id	sid	tid	token	lemma	pos
ejpam-5171	1	1	european	european	PROPN
ejpam-5171	1	2	journal	journal	PROPN
ejpam-5171	1	3	of	of	ADP
ejpam-5171	1	4	pure	pure	ADJ
ejpam-5171	1	5	and	and	CCONJ
ejpam-5171	1	6	applied	apply	VERB
ejpam-5171	1	7	mathematics	mathematic	NOUN
ejpam-5171	1	8	vol	vol	NOUN
ejpam-5171	1	9	.	.	PROPN
ejpam-5171	2	1	17	17	NUM
ejpam-5171	2	2	,	,	PUNCT
ejpam-5171	2	3	no	no	INTJ
ejpam-5171	2	4	.	.	NOUN
ejpam-5171	2	5	2	2	NUM
ejpam-5171	2	6	,	,	PUNCT
ejpam-5171	2	7	2024	2024	NUM
ejpam-5171	2	8	,	,	PUNCT
ejpam-5171	2	9	1352	1352	NUM
ejpam-5171	2	10	-	-	SYM
ejpam-5171	2	11	1368	1368	NUM
ejpam-5171	2	12	issn	issn	PROPN
ejpam-5171	2	13	1307	1307	NUM
ejpam-5171	2	14	-	-	SYM
ejpam-5171	2	15	5543	5543	NUM
ejpam-5171	2	16	–	–	PUNCT
ejpam-5171	2	17	ejpam.com	ejpam.com	X
ejpam-5171	2	18	published	publish	VERB
ejpam-5171	2	19	by	by	ADP
ejpam-5171	2	20	new	new	PROPN
ejpam-5171	2	21	york	york	PROPN
ejpam-5171	2	22	business	business	PROPN
ejpam-5171	2	23	global	global	ADJ
ejpam-5171	2	24	sets	set	NOUN
ejpam-5171	2	25	related	relate	VERB
ejpam-5171	2	26	to	to	ADP
ejpam-5171	2	27	openness	openness	NOUN
ejpam-5171	2	28	and	and	CCONJ
ejpam-5171	2	29	continuity	continuity	NOUN
ejpam-5171	2	30	decompositions	decomposition	NOUN
ejpam-5171	2	31	in	in	ADP
ejpam-5171	2	32	primal	primal	ADJ
ejpam-5171	2	33	topological	topological	ADJ
ejpam-5171	2	34	spaces	space	NOUN
ejpam-5171	2	35	hanan	hanan	PROPN
ejpam-5171	2	36	al	al	PROPN
ejpam-5171	2	37	-	-	PUNCT
ejpam-5171	2	38	saadi1,∗	saadi1,∗	PROPN
ejpam-5171	2	39	,	,	PUNCT
ejpam-5171	2	40	muna	muna	PROPN
ejpam-5171	2	41	al	al	PROPN
ejpam-5171	2	42	-	-	PUNCT
ejpam-5171	2	43	hodieb2	hodieb2	PROPN
ejpam-5171	2	44	1	1	NUM
ejpam-5171	2	45	department	department	NOUN
ejpam-5171	2	46	of	of	ADP
ejpam-5171	2	47	mathematics	mathematic	NOUN
ejpam-5171	2	48	,	,	PUNCT
ejpam-5171	2	49	faculty	faculty	NOUN
ejpam-5171	2	50	of	of	ADP
ejpam-5171	2	51	sciences	science	NOUN
ejpam-5171	2	52	,	,	PUNCT
ejpam-5171	2	53	umm	umm	INTJ
ejpam-5171	2	54	al	al	PROPN
ejpam-5171	2	55	-	-	PUNCT
ejpam-5171	2	56	qura	qura	PROPN
ejpam-5171	2	57	university	university	PROPN
ejpam-5171	2	58	,	,	PUNCT
ejpam-5171	2	59	makkah	makkah	PROPN
ejpam-5171	2	60	21955	21955	NUM
ejpam-5171	2	61	,	,	PUNCT
ejpam-5171	2	62	saudi	saudi	PROPN
ejpam-5171	2	63	arabia	arabia	PROPN
ejpam-5171	2	64	2	2	NUM
ejpam-5171	2	65	department	department	NOUN
ejpam-5171	2	66	of	of	ADP
ejpam-5171	2	67	mathematics	mathematic	NOUN
ejpam-5171	2	68	,	,	PUNCT
ejpam-5171	2	69	college	college	NOUN
ejpam-5171	2	70	of	of	ADP
ejpam-5171	2	71	sciences	sciences	PROPN
ejpam-5171	2	72	,	,	PUNCT
ejpam-5171	2	73	qassim	qassim	PROPN
ejpam-5171	2	74	university	university	PROPN
ejpam-5171	2	75	,	,	PUNCT
ejpam-5171	2	76	buraidah	buraidah	PROPN
ejpam-5171	2	77	,	,	PUNCT
ejpam-5171	3	1	saudi	saudi	PROPN
ejpam-5171	3	2	arabia	arabia	PROPN
ejpam-5171	3	3	abstract	abstract	NOUN
ejpam-5171	3	4	.	.	PUNCT
ejpam-5171	4	1	this	this	DET
ejpam-5171	4	2	paper	paper	NOUN
ejpam-5171	4	3	introduces	introduce	NOUN
ejpam-5171	4	4	and	and	CCONJ
ejpam-5171	4	5	investigates	investigate	VERB
ejpam-5171	4	6	several	several	ADJ
ejpam-5171	4	7	new	new	ADJ
ejpam-5171	4	8	classes	class	NOUN
ejpam-5171	4	9	of	of	ADP
ejpam-5171	4	10	sets	set	NOUN
ejpam-5171	4	11	called	call	VERB
ejpam-5171	4	12	p	p	NOUN
ejpam-5171	4	13	-	-	PUNCT
ejpam-5171	4	14	α	α	NOUN
ejpam-5171	4	15	-	-	ADJ
ejpam-5171	4	16	open	open	ADJ
ejpam-5171	4	17	sets	set	NOUN
ejpam-5171	4	18	,	,	PUNCT
ejpam-5171	4	19	p	p	NOUN
ejpam-5171	4	20	-	-	PUNCT
ejpam-5171	4	21	semiopen	semiopen	ADJ
ejpam-5171	4	22	sets	set	NOUN
ejpam-5171	4	23	,	,	PUNCT
ejpam-5171	4	24	p	p	ADJ
ejpam-5171	4	25	-	-	PUNCT
ejpam-5171	4	26	preopen	preopen	ADJ
ejpam-5171	4	27	sets	set	NOUN
ejpam-5171	4	28	,	,	PUNCT
ejpam-5171	4	29	and	and	CCONJ
ejpam-5171	4	30	p	p	X
ejpam-5171	4	31	-	-	PUNCT
ejpam-5171	4	32	β	β	NOUN
ejpam-5171	4	33	-	-	ADJ
ejpam-5171	4	34	open	open	ADJ
ejpam-5171	4	35	sets	set	NOUN
ejpam-5171	4	36	within	within	ADP
ejpam-5171	4	37	the	the	DET
ejpam-5171	4	38	framework	framework	NOUN
ejpam-5171	4	39	of	of	ADP
ejpam-5171	4	40	primal	primal	ADJ
ejpam-5171	4	41	topological	topological	ADJ
ejpam-5171	4	42	spaces	space	NOUN
ejpam-5171	4	43	.	.	PUNCT
ejpam-5171	5	1	their	their	PRON
ejpam-5171	5	2	properties	property	NOUN
ejpam-5171	5	3	and	and	CCONJ
ejpam-5171	5	4	relationships	relationship	NOUN
ejpam-5171	5	5	with	with	ADP
ejpam-5171	5	6	other	other	ADJ
ejpam-5171	5	7	open	open	ADJ
ejpam-5171	5	8	set	set	NOUN
ejpam-5171	5	9	generalizations	generalization	NOUN
ejpam-5171	5	10	are	be	AUX
ejpam-5171	5	11	studied	study	VERB
ejpam-5171	5	12	through	through	ADP
ejpam-5171	5	13	examples	example	NOUN
ejpam-5171	5	14	.	.	PUNCT
ejpam-5171	6	1	additionally	additionally	ADV
ejpam-5171	6	2	,	,	PUNCT
ejpam-5171	6	3	the	the	DET
ejpam-5171	6	4	concepts	concept	NOUN
ejpam-5171	6	5	of	of	ADP
ejpam-5171	6	6	pr	pr	NOUN
ejpam-5171	6	7	-	-	PUNCT
ejpam-5171	6	8	sets	set	NOUN
ejpam-5171	6	9	and	and	CCONJ
ejpam-5171	6	10	prα	prα	VERB
ejpam-5171	6	11	-sets	-set	NOUN
ejpam-5171	6	12	are	be	AUX
ejpam-5171	6	13	defined	define	VERB
ejpam-5171	6	14	and	and	CCONJ
ejpam-5171	6	15	their	their	PRON
ejpam-5171	6	16	characteristics	characteristic	NOUN
ejpam-5171	6	17	examined	examine	VERB
ejpam-5171	6	18	.	.	PUNCT
ejpam-5171	7	1	also	also	ADV
ejpam-5171	7	2	,	,	PUNCT
ejpam-5171	7	3	the	the	DET
ejpam-5171	7	4	notions	notion	NOUN
ejpam-5171	7	5	of	of	ADP
ejpam-5171	7	6	p	p	NOUN
ejpam-5171	7	7	-	-	PUNCT
ejpam-5171	7	8	α	α	NOUN
ejpam-5171	7	9	-	-	ADJ
ejpam-5171	7	10	continuous	continuous	ADJ
ejpam-5171	7	11	,	,	PUNCT
ejpam-5171	7	12	p	p	NOUN
ejpam-5171	7	13	-	-	PUNCT
ejpam-5171	7	14	semicontinuous	semicontinuous	ADJ
ejpam-5171	7	15	,	,	PUNCT
ejpam-5171	7	16	p	p	NOUN
ejpam-5171	7	17	-	-	NOUN
ejpam-5171	7	18	precontinuous	precontinuous	ADJ
ejpam-5171	7	19	and	and	CCONJ
ejpam-5171	7	20	p	p	NOUN
ejpam-5171	7	21	-	-	PUNCT
ejpam-5171	7	22	β	β	NOUN
ejpam-5171	7	23	-	-	ADJ
ejpam-5171	7	24	continuous	continuous	ADJ
ejpam-5171	7	25	mappings	mapping	NOUN
ejpam-5171	7	26	are	be	AUX
ejpam-5171	7	27	initiated	initiate	VERB
ejpam-5171	7	28	and	and	CCONJ
ejpam-5171	7	29	their	their	PRON
ejpam-5171	7	30	features	feature	NOUN
ejpam-5171	7	31	and	and	CCONJ
ejpam-5171	7	32	main	main	ADJ
ejpam-5171	7	33	characterizations	characterization	NOUN
ejpam-5171	7	34	determined	determine	VERB
ejpam-5171	7	35	.	.	PUNCT
ejpam-5171	8	1	a	a	DET
ejpam-5171	8	2	new	new	ADJ
ejpam-5171	8	3	class	class	NOUN
ejpam-5171	8	4	of	of	ADP
ejpam-5171	8	5	sets	set	NOUN
ejpam-5171	8	6	called	call	VERB
ejpam-5171	8	7	ψ̃p	ψ̃p	NOUN
ejpam-5171	8	8	-sets	-set	NOUN
ejpam-5171	8	9	is	be	AUX
ejpam-5171	8	10	also	also	ADV
ejpam-5171	8	11	introduced	introduce	VERB
ejpam-5171	8	12	in	in	ADP
ejpam-5171	8	13	primal	primal	ADJ
ejpam-5171	8	14	topological	topological	ADJ
ejpam-5171	8	15	spaces	space	NOUN
ejpam-5171	8	16	using	use	VERB
ejpam-5171	8	17	the	the	DET
ejpam-5171	8	18	ψp	ψp	NOUN
ejpam-5171	8	19	-operator	-operator	NOUN
ejpam-5171	8	20	.	.	PUNCT
ejpam-5171	9	1	their	their	PRON
ejpam-5171	9	2	properties	property	NOUN
ejpam-5171	9	3	and	and	CCONJ
ejpam-5171	9	4	relationships	relationship	NOUN
ejpam-5171	9	5	between	between	ADP
ejpam-5171	9	6	ψ̃p	ψ̃p	NOUN
ejpam-5171	9	7	-sets	-set	NOUN
ejpam-5171	9	8	,	,	PUNCT
ejpam-5171	9	9	α	α	NOUN
ejpam-5171	9	10	-	-	ADJ
ejpam-5171	9	11	open	open	ADJ
ejpam-5171	9	12	,	,	PUNCT
ejpam-5171	9	13	semi	semi	ADJ
ejpam-5171	9	14	-	-	ADJ
ejpam-5171	9	15	open	open	ADJ
ejpam-5171	9	16	,	,	PUNCT
ejpam-5171	9	17	and	and	CCONJ
ejpam-5171	9	18	pre	pre	ADJ
ejpam-5171	9	19	-	-	ADJ
ejpam-5171	9	20	open	open	ADJ
ejpam-5171	9	21	are	be	AUX
ejpam-5171	9	22	investigated	investigate	VERB
ejpam-5171	9	23	.	.	PUNCT
ejpam-5171	10	1	theorems	theorem	NOUN
ejpam-5171	10	2	on	on	ADP
ejpam-5171	10	3	arbitrary	arbitrary	ADJ
ejpam-5171	10	4	unions	union	NOUN
ejpam-5171	10	5	and	and	CCONJ
ejpam-5171	10	6	finite	finite	ADJ
ejpam-5171	10	7	intersections	intersection	NOUN
ejpam-5171	10	8	of	of	ADP
ejpam-5171	10	9	ψ̃p	ψ̃p	NOUN
ejpam-5171	10	10	are	be	AUX
ejpam-5171	10	11	discussed	discuss	VERB
ejpam-5171	10	12	.	.	PUNCT
ejpam-5171	11	1	2020	2020	NUM
ejpam-5171	11	2	mathematics	mathematic	NOUN
ejpam-5171	11	3	subject	subject	NOUN
ejpam-5171	11	4	classifications	classification	NOUN
ejpam-5171	11	5	:	:	PUNCT
ejpam-5171	11	6	54a05	54a05	NUM
ejpam-5171	11	7	,	,	PUNCT
ejpam-5171	11	8	54b99	54b99	NUM
ejpam-5171	11	9	,	,	PUNCT
ejpam-5171	11	10	94a60	94a60	PRON
ejpam-5171	11	11	key	key	ADJ
ejpam-5171	11	12	words	word	NOUN
ejpam-5171	11	13	and	and	CCONJ
ejpam-5171	11	14	phrases	phrase	NOUN
ejpam-5171	11	15	:	:	PUNCT
ejpam-5171	11	16	primal	primal	ADJ
ejpam-5171	11	17	topological	topological	ADJ
ejpam-5171	11	18	spaces	space	NOUN
ejpam-5171	11	19	,	,	PUNCT
ejpam-5171	11	20	p	p	NOUN
ejpam-5171	11	21	-	-	PUNCT
ejpam-5171	11	22	open	open	ADJ
ejpam-5171	11	23	set	set	NOUN
ejpam-5171	11	24	,	,	PUNCT
ejpam-5171	11	25	pr	pr	NOUN
ejpam-5171	11	26	-	-	PUNCT
ejpam-5171	11	27	sets	set	NOUN
ejpam-5171	11	28	,	,	PUNCT
ejpam-5171	11	29	ψp	ψp	ADP
ejpam-5171	11	30	-sets	-set	NOUN
ejpam-5171	11	31	,	,	PUNCT
ejpam-5171	11	32	and	and	CCONJ
ejpam-5171	11	33	ψ̃p	ψ̃p	NOUN
ejpam-5171	11	34	sets	set	NOUN
ejpam-5171	11	35	,	,	PUNCT
ejpam-5171	11	36	p	p	NOUN
ejpam-5171	11	37	-	-	PUNCT
ejpam-5171	11	38	continuous	continuous	ADJ
ejpam-5171	11	39	1	1	NUM
ejpam-5171	11	40	.	.	PUNCT
ejpam-5171	11	41	introduction	introduction	NOUN
ejpam-5171	11	42	and	and	CCONJ
ejpam-5171	11	43	preliminaries	preliminary	NOUN
ejpam-5171	11	44	topology	topology	NOUN
ejpam-5171	11	45	is	be	AUX
ejpam-5171	11	46	one	one	NUM
ejpam-5171	11	47	of	of	ADP
ejpam-5171	11	48	the	the	DET
ejpam-5171	11	49	important	important	ADJ
ejpam-5171	11	50	scientific	scientific	ADJ
ejpam-5171	11	51	fields	field	NOUN
ejpam-5171	11	52	in	in	ADP
ejpam-5171	11	53	mathematics	mathematic	NOUN
ejpam-5171	11	54	and	and	CCONJ
ejpam-5171	11	55	physics	physics	NOUN
ejpam-5171	11	56	.	.	PUNCT
ejpam-5171	12	1	it	it	PRON
ejpam-5171	12	2	can	can	AUX
ejpam-5171	12	3	be	be	AUX
ejpam-5171	12	4	used	use	VERB
ejpam-5171	12	5	in	in	ADP
ejpam-5171	12	6	many	many	ADJ
ejpam-5171	12	7	different	different	ADJ
ejpam-5171	12	8	areas	area	NOUN
ejpam-5171	12	9	of	of	ADP
ejpam-5171	12	10	mathematics	mathematic	NOUN
ejpam-5171	12	11	,	,	PUNCT
ejpam-5171	12	12	including	include	VERB
ejpam-5171	12	13	algebra	algebra	NOUN
ejpam-5171	12	14	,	,	PUNCT
ejpam-5171	12	15	riemann	riemann	PROPN
ejpam-5171	12	16	integration	integration	NOUN
ejpam-5171	12	17	,	,	PUNCT
ejpam-5171	12	18	perron	perron	PROPN
ejpam-5171	12	19	integration	integration	NOUN
ejpam-5171	12	20	,	,	PUNCT
ejpam-5171	12	21	operations	operation	NOUN
ejpam-5171	12	22	research	research	NOUN
ejpam-5171	12	23	,	,	PUNCT
ejpam-5171	12	24	probability	probability	NOUN
ejpam-5171	12	25	theory	theory	NOUN
ejpam-5171	12	26	,	,	PUNCT
ejpam-5171	12	27	game	game	NOUN
ejpam-5171	12	28	theory	theory	NOUN
ejpam-5171	12	29	,	,	PUNCT
ejpam-5171	12	30	smoothness	smoothness	NOUN
ejpam-5171	12	31	of	of	ADP
ejpam-5171	12	32	functions	function	NOUN
ejpam-5171	12	33	,	,	PUNCT
ejpam-5171	12	34	and	and	CCONJ
ejpam-5171	12	35	measurement	measurement	NOUN
ejpam-5171	12	36	theory	theory	NOUN
ejpam-5171	12	37	.	.	PUNCT
ejpam-5171	13	1	also	also	ADV
ejpam-5171	13	2	,	,	PUNCT
ejpam-5171	13	3	it	it	PRON
ejpam-5171	13	4	is	be	AUX
ejpam-5171	13	5	relevant	relevant	ADJ
ejpam-5171	13	6	to	to	ADP
ejpam-5171	13	7	various	various	ADJ
ejpam-5171	13	8	fields	field	NOUN
ejpam-5171	13	9	in	in	ADP
ejpam-5171	13	10	physics	physics	NOUN
ejpam-5171	13	11	such	such	ADJ
ejpam-5171	13	12	as	as	ADP
ejpam-5171	13	13	condensed	condense	VERB
ejpam-5171	13	14	matter	matter	NOUN
ejpam-5171	13	15	physics	physics	NOUN
ejpam-5171	13	16	,	,	PUNCT
ejpam-5171	13	17	quantum	quantum	ADJ
ejpam-5171	13	18	field	field	NOUN
ejpam-5171	13	19	theory	theory	NOUN
ejpam-5171	13	20	,	,	PUNCT
ejpam-5171	13	21	physical	physical	ADJ
ejpam-5171	13	22	cosmology	cosmology	NOUN
ejpam-5171	13	23	,	,	PUNCT
ejpam-5171	13	24	mechanical	mechanical	ADJ
ejpam-5171	13	25	engineering	engineering	NOUN
ejpam-5171	13	26	,	,	PUNCT
ejpam-5171	13	27	and	and	CCONJ
ejpam-5171	13	28	materials	material	NOUN
ejpam-5171	13	29	science	science	NOUN
ejpam-5171	13	30	.	.	PUNCT
ejpam-5171	14	1	some	some	DET
ejpam-5171	14	2	applications	application	NOUN
ejpam-5171	14	3	of	of	ADP
ejpam-5171	14	4	these	these	DET
ejpam-5171	14	5	mathematical	mathematical	ADJ
ejpam-5171	14	6	concepts	concept	NOUN
ejpam-5171	14	7	influence	influence	VERB
ejpam-5171	14	8	the	the	DET
ejpam-5171	14	9	mechanical	mechanical	ADJ
ejpam-5171	14	10	properties	property	NOUN
ejpam-5171	14	11	of	of	ADP
ejpam-5171	14	12	solids	solid	NOUN
ejpam-5171	14	13	,	,	PUNCT
ejpam-5171	14	14	as	as	ADV
ejpam-5171	14	15	well	well	ADV
ejpam-5171	14	16	as	as	ADP
ejpam-5171	14	17	the	the	DET
ejpam-5171	14	18	electrical	electrical	ADJ
ejpam-5171	14	19	and	and	CCONJ
ejpam-5171	14	20	mechanical	mechanical	ADJ
ejpam-5171	14	21	characteristics	characteristic	NOUN
ejpam-5171	14	22	that	that	PRON
ejpam-5171	14	23	rely	rely	VERB
ejpam-5171	14	24	on	on	ADP
ejpam-5171	14	25	the	the	DET
ejpam-5171	14	26	arrangement	arrangement	NOUN
ejpam-5171	14	27	and	and	CCONJ
ejpam-5171	14	28	network	network	NOUN
ejpam-5171	14	29	structures	structure	NOUN
ejpam-5171	14	30	of	of	ADP
ejpam-5171	14	31	molecules	molecule	NOUN
ejpam-5171	14	32	and	and	CCONJ
ejpam-5171	14	33	primary	primary	ADJ
ejpam-5171	14	34	units	unit	NOUN
ejpam-5171	14	35	in	in	ADP
ejpam-5171	14	36	materials	material	NOUN
ejpam-5171	14	37	.	.	PUNCT
ejpam-5171	15	1	∗corresponding	∗corresponde	VERB
ejpam-5171	15	2	author	author	NOUN
ejpam-5171	15	3	.	.	PUNCT
ejpam-5171	16	1	doi	doi	NOUN
ejpam-5171	16	2	:	:	PUNCT
ejpam-5171	16	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5171	https://doi.org/10.29020/nybg.ejpam.v17i2.5171	PROPN
ejpam-5171	16	4	email	email	NOUN
ejpam-5171	16	5	addresses	address	NOUN
ejpam-5171	16	6	:	:	PUNCT
ejpam-5171	16	7	hsssaadi@uqu.edu.sa	hsssaadi@uqu.edu.sa	PROPN
ejpam-5171	16	8	(	(	PUNCT
ejpam-5171	16	9	h.	h.	PROPN
ejpam-5171	16	10	al	al	PROPN
ejpam-5171	16	11	-	-	PUNCT
ejpam-5171	16	12	saadi	saadi	PROPN
ejpam-5171	16	13	)	)	PUNCT
ejpam-5171	16	14	,	,	PUNCT
ejpam-5171	16	15	mmhdieb@qu.edu.sa	mmhdieb@qu.edu.sa	PROPN
ejpam-5171	16	16	(	(	PUNCT
ejpam-5171	16	17	m.	m.	PROPN
ejpam-5171	16	18	al	al	PROPN
ejpam-5171	16	19	-	-	PUNCT
ejpam-5171	16	20	hodieb	hodieb	PROPN
ejpam-5171	16	21	)	)	PUNCT
ejpam-5171	16	22	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5171	16	23	1352	1352	NUM
ejpam-5171	17	1	©	©	ADP
ejpam-5171	17	2	2024	2024	NUM
ejpam-5171	17	3	ejpam	ejpam	NOUN
ejpam-5171	17	4	all	all	DET
ejpam-5171	17	5	rights	right	NOUN
ejpam-5171	17	6	reserved	reserve	VERB
ejpam-5171	17	7	.	.	PUNCT
ejpam-5171	18	1	h.	h.	PROPN
ejpam-5171	18	2	al	al	PROPN
ejpam-5171	18	3	-	-	PUNCT
ejpam-5171	18	4	saadi	saadi	PROPN
ejpam-5171	18	5	,	,	PUNCT
ejpam-5171	18	6	m.	m.	NOUN
ejpam-5171	18	7	al	al	PROPN
ejpam-5171	18	8	-	-	PUNCT
ejpam-5171	18	9	hodieb	hodieb	PROPN
ejpam-5171	18	10	/	/	SYM
ejpam-5171	18	11	eur	eur	PROPN
ejpam-5171	18	12	.	.	PUNCT
ejpam-5171	19	1	j.	j.	PROPN
ejpam-5171	19	2	pure	pure	PROPN
ejpam-5171	19	3	appl	appl	PROPN
ejpam-5171	19	4	.	.	PROPN
ejpam-5171	19	5	math	math	PROPN
ejpam-5171	19	6	,	,	PUNCT
ejpam-5171	19	7	17	17	NUM
ejpam-5171	19	8	(	(	PUNCT
ejpam-5171	19	9	2	2	NUM
ejpam-5171	19	10	)	)	PUNCT
ejpam-5171	19	11	(	(	PUNCT
ejpam-5171	19	12	2024	2024	NUM
ejpam-5171	19	13	)	)	PUNCT
ejpam-5171	19	14	,	,	PUNCT
ejpam-5171	19	15	1352	1352	NUM
ejpam-5171	19	16	-	-	SYM
ejpam-5171	19	17	1368	1368	NUM
ejpam-5171	19	18	1353	1353	NUM
ejpam-5171	19	19	over	over	ADP
ejpam-5171	19	20	the	the	DET
ejpam-5171	19	21	past	past	ADJ
ejpam-5171	19	22	years	year	NOUN
ejpam-5171	19	23	,	,	PUNCT
ejpam-5171	19	24	open	open	ADJ
ejpam-5171	19	25	-	-	PUNCT
ejpam-5171	19	26	set	set	VERB
ejpam-5171	19	27	generalizations	generalization	NOUN
ejpam-5171	19	28	have	have	AUX
ejpam-5171	19	29	been	be	AUX
ejpam-5171	19	30	discussed	discuss	VERB
ejpam-5171	19	31	by	by	ADP
ejpam-5171	19	32	many	many	ADJ
ejpam-5171	19	33	researchers	researcher	NOUN
ejpam-5171	19	34	.	.	PUNCT
ejpam-5171	20	1	the	the	DET
ejpam-5171	20	2	initial	initial	ADJ
ejpam-5171	20	3	concept	concept	NOUN
ejpam-5171	20	4	of	of	ADP
ejpam-5171	20	5	semi	semi	ADJ
ejpam-5171	20	6	-	-	ADJ
ejpam-5171	20	7	open	open	ADJ
ejpam-5171	20	8	sets	set	NOUN
ejpam-5171	20	9	was	be	AUX
ejpam-5171	20	10	introduced	introduce	VERB
ejpam-5171	20	11	by	by	ADP
ejpam-5171	20	12	levine	levine	PROPN
ejpam-5171	20	13	[	[	X
ejpam-5171	20	14	1	1	NUM
ejpam-5171	20	15	]	]	PUNCT
ejpam-5171	20	16	in	in	ADP
ejpam-5171	20	17	1963	1963	NUM
ejpam-5171	20	18	.	.	PUNCT
ejpam-5171	20	19	nj̊astad	nj̊astad	NOUN
ejpam-5171	21	1	[	[	X
ejpam-5171	21	2	2	2	X
ejpam-5171	21	3	]	]	PUNCT
ejpam-5171	21	4	introduced	introduce	VERB
ejpam-5171	21	5	several	several	ADJ
ejpam-5171	21	6	classes	class	NOUN
ejpam-5171	21	7	of	of	ADP
ejpam-5171	21	8	almost	almost	ADV
ejpam-5171	21	9	open	open	ADJ
ejpam-5171	21	10	sets	set	NOUN
ejpam-5171	21	11	in	in	ADP
ejpam-5171	21	12	1965	1965	NUM
ejpam-5171	21	13	;	;	PUNCT
ejpam-5171	21	14	specifically	specifically	ADV
ejpam-5171	21	15	,	,	PUNCT
ejpam-5171	21	16	they	they	PRON
ejpam-5171	21	17	looked	look	VERB
ejpam-5171	21	18	into	into	ADP
ejpam-5171	21	19	the	the	DET
ejpam-5171	21	20	structure	structure	NOUN
ejpam-5171	21	21	of	of	ADP
ejpam-5171	21	22	α	α	NOUN
ejpam-5171	21	23	-	-	ADJ
ejpam-5171	21	24	open	open	ADJ
ejpam-5171	21	25	sets	set	NOUN
ejpam-5171	21	26	and	and	CCONJ
ejpam-5171	21	27	provided	provide	VERB
ejpam-5171	21	28	several	several	ADJ
ejpam-5171	21	29	applications	application	NOUN
ejpam-5171	21	30	.	.	PUNCT
ejpam-5171	22	1	pre	pre	ADJ
ejpam-5171	22	2	-	-	ADJ
ejpam-5171	22	3	open	open	ADJ
ejpam-5171	22	4	sets	set	NOUN
ejpam-5171	22	5	and	and	CCONJ
ejpam-5171	22	6	precontinuous	precontinuous	ADJ
ejpam-5171	22	7	functions	function	NOUN
ejpam-5171	22	8	were	be	AUX
ejpam-5171	22	9	presented	present	VERB
ejpam-5171	22	10	and	and	CCONJ
ejpam-5171	22	11	investigated	investigate	VERB
ejpam-5171	22	12	by	by	ADP
ejpam-5171	22	13	mashhour	mashhour	PROPN
ejpam-5171	22	14	et	et	PROPN
ejpam-5171	22	15	al	al	PROPN
ejpam-5171	22	16	.	.	PROPN
ejpam-5171	23	1	in	in	ADP
ejpam-5171	23	2	1982	1982	NUM
ejpam-5171	23	3	,	,	PUNCT
ejpam-5171	23	4	[	[	X
ejpam-5171	23	5	3	3	NUM
ejpam-5171	23	6	]	]	PUNCT
ejpam-5171	23	7	presented	present	VERB
ejpam-5171	23	8	and	and	CCONJ
ejpam-5171	23	9	investigated	investigate	VERB
ejpam-5171	23	10	the	the	DET
ejpam-5171	23	11	concepts	concept	NOUN
ejpam-5171	23	12	of	of	ADP
ejpam-5171	23	13	pre	pre	ADJ
ejpam-5171	23	14	-	-	ADJ
ejpam-5171	23	15	open	open	ADJ
ejpam-5171	23	16	and	and	CCONJ
ejpam-5171	23	17	pre	pre	ADJ
ejpam-5171	23	18	-	-	ADJ
ejpam-5171	23	19	continuous	continuous	ADJ
ejpam-5171	23	20	functions	function	NOUN
ejpam-5171	23	21	.	.	PUNCT
ejpam-5171	24	1	the	the	DET
ejpam-5171	24	2	new	new	ADJ
ejpam-5171	24	3	notions	notion	NOUN
ejpam-5171	24	4	of	of	ADP
ejpam-5171	24	5	β	β	ADJ
ejpam-5171	24	6	-	-	ADJ
ejpam-5171	24	7	open	open	ADJ
ejpam-5171	24	8	sets	set	NOUN
ejpam-5171	24	9	,	,	PUNCT
ejpam-5171	24	10	β	β	ADJ
ejpam-5171	24	11	-	-	ADJ
ejpam-5171	24	12	continuous	continuous	ADJ
ejpam-5171	24	13	mappings	mapping	NOUN
ejpam-5171	24	14	,	,	PUNCT
ejpam-5171	24	15	and	and	CCONJ
ejpam-5171	24	16	β	β	X
ejpam-5171	24	17	-	-	ADJ
ejpam-5171	24	18	open	open	ADJ
ejpam-5171	24	19	mappings	mapping	NOUN
ejpam-5171	24	20	were	be	AUX
ejpam-5171	24	21	first	first	ADV
ejpam-5171	24	22	presented	present	VERB
ejpam-5171	24	23	by	by	ADP
ejpam-5171	24	24	abd	abd	PROPN
ejpam-5171	24	25	el	el	PROPN
ejpam-5171	24	26	-	-	PROPN
ejpam-5171	24	27	monsef	monsef	PROPN
ejpam-5171	24	28	et	et	PROPN
ejpam-5171	24	29	al	al	PROPN
ejpam-5171	24	30	.	.	PUNCT
ejpam-5171	25	1	[	[	X
ejpam-5171	25	2	4	4	X
ejpam-5171	25	3	]	]	PUNCT
ejpam-5171	25	4	in	in	ADP
ejpam-5171	25	5	1983	1983	NUM
ejpam-5171	25	6	.	.	PUNCT
ejpam-5171	26	1	topology	topology	NOUN
ejpam-5171	26	2	’s	’s	PART
ejpam-5171	26	3	application	application	NOUN
ejpam-5171	26	4	in	in	ADP
ejpam-5171	26	5	social	social	ADJ
ejpam-5171	26	6	science	science	NOUN
ejpam-5171	26	7	and	and	CCONJ
ejpam-5171	26	8	science	science	NOUN
ejpam-5171	26	9	has	have	AUX
ejpam-5171	26	10	led	lead	VERB
ejpam-5171	26	11	to	to	ADP
ejpam-5171	26	12	the	the	DET
ejpam-5171	26	13	development	development	NOUN
ejpam-5171	26	14	of	of	ADP
ejpam-5171	26	15	many	many	ADJ
ejpam-5171	26	16	new	new	ADJ
ejpam-5171	26	17	ideas	idea	NOUN
ejpam-5171	26	18	in	in	ADP
ejpam-5171	26	19	addition	addition	NOUN
ejpam-5171	26	20	to	to	ADP
ejpam-5171	26	21	traditional	traditional	ADJ
ejpam-5171	26	22	structures	structure	NOUN
ejpam-5171	26	23	.	.	PUNCT
ejpam-5171	27	1	kuratowski	kuratowski	PROPN
ejpam-5171	27	2	presented	present	VERB
ejpam-5171	27	3	the	the	DET
ejpam-5171	27	4	concept	concept	NOUN
ejpam-5171	27	5	of	of	ADP
ejpam-5171	27	6	the	the	DET
ejpam-5171	27	7	ideal	ideal	NOUN
ejpam-5171	27	8	derived	derive	VERB
ejpam-5171	27	9	from	from	ADP
ejpam-5171	27	10	a	a	DET
ejpam-5171	27	11	filter	filter	NOUN
ejpam-5171	27	12	.	.	PUNCT
ejpam-5171	28	1	the	the	DET
ejpam-5171	28	2	concept	concept	NOUN
ejpam-5171	28	3	of	of	ADP
ejpam-5171	28	4	an	an	DET
ejpam-5171	28	5	ideal	ideal	NOUN
ejpam-5171	28	6	can	can	AUX
ejpam-5171	28	7	be	be	AUX
ejpam-5171	28	8	thought	think	VERB
ejpam-5171	28	9	of	of	ADP
ejpam-5171	28	10	as	as	ADP
ejpam-5171	28	11	the	the	DET
ejpam-5171	28	12	dual	dual	ADJ
ejpam-5171	28	13	counterpart	counterpart	NOUN
ejpam-5171	28	14	of	of	ADP
ejpam-5171	28	15	a	a	DET
ejpam-5171	28	16	filter	filter	NOUN
ejpam-5171	28	17	.	.	PUNCT
ejpam-5171	29	1	likewise	likewise	ADV
ejpam-5171	29	2	,	,	PUNCT
ejpam-5171	29	3	among	among	ADP
ejpam-5171	29	4	the	the	DET
ejpam-5171	29	5	new	new	ADJ
ejpam-5171	29	6	constructs	construct	NOUN
ejpam-5171	29	7	in	in	ADP
ejpam-5171	29	8	topology	topology	NOUN
ejpam-5171	29	9	is	be	AUX
ejpam-5171	29	10	the	the	DET
ejpam-5171	29	11	notion	notion	NOUN
ejpam-5171	29	12	of	of	ADP
ejpam-5171	29	13	a	a	DET
ejpam-5171	29	14	grill	grill	NOUN
ejpam-5171	29	15	,	,	PUNCT
ejpam-5171	29	16	which	which	PRON
ejpam-5171	29	17	was	be	AUX
ejpam-5171	29	18	first	first	ADV
ejpam-5171	29	19	defined	define	VERB
ejpam-5171	29	20	by	by	ADP
ejpam-5171	29	21	choquet	choquet	NOUN
ejpam-5171	29	22	in	in	ADP
ejpam-5171	29	23	1947	1947	NUM
ejpam-5171	29	24	[	[	X
ejpam-5171	29	25	5	5	NUM
ejpam-5171	29	26	]	]	PUNCT
ejpam-5171	29	27	and	and	CCONJ
ejpam-5171	29	28	thron	thron	X
ejpam-5171	29	29	[	[	X
ejpam-5171	29	30	6	6	NUM
ejpam-5171	29	31	]	]	PUNCT
ejpam-5171	29	32	introduced	introduce	VERB
ejpam-5171	29	33	proximity	proximity	NOUN
ejpam-5171	29	34	structures	structure	NOUN
ejpam-5171	29	35	within	within	ADP
ejpam-5171	29	36	the	the	DET
ejpam-5171	29	37	domain	domain	NOUN
ejpam-5171	29	38	of	of	ADP
ejpam-5171	29	39	grills	grill	NOUN
ejpam-5171	29	40	.	.	PUNCT
ejpam-5171	30	1	in	in	ADP
ejpam-5171	30	2	1977	1977	NUM
ejpam-5171	30	3	,	,	PUNCT
ejpam-5171	30	4	chattopadhyay	chattopadhyay	NOUN
ejpam-5171	30	5	and	and	CCONJ
ejpam-5171	30	6	thron	thron	PROPN
ejpam-5171	31	1	[	[	X
ejpam-5171	31	2	7	7	NUM
ejpam-5171	31	3	]	]	PUNCT
ejpam-5171	31	4	expanded	expand	VERB
ejpam-5171	31	5	the	the	DET
ejpam-5171	31	6	concepts	concept	NOUN
ejpam-5171	31	7	of	of	ADP
ejpam-5171	31	8	closure	closure	NOUN
ejpam-5171	31	9	spaces	space	NOUN
ejpam-5171	31	10	in	in	ADP
ejpam-5171	31	11	conjunction	conjunction	NOUN
ejpam-5171	31	12	with	with	ADP
ejpam-5171	31	13	grills	grill	NOUN
ejpam-5171	31	14	.	.	PUNCT
ejpam-5171	32	1	furthermore	furthermore	ADV
ejpam-5171	32	2	,	,	PUNCT
ejpam-5171	32	3	chattopadhyay	chattopadhyay	NOUN
ejpam-5171	32	4	and	and	CCONJ
ejpam-5171	32	5	colleagues	colleague	NOUN
ejpam-5171	33	1	[	[	X
ejpam-5171	33	2	8	8	NUM
ejpam-5171	33	3	]	]	PUNCT
ejpam-5171	33	4	expanded	expand	VERB
ejpam-5171	33	5	the	the	DET
ejpam-5171	33	6	concept	concept	NOUN
ejpam-5171	33	7	of	of	ADP
ejpam-5171	33	8	grills	grill	NOUN
ejpam-5171	33	9	to	to	PART
ejpam-5171	33	10	investigate	investigate	VERB
ejpam-5171	33	11	merotopic	merotopic	ADJ
ejpam-5171	33	12	spaces	space	NOUN
ejpam-5171	33	13	.	.	PUNCT
ejpam-5171	34	1	since	since	SCONJ
ejpam-5171	34	2	that	that	DET
ejpam-5171	34	3	time	time	NOUN
ejpam-5171	34	4	,	,	PUNCT
ejpam-5171	34	5	the	the	DET
ejpam-5171	34	6	grill	grill	NOUN
ejpam-5171	34	7	structure	structure	NOUN
ejpam-5171	34	8	has	have	AUX
ejpam-5171	34	9	found	find	VERB
ejpam-5171	34	10	extensive	extensive	ADJ
ejpam-5171	34	11	application	application	NOUN
ejpam-5171	34	12	within	within	ADP
ejpam-5171	34	13	the	the	DET
ejpam-5171	34	14	field	field	NOUN
ejpam-5171	34	15	of	of	ADP
ejpam-5171	34	16	topology	topology	NOUN
ejpam-5171	34	17	.	.	PUNCT
ejpam-5171	35	1	roy	roy	PROPN
ejpam-5171	35	2	and	and	CCONJ
ejpam-5171	35	3	mukherjee	mukherjee	PROPN
ejpam-5171	36	1	[	[	X
ejpam-5171	36	2	9–11	9–11	X
ejpam-5171	36	3	]	]	PUNCT
ejpam-5171	36	4	conducted	conduct	VERB
ejpam-5171	36	5	the	the	DET
ejpam-5171	36	6	initial	initial	ADJ
ejpam-5171	36	7	attempt	attempt	NOUN
ejpam-5171	36	8	to	to	PART
ejpam-5171	36	9	identify	identify	VERB
ejpam-5171	36	10	the	the	DET
ejpam-5171	36	11	topological	topological	ADJ
ejpam-5171	36	12	characteristics	characteristic	NOUN
ejpam-5171	36	13	associated	associate	VERB
ejpam-5171	36	14	with	with	ADP
ejpam-5171	36	15	grills	grill	NOUN
ejpam-5171	36	16	.	.	PUNCT
ejpam-5171	37	1	the	the	DET
ejpam-5171	37	2	authors	author	NOUN
ejpam-5171	37	3	in	in	ADP
ejpam-5171	37	4	[	[	X
ejpam-5171	37	5	12	12	NUM
ejpam-5171	37	6	,	,	PUNCT
ejpam-5171	37	7	13	13	NUM
ejpam-5171	37	8	]	]	PUNCT
ejpam-5171	37	9	defined	define	VERB
ejpam-5171	37	10	operators	operator	NOUN
ejpam-5171	37	11	on	on	ADP
ejpam-5171	37	12	grill	grill	ADJ
ejpam-5171	37	13	topological	topological	ADJ
ejpam-5171	37	14	space	space	NOUN
ejpam-5171	37	15	.	.	PUNCT
ejpam-5171	38	1	then	then	ADV
ejpam-5171	38	2	,	,	PUNCT
ejpam-5171	38	3	several	several	ADJ
ejpam-5171	38	4	variations	variation	NOUN
ejpam-5171	38	5	on	on	ADP
ejpam-5171	38	6	operators	operator	NOUN
ejpam-5171	38	7	appeared	appear	VERB
ejpam-5171	38	8	from	from	ADP
ejpam-5171	38	9	other	other	ADJ
ejpam-5171	38	10	researchers	researcher	NOUN
ejpam-5171	38	11	.	.	PUNCT
ejpam-5171	39	1	following	follow	VERB
ejpam-5171	39	2	that	that	PRON
ejpam-5171	39	3	,	,	PUNCT
ejpam-5171	39	4	topologists	topologist	NOUN
ejpam-5171	39	5	have	have	AUX
ejpam-5171	39	6	defined	define	VERB
ejpam-5171	39	7	new	new	ADJ
ejpam-5171	39	8	concepts	concept	NOUN
ejpam-5171	39	9	related	relate	VERB
ejpam-5171	39	10	to	to	ADP
ejpam-5171	39	11	grill	grill	ADJ
ejpam-5171	39	12	topological	topological	ADJ
ejpam-5171	39	13	space	space	NOUN
ejpam-5171	39	14	,	,	PUNCT
ejpam-5171	39	15	their	their	PRON
ejpam-5171	39	16	subsets	subset	NOUN
ejpam-5171	39	17	,	,	PUNCT
ejpam-5171	39	18	and	and	CCONJ
ejpam-5171	39	19	continuity	continuity	NOUN
ejpam-5171	39	20	[	[	X
ejpam-5171	39	21	14–18	14–18	NUM
ejpam-5171	39	22	]	]	PUNCT
ejpam-5171	39	23	.	.	PUNCT
ejpam-5171	40	1	it	it	PRON
ejpam-5171	40	2	is	be	AUX
ejpam-5171	40	3	worth	worth	ADJ
ejpam-5171	40	4	noting	note	VERB
ejpam-5171	40	5	that	that	SCONJ
ejpam-5171	40	6	the	the	DET
ejpam-5171	40	7	literature	literature	NOUN
ejpam-5171	40	8	concerning	concern	VERB
ejpam-5171	40	9	grill	grill	NOUN
ejpam-5171	40	10	structures	structure	NOUN
ejpam-5171	40	11	is	be	AUX
ejpam-5171	40	12	relatively	relatively	ADV
ejpam-5171	40	13	limited	limited	ADJ
ejpam-5171	40	14	compared	compare	VERB
ejpam-5171	40	15	to	to	ADP
ejpam-5171	40	16	filter	filter	VERB
ejpam-5171	40	17	,	,	PUNCT
ejpam-5171	40	18	ideal	ideal	ADJ
ejpam-5171	40	19	,	,	PUNCT
ejpam-5171	40	20	and	and	CCONJ
ejpam-5171	40	21	other	other	ADJ
ejpam-5171	40	22	topics	topic	NOUN
ejpam-5171	40	23	;	;	PUNCT
ejpam-5171	40	24	additionally	additionally	ADV
ejpam-5171	40	25	,	,	PUNCT
ejpam-5171	40	26	interdisciplinary	interdisciplinary	ADJ
ejpam-5171	40	27	applications	application	NOUN
ejpam-5171	40	28	of	of	ADP
ejpam-5171	40	29	grill	grill	NOUN
ejpam-5171	40	30	structures	structure	NOUN
ejpam-5171	40	31	are	be	AUX
ejpam-5171	40	32	scarce	scarce	ADJ
ejpam-5171	40	33	.	.	PUNCT
ejpam-5171	41	1	njastad	njastad	PROPN
ejpam-5171	41	2	was	be	AUX
ejpam-5171	41	3	the	the	DET
ejpam-5171	41	4	first	first	ADJ
ejpam-5171	41	5	to	to	PART
ejpam-5171	41	6	define	define	VERB
ejpam-5171	41	7	the	the	DET
ejpam-5171	41	8	topology	topology	NOUN
ejpam-5171	41	9	’s	’s	PART
ejpam-5171	41	10	compatibility	compatibility	NOUN
ejpam-5171	41	11	with	with	ADP
ejpam-5171	41	12	an	an	DET
ejpam-5171	41	13	ideal	ideal	NOUN
ejpam-5171	42	1	i	i	PRON
ejpam-5171	42	2	[	[	X
ejpam-5171	42	3	19	19	NUM
ejpam-5171	42	4	]	]	PUNCT
ejpam-5171	42	5	.	.	PUNCT
ejpam-5171	43	1	in	in	ADP
ejpam-5171	43	2	1990	1990	NUM
ejpam-5171	43	3	,	,	PUNCT
ejpam-5171	43	4	jankovic	jankovic	PROPN
ejpam-5171	43	5	and	and	CCONJ
ejpam-5171	43	6	hamlett	hamlett	PROPN
ejpam-5171	43	7	[	[	X
ejpam-5171	43	8	20	20	NUM
ejpam-5171	43	9	,	,	PUNCT
ejpam-5171	43	10	21	21	NUM
ejpam-5171	43	11	]	]	PUNCT
ejpam-5171	43	12	obtained	obtain	VERB
ejpam-5171	43	13	other	other	ADJ
ejpam-5171	43	14	characteristics	characteristic	NOUN
ejpam-5171	43	15	of	of	ADP
ejpam-5171	43	16	ideal	ideal	ADJ
ejpam-5171	43	17	topological	topological	ADJ
ejpam-5171	43	18	spaces	space	NOUN
ejpam-5171	43	19	and	and	CCONJ
ejpam-5171	43	20	ψ	ψ	NOUN
ejpam-5171	43	21	-	-	NOUN
ejpam-5171	43	22	operator	operator	NOUN
ejpam-5171	43	23	,	,	PUNCT
ejpam-5171	43	24	for	for	ADP
ejpam-5171	43	25	the	the	DET
ejpam-5171	43	26	ideal	ideal	ADJ
ejpam-5171	43	27	topological	topological	ADJ
ejpam-5171	43	28	space	space	NOUN
ejpam-5171	43	29	(	(	PUNCT
ejpam-5171	43	30	x	x	NOUN
ejpam-5171	43	31	,	,	PUNCT
ejpam-5171	43	32	δ	δ	PROPN
ejpam-5171	43	33	,	,	PUNCT
ejpam-5171	43	34	i	i	PROPN
ejpam-5171	43	35	)	)	PUNCT
ejpam-5171	43	36	,	,	PUNCT
ejpam-5171	43	37	local	local	ADJ
ejpam-5171	43	38	function	function	NOUN
ejpam-5171	43	39	of	of	ADP
ejpam-5171	43	40	l	l	NOUN
ejpam-5171	43	41	⊆	⊆	NUM
ejpam-5171	43	42	x	x	PUNCT
ejpam-5171	43	43	is	be	AUX
ejpam-5171	43	44	defined	define	VERB
ejpam-5171	43	45	as	as	ADP
ejpam-5171	43	46	:	:	PUNCT
ejpam-5171	43	47	l⋆(i	l⋆(i	PROPN
ejpam-5171	43	48	)	)	PUNCT
ejpam-5171	43	49	(	(	PUNCT
ejpam-5171	43	50	or	or	CCONJ
ejpam-5171	43	51	simply	simply	ADV
ejpam-5171	43	52	l⋆	l⋆	NUM
ejpam-5171	43	53	)	)	PUNCT
ejpam-5171	44	1	=	=	PRON
ejpam-5171	44	2	{	{	PUNCT
ejpam-5171	44	3	x	x	PUNCT
ejpam-5171	44	4	∈	∈	PROPN
ejpam-5171	44	5	x	x	X
ejpam-5171	44	6	:	:	PUNCT
ejpam-5171	44	7	u	u	NOUN
ejpam-5171	44	8	∩l	∩l	NOUN
ejpam-5171	44	9	/∈	/∈	PUNCT
ejpam-5171	45	1	i	i	PRON
ejpam-5171	45	2	,	,	PUNCT
ejpam-5171	45	3	u	u	PROPN
ejpam-5171	45	4	∈	∈	PROPN
ejpam-5171	45	5	δ(x	δ(x	PROPN
ejpam-5171	45	6	)	)	PUNCT
ejpam-5171	45	7	}	}	PUNCT
ejpam-5171	45	8	,	,	PUNCT
ejpam-5171	45	9	where	where	SCONJ
ejpam-5171	45	10	δ(x	δ(x	ADJ
ejpam-5171	45	11	)	)	PUNCT
ejpam-5171	45	12	=	=	PRON
ejpam-5171	45	13	{	{	PUNCT
ejpam-5171	45	14	u	u	NOUN
ejpam-5171	45	15	∈	∈	PROPN
ejpam-5171	45	16	δ	δ	NOUN
ejpam-5171	45	17	:	:	PUNCT
ejpam-5171	45	18	x	x	X
ejpam-5171	45	19	∈	∈	PROPN
ejpam-5171	45	20	u	u	NOUN
ejpam-5171	45	21	}	}	PUNCT
ejpam-5171	45	22	,	,	PUNCT
ejpam-5171	45	23	whereas	whereas	SCONJ
ejpam-5171	45	24	ψ	ψ	X
ejpam-5171	45	25	-	-	NOUN
ejpam-5171	45	26	operator	operator	NOUN
ejpam-5171	45	27	is	be	AUX
ejpam-5171	45	28	defined	define	VERB
ejpam-5171	45	29	as	as	ADP
ejpam-5171	45	30	ψ(l	ψ(l	ADJ
ejpam-5171	45	31	)	)	PUNCT
ejpam-5171	45	32	=	=	PUNCT
ejpam-5171	46	1	x	x	X
ejpam-5171	46	2	−	−	PROPN
ejpam-5171	46	3	(	(	PUNCT
ejpam-5171	46	4	x	x	X
ejpam-5171	46	5	−	−	X
ejpam-5171	46	6	l)⋆.	l)⋆.	PROPN
ejpam-5171	46	7	the	the	DET
ejpam-5171	46	8	ψ	ψ	NOUN
ejpam-5171	46	9	-	-	NOUN
ejpam-5171	46	10	operator	operator	NOUN
ejpam-5171	46	11	was	be	AUX
ejpam-5171	46	12	used	use	VERB
ejpam-5171	46	13	in	in	ADP
ejpam-5171	46	14	2007	2007	NUM
ejpam-5171	46	15	by	by	ADP
ejpam-5171	46	16	modak	modak	NOUN
ejpam-5171	46	17	and	and	CCONJ
ejpam-5171	46	18	bandyopadhyay	bandyopadhyay	NOUN
ejpam-5171	47	1	[	[	X
ejpam-5171	47	2	22	22	NUM
ejpam-5171	47	3	]	]	PUNCT
ejpam-5171	47	4	to	to	PART
ejpam-5171	47	5	define	define	VERB
ejpam-5171	47	6	the	the	DET
ejpam-5171	47	7	notion	notion	NOUN
ejpam-5171	47	8	of	of	ADP
ejpam-5171	47	9	generalized	generalized	ADJ
ejpam-5171	47	10	open	open	ADJ
ejpam-5171	47	11	sets	set	NOUN
ejpam-5171	47	12	.	.	PUNCT
ejpam-5171	48	1	in	in	ADP
ejpam-5171	48	2	2012	2012	NUM
ejpam-5171	48	3	,	,	PUNCT
ejpam-5171	48	4	al	al	PROPN
ejpam-5171	48	5	-	-	PUNCT
ejpam-5171	48	6	omari	omari	PROPN
ejpam-5171	48	7	and	and	CCONJ
ejpam-5171	48	8	takashi	takashi	PROPN
ejpam-5171	49	1	[	[	X
ejpam-5171	49	2	23	23	NUM
ejpam-5171	49	3	]	]	PUNCT
ejpam-5171	49	4	studied	study	VERB
ejpam-5171	49	5	features	feature	NOUN
ejpam-5171	49	6	of	of	ADP
ejpam-5171	49	7	grill	grill	ADJ
ejpam-5171	49	8	topological	topological	ADJ
ejpam-5171	49	9	space	space	NOUN
ejpam-5171	49	10	and	and	CCONJ
ejpam-5171	49	11	a	a	DET
ejpam-5171	49	12	different	different	ADJ
ejpam-5171	49	13	operator	operator	NOUN
ejpam-5171	49	14	denoted	denote	VERB
ejpam-5171	49	15	by	by	ADP
ejpam-5171	49	16	ψ	ψ	NOUN
ejpam-5171	49	17	-	-	NOUN
ejpam-5171	49	18	operators	operator	NOUN
ejpam-5171	49	19	where	where	SCONJ
ejpam-5171	49	20	ψ(l	ψ(l	ADJ
ejpam-5171	49	21	)	)	PUNCT
ejpam-5171	49	22	=	=	SYM
ejpam-5171	49	23	x−	x−	PROPN
ejpam-5171	49	24	φ(x−	φ(x−	PROPN
ejpam-5171	49	25	l	l	NOUN
ejpam-5171	49	26	)	)	PUNCT
ejpam-5171	49	27	.	.	PUNCT
ejpam-5171	50	1	ψ̃g	ψ̃g	PROPN
ejpam-5171	50	2	was	be	AUX
ejpam-5171	50	3	introduced	introduce	VERB
ejpam-5171	50	4	and	and	CCONJ
ejpam-5171	50	5	studied	study	VERB
ejpam-5171	50	6	by	by	ADP
ejpam-5171	50	7	al	al	PROPN
ejpam-5171	50	8	-	-	PUNCT
ejpam-5171	50	9	omari	omari	PROPN
ejpam-5171	50	10	and	and	CCONJ
ejpam-5171	50	11	takashi	takashi	PROPN
ejpam-5171	50	12	in	in	ADP
ejpam-5171	50	13	[	[	X
ejpam-5171	50	14	24	24	NUM
ejpam-5171	50	15	]	]	PUNCT
ejpam-5171	50	16	,	,	PUNCT
ejpam-5171	50	17	they	they	PRON
ejpam-5171	50	18	also	also	ADV
ejpam-5171	50	19	used	use	VERB
ejpam-5171	50	20	the	the	DET
ejpam-5171	50	21	ψg	ψg	NOUN
ejpam-5171	50	22	-	-	NOUN
ejpam-5171	50	23	operator	operator	NOUN
ejpam-5171	50	24	to	to	PART
ejpam-5171	50	25	define	define	VERB
ejpam-5171	50	26	a	a	DET
ejpam-5171	50	27	new	new	ADJ
ejpam-5171	50	28	class	class	NOUN
ejpam-5171	50	29	of	of	ADP
ejpam-5171	50	30	open	open	ADJ
ejpam-5171	50	31	sets	set	NOUN
ejpam-5171	50	32	.	.	PUNCT
ejpam-5171	51	1	recently	recently	ADV
ejpam-5171	51	2	,	,	PUNCT
ejpam-5171	51	3	the	the	DET
ejpam-5171	51	4	notion	notion	NOUN
ejpam-5171	51	5	of	of	ADP
ejpam-5171	51	6	primal	primal	ADJ
ejpam-5171	51	7	topological	topological	ADJ
ejpam-5171	51	8	space	space	NOUN
ejpam-5171	51	9	was	be	AUX
ejpam-5171	51	10	introduced	introduce	VERB
ejpam-5171	51	11	by	by	ADP
ejpam-5171	51	12	acharjee	acharjee	NOUN
ejpam-5171	51	13	et	et	PROPN
ejpam-5171	51	14	al	al	PROPN
ejpam-5171	51	15	.	.	PUNCT
ejpam-5171	52	1	[	[	X
ejpam-5171	52	2	25	25	NUM
ejpam-5171	52	3	,	,	PUNCT
ejpam-5171	52	4	26	26	NUM
ejpam-5171	52	5	]	]	PUNCT
ejpam-5171	52	6	as	as	ADP
ejpam-5171	52	7	the	the	DET
ejpam-5171	52	8	dual	dual	ADJ
ejpam-5171	52	9	structure	structure	NOUN
ejpam-5171	52	10	of	of	ADP
ejpam-5171	52	11	the	the	DET
ejpam-5171	52	12	grill	grill	NOUN
ejpam-5171	52	13	and	and	CCONJ
ejpam-5171	52	14	the	the	DET
ejpam-5171	52	15	authors	author	NOUN
ejpam-5171	52	16	obtained	obtain	VERB
ejpam-5171	52	17	many	many	ADJ
ejpam-5171	52	18	fundamental	fundamental	ADJ
ejpam-5171	52	19	properties	property	NOUN
ejpam-5171	52	20	of	of	ADP
ejpam-5171	52	21	it	it	PRON
ejpam-5171	52	22	.	.	PUNCT
ejpam-5171	53	1	in	in	ADP
ejpam-5171	53	2	2023	2023	NUM
ejpam-5171	53	3	,	,	PUNCT
ejpam-5171	53	4	al	al	PROPN
ejpam-5171	53	5	-	-	PUNCT
ejpam-5171	53	6	omari	omari	PROPN
ejpam-5171	53	7	,	,	PUNCT
ejpam-5171	53	8	acharjee	acharjee	NOUN
ejpam-5171	53	9	,	,	PUNCT
ejpam-5171	53	10	and	and	CCONJ
ejpam-5171	53	11	özkoç	özkoç	NOUN
ejpam-5171	54	1	[	[	X
ejpam-5171	54	2	26	26	NUM
ejpam-5171	54	3	]	]	PUNCT
ejpam-5171	54	4	defined	define	VERB
ejpam-5171	54	5	and	and	CCONJ
ejpam-5171	54	6	studied	study	VERB
ejpam-5171	54	7	operator	operator	NOUN
ejpam-5171	54	8	ψ	ψ	NOUN
ejpam-5171	54	9	by	by	ADP
ejpam-5171	54	10	using	use	VERB
ejpam-5171	54	11	primal	primal	ADJ
ejpam-5171	54	12	topological	topological	ADJ
ejpam-5171	54	13	spaces	space	NOUN
ejpam-5171	54	14	as	as	ADP
ejpam-5171	54	15	ψ(l	ψ(l	ADJ
ejpam-5171	54	16	)	)	PUNCT
ejpam-5171	54	17	=	=	SYM
ejpam-5171	54	18	x−	x−	PROPN
ejpam-5171	54	19	(	(	PUNCT
ejpam-5171	54	20	x−	x−	PROPN
ejpam-5171	54	21	l)	l)	PROPN
ejpam-5171	54	22	♢	♢	PROPN
ejpam-5171	54	23	.	.	PUNCT
ejpam-5171	55	1	the	the	DET
ejpam-5171	55	2	authors	author	NOUN
ejpam-5171	55	3	in	in	ADP
ejpam-5171	55	4	[	[	X
ejpam-5171	55	5	27	27	NUM
ejpam-5171	55	6	]	]	PUNCT
ejpam-5171	55	7	expand	expand	VERB
ejpam-5171	55	8	the	the	DET
ejpam-5171	55	9	class	class	NOUN
ejpam-5171	55	10	of	of	ADP
ejpam-5171	55	11	primal	primal	ADJ
ejpam-5171	55	12	lower	low	ADJ
ejpam-5171	55	13	pleasant	pleasant	ADJ
ejpam-5171	55	14	functions	function	NOUN
ejpam-5171	55	15	to	to	ADP
ejpam-5171	55	16	the	the	DET
ejpam-5171	55	17	setting	setting	NOUN
ejpam-5171	55	18	of	of	ADP
ejpam-5171	55	19	reflexive	reflexive	ADJ
ejpam-5171	55	20	smooth	smooth	ADJ
ejpam-5171	55	21	banach	banach	NOUN
ejpam-5171	55	22	spaces	space	VERB
ejpam-5171	55	23	.	.	PUNCT
ejpam-5171	56	1	furthermore	furthermore	ADV
ejpam-5171	56	2	,	,	PUNCT
ejpam-5171	56	3	generalized	generalized	ADJ
ejpam-5171	56	4	primal	primal	ADJ
ejpam-5171	56	5	topological	topological	ADJ
ejpam-5171	56	6	spaces	space	NOUN
ejpam-5171	56	7	are	be	AUX
ejpam-5171	56	8	a	a	DET
ejpam-5171	56	9	new	new	ADJ
ejpam-5171	56	10	category	category	NOUN
ejpam-5171	56	11	of	of	ADP
ejpam-5171	56	12	generalized	generalized	ADJ
ejpam-5171	56	13	topology	topology	NOUN
ejpam-5171	56	14	that	that	PRON
ejpam-5171	56	15	al	al	PROPN
ejpam-5171	56	16	-	-	PUNCT
ejpam-5171	56	17	saadi	saadi	PROPN
ejpam-5171	56	18	and	and	CCONJ
ejpam-5171	56	19	al	al	PROPN
ejpam-5171	56	20	-	-	PUNCT
ejpam-5171	56	21	malki	malki	PROPN
ejpam-5171	56	22	recently	recently	ADV
ejpam-5171	56	23	introduced	introduce	VERB
ejpam-5171	56	24	with	with	ADP
ejpam-5171	56	25	the	the	DET
ejpam-5171	56	26	concept	concept	NOUN
ejpam-5171	56	27	of	of	ADP
ejpam-5171	56	28	the	the	DET
ejpam-5171	56	29	primal	primal	ADJ
ejpam-5171	56	30	[	[	X
ejpam-5171	56	31	28	28	NUM
ejpam-5171	56	32	]	]	PUNCT
ejpam-5171	56	33	.	.	PUNCT
ejpam-5171	57	1	in	in	ADP
ejpam-5171	57	2	[	[	X
ejpam-5171	57	3	29	29	NUM
ejpam-5171	57	4	]	]	PUNCT
ejpam-5171	57	5	,	,	PUNCT
ejpam-5171	57	6	soft	soft	ADJ
ejpam-5171	57	7	spaces	space	NOUN
ejpam-5171	57	8	were	be	AUX
ejpam-5171	57	9	also	also	ADV
ejpam-5171	57	10	investigated	investigate	VERB
ejpam-5171	57	11	,	,	PUNCT
ejpam-5171	57	12	and	and	CCONJ
ejpam-5171	57	13	these	these	DET
ejpam-5171	57	14	concepts	concept	NOUN
ejpam-5171	57	15	were	be	AUX
ejpam-5171	57	16	h.	h.	PROPN
ejpam-5171	57	17	al	al	PROPN
ejpam-5171	57	18	-	-	PUNCT
ejpam-5171	57	19	saadi	saadi	PROPN
ejpam-5171	57	20	,	,	PUNCT
ejpam-5171	57	21	m.	m.	NOUN
ejpam-5171	57	22	al	al	PROPN
ejpam-5171	57	23	-	-	PUNCT
ejpam-5171	57	24	hodieb	hodieb	PROPN
ejpam-5171	57	25	/	/	SYM
ejpam-5171	57	26	eur	eur	PROPN
ejpam-5171	57	27	.	.	PUNCT
ejpam-5171	58	1	j.	j.	PROPN
ejpam-5171	58	2	pure	pure	PROPN
ejpam-5171	58	3	appl	appl	PROPN
ejpam-5171	58	4	.	.	PROPN
ejpam-5171	58	5	math	math	PROPN
ejpam-5171	58	6	,	,	PUNCT
ejpam-5171	58	7	17	17	NUM
ejpam-5171	58	8	(	(	PUNCT
ejpam-5171	58	9	2	2	NUM
ejpam-5171	58	10	)	)	PUNCT
ejpam-5171	58	11	(	(	PUNCT
ejpam-5171	58	12	2024	2024	NUM
ejpam-5171	58	13	)	)	PUNCT
ejpam-5171	58	14	,	,	PUNCT
ejpam-5171	58	15	1352	1352	NUM
ejpam-5171	58	16	-	-	SYM
ejpam-5171	58	17	1368	1368	NUM
ejpam-5171	58	18	1354	1354	NUM
ejpam-5171	58	19	applied	apply	VERB
ejpam-5171	58	20	in	in	ADP
ejpam-5171	58	21	primal	primal	ADJ
ejpam-5171	58	22	topological	topological	ADJ
ejpam-5171	58	23	spaces	space	NOUN
ejpam-5171	58	24	.	.	PUNCT
ejpam-5171	59	1	in	in	ADP
ejpam-5171	59	2	this	this	DET
ejpam-5171	59	3	paper	paper	NOUN
ejpam-5171	59	4	,	,	PUNCT
ejpam-5171	59	5	new	new	ADJ
ejpam-5171	59	6	classes	class	NOUN
ejpam-5171	59	7	of	of	ADP
ejpam-5171	59	8	weaker	weak	ADJ
ejpam-5171	59	9	sets	set	NOUN
ejpam-5171	59	10	are	be	AUX
ejpam-5171	59	11	defined	define	VERB
ejpam-5171	59	12	as	as	ADP
ejpam-5171	59	13	some	some	PRON
ejpam-5171	59	14	of	of	ADP
ejpam-5171	59	15	the	the	DET
ejpam-5171	59	16	weak	weak	ADJ
ejpam-5171	59	17	continuity	continuity	NOUN
ejpam-5171	59	18	on	on	ADP
ejpam-5171	59	19	primal	primal	ADJ
ejpam-5171	59	20	topological	topological	ADJ
ejpam-5171	59	21	spaces	space	NOUN
ejpam-5171	59	22	,	,	PUNCT
ejpam-5171	59	23	and	and	CCONJ
ejpam-5171	59	24	some	some	PRON
ejpam-5171	59	25	of	of	ADP
ejpam-5171	59	26	their	their	PRON
ejpam-5171	59	27	basic	basic	ADJ
ejpam-5171	59	28	properties	property	NOUN
ejpam-5171	59	29	are	be	AUX
ejpam-5171	59	30	investigated	investigate	VERB
ejpam-5171	59	31	.	.	PUNCT
ejpam-5171	60	1	additionally	additionally	ADV
ejpam-5171	60	2	,	,	PUNCT
ejpam-5171	60	3	we	we	PRON
ejpam-5171	60	4	investigated	investigate	VERB
ejpam-5171	60	5	the	the	DET
ejpam-5171	60	6	relationship	relationship	NOUN
ejpam-5171	60	7	between	between	ADP
ejpam-5171	60	8	them	they	PRON
ejpam-5171	60	9	,	,	PUNCT
ejpam-5171	60	10	and	and	CCONJ
ejpam-5171	60	11	we	we	PRON
ejpam-5171	60	12	provided	provide	VERB
ejpam-5171	60	13	examples	example	NOUN
ejpam-5171	60	14	of	of	ADP
ejpam-5171	60	15	the	the	DET
ejpam-5171	60	16	opposite	opposite	NOUN
ejpam-5171	60	17	of	of	ADP
ejpam-5171	60	18	relationships	relationship	NOUN
ejpam-5171	60	19	that	that	PRON
ejpam-5171	60	20	were	be	AUX
ejpam-5171	60	21	not	not	PART
ejpam-5171	60	22	satisfying	satisfy	VERB
ejpam-5171	60	23	.	.	PUNCT
ejpam-5171	61	1	we	we	PRON
ejpam-5171	61	2	define	define	VERB
ejpam-5171	61	3	some	some	DET
ejpam-5171	61	4	new	new	ADJ
ejpam-5171	61	5	classes	class	NOUN
ejpam-5171	61	6	of	of	ADP
ejpam-5171	61	7	functions	function	NOUN
ejpam-5171	61	8	and	and	CCONJ
ejpam-5171	61	9	use	use	VERB
ejpam-5171	61	10	these	these	DET
ejpam-5171	61	11	functions	function	NOUN
ejpam-5171	61	12	to	to	PART
ejpam-5171	61	13	introduce	introduce	VERB
ejpam-5171	61	14	several	several	ADJ
ejpam-5171	61	15	interesting	interesting	ADJ
ejpam-5171	61	16	decomposition	decomposition	NOUN
ejpam-5171	61	17	theorems	theorem	NOUN
ejpam-5171	61	18	of	of	ADP
ejpam-5171	61	19	continuity	continuity	NOUN
ejpam-5171	61	20	.	.	PUNCT
ejpam-5171	62	1	finally	finally	ADV
ejpam-5171	62	2	,	,	PUNCT
ejpam-5171	62	3	we	we	PRON
ejpam-5171	62	4	use	use	VERB
ejpam-5171	62	5	the	the	DET
ejpam-5171	62	6	ψp	ψp	NOUN
ejpam-5171	62	7	-operator	-operator	NOUN
ejpam-5171	62	8	to	to	PART
