NUM
ejpam-5369	98	29	=	=	SYM
ejpam-5369	98	30	(	(	PUNCT
ejpam-5369	98	31	a	a	DET
ejpam-5369	98	32	∪b)⋄ω	∪b)⋄ω	NOUN
ejpam-5369	98	33	,	,	PUNCT
ejpam-5369	98	34	(	(	PUNCT
ejpam-5369	98	35	f	f	X
ejpam-5369	98	36	)	)	PUNCT
ejpam-5369	98	37	(	(	PUNCT
ejpam-5369	98	38	a	a	DET
ejpam-5369	98	39	∩b)⋄ω	∩b)⋄ω	NOUN
ejpam-5369	98	40	⊆	⊆	NUM
ejpam-5369	98	41	a⋄	a⋄	NOUN
ejpam-5369	98	42	ω	ω	X
ejpam-5369	98	43	∩b⋄	∩b⋄	X
ejpam-5369	98	44	ω	ω	PROPN
ejpam-5369	98	45	.	.	PUNCT
ejpam-5369	99	1	proof	proof	NOUN
ejpam-5369	99	2	.	.	PUNCT
ejpam-5369	100	1	(	(	PUNCT
ejpam-5369	100	2	a	a	X
ejpam-5369	100	3	)	)	PUNCT
ejpam-5369	100	4	suppose	suppose	VERB
ejpam-5369	100	5	that	that	SCONJ
ejpam-5369	100	6	∅⋄ω	∅⋄ω	PROPN
ejpam-5369	100	7	̸=	̸=	PROPN
ejpam-5369	100	8	∅.	∅.	NOUN
ejpam-5369	100	9	then	then	ADV
ejpam-5369	100	10	,	,	PUNCT
ejpam-5369	100	11	there	there	PRON
ejpam-5369	100	12	exists	exist	VERB
ejpam-5369	100	13	x	x	X
ejpam-5369	100	14	∈	∈	PROPN
ejpam-5369	100	15	x	x	X
ejpam-5369	100	16	such	such	ADJ
ejpam-5369	100	17	that	that	SCONJ
ejpam-5369	100	18	x	x	SYM
ejpam-5369	100	19	∈	∈	PROPN
ejpam-5369	100	20	∅⋄ω	∅⋄ω	PROPN
ejpam-5369	100	21	.	.	PUNCT
ejpam-5369	101	1	thus	thus	ADV
ejpam-5369	101	2	,	,	PUNCT
ejpam-5369	101	3	we	we	PRON
ejpam-5369	101	4	have	have	VERB
ejpam-5369	101	5	u	u	NOUN
ejpam-5369	101	6	c	c	NOUN
ejpam-5369	101	7	∪	∪	X
ejpam-5369	101	8	∅c	∅c	NOUN
ejpam-5369	101	9	=	=	SYM
ejpam-5369	101	10	u	u	PROPN
ejpam-5369	101	11	c	c	NOUN
ejpam-5369	101	12	∪x	∪x	NOUN
ejpam-5369	102	1	=	=	SYM
ejpam-5369	102	2	x	x	SYM
ejpam-5369	102	3	∈	∈	PROPN
ejpam-5369	102	4	p	p	NOUN
ejpam-5369	102	5	for	for	ADP
ejpam-5369	102	6	every	every	DET
ejpam-5369	102	7	u	u	PROPN
ejpam-5369	102	8	∈	∈	PROPN
ejpam-5369	102	9	ωo(x	ωo(x	NUM
ejpam-5369	102	10	,	,	PUNCT
ejpam-5369	102	11	x	x	X
ejpam-5369	102	12	)	)	PUNCT
ejpam-5369	102	13	which	which	PRON
ejpam-5369	102	14	is	be	AUX
ejpam-5369	102	15	a	a	DET
ejpam-5369	102	16	contradiction	contradiction	NOUN
ejpam-5369	102	17	.	.	PUNCT
ejpam-5369	103	1	(	(	PUNCT
ejpam-5369	103	2	b	b	X
ejpam-5369	103	3	)	)	PUNCT
ejpam-5369	103	4	we	we	PRON
ejpam-5369	103	5	have	have	VERB
ejpam-5369	103	6	always	always	ADV
ejpam-5369	103	7	a⋄	a⋄	NOUN
ejpam-5369	103	8	ω	ω	PROPN
ejpam-5369	103	9	⊆	⊆	NUM
ejpam-5369	103	10	ω	ω	NUM
ejpam-5369	103	11	-	-	PUNCT
ejpam-5369	103	12	cl(a⋄	cl(a⋄	NOUN
ejpam-5369	103	13	ω	ω	NOUN
ejpam-5369	103	14	)	)	PUNCT
ejpam-5369	103	15	.	.	PUNCT
ejpam-5369	103	16	.	.	PUNCT
ejpam-5369	103	17	.	.	PUNCT
ejpam-5369	104	1	(	(	PUNCT
ejpam-5369	104	2	1	1	X
ejpam-5369	104	3	)	)	PUNCT
ejpam-5369	104	4	conversely	conversely	ADV
ejpam-5369	104	5	,	,	PUNCT
ejpam-5369	104	6	now	now	ADV
ejpam-5369	104	7	let	let	VERB
ejpam-5369	104	8	x	x	X
ejpam-5369	104	9	∈	∈	PROPN
ejpam-5369	104	10	ω	ω	PROPN
ejpam-5369	104	11	-	-	PUNCT
ejpam-5369	104	12	cl(a⋄	cl(a⋄	NOUN
ejpam-5369	104	13	ω	ω	NOUN
ejpam-5369	104	14	)	)	PUNCT
ejpam-5369	104	15	.	.	PUNCT
ejpam-5369	105	1	x	x	X
ejpam-5369	105	2	∈	∈	PROPN
ejpam-5369	105	3	ω	ω	PROPN
ejpam-5369	105	4	-	-	PUNCT
ejpam-5369	105	5	cl(a⋄	cl(a⋄	ADJ
ejpam-5369	105	6	ω	ω	NOUN
ejpam-5369	105	7	)	)	PUNCT
ejpam-5369	105	8	⇒	⇒	NOUN
ejpam-5369	105	9	(	(	PUNCT
ejpam-5369	105	10	∀u	∀u	NOUN
ejpam-5369	105	11	∈	∈	NOUN
ejpam-5369	105	12	ωo(x	ωo(x	NUM
ejpam-5369	105	13	,	,	PUNCT
ejpam-5369	105	14	x))(u	x))(u	PROPN
ejpam-5369	105	15	∩a⋄	∩a⋄	PROPN
ejpam-5369	105	16	ω	ω	NUM
ejpam-5369	105	17	̸=	̸=	PROPN
ejpam-5369	105	18	∅	∅	NOUN
ejpam-5369	105	19	)	)	PUNCT
ejpam-5369	105	20	⇒	⇒	NOUN
ejpam-5369	105	21	(	(	PUNCT
ejpam-5369	105	22	∀u	∀u	NOUN
ejpam-5369	105	23	∈	∈	NOUN
ejpam-5369	105	24	ωo(x	ωo(x	NUM
ejpam-5369	105	25	,	,	PUNCT
ejpam-5369	105	26	x))(∃y	x))(∃y	PROPN
ejpam-5369	105	27	∈	∈	PROPN
ejpam-5369	105	28	x)(y	x)(y	PUNCT
ejpam-5369	106	1	∈	∈	PROPN
ejpam-5369	106	2	u)(y	u)(y	PROPN
ejpam-5369	106	3	∈	∈	PROPN
ejpam-5369	106	4	a⋄	a⋄	PROPN
ejpam-5369	106	5	ω	ω	NUM
ejpam-5369	106	6	)	)	PUNCT
ejpam-5369	106	7	⇒	⇒	NOUN
ejpam-5369	106	8	(	(	PUNCT
ejpam-5369	106	9	∀u	∀u	NOUN
ejpam-5369	106	10	∈	∈	NOUN
ejpam-5369	106	11	ωo(x	ωo(x	NUM
ejpam-5369	106	12	,	,	PUNCT
ejpam-5369	106	13	x))(∃y	x))(∃y	PROPN
ejpam-5369	106	14	∈	∈	PROPN
ejpam-5369	106	15	x)(y	x)(y	PUNCT
ejpam-5369	106	16	∈	∈	PROPN
ejpam-5369	106	17	u)(∀v	u)(∀v	PROPN
ejpam-5369	106	18	∈	∈	PROPN
ejpam-5369	106	19	ωo(x	ωo(x	NUM
ejpam-5369	106	20	,	,	PUNCT
ejpam-5369	106	21	y))(v	y))(v	PRON
ejpam-5369	106	22	c	c	PROPN
ejpam-5369	106	23	∪ac	∪ac	PROPN
ejpam-5369	106	24	∈	∈	PROPN
ejpam-5369	106	25	p	p	X
ejpam-5369	106	26	)	)	PUNCT
ejpam-5369	106	27	v	v	NOUN
ejpam-5369	106	28	:	:	PUNCT
ejpam-5369	106	29	=	=	SYM
ejpam-5369	106	30	u	u	NOUN
ejpam-5369	106	31	}	}	PUNCT
ejpam-5369	106	32	⇒	⇒	VERB
ejpam-5369	106	33	⇒	⇒	NOUN
ejpam-5369	106	34	(	(	PUNCT
ejpam-5369	106	35	∀u	∀u	NOUN
ejpam-5369	106	36	∈	∈	NOUN
ejpam-5369	106	37	ωo(x	ωo(x	NUM
ejpam-5369	106	38	,	,	PUNCT
ejpam-5369	106	39	x))(u	x))(u	PROPN
ejpam-5369	106	40	c	c	PROPN
ejpam-5369	106	41	∪ac	∪ac	PROPN
ejpam-5369	106	42	∈	∈	PROPN
ejpam-5369	106	43	p	p	NOUN
ejpam-5369	106	44	)	)	PUNCT
ejpam-5369	106	45	⇒	⇒	NOUN
ejpam-5369	106	46	x	x	SYM
ejpam-5369	106	47	∈	∈	PROPN
ejpam-5369	106	48	a⋄	a⋄	PROPN
ejpam-5369	106	49	ω	ω	NOUN
ejpam-5369	106	50	.	.	PUNCT
ejpam-5369	107	1	then	then	ADV
ejpam-5369	107	2	,	,	PUNCT
ejpam-5369	107	3	we	we	PRON
ejpam-5369	107	4	have	have	VERB
ejpam-5369	107	5	ω	ω	VERB
ejpam-5369	107	6	-	-	PUNCT
ejpam-5369	107	7	cl(a⋄	cl(a⋄	ADJ
ejpam-5369	107	8	ω	ω	NOUN
ejpam-5369	107	9	)	)	PUNCT
ejpam-5369	107	10	⊆	⊆	NUM
ejpam-5369	107	11	a⋄	a⋄	NOUN
ejpam-5369	107	12	ω	ω	NOUN
ejpam-5369	107	13	.	.	PUNCT
ejpam-5369	107	14	.	.	PUNCT
ejpam-5369	107	15	.	.	PUNCT
ejpam-5369	108	1	(	(	PUNCT
ejpam-5369	108	2	2	2	X
ejpam-5369	108	3	)	)	PUNCT
ejpam-5369	108	4	(	(	PUNCT
ejpam-5369	108	5	1	1	NUM
ejpam-5369	108	6	)	)	PUNCT
ejpam-5369	108	7	,	,	PUNCT
ejpam-5369	108	8	(	(	PUNCT
ejpam-5369	108	9	2	2	X
ejpam-5369	108	10	)	)	PUNCT
ejpam-5369	108	11	⇒	⇒	NOUN
ejpam-5369	108	12	a⋄	a⋄	PROPN
ejpam-5369	108	13	ω	ω	PROPN
ejpam-5369	108	14	=	=	SYM
ejpam-5369	108	15	ω	ω	NUM
ejpam-5369	108	16	-	-	PUNCT
ejpam-5369	108	17	cl(a⋄	cl(a⋄	ADJ
ejpam-5369	108	18	ω	ω	NOUN
ejpam-5369	108	19	)	)	PUNCT
ejpam-5369	108	20	⇒	⇒	NOUN
ejpam-5369	108	21	a⋄	a⋄	PROPN
ejpam-5369	108	22	ω	ω	PROPN
ejpam-5369	108	23	∈	∈	PROPN
ejpam-5369	108	24	ωc(x	ωc(x	NOUN
ejpam-5369	108	25	)	)	PUNCT
ejpam-5369	108	26	.	.	PUNCT
ejpam-5369	109	1	(	(	PUNCT
ejpam-5369	109	2	c	c	X
ejpam-5369	109	3	)	)	PUNCT
ejpam-5369	109	4	let	let	VERB
ejpam-5369	109	5	a	a	DET
ejpam-5369	109	6	⊆	⊆	NUM
ejpam-5369	109	7	x.	x.	NOUN
ejpam-5369	109	8	a	a	PRON
ejpam-5369	109	9	⊆	⊆	NUM
ejpam-5369	109	10	x	x	SYM
ejpam-5369	109	11	(	(	PUNCT
ejpam-5369	109	12	b)⇒	b)⇒	PROPN
ejpam-5369	109	13	a⋄	a⋄	PROPN
ejpam-5369	109	14	ω	ω	PROPN
ejpam-5369	109	15	∈	∈	PROPN
ejpam-5369	109	16	ωc(x	ωc(x	NOUN
ejpam-5369	109	17	)	)	PUNCT
ejpam-5369	109	18	theorem	theorem	VERB
ejpam-5369	109	19	1⇒	1⇒	PROPN
ejpam-5369	109	20	(	(	PUNCT
ejpam-5369	109	21	a⋄	a⋄	PROPN
ejpam-5369	109	22	ω	ω	NUM
ejpam-5369	109	23	)	)	PUNCT
ejpam-5369	109	24	⋄	⋄	PROPN
ejpam-5369	109	25	ω	ω	NUM
ejpam-5369	109	26	⊆	⊆	NUM
ejpam-5369	109	27	a⋄	a⋄	NOUN
ejpam-5369	109	28	ω	ω	NOUN
ejpam-5369	109	29	.	.	PUNCT
ejpam-5369	110	1	(	(	PUNCT
ejpam-5369	110	2	d	d	X
ejpam-5369	110	3	)	)	PUNCT
ejpam-5369	110	4	let	let	VERB
ejpam-5369	110	5	a	a	DET
ejpam-5369	110	6	⊆	⊆	NUM
ejpam-5369	110	7	b	b	NOUN
ejpam-5369	110	8	and	and	CCONJ
ejpam-5369	110	9	x	x	PROPN
ejpam-5369	110	10	∈	∈	PROPN
ejpam-5369	110	11	a⋄	a⋄	PROPN
ejpam-5369	110	12	ω	ω	NOUN
ejpam-5369	110	13	.	.	PUNCT
ejpam-5369	111	1	we	we	PRON
ejpam-5369	111	2	will	will	AUX
ejpam-5369	111	3	prove	prove	VERB
ejpam-5369	111	4	that	that	SCONJ
ejpam-5369	111	5	x	x	PUNCT
ejpam-5369	111	6	∈	∈	PROPN
ejpam-5369	111	7	b⋄	b⋄	PROPN
ejpam-5369	111	8	ω	ω	NOUN
ejpam-5369	111	9	.	.	PUNCT
ejpam-5369	112	1	x	x	SYM
ejpam-5369	112	2	∈	∈	PROPN
ejpam-5369	112	3	a⋄	a⋄	NOUN
ejpam-5369	112	4	ω	ω	NOUN
ejpam-5369	112	5	⇒	⇒	NOUN
ejpam-5369	112	6	(	(	PUNCT
ejpam-5369	112	7	∀u	∀u	NOUN
ejpam-5369	112	8	∈	∈	NOUN
ejpam-5369	112	9	ωo(x	ωo(x	NUM
ejpam-5369	112	10	,	,	PUNCT
ejpam-5369	112	11	x))(u	x))(u	PROPN
ejpam-5369	112	12	c	c	PROPN
ejpam-5369	112	13	∪ac	∪ac	PROPN
ejpam-5369	112	14	∈	∈	PROPN
ejpam-5369	112	15	p	p	NOUN
ejpam-5369	112	16	)	)	PUNCT
ejpam-5369	112	17	a	a	DET
ejpam-5369	112	18	⊆	⊆	NUM
ejpam-5369	112	19	b	b	X
ejpam-5369	112	20	}	}	PUNCT
ejpam-5369	112	21	⇒	⇒	NOUN
ejpam-5369	112	22	(	(	PUNCT
ejpam-5369	112	23	∀u	∀u	NOUN
ejpam-5369	112	24	∈	∈	NOUN
ejpam-5369	112	25	ωo(x	ωo(x	NUM
ejpam-5369	112	26	,	,	PUNCT
ejpam-5369	112	27	x))(u	x))(u	PROPN
ejpam-5369	112	28	c	c	X
ejpam-5369	112	29	∪bc	∪bc	VERB
ejpam-5369	112	30	∈	∈	PROPN
ejpam-5369	112	31	p	p	NOUN
ejpam-5369	112	32	)	)	PUNCT
ejpam-5369	112	33	⇒	⇒	NOUN
ejpam-5369	112	34	x	x	SYM
ejpam-5369	112	35	∈	∈	PROPN
ejpam-5369	112	36	b⋄	b⋄	PROPN
ejpam-5369	112	37	ω	ω	NOUN
ejpam-5369	112	38	.	.	PUNCT
ejpam-5369	113	1	(	(	PUNCT
ejpam-5369	113	2	e	e	X
ejpam-5369	113	3	)	)	PUNCT
ejpam-5369	113	4	let	let	VERB
ejpam-5369	113	5	a	a	DET
ejpam-5369	113	6	,	,	PUNCT
ejpam-5369	113	7	b	b	PROPN
ejpam-5369	113	8	⊆	⊆	NUM
ejpam-5369	113	9	x.	x.	NOUN
ejpam-5369	113	10	a	a	DET
ejpam-5369	113	11	⊆	⊆	NUM
ejpam-5369	113	12	x	x	X
ejpam-5369	113	13	⇒	⇒	VERB
ejpam-5369	113	14	a	a	DET
ejpam-5369	113	15	⊆	⊆	NUM
ejpam-5369	113	16	a	a	PRON
ejpam-5369	113	17	∪b	∪b	PUNCT
ejpam-5369	113	18	(	(	PUNCT
ejpam-5369	113	19	d)⇒	d)⇒	PROPN
ejpam-5369	113	20	a⋄	a⋄	NOUN
ejpam-5369	113	21	ω	ω	NOUN
ejpam-5369	113	22	⊆	⊆	NUM
ejpam-5369	113	23	(	(	PUNCT
ejpam-5369	113	24	a	a	DET
ejpam-5369	113	25	∪b)⋄ω	∪b)⋄ω	X
ejpam-5369	113	26	b	b	NOUN
ejpam-5369	113	27	⊆	⊆	NUM
ejpam-5369	113	28	x	x	X
ejpam-5369	113	29	⇒	⇒	NOUN
ejpam-5369	113	30	b	b	NOUN
ejpam-5369	113	31	⊆	⊆	NUM
ejpam-5369	113	32	a	a	DET
ejpam-5369	113	33	∪b	∪b	PUNCT
ejpam-5369	113	34	(	(	PUNCT
ejpam-5369	113	35	d)⇒	d)⇒	PROPN
ejpam-5369	113	36	b⋄	b⋄	PROPN
ejpam-5369	113	37	ω	ω	NOUN
ejpam-5369	113	38	⊆	⊆	NUM
ejpam-5369	113	39	(	(	PUNCT
ejpam-5369	113	40	a	a	DET
ejpam-5369	113	41	∪b)⋄ω	∪b)⋄ω	ADJ
ejpam-5369	113	42			NOUN
ejpam-5369	113	43	⇒	⇒	NOUN
ejpam-5369	113	44	a⋄	a⋄	PROPN
ejpam-5369	113	45	ω	ω	PROPN
ejpam-5369	113	46	∪b⋄	∪b⋄	NOUN
ejpam-5369	113	47	ω	ω	NUM
ejpam-5369	113	48	⊆	⊆	NUM
ejpam-5369	113	49	(	(	PUNCT
ejpam-5369	113	50	a	a	DET
ejpam-5369	113	51	∪b)⋄ω	∪b)⋄ω	NOUN
ejpam-5369	113	52	.	.	PUNCT
ejpam-5369	113	53	.	.	PUNCT
ejpam-5369	113	54	.	.	PUNCT
ejpam-5369	114	1	(	(	PUNCT
ejpam-5369	114	2	1	1	X
ejpam-5369	114	3	)	)	PUNCT
ejpam-5369	114	4	conversely	conversely	ADV
ejpam-5369	114	5	,	,	PUNCT
ejpam-5369	114	6	let	let	VERB
ejpam-5369	114	7	x	x	PRON
ejpam-5369	114	8	/∈	/∈	PUNCT
ejpam-5369	115	1	a⋄	a⋄	NOUN
ejpam-5369	115	2	ω	ω	PROPN
ejpam-5369	115	3	∪b⋄	∪b⋄	NUM
ejpam-5369	115	4	ω	ω	NOUN
ejpam-5369	115	5	.	.	PUNCT
ejpam-5369	116	1	x	x	SYM
ejpam-5369	116	2	/∈	/∈	PUNCT
ejpam-5369	116	3	a⋄	a⋄	NOUN
ejpam-5369	116	4	ω	ω	NUM
ejpam-5369	116	5	∪b⋄	∪b⋄	NUM
ejpam-5369	116	6	ω	ω	NUM
ejpam-5369	116	7	⇒	⇒	NOUN
ejpam-5369	116	8	(	(	PUNCT
ejpam-5369	116	9	x	x	SYM
ejpam-5369	116	10	/∈	/∈	PUNCT
ejpam-5369	116	11	a⋄	a⋄	NOUN
ejpam-5369	116	12	ω)(x	ω)(x	NUM
ejpam-5369	116	13	/∈	/∈	PUNCT
ejpam-5369	117	1	b⋄	b⋄	PROPN
ejpam-5369	117	2	ω	ω	NUM
ejpam-5369	117	3	)	)	PUNCT
ejpam-5369	117	4	⇒	⇒	NOUN
ejpam-5369	117	5	(	(	PUNCT
ejpam-5369	117	6	∃u	∃u	PROPN
ejpam-5369	117	7	,	,	PUNCT
ejpam-5369	117	8	v	v	NOUN
ejpam-5369	117	9	∈	∈	PROPN
ejpam-5369	117	10	ωo(x	ωo(x	NUM
ejpam-5369	117	11	,	,	PUNCT
ejpam-5369	117	12	x))(u	x))(u	PROPN
ejpam-5369	117	13	c	c	PROPN
ejpam-5369	117	14	∪ac	∪ac	PROPN
ejpam-5369	117	15	/∈	/∈	PUNCT
ejpam-5369	118	1	p)(v	p)(v	X
ejpam-5369	119	1	c	c	AUX
ejpam-5369	119	2	∪bc	∪bc	VERB
ejpam-5369	119	3	/∈	/∈	PUNCT
ejpam-5369	120	1	p	p	X
ejpam-5369	120	2	)	)	PUNCT
ejpam-5369	120	3	w	w	NOUN
ejpam-5369	120	4	:	:	PUNCT
ejpam-5369	120	5	=	=	SYM
ejpam-5369	120	6	u	u	NOUN
ejpam-5369	120	7	∩	∩	NOUN
ejpam-5369	120	8	v	v	ADP
ejpam-5369	120	9	}	}	PUNCT
ejpam-5369	120	10	⇒	⇒	NOUN
ejpam-5369	120	11	⇒	⇒	NOUN
ejpam-5369	120	12	(	(	PUNCT
ejpam-5369	120	13	w	w	PROPN
ejpam-5369	120	14	∈	∈	PROPN
ejpam-5369	120	15	ωo(x	ωo(x	NUM
ejpam-5369	120	16	,	,	PUNCT
ejpam-5369	120	17	x))(w	x))(w	PROPN
ejpam-5369	120	18	c	c	PROPN
ejpam-5369	120	19	∪ac	∪ac	PROPN
ejpam-5369	120	20	/∈	/∈	PUNCT
ejpam-5369	121	1	p)(w	p)(w	NOUN
ejpam-5369	121	2	c	c	NOUN
ejpam-5369	121	3	∪bc	∪bc	VERB
ejpam-5369	121	4	/∈	/∈	PUNCT
ejpam-5369	122	1	p	p	X
ejpam-5369	122	2	)	)	PUNCT
ejpam-5369	122	3	p.	p.	NOUN
ejpam-5369	122	4	şaşmaz	şaşmaz	NUM
ejpam-5369	122	5	,	,	PUNCT
ejpam-5369	122	6	m.	m.	NOUN
ejpam-5369	122	7	özkoç	özkoç	PROPN
ejpam-5369	122	8	/	/	SYM
ejpam-5369	122	9	eur	eur	PROPN
ejpam-5369	122	10	.	.	PUNCT
ejpam-5369	123	1	j.	j.	PROPN
ejpam-5369	123	2	pure	pure	PROPN
ejpam-5369	123	3	appl	appl	PROPN
ejpam-5369	123	4	.	.	PROPN
ejpam-5369	123	5	math	math	PROPN
ejpam-5369	123	6	,	,	PUNCT
ejpam-5369	123	7	17	17	NUM
ejpam-5369	123	8	(	(	PUNCT
ejpam-5369	123	9	4	4	NUM
ejpam-5369	123	10	)	)	PUNCT
ejpam-5369	123	11	(	(	PUNCT
ejpam-5369	123	12	2024	2024	NUM
ejpam-5369	123	13	)	)	PUNCT
ejpam-5369	123	14	,	,	PUNCT
ejpam-5369	123	15	2800	2800	NUM
ejpam-5369	123	16	-	-	SYM
ejpam-5369	123	17	2811	2811	NUM
ejpam-5369	123	18	2804	2804	NUM
ejpam-5369	123	19	⇒	⇒	NOUN
ejpam-5369	123	20	(	(	PUNCT
ejpam-5369	123	21	w	w	PROPN
ejpam-5369	123	22	∈	∈	PROPN
ejpam-5369	123	23	ωo(x	ωo(x	NUM
ejpam-5369	123	24	,	,	PUNCT
ejpam-5369	123	25	x))(w	x))(w	PROPN
ejpam-5369	123	26	c	c	PROPN
ejpam-5369	123	27	∪	∪	X
ejpam-5369	123	28	(	(	PUNCT
ejpam-5369	123	29	a	a	DET
ejpam-5369	123	30	∪b)c	∪b)c	PROPN
ejpam-5369	123	31	=	=	SYM
ejpam-5369	123	32	(	(	PUNCT
ejpam-5369	123	33	w	w	PROPN
ejpam-5369	123	34	c	c	PROPN
ejpam-5369	123	35	∪ac	∪ac	PROPN
ejpam-5369	123	36	)	)	PUNCT
ejpam-5369	123	37	∩	∩	NOUN
ejpam-5369	123	38	(	(	PUNCT
ejpam-5369	123	39	w	w	PROPN
ejpam-5369	123	40	c	c	NOUN
ejpam-5369	123	41	∪bc	∪bc	PROPN
ejpam-5369	123	42	)	)	PUNCT
ejpam-5369	123	43	/∈	/∈	PUNCT
ejpam-5369	124	1	p	p	NOUN
ejpam-5369	124	2	)	)	PUNCT
ejpam-5369	124	3	⇒	⇒	NOUN
ejpam-5369	124	4	x	x	X
ejpam-5369	124	5	/∈	/∈	INTJ
ejpam-5369	125	1	(	(	PUNCT
ejpam-5369	125	2	a	a	PRON
ejpam-5369	125	3	∪b)⋄ω	∪b)⋄ω	X
ejpam-5369	125	4	then	then	ADV
ejpam-5369	125	5	,	,	PUNCT
ejpam-5369	125	6	we	we	PRON
ejpam-5369	125	7	have	have	VERB
ejpam-5369	125	8	(	(	PUNCT
ejpam-5369	125	9	a	a	DET
ejpam-5369	125	10	∪b)⋄ω	∪b)⋄ω	NOUN
ejpam-5369	125	11	⊆	⊆	NUM
ejpam-5369	125	12	a⋄	a⋄	NOUN
ejpam-5369	125	13	ω	ω	NUM
ejpam-5369	125	14	∪b⋄	∪b⋄	NOUN
ejpam-5369	125	15	ω	ω	NOUN
ejpam-5369	125	16	.	.	PUNCT
ejpam-5369	125	17	.	.	PUNCT
ejpam-5369	125	18	.	.	PUNCT
ejpam-5369	126	1	(	(	PUNCT
ejpam-5369	126	2	2	2	X
ejpam-5369	126	3	)	)	PUNCT
ejpam-5369	126	4	(	(	PUNCT
ejpam-5369	126	5	1	1	NUM
ejpam-5369	126	6	)	)	PUNCT
ejpam-5369	126	7	,	,	PUNCT
ejpam-5369	126	8	(	(	PUNCT
ejpam-5369	126	9	2	2	X
ejpam-5369	126	10	)	)	PUNCT
ejpam-5369	126	11	⇒	⇒	NOUN
ejpam-5369	126	12	(	(	PUNCT
ejpam-5369	126	13	a	a	DET
ejpam-5369	126	14	∪b)⋄ω	∪b)⋄ω	NOUN
ejpam-5369	126	15	=	=	SYM
ejpam-5369	126	16	a⋄	a⋄	NOUN
ejpam-5369	126	17	ω	ω	NUM
ejpam-5369	126	18	∪b⋄	∪b⋄	NUM
ejpam-5369	126	19	ω	ω	NOUN
ejpam-5369	126	20	.	.	PUNCT
ejpam-5369	127	1	(	(	PUNCT
ejpam-5369	127	2	f	f	X
ejpam-5369	127	3	)	)	PUNCT
ejpam-5369	127	4	it	it	PRON
ejpam-5369	127	5	is	be	AUX
ejpam-5369	127	6	clear	clear	ADJ
ejpam-5369	127	7	from	from	ADP
ejpam-5369	127	8	(	(	PUNCT
ejpam-5369	127	9	d	d	NOUN
ejpam-5369	127	10	)	)	PUNCT
ejpam-5369	127	11	.	.	PUNCT
ejpam-5369	128	1	theorem	theorem	NOUN
ejpam-5369	128	2	3	3	X
ejpam-5369	128	3	.	.	PUNCT
ejpam-5369	129	1	let	let	VERB
ejpam-5369	129	2	(	(	PUNCT
ejpam-5369	129	3	x	x	X
ejpam-5369	129	4	,	,	PUNCT
ejpam-5369	129	5	τ	τ	PROPN
ejpam-5369	129	6	,	,	PUNCT
ejpam-5369	129	7	p	p	NOUN
ejpam-5369	129	8	)	)	PUNCT
ejpam-5369	129	9	and	and	CCONJ
ejpam-5369	129	10	(	(	PUNCT
ejpam-5369	129	11	x	x	X
ejpam-5369	129	12	,	,	PUNCT
ejpam-5369	129	13	τ	τ	PROPN
ejpam-5369	129	14	,	,	PUNCT
ejpam-5369	129	15	q	q	NOUN
ejpam-5369	129	16	)	)	PUNCT
ejpam-5369	129	17	be	be	VERB
ejpam-5369	129	18	two	two	NUM
ejpam-5369	129	19	primal	primal	ADJ
ejpam-5369	129	20	topological	topological	ADJ
