id	sid	tid	token	lemma	pos
ejpam-5135	1	1	european	european	PROPN
ejpam-5135	1	2	journal	journal	PROPN
ejpam-5135	1	3	of	of	ADP
ejpam-5135	1	4	pure	pure	ADJ
ejpam-5135	1	5	and	and	CCONJ
ejpam-5135	1	6	applied	apply	VERB
ejpam-5135	1	7	mathematics	mathematic	NOUN
ejpam-5135	1	8	vol	vol	NOUN
ejpam-5135	1	9	.	.	PROPN
ejpam-5135	2	1	17	17	NUM
ejpam-5135	2	2	,	,	PUNCT
ejpam-5135	2	3	no	no	INTJ
ejpam-5135	2	4	.	.	NOUN
ejpam-5135	2	5	2	2	NUM
ejpam-5135	2	6	,	,	PUNCT
ejpam-5135	2	7	2024	2024	NUM
ejpam-5135	2	8	,	,	PUNCT
ejpam-5135	2	9	663	663	NUM
ejpam-5135	2	10	-	-	SYM
ejpam-5135	2	11	675	675	NUM
ejpam-5135	2	12	issn	issn	PROPN
ejpam-5135	2	13	1307	1307	NUM
ejpam-5135	2	14	-	-	SYM
ejpam-5135	2	15	5543	5543	NUM
ejpam-5135	2	16	–	–	PUNCT
ejpam-5135	2	17	ejpam.com	ejpam.com	X
ejpam-5135	2	18	published	publish	VERB
ejpam-5135	2	19	by	by	ADP
ejpam-5135	2	20	new	new	PROPN
ejpam-5135	2	21	york	york	PROPN
ejpam-5135	2	22	business	business	PROPN
ejpam-5135	2	23	global	global	PROPN
ejpam-5135	2	24	the	the	DET
ejpam-5135	2	25	block	block	NOUN
ejpam-5135	2	26	topological	topological	ADJ
ejpam-5135	2	27	space	space	NOUN
ejpam-5135	2	28	and	and	CCONJ
ejpam-5135	2	29	block	block	NOUN
ejpam-5135	2	30	topological	topological	ADJ
ejpam-5135	2	31	graph	graph	NOUN
ejpam-5135	2	32	induced	induce	VERB
ejpam-5135	2	33	by	by	ADP
ejpam-5135	2	34	undirected	undirected	ADJ
ejpam-5135	2	35	graphs	graph	NOUN
ejpam-5135	2	36	justine	justine	PROPN
ejpam-5135	2	37	bryle	bryle	PROPN
ejpam-5135	2	38	c.	c.	PROPN
ejpam-5135	2	39	macaso1,∗	macaso1,∗	PROPN
ejpam-5135	2	40	,	,	PUNCT
ejpam-5135	2	41	cherry	cherry	PROPN
ejpam-5135	2	42	mae	mae	PROPN
ejpam-5135	2	43	r.	r.	PROPN
ejpam-5135	2	44	balingit1	balingit1	PROPN
ejpam-5135	2	45	1	1	NUM
ejpam-5135	2	46	department	department	NOUN
ejpam-5135	2	47	of	of	ADP
ejpam-5135	2	48	mathematics	mathematic	NOUN
ejpam-5135	2	49	,	,	PUNCT
ejpam-5135	2	50	college	college	NOUN
ejpam-5135	2	51	of	of	ADP
ejpam-5135	2	52	arts	art	NOUN
ejpam-5135	2	53	and	and	CCONJ
ejpam-5135	2	54	sciences	science	NOUN
ejpam-5135	2	55	,	,	PUNCT
ejpam-5135	2	56	central	central	ADJ
ejpam-5135	2	57	mindanao	mindanao	PROPN
ejpam-5135	2	58	university	university	PROPN
ejpam-5135	2	59	,	,	PUNCT
ejpam-5135	2	60	university	university	NOUN
ejpam-5135	2	61	town	town	NOUN
ejpam-5135	2	62	,	,	PUNCT
ejpam-5135	2	63	musuan	musuan	PROPN
ejpam-5135	2	64	,	,	PUNCT
ejpam-5135	2	65	8710	8710	NUM
ejpam-5135	2	66	maramag	maramag	NOUN
ejpam-5135	2	67	,	,	PUNCT
ejpam-5135	2	68	bukidnon	bukidnon	NOUN
ejpam-5135	2	69	,	,	PUNCT
ejpam-5135	2	70	philippines	philippine	NOUN
ejpam-5135	2	71	abstract	abstract	ADJ
ejpam-5135	2	72	.	.	PUNCT
ejpam-5135	3	1	let	let	VERB
ejpam-5135	3	2	g	g	PROPN
ejpam-5135	3	3	=	=	SYM
ejpam-5135	3	4	(	(	PUNCT
ejpam-5135	3	5	v	v	NOUN
ejpam-5135	3	6	(	(	PUNCT
ejpam-5135	3	7	g	g	NOUN
ejpam-5135	3	8	)	)	PUNCT
ejpam-5135	3	9	,	,	PUNCT
ejpam-5135	3	10	e(g	e(g	PROPN
ejpam-5135	3	11	)	)	PUNCT
ejpam-5135	3	12	)	)	PUNCT
ejpam-5135	4	1	be	be	AUX
ejpam-5135	4	2	a	a	DET
ejpam-5135	4	3	simple	simple	ADJ
ejpam-5135	4	4	undirected	undirected	ADJ
ejpam-5135	4	5	graph	graph	NOUN
ejpam-5135	4	6	.	.	PUNCT
ejpam-5135	5	1	a	a	DET
ejpam-5135	5	2	block	block	NOUN
ejpam-5135	5	3	of	of	ADP
ejpam-5135	5	4	g	g	PROPN
ejpam-5135	5	5	is	be	AUX
ejpam-5135	5	6	a	a	DET
ejpam-5135	5	7	maximal	maximal	ADJ
ejpam-5135	5	8	connected	connected	ADJ
ejpam-5135	5	9	subgraph	subgraph	NOUN
ejpam-5135	5	10	of	of	ADP
ejpam-5135	5	11	g	g	PROPN
ejpam-5135	5	12	that	that	PRON
ejpam-5135	5	13	contains	contain	VERB
ejpam-5135	5	14	no	no	DET
ejpam-5135	5	15	cut	cut	NOUN
ejpam-5135	5	16	-	-	PUNCT
ejpam-5135	5	17	vertices	vertex	NOUN
ejpam-5135	5	18	[	[	X
ejpam-5135	5	19	11	11	NUM
ejpam-5135	5	20	]	]	PUNCT
ejpam-5135	5	21	.	.	PUNCT
ejpam-5135	6	1	the	the	DET
ejpam-5135	6	2	family	family	NOUN
ejpam-5135	6	3	of	of	ADP
ejpam-5135	6	4	vertex	vertex	NOUN
ejpam-5135	6	5	sets	set	NOUN
ejpam-5135	6	6	of	of	ADP
ejpam-5135	6	7	blocks	block	NOUN
ejpam-5135	6	8	of	of	ADP
ejpam-5135	6	9	g	g	PROPN
ejpam-5135	6	10	generates	generate	VERB
ejpam-5135	6	11	a	a	DET
ejpam-5135	6	12	unique	unique	ADJ
ejpam-5135	6	13	topology	topology	NOUN
ejpam-5135	6	14	.	.	PUNCT
ejpam-5135	7	1	in	in	ADP
ejpam-5135	7	2	this	this	DET
ejpam-5135	7	3	paper	paper	NOUN
ejpam-5135	7	4	,	,	PUNCT
ejpam-5135	7	5	we	we	PRON
ejpam-5135	7	6	formally	formally	ADV
ejpam-5135	7	7	define	define	VERB
ejpam-5135	7	8	the	the	DET
ejpam-5135	7	9	topology	topology	NOUN
ejpam-5135	7	10	generated	generate	VERB
ejpam-5135	7	11	by	by	ADP
ejpam-5135	7	12	the	the	DET
ejpam-5135	7	13	family	family	NOUN
ejpam-5135	7	14	of	of	ADP
ejpam-5135	7	15	blocks	block	NOUN
ejpam-5135	7	16	in	in	ADP
ejpam-5135	7	17	a	a	DET
ejpam-5135	7	18	graph	graph	NOUN
ejpam-5135	7	19	called	call	VERB
ejpam-5135	7	20	the	the	DET
ejpam-5135	7	21	block	block	NOUN
ejpam-5135	7	22	topological	topological	ADJ
ejpam-5135	7	23	space	space	NOUN
ejpam-5135	7	24	.	.	PUNCT
ejpam-5135	8	1	moreover	moreover	ADV
ejpam-5135	8	2	,	,	PUNCT
ejpam-5135	8	3	we	we	PRON
ejpam-5135	8	4	characterize	characterize	VERB
ejpam-5135	8	5	and	and	CCONJ
ejpam-5135	8	6	describe	describe	VERB
ejpam-5135	8	7	some	some	DET
ejpam-5135	8	8	special	special	ADJ
ejpam-5135	8	9	attributes	attribute	NOUN
ejpam-5135	8	10	of	of	ADP
ejpam-5135	8	11	the	the	DET
ejpam-5135	8	12	block	block	NOUN
ejpam-5135	8	13	topological	topological	ADJ
ejpam-5135	8	14	space	space	NOUN
ejpam-5135	8	15	.	.	PUNCT
ejpam-5135	9	1	finally	finally	ADV
ejpam-5135	9	2	,	,	PUNCT
ejpam-5135	9	3	we	we	PRON
ejpam-5135	9	4	associate	associate	VERB
ejpam-5135	9	5	a	a	DET
ejpam-5135	9	6	corresponding	corresponding	ADJ
ejpam-5135	9	7	graph	graph	NOUN
ejpam-5135	9	8	from	from	ADP
ejpam-5135	9	9	a	a	DET
ejpam-5135	9	10	given	give	VERB
ejpam-5135	9	11	block	block	NOUN
ejpam-5135	9	12	topological	topological	ADJ
ejpam-5135	9	13	space	space	NOUN
ejpam-5135	9	14	by	by	ADP
ejpam-5135	9	15	defining	define	VERB
ejpam-5135	9	16	the	the	DET
ejpam-5135	9	17	block	block	NOUN
ejpam-5135	9	18	topological	topological	ADJ
ejpam-5135	9	19	graph	graph	NOUN
ejpam-5135	9	20	.	.	PUNCT
ejpam-5135	10	1	2020	2020	NUM
ejpam-5135	10	2	mathematics	mathematic	NOUN
ejpam-5135	10	3	subject	subject	NOUN
ejpam-5135	10	4	classifications	classification	NOUN
ejpam-5135	10	5	:	:	PUNCT
ejpam-5135	10	6	37f20	37f20	NUM
ejpam-5135	10	7	,	,	PUNCT
ejpam-5135	10	8	05c10	05c10	ADJ
ejpam-5135	10	9	,	,	PUNCT
ejpam-5135	10	10	54c35	54c35	NUM
ejpam-5135	10	11	key	key	ADJ
ejpam-5135	10	12	words	word	NOUN
ejpam-5135	10	13	and	and	CCONJ
ejpam-5135	10	14	phrases	phrase	NOUN
ejpam-5135	10	15	:	:	PUNCT
ejpam-5135	10	16	block	block	VERB
ejpam-5135	10	17	topological	topological	ADJ
ejpam-5135	10	18	space	space	NOUN
ejpam-5135	10	19	,	,	PUNCT
ejpam-5135	10	20	block	block	VERB
ejpam-5135	10	21	topological	topological	ADJ
ejpam-5135	10	22	graph	graph	NOUN
ejpam-5135	10	23	,	,	PUNCT
ejpam-5135	10	24	graph	graph	NOUN
ejpam-5135	10	25	,	,	PUNCT
ejpam-5135	10	26	block	block	NOUN
ejpam-5135	10	27	,	,	PUNCT
ejpam-5135	10	28	hausdorff	hausdorff	NOUN
ejpam-5135	10	29	space	space	NOUN
ejpam-5135	10	30	,	,	PUNCT
ejpam-5135	10	31	continuous	continuous	ADJ
ejpam-5135	10	32	1	1	NUM
ejpam-5135	10	33	.	.	PUNCT
ejpam-5135	11	1	introduction	introduction	NOUN
ejpam-5135	11	2	there	there	PRON
ejpam-5135	11	3	are	be	VERB
ejpam-5135	11	4	many	many	ADJ
ejpam-5135	11	5	ways	way	NOUN
ejpam-5135	11	6	of	of	ADP
ejpam-5135	11	7	associating	associate	VERB
ejpam-5135	11	8	topology	topology	NOUN
ejpam-5135	11	9	from	from	ADP
ejpam-5135	11	10	a	a	DET
ejpam-5135	11	11	graph	graph	NOUN
