id	sid	tid	token	lemma	pos
ejpam-4803	1	1	european	european	PROPN
ejpam-4803	1	2	journal	journal	PROPN
ejpam-4803	1	3	of	of	ADP
ejpam-4803	1	4	pure	pure	ADJ
ejpam-4803	1	5	and	and	CCONJ
ejpam-4803	1	6	applied	apply	VERB
ejpam-4803	1	7	mathematics	mathematic	NOUN
ejpam-4803	1	8	vol	vol	NOUN
ejpam-4803	1	9	.	.	PROPN
ejpam-4803	2	1	17	17	NUM
ejpam-4803	2	2	,	,	PUNCT
ejpam-4803	2	3	no	no	INTJ
ejpam-4803	2	4	.	.	NOUN
ejpam-4803	2	5	1	1	NUM
ejpam-4803	2	6	,	,	PUNCT
ejpam-4803	2	7	2024	2024	NUM
ejpam-4803	2	8	,	,	PUNCT
ejpam-4803	2	9	356	356	NUM
ejpam-4803	2	10	-	-	SYM
ejpam-4803	2	11	361	361	NUM
ejpam-4803	2	12	issn	issn	PROPN
ejpam-4803	2	13	1307	1307	NUM
ejpam-4803	2	14	-	-	SYM
ejpam-4803	2	15	5543	5543	NUM
ejpam-4803	2	16	–	–	PUNCT
ejpam-4803	3	1	ejpam.com	ejpam.com	X
ejpam-4803	3	2	published	publish	VERB
ejpam-4803	3	3	by	by	ADP
ejpam-4803	3	4	new	new	PROPN
ejpam-4803	3	5	york	york	PROPN
ejpam-4803	3	6	business	business	PROPN
ejpam-4803	3	7	global	global	ADJ
ejpam-4803	3	8	codimension	codimension	NOUN
ejpam-4803	3	9	one	one	NUM
ejpam-4803	3	10	foliation	foliation	NOUN
ejpam-4803	3	11	and	and	CCONJ
ejpam-4803	3	12	the	the	DET
ejpam-4803	3	13	prime	prime	ADJ
ejpam-4803	3	14	spectrum	spectrum	NOUN
ejpam-4803	3	15	of	of	ADP
ejpam-4803	3	16	a	a	DET
ejpam-4803	3	17	ring	ring	NOUN
ejpam-4803	3	18	badr	badr	PROPN
ejpam-4803	3	19	alharbi	alharbi	PROPN
ejpam-4803	3	20	department	department	PROPN
ejpam-4803	3	21	of	of	ADP
ejpam-4803	3	22	mathematics	mathematics	PROPN
ejpam-4803	3	23	,	,	PUNCT
ejpam-4803	3	24	al	al	PROPN
ejpam-4803	3	25	jumum	jumum	PROPN
ejpam-4803	3	26	university	university	PROPN
ejpam-4803	3	27	college	college	NOUN
ejpam-4803	3	28	,	,	PUNCT
ejpam-4803	3	29	umm	umm	INTJ
ejpam-4803	3	30	al	al	PROPN
ejpam-4803	3	31	-	-	PUNCT
ejpam-4803	3	32	qura	qura	PROPN
ejpam-4803	3	33	university	university	NOUN
ejpam-4803	3	34	,	,	PUNCT
ejpam-4803	3	35	,	,	PUNCT
ejpam-4803	3	36	saudi	saudi	PROPN
ejpam-4803	3	37	arabia	arabia	PROPN
ejpam-4803	3	38	abstract	abstract	NOUN
ejpam-4803	3	39	.	.	PUNCT
ejpam-4803	4	1	let	let	VERB
ejpam-4803	4	2	f	f	PRON
ejpam-4803	4	3	be	be	AUX
ejpam-4803	4	4	a	a	DET
ejpam-4803	4	5	transversally	transversally	ADV
ejpam-4803	4	6	oriented	orient	VERB
ejpam-4803	4	7	codimension	codimension	NOUN
ejpam-4803	4	8	-	-	PUNCT
ejpam-4803	4	9	one	one	NUM
ejpam-4803	4	10	foliation	foliation	NOUN
ejpam-4803	4	11	of	of	ADP
ejpam-4803	4	12	class	class	NOUN
ejpam-4803	4	13	cr	cr	PROPN
ejpam-4803	4	14	,	,	PUNCT
ejpam-4803	4	15	r	r	NOUN
ejpam-4803	4	16	≥	≥	NOUN
ejpam-4803	4	17	0	0	NUM
ejpam-4803	4	18	,	,	PUNCT
ejpam-4803	4	19	on	on	ADP
ejpam-4803	4	20	a	a	DET
ejpam-4803	4	21	closed	closed	ADJ
ejpam-4803	4	22	manifold	manifold	ADJ
ejpam-4803	4	23	m	m	NOUN
ejpam-4803	4	24	.	.	PUNCT
ejpam-4803	5	1	a	a	DET
ejpam-4803	5	2	leaf	leaf	NOUN
ejpam-4803	5	3	class	class	NOUN
ejpam-4803	5	4	of	of	ADP
ejpam-4803	5	5	a	a	DET
ejpam-4803	5	6	leaf	leaf	NOUN
ejpam-4803	5	7	f	f	NOUN
ejpam-4803	5	8	is	be	AUX
ejpam-4803	5	9	the	the	DET
ejpam-4803	5	10	union	union	NOUN
ejpam-4803	5	11	of	of	ADP
ejpam-4803	5	12	all	all	DET
ejpam-4803	5	13	leaves	leave	NOUN
ejpam-4803	5	14	having	have	VERB
ejpam-4803	5	15	the	the	DET
ejpam-4803	5	16	same	same	ADJ
ejpam-4803	5	17	closure	closure	NOUN
ejpam-4803	5	18	as	as	ADP
ejpam-4803	5	19	f	f	PROPN
ejpam-4803	5	20	.	.	PUNCT
ejpam-4803	6	1	let	let	VERB
ejpam-4803	6	2	x	x	PRON
ejpam-4803	6	3	be	be	AUX
ejpam-4803	6	4	the	the	DET
ejpam-4803	6	5	leaf	leaf	NOUN
ejpam-4803	6	6	classes	class	NOUN
ejpam-4803	6	7	space	space	NOUN
ejpam-4803	6	8	and	and	CCONJ
ejpam-4803	6	9	x0	x0	PROPN
ejpam-4803	6	10	be	be	VERB
ejpam-4803	6	11	the	the	DET
ejpam-4803	6	12	union	union	NOUN
ejpam-4803	6	13	of	of	ADP
ejpam-4803	6	14	all	all	DET
ejpam-4803	6	15	open	open	ADJ
ejpam-4803	6	16	subsets	subset	NOUN
ejpam-4803	6	17	of	of	ADP
ejpam-4803	6	18	x	x	X
ejpam-4803	6	19	homeomorphic	homeomorphic	ADJ
ejpam-4803	6	20	to	to	ADP
ejpam-4803	6	21	r	r	NOUN
ejpam-4803	6	22	or	or	CCONJ
ejpam-4803	6	23	s1	s1	NOUN
ejpam-4803	6	24	.	.	PUNCT
ejpam-4803	7	1	in	in	ADP
ejpam-4803	7	2	[	[	X
ejpam-4803	7	3	3	3	NUM
ejpam-4803	7	4	,	,	PUNCT
ejpam-4803	7	5	theorem	theorem	VERB
ejpam-4803	7	6	3.15	3.15	NUM
ejpam-4803	7	7	]	]	X
ejpam-4803	7	8	it	it	PRON
ejpam-4803	7	9	is	be	AUX
ejpam-4803	7	10	shown	show	VERB
ejpam-4803	7	11	that	that	SCONJ
ejpam-4803	7	12	if	if	SCONJ
ejpam-4803	7	13	a	a	DET
ejpam-4803	7	14	codimension	codimension	NOUN
ejpam-4803	7	15	one	one	NUM
ejpam-4803	7	16	foliation	foliation	NOUN
ejpam-4803	7	17	has	have	VERB
ejpam-4803	7	18	a	a	DET
ejpam-4803	7	19	finite	finite	ADJ
ejpam-4803	7	20	height	height	NOUN
ejpam-4803	7	21	,	,	PUNCT
ejpam-4803	7	22	then	then	ADV
ejpam-4803	7	23	the	the	DET
ejpam-4803	7	24	singular	singular	ADJ
ejpam-4803	7	25	part	part	NOUN
ejpam-4803	7	26	of	of	ADP
ejpam-4803	7	27	the	the	DET
ejpam-4803	7	28	space	space	NOUN
ejpam-4803	7	29	of	of	ADP
ejpam-4803	7	30	leaf	leaf	NOUN
ejpam-4803	7	31	classes	class	NOUN
ejpam-4803	7	32	is	be	AUX
ejpam-4803	7	33	homeomorphic	homeomorphic	ADJ
ejpam-4803	7	34	to	to	ADP
ejpam-4803	7	35	the	the	DET
ejpam-4803	7	36	prime	prime	ADJ
ejpam-4803	7	37	spectrum	spectrum	NOUN
ejpam-4803	7	38	(	(	PUNCT
ejpam-4803	7	39	or	or	CCONJ
ejpam-4803	7	40	simply	simply	ADV
ejpam-4803	7	41	the	the	DET
ejpam-4803	7	42	spectrum	spectrum	NOUN
ejpam-4803	7	43	)	)	PUNCT
ejpam-4803	7	44	of	of	ADP
ejpam-4803	7	45	unitary	unitary	ADJ
ejpam-4803	7	46	commutative	commutative	ADJ
ejpam-4803	7	47	ring	ring	NOUN
ejpam-4803	7	48	.	.	PUNCT
ejpam-4803	8	1	in	in	ADP
ejpam-4803	8	2	this	this	DET
ejpam-4803	8	3	paper	paper	NOUN
ejpam-4803	8	4	we	we	PRON
ejpam-4803	8	5	prove	prove	VERB
ejpam-4803	8	6	that	that	SCONJ
ejpam-4803	8	7	the	the	DET
ejpam-4803	8	8	singular	singular	ADJ
ejpam-4803	8	9	part	part	NOUN
ejpam-4803	8	10	of	of	ADP
ejpam-4803	8	11	the	the	DET
ejpam-4803	8	12	space	space	NOUN
ejpam-4803	8	13	of	of	ADP
ejpam-4803	8	14	leaf	leaf	NOUN
ejpam-4803	8	15	classes	class	NOUN
ejpam-4803	8	16	is	be	AUX
ejpam-4803	8	17	homeomorphic	homeomorphic	ADJ
ejpam-4803	8	18	to	to	ADP
ejpam-4803	8	19	the	the	DET
ejpam-4803	8	20	spectrum	spectrum	NOUN
ejpam-4803	8	21	of	of	ADP
ejpam-4803	8	22	unitary	unitary	ADJ
ejpam-4803	8	23	commutative	commutative	ADJ
ejpam-4803	8	24	ring	ring	NOUN
ejpam-4803	8	25	if	if	SCONJ
ejpam-4803	8	26	and	and	CCONJ
ejpam-4803	8	27	only	only	ADV
ejpam-4803	8	28	if	if	SCONJ
ejpam-4803	8	29	every	every	DET
ejpam-4803	8	30	family	family	NOUN
ejpam-4803	8	31	of	of	ADP
ejpam-4803	8	32	totaly	totaly	PROPN
ejpam-4803	8	33	ordered	order	VERB
ejpam-4803	8	34	leaves	leave	NOUN
ejpam-4803	8	35	is	be	AUX
ejpam-4803	8	36	bounded	bound	VERB
ejpam-4803	8	37	below	below	ADV
ejpam-4803	8	38	.	.	PUNCT
ejpam-4803	9	1	2020	2020	NUM
ejpam-4803	9	2	mathematics	mathematic	NOUN
ejpam-4803	9	3	subject	subject	NOUN
ejpam-4803	9	4	classifications	classification	NOUN
ejpam-4803	9	5	:	:	PUNCT
ejpam-4803	9	6	54f65	54f65	NUM
ejpam-4803	9	7	,	,	PUNCT
ejpam-4803	9	8	54h20	54h20	NUM
ejpam-4803	9	9	key	key	ADJ
ejpam-4803	9	10	words	word	NOUN
ejpam-4803	9	11	and	and	CCONJ
ejpam-4803	9	12	phrases	phrase	NOUN
ejpam-4803	9	13	:	:	PUNCT
ejpam-4803	9	14	foliation	foliation	NOUN
ejpam-4803	9	15	,	,	PUNCT
ejpam-4803	9	16	prime	prime	ADJ
ejpam-4803	9	17	spectrum	spectrum	NOUN
ejpam-4803	9	18	,	,	PUNCT
ejpam-4803	9	19	ring	ring	NOUN
ejpam-4803	9	20	,	,	PUNCT
ejpam-4803	9	21	the	the	DET
ejpam-4803	9	22	space	space	NOUN
ejpam-4803	9	23	of	of	ADP
ejpam-4803	9	24	leaf	leaf	NOUN
ejpam-4803	9	25	classes	class	NOUN
ejpam-4803	9	26	1	1	NUM
ejpam-4803	9	27	.	.	PUNCT
ejpam-4803	10	1	introduction	introduction	NOUN
ejpam-4803	10	2	a	a	DET
ejpam-4803	10	3	space	space	NOUN
ejpam-4803	10	4	x	x	PUNCT
ejpam-4803	10	5	is	be	AUX
ejpam-4803	10	6	a	a	DET
ejpam-4803	10	7	spectral	spectral	ADJ
ejpam-4803	10	8	space	space	NOUN
ejpam-4803	10	9	[	[	X
ejpam-4803	10	10	5	5	X
ejpam-4803	10	11	]	]	PUNCT
ejpam-4803	10	12	if	if	SCONJ
ejpam-4803	10	13	it	it	PRON
ejpam-4803	10	14	is	be	AUX
ejpam-4803	10	15	(	(	PUNCT
ejpam-4803	10	16	1	1	X
ejpam-4803	10	17	)	)	PUNCT
ejpam-4803	10	18	sober	sober	ADJ
ejpam-4803	10	19	(	(	PUNCT
ejpam-4803	10	20	i.e.	i.e.	X
ejpam-4803	10	21	,	,	PUNCT
ejpam-4803	10	22	every	every	PRON
ejpam-4803	10	23	nonempty	nonempty	ADV
ejpam-4803	10	24	irreducible	irreducible	ADJ
ejpam-4803	10	25	closed	closed	ADJ
ejpam-4803	10	26	subset	subset	NOUN
ejpam-4803	10	27	of	of	ADP
ejpam-4803	10	28	y	y	PROPN
ejpam-4803	10	29	is	be	AUX
ejpam-4803	10	30	the	the	DET
ejpam-4803	10	31	closure	closure	NOUN
ejpam-4803	10	32	of	of	ADP
ejpam-4803	10	33	a	a	DET
ejpam-4803	10	34	unique	unique	ADJ
ejpam-4803	10	35	point	point	NOUN
ejpam-4803	10	36	)	)	PUNCT
ejpam-4803	10	37	,	,	PUNCT
ejpam-4803	10	38	(	(	PUNCT
ejpam-4803	10	39	2	2	X
ejpam-4803	10	40	)	)	PUNCT
ejpam-4803	10	41	quasi	quasi	ADJ
ejpam-4803	10	42	-	-	ADJ
ejpam-4803	10	43	compact	compact	ADJ
ejpam-4803	10	44	,	,	PUNCT
ejpam-4803	10	45	(	(	PUNCT
ejpam-4803	10	46	3	3	X
ejpam-4803	10	47	)	)	PUNCT
ejpam-4803	10	48	the	the	DET
ejpam-4803	10	49	quasi	quasi	ADJ
ejpam-4803	10	50	-	-	ADJ
ejpam-4803	10	51	compact	compact	ADJ
ejpam-4803	10	52	open	open	ADJ
ejpam-4803	10	53	subsets	subset	NOUN
ejpam-4803	10	54	of	of	ADP
ejpam-4803	10	55	x	x	PUNCT
ejpam-4803	10	56	form	form	VERB
ejpam-4803	10	57	a	a	DET
ejpam-4803	10	58	basis	basis	NOUN
ejpam-4803	10	59	and	and	CCONJ
ejpam-4803	10	60	(	(	PUNCT
ejpam-4803	10	61	4	4	X
ejpam-4803	10	62	)	)	PUNCT
ejpam-4803	10	63	the	the	DET
ejpam-4803	10	64	family	family	NOUN
ejpam-4803	10	65	of	of	ADP
ejpam-4803	10	66	quasi	quasi	ADJ
ejpam-4803	10	67	-	-	ADJ
ejpam-4803	10	68	compact	compact	ADJ
ejpam-4803	10	69	open	open	ADJ
ejpam-4803	10	70	subsets	subset	NOUN
ejpam-4803	10	71	of	of	ADP
ejpam-4803	10	72	x	x	PUNCT
ejpam-4803	10	73	is	be	AUX
ejpam-4803	10	74	closed	close	VERB
ejpam-4803	10	75	under	under	ADP
ejpam-4803	10	76	finite	finite	ADJ
ejpam-4803	10	77	intersections	intersection	NOUN
ejpam-4803	10	78	.	.	PUNCT
ejpam-4803	11	1	in	in	ADP
ejpam-4803	11	2	particular	particular	ADJ
ejpam-4803	11	3	a	a	DET
ejpam-4803	11	4	finite	finite	PROPN
ejpam-4803	11	5	t0	t0	NOUN
ejpam-4803	11	6	-	-	NOUN
ejpam-4803	11	7	space	space	NOUN
ejpam-4803	11	8	is	be	AUX
ejpam-4803	11	9	a	a	DET
ejpam-4803	11	10	spectral	spectral	ADJ
ejpam-4803	11	11	space	space	NOUN
ejpam-4803	11	12	.	.	PUNCT
ejpam-4803	12	1	(	(	PUNCT
ejpam-4803	12	2	1	1	NUM
ejpam-4803	12	3	)	)	PUNCT
ejpam-4803	12	4	,	,	PUNCT
ejpam-4803	12	5	(	(	PUNCT
ejpam-4803	12	6	2	2	NUM
ejpam-4803	12	7	)	)	PUNCT
ejpam-4803	12	8	,	,	PUNCT
ejpam-4803	12	9	(	(	PUNCT
ejpam-4803	12	10	3	3	X
ejpam-4803	12	11	)	)	PUNCT
ejpam-4803	12	12	and	and	CCONJ
ejpam-4803	12	13	(	(	PUNCT
ejpam-4803	12	14	4	4	X
ejpam-4803	12	15	)	)	PUNCT
ejpam-4803	12	16	are	be	AUX
ejpam-4803	12	17	called	call	VERB
ejpam-4803	12	18	spectral	spectral	ADJ
ejpam-4803	12	19	properties	property	NOUN
ejpam-4803	12	20	.	.	PUNCT
ejpam-4803	13	1	a	a	DET
ejpam-4803	13	2	foliation	foliation	NOUN
ejpam-4803	13	3	of	of	ADP
ejpam-4803	13	4	codimension	codimension	NOUN
ejpam-4803	13	5	one	one	NUM
ejpam-4803	13	6	on	on	ADP
ejpam-4803	13	7	a	a	DET
ejpam-4803	13	8	smooth	smooth	ADJ
ejpam-4803	13	9	manifold	manifold	ADJ
ejpam-4803	13	10	m	m	NOUN
ejpam-4803	13	11	of	of	ADP
ejpam-4803	13	12	dimension	dimension	NOUN
ejpam-4803	13	13	m	m	VERB
ejpam-4803	13	14	is	be	AUX
ejpam-4803	13	15	an	an	DET
ejpam-4803	13	16	open	open	ADJ
ejpam-4803	13	17	equivalence	equivalence	NOUN
ejpam-4803	13	18	relation	relation	NOUN
ejpam-4803	13	19	f	f	PROPN
ejpam-4803	13	20	on	on	ADP
ejpam-4803	13	21	m	m	PROPN
ejpam-4803	13	22	with	with	ADP
ejpam-4803	13	23	each	each	DET
ejpam-4803	13	24	equivalence	equivalence	NOUN
ejpam-4803	13	25	class	class	NOUN
ejpam-4803	13	26	(	(	PUNCT
ejpam-4803	13	27	called	call	VERB
ejpam-4803	13	28	a	a	DET
ejpam-4803	13	29	leaf	leaf	NOUN
ejpam-4803	13	30	)	)	PUNCT
ejpam-4803	13	31	is	be	AUX
ejpam-4803	13	32	a	a	DET
ejpam-4803	13	33	weakly	weakly	ADV
ejpam-4803	13	34	embedded	embed	VERB
ejpam-4803	13	35	m−	m−	PROPN
ejpam-4803	13	36	1	1	NUM
ejpam-4803	13	37	sub	sub	ADJ
ejpam-4803	13	38	-	-	ADJ
ejpam-4803	13	39	manifold	manifold	ADJ
ejpam-4803	13	40	such	such	ADJ
ejpam-4803	13	41	as	as	ADP
ejpam-4803	13	42	the	the	DET
ejpam-4803	13	43	canonical	canonical	ADJ
ejpam-4803	13	44	projection	projection	NOUN
ejpam-4803	13	45	of	of	ADP
ejpam-4803	13	46	m	m	PROPN
ejpam-4803	13	47	on	on	ADP
ejpam-4803	13	48	the	the	DET
ejpam-4803	13	49	space	space	NOUN
ejpam-4803	13	50	of	of	ADP
ejpam-4803	13	51	leaves	leave	NOUN
ejpam-4803	13	52	m	m	PROPN