ejpam-5369	129	21	spaces	space	NOUN
ejpam-5369	129	22	and	and	CCONJ
ejpam-5369	129	23	a	a	DET
ejpam-5369	129	24	⊆	⊆	NUM
ejpam-5369	129	25	x.	x.	NOUN
ejpam-5369	129	26	if	if	SCONJ
ejpam-5369	129	27	p	p	PROPN
ejpam-5369	129	28	⊆	⊆	NUM
ejpam-5369	129	29	q	q	NOUN
ejpam-5369	129	30	,	,	PUNCT
ejpam-5369	129	31	then	then	ADV
ejpam-5369	129	32	a⋄	a⋄	NOUN
ejpam-5369	129	33	ω(p	ω(p	NOUN
ejpam-5369	129	34	)	)	PUNCT
ejpam-5369	129	35	⊆	⊆	NUM
ejpam-5369	129	36	a⋄	a⋄	NOUN
ejpam-5369	129	37	ω(q	ω(q	NOUN
ejpam-5369	129	38	)	)	PUNCT
ejpam-5369	129	39	.	.	PUNCT
ejpam-5369	130	1	proof	proof	NOUN
ejpam-5369	130	2	.	.	PUNCT
ejpam-5369	131	1	let	let	VERB
ejpam-5369	131	2	x	x	SYM
ejpam-5369	131	3	∈	∈	PROPN
ejpam-5369	131	4	a⋄	a⋄	NOUN
ejpam-5369	131	5	ω(p	ω(p	NOUN
ejpam-5369	131	6	)	)	PUNCT
ejpam-5369	131	7	and	and	CCONJ
ejpam-5369	131	8	p	p	X
ejpam-5369	131	9	⊆	⊆	NUM
ejpam-5369	131	10	q.	q.	NOUN
ejpam-5369	131	11	x	x	SYM
ejpam-5369	131	12	∈	∈	NOUN
ejpam-5369	131	13	a⋄	a⋄	VERB
ejpam-5369	131	14	ω(p	ω(p	NOUN
ejpam-5369	131	15	)	)	PUNCT
ejpam-5369	131	16	⇒	⇒	NOUN
ejpam-5369	131	17	(	(	PUNCT
ejpam-5369	131	18	∀u	∀u	NOUN
ejpam-5369	131	19	∈	∈	NOUN
ejpam-5369	131	20	ωo(x	ωo(x	NUM
ejpam-5369	131	21	,	,	PUNCT
ejpam-5369	131	22	x))(u	x))(u	PROPN
ejpam-5369	131	23	c	c	PROPN
ejpam-5369	131	24	∪ac	∪ac	PROPN
ejpam-5369	131	25	∈	∈	PROPN
ejpam-5369	131	26	p	p	X
ejpam-5369	131	27	)	)	PUNCT
ejpam-5369	131	28	p	p	NOUN
ejpam-5369	131	29	⊆	⊆	NUM
ejpam-5369	131	30	q	q	PRON
ejpam-5369	131	31	}	}	PUNCT
ejpam-5369	131	32	⇒	⇒	NOUN
ejpam-5369	131	33	(	(	PUNCT
ejpam-5369	131	34	∀u	∀u	NOUN
ejpam-5369	131	35	∈	∈	NOUN
ejpam-5369	131	36	ωo(x	ωo(x	NUM
ejpam-5369	131	37	,	,	PUNCT
ejpam-5369	131	38	x))(u	x))(u	PROPN
ejpam-5369	131	39	c	c	PROPN
ejpam-5369	131	40	∪ac	∪ac	PROPN
ejpam-5369	131	41	∈	∈	PROPN
ejpam-5369	131	42	q	q	NOUN
ejpam-5369	131	43	)	)	PUNCT
ejpam-5369	131	44	⇒	⇒	NOUN
ejpam-5369	131	45	x	x	SYM
ejpam-5369	131	46	∈	∈	NOUN
ejpam-5369	131	47	a⋄	a⋄	NOUN
ejpam-5369	131	48	ω(q	ω(q	NOUN
ejpam-5369	131	49	)	)	PUNCT
ejpam-5369	131	50	.	.	PUNCT
ejpam-5369	132	1	theorem	theorem	ADJ
ejpam-5369	132	2	4	4	NUM
ejpam-5369	132	3	.	.	PUNCT
ejpam-5369	133	1	let	let	VERB
ejpam-5369	133	2	(	(	PUNCT
ejpam-5369	133	3	x	x	X
ejpam-5369	133	4	,	,	PUNCT
ejpam-5369	133	5	τ	τ	PROPN
ejpam-5369	133	6	,	,	PUNCT
ejpam-5369	133	7	p	p	NOUN
ejpam-5369	133	8	)	)	PUNCT
ejpam-5369	133	9	and	and	CCONJ
ejpam-5369	133	10	(	(	PUNCT
ejpam-5369	133	11	x	x	X
ejpam-5369	133	12	,	,	PUNCT
ejpam-5369	133	13	σ	σ	PROPN
ejpam-5369	133	14	,	,	PUNCT
ejpam-5369	133	15	p	p	X
ejpam-5369	133	16	)	)	PUNCT
ejpam-5369	133	17	be	be	AUX
ejpam-5369	133	18	two	two	NUM
ejpam-5369	133	19	primal	primal	ADJ
ejpam-5369	133	20	topological	topological	ADJ
ejpam-5369	133	21	spaces	space	NOUN
ejpam-5369	133	22	and	and	CCONJ
ejpam-5369	133	23	a	a	DET
ejpam-5369	133	24	⊆	⊆	NUM
ejpam-5369	133	25	x.	x.	NOUN
ejpam-5369	133	26	if	if	SCONJ
ejpam-5369	133	27	τ	τ	PROPN
ejpam-5369	133	28	⊆	⊆	NUM
ejpam-5369	133	29	σ	σ	NOUN
ejpam-5369	133	30	,	,	PUNCT
ejpam-5369	133	31	then	then	ADV
ejpam-5369	133	32	a⋄	a⋄	NOUN
ejpam-5369	133	33	ω(x	ω(x	NOUN
ejpam-5369	133	34	,	,	PUNCT
ejpam-5369	133	35	σ	σ	PROPN
ejpam-5369	133	36	,	,	PUNCT
ejpam-5369	133	37	p	p	NOUN
ejpam-5369	133	38	)	)	PUNCT
ejpam-5369	133	39	⊆	⊆	NUM
ejpam-5369	133	40	a⋄	a⋄	NOUN
ejpam-5369	133	41	ω(x	ω(x	NOUN
ejpam-5369	133	42	,	,	PUNCT
ejpam-5369	133	43	τ	τ	X
ejpam-5369	133	44	,	,	PUNCT
ejpam-5369	133	45	p	p	NOUN
ejpam-5369	133	46	)	)	PUNCT
ejpam-5369	133	47	.	.	PUNCT
ejpam-5369	134	1	proof	proof	NOUN
ejpam-5369	134	2	.	.	PUNCT
ejpam-5369	135	1	let	let	VERB
ejpam-5369	135	2	x	x	SYM
ejpam-5369	135	3	∈	∈	NOUN
ejpam-5369	135	4	a⋄	a⋄	NOUN
ejpam-5369	135	5	ω(x	ω(x	NOUN
ejpam-5369	135	6	,	,	PUNCT
ejpam-5369	135	7	σ	σ	PROPN
ejpam-5369	135	8	,	,	PUNCT
ejpam-5369	135	9	p	p	NOUN
ejpam-5369	135	10	)	)	PUNCT
ejpam-5369	135	11	and	and	CCONJ
ejpam-5369	135	12	τ	τ	PROPN
ejpam-5369	135	13	⊆	⊆	NUM
ejpam-5369	135	14	σ	σ	PROPN
ejpam-5369	135	15	.	.	PUNCT
ejpam-5369	135	16	x	x	SYM
ejpam-5369	135	17	∈	∈	NOUN
ejpam-5369	135	18	a⋄	a⋄	NOUN
ejpam-5369	135	19	ω(x	ω(x	NOUN
ejpam-5369	135	20	,	,	PUNCT
ejpam-5369	135	21	σ	σ	PROPN
ejpam-5369	135	22	,	,	PUNCT
ejpam-5369	135	23	p	p	NOUN
ejpam-5369	135	24	)	)	PUNCT
ejpam-5369	135	25	⇒	⇒	NOUN
ejpam-5369	135	26	(	(	PUNCT
ejpam-5369	135	27	∀u	∀u	NOUN
ejpam-5369	135	28	∈	∈	NOUN
ejpam-5369	135	29	ωoσ(x	ωoσ(x	PROPN
ejpam-5369	135	30	,	,	PUNCT
ejpam-5369	135	31	x))(u	x))(u	PROPN
ejpam-5369	135	32	c	c	PROPN
ejpam-5369	135	33	∪ac	∪ac	PROPN
ejpam-5369	135	34	∈	∈	PROPN
ejpam-5369	136	1	p	p	X
ejpam-5369	136	2	)	)	PUNCT
ejpam-5369	136	3	τ	τ	PROPN
ejpam-5369	136	4	⊆	⊆	NUM
ejpam-5369	136	5	σ	σ	PROPN
ejpam-5369	136	6	}	}	PUNCT
ejpam-5369	136	7	⇒	⇒	NOUN
ejpam-5369	136	8	⇒	⇒	NOUN
ejpam-5369	136	9	(	(	PUNCT
ejpam-5369	136	10	∀u	∀u	NOUN
ejpam-5369	136	11	∈	∈	NOUN
ejpam-5369	136	12	ωoτ	ωoτ	ADJ
ejpam-5369	136	13	(	(	PUNCT
ejpam-5369	136	14	x	x	X
ejpam-5369	136	15	,	,	PUNCT
ejpam-5369	136	16	x))(u	x))(u	PROPN
ejpam-5369	136	17	c	c	PROPN
ejpam-5369	136	18	∪ac	∪ac	PROPN
ejpam-5369	136	19	∈	∈	PROPN
ejpam-5369	136	20	p	p	NOUN
ejpam-5369	136	21	)	)	PUNCT
ejpam-5369	136	22	⇒	⇒	NOUN
ejpam-5369	136	23	x	x	SYM
ejpam-5369	136	24	∈	∈	NOUN
ejpam-5369	136	25	a⋄	a⋄	NOUN
ejpam-5369	136	26	ω(x	ω(x	NOUN
ejpam-5369	136	27	,	,	PUNCT
ejpam-5369	136	28	τ	τ	X
ejpam-5369	136	29	,	,	PUNCT
ejpam-5369	136	30	p	p	NOUN
ejpam-5369	136	31	)	)	PUNCT
ejpam-5369	136	32	.	.	PUNCT
ejpam-5369	137	1	theorem	theorem	NOUN
ejpam-5369	137	2	5	5	NUM
ejpam-5369	137	3	.	.	PUNCT
ejpam-5369	138	1	let	let	VERB
ejpam-5369	138	2	(	(	PUNCT
ejpam-5369	138	3	x	x	X
ejpam-5369	138	4	,	,	PUNCT
ejpam-5369	138	5	τ	τ	PROPN
ejpam-5369	138	6	,	,	PUNCT
ejpam-5369	138	7	p	p	NOUN
ejpam-5369	138	8	)	)	PUNCT
ejpam-5369	138	9	be	be	AUX
ejpam-5369	138	10	a	a	DET
ejpam-5369	138	11	primal	primal	ADJ
ejpam-5369	138	12	topological	topological	ADJ
ejpam-5369	138	13	space	space	NOUN
ejpam-5369	138	14	.	.	PUNCT
ejpam-5369	139	1	then	then	ADV
ejpam-5369	139	2	,	,	PUNCT
ejpam-5369	139	3	the	the	DET
ejpam-5369	139	4	following	follow	VERB
ejpam-5369	139	5	statements	statement	NOUN
ejpam-5369	139	6	hold	hold	VERB
ejpam-5369	139	7	for	for	ADP
ejpam-5369	139	8	any	any	DET
ejpam-5369	139	9	two	two	NUM
ejpam-5369	139	10	subsets	subset	NOUN
ejpam-5369	139	11	a	a	PRON
ejpam-5369	139	12	and	and	CCONJ
ejpam-5369	139	13	b	b	NOUN
ejpam-5369	139	14	of	of	ADP
ejpam-5369	139	15	x.	x.	NOUN
ejpam-5369	139	16	(	(	PUNCT
ejpam-5369	139	17	a	a	X
ejpam-5369	139	18	)	)	PUNCT
ejpam-5369	139	19	a⋄	a⋄	PROPN
ejpam-5369	139	20	ω	ω	NOUN
ejpam-5369	139	21	⊆	⊆	NUM
ejpam-5369	139	22	cl(a	cl(a	NUM
ejpam-5369	139	23	)	)	PUNCT
ejpam-5369	139	24	,	,	PUNCT
ejpam-5369	139	25	(	(	PUNCT
ejpam-5369	139	26	b	b	X
ejpam-5369	139	27	)	)	PUNCT
ejpam-5369	139	28	cl(a⋄	cl(a⋄	NOUN
ejpam-5369	139	29	ω	ω	NUM
ejpam-5369	139	30	)	)	PUNCT
ejpam-5369	139	31	⊆	⊆	NUM
ejpam-5369	139	32	cl(a	cl(a	NUM
ejpam-5369	139	33	)	)	PUNCT
ejpam-5369	139	34	,	,	PUNCT
ejpam-5369	139	35	(	(	PUNCT
ejpam-5369	139	36	c	c	X
ejpam-5369	139	37	)	)	PUNCT
ejpam-5369	139	38	a⋄	a⋄	PROPN
ejpam-5369	139	39	ω	ω	PROPN
ejpam-5369	139	40	\b⋄	\b⋄	PUNCT
ejpam-5369	139	41	ω	ω	NOUN
ejpam-5369	139	42	⊆	⊆	NUM
ejpam-5369	139	43	(	(	PUNCT
ejpam-5369	139	44	a	a	DET
ejpam-5369	139	45	\b)⋄ω	\b)⋄ω	NOUN
ejpam-5369	139	46	,	,	PUNCT
ejpam-5369	139	47	(	(	PUNCT
ejpam-5369	139	48	d	d	X
ejpam-5369	139	49	)	)	PUNCT
ejpam-5369	139	50	a⋄	a⋄	PROPN
ejpam-5369	139	51	ω	ω	PROPN
ejpam-5369	139	52	\b⋄	\b⋄	X
ejpam-5369	139	53	ω	ω	NOUN
ejpam-5369	139	54	=	=	SYM
ejpam-5369	139	55	(	(	PUNCT
ejpam-5369	139	56	a	a	DET
ejpam-5369	139	57	\b)⋄ω	\b)⋄ω	PROPN
ejpam-5369	139	58	\b⋄	\b⋄	PUNCT
ejpam-5369	139	59	ω	ω	NOUN
ejpam-5369	139	60	.	.	PUNCT
ejpam-5369	140	1	proof	proof	NOUN
ejpam-5369	140	2	.	.	PUNCT
ejpam-5369	141	1	(	(	PUNCT
ejpam-5369	141	2	a	a	X
ejpam-5369	141	3	)	)	PUNCT
ejpam-5369	141	4	let	let	VERB
ejpam-5369	141	5	x	x	PRON
ejpam-5369	141	6	/∈	/∈	PUNCT
ejpam-5369	141	7	cl(a	cl(a	NUM
ejpam-5369	141	8	)	)	PUNCT
ejpam-5369	141	9	.	.	PUNCT
ejpam-5369	142	1	our	our	PRON
ejpam-5369	142	2	aim	aim	NOUN
ejpam-5369	142	3	is	be	AUX
ejpam-5369	142	4	to	to	PART
ejpam-5369	142	5	show	show	VERB
ejpam-5369	142	6	that	that	SCONJ
ejpam-5369	142	7	x	x	SYM
ejpam-5369	142	8	/∈	/∈	PUNCT
ejpam-5369	142	9	a⋄	a⋄	PROPN
ejpam-5369	142	10	ω	ω	NOUN
ejpam-5369	142	11	.	.	PUNCT
ejpam-5369	142	12	x	x	X
ejpam-5369	142	13	/∈	/∈	PUNCT
ejpam-5369	142	14	cl(a	cl(a	NUM
ejpam-5369	142	15	)	)	PUNCT
ejpam-5369	142	16	⇒	⇒	NOUN
ejpam-5369	142	17	(	(	PUNCT
ejpam-5369	142	18	∃u	∃u	PROPN
ejpam-5369	142	19	∈	∈	PROPN
ejpam-5369	142	20	o(x	o(x	PROPN
ejpam-5369	142	21	,	,	PUNCT
ejpam-5369	142	22	x))(u	x))(u	ADJ
ejpam-5369	142	23	∩a	∩a	NOUN
ejpam-5369	142	24	=	=	PUNCT
ejpam-5369	142	25	∅	∅	NOUN
ejpam-5369	142	26	)	)	PUNCT
ejpam-5369	142	27	o(x	o(x	PROPN
ejpam-5369	142	28	,	,	PUNCT
ejpam-5369	142	29	x	x	X
ejpam-5369	142	30	)	)	PUNCT
ejpam-5369	142	31	⊆	⊆	NUM
ejpam-5369	142	32	ωo(x	ωo(x	NUM
ejpam-5369	142	33	,	,	PUNCT
ejpam-5369	142	34	x	x	NOUN
ejpam-5369	142	35	)	)	PUNCT
ejpam-5369	142	36	}	}	PUNCT
ejpam-5369	142	37	⇒	⇒	NOUN
ejpam-5369	142	38	(	(	PUNCT
ejpam-5369	142	39	∃u	∃u	PROPN
ejpam-5369	142	40	∈	∈	PROPN
ejpam-5369	142	41	ωo(x	ωo(x	NUM
ejpam-5369	142	42	,	,	PUNCT
ejpam-5369	142	43	x))(a	x))(a	PROPN
ejpam-5369	142	44	⊆	⊆	NUM
ejpam-5369	142	45	u	u	PROPN
ejpam-5369	142	46	c	c	NOUN
ejpam-5369	142	47	)	)	PUNCT
ejpam-5369	142	48	⇒	⇒	NOUN
ejpam-5369	142	49	(	(	PUNCT
ejpam-5369	142	50	∃u	∃u	PROPN
ejpam-5369	142	51	∈	∈	PROPN
ejpam-5369	142	52	ωo(x	ωo(x	NUM
ejpam-5369	142	53	,	,	PUNCT
ejpam-5369	142	54	x))(x	x))(x	NOUN
ejpam-5369	142	55	=	=	PUNCT
ejpam-5369	143	1	a	a	DET
ejpam-5369	143	2	∪ac	∪ac	PROPN
ejpam-5369	143	3	⊆	⊆	NUM
ejpam-5369	143	4	u	u	NOUN
ejpam-5369	143	5	c	c	PROPN
ejpam-5369	143	6	∪ac	∪ac	PROPN
ejpam-5369	143	7	/∈	/∈	PUNCT
ejpam-5369	144	1	p	p	X
ejpam-5369	144	2	)	)	PUNCT
ejpam-5369	144	3	⇒	⇒	NOUN
ejpam-5369	144	4	x	x	SYM
ejpam-5369	144	5	/∈	/∈	PUNCT
ejpam-5369	144	6	a⋄	a⋄	PROPN
ejpam-5369	144	7	ω	ω	NOUN
ejpam-5369	144	8	.	.	PUNCT
ejpam-5369	145	1	(	(	PUNCT
ejpam-5369	145	2	b	b	X
ejpam-5369	145	3	)	)	PUNCT
ejpam-5369	145	4	let	let	VERB
ejpam-5369	145	5	a	a	DET
ejpam-5369	145	6	⊆	⊆	NUM
ejpam-5369	145	7	x.	x.	NOUN
ejpam-5369	145	8	a	a	DET
ejpam-5369	145	9	⊆	⊆	NUM
ejpam-5369	145	10	x	x	SYM
ejpam-5369	145	11	(	(	PUNCT
ejpam-5369	145	12	a)⇒	a)⇒	PROPN
ejpam-5369	145	13	a⋄	a⋄	NOUN
ejpam-5369	145	14	ω	ω	NOUN
ejpam-5369	145	15	⊆	⊆	NUM
ejpam-5369	145	16	cl(a	cl(a	NUM
ejpam-5369	145	17	)	)	PUNCT
ejpam-5369	145	18	⇒	⇒	PROPN
ejpam-5369	145	19	cl(a⋄	cl(a⋄	PROPN
ejpam-5369	145	20	ω	ω	PROPN
ejpam-5369	145	21	)	)	PUNCT
ejpam-5369	145	22	⊆	⊆	NUM
ejpam-5369	145	23	cl(cl(a	cl(cl(a	PROPN
ejpam-5369	145	24	)	)	PUNCT
ejpam-5369	145	25	)	)	PUNCT
ejpam-5369	146	1	=	=	SYM
ejpam-5369	146	2	cl(a	cl(a	X
ejpam-5369	146	3	)	)	PUNCT
ejpam-5369	146	4	.	.	PUNCT
ejpam-5369	147	1	p.	p.	NOUN
ejpam-5369	147	2	şaşmaz	şaşmaz	NUM
ejpam-5369	147	3	,	,	PUNCT
ejpam-5369	147	4	m.	m.	NOUN
ejpam-5369	147	5	özkoç	özkoç	PROPN
ejpam-5369	147	6	/	/	SYM
ejpam-5369	147	7	eur	eur	PROPN
ejpam-5369	147	8	.	.	PUNCT
ejpam-5369	148	1	j.	j.	PROPN
ejpam-5369	148	2	pure	pure	PROPN
ejpam-5369	148	3	appl	appl	PROPN
ejpam-5369	148	4	.	.	PROPN
ejpam-5369	148	5	math	math	PROPN
ejpam-5369	148	6	,	,	PUNCT
ejpam-5369	148	7	17	17	NUM
ejpam-5369	148	8	(	(	PUNCT
ejpam-5369	148	9	4	4	NUM
ejpam-5369	148	10	)	)	PUNCT
ejpam-5369	148	11	(	(	PUNCT
ejpam-5369	148	12	2024	2024	NUM
ejpam-5369	148	13	)	)	PUNCT
ejpam-5369	148	14	,	,	PUNCT
ejpam-5369	148	15	2800	2800	NUM
ejpam-5369	148	16	-	-	SYM
ejpam-5369	148	17	2811	2811	NUM
ejpam-5369	148	18	2805	2805	NUM
ejpam-5369	148	19	(	(	PUNCT
ejpam-5369	148	20	c	c	X
ejpam-5369	148	21	)	)	PUNCT
ejpam-5369	148	22	let	let	VERB
ejpam-5369	148	23	a	a	PRON
ejpam-5369	148	24	,	,	PUNCT
ejpam-5369	148	25	b	b	PROPN
ejpam-5369	148	26	⊆	⊆	NUM
ejpam-5369	148	27	x.	x.	NOUN
ejpam-5369	148	28	a	a	NOUN
ejpam-5369	148	29	,	,	PUNCT
ejpam-5369	148	30	b	b	PROPN
ejpam-5369	148	31	⊆	⊆	NUM
ejpam-5369	148	32	x	x	X
ejpam-5369	148	33	⇒	⇒	VERB
ejpam-5369	148	34	a	a	DET
ejpam-5369	148	35	⊆	⊆	NUM
ejpam-5369	148	36	(	(	PUNCT
ejpam-5369	148	37	a	a	DET
ejpam-5369	148	38	\b	\b	ADJ
ejpam-5369	148	39	)	)	PUNCT
ejpam-5369	148	40	∪b	∪b	VERB
ejpam-5369	148	41	⇒	⇒	VERB
ejpam-5369	148	42	a⋄	a⋄	ADV
ejpam-5369	148	43	ω	ω	PROPN
ejpam-5369	148	44	⊆	⊆	NUM
ejpam-5369	148	45	[	[	X
ejpam-5369	148	46	(	(	PUNCT
ejpam-5369	148	47	a	a	DET
ejpam-5369	148	48	\b	\b	NOUN
ejpam-5369	148	49	)	)	PUNCT
ejpam-5369	148	50	∪b]⋄ω	∪b]⋄ω	PUNCT
ejpam-5369	149	1	=	=	SYM
ejpam-5369	149	2	(	(	PUNCT
ejpam-5369	149	3	a	a	DET
ejpam-5369	149	4	\b)⋄ω	\b)⋄ω	PROPN
ejpam-5369	149	5	∪b⋄	∪b⋄	PRON
ejpam-5369	149	6	ω	ω	ADJ
ejpam-5369	149	7	⇒	⇒	PROPN
ejpam-5369	149	8	a⋄	a⋄	PROPN
ejpam-5369	149	9	ω	ω	PROPN
ejpam-5369	149	10	\b⋄	\b⋄	PUNCT
ejpam-5369	149	11	ω	ω	NOUN
ejpam-5369	149	12	⊆	⊆	NUM
ejpam-5369	149	13	(	(	PUNCT
ejpam-5369	149	14	a	a	DET
ejpam-5369	149	15	\b)⋄ω	\b)⋄ω	NOUN
ejpam-5369	149	16	.	.	PUNCT
ejpam-5369	150	1	(	(	PUNCT
ejpam-5369	150	2	d	d	X
ejpam-5369	150	3	)	)	PUNCT
ejpam-5369	150	4	let	let	VERB
ejpam-5369	150	5	a	a	PRON
ejpam-5369	150	6	,	,	PUNCT
ejpam-5369	150	7	b	b	PROPN
ejpam-5369	150	8	⊆	⊆	NUM
ejpam-5369	150	9	x.	x.	NOUN
ejpam-5369	150	10	a	a	NOUN
ejpam-5369	150	11	,	,	PUNCT
ejpam-5369	150	12	b	b	PROPN
ejpam-5369	150	13	⊆	⊆	NUM
ejpam-5369	150	14	x	x	X
ejpam-5369	150	15	⇒	⇒	VERB
ejpam-5369	150	16	a	a	DET
ejpam-5369	150	17	\b	\b	NOUN
ejpam-5369	150	18	⊆	⊆	NUM
ejpam-5369	150	19	a	a	DET
ejpam-5369	150	20	⇒	⇒	NOUN
ejpam-5369	150	21	(	(	PUNCT
ejpam-5369	150	22	a	a	DET
ejpam-5369	150	23	\b)⋄ω	\b)⋄ω	PROPN
ejpam-5369	150	24	⊆	⊆	NUM
ejpam-5369	150	25	a⋄	a⋄	NOUN
ejpam-5369	150	26	ω	ω	NOUN
ejpam-5369	150	27	⇒	⇒	NOUN
ejpam-5369	150	28	(	(	PUNCT
ejpam-5369	150	29	a	a	DET
ejpam-5369	150	30	\b)⋄ω	\b)⋄ω	NOUN
ejpam-5369	150	31	\b⋄	\b⋄	PUNCT
ejpam-5369	150	32	ω	ω	ADP
ejpam-5369	150	33	⊆	⊆	NUM
ejpam-5369	150	34	a⋄	a⋄	NOUN
ejpam-5369	150	35	ω	ω	NUM
ejpam-5369	150	36	\b⋄	\b⋄	PUNCT
ejpam-5369	150	37	ω	ω	NOUN
ejpam-5369	150	38	a	a	X
ejpam-5369	150	39	,	,	PUNCT
ejpam-5369	150	40	b	b	NOUN
ejpam-5369	150	41	⊆	⊆	NUM
ejpam-5369	150	42	x	x	SYM
ejpam-5369	150	43	(	(	PUNCT
ejpam-5369	150	44	c)⇒	c)⇒	PROPN
ejpam-5369	150	45	a⋄	a⋄	PROPN
ejpam-5369	150	46	ω	ω	PROPN
ejpam-5369	150	47	\b⋄	\b⋄	PUNCT
ejpam-5369	150	48	ω	ω	NOUN
ejpam-5369	150	49	⊆	⊆	NUM
ejpam-5369	150	50	(	(	PUNCT
ejpam-5369	150	51	a	a	DET
ejpam-5369	150	52	\b)⋄ω	\b)⋄ω	ADJ
ejpam-5369	150	53	⇒	⇒	NOUN
ejpam-5369	150	54	(	(	PUNCT
ejpam-5369	150	55	a⋄	a⋄	PROPN
ejpam-5369	150	56	ω	ω	PROPN
ejpam-5369	150	57	\b⋄	\b⋄	X
ejpam-5369	150	58	ω	ω	NOUN
ejpam-5369	150	59	)	)	PUNCT
ejpam-5369	150	60	\b⋄	\b⋄	PUNCT
ejpam-5369	150	61	ω	ω	NOUN
ejpam-5369	150	62	=	=	SYM
ejpam-5369	150	63	a⋄	a⋄	PROPN
ejpam-5369	150	64	ω	ω	NUM
ejpam-5369	150	65	\b⋄	\b⋄	PUNCT
ejpam-5369	150	66	ω	ω	NOUN
ejpam-5369	150	67	⊆	⊆	NUM
ejpam-5369	150	68	(	(	PUNCT
ejpam-5369	150	69	a	a	DET
ejpam-5369	150	70	\b)⋄ω	\b)⋄ω	PROPN
ejpam-5369	150	71	\b⋄	\b⋄	PUNCT
ejpam-5369	150	72	ω	ω	NOUN
ejpam-5369	150	73	}	}	PUNCT
ejpam-5369	150	74	⇒	⇒	NOUN
ejpam-5369	150	75	⇒	⇒	NOUN
ejpam-5369	150	76	(	(	PUNCT
ejpam-5369	150	77	a	a	DET
ejpam-5369	150	78	\b)⋄ω	\b)⋄ω	NOUN
ejpam-5369	150	79	\b⋄	\b⋄	PUNCT
ejpam-5369	150	80	ω	ω	NOUN
ejpam-5369	150	81	=	=	SYM
ejpam-5369	150	82	a⋄	a⋄	PROPN
ejpam-5369	150	83	ω	ω	NUM
ejpam-5369	150	84	\b⋄	\b⋄	X
ejpam-5369	150	85	ω	ω	PROPN
ejpam-5369	150	86	.	.	PUNCT
ejpam-5369	151	1	theorem	theorem	VERB
ejpam-5369	151	2	6	6	NUM
ejpam-5369	151	3	.	.	PUNCT
ejpam-5369	152	1	let	let	VERB
ejpam-5369	152	2	(	(	PUNCT
ejpam-5369	152	3	x	x	X
ejpam-5369	152	4	,	,	PUNCT
ejpam-5369	152	5	τ	τ	PROPN
ejpam-5369	152	6	,	,	PUNCT
ejpam-5369	152	7	p	p	NOUN
ejpam-5369	152	8	)	)	PUNCT
ejpam-5369	152	9	be	be	AUX
ejpam-5369	152	10	a	a	DET
ejpam-5369	152	11	primal	primal	ADJ
ejpam-5369	152	12	topological	topological	ADJ
ejpam-5369	152	13	space	space	NOUN
ejpam-5369	152	14	and	and	CCONJ
ejpam-5369	152	15	a	a	PRON
ejpam-5369	152	16	,	,	PUNCT
ejpam-5369	152	17	b	b	PROPN
ejpam-5369	152	18	⊆	⊆	NUM