ejpam-5171	62	9	introduce	introduce	VERB
ejpam-5171	62	10	and	and	CCONJ
ejpam-5171	62	11	study	study	VERB
ejpam-5171	62	12	ψ̃p	ψ̃p	NOUN
ejpam-5171	62	13	-sets	-set	NOUN
ejpam-5171	62	14	as	as	ADP
ejpam-5171	62	15	a	a	DET
ejpam-5171	62	16	new	new	ADJ
ejpam-5171	62	17	class	class	NOUN
ejpam-5171	62	18	of	of	ADP
ejpam-5171	62	19	sets	set	NOUN
ejpam-5171	62	20	in	in	ADP
ejpam-5171	62	21	the	the	DET
ejpam-5171	62	22	structure	structure	NOUN
ejpam-5171	62	23	of	of	ADP
ejpam-5171	62	24	primal	primal	ADJ
ejpam-5171	62	25	topological	topological	ADJ
ejpam-5171	62	26	spaces	space	NOUN
ejpam-5171	62	27	,	,	PUNCT
ejpam-5171	62	28	and	and	CCONJ
ejpam-5171	62	29	we	we	PRON
ejpam-5171	62	30	obtain	obtain	VERB
ejpam-5171	62	31	their	their	PRON
ejpam-5171	62	32	features	feature	NOUN
ejpam-5171	62	33	.	.	PUNCT
ejpam-5171	63	1	a	a	DET
ejpam-5171	63	2	counter	counter	NOUN
ejpam-5171	63	3	-	-	NOUN
ejpam-5171	63	4	example	example	NOUN
ejpam-5171	63	5	to	to	ADP
ejpam-5171	63	6	the	the	DET
ejpam-5171	63	7	theorems	theorem	NOUN
ejpam-5171	63	8	based	base	VERB
ejpam-5171	63	9	on	on	ADP
ejpam-5171	63	10	arbitrary	arbitrary	ADJ
ejpam-5171	63	11	unions	union	NOUN
ejpam-5171	63	12	and	and	CCONJ
ejpam-5171	63	13	finite	finite	ADJ
ejpam-5171	63	14	intersections	intersection	NOUN
ejpam-5171	63	15	is	be	AUX
ejpam-5171	63	16	discussed	discuss	VERB
ejpam-5171	63	17	.	.	PUNCT
ejpam-5171	64	1	moreover	moreover	ADV
ejpam-5171	64	2	,	,	PUNCT
ejpam-5171	64	3	we	we	PRON
ejpam-5171	64	4	study	study	VERB
ejpam-5171	64	5	the	the	DET
ejpam-5171	64	6	relationships	relationship	NOUN
ejpam-5171	64	7	between	between	ADP
ejpam-5171	64	8	ψ̃p	ψ̃p	NOUN
ejpam-5171	64	9	-sets	-set	NOUN
ejpam-5171	64	10	and	and	CCONJ
ejpam-5171	64	11	their	their	PRON
ejpam-5171	64	12	analogous	analogous	ADJ
ejpam-5171	64	13	topological	topological	ADJ
ejpam-5171	64	14	concepts	concept	NOUN
ejpam-5171	64	15	.	.	PUNCT
ejpam-5171	65	1	assume	assume	VERB
ejpam-5171	65	2	that	that	SCONJ
ejpam-5171	65	3	(	(	PUNCT
ejpam-5171	65	4	x	x	NOUN
ejpam-5171	65	5	,	,	PUNCT
ejpam-5171	65	6	δ	δ	PROPN
ejpam-5171	65	7	)	)	PUNCT
ejpam-5171	65	8	be	be	VERB
ejpam-5171	65	9	a	a	DET
ejpam-5171	65	10	topological	topological	ADJ
ejpam-5171	65	11	space	space	NOUN
ejpam-5171	65	12	(	(	PUNCT
ejpam-5171	65	13	ts	ts	NOUN
ejpam-5171	65	14	,	,	PUNCT
ejpam-5171	65	15	for	for	ADP
ejpam-5171	65	16	short	short	ADJ
ejpam-5171	65	17	)	)	PUNCT
ejpam-5171	65	18	,	,	PUNCT
ejpam-5171	65	19	and	and	CCONJ
ejpam-5171	65	20	cl(l	cl(l	NUM
ejpam-5171	65	21	)	)	PUNCT
ejpam-5171	65	22	,	,	PUNCT
ejpam-5171	65	23	int(l	int(l	PROPN
ejpam-5171	65	24	)	)	PUNCT
ejpam-5171	65	25	,	,	PUNCT
ejpam-5171	65	26	respectively	respectively	ADV
ejpam-5171	65	27	,	,	PUNCT
ejpam-5171	65	28	will	will	AUX
ejpam-5171	65	29	be	be	AUX
ejpam-5171	65	30	used	use	VERB
ejpam-5171	65	31	to	to	PART
ejpam-5171	65	32	refer	refer	VERB
ejpam-5171	65	33	to	to	ADP
ejpam-5171	65	34	the	the	DET
ejpam-5171	65	35	interior	interior	NOUN
ejpam-5171	65	36	of	of	ADP
ejpam-5171	65	37	l	l	NOUN
ejpam-5171	65	38	in	in	ADP
ejpam-5171	65	39	(	(	PUNCT
ejpam-5171	65	40	x	x	NOUN
ejpam-5171	65	41	,	,	PUNCT
ejpam-5171	65	42	δ	δ	PROPN
ejpam-5171	65	43	)	)	PUNCT
ejpam-5171	65	44	and	and	CCONJ
ejpam-5171	65	45	the	the	DET
ejpam-5171	65	46	closure	closure	NOUN
ejpam-5171	65	47	of	of	ADP
ejpam-5171	65	48	l	l	NOUN
ejpam-5171	65	49	in	in	ADP
ejpam-5171	65	50	(	(	PUNCT
ejpam-5171	65	51	x	x	NOUN
ejpam-5171	65	52	,	,	PUNCT
ejpam-5171	65	53	δ	δ	PROPN
ejpam-5171	65	54	)	)	PUNCT
ejpam-5171	65	55	.	.	PUNCT
ejpam-5171	66	1	the	the	DET
ejpam-5171	66	2	family	family	NOUN
ejpam-5171	66	3	of	of	ADP
ejpam-5171	66	4	all	all	DET
ejpam-5171	66	5	open	open	ADJ
ejpam-5171	66	6	neighborhoods	neighborhood	NOUN
ejpam-5171	66	7	of	of	ADP
ejpam-5171	66	8	a	a	DET
ejpam-5171	66	9	point	point	NOUN
ejpam-5171	66	10	x	x	X
ejpam-5171	66	11	∈	∈	NOUN
ejpam-5171	66	12	x	x	AUX
ejpam-5171	66	13	is	be	AUX
ejpam-5171	66	14	denoted	denote	VERB
ejpam-5171	66	15	by	by	ADP
ejpam-5171	66	16	n	n	PROPN
ejpam-5171	66	17	(	(	PUNCT
ejpam-5171	66	18	x	x	NOUN
ejpam-5171	66	19	)	)	PUNCT
ejpam-5171	66	20	.	.	PUNCT
ejpam-5171	67	1	definition	definition	NOUN
ejpam-5171	67	2	1.1	1.1	NUM
ejpam-5171	67	3	.	.	PUNCT
ejpam-5171	68	1	(	(	PUNCT
ejpam-5171	68	2	[	[	X
ejpam-5171	68	3	5	5	NUM
ejpam-5171	68	4	]	]	PUNCT
ejpam-5171	68	5	)	)	PUNCT
ejpam-5171	68	6	a	a	DET
ejpam-5171	68	7	family	family	NOUN
ejpam-5171	68	8	g	g	NOUN
ejpam-5171	68	9	of	of	ADP
ejpam-5171	68	10	2x	2x	NUM
ejpam-5171	68	11	is	be	AUX
ejpam-5171	68	12	called	call	VERB
ejpam-5171	68	13	a	a	DET
ejpam-5171	68	14	grill	grill	NOUN
ejpam-5171	68	15	on	on	ADP
ejpam-5171	68	16	x	x	PUNCT
ejpam-5171	68	17	if	if	SCONJ
ejpam-5171	68	18	g	g	PROPN
ejpam-5171	68	19	satisfies	satisfy	VERB
ejpam-5171	68	20	the	the	DET
ejpam-5171	68	21	following	follow	VERB
ejpam-5171	68	22	conditions	condition	NOUN
ejpam-5171	68	23	:	:	PUNCT
ejpam-5171	68	24	(	(	PUNCT
ejpam-5171	68	25	a	a	X
ejpam-5171	68	26	)	)	PUNCT
ejpam-5171	68	27	ϕ	ϕ	NOUN
ejpam-5171	68	28	/∈	/∈	PUNCT
ejpam-5171	69	1	g	g	NOUN
ejpam-5171	69	2	,	,	PUNCT
ejpam-5171	69	3	(	(	PUNCT
ejpam-5171	69	4	b	b	X
ejpam-5171	69	5	)	)	PUNCT
ejpam-5171	69	6	if	if	SCONJ
ejpam-5171	69	7	l	l	PROPN
ejpam-5171	69	8	∈	∈	PROPN
ejpam-5171	69	9	g	g	NOUN
ejpam-5171	69	10	and	and	CCONJ
ejpam-5171	69	11	l	l	NOUN
ejpam-5171	69	12	⊆	⊆	NUM
ejpam-5171	69	13	e	e	NOUN
ejpam-5171	69	14	,	,	PUNCT
ejpam-5171	69	15	then	then	ADV
ejpam-5171	69	16	e	e	PROPN
ejpam-5171	69	17	∈	∈	PROPN
ejpam-5171	69	18	g	g	PROPN
ejpam-5171	69	19	,	,	PUNCT
ejpam-5171	69	20	(	(	PUNCT
ejpam-5171	69	21	c	c	X
ejpam-5171	69	22	)	)	PUNCT
ejpam-5171	69	23	if	if	SCONJ
ejpam-5171	69	24	l	l	NOUN
ejpam-5171	69	25	∪	∪	X
ejpam-5171	69	26	e	e	PROPN
ejpam-5171	69	27	∈	∈	PROPN
ejpam-5171	69	28	g	g	PROPN
ejpam-5171	69	29	,	,	PUNCT
ejpam-5171	69	30	then	then	ADV
ejpam-5171	69	31	l	l	PROPN
ejpam-5171	69	32	∈	∈	PROPN
ejpam-5171	69	33	g	g	PROPN
ejpam-5171	69	34	or	or	CCONJ
ejpam-5171	69	35	e	e	PROPN
ejpam-5171	69	36	∈	∈	PROPN
ejpam-5171	69	37	g.	g.	NOUN
ejpam-5171	70	1	in	in	ADP
ejpam-5171	70	2	[	[	X
ejpam-5171	70	3	5	5	NUM
ejpam-5171	70	4	]	]	PUNCT
ejpam-5171	70	5	,	,	PUNCT
ejpam-5171	70	6	define	define	VERB
ejpam-5171	70	7	an	an	DET
ejpam-5171	70	8	operator	operator	NOUN
ejpam-5171	70	9	φ	φ	NOUN
ejpam-5171	70	10	:	:	PUNCT
ejpam-5171	70	11	2x	2x	NUM
ejpam-5171	70	12	→	→	SYM
ejpam-5171	70	13	2x	2x	NUM
ejpam-5171	70	14	for	for	ADP
ejpam-5171	70	15	a	a	DET
ejpam-5171	70	16	grill	grill	NOUN
ejpam-5171	70	17	g	g	NOUN
ejpam-5171	70	18	on	on	ADP
ejpam-5171	70	19	a	a	DET
ejpam-5171	70	20	ts	ts	X
ejpam-5171	70	21	(	(	PUNCT
ejpam-5171	70	22	x	x	NOUN
ejpam-5171	70	23	,	,	PUNCT
ejpam-5171	70	24	δ	δ	PROPN
ejpam-5171	70	25	)	)	PUNCT
ejpam-5171	70	26	,	,	PUNCT
ejpam-5171	70	27	and	and	CCONJ
ejpam-5171	70	28	for	for	ADP
ejpam-5171	70	29	any	any	DET
ejpam-5171	70	30	l	l	NOUN
ejpam-5171	70	31	∈	∈	NOUN
ejpam-5171	70	32	2x	2x	NUM
ejpam-5171	70	33	,	,	PUNCT
ejpam-5171	70	34	φ(l	φ(l	PROPN
ejpam-5171	70	35	)	)	PUNCT
ejpam-5171	70	36	=	=	SYM
ejpam-5171	70	37	{	{	PUNCT
ejpam-5171	70	38	x	x	PUNCT
ejpam-5171	70	39	∈	∈	PROPN
ejpam-5171	70	40	x	x	X
ejpam-5171	70	41	:	:	PUNCT
ejpam-5171	70	42	u	u	NOUN
ejpam-5171	70	43	∩	∩	NOUN
ejpam-5171	70	44	l	l	NOUN
ejpam-5171	70	45	∈	∈	PROPN
ejpam-5171	70	46	g	g	NOUN
ejpam-5171	70	47	,	,	PUNCT
ejpam-5171	70	48	∀u	∀u	NOUN
ejpam-5171	70	49	∈	∈	NOUN
ejpam-5171	70	50	n	n	CCONJ
ejpam-5171	70	51	(	(	PUNCT
ejpam-5171	70	52	x	x	NOUN
ejpam-5171	70	53	)	)	PUNCT
ejpam-5171	70	54	}	}	PUNCT
ejpam-5171	70	55	.	.	PUNCT
ejpam-5171	71	1	then	then	ADV
ejpam-5171	71	2	,	,	PUNCT
ejpam-5171	71	3	the	the	DET
ejpam-5171	71	4	author	author	NOUN
ejpam-5171	71	5	defined	define	VERB
ejpam-5171	71	6	another	another	DET
ejpam-5171	71	7	operator	operator	NOUN
ejpam-5171	71	8	,	,	PUNCT
ejpam-5171	71	9	ψ	ψ	X
ejpam-5171	71	10	:	:	PUNCT
ejpam-5171	71	11	2x	2x	NUM
ejpam-5171	71	12	→	→	SYM
ejpam-5171	71	13	2x	2x	NUM
ejpam-5171	71	14	,	,	PUNCT
ejpam-5171	71	15	as	as	ADP
ejpam-5171	71	16	ψ(l	ψ(l	ADJ
ejpam-5171	71	17	)	)	PUNCT
ejpam-5171	71	18	=	=	SYM
ejpam-5171	71	19	l	l	NOUN
ejpam-5171	71	20	∪	∪	X
ejpam-5171	71	21	φ(l	φ(l	NOUN
ejpam-5171	71	22	)	)	PUNCT
ejpam-5171	71	23	for	for	ADP
ejpam-5171	71	24	l	l	NOUN
ejpam-5171	71	25	⊆	⊆	NUM
ejpam-5171	71	26	x	x	X
ejpam-5171	71	27	,	,	PUNCT
ejpam-5171	71	28	is	be	AUX
ejpam-5171	71	29	a	a	DET
ejpam-5171	71	30	kuratowski	kuratowski	ADJ
ejpam-5171	71	31	closure	closure	NOUN
ejpam-5171	71	32	operator	operator	NOUN
ejpam-5171	71	33	,	,	PUNCT
ejpam-5171	71	34	defining	define	VERB
ejpam-5171	71	35	a	a	DET
ejpam-5171	71	36	distinct	distinct	ADJ
ejpam-5171	71	37	topology	topology	NOUN
ejpam-5171	71	38	δg	δg	VERB
ejpam-5171	71	39	on	on	ADP
ejpam-5171	71	40	x	x	PUNCT
ejpam-5171	71	41	that	that	PRON
ejpam-5171	71	42	is	is	ADV
ejpam-5171	71	43	,	,	PUNCT
ejpam-5171	71	44	δ	δ	PROPN
ejpam-5171	71	45	⊆	⊆	NUM
ejpam-5171	71	46	δg	δg	PROPN
ejpam-5171	71	47	.	.	PUNCT
ejpam-5171	72	1	definition	definition	NOUN
ejpam-5171	72	2	1.2	1.2	NUM
ejpam-5171	72	3	.	.	PUNCT
ejpam-5171	72	4	suppose	suppose	VERB
ejpam-5171	72	5	that	that	SCONJ
ejpam-5171	72	6	(	(	PUNCT
ejpam-5171	72	7	x	x	NOUN
ejpam-5171	72	8	,	,	PUNCT
ejpam-5171	72	9	δ	δ	PROPN
ejpam-5171	72	10	)	)	PUNCT
ejpam-5171	72	11	is	be	AUX
ejpam-5171	72	12	a	a	DET
ejpam-5171	72	13	ts	ts	NOUN
ejpam-5171	72	14	.	.	PUNCT
ejpam-5171	73	1	hence	hence	ADV
ejpam-5171	73	2	,	,	PUNCT
ejpam-5171	73	3	a	a	DET
ejpam-5171	73	4	subset	subset	ADJ
ejpam-5171	73	5	l	l	NOUN
ejpam-5171	73	6	of	of	ADP
ejpam-5171	73	7	x	x	PRON
ejpam-5171	73	8	can	can	AUX
ejpam-5171	73	9	be	be	AUX
ejpam-5171	73	10	defined	define	VERB
ejpam-5171	73	11	as	as	ADP
ejpam-5171	73	12	:	:	PUNCT
ejpam-5171	73	13	(	(	PUNCT
ejpam-5171	73	14	a	a	X
ejpam-5171	73	15	)	)	PUNCT
ejpam-5171	73	16	α	α	NOUN
ejpam-5171	73	17	-	-	ADJ
ejpam-5171	73	18	open	open	ADJ
ejpam-5171	73	19	(	(	PUNCT
ejpam-5171	73	20	[	[	X
ejpam-5171	73	21	2	2	NUM
ejpam-5171	73	22	]	]	NUM
ejpam-5171	73	23	)	)	PUNCT
ejpam-5171	73	24	,	,	PUNCT
ejpam-5171	73	25	if	if	SCONJ
ejpam-5171	73	26	l	l	PROPN
ejpam-5171	73	27	⊆	⊆	NUM
ejpam-5171	73	28	int(cl(int(l	int(cl(int(l	PROPN
ejpam-5171	73	29	)	)	PUNCT
ejpam-5171	73	30	)	)	PUNCT
ejpam-5171	73	31	)	)	PUNCT
ejpam-5171	73	32	,	,	PUNCT
ejpam-5171	73	33	(	(	PUNCT
ejpam-5171	73	34	b	b	X
ejpam-5171	73	35	)	)	PUNCT
ejpam-5171	73	36	semi	semi	ADJ
ejpam-5171	73	37	-	-	ADJ
ejpam-5171	73	38	open([1	open([1	ADJ
ejpam-5171	73	39	]	]	X
ejpam-5171	73	40	)	)	PUNCT
ejpam-5171	73	41	,	,	PUNCT
ejpam-5171	73	42	if	if	SCONJ
ejpam-5171	73	43	l	l	NOUN
ejpam-5171	73	44	⊆	⊆	NUM
ejpam-5171	73	45	cl(int(l	cl(int(l	NOUN
ejpam-5171	73	46	)	)	PUNCT
ejpam-5171	73	47	)	)	PUNCT
ejpam-5171	73	48	,	,	PUNCT
ejpam-5171	73	49	(	(	PUNCT
ejpam-5171	73	50	c	c	X
ejpam-5171	73	51	)	)	PUNCT
ejpam-5171	73	52	pre	pre	ADJ
ejpam-5171	73	53	-	-	ADJ
ejpam-5171	73	54	open	open	ADJ
ejpam-5171	73	55	(	(	PUNCT
ejpam-5171	73	56	[	[	X
ejpam-5171	73	57	3	3	NUM
ejpam-5171	73	58	]	]	NUM
ejpam-5171	73	59	)	)	PUNCT
ejpam-5171	73	60	,	,	PUNCT
ejpam-5171	73	61	if	if	SCONJ
ejpam-5171	73	62	l	l	PROPN
ejpam-5171	73	63	⊆	⊆	NUM
ejpam-5171	73	64	int(cl(l	int(cl(l	NOUN
ejpam-5171	73	65	)	)	PUNCT
ejpam-5171	73	66	)	)	PUNCT
ejpam-5171	73	67	,	,	PUNCT
ejpam-5171	73	68	(	(	PUNCT
ejpam-5171	73	69	d	d	X
ejpam-5171	73	70	)	)	PUNCT
ejpam-5171	73	71	β	β	X
ejpam-5171	73	72	-	-	PUNCT
ejpam-5171	73	73	open	open	ADJ
ejpam-5171	73	74	(	(	PUNCT
ejpam-5171	73	75	[	[	X
ejpam-5171	73	76	4	4	NUM
ejpam-5171	73	77	]	]	PUNCT
ejpam-5171	73	78	)	)	PUNCT
ejpam-5171	73	79	or	or	CCONJ
ejpam-5171	73	80	semi	semi	ADJ
ejpam-5171	73	81	-	-	ADJ
ejpam-5171	73	82	pre	pre	ADJ
ejpam-5171	73	83	-	-	ADJ
ejpam-5171	73	84	open	open	ADJ
ejpam-5171	73	85	(	(	PUNCT
ejpam-5171	73	86	[	[	X
ejpam-5171	73	87	30	30	NUM
ejpam-5171	73	88	]	]	NUM
ejpam-5171	73	89	)	)	PUNCT
ejpam-5171	73	90	,	,	PUNCT
ejpam-5171	73	91	if	if	SCONJ
ejpam-5171	73	92	l	l	NOUN
ejpam-5171	73	93	⊆	⊆	NUM
ejpam-5171	73	94	cl(int(cl(l	cl(int(cl(l	NOUN
ejpam-5171	73	95	)	)	PUNCT
ejpam-5171	73	96	)	)	PUNCT
ejpam-5171	73	97	)	)	PUNCT
ejpam-5171	73	98	,	,	PUNCT
ejpam-5171	73	99	(	(	PUNCT
ejpam-5171	73	100	e	e	NOUN
ejpam-5171	73	101	)	)	PUNCT
ejpam-5171	73	102	t	t	NOUN
ejpam-5171	73	103	-	-	PUNCT
ejpam-5171	73	104	set	set	VERB
ejpam-5171	73	105	(	(	PUNCT
ejpam-5171	73	106	[	[	X
ejpam-5171	73	107	31	31	NUM
ejpam-5171	73	108	]	]	PUNCT
ejpam-5171	73	109	)	)	PUNCT
ejpam-5171	73	110	,	,	PUNCT
ejpam-5171	73	111	if	if	SCONJ
ejpam-5171	73	112	int(l	int(l	PROPN
ejpam-5171	73	113	)	)	PUNCT
ejpam-5171	73	114	=	=	SYM
ejpam-5171	73	115	int(cl(l	int(cl(l	PROPN
ejpam-5171	73	116	)	)	PUNCT
ejpam-5171	73	117	)	)	PUNCT
ejpam-5171	73	118	,	,	PUNCT
ejpam-5171	73	119	(	(	PUNCT
ejpam-5171	73	120	f	f	X
ejpam-5171	73	121	)	)	PUNCT
ejpam-5171	73	122	r	r	NOUN
ejpam-5171	73	123	-	-	PUNCT
ejpam-5171	73	124	set	set	VERB
ejpam-5171	73	125	(	(	PUNCT
ejpam-5171	73	126	[	[	X
ejpam-5171	73	127	31	31	NUM
ejpam-5171	73	128	]	]	PUNCT
ejpam-5171	73	129	)	)	PUNCT
ejpam-5171	73	130	,	,	PUNCT
ejpam-5171	73	131	if	if	SCONJ
ejpam-5171	73	132	l	l	NOUN
ejpam-5171	73	133	=	=	SYM
ejpam-5171	73	134	l1	l1	PROPN
ejpam-5171	73	135	∩	∩	ADJ
ejpam-5171	73	136	l2	l2	NOUN
ejpam-5171	73	137	,	,	PUNCT
ejpam-5171	73	138	where	where	SCONJ
ejpam-5171	73	139	l1	l1	PROPN
ejpam-5171	73	140	is	be	AUX
ejpam-5171	73	141	an	an	DET
ejpam-5171	73	142	open	open	ADJ
ejpam-5171	73	143	set	set	NOUN
ejpam-5171	73	144	and	and	CCONJ
ejpam-5171	73	145	l2	l2	NOUN
ejpam-5171	73	146	is	be	AUX
ejpam-5171	73	147	a	a	DET
ejpam-5171	73	148	t	t	NOUN
ejpam-5171	73	149	-	-	PUNCT
ejpam-5171	73	150	set	set	NOUN
ejpam-5171	73	151	,	,	PUNCT
ejpam-5171	73	152	(	(	PUNCT
ejpam-5171	73	153	g	g	NOUN
ejpam-5171	73	154	)	)	PUNCT
ejpam-5171	73	155	tα	tα	NOUN
ejpam-5171	73	156	-	-	PUNCT
ejpam-5171	73	157	set	set	NOUN
ejpam-5171	73	158	(	(	PUNCT
ejpam-5171	73	159	[	[	X
ejpam-5171	73	160	32	32	NUM
ejpam-5171	73	161	]	]	PUNCT
ejpam-5171	73	162	)	)	PUNCT
ejpam-5171	73	163	,	,	PUNCT
ejpam-5171	73	164	if	if	SCONJ
ejpam-5171	73	165	int(l	int(l	PROPN
ejpam-5171	73	166	)	)	PUNCT
ejpam-5171	73	167	=	=	SYM
ejpam-5171	73	168	int(cl(int(l	int(cl(int(l	PROPN
ejpam-5171	73	169	)	)	PUNCT
ejpam-5171	73	170	)	)	PUNCT
ejpam-5171	73	171	)	)	PUNCT
ejpam-5171	73	172	,	,	PUNCT
ejpam-5171	73	173	(	(	PUNCT
ejpam-5171	73	174	h	h	NOUN
ejpam-5171	73	175	)	)	PUNCT
ejpam-5171	73	176	rα	rα	ADJ
ejpam-5171	73	177	-	-	PUNCT
ejpam-5171	73	178	set	set	VERB
ejpam-5171	73	179	(	(	PUNCT
ejpam-5171	73	180	[	[	X
ejpam-5171	73	181	32	32	NUM
ejpam-5171	73	182	]	]	PUNCT
ejpam-5171	73	183	)	)	PUNCT
ejpam-5171	73	184	,	,	PUNCT
ejpam-5171	73	185	if	if	SCONJ
ejpam-5171	73	186	l	l	NOUN
ejpam-5171	73	187	=	=	SYM
ejpam-5171	73	188	l1	l1	PROPN
ejpam-5171	73	189	∩	∩	ADJ
ejpam-5171	73	190	l2	l2	NOUN
ejpam-5171	73	191	,	,	PUNCT
ejpam-5171	73	192	where	where	SCONJ
ejpam-5171	73	193	l1	l1	PROPN
ejpam-5171	73	194	is	be	AUX
ejpam-5171	73	195	an	an	DET
ejpam-5171	73	196	open	open	ADJ
ejpam-5171	73	197	set	set	NOUN
ejpam-5171	73	198	and	and	CCONJ
ejpam-5171	73	199	l2	l2	NOUN
ejpam-5171	73	200	is	be	AUX
ejpam-5171	73	201	a	a	DET
ejpam-5171	73	202	tα	tα	ADV
ejpam-5171	73	203	-	-	PUNCT
ejpam-5171	73	204	set	set	NOUN
ejpam-5171	73	205	.	.	PUNCT
ejpam-5171	74	1	for	for	ADP
ejpam-5171	74	2	any	any	DET
ejpam-5171	74	3	collection	collection	NOUN
ejpam-5171	74	4	of	of	ADP
ejpam-5171	74	5	α	α	NOUN
ejpam-5171	74	6	-	-	ADJ
ejpam-5171	74	7	open	open	ADJ
ejpam-5171	74	8	(	(	PUNCT
ejpam-5171	74	9	resp	resp	NOUN
ejpam-5171	74	10	.	.	PUNCT
ejpam-5171	74	11	semi	semi	ADJ
ejpam-5171	74	12	-	-	ADJ
ejpam-5171	74	13	open	open	ADJ
ejpam-5171	74	14	,	,	PUNCT
ejpam-5171	74	15	pre	pre	ADJ
ejpam-5171	74	16	-	-	ADJ
ejpam-5171	74	17	open	open	ADJ
ejpam-5171	74	18	,	,	PUNCT
ejpam-5171	74	19	and	and	CCONJ
ejpam-5171	74	20	β	β	X
ejpam-5171	74	21	-	-	ADJ
ejpam-5171	74	22	open	open	ADJ
ejpam-5171	74	23	)	)	PUNCT
ejpam-5171	74	24	sets	set	NOUN
ejpam-5171	74	25	is	be	AUX
ejpam-5171	74	26	denoted	denote	VERB
ejpam-5171	74	27	by	by	ADP
ejpam-5171	74	28	δα	δα	PROPN
ejpam-5171	74	29	(	(	PUNCT
ejpam-5171	74	30	resp	resp	PROPN
ejpam-5171	74	31	.	.	PUNCT
ejpam-5171	74	32	so(x	so(x	NUM
ejpam-5171	74	33	)	)	PUNCT
ejpam-5171	74	34	,	,	PUNCT
ejpam-5171	74	35	po(x	po(x	NUM
ejpam-5171	74	36	)	)	PUNCT
ejpam-5171	74	37	,	,	PUNCT
ejpam-5171	74	38	and	and	CCONJ
ejpam-5171	74	39	βo(x	βo(x	NUM
ejpam-5171	74	40	)	)	PUNCT
ejpam-5171	74	41	)	)	PUNCT
ejpam-5171	74	42	.	.	PUNCT
ejpam-5171	75	1	h.	h.	PROPN
ejpam-5171	75	2	al	al	PROPN
ejpam-5171	75	3	-	-	PUNCT
ejpam-5171	75	4	saadi	saadi	PROPN
ejpam-5171	75	5	,	,	PUNCT
ejpam-5171	75	6	m.	m.	NOUN
ejpam-5171	75	7	al	al	PROPN
ejpam-5171	75	8	-	-	PUNCT
ejpam-5171	75	9	hodieb	hodieb	PROPN
ejpam-5171	75	10	/	/	SYM
ejpam-5171	75	11	eur	eur	PROPN
ejpam-5171	75	12	.	.	PUNCT
ejpam-5171	76	1	j.	j.	PROPN
ejpam-5171	76	2	pure	pure	PROPN
ejpam-5171	76	3	appl	appl	PROPN
ejpam-5171	76	4	.	.	PROPN
ejpam-5171	76	5	math	math	PROPN
ejpam-5171	76	6	,	,	PUNCT
ejpam-5171	76	7	17	17	NUM
ejpam-5171	76	8	(	(	PUNCT
ejpam-5171	76	9	2	2	NUM
ejpam-5171	76	10	)	)	PUNCT
ejpam-5171	76	11	(	(	PUNCT
ejpam-5171	76	12	2024	2024	NUM
ejpam-5171	76	13	)	)	PUNCT
ejpam-5171	76	14	,	,	PUNCT
ejpam-5171	76	15	1352	1352	NUM
ejpam-5171	76	16	-	-	SYM
ejpam-5171	76	17	1368	1368	NUM
ejpam-5171	76	18	1355	1355	NUM
ejpam-5171	76	19	definition	definition	NOUN
ejpam-5171	76	20	1.3	1.3	NUM
ejpam-5171	76	21	.	.	PUNCT
ejpam-5171	77	1	(	(	PUNCT
ejpam-5171	77	2	[	[	X
ejpam-5171	77	3	25	25	NUM
ejpam-5171	77	4	,	,	PUNCT
ejpam-5171	77	5	26	26	NUM
ejpam-5171	77	6	]	]	PUNCT
ejpam-5171	77	7	)	)	PUNCT
ejpam-5171	77	8	for	for	ADP
ejpam-5171	77	9	a	a	DET
ejpam-5171	77	10	collection	collection	NOUN
ejpam-5171	77	11	p	p	NOUN
ejpam-5171	77	12	⊆	⊆	NUM
ejpam-5171	77	13	2x	2x	NUM
ejpam-5171	77	14	on	on	ADP
ejpam-5171	77	15	x	x	PUNCT
ejpam-5171	77	16	̸=	̸=	PROPN
ejpam-5171	77	17	ϕ.	ϕ.	NOUN
ejpam-5171	77	18	we	we	PRON
ejpam-5171	77	19	define	define	VERB
ejpam-5171	77	20	a	a	DET
ejpam-5171	77	21	primal	primal	NOUN
ejpam-5171	77	22	on	on	ADP
ejpam-5171	77	23	x	x	PART
ejpam-5171	77	24	as	as	ADP
ejpam-5171	77	25	:	:	PUNCT
ejpam-5171	77	26	(	(	PUNCT
ejpam-5171	77	27	a	a	X
ejpam-5171	77	28	)	)	PUNCT
ejpam-5171	77	29	x	x	SYM
ejpam-5171	77	30	/∈	/∈	PUNCT
ejpam-5171	78	1	p	p	X
ejpam-5171	78	2	,	,	PUNCT
ejpam-5171	78	3	(	(	PUNCT
ejpam-5171	78	4	b	b	X
ejpam-5171	78	5	)	)	PUNCT
ejpam-5171	78	6	if	if	SCONJ
ejpam-5171	78	7	l	l	PROPN
ejpam-5171	78	8	∈	∈	PROPN
ejpam-5171	78	9	p	p	NOUN
ejpam-5171	78	10	and	and	CCONJ
ejpam-5171	78	11	e	e	NOUN
ejpam-5171	78	12	⊆	⊆	NUM
ejpam-5171	78	13	l	l	NOUN
ejpam-5171	78	14	,	,	PUNCT
ejpam-5171	78	15	thus	thus	ADV
ejpam-5171	78	16	e	e	X
ejpam-5171	78	17	∈	∈	PROPN
ejpam-5171	78	18	p	p	X
ejpam-5171	78	19	,	,	PUNCT
ejpam-5171	78	20	(	(	PUNCT
ejpam-5171	78	21	c	c	X
ejpam-5171	78	22	)	)	PUNCT
ejpam-5171	79	1	if	if	SCONJ
ejpam-5171	79	2	l	l	NOUN
ejpam-5171	79	3	∩	∩	X
ejpam-5171	79	4	e	e	X
ejpam-5171	79	5	∈	∈	PROPN
ejpam-5171	79	6	p	p	X
ejpam-5171	79	7	,	,	PUNCT
ejpam-5171	79	8	then	then	ADV
ejpam-5171	79	9	l	l	PROPN
ejpam-5171	79	10	∈	∈	PROPN
ejpam-5171	79	11	p	p	NOUN
ejpam-5171	79	12	or	or	CCONJ
ejpam-5171	79	13	e	e	NOUN
ejpam-5171	79	14	∈	∈	PROPN
ejpam-5171	79	15	p.	p.	NOUN
ejpam-5171	79	16	definition	definition	NOUN
ejpam-5171	79	17	1.4	1.4	NUM
ejpam-5171	79	18	.	.	PUNCT
ejpam-5171	80	1	(	(	PUNCT
ejpam-5171	80	2	[	[	X
ejpam-5171	80	3	25	25	NUM
ejpam-5171	80	4	,	,	PUNCT
ejpam-5171	80	5	26	26	NUM
ejpam-5171	80	6	]	]	PUNCT
ejpam-5171	80	7	)	)	PUNCT
ejpam-5171	80	8	the	the	DET
ejpam-5171	80	9	ts	ts	X
ejpam-5171	80	10	(	(	PUNCT
ejpam-5171	80	11	x	x	PROPN
ejpam-5171	80	12	,	,	PUNCT
ejpam-5171	80	13	δ	δ	PROPN
ejpam-5171	80	14	)	)	PUNCT
ejpam-5171	80	15	with	with	ADP
ejpam-5171	80	16	a	a	DET
ejpam-5171	80	17	primal	primal	ADJ
ejpam-5171	80	18	p	p	NOUN
ejpam-5171	80	19	defined	define	VERB
ejpam-5171	80	20	on	on	ADP
ejpam-5171	80	21	x	x	PUNCT
ejpam-5171	80	22	as	as	ADP
ejpam-5171	80	23	(	(	PUNCT
ejpam-5171	80	24	x	x	NOUN
ejpam-5171	80	25	,	,	PUNCT
ejpam-5171	80	26	δ	δ	PROPN
ejpam-5171	80	27	,	,	PUNCT
ejpam-5171	80	28	p	p	NOUN
ejpam-5171	80	29	)	)	PUNCT
ejpam-5171	80	30	is	be	AUX
ejpam-5171	80	31	called	call	VERB
ejpam-5171	80	32	a	a	DET
ejpam-5171	80	33	primal	primal	ADJ
ejpam-5171	80	34	topological	topological	ADJ
ejpam-5171	80	35	space	space	NOUN
ejpam-5171	80	36	(	(	PUNCT
ejpam-5171	80	37	pts	pt	NOUN
ejpam-5171	80	38	,	,	PUNCT
ejpam-5171	80	39	for	for	ADP
ejpam-5171	80	40	short	short	ADJ
ejpam-5171	80	41	)	)	PUNCT
ejpam-5171	80	42	.	.	PUNCT
ejpam-5171	81	1	definition	definition	NOUN
ejpam-5171	81	2	1.5	1.5	NUM
ejpam-5171	81	3	.	.	PUNCT
ejpam-5171	82	1	(	(	PUNCT
ejpam-5171	82	2	[	[	X
ejpam-5171	82	3	25	25	NUM
ejpam-5171	82	4	,	,	PUNCT
ejpam-5171	82	5	26	26	NUM
ejpam-5171	82	6	]	]	PUNCT
ejpam-5171	82	7	)	)	PUNCT
ejpam-5171	82	8	assume	assume	VERB
ejpam-5171	82	9	that	that	SCONJ
ejpam-5171	82	10	the	the	DET
ejpam-5171	82	11	pts	pt	NOUN
ejpam-5171	82	12	is	be	AUX
ejpam-5171	82	13	(	(	PUNCT
ejpam-5171	82	14	x	x	NOUN
ejpam-5171	82	15	,	,	PUNCT
ejpam-5171	82	16	δ	δ	PROPN
ejpam-5171	82	17	,	,	PUNCT
ejpam-5171	82	18	p	p	NOUN
ejpam-5171	82	19	)	)	PUNCT
ejpam-5171	82	20	.	.	PUNCT
ejpam-5171	83	1	defined	define	VERB
ejpam-5171	83	2	an	an	DET
ejpam-5171	83	3	operator	operator	NOUN
ejpam-5171	83	4	(	(	PUNCT
ejpam-5171	83	5	.	.	PUNCT
ejpam-5171	83	6	)	)	PUNCT
ejpam-5171	84	1	♢	♢	PROPN
ejpam-5171	84	2	:	:	PUNCT
ejpam-5171	85	1	2x	2x	NUM
ejpam-5171	85	2	→	→	SYM
ejpam-5171	85	3	2x	2x	NUM
ejpam-5171	85	4	as	as	ADP
ejpam-5171	85	5	l	l	NOUN
ejpam-5171	85	6	♢	♢	PROPN
ejpam-5171	85	7	(x	(x	PROPN
ejpam-5171	85	8	,	,	PUNCT
ejpam-5171	85	9	δ	δ	PROPN
ejpam-5171	85	10	,	,	PUNCT
ejpam-5171	85	11	p	p	NOUN
ejpam-5171	85	12	)	)	PUNCT
ejpam-5171	85	13	=	=	SYM
ejpam-5171	85	14	{	{	PUNCT
ejpam-5171	85	15	x	x	PUNCT
ejpam-5171	85	16	∈	∈	PROPN
ejpam-5171	85	17	x	x	X
ejpam-5171	85	18	:	:	PUNCT
ejpam-5171	85	19	(	(	PUNCT
ejpam-5171	85	20	∀u	∀u	NOUN
ejpam-5171	85	21	∈	∈	NOUN
ejpam-5171	85	22	n	n	CCONJ
ejpam-5171	85	23	(	(	PUNCT
ejpam-5171	85	24	x))(lc	x))(lc	PROPN
ejpam-5171	85	25	∪	∪	ADJ
ejpam-5171	85	26	uc	uc	PROPN
ejpam-5171	85	27	∈	∈	PROPN
ejpam-5171	85	28	p	p	NOUN
ejpam-5171	85	29	)	)	PUNCT
ejpam-5171	85	30	}	}	PUNCT
ejpam-5171	85	31	for	for	ADP
ejpam-5171	85	32	each	each	DET
ejpam-5171	85	33	subset	subset	NOUN
ejpam-5171	85	34	l	l	NOUN
ejpam-5171	85	35	of	of	ADP
ejpam-5171	85	36	x	x	PUNCT
ejpam-5171	85	37	the	the	DET
ejpam-5171	85	38	primal	primal	NOUN
ejpam-5171	85	39	by	by	ADP
ejpam-5171	85	40	our	our	PRON
ejpam-5171	85	41	needs	need	NOUN
ejpam-5171	85	42	,	,	PUNCT
ejpam-5171	85	43	will	will	AUX
ejpam-5171	85	44	be	be	AUX
ejpam-5171	85	45	used	use	VERB
ejpam-5171	85	46	l	l	PROPN
ejpam-5171	85	47	♢	♢	PROPN
ejpam-5171	85	48	p	p	NOUN
ejpam-5171	85	49	or	or	CCONJ
ejpam-5171	85	50	l	l	NOUN
ejpam-5171	85	51	♢	♢	PROPN
ejpam-5171	85	52	(x	(x	PROPN
ejpam-5171	85	53	,	,	PUNCT
ejpam-5171	85	54	δ	δ	PROPN
ejpam-5171	85	55	,	,	PUNCT
ejpam-5171	85	56	p	p	NOUN
ejpam-5171	85	57	)	)	PUNCT
ejpam-5171	85	58	to	to	PART
ejpam-5171	85	59	refer	refer	VERB
ejpam-5171	85	60	to	to	ADP
ejpam-5171	85	61	this	this	DET
ejpam-5171	85	62	operator	operator	NOUN
ejpam-5171	85	63	.	.	PUNCT
ejpam-5171	86	1	definition	definition	NOUN
ejpam-5171	86	2	1.6	1.6	NUM
ejpam-5171	86	3	.	.	PUNCT
ejpam-5171	87	1	(	(	PUNCT
ejpam-5171	87	2	[	[	X
ejpam-5171	87	3	25	25	NUM
ejpam-5171	87	4	,	,	PUNCT
ejpam-5171	87	5	26	26	NUM
ejpam-5171	87	6	]	]	PUNCT
ejpam-5171	87	7	)	)	PUNCT
ejpam-5171	87	8	consider	consider	VERB
ejpam-5171	87	9	a	a	DET
ejpam-5171	87	10	map	map	NOUN
ejpam-5171	87	11	cl	cl	NOUN
ejpam-5171	87	12	♢	♢	PROPN
ejpam-5171	87	13	:	:	PUNCT
ejpam-5171	87	14	2x	2x	NUM
ejpam-5171	87	15	→	→	SYM
ejpam-5171	87	16	2x	2x	NUM
ejpam-5171	87	17	in	in	ADP
ejpam-5171	87	18	a	a	DET
ejpam-5171	87	19	pts	pts	X
ejpam-5171	87	20	(	(	PUNCT
ejpam-5171	87	21	x	x	NOUN
ejpam-5171	87	22	,	,	PUNCT
ejpam-5171	87	23	δ	δ	PROPN
ejpam-5171	87	24	,	,	PUNCT
ejpam-5171	87	25	p	p	NOUN
ejpam-5171	87	26	)	)	PUNCT
ejpam-5171	87	27	,	,	PUNCT
ejpam-5171	87	28	defined	define	VERB
ejpam-5171	87	29	as	as	ADP
ejpam-5171	87	30	cl	cl	NOUN
ejpam-5171	87	31	♢	♢	PROPN
ejpam-5171	87	32	(l	(l	PROPN
ejpam-5171	87	33	)	)	PUNCT
ejpam-5171	87	34	=	=	SYM
ejpam-5171	88	1	l	l	NOUN
ejpam-5171	88	2	∪	∪	X
ejpam-5171	88	3	l	l	NOUN
ejpam-5171	88	4	♢	♢	PROPN
ejpam-5171	88	5	,	,	PUNCT
ejpam-5171	88	6	where	where	SCONJ
ejpam-5171	88	7	l	l	NOUN
ejpam-5171	88	8	is	be	AUX
ejpam-5171	88	9	any	any	DET
ejpam-5171	88	10	subset	subset	NOUN
ejpam-5171	88	11	of	of	ADP
ejpam-5171	88	12	x.	x.	NOUN
ejpam-5171	88	13	definition	definition	NOUN
ejpam-5171	88	14	1.7	1.7	NUM
ejpam-5171	88	15	.	.	PUNCT
ejpam-5171	89	1	(	(	PUNCT
ejpam-5171	89	2	[	[	X
ejpam-5171	89	3	25	25	NUM
ejpam-5171	89	4	,	,	PUNCT
ejpam-5171	89	5	26	26	NUM
ejpam-5171	89	6	]	]	PUNCT
ejpam-5171	89	7	)	)	PUNCT
ejpam-5171	89	8	in	in	ADP
ejpam-5171	89	9	a	a	DET
ejpam-5171	89	10	pts	pts	X
ejpam-5171	89	11	(	(	PUNCT
ejpam-5171	89	12	x	x	NOUN
ejpam-5171	89	13	,	,	PUNCT
ejpam-5171	89	14	δ	δ	PROPN
ejpam-5171	89	15	,	,	PUNCT
ejpam-5171	89	16	p	p	NOUN
ejpam-5171	89	17	)	)	PUNCT
ejpam-5171	89	18	,	,	PUNCT
ejpam-5171	89	19	the	the	DET
ejpam-5171	89	20	collection	collection	NOUN
ejpam-5171	89	21	δ	δ	PROPN
ejpam-5171	89	22	♢	♢	PROPN
ejpam-5171	89	23	=	=	SYM
ejpam-5171	89	24	{	{	PUNCT
ejpam-5171	89	25	l	l	NOUN
ejpam-5171	89	26	⊆	⊆	NUM
ejpam-5171	89	27	x	x	SYM
ejpam-5171	89	28	:	:	PUNCT
ejpam-5171	89	29	cl	cl	NOUN
ejpam-5171	89	30	♢	♢	PROPN
ejpam-5171	89	31	(lc	(lc	NUM
ejpam-5171	89	32	)	)	PUNCT
ejpam-5171	89	33	=	=	SYM
ejpam-5171	89	34	lc	lc	PROPN
ejpam-5171	89	35	}	}	PUNCT
ejpam-5171	89	36	is	be	AUX
ejpam-5171	89	37	characterized	characterize	VERB
ejpam-5171	89	38	as	as	ADP
ejpam-5171	89	39	a	a	DET
ejpam-5171	89	40	topology	topology	NOUN
ejpam-5171	89	41	on	on	ADP
ejpam-5171	89	42	x	x	SYM
ejpam-5171	89	43	that	that	PRON
ejpam-5171	89	44	is	be	AUX
ejpam-5171	89	45	generated	generate	VERB
ejpam-5171	89	46	by	by	ADP
ejpam-5171	89	47	primal	primal	ADJ
ejpam-5171	89	48	p	p	NOUN
ejpam-5171	89	49	and	and	CCONJ
ejpam-5171	89	50	topology	topology	PROPN
ejpam-5171	89	51	δ	δ	PROPN
ejpam-5171	89	52	.	.	PUNCT
ejpam-5171	90	1	the	the	DET
ejpam-5171	90	2	primal	primal	ADJ
ejpam-5171	90	3	topology	topology	NOUN
ejpam-5171	90	4	on	on	ADP
ejpam-5171	90	5	x	x	X
ejpam-5171	90	6	is	be	AUX
ejpam-5171	90	7	the	the	DET
ejpam-5171	90	8	term	term	NOUN
ejpam-5171	90	9	for	for	ADP
ejpam-5171	90	10	it	it	PRON
ejpam-5171	90	11	and	and	CCONJ
ejpam-5171	90	12	we	we	PRON
ejpam-5171	90	13	can	can	AUX
ejpam-5171	90	14	write	write	VERB
ejpam-5171	90	15	δ	δ	PROPN
ejpam-5171	90	16	♢	♢	PROPN
ejpam-5171	90	17	p	p	PROPN
ejpam-5171	90	18	instead	instead	ADV
ejpam-5171	90	19	of	of	ADP
ejpam-5171	90	20	δ	δ	PROPN
ejpam-5171	90	21	♢	♢	PROPN
ejpam-5171	90	22	.	.	PUNCT
ejpam-5171	91	1	clearly	clearly	ADV
ejpam-5171	91	2	,	,	PUNCT
ejpam-5171	91	3	δ	δ	PROPN
ejpam-5171	91	4	⊆	⊆	NUM
ejpam-5171	91	5	δ	δ	PROPN
ejpam-5171	91	6	♢	♢	PROPN
ejpam-5171	91	7	for	for	ADP
ejpam-5171	91	8	any	any	DET
ejpam-5171	91	9	primal	primal	ADJ
ejpam-5171	91	10	p	p	NOUN
ejpam-5171	91	11	on	on	ADP
ejpam-5171	91	12	a	a	DET
ejpam-5171	91	13	topological	topological	ADJ
ejpam-5171	91	14	(	(	PUNCT
ejpam-5171	91	15	x	x	NOUN
ejpam-5171	91	16	,	,	PUNCT
ejpam-5171	91	17	δ	δ	PROPN
ejpam-5171	91	18	)	)	PUNCT
ejpam-5171	91	19	.	.	PUNCT
ejpam-5171	92	1	we	we	PRON
ejpam-5171	92	2	will	will	AUX
ejpam-5171	92	3	use	use	VERB
ejpam-5171	92	4	δ	δ	PROPN
ejpam-5171	92	5	♢	♢	NOUN
ejpam-5171	92	6	-int(l	-int(l	PROPN
ejpam-5171	92	7	)	)	PUNCT
ejpam-5171	92	8	to	to	PART
ejpam-5171	92	9	refer	refer	VERB
ejpam-5171	92	10	to	to	ADP
ejpam-5171	92	11	the	the	DET
ejpam-5171	92	12	interior	interior	NOUN
ejpam-5171	92	13	of	of	ADP
ejpam-5171	92	14	l	l	NOUN
ejpam-5171	92	15	relative	relative	ADJ
ejpam-5171	92	16	to	to	ADP
ejpam-5171	92	17	δ	δ	PROPN
ejpam-5171	92	18	♢	♢	PROPN
ejpam-5171	92	19	.	.	PROPN
ejpam-5171	92	20	theorem	theorem	VERB
ejpam-5171	92	21	1.8	1.8	NUM
ejpam-5171	92	22	.	.	PUNCT
ejpam-5171	93	1	(	(	PUNCT
ejpam-5171	93	2	[	[	X
ejpam-5171	93	3	25	25	NUM
ejpam-5171	93	4	,	,	PUNCT
ejpam-5171	93	5	26	26	NUM
ejpam-5171	93	6	]	]	PUNCT
ejpam-5171	93	7	)	)	PUNCT
ejpam-5171	93	8	if	if	SCONJ
ejpam-5171	93	9	(	(	PUNCT
ejpam-5171	93	10	x	x	NOUN
ejpam-5171	93	11	,	,	PUNCT
ejpam-5171	93	12	δ	δ	PROPN
ejpam-5171	93	13	,	,	PUNCT
ejpam-5171	93	14	p	p	NOUN
ejpam-5171	93	15	)	)	PUNCT
ejpam-5171	93	16	is	be	AUX
ejpam-5171	93	17	pts	pt	NOUN
ejpam-5171	93	18	.	.	PUNCT
ejpam-5171	94	1	consequently	consequently	ADV
ejpam-5171	94	2	,	,	PUNCT
ejpam-5171	94	3	the	the	DET
ejpam-5171	94	4	primal	primal	ADJ
ejpam-5171	94	5	topology	topology	NOUN
ejpam-5171	94	6	δ	δ	PROPN
ejpam-5171	94	7	♢	♢	PROPN
ejpam-5171	94	8	is	be	AUX
ejpam-5171	94	9	finer	fine	ADJ
ejpam-5171	94	10	than	than	SCONJ
ejpam-5171	94	11	δ	δ	PROPN
ejpam-5171	94	12	.	.	PUNCT
ejpam-5171	94	13	theorem	theorem	VERB
ejpam-5171	94	14	1.9	1.9	NUM
ejpam-5171	94	15	.	.	PUNCT
ejpam-5171	95	1	(	(	PUNCT
ejpam-5171	95	2	[	[	X
ejpam-5171	95	3	25	25	NUM
ejpam-5171	95	4	,	,	PUNCT
ejpam-5171	95	5	26	26	NUM
ejpam-5171	95	6	]	]	PUNCT
ejpam-5171	95	7	)	)	PUNCT
ejpam-5171	95	8	considering	consider	VERB
ejpam-5171	95	9	a	a	DET
ejpam-5171	95	10	pts	pts	X
ejpam-5171	95	11	(	(	PUNCT
ejpam-5171	95	12	x	x	NOUN
ejpam-5171	95	13	,	,	PUNCT
ejpam-5171	95	14	δ	δ	PROPN
ejpam-5171	95	15	,	,	PUNCT
ejpam-5171	95	16	p	p	NOUN
ejpam-5171	95	17	)	)	PUNCT
ejpam-5171	95	18	,	,	PUNCT
ejpam-5171	95	19	the	the	DET
ejpam-5171	95	20	following	follow	VERB
ejpam-5171	95	21	is	be	AUX
ejpam-5171	95	22	true	true	ADJ
ejpam-5171	95	23	for	for	ADP
ejpam-5171	95	24	any	any	DET
ejpam-5171	95	25	two	two	NUM
ejpam-5171	95	26	subsets	subset	NOUN
ejpam-5171	95	27	l	l	NOUN
ejpam-5171	95	28	and	and	CCONJ
ejpam-5171	95	29	e	e	X
ejpam-5171	95	30	of	of	ADP
ejpam-5171	95	31	x	x	PROPN
ejpam-5171	95	32	:	:	PUNCT
ejpam-5171	95	33	(	(	PUNCT
ejpam-5171	95	34	a	a	X
ejpam-5171	95	35	)	)	PUNCT
ejpam-5171	95	36	if	if	SCONJ
ejpam-5171	95	37	lc	lc	PROPN
ejpam-5171	95	38	∈	∈	PROPN
ejpam-5171	95	39	δ	δ	PROPN
ejpam-5171	95	40	,	,	PUNCT
ejpam-5171	95	41	then	then	ADV
ejpam-5171	95	42	l	l	NOUN
ejpam-5171	95	43	♢	♢	PROPN
ejpam-5171	95	44	⊆	⊆	NUM
ejpam-5171	95	45	l	l	NOUN
ejpam-5171	95	46	,	,	PUNCT
ejpam-5171	95	47	(	(	PUNCT
ejpam-5171	95	48	b	b	X
ejpam-5171	95	49	)	)	PUNCT
ejpam-5171	95	50	ϕ	ϕ	NOUN
ejpam-5171	95	51	♢	♢	PROPN
ejpam-5171	95	52	=	=	SYM
ejpam-5171	95	53	ϕ	ϕ	PROPN
ejpam-5171	95	54	,	,	PUNCT
ejpam-5171	95	55	(	(	PUNCT
ejpam-5171	95	56	c	c	NOUN
ejpam-5171	95	57	)	)	PUNCT
ejpam-5171	95	58	cl(l	cl(l	NOUN
ejpam-5171	95	59	♢	♢	NOUN
ejpam-5171	95	60	)	)	PUNCT
ejpam-5171	95	61	=	=	PUNCT
ejpam-5171	96	1	l	l	NOUN
ejpam-5171	96	2	♢	♢	PROPN
ejpam-5171	96	3	,	,	PUNCT
ejpam-5171	96	4	(	(	PUNCT
ejpam-5171	96	5	d	d	X
ejpam-5171	96	6	)	)	PUNCT
ejpam-5171	96	7	(	(	PUNCT
ejpam-5171	96	8	l	l	NOUN
ejpam-5171	96	9	♢	♢	PROPN
ejpam-5171	96	10	)	)	PUNCT
ejpam-5171	96	11	♢	♢	PROPN
ejpam-5171	96	12	⊆	⊆	NUM
ejpam-5171	96	13	l	l	NOUN
ejpam-5171	96	14	♢	♢	PROPN
ejpam-5171	96	15	,	,	PUNCT
ejpam-5171	96	16	(	(	PUNCT
ejpam-5171	96	17	e	e	NOUN
ejpam-5171	96	18	)	)	PUNCT
ejpam-5171	96	19	if	if	SCONJ
ejpam-5171	96	20	l	l	PROPN
ejpam-5171	96	21	⊆	⊆	NUM
ejpam-5171	96	22	e	e	NOUN
ejpam-5171	96	23	,	,	PUNCT
ejpam-5171	96	24	then	then	ADV
ejpam-5171	96	25	l	l	NOUN
ejpam-5171	96	26	♢	♢	PROPN
ejpam-5171	96	27	⊆	⊆	NUM
ejpam-5171	96	28	e	e	SYM
ejpam-5171	96	29	♢	♢	PROPN
ejpam-5171	96	30	,	,	PUNCT
ejpam-5171	96	31	(	(	PUNCT
ejpam-5171	96	32	f	f	X
ejpam-5171	96	33	)	)	PUNCT
ejpam-5171	96	34	l	l	NOUN
ejpam-5171	96	35	♢	♢	PROPN
ejpam-5171	96	36	∪	∪	PROPN
ejpam-5171	96	37	e	e	PROPN
ejpam-5171	96	38	♢	♢	NOUN
ejpam-5171	96	39	=	=	SYM
ejpam-5171	96	40	(	(	PUNCT
ejpam-5171	96	41	l	l	NOUN
ejpam-5171	96	42	∪	∪	X
ejpam-5171	96	43	e	e	NOUN
ejpam-5171	96	44	)	)	PUNCT
ejpam-5171	96	45	♢	♢	PROPN
ejpam-5171	96	46	,	,	PUNCT
ejpam-5171	96	47	(	(	PUNCT
ejpam-5171	96	48	g	g	NOUN
ejpam-5171	96	49	)	)	PUNCT
ejpam-5171	96	50	(	(	PUNCT
ejpam-5171	96	51	l	l	NOUN
ejpam-5171	96	52	∩	∩	X
ejpam-5171	96	53	e	e	NOUN
ejpam-5171	96	54	)	)	PUNCT
ejpam-5171	96	55	♢	♢	PROPN
ejpam-5171	96	56	⊆	⊆	NUM
ejpam-5171	96	57	l	l	NOUN
ejpam-5171	96	58	♢	♢	PROPN
ejpam-5171	96	59	∩	∩	PROPN
ejpam-5171	96	60	e	e	PROPN
ejpam-5171	96	61	♢	♢	PROPN
ejpam-5171	96	62	.	.	PUNCT
ejpam-5171	96	63	lemma	lemma	PROPN
ejpam-5171	96	64	1.10	1.10	NUM
ejpam-5171	96	65	.	.	PUNCT
ejpam-5171	97	1	(	(	PUNCT
ejpam-5171	97	2	[	[	X
ejpam-5171	97	3	26	26	NUM
ejpam-5171	97	4	]	]	PUNCT
ejpam-5171	97	5	)	)	PUNCT
ejpam-5171	97	6	in	in	ADP
ejpam-5171	97	7	a	a	DET
ejpam-5171	97	8	pts	pts	X
ejpam-5171	97	9	(	(	PUNCT
ejpam-5171	97	10	x	x	NOUN
ejpam-5171	97	11	,	,	PUNCT
ejpam-5171	97	12	δ	δ	PROPN
ejpam-5171	97	13	,	,	PUNCT
ejpam-5171	97	14	p	p	NOUN
ejpam-5171	97	15	)	)	PUNCT
ejpam-5171	97	16	,	,	PUNCT
ejpam-5171	97	17	if	if	SCONJ
ejpam-5171	97	18	lc	lc	PROPN
ejpam-5171	97	19	/∈	/∈	PUNCT
ejpam-5171	98	1	p	p	X
ejpam-5171	98	2	,	,	PUNCT
ejpam-5171	98	3	then	then	ADV
ejpam-5171	98	4	l	l	NOUN
ejpam-5171	98	5	♢	♢	PROPN
ejpam-5171	98	6	=	=	PROPN
ejpam-5171	98	7	ϕ.	ϕ.	PROPN
ejpam-5171	98	8	theorem	theorem	VERB
ejpam-5171	98	9	1.11	1.11	NUM
ejpam-5171	98	10	.	.	PUNCT
ejpam-5171	99	1	(	(	PUNCT
ejpam-5171	99	2	[	[	X
ejpam-5171	99	3	25	25	NUM
ejpam-5171	99	4	,	,	PUNCT
ejpam-5171	99	5	26	26	NUM
ejpam-5171	99	6	]	]	PUNCT
ejpam-5171	99	7	)	)	PUNCT
ejpam-5171	99	8	assume	assume	VERB
ejpam-5171	99	9	that	that	SCONJ
ejpam-5171	99	10	(	(	PUNCT
ejpam-5171	99	11	x	x	NOUN
ejpam-5171	99	12	,	,	PUNCT
ejpam-5171	99	13	δ	δ	PROPN
ejpam-5171	99	14	,	,	PUNCT
ejpam-5171	99	15	p	p	NOUN
ejpam-5171	99	16	)	)	PUNCT
ejpam-5171	99	17	is	be	AUX
ejpam-5171	99	18	a	a	DET
ejpam-5171	99	19	pts	pt	NOUN
ejpam-5171	99	20	.	.	PUNCT
ejpam-5171	100	1	then	then	ADV
ejpam-5171	100	2	,	,	PUNCT
ejpam-5171	100	3	the	the	DET
ejpam-5171	100	4	family	family	NOUN
ejpam-5171	100	5	bp	bp	PROPN
ejpam-5171	100	6	=	=	SYM
ejpam-5171	100	7	{	{	PUNCT
ejpam-5171	100	8	t	t	PROPN
ejpam-5171	100	9	∩	∩	PROPN
ejpam-5171	100	10	p	p	X
ejpam-5171	100	11	:	:	PUNCT
ejpam-5171	100	12	t	t	PROPN
ejpam-5171	100	13	∈	∈	PROPN
ejpam-5171	100	14	δ	δ	PROPN
ejpam-5171	100	15	and	and	CCONJ
ejpam-5171	100	16	p	p	NOUN
ejpam-5171	100	17	/∈	/∈	PUNCT
ejpam-5171	101	1	p	p	X
ejpam-5171	101	2	}	}	PUNCT
ejpam-5171	101	3	is	be	AUX
ejpam-5171	101	4	a	a	DET
ejpam-5171	101	5	base	base	NOUN
ejpam-5171	101	6	for	for	ADP
ejpam-5171	101	7	the	the	DET
ejpam-5171	101	8	primal	primal	ADJ
ejpam-5171	101	9	topology	topology	NOUN
ejpam-5171	101	10	δ	δ	PROPN
ejpam-5171	101	11	♢	♢	PROPN
ejpam-5171	101	12	on	on	ADP
ejpam-5171	101	13	x.	x.	PROPN
ejpam-5171	101	14	definition	definition	NOUN
ejpam-5171	101	15	1.12	1.12	NUM
ejpam-5171	101	16	.	.	PUNCT
ejpam-5171	102	1	(	(	PUNCT
ejpam-5171	102	2	[	[	X
ejpam-5171	102	3	26	26	NUM
ejpam-5171	102	4	]	]	PUNCT
ejpam-5171	102	5	)	)	PUNCT
ejpam-5171	102	6	assume	assume	VERB
ejpam-5171	102	7	that	that	SCONJ
ejpam-5171	102	8	(	(	PUNCT
ejpam-5171	102	9	x	x	NOUN
ejpam-5171	102	10	,	,	PUNCT
ejpam-5171	102	11	δ	δ	PROPN
ejpam-5171	102	12	,	,	PUNCT
ejpam-5171	102	13	p	p	NOUN
ejpam-5171	102	14	)	)	PUNCT
ejpam-5171	102	15	is	be	AUX
ejpam-5171	102	16	a	a	DET
ejpam-5171	102	17	pts	pt	NOUN
ejpam-5171	102	18	.	.	PUNCT
ejpam-5171	103	1	an	an	DET
ejpam-5171	103	2	operator	operator	NOUN
ejpam-5171	103	3	cl	cl	NOUN
ejpam-5171	103	4	♢	♢	PROPN
ejpam-5171	103	5	p	p	NOUN
ejpam-5171	103	6	:	:	PUNCT
ejpam-5171	103	7	2x	2x	NUM
ejpam-5171	103	8	→	→	SYM
ejpam-5171	103	9	2x	2x	NUM
ejpam-5171	103	10	is	be	AUX
ejpam-5171	103	11	defined	define	VERB
ejpam-5171	103	12	as	as	ADP
ejpam-5171	103	13	cl	cl	NOUN
ejpam-5171	103	14	♢	♢	NOUN
ejpam-5171	103	15	p(l	p(l	PROPN
ejpam-5171	103	16	)	)	PUNCT
ejpam-5171	103	17	=	=	PRON
ejpam-5171	104	1	{	{	PUNCT
ejpam-5171	104	2	x	x	PUNCT
ejpam-5171	104	3	∈	∈	PROPN
ejpam-5171	104	4	x	x	X
ejpam-5171	104	5	:	:	PUNCT
ejpam-5171	104	6	(	(	PUNCT
ejpam-5171	104	7	∃	∃	PROPN
ejpam-5171	104	8	u	u	PROPN
ejpam-5171	104	9	∈	∈	PROPN
ejpam-5171	104	10	δ(x))((u	δ(x))((u	VERB
ejpam-5171	104	11	−	−	NOUN
ejpam-5171	104	12	l)c	l)c	NOUN
ejpam-5171	104	13	/∈	/∈	PUNCT
ejpam-5171	105	1	p	p	X
ejpam-5171	105	2	)	)	PUNCT
ejpam-5171	105	3	}	}	PUNCT
ejpam-5171	105	4	for	for	ADP
ejpam-5171	105	5	every	every	DET
ejpam-5171	105	6	l	l	NOUN
ejpam-5171	105	7	⊆	⊆	NUM
ejpam-5171	105	8	x.	x.	PROPN
ejpam-5171	105	9	h.	h.	PROPN
ejpam-5171	105	10	al	al	PROPN
ejpam-5171	105	11	-	-	PUNCT
ejpam-5171	105	12	saadi	saadi	PROPN
ejpam-5171	105	13	,	,	PUNCT
ejpam-5171	105	14	m.	m.	NOUN
ejpam-5171	105	15	al	al	PROPN
ejpam-5171	105	16	-	-	PUNCT
ejpam-5171	105	17	hodieb	hodieb	PROPN
ejpam-5171	105	18	/	/	SYM
ejpam-5171	105	19	eur	eur	PROPN
ejpam-5171	105	20	.	.	PUNCT
ejpam-5171	106	1	j.	j.	PROPN
ejpam-5171	106	2	pure	pure	PROPN
ejpam-5171	106	3	appl	appl	PROPN
ejpam-5171	106	4	.	.	PROPN
ejpam-5171	106	5	math	math	PROPN
ejpam-5171	106	6	,	,	PUNCT
ejpam-5171	106	7	17	17	NUM
ejpam-5171	106	8	(	(	PUNCT
ejpam-5171	106	9	2	2	NUM
ejpam-5171	106	10	)	)	PUNCT
ejpam-5171	106	11	(	(	PUNCT
ejpam-5171	106	12	2024	2024	NUM
ejpam-5171	106	13	)	)	PUNCT
ejpam-5171	106	14	,	,	PUNCT
ejpam-5171	106	15	1352	1352	NUM
ejpam-5171	106	16	-	-	SYM
ejpam-5171	106	17	1368	1368	NUM
ejpam-5171	106	18	1356	1356	NUM
ejpam-5171	106	19	the	the	DET
ejpam-5171	106	20	theorem	theorem	NOUN
ejpam-5171	106	21	below	below	ADV
ejpam-5171	106	22	demonstrates	demonstrate	VERB
ejpam-5171	106	23	several	several	ADJ
ejpam-5171	106	24	characterizations	characterization	NOUN
ejpam-5171	106	25	of	of	ADP
ejpam-5171	106	26	the	the	DET
ejpam-5171	106	27	operator	operator	NOUN
ejpam-5171	106	28	cl	cl	NOUN
ejpam-5171	106	29	♢	♢	PROPN
ejpam-5171	106	30	p	p	NOUN
ejpam-5171	106	31	.	.	PUNCT
ejpam-5171	107	1	theorem	theorem	VERB
ejpam-5171	107	2	1.13	1.13	NUM
ejpam-5171	107	3	.	.	PUNCT
ejpam-5171	108	1	(	(	PUNCT
ejpam-5171	108	2	[	[	X
ejpam-5171	108	3	26	26	NUM
ejpam-5171	108	4	]	]	PUNCT
ejpam-5171	108	5	)	)	PUNCT
ejpam-5171	108	6	assume	assume	VERB
ejpam-5171	108	7	that	that	SCONJ
ejpam-5171	108	8	(	(	PUNCT
ejpam-5171	108	9	x	x	NOUN
ejpam-5171	108	10	,	,	PUNCT
ejpam-5171	108	11	δ	δ	PROPN
ejpam-5171	108	12	,	,	PUNCT
ejpam-5171	108	13	p	p	NOUN
ejpam-5171	108	14	)	)	PUNCT
ejpam-5171	108	15	is	be	AUX
ejpam-5171	108	16	a	a	DET
ejpam-5171	108	17	pts	pt	NOUN
ejpam-5171	108	18	.	.	PUNCT
ejpam-5171	109	1	consequently	consequently	ADV
ejpam-5171	109	2	,	,	PUNCT
ejpam-5171	109	3	these	these	DET
ejpam-5171	109	4	characteristics	characteristic	NOUN
ejpam-5171	109	5	are	be	AUX
ejpam-5171	109	6	true	true	ADJ
ejpam-5171	109	7	:	:	PUNCT
ejpam-5171	109	8	(	(	PUNCT
ejpam-5171	109	9	a	a	X
ejpam-5171	109	10	)	)	PUNCT
ejpam-5171	109	11	if	if	SCONJ
ejpam-5171	109	12	l	l	NOUN
ejpam-5171	109	13	⊆	⊆	NUM
ejpam-5171	109	14	x	x	SYM
ejpam-5171	109	15	,	,	PUNCT
ejpam-5171	109	16	then	then	ADV
ejpam-5171	109	17	ψp(l	ψp(l	PUNCT
ejpam-5171	109	18	)	)	PUNCT
ejpam-5171	110	1	=	=	SYM
ejpam-5171	110	2	x−	x−	PROPN
ejpam-5171	110	3	(	(	PUNCT
ejpam-5171	110	4	x−	x−	PROPN
ejpam-5171	110	5	l	l	PROPN
ejpam-5171	110	6	)	)	PUNCT
ejpam-5171	110	7	♢	♢	PROPN
ejpam-5171	110	8	,	,	PUNCT
ejpam-5171	110	9	(	(	PUNCT
ejpam-5171	110	10	b	b	X
ejpam-5171	110	11	)	)	PUNCT
ejpam-5171	110	12	if	if	SCONJ
ejpam-5171	110	13	l	l	PROPN
ejpam-5171	110	14	⊆	⊆	NUM
ejpam-5171	110	15	x	x	X
ejpam-5171	110	16	,	,	PUNCT
ejpam-5171	110	17	then	then	ADV
ejpam-5171	110	18	ψp(l	ψp(l	PUNCT
ejpam-5171	110	19	)	)	PUNCT
ejpam-5171	110	20	is	be	AUX
ejpam-5171	110	21	open	open	ADJ
ejpam-5171	110	22	,	,	PUNCT
ejpam-5171	110	23	(	(	PUNCT
ejpam-5171	110	24	c	c	X
ejpam-5171	110	25	)	)	PUNCT
ejpam-5171	110	26	if	if	SCONJ
ejpam-5171	110	27	l	l	PROPN
ejpam-5171	110	28	⊆	⊆	NUM
ejpam-5171	110	29	e	e	NOUN
ejpam-5171	110	30	,	,	PUNCT
ejpam-5171	110	31	then	then	ADV
ejpam-5171	110	32	ψp(l	ψp(l	PUNCT
ejpam-5171	110	33	)	)	PUNCT
ejpam-5171	110	34	⊆	⊆	NUM
ejpam-5171	110	35	ψp(e	ψp(e	NOUN
ejpam-5171	110	36	)	)	PUNCT
ejpam-5171	110	37	,	,	PUNCT
ejpam-5171	110	38	(	(	PUNCT
ejpam-5171	110	39	d	d	X
ejpam-5171	110	40	)	)	PUNCT
ejpam-5171	110	41	if	if	SCONJ
ejpam-5171	110	42	l	l	NOUN
ejpam-5171	110	43	,	,	PUNCT
ejpam-5171	110	44	e	e	PROPN
ejpam-5171	110	45	⊆	⊆	NUM
ejpam-5171	110	46	x	x	NUM
ejpam-5171	110	47	,	,	PUNCT
ejpam-5171	110	48	then	then	ADV
ejpam-5171	110	49	ψp(l	ψp(l	PUNCT
ejpam-5171	110	50	∩	∩	ADJ
ejpam-5171	110	51	e	e	NOUN
ejpam-5171	110	52	)	)	PUNCT
ejpam-5171	110	53	=	=	SYM
ejpam-5171	110	54	ψp(l	ψp(l	X
ejpam-5171	110	55	)	)	PUNCT
ejpam-5171	110	56	∩ψp(e	∩ψp(e	PROPN
ejpam-5171	110	57	)	)	PUNCT
ejpam-5171	110	58	,	,	PUNCT
ejpam-5171	110	59	(	(	PUNCT
ejpam-5171	110	60	e	e	X
ejpam-5171	110	61	)	)	PUNCT
ejpam-5171	110	62	if	if	SCONJ
ejpam-5171	110	63	u	u	PROPN
ejpam-5171	110	64	∈	∈	PROPN
ejpam-5171	110	65	δ	δ	PROPN
ejpam-5171	110	66	♢	♢	PROPN
ejpam-5171	110	67	,	,	PUNCT
ejpam-5171	110	68	then	then	ADV
ejpam-5171	110	69	u	u	NOUN
ejpam-5171	110	70	⊆	⊆	NUM
ejpam-5171	110	71	ψp(u	ψp(u	NUM
ejpam-5171	110	72	)	)	PUNCT
ejpam-5171	110	73	,	,	PUNCT
ejpam-5171	110	74	(	(	PUNCT
ejpam-5171	110	75	f	f	X
ejpam-5171	110	76	)	)	PUNCT
ejpam-5171	110	77	if	if	SCONJ
ejpam-5171	110	78	l	l	PROPN
ejpam-5171	110	79	⊆	⊆	NUM
ejpam-5171	110	80	x	x	X
ejpam-5171	110	81	,	,	PUNCT
ejpam-5171	110	82	then	then	ADV
ejpam-5171	110	83	ψp(l	ψp(l	PUNCT
ejpam-5171	110	84	)	)	PUNCT
ejpam-5171	110	85	⊆	⊆	NUM
ejpam-5171	110	86	ψp(ψp(l	ψp(ψp(l	NOUN
ejpam-5171	110	87	)	)	PUNCT
ejpam-5171	110	88	)	)	PUNCT
ejpam-5171	110	89	,	,	PUNCT
ejpam-5171	110	90	(	(	PUNCT
ejpam-5171	110	91	g	g	NOUN
ejpam-5171	110	92	)	)	PUNCT
ejpam-5171	110	93	if	if	SCONJ
ejpam-5171	110	94	l	l	PROPN
ejpam-5171	110	95	⊆	⊆	NUM
ejpam-5171	110	96	x	x	X
ejpam-5171	110	97	,	,	PUNCT
ejpam-5171	110	98	then	then	ADV
ejpam-5171	110	99	l	l	PROPN
ejpam-5171	110	100	∩ψp(l	∩ψp(l	PROPN
ejpam-5171	110	101	)	)	PUNCT
ejpam-5171	110	102	=	=	PUNCT
ejpam-5171	111	1	int	int	PROPN
ejpam-5171	111	2	♢	♢	PROPN
ejpam-5171	111	3	(l	(l	PROPN
ejpam-5171	111	4	)	)	PUNCT
ejpam-5171	111	5	.	.	PUNCT
ejpam-5171	112	1	corollary	corollary	ADJ
ejpam-5171	112	2	1.14	1.14	NUM
ejpam-5171	112	3	.	.	PUNCT
ejpam-5171	113	1	(	(	PUNCT
ejpam-5171	113	2	[	[	X
ejpam-5171	113	3	26	26	NUM
ejpam-5171	113	4	]	]	PUNCT
ejpam-5171	113	5	)	)	PUNCT
ejpam-5171	113	6	assume	assume	VERB
ejpam-5171	113	7	that	that	SCONJ
ejpam-5171	113	8	(	(	PUNCT
ejpam-5171	113	9	x	x	NOUN
ejpam-5171	113	10	,	,	PUNCT
ejpam-5171	113	11	δ	δ	PROPN
ejpam-5171	113	12	,	,	PUNCT
ejpam-5171	113	13	p	p	NOUN
ejpam-5171	113	14	)	)	PUNCT
ejpam-5171	113	15	is	be	AUX
ejpam-5171	113	16	a	a	DET
ejpam-5171	113	17	pts	pt	NOUN
ejpam-5171	113	18	.	.	PUNCT
ejpam-5171	114	1	then	then	ADV
ejpam-5171	114	2	,	,	PUNCT
ejpam-5171	114	3	u	u	NOUN
ejpam-5171	114	4	⊆	⊆	NUM
ejpam-5171	114	5	ψp(u	ψp(u	NUM
ejpam-5171	114	6	)	)	PUNCT
ejpam-5171	114	7	for	for	ADP
ejpam-5171	114	8	each	each	DET
ejpam-5171	114	9	open	open	ADJ