ejpam-5135	11	12	,	,	PUNCT
ejpam-5135	11	13	as	as	SCONJ
ejpam-5135	11	14	seen	see	VERB
ejpam-5135	11	15	in	in	ADP
ejpam-5135	11	16	[	[	X
ejpam-5135	11	17	1	1	NUM
ejpam-5135	11	18	]	]	PUNCT
ejpam-5135	11	19	,	,	PUNCT
ejpam-5135	11	20	[	[	X
ejpam-5135	11	21	3	3	NUM
ejpam-5135	11	22	]	]	PUNCT
ejpam-5135	11	23	,	,	PUNCT
ejpam-5135	11	24	[	[	X
ejpam-5135	11	25	5	5	NUM
ejpam-5135	11	26	]	]	PUNCT
ejpam-5135	11	27	,	,	PUNCT
ejpam-5135	11	28	[	[	X
ejpam-5135	11	29	6	6	NUM
ejpam-5135	11	30	]	]	PUNCT
ejpam-5135	11	31	,	,	PUNCT
ejpam-5135	11	32	[	[	X
ejpam-5135	11	33	7	7	NUM
ejpam-5135	11	34	]	]	PUNCT
ejpam-5135	11	35	,	,	PUNCT
ejpam-5135	11	36	and	and	CCONJ
ejpam-5135	11	37	[	[	X
ejpam-5135	11	38	8	8	NUM
ejpam-5135	11	39	]	]	PUNCT
ejpam-5135	11	40	.	.	PUNCT
ejpam-5135	12	1	the	the	DET
ejpam-5135	12	2	most	most	ADV
ejpam-5135	12	3	common	common	ADJ
ejpam-5135	12	4	method	method	NOUN
ejpam-5135	12	5	among	among	ADP
ejpam-5135	12	6	these	these	PRON
ejpam-5135	12	7	is	be	AUX
ejpam-5135	12	8	by	by	ADP
ejpam-5135	12	9	treating	treat	VERB
ejpam-5135	12	10	a	a	DET
ejpam-5135	12	11	collection	collection	NOUN
ejpam-5135	12	12	of	of	ADP
ejpam-5135	12	13	subsets	subset	NOUN
ejpam-5135	12	14	of	of	ADP
ejpam-5135	12	15	a	a	DET
ejpam-5135	12	16	nonempty	nonempty	ADJ
ejpam-5135	12	17	set	set	VERB
ejpam-5135	12	18	(	(	PUNCT
ejpam-5135	12	19	e.g.	e.g.	ADV
ejpam-5135	12	20	vertex	vertex	NOUN
ejpam-5135	12	21	set	set	NOUN
ejpam-5135	12	22	or	or	CCONJ
ejpam-5135	12	23	edge	edge	NOUN
ejpam-5135	12	24	set	set	NOUN
ejpam-5135	12	25	)	)	PUNCT
ejpam-5135	12	26	as	as	ADP
ejpam-5135	12	27	a	a	DET
ejpam-5135	12	28	subbase	subbase	NOUN
ejpam-5135	12	29	to	to	PART
ejpam-5135	12	30	generate	generate	VERB
ejpam-5135	12	31	the	the	DET
ejpam-5135	12	32	desired	desire	VERB
ejpam-5135	12	33	topology	topology	NOUN
ejpam-5135	12	34	which	which	PRON
ejpam-5135	12	35	is	be	AUX
ejpam-5135	12	36	reflected	reflect	VERB
ejpam-5135	12	37	in	in	ADP
ejpam-5135	12	38	the	the	DET
ejpam-5135	12	39	paper	paper	NOUN
ejpam-5135	12	40	of	of	ADP
ejpam-5135	12	41	hassan	hassan	PROPN
ejpam-5135	12	42	and	and	CCONJ
ejpam-5135	12	43	abed	abe	VERB
ejpam-5135	12	44	in	in	ADP
ejpam-5135	12	45	[	[	X
ejpam-5135	12	46	7	7	NUM
ejpam-5135	12	47	]	]	PUNCT
ejpam-5135	12	48	.	.	PUNCT
ejpam-5135	13	1	this	this	DET
ejpam-5135	13	2	topology	topology	NOUN
ejpam-5135	13	3	is	be	AUX
ejpam-5135	13	4	called	call	VERB
ejpam-5135	13	5	the	the	DET
ejpam-5135	13	6	independent	independent	ADJ
ejpam-5135	13	7	topology	topology	NOUN
ejpam-5135	13	8	and	and	CCONJ
ejpam-5135	13	9	is	be	AUX
ejpam-5135	13	10	generated	generate	VERB
ejpam-5135	13	11	from	from	ADP
ejpam-5135	13	12	the	the	DET
ejpam-5135	13	13	family	family	NOUN
ejpam-5135	13	14	of	of	ADP
ejpam-5135	13	15	independent	independent	ADJ
ejpam-5135	13	16	sets	set	NOUN
ejpam-5135	13	17	of	of	ADP
ejpam-5135	13	18	each	each	PRON
ejpam-5135	13	19	of	of	ADP
ejpam-5135	13	20	the	the	DET
ejpam-5135	13	21	vertices	vertex	NOUN
ejpam-5135	13	22	in	in	ADP
ejpam-5135	13	23	the	the	DET
ejpam-5135	13	24	graph	graph	NOUN
ejpam-5135	13	25	.	.	PUNCT
ejpam-5135	14	1	the	the	DET
ejpam-5135	14	2	same	same	ADJ
ejpam-5135	14	3	method	method	NOUN
ejpam-5135	14	4	was	be	AUX
ejpam-5135	14	5	applied	apply	VERB
ejpam-5135	14	6	in	in	ADP
ejpam-5135	14	7	the	the	DET
ejpam-5135	14	8	study	study	NOUN
ejpam-5135	14	9	of	of	ADP
ejpam-5135	14	10	abdu	abdu	PROPN
ejpam-5135	14	11	and	and	CCONJ
ejpam-5135	14	12	kilicman	kilicman	NOUN
ejpam-5135	14	13	in	in	ADP
ejpam-5135	14	14	[	[	X
ejpam-5135	14	15	1	1	NUM
ejpam-5135	14	16	]	]	PUNCT
ejpam-5135	14	17	where	where	SCONJ
ejpam-5135	14	18	they	they	PRON
ejpam-5135	14	19	associated	associate	VERB
ejpam-5135	14	20	two	two	NUM
ejpam-5135	14	21	topologies	topology	NOUN
ejpam-5135	14	22	on	on	ADP
ejpam-5135	14	23	the	the	DET
ejpam-5135	14	24	set	set	NOUN
ejpam-5135	14	25	of	of	ADP
ejpam-5135	14	26	edges	edge	NOUN
ejpam-5135	14	27	from	from	ADP
ejpam-5135	14	28	a	a	DET
ejpam-5135	14	29	particular	particular	ADJ
ejpam-5135	14	30	directed	direct	VERB
ejpam-5135	14	31	graph	graph	NOUN
ejpam-5135	14	32	called	call	VERB
ejpam-5135	14	33	edge	edge	NOUN
ejpam-5135	14	34	-	-	PUNCT
ejpam-5135	14	35	compatible	compatible	ADJ
ejpam-5135	14	36	topology	topology	NOUN
ejpam-5135	14	37	and	and	CCONJ
ejpam-5135	14	38	edge	edge	NOUN
ejpam-5135	14	39	-	-	PUNCT
ejpam-5135	14	40	incompatible	incompatible	ADJ
ejpam-5135	14	41	topology	topology	NOUN
ejpam-5135	14	42	.	.	PUNCT
ejpam-5135	15	1	another	another	DET
ejpam-5135	15	2	fascinating	fascinating	ADJ
ejpam-5135	15	3	intercrossing	intercrossing	NOUN
ejpam-5135	15	4	of	of	ADP
ejpam-5135	15	5	topology	topology	NOUN
ejpam-5135	15	6	and	and	CCONJ
ejpam-5135	15	7	graph	graph	NOUN
ejpam-5135	15	8	theory	theory	NOUN
ejpam-5135	15	9	is	be	AUX
ejpam-5135	15	10	establishing	establish	VERB
ejpam-5135	15	11	an	an	DET
ejpam-5135	15	12	adjacency	adjacency	NOUN
ejpam-5135	15	13	condition	condition	NOUN
ejpam-5135	15	14	to	to	PART
ejpam-5135	15	15	obtain	obtain	VERB
ejpam-5135	15	16	the	the	DET
ejpam-5135	15	17	desired	desire	VERB
ejpam-5135	15	18	graph	graph	NOUN
ejpam-5135	15	19	from	from	ADP
ejpam-5135	15	20	a	a	DET
ejpam-5135	15	21	given	give	VERB
ejpam-5135	15	22	finite	finite	ADJ
ejpam-5135	15	23	topological	topological	ADJ
ejpam-5135	15	24	space	space	NOUN
ejpam-5135	15	25	.	.	PUNCT
ejpam-5135	16	1	this	this	DET
ejpam-5135	16	2	idea	idea	NOUN
ejpam-5135	16	3	was	be	AUX
ejpam-5135	16	4	reflected	reflect	VERB
ejpam-5135	16	5	in	in	ADP
ejpam-5135	16	6	the	the	DET
ejpam-5135	16	7	paper	paper	NOUN
ejpam-5135	16	8	of	of	ADP
ejpam-5135	16	9	alsanaia	alsanaia	PROPN
ejpam-5135	16	10	et.al	et.al	PROPN
ejpam-5135	16	11	.	.	PUNCT
ejpam-5135	17	1	in	in	ADP
ejpam-5135	17	2	[	[	X
ejpam-5135	17	3	2	2	NUM
ejpam-5135	17	4	]	]	PUNCT
ejpam-5135	17	5	as	as	SCONJ
ejpam-5135	17	6	they	they	PRON
ejpam-5135	17	7	gave	give	VERB
ejpam-5135	17	8	a	a	DET
ejpam-5135	17	9	formal	formal	ADJ
ejpam-5135	17	10	definition	definition	NOUN
ejpam-5135	17	11	of	of	ADP
ejpam-5135	17	12	converting	convert	VERB
ejpam-5135	17	13	the	the	DET
ejpam-5135	17	14	finite	finite	ADJ
ejpam-5135	17	15	discrete	discrete	ADJ
ejpam-5135	17	16	topological	topological	ADJ
ejpam-5135	17	17	space	space	NOUN
ejpam-5135	17	18	using	use	VERB
ejpam-5135	17	19	a	a	DET
ejpam-5135	17	20	suitable	suitable	ADJ
ejpam-5135	17	21	adjacency	adjacency	NOUN
ejpam-5135	17	22	condition	condition	NOUN
ejpam-5135	17	23	to	to	PART
ejpam-5135	17	24	obtain	obtain	VERB
ejpam-5135	17	25	the	the	DET
ejpam-5135	17	26	graph	graph	NOUN
ejpam-5135	17	27	called	call	VERB
ejpam-5135	17	28	the	the	DET
ejpam-5135	17	29	discrete	discrete	ADJ
ejpam-5135	17	30	topological	topological	ADJ
ejpam-5135	17	31	graph	graph	NOUN
ejpam-5135	17	32	.	.	PUNCT
ejpam-5135	17	33	∗corresponding	∗corresponde	VERB
ejpam-5135	17	34	author	author	NOUN
ejpam-5135	17	35	.	.	PUNCT
ejpam-5135	18	1	doi	doi	NOUN
ejpam-5135	18	2	:	:	PUNCT
ejpam-5135	18	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5135	https://doi.org/10.29020/nybg.ejpam.v17i2.5135	ADP
ejpam-5135	18	4	email	email	NOUN
ejpam-5135	18	5	addresses	address	NOUN
ejpam-5135	18	6	:	:	PUNCT
ejpam-5135	18	7	s.macaso.justinebryle@cmu.edu.ph	s.macaso.justinebryle@cmu.edu.ph	PROPN
ejpam-5135	18	8	(	(	PUNCT
ejpam-5135	18	9	jb	jb	PROPN
ejpam-5135	18	10	.	.	PUNCT
ejpam-5135	18	11	macaso	macaso	PROPN
ejpam-5135	18	12	)	)	PUNCT
ejpam-5135	18	13	,	,	PUNCT
ejpam-5135	18	14	f.cherrymae.balingit@cmu.edu.ph	f.cherrymae.balingit@cmu.edu.ph	PROPN
ejpam-5135	18	15	(	(	PUNCT
ejpam-5135	18	16	cm	cm	NOUN