ejpam-5369	152	19	x.	x.	NOUN
ejpam-5369	152	20	if	if	SCONJ
ejpam-5369	152	21	a	a	PRON
ejpam-5369	152	22	is	be	AUX
ejpam-5369	152	23	ω	ω	NOUN
ejpam-5369	152	24	-	-	NOUN
ejpam-5369	152	25	open	open	ADJ
ejpam-5369	152	26	in	in	ADP
ejpam-5369	152	27	x	x	NOUN
ejpam-5369	152	28	,	,	PUNCT
ejpam-5369	152	29	then	then	ADV
ejpam-5369	152	30	a	a	DET
ejpam-5369	152	31	∩b⋄	∩b⋄	NOUN
ejpam-5369	152	32	ω	ω	NUM
ejpam-5369	152	33	⊆	⊆	NUM
ejpam-5369	152	34	(	(	PUNCT
ejpam-5369	152	35	a	a	DET
ejpam-5369	152	36	∩b)⋄ω	∩b)⋄ω	NOUN
ejpam-5369	152	37	.	.	PUNCT
ejpam-5369	153	1	proof	proof	NOUN
ejpam-5369	153	2	.	.	PUNCT
ejpam-5369	154	1	let	let	VERB
ejpam-5369	154	2	x	x	SYM
ejpam-5369	154	3	∈	∈	VERB
ejpam-5369	154	4	a	a	DET
ejpam-5369	154	5	∩b⋄	∩b⋄	NOUN
ejpam-5369	154	6	ω	ω	NOUN
ejpam-5369	154	7	.	.	PUNCT
ejpam-5369	155	1	x	x	X
ejpam-5369	155	2	∈	∈	PROPN
ejpam-5369	155	3	a	a	DET
ejpam-5369	155	4	∩b⋄	∩b⋄	NOUN
ejpam-5369	155	5	ω	ω	NUM
ejpam-5369	155	6	⇒	⇒	NOUN
ejpam-5369	155	7	(	(	PUNCT
ejpam-5369	155	8	x	x	SYM
ejpam-5369	155	9	∈	∈	PROPN
ejpam-5369	155	10	a)(x	a)(x	NOUN
ejpam-5369	155	11	∈	∈	PROPN
ejpam-5369	155	12	b⋄	b⋄	PROPN
ejpam-5369	155	13	ω	ω	NUM
ejpam-5369	155	14	)	)	PUNCT
ejpam-5369	155	15	⇒	⇒	NOUN
ejpam-5369	155	16	(	(	PUNCT
ejpam-5369	155	17	x	x	SYM
ejpam-5369	155	18	∈	∈	PROPN
ejpam-5369	155	19	a)(∀u	a)(∀u	NOUN
ejpam-5369	155	20	∈	∈	PROPN
ejpam-5369	155	21	ωo(x	ωo(x	NUM
ejpam-5369	155	22	,	,	PUNCT
ejpam-5369	155	23	x))(u	x))(u	PROPN
ejpam-5369	155	24	c	c	X
ejpam-5369	155	25	∪bc	∪bc	VERB
ejpam-5369	155	26	∈	∈	PROPN
ejpam-5369	155	27	p	p	NOUN
ejpam-5369	155	28	)	)	PUNCT
ejpam-5369	155	29	a	a	DET
ejpam-5369	155	30	∈	∈	PROPN
ejpam-5369	155	31	ωo(x	ωo(x	NUM
ejpam-5369	155	32	)	)	PUNCT
ejpam-5369	155	33	}	}	PUNCT
ejpam-5369	155	34	⇒	⇒	VERB
ejpam-5369	155	35	⇒	⇒	NOUN
ejpam-5369	155	36	(	(	PUNCT
ejpam-5369	155	37	∀u	∀u	NOUN
ejpam-5369	155	38	∈	∈	NOUN
ejpam-5369	155	39	ωo(x	ωo(x	NUM
ejpam-5369	155	40	,	,	PUNCT
ejpam-5369	155	41	x))(u	x))(u	PROPN
ejpam-5369	155	42	∩a	∩a	PROPN
ejpam-5369	155	43	∈	∈	PROPN
ejpam-5369	155	44	ωo(x	ωo(x	PROPN
ejpam-5369	155	45	,	,	PUNCT
ejpam-5369	155	46	x))((u	x))((u	NOUN
ejpam-5369	155	47	∩a)c	∩a)c	PROPN
ejpam-5369	155	48	∪bc	∪bc	ADJ
ejpam-5369	155	49	=	=	SYM
ejpam-5369	155	50	u	u	NOUN
ejpam-5369	155	51	c	c	NOUN
ejpam-5369	155	52	∪	∪	X
ejpam-5369	155	53	(	(	PUNCT
ejpam-5369	155	54	a	a	DET
ejpam-5369	155	55	∩b)c	∩b)c	PROPN
ejpam-5369	155	56	∈	∈	PROPN
ejpam-5369	155	57	p	p	NOUN
ejpam-5369	155	58	)	)	PUNCT
ejpam-5369	155	59	⇒	⇒	NOUN
ejpam-5369	156	1	x	x	X
ejpam-5369	156	2	∈	∈	PROPN
ejpam-5369	156	3	(	(	PUNCT
ejpam-5369	156	4	a	a	DET
ejpam-5369	156	5	∩b)⋄ω	∩b)⋄ω	NOUN
ejpam-5369	156	6	.	.	NOUN
ejpam-5369	156	7	corollary	corollary	ADJ
ejpam-5369	156	8	2	2	NUM
ejpam-5369	156	9	.	.	PUNCT
ejpam-5369	157	1	let	let	VERB
ejpam-5369	157	2	(	(	PUNCT
ejpam-5369	157	3	x	x	X
ejpam-5369	157	4	,	,	PUNCT
ejpam-5369	157	5	τ	τ	PROPN
ejpam-5369	157	6	,	,	PUNCT
ejpam-5369	157	7	p	p	NOUN
ejpam-5369	157	8	)	)	PUNCT
ejpam-5369	157	9	be	be	AUX
ejpam-5369	157	10	a	a	DET
ejpam-5369	157	11	primal	primal	ADJ
ejpam-5369	157	12	topological	topological	ADJ
ejpam-5369	157	13	space	space	NOUN
ejpam-5369	157	14	and	and	CCONJ
ejpam-5369	157	15	a	a	PRON
ejpam-5369	157	16	,	,	PUNCT
ejpam-5369	157	17	b	b	PROPN
ejpam-5369	157	18	⊆	⊆	NUM
ejpam-5369	157	19	x.	x.	NOUN
ejpam-5369	157	20	if	if	SCONJ
ejpam-5369	157	21	a	a	PRON
ejpam-5369	157	22	is	be	AUX
ejpam-5369	157	23	open	open	ADJ
ejpam-5369	157	24	in	in	ADP
ejpam-5369	157	25	x	x	NOUN
ejpam-5369	157	26	,	,	PUNCT
ejpam-5369	157	27	then	then	ADV
ejpam-5369	157	28	a	a	DET
ejpam-5369	157	29	∩b⋄	∩b⋄	NOUN
ejpam-5369	157	30	ω	ω	NUM
ejpam-5369	157	31	⊆	⊆	NUM
ejpam-5369	157	32	(	(	PUNCT
ejpam-5369	157	33	a	a	DET
ejpam-5369	157	34	∩b)⋄ω	∩b)⋄ω	NOUN
ejpam-5369	157	35	.	.	PUNCT
ejpam-5369	158	1	theorem	theorem	NOUN
ejpam-5369	158	2	7	7	NUM
ejpam-5369	158	3	.	.	PUNCT
ejpam-5369	159	1	let	let	VERB
ejpam-5369	159	2	(	(	PUNCT
ejpam-5369	159	3	x	x	X
ejpam-5369	159	4	,	,	PUNCT
ejpam-5369	159	5	τ	τ	PROPN
ejpam-5369	159	6	,	,	PUNCT
ejpam-5369	159	7	p	p	NOUN
ejpam-5369	159	8	)	)	PUNCT
ejpam-5369	159	9	be	be	AUX
ejpam-5369	159	10	a	a	DET
ejpam-5369	159	11	primal	primal	ADJ
ejpam-5369	159	12	topological	topological	ADJ
ejpam-5369	159	13	space	space	NOUN
ejpam-5369	159	14	.	.	PUNCT
ejpam-5369	160	1	(	(	PUNCT
ejpam-5369	160	2	a	a	X
ejpam-5369	160	3	)	)	PUNCT
ejpam-5369	160	4	if	if	SCONJ
ejpam-5369	160	5	ωc(x	ωc(x	NUM
ejpam-5369	160	6	)	)	PUNCT
ejpam-5369	160	7	\	\	NOUN
ejpam-5369	160	8	{	{	PUNCT
ejpam-5369	160	9	x	x	X
ejpam-5369	160	10	}	}	PUNCT
ejpam-5369	160	11	⊆	⊆	NUM
ejpam-5369	160	12	p	p	NOUN
ejpam-5369	160	13	,	,	PUNCT
ejpam-5369	160	14	then	then	ADV
ejpam-5369	160	15	x⋄	x⋄	PUNCT
ejpam-5369	161	1	ω	ω	X
ejpam-5369	161	2	=	=	SYM
ejpam-5369	161	3	x	x	X
ejpam-5369	161	4	;	;	PUNCT
ejpam-5369	161	5	(	(	PUNCT
ejpam-5369	161	6	b	b	X
ejpam-5369	161	7	)	)	PUNCT
ejpam-5369	161	8	if	if	SCONJ
ejpam-5369	161	9	ωc(x	ωc(x	NUM
ejpam-5369	161	10	)	)	PUNCT
ejpam-5369	161	11	\	\	NOUN
ejpam-5369	161	12	{	{	PUNCT
ejpam-5369	161	13	x	x	X
ejpam-5369	161	14	}	}	PUNCT
ejpam-5369	161	15	⊆	⊆	NUM
ejpam-5369	161	16	p	p	NOUN
ejpam-5369	161	17	,	,	PUNCT
ejpam-5369	161	18	then	then	ADV
ejpam-5369	161	19	a	a	DET
ejpam-5369	161	20	⊆	⊆	NUM
ejpam-5369	161	21	a⋄	a⋄	NOUN
ejpam-5369	161	22	ω	ω	NOUN
ejpam-5369	161	23	for	for	ADP
ejpam-5369	161	24	all	all	DET
ejpam-5369	161	25	a	a	DET
ejpam-5369	161	26	∈	∈	NOUN
ejpam-5369	161	27	ωo(x	ωo(x	NUM
ejpam-5369	161	28	)	)	PUNCT
ejpam-5369	161	29	.	.	PUNCT
ejpam-5369	162	1	proof	proof	NOUN
ejpam-5369	162	2	.	.	PUNCT
ejpam-5369	163	1	(	(	PUNCT
ejpam-5369	163	2	a	a	X
ejpam-5369	163	3	)	)	PUNCT
ejpam-5369	163	4	let	let	VERB
ejpam-5369	163	5	x	x	PUNCT
ejpam-5369	163	6	∈	∈	PROPN
ejpam-5369	163	7	x	x	X
ejpam-5369	163	8	and	and	CCONJ
ejpam-5369	163	9	u	u	PROPN
ejpam-5369	163	10	∈	∈	PROPN
ejpam-5369	163	11	ωo(x	ωo(x	NUM
ejpam-5369	163	12	,	,	PUNCT
ejpam-5369	163	13	x	x	NOUN
ejpam-5369	163	14	)	)	PUNCT
ejpam-5369	163	15	.	.	PUNCT
ejpam-5369	164	1	u	u	PROPN
ejpam-5369	164	2	∈	∈	PROPN
ejpam-5369	164	3	ωo(x	ωo(x	NUM
ejpam-5369	164	4	,	,	PUNCT
ejpam-5369	164	5	x	x	NOUN
ejpam-5369	164	6	)	)	PUNCT
ejpam-5369	164	7	⇒	⇒	VERB
ejpam-5369	164	8	u	u	NOUN
ejpam-5369	164	9	c	c	PROPN
ejpam-5369	164	10	∈	∈	PROPN
ejpam-5369	164	11	ωc(x	ωc(x	NOUN
ejpam-5369	164	12	)	)	PUNCT
ejpam-5369	164	13	\	\	NOUN
ejpam-5369	164	14	{	{	PUNCT
ejpam-5369	164	15	x	x	NOUN
ejpam-5369	164	16	}	}	PUNCT
ejpam-5369	164	17	ωc(x	ωc(x	NOUN
ejpam-5369	164	18	)	)	PUNCT
ejpam-5369	164	19	\	\	NOUN
ejpam-5369	164	20	{	{	PUNCT
ejpam-5369	164	21	x	x	NOUN
ejpam-5369	164	22	}	}	PUNCT
ejpam-5369	164	23	⊆	⊆	NUM
ejpam-5369	164	24	p	p	NOUN
ejpam-5369	164	25	}	}	PUNCT
ejpam-5369	164	26	⇒	⇒	VERB
ejpam-5369	164	27	u	u	PROPN
ejpam-5369	164	28	c	c	PROPN
ejpam-5369	164	29	∪xc	∪xc	PROPN
ejpam-5369	164	30	=	=	SYM
ejpam-5369	164	31	u	u	NOUN
ejpam-5369	164	32	c	c	NOUN
ejpam-5369	164	33	∪	∪	NOUN
ejpam-5369	164	34	∅	∅	NOUN
ejpam-5369	164	35	=	=	SYM
ejpam-5369	164	36	u	u	X
ejpam-5369	164	37	c	c	NOUN
ejpam-5369	164	38	∈	∈	PROPN
ejpam-5369	165	1	p	p	NOUN
ejpam-5369	165	2	then	then	ADV
ejpam-5369	165	3	,	,	PUNCT
ejpam-5369	165	4	we	we	PRON
ejpam-5369	165	5	have	have	VERB
ejpam-5369	165	6	x	x	PROPN
ejpam-5369	165	7	∈	∈	PROPN
ejpam-5369	165	8	x⋄	x⋄	PROPN
ejpam-5369	165	9	ω	ω	PROPN
ejpam-5369	165	10	.	.	PUNCT
ejpam-5369	166	1	thus	thus	ADV
ejpam-5369	166	2	,	,	PUNCT
ejpam-5369	166	3	x	x	PUNCT
ejpam-5369	166	4	⊆	⊆	X
ejpam-5369	166	5	x⋄	x⋄	SYM
ejpam-5369	166	6	ω	ω	NUM
ejpam-5369	166	7	which	which	PRON
ejpam-5369	166	8	means	mean	VERB
ejpam-5369	166	9	x⋄	x⋄	X
ejpam-5369	166	10	ω	ω	PROPN
ejpam-5369	166	11	=	=	PUNCT
ejpam-5369	166	12	x.	x.	NOUN
ejpam-5369	166	13	(	(	PUNCT
ejpam-5369	166	14	b	b	X
ejpam-5369	166	15	)	)	PUNCT
ejpam-5369	166	16	let	let	VERB
ejpam-5369	166	17	a	a	DET
ejpam-5369	166	18	∈	∈	NOUN
ejpam-5369	166	19	ωo(x	ωo(x	NUM
ejpam-5369	166	20	)	)	PUNCT
ejpam-5369	166	21	.	.	PUNCT
ejpam-5369	167	1	a	a	DET
ejpam-5369	167	2	∈	∈	PROPN
ejpam-5369	167	3	ωo(x	ωo(x	NUM
ejpam-5369	167	4	)	)	PUNCT
ejpam-5369	167	5	theorem	theorem	VERB
ejpam-5369	167	6	6⇒	6⇒	NOUN
ejpam-5369	167	7	a	a	DET
ejpam-5369	167	8	∩x⋄	∩x⋄	PROPN
ejpam-5369	167	9	ω	ω	NUM
ejpam-5369	167	10	⊆	⊆	NUM
ejpam-5369	167	11	(	(	PUNCT
ejpam-5369	167	12	a	a	DET
ejpam-5369	167	13	∩x)⋄ω	∩x)⋄ω	ADJ
ejpam-5369	167	14	=	=	NOUN
ejpam-5369	167	15	a⋄	a⋄	NOUN
ejpam-5369	167	16	ω	ω	NUM
ejpam-5369	167	17	ωc(x	ωc(x	NOUN
ejpam-5369	167	18	)	)	PUNCT
ejpam-5369	167	19	\	\	NOUN
ejpam-5369	168	1	{	{	PUNCT
ejpam-5369	168	2	x	x	NOUN
ejpam-5369	168	3	}	}	PUNCT
ejpam-5369	168	4	⊆	⊆	NUM
ejpam-5369	168	5	p	p	NOUN
ejpam-5369	168	6	(	(	PUNCT
ejpam-5369	168	7	a)⇒	a)⇒	PROPN
ejpam-5369	168	8	x⋄	x⋄	PROPN
ejpam-5369	168	9	ω	ω	PROPN
ejpam-5369	168	10	=	=	PUNCT
ejpam-5369	168	11	x	x	SYM
ejpam-5369	168	12	}	}	PUNCT
ejpam-5369	168	13	⇒	⇒	VERB
ejpam-5369	168	14	a	a	DET
ejpam-5369	168	15	⊆	⊆	NUM
ejpam-5369	168	16	a⋄	a⋄	NOUN
ejpam-5369	168	17	ω	ω	PROPN
ejpam-5369	168	18	.	.	PUNCT
ejpam-5369	168	19	theorem	theorem	NOUN
ejpam-5369	168	20	8	8	NUM
ejpam-5369	168	21	.	.	PUNCT
ejpam-5369	169	1	let	let	VERB
ejpam-5369	169	2	(	(	PUNCT
ejpam-5369	169	3	x	x	X
ejpam-5369	169	4	,	,	PUNCT
ejpam-5369	169	5	τ	τ	PROPN
ejpam-5369	169	6	,	,	PUNCT
ejpam-5369	169	7	p	p	NOUN
ejpam-5369	169	8	)	)	PUNCT
ejpam-5369	169	9	be	be	AUX
ejpam-5369	169	10	a	a	DET
ejpam-5369	169	11	primal	primal	ADJ
ejpam-5369	169	12	topological	topological	ADJ
ejpam-5369	169	13	space	space	NOUN
ejpam-5369	169	14	and	and	CCONJ
ejpam-5369	169	15	a	a	PRON
ejpam-5369	169	16	,	,	PUNCT
ejpam-5369	169	17	b	b	PROPN
ejpam-5369	169	18	⊆	⊆	NUM
ejpam-5369	169	19	x.	x.	NOUN
ejpam-5369	169	20	if	if	SCONJ
ejpam-5369	169	21	b	b	PROPN
ejpam-5369	169	22	∈	∈	PROPN
ejpam-5369	169	23	p	p	X
ejpam-5369	169	24	,	,	PUNCT
ejpam-5369	169	25	then	then	ADV
ejpam-5369	169	26	(	(	PUNCT
ejpam-5369	169	27	a	a	DET
ejpam-5369	169	28	∪b)⋄ω	∪b)⋄ω	NOUN
ejpam-5369	169	29	=	=	NOUN
ejpam-5369	169	30	a⋄	a⋄	NOUN
ejpam-5369	169	31	ω	ω	NOUN
ejpam-5369	169	32	=	=	SYM
ejpam-5369	169	33	(	(	PUNCT
ejpam-5369	169	34	a	a	DET
ejpam-5369	169	35	\b)⋄ω	\b)⋄ω	NOUN
ejpam-5369	169	36	.	.	PUNCT
ejpam-5369	170	1	proof	proof	NOUN
ejpam-5369	170	2	.	.	PUNCT
ejpam-5369	171	1	let	let	VERB
ejpam-5369	171	2	a	a	DET
ejpam-5369	171	3	,	,	PUNCT
ejpam-5369	171	4	b	b	PROPN
ejpam-5369	171	5	⊆	⊆	NUM
ejpam-5369	171	6	x.	x.	NOUN
ejpam-5369	171	7	a	a	NOUN
ejpam-5369	171	8	,	,	PUNCT
ejpam-5369	171	9	b	b	PROPN
ejpam-5369	171	10	⊆	⊆	NUM
ejpam-5369	171	11	x	x	SYM
ejpam-5369	171	12	theorem	theorem	VERB
ejpam-5369	171	13	5⇒	5⇒	PROPN
ejpam-5369	171	14	a⋄	a⋄	PROPN
ejpam-5369	171	15	ω	ω	NUM
ejpam-5369	171	16	\b⋄	\b⋄	X
ejpam-5369	171	17	ω	ω	NOUN
ejpam-5369	171	18	=	=	SYM
ejpam-5369	171	19	(	(	PUNCT
ejpam-5369	171	20	a	a	DET
ejpam-5369	171	21	\b)⋄ω	\b)⋄ω	PROPN
ejpam-5369	171	22	\b⋄	\b⋄	PUNCT
ejpam-5369	171	23	ω	ω	NOUN
ejpam-5369	171	24	b	b	PROPN
ejpam-5369	171	25	∈	∈	PROPN
ejpam-5369	171	26	p	p	PROPN
ejpam-5369	171	27	⇒	⇒	PROPN
ejpam-5369	171	28	b⋄	b⋄	PROPN
ejpam-5369	171	29	ω	ω	NOUN
ejpam-5369	171	30	=	=	NOUN
ejpam-5369	171	31	∅	∅	NOUN
ejpam-5369	171	32	}	}	PUNCT
ejpam-5369	171	33	⇒	⇒	VERB
ejpam-5369	171	34	a⋄	a⋄	NOUN
ejpam-5369	171	35	ω	ω	PROPN
ejpam-5369	171	36	=	=	SYM
ejpam-5369	171	37	(	(	PUNCT
ejpam-5369	171	38	a	a	DET
ejpam-5369	171	39	\b)⋄ω	\b)⋄ω	PROPN
ejpam-5369	171	40	.	.	PUNCT
ejpam-5369	171	41	.	.	PUNCT
ejpam-5369	171	42	.	.	PUNCT
ejpam-5369	172	1	(	(	PUNCT
ejpam-5369	172	2	1	1	X
ejpam-5369	172	3	)	)	PUNCT
ejpam-5369	172	4	a	a	PRON
ejpam-5369	172	5	,	,	PUNCT
ejpam-5369	172	6	b	b	NOUN
ejpam-5369	172	7	⊆	⊆	NUM
ejpam-5369	172	8	x	x	SYM
ejpam-5369	172	9	theorem	theorem	ADJ
ejpam-5369	172	10	2⇒	2⇒	PROPN
ejpam-5369	172	11	a⋄	a⋄	PROPN
ejpam-5369	172	12	ω	ω	PROPN
ejpam-5369	172	13	∪b⋄	∪b⋄	NOUN
ejpam-5369	172	14	ω	ω	NOUN
ejpam-5369	172	15	=	=	X
ejpam-5369	172	16	(	(	PUNCT
ejpam-5369	172	17	a	a	DET
ejpam-5369	172	18	∪b)⋄ω	∪b)⋄ω	X
ejpam-5369	172	19	b	b	NOUN
ejpam-5369	172	20	∈	∈	PROPN
ejpam-5369	172	21	p	p	PROPN
ejpam-5369	172	22	⇒	⇒	PROPN
ejpam-5369	172	23	b⋄	b⋄	PROPN
ejpam-5369	172	24	ω	ω	NOUN
ejpam-5369	172	25	=	=	NOUN
ejpam-5369	172	26	∅	∅	NOUN
ejpam-5369	172	27	}	}	PUNCT
ejpam-5369	172	28	⇒	⇒	VERB
ejpam-5369	172	29	a⋄	a⋄	NOUN
ejpam-5369	172	30	ω	ω	PROPN
ejpam-5369	172	31	=	=	SYM
ejpam-5369	172	32	(	(	PUNCT
ejpam-5369	172	33	a	a	DET
ejpam-5369	172	34	∪b)⋄ω	∪b)⋄ω	NOUN
ejpam-5369	172	35	.	.	PUNCT
ejpam-5369	172	36	.	.	PUNCT
ejpam-5369	172	37	.	.	PUNCT
ejpam-5369	173	1	(	(	PUNCT
ejpam-5369	173	2	2	2	X
ejpam-5369	173	3	)	)	PUNCT
ejpam-5369	173	4	p.	p.	NOUN
ejpam-5369	173	5	şaşmaz	şaşmaz	NUM
ejpam-5369	173	6	,	,	PUNCT
ejpam-5369	173	7	m.	m.	NOUN
ejpam-5369	173	8	özkoç	özkoç	PROPN
ejpam-5369	173	9	/	/	SYM
ejpam-5369	173	10	eur	eur	PROPN
ejpam-5369	173	11	.	.	PUNCT
ejpam-5369	174	1	j.	j.	PROPN
ejpam-5369	174	2	pure	pure	PROPN
ejpam-5369	174	3	appl	appl	PROPN
ejpam-5369	174	4	.	.	PROPN
ejpam-5369	174	5	math	math	PROPN
ejpam-5369	174	6	,	,	PUNCT
ejpam-5369	174	7	17	17	NUM
ejpam-5369	174	8	(	(	PUNCT
ejpam-5369	174	9	4	4	NUM
ejpam-5369	174	10	)	)	PUNCT
ejpam-5369	174	11	(	(	PUNCT
ejpam-5369	174	12	2024	2024	NUM
ejpam-5369	174	13	)	)	PUNCT
ejpam-5369	174	14	,	,	PUNCT
ejpam-5369	174	15	2800	2800	NUM
ejpam-5369	174	16	-	-	SYM
ejpam-5369	174	17	2811	2811	NUM
ejpam-5369	174	18	2806	2806	NUM
ejpam-5369	174	19	(	(	PUNCT
ejpam-5369	174	20	1	1	NUM
ejpam-5369	174	21	)	)	PUNCT
ejpam-5369	174	22	,	,	PUNCT
ejpam-5369	174	23	(	(	PUNCT
ejpam-5369	174	24	2	2	X
ejpam-5369	174	25	)	)	PUNCT
ejpam-5369	174	26	⇒	⇒	NOUN
ejpam-5369	174	27	(	(	PUNCT
ejpam-5369	174	28	a	a	DET
ejpam-5369	174	29	∪b)⋄ω	∪b)⋄ω	NOUN
ejpam-5369	174	30	=	=	NOUN
ejpam-5369	174	31	a⋄	a⋄	NOUN
ejpam-5369	174	32	ω	ω	NOUN
ejpam-5369	174	33	=	=	SYM
ejpam-5369	174	34	(	(	PUNCT
ejpam-5369	174	35	a	a	DET
ejpam-5369	174	36	\b)⋄ω	\b)⋄ω	NOUN
ejpam-5369	174	37	.	.	PUNCT
ejpam-5369	174	38	theorem	theorem	NOUN
ejpam-5369	174	39	9	9	NUM
ejpam-5369	174	40	.	.	PUNCT
ejpam-5369	175	1	let	let	VERB
ejpam-5369	175	2	p	p	PRON
ejpam-5369	175	3	be	be	AUX
ejpam-5369	175	4	a	a	DET
ejpam-5369	175	5	primal	primal	ADJ
ejpam-5369	175	6	on	on	ADP
ejpam-5369	175	7	topological	topological	ADJ
ejpam-5369	175	8	space	space	NOUN
ejpam-5369	175	9	(	(	PUNCT
ejpam-5369	175	10	x	x	X
ejpam-5369	175	11	,	,	PUNCT
ejpam-5369	175	12	τ	τ	X
ejpam-5369	175	13	)	)	PUNCT
ejpam-5369	175	14	and	and	CCONJ
ejpam-5369	175	15	a	a	DET
ejpam-5369	175	16	⊆	⊆	NUM
ejpam-5369	175	17	x.	x.	NOUN
ejpam-5369	175	18	if	if	SCONJ
ejpam-5369	175	19	ac	ac	PROPN
ejpam-5369	175	20	/∈	/∈	PUNCT
ejpam-5369	176	1	p	p	X
ejpam-5369	176	2	,	,	PUNCT
ejpam-5369	176	3	then	then	ADV
ejpam-5369	176	4	a⋄	a⋄	PROPN
ejpam-5369	176	5	ω	ω	NOUN
ejpam-5369	176	6	=	=	PUNCT
ejpam-5369	176	7	∅.	∅.	NOUN
ejpam-5369	176	8	proof	proof	NOUN
ejpam-5369	176	9	.	.	PUNCT
ejpam-5369	177	1	suppose	suppose	VERB
ejpam-5369	177	2	that	that	SCONJ
ejpam-5369	177	3	a⋄	a⋄	NOUN
ejpam-5369	177	4	ω	ω	NUM
ejpam-5369	177	5	̸=	̸=	PROPN
ejpam-5369	177	6	∅.	∅.	PROPN
ejpam-5369	177	7	a⋄	a⋄	NOUN
ejpam-5369	177	8	ω	ω	NUM
ejpam-5369	177	9	̸=	̸=	PROPN
ejpam-5369	177	10	∅	∅	NOUN
ejpam-5369	177	11	⇒	⇒	NOUN
ejpam-5369	177	12	(	(	PUNCT
ejpam-5369	177	13	∃x	∃x	PROPN
ejpam-5369	177	14	∈	∈	NOUN
ejpam-5369	177	15	x)(x	x)(x	PROPN
ejpam-5369	177	16	∈	∈	PROPN
ejpam-5369	177	17	a⋄	a⋄	PROPN
ejpam-5369	177	18	ω	ω	NUM
ejpam-5369	177	19	)	)	PUNCT
ejpam-5369	177	20	⇒	⇒	NOUN
ejpam-5369	177	21	(	(	PUNCT
ejpam-5369	177	22	∀u	∀u	NOUN
ejpam-5369	177	23	∈	∈	NOUN
ejpam-5369	177	24	ωo(x	ωo(x	NUM
ejpam-5369	177	25	,	,	PUNCT
ejpam-5369	177	26	x))(ac	x))(ac	PROPN
ejpam-5369	177	27	⊆	⊆	NUM
ejpam-5369	177	28	u	u	NOUN
ejpam-5369	177	29	c	c	PROPN
ejpam-5369	177	30	∪ac	∪ac	PROPN
ejpam-5369	177	31	∈	∈	PROPN
ejpam-5369	177	32	p	p	X
ejpam-5369	177	33	)	)	PUNCT
ejpam-5369	177	34	p	p	NOUN
ejpam-5369	177	35	is	be	AUX
ejpam-5369	177	36	a	a	DET
ejpam-5369	177	37	primal	primal	ADJ
ejpam-5369	177	38	on	on	ADP
ejpam-5369	177	39	x	x	SYM
ejpam-5369	177	40	}	}	PUNCT
ejpam-5369	177	41	⇒	⇒	NOUN
ejpam-5369	177	42	ac	ac	PROPN
ejpam-5369	177	43	∈	∈	PROPN
ejpam-5369	177	44	p	p	NOUN
ejpam-5369	177	45	this	this	PRON