ejpam-4803	13	53	/	/	SYM
ejpam-4803	13	54	f	f	PROPN
ejpam-4803	13	55	is	be	AUX
ejpam-4803	13	56	a	a	DET
ejpam-4803	13	57	locally	locally	ADV
ejpam-4803	13	58	submersion	submersion	NOUN
ejpam-4803	13	59	.	.	PUNCT
ejpam-4803	14	1	in	in	ADP
ejpam-4803	14	2	that	that	DET
ejpam-4803	14	3	event	event	NOUN
ejpam-4803	14	4	for	for	ADP
ejpam-4803	14	5	each	each	DET
ejpam-4803	14	6	x	x	SYM
ejpam-4803	14	7	∈	∈	PROPN
ejpam-4803	14	8	m	m	NOUN
ejpam-4803	14	9	,	,	PUNCT
ejpam-4803	14	10	there	there	PRON
ejpam-4803	14	11	is	be	VERB
ejpam-4803	14	12	a	a	DET
ejpam-4803	14	13	chart	chart	NOUN
ejpam-4803	14	14	(	(	PUNCT
ejpam-4803	14	15	u	u	NOUN
ejpam-4803	14	16	,	,	PUNCT
ejpam-4803	14	17	φ	φ	NOUN
ejpam-4803	14	18	)	)	PUNCT
ejpam-4803	14	19	such	such	ADJ
ejpam-4803	14	20	that	that	SCONJ
ejpam-4803	14	21	φ(u	φ(u	NOUN
ejpam-4803	14	22	)	)	PUNCT
ejpam-4803	14	23	=	=	SYM
ejpam-4803	14	24	rm	rm	NOUN
ejpam-4803	14	25	and	and	CCONJ
ejpam-4803	14	26	each	each	DET
ejpam-4803	14	27	equivalence	equivalence	NOUN
ejpam-4803	14	28	class	class	NOUN
ejpam-4803	14	29	of	of	ADP
ejpam-4803	14	30	the	the	DET
ejpam-4803	14	31	restriction	restriction	NOUN
ejpam-4803	14	32	of	of	ADP
ejpam-4803	14	33	f	f	PROPN
ejpam-4803	14	34	to	to	ADP
ejpam-4803	14	35	u	u	PRON
ejpam-4803	14	36	is	be	AUX
ejpam-4803	14	37	homeomorphic	homeomorphic	ADJ
ejpam-4803	14	38	to	to	ADP
ejpam-4803	14	39	rp	rp	PROPN
ejpam-4803	14	40	×	×	PROPN
ejpam-4803	14	41	{	{	PUNCT
ejpam-4803	14	42	y	y	NOUN
ejpam-4803	14	43	}	}	PUNCT
ejpam-4803	14	44	where	where	SCONJ
ejpam-4803	14	45	y	y	PROPN
ejpam-4803	14	46	∈	∈	PROPN
ejpam-4803	14	47	r.	r.	PROPN
ejpam-4803	14	48	such	such	ADJ
ejpam-4803	14	49	chart	chart	NOUN
ejpam-4803	14	50	(	(	PUNCT
ejpam-4803	14	51	u	u	NOUN
ejpam-4803	14	52	,	,	PUNCT
ejpam-4803	14	53	φ	φ	NUM
ejpam-4803	14	54	)	)	PUNCT
ejpam-4803	14	55	is	be	AUX
ejpam-4803	14	56	a	a	DET
ejpam-4803	14	57	distinguished	distinguished	ADJ
ejpam-4803	14	58	chart	chart	NOUN
ejpam-4803	14	59	.	.	PUNCT
ejpam-4803	15	1	the	the	DET
ejpam-4803	15	2	notions	notion	NOUN
ejpam-4803	15	3	of	of	ADP
ejpam-4803	15	4	proper	proper	ADJ
ejpam-4803	15	5	leaf	leaf	NOUN
ejpam-4803	15	6	,	,	PUNCT
ejpam-4803	15	7	minimal	minimal	ADJ
ejpam-4803	15	8	set	set	NOUN
ejpam-4803	15	9	,	,	PUNCT
ejpam-4803	15	10	local	local	ADJ
ejpam-4803	15	11	minimal	minimal	ADJ
ejpam-4803	15	12	set	set	NOUN
ejpam-4803	15	13	are	be	AUX
ejpam-4803	15	14	introduced	introduce	VERB
ejpam-4803	15	15	in	in	ADP
ejpam-4803	15	16	[	[	X
ejpam-4803	15	17	4	4	NUM
ejpam-4803	15	18	,	,	PUNCT
ejpam-4803	15	19	chapter	chapter	NOUN
ejpam-4803	15	20	4.4	4.4	NUM
ejpam-4803	15	21	]	]	PUNCT
ejpam-4803	15	22	.	.	PUNCT
ejpam-4803	16	1	doi	doi	NOUN
ejpam-4803	16	2	:	:	PUNCT
ejpam-4803	16	3	https://doi.org/10.29020/nybg.ejpam.v17i1.4803	https://doi.org/10.29020/nybg.ejpam.v17i1.4803	NOUN
ejpam-4803	16	4	email	email	NOUN
ejpam-4803	16	5	address	address	NOUN
ejpam-4803	16	6	:	:	PUNCT
ejpam-4803	16	7	bhharbi@uqu.edu.sa	bhharbi@uqu.edu.sa	PROPN
ejpam-4803	16	8	(	(	PUNCT
ejpam-4803	16	9	b.	b.	PROPN
ejpam-4803	16	10	alharbi	alharbi	PROPN
ejpam-4803	16	11	)	)	PUNCT
ejpam-4803	16	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4803	16	13	356	356	NUM
ejpam-4803	16	14	©	©	ADP
ejpam-4803	16	15	2024	2024	NUM
ejpam-4803	16	16	ejpam	ejpam	NOUN
ejpam-4803	16	17	all	all	DET
ejpam-4803	16	18	rights	right	NOUN
ejpam-4803	16	19	reserved	reserve	VERB
ejpam-4803	16	20	.	.	PUNCT
ejpam-4803	17	1	b.	b.	PROPN
ejpam-4803	17	2	alharbi	alharbi	PROPN
ejpam-4803	17	3	/	/	SYM
ejpam-4803	17	4	eur	eur	PROPN
ejpam-4803	17	5	.	.	PUNCT
ejpam-4803	18	1	j.	j.	PROPN
ejpam-4803	18	2	pure	pure	PROPN
ejpam-4803	18	3	appl	appl	PROPN
ejpam-4803	18	4	.	.	PROPN
ejpam-4803	18	5	math	math	PROPN
ejpam-4803	18	6	,	,	PUNCT
ejpam-4803	18	7	17	17	NUM
ejpam-4803	18	8	(	(	PUNCT
ejpam-4803	18	9	1	1	NUM
ejpam-4803	18	10	)	)	PUNCT
ejpam-4803	18	11	(	(	PUNCT
ejpam-4803	18	12	2024	2024	NUM
ejpam-4803	18	13	)	)	PUNCT
ejpam-4803	18	14	,	,	PUNCT
ejpam-4803	18	15	356	356	NUM
ejpam-4803	18	16	-	-	SYM
ejpam-4803	18	17	361	361	NUM
ejpam-4803	18	18	357	357	NUM
ejpam-4803	18	19	recently	recently	ADV
ejpam-4803	19	1	,	,	PUNCT
ejpam-4803	19	2	we	we	PRON
ejpam-4803	19	3	study	study	VERB
ejpam-4803	19	4	the	the	DET
ejpam-4803	19	5	relationships	relationship	NOUN
ejpam-4803	19	6	between	between	ADP
ejpam-4803	19	7	graphs	graph	NOUN
ejpam-4803	19	8	and	and	CCONJ
ejpam-4803	19	9	the	the	DET
ejpam-4803	19	10	prime	prime	ADJ
ejpam-4803	19	11	spectrum	spectrum	NOUN
ejpam-4803	19	12	of	of	ADP
ejpam-4803	19	13	unitary	unitary	ADJ
ejpam-4803	19	14	commutative	commutative	ADJ
ejpam-4803	19	15	rings	ring	NOUN
ejpam-4803	19	16	[	[	X
ejpam-4803	19	17	1	1	NUM
ejpam-4803	19	18	]	]	PUNCT
ejpam-4803	19	19	.	.	PUNCT
ejpam-4803	20	1	in	in	ADP
ejpam-4803	20	2	[	[	X
ejpam-4803	20	3	3	3	X
ejpam-4803	20	4	]	]	PUNCT
ejpam-4803	20	5	the	the	DET
ejpam-4803	20	6	authors	author	NOUN
ejpam-4803	20	7	studied	study	VERB
ejpam-4803	20	8	relationships	relationship	NOUN
ejpam-4803	20	9	between	between	ADP
ejpam-4803	20	10	foliations	foliation	NOUN
ejpam-4803	20	11	and	and	CCONJ
ejpam-4803	20	12	spectral	spectral	ADJ
ejpam-4803	20	13	space	space	NOUN
ejpam-4803	20	14	.	.	PUNCT
ejpam-4803	21	1	in	in	ADP
ejpam-4803	21	2	particular	particular	ADJ
ejpam-4803	21	3	,	,	PUNCT
ejpam-4803	21	4	if	if	SCONJ
ejpam-4803	21	5	a	a	DET
ejpam-4803	21	6	codimension	codimension	NOUN
ejpam-4803	21	7	one	one	NUM
ejpam-4803	21	8	foliation	foliation	NOUN
ejpam-4803	21	9	has	have	VERB
ejpam-4803	21	10	a	a	DET
ejpam-4803	21	11	finite	finite	ADJ
ejpam-4803	21	12	height	height	NOUN
ejpam-4803	21	13	,	,	PUNCT
ejpam-4803	21	14	then	then	ADV
ejpam-4803	21	15	the	the	DET
ejpam-4803	21	16	singular	singular	ADJ
ejpam-4803	21	17	part	part	NOUN
ejpam-4803	21	18	of	of	ADP
ejpam-4803	21	19	the	the	DET
ejpam-4803	21	20	space	space	NOUN
ejpam-4803	21	21	of	of	ADP
ejpam-4803	21	22	leaf	leaf	NOUN
ejpam-4803	21	23	classes	class	NOUN
ejpam-4803	21	24	is	be	AUX
ejpam-4803	21	25	homeomorphic	homeomorphic	ADJ
ejpam-4803	21	26	to	to	ADP
ejpam-4803	21	27	the	the	DET
ejpam-4803	21	28	spectrum	spectrum	NOUN
ejpam-4803	21	29	of	of	ADP
ejpam-4803	21	30	unitary	unitary	ADJ
ejpam-4803	21	31	commutative	commutative	ADJ
ejpam-4803	21	32	ring	ring	NOUN
ejpam-4803	21	33	.	.	PUNCT
ejpam-4803	22	1	in	in	ADP
ejpam-4803	22	2	this	this	DET
ejpam-4803	22	3	paper	paper	NOUN
ejpam-4803	22	4	we	we	PRON
ejpam-4803	22	5	prove	prove	VERB
ejpam-4803	22	6	that	that	SCONJ
ejpam-4803	22	7	the	the	DET
ejpam-4803	22	8	singular	singular	ADJ
ejpam-4803	22	9	part	part	NOUN
ejpam-4803	22	10	of	of	ADP
ejpam-4803	22	11	the	the	DET
ejpam-4803	22	12	space	space	NOUN
ejpam-4803	22	13	of	of	ADP
ejpam-4803	22	14	leaf	leaf	NOUN
ejpam-4803	22	15	classes	class	NOUN
ejpam-4803	22	16	is	be	AUX
ejpam-4803	22	17	homeomorphic	homeomorphic	ADJ
ejpam-4803	22	18	to	to	ADP
ejpam-4803	22	19	the	the	DET
ejpam-4803	22	20	spectrum	spectrum	NOUN
ejpam-4803	22	21	of	of	ADP
ejpam-4803	22	22	unitary	unitary	ADJ
ejpam-4803	22	23	commutative	commutative	ADJ
ejpam-4803	22	24	ring	ring	NOUN
ejpam-4803	22	25	if	if	SCONJ
ejpam-4803	22	26	and	and	CCONJ
ejpam-4803	22	27	only	only	ADV
ejpam-4803	22	28	if	if	SCONJ
ejpam-4803	22	29	every	every	DET
ejpam-4803	22	30	family	family	NOUN
ejpam-4803	22	31	of	of	ADP
ejpam-4803	22	32	totaly	totaly	PROPN
ejpam-4803	22	33	ordered	order	VERB
ejpam-4803	22	34	leaves	leave	NOUN
ejpam-4803	22	35	is	be	AUX
ejpam-4803	22	36	bounded	bound	VERB
ejpam-4803	22	37	below	below	ADV
ejpam-4803	22	38	.	.	PUNCT
ejpam-4803	23	1	2	2	X
ejpam-4803	23	2	.	.	X
ejpam-4803	23	3	useful	useful	ADJ
ejpam-4803	23	4	notions	notion	NOUN
ejpam-4803	23	5	a	a	DET
ejpam-4803	23	6	topological	topological	ADJ
ejpam-4803	23	7	space	space	NOUN
ejpam-4803	23	8	x	x	PUNCT
ejpam-4803	23	9	is	be	AUX
ejpam-4803	23	10	a	a	DET
ejpam-4803	23	11	t0	t0	NOUN
ejpam-4803	23	12	-	-	NOUN
ejpam-4803	23	13	space	space	NOUN
ejpam-4803	23	14	(	(	PUNCT
ejpam-4803	23	15	or	or	CCONJ
ejpam-4803	23	16	kolmogorov	kolmogorov	ADJ
ejpam-4803	23	17	space	space	NOUN
ejpam-4803	23	18	)	)	PUNCT
ejpam-4803	23	19	if	if	SCONJ
ejpam-4803	23	20	for	for	ADP
ejpam-4803	23	21	every	every	DET
ejpam-4803	23	22	x	x	SYM
ejpam-4803	23	23	̸=	̸=	PROPN
ejpam-4803	23	24	y	y	PROPN
ejpam-4803	23	25	,	,	PUNCT
ejpam-4803	23	26	there	there	PRON
ejpam-4803	23	27	is	be	VERB
ejpam-4803	23	28	a	a	DET
ejpam-4803	23	29	neighborhood	neighborhood	NOUN
ejpam-4803	23	30	containing	contain	VERB
ejpam-4803	23	31	one	one	NUM
ejpam-4803	23	32	of	of	ADP
ejpam-4803	23	33	them	they	PRON
ejpam-4803	23	34	but	but	CCONJ
ejpam-4803	23	35	not	not	PART
ejpam-4803	23	36	the	the	DET
ejpam-4803	23	37	other	other	ADJ
ejpam-4803	23	38	;	;	PUNCT
ejpam-4803	23	39	which	which	PRON
ejpam-4803	23	40	is	be	AUX
ejpam-4803	23	41	equivalent	equivalent	ADJ
ejpam-4803	23	42	to	to	ADP
ejpam-4803	23	43	the	the	DET
ejpam-4803	23	44	following	follow	VERB
ejpam-4803	23	45	implication	implication	NOUN
ejpam-4803	23	46	(	(	PUNCT
ejpam-4803	23	47	{	{	PUNCT
ejpam-4803	23	48	x	x	NOUN
ejpam-4803	23	49	}	}	PUNCT
ejpam-4803	23	50	=	=	SYM
ejpam-4803	23	51	{	{	PUNCT
ejpam-4803	23	52	y	y	NOUN
ejpam-4803	23	53	}	}	PUNCT
ejpam-4803	23	54	⇒	⇒	NOUN
ejpam-4803	23	55	x	x	PUNCT
ejpam-4803	23	56	=	=	SYM
ejpam-4803	23	57	y	y	PROPN
ejpam-4803	23	58	)	)	PUNCT
ejpam-4803	23	59	.	.	PUNCT
ejpam-4803	24	1	let	let	VERB
ejpam-4803	24	2	(	(	PUNCT
ejpam-4803	24	3	x,≤	x,≤	PUNCT
ejpam-4803	24	4	)	)	PUNCT
ejpam-4803	24	5	be	be	AUX
ejpam-4803	24	6	an	an	DET
ejpam-4803	24	7	ordered	order	VERB
ejpam-4803	24	8	set	set	NOUN
ejpam-4803	24	9	and	and	CCONJ
ejpam-4803	24	10	t	t	PROPN
ejpam-4803	24	11	be	be	AUX
ejpam-4803	24	12	a	a	DET
ejpam-4803	24	13	topology	topology	NOUN
ejpam-4803	24	14	on	on	ADP
ejpam-4803	24	15	x.	x.	NOUN
ejpam-4803	25	1	we	we	PRON
ejpam-4803	25	2	say	say	VERB
ejpam-4803	25	3	that	that	SCONJ
ejpam-4803	25	4	t	t	PROPN
ejpam-4803	25	5	is	be	AUX
ejpam-4803	25	6	compatible	compatible	ADJ
ejpam-4803	25	7	with	with	ADP
ejpam-4803	25	8	≤	≤	NUM
ejpam-4803	25	9	if	if	SCONJ
ejpam-4803	25	10	,	,	PUNCT
ejpam-4803	25	11	for	for	ADP
ejpam-4803	25	12	each	each	DET
ejpam-4803	25	13	element	element	NOUN
ejpam-4803	25	14	x	x	SYM
ejpam-4803	25	15	∈	∈	PROPN
ejpam-4803	25	16	x	x	X
ejpam-4803	25	17	,	,	PUNCT
ejpam-4803	25	18	{	{	PUNCT
ejpam-4803	25	19	x	x	NOUN
ejpam-4803	25	20	}	}	PUNCT
ejpam-4803	25	21	=	=	SYM
ejpam-4803	25	22	{	{	PUNCT
ejpam-4803	25	23	y	y	PROPN
ejpam-4803	25	24	∈	∈	PROPN
ejpam-4803	25	25	x	x	X
ejpam-4803	25	26	:	:	PUNCT
ejpam-4803	25	27	x	x	SYM
ejpam-4803	25	28	≤	≤	NUM
ejpam-4803	25	29	y	y	NOUN
ejpam-4803	25	30	}	}	PUNCT
ejpam-4803	25	31	=	=	NOUN
ejpam-4803	26	1	[	[	X
ejpam-4803	26	2	x,→	x,→	X
ejpam-4803	26	3	[	[	PUNCT
ejpam-4803	26	4	(	(	PUNCT
ejpam-4803	26	5	{	{	PUNCT
ejpam-4803	26	6	x	x	NOUN
ejpam-4803	26	7	}	}	PUNCT
ejpam-4803	26	8	is	be	AUX
ejpam-4803	26	9	the	the	DET
ejpam-4803	26	10	closure	closure	NOUN
ejpam-4803	26	11	of	of	ADP
ejpam-4803	26	12	{	{	PUNCT
ejpam-4803	26	13	x	x	NOUN
ejpam-4803	26	14	}	}	PUNCT
ejpam-4803	26	15	)	)	PUNCT
ejpam-4803	26	16	.	.	PUNCT
ejpam-4803	27	1	proposition	proposition	NOUN
ejpam-4803	27	2	2.1	2.1	NUM
ejpam-4803	27	3	.	.	PUNCT
ejpam-4803	28	1	let	let	VERB
ejpam-4803	28	2	(	(	PUNCT
ejpam-4803	28	3	x,≤	x,≤	PUNCT
ejpam-4803	28	4	)	)	PUNCT
ejpam-4803	28	5	be	be	AUX
ejpam-4803	28	6	an	an	DET
ejpam-4803	28	7	ordered	order	VERB
ejpam-4803	28	8	set	set	NOUN
ejpam-4803	28	9	and	and	CCONJ
ejpam-4803	28	10	t	t	PROPN
ejpam-4803	28	11	be	be	AUX
ejpam-4803	28	12	a	a	DET
ejpam-4803	28	13	topology	topology	NOUN
ejpam-4803	28	14	on	on	ADP
ejpam-4803	28	15	x.	x.	NOUN
ejpam-4803	28	16	if	if	SCONJ
ejpam-4803	28	17	t	t	PROPN
ejpam-4803	28	18	is	be	AUX
ejpam-4803	28	19	compatible	compatible	ADJ
ejpam-4803	28	20	with	with	ADP
ejpam-4803	28	21	≤	≤	NUM
ejpam-4803	28	22	,	,	PUNCT
ejpam-4803	28	23	then	then	ADV
ejpam-4803	28	24	(	(	PUNCT
ejpam-4803	28	25	x	x	X
ejpam-4803	28	26	,	,	PUNCT
ejpam-4803	28	27	t	t	PROPN
ejpam-4803	28	28	)	)	PUNCT
ejpam-4803	28	29	is	be	AUX
ejpam-4803	28	30	a	a	DET
ejpam-4803	28	31	t0	t0	NOUN
ejpam-4803	28	32	-	-	NOUN
ejpam-4803	28	33	space	space	NOUN
ejpam-4803	28	34	.	.	PUNCT
ejpam-4803	29	1	proof	proof	NOUN
ejpam-4803	29	2	.	.	PUNCT
ejpam-4803	30	1	let	let	VERB
ejpam-4803	30	2	x	x	PRON
ejpam-4803	30	3	and	and	CCONJ
ejpam-4803	30	4	y	y	PROPN
ejpam-4803	30	5	be	be	VERB
ejpam-4803	30	6	two	two	NUM
ejpam-4803	30	7	points	point	NOUN
ejpam-4803	30	8	of	of	ADP
ejpam-4803	30	9	x.	x.	NOUN
ejpam-4803	30	10	•	•	NOUN
ejpam-4803	31	1	if	if	SCONJ
