id	sid	tid	token	lemma	pos
ejpam-4654	1	1	european	european	PROPN
ejpam-4654	1	2	journal	journal	PROPN
ejpam-4654	1	3	of	of	ADP
ejpam-4654	1	4	pure	pure	ADJ
ejpam-4654	1	5	and	and	CCONJ
ejpam-4654	1	6	applied	apply	VERB
ejpam-4654	1	7	mathematics	mathematic	NOUN
ejpam-4654	1	8	vol	vol	NOUN
ejpam-4654	1	9	.	.	PUNCT
ejpam-4654	2	1	16	16	NUM
ejpam-4654	2	2	,	,	PUNCT
ejpam-4654	2	3	no	no	INTJ
ejpam-4654	2	4	.	.	NOUN
ejpam-4654	2	5	1	1	NUM
ejpam-4654	2	6	,	,	PUNCT
ejpam-4654	2	7	2023	2023	NUM
ejpam-4654	2	8	,	,	PUNCT
ejpam-4654	2	9	314	314	NUM
ejpam-4654	2	10	-	-	SYM
ejpam-4654	2	11	318	318	NUM
ejpam-4654	2	12	issn	issn	PROPN
ejpam-4654	2	13	1307	1307	NUM
ejpam-4654	2	14	-	-	SYM
ejpam-4654	2	15	5543	5543	NUM
ejpam-4654	2	16	–	–	PUNCT
ejpam-4654	2	17	ejpam.com	ejpam.com	X
ejpam-4654	2	18	published	publish	VERB
ejpam-4654	2	19	by	by	ADP
ejpam-4654	2	20	new	new	PROPN
ejpam-4654	2	21	york	york	PROPN
ejpam-4654	2	22	business	business	NOUN
ejpam-4654	2	23	global	global	ADJ
ejpam-4654	2	24	graphs	graph	NOUN
ejpam-4654	2	25	and	and	CCONJ
ejpam-4654	2	26	the	the	DET
ejpam-4654	2	27	prime	prime	ADJ
ejpam-4654	2	28	spectrum	spectrum	NOUN
ejpam-4654	2	29	of	of	ADP
ejpam-4654	2	30	unitary	unitary	ADJ
ejpam-4654	2	31	commutative	commutative	ADJ
ejpam-4654	2	32	rings	ring	NOUN
ejpam-4654	2	33	badr	badr	PROPN
ejpam-4654	2	34	alharbi	alharbi	PROPN
ejpam-4654	2	35	umm	umm	INTJ
ejpam-4654	2	36	al	al	PROPN
ejpam-4654	2	37	-	-	PUNCT
ejpam-4654	2	38	qura	qura	PROPN
ejpam-4654	2	39	university	university	PROPN
ejpam-4654	2	40	,	,	PUNCT
ejpam-4654	2	41	al	al	PROPN
ejpam-4654	2	42	jumum	jumum	PROPN
ejpam-4654	2	43	university	university	PROPN
ejpam-4654	2	44	college	college	PROPN
ejpam-4654	2	45	,	,	PUNCT
ejpam-4654	2	46	department	department	NOUN
ejpam-4654	2	47	of	of	ADP
ejpam-4654	2	48	mathematics	mathematics	PROPN
ejpam-4654	2	49	abstract	abstract	NOUN
ejpam-4654	2	50	.	.	PUNCT
ejpam-4654	3	1	in	in	ADP
ejpam-4654	3	2	this	this	DET
ejpam-4654	3	3	paper	paper	NOUN
ejpam-4654	3	4	,	,	PUNCT
ejpam-4654	3	5	we	we	PRON
ejpam-4654	3	6	study	study	VERB
ejpam-4654	3	7	the	the	DET
ejpam-4654	3	8	relationships	relationship	NOUN
ejpam-4654	3	9	between	between	ADP
ejpam-4654	3	10	graphs	graph	NOUN
ejpam-4654	3	11	and	and	CCONJ
ejpam-4654	3	12	the	the	DET
ejpam-4654	3	13	prime	prime	ADJ
ejpam-4654	3	14	spectrum	spectrum	NOUN
ejpam-4654	3	15	of	of	ADP
ejpam-4654	3	16	unitary	unitary	ADJ
ejpam-4654	3	17	commutative	commutative	ADJ
ejpam-4654	3	18	rings	ring	NOUN
ejpam-4654	3	19	.	.	PUNCT
ejpam-4654	4	1	it	it	PRON
ejpam-4654	4	2	is	be	AUX
ejpam-4654	4	3	shown	show	VERB
ejpam-4654	4	4	that	that	SCONJ
ejpam-4654	4	5	a	a	DET
ejpam-4654	4	6	graph	graph	NOUN
ejpam-4654	4	7	g	g	NOUN
ejpam-4654	4	8	equipped	equip	VERB
ejpam-4654	4	9	with	with	ADP
ejpam-4654	4	10	the	the	DET
ejpam-4654	4	11	g	g	NOUN
ejpam-4654	4	12	-	-	PUNCT
ejpam-4654	4	13	right	right	NOUN
ejpam-4654	4	14	topology	topology	NOUN
ejpam-4654	4	15	satisfies	satisfy	VERB
ejpam-4654	4	16	some	some	DET
ejpam-4654	4	17	spectral	spectral	ADJ
ejpam-4654	4	18	properties	property	NOUN
ejpam-4654	4	19	.	.	PUNCT
ejpam-4654	5	1	in	in	ADP
ejpam-4654	5	2	particular	particular	ADJ
ejpam-4654	5	3	we	we	PRON
ejpam-4654	5	4	give	give	VERB
ejpam-4654	5	5	a	a	DET
ejpam-4654	5	6	necessarily	necessarily	ADV
ejpam-4654	5	7	and	and	CCONJ
ejpam-4654	5	8	sufficient	sufficient	ADJ
ejpam-4654	5	9	condition	condition	NOUN
ejpam-4654	5	10	to	to	PART
ejpam-4654	5	11	obtain	obtain	VERB
ejpam-4654	5	12	a	a	DET
ejpam-4654	5	13	spectral	spectral	ADJ
ejpam-4654	5	14	graph	graph	NOUN
ejpam-4654	5	15	.	.	PUNCT
ejpam-4654	6	1	2020	2020	NUM
ejpam-4654	6	2	mathematics	mathematic	NOUN
ejpam-4654	6	3	subject	subject	NOUN
ejpam-4654	6	4	classifications	classification	NOUN
ejpam-4654	6	5	:	:	PUNCT
ejpam-4654	6	6	54f65	54f65	NUM
ejpam-4654	6	7	,	,	PUNCT
ejpam-4654	6	8	54h20	54h20	NUM
ejpam-4654	6	9	key	key	ADJ
ejpam-4654	6	10	words	word	NOUN
ejpam-4654	6	11	and	and	CCONJ
ejpam-4654	6	12	phrases	phrase	NOUN
ejpam-4654	6	13	:	:	PUNCT
ejpam-4654	6	14	graph	graph	NOUN
ejpam-4654	6	15	,	,	PUNCT
ejpam-4654	6	16	spectral	spectral	ADJ
ejpam-4654	6	17	,	,	PUNCT
ejpam-4654	6	18	prime	prime	ADJ
ejpam-4654	6	19	spectrum	spectrum	NOUN
ejpam-4654	6	20	,	,	PUNCT
ejpam-4654	6	21	ring	ring	NOUN
ejpam-4654	6	22	,	,	PUNCT
ejpam-4654	6	23	alexandroff	alexandroff	ADJ
ejpam-4654	6	24	space	space	NOUN
ejpam-4654	6	25	1	1	NUM
ejpam-4654	6	26	.	.	PUNCT
ejpam-4654	6	27	introduction	introduction	NOUN
ejpam-4654	6	28	in	in	ADP
ejpam-4654	6	29	[	[	X
ejpam-4654	6	30	4	4	NUM
ejpam-4654	6	31	]	]	PUNCT
ejpam-4654	6	32	,	,	PUNCT
ejpam-4654	6	33	hochster	hochster	PROPN
ejpam-4654	6	34	proved	prove	VERB
ejpam-4654	6	35	that	that	SCONJ
ejpam-4654	6	36	an	an	DET
ejpam-4654	6	37	ordered	order	VERB
ejpam-4654	6	38	set	set	NOUN
ejpam-4654	6	39	(	(	PUNCT
ejpam-4654	6	40	y,≤	y,≤	ADJ
ejpam-4654	6	41	)	)	PUNCT
ejpam-4654	6	42	is	be	AUX
ejpam-4654	6	43	order	order	NOUN
ejpam-4654	6	44	-	-	PUNCT
ejpam-4654	6	45	isomorphic	isomorphic	ADJ
ejpam-4654	6	46	to	to	ADP
ejpam-4654	6	47	the	the	DET
ejpam-4654	6	48	prime	prime	ADJ
ejpam-4654	6	49	spectrum	spectrum	NOUN
ejpam-4654	6	50	of	of	ADP
ejpam-4654	6	51	a	a	DET
ejpam-4654	6	52	commutative	commutative	ADJ
ejpam-4654	6	53	ring	ring	NOUN
ejpam-4654	6	54	with	with	ADP
ejpam-4654	6	55	unit	unit	NOUN
ejpam-4654	6	56	equipped	equip	VERB
ejpam-4654	6	57	with	with	ADP
ejpam-4654	6	58	the	the	DET
ejpam-4654	6	59	inclusion	inclusion	NOUN
ejpam-4654	6	60	if	if	SCONJ
ejpam-4654	6	61	and	and	CCONJ
ejpam-4654	6	62	only	only	ADV
ejpam-4654	6	63	if	if	SCONJ
ejpam-4654	6	64	the	the	DET
ejpam-4654	6	65	set	set	NOUN
ejpam-4654	6	66	y	y	PROPN
ejpam-4654	6	67	is	be	AUX
ejpam-4654	6	68	equipped	equip	VERB
ejpam-4654	6	69	with	with	ADP
ejpam-4654	6	70	a	a	DET
ejpam-4654	6	71	topology	topology	NOUN
ejpam-4654	6	72	compatible	compatible	ADJ
ejpam-4654	6	73	with	with	ADP
ejpam-4654	6	74	the	the	DET
ejpam-4654	6	75	order	order	NOUN
ejpam-4654	6	76	and	and	CCONJ
ejpam-4654	6	77	satisfying	satisfy	VERB
ejpam-4654	6	78	the	the	DET
ejpam-4654	6	79	following	follow	VERB
ejpam-4654	6	80	properties	property	NOUN
ejpam-4654	6	81	:	:	PUNCT
ejpam-4654	6	82	i	i	X
ejpam-4654	6	83	)	)	PUNCT
ejpam-4654	6	84	x	x	X
ejpam-4654	6	85	is	be	AUX
ejpam-4654	6	86	a	a	DET
ejpam-4654	6	87	quasi	quasi	ADJ
ejpam-4654	6	88	-	-	ADJ
ejpam-4654	6	89	compact	compact	ADJ
ejpam-4654	6	90	space	space	NOUN
ejpam-4654	6	91	.	.	PUNCT
ejpam-4654	7	1	ii	ii	X
ejpam-4654	7	2	)	)	PUNCT
ejpam-4654	7	3	x	x	PUNCT
ejpam-4654	7	4	is	be	AUX
ejpam-4654	7	5	a	a	DET
ejpam-4654	7	6	t0	t0	NOUN
ejpam-4654	7	7	-	-	NOUN
ejpam-4654	7	8	space	space	NOUN
ejpam-4654	7	9	.	.	PUNCT
ejpam-4654	8	1	iii	iii	X
ejpam-4654	8	2	)	)	PUNCT
ejpam-4654	8	3	each	each	DET
ejpam-4654	8	4	irreducible	irreducible	ADJ
ejpam-4654	8	5	closed	close	VERB
ejpam-4654	8	6	subset	subset	NOUN
ejpam-4654	8	7	has	have	VERB
ejpam-4654	8	8	a	a	DET
ejpam-4654	8	9	generic	generic	ADJ
ejpam-4654	8	10	point	point	NOUN
ejpam-4654	8	11	.	.	PUNCT
ejpam-4654	9	1	iv	iv	X
ejpam-4654	9	2	)	)	PUNCT
ejpam-4654	9	3	x	x	PUNCT
ejpam-4654	9	4	has	have	VERB
ejpam-4654	9	5	a	a	DET
ejpam-4654	9	6	basis	basis	NOUN
ejpam-4654	9	7	of	of	ADP
ejpam-4654	9	8	quasi	quasi	ADJ
ejpam-4654	9	9	-	-	ADJ
ejpam-4654	9	10	compact	compact	ADJ
ejpam-4654	9	11	open	open	ADJ
ejpam-4654	9	12	subsets	subset	NOUN
ejpam-4654	9	13	.	.	PUNCT
ejpam-4654	10	1	v	v	X
ejpam-4654	10	2	)	)	PUNCT
ejpam-4654	10	3	the	the	DET
ejpam-4654	10	4	intersection	intersection	NOUN
ejpam-4654	10	5	of	of	ADP
ejpam-4654	10	6	two	two	NUM
ejpam-4654	10	7	quasi	quasi	ADJ
ejpam-4654	10	8	-	-	ADJ
ejpam-4654	10	9	compact	compact	ADJ
ejpam-4654	10	10	open	open	ADJ
ejpam-4654	10	11	subsets	subset	NOUN
ejpam-4654	10	12	is	be	AUX
ejpam-4654	10	13	quasi	quasi	ADJ
ejpam-4654	10	14	-	-	ADJ
ejpam-4654	10	15	compact	compact	ADJ
ejpam-4654	10	16	.	.	PUNCT
ejpam-4654	11	1	the	the	DET
ejpam-4654	11	2	above	above	ADJ
ejpam-4654	11	3	five	five	NUM
ejpam-4654	11	4	properties	property	NOUN
ejpam-4654	11	5	are	be	AUX
ejpam-4654	11	6	called	call	VERB
ejpam-4654	11	7	spectral	spectral	ADJ
ejpam-4654	11	8	properties	property	NOUN
ejpam-4654	11	9	.	.	PUNCT
ejpam-4654	12	1	note	note	VERB
ejpam-4654	12	2	that	that	SCONJ
ejpam-4654	12	3	a	a	DET
ejpam-4654	12	4	topology	topology	NOUN
ejpam-4654	12	5	compatible	compatible	ADJ
ejpam-4654	12	6	with	with	ADP
ejpam-4654	12	7	the	the	DET
ejpam-4654	12	8	order	order	NOUN
ejpam-4654	12	9	is	be	AUX
ejpam-4654	12	10	always	always	ADV
ejpam-4654	12	11	t0	t0	X
ejpam-4654	12	12	[	[	X
ejpam-4654	12	13	2	2	NUM
ejpam-4654	12	14	]	]	PUNCT
ejpam-4654	12	15	.	.	PUNCT
ejpam-4654	13	1	a	a	DET
ejpam-4654	13	2	topology	topology	NOUN
ejpam-4654	13	3	defined	define	VERB
ejpam-4654	13	4	on	on	ADP
ejpam-4654	13	5	the	the	DET
ejpam-4654	13	6	set	set	NOUN
ejpam-4654	13	7	y	y	PROPN
ejpam-4654	13	8	satisfying	satisfy	VERB
ejpam-4654	13	9	the	the	DET
ejpam-4654	13	10	properties	property	NOUN
ejpam-4654	13	11	i	i	PRON
ejpam-4654	13	12	)	)	PUNCT
ejpam-4654	13	13	,	,	PUNCT
ejpam-4654	13	14	iii	iii	PROPN
ejpam-4654	13	15	)	)	PUNCT
ejpam-4654	13	16	,	,	PUNCT
ejpam-4654	13	17	iv	iv	X
ejpam-4654	13	18	)	)	PUNCT
ejpam-4654	13	19	and	and	CCONJ
ejpam-4654	13	20	v	v	NOUN
ejpam-4654	13	21	)	)	PUNCT
ejpam-4654	13	22	is	be	AUX
ejpam-4654	13	23	called	call	VERB
ejpam-4654	13	24	a	a	DET
ejpam-4654	13	25	quasi	quasi	ADJ
ejpam-4654	13	26	-	-	ADJ
ejpam-4654	13	27	spectral	spectral	ADJ
ejpam-4654	13	28	topology	topology	NOUN
ejpam-4654	13	29	.	.	PUNCT
ejpam-4654	14	1	doi	doi	NOUN
ejpam-4654	14	2	:	:	PUNCT
ejpam-4654	14	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4654	https://doi.org/10.29020/nybg.ejpam.v16i1.4654	ADJ
ejpam-4654	14	4	email	email	NOUN
ejpam-4654	14	5	address	address	NOUN
ejpam-4654	14	6	:	:	PUNCT
ejpam-4654	14	7	bhharbi@uqu.edu.sa	bhharbi@uqu.edu.sa	PROPN
ejpam-4654	14	8	(	(	PUNCT
ejpam-4654	14	9	b.	b.	PROPN
ejpam-4654	14	10	alharbi	alharbi	PROPN
ejpam-4654	14	11	)	)	PUNCT
ejpam-4654	14	12	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4654	14	13	314	314	NUM
ejpam-4654	15	1	©	©	ADP
ejpam-4654	15	2	2023	2023	NUM
ejpam-4654	15	3	ejpam	ejpam	NOUN
ejpam-4654	15	4	all	all	DET
ejpam-4654	15	5	rights	right	NOUN
ejpam-4654	15	6	reserved	reserve	VERB
ejpam-4654	15	7	.	.	PUNCT
ejpam-4654	16	1	b.	b.	PROPN
ejpam-4654	16	2	alharbi	alharbi	PROPN
ejpam-4654	16	3	/	/	SYM
ejpam-4654	16	4	eur	eur	PROPN
ejpam-4654	16	5	.	.	PUNCT
ejpam-4654	17	1	j.	j.	PROPN
ejpam-4654	17	2	pure	pure	PROPN
ejpam-4654	17	3	appl	appl	PROPN
ejpam-4654	17	4	.	.	PROPN
ejpam-4654	17	5	math	math	PROPN
ejpam-4654	17	6	,	,	PUNCT
ejpam-4654	17	7	16	16	NUM
ejpam-4654	17	8	(	(	PUNCT
ejpam-4654	17	9	1	1	NUM
ejpam-4654	17	10	)	)	PUNCT
ejpam-4654	17	11	(	(	PUNCT
ejpam-4654	17	12	2023	2023	NUM
ejpam-4654	17	13	)	)	PUNCT
ejpam-4654	17	14	,	,	PUNCT
ejpam-4654	17	15	314	314	NUM