ejpam-5369	177	46	contradicts	contradict	VERB
ejpam-5369	177	47	with	with	ADP
ejpam-5369	177	48	the	the	DET
ejpam-5369	177	49	hypothesis	hypothesis	NOUN
ejpam-5369	177	50	.	.	PUNCT
ejpam-5369	178	1	4	4	X
ejpam-5369	178	2	.	.	X
ejpam-5369	179	1	the	the	DET
ejpam-5369	179	2	operator	operator	NOUN
ejpam-5369	179	3	cl⋄ω	cl⋄ω	PROPN
ejpam-5369	179	4	and	and	CCONJ
ejpam-5369	179	5	its	its	PRON
ejpam-5369	179	6	associated	associated	ADJ
ejpam-5369	179	7	topology	topology	NOUN
ejpam-5369	179	8	definition	definition	NOUN
ejpam-5369	179	9	8	8	NUM
ejpam-5369	179	10	.	.	PUNCT
ejpam-5369	180	1	let	let	VERB
ejpam-5369	180	2	(	(	PUNCT
ejpam-5369	180	3	x	x	X
ejpam-5369	180	4	,	,	PUNCT
ejpam-5369	180	5	τ	τ	PROPN
ejpam-5369	180	6	,	,	PUNCT
ejpam-5369	180	7	p	p	NOUN
ejpam-5369	180	8	)	)	PUNCT
ejpam-5369	180	9	be	be	AUX
ejpam-5369	180	10	a	a	DET
ejpam-5369	180	11	primal	primal	ADJ
ejpam-5369	180	12	topological	topological	ADJ
ejpam-5369	180	13	space	space	NOUN
ejpam-5369	180	14	.	.	PUNCT
ejpam-5369	181	1	we	we	PRON
ejpam-5369	181	2	consider	consider	VERB
ejpam-5369	181	3	a	a	DET
ejpam-5369	181	4	map	map	NOUN
ejpam-5369	182	1	cl⋄ω	cl⋄ω	PROPN
ejpam-5369	182	2	:	:	PUNCT
ejpam-5369	182	3	2x	2x	NUM
ejpam-5369	182	4	→	→	SYM
ejpam-5369	182	5	2x	2x	NUM
ejpam-5369	182	6	as	as	ADP
ejpam-5369	182	7	cl⋄ω(a	cl⋄ω(a	NOUN
ejpam-5369	182	8	)	)	PUNCT
ejpam-5369	182	9	=	=	PUNCT
ejpam-5369	182	10	a	a	DET
ejpam-5369	182	11	∪a⋄	∪a⋄	X
ejpam-5369	182	12	ω	ω	NOUN
ejpam-5369	182	13	,	,	PUNCT
ejpam-5369	182	14	where	where	SCONJ
ejpam-5369	182	15	a	a	PRON
ejpam-5369	182	16	is	be	AUX
ejpam-5369	182	17	any	any	DET
ejpam-5369	182	18	subset	subset	NOUN
ejpam-5369	182	19	of	of	ADP
ejpam-5369	182	20	x.	x.	PROPN
ejpam-5369	182	21	theorem	theorem	VERB
ejpam-5369	182	22	10	10	NUM
ejpam-5369	182	23	.	.	PUNCT
ejpam-5369	183	1	let	let	VERB
ejpam-5369	183	2	(	(	PUNCT
ejpam-5369	183	3	x	x	X
ejpam-5369	183	4	,	,	PUNCT
ejpam-5369	183	5	τ	τ	PROPN
ejpam-5369	183	6	,	,	PUNCT
ejpam-5369	183	7	p	p	NOUN
ejpam-5369	183	8	)	)	PUNCT
ejpam-5369	183	9	be	be	AUX
ejpam-5369	183	10	a	a	DET
ejpam-5369	183	11	primal	primal	ADJ
ejpam-5369	183	12	topological	topological	ADJ
ejpam-5369	183	13	space	space	NOUN
ejpam-5369	183	14	and	and	CCONJ
ejpam-5369	183	15	a	a	PRON
ejpam-5369	183	16	,	,	PUNCT
ejpam-5369	183	17	b	b	PROPN
ejpam-5369	183	18	⊆	⊆	NUM
ejpam-5369	183	19	x.	x.	NOUN
ejpam-5369	183	20	then	then	ADV
ejpam-5369	183	21	,	,	PUNCT
ejpam-5369	183	22	the	the	DET
ejpam-5369	183	23	following	follow	VERB
ejpam-5369	183	24	statements	statement	NOUN
ejpam-5369	183	25	hold	hold	VERB
ejpam-5369	183	26	:	:	PUNCT
ejpam-5369	183	27	(	(	PUNCT
ejpam-5369	183	28	a	a	X
ejpam-5369	183	29	)	)	PUNCT
ejpam-5369	183	30	cl⋄ω(∅	cl⋄ω(∅	PROPN
ejpam-5369	183	31	)	)	PUNCT
ejpam-5369	183	32	=	=	SYM
ejpam-5369	183	33	∅	∅	NOUN
ejpam-5369	183	34	,	,	PUNCT
ejpam-5369	183	35	(	(	PUNCT
ejpam-5369	183	36	b	b	NOUN
ejpam-5369	183	37	)	)	PUNCT
ejpam-5369	183	38	cl⋄ω(x	cl⋄ω(x	NOUN
ejpam-5369	183	39	)	)	PUNCT
ejpam-5369	183	40	=	=	SYM
ejpam-5369	184	1	x	x	X
ejpam-5369	184	2	,	,	PUNCT
ejpam-5369	184	3	(	(	PUNCT
ejpam-5369	184	4	c	c	X
ejpam-5369	184	5	)	)	PUNCT
ejpam-5369	184	6	a	a	DET
ejpam-5369	184	7	⊆	⊆	NUM
ejpam-5369	184	8	cl⋄ω(a	cl⋄ω(a	NOUN
ejpam-5369	184	9	)	)	PUNCT
ejpam-5369	184	10	⊆	⊆	NUM
ejpam-5369	184	11	cl⋄(a	cl⋄(a	NOUN
ejpam-5369	184	12	)	)	PUNCT
ejpam-5369	184	13	,	,	PUNCT
ejpam-5369	184	14	(	(	PUNCT
ejpam-5369	184	15	d	d	X
ejpam-5369	184	16	)	)	PUNCT
ejpam-5369	184	17	if	if	SCONJ
ejpam-5369	184	18	a	a	DET
ejpam-5369	184	19	⊆	⊆	NUM
ejpam-5369	184	20	b	b	NOUN
ejpam-5369	184	21	⊆	⊆	NUM
ejpam-5369	184	22	x	x	NUM
ejpam-5369	184	23	,	,	PUNCT
ejpam-5369	184	24	then	then	ADV
ejpam-5369	184	25	cl⋄ω(a	cl⋄ω(a	NOUN
ejpam-5369	184	26	)	)	PUNCT
ejpam-5369	184	27	⊆	⊆	NUM
ejpam-5369	184	28	cl⋄ω(b	cl⋄ω(b	NOUN
ejpam-5369	184	29	)	)	PUNCT
ejpam-5369	184	30	,	,	PUNCT
ejpam-5369	184	31	(	(	PUNCT
ejpam-5369	184	32	e	e	NOUN
ejpam-5369	184	33	)	)	PUNCT
ejpam-5369	184	34	cl⋄ω(a	cl⋄ω(a	NOUN
ejpam-5369	184	35	)	)	PUNCT
ejpam-5369	184	36	∪	∪	ADP
ejpam-5369	184	37	cl⋄ω(b	cl⋄ω(b	NOUN
ejpam-5369	184	38	)	)	PUNCT
ejpam-5369	184	39	=	=	SYM
ejpam-5369	184	40	cl⋄ω(a	cl⋄ω(a	PROPN
ejpam-5369	184	41	∪b	∪b	NOUN
ejpam-5369	184	42	)	)	PUNCT
ejpam-5369	184	43	,	,	PUNCT
ejpam-5369	184	44	(	(	PUNCT
ejpam-5369	184	45	f	f	X
ejpam-5369	184	46	)	)	PUNCT
ejpam-5369	184	47	cl⋄ω(cl	cl⋄ω(cl	PROPN
ejpam-5369	184	48	⋄	⋄	PROPN
ejpam-5369	184	49	ω(a	ω(a	PROPN
ejpam-5369	184	50	)	)	PUNCT
ejpam-5369	184	51	)	)	PUNCT
ejpam-5369	185	1	=	=	PUNCT
ejpam-5369	185	2	cl⋄ω(a	cl⋄ω(a	NOUN
ejpam-5369	185	3	)	)	PUNCT
ejpam-5369	185	4	.	.	PUNCT
ejpam-5369	186	1	proof	proof	NOUN
ejpam-5369	186	2	.	.	PUNCT
ejpam-5369	187	1	(	(	PUNCT
ejpam-5369	187	2	a	a	X
ejpam-5369	187	3	)	)	PUNCT
ejpam-5369	187	4	since	since	SCONJ
ejpam-5369	187	5	∅⋄ω	∅⋄ω	PROPN
ejpam-5369	187	6	=	=	SYM
ejpam-5369	187	7	∅	∅	NOUN
ejpam-5369	187	8	,	,	PUNCT
ejpam-5369	187	9	we	we	PRON
ejpam-5369	187	10	have	have	VERB
ejpam-5369	187	11	cl⋄ω(∅	cl⋄ω(∅	NOUN
ejpam-5369	187	12	)	)	PUNCT
ejpam-5369	187	13	=	=	NOUN
ejpam-5369	187	14	∅	∅	NOUN
ejpam-5369	187	15	∪	∪	VERB
ejpam-5369	187	16	∅⋄ω	∅⋄ω	PROPN
ejpam-5369	187	17	=	=	PUNCT
ejpam-5369	187	18	∅.	∅.	X
ejpam-5369	187	19	(	(	PUNCT
ejpam-5369	187	20	b	b	NOUN
ejpam-5369	187	21	)	)	PUNCT
ejpam-5369	187	22	since	since	SCONJ
ejpam-5369	187	23	x⋄	x⋄	PROPN
ejpam-5369	187	24	ω	ω	PROPN
ejpam-5369	187	25	⊆	⊆	NUM
ejpam-5369	187	26	x	x	X
ejpam-5369	187	27	,	,	PUNCT
ejpam-5369	187	28	we	we	PRON
ejpam-5369	187	29	have	have	VERB
ejpam-5369	187	30	cl⋄ω(x	cl⋄ω(x	NOUN
ejpam-5369	187	31	)	)	PUNCT
ejpam-5369	187	32	=	=	PUNCT
ejpam-5369	188	1	x	x	X
ejpam-5369	188	2	∪x⋄	∪x⋄	PROPN
ejpam-5369	188	3	ω	ω	X
ejpam-5369	188	4	=	=	PUNCT
ejpam-5369	188	5	x.	x.	NOUN
ejpam-5369	188	6	(	(	PUNCT
ejpam-5369	188	7	c	c	X
ejpam-5369	188	8	)	)	PUNCT
ejpam-5369	188	9	let	let	VERB
ejpam-5369	188	10	a	a	DET
ejpam-5369	188	11	⊆	⊆	NUM
ejpam-5369	188	12	x.	x.	NOUN
ejpam-5369	188	13	a	a	DET
ejpam-5369	188	14	⊆	⊆	NUM
ejpam-5369	188	15	x	x	SYM
ejpam-5369	188	16	⇒	⇒	NOUN
ejpam-5369	188	17	a⋄	a⋄	PUNCT
ejpam-5369	188	18	ω	ω	PROPN
ejpam-5369	188	19	⊆	⊆	NUM
ejpam-5369	188	20	a⋄	a⋄	ADJ
ejpam-5369	188	21	⇒	⇒	VERB
ejpam-5369	188	22	a	a	PRON
ejpam-5369	188	23	⊆	⊆	NUM
ejpam-5369	188	24	a	a	DET
ejpam-5369	188	25	∪a⋄	∪a⋄	X
ejpam-5369	188	26	ω	ω	NUM
ejpam-5369	188	27	=	=	SYM
ejpam-5369	188	28	cl⋄ω(a	cl⋄ω(a	NOUN
ejpam-5369	188	29	)	)	PUNCT
ejpam-5369	188	30	⊆	⊆	NUM
ejpam-5369	188	31	a	a	DET
ejpam-5369	188	32	∪a⋄	∪a⋄	X
ejpam-5369	188	33	=	=	PUNCT
ejpam-5369	188	34	cl⋄(a	cl⋄(a	PROPN
ejpam-5369	188	35	)	)	PUNCT
ejpam-5369	188	36	.	.	PUNCT
ejpam-5369	189	1	(	(	PUNCT
ejpam-5369	189	2	d	d	X
ejpam-5369	189	3	)	)	PUNCT
ejpam-5369	189	4	let	let	VERB
ejpam-5369	190	1	a	a	DET
ejpam-5369	190	2	⊆	⊆	NUM
ejpam-5369	190	3	b	b	SYM
ejpam-5369	190	4	⊆	⊆	NUM
ejpam-5369	190	5	x.	x.	NOUN
ejpam-5369	190	6	a	a	DET
ejpam-5369	190	7	⊆	⊆	NUM
ejpam-5369	190	8	b	b	NOUN
ejpam-5369	190	9	⇒	⇒	NOUN
ejpam-5369	190	10	a⋄	a⋄	PUNCT
ejpam-5369	190	11	ω	ω	PROPN
ejpam-5369	190	12	⊆	⊆	NUM
ejpam-5369	190	13	b⋄	b⋄	PROPN
ejpam-5369	190	14	ω	ω	PROPN
ejpam-5369	190	15	⇒	⇒	PROPN
ejpam-5369	190	16	cl⋄ω(a	cl⋄ω(a	PROPN
ejpam-5369	190	17	)	)	PUNCT
ejpam-5369	190	18	=	=	PUNCT
ejpam-5369	190	19	a	a	DET
ejpam-5369	190	20	∪a⋄	∪a⋄	X
ejpam-5369	190	21	ω	ω	NUM
ejpam-5369	190	22	⊆	⊆	NUM
ejpam-5369	190	23	b	b	PROPN
ejpam-5369	190	24	∪b⋄	∪b⋄	NUM
ejpam-5369	190	25	ω	ω	PROPN
ejpam-5369	190	26	=	=	PUNCT
ejpam-5369	190	27	cl⋄ω(b	cl⋄ω(b	PROPN
ejpam-5369	190	28	)	)	PUNCT
ejpam-5369	190	29	.	.	PUNCT
ejpam-5369	191	1	(	(	PUNCT
ejpam-5369	191	2	e	e	X
ejpam-5369	191	3	)	)	PUNCT
ejpam-5369	191	4	let	let	VERB
ejpam-5369	191	5	a	a	DET
ejpam-5369	191	6	,	,	PUNCT
ejpam-5369	191	7	b	b	PROPN
ejpam-5369	191	8	⊆	⊆	NUM
ejpam-5369	191	9	x.	x.	NOUN
ejpam-5369	191	10	cl⋄ω(a	cl⋄ω(a	PROPN
ejpam-5369	191	11	∪b	∪b	X
ejpam-5369	191	12	)	)	PUNCT
ejpam-5369	191	13	=	=	SYM
ejpam-5369	192	1	(	(	PUNCT
ejpam-5369	192	2	a	a	DET
ejpam-5369	192	3	∪b	∪b	NOUN
ejpam-5369	192	4	)	)	PUNCT
ejpam-5369	192	5	∪	∪	NOUN
ejpam-5369	192	6	(	(	PUNCT
ejpam-5369	192	7	a	a	DET
ejpam-5369	192	8	∪b)⋄ω	∪b)⋄ω	NOUN
ejpam-5369	192	9	=	=	X
ejpam-5369	192	10	(	(	PUNCT
ejpam-5369	192	11	a	a	DET
ejpam-5369	192	12	∪b	∪b	NOUN
ejpam-5369	192	13	)	)	PUNCT
ejpam-5369	192	14	∪	∪	NOUN
ejpam-5369	192	15	(	(	PUNCT
ejpam-5369	192	16	a⋄	a⋄	NOUN
ejpam-5369	192	17	ω	ω	NUM
ejpam-5369	192	18	∪b⋄	∪b⋄	NUM
ejpam-5369	192	19	ω	ω	NOUN
ejpam-5369	192	20	)	)	PUNCT
ejpam-5369	192	21	=	=	PUNCT
ejpam-5369	192	22	(	(	PUNCT
ejpam-5369	192	23	a	a	DET
ejpam-5369	192	24	∪a⋄	∪a⋄	X
ejpam-5369	192	25	ω	ω	NOUN
ejpam-5369	192	26	)	)	PUNCT
ejpam-5369	192	27	∪	∪	NOUN
ejpam-5369	192	28	(	(	PUNCT
ejpam-5369	192	29	b	b	NOUN
ejpam-5369	192	30	∪b⋄	∪b⋄	NUM
ejpam-5369	192	31	ω	ω	NOUN
ejpam-5369	192	32	)	)	PUNCT
ejpam-5369	192	33	=	=	SYM
ejpam-5369	192	34	cl⋄ω(a	cl⋄ω(a	NOUN
ejpam-5369	192	35	)	)	PUNCT
ejpam-5369	192	36	∪	∪	ADP
ejpam-5369	192	37	cl⋄ω(b	cl⋄ω(b	NOUN
ejpam-5369	192	38	)	)	PUNCT
ejpam-5369	192	39	.	.	PUNCT
ejpam-5369	193	1	p.	p.	NOUN
ejpam-5369	193	2	şaşmaz	şaşmaz	NUM
ejpam-5369	193	3	,	,	PUNCT
ejpam-5369	193	4	m.	m.	NOUN
ejpam-5369	193	5	özkoç	özkoç	PROPN
ejpam-5369	193	6	/	/	SYM
ejpam-5369	193	7	eur	eur	PROPN
ejpam-5369	193	8	.	.	PUNCT
ejpam-5369	194	1	j.	j.	PROPN
ejpam-5369	194	2	pure	pure	PROPN
ejpam-5369	194	3	appl	appl	PROPN
ejpam-5369	194	4	.	.	PROPN
ejpam-5369	194	5	math	math	PROPN
ejpam-5369	194	6	,	,	PUNCT
ejpam-5369	194	7	17	17	NUM
ejpam-5369	194	8	(	(	PUNCT
ejpam-5369	194	9	4	4	NUM
ejpam-5369	194	10	)	)	PUNCT
ejpam-5369	194	11	(	(	PUNCT
ejpam-5369	194	12	2024	2024	NUM
ejpam-5369	194	13	)	)	PUNCT
ejpam-5369	194	14	,	,	PUNCT
ejpam-5369	194	15	2800	2800	NUM
ejpam-5369	194	16	-	-	SYM
ejpam-5369	194	17	2811	2811	NUM
ejpam-5369	194	18	2807	2807	NUM
ejpam-5369	194	19	(	(	PUNCT
ejpam-5369	194	20	f	f	X
ejpam-5369	194	21	)	)	PUNCT
ejpam-5369	194	22	let	let	VERB
ejpam-5369	194	23	a	a	DET
ejpam-5369	194	24	⊆	⊆	NUM
ejpam-5369	194	25	x.	x.	NOUN
ejpam-5369	194	26	it	it	PRON
ejpam-5369	194	27	is	be	AUX
ejpam-5369	194	28	obvious	obvious	ADJ
ejpam-5369	194	29	from	from	ADP
ejpam-5369	194	30	(	(	PUNCT
ejpam-5369	194	31	c	c	NOUN
ejpam-5369	194	32	)	)	PUNCT
ejpam-5369	194	33	and	and	CCONJ
ejpam-5369	194	34	(	(	PUNCT
ejpam-5369	194	35	d	d	X
ejpam-5369	194	36	)	)	PUNCT
ejpam-5369	194	37	that	that	SCONJ
ejpam-5369	194	38	cl⋄ω(a	cl⋄ω(a	NOUN
ejpam-5369	194	39	)	)	PUNCT
ejpam-5369	194	40	⊆	⊆	NUM
ejpam-5369	194	41	cl⋄ω(cl	cl⋄ω(cl	ADP
ejpam-5369	194	42	⋄	⋄	PROPN
ejpam-5369	194	43	ω(a	ω(a	PROPN
ejpam-5369	194	44	)	)	PUNCT
ejpam-5369	194	45	)	)	PUNCT
ejpam-5369	194	46	.	.	PUNCT
ejpam-5369	194	47	.	.	PUNCT
ejpam-5369	194	48	.	.	PUNCT
ejpam-5369	195	1	(	(	PUNCT
ejpam-5369	195	2	1	1	X
ejpam-5369	195	3	)	)	PUNCT
ejpam-5369	195	4	cl⋄ω(cl	cl⋄ω(cl	NOUN
ejpam-5369	195	5	⋄	⋄	PROPN
ejpam-5369	195	6	ω(a	ω(a	PROPN
ejpam-5369	195	7	)	)	PUNCT
ejpam-5369	195	8	)	)	PUNCT
ejpam-5369	196	1	=	=	SYM
ejpam-5369	196	2	cl⋄ω(a	cl⋄ω(a	NOUN
ejpam-5369	196	3	)	)	PUNCT
ejpam-5369	196	4	∪	∪	NOUN
ejpam-5369	196	5	(	(	PUNCT
ejpam-5369	196	6	cl⋄ω(a))⋄ω	cl⋄ω(a))⋄ω	NOUN
ejpam-5369	196	7	=	=	SYM
ejpam-5369	196	8	cl⋄ω(a	cl⋄ω(a	NOUN
ejpam-5369	196	9	)	)	PUNCT
ejpam-5369	196	10	∪	∪	NOUN
ejpam-5369	196	11	(	(	PUNCT
ejpam-5369	196	12	a	a	DET
ejpam-5369	196	13	∪a⋄	∪a⋄	NUM
ejpam-5369	196	14	ω	ω	NUM
ejpam-5369	196	15	)	)	PUNCT
ejpam-5369	196	16	⋄	⋄	PROPN
ejpam-5369	196	17	ω	ω	NUM
ejpam-5369	197	1	=	=	SYM
ejpam-5369	197	2	cl⋄ω(a	cl⋄ω(a	NOUN
ejpam-5369	197	3	)	)	PUNCT
ejpam-5369	198	1	∪a⋄	∪a⋄	X
ejpam-5369	198	2	ω	ω	X
ejpam-5369	198	3	∪	∪	X
ejpam-5369	198	4	(	(	PUNCT
ejpam-5369	198	5	a⋄	a⋄	PROPN
ejpam-5369	198	6	ω	ω	NUM
ejpam-5369	198	7	)	)	PUNCT
ejpam-5369	198	8	⋄	⋄	PROPN
ejpam-5369	198	9	ω	ω	NUM
ejpam-5369	198	10	a	a	DET
ejpam-5369	198	11	⊆	⊆	NUM
ejpam-5369	198	12	x	x	SYM
ejpam-5369	198	13	⇒	⇒	NOUN
ejpam-5369	198	14	a⋄	a⋄	PROPN
ejpam-5369	198	15	ω	ω	PROPN
ejpam-5369	198	16	∈	∈	PROPN
ejpam-5369	198	17	ωc(x	ωc(x	NOUN
ejpam-5369	198	18	)	)	PUNCT
ejpam-5369	198	19	⇒	⇒	NOUN
ejpam-5369	198	20	(	(	PUNCT
ejpam-5369	198	21	a⋄	a⋄	PROPN
ejpam-5369	198	22	ω	ω	NUM
ejpam-5369	198	23	)	)	PUNCT
ejpam-5369	198	24	⋄	⋄	PROPN
ejpam-5369	198	25	ω	ω	NUM
ejpam-5369	198	26	⊆	⊆	NUM
ejpam-5369	198	27	a⋄	a⋄	NOUN
ejpam-5369	198	28	ω	ω	NUM
ejpam-5369	198	29	}	}	PUNCT
ejpam-5369	198	30	⇒	⇒	VERB
ejpam-5369	198	31	⇒	⇒	NOUN
ejpam-5369	198	32	cl⋄ω(cl	cl⋄ω(cl	SYM
ejpam-5369	198	33	⋄	⋄	PROPN
ejpam-5369	198	34	ω(a	ω(a	PROPN
ejpam-5369	198	35	)	)	PUNCT
ejpam-5369	198	36	)	)	PUNCT
ejpam-5369	199	1	⊆	⊆	NUM
ejpam-5369	199	2	cl⋄ω(a	cl⋄ω(a	NOUN
ejpam-5369	199	3	)	)	PUNCT
ejpam-5369	199	4	.	.	PUNCT
ejpam-5369	199	5	.	.	PUNCT
ejpam-5369	199	6	.	.	PUNCT
ejpam-5369	200	1	(	(	PUNCT
ejpam-5369	200	2	2	2	X
ejpam-5369	200	3	)	)	PUNCT
ejpam-5369	200	4	(	(	PUNCT
ejpam-5369	200	5	1	1	NUM
ejpam-5369	200	6	)	)	PUNCT
ejpam-5369	200	7	,	,	PUNCT
ejpam-5369	200	8	(	(	PUNCT
ejpam-5369	200	9	2	2	X
ejpam-5369	200	10	)	)	PUNCT
ejpam-5369	200	11	⇒	⇒	NOUN
ejpam-5369	200	12	cl⋄ω(a	cl⋄ω(a	NOUN
ejpam-5369	200	13	)	)	PUNCT
ejpam-5369	200	14	=	=	SYM
ejpam-5369	200	15	cl⋄ω(cl	cl⋄ω(cl	X
ejpam-5369	200	16	⋄	⋄	PROPN
ejpam-5369	200	17	ω(a	ω(a	PROPN
ejpam-5369	200	18	)	)	PUNCT
ejpam-5369	200	19	)	)	PUNCT
ejpam-5369	200	20	.	.	PUNCT
ejpam-5369	201	1	corollary	corollary	ADJ
ejpam-5369	201	2	3	3	X
ejpam-5369	201	3	.	.	PUNCT
ejpam-5369	202	1	let	let	VERB
ejpam-5369	202	2	(	(	PUNCT
ejpam-5369	202	3	x	x	X
ejpam-5369	202	4	,	,	PUNCT
ejpam-5369	202	5	τ	τ	PROPN
ejpam-5369	202	6	,	,	PUNCT
ejpam-5369	202	7	p	p	NOUN
ejpam-5369	202	8	)	)	PUNCT
ejpam-5369	202	9	be	be	AUX
ejpam-5369	202	10	a	a	DET
ejpam-5369	202	11	primal	primal	ADJ
ejpam-5369	202	12	topological	topological	ADJ
ejpam-5369	202	13	space	space	NOUN
ejpam-5369	202	14	.	.	PUNCT
ejpam-5369	203	1	then	then	ADV
ejpam-5369	203	2	,	,	PUNCT
ejpam-5369	203	3	the	the	DET
ejpam-5369	203	4	operator	operator	NOUN
ejpam-5369	203	5	cl⋄ω	cl⋄ω	PROPN
ejpam-5369	203	6	:	:	PUNCT
ejpam-5369	203	7	2x	2x	NUM
ejpam-5369	203	8	→	→	SYM
ejpam-5369	203	9	2x	2x	NUM
ejpam-5369	203	10	defined	define	VERB
ejpam-5369	203	11	by	by	ADP
ejpam-5369	203	12	cl⋄ω(a	cl⋄ω(a	NOUN
ejpam-5369	203	13	)	)	PUNCT
ejpam-5369	203	14	=	=	NOUN
ejpam-5369	203	15	a	a	DET
ejpam-5369	203	16	∪	∪	ADJ
ejpam-5369	203	17	a⋄	a⋄	ADJ
ejpam-5369	203	18	ω	ω	NOUN
ejpam-5369	203	19	,	,	PUNCT
ejpam-5369	203	20	where	where	SCONJ
ejpam-5369	203	21	a	a	PRON
ejpam-5369	203	22	is	be	AUX
ejpam-5369	203	23	any	any	DET
ejpam-5369	203	24	subset	subset	NOUN
ejpam-5369	203	25	of	of	ADP
ejpam-5369	203	26	x	x	X
ejpam-5369	203	27	,	,	PUNCT
ejpam-5369	203	28	is	be	AUX
ejpam-5369	203	29	a	a	DET
ejpam-5369	203	30	kuratowski	kuratowski	ADJ
ejpam-5369	203	31	closure	closure	NOUN
ejpam-5369	203	32	operator	operator	NOUN
ejpam-5369	203	33	.	.	PUNCT
ejpam-5369	204	1	definition	definition	NOUN
ejpam-5369	204	2	9	9	NUM
ejpam-5369	204	3	.	.	PUNCT
ejpam-5369	205	1	let	let	VERB
ejpam-5369	205	2	(	(	PUNCT
ejpam-5369	205	3	x	x	X
ejpam-5369	205	4	,	,	PUNCT
ejpam-5369	205	5	τ	τ	PROPN
ejpam-5369	205	6	,	,	PUNCT
ejpam-5369	205	7	p	p	NOUN
ejpam-5369	205	8	)	)	PUNCT
ejpam-5369	205	9	be	be	AUX
ejpam-5369	205	10	a	a	DET
ejpam-5369	205	11	primal	primal	ADJ
ejpam-5369	205	12	topological	topological	ADJ
ejpam-5369	205	13	space	space	NOUN
ejpam-5369	205	14	.	.	PUNCT
ejpam-5369	206	1	then	then	ADV
ejpam-5369	206	2	,	,	PUNCT
ejpam-5369	206	3	the	the	DET
ejpam-5369	206	4	family	family	NOUN
ejpam-5369	206	5	τ⋄ω	τ⋄ω	PUNCT
ejpam-5369	206	6	=	=	SYM
ejpam-5369	206	7	{	{	PUNCT
ejpam-5369	206	8	a	a	PRON
ejpam-5369	206	9	⊆	⊆	NUM
ejpam-5369	206	10	x|cl⋄ω(ac	x|cl⋄ω(ac	PRON
ejpam-5369	206	11	)	)	PUNCT
ejpam-5369	207	1	=	=	PUNCT
ejpam-5369	207	2	ac	ac	PROPN
ejpam-5369	207	3	}	}	PUNCT
ejpam-5369	207	4	is	be	AUX
ejpam-5369	207	5	a	a	DET
ejpam-5369	207	6	topology	topology	NOUN
ejpam-5369	207	7	on	on	ADP
ejpam-5369	207	8	x	x	PUNCT
ejpam-5369	207	9	induced	induce	VERB
ejpam-5369	207	10	by	by	ADP
ejpam-5369	207	11	topology	topology	NOUN
ejpam-5369	207	12	τ	τ	PROPN
ejpam-5369	207	13	and	and	CCONJ
ejpam-5369	207	14	primal	primal	ADJ
ejpam-5369	207	15	p.	p.	NOUN