ejpam-4803	31	2	x	x	X
ejpam-4803	31	3	<	<	X
ejpam-4803	31	4	y	y	PROPN
ejpam-4803	31	5	,	,	PUNCT
ejpam-4803	31	6	then	then	ADV
ejpam-4803	31	7	x	x	SYM
ejpam-4803	31	8	∈	∈	PROPN
ejpam-4803	31	9	x	x	X
ejpam-4803	31	10	−	−	PROPN
ejpam-4803	32	1	[	[	X
ejpam-4803	32	2	y,→	y,→	PRON
ejpam-4803	32	3	[	[	PUNCT
ejpam-4803	32	4	and	and	CCONJ
ejpam-4803	32	5	so	so	ADV
ejpam-4803	32	6	the	the	DET
ejpam-4803	32	7	open	open	ADJ
ejpam-4803	32	8	set	set	NOUN
ejpam-4803	32	9	x	x	X
ejpam-4803	32	10	−	−	PROPN
ejpam-4803	33	1	[	[	X
ejpam-4803	33	2	y,→	y,→	PRON
ejpam-4803	33	3	[	[	PUNCT
ejpam-4803	33	4	contains	contain	VERB
ejpam-4803	33	5	x	x	PUNCT
ejpam-4803	33	6	and	and	CCONJ
ejpam-4803	33	7	not	not	PART
ejpam-4803	33	8	contains	contain	VERB
ejpam-4803	33	9	y.	y.	NOUN
ejpam-4803	33	10	•	•	NOUN
ejpam-4803	33	11	if	if	SCONJ
ejpam-4803	33	12	x	x	PRON
ejpam-4803	33	13	and	and	CCONJ
ejpam-4803	33	14	y	y	PROPN
ejpam-4803	33	15	are	be	AUX
ejpam-4803	33	16	not	not	PART
ejpam-4803	33	17	comparable	comparable	ADJ
ejpam-4803	33	18	,	,	PUNCT
ejpam-4803	33	19	then	then	ADV
ejpam-4803	33	20	the	the	DET
ejpam-4803	33	21	open	open	ADJ
ejpam-4803	33	22	set	set	NOUN
ejpam-4803	33	23	x	x	X
ejpam-4803	33	24	−	−	PROPN
ejpam-4803	34	1	[	[	X
ejpam-4803	34	2	x,→	x,→	X
ejpam-4803	34	3	[	[	PUNCT
ejpam-4803	34	4	contains	contain	VERB
ejpam-4803	34	5	y	y	PROPN
ejpam-4803	34	6	and	and	CCONJ
ejpam-4803	34	7	not	not	PART
ejpam-4803	34	8	contains	contain	VERB
ejpam-4803	34	9	x.	x.	NOUN
ejpam-4803	34	10	remark	remark	PROPN
ejpam-4803	34	11	2.2	2.2	NUM
ejpam-4803	34	12	.	.	PUNCT
ejpam-4803	35	1	if	if	SCONJ
ejpam-4803	35	2	(	(	PUNCT
ejpam-4803	35	3	x	x	X
ejpam-4803	35	4	,	,	PUNCT
ejpam-4803	35	5	t	t	PROPN
ejpam-4803	35	6	)	)	PUNCT
ejpam-4803	35	7	is	be	AUX
ejpam-4803	35	8	a	a	DET
ejpam-4803	35	9	t0	t0	NOUN
ejpam-4803	35	10	-	-	NOUN
ejpam-4803	35	11	space	space	NOUN
ejpam-4803	35	12	,	,	PUNCT
ejpam-4803	35	13	then	then	ADV
ejpam-4803	35	14	x	x	PUNCT
ejpam-4803	35	15	is	be	AUX
ejpam-4803	35	16	an	an	DET
ejpam-4803	35	17	ordered	order	VERB
ejpam-4803	35	18	set	set	VERB
ejpam-4803	35	19	by	by	ADP
ejpam-4803	35	20	the	the	DET
ejpam-4803	35	21	order	order	NOUN
ejpam-4803	35	22	defined	define	VERB
ejpam-4803	35	23	by	by	ADP
ejpam-4803	35	24	x	x	SYM
ejpam-4803	35	25	≤t	≤t	PROPN
ejpam-4803	35	26	y	y	PROPN
ejpam-4803	35	27	if	if	SCONJ
ejpam-4803	35	28	and	and	CCONJ
ejpam-4803	35	29	only	only	ADV
ejpam-4803	35	30	if	if	SCONJ
ejpam-4803	35	31	x	x	SYM
ejpam-4803	35	32	∈	∈	PROPN
ejpam-4803	35	33	{	{	PUNCT
ejpam-4803	35	34	y	y	NOUN
ejpam-4803	35	35	}	}	PUNCT
ejpam-4803	35	36	.	.	PUNCT
ejpam-4803	36	1	according	accord	VERB
ejpam-4803	36	2	to	to	ADP
ejpam-4803	36	3	[	[	X
ejpam-4803	36	4	2	2	X
ejpam-4803	36	5	]	]	PUNCT
ejpam-4803	36	6	we	we	PRON
ejpam-4803	36	7	have	have	VERB
ejpam-4803	36	8	the	the	DET
ejpam-4803	36	9	following	follow	VERB
ejpam-4803	36	10	proposition	proposition	NOUN
ejpam-4803	36	11	:	:	PUNCT
ejpam-4803	36	12	proposition	proposition	NOUN
ejpam-4803	36	13	2.3	2.3	NUM
ejpam-4803	36	14	.	.	PUNCT
ejpam-4803	37	1	if	if	SCONJ
ejpam-4803	37	2	(	(	PUNCT
ejpam-4803	37	3	x	x	NOUN
ejpam-4803	37	4	,	,	PUNCT
ejpam-4803	37	5	t	t	PROPN
ejpam-4803	37	6	)	)	PUNCT
ejpam-4803	37	7	and	and	CCONJ
ejpam-4803	37	8	(	(	PUNCT
ejpam-4803	37	9	x	x	PROPN
ejpam-4803	37	10	′	′	NUM
ejpam-4803	37	11	,	,	PUNCT
ejpam-4803	37	12	t	t	PROPN
ejpam-4803	37	13	′	′	NUM
ejpam-4803	37	14	)	)	PUNCT
ejpam-4803	37	15	are	be	AUX
ejpam-4803	37	16	two	two	NUM
ejpam-4803	37	17	homeomorphic	homeomorphic	ADJ
ejpam-4803	37	18	t0	t0	NOUN
ejpam-4803	37	19	-	-	NOUN
ejpam-4803	37	20	spaces	space	NOUN
ejpam-4803	37	21	,	,	PUNCT
ejpam-4803	37	22	then	then	ADV
ejpam-4803	37	23	the	the	DET
ejpam-4803	37	24	ordered	order	VERB
ejpam-4803	37	25	sets	set	NOUN
ejpam-4803	37	26	(	(	PUNCT
ejpam-4803	37	27	x,≤t	x,≤t	PROPN
ejpam-4803	37	28	)	)	PUNCT
ejpam-4803	37	29	and	and	CCONJ
ejpam-4803	37	30	(	(	PUNCT
ejpam-4803	37	31	x	x	PROPN
ejpam-4803	37	32	′,≤t	′,≤t	PROPN
ejpam-4803	37	33	′	′	NOUN
ejpam-4803	37	34	)	)	PUNCT
ejpam-4803	37	35	are	be	AUX
ejpam-4803	37	36	isomorphic	isomorphic	ADJ
ejpam-4803	37	37	.	.	PUNCT
ejpam-4803	38	1	proof	proof	NOUN
ejpam-4803	38	2	.	.	PUNCT
ejpam-4803	39	1	let	let	VERB
ejpam-4803	39	2	h	h	PRON
ejpam-4803	39	3	be	be	AUX
ejpam-4803	39	4	a	a	DET
ejpam-4803	39	5	homeomorphism	homeomorphism	NOUN
ejpam-4803	39	6	between	between	ADP
ejpam-4803	39	7	(	(	PUNCT
ejpam-4803	39	8	x	x	NOUN
ejpam-4803	39	9	,	,	PUNCT
ejpam-4803	39	10	t	t	PROPN
ejpam-4803	39	11	)	)	PUNCT
ejpam-4803	39	12	and	and	CCONJ
ejpam-4803	39	13	(	(	PUNCT
ejpam-4803	39	14	x	x	PROPN
ejpam-4803	39	15	′	′	NUM
ejpam-4803	39	16	,	,	PUNCT
ejpam-4803	39	17	t	t	PROPN
ejpam-4803	39	18	′	′	NUM
ejpam-4803	39	19	)	)	PUNCT
ejpam-4803	39	20	.	.	PUNCT
ejpam-4803	40	1	if	if	SCONJ
ejpam-4803	40	2	x	x	PRON
ejpam-4803	40	3	≤t	≤t	PROPN
ejpam-4803	40	4	y	y	PROPN
ejpam-4803	40	5	,	,	PUNCT
ejpam-4803	40	6	then	then	ADV
ejpam-4803	40	7	x	x	SYM
ejpam-4803	40	8	∈	∈	PROPN
ejpam-4803	40	9	{	{	PUNCT
ejpam-4803	40	10	y}t	y}t	PROPN
ejpam-4803	40	11	.	.	PUNCT
ejpam-4803	41	1	since	since	SCONJ
ejpam-4803	41	2	h	h	NOUN
ejpam-4803	41	3	is	be	AUX
ejpam-4803	41	4	continuous	continuous	ADJ
ejpam-4803	41	5	,	,	PUNCT
ejpam-4803	41	6	h(x	h(x	PROPN
ejpam-4803	41	7	)	)	PUNCT
ejpam-4803	41	8	∈	∈	PROPN
ejpam-4803	41	9	{	{	PUNCT
ejpam-4803	41	10	h(y)}t	h(y)}t	NOUN
ejpam-4803	41	11	′	′	NOUN
ejpam-4803	42	1	and	and	CCONJ
ejpam-4803	42	2	so	so	ADV
ejpam-4803	42	3	h(x	h(x	PROPN
ejpam-4803	42	4	)	)	PUNCT
ejpam-4803	42	5	≤t	≤t	NOUN
ejpam-4803	42	6	′	′	NUM
ejpam-4803	42	7	h(y	h(y	NOUN
ejpam-4803	42	8	)	)	PUNCT
ejpam-4803	42	9	.	.	PUNCT
ejpam-4803	43	1	if	if	SCONJ
ejpam-4803	43	2	now	now	ADV
ejpam-4803	43	3	h(x	h(x	PROPN
ejpam-4803	43	4	)	)	PUNCT
ejpam-4803	43	5	≤t	≤t	NOUN
ejpam-4803	43	6	′	′	NUM
ejpam-4803	43	7	h(y	h(y	NOUN
ejpam-4803	43	8	)	)	PUNCT
ejpam-4803	43	9	,	,	PUNCT
ejpam-4803	43	10	then	then	ADV
ejpam-4803	43	11	,	,	PUNCT
ejpam-4803	43	12	by	by	ADP
ejpam-4803	43	13	the	the	DET
ejpam-4803	43	14	continuity	continuity	NOUN
ejpam-4803	43	15	of	of	ADP
ejpam-4803	43	16	h−1	h−1	PROPN
ejpam-4803	43	17	,	,	PUNCT
ejpam-4803	43	18	x	x	PUNCT
ejpam-4803	43	19	≤t	≤t	PROPN
ejpam-4803	43	20	y.	y.	PROPN
ejpam-4803	43	21	therefore	therefore	ADV
ejpam-4803	43	22	h	h	PROPN
ejpam-4803	43	23	is	be	AUX
ejpam-4803	43	24	an	an	DET
ejpam-4803	43	25	isomorphism	isomorphism	NOUN
ejpam-4803	43	26	.	.	PUNCT
ejpam-4803	44	1	the	the	DET
ejpam-4803	44	2	converse	converse	NOUN
ejpam-4803	44	3	of	of	ADP
ejpam-4803	44	4	the	the	DET
ejpam-4803	44	5	proposition	proposition	NOUN
ejpam-4803	44	6	2.3	2.3	NUM
ejpam-4803	44	7	is	be	AUX
ejpam-4803	44	8	false	false	ADJ
ejpam-4803	44	9	.	.	PUNCT
ejpam-4803	45	1	indeed	indeed	ADV
ejpam-4803	45	2	,	,	PUNCT
ejpam-4803	45	3	all	all	DET
ejpam-4803	45	4	the	the	DET
ejpam-4803	45	5	compatible	compatible	ADJ
ejpam-4803	45	6	topologies	topology	NOUN
ejpam-4803	45	7	with	with	ADP
ejpam-4803	45	8	an	an	DET
ejpam-4803	45	9	order	order	NOUN
ejpam-4803	45	10	≤	≤	X
ejpam-4803	45	11	induce	induce	VERB
ejpam-4803	45	12	the	the	DET
ejpam-4803	45	13	same	same	ADJ
ejpam-4803	45	14	order	order	NOUN
ejpam-4803	45	15	≤	≤	NOUN
ejpam-4803	45	16	but	but	CCONJ
ejpam-4803	45	17	are	be	AUX
ejpam-4803	45	18	not	not	PART
ejpam-4803	45	19	necessarily	necessarily	ADV
ejpam-4803	45	20	homeomorphic	homeomorphic	ADJ
ejpam-4803	45	21	.	.	PUNCT
ejpam-4803	46	1	a	a	DET
ejpam-4803	46	2	topological	topological	ADJ
ejpam-4803	46	3	space	space	NOUN
ejpam-4803	46	4	x	x	PUNCT
ejpam-4803	46	5	is	be	AUX
ejpam-4803	46	6	quasi	quasi	ADJ
ejpam-4803	46	7	-	-	ADJ
ejpam-4803	46	8	compact	compact	ADJ
ejpam-4803	46	9	if	if	SCONJ
ejpam-4803	46	10	it	it	PRON
ejpam-4803	46	11	satisfies	satisfy	VERB
ejpam-4803	46	12	the	the	DET
ejpam-4803	46	13	property	property	NOUN
ejpam-4803	46	14	of	of	ADP
ejpam-4803	46	15	borel	borel	NOUN
ejpam-4803	46	16	-	-	PUNCT
ejpam-4803	46	17	lebesgue	lebesgue	PROPN
ejpam-4803	47	1	but	but	CCONJ
ejpam-4803	47	2	it	it	PRON
ejpam-4803	47	3	is	be	AUX
ejpam-4803	47	4	not	not	PART
ejpam-4803	47	5	necessarily	necessarily	ADV
ejpam-4803	47	6	a	a	DET
ejpam-4803	47	7	hausdorff	hausdorff	NOUN
ejpam-4803	47	8	space	space	NOUN
ejpam-4803	47	9	.	.	PUNCT
ejpam-4803	48	1	a	a	DET
ejpam-4803	48	2	subset	subset	NOUN
ejpam-4803	48	3	a	a	PRON
ejpam-4803	48	4	of	of	ADP
ejpam-4803	48	5	x	x	PUNCT
ejpam-4803	48	6	is	be	AUX
ejpam-4803	48	7	quasi	quasi	ADJ
ejpam-4803	48	8	-	-	ADJ
ejpam-4803	48	9	compact	compact	ADJ
ejpam-4803	48	10	if	if	SCONJ
ejpam-4803	48	11	it	it	PRON
ejpam-4803	48	12	is	be	AUX
ejpam-4803	48	13	a	a	DET
ejpam-4803	48	14	quasi	quasi	ADJ
ejpam-4803	48	15	-	-	ADJ
ejpam-4803	48	16	compact	compact	ADJ
ejpam-4803	48	17	space	space	NOUN
ejpam-4803	48	18	equipped	equip	VERB
ejpam-4803	48	19	with	with	ADP
ejpam-4803	48	20	the	the	DET
ejpam-4803	48	21	relative	relative	ADJ
ejpam-4803	48	22	topology	topology	NOUN
ejpam-4803	48	23	of	of	ADP
ejpam-4803	48	24	x.	x.	NOUN
ejpam-4803	48	25	we	we	PRON
ejpam-4803	48	26	have	have	VERB
ejpam-4803	48	27	the	the	DET
ejpam-4803	48	28	following	follow	VERB
ejpam-4803	48	29	properties	property	NOUN
ejpam-4803	48	30	:	:	PUNCT
ejpam-4803	48	31	b.	b.	PROPN
ejpam-4803	48	32	alharbi	alharbi	PROPN
ejpam-4803	48	33	/	/	SYM
ejpam-4803	48	34	eur	eur	PROPN
ejpam-4803	48	35	.	.	PUNCT
ejpam-4803	49	1	j.	j.	PROPN
ejpam-4803	49	2	pure	pure	PROPN
ejpam-4803	49	3	appl	appl	PROPN
ejpam-4803	49	4	.	.	PROPN
ejpam-4803	49	5	math	math	PROPN
ejpam-4803	49	6	,	,	PUNCT
ejpam-4803	49	7	17	17	NUM
ejpam-4803	49	8	(	(	PUNCT
ejpam-4803	49	9	1	1	NUM
ejpam-4803	49	10	)	)	PUNCT
ejpam-4803	49	11	(	(	PUNCT
ejpam-4803	49	12	2024	2024	NUM
ejpam-4803	49	13	)	)	PUNCT
ejpam-4803	49	14	,	,	PUNCT
ejpam-4803	49	15	356	356	NUM
ejpam-4803	49	16	-	-	SYM
ejpam-4803	49	17	361	361	NUM
ejpam-4803	49	18	358	358	NUM
ejpam-4803	49	19	1	1	NUM
ejpam-4803	49	20	.	.	PUNCT
ejpam-4803	50	1	the	the	DET
ejpam-4803	50	2	quasi	quasi	NOUN
ejpam-4803	50	3	-	-	NOUN
ejpam-4803	50	4	compactness	compactness	NOUN
ejpam-4803	50	5	is	be	AUX
ejpam-4803	50	6	invariant	invariant	ADJ
ejpam-4803	50	7	under	under	ADP
ejpam-4803	50	8	continuous	continuous	ADJ
ejpam-4803	50	9	map	map	NOUN
ejpam-4803	50	10	.	.	PUNCT
ejpam-4803	51	1	2	2	X
ejpam-4803	51	2	.	.	NUM
ejpam-4803	51	3	closed	close	VERB
ejpam-4803	51	4	subsets	subset	NOUN
ejpam-4803	51	5	of	of	ADP
ejpam-4803	51	6	a	a	DET
ejpam-4803	51	7	quasi	quasi	ADJ
ejpam-4803	51	8	-	-	ADJ
ejpam-4803	51	9	compact	compact	ADJ
ejpam-4803	51	10	space	space	NOUN
ejpam-4803	51	11	are	be	AUX
ejpam-4803	51	12	quasi	quasi	ADJ
ejpam-4803	51	13	-	-	ADJ
ejpam-4803	51	14	compact	compact	ADJ
ejpam-4803	51	15	.	.	PUNCT
ejpam-4803	52	1	3	3	X
ejpam-4803	52	2	.	.	X
ejpam-4803	52	3	the	the	DET
ejpam-4803	52	4	union	union	NOUN
ejpam-4803	52	5	of	of	ADP
ejpam-4803	52	6	finitely	finitely	ADV
ejpam-4803	52	7	many	many	ADJ
ejpam-4803	52	8	quasi	quasi	ADJ
ejpam-4803	52	9	-	-	ADJ
ejpam-4803	52	10	compact	compact	ADJ
ejpam-4803	52	11	subsets	subset	NOUN
ejpam-4803	52	12	is	be	AUX
ejpam-4803	52	13	quasi	quasi	ADJ
ejpam-4803	52	14	-	-	ADJ
ejpam-4803	52	15	compact	compact	ADJ
ejpam-4803	52	16	.	.	PUNCT
ejpam-4803	53	1	the	the	DET
ejpam-4803	53	2	intersection	intersection	NOUN
ejpam-4803	53	3	of	of	ADP
ejpam-4803	53	4	tow	tow	NOUN
ejpam-4803	53	5	quasi	quasi	ADJ
ejpam-4803	53	6	-	-	ADJ
ejpam-4803	53	7	compact	compact	ADJ
ejpam-4803	53	8	open	open	ADJ
ejpam-4803	53	9	subsets	subset	NOUN
ejpam-4803	53	10	is	be	AUX
ejpam-4803	53	11	not	not	PART
ejpam-4803	53	12	necessarily	necessarily	ADV
ejpam-4803	53	13	quasi	quasi	ADJ
ejpam-4803	53	14	-	-	ADJ
ejpam-4803	53	15	compact	compact	ADJ
ejpam-4803	53	16	.	.	PUNCT
ejpam-4803	54	1	the	the	DET
ejpam-4803	54	2	following	follow	VERB
ejpam-4803	54	3	example	example	NOUN
ejpam-4803	54	4	confirm	confirm	VERB
ejpam-4803	54	5	this	this	DET
ejpam-4803	54	6	result	result	NOUN
ejpam-4803	54	7	:	:	PUNCT
ejpam-4803	54	8	example	example	NOUN
ejpam-4803	54	9	2.4	2.4	NUM
ejpam-4803	54	10	.	.	PUNCT
ejpam-4803	55	1	in	in	ADP
ejpam-4803	55	2	the	the	DET
ejpam-4803	55	3	two	two	NUM
ejpam-4803	55	4	euclidean	euclidean	ADJ
ejpam-4803	55	5	space	space	NOUN
ejpam-4803	55	6	we	we	PRON
ejpam-4803	55	7	consider	consider	VERB
ejpam-4803	55	8	the	the	DET
ejpam-4803	55	9	following	follow	VERB
ejpam-4803	55	10	points	point	NOUN
ejpam-4803	55	11	:	:	PUNCT
ejpam-4803	55	12	c(0	c(0	NOUN
ejpam-4803	55	13	,	,	PUNCT
ejpam-4803	55	14	1	1	NUM
ejpam-4803	55	15	)	)	PUNCT
ejpam-4803	55	16	,	,	PUNCT
ejpam-4803	55	17	a(−1	a(−1	PROPN
ejpam-4803	55	18	,	,	PUNCT