ejpam-4654	17	16	-	-	SYM
ejpam-4654	17	17	318	318	NUM
ejpam-4654	17	18	315	315	NUM
ejpam-4654	17	19	•	•	NOUN
ejpam-4654	17	20	the	the	DET
ejpam-4654	17	21	space	space	NOUN
ejpam-4654	17	22	x	x	PUNCT
ejpam-4654	17	23	is	be	AUX
ejpam-4654	17	24	said	say	VERB
ejpam-4654	17	25	to	to	PART
ejpam-4654	17	26	be	be	AUX
ejpam-4654	17	27	quasi	quasi	ADJ
ejpam-4654	17	28	-	-	ADJ
ejpam-4654	17	29	compact	compact	ADJ
ejpam-4654	17	30	if	if	SCONJ
ejpam-4654	17	31	it	it	PRON
ejpam-4654	17	32	satisfies	satisfy	VERB
ejpam-4654	17	33	the	the	DET
ejpam-4654	17	34	property	property	NOUN
ejpam-4654	17	35	of	of	ADP
ejpam-4654	17	36	borel	borel	NOUN
ejpam-4654	17	37	-	-	PUNCT
ejpam-4654	17	38	lebesgue	lebesgue	PROPN
ejpam-4654	17	39	but	but	CCONJ
ejpam-4654	17	40	it	it	PRON
ejpam-4654	17	41	is	be	AUX
ejpam-4654	17	42	not	not	PART
ejpam-4654	17	43	necessarily	necessarily	ADV
ejpam-4654	17	44	a	a	DET
ejpam-4654	17	45	hausdorff	hausdorff	NOUN
ejpam-4654	17	46	space	space	NOUN
ejpam-4654	17	47	.	.	PUNCT
ejpam-4654	18	1	•	•	ADP
ejpam-4654	18	2	a	a	DET
ejpam-4654	18	3	topological	topological	ADJ
ejpam-4654	18	4	spacex	spacex	NOUN
ejpam-4654	18	5	is	be	AUX
ejpam-4654	18	6	a	a	DET
ejpam-4654	18	7	t0	t0	NOUN
ejpam-4654	18	8	-	-	NOUN
ejpam-4654	18	9	space	space	NOUN
ejpam-4654	18	10	(	(	PUNCT
ejpam-4654	18	11	or	or	CCONJ
ejpam-4654	18	12	kolmogorov	kolmogorov	ADJ
ejpam-4654	18	13	space	space	NOUN
ejpam-4654	18	14	)	)	PUNCT
ejpam-4654	18	15	if	if	SCONJ
ejpam-4654	18	16	for	for	ADP
ejpam-4654	18	17	every	every	DET
ejpam-4654	18	18	pair	pair	NOUN
ejpam-4654	18	19	of	of	ADP
ejpam-4654	18	20	distinct	distinct	ADJ
ejpam-4654	18	21	points	point	NOUN
ejpam-4654	18	22	x	x	PUNCT
ejpam-4654	18	23	and	and	CCONJ
ejpam-4654	18	24	y	y	PROPN
ejpam-4654	18	25	,	,	PUNCT
ejpam-4654	18	26	there	there	PRON
ejpam-4654	18	27	exists	exist	VERB
ejpam-4654	18	28	a	a	DET
ejpam-4654	18	29	neighborhood	neighborhood	NOUN
ejpam-4654	18	30	containing	contain	VERB
ejpam-4654	18	31	one	one	NUM
ejpam-4654	18	32	of	of	ADP
ejpam-4654	18	33	them	they	PRON
ejpam-4654	18	34	but	but	CCONJ
ejpam-4654	18	35	not	not	PART
ejpam-4654	18	36	the	the	DET
ejpam-4654	18	37	other	other	ADJ
ejpam-4654	18	38	;	;	PUNCT
ejpam-4654	18	39	which	which	PRON
ejpam-4654	18	40	is	be	AUX
ejpam-4654	18	41	equivalent	equivalent	ADJ
ejpam-4654	18	42	to	to	ADP
ejpam-4654	18	43	the	the	DET
ejpam-4654	18	44	following	follow	VERB
ejpam-4654	18	45	implication	implication	NOUN
ejpam-4654	18	46	(	(	PUNCT
ejpam-4654	18	47	{	{	PUNCT
ejpam-4654	18	48	x	x	NOUN
ejpam-4654	18	49	}	}	PUNCT
ejpam-4654	18	50	=	=	SYM
ejpam-4654	18	51	{	{	PUNCT
ejpam-4654	18	52	y	y	NOUN
ejpam-4654	18	53	}	}	PUNCT
ejpam-4654	18	54	⇒	⇒	NOUN
ejpam-4654	18	55	x	x	PUNCT
ejpam-4654	18	56	=	=	SYM
ejpam-4654	18	57	y	y	PROPN
ejpam-4654	18	58	)	)	PUNCT
ejpam-4654	18	59	.	.	PUNCT
ejpam-4654	19	1	•	•	NUM
ejpam-4654	19	2	a	a	DET
ejpam-4654	19	3	closed	closed	ADJ
ejpam-4654	19	4	subset	subset	NOUN
ejpam-4654	19	5	c	c	NOUN
ejpam-4654	19	6	is	be	AUX
ejpam-4654	19	7	irreducible	irreducible	ADJ
ejpam-4654	19	8	if	if	SCONJ
ejpam-4654	19	9	it	it	PRON
ejpam-4654	19	10	is	be	AUX
ejpam-4654	19	11	not	not	PART
ejpam-4654	19	12	the	the	DET
ejpam-4654	19	13	union	union	NOUN
ejpam-4654	19	14	of	of	ADP
ejpam-4654	19	15	two	two	NUM
ejpam-4654	19	16	proper	proper	ADJ
ejpam-4654	19	17	closed	closed	ADJ
ejpam-4654	19	18	subsets	subset	NOUN
ejpam-4654	19	19	or	or	CCONJ
ejpam-4654	19	20	if	if	SCONJ
ejpam-4654	19	21	the	the	DET
ejpam-4654	19	22	intersection	intersection	NOUN
ejpam-4654	19	23	of	of	ADP
ejpam-4654	19	24	two	two	NUM
ejpam-4654	19	25	nonempty	nonempty	ADJ
ejpam-4654	19	26	open	open	ADJ
ejpam-4654	19	27	subsets	subset	NOUN
ejpam-4654	19	28	is	be	AUX
ejpam-4654	19	29	nonempty	nonempty	ADJ
ejpam-4654	19	30	.	.	PUNCT
ejpam-4654	20	1	an	an	DET
ejpam-4654	20	2	element	element	NOUN
ejpam-4654	20	3	x	x	PUNCT
ejpam-4654	20	4	of	of	ADP
ejpam-4654	20	5	c	c	PROPN
ejpam-4654	20	6	is	be	AUX
ejpam-4654	20	7	called	call	VERB
ejpam-4654	20	8	a	a	DET
ejpam-4654	20	9	generic	generic	ADJ
ejpam-4654	20	10	point	point	NOUN
ejpam-4654	20	11	if	if	SCONJ
ejpam-4654	20	12	the	the	DET
ejpam-4654	20	13	closure	closure	NOUN
ejpam-4654	20	14	of	of	ADP
ejpam-4654	20	15	the	the	DET
ejpam-4654	20	16	singleton	singleton	NOUN
ejpam-4654	20	17	{	{	PUNCT
ejpam-4654	20	18	x	x	NOUN
ejpam-4654	20	19	}	}	PUNCT
ejpam-4654	20	20	is	be	AUX
ejpam-4654	20	21	equal	equal	ADJ
ejpam-4654	20	22	to	to	ADP
ejpam-4654	20	23	c	c	NOUN
ejpam-4654	20	24	:	:	PUNCT
ejpam-4654	20	25	{	{	PUNCT
ejpam-4654	20	26	x	x	NOUN
ejpam-4654	20	27	}	}	PUNCT
ejpam-4654	20	28	=	=	SYM
ejpam-4654	21	1	c.	c.	NOUN
ejpam-4654	21	2	we	we	PRON
ejpam-4654	21	3	have	have	VERB
ejpam-4654	21	4	the	the	DET
ejpam-4654	21	5	following	follow	VERB
ejpam-4654	21	6	properties	property	NOUN
ejpam-4654	21	7	:	:	PUNCT
ejpam-4654	22	1	1	1	X
ejpam-4654	22	2	.	.	X
ejpam-4654	23	1	the	the	DET
ejpam-4654	23	2	quasi	quasi	NOUN
ejpam-4654	23	3	-	-	NOUN
ejpam-4654	23	4	compactness	compactness	NOUN
ejpam-4654	23	5	is	be	AUX
ejpam-4654	23	6	invariant	invariant	ADJ
ejpam-4654	23	7	under	under	ADP
ejpam-4654	23	8	continuous	continuous	ADJ
ejpam-4654	23	9	map	map	NOUN
ejpam-4654	23	10	.	.	PUNCT
ejpam-4654	24	1	2	2	X
ejpam-4654	24	2	.	.	X
ejpam-4654	24	3	each	each	DET
ejpam-4654	24	4	closed	close	VERB
ejpam-4654	24	5	subset	subset	NOUN
ejpam-4654	24	6	of	of	ADP
ejpam-4654	24	7	a	a	DET
ejpam-4654	24	8	quasi	quasi	ADJ
ejpam-4654	24	9	-	-	ADJ
ejpam-4654	24	10	compact	compact	ADJ
ejpam-4654	24	11	space	space	NOUN
ejpam-4654	24	12	is	be	AUX
ejpam-4654	24	13	quasi	quasi	ADJ
ejpam-4654	24	14	-	-	ADJ
ejpam-4654	24	15	compact	compact	ADJ
ejpam-4654	24	16	.	.	PUNCT
ejpam-4654	25	1	3	3	X
ejpam-4654	25	2	.	.	X
ejpam-4654	25	3	the	the	DET
ejpam-4654	25	4	union	union	NOUN
ejpam-4654	25	5	of	of	ADP
ejpam-4654	25	6	finitely	finitely	ADV
ejpam-4654	25	7	many	many	ADJ
ejpam-4654	25	8	quasi	quasi	ADJ
ejpam-4654	25	9	-	-	ADJ
ejpam-4654	25	10	compact	compact	ADJ
ejpam-4654	25	11	subsets	subset	NOUN
ejpam-4654	25	12	is	be	AUX
ejpam-4654	25	13	quasi	quasi	ADJ
ejpam-4654	25	14	-	-	ADJ
ejpam-4654	25	15	compact	compact	ADJ
ejpam-4654	25	16	.	.	PUNCT
ejpam-4654	26	1	the	the	DET
ejpam-4654	26	2	intersection	intersection	NOUN
ejpam-4654	26	3	of	of	ADP
ejpam-4654	26	4	tow	tow	NOUN
ejpam-4654	26	5	quasi	quasi	ADJ
ejpam-4654	26	6	-	-	ADJ
ejpam-4654	26	7	compact	compact	ADJ
ejpam-4654	26	8	open	open	ADJ
ejpam-4654	26	9	subsets	subset	NOUN
ejpam-4654	26	10	is	be	AUX
ejpam-4654	26	11	not	not	PART
ejpam-4654	26	12	necessarily	necessarily	ADV
ejpam-4654	26	13	quasi	quasi	ADJ
ejpam-4654	26	14	-	-	ADJ
ejpam-4654	26	15	compact	compact	ADJ
ejpam-4654	26	16	.	.	PUNCT
ejpam-4654	27	1	[	[	X
ejpam-4654	27	2	1	1	NUM
ejpam-4654	27	3	,	,	PUNCT
ejpam-4654	27	4	example	example	NOUN
ejpam-4654	27	5	2.1	2.1	NUM
ejpam-4654	27	6	]	]	PUNCT
ejpam-4654	27	7	confirm	confirm	VERB
ejpam-4654	27	8	this	this	DET
ejpam-4654	27	9	result	result	NOUN
ejpam-4654	27	10	.	.	PUNCT
ejpam-4654	28	1	by	by	ADP
ejpam-4654	28	2	[	[	X
ejpam-4654	28	3	5	5	NUM
ejpam-4654	28	4	]	]	PUNCT
ejpam-4654	28	5	,	,	PUNCT
ejpam-4654	28	6	a	a	DET
ejpam-4654	28	7	spectral	spectral	ADJ
ejpam-4654	28	8	set	set	NOUN
ejpam-4654	28	9	satisfies	satisfy	VERB
ejpam-4654	28	10	the	the	DET
ejpam-4654	28	11	following	follow	VERB
ejpam-4654	28	12	conditions	condition	NOUN
ejpam-4654	28	13	:	:	PUNCT
ejpam-4654	28	14	(	(	PUNCT
ejpam-4654	28	15	k1	k1	NOUN
ejpam-4654	28	16	)	)	PUNCT
ejpam-4654	28	17	each	each	PRON
ejpam-4654	28	18	totally	totally	ADV
ejpam-4654	28	19	ordered	order	VERB
ejpam-4654	28	20	family	family	NOUN
ejpam-4654	28	21	of	of	ADP
ejpam-4654	28	22	elements	element	NOUN
ejpam-4654	28	23	in	in	ADP
ejpam-4654	28	24	(	(	PUNCT
ejpam-4654	28	25	y,≤	y,≤	ADJ
ejpam-4654	28	26	)	)	PUNCT
ejpam-4654	28	27	has	have	VERB
ejpam-4654	28	28	a	a	DET
ejpam-4654	28	29	supremum	supremum	ADJ
ejpam-4654	28	30	and	and	CCONJ
ejpam-4654	28	31	an	an	DET
ejpam-4654	28	32	infimum	infimum	NOUN
ejpam-4654	28	33	.	.	PUNCT
ejpam-4654	29	1	(	(	PUNCT
ejpam-4654	29	2	k2	k2	NOUN
ejpam-4654	29	3	)	)	PUNCT
ejpam-4654	29	4	for	for	ADP
ejpam-4654	29	5	every	every	DET
ejpam-4654	29	6	elements	element	NOUN
ejpam-4654	29	7	a	a	DET
ejpam-4654	29	8	<	<	X
ejpam-4654	29	9	b	b	PROPN
ejpam-4654	29	10	in	in	ADP
ejpam-4654	29	11	y	y	PROPN
ejpam-4654	29	12	,	,	PUNCT
ejpam-4654	29	13	there	there	PRON
ejpam-4654	29	14	exist	exist	VERB
ejpam-4654	29	15	two	two	NUM
ejpam-4654	29	16	consecutive	consecutive	ADJ
ejpam-4654	29	17	elements	element	NOUN
ejpam-4654	29	18	a1	a1	VERB
ejpam-4654	29	19	<	<	X
ejpam-4654	29	20	b1	b1	NOUN
ejpam-4654	29	21	with	with	ADP
ejpam-4654	29	22	a	a	DET
ejpam-4654	29	23	≤	≤	NUM
ejpam-4654	29	24	a1	a1	NOUN
ejpam-4654	29	25	<	<	X
ejpam-4654	29	26	b1	b1	PROPN
ejpam-4654	29	27	≤	≤	PROPN
ejpam-4654	29	28	b.	b.	PROPN
ejpam-4654	29	29	lewis	lewis	PROPN
ejpam-4654	29	30	and	and	CCONJ
ejpam-4654	29	31	ohm	ohm	NOUN
ejpam-4654	29	32	showed	show	VERB
ejpam-4654	29	33	in	in	ADP
ejpam-4654	29	34	[	[	X
ejpam-4654	29	35	6	6	NUM
ejpam-4654	29	36	]	]	PUNCT
ejpam-4654	29	37	that	that	SCONJ
ejpam-4654	29	38	these	these	DET
ejpam-4654	29	39	two	two	NUM
ejpam-4654	29	40	conditions	condition	NOUN
ejpam-4654	29	41	are	be	AUX
ejpam-4654	29	42	not	not	PART
ejpam-4654	29	43	sufficient	sufficient	ADJ
ejpam-4654	29	44	to	to	PART
ejpam-4654	29	45	characterize	characterize	VERB
ejpam-4654	29	46	ordered	order	VERB
ejpam-4654	29	47	spectral	spectral	ADJ
ejpam-4654	29	48	sets	set	NOUN
ejpam-4654	29	49	.	.	PUNCT
ejpam-4654	30	1	they	they	PRON
ejpam-4654	30	2	even	even	ADV
ejpam-4654	30	3	added	add	VERB
ejpam-4654	30	4	a	a	DET
ejpam-4654	30	5	third	third	ADJ
ejpam-4654	30	6	independent	independent	NOUN
ejpam-4654	30	7	of	of	ADP
ejpam-4654	30	8	(	(	PUNCT
ejpam-4654	30	9	k1	k1	NOUN
ejpam-4654	30	10	)	)	PUNCT
ejpam-4654	30	11	and	and	CCONJ
ejpam-4654	30	12	(	(	PUNCT
ejpam-4654	30	13	k2	k2	NOUN
ejpam-4654	30	14	)	)	PUNCT
ejpam-4654	30	15	(	(	PUNCT
ejpam-4654	30	16	still	still	ADV
ejpam-4654	30	17	necessary	necessary	ADJ
ejpam-4654	30	18	not	not	PART
ejpam-4654	30	19	sufficient	sufficient	ADJ
ejpam-4654	30	20	):	):	PUNCT
ejpam-4654	30	21	(	(	PUNCT
ejpam-4654	30	22	h	h	NOUN
ejpam-4654	30	23	)	)	PUNCT
ejpam-4654	30	24	let	let	VERB
ejpam-4654	30	25	f	f	PRON
ejpam-4654	30	26	be	be	AUX
ejpam-4654	30	27	a	a	DET
ejpam-4654	30	28	subset	subset	NOUN
ejpam-4654	30	29	of	of	ADP
ejpam-4654	30	30	l	l	NOUN
ejpam-4654	30	31	=	=	PUNCT
ejpam-4654	30	32	{	{	PUNCT
ejpam-4654	30	33	]	]	X
ejpam-4654	30	34	←	←	PROPN
ejpam-4654	30	35	,	,	PUNCT
ejpam-4654	30	36	x	x	X
ejpam-4654	30	37	]	]	X
ejpam-4654	30	38	:	:	PUNCT
ejpam-4654	30	39	x	x	SYM
ejpam-4654	30	40	∈	∈	NOUN
ejpam-4654	30	41	x	x	X
ejpam-4654	30	42	}	}	PUNCT
ejpam-4654	30	43	or	or	CCONJ
ejpam-4654	30	44	r	r	NOUN
ejpam-4654	30	45	=	=	SYM
ejpam-4654	30	46	{	{	PUNCT