ejpam-5171	114	10	set	set	VERB
ejpam-5171	114	11	u	u	PROPN
ejpam-5171	114	12	∈	∈	PROPN
ejpam-5171	114	13	δ	δ	PROPN
ejpam-5171	114	14	.	.	PUNCT
ejpam-5171	114	15	theorem	theorem	VERB
ejpam-5171	114	16	1.15	1.15	NUM
ejpam-5171	114	17	.	.	PUNCT
ejpam-5171	115	1	(	(	PUNCT
ejpam-5171	115	2	[	[	X
ejpam-5171	115	3	26	26	NUM
ejpam-5171	115	4	]	]	PUNCT
ejpam-5171	115	5	)	)	PUNCT
ejpam-5171	115	6	consider	consider	VERB
ejpam-5171	115	7	(	(	PUNCT
ejpam-5171	115	8	x	x	NOUN
ejpam-5171	115	9	,	,	PUNCT
ejpam-5171	115	10	δ	δ	PROPN
ejpam-5171	115	11	,	,	PUNCT
ejpam-5171	115	12	p	p	NOUN
ejpam-5171	115	13	)	)	PUNCT
ejpam-5171	115	14	as	as	ADP
ejpam-5171	115	15	a	a	DET
ejpam-5171	115	16	pts	pt	NOUN
ejpam-5171	115	17	and	and	CCONJ
ejpam-5171	115	18	l	l	NOUN
ejpam-5171	115	19	⊆	⊆	NUM
ejpam-5171	115	20	x.	x.	NOUN
ejpam-5171	115	21	then	then	ADV
ejpam-5171	115	22	,	,	PUNCT
ejpam-5171	115	23	the	the	DET
ejpam-5171	115	24	following	follow	VERB
ejpam-5171	115	25	properties	property	NOUN
ejpam-5171	115	26	hold	hold	VERB
ejpam-5171	115	27	:	:	PUNCT
ejpam-5171	115	28	(	(	PUNCT
ejpam-5171	115	29	a	a	NOUN
ejpam-5171	115	30	)	)	PUNCT
ejpam-5171	115	31	ψp(l	ψp(l	PUNCT
ejpam-5171	115	32	)	)	PUNCT
ejpam-5171	115	33	=	=	PUNCT
ejpam-5171	116	1	∪{u	∪{u	PROPN
ejpam-5171	116	2	∈	∈	PROPN
ejpam-5171	116	3	δ	δ	NOUN
ejpam-5171	116	4	:	:	PUNCT
ejpam-5171	116	5	(	(	PUNCT
ejpam-5171	116	6	u	u	NOUN
ejpam-5171	116	7	−	−	NOUN
ejpam-5171	116	8	l)c	l)c	NOUN
ejpam-5171	116	9	/∈	/∈	PUNCT
ejpam-5171	117	1	p	p	X
ejpam-5171	117	2	}	}	PUNCT
ejpam-5171	117	3	,	,	PUNCT
ejpam-5171	117	4	(	(	PUNCT
ejpam-5171	117	5	b	b	NOUN
ejpam-5171	117	6	)	)	PUNCT
ejpam-5171	117	7	ψp(l	ψp(l	PUNCT
ejpam-5171	117	8	)	)	PUNCT
ejpam-5171	117	9	⊇	⊇	PROPN
ejpam-5171	117	10	∪{u	∪{u	PROPN
ejpam-5171	117	11	∈	∈	PROPN
ejpam-5171	117	12	δ	δ	PROPN
ejpam-5171	117	13	:	:	PUNCT
ejpam-5171	117	14	(	(	PUNCT
ejpam-5171	117	15	u	u	NOUN
ejpam-5171	117	16	−	−	NOUN
ejpam-5171	117	17	l)c	l)c	NOUN
ejpam-5171	117	18	∪	∪	X
ejpam-5171	117	19	(	(	PUNCT
ejpam-5171	117	20	l−	l−	NOUN
ejpam-5171	117	21	u)c	u)c	ADJ
ejpam-5171	117	22	/∈	/∈	PUNCT
ejpam-5171	118	1	p	p	X
ejpam-5171	118	2	}	}	PUNCT
ejpam-5171	118	3	.	.	PUNCT
ejpam-5171	119	1	2	2	X
ejpam-5171	119	2	.	.	X
ejpam-5171	119	3	new	new	ADJ
ejpam-5171	119	4	classes	class	NOUN
ejpam-5171	119	5	of	of	ADP
ejpam-5171	119	6	sets	set	NOUN
ejpam-5171	119	7	in	in	ADP
ejpam-5171	119	8	primal	primal	ADJ
ejpam-5171	119	9	topological	topological	ADJ
ejpam-5171	119	10	spaces	space	NOUN
ejpam-5171	119	11	this	this	DET
ejpam-5171	119	12	section	section	NOUN
ejpam-5171	119	13	aims	aim	VERB
ejpam-5171	119	14	to	to	PART
ejpam-5171	119	15	describe	describe	VERB
ejpam-5171	119	16	,	,	PUNCT
ejpam-5171	119	17	introduce	introduce	VERB
ejpam-5171	119	18	,	,	PUNCT
ejpam-5171	119	19	and	and	CCONJ
ejpam-5171	119	20	examine	examine	VERB
ejpam-5171	119	21	several	several	ADJ
ejpam-5171	119	22	classes	class	NOUN
ejpam-5171	119	23	of	of	ADP
ejpam-5171	119	24	open	open	ADJ
ejpam-5171	119	25	sets	set	NOUN
ejpam-5171	119	26	in	in	ADP
ejpam-5171	119	27	primal	primal	ADJ
ejpam-5171	119	28	topological	topological	ADJ
ejpam-5171	119	29	spaces	space	NOUN
ejpam-5171	119	30	,	,	PUNCT
ejpam-5171	119	31	as	as	ADV
ejpam-5171	119	32	well	well	ADV
ejpam-5171	119	33	as	as	ADP
ejpam-5171	119	34	their	their	PRON
ejpam-5171	119	35	fundamental	fundamental	ADJ
ejpam-5171	119	36	characteristics	characteristic	NOUN
ejpam-5171	119	37	and	and	CCONJ
ejpam-5171	119	38	relationships	relationship	NOUN
ejpam-5171	119	39	.	.	PUNCT
ejpam-5171	120	1	definition	definition	NOUN
ejpam-5171	120	2	2.1	2.1	NUM
ejpam-5171	120	3	.	.	PUNCT
ejpam-5171	120	4	suppose	suppose	VERB
ejpam-5171	120	5	that	that	SCONJ
ejpam-5171	120	6	a	a	DET
ejpam-5171	120	7	pts	pts	X
ejpam-5171	120	8	(	(	PUNCT
ejpam-5171	120	9	x	x	NOUN
ejpam-5171	120	10	,	,	PUNCT
ejpam-5171	120	11	δ	δ	PROPN
ejpam-5171	120	12	,	,	PUNCT
ejpam-5171	120	13	p	p	NOUN
ejpam-5171	120	14	)	)	PUNCT
ejpam-5171	120	15	.	.	PUNCT
ejpam-5171	121	1	so	so	ADV
ejpam-5171	121	2	,	,	PUNCT
ejpam-5171	121	3	we	we	PRON
ejpam-5171	121	4	may	may	AUX
ejpam-5171	121	5	define	define	VERB
ejpam-5171	121	6	a	a	DET
ejpam-5171	121	7	subset	subset	NOUN
ejpam-5171	121	8	l	l	NOUN
ejpam-5171	121	9	of	of	ADP
ejpam-5171	121	10	x	x	PRON
ejpam-5171	121	11	as	as	SCONJ
ejpam-5171	121	12	follows	follow	VERB
ejpam-5171	121	13	:	:	PUNCT
ejpam-5171	121	14	(	(	PUNCT
ejpam-5171	121	15	a	a	X
ejpam-5171	121	16	)	)	PUNCT
ejpam-5171	121	17	p	p	NOUN
ejpam-5171	121	18	-	-	PUNCT
ejpam-5171	121	19	open	open	ADJ
ejpam-5171	121	20	(	(	PUNCT
ejpam-5171	121	21	[	[	X
ejpam-5171	121	22	25	25	NUM
ejpam-5171	121	23	,	,	PUNCT
ejpam-5171	121	24	26	26	NUM
ejpam-5171	121	25	]	]	PUNCT
ejpam-5171	121	26	)	)	PUNCT
ejpam-5171	121	27	,	,	PUNCT
ejpam-5171	121	28	if	if	SCONJ
ejpam-5171	121	29	l	l	PROPN
ejpam-5171	121	30	⊆	⊆	NUM
ejpam-5171	121	31	int(l	int(l	PROPN
ejpam-5171	121	32	♢	♢	PROPN
ejpam-5171	121	33	p	p	NOUN
ejpam-5171	121	34	)	)	PUNCT
ejpam-5171	121	35	,	,	PUNCT
ejpam-5171	121	36	(	(	PUNCT
ejpam-5171	121	37	b	b	X
ejpam-5171	121	38	)	)	PUNCT
ejpam-5171	121	39	p	p	NOUN
ejpam-5171	121	40	-	-	PUNCT
ejpam-5171	121	41	α	α	NOUN
ejpam-5171	121	42	-	-	NOUN
ejpam-5171	121	43	open	open	ADJ
ejpam-5171	121	44	,	,	PUNCT
ejpam-5171	121	45	if	if	SCONJ
ejpam-5171	121	46	l	l	PROPN
ejpam-5171	121	47	⊆	⊆	NUM
ejpam-5171	121	48	int(cl	int(cl	ADJ
ejpam-5171	121	49	♢	♢	PROPN
ejpam-5171	121	50	(int(l	(int(l	PROPN
ejpam-5171	121	51	)	)	PUNCT
ejpam-5171	121	52	)	)	PUNCT
ejpam-5171	121	53	)	)	PUNCT
ejpam-5171	121	54	,	,	PUNCT
ejpam-5171	121	55	(	(	PUNCT
ejpam-5171	121	56	c	c	X
ejpam-5171	121	57	)	)	PUNCT
ejpam-5171	121	58	p	p	NOUN
ejpam-5171	121	59	-	-	PUNCT
ejpam-5171	121	60	semi	semi	ADV
ejpam-5171	121	61	-	-	ADJ
ejpam-5171	121	62	open	open	ADJ
ejpam-5171	121	63	,	,	PUNCT
ejpam-5171	121	64	if	if	SCONJ
ejpam-5171	121	65	l	l	NOUN
ejpam-5171	121	66	⊆	⊆	NUM
ejpam-5171	121	67	cl	cl	NOUN
ejpam-5171	121	68	♢	♢	PROPN
ejpam-5171	121	69	(int(l	(int(l	PROPN
ejpam-5171	121	70	)	)	PUNCT
ejpam-5171	121	71	)	)	PUNCT
ejpam-5171	121	72	,	,	PUNCT
ejpam-5171	121	73	(	(	PUNCT
ejpam-5171	121	74	d	d	X
ejpam-5171	121	75	)	)	PUNCT
ejpam-5171	121	76	p	p	NOUN
ejpam-5171	121	77	-	-	PUNCT
ejpam-5171	121	78	pre	pre	NOUN
ejpam-5171	121	79	-	-	ADJ
ejpam-5171	121	80	open	open	ADJ
ejpam-5171	121	81	,	,	PUNCT
ejpam-5171	121	82	if	if	SCONJ
ejpam-5171	121	83	l	l	PROPN
ejpam-5171	121	84	⊆	⊆	NUM
ejpam-5171	121	85	int(cl	int(cl	PROPN
ejpam-5171	121	86	♢	♢	PROPN
ejpam-5171	121	87	(l	(l	PROPN
ejpam-5171	121	88	)	)	PUNCT
ejpam-5171	121	89	)	)	PUNCT
ejpam-5171	121	90	,	,	PUNCT
ejpam-5171	121	91	(	(	PUNCT
ejpam-5171	121	92	e	e	NOUN
ejpam-5171	121	93	)	)	PUNCT
ejpam-5171	121	94	p	p	NOUN
ejpam-5171	121	95	-	-	PUNCT
ejpam-5171	121	96	β	β	NOUN
ejpam-5171	121	97	-	-	ADJ
ejpam-5171	121	98	open	open	ADJ
ejpam-5171	121	99	,	,	PUNCT
ejpam-5171	121	100	if	if	SCONJ
ejpam-5171	121	101	l	l	PROPN
ejpam-5171	121	102	⊆	⊆	NUM
ejpam-5171	121	103	cl(int(cl	cl(int(cl	PROPN
ejpam-5171	121	104	♢	♢	PROPN
ejpam-5171	121	105	(l	(l	PROPN
ejpam-5171	121	106	)	)	PUNCT
ejpam-5171	121	107	)	)	PUNCT
ejpam-5171	121	108	)	)	PUNCT
ejpam-5171	121	109	.	.	PUNCT
ejpam-5171	122	1	theorem	theorem	VERB
ejpam-5171	122	2	2.2	2.2	NUM
ejpam-5171	122	3	.	.	PUNCT
ejpam-5171	123	1	in	in	ADP
ejpam-5171	123	2	a	a	DET
ejpam-5171	123	3	pts	pts	X
ejpam-5171	123	4	(	(	PUNCT
ejpam-5171	123	5	x	x	NOUN
ejpam-5171	123	6	,	,	PUNCT
ejpam-5171	123	7	δ	δ	PROPN
ejpam-5171	123	8	,	,	PUNCT
ejpam-5171	123	9	p	p	NOUN
ejpam-5171	123	10	)	)	PUNCT
ejpam-5171	123	11	,	,	PUNCT
ejpam-5171	123	12	the	the	DET
ejpam-5171	123	13	next	next	ADJ
ejpam-5171	123	14	characteristics	characteristic	NOUN
ejpam-5171	123	15	are	be	AUX
ejpam-5171	123	16	true	true	ADJ
ejpam-5171	123	17	:	:	PUNCT
ejpam-5171	123	18	(	(	PUNCT
ejpam-5171	123	19	a	a	X
ejpam-5171	123	20	)	)	PUNCT
ejpam-5171	123	21	each	each	DET
ejpam-5171	123	22	p	p	PROPN
ejpam-5171	123	23	-	-	PUNCT
ejpam-5171	123	24	α	α	NOUN
ejpam-5171	123	25	-	-	ADJ
ejpam-5171	123	26	open	open	ADJ
ejpam-5171	123	27	set	set	NOUN
ejpam-5171	123	28	is	be	AUX
ejpam-5171	123	29	α	α	NOUN
ejpam-5171	123	30	-	-	ADJ
ejpam-5171	123	31	open	open	ADJ
ejpam-5171	123	32	,	,	PUNCT
ejpam-5171	123	33	(	(	PUNCT
ejpam-5171	123	34	b	b	X
ejpam-5171	123	35	)	)	PUNCT
ejpam-5171	123	36	each	each	DET
ejpam-5171	123	37	p	p	NOUN
ejpam-5171	123	38	-	-	PUNCT
ejpam-5171	123	39	semi	semi	ADV
ejpam-5171	123	40	-	-	ADJ
ejpam-5171	123	41	open	open	ADJ
ejpam-5171	123	42	set	set	NOUN
ejpam-5171	123	43	is	be	AUX
ejpam-5171	123	44	semi	semi	ADJ
ejpam-5171	123	45	-	-	ADJ
ejpam-5171	123	46	open	open	ADJ
ejpam-5171	123	47	,	,	PUNCT
ejpam-5171	123	48	(	(	PUNCT
ejpam-5171	123	49	c	c	X
ejpam-5171	123	50	)	)	PUNCT
ejpam-5171	123	51	each	each	DET
ejpam-5171	123	52	p	p	PROPN
ejpam-5171	123	53	-	-	PUNCT
ejpam-5171	123	54	pre	pre	ADJ
ejpam-5171	123	55	-	-	ADJ
ejpam-5171	123	56	open	open	ADJ
ejpam-5171	123	57	set	set	NOUN
ejpam-5171	123	58	is	be	AUX
ejpam-5171	123	59	pre	pre	ADJ
ejpam-5171	123	60	-	-	ADJ
ejpam-5171	123	61	open	open	ADJ
ejpam-5171	123	62	,	,	PUNCT
ejpam-5171	123	63	(	(	PUNCT
ejpam-5171	123	64	d	d	X
ejpam-5171	123	65	)	)	PUNCT
ejpam-5171	123	66	each	each	DET
ejpam-5171	123	67	p	p	PROPN
ejpam-5171	123	68	-	-	PUNCT
ejpam-5171	123	69	β	β	NOUN
ejpam-5171	123	70	-	-	ADJ
ejpam-5171	123	71	open	open	ADJ
ejpam-5171	123	72	set	set	NOUN
ejpam-5171	123	73	is	be	AUX
ejpam-5171	123	74	β	β	NOUN
ejpam-5171	123	75	-	-	ADJ
ejpam-5171	123	76	open	open	ADJ
ejpam-5171	123	77	.	.	PUNCT
ejpam-5171	124	1	h.	h.	PROPN
ejpam-5171	124	2	al	al	PROPN
ejpam-5171	124	3	-	-	PUNCT
ejpam-5171	124	4	saadi	saadi	PROPN
ejpam-5171	124	5	,	,	PUNCT
ejpam-5171	124	6	m.	m.	NOUN
ejpam-5171	124	7	al	al	PROPN
ejpam-5171	124	8	-	-	PUNCT
ejpam-5171	124	9	hodieb	hodieb	PROPN
ejpam-5171	124	10	/	/	SYM
ejpam-5171	124	11	eur	eur	PROPN
ejpam-5171	124	12	.	.	PUNCT
ejpam-5171	125	1	j.	j.	PROPN
ejpam-5171	125	2	pure	pure	PROPN
ejpam-5171	125	3	appl	appl	PROPN
ejpam-5171	125	4	.	.	PROPN
ejpam-5171	125	5	math	math	PROPN
ejpam-5171	125	6	,	,	PUNCT
ejpam-5171	125	7	17	17	NUM
ejpam-5171	125	8	(	(	PUNCT
ejpam-5171	125	9	2	2	NUM
ejpam-5171	125	10	)	)	PUNCT
ejpam-5171	125	11	(	(	PUNCT
ejpam-5171	125	12	2024	2024	NUM
ejpam-5171	125	13	)	)	PUNCT
ejpam-5171	125	14	,	,	PUNCT
ejpam-5171	125	15	1352	1352	NUM
ejpam-5171	125	16	-	-	SYM
ejpam-5171	125	17	1368	1368	NUM
ejpam-5171	125	18	1357	1357	NUM
ejpam-5171	125	19	proof	proof	NOUN
ejpam-5171	125	20	.	.	PUNCT
ejpam-5171	126	1	(	(	PUNCT
ejpam-5171	126	2	a	a	X
ejpam-5171	126	3	)	)	PUNCT
ejpam-5171	126	4	suppose	suppose	VERB
ejpam-5171	126	5	that	that	SCONJ
ejpam-5171	126	6	l	l	NOUN
ejpam-5171	126	7	be	be	AUX
ejpam-5171	126	8	a	a	DET
ejpam-5171	126	9	p	p	NOUN
ejpam-5171	126	10	-	-	PUNCT
ejpam-5171	126	11	α	α	NOUN
ejpam-5171	126	12	-	-	NOUN
ejpam-5171	126	13	open	open	ADJ
ejpam-5171	126	14	.	.	PUNCT
ejpam-5171	127	1	hence	hence	ADV
ejpam-5171	127	2	,	,	PUNCT
ejpam-5171	127	3	l	l	PROPN
ejpam-5171	127	4	⊂	⊂	PROPN
ejpam-5171	127	5	int(cl	int(cl	PROPN
ejpam-5171	127	6	♢	♢	PROPN
ejpam-5171	127	7	(int(l	(int(l	PROPN
ejpam-5171	127	8	)	)	PUNCT
ejpam-5171	127	9	)	)	PUNCT
ejpam-5171	127	10	)	)	PUNCT
ejpam-5171	128	1	=	=	SYM
ejpam-5171	128	2	int(int(l)∪	int(int(l)∪	PROPN
ejpam-5171	128	3	(	(	PUNCT
ejpam-5171	128	4	int(l	int(l	PROPN
ejpam-5171	128	5	)	)	PUNCT
ejpam-5171	128	6	)	)	PUNCT
ejpam-5171	128	7	♢	♢	PROPN
ejpam-5171	128	8	)	)	PUNCT
ejpam-5171	128	9	⊂	⊂	PROPN
ejpam-5171	128	10	int(cl(int(l	int(cl(int(l	PROPN
ejpam-5171	128	11	)	)	PUNCT
ejpam-5171	128	12	)	)	PUNCT
ejpam-5171	128	13	∪	∪	ADP
ejpam-5171	128	14	int(l	int(l	PROPN
ejpam-5171	128	15	)	)	PUNCT
ejpam-5171	128	16	)	)	PUNCT
ejpam-5171	129	1	⊂	⊂	PROPN
ejpam-5171	129	2	int(cl(int(l	int(cl(int(l	PROPN
ejpam-5171	129	3	)	)	PUNCT
ejpam-5171	129	4	)	)	PUNCT
ejpam-5171	129	5	)	)	PUNCT
ejpam-5171	129	6	.	.	PUNCT
ejpam-5171	130	1	thus	thus	ADV
ejpam-5171	130	2	,	,	PUNCT
ejpam-5171	130	3	l	l	PROPN
ejpam-5171	130	4	is	be	AUX
ejpam-5171	130	5	α	α	NOUN
ejpam-5171	130	6	-	-	NOUN
ejpam-5171	130	7	open	open	ADJ
ejpam-5171	130	8	.	.	PUNCT
ejpam-5171	131	1	(	(	PUNCT
ejpam-5171	131	2	b	b	X
ejpam-5171	131	3	)	)	PUNCT
ejpam-5171	131	4	suppose	suppose	VERB
ejpam-5171	131	5	that	that	SCONJ
ejpam-5171	131	6	l	l	NOUN
ejpam-5171	131	7	be	be	AUX
ejpam-5171	131	8	a	a	DET
ejpam-5171	131	9	p	p	NOUN
ejpam-5171	131	10	-	-	PUNCT
ejpam-5171	131	11	semi	semi	ADV
ejpam-5171	131	12	-	-	ADJ
ejpam-5171	131	13	open	open	ADJ
ejpam-5171	131	14	.	.	PUNCT
ejpam-5171	132	1	hence	hence	ADV
ejpam-5171	132	2	,	,	PUNCT
ejpam-5171	132	3	l	l	PROPN
ejpam-5171	132	4	⊆	⊆	NUM
ejpam-5171	132	5	cl	cl	NOUN
ejpam-5171	132	6	♢	♢	PROPN
ejpam-5171	132	7	(int(l	(int(l	PROPN
ejpam-5171	132	8	)	)	PUNCT
ejpam-5171	132	9	)	)	PUNCT
ejpam-5171	133	1	=	=	SYM
ejpam-5171	133	2	int(l	int(l	PROPN
ejpam-5171	133	3	)	)	PUNCT
ejpam-5171	133	4	∪	∪	NOUN
ejpam-5171	133	5	(	(	PUNCT
ejpam-5171	133	6	int(l	int(l	PROPN
ejpam-5171	133	7	)	)	PUNCT
ejpam-5171	133	8	)	)	PUNCT
ejpam-5171	134	1	♢	♢	PROPN
ejpam-5171	134	2	⊆	⊆	NUM
ejpam-5171	134	3	int(l	int(l	PROPN
ejpam-5171	134	4	)	)	PUNCT
ejpam-5171	134	5	∪	∪	ADP
ejpam-5171	134	6	cl(int(l	cl(int(l	PROPN
ejpam-5171	134	7	)	)	PUNCT
ejpam-5171	134	8	)	)	PUNCT
ejpam-5171	134	9	(	(	PUNCT
ejpam-5171	134	10	from	from	ADP
ejpam-5171	134	11	theorem	theorem	ADJ
ejpam-5171	134	12	1.9	1.9	NUM
ejpam-5171	134	13	)	)	PUNCT
ejpam-5171	134	14	=	=	SYM
ejpam-5171	134	15	cl(int(l	cl(int(l	PROPN
ejpam-5171	134	16	)	)	PUNCT
ejpam-5171	134	17	)	)	PUNCT
ejpam-5171	134	18	.	.	PUNCT
ejpam-5171	135	1	thus	thus	ADV
ejpam-5171	135	2	,	,	PUNCT
ejpam-5171	135	3	l	l	NOUN
ejpam-5171	135	4	is	be	AUX
ejpam-5171	135	5	semi	semi	ADJ
ejpam-5171	135	6	-	-	ADJ
ejpam-5171	135	7	open	open	ADJ
ejpam-5171	135	8	.	.	PUNCT
ejpam-5171	136	1	(	(	PUNCT
ejpam-5171	136	2	c	c	X
ejpam-5171	136	3	)	)	PUNCT
ejpam-5171	136	4	suppose	suppose	VERB
ejpam-5171	136	5	that	that	SCONJ
ejpam-5171	136	6	l	l	NOUN
ejpam-5171	136	7	be	be	AUX
ejpam-5171	136	8	a	a	DET
ejpam-5171	136	9	p	p	NOUN
ejpam-5171	136	10	-	-	PUNCT
ejpam-5171	136	11	pre	pre	NOUN
ejpam-5171	136	12	-	-	ADJ
ejpam-5171	136	13	open	open	ADJ
ejpam-5171	136	14	.	.	PUNCT
ejpam-5171	137	1	hence	hence	ADV
ejpam-5171	137	2	,	,	PUNCT
ejpam-5171	137	3	l	l	PROPN
ejpam-5171	137	4	⊆	⊆	NUM
ejpam-5171	137	5	int(cl	int(cl	PROPN
ejpam-5171	137	6	♢	♢	PROPN
ejpam-5171	137	7	(l	(l	PROPN
ejpam-5171	137	8	)	)	PUNCT
ejpam-5171	137	9	)	)	PUNCT
ejpam-5171	138	1	=	=	SYM
ejpam-5171	138	2	int(l	int(l	PROPN
ejpam-5171	138	3	∪	∪	PROPN
ejpam-5171	138	4	l	l	PROPN
ejpam-5171	138	5	♢	♢	NOUN
ejpam-5171	138	6	)	)	PUNCT
ejpam-5171	138	7	⊆	⊆	NUM
ejpam-5171	138	8	int(l	int(l	PROPN
ejpam-5171	138	9	∪	∪	ADJ
ejpam-5171	138	10	cl(l	cl(l	NOUN
ejpam-5171	138	11	)	)	PUNCT
ejpam-5171	138	12	)	)	PUNCT
ejpam-5171	139	1	=	=	SYM
ejpam-5171	139	2	int(cl(l	int(cl(l	PROPN
ejpam-5171	139	3	)	)	PUNCT
ejpam-5171	139	4	)	)	PUNCT
ejpam-5171	139	5	.	.	PUNCT
ejpam-5171	140	1	therefore	therefore	ADV
ejpam-5171	140	2	,	,	PUNCT
ejpam-5171	140	3	l	l	NOUN
ejpam-5171	140	4	is	be	AUX
ejpam-5171	140	5	a	a	DET
ejpam-5171	140	6	pre	pre	ADJ
ejpam-5171	140	7	-	-	ADJ
ejpam-5171	140	8	open	open	ADJ
ejpam-5171	140	9	set	set	NOUN
ejpam-5171	140	10	.	.	PUNCT
ejpam-5171	141	1	(	(	PUNCT
ejpam-5171	141	2	d	d	X
ejpam-5171	141	3	)	)	PUNCT
ejpam-5171	141	4	suppose	suppose	VERB
ejpam-5171	141	5	that	that	SCONJ
ejpam-5171	141	6	l	l	NOUN
ejpam-5171	141	7	be	be	AUX
ejpam-5171	141	8	a	a	DET
ejpam-5171	141	9	p	p	NOUN
ejpam-5171	141	10	-	-	PUNCT
ejpam-5171	141	11	β	β	NOUN
ejpam-5171	141	12	-	-	ADJ
ejpam-5171	141	13	open	open	ADJ
ejpam-5171	141	14	set	set	NOUN
ejpam-5171	141	15	.	.	PUNCT
ejpam-5171	142	1	hence	hence	ADV
ejpam-5171	142	2	,	,	PUNCT
ejpam-5171	142	3	l	l	PROPN
ejpam-5171	142	4	⊆	⊆	NUM
ejpam-5171	142	5	cl(int(cl	cl(int(cl	PROPN
ejpam-5171	142	6	♢	♢	PROPN
ejpam-5171	142	7	(l	(l	PROPN
ejpam-5171	142	8	)	)	PUNCT
ejpam-5171	142	9	)	)	PUNCT
ejpam-5171	142	10	)	)	PUNCT
ejpam-5171	143	1	=	=	SYM
ejpam-5171	143	2	cl(int(l	cl(int(l	PROPN
ejpam-5171	143	3	∪	∪	PROPN
ejpam-5171	143	4	l	l	PROPN
ejpam-5171	143	5	♢	♢	PROPN
ejpam-5171	143	6	)	)	PUNCT
ejpam-5171	143	7	)	)	PUNCT
ejpam-5171	144	1	⊂	⊂	PROPN
ejpam-5171	144	2	cl(int(cl(l	cl(int(cl(l	X
ejpam-5171	144	3	)	)	PUNCT
ejpam-5171	144	4	∪	∪	ADP
ejpam-5171	144	5	l	l	NOUN
ejpam-5171	144	6	)	)	PUNCT
ejpam-5171	144	7	)	)	PUNCT
ejpam-5171	145	1	=	=	SYM
ejpam-5171	145	2	cl(int(cl(l	cl(int(cl(l	ADJ
ejpam-5171	145	3	)	)	PUNCT
ejpam-5171	145	4	)	)	PUNCT
ejpam-5171	145	5	)	)	PUNCT
ejpam-5171	145	6	.	.	PUNCT
ejpam-5171	146	1	therefore	therefore	ADV
ejpam-5171	146	2	,	,	PUNCT
ejpam-5171	146	3	l	l	NOUN
ejpam-5171	146	4	is	be	AUX
ejpam-5171	146	5	a	a	DET
ejpam-5171	146	6	β	β	NOUN
ejpam-5171	146	7	-	-	ADJ
ejpam-5171	146	8	open	open	ADJ
ejpam-5171	146	9	set	set	NOUN
ejpam-5171	146	10	.	.	PUNCT
ejpam-5171	147	1	remark	remark	VERB
ejpam-5171	147	2	2.3	2.3	NUM
ejpam-5171	147	3	.	.	PUNCT
ejpam-5171	148	1	in	in	ADP
ejpam-5171	148	2	general	general	ADJ
ejpam-5171	148	3	,	,	PUNCT
ejpam-5171	148	4	the	the	DET
ejpam-5171	148	5	following	follow	VERB
ejpam-5171	148	6	examples	example	NOUN
ejpam-5171	148	7	demonstrate	demonstrate	VERB
ejpam-5171	148	8	that	that	SCONJ
ejpam-5171	148	9	the	the	DET
ejpam-5171	148	10	opposite	opposite	NOUN
ejpam-5171	148	11	of	of	ADP
ejpam-5171	148	12	theorem	theorem	ADJ
ejpam-5171	148	13	2.2	2.2	NUM
ejpam-5171	148	14	is	be	AUX
ejpam-5171	148	15	not	not	PART
ejpam-5171	148	16	true	true	ADJ
ejpam-5171	148	17	.	.	PUNCT
ejpam-5171	149	1	example	example	NOUN
ejpam-5171	149	2	2.4	2.4	NUM
ejpam-5171	149	3	.	.	PUNCT
ejpam-5171	150	1	assuming	assume	VERB
ejpam-5171	150	2	that	that	SCONJ
ejpam-5171	150	3	x	x	SYM
ejpam-5171	150	4	=	=	PRON
ejpam-5171	150	5	{	{	PUNCT
ejpam-5171	150	6	a1	a1	PROPN
ejpam-5171	150	7	,	,	PUNCT
ejpam-5171	150	8	a2	a2	PROPN
ejpam-5171	150	9	,	,	PUNCT
ejpam-5171	150	10	a3	a3	NOUN
ejpam-5171	150	11	}	}	PUNCT
ejpam-5171	150	12	,	,	PUNCT
ejpam-5171	150	13	δ	δ	PROPN
ejpam-5171	150	14	=	=	PRON
ejpam-5171	150	15	{	{	PUNCT
ejpam-5171	150	16	ϕ	ϕ	NOUN
ejpam-5171	150	17	,	,	PUNCT
ejpam-5171	150	18	{	{	PUNCT
ejpam-5171	150	19	a1},x	a1},x	NOUN
ejpam-5171	150	20	}	}	PUNCT
ejpam-5171	150	21	,	,	PUNCT
ejpam-5171	150	22	with	with	ADP
ejpam-5171	150	23	the	the	DET
ejpam-5171	150	24	primal	primal	ADJ
ejpam-5171	150	25	p	p	X
ejpam-5171	150	26	=	=	X
ejpam-5171	150	27	{	{	PUNCT
ejpam-5171	150	28	ϕ	ϕ	NOUN
ejpam-5171	150	29	,	,	PUNCT
ejpam-5171	150	30	{	{	PUNCT
ejpam-5171	150	31	a1	a1	NOUN
ejpam-5171	150	32	}	}	PUNCT
ejpam-5171	150	33	,	,	PUNCT
ejpam-5171	150	34	{	{	PUNCT
ejpam-5171	150	35	a3	a3	NOUN
ejpam-5171	150	36	}	}	PUNCT
ejpam-5171	150	37	,	,	PUNCT
ejpam-5171	150	38	{	{	PUNCT
ejpam-5171	150	39	a1	a1	NOUN
ejpam-5171	150	40	,	,	PUNCT
ejpam-5171	150	41	a3	a3	NOUN
ejpam-5171	150	42	}	}	PUNCT
ejpam-5171	150	43	}	}	PUNCT
ejpam-5171	150	44	.	.	PUNCT
ejpam-5171	151	1	thus	thus	ADV
ejpam-5171	151	2	,	,	PUNCT
ejpam-5171	151	3	(	(	PUNCT
ejpam-5171	151	4	a	a	X
ejpam-5171	151	5	)	)	PUNCT
ejpam-5171	151	6	l	l	NOUN
ejpam-5171	151	7	=	=	SYM
ejpam-5171	151	8	{	{	PUNCT
ejpam-5171	151	9	a1	a1	NOUN
ejpam-5171	151	10	,	,	PUNCT
ejpam-5171	151	11	a3	a3	NOUN
ejpam-5171	151	12	}	}	PUNCT
ejpam-5171	151	13	is	be	AUX
ejpam-5171	151	14	a	a	DET
ejpam-5171	151	15	α	α	NOUN
ejpam-5171	151	16	-	-	ADJ
ejpam-5171	151	17	open	open	ADJ
ejpam-5171	151	18	set	set	NOUN
ejpam-5171	151	19	that	that	PRON
ejpam-5171	151	20	is	be	AUX
ejpam-5171	151	21	not	not	PART
ejpam-5171	151	22	p	p	NOUN
ejpam-5171	151	23	-	-	PUNCT
ejpam-5171	151	24	α	α	NOUN
ejpam-5171	151	25	-	-	NOUN
ejpam-5171	151	26	open	open	ADJ
ejpam-5171	151	27	,	,	PUNCT
ejpam-5171	151	28	since	since	SCONJ
ejpam-5171	151	29	l	l	NOUN
ejpam-5171	151	30	⊆	⊆	NUM
ejpam-5171	151	31	int(cl(int(l	int(cl(int(l	PROPN
ejpam-5171	151	32	)	)	PUNCT
ejpam-5171	151	33	)	)	PUNCT
ejpam-5171	151	34	)	)	PUNCT
ejpam-5171	152	1	=	=	PUNCT
ejpam-5171	152	2	x	x	NOUN
ejpam-5171	152	3	,	,	PUNCT
ejpam-5171	152	4	but	but	CCONJ
ejpam-5171	152	5	l	l	PROPN
ejpam-5171	152	6	⊈	⊈	PROPN
ejpam-5171	152	7	int(cl	int(cl	NOUN
ejpam-5171	152	8	♢	♢	PROPN
ejpam-5171	152	9	(int(l	(int(l	PROPN
ejpam-5171	152	10	)	)	PUNCT
ejpam-5171	152	11	)	)	PUNCT
ejpam-5171	152	12	)	)	PUNCT
ejpam-5171	152	13	=	=	PRON
ejpam-5171	152	14	{	{	PUNCT
ejpam-5171	152	15	a1	a1	NOUN
ejpam-5171	152	16	}	}	PUNCT
ejpam-5171	152	17	.	.	PUNCT
ejpam-5171	153	1	(	(	PUNCT
ejpam-5171	153	2	b	b	X
ejpam-5171	153	3	)	)	PUNCT
ejpam-5171	153	4	l	l	NOUN
ejpam-5171	153	5	=	=	SYM
ejpam-5171	153	6	{	{	PUNCT
ejpam-5171	153	7	a1	a1	NOUN
ejpam-5171	153	8	,	,	PUNCT
ejpam-5171	153	9	a3	a3	NOUN
ejpam-5171	153	10	}	}	PUNCT
ejpam-5171	153	11	is	be	AUX
ejpam-5171	153	12	a	a	DET
ejpam-5171	153	13	semi	semi	ADJ
ejpam-5171	153	14	-	-	ADJ
ejpam-5171	153	15	open	open	ADJ
ejpam-5171	153	16	set	set	NOUN
ejpam-5171	153	17	that	that	PRON
ejpam-5171	153	18	is	be	AUX
ejpam-5171	153	19	not	not	PART
ejpam-5171	153	20	p	p	NOUN
ejpam-5171	153	21	-	-	PUNCT
ejpam-5171	153	22	semi	semi	ADV
ejpam-5171	153	23	-	-	ADJ
ejpam-5171	153	24	open	open	ADJ
ejpam-5171	153	25	,	,	PUNCT
ejpam-5171	153	26	since	since	SCONJ
ejpam-5171	153	27	l	l	NOUN
ejpam-5171	153	28	⊆	⊆	NUM
ejpam-5171	153	29	cl(int(l	cl(int(l	NOUN
ejpam-5171	153	30	)	)	PUNCT
ejpam-5171	153	31	)	)	PUNCT
ejpam-5171	154	1	=	=	PUNCT
ejpam-5171	154	2	x	x	NOUN
ejpam-5171	154	3	,	,	PUNCT
ejpam-5171	154	4	but	but	CCONJ
ejpam-5171	154	5	l	l	PROPN
ejpam-5171	154	6	⊈	⊈	PROPN
ejpam-5171	154	7	cl	cl	NOUN
ejpam-5171	154	8	♢	♢	NOUN
ejpam-5171	154	9	(int(l	(int(l	PROPN
ejpam-5171	154	10	)	)	PUNCT
ejpam-5171	154	11	)	)	PUNCT
ejpam-5171	155	1	=	=	PRON
ejpam-5171	155	2	{	{	PUNCT
ejpam-5171	155	3	a1	a1	NOUN
ejpam-5171	155	4	}	}	PUNCT
ejpam-5171	155	5	.	.	PUNCT
ejpam-5171	156	1	(	(	PUNCT
ejpam-5171	156	2	c	c	X
ejpam-5171	156	3	)	)	PUNCT
ejpam-5171	156	4	l	l	NOUN
ejpam-5171	156	5	=	=	SYM
ejpam-5171	156	6	{	{	PUNCT
ejpam-5171	156	7	a1	a1	NOUN
ejpam-5171	156	8	,	,	PUNCT
ejpam-5171	156	9	a3	a3	NOUN
ejpam-5171	156	10	}	}	PUNCT
ejpam-5171	156	11	is	be	AUX
ejpam-5171	156	12	a	a	DET
ejpam-5171	156	13	pre	pre	ADJ
ejpam-5171	156	14	-	-	ADJ
ejpam-5171	156	15	open	open	ADJ
ejpam-5171	156	16	set	set	NOUN
ejpam-5171	156	17	that	that	PRON
ejpam-5171	156	18	is	be	AUX
ejpam-5171	156	19	not	not	PART
ejpam-5171	156	20	p	p	NOUN
ejpam-5171	156	21	-	-	PUNCT
ejpam-5171	156	22	pre	pre	NOUN
ejpam-5171	156	23	-	-	ADJ
ejpam-5171	156	24	open	open	ADJ
ejpam-5171	156	25	,	,	PUNCT
ejpam-5171	156	26	since	since	SCONJ
ejpam-5171	156	27	l	l	NOUN
ejpam-5171	156	28	⊆	⊆	NUM
ejpam-5171	156	29	int(cl(l	int(cl(l	NOUN
ejpam-5171	156	30	)	)	PUNCT
ejpam-5171	156	31	)	)	PUNCT
ejpam-5171	157	1	=	=	SYM
ejpam-5171	157	2	x	x	NOUN
ejpam-5171	157	3	,	,	PUNCT
ejpam-5171	157	4	but	but	CCONJ
ejpam-5171	157	5	l	l	PROPN
ejpam-5171	157	6	⊈	⊈	PROPN
ejpam-5171	157	7	int(cl	int(cl	NOUN
ejpam-5171	157	8	♢	♢	PROPN
ejpam-5171	157	9	(l	(l	PROPN
ejpam-5171	157	10	)	)	PUNCT
ejpam-5171	157	11	)	)	PUNCT
ejpam-5171	157	12	=	=	PRON
ejpam-5171	157	13	{	{	PUNCT
ejpam-5171	157	14	a1	a1	PROPN
ejpam-5171	157	15	}	}	PUNCT
ejpam-5171	157	16	.	.	PUNCT
ejpam-5171	158	1	example	example	NOUN
ejpam-5171	158	2	2.5	2.5	NUM
ejpam-5171	158	3	.	.	PUNCT
ejpam-5171	159	1	assuming	assume	VERB
ejpam-5171	159	2	that	that	SCONJ
ejpam-5171	159	3	x	x	SYM
ejpam-5171	159	4	=	=	PRON
ejpam-5171	159	5	{	{	PUNCT
ejpam-5171	159	6	a1	a1	PROPN
ejpam-5171	159	7	,	,	PUNCT
ejpam-5171	159	8	a2	a2	PROPN
ejpam-5171	159	9	,	,	PUNCT
ejpam-5171	159	10	a3	a3	NOUN
ejpam-5171	159	11	}	}	PUNCT
ejpam-5171	159	12	,	,	PUNCT
ejpam-5171	159	13	δ	δ	PROPN
ejpam-5171	159	14	=	=	PRON
ejpam-5171	159	15	{	{	PUNCT
ejpam-5171	159	16	ϕ	ϕ	NOUN
ejpam-5171	159	17	,	,	PUNCT
ejpam-5171	159	18	{	{	PUNCT
ejpam-5171	159	19	a1	a1	NOUN
ejpam-5171	159	20	}	}	PUNCT
ejpam-5171	159	21	,	,	PUNCT
ejpam-5171	159	22	{	{	PUNCT
ejpam-5171	159	23	a2	a2	NOUN
ejpam-5171	159	24	,	,	PUNCT
ejpam-5171	159	25	a3},x	a3},x	PROPN
ejpam-5171	159	26	}	}	PUNCT
ejpam-5171	159	27	,	,	PUNCT
ejpam-5171	159	28	with	with	ADP
ejpam-5171	159	29	the	the	DET
ejpam-5171	159	30	primal	primal	ADJ
ejpam-5171	159	31	p	p	X
ejpam-5171	159	32	=	=	X
ejpam-5171	159	33	{	{	PUNCT
ejpam-5171	159	34	ϕ	ϕ	NOUN
ejpam-5171	159	35	,	,	PUNCT
ejpam-5171	159	36	{	{	PUNCT
ejpam-5171	159	37	a1	a1	NOUN
ejpam-5171	159	38	}	}	PUNCT
ejpam-5171	159	39	,	,	PUNCT
ejpam-5171	159	40	{	{	PUNCT
ejpam-5171	159	41	a3	a3	NOUN
ejpam-5171	159	42	}	}	PUNCT
ejpam-5171	159	43	,	,	PUNCT
ejpam-5171	159	44	{	{	PUNCT
ejpam-5171	159	45	a1	a1	NOUN
ejpam-5171	159	46	,	,	PUNCT
ejpam-5171	159	47	a3	a3	NOUN
ejpam-5171	159	48	}	}	PUNCT
ejpam-5171	159	49	}	}	PUNCT
ejpam-5171	159	50	.	.	PUNCT
ejpam-5171	160	1	thus	thus	ADV
ejpam-5171	160	2	,	,	PUNCT
ejpam-5171	160	3	l	l	NOUN
ejpam-5171	160	4	=	=	SYM
ejpam-5171	160	5	{	{	PUNCT
ejpam-5171	160	6	a1	a1	NOUN
ejpam-5171	160	7	,	,	PUNCT
ejpam-5171	160	8	a3	a3	NOUN
ejpam-5171	160	9	}	}	PUNCT
ejpam-5171	160	10	is	be	AUX
ejpam-5171	160	11	a	a	DET
ejpam-5171	160	12	β	β	NOUN
ejpam-5171	160	13	-	-	ADJ
ejpam-5171	160	14	open	open	ADJ
ejpam-5171	160	15	set	set	NOUN
ejpam-5171	160	16	,	,	PUNCT
ejpam-5171	160	17	which	which	PRON
ejpam-5171	160	18	is	be	AUX
ejpam-5171	160	19	not	not	PART
ejpam-5171	160	20	p	p	NOUN
ejpam-5171	160	21	-	-	PUNCT
ejpam-5171	160	22	β	β	NOUN
ejpam-5171	160	23	-	-	NOUN
ejpam-5171	160	24	open	open	ADJ
ejpam-5171	160	25	since	since	SCONJ
ejpam-5171	160	26	l	l	NOUN
ejpam-5171	160	27	⊆	⊆	NUM
ejpam-5171	160	28	cl(int(cl(l	cl(int(cl(l	NOUN
ejpam-5171	160	29	)	)	PUNCT
ejpam-5171	160	30	)	)	PUNCT
ejpam-5171	160	31	)	)	PUNCT
ejpam-5171	161	1	=	=	PUNCT
ejpam-5171	161	2	x	x	NOUN
ejpam-5171	161	3	,	,	PUNCT
ejpam-5171	161	4	but	but	CCONJ
ejpam-5171	161	5	l	l	NOUN
ejpam-5171	161	6	⊈	⊈	PROPN
ejpam-5171	161	7	cl(int(cl	cl(int(cl	PROPN
ejpam-5171	161	8	♢	♢	PROPN
ejpam-5171	161	9	(l	(l	PROPN
ejpam-5171	161	10	)	)	PUNCT
ejpam-5171	161	11	)	)	PUNCT
ejpam-5171	161	12	)	)	PUNCT
ejpam-5171	162	1	=	=	PRON
ejpam-5171	162	2	{	{	PUNCT
ejpam-5171	162	3	a1	a1	PROPN
ejpam-5171	162	4	}	}	PUNCT
ejpam-5171	162	5	.	.	PUNCT
ejpam-5171	163	1	remark	remark	PROPN
ejpam-5171	163	2	2.6	2.6	NUM
ejpam-5171	163	3	.	.	PUNCT
ejpam-5171	164	1	let	let	VERB
ejpam-5171	164	2	(	(	PUNCT
ejpam-5171	164	3	x	x	NOUN
ejpam-5171	164	4	,	,	PUNCT
ejpam-5171	164	5	δ	δ	PROPN
ejpam-5171	164	6	,	,	PUNCT
ejpam-5171	164	7	p	p	NOUN
ejpam-5171	164	8	)	)	PUNCT
ejpam-5171	164	9	be	be	AUX
ejpam-5171	164	10	a	a	DET
ejpam-5171	164	11	pts	pts	NOUN
ejpam-5171	164	12	,	,	PUNCT
ejpam-5171	164	13	then	then	ADV
ejpam-5171	164	14	the	the	DET
ejpam-5171	164	15	concept	concept	NOUN
ejpam-5171	164	16	of	of	ADP
ejpam-5171	164	17	openness	openness	NOUN
ejpam-5171	164	18	and	and	CCONJ
ejpam-5171	164	19	p	p	NOUN
ejpam-5171	164	20	-	-	PUNCT
ejpam-5171	164	21	openness	openness	NOUN
ejpam-5171	164	22	are	be	AUX
ejpam-5171	164	23	independence	independence	NOUN
ejpam-5171	164	24	.	.	PUNCT
ejpam-5171	165	1	example	example	NOUN
ejpam-5171	165	2	2.7	2.7	NUM
ejpam-5171	165	3	.	.	PUNCT
ejpam-5171	166	1	(	(	PUNCT
ejpam-5171	166	2	a	a	X
ejpam-5171	166	3	)	)	PUNCT
ejpam-5171	166	4	assuming	assume	VERB
ejpam-5171	166	5	that	that	SCONJ
ejpam-5171	166	6	x	x	SYM
ejpam-5171	166	7	=	=	PRON
ejpam-5171	166	8	{	{	PUNCT
ejpam-5171	166	9	a1	a1	PROPN
ejpam-5171	166	10	,	,	PUNCT
ejpam-5171	166	11	a2	a2	PROPN
ejpam-5171	166	12	,	,	PUNCT
ejpam-5171	166	13	a3	a3	NOUN
ejpam-5171	166	14	}	}	PUNCT
ejpam-5171	166	15	,	,	PUNCT
ejpam-5171	166	16	δ	δ	PROPN
ejpam-5171	166	17	=	=	PRON
ejpam-5171	166	18	{	{	PUNCT
ejpam-5171	166	19	ϕ	ϕ	NOUN
ejpam-5171	166	20	,	,	PUNCT
ejpam-5171	166	21	{	{	PUNCT
ejpam-5171	166	22	a1	a1	NOUN
ejpam-5171	166	23	}	}	PUNCT
ejpam-5171	166	24	,	,	PUNCT
ejpam-5171	166	25	{	{	PUNCT
ejpam-5171	166	26	a3	a3	NOUN
ejpam-5171	166	27	}	}	PUNCT
ejpam-5171	166	28	,	,	PUNCT
ejpam-5171	166	29	{	{	PUNCT
ejpam-5171	166	30	a1	a1	NOUN
ejpam-5171	166	31	,	,	PUNCT
ejpam-5171	166	32	a3},x	a3},x	NOUN
ejpam-5171	166	33	}	}	PUNCT
ejpam-5171	166	34	,	,	PUNCT
ejpam-5171	166	35	and	and	CCONJ
ejpam-5171	166	36	p	p	NOUN
ejpam-5171	166	37	=	=	X
ejpam-5171	166	38	{	{	PUNCT
ejpam-5171	166	39	ϕ	ϕ	NOUN
ejpam-5171	166	40	,	,	PUNCT
ejpam-5171	166	41	{	{	PUNCT
ejpam-5171	166	42	a1	a1	NOUN
ejpam-5171	166	43	}	}	PUNCT
ejpam-5171	166	44	,	,	PUNCT
ejpam-5171	166	45	{	{	PUNCT
ejpam-5171	166	46	a2	a2	PROPN
ejpam-5171	166	47	}	}	PUNCT
ejpam-5171	166	48	,	,	PUNCT
ejpam-5171	166	49	{	{	PUNCT
ejpam-5171	166	50	a1	a1	NOUN
ejpam-5171	166	51	,	,	PUNCT
ejpam-5171	166	52	a2	a2	PROPN
ejpam-5171	166	53	}	}	PUNCT
ejpam-5171	166	54	}	}	PUNCT
ejpam-5171	166	55	.	.	PUNCT
ejpam-5171	167	1	thus	thus	ADV
ejpam-5171	167	2	,	,	PUNCT
ejpam-5171	167	3	(	(	PUNCT
ejpam-5171	167	4	x	x	NOUN
ejpam-5171	167	5	,	,	PUNCT
ejpam-5171	167	6	δ	δ	PROPN
ejpam-5171	167	7	)	)	PUNCT
ejpam-5171	167	8	is	be	AUX
ejpam-5171	167	9	a	a	DET
ejpam-5171	167	10	ts	ts	NOUN
ejpam-5171	167	11	.	.	PUNCT
ejpam-5171	168	1	moreover	moreover	ADV
ejpam-5171	168	2	,	,	PUNCT
ejpam-5171	168	3	p	p	PRON
ejpam-5171	168	4	is	be	AUX
ejpam-5171	168	5	a	a	DET
ejpam-5171	168	6	primal	primal	NOUN
ejpam-5171	168	7	on	on	ADP
ejpam-5171	168	8	x.	x.	NOUN
ejpam-5171	168	9	put	put	VERB
ejpam-5171	168	10	u	u	NOUN
ejpam-5171	168	11	=	=	NOUN
ejpam-5171	168	12	{	{	PUNCT
ejpam-5171	168	13	a1	a1	NOUN
ejpam-5171	168	14	,	,	PUNCT
ejpam-5171	168	15	a3	a3	NOUN
ejpam-5171	168	16	}	}	PUNCT
ejpam-5171	168	17	∈	∈	PROPN
ejpam-5171	168	18	δ	δ	PROPN
ejpam-5171	168	19	.	.	PUNCT
ejpam-5171	169	1	however	however	ADV
ejpam-5171	169	2	,	,	PUNCT
ejpam-5171	169	3	u	u	NOUN
ejpam-5171	169	4	♢	♢	NOUN
ejpam-5171	169	5	p	p	NOUN
ejpam-5171	169	6	=	=	X
ejpam-5171	169	7	{	{	PUNCT
ejpam-5171	169	8	a2	a2	PROPN
ejpam-5171	169	9	,	,	PUNCT
ejpam-5171	169	10	a3	a3	NOUN
ejpam-5171	169	11	}	}	PUNCT
ejpam-5171	169	12	in	in	ADP
ejpam-5171	169	13	order	order	NOUN
ejpam-5171	169	14	that	that	SCONJ
ejpam-5171	169	15	u	u	NOUN
ejpam-5171	169	16	is	be	AUX
ejpam-5171	169	17	not	not	PART
ejpam-5171	169	18	p	p	NOUN
ejpam-5171	169	19	-	-	NOUN
ejpam-5171	169	20	open	open	ADJ
ejpam-5171	169	21	.	.	PUNCT
ejpam-5171	170	1	(	(	PUNCT
ejpam-5171	170	2	b	b	X
ejpam-5171	170	3	)	)	PUNCT
ejpam-5171	170	4	assuming	assume	VERB
ejpam-5171	170	5	that	that	SCONJ
ejpam-5171	170	6	x	x	SYM
ejpam-5171	170	7	=	=	PRON
ejpam-5171	170	8	{	{	PUNCT
ejpam-5171	170	9	a1	a1	PROPN
ejpam-5171	170	10	,	,	PUNCT
ejpam-5171	170	11	a2	a2	PROPN
ejpam-5171	170	12	,	,	PUNCT
ejpam-5171	170	13	a3	a3	NOUN
ejpam-5171	170	14	}	}	PUNCT
ejpam-5171	170	15	,	,	PUNCT
ejpam-5171	170	16	δ	δ	PROPN
ejpam-5171	170	17	=	=	PRON
ejpam-5171	170	18	{	{	PUNCT
ejpam-5171	170	19	ϕ,x	ϕ,x	NOUN
ejpam-5171	170	20	}	}	PUNCT
ejpam-5171	170	21	and	and	CCONJ
ejpam-5171	170	22	p	p	NOUN
ejpam-5171	170	23	=	=	X
ejpam-5171	170	24	{	{	PUNCT
ejpam-5171	170	25	ϕ	ϕ	NOUN
ejpam-5171	170	26	,	,	PUNCT
ejpam-5171	170	27	{	{	PUNCT
ejpam-5171	170	28	a1	a1	NOUN
ejpam-5171	170	29	}	}	PUNCT
ejpam-5171	170	30	,	,	PUNCT
ejpam-5171	170	31	{	{	PUNCT
ejpam-5171	170	32	a2	a2	PROPN
ejpam-5171	170	33	}	}	PUNCT
ejpam-5171	170	34	,	,	PUNCT
ejpam-5171	170	35	{	{	PUNCT
ejpam-5171	170	36	a1	a1	NOUN
ejpam-5171	170	37	,	,	PUNCT
ejpam-5171	170	38	a2	a2	PROPN
ejpam-5171	170	39	}	}	PUNCT
ejpam-5171	170	40	}	}	PUNCT
ejpam-5171	170	41	.	.	PUNCT
ejpam-5171	171	1	thus	thus	ADV
ejpam-5171	171	2	,	,	PUNCT
ejpam-5171	171	3	(	(	PUNCT
ejpam-5171	171	4	x	x	NOUN
ejpam-5171	171	5	,	,	PUNCT
ejpam-5171	171	6	δ	δ	PROPN
ejpam-5171	171	7	)	)	PUNCT
ejpam-5171	171	8	is	be	AUX
ejpam-5171	171	9	a	a	DET
ejpam-5171	171	10	ts	ts	NOUN
ejpam-5171	171	11	.	.	PUNCT
ejpam-5171	172	1	moreover	moreover	ADV
ejpam-5171	172	2	,	,	PUNCT
ejpam-5171	172	3	p	p	PRON
ejpam-5171	172	4	is	be	AUX
ejpam-5171	172	5	a	a	DET
ejpam-5171	172	6	primal	primal	NOUN
ejpam-5171	172	7	on	on	ADP
ejpam-5171	172	8	x.	x.	NOUN
ejpam-5171	172	9	put	put	VERB
ejpam-5171	172	10	l	l	NOUN
ejpam-5171	172	11	=	=	SYM
ejpam-5171	172	12	{	{	PUNCT
ejpam-5171	172	13	a2	a2	PROPN
ejpam-5171	172	14	}	}	PUNCT
ejpam-5171	172	15	.	.	PUNCT
ejpam-5171	173	1	thus	thus	ADV
ejpam-5171	173	2	,	,	PUNCT
ejpam-5171	173	3	l	l	PROPN
ejpam-5171	173	4	♢	♢	PROPN
ejpam-5171	173	5	p	p	X
ejpam-5171	173	6	=	=	X
ejpam-5171	173	7	ϕ	ϕ	PROPN
ejpam-5171	173	8	,	,	PUNCT
ejpam-5171	173	9	so	so	SCONJ
ejpam-5171	173	10	that	that	SCONJ
ejpam-5171	173	11	l	l	NOUN
ejpam-5171	173	12	is	be	AUX
ejpam-5171	173	13	p	p	NOUN
ejpam-5171	173	14	-	-	ADV
ejpam-5171	173	15	open	open	ADJ
ejpam-5171	173	16	.	.	PUNCT
ejpam-5171	174	1	however	however	ADV
ejpam-5171	174	2	,	,	PUNCT
ejpam-5171	174	3	l	l	NOUN
ejpam-5171	174	4	is	be	AUX
ejpam-5171	174	5	not	not	PART
ejpam-5171	174	6	open	open	ADJ
ejpam-5171	174	7	in	in	ADP
ejpam-5171	174	8	(	(	PUNCT
ejpam-5171	174	9	x	x	NOUN
ejpam-5171	174	10	,	,	PUNCT
ejpam-5171	174	11	δ	δ	PROPN
ejpam-5171	174	12	)	)	PUNCT
ejpam-5171	174	13	.	.	PUNCT
ejpam-5171	175	1	theorem	theorem	VERB
ejpam-5171	175	2	2.8	2.8	NUM
ejpam-5171	175	3	.	.	PUNCT
ejpam-5171	176	1	if	if	SCONJ
ejpam-5171	176	2	(	(	PUNCT
ejpam-5171	176	3	x	x	NOUN
ejpam-5171	176	4	,	,	PUNCT
ejpam-5171	176	5	δ	δ	PROPN
ejpam-5171	176	6	,	,	PUNCT
ejpam-5171	176	7	p	p	NOUN
ejpam-5171	176	8	)	)	PUNCT
ejpam-5171	176	9	is	be	AUX
ejpam-5171	176	10	a	a	DET
ejpam-5171	176	11	pts	pt	NOUN
ejpam-5171	176	12	,	,	PUNCT
ejpam-5171	176	13	the	the	DET
ejpam-5171	176	14	next	next	ADJ
ejpam-5171	176	15	characteristics	characteristic	NOUN
ejpam-5171	176	16	apply	apply	VERB
ejpam-5171	176	17	for	for	ADP
ejpam-5171	176	18	l	l	NOUN
ejpam-5171	176	19	⊆	⊆	NUM
ejpam-5171	176	20	x.	x.	NOUN
ejpam-5171	176	21	(	(	PUNCT
ejpam-5171	176	22	a	a	X
ejpam-5171	176	23	)	)	PUNCT
ejpam-5171	176	24	l	l	NOUN
ejpam-5171	176	25	is	be	AUX
ejpam-5171	176	26	p	p	AUX
ejpam-5171	176	27	-	-	PUNCT
ejpam-5171	176	28	α	α	NOUN
ejpam-5171	176	29	-	-	NOUN
ejpam-5171	176	30	open	open	ADJ
ejpam-5171	176	31	if	if	SCONJ
ejpam-5171	176	32	and	and	CCONJ
ejpam-5171	176	33	only	only	ADV
ejpam-5171	176	34	if	if	SCONJ
ejpam-5171	176	35	it	it	PRON
ejpam-5171	176	36	is	be	AUX
ejpam-5171	176	37	p	p	NOUN
ejpam-5171	176	38	-	-	PUNCT
ejpam-5171	176	39	semi	semi	ADV
ejpam-5171	176	40	-	-	ADJ
ejpam-5171	176	41	open	open	ADJ
ejpam-5171	176	42	and	and	CCONJ
ejpam-5171	176	43	p	p	NOUN
ejpam-5171	176	44	-	-	PUNCT
ejpam-5171	176	45	pre	pre	NOUN
ejpam-5171	176	46	-	-	ADJ
ejpam-5171	176	47	open	open	ADJ
ejpam-5171	176	48	,	,	PUNCT
ejpam-5171	176	49	(	(	PUNCT
ejpam-5171	176	50	b	b	X
ejpam-5171	176	51	)	)	PUNCT
ejpam-5171	176	52	l	l	NOUN
ejpam-5171	176	53	is	be	AUX
ejpam-5171	176	54	p	p	ADJ
ejpam-5171	176	55	-	-	PUNCT
ejpam-5171	176	56	β	β	NOUN
ejpam-5171	176	57	-	-	ADJ
ejpam-5171	176	58	open	open	ADJ
ejpam-5171	176	59	,	,	PUNCT
ejpam-5171	176	60	if	if	SCONJ
ejpam-5171	176	61	l	l	NOUN
ejpam-5171	176	62	is	be	AUX
ejpam-5171	176	63	p	p	NOUN
ejpam-5171	176	64	-	-	PUNCT
ejpam-5171	176	65	semi	semi	ADV
ejpam-5171	176	66	-	-	ADJ
ejpam-5171	176	67	open	open	ADJ
ejpam-5171	176	68	,	,	PUNCT
ejpam-5171	176	69	(	(	PUNCT
ejpam-5171	176	70	c	c	X
ejpam-5171	176	71	)	)	PUNCT
ejpam-5171	176	72	l	l	NOUN
ejpam-5171	176	73	is	be	AUX
ejpam-5171	176	74	p	p	ADJ
ejpam-5171	176	75	-	-	PUNCT
ejpam-5171	176	76	β	β	NOUN
ejpam-5171	176	77	-	-	ADJ
ejpam-5171	176	78	open	open	ADJ
ejpam-5171	176	79	,	,	PUNCT
ejpam-5171	176	80	if	if	SCONJ
ejpam-5171	176	81	l	l	NOUN
ejpam-5171	176	82	is	be	AUX
ejpam-5171	176	83	p	p	NOUN
ejpam-5171	176	84	-	-	PUNCT
ejpam-5171	176	85	pre	pre	NOUN
ejpam-5171	176	86	-	-	ADJ
ejpam-5171	176	87	open	open	ADJ
ejpam-5171	176	88	,	,	PUNCT
ejpam-5171	176	89	(	(	PUNCT
ejpam-5171	176	90	d	d	X
ejpam-5171	176	91	)	)	PUNCT
ejpam-5171	176	92	l	l	NOUN
ejpam-5171	176	93	is	be	AUX
ejpam-5171	176	94	p	p	NOUN
ejpam-5171	176	95	-	-	PUNCT
ejpam-5171	176	96	pre	pre	NOUN
ejpam-5171	176	97	-	-	ADJ
ejpam-5171	176	98	open	open	ADJ
ejpam-5171	176	99	,	,	PUNCT
ejpam-5171	176	100	if	if	SCONJ
ejpam-5171	176	101	l	l	NOUN
ejpam-5171	176	102	is	be	AUX
ejpam-5171	176	103	p	p	NOUN
ejpam-5171	176	104	-	-	ADV
ejpam-5171	176	105	open	open	ADJ
ejpam-5171	176	106	.	.	PUNCT
ejpam-5171	177	1	proof	proof	NOUN
ejpam-5171	177	2	.	.	PUNCT
ejpam-5171	178	1	(	(	PUNCT
ejpam-5171	178	2	a	a	X
ejpam-5171	178	3	)	)	PUNCT
ejpam-5171	178	4	necessity	necessity	NOUN
ejpam-5171	178	5	.	.	PUNCT
ejpam-5171	179	1	it	it	PRON
ejpam-5171	179	2	is	be	AUX
ejpam-5171	179	3	clear	clear	ADJ
ejpam-5171	179	4	.	.	PUNCT
ejpam-5171	180	1	sufficiency	sufficiency	NOUN
ejpam-5171	180	2	.	.	PUNCT
ejpam-5171	181	1	let	let	VERB
ejpam-5171	181	2	l	l	NOUN
ejpam-5171	181	3	be	be	AUX
ejpam-5171	181	4	a	a	DET
ejpam-5171	181	5	p	p	NOUN
ejpam-5171	181	6	-	-	PUNCT
ejpam-5171	181	7	semi	semi	NOUN
ejpam-5171	181	8	-	-	ADJ
ejpam-5171	181	9	open	open	ADJ
ejpam-5171	181	10	and	and	CCONJ
ejpam-5171	181	11	a	a	DET
ejpam-5171	181	12	p	p	NOUN
ejpam-5171	181	13	-	-	PUNCT
ejpam-5171	181	14	pre	pre	NOUN
ejpam-5171	181	15	-	-	ADJ
ejpam-5171	181	16	open	open	ADJ
ejpam-5171	181	17	.	.	PUNCT
ejpam-5171	182	1	hence	hence	ADV
ejpam-5171	182	2	,	,	PUNCT
ejpam-5171	182	3	l	l	PROPN
ejpam-5171	182	4	⊆	⊆	NUM
ejpam-5171	182	5	int(cl	int(cl	PROPN
ejpam-5171	182	6	♢	♢	PROPN
ejpam-5171	182	7	(l	(l	PROPN
ejpam-5171	182	8	)	)	PUNCT
ejpam-5171	182	9	)	)	PUNCT
ejpam-5171	183	1	⊆	⊆	NUM
ejpam-5171	183	2	h.	h.	PROPN
ejpam-5171	183	3	al	al	PROPN
ejpam-5171	183	4	-	-	PUNCT
ejpam-5171	183	5	saadi	saadi	PROPN
ejpam-5171	183	6	,	,	PUNCT
ejpam-5171	183	7	m.	m.	NOUN
ejpam-5171	183	8	al	al	PROPN
ejpam-5171	183	9	-	-	PUNCT
ejpam-5171	183	10	hodieb	hodieb	PROPN
ejpam-5171	183	11	/	/	SYM
ejpam-5171	183	12	eur	eur	PROPN
ejpam-5171	183	13	.	.	PUNCT
ejpam-5171	184	1	j.	j.	PROPN
ejpam-5171	184	2	pure	pure	PROPN
ejpam-5171	184	3	appl	appl	PROPN
ejpam-5171	184	4	.	.	PROPN
ejpam-5171	184	5	math	math	PROPN
ejpam-5171	184	6	,	,	PUNCT
ejpam-5171	184	7	17	17	NUM
ejpam-5171	184	8	(	(	PUNCT
ejpam-5171	184	9	2	2	NUM
ejpam-5171	184	10	)	)	PUNCT
ejpam-5171	184	11	(	(	PUNCT
ejpam-5171	184	12	2024	2024	NUM
ejpam-5171	184	13	)	)	PUNCT
ejpam-5171	184	14	,	,	PUNCT
ejpam-5171	184	15	1352	1352	NUM
ejpam-5171	184	16	-	-	SYM
ejpam-5171	184	17	1368	1368	NUM
ejpam-5171	184	18	1358	1358	NUM
ejpam-5171	184	19	int(cl	int(cl	PROPN
ejpam-5171	184	20	♢	♢	PROPN
ejpam-5171	184	21	(cl	(cl	PROPN
ejpam-5171	184	22	♢	♢	PROPN
ejpam-5171	184	23	(int(l	(int(l	PROPN
ejpam-5171	184	24	)	)	PUNCT
ejpam-5171	184	25	)	)	PUNCT
ejpam-5171	184	26	)	)	PUNCT
ejpam-5171	184	27	)	)	PUNCT
ejpam-5171	185	1	⊆	⊆	NUM
ejpam-5171	185	2	int(cl	int(cl	ADJ
ejpam-5171	185	3	♢	♢	PROPN
ejpam-5171	185	4	(int(l	(int(l	PROPN
ejpam-5171	185	5	)	)	PUNCT
ejpam-5171	185	6	)	)	PUNCT
ejpam-5171	185	7	)	)	PUNCT
ejpam-5171	185	8	.	.	PUNCT
ejpam-5171	186	1	thus	thus	ADV
ejpam-5171	186	2	,	,	PUNCT
ejpam-5171	186	3	l	l	PROPN
ejpam-5171	186	4	is	be	AUX
ejpam-5171	186	5	p	p	PROPN
ejpam-5171	186	6	-	-	PUNCT
ejpam-5171	186	7	α	α	NOUN
ejpam-5171	186	8	-	-	NOUN
ejpam-5171	186	9	open	open	ADJ
ejpam-5171	186	10	.	.	PUNCT
ejpam-5171	187	1	(	(	PUNCT
ejpam-5171	187	2	b	b	X
ejpam-5171	187	3	)	)	PUNCT
ejpam-5171	187	4	since	since	SCONJ
ejpam-5171	187	5	l	l	NOUN
ejpam-5171	187	6	is	be	AUX
ejpam-5171	187	7	p	p	NOUN
ejpam-5171	187	8	-	-	PUNCT
ejpam-5171	187	9	semi	semi	ADV
ejpam-5171	187	10	-	-	ADJ
ejpam-5171	187	11	open	open	ADJ
ejpam-5171	187	12	and	and	CCONJ
ejpam-5171	187	13	δ	δ	PROPN
ejpam-5171	187	14	⊆	⊆	NUM
ejpam-5171	187	15	δ	δ	PROPN
ejpam-5171	187	16	♢	♢	PROPN
ejpam-5171	187	17	,	,	PUNCT
ejpam-5171	187	18	we	we	PRON
ejpam-5171	187	19	already	already	ADV
ejpam-5171	187	20	have	have	VERB
ejpam-5171	187	21	l	l	NOUN
ejpam-5171	187	22	⊆	⊆	NUM
ejpam-5171	187	23	cl	cl	NOUN
ejpam-5171	187	24	♢	♢	NOUN
ejpam-5171	187	25	(int(l	(int(l	PROPN
ejpam-5171	187	26	)	)	PUNCT
ejpam-5171	187	27	)	)	PUNCT
ejpam-5171	188	1	⊆	⊆	NUM
ejpam-5171	188	2	cl(int(l	cl(int(l	NOUN
ejpam-5171	188	3	)	)	PUNCT
ejpam-5171	188	4	)	)	PUNCT
ejpam-5171	189	1	⊆	⊆	NUM
ejpam-5171	189	2	cl(int(cl	cl(int(cl	PROPN
ejpam-5171	189	3	♢	♢	PROPN
ejpam-5171	189	4	(l	(l	PROPN
ejpam-5171	189	5	)	)	PUNCT
ejpam-5171	189	6	)	)	PUNCT
ejpam-5171	189	7	)	)	PUNCT
ejpam-5171	189	8	.	.	PUNCT
ejpam-5171	190	1	thus	thus	ADV
ejpam-5171	190	2	,	,	PUNCT
ejpam-5171	190	3	l	l	PROPN
ejpam-5171	190	4	is	be	AUX
ejpam-5171	190	5	p	p	ADJ
ejpam-5171	190	6	-	-	PUNCT
ejpam-5171	190	7	β	β	NOUN
ejpam-5171	190	8	-	-	ADJ
ejpam-5171	190	9	open	open	ADJ
ejpam-5171	190	10	.	.	PUNCT
ejpam-5171	191	1	(	(	PUNCT
ejpam-5171	191	2	c	c	X
ejpam-5171	191	3	)	)	PUNCT
ejpam-5171	191	4	it	it	PRON
ejpam-5171	191	5	is	be	AUX
ejpam-5171	191	6	clear	clear	ADJ
ejpam-5171	191	7	.	.	PUNCT
ejpam-5171	192	1	(	(	PUNCT
ejpam-5171	192	2	d	d	X
ejpam-5171	192	3	)	)	PUNCT
ejpam-5171	192	4	let	let	VERB
ejpam-5171	192	5	l	l	NOUN
ejpam-5171	192	6	be	be	AUX
ejpam-5171	192	7	a	a	DET
ejpam-5171	192	8	p	p	NOUN
ejpam-5171	192	9	-	-	PUNCT
ejpam-5171	192	10	open	open	ADJ
ejpam-5171	192	11	.	.	PUNCT
ejpam-5171	193	1	thus	thus	ADV
ejpam-5171	193	2	,	,	PUNCT
ejpam-5171	193	3	l	l	PROPN
ejpam-5171	193	4	⊂	⊂	PROPN
ejpam-5171	193	5	int(l	int(l	PROPN
ejpam-5171	193	6	♢	♢	PROPN
ejpam-5171	193	7	p	p	PROPN
ejpam-5171	193	8	)	)	PUNCT
ejpam-5171	194	1	⊂	⊂	PROPN
ejpam-5171	194	2	int(l	int(l	PROPN
ejpam-5171	194	3	∪	∪	PROPN
ejpam-5171	194	4	l	l	PROPN
ejpam-5171	194	5	♢	♢	PROPN
ejpam-5171	194	6	p	p	X
ejpam-5171	194	7	)	)	PUNCT
ejpam-5171	194	8	=	=	SYM
ejpam-5171	194	9	int(cl	int(cl	PROPN
ejpam-5171	194	10	♢	♢	PROPN
ejpam-5171	194	11	(l	(l	PROPN
ejpam-5171	194	12	)	)	PUNCT
ejpam-5171	194	13	)	)	PUNCT
ejpam-5171	194	14	.	.	PUNCT
ejpam-5171	195	1	therefore	therefore	ADV
ejpam-5171	195	2	,	,	PUNCT
ejpam-5171	195	3	l	l	PROPN
ejpam-5171	195	4	is	be	AUX
ejpam-5171	195	5	p	p	NOUN
ejpam-5171	195	6	-	-	PUNCT
ejpam-5171	195	7	pre	pre	NOUN
ejpam-5171	195	8	-	-	ADJ
ejpam-5171	195	9	open	open	ADJ
ejpam-5171	195	10	.	.	PUNCT
ejpam-5171	196	1	theorem	theorem	VERB
ejpam-5171	196	2	2.9	2.9	NUM
ejpam-5171	196	3	.	.	PUNCT
ejpam-5171	197	1	each	each	DET
ejpam-5171	197	2	open	open	ADJ
ejpam-5171	197	3	set	set	NOUN
ejpam-5171	197	4	in	in	ADP
ejpam-5171	197	5	a	a	DET
ejpam-5171	197	6	pts	pt	NOUN
ejpam-5171	197	7	is	be	AUX
ejpam-5171	197	8	p	p	PROPN
ejpam-5171	197	9	-	-	PUNCT
ejpam-5171	197	10	α	α	NOUN
ejpam-5171	197	11	-	-	NOUN
ejpam-5171	197	12	open	open	ADJ
ejpam-5171	197	13	.	.	PUNCT
ejpam-5171	198	1	proof	proof	NOUN
ejpam-5171	198	2	.	.	PUNCT
ejpam-5171	199	1	if	if	SCONJ
ejpam-5171	199	2	l	l	NOUN
ejpam-5171	199	3	is	be	AUX
ejpam-5171	199	4	any	any	DET
ejpam-5171	199	5	open	open	ADJ
ejpam-5171	199	6	set	set	NOUN
ejpam-5171	199	7	,	,	PUNCT
ejpam-5171	199	8	then	then	ADV
ejpam-5171	199	9	l	l	NOUN
ejpam-5171	199	10	=	=	SYM
ejpam-5171	199	11	int(l	int(l	PROPN
ejpam-5171	199	12	)	)	PUNCT
ejpam-5171	199	13	⊂	⊂	PROPN
ejpam-5171	199	14	int((int(l))	int((int(l))	PROPN
ejpam-5171	199	15	♢	♢	NOUN
ejpam-5171	199	16	∪int(l	∪int(l	NUM
ejpam-5171	199	17	)	)	PUNCT
ejpam-5171	199	18	)	)	PUNCT
ejpam-5171	200	1	=	=	SYM
ejpam-5171	200	2	int(cl	int(cl	PROPN
ejpam-5171	200	3	♢	♢	PROPN
ejpam-5171	200	4	(int(l	(int(l	PROPN