ejpam-4803	55	19	0	0	NUM
ejpam-4803	55	20	)	)	PUNCT
ejpam-4803	55	21	,	,	PUNCT
ejpam-4803	55	22	b(1	b(1	PROPN
ejpam-4803	55	23	,	,	PUNCT
ejpam-4803	55	24	0	0	NUM
ejpam-4803	55	25	)	)	PUNCT
ejpam-4803	55	26	,	,	PUNCT
ejpam-4803	55	27	an(−1	an(−1	PROPN
ejpam-4803	55	28	,	,	PUNCT
ejpam-4803	55	29	−1	−1	NOUN
ejpam-4803	55	30	n	n	NOUN
ejpam-4803	55	31	)	)	PUNCT
ejpam-4803	55	32	)	)	PUNCT
ejpam-4803	55	33	and	and	CCONJ
ejpam-4803	55	34	bn(1	bn(1	NOUN
ejpam-4803	55	35	,	,	PUNCT
ejpam-4803	55	36	−1	−1	NOUN
ejpam-4803	55	37	n	n	NOUN
ejpam-4803	55	38	)	)	PUNCT
ejpam-4803	55	39	)	)	PUNCT
ejpam-4803	55	40	.	.	PUNCT
ejpam-4803	56	1	let	let	VERB
ejpam-4803	56	2	x	x	PRON
ejpam-4803	56	3	be	be	AUX
ejpam-4803	56	4	the	the	DET
ejpam-4803	56	5	set	set	NOUN
ejpam-4803	56	6	{	{	PUNCT
ejpam-4803	56	7	c	c	NOUN
ejpam-4803	56	8	,	,	PUNCT
ejpam-4803	56	9	a	a	DET
ejpam-4803	56	10	,	,	PUNCT
ejpam-4803	56	11	b	b	NOUN
ejpam-4803	56	12	,	,	PUNCT
ejpam-4803	56	13	an	an	PRON
ejpam-4803	56	14	,	,	PUNCT
ejpam-4803	56	15	bn	bn	NOUN
ejpam-4803	56	16	:	:	PUNCT
ejpam-4803	56	17	n	n	PRON
ejpam-4803	56	18	≥	≥	NOUN
ejpam-4803	56	19	1	1	NUM
ejpam-4803	56	20	}	}	PUNCT
ejpam-4803	56	21	equipped	equip	VERB
ejpam-4803	56	22	with	with	ADP
ejpam-4803	56	23	the	the	DET
ejpam-4803	56	24	following	follow	VERB
ejpam-4803	56	25	topology	topology	NOUN
ejpam-4803	56	26	:	:	PUNCT
ejpam-4803	56	27	{	{	PUNCT
ejpam-4803	56	28	∅	∅	NOUN
ejpam-4803	56	29	,	,	PUNCT
ejpam-4803	56	30	x	x	X
ejpam-4803	56	31	,	,	PUNCT
ejpam-4803	56	32	u	u	NOUN
ejpam-4803	56	33	=	=	X
ejpam-4803	56	34	{	{	PUNCT
ejpam-4803	56	35	a	a	NOUN
ejpam-4803	56	36	,	,	PUNCT
ejpam-4803	56	37	an	an	PRON
ejpam-4803	56	38	:	:	PUNCT
ejpam-4803	56	39	n	n	PRON
ejpam-4803	56	40	≥	≥	NOUN
ejpam-4803	56	41	1	1	NUM
ejpam-4803	56	42	}	}	PUNCT
ejpam-4803	56	43	,	,	PUNCT
ejpam-4803	56	44	v	v	X
ejpam-4803	56	45	=	=	SYM
ejpam-4803	56	46	{	{	PUNCT
ejpam-4803	56	47	b	b	NOUN
ejpam-4803	56	48	,	,	PUNCT
ejpam-4803	56	49	bn	bn	NOUN
ejpam-4803	56	50	:	:	PUNCT
ejpam-4803	56	51	n	n	PRON
ejpam-4803	56	52	≥	≥	NOUN
ejpam-4803	56	53	1	1	NUM
ejpam-4803	56	54	}	}	PUNCT
ejpam-4803	56	55	,	,	PUNCT
ejpam-4803	56	56	un	un	PROPN
ejpam-4803	56	57	=	=	PRON
ejpam-4803	56	58	{	{	PUNCT
ejpam-4803	56	59	ap	ap	NOUN
ejpam-4803	56	60	:	:	PUNCT
ejpam-4803	56	61	n	n	PRON
ejpam-4803	56	62	≥	≥	NOUN
ejpam-4803	56	63	p	p	NOUN
ejpam-4803	56	64	≥	≥	NUM
ejpam-4803	56	65	1	1	NUM
ejpam-4803	56	66	}	}	PUNCT
ejpam-4803	56	67	,	,	PUNCT
ejpam-4803	56	68	vn	vn	PROPN
ejpam-4803	56	69	=	=	SYM
ejpam-4803	56	70	{	{	PUNCT
ejpam-4803	56	71	bp	bp	PROPN
ejpam-4803	56	72	:	:	PUNCT
ejpam-4803	56	73	n	n	PRON
ejpam-4803	56	74	≥	≥	NOUN
ejpam-4803	56	75	p	p	NOUN
ejpam-4803	56	76	≥	≥	NUM
ejpam-4803	56	77	1	1	NUM
ejpam-4803	56	78	}	}	PUNCT
ejpam-4803	56	79	}	}	PUNCT
ejpam-4803	56	80	.	.	PUNCT
ejpam-4803	57	1	note	note	VERB
ejpam-4803	57	2	that	that	SCONJ
ejpam-4803	57	3	u	u	PROPN
ejpam-4803	57	4	and	and	CCONJ
ejpam-4803	57	5	v	v	NOUN
ejpam-4803	57	6	are	be	AUX
ejpam-4803	57	7	quasi	quasi	ADJ
ejpam-4803	57	8	-	-	ADJ
ejpam-4803	57	9	compact	compact	ADJ
ejpam-4803	57	10	.	.	PUNCT
ejpam-4803	58	1	since	since	SCONJ
ejpam-4803	58	2	u	u	NOUN
ejpam-4803	58	3	∩	∩	NOUN
ejpam-4803	58	4	v	v	NOUN
ejpam-4803	58	5	=	=	SYM
ejpam-4803	58	6	⋃	⋃	PROPN
ejpam-4803	58	7	n	n	X
ejpam-4803	58	8	un	un	PROPN
ejpam-4803	58	9	∪	∪	PROPN
ejpam-4803	58	10	vn	vn	PROPN
ejpam-4803	58	11	and	and	CCONJ
ejpam-4803	58	12	un	un	PROPN
ejpam-4803	58	13	∪	∪	PROPN
ejpam-4803	58	14	vn	vn	PROPN
ejpam-4803	58	15	is	be	AUX
ejpam-4803	58	16	an	an	DET
ejpam-4803	58	17	increasing	increase	VERB
ejpam-4803	58	18	sequence	sequence	NOUN
ejpam-4803	58	19	of	of	ADP
ejpam-4803	58	20	open	open	ADJ
ejpam-4803	58	21	subsets	subset	NOUN
ejpam-4803	58	22	,	,	PUNCT
ejpam-4803	58	23	u	u	PROPN
ejpam-4803	58	24	∩	∩	NOUN
ejpam-4803	58	25	v	v	NOUN
ejpam-4803	58	26	is	be	AUX
ejpam-4803	58	27	not	not	PART
ejpam-4803	58	28	a	a	DET
ejpam-4803	58	29	quasi	quasi	ADJ
ejpam-4803	58	30	-	-	ADJ
ejpam-4803	58	31	compact	compact	ADJ
ejpam-4803	58	32	subset	subset	NOUN
ejpam-4803	58	33	.	.	PUNCT
ejpam-4803	59	1	a	a	DET
ejpam-4803	59	2	closed	closed	ADJ
ejpam-4803	59	3	subset	subset	NOUN
ejpam-4803	59	4	c	c	NOUN
ejpam-4803	59	5	is	be	AUX
ejpam-4803	59	6	irreducible	irreducible	ADJ
ejpam-4803	59	7	if	if	SCONJ
ejpam-4803	59	8	it	it	PRON
ejpam-4803	59	9	is	be	AUX
ejpam-4803	59	10	not	not	PART
ejpam-4803	59	11	the	the	DET
ejpam-4803	59	12	union	union	NOUN
ejpam-4803	59	13	of	of	ADP
ejpam-4803	59	14	two	two	NUM
ejpam-4803	59	15	proper	proper	ADJ
ejpam-4803	59	16	closed	closed	ADJ
ejpam-4803	59	17	subsets	subset	NOUN
ejpam-4803	59	18	or	or	CCONJ
ejpam-4803	59	19	if	if	SCONJ
ejpam-4803	59	20	the	the	DET
ejpam-4803	59	21	intersection	intersection	NOUN
ejpam-4803	59	22	of	of	ADP
ejpam-4803	59	23	two	two	NUM
ejpam-4803	59	24	nonempty	nonempty	ADJ
ejpam-4803	59	25	open	open	ADJ
ejpam-4803	59	26	subsets	subset	NOUN
ejpam-4803	59	27	is	be	AUX
ejpam-4803	59	28	nonempty	nonempty	ADJ
ejpam-4803	59	29	.	.	PUNCT
ejpam-4803	60	1	an	an	DET
ejpam-4803	60	2	element	element	NOUN
ejpam-4803	60	3	x	x	PUNCT
ejpam-4803	60	4	of	of	ADP
ejpam-4803	60	5	c	c	PROPN
ejpam-4803	60	6	is	be	AUX
ejpam-4803	60	7	called	call	VERB
ejpam-4803	60	8	a	a	DET
ejpam-4803	60	9	generic	generic	ADJ
ejpam-4803	60	10	point	point	NOUN
ejpam-4803	60	11	if	if	SCONJ
ejpam-4803	60	12	the	the	DET
ejpam-4803	60	13	closure	closure	NOUN
ejpam-4803	60	14	of	of	ADP
ejpam-4803	60	15	the	the	DET
ejpam-4803	60	16	singleton	singleton	NOUN
ejpam-4803	60	17	{	{	PUNCT
ejpam-4803	60	18	x	x	NOUN
ejpam-4803	60	19	}	}	PUNCT
ejpam-4803	60	20	is	be	AUX
ejpam-4803	60	21	equal	equal	ADJ
ejpam-4803	60	22	to	to	ADP
ejpam-4803	60	23	c	c	NOUN
ejpam-4803	60	24	:	:	PUNCT
ejpam-4803	60	25	{	{	PUNCT
ejpam-4803	60	26	x	x	NOUN
ejpam-4803	60	27	}	}	PUNCT
ejpam-4803	60	28	=	=	SYM
ejpam-4803	60	29	c.	c.	NOUN
ejpam-4803	60	30	let	let	VERB
ejpam-4803	60	31	a	a	PRON
ejpam-4803	60	32	be	be	AUX
ejpam-4803	60	33	a	a	DET
ejpam-4803	60	34	commutative	commutative	ADJ
ejpam-4803	60	35	and	and	CCONJ
ejpam-4803	60	36	unitary	unitary	ADJ
ejpam-4803	60	37	ring	ring	NOUN
ejpam-4803	60	38	and	and	CCONJ
ejpam-4803	60	39	spec(a	spec(a	NOUN
ejpam-4803	60	40	)	)	PUNCT
ejpam-4803	60	41	be	be	VERB
ejpam-4803	60	42	the	the	DET
ejpam-4803	60	43	set	set	NOUN
ejpam-4803	60	44	of	of	ADP
ejpam-4803	60	45	prime	prime	ADJ
ejpam-4803	60	46	ideals	ideal	NOUN
ejpam-4803	60	47	of	of	ADP
ejpam-4803	60	48	a.	a.	NOUN
ejpam-4803	60	49	if	if	SCONJ
ejpam-4803	60	50	p	p	NOUN
ejpam-4803	60	51	is	be	AUX
ejpam-4803	60	52	an	an	DET
ejpam-4803	60	53	ideal	ideal	NOUN
ejpam-4803	60	54	of	of	ADP
ejpam-4803	60	55	a	a	PRON
ejpam-4803	60	56	,	,	PUNCT
ejpam-4803	60	57	the	the	DET
ejpam-4803	60	58	family	family	NOUN
ejpam-4803	60	59	{	{	PUNCT
ejpam-4803	60	60	v	v	NOUN
ejpam-4803	60	61	(	(	PUNCT
ejpam-4803	60	62	p	p	NOUN
ejpam-4803	60	63	)	)	PUNCT
ejpam-4803	60	64	=	=	PUNCT
ejpam-4803	60	65	{	{	PUNCT
ejpam-4803	60	66	q	q	PROPN
ejpam-4803	60	67	∈	∈	PROPN
ejpam-4803	60	68	spec(a	spec(a	PROPN
ejpam-4803	60	69	)	)	PUNCT
ejpam-4803	60	70	:	:	PUNCT
ejpam-4803	61	1	p	p	X
ejpam-4803	61	2	⊂	⊂	PROPN
ejpam-4803	61	3	q	q	NOUN
ejpam-4803	61	4	}	}	PUNCT
ejpam-4803	61	5	}	}	PUNCT
ejpam-4803	61	6	defines	define	VERB
ejpam-4803	61	7	the	the	DET
ejpam-4803	61	8	closed	closed	ADJ
ejpam-4803	61	9	subsets	subset	NOUN
ejpam-4803	61	10	of	of	ADP
ejpam-4803	61	11	the	the	DET
ejpam-4803	61	12	zariski	zariski	ADJ
ejpam-4803	61	13	topology	topology	NOUN
ejpam-4803	61	14	in	in	ADP
ejpam-4803	61	15	spec(a	spec(a	NOUN
ejpam-4803	61	16	)	)	PUNCT
ejpam-4803	61	17	.	.	PUNCT
ejpam-4803	62	1	equipped	equip	VERB
ejpam-4803	62	2	with	with	ADP
ejpam-4803	62	3	this	this	DET
ejpam-4803	62	4	topology	topology	NOUN
ejpam-4803	62	5	,	,	PUNCT
ejpam-4803	62	6	spec(a	spec(a	PROPN
ejpam-4803	62	7	)	)	PUNCT
ejpam-4803	62	8	satisfies	satisfy	VERB
ejpam-4803	62	9	the	the	DET
ejpam-4803	62	10	following	follow	VERB
ejpam-4803	62	11	properties	property	NOUN
ejpam-4803	62	12	:	:	PUNCT
ejpam-4803	62	13	1	1	X
ejpam-4803	62	14	.	.	X
ejpam-4803	62	15	spec(a	spec(a	NOUN
ejpam-4803	62	16	)	)	PUNCT
ejpam-4803	62	17	is	be	AUX
ejpam-4803	62	18	kolmogorov	kolmogorov	ADJ
ejpam-4803	62	19	.	.	PUNCT
ejpam-4803	63	1	2	2	NUM
ejpam-4803	63	2	.	.	X
ejpam-4803	64	1	every	every	DET
ejpam-4803	64	2	irreducible	irreducible	ADJ
ejpam-4803	64	3	closed	closed	ADJ
ejpam-4803	64	4	subset	subset	NOUN
ejpam-4803	64	5	of	of	ADP
ejpam-4803	64	6	spec(a	spec(a	NOUN
ejpam-4803	64	7	)	)	PUNCT
ejpam-4803	64	8	has	have	VERB
ejpam-4803	64	9	a	a	DET
ejpam-4803	64	10	generic	generic	ADJ
ejpam-4803	64	11	point	point	NOUN
ejpam-4803	64	12	.	.	PUNCT
ejpam-4803	65	1	3	3	X
ejpam-4803	65	2	.	.	X
ejpam-4803	65	3	spec(a	spec(a	NOUN
ejpam-4803	65	4	)	)	PUNCT
ejpam-4803	65	5	is	be	AUX
ejpam-4803	65	6	a	a	DET
ejpam-4803	65	7	quasi	quasi	ADJ
ejpam-4803	65	8	-	-	ADJ
ejpam-4803	65	9	compact	compact	ADJ
ejpam-4803	65	10	space	space	NOUN
ejpam-4803	65	11	.	.	PUNCT
ejpam-4803	66	1	4	4	X
ejpam-4803	66	2	.	.	X
ejpam-4803	66	3	there	there	PRON
ejpam-4803	66	4	is	be	VERB
ejpam-4803	66	5	a	a	DET
ejpam-4803	66	6	basis	basis	NOUN
ejpam-4803	66	7	of	of	ADP
ejpam-4803	66	8	quasi	quasi	ADJ
ejpam-4803	66	9	-	-	ADJ
ejpam-4803	66	10	compact	compact	ADJ
ejpam-4803	66	11	open	open	ADJ
ejpam-4803	66	12	subsets	subset	NOUN
ejpam-4803	66	13	of	of	ADP
ejpam-4803	66	14	spec(a	spec(a	NOUN
ejpam-4803	66	15	)	)	PUNCT
ejpam-4803	66	16	.	.	PUNCT
ejpam-4803	67	1	5	5	X
ejpam-4803	67	2	.	.	X
ejpam-4803	67	3	the	the	DET
ejpam-4803	67	4	family	family	NOUN
ejpam-4803	67	5	of	of	ADP
ejpam-4803	67	6	quasi	quasi	ADJ
ejpam-4803	67	7	-	-	ADJ
ejpam-4803	67	8	compact	compact	ADJ
ejpam-4803	67	9	open	open	ADJ
ejpam-4803	67	10	subsets	subset	NOUN
ejpam-4803	67	11	of	of	ADP
ejpam-4803	67	12	spec(a	spec(a	NOUN
ejpam-4803	67	13	)	)	PUNCT
ejpam-4803	67	14	is	be	AUX
ejpam-4803	67	15	stable	stable	ADJ
ejpam-4803	67	16	under	under	ADP
ejpam-4803	67	17	finite	finite	ADJ
ejpam-4803	67	18	intersection	intersection	NOUN
ejpam-4803	67	19	.	.	PUNCT
ejpam-4803	68	1	if	if	SCONJ
ejpam-4803	68	2	a	a	DET
ejpam-4803	68	3	topological	topological	ADJ
ejpam-4803	68	4	space	space	NOUN
ejpam-4803	68	5	x	x	NOUN
ejpam-4803	68	6	satisfies	satisfy	VERB
ejpam-4803	68	7	the	the	DET
ejpam-4803	68	8	above	above	ADJ
ejpam-4803	68	9	five	five	NUM
ejpam-4803	68	10	properties	property	NOUN
ejpam-4803	68	11	,	,	PUNCT
ejpam-4803	68	12	then	then	ADV
ejpam-4803	68	13	there	there	PRON
ejpam-4803	68	14	exists	exist	VERB
ejpam-4803	68	15	a	a	DET
ejpam-4803	68	16	commutative	commutative	ADJ
ejpam-4803	68	17	and	and	CCONJ
ejpam-4803	68	18	unitary	unitary	ADJ
ejpam-4803	68	19	ring	ring	NOUN
ejpam-4803	68	20	a	a	DET
ejpam-4803	68	21	such	such	ADJ
ejpam-4803	68	22	that	that	PRON
ejpam-4803	68	23	x	x	PRON
ejpam-4803	68	24	is	be	AUX
ejpam-4803	68	25	homeomorphic	homeomorphic	ADJ
ejpam-4803	68	26	to	to	ADP
ejpam-4803	68	27	spec(a	spec(a	NOUN
ejpam-4803	68	28	)	)	PUNCT
ejpam-4803	68	29	equipped	equip	VERB
ejpam-4803	68	30	with	with	ADP
ejpam-4803	68	31	the	the	DET
ejpam-4803	68	32	zariski	zariski	ADJ
ejpam-4803	68	33	topology	topology	NOUN
ejpam-4803	68	34	[	[	X
ejpam-4803	68	35	5	5	NUM
ejpam-4803	68	36	]	]	PUNCT
ejpam-4803	68	37	.	.	PUNCT
ejpam-4803	69	1	let	let	VERB
ejpam-4803	69	2	f	f	PRON
ejpam-4803	69	3	be	be	AUX
ejpam-4803	69	4	a	a	DET
ejpam-4803	69	5	codimension	codimension	NOUN
ejpam-4803	69	6	-	-	PUNCT
ejpam-4803	69	7	one	one	NUM
ejpam-4803	69	8	transversally	transversally	ADV
ejpam-4803	69	9	oriented	orient	VERB
ejpam-4803	69	10	foliation	foliation	NOUN
ejpam-4803	69	11	of	of	ADP
ejpam-4803	69	12	class	class	NOUN
ejpam-4803	69	13	cr	cr	PROPN
ejpam-4803	69	14	,	,	PUNCT
ejpam-4803	69	15	r	r	NOUN
ejpam-4803	69	16	≥	≥	NOUN
ejpam-4803	69	17	0	0	NUM
ejpam-4803	69	18	,	,	PUNCT
ejpam-4803	69	19	on	on	ADP
ejpam-4803	69	20	a	a	DET
ejpam-4803	69	21	closed	closed	ADJ
ejpam-4803	69	22	m	m	NOUN
ejpam-4803	69	23	-	-	ADJ
ejpam-4803	69	24	manifold	manifold	ADJ
ejpam-4803	69	25	m	m	NOUN
ejpam-4803	69	26	.	.	PUNCT
ejpam-4803	70	1	dippolito	dippolito	PROPN
ejpam-4803	71	1	[	[	X
ejpam-4803	71	2	4	4	NUM
ejpam-4803	71	3	,	,	PUNCT
ejpam-4803	71	4	chapter	chapter	NOUN
ejpam-4803	71	5	4.4	4.4	NUM
ejpam-4803	71	6	]	]	PUNCT
ejpam-4803	71	7	defined	define	VERB
ejpam-4803	71	8	the	the	DET
ejpam-4803	71	9	boundary	boundary	NOUN
ejpam-4803	71	10	δu	δu	NOUN
ejpam-4803	71	11	of	of	ADP
ejpam-4803	71	12	a	a	DET
ejpam-4803	71	13	nonempty	nonempty	ADV
ejpam-4803	71	14	saturated	saturate	VERB
ejpam-4803	71	15	connected	connect	VERB