ejpam-4654	30	47	[	[	X
ejpam-4654	30	48	x,→	x,→	X
ejpam-4654	30	49	[:	[:	X
ejpam-4654	30	50	x	x	X
ejpam-4654	30	51	∈	∈	NOUN
ejpam-4654	30	52	x	x	X
ejpam-4654	30	53	}	}	PUNCT
ejpam-4654	30	54	.	.	PUNCT
ejpam-4654	31	1	if⋂	if⋂	ADJ
ejpam-4654	31	2	f∈f	f∈f	NOUN
ejpam-4654	31	3	f	f	NOUN
ejpam-4654	31	4	=	=	SYM
ejpam-4654	31	5	∅	∅	NOUN
ejpam-4654	31	6	,	,	PUNCT
ejpam-4654	31	7	then	then	ADV
ejpam-4654	31	8	f	f	PROPN
ejpam-4654	31	9	contains	contain	VERB
ejpam-4654	31	10	a	a	DET
ejpam-4654	31	11	finitely	finitely	ADV
ejpam-4654	31	12	many	many	ADJ
ejpam-4654	31	13	elements	element	NOUN
ejpam-4654	31	14	with	with	ADP
ejpam-4654	31	15	empty	empty	ADJ
ejpam-4654	31	16	intersection	intersection	NOUN
ejpam-4654	31	17	.	.	PUNCT
ejpam-4654	32	1	where	where	SCONJ
ejpam-4654	32	2	]	]	PUNCT
ejpam-4654	32	3	←	←	PROPN
ejpam-4654	32	4	,	,	PUNCT
ejpam-4654	32	5	x	x	X
ejpam-4654	32	6	]	]	X
ejpam-4654	32	7	=	=	X
ejpam-4654	32	8	{	{	PUNCT
ejpam-4654	32	9	y	y	PROPN
ejpam-4654	32	10	∈	∈	PROPN
ejpam-4654	32	11	x|y	x|y	PUNCT
ejpam-4654	33	1	≤	≤	NUM
ejpam-4654	33	2	x	x	PUNCT
ejpam-4654	33	3	}	}	PUNCT
ejpam-4654	33	4	and	and	CCONJ
ejpam-4654	33	5	[	[	X
ejpam-4654	33	6	x,←	x,←	PROPN
ejpam-4654	33	7	,	,	PUNCT
ejpam-4654	33	8	x[=	x[=	PROPN
ejpam-4654	33	9	{	{	PUNCT
ejpam-4654	33	10	y	y	PROPN
ejpam-4654	33	11	∈	∈	PROPN
ejpam-4654	33	12	x|x	x|x	PUNCT
ejpam-4654	34	1	≤	≤	NUM
ejpam-4654	34	2	y	y	X
ejpam-4654	34	3	}	}	PUNCT
ejpam-4654	34	4	.	.	PUNCT
ejpam-4654	35	1	note	note	VERB
ejpam-4654	35	2	that	that	SCONJ
ejpam-4654	35	3	the	the	DET
ejpam-4654	35	4	problem	problem	NOUN
ejpam-4654	35	5	of	of	ADP
ejpam-4654	35	6	characterization	characterization	NOUN
ejpam-4654	35	7	of	of	ADP
ejpam-4654	35	8	spectral	spectral	ADJ
ejpam-4654	35	9	set	set	NOUN
ejpam-4654	35	10	is	be	AUX
ejpam-4654	35	11	still	still	ADV
ejpam-4654	35	12	open	open	ADJ
ejpam-4654	35	13	.	.	PUNCT
ejpam-4654	36	1	in	in	ADP
ejpam-4654	36	2	this	this	DET
ejpam-4654	36	3	paper	paper	NOUN
ejpam-4654	36	4	we	we	PRON
ejpam-4654	36	5	define	define	VERB
ejpam-4654	36	6	and	and	CCONJ
ejpam-4654	36	7	characterise	characterise	VERB
ejpam-4654	36	8	spectral	spectral	ADJ
ejpam-4654	36	9	graph	graph	NOUN
ejpam-4654	36	10	.	.	PUNCT
ejpam-4654	37	1	2	2	X
ejpam-4654	37	2	.	.	X
ejpam-4654	37	3	quasi	quasi	NOUN
ejpam-4654	37	4	-	-	PROPN
ejpam-4654	37	5	homeomorphism	homeomorphism	ADJ
ejpam-4654	37	6	and	and	CCONJ
ejpam-4654	37	7	spectral	spectral	ADJ
ejpam-4654	37	8	properties	property	NOUN
ejpam-4654	37	9	according	accord	VERB
ejpam-4654	37	10	to	to	ADP
ejpam-4654	37	11	[	[	X
ejpam-4654	37	12	3	3	NUM
ejpam-4654	37	13	]	]	PUNCT
ejpam-4654	37	14	,	,	PUNCT
ejpam-4654	37	15	a	a	DET
ejpam-4654	37	16	continuous	continuous	ADJ
ejpam-4654	37	17	mapping	mapping	NOUN
ejpam-4654	37	18	f	f	NOUN
ejpam-4654	37	19	:	:	PUNCT
ejpam-4654	37	20	x	x	X
ejpam-4654	37	21	→	→	SYM
ejpam-4654	37	22	y	y	NOUN
ejpam-4654	37	23	between	between	ADP
ejpam-4654	37	24	two	two	NUM
ejpam-4654	37	25	topological	topological	ADJ
ejpam-4654	37	26	spaces	space	NOUN
ejpam-4654	37	27	is	be	AUX
ejpam-4654	37	28	a	a	DET
ejpam-4654	37	29	quasi	quasi	NOUN
ejpam-4654	37	30	-	-	NOUN
ejpam-4654	37	31	homeomorphism	homeomorphism	X
ejpam-4654	37	32	if	if	SCONJ
ejpam-4654	37	33	the	the	DET
ejpam-4654	37	34	map	map	NOUN
ejpam-4654	37	35	which	which	PRON
ejpam-4654	37	36	associates	associate	VERB
ejpam-4654	37	37	to	to	ADP
ejpam-4654	37	38	each	each	DET
ejpam-4654	37	39	open	open	ADJ
ejpam-4654	37	40	subset	subset	VERB
ejpam-4654	37	41	v	v	ADP
ejpam-4654	37	42	⊂	⊂	PROPN
ejpam-4654	37	43	y	y	PROPN
ejpam-4654	37	44	the	the	DET
ejpam-4654	37	45	open	open	ADJ
ejpam-4654	37	46	subset	subset	NOUN
ejpam-4654	37	47	u	u	NOUN
ejpam-4654	37	48	=	=	NOUN
ejpam-4654	37	49	f−1(v	f−1(v	PROPN
ejpam-4654	37	50	)	)	PUNCT
ejpam-4654	38	1	⊂	⊂	PROPN
ejpam-4654	38	2	x	x	X
ejpam-4654	38	3	is	be	AUX
ejpam-4654	38	4	a	a	DET
ejpam-4654	38	5	bijective	bijective	ADJ
ejpam-4654	38	6	mapping	mapping	NOUN
ejpam-4654	38	7	.	.	PUNCT
ejpam-4654	39	1	equivalently	equivalently	ADV
ejpam-4654	39	2	,	,	PUNCT
ejpam-4654	39	3	the	the	DET
ejpam-4654	39	4	map	map	NOUN
ejpam-4654	39	5	which	which	PRON
ejpam-4654	39	6	assigns	assign	VERB
ejpam-4654	39	7	to	to	ADP
ejpam-4654	39	8	each	each	DET
ejpam-4654	39	9	closed	close	VERB
ejpam-4654	39	10	subset	subset	VERB
ejpam-4654	39	11	g	g	PROPN
ejpam-4654	39	12	⊂	⊂	PROPN
ejpam-4654	39	13	y	y	PROPN
ejpam-4654	39	14	the	the	DET
ejpam-4654	39	15	closed	close	VERB
ejpam-4654	39	16	subset	subset	NOUN
ejpam-4654	39	17	f	f	PROPN
ejpam-4654	39	18	=	=	SYM
ejpam-4654	39	19	f−1(g	f−1(g	PROPN
ejpam-4654	39	20	)	)	PUNCT
ejpam-4654	40	1	⊂	⊂	PROPN
ejpam-4654	40	2	x	x	X
ejpam-4654	40	3	is	be	AUX
ejpam-4654	40	4	also	also	ADV
ejpam-4654	40	5	a	a	DET
ejpam-4654	40	6	bijective	bijective	ADJ
ejpam-4654	40	7	mapping	mapping	NOUN
ejpam-4654	40	8	.	.	PUNCT
ejpam-4654	41	1	we	we	PRON
ejpam-4654	41	2	have	have	VERB
ejpam-4654	41	3	the	the	DET
ejpam-4654	41	4	following	follow	VERB
ejpam-4654	41	5	properties	property	NOUN
ejpam-4654	41	6	:	:	PUNCT
ejpam-4654	41	7	let	let	VERB
ejpam-4654	41	8	f	f	PRON
ejpam-4654	41	9	:	:	PUNCT
ejpam-4654	41	10	x	x	X
ejpam-4654	41	11	→	→	SYM
ejpam-4654	41	12	y	y	X
ejpam-4654	41	13	be	be	AUX
ejpam-4654	41	14	a	a	DET
ejpam-4654	41	15	quasi	quasi	NOUN
ejpam-4654	41	16	-	-	NOUN
ejpam-4654	41	17	homeomorphism	homeomorphism	ADJ
ejpam-4654	41	18	.	.	PUNCT
ejpam-4654	42	1	1	1	X
ejpam-4654	42	2	.	.	X
ejpam-4654	42	3	the	the	DET
ejpam-4654	42	4	composition	composition	NOUN
ejpam-4654	42	5	of	of	ADP
ejpam-4654	42	6	two	two	NUM
ejpam-4654	42	7	quasi	quasi	NOUN
ejpam-4654	42	8	-	-	NOUN
ejpam-4654	42	9	homeomorphisms	homeomorphisms	PROPN
ejpam-4654	42	10	is	be	AUX
ejpam-4654	42	11	a	a	DET
ejpam-4654	42	12	quasi	quasi	NOUN
ejpam-4654	42	13	-	-	NOUN
ejpam-4654	42	14	homeomorphism	homeomorphism	X
ejpam-4654	42	15	.	.	PUNCT
ejpam-4654	43	1	b.	b.	PROPN
ejpam-4654	43	2	alharbi	alharbi	PROPN
ejpam-4654	43	3	/	/	SYM
ejpam-4654	43	4	eur	eur	PROPN
ejpam-4654	43	5	.	.	PUNCT
ejpam-4654	44	1	j.	j.	PROPN
ejpam-4654	44	2	pure	pure	PROPN
ejpam-4654	44	3	appl	appl	PROPN
ejpam-4654	44	4	.	.	PROPN
ejpam-4654	44	5	math	math	PROPN
ejpam-4654	44	6	,	,	PUNCT
ejpam-4654	44	7	16	16	NUM
ejpam-4654	44	8	(	(	PUNCT
ejpam-4654	44	9	1	1	NUM
ejpam-4654	44	10	)	)	PUNCT
ejpam-4654	44	11	(	(	PUNCT
ejpam-4654	44	12	2023	2023	NUM
ejpam-4654	44	13	)	)	PUNCT
ejpam-4654	44	14	,	,	PUNCT
ejpam-4654	44	15	314	314	NUM
ejpam-4654	44	16	-	-	SYM
ejpam-4654	44	17	318	318	NUM
ejpam-4654	44	18	316	316	NUM
ejpam-4654	44	19	2	2	NUM
ejpam-4654	44	20	.	.	PUNCT
ejpam-4654	45	1	f	f	PROPN
ejpam-4654	45	2	is	be	AUX
ejpam-4654	45	3	open	open	ADJ
ejpam-4654	45	4	,	,	PUNCT
ejpam-4654	45	5	closed	closed	ADJ
ejpam-4654	45	6	.	.	PUNCT
ejpam-4654	46	1	3	3	X
ejpam-4654	46	2	.	.	X
ejpam-4654	46	3	for	for	ADP
ejpam-4654	46	4	every	every	DET
ejpam-4654	46	5	locally	locally	ADV
ejpam-4654	46	6	closed	close	VERB
ejpam-4654	46	7	subset	subset	VERB
ejpam-4654	46	8	a	a	DET
ejpam-4654	46	9	⊂	⊂	PROPN
ejpam-4654	46	10	x	x	NOUN
ejpam-4654	46	11	,	,	PUNCT
ejpam-4654	46	12	we	we	PRON
ejpam-4654	46	13	have	have	VERB
ejpam-4654	46	14	a	a	DET
ejpam-4654	46	15	=	=	SYM
ejpam-4654	46	16	f−1(f(a	f−1(f(a	NOUN
ejpam-4654	46	17	)	)	PUNCT
ejpam-4654	46	18	)	)	PUNCT
ejpam-4654	46	19	.	.	PUNCT
ejpam-4654	47	1	we	we	PRON
ejpam-4654	47	2	say	say	VERB
ejpam-4654	47	3	that	that	SCONJ
ejpam-4654	47	4	every	every	DET
ejpam-4654	47	5	locally	locally	ADV
ejpam-4654	47	6	closed	close	VERB
ejpam-4654	47	7	subset	subset	NOUN
ejpam-4654	47	8	of	of	ADP
ejpam-4654	47	9	x	x	SYM
ejpam-4654	47	10	is	be	AUX
ejpam-4654	47	11	f	f	PROPN
ejpam-4654	47	12	-saturated	-saturated	PROPN
ejpam-4654	47	13	.	.	PUNCT
ejpam-4654	48	1	4	4	X
ejpam-4654	48	2	.	.	X
ejpam-4654	48	3	for	for	ADP
ejpam-4654	48	4	every	every	DET
ejpam-4654	48	5	x	x	NOUN
ejpam-4654	48	6	,	,	PUNCT
ejpam-4654	48	7	y	y	PROPN
ejpam-4654	48	8	∈	∈	PROPN
ejpam-4654	48	9	x	x	X
ejpam-4654	48	10	,	,	PUNCT
ejpam-4654	48	11	we	we	PRON
ejpam-4654	48	12	have	have	VERB
ejpam-4654	48	13	the	the	DET
ejpam-4654	48	14	following	following	ADJ
ejpam-4654	48	15	implication	implication	NOUN
ejpam-4654	48	16	:	:	PUNCT
ejpam-4654	48	17	f(x	f(x	PROPN
ejpam-4654	48	18	)	)	PUNCT
ejpam-4654	48	19	=	=	SYM
ejpam-4654	48	20	f(y	f(y	NOUN
ejpam-4654	48	21	)	)	PUNCT
ejpam-4654	48	22	⇒	⇒	NOUN
ejpam-4654	48	23	{	{	PUNCT
ejpam-4654	48	24	x	x	NOUN
ejpam-4654	48	25	}	}	PUNCT
ejpam-4654	48	26	=	=	SYM
ejpam-4654	48	27	{	{	PUNCT
ejpam-4654	48	28	y	y	NOUN
ejpam-4654	48	29	}	}	PUNCT
ejpam-4654	48	30	5	5	NUM
ejpam-4654	48	31	.	.	PUNCT
ejpam-4654	49	1	if	if	SCONJ
ejpam-4654	49	2	moreover	moreover	ADV
ejpam-4654	49	3	x	x	VERB
ejpam-4654	49	4	is	be	AUX
ejpam-4654	49	5	a	a	DET
ejpam-4654	49	6	t0	t0	NOUN
ejpam-4654	49	7	-	-	NOUN
ejpam-4654	49	8	space	space	NOUN
ejpam-4654	49	9	,	,	PUNCT
ejpam-4654	49	10	then	then	ADV
ejpam-4654	49	11	f	f	PROPN
ejpam-4654	49	12	is	be	AUX
ejpam-4654	49	13	an	an	DET
ejpam-4654	49	14	embedding	embed	VERB
ejpam-4654	49	15	(	(	PUNCT
ejpam-4654	49	16	f	f	NOUN
ejpam-4654	49	17	:	:	PUNCT
ejpam-4654	49	18	x	x	X
ejpam-4654	49	19	→	→	SYM
ejpam-4654	49	20	f(x	f(x	PROPN
ejpam-4654	49	21	)	)	PUNCT
ejpam-4654	49	22	is	be	AUX
ejpam-4654	49	23	a	a	DET
ejpam-4654	49	24	homeomorphism	homeomorphism	NOUN
ejpam-4654	49	25	)	)	PUNCT
ejpam-4654	49	26	.	.	PUNCT
ejpam-4654	50	1	theorem	theorem	VERB
ejpam-4654	50	2	2.1	2.1	NUM
ejpam-4654	50	3	.	.	PUNCT
ejpam-4654	51	1	if	if	SCONJ
ejpam-4654	51	2	f	f	PROPN
ejpam-4654	51	3	:	:	PUNCT
ejpam-4654	51	4	(	(	PUNCT
ejpam-4654	51	5	x	x	X
ejpam-4654	51	6	,	,	PUNCT
ejpam-4654	51	7	t	t	NOUN
ejpam-4654	51	8	)	)	PUNCT
ejpam-4654	51	9	→	→	SYM
ejpam-4654	51	10	(	(	PUNCT
ejpam-4654	51	11	y	y	PROPN
ejpam-4654	51	12	,	,	PUNCT
ejpam-4654	51	13	t	t	PROPN
ejpam-4654	51	14	′	′	NUM
ejpam-4654	51	15	)	)	PUNCT
ejpam-4654	51	16	is	be	AUX
ejpam-4654	51	17	a	a	PRON
ejpam-4654	51	18	onto	onto	ADP
ejpam-4654	51	19	quasi	quasi	NOUN
ejpam-4654	51	20	-	-	NOUN
ejpam-4654	51	21	homeomorphism	homeomorphism	ADJ
ejpam-4654	51	22	,	,	PUNCT
ejpam-4654	51	23	then	then	ADV
ejpam-4654	51	24	t	t	PROPN
ejpam-4654	51	25	is	be	AUX
ejpam-4654	51	26	quasispectral	quasispectral	ADJ
ejpam-4654	51	27	if	if	SCONJ
ejpam-4654	51	28	and	and	CCONJ
ejpam-4654	51	29	only	only	ADV
ejpam-4654	51	30	if	if	SCONJ
ejpam-4654	51	31	t	t	PROPN
ejpam-4654	51	32	′	′	NOUN
ejpam-4654	51	33	is	be	AUX
ejpam-4654	51	34	quasi	quasi	ADJ
ejpam-4654	51	35	-	-	ADJ
ejpam-4654	51	36	spectral	spectral	ADJ
ejpam-4654	51	37	.	.	PUNCT
ejpam-4654	52	1	proof	proof	NOUN
ejpam-4654	52	2	.	.	PUNCT
ejpam-4654	53	1	we	we	PRON
ejpam-4654	53	2	start	start	VERB
ejpam-4654	53	3	by	by	ADP
ejpam-4654	53	4	showing	show	VERB
ejpam-4654	53	5	the	the	DET
ejpam-4654	53	6	following	following	NOUN
ejpam-4654	53	7	:	:	PUNCT
ejpam-4654	53	8	let	let	VERB
ejpam-4654	53	9	f	f	PRON
ejpam-4654	53	10	:	:	PUNCT