ejpam-5171	200	5	)	)	PUNCT
ejpam-5171	200	6	)	)	PUNCT
ejpam-5171	200	7	)	)	PUNCT
ejpam-5171	200	8	.	.	PUNCT
ejpam-5171	201	1	therefore	therefore	ADV
ejpam-5171	201	2	,	,	PUNCT
ejpam-5171	201	3	l	l	PROPN
ejpam-5171	201	4	is	be	AUX
ejpam-5171	201	5	p	p	PROPN
ejpam-5171	201	6	-	-	PUNCT
ejpam-5171	201	7	α	α	NOUN
ejpam-5171	201	8	-	-	ADJ
ejpam-5171	201	9	open	open	ADJ
ejpam-5171	201	10	.	.	PUNCT
ejpam-5171	202	1	remark	remark	PROPN
ejpam-5171	202	2	2.10	2.10	NUM
ejpam-5171	202	3	.	.	PUNCT
ejpam-5171	203	1	the	the	DET
ejpam-5171	203	2	following	follow	VERB
ejpam-5171	203	3	figure	figure	NOUN
ejpam-5171	203	4	represents	represent	VERB
ejpam-5171	203	5	several	several	ADJ
ejpam-5171	203	6	of	of	ADP
ejpam-5171	203	7	the	the	DET
ejpam-5171	203	8	above	above	ADV
ejpam-5171	203	9	-	-	PUNCT
ejpam-5171	203	10	described	describe	VERB
ejpam-5171	203	11	sets	set	NOUN
ejpam-5171	203	12	,	,	PUNCT
ejpam-5171	203	13	where	where	SCONJ
ejpam-5171	203	14	the	the	DET
ejpam-5171	203	15	opposite	opposite	NOUN
ejpam-5171	203	16	of	of	ADP
ejpam-5171	203	17	the	the	DET
ejpam-5171	203	18	figure	figure	NOUN
ejpam-5171	203	19	may	may	AUX
ejpam-5171	203	20	not	not	PART
ejpam-5171	203	21	be	be	AUX
ejpam-5171	203	22	as	as	ADV
ejpam-5171	203	23	correct	correct	ADJ
ejpam-5171	203	24	as	as	ADP
ejpam-5171	203	25	the	the	DET
ejpam-5171	203	26	next	next	ADJ
ejpam-5171	203	27	.	.	PUNCT
ejpam-5171	204	1	open	open	VERB
ejpam-5171	204	2	p	p	PROPN
ejpam-5171	204	3	-	-	PUNCT
ejpam-5171	204	4	α	α	NOUN
ejpam-5171	204	5	-	-	ADJ
ejpam-5171	204	6	open	open	ADJ
ejpam-5171	204	7	p	p	NOUN
ejpam-5171	204	8	-	-	PUNCT
ejpam-5171	204	9	open	open	ADJ
ejpam-5171	204	10	p	p	NOUN
ejpam-5171	204	11	-	-	PUNCT
ejpam-5171	204	12	pre	pre	NOUN
ejpam-5171	204	13	-	-	ADJ
ejpam-5171	204	14	open	open	ADJ
ejpam-5171	204	15	p	p	NOUN
ejpam-5171	204	16	-	-	PUNCT
ejpam-5171	204	17	semi	semi	ADV
ejpam-5171	204	18	-	-	ADJ
ejpam-5171	204	19	open	open	ADJ
ejpam-5171	204	20	p	p	NOUN
ejpam-5171	204	21	-	-	PUNCT
ejpam-5171	204	22	β	β	NOUN
ejpam-5171	204	23	-	-	ADJ
ejpam-5171	204	24	open	open	ADJ
ejpam-5171	204	25	α	α	NOUN
ejpam-5171	204	26	-	-	ADJ
ejpam-5171	204	27	open	open	ADJ
ejpam-5171	204	28	β	β	NOUN
ejpam-5171	204	29	-	-	ADJ
ejpam-5171	204	30	open	open	ADJ
ejpam-5171	204	31	pre	pre	ADJ
ejpam-5171	204	32	-	-	ADJ
ejpam-5171	204	33	open	open	ADJ
ejpam-5171	204	34	semi	semi	ADJ
ejpam-5171	204	35	-	-	ADJ
ejpam-5171	204	36	open	open	ADJ
ejpam-5171	204	37	example	example	NOUN
ejpam-5171	204	38	2.11	2.11	NUM
ejpam-5171	204	39	.	.	PUNCT
ejpam-5171	205	1	consider	consider	VERB
ejpam-5171	205	2	x	x	PUNCT
ejpam-5171	205	3	=	=	PRON
ejpam-5171	205	4	{	{	PUNCT
ejpam-5171	205	5	a1	a1	PROPN
ejpam-5171	205	6	,	,	PUNCT
ejpam-5171	205	7	a2	a2	PROPN
ejpam-5171	205	8	,	,	PUNCT
ejpam-5171	205	9	a3	a3	NOUN
ejpam-5171	205	10	}	}	PUNCT
ejpam-5171	205	11	,	,	PUNCT
ejpam-5171	205	12	δ	δ	PROPN
ejpam-5171	205	13	=	=	PRON
ejpam-5171	205	14	{	{	PUNCT
ejpam-5171	205	15	ϕ	ϕ	NOUN
ejpam-5171	205	16	,	,	PUNCT
ejpam-5171	205	17	{	{	PUNCT
ejpam-5171	205	18	a1},x	a1},x	NOUN
ejpam-5171	205	19	}	}	PUNCT
ejpam-5171	205	20	,	,	PUNCT
ejpam-5171	205	21	with	with	ADP
ejpam-5171	205	22	the	the	DET
ejpam-5171	205	23	primal	primal	ADJ
ejpam-5171	205	24	p	p	X
ejpam-5171	205	25	=	=	X
ejpam-5171	205	26	{	{	PUNCT
ejpam-5171	205	27	ϕ	ϕ	NOUN
ejpam-5171	205	28	,	,	PUNCT
ejpam-5171	205	29	{	{	PUNCT
ejpam-5171	205	30	a1	a1	NOUN
ejpam-5171	205	31	}	}	PUNCT
ejpam-5171	205	32	,	,	PUNCT
ejpam-5171	205	33	{	{	PUNCT
ejpam-5171	205	34	a2	a2	PROPN
ejpam-5171	205	35	}	}	PUNCT
ejpam-5171	205	36	,	,	PUNCT
ejpam-5171	205	37	{	{	PUNCT
ejpam-5171	205	38	a3	a3	NOUN
ejpam-5171	205	39	}	}	PUNCT
ejpam-5171	205	40	,	,	PUNCT
ejpam-5171	205	41	{	{	PUNCT
ejpam-5171	205	42	a1	a1	NOUN
ejpam-5171	205	43	,	,	PUNCT
ejpam-5171	205	44	a2	a2	PROPN
ejpam-5171	205	45	}	}	PUNCT
ejpam-5171	205	46	,	,	PUNCT
ejpam-5171	205	47	{	{	PUNCT
ejpam-5171	205	48	a1	a1	NOUN
ejpam-5171	205	49	,	,	PUNCT
ejpam-5171	205	50	a3	a3	NOUN
ejpam-5171	205	51	}	}	PUNCT
ejpam-5171	205	52	,	,	PUNCT
ejpam-5171	205	53	{	{	PUNCT
ejpam-5171	205	54	a2	a2	NOUN
ejpam-5171	205	55	,	,	PUNCT
ejpam-5171	205	56	a3	a3	NOUN
ejpam-5171	205	57	}	}	PUNCT
ejpam-5171	205	58	}	}	PUNCT
ejpam-5171	205	59	.	.	PUNCT
ejpam-5171	206	1	thus	thus	ADV
ejpam-5171	206	2	,	,	PUNCT
ejpam-5171	206	3	l	l	NOUN
ejpam-5171	206	4	=	=	SYM
ejpam-5171	206	5	{	{	PUNCT
ejpam-5171	206	6	a1	a1	NOUN
ejpam-5171	206	7	,	,	PUNCT
ejpam-5171	206	8	a3	a3	NOUN
ejpam-5171	206	9	}	}	PUNCT
ejpam-5171	206	10	is	be	AUX
ejpam-5171	206	11	a	a	DET
ejpam-5171	206	12	p	p	NOUN
ejpam-5171	206	13	-	-	PUNCT
ejpam-5171	206	14	α	α	NOUN
ejpam-5171	206	15	-	-	NOUN
ejpam-5171	206	16	open	open	ADJ
ejpam-5171	206	17	that	that	PRON
ejpam-5171	206	18	is	be	AUX
ejpam-5171	206	19	not	not	PART
ejpam-5171	206	20	open	open	ADJ
ejpam-5171	206	21	,	,	PUNCT
ejpam-5171	206	22	since	since	SCONJ
ejpam-5171	206	23	l	l	PROPN
ejpam-5171	206	24	⊆	⊆	NUM
ejpam-5171	206	25	int(cl	int(cl	NOUN
ejpam-5171	206	26	♢	♢	PROPN
ejpam-5171	206	27	(int(l	(int(l	PROPN
ejpam-5171	206	28	)	)	PUNCT
ejpam-5171	206	29	)	)	PUNCT
ejpam-5171	206	30	)	)	PUNCT
ejpam-5171	207	1	=	=	PUNCT
ejpam-5171	207	2	x	x	NOUN
ejpam-5171	207	3	,	,	PUNCT
ejpam-5171	207	4	but	but	CCONJ
ejpam-5171	207	5	l	l	NOUN
ejpam-5171	207	6	/∈	/∈	PUNCT
ejpam-5171	208	1	δ	δ	PROPN
ejpam-5171	208	2	.	.	PUNCT
ejpam-5171	208	3	example	example	NOUN
ejpam-5171	209	1	2.12	2.12	NUM
ejpam-5171	209	2	.	.	PUNCT
ejpam-5171	210	1	consider	consider	VERB
ejpam-5171	210	2	x	x	PUNCT
ejpam-5171	210	3	=	=	PRON
ejpam-5171	210	4	{	{	PUNCT
ejpam-5171	210	5	a1	a1	PROPN
ejpam-5171	210	6	,	,	PUNCT
ejpam-5171	210	7	a2	a2	PROPN
ejpam-5171	210	8	,	,	PUNCT
ejpam-5171	210	9	a3	a3	NOUN
ejpam-5171	210	10	,	,	PUNCT
ejpam-5171	210	11	a4	a4	PROPN
ejpam-5171	210	12	}	}	PUNCT
ejpam-5171	210	13	,	,	PUNCT
ejpam-5171	210	14	δ	δ	PROPN
ejpam-5171	210	15	=	=	PRON
ejpam-5171	210	16	{	{	PUNCT
ejpam-5171	210	17	ϕ	ϕ	NOUN
ejpam-5171	210	18	,	,	PUNCT
ejpam-5171	210	19	{	{	PUNCT
ejpam-5171	210	20	a1	a1	NOUN
ejpam-5171	210	21	}	}	PUNCT
ejpam-5171	210	22	,	,	PUNCT
ejpam-5171	210	23	{	{	PUNCT
ejpam-5171	210	24	a1	a1	NOUN
ejpam-5171	210	25	,	,	PUNCT
ejpam-5171	210	26	a2	a2	PROPN
ejpam-5171	210	27	}	}	PUNCT
ejpam-5171	210	28	,	,	PUNCT
ejpam-5171	210	29	{	{	PUNCT
ejpam-5171	210	30	a1	a1	NOUN
ejpam-5171	210	31	,	,	PUNCT
ejpam-5171	210	32	a4	a4	NOUN
ejpam-5171	210	33	}	}	PUNCT
ejpam-5171	210	34	,	,	PUNCT
ejpam-5171	210	35	{	{	PUNCT
ejpam-5171	210	36	a1	a1	NOUN
ejpam-5171	210	37	,	,	PUNCT
ejpam-5171	210	38	a2	a2	PROPN
ejpam-5171	210	39	,	,	PUNCT
ejpam-5171	210	40	a4},x	a4},x	PROPN
ejpam-5171	210	41	}	}	PUNCT
ejpam-5171	210	42	,	,	PUNCT
ejpam-5171	210	43	with	with	ADP
ejpam-5171	210	44	the	the	DET
ejpam-5171	210	45	primal	primal	ADJ
ejpam-5171	210	46	p	p	X
ejpam-5171	210	47	=	=	X
ejpam-5171	210	48	{	{	PUNCT
ejpam-5171	210	49	ϕ	ϕ	NOUN
ejpam-5171	210	50	,	,	PUNCT
ejpam-5171	210	51	{	{	PUNCT
ejpam-5171	210	52	a1	a1	NOUN
ejpam-5171	210	53	}	}	PUNCT
ejpam-5171	210	54	,	,	PUNCT
ejpam-5171	210	55	{	{	PUNCT
ejpam-5171	210	56	a2	a2	PROPN
ejpam-5171	210	57	}	}	PUNCT
ejpam-5171	210	58	,	,	PUNCT
ejpam-5171	210	59	{	{	PUNCT
ejpam-5171	210	60	a3	a3	NOUN
ejpam-5171	210	61	}	}	PUNCT
ejpam-5171	210	62	,	,	PUNCT
ejpam-5171	210	63	{	{	PUNCT
ejpam-5171	210	64	a1	a1	NOUN
ejpam-5171	210	65	,	,	PUNCT
ejpam-5171	210	66	a2	a2	PROPN
ejpam-5171	210	67	}	}	PUNCT
ejpam-5171	210	68	,	,	PUNCT
ejpam-5171	210	69	{	{	PUNCT
ejpam-5171	210	70	a2	a2	NOUN
ejpam-5171	210	71	,	,	PUNCT
ejpam-5171	210	72	a3	a3	NOUN
ejpam-5171	210	73	}	}	PUNCT
ejpam-5171	210	74	,	,	PUNCT
ejpam-5171	210	75	{	{	PUNCT
ejpam-5171	210	76	a1	a1	NOUN
ejpam-5171	210	77	,	,	PUNCT
ejpam-5171	210	78	a3	a3	NOUN
ejpam-5171	210	79	}	}	PUNCT
ejpam-5171	210	80	,	,	PUNCT
ejpam-5171	210	81	{	{	PUNCT
ejpam-5171	210	82	a1	a1	NOUN
ejpam-5171	210	83	,	,	PUNCT
ejpam-5171	210	84	a2	a2	PROPN
ejpam-5171	210	85	,	,	PUNCT
ejpam-5171	210	86	a3	a3	NOUN
ejpam-5171	210	87	}	}	PUNCT
ejpam-5171	210	88	}	}	PUNCT
ejpam-5171	210	89	.	.	PUNCT
ejpam-5171	211	1	thus	thus	ADV
ejpam-5171	211	2	,	,	PUNCT
ejpam-5171	211	3	l	l	NOUN
ejpam-5171	211	4	=	=	SYM
ejpam-5171	211	5	{	{	PUNCT
ejpam-5171	211	6	a1	a1	NOUN
ejpam-5171	211	7	,	,	PUNCT
ejpam-5171	211	8	a3	a3	NOUN
ejpam-5171	211	9	,	,	PUNCT
ejpam-5171	211	10	a4	a4	PROPN
ejpam-5171	211	11	}	}	PUNCT
ejpam-5171	211	12	is	be	AUX
ejpam-5171	211	13	a	a	DET
ejpam-5171	211	14	p	p	NOUN
ejpam-5171	211	15	-	-	PUNCT
ejpam-5171	211	16	semi	semi	ADV
ejpam-5171	211	17	-	-	ADJ
ejpam-5171	211	18	open	open	ADJ
ejpam-5171	211	19	set	set	NOUN
ejpam-5171	211	20	that	that	PRON
ejpam-5171	211	21	is	be	AUX
ejpam-5171	211	22	not	not	PART
ejpam-5171	211	23	p	p	NOUN
ejpam-5171	211	24	-	-	PUNCT
ejpam-5171	211	25	α	α	NOUN
ejpam-5171	211	26	-	-	NOUN
ejpam-5171	211	27	open	open	ADJ
ejpam-5171	211	28	,	,	PUNCT
ejpam-5171	211	29	since	since	SCONJ
ejpam-5171	211	30	l	l	NOUN
ejpam-5171	211	31	⊆	⊆	NUM
ejpam-5171	211	32	cl	cl	NOUN
ejpam-5171	211	33	♢	♢	PROPN
ejpam-5171	211	34	(int(l	(int(l	PROPN
ejpam-5171	211	35	)	)	PUNCT
ejpam-5171	211	36	)	)	PUNCT
ejpam-5171	212	1	=	=	PUNCT
ejpam-5171	212	2	l	l	NOUN
ejpam-5171	212	3	,	,	PUNCT
ejpam-5171	212	4	but	but	CCONJ
ejpam-5171	212	5	l	l	PROPN
ejpam-5171	212	6	⊈	⊈	PROPN
ejpam-5171	212	7	int(cl	int(cl	NOUN
ejpam-5171	212	8	♢	♢	PROPN
ejpam-5171	212	9	(int(l	(int(l	PROPN
ejpam-5171	212	10	)	)	PUNCT
ejpam-5171	212	11	)	)	PUNCT
ejpam-5171	212	12	)	)	PUNCT
ejpam-5171	213	1	=	=	PRON
ejpam-5171	213	2	{	{	PUNCT
ejpam-5171	213	3	a1	a1	NOUN
ejpam-5171	213	4	,	,	PUNCT
ejpam-5171	213	5	a4	a4	NOUN
ejpam-5171	213	6	}	}	PUNCT
ejpam-5171	213	7	.	.	PUNCT
ejpam-5171	214	1	h.	h.	PROPN
ejpam-5171	214	2	al	al	PROPN
ejpam-5171	214	3	-	-	PUNCT
ejpam-5171	214	4	saadi	saadi	PROPN
ejpam-5171	214	5	,	,	PUNCT
ejpam-5171	214	6	m.	m.	NOUN
ejpam-5171	214	7	al	al	PROPN
ejpam-5171	214	8	-	-	PUNCT
ejpam-5171	214	9	hodieb	hodieb	PROPN
ejpam-5171	214	10	/	/	SYM
ejpam-5171	214	11	eur	eur	PROPN
ejpam-5171	214	12	.	.	PUNCT
ejpam-5171	215	1	j.	j.	PROPN
ejpam-5171	215	2	pure	pure	PROPN
ejpam-5171	215	3	appl	appl	PROPN
ejpam-5171	215	4	.	.	PROPN
ejpam-5171	215	5	math	math	PROPN
ejpam-5171	215	6	,	,	PUNCT
ejpam-5171	215	7	17	17	NUM
ejpam-5171	215	8	(	(	PUNCT
ejpam-5171	215	9	2	2	NUM
ejpam-5171	215	10	)	)	PUNCT
ejpam-5171	215	11	(	(	PUNCT
ejpam-5171	215	12	2024	2024	NUM
ejpam-5171	215	13	)	)	PUNCT
ejpam-5171	215	14	,	,	PUNCT
ejpam-5171	215	15	1352	1352	NUM
ejpam-5171	215	16	-	-	SYM
ejpam-5171	215	17	1368	1368	NUM
ejpam-5171	215	18	1359	1359	NUM
ejpam-5171	215	19	example	example	NOUN
ejpam-5171	215	20	2.13	2.13	NUM
ejpam-5171	215	21	.	.	PUNCT
ejpam-5171	216	1	consider	consider	VERB
ejpam-5171	216	2	x	x	PUNCT
ejpam-5171	216	3	=	=	PRON
ejpam-5171	216	4	{	{	PUNCT
ejpam-5171	216	5	a1	a1	PROPN
ejpam-5171	216	6	,	,	PUNCT
ejpam-5171	216	7	a2	a2	PROPN
ejpam-5171	216	8	,	,	PUNCT
ejpam-5171	216	9	a3	a3	NOUN
ejpam-5171	216	10	,	,	PUNCT
ejpam-5171	216	11	a4	a4	PROPN
ejpam-5171	216	12	}	}	PUNCT
ejpam-5171	216	13	,	,	PUNCT
ejpam-5171	216	14	δ	δ	PROPN
ejpam-5171	216	15	=	=	PRON
ejpam-5171	216	16	{	{	PUNCT
ejpam-5171	216	17	ϕ	ϕ	NOUN
ejpam-5171	216	18	,	,	PUNCT
ejpam-5171	216	19	{	{	PUNCT
ejpam-5171	216	20	a1	a1	NOUN
ejpam-5171	216	21	}	}	PUNCT
ejpam-5171	216	22	,	,	PUNCT
ejpam-5171	216	23	{	{	PUNCT
ejpam-5171	216	24	a1	a1	NOUN
ejpam-5171	216	25	,	,	PUNCT
ejpam-5171	216	26	a2	a2	PROPN
ejpam-5171	216	27	}	}	PUNCT
ejpam-5171	216	28	,	,	PUNCT
ejpam-5171	216	29	{	{	PUNCT
ejpam-5171	216	30	a1	a1	NOUN
ejpam-5171	216	31	,	,	PUNCT
ejpam-5171	216	32	a4	a4	NOUN
ejpam-5171	216	33	}	}	PUNCT
ejpam-5171	216	34	,	,	PUNCT
ejpam-5171	216	35	{	{	PUNCT
ejpam-5171	216	36	a1	a1	NOUN
ejpam-5171	216	37	,	,	PUNCT
ejpam-5171	216	38	a2	a2	PROPN
ejpam-5171	216	39	,	,	PUNCT
ejpam-5171	216	40	a4},x	a4},x	PROPN
ejpam-5171	216	41	}	}	PUNCT
ejpam-5171	216	42	,	,	PUNCT
ejpam-5171	216	43	with	with	ADP
ejpam-5171	216	44	the	the	DET
ejpam-5171	216	45	primal	primal	ADJ
ejpam-5171	216	46	p	p	X
ejpam-5171	216	47	=	=	X
ejpam-5171	216	48	{	{	PUNCT
ejpam-5171	216	49	ϕ	ϕ	NOUN
ejpam-5171	216	50	,	,	PUNCT
ejpam-5171	216	51	{	{	PUNCT
ejpam-5171	216	52	a1	a1	NOUN
ejpam-5171	216	53	}	}	PUNCT
ejpam-5171	216	54	,	,	PUNCT
ejpam-5171	216	55	{	{	PUNCT
ejpam-5171	216	56	a2	a2	PROPN
ejpam-5171	216	57	}	}	PUNCT
ejpam-5171	216	58	,	,	PUNCT
ejpam-5171	216	59	{	{	PUNCT
ejpam-5171	216	60	a3	a3	NOUN
ejpam-5171	216	61	}	}	PUNCT
ejpam-5171	216	62	,	,	PUNCT
ejpam-5171	216	63	{	{	PUNCT
ejpam-5171	216	64	a1	a1	NOUN
ejpam-5171	216	65	,	,	PUNCT
ejpam-5171	216	66	a2	a2	PROPN
ejpam-5171	216	67	}	}	PUNCT
ejpam-5171	216	68	,	,	PUNCT
ejpam-5171	216	69	{	{	PUNCT
ejpam-5171	216	70	a2	a2	NOUN
ejpam-5171	216	71	,	,	PUNCT
ejpam-5171	216	72	a3	a3	NOUN
ejpam-5171	216	73	}	}	PUNCT
ejpam-5171	216	74	,	,	PUNCT
ejpam-5171	216	75	{	{	PUNCT
ejpam-5171	216	76	a1	a1	NOUN
ejpam-5171	216	77	,	,	PUNCT
ejpam-5171	216	78	a3	a3	NOUN
ejpam-5171	216	79	}	}	PUNCT
ejpam-5171	216	80	,	,	PUNCT
ejpam-5171	216	81	{	{	PUNCT
ejpam-5171	216	82	a1	a1	NOUN
ejpam-5171	216	83	,	,	PUNCT
ejpam-5171	216	84	a2	a2	PROPN
ejpam-5171	216	85	,	,	PUNCT
ejpam-5171	216	86	a3	a3	NOUN
ejpam-5171	216	87	}	}	PUNCT
ejpam-5171	216	88	}	}	PUNCT
ejpam-5171	216	89	.	.	PUNCT
ejpam-5171	217	1	thus	thus	ADV
ejpam-5171	217	2	,	,	PUNCT
ejpam-5171	217	3	l	l	NOUN
ejpam-5171	217	4	=	=	SYM
ejpam-5171	217	5	{	{	PUNCT
ejpam-5171	217	6	a1	a1	NOUN
ejpam-5171	217	7	,	,	PUNCT
ejpam-5171	217	8	a3	a3	NOUN
ejpam-5171	217	9	,	,	PUNCT
ejpam-5171	217	10	a4	a4	PROPN
ejpam-5171	217	11	}	}	PUNCT
ejpam-5171	217	12	is	be	AUX
ejpam-5171	217	13	a	a	DET
ejpam-5171	217	14	p	p	NOUN
ejpam-5171	217	15	-	-	PUNCT
ejpam-5171	217	16	β	β	NOUN
ejpam-5171	217	17	-	-	ADJ
ejpam-5171	217	18	open	open	ADJ
ejpam-5171	217	19	set	set	NOUN
ejpam-5171	217	20	that	that	PRON
ejpam-5171	217	21	is	be	AUX
ejpam-5171	217	22	not	not	PART
ejpam-5171	217	23	p	p	NOUN
ejpam-5171	217	24	-	-	PUNCT
ejpam-5171	217	25	pre	pre	NOUN
ejpam-5171	217	26	-	-	ADJ
ejpam-5171	217	27	open	open	ADJ
ejpam-5171	217	28	,	,	PUNCT
ejpam-5171	217	29	since	since	SCONJ
ejpam-5171	217	30	l	l	NOUN
ejpam-5171	217	31	⊆	⊆	NUM
ejpam-5171	217	32	cl(int(cl	cl(int(cl	PROPN
ejpam-5171	217	33	♢	♢	PROPN
ejpam-5171	217	34	(l	(l	PROPN
ejpam-5171	217	35	)	)	PUNCT
ejpam-5171	217	36	)	)	PUNCT
ejpam-5171	217	37	)	)	PUNCT
ejpam-5171	218	1	=	=	PUNCT
ejpam-5171	218	2	x	x	NOUN
ejpam-5171	218	3	,	,	PUNCT
ejpam-5171	218	4	but	but	CCONJ
ejpam-5171	218	5	l	l	PROPN
ejpam-5171	218	6	⊈	⊈	PROPN
ejpam-5171	218	7	int(cl	int(cl	NOUN
ejpam-5171	218	8	♢	♢	PROPN
ejpam-5171	218	9	(l	(l	PROPN
ejpam-5171	218	10	)	)	PUNCT
ejpam-5171	218	11	)	)	PUNCT
ejpam-5171	218	12	=	=	PRON
ejpam-5171	218	13	{	{	PUNCT
ejpam-5171	218	14	a1	a1	NOUN
ejpam-5171	218	15	,	,	PUNCT
ejpam-5171	218	16	a4	a4	NOUN
ejpam-5171	218	17	}	}	PUNCT
ejpam-5171	218	18	.	.	PUNCT
ejpam-5171	219	1	example	example	NOUN
ejpam-5171	219	2	2.14	2.14	NUM
ejpam-5171	219	3	.	.	PUNCT
ejpam-5171	220	1	consider	consider	VERB
ejpam-5171	220	2	x	x	PUNCT
ejpam-5171	220	3	=	=	PRON
ejpam-5171	220	4	{	{	PUNCT
ejpam-5171	220	5	a1	a1	PROPN
ejpam-5171	220	6	,	,	PUNCT
ejpam-5171	220	7	a2	a2	PROPN
ejpam-5171	220	8	,	,	PUNCT
ejpam-5171	220	9	a3	a3	NOUN
ejpam-5171	220	10	}	}	PUNCT
ejpam-5171	220	11	,	,	PUNCT
ejpam-5171	220	12	δ	δ	PROPN
ejpam-5171	220	13	=	=	PRON
ejpam-5171	220	14	{	{	PUNCT
ejpam-5171	220	15	ϕ,x	ϕ,x	NOUN
ejpam-5171	220	16	}	}	PUNCT
ejpam-5171	220	17	,	,	PUNCT
ejpam-5171	220	18	with	with	ADP
ejpam-5171	220	19	the	the	DET
ejpam-5171	220	20	primal	primal	ADJ
ejpam-5171	220	21	p	p	X
ejpam-5171	220	22	=	=	X
ejpam-5171	220	23	{	{	PUNCT
ejpam-5171	220	24	ϕ	ϕ	NOUN
ejpam-5171	220	25	,	,	PUNCT
ejpam-5171	220	26	{	{	PUNCT
ejpam-5171	220	27	a1	a1	NOUN
ejpam-5171	220	28	}	}	PUNCT
ejpam-5171	220	29	,	,	PUNCT
ejpam-5171	220	30	{	{	PUNCT
ejpam-5171	220	31	a2	a2	PROPN
ejpam-5171	220	32	}	}	PUNCT
ejpam-5171	220	33	,	,	PUNCT
ejpam-5171	220	34	{	{	PUNCT
ejpam-5171	220	35	a3	a3	NOUN
ejpam-5171	220	36	}	}	PUNCT
ejpam-5171	220	37	,	,	PUNCT
ejpam-5171	220	38	{	{	PUNCT
ejpam-5171	220	39	a1	a1	NOUN
ejpam-5171	220	40	,	,	PUNCT
ejpam-5171	220	41	a2	a2	PROPN
ejpam-5171	220	42	}	}	PUNCT
ejpam-5171	220	43	,	,	PUNCT
ejpam-5171	220	44	{	{	PUNCT
ejpam-5171	220	45	a2	a2	NOUN
ejpam-5171	220	46	,	,	PUNCT
ejpam-5171	220	47	a3	a3	NOUN
ejpam-5171	220	48	}	}	PUNCT
ejpam-5171	220	49	}	}	PUNCT
ejpam-5171	220	50	.	.	PUNCT
ejpam-5171	221	1	thus	thus	ADV
ejpam-5171	221	2	,	,	PUNCT
ejpam-5171	221	3	(	(	PUNCT
ejpam-5171	221	4	a	a	X
ejpam-5171	221	5	)	)	PUNCT
ejpam-5171	221	6	l	l	NOUN
ejpam-5171	221	7	=	=	SYM
ejpam-5171	221	8	{	{	PUNCT
ejpam-5171	221	9	a3	a3	NOUN
ejpam-5171	221	10	}	}	PUNCT
ejpam-5171	221	11	is	be	AUX
ejpam-5171	221	12	a	a	DET
ejpam-5171	221	13	set	set	NOUN
ejpam-5171	221	14	that	that	PRON
ejpam-5171	221	15	is	be	AUX
ejpam-5171	221	16	p	p	AUX
ejpam-5171	221	17	-	-	PUNCT
ejpam-5171	221	18	β	β	NOUN
ejpam-5171	221	19	-	-	ADJ
ejpam-5171	221	20	open	open	ADJ
ejpam-5171	221	21	but	but	CCONJ
ejpam-5171	221	22	not	not	PART
ejpam-5171	221	23	p	p	NOUN
ejpam-5171	221	24	-	-	PUNCT
ejpam-5171	221	25	semi	semi	ADV
ejpam-5171	221	26	-	-	ADJ
ejpam-5171	221	27	open	open	ADJ
ejpam-5171	221	28	,	,	PUNCT
ejpam-5171	221	29	since	since	SCONJ
ejpam-5171	221	30	l	l	NOUN
ejpam-5171	221	31	⊆	⊆	NUM
ejpam-5171	221	32	cl(int(cl	cl(int(cl	PROPN
ejpam-5171	221	33	♢	♢	PROPN
ejpam-5171	221	34	(l	(l	PROPN
ejpam-5171	221	35	)	)	PUNCT
ejpam-5171	221	36	)	)	PUNCT
ejpam-5171	221	37	)	)	PUNCT
ejpam-5171	222	1	=	=	PUNCT
ejpam-5171	222	2	x	x	NOUN
ejpam-5171	222	3	,	,	PUNCT
ejpam-5171	222	4	but	but	CCONJ
ejpam-5171	222	5	l	l	PROPN
ejpam-5171	222	6	⊈	⊈	PROPN
ejpam-5171	222	7	cl	cl	NOUN
ejpam-5171	222	8	♢	♢	NOUN
ejpam-5171	222	9	(int(l	(int(l	PROPN
ejpam-5171	222	10	)	)	PUNCT
ejpam-5171	222	11	)	)	PUNCT
ejpam-5171	223	1	=	=	PUNCT
ejpam-5171	223	2	ϕ.	ϕ.	NOUN
ejpam-5171	223	3	(	(	PUNCT
ejpam-5171	223	4	b	b	NOUN
ejpam-5171	223	5	)	)	PUNCT
ejpam-5171	223	6	l	l	NOUN
ejpam-5171	223	7	=	=	SYM
ejpam-5171	223	8	{	{	PUNCT
ejpam-5171	223	9	a3	a3	NOUN
ejpam-5171	223	10	}	}	PUNCT
ejpam-5171	223	11	is	be	AUX
ejpam-5171	223	12	a	a	DET
ejpam-5171	223	13	set	set	NOUN
ejpam-5171	223	14	that	that	PRON
ejpam-5171	223	15	is	be	AUX
ejpam-5171	223	16	p	p	ADJ
ejpam-5171	223	17	-	-	PUNCT
ejpam-5171	223	18	pre	pre	NOUN
ejpam-5171	223	19	-	-	ADJ
ejpam-5171	223	20	open	open	ADJ
ejpam-5171	223	21	but	but	CCONJ
ejpam-5171	223	22	not	not	PART
ejpam-5171	223	23	p	p	NOUN
ejpam-5171	223	24	-	-	PUNCT
ejpam-5171	223	25	α	α	NOUN
ejpam-5171	223	26	-	-	NOUN
ejpam-5171	223	27	open	open	ADJ
ejpam-5171	223	28	,	,	PUNCT
ejpam-5171	223	29	since	since	SCONJ
ejpam-5171	223	30	l	l	PROPN
ejpam-5171	223	31	⊆	⊆	NUM
ejpam-5171	223	32	int(cl	int(cl	PROPN
ejpam-5171	223	33	♢	♢	PROPN
ejpam-5171	223	34	(l	(l	PROPN
ejpam-5171	223	35	)	)	PUNCT
ejpam-5171	223	36	)	)	PUNCT
ejpam-5171	224	1	=	=	SYM
ejpam-5171	224	2	x	x	NOUN
ejpam-5171	224	3	,	,	PUNCT
ejpam-5171	224	4	but	but	CCONJ
ejpam-5171	224	5	l	l	PROPN
ejpam-5171	224	6	⊈	⊈	PROPN
ejpam-5171	224	7	int(cl	int(cl	NOUN
ejpam-5171	224	8	♢	♢	PROPN
ejpam-5171	224	9	(int(l	(int(l	PROPN
ejpam-5171	224	10	)	)	PUNCT
ejpam-5171	224	11	)	)	PUNCT
ejpam-5171	224	12	)	)	PUNCT
ejpam-5171	225	1	=	=	PUNCT
ejpam-5171	225	2	ϕ.	ϕ.	NOUN
ejpam-5171	225	3	(	(	PUNCT
ejpam-5171	225	4	c	c	NOUN
ejpam-5171	225	5	)	)	PUNCT
ejpam-5171	225	6	l	l	NOUN
ejpam-5171	226	1	=	=	SYM
ejpam-5171	226	2	{	{	PUNCT
ejpam-5171	226	3	a1	a1	NOUN
ejpam-5171	226	4	,	,	PUNCT
ejpam-5171	226	5	a3	a3	NOUN
ejpam-5171	226	6	}	}	PUNCT
ejpam-5171	226	7	is	be	AUX
ejpam-5171	226	8	a	a	DET
ejpam-5171	226	9	set	set	NOUN
ejpam-5171	226	10	that	that	PRON
ejpam-5171	226	11	is	be	AUX
ejpam-5171	226	12	p	p	ADJ
ejpam-5171	226	13	-	-	PUNCT
ejpam-5171	226	14	pre	pre	NOUN
ejpam-5171	226	15	-	-	ADJ
ejpam-5171	226	16	open	open	ADJ
ejpam-5171	226	17	but	but	CCONJ
ejpam-5171	226	18	not	not	PART
ejpam-5171	226	19	p	p	NOUN
ejpam-5171	226	20	-	-	PUNCT
ejpam-5171	226	21	open	open	ADJ
ejpam-5171	226	22	,	,	PUNCT
ejpam-5171	226	23	since	since	SCONJ
ejpam-5171	226	24	l	l	PROPN
ejpam-5171	226	25	⊆	⊆	NUM
ejpam-5171	226	26	int(cl	int(cl	PROPN
ejpam-5171	226	27	♢	♢	PROPN
ejpam-5171	226	28	(l	(l	PROPN
ejpam-5171	226	29	)	)	PUNCT
ejpam-5171	226	30	)	)	PUNCT
ejpam-5171	227	1	=	=	SYM
ejpam-5171	227	2	x	x	NOUN
ejpam-5171	227	3	,	,	PUNCT
ejpam-5171	227	4	but	but	CCONJ
ejpam-5171	227	5	l	l	NOUN
ejpam-5171	227	6	/∈	/∈	PUNCT
ejpam-5171	228	1	p.	p.	NOUN
ejpam-5171	228	2	example	example	NOUN
ejpam-5171	229	1	2.15	2.15	NUM
ejpam-5171	229	2	.	.	PUNCT
ejpam-5171	230	1	consider	consider	VERB
ejpam-5171	230	2	x	x	PUNCT
ejpam-5171	230	3	=	=	PRON
ejpam-5171	230	4	{	{	PUNCT
ejpam-5171	230	5	a1	a1	PROPN
ejpam-5171	230	6	,	,	PUNCT
ejpam-5171	230	7	a2	a2	PROPN
ejpam-5171	230	8	,	,	PUNCT
ejpam-5171	230	9	a3	a3	NOUN
ejpam-5171	230	10	}	}	PUNCT
ejpam-5171	230	11	,	,	PUNCT
ejpam-5171	230	12	δ	δ	PROPN
ejpam-5171	230	13	=	=	PRON
ejpam-5171	230	14	{	{	PUNCT
ejpam-5171	230	15	ϕ,x	ϕ,x	NOUN
ejpam-5171	230	16	}	}	PUNCT
ejpam-5171	230	17	,	,	PUNCT
ejpam-5171	230	18	with	with	ADP
ejpam-5171	230	19	the	the	DET
ejpam-5171	230	20	primal	primal	ADJ
ejpam-5171	230	21	set	set	NOUN
ejpam-5171	230	22	given	give	VERB
ejpam-5171	230	23	by	by	ADP
ejpam-5171	230	24	p	p	PROPN
ejpam-5171	230	25	=	=	X
ejpam-5171	230	26	{	{	PUNCT
ejpam-5171	230	27	ϕ	ϕ	NOUN
ejpam-5171	230	28	,	,	PUNCT
ejpam-5171	230	29	{	{	PUNCT
ejpam-5171	230	30	a1	a1	NOUN
ejpam-5171	230	31	}	}	PUNCT
ejpam-5171	230	32	,	,	PUNCT
ejpam-5171	230	33	{	{	PUNCT
ejpam-5171	230	34	a2	a2	PROPN
ejpam-5171	230	35	}	}	PUNCT
ejpam-5171	230	36	,	,	PUNCT
ejpam-5171	230	37	{	{	PUNCT
ejpam-5171	230	38	a3	a3	NOUN
ejpam-5171	230	39	}	}	PUNCT
ejpam-5171	230	40	,	,	PUNCT
ejpam-5171	230	41	{	{	PUNCT
ejpam-5171	230	42	a1	a1	NOUN
ejpam-5171	230	43	,	,	PUNCT
ejpam-5171	230	44	a2	a2	PROPN
ejpam-5171	230	45	}	}	PUNCT
ejpam-5171	230	46	,	,	PUNCT
ejpam-5171	230	47	{	{	PUNCT
ejpam-5171	230	48	a1	a1	NOUN
ejpam-5171	230	49	,	,	PUNCT
ejpam-5171	230	50	a3	a3	NOUN
ejpam-5171	230	51	}	}	PUNCT
ejpam-5171	230	52	}	}	PUNCT
ejpam-5171	230	53	.	.	PUNCT
ejpam-5171	231	1	thus	thus	ADV
ejpam-5171	231	2	,	,	PUNCT
ejpam-5171	231	3	l	l	NOUN
ejpam-5171	231	4	=	=	SYM
ejpam-5171	231	5	{	{	PUNCT
ejpam-5171	231	6	a3	a3	NOUN
ejpam-5171	231	7	}	}	PUNCT
ejpam-5171	231	8	is	be	AUX
ejpam-5171	231	9	a	a	DET
ejpam-5171	231	10	set	set	NOUN
ejpam-5171	231	11	that	that	PRON
ejpam-5171	231	12	is	be	AUX
ejpam-5171	231	13	p	p	X
ejpam-5171	231	14	-	-	PUNCT
ejpam-5171	231	15	open	open	ADJ
ejpam-5171	231	16	but	but	CCONJ
ejpam-5171	231	17	not	not	PART
ejpam-5171	231	18	p	p	NOUN
ejpam-5171	231	19	-	-	PUNCT
ejpam-5171	231	20	semi	semi	ADV
ejpam-5171	231	21	-	-	ADJ
ejpam-5171	231	22	open	open	ADJ
ejpam-5171	231	23	,	,	PUNCT
ejpam-5171	231	24	since	since	SCONJ
ejpam-5171	231	25	l	l	NOUN
ejpam-5171	231	26	⊆	⊆	NUM
ejpam-5171	231	27	int(l	int(l	PROPN
ejpam-5171	231	28	♢	♢	PROPN
ejpam-5171	231	29	p	p	NOUN
ejpam-5171	231	30	)	)	PUNCT
ejpam-5171	231	31	=	=	SYM
ejpam-5171	231	32	x	x	NOUN
ejpam-5171	231	33	,	,	PUNCT
ejpam-5171	231	34	but	but	CCONJ
ejpam-5171	231	35	l	l	PROPN
ejpam-5171	231	36	⊈	⊈	PROPN
ejpam-5171	231	37	cl	cl	NOUN
ejpam-5171	231	38	♢	♢	NOUN
ejpam-5171	231	39	(int(l	(int(l	PROPN
ejpam-5171	231	40	)	)	PUNCT
ejpam-5171	231	41	)	)	PUNCT
ejpam-5171	232	1	=	=	PUNCT
ejpam-5171	232	2	ϕ.	ϕ.	NOUN
ejpam-5171	232	3	definition	definition	NOUN
ejpam-5171	232	4	2.16	2.16	NUM
ejpam-5171	232	5	.	.	PUNCT
ejpam-5171	233	1	a	a	DET
ejpam-5171	233	2	subset	subset	ADJ
ejpam-5171	233	3	l	l	NOUN
ejpam-5171	233	4	of	of	ADP
ejpam-5171	233	5	a	a	DET
ejpam-5171	233	6	pts	pts	X
ejpam-5171	233	7	(	(	PUNCT
ejpam-5171	233	8	x	x	NOUN
ejpam-5171	233	9	,	,	PUNCT
ejpam-5171	233	10	δ	δ	PROPN
ejpam-5171	233	11	,	,	PUNCT
ejpam-5171	233	12	p	p	NOUN
ejpam-5171	233	13	)	)	PUNCT
ejpam-5171	233	14	is	be	AUX
ejpam-5171	233	15	called	call	VERB
ejpam-5171	233	16	p	p	NOUN
ejpam-5171	233	17	-	-	PUNCT
ejpam-5171	233	18	dense	dense	ADJ
ejpam-5171	233	19	in	in	ADP
ejpam-5171	233	20	x	x	PUNCT
ejpam-5171	233	21	if	if	SCONJ
ejpam-5171	233	22	cl	cl	NOUN
ejpam-5171	233	23	♢	♢	PROPN
ejpam-5171	233	24	(l	(l	PROPN
ejpam-5171	233	25	)	)	PUNCT
ejpam-5171	233	26	=	=	SYM
ejpam-5171	233	27	x.	x.	NOUN
ejpam-5171	233	28	theorem	theorem	VERB
ejpam-5171	233	29	2.17	2.17	NUM
ejpam-5171	233	30	.	.	PUNCT
ejpam-5171	234	1	assume	assume	VERB
ejpam-5171	234	2	that	that	SCONJ
ejpam-5171	234	3	(	(	PUNCT
ejpam-5171	234	4	x	x	NOUN
ejpam-5171	234	5	,	,	PUNCT
ejpam-5171	234	6	δ	δ	PROPN
ejpam-5171	234	7	,	,	PUNCT
ejpam-5171	234	8	p	p	NOUN
ejpam-5171	234	9	)	)	PUNCT
ejpam-5171	234	10	be	be	AUX
ejpam-5171	234	11	pts	pt	NOUN
ejpam-5171	234	12	.	.	PUNCT
ejpam-5171	235	1	thus	thus	ADV
ejpam-5171	235	2	,	,	PUNCT
ejpam-5171	235	3	for	for	ADP
ejpam-5171	235	4	a	a	DET
ejpam-5171	235	5	subset	subset	ADJ
ejpam-5171	235	6	l	l	NOUN
ejpam-5171	235	7	of	of	ADP
ejpam-5171	235	8	x	x	PRON
ejpam-5171	235	9	,	,	PUNCT
ejpam-5171	235	10	the	the	DET
ejpam-5171	235	11	next	next	ADJ
ejpam-5171	235	12	is	be	AUX
ejpam-5171	235	13	true	true	ADJ
ejpam-5171	235	14	:	:	PUNCT
ejpam-5171	235	15	(	(	PUNCT
ejpam-5171	235	16	a	a	X
ejpam-5171	235	17	)	)	PUNCT
ejpam-5171	235	18	if	if	SCONJ
ejpam-5171	235	19	p	p	NOUN
ejpam-5171	235	20	=	=	SYM
ejpam-5171	235	21	2x	2x	NUM
ejpam-5171	235	22	\	\	NOUN
ejpam-5171	235	23	{	{	PUNCT
ejpam-5171	235	24	x	x	X
ejpam-5171	235	25	}	}	PUNCT
ejpam-5171	235	26	,	,	PUNCT
ejpam-5171	235	27	l	l	NOUN
ejpam-5171	235	28	is	be	AUX
ejpam-5171	235	29	p	p	AUX
ejpam-5171	235	30	-	-	PUNCT
ejpam-5171	235	31	β	β	NOUN
ejpam-5171	235	32	-	-	ADJ
ejpam-5171	235	33	open	open	ADJ
ejpam-5171	235	34	iff	iff	PROPN
ejpam-5171	235	35	l	l	PROPN
ejpam-5171	235	36	is	be	AUX
ejpam-5171	235	37	semi	semi	ADJ
ejpam-5171	235	38	-	-	ADJ
ejpam-5171	235	39	open	open	ADJ
ejpam-5171	235	40	,	,	PUNCT
ejpam-5171	235	41	(	(	PUNCT
ejpam-5171	235	42	b	b	X
ejpam-5171	235	43	)	)	PUNCT
ejpam-5171	235	44	let	let	VERB
ejpam-5171	235	45	p	p	NOUN
ejpam-5171	235	46	=	=	X
ejpam-5171	235	47	{	{	PUNCT
ejpam-5171	235	48	n	n	CCONJ
ejpam-5171	235	49	⊆	⊆	NUM
ejpam-5171	235	50	x	x	SYM
ejpam-5171	235	51	\	\	NOUN
ejpam-5171	235	52	n	n	PRON
ejpam-5171	235	53	is	be	AUX
ejpam-5171	235	54	the	the	DET
ejpam-5171	235	55	primal	primal	ADJ
ejpam-5171	235	56	dense	dense	NOUN
ejpam-5171	235	57	for	for	ADP
ejpam-5171	235	58	all	all	DET
ejpam-5171	235	59	nowhere	nowhere	ADV
ejpam-5171	235	60	dense	dense	ADJ
ejpam-5171	235	61	set	set	NOUN
ejpam-5171	235	62	}	}	PUNCT
ejpam-5171	235	63	and	and	CCONJ
ejpam-5171	235	64	l	l	NOUN
ejpam-5171	235	65	⊆	⊆	NUM
ejpam-5171	235	66	x.	x.	NOUN
ejpam-5171	235	67	then	then	ADV
ejpam-5171	235	68	,	,	PUNCT
ejpam-5171	235	69	l	l	PROPN
ejpam-5171	235	70	is	be	AUX
ejpam-5171	235	71	p	p	AUX
ejpam-5171	235	72	-	-	PUNCT
ejpam-5171	235	73	β	β	NOUN
ejpam-5171	235	74	-	-	ADJ
ejpam-5171	235	75	open	open	ADJ
ejpam-5171	235	76	iff	iff	PROPN
ejpam-5171	235	77	l	l	PROPN
ejpam-5171	235	78	is	be	AUX
ejpam-5171	235	79	β	β	NOUN
ejpam-5171	235	80	-	-	ADJ
ejpam-5171	235	81	open	open	ADJ
ejpam-5171	235	82	.	.	PUNCT
ejpam-5171	236	1	proof	proof	NOUN
ejpam-5171	236	2	.	.	PUNCT
ejpam-5171	237	1	(	(	PUNCT
ejpam-5171	237	2	a	a	X
ejpam-5171	237	3	)	)	PUNCT
ejpam-5171	237	4	when	when	SCONJ
ejpam-5171	237	5	p	p	PROPN
ejpam-5171	237	6	=	=	SYM
ejpam-5171	237	7	2x	2x	NUM
ejpam-5171	237	8	\	\	NOUN
ejpam-5171	237	9	{	{	PUNCT
ejpam-5171	237	10	x	x	X
ejpam-5171	237	11	}	}	PUNCT
ejpam-5171	237	12	,	,	PUNCT
ejpam-5171	237	13	thus	thus	ADV
ejpam-5171	237	14	l	l	NOUN
ejpam-5171	237	15	♢	♢	PROPN
ejpam-5171	237	16	p	p	PROPN
ejpam-5171	237	17	=	=	PROPN
ejpam-5171	237	18	ϕ	ϕ	PROPN
ejpam-5171	237	19	for	for	ADP
ejpam-5171	237	20	any	any	DET
ejpam-5171	237	21	l	l	NOUN
ejpam-5171	237	22	⊂	⊂	X
ejpam-5171	237	23	x.	x.	NOUN
ejpam-5171	238	1	consequently	consequently	ADV
ejpam-5171	238	2	,	,	PUNCT
ejpam-5171	238	3	we	we	PRON
ejpam-5171	238	4	have	have	VERB
ejpam-5171	238	5	cl(int(cl	cl(int(cl	PROPN
ejpam-5171	238	6	♢	♢	PROPN
ejpam-5171	238	7	(l	(l	PROPN
ejpam-5171	238	8	)	)	PUNCT
ejpam-5171	238	9	)	)	PUNCT
ejpam-5171	238	10	)	)	PUNCT
ejpam-5171	239	1	=	=	SYM
ejpam-5171	239	2	cl(int(l	cl(int(l	PROPN
ejpam-5171	239	3	♢	♢	PROPN
ejpam-5171	239	4	∪	∪	PROPN
ejpam-5171	239	5	l	l	NOUN
ejpam-5171	239	6	)	)	PUNCT
ejpam-5171	239	7	)	)	PUNCT
ejpam-5171	239	8	=	=	SYM
ejpam-5171	239	9	cl(int(l	cl(int(l	PROPN
ejpam-5171	239	10	)	)	PUNCT
ejpam-5171	239	11	)	)	PUNCT
ejpam-5171	239	12	.	.	PUNCT
ejpam-5171	240	1	thus	thus	ADV
ejpam-5171	240	2	,	,	PUNCT
ejpam-5171	240	3	p	p	PROPN
ejpam-5171	240	4	-	-	PUNCT
ejpam-5171	240	5	β	β	NOUN
ejpam-5171	240	6	-	-	NOUN
ejpam-5171	240	7	openness	openness	NOUN
ejpam-5171	240	8	and	and	CCONJ
ejpam-5171	240	9	semi	semi	ADJ
ejpam-5171	240	10	-	-	ADJ
ejpam-5171	240	11	openness	openness	NOUN
ejpam-5171	240	12	are	be	AUX
ejpam-5171	240	13	equivalent	equivalent	ADJ
ejpam-5171	240	14	.	.	PUNCT
ejpam-5171	241	1	(	(	PUNCT
ejpam-5171	241	2	b	b	X
ejpam-5171	241	3	)	)	PUNCT
ejpam-5171	241	4	by	by	ADP
ejpam-5171	241	5	theorem	theorem	ADJ
ejpam-5171	241	6	2.2	2.2	NUM
ejpam-5171	241	7	,	,	PUNCT
ejpam-5171	241	8	every	every	DET
ejpam-5171	241	9	p	p	PROPN
ejpam-5171	241	10	-	-	PUNCT
ejpam-5171	241	11	β	β	NOUN
ejpam-5171	241	12	-	-	ADJ
ejpam-5171	241	13	open	open	ADJ
ejpam-5171	241	14	set	set	NOUN
ejpam-5171	241	15	is	be	AUX
ejpam-5171	241	16	β	β	NOUN
ejpam-5171	241	17	-	-	NOUN
ejpam-5171	241	18	open	open	ADJ
ejpam-5171	241	19	.	.	PUNCT
ejpam-5171	242	1	if	if	SCONJ
ejpam-5171	242	2	p	p	NOUN
ejpam-5171	242	3	=	=	NOUN
ejpam-5171	242	4	n	n	CCONJ
ejpam-5171	242	5	,	,	PUNCT
ejpam-5171	242	6	then	then	ADV
ejpam-5171	242	7	it	it	PRON
ejpam-5171	242	8	is	be	AUX
ejpam-5171	242	9	well	well	ADV
ejpam-5171	242	10	-	-	PUNCT
ejpam-5171	242	11	known	know	VERB
ejpam-5171	242	12	that	that	SCONJ
ejpam-5171	242	13	l	l	NOUN
ejpam-5171	242	14	♢	♢	NOUN
ejpam-5171	242	15	=	=	SYM
ejpam-5171	242	16	cl(int(cl(l	cl(int(cl(l	ADJ
ejpam-5171	242	17	)	)	PUNCT
ejpam-5171	242	18	)	)	PUNCT
ejpam-5171	242	19	)	)	PUNCT
ejpam-5171	242	20	.	.	PUNCT
ejpam-5171	243	1	therefore	therefore	ADV
ejpam-5171	243	2	,	,	PUNCT
ejpam-5171	243	3	if	if	SCONJ
ejpam-5171	243	4	l	l	NOUN
ejpam-5171	243	5	is	be	AUX
ejpam-5171	243	6	β	β	NOUN
ejpam-5171	243	7	-	-	ADJ
ejpam-5171	243	8	open	open	ADJ
ejpam-5171	243	9	,	,	PUNCT
ejpam-5171	243	10	we	we	PRON
ejpam-5171	243	11	obtain	obtain	VERB
ejpam-5171	243	12	l	l	NOUN
ejpam-5171	243	13	⊂	⊂	X
ejpam-5171	243	14	cl(int(cl(l	cl(int(cl(l	ADJ
ejpam-5171	243	15	)	)	PUNCT
ejpam-5171	243	16	)	)	PUNCT
ejpam-5171	243	17	)	)	PUNCT
ejpam-5171	244	1	=	=	PUNCT
ejpam-5171	245	1	l	l	NOUN
ejpam-5171	245	2	♢	♢	PROPN
ejpam-5171	245	3	=	=	SYM
ejpam-5171	245	4	cl	cl	NOUN
ejpam-5171	245	5	♢	♢	PROPN
ejpam-5171	245	6	(l	(l	PROPN
ejpam-5171	245	7	)	)	PUNCT
ejpam-5171	245	8	,	,	PUNCT
ejpam-5171	245	9	and	and	CCONJ
ejpam-5171	245	10	hence	hence	ADV
ejpam-5171	245	11	l	l	PROPN
ejpam-5171	245	12	⊂	⊂	X
ejpam-5171	245	13	cl(int(cl(l	cl(int(cl(l	ADJ
ejpam-5171	245	14	)	)	PUNCT
ejpam-5171	245	15	)	)	PUNCT
ejpam-5171	245	16	)	)	PUNCT
ejpam-5171	246	1	=	=	PUNCT
ejpam-5171	246	2	cl(int[cl(int(cl(l	cl(int[cl(int(cl(l	NOUN
ejpam-5171	246	3	)	)	PUNCT
ejpam-5171	246	4	)	)	PUNCT
ejpam-5171	246	5	)	)	PUNCT
ejpam-5171	246	6	]	]	X
ejpam-5171	246	7	)	)	PUNCT
ejpam-5171	246	8	=	=	SYM
ejpam-5171	246	9	cl(int(cl	cl(int(cl	PROPN
ejpam-5171	246	10	♢	♢	PROPN
ejpam-5171	246	11	(l	(l	PROPN
ejpam-5171	246	12	)	)	PUNCT
ejpam-5171	246	13	)	)	PUNCT
ejpam-5171	246	14	)	)	PUNCT
ejpam-5171	246	15	.	.	PUNCT
ejpam-5171	247	1	3	3	X
ejpam-5171	247	2	.	.	X
ejpam-5171	247	3	pr	pr	NOUN
ejpam-5171	247	4	-	-	PUNCT
ejpam-5171	247	5	sets	set	NOUN
ejpam-5171	247	6	and	and	CCONJ
ejpam-5171	247	7	prα	prα	NOUN
ejpam-5171	247	8	-	-	PUNCT
ejpam-5171	247	9	sets	set	NOUN
ejpam-5171	247	10	in	in	ADP
ejpam-5171	247	11	this	this	DET
ejpam-5171	247	12	section	section	NOUN
ejpam-5171	247	13	,	,	PUNCT
ejpam-5171	247	14	we	we	PRON
ejpam-5171	247	15	focus	focus	VERB
ejpam-5171	247	16	on	on	ADP
ejpam-5171	247	17	using	use	VERB
ejpam-5171	247	18	the	the	DET
ejpam-5171	247	19	pts	pt	NOUN
ejpam-5171	247	20	of	of	ADP
ejpam-5171	247	21	some	some	DET
ejpam-5171	247	22	defined	define	VERB
ejpam-5171	247	23	sets	set	NOUN
ejpam-5171	247	24	,	,	PUNCT
ejpam-5171	247	25	namely	namely	ADV
ejpam-5171	247	26	the	the	DET
ejpam-5171	247	27	pr	pr	NOUN
ejpam-5171	247	28	-	-	PUNCT
ejpam-5171	247	29	sets	set	NOUN
ejpam-5171	247	30	and	and	CCONJ
ejpam-5171	247	31	prα	prα	NOUN
ejpam-5171	247	32	-	-	PUNCT
ejpam-5171	247	33	sets	set	NOUN
ejpam-5171	247	34	.	.	PUNCT
ejpam-5171	248	1	furthermore	furthermore	ADV
ejpam-5171	248	2	,	,	PUNCT
ejpam-5171	248	3	their	their	PRON
ejpam-5171	248	4	characterizations	characterization	NOUN
ejpam-5171	248	5	and	and	CCONJ
ejpam-5171	248	6	main	main	ADJ
ejpam-5171	248	7	features	feature	NOUN
ejpam-5171	248	8	are	be	AUX
ejpam-5171	248	9	determined	determine	VERB
ejpam-5171	248	10	,	,	PUNCT
ejpam-5171	248	11	and	and	CCONJ
ejpam-5171	248	12	their	their	PRON
ejpam-5171	248	13	relationships	relationship	NOUN
ejpam-5171	248	14	with	with	ADP
ejpam-5171	248	15	another	another	DET
ejpam-5171	248	16	set	set	NOUN
ejpam-5171	248	17	are	be	AUX
ejpam-5171	248	18	investigated	investigate	VERB
ejpam-5171	248	19	.	.	PUNCT
ejpam-5171	249	1	definition	definition	NOUN
ejpam-5171	249	2	3.1	3.1	NUM
ejpam-5171	249	3	.	.	PUNCT
ejpam-5171	249	4	assume	assume	VERB
ejpam-5171	249	5	that	that	SCONJ
ejpam-5171	249	6	(	(	PUNCT
ejpam-5171	249	7	x	x	NOUN
ejpam-5171	249	8	,	,	PUNCT
ejpam-5171	249	9	δ	δ	PROPN
ejpam-5171	249	10	,	,	PUNCT
ejpam-5171	249	11	p	p	NOUN
ejpam-5171	249	12	)	)	PUNCT
ejpam-5171	249	13	be	be	AUX
ejpam-5171	249	14	pts	pt	NOUN
ejpam-5171	249	15	.	.	PUNCT
ejpam-5171	250	1	thus	thus	ADV
ejpam-5171	250	2	,	,	PUNCT
ejpam-5171	250	3	l	l	PROPN
ejpam-5171	250	4	⊆	⊆	NUM
ejpam-5171	250	5	x	x	PUNCT
ejpam-5171	250	6	has	have	VERB
ejpam-5171	250	7	the	the	DET
ejpam-5171	250	8	following	follow	VERB
ejpam-5171	250	9	definition	definition	NOUN
ejpam-5171	250	10	:	:	PUNCT
ejpam-5171	250	11	(	(	PUNCT
ejpam-5171	250	12	a	a	X
ejpam-5171	250	13	)	)	PUNCT
ejpam-5171	250	14	primal	primal	ADJ
ejpam-5171	250	15	t	t	PROPN
ejpam-5171	250	16	-	-	PUNCT
ejpam-5171	250	17	set	set	NOUN
ejpam-5171	250	18	(	(	PUNCT
ejpam-5171	250	19	briefly	briefly	ADV
ejpam-5171	250	20	,	,	PUNCT
ejpam-5171	250	21	pt	pt	NOUN
ejpam-5171	250	22	-	-	PUNCT
ejpam-5171	250	23	set	set	NOUN
ejpam-5171	250	24	)	)	PUNCT
ejpam-5171	250	25	,	,	PUNCT
ejpam-5171	250	26	if	if	SCONJ
ejpam-5171	250	27	int(l	int(l	PROPN
ejpam-5171	250	28	)	)	PUNCT
ejpam-5171	250	29	=	=	PUNCT
ejpam-5171	250	30	int(cl	int(cl	PROPN
ejpam-5171	250	31	♢	♢	PROPN
ejpam-5171	250	32	(l	(l	PROPN
ejpam-5171	250	33	)	)	PUNCT
ejpam-5171	250	34	)	)	PUNCT
ejpam-5171	250	35	.	.	PUNCT
ejpam-5171	251	1	h.	h.	PROPN
ejpam-5171	251	2	al	al	PROPN
ejpam-5171	251	3	-	-	PUNCT
ejpam-5171	251	4	saadi	saadi	PROPN
ejpam-5171	251	5	,	,	PUNCT
ejpam-5171	251	6	m.	m.	NOUN
ejpam-5171	251	7	al	al	PROPN
ejpam-5171	251	8	-	-	PUNCT
ejpam-5171	251	9	hodieb	hodieb	PROPN
ejpam-5171	251	10	/	/	SYM
ejpam-5171	251	11	eur	eur	PROPN
ejpam-5171	251	12	.	.	PUNCT
ejpam-5171	252	1	j.	j.	PROPN
ejpam-5171	252	2	pure	pure	PROPN
ejpam-5171	252	3	appl	appl	PROPN
ejpam-5171	252	4	.	.	PROPN
ejpam-5171	252	5	math	math	PROPN
ejpam-5171	252	6	,	,	PUNCT
ejpam-5171	252	7	17	17	NUM
ejpam-5171	252	8	(	(	PUNCT
ejpam-5171	252	9	2	2	NUM
ejpam-5171	252	10	)	)	PUNCT
ejpam-5171	252	11	(	(	PUNCT
ejpam-5171	252	12	2024	2024	NUM
ejpam-5171	252	13	)	)	PUNCT
ejpam-5171	252	14	,	,	PUNCT
ejpam-5171	252	15	1352	1352	NUM
ejpam-5171	252	16	-	-	SYM
ejpam-5171	252	17	1368	1368	NUM
ejpam-5171	252	18	1360	1360	NUM
ejpam-5171	252	19	(	(	PUNCT
ejpam-5171	252	20	b	b	NOUN
ejpam-5171	252	21	)	)	PUNCT
ejpam-5171	252	22	primal	primal	ADJ
ejpam-5171	252	23	tα	tα	NOUN
ejpam-5171	252	24	-	-	PUNCT
ejpam-5171	252	25	set	set	NOUN
ejpam-5171	252	26	(	(	PUNCT
ejpam-5171	252	27	briefly	briefly	ADV
ejpam-5171	252	28	,	,	PUNCT
ejpam-5171	252	29	ptα	ptα	NOUN
ejpam-5171	252	30	-	-	PUNCT
ejpam-5171	252	31	set	set	NOUN
ejpam-5171	252	32	)	)	PUNCT
ejpam-5171	252	33	,	,	PUNCT
ejpam-5171	252	34	if	if	SCONJ
ejpam-5171	252	35	int(l	int(l	PROPN
ejpam-5171	252	36	)	)	PUNCT
ejpam-5171	252	37	=	=	PUNCT
ejpam-5171	252	38	int(cl	int(cl	PROPN
ejpam-5171	252	39	♢	♢	PROPN
ejpam-5171	252	40	(int(l	(int(l	PROPN
ejpam-5171	252	41	)	)	PUNCT
ejpam-5171	252	42	)	)	PUNCT
ejpam-5171	252	43	)	)	PUNCT
ejpam-5171	252	44	.	.	PUNCT
ejpam-5171	253	1	(	(	PUNCT
ejpam-5171	253	2	c	c	X
ejpam-5171	253	3	)	)	PUNCT
ejpam-5171	253	4	primal	primal	ADJ
ejpam-5171	253	5	r	r	NOUN
ejpam-5171	253	6	-	-	PUNCT
ejpam-5171	253	7	set	set	ADJ
ejpam-5171	253	8	(	(	PUNCT
ejpam-5171	253	9	briefly	briefly	ADV
ejpam-5171	253	10	,	,	PUNCT
ejpam-5171	253	11	pr	pr	NOUN
ejpam-5171	253	12	-	-	PUNCT
ejpam-5171	253	13	set	set	NOUN
ejpam-5171	253	14	)	)	PUNCT
ejpam-5171	253	15	,	,	PUNCT
ejpam-5171	253	16	if	if	SCONJ
ejpam-5171	253	17	l	l	NOUN
ejpam-5171	253	18	=	=	SYM
ejpam-5171	253	19	l1	l1	PROPN
ejpam-5171	253	20	∩	∩	ADJ
ejpam-5171	253	21	l2	l2	NOUN
ejpam-5171	253	22	,	,	PUNCT
ejpam-5171	253	23	where	where	SCONJ
ejpam-5171	253	24	l1	l1	PROPN
ejpam-5171	253	25	is	be	AUX
ejpam-5171	253	26	open	open	ADJ
ejpam-5171	253	27	and	and	CCONJ
ejpam-5171	253	28	l2	l2	NOUN
ejpam-5171	253	29	is	be	AUX
ejpam-5171	253	30	pt	pt	NOUN
ejpam-5171	253	31	-	-	PUNCT
ejpam-5171	253	32	set	set	NOUN
ejpam-5171	253	33	.	.	PUNCT
ejpam-5171	254	1	(	(	PUNCT
ejpam-5171	254	2	d	d	X
ejpam-5171	254	3	)	)	PUNCT
ejpam-5171	254	4	primal	primal	ADJ
ejpam-5171	254	5	rα	rα	ADV
ejpam-5171	254	6	-	-	PUNCT
ejpam-5171	254	7	set	set	ADJ
ejpam-5171	254	8	(	(	PUNCT
ejpam-5171	254	9	briefly	briefly	ADV
ejpam-5171	254	10	,	,	PUNCT
ejpam-5171	254	11	prα	prα	NOUN
ejpam-5171	254	12	-	-	PUNCT
ejpam-5171	254	13	set	set	NOUN
ejpam-5171	254	14	)	)	PUNCT
ejpam-5171	254	15	,	,	PUNCT
ejpam-5171	254	16	if	if	SCONJ
ejpam-5171	254	17	l	l	NOUN
ejpam-5171	254	18	=	=	SYM
ejpam-5171	254	19	l1∩l2	l1∩l2	PROPN
ejpam-5171	254	20	,	,	PUNCT
ejpam-5171	254	21	where	where	SCONJ
ejpam-5171	254	22	l1	l1	PROPN
ejpam-5171	254	23	is	be	AUX
ejpam-5171	254	24	open	open	ADJ
ejpam-5171	254	25	and	and	CCONJ
ejpam-5171	254	26	l2	l2	NOUN
ejpam-5171	254	27	is	be	AUX
ejpam-5171	254	28	ptα	ptα	NOUN
ejpam-5171	254	29	-	-	PUNCT
ejpam-5171	254	30	set	set	NOUN
ejpam-5171	254	31	.	.	PUNCT
ejpam-5171	255	1	example	example	NOUN
ejpam-5171	255	2	3.2	3.2	NUM
ejpam-5171	255	3	.	.	PUNCT
ejpam-5171	256	1	let	let	VERB
ejpam-5171	256	2	x	x	PUNCT
ejpam-5171	256	3	=	=	PRON
ejpam-5171	256	4	{	{	PUNCT
ejpam-5171	256	5	a1	a1	PROPN
ejpam-5171	256	6	,	,	PUNCT
ejpam-5171	256	7	a2	a2	PROPN
ejpam-5171	256	8	}	}	PUNCT
ejpam-5171	256	9	and	and	CCONJ
ejpam-5171	256	10	δ	δ	PROPN
ejpam-5171	256	11	=	=	PRON
ejpam-5171	256	12	{	{	PUNCT
ejpam-5171	256	13	ϕ	ϕ	NOUN
ejpam-5171	256	14	,	,	PUNCT
ejpam-5171	256	15	{	{	PUNCT
ejpam-5171	256	16	a1},x	a1},x	NOUN
ejpam-5171	256	17	}	}	PUNCT
ejpam-5171	256	18	.	.	PUNCT
ejpam-5171	257	1	if	if	SCONJ
ejpam-5171	257	2	p	p	NOUN
ejpam-5171	257	3	=	=	X
ejpam-5171	257	4	{	{	PUNCT
ejpam-5171	257	5	ϕ	ϕ	NOUN
ejpam-5171	257	6	,	,	PUNCT
ejpam-5171	257	7	{	{	PUNCT
ejpam-5171	257	8	a1	a1	NOUN
ejpam-5171	257	9	}	}	PUNCT
ejpam-5171	257	10	}	}	PUNCT
ejpam-5171	257	11	,	,	PUNCT
ejpam-5171	257	12	then	then	ADV
ejpam-5171	257	13	{	{	PUNCT
ejpam-5171	257	14	a1	a1	NOUN
ejpam-5171	257	15	}	}	PUNCT
ejpam-5171	257	16	is	be	AUX
ejpam-5171	257	17	ptset	ptset	VERB
ejpam-5171	257	18	,	,	PUNCT
ejpam-5171	257	19	ptα	ptα	NOUN
ejpam-5171	257	20	-	-	PUNCT
ejpam-5171	257	21	set	set	NOUN
ejpam-5171	257	22	,	,	PUNCT
ejpam-5171	257	23	pr	pr	NOUN
ejpam-5171	257	24	-	-	PUNCT
ejpam-5171	257	25	set	set	VERB
ejpam-5171	257	26	,	,	PUNCT
ejpam-5171	257	27	and	and	CCONJ
ejpam-5171	257	28	prα	prα	VERB
ejpam-5171	257	29	-	-	PUNCT
ejpam-5171	257	30	set	set	NOUN
ejpam-5171	257	31	,	,	PUNCT
ejpam-5171	257	32	since	since	SCONJ
ejpam-5171	257	33	int({a1	int({a1	NOUN
ejpam-5171	257	34	}	}	PUNCT
ejpam-5171	257	35	)	)	PUNCT
ejpam-5171	257	36	=	=	SYM
ejpam-5171	257	37	int(cl	int(cl	PROPN
ejpam-5171	257	38	♢	♢	PROPN
ejpam-5171	257	39	({a1	({a1	PROPN
ejpam-5171	257	40	}	}	PUNCT
ejpam-5171	257	41	)	)	PUNCT
ejpam-5171	257	42	)	)	PUNCT
ejpam-5171	258	1	=	=	SYM
ejpam-5171	258	2	int(cl	int(cl	NOUN
ejpam-5171	258	3	♢	♢	PROPN
ejpam-5171	258	4	(int({a1	(int({a1	NOUN
ejpam-5171	258	5	}	}	PUNCT
ejpam-5171	258	6	)	)	PUNCT
ejpam-5171	258	7	)	)	PUNCT
ejpam-5171	258	8	)	)	PUNCT
ejpam-5171	259	1	=	=	PRON
ejpam-5171	259	2	{	{	PUNCT
ejpam-5171	259	3	a1	a1	PROPN
ejpam-5171	259	4	}	}	PUNCT
ejpam-5171	259	5	.	.	PUNCT
ejpam-5171	260	1	theorem	theorem	VERB
ejpam-5171	260	2	3.3	3.3	NUM
ejpam-5171	260	3	.	.	PUNCT
ejpam-5171	261	1	assume	assume	VERB
ejpam-5171	261	2	that	that	SCONJ
ejpam-5171	261	3	(	(	PUNCT
ejpam-5171	261	4	x	x	NOUN
ejpam-5171	261	5	,	,	PUNCT
ejpam-5171	261	6	δ	δ	PROPN
ejpam-5171	261	7	,	,	PUNCT
ejpam-5171	261	8	p	p	NOUN
ejpam-5171	261	9	)	)	PUNCT
ejpam-5171	261	10	be	be	AUX
ejpam-5171	261	11	pts	pt	NOUN
ejpam-5171	261	12	.	.	PUNCT
ejpam-5171	262	1	therefore	therefore	ADV
ejpam-5171	262	2	,	,	PUNCT
ejpam-5171	262	3	(	(	PUNCT
ejpam-5171	262	4	a	a	X
ejpam-5171	262	5	)	)	PUNCT
ejpam-5171	262	6	each	each	DET
ejpam-5171	262	7	open	open	ADJ
ejpam-5171	262	8	set	set	NOUN
ejpam-5171	262	9	u	u	NOUN
ejpam-5171	262	10	is	be	AUX
ejpam-5171	262	11	pr	pr	NOUN
ejpam-5171	262	12	-	-	PUNCT
ejpam-5171	262	13	set	set	VERB
ejpam-5171	262	14	.	.	PUNCT
ejpam-5171	263	1	(	(	PUNCT
ejpam-5171	263	2	b	b	X
ejpam-5171	263	3	)	)	PUNCT
ejpam-5171	263	4	each	each	DET
ejpam-5171	263	5	pt	pt	NOUN
ejpam-5171	263	6	-	-	PUNCT
ejpam-5171	263	7	set	set	NOUN
ejpam-5171	263	8	is	be	AUX
ejpam-5171	263	9	pr	pr	NOUN
ejpam-5171	263	10	-	-	PUNCT
ejpam-5171	263	11	set	set	VERB
ejpam-5171	263	12	.	.	PUNCT
ejpam-5171	264	1	proof	proof	NOUN
ejpam-5171	264	2	.	.	PUNCT
ejpam-5171	265	1	(	(	PUNCT
ejpam-5171	265	2	a	a	X
ejpam-5171	265	3	)	)	PUNCT
ejpam-5171	265	4	put	put	VERB
ejpam-5171	265	5	u	u	NOUN
ejpam-5171	265	6	=	=	NOUN
ejpam-5171	265	7	u	u	NOUN
ejpam-5171	265	8	∩	∩	NOUN
ejpam-5171	265	9	x.	x.	NOUN
ejpam-5171	265	10	thus	thus	ADV
ejpam-5171	265	11	,	,	PUNCT
ejpam-5171	265	12	int(cl	int(cl	PROPN
ejpam-5171	265	13	♢	♢	PROPN
ejpam-5171	265	14	(u	(u	PROPN
ejpam-5171	265	15	)	)	PUNCT
ejpam-5171	265	16	)	)	PUNCT
ejpam-5171	266	1	=	=	SYM
ejpam-5171	266	2	int(u	int(u	PROPN
ejpam-5171	266	3	)	)	PUNCT
ejpam-5171	266	4	.	.	PUNCT
ejpam-5171	267	1	(	(	PUNCT
ejpam-5171	267	2	b	b	X
ejpam-5171	267	3	)	)	PUNCT
ejpam-5171	267	4	let	let	VERB
ejpam-5171	267	5	l	l	NOUN
ejpam-5171	267	6	be	be	AUX
ejpam-5171	267	7	a	a	DET
ejpam-5171	267	8	pt	pt	NOUN
ejpam-5171	267	9	-	-	PUNCT
ejpam-5171	267	10	set	set	NOUN
ejpam-5171	267	11	.	.	PUNCT
ejpam-5171	268	1	if	if	SCONJ
ejpam-5171	268	2	we	we	PRON
ejpam-5171	268	3	assume	assume	VERB
ejpam-5171	268	4	that	that	SCONJ
ejpam-5171	268	5	u	u	PRON
ejpam-5171	268	6	=	=	NOUN
ejpam-5171	268	7	x	x	SYM