ejpam-4803	71	16	open	open	ADJ
ejpam-4803	71	17	subset	subset	ADJ
ejpam-4803	71	18	distinct	distinct	ADJ
ejpam-4803	71	19	of	of	ADP
ejpam-4803	71	20	m	m	PROPN
ejpam-4803	71	21	.	.	PUNCT
ejpam-4803	72	1	the	the	DET
ejpam-4803	72	2	boundary	boundary	ADJ
ejpam-4803	72	3	δu	δu	NOUN
ejpam-4803	72	4	is	be	AUX
ejpam-4803	72	5	equal	equal	ADJ
ejpam-4803	72	6	to	to	ADP
ejpam-4803	72	7	the	the	DET
ejpam-4803	72	8	set	set	NOUN
ejpam-4803	72	9	of	of	ADP
ejpam-4803	72	10	points	point	NOUN
ejpam-4803	72	11	x	x	X
ejpam-4803	72	12	∈	∈	NOUN
ejpam-4803	72	13	m	m	VERB
ejpam-4803	72	14	−	−	NOUN
ejpam-4803	72	15	u	u	NOUN
ejpam-4803	72	16	such	such	ADJ
ejpam-4803	72	17	as	as	SCONJ
ejpam-4803	72	18	there	there	PRON
ejpam-4803	72	19	is	be	VERB
ejpam-4803	72	20	a	a	DET
ejpam-4803	72	21	curve	curve	NOUN
ejpam-4803	72	22	c	c	NOUN
ejpam-4803	72	23	:	:	PUNCT
ejpam-4803	73	1	[	[	X
ejpam-4803	73	2	0	0	NUM
ejpam-4803	73	3	,	,	PUNCT
ejpam-4803	73	4	1	1	NUM
ejpam-4803	73	5	]	]	PUNCT
ejpam-4803	73	6	→	→	SYM
ejpam-4803	73	7	m	m	VERB
ejpam-4803	73	8	such	such	ADJ
ejpam-4803	73	9	that	that	DET
ejpam-4803	73	10	c(0	c(0	NOUN
ejpam-4803	73	11	)	)	PUNCT
ejpam-4803	74	1	=	=	SYM
ejpam-4803	74	2	x	x	PROPN
ejpam-4803	74	3	and	and	CCONJ
ejpam-4803	74	4	c(]0	c(]0	PROPN
ejpam-4803	74	5	,	,	PUNCT
ejpam-4803	74	6	1	1	NUM
ejpam-4803	74	7	]	]	PUNCT
ejpam-4803	74	8	)	)	PUNCT
ejpam-4803	75	1	⊂	⊂	PROPN
ejpam-4803	75	2	u	u	PROPN
ejpam-4803	75	3	.	.	PUNCT
ejpam-4803	75	4	dippolito	dippolito	PROPN
ejpam-4803	75	5	proved	prove	VERB
ejpam-4803	75	6	that	that	SCONJ
ejpam-4803	75	7	δu	δu	PRON
ejpam-4803	75	8	is	be	AUX
ejpam-4803	75	9	a	a	DET
ejpam-4803	75	10	union	union	NOUN
ejpam-4803	75	11	of	of	ADP
ejpam-4803	75	12	a	a	DET
ejpam-4803	75	13	finitely	finitely	ADV
ejpam-4803	75	14	many	many	ADJ
ejpam-4803	75	15	leaves	leave	NOUN
ejpam-4803	75	16	(	(	PUNCT
ejpam-4803	75	17	[	[	X
ejpam-4803	75	18	4	4	NUM
ejpam-4803	75	19	,	,	PUNCT
ejpam-4803	75	20	chapter	chapter	NOUN
ejpam-4803	75	21	4.4	4.4	NUM
ejpam-4803	75	22	]	]	PUNCT
ejpam-4803	75	23	)	)	PUNCT
ejpam-4803	75	24	.	.	PUNCT
ejpam-4803	76	1	we	we	PRON
ejpam-4803	76	2	have	have	VERB
ejpam-4803	76	3	δu	δu	NOUN
ejpam-4803	76	4	=	=	SYM
ejpam-4803	76	5	u	u	NOUN
ejpam-4803	76	6	−	−	PROPN
ejpam-4803	76	7	u	u	PROPN
ejpam-4803	76	8	.	.	PUNCT
ejpam-4803	77	1	note	note	VERB
ejpam-4803	77	2	that	that	SCONJ
ejpam-4803	77	3	an	an	PRON
ejpam-4803	77	4	attracting	attract	VERB
ejpam-4803	77	5	proper	proper	ADJ
ejpam-4803	77	6	leaf	leaf	NOUN
ejpam-4803	77	7	from	from	ADP
ejpam-4803	77	8	one	one	NUM
ejpam-4803	77	9	side	side	NOUN
ejpam-4803	77	10	is	be	AUX
ejpam-4803	77	11	introduced	introduce	VERB
ejpam-4803	77	12	in	in	ADP
ejpam-4803	77	13	[	[	X
ejpam-4803	77	14	4	4	NUM
ejpam-4803	77	15	,	,	PUNCT
ejpam-4803	77	16	chapter	chapter	NOUN
ejpam-4803	77	17	4.4	4.4	NUM
ejpam-4803	77	18	]	]	PUNCT
ejpam-4803	77	19	.	.	PUNCT
ejpam-4803	78	1	recall	recall	VERB
ejpam-4803	78	2	that	that	SCONJ
ejpam-4803	78	3	if	if	SCONJ
ejpam-4803	78	4	a	a	DET
ejpam-4803	78	5	⊂	⊂	PROPN
ejpam-4803	78	6	x	x	X
ejpam-4803	78	7	,	,	PUNCT
ejpam-4803	78	8	the	the	DET
ejpam-4803	78	9	saturation	saturation	NOUN
ejpam-4803	78	10	satr(a	satr(a	NOUN
ejpam-4803	78	11	)	)	PUNCT
ejpam-4803	78	12	of	of	ADP
ejpam-4803	78	13	a	a	PRON
ejpam-4803	78	14	is	be	AUX
ejpam-4803	78	15	the	the	DET
ejpam-4803	78	16	union	union	NOUN
ejpam-4803	78	17	of	of	ADP
ejpam-4803	78	18	all	all	DET
ejpam-4803	78	19	equivalence	equivalence	NOUN
ejpam-4803	78	20	classes	class	NOUN
ejpam-4803	78	21	meeting	meet	VERB
ejpam-4803	78	22	a.	a.	NOUN
ejpam-4803	78	23	the	the	DET
ejpam-4803	78	24	subset	subset	NOUN
ejpam-4803	78	25	a	a	PRON
ejpam-4803	78	26	is	be	AUX
ejpam-4803	78	27	called	call	VERB
ejpam-4803	78	28	invariant	invariant	ADJ
ejpam-4803	78	29	(	(	PUNCT
ejpam-4803	78	30	or	or	CCONJ
ejpam-4803	78	31	saturated	saturate	VERB
ejpam-4803	78	32	)	)	PUNCT
ejpam-4803	78	33	if	if	SCONJ
ejpam-4803	78	34	a	a	DET
ejpam-4803	78	35	=	=	PUNCT
ejpam-4803	78	36	satr(a	satr(a	NOUN
ejpam-4803	78	37	)	)	PUNCT
ejpam-4803	78	38	.	.	PUNCT
ejpam-4803	79	1	note	note	VERB
ejpam-4803	79	2	b.	b.	PROPN
ejpam-4803	79	3	alharbi	alharbi	PROPN
ejpam-4803	79	4	/	/	SYM
ejpam-4803	79	5	eur	eur	PROPN
ejpam-4803	79	6	.	.	PUNCT
ejpam-4803	80	1	j.	j.	PROPN
ejpam-4803	80	2	pure	pure	PROPN
ejpam-4803	80	3	appl	appl	PROPN
ejpam-4803	80	4	.	.	PROPN
ejpam-4803	80	5	math	math	PROPN
ejpam-4803	80	6	,	,	PUNCT
ejpam-4803	80	7	17	17	NUM
ejpam-4803	80	8	(	(	PUNCT
ejpam-4803	80	9	1	1	NUM
ejpam-4803	80	10	)	)	PUNCT
ejpam-4803	80	11	(	(	PUNCT
ejpam-4803	80	12	2024	2024	NUM
ejpam-4803	80	13	)	)	PUNCT
ejpam-4803	80	14	,	,	PUNCT
ejpam-4803	80	15	356	356	NUM
ejpam-4803	80	16	-	-	SYM
ejpam-4803	80	17	361	361	NUM
ejpam-4803	80	18	359	359	NUM
ejpam-4803	80	19	that	that	PRON
ejpam-4803	80	20	,	,	PUNCT
ejpam-4803	80	21	the	the	DET
ejpam-4803	80	22	interior	interior	NOUN
ejpam-4803	80	23	,	,	PUNCT
ejpam-4803	80	24	the	the	DET
ejpam-4803	80	25	closure	closure	NOUN
ejpam-4803	80	26	,	,	PUNCT
ejpam-4803	80	27	the	the	DET
ejpam-4803	80	28	boundary	boundary	NOUN
ejpam-4803	80	29	of	of	ADP
ejpam-4803	80	30	each	each	DET
ejpam-4803	80	31	saturated	saturate	VERB
ejpam-4803	80	32	subset	subset	NOUN
ejpam-4803	80	33	is	be	AUX
ejpam-4803	80	34	also	also	ADV
ejpam-4803	80	35	saturated	saturate	VERB
ejpam-4803	81	1	;	;	PUNCT
ejpam-4803	81	2	indeed	indeed	ADV
ejpam-4803	81	3	the	the	DET
ejpam-4803	81	4	relation	relation	NOUN
ejpam-4803	81	5	r	r	NOUN
ejpam-4803	81	6	is	be	AUX
ejpam-4803	81	7	open	open	ADJ
ejpam-4803	81	8	.	.	PUNCT
ejpam-4803	82	1	we	we	PRON
ejpam-4803	82	2	denote	denote	VERB
ejpam-4803	82	3	by	by	ADP
ejpam-4803	82	4	ts	ts	ADP
ejpam-4803	82	5	the	the	DET
ejpam-4803	82	6	invariant	invariant	ADJ
ejpam-4803	82	7	topology	topology	NOUN
ejpam-4803	82	8	on	on	ADP
ejpam-4803	82	9	x	x	PUNCT
ejpam-4803	82	10	formed	form	VERB
ejpam-4803	82	11	by	by	ADP
ejpam-4803	82	12	the	the	DET
ejpam-4803	82	13	invariant	invariant	ADJ
ejpam-4803	82	14	open	open	ADJ
ejpam-4803	82	15	subsets	subset	NOUN
ejpam-4803	82	16	of	of	ADP
ejpam-4803	82	17	x.	x.	NOUN
ejpam-4803	82	18	an	an	DET
ejpam-4803	82	19	invariant	invariant	ADJ
ejpam-4803	82	20	open	open	NOUN
ejpam-4803	82	21	subset	subset	VERB
ejpam-4803	82	22	u	u	NOUN
ejpam-4803	82	23	⊂	⊂	PROPN
ejpam-4803	82	24	x	x	AUX
ejpam-4803	82	25	is	be	AUX
ejpam-4803	82	26	called	call	VERB
ejpam-4803	82	27	compact	compact	ADJ
ejpam-4803	82	28	by	by	ADP
ejpam-4803	82	29	saturation	saturation	NOUN
ejpam-4803	82	30	if	if	SCONJ
ejpam-4803	82	31	it	it	PRON
ejpam-4803	82	32	is	be	AUX
ejpam-4803	82	33	quasi	quasi	ADJ
ejpam-4803	82	34	-	-	ADJ
ejpam-4803	82	35	compact	compact	ADJ
ejpam-4803	82	36	for	for	ADP
ejpam-4803	82	37	the	the	DET
ejpam-4803	82	38	invariant	invariant	ADJ
ejpam-4803	82	39	topology	topology	NOUN
ejpam-4803	82	40	ts	ts	NOUN
ejpam-4803	82	41	.	.	PUNCT
ejpam-4803	83	1	that	that	PRON
ejpam-4803	83	2	is	be	AUX
ejpam-4803	83	3	,	,	PUNCT
ejpam-4803	83	4	every	every	DET
ejpam-4803	83	5	covering	covering	NOUN
ejpam-4803	83	6	(	(	PUNCT
ejpam-4803	83	7	ui	ui	NOUN
ejpam-4803	83	8	)	)	PUNCT
ejpam-4803	83	9	of	of	ADP
ejpam-4803	83	10	u	u	NOUN
ejpam-4803	83	11	by	by	ADP
ejpam-4803	83	12	invariant	invariant	ADJ
ejpam-4803	83	13	open	open	ADJ
ejpam-4803	83	14	subsets	subset	NOUN
ejpam-4803	83	15	ui	ui	PROPN
ejpam-4803	83	16	contains	contain	VERB
ejpam-4803	83	17	a	a	DET
ejpam-4803	83	18	finite	finite	ADJ
ejpam-4803	83	19	sub	sub	NOUN
ejpam-4803	83	20	-	-	NOUN
ejpam-4803	83	21	cover	cover	NOUN
ejpam-4803	83	22	.	.	PUNCT
ejpam-4803	84	1	lemma	lemma	PROPN
ejpam-4803	84	2	2.5	2.5	NUM
ejpam-4803	84	3	.	.	PUNCT
ejpam-4803	85	1	let	let	VERB
ejpam-4803	85	2	r	r	PRON
ejpam-4803	85	3	be	be	AUX
ejpam-4803	85	4	an	an	DET
ejpam-4803	85	5	open	open	ADJ
ejpam-4803	85	6	equivalence	equivalence	NOUN
ejpam-4803	85	7	relation	relation	NOUN
ejpam-4803	85	8	on	on	ADP
ejpam-4803	85	9	a	a	DET
ejpam-4803	85	10	topological	topological	ADJ
ejpam-4803	85	11	space	space	NOUN
ejpam-4803	85	12	x.	x.	NOUN
ejpam-4803	86	1	an	an	DET
ejpam-4803	86	2	open	open	ADJ
ejpam-4803	86	3	subset	subset	NOUN
ejpam-4803	86	4	v	v	NOUN
ejpam-4803	86	5	of	of	ADP
ejpam-4803	86	6	the	the	DET
ejpam-4803	86	7	quotient	quotient	NOUN
ejpam-4803	86	8	space	space	NOUN
ejpam-4803	86	9	x	x	X
ejpam-4803	86	10	/	/	SYM
ejpam-4803	86	11	r	r	NOUN
ejpam-4803	86	12	is	be	AUX
ejpam-4803	86	13	quasi	quasi	ADJ
ejpam-4803	86	14	-	-	ADJ
ejpam-4803	86	15	compact	compact	ADJ
ejpam-4803	86	16	if	if	SCONJ
ejpam-4803	87	1	and	and	CCONJ
ejpam-4803	87	2	only	only	ADV
ejpam-4803	87	3	if	if	SCONJ
ejpam-4803	87	4	the	the	DET
ejpam-4803	87	5	open	open	ADJ
ejpam-4803	87	6	subset	subset	NOUN
ejpam-4803	87	7	u	u	NOUN
ejpam-4803	87	8	=	=	PROPN
ejpam-4803	87	9	q−1(v	q−1(v	PROPN
ejpam-4803	87	10	)	)	PUNCT
ejpam-4803	87	11	is	be	AUX
ejpam-4803	87	12	compact	compact	ADJ
ejpam-4803	87	13	by	by	ADP
ejpam-4803	87	14	saturation	saturation	NOUN
ejpam-4803	87	15	.	.	PUNCT
ejpam-4803	88	1	proof	proof	NOUN
ejpam-4803	88	2	.	.	PUNCT
ejpam-4803	89	1	suppose	suppose	VERB
ejpam-4803	89	2	that	that	SCONJ
ejpam-4803	89	3	v	v	NOUN
ejpam-4803	89	4	is	be	AUX
ejpam-4803	89	5	quasi	quasi	ADJ
ejpam-4803	89	6	-	-	ADJ
ejpam-4803	89	7	compact	compact	ADJ
ejpam-4803	89	8	,	,	PUNCT
ejpam-4803	89	9	and	and	CCONJ
ejpam-4803	89	10	let	let	VERB
ejpam-4803	89	11	(	(	PUNCT
ejpam-4803	89	12	ui	ui	NOUN
ejpam-4803	89	13	,	,	PUNCT
ejpam-4803	89	14	i	i	PRON
ejpam-4803	89	15	∈	∈	PROPN
ejpam-4803	89	16	i	i	PRON
ejpam-4803	89	17	)	)	PUNCT
ejpam-4803	89	18	be	be	VERB
ejpam-4803	89	19	a	a	DET
ejpam-4803	89	20	covering	covering	NOUN
ejpam-4803	89	21	of	of	ADP
ejpam-4803	89	22	u	u	NOUN
ejpam-4803	89	23	=	=	PROPN
ejpam-4803	89	24	q−1(v	q−1(v	PROPN
ejpam-4803	89	25	)	)	PUNCT
ejpam-4803	89	26	by	by	ADP
ejpam-4803	89	27	saturated	saturate	VERB
ejpam-4803	89	28	open	open	ADJ
ejpam-4803	89	29	subsets	subset	NOUN
ejpam-4803	89	30	.	.	PUNCT
ejpam-4803	90	1	thus	thus	ADV
ejpam-4803	90	2	the	the	DET
ejpam-4803	90	3	open	open	ADJ
ejpam-4803	90	4	subsets	subset	NOUN
ejpam-4803	90	5	(	(	PUNCT
ejpam-4803	90	6	q(ui	q(ui	NOUN
ejpam-4803	90	7	)	)	PUNCT
ejpam-4803	90	8	)	)	PUNCT
ejpam-4803	90	9	cover	cover	VERB
ejpam-4803	90	10	v	v	NOUN
ejpam-4803	90	11	,	,	PUNCT
ejpam-4803	90	12	and	and	CCONJ
ejpam-4803	90	13	some	some	DET
ejpam-4803	90	14	finite	finite	ADJ
ejpam-4803	90	15	number	number	NOUN
ejpam-4803	90	16	of	of	ADP
ejpam-4803	90	17	these	these	PRON
ejpam-4803	90	18	,	,	PUNCT
ejpam-4803	90	19	q(ui1	q(ui1	NOUN
ejpam-4803	90	20	)	)	PUNCT
ejpam-4803	90	21	,	,	PUNCT
ejpam-4803	90	22	...	...	PUNCT
ejpam-4803	90	23	,	,	PUNCT
ejpam-4803	90	24	q(uin	q(uin	PROPN
ejpam-4803	90	25	)	)	PUNCT
ejpam-4803	90	26	,	,	PUNCT
ejpam-4803	90	27	covers	cover	VERB
ejpam-4803	90	28	v	v	NOUN
ejpam-4803	90	29	.	.	PUNCT
ejpam-4803	91	1	because	because	SCONJ
ejpam-4803	91	2	every	every	DET
ejpam-4803	91	3	ui	ui	NOUN
ejpam-4803	91	4	is	be	AUX
ejpam-4803	91	5	saturated	saturate	VERB
ejpam-4803	91	6	,	,	PUNCT
ejpam-4803	91	7	q−1(q(ui	q−1(q(ui	PROPN
ejpam-4803	91	8	)	)	PUNCT
ejpam-4803	91	9	)	)	PUNCT
ejpam-4803	92	1	=	=	SYM
ejpam-4803	93	1	ui	ui	NOUN
ejpam-4803	94	1	and	and	CCONJ
ejpam-4803	94	2	hence	hence	ADV
ejpam-4803	94	3	u	u	X
ejpam-4803	95	1	=	=	NOUN
ejpam-4803	95	2	ui1	ui1	ADV
ejpam-4803	95	3	∪	∪	ADV
ejpam-4803	95	4	...	...	PUNCT
ejpam-4803	95	5	∪	∪	ADP
ejpam-4803	95	6	uin	uin	PROPN
ejpam-4803	95	7	.	.	PUNCT
ejpam-4803	96	1	conversely	conversely	ADV
ejpam-4803	96	2	,	,	PUNCT
ejpam-4803	96	3	let	let	VERB
ejpam-4803	96	4	(	(	PUNCT
ejpam-4803	96	5	vi	vi	VERB
ejpam-4803	96	6	,	,	PUNCT
ejpam-4803	96	7	i	i	PRON
ejpam-4803	96	8	∈	∈	PROPN
ejpam-4803	97	1	i	i	PRON
ejpam-4803	97	2	)	)	PUNCT
ejpam-4803	97	3	be	be	VERB
ejpam-4803	97	4	a	a	DET
ejpam-4803	97	5	family	family	NOUN
ejpam-4803	97	6	of	of	ADP
ejpam-4803	97	7	open	open	ADJ
ejpam-4803	97	8	subsets	subset	NOUN
ejpam-4803	97	9	of	of	ADP
ejpam-4803	97	10	x	x	NOUN
ejpam-4803	97	11	/	/	SYM
ejpam-4803	97	12	r	r	NOUN
ejpam-4803	97	13	such	such	ADJ
ejpam-4803	97	14	that	that	DET
ejpam-4803	97	15	v	v	NOUN
ejpam-4803	97	16	=	=	SYM
ejpam-4803	97	17	⋃	⋃	PROPN
ejpam-4803	97	18	i	i	PRON
ejpam-4803	97	19	vi	vi	PROPN
ejpam-4803	97	20	.	.	PUNCT
ejpam-4803	98	1	since	since	SCONJ
ejpam-4803	98	2	q−1(vi	q−1(vi	PROPN
ejpam-4803	98	3	)	)	PUNCT
ejpam-4803	98	4	is	be	AUX
ejpam-4803	98	5	a	a	DET
ejpam-4803	98	6	saturated	saturate	VERB
ejpam-4803	98	7	open	open	ADJ
ejpam-4803	98	8	subset	subset	NOUN
ejpam-4803	98	9	and	and	CCONJ
ejpam-4803	98	10	u	u	NOUN
ejpam-4803	98	11	is	be	AUX
ejpam-4803	98	12	compact	compact	ADJ