ejpam-4654	53	11	x	x	X
ejpam-4654	53	12	→	→	SYM
ejpam-4654	53	13	y	y	X
ejpam-4654	53	14	be	be	AUX
ejpam-4654	53	15	a	a	DET
ejpam-4654	53	16	quasi	quasi	NOUN
ejpam-4654	53	17	-	-	NOUN
ejpam-4654	53	18	homeomorphism	homeomorphism	PROPN
ejpam-4654	53	19	and	and	CCONJ
ejpam-4654	53	20	s	s	AUX
ejpam-4654	53	21	be	be	AUX
ejpam-4654	53	22	a	a	DET
ejpam-4654	53	23	subset	subset	NOUN
ejpam-4654	53	24	of	of	ADP
ejpam-4654	53	25	y	y	PROPN
ejpam-4654	53	26	.	.	PUNCT
ejpam-4654	54	1	1	1	X
ejpam-4654	54	2	.	.	X
ejpam-4654	55	1	if	if	SCONJ
ejpam-4654	55	2	s	s	NOUN
ejpam-4654	55	3	is	be	AUX
ejpam-4654	55	4	an	an	DET
ejpam-4654	55	5	open	open	ADJ
ejpam-4654	55	6	set	set	NOUN
ejpam-4654	55	7	,	,	PUNCT
ejpam-4654	55	8	then	then	ADV
ejpam-4654	55	9	s	s	VERB
ejpam-4654	55	10	is	be	AUX
ejpam-4654	55	11	quasi	quasi	ADJ
ejpam-4654	55	12	-	-	ADJ
ejpam-4654	55	13	compact	compact	ADJ
ejpam-4654	55	14	in	in	ADP
ejpam-4654	55	15	y	y	PROPN
ejpam-4654	55	16	if	if	SCONJ
ejpam-4654	56	1	and	and	CCONJ
ejpam-4654	56	2	only	only	ADV
ejpam-4654	56	3	if	if	SCONJ
ejpam-4654	56	4	,	,	PUNCT
ejpam-4654	56	5	f−1(s	f−1(s	PROPN
ejpam-4654	56	6	)	)	PUNCT
ejpam-4654	56	7	is	be	AUX
ejpam-4654	56	8	quasicompact	quasicompact	ADJ
ejpam-4654	56	9	in	in	ADP
ejpam-4654	56	10	x.	x.	NOUN
ejpam-4654	56	11	2	2	X
ejpam-4654	56	12	.	.	PUNCT
ejpam-4654	57	1	if	if	SCONJ
ejpam-4654	57	2	s	s	PROPN
ejpam-4654	57	3	is	be	AUX
ejpam-4654	57	4	a	a	DET
ejpam-4654	57	5	closed	closed	ADJ
ejpam-4654	57	6	set	set	NOUN
ejpam-4654	57	7	,	,	PUNCT
ejpam-4654	57	8	then	then	ADV
ejpam-4654	57	9	s	s	VERB
ejpam-4654	57	10	is	be	AUX
ejpam-4654	57	11	irreducible	irreducible	ADJ
ejpam-4654	57	12	in	in	ADP
ejpam-4654	57	13	y	y	PROPN
ejpam-4654	57	14	if	if	SCONJ
ejpam-4654	58	1	and	and	CCONJ
ejpam-4654	58	2	only	only	ADV
ejpam-4654	58	3	if	if	SCONJ
ejpam-4654	58	4	,	,	PUNCT
ejpam-4654	58	5	f−1(s	f−1(s	PROPN
ejpam-4654	58	6	)	)	PUNCT
ejpam-4654	58	7	is	be	AUX
ejpam-4654	58	8	irreducible	irreducible	ADJ
ejpam-4654	58	9	in	in	ADP
ejpam-4654	58	10	x.	x.	NOUN
ejpam-4654	58	11	1	1	NUM
ejpam-4654	58	12	.	.	PUNCT
ejpam-4654	58	13	suppose	suppose	VERB
ejpam-4654	58	14	that	that	SCONJ
ejpam-4654	58	15	s	s	VERB
ejpam-4654	58	16	is	be	AUX
ejpam-4654	58	17	a	a	DET
ejpam-4654	58	18	quasi	quasi	ADJ
ejpam-4654	58	19	-	-	ADJ
ejpam-4654	58	20	compact	compact	ADJ
ejpam-4654	58	21	open	open	ADJ
ejpam-4654	58	22	subset	subset	NOUN
ejpam-4654	58	23	in	in	ADP
ejpam-4654	58	24	y	y	PROPN
ejpam-4654	58	25	.	.	PUNCT
ejpam-4654	59	1	let	let	VERB
ejpam-4654	59	2	(	(	PUNCT
ejpam-4654	59	3	ui	ui	NOUN
ejpam-4654	59	4	,	,	PUNCT
ejpam-4654	59	5	i	i	PRON
ejpam-4654	59	6	∈	∈	PROPN
ejpam-4654	60	1	i	i	PRON
ejpam-4654	60	2	)	)	PUNCT
ejpam-4654	60	3	be	be	VERB
ejpam-4654	60	4	an	an	DET
ejpam-4654	60	5	open	open	ADJ
ejpam-4654	60	6	covering	covering	NOUN
ejpam-4654	60	7	of	of	ADP
ejpam-4654	60	8	f−1(s	f−1(s	PROPN
ejpam-4654	60	9	)	)	PUNCT
ejpam-4654	60	10	.	.	PUNCT
ejpam-4654	61	1	the	the	DET
ejpam-4654	61	2	fact	fact	NOUN
ejpam-4654	61	3	that	that	SCONJ
ejpam-4654	61	4	f	f	PROPN
ejpam-4654	61	5	is	be	AUX
ejpam-4654	61	6	a	a	DET
ejpam-4654	61	7	quasi	quasi	NOUN
ejpam-4654	61	8	-	-	NOUN
ejpam-4654	61	9	homeomorphism	homeomorphism	PROPN
ejpam-4654	61	10	implies	imply	VERB
ejpam-4654	61	11	that	that	SCONJ
ejpam-4654	61	12	,	,	PUNCT
ejpam-4654	61	13	for	for	ADP
ejpam-4654	61	14	each	each	DET
ejpam-4654	61	15	i	i	PRON
ejpam-4654	61	16	∈	∈	PROPN
ejpam-4654	61	17	i	i	PRON
ejpam-4654	61	18	,	,	PUNCT
ejpam-4654	61	19	there	there	PRON
ejpam-4654	61	20	exist	exist	VERB
ejpam-4654	61	21	an	an	DET
ejpam-4654	61	22	open	open	ADJ
ejpam-4654	61	23	subset	subset	NOUN
ejpam-4654	61	24	vi	vi	PROPN
ejpam-4654	61	25	of	of	ADP
ejpam-4654	61	26	y	y	PRON
ejpam-4654	61	27	such	such	ADJ
ejpam-4654	61	28	that	that	PRON
ejpam-4654	61	29	ui	ui	PROPN
ejpam-4654	61	30	=	=	PUNCT
ejpam-4654	61	31	f−1(vi	f−1(vi	PROPN
ejpam-4654	61	32	)	)	PUNCT
ejpam-4654	61	33	.	.	PUNCT
ejpam-4654	62	1	therefore	therefore	ADV
ejpam-4654	62	2	f−1(s	f−1(s	PROPN
ejpam-4654	62	3	)	)	PUNCT
ejpam-4654	63	1	=	=	SYM
ejpam-4654	63	2	f−1	f−1	PROPN
ejpam-4654	63	3	(	(	PUNCT
ejpam-4654	63	4	⋃	⋃	PROPN
ejpam-4654	63	5	i∈i	i∈i	ADJ
ejpam-4654	63	6	vi	vi	NOUN
ejpam-4654	63	7	)	)	PUNCT
ejpam-4654	63	8	and	and	CCONJ
ejpam-4654	63	9	so	so	ADV
ejpam-4654	63	10	s	s	PART
ejpam-4654	63	11	=	=	PUNCT
ejpam-4654	63	12	⋃	⋃	PROPN
ejpam-4654	63	13	i∈i	i∈i	ADJ
ejpam-4654	63	14	vi	vi	NOUN
ejpam-4654	63	15	.	.	PUNCT
ejpam-4654	64	1	it	it	PRON
ejpam-4654	64	2	follows	follow	VERB
ejpam-4654	64	3	from	from	ADP
ejpam-4654	64	4	the	the	DET
ejpam-4654	64	5	fact	fact	NOUN
ejpam-4654	64	6	that	that	SCONJ
ejpam-4654	64	7	s	s	VERB
ejpam-4654	64	8	is	be	AUX
ejpam-4654	64	9	quasicompact	quasicompact	ADJ
ejpam-4654	64	10	in	in	ADP
ejpam-4654	64	11	y	y	PROPN
ejpam-4654	64	12	,	,	PUNCT
ejpam-4654	64	13	that	that	SCONJ
ejpam-4654	64	14	there	there	PRON
ejpam-4654	64	15	exists	exist	VERB
ejpam-4654	64	16	a	a	DET
ejpam-4654	64	17	finite	finite	NOUN
ejpam-4654	64	18	subset	subset	VERB
ejpam-4654	64	19	j	j	PROPN
ejpam-4654	64	20	of	of	ADP
ejpam-4654	64	21	i	i	PRON
ejpam-4654	64	22	such	such	ADJ
ejpam-4654	64	23	that	that	DET
ejpam-4654	64	24	s	s	NOUN
ejpam-4654	64	25	=	=	PUNCT
ejpam-4654	64	26	⋃	⋃	PROPN
ejpam-4654	64	27	i∈j	i∈j	NOUN
ejpam-4654	64	28	vi	vi	NOUN
ejpam-4654	64	29	,	,	PUNCT
ejpam-4654	64	30	which	which	PRON
ejpam-4654	64	31	gives	give	VERB
ejpam-4654	64	32	f−1(s	f−1(s	PROPN
ejpam-4654	64	33	)	)	PUNCT
ejpam-4654	64	34	=	=	PUNCT
ejpam-4654	64	35	⋃	⋃	NOUN
ejpam-4654	64	36	i∈j	i∈j	NOUN
ejpam-4654	64	37	ui	ui	NOUN
ejpam-4654	64	38	and	and	CCONJ
ejpam-4654	64	39	so	so	ADV
ejpam-4654	64	40	f−1(s	f−1(s	ADJ
ejpam-4654	64	41	)	)	PUNCT
ejpam-4654	64	42	is	be	AUX
ejpam-4654	64	43	quasi	quasi	ADJ
ejpam-4654	64	44	-	-	ADJ
ejpam-4654	64	45	compact	compact	ADJ
ejpam-4654	64	46	in	in	ADP
ejpam-4654	64	47	x.	x.	NOUN
ejpam-4654	64	48	conversely	conversely	ADV
ejpam-4654	64	49	,	,	PUNCT
ejpam-4654	64	50	suppose	suppose	VERB
ejpam-4654	64	51	that	that	SCONJ
ejpam-4654	64	52	f−1(s	f−1(s	PROPN
ejpam-4654	64	53	)	)	PUNCT
ejpam-4654	64	54	is	be	AUX
ejpam-4654	64	55	a	a	DET
ejpam-4654	64	56	quasi	quasi	ADJ
ejpam-4654	64	57	-	-	ADJ
ejpam-4654	64	58	compact	compact	ADJ
ejpam-4654	64	59	open	open	ADJ
ejpam-4654	64	60	subset	subset	NOUN
ejpam-4654	64	61	inx	inx	PROPN
ejpam-4654	65	1	.	.	PUNCT
ejpam-4654	65	2	let	let	VERB
ejpam-4654	65	3	(	(	PUNCT
ejpam-4654	65	4	vi	vi	VERB
ejpam-4654	65	5	,	,	PUNCT
ejpam-4654	65	6	i	i	PRON
ejpam-4654	65	7	∈	∈	PROPN
ejpam-4654	65	8	i	i	PRON
ejpam-4654	65	9	)	)	PUNCT
ejpam-4654	65	10	be	be	VERB
ejpam-4654	65	11	an	an	DET
ejpam-4654	65	12	open	open	ADJ
ejpam-4654	65	13	covering	covering	NOUN
ejpam-4654	65	14	of	of	ADP
ejpam-4654	65	15	s.	s.	PROPN
ejpam-4654	65	16	then	then	ADV
ejpam-4654	65	17	f−1(s	f−1(s	PROPN
ejpam-4654	65	18	)	)	PUNCT
ejpam-4654	65	19	=	=	PUNCT
ejpam-4654	66	1	⋃	⋃	ADP
ejpam-4654	66	2	i∈i	i∈i	ADJ
ejpam-4654	66	3	f	f	PROPN
ejpam-4654	66	4	−1(vi	−1(vi	NOUN
ejpam-4654	66	5	)	)	PUNCT
ejpam-4654	67	1	and	and	CCONJ
ejpam-4654	67	2	so	so	ADV
ejpam-4654	67	3	there	there	PRON
ejpam-4654	67	4	exists	exist	VERB
ejpam-4654	67	5	a	a	DET
ejpam-4654	67	6	finite	finite	NOUN
ejpam-4654	67	7	subset	subset	VERB
ejpam-4654	67	8	j	j	PROPN
ejpam-4654	67	9	of	of	ADP
ejpam-4654	67	10	i	i	PRON
ejpam-4654	67	11	such	such	ADJ
ejpam-4654	67	12	that	that	PRON
ejpam-4654	67	13	f−1(s	f−1(s	PROPN
ejpam-4654	67	14	)	)	PUNCT
ejpam-4654	67	15	=	=	PUNCT
ejpam-4654	67	16	⋃	⋃	ADP
ejpam-4654	67	17	i∈j	i∈j	NOUN
ejpam-4654	67	18	f−1(vi	f−1(vi	NOUN
ejpam-4654	67	19	)	)	PUNCT
ejpam-4654	67	20	=	=	SYM
ejpam-4654	67	21	f−1	f−1	PROPN
ejpam-4654	67	22	(	(	PUNCT
ejpam-4654	67	23	⋃	⋃	NOUN
ejpam-4654	67	24	i∈j	i∈j	NOUN
ejpam-4654	67	25	vi	vi	NOUN
ejpam-4654	67	26	)	)	PUNCT
ejpam-4654	67	27	using	use	VERB
ejpam-4654	67	28	the	the	DET
ejpam-4654	67	29	fact	fact	NOUN
ejpam-4654	67	30	that	that	SCONJ
ejpam-4654	67	31	f	f	PROPN
ejpam-4654	67	32	is	be	AUX
ejpam-4654	67	33	a	a	DET
ejpam-4654	67	34	quasi	quasi	NOUN
ejpam-4654	67	35	-	-	NOUN
ejpam-4654	67	36	homeomorphism	homeomorphism	ADJ
ejpam-4654	67	37	we	we	PRON
ejpam-4654	67	38	obtain	obtain	VERB
ejpam-4654	67	39	s	s	VERB
ejpam-4654	67	40	=	=	PUNCT
ejpam-4654	67	41	⋃	⋃	NOUN
ejpam-4654	67	42	i∈j	i∈j	NOUN
ejpam-4654	67	43	vi	vi	NOUN
ejpam-4654	68	1	and	and	CCONJ
ejpam-4654	68	2	so	so	ADV
ejpam-4654	68	3	s	s	VERB
ejpam-4654	68	4	is	be	AUX
ejpam-4654	68	5	quasi	quasi	ADJ
ejpam-4654	68	6	-	-	ADJ
ejpam-4654	68	7	compact	compact	ADJ
ejpam-4654	68	8	in	in	ADP
ejpam-4654	68	9	y	y	PROPN
ejpam-4654	68	10	.	.	PUNCT
ejpam-4654	69	1	2	2	X
ejpam-4654	69	2	.	.	X
ejpam-4654	69	3	suppose	suppose	VERB
ejpam-4654	69	4	that	that	SCONJ
ejpam-4654	69	5	s	s	VERB
ejpam-4654	69	6	is	be	AUX
ejpam-4654	69	7	an	an	DET
ejpam-4654	69	8	irreducible	irreducible	ADJ
ejpam-4654	69	9	closed	closed	ADJ
ejpam-4654	69	10	subset	subset	NOUN
ejpam-4654	69	11	of	of	ADP
ejpam-4654	69	12	y	y	PROPN
ejpam-4654	69	13	.	.	PUNCT
ejpam-4654	70	1	let	let	VERB
ejpam-4654	70	2	f	f	PROPN
ejpam-4654	70	3	and	and	CCONJ
ejpam-4654	70	4	k	k	PROPN
ejpam-4654	70	5	be	be	AUX
ejpam-4654	70	6	two	two	NUM
ejpam-4654	70	7	closed	closed	ADJ
ejpam-4654	70	8	subset	subset	NOUN
ejpam-4654	70	9	of	of	ADP
ejpam-4654	70	10	x	x	SYM
ejpam-4654	70	11	such	such	ADJ
ejpam-4654	70	12	that	that	DET
ejpam-4654	70	13	f−1(s	f−1(s	PROPN
ejpam-4654	70	14	)	)	PUNCT
ejpam-4654	70	15	=	=	SYM
ejpam-4654	71	1	f	f	PROPN
ejpam-4654	71	2	∪	∪	PROPN
ejpam-4654	71	3	k.	k.	PROPN
ejpam-4654	71	4	since	since	SCONJ
ejpam-4654	71	5	f	f	PROPN
ejpam-4654	71	6	is	be	AUX
ejpam-4654	71	7	a	a	DET
ejpam-4654	71	8	quasi	quasi	NOUN
ejpam-4654	71	9	-	-	NOUN
ejpam-4654	71	10	homeomorphism	homeomorphism	ADJ
ejpam-4654	71	11	there	there	PRON
ejpam-4654	71	12	exists	exist	VERB
ejpam-4654	71	13	two	two	NUM
ejpam-4654	71	14	closed	closed	ADJ
ejpam-4654	71	15	subsets	subset	NOUN
ejpam-4654	71	16	f	f	NOUN
ejpam-4654	72	1	′	′	NOUN
ejpam-4654	73	1	and	and	CCONJ
ejpam-4654	73	2	k	k	NOUN
ejpam-4654	74	1	′	′	NOUN
ejpam-4654	74	2	of	of	ADP
ejpam-4654	74	3	y	y	PRON
ejpam-4654	74	4	such	such	ADJ
ejpam-4654	74	5	that	that	DET
ejpam-4654	74	6	f−1(f	f−1(f	PROPN
ejpam-4654	74	7	′	′	NOUN
ejpam-4654	74	8	)	)	PUNCT
ejpam-4654	75	1	=	=	SYM
ejpam-4654	75	2	f	f	PROPN
ejpam-4654	75	3	and	and	CCONJ
ejpam-4654	75	4	f−1(k	f−1(k	PROPN
ejpam-4654	75	5	′	′	NUM
ejpam-4654	75	6	)	)	PUNCT
ejpam-4654	76	1	=	=	PUNCT
ejpam-4654	76	2	k.	k.	PROPN
ejpam-4654	76	3	hence	hence	ADV
ejpam-4654	76	4	f−1(s	f−1(s	PROPN
ejpam-4654	76	5	)	)	PUNCT
ejpam-4654	77	1	=	=	SYM
ejpam-4654	77	2	f−1(f	f−1(f	NOUN
ejpam-4654	77	3	′	′	NUM
ejpam-4654	77	4	∪	∪	PROPN
ejpam-4654	77	5	k	k	PROPN
ejpam-4654	77	6	′	′	PROPN
ejpam-4654	77	7	)	)	PUNCT
ejpam-4654	77	8	,	,	PUNCT
ejpam-4654	77	9	which	which	PRON
ejpam-4654	77	10	gives	give	VERB
ejpam-4654	77	11	s	s	NOUN