ejpam-5369	207	16	theorem	theorem	VERB
ejpam-5369	207	17	11	11	NUM
ejpam-5369	207	18	.	.	PUNCT
ejpam-5369	208	1	let	let	VERB
ejpam-5369	208	2	(	(	PUNCT
ejpam-5369	208	3	x	x	X
ejpam-5369	208	4	,	,	PUNCT
ejpam-5369	208	5	τ	τ	PROPN
ejpam-5369	208	6	,	,	PUNCT
ejpam-5369	208	7	p	p	NOUN
ejpam-5369	208	8	)	)	PUNCT
ejpam-5369	208	9	be	be	AUX
ejpam-5369	208	10	a	a	DET
ejpam-5369	208	11	primal	primal	ADJ
ejpam-5369	208	12	topological	topological	ADJ
ejpam-5369	208	13	space	space	NOUN
ejpam-5369	208	14	.	.	PUNCT
ejpam-5369	209	1	then	then	ADV
ejpam-5369	209	2	,	,	PUNCT
ejpam-5369	209	3	we	we	PRON
ejpam-5369	209	4	have	have	VERB
ejpam-5369	209	5	τ	τ	PROPN
ejpam-5369	209	6	⊆	⊆	NUM
ejpam-5369	209	7	τ⋄	τ⋄	X
ejpam-5369	209	8	⊆	⊆	NUM
ejpam-5369	209	9	τ⋄ω	τ⋄ω	NUM
ejpam-5369	209	10	.	.	PUNCT
ejpam-5369	210	1	proof	proof	NOUN
ejpam-5369	210	2	.	.	PUNCT
ejpam-5369	211	1	we	we	PRON
ejpam-5369	211	2	have	have	VERB
ejpam-5369	211	3	τ	τ	PROPN
ejpam-5369	211	4	⊆	⊆	NUM
ejpam-5369	211	5	τ⋄	τ⋄	PUNCT
ejpam-5369	211	6	from	from	ADP
ejpam-5369	211	7	theorem	theorem	ADJ
ejpam-5369	211	8	3.6	3.6	NUM
ejpam-5369	211	9	in	in	ADP
ejpam-5369	211	10	[	[	X
ejpam-5369	211	11	1	1	NUM
ejpam-5369	211	12	]	]	PUNCT
ejpam-5369	211	13	.	.	PUNCT
ejpam-5369	212	1	now	now	ADV
ejpam-5369	212	2	,	,	PUNCT
ejpam-5369	212	3	let	let	VERB
ejpam-5369	212	4	a	a	DET
ejpam-5369	212	5	∈	∈	NOUN
ejpam-5369	212	6	τ⋄.	τ⋄.	NOUN
ejpam-5369	212	7	we	we	PRON
ejpam-5369	212	8	will	will	AUX
ejpam-5369	212	9	prove	prove	VERB
ejpam-5369	212	10	that	that	SCONJ
ejpam-5369	212	11	a	a	DET
ejpam-5369	212	12	∈	∈	PROPN
ejpam-5369	212	13	τ⋄ω	τ⋄ω	NUM
ejpam-5369	212	14	.	.	PUNCT
ejpam-5369	213	1	a	a	DET
ejpam-5369	213	2	∈	∈	NOUN
ejpam-5369	213	3	τ⋄	τ⋄	X
ejpam-5369	213	4	⇒	⇒	NOUN
ejpam-5369	213	5	cl⋄(ac	cl⋄(ac	PROPN
ejpam-5369	213	6	)	)	PUNCT
ejpam-5369	214	1	=	=	PRON
ejpam-5369	214	2	ac	ac	PROPN
ejpam-5369	214	3	a	a	DET
ejpam-5369	214	4	⊆	⊆	NUM
ejpam-5369	214	5	x	x	SYM
ejpam-5369	214	6	⇒	⇒	NOUN
ejpam-5369	214	7	(	(	PUNCT
ejpam-5369	214	8	ac)⋄ω	ac)⋄ω	X
ejpam-5369	214	9	⊆	⊆	NUM
ejpam-5369	214	10	(	(	PUNCT
ejpam-5369	214	11	ac)⋄	ac)⋄	NOUN
ejpam-5369	214	12	⇒	⇒	PROPN
ejpam-5369	214	13	cl⋄ω(a	cl⋄ω(a	PROPN
ejpam-5369	214	14	c	c	PROPN
ejpam-5369	214	15	)	)	PUNCT
ejpam-5369	214	16	⊆	⊆	NUM
ejpam-5369	214	17	cl⋄(ac	cl⋄(ac	PROPN
ejpam-5369	214	18	)	)	PUNCT
ejpam-5369	214	19	}	}	PUNCT
ejpam-5369	214	20	⇒	⇒	VERB
ejpam-5369	214	21	cl⋄ω(a	cl⋄ω(a	PROPN
ejpam-5369	214	22	c	c	PROPN
ejpam-5369	214	23	)	)	PUNCT
ejpam-5369	214	24	⊆	⊆	NUM
ejpam-5369	214	25	ac	ac	PROPN
ejpam-5369	214	26	ac	ac	PROPN
ejpam-5369	214	27	⊆	⊆	NUM
ejpam-5369	214	28	cl⋄ω(a	cl⋄ω(a	PROPN
ejpam-5369	214	29	c	c	PROPN
ejpam-5369	214	30	)	)	PUNCT
ejpam-5369	214	31	}	}	PUNCT
ejpam-5369	214	32	⇒	⇒	VERB
ejpam-5369	214	33	ac	ac	X
ejpam-5369	215	1	=	=	SYM
ejpam-5369	215	2	cl⋄ω(a	cl⋄ω(a	PROPN
ejpam-5369	215	3	c	c	PROPN
ejpam-5369	215	4	)	)	PUNCT
ejpam-5369	215	5	⇒	⇒	VERB
ejpam-5369	215	6	a	a	DET
ejpam-5369	215	7	∈	∈	PROPN
ejpam-5369	215	8	τ⋄ω	τ⋄ω	NUM
ejpam-5369	215	9	.	.	PUNCT
ejpam-5369	216	1	theorem	theorem	NOUN
ejpam-5369	216	2	12	12	NUM
ejpam-5369	216	3	.	.	PUNCT
ejpam-5369	217	1	let	let	VERB
ejpam-5369	217	2	(	(	PUNCT
ejpam-5369	217	3	x	x	X
ejpam-5369	217	4	,	,	PUNCT
ejpam-5369	217	5	τ	τ	PROPN
ejpam-5369	217	6	,	,	PUNCT
ejpam-5369	217	7	p	p	NOUN
ejpam-5369	217	8	)	)	PUNCT
ejpam-5369	217	9	be	be	AUX
ejpam-5369	217	10	a	a	DET
ejpam-5369	217	11	primal	primal	ADJ
ejpam-5369	217	12	topological	topological	ADJ
ejpam-5369	217	13	space	space	NOUN
ejpam-5369	217	14	.	.	PUNCT
ejpam-5369	218	1	then	then	ADV
ejpam-5369	218	2	,	,	PUNCT
ejpam-5369	218	3	we	we	PRON
ejpam-5369	218	4	have	have	VERB
ejpam-5369	218	5	τ	τ	PROPN
ejpam-5369	218	6	⊆	⊆	NUM
ejpam-5369	218	7	τω	τω	ADP
ejpam-5369	218	8	⊆	⊆	NUM
ejpam-5369	218	9	τ⋄ω	τ⋄ω	NUM
ejpam-5369	218	10	.	.	PUNCT
ejpam-5369	219	1	proof	proof	NOUN
ejpam-5369	219	2	.	.	PUNCT
ejpam-5369	220	1	we	we	PRON
ejpam-5369	220	2	have	have	VERB
ejpam-5369	220	3	τ	τ	PROPN
ejpam-5369	220	4	⊆	⊆	NUM
ejpam-5369	220	5	τω	τω	ADV
ejpam-5369	220	6	from	from	ADP
ejpam-5369	220	7	[	[	X
ejpam-5369	220	8	10	10	NUM
ejpam-5369	220	9	]	]	PUNCT
ejpam-5369	220	10	.	.	PUNCT
ejpam-5369	221	1	now	now	ADV
ejpam-5369	221	2	,	,	PUNCT
ejpam-5369	221	3	let	let	VERB
ejpam-5369	221	4	a	a	DET
ejpam-5369	221	5	∈	∈	NOUN
ejpam-5369	221	6	τω	τω	INTJ
ejpam-5369	221	7	.	.	PUNCT
ejpam-5369	222	1	we	we	PRON
ejpam-5369	222	2	will	will	AUX
ejpam-5369	222	3	prove	prove	VERB
ejpam-5369	222	4	that	that	SCONJ
ejpam-5369	222	5	a	a	DET
ejpam-5369	222	6	∈	∈	PROPN
ejpam-5369	222	7	τ⋄ω	τ⋄ω	NUM
ejpam-5369	222	8	.	.	PUNCT
ejpam-5369	223	1	a	a	DET
ejpam-5369	223	2	∈	∈	NOUN
ejpam-5369	223	3	τω	τω	SCONJ
ejpam-5369	223	4	theorem	theorem	ADJ
ejpam-5369	223	5	1⇒	1⇒	PROPN
ejpam-5369	223	6	(	(	PUNCT
ejpam-5369	223	7	ac)⋄ω	ac)⋄ω	X
ejpam-5369	223	8	⊆	⊆	NUM
ejpam-5369	223	9	ac	ac	ADJ
ejpam-5369	223	10	⇒	⇒	NOUN
ejpam-5369	223	11	cl⋄ω(a	cl⋄ω(a	PROPN
ejpam-5369	223	12	c	c	NOUN
ejpam-5369	223	13	)	)	PUNCT
ejpam-5369	223	14	=	=	PUNCT
ejpam-5369	224	1	ac	ac	ADP
ejpam-5369	224	2	∪	∪	ADV
ejpam-5369	224	3	(	(	PUNCT
ejpam-5369	224	4	ac)⋄ω	ac)⋄ω	X
ejpam-5369	224	5	⊆	⊆	NUM
ejpam-5369	224	6	ac	ac	ADJ
ejpam-5369	224	7	∪ac	∪ac	PROPN
ejpam-5369	224	8	=	=	SYM
ejpam-5369	224	9	ac	ac	PROPN
ejpam-5369	224	10	a	a	DET
ejpam-5369	224	11	⊆	⊆	NUM
ejpam-5369	224	12	x	x	SYM
ejpam-5369	224	13	⇒	⇒	NOUN
ejpam-5369	224	14	ac	ac	PROPN
ejpam-5369	225	1	⊆	⊆	NUM
ejpam-5369	225	2	cl⋄ω(a	cl⋄ω(a	PROPN
ejpam-5369	225	3	c	c	PROPN
ejpam-5369	225	4	)	)	PUNCT
ejpam-5369	225	5	}	}	PUNCT
ejpam-5369	225	6	⇒	⇒	VERB
ejpam-5369	225	7	⇒	⇒	NOUN
ejpam-5369	225	8	ac	ac	PROPN
ejpam-5369	226	1	=	=	PUNCT
ejpam-5369	226	2	cl⋄ω(a	cl⋄ω(a	PROPN
ejpam-5369	226	3	c	c	PROPN
ejpam-5369	226	4	)	)	PUNCT
ejpam-5369	226	5	⇒	⇒	VERB
ejpam-5369	226	6	a	a	DET
ejpam-5369	226	7	∈	∈	PROPN
ejpam-5369	226	8	τ⋄ω	τ⋄ω	NUM
ejpam-5369	226	9	.	.	PUNCT
ejpam-5369	227	1	corollary	corollary	ADJ
ejpam-5369	227	2	4	4	NUM
ejpam-5369	227	3	.	.	PUNCT
ejpam-5369	228	1	we	we	PRON
ejpam-5369	228	2	have	have	VERB
ejpam-5369	228	3	the	the	DET
ejpam-5369	228	4	following	follow	VERB
ejpam-5369	228	5	diagram	diagram	NOUN
ejpam-5369	228	6	from	from	ADP
ejpam-5369	228	7	definitions	definition	NOUN
ejpam-5369	228	8	1	1	NUM
ejpam-5369	228	9	,	,	PUNCT
ejpam-5369	228	10	6	6	NUM
ejpam-5369	228	11	,	,	PUNCT
ejpam-5369	228	12	9	9	NUM
ejpam-5369	228	13	.	.	X
ejpam-5369	228	14	τ⋄r	τ⋄r	NOUN
ejpam-5369	228	15	-	-	NOUN
ejpam-5369	228	16	open	open	ADJ
ejpam-5369	228	17	→	→	SYM
ejpam-5369	228	18	τ⋄-open	τ⋄-open	ADJ
ejpam-5369	228	19	→	→	SYM
ejpam-5369	228	20	τ⋄ω	τ⋄ω	NUM
ejpam-5369	228	21	-	-	PUNCT
ejpam-5369	228	22	open	open	ADJ
ejpam-5369	228	23	↑	↑	PROPN
ejpam-5369	228	24	↑	↑	PROPN
ejpam-5369	228	25	↑	↑	PROPN
ejpam-5369	228	26	τδ	τδ	ADV
ejpam-5369	228	27	-	-	PUNCT
ejpam-5369	228	28	open	open	ADJ
ejpam-5369	228	29	→	→	ADP
ejpam-5369	228	30	τ	τ	X
ejpam-5369	228	31	-open	-open	NOUN
ejpam-5369	228	32	→	→	SYM
ejpam-5369	228	33	τω	τω	ADJ
ejpam-5369	228	34	-	-	ADJ
ejpam-5369	228	35	open	open	ADJ
ejpam-5369	228	36	remark	remark	NOUN
ejpam-5369	228	37	2	2	NUM
ejpam-5369	228	38	.	.	PUNCT
ejpam-5369	229	1	the	the	DET
ejpam-5369	229	2	converses	converse	NOUN
ejpam-5369	229	3	of	of	ADP
ejpam-5369	229	4	the	the	DET
ejpam-5369	229	5	implications	implication	NOUN
ejpam-5369	229	6	given	give	VERB
ejpam-5369	229	7	in	in	ADP
ejpam-5369	229	8	the	the	DET
ejpam-5369	229	9	above	above	ADJ
ejpam-5369	229	10	diagram	diagram	NOUN
ejpam-5369	229	11	need	need	VERB
ejpam-5369	229	12	not	not	PART
ejpam-5369	229	13	to	to	PART
ejpam-5369	229	14	be	be	AUX
ejpam-5369	229	15	true	true	ADJ
ejpam-5369	229	16	as	as	SCONJ
ejpam-5369	229	17	shown	show	VERB
ejpam-5369	229	18	by	by	ADP
ejpam-5369	229	19	the	the	DET
ejpam-5369	229	20	following	follow	VERB
ejpam-5369	229	21	examples	example	NOUN
ejpam-5369	229	22	.	.	PUNCT
ejpam-5369	230	1	example	example	NOUN
ejpam-5369	231	1	3	3	X
ejpam-5369	231	2	.	.	X
ejpam-5369	231	3	consider	consider	VERB
ejpam-5369	231	4	the	the	DET
ejpam-5369	231	5	topology	topology	NOUN
ejpam-5369	231	6	τ	τ	NOUN
ejpam-5369	231	7	=	=	PUNCT
ejpam-5369	231	8	{	{	PUNCT
ejpam-5369	231	9	u	u	NOUN
ejpam-5369	231	10	|0	|0	NUM
ejpam-5369	231	11	/∈	/∈	PUNCT
ejpam-5369	232	1	u	u	NOUN
ejpam-5369	232	2	}	}	PUNCT
ejpam-5369	232	3	∪	∪	VERB
ejpam-5369	232	4	{	{	PUNCT
ejpam-5369	232	5	r	r	NOUN
ejpam-5369	232	6	}	}	PUNCT
ejpam-5369	232	7	with	with	ADP
ejpam-5369	232	8	the	the	DET
ejpam-5369	232	9	primal	primal	ADJ
ejpam-5369	232	10	p	p	X
ejpam-5369	232	11	=	=	NOUN
ejpam-5369	232	12	2r\{0	2r\{0	NUM
ejpam-5369	232	13	}	}	PUNCT
ejpam-5369	232	14	on	on	ADP
ejpam-5369	232	15	r.	r.	PROPN
ejpam-5369	232	16	then	then	ADV
ejpam-5369	232	17	,	,	PUNCT
ejpam-5369	232	18	[	[	X
ejpam-5369	232	19	0,∞	0,∞	X
ejpam-5369	232	20	)	)	PUNCT
ejpam-5369	232	21	∈	∈	PROPN
ejpam-5369	232	22	τ⋄ω	τ⋄ω	PUNCT
ejpam-5369	233	1	but	but	CCONJ
ejpam-5369	233	2	[	[	X
ejpam-5369	233	3	0,∞	0,∞	NOUN
ejpam-5369	233	4	)	)	PUNCT
ejpam-5369	233	5	/∈	/∈	PUNCT
ejpam-5369	234	1	τω	τω	INTJ
ejpam-5369	234	2	.	.	NOUN
ejpam-5369	234	3	example	example	NOUN
ejpam-5369	235	1	4	4	X
ejpam-5369	235	2	.	.	PUNCT
ejpam-5369	235	3	let	let	VERB
ejpam-5369	235	4	x	x	PUNCT
ejpam-5369	235	5	=	=	PRON
ejpam-5369	235	6	{	{	PUNCT
ejpam-5369	235	7	a	a	PRON
ejpam-5369	235	8	,	,	PUNCT
ejpam-5369	235	9	b	b	NOUN
ejpam-5369	235	10	,	,	PUNCT
ejpam-5369	235	11	c	c	NOUN
ejpam-5369	235	12	}	}	PUNCT
ejpam-5369	235	13	with	with	ADP
ejpam-5369	235	14	the	the	DET
ejpam-5369	235	15	topology	topology	NOUN
ejpam-5369	235	16	τ	τ	X
ejpam-5369	235	17	=	=	PUNCT
ejpam-5369	235	18	{	{	PUNCT
ejpam-5369	235	19	∅	∅	NOUN
ejpam-5369	235	20	,	,	PUNCT
ejpam-5369	235	21	x	x	X
ejpam-5369	235	22	,	,	PUNCT
ejpam-5369	235	23	{	{	PUNCT
ejpam-5369	235	24	a	a	PRON
ejpam-5369	235	25	,	,	PUNCT
ejpam-5369	235	26	b	b	NOUN
ejpam-5369	235	27	}	}	PUNCT
ejpam-5369	235	28	}	}	PUNCT
ejpam-5369	235	29	.	.	PUNCT
ejpam-5369	236	1	we	we	PRON
ejpam-5369	236	2	consider	consider	VERB
ejpam-5369	236	3	the	the	DET
ejpam-5369	236	4	primal	primal	ADJ
ejpam-5369	236	5	p	p	X
ejpam-5369	236	6	=	=	PUNCT
ejpam-5369	236	7	2x	2x	NUM
ejpam-5369	236	8	\	\	NOUN
ejpam-5369	236	9	{	{	PUNCT
ejpam-5369	236	10	x	x	NOUN
ejpam-5369	236	11	,	,	PUNCT
ejpam-5369	236	12	{	{	PUNCT
ejpam-5369	236	13	a	a	DET
ejpam-5369	236	14	,	,	PUNCT
ejpam-5369	236	15	b	b	NOUN
ejpam-5369	236	16	}	}	PUNCT
ejpam-5369	236	17	}	}	PUNCT
ejpam-5369	236	18	on	on	ADP
ejpam-5369	236	19	x.	x.	NOUN
ejpam-5369	236	20	then	then	ADV
ejpam-5369	236	21	,	,	PUNCT
ejpam-5369	236	22	{	{	PUNCT
ejpam-5369	236	23	a	a	PRON
ejpam-5369	236	24	,	,	PUNCT
ejpam-5369	236	25	c	c	NOUN
ejpam-5369	236	26	}	}	PUNCT
ejpam-5369	236	27	∈	∈	PROPN
ejpam-5369	236	28	τ⋄ω	τ⋄ω	X
ejpam-5369	236	29	=	=	PUNCT
ejpam-5369	236	30	τω	τω	NOUN
ejpam-5369	236	31	=	=	NOUN
ejpam-5369	236	32	2x	2x	NOUN
ejpam-5369	236	33	but	but	CCONJ
ejpam-5369	236	34	{	{	PUNCT
ejpam-5369	236	35	a	a	X
ejpam-5369	236	36	,	,	PUNCT
ejpam-5369	236	37	c	c	NOUN
ejpam-5369	236	38	}	}	PUNCT
ejpam-5369	236	39	/∈	/∈	PUNCT
ejpam-5369	236	40	τ⋄	τ⋄	X
ejpam-5369	236	41	=	=	SYM
ejpam-5369	236	42	τ	τ	PROPN
ejpam-5369	236	43	.	.	PUNCT
ejpam-5369	237	1	p.	p.	NOUN
ejpam-5369	237	2	şaşmaz	şaşmaz	NUM
ejpam-5369	237	3	,	,	PUNCT
ejpam-5369	237	4	m.	m.	NOUN
ejpam-5369	237	5	özkoç	özkoç	PROPN
ejpam-5369	237	6	/	/	SYM
ejpam-5369	237	7	eur	eur	PROPN
ejpam-5369	237	8	.	.	PUNCT
ejpam-5369	238	1	j.	j.	PROPN
ejpam-5369	238	2	pure	pure	PROPN
ejpam-5369	238	3	appl	appl	PROPN
ejpam-5369	238	4	.	.	PROPN
ejpam-5369	238	5	math	math	PROPN
ejpam-5369	238	6	,	,	PUNCT
ejpam-5369	238	7	17	17	NUM
ejpam-5369	238	8	(	(	PUNCT
ejpam-5369	238	9	4	4	NUM
ejpam-5369	238	10	)	)	PUNCT
ejpam-5369	238	11	(	(	PUNCT
ejpam-5369	238	12	2024	2024	NUM
ejpam-5369	238	13	)	)	PUNCT
ejpam-5369	238	14	,	,	PUNCT
ejpam-5369	238	15	2800	2800	NUM
ejpam-5369	238	16	-	-	SYM
ejpam-5369	238	17	2811	2811	NUM
ejpam-5369	238	18	2808	2808	NUM
ejpam-5369	238	19	theorem	theorem	VERB
ejpam-5369	238	20	13	13	NUM
ejpam-5369	238	21	.	.	PUNCT
ejpam-5369	239	1	let	let	VERB
ejpam-5369	239	2	(	(	PUNCT
ejpam-5369	239	3	x	x	X
ejpam-5369	239	4	,	,	PUNCT
ejpam-5369	239	5	τ	τ	PROPN
ejpam-5369	239	6	,	,	PUNCT
ejpam-5369	239	7	p	p	NOUN
ejpam-5369	239	8	)	)	PUNCT
ejpam-5369	239	9	be	be	AUX
ejpam-5369	239	10	a	a	DET
ejpam-5369	239	11	primal	primal	ADJ
ejpam-5369	239	12	topological	topological	ADJ
ejpam-5369	239	13	space	space	NOUN
ejpam-5369	239	14	.	.	PUNCT
ejpam-5369	240	1	then	then	ADV
ejpam-5369	240	2	,	,	PUNCT
ejpam-5369	240	3	the	the	DET
ejpam-5369	240	4	following	follow	VERB
ejpam-5369	240	5	statements	statement	NOUN
ejpam-5369	240	6	hold	hold	VERB
ejpam-5369	240	7	:	:	PUNCT
ejpam-5369	240	8	(	(	PUNCT
ejpam-5369	240	9	a	a	X
ejpam-5369	240	10	)	)	PUNCT
ejpam-5369	240	11	if	if	SCONJ
ejpam-5369	240	12	p	p	NOUN
ejpam-5369	240	13	=	=	NOUN
ejpam-5369	240	14	∅	∅	NOUN
ejpam-5369	240	15	,	,	PUNCT
ejpam-5369	240	16	then	then	ADV
ejpam-5369	240	17	τ⋄ω	τ⋄ω	NUM
ejpam-5369	240	18	=	=	SYM
ejpam-5369	240	19	2x	2x	NUM
ejpam-5369	240	20	,	,	PUNCT
ejpam-5369	240	21	(	(	PUNCT
ejpam-5369	240	22	b	b	X
ejpam-5369	240	23	)	)	PUNCT
ejpam-5369	240	24	if	if	SCONJ
ejpam-5369	240	25	p	p	NOUN
ejpam-5369	240	26	=	=	SYM
ejpam-5369	240	27	2x	2x	NUM
ejpam-5369	240	28	\	\	NOUN
ejpam-5369	240	29	{	{	PUNCT
ejpam-5369	240	30	x	x	X
ejpam-5369	240	31	}	}	PUNCT
ejpam-5369	240	32	,	,	PUNCT
ejpam-5369	240	33	then	then	ADV
ejpam-5369	240	34	τω	τω	X
ejpam-5369	240	35	=	=	NOUN
ejpam-5369	240	36	τ⋄ω	τ⋄ω	NUM
ejpam-5369	240	37	.	.	PUNCT
ejpam-5369	241	1	proof	proof	NOUN
ejpam-5369	241	2	.	.	PUNCT
ejpam-5369	242	1	(	(	PUNCT
ejpam-5369	242	2	a	a	X
ejpam-5369	242	3	)	)	PUNCT
ejpam-5369	242	4	we	we	PRON
ejpam-5369	242	5	have	have	VERB
ejpam-5369	242	6	always	always	ADV
ejpam-5369	242	7	τ⋄ω	τ⋄ω	NUM
ejpam-5369	242	8	⊆	⊆	NUM
ejpam-5369	242	9	2x	2x	NUM
ejpam-5369	242	10	.	.	PUNCT
ejpam-5369	242	11	.	.	PUNCT
ejpam-5369	242	12	.	.	PUNCT
ejpam-5369	243	1	(	(	PUNCT
ejpam-5369	243	2	1	1	NUM
ejpam-5369	243	3	)	)	PUNCT
ejpam-5369	243	4	.	.	PUNCT
ejpam-5369	244	1	now	now	ADV
ejpam-5369	244	2	,	,	PUNCT
ejpam-5369	244	3	let	let	VERB
ejpam-5369	244	4	a	a	DET
ejpam-5369	244	5	∈	∈	NOUN
ejpam-5369	244	6	2x	2x	NUM
ejpam-5369	244	7	.	.	PUNCT
ejpam-5369	245	1	a	a	DET
ejpam-5369	245	2	∈	∈	PROPN
ejpam-5369	245	3	2x	2x	NUM
ejpam-5369	245	4	⇒	⇒	NOUN
ejpam-5369	245	5	cl⋄ω(a	cl⋄ω(a	PROPN
ejpam-5369	245	6	c	c	NOUN
ejpam-5369	245	7	)	)	PUNCT
ejpam-5369	245	8	=	=	NOUN
ejpam-5369	246	1	(	(	PUNCT
ejpam-5369	246	2	ac)⋄ω	ac)⋄ω	X
ejpam-5369	246	3	∪ac	∪ac	PROPN
ejpam-5369	246	4	p	p	NOUN
ejpam-5369	246	5	=	=	NOUN
ejpam-5369	246	6	∅	∅	NOUN
ejpam-5369	246	7	⇒	⇒	NOUN
ejpam-5369	246	8	(	(	PUNCT
ejpam-5369	246	9	ac)⋄ω	ac)⋄ω	X
ejpam-5369	246	10	=	=	NOUN
ejpam-5369	246	11	∅	∅	NOUN
ejpam-5369	246	12	}	}	PUNCT
ejpam-5369	246	13	⇒	⇒	VERB
ejpam-5369	246	14	cl⋄ω(a	cl⋄ω(a	PROPN
ejpam-5369	246	15	c	c	NOUN
ejpam-5369	246	16	)	)	PUNCT
ejpam-5369	246	17	=	=	PUNCT
ejpam-5369	246	18	ac	ac	PROPN
ejpam-5369	246	19	⇒	⇒	VERB
ejpam-5369	246	20	a	a	DET
ejpam-5369	246	21	∈	∈	PROPN
ejpam-5369	246	22	τ⋄ω	τ⋄ω	PUNCT
ejpam-5369	246	23	then	then	ADV
ejpam-5369	246	24	,	,	PUNCT
ejpam-5369	246	25	we	we	PRON
ejpam-5369	246	26	have	have	VERB
ejpam-5369	246	27	2x	2x	NUM
ejpam-5369	246	28	⊆	⊆	NUM
ejpam-5369	246	29	τ⋄ω	τ⋄ω	NUM
ejpam-5369	246	30	.	.	PUNCT
ejpam-5369	246	31	.	.	PUNCT
ejpam-5369	246	32	.	.	PUNCT
ejpam-5369	247	1	(	(	PUNCT
ejpam-5369	247	2	2	2	X
ejpam-5369	247	3	)	)	PUNCT
ejpam-5369	247	4	(	(	PUNCT
ejpam-5369	247	5	1	1	NUM
ejpam-5369	247	6	)	)	PUNCT
ejpam-5369	247	7	,	,	PUNCT
ejpam-5369	247	8	(	(	PUNCT
ejpam-5369	247	9	2	2	X
ejpam-5369	247	10	)	)	PUNCT
ejpam-5369	247	11	⇒	⇒	NOUN
ejpam-5369	247	12	τ⋄ω	τ⋄ω	NUM
ejpam-5369	248	1	=	=	SYM
ejpam-5369	248	2	2x	2x	NUM
ejpam-5369	248	3	.	.	PUNCT
ejpam-5369	249	1	(	(	PUNCT
ejpam-5369	249	2	b	b	X
ejpam-5369	249	3	)	)	PUNCT
ejpam-5369	249	4	we	we	PRON
ejpam-5369	249	5	have	have	VERB
ejpam-5369	249	6	τω	τω	PRON
ejpam-5369	249	7	⊆	⊆	NUM
ejpam-5369	249	8	τ⋄ω	τ⋄ω	NUM
ejpam-5369	249	9	.	.	PUNCT
ejpam-5369	249	10	.	.	PUNCT
ejpam-5369	249	11	.	.	PUNCT
ejpam-5369	250	1	(	(	PUNCT
ejpam-5369	250	2	1	1	NUM