ejpam-4803	98	13	by	by	ADP
ejpam-4803	98	14	saturation	saturation	NOUN
ejpam-4803	98	15	,	,	PUNCT
ejpam-4803	98	16	it	it	PRON
ejpam-4803	98	17	follows	follow	VERB
ejpam-4803	98	18	that	that	SCONJ
ejpam-4803	98	19	u	u	NOUN
ejpam-4803	98	20	=	=	NOUN
ejpam-4803	98	21	q−1(vi1	q−1(vi1	ADV
ejpam-4803	98	22	)	)	PUNCT
ejpam-4803	98	23	∪	∪	ADV
ejpam-4803	98	24	...	...	PUNCT
ejpam-4803	98	25	∪	∪	ADP
ejpam-4803	98	26	q−1(vin	q−1(vin	NOUN
ejpam-4803	98	27	)	)	PUNCT
ejpam-4803	98	28	which	which	PRON
ejpam-4803	98	29	implies	imply	VERB
ejpam-4803	98	30	that	that	SCONJ
ejpam-4803	98	31	v	v	NOUN
ejpam-4803	98	32	=	=	PUNCT
ejpam-4803	98	33	vi1	vi1	NOUN
ejpam-4803	98	34	∪	∪	ADV
ejpam-4803	98	35	...	...	PUNCT
ejpam-4803	98	36	∪	∪	X
ejpam-4803	98	37	vin	vin	NOUN
ejpam-4803	98	38	.	.	PUNCT
ejpam-4803	99	1	lemma	lemma	PROPN
ejpam-4803	99	2	2.6	2.6	NUM
ejpam-4803	99	3	.	.	PUNCT
ejpam-4803	100	1	[	[	X
ejpam-4803	100	2	3	3	X
ejpam-4803	100	3	]	]	PUNCT
ejpam-4803	100	4	let	let	VERB
ejpam-4803	100	5	u	u	PRON
ejpam-4803	100	6	be	be	AUX
ejpam-4803	100	7	a	a	DET
ejpam-4803	100	8	connected	connect	VERB
ejpam-4803	100	9	nonempty	nonempty	ADV
ejpam-4803	100	10	invariant	invariant	ADJ
ejpam-4803	100	11	open	open	ADJ
ejpam-4803	100	12	subset	subset	NOUN
ejpam-4803	100	13	of	of	ADP
ejpam-4803	100	14	m	m	PROPN
ejpam-4803	100	15	.	.	PUNCT
ejpam-4803	101	1	then	then	ADV
ejpam-4803	101	2	the	the	DET
ejpam-4803	101	3	following	follow	VERB
ejpam-4803	101	4	properties	property	NOUN
ejpam-4803	101	5	are	be	AUX
ejpam-4803	101	6	equivalent	equivalent	ADJ
ejpam-4803	101	7	:	:	PUNCT
ejpam-4803	101	8	a	a	X
ejpam-4803	101	9	)	)	PUNCT
ejpam-4803	101	10	the	the	DET
ejpam-4803	101	11	following	follow	VERB
ejpam-4803	101	12	two	two	NUM
ejpam-4803	101	13	properties	property	NOUN
ejpam-4803	101	14	hold	hold	VERB
ejpam-4803	101	15	:	:	PUNCT
ejpam-4803	101	16	i	i	PRON
ejpam-4803	101	17	)	)	PUNCT
ejpam-4803	101	18	each	each	DET
ejpam-4803	101	19	leaf	leaf	NOUN
ejpam-4803	102	1	l	l	PROPN
ejpam-4803	102	2	⊂	⊂	X
ejpam-4803	102	3	δϵu	δϵu	PROPN
ejpam-4803	102	4	,	,	PUNCT
ejpam-4803	102	5	ϵ	ϵ	X
ejpam-4803	102	6	=	=	SYM
ejpam-4803	102	7	±	±	PROPN
ejpam-4803	102	8	,	,	PUNCT
ejpam-4803	102	9	is	be	AUX
ejpam-4803	102	10	attracting	attract	VERB
ejpam-4803	102	11	from	from	ADP
ejpam-4803	102	12	the	the	DET
ejpam-4803	102	13	side	side	NOUN
ejpam-4803	102	14	ϵ	ϵ	X
ejpam-4803	102	15	(	(	PUNCT
ejpam-4803	102	16	i.e	i.e	DET
ejpam-4803	102	17	l	l	NOUN
ejpam-4803	102	18	is	be	AUX
ejpam-4803	102	19	attracting	attract	VERB
ejpam-4803	102	20	from	from	ADP
ejpam-4803	102	21	the	the	DET
ejpam-4803	102	22	side	side	NOUN
ejpam-4803	102	23	of	of	ADP
ejpam-4803	102	24	u	u	NOUN
ejpam-4803	102	25	)	)	PUNCT
ejpam-4803	102	26	.	.	PUNCT
ejpam-4803	103	1	ii	ii	PROPN
ejpam-4803	103	2	)	)	PUNCT
ejpam-4803	103	3	for	for	ADP
ejpam-4803	103	4	each	each	DET
ejpam-4803	103	5	leaf	leaf	NOUN
ejpam-4803	103	6	f	f	PROPN
ejpam-4803	103	7	⊂	⊂	PROPN
ejpam-4803	103	8	u	u	PROPN
ejpam-4803	103	9	,	,	PUNCT
ejpam-4803	103	10	the	the	DET
ejpam-4803	103	11	intersection	intersection	NOUN
ejpam-4803	103	12	f	f	PROPN
ejpam-4803	103	13	∩	∩	NOUN
ejpam-4803	103	14	u	u	NOUN
ejpam-4803	103	15	contains	contain	VERB
ejpam-4803	103	16	a	a	DET
ejpam-4803	103	17	local	local	ADJ
ejpam-4803	103	18	minimal	minimal	ADJ
ejpam-4803	103	19	set	set	NOUN
ejpam-4803	103	20	in	in	ADP
ejpam-4803	103	21	u	u	PROPN
ejpam-4803	103	22	.	.	PUNCT
ejpam-4803	104	1	b	b	X
ejpam-4803	104	2	)	)	PUNCT
ejpam-4803	104	3	u	u	NOUN
ejpam-4803	104	4	is	be	AUX
ejpam-4803	104	5	compact	compact	ADJ
ejpam-4803	104	6	by	by	ADP
ejpam-4803	104	7	saturation	saturation	NOUN
ejpam-4803	104	8	.	.	PUNCT
ejpam-4803	105	1	lemma	lemma	PROPN
ejpam-4803	105	2	2.7	2.7	NUM
ejpam-4803	105	3	.	.	PUNCT
ejpam-4803	106	1	[	[	X
ejpam-4803	106	2	4	4	NUM
ejpam-4803	106	3	,	,	PUNCT
ejpam-4803	106	4	chapter	chapter	NOUN
ejpam-4803	106	5	4.4	4.4	NUM
ejpam-4803	106	6	]	]	PUNCT
ejpam-4803	106	7	for	for	ADP
ejpam-4803	106	8	each	each	DET
ejpam-4803	106	9	leaf	leaf	NOUN
ejpam-4803	106	10	f	f	NOUN
ejpam-4803	106	11	of	of	ADP
ejpam-4803	106	12	a	a	DET
ejpam-4803	106	13	nonempty	nonempty	ADV
ejpam-4803	106	14	invariant	invariant	ADJ
ejpam-4803	106	15	open	open	ADJ
ejpam-4803	106	16	subset	subset	NOUN
ejpam-4803	106	17	u	u	PROPN
ejpam-4803	106	18	⊂	⊂	PROPN
ejpam-4803	106	19	m	m	PROPN
ejpam-4803	106	20	,	,	PUNCT
ejpam-4803	106	21	the	the	DET
ejpam-4803	106	22	intersection	intersection	NOUN
ejpam-4803	106	23	f	f	PROPN
ejpam-4803	106	24	∩	∩	NOUN
ejpam-4803	106	25	u	u	NOUN
ejpam-4803	106	26	contains	contain	VERB
ejpam-4803	106	27	at	at	ADP
ejpam-4803	106	28	most	most	ADV
ejpam-4803	106	29	finitely	finitely	ADV
ejpam-4803	106	30	many	many	ADJ
ejpam-4803	106	31	local	local	ADJ
ejpam-4803	106	32	minimal	minimal	ADJ
ejpam-4803	106	33	sets	set	NOUN
ejpam-4803	106	34	in	in	ADP
ejpam-4803	106	35	u	u	NOUN
ejpam-4803	106	36	.	.	PUNCT
ejpam-4803	107	1	let	let	VERB
ejpam-4803	107	2	x	x	SYM
ejpam-4803	107	3	=	=	NOUN
ejpam-4803	107	4	m	m	PROPN
ejpam-4803	107	5	/	/	SYM
ejpam-4803	107	6	f̃	f̃	PROPN
ejpam-4803	107	7	be	be	VERB
ejpam-4803	107	8	the	the	DET
ejpam-4803	107	9	leaf	leaf	NOUN
ejpam-4803	107	10	classes	class	NOUN
ejpam-4803	107	11	space	space	NOUN
ejpam-4803	107	12	.	.	PUNCT
ejpam-4803	108	1	consider	consider	VERB
ejpam-4803	108	2	x0	x0	PROPN
ejpam-4803	108	3	the	the	DET
ejpam-4803	108	4	union	union	NOUN
ejpam-4803	108	5	of	of	ADP
ejpam-4803	108	6	all	all	DET
ejpam-4803	108	7	open	open	ADJ
ejpam-4803	108	8	subsets	subset	NOUN
ejpam-4803	108	9	of	of	ADP
ejpam-4803	108	10	x	x	X
ejpam-4803	108	11	homeomorphic	homeomorphic	ADJ
ejpam-4803	108	12	to	to	ADP
ejpam-4803	108	13	r	r	NOUN
ejpam-4803	108	14	or	or	CCONJ
ejpam-4803	108	15	s1	s1	NOUN
ejpam-4803	108	16	.	.	PUNCT
ejpam-4803	109	1	proposition	proposition	NOUN
ejpam-4803	109	2	2.8	2.8	NUM
ejpam-4803	109	3	.	.	PUNCT
ejpam-4803	110	1	[	[	X
ejpam-4803	110	2	3	3	X
ejpam-4803	110	3	]	]	X
ejpam-4803	110	4	the	the	DET
ejpam-4803	110	5	inverse	inverse	NOUN
ejpam-4803	110	6	image	image	NOUN
ejpam-4803	110	7	of	of	ADP
ejpam-4803	110	8	x0	x0	PROPN
ejpam-4803	110	9	by	by	ADP
ejpam-4803	110	10	the	the	DET
ejpam-4803	110	11	canonical	canonical	ADJ
ejpam-4803	110	12	projection	projection	NOUN
ejpam-4803	110	13	p	p	NOUN
ejpam-4803	110	14	is	be	AUX
ejpam-4803	110	15	the	the	DET
ejpam-4803	110	16	union	union	NOUN
ejpam-4803	110	17	of	of	ADP
ejpam-4803	110	18	all	all	DET
ejpam-4803	110	19	stable	stable	ADJ
ejpam-4803	110	20	proper	proper	ADJ
ejpam-4803	110	21	leaves	leave	NOUN
ejpam-4803	110	22	.	.	PUNCT
ejpam-4803	111	1	bouacida	bouacida	PROPN
ejpam-4803	111	2	et	et	PROPN
ejpam-4803	111	3	all	all	PRON
ejpam-4803	111	4	showed	show	VERB
ejpam-4803	111	5	,	,	PUNCT
ejpam-4803	111	6	in	in	ADP
ejpam-4803	111	7	[	[	PUNCT
ejpam-4803	111	8	3	3	NUM
ejpam-4803	111	9	]	]	PUNCT
ejpam-4803	111	10	,	,	PUNCT
ejpam-4803	111	11	that	that	SCONJ
ejpam-4803	111	12	if	if	SCONJ
ejpam-4803	111	13	f	f	PROPN
ejpam-4803	111	14	has	have	VERB
ejpam-4803	111	15	a	a	DET
ejpam-4803	111	16	well	well	ADV
ejpam-4803	111	17	defined	define	VERB
ejpam-4803	111	18	height	height	NOUN
ejpam-4803	111	19	,	,	PUNCT
ejpam-4803	111	20	then	then	ADV
ejpam-4803	111	21	the	the	DET
ejpam-4803	111	22	singular	singular	ADJ
ejpam-4803	111	23	part	part	NOUN
ejpam-4803	111	24	x−x0	x−x0	NOUN
ejpam-4803	111	25	of	of	ADP
ejpam-4803	111	26	the	the	DET
ejpam-4803	111	27	leaf	leaf	NOUN
ejpam-4803	111	28	classes	class	NOUN
ejpam-4803	111	29	space	space	NOUN
ejpam-4803	111	30	is	be	AUX
ejpam-4803	111	31	homeomorphic	homeomorphic	ADJ
ejpam-4803	111	32	to	to	ADP
ejpam-4803	111	33	the	the	DET
ejpam-4803	111	34	spectrum	spectrum	NOUN
ejpam-4803	111	35	of	of	ADP
ejpam-4803	111	36	a	a	DET
ejpam-4803	111	37	unitary	unitary	ADJ
ejpam-4803	111	38	commutative	commutative	ADJ
ejpam-4803	111	39	ring	ring	NOUN
ejpam-4803	111	40	equipped	equip	VERB
ejpam-4803	111	41	with	with	ADP
ejpam-4803	111	42	the	the	DET
ejpam-4803	111	43	zariski	zariski	NOUN
ejpam-4803	111	44	topology	topology	NOUN
ejpam-4803	111	45	.	.	PUNCT
ejpam-4803	112	1	note	note	VERB
ejpam-4803	112	2	that	that	SCONJ
ejpam-4803	112	3	,	,	PUNCT
ejpam-4803	112	4	the	the	DET
ejpam-4803	112	5	height	height	NOUN
ejpam-4803	112	6	of	of	ADP
ejpam-4803	112	7	a	a	DET
ejpam-4803	112	8	foliation	foliation	NOUN
ejpam-4803	112	9	is	be	AUX
ejpam-4803	112	10	well	well	ADV
ejpam-4803	112	11	defined	define	VERB
ejpam-4803	112	12	[	[	PUNCT
ejpam-4803	112	13	4	4	NUM
ejpam-4803	112	14	,	,	PUNCT
ejpam-4803	112	15	chapter	chapter	NOUN
ejpam-4803	112	16	4.4	4.4	NUM
ejpam-4803	112	17	]	]	PUNCT
ejpam-4803	112	18	if	if	SCONJ
ejpam-4803	112	19	and	and	CCONJ
ejpam-4803	112	20	only	only	ADV
ejpam-4803	112	21	if	if	SCONJ
ejpam-4803	112	22	every	every	PRON
ejpam-4803	112	23	totally	totally	ADV
ejpam-4803	112	24	ordered	order	VERB
ejpam-4803	112	25	family	family	NOUN
ejpam-4803	112	26	of	of	ADP
ejpam-4803	112	27	leaves	leave	NOUN
ejpam-4803	112	28	is	be	AUX
ejpam-4803	112	29	well	well	ADV
ejpam-4803	112	30	-	-	PUNCT
ejpam-4803	112	31	ordered	order	VERB
ejpam-4803	112	32	(	(	PUNCT
ejpam-4803	112	33	i.e.	i.e.	X
ejpam-4803	112	34	it	it	PRON
ejpam-4803	112	35	has	have	AUX
ejpam-4803	112	36	a	a	DET
ejpam-4803	112	37	minimal	minimal	ADJ
ejpam-4803	112	38	element	element	NOUN
ejpam-4803	112	39	)	)	PUNCT
ejpam-4803	112	40	.	.	PUNCT
ejpam-4803	113	1	recall	recall	VERB
ejpam-4803	113	2	that	that	SCONJ
ejpam-4803	113	3	a	a	DET
ejpam-4803	113	4	family	family	NOUN
ejpam-4803	113	5	of	of	ADP
ejpam-4803	113	6	leaves	leave	NOUN
ejpam-4803	113	7	is	be	AUX
ejpam-4803	113	8	ordered	order	VERB
ejpam-4803	113	9	by	by	ADP
ejpam-4803	113	10	inclusion	inclusion	NOUN
ejpam-4803	113	11	of	of	ADP
ejpam-4803	113	12	their	their	PRON
ejpam-4803	113	13	closures	closure	NOUN
ejpam-4803	113	14	.	.	PUNCT
ejpam-4803	114	1	precisely	precisely	ADV
ejpam-4803	114	2	,	,	PUNCT
ejpam-4803	114	3	the	the	DET
ejpam-4803	114	4	authors	author	NOUN
ejpam-4803	114	5	of	of	ADP
ejpam-4803	114	6	[	[	X
ejpam-4803	114	7	3	3	NUM
ejpam-4803	114	8	]	]	PUNCT
ejpam-4803	114	9	showed	show	VERB
ejpam-4803	114	10	that	that	SCONJ
ejpam-4803	114	11	x	x	PUNCT
ejpam-4803	114	12	−x0	−x0	NOUN
ejpam-4803	114	13	verifies	verify	VERB
ejpam-4803	114	14	the	the	DET
ejpam-4803	114	15	following	follow	VERB
ejpam-4803	114	16	properties	property	NOUN
ejpam-4803	114	17	:	:	PUNCT
ejpam-4803	114	18	(	(	PUNCT
ejpam-4803	114	19	1	1	X
ejpam-4803	114	20	)	)	PUNCT
ejpam-4803	114	21	x	x	SYM
ejpam-4803	114	22	−x0	−x0	NOUN
ejpam-4803	114	23	is	be	AUX
ejpam-4803	114	24	a	a	DET
ejpam-4803	114	25	sober	sober	ADJ
ejpam-4803	114	26	space	space	NOUN
ejpam-4803	114	27	.	.	PUNCT
ejpam-4803	115	1	b.	b.	PROPN
ejpam-4803	115	2	alharbi	alharbi	PROPN
ejpam-4803	115	3	/	/	SYM
ejpam-4803	115	4	eur	eur	PROPN
ejpam-4803	115	5	.	.	PUNCT
ejpam-4803	116	1	j.	j.	PROPN
ejpam-4803	116	2	pure	pure	PROPN
ejpam-4803	116	3	appl	appl	PROPN
ejpam-4803	116	4	.	.	PROPN
ejpam-4803	116	5	math	math	PROPN
ejpam-4803	116	6	,	,	PUNCT
ejpam-4803	116	7	17	17	NUM
ejpam-4803	116	8	(	(	PUNCT
ejpam-4803	116	9	1	1	NUM
ejpam-4803	116	10	)	)	PUNCT
ejpam-4803	116	11	(	(	PUNCT
ejpam-4803	116	12	2024	2024	NUM
ejpam-4803	116	13	)	)	PUNCT
ejpam-4803	116	14	,	,	PUNCT
ejpam-4803	116	15	356	356	NUM
ejpam-4803	116	16	-	-	SYM
ejpam-4803	116	17	361	361	NUM
ejpam-4803	116	18	360	360	NUM
ejpam-4803	116	19	(	(	PUNCT
ejpam-4803	116	20	2	2	NUM
ejpam-4803	116	21	)	)	PUNCT
ejpam-4803	116	22	x	x	SYM
ejpam-4803	117	1	−x0	−x0	NOUN
ejpam-4803	117	2	is	be	AUX
ejpam-4803	117	3	a	a	DET
ejpam-4803	117	4	quasi	quasi	ADJ
ejpam-4803	117	5	-	-	ADJ
ejpam-4803	117	6	compact	compact	ADJ
ejpam-4803	117	7	space	space	NOUN
ejpam-4803	117	8	.	.	PUNCT
ejpam-4803	118	1	(	(	PUNCT
ejpam-4803	118	2	3	3	X
ejpam-4803	118	3	)	)	PUNCT
ejpam-4803	118	4	x	x	SYM
ejpam-4803	118	5	−x0	−x0	NOUN
ejpam-4803	118	6	has	have	VERB
ejpam-4803	118	7	a	a	DET
ejpam-4803	118	8	basis	basis	NOUN
ejpam-4803	118	9	of	of	ADP
ejpam-4803	118	10	quasi	quasi	ADJ
ejpam-4803	118	11	-	-	ADJ
ejpam-4803	118	12	compact	compact	ADJ
ejpam-4803	118	13	open	open	ADJ
ejpam-4803	118	14	subsets	subset	NOUN
ejpam-4803	118	15	.	.	PUNCT
ejpam-4803	119	1	(	(	PUNCT
ejpam-4803	119	2	4	4	X
ejpam-4803	119	3	)	)	PUNCT
ejpam-4803	119	4	if	if	SCONJ
ejpam-4803	119	5	f	f	PROPN
ejpam-4803	119	6	has	have	VERB
ejpam-4803	119	7	a	a	DET
ejpam-4803	119	8	well	well	ADV
ejpam-4803	119	9	defined	define	VERB
ejpam-4803	119	10	height	height	NOUN
ejpam-4803	119	11	,	,	PUNCT
ejpam-4803	119	12	then	then	ADV
ejpam-4803	119	13	the	the	DET
ejpam-4803	119	14	family	family	NOUN