ejpam-4654	77	12	=	=	SYM
ejpam-4654	77	13	f	f	NOUN
ejpam-4654	77	14	′	′	NOUN
ejpam-4654	77	15	∪	∪	PROPN
ejpam-4654	77	16	k	k	PROPN
ejpam-4654	77	17	′.	′.	NOUN
ejpam-4654	77	18	from	from	ADP
ejpam-4654	77	19	the	the	DET
ejpam-4654	77	20	fact	fact	NOUN
ejpam-4654	77	21	that	that	SCONJ
ejpam-4654	77	22	s	s	VERB
ejpam-4654	77	23	is	be	AUX
ejpam-4654	77	24	an	an	DET
ejpam-4654	77	25	irreducible	irreducible	ADJ
ejpam-4654	77	26	closed	closed	ADJ
ejpam-4654	77	27	subset	subset	NOUN
ejpam-4654	77	28	of	of	ADP
ejpam-4654	77	29	y	y	PROPN
ejpam-4654	77	30	,	,	PUNCT
ejpam-4654	77	31	it	it	PRON
ejpam-4654	77	32	follows	follow	VERB
ejpam-4654	77	33	that	that	PRON
ejpam-4654	77	34	s	s	VERB
ejpam-4654	77	35	=	=	ADJ
ejpam-4654	77	36	f	f	X
ejpam-4654	77	37	′	′	NOUN
ejpam-4654	77	38	or	or	CCONJ
ejpam-4654	77	39	f	f	PROPN
ejpam-4654	77	40	=	=	SYM
ejpam-4654	77	41	k	k	PROPN
ejpam-4654	77	42	′	′	PROPN
ejpam-4654	77	43	,	,	PUNCT
ejpam-4654	77	44	this	this	DET
ejpam-4654	77	45	yields	yield	NOUN
ejpam-4654	77	46	f−1(s	f−1(s	PROPN
ejpam-4654	77	47	)	)	PUNCT
ejpam-4654	77	48	=	=	SYM
ejpam-4654	77	49	f	f	PROPN
ejpam-4654	77	50	or	or	CCONJ
ejpam-4654	77	51	f−1(s	f−1(s	PROPN
ejpam-4654	77	52	)	)	PUNCT
ejpam-4654	78	1	=	=	PUNCT
ejpam-4654	78	2	k.	k.	PROPN
ejpam-4654	78	3	therefore	therefore	ADV
ejpam-4654	78	4	f−1(s	f−1(s	PROPN
ejpam-4654	78	5	)	)	PUNCT
ejpam-4654	78	6	is	be	AUX
ejpam-4654	78	7	an	an	DET
ejpam-4654	78	8	irreducible	irreducible	ADJ
ejpam-4654	78	9	closed	closed	ADJ
ejpam-4654	78	10	subset	subset	NOUN
ejpam-4654	78	11	of	of	ADP
ejpam-4654	78	12	x.	x.	PROPN
ejpam-4654	78	13	b.	b.	PROPN
ejpam-4654	78	14	alharbi	alharbi	PROPN
ejpam-4654	78	15	/	/	SYM
ejpam-4654	78	16	eur	eur	PROPN
ejpam-4654	78	17	.	.	PUNCT
ejpam-4654	79	1	j.	j.	PROPN
ejpam-4654	79	2	pure	pure	PROPN
ejpam-4654	79	3	appl	appl	PROPN
ejpam-4654	79	4	.	.	PROPN
ejpam-4654	79	5	math	math	PROPN
ejpam-4654	79	6	,	,	PUNCT
ejpam-4654	79	7	16	16	NUM
ejpam-4654	79	8	(	(	PUNCT
ejpam-4654	79	9	1	1	NUM
ejpam-4654	79	10	)	)	PUNCT
ejpam-4654	79	11	(	(	PUNCT
ejpam-4654	79	12	2023	2023	NUM
ejpam-4654	79	13	)	)	PUNCT
ejpam-4654	79	14	,	,	PUNCT
ejpam-4654	79	15	314	314	NUM
ejpam-4654	79	16	-	-	SYM
ejpam-4654	79	17	318	318	NUM
ejpam-4654	79	18	317	317	NUM
ejpam-4654	79	19	conversely	conversely	ADV
ejpam-4654	79	20	,	,	PUNCT
ejpam-4654	79	21	let	let	VERB
ejpam-4654	79	22	f	f	PRON
ejpam-4654	79	23	′	′	NOUN
ejpam-4654	80	1	and	and	CCONJ
ejpam-4654	80	2	k	k	PROPN
ejpam-4654	80	3	′	′	NUM
ejpam-4654	80	4	be	be	VERB
ejpam-4654	80	5	two	two	NUM
ejpam-4654	80	6	closed	closed	ADJ
ejpam-4654	80	7	subset	subset	NOUN
ejpam-4654	80	8	of	of	ADP
ejpam-4654	80	9	y	y	PRON
ejpam-4654	81	1	such	such	ADJ
ejpam-4654	81	2	that	that	DET
ejpam-4654	81	3	s	s	VERB
ejpam-4654	81	4	=	=	SYM
ejpam-4654	81	5	f	f	NOUN
ejpam-4654	81	6	′	′	NUM
ejpam-4654	81	7	∪k	∪k	PROPN
ejpam-4654	81	8	′.	′.	PROPN
ejpam-4654	81	9	then	then	ADV
ejpam-4654	81	10	f−1(s	f−1(s	PROPN
ejpam-4654	81	11	)	)	PUNCT
ejpam-4654	82	1	=	=	SYM
ejpam-4654	82	2	f−1(f	f−1(f	PROPN
ejpam-4654	82	3	′	′	NUM
ejpam-4654	82	4	)	)	PUNCT
ejpam-4654	82	5	∪	∪	X
ejpam-4654	82	6	f−1(k	f−1(k	PROPN
ejpam-4654	82	7	′	′	NUM
ejpam-4654	82	8	)	)	PUNCT
ejpam-4654	82	9	and	and	CCONJ
ejpam-4654	82	10	from	from	ADP
ejpam-4654	82	11	the	the	DET
ejpam-4654	82	12	fact	fact	NOUN
ejpam-4654	82	13	that	that	SCONJ
ejpam-4654	82	14	f−1(s	f−1(s	PROPN
ejpam-4654	82	15	)	)	PUNCT
ejpam-4654	82	16	is	be	AUX
ejpam-4654	82	17	an	an	DET
ejpam-4654	82	18	irreducible	irreducible	ADJ
ejpam-4654	82	19	closed	closed	ADJ
ejpam-4654	82	20	subset	subset	NOUN
ejpam-4654	82	21	of	of	ADP
ejpam-4654	82	22	x	x	PRON
ejpam-4654	82	23	it	it	PRON
ejpam-4654	82	24	follows	follow	VERB
ejpam-4654	82	25	that	that	SCONJ
ejpam-4654	82	26	f−1(s	f−1(s	PROPN
ejpam-4654	82	27	)	)	PUNCT
ejpam-4654	82	28	=	=	SYM
ejpam-4654	82	29	f−1(f	f−1(f	PROPN
ejpam-4654	82	30	′	′	NUM
ejpam-4654	82	31	)	)	PUNCT
ejpam-4654	82	32	or	or	CCONJ
ejpam-4654	82	33	f−1(s	f−1(s	ADJ
ejpam-4654	82	34	)	)	PUNCT
ejpam-4654	82	35	=	=	SYM
ejpam-4654	82	36	f−1(k	f−1(k	PROPN
ejpam-4654	82	37	′	′	NUM
ejpam-4654	82	38	)	)	PUNCT
ejpam-4654	82	39	.	.	PUNCT
ejpam-4654	83	1	since	since	SCONJ
ejpam-4654	83	2	f	f	PROPN
ejpam-4654	83	3	is	be	AUX
ejpam-4654	83	4	a	a	DET
ejpam-4654	83	5	quasi	quasi	NOUN
ejpam-4654	83	6	-	-	NOUN
ejpam-4654	83	7	homeomorphism	homeomorphism	ADJ
ejpam-4654	83	8	,	,	PUNCT
ejpam-4654	83	9	s	s	PART
ejpam-4654	83	10	=	=	NOUN
ejpam-4654	83	11	f	f	X
ejpam-4654	84	1	′	′	NUM
ejpam-4654	84	2	or	or	CCONJ
ejpam-4654	84	3	s	s	VERB
ejpam-4654	84	4	=	=	SYM
ejpam-4654	84	5	k	k	PROPN
ejpam-4654	84	6	′	′	NUM
ejpam-4654	84	7	which	which	PRON
ejpam-4654	84	8	implies	imply	VERB
ejpam-4654	84	9	that	that	SCONJ
ejpam-4654	84	10	s	s	VERB
ejpam-4654	84	11	is	be	AUX
ejpam-4654	84	12	an	an	DET
ejpam-4654	84	13	irreducible	irreducible	ADJ
ejpam-4654	84	14	closed	closed	ADJ
ejpam-4654	84	15	subset	subset	NOUN
ejpam-4654	84	16	of	of	ADP
ejpam-4654	84	17	y	y	PROPN
ejpam-4654	84	18	.	.	PUNCT
ejpam-4654	85	1	ifx	ifx	PROPN
ejpam-4654	85	2	is	be	AUX
ejpam-4654	85	3	quasi	quasi	ADJ
ejpam-4654	85	4	-	-	ADJ
ejpam-4654	85	5	compact	compact	ADJ
ejpam-4654	85	6	,	,	PUNCT
ejpam-4654	85	7	then	then	ADV
ejpam-4654	85	8	since	since	SCONJ
ejpam-4654	85	9	f	f	PROPN
ejpam-4654	85	10	is	be	AUX
ejpam-4654	85	11	onto	onto	ADP
ejpam-4654	85	12	and	and	CCONJ
ejpam-4654	85	13	continuous	continuous	ADJ
ejpam-4654	85	14	,	,	PUNCT
ejpam-4654	85	15	f(x	f(x	PROPN
ejpam-4654	85	16	)	)	PUNCT
ejpam-4654	86	1	=	=	SYM
ejpam-4654	86	2	y	y	PROPN
ejpam-4654	86	3	is	be	AUX
ejpam-4654	86	4	quasi	quasi	ADJ
ejpam-4654	86	5	-	-	ADJ
ejpam-4654	86	6	compact	compact	ADJ
ejpam-4654	86	7	.	.	PUNCT
ejpam-4654	87	1	by	by	ADP
ejpam-4654	87	2	the	the	DET
ejpam-4654	87	3	above	above	ADJ
ejpam-4654	87	4	item	item	NOUN
ejpam-4654	87	5	(	(	PUNCT
ejpam-4654	87	6	1	1	NUM
ejpam-4654	87	7	)	)	PUNCT
ejpam-4654	87	8	,	,	PUNCT
ejpam-4654	87	9	if	if	SCONJ
ejpam-4654	87	10	y	y	PROPN
ejpam-4654	87	11	is	be	AUX
ejpam-4654	87	12	quasi	quasi	ADJ
ejpam-4654	87	13	-	-	ADJ
ejpam-4654	87	14	compact	compact	ADJ
ejpam-4654	87	15	,	,	PUNCT
ejpam-4654	87	16	then	then	ADV
ejpam-4654	87	17	f−1(y	f−1(y	PROPN
ejpam-4654	87	18	)	)	PUNCT
ejpam-4654	88	1	=	=	PUNCT
ejpam-4654	88	2	x	x	X
ejpam-4654	88	3	is	be	AUX
ejpam-4654	88	4	quasi	quasi	ADJ
ejpam-4654	88	5	-	-	ADJ
ejpam-4654	88	6	compact	compact	ADJ
ejpam-4654	88	7	.	.	PUNCT
ejpam-4654	89	1	by	by	ADP
ejpam-4654	89	2	the	the	DET
ejpam-4654	89	3	above	above	ADJ
ejpam-4654	89	4	item	item	NOUN
ejpam-4654	89	5	(	(	PUNCT
ejpam-4654	89	6	1	1	NUM
ejpam-4654	89	7	)	)	PUNCT
ejpam-4654	89	8	,	,	PUNCT
ejpam-4654	89	9	(	(	PUNCT
ejpam-4654	89	10	x	x	X
ejpam-4654	89	11	,	,	PUNCT
ejpam-4654	89	12	t	t	PROPN
ejpam-4654	89	13	)	)	PUNCT
ejpam-4654	89	14	has	have	VERB
ejpam-4654	89	15	a	a	DET
ejpam-4654	89	16	base	base	NOUN
ejpam-4654	89	17	of	of	ADP
ejpam-4654	89	18	quasi	quasi	ADJ
ejpam-4654	89	19	-	-	ADJ
ejpam-4654	89	20	compact	compact	ADJ
ejpam-4654	89	21	open	open	ADJ
ejpam-4654	89	22	subsets	subset	NOUN
ejpam-4654	89	23	if	if	SCONJ
ejpam-4654	90	1	and	and	CCONJ
ejpam-4654	90	2	only	only	ADV
ejpam-4654	90	3	if	if	SCONJ
ejpam-4654	90	4	(	(	PUNCT
ejpam-4654	90	5	y	y	PROPN
ejpam-4654	90	6	,	,	PUNCT
ejpam-4654	90	7	t	t	PROPN
ejpam-4654	90	8	′	′	NUM
ejpam-4654	90	9	)	)	PUNCT
ejpam-4654	90	10	has	have	VERB
ejpam-4654	90	11	a	a	DET
ejpam-4654	90	12	base	base	NOUN
ejpam-4654	90	13	of	of	ADP
ejpam-4654	90	14	quasi	quasi	ADJ
ejpam-4654	90	15	-	-	ADJ
ejpam-4654	90	16	compact	compact	ADJ
ejpam-4654	90	17	open	open	ADJ
ejpam-4654	90	18	subsets	subset	NOUN
ejpam-4654	90	19	.	.	PUNCT
ejpam-4654	91	1	by	by	ADP
ejpam-4654	91	2	the	the	DET
ejpam-4654	91	3	above	above	ADJ
ejpam-4654	91	4	item	item	NOUN
ejpam-4654	91	5	(	(	PUNCT
ejpam-4654	91	6	1	1	NUM
ejpam-4654	91	7	)	)	PUNCT
ejpam-4654	91	8	and	and	CCONJ
ejpam-4654	91	9	the	the	DET
ejpam-4654	91	10	fact	fact	NOUN
ejpam-4654	91	11	that	that	SCONJ
ejpam-4654	91	12	f	f	PROPN
ejpam-4654	91	13	is	be	AUX
ejpam-4654	91	14	onto	onto	ADP
ejpam-4654	91	15	and	and	CCONJ
ejpam-4654	91	16	continuous	continuous	ADJ
ejpam-4654	91	17	,	,	PUNCT
ejpam-4654	91	18	the	the	DET
ejpam-4654	91	19	family	family	NOUN
ejpam-4654	91	20	of	of	ADP
ejpam-4654	91	21	quasicompact	quasicompact	PROPN
ejpam-4654	91	22	open	open	ADJ
ejpam-4654	91	23	subsets	subset	NOUN
ejpam-4654	91	24	of	of	ADP
ejpam-4654	91	25	(	(	PUNCT
ejpam-4654	91	26	x	x	PROPN
ejpam-4654	91	27	,	,	PUNCT
ejpam-4654	91	28	t	t	PROPN
ejpam-4654	91	29	)	)	PUNCT
ejpam-4654	91	30	is	be	AUX
ejpam-4654	91	31	stable	stable	ADJ
ejpam-4654	91	32	by	by	ADP
ejpam-4654	91	33	finite	finite	ADJ
ejpam-4654	91	34	intersection	intersection	NOUN
ejpam-4654	91	35	if	if	SCONJ
ejpam-4654	91	36	and	and	CCONJ
ejpam-4654	91	37	only	only	ADV
ejpam-4654	91	38	if	if	SCONJ
ejpam-4654	91	39	the	the	DET
ejpam-4654	91	40	family	family	NOUN
ejpam-4654	91	41	of	of	ADP
ejpam-4654	91	42	quasi	quasi	ADJ
ejpam-4654	91	43	-	-	ADJ
ejpam-4654	91	44	compact	compact	ADJ
ejpam-4654	91	45	open	open	ADJ
ejpam-4654	91	46	subsets	subset	NOUN
ejpam-4654	91	47	of	of	ADP
ejpam-4654	91	48	(	(	PUNCT
ejpam-4654	91	49	y	y	PROPN
ejpam-4654	91	50	,	,	PUNCT
ejpam-4654	91	51	t	t	PROPN
ejpam-4654	91	52	′	′	NUM
ejpam-4654	91	53	)	)	PUNCT
ejpam-4654	91	54	is	be	AUX
ejpam-4654	91	55	stable	stable	ADJ
ejpam-4654	91	56	by	by	ADP
ejpam-4654	91	57	finite	finite	ADJ
ejpam-4654	91	58	intersection	intersection	NOUN
ejpam-4654	91	59	.	.	PUNCT
ejpam-4654	92	1	by	by	ADP
ejpam-4654	92	2	the	the	DET
ejpam-4654	92	3	above	above	ADJ
ejpam-4654	92	4	item	item	NOUN
ejpam-4654	92	5	(	(	PUNCT
ejpam-4654	92	6	2	2	NUM
ejpam-4654	92	7	)	)	PUNCT
ejpam-4654	92	8	and	and	CCONJ
ejpam-4654	92	9	the	the	DET
ejpam-4654	92	10	fact	fact	NOUN
ejpam-4654	92	11	that	that	SCONJ
ejpam-4654	92	12	f	f	PROPN
ejpam-4654	92	13	is	be	AUX
ejpam-4654	92	14	onto	onto	ADP
ejpam-4654	92	15	and	and	CCONJ
ejpam-4654	92	16	continuous	continuous	ADJ
ejpam-4654	92	17	,	,	PUNCT
ejpam-4654	92	18	every	every	DET
ejpam-4654	92	19	irreducible	irreducible	ADJ
ejpam-4654	92	20	closed	closed	ADJ
ejpam-4654	92	21	subset	subset	NOUN
ejpam-4654	92	22	of	of	ADP
ejpam-4654	92	23	(	(	PUNCT
ejpam-4654	92	24	x	x	PROPN
ejpam-4654	92	25	,	,	PUNCT
ejpam-4654	92	26	t	t	PROPN
ejpam-4654	92	27	)	)	PUNCT
ejpam-4654	92	28	has	have	VERB
ejpam-4654	92	29	a	a	DET
ejpam-4654	92	30	generic	generic	ADJ
ejpam-4654	92	31	point	point	NOUN
ejpam-4654	92	32	if	if	SCONJ
ejpam-4654	93	1	and	and	CCONJ
ejpam-4654	93	2	only	only	ADV
ejpam-4654	93	3	if	if	SCONJ
ejpam-4654	93	4	every	every	DET
ejpam-4654	93	5	irreducible	irreducible	ADJ
ejpam-4654	93	6	closed	closed	ADJ
ejpam-4654	93	7	subset	subset	NOUN
ejpam-4654	93	8	of	of	ADP
ejpam-4654	93	9	(	(	PUNCT
ejpam-4654	93	10	y	y	PROPN
ejpam-4654	93	11	,	,	PUNCT
ejpam-4654	93	12	t	t	PROPN
ejpam-4654	93	13	′	′	NUM