ejpam-5135	18	17	.	.	PUNCT
ejpam-5135	18	18	balingit	balingit	ADJ
ejpam-5135	18	19	)	)	PUNCT
ejpam-5135	18	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5135	18	21	663	663	NUM
ejpam-5135	18	22	©	©	ADP
ejpam-5135	18	23	2024	2024	NUM
ejpam-5135	18	24	ejpam	ejpam	NOUN
ejpam-5135	18	25	all	all	DET
ejpam-5135	18	26	rights	right	NOUN
ejpam-5135	18	27	reserved	reserve	VERB
ejpam-5135	18	28	.	.	PUNCT
ejpam-5135	19	1	justine	justine	PROPN
ejpam-5135	19	2	bryle	bryle	PROPN
ejpam-5135	19	3	c.	c.	PROPN
ejpam-5135	19	4	macaso	macaso	PROPN
ejpam-5135	19	5	,	,	PUNCT
ejpam-5135	19	6	cherry	cherry	PROPN
ejpam-5135	19	7	mae	mae	PROPN
ejpam-5135	19	8	r.	r.	PROPN
ejpam-5135	19	9	balingit	balingit	PROPN
ejpam-5135	19	10	/	/	SYM
ejpam-5135	19	11	eur	eur	PROPN
ejpam-5135	19	12	.	.	PUNCT
ejpam-5135	20	1	j.	j.	PROPN
ejpam-5135	20	2	pure	pure	PROPN
ejpam-5135	20	3	appl	appl	PROPN
ejpam-5135	20	4	.	.	PROPN
ejpam-5135	20	5	math	math	PROPN
ejpam-5135	20	6	,	,	PUNCT
ejpam-5135	20	7	17	17	NUM
ejpam-5135	20	8	(	(	PUNCT
ejpam-5135	20	9	2	2	NUM
ejpam-5135	20	10	)	)	PUNCT
ejpam-5135	20	11	(	(	PUNCT
ejpam-5135	20	12	2024	2024	NUM
ejpam-5135	20	13	)	)	PUNCT
ejpam-5135	20	14	,	,	PUNCT
ejpam-5135	20	15	663	663	NUM
ejpam-5135	20	16	-	-	SYM
ejpam-5135	20	17	675	675	NUM
ejpam-5135	20	18	664	664	NUM
ejpam-5135	20	19	let	let	VERB
ejpam-5135	20	20	g	g	NOUN
ejpam-5135	20	21	=	=	SYM
ejpam-5135	20	22	(	(	PUNCT
ejpam-5135	20	23	v	v	NOUN
ejpam-5135	20	24	(	(	PUNCT
ejpam-5135	20	25	g	g	NOUN
ejpam-5135	20	26	)	)	PUNCT
ejpam-5135	20	27	,	,	PUNCT
ejpam-5135	20	28	e(g	e(g	PROPN
ejpam-5135	20	29	)	)	PUNCT
ejpam-5135	20	30	)	)	PUNCT
ejpam-5135	20	31	be	be	AUX
ejpam-5135	20	32	a	a	DET
ejpam-5135	20	33	simple	simple	ADJ
ejpam-5135	20	34	undirected	undirected	ADJ
ejpam-5135	20	35	graph	graph	NOUN
ejpam-5135	20	36	.	.	PUNCT
ejpam-5135	21	1	for	for	ADP
ejpam-5135	21	2	a	a	DET
ejpam-5135	21	3	nonempty	nonempty	ADJ
ejpam-5135	21	4	subset	subset	NOUN
ejpam-5135	21	5	s	s	NOUN
ejpam-5135	21	6	of	of	ADP
ejpam-5135	21	7	v	v	NOUN
ejpam-5135	21	8	(	(	PUNCT
ejpam-5135	21	9	g	g	NOUN
ejpam-5135	21	10	)	)	PUNCT
ejpam-5135	21	11	,	,	PUNCT
ejpam-5135	21	12	the	the	DET
ejpam-5135	21	13	subgraph	subgraph	NOUN
ejpam-5135	21	14	induced	induce	VERB
ejpam-5135	21	15	by	by	ADP
ejpam-5135	21	16	s	s	PROPN
ejpam-5135	21	17	,	,	PUNCT
ejpam-5135	21	18	denoted	denote	VERB
ejpam-5135	21	19	by	by	ADP
ejpam-5135	21	20	g[s	g[	NOUN
ejpam-5135	21	21	]	]	PUNCT
ejpam-5135	21	22	,	,	PUNCT
ejpam-5135	21	23	has	have	VERB
ejpam-5135	21	24	s	s	NOUN
ejpam-5135	21	25	as	as	ADP
ejpam-5135	21	26	its	its	PRON
ejpam-5135	21	27	vertex	vertex	NOUN
ejpam-5135	21	28	set	set	NOUN
ejpam-5135	21	29	and	and	CCONJ
ejpam-5135	21	30	two	two	NUM
ejpam-5135	21	31	vertices	vertex	NOUN
ejpam-5135	21	32	u	u	NOUN
ejpam-5135	21	33	and	and	CCONJ
ejpam-5135	21	34	v	v	NOUN
ejpam-5135	21	35	are	be	AUX
ejpam-5135	21	36	adjacent	adjacent	ADJ
ejpam-5135	21	37	in	in	ADP
ejpam-5135	21	38	g[s	g[	NOUN
ejpam-5135	21	39	]	]	PUNCT
ejpam-5135	21	40	if	if	SCONJ
ejpam-5135	21	41	and	and	CCONJ
ejpam-5135	21	42	only	only	ADV
ejpam-5135	21	43	if	if	SCONJ
ejpam-5135	21	44	u	u	NOUN
ejpam-5135	21	45	and	and	CCONJ
ejpam-5135	21	46	v	v	NOUN
ejpam-5135	21	47	are	be	AUX
ejpam-5135	21	48	adjacent	adjacent	ADJ
ejpam-5135	21	49	in	in	ADP
ejpam-5135	21	50	g.	g.	PROPN
ejpam-5135	21	51	a	a	DET
ejpam-5135	21	52	subgraph	subgraph	NOUN
ejpam-5135	21	53	h	h	NOUN
ejpam-5135	21	54	of	of	ADP
ejpam-5135	21	55	a	a	DET
ejpam-5135	21	56	graph	graph	NOUN
ejpam-5135	21	57	g	g	NOUN
ejpam-5135	21	58	is	be	AUX
ejpam-5135	21	59	called	call	VERB
ejpam-5135	21	60	an	an	DET
ejpam-5135	21	61	induced	induced	ADJ
ejpam-5135	21	62	subgraph	subgraph	NOUN
ejpam-5135	21	63	if	if	SCONJ
ejpam-5135	21	64	there	there	PRON
ejpam-5135	21	65	is	be	VERB
ejpam-5135	21	66	a	a	DET
ejpam-5135	21	67	nonempty	nonempty	ADJ
ejpam-5135	21	68	subset	subset	VERB
ejpam-5135	21	69	s	s	NOUN
ejpam-5135	21	70	of	of	ADP
ejpam-5135	21	71	v	v	NOUN
ejpam-5135	21	72	(	(	PUNCT
ejpam-5135	21	73	g	g	NOUN
ejpam-5135	21	74	)	)	PUNCT
ejpam-5135	21	75	such	such	ADJ
ejpam-5135	21	76	that	that	DET
ejpam-5135	21	77	h	h	NOUN
ejpam-5135	21	78	=	=	SYM
ejpam-5135	21	79	g[s	g[s	PROPN
ejpam-5135	21	80	]	]	PUNCT
ejpam-5135	21	81	.	.	PUNCT
ejpam-5135	22	1	a	a	DET
ejpam-5135	22	2	vertex	vertex	NOUN
ejpam-5135	22	3	v	v	NOUN
ejpam-5135	22	4	of	of	ADP
ejpam-5135	22	5	g	g	PROPN
ejpam-5135	22	6	is	be	AUX
ejpam-5135	22	7	an	an	DET
ejpam-5135	22	8	isolated	isolated	ADJ
ejpam-5135	22	9	vertex	vertex	NOUN
ejpam-5135	22	10	if	if	SCONJ
ejpam-5135	22	11	it	it	PRON
ejpam-5135	22	12	is	be	AUX
ejpam-5135	22	13	not	not	PART
ejpam-5135	22	14	adjacent	adjacent	ADJ
ejpam-5135	22	15	to	to	ADP
ejpam-5135	22	16	any	any	DET
ejpam-5135	22	17	other	other	ADJ
ejpam-5135	22	18	vertices	vertex	NOUN
ejpam-5135	22	19	of	of	ADP
ejpam-5135	22	20	g.	g.	PROPN
ejpam-5135	22	21	two	two	NUM
ejpam-5135	22	22	vertices	vertex	NOUN
ejpam-5135	22	23	of	of	ADP
ejpam-5135	22	24	g	g	NOUN
ejpam-5135	22	25	are	be	AUX
ejpam-5135	22	26	connected	connect	VERB
ejpam-5135	22	27	if	if	SCONJ
ejpam-5135	22	28	there	there	PRON
ejpam-5135	22	29	is	be	VERB
ejpam-5135	22	30	a	a	DET
ejpam-5135	22	31	path	path	NOUN
ejpam-5135	22	32	that	that	PRON
ejpam-5135	22	33	connect	connect	VERB
ejpam-5135	22	34	them	they	PRON
ejpam-5135	22	35	.	.	PUNCT
ejpam-5135	23	1	if	if	SCONJ
ejpam-5135	23	2	every	every	DET
ejpam-5135	23	3	two	two	NUM
ejpam-5135	23	4	vertices	vertex	NOUN
ejpam-5135	23	5	of	of	ADP
ejpam-5135	23	6	g	g	NOUN
ejpam-5135	23	7	are	be	AUX
ejpam-5135	23	8	connected	connect	VERB
ejpam-5135	23	9	,	,	PUNCT
ejpam-5135	23	10	then	then	ADV
ejpam-5135	23	11	the	the	DET
ejpam-5135	23	12	graph	graph	NOUN
ejpam-5135	23	13	g	g	NOUN
ejpam-5135	23	14	is	be	AUX
ejpam-5135	23	15	connected	connect	VERB
ejpam-5135	23	16	.	.	PUNCT
ejpam-5135	24	1	a	a	DET
ejpam-5135	24	2	component	component	NOUN
ejpam-5135	24	3	of	of	ADP
ejpam-5135	24	4	g	g	PROPN
ejpam-5135	24	5	is	be	AUX
ejpam-5135	24	6	a	a	DET
ejpam-5135	24	7	connected	connected	ADJ
ejpam-5135	24	8	subgraph	subgraph	NOUN
ejpam-5135	24	9	of	of	ADP
ejpam-5135	24	10	g	g	PROPN
ejpam-5135	24	11	that	that	PRON
ejpam-5135	24	12	is	be	AUX
ejpam-5135	24	13	not	not	PART
ejpam-5135	24	14	contained	contain	VERB
ejpam-5135	24	15	in	in	ADP
ejpam-5135	24	16	any	any	DET
ejpam-5135	24	17	larger	large	ADJ
ejpam-5135	24	18	connected	connected	ADJ
ejpam-5135	24	19	subgraph	subgraph	NOUN
ejpam-5135	24	20	of	of	ADP
ejpam-5135	24	21	g.	g.	PROPN
ejpam-5135	24	22	the	the	DET
ejpam-5135	24	23	number	number	NOUN
ejpam-5135	24	24	of	of	ADP
ejpam-5135	24	25	components	component	NOUN
ejpam-5135	24	26	of	of	ADP
ejpam-5135	24	27	g	g	PROPN
ejpam-5135	24	28	is	be	AUX
ejpam-5135	24	29	denoted	denote	VERB
ejpam-5135	24	30	by	by	ADP
ejpam-5135	24	31	κ(g	κ(g	PROPN
ejpam-5135	24	32	)	)	PUNCT
ejpam-5135	24	33	.	.	PUNCT
ejpam-5135	25	1	a	a	DET
ejpam-5135	25	2	vertex	vertex	NOUN
ejpam-5135	25	3	v	v	NOUN
ejpam-5135	25	4	of	of	ADP
ejpam-5135	25	5	g	g	PROPN
ejpam-5135	25	6	is	be	AUX
ejpam-5135	25	7	a	a	DET
ejpam-5135	25	8	cut	cut	NOUN
ejpam-5135	25	9	-	-	PUNCT
ejpam-5135	25	10	vertex	vertex	NOUN
ejpam-5135	25	11	of	of	ADP
ejpam-5135	25	12	g	g	NOUN
ejpam-5135	25	13	if	if	SCONJ
ejpam-5135	25	14	κ(g	κ(g	PROPN
ejpam-5135	25	15	−	−	PROPN
ejpam-5135	25	16	v	v	NOUN
ejpam-5135	25	17	)	)	PUNCT
ejpam-5135	25	18	>	>	X
ejpam-5135	25	19	κ(g	κ(g	NOUN
ejpam-5135	25	20	)	)	PUNCT
ejpam-5135	25	21	.	.	PUNCT
ejpam-5135	26	1	if	if	SCONJ
ejpam-5135	26	2	g	g	PROPN
ejpam-5135	26	3	is	be	AUX
ejpam-5135	26	4	a	a	DET
ejpam-5135	26	5	nontrivial	nontrivial	ADJ