ejpam-4803	119	15	of	of	ADP
ejpam-4803	119	16	quasi	quasi	ADJ
ejpam-4803	119	17	-	-	ADJ
ejpam-4803	119	18	compact	compact	ADJ
ejpam-4803	119	19	open	open	ADJ
ejpam-4803	119	20	subsets	subset	NOUN
ejpam-4803	119	21	of	of	ADP
ejpam-4803	119	22	x	x	PART
ejpam-4803	119	23	−x0	−x0	NOUN
ejpam-4803	119	24	is	be	AUX
ejpam-4803	119	25	closed	close	VERB
ejpam-4803	119	26	under	under	ADP
ejpam-4803	119	27	finite	finite	ADJ
ejpam-4803	119	28	intersections	intersection	NOUN
ejpam-4803	119	29	.	.	PUNCT
ejpam-4803	120	1	in	in	ADP
ejpam-4803	120	2	this	this	DET
ejpam-4803	120	3	paper	paper	NOUN
ejpam-4803	120	4	we	we	PRON
ejpam-4803	120	5	prove	prove	VERB
ejpam-4803	120	6	that	that	SCONJ
ejpam-4803	120	7	the	the	DET
ejpam-4803	120	8	singular	singular	ADJ
ejpam-4803	120	9	part	part	NOUN
ejpam-4803	120	10	of	of	ADP
ejpam-4803	120	11	the	the	DET
ejpam-4803	120	12	space	space	NOUN
ejpam-4803	120	13	of	of	ADP
ejpam-4803	120	14	leaf	leaf	NOUN
ejpam-4803	120	15	classes	class	NOUN
ejpam-4803	120	16	is	be	AUX
ejpam-4803	120	17	homeomorphic	homeomorphic	ADJ
ejpam-4803	120	18	to	to	ADP
ejpam-4803	120	19	the	the	DET
ejpam-4803	120	20	spectrum	spectrum	NOUN
ejpam-4803	120	21	of	of	ADP
ejpam-4803	120	22	unitary	unitary	ADJ
ejpam-4803	120	23	commutative	commutative	ADJ
ejpam-4803	120	24	ring	ring	NOUN
ejpam-4803	120	25	if	if	SCONJ
ejpam-4803	120	26	and	and	CCONJ
ejpam-4803	120	27	only	only	ADV
ejpam-4803	120	28	if	if	SCONJ
ejpam-4803	120	29	every	every	DET
ejpam-4803	120	30	family	family	NOUN
ejpam-4803	120	31	of	of	ADP
ejpam-4803	120	32	totaly	totaly	PROPN
ejpam-4803	120	33	ordered	order	VERB
ejpam-4803	120	34	leaves	leave	NOUN
ejpam-4803	120	35	is	be	AUX
ejpam-4803	120	36	bounded	bound	VERB
ejpam-4803	120	37	below	below	ADV
ejpam-4803	120	38	(	(	PUNCT
ejpam-4803	120	39	theorem	theorem	ADJ
ejpam-4803	120	40	3.1	3.1	NUM
ejpam-4803	120	41	)	)	PUNCT
ejpam-4803	120	42	.	.	PUNCT
ejpam-4803	121	1	3	3	X
ejpam-4803	121	2	.	.	X
ejpam-4803	121	3	main	main	ADJ
ejpam-4803	121	4	result	result	NOUN
ejpam-4803	121	5	theorem	theorem	VERB
ejpam-4803	121	6	3.1	3.1	NUM
ejpam-4803	121	7	.	.	PUNCT
ejpam-4803	122	1	let	let	VERB
ejpam-4803	122	2	f	f	PRON
ejpam-4803	122	3	be	be	AUX
ejpam-4803	122	4	a	a	DET
ejpam-4803	122	5	codimension	codimension	NOUN
ejpam-4803	122	6	-	-	PUNCT
ejpam-4803	122	7	one	one	NUM
ejpam-4803	122	8	transversally	transversally	ADV
ejpam-4803	122	9	oriented	orient	VERB
ejpam-4803	122	10	foliation	foliation	NOUN
ejpam-4803	122	11	of	of	ADP
ejpam-4803	122	12	class	class	NOUN
ejpam-4803	122	13	cr	cr	PROPN
ejpam-4803	122	14	,	,	PUNCT
ejpam-4803	122	15	r	r	NOUN
ejpam-4803	122	16	≥	≥	NOUN
ejpam-4803	122	17	0	0	NUM
ejpam-4803	122	18	,	,	PUNCT
ejpam-4803	122	19	on	on	ADP
ejpam-4803	122	20	a	a	DET
ejpam-4803	122	21	closed	closed	ADJ
ejpam-4803	122	22	manifold	manifold	ADJ
ejpam-4803	122	23	m	m	NOUN
ejpam-4803	122	24	.	.	PUNCT
ejpam-4803	123	1	consider	consider	VERB
ejpam-4803	123	2	x	x	PUNCT
ejpam-4803	123	3	the	the	DET
ejpam-4803	123	4	leaf	leaf	NOUN
ejpam-4803	123	5	classes	class	NOUN
ejpam-4803	123	6	space	space	NOUN
ejpam-4803	123	7	and	and	CCONJ
ejpam-4803	123	8	let	let	VERB
ejpam-4803	123	9	x0	x0	PROPN
ejpam-4803	123	10	be	be	AUX
ejpam-4803	123	11	the	the	DET
ejpam-4803	123	12	union	union	NOUN
ejpam-4803	123	13	of	of	ADP
ejpam-4803	123	14	all	all	DET
ejpam-4803	123	15	open	open	ADJ
ejpam-4803	123	16	subsets	subset	NOUN
ejpam-4803	123	17	of	of	ADP
ejpam-4803	123	18	x	x	X
ejpam-4803	123	19	homeomorphic	homeomorphic	ADJ
ejpam-4803	123	20	to	to	ADP
ejpam-4803	123	21	r	r	NOUN
ejpam-4803	123	22	or	or	CCONJ
ejpam-4803	123	23	s1	s1	NOUN
ejpam-4803	123	24	.	.	PUNCT
ejpam-4803	124	1	then	then	ADV
ejpam-4803	124	2	,	,	PUNCT
ejpam-4803	124	3	the	the	DET
ejpam-4803	124	4	space	space	NOUN
ejpam-4803	124	5	x	x	PUNCT
ejpam-4803	124	6	−	−	NOUN
ejpam-4803	124	7	x0	x0	PROPN
ejpam-4803	124	8	is	be	AUX
ejpam-4803	124	9	homeomorphic	homeomorphic	ADJ
ejpam-4803	124	10	to	to	ADP
ejpam-4803	124	11	the	the	DET
ejpam-4803	124	12	spectrum	spectrum	NOUN
ejpam-4803	124	13	of	of	ADP
ejpam-4803	124	14	unitary	unitary	ADJ
ejpam-4803	124	15	commutative	commutative	ADJ
ejpam-4803	124	16	ring	ring	NOUN
ejpam-4803	124	17	if	if	SCONJ
ejpam-4803	125	1	and	and	CCONJ
ejpam-4803	125	2	only	only	ADV
ejpam-4803	125	3	if	if	SCONJ
ejpam-4803	125	4	every	every	DET
ejpam-4803	125	5	family	family	NOUN
ejpam-4803	125	6	of	of	ADP
ejpam-4803	125	7	totaly	totaly	PROPN
ejpam-4803	125	8	ordered	order	VERB
ejpam-4803	125	9	leaves	leave	NOUN
ejpam-4803	125	10	is	be	AUX
ejpam-4803	125	11	bounded	bound	VERB
ejpam-4803	125	12	below	below	ADV
ejpam-4803	125	13	.	.	PUNCT
ejpam-4803	126	1	we	we	PRON
ejpam-4803	126	2	need	need	VERB
ejpam-4803	126	3	the	the	DET
ejpam-4803	126	4	following	follow	VERB
ejpam-4803	126	5	lemmas	lemmas	NOUN
ejpam-4803	126	6	.	.	PUNCT
ejpam-4803	127	1	lemma	lemma	PROPN
ejpam-4803	127	2	3.2	3.2	NUM
ejpam-4803	127	3	.	.	PUNCT
ejpam-4803	128	1	[	[	X
ejpam-4803	128	2	3	3	X
ejpam-4803	128	3	]	]	PUNCT
ejpam-4803	128	4	let	let	VERB
ejpam-4803	128	5	f	f	PRON
ejpam-4803	128	6	be	be	AUX
ejpam-4803	128	7	a	a	DET
ejpam-4803	128	8	codimension	codimension	NOUN
ejpam-4803	128	9	-	-	PUNCT
ejpam-4803	128	10	one	one	NUM
ejpam-4803	128	11	transversally	transversally	ADV
ejpam-4803	128	12	oriented	orient	VERB
ejpam-4803	128	13	foliation	foliation	NOUN
ejpam-4803	128	14	of	of	ADP
ejpam-4803	128	15	class	class	NOUN
ejpam-4803	128	16	cr	cr	PROPN
ejpam-4803	128	17	,	,	PUNCT
ejpam-4803	128	18	r	r	NOUN
ejpam-4803	128	19	≥	≥	NOUN
ejpam-4803	128	20	0	0	NUM
ejpam-4803	128	21	,	,	PUNCT
ejpam-4803	128	22	on	on	ADP
ejpam-4803	128	23	a	a	DET
ejpam-4803	128	24	closed	closed	ADJ
ejpam-4803	128	25	manifold	manifold	ADJ
ejpam-4803	128	26	m	m	NOUN
ejpam-4803	128	27	.	.	PUNCT
ejpam-4803	129	1	consider	consider	VERB
ejpam-4803	129	2	x	x	PUNCT
ejpam-4803	129	3	the	the	DET
ejpam-4803	129	4	leaf	leaf	NOUN
ejpam-4803	129	5	classes	class	NOUN
ejpam-4803	129	6	space	space	NOUN
ejpam-4803	129	7	and	and	CCONJ
ejpam-4803	129	8	let	let	VERB
ejpam-4803	129	9	x0	x0	PROPN
ejpam-4803	129	10	be	be	AUX
ejpam-4803	129	11	the	the	DET
ejpam-4803	129	12	union	union	NOUN
ejpam-4803	129	13	of	of	ADP
ejpam-4803	129	14	all	all	DET
ejpam-4803	129	15	open	open	ADJ
ejpam-4803	129	16	subsets	subset	NOUN
ejpam-4803	129	17	of	of	ADP
ejpam-4803	129	18	x	x	X
ejpam-4803	129	19	homeomorphic	homeomorphic	ADJ
ejpam-4803	129	20	to	to	ADP
ejpam-4803	129	21	r	r	NOUN
ejpam-4803	129	22	or	or	CCONJ
ejpam-4803	129	23	s1	s1	NOUN
ejpam-4803	129	24	.	.	PUNCT
ejpam-4803	130	1	then	then	ADV
ejpam-4803	130	2	,	,	PUNCT
ejpam-4803	130	3	e	e	PRON
ejpam-4803	130	4	get	get	VERB
ejpam-4803	130	5	the	the	DET
ejpam-4803	130	6	following	follow	VERB
ejpam-4803	130	7	properties	property	NOUN
ejpam-4803	130	8	:	:	PUNCT
ejpam-4803	130	9	(	(	PUNCT
ejpam-4803	130	10	1	1	X
ejpam-4803	130	11	)	)	PUNCT
ejpam-4803	130	12	the	the	DET
ejpam-4803	130	13	space	space	NOUN
ejpam-4803	130	14	x	x	PUNCT
ejpam-4803	130	15	−x0	−x0	NOUN
ejpam-4803	130	16	is	be	AUX
ejpam-4803	130	17	sober	sober	ADJ
ejpam-4803	130	18	.	.	PUNCT
ejpam-4803	131	1	(	(	PUNCT
ejpam-4803	131	2	2	2	X
ejpam-4803	131	3	)	)	PUNCT
ejpam-4803	131	4	the	the	DET
ejpam-4803	131	5	space	space	NOUN
ejpam-4803	131	6	x	x	PUNCT
ejpam-4803	131	7	−x0	−x0	NOUN
ejpam-4803	131	8	is	be	AUX
ejpam-4803	131	9	quasi	quasi	ADJ
ejpam-4803	131	10	-	-	ADJ
ejpam-4803	131	11	compact	compact	ADJ
ejpam-4803	131	12	.	.	PUNCT
ejpam-4803	132	1	(	(	PUNCT
ejpam-4803	132	2	3	3	X
ejpam-4803	132	3	)	)	PUNCT
ejpam-4803	132	4	the	the	DET
ejpam-4803	132	5	space	space	NOUN
ejpam-4803	132	6	x	x	PUNCT
ejpam-4803	132	7	−x0	−x0	NOUN
ejpam-4803	132	8	has	have	VERB
ejpam-4803	132	9	a	a	DET
ejpam-4803	132	10	basis	basis	NOUN
ejpam-4803	132	11	of	of	ADP
ejpam-4803	132	12	quasi	quasi	ADJ
ejpam-4803	132	13	-	-	ADJ
ejpam-4803	132	14	compact	compact	ADJ
ejpam-4803	132	15	open	open	ADJ
ejpam-4803	132	16	subsets	subset	NOUN
ejpam-4803	132	17	.	.	PUNCT
ejpam-4803	133	1	proof	proof	NOUN
ejpam-4803	133	2	.	.	PUNCT
ejpam-4803	134	1	of	of	ADP
ejpam-4803	134	2	theorem	theorem	NOUN
ejpam-4803	134	3	3.1	3.1	NUM
ejpam-4803	134	4	.	.	PUNCT
ejpam-4803	135	1	if	if	SCONJ
ejpam-4803	135	2	x	x	SYM
ejpam-4803	135	3	−x0	−x0	NOUN
ejpam-4803	135	4	is	be	AUX
ejpam-4803	135	5	homeomorphic	homeomorphic	ADJ
ejpam-4803	135	6	to	to	ADP
ejpam-4803	135	7	the	the	DET
ejpam-4803	135	8	prime	prime	ADJ
ejpam-4803	135	9	spectrum	spectrum	NOUN
ejpam-4803	135	10	of	of	ADP
ejpam-4803	135	11	unitary	unitary	ADJ
ejpam-4803	135	12	commutative	commutative	ADJ
ejpam-4803	135	13	ring	ring	NOUN
ejpam-4803	135	14	,	,	PUNCT
ejpam-4803	135	15	then	then	ADV
ejpam-4803	135	16	it	it	PRON
ejpam-4803	135	17	satisfies	satisfy	VERB
ejpam-4803	135	18	the	the	DET
ejpam-4803	135	19	condition	condition	NOUN
ejpam-4803	135	20	(	(	PUNCT
ejpam-4803	135	21	k1	k1	NOUN
ejpam-4803	135	22	)	)	PUNCT
ejpam-4803	135	23	of	of	ADP
ejpam-4803	135	24	kaplansky	kaplansky	NOUN
ejpam-4803	135	25	and	and	CCONJ
ejpam-4803	135	26	so	so	ADV
ejpam-4803	135	27	every	every	DET
ejpam-4803	135	28	totally	totally	ADV
ejpam-4803	135	29	ordered	order	VERB
ejpam-4803	135	30	family	family	NOUN
ejpam-4803	135	31	of	of	ADP
ejpam-4803	135	32	orbits	orbit	NOUN
ejpam-4803	135	33	has	have	VERB
ejpam-4803	135	34	an	an	DET
ejpam-4803	135	35	infimum	infimum	NOUN
ejpam-4803	135	36	.	.	PUNCT
ejpam-4803	136	1	by	by	ADP
ejpam-4803	136	2	lemma	lemma	PROPN
ejpam-4803	136	3	3.2	3.2	NUM
ejpam-4803	136	4	,	,	PUNCT
ejpam-4803	136	5	x	x	PUNCT
ejpam-4803	136	6	−x0	−x0	NOUN
ejpam-4803	136	7	satisfies	satisfy	VERB
ejpam-4803	136	8	three	three	NUM
ejpam-4803	136	9	spectral	spectral	ADJ
ejpam-4803	136	10	properties	property	NOUN
ejpam-4803	136	11	(	(	PUNCT
ejpam-4803	136	12	1	1	NUM
ejpam-4803	136	13	)	)	PUNCT
ejpam-4803	136	14	,	,	PUNCT
ejpam-4803	136	15	(	(	PUNCT
ejpam-4803	136	16	2	2	X
ejpam-4803	136	17	)	)	PUNCT
ejpam-4803	136	18	and	and	CCONJ
ejpam-4803	136	19	(	(	PUNCT
ejpam-4803	136	20	3	3	NUM
ejpam-4803	136	21	)	)	PUNCT
ejpam-4803	136	22	.	.	PUNCT
ejpam-4803	137	1	it	it	PRON
ejpam-4803	137	2	suffices	suffice	VERB
ejpam-4803	137	3	to	to	PART
ejpam-4803	137	4	show	show	VERB
ejpam-4803	137	5	the	the	DET
ejpam-4803	137	6	fourth	fourth	ADJ
ejpam-4803	137	7	spectral	spectral	ADJ
ejpam-4803	137	8	property	property	NOUN
ejpam-4803	137	9	,	,	PUNCT
ejpam-4803	137	10	that	that	ADV
ejpam-4803	137	11	is	is	ADV
ejpam-4803	137	12	,	,	PUNCT
ejpam-4803	137	13	if	if	SCONJ
ejpam-4803	137	14	every	every	DET
ejpam-4803	137	15	family	family	NOUN
ejpam-4803	137	16	of	of	ADP
ejpam-4803	137	17	totaly	totaly	PROPN
ejpam-4803	137	18	ordered	order	VERB
ejpam-4803	137	19	leaves	leave	NOUN
ejpam-4803	137	20	is	be	AUX
ejpam-4803	137	21	bounded	bound	VERB
ejpam-4803	137	22	below	below	ADV
ejpam-4803	137	23	,	,	PUNCT
ejpam-4803	137	24	then	then	ADV
ejpam-4803	137	25	the	the	DET
ejpam-4803	137	26	family	family	NOUN
ejpam-4803	137	27	of	of	ADP
ejpam-4803	137	28	quasi	quasi	ADJ
ejpam-4803	137	29	-	-	ADJ
ejpam-4803	137	30	compact	compact	ADJ
ejpam-4803	137	31	open	open	ADJ
ejpam-4803	137	32	subsets	subset	NOUN
ejpam-4803	137	33	of	of	ADP
ejpam-4803	137	34	x	x	PART
ejpam-4803	137	35	−x0	−x0	NOUN
ejpam-4803	137	36	is	be	AUX
ejpam-4803	137	37	closed	close	VERB
ejpam-4803	137	38	under	under	ADP
ejpam-4803	137	39	finite	finite	ADJ
ejpam-4803	137	40	intersections	intersection	NOUN
ejpam-4803	137	41	.	.	PUNCT
ejpam-4803	138	1	according	accord	VERB
ejpam-4803	138	2	to	to	ADP
ejpam-4803	138	3	lemma	lemma	PROPN
ejpam-4803	138	4	2.6	2.6	NUM
ejpam-4803	138	5	,	,	PUNCT
ejpam-4803	138	6	it	it	PRON
ejpam-4803	138	7	suffices	suffice	VERB
ejpam-4803	138	8	to	to	PART
ejpam-4803	138	9	show	show	VERB
ejpam-4803	138	10	that	that	SCONJ
ejpam-4803	138	11	the	the	DET
ejpam-4803	138	12	intersection	intersection	NOUN
ejpam-4803	138	13	w	w	NOUN
ejpam-4803	138	14	=	=	SYM
ejpam-4803	138	15	u	u	PROPN
ejpam-4803	138	16	∩	∩	NOUN
ejpam-4803	138	17	v	v	NOUN
ejpam-4803	138	18	of	of	ADP
ejpam-4803	138	19	two	two	NUM
ejpam-4803	138	20	compact	compact	ADJ
ejpam-4803	138	21	by	by	ADP
ejpam-4803	138	22	saturation	saturation	NOUN
ejpam-4803	138	23	open	open	ADJ
ejpam-4803	138	24	sets	set	NOUN
ejpam-4803	138	25	is	be	AUX
ejpam-4803	138	26	also	also	ADV
ejpam-4803	138	27	compact	compact	ADJ
ejpam-4803	138	28	by	by	ADP
ejpam-4803	138	29	saturation	saturation	NOUN
ejpam-4803	138	30	.	.	PUNCT
ejpam-4803	139	1	according	accord	VERB
ejpam-4803	139	2	to	to	ADP
ejpam-4803	139	3	that	that	DET
ejpam-4803	139	4	fact	fact	NOUN
ejpam-4803	139	5	that	that	SCONJ