ejpam-5171	268	8	∈	∈	PROPN
ejpam-5171	268	9	δ	δ	PROPN
ejpam-5171	268	10	,	,	PUNCT
ejpam-5171	268	11	then	then	ADV
ejpam-5171	268	12	l	l	NOUN
ejpam-5171	268	13	=	=	SYM
ejpam-5171	268	14	u	u	NOUN
ejpam-5171	268	15	∩	∩	NOUN
ejpam-5171	268	16	l	l	NOUN
ejpam-5171	268	17	,	,	PUNCT
ejpam-5171	268	18	and	and	CCONJ
ejpam-5171	268	19	hence	hence	ADV
ejpam-5171	268	20	l	l	NOUN
ejpam-5171	268	21	is	be	AUX
ejpam-5171	268	22	pr	pr	NOUN
ejpam-5171	268	23	-	-	PUNCT
ejpam-5171	268	24	set	set	VERB
ejpam-5171	268	25	.	.	PUNCT
ejpam-5171	269	1	remark	remark	PROPN
ejpam-5171	269	2	3.4	3.4	NUM
ejpam-5171	269	3	.	.	PUNCT
ejpam-5171	270	1	the	the	DET
ejpam-5171	270	2	opposite	opposite	NOUN
ejpam-5171	270	3	of	of	ADP
ejpam-5171	270	4	theorem	theorem	ADJ
ejpam-5171	270	5	3.3	3.3	NUM
ejpam-5171	270	6	is	be	AUX
ejpam-5171	270	7	untrue	untrue	ADJ
ejpam-5171	270	8	in	in	ADP
ejpam-5171	270	9	all	all	DET
ejpam-5171	270	10	cases	case	NOUN
ejpam-5171	270	11	,	,	PUNCT
ejpam-5171	270	12	as	as	SCONJ
ejpam-5171	270	13	proved	prove	VERB
ejpam-5171	270	14	in	in	ADP
ejpam-5171	270	15	the	the	DET
ejpam-5171	270	16	following	follow	VERB
ejpam-5171	270	17	examples	example	NOUN
ejpam-5171	270	18	.	.	PUNCT
ejpam-5171	271	1	example	example	NOUN
ejpam-5171	271	2	3.5	3.5	NUM
ejpam-5171	271	3	.	.	PUNCT
ejpam-5171	272	1	in	in	ADP
ejpam-5171	272	2	example	example	NOUN
ejpam-5171	272	3	3.2	3.2	NUM
ejpam-5171	272	4	,	,	PUNCT
ejpam-5171	272	5	the	the	DET
ejpam-5171	272	6	set	set	NOUN
ejpam-5171	272	7	{	{	PUNCT
ejpam-5171	272	8	a2	a2	PROPN
ejpam-5171	272	9	}	}	PUNCT
ejpam-5171	272	10	is	be	AUX
ejpam-5171	272	11	pr	pr	NOUN
ejpam-5171	272	12	-	-	PUNCT
ejpam-5171	272	13	set	set	VERB
ejpam-5171	272	14	.	.	PUNCT
ejpam-5171	273	1	however	however	ADV
ejpam-5171	273	2	,	,	PUNCT
ejpam-5171	273	3	it	it	PRON
ejpam-5171	273	4	is	be	AUX
ejpam-5171	273	5	not	not	PART
ejpam-5171	273	6	an	an	DET
ejpam-5171	273	7	open	open	ADJ
ejpam-5171	273	8	set	set	NOUN
ejpam-5171	273	9	.	.	PUNCT
ejpam-5171	273	10	example	example	NOUN
ejpam-5171	274	1	3.6	3.6	NUM
ejpam-5171	274	2	.	.	PUNCT
ejpam-5171	275	1	consider	consider	VERB
ejpam-5171	275	2	x	x	PUNCT
ejpam-5171	275	3	=	=	PRON
ejpam-5171	275	4	{	{	PUNCT
ejpam-5171	275	5	a1	a1	PROPN
ejpam-5171	275	6	,	,	PUNCT
ejpam-5171	275	7	a2	a2	PROPN
ejpam-5171	275	8	,	,	PUNCT
ejpam-5171	275	9	a3	a3	NOUN
ejpam-5171	275	10	}	}	PUNCT
ejpam-5171	275	11	,	,	PUNCT
ejpam-5171	275	12	δ	δ	PROPN
ejpam-5171	275	13	=	=	PRON
ejpam-5171	275	14	{	{	PUNCT
ejpam-5171	275	15	ϕ	ϕ	NOUN
ejpam-5171	275	16	,	,	PUNCT
ejpam-5171	275	17	{	{	PUNCT
ejpam-5171	275	18	a3},x	a3},x	NOUN
ejpam-5171	275	19	}	}	PUNCT
ejpam-5171	275	20	and	and	CCONJ
ejpam-5171	275	21	p	p	NOUN
ejpam-5171	275	22	=	=	X
ejpam-5171	275	23	{	{	PUNCT
ejpam-5171	275	24	ϕ	ϕ	NOUN
ejpam-5171	275	25	,	,	PUNCT
ejpam-5171	275	26	{	{	PUNCT
ejpam-5171	275	27	a1	a1	NOUN
ejpam-5171	275	28	}	}	PUNCT
ejpam-5171	275	29	,	,	PUNCT
ejpam-5171	275	30	{	{	PUNCT
ejpam-5171	275	31	a2	a2	PROPN
ejpam-5171	275	32	}	}	PUNCT
ejpam-5171	275	33	,	,	PUNCT
ejpam-5171	275	34	{	{	PUNCT
ejpam-5171	275	35	a1	a1	NOUN
ejpam-5171	275	36	,	,	PUNCT
ejpam-5171	275	37	a2	a2	PROPN
ejpam-5171	275	38	}	}	PUNCT
ejpam-5171	275	39	}	}	PUNCT
ejpam-5171	275	40	.	.	PUNCT
ejpam-5171	276	1	then	then	ADV
ejpam-5171	276	2	,	,	PUNCT
ejpam-5171	276	3	{	{	PUNCT
ejpam-5171	276	4	a3	a3	NOUN
ejpam-5171	276	5	}	}	PUNCT
ejpam-5171	276	6	is	be	AUX
ejpam-5171	276	7	pr	pr	NOUN
ejpam-5171	276	8	-	-	PUNCT
ejpam-5171	276	9	set	set	VERB
ejpam-5171	276	10	but	but	CCONJ
ejpam-5171	276	11	not	not	PART
ejpam-5171	276	12	pt	pt	NOUN
ejpam-5171	276	13	-	-	PUNCT
ejpam-5171	276	14	set	set	NOUN
ejpam-5171	276	15	,	,	PUNCT
ejpam-5171	276	16	since	since	SCONJ
ejpam-5171	276	17	{	{	PUNCT
ejpam-5171	276	18	a3	a3	VERB
ejpam-5171	276	19	}	}	PUNCT
ejpam-5171	276	20	=	=	SYM
ejpam-5171	276	21	int({a3	int({a3	PROPN
ejpam-5171	276	22	}	}	PUNCT
ejpam-5171	276	23	)	)	PUNCT
ejpam-5171	277	1	̸=	̸=	PROPN
ejpam-5171	277	2	int(cl	int(cl	ADJ
ejpam-5171	277	3	♢	♢	PROPN
ejpam-5171	277	4	({a3	({a3	PROPN
ejpam-5171	277	5	}	}	PUNCT
ejpam-5171	277	6	)	)	PUNCT
ejpam-5171	277	7	)	)	PUNCT
ejpam-5171	278	1	=	=	PUNCT
ejpam-5171	278	2	x.	x.	NOUN
ejpam-5171	278	3	proposition	proposition	NOUN
ejpam-5171	278	4	3.7	3.7	NUM
ejpam-5171	278	5	.	.	PUNCT
ejpam-5171	278	6	suppose	suppose	VERB
ejpam-5171	278	7	that	that	SCONJ
ejpam-5171	278	8	l	l	PROPN
ejpam-5171	278	9	and	and	CCONJ
ejpam-5171	278	10	e	e	PROPN
ejpam-5171	278	11	are	be	AUX
ejpam-5171	278	12	subsets	subset	NOUN
ejpam-5171	278	13	of	of	ADP
ejpam-5171	278	14	the	the	DET
ejpam-5171	278	15	space	space	NOUN
ejpam-5171	278	16	(	(	PUNCT
ejpam-5171	278	17	x	x	NOUN
ejpam-5171	278	18	,	,	PUNCT
ejpam-5171	278	19	δ	δ	PROPN
ejpam-5171	278	20	,	,	PUNCT
ejpam-5171	278	21	p	p	NOUN
ejpam-5171	278	22	)	)	PUNCT
ejpam-5171	278	23	.	.	PUNCT
ejpam-5171	279	1	if	if	SCONJ
ejpam-5171	279	2	l	l	PROPN
ejpam-5171	279	3	and	and	CCONJ
ejpam-5171	279	4	e	e	PROPN
ejpam-5171	279	5	are	be	AUX
ejpam-5171	279	6	pt	pt	NOUN
ejpam-5171	279	7	-	-	PUNCT
ejpam-5171	279	8	sets	set	NOUN
ejpam-5171	279	9	,	,	PUNCT
ejpam-5171	279	10	then	then	ADV
ejpam-5171	279	11	l	l	NOUN
ejpam-5171	279	12	∩	∩	NOUN
ejpam-5171	279	13	e	e	NOUN
ejpam-5171	279	14	is	be	AUX
ejpam-5171	279	15	a	a	DET
ejpam-5171	279	16	pt	pt	NOUN
ejpam-5171	279	17	-	-	PUNCT
ejpam-5171	279	18	set	set	NOUN
ejpam-5171	279	19	.	.	PUNCT
ejpam-5171	280	1	proof	proof	NOUN
ejpam-5171	280	2	.	.	PUNCT
ejpam-5171	281	1	let	let	VERB
ejpam-5171	281	2	l	l	NOUN
ejpam-5171	281	3	and	and	CCONJ
ejpam-5171	281	4	e	e	NOUN
ejpam-5171	281	5	be	be	AUX
ejpam-5171	281	6	pt	pt	NOUN
ejpam-5171	281	7	-	-	PUNCT
ejpam-5171	281	8	sets	set	NOUN
ejpam-5171	281	9	.	.	PUNCT
ejpam-5171	282	1	we	we	PRON
ejpam-5171	282	2	have	have	VERB
ejpam-5171	282	3	int(l∩e	int(l∩e	NOUN
ejpam-5171	282	4	)	)	PUNCT
ejpam-5171	283	1	⊂	⊂	PROPN
ejpam-5171	283	2	int(cl	int(cl	PROPN
ejpam-5171	283	3	♢	♢	PROPN
ejpam-5171	283	4	(l∩e	(l∩e	PROPN
ejpam-5171	283	5	)	)	PUNCT
ejpam-5171	283	6	)	)	PUNCT
ejpam-5171	284	1	⊂	⊂	PROPN
ejpam-5171	284	2	int(cl	int(cl	PROPN
ejpam-5171	284	3	♢	♢	PROPN
ejpam-5171	284	4	(l)∩	(l)∩	PROPN
ejpam-5171	284	5	cl	cl	PROPN
ejpam-5171	284	6	♢	♢	PROPN
ejpam-5171	284	7	(e	(e	NOUN
ejpam-5171	284	8	)	)	PUNCT
ejpam-5171	284	9	)	)	PUNCT
ejpam-5171	284	10	=	=	SYM
ejpam-5171	284	11	int(cl	int(cl	PROPN
ejpam-5171	284	12	♢	♢	PROPN
ejpam-5171	284	13	(l))∩	(l))∩	PROPN
ejpam-5171	284	14	int(cl	int(cl	PROPN
ejpam-5171	284	15	♢	♢	PROPN
ejpam-5171	284	16	(e	(e	NOUN
ejpam-5171	284	17	)	)	PUNCT
ejpam-5171	284	18	)	)	PUNCT
ejpam-5171	284	19	=	=	PUNCT
ejpam-5171	284	20	int(l)∩	int(l)∩	NOUN
ejpam-5171	284	21	int(e	int(e	NOUN
ejpam-5171	284	22	)	)	PUNCT
ejpam-5171	284	23	=	=	SYM
ejpam-5171	284	24	int(l∩e	int(l∩e	NOUN
ejpam-5171	284	25	)	)	PUNCT
ejpam-5171	284	26	.	.	PUNCT
ejpam-5171	285	1	then	then	ADV
ejpam-5171	285	2	int(l∩e	int(l∩e	VERB
ejpam-5171	285	3	)	)	PUNCT
ejpam-5171	286	1	=	=	SYM
ejpam-5171	286	2	int(cl	int(cl	PROPN
ejpam-5171	286	3	♢	♢	PROPN
ejpam-5171	286	4	(l	(l	PROPN
ejpam-5171	286	5	∩	∩	PROPN
ejpam-5171	286	6	e	e	NOUN
ejpam-5171	286	7	)	)	PUNCT
ejpam-5171	286	8	)	)	PUNCT
ejpam-5171	286	9	,	,	PUNCT
ejpam-5171	286	10	and	and	CCONJ
ejpam-5171	286	11	hence	hence	ADV
ejpam-5171	286	12	l	l	NOUN
ejpam-5171	286	13	∩	∩	NOUN
ejpam-5171	286	14	e	e	NOUN
ejpam-5171	286	15	is	be	AUX
ejpam-5171	286	16	a	a	DET
ejpam-5171	286	17	pt	pt	NOUN
ejpam-5171	286	18	-	-	PUNCT
ejpam-5171	286	19	set	set	NOUN
ejpam-5171	286	20	.	.	PUNCT
ejpam-5171	287	1	the	the	DET
ejpam-5171	287	2	example	example	NOUN
ejpam-5171	287	3	below	below	ADP
ejpam-5171	287	4	shows	show	VERB
ejpam-5171	287	5	that	that	SCONJ
ejpam-5171	287	6	the	the	DET
ejpam-5171	287	7	union	union	NOUN
ejpam-5171	287	8	of	of	ADP
ejpam-5171	287	9	two	two	NUM
ejpam-5171	287	10	pt	pt	NOUN
ejpam-5171	287	11	-	-	PUNCT
ejpam-5171	287	12	sets	set	NOUN
ejpam-5171	287	13	need	need	AUX
ejpam-5171	287	14	not	not	PART
ejpam-5171	287	15	be	be	AUX
ejpam-5171	287	16	a	a	DET
ejpam-5171	287	17	pt	pt	NOUN
ejpam-5171	287	18	-	-	PUNCT
ejpam-5171	287	19	sets	set	NOUN
ejpam-5171	287	20	.	.	PUNCT
ejpam-5171	288	1	example	example	NOUN
ejpam-5171	288	2	3.8	3.8	NUM
ejpam-5171	288	3	.	.	PUNCT
ejpam-5171	289	1	consider	consider	VERB
ejpam-5171	289	2	x	x	PUNCT
ejpam-5171	289	3	=	=	PRON
ejpam-5171	289	4	{	{	PUNCT
ejpam-5171	289	5	a1	a1	PROPN
ejpam-5171	289	6	,	,	PUNCT
ejpam-5171	289	7	a2	a2	PROPN
ejpam-5171	289	8	,	,	PUNCT
ejpam-5171	289	9	a3	a3	NOUN
ejpam-5171	289	10	,	,	PUNCT
ejpam-5171	289	11	a4	a4	PROPN
ejpam-5171	289	12	}	}	PUNCT
ejpam-5171	289	13	,	,	PUNCT
ejpam-5171	289	14	δ	δ	PROPN
ejpam-5171	289	15	=	=	PRON
ejpam-5171	289	16	{	{	PUNCT
ejpam-5171	289	17	ϕ	ϕ	NOUN
ejpam-5171	289	18	,	,	PUNCT
ejpam-5171	289	19	{	{	PUNCT
ejpam-5171	289	20	a1	a1	NOUN
ejpam-5171	289	21	,	,	PUNCT
ejpam-5171	289	22	a3},x	a3},x	NOUN
ejpam-5171	289	23	}	}	PUNCT
ejpam-5171	289	24	,	,	PUNCT
ejpam-5171	289	25	with	with	ADP
ejpam-5171	289	26	the	the	DET
ejpam-5171	289	27	primal	primal	ADJ
ejpam-5171	289	28	p	p	X
ejpam-5171	289	29	=	=	X
ejpam-5171	289	30	{	{	PUNCT
ejpam-5171	289	31	ϕ	ϕ	NOUN
ejpam-5171	289	32	,	,	PUNCT
ejpam-5171	289	33	{	{	PUNCT
ejpam-5171	289	34	a1	a1	NOUN
ejpam-5171	289	35	}	}	PUNCT
ejpam-5171	289	36	,	,	PUNCT
ejpam-5171	289	37	{	{	PUNCT
ejpam-5171	289	38	a2	a2	PROPN
ejpam-5171	289	39	}	}	PUNCT
ejpam-5171	289	40	,	,	PUNCT
ejpam-5171	289	41	{	{	PUNCT
ejpam-5171	289	42	a3	a3	NOUN
ejpam-5171	289	43	}	}	PUNCT
ejpam-5171	289	44	,	,	PUNCT
ejpam-5171	289	45	{	{	PUNCT
ejpam-5171	289	46	a1	a1	NOUN
ejpam-5171	289	47	,	,	PUNCT
ejpam-5171	289	48	a2	a2	PROPN
ejpam-5171	289	49	}	}	PUNCT
ejpam-5171	289	50	,	,	PUNCT
ejpam-5171	289	51	{	{	PUNCT
ejpam-5171	289	52	a1	a1	NOUN
ejpam-5171	289	53	,	,	PUNCT
ejpam-5171	289	54	a3	a3	NOUN
ejpam-5171	289	55	}	}	PUNCT
ejpam-5171	289	56	,	,	PUNCT
ejpam-5171	289	57	{	{	PUNCT
ejpam-5171	289	58	a2	a2	NOUN
ejpam-5171	289	59	,	,	PUNCT
ejpam-5171	289	60	a3	a3	NOUN
ejpam-5171	289	61	}	}	PUNCT
ejpam-5171	289	62	,	,	PUNCT
ejpam-5171	289	63	{	{	PUNCT
ejpam-5171	289	64	a1	a1	NOUN
ejpam-5171	289	65	,	,	PUNCT
ejpam-5171	289	66	a2	a2	PROPN
ejpam-5171	289	67	,	,	PUNCT
ejpam-5171	289	68	a3	a3	NOUN
ejpam-5171	289	69	}	}	PUNCT
ejpam-5171	289	70	}	}	PUNCT
ejpam-5171	289	71	.	.	PUNCT
ejpam-5171	290	1	then	then	ADV
ejpam-5171	290	2	,	,	PUNCT
ejpam-5171	290	3	l	l	NOUN
ejpam-5171	290	4	=	=	SYM
ejpam-5171	290	5	{	{	PUNCT
ejpam-5171	290	6	a1	a1	NOUN
ejpam-5171	290	7	,	,	PUNCT
ejpam-5171	290	8	a3	a3	NOUN
ejpam-5171	290	9	}	}	PUNCT
ejpam-5171	290	10	and	and	CCONJ
ejpam-5171	290	11	e	e	X
ejpam-5171	290	12	=	=	SYM
ejpam-5171	290	13	{	{	PUNCT
ejpam-5171	290	14	a1	a1	PROPN
ejpam-5171	290	15	,	,	PUNCT
ejpam-5171	290	16	a4	a4	NOUN
ejpam-5171	290	17	}	}	PUNCT
ejpam-5171	290	18	are	be	AUX
ejpam-5171	290	19	ptsets	ptset	NOUN
ejpam-5171	290	20	,	,	PUNCT
ejpam-5171	290	21	since	since	SCONJ
ejpam-5171	290	22	int({a1	int({a1	NUM
ejpam-5171	290	23	,	,	PUNCT
ejpam-5171	290	24	a3	a3	NOUN
ejpam-5171	290	25	}	}	PUNCT
ejpam-5171	290	26	)	)	PUNCT
ejpam-5171	291	1	=	=	SYM
ejpam-5171	291	2	int(cl	int(cl	PROPN
ejpam-5171	291	3	♢	♢	PROPN
ejpam-5171	291	4	({a1	({a1	PROPN
ejpam-5171	291	5	,	,	PUNCT
ejpam-5171	291	6	a3	a3	NOUN
ejpam-5171	291	7	}	}	PUNCT
ejpam-5171	291	8	)	)	PUNCT
ejpam-5171	292	1	=	=	PRON
ejpam-5171	292	2	{	{	PUNCT
ejpam-5171	292	3	a1	a1	NOUN
ejpam-5171	292	4	,	,	PUNCT
ejpam-5171	292	5	a3	a3	NOUN
ejpam-5171	292	6	}	}	PUNCT
ejpam-5171	292	7	and	and	CCONJ
ejpam-5171	292	8	int({a1	int({a1	NUM
ejpam-5171	292	9	,	,	PUNCT
ejpam-5171	292	10	a4	a4	NOUN
ejpam-5171	292	11	}	}	PUNCT
ejpam-5171	292	12	)	)	PUNCT
ejpam-5171	292	13	=	=	SYM
ejpam-5171	292	14	int(cl	int(cl	PROPN
ejpam-5171	292	15	♢	♢	PROPN
ejpam-5171	292	16	({a1	({a1	PROPN
ejpam-5171	292	17	,	,	PUNCT
ejpam-5171	292	18	a4	a4	PROPN
ejpam-5171	292	19	}	}	PUNCT
ejpam-5171	292	20	)	)	PUNCT
ejpam-5171	292	21	=	=	SYM
ejpam-5171	292	22	ϕ	ϕ	NOUN
ejpam-5171	292	23	,	,	PUNCT
ejpam-5171	292	24	but	but	CCONJ
ejpam-5171	292	25	l	l	NOUN
ejpam-5171	292	26	∪	∪	X
ejpam-5171	292	27	e	e	X
ejpam-5171	292	28	=	=	SYM
ejpam-5171	292	29	{	{	PUNCT
ejpam-5171	292	30	a1	a1	PROPN
ejpam-5171	292	31	,	,	PUNCT
ejpam-5171	292	32	a3	a3	NOUN
ejpam-5171	292	33	a4	a4	PROPN
ejpam-5171	292	34	}	}	PUNCT
ejpam-5171	292	35	is	be	AUX
ejpam-5171	292	36	not	not	PART
ejpam-5171	292	37	pt	pt	NOUN
ejpam-5171	292	38	-	-	PUNCT
ejpam-5171	292	39	set	set	NOUN
ejpam-5171	292	40	.	.	PUNCT
ejpam-5171	293	1	proposition	proposition	NOUN
ejpam-5171	293	2	3.9	3.9	NUM
ejpam-5171	293	3	.	.	PUNCT
ejpam-5171	294	1	assume	assume	VERB
ejpam-5171	294	2	that	that	SCONJ
ejpam-5171	294	3	(	(	PUNCT
ejpam-5171	294	4	x	x	NOUN
ejpam-5171	294	5	,	,	PUNCT
ejpam-5171	294	6	δ	δ	PROPN
ejpam-5171	294	7	,	,	PUNCT
ejpam-5171	294	8	p	p	NOUN
ejpam-5171	294	9	)	)	PUNCT
ejpam-5171	294	10	is	be	AUX
ejpam-5171	294	11	a	a	DET
ejpam-5171	294	12	pts	pt	NOUN
ejpam-5171	294	13	.	.	PUNCT
ejpam-5171	295	1	the	the	DET
ejpam-5171	295	2	following	follow	VERB
ejpam-5171	295	3	statements	statement	NOUN
ejpam-5171	295	4	are	be	AUX
ejpam-5171	295	5	equivalent	equivalent	ADJ
ejpam-5171	295	6	for	for	ADP
ejpam-5171	295	7	a	a	DET
ejpam-5171	295	8	subset	subset	NOUN
ejpam-5171	295	9	l	l	NOUN
ejpam-5171	295	10	of	of	ADP
ejpam-5171	295	11	x	x	NOUN
ejpam-5171	295	12	:	:	PUNCT
ejpam-5171	295	13	(	(	PUNCT
ejpam-5171	295	14	a	a	X
ejpam-5171	295	15	)	)	PUNCT
ejpam-5171	295	16	l	l	NOUN
ejpam-5171	295	17	is	be	AUX
ejpam-5171	295	18	open	open	ADJ
ejpam-5171	295	19	,	,	PUNCT
ejpam-5171	295	20	(	(	PUNCT
ejpam-5171	295	21	b	b	X
ejpam-5171	295	22	)	)	PUNCT
ejpam-5171	295	23	l	l	NOUN
ejpam-5171	295	24	is	be	AUX
ejpam-5171	295	25	p	p	NOUN
ejpam-5171	295	26	-	-	PUNCT
ejpam-5171	295	27	pre	pre	NOUN
ejpam-5171	295	28	-	-	ADJ
ejpam-5171	295	29	open	open	ADJ
ejpam-5171	295	30	and	and	CCONJ
ejpam-5171	295	31	pr	pr	NOUN
ejpam-5171	295	32	-	-	PUNCT
ejpam-5171	295	33	set	set	NOUN
ejpam-5171	295	34	.	.	PUNCT
ejpam-5171	296	1	h.	h.	PROPN
ejpam-5171	296	2	al	al	PROPN
ejpam-5171	296	3	-	-	PUNCT
ejpam-5171	296	4	saadi	saadi	PROPN
ejpam-5171	296	5	,	,	PUNCT
ejpam-5171	296	6	m.	m.	NOUN
ejpam-5171	296	7	al	al	PROPN
ejpam-5171	296	8	-	-	PUNCT
ejpam-5171	296	9	hodieb	hodieb	PROPN
ejpam-5171	296	10	/	/	SYM
ejpam-5171	296	11	eur	eur	PROPN
ejpam-5171	296	12	.	.	PUNCT
ejpam-5171	297	1	j.	j.	PROPN
ejpam-5171	297	2	pure	pure	PROPN
ejpam-5171	297	3	appl	appl	PROPN
ejpam-5171	297	4	.	.	PROPN
ejpam-5171	297	5	math	math	PROPN
ejpam-5171	297	6	,	,	PUNCT
ejpam-5171	297	7	17	17	NUM
ejpam-5171	297	8	(	(	PUNCT
ejpam-5171	297	9	2	2	NUM
ejpam-5171	297	10	)	)	PUNCT
ejpam-5171	297	11	(	(	PUNCT
ejpam-5171	297	12	2024	2024	NUM
ejpam-5171	297	13	)	)	PUNCT
ejpam-5171	297	14	,	,	PUNCT
ejpam-5171	297	15	1352	1352	NUM
ejpam-5171	297	16	-	-	SYM
ejpam-5171	297	17	1368	1368	NUM
ejpam-5171	297	18	1361	1361	NUM
ejpam-5171	297	19	proof	proof	NOUN
ejpam-5171	297	20	.	.	PUNCT
ejpam-5171	298	1	(	(	PUNCT
ejpam-5171	298	2	a)⇒(b	a)⇒(b	PROPN
ejpam-5171	298	3	)	)	PUNCT
ejpam-5171	298	4	:	:	PUNCT
ejpam-5171	298	5	consider	consider	VERB
ejpam-5171	298	6	l	l	NOUN
ejpam-5171	298	7	as	as	ADV
ejpam-5171	298	8	open	open	ADJ
ejpam-5171	298	9	.	.	PUNCT
ejpam-5171	299	1	thus	thus	ADV
ejpam-5171	299	2	,	,	PUNCT
ejpam-5171	299	3	l	l	NOUN
ejpam-5171	299	4	=	=	SYM
ejpam-5171	299	5	int(l	int(l	PROPN
ejpam-5171	299	6	)	)	PUNCT
ejpam-5171	299	7	⊂	⊂	PROPN
ejpam-5171	299	8	int(cl	int(cl	PROPN
ejpam-5171	299	9	♢	♢	PROPN
ejpam-5171	299	10	(l	(l	PROPN
ejpam-5171	299	11	)	)	PUNCT
ejpam-5171	299	12	)	)	PUNCT
ejpam-5171	299	13	,	,	PUNCT
ejpam-5171	299	14	and	and	CCONJ
ejpam-5171	299	15	l	l	NOUN
ejpam-5171	299	16	is	be	AUX
ejpam-5171	299	17	p	p	NOUN
ejpam-5171	299	18	-	-	PUNCT
ejpam-5171	299	19	pre	pre	NOUN
ejpam-5171	299	20	-	-	ADJ
ejpam-5171	299	21	open	open	ADJ
ejpam-5171	299	22	.	.	PUNCT
ejpam-5171	300	1	also	also	ADV
ejpam-5171	300	2	by	by	ADP
ejpam-5171	300	3	theorem	theorem	NOUN
ejpam-5171	300	4	3.3	3.3	NUM
ejpam-5171	300	5	,	,	PUNCT
ejpam-5171	300	6	l	l	NOUN
ejpam-5171	300	7	is	be	AUX
ejpam-5171	300	8	pr	pr	NOUN
ejpam-5171	300	9	-	-	PUNCT
ejpam-5171	300	10	set	set	VERB
ejpam-5171	300	11	.	.	PUNCT
ejpam-5171	301	1	(	(	PUNCT
ejpam-5171	301	2	b	b	X
ejpam-5171	301	3	)	)	PUNCT
ejpam-5171	301	4	⇒	⇒	NOUN
ejpam-5171	301	5	(	(	PUNCT
ejpam-5171	301	6	a	a	X
ejpam-5171	301	7	):	):	PUNCT
ejpam-5171	301	8	consider	consider	VERB
ejpam-5171	301	9	l	l	NOUN
ejpam-5171	301	10	as	as	ADP
ejpam-5171	301	11	a	a	DET
ejpam-5171	301	12	pr	pr	NOUN
ejpam-5171	301	13	-	-	PUNCT
ejpam-5171	301	14	set	set	NOUN
ejpam-5171	301	15	.	.	PUNCT
ejpam-5171	302	1	so	so	ADV
ejpam-5171	302	2	l	l	NOUN
ejpam-5171	302	3	=	=	SYM
ejpam-5171	302	4	l1	l1	PROPN
ejpam-5171	302	5	∩	∩	ADJ
ejpam-5171	302	6	l2	l2	NOUN
ejpam-5171	302	7	,	,	PUNCT
ejpam-5171	302	8	where	where	SCONJ
ejpam-5171	302	9	l1	l1	PROPN
ejpam-5171	302	10	is	be	AUX
ejpam-5171	302	11	open	open	ADJ
ejpam-5171	302	12	,	,	PUNCT
ejpam-5171	302	13	and	and	CCONJ
ejpam-5171	302	14	int(q	int(q	NOUN
ejpam-5171	302	15	)	)	PUNCT
ejpam-5171	302	16	=	=	SYM
ejpam-5171	302	17	int(cl(q	int(cl(q	PROPN
ejpam-5171	302	18	)	)	PUNCT
ejpam-5171	302	19	)	)	PUNCT
ejpam-5171	302	20	.	.	PUNCT
ejpam-5171	303	1	thus	thus	ADV
ejpam-5171	303	2	,	,	PUNCT
ejpam-5171	303	3	l	l	PROPN
ejpam-5171	303	4	⊆	⊆	NUM
ejpam-5171	303	5	l1	l1	PROPN
ejpam-5171	303	6	=	=	SYM
ejpam-5171	303	7	int(l1	int(l1	PROPN
ejpam-5171	303	8	)	)	PUNCT
ejpam-5171	303	9	.	.	PUNCT
ejpam-5171	304	1	also	also	ADV
ejpam-5171	304	2	,	,	PUNCT
ejpam-5171	304	3	l	l	PROPN
ejpam-5171	304	4	is	be	AUX
ejpam-5171	304	5	p	p	NOUN
ejpam-5171	304	6	-	-	PUNCT
ejpam-5171	304	7	pre	pre	VERB
ejpam-5171	304	8	-	-	ADJ
ejpam-5171	304	9	open	open	ADJ
ejpam-5171	304	10	implies	imply	VERB
ejpam-5171	304	11	l	l	NOUN
ejpam-5171	304	12	⊆	⊆	NUM
ejpam-5171	304	13	int(cl(l	int(cl(l	NOUN
ejpam-5171	304	14	)	)	PUNCT
ejpam-5171	304	15	)	)	PUNCT
ejpam-5171	305	1	⊂	⊂	PROPN
ejpam-5171	305	2	int(cl	int(cl	PROPN
ejpam-5171	305	3	♢	♢	PROPN
ejpam-5171	305	4	(l2	(l2	X
ejpam-5171	305	5	)	)	PUNCT
ejpam-5171	305	6	)	)	PUNCT
ejpam-5171	306	1	=	=	PUNCT
ejpam-5171	306	2	int(l2	int(l2	NOUN
ejpam-5171	306	3	)	)	PUNCT
ejpam-5171	306	4	by	by	ADP
ejpam-5171	306	5	assumption	assumption	NOUN
ejpam-5171	306	6	.	.	PUNCT
ejpam-5171	307	1	consequently	consequently	ADV
ejpam-5171	307	2	,	,	PUNCT
ejpam-5171	307	3	l	l	PROPN
ejpam-5171	307	4	⊆	⊆	NUM
ejpam-5171	307	5	int(l1	int(l1	NOUN
ejpam-5171	307	6	)	)	PUNCT
ejpam-5171	307	7	∩	∩	NOUN
ejpam-5171	307	8	int(l2	int(l2	NOUN
ejpam-5171	307	9	)	)	PUNCT
ejpam-5171	307	10	=	=	SYM
ejpam-5171	307	11	int(l1	int(l1	PROPN
ejpam-5171	307	12	∩	∩	ADJ
ejpam-5171	307	13	l2	l2	NOUN
ejpam-5171	307	14	)	)	PUNCT
ejpam-5171	307	15	=	=	SYM
ejpam-5171	307	16	int(l	int(l	PROPN
ejpam-5171	307	17	)	)	PUNCT
ejpam-5171	307	18	,	,	PUNCT
ejpam-5171	307	19	and	and	CCONJ
ejpam-5171	307	20	so	so	ADV
ejpam-5171	307	21	l	l	NOUN
ejpam-5171	307	22	is	be	AUX
ejpam-5171	307	23	open	open	ADJ
ejpam-5171	307	24	.	.	PUNCT
ejpam-5171	308	1	remark	remark	PROPN
ejpam-5171	308	2	3.10	3.10	NUM
ejpam-5171	308	3	.	.	PUNCT
ejpam-5171	309	1	suppose	suppose	VERB
ejpam-5171	309	2	that	that	SCONJ
ejpam-5171	309	3	(	(	PUNCT
ejpam-5171	309	4	x	x	X
ejpam-5171	309	5	,	,	PUNCT
ejpam-5171	309	6	δ	δ	PROPN
ejpam-5171	309	7	,	,	PUNCT
ejpam-5171	309	8	p	p	NOUN
ejpam-5171	309	9	)	)	PUNCT
ejpam-5171	309	10	is	be	AUX
ejpam-5171	309	11	a	a	DET
ejpam-5171	309	12	pts	pt	NOUN
ejpam-5171	309	13	.	.	PUNCT
ejpam-5171	310	1	so	so	ADV
ejpam-5171	310	2	,	,	PUNCT
ejpam-5171	310	3	the	the	DET
ejpam-5171	310	4	concepts	concept	NOUN
ejpam-5171	310	5	of	of	ADP
ejpam-5171	310	6	p	p	NOUN
ejpam-5171	310	7	-	-	PUNCT
ejpam-5171	310	8	pre	pre	ADJ
ejpam-5171	310	9	-	-	ADJ
ejpam-5171	310	10	open	open	ADJ
ejpam-5171	310	11	sets	set	NOUN
ejpam-5171	310	12	and	and	CCONJ
ejpam-5171	310	13	pr	pr	NOUN
ejpam-5171	310	14	-	-	PUNCT
ejpam-5171	310	15	sets	set	NOUN
ejpam-5171	310	16	are	be	AUX
ejpam-5171	310	17	independent	independent	ADJ
ejpam-5171	310	18	.	.	PUNCT
ejpam-5171	310	19	example	example	NOUN
ejpam-5171	311	1	3.11	3.11	NUM
ejpam-5171	311	2	.	.	PUNCT
ejpam-5171	312	1	(	(	PUNCT
ejpam-5171	312	2	a	a	X
ejpam-5171	312	3	)	)	PUNCT
ejpam-5171	312	4	consider	consider	VERB
ejpam-5171	312	5	x	x	X
ejpam-5171	312	6	=	=	PRON
ejpam-5171	312	7	{	{	PUNCT
ejpam-5171	312	8	a1	a1	PROPN
ejpam-5171	312	9	,	,	PUNCT
ejpam-5171	312	10	a2	a2	PROPN
ejpam-5171	312	11	,	,	PUNCT
ejpam-5171	312	12	a3	a3	NOUN
ejpam-5171	312	13	,	,	PUNCT
ejpam-5171	312	14	a4	a4	PROPN
ejpam-5171	312	15	}	}	PUNCT
ejpam-5171	312	16	,	,	PUNCT
ejpam-5171	312	17	δ	δ	PROPN
ejpam-5171	312	18	=	=	PRON
ejpam-5171	312	19	{	{	PUNCT
ejpam-5171	312	20	ϕ	ϕ	NOUN
ejpam-5171	312	21	,	,	PUNCT
ejpam-5171	312	22	{	{	PUNCT
ejpam-5171	312	23	a1	a1	NOUN
ejpam-5171	312	24	,	,	PUNCT
ejpam-5171	312	25	a3},x	a3},x	NOUN
ejpam-5171	312	26	}	}	PUNCT
ejpam-5171	312	27	,	,	PUNCT
ejpam-5171	312	28	with	with	ADP
ejpam-5171	312	29	the	the	DET
ejpam-5171	312	30	primal	primal	ADJ
ejpam-5171	312	31	p	p	X
ejpam-5171	312	32	=	=	X
ejpam-5171	312	33	{	{	PUNCT
ejpam-5171	312	34	ϕ	ϕ	NOUN
ejpam-5171	312	35	,	,	PUNCT
ejpam-5171	312	36	{	{	PUNCT
ejpam-5171	312	37	a1	a1	NOUN
ejpam-5171	312	38	}	}	PUNCT
ejpam-5171	312	39	,	,	PUNCT
ejpam-5171	312	40	{	{	PUNCT
ejpam-5171	312	41	a2	a2	PROPN
ejpam-5171	312	42	}	}	PUNCT
ejpam-5171	312	43	,	,	PUNCT
ejpam-5171	312	44	{	{	PUNCT
ejpam-5171	312	45	a3	a3	NOUN
ejpam-5171	312	46	}	}	PUNCT
ejpam-5171	312	47	,	,	PUNCT
ejpam-5171	312	48	{	{	PUNCT
ejpam-5171	312	49	a1	a1	NOUN
ejpam-5171	312	50	,	,	PUNCT
ejpam-5171	312	51	a2	a2	PROPN
ejpam-5171	312	52	}	}	PUNCT
ejpam-5171	312	53	,	,	PUNCT
ejpam-5171	312	54	{	{	PUNCT
ejpam-5171	312	55	a1	a1	NOUN
ejpam-5171	312	56	,	,	PUNCT
ejpam-5171	312	57	a3	a3	NOUN
ejpam-5171	312	58	}	}	PUNCT
ejpam-5171	312	59	,	,	PUNCT
ejpam-5171	312	60	{	{	PUNCT
ejpam-5171	312	61	a2	a2	NOUN
ejpam-5171	312	62	,	,	PUNCT
ejpam-5171	312	63	a3	a3	NOUN
ejpam-5171	312	64	}	}	PUNCT
ejpam-5171	312	65	,	,	PUNCT
ejpam-5171	312	66	{	{	PUNCT
ejpam-5171	312	67	a1	a1	NOUN
ejpam-5171	312	68	,	,	PUNCT
ejpam-5171	312	69	a2	a2	PROPN
ejpam-5171	312	70	,	,	PUNCT
ejpam-5171	312	71	a3	a3	NOUN
ejpam-5171	312	72	}	}	PUNCT
ejpam-5171	312	73	}	}	PUNCT
ejpam-5171	312	74	.	.	PUNCT
ejpam-5171	313	1	thus	thus	ADV
ejpam-5171	313	2	,	,	PUNCT
ejpam-5171	313	3	l	l	NOUN
ejpam-5171	313	4	=	=	SYM
ejpam-5171	313	5	{	{	PUNCT
ejpam-5171	313	6	a1	a1	NOUN
ejpam-5171	313	7	,	,	PUNCT
ejpam-5171	313	8	a3	a3	NOUN
ejpam-5171	313	9	,	,	PUNCT
ejpam-5171	313	10	a4	a4	PROPN
ejpam-5171	313	11	}	}	PUNCT
ejpam-5171	313	12	is	be	AUX
ejpam-5171	313	13	p	p	ADJ
ejpam-5171	313	14	-	-	PUNCT
ejpam-5171	313	15	pre	pre	NOUN
ejpam-5171	313	16	-	-	ADJ
ejpam-5171	313	17	open	open	ADJ
ejpam-5171	313	18	but	but	CCONJ
ejpam-5171	313	19	not	not	PART
ejpam-5171	313	20	pr	pr	NOUN
ejpam-5171	313	21	-	-	PUNCT
ejpam-5171	313	22	sets	set	NOUN
ejpam-5171	313	23	,	,	PUNCT
ejpam-5171	313	24	since	since	SCONJ
ejpam-5171	313	25	l	l	PROPN
ejpam-5171	313	26	⊆	⊆	NUM
ejpam-5171	313	27	int(cl	int(cl	PROPN
ejpam-5171	313	28	♢	♢	PROPN
ejpam-5171	313	29	(l	(l	PROPN
ejpam-5171	313	30	)	)	PUNCT
ejpam-5171	313	31	)	)	PUNCT
ejpam-5171	314	1	=	=	SYM
ejpam-5171	314	2	x	x	NOUN
ejpam-5171	314	3	,	,	PUNCT
ejpam-5171	314	4	but	but	CCONJ
ejpam-5171	314	5	l	l	NOUN
ejpam-5171	314	6	=	=	PUNCT
ejpam-5171	315	1	x∩l	x∩l	PROPN
ejpam-5171	315	2	and	and	CCONJ
ejpam-5171	315	3	{	{	PUNCT
ejpam-5171	315	4	a1	a1	NOUN
ejpam-5171	315	5	,	,	PUNCT
ejpam-5171	315	6	a3	a3	NOUN
ejpam-5171	315	7	}	}	PUNCT
ejpam-5171	315	8	=	=	SYM
ejpam-5171	315	9	int(l	int(l	PROPN
ejpam-5171	315	10	)	)	PUNCT
ejpam-5171	315	11	̸=	̸=	PROPN
ejpam-5171	315	12	int(cl	int(cl	ADJ
ejpam-5171	315	13	♢	♢	PROPN
ejpam-5171	315	14	(l	(l	PROPN
ejpam-5171	315	15	)	)	PUNCT
ejpam-5171	315	16	)	)	PUNCT
ejpam-5171	316	1	=	=	PUNCT
ejpam-5171	316	2	x.	x.	NOUN
ejpam-5171	316	3	(	(	PUNCT
ejpam-5171	316	4	b	b	NOUN
ejpam-5171	316	5	)	)	PUNCT
ejpam-5171	316	6	in	in	ADP
ejpam-5171	316	7	example	example	NOUN
ejpam-5171	316	8	2.13	2.13	NUM
ejpam-5171	316	9	,	,	PUNCT
ejpam-5171	316	10	{	{	PUNCT
ejpam-5171	316	11	a1	a1	NOUN
ejpam-5171	316	12	,	,	PUNCT
ejpam-5171	316	13	a3	a3	NOUN
ejpam-5171	316	14	,	,	PUNCT
ejpam-5171	316	15	a4	a4	PROPN
ejpam-5171	316	16	}	}	PUNCT
ejpam-5171	316	17	is	be	AUX
ejpam-5171	316	18	pr	pr	NOUN
ejpam-5171	316	19	-	-	PUNCT
ejpam-5171	316	20	sets	set	NOUN
ejpam-5171	316	21	but	but	CCONJ
ejpam-5171	316	22	not	not	PART
ejpam-5171	316	23	p	p	NOUN
ejpam-5171	316	24	-	-	PUNCT
ejpam-5171	316	25	pre	pre	NOUN
ejpam-5171	316	26	-	-	ADJ
ejpam-5171	316	27	open	open	ADJ
ejpam-5171	316	28	.	.	PUNCT
ejpam-5171	317	1	theorem	theorem	VERB
ejpam-5171	317	2	3.12	3.12	NUM
ejpam-5171	317	3	.	.	PUNCT
ejpam-5171	318	1	suppose	suppose	VERB
ejpam-5171	318	2	that	that	SCONJ
ejpam-5171	318	3	(	(	PUNCT
ejpam-5171	318	4	x	x	X
ejpam-5171	318	5	,	,	PUNCT
ejpam-5171	318	6	δ	δ	PROPN
ejpam-5171	318	7	,	,	PUNCT
ejpam-5171	318	8	p	p	NOUN
ejpam-5171	318	9	)	)	PUNCT
ejpam-5171	318	10	is	be	AUX
ejpam-5171	318	11	a	a	DET
ejpam-5171	318	12	pts	pt	NOUN
ejpam-5171	318	13	.	.	PUNCT
ejpam-5171	319	1	so	so	ADV
ejpam-5171	319	2	,	,	PUNCT
ejpam-5171	319	3	(	(	PUNCT
ejpam-5171	319	4	a	a	X
ejpam-5171	319	5	)	)	PUNCT
ejpam-5171	319	6	each	each	DET
ejpam-5171	319	7	open	open	ADJ
ejpam-5171	319	8	set	set	NOUN
ejpam-5171	319	9	is	be	AUX
ejpam-5171	319	10	prα	prα	VERB
ejpam-5171	319	11	-	-	PUNCT
ejpam-5171	319	12	set	set	VERB
ejpam-5171	319	13	,	,	PUNCT
ejpam-5171	319	14	(	(	PUNCT
ejpam-5171	319	15	b	b	X
ejpam-5171	319	16	)	)	PUNCT
ejpam-5171	319	17	each	each	DET
ejpam-5171	319	18	ptα	ptα	NOUN
ejpam-5171	319	19	-	-	PUNCT
ejpam-5171	319	20	set	set	NOUN
ejpam-5171	319	21	is	be	AUX
ejpam-5171	319	22	prα	prα	VERB
ejpam-5171	319	23	-	-	PUNCT
ejpam-5171	319	24	set	set	NOUN
ejpam-5171	319	25	.	.	PUNCT
ejpam-5171	320	1	proof	proof	NOUN
ejpam-5171	320	2	.	.	PUNCT
ejpam-5171	321	1	obvious	obvious	ADJ
ejpam-5171	321	2	.	.	PUNCT
ejpam-5171	322	1	example	example	NOUN
ejpam-5171	322	2	3.13	3.13	NUM
ejpam-5171	322	3	.	.	PUNCT
ejpam-5171	323	1	(	(	PUNCT
ejpam-5171	323	2	a	a	X
ejpam-5171	323	3	)	)	PUNCT
ejpam-5171	323	4	in	in	ADP
ejpam-5171	323	5	example	example	NOUN
ejpam-5171	323	6	3.2	3.2	NUM
ejpam-5171	323	7	,	,	PUNCT
ejpam-5171	323	8	the	the	DET
ejpam-5171	323	9	set	set	NOUN
ejpam-5171	323	10	{	{	PUNCT
ejpam-5171	323	11	a2	a2	PROPN
ejpam-5171	323	12	}	}	PUNCT
ejpam-5171	323	13	is	be	AUX
ejpam-5171	323	14	prα	prα	VERB
ejpam-5171	323	15	-	-	PUNCT
ejpam-5171	323	16	set	set	NOUN
ejpam-5171	323	17	.	.	PUNCT
ejpam-5171	324	1	however	however	ADV
ejpam-5171	324	2	,	,	PUNCT
ejpam-5171	324	3	it	it	PRON
ejpam-5171	324	4	is	be	AUX
ejpam-5171	324	5	not	not	PART
ejpam-5171	324	6	open	open	ADJ
ejpam-5171	324	7	.	.	PUNCT
ejpam-5171	325	1	(	(	PUNCT
ejpam-5171	325	2	b	b	X
ejpam-5171	325	3	)	)	PUNCT
ejpam-5171	325	4	in	in	ADP
ejpam-5171	325	5	example	example	NOUN
ejpam-5171	325	6	3.6	3.6	NUM
ejpam-5171	325	7	,	,	PUNCT
ejpam-5171	325	8	the	the	DET
ejpam-5171	325	9	set	set	NOUN
ejpam-5171	325	10	{	{	PUNCT
ejpam-5171	325	11	a3	a3	NOUN
ejpam-5171	325	12	}	}	PUNCT
ejpam-5171	325	13	is	be	AUX
ejpam-5171	325	14	prα	prα	VERB
ejpam-5171	325	15	-	-	PUNCT
ejpam-5171	325	16	set	set	NOUN
ejpam-5171	325	17	.	.	PUNCT
ejpam-5171	326	1	however	however	ADV
ejpam-5171	326	2	,	,	PUNCT
ejpam-5171	326	3	it	it	PRON
ejpam-5171	326	4	is	be	AUX
ejpam-5171	326	5	not	not	PART
ejpam-5171	326	6	ptα	ptα	NOUN
ejpam-5171	326	7	-	-	PUNCT
ejpam-5171	326	8	set	set	NOUN
ejpam-5171	326	9	.	.	PUNCT
ejpam-5171	327	1	proposition	proposition	NOUN
ejpam-5171	327	2	3.14	3.14	NUM
ejpam-5171	327	3	.	.	PUNCT
ejpam-5171	328	1	if	if	SCONJ
ejpam-5171	328	2	l1	l1	PROPN
ejpam-5171	328	3	and	and	CCONJ
ejpam-5171	328	4	l2	l2	NOUN
ejpam-5171	328	5	are	be	AUX
ejpam-5171	328	6	ptα	ptα	NOUN
ejpam-5171	328	7	-	-	PUNCT
ejpam-5171	328	8	sets	set	NOUN
ejpam-5171	328	9	,	,	PUNCT
ejpam-5171	328	10	then	then	ADV
ejpam-5171	328	11	l1	l1	PROPN
ejpam-5171	328	12	∩	∩	ADJ
ejpam-5171	328	13	l2	l2	NOUN
ejpam-5171	328	14	is	be	AUX
ejpam-5171	328	15	a	a	DET
ejpam-5171	328	16	ptα	ptα	NOUN
ejpam-5171	328	17	-	-	PUNCT
ejpam-5171	328	18	set	set	NOUN
ejpam-5171	328	19	.	.	PUNCT
ejpam-5171	329	1	proof	proof	NOUN
ejpam-5171	329	2	.	.	PUNCT
ejpam-5171	330	1	let	let	VERB
ejpam-5171	330	2	l1	l1	PROPN
ejpam-5171	330	3	and	and	CCONJ
ejpam-5171	330	4	l2	l2	NOUN
ejpam-5171	330	5	be	be	VERB
ejpam-5171	330	6	ptα	ptα	NOUN
ejpam-5171	330	7	-	-	PUNCT
ejpam-5171	330	8	sets	set	NOUN
ejpam-5171	330	9	.	.	PUNCT
ejpam-5171	331	1	next	next	ADV
ejpam-5171	331	2	,	,	PUNCT
ejpam-5171	331	3	we	we	PRON
ejpam-5171	331	4	have	have	VERB
ejpam-5171	331	5	int(l1	int(l1	PROPN
ejpam-5171	331	6	∩	∩	ADJ
ejpam-5171	331	7	l2	l2	NOUN
ejpam-5171	331	8	)	)	PUNCT
ejpam-5171	332	1	⊂	⊂	PROPN
ejpam-5171	332	2	int(cl	int(cl	PROPN
ejpam-5171	332	3	♢	♢	PROPN
ejpam-5171	332	4	(int(l1	(int(l1	PROPN
ejpam-5171	332	5	∩	∩	ADJ
ejpam-5171	332	6	l2	l2	NOUN
ejpam-5171	332	7	)	)	PUNCT
ejpam-5171	332	8	)	)	PUNCT
ejpam-5171	332	9	)	)	PUNCT
ejpam-5171	333	1	⊆	⊆	NUM
ejpam-5171	333	2	int[cl	int[cl	PROPN
ejpam-5171	333	3	♢	♢	PROPN
ejpam-5171	333	4	(int(l1))∩cl	(int(l1))∩cl	PROPN
ejpam-5171	333	5	♢	♢	PROPN
ejpam-5171	333	6	(int(l2	(int(l2	PROPN
ejpam-5171	333	7	)	)	PUNCT
ejpam-5171	333	8	)	)	PUNCT
ejpam-5171	333	9	]	]	PUNCT
ejpam-5171	333	10	=	=	SYM
ejpam-5171	333	11	int(cl	int(cl	PROPN
ejpam-5171	333	12	♢	♢	PROPN
ejpam-5171	333	13	(int(l1)))∩int(cl	(int(l1)))∩int(cl	PROPN
ejpam-5171	333	14	♢	♢	PROPN
ejpam-5171	333	15	(int(l2	(int(l2	NOUN
ejpam-5171	333	16	)	)	PUNCT
ejpam-5171	333	17	)	)	PUNCT
ejpam-5171	333	18	)	)	PUNCT
ejpam-5171	334	1	=	=	PUNCT
ejpam-5171	334	2	int(l1)∩	int(l1)∩	VERB
ejpam-5171	334	3	int(l2	int(l2	NOUN
ejpam-5171	334	4	)	)	PUNCT
ejpam-5171	334	5	=	=	PUNCT
ejpam-5171	335	1	int(l1	int(l1	PROPN
ejpam-5171	335	2	∩l2	∩l2	PROPN
ejpam-5171	335	3	)	)	PUNCT
ejpam-5171	335	4	.	.	PUNCT
ejpam-5171	336	1	then	then	ADV
ejpam-5171	336	2	,	,	PUNCT
ejpam-5171	336	3	int(l1	int(l1	PROPN
ejpam-5171	336	4	∩l2	∩l2	PROPN
ejpam-5171	336	5	)	)	PUNCT
ejpam-5171	336	6	=	=	SYM
ejpam-5171	336	7	int(cl	int(cl	PROPN
ejpam-5171	336	8	♢	♢	PROPN
ejpam-5171	336	9	(int(l1	(int(l1	PROPN
ejpam-5171	336	10	∩l2	∩l2	PROPN
ejpam-5171	336	11	)	)	PUNCT
ejpam-5171	336	12	)	)	PUNCT
ejpam-5171	336	13	)	)	PUNCT
ejpam-5171	336	14	.	.	PUNCT
ejpam-5171	337	1	therefore	therefore	ADV
ejpam-5171	337	2	,	,	PUNCT
ejpam-5171	337	3	l1	l1	PROPN
ejpam-5171	337	4	∩l2	∩l2	PROPN
ejpam-5171	337	5	is	be	AUX
ejpam-5171	337	6	a	a	DET
ejpam-5171	337	7	ptα	ptα	NOUN
ejpam-5171	337	8	-	-	PUNCT
ejpam-5171	337	9	set	set	NOUN
ejpam-5171	337	10	.	.	PUNCT
ejpam-5171	338	1	proposition	proposition	NOUN
ejpam-5171	338	2	3.15	3.15	NUM
ejpam-5171	338	3	.	.	PUNCT
ejpam-5171	339	1	assume	assume	VERB
ejpam-5171	339	2	that	that	SCONJ
ejpam-5171	339	3	(	(	PUNCT
ejpam-5171	339	4	x	x	NOUN
ejpam-5171	339	5	,	,	PUNCT
ejpam-5171	339	6	δ	δ	PROPN
ejpam-5171	339	7	,	,	PUNCT
ejpam-5171	339	8	p	p	NOUN
ejpam-5171	339	9	)	)	PUNCT
ejpam-5171	339	10	is	be	AUX
ejpam-5171	339	11	a	a	DET
ejpam-5171	339	12	pts	pt	NOUN
ejpam-5171	339	13	.	.	PUNCT
ejpam-5171	340	1	the	the	DET
ejpam-5171	340	2	following	follow	VERB
ejpam-5171	340	3	statements	statement	NOUN
ejpam-5171	340	4	are	be	AUX
ejpam-5171	340	5	equivalent	equivalent	ADJ
ejpam-5171	340	6	for	for	ADP
ejpam-5171	340	7	a	a	DET
ejpam-5171	340	8	subset	subset	NOUN
ejpam-5171	340	9	l	l	NOUN
ejpam-5171	340	10	of	of	ADP
ejpam-5171	340	11	x	x	NOUN
ejpam-5171	340	12	:	:	PUNCT
ejpam-5171	340	13	(	(	PUNCT
ejpam-5171	340	14	a	a	X
ejpam-5171	340	15	)	)	PUNCT
ejpam-5171	340	16	l	l	NOUN
ejpam-5171	340	17	is	be	AUX
ejpam-5171	340	18	open	open	ADJ
ejpam-5171	340	19	,	,	PUNCT
ejpam-5171	340	20	(	(	PUNCT
ejpam-5171	340	21	b	b	X
ejpam-5171	340	22	)	)	PUNCT
ejpam-5171	340	23	l	l	NOUN
ejpam-5171	340	24	is	be	AUX
ejpam-5171	340	25	p	p	AUX
ejpam-5171	340	26	-	-	PUNCT
ejpam-5171	340	27	α	α	NOUN
ejpam-5171	340	28	-	-	ADJ
ejpam-5171	340	29	open	open	ADJ
ejpam-5171	340	30	and	and	CCONJ
ejpam-5171	340	31	prα	prα	VERB
ejpam-5171	340	32	-	-	PUNCT
ejpam-5171	340	33	set	set	NOUN
ejpam-5171	340	34	.	.	PUNCT
ejpam-5171	341	1	proof	proof	NOUN
ejpam-5171	341	2	.	.	PUNCT
ejpam-5171	342	1	(	(	PUNCT
ejpam-5171	342	2	a	a	X
ejpam-5171	342	3	)	)	PUNCT
ejpam-5171	342	4	⇒	⇒	NOUN
ejpam-5171	342	5	(	(	PUNCT
ejpam-5171	342	6	b	b	NOUN
ejpam-5171	342	7	):	):	PUNCT
ejpam-5171	342	8	suppose	suppose	VERB
ejpam-5171	342	9	that	that	SCONJ
ejpam-5171	342	10	l	l	NOUN
ejpam-5171	342	11	is	be	AUX
ejpam-5171	342	12	an	an	DET
ejpam-5171	342	13	open	open	ADJ
ejpam-5171	342	14	set	set	NOUN
ejpam-5171	342	15	.	.	PUNCT
ejpam-5171	343	1	thus	thus	ADV
ejpam-5171	343	2	,	,	PUNCT
ejpam-5171	343	3	l	l	NOUN
ejpam-5171	343	4	=	=	SYM
ejpam-5171	343	5	int(l	int(l	PROPN
ejpam-5171	343	6	)	)	PUNCT
ejpam-5171	343	7	⊆	⊆	NUM
ejpam-5171	343	8	cl	cl	NOUN
ejpam-5171	343	9	♢	♢	NOUN
ejpam-5171	343	10	(int(l	(int(l	PROPN
ejpam-5171	343	11	)	)	PUNCT
ejpam-5171	343	12	)	)	PUNCT
ejpam-5171	343	13	and	and	CCONJ
ejpam-5171	343	14	l	l	NOUN
ejpam-5171	343	15	=	=	SYM
ejpam-5171	343	16	int(l	int(l	PROPN
ejpam-5171	343	17	)	)	PUNCT
ejpam-5171	343	18	⊆	⊆	NUM
ejpam-5171	343	19	int(cl	int(cl	PROPN
ejpam-5171	343	20	♢	♢	PROPN
ejpam-5171	343	21	(int(l	(int(l	PROPN
ejpam-5171	343	22	)	)	PUNCT
ejpam-5171	343	23	)	)	PUNCT
ejpam-5171	343	24	)	)	PUNCT
ejpam-5171	343	25	.	.	PUNCT
ejpam-5171	344	1	therefore	therefore	ADV
ejpam-5171	344	2	,	,	PUNCT
ejpam-5171	344	3	l	l	PROPN
ejpam-5171	344	4	is	be	AUX
ejpam-5171	344	5	p	p	PROPN
ejpam-5171	344	6	-	-	PUNCT
ejpam-5171	344	7	α	α	NOUN
ejpam-5171	344	8	-	-	NOUN
ejpam-5171	344	9	open	open	ADJ
ejpam-5171	344	10	.	.	PUNCT
ejpam-5171	345	1	also	also	ADV
ejpam-5171	345	2	by	by	ADP
ejpam-5171	345	3	theorem	theorem	NOUN
ejpam-5171	345	4	3.12	3.12	NUM
ejpam-5171	345	5	,	,	PUNCT
ejpam-5171	345	6	l	l	NOUN
ejpam-5171	345	7	is	be	AUX
ejpam-5171	345	8	prα	prα	VERB
ejpam-5171	345	9	-	-	PUNCT
ejpam-5171	345	10	set	set	NOUN
ejpam-5171	345	11	.	.	PUNCT
ejpam-5171	346	1	(	(	PUNCT
ejpam-5171	346	2	b)⇒	b)⇒	PROPN
ejpam-5171	346	3	(	(	PUNCT
ejpam-5171	346	4	a	a	X
ejpam-5171	346	5	):	):	PUNCT
ejpam-5171	346	6	let	let	VERB
ejpam-5171	346	7	l	l	NOUN
ejpam-5171	346	8	be	be	AUX
ejpam-5171	346	9	the	the	DET
ejpam-5171	346	10	prα	prα	NOUN
ejpam-5171	346	11	-	-	PUNCT
ejpam-5171	346	12	set	set	NOUN
ejpam-5171	346	13	.	.	PUNCT
ejpam-5171	347	1	so	so	ADV
ejpam-5171	347	2	,	,	PUNCT
ejpam-5171	347	3	l	l	PROPN
ejpam-5171	347	4	=	=	SYM
ejpam-5171	347	5	l1	l1	PROPN
ejpam-5171	347	6	∩	∩	ADJ
ejpam-5171	347	7	l2	l2	NOUN
ejpam-5171	347	8	,	,	PUNCT
ejpam-5171	347	9	where	where	SCONJ
ejpam-5171	347	10	l1	l1	PROPN
ejpam-5171	347	11	is	be	AUX
ejpam-5171	347	12	open	open	ADJ
ejpam-5171	347	13	and	and	CCONJ
ejpam-5171	347	14	int(l2	int(l2	NOUN
ejpam-5171	347	15	)	)	PUNCT
ejpam-5171	347	16	=	=	SYM
ejpam-5171	347	17	int(cl	int(cl	PROPN
ejpam-5171	347	18	♢	♢	PROPN
ejpam-5171	347	19	(int(l2	(int(l2	NUM
ejpam-5171	347	20	)	)	PUNCT
ejpam-5171	347	21	)	)	PUNCT
ejpam-5171	347	22	)	)	PUNCT
ejpam-5171	347	23	.	.	PUNCT
ejpam-5171	348	1	thus	thus	ADV
ejpam-5171	348	2	,	,	PUNCT
ejpam-5171	348	3	l	l	PROPN
ejpam-5171	348	4	⊆	⊆	NUM
ejpam-5171	348	5	l1	l1	PROPN
ejpam-5171	348	6	=	=	SYM
ejpam-5171	348	7	int(l1	int(l1	PROPN
ejpam-5171	348	8	)	)	PUNCT
ejpam-5171	348	9	.	.	PUNCT
ejpam-5171	349	1	also	also	ADV
ejpam-5171	349	2	,	,	PUNCT
ejpam-5171	349	3	l	l	PROPN
ejpam-5171	349	4	is	be	AUX
ejpam-5171	349	5	p	p	PROPN
ejpam-5171	349	6	-	-	PUNCT
ejpam-5171	349	7	α	α	NOUN
ejpam-5171	349	8	-	-	ADJ
ejpam-5171	349	9	open	open	ADJ
ejpam-5171	349	10	implies	imply	VERB
ejpam-5171	349	11	l	l	PROPN
ejpam-5171	349	12	⊆	⊆	NUM
ejpam-5171	349	13	int(cl	int(cl	NOUN
ejpam-5171	349	14	♢	♢	PROPN
ejpam-5171	349	15	(int(l	(int(l	PROPN
ejpam-5171	349	16	)	)	PUNCT
ejpam-5171	349	17	)	)	PUNCT
ejpam-5171	349	18	)	)	PUNCT
ejpam-5171	350	1	⊆	⊆	NUM
ejpam-5171	350	2	int(cl	int(cl	ADP
ejpam-5171	350	3	♢	♢	PROPN
ejpam-5171	350	4	(int(l2	(int(l2	NUM
ejpam-5171	350	5	)	)	PUNCT
ejpam-5171	350	6	)	)	PUNCT
ejpam-5171	350	7	)	)	PUNCT
ejpam-5171	351	1	=	=	PUNCT
ejpam-5171	351	2	int(l2	int(l2	NOUN
ejpam-5171	351	3	)	)	PUNCT
ejpam-5171	351	4	by	by	ADP
ejpam-5171	351	5	assumption	assumption	NOUN
ejpam-5171	351	6	.	.	PUNCT
ejpam-5171	352	1	thus	thus	ADV
ejpam-5171	352	2	,	,	PUNCT
ejpam-5171	352	3	l	l	PROPN
ejpam-5171	352	4	⊆	⊆	NUM
ejpam-5171	352	5	int(l1)∩int(l2	int(l1)∩int(l2	PROPN
ejpam-5171	352	6	)	)	PUNCT
ejpam-5171	352	7	=	=	SYM
ejpam-5171	352	8	int(l1∩l2	int(l1∩l2	PROPN
ejpam-5171	352	9	)	)	PUNCT
ejpam-5171	352	10	=	=	SYM
ejpam-5171	352	11	int(l	int(l	PROPN
ejpam-5171	352	12	)	)	PUNCT
ejpam-5171	352	13	,	,	PUNCT
ejpam-5171	352	14	and	and	CCONJ
ejpam-5171	352	15	l	l	NOUN
ejpam-5171	352	16	is	be	AUX
ejpam-5171	352	17	open	open	ADJ
ejpam-5171	352	18	.	.	PUNCT
ejpam-5171	353	1	h.	h.	PROPN
ejpam-5171	353	2	al	al	PROPN
ejpam-5171	353	3	-	-	PUNCT
ejpam-5171	353	4	saadi	saadi	PROPN
ejpam-5171	353	5	,	,	PUNCT
ejpam-5171	353	6	m.	m.	NOUN
ejpam-5171	353	7	al	al	PROPN
ejpam-5171	353	8	-	-	PUNCT
ejpam-5171	353	9	hodieb	hodieb	PROPN
ejpam-5171	353	10	/	/	SYM
ejpam-5171	353	11	eur	eur	PROPN
ejpam-5171	353	12	.	.	PUNCT
ejpam-5171	354	1	j.	j.	PROPN
ejpam-5171	354	2	pure	pure	PROPN
ejpam-5171	354	3	appl	appl	PROPN
ejpam-5171	354	4	.	.	PROPN
ejpam-5171	354	5	math	math	PROPN
ejpam-5171	354	6	,	,	PUNCT
ejpam-5171	354	7	17	17	NUM
ejpam-5171	354	8	(	(	PUNCT
ejpam-5171	354	9	2	2	NUM
ejpam-5171	354	10	)	)	PUNCT
ejpam-5171	354	11	(	(	PUNCT
ejpam-5171	354	12	2024	2024	NUM
ejpam-5171	354	13	)	)	PUNCT
ejpam-5171	354	14	,	,	PUNCT
ejpam-5171	354	15	1352	1352	NUM
ejpam-5171	354	16	-	-	SYM
ejpam-5171	354	17	1368	1368	NUM
ejpam-5171	354	18	1362	1362	NUM
ejpam-5171	354	19	remark	remark	NOUN
ejpam-5171	354	20	3.16	3.16	NUM
ejpam-5171	354	21	.	.	PUNCT
ejpam-5171	355	1	the	the	DET
ejpam-5171	355	2	relationships	relationship	NOUN
ejpam-5171	355	3	between	between	ADP
ejpam-5171	355	4	the	the	DET
ejpam-5171	355	5	above	above	ADJ
ejpam-5171	355	6	open	open	ADJ
ejpam-5171	355	7	sets	set	NOUN
ejpam-5171	355	8	are	be	AUX
ejpam-5171	355	9	shown	show	VERB
ejpam-5171	355	10	in	in	ADP
ejpam-5171	355	11	the	the	DET
ejpam-5171	355	12	following	follow	VERB
ejpam-5171	355	13	figure	figure	NOUN
ejpam-5171	355	14	:	:	PUNCT
ejpam-5171	355	15	open	open	ADJ
ejpam-5171	355	16	set	set	VERB
ejpam-5171	355	17	pr	pr	NOUN
ejpam-5171	355	18	set	set	VERB
ejpam-5171	355	19	ptα	ptα	CCONJ
ejpam-5171	355	20	-set	-set	ADV
ejpam-5171	355	21	prα	prα	VERB
ejpam-5171	355	22	-set	-set	PUNCT
ejpam-5171	355	23	p	p	NOUN
ejpam-5171	355	24	-	-	PUNCT
ejpam-5171	355	25	pre	pre	ADJ
ejpam-5171	355	26	-	-	ADJ
ejpam-5171	355	27	open	open	ADJ
ejpam-5171	355	28	set	set	VERB
ejpam-5171	355	29	pt	pt	X
ejpam-5171	355	30	-set	-set	X
ejpam-5171	355	31	/	/	SYM
ejpam-5171	355	32	4	4	X
ejpam-5171	355	33	.	.	PUNCT
ejpam-5171	355	34	decomposition	decomposition	NOUN
ejpam-5171	355	35	of	of	ADP
ejpam-5171	355	36	generalized	generalized	ADJ
ejpam-5171	355	37	continuity	continuity	NOUN
ejpam-5171	355	38	in	in	ADP
ejpam-5171	355	39	this	this	DET
ejpam-5171	355	40	section	section	NOUN
ejpam-5171	355	41	,	,	PUNCT
ejpam-5171	355	42	we	we	PRON
ejpam-5171	355	43	focus	focus	VERB
ejpam-5171	355	44	on	on	ADP
ejpam-5171	355	45	defining	define	VERB
ejpam-5171	355	46	some	some	DET
ejpam-5171	355	47	classes	class	NOUN
ejpam-5171	355	48	of	of	ADP
ejpam-5171	355	49	primal	primal	ADJ
ejpam-5171	355	50	continuous	continuous	ADJ
ejpam-5171	355	51	functions	function	NOUN
ejpam-5171	355	52	to	to	PART
ejpam-5171	355	53	obtain	obtain	VERB
ejpam-5171	355	54	decompositions	decomposition	NOUN
ejpam-5171	355	55	of	of	ADP
ejpam-5171	355	56	continuity	continuity	NOUN
ejpam-5171	355	57	.	.	PUNCT
ejpam-5171	356	1	definition	definition	NOUN
ejpam-5171	356	2	4.1	4.1	NUM
ejpam-5171	356	3	.	.	PUNCT
ejpam-5171	357	1	a	a	DET
ejpam-5171	357	2	function	function	NOUN
ejpam-5171	357	3	f	f	NOUN
ejpam-5171	357	4	:	:	PUNCT
ejpam-5171	357	5	(	(	PUNCT
ejpam-5171	357	6	x	x	X
ejpam-5171	357	7	,	,	PUNCT
ejpam-5171	357	8	δ	δ	PROPN
ejpam-5171	357	9	,	,	PUNCT
ejpam-5171	357	10	p	p	NOUN
ejpam-5171	357	11	)	)	PUNCT
ejpam-5171	357	12	→	→	SYM
ejpam-5171	357	13	(	(	PUNCT
ejpam-5171	357	14	y	y	NOUN
ejpam-5171	357	15	,	,	PUNCT
ejpam-5171	357	16	ς	ς	NOUN
ejpam-5171	357	17	)	)	PUNCT
ejpam-5171	357	18	is	be	AUX
ejpam-5171	357	19	said	say	VERB
ejpam-5171	357	20	to	to	PART
ejpam-5171	357	21	be	be	AUX
ejpam-5171	357	22	p	p	NOUN
ejpam-5171	357	23	-	-	PUNCT
ejpam-5171	357	24	α	α	NOUN
ejpam-5171	357	25	-	-	ADJ
ejpam-5171	357	26	continuous	continuous	ADJ
ejpam-5171	357	27	(	(	PUNCT
ejpam-5171	357	28	resp	resp	NOUN
ejpam-5171	357	29	.	.	PUNCT
ejpam-5171	358	1	p	p	X
ejpam-5171	358	2	-	-	PUNCT
ejpam-5171	358	3	semicontinuous	semicontinuous	ADJ
ejpam-5171	358	4	,	,	PUNCT
ejpam-5171	358	5	p	p	NOUN
ejpam-5171	358	6	-	-	NOUN
ejpam-5171	358	7	precontinuous	precontinuous	ADJ
ejpam-5171	358	8	,	,	PUNCT
ejpam-5171	358	9	p	p	NOUN
ejpam-5171	358	10	-	-	PUNCT
ejpam-5171	358	11	β	β	NOUN
ejpam-5171	358	12	-	-	ADJ
ejpam-5171	358	13	continuous	continuous	ADJ
ejpam-5171	358	14	)	)	PUNCT
ejpam-5171	358	15	if	if	SCONJ
ejpam-5171	358	16	the	the	DET
ejpam-5171	358	17	inverse	inverse	ADJ
ejpam-5171	358	18	image	image	NOUN
ejpam-5171	358	19	of	of	ADP
ejpam-5171	358	20	each	each	DET
ejpam-5171	358	21	open	open	ADJ
ejpam-5171	358	22	set	set	NOUN
ejpam-5171	358	23	in	in	ADP
ejpam-5171	358	24	y	y	PROPN
ejpam-5171	358	25	is	be	AUX
ejpam-5171	358	26	p	p	PROPN
ejpam-5171	358	27	-	-	PUNCT
ejpam-5171	358	28	α	α	NOUN
ejpam-5171	358	29	-	-	ADJ
ejpam-5171	358	30	open	open	ADJ
ejpam-5171	358	31	(	(	PUNCT
ejpam-5171	358	32	resp	resp	NOUN
ejpam-5171	358	33	.	.	PUNCT
ejpam-5171	359	1	p	p	X
ejpam-5171	359	2	-	-	PUNCT
ejpam-5171	359	3	semi	semi	ADV
ejpam-5171	359	4	-	-	ADJ
ejpam-5171	359	5	open	open	ADJ
ejpam-5171	359	6	,	,	PUNCT
ejpam-5171	359	7	p	p	NOUN
ejpam-5171	359	8	-	-	PUNCT
ejpam-5171	359	9	pre	pre	NOUN
ejpam-5171	359	10	-	-	ADJ
ejpam-5171	359	11	open	open	ADJ
ejpam-5171	359	12	,	,	PUNCT
ejpam-5171	359	13	p	p	NOUN
ejpam-5171	359	14	-	-	PUNCT
ejpam-5171	359	15	β	β	NOUN
ejpam-5171	359	16	-	-	ADJ
ejpam-5171	359	17	open	open	ADJ
ejpam-5171	359	18	)	)	PUNCT
ejpam-5171	359	19	in	in	ADP
ejpam-5171	359	20	(	(	PUNCT
ejpam-5171	359	21	x	x	NOUN
ejpam-5171	359	22	,	,	PUNCT
ejpam-5171	359	23	δ	δ	PROPN
ejpam-5171	359	24	,	,	PUNCT
ejpam-5171	359	25	p	p	NOUN
ejpam-5171	359	26	)	)	PUNCT
ejpam-5171	359	27	.	.	PUNCT
ejpam-5171	360	1	theorem	theorem	VERB
ejpam-5171	360	2	4.2	4.2	NUM
ejpam-5171	360	3	.	.	PUNCT
ejpam-5171	361	1	let	let	VERB
ejpam-5171	361	2	f	f	NOUN
ejpam-5171	361	3	:	:	PUNCT
ejpam-5171	361	4	(	(	PUNCT
ejpam-5171	361	5	x	x	X
ejpam-5171	361	6	,	,	PUNCT
ejpam-5171	361	7	δ	δ	PROPN
ejpam-5171	361	8	,	,	PUNCT
ejpam-5171	361	9	p	p	NOUN
ejpam-5171	361	10	)	)	PUNCT
ejpam-5171	361	11	→	→	SYM
ejpam-5171	361	12	(	(	PUNCT
ejpam-5171	361	13	y	y	NOUN
ejpam-5171	361	14	,	,	PUNCT
ejpam-5171	361	15	ς	ς	PROPN