ejpam-5135	26	6	graph	graph	NOUN
ejpam-5135	26	7	and	and	CCONJ
ejpam-5135	26	8	v	v	NOUN
ejpam-5135	26	9	is	be	AUX
ejpam-5135	26	10	a	a	DET
ejpam-5135	26	11	cut	cut	NOUN
ejpam-5135	26	12	-	-	PUNCT
ejpam-5135	26	13	vertex	vertex	NOUN
ejpam-5135	26	14	of	of	ADP
ejpam-5135	26	15	component	component	NOUN
ejpam-5135	26	16	cj	cj	NOUN
ejpam-5135	26	17	of	of	ADP
ejpam-5135	26	18	g	g	PROPN
ejpam-5135	26	19	,	,	PUNCT
ejpam-5135	26	20	then	then	ADV
ejpam-5135	26	21	the	the	DET
ejpam-5135	26	22	subgraph	subgraph	NOUN
ejpam-5135	26	23	cj	cj	PROPN
ejpam-5135	26	24	−	−	PROPN
ejpam-5135	26	25	v	v	NOUN
ejpam-5135	26	26	has	have	VERB
ejpam-5135	26	27	m	m	PROPN
ejpam-5135	26	28	components	component	NOUN
ejpam-5135	26	29	g1	g1	NOUN
ejpam-5135	26	30	,	,	PUNCT
ejpam-5135	26	31	g2	g2	PROPN
ejpam-5135	26	32	,	,	PUNCT
ejpam-5135	26	33	·	·	PUNCT
ejpam-5135	26	34	·	·	PUNCT
ejpam-5135	26	35	·	·	PUNCT
ejpam-5135	26	36	,	,	PUNCT
ejpam-5135	26	37	gm	gm	PROPN
ejpam-5135	26	38	for	for	ADP
ejpam-5135	26	39	m	m	PROPN
ejpam-5135	26	40	≥	≥	NOUN
ejpam-5135	26	41	2	2	NUM
ejpam-5135	26	42	and	and	CCONJ
ejpam-5135	26	43	the	the	DET
ejpam-5135	26	44	induced	induced	ADJ
ejpam-5135	26	45	subgraphs	subgraphs	NOUN
ejpam-5135	26	46	brji	brji	PROPN
ejpam-5135	26	47	=	=	SYM
ejpam-5135	26	48	g[v	g[v	NOUN
ejpam-5135	26	49	(	(	PUNCT
ejpam-5135	26	50	gi)∪	gi)∪	X
ejpam-5135	26	51	{	{	PUNCT
ejpam-5135	26	52	v	v	NOUN
ejpam-5135	26	53	}	}	PUNCT
ejpam-5135	26	54	]	]	PUNCT
ejpam-5135	26	55	are	be	AUX
ejpam-5135	26	56	connected	connect	VERB
ejpam-5135	26	57	and	and	CCONJ
ejpam-5135	26	58	referred	refer	VERB
ejpam-5135	26	59	to	to	ADP
ejpam-5135	26	60	as	as	ADP
ejpam-5135	26	61	branches	branch	NOUN
ejpam-5135	26	62	of	of	ADP
ejpam-5135	26	63	cj	cj	NOUN
ejpam-5135	26	64	at	at	ADP
ejpam-5135	26	65	v	v	NUM
ejpam-5135	26	66	[	[	X
ejpam-5135	26	67	4	4	NUM
ejpam-5135	26	68	]	]	PUNCT
ejpam-5135	26	69	.	.	PUNCT
ejpam-5135	27	1	a	a	DET
ejpam-5135	27	2	block	block	NOUN
ejpam-5135	27	3	of	of	ADP
ejpam-5135	27	4	a	a	DET
ejpam-5135	27	5	graph	graph	NOUN
ejpam-5135	27	6	is	be	AUX
ejpam-5135	27	7	a	a	DET
ejpam-5135	27	8	maximal	maximal	ADJ
ejpam-5135	27	9	connected	connected	ADJ
ejpam-5135	27	10	subgraph	subgraph	NOUN
ejpam-5135	27	11	that	that	PRON
ejpam-5135	27	12	contains	contain	VERB
ejpam-5135	27	13	no	no	DET
ejpam-5135	27	14	cut	cut	NOUN
ejpam-5135	27	15	-	-	PUNCT
ejpam-5135	27	16	vertices	vertex	NOUN
ejpam-5135	27	17	[	[	X
ejpam-5135	27	18	11	11	NUM
ejpam-5135	27	19	]	]	PUNCT
ejpam-5135	27	20	.	.	PUNCT
ejpam-5135	28	1	the	the	DET
ejpam-5135	28	2	smallest	small	ADJ
ejpam-5135	28	3	possible	possible	ADJ
ejpam-5135	28	4	block	block	NOUN
ejpam-5135	28	5	in	in	ADP
ejpam-5135	28	6	a	a	DET
ejpam-5135	28	7	graph	graph	NOUN
ejpam-5135	28	8	is	be	AUX
ejpam-5135	28	9	a	a	DET
ejpam-5135	28	10	subgraph	subgraph	NOUN
ejpam-5135	28	11	induced	induce	VERB
ejpam-5135	28	12	by	by	ADP
ejpam-5135	28	13	a	a	DET
ejpam-5135	28	14	single	single	ADJ
ejpam-5135	28	15	vertex	vertex	NOUN
ejpam-5135	28	16	with	with	ADP
ejpam-5135	28	17	a	a	DET
ejpam-5135	28	18	degree	degree	NOUN
ejpam-5135	28	19	equal	equal	ADJ
ejpam-5135	28	20	to	to	ADP
ejpam-5135	28	21	zero	zero	NUM
ejpam-5135	28	22	.	.	PUNCT
ejpam-5135	29	1	moreover	moreover	ADV
ejpam-5135	29	2	,	,	PUNCT
ejpam-5135	29	3	two	two	NUM
ejpam-5135	29	4	distinct	distinct	ADJ
ejpam-5135	29	5	blocks	block	NOUN
ejpam-5135	29	6	have	have	VERB
ejpam-5135	29	7	at	at	ADP
ejpam-5135	29	8	most	most	ADV
ejpam-5135	29	9	one	one	NUM
ejpam-5135	29	10	vertex	vertex	NOUN
ejpam-5135	29	11	in	in	ADP
ejpam-5135	29	12	common	common	ADJ
ejpam-5135	29	13	and	and	CCONJ
ejpam-5135	29	14	if	if	SCONJ
ejpam-5135	29	15	they	they	PRON
ejpam-5135	29	16	share	share	VERB
ejpam-5135	29	17	the	the	DET
ejpam-5135	29	18	same	same	ADJ
ejpam-5135	29	19	vertex	vertex	NOUN
ejpam-5135	29	20	,	,	PUNCT
ejpam-5135	29	21	then	then	ADV
ejpam-5135	29	22	this	this	DET
ejpam-5135	29	23	vertex	vertex	NOUN
ejpam-5135	29	24	is	be	AUX
ejpam-5135	29	25	a	a	DET
ejpam-5135	29	26	cut	cut	NOUN
ejpam-5135	29	27	-	-	PUNCT
ejpam-5135	29	28	vertex	vertex	NOUN
ejpam-5135	29	29	[	[	X
ejpam-5135	29	30	4	4	NUM
ejpam-5135	29	31	]	]	PUNCT
ejpam-5135	29	32	.	.	PUNCT
ejpam-5135	30	1	in	in	ADP
ejpam-5135	30	2	addition	addition	NOUN
ejpam-5135	30	3	,	,	PUNCT
ejpam-5135	30	4	if	if	SCONJ
ejpam-5135	30	5	b1	b1	NOUN
ejpam-5135	30	6	,	,	PUNCT
ejpam-5135	30	7	b2	b2	NOUN
ejpam-5135	30	8	,	,	PUNCT
ejpam-5135	30	9	·	·	PUNCT
ejpam-5135	30	10	·	·	PUNCT
ejpam-5135	30	11	·	·	PUNCT
ejpam-5135	30	12	,	,	PUNCT
ejpam-5135	30	13	bk	bk	NOUN
ejpam-5135	30	14	are	be	AUX
ejpam-5135	30	15	the	the	DET
ejpam-5135	30	16	blocks	block	NOUN
ejpam-5135	30	17	of	of	ADP
ejpam-5135	30	18	g	g	NOUN
ejpam-5135	30	19	,	,	PUNCT
ejpam-5135	30	20	then	then	ADV
ejpam-5135	30	21	⋃k	⋃k	NUM
ejpam-5135	30	22	i=1	i=1	PROPN
ejpam-5135	30	23	v	v	PROPN
ejpam-5135	30	24	(	(	PUNCT
ejpam-5135	30	25	bi	bi	NOUN
ejpam-5135	30	26	)	)	PUNCT
ejpam-5135	30	27	=	=	SYM
ejpam-5135	30	28	v	v	NOUN
ejpam-5135	30	29	(	(	PUNCT
ejpam-5135	30	30	g	g	NOUN
ejpam-5135	30	31	)	)	PUNCT
ejpam-5135	30	32	.	.	PUNCT
ejpam-5135	31	1	a	a	DET
ejpam-5135	31	2	topology	topology	NOUN
ejpam-5135	31	3	τ	τ	X
ejpam-5135	31	4	on	on	ADP
ejpam-5135	31	5	a	a	DET
ejpam-5135	31	6	nonempty	nonempty	ADV
ejpam-5135	31	7	set	set	VERB
ejpam-5135	31	8	x	x	PUNCT
ejpam-5135	31	9	is	be	AUX
ejpam-5135	31	10	a	a	DET
ejpam-5135	31	11	class	class	NOUN
ejpam-5135	31	12	of	of	ADP
ejpam-5135	31	13	subsets	subset	NOUN
ejpam-5135	31	14	of	of	ADP
ejpam-5135	31	15	x	x	PRON
ejpam-5135	31	16	that	that	PRON
ejpam-5135	31	17	is	be	AUX
ejpam-5135	31	18	closed	close	VERB
ejpam-5135	31	19	under	under	ADP
ejpam-5135	31	20	arbitrary	arbitrary	ADJ
ejpam-5135	31	21	union	union	NOUN
ejpam-5135	31	22	and	and	CCONJ
ejpam-5135	31	23	finite	finite	ADJ
ejpam-5135	31	24	intersection	intersection	NOUN
ejpam-5135	31	25	,	,	PUNCT
ejpam-5135	31	26	and	and	CCONJ
ejpam-5135	31	27	x	x	PUNCT
ejpam-5135	31	28	and	and	CCONJ
ejpam-5135	31	29	∅	∅	NOUN
ejpam-5135	31	30	belong	belong	VERB
ejpam-5135	31	31	to	to	ADP
ejpam-5135	31	32	τ	τ	PROPN
ejpam-5135	31	33	.	.	PUNCT
ejpam-5135	32	1	the	the	DET
ejpam-5135	32	2	member	member	NOUN
ejpam-5135	32	3	of	of	ADP
ejpam-5135	32	4	τ	τ	PROPN
ejpam-5135	32	5	is	be	AUX
ejpam-5135	32	6	called	call	VERB
ejpam-5135	32	7	an	an	DET
ejpam-5135	32	8	open	open	ADJ
ejpam-5135	32	9	set	set	NOUN
ejpam-5135	32	10	and	and	CCONJ
ejpam-5135	32	11	the	the	DET
ejpam-5135	32	12	pair	pair	NOUN
ejpam-5135	32	13	(	(	PUNCT
ejpam-5135	32	14	x	x	X
ejpam-5135	32	15	,	,	PUNCT
ejpam-5135	32	16	τ	τ	X
ejpam-5135	32	17	)	)	PUNCT
ejpam-5135	32	18	is	be	AUX
ejpam-5135	32	19	called	call	VERB
ejpam-5135	32	20	a	a	DET
ejpam-5135	32	21	topological	topological	ADJ
ejpam-5135	32	22	space	space	NOUN
ejpam-5135	32	23	.	.	PUNCT
ejpam-5135	33	1	the	the	DET
ejpam-5135	33	2	topology	topology	NOUN
ejpam-5135	33	3	containing	contain	VERB
ejpam-5135	33	4	all	all	DET
ejpam-5135	33	5	the	the	DET
ejpam-5135	33	6	subsets	subset	NOUN
ejpam-5135	33	7	of	of	ADP
ejpam-5135	33	8	x	x	PROPN
ejpam-5135	33	9	is	be	AUX
ejpam-5135	33	10	called	call	VERB
ejpam-5135	33	11	the	the	DET
ejpam-5135	33	12	discrete	discrete	ADJ
ejpam-5135	33	13	topology	topology	NOUN
ejpam-5135	33	14	on	on	ADP
ejpam-5135	33	15	x	x	PUNCT
ejpam-5135	33	16	and	and	CCONJ
ejpam-5135	33	17	the	the	DET
ejpam-5135	33	18	topology	topology	NOUN
ejpam-5135	33	19	containing	contain	VERB
ejpam-5135	33	20	exactly	exactly	ADV
ejpam-5135	33	21	x	x	PUNCT
ejpam-5135	33	22	and	and	CCONJ
ejpam-5135	33	23	∅	∅	NOUN
ejpam-5135	33	24	is	be	AUX
ejpam-5135	33	25	called	call	VERB