ejpam-5369	250	3	)	)	PUNCT
ejpam-5369	250	4	.	.	PUNCT
ejpam-5369	251	1	now	now	ADV
ejpam-5369	251	2	,	,	PUNCT
ejpam-5369	251	3	let	let	VERB
ejpam-5369	251	4	a	a	DET
ejpam-5369	251	5	∈	∈	NOUN
ejpam-5369	251	6	τ⋄ω	τ⋄ω	NUM
ejpam-5369	251	7	.	.	PUNCT
ejpam-5369	252	1	we	we	PRON
ejpam-5369	252	2	will	will	AUX
ejpam-5369	252	3	prove	prove	VERB
ejpam-5369	252	4	that	that	SCONJ
ejpam-5369	252	5	a	a	DET
ejpam-5369	252	6	∈	∈	PROPN
ejpam-5369	252	7	τω	τω	INTJ
ejpam-5369	252	8	.	.	PUNCT
ejpam-5369	253	1	a	a	DET
ejpam-5369	253	2	∈	∈	PROPN
ejpam-5369	253	3	τ⋄ω	τ⋄ω	NUM
ejpam-5369	253	4	⇒	⇒	PROPN
ejpam-5369	253	5	cl⋄ω(a	cl⋄ω(a	PROPN
ejpam-5369	253	6	c	c	NOUN
ejpam-5369	253	7	)	)	PUNCT
ejpam-5369	253	8	=	=	PUNCT
ejpam-5369	253	9	ac	ac	PROPN
ejpam-5369	253	10	⇒	⇒	PROPN
ejpam-5369	253	11	ac	ac	PROPN
ejpam-5369	253	12	∪	∪	ADV
ejpam-5369	253	13	(	(	PUNCT
ejpam-5369	253	14	ac)⋄ω	ac)⋄ω	X
ejpam-5369	253	15	=	=	SYM
ejpam-5369	253	16	ac	ac	ADJ
ejpam-5369	253	17	⇒	⇒	NOUN
ejpam-5369	253	18	(	(	PUNCT
ejpam-5369	253	19	ac)⋄ω	ac)⋄ω	X
ejpam-5369	253	20	⊆	⊆	NUM
ejpam-5369	253	21	ac	ac	NOUN
ejpam-5369	253	22	.	.	PUNCT
ejpam-5369	253	23	.	.	PUNCT
ejpam-5369	253	24	.	.	PUNCT
ejpam-5369	254	1	(	(	PUNCT
ejpam-5369	254	2	2	2	X
ejpam-5369	254	3	)	)	PUNCT
ejpam-5369	254	4	now	now	ADV
ejpam-5369	254	5	,	,	PUNCT
ejpam-5369	254	6	let	let	VERB
ejpam-5369	254	7	x	x	PRON
ejpam-5369	254	8	/∈	/∈	VERB
ejpam-5369	254	9	(	(	PUNCT
ejpam-5369	254	10	ac)⋄ω	ac)⋄ω	NOUN
ejpam-5369	254	11	.	.	NOUN
ejpam-5369	254	12	x	x	X
ejpam-5369	254	13	/∈	/∈	PUNCT
ejpam-5369	255	1	(	(	PUNCT
ejpam-5369	255	2	ac)⋄ω	ac)⋄ω	X
ejpam-5369	255	3	⇒	⇒	NOUN
ejpam-5369	255	4	(	(	PUNCT
ejpam-5369	255	5	∃u	∃u	PROPN
ejpam-5369	255	6	∈	∈	PROPN
ejpam-5369	255	7	ωo(x	ωo(x	NUM
ejpam-5369	255	8	,	,	PUNCT
ejpam-5369	255	9	x))(u	x))(u	PROPN
ejpam-5369	255	10	c	c	NOUN
ejpam-5369	255	11	∪a	∪a	NUM
ejpam-5369	255	12	/∈	/∈	PUNCT
ejpam-5369	256	1	p	p	X
ejpam-5369	256	2	)	)	PUNCT
ejpam-5369	256	3	p	p	NOUN
ejpam-5369	256	4	=	=	PUNCT
ejpam-5369	256	5	2x	2x	NUM
ejpam-5369	256	6	\	\	NOUN
ejpam-5369	256	7	{	{	PUNCT
ejpam-5369	256	8	x	x	NOUN
ejpam-5369	256	9	}	}	PUNCT
ejpam-5369	256	10	}	}	PUNCT
ejpam-5369	256	11	⇒	⇒	NOUN
ejpam-5369	256	12	(	(	PUNCT
ejpam-5369	256	13	∃u	∃u	PROPN
ejpam-5369	256	14	∈	∈	PROPN
ejpam-5369	256	15	ωo(x	ωo(x	NUM
ejpam-5369	256	16	,	,	PUNCT
ejpam-5369	256	17	x))(u	x))(u	PROPN
ejpam-5369	256	18	c	c	NOUN
ejpam-5369	256	19	∪a	∪a	NUM
ejpam-5369	256	20	=	=	SYM
ejpam-5369	256	21	x	x	X
ejpam-5369	256	22	)	)	PUNCT
ejpam-5369	256	23	⇒	⇒	NOUN
ejpam-5369	256	24	(	(	PUNCT
ejpam-5369	256	25	∃u	∃u	PROPN
ejpam-5369	256	26	∈	∈	PROPN
ejpam-5369	256	27	ωo(x	ωo(x	NUM
ejpam-5369	256	28	,	,	PUNCT
ejpam-5369	256	29	x))(u	x))(u	ADJ
ejpam-5369	256	30	∩ac	∩ac	NOUN
ejpam-5369	256	31	=	=	SYM
ejpam-5369	256	32	∅	∅	NOUN
ejpam-5369	256	33	)	)	PUNCT
ejpam-5369	256	34	⇒	⇒	NOUN
ejpam-5369	256	35	x	x	X
ejpam-5369	256	36	/∈	/∈	PUNCT
ejpam-5369	257	1	ω	ω	X
ejpam-5369	257	2	-	-	PUNCT
ejpam-5369	257	3	cl(ac	cl(ac	PROPN
ejpam-5369	257	4	)	)	PUNCT
ejpam-5369	257	5	then	then	ADV
ejpam-5369	257	6	,	,	PUNCT
ejpam-5369	257	7	we	we	PRON
ejpam-5369	257	8	get	get	VERB
ejpam-5369	257	9	ω	ω	NOUN
ejpam-5369	257	10	-	-	NOUN
ejpam-5369	257	11	cl(ac	cl(ac	PROPN
ejpam-5369	257	12	)	)	PUNCT
ejpam-5369	258	1	⊆	⊆	NUM
ejpam-5369	258	2	(	(	PUNCT
ejpam-5369	258	3	ac)⋄ω	ac)⋄ω	NOUN
ejpam-5369	258	4	.	.	PUNCT
ejpam-5369	258	5	.	.	PUNCT
ejpam-5369	258	6	.	.	PUNCT
ejpam-5369	259	1	(	(	PUNCT
ejpam-5369	259	2	3	3	NUM
ejpam-5369	259	3	)	)	PUNCT
ejpam-5369	259	4	.	.	PUNCT
ejpam-5369	260	1	thus	thus	ADV
ejpam-5369	260	2	,	,	PUNCT
ejpam-5369	260	3	we	we	PRON
ejpam-5369	260	4	have	have	VERB
ejpam-5369	260	5	ω	ω	VERB
ejpam-5369	260	6	-	-	NOUN
ejpam-5369	260	7	cl(ac	cl(ac	PROPN
ejpam-5369	260	8	)	)	PUNCT
ejpam-5369	261	1	⊆	⊆	NUM
ejpam-5369	261	2	ac	ac	ADV
ejpam-5369	261	3	from	from	ADP
ejpam-5369	261	4	(	(	PUNCT
ejpam-5369	261	5	2	2	NUM
ejpam-5369	261	6	)	)	PUNCT
ejpam-5369	261	7	and	and	CCONJ
ejpam-5369	261	8	(	(	PUNCT
ejpam-5369	261	9	3	3	NUM
ejpam-5369	261	10	)	)	PUNCT
ejpam-5369	261	11	.	.	PUNCT
ejpam-5369	262	1	therefore	therefore	ADV
ejpam-5369	262	2	,	,	PUNCT
ejpam-5369	262	3	ω	ω	PROPN
ejpam-5369	262	4	-	-	NOUN
ejpam-5369	262	5	cl(ac	cl(ac	PROPN
ejpam-5369	262	6	)	)	PUNCT
ejpam-5369	263	1	=	=	PUNCT
ejpam-5369	263	2	ac	ac	PROPN
ejpam-5369	263	3	.	.	PUNCT
ejpam-5369	264	1	hence	hence	ADV
ejpam-5369	264	2	,	,	PUNCT
ejpam-5369	264	3	a	a	PRON
ejpam-5369	264	4	is	be	AUX
ejpam-5369	264	5	ω	ω	NOUN
ejpam-5369	264	6	-	-	ADJ
ejpam-5369	264	7	open	open	ADJ
ejpam-5369	264	8	.	.	PUNCT
ejpam-5369	265	1	remark	remark	NOUN
ejpam-5369	265	2	3	3	NUM
ejpam-5369	265	3	.	.	PUNCT
ejpam-5369	266	1	the	the	DET
ejpam-5369	266	2	converse	converse	NOUN
ejpam-5369	266	3	of	of	ADP
ejpam-5369	266	4	theorem	theorem	PROPN
ejpam-5369	266	5	13(b	13(b	NUM
ejpam-5369	266	6	)	)	PUNCT
ejpam-5369	266	7	need	need	VERB
ejpam-5369	266	8	not	not	PART
ejpam-5369	266	9	to	to	PART
ejpam-5369	266	10	be	be	AUX
ejpam-5369	266	11	true	true	ADJ
ejpam-5369	266	12	as	as	SCONJ
ejpam-5369	266	13	shown	show	VERB
ejpam-5369	266	14	by	by	ADP
ejpam-5369	266	15	the	the	DET
ejpam-5369	266	16	following	follow	VERB
ejpam-5369	266	17	example	example	NOUN
ejpam-5369	266	18	.	.	PUNCT
ejpam-5369	267	1	example	example	NOUN
ejpam-5369	268	1	5	5	NUM
ejpam-5369	268	2	.	.	PUNCT
ejpam-5369	268	3	let	let	VERB
ejpam-5369	268	4	x	x	PUNCT
ejpam-5369	268	5	=	=	PRON
ejpam-5369	268	6	{	{	PUNCT
ejpam-5369	268	7	a	a	PRON
ejpam-5369	268	8	,	,	PUNCT
ejpam-5369	268	9	b	b	NOUN
ejpam-5369	268	10	,	,	PUNCT
ejpam-5369	268	11	c	c	NOUN
ejpam-5369	268	12	}	}	PUNCT
ejpam-5369	268	13	with	with	ADP
ejpam-5369	268	14	the	the	DET
ejpam-5369	268	15	discrete	discrete	ADJ
ejpam-5369	268	16	topology	topology	NOUN
ejpam-5369	268	17	τ	τ	PROPN
ejpam-5369	268	18	and	and	CCONJ
ejpam-5369	268	19	p	p	NOUN
ejpam-5369	268	20	=	=	PROPN
ejpam-5369	268	21	2x	2x	NUM
ejpam-5369	268	22	\{x	\{x	NOUN
ejpam-5369	268	23	,	,	PUNCT
ejpam-5369	268	24	{	{	PUNCT
ejpam-5369	268	25	b	b	NOUN
ejpam-5369	268	26	,	,	PUNCT
ejpam-5369	268	27	c	c	NOUN
ejpam-5369	268	28	}	}	PUNCT
ejpam-5369	268	29	}	}	PUNCT
ejpam-5369	268	30	.	.	PUNCT
ejpam-5369	269	1	then	then	ADV
ejpam-5369	269	2	,	,	PUNCT
ejpam-5369	269	3	τω	τω	X
ejpam-5369	269	4	=	=	PUNCT
ejpam-5369	269	5	τ⋄ω	τ⋄ω	PROPN
ejpam-5369	270	1	but	but	CCONJ
ejpam-5369	270	2	p	p	NOUN
ejpam-5369	270	3	=	=	NOUN
ejpam-5369	270	4	̸	̸	NUM
ejpam-5369	270	5	2x	2x	NUM
ejpam-5369	270	6	\	\	NOUN
ejpam-5369	270	7	{	{	PUNCT
ejpam-5369	270	8	x	x	NOUN
ejpam-5369	270	9	}	}	PUNCT
ejpam-5369	270	10	.	.	PUNCT
ejpam-5369	271	1	theorem	theorem	NOUN
ejpam-5369	271	2	14	14	NUM
ejpam-5369	271	3	.	.	PUNCT
ejpam-5369	272	1	let	let	VERB
ejpam-5369	272	2	(	(	PUNCT
ejpam-5369	272	3	x	x	X
ejpam-5369	272	4	,	,	PUNCT
ejpam-5369	272	5	τ	τ	PROPN
ejpam-5369	272	6	,	,	PUNCT
ejpam-5369	272	7	p	p	NOUN
ejpam-5369	272	8	)	)	PUNCT
ejpam-5369	272	9	be	be	AUX
ejpam-5369	272	10	a	a	DET
ejpam-5369	272	11	primal	primal	ADJ
ejpam-5369	272	12	topological	topological	ADJ
ejpam-5369	272	13	space	space	NOUN
ejpam-5369	272	14	and	and	CCONJ
ejpam-5369	272	15	a	a	DET
ejpam-5369	272	16	⊆	⊆	NUM
ejpam-5369	272	17	x.	x.	NOUN
ejpam-5369	272	18	then	then	ADV
ejpam-5369	272	19	,	,	PUNCT
ejpam-5369	272	20	a	a	DET
ejpam-5369	272	21	∈	∈	NOUN
ejpam-5369	272	22	τ⋄ω	τ⋄ω	PUNCT
ejpam-5369	273	1	if	if	SCONJ
ejpam-5369	273	2	and	and	CCONJ
ejpam-5369	273	3	only	only	ADV
ejpam-5369	273	4	if	if	SCONJ
ejpam-5369	273	5	for	for	ADP
ejpam-5369	273	6	all	all	DET
ejpam-5369	273	7	x	x	NOUN
ejpam-5369	273	8	in	in	ADP
ejpam-5369	273	9	a	a	PRON
ejpam-5369	273	10	,	,	PUNCT
ejpam-5369	273	11	there	there	PRON
ejpam-5369	273	12	exists	exist	VERB
ejpam-5369	273	13	an	an	DET
ejpam-5369	273	14	ω	ω	ADJ
ejpam-5369	273	15	-	-	ADJ
ejpam-5369	273	16	open	open	ADJ
ejpam-5369	273	17	set	set	NOUN
ejpam-5369	273	18	u	u	NOUN
ejpam-5369	273	19	containing	contain	VERB
ejpam-5369	273	20	x	x	PUNCT
ejpam-5369	273	21	such	such	ADJ
ejpam-5369	273	22	that	that	SCONJ
ejpam-5369	273	23	u	u	NOUN
ejpam-5369	273	24	c∪a	c∪a	NOUN
ejpam-5369	273	25	/∈	/∈	PUNCT
ejpam-5369	274	1	p.	p.	NOUN
ejpam-5369	274	2	proof	proof	NOUN
ejpam-5369	274	3	.	.	PUNCT
ejpam-5369	275	1	let	let	VERB
ejpam-5369	275	2	a	a	DET
ejpam-5369	275	3	∈	∈	NOUN
ejpam-5369	275	4	τ⋄ω	τ⋄ω	NUM
ejpam-5369	275	5	.	.	PUNCT
ejpam-5369	276	1	a	a	DET
ejpam-5369	276	2	∈	∈	PROPN
ejpam-5369	276	3	τ⋄ω	τ⋄ω	NUM
ejpam-5369	276	4	⇔	⇔	PROPN
ejpam-5369	276	5	cl⋄ω(a	cl⋄ω(a	PROPN
ejpam-5369	276	6	c	c	PROPN
ejpam-5369	276	7	)	)	PUNCT
ejpam-5369	276	8	=	=	SYM
ejpam-5369	276	9	ac	ac	PROPN
ejpam-5369	276	10	⇔	⇔	PROPN
ejpam-5369	276	11	ac	ac	PROPN
ejpam-5369	276	12	∪	∪	ADV
ejpam-5369	276	13	(	(	PUNCT
ejpam-5369	276	14	ac)⋄ω	ac)⋄ω	X
ejpam-5369	276	15	=	=	SYM
ejpam-5369	276	16	ac	ac	PROPN
ejpam-5369	276	17	⇔	⇔	PROPN
ejpam-5369	276	18	(	(	PUNCT
ejpam-5369	276	19	ac)⋄ω	ac)⋄ω	PROPN
ejpam-5369	276	20	⊆	⊆	NUM
ejpam-5369	276	21	ac	ac	PROPN
ejpam-5369	276	22	⇔	⇔	PROPN
ejpam-5369	276	23	a	a	PRON
ejpam-5369	276	24	⊆	⊆	NUM
ejpam-5369	276	25	(	(	PUNCT
ejpam-5369	276	26	(	(	PUNCT
ejpam-5369	276	27	ac)⋄ω	ac)⋄ω	NOUN
ejpam-5369	276	28	)	)	PUNCT
ejpam-5369	276	29	c	c	NOUN
ejpam-5369	276	30	⇔	⇔	X
ejpam-5369	276	31	(	(	PUNCT
ejpam-5369	276	32	∀x	∀x	X
ejpam-5369	276	33	∈	∈	PROPN
ejpam-5369	276	34	a)(x	a)(x	NOUN
ejpam-5369	276	35	/∈	/∈	PUNCT
ejpam-5369	276	36	(	(	PUNCT
ejpam-5369	276	37	ac)⋄ω	ac)⋄ω	NOUN
ejpam-5369	276	38	)	)	PUNCT
ejpam-5369	276	39	⇔	⇔	X
ejpam-5369	276	40	(	(	PUNCT
ejpam-5369	276	41	∀x	∀x	X
ejpam-5369	276	42	∈	∈	PROPN
ejpam-5369	276	43	a)(∃u	a)(∃u	NOUN
ejpam-5369	276	44	∈	∈	PROPN
ejpam-5369	276	45	ωo(x	ωo(x	NUM
ejpam-5369	276	46	,	,	PUNCT
ejpam-5369	276	47	x))(u	x))(u	PROPN
ejpam-5369	276	48	c	c	PROPN
ejpam-5369	276	49	∪	∪	X
ejpam-5369	276	50	(	(	PUNCT
ejpam-5369	276	51	ac)c	ac)c	PROPN
ejpam-5369	276	52	=	=	SYM
ejpam-5369	276	53	u	u	NOUN
ejpam-5369	276	54	c	c	NOUN
ejpam-5369	276	55	∪a	∪a	NUM
ejpam-5369	276	56	/∈	/∈	PUNCT
ejpam-5369	277	1	p	p	X
ejpam-5369	277	2	)	)	PUNCT
ejpam-5369	277	3	.	.	PUNCT
ejpam-5369	278	1	theorem	theorem	NOUN
ejpam-5369	278	2	15	15	NUM
ejpam-5369	278	3	.	.	PUNCT
ejpam-5369	279	1	let	let	VERB
ejpam-5369	279	2	(	(	PUNCT
ejpam-5369	279	3	x	x	X
ejpam-5369	279	4	,	,	PUNCT
ejpam-5369	279	5	τ	τ	PROPN
ejpam-5369	279	6	,	,	PUNCT
ejpam-5369	279	7	p	p	NOUN
ejpam-5369	279	8	)	)	PUNCT
ejpam-5369	279	9	be	be	AUX
ejpam-5369	279	10	a	a	DET
ejpam-5369	279	11	primal	primal	ADJ
ejpam-5369	279	12	topological	topological	ADJ
ejpam-5369	279	13	space	space	NOUN
ejpam-5369	279	14	and	and	CCONJ
ejpam-5369	279	15	a	a	DET
ejpam-5369	279	16	⊆	⊆	NUM
ejpam-5369	279	17	x.	x.	NOUN
ejpam-5369	279	18	if	if	SCONJ
ejpam-5369	279	19	a	a	PRON
ejpam-5369	279	20	/∈	/∈	NOUN
ejpam-5369	280	1	p	p	NOUN
ejpam-5369	280	2	,	,	PUNCT
ejpam-5369	280	3	then	then	ADV
ejpam-5369	280	4	a	a	DET
ejpam-5369	280	5	∈	∈	NOUN
ejpam-5369	280	6	τ⋄ω	τ⋄ω	NUM
ejpam-5369	280	7	.	.	PUNCT
ejpam-5369	281	1	p.	p.	NOUN
ejpam-5369	281	2	şaşmaz	şaşmaz	NUM
ejpam-5369	281	3	,	,	PUNCT
ejpam-5369	281	4	m.	m.	NOUN
ejpam-5369	281	5	özkoç	özkoç	PROPN
ejpam-5369	281	6	/	/	SYM
ejpam-5369	281	7	eur	eur	PROPN
ejpam-5369	281	8	.	.	PUNCT
ejpam-5369	282	1	j.	j.	PROPN
ejpam-5369	282	2	pure	pure	PROPN
ejpam-5369	282	3	appl	appl	PROPN
ejpam-5369	282	4	.	.	PROPN
ejpam-5369	282	5	math	math	PROPN
ejpam-5369	282	6	,	,	PUNCT
ejpam-5369	282	7	17	17	NUM
ejpam-5369	282	8	(	(	PUNCT
ejpam-5369	282	9	4	4	NUM
ejpam-5369	282	10	)	)	PUNCT
ejpam-5369	282	11	(	(	PUNCT
ejpam-5369	282	12	2024	2024	NUM
ejpam-5369	282	13	)	)	PUNCT
ejpam-5369	282	14	,	,	PUNCT
ejpam-5369	282	15	2800	2800	NUM
ejpam-5369	282	16	-	-	SYM
ejpam-5369	282	17	2811	2811	NUM
ejpam-5369	282	18	2809	2809	NUM
ejpam-5369	282	19	proof	proof	NOUN
ejpam-5369	282	20	.	.	PUNCT
ejpam-5369	283	1	let	let	VERB
ejpam-5369	283	2	a	a	DET
ejpam-5369	283	3	/∈	/∈	PUNCT
ejpam-5369	283	4	p	p	NOUN
ejpam-5369	284	1	and	and	CCONJ
ejpam-5369	284	2	x	x	SYM
ejpam-5369	284	3	∈	∈	NOUN
ejpam-5369	284	4	a.	a.	NOUN
ejpam-5369	284	5	(	(	PUNCT
ejpam-5369	284	6	u	u	NOUN
ejpam-5369	284	7	:	:	PUNCT
ejpam-5369	284	8	=	=	SYM
ejpam-5369	284	9	x)(x	x)(x	PROPN
ejpam-5369	284	10	∈	∈	PROPN
ejpam-5369	284	11	a	a	PRON
ejpam-5369	284	12	)	)	PUNCT
ejpam-5369	284	13	⇒	⇒	NOUN
ejpam-5369	284	14	(	(	PUNCT
ejpam-5369	284	15	u	u	NOUN
ejpam-5369	284	16	∈	∈	PROPN
ejpam-5369	284	17	ωo(x	ωo(x	NUM
ejpam-5369	284	18	,	,	PUNCT
ejpam-5369	284	19	x))(a	x))(a	X
ejpam-5369	284	20	=	=	SYM
ejpam-5369	284	21	u	u	PROPN
ejpam-5369	284	22	c	c	NOUN
ejpam-5369	284	23	∪a	∪a	NUM
ejpam-5369	284	24	)	)	PUNCT
ejpam-5369	285	1	a	a	PRON
ejpam-5369	285	2	/∈	/∈	NOUN
ejpam-5369	285	3	p	p	NOUN
ejpam-5369	285	4	}	}	PUNCT
ejpam-5369	285	5	⇒	⇒	VERB
ejpam-5369	285	6	u	u	NOUN
ejpam-5369	285	7	c	c	PROPN
ejpam-5369	285	8	∪a	∪a	NUM
ejpam-5369	285	9	/∈	/∈	PUNCT
ejpam-5369	286	1	p	p	X
ejpam-5369	286	2	therefore	therefore	ADV
ejpam-5369	286	3	,	,	PUNCT
ejpam-5369	286	4	we	we	PRON
ejpam-5369	286	5	get	get	VERB
ejpam-5369	286	6	a	a	DET
ejpam-5369	286	7	∈	∈	NOUN
ejpam-5369	286	8	τ⋄ω	τ⋄ω	NUM
ejpam-5369	286	9	from	from	ADP
ejpam-5369	286	10	theorem	theorem	ADJ
ejpam-5369	286	11	14	14	NUM
ejpam-5369	286	12	.	.	PUNCT
ejpam-5369	287	1	theorem	theorem	VERB
ejpam-5369	287	2	16	16	NUM
ejpam-5369	287	3	.	.	PUNCT
ejpam-5369	288	1	let	let	VERB
ejpam-5369	288	2	(	(	PUNCT
ejpam-5369	288	3	x	x	X
ejpam-5369	288	4	,	,	PUNCT
ejpam-5369	288	5	τ	τ	PROPN
ejpam-5369	288	6	,	,	PUNCT
ejpam-5369	288	7	p	p	NOUN
ejpam-5369	288	8	)	)	PUNCT
ejpam-5369	288	9	be	be	AUX
ejpam-5369	288	10	a	a	DET
ejpam-5369	288	11	primal	primal	ADJ
ejpam-5369	288	12	topological	topological	ADJ
ejpam-5369	288	13	space	space	NOUN
ejpam-5369	288	14	.	.	PUNCT
ejpam-5369	289	1	then	then	ADV
ejpam-5369	289	2	,	,	PUNCT
ejpam-5369	289	3	the	the	DET
ejpam-5369	289	4	family	family	NOUN
ejpam-5369	289	5	b	b	PROPN
ejpam-5369	289	6	=	=	SYM
ejpam-5369	289	7	{	{	PUNCT
ejpam-5369	289	8	t	t	PROPN
ejpam-5369	289	9	∩	∩	PROPN
ejpam-5369	289	10	p	p	PROPN
ejpam-5369	289	11	|	|	NOUN
ejpam-5369	289	12	t	t	PROPN
ejpam-5369	289	13	∈	∈	PROPN
ejpam-5369	289	14	τω	τω	INTJ
ejpam-5369	289	15	and	and	CCONJ
ejpam-5369	289	16	p	p	NOUN
ejpam-5369	289	17	/∈	/∈	PUNCT
ejpam-5369	290	1	p	p	X
ejpam-5369	290	2	}	}	PUNCT
ejpam-5369	290	3	is	be	AUX
ejpam-5369	290	4	a	a	DET
ejpam-5369	290	5	base	base	NOUN
ejpam-5369	290	6	for	for	ADP
ejpam-5369	290	7	the	the	DET
ejpam-5369	290	8	topology	topology	NOUN
ejpam-5369	290	9	τ⋄ω	τ⋄ω	PUNCT
ejpam-5369	290	10	on	on	ADP
ejpam-5369	290	11	x.	x.	NOUN
ejpam-5369	290	12	proof	proof	NOUN
ejpam-5369	290	13	.	.	PUNCT
ejpam-5369	291	1	let	let	VERB
ejpam-5369	291	2	b	b	X
ejpam-5369	291	3	∈	∈	PROPN
ejpam-5369	291	4	b.	b.	PROPN
ejpam-5369	291	5	b	b	PROPN
ejpam-5369	291	6	∈	∈	PROPN
ejpam-5369	291	7	b	b	PROPN
ejpam-5369	291	8	⇒	⇒	NOUN
ejpam-5369	291	9	(	(	PUNCT
ejpam-5369	291	10	∃t	∃t	NOUN
ejpam-5369	291	11	∈	∈	PROPN
ejpam-5369	291	12	τω)(∃p	τω)(∃p	PUNCT
ejpam-5369	291	13	/∈	/∈	PUNCT
ejpam-5369	292	1	p)(b	p)(b	PUNCT
ejpam-5369	293	1	=	=	PUNCT
ejpam-5369	293	2	t	t	PROPN
ejpam-5369	293	3	∩	∩	NOUN
ejpam-5369	293	4	p	p	NOUN
ejpam-5369	293	5	)	)	PUNCT
ejpam-5369	293	6	τω	τω	ADP
ejpam-5369	293	7	⊆	⊆	NUM
ejpam-5369	293	8	τ⋄ω	τ⋄ω	NUM
ejpam-5369	293	9	}	}	PUNCT
ejpam-5369	293	10	theorem	theorem	VERB
ejpam-5369	293	11	15⇒	15⇒	NUM
ejpam-5369	293	12	(	(	PUNCT
ejpam-5369	293	13	t	t	PROPN
ejpam-5369	293	14	,	,	PUNCT
ejpam-5369	293	15	p	p	PROPN
ejpam-5369	293	16	∈	∈	PROPN
ejpam-5369	293	17	τ⋄ω)(b	τ⋄ω)(b	PROPN
ejpam-5369	293	18	=	=	SYM
ejpam-5369	293	19	t	t	PROPN
ejpam-5369	293	20	∩	∩	PROPN
ejpam-5369	293	21	p	p	X
ejpam-5369	293	22	)	)	PUNCT
ejpam-5369	293	23	⇒	⇒	PROPN
ejpam-5369	293	24	b	b	PROPN
ejpam-5369	293	25	∈	∈	PROPN
ejpam-5369	293	26	τ⋄ω	τ⋄ω	PUNCT
ejpam-5369	294	1	then	then	ADV
ejpam-5369	294	2	,	,	PUNCT
ejpam-5369	294	3	we	we	PRON
ejpam-5369	294	4	have	have	VERB
ejpam-5369	294	5	b	b	NUM
ejpam-5369	294	6	⊆	⊆	NUM
ejpam-5369	294	7	τ⋄ω	τ⋄ω	NUM
ejpam-5369	294	8	.	.	PUNCT
ejpam-5369	294	9	.	.	PUNCT
ejpam-5369	294	10	.	.	PUNCT
ejpam-5369	295	1	(	(	PUNCT
ejpam-5369	295	2	1	1	X
ejpam-5369	295	3	)	)	PUNCT
ejpam-5369	295	4	now	now	ADV
ejpam-5369	295	5	,	,	PUNCT
ejpam-5369	295	6	let	let	VERB