ejpam-4654	93	14	)	)	PUNCT
ejpam-4654	93	15	has	have	VERB
ejpam-4654	93	16	a	a	DET
ejpam-4654	93	17	generic	generic	ADJ
ejpam-4654	93	18	point	point	NOUN
ejpam-4654	93	19	.	.	PUNCT
ejpam-4654	94	1	this	this	PRON
ejpam-4654	94	2	ends	end	VERB
ejpam-4654	94	3	the	the	DET
ejpam-4654	94	4	proof	proof	NOUN
ejpam-4654	94	5	of	of	ADP
ejpam-4654	94	6	the	the	DET
ejpam-4654	94	7	theorem	theorem	NOUN
ejpam-4654	94	8	.	.	PROPN
ejpam-4654	95	1	3	3	X
ejpam-4654	95	2	.	.	X
ejpam-4654	95	3	spectral	spectral	ADJ
ejpam-4654	95	4	graph	graph	NOUN
ejpam-4654	95	5	let	let	VERB
ejpam-4654	95	6	g	g	NOUN
ejpam-4654	95	7	=	=	SYM
ejpam-4654	95	8	(	(	PUNCT
ejpam-4654	95	9	v	v	NOUN
ejpam-4654	95	10	,	,	PUNCT
ejpam-4654	95	11	e	e	NOUN
ejpam-4654	95	12	)	)	PUNCT
ejpam-4654	95	13	be	be	AUX
ejpam-4654	95	14	a	a	DET
ejpam-4654	95	15	graph	graph	NOUN
ejpam-4654	95	16	(	(	PUNCT
ejpam-4654	95	17	finite	finite	NOUN
ejpam-4654	95	18	or	or	CCONJ
ejpam-4654	95	19	infinite	infinite	VERB
ejpam-4654	95	20	)	)	PUNCT
ejpam-4654	95	21	and	and	CCONJ
ejpam-4654	95	22	let	let	VERB
ejpam-4654	95	23	u	u	NOUN
ejpam-4654	95	24	,	,	PUNCT
ejpam-4654	95	25	v	v	PROPN
ejpam-4654	95	26	∈	∈	PROPN
ejpam-4654	95	27	v	v	NOUN
ejpam-4654	95	28	.	.	PUNCT
ejpam-4654	96	1	a	a	DET
ejpam-4654	96	2	path	path	NOUN
ejpam-4654	96	3	from	from	ADP
ejpam-4654	96	4	u	u	NOUN
ejpam-4654	96	5	to	to	ADP
ejpam-4654	96	6	v	v	NOUN
ejpam-4654	96	7	in	in	ADP
ejpam-4654	96	8	g	g	PROPN
ejpam-4654	96	9	is	be	AUX
ejpam-4654	96	10	a	a	DET
ejpam-4654	96	11	sequence	sequence	NOUN
ejpam-4654	96	12	of	of	ADP
ejpam-4654	96	13	edges	edge	NOUN
ejpam-4654	96	14	e1	e1	NOUN
ejpam-4654	96	15	,	,	PUNCT
ejpam-4654	96	16	.	.	PUNCT
ejpam-4654	96	17	.	.	PUNCT
ejpam-4654	97	1	.	.	PUNCT
ejpam-4654	98	1	,	,	PUNCT
ejpam-4654	98	2	en	en	X
ejpam-4654	98	3	of	of	ADP
ejpam-4654	98	4	e	e	PROPN
ejpam-4654	98	5	for	for	ADP
ejpam-4654	98	6	which	which	PRON
ejpam-4654	98	7	there	there	PRON
ejpam-4654	98	8	exists	exist	VERB
ejpam-4654	98	9	a	a	DET
ejpam-4654	98	10	sequence	sequence	NOUN
ejpam-4654	98	11	x0	x0	PROPN
ejpam-4654	98	12	=	=	PUNCT
ejpam-4654	98	13	u	u	PROPN
ejpam-4654	98	14	,	,	PUNCT
ejpam-4654	98	15	x1	x1	PROPN
ejpam-4654	98	16	,	,	PUNCT
ejpam-4654	98	17	.	.	PUNCT
ejpam-4654	98	18	.	.	PUNCT
ejpam-4654	98	19	.	.	PUNCT
ejpam-4654	99	1	,	,	PUNCT
ejpam-4654	99	2	xn−1	xn−1	PROPN
ejpam-4654	99	3	,	,	PUNCT
ejpam-4654	99	4	xn	xn	PUNCT
ejpam-4654	100	1	=	=	SYM
ejpam-4654	100	2	v	v	NOUN
ejpam-4654	100	3	of	of	ADP
ejpam-4654	100	4	vertices	vertex	NOUN
ejpam-4654	100	5	such	such	ADJ
ejpam-4654	100	6	that	that	SCONJ
ejpam-4654	100	7	ei	ei	NOUN
ejpam-4654	100	8	has	have	VERB
ejpam-4654	100	9	,	,	PUNCT
ejpam-4654	100	10	for	for	ADP
ejpam-4654	100	11	i	i	PROPN
ejpam-4654	100	12	=	=	NOUN
ejpam-4654	100	13	1	1	NUM
ejpam-4654	100	14	,	,	PUNCT
ejpam-4654	100	15	...	...	PUNCT
ejpam-4654	100	16	,	,	PUNCT
ejpam-4654	100	17	n	n	CCONJ
ejpam-4654	100	18	,	,	PUNCT
ejpam-4654	100	19	the	the	DET
ejpam-4654	100	20	endpoints	endpoint	NOUN
ejpam-4654	100	21	xi−1	xi−1	PROPN
ejpam-4654	100	22	and	and	CCONJ
ejpam-4654	100	23	xi	xi	PROPN
ejpam-4654	100	24	.	.	PUNCT
ejpam-4654	101	1	we	we	PRON
ejpam-4654	101	2	denote	denote	VERB
ejpam-4654	101	3	by	by	ADP
ejpam-4654	101	4	r(u	r(u	NOUN
ejpam-4654	101	5	)	)	PUNCT
ejpam-4654	102	1	=	=	PRON
ejpam-4654	102	2	{	{	PUNCT
ejpam-4654	102	3	u	u	NOUN
ejpam-4654	102	4	}	}	PUNCT
ejpam-4654	102	5	∪	∪	ADJ
ejpam-4654	102	6	{	{	PUNCT
ejpam-4654	102	7	v	v	NOUN
ejpam-4654	102	8	:	:	PUNCT
ejpam-4654	102	9	if	if	SCONJ
ejpam-4654	102	10	there	there	PRON
ejpam-4654	102	11	exists	exist	VERB
ejpam-4654	102	12	a	a	DET
ejpam-4654	102	13	path	path	NOUN
ejpam-4654	102	14	from	from	ADP
ejpam-4654	102	15	u	u	NOUN
ejpam-4654	102	16	to	to	ADP
ejpam-4654	102	17	v	v	PROPN
ejpam-4654	102	18	}	}	PUNCT
ejpam-4654	102	19	l(u	l(u	PROPN
ejpam-4654	102	20	)	)	PUNCT
ejpam-4654	102	21	=	=	PRON
ejpam-4654	102	22	{	{	PUNCT
ejpam-4654	102	23	u	u	NOUN
ejpam-4654	102	24	}	}	PUNCT
ejpam-4654	102	25	∪	∪	ADJ
ejpam-4654	102	26	{	{	PUNCT
ejpam-4654	102	27	v	v	NOUN
ejpam-4654	102	28	:	:	PUNCT
ejpam-4654	102	29	if	if	SCONJ
ejpam-4654	102	30	there	there	PRON
ejpam-4654	102	31	exists	exist	VERB
ejpam-4654	102	32	a	a	DET
ejpam-4654	102	33	path	path	NOUN
ejpam-4654	102	34	from	from	ADP
ejpam-4654	102	35	v	v	NUM
ejpam-4654	102	36	to	to	ADP
ejpam-4654	102	37	u	u	NOUN
ejpam-4654	102	38	}	}	PUNCT
ejpam-4654	102	39	.	.	PUNCT
ejpam-4654	103	1	the	the	DET
ejpam-4654	103	2	family	family	NOUN
ejpam-4654	103	3	{	{	PUNCT
ejpam-4654	103	4	r(u	r(u	PROPN
ejpam-4654	103	5	)	)	PUNCT
ejpam-4654	103	6	:	:	PUNCT
ejpam-4654	103	7	u	u	NOUN
ejpam-4654	103	8	∈	∈	PROPN
ejpam-4654	103	9	g	g	PROPN
ejpam-4654	103	10	}	}	PUNCT
ejpam-4654	103	11	(	(	PUNCT
ejpam-4654	103	12	respectively	respectively	ADV
ejpam-4654	103	13	{	{	PUNCT
ejpam-4654	103	14	l(u	l(u	PROPN
ejpam-4654	103	15	)	)	PUNCT
ejpam-4654	103	16	:	:	PUNCT
ejpam-4654	103	17	u	u	NOUN
ejpam-4654	103	18	∈	∈	PROPN
ejpam-4654	103	19	g	g	NOUN
ejpam-4654	103	20	}	}	PUNCT
ejpam-4654	103	21	)	)	PUNCT
ejpam-4654	103	22	forms	form	VERB
ejpam-4654	103	23	a	a	DET
ejpam-4654	103	24	base	base	NOUN
ejpam-4654	103	25	of	of	ADP
ejpam-4654	103	26	a	a	DET
ejpam-4654	103	27	topology	topology	NOUN
ejpam-4654	103	28	on	on	ADP
ejpam-4654	103	29	g	g	PROPN
ejpam-4654	103	30	called	call	VERB
ejpam-4654	103	31	the	the	DET
ejpam-4654	103	32	g	g	NOUN
ejpam-4654	103	33	-	-	PUNCT
ejpam-4654	103	34	right	right	NOUN
ejpam-4654	103	35	τ(gr	τ(gr	PROPN
ejpam-4654	103	36	)	)	PUNCT
ejpam-4654	103	37	(	(	PUNCT
ejpam-4654	103	38	respectively	respectively	ADV
ejpam-4654	103	39	g	g	NOUN
ejpam-4654	103	40	-	-	PUNCT
ejpam-4654	103	41	left	leave	VERB
ejpam-4654	103	42	τ(gl	τ(gl	NUM
ejpam-4654	103	43	)	)	PUNCT
ejpam-4654	103	44	)	)	PUNCT
ejpam-4654	103	45	topology	topology	NOUN
ejpam-4654	103	46	.	.	PUNCT
ejpam-4654	104	1	two	two	NUM
ejpam-4654	104	2	vertices	vertex	NOUN
ejpam-4654	104	3	a	a	PRON
ejpam-4654	104	4	and	and	CCONJ
ejpam-4654	104	5	b	b	NOUN
ejpam-4654	104	6	in	in	ADP
ejpam-4654	104	7	a	a	DET
ejpam-4654	104	8	graph	graph	NOUN
ejpam-4654	104	9	g	g	NOUN
ejpam-4654	104	10	are	be	AUX
ejpam-4654	104	11	called	call	VERB
ejpam-4654	104	12	adjacent	adjacent	ADJ
ejpam-4654	104	13	in	in	ADP
ejpam-4654	104	14	g	g	PROPN
ejpam-4654	104	15	if	if	SCONJ
ejpam-4654	104	16	a	a	PRON
ejpam-4654	104	17	and	and	CCONJ
ejpam-4654	104	18	b	b	NOUN
ejpam-4654	104	19	are	be	AUX
ejpam-4654	104	20	endpoints	endpoint	NOUN
ejpam-4654	104	21	of	of	ADP
ejpam-4654	104	22	an	an	DET
ejpam-4654	104	23	edge	edge	NOUN
ejpam-4654	104	24	e	e	NOUN
ejpam-4654	104	25	of	of	ADP
ejpam-4654	104	26	g.	g.	PROPN
ejpam-4654	105	1	the	the	DET
ejpam-4654	105	2	graphs	graph	NOUN
ejpam-4654	105	3	g1	g1	PROPN
ejpam-4654	105	4	=	=	SYM
ejpam-4654	105	5	(	(	PUNCT
ejpam-4654	105	6	v1	v1	PROPN
ejpam-4654	105	7	,	,	PUNCT
ejpam-4654	105	8	e1	e1	NOUN
ejpam-4654	105	9	)	)	PUNCT
ejpam-4654	105	10	and	and	CCONJ
ejpam-4654	105	11	g2	g2	PROPN
ejpam-4654	105	12	=	=	PUNCT
ejpam-4654	105	13	(	(	PUNCT
ejpam-4654	105	14	v2	v2	PROPN
ejpam-4654	105	15	,	,	PUNCT
ejpam-4654	105	16	e2	e2	PROPN
ejpam-4654	105	17	)	)	PUNCT
ejpam-4654	105	18	are	be	AUX
ejpam-4654	105	19	isomorphic	isomorphic	ADJ
ejpam-4654	105	20	if	if	SCONJ
ejpam-4654	105	21	there	there	PRON
ejpam-4654	105	22	exists	exist	VERB
ejpam-4654	105	23	a	a	DET
ejpam-4654	105	24	one	one	NUM
ejpam-4654	105	25	-	-	PUNCT
ejpam-4654	105	26	to	to	ADP
ejpam-4654	105	27	-	-	PUNCT
ejpam-4654	105	28	one	one	NUM
ejpam-4654	105	29	and	and	CCONJ
ejpam-4654	105	30	onto	onto	ADP
ejpam-4654	105	31	function	function	NOUN
ejpam-4654	105	32	f	f	PROPN
ejpam-4654	105	33	from	from	ADP
ejpam-4654	105	34	v1	v1	NOUN
ejpam-4654	105	35	to	to	PART
ejpam-4654	105	36	v2	v2	VERB
ejpam-4654	105	37	with	with	ADP
ejpam-4654	105	38	the	the	DET
ejpam-4654	105	39	property	property	NOUN
ejpam-4654	105	40	that	that	PRON
ejpam-4654	105	41	a	a	PRON
ejpam-4654	105	42	and	and	CCONJ
ejpam-4654	105	43	b	b	NOUN
ejpam-4654	105	44	are	be	AUX
ejpam-4654	105	45	adjacent	adjacent	ADJ
ejpam-4654	105	46	in	in	ADP
ejpam-4654	105	47	g1	g1	PROPN
ejpam-4654	105	48	if	if	SCONJ
ejpam-4654	105	49	and	and	CCONJ
ejpam-4654	105	50	only	only	ADV
ejpam-4654	105	51	if	if	SCONJ
ejpam-4654	105	52	f(a	f(a	NOUN
ejpam-4654	105	53	)	)	PUNCT
ejpam-4654	105	54	and	and	CCONJ
ejpam-4654	105	55	f(b	f(b	PROPN
ejpam-4654	105	56	)	)	PUNCT
ejpam-4654	105	57	are	be	AUX
ejpam-4654	105	58	adjacent	adjacent	ADJ
ejpam-4654	105	59	in	in	ADP
ejpam-4654	105	60	g2	g2	PROPN
ejpam-4654	105	61	,	,	PUNCT
ejpam-4654	105	62	for	for	ADP
ejpam-4654	105	63	all	all	DET
ejpam-4654	105	64	a	a	PRON
ejpam-4654	105	65	and	and	CCONJ
ejpam-4654	105	66	b	b	NOUN
ejpam-4654	105	67	in	in	ADP
ejpam-4654	105	68	v1	v1	NOUN
ejpam-4654	105	69	.	.	PUNCT
ejpam-4654	106	1	such	such	DET
ejpam-4654	106	2	a	a	DET
ejpam-4654	106	3	function	function	NOUN
ejpam-4654	106	4	f	f	PROPN
ejpam-4654	106	5	is	be	AUX
ejpam-4654	106	6	called	call	VERB
ejpam-4654	106	7	an	an	DET
ejpam-4654	106	8	isomorphism	isomorphism	NOUN
ejpam-4654	106	9	.	.	PUNCT
ejpam-4654	107	1	definition	definition	NOUN
ejpam-4654	107	2	3.1	3.1	NUM
ejpam-4654	107	3	.	.	PUNCT
ejpam-4654	108	1	[	[	X
ejpam-4654	108	2	1	1	X
ejpam-4654	108	3	]	]	PUNCT
ejpam-4654	108	4	the	the	DET
ejpam-4654	108	5	graphs	graph	NOUN
ejpam-4654	108	6	g1	g1	PROPN
ejpam-4654	108	7	=	=	SYM
ejpam-4654	108	8	(	(	PUNCT
ejpam-4654	108	9	v1	v1	PROPN
ejpam-4654	108	10	,	,	PUNCT
ejpam-4654	108	11	e1	e1	NOUN
ejpam-4654	108	12	)	)	PUNCT
ejpam-4654	108	13	and	and	CCONJ
ejpam-4654	108	14	g2	g2	PROPN
ejpam-4654	108	15	=	=	PUNCT
ejpam-4654	108	16	(	(	PUNCT
ejpam-4654	108	17	v2	v2	PROPN
ejpam-4654	108	18	,	,	PUNCT
ejpam-4654	108	19	e2	e2	PROPN
ejpam-4654	108	20	)	)	PUNCT
ejpam-4654	108	21	are	be	AUX
ejpam-4654	108	22	homeomorphic	homeomorphic	ADJ
ejpam-4654	108	23	if	if	SCONJ
ejpam-4654	108	24	(	(	PUNCT
ejpam-4654	108	25	g1	g1	PROPN
ejpam-4654	108	26	,	,	PUNCT
ejpam-4654	108	27	τ(g	τ(g	PROPN
ejpam-4654	108	28	r	r	NOUN
ejpam-4654	108	29	1	1	NUM
ejpam-4654	108	30	)	)	PUNCT
ejpam-4654	108	31	)	)	PUNCT
ejpam-4654	108	32	and	and	CCONJ
ejpam-4654	108	33	(	(	PUNCT
ejpam-4654	108	34	g2	g2	PROPN
ejpam-4654	108	35	,	,	PUNCT
ejpam-4654	108	36	τ(g	τ(g	X
ejpam-4654	108	37	r	r	NOUN
ejpam-4654	108	38	2	2	NUM
ejpam-4654	108	39	)	)	PUNCT
ejpam-4654	108	40	)	)	PUNCT
ejpam-4654	108	41	are	be	AUX
ejpam-4654	108	42	homeomorphic	homeomorphic	ADJ
ejpam-4654	108	43	.	.	PUNCT
ejpam-4654	109	1	note	note	VERB
ejpam-4654	109	2	that	that	SCONJ
ejpam-4654	109	3	,	,	PUNCT
ejpam-4654	109	4	according	accord	VERB
ejpam-4654	109	5	to	to	ADP
ejpam-4654	109	6	[	[	X
ejpam-4654	109	7	1	1	NUM
ejpam-4654	109	8	]	]	PUNCT
ejpam-4654	109	9	,	,	PUNCT
ejpam-4654	109	10	if	if	SCONJ
ejpam-4654	109	11	g1	g1	PROPN
ejpam-4654	109	12	=	=	SYM
ejpam-4654	109	13	(	(	PUNCT
ejpam-4654	109	14	v1	v1	NOUN
ejpam-4654	109	15	,	,	PUNCT