ejpam-5135	33	26	the	the	DET
ejpam-5135	33	27	indiscrete	indiscrete	ADJ
ejpam-5135	33	28	topology	topology	NOUN
ejpam-5135	33	29	on	on	ADP
ejpam-5135	33	30	x.	x.	NOUN
ejpam-5135	33	31	a	a	DET
ejpam-5135	33	32	collection	collection	NOUN
ejpam-5135	33	33	γ	γ	NOUN
ejpam-5135	33	34	of	of	ADP
ejpam-5135	33	35	open	open	ADJ
ejpam-5135	33	36	sets	set	NOUN
ejpam-5135	33	37	is	be	AUX
ejpam-5135	33	38	a	a	DET
ejpam-5135	33	39	base	base	NOUN
ejpam-5135	33	40	for	for	ADP
ejpam-5135	33	41	a	a	DET
ejpam-5135	33	42	topology	topology	NOUN
ejpam-5135	33	43	of	of	ADP
ejpam-5135	33	44	x	x	PRON
ejpam-5135	33	45	if	if	SCONJ
ejpam-5135	33	46	each	each	DET
ejpam-5135	33	47	nonempty	nonempty	ADV
ejpam-5135	33	48	open	open	ADJ
ejpam-5135	33	49	is	be	AUX
ejpam-5135	33	50	a	a	DET
ejpam-5135	33	51	union	union	NOUN
ejpam-5135	33	52	of	of	ADP
ejpam-5135	33	53	sets	set	NOUN
ejpam-5135	33	54	belonging	belong	VERB
ejpam-5135	33	55	to	to	ADP
ejpam-5135	33	56	γ	γ	PROPN
ejpam-5135	33	57	.	.	PUNCT
ejpam-5135	34	1	a	a	DET
ejpam-5135	34	2	collection	collection	NOUN
ejpam-5135	34	3	σ	σ	NOUN
ejpam-5135	34	4	of	of	ADP
ejpam-5135	34	5	open	open	ADJ
ejpam-5135	34	6	sets	set	NOUN
ejpam-5135	34	7	is	be	AUX
ejpam-5135	34	8	called	call	VERB
ejpam-5135	34	9	a	a	DET
ejpam-5135	34	10	subbase	subbase	NOUN
ejpam-5135	34	11	if	if	SCONJ
ejpam-5135	34	12	the	the	DET
ejpam-5135	34	13	set	set	NOUN
ejpam-5135	34	14	{	{	PUNCT
ejpam-5135	34	15	a	a	X
ejpam-5135	34	16	:	:	PUNCT
ejpam-5135	34	17	a	a	DET
ejpam-5135	34	18	=	=	PROPN
ejpam-5135	34	19	⋂k	⋂k	PROPN
ejpam-5135	34	20	i=1wi	i=1wi	PROPN
ejpam-5135	34	21	,	,	PUNCT
ejpam-5135	34	22	k	k	PROPN
ejpam-5135	34	23	∈	∈	PROPN
ejpam-5135	34	24	z+,wi	z+,wi	PROPN
ejpam-5135	34	25	∈	∈	PROPN
ejpam-5135	34	26	σ	σ	PROPN
ejpam-5135	34	27	}	}	PUNCT
ejpam-5135	34	28	is	be	AUX
ejpam-5135	34	29	a	a	DET
ejpam-5135	34	30	base	base	NOUN
ejpam-5135	34	31	for	for	ADP
ejpam-5135	34	32	a	a	DET
ejpam-5135	34	33	topology	topology	NOUN
ejpam-5135	34	34	on	on	ADP
ejpam-5135	34	35	x[10	x[10	PROPN
ejpam-5135	34	36	]	]	PUNCT
ejpam-5135	34	37	.	.	PUNCT
ejpam-5135	35	1	any	any	DET
ejpam-5135	35	2	class	class	NOUN
ejpam-5135	35	3	a	a	PRON
ejpam-5135	35	4	of	of	ADP
ejpam-5135	35	5	subsets	subset	NOUN
ejpam-5135	35	6	of	of	ADP
ejpam-5135	35	7	x	x	X
ejpam-5135	35	8	is	be	AUX
ejpam-5135	35	9	a	a	DET
ejpam-5135	35	10	subbase	subbase	NOUN
ejpam-5135	35	11	of	of	ADP
ejpam-5135	35	12	for	for	ADP
ejpam-5135	35	13	a	a	DET
ejpam-5135	35	14	unique	unique	ADJ
ejpam-5135	35	15	topology	topology	NOUN
ejpam-5135	35	16	on	on	ADP
ejpam-5135	35	17	x.	x.	NOUN
ejpam-5135	35	18	that	that	PRON
ejpam-5135	35	19	is	is	ADV
ejpam-5135	35	20	,	,	PUNCT
ejpam-5135	35	21	the	the	DET
ejpam-5135	35	22	finite	finite	ADJ
ejpam-5135	35	23	intersection	intersection	NOUN
ejpam-5135	35	24	of	of	ADP
ejpam-5135	35	25	sets	set	NOUN
ejpam-5135	35	26	in	in	ADP
ejpam-5135	35	27	a	a	DET
ejpam-5135	35	28	form	form	NOUN
ejpam-5135	35	29	a	a	DET
ejpam-5135	35	30	base	base	NOUN
ejpam-5135	35	31	for	for	ADP
ejpam-5135	35	32	a	a	DET
ejpam-5135	35	33	topology	topology	NOUN
ejpam-5135	35	34	on	on	ADP
ejpam-5135	35	35	x	x	PUNCT
ejpam-5135	36	1	[	[	X
ejpam-5135	36	2	9	9	NUM
ejpam-5135	36	3	]	]	PUNCT
ejpam-5135	36	4	.	.	PUNCT
ejpam-5135	37	1	if	if	SCONJ
ejpam-5135	37	2	(	(	PUNCT
ejpam-5135	37	3	x	x	NOUN
ejpam-5135	37	4	,	,	PUNCT
ejpam-5135	37	5	τ1	τ1	NOUN
ejpam-5135	37	6	)	)	PUNCT
ejpam-5135	37	7	and	and	CCONJ
ejpam-5135	37	8	(	(	PUNCT
ejpam-5135	37	9	y	y	PROPN
ejpam-5135	37	10	,	,	PUNCT
ejpam-5135	37	11	τ2	τ2	PROPN
ejpam-5135	37	12	)	)	PUNCT
ejpam-5135	37	13	are	be	AUX
ejpam-5135	37	14	two	two	NUM
ejpam-5135	37	15	topological	topological	ADJ
ejpam-5135	37	16	space	space	NOUN
ejpam-5135	37	17	,	,	PUNCT
ejpam-5135	37	18	then	then	ADV
ejpam-5135	37	19	f	f	X
ejpam-5135	37	20	:	:	PUNCT
ejpam-5135	37	21	(	(	PUNCT
ejpam-5135	37	22	x	x	NOUN
ejpam-5135	37	23	,	,	PUNCT
ejpam-5135	37	24	τ1	τ1	NOUN
ejpam-5135	37	25	)	)	PUNCT
ejpam-5135	37	26	→	→	SYM
ejpam-5135	37	27	(	(	PUNCT
ejpam-5135	37	28	y	y	PROPN
ejpam-5135	37	29	,	,	PUNCT
ejpam-5135	37	30	τ2	τ2	NOUN
ejpam-5135	37	31	)	)	PUNCT
ejpam-5135	37	32	is	be	AUX
ejpam-5135	37	33	continuous	continuous	ADJ
ejpam-5135	37	34	if	if	SCONJ
ejpam-5135	37	35	the	the	DET
ejpam-5135	37	36	preimage	preimage	NOUN
ejpam-5135	37	37	of	of	ADP
ejpam-5135	37	38	any	any	DET
ejpam-5135	37	39	open	open	ADJ
ejpam-5135	37	40	subset	subset	NOUN
ejpam-5135	37	41	of	of	ADP
ejpam-5135	37	42	y	y	PROPN
ejpam-5135	37	43	is	be	AUX
ejpam-5135	37	44	an	an	DET
ejpam-5135	37	45	open	open	ADJ
ejpam-5135	37	46	subset	subset	NOUN
ejpam-5135	37	47	of	of	ADP
ejpam-5135	37	48	x[10	x[10	PROPN
ejpam-5135	37	49	]	]	PUNCT
ejpam-5135	37	50	.	.	PUNCT
ejpam-5135	38	1	as	as	SCONJ
ejpam-5135	38	2	seen	see	VERB
ejpam-5135	38	3	in	in	ADP
ejpam-5135	38	4	the	the	DET
ejpam-5135	38	5	above	above	ADJ
ejpam-5135	38	6	discussion	discussion	NOUN
ejpam-5135	38	7	,	,	PUNCT
ejpam-5135	38	8	it	it	PRON
ejpam-5135	38	9	is	be	AUX
ejpam-5135	38	10	possible	possible	ADJ
ejpam-5135	38	11	to	to	PART
ejpam-5135	38	12	exhaust	exhaust	VERB
ejpam-5135	38	13	the	the	DET
ejpam-5135	38	14	distinct	distinct	ADJ
ejpam-5135	38	15	blocks	block	NOUN
ejpam-5135	38	16	of	of	ADP
ejpam-5135	38	17	a	a	DET
ejpam-5135	38	18	given	give	VERB
ejpam-5135	38	19	graph	graph	NOUN
ejpam-5135	38	20	and	and	CCONJ
ejpam-5135	38	21	apply	apply	VERB
ejpam-5135	38	22	various	various	ADJ
ejpam-5135	38	23	methods	method	NOUN
ejpam-5135	38	24	of	of	ADP
ejpam-5135	38	25	topologizing	topologize	VERB
ejpam-5135	38	26	the	the	DET
ejpam-5135	38	27	family	family	NOUN
ejpam-5135	38	28	of	of	ADP
ejpam-5135	38	29	the	the	DET
ejpam-5135	38	30	vertex	vertex	NOUN
ejpam-5135	38	31	sets	set	NOUN
ejpam-5135	38	32	of	of	ADP
ejpam-5135	38	33	these	these	DET
ejpam-5135	38	34	blocks	block	NOUN
ejpam-5135	38	35	.	.	PUNCT
ejpam-5135	39	1	it	it	PRON
ejpam-5135	39	2	is	be	AUX
ejpam-5135	39	3	with	with	ADP
ejpam-5135	39	4	this	this	DET
ejpam-5135	39	5	motivation	motivation	NOUN
ejpam-5135	39	6	that	that	PRON
ejpam-5135	39	7	we	we	PRON
ejpam-5135	39	8	aim	aim	VERB
ejpam-5135	39	9	to	to	PART
ejpam-5135	39	10	introduce	introduce	VERB
ejpam-5135	39	11	a	a	DET
ejpam-5135	39	12	novel	novel	ADJ
ejpam-5135	39	13	approach	approach	NOUN
ejpam-5135	39	14	to	to	ADP
ejpam-5135	39	15	topologizing	topologize	VERB
ejpam-5135	39	16	a	a	DET
ejpam-5135	39	17	graph	graph	NOUN
ejpam-5135	39	18	using	use	VERB
ejpam-5135	39	19	the	the	DET
ejpam-5135	39	20	blocks	block	NOUN
ejpam-5135	39	21	in	in	ADP
ejpam-5135	39	22	a	a	DET
ejpam-5135	39	23	graph	graph	NOUN
ejpam-5135	39	24	.	.	PUNCT
ejpam-5135	40	1	the	the	DET
ejpam-5135	40	2	generated	generate	VERB
ejpam-5135	40	3	topology	topology	NOUN
ejpam-5135	40	4	will	will	AUX
ejpam-5135	40	5	then	then	ADV
ejpam-5135	40	6	be	be	AUX
ejpam-5135	40	7	called	call	VERB
ejpam-5135	40	8	the	the	DET
ejpam-5135	40	9	block	block	NOUN
ejpam-5135	40	10	topological	topological	ADJ
ejpam-5135	40	11	space	space	NOUN
ejpam-5135	40	12	of	of	ADP
ejpam-5135	40	13	a	a	DET
ejpam-5135	40	14	graph	graph	NOUN
ejpam-5135	40	15	.	.	PUNCT
ejpam-5135	41	1	moreover	moreover	ADV
ejpam-5135	41	2	,	,	PUNCT
ejpam-5135	41	3	we	we	PRON
ejpam-5135	41	4	examine	examine	VERB
ejpam-5135	41	5	and	and	CCONJ
ejpam-5135	41	6	investigate	investigate	VERB
ejpam-5135	41	7	some	some	DET
ejpam-5135	41	8	elementary	elementary	ADJ
ejpam-5135	41	9	properties	property	NOUN
ejpam-5135	41	10	of	of	ADP
ejpam-5135	41	11	sets	set	NOUN
ejpam-5135	41	12	in	in	ADP
ejpam-5135	41	13	a	a	DET
ejpam-5135	41	14	block	block	NOUN
ejpam-5135	41	15	topological	topological	ADJ