ejpam-5369	295	7	a	a	DET
ejpam-5369	295	8	∈	∈	NOUN
ejpam-5369	295	9	τ⋄ω	τ⋄ω	PUNCT
ejpam-5369	295	10	and	and	CCONJ
ejpam-5369	295	11	x	x	PUNCT
ejpam-5369	295	12	∈	∈	NOUN
ejpam-5369	295	13	a.	a.	NOUN
ejpam-5369	295	14	x	x	PUNCT
ejpam-5369	295	15	∈	∈	PROPN
ejpam-5369	295	16	a	a	DET
ejpam-5369	295	17	∈	∈	PROPN
ejpam-5369	295	18	τ⋄ω	τ⋄ω	NUM
ejpam-5369	295	19	⇒	⇒	NOUN
ejpam-5369	295	20	(	(	PUNCT
ejpam-5369	295	21	∃u	∃u	PROPN
ejpam-5369	295	22	∈	∈	PROPN
ejpam-5369	295	23	ωo(x	ωo(x	NUM
ejpam-5369	295	24	,	,	PUNCT
ejpam-5369	295	25	x))(u	x))(u	PROPN
ejpam-5369	295	26	c	c	NOUN
ejpam-5369	295	27	∪a	∪a	NUM
ejpam-5369	295	28	/∈	/∈	PUNCT
ejpam-5369	296	1	p	p	X
ejpam-5369	296	2	)	)	PUNCT
ejpam-5369	296	3	b	b	NOUN
ejpam-5369	296	4	:	:	PUNCT
ejpam-5369	296	5	=	=	SYM
ejpam-5369	296	6	u	u	NOUN
ejpam-5369	296	7	∩	∩	NOUN
ejpam-5369	296	8	(	(	PUNCT
ejpam-5369	296	9	u	u	X
ejpam-5369	296	10	c	c	NOUN
ejpam-5369	296	11	∪a	∪a	NUM
ejpam-5369	296	12	)	)	PUNCT
ejpam-5369	296	13	}	}	PUNCT
ejpam-5369	296	14	⇒	⇒	NOUN
ejpam-5369	296	15	(	(	PUNCT
ejpam-5369	296	16	b	b	X
ejpam-5369	296	17	∈	∈	ADJ
ejpam-5369	296	18	b)(x	b)(x	PROPN
ejpam-5369	296	19	∈	∈	PROPN
ejpam-5369	296	20	b	b	PROPN
ejpam-5369	296	21	⊆	⊆	NUM
ejpam-5369	296	22	a	a	PRON
ejpam-5369	296	23	)	)	PUNCT
ejpam-5369	296	24	.	.	PUNCT
ejpam-5369	296	25	.	.	PUNCT
ejpam-5369	296	26	.	.	PUNCT
ejpam-5369	297	1	(	(	PUNCT
ejpam-5369	297	2	2	2	X
ejpam-5369	297	3	)	)	PUNCT
ejpam-5369	297	4	therefore	therefore	ADV
ejpam-5369	297	5	,	,	PUNCT
ejpam-5369	297	6	b	b	PROPN
ejpam-5369	297	7	is	be	AUX
ejpam-5369	297	8	a	a	DET
ejpam-5369	297	9	base	base	NOUN
ejpam-5369	297	10	for	for	ADP
ejpam-5369	297	11	the	the	DET
ejpam-5369	297	12	topology	topology	NOUN
ejpam-5369	297	13	τ⋄ω	τ⋄ω	PUNCT
ejpam-5369	297	14	on	on	ADP
ejpam-5369	297	15	x	x	SYM
ejpam-5369	297	16	due	due	ADP
ejpam-5369	297	17	to	to	ADP
ejpam-5369	297	18	(	(	PUNCT
ejpam-5369	297	19	1	1	NUM
ejpam-5369	297	20	)	)	PUNCT
ejpam-5369	297	21	and	and	CCONJ
ejpam-5369	297	22	(	(	PUNCT
ejpam-5369	297	23	2	2	NUM
ejpam-5369	297	24	)	)	PUNCT
ejpam-5369	297	25	.	.	PUNCT
ejpam-5369	298	1	theorem	theorem	NOUN
ejpam-5369	298	2	17	17	NUM
ejpam-5369	298	3	.	.	PUNCT
ejpam-5369	299	1	let	let	VERB
ejpam-5369	299	2	(	(	PUNCT
ejpam-5369	299	3	x	x	X
ejpam-5369	299	4	,	,	PUNCT
ejpam-5369	299	5	τ	τ	PROPN
ejpam-5369	299	6	,	,	PUNCT
ejpam-5369	299	7	p	p	NOUN
ejpam-5369	299	8	)	)	PUNCT
ejpam-5369	299	9	and	and	CCONJ
ejpam-5369	299	10	(	(	PUNCT
ejpam-5369	299	11	x	x	X
ejpam-5369	299	12	,	,	PUNCT
ejpam-5369	299	13	τ	τ	PROPN
ejpam-5369	299	14	,	,	PUNCT
ejpam-5369	299	15	q	q	NOUN
ejpam-5369	299	16	)	)	PUNCT
ejpam-5369	299	17	be	be	VERB
ejpam-5369	299	18	two	two	NUM
ejpam-5369	299	19	primal	primal	ADJ
ejpam-5369	299	20	topological	topological	ADJ
ejpam-5369	299	21	spaces	space	NOUN
ejpam-5369	299	22	.	.	PUNCT
ejpam-5369	300	1	if	if	SCONJ
ejpam-5369	300	2	p	p	PRON
ejpam-5369	300	3	⊆	⊆	NUM
ejpam-5369	300	4	q	q	NOUN
ejpam-5369	300	5	,	,	PUNCT
ejpam-5369	300	6	then	then	ADV
ejpam-5369	300	7	τ⋄ω(q	τ⋄ω(q	PROPN
ejpam-5369	300	8	)	)	PUNCT
ejpam-5369	300	9	⊆	⊆	NUM
ejpam-5369	300	10	τ⋄ω(p	τ⋄ω(p	NUM
ejpam-5369	300	11	)	)	PUNCT
ejpam-5369	300	12	.	.	PUNCT
ejpam-5369	301	1	proof	proof	NOUN
ejpam-5369	301	2	.	.	PUNCT
ejpam-5369	302	1	let	let	VERB
ejpam-5369	302	2	a	a	DET
ejpam-5369	302	3	∈	∈	PROPN
ejpam-5369	302	4	τ⋄ω(q	τ⋄ω(q	NOUN
ejpam-5369	302	5	)	)	PUNCT
ejpam-5369	302	6	.	.	PUNCT
ejpam-5369	303	1	a	a	DET
ejpam-5369	303	2	∈	∈	PROPN
ejpam-5369	303	3	τ⋄ω(q	τ⋄ω(q	NOUN
ejpam-5369	303	4	)	)	PUNCT
ejpam-5369	303	5	⇒	⇒	NOUN
ejpam-5369	303	6	(	(	PUNCT
ejpam-5369	303	7	∀x	∀x	X
ejpam-5369	303	8	∈	∈	PROPN
ejpam-5369	303	9	a)(∃u	a)(∃u	NOUN
ejpam-5369	303	10	∈	∈	PROPN
ejpam-5369	303	11	ωo(x	ωo(x	NUM
ejpam-5369	303	12	,	,	PUNCT
ejpam-5369	303	13	x))(u	x))(u	PROPN
ejpam-5369	303	14	c	c	NOUN
ejpam-5369	303	15	∪a	∪a	NUM
ejpam-5369	303	16	/∈	/∈	PUNCT
ejpam-5369	304	1	q	q	X
ejpam-5369	304	2	)	)	PUNCT
ejpam-5369	304	3	p	p	NOUN
ejpam-5369	304	4	⊆	⊆	NUM
ejpam-5369	304	5	q	q	DET
ejpam-5369	304	6	}	}	PUNCT
ejpam-5369	304	7	⇒	⇒	NOUN
ejpam-5369	304	8	⇒	⇒	NOUN
ejpam-5369	304	9	(	(	PUNCT
ejpam-5369	304	10	∀x	∀x	X
ejpam-5369	304	11	∈	∈	PROPN
ejpam-5369	304	12	a)(∃u	a)(∃u	NOUN
ejpam-5369	304	13	∈	∈	PROPN
ejpam-5369	304	14	ωo(x	ωo(x	NUM
ejpam-5369	304	15	,	,	PUNCT
ejpam-5369	304	16	x))(u	x))(u	PROPN
ejpam-5369	304	17	c	c	NOUN
ejpam-5369	304	18	∪a	∪a	NUM
ejpam-5369	304	19	/∈	/∈	PUNCT
ejpam-5369	305	1	p	p	X
ejpam-5369	305	2	)	)	PUNCT
ejpam-5369	305	3	⇒	⇒	VERB
ejpam-5369	305	4	a	a	DET
ejpam-5369	305	5	∈	∈	PROPN
ejpam-5369	305	6	τ⋄ω(p	τ⋄ω(p	NUM
ejpam-5369	305	7	)	)	PUNCT
ejpam-5369	305	8	.	.	PUNCT
ejpam-5369	306	1	5	5	X
ejpam-5369	306	2	.	.	X
ejpam-5369	306	3	conclusion	conclusion	NOUN
ejpam-5369	306	4	in	in	ADP
ejpam-5369	306	5	this	this	DET
ejpam-5369	306	6	article	article	NOUN
ejpam-5369	306	7	,	,	PUNCT
ejpam-5369	306	8	we	we	PRON
ejpam-5369	306	9	introduced	introduce	VERB
ejpam-5369	306	10	and	and	CCONJ
ejpam-5369	306	11	studied	study	VERB
ejpam-5369	306	12	two	two	NUM
ejpam-5369	306	13	new	new	ADJ
ejpam-5369	306	14	operators	operator	NOUN
ejpam-5369	306	15	,	,	PUNCT
ejpam-5369	306	16	denoted	denote	VERB
ejpam-5369	306	17	by	by	ADP
ejpam-5369	306	18	(	(	PUNCT
ejpam-5369	306	19	·	·	PUNCT
ejpam-5369	306	20	)	)	PUNCT
ejpam-5369	306	21	⋄ω	⋄ω	NOUN
ejpam-5369	306	22	and	and	CCONJ
ejpam-5369	306	23	cl⋄ω	cl⋄ω	PROPN
ejpam-5369	306	24	(	(	PUNCT
ejpam-5369	306	25	·	·	PUNCT
ejpam-5369	306	26	)	)	PUNCT
ejpam-5369	306	27	,	,	PUNCT
ejpam-5369	306	28	via	via	ADP
ejpam-5369	306	29	the	the	DET
ejpam-5369	306	30	notions	notion	NOUN
ejpam-5369	306	31	of	of	ADP
ejpam-5369	306	32	primal	primal	ADJ
ejpam-5369	306	33	and	and	CCONJ
ejpam-5369	306	34	ω	ω	VERB
ejpam-5369	306	35	-	-	ADJ
ejpam-5369	306	36	open	open	ADJ
ejpam-5369	306	37	set	set	NOUN
ejpam-5369	306	38	.	.	PUNCT
ejpam-5369	307	1	also	also	ADV
ejpam-5369	307	2	,	,	PUNCT
ejpam-5369	307	3	we	we	PRON
ejpam-5369	307	4	revealed	reveal	VERB
ejpam-5369	307	5	their	their	PRON
ejpam-5369	307	6	fundamental	fundamental	ADJ
ejpam-5369	307	7	properties	property	NOUN
ejpam-5369	307	8	.	.	PUNCT
ejpam-5369	308	1	although	although	SCONJ
ejpam-5369	308	2	the	the	DET
ejpam-5369	308	3	first	first	ADJ
ejpam-5369	308	4	one	one	NOUN
ejpam-5369	308	5	is	be	AUX
ejpam-5369	308	6	not	not	PART
ejpam-5369	308	7	a	a	DET
ejpam-5369	308	8	kuratowski	kuratowski	ADJ
ejpam-5369	308	9	closure	closure	NOUN
ejpam-5369	308	10	operator	operator	NOUN
ejpam-5369	308	11	,	,	PUNCT
ejpam-5369	308	12	the	the	DET
ejpam-5369	308	13	second	second	ADJ
ejpam-5369	308	14	one	one	NOUN
ejpam-5369	308	15	appears	appear	VERB
ejpam-5369	308	16	as	as	ADP
ejpam-5369	308	17	a	a	DET
ejpam-5369	308	18	kuratowski	kuratowski	ADJ
ejpam-5369	308	19	closure	closure	NOUN
ejpam-5369	308	20	operator	operator	NOUN
ejpam-5369	308	21	.	.	PUNCT
ejpam-5369	309	1	thus	thus	ADV
ejpam-5369	309	2	,	,	PUNCT
ejpam-5369	309	3	we	we	PRON
ejpam-5369	309	4	obtained	obtain	VERB
ejpam-5369	309	5	a	a	DET
ejpam-5369	309	6	new	new	ADJ
ejpam-5369	309	7	topology	topology	NOUN
ejpam-5369	309	8	τ⋄ω	τ⋄ω	NUM
ejpam-5369	309	9	which	which	PRON
ejpam-5369	309	10	is	be	AUX
ejpam-5369	309	11	finer	fine	ADJ
ejpam-5369	309	12	than	than	ADP
ejpam-5369	309	13	both	both	PRON
ejpam-5369	309	14	τ⋄	τ⋄	NUM
ejpam-5369	309	15	and	and	CCONJ
ejpam-5369	309	16	τω	τω	INTJ
ejpam-5369	309	17	.	.	PUNCT
ejpam-5369	310	1	also	also	ADV
ejpam-5369	310	2	,	,	PUNCT
ejpam-5369	310	3	we	we	PRON
ejpam-5369	310	4	built	build	VERB
ejpam-5369	310	5	a	a	DET
ejpam-5369	310	6	basis	basis	NOUN
ejpam-5369	310	7	for	for	ADP
ejpam-5369	310	8	this	this	DET
ejpam-5369	310	9	new	new	ADJ
ejpam-5369	310	10	topology	topology	NOUN
ejpam-5369	310	11	τ⋄ω	τ⋄ω	PUNCT
ejpam-5369	310	12	and	and	CCONJ
ejpam-5369	310	13	revealed	reveal	VERB
ejpam-5369	310	14	several	several	ADJ
ejpam-5369	310	15	fundamental	fundamental	ADJ
ejpam-5369	310	16	results	result	NOUN
ejpam-5369	310	17	.	.	PUNCT
ejpam-5369	311	1	moreover	moreover	ADV
ejpam-5369	311	2	,	,	PUNCT
ejpam-5369	311	3	we	we	PRON
ejpam-5369	311	4	obtained	obtain	VERB
ejpam-5369	311	5	some	some	DET
ejpam-5369	311	6	relationships	relationship	NOUN
ejpam-5369	311	7	between	between	ADP
ejpam-5369	311	8	this	this	DET
ejpam-5369	311	9	new	new	ADJ
ejpam-5369	311	10	topology	topology	NOUN
ejpam-5369	311	11	and	and	CCONJ
ejpam-5369	311	12	the	the	DET
ejpam-5369	311	13	other	other	ADJ
ejpam-5369	311	14	topologies	topology	NOUN
ejpam-5369	311	15	existed	exist	VERB
ejpam-5369	311	16	in	in	ADP
ejpam-5369	311	17	the	the	DET
ejpam-5369	311	18	literature	literature	NOUN
ejpam-5369	311	19	.	.	PUNCT
ejpam-5369	312	1	we	we	PRON
ejpam-5369	312	2	hope	hope	VERB
ejpam-5369	312	3	that	that	SCONJ
ejpam-5369	312	4	this	this	DET
ejpam-5369	312	5	paper	paper	NOUN
ejpam-5369	312	6	will	will	AUX
ejpam-5369	312	7	stimulate	stimulate	VERB
ejpam-5369	312	8	further	further	ADJ
ejpam-5369	312	9	research	research	NOUN
ejpam-5369	312	10	on	on	ADP
ejpam-5369	312	11	primals	primal	NOUN
ejpam-5369	312	12	and	and	CCONJ
ejpam-5369	312	13	rough	rough	ADJ
ejpam-5369	312	14	sets	set	NOUN
ejpam-5369	312	15	as	as	ADP
ejpam-5369	312	16	ideals	ideal	NOUN
ejpam-5369	312	17	.	.	PUNCT
ejpam-5369	313	1	in	in	ADP
ejpam-5369	313	2	future	future	ADJ
ejpam-5369	313	3	work	work	NOUN
ejpam-5369	313	4	,	,	PUNCT
ejpam-5369	313	5	we	we	PRON
ejpam-5369	313	6	will	will	AUX
ejpam-5369	313	7	study	study	VERB
ejpam-5369	313	8	different	different	ADJ
ejpam-5369	313	9	operators	operator	NOUN
ejpam-5369	313	10	by	by	ADP
ejpam-5369	313	11	utilizing	utilize	VERB
ejpam-5369	313	12	soft	soft	ADJ
ejpam-5369	313	13	sets	set	NOUN
ejpam-5369	313	14	and	and	CCONJ
ejpam-5369	313	15	rough	rough	ADJ
ejpam-5369	313	16	sets	set	NOUN
ejpam-5369	313	17	via	via	ADP
ejpam-5369	313	18	primals	primal	NOUN
ejpam-5369	313	19	.	.	PUNCT
ejpam-5369	314	1	also	also	ADV
ejpam-5369	314	2	,	,	PUNCT
ejpam-5369	314	3	we	we	PRON
ejpam-5369	314	4	will	will	AUX
ejpam-5369	314	5	generate	generate	VERB
ejpam-5369	314	6	new	new	ADJ
ejpam-5369	314	7	topologies	topology	NOUN
ejpam-5369	314	8	from	from	ADP
ejpam-5369	314	9	primals	primal	NOUN
ejpam-5369	314	10	and	and	CCONJ
ejpam-5369	314	11	other	other	ADJ
ejpam-5369	314	12	types	type	NOUN
ejpam-5369	314	13	of	of	ADP
ejpam-5369	314	14	sets	set	NOUN
ejpam-5369	314	15	in	in	ADP
ejpam-5369	314	16	the	the	DET
ejpam-5369	314	17	literature	literature	NOUN
ejpam-5369	314	18	.	.	PUNCT
ejpam-5369	315	1	references	reference	NOUN
ejpam-5369	315	2	2810	2810	NUM
ejpam-5369	315	3	acknowledgements	acknowledgement	NOUN
ejpam-5369	315	4	the	the	DET
ejpam-5369	315	5	authors	author	NOUN
ejpam-5369	315	6	would	would	AUX
ejpam-5369	315	7	like	like	VERB
ejpam-5369	315	8	to	to	PART
ejpam-5369	315	9	thank	thank	VERB
ejpam-5369	315	10	the	the	DET
ejpam-5369	315	11	referees	referee	NOUN
ejpam-5369	315	12	and	and	CCONJ
ejpam-5369	315	13	the	the	DET
ejpam-5369	315	14	editor	editor	NOUN
ejpam-5369	315	15	for	for	ADP
ejpam-5369	315	16	their	their	PRON
ejpam-5369	315	17	helpful	helpful	ADJ
ejpam-5369	315	18	suggestions	suggestion	NOUN
ejpam-5369	315	19	which	which	PRON
ejpam-5369	315	20	improved	improve	VERB
ejpam-5369	315	21	the	the	DET
ejpam-5369	315	22	paper	paper	NOUN
ejpam-5369	315	23	.	.	PUNCT
ejpam-5369	316	1	we	we	PRON
ejpam-5369	316	2	would	would	AUX
ejpam-5369	316	3	like	like	VERB
ejpam-5369	316	4	to	to	PART
ejpam-5369	316	5	thank	thank	VERB
ejpam-5369	316	6	professor	professor	NOUN
ejpam-5369	316	7	can	can	AUX
ejpam-5369	316	8	dalkiran	dalkiran	VERB
ejpam-5369	316	9	for	for	ADP
ejpam-5369	316	10	his	his	PRON
ejpam-5369	316	11	valuable	valuable	ADJ
ejpam-5369	316	12	suggestions	suggestion	NOUN
ejpam-5369	316	13	as	as	ADV
ejpam-5369	316	14	well	well	ADV
ejpam-5369	316	15	.	.	PUNCT
ejpam-5369	317	1	references	reference	NOUN
ejpam-5369	317	2	[	[	X
ejpam-5369	317	3	1	1	X
ejpam-5369	317	4	]	]	PUNCT
ejpam-5369	317	5	s.	s.	PROPN
ejpam-5369	317	6	acharjee	acharjee	PROPN
ejpam-5369	317	7	,	,	PUNCT
ejpam-5369	317	8	m.	m.	NOUN
ejpam-5369	317	9	özkoç	özkoç	PROPN
ejpam-5369	317	10	,	,	PUNCT
ejpam-5369	317	11	and	and	CCONJ
ejpam-5369	317	12	f.	f.	PROPN
ejpam-5369	317	13	y.	y.	PROPN
ejpam-5369	317	14	issaka	issaka	PROPN
ejpam-5369	317	15	.	.	PUNCT
ejpam-5369	318	1	primal	primal	ADJ
ejpam-5369	318	2	topological	topological	ADJ
ejpam-5369	318	3	spaces	space	NOUN
ejpam-5369	318	4	.	.	PUNCT
ejpam-5369	319	1	bspm	bspm	PROPN
ejpam-5369	319	2	,	,	PUNCT
ejpam-5369	319	3	2024	2024	NUM
ejpam-5369	319	4	.	.	PUNCT
ejpam-5369	319	5	accepted	accept	VERB
ejpam-5369	319	6	for	for	ADP
ejpam-5369	319	7	publication	publication	NOUN
ejpam-5369	319	8	.	.	PUNCT
ejpam-5369	320	1	[	[	X
ejpam-5369	320	2	2	2	NUM
ejpam-5369	320	3	]	]	PUNCT
ejpam-5369	320	4	a.	a.	PROPN
ejpam-5369	320	5	al	al	PROPN
ejpam-5369	320	6	-	-	PUNCT
ejpam-5369	320	7	omari	omari	PROPN
ejpam-5369	320	8	,	,	PUNCT
ejpam-5369	320	9	s.	s.	PROPN
ejpam-5369	320	10	acharjee	acharjee	PROPN
ejpam-5369	320	11	,	,	PUNCT
ejpam-5369	320	12	and	and	CCONJ
ejpam-5369	320	13	m.	m.	NOUN
ejpam-5369	320	14	özkoç.	özkoç.	NOUN
ejpam-5369	320	15	a	a	DET
ejpam-5369	320	16	new	new	ADJ
ejpam-5369	320	17	operator	operator	NOUN
ejpam-5369	320	18	of	of	ADP
ejpam-5369	320	19	primal	primal	ADJ
ejpam-5369	320	20	topological	topological	ADJ
ejpam-5369	320	21	spaces	space	NOUN
ejpam-5369	320	22	.	.	PUNCT
ejpam-5369	321	1	mathematica	mathematica	PROPN
ejpam-5369	321	2	,	,	PUNCT
ejpam-5369	321	3	6:175–183	6:175–183	NUM
ejpam-5369	321	4	,	,	PUNCT
ejpam-5369	321	5	2023	2023	NUM
ejpam-5369	321	6	.	.	PUNCT
ejpam-5369	322	1	[	[	X
ejpam-5369	322	2	3	3	NUM
ejpam-5369	322	3	]	]	PUNCT
ejpam-5369	322	4	a.	a.	PROPN
ejpam-5369	322	5	al	al	PROPN
ejpam-5369	322	6	-	-	PUNCT
ejpam-5369	322	7	omari	omari	PROPN
ejpam-5369	322	8	and	and	CCONJ
ejpam-5369	322	9	o.	o.	PROPN
ejpam-5369	322	10	alghamdi	alghamdi	NOUN
ejpam-5369	322	11	.	.	PUNCT
ejpam-5369	323	1	regularity	regularity	NOUN
ejpam-5369	323	2	and	and	CCONJ
ejpam-5369	323	3	normality	normality	NOUN
ejpam-5369	323	4	on	on	ADP
ejpam-5369	323	5	primal	primal	ADJ
ejpam-5369	323	6	spaces	space	NOUN
ejpam-5369	323	7	.	.	PUNCT
ejpam-5369	324	1	aims	aim	VERB
ejpam-5369	324	2	mathematics	mathematic	NOUN
ejpam-5369	324	3	,	,	PUNCT
ejpam-5369	324	4	9:7662–7672	9:7662–7672	NUM
ejpam-5369	324	5	,	,	PUNCT
ejpam-5369	324	6	2024	2024	NUM
ejpam-5369	324	7	.	.	PUNCT
ejpam-5369	325	1	[	[	X
ejpam-5369	325	2	4	4	X
ejpam-5369	325	3	]	]	PUNCT
ejpam-5369	325	4	a.	a.	PROPN
ejpam-5369	325	5	al	al	PROPN
ejpam-5369	325	6	-	-	PUNCT
ejpam-5369	325	7	omari	omari	PROPN
ejpam-5369	325	8	and	and	CCONJ
ejpam-5369	325	9	m.	m.	PROPN
ejpam-5369	325	10	h.	h.	PROPN
ejpam-5369	325	11	alqahtani	alqahtani	PROPN
ejpam-5369	325	12	.	.	PUNCT
ejpam-5369	326	1	primal	primal	ADJ
ejpam-5369	326	2	structure	structure	NOUN
ejpam-5369	326	3	with	with	ADP
ejpam-5369	326	4	closure	closure	NOUN
ejpam-5369	326	5	operators	operator	NOUN
ejpam-5369	326	6	and	and	CCONJ
ejpam-5369	326	7	their	their	PRON
ejpam-5369	326	8	applications	application	NOUN
ejpam-5369	326	9	.	.	PUNCT
ejpam-5369	327	1	mathematics	mathematic	NOUN
ejpam-5369	327	2	mpdi	mpdi	PROPN
ejpam-5369	327	3	,	,	PUNCT
ejpam-5369	327	4	11:4946	11:4946	NUM
ejpam-5369	327	5	,	,	PUNCT
ejpam-5369	327	6	2023	2023	NUM
ejpam-5369	327	7	.	.	PUNCT
ejpam-5369	328	1	[	[	X
ejpam-5369	328	2	5	5	NUM
ejpam-5369	328	3	]	]	PUNCT
ejpam-5369	328	4	a.	a.	PROPN
ejpam-5369	328	5	al	al	PROPN
ejpam-5369	328	6	-	-	PUNCT
ejpam-5369	328	7	omari	omari	PROPN
ejpam-5369	328	8	and	and	CCONJ
ejpam-5369	328	9	m.	m.	PROPN
ejpam-5369	328	10	h.	h.	PROPN
ejpam-5369	328	11	alqahtani	alqahtani	PROPN
ejpam-5369	328	12	.	.	PUNCT
ejpam-5369	329	1	some	some	DET
ejpam-5369	329	2	operators	operator	NOUN
ejpam-5369	329	3	in	in	ADP
ejpam-5369	329	4	soft	soft	ADJ
ejpam-5369	329	5	primal	primal	ADJ
ejpam-5369	329	6	spaces	space	NOUN
ejpam-5369	329	7	.	.	PUNCT
ejpam-5369	330	1	aims	aim	VERB
ejpam-5369	330	2	mathematics	mathematic	NOUN
ejpam-5369	330	3	,	,	PUNCT
ejpam-5369	330	4	96(5):10756–10774	96(5):10756–10774	NUM
ejpam-5369	330	5	,	,	PUNCT
ejpam-5369	330	6	2024	2024	NUM
ejpam-5369	330	7	.	.	PUNCT
ejpam-5369	331	1	[	[	X