ejpam-4654	109	16	e1	e1	NOUN
ejpam-4654	109	17	)	)	PUNCT
ejpam-4654	109	18	and	and	CCONJ
ejpam-4654	109	19	g2	g2	PROPN
ejpam-4654	109	20	=	=	PUNCT
ejpam-4654	109	21	(	(	PUNCT
ejpam-4654	109	22	v2	v2	PROPN
ejpam-4654	109	23	,	,	PUNCT
ejpam-4654	109	24	e2	e2	PROPN
ejpam-4654	109	25	)	)	PUNCT
ejpam-4654	109	26	are	be	AUX
ejpam-4654	109	27	isomorphic	isomorphic	ADJ
ejpam-4654	109	28	,	,	PUNCT
ejpam-4654	109	29	then	then	ADV
ejpam-4654	109	30	they	they	PRON
ejpam-4654	109	31	are	be	AUX
ejpam-4654	109	32	homeomorphic	homeomorphic	ADJ
ejpam-4654	109	33	.	.	PUNCT
ejpam-4654	110	1	if	if	SCONJ
ejpam-4654	110	2	moreover	moreover	ADV
ejpam-4654	110	3	every	every	DET
ejpam-4654	110	4	vertex	vertex	NOUN
ejpam-4654	110	5	of	of	ADP
ejpam-4654	110	6	g1	g1	PROPN
ejpam-4654	110	7	and	and	CCONJ
ejpam-4654	110	8	g2	g2	PROPN
ejpam-4654	110	9	has	have	VERB
ejpam-4654	110	10	a	a	DET
ejpam-4654	110	11	loop	loop	NOUN
ejpam-4654	110	12	,	,	PUNCT
ejpam-4654	110	13	then	then	ADV
ejpam-4654	110	14	isomorphic	isomorphic	ADJ
ejpam-4654	110	15	and	and	CCONJ
ejpam-4654	110	16	homeomorphic	homeomorphic	ADJ
ejpam-4654	110	17	properties	property	NOUN
ejpam-4654	110	18	are	be	AUX
ejpam-4654	110	19	equivalent	equivalent	ADJ
ejpam-4654	110	20	.	.	PUNCT
ejpam-4654	111	1	references	reference	NOUN
ejpam-4654	111	2	318	318	NUM
ejpam-4654	111	3	let	let	VERB
ejpam-4654	111	4	g	g	NOUN
ejpam-4654	111	5	=	=	SYM
ejpam-4654	111	6	(	(	PUNCT
ejpam-4654	111	7	v	v	NOUN
ejpam-4654	111	8	,	,	PUNCT
ejpam-4654	111	9	e	e	NOUN
ejpam-4654	111	10	)	)	PUNCT
ejpam-4654	111	11	be	be	AUX
ejpam-4654	111	12	a	a	DET
ejpam-4654	111	13	graph	graph	NOUN
ejpam-4654	111	14	equipped	equip	VERB
ejpam-4654	111	15	with	with	ADP
ejpam-4654	111	16	a	a	DET
ejpam-4654	111	17	topology	topology	NOUN
ejpam-4654	111	18	t	t	NOUN
ejpam-4654	111	19	.	.	PUNCT
ejpam-4654	112	1	we	we	PRON
ejpam-4654	112	2	say	say	VERB
ejpam-4654	112	3	that	that	SCONJ
ejpam-4654	112	4	t	t	PROPN
ejpam-4654	112	5	is	be	AUX
ejpam-4654	112	6	compatible	compatible	ADJ
ejpam-4654	112	7	with	with	ADP
ejpam-4654	112	8	the	the	DET
ejpam-4654	112	9	graph	graph	NOUN
ejpam-4654	112	10	structure	structure	NOUN
ejpam-4654	112	11	g	g	NOUN
ejpam-4654	112	12	,	,	PUNCT
ejpam-4654	112	13	if	if	SCONJ
ejpam-4654	112	14	for	for	ADP
ejpam-4654	112	15	all	all	PRON
ejpam-4654	112	16	u	u	NOUN
ejpam-4654	112	17	∈	∈	PROPN
ejpam-4654	112	18	v	v	NOUN
ejpam-4654	112	19	,	,	PUNCT
ejpam-4654	112	20	{	{	PUNCT
ejpam-4654	112	21	u	u	NOUN
ejpam-4654	112	22	}	}	PUNCT
ejpam-4654	112	23	=	=	SYM
ejpam-4654	112	24	r(u	r(u	PROPN
ejpam-4654	112	25	)	)	PUNCT
ejpam-4654	112	26	.	.	PUNCT
ejpam-4654	113	1	we	we	PRON
ejpam-4654	113	2	remark	remark	VERB
ejpam-4654	113	3	that	that	SCONJ
ejpam-4654	113	4	the	the	DET
ejpam-4654	113	5	g	g	NOUN
ejpam-4654	113	6	-	-	PUNCT
ejpam-4654	113	7	left	leave	VERB
ejpam-4654	113	8	τ(gl	τ(gl	NOUN
ejpam-4654	113	9	)	)	PUNCT
ejpam-4654	113	10	topology	topology	NOUN
ejpam-4654	113	11	is	be	AUX
ejpam-4654	113	12	the	the	DET
ejpam-4654	113	13	finer	fine	ADJ
ejpam-4654	113	14	topology	topology	NOUN
ejpam-4654	113	15	compatible	compatible	ADJ
ejpam-4654	113	16	with	with	ADP
ejpam-4654	113	17	the	the	DET
ejpam-4654	113	18	graph	graph	NOUN
ejpam-4654	113	19	structure	structure	NOUN
ejpam-4654	113	20	g.	g.	NOUN
ejpam-4654	113	21	we	we	PRON
ejpam-4654	113	22	define	define	VERB
ejpam-4654	113	23	on	on	ADP
ejpam-4654	113	24	g	g	PROPN
ejpam-4654	113	25	the	the	DET
ejpam-4654	113	26	following	follow	VERB
ejpam-4654	113	27	relation	relation	NOUN
ejpam-4654	113	28	u	u	PROPN
ejpam-4654	113	29	⪯	⪯	VERB
ejpam-4654	113	30	v	v	INTJ
ejpam-4654	113	31	if	if	SCONJ
ejpam-4654	113	32	u	u	PROPN
ejpam-4654	113	33	∈	∈	PROPN
ejpam-4654	113	34	r(v	r(v	PROPN
ejpam-4654	113	35	)	)	PUNCT
ejpam-4654	113	36	.	.	PUNCT
ejpam-4654	114	1	it	it	PRON
ejpam-4654	114	2	is	be	AUX
ejpam-4654	114	3	easy	easy	ADJ
ejpam-4654	114	4	to	to	PART
ejpam-4654	114	5	see	see	VERB
ejpam-4654	114	6	that	that	DET
ejpam-4654	114	7	⪯	⪯	NOUN
ejpam-4654	114	8	is	be	AUX
ejpam-4654	114	9	reflexive	reflexive	ADJ
ejpam-4654	114	10	and	and	CCONJ
ejpam-4654	114	11	transitive	transitive	ADJ
ejpam-4654	114	12	.	.	PUNCT
ejpam-4654	115	1	then	then	ADV
ejpam-4654	115	2	⪯	⪯	PROPN
ejpam-4654	115	3	is	be	AUX
ejpam-4654	115	4	a	a	DET
ejpam-4654	115	5	preorder	preorder	NOUN
ejpam-4654	115	6	.	.	PUNCT
ejpam-4654	116	1	we	we	PRON
ejpam-4654	116	2	define	define	VERB
ejpam-4654	116	3	an	an	DET
ejpam-4654	116	4	equivalence	equivalence	NOUN
ejpam-4654	116	5	relation	relation	NOUN
ejpam-4654	116	6	on	on	ADP
ejpam-4654	116	7	g	g	PROPN
ejpam-4654	116	8	by	by	ADV
ejpam-4654	116	9	urv	urv	ADP
ejpam-4654	116	10	if	if	SCONJ
ejpam-4654	116	11	and	and	CCONJ
ejpam-4654	116	12	only	only	ADV
ejpam-4654	116	13	if	if	SCONJ
ejpam-4654	116	14	r(u	r(u	PROPN
ejpam-4654	116	15	)	)	PUNCT
ejpam-4654	116	16	=	=	SYM
ejpam-4654	116	17	r(v	r(v	PROPN
ejpam-4654	116	18	)	)	PUNCT
ejpam-4654	116	19	.	.	PUNCT
ejpam-4654	117	1	the	the	DET
ejpam-4654	117	2	quotient	quotient	NOUN
ejpam-4654	117	3	set	set	NOUN
ejpam-4654	117	4	(	(	PUNCT
ejpam-4654	117	5	the	the	DET
ejpam-4654	117	6	set	set	NOUN
ejpam-4654	117	7	of	of	ADP
ejpam-4654	117	8	equivalence	equivalence	NOUN
ejpam-4654	117	9	classes	class	NOUN
ejpam-4654	117	10	)	)	PUNCT
ejpam-4654	117	11	is	be	AUX
ejpam-4654	117	12	denoted	denote	VERB
ejpam-4654	117	13	by	by	ADP
ejpam-4654	117	14	g	g	PROPN
ejpam-4654	117	15	/	/	SYM
ejpam-4654	117	16	r.	r.	PROPN
ejpam-4654	117	17	(	(	PUNCT
ejpam-4654	117	18	g	g	NOUN
ejpam-4654	117	19	/	/	SYM
ejpam-4654	117	20	r,⪯	r,⪯	PROPN
ejpam-4654	117	21	)	)	PUNCT
ejpam-4654	117	22	is	be	AUX
ejpam-4654	117	23	a	a	DET
ejpam-4654	117	24	pre	pre	ADJ
ejpam-4654	117	25	-	-	ADJ
ejpam-4654	117	26	ordered	ordered	ADJ
ejpam-4654	117	27	set	set	NOUN
ejpam-4654	117	28	.	.	PUNCT
ejpam-4654	118	1	let	let	VERB
ejpam-4654	118	2	g	g	NOUN
ejpam-4654	118	3	/	/	SYM
ejpam-4654	118	4	r̃	r̃	NOUN
ejpam-4654	118	5	be	be	VERB
ejpam-4654	118	6	the	the	DET
ejpam-4654	118	7	universal	universal	PROPN
ejpam-4654	118	8	t0	t0	PROPN
ejpam-4654	118	9	-	-	PUNCT
ejpam-4654	118	10	space	space	NOUN
ejpam-4654	118	11	associated	associate	VERB
ejpam-4654	118	12	to	to	ADP
ejpam-4654	118	13	the	the	DET
ejpam-4654	118	14	space	space	NOUN
ejpam-4654	118	15	g	g	NOUN
ejpam-4654	118	16	/	/	SYM
ejpam-4654	118	17	r	r	NOUN
ejpam-4654	118	18	as	as	ADP
ejpam-4654	118	19	in	in	ADP
ejpam-4654	118	20	bourbaki	bourbaki	NOUN
ejpam-4654	119	1	[	[	X
ejpam-4654	119	2	2	2	NUM
ejpam-4654	119	3	,	,	PUNCT
ejpam-4654	119	4	exercise	exercise	VERB
ejpam-4654	119	5	27	27	NUM
ejpam-4654	119	6	p	p	NOUN
ejpam-4654	119	7	:	:	PUNCT
ejpam-4654	119	8	1	1	NUM
ejpam-4654	119	9	-	-	SYM
ejpam-4654	119	10	104	104	NUM
ejpam-4654	119	11	]	]	PUNCT
ejpam-4654	119	12	.	.	PUNCT
ejpam-4654	120	1	definition	definition	NOUN
ejpam-4654	120	2	3.2	3.2	NUM
ejpam-4654	120	3	.	.	PUNCT
ejpam-4654	121	1	g	g	PROPN
ejpam-4654	121	2	is	be	AUX
ejpam-4654	121	3	a	a	DET
ejpam-4654	121	4	spectral	spectral	ADJ
ejpam-4654	121	5	graph	graph	NOUN
ejpam-4654	121	6	if	if	SCONJ
ejpam-4654	121	7	there	there	PRON
ejpam-4654	121	8	exists	exist	VERB
ejpam-4654	121	9	a	a	DET
ejpam-4654	121	10	quasi	quasi	ADJ
ejpam-4654	121	11	-	-	ADJ
ejpam-4654	121	12	spectral	spectral	ADJ
ejpam-4654	121	13	topology	topology	NOUN
ejpam-4654	121	14	t	t	NOUN
ejpam-4654	121	15	compatible	compatible	ADJ
ejpam-4654	121	16	with	with	ADP
ejpam-4654	121	17	the	the	DET
ejpam-4654	121	18	graph	graph	NOUN
ejpam-4654	121	19	structure	structure	NOUN
ejpam-4654	121	20	g.	g.	PROPN
ejpam-4654	121	21	theorem	theorem	VERB
ejpam-4654	121	22	3.3	3.3	NUM
ejpam-4654	121	23	.	.	PUNCT
ejpam-4654	122	1	g	g	PROPN
ejpam-4654	122	2	is	be	AUX
ejpam-4654	122	3	a	a	DET
ejpam-4654	122	4	spectral	spectral	ADJ
ejpam-4654	122	5	graph	graph	NOUN
ejpam-4654	122	6	if	if	SCONJ
ejpam-4654	122	7	and	and	CCONJ
ejpam-4654	122	8	only	only	ADV
ejpam-4654	122	9	if	if	SCONJ
ejpam-4654	122	10	(	(	PUNCT
ejpam-4654	122	11	g	g	NOUN
ejpam-4654	122	12	/	/	SYM
ejpam-4654	122	13	r̃,⪯	r̃,⪯	NOUN
ejpam-4654	122	14	)	)	PUNCT
ejpam-4654	122	15	is	be	AUX
ejpam-4654	122	16	order	order	NOUN
ejpam-4654	122	17	-	-	PUNCT
ejpam-4654	122	18	isomorphic	isomorphic	ADJ
ejpam-4654	122	19	to	to	ADP
ejpam-4654	122	20	the	the	DET
ejpam-4654	122	21	prime	prime	ADJ
ejpam-4654	122	22	spectrum	spectrum	NOUN
ejpam-4654	122	23	of	of	ADP
ejpam-4654	122	24	a	a	DET
ejpam-4654	122	25	unitary	unitary	ADJ
ejpam-4654	122	26	commutative	commutative	ADJ
ejpam-4654	122	27	ring	ring	NOUN
ejpam-4654	122	28	equipped	equip	VERB
ejpam-4654	122	29	with	with	ADP
ejpam-4654	122	30	the	the	DET
ejpam-4654	122	31	inclusion	inclusion	NOUN
ejpam-4654	122	32	.	.	PUNCT
ejpam-4654	123	1	proof	proof	NOUN
ejpam-4654	123	2	.	.	PUNCT
ejpam-4654	124	1	let	let	VERB
ejpam-4654	124	2	projection	projection	NOUN
ejpam-4654	124	3	q	q	NOUN
ejpam-4654	124	4	:	:	PUNCT
ejpam-4654	124	5	(	(	PUNCT
ejpam-4654	124	6	g	g	NOUN
ejpam-4654	124	7	,	,	PUNCT
ejpam-4654	124	8	t	t	NOUN
ejpam-4654	124	9	)	)	PUNCT
ejpam-4654	124	10	→	→	PUNCT
ejpam-4654	124	11	g	g	X
ejpam-4654	124	12	/	/	SYM
ejpam-4654	124	13	r	r	NOUN
ejpam-4654	124	14	be	be	VERB
ejpam-4654	124	15	the	the	DET
ejpam-4654	124	16	canonical	canonical	NOUN
ejpam-4654	124	17	.	.	PUNCT
ejpam-4654	125	1	let	let	VERB
ejpam-4654	125	2	t	t	NOUN
ejpam-4654	125	3	be	be	AUX
ejpam-4654	125	4	the	the	DET
ejpam-4654	125	5	quotient	quotient	NOUN
ejpam-4654	125	6	topology	topology	NOUN
ejpam-4654	125	7	on	on	ADP
ejpam-4654	125	8	g	g	PROPN
ejpam-4654	125	9	/	/	SYM
ejpam-4654	125	10	r.	r.	PROPN
ejpam-4654	125	11	let	let	VERB
ejpam-4654	125	12	φ	φ	PROPN
ejpam-4654	125	13	:	:	PUNCT
ejpam-4654	125	14	t	t	PROPN
ejpam-4654	125	15	→	→	SYM
ejpam-4654	125	16	t	t	PROPN
ejpam-4654	125	17	be	be	AUX
ejpam-4654	125	18	the	the	DET
ejpam-4654	125	19	defined	define	VERB
ejpam-4654	125	20	by	by	ADP
ejpam-4654	125	21	φ(u	φ(u	NOUN
ejpam-4654	125	22	)	)	PUNCT
ejpam-4654	125	23	=	=	SYM
ejpam-4654	125	24	q−1(u	q−1(u	PROPN
ejpam-4654	125	25	)	)	PUNCT
ejpam-4654	125	26	,	,	PUNCT
ejpam-4654	125	27	for	for	ADP
ejpam-4654	125	28	all	all	PRON
ejpam-4654	125	29	u	u	PROPN
ejpam-4654	125	30	∈	∈	PROPN
ejpam-4654	125	31	t	t	NOUN
ejpam-4654	125	32	.	.	PUNCT
ejpam-4654	126	1	first	first	ADV
ejpam-4654	126	2	,	,	PUNCT
ejpam-4654	126	3	we	we	PRON
ejpam-4654	126	4	show	show	VERB
ejpam-4654	126	5	that	that	SCONJ
ejpam-4654	126	6	φ	φ	PROPN
ejpam-4654	126	7	is	be	AUX
ejpam-4654	126	8	onto	onto	ADP
ejpam-4654	126	9	.	.	PUNCT
ejpam-4654	127	1	it	it	PRON
ejpam-4654	127	2	suffices	suffice	VERB
ejpam-4654	127	3	to	to	PART
ejpam-4654	127	4	show	show	VERB
ejpam-4654	127	5	that	that	SCONJ
ejpam-4654	127	6	q−1(q(u	q−1(q(u	NOUN
ejpam-4654	127	7	)	)	PUNCT
ejpam-4654	127	8	)	)	PUNCT
ejpam-4654	128	1	=	=	SYM
ejpam-4654	128	2	u	u	NOUN
ejpam-4654	128	3	.	.	PUNCT
ejpam-4654	129	1	it	it	PRON
ejpam-4654	129	2	is	be	AUX