ejpam-5135	41	16	space	space	NOUN
ejpam-5135	41	17	.	.	PUNCT
ejpam-5135	42	1	finally	finally	ADV
ejpam-5135	42	2	,	,	PUNCT
ejpam-5135	42	3	we	we	PRON
ejpam-5135	42	4	introduce	introduce	VERB
ejpam-5135	42	5	the	the	DET
ejpam-5135	42	6	notion	notion	NOUN
ejpam-5135	42	7	of	of	ADP
ejpam-5135	42	8	a	a	DET
ejpam-5135	42	9	block	block	NOUN
ejpam-5135	42	10	topological	topological	ADJ
ejpam-5135	42	11	graph	graph	NOUN
ejpam-5135	42	12	.	.	PUNCT
ejpam-5135	43	1	2	2	X
ejpam-5135	43	2	.	.	NOUN
ejpam-5135	43	3	steps	step	NOUN
ejpam-5135	43	4	in	in	ADP
ejpam-5135	43	5	enumerating	enumerate	VERB
ejpam-5135	43	6	the	the	DET
ejpam-5135	43	7	blocks	block	NOUN
ejpam-5135	43	8	in	in	ADP
ejpam-5135	43	9	a	a	DET
ejpam-5135	43	10	graph	graph	NOUN
ejpam-5135	43	11	general	general	ADJ
ejpam-5135	43	12	assumption	assumption	NOUN
ejpam-5135	43	13	:	:	PUNCT
ejpam-5135	43	14	let	let	VERB
ejpam-5135	43	15	g	g	PRON
ejpam-5135	43	16	be	be	AUX
ejpam-5135	43	17	a	a	DET
ejpam-5135	43	18	simple	simple	ADJ
ejpam-5135	43	19	undirected	undirected	ADJ
ejpam-5135	43	20	graph	graph	NOUN
ejpam-5135	43	21	with	with	ADP
ejpam-5135	43	22	components	component	NOUN
ejpam-5135	43	23	c1	c1	PROPN
ejpam-5135	43	24	,	,	PUNCT
ejpam-5135	43	25	·	·	PUNCT
ejpam-5135	43	26	·	·	PUNCT
ejpam-5135	43	27	·	·	PUNCT
ejpam-5135	43	28	,	,	PUNCT
ejpam-5135	43	29	cj	cj	NOUN
ejpam-5135	43	30	for	for	ADP
ejpam-5135	43	31	some	some	DET
ejpam-5135	43	32	j	j	PROPN
ejpam-5135	43	33	∈	∈	PROPN
ejpam-5135	43	34	z+	z+	PUNCT
ejpam-5135	43	35	.	.	PUNCT
ejpam-5135	44	1	the	the	DET
ejpam-5135	44	2	following	follow	VERB
ejpam-5135	44	3	steps	step	NOUN
ejpam-5135	44	4	are	be	AUX
ejpam-5135	44	5	ways	way	NOUN
ejpam-5135	44	6	on	on	ADP
ejpam-5135	44	7	enumerating	enumerate	VERB
ejpam-5135	44	8	the	the	DET
ejpam-5135	44	9	blocks	block	NOUN
ejpam-5135	44	10	in	in	ADP
ejpam-5135	44	11	a	a	DET
ejpam-5135	44	12	graph	graph	NOUN
ejpam-5135	44	13	.	.	PUNCT
ejpam-5135	45	1	justine	justine	PROPN
ejpam-5135	45	2	bryle	bryle	PROPN
ejpam-5135	45	3	c.	c.	PROPN
ejpam-5135	45	4	macaso	macaso	PROPN
ejpam-5135	45	5	,	,	PUNCT
ejpam-5135	45	6	cherry	cherry	PROPN
ejpam-5135	45	7	mae	mae	PROPN
ejpam-5135	45	8	r.	r.	PROPN
ejpam-5135	45	9	balingit	balingit	PROPN
ejpam-5135	45	10	/	/	SYM
ejpam-5135	45	11	eur	eur	PROPN
ejpam-5135	45	12	.	.	PUNCT
ejpam-5135	46	1	j.	j.	PROPN
ejpam-5135	46	2	pure	pure	PROPN
ejpam-5135	46	3	appl	appl	PROPN
ejpam-5135	46	4	.	.	PROPN
ejpam-5135	46	5	math	math	PROPN
ejpam-5135	46	6	,	,	PUNCT
ejpam-5135	46	7	17	17	NUM
ejpam-5135	46	8	(	(	PUNCT
ejpam-5135	46	9	2	2	NUM
ejpam-5135	46	10	)	)	PUNCT
ejpam-5135	46	11	(	(	PUNCT
ejpam-5135	46	12	2024	2024	NUM
ejpam-5135	46	13	)	)	PUNCT
ejpam-5135	46	14	,	,	PUNCT
ejpam-5135	46	15	663	663	NUM
ejpam-5135	46	16	-	-	SYM
ejpam-5135	46	17	675	675	NUM
ejpam-5135	46	18	665	665	NUM
ejpam-5135	46	19	step	step	NOUN
ejpam-5135	46	20	1	1	NUM
ejpam-5135	46	21	:	:	PUNCT
ejpam-5135	46	22	for	for	ADP
ejpam-5135	46	23	any	any	DET
ejpam-5135	46	24	1	1	NUM
ejpam-5135	46	25	≤	≤	NUM
ejpam-5135	46	26	i	i	NOUN
ejpam-5135	47	1	≤	≤	PROPN
ejpam-5135	47	2	j	j	PROPN
ejpam-5135	47	3	,	,	PUNCT
ejpam-5135	47	4	if	if	SCONJ
ejpam-5135	47	5	ci	ci	PROPN
ejpam-5135	47	6	contains	contain	VERB
ejpam-5135	47	7	no	no	DET
ejpam-5135	47	8	cut	cut	NOUN
ejpam-5135	47	9	-	-	PUNCT
ejpam-5135	47	10	vertices	vertex	NOUN
ejpam-5135	47	11	,	,	PUNCT
ejpam-5135	47	12	then	then	ADV
ejpam-5135	47	13	ci	ci	PROPN
ejpam-5135	47	14	is	be	AUX
ejpam-5135	47	15	a	a	DET
ejpam-5135	47	16	block	block	NOUN
ejpam-5135	47	17	of	of	ADP
ejpam-5135	47	18	g.	g.	PROPN
ejpam-5135	47	19	consequently	consequently	ADV
ejpam-5135	47	20	,	,	PUNCT
ejpam-5135	47	21	if	if	SCONJ
ejpam-5135	47	22	g	g	PROPN
ejpam-5135	47	23	has	have	VERB
ejpam-5135	47	24	no	no	DET
ejpam-5135	47	25	cut	cut	NOUN
ejpam-5135	47	26	-	-	PUNCT
ejpam-5135	47	27	vertex	vertex	NOUN
ejpam-5135	47	28	,	,	PUNCT
ejpam-5135	47	29	then	then	ADV
ejpam-5135	47	30	c1	c1	PROPN
ejpam-5135	47	31	,	,	PUNCT
ejpam-5135	47	32	c2	c2	PROPN
ejpam-5135	47	33	,	,	PUNCT
ejpam-5135	47	34	·	·	PUNCT
ejpam-5135	47	35	·	·	PUNCT
ejpam-5135	47	36	·	·	PUNCT
ejpam-5135	47	37	,	,	PUNCT
ejpam-5135	47	38	cj	cj	NOUN
ejpam-5135	47	39	are	be	AUX
ejpam-5135	47	40	precisely	precisely	ADV
ejpam-5135	47	41	the	the	DET
ejpam-5135	47	42	blocks	block	NOUN
ejpam-5135	47	43	of	of	ADP
ejpam-5135	47	44	g.	g.	PROPN
ejpam-5135	47	45	step	step	NOUN
ejpam-5135	47	46	2	2	NUM
ejpam-5135	47	47	:	:	PUNCT
ejpam-5135	47	48	if	if	SCONJ
ejpam-5135	47	49	ci	ci	PROPN
ejpam-5135	47	50	contains	contain	VERB
ejpam-5135	47	51	a	a	DET
ejpam-5135	47	52	cut	cut	VERB
ejpam-5135	47	53	-	-	PUNCT
ejpam-5135	47	54	vertex	vertex	NOUN
ejpam-5135	47	55	vi1	vi1	NOUN
ejpam-5135	47	56	,	,	PUNCT
ejpam-5135	47	57	then	then	ADV
ejpam-5135	47	58	obtain	obtain	VERB
ejpam-5135	47	59	the	the	DET
ejpam-5135	47	60	branches	branch	NOUN
ejpam-5135	47	61	of	of	ADP
ejpam-5135	47	62	ci	ci	PROPN
ejpam-5135	47	63	at	at	ADP
ejpam-5135	47	64	vi1	vi1	PROPN
ejpam-5135	47	65	.	.	PUNCT
ejpam-5135	48	1	step	step	VERB
ejpam-5135	48	2	3	3	NUM
ejpam-5135	48	3	:	:	PUNCT
ejpam-5135	48	4	if	if	SCONJ
ejpam-5135	48	5	all	all	DET
ejpam-5135	48	6	the	the	DET
ejpam-5135	48	7	branches	branch	NOUN
ejpam-5135	48	8	of	of	ADP
ejpam-5135	48	9	ci	ci	PROPN
ejpam-5135	48	10	at	at	ADP
ejpam-5135	48	11	vi1	vi1	PROPN
ejpam-5135	48	12	contains	contain	VERB
ejpam-5135	48	13	no	no	DET
ejpam-5135	48	14	cut	cut	NOUN
ejpam-5135	48	15	-	-	PUNCT
ejpam-5135	48	16	vertices	vertex	NOUN
ejpam-5135	48	17	,	,	PUNCT
ejpam-5135	48	18	then	then	ADV
ejpam-5135	48	19	of	of	ADP
ejpam-5135	48	20	these	these	DET
ejpam-5135	48	21	branches	branch	NOUN
ejpam-5135	48	22	is	be	AUX
ejpam-5135	48	23	a	a	DET
ejpam-5135	48	24	block	block	NOUN
ejpam-5135	48	25	of	of	ADP
ejpam-5135	48	26	g.	g.	PROPN
ejpam-5135	48	27	otherwise	otherwise	ADV
ejpam-5135	48	28	,	,	PUNCT
ejpam-5135	48	29	take	take	VERB
ejpam-5135	48	30	the	the	DET
ejpam-5135	48	31	branches	branch	NOUN
ejpam-5135	48	32	of	of	ADP
ejpam-5135	48	33	ci	ci	NOUN
ejpam-5135	48	34	at	at	ADP
ejpam-5135	48	35	vi1	vi1	PROPN
ejpam-5135	48	36	with	with	ADP
ejpam-5135	48	37	cut	cut	NOUN
ejpam-5135	48	38	-	-	PUNCT
ejpam-5135	48	39	vertices	vertex	NOUN
ejpam-5135	48	40	.	.	PUNCT
ejpam-5135	49	1	step	step	NOUN
ejpam-5135	49	2	4	4	NUM
ejpam-5135	49	3	:	:	PUNCT
ejpam-5135	49	4	for	for	ADP
ejpam-5135	49	5	each	each	DET
ejpam-5135	49	6	branch	branch	NOUN
ejpam-5135	49	7	of	of	ADP
ejpam-5135	49	8	ci	ci	NOUN
ejpam-5135	49	9	with	with	ADP
ejpam-5135	49	10	a	a	DET
ejpam-5135	49	11	cut	cut	NOUN
ejpam-5135	49	12	-	-	PUNCT
ejpam-5135	49	13	vertex	vertex	NOUN
ejpam-5135	49	14	,	,	PUNCT
ejpam-5135	49	15	choose	choose	VERB
ejpam-5135	49	16	one	one	NUM
ejpam-5135	49	17	cut	cut	NOUN
ejpam-5135	49	18	-	-	PUNCT
ejpam-5135	49	19	vertex	vertex	NOUN
ejpam-5135	49	20	vi2	vi2	NOUN
ejpam-5135	49	21	and	and	CCONJ
ejpam-5135	49	22	obtain	obtain	VERB
ejpam-5135	49	23	the	the	DET
ejpam-5135	49	24	sub	sub	NOUN
ejpam-5135	49	25	-	-	NOUN
ejpam-5135	49	26	branches	branch	NOUN
ejpam-5135	49	27	at	at	ADP
ejpam-5135	49	28	vi2	vi2	NOUN
ejpam-5135	49	29	.	.	PUNCT
ejpam-5135	50	1	step	step	NOUN
ejpam-5135	50	2	5	5	NUM
ejpam-5135	50	3	:	:	PUNCT
ejpam-5135	50	4	repeat	repeat	VERB
ejpam-5135	50	5	the	the	DET
ejpam-5135	50	6	steps	step	NOUN
ejpam-5135	50	7	of	of	ADP
ejpam-5135	50	8	separating	separate	VERB
ejpam-5135	50	9	the	the	DET
ejpam-5135	50	10	branch	branch	NOUN
ejpam-5135	50	11	until	until	SCONJ
ejpam-5135	50	12	all	all	DET
ejpam-5135	50	13	the	the	DET
ejpam-5135	50	14	resulting	result	VERB
ejpam-5135	50	15	sub	sub	NOUN