ejpam-4803	139	6	δϵw	δϵw	NOUN
ejpam-4803	139	7	⊂	⊂	PROPN
ejpam-4803	139	8	δϵu	δϵu	PROPN
ejpam-4803	139	9	∪	∪	PROPN
ejpam-4803	139	10	δϵv	δϵv	PROPN
ejpam-4803	139	11	,	,	PUNCT
ejpam-4803	139	12	ϵ	ϵ	X
ejpam-4803	139	13	=	=	SYM
ejpam-4803	139	14	±	±	PROPN
ejpam-4803	139	15	,	,	PUNCT
ejpam-4803	139	16	we	we	PRON
ejpam-4803	139	17	prove	prove	VERB
ejpam-4803	139	18	that	that	SCONJ
ejpam-4803	139	19	w	w	ADJ
ejpam-4803	139	20	verifies	verifie	NOUN
ejpam-4803	139	21	the	the	DET
ejpam-4803	139	22	property	property	NOUN
ejpam-4803	139	23	a	a	DET
ejpam-4803	139	24	−	−	PROPN
ejpam-4803	139	25	ii	ii	NOUN
ejpam-4803	139	26	)	)	PUNCT
ejpam-4803	139	27	of	of	ADP
ejpam-4803	139	28	lemma	lemma	PROPN
ejpam-4803	139	29	2.6	2.6	NUM
ejpam-4803	139	30	.	.	PUNCT
ejpam-4803	140	1	we	we	PRON
ejpam-4803	140	2	can	can	AUX
ejpam-4803	140	3	suppose	suppose	VERB
ejpam-4803	140	4	that	that	SCONJ
ejpam-4803	140	5	w	w	PROPN
ejpam-4803	140	6	is	be	AUX
ejpam-4803	140	7	a	a	DET
ejpam-4803	140	8	connected	connected	ADJ
ejpam-4803	140	9	set	set	NOUN
ejpam-4803	140	10	,	,	PUNCT
ejpam-4803	140	11	differently	differently	ADV
ejpam-4803	140	12	we	we	PRON
ejpam-4803	140	13	can	can	AUX
ejpam-4803	140	14	take	take	VERB
ejpam-4803	140	15	the	the	DET
ejpam-4803	140	16	connected	connected	ADJ
ejpam-4803	140	17	component	component	NOUN
ejpam-4803	140	18	of	of	ADP
ejpam-4803	140	19	w	w	NOUN
ejpam-4803	140	20	containing	contain	VERB
ejpam-4803	140	21	a	a	DET
ejpam-4803	140	22	leaf	leaf	NOUN
ejpam-4803	141	1	f	f	X
ejpam-4803	142	1	⊂	⊂	PROPN
ejpam-4803	142	2	w	w	PROPN
ejpam-4803	142	3	.	.	PUNCT
ejpam-4803	143	1	consider	consider	VERB
ejpam-4803	143	2	{	{	PUNCT
ejpam-4803	143	3	fi	fi	NOUN
ejpam-4803	143	4	}	}	PUNCT
ejpam-4803	143	5	a	a	DET
ejpam-4803	143	6	maximal	maximal	ADJ
ejpam-4803	143	7	totally	totally	ADV
ejpam-4803	143	8	ordered	order	VERB
ejpam-4803	143	9	family	family	NOUN
ejpam-4803	143	10	of	of	ADP
ejpam-4803	143	11	leaves	leave	NOUN
ejpam-4803	143	12	such	such	ADJ
ejpam-4803	143	13	that	that	DET
ejpam-4803	143	14	fi	fi	NOUN
ejpam-4803	144	1	⊂	⊂	PROPN
ejpam-4803	144	2	f	f	X
ejpam-4803	145	1	∩w	∩w	ADV
ejpam-4803	145	2	,	,	PUNCT
ejpam-4803	145	3	for	for	ADP
ejpam-4803	145	4	every	every	DET
ejpam-4803	145	5	i	i	PROPN
ejpam-4803	145	6	,	,	PUNCT
ejpam-4803	145	7	and	and	CCONJ
ejpam-4803	145	8	we	we	PRON
ejpam-4803	145	9	denote	denote	VERB
ejpam-4803	145	10	by	by	ADP
ejpam-4803	145	11	l	l	PROPN
ejpam-4803	145	12	the	the	DET
ejpam-4803	145	13	greatest	greatest	ADV
ejpam-4803	145	14	lower	low	ADJ
ejpam-4803	145	15	bound	bind	VERB
ejpam-4803	145	16	leaf	leaf	NOUN
ejpam-4803	145	17	of	of	ADP
ejpam-4803	145	18	this	this	DET
ejpam-4803	145	19	family	family	NOUN
ejpam-4803	145	20	(	(	PUNCT
ejpam-4803	145	21	this	this	DET
ejpam-4803	145	22	leaf	leaf	NOUN
ejpam-4803	145	23	l	l	NOUN
ejpam-4803	145	24	exists	exist	VERB
ejpam-4803	145	25	from	from	ADP
ejpam-4803	145	26	the	the	DET
ejpam-4803	145	27	hypothesis	hypothesis	NOUN
ejpam-4803	145	28	)	)	PUNCT
ejpam-4803	145	29	.	.	PUNCT
ejpam-4803	146	1	according	accord	VERB
ejpam-4803	146	2	to	to	ADP
ejpam-4803	146	3	lemmas	lemmas	PROPN
ejpam-4803	146	4	2.7	2.7	NUM
ejpam-4803	146	5	and	and	CCONJ
ejpam-4803	146	6	2.6	2.6	NUM
ejpam-4803	146	7	-	-	PUNCT
ejpam-4803	146	8	a	a	DET
ejpam-4803	146	9	-	-	PUNCT
ejpam-4803	146	10	ii	ii	NOUN
ejpam-4803	146	11	)	)	PUNCT
ejpam-4803	146	12	,	,	PUNCT
ejpam-4803	146	13	there	there	PRON
ejpam-4803	146	14	exist	exist	VERB
ejpam-4803	146	15	two	two	NUM
ejpam-4803	146	16	local	local	ADJ
ejpam-4803	146	17	minimal	minimal	ADJ
ejpam-4803	146	18	references	reference	NOUN
ejpam-4803	146	19	361	361	NUM
ejpam-4803	146	20	sets	set	NOUN
ejpam-4803	146	21	e1	e1	NOUN
ejpam-4803	146	22	and	and	CCONJ
ejpam-4803	146	23	e2	e2	PROPN
ejpam-4803	146	24	of	of	ADP
ejpam-4803	146	25	f	f	PROPN
ejpam-4803	146	26	restricted	restrict	VERB
ejpam-4803	146	27	to	to	ADP
ejpam-4803	146	28	u	u	NOUN
ejpam-4803	146	29	and	and	CCONJ
ejpam-4803	146	30	v	v	NOUN
ejpam-4803	146	31	respectively	respectively	ADV
ejpam-4803	146	32	which	which	PRON
ejpam-4803	146	33	are	be	AUX
ejpam-4803	146	34	subsets	subset	NOUN
ejpam-4803	146	35	of	of	ADP
ejpam-4803	146	36	the	the	DET
ejpam-4803	146	37	closure	closure	NOUN
ejpam-4803	146	38	fi	fi	NOUN
ejpam-4803	146	39	,	,	PUNCT
ejpam-4803	146	40	for	for	ADP
ejpam-4803	146	41	every	every	DET
ejpam-4803	146	42	i.	i.	NOUN
ejpam-4803	146	43	consider	consider	VERB
ejpam-4803	146	44	l1	l1	PROPN
ejpam-4803	146	45	and	and	CCONJ
ejpam-4803	146	46	l2	l2	VERB
ejpam-4803	146	47	two	two	NUM
ejpam-4803	146	48	leaves	leave	NOUN
ejpam-4803	146	49	such	such	ADJ
ejpam-4803	146	50	as	as	ADP
ejpam-4803	146	51	l1	l1	PROPN
ejpam-4803	146	52	⊂	⊂	PROPN
ejpam-4803	146	53	e1	e1	PROPN
ejpam-4803	146	54	and	and	CCONJ
ejpam-4803	146	55	l2	l2	PROPN
ejpam-4803	146	56	⊂	⊂	PROPN
ejpam-4803	146	57	e2	e2	PROPN
ejpam-4803	146	58	.	.	PUNCT
ejpam-4803	147	1	therefore	therefore	ADV
ejpam-4803	147	2	l1	l1	PROPN
ejpam-4803	147	3	=	=	PROPN
ejpam-4803	147	4	e1	e1	PROPN
ejpam-4803	147	5	⊂	⊂	PROPN
ejpam-4803	147	6	l	l	NOUN
ejpam-4803	147	7	and	and	CCONJ
ejpam-4803	147	8	l2	l2	PROPN
ejpam-4803	147	9	=	=	SYM
ejpam-4803	147	10	e2	e2	PROPN
ejpam-4803	147	11	⊂	⊂	PROPN
ejpam-4803	147	12	l.	l.	PROPN
ejpam-4803	147	13	consequently	consequently	ADV
ejpam-4803	147	14	,	,	PUNCT
ejpam-4803	147	15	l	l	PROPN
ejpam-4803	147	16	⊂	⊂	PUNCT
ejpam-4803	147	17	u	u	NOUN
ejpam-4803	147	18	and	and	CCONJ
ejpam-4803	147	19	l	l	PROPN
ejpam-4803	147	20	⊂	⊂	PROPN
ejpam-4803	147	21	v	v	X
ejpam-4803	147	22	,	,	PUNCT
ejpam-4803	147	23	thus	thus	ADV
ejpam-4803	147	24	l	l	X
ejpam-4803	147	25	⊂	⊂	PROPN
ejpam-4803	147	26	w	w	NOUN
ejpam-4803	147	27	and	and	CCONJ
ejpam-4803	147	28	l∩w	l∩w	NOUN
ejpam-4803	147	29	is	be	AUX
ejpam-4803	147	30	a	a	DET
ejpam-4803	147	31	local	local	ADJ
ejpam-4803	147	32	minimal	minimal	ADJ
ejpam-4803	147	33	set	set	NOUN
ejpam-4803	147	34	of	of	ADP
ejpam-4803	147	35	f	f	PROPN
ejpam-4803	147	36	restricted	restrict	VERB
ejpam-4803	147	37	to	to	ADP
ejpam-4803	147	38	w	w	PROPN
ejpam-4803	147	39	.	.	PUNCT
ejpam-4803	148	1	differently	differently	ADV
ejpam-4803	148	2	,	,	PUNCT
ejpam-4803	148	3	there	there	PRON
ejpam-4803	148	4	is	be	VERB
ejpam-4803	148	5	a	a	DET
ejpam-4803	148	6	leaf	leaf	NOUN
ejpam-4803	148	7	s	s	NOUN
ejpam-4803	148	8	such	such	ADJ
ejpam-4803	148	9	that	that	PRON
ejpam-4803	148	10	s	s	VERB
ejpam-4803	148	11	̸=	̸=	PROPN
ejpam-4803	148	12	l	l	NOUN
ejpam-4803	148	13	and	and	CCONJ
ejpam-4803	148	14	s	s	NOUN
ejpam-4803	148	15	⊂	⊂	PROPN
ejpam-4803	148	16	l	l	NOUN
ejpam-4803	148	17	∩	∩	PROPN
ejpam-4803	148	18	w	w	X
ejpam-4803	148	19	.	.	PUNCT
ejpam-4803	149	1	thus	thus	ADV
ejpam-4803	149	2	the	the	DET
ejpam-4803	149	3	family	family	NOUN
ejpam-4803	149	4	{	{	PUNCT
ejpam-4803	149	5	fi	fi	NOUN
ejpam-4803	149	6	}	}	PUNCT
ejpam-4803	149	7	is	be	AUX
ejpam-4803	149	8	not	not	PART
ejpam-4803	149	9	maximal	maximal	ADJ
ejpam-4803	149	10	which	which	PRON
ejpam-4803	149	11	leads	lead	VERB
ejpam-4803	149	12	to	to	ADP
ejpam-4803	149	13	a	a	DET
ejpam-4803	149	14	contradiction	contradiction	NOUN
ejpam-4803	149	15	.	.	PUNCT
ejpam-4803	150	1	we	we	PRON
ejpam-4803	150	2	deduce	deduce	VERB
ejpam-4803	150	3	that	that	SCONJ
ejpam-4803	150	4	the	the	DET
ejpam-4803	150	5	open	open	ADJ
ejpam-4803	150	6	set	set	NOUN
ejpam-4803	150	7	w	w	NOUN
ejpam-4803	150	8	verifies	verifie	NOUN
ejpam-4803	150	9	the	the	DET
ejpam-4803	150	10	two	two	NUM
ejpam-4803	150	11	items	item	NOUN
ejpam-4803	150	12	of	of	ADP
ejpam-4803	150	13	the	the	DET
ejpam-4803	150	14	property	property	NOUN
ejpam-4803	150	15	a	a	NOUN
ejpam-4803	150	16	)	)	PUNCT
ejpam-4803	150	17	in	in	ADP
ejpam-4803	150	18	lemma	lemma	PROPN
ejpam-4803	150	19	2.6	2.6	NUM
ejpam-4803	150	20	.	.	PUNCT
ejpam-4803	151	1	therefore	therefore	ADV
ejpam-4803	151	2	w	w	ADP
ejpam-4803	151	3	it	it	PRON
ejpam-4803	151	4	is	be	AUX
ejpam-4803	151	5	a	a	DET
ejpam-4803	151	6	compact	compact	NOUN
ejpam-4803	151	7	by	by	ADP
ejpam-4803	151	8	saturation	saturation	NOUN
ejpam-4803	151	9	open	open	ADJ
ejpam-4803	151	10	set	set	NOUN
ejpam-4803	151	11	.	.	PUNCT
ejpam-4803	152	1	this	this	PRON
ejpam-4803	152	2	ends	end	VERB
ejpam-4803	152	3	the	the	DET
ejpam-4803	152	4	proof	proof	NOUN
ejpam-4803	152	5	of	of	ADP
ejpam-4803	152	6	theorem	theorem	ADJ
ejpam-4803	152	7	3.1	3.1	NUM
ejpam-4803	152	8	.	.	PUNCT
ejpam-4803	153	1	references	reference	NOUN
ejpam-4803	153	2	[	[	X
ejpam-4803	153	3	1	1	NUM
ejpam-4803	153	4	]	]	PUNCT
ejpam-4803	153	5	b.	b.	PROPN
ejpam-4803	153	6	alharbi	alharbi	PROPN
ejpam-4803	153	7	.	.	PUNCT
ejpam-4803	154	1	graphs	graph	NOUN
ejpam-4803	154	2	and	and	CCONJ
ejpam-4803	154	3	the	the	DET
ejpam-4803	154	4	prime	prime	ADJ
ejpam-4803	154	5	spectrum	spectrum	NOUN
ejpam-4803	154	6	of	of	ADP
ejpam-4803	154	7	unitary	unitary	ADJ
ejpam-4803	154	8	commutative	commutative	ADJ
ejpam-4803	154	9	rings	ring	NOUN
ejpam-4803	154	10	.	.	PUNCT
ejpam-4803	155	1	european	european	PROPN
ejpam-4803	155	2	journal	journal	PROPN
ejpam-4803	155	3	of	of	ADP
ejpam-4803	155	4	pure	pure	ADJ
ejpam-4803	155	5	and	and	CCONJ
ejpam-4803	155	6	applied	applied	ADJ
ejpam-4803	155	7	mathematics	mathematic	NOUN
ejpam-4803	155	8	,	,	PUNCT
ejpam-4803	155	9	16:314–318	16:314–318	NUM
ejpam-4803	155	10	,	,	PUNCT
ejpam-4803	155	11	2023	2023	NUM
ejpam-4803	155	12	.	.	PUNCT
ejpam-4803	156	1	[	[	X
ejpam-4803	156	2	2	2	X
ejpam-4803	156	3	]	]	PUNCT
ejpam-4803	156	4	e.	e.	PROPN
ejpam-4803	156	5	salhi	salhi	PROPN
ejpam-4803	156	6	e.	e.	PROPN
ejpam-4803	156	7	bouacida	bouacida	PROPN
ejpam-4803	156	8	,	,	PUNCT
ejpam-4803	156	9	o.	o.	PROPN
ejpam-4803	156	10	echi	echi	PROPN
ejpam-4803	156	11	.	.	PUNCT
ejpam-4803	157	1	foliations	foliation	NOUN
ejpam-4803	157	2	,	,	PUNCT
ejpam-4803	157	3	spectral	spectral	ADJ
ejpam-4803	157	4	topology	topology	NOUN
ejpam-4803	157	5	and	and	CCONJ
ejpam-4803	157	6	special	special	ADJ
ejpam-4803	157	7	morphism	morphism	NOUN
ejpam-4803	157	8	.	.	PUNCT
ejpam-4803	158	1	comm.ring.theory	comm.ring.theory	PROPN
ejpam-4803	158	2	iii	iii	NUM
ejpam-4803	158	3	lect.not.pure.appl.math.m.dekker	lect.not.pure.appl.math.m.dekker	NOUN
ejpam-4803	158	4	,	,	PUNCT
ejpam-4803	158	5	205:111–132	205:111–132	NUM
ejpam-4803	158	6	,	,	PUNCT
ejpam-4803	158	7	1999	1999	NUM
ejpam-4803	158	8	.	.	PUNCT
ejpam-4803	159	1	[	[	X
ejpam-4803	159	2	3	3	X
ejpam-4803	159	3	]	]	X
ejpam-4803	159	4	e.	e.	PROPN
ejpam-4803	159	5	salhi	salhi	PROPN
ejpam-4803	159	6	e.	e.	PROPN
ejpam-4803	159	7	bouacida	bouacida	PROPN
ejpam-4803	159	8	,	,	PUNCT
ejpam-4803	159	9	o.	o.	PROPN
ejpam-4803	159	10	echi	echi	PROPN
ejpam-4803	159	11	.	.	PUNCT
ejpam-4803	160	1	foliation	foliation	NOUN
ejpam-4803	160	2	and	and	CCONJ
ejpam-4803	160	3	spectral	spectral	ADJ
ejpam-4803	160	4	topology	topology	NOUN
ejpam-4803	160	5	.	.	PUNCT
ejpam-4803	161	1	j.	j.	PROPN
ejpam-4803	161	2	math	math	PROPN
ejpam-4803	161	3	.	.	PUNCT
ejpam-4803	162	1	soc	soc	PROPN
ejpam-4803	162	2	.	.	PUNCT
ejpam-4803	163	1	japan	japan	PROPN
ejpam-4803	163	2	,	,	PUNCT
ejpam-4803	163	3	52:447–464	52:447–464	PROPN
ejpam-4803	163	4	,	,	PUNCT
ejpam-4803	163	5	2000	2000	NUM
ejpam-4803	163	6	.	.	PUNCT
ejpam-4803	164	1	[	[	X
ejpam-4803	164	2	4	4	NUM
ejpam-4803	164	3	]	]	X
ejpam-4803	164	4	c.	c.	PROPN
ejpam-4803	164	5	godbillon	godbillon	PROPN
ejpam-4803	164	6	.	.	PROPN
ejpam-4803	164	7	feuilletages	feuilletage	NOUN
ejpam-4803	164	8	.	.	PUNCT
ejpam-4803	165	1	etudes	etude	VERB
ejpam-4803	165	2	géométriques	géométrique	NOUN
ejpam-4803	165	3	.	.	PUNCT
ejpam-4803	166	1	birkauser	birkauser	PROPN
ejpam-4803	166	2	-verlag	-verlag	PROPN
ejpam-4803	166	3	,	,	PUNCT
ejpam-4803	166	4	new	new	PROPN
ejpam-4803	166	5	york	york	PROPN
ejpam-4803	166	6	,	,	PUNCT
ejpam-4803	166	7	1991	1991	NUM
ejpam-4803	166	8	.	.	PUNCT
ejpam-4803	167	1	[	[	X
ejpam-4803	167	2	5	5	X
ejpam-4803	167	3	]	]	PUNCT
ejpam-4803	167	4	m.	m.	NOUN
ejpam-4803	167	5	hochster	hochster	NOUN
ejpam-4803	167	6	.	.	PUNCT
ejpam-4803	168	1	prime	prime	ADJ
ejpam-4803	168	2	ideal	ideal	ADJ
ejpam-4803	168	3	structure	structure	NOUN
ejpam-4803	168	4	in	in	ADP
ejpam-4803	168	5	commutative	commutative	ADJ
ejpam-4803	168	6	rings	ring	NOUN
ejpam-4803	168	7	.	.	PUNCT
ejpam-4803	169	1	trans	trans	PROPN
ejpam-4803	169	2	.	.	PUNCT
ejpam-4803	170	1	amer	amer	PROPN
ejpam-4803	170	2	.	.	PUNCT
ejpam-4803	170	3	math	math	PROPN
ejpam-4803	170	4	.	.	PUNCT
ejpam-4803	171	1	soc	soc	PROPN
ejpam-4803	171	2	.	.	PUNCT
ejpam-4803	171	3	,	,	PUNCT
ejpam-4803	171	4	142:43–60	142:43–60	NUM
ejpam-4803	171	5	,	,	PUNCT
ejpam-4803	171	6	1969	1969	NUM
ejpam-4803	171	7	.	.	PUNCT