ejpam-4654	129	3	easy	easy	ADJ
ejpam-4654	129	4	to	to	PART
ejpam-4654	129	5	see	see	VERB
ejpam-4654	129	6	that	that	SCONJ
ejpam-4654	129	7	u	u	PROPN
ejpam-4654	129	8	⊂	⊂	PROPN
ejpam-4654	129	9	q−1(q(u	q−1(q(u	NOUN
ejpam-4654	129	10	)	)	PUNCT
ejpam-4654	129	11	)	)	PUNCT
ejpam-4654	129	12	.	.	PUNCT
ejpam-4654	130	1	let	let	VERB
ejpam-4654	130	2	x	x	PUNCT
ejpam-4654	130	3	∈	∈	PROPN
ejpam-4654	130	4	q−1(q(u	q−1(q(u	NOUN
ejpam-4654	130	5	)	)	PUNCT
ejpam-4654	130	6	)	)	PUNCT
ejpam-4654	130	7	.	.	PUNCT
ejpam-4654	131	1	then	then	ADV
ejpam-4654	131	2	q(x	q(x	PROPN
ejpam-4654	131	3	)	)	PUNCT
ejpam-4654	131	4	∈	∈	PROPN
ejpam-4654	131	5	q(u	q(u	NOUN
ejpam-4654	131	6	)	)	PUNCT
ejpam-4654	131	7	which	which	PRON
ejpam-4654	131	8	implies	imply	VERB
ejpam-4654	131	9	that	that	SCONJ
ejpam-4654	131	10	there	there	PRON
ejpam-4654	131	11	exits	exit	VERB
ejpam-4654	131	12	y	y	PROPN
ejpam-4654	131	13	∈	∈	PROPN
ejpam-4654	131	14	u	u	NOUN
ejpam-4654	131	15	such	such	ADJ
ejpam-4654	131	16	that	that	SCONJ
ejpam-4654	131	17	q(x	q(x	PROPN
ejpam-4654	131	18	)	)	PUNCT
ejpam-4654	131	19	=	=	SYM
ejpam-4654	131	20	q(y	q(y	NOUN
ejpam-4654	131	21	)	)	PUNCT
ejpam-4654	131	22	.	.	PUNCT
ejpam-4654	132	1	therefore	therefore	ADV
ejpam-4654	132	2	r(x	r(x	PROPN
ejpam-4654	132	3	)	)	PUNCT
ejpam-4654	132	4	=	=	PUNCT
ejpam-4654	132	5	r(y	r(y	VERB
ejpam-4654	132	6	)	)	PUNCT
ejpam-4654	132	7	.	.	PUNCT
ejpam-4654	133	1	since	since	SCONJ
ejpam-4654	133	2	t	t	PROPN
ejpam-4654	133	3	is	be	AUX
ejpam-4654	133	4	compatible	compatible	ADJ
ejpam-4654	133	5	with	with	ADP
ejpam-4654	133	6	g	g	PROPN
ejpam-4654	133	7	,	,	PUNCT
ejpam-4654	133	8	r(x	r(x	PROPN
ejpam-4654	133	9	)	)	PUNCT
ejpam-4654	134	1	⊂	⊂	PROPN
ejpam-4654	134	2	u	u	PROPN
ejpam-4654	134	3	which	which	PRON
ejpam-4654	134	4	implies	imply	VERB
ejpam-4654	134	5	that	that	SCONJ
ejpam-4654	134	6	x	x	PUNCT
ejpam-4654	134	7	∈	∈	PROPN
ejpam-4654	134	8	u	u	NOUN
ejpam-4654	134	9	.	.	PUNCT
ejpam-4654	135	1	thus	thus	ADV
ejpam-4654	135	2	q−1(q(u	q−1(q(u	NOUN
ejpam-4654	135	3	)	)	PUNCT
ejpam-4654	135	4	)	)	PUNCT
ejpam-4654	136	1	=	=	SYM
ejpam-4654	136	2	u	u	PROPN
ejpam-4654	136	3	.	.	PUNCT
ejpam-4654	137	1	second	second	ADJ
ejpam-4654	137	2	,	,	PUNCT
ejpam-4654	137	3	since	since	SCONJ
ejpam-4654	137	4	q	q	NOUN
ejpam-4654	137	5	is	be	AUX
ejpam-4654	137	6	onto	onto	ADP
ejpam-4654	137	7	,	,	PUNCT
ejpam-4654	137	8	we	we	PRON
ejpam-4654	137	9	get	get	VERB
ejpam-4654	137	10	q(q−1(v	q(q−1(v	PROPN
ejpam-4654	137	11	)	)	PUNCT
ejpam-4654	137	12	)	)	PUNCT
ejpam-4654	138	1	=	=	SYM
ejpam-4654	138	2	v	v	NOUN
ejpam-4654	138	3	for	for	ADP
ejpam-4654	138	4	all	all	PRON
ejpam-4654	138	5	v	v	ADP
ejpam-4654	138	6	∈	∈	PROPN
ejpam-4654	138	7	t	t	NOUN
ejpam-4654	138	8	.	.	PUNCT
ejpam-4654	139	1	then	then	ADV
ejpam-4654	139	2	φ	φ	PROPN
ejpam-4654	139	3	is	be	AUX
ejpam-4654	139	4	injective	injective	ADJ
ejpam-4654	139	5	.	.	PUNCT
ejpam-4654	140	1	consequently	consequently	ADV
ejpam-4654	140	2	,	,	PUNCT
ejpam-4654	140	3	φ	φ	PROPN
ejpam-4654	140	4	is	be	AUX
ejpam-4654	140	5	bijective	bijective	ADJ
ejpam-4654	140	6	and	and	CCONJ
ejpam-4654	140	7	so	so	ADV
ejpam-4654	140	8	q	q	X
ejpam-4654	140	9	is	be	AUX
ejpam-4654	140	10	an	an	PRON
ejpam-4654	140	11	onto	onto	ADP
ejpam-4654	140	12	quasi	quasi	NOUN
ejpam-4654	140	13	-	-	NOUN
ejpam-4654	140	14	homeomorphism	homeomorphism	X
ejpam-4654	140	15	.	.	PUNCT
ejpam-4654	141	1	by	by	ADP
ejpam-4654	141	2	a	a	DET
ejpam-4654	141	3	same	same	ADJ
ejpam-4654	141	4	method	method	NOUN
ejpam-4654	141	5	as	as	ADP
ejpam-4654	141	6	above	above	ADV
ejpam-4654	141	7	we	we	PRON
ejpam-4654	141	8	get	get	VERB
ejpam-4654	141	9	ψ	ψ	X
ejpam-4654	141	10	:	:	PUNCT
ejpam-4654	141	11	g	g	X
ejpam-4654	141	12	/	/	SYM
ejpam-4654	141	13	r	r	NOUN
ejpam-4654	141	14	→	→	SYM
ejpam-4654	141	15	g	g	NOUN
ejpam-4654	141	16	/	/	SYM
ejpam-4654	141	17	r̃	r̃	NOUN
ejpam-4654	141	18	which	which	PRON
ejpam-4654	141	19	associates	associate	VERB
ejpam-4654	141	20	to	to	ADP
ejpam-4654	141	21	each	each	DET
ejpam-4654	141	22	r(u	r(u	PROPN
ejpam-4654	141	23	)	)	PUNCT
ejpam-4654	141	24	its	its	PRON
ejpam-4654	141	25	class	class	NOUN
ejpam-4654	141	26	r̃(u	r̃(u	NOUN
ejpam-4654	141	27	)	)	PUNCT
ejpam-4654	141	28	=	=	PRON
ejpam-4654	141	29	{	{	PUNCT
ejpam-4654	141	30	v	v	NUM
ejpam-4654	141	31	∈	∈	NOUN
ejpam-4654	141	32	g	g	NOUN
ejpam-4654	141	33	:	:	PUNCT
ejpam-4654	141	34	{	{	PUNCT
ejpam-4654	141	35	r(u	r(u	PROPN
ejpam-4654	141	36	)	)	PUNCT
ejpam-4654	141	37	}	}	PUNCT
ejpam-4654	141	38	=	=	SYM
ejpam-4654	141	39	{	{	PUNCT
ejpam-4654	141	40	r(v	r(v	PROPN
ejpam-4654	141	41	)	)	PUNCT
ejpam-4654	141	42	}	}	PUNCT
ejpam-4654	141	43	}	}	PUNCT
ejpam-4654	141	44	is	be	AUX
ejpam-4654	141	45	a	a	DET
ejpam-4654	141	46	quasi	quasi	NOUN
ejpam-4654	141	47	-	-	NOUN
ejpam-4654	141	48	homeomorphism	homeomorphism	X
ejpam-4654	141	49	.	.	PUNCT
ejpam-4654	142	1	therefore	therefore	ADV
ejpam-4654	142	2	ψ	ψ	X
ejpam-4654	142	3	◦	◦	NOUN
ejpam-4654	142	4	q	q	NOUN
ejpam-4654	142	5	:	:	PUNCT
ejpam-4654	142	6	(	(	PUNCT
ejpam-4654	142	7	g	g	NOUN
ejpam-4654	142	8	,	,	PUNCT
ejpam-4654	142	9	t	t	NOUN
ejpam-4654	142	10	)	)	PUNCT
ejpam-4654	142	11	→	→	SYM
ejpam-4654	142	12	g	g	X
ejpam-4654	142	13	/	/	SYM
ejpam-4654	142	14	r̃	r̃	NOUN
ejpam-4654	142	15	is	be	AUX
ejpam-4654	142	16	a	a	DET
ejpam-4654	142	17	quasi	quasi	NOUN
ejpam-4654	142	18	-	-	NOUN
ejpam-4654	142	19	homeomorphism	homeomorphism	X
ejpam-4654	142	20	.	.	PUNCT
ejpam-4654	143	1	hence	hence	ADV
ejpam-4654	143	2	,	,	PUNCT
ejpam-4654	143	3	by	by	ADP
ejpam-4654	143	4	theorem	theorem	VERB
ejpam-4654	143	5	2.1	2.1	NUM
ejpam-4654	143	6	we	we	PRON
ejpam-4654	143	7	get	get	VERB
ejpam-4654	143	8	(	(	PUNCT
ejpam-4654	143	9	g	g	NOUN
ejpam-4654	143	10	,	,	PUNCT
ejpam-4654	143	11	t	t	NOUN
ejpam-4654	143	12	)	)	PUNCT
ejpam-4654	143	13	to	to	PART
ejpam-4654	143	14	be	be	AUX
ejpam-4654	143	15	quasi	quasi	ADJ
ejpam-4654	143	16	-	-	ADJ
ejpam-4654	143	17	spectral	spectral	ADJ
ejpam-4654	143	18	if	if	SCONJ
ejpam-4654	143	19	and	and	CCONJ
ejpam-4654	143	20	only	only	ADV
ejpam-4654	143	21	if	if	SCONJ
ejpam-4654	143	22	g	g	PROPN
ejpam-4654	143	23	/	/	SYM
ejpam-4654	143	24	r̃	r̃	NOUN
ejpam-4654	143	25	is	be	AUX
ejpam-4654	143	26	quasispectral	quasispectral	ADJ
ejpam-4654	143	27	.	.	PUNCT
ejpam-4654	144	1	since	since	SCONJ
ejpam-4654	144	2	g	g	PROPN
ejpam-4654	144	3	/	/	SYM
ejpam-4654	144	4	r̃	r̃	NOUN
ejpam-4654	144	5	is	be	AUX
ejpam-4654	144	6	a	a	DET
ejpam-4654	144	7	t0	t0	NOUN
ejpam-4654	144	8	-	-	NOUN
ejpam-4654	144	9	space	space	NOUN
ejpam-4654	144	10	we	we	PRON
ejpam-4654	144	11	obtain	obtain	VERB
ejpam-4654	144	12	theorem	theorem	VERB
ejpam-4654	144	13	3.3	3.3	NUM
ejpam-4654	144	14	.	.	PUNCT
ejpam-4654	145	1	note	note	VERB
ejpam-4654	145	2	that	that	SCONJ
ejpam-4654	145	3	a	a	DET
ejpam-4654	145	4	finite	finite	ADJ
ejpam-4654	145	5	graph	graph	NOUN
ejpam-4654	145	6	is	be	AUX
ejpam-4654	145	7	spectral	spectral	ADJ
ejpam-4654	145	8	.	.	PUNCT
ejpam-4654	146	1	references	reference	NOUN
ejpam-4654	146	2	[	[	X
ejpam-4654	146	3	1	1	NUM
ejpam-4654	146	4	]	]	PUNCT
ejpam-4654	146	5	b.	b.	PROPN
ejpam-4654	146	6	alharbi	alharbi	PROPN
ejpam-4654	146	7	.	.	PUNCT
ejpam-4654	147	1	graphs	graph	NOUN
ejpam-4654	147	2	and	and	CCONJ
ejpam-4654	147	3	alexandroff	alexandroff	ADJ
ejpam-4654	147	4	spaces	space	NOUN
ejpam-4654	147	5	.	.	PUNCT
ejpam-4654	148	1	submitted	submit	VERB
ejpam-4654	148	2	.	.	PUNCT
ejpam-4654	149	1	[	[	X
ejpam-4654	149	2	2	2	NUM
ejpam-4654	149	3	]	]	X
ejpam-4654	149	4	n.	n.	NOUN
ejpam-4654	149	5	bourbaki	bourbaki	PROPN
ejpam-4654	149	6	.	.	PUNCT
ejpam-4654	150	1	general	general	ADJ
ejpam-4654	150	2	topology	topology	NOUN
ejpam-4654	150	3	chapter	chapter	NOUN
ejpam-4654	150	4	1	1	NUM
ejpam-4654	150	5	to	to	ADP
ejpam-4654	150	6	4	4	NUM
ejpam-4654	150	7	.	.	PUNCT
ejpam-4654	151	1	masson	masson	PROPN
ejpam-4654	151	2	,	,	PUNCT
ejpam-4654	151	3	new	new	PROPN
ejpam-4654	151	4	york	york	PROPN
ejpam-4654	151	5	,	,	PUNCT
ejpam-4654	151	6	1990	1990	NUM
ejpam-4654	151	7	.	.	PUNCT
ejpam-4654	152	1	[	[	X
ejpam-4654	152	2	3	3	NUM
ejpam-4654	152	3	]	]	PUNCT
ejpam-4654	152	4	a.	a.	NOUN
ejpam-4654	152	5	grothendieck	grothendieck	NOUN
ejpam-4654	152	6	and	and	CCONJ
ejpam-4654	152	7	j.	j.	PROPN
ejpam-4654	152	8	dieudonné.	dieudonné.	PROPN
ejpam-4654	152	9	éléments	éléments	PROPN
ejpam-4654	152	10	de	de	X
ejpam-4654	152	11	géométrie	géométrie	X
ejpam-4654	152	12	algébrique	algébrique	PROPN
ejpam-4654	152	13	.	.	PUNCT
ejpam-4654	153	1	springerverlag	springerverlag	PROPN
ejpam-4654	153	2	,	,	PUNCT
ejpam-4654	153	3	new	new	PROPN
ejpam-4654	153	4	york	york	PROPN
ejpam-4654	153	5	,	,	PUNCT
ejpam-4654	153	6	1971	1971	NUM
ejpam-4654	153	7	.	.	PUNCT
ejpam-4654	154	1	[	[	X
ejpam-4654	154	2	4	4	X
ejpam-4654	154	3	]	]	PUNCT
ejpam-4654	154	4	m.	m.	NOUN
ejpam-4654	154	5	hochster	hochster	NOUN
ejpam-4654	154	6	.	.	PUNCT
ejpam-4654	155	1	prime	prime	ADJ
ejpam-4654	155	2	ideal	ideal	ADJ
ejpam-4654	155	3	structure	structure	NOUN
ejpam-4654	155	4	in	in	ADP
ejpam-4654	155	5	commutative	commutative	ADJ
ejpam-4654	155	6	rings	ring	NOUN
ejpam-4654	155	7	.	.	PUNCT
ejpam-4654	156	1	trans	trans	PROPN
ejpam-4654	156	2	.	.	PUNCT
ejpam-4654	157	1	amer	amer	PROPN
ejpam-4654	157	2	.	.	PUNCT
ejpam-4654	157	3	math	math	PROPN
ejpam-4654	157	4	.	.	PUNCT
ejpam-4654	158	1	soc	soc	PROPN
ejpam-4654	158	2	.	.	PUNCT
ejpam-4654	158	3	,	,	PUNCT
ejpam-4654	158	4	142:43–60	142:43–60	NUM
ejpam-4654	158	5	,	,	PUNCT
ejpam-4654	158	6	1969	1969	NUM
ejpam-4654	158	7	.	.	PUNCT
ejpam-4654	159	1	[	[	X
ejpam-4654	159	2	5	5	X
ejpam-4654	159	3	]	]	PUNCT
ejpam-4654	159	4	l.	l.	PROPN
ejpam-4654	159	5	kaplansky	kaplansky	PROPN
ejpam-4654	159	6	.	.	PUNCT
ejpam-4654	160	1	graphs	graph	NOUN
ejpam-4654	160	2	and	and	CCONJ
ejpam-4654	160	3	alexandroff	alexandroff	ADJ
ejpam-4654	160	4	spaces	space	NOUN
ejpam-4654	160	5	(	(	PUNCT
ejpam-4654	160	6	revised	revise	VERB
ejpam-4654	160	7	edition	edition	NOUN
ejpam-4654	160	8	)	)	PUNCT
ejpam-4654	160	9	.	.	PUNCT
ejpam-4654	161	1	the	the	DET
ejpam-4654	161	2	universty	universty	PROPN
ejpam-4654	161	3	of	of	ADP
ejpam-4654	161	4	chicago	chicago	PROPN
ejpam-4654	161	5	,	,	PUNCT
ejpam-4654	161	6	press	press	NOUN
ejpam-4654	161	7	,	,	PUNCT
ejpam-4654	161	8	1974	1974	NUM
ejpam-4654	161	9	.	.	PUNCT
ejpam-4654	162	1	[	[	X
ejpam-4654	162	2	6	6	NUM
ejpam-4654	162	3	]	]	PUNCT
ejpam-4654	162	4	w.j.lewis	w.j.lewis	NOUN
ejpam-4654	162	5	and	and	CCONJ
ejpam-4654	162	6	j.ohm	j.ohm	PROPN
ejpam-4654	162	7	.	.	PUNCT
ejpam-4654	163	1	the	the	DET
ejpam-4654	163	2	ordring	ordring	NOUN
ejpam-4654	163	3	of	of	ADP
ejpam-4654	163	4	spec	spec	NOUN
ejpam-4654	163	5	.	.	PUNCT
ejpam-4654	164	1	r.can.j.math	r.can.j.math	PROPN
ejpam-4654	164	2	vol	vol	NOUN
ejpam-4654	164	3	,	,	PUNCT
ejpam-4654	164	4	28:820–835	28:820–835	NUM
ejpam-4654	164	5	,	,	PUNCT
ejpam-4654	164	6	1973	1973	NUM
ejpam-4654	164	7	.	.	PUNCT