ejpam-5135	50	16	-	-	NOUN
ejpam-5135	50	17	branches	branch	NOUN
ejpam-5135	50	18	contain	contain	VERB
ejpam-5135	50	19	no	no	DET
ejpam-5135	50	20	cut	cut	NOUN
ejpam-5135	50	21	-	-	PUNCT
ejpam-5135	50	22	vertices	vertex	NOUN
ejpam-5135	50	23	.	.	PUNCT
ejpam-5135	51	1	step	step	NOUN
ejpam-5135	51	2	6	6	NUM
ejpam-5135	51	3	:	:	PUNCT
ejpam-5135	51	4	do	do	VERB
ejpam-5135	51	5	these	these	PRON
ejpam-5135	51	6	for	for	ADP
ejpam-5135	51	7	all	all	DET
ejpam-5135	51	8	the	the	DET
ejpam-5135	51	9	components	component	NOUN
ejpam-5135	51	10	of	of	ADP
ejpam-5135	51	11	g	g	PROPN
ejpam-5135	51	12	that	that	PRON
ejpam-5135	51	13	contains	contain	VERB
ejpam-5135	51	14	cut	cut	VERB
ejpam-5135	51	15	-	-	PUNCT
ejpam-5135	51	16	vertices	vertex	NOUN
ejpam-5135	51	17	.	.	PUNCT
ejpam-5135	52	1	step	step	NOUN
ejpam-5135	52	2	7	7	NUM
ejpam-5135	52	3	:	:	PUNCT
ejpam-5135	52	4	collect	collect	VERB
ejpam-5135	52	5	all	all	DET
ejpam-5135	52	6	the	the	DET
ejpam-5135	52	7	components	component	NOUN
ejpam-5135	52	8	,	,	PUNCT
ejpam-5135	52	9	branches	branch	NOUN
ejpam-5135	52	10	,	,	PUNCT
ejpam-5135	52	11	and	and	CCONJ
ejpam-5135	52	12	sub	sub	NOUN
ejpam-5135	52	13	-	-	NOUN
ejpam-5135	52	14	branches	branch	NOUN
ejpam-5135	52	15	of	of	ADP
ejpam-5135	52	16	g	g	PROPN
ejpam-5135	52	17	that	that	PRON
ejpam-5135	52	18	contain	contain	VERB
ejpam-5135	52	19	no	no	DET
ejpam-5135	52	20	cut	cut	NOUN
ejpam-5135	52	21	-	-	PUNCT
ejpam-5135	52	22	vertices	vertex	NOUN
ejpam-5135	52	23	.	.	PUNCT
ejpam-5135	53	1	these	these	PRON
ejpam-5135	53	2	are	be	AUX
ejpam-5135	53	3	precisely	precisely	ADV
ejpam-5135	53	4	the	the	DET
ejpam-5135	53	5	blocks	block	NOUN
ejpam-5135	53	6	of	of	ADP
ejpam-5135	53	7	g.	g.	PROPN
ejpam-5135	53	8	for	for	ADP
ejpam-5135	53	9	example	example	NOUN
ejpam-5135	53	10	,	,	PUNCT
ejpam-5135	53	11	consider	consider	VERB
ejpam-5135	53	12	the	the	DET
ejpam-5135	53	13	graph	graph	NOUN
ejpam-5135	53	14	g	g	NOUN
ejpam-5135	53	15	in	in	ADP
ejpam-5135	53	16	figure	figure	NOUN
ejpam-5135	53	17	1	1	NUM
ejpam-5135	53	18	.	.	PUNCT
ejpam-5135	54	1	g	g	NOUN
ejpam-5135	54	2	:	:	PUNCT
ejpam-5135	54	3	figure	figure	NOUN
ejpam-5135	54	4	1	1	NUM
ejpam-5135	54	5	:	:	PUNCT
ejpam-5135	54	6	the	the	DET
ejpam-5135	54	7	graph	graph	NOUN
ejpam-5135	54	8	g	g	ADP
ejpam-5135	54	9	the	the	DET
ejpam-5135	54	10	following	following	NOUN
ejpam-5135	54	11	are	be	AUX
ejpam-5135	54	12	the	the	DET
ejpam-5135	54	13	components	component	NOUN
ejpam-5135	54	14	of	of	ADP
ejpam-5135	54	15	g	g	NOUN
ejpam-5135	54	16	,	,	PUNCT
ejpam-5135	54	17	each	each	PRON
ejpam-5135	54	18	containing	contain	VERB
ejpam-5135	54	19	cut	cut	NOUN
ejpam-5135	54	20	-	-	PUNCT
ejpam-5135	54	21	vertices	vertex	NOUN
ejpam-5135	54	22	as	as	SCONJ
ejpam-5135	54	23	shown	show	VERB
ejpam-5135	54	24	in	in	ADP
ejpam-5135	54	25	figure	figure	NOUN
ejpam-5135	54	26	2	2	NUM
ejpam-5135	54	27	.	.	PUNCT
ejpam-5135	54	28	justine	justine	PROPN
ejpam-5135	54	29	bryle	bryle	PROPN
ejpam-5135	54	30	c.	c.	PROPN
ejpam-5135	54	31	macaso	macaso	PROPN
ejpam-5135	54	32	,	,	PUNCT
ejpam-5135	54	33	cherry	cherry	PROPN
ejpam-5135	54	34	mae	mae	PROPN
ejpam-5135	54	35	r.	r.	PROPN
ejpam-5135	54	36	balingit	balingit	PROPN
ejpam-5135	54	37	/	/	SYM
ejpam-5135	54	38	eur	eur	PROPN
ejpam-5135	54	39	.	.	PUNCT
ejpam-5135	55	1	j.	j.	PROPN
ejpam-5135	55	2	pure	pure	PROPN
ejpam-5135	55	3	appl	appl	PROPN
ejpam-5135	55	4	.	.	PROPN
ejpam-5135	55	5	math	math	PROPN
ejpam-5135	55	6	,	,	PUNCT
ejpam-5135	55	7	17	17	NUM
ejpam-5135	55	8	(	(	PUNCT
ejpam-5135	55	9	2	2	NUM
ejpam-5135	55	10	)	)	PUNCT
ejpam-5135	55	11	(	(	PUNCT
ejpam-5135	55	12	2024	2024	NUM
ejpam-5135	55	13	)	)	PUNCT
ejpam-5135	55	14	,	,	PUNCT
ejpam-5135	55	15	663	663	NUM
ejpam-5135	55	16	-	-	SYM
ejpam-5135	55	17	675	675	NUM
ejpam-5135	55	18	666	666	NUM
ejpam-5135	55	19	c1	c1	NOUN
ejpam-5135	55	20	:	:	PUNCT
ejpam-5135	55	21	c2	c2	PROPN
ejpam-5135	55	22	:	:	PUNCT
ejpam-5135	55	23	c3	c3	PROPN
ejpam-5135	55	24	:	:	PUNCT
ejpam-5135	55	25	figure	figure	NOUN
ejpam-5135	55	26	2	2	NUM
ejpam-5135	55	27	:	:	PUNCT
ejpam-5135	55	28	components	component	NOUN
ejpam-5135	55	29	of	of	ADP
ejpam-5135	55	30	g	g	PROPN
ejpam-5135	55	31	for	for	ADP
ejpam-5135	55	32	c1	c1	NOUN
ejpam-5135	55	33	,	,	PUNCT
ejpam-5135	55	34	choose	choose	VERB
ejpam-5135	55	35	a	a	DET
ejpam-5135	55	36	cut	cut	VERB
ejpam-5135	55	37	-	-	PUNCT
ejpam-5135	55	38	vertex	vertex	NOUN
ejpam-5135	55	39	v11	v11	NOUN
ejpam-5135	55	40	so	so	SCONJ
ejpam-5135	55	41	that	that	SCONJ
ejpam-5135	55	42	the	the	DET
ejpam-5135	55	43	branches	branch	NOUN
ejpam-5135	55	44	of	of	ADP
ejpam-5135	55	45	c1	c1	PROPN
ejpam-5135	55	46	at	at	ADP
ejpam-5135	55	47	v11	v11	NOUN
ejpam-5135	55	48	are	be	AUX
ejpam-5135	55	49	shown	show	VERB
ejpam-5135	55	50	in	in	ADP
ejpam-5135	55	51	figure	figure	NOUN
ejpam-5135	55	52	3	3	NUM
ejpam-5135	55	53	.	.	PUNCT
ejpam-5135	55	54	v11	v11	NOUN
ejpam-5135	55	55	v11	v11	NOUN
ejpam-5135	55	56	figure	figure	NOUN
ejpam-5135	55	57	3	3	NUM
ejpam-5135	55	58	:	:	PUNCT
ejpam-5135	55	59	branches	branch	NOUN
ejpam-5135	55	60	of	of	ADP
ejpam-5135	55	61	c1	c1	PROPN
ejpam-5135	55	62	at	at	ADP
ejpam-5135	55	63	v11	v11	NOUN
ejpam-5135	55	64	notice	notice	NOUN
ejpam-5135	55	65	that	that	SCONJ
ejpam-5135	55	66	one	one	NUM
ejpam-5135	55	67	of	of	ADP
ejpam-5135	55	68	the	the	DET
ejpam-5135	55	69	branches	branch	NOUN
ejpam-5135	55	70	of	of	ADP
ejpam-5135	55	71	c1	c1	PROPN
ejpam-5135	55	72	at	at	ADP
ejpam-5135	55	73	v11	v11	PROPN
ejpam-5135	55	74	has	have	AUX
ejpam-5135	55	75	cut	cut	VERB
ejpam-5135	55	76	-	-	PUNCT
ejpam-5135	55	77	vertices	vertex	NOUN
ejpam-5135	55	78	.	.	PUNCT
ejpam-5135	56	1	choose	choose	VERB
ejpam-5135	56	2	another	another	DET
ejpam-5135	56	3	cutvertex	cutvertex	NOUN
ejpam-5135	56	4	v12	v12	VERB
ejpam-5135	56	5	and	and	CCONJ
ejpam-5135	56	6	obtain	obtain	VERB
ejpam-5135	56	7	the	the	DET
ejpam-5135	56	8	sub	sub	NOUN
ejpam-5135	56	9	-	-	NOUN
ejpam-5135	56	10	branches	branch	NOUN
ejpam-5135	56	11	at	at	ADP
ejpam-5135	56	12	v12	v12	VERB
ejpam-5135	56	13	.	.	PUNCT
ejpam-5135	57	1	the	the	DET
ejpam-5135	57	2	sub	sub	NOUN
ejpam-5135	57	3	-	-	NOUN
ejpam-5135	57	4	branches	branch	NOUN
ejpam-5135	57	5	at	at	ADP
ejpam-5135	57	6	v12	v12	PROPN
ejpam-5135	57	7	are	be	AUX
ejpam-5135	57	8	as	as	SCONJ
ejpam-5135	57	9	shown	show	VERB
ejpam-5135	57	10	in	in	ADP
ejpam-5135	57	11	the	the	DET
ejpam-5135	57	12	figure	figure	NOUN
ejpam-5135	57	13	4	4	NUM
ejpam-5135	57	14	.	.	PUNCT
ejpam-5135	57	15	v11	v11	NOUN
ejpam-5135	57	16	v12	v12	VERB
ejpam-5135	57	17	v12	v12	VERB
ejpam-5135	57	18	figure	figure	NOUN
ejpam-5135	57	19	4	4	NUM
ejpam-5135	57	20	:	:	PUNCT
ejpam-5135	57	21	sub	sub	NOUN
ejpam-5135	57	22	-	-	NOUN
ejpam-5135	57	23	branches	branch	NOUN
ejpam-5135	57	24	at	at	ADP
ejpam-5135	57	25	v12	v12	ADJ
ejpam-5135	57	26	repeat	repeat	NOUN
ejpam-5135	57	27	the	the	DET
ejpam-5135	57	28	steps	step	NOUN
ejpam-5135	57	29	of	of	ADP
ejpam-5135	57	30	separating	separate	VERB
ejpam-5135	57	31	the	the	DET
ejpam-5135	57	32	branch	branch	NOUN
ejpam-5135	57	33	until	until	SCONJ
ejpam-5135	57	34	the	the	DET
ejpam-5135	57	35	resulting	result	VERB
ejpam-5135	57	36	sub	sub	NOUN
ejpam-5135	57	37	-	-	NOUN
ejpam-5135	57	38	branches	branch	NOUN
ejpam-5135	57	39	contain	contain	VERB
ejpam-5135	57	40	no	no	DET
ejpam-5135	57	41	justine	justine	PROPN
ejpam-5135	57	42	bryle	bryle	PROPN
ejpam-5135	57	43	c.	c.	PROPN
ejpam-5135	57	44	macaso	macaso	PROPN
ejpam-5135	57	45	,	,	PUNCT
ejpam-5135	57	46	cherry	cherry	PROPN
ejpam-5135	57	47	mae	mae	PROPN
ejpam-5135	57	48	r.	r.	PROPN
ejpam-5135	57	49	balingit	balingit	PROPN