ejpam-5369	331	2	6	6	NUM
ejpam-5369	331	3	]	]	PUNCT
ejpam-5369	331	4	a.	a.	PROPN
ejpam-5369	331	5	al	al	PROPN
ejpam-5369	331	6	-	-	PUNCT
ejpam-5369	331	7	omari	omari	PROPN
ejpam-5369	331	8	,	,	PUNCT
ejpam-5369	331	9	m.	m.	NOUN
ejpam-5369	331	10	özkoç	özkoç	PROPN
ejpam-5369	331	11	,	,	PUNCT
ejpam-5369	331	12	and	and	CCONJ
ejpam-5369	331	13	s.	s.	PROPN
ejpam-5369	331	14	acharjee	acharjee	PROPN
ejpam-5369	331	15	.	.	PUNCT
ejpam-5369	332	1	primal	primal	ADJ
ejpam-5369	332	2	-	-	PUNCT
ejpam-5369	332	3	proximity	proximity	NOUN
ejpam-5369	332	4	spaces	space	NOUN
ejpam-5369	332	5	.	.	PUNCT
ejpam-5369	333	1	mathematica	mathematica	PROPN
ejpam-5369	333	2	,	,	PUNCT
ejpam-5369	333	3	2024	2024	NUM
ejpam-5369	333	4	.	.	PUNCT
ejpam-5369	333	5	accepted	accept	VERB
ejpam-5369	333	6	for	for	ADP
ejpam-5369	333	7	publication	publication	NOUN
ejpam-5369	333	8	.	.	PUNCT
ejpam-5369	334	1	[	[	X
ejpam-5369	334	2	7	7	X
ejpam-5369	334	3	]	]	X
ejpam-5369	334	4	h.	h.	PROPN
ejpam-5369	334	5	al	al	PROPN
ejpam-5369	334	6	-	-	PUNCT
ejpam-5369	334	7	saadi	saadi	PROPN
ejpam-5369	334	8	and	and	CCONJ
ejpam-5369	334	9	h.	h.	PROPN
ejpam-5369	334	10	al	al	PROPN
ejpam-5369	334	11	-	-	PUNCT
ejpam-5369	334	12	malki	malki	PROPN
ejpam-5369	334	13	.	.	PUNCT
ejpam-5369	335	1	generalized	generalize	VERB
ejpam-5369	335	2	primal	primal	ADJ
ejpam-5369	335	3	topological	topological	ADJ
ejpam-5369	335	4	spaces	space	NOUN
ejpam-5369	335	5	.	.	PUNCT
ejpam-5369	336	1	aims	aim	VERB
ejpam-5369	336	2	mathematics	mathematic	NOUN
ejpam-5369	336	3	,	,	PUNCT
ejpam-5369	336	4	8(10):24162–24175	8(10):24162–24175	NUM
ejpam-5369	336	5	,	,	PUNCT
ejpam-5369	336	6	2023	2023	NUM
ejpam-5369	336	7	.	.	PUNCT
ejpam-5369	337	1	[	[	X
ejpam-5369	337	2	8	8	NUM
ejpam-5369	337	3	]	]	X
ejpam-5369	337	4	h.	h.	PROPN
ejpam-5369	337	5	al	al	PROPN
ejpam-5369	337	6	-	-	PUNCT
ejpam-5369	337	7	saadi	saadi	PROPN
ejpam-5369	337	8	and	and	CCONJ
ejpam-5369	337	9	h.	h.	PROPN
ejpam-5369	337	10	al	al	PROPN
ejpam-5369	337	11	-	-	PUNCT
ejpam-5369	337	12	malki	malki	NOUN
ejpam-5369	337	13	.	.	PUNCT
ejpam-5369	338	1	categories	category	NOUN
ejpam-5369	338	2	of	of	ADP
ejpam-5369	338	3	open	open	ADJ
ejpam-5369	338	4	sets	set	NOUN
ejpam-5369	338	5	in	in	ADP
ejpam-5369	338	6	generalized	generalized	ADJ
ejpam-5369	338	7	primal	primal	ADJ
ejpam-5369	338	8	topological	topological	ADJ
ejpam-5369	338	9	spaces	space	NOUN
ejpam-5369	338	10	.	.	PUNCT
ejpam-5369	339	1	mathematics	mathematic	NOUN
ejpam-5369	339	2	mpdi	mpdi	PROPN
ejpam-5369	339	3	,	,	PUNCT
ejpam-5369	339	4	12:207	12:207	NUM
ejpam-5369	339	5	,	,	PUNCT
ejpam-5369	339	6	2024	2024	NUM
ejpam-5369	339	7	.	.	PUNCT
ejpam-5369	340	1	[	[	X
ejpam-5369	340	2	9	9	NUM
ejpam-5369	340	3	]	]	PUNCT
ejpam-5369	340	4	t.	t.	PROPN
ejpam-5369	340	5	m.	m.	PROPN
ejpam-5369	340	6	al	al	PROPN
ejpam-5369	340	7	-	-	PUNCT
ejpam-5369	340	8	shami	shami	PROPN
ejpam-5369	340	9	,	,	PUNCT
ejpam-5369	340	10	z.	z.	PROPN
ejpam-5369	340	11	a.	a.	PROPN
ejpam-5369	340	12	ameen	ameen	PROPN
ejpam-5369	340	13	,	,	PUNCT
ejpam-5369	340	14	r.	r.	PROPN
ejpam-5369	340	15	a.	a.	PROPN
ejpam-5369	340	16	gdairi	gdairi	PROPN
ejpam-5369	340	17	,	,	PUNCT
ejpam-5369	340	18	and	and	CCONJ
ejpam-5369	340	19	a.	a.	NOUN
ejpam-5369	340	20	mhemdi	mhemdi	PROPN
ejpam-5369	340	21	.	.	PUNCT
ejpam-5369	341	1	on	on	ADP
ejpam-5369	341	2	primal	primal	ADJ
ejpam-5369	341	3	soft	soft	ADJ
ejpam-5369	341	4	topology	topology	NOUN
ejpam-5369	341	5	.	.	PUNCT
ejpam-5369	342	1	mathematics	mathematic	NOUN
ejpam-5369	342	2	,	,	PUNCT
ejpam-5369	342	3	11:2329	11:2329	NUM
ejpam-5369	342	4	,	,	PUNCT
ejpam-5369	342	5	2023	2023	NUM
ejpam-5369	342	6	.	.	PUNCT
ejpam-5369	343	1	[	[	X
ejpam-5369	343	2	10	10	NUM
ejpam-5369	343	3	]	]	PUNCT
ejpam-5369	343	4	k.	k.	PROPN
ejpam-5369	344	1	y.	y.	PROPN
ejpam-5369	344	2	al	al	PROPN
ejpam-5369	344	3	-	-	PROPN
ejpam-5369	344	4	zoubi	zoubi	PROPN
ejpam-5369	344	5	and	and	CCONJ
ejpam-5369	344	6	b.	b.	PROPN
ejpam-5369	344	7	al	al	PROPN
ejpam-5369	344	8	-	-	PUNCT
ejpam-5369	344	9	nashef	nashef	PROPN
ejpam-5369	344	10	.	.	PUNCT
ejpam-5369	345	1	the	the	DET
ejpam-5369	345	2	topology	topology	NOUN
ejpam-5369	345	3	of	of	ADP
ejpam-5369	345	4	ω	ω	VERB
ejpam-5369	345	5	-	-	ADJ
ejpam-5369	345	6	open	open	ADJ
ejpam-5369	345	7	subsets	subset	NOUN
ejpam-5369	345	8	.	.	PUNCT
ejpam-5369	346	1	al	al	PROPN
ejpam-5369	346	2	-	-	PUNCT
ejpam-5369	346	3	manarah	manarah	PROPN
ejpam-5369	346	4	journal	journal	NOUN
ejpam-5369	346	5	,	,	PUNCT
ejpam-5369	346	6	9:169–179	9:169–179	PROPN
ejpam-5369	346	7	,	,	PUNCT
ejpam-5369	346	8	2003	2003	NUM
ejpam-5369	346	9	.	.	PUNCT
ejpam-5369	347	1	[	[	X
ejpam-5369	347	2	11	11	NUM
ejpam-5369	347	3	]	]	X
ejpam-5369	347	4	o.	o.	NOUN
ejpam-5369	347	5	alghamdi	alghamdi	NOUN
ejpam-5369	347	6	,	,	PUNCT
ejpam-5369	347	7	a.	a.	PROPN
ejpam-5369	347	8	al	al	PROPN
ejpam-5369	347	9	-	-	PUNCT
ejpam-5369	347	10	omari	omari	PROPN
ejpam-5369	347	11	,	,	PUNCT
ejpam-5369	347	12	and	and	CCONJ
ejpam-5369	347	13	m.	m.	PROPN
ejpam-5369	347	14	h.	h.	PROPN
ejpam-5369	347	15	alqahtani	alqahtani	PROPN
ejpam-5369	347	16	.	.	PUNCT
ejpam-5369	348	1	novel	novel	ADJ
ejpam-5369	348	2	operators	operator	NOUN
ejpam-5369	348	3	in	in	ADP
ejpam-5369	348	4	the	the	DET
ejpam-5369	348	5	frame	frame	NOUN
ejpam-5369	348	6	of	of	ADP
ejpam-5369	348	7	primal	primal	ADJ
ejpam-5369	348	8	topological	topological	ADJ
ejpam-5369	348	9	spaces	space	NOUN
ejpam-5369	348	10	.	.	PUNCT
ejpam-5369	349	1	aims	aim	VERB
ejpam-5369	349	2	mathematics	mathematic	NOUN
ejpam-5369	349	3	,	,	PUNCT
ejpam-5369	349	4	9(9):25792–25808	9(9):25792–25808	NUM
ejpam-5369	349	5	,	,	PUNCT
ejpam-5369	349	6	2024	2024	NUM
ejpam-5369	349	7	.	.	PUNCT
ejpam-5369	350	1	[	[	X
ejpam-5369	350	2	12	12	NUM
ejpam-5369	350	3	]	]	X
ejpam-5369	350	4	g.	g.	PROPN
ejpam-5369	350	5	chóquet	chóquet	PROPN
ejpam-5369	350	6	.	.	PUNCT
ejpam-5369	351	1	sur	sur	PROPN
ejpam-5369	351	2	les	les	PROPN
ejpam-5369	351	3	notions	notion	NOUN
ejpam-5369	351	4	de	de	ADP
ejpam-5369	351	5	filter	filter	NOUN
ejpam-5369	351	6	et	et	NOUN
ejpam-5369	351	7	grille	grille	NOUN
ejpam-5369	351	8	.	.	PUNCT
ejpam-5369	352	1	comptes	compte	VERB
ejpam-5369	352	2	rendus	rendus	PROPN
ejpam-5369	352	3	acad	acad	PROPN
ejpam-5369	352	4	.	.	PUNCT
ejpam-5369	353	1	sci	sci	PROPN
ejpam-5369	353	2	.	.	PROPN
ejpam-5369	353	3	paris	paris	PROPN
ejpam-5369	353	4	,	,	PUNCT
ejpam-5369	353	5	224:171–173	224:171–173	NUM
ejpam-5369	353	6	,	,	PUNCT
ejpam-5369	353	7	1947	1947	NUM
ejpam-5369	353	8	.	.	PUNCT
ejpam-5369	354	1	[	[	X
ejpam-5369	354	2	13	13	NUM
ejpam-5369	354	3	]	]	SYM
ejpam-5369	354	4	ş.	ş.	PROPN
ejpam-5369	354	5	güzide	güzide	NOUN
ejpam-5369	354	6	.	.	PUNCT
ejpam-5369	355	1	a	a	DET
ejpam-5369	355	2	new	new	ADJ
ejpam-5369	355	3	approach	approach	NOUN
ejpam-5369	355	4	to	to	ADP
ejpam-5369	355	5	hausdorff	hausdorff	NOUN
ejpam-5369	355	6	space	space	NOUN
ejpam-5369	355	7	theory	theory	NOUN
ejpam-5369	355	8	via	via	ADP
ejpam-5369	355	9	the	the	DET
ejpam-5369	355	10	soft	soft	ADJ
ejpam-5369	355	11	sets	set	NOUN
ejpam-5369	355	12	.	.	PUNCT
ejpam-5369	356	1	math	math	NOUN
ejpam-5369	356	2	.	.	PUNCT
ejpam-5369	357	1	probl	probl	PROPN
ejpam-5369	357	2	.	.	PUNCT
ejpam-5369	358	1	eng	eng	PROPN
ejpam-5369	358	2	.	.	PROPN
ejpam-5369	358	3	,	,	PUNCT
ejpam-5369	358	4	9:1–6	9:1–6	NUM
ejpam-5369	358	5	,	,	PUNCT
ejpam-5369	358	6	2016	2016	NUM
ejpam-5369	358	7	.	.	PUNCT
ejpam-5369	359	1	references	reference	NOUN
ejpam-5369	359	2	2811	2811	NUM
ejpam-5369	360	1	[	[	X
ejpam-5369	360	2	14	14	NUM
ejpam-5369	360	3	]	]	X
ejpam-5369	360	4	ş.	ş.	PROPN
ejpam-5369	360	5	güzide	güzide	PROPN
ejpam-5369	360	6	,	,	PUNCT
ejpam-5369	360	7	l.	l.	PROPN
ejpam-5369	360	8	j.	j.	PROPN
ejpam-5369	360	9	gon	gon	PROPN
ejpam-5369	360	10	,	,	PUNCT
ejpam-5369	360	11	y.	y.	PROPN
ejpam-5369	360	12	b.	b.	PROPN
ejpam-5369	360	13	jun	jun	PROPN
ejpam-5369	360	14	,	,	PUNCT
ejpam-5369	360	15	a.	a.	NOUN
ejpam-5369	360	16	fadhil	fadhil	PROPN
ejpam-5369	360	17	,	,	PUNCT
ejpam-5369	360	18	and	and	CCONJ
ejpam-5369	360	19	k.	k.	PROPN
ejpam-5369	360	20	hur	hur	PROPN
ejpam-5369	360	21	.	.	PUNCT
ejpam-5369	361	1	topological	topological	ADJ
ejpam-5369	361	2	structures	structure	NOUN
ejpam-5369	361	3	via	via	ADP
ejpam-5369	361	4	interval	interval	NOUN
ejpam-5369	361	5	-	-	PUNCT
ejpam-5369	361	6	valued	value	VERB
ejpam-5369	361	7	soft	soft	ADJ
ejpam-5369	361	8	sets	set	NOUN
ejpam-5369	361	9	.	.	PUNCT
ejpam-5369	362	1	ann	ann	PROPN
ejpam-5369	362	2	.	.	PUNCT
ejpam-5369	362	3	fuzzy	fuzzy	ADJ
ejpam-5369	362	4	math	math	NOUN
ejpam-5369	362	5	.	.	PUNCT
ejpam-5369	363	1	inform	inform	NOUN
ejpam-5369	363	2	.	.	PUNCT
ejpam-5369	363	3	,	,	PUNCT
ejpam-5369	363	4	22(2):133–16	22(2):133–16	NUM
ejpam-5369	363	5	,	,	PUNCT
ejpam-5369	363	6	2021	2021	NUM
ejpam-5369	363	7	.	.	PUNCT
ejpam-5369	364	1	[	[	X
ejpam-5369	364	2	15	15	NUM
ejpam-5369	364	3	]	]	X
ejpam-5369	364	4	h.	h.	PROPN
ejpam-5369	364	5	z.	z.	PROPN
ejpam-5369	364	6	hdeib	hdeib	PROPN
ejpam-5369	364	7	.	.	PUNCT
ejpam-5369	365	1	ω	ω	VERB
ejpam-5369	365	2	-	-	PUNCT
ejpam-5369	365	3	closed	close	VERB
ejpam-5369	365	4	mappings	mapping	NOUN
ejpam-5369	365	5	.	.	PUNCT
ejpam-5369	366	1	rev	rev	PROPN
ejpam-5369	366	2	.	.	PUNCT
ejpam-5369	367	1	colombiana	colombiana	PROPN
ejpam-5369	367	2	mat	mat	PROPN
ejpam-5369	367	3	.	.	PROPN
ejpam-5369	367	4	,	,	PUNCT
ejpam-5369	367	5	16:65–78	16:65–78	NUM
ejpam-5369	367	6	,	,	PUNCT
ejpam-5369	367	7	1982	1982	NUM
ejpam-5369	367	8	.	.	PUNCT
ejpam-5369	368	1	[	[	X
ejpam-5369	368	2	16	16	NUM
ejpam-5369	368	3	]	]	PUNCT
ejpam-5369	368	4	k.	k.	PROPN
ejpam-5369	368	5	kuratowski	kuratowski	PROPN
ejpam-5369	368	6	.	.	PUNCT
ejpam-5369	369	1	topology	topology	NOUN
ejpam-5369	369	2	:	:	PUNCT
ejpam-5369	369	3	volume	volume	NOUN
ejpam-5369	369	4	i.	i.	PROPN
ejpam-5369	369	5	elsevier	elsevier	PROPN
ejpam-5369	369	6	,	,	PUNCT
ejpam-5369	369	7	2014	2014	NUM
ejpam-5369	369	8	.	.	PUNCT
ejpam-5369	370	1	[	[	X
ejpam-5369	370	2	17	17	NUM
ejpam-5369	370	3	]	]	PUNCT
ejpam-5369	370	4	s.	s.	PROPN
ejpam-5369	370	5	modak	modak	PROPN
ejpam-5369	370	6	.	.	PUNCT
ejpam-5369	371	1	grill	grill	ADJ
ejpam-5369	371	2	-	-	PUNCT
ejpam-5369	371	3	filter	filter	NOUN
ejpam-5369	371	4	space	space	NOUN
ejpam-5369	371	5	.	.	PUNCT
ejpam-5369	372	1	jour	jour	X
ejpam-5369	372	2	.	.	PUNCT
ejpam-5369	372	3	indian	indian	PROPN
ejpam-5369	372	4	math	math	PROPN
ejpam-5369	372	5	.	.	PUNCT
ejpam-5369	373	1	soc	soc	PROPN
ejpam-5369	373	2	.	.	PROPN
ejpam-5369	373	3	,	,	PUNCT
ejpam-5369	373	4	80(3–4):313–320	80(3–4):313–320	PROPN
ejpam-5369	373	5	,	,	PUNCT
ejpam-5369	373	6	2013	2013	NUM
ejpam-5369	373	7	.	.	PUNCT
ejpam-5369	374	1	[	[	X
ejpam-5369	374	2	18	18	NUM
ejpam-5369	374	3	]	]	X
ejpam-5369	374	4	s.	s.	PROPN
ejpam-5369	374	5	modak	modak	PROPN
ejpam-5369	374	6	.	.	PUNCT
ejpam-5369	375	1	topology	topology	NOUN
ejpam-5369	375	2	on	on	ADP
ejpam-5369	375	3	grill	grill	ADJ
ejpam-5369	375	4	-	-	PUNCT
ejpam-5369	375	5	filter	filter	NOUN
ejpam-5369	375	6	space	space	NOUN
ejpam-5369	375	7	and	and	CCONJ
ejpam-5369	375	8	continuity	continuity	NOUN
ejpam-5369	375	9	.	.	PUNCT
ejpam-5369	376	1	bol	bol	NOUN
ejpam-5369	376	2	.	.	PUNCT
ejpam-5369	377	1	soc	soc	PROPN
ejpam-5369	377	2	.	.	PUNCT
ejpam-5369	378	1	paran	paran	PROPN
ejpam-5369	378	2	.	.	PUNCT
ejpam-5369	379	1	mat	mat	PROPN
ejpam-5369	379	2	.	.	PROPN
ejpam-5369	379	3	,	,	PUNCT
ejpam-5369	379	4	31(2):219–230	31(2):219–230	PROPN
ejpam-5369	379	5	,	,	PUNCT
ejpam-5369	379	6	2013	2013	NUM
ejpam-5369	379	7	.	.	PUNCT
ejpam-5369	380	1	[	[	X
ejpam-5369	380	2	19	19	NUM
ejpam-5369	380	3	]	]	X
ejpam-5369	380	4	d.	d.	PROPN
ejpam-5369	380	5	molodtsov	molodtsov	PROPN
ejpam-5369	380	6	.	.	PUNCT
ejpam-5369	381	1	soft	soft	ADJ
ejpam-5369	381	2	set	set	NOUN
ejpam-5369	381	3	theory	theory	NOUN
ejpam-5369	381	4	-	-	PUNCT
ejpam-5369	381	5	first	first	ADJ
ejpam-5369	381	6	results	result	NOUN
ejpam-5369	381	7	.	.	PUNCT
ejpam-5369	382	1	computers	computer	NOUN
ejpam-5369	382	2	and	and	CCONJ
ejpam-5369	382	3	mathematics	mathematic	NOUN
ejpam-5369	382	4	with	with	ADP
ejpam-5369	382	5	applications	application	NOUN
ejpam-5369	382	6	,	,	PUNCT
ejpam-5369	382	7	37:19–31	37:19–31	NUM
ejpam-5369	382	8	,	,	PUNCT
ejpam-5369	382	9	1999	1999	NUM
ejpam-5369	382	10	.	.	PUNCT
ejpam-5369	383	1	[	[	X
ejpam-5369	383	2	20	20	NUM
ejpam-5369	383	3	]	]	PUNCT
ejpam-5369	383	4	m.	m.	NOUN
ejpam-5369	383	5	özkoç	özkoç	PROPN
ejpam-5369	383	6	and	and	CCONJ
ejpam-5369	383	7	b.	b.	PROPN
ejpam-5369	383	8	köstel	köstel	PROPN
ejpam-5369	383	9	.	.	PUNCT
ejpam-5369	384	1	on	on	ADP
ejpam-5369	384	2	the	the	DET
ejpam-5369	384	3	topology	topology	NOUN
ejpam-5369	384	4	τ⋄r	τ⋄r	NUM
ejpam-5369	384	5	of	of	ADP
ejpam-5369	384	6	primal	primal	ADJ
ejpam-5369	384	7	topological	topological	ADJ
ejpam-5369	384	8	spaces	space	NOUN
ejpam-5369	384	9	.	.	PUNCT
ejpam-5369	385	1	aims	aim	VERB
ejpam-5369	385	2	mathematics	mathematic	NOUN
ejpam-5369	385	3	,	,	PUNCT
ejpam-5369	385	4	9(7):17171–17183	9(7):17171–17183	NUM
ejpam-5369	385	5	,	,	PUNCT
ejpam-5369	385	6	2024	2024	NUM
ejpam-5369	385	7	.	.	PUNCT
ejpam-5369	386	1	[	[	X
ejpam-5369	386	2	21	21	NUM
ejpam-5369	386	3	]	]	PUNCT
ejpam-5369	386	4	z.	z.	PROPN
ejpam-5369	386	5	a.	a.	PROPN
ejpam-5369	386	6	pawlak	pawlak	PROPN
ejpam-5369	386	7	.	.	PUNCT
ejpam-5369	387	1	rough	rough	ADJ
ejpam-5369	387	2	sets	set	NOUN
ejpam-5369	387	3	.	.	PUNCT
ejpam-5369	388	1	internat	internat	PROPN
ejpam-5369	388	2	.	.	PUNCT
ejpam-5369	389	1	j.	j.	PROPN
ejpam-5369	389	2	comput	comput	PROPN
ejpam-5369	389	3	.	.	PUNCT
ejpam-5369	389	4	&	&	CCONJ
ejpam-5369	389	5	inform	inform	VERB
ejpam-5369	389	6	.	.	PUNCT
ejpam-5369	390	1	sci	sci	PROPN
ejpam-5369	390	2	.	.	PROPN
ejpam-5369	390	3	,	,	PUNCT
ejpam-5369	390	4	5:341–356	5:341–356	NUM
ejpam-5369	390	5	,	,	PUNCT
ejpam-5369	390	6	1982	1982	NUM
ejpam-5369	390	7	.	.	PUNCT
ejpam-5369	391	1	[	[	X
ejpam-5369	391	2	22	22	NUM
ejpam-5369	391	3	]	]	PUNCT
ejpam-5369	391	4	m.	m.	NOUN
ejpam-5369	391	5	h.	h.	PROPN
ejpam-5369	391	6	stone	stone	PROPN
ejpam-5369	391	7	.	.	PUNCT
ejpam-5369	392	1	applications	application	NOUN
ejpam-5369	392	2	of	of	ADP
ejpam-5369	392	3	the	the	DET
ejpam-5369	392	4	theory	theory	NOUN
ejpam-5369	392	5	of	of	ADP
ejpam-5369	392	6	boolean	boolean	ADJ
ejpam-5369	392	7	rings	ring	NOUN
ejpam-5369	392	8	to	to	ADP
ejpam-5369	392	9	general	general	ADJ
ejpam-5369	392	10	topology	topology	NOUN
ejpam-5369	392	11	.	.	PUNCT
ejpam-5369	393	1	trans	trans	PROPN
ejpam-5369	393	2	.	.	PUNCT
ejpam-5369	394	1	amer	amer	PROPN
ejpam-5369	394	2	.	.	PUNCT
ejpam-5369	394	3	math	math	PROPN
ejpam-5369	394	4	.	.	PUNCT
ejpam-5369	395	1	soc	soc	PROPN
ejpam-5369	395	2	.	.	PUNCT
ejpam-5369	395	3	,	,	PUNCT
ejpam-5369	395	4	41:375–381	41:375–381	PROPN
ejpam-5369	395	5	,	,	PUNCT
ejpam-5369	395	6	1937	1937	NUM
ejpam-5369	395	7	.	.	PUNCT
ejpam-5369	396	1	[	[	X
ejpam-5369	396	2	23	23	NUM
ejpam-5369	396	3	]	]	X
ejpam-5369	396	4	n.	n.	PROPN
ejpam-5369	396	5	v.	v.	PROPN
ejpam-5369	396	6	velic̆ko	velic̆ko	PROPN
ejpam-5369	396	7	.	.	PUNCT
ejpam-5369	397	1	h	h	NOUN
ejpam-5369	397	2	-	-	PUNCT
ejpam-5369	397	3	closed	close	VERB
ejpam-5369	397	4	topological	topological	ADJ
ejpam-5369	397	5	spaces	space	NOUN
ejpam-5369	397	6	.	.	PUNCT
ejpam-5369	398	1	amer	amer	PROPN
ejpam-5369	398	2	.	.	PUNCT
ejpam-5369	398	3	math	math	PROPN
ejpam-5369	398	4	.	.	PUNCT
ejpam-5369	399	1	soc	soc	PROPN
ejpam-5369	399	2	.	.	PUNCT
ejpam-5369	400	1	transl	transl	PROPN
ejpam-5369	400	2	.	.	PUNCT
ejpam-5369	400	3	,	,	PUNCT
ejpam-5369	401	1	78:103–118	78:103–118	PROPN
ejpam-5369	401	2	,	,	PUNCT
ejpam-5369	401	3	1968	1968	NUM
ejpam-5369	401	4	.	.	PUNCT
ejpam-5369	402	1	[	[	X
ejpam-5369	402	2	24	24	NUM
ejpam-5369	402	3	]	]	PUNCT
ejpam-5369	402	4	l.	l.	PROPN
ejpam-5369	402	5	a.	a.	PROPN
ejpam-5369	402	6	zadeh	zadeh	PROPN
ejpam-5369	402	7	.	.	PUNCT
ejpam-5369	402	8	fuzzy	fuzzy	ADJ
ejpam-5369	402	9	sets	set	NOUN
ejpam-5369	402	10	.	.	PUNCT
ejpam-5369	403	1	information	information	NOUN
ejpam-5369	403	2	control	control	NOUN
ejpam-5369	403	3	,	,	PUNCT
ejpam-5369	403	4	8:338–353	8:338–353	NUM
ejpam-5369	403	5	,	,	PUNCT
ejpam-5369	403	6	1965	1965	NUM
ejpam-5369	403	7	.	.	PUNCT