ejpam-5171	361	16	)	)	PUNCT
ejpam-5171	361	17	be	be	AUX
ejpam-5171	361	18	a	a	DET
ejpam-5171	361	19	function	function	NOUN
ejpam-5171	361	20	.	.	PUNCT
ejpam-5171	362	1	hence	hence	ADV
ejpam-5171	362	2	,	,	PUNCT
ejpam-5171	362	3	f	f	PROPN
ejpam-5171	362	4	is	be	AUX
ejpam-5171	362	5	a	a	DET
ejpam-5171	362	6	p	p	NOUN
ejpam-5171	362	7	-	-	PUNCT
ejpam-5171	362	8	α	α	NOUN
ejpam-5171	362	9	-	-	ADJ
ejpam-5171	362	10	continuous	continuous	ADJ
ejpam-5171	362	11	iff	iff	PROPN
ejpam-5171	362	12	it	it	PRON
ejpam-5171	362	13	is	be	AUX
ejpam-5171	362	14	p	p	ADJ
ejpam-5171	362	15	-	-	PUNCT
ejpam-5171	362	16	semicontinuous	semicontinuous	ADJ
ejpam-5171	362	17	and	and	CCONJ
ejpam-5171	362	18	p	p	NOUN
ejpam-5171	362	19	-	-	NOUN
ejpam-5171	362	20	precontinuous	precontinuous	ADJ
ejpam-5171	362	21	.	.	PUNCT
ejpam-5171	363	1	proof	proof	NOUN
ejpam-5171	363	2	.	.	PUNCT
ejpam-5171	364	1	clearly	clearly	ADV
ejpam-5171	364	2	from	from	ADP
ejpam-5171	364	3	theorem	theorem	ADJ
ejpam-5171	364	4	2.8	2.8	NUM
ejpam-5171	364	5	.	.	PUNCT
ejpam-5171	364	6	definition	definition	NOUN
ejpam-5171	364	7	4.3	4.3	NUM
ejpam-5171	364	8	.	.	PUNCT
ejpam-5171	365	1	let	let	VERB
ejpam-5171	365	2	f	f	NOUN
ejpam-5171	365	3	:	:	PUNCT
ejpam-5171	365	4	(	(	PUNCT
ejpam-5171	365	5	x	x	X
ejpam-5171	365	6	,	,	PUNCT
ejpam-5171	365	7	δ	δ	PROPN
ejpam-5171	365	8	,	,	PUNCT
ejpam-5171	365	9	p	p	NOUN
ejpam-5171	365	10	)	)	PUNCT
ejpam-5171	365	11	→	→	SYM
ejpam-5171	365	12	(	(	PUNCT
ejpam-5171	365	13	y	y	NOUN
ejpam-5171	365	14	,	,	PUNCT
ejpam-5171	365	15	ς	ς	PROPN
ejpam-5171	365	16	)	)	PUNCT
ejpam-5171	365	17	be	be	AUX
ejpam-5171	365	18	a	a	DET
ejpam-5171	365	19	function	function	NOUN
ejpam-5171	365	20	.	.	PUNCT
ejpam-5171	366	1	hence	hence	ADV
ejpam-5171	366	2	,	,	PUNCT
ejpam-5171	366	3	f	f	PROPN
ejpam-5171	366	4	is	be	AUX
ejpam-5171	366	5	said	say	VERB
ejpam-5171	366	6	to	to	PART
ejpam-5171	366	7	be	be	AUX
ejpam-5171	366	8	αcontinuous	αcontinuous	ADJ
ejpam-5171	366	9	(	(	PUNCT
ejpam-5171	366	10	[	[	X
ejpam-5171	366	11	33	33	NUM
ejpam-5171	366	12	]	]	SYM
ejpam-5171	366	13	)	)	PUNCT
ejpam-5171	366	14	(	(	PUNCT
ejpam-5171	366	15	resp	resp	NOUN
ejpam-5171	366	16	.	.	PUNCT
ejpam-5171	367	1	semicontinuous	semicontinuous	ADJ
ejpam-5171	367	2	(	(	PUNCT
ejpam-5171	367	3	[	[	X
ejpam-5171	367	4	1	1	NUM
ejpam-5171	367	5	]	]	NUM
ejpam-5171	367	6	)	)	PUNCT
ejpam-5171	367	7	,	,	PUNCT
ejpam-5171	367	8	precontinuous	precontinuous	ADJ
ejpam-5171	367	9	(	(	PUNCT
ejpam-5171	367	10	[	[	X
ejpam-5171	367	11	3	3	NUM
ejpam-5171	367	12	]	]	NUM
ejpam-5171	367	13	)	)	PUNCT
ejpam-5171	367	14	,	,	PUNCT
ejpam-5171	367	15	β	β	X
ejpam-5171	367	16	-	-	ADJ
ejpam-5171	367	17	continuous	continuous	ADJ
ejpam-5171	367	18	(	(	PUNCT
ejpam-5171	367	19	[	[	X
ejpam-5171	367	20	4	4	NUM
ejpam-5171	367	21	]	]	NUM
ejpam-5171	367	22	)	)	PUNCT
ejpam-5171	367	23	)	)	PUNCT
ejpam-5171	368	1	if	if	SCONJ
ejpam-5171	368	2	the	the	DET
ejpam-5171	368	3	inverse	inverse	ADJ
ejpam-5171	368	4	image	image	NOUN
ejpam-5171	368	5	of	of	ADP
ejpam-5171	368	6	any	any	DET
ejpam-5171	368	7	open	open	ADJ
ejpam-5171	368	8	set	set	NOUN
ejpam-5171	368	9	of	of	ADP
ejpam-5171	368	10	(	(	PUNCT
ejpam-5171	368	11	y	y	PROPN
ejpam-5171	368	12	,	,	PUNCT
ejpam-5171	368	13	ς	ς	NOUN
ejpam-5171	368	14	)	)	PUNCT
ejpam-5171	368	15	is	be	AUX
ejpam-5171	368	16	an	an	DET
ejpam-5171	368	17	α	α	NOUN
ejpam-5171	368	18	-	-	ADJ
ejpam-5171	368	19	open	open	ADJ
ejpam-5171	368	20	(	(	PUNCT
ejpam-5171	368	21	resp	resp	NOUN
ejpam-5171	368	22	.	.	PUNCT
ejpam-5171	368	23	semi	semi	ADJ
ejpam-5171	368	24	-	-	ADJ
ejpam-5171	368	25	open	open	ADJ
ejpam-5171	368	26	,	,	PUNCT
ejpam-5171	368	27	pre	pre	ADJ
ejpam-5171	368	28	-	-	ADJ
ejpam-5171	368	29	open	open	ADJ
ejpam-5171	368	30	,	,	PUNCT
ejpam-5171	368	31	β	β	NOUN
ejpam-5171	368	32	-	-	ADJ
ejpam-5171	368	33	open	open	ADJ
ejpam-5171	368	34	)	)	PUNCT
ejpam-5171	368	35	in	in	ADP
ejpam-5171	368	36	(	(	PUNCT
ejpam-5171	368	37	x	x	NOUN
ejpam-5171	368	38	,	,	PUNCT
ejpam-5171	368	39	δ	δ	PROPN
ejpam-5171	368	40	,	,	PUNCT
ejpam-5171	368	41	p	p	NOUN
ejpam-5171	368	42	)	)	PUNCT
ejpam-5171	368	43	.	.	PUNCT
ejpam-5171	369	1	proposition	proposition	NOUN
ejpam-5171	369	2	4.4	4.4	NUM
ejpam-5171	369	3	.	.	PUNCT
ejpam-5171	370	1	if	if	SCONJ
ejpam-5171	370	2	a	a	DET
ejpam-5171	370	3	function	function	NOUN
ejpam-5171	370	4	f	f	X
ejpam-5171	370	5	:	:	PUNCT
ejpam-5171	370	6	(	(	PUNCT
ejpam-5171	370	7	x	x	X
ejpam-5171	370	8	,	,	PUNCT
ejpam-5171	370	9	δ	δ	PROPN
ejpam-5171	370	10	,	,	PUNCT
ejpam-5171	370	11	p	p	NOUN
ejpam-5171	370	12	)	)	PUNCT
ejpam-5171	370	13	→	→	SYM
ejpam-5171	370	14	(	(	PUNCT
ejpam-5171	370	15	y	y	NOUN
ejpam-5171	370	16	,	,	PUNCT
ejpam-5171	370	17	ς	ς	NOUN
ejpam-5171	370	18	)	)	PUNCT
ejpam-5171	370	19	is	be	AUX
ejpam-5171	370	20	p	p	PROPN
ejpam-5171	370	21	-	-	PUNCT
ejpam-5171	370	22	α	α	NOUN
ejpam-5171	370	23	-	-	ADJ
ejpam-5171	370	24	continuous	continuous	ADJ
ejpam-5171	370	25	(	(	PUNCT
ejpam-5171	370	26	resp	resp	NOUN
ejpam-5171	370	27	.	.	PUNCT
ejpam-5171	371	1	psemicontinuous	psemicontinuous	ADJ
ejpam-5171	371	2	,	,	PUNCT
ejpam-5171	371	3	p	p	NOUN
ejpam-5171	371	4	-	-	NOUN
ejpam-5171	371	5	precontinuous	precontinuous	ADJ
ejpam-5171	371	6	,	,	PUNCT
ejpam-5171	371	7	p	p	NOUN
ejpam-5171	371	8	-	-	PUNCT
ejpam-5171	371	9	β	β	NOUN
ejpam-5171	371	10	-	-	ADJ
ejpam-5171	371	11	continuous	continuous	ADJ
ejpam-5171	371	12	)	)	PUNCT
ejpam-5171	371	13	,	,	PUNCT
ejpam-5171	371	14	thus	thus	ADV
ejpam-5171	371	15	f	f	PROPN
ejpam-5171	371	16	is	be	AUX
ejpam-5171	371	17	α	α	NOUN
ejpam-5171	371	18	-	-	ADJ
ejpam-5171	371	19	continuous	continuous	ADJ
ejpam-5171	371	20	(	(	PUNCT
ejpam-5171	371	21	resp	resp	NOUN
ejpam-5171	371	22	.	.	PUNCT
ejpam-5171	371	23	semicontinuous	semicontinuous	ADJ
ejpam-5171	371	24	,	,	PUNCT
ejpam-5171	371	25	precontinuous	precontinuous	ADJ
ejpam-5171	371	26	,	,	PUNCT
ejpam-5171	371	27	β	β	NOUN
ejpam-5171	371	28	-	-	ADJ
ejpam-5171	371	29	continuous	continuous	ADJ
ejpam-5171	371	30	)	)	PUNCT
ejpam-5171	371	31	.	.	PUNCT
ejpam-5171	372	1	proof	proof	NOUN
ejpam-5171	372	2	.	.	PUNCT
ejpam-5171	373	1	clearly	clearly	ADV
ejpam-5171	373	2	from	from	ADP
ejpam-5171	373	3	theorem	theorem	ADJ
ejpam-5171	373	4	2.2	2.2	NUM
ejpam-5171	373	5	.	.	PUNCT
ejpam-5171	373	6	example	example	NOUN
ejpam-5171	373	7	4.5	4.5	NUM
ejpam-5171	373	8	.	.	PUNCT
ejpam-5171	374	1	consider	consider	VERB
ejpam-5171	374	2	x	x	PUNCT
ejpam-5171	374	3	=	=	PRON
ejpam-5171	374	4	{	{	PUNCT
ejpam-5171	374	5	a1	a1	PROPN
ejpam-5171	374	6	,	,	PUNCT
ejpam-5171	374	7	a2	a2	PROPN
ejpam-5171	374	8	,	,	PUNCT
ejpam-5171	374	9	a3	a3	NOUN
ejpam-5171	374	10	,	,	PUNCT
ejpam-5171	374	11	a4	a4	PROPN
ejpam-5171	374	12	}	}	PUNCT
ejpam-5171	374	13	,	,	PUNCT
ejpam-5171	374	14	δ	δ	PROPN
ejpam-5171	374	15	=	=	PRON
ejpam-5171	374	16	{	{	PUNCT
ejpam-5171	374	17	ϕ	ϕ	NOUN
ejpam-5171	374	18	,	,	PUNCT
ejpam-5171	374	19	{	{	PUNCT
ejpam-5171	374	20	a1	a1	NOUN
ejpam-5171	374	21	}	}	PUNCT
ejpam-5171	374	22	,	,	PUNCT
ejpam-5171	374	23	{	{	PUNCT
ejpam-5171	374	24	a1	a1	NOUN
ejpam-5171	374	25	,	,	PUNCT
ejpam-5171	374	26	a2	a2	PROPN
ejpam-5171	374	27	}	}	PUNCT
ejpam-5171	374	28	,	,	PUNCT
ejpam-5171	374	29	{	{	PUNCT
ejpam-5171	374	30	a1	a1	NOUN
ejpam-5171	374	31	,	,	PUNCT
ejpam-5171	374	32	a4	a4	NOUN
ejpam-5171	374	33	}	}	PUNCT
ejpam-5171	374	34	,	,	PUNCT
ejpam-5171	374	35	{	{	PUNCT
ejpam-5171	374	36	a1	a1	NOUN
ejpam-5171	374	37	,	,	PUNCT
ejpam-5171	374	38	a2	a2	PROPN
ejpam-5171	374	39	,	,	PUNCT
ejpam-5171	374	40	a4},x	a4},x	PROPN
ejpam-5171	374	41	}	}	PUNCT
ejpam-5171	374	42	,	,	PUNCT
ejpam-5171	374	43	with	with	ADP
ejpam-5171	374	44	the	the	DET
ejpam-5171	374	45	primal	primal	ADJ
ejpam-5171	374	46	p	p	X
ejpam-5171	374	47	=	=	X
ejpam-5171	374	48	{	{	PUNCT
ejpam-5171	374	49	ϕ	ϕ	NOUN
ejpam-5171	374	50	,	,	PUNCT
ejpam-5171	374	51	{	{	PUNCT
ejpam-5171	374	52	a1	a1	NOUN
ejpam-5171	374	53	}	}	PUNCT
ejpam-5171	374	54	,	,	PUNCT
ejpam-5171	374	55	{	{	PUNCT
ejpam-5171	374	56	a2	a2	PROPN
ejpam-5171	374	57	}	}	PUNCT
ejpam-5171	374	58	,	,	PUNCT
ejpam-5171	374	59	{	{	PUNCT
ejpam-5171	374	60	a3	a3	NOUN
ejpam-5171	374	61	}	}	PUNCT
ejpam-5171	374	62	,	,	PUNCT
ejpam-5171	374	63	{	{	PUNCT
ejpam-5171	374	64	a1	a1	NOUN
ejpam-5171	374	65	,	,	PUNCT
ejpam-5171	374	66	a2	a2	PROPN
ejpam-5171	374	67	}	}	PUNCT
ejpam-5171	374	68	,	,	PUNCT
ejpam-5171	374	69	{	{	PUNCT
ejpam-5171	374	70	a2	a2	NOUN
ejpam-5171	374	71	,	,	PUNCT
ejpam-5171	374	72	a3	a3	NOUN
ejpam-5171	374	73	}	}	PUNCT
ejpam-5171	374	74	,	,	PUNCT
ejpam-5171	374	75	{	{	PUNCT
ejpam-5171	374	76	a1	a1	NOUN
ejpam-5171	374	77	,	,	PUNCT
ejpam-5171	374	78	a3	a3	NOUN
ejpam-5171	374	79	}	}	PUNCT
ejpam-5171	374	80	,	,	PUNCT
ejpam-5171	374	81	{	{	PUNCT
ejpam-5171	374	82	a1	a1	NOUN
ejpam-5171	374	83	,	,	PUNCT
ejpam-5171	374	84	a2	a2	PROPN
ejpam-5171	374	85	,	,	PUNCT
ejpam-5171	374	86	a3	a3	NOUN
ejpam-5171	374	87	}	}	PUNCT
ejpam-5171	374	88	}	}	PUNCT
ejpam-5171	374	89	.	.	PUNCT
ejpam-5171	375	1	we	we	PRON
ejpam-5171	375	2	define	define	VERB
ejpam-5171	375	3	a	a	DET
ejpam-5171	375	4	function	function	NOUN
ejpam-5171	375	5	f	f	NOUN
ejpam-5171	375	6	:	:	PUNCT
ejpam-5171	375	7	(	(	PUNCT
ejpam-5171	375	8	x	x	X
ejpam-5171	375	9	,	,	PUNCT
ejpam-5171	375	10	δ	δ	PROPN
ejpam-5171	375	11	,	,	PUNCT
ejpam-5171	375	12	p	p	NOUN
ejpam-5171	375	13	)	)	PUNCT
ejpam-5171	375	14	→	→	SYM
ejpam-5171	375	15	(	(	PUNCT
ejpam-5171	375	16	x	x	NOUN
ejpam-5171	375	17	,	,	PUNCT
ejpam-5171	375	18	δ	δ	PROPN
ejpam-5171	375	19	)	)	PUNCT
ejpam-5171	375	20	as	as	SCONJ
ejpam-5171	375	21	follows	follow	VERB
ejpam-5171	375	22	:	:	PUNCT
ejpam-5171	375	23	f(a1	f(a1	NOUN
ejpam-5171	375	24	)	)	PUNCT
ejpam-5171	375	25	=	=	SYM
ejpam-5171	375	26	a1	a1	NOUN
ejpam-5171	375	27	,	,	PUNCT
ejpam-5171	375	28	f(a2	f(a2	NOUN
ejpam-5171	375	29	)	)	PUNCT
ejpam-5171	375	30	=	=	SYM
ejpam-5171	375	31	a2	a2	PROPN
ejpam-5171	375	32	,	,	PUNCT
ejpam-5171	375	33	and	and	CCONJ
ejpam-5171	375	34	f(a3	f(a3	NOUN
ejpam-5171	375	35	)	)	PUNCT
ejpam-5171	375	36	=	=	SYM
ejpam-5171	375	37	f(a4	f(a4	PROPN
ejpam-5171	375	38	)	)	PUNCT
ejpam-5171	375	39	=	=	NOUN
ejpam-5171	375	40	a3	a3	NOUN
ejpam-5171	375	41	.	.	PUNCT
ejpam-5171	376	1	thus	thus	ADV
ejpam-5171	376	2	,	,	PUNCT
ejpam-5171	376	3	f	f	PROPN
ejpam-5171	376	4	is	be	AUX
ejpam-5171	376	5	not	not	PART
ejpam-5171	376	6	continuous	continuous	ADJ
ejpam-5171	376	7	since	since	SCONJ
ejpam-5171	376	8	f−1({a1	f−1({a1	NOUN
ejpam-5171	376	9	,	,	PUNCT
ejpam-5171	376	10	a3	a3	NOUN
ejpam-5171	376	11	}	}	PUNCT
ejpam-5171	376	12	)	)	PUNCT
ejpam-5171	377	1	=	=	PRON
ejpam-5171	377	2	{	{	PUNCT
ejpam-5171	377	3	a1	a1	PROPN
ejpam-5171	377	4	,	,	PUNCT
ejpam-5171	377	5	a4	a4	NOUN
ejpam-5171	377	6	}	}	PUNCT
ejpam-5171	377	7	is	be	AUX
ejpam-5171	377	8	not	not	PART
ejpam-5171	377	9	p	p	NOUN
ejpam-5171	377	10	-	-	NOUN
ejpam-5171	377	11	open	open	ADJ
ejpam-5171	377	12	.	.	PUNCT
ejpam-5171	378	1	however	however	ADV
ejpam-5171	378	2	,	,	PUNCT
ejpam-5171	378	3	f	f	PROPN
ejpam-5171	378	4	is	be	AUX
ejpam-5171	378	5	p	p	ADJ
ejpam-5171	378	6	-	-	PUNCT
ejpam-5171	378	7	semicontinuous	semicontinuous	ADJ
ejpam-5171	378	8	.	.	PUNCT
ejpam-5171	379	1	definition	definition	NOUN
ejpam-5171	379	2	4.6	4.6	NUM
ejpam-5171	379	3	.	.	PUNCT
ejpam-5171	380	1	a	a	DET
ejpam-5171	380	2	function	function	NOUN
ejpam-5171	380	3	f	f	NOUN
ejpam-5171	380	4	:	:	PUNCT
ejpam-5171	380	5	(	(	PUNCT
ejpam-5171	380	6	x	x	X
ejpam-5171	380	7	,	,	PUNCT
ejpam-5171	380	8	δ	δ	PROPN
ejpam-5171	380	9	,	,	PUNCT
ejpam-5171	380	10	p	p	NOUN
ejpam-5171	380	11	)	)	PUNCT
ejpam-5171	380	12	→	→	SYM
ejpam-5171	380	13	(	(	PUNCT
ejpam-5171	380	14	y	y	NOUN
ejpam-5171	380	15	,	,	PUNCT
ejpam-5171	380	16	ς	ς	NOUN
ejpam-5171	380	17	)	)	PUNCT
ejpam-5171	380	18	is	be	AUX
ejpam-5171	380	19	said	say	VERB
ejpam-5171	380	20	to	to	PART
ejpam-5171	380	21	be	be	AUX
ejpam-5171	380	22	pr	pr	NOUN
ejpam-5171	380	23	-	-	ADJ
ejpam-5171	380	24	continuous	continuous	ADJ
ejpam-5171	380	25	(	(	PUNCT
ejpam-5171	380	26	resp	resp	NOUN
ejpam-5171	380	27	.	.	PUNCT
ejpam-5171	381	1	prα	prα	VERB
ejpam-5171	381	2	-	-	ADJ
ejpam-5171	381	3	continuous	continuous	ADJ
ejpam-5171	381	4	)	)	PUNCT
ejpam-5171	381	5	,	,	PUNCT
ejpam-5171	381	6	if	if	SCONJ
ejpam-5171	381	7	the	the	DET
ejpam-5171	381	8	inverse	inverse	ADJ
ejpam-5171	381	9	image	image	NOUN
ejpam-5171	381	10	of	of	ADP
ejpam-5171	381	11	each	each	DET
ejpam-5171	381	12	open	open	ADJ
ejpam-5171	381	13	set	set	NOUN
ejpam-5171	381	14	in	in	ADP
ejpam-5171	381	15	y	y	PROPN
ejpam-5171	381	16	is	be	AUX
ejpam-5171	381	17	pr	pr	NOUN
ejpam-5171	381	18	-	-	PUNCT
ejpam-5171	381	19	set	set	VERB
ejpam-5171	381	20	(	(	PUNCT
ejpam-5171	381	21	resp	resp	NOUN
ejpam-5171	381	22	.	.	PUNCT
ejpam-5171	382	1	prα	prα	VERB
ejpam-5171	382	2	-	-	PUNCT
ejpam-5171	382	3	set	set	NOUN
ejpam-5171	382	4	)	)	PUNCT
ejpam-5171	382	5	in	in	ADP
ejpam-5171	382	6	(	(	PUNCT
ejpam-5171	382	7	x	x	NOUN
ejpam-5171	382	8	,	,	PUNCT
ejpam-5171	382	9	δ	δ	PROPN
ejpam-5171	382	10	,	,	PUNCT
ejpam-5171	382	11	p	p	NOUN
ejpam-5171	382	12	)	)	PUNCT
ejpam-5171	382	13	.	.	PUNCT
ejpam-5171	383	1	h.	h.	PROPN
ejpam-5171	383	2	al	al	PROPN
ejpam-5171	383	3	-	-	PUNCT
ejpam-5171	383	4	saadi	saadi	PROPN
ejpam-5171	383	5	,	,	PUNCT
ejpam-5171	383	6	m.	m.	NOUN
ejpam-5171	383	7	al	al	PROPN
ejpam-5171	383	8	-	-	PUNCT
ejpam-5171	383	9	hodieb	hodieb	PROPN
ejpam-5171	383	10	/	/	SYM
ejpam-5171	383	11	eur	eur	PROPN
ejpam-5171	383	12	.	.	PUNCT
ejpam-5171	384	1	j.	j.	PROPN
ejpam-5171	384	2	pure	pure	PROPN
ejpam-5171	384	3	appl	appl	PROPN
ejpam-5171	384	4	.	.	PROPN
ejpam-5171	384	5	math	math	PROPN
ejpam-5171	384	6	,	,	PUNCT
ejpam-5171	384	7	17	17	NUM
ejpam-5171	384	8	(	(	PUNCT
ejpam-5171	384	9	2	2	NUM
ejpam-5171	384	10	)	)	PUNCT
ejpam-5171	384	11	(	(	PUNCT
ejpam-5171	384	12	2024	2024	NUM
ejpam-5171	384	13	)	)	PUNCT
ejpam-5171	384	14	,	,	PUNCT
ejpam-5171	384	15	1352	1352	NUM
ejpam-5171	384	16	-	-	SYM
ejpam-5171	384	17	1368	1368	NUM
ejpam-5171	384	18	1363	1363	NUM
ejpam-5171	384	19	definition	definition	NOUN
ejpam-5171	384	20	4.7	4.7	NUM
ejpam-5171	384	21	.	.	PUNCT
ejpam-5171	385	1	a	a	DET
ejpam-5171	385	2	function	function	NOUN
ejpam-5171	385	3	f	f	NOUN
ejpam-5171	385	4	:	:	PUNCT
ejpam-5171	385	5	(	(	PUNCT
ejpam-5171	385	6	x	x	NOUN
ejpam-5171	385	7	,	,	PUNCT
ejpam-5171	385	8	δ	δ	PROPN
ejpam-5171	385	9	)	)	PUNCT
ejpam-5171	385	10	→	→	SYM
ejpam-5171	385	11	(	(	PUNCT
ejpam-5171	385	12	y	y	NOUN
ejpam-5171	385	13	,	,	PUNCT
ejpam-5171	385	14	ς	ς	NOUN
ejpam-5171	385	15	)	)	PUNCT
ejpam-5171	385	16	is	be	AUX
ejpam-5171	385	17	said	say	VERB
ejpam-5171	385	18	to	to	PART
ejpam-5171	385	19	be	be	AUX
ejpam-5171	385	20	r	r	NOUN
ejpam-5171	385	21	-	-	ADJ
ejpam-5171	385	22	continuous	continuous	ADJ
ejpam-5171	385	23	[	[	X
ejpam-5171	385	24	31	31	NUM
ejpam-5171	385	25	]	]	PUNCT
ejpam-5171	385	26	(	(	PUNCT
ejpam-5171	385	27	resp	resp	NOUN
ejpam-5171	385	28	.	.	PUNCT
ejpam-5171	386	1	rα	rα	ADJ
ejpam-5171	387	1	-	-	ADJ
ejpam-5171	387	2	continuous	continuous	ADJ
ejpam-5171	387	3	[	[	X
ejpam-5171	387	4	32	32	NUM
ejpam-5171	387	5	]	]	PUNCT
ejpam-5171	387	6	)	)	PUNCT
ejpam-5171	387	7	,	,	PUNCT
ejpam-5171	387	8	if	if	SCONJ
ejpam-5171	387	9	the	the	DET
ejpam-5171	387	10	inverse	inverse	ADJ
ejpam-5171	387	11	image	image	NOUN
ejpam-5171	387	12	of	of	ADP
ejpam-5171	387	13	each	each	DET
ejpam-5171	387	14	open	open	ADJ
ejpam-5171	387	15	set	set	NOUN
ejpam-5171	387	16	in	in	ADP
ejpam-5171	387	17	y	y	PROPN
ejpam-5171	387	18	is	be	AUX
ejpam-5171	387	19	r	r	NOUN
ejpam-5171	387	20	-	-	PUNCT
ejpam-5171	387	21	set	set	VERB
ejpam-5171	387	22	(	(	PUNCT
ejpam-5171	387	23	resp	resp	NOUN
ejpam-5171	387	24	.	.	PUNCT
ejpam-5171	388	1	rα	rα	VERB
ejpam-5171	388	2	-	-	PUNCT
ejpam-5171	388	3	set	set	NOUN
ejpam-5171	388	4	)	)	PUNCT
ejpam-5171	388	5	in	in	ADP
ejpam-5171	388	6	(	(	PUNCT
ejpam-5171	388	7	x	x	NOUN
ejpam-5171	388	8	,	,	PUNCT
ejpam-5171	388	9	δ	δ	PROPN
ejpam-5171	388	10	)	)	PUNCT
ejpam-5171	388	11	.	.	PUNCT
ejpam-5171	389	1	proposition	proposition	NOUN
ejpam-5171	389	2	4.8	4.8	NUM
ejpam-5171	389	3	.	.	PUNCT
ejpam-5171	390	1	if	if	SCONJ
ejpam-5171	390	2	a	a	DET
ejpam-5171	390	3	function	function	NOUN
ejpam-5171	390	4	f	f	X
ejpam-5171	390	5	:	:	PUNCT
ejpam-5171	390	6	(	(	PUNCT
ejpam-5171	390	7	x	x	X
ejpam-5171	390	8	,	,	PUNCT
ejpam-5171	390	9	δ	δ	PROPN
ejpam-5171	390	10	,	,	PUNCT
ejpam-5171	390	11	p	p	NOUN
ejpam-5171	390	12	)	)	PUNCT
ejpam-5171	390	13	→	→	SYM
ejpam-5171	390	14	(	(	PUNCT
ejpam-5171	390	15	y	y	NOUN
ejpam-5171	390	16	,	,	PUNCT
ejpam-5171	390	17	ς	ς	NOUN
ejpam-5171	390	18	)	)	PUNCT
ejpam-5171	390	19	is	be	AUX
ejpam-5171	390	20	r	r	NOUN
ejpam-5171	390	21	-	-	ADJ
ejpam-5171	390	22	continuous	continuous	ADJ
ejpam-5171	390	23	(	(	PUNCT
ejpam-5171	390	24	resp	resp	NOUN
ejpam-5171	390	25	.	.	PUNCT
ejpam-5171	391	1	rαcontinuous	rαcontinuous	ADJ
ejpam-5171	391	2	)	)	PUNCT
ejpam-5171	391	3	,	,	PUNCT
ejpam-5171	391	4	it	it	PRON
ejpam-5171	391	5	is	be	AUX
ejpam-5171	391	6	also	also	ADV
ejpam-5171	391	7	pr	pr	NOUN
ejpam-5171	391	8	-	-	ADJ
ejpam-5171	391	9	continuous	continuous	ADJ
ejpam-5171	391	10	(	(	PUNCT
ejpam-5171	391	11	resp	resp	NOUN
ejpam-5171	391	12	.	.	PUNCT
ejpam-5171	392	1	prα	prα	VERB
ejpam-5171	392	2	-	-	ADJ
ejpam-5171	392	3	continuous	continuous	ADJ
ejpam-5171	392	4	)	)	PUNCT
ejpam-5171	392	5	.	.	PUNCT
ejpam-5171	393	1	proof	proof	NOUN
ejpam-5171	393	2	.	.	PUNCT
ejpam-5171	394	1	straightforward	straightforward	ADJ
ejpam-5171	394	2	.	.	PUNCT
ejpam-5171	395	1	theorem	theorem	VERB
ejpam-5171	395	2	4.9	4.9	NUM
ejpam-5171	395	3	.	.	PUNCT
ejpam-5171	396	1	let	let	VERB
ejpam-5171	396	2	f	f	NOUN
ejpam-5171	396	3	:	:	PUNCT
ejpam-5171	396	4	(	(	PUNCT
ejpam-5171	396	5	x	x	X
ejpam-5171	396	6	,	,	PUNCT
ejpam-5171	396	7	δ	δ	PROPN
ejpam-5171	396	8	,	,	PUNCT
ejpam-5171	396	9	p	p	NOUN
ejpam-5171	396	10	)	)	PUNCT
ejpam-5171	396	11	→	→	SYM
ejpam-5171	396	12	(	(	PUNCT
ejpam-5171	396	13	y	y	NOUN
ejpam-5171	396	14	,	,	PUNCT
ejpam-5171	396	15	ς	ς	PROPN
ejpam-5171	396	16	)	)	PUNCT
ejpam-5171	396	17	be	be	AUX
ejpam-5171	396	18	a	a	DET
ejpam-5171	396	19	function	function	NOUN
ejpam-5171	396	20	.	.	PUNCT
ejpam-5171	397	1	hence	hence	ADV
ejpam-5171	397	2	,	,	PUNCT
ejpam-5171	397	3	the	the	DET
ejpam-5171	397	4	following	follow	VERB
ejpam-5171	397	5	are	be	AUX
ejpam-5171	397	6	equivalent	equivalent	ADJ
ejpam-5171	397	7	:	:	PUNCT
ejpam-5171	397	8	(	(	PUNCT
ejpam-5171	397	9	a	a	X
ejpam-5171	397	10	)	)	PUNCT
ejpam-5171	397	11	f	f	PROPN
ejpam-5171	397	12	is	be	AUX
ejpam-5171	397	13	continuous	continuous	ADJ
ejpam-5171	397	14	;	;	PUNCT
ejpam-5171	397	15	(	(	PUNCT
ejpam-5171	397	16	b	b	X
ejpam-5171	397	17	)	)	PUNCT
ejpam-5171	397	18	f	f	PROPN
ejpam-5171	397	19	is	be	AUX
ejpam-5171	397	20	a	a	DET
ejpam-5171	397	21	p	p	NOUN
ejpam-5171	397	22	-	-	PUNCT
ejpam-5171	397	23	precontinuous	precontinuous	NOUN
ejpam-5171	397	24	and	and	CCONJ
ejpam-5171	397	25	a	a	DET
ejpam-5171	397	26	pr	pr	NOUN
ejpam-5171	397	27	-	-	NOUN
ejpam-5171	397	28	continuous	continuous	ADJ
ejpam-5171	397	29	;	;	PUNCT
ejpam-5171	397	30	(	(	PUNCT
ejpam-5171	397	31	c	c	X
ejpam-5171	397	32	)	)	PUNCT
ejpam-5171	397	33	f	f	PROPN
ejpam-5171	397	34	is	be	AUX
ejpam-5171	397	35	a	a	DET
ejpam-5171	397	36	p	p	NOUN
ejpam-5171	397	37	-	-	PUNCT
ejpam-5171	397	38	α	α	NOUN
ejpam-5171	397	39	-	-	ADJ
ejpam-5171	397	40	continuous	continuous	ADJ
ejpam-5171	397	41	and	and	CCONJ
ejpam-5171	397	42	a	a	DET
ejpam-5171	397	43	prα	prα	ADJ
ejpam-5171	397	44	-	-	ADJ
ejpam-5171	397	45	continuous	continuous	ADJ
ejpam-5171	397	46	.	.	PUNCT
ejpam-5171	398	1	proof	proof	NOUN
ejpam-5171	398	2	.	.	PUNCT
ejpam-5171	399	1	it	it	PRON
ejpam-5171	399	2	is	be	AUX
ejpam-5171	399	3	a	a	DET
ejpam-5171	399	4	direct	direct	ADJ
ejpam-5171	399	5	result	result	NOUN
ejpam-5171	399	6	of	of	ADP
ejpam-5171	399	7	propositions	proposition	NOUN
ejpam-5171	399	8	3.9	3.9	NUM
ejpam-5171	399	9	and	and	CCONJ
ejpam-5171	399	10	propositions	proposition	NOUN
ejpam-5171	399	11	3.15	3.15	NUM
ejpam-5171	399	12	.	.	PUNCT
ejpam-5171	400	1	5	5	NUM
ejpam-5171	400	2	.	.	X
ejpam-5171	400	3	ψ̃p	ψ̃p	NOUN
ejpam-5171	400	4	-	-	PUNCT
ejpam-5171	400	5	sets	set	NOUN
ejpam-5171	400	6	in	in	ADP
ejpam-5171	400	7	this	this	DET
ejpam-5171	400	8	section	section	NOUN
ejpam-5171	400	9	,	,	PUNCT
ejpam-5171	400	10	we	we	PRON
ejpam-5171	400	11	describe	describe	VERB
ejpam-5171	400	12	a	a	DET
ejpam-5171	400	13	new	new	ADJ
ejpam-5171	400	14	class	class	NOUN
ejpam-5171	400	15	of	of	ADP
ejpam-5171	400	16	sets	set	NOUN
ejpam-5171	400	17	in	in	ADP
ejpam-5171	400	18	pts	pt	NOUN
ejpam-5171	400	19	that	that	PRON
ejpam-5171	400	20	contain	contain	VERB
ejpam-5171	400	21	the	the	DET
ejpam-5171	400	22	class	class	NOUN
ejpam-5171	400	23	of	of	ADP
ejpam-5171	400	24	all	all	DET
ejpam-5171	400	25	open	open	ADJ
ejpam-5171	400	26	sets	set	NOUN
ejpam-5171	400	27	,	,	PUNCT
ejpam-5171	400	28	using	use	VERB
ejpam-5171	400	29	the	the	DET
ejpam-5171	400	30	ψp	ψp	NOUN
ejpam-5171	400	31	-operator	-operator	PROPN
ejpam-5171	400	32	.	.	PUNCT
ejpam-5171	401	1	definition	definition	NOUN
ejpam-5171	401	2	5.1	5.1	NUM
ejpam-5171	401	3	.	.	PUNCT
ejpam-5171	402	1	a	a	DET
ejpam-5171	402	2	subset	subset	ADJ
ejpam-5171	402	3	l	l	NOUN
ejpam-5171	402	4	of	of	ADP
ejpam-5171	402	5	a	a	DET
ejpam-5171	402	6	pts	pts	X
ejpam-5171	402	7	(	(	PUNCT
ejpam-5171	402	8	x	x	NOUN
ejpam-5171	402	9	,	,	PUNCT
ejpam-5171	402	10	δ	δ	PROPN
ejpam-5171	402	11	,	,	PUNCT
ejpam-5171	402	12	p	p	NOUN
ejpam-5171	402	13	)	)	PUNCT
ejpam-5171	402	14	is	be	AUX
ejpam-5171	402	15	called	call	VERB
ejpam-5171	402	16	ψ̃p	ψ̃p	NOUN
ejpam-5171	402	17	-	-	PUNCT
ejpam-5171	402	18	set	set	VERB
ejpam-5171	402	19	if	if	SCONJ
ejpam-5171	402	20	l	l	NOUN
ejpam-5171	402	21	⊆	⊆	NUM
ejpam-5171	402	22	cl(ψp(l	cl(ψp(l	NOUN
ejpam-5171	402	23	)	)	PUNCT
ejpam-5171	402	24	)	)	PUNCT
ejpam-5171	402	25	.	.	PUNCT
ejpam-5171	403	1	the	the	DET
ejpam-5171	403	2	family	family	NOUN
ejpam-5171	403	3	of	of	ADP
ejpam-5171	403	4	all	all	DET
ejpam-5171	403	5	ψ̃p	ψ̃p	NOUN
ejpam-5171	403	6	-sets	-set	NOUN
ejpam-5171	403	7	in	in	ADP
ejpam-5171	403	8	(	(	PUNCT
ejpam-5171	403	9	x	x	NOUN
ejpam-5171	403	10	,	,	PUNCT
ejpam-5171	403	11	δ	δ	PROPN
ejpam-5171	403	12	,	,	PUNCT
ejpam-5171	403	13	p	p	NOUN
ejpam-5171	403	14	)	)	PUNCT
ejpam-5171	403	15	is	be	AUX
ejpam-5171	403	16	denoted	denote	VERB
ejpam-5171	403	17	by	by	ADP
ejpam-5171	403	18	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	403	19	,	,	PUNCT
ejpam-5171	403	20	δ	δ	PROPN
ejpam-5171	403	21	)	)	PUNCT
ejpam-5171	403	22	.	.	PUNCT
ejpam-5171	404	1	theorem	theorem	VERB
ejpam-5171	404	2	5.2	5.2	NUM
ejpam-5171	404	3	.	.	PUNCT
ejpam-5171	405	1	suppose	suppose	VERB
ejpam-5171	405	2	that	that	SCONJ
ejpam-5171	405	3	(	(	PUNCT
ejpam-5171	405	4	x	x	X
ejpam-5171	405	5	,	,	PUNCT
ejpam-5171	405	6	δ	δ	PROPN
ejpam-5171	405	7	,	,	PUNCT
ejpam-5171	405	8	p	p	NOUN
ejpam-5171	405	9	)	)	PUNCT
ejpam-5171	405	10	is	be	AUX
ejpam-5171	405	11	a	a	DET
ejpam-5171	405	12	pts	pt	NOUN
ejpam-5171	405	13	.	.	PUNCT
ejpam-5171	406	1	if	if	SCONJ
ejpam-5171	406	2	l	l	PROPN
ejpam-5171	406	3	∈	∈	PROPN
ejpam-5171	406	4	δ	δ	PROPN
ejpam-5171	406	5	,	,	PUNCT
ejpam-5171	406	6	then	then	ADV
ejpam-5171	406	7	l	l	PROPN
ejpam-5171	406	8	∈	∈	PROPN
ejpam-5171	406	9	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	406	10	,	,	PUNCT
ejpam-5171	406	11	δ	δ	PROPN
ejpam-5171	406	12	)	)	PUNCT
ejpam-5171	406	13	.	.	PUNCT
ejpam-5171	407	1	proof	proof	NOUN
ejpam-5171	407	2	.	.	PUNCT
ejpam-5171	408	1	by	by	ADP
ejpam-5171	408	2	corollary	corollary	ADJ
ejpam-5171	408	3	1.14	1.14	NUM
ejpam-5171	408	4	,	,	PUNCT
ejpam-5171	408	5	δ	δ	PROPN
ejpam-5171	408	6	⊂	⊂	PROPN
ejpam-5171	408	7	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	408	8	,	,	PUNCT
ejpam-5171	408	9	δ	δ	PROPN
ejpam-5171	408	10	)	)	PUNCT
ejpam-5171	408	11	is	be	AUX
ejpam-5171	408	12	obtained	obtain	VERB
ejpam-5171	408	13	in	in	ADP
ejpam-5171	408	14	the	the	DET
ejpam-5171	408	15	topological	topological	ADJ
ejpam-5171	408	16	space	space	NOUN
ejpam-5171	408	17	(	(	PUNCT
ejpam-5171	408	18	x	x	NOUN
ejpam-5171	408	19	,	,	PUNCT
ejpam-5171	408	20	δ	δ	PROPN
ejpam-5171	408	21	,	,	PUNCT
ejpam-5171	408	22	p	p	NOUN
ejpam-5171	408	23	)	)	PUNCT
ejpam-5171	408	24	.	.	PUNCT
ejpam-5171	409	1	in	in	ADP
ejpam-5171	409	2	general	general	ADJ
ejpam-5171	409	3	,	,	PUNCT
ejpam-5171	409	4	the	the	DET
ejpam-5171	409	5	following	follow	VERB
ejpam-5171	409	6	example	example	NOUN
ejpam-5171	409	7	demonstrates	demonstrate	VERB
ejpam-5171	409	8	that	that	SCONJ
ejpam-5171	409	9	the	the	DET
ejpam-5171	409	10	opposite	opposite	NOUN
ejpam-5171	409	11	of	of	ADP
ejpam-5171	409	12	theorem	theorem	ADJ
ejpam-5171	409	13	5.2	5.2	NUM
ejpam-5171	409	14	is	be	AUX
ejpam-5171	409	15	not	not	PART
ejpam-5171	409	16	true	true	ADJ
ejpam-5171	409	17	.	.	PUNCT
ejpam-5171	410	1	example	example	NOUN
ejpam-5171	410	2	5.3	5.3	NUM
ejpam-5171	410	3	.	.	PUNCT
ejpam-5171	411	1	let	let	VERB
ejpam-5171	411	2	x	x	PUNCT
ejpam-5171	411	3	=	=	PRON
ejpam-5171	411	4	{	{	PUNCT
ejpam-5171	411	5	a1	a1	PROPN
ejpam-5171	411	6	,	,	PUNCT
ejpam-5171	411	7	a2	a2	PROPN
ejpam-5171	411	8	,	,	PUNCT
ejpam-5171	411	9	a3	a3	NOUN
ejpam-5171	411	10	}	}	PUNCT
ejpam-5171	411	11	,	,	PUNCT
ejpam-5171	411	12	and	and	CCONJ
ejpam-5171	411	13	δ	δ	PROPN
ejpam-5171	411	14	=	=	PRON
ejpam-5171	411	15	{	{	PUNCT
ejpam-5171	411	16	ϕ	ϕ	NOUN
ejpam-5171	411	17	,	,	PUNCT
ejpam-5171	411	18	{	{	PUNCT
ejpam-5171	411	19	a1	a1	NOUN
ejpam-5171	411	20	}	}	PUNCT
ejpam-5171	411	21	,	,	PUNCT
ejpam-5171	411	22	{	{	PUNCT
ejpam-5171	411	23	a2	a2	PROPN
ejpam-5171	411	24	}	}	PUNCT
ejpam-5171	411	25	,	,	PUNCT
ejpam-5171	411	26	{	{	PUNCT
ejpam-5171	411	27	a1	a1	NOUN
ejpam-5171	411	28	,	,	PUNCT
ejpam-5171	411	29	a2},x	a2},x	PROPN
ejpam-5171	411	30	}	}	PUNCT
ejpam-5171	411	31	,	,	PUNCT
ejpam-5171	411	32	with	with	ADP
ejpam-5171	411	33	the	the	DET
ejpam-5171	411	34	primal	primal	ADJ
ejpam-5171	411	35	p	p	X
ejpam-5171	411	36	=	=	X
ejpam-5171	411	37	{	{	PUNCT
ejpam-5171	411	38	ϕ	ϕ	NOUN
ejpam-5171	411	39	,	,	PUNCT
ejpam-5171	411	40	{	{	PUNCT
ejpam-5171	411	41	a1	a1	NOUN
ejpam-5171	411	42	}	}	PUNCT
ejpam-5171	411	43	,	,	PUNCT
ejpam-5171	411	44	{	{	PUNCT
ejpam-5171	411	45	a2	a2	PROPN
ejpam-5171	411	46	}	}	PUNCT
ejpam-5171	411	47	,	,	PUNCT
ejpam-5171	411	48	{	{	PUNCT
ejpam-5171	411	49	a1	a1	NOUN
ejpam-5171	411	50	,	,	PUNCT
ejpam-5171	411	51	a2	a2	PROPN
ejpam-5171	411	52	}	}	PUNCT
ejpam-5171	411	53	}	}	PUNCT
ejpam-5171	411	54	.	.	PUNCT
ejpam-5171	412	1	now	now	ADV
ejpam-5171	412	2	,	,	PUNCT
ejpam-5171	412	3	ψp({a3	ψp({a3	PROPN
ejpam-5171	412	4	}	}	PUNCT
ejpam-5171	412	5	)	)	PUNCT
ejpam-5171	413	1	=	=	PUNCT
ejpam-5171	413	2	x	x	PUNCT
ejpam-5171	413	3	−	−	PROPN
ejpam-5171	413	4	{	{	PUNCT
ejpam-5171	413	5	a1	a1	PROPN
ejpam-5171	413	6	,	,	PUNCT
ejpam-5171	413	7	a2	a2	PROPN
ejpam-5171	413	8	}	}	PUNCT
ejpam-5171	413	9	♢	♢	PROPN
ejpam-5171	413	10	=	=	PUNCT
ejpam-5171	413	11	x	x	PROPN
ejpam-5171	414	1	−	−	NOUN
ejpam-5171	414	2	ϕ	ϕ	X
ejpam-5171	414	3	=	=	PUNCT
ejpam-5171	414	4	x.	x.	NOUN
ejpam-5171	414	5	thus	thus	ADV
ejpam-5171	414	6	,	,	PUNCT
ejpam-5171	414	7	cl(ψp({a3	cl(ψp({a3	NOUN
ejpam-5171	414	8	}	}	PUNCT
ejpam-5171	414	9	)	)	PUNCT
ejpam-5171	414	10	)	)	PUNCT
ejpam-5171	415	1	=	=	PUNCT
ejpam-5171	415	2	x.	x.	NOUN
ejpam-5171	415	3	therefore	therefore	ADV
ejpam-5171	415	4	,	,	PUNCT
ejpam-5171	415	5	{	{	PUNCT
ejpam-5171	415	6	a3	a3	NOUN
ejpam-5171	415	7	}	}	PUNCT
ejpam-5171	415	8	⊆	⊆	NUM
ejpam-5171	415	9	cl(cl	cl(cl	PROPN
ejpam-5171	415	10	♢	♢	NOUN
ejpam-5171	415	11	p({a3	p({a3	PROPN
ejpam-5171	415	12	}	}	PUNCT
ejpam-5171	415	13	)	)	PUNCT
ejpam-5171	415	14	)	)	PUNCT
ejpam-5171	415	15	,	,	PUNCT
ejpam-5171	415	16	but	but	CCONJ
ejpam-5171	415	17	{	{	PUNCT
ejpam-5171	415	18	a3	a3	NOUN
ejpam-5171	415	19	}	}	PUNCT
ejpam-5171	415	20	is	be	AUX
ejpam-5171	415	21	not	not	PART
ejpam-5171	415	22	open	open	ADJ
ejpam-5171	415	23	in	in	ADP
ejpam-5171	415	24	δ	δ	PROPN
ejpam-5171	415	25	.	.	PUNCT
ejpam-5171	416	1	now	now	ADV
ejpam-5171	416	2	,	,	PUNCT
ejpam-5171	416	3	we	we	PRON
ejpam-5171	416	4	show	show	VERB
ejpam-5171	416	5	that	that	SCONJ
ejpam-5171	416	6	any	any	DET
ejpam-5171	416	7	union	union	NOUN
ejpam-5171	416	8	of	of	ADP
ejpam-5171	416	9	ψ̃p	ψ̃p	NOUN
ejpam-5171	416	10	-sets	-set	NOUN
ejpam-5171	416	11	is	be	AUX
ejpam-5171	416	12	a	a	DET
ejpam-5171	416	13	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	416	14	,	,	PUNCT
ejpam-5171	416	15	δ	δ	PROPN
ejpam-5171	416	16	)	)	PUNCT
ejpam-5171	416	17	.	.	PUNCT
ejpam-5171	417	1	proposition	proposition	NOUN
ejpam-5171	417	2	5.4	5.4	NUM
ejpam-5171	417	3	.	.	PUNCT
ejpam-5171	417	4	suppose	suppose	VERB
ejpam-5171	417	5	that	that	SCONJ
ejpam-5171	417	6	{	{	PUNCT
ejpam-5171	417	7	lα	lα	NOUN
ejpam-5171	417	8	:	:	PUNCT
ejpam-5171	417	9	α	α	PROPN
ejpam-5171	417	10	∈	∈	PROPN
ejpam-5171	417	11	∆	∆	X
ejpam-5171	417	12	}	}	PUNCT
ejpam-5171	417	13	is	be	AUX
ejpam-5171	417	14	a	a	DET
ejpam-5171	417	15	set	set	NOUN
ejpam-5171	417	16	of	of	ADP
ejpam-5171	417	17	non	non	ADJ
ejpam-5171	417	18	-	-	ADJ
ejpam-5171	417	19	empty	empty	ADJ
ejpam-5171	417	20	ψ̃p	ψ̃p	NOUN
ejpam-5171	417	21	-	-	PUNCT
ejpam-5171	417	22	sets	set	NOUN
ejpam-5171	417	23	in	in	ADP
ejpam-5171	417	24	a	a	DET
ejpam-5171	417	25	pts	pts	X
ejpam-5171	417	26	(	(	PUNCT
ejpam-5171	417	27	x	x	NOUN
ejpam-5171	417	28	,	,	PUNCT
ejpam-5171	417	29	δ	δ	PROPN
ejpam-5171	417	30	,	,	PUNCT
ejpam-5171	417	31	p	p	NOUN
ejpam-5171	417	32	)	)	PUNCT
ejpam-5171	417	33	,	,	PUNCT
ejpam-5171	417	34	then	then	ADV
ejpam-5171	417	35	∪α∈∆lα	∪α∈∆lα	VERB
ejpam-5171	417	36	∈	∈	PROPN
ejpam-5171	417	37	ψ̃p(x	ψ̃p(x	NOUN
ejpam-5171	417	38	,	,	PUNCT
ejpam-5171	417	39	δ	δ	PROPN
ejpam-5171	417	40	)	)	PUNCT
ejpam-5171	417	41	.	.	PUNCT
ejpam-5171	418	1	proof	proof	NOUN
ejpam-5171	418	2	.	.	PUNCT
ejpam-5171	419	1	for	for	ADP
ejpam-5171	419	2	every	every	DET
ejpam-5171	419	3	α	α	PROPN
ejpam-5171	419	4	∈	∈	NOUN
ejpam-5171	419	5	∆	∆	PROPN
ejpam-5171	419	6	,	,	PUNCT
ejpam-5171	419	7	lα	lα	ADP
ejpam-5171	419	8	⊆	⊆	NUM
ejpam-5171	419	9	cl(ψp(lα	cl(ψp(lα	NUM
ejpam-5171	419	10	)	)	PUNCT
ejpam-5171	419	11	)	)	PUNCT
ejpam-5171	420	1	⊆	⊆	NUM
ejpam-5171	420	2	cl(ψp(∪α∈∆lα	cl(ψp(∪α∈∆lα	NOUN
ejpam-5171	420	3	)	)	PUNCT
ejpam-5171	420	4	)	)	PUNCT
ejpam-5171	420	5	.	.	PUNCT
ejpam-5171	421	1	this	this	PRON
ejpam-5171	421	2	implies	imply	VERB
ejpam-5171	421	3	that	that	SCONJ
ejpam-5171	421	4	∪α∈∆lα	∪α∈∆lα	VERB
ejpam-5171	421	5	⊆	⊆	NUM
ejpam-5171	421	6	cl(ψp(∪α∈∆lα	cl(ψp(∪α∈∆lα	NOUN
ejpam-5171	421	7	)	)	PUNCT
ejpam-5171	421	8	)	)	PUNCT
ejpam-5171	421	9	.	.	PUNCT
ejpam-5171	422	1	hence	hence	ADV
ejpam-5171	422	2	,	,	PUNCT
ejpam-5171	422	3	∪α∈∆lα	∪α∈∆lα	NOUN
ejpam-5171	422	4	∈	∈	ADJ
ejpam-5171	422	5	ψ̃p(x	ψ̃p(x	NOUN
ejpam-5171	422	6	,	,	PUNCT
ejpam-5171	422	7	δ	δ	PROPN
ejpam-5171	422	8	)	)	PUNCT
ejpam-5171	422	9	.	.	PUNCT
ejpam-5171	423	1	the	the	DET
ejpam-5171	423	2	example	example	NOUN
ejpam-5171	423	3	below	below	ADV
ejpam-5171	423	4	demonstrates	demonstrate	VERB
ejpam-5171	423	5	an	an	DET
ejpam-5171	423	6	intersection	intersection	NOUN
ejpam-5171	423	7	of	of	ADP
ejpam-5171	423	8	two	two	NUM
ejpam-5171	423	9	ψ̃p	ψ̃p	NOUN
ejpam-5171	423	10	-sets	-set	NOUN
ejpam-5171	423	11	not	not	PART
ejpam-5171	423	12	necessarily	necessarily	ADV
ejpam-5171	423	13	a	a	DET
ejpam-5171	423	14	ψ̃p	ψ̃p	NOUN
ejpam-5171	423	15	-set	-set	ADJ
ejpam-5171	423	16	.	.	PUNCT
ejpam-5171	424	1	h.	h.	PROPN
ejpam-5171	424	2	al	al	PROPN
ejpam-5171	424	3	-	-	PUNCT
ejpam-5171	424	4	saadi	saadi	PROPN
ejpam-5171	424	5	,	,	PUNCT
ejpam-5171	424	6	m.	m.	NOUN
ejpam-5171	424	7	al	al	PROPN
ejpam-5171	424	8	-	-	PUNCT
ejpam-5171	424	9	hodieb	hodieb	PROPN
ejpam-5171	424	10	/	/	SYM
ejpam-5171	424	11	eur	eur	PROPN
ejpam-5171	424	12	.	.	PUNCT
ejpam-5171	425	1	j.	j.	PROPN
ejpam-5171	425	2	pure	pure	PROPN
ejpam-5171	425	3	appl	appl	PROPN
ejpam-5171	425	4	.	.	PROPN
ejpam-5171	425	5	math	math	PROPN
ejpam-5171	425	6	,	,	PUNCT
ejpam-5171	425	7	17	17	NUM
ejpam-5171	425	8	(	(	PUNCT
ejpam-5171	425	9	2	2	NUM
ejpam-5171	425	10	)	)	PUNCT
ejpam-5171	425	11	(	(	PUNCT
ejpam-5171	425	12	2024	2024	NUM
ejpam-5171	425	13	)	)	PUNCT
ejpam-5171	425	14	,	,	PUNCT
ejpam-5171	425	15	1352	1352	NUM
ejpam-5171	425	16	-	-	SYM
ejpam-5171	425	17	1368	1368	NUM
ejpam-5171	425	18	1364	1364	NUM
ejpam-5171	425	19	example	example	NOUN
ejpam-5171	425	20	5.5	5.5	NUM
ejpam-5171	425	21	.	.	PUNCT
ejpam-5171	426	1	assuming	assume	VERB
ejpam-5171	426	2	that	that	SCONJ
ejpam-5171	426	3	x	x	SYM
ejpam-5171	426	4	=	=	PRON
ejpam-5171	426	5	{	{	PUNCT
ejpam-5171	426	6	a1	a1	PROPN
ejpam-5171	426	7	,	,	PUNCT
ejpam-5171	426	8	a2	a2	PROPN
ejpam-5171	426	9	,	,	PUNCT
ejpam-5171	426	10	a3	a3	NOUN
ejpam-5171	426	11	}	}	PUNCT
ejpam-5171	426	12	,	,	PUNCT
ejpam-5171	426	13	δ	δ	PROPN
ejpam-5171	426	14	=	=	PRON
ejpam-5171	426	15	{	{	PUNCT
ejpam-5171	426	16	ϕ	ϕ	NOUN
ejpam-5171	426	17	,	,	PUNCT
ejpam-5171	426	18	{	{	PUNCT
ejpam-5171	426	19	a1	a1	NOUN
ejpam-5171	426	20	,	,	PUNCT
ejpam-5171	426	21	a3},x	a3},x	NOUN
ejpam-5171	426	22	}	}	PUNCT
ejpam-5171	426	23	,	,	PUNCT
ejpam-5171	426	24	with	with	ADP
ejpam-5171	426	25	the	the	DET
ejpam-5171	426	26	primal	primal	ADJ
ejpam-5171	426	27	p	p	X
ejpam-5171	426	28	=	=	X
ejpam-5171	426	29	{	{	PUNCT
ejpam-5171	426	30	ϕ	ϕ	NOUN
ejpam-5171	426	31	,	,	PUNCT
ejpam-5171	426	32	{	{	PUNCT
ejpam-5171	426	33	a2	a2	PROPN
ejpam-5171	426	34	}	}	PUNCT
ejpam-5171	426	35	,	,	PUNCT
ejpam-5171	426	36	{	{	PUNCT
ejpam-5171	426	37	a3	a3	NOUN
ejpam-5171	426	38	}	}	PUNCT
ejpam-5171	426	39	,	,	PUNCT
ejpam-5171	426	40	{	{	PUNCT
ejpam-5171	426	41	a2	a2	NOUN
ejpam-5171	426	42	,	,	PUNCT
ejpam-5171	426	43	a3	a3	NOUN
ejpam-5171	426	44	}	}	PUNCT
ejpam-5171	426	45	}	}	PUNCT
ejpam-5171	426	46	.	.	PUNCT
ejpam-5171	427	1	then	then	ADV
ejpam-5171	427	2	l	l	NOUN
ejpam-5171	427	3	=	=	PUNCT
ejpam-5171	427	4	{	{	PUNCT
ejpam-5171	427	5	a1	a1	PROPN
ejpam-5171	427	6	,	,	PUNCT
ejpam-5171	427	7	a2	a2	NOUN
ejpam-5171	427	8	}	}	PUNCT
ejpam-5171	427	9	and	and	CCONJ
ejpam-5171	427	10	e	e	NOUN
ejpam-5171	427	11	=	=	SYM
ejpam-5171	427	12	{	{	PUNCT
ejpam-5171	427	13	a1	a1	NOUN
ejpam-5171	427	14	,	,	PUNCT
ejpam-5171	427	15	a3	a3	NOUN
ejpam-5171	427	16	}	}	PUNCT
ejpam-5171	427	17	are	be	AUX
ejpam-5171	427	18	ψ̃p	ψ̃p	NOUN
ejpam-5171	427	19	-	-	PUNCT
ejpam-5171	427	20	sets	set	NOUN
ejpam-5171	427	21	,	,	PUNCT
ejpam-5171	427	22	since	since	SCONJ
ejpam-5171	427	23	ψp({a1	ψp({a1	ADJ
ejpam-5171	427	24	,	,	PUNCT
ejpam-5171	427	25	a2	a2	PROPN
ejpam-5171	427	26	}	}	PUNCT
ejpam-5171	427	27	)	)	PUNCT
ejpam-5171	428	1	=	=	PUNCT
ejpam-5171	428	2	x	x	PUNCT
ejpam-5171	428	3	−	−	NOUN
ejpam-5171	428	4	{	{	PUNCT
ejpam-5171	428	5	a3	a3	NOUN
ejpam-5171	428	6	}	}	PUNCT
ejpam-5171	428	7	♢	♢	PROPN
ejpam-5171	428	8	=	=	SYM
ejpam-5171	428	9	x	x	PROPN
ejpam-5171	428	10	,	,	PUNCT
ejpam-5171	428	11	{	{	PUNCT
ejpam-5171	428	12	a1	a1	NOUN
ejpam-5171	428	13	,	,	PUNCT
ejpam-5171	428	14	a2	a2	PROPN
ejpam-5171	428	15	}	}	PUNCT
ejpam-5171	428	16	⊆	⊆	NUM
ejpam-5171	428	17	cl(ψp({a1	cl(ψp({a1	ADJ
ejpam-5171	428	18	,	,	PUNCT
ejpam-5171	428	19	a2	a2	NOUN
ejpam-5171	428	20	}	}	PUNCT
ejpam-5171	428	21	)	)	PUNCT
ejpam-5171	428	22	)	)	PUNCT
ejpam-5171	429	1	=	=	PUNCT
ejpam-5171	429	2	x	x	X
ejpam-5171	429	3	and	and	CCONJ
ejpam-5171	429	4	ψp({a1	ψp({a1	ADJ
ejpam-5171	429	5	,	,	PUNCT
ejpam-5171	429	6	a3	a3	NOUN
ejpam-5171	429	7	}	}	PUNCT
ejpam-5171	429	8	)	)	PUNCT
ejpam-5171	429	9	=	=	PUNCT
ejpam-5171	430	1	x	x	PUNCT
ejpam-5171	430	2	−	−	PROPN
ejpam-5171	430	3	{	{	PUNCT
ejpam-5171	430	4	a2	a2	PROPN
ejpam-5171	430	5	}	}	PUNCT
ejpam-5171	430	6	♢	♢	PROPN
ejpam-5171	430	7	=	=	SYM
ejpam-5171	430	8	x	x	PROPN
ejpam-5171	430	9	,	,	PUNCT
ejpam-5171	430	10	{	{	PUNCT
ejpam-5171	430	11	a1	a1	NOUN
ejpam-5171	430	12	,	,	PUNCT
ejpam-5171	430	13	a3	a3	NOUN
ejpam-5171	430	14	}	}	PUNCT
ejpam-5171	430	15	⊆	⊆	NUM
ejpam-5171	430	16	cl(ψp({a1	cl(ψp({a1	ADJ
ejpam-5171	430	17	,	,	PUNCT
ejpam-5171	430	18	a3	a3	NOUN
ejpam-5171	430	19	}	}	PUNCT
ejpam-5171	430	20	)	)	PUNCT
ejpam-5171	430	21	)	)	PUNCT
ejpam-5171	431	1	=	=	PUNCT
ejpam-5171	431	2	x.	x.	NOUN
ejpam-5171	431	3	therefore	therefore	ADV
ejpam-5171	431	4	,	,	PUNCT
ejpam-5171	431	5	l	l	NOUN
ejpam-5171	431	6	∩	∩	X
ejpam-5171	431	7	e	e	NOUN
ejpam-5171	431	8	=	=	SYM
ejpam-5171	431	9	{	{	PUNCT
ejpam-5171	431	10	a1	a1	PROPN
ejpam-5171	431	11	}	}	PUNCT
ejpam-5171	431	12	is	be	AUX
ejpam-5171	431	13	not	not	PART
ejpam-5171	431	14	ψ̃p	ψ̃p	NOUN
ejpam-5171	431	15	-	-	PUNCT
ejpam-5171	431	16	set	set	NOUN
ejpam-5171	431	17	,	,	PUNCT
ejpam-5171	431	18	since	since	SCONJ
ejpam-5171	431	19	ψp({a1	ψp({a1	ADV
ejpam-5171	431	20	}	}	PUNCT
ejpam-5171	431	21	)	)	PUNCT
ejpam-5171	432	1	=	=	SYM
ejpam-5171	432	2	x−	x−	PROPN
ejpam-5171	432	3	{	{	PUNCT
ejpam-5171	432	4	a2	a2	PROPN
ejpam-5171	432	5	,	,	PUNCT
ejpam-5171	432	6	a3	a3	NOUN
ejpam-5171	432	7	}	}	PUNCT
ejpam-5171	432	8	♢	♢	PROPN
ejpam-5171	432	9	=	=	SYM
ejpam-5171	432	10	ϕ	ϕ	PROPN
ejpam-5171	432	11	,	,	PUNCT
ejpam-5171	432	12	{	{	PUNCT
ejpam-5171	432	13	a1	a1	NOUN
ejpam-5171	432	14	}	}	PUNCT
ejpam-5171	432	15	⊈	⊈	X
ejpam-5171	432	16	cl(ψp({a1	cl(ψp({a1	NOUN
ejpam-5171	432	17	}	}	PUNCT
ejpam-5171	432	18	)	)	PUNCT
ejpam-5171	432	19	)	)	PUNCT
ejpam-5171	433	1	=	=	PUNCT
ejpam-5171	434	1	ϕ.	ϕ.	NOUN
ejpam-5171	434	2	we	we	PRON
ejpam-5171	434	3	will	will	AUX
ejpam-5171	434	4	demonstrate	demonstrate	VERB
ejpam-5171	434	5	that	that	SCONJ
ejpam-5171	434	6	the	the	DET
ejpam-5171	434	7	intersection	intersection	NOUN
ejpam-5171	434	8	of	of	ADP
ejpam-5171	434	9	two	two	NUM
ejpam-5171	434	10	ψ̃p	ψ̃p	NOUN
ejpam-5171	434	11	-sets	-set	NOUN
ejpam-5171	434	12	are	be	AUX
ejpam-5171	434	13	not	not	PART
ejpam-5171	434	14	often	often	ADV
ejpam-5171	434	15	be	be	AUX
ejpam-5171	434	16	a	a	DET
ejpam-5171	434	17	ψ̃p	ψ̃p	NOUN
ejpam-5171	434	18	-set	-set	ADJ
ejpam-5171	434	19	,	,	PUNCT
ejpam-5171	434	20	we	we	PRON
ejpam-5171	434	21	will	will	AUX
ejpam-5171	434	22	show	show	VERB
ejpam-5171	434	23	that	that	SCONJ
ejpam-5171	434	24	the	the	DET
ejpam-5171	434	25	intersection	intersection	NOUN
ejpam-5171	434	26	of	of	ADP
ejpam-5171	434	27	a	a	DET
ejpam-5171	434	28	δα	δα	NOUN
ejpam-5171	434	29	with	with	ADP
ejpam-5171	434	30	a	a	DET
ejpam-5171	434	31	ψ̃p	ψ̃p	NOUN
ejpam-5171	434	32	-set	-set	ADJ
ejpam-5171	434	33	is	be	AUX
ejpam-5171	434	34	a	a	DET
ejpam-5171	434	35	ψ̃p	ψ̃p	NOUN
ejpam-5171	434	36	-set	-set	ADJ
ejpam-5171	434	37	.	.	PUNCT
ejpam-5171	435	1	theorem	theorem	NOUN
ejpam-5171	435	2	5.6	5.6	NUM
ejpam-5171	435	3	.	.	PUNCT
ejpam-5171	436	1	suppose	suppose	VERB
ejpam-5171	436	2	that	that	SCONJ
ejpam-5171	436	3	we	we	PRON
ejpam-5171	436	4	have	have	VERB
ejpam-5171	436	5	a	a	DET
ejpam-5171	436	6	pts	pts	X
ejpam-5171	436	7	(	(	PUNCT
ejpam-5171	436	8	x	x	NOUN
ejpam-5171	436	9	,	,	PUNCT
ejpam-5171	436	10	δ	δ	PROPN
ejpam-5171	436	11	,	,	PUNCT
ejpam-5171	436	12	p	p	NOUN
ejpam-5171	436	13	)	)	PUNCT
ejpam-5171	436	14	,	,	PUNCT
ejpam-5171	436	15	and	and	CCONJ
ejpam-5171	436	16	let	let	VERB
ejpam-5171	436	17	l	l	NOUN
ejpam-5171	436	18	belong	belong	VERB
ejpam-5171	436	19	to	to	ADP
ejpam-5171	436	20	the	the	DET
ejpam-5171	436	21	set	set	NOUN
ejpam-5171	436	22	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	436	23	,	,	PUNCT
ejpam-5171	436	24	δ	δ	PROPN
ejpam-5171	436	25	)	)	PUNCT
ejpam-5171	436	26	.	.	PUNCT
ejpam-5171	437	1	thus	thus	ADV
ejpam-5171	437	2	,	,	PUNCT
ejpam-5171	437	3	if	if	SCONJ
ejpam-5171	437	4	u	u	NOUN
ejpam-5171	437	5	is	be	AUX
ejpam-5171	437	6	an	an	DET
ejpam-5171	437	7	element	element	NOUN
ejpam-5171	437	8	of	of	ADP
ejpam-5171	437	9	δα	δα	PRON
ejpam-5171	437	10	,	,	PUNCT
ejpam-5171	437	11	then	then	ADV
ejpam-5171	437	12	it	it	PRON
ejpam-5171	437	13	follows	follow	VERB
ejpam-5171	437	14	that	that	SCONJ
ejpam-5171	437	15	the	the	DET
ejpam-5171	437	16	intersection	intersection	NOUN
ejpam-5171	437	17	of	of	ADP
ejpam-5171	437	18	u	u	NOUN
ejpam-5171	437	19	with	with	ADP
ejpam-5171	437	20	l	l	NOUN
ejpam-5171	437	21	also	also	ADV
ejpam-5171	437	22	belongs	belong	VERB
ejpam-5171	437	23	to	to	ADP
ejpam-5171	437	24	the	the	DET
ejpam-5171	437	25	set	set	NOUN
ejpam-5171	437	26	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	437	27	,	,	PUNCT
ejpam-5171	437	28	δ	δ	PROPN
ejpam-5171	437	29	)	)	PUNCT
ejpam-5171	437	30	.	.	PUNCT
ejpam-5171	438	1	proof	proof	NOUN
ejpam-5171	438	2	.	.	PUNCT
ejpam-5171	439	1	we	we	PRON
ejpam-5171	439	2	note	note	VERB
ejpam-5171	439	3	that	that	SCONJ
ejpam-5171	439	4	if	if	SCONJ
ejpam-5171	439	5	g	g	PROPN
ejpam-5171	439	6	is	be	AUX
ejpam-5171	439	7	open	open	ADJ
ejpam-5171	439	8	,	,	PUNCT
ejpam-5171	439	9	for	for	ADP
ejpam-5171	439	10	any	any	DET
ejpam-5171	439	11	l	l	NOUN
ejpam-5171	439	12	⊆	⊆	NUM
ejpam-5171	439	13	x	x	SYM
ejpam-5171	439	14	,	,	PUNCT
ejpam-5171	439	15	g	g	PROPN
ejpam-5171	439	16	∩	∩	NOUN
ejpam-5171	439	17	cl(l	cl(l	NOUN
ejpam-5171	439	18	)	)	PUNCT
ejpam-5171	440	1	⊆	⊆	NUM
ejpam-5171	440	2	cl(g	cl(g	NOUN
ejpam-5171	440	3	∩	∩	NOUN
ejpam-5171	440	4	l	l	NOUN
ejpam-5171	440	5	)	)	PUNCT
ejpam-5171	440	6	.	.	PUNCT
ejpam-5171	441	1	let	let	VERB
ejpam-5171	441	2	u	u	PRON
ejpam-5171	441	3	∈	∈	VERB
ejpam-5171	441	4	δα	δα	PROPN
ejpam-5171	441	5	and	and	CCONJ
ejpam-5171	441	6	l	l	PROPN
ejpam-5171	441	7	∈	∈	PROPN
ejpam-5171	441	8	˜	˜	PROPN
ejpam-5171	441	9	cl	cl	NOUN
ejpam-5171	441	10	♢	♢	PROPN
ejpam-5171	441	11	p(x	p(x	PROPN
ejpam-5171	441	12	,	,	PUNCT
ejpam-5171	441	13	δ	δ	PROPN
ejpam-5171	441	14	)	)	PUNCT
ejpam-5171	441	15	.	.	PUNCT
ejpam-5171	442	1	then	then	ADV
ejpam-5171	442	2	by	by	ADP
ejpam-5171	442	3	theorem	theorem	ADJ
ejpam-5171	442	4	1.15	1.15	NUM
ejpam-5171	442	5	and	and	CCONJ
ejpam-5171	442	6	corollary	corollary	ADJ
ejpam-5171	442	7	1.14	1.14	NUM
ejpam-5171	442	8	we	we	PRON
ejpam-5171	442	9	have	have	VERB
ejpam-5171	442	10	u	u	NOUN
ejpam-5171	442	11	∩	∩	NOUN
ejpam-5171	442	12	l	l	PROPN
ejpam-5171	442	13	⊆	⊆	NUM
ejpam-5171	442	14	int(cl(int(u)))∩	int(cl(int(u)))∩	NOUN
ejpam-5171	442	15	cl(ψp(l	cl(ψp(l	NOUN
ejpam-5171	442	16	)	)	PUNCT
ejpam-5171	442	17	)	)	PUNCT
ejpam-5171	443	1	⊆	⊆	X
ejpam-5171	443	2	int(cl(ψp(u)))∩	int(cl(ψp(u)))∩	PROPN
ejpam-5171	443	3	cl(ψp(l	cl(ψp(l	NOUN
ejpam-5171	443	4	)	)	PUNCT
ejpam-5171	443	5	)	)	PUNCT
ejpam-5171	443	6	⊆	⊆	NUM
ejpam-5171	443	7	cl[int(cl(ψp(u)))∩ψp(l	cl[int(cl(ψp(u)))∩ψp(l	NOUN
ejpam-5171	443	8	)	)	PUNCT
ejpam-5171	443	9	]	]	PUNCT
ejpam-5171	443	10	=	=	PUNCT
ejpam-5171	443	11	cl[int(cl[ψp(u	cl[int(cl[ψp(u	NOUN
ejpam-5171	443	12	)	)	PUNCT
ejpam-5171	443	13	∩	∩	NOUN
ejpam-5171	443	14	ψp(l	ψp(l	NUM
ejpam-5171	443	15	)	)	PUNCT
ejpam-5171	443	16	]	]	PUNCT
ejpam-5171	443	17	)	)	PUNCT
ejpam-5171	443	18	]	]	PUNCT
ejpam-5171	443	19	=	=	SYM
ejpam-5171	443	20	cl[ψp(u	cl[ψp(u	NUM
ejpam-5171	443	21	)	)	PUNCT
ejpam-5171	443	22	∩	∩	NOUN
ejpam-5171	443	23	ψp(l	ψp(l	NUM
ejpam-5171	443	24	)	)	PUNCT
ejpam-5171	443	25	]	]	PUNCT
ejpam-5171	444	1	=	=	PUNCT
ejpam-5171	444	2	cl[ψp(u	cl[ψp(u	ADJ
ejpam-5171	444	3	∩	∩	ADJ
ejpam-5171	444	4	l	l	NOUN
ejpam-5171	444	5	)	)	PUNCT
ejpam-5171	444	6	]	]	PUNCT
ejpam-5171	444	7	.	.	PUNCT
ejpam-5171	445	1	hence	hence	ADV
ejpam-5171	445	2	,	,	PUNCT
ejpam-5171	445	3	u	u	PROPN
ejpam-5171	445	4	∩	∩	PROPN
ejpam-5171	445	5	l	l	PROPN
ejpam-5171	445	6	∈	∈	PROPN
ejpam-5171	445	7	ψ̃p(x	ψ̃p(x	NOUN
ejpam-5171	445	8	,	,	PUNCT
ejpam-5171	445	9	δ	δ	PROPN
ejpam-5171	445	10	)	)	PUNCT
ejpam-5171	445	11	.	.	PUNCT
ejpam-5171	446	1	corollary	corollary	ADJ
ejpam-5171	446	2	5.7	5.7	NUM
ejpam-5171	446	3	.	.	PUNCT
ejpam-5171	447	1	let	let	VERB
ejpam-5171	447	2	(	(	PUNCT
ejpam-5171	447	3	x	x	NOUN
ejpam-5171	447	4	,	,	PUNCT
ejpam-5171	447	5	δ	δ	PROPN
ejpam-5171	447	6	,	,	PUNCT
ejpam-5171	447	7	p	p	NOUN
ejpam-5171	447	8	)	)	PUNCT
ejpam-5171	447	9	be	be	AUX
ejpam-5171	447	10	a	a	DET
ejpam-5171	447	11	pts	pts	NOUN
ejpam-5171	447	12	,	,	PUNCT
ejpam-5171	447	13	and	and	CCONJ
ejpam-5171	447	14	let	let	VERB
ejpam-5171	447	15	l	l	NOUN
ejpam-5171	447	16	belong	belong	VERB
ejpam-5171	447	17	to	to	ADP
ejpam-5171	447	18	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	447	19	,	,	PUNCT
ejpam-5171	447	20	δ	δ	PROPN
ejpam-5171	447	21	)	)	PUNCT
ejpam-5171	447	22	.	.	PUNCT
ejpam-5171	448	1	if	if	SCONJ
ejpam-5171	448	2	u	u	NOUN
ejpam-5171	448	3	is	be	AUX
ejpam-5171	448	4	an	an	DET
ejpam-5171	448	5	element	element	NOUN
ejpam-5171	448	6	of	of	ADP
ejpam-5171	448	7	δ	δ	PROPN
ejpam-5171	448	8	,	,	PUNCT
ejpam-5171	448	9	then	then	ADV
ejpam-5171	448	10	their	their	PRON
ejpam-5171	448	11	intersection	intersection	NOUN
ejpam-5171	448	12	u	u	NOUN
ejpam-5171	448	13	∩	∩	NOUN
ejpam-5171	448	14	l	l	NOUN
ejpam-5171	448	15	also	also	ADV
ejpam-5171	448	16	belongs	belong	VERB
ejpam-5171	448	17	to	to	ADP
ejpam-5171	448	18	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	448	19	,	,	PUNCT
ejpam-5171	448	20	δ	δ	PROPN
ejpam-5171	448	21	)	)	PUNCT
ejpam-5171	448	22	.	.	PUNCT
ejpam-5171	449	1	for	for	ADP
ejpam-5171	449	2	any	any	DET
ejpam-5171	449	3	non	non	ADJ
ejpam-5171	449	4	-	-	ADJ
ejpam-5171	449	5	empty	empty	ADJ
ejpam-5171	449	6	relative	relative	NOUN
ejpam-5171	449	7	to	to	ADP
ejpam-5171	449	8	an	an	DET
ejpam-5171	449	9	open	open	ADJ
ejpam-5171	449	10	set	set	NOUN
ejpam-5171	449	11	u	u	NOUN
ejpam-5171	449	12	∩l	∩l	VERB
ejpam-5171	449	13	,	,	PUNCT
ejpam-5171	449	14	it	it	PRON
ejpam-5171	449	15	holds	hold	VERB
ejpam-5171	449	16	that	that	SCONJ
ejpam-5171	449	17	(	(	PUNCT
ejpam-5171	449	18	u	u	NOUN
ejpam-5171	449	19	∩l)∩d	∩l)∩d	NOUN
ejpam-5171	449	20	∈	∈	PROPN
ejpam-5171	449	21	p	p	NOUN
ejpam-5171	449	22	when	when	SCONJ
ejpam-5171	449	23	u	u	PROPN
ejpam-5171	449	24	∈	∈	PROPN
ejpam-5171	449	25	δ	δ	PROPN
ejpam-5171	449	26	,	,	PUNCT
ejpam-5171	449	27	then	then	ADV
ejpam-5171	449	28	we	we	PRON
ejpam-5171	449	29	refer	refer	VERB
ejpam-5171	449	30	to	to	ADP
ejpam-5171	449	31	a	a	DET
ejpam-5171	449	32	set	set	NOUN
ejpam-5171	449	33	d	d	NOUN
ejpam-5171	449	34	as	as	ADP
ejpam-5171	449	35	being	be	AUX
ejpam-5171	449	36	relative	relative	ADJ
ejpam-5171	449	37	p	p	NOUN
ejpam-5171	449	38	-	-	PUNCT
ejpam-5171	449	39	dense	dense	ADJ
ejpam-5171	449	40	in	in	ADP
ejpam-5171	449	41	the	the	DET
ejpam-5171	449	42	set	set	NOUN
ejpam-5171	449	43	l.	l.	PROPN
ejpam-5171	449	44	theorem	theorem	VERB
ejpam-5171	449	45	5.8	5.8	NUM
ejpam-5171	449	46	.	.	PUNCT
ejpam-5171	450	1	let	let	VERB
ejpam-5171	450	2	(	(	PUNCT
ejpam-5171	450	3	x	x	NOUN
ejpam-5171	450	4	,	,	PUNCT
ejpam-5171	450	5	δ	δ	PROPN
ejpam-5171	450	6	,	,	PUNCT
ejpam-5171	450	7	p	p	NOUN
ejpam-5171	450	8	)	)	PUNCT
ejpam-5171	450	9	be	be	AUX
ejpam-5171	450	10	a	a	DET
ejpam-5171	450	11	pts	pts	NOUN
ejpam-5171	450	12	.	.	PUNCT
ejpam-5171	451	1	a	a	DET
ejpam-5171	451	2	set	set	ADJ
ejpam-5171	451	3	l	l	NOUN
ejpam-5171	451	4	/∈	/∈	PUNCT
ejpam-5171	452	1	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	452	2	,	,	PUNCT
ejpam-5171	452	3	δ	δ	PROPN
ejpam-5171	452	4	)	)	PUNCT
ejpam-5171	452	5	if	if	SCONJ
ejpam-5171	452	6	and	and	CCONJ
ejpam-5171	452	7	only	only	ADV
ejpam-5171	452	8	if	if	SCONJ
ejpam-5171	452	9	there	there	PRON
ejpam-5171	452	10	exists	exist	VERB
ejpam-5171	452	11	an	an	DET
ejpam-5171	452	12	element	element	NOUN
ejpam-5171	452	13	x	x	PUNCT
ejpam-5171	452	14	in	in	ADP
ejpam-5171	452	15	l	l	NOUN
ejpam-5171	452	16	such	such	ADJ
ejpam-5171	452	17	that	that	SCONJ
ejpam-5171	452	18	there	there	PRON
ejpam-5171	452	19	is	be	VERB
ejpam-5171	452	20	a	a	DET
ejpam-5171	452	21	neighborhood	neighborhood	NOUN
ejpam-5171	452	22	vx	vx	ADP
ejpam-5171	452	23	∈	∈	PROPN
ejpam-5171	452	24	δ	δ	PROPN
ejpam-5171	452	25	of	of	ADP
ejpam-5171	452	26	x	x	PUNCT
ejpam-5171	452	27	for	for	ADP
ejpam-5171	452	28	which	which	PRON
ejpam-5171	452	29	x	x	PUNCT
ejpam-5171	452	30	−	−	PROPN
ejpam-5171	452	31	l	l	NOUN
ejpam-5171	452	32	is	be	AUX
ejpam-5171	452	33	relative	relative	ADJ
ejpam-5171	452	34	to	to	ADP
ejpam-5171	452	35	p	p	NOUN
ejpam-5171	452	36	-	-	PUNCT
ejpam-5171	452	37	dense	dense	ADJ
ejpam-5171	452	38	in	in	ADP
ejpam-5171	452	39	vx	vx	PROPN
ejpam-5171	452	40	.	.	PROPN
ejpam-5171	452	41	proof	proof	NOUN
ejpam-5171	452	42	.	.	PUNCT
ejpam-5171	453	1	suppose	suppose	VERB
ejpam-5171	453	2	that	that	SCONJ
ejpam-5171	453	3	a	a	DET
ejpam-5171	453	4	set	set	NOUN
ejpam-5171	453	5	l	l	NOUN
ejpam-5171	453	6	/∈	/∈	PUNCT
ejpam-5171	454	1	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	454	2	,	,	PUNCT
ejpam-5171	454	3	δ	δ	PROPN
ejpam-5171	454	4	)	)	PUNCT
ejpam-5171	454	5	.	.	PUNCT
ejpam-5171	455	1	we	we	PRON
ejpam-5171	455	2	need	need	VERB
ejpam-5171	455	3	to	to	PART
ejpam-5171	455	4	show	show	VERB
ejpam-5171	455	5	the	the	DET
ejpam-5171	455	6	existence	existence	NOUN
ejpam-5171	455	7	of	of	ADP
ejpam-5171	455	8	x	x	X
ejpam-5171	455	9	∈	∈	PROPN
ejpam-5171	455	10	l	l	NOUN
ejpam-5171	455	11	and	and	CCONJ
ejpam-5171	455	12	a	a	DET
ejpam-5171	455	13	neighborhood	neighborhood	NOUN
ejpam-5171	455	14	vx	vx	PROPN
ejpam-5171	455	15	∈	∈	PROPN
ejpam-5171	455	16	δ(x	δ(x	PROPN
ejpam-5171	455	17	)	)	PUNCT
ejpam-5171	455	18	,	,	PUNCT
ejpam-5171	455	19	then	then	ADV
ejpam-5171	455	20	(	(	PUNCT
ejpam-5171	455	21	x	x	X
ejpam-5171	455	22	−	−	PROPN
ejpam-5171	455	23	l	l	NOUN
ejpam-5171	455	24	)	)	PUNCT
ejpam-5171	455	25	is	be	AUX
ejpam-5171	455	26	relative	relative	ADJ
ejpam-5171	455	27	p	p	NOUN
ejpam-5171	455	28	-	-	PUNCT
ejpam-5171	455	29	dense	dense	ADJ
ejpam-5171	455	30	in	in	ADP
ejpam-5171	455	31	vx	vx	PROPN
ejpam-5171	455	32	.	.	PUNCT
ejpam-5171	455	33	now	now	ADV
ejpam-5171	455	34	,	,	PUNCT
ejpam-5171	455	35	since	since	SCONJ
ejpam-5171	455	36	l	l	NOUN
ejpam-5171	455	37	⊈	⊈	PROPN
ejpam-5171	455	38	cl(ψp(l	cl(ψp(l	NOUN
ejpam-5171	455	39	)	)	PUNCT
ejpam-5171	455	40	)	)	PUNCT
ejpam-5171	455	41	,	,	PUNCT
ejpam-5171	455	42	and	and	CCONJ
ejpam-5171	455	43	so	so	ADV
ejpam-5171	455	44	there	there	PRON
ejpam-5171	455	45	exists	exist	VERB
ejpam-5171	455	46	an	an	DET
ejpam-5171	455	47	element	element	NOUN
ejpam-5171	455	48	x	x	SYM
ejpam-5171	455	49	∈	∈	PROPN
ejpam-5171	455	50	x	x	PUNCT
ejpam-5171	455	51	such	such	ADJ
ejpam-5171	455	52	that	that	SCONJ
ejpam-5171	455	53	x	x	PRON
ejpam-5171	455	54	is	be	AUX
ejpam-5171	455	55	in	in	ADP
ejpam-5171	455	56	l	l	NOUN
ejpam-5171	455	57	but	but	CCONJ
ejpam-5171	455	58	not	not	PART
ejpam-5171	455	59	in	in	ADP
ejpam-5171	455	60	the	the	DET
ejpam-5171	455	61	closure	closure	NOUN
ejpam-5171	455	62	of	of	ADP
ejpam-5171	455	63	ψp(l	ψp(l	NOUN
ejpam-5171	455	64	)	)	PUNCT
ejpam-5171	455	65	.	.	PUNCT
ejpam-5171	456	1	consequently	consequently	ADV
ejpam-5171	456	2	,	,	PUNCT
ejpam-5171	456	3	there	there	PRON
ejpam-5171	456	4	is	be	VERB
ejpam-5171	456	5	a	a	DET
ejpam-5171	456	6	neighborhood	neighborhood	NOUN
ejpam-5171	456	7	vx	vx	PROPN
ejpam-5171	456	8	∈	∈	PROPN
ejpam-5171	456	9	δ(x	δ(x	PROPN
ejpam-5171	456	10	)	)	PUNCT
ejpam-5171	456	11	so	so	SCONJ
ejpam-5171	456	12	that	that	SCONJ
ejpam-5171	456	13	vx	vx	PROPN
ejpam-5171	456	14	∩	∩	NOUN
ejpam-5171	456	15	ψp(l	ψp(l	NUM
ejpam-5171	456	16	)	)	PUNCT
ejpam-5171	456	17	=	=	SYM
ejpam-5171	456	18	ϕ.	ϕ.	NOUN
ejpam-5171	456	19	hence	hence	ADV
ejpam-5171	456	20	,	,	PUNCT
ejpam-5171	456	21	vx	vx	PROPN
ejpam-5171	456	22	∩	∩	X
ejpam-5171	456	23	(	(	PUNCT
ejpam-5171	456	24	x	x	SYM
ejpam-5171	456	25	−	−	PROPN
ejpam-5171	456	26	(	(	PUNCT
ejpam-5171	456	27	x	x	X
ejpam-5171	456	28	−	−	PROPN
ejpam-5171	456	29	l	l	NOUN
ejpam-5171	456	30	)	)	PUNCT
ejpam-5171	456	31	♢	♢	PROPN
ejpam-5171	456	32	)	)	PUNCT
ejpam-5171	456	33	=	=	SYM
ejpam-5171	456	34	ϕ	ϕ	NOUN
ejpam-5171	456	35	,	,	PUNCT
ejpam-5171	456	36	and	and	CCONJ
ejpam-5171	456	37	therefore	therefore	ADV
ejpam-5171	456	38	,	,	PUNCT
ejpam-5171	456	39	vx	vx	PROPN
ejpam-5171	456	40	⊆	⊆	NUM
ejpam-5171	456	41	(	(	PUNCT
ejpam-5171	456	42	x	x	NOUN
ejpam-5171	456	43	−	−	PROPN
ejpam-5171	456	44	l)	l)	PROPN
ejpam-5171	456	45	♢	♢	PROPN
ejpam-5171	456	46	.	.	PUNCT
ejpam-5171	457	1	now	now	ADV
ejpam-5171	457	2	,	,	PUNCT
ejpam-5171	457	3	consider	consider	VERB
ejpam-5171	457	4	any	any	DET
ejpam-5171	457	5	non	non	ADJ
ejpam-5171	457	6	-	-	ADJ
ejpam-5171	457	7	empty	empty	ADJ
ejpam-5171	457	8	open	open	ADJ
ejpam-5171	457	9	set	set	NOUN
ejpam-5171	457	10	u	u	NOUN
ejpam-5171	457	11	in	in	ADP
ejpam-5171	457	12	vx	vx	PROPN
ejpam-5171	457	13	.	.	PROPN
ejpam-5171	457	14	since	since	SCONJ
ejpam-5171	457	15	vx	vx	PROPN
ejpam-5171	457	16	⊆	⊆	NUM
ejpam-5171	457	17	(	(	PUNCT
ejpam-5171	457	18	x	x	SYM
ejpam-5171	457	19	−	−	PROPN
ejpam-5171	457	20	l	l	NOUN
ejpam-5171	457	21	)	)	PUNCT
ejpam-5171	457	22	♢	♢	PROPN
ejpam-5171	457	23	,	,	PUNCT
ejpam-5171	457	24	it	it	PRON
ejpam-5171	457	25	follows	follow	VERB
ejpam-5171	457	26	that	that	SCONJ
ejpam-5171	457	27	u	u	NOUN
ejpam-5171	457	28	∩	∩	NOUN
ejpam-5171	457	29	(	(	PUNCT
ejpam-5171	457	30	x−	x−	PROPN
ejpam-5171	457	31	l	l	PROPN
ejpam-5171	457	32	)	)	PUNCT
ejpam-5171	457	33	∈	∈	PROPN
ejpam-5171	458	1	p.	p.	NOUN
ejpam-5171	458	2	this	this	PRON
ejpam-5171	458	3	demonstrates	demonstrate	VERB
ejpam-5171	458	4	that	that	SCONJ
ejpam-5171	458	5	(	(	PUNCT
ejpam-5171	458	6	x−	x−	PROPN
ejpam-5171	458	7	l	l	PROPN
ejpam-5171	458	8	)	)	PUNCT
ejpam-5171	458	9	is	be	AUX
ejpam-5171	458	10	relatively	relatively	ADV
ejpam-5171	458	11	p	p	NOUN
ejpam-5171	458	12	-	-	PUNCT
ejpam-5171	458	13	dense	dense	ADJ
ejpam-5171	458	14	in	in	ADP
ejpam-5171	458	15	vx	vx	PROPN
ejpam-5171	458	16	.	.	PROPN
ejpam-5171	458	17	definition	definition	NOUN
ejpam-5171	458	18	5.9	5.9	NUM
ejpam-5171	458	19	.	.	PUNCT
ejpam-5171	459	1	let	let	VERB
ejpam-5171	459	2	(	(	PUNCT
ejpam-5171	459	3	x	x	NOUN
ejpam-5171	459	4	,	,	PUNCT
ejpam-5171	459	5	δ	δ	PROPN
ejpam-5171	459	6	,	,	PUNCT
ejpam-5171	459	7	p	p	NOUN
ejpam-5171	459	8	)	)	PUNCT
ejpam-5171	459	9	is	be	AUX
ejpam-5171	459	10	a	a	DET
ejpam-5171	459	11	pts	pts	NOUN
ejpam-5171	459	12	.	.	PUNCT
ejpam-5171	460	1	p	p	NOUN
ejpam-5171	460	2	is	be	AUX
ejpam-5171	460	3	said	say	VERB
ejpam-5171	460	4	to	to	PART
ejpam-5171	460	5	be	be	AUX
ejpam-5171	460	6	primal	primal	ADJ
ejpam-5171	460	7	anti	anti	ADJ
ejpam-5171	460	8	-	-	NOUN
ejpam-5171	460	9	codense	codense	ADJ
ejpam-5171	460	10	if	if	SCONJ
ejpam-5171	460	11	δ−{ϕ	δ−{ϕ	NOUN
ejpam-5171	460	12	}	}	PUNCT
ejpam-5171	460	13	⊆	⊆	NUM
ejpam-5171	460	14	p.	p.	NOUN
ejpam-5171	460	15	theorem	theorem	VERB
ejpam-5171	460	16	5.10	5.10	NUM
ejpam-5171	460	17	.	.	PUNCT
ejpam-5171	461	1	in	in	ADP
ejpam-5171	461	2	the	the	DET
ejpam-5171	461	3	pts	pt	NOUN
ejpam-5171	461	4	(	(	PUNCT
ejpam-5171	461	5	x	x	NOUN
ejpam-5171	461	6	,	,	PUNCT
ejpam-5171	461	7	δ	δ	PROPN
ejpam-5171	461	8	,	,	PUNCT
ejpam-5171	461	9	p	p	NOUN
ejpam-5171	461	10	)	)	PUNCT
ejpam-5171	461	11	,	,	PUNCT
ejpam-5171	461	12	if	if	SCONJ
ejpam-5171	461	13	p	p	NOUN
ejpam-5171	461	14	is	be	AUX
ejpam-5171	461	15	characterized	characterize	VERB
ejpam-5171	461	16	as	as	ADP
ejpam-5171	461	17	a	a	DET
ejpam-5171	461	18	primal	primal	ADJ
ejpam-5171	461	19	anti	anti	ADJ
ejpam-5171	461	20	-	-	NOUN
ejpam-5171	461	21	codense	codense	NOUN
ejpam-5171	461	22	,	,	PUNCT
ejpam-5171	461	23	then	then	ADV
ejpam-5171	461	24	so(x	so(x	PUNCT
ejpam-5171	461	25	,	,	PUNCT
ejpam-5171	461	26	δ	δ	PROPN
ejpam-5171	461	27	♢	♢	PROPN
ejpam-5171	461	28	)	)	PUNCT
ejpam-5171	461	29	=	=	SYM
ejpam-5171	461	30	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	461	31	,	,	PUNCT
ejpam-5171	461	32	δ	δ	PROPN
ejpam-5171	461	33	)	)	PUNCT
ejpam-5171	461	34	.	.	PUNCT
ejpam-5171	462	1	proof	proof	NOUN
ejpam-5171	462	2	.	.	PUNCT
ejpam-5171	463	1	first	first	ADV
ejpam-5171	463	2	assume	assume	VERB
ejpam-5171	463	3	that	that	SCONJ
ejpam-5171	463	4	l	l	NOUN
ejpam-5171	463	5	is	be	AUX
ejpam-5171	463	6	an	an	DET
ejpam-5171	463	7	element	element	NOUN
ejpam-5171	463	8	of	of	ADP
ejpam-5171	463	9	so(x	so(x	NOUN
ejpam-5171	463	10	,	,	PUNCT
ejpam-5171	463	11	δ	δ	PROPN
ejpam-5171	463	12	♢	♢	PROPN
ejpam-5171	463	13	)	)	PUNCT
ejpam-5171	463	14	.	.	PUNCT
ejpam-5171	464	1	according	accord	VERB
ejpam-5171	464	2	to	to	ADP
ejpam-5171	464	3	theorem	theorem	NOUN
ejpam-5171	464	4	1.15	1.15	NUM
ejpam-5171	464	5	,	,	PUNCT
ejpam-5171	464	6	we	we	PRON
ejpam-5171	464	7	have	have	VERB
ejpam-5171	464	8	l	l	NOUN
ejpam-5171	464	9	⊆	⊆	NUM
ejpam-5171	464	10	δ	δ	PROPN
ejpam-5171	464	11	♢	♢	PROPN
ejpam-5171	464	12	-cl(δ	-cl(δ	PROPN
ejpam-5171	464	13	♢	♢	NOUN
ejpam-5171	464	14	-int(l	-int(l	PROPN
ejpam-5171	464	15	)	)	PUNCT
ejpam-5171	464	16	)	)	PUNCT
ejpam-5171	465	1	=	=	SYM
ejpam-5171	465	2	δ	δ	PROPN
ejpam-5171	465	3	♢	♢	PROPN
ejpam-5171	465	4	-cl(ψp(l)∩l	-cl(ψp(l)∩l	PROPN
ejpam-5171	465	5	)	)	PUNCT
ejpam-5171	465	6	.	.	PUNCT
ejpam-5171	466	1	this	this	PRON
ejpam-5171	466	2	implies	imply	VERB
ejpam-5171	466	3	that	that	SCONJ
ejpam-5171	466	4	l	l	NOUN
ejpam-5171	466	5	⊆	⊆	NUM
ejpam-5171	466	6	cl(ψp(l)∩l	cl(ψp(l)∩l	NOUN
ejpam-5171	466	7	)	)	PUNCT
ejpam-5171	466	8	⊆	⊆	PROPN
ejpam-5171	466	9	h.	h.	PROPN
ejpam-5171	466	10	al	al	PROPN
ejpam-5171	466	11	-	-	PUNCT
ejpam-5171	466	12	saadi	saadi	PROPN
ejpam-5171	466	13	,	,	PUNCT
ejpam-5171	466	14	m.	m.	NOUN
ejpam-5171	466	15	al	al	PROPN
ejpam-5171	466	16	-	-	PUNCT
ejpam-5171	466	17	hodieb	hodieb	PROPN
ejpam-5171	466	18	/	/	SYM
ejpam-5171	466	19	eur	eur	PROPN
ejpam-5171	466	20	.	.	PUNCT
ejpam-5171	467	1	j.	j.	PROPN
ejpam-5171	467	2	pure	pure	PROPN
ejpam-5171	467	3	appl	appl	PROPN
ejpam-5171	467	4	.	.	PROPN
ejpam-5171	467	5	math	math	PROPN
ejpam-5171	467	6	,	,	PUNCT
ejpam-5171	467	7	17	17	NUM
ejpam-5171	467	8	(	(	PUNCT
ejpam-5171	467	9	2	2	NUM
ejpam-5171	467	10	)	)	PUNCT
ejpam-5171	467	11	(	(	PUNCT
ejpam-5171	467	12	2024	2024	NUM
ejpam-5171	467	13	)	)	PUNCT
ejpam-5171	467	14	,	,	PUNCT
ejpam-5171	467	15	1352	1352	NUM
ejpam-5171	467	16	-	-	SYM
ejpam-5171	467	17	1368	1368	NUM
ejpam-5171	467	18	1365	1365	NUM
ejpam-5171	467	19	cl(ψp(l	cl(ψp(l	NOUN
ejpam-5171	467	20	)	)	PUNCT
ejpam-5171	467	21	)	)	PUNCT
ejpam-5171	467	22	.	.	PUNCT
ejpam-5171	468	1	consequently	consequently	ADV
ejpam-5171	468	2	,	,	PUNCT
ejpam-5171	468	3	we	we	PRON
ejpam-5171	468	4	can	can	AUX
ejpam-5171	468	5	conclude	conclude	VERB
ejpam-5171	468	6	that	that	SCONJ
ejpam-5171	468	7	l	l	NOUN
ejpam-5171	468	8	belongs	belong	VERB
ejpam-5171	468	9	to	to	ADP
ejpam-5171	468	10	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	468	11	,	,	PUNCT
ejpam-5171	468	12	δ	δ	PROPN
ejpam-5171	468	13	)	)	PUNCT
ejpam-5171	468	14	.	.	PUNCT
ejpam-5171	469	1	therefore	therefore	ADV
ejpam-5171	469	2	,	,	PUNCT
ejpam-5171	469	3	so(x	so(x	NOUN
ejpam-5171	469	4	,	,	PUNCT
ejpam-5171	469	5	δ	δ	PROPN
ejpam-5171	469	6	♢	♢	PROPN
ejpam-5171	469	7	)	)	PUNCT
ejpam-5171	469	8	⊆	⊆	NUM
ejpam-5171	469	9	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	469	10	,	,	PUNCT
ejpam-5171	469	11	δ	δ	PROPN
ejpam-5171	469	12	)	)	PUNCT
ejpam-5171	469	13	.	.	PUNCT
ejpam-5171	470	1	conversely	conversely	ADV
ejpam-5171	470	2	,	,	PUNCT
ejpam-5171	470	3	assume	assume	VERB
ejpam-5171	470	4	that	that	SCONJ
ejpam-5171	470	5	l	l	NOUN
ejpam-5171	470	6	is	be	AUX
ejpam-5171	470	7	an	an	DET
ejpam-5171	470	8	element	element	NOUN
ejpam-5171	470	9	of	of	ADP
ejpam-5171	470	10	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	470	11	,	,	PUNCT
ejpam-5171	470	12	δ	δ	PROPN
ejpam-5171	470	13	)	)	PUNCT
ejpam-5171	470	14	,	,	PUNCT
ejpam-5171	470	15	and	and	CCONJ
ejpam-5171	470	16	let	let	VERB
ejpam-5171	470	17	x	x	PRON
ejpam-5171	470	18	be	be	AUX
ejpam-5171	470	19	an	an	DET
ejpam-5171	470	20	element	element	NOUN
ejpam-5171	470	21	of	of	ADP
ejpam-5171	470	22	l.	l.	PROPN
ejpam-5171	470	23	consider	consider	VERB
ejpam-5171	470	24	a	a	DET
ejpam-5171	470	25	basic	basic	ADJ
ejpam-5171	470	26	neighborhood	neighborhood	NOUN
ejpam-5171	470	27	u1	u1	NOUN
ejpam-5171	470	28	of	of	ADP
ejpam-5171	470	29	x	x	PUNCT
ejpam-5171	470	30	in	in	ADP
ejpam-5171	470	31	(	(	PUNCT
ejpam-5171	470	32	x	x	NOUN
ejpam-5171	470	33	,	,	PUNCT
ejpam-5171	470	34	δ	δ	PROPN
ejpam-5171	470	35	♢	♢	PROPN
ejpam-5171	470	36	)	)	PUNCT
ejpam-5171	470	37	.	.	PUNCT
ejpam-5171	471	1	the	the	DET
ejpam-5171	471	2	neighborhood	neighborhood	NOUN
ejpam-5171	471	3	u1	u1	NOUN
ejpam-5171	471	4	can	can	AUX
ejpam-5171	471	5	be	be	AUX
ejpam-5171	471	6	represented	represent	VERB
ejpam-5171	471	7	as	as	ADP
ejpam-5171	471	8	u	u	NOUN
ejpam-5171	471	9	−	−	PROPN
ejpam-5171	471	10	g	g	NOUN
ejpam-5171	471	11	,	,	PUNCT
ejpam-5171	471	12	where	where	SCONJ
ejpam-5171	471	13	u	u	PROPN
ejpam-5171	471	14	∈	∈	PROPN
ejpam-5171	471	15	δ	δ	PROPN
ejpam-5171	471	16	and	and	CCONJ
ejpam-5171	471	17	g	g	PROPN
ejpam-5171	471	18	/∈	/∈	PUNCT
ejpam-5171	472	1	p.	p.	NOUN
ejpam-5171	472	2	this	this	PRON
ejpam-5171	472	3	implies	imply	VERB
ejpam-5171	472	4	that	that	SCONJ
ejpam-5171	472	5	x	x	PRON
ejpam-5171	472	6	is	be	AUX
ejpam-5171	472	7	in	in	ADP
ejpam-5171	472	8	u	u	NOUN
ejpam-5171	472	9	,	,	PUNCT
ejpam-5171	472	10	and	and	CCONJ
ejpam-5171	472	11	consequently	consequently	ADV
ejpam-5171	472	12	,	,	PUNCT
ejpam-5171	472	13	l	l	NOUN
ejpam-5171	472	14	⊆	⊆	NUM
ejpam-5171	472	15	cl(ψp(l	cl(ψp(l	NOUN
ejpam-5171	472	16	)	)	PUNCT
ejpam-5171	472	17	)	)	PUNCT
ejpam-5171	472	18	.	.	PUNCT
ejpam-5171	473	1	also	also	ADV
ejpam-5171	473	2	,	,	PUNCT
ejpam-5171	473	3	u	u	PROPN
ejpam-5171	473	4	∈	∈	PROPN
ejpam-5171	473	5	δ(x	δ(x	PROPN
ejpam-5171	473	6	)	)	PUNCT
ejpam-5171	473	7	,	,	PUNCT
ejpam-5171	473	8	which	which	PRON
ejpam-5171	473	9	means	mean	VERB
ejpam-5171	473	10	u	u	NOUN
ejpam-5171	473	11	∩ψp(l	∩ψp(l	PROPN
ejpam-5171	473	12	)	)	PUNCT
ejpam-5171	473	13	̸=	̸=	PROPN
ejpam-5171	473	14	ϕ.	ϕ.	NOUN
ejpam-5171	473	15	now	now	ADV
ejpam-5171	473	16	,	,	PUNCT
ejpam-5171	473	17	let	let	VERB
ejpam-5171	473	18	y	y	PROPN
ejpam-5171	473	19	∈	∈	PROPN
ejpam-5171	473	20	u	u	NOUN
ejpam-5171	473	21	∩ψp(l	∩ψp(l	PROPN
ejpam-5171	473	22	)	)	PUNCT
ejpam-5171	473	23	.	.	PUNCT
ejpam-5171	474	1	then	then	ADV
ejpam-5171	474	2	,	,	PUNCT
ejpam-5171	474	3	there	there	PRON
ejpam-5171	474	4	is	be	VERB
ejpam-5171	474	5	exists	exist	VERB
ejpam-5171	474	6	a	a	DET
ejpam-5171	474	7	neighborhood	neighborhood	NOUN
ejpam-5171	474	8	wy	wy	NOUN
ejpam-5171	474	9	of	of	ADP
ejpam-5171	474	10	y	y	PRON
ejpam-5171	475	1	such	such	ADJ
ejpam-5171	475	2	that	that	SCONJ
ejpam-5171	475	3	wy	wy	PROPN
ejpam-5171	475	4	−	−	PROPN
ejpam-5171	476	1	l	l	NOUN
ejpam-5171	476	2	/∈	/∈	PUNCT
ejpam-5171	477	1	p	p	X
ejpam-5171	477	2	(	(	PUNCT
ejpam-5171	477	3	by	by	ADP
ejpam-5171	477	4	definition	definition	NOUN
ejpam-5171	477	5	of	of	ADP
ejpam-5171	477	6	ψp(l	ψp(l	NOUN
ejpam-5171	477	7	)	)	PUNCT
ejpam-5171	477	8	)	)	PUNCT
ejpam-5171	477	9	.	.	PUNCT
ejpam-5171	478	1	now	now	ADV
ejpam-5171	478	2	,	,	PUNCT
ejpam-5171	478	3	assume	assume	VERB
ejpam-5171	478	4	that	that	SCONJ
ejpam-5171	478	5	u	u	PROPN
ejpam-5171	478	6	∩wy	∩wy	NOUN
ejpam-5171	478	7	=	=	PUNCT
ejpam-5171	478	8	v.	v.	NOUN
ejpam-5171	478	9	consider	consider	VERB
ejpam-5171	478	10	g1	g1	NOUN
ejpam-5171	478	11	=	=	SYM
ejpam-5171	478	12	v−l	v−l	NOUN
ejpam-5171	478	13	/∈	/∈	PUNCT
ejpam-5171	479	1	p.	p.	NOUN
ejpam-5171	479	2	since	since	SCONJ
ejpam-5171	479	3	v	v	NOUN
ejpam-5171	479	4	=	=	NOUN
ejpam-5171	479	5	̸	̸	NUM
ejpam-5171	479	6	ϕ	ϕ	NOUN
ejpam-5171	479	7	,	,	PUNCT
ejpam-5171	479	8	v	v	NOUN
ejpam-5171	479	9	∈	∈	PROPN
ejpam-5171	479	10	δ	δ	PROPN
ejpam-5171	479	11	,	,	PUNCT
ejpam-5171	479	12	and	and	CCONJ
ejpam-5171	479	13	v	v	ADP
ejpam-5171	479	14	−	−	PROPN
ejpam-5171	479	15	g1	g1	PROPN
ejpam-5171	479	16	⊆	⊆	NUM
ejpam-5171	479	17	l	l	NOUN
ejpam-5171	479	18	,	,	PUNCT
ejpam-5171	479	19	it	it	PRON
ejpam-5171	479	20	follows	follow	VERB
ejpam-5171	479	21	that	that	SCONJ
ejpam-5171	479	22	v	v	ADP
ejpam-5171	479	23	⊆	⊆	NUM
ejpam-5171	479	24	u	u	NOUN
ejpam-5171	479	25	.	.	PUNCT
ejpam-5171	480	1	consequently	consequently	ADV
ejpam-5171	480	2	,	,	PUNCT
ejpam-5171	480	3	m	m	VERB
ejpam-5171	480	4	=	=	NOUN
ejpam-5171	480	5	v	v	ADJ
ejpam-5171	480	6	−	−	PROPN
ejpam-5171	480	7	(	(	PUNCT
ejpam-5171	480	8	g1	g1	PROPN
ejpam-5171	480	9	∪	∪	ADP
ejpam-5171	480	10	g	g	NOUN
ejpam-5171	480	11	)	)	PUNCT
ejpam-5171	480	12	⊆	⊆	NUM
ejpam-5171	480	13	l	l	NOUN
ejpam-5171	480	14	and	and	CCONJ
ejpam-5171	480	15	m	m	PROPN
ejpam-5171	480	16	=	=	NOUN
ejpam-5171	480	17	v	v	ADJ
ejpam-5171	480	18	−	−	PROPN
ejpam-5171	480	19	(	(	PUNCT
ejpam-5171	480	20	g1∪g	g1∪g	NOUN
ejpam-5171	480	21	)	)	PUNCT
ejpam-5171	480	22	̸=	̸=	PROPN
ejpam-5171	480	23	ϕ	ϕ	NOUN
ejpam-5171	480	24	,	,	PUNCT
ejpam-5171	480	25	since	since	SCONJ
ejpam-5171	480	26	p	p	NOUN
ejpam-5171	480	27	is	be	AUX
ejpam-5171	480	28	a	a	DET
ejpam-5171	480	29	primal	primal	ADJ
ejpam-5171	480	30	anti	anti	ADJ
ejpam-5171	480	31	-	-	NOUN
ejpam-5171	480	32	codense	codense	NOUN
ejpam-5171	480	33	,	,	PUNCT
ejpam-5171	480	34	then	then	ADV
ejpam-5171	480	35	m	m	VERB
ejpam-5171	480	36	⊆	⊆	NUM
ejpam-5171	480	37	l∩	l∩	ADJ
ejpam-5171	480	38	(	(	PUNCT
ejpam-5171	480	39	u	u	NOUN
ejpam-5171	480	40	−g	−g	NOUN
ejpam-5171	480	41	)	)	PUNCT
ejpam-5171	480	42	.	.	PUNCT
ejpam-5171	481	1	hence	hence	ADV
ejpam-5171	481	2	,	,	PUNCT
ejpam-5171	481	3	we	we	PRON
ejpam-5171	481	4	have	have	AUX
ejpam-5171	481	5	shown	show	VERB
ejpam-5171	481	6	that	that	SCONJ
ejpam-5171	481	7	l	l	NOUN
ejpam-5171	481	8	includes	include	VERB
ejpam-5171	481	9	a	a	DET
ejpam-5171	481	10	nonempty	nonempty	ADJ
ejpam-5171	481	11	δ	δ	PROPN
ejpam-5171	481	12	♢	♢	NOUN
ejpam-5171	481	13	-open	-open	NOUN
ejpam-5171	481	14	set	set	NOUN
ejpam-5171	481	15	m	m	AUX
ejpam-5171	481	16	included	include	VERB
ejpam-5171	481	17	in	in	ADP
ejpam-5171	481	18	u	u	PROPN
ejpam-5171	481	19	−g	−g	NOUN
ejpam-5171	481	20	.	.	PUNCT
ejpam-5171	482	1	choose	choose	VERB
ejpam-5171	482	2	x	x	PUNCT
ejpam-5171	482	3	∈	∈	PROPN
ejpam-5171	482	4	l	l	NOUN
ejpam-5171	482	5	,	,	PUNCT
ejpam-5171	482	6	we	we	PRON
ejpam-5171	482	7	have	have	VERB
ejpam-5171	482	8	that	that	PRON
ejpam-5171	482	9	l	l	NOUN
ejpam-5171	482	10	⊆	⊆	NUM
ejpam-5171	482	11	δ	δ	PROPN
ejpam-5171	482	12	♢	♢	PROPN
ejpam-5171	482	13	-cl(δ	-cl(δ	PROPN
ejpam-5171	482	14	♢	♢	NOUN
ejpam-5171	482	15	-int(l	-int(l	PROPN
ejpam-5171	482	16	)	)	PUNCT
ejpam-5171	482	17	)	)	PUNCT
ejpam-5171	482	18	.	.	PUNCT
ejpam-5171	483	1	therefore	therefore	ADV
ejpam-5171	483	2	,	,	PUNCT
ejpam-5171	483	3	l	l	NOUN
ejpam-5171	483	4	is	be	AUX
ejpam-5171	483	5	an	an	DET
ejpam-5171	483	6	element	element	NOUN
ejpam-5171	483	7	of	of	ADP
ejpam-5171	483	8	so(x	so(x	NOUN
ejpam-5171	483	9	,	,	PUNCT
ejpam-5171	483	10	δ	δ	PROPN
ejpam-5171	483	11	♢	♢	PROPN
ejpam-5171	483	12	)	)	PUNCT
ejpam-5171	483	13	.	.	PUNCT
ejpam-5171	484	1	thus	thus	ADV
ejpam-5171	484	2	,	,	PUNCT
ejpam-5171	484	3	we	we	PRON
ejpam-5171	484	4	have	have	AUX
ejpam-5171	484	5	shown	show	VERB
ejpam-5171	484	6	that	that	SCONJ
ejpam-5171	484	7	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	484	8	,	,	PUNCT
ejpam-5171	484	9	δ	δ	PROPN
ejpam-5171	484	10	)	)	PUNCT
ejpam-5171	484	11	⊆	⊆	NUM
ejpam-5171	484	12	so(x	so(x	NOUN
ejpam-5171	484	13	,	,	PUNCT
ejpam-5171	484	14	δ	δ	PROPN
ejpam-5171	484	15	♢	♢	PROPN
ejpam-5171	484	16	)	)	PUNCT
ejpam-5171	484	17	.	.	PUNCT
ejpam-5171	485	1	thus	thus	ADV
ejpam-5171	485	2	,	,	PUNCT
ejpam-5171	485	3	so(x	so(x	NOUN
ejpam-5171	485	4	,	,	PUNCT
ejpam-5171	485	5	δ	δ	PROPN
ejpam-5171	485	6	♢	♢	PROPN
ejpam-5171	485	7	)	)	PUNCT
ejpam-5171	486	1	=	=	SYM
ejpam-5171	486	2	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	486	3	,	,	PUNCT
ejpam-5171	486	4	δ	δ	PROPN
ejpam-5171	486	5	)	)	PUNCT
ejpam-5171	486	6	.	.	PUNCT
ejpam-5171	487	1	definition	definition	NOUN
ejpam-5171	487	2	5.11	5.11	NUM
ejpam-5171	487	3	.	.	PUNCT
ejpam-5171	488	1	a	a	DET
ejpam-5171	488	2	subset	subset	ADJ
ejpam-5171	488	3	l	l	NOUN
ejpam-5171	488	4	of	of	ADP
ejpam-5171	488	5	a	a	DET
ejpam-5171	488	6	pts	pts	X
ejpam-5171	488	7	(	(	PUNCT
ejpam-5171	488	8	x	x	NOUN
ejpam-5171	488	9	,	,	PUNCT
ejpam-5171	488	10	δ	δ	PROPN
ejpam-5171	488	11	,	,	PUNCT
ejpam-5171	488	12	p	p	NOUN
ejpam-5171	488	13	)	)	PUNCT
ejpam-5171	488	14	is	be	AUX
ejpam-5171	488	15	called	call	VERB
ejpam-5171	488	16	a	a	DET
ejpam-5171	488	17	ψl	ψl	NOUN
ejpam-5171	488	18	-	-	PUNCT
ejpam-5171	488	19	set	set	VERB
ejpam-5171	488	20	if	if	SCONJ
ejpam-5171	488	21	l	l	NOUN
ejpam-5171	488	22	⊆	⊆	NUM
ejpam-5171	488	23	int(cl(ψp(l	int(cl(ψp(l	NOUN
ejpam-5171	488	24	)	)	PUNCT
ejpam-5171	488	25	)	)	PUNCT
ejpam-5171	488	26	)	)	PUNCT
ejpam-5171	488	27	.	.	PUNCT
ejpam-5171	489	1	the	the	DET
ejpam-5171	489	2	set	set	NOUN
ejpam-5171	489	3	of	of	ADP
ejpam-5171	489	4	all	all	DET
ejpam-5171	489	5	ψl	ψl	NOUN
ejpam-5171	489	6	-	-	PUNCT
ejpam-5171	489	7	sets	set	NOUN
ejpam-5171	489	8	in	in	ADP
ejpam-5171	489	9	(	(	PUNCT
ejpam-5171	489	10	x	x	NOUN
ejpam-5171	489	11	,	,	PUNCT
ejpam-5171	489	12	δ	δ	PROPN
ejpam-5171	489	13	,	,	PUNCT
ejpam-5171	489	14	p	p	NOUN
ejpam-5171	489	15	)	)	PUNCT
ejpam-5171	489	16	is	be	AUX
ejpam-5171	489	17	represented	represent	VERB
ejpam-5171	489	18	as	as	ADP
ejpam-5171	489	19	δl	δl	X
ejpam-5171	489	20	.	.	PUNCT
ejpam-5171	489	21	by	by	ADP
ejpam-5171	489	22	definitions	definition	NOUN
ejpam-5171	489	23	5.1	5.1	NUM
ejpam-5171	489	24	and	and	CCONJ
ejpam-5171	489	25	definitions	definition	NOUN
ejpam-5171	489	26	5.9	5.9	NUM
ejpam-5171	489	27	,	,	PUNCT
ejpam-5171	489	28	it	it	PRON
ejpam-5171	489	29	can	can	AUX
ejpam-5171	489	30	be	be	AUX
ejpam-5171	489	31	deduced	deduce	VERB
ejpam-5171	489	32	that	that	SCONJ
ejpam-5171	489	33	δl	δl	PROPN
ejpam-5171	489	34	is	be	AUX
ejpam-5171	489	35	a	a	DET
ejpam-5171	489	36	subset	subset	NOUN
ejpam-5171	489	37	of	of	ADP
ejpam-5171	489	38	δl	δl	PROPN
ejpam-5171	489	39	⊆	⊆	NUM
ejpam-5171	489	40	ψ̃p(x	ψ̃p(x	PROPN
ejpam-5171	489	41	,	,	PUNCT
ejpam-5171	489	42	δ	δ	PROPN
ejpam-5171	489	43	)	)	PUNCT
ejpam-5171	489	44	.	.	PUNCT
ejpam-5171	490	1	we	we	PRON
ejpam-5171	490	2	demonstrate	demonstrate	VERB
ejpam-5171	490	3	that	that	SCONJ
ejpam-5171	490	4	the	the	DET
ejpam-5171	490	5	collection	collection	NOUN
ejpam-5171	490	6	δl	δl	INTJ
ejpam-5171	490	7	forms	form	VERB
ejpam-5171	490	8	a	a	DET
ejpam-5171	490	9	topology	topology	NOUN
ejpam-5171	490	10	.	.	PUNCT
ejpam-5171	491	1	theorem	theorem	VERB
ejpam-5171	491	2	5.12	5.12	NUM
ejpam-5171	491	3	.	.	PUNCT
ejpam-5171	492	1	suppose	suppose	VERB
ejpam-5171	492	2	that	that	SCONJ
ejpam-5171	492	3	(	(	PUNCT
ejpam-5171	492	4	x	x	X
ejpam-5171	492	5	,	,	PUNCT
ejpam-5171	492	6	δ	δ	PROPN
ejpam-5171	492	7	,	,	PUNCT
ejpam-5171	492	8	p	p	NOUN
ejpam-5171	492	9	)	)	PUNCT
ejpam-5171	492	10	is	be	AUX
ejpam-5171	492	11	a	a	DET
ejpam-5171	492	12	pts	pt	NOUN
ejpam-5171	492	13	.	.	PUNCT
ejpam-5171	493	1	if	if	SCONJ
ejpam-5171	493	2	p	p	NOUN
ejpam-5171	493	3	is	be	AUX
ejpam-5171	493	4	primal	primal	ADJ
ejpam-5171	493	5	anti	anti	ADJ
ejpam-5171	493	6	-	-	NOUN
ejpam-5171	493	7	codense	codense	NOUN
ejpam-5171	493	8	,	,	PUNCT
ejpam-5171	493	9	then	then	ADV
ejpam-5171	493	10	the	the	DET
ejpam-5171	493	11	collection	collection	NOUN
ejpam-5171	493	12	δl	δl	X
ejpam-5171	493	13	=	=	SYM
ejpam-5171	493	14	{	{	PUNCT
ejpam-5171	493	15	l	l	NOUN
ejpam-5171	493	16	⊆	⊆	NUM
ejpam-5171	493	17	x	x	SYM
ejpam-5171	493	18	:	:	PUNCT
ejpam-5171	493	19	l	l	NOUN
ejpam-5171	493	20	⊆	⊆	NUM
ejpam-5171	493	21	int(cl(ψp(l	int(cl(ψp(l	NOUN
ejpam-5171	493	22	)	)	PUNCT
ejpam-5171	493	23	)	)	PUNCT
ejpam-5171	493	24	)	)	PUNCT
ejpam-5171	493	25	}	}	PUNCT
ejpam-5171	493	26	forms	form	VERB
ejpam-5171	493	27	a	a	DET
ejpam-5171	493	28	topology	topology	NOUN
ejpam-5171	493	29	on	on	ADP
ejpam-5171	493	30	x.	x.	NOUN
ejpam-5171	493	31	proof	proof	NOUN
ejpam-5171	493	32	.	.	PUNCT
ejpam-5171	494	1	we	we	PRON
ejpam-5171	494	2	have	have	AUX
ejpam-5171	494	3	show	show	VERB
ejpam-5171	494	4	that	that	SCONJ
ejpam-5171	494	5	both	both	DET
ejpam-5171	494	6	ϕ	ϕ	NOUN
ejpam-5171	494	7	and	and	CCONJ
ejpam-5171	494	8	x	x	PART
ejpam-5171	494	9	satisfy	satisfy	VERB
ejpam-5171	494	10	the	the	DET
ejpam-5171	494	11	conditions	condition	NOUN
ejpam-5171	494	12	ϕ	ϕ	ADP
ejpam-5171	494	13	⊆	⊆	NUM
ejpam-5171	494	14	int(cl(ψp(ϕ	int(cl(ψp(ϕ	NOUN
ejpam-5171	494	15	)	)	PUNCT
ejpam-5171	494	16	)	)	PUNCT
ejpam-5171	494	17	)	)	PUNCT
ejpam-5171	495	1	and	and	CCONJ
ejpam-5171	495	2	x	x	SYM
ejpam-5171	495	3	⊆	⊆	NUM
ejpam-5171	495	4	int(cl(ψp(x	int(cl(ψp(x	NOUN
ejpam-5171	495	5	)	)	PUNCT
ejpam-5171	495	6	)	)	PUNCT
ejpam-5171	495	7	)	)	PUNCT
ejpam-5171	495	8	,	,	PUNCT
ejpam-5171	496	1	which	which	PRON
ejpam-5171	496	2	means	mean	VERB
ejpam-5171	496	3	that	that	SCONJ
ejpam-5171	496	4	ϕ	ϕ	NOUN
ejpam-5171	496	5	and	and	CCONJ
ejpam-5171	496	6	x	x	AUX
ejpam-5171	496	7	belong	belong	VERB
ejpam-5171	496	8	to	to	ADP
ejpam-5171	496	9	the	the	DET
ejpam-5171	496	10	collection	collection	NOUN
ejpam-5171	496	11	δl	δl	X
ejpam-5171	496	12	.	.	PROPN
ejpam-5171	496	13	suppose	suppose	VERB
ejpam-5171	496	14	that	that	SCONJ
ejpam-5171	496	15	a	a	DET
ejpam-5171	496	16	family	family	NOUN
ejpam-5171	496	17	of	of	ADP
ejpam-5171	496	18	sets	set	NOUN
ejpam-5171	496	19	{	{	PUNCT
ejpam-5171	496	20	lα	lα	NOUN
ejpam-5171	496	21	:	:	PUNCT
ejpam-5171	496	22	α	α	PROPN
ejpam-5171	496	23	∈	∈	NOUN
ejpam-5171	496	24	∆	∆	PROPN
ejpam-5171	496	25	}	}	PUNCT
ejpam-5171	496	26	⊆	⊆	NUM
ejpam-5171	496	27	δl	δl	NOUN
ejpam-5171	496	28	.	.	PROPN
ejpam-5171	496	29	for	for	ADP
ejpam-5171	496	30	any	any	DET
ejpam-5171	496	31	α	α	NOUN
ejpam-5171	496	32	∈	∈	NOUN
ejpam-5171	496	33	∆	∆	PROPN
ejpam-5171	496	34	,	,	PUNCT
ejpam-5171	496	35	it	it	PRON
ejpam-5171	496	36	holds	hold	VERB
ejpam-5171	496	37	that	that	PRON
ejpam-5171	496	38	ψp(lα	ψp(lα	PROPN
ejpam-5171	496	39	)	)	PUNCT
ejpam-5171	496	40	⊆	⊆	NUM
ejpam-5171	496	41	ψp(∪lα	ψp(∪lα	ADJ
ejpam-5171	496	42	)	)	PUNCT
ejpam-5171	496	43	.	.	PUNCT
ejpam-5171	497	1	consequently	consequently	ADV
ejpam-5171	497	2	,	,	PUNCT
ejpam-5171	497	3	lα	lα	ADP
ejpam-5171	497	4	⊆	⊆	NUM
ejpam-5171	497	5	int(cl(ψp(lα	int(cl(ψp(lα	NUM
ejpam-5171	497	6	)	)	PUNCT
ejpam-5171	497	7	)	)	PUNCT
ejpam-5171	497	8	)	)	PUNCT
ejpam-5171	498	1	⊆	⊆	NUM
ejpam-5171	498	2	int(cl(ψp(∪lα	int(cl(ψp(∪lα	NOUN
ejpam-5171	498	3	)	)	PUNCT
ejpam-5171	498	4	)	)	PUNCT
ejpam-5171	498	5	)	)	PUNCT
ejpam-5171	498	6	for	for	ADP
ejpam-5171	498	7	any	any	DET
ejpam-5171	498	8	α	α	NOUN
ejpam-5171	498	9	∈	∈	PROPN
ejpam-5171	499	1	∆.	∆.	ADP
ejpam-5171	499	2	this	this	PRON
ejpam-5171	499	3	implies	imply	VERB
ejpam-5171	499	4	that	that	PRON
ejpam-5171	499	5	∪lα	∪lα	VERB
ejpam-5171	499	6	⊆	⊆	NUM
ejpam-5171	499	7	int(cl(ψp(∪lα	int(cl(ψp(∪lα	NOUN
ejpam-5171	499	8	)	)	PUNCT
ejpam-5171	499	9	)	)	PUNCT
ejpam-5171	499	10	)	)	PUNCT
ejpam-5171	499	11	.	.	PUNCT
ejpam-5171	500	1	thus	thus	ADV
ejpam-5171	500	2	,	,	PUNCT
ejpam-5171	500	3	∪lα	∪lα	PROPN
ejpam-5171	500	4	is	be	AUX
ejpam-5171	500	5	an	an	DET
ejpam-5171	500	6	element	element	NOUN
ejpam-5171	500	7	of	of	ADP
ejpam-5171	500	8	δl	δl	PROPN
ejpam-5171	500	9	.	.	PUNCT
ejpam-5171	501	1	let	let	VERB
ejpam-5171	501	2	l	l	NOUN
ejpam-5171	501	3	and	and	CCONJ
ejpam-5171	501	4	e	e	NOUN
ejpam-5171	501	5	be	be	AUX
ejpam-5171	501	6	two	two	NUM
ejpam-5171	501	7	sets	set	NOUN
ejpam-5171	501	8	in	in	ADP
ejpam-5171	501	9	δl	δl	PROPN
ejpam-5171	501	10	.	.	PUNCT
ejpam-5171	502	1	as	as	ADP
ejpam-5171	502	2	ψp(l	ψp(l	PUNCT
ejpam-5171	502	3	)	)	PUNCT
ejpam-5171	502	4	is	be	AUX
ejpam-5171	502	5	open	open	ADJ
ejpam-5171	502	6	in	in	ADP
ejpam-5171	502	7	(	(	PUNCT
ejpam-5171	502	8	x	x	NOUN
ejpam-5171	502	9	,	,	PUNCT
ejpam-5171	502	10	δ	δ	PROPN
ejpam-5171	502	11	)	)	PUNCT
ejpam-5171	502	12	,	,	PUNCT
ejpam-5171	502	13	we	we	PRON
ejpam-5171	502	14	can	can	AUX
ejpam-5171	502	15	apply	apply	VERB
ejpam-5171	502	16	theorem	theorem	ADJ
ejpam-5171	502	17	1.15	1.15	NUM
ejpam-5171	502	18	,	,	PUNCT
ejpam-5171	502	19	which	which	PRON
ejpam-5171	502	20	leads	lead	VERB
ejpam-5171	502	21	to	to	ADP
ejpam-5171	502	22	the	the	DET
ejpam-5171	502	23	conclusion	conclusion	NOUN
ejpam-5171	502	24	that	that	SCONJ
ejpam-5171	502	25	l	l	NOUN
ejpam-5171	502	26	∩	∩	NOUN
ejpam-5171	502	27	e	e	PROPN
ejpam-5171	502	28	⊆	⊆	NUM
ejpam-5171	502	29	int(cl(ψp(l	int(cl(ψp(l	NOUN
ejpam-5171	502	30	)	)	PUNCT
ejpam-5171	502	31	)	)	PUNCT
ejpam-5171	502	32	)	)	PUNCT
ejpam-5171	502	33	∩	∩	PROPN
ejpam-5171	502	34	int(cl(ψp(e	int(cl(ψp(e	NOUN
ejpam-5171	502	35	)	)	PUNCT
ejpam-5171	502	36	)	)	PUNCT
ejpam-5171	502	37	)	)	PUNCT
ejpam-5171	503	1	=	=	PUNCT
ejpam-5171	503	2	int(cl(ψp(l	int(cl(ψp(l	X
ejpam-5171	503	3	)	)	PUNCT
ejpam-5171	503	4	∩ψp(e	∩ψp(e	NOUN
ejpam-5171	503	5	)	)	PUNCT
ejpam-5171	503	6	)	)	PUNCT
ejpam-5171	503	7	)	)	PUNCT
ejpam-5171	504	1	=	=	PUNCT
ejpam-5171	504	2	int(cl(ψp(l	int(cl(ψp(l	ADP
ejpam-5171	504	3	∩e	∩e	NOUN
ejpam-5171	504	4	)	)	PUNCT
ejpam-5171	504	5	)	)	PUNCT
ejpam-5171	504	6	)	)	PUNCT
ejpam-5171	504	7	.	.	PUNCT
ejpam-5171	505	1	therefore	therefore	ADV
ejpam-5171	505	2	,	,	PUNCT
ejpam-5171	505	3	l	l	NOUN
ejpam-5171	505	4	∩e	∩e	NOUN
ejpam-5171	506	1	⊆	⊆	X
ejpam-5171	506	2	int(cl(ψp(l	int(cl(ψp(l	ADP
ejpam-5171	506	3	∩e	∩e	NOUN
ejpam-5171	506	4	)	)	PUNCT
ejpam-5171	506	5	)	)	PUNCT
ejpam-5171	506	6	)	)	PUNCT
ejpam-5171	507	1	and	and	CCONJ
ejpam-5171	507	2	l	l	NOUN
ejpam-5171	507	3	∩	∩	X
ejpam-5171	507	4	e	e	X
ejpam-5171	507	5	∈	∈	PROPN
ejpam-5171	507	6	δl	δl	AUX
ejpam-5171	507	7	.	.	PUNCT
ejpam-5171	508	1	this	this	PRON
ejpam-5171	508	2	is	be	AUX
ejpam-5171	508	3	the	the	DET
ejpam-5171	508	4	end	end	NOUN
ejpam-5171	508	5	of	of	ADP
ejpam-5171	508	6	the	the	DET
ejpam-5171	508	7	proof	proof	NOUN
ejpam-5171	508	8	.	.	PUNCT
ejpam-5171	509	1	proposition	proposition	NOUN
ejpam-5171	509	2	5.13	5.13	NUM
ejpam-5171	509	3	.	.	PUNCT
ejpam-5171	509	4	suppose	suppose	VERB
ejpam-5171	509	5	that	that	SCONJ
ejpam-5171	509	6	(	(	PUNCT
ejpam-5171	509	7	x	x	X
ejpam-5171	509	8	,	,	PUNCT
ejpam-5171	509	9	δ	δ	PROPN
ejpam-5171	509	10	,	,	PUNCT
ejpam-5171	509	11	p	p	NOUN
ejpam-5171	509	12	)	)	PUNCT
ejpam-5171	509	13	is	be	AUX
ejpam-5171	509	14	a	a	DET
ejpam-5171	509	15	pts	pt	NOUN
ejpam-5171	509	16	.	.	PUNCT
ejpam-5171	510	1	then	then	ADV
ejpam-5171	510	2	,	,	PUNCT
ejpam-5171	510	3	ψp(l	ψp(l	PUNCT
ejpam-5171	510	4	)	)	PUNCT
ejpam-5171	510	5	̸=	̸=	PROPN
ejpam-5171	510	6	ϕ	ϕ	NOUN
ejpam-5171	510	7	if	if	SCONJ
ejpam-5171	510	8	and	and	CCONJ
ejpam-5171	510	9	only	only	ADV
ejpam-5171	510	10	if	if	SCONJ
ejpam-5171	510	11	l	l	NOUN
ejpam-5171	510	12	has	have	VERB
ejpam-5171	510	13	a	a	DET
ejpam-5171	510	14	non	non	ADJ
ejpam-5171	510	15	-	-	ADJ
ejpam-5171	510	16	empty	empty	ADJ
ejpam-5171	510	17	δ	δ	PROPN
ejpam-5171	510	18	♢	♢	NOUN
ejpam-5171	510	19	-interior	-interior	NOUN
ejpam-5171	510	20	.	.	PUNCT
ejpam-5171	511	1	proof	proof	NOUN
ejpam-5171	511	2	.	.	PUNCT
ejpam-5171	512	1	first	first	ADV
ejpam-5171	512	2	,	,	PUNCT
ejpam-5171	512	3	suppose	suppose	VERB
ejpam-5171	512	4	that	that	SCONJ
ejpam-5171	512	5	ψp(l	ψp(l	PUNCT
ejpam-5171	512	6	)	)	PUNCT
ejpam-5171	512	7	̸=	̸=	PROPN
ejpam-5171	512	8	ϕ.	ϕ.	NOUN
ejpam-5171	512	9	however	however	ADV
ejpam-5171	512	10	,	,	PUNCT
ejpam-5171	512	11	according	accord	VERB
ejpam-5171	512	12	to	to	ADP
ejpam-5171	512	13	theorem	theorem	ADJ
ejpam-5171	512	14	1.15	1.15	NUM
ejpam-5171	512	15	,	,	PUNCT
ejpam-5171	512	16	ψp(l	ψp(l	PUNCT
ejpam-5171	512	17	)	)	PUNCT
ejpam-5171	512	18	we	we	PRON
ejpam-5171	512	19	can	can	AUX
ejpam-5171	512	20	write	write	VERB
ejpam-5171	512	21	ψp(l	ψp(l	PUNCT
ejpam-5171	512	22	)	)	PUNCT
ejpam-5171	512	23	=	=	PUNCT
ejpam-5171	512	24	∪{u	∪{u	PROPN
ejpam-5171	512	25	∈	∈	PROPN
ejpam-5171	512	26	δ	δ	NOUN
ejpam-5171	512	27	:	:	PUNCT
ejpam-5171	512	28	(	(	PUNCT
ejpam-5171	512	29	u	u	NOUN
ejpam-5171	512	30	−	−	PROPN
ejpam-5171	512	31	l	l	NOUN
ejpam-5171	512	32	)	)	PUNCT
ejpam-5171	512	33	♢	♢	PROPN
ejpam-5171	512	34	/∈	/∈	PUNCT
ejpam-5171	513	1	p	p	X
ejpam-5171	513	2	}	}	PUNCT
ejpam-5171	513	3	.	.	PUNCT
ejpam-5171	514	1	this	this	PRON
ejpam-5171	514	2	implies	imply	VERB
ejpam-5171	514	3	that	that	SCONJ
ejpam-5171	514	4	there	there	PRON
ejpam-5171	514	5	exists	exist	VERB
ejpam-5171	514	6	a	a	DET
ejpam-5171	514	7	non	non	ADJ
ejpam-5171	514	8	-	-	ADJ
ejpam-5171	514	9	empty	empty	ADJ
ejpam-5171	514	10	set	set	VERB
ejpam-5171	514	11	u	u	PROPN
ejpam-5171	514	12	∈	∈	PROPN
ejpam-5171	514	13	δ	δ	PROPN
ejpam-5171	514	14	for	for	ADP
ejpam-5171	514	15	which	which	PRON
ejpam-5171	514	16	(	(	PUNCT
ejpam-5171	514	17	u	u	NOUN
ejpam-5171	514	18	−	−	PROPN
ejpam-5171	514	19	l)c	l)c	NOUN
ejpam-5171	514	20	/∈	/∈	PUNCT
ejpam-5171	515	1	p.	p.	NOUN
ejpam-5171	515	2	let	let	VERB
ejpam-5171	515	3	(	(	PUNCT
ejpam-5171	515	4	u	u	NOUN
ejpam-5171	515	5	−	−	NOUN
ejpam-5171	515	6	l)c	l)c	NOUN
ejpam-5171	516	1	=	=	SYM
ejpam-5171	516	2	t	t	PROPN
ejpam-5171	516	3	,	,	PUNCT
ejpam-5171	516	4	where	where	SCONJ
ejpam-5171	516	5	t	t	NOUN
ejpam-5171	516	6	/∈	/∈	PUNCT
ejpam-5171	517	1	p.	p.	NOUN
ejpam-5171	517	2	now	now	ADV
ejpam-5171	517	3	,	,	PUNCT
ejpam-5171	517	4	u	u	PRON
ejpam-5171	517	5	−t	−t	VERB
ejpam-5171	517	6	⊆	⊆	NUM
ejpam-5171	517	7	l	l	NOUN
ejpam-5171	517	8	,	,	PUNCT
ejpam-5171	517	9	and	and	CCONJ
ejpam-5171	517	10	since	since	SCONJ
ejpam-5171	517	11	u	u	NOUN
ejpam-5171	517	12	−t	−t	NOUN
ejpam-5171	517	13	is	be	AUX
ejpam-5171	517	14	a	a	DET
ejpam-5171	517	15	δ	δ	PROPN
ejpam-5171	517	16	♢	♢	NOUN
ejpam-5171	517	17	-open	-open	NOUN
ejpam-5171	517	18	set	set	NOUN
ejpam-5171	517	19	according	accord	VERB
ejpam-5171	517	20	to	to	ADP
ejpam-5171	517	21	theorem	theorem	NOUN
ejpam-5171	517	22	1.11	1.11	NUM
ejpam-5171	517	23	,	,	PUNCT
ejpam-5171	517	24	we	we	PRON
ejpam-5171	517	25	can	can	AUX
ejpam-5171	517	26	conclude	conclude	VERB
ejpam-5171	517	27	that	that	SCONJ
ejpam-5171	517	28	l	l	NOUN
ejpam-5171	517	29	includes	include	VERB
ejpam-5171	517	30	a	a	DET
ejpam-5171	517	31	non	non	ADJ
ejpam-5171	517	32	-	-	ADJ
ejpam-5171	517	33	empty	empty	ADJ
ejpam-5171	517	34	δ	δ	PROPN
ejpam-5171	517	35	♢	♢	NOUN
ejpam-5171	517	36	-interior	-interior	NOUN
ejpam-5171	517	37	.	.	PUNCT
ejpam-5171	518	1	conversely	conversely	ADV
ejpam-5171	518	2	,	,	PUNCT
ejpam-5171	518	3	assume	assume	VERB
ejpam-5171	518	4	that	that	SCONJ
ejpam-5171	518	5	l	l	NOUN
ejpam-5171	518	6	includes	include	VERB
ejpam-5171	518	7	a	a	DET
ejpam-5171	518	8	non	non	ADJ
ejpam-5171	518	9	-	-	ADJ
ejpam-5171	518	10	empty	empty	ADJ
ejpam-5171	518	11	δ	δ	PROPN
ejpam-5171	518	12	♢	♢	NOUN
ejpam-5171	518	13	-interior	-interior	PROPN
ejpam-5171	518	14	.	.	PUNCT
ejpam-5171	519	1	this	this	PRON
ejpam-5171	519	2	implies	imply	VERB
ejpam-5171	519	3	that	that	SCONJ
ejpam-5171	519	4	u	u	PROPN
ejpam-5171	519	5	∈	∈	PROPN
ejpam-5171	519	6	δ	δ	PROPN
ejpam-5171	519	7	and	and	CCONJ
ejpam-5171	519	8	t	t	PROPN
ejpam-5171	519	9	/∈	/∈	PUNCT
ejpam-5171	520	1	p	p	X
ejpam-5171	520	2	such	such	ADJ
ejpam-5171	520	3	that	that	DET
ejpam-5171	520	4	u	u	NOUN
ejpam-5171	520	5	−	−	PROPN
ejpam-5171	520	6	t	t	PROPN
ejpam-5171	520	7	⊆	⊆	NUM
ejpam-5171	520	8	l.	l.	PROPN
ejpam-5171	520	9	consequently	consequently	ADV
ejpam-5171	520	10	,	,	PUNCT
ejpam-5171	520	11	u	u	NOUN
ejpam-5171	520	12	−	−	PROPN
ejpam-5171	520	13	l	l	NOUN
ejpam-5171	521	1	⊆	⊆	NUM
ejpam-5171	521	2	t	t	NOUN
ejpam-5171	521	3	.	.	PUNCT
ejpam-5171	522	1	let	let	VERB
ejpam-5171	522	2	h	h	NOUN
ejpam-5171	522	3	=	=	PUNCT
ejpam-5171	522	4	u	u	NOUN
ejpam-5171	522	5	−	−	PROPN
ejpam-5171	522	6	l	l	NOUN
ejpam-5171	522	7	⊆	⊆	NUM
ejpam-5171	522	8	t	t	NOUN
ejpam-5171	522	9	,	,	PUNCT
ejpam-5171	522	10	and	and	CCONJ
ejpam-5171	522	11	thus	thus	ADV
ejpam-5171	522	12	h	h	NOUN
ejpam-5171	522	13	/∈	/∈	PUNCT
ejpam-5171	523	1	p.	p.	NOUN
ejpam-5171	523	2	hence	hence	ADV
ejpam-5171	523	3	,	,	PUNCT
ejpam-5171	523	4	∪{u	∪{u	PROPN
ejpam-5171	523	5	∈	∈	PROPN
ejpam-5171	523	6	δ	δ	NOUN
ejpam-5171	523	7	:	:	PUNCT
ejpam-5171	523	8	(	(	PUNCT
ejpam-5171	523	9	u	u	NOUN
ejpam-5171	523	10	−	−	NOUN
ejpam-5171	523	11	l)c	l)c	NOUN
ejpam-5171	523	12	/∈	/∈	PUNCT
ejpam-5171	524	1	p	p	X
ejpam-5171	524	2	}	}	PUNCT
ejpam-5171	524	3	=	=	SYM
ejpam-5171	524	4	ψp(l	ψp(l	X
ejpam-5171	524	5	)	)	PUNCT
ejpam-5171	524	6	̸=	̸=	PROPN
ejpam-5171	524	7	ϕ.	ϕ.	NOUN
ejpam-5171	524	8	references	reference	NOUN
ejpam-5171	524	9	1366	1366	NUM
ejpam-5171	524	10	corollary	corollary	NOUN
ejpam-5171	524	11	5.14	5.14	NUM
ejpam-5171	524	12	.	.	PUNCT
ejpam-5171	524	13	suppose	suppose	VERB
ejpam-5171	524	14	that	that	SCONJ
ejpam-5171	524	15	(	(	PUNCT
ejpam-5171	524	16	x	x	X
ejpam-5171	524	17	,	,	PUNCT
ejpam-5171	524	18	δ	δ	PROPN
ejpam-5171	524	19	,	,	PUNCT
ejpam-5171	524	20	p	p	NOUN
ejpam-5171	524	21	)	)	PUNCT
ejpam-5171	524	22	is	be	AUX
ejpam-5171	524	23	a	a	DET
ejpam-5171	524	24	pts	pt	NOUN
ejpam-5171	524	25	.	.	PUNCT
ejpam-5171	525	1	then	then	ADV
ejpam-5171	525	2	,	,	PUNCT
ejpam-5171	525	3	{	{	PUNCT
ejpam-5171	525	4	ax	ax	NOUN
ejpam-5171	525	5	}	}	PUNCT
ejpam-5171	525	6	∈	∈	PROPN
ejpam-5171	525	7	ψ̃p(x	ψ̃p(x	NOUN
ejpam-5171	525	8	,	,	PUNCT
ejpam-5171	525	9	δ	δ	PROPN
ejpam-5171	525	10	)	)	PUNCT
ejpam-5171	526	1	if	if	SCONJ
ejpam-5171	526	2	and	and	CCONJ
ejpam-5171	526	3	only	only	ADV
ejpam-5171	526	4	if	if	SCONJ
ejpam-5171	526	5	{	{	PUNCT
ejpam-5171	526	6	ax	ax	NOUN
ejpam-5171	526	7	}	}	PUNCT
ejpam-5171	526	8	∈	∈	PROPN
ejpam-5171	526	9	δl	δl	NOUN
ejpam-5171	526	10	.	.	PUNCT
ejpam-5171	526	11	proof	proof	NOUN
ejpam-5171	526	12	.	.	PUNCT
ejpam-5171	527	1	first	first	ADV
ejpam-5171	527	2	,	,	PUNCT
ejpam-5171	527	3	suppose	suppose	VERB
ejpam-5171	527	4	that	that	SCONJ
ejpam-5171	527	5	{	{	PUNCT
ejpam-5171	527	6	ax	ax	NOUN
ejpam-5171	527	7	}	}	PUNCT
ejpam-5171	527	8	∈	∈	PROPN
ejpam-5171	527	9	ψ̃p(x	ψ̃p(x	NOUN
ejpam-5171	527	10	,	,	PUNCT
ejpam-5171	527	11	δ	δ	PROPN
ejpam-5171	527	12	)	)	PUNCT
ejpam-5171	527	13	.	.	PUNCT
ejpam-5171	528	1	this	this	PRON
ejpam-5171	528	2	means	mean	VERB
ejpam-5171	528	3	that	that	SCONJ
ejpam-5171	528	4	{	{	PUNCT
ejpam-5171	528	5	ax	ax	NOUN
ejpam-5171	528	6	}	}	PUNCT
ejpam-5171	528	7	is	be	AUX
ejpam-5171	528	8	open	open	ADJ
ejpam-5171	528	9	in	in	ADP
ejpam-5171	528	10	(	(	PUNCT
ejpam-5171	528	11	x	x	NOUN
ejpam-5171	528	12	,	,	PUNCT
ejpam-5171	528	13	δ	δ	PROPN
ejpam-5171	528	14	♢	♢	PROPN
ejpam-5171	528	15	)	)	PUNCT
ejpam-5171	528	16	through	through	ADP
ejpam-5171	528	17	proposition	proposition	NOUN
ejpam-5171	528	18	5.13	5.13	NUM
ejpam-5171	528	19	.	.	PUNCT
ejpam-5171	529	1	since	since	SCONJ
ejpam-5171	529	2	{	{	PUNCT
ejpam-5171	529	3	ax	ax	NOUN
ejpam-5171	529	4	}	}	PUNCT
ejpam-5171	529	5	⊆	⊆	NUM
ejpam-5171	529	6	ψp({ax	ψp({ax	NOUN
ejpam-5171	529	7	}	}	PUNCT
ejpam-5171	529	8	)	)	PUNCT
ejpam-5171	529	9	and	and	CCONJ
ejpam-5171	529	10	ψp({ax	ψp({ax	NOUN
ejpam-5171	529	11	}	}	PUNCT
ejpam-5171	529	12	)	)	PUNCT
ejpam-5171	529	13	is	be	AUX
ejpam-5171	529	14	open	open	ADJ
ejpam-5171	529	15	in	in	ADP
ejpam-5171	529	16	(	(	PUNCT
ejpam-5171	529	17	x	x	NOUN
ejpam-5171	529	18	,	,	PUNCT
ejpam-5171	529	19	δ	δ	PROPN
ejpam-5171	529	20	)	)	PUNCT
ejpam-5171	529	21	,	,	PUNCT
ejpam-5171	529	22	we	we	PRON
ejpam-5171	529	23	can	can	AUX
ejpam-5171	529	24	conclude	conclude	VERB
ejpam-5171	529	25	that	that	SCONJ
ejpam-5171	529	26	{	{	PUNCT
ejpam-5171	529	27	ax	ax	NOUN
ejpam-5171	529	28	}	}	PUNCT
ejpam-5171	529	29	⊆	⊆	NUM
ejpam-5171	529	30	int(cl(ψp({ax	int(cl(ψp({ax	X
ejpam-5171	529	31	}	}	PUNCT
ejpam-5171	529	32	)	)	PUNCT
ejpam-5171	529	33	)	)	PUNCT
ejpam-5171	529	34	)	)	PUNCT
ejpam-5171	529	35	.	.	PUNCT
ejpam-5171	530	1	thus	thus	ADV
ejpam-5171	530	2	,	,	PUNCT
ejpam-5171	530	3	we	we	PRON
ejpam-5171	530	4	have	have	AUX
ejpam-5171	530	5	shown	show	VERB
ejpam-5171	530	6	that	that	SCONJ
ejpam-5171	530	7	{	{	PUNCT
ejpam-5171	530	8	ax	ax	NOUN
ejpam-5171	530	9	}	}	PUNCT
ejpam-5171	530	10	∈	∈	PROPN
ejpam-5171	530	11	δl	δl	AUX
ejpam-5171	530	12	.	.	PUNCT
ejpam-5171	530	13	conversely	conversely	ADV
ejpam-5171	530	14	,	,	PUNCT
ejpam-5171	530	15	suppose	suppose	VERB
ejpam-5171	530	16	that	that	SCONJ
ejpam-5171	530	17	{	{	PUNCT
ejpam-5171	530	18	ax	ax	NOUN
ejpam-5171	530	19	}	}	PUNCT
ejpam-5171	530	20	⊆	⊆	NUM
ejpam-5171	530	21	int(cl(ψp({ax	int(cl(ψp({ax	X
ejpam-5171	530	22	}	}	PUNCT
ejpam-5171	530	23	)	)	PUNCT
ejpam-5171	530	24	)	)	PUNCT
ejpam-5171	530	25	)	)	PUNCT
ejpam-5171	531	1	and	and	CCONJ
ejpam-5171	531	2	{	{	PUNCT
ejpam-5171	531	3	ax	ax	NOUN
ejpam-5171	531	4	}	}	PUNCT
ejpam-5171	531	5	⊆	⊆	NUM
ejpam-5171	531	6	(	(	PUNCT
ejpam-5171	531	7	cl(ψp({ax	cl(ψp({ax	X
ejpam-5171	531	8	}	}	PUNCT
ejpam-5171	531	9	)	)	PUNCT
ejpam-5171	531	10	)	)	PUNCT
ejpam-5171	531	11	)	)	PUNCT
ejpam-5171	531	12	.	.	PUNCT
ejpam-5171	532	1	therefore	therefore	ADV
ejpam-5171	532	2	,	,	PUNCT
ejpam-5171	532	3	it	it	PRON
ejpam-5171	532	4	follows	follow	VERB
ejpam-5171	532	5	that	that	SCONJ
ejpam-5171	532	6	{	{	PUNCT
ejpam-5171	532	7	ax	ax	NOUN
ejpam-5171	532	8	}	}	PUNCT
ejpam-5171	532	9	∈	∈	PROPN
ejpam-5171	532	10	ψ̃p(x	ψ̃p(x	NOUN
ejpam-5171	532	11	,	,	PUNCT
ejpam-5171	532	12	δ	δ	PROPN
ejpam-5171	532	13	)	)	PUNCT
ejpam-5171	532	14	.	.	PUNCT
ejpam-5171	533	1	6	6	X
ejpam-5171	533	2	.	.	X
ejpam-5171	533	3	conclusions	conclusion	NOUN
ejpam-5171	533	4	new	new	ADJ
ejpam-5171	533	5	classes	class	NOUN
ejpam-5171	533	6	of	of	ADP
ejpam-5171	533	7	sets	set	NOUN
ejpam-5171	533	8	,	,	PUNCT
ejpam-5171	533	9	namely	namely	ADV
ejpam-5171	533	10	p	p	NOUN
ejpam-5171	533	11	-	-	PUNCT
ejpam-5171	533	12	α	α	NOUN
ejpam-5171	533	13	-	-	ADJ
ejpam-5171	533	14	open	open	ADJ
ejpam-5171	533	15	,	,	PUNCT
ejpam-5171	533	16	p	p	NOUN
ejpam-5171	533	17	-	-	PUNCT
ejpam-5171	533	18	semi	semi	ADV
ejpam-5171	533	19	-	-	ADJ
ejpam-5171	533	20	open	open	ADJ
ejpam-5171	533	21	,	,	PUNCT
ejpam-5171	533	22	p	p	NOUN
ejpam-5171	533	23	-	-	PUNCT
ejpam-5171	533	24	pre	pre	NOUN
ejpam-5171	533	25	-	-	ADJ
ejpam-5171	533	26	open	open	ADJ
ejpam-5171	533	27	,	,	PUNCT
ejpam-5171	533	28	p	p	NOUN
ejpam-5171	533	29	-	-	PUNCT
ejpam-5171	533	30	β	β	NOUN
ejpam-5171	533	31	-	-	ADJ
ejpam-5171	533	32	open	open	ADJ
ejpam-5171	533	33	,	,	PUNCT
ejpam-5171	533	34	pr	pr	NOUN
ejpam-5171	533	35	-	-	PUNCT
ejpam-5171	533	36	sets	set	NOUN
ejpam-5171	533	37	,	,	PUNCT
ejpam-5171	533	38	and	and	CCONJ
ejpam-5171	533	39	prα	prα	VERB
ejpam-5171	533	40	-	-	PUNCT
ejpam-5171	533	41	sets	set	NOUN
ejpam-5171	533	42	in	in	ADP
ejpam-5171	533	43	ptss	ptss	NOUN
ejpam-5171	533	44	,	,	PUNCT
ejpam-5171	533	45	have	have	AUX
ejpam-5171	533	46	been	be	AUX
ejpam-5171	533	47	studied	study	VERB
ejpam-5171	533	48	along	along	ADP
ejpam-5171	533	49	with	with	ADP
ejpam-5171	533	50	results	result	NOUN
ejpam-5171	533	51	about	about	ADP
ejpam-5171	533	52	the	the	DET
ejpam-5171	533	53	relationships	relationship	NOUN
ejpam-5171	533	54	between	between	ADP
ejpam-5171	533	55	class	class	NOUN
ejpam-5171	533	56	sets	set	NOUN
ejpam-5171	533	57	in	in	ADP
ejpam-5171	533	58	tss	tss	NOUN
ejpam-5171	533	59	and	and	CCONJ
ejpam-5171	533	60	a	a	DET
ejpam-5171	533	61	new	new	ADJ
ejpam-5171	533	62	class	class	NOUN
ejpam-5171	533	63	of	of	ADP
ejpam-5171	533	64	sets	set	NOUN
ejpam-5171	533	65	in	in	ADP
ejpam-5171	533	66	ptss	ptss	NOUN
ejpam-5171	533	67	.	.	PUNCT
ejpam-5171	534	1	moreover	moreover	ADV
ejpam-5171	534	2	,	,	PUNCT
ejpam-5171	534	3	the	the	DET
ejpam-5171	534	4	relationships	relationship	NOUN
ejpam-5171	534	5	between	between	ADP
ejpam-5171	534	6	these	these	DET
ejpam-5171	534	7	classes	class	NOUN
ejpam-5171	534	8	of	of	ADP
ejpam-5171	534	9	subsets	subset	NOUN
ejpam-5171	534	10	and	and	CCONJ
ejpam-5171	534	11	some	some	DET
ejpam-5171	534	12	generalizations	generalization	NOUN
ejpam-5171	534	13	of	of	ADP
ejpam-5171	534	14	open	open	ADJ
ejpam-5171	534	15	have	have	AUX
ejpam-5171	534	16	been	be	AUX
ejpam-5171	534	17	introduced	introduce	VERB
ejpam-5171	534	18	.	.	PUNCT
ejpam-5171	535	1	many	many	ADJ
ejpam-5171	535	2	theorems	theorem	NOUN
ejpam-5171	535	3	are	be	AUX
ejpam-5171	535	4	discussed	discuss	VERB
ejpam-5171	535	5	together	together	ADV
ejpam-5171	535	6	with	with	ADP
ejpam-5171	535	7	the	the	DET
ejpam-5171	535	8	counterexamples	counterexample	NOUN
ejpam-5171	535	9	.	.	PUNCT
ejpam-5171	536	1	in	in	ADP
ejpam-5171	536	2	addition	addition	NOUN
ejpam-5171	536	3	,	,	PUNCT
ejpam-5171	536	4	examples	example	NOUN
ejpam-5171	536	5	are	be	AUX
ejpam-5171	536	6	provided	provide	VERB
ejpam-5171	536	7	in	in	ADP
ejpam-5171	536	8	such	such	DET
ejpam-5171	536	9	a	a	DET
ejpam-5171	536	10	way	way	NOUN
ejpam-5171	536	11	as	as	SCONJ
ejpam-5171	536	12	to	to	PART
ejpam-5171	536	13	illustrate	illustrate	VERB
ejpam-5171	536	14	the	the	DET
ejpam-5171	536	15	independence	independence	NOUN
ejpam-5171	536	16	between	between	ADP
ejpam-5171	536	17	openness	openness	NOUN
ejpam-5171	536	18	and	and	CCONJ
ejpam-5171	536	19	popenness	popenness	NOUN
ejpam-5171	536	20	,	,	PUNCT
ejpam-5171	536	21	as	as	ADV
ejpam-5171	536	22	well	well	ADV
ejpam-5171	536	23	as	as	ADP
ejpam-5171	536	24	the	the	DET
ejpam-5171	536	25	independence	independence	NOUN
ejpam-5171	536	26	between	between	ADP
ejpam-5171	536	27	p	p	NOUN
ejpam-5171	536	28	-	-	PUNCT
ejpam-5171	536	29	pre	pre	NOUN
ejpam-5171	536	30	-	-	ADJ
ejpam-5171	536	31	open	open	ADJ
ejpam-5171	536	32	and	and	CCONJ
ejpam-5171	536	33	pr	pr	NOUN
ejpam-5171	536	34	-	-	PUNCT
ejpam-5171	536	35	sets	set	NOUN
ejpam-5171	536	36	.	.	PUNCT
ejpam-5171	537	1	furthermore	furthermore	ADV
ejpam-5171	537	2	,	,	PUNCT
ejpam-5171	537	3	the	the	DET
ejpam-5171	537	4	decomposition	decomposition	NOUN
ejpam-5171	537	5	of	of	ADP
ejpam-5171	537	6	continuity	continuity	NOUN
ejpam-5171	537	7	by	by	ADP
ejpam-5171	537	8	using	use	VERB
ejpam-5171	537	9	a	a	DET
ejpam-5171	537	10	new	new	ADJ
ejpam-5171	537	11	class	class	NOUN
ejpam-5171	537	12	of	of	ADP
ejpam-5171	537	13	sets	set	NOUN
ejpam-5171	537	14	in	in	ADP
ejpam-5171	537	15	ptss	ptss	NOUN
ejpam-5171	537	16	has	have	AUX
ejpam-5171	537	17	been	be	AUX
ejpam-5171	537	18	obtained	obtain	VERB
ejpam-5171	537	19	.	.	PUNCT
ejpam-5171	538	1	finally	finally	ADV
ejpam-5171	538	2	,	,	PUNCT
ejpam-5171	538	3	ψ̃p	ψ̃p	NOUN
ejpam-5171	538	4	-sets	-set	NOUN
ejpam-5171	538	5	were	be	AUX
ejpam-5171	538	6	introduced	introduce	VERB
ejpam-5171	538	7	and	and	CCONJ
ejpam-5171	538	8	investigated	investigate	VERB
ejpam-5171	538	9	by	by	ADP
ejpam-5171	538	10	defining	define	VERB
ejpam-5171	538	11	intriguing	intriguing	ADJ
ejpam-5171	538	12	generalized	generalized	ADJ
ejpam-5171	538	13	open	open	ADJ
ejpam-5171	538	14	sets	set	NOUN
ejpam-5171	538	15	in	in	ADP
ejpam-5171	538	16	pts	pt	NOUN
ejpam-5171	538	17	using	use	VERB
ejpam-5171	538	18	the	the	DET
ejpam-5171	538	19	ψ	ψ	NOUN
ejpam-5171	538	20	-	-	NOUN
ejpam-5171	538	21	operator	operator	NOUN
ejpam-5171	538	22	,	,	PUNCT
ejpam-5171	538	23	besides	besides	SCONJ
ejpam-5171	538	24	investigating	investigate	VERB
ejpam-5171	538	25	some	some	PRON
ejpam-5171	538	26	of	of	ADP
ejpam-5171	538	27	their	their	PRON
ejpam-5171	538	28	important	important	ADJ
ejpam-5171	538	29	properties	property	NOUN
ejpam-5171	538	30	.	.	PUNCT
ejpam-5171	539	1	in	in	ADP
ejpam-5171	539	2	future	future	ADJ
ejpam-5171	539	3	work	work	NOUN
ejpam-5171	539	4	,	,	PUNCT
ejpam-5171	539	5	the	the	DET
ejpam-5171	539	6	same	same	ADJ
ejpam-5171	539	7	concepts	concept	NOUN
ejpam-5171	539	8	presented	present	VERB
ejpam-5171	539	9	in	in	ADP
ejpam-5171	539	10	this	this	DET
ejpam-5171	539	11	article	article	NOUN
ejpam-5171	539	12	can	can	AUX
ejpam-5171	539	13	be	be	AUX
ejpam-5171	539	14	introduced	introduce	VERB
ejpam-5171	539	15	in	in	ADP
ejpam-5171	539	16	the	the	DET
ejpam-5171	539	17	context	context	NOUN
ejpam-5171	539	18	of	of	ADP
ejpam-5171	539	19	primal	primal	ADJ
ejpam-5171	539	20	topological	topological	ADJ
ejpam-5171	539	21	spaces	space	NOUN
ejpam-5171	539	22	[	[	X
ejpam-5171	539	23	29	29	NUM
ejpam-5171	539	24	,	,	PUNCT
ejpam-5171	539	25	34	34	NUM
ejpam-5171	539	26	,	,	PUNCT
ejpam-5171	539	27	35	35	NUM
ejpam-5171	539	28	]	]	PUNCT
ejpam-5171	539	29	by	by	ADP
ejpam-5171	539	30	the	the	DET
ejpam-5171	539	31	techniques	technique	NOUN
ejpam-5171	539	32	in	in	ADP
ejpam-5171	539	33	soft	soft	ADJ
ejpam-5171	539	34	sets	set	NOUN
ejpam-5171	539	35	or	or	CCONJ
ejpam-5171	539	36	rough	rough	ADJ
ejpam-5171	539	37	sets	set	NOUN
ejpam-5171	539	38	.	.	PUNCT
ejpam-5171	540	1	additionally	additionally	ADV
ejpam-5171	540	2	,	,	PUNCT
ejpam-5171	540	3	we	we	PRON
ejpam-5171	540	4	hope	hope	VERB
ejpam-5171	540	5	to	to	PART
ejpam-5171	540	6	relate	relate	VERB
ejpam-5171	540	7	these	these	DET
ejpam-5171	540	8	classes	class	NOUN
ejpam-5171	540	9	of	of	ADP
ejpam-5171	540	10	sets	set	NOUN
ejpam-5171	540	11	to	to	ADP
ejpam-5171	540	12	some	some	DET
ejpam-5171	540	13	concepts	concept	NOUN
ejpam-5171	540	14	in	in	ADP
ejpam-5171	540	15	different	different	ADJ
ejpam-5171	540	16	topological	topological	ADJ
ejpam-5171	540	17	structures	structure	NOUN
ejpam-5171	540	18	.	.	PUNCT
ejpam-5171	541	1	references	reference	NOUN
ejpam-5171	541	2	[	[	X
ejpam-5171	541	3	1	1	NUM
ejpam-5171	541	4	]	]	PUNCT
ejpam-5171	541	5	n.levine	n.levine	NOUN
ejpam-5171	541	6	.	.	PUNCT
ejpam-5171	542	1	semi	semi	ADJ
ejpam-5171	542	2	-	-	ADJ
ejpam-5171	542	3	open	open	ADJ
ejpam-5171	542	4	sets	set	NOUN
ejpam-5171	542	5	and	and	CCONJ
ejpam-5171	542	6	semi	semi	ADJ
ejpam-5171	542	7	-	-	NOUN
ejpam-5171	542	8	continuity	continuity	NOUN
ejpam-5171	542	9	in	in	ADP
ejpam-5171	542	10	topological	topological	ADJ
ejpam-5171	542	11	spaces	space	NOUN
ejpam-5171	542	12	.	.	PUNCT
ejpam-5171	543	1	am	be	AUX
ejpam-5171	543	2	.	.	PUNCT
ejpam-5171	544	1	math	math	NOUN
ejpam-5171	544	2	.	.	PUNCT
ejpam-5171	545	1	mon	mon	PROPN
ejpam-5171	545	2	,	,	PUNCT
ejpam-5171	545	3	70:36–41	70:36–41	NUM
ejpam-5171	545	4	,	,	PUNCT
ejpam-5171	545	5	1963	1963	NUM
ejpam-5171	545	6	.	.	PUNCT
ejpam-5171	546	1	[	[	X
ejpam-5171	546	2	2	2	X
ejpam-5171	546	3	]	]	X
ejpam-5171	546	4	o.	o.	NOUN
ejpam-5171	546	5	nj̊astad	nj̊astad	NOUN
ejpam-5171	546	6	.	.	PUNCT
ejpam-5171	547	1	on	on	ADP
ejpam-5171	547	2	some	some	DET
ejpam-5171	547	3	classes	class	NOUN
ejpam-5171	547	4	of	of	ADP
ejpam-5171	547	5	nearly	nearly	ADV
ejpam-5171	547	6	open	open	ADJ
ejpam-5171	547	7	sets	set	NOUN
ejpam-5171	547	8	.	.	PUNCT
ejpam-5171	548	1	pacific	pacific	PROPN
ejpam-5171	548	2	journal	journal	PROPN
ejpam-5171	548	3	of	of	ADP
ejpam-5171	548	4	mathematics	mathematic	NOUN
ejpam-5171	548	5	,	,	PUNCT
ejpam-5171	548	6	15:961–970	15:961–970	PROPN
ejpam-5171	548	7	,	,	PUNCT
ejpam-5171	548	8	1965	1965	NUM
ejpam-5171	548	9	.	.	PUNCT
ejpam-5171	549	1	[	[	X
ejpam-5171	549	2	3	3	NUM
ejpam-5171	549	3	]	]	PUNCT
ejpam-5171	549	4	a.	a.	NOUN
ejpam-5171	549	5	s.	s.	PROPN
ejpam-5171	549	6	mashhour	mashhour	PROPN
ejpam-5171	549	7	.	.	PUNCT
ejpam-5171	550	1	on	on	ADP
ejpam-5171	550	2	precontinuous	precontinuous	ADJ
ejpam-5171	550	3	and	and	CCONJ
ejpam-5171	550	4	weak	weak	ADJ
ejpam-5171	550	5	precontinuous	precontinuous	ADJ
ejpam-5171	550	6	mappings	mapping	NOUN
ejpam-5171	550	7	.	.	PUNCT
ejpam-5171	551	1	proceedings	proceeding	NOUN
ejpam-5171	551	2	of	of	ADP
ejpam-5171	551	3	the	the	DET
ejpam-5171	551	4	mathematical	mathematical	ADJ
ejpam-5171	551	5	and	and	CCONJ
ejpam-5171	551	6	physical	physical	ADJ
ejpam-5171	551	7	society	society	NOUN
ejpam-5171	551	8	of	of	ADP
ejpam-5171	551	9	egypt	egypt	PROPN
ejpam-5171	551	10	,	,	PUNCT
ejpam-5171	551	11	53:47–53	53:47–53	NUM
ejpam-5171	551	12	,	,	PUNCT
ejpam-5171	551	13	1982	1982	NUM
ejpam-5171	551	14	.	.	PUNCT
ejpam-5171	552	1	[	[	X
ejpam-5171	552	2	4	4	X
ejpam-5171	552	3	]	]	PUNCT
ejpam-5171	552	4	m.	m.	NOUN
ejpam-5171	552	5	e.	e.	PROPN
ejpam-5171	552	6	abd	abd	PROPN
ejpam-5171	553	1	el	el	PROPN
ejpam-5171	553	2	-	-	PROPN
ejpam-5171	553	3	monsef	monsef	PROPN
ejpam-5171	553	4	,	,	PUNCT
ejpam-5171	553	5	s.	s.	PROPN
ejpam-5171	553	6	n.	n.	PROPN
ejpam-5171	553	7	el	el	PROPN
ejpam-5171	553	8	-	-	PROPN
ejpam-5171	553	9	deeb	deeb	PROPN
ejpam-5171	553	10	,	,	PUNCT
ejpam-5171	553	11	and	and	CCONJ
ejpam-5171	553	12	r.	r.	PROPN
ejpam-5171	553	13	a.	a.	PROPN
ejpam-5171	553	14	mahmoud	mahmoud	PROPN
ejpam-5171	553	15	.	.	PUNCT
ejpam-5171	554	1	β	β	X
ejpam-5171	554	2	-	-	ADJ
ejpam-5171	554	3	open	open	ADJ
ejpam-5171	554	4	sets	set	NOUN
ejpam-5171	554	5	and	and	CCONJ
ejpam-5171	554	6	βcontinuous	βcontinuous	ADJ
ejpam-5171	554	7	mappings	mapping	NOUN
ejpam-5171	554	8	.	.	PUNCT
ejpam-5171	555	1	bull	bull	NOUN
ejpam-5171	555	2	.	.	PUNCT
ejpam-5171	556	1	fac	fac	PROPN
ejpam-5171	556	2	.	.	PUNCT
ejpam-5171	557	1	sci	sci	PROPN
ejpam-5171	557	2	.	.	PUNCT
ejpam-5171	557	3	assiut	assiut	PROPN
ejpam-5171	557	4	univ	univ	PROPN
ejpam-5171	557	5	,	,	PUNCT
ejpam-5171	557	6	12:77–90	12:77–90	NUM
ejpam-5171	557	7	,	,	PUNCT
ejpam-5171	557	8	1983	1983	NUM
ejpam-5171	557	9	.	.	PUNCT
ejpam-5171	558	1	[	[	X
ejpam-5171	558	2	5	5	NUM
ejpam-5171	558	3	]	]	PUNCT
ejpam-5171	558	4	g.	g.	NOUN
ejpam-5171	558	5	choquet	choquet	PROPN
ejpam-5171	558	6	.	.	PUNCT
ejpam-5171	559	1	théorie	théorie	PROPN
ejpam-5171	559	2	des	des	PROPN
ejpam-5171	559	3	ensembles	ensembles	PROPN
ejpam-5171	559	4	-	-	PUNCT
ejpam-5171	559	5	sur	sur	NOUN
ejpam-5171	559	6	les	les	X
ejpam-5171	559	7	notions	notion	NOUN
ejpam-5171	559	8	de	de	X
ejpam-5171	559	9	filtre	filtre	NOUN
ejpam-5171	559	10	et	et	NOUN
ejpam-5171	559	11	de	de	NOUN
ejpam-5171	559	12	grille	grille	NOUN
ejpam-5171	559	13	.	.	PUNCT
ejpam-5171	560	1	comptes	compte	VERB
ejpam-5171	560	2	rendus	rendus	PROPN
ejpam-5171	560	3	hebd	hebd	PROPN
ejpam-5171	560	4	.	.	PUNCT
ejpam-5171	561	1	des	des	PROPN
ejpam-5171	561	2	séances	séances	PROPN
ejpam-5171	561	3	l	l	NOUN
ejpam-5171	561	4	acad	acad	NOUN
ejpam-5171	561	5	.	.	PUNCT
ejpam-5171	562	1	des	des	PROPN
ejpam-5171	562	2	sci	sci	PROPN
ejpam-5171	562	3	,	,	PUNCT
ejpam-5171	562	4	224:171–173	224:171–173	NUM
ejpam-5171	562	5	,	,	PUNCT
ejpam-5171	562	6	1947	1947	NUM
ejpam-5171	562	7	.	.	PUNCT
ejpam-5171	563	1	[	[	X
ejpam-5171	563	2	6	6	NUM
ejpam-5171	563	3	]	]	PUNCT
ejpam-5171	563	4	w.	w.	PROPN
ejpam-5171	563	5	j.	j.	PROPN
ejpam-5171	563	6	thron	thron	PROPN
ejpam-5171	563	7	.	.	PUNCT
ejpam-5171	563	8	proximity	proximity	NOUN
ejpam-5171	563	9	structures	structure	NOUN
ejpam-5171	563	10	and	and	CCONJ
ejpam-5171	563	11	grills	grill	NOUN
ejpam-5171	563	12	.	.	PUNCT
ejpam-5171	564	1	mathematische	mathematische	PROPN
ejpam-5171	564	2	annalen	annalen	PROPN
ejpam-5171	564	3	,	,	PUNCT
ejpam-5171	564	4	260:35–62	260:35–62	NUM
ejpam-5171	564	5	,	,	PUNCT
ejpam-5171	564	6	1973	1973	NUM
ejpam-5171	564	7	references	reference	NOUN
ejpam-5171	564	8	1367	1367	NUM
ejpam-5171	564	9	[	[	X
ejpam-5171	564	10	7	7	NUM
ejpam-5171	564	11	]	]	PUNCT
ejpam-5171	564	12	k.	k.	PROPN
ejpam-5171	565	1	c.	c.	PROPN
ejpam-5171	565	2	chattopadhyay	chattopadhyay	PROPN
ejpam-5171	565	3	and	and	CCONJ
ejpam-5171	565	4	w.	w.	PROPN
ejpam-5171	565	5	j.	j.	PROPN
ejpam-5171	565	6	thron	thron	PROPN
ejpam-5171	565	7	.	.	PUNCT
ejpam-5171	566	1	extensions	extension	NOUN
ejpam-5171	566	2	of	of	ADP
ejpam-5171	566	3	closure	closure	NOUN
ejpam-5171	566	4	spaces	space	NOUN
ejpam-5171	566	5	.	.	PUNCT
ejpam-5171	567	1	canadian	canadian	ADJ
ejpam-5171	567	2	journal	journal	PROPN
ejpam-5171	567	3	of	of	ADP
ejpam-5171	567	4	mathematics	mathematic	NOUN
ejpam-5171	567	5	,	,	PUNCT
ejpam-5171	567	6	29:1277–1286	29:1277–1286	NUM
ejpam-5171	567	7	,	,	PUNCT
ejpam-5171	567	8	1977	1977	NUM
ejpam-5171	567	9	.	.	PUNCT
ejpam-5171	568	1	[	[	X
ejpam-5171	568	2	8	8	NUM
ejpam-5171	568	3	]	]	PUNCT
ejpam-5171	568	4	k.	k.	PROPN
ejpam-5171	569	1	c.	c.	PROPN
ejpam-5171	569	2	chattopadhyay	chattopadhyay	PROPN
ejpam-5171	569	3	,	,	PUNCT
ejpam-5171	569	4	o.	o.	NOUN
ejpam-5171	569	5	nj̊astad	nj̊astad	NOUN
ejpam-5171	569	6	,	,	PUNCT
ejpam-5171	569	7	and	and	CCONJ
ejpam-5171	569	8	w.	w.	PROPN
ejpam-5171	569	9	j.	j.	PROPN
ejpam-5171	569	10	thron	thron	PROPN
ejpam-5171	569	11	.	.	PUNCT
ejpam-5171	570	1	merotopic	merotopic	ADJ
ejpam-5171	570	2	spaces	space	NOUN
ejpam-5171	570	3	and	and	CCONJ
ejpam-5171	570	4	extensions	extension	NOUN
ejpam-5171	570	5	of	of	ADP
ejpam-5171	570	6	closure	closure	NOUN
ejpam-5171	570	7	spaces	space	NOUN
ejpam-5171	570	8	.	.	PUNCT
ejpam-5171	571	1	canadian	canadian	ADJ
ejpam-5171	571	2	journal	journal	PROPN
ejpam-5171	571	3	of	of	ADP
ejpam-5171	571	4	mathematics	mathematic	NOUN
ejpam-5171	571	5	,	,	PUNCT
ejpam-5171	571	6	35:613–629	35:613–629	NUM
ejpam-5171	571	7	,	,	PUNCT
ejpam-5171	571	8	1983	1983	NUM
ejpam-5171	571	9	.	.	PUNCT
ejpam-5171	572	1	[	[	X
ejpam-5171	572	2	9	9	NUM
ejpam-5171	572	3	]	]	X
ejpam-5171	572	4	b.	b.	PROPN
ejpam-5171	572	5	roy	roy	PROPN
ejpam-5171	572	6	and	and	CCONJ
ejpam-5171	572	7	m.n	m.n	PROPN
ejpam-5171	572	8	.	.	PROPN
ejpam-5171	572	9	mukherjee	mukherjee	PROPN
ejpam-5171	572	10	.	.	PUNCT
ejpam-5171	573	1	on	on	ADP
ejpam-5171	573	2	a	a	DET
ejpam-5171	573	3	typical	typical	ADJ
ejpam-5171	573	4	topology	topology	NOUN
ejpam-5171	573	5	induced	induce	VERB
ejpam-5171	573	6	by	by	ADP
ejpam-5171	573	7	a	a	DET
ejpam-5171	573	8	grill	grill	NOUN
ejpam-5171	573	9	.	.	PUNCT
ejpam-5171	574	1	soochow	soochow	PROPN
ejpam-5171	574	2	j.	j.	PROPN
ejpam-5171	574	3	math	math	PROPN
ejpam-5171	574	4	,	,	PUNCT
ejpam-5171	574	5	33:771–786	33:771–786	PROPN
ejpam-5171	574	6	,	,	PUNCT
ejpam-5171	574	7	2007	2007	NUM
ejpam-5171	574	8	.	.	PUNCT
ejpam-5171	575	1	[	[	X
ejpam-5171	575	2	10	10	NUM
ejpam-5171	575	3	]	]	X
ejpam-5171	575	4	b.	b.	PROPN
ejpam-5171	575	5	roy	roy	PROPN
ejpam-5171	575	6	and	and	CCONJ
ejpam-5171	575	7	m.n	m.n	PROPN
ejpam-5171	575	8	.	.	PROPN
ejpam-5171	575	9	mukherjee	mukherjee	PROPN
ejpam-5171	575	10	.	.	PUNCT
ejpam-5171	576	1	concerning	concern	VERB
ejpam-5171	576	2	topologies	topology	NOUN
ejpam-5171	576	3	induced	induce	VERB
ejpam-5171	576	4	by	by	ADP
ejpam-5171	576	5	principal	principal	ADJ
ejpam-5171	576	6	grills	grill	NOUN
ejpam-5171	576	7	.	.	PUNCT
ejpam-5171	577	1	an	an	DET
ejpam-5171	577	2	.	.	NOUN
ejpam-5171	577	3	stiint	stiint	PROPN
ejpam-5171	577	4	.	.	PUNCT
ejpam-5171	578	1	univ	univ	PROPN
ejpam-5171	578	2	.	.	PUNCT
ejpam-5171	579	1	al	al	PROPN
ejpam-5171	579	2	.	.	PROPN
ejpam-5171	579	3	i.	i.	PROPN
ejpam-5171	579	4	cuza	cuza	PROPN
ejpam-5171	579	5	iasi	iasi	PROPN
ejpam-5171	579	6	.	.	PUNCT
ejpam-5171	580	1	mat.(ns	mat.(ns	NOUN
ejpam-5171	580	2	)	)	PUNCT
ejpam-5171	581	1	,	,	PUNCT
ejpam-5171	581	2	55:285–294	55:285–294	NUM
ejpam-5171	581	3	,	,	PUNCT
ejpam-5171	581	4	2009	2009	NUM
ejpam-5171	581	5	.	.	PUNCT
ejpam-5171	582	1	[	[	X
ejpam-5171	582	2	11	11	NUM
ejpam-5171	582	3	]	]	X
ejpam-5171	582	4	b.	b.	PROPN
ejpam-5171	582	5	roy	roy	PROPN
ejpam-5171	582	6	and	and	CCONJ
ejpam-5171	582	7	m.n	m.n	PROPN
ejpam-5171	582	8	.	.	PROPN
ejpam-5171	582	9	mukherjee	mukherjee	PROPN
ejpam-5171	582	10	.	.	PUNCT
ejpam-5171	583	1	on	on	ADP
ejpam-5171	583	2	a	a	DET
ejpam-5171	583	3	type	type	NOUN
ejpam-5171	583	4	of	of	ADP
ejpam-5171	583	5	compactness	compactness	NOUN
ejpam-5171	583	6	via	via	ADP
ejpam-5171	583	7	grills	grill	NOUN
ejpam-5171	583	8	.	.	PUNCT
ejpam-5171	584	1	matematichki	matematichki	PROPN
ejpam-5171	584	2	vesnik	vesnik	PROPN
ejpam-5171	584	3	,	,	PUNCT
ejpam-5171	584	4	59:113–120	59:113–120	NUM
ejpam-5171	584	5	,	,	PUNCT
ejpam-5171	584	6	2007	2007	NUM
ejpam-5171	584	7	.	.	PUNCT
ejpam-5171	585	1	[	[	X
ejpam-5171	585	2	12	12	NUM
ejpam-5171	585	3	]	]	X
ejpam-5171	585	4	b.	b.	PROPN
ejpam-5171	585	5	roy	roy	PROPN
ejpam-5171	585	6	,	,	PUNCT
ejpam-5171	585	7	m.n	m.n	PROPN
ejpam-5171	585	8	.	.	PROPN
ejpam-5171	585	9	mukherjee	mukherjee	PROPN
ejpam-5171	585	10	,	,	PUNCT
ejpam-5171	585	11	and	and	CCONJ
ejpam-5171	585	12	s.	s.	PROPN
ejpam-5171	585	13	k.	k.	PROPN
ejpam-5171	585	14	ghosh	ghosh	PROPN
ejpam-5171	585	15	.	.	PUNCT
ejpam-5171	586	1	on	on	ADP
ejpam-5171	586	2	a	a	DET
ejpam-5171	586	3	new	new	ADJ
ejpam-5171	586	4	operator	operator	NOUN
ejpam-5171	586	5	based	base	VERB
ejpam-5171	586	6	on	on	ADP
ejpam-5171	586	7	a	a	DET
ejpam-5171	586	8	grill	grill	NOUN
ejpam-5171	586	9	and	and	CCONJ
ejpam-5171	586	10	its	its	PRON
ejpam-5171	586	11	associated	associated	ADJ
ejpam-5171	586	12	topology	topology	NOUN
ejpam-5171	586	13	.	.	PUNCT
ejpam-5171	587	1	arab	arab	PROPN
ejpam-5171	587	2	jour	jour	PROPN
ejpam-5171	587	3	.	.	PROPN
ejpam-5171	587	4	math	math	PROPN
ejpam-5171	587	5	sc	sc	PROPN
ejpam-5171	587	6	,	,	PUNCT
ejpam-5171	587	7	14:21–32	14:21–32	NUM
ejpam-5171	587	8	,	,	PUNCT
ejpam-5171	587	9	2008	2008	NUM
ejpam-5171	587	10	.	.	PUNCT
ejpam-5171	588	1	[	[	X
ejpam-5171	588	2	13	13	NUM
ejpam-5171	588	3	]	]	PUNCT
ejpam-5171	588	4	a.	a.	NOUN
ejpam-5171	588	5	a.	a.	NOUN
ejpam-5171	588	6	nasef	nasef	PROPN
ejpam-5171	588	7	and	and	CCONJ
ejpam-5171	588	8	a.	a.	NOUN
ejpam-5171	588	9	azzam	azzam	PROPN
ejpam-5171	588	10	.	.	PUNCT
ejpam-5171	589	1	some	some	DET
ejpam-5171	589	2	topological	topological	ADJ
ejpam-5171	589	3	operators	operator	NOUN
ejpam-5171	589	4	via	via	ADP
ejpam-5171	589	5	grills	grill	NOUN
ejpam-5171	589	6	.	.	PUNCT
ejpam-5171	590	1	journal	journal	PROPN
ejpam-5171	590	2	of	of	ADP
ejpam-5171	590	3	linear	linear	PROPN
ejpam-5171	590	4	and	and	CCONJ
ejpam-5171	590	5	topological	topological	ADJ
ejpam-5171	590	6	algebra	algebra	NOUN
ejpam-5171	590	7	,	,	PUNCT
ejpam-5171	590	8	5:199–204	5:199–204	PROPN
ejpam-5171	590	9	,	,	PUNCT
ejpam-5171	590	10	2016	2016	NUM
ejpam-5171	590	11	.	.	PUNCT
ejpam-5171	591	1	[	[	X
ejpam-5171	591	2	14	14	NUM
ejpam-5171	591	3	]	]	X
ejpam-5171	591	4	e.	e.	PROPN
ejpam-5171	591	5	hatir	hatir	PROPN
ejpam-5171	591	6	and	and	CCONJ
ejpam-5171	591	7	s.	s.	PROPN
ejpam-5171	591	8	jafari	jafari	PROPN
ejpam-5171	591	9	.	.	PUNCT
ejpam-5171	592	1	on	on	ADP
ejpam-5171	592	2	some	some	DET
ejpam-5171	592	3	new	new	ADJ
ejpam-5171	592	4	classes	class	NOUN
ejpam-5171	592	5	of	of	ADP
ejpam-5171	592	6	sets	set	NOUN
ejpam-5171	592	7	and	and	CCONJ
ejpam-5171	592	8	a	a	DET
ejpam-5171	592	9	new	new	ADJ
ejpam-5171	592	10	decomposition	decomposition	NOUN
ejpam-5171	592	11	of	of	ADP
ejpam-5171	592	12	continuity	continuity	NOUN
ejpam-5171	592	13	via	via	ADP
ejpam-5171	592	14	grills	grill	NOUN
ejpam-5171	592	15	.	.	PUNCT
ejpam-5171	593	1	journal	journal	NOUN
ejpam-5171	593	2	of	of	ADP
ejpam-5171	593	3	advanced	advanced	ADJ
ejpam-5171	593	4	mathematical	mathematical	ADJ
ejpam-5171	593	5	studies	study	NOUN
ejpam-5171	593	6	,	,	PUNCT
ejpam-5171	593	7	3:33–40	3:33–40	NUM
ejpam-5171	593	8	,	,	PUNCT
ejpam-5171	593	9	2010	2010	NUM
ejpam-5171	593	10	.	.	PUNCT
ejpam-5171	594	1	[	[	X
ejpam-5171	594	2	15	15	NUM
ejpam-5171	594	3	]	]	X
ejpam-5171	594	4	a.	a.	PROPN
ejpam-5171	594	5	al	al	PROPN
ejpam-5171	594	6	-	-	PUNCT
ejpam-5171	594	7	omari	omari	PROPN
ejpam-5171	594	8	and	and	CCONJ
ejpam-5171	594	9	t.	t.	PROPN
ejpam-5171	594	10	noiri	noiri	PROPN
ejpam-5171	594	11	.	.	PUNCT
ejpam-5171	595	1	decompositions	decomposition	NOUN
ejpam-5171	595	2	of	of	ADP
ejpam-5171	595	3	continuity	continuity	NOUN
ejpam-5171	595	4	via	via	ADP
ejpam-5171	595	5	grills	grill	NOUN
ejpam-5171	595	6	.	.	PUNCT
ejpam-5171	596	1	jordan	jordan	PROPN
ejpam-5171	596	2	j.	j.	PROPN
ejpam-5171	596	3	math	math	PROPN
ejpam-5171	596	4	.	.	PUNCT
ejpam-5171	597	1	stat	stat	PROPN
ejpam-5171	597	2	,	,	PUNCT
ejpam-5171	597	3	4:33	4:33	NUM
ejpam-5171	597	4	-	-	SYM
ejpam-5171	597	5	46	46	NUM
ejpam-5171	597	6	,	,	PUNCT
ejpam-5171	597	7	2011	2011	NUM
ejpam-5171	597	8	.	.	PUNCT
ejpam-5171	598	1	[	[	X
ejpam-5171	598	2	16	16	NUM
ejpam-5171	598	3	]	]	X
ejpam-5171	598	4	d.	d.	PROPN
ejpam-5171	598	5	mandal	mandal	PROPN
ejpam-5171	598	6	and	and	CCONJ
ejpam-5171	598	7	m.	m.	PROPN
ejpam-5171	598	8	mukherjee	mukherjee	PROPN
ejpam-5171	598	9	.	.	PUNCT
ejpam-5171	599	1	on	on	ADP
ejpam-5171	599	2	a	a	DET
ejpam-5171	599	3	class	class	NOUN
ejpam-5171	599	4	of	of	ADP
ejpam-5171	599	5	sets	set	NOUN
ejpam-5171	599	6	via	via	ADP
ejpam-5171	599	7	grill	grill	NOUN
ejpam-5171	599	8	:	:	PUNCT
ejpam-5171	599	9	a	a	DET
ejpam-5171	599	10	decomposition	decomposition	NOUN
ejpam-5171	599	11	of	of	ADP
ejpam-5171	599	12	continuity	continuity	NOUN
ejpam-5171	599	13	.	.	PUNCT
ejpam-5171	600	1	analele	analele	ADP
ejpam-5171	600	2	ştiinţifice	ştiinţifice	PROPN
ejpam-5171	600	3	ale	ale	NOUN
ejpam-5171	600	4	universităţii	universităţii	PROPN
ejpam-5171	600	5	”	"	PUNCT
ejpam-5171	600	6	ovidius	ovidius	ADJ
ejpam-5171	600	7	”	"	PUNCT
ejpam-5171	600	8	constanţa	constanţa	NOUN
ejpam-5171	600	9	.	.	PUNCT
ejpam-5171	601	1	seria	seria	PROPN
ejpam-5171	601	2	matematică	matematică	PROPN
ejpam-5171	601	3	,	,	PUNCT
ejpam-5171	601	4	20:307–316	20:307–316	NUM
ejpam-5171	601	5	,	,	PUNCT
ejpam-5171	601	6	2012	2012	NUM
ejpam-5171	601	7	.	.	PUNCT
ejpam-5171	602	1	[	[	X
ejpam-5171	602	2	17	17	NUM
ejpam-5171	602	3	]	]	PUNCT
ejpam-5171	602	4	i.	i.	NOUN
ejpam-5171	602	5	rajasekaran	rajasekaran	PROPN
ejpam-5171	602	6	,	,	PUNCT
ejpam-5171	602	7	o.	o.	PROPN
ejpam-5171	602	8	nethaji	nethaji	PROPN
ejpam-5171	602	9	,	,	PUNCT
ejpam-5171	602	10	s.	s.	PROPN
ejpam-5171	602	11	jackson	jackson	PROPN
ejpam-5171	602	12	,	,	PUNCT
ejpam-5171	602	13	and	and	CCONJ
ejpam-5171	602	14	n.	n.	PROPN
ejpam-5171	602	15	sekar	sekar	PROPN
ejpam-5171	602	16	.	.	PUNCT
ejpam-5171	603	1	some	some	DET
ejpam-5171	603	2	improvised	improvise	VERB
ejpam-5171	603	3	sets	set	NOUN
ejpam-5171	603	4	in	in	ADP
ejpam-5171	603	5	grill	grill	ADJ
ejpam-5171	603	6	topological	topological	ADJ
ejpam-5171	603	7	spaces	space	NOUN
ejpam-5171	603	8	.	.	PUNCT
ejpam-5171	604	1	annal	annal	ADJ
ejpam-5171	604	2	of	of	ADP
ejpam-5171	604	3	communications	communication	NOUN
ejpam-5171	604	4	in	in	ADP
ejpam-5171	604	5	mathematics	mathematic	NOUN
ejpam-5171	604	6	,	,	PUNCT
ejpam-5171	604	7	5:207–211	5:207–211	NUM
ejpam-5171	604	8	,	,	PUNCT
ejpam-5171	604	9	2022	2022	NUM
ejpam-5171	604	10	.	.	PUNCT
ejpam-5171	605	1	[	[	X
ejpam-5171	605	2	18	18	NUM
ejpam-5171	605	3	]	]	PUNCT
ejpam-5171	605	4	]	]	PUNCT
ejpam-5171	605	5	e.	e.	PROPN
ejpam-5171	605	6	hatir	hatir	PROPN
ejpam-5171	605	7	and	and	CCONJ
ejpam-5171	605	8	t.	t.	PROPN
ejpam-5171	605	9	noiri	noiri	PROPN
ejpam-5171	605	10	.	.	PUNCT
ejpam-5171	606	1	on	on	ADP
ejpam-5171	606	2	decompositions	decomposition	NOUN
ejpam-5171	606	3	of	of	ADP
ejpam-5171	606	4	continuity	continuity	NOUN
ejpam-5171	606	5	via	via	ADP
ejpam-5171	606	6	idealization	idealization	NOUN
ejpam-5171	606	7	.	.	PUNCT
ejpam-5171	607	1	acta	acta	PROPN
ejpam-5171	607	2	mathematica	mathematica	PROPN
ejpam-5171	607	3	hungarica	hungarica	PROPN
ejpam-5171	607	4	,	,	PUNCT
ejpam-5171	607	5	96:341–349	96:341–349	PROPN
ejpam-5171	607	6	,	,	PUNCT
ejpam-5171	607	7	2002	2002	NUM
ejpam-5171	607	8	.	.	PUNCT
ejpam-5171	608	1	[	[	X
ejpam-5171	608	2	19	19	NUM
ejpam-5171	608	3	]	]	X
ejpam-5171	608	4	o.	o.	NOUN
ejpam-5171	608	5	nj̊astad	nj̊astad	PROPN
ejpam-5171	608	6	.	.	PUNCT
ejpam-5171	609	1	remark	remark	NOUN
ejpam-5171	609	2	on	on	ADP
ejpam-5171	609	3	topologies	topology	NOUN
ejpam-5171	609	4	defined	define	VERB
ejpam-5171	609	5	by	by	ADP
ejpam-5171	609	6	local	local	ADJ
ejpam-5171	609	7	properties	property	NOUN
ejpam-5171	609	8	.	.	PUNCT
ejpam-5171	610	1	avh	avh	PROPN
ejpam-5171	610	2	.	.	PUNCT
ejpam-5171	611	1	norske	norske	PROPN
ejpam-5171	611	2	vid	vid	PROPN
ejpam-5171	611	3	.	.	PUNCT
ejpam-5171	612	1	akad	akad	PROPN
ejpam-5171	612	2	.	.	PUNCT
ejpam-5171	613	1	oslo	oslo	PROPN
ejpam-5171	614	1	i	i	PRON
ejpam-5171	614	2	(	(	PUNCT
ejpam-5171	614	3	n.	n.	PROPN
ejpam-5171	614	4	s	s	PROPN
ejpam-5171	614	5	)	)	PUNCT
ejpam-5171	614	6	,	,	PUNCT
ejpam-5171	614	7	8:1–16	8:1–16	NUM
ejpam-5171	614	8	,	,	PUNCT
ejpam-5171	614	9	1966	1966	NUM
ejpam-5171	614	10	.	.	PUNCT
ejpam-5171	615	1	[	[	X
ejpam-5171	615	2	20	20	NUM
ejpam-5171	615	3	]	]	X
ejpam-5171	615	4	d.	d.	PROPN
ejpam-5171	615	5	janković	janković	PROPN
ejpam-5171	615	6	and	and	CCONJ
ejpam-5171	615	7	t.	t.	PROPN
ejpam-5171	615	8	r.	r.	PROPN
ejpam-5171	615	9	hamlett	hamlett	PROPN
ejpam-5171	615	10	.	.	PUNCT
ejpam-5171	616	1	new	new	ADJ
ejpam-5171	616	2	topologies	topology	NOUN
ejpam-5171	616	3	from	from	ADP
ejpam-5171	616	4	old	old	ADJ
ejpam-5171	616	5	via	via	ADP
ejpam-5171	616	6	ideals	ideal	NOUN
ejpam-5171	616	7	.	.	PUNCT
ejpam-5171	617	1	the	the	DET
ejpam-5171	617	2	american	american	PROPN
ejpam-5171	617	3	mathematical	mathematical	PROPN
ejpam-5171	617	4	monthly	monthly	ADV
ejpam-5171	617	5	,	,	PUNCT
ejpam-5171	617	6	97:295–310	97:295–310	PROPN
ejpam-5171	617	7	,	,	PUNCT
ejpam-5171	617	8	1990	1990	NUM
ejpam-5171	617	9	.	.	PUNCT
ejpam-5171	618	1	[	[	X
ejpam-5171	618	2	21	21	NUM
ejpam-5171	618	3	]	]	X
ejpam-5171	618	4	t.r	t.r	PROPN
ejpam-5171	618	5	.	.	PROPN
ejpam-5171	618	6	hamlett	hamlett	PROPN
ejpam-5171	618	7	and	and	CCONJ
ejpam-5171	618	8	d.	d.	PROPN
ejpam-5171	618	9	janković.	janković.	PROPN
ejpam-5171	618	10	ideals	ideal	NOUN
ejpam-5171	618	11	in	in	ADP
ejpam-5171	618	12	topological	topological	ADJ
ejpam-5171	618	13	spaces	space	NOUN
ejpam-5171	618	14	and	and	CCONJ
ejpam-5171	618	15	the	the	DET
ejpam-5171	618	16	set	set	NOUN
ejpam-5171	618	17	operator	operator	NOUN
ejpam-5171	618	18	ψ	ψ	PROPN
ejpam-5171	618	19	.	.	PUNCT
ejpam-5171	618	20	boll	boll	PROPN
ejpam-5171	618	21	.	.	PUNCT
ejpam-5171	619	1	un	un	PROPN
ejpam-5171	619	2	.	.	PROPN
ejpam-5171	619	3	mat	mat	PROPN
ejpam-5171	619	4	.	.	PUNCT
ejpam-5171	619	5	ital	ital	PROPN
ejpam-5171	619	6	,	,	PUNCT
ejpam-5171	619	7	7:863–874	7:863–874	NOUN
ejpam-5171	619	8	,	,	PUNCT
ejpam-5171	619	9	1990	1990	NUM
ejpam-5171	619	10	.	.	PUNCT
ejpam-5171	620	1	[	[	X
ejpam-5171	620	2	22	22	NUM
ejpam-5171	620	3	]	]	X
ejpam-5171	620	4	s.	s.	PROPN
ejpam-5171	620	5	modak	modak	PROPN
ejpam-5171	620	6	and	and	CCONJ
ejpam-5171	620	7	c.	c.	PROPN
ejpam-5171	620	8	bandyopadyay	bandyopadyay	PROPN
ejpam-5171	620	9	.	.	PUNCT
ejpam-5171	621	1	a	a	DET
ejpam-5171	621	2	note	note	NOUN
ejpam-5171	621	3	on	on	ADP
ejpam-5171	621	4	ψ	ψ	NOUN
ejpam-5171	621	5	-	-	NOUN
ejpam-5171	621	6	operator	operator	NOUN
ejpam-5171	621	7	.	.	PUNCT
ejpam-5171	622	1	bulletin	bulletin	NOUN
ejpam-5171	622	2	of	of	ADP
ejpam-5171	622	3	the	the	DET
ejpam-5171	622	4	malaysian	malaysian	PROPN
ejpam-5171	622	5	mathematical	mathematical	PROPN
ejpam-5171	622	6	sciences	sciences	PROPN
ejpam-5171	622	7	society	society	NOUN
ejpam-5171	622	8	.	.	PUNCT
ejpam-5171	623	1	second	second	ADJ
ejpam-5171	623	2	series	series	NOUN
ejpam-5171	623	3	,	,	PUNCT
ejpam-5171	623	4	30:43–48	30:43–48	PROPN
ejpam-5171	623	5	,	,	PUNCT
ejpam-5171	623	6	2007	2007	NUM
ejpam-5171	623	7	.	.	PUNCT
ejpam-5171	624	1	references	reference	NOUN
ejpam-5171	624	2	1368	1368	NUM
ejpam-5171	625	1	[	[	X
ejpam-5171	625	2	23	23	NUM
ejpam-5171	625	3	]	]	PUNCT
ejpam-5171	625	4	a.	a.	PROPN
ejpam-5171	625	5	al	al	PROPN
ejpam-5171	625	6	-	-	PUNCT
ejpam-5171	625	7	omari	omari	PROPN
ejpam-5171	625	8	and	and	CCONJ
ejpam-5171	625	9	t.	t.	PROPN
ejpam-5171	625	10	noiri	noiri	PROPN
ejpam-5171	625	11	.	.	PUNCT
ejpam-5171	626	1	on	on	ADP
ejpam-5171	626	2	ψg	ψg	NOUN
ejpam-5171	626	3	-	-	NOUN
ejpam-5171	626	4	operator	operator	NOUN
ejpam-5171	626	5	in	in	ADP
ejpam-5171	626	6	grill	grill	ADJ
ejpam-5171	626	7	topological	topological	ADJ
ejpam-5171	626	8	spaces	space	NOUN
ejpam-5171	626	9	.	.	PUNCT
ejpam-5171	627	1	ann	ann	PROPN
ejpam-5171	627	2	.	.	PROPN
ejpam-5171	627	3	univ	univ	PROPN
ejpam-5171	627	4	.	.	PUNCT
ejpam-5171	628	1	oradea	oradea	PROPN
ejpam-5171	628	2	fasc	fasc	PROPN
ejpam-5171	628	3	.	.	PROPN
ejpam-5171	628	4	mat	mat	PROPN
ejpam-5171	628	5	,	,	PUNCT
ejpam-5171	628	6	19:187–196	19:187–196	NUM
ejpam-5171	628	7	,	,	PUNCT
ejpam-5171	628	8	2012	2012	NUM
ejpam-5171	628	9	.	.	PUNCT
ejpam-5171	629	1	[	[	X
ejpam-5171	629	2	24	24	NUM
ejpam-5171	629	3	]	]	PUNCT
ejpam-5171	629	4	a.	a.	PROPN
ejpam-5171	629	5	al	al	PROPN
ejpam-5171	629	6	-	-	PUNCT
ejpam-5171	629	7	omari	omari	PROPN
ejpam-5171	629	8	and	and	CCONJ
ejpam-5171	629	9	t.	t.	PROPN
ejpam-5171	629	10	noiri	noiri	PROPN
ejpam-5171	629	11	.	.	PUNCT
ejpam-5171	630	1	on	on	ADP
ejpam-5171	630	2	ψ̃g	ψ̃g	NOUN
ejpam-5171	630	3	-	-	NOUN
ejpam-5171	630	4	sets	set	NOUN
ejpam-5171	630	5	in	in	ADP
ejpam-5171	630	6	grill	grill	ADJ
ejpam-5171	630	7	topological	topological	ADJ
ejpam-5171	630	8	spaces	space	NOUN
ejpam-5171	630	9	.	.	PUNCT
ejpam-5171	631	1	filomat	filomat	NOUN
ejpam-5171	631	2	,	,	PUNCT
ejpam-5171	631	3	25:187	25:187	NUM
ejpam-5171	631	4	–	–	PUNCT
ejpam-5171	631	5	196	196	NUM
ejpam-5171	631	6	,	,	PUNCT
ejpam-5171	631	7	2011	2011	NUM
ejpam-5171	631	8	.	.	PUNCT
ejpam-5171	632	1	[	[	X
ejpam-5171	632	2	25	25	NUM
ejpam-5171	632	3	]	]	X
ejpam-5171	632	4	s.	s.	PROPN
ejpam-5171	632	5	acharjee	acharjee	PROPN
ejpam-5171	632	6	and	and	CCONJ
ejpam-5171	632	7	m.	m.	NOUN
ejpam-5171	632	8	özkoç	özkoç	PROPN
ejpam-5171	632	9	,	,	PUNCT
ejpam-5171	632	10	and	and	CCONJ
ejpam-5171	632	11	f.	f.	PROPN
ejpam-5171	632	12	y.	y.	PROPN
ejpam-5171	632	13	issaka	issaka	PROPN
ejpam-5171	632	14	.	.	PUNCT
ejpam-5171	633	1	primal	primal	ADJ
ejpam-5171	633	2	topological	topological	ADJ
ejpam-5171	633	3	spaces	space	NOUN
ejpam-5171	633	4	.	.	PUNCT
ejpam-5171	634	1	arxiv	arxiv	PROPN
ejpam-5171	634	2	preprint	preprint	PROPN
ejpam-5171	634	3	arxiv:2209.12676	arxiv:2209.12676	NUM
ejpam-5171	634	4	,	,	PUNCT
ejpam-5171	634	5	2022	2022	NUM
ejpam-5171	634	6	.	.	PUNCT
ejpam-5171	635	1	[	[	X
ejpam-5171	635	2	26	26	NUM
ejpam-5171	635	3	]	]	PUNCT
ejpam-5171	635	4	a.	a.	PROPN
ejpam-5171	635	5	al	al	PROPN
ejpam-5171	635	6	-	-	PUNCT
ejpam-5171	635	7	omari	omari	PROPN
ejpam-5171	635	8	and	and	CCONJ
ejpam-5171	635	9	s.	s.	PROPN
ejpam-5171	635	10	acharjee	acharjee	PROPN
ejpam-5171	635	11	,	,	PUNCT
ejpam-5171	635	12	and	and	CCONJ
ejpam-5171	635	13	m.	m.	NOUN
ejpam-5171	635	14	özkoç.	özkoç.	NOUN
ejpam-5171	635	15	a	a	DET
ejpam-5171	635	16	new	new	ADJ
ejpam-5171	635	17	operator	operator	NOUN
ejpam-5171	635	18	of	of	ADP
ejpam-5171	635	19	primal	primal	ADJ
ejpam-5171	635	20	topological	topological	ADJ
ejpam-5171	635	21	spaces	space	NOUN
ejpam-5171	635	22	.	.	PUNCT
ejpam-5171	636	1	mathematica	mathematica	PROPN
ejpam-5171	636	2	,	,	PUNCT
ejpam-5171	636	3	88:1–11	88:1–11	NOUN
ejpam-5171	636	4	,	,	PUNCT
ejpam-5171	636	5	2023	2023	NUM
ejpam-5171	636	6	.	.	PUNCT
ejpam-5171	637	1	[	[	X
ejpam-5171	637	2	27	27	NUM
ejpam-5171	637	3	]	]	PUNCT
ejpam-5171	637	4	m.	m.	NOUN
ejpam-5171	637	5	bounkhel	bounkhel	PROPN
ejpam-5171	637	6	and	and	CCONJ
ejpam-5171	637	7	m.	m.	PROPN
ejpam-5171	637	8	bachar	bachar	PROPN
ejpam-5171	637	9	.	.	PUNCT
ejpam-5171	638	1	primal	primal	ADJ
ejpam-5171	638	2	lower	low	ADJ
ejpam-5171	638	3	nice	nice	ADJ
ejpam-5171	638	4	functions	function	NOUN
ejpam-5171	638	5	in	in	ADP
ejpam-5171	638	6	reflexive	reflexive	ADJ
ejpam-5171	638	7	smooth	smooth	ADJ
ejpam-5171	638	8	banach	banach	NOUN
ejpam-5171	638	9	spaces	space	NOUN
ejpam-5171	638	10	.	.	PUNCT
ejpam-5171	639	1	mathematics	mathematic	NOUN
ejpam-5171	639	2	,	,	PUNCT
ejpam-5171	639	3	8:2066	8:2066	NUM
ejpam-5171	639	4	,	,	PUNCT
ejpam-5171	639	5	2020	2020	NUM
ejpam-5171	639	6	.	.	PUNCT
ejpam-5171	640	1	[	[	X
ejpam-5171	640	2	28	28	NUM
ejpam-5171	640	3	]	]	X
ejpam-5171	640	4	h.	h.	PROPN
ejpam-5171	640	5	al	al	PROPN
ejpam-5171	640	6	-	-	PUNCT
ejpam-5171	640	7	saadi	saadi	PROPN
ejpam-5171	640	8	and	and	CCONJ
ejpam-5171	640	9	h.	h.	PROPN
ejpam-5171	640	10	al	al	PROPN
ejpam-5171	640	11	-	-	PUNCT
ejpam-5171	640	12	malki	malki	PROPN
ejpam-5171	640	13	.	.	PUNCT
ejpam-5171	641	1	generalized	generalize	VERB
ejpam-5171	641	2	primal	primal	ADJ
ejpam-5171	641	3	topological	topological	ADJ
ejpam-5171	641	4	spaces	space	NOUN
ejpam-5171	641	5	.	.	PUNCT
ejpam-5171	642	1	aims	aim	VERB
ejpam-5171	642	2	math	math	NOUN
ejpam-5171	642	3	,	,	PUNCT
ejpam-5171	642	4	8:24162–24175	8:24162–24175	NUM
ejpam-5171	642	5	,	,	PUNCT
ejpam-5171	642	6	2023	2023	NUM
ejpam-5171	642	7	.	.	PUNCT
ejpam-5171	643	1	[	[	X
ejpam-5171	643	2	29	29	NUM
ejpam-5171	643	3	]	]	PUNCT
ejpam-5171	643	4	t.	t.	PROPN
ejpam-5171	643	5	m.	m.	PROPN
ejpam-5171	643	6	al	al	PROPN
ejpam-5171	643	7	-	-	PUNCT
ejpam-5171	643	8	shami	shami	PROPN
ejpam-5171	643	9	,	,	PUNCT
ejpam-5171	643	10	z.	z.	PROPN
ejpam-5171	643	11	a.	a.	PROPN
ejpam-5171	643	12	ameen	ameen	PROPN
ejpam-5171	643	13	,	,	PUNCT
ejpam-5171	643	14	r.	r.	PROPN
ejpam-5171	643	15	abu	abu	PROPN
ejpam-5171	643	16	-	-	PUNCT
ejpam-5171	643	17	gdairi	gdairi	PROPN
ejpam-5171	643	18	,	,	PUNCT
ejpam-5171	643	19	and	and	CCONJ
ejpam-5171	643	20	a	a	DET
ejpam-5171	643	21	mhemdi	mhemdi	NOUN
ejpam-5171	643	22	.	.	PUNCT
ejpam-5171	644	1	on	on	ADP
ejpam-5171	644	2	primal	primal	ADJ
ejpam-5171	644	3	soft	soft	ADJ
ejpam-5171	644	4	topology	topology	NOUN
ejpam-5171	644	5	.	.	PUNCT
ejpam-5171	645	1	mathematics	mathematic	NOUN
ejpam-5171	645	2	,	,	PUNCT
ejpam-5171	645	3	11:2329	11:2329	NUM
ejpam-5171	645	4	,	,	PUNCT
ejpam-5171	645	5	2023	2023	NUM
ejpam-5171	645	6	.	.	PUNCT
ejpam-5171	646	1	[	[	X
ejpam-5171	646	2	30	30	NUM
ejpam-5171	646	3	]	]	X
ejpam-5171	646	4	d.	d.	PROPN
ejpam-5171	646	5	andrijevic	andrijevic	PROPN
ejpam-5171	646	6	.	.	PUNCT
ejpam-5171	647	1	semi	semi	ADJ
ejpam-5171	647	2	-	-	ADJ
ejpam-5171	647	3	pre	pre	ADJ
ejpam-5171	647	4	-	-	ADJ
ejpam-5171	647	5	open	open	ADJ
ejpam-5171	647	6	sets	set	NOUN
ejpam-5171	647	7	.	.	PUNCT
ejpam-5171	648	1	mat.vesnik	mat.vesnik	X
ejpam-5171	648	2	,	,	PUNCT
ejpam-5171	648	3	38:24–32	38:24–32	NUM
ejpam-5171	648	4	,	,	PUNCT
ejpam-5171	648	5	1986	1986	NUM
ejpam-5171	648	6	.	.	PUNCT
ejpam-5171	649	1	[	[	X
ejpam-5171	649	2	31	31	NUM
ejpam-5171	649	3	]	]	PUNCT
ejpam-5171	649	4	j.	j.	PROPN
ejpam-5171	649	5	tong	tong	PROPN
ejpam-5171	649	6	.	.	PUNCT
ejpam-5171	650	1	on	on	ADP
ejpam-5171	650	2	decomposition	decomposition	NOUN
ejpam-5171	650	3	of	of	ADP
ejpam-5171	650	4	continuity	continuity	NOUN
ejpam-5171	650	5	in	in	ADP
ejpam-5171	650	6	topological	topological	ADJ
ejpam-5171	650	7	spaces	space	NOUN
ejpam-5171	650	8	.	.	PUNCT
ejpam-5171	651	1	acta	acta	PROPN
ejpam-5171	651	2	mathematical	mathematical	PROPN
ejpam-5171	651	3	hungarica	hungarica	PROPN
ejpam-5171	651	4	,	,	PUNCT
ejpam-5171	651	5	54:51–55	54:51–55	NUM
ejpam-5171	651	6	,	,	PUNCT
ejpam-5171	651	7	1989	1989	NUM
ejpam-5171	651	8	.	.	PUNCT
ejpam-5171	652	1	[	[	X
ejpam-5171	652	2	32	32	NUM
ejpam-5171	652	3	]	]	PUNCT
ejpam-5171	652	4	e.	e.	PROPN
ejpam-5171	652	5	hatir	hatir	PROPN
ejpam-5171	652	6	,	,	PUNCT
ejpam-5171	652	7	t.	t.	PROPN
ejpam-5171	652	8	noiri	noiri	PROPN
ejpam-5171	652	9	,	,	PUNCT
ejpam-5171	652	10	and	and	CCONJ
ejpam-5171	652	11	s.	s.	PROPN
ejpam-5171	652	12	yüksel	yüksel	PROPN
ejpam-5171	652	13	.	.	PUNCT
ejpam-5171	653	1	a	a	DET
ejpam-5171	653	2	decomposition	decomposition	NOUN
ejpam-5171	653	3	of	of	ADP
ejpam-5171	653	4	continuity	continuity	NOUN
ejpam-5171	653	5	.	.	PUNCT
ejpam-5171	654	1	acta	acta	PROPN
ejpam-5171	654	2	mathematica	mathematica	PROPN
ejpam-5171	654	3	hungar	hungar	PROPN
ejpam-5171	654	4	,	,	PUNCT
ejpam-5171	654	5	70:145–150	70:145–150	PROPN
ejpam-5171	654	6	,	,	PUNCT
ejpam-5171	654	7	1996	1996	NUM
ejpam-5171	654	8	.	.	PUNCT
ejpam-5171	655	1	[	[	X
ejpam-5171	655	2	33	33	NUM
ejpam-5171	655	3	]	]	PUNCT
ejpam-5171	655	4	a.	a.	NOUN
ejpam-5171	655	5	mashhour	mashhour	PROPN
ejpam-5171	655	6	,	,	PUNCT
ejpam-5171	655	7	i.	i.	PROPN
ejpam-5171	655	8	hasanein	hasanein	PROPN
ejpam-5171	655	9	,	,	PUNCT
ejpam-5171	655	10	and	and	CCONJ
ejpam-5171	655	11	s.	s.	PROPN
ejpam-5171	655	12	el	el	PROPN
ejpam-5171	655	13	-	-	PROPN
ejpam-5171	655	14	deeb	deeb	PROPN
ejpam-5171	655	15	.	.	PUNCT
ejpam-5171	656	1	α	α	X
ejpam-5171	656	2	-	-	ADJ
ejpam-5171	656	3	continuous	continuous	ADJ
ejpam-5171	656	4	and	and	CCONJ
ejpam-5171	656	5	α	α	NOUN
ejpam-5171	656	6	-	-	ADJ
ejpam-5171	656	7	open	open	ADJ
ejpam-5171	656	8	mappings	mapping	NOUN
ejpam-5171	656	9	.	.	PUNCT
ejpam-5171	657	1	acta	acta	PROPN
ejpam-5171	657	2	mathematica	mathematica	PROPN
ejpam-5171	657	3	hungar	hungar	PROPN
ejpam-5171	657	4	,	,	PUNCT
ejpam-5171	657	5	41:213–218	41:213–218	PROPN
ejpam-5171	657	6	,	,	PUNCT
ejpam-5171	657	7	1983	1983	NUM
ejpam-5171	657	8	.	.	PUNCT
ejpam-5171	658	1	[	[	X
ejpam-5171	658	2	34	34	NUM
ejpam-5171	658	3	]	]	X
ejpam-5171	658	4	t.	t.	PROPN
ejpam-5171	658	5	m.	m.	PROPN
ejpam-5171	658	6	al	al	PROPN
ejpam-5171	658	7	-	-	PUNCT
ejpam-5171	658	8	shami	shami	PROPN
ejpam-5171	658	9	.	.	PUNCT
ejpam-5171	659	1	topological	topological	ADJ
ejpam-5171	659	2	approach	approach	NOUN
ejpam-5171	659	3	to	to	PART
ejpam-5171	659	4	generate	generate	VERB
ejpam-5171	659	5	new	new	ADJ
ejpam-5171	659	6	rough	rough	ADJ
ejpam-5171	659	7	set	set	NOUN
ejpam-5171	659	8	models	model	NOUN
ejpam-5171	659	9	.	.	PUNCT
ejpam-5171	660	1	complex	complex	ADJ
ejpam-5171	660	2	intelligent	intelligent	ADJ
ejpam-5171	660	3	systems	system	NOUN
ejpam-5171	660	4	,	,	PUNCT
ejpam-5171	660	5	85:4101–4113	85:4101–4113	PROPN
ejpam-5171	660	6	,	,	PUNCT
ejpam-5171	660	7	2022	2022	NUM
ejpam-5171	660	8	.	.	PUNCT
ejpam-5171	661	1	[	[	X
ejpam-5171	661	2	35	35	NUM
ejpam-5171	661	3	]	]	X
ejpam-5171	661	4	t.	t.	PROPN
ejpam-5171	661	5	m.	m.	PROPN
ejpam-5171	661	6	al	al	PROPN
ejpam-5171	661	7	-	-	PUNCT
ejpam-5171	661	8	shami	shami	PROPN
ejpam-5171	661	9	.	.	PUNCT
ejpam-5171	662	1	improvement	improvement	NOUN
ejpam-5171	662	2	of	of	ADP
ejpam-5171	662	3	the	the	DET
ejpam-5171	662	4	approximations	approximation	NOUN
ejpam-5171	662	5	and	and	CCONJ
ejpam-5171	662	6	accuracy	accuracy	NOUN
ejpam-5171	662	7	measure	measure	NOUN
ejpam-5171	662	8	of	of	ADP
ejpam-5171	662	9	a	a	DET
ejpam-5171	662	10	rough	rough	ADJ
ejpam-5171	662	11	set	set	NOUN
ejpam-5171	662	12	using	use	VERB
ejpam-5171	662	13	somewhere	somewhere	ADV
ejpam-5171	662	14	dense	dense	ADJ
ejpam-5171	662	15	sets	set	NOUN
ejpam-5171	662	16	.	.	PUNCT
ejpam-5171	663	1	soft	soft	ADJ
ejpam-5171	663	2	computing	computing	NOUN
ejpam-5171	663	3	,	,	PUNCT
ejpam-5171	663	4	2523:14449–14460	2523:14449–14460	NUM
ejpam-5171	663	5	,	,	PUNCT
ejpam-5171	663	6	2021	2021	NUM
ejpam-5171	663	7	.	.	PUNCT