ejpam-5135	57	50	/	/	SYM
ejpam-5135	57	51	eur	eur	PROPN
ejpam-5135	57	52	.	.	PUNCT
ejpam-5135	58	1	j.	j.	PROPN
ejpam-5135	58	2	pure	pure	PROPN
ejpam-5135	58	3	appl	appl	PROPN
ejpam-5135	58	4	.	.	PROPN
ejpam-5135	58	5	math	math	PROPN
ejpam-5135	58	6	,	,	PUNCT
ejpam-5135	58	7	17	17	NUM
ejpam-5135	58	8	(	(	PUNCT
ejpam-5135	58	9	2	2	NUM
ejpam-5135	58	10	)	)	PUNCT
ejpam-5135	58	11	(	(	PUNCT
ejpam-5135	58	12	2024	2024	NUM
ejpam-5135	58	13	)	)	PUNCT
ejpam-5135	58	14	,	,	PUNCT
ejpam-5135	58	15	663	663	NUM
ejpam-5135	58	16	-	-	SYM
ejpam-5135	58	17	675	675	NUM
ejpam-5135	58	18	667	667	NUM
ejpam-5135	58	19	cut	cut	NOUN
ejpam-5135	58	20	-	-	PUNCT
ejpam-5135	58	21	vertices	vertex	NOUN
ejpam-5135	58	22	.	.	PUNCT
ejpam-5135	59	1	thus	thus	ADV
ejpam-5135	59	2	,	,	PUNCT
ejpam-5135	59	3	the	the	DET
ejpam-5135	59	4	following	follow	VERB
ejpam-5135	59	5	are	be	AUX
ejpam-5135	59	6	the	the	DET
ejpam-5135	59	7	sub	sub	NOUN
ejpam-5135	59	8	-	-	NOUN
ejpam-5135	59	9	branches	branch	NOUN
ejpam-5135	59	10	at	at	ADP
ejpam-5135	59	11	every	every	DET
ejpam-5135	59	12	cut	cut	NOUN
ejpam-5135	59	13	-	-	PUNCT
ejpam-5135	59	14	vertices	vertex	NOUN
ejpam-5135	59	15	of	of	ADP
ejpam-5135	59	16	c1	c1	PROPN
ejpam-5135	59	17	as	as	SCONJ
ejpam-5135	59	18	shown	show	VERB
ejpam-5135	59	19	in	in	ADP
ejpam-5135	59	20	figure	figure	NOUN
ejpam-5135	59	21	5	5	NUM
ejpam-5135	59	22	.	.	PUNCT
ejpam-5135	60	1	furthermore	furthermore	ADV
ejpam-5135	60	2	,	,	PUNCT
ejpam-5135	60	3	the	the	DET
ejpam-5135	60	4	blocks	block	NOUN
ejpam-5135	60	5	of	of	ADP
ejpam-5135	60	6	g	g	PROPN
ejpam-5135	60	7	at	at	ADP
ejpam-5135	60	8	c1	c1	PROPN
ejpam-5135	60	9	are	be	AUX
ejpam-5135	60	10	as	as	SCONJ
ejpam-5135	60	11	shown	show	VERB
ejpam-5135	60	12	in	in	ADP
ejpam-5135	60	13	figure	figure	NOUN
ejpam-5135	60	14	5	5	NUM
ejpam-5135	60	15	.	.	PUNCT
ejpam-5135	60	16	v11	v11	NOUN
ejpam-5135	60	17	v11	v11	NOUN
ejpam-5135	60	18	v12	v12	VERB
ejpam-5135	60	19	v12	v12	VERB
ejpam-5135	60	20	v14	v14	NOUN
ejpam-5135	60	21	v14	v14	NOUN
ejpam-5135	60	22	v13	v13	NOUN
ejpam-5135	60	23	v13	v13	NOUN
ejpam-5135	60	24	figure	figure	NOUN
ejpam-5135	60	25	5	5	NUM
ejpam-5135	60	26	:	:	PUNCT
ejpam-5135	60	27	the	the	DET
ejpam-5135	60	28	blocks	block	NOUN
ejpam-5135	60	29	of	of	ADP
ejpam-5135	60	30	g	g	NOUN
ejpam-5135	60	31	at	at	ADP
ejpam-5135	60	32	c1	c1	PROPN
ejpam-5135	60	33	doing	do	VERB
ejpam-5135	60	34	the	the	DET
ejpam-5135	60	35	preceding	precede	VERB
ejpam-5135	60	36	steps	step	NOUN
ejpam-5135	60	37	for	for	ADP
ejpam-5135	60	38	all	all	DET
ejpam-5135	60	39	the	the	DET
ejpam-5135	60	40	components	component	NOUN
ejpam-5135	60	41	of	of	ADP
ejpam-5135	60	42	g	g	PROPN
ejpam-5135	60	43	gives	give	VERB
ejpam-5135	60	44	the	the	DET
ejpam-5135	60	45	distinct	distinct	ADJ
ejpam-5135	60	46	blocks	block	NOUN
ejpam-5135	60	47	of	of	ADP
ejpam-5135	60	48	g	g	NOUN
ejpam-5135	60	49	as	as	SCONJ
ejpam-5135	60	50	shown	show	VERB
ejpam-5135	60	51	in	in	ADP
ejpam-5135	60	52	the	the	DET
ejpam-5135	60	53	figure	figure	NOUN
ejpam-5135	60	54	6	6	NUM
ejpam-5135	60	55	.	.	PUNCT
ejpam-5135	60	56	figure	figure	VERB
ejpam-5135	60	57	6	6	NUM
ejpam-5135	60	58	:	:	PUNCT
ejpam-5135	60	59	the	the	DET
ejpam-5135	60	60	blocks	block	NOUN
ejpam-5135	60	61	of	of	ADP
ejpam-5135	60	62	g	g	PROPN
ejpam-5135	60	63	3	3	NUM
ejpam-5135	60	64	.	.	PUNCT
ejpam-5135	61	1	the	the	DET
ejpam-5135	61	2	block	block	NOUN
ejpam-5135	61	3	topological	topological	ADJ
ejpam-5135	61	4	space	space	NOUN
ejpam-5135	61	5	definition	definition	NOUN
ejpam-5135	61	6	1	1	X
ejpam-5135	61	7	.	.	PUNCT
ejpam-5135	62	1	let	let	VERB
ejpam-5135	62	2	g	g	PRON
ejpam-5135	62	3	be	be	AUX
ejpam-5135	62	4	a	a	DET
ejpam-5135	62	5	graph	graph	NOUN
ejpam-5135	62	6	and	and	CCONJ
ejpam-5135	62	7	let	let	VERB
ejpam-5135	62	8	b1	b1	NOUN
ejpam-5135	62	9	,	,	PUNCT
ejpam-5135	62	10	b2	b2	NOUN
ejpam-5135	62	11	,	,	PUNCT
ejpam-5135	62	12	·	·	PUNCT
ejpam-5135	62	13	·	·	PUNCT
ejpam-5135	62	14	·	·	PUNCT
ejpam-5135	62	15	,	,	PUNCT
ejpam-5135	62	16	bk	bk	NOUN
ejpam-5135	62	17	be	be	AUX
ejpam-5135	62	18	the	the	DET
ejpam-5135	62	19	distinct	distinct	ADJ
ejpam-5135	62	20	blocks	block	NOUN
ejpam-5135	62	21	of	of	ADP
ejpam-5135	62	22	g	g	NOUN
ejpam-5135	62	23	for	for	ADP
ejpam-5135	62	24	some	some	DET
ejpam-5135	62	25	k	k	PROPN
ejpam-5135	62	26	∈	∈	PROPN
ejpam-5135	62	27	z+	z+	PUNCT
ejpam-5135	62	28	.	.	PUNCT
ejpam-5135	63	1	then	then	ADV
ejpam-5135	63	2	the	the	DET
ejpam-5135	63	3	topology	topology	NOUN
ejpam-5135	63	4	on	on	ADP
ejpam-5135	63	5	v	v	ADP
ejpam-5135	63	6	(	(	PUNCT
ejpam-5135	63	7	g	g	NOUN
ejpam-5135	63	8	)	)	PUNCT
ejpam-5135	63	9	generated	generate	VERB
ejpam-5135	63	10	by	by	ADP
ejpam-5135	63	11	the	the	DET
ejpam-5135	63	12	family	family	NOUN
ejpam-5135	63	13	σb(g	σb(g	NOUN
ejpam-5135	63	14	)	)	PUNCT
ejpam-5135	63	15	=	=	SYM
ejpam-5135	63	16	{	{	PUNCT
ejpam-5135	63	17	v	v	NOUN
ejpam-5135	63	18	(	(	PUNCT
ejpam-5135	63	19	b1	b1	NOUN
ejpam-5135	63	20	)	)	PUNCT
ejpam-5135	63	21	,	,	PUNCT
ejpam-5135	63	22	v	v	NOUN
ejpam-5135	63	23	(	(	PUNCT
ejpam-5135	63	24	b2	b2	NOUN
ejpam-5135	63	25	)	)	PUNCT
ejpam-5135	63	26	,	,	PUNCT
ejpam-5135	63	27	·	·	PUNCT
ejpam-5135	63	28	·	·	PUNCT
ejpam-5135	63	29	·	·	PUNCT
ejpam-5135	63	30	,	,	PUNCT
ejpam-5135	63	31	v	v	X
ejpam-5135	63	32	(	(	PUNCT
ejpam-5135	63	33	bk	bk	NOUN
ejpam-5135	63	34	)	)	PUNCT
ejpam-5135	63	35	}	}	PUNCT
ejpam-5135	63	36	is	be	AUX
ejpam-5135	63	37	called	call	VERB
ejpam-5135	63	38	the	the	DET
ejpam-5135	63	39	block	block	NOUN
ejpam-5135	63	40	topology	topology	NOUN
ejpam-5135	63	41	of	of	ADP
ejpam-5135	63	42	g	g	NOUN
ejpam-5135	63	43	,	,	PUNCT
ejpam-5135	63	44	denoted	denote	VERB
ejpam-5135	63	45	by	by	ADP
ejpam-5135	63	46	τb(g	τb(g	NOUN
ejpam-5135	63	47	)	)	PUNCT
ejpam-5135	63	48	and	and	CCONJ
ejpam-5135	63	49	the	the	DET
ejpam-5135	63	50	pair	pair	NOUN
ejpam-5135	63	51	(	(	PUNCT
ejpam-5135	63	52	v	v	NOUN
ejpam-5135	63	53	(	(	PUNCT
ejpam-5135	63	54	g	g	NOUN
ejpam-5135	63	55	)	)	PUNCT
ejpam-5135	63	56	,	,	PUNCT
ejpam-5135	63	57	τb(g	τb(g	NUM
ejpam-5135	63	58	)	)	PUNCT
ejpam-5135	63	59	)	)	PUNCT
ejpam-5135	63	60	is	be	AUX
ejpam-5135	63	61	called	call	VERB
ejpam-5135	63	62	the	the	DET
ejpam-5135	63	63	block	block	NOUN
ejpam-5135	63	64	topological	topological	ADJ
ejpam-5135	63	65	space	space	NOUN
ejpam-5135	63	66	of	of	ADP
ejpam-5135	63	67	g.	g.	PROPN
ejpam-5135	63	68	denote	denote	PROPN
ejpam-5135	63	69	γb(g	γb(g	NOUN
ejpam-5135	63	70	)	)	PUNCT
ejpam-5135	63	71	to	to	PART
ejpam-5135	63	72	be	be	AUX
ejpam-5135	63	73	the	the	DET
ejpam-5135	63	74	family	family	NOUN
ejpam-5135	63	75	of	of	ADP
ejpam-5135	63	76	finite	finite	ADJ
ejpam-5135	63	77	intersections	intersection	NOUN
ejpam-5135	63	78	of	of	ADP
ejpam-5135	63	79	sets	set	NOUN
ejpam-5135	63	80	in	in	ADP
ejpam-5135	63	81	σb(g	σb(g	NOUN
ejpam-5135	63	82	)	)	PUNCT
ejpam-5135	63	83	.	.	PUNCT
ejpam-5135	64	1	in	in	ADP
ejpam-5135	64	2	this	this	DET
ejpam-5135	64	3	case	case	NOUN
ejpam-5135	64	4	,	,	PUNCT
ejpam-5135	64	5	γb(g	γb(g	NUM
ejpam-5135	64	6	)	)	PUNCT
ejpam-5135	64	7	is	be	AUX
ejpam-5135	64	8	a	a	DET
ejpam-5135	64	9	base	base	NOUN
ejpam-5135	64	10	for	for	ADP
ejpam-5135	64	11	τb(g	τb(g	NUM
ejpam-5135	64	12	)	)	PUNCT
ejpam-5135	64	13	.	.	PUNCT
ejpam-5135	65	1	a	a	DET
ejpam-5135	65	2	subset	subset	NOUN
ejpam-5135	65	3	a	a	PRON
ejpam-5135	65	4	of	of	ADP
ejpam-5135	65	5	v	v	NOUN
ejpam-5135	65	6	(	(	PUNCT
ejpam-5135	65	7	g	g	NOUN
ejpam-5135	65	8	)	)	PUNCT
ejpam-5135	65	9	is	be	AUX
ejpam-5135	65	10	τb(g)-open	τb(g)-open	VERB
ejpam-5135	65	11	if	if	SCONJ
ejpam-5135	65	12	a	a	PRON
ejpam-5135	65	13	belongs	belong	VERB
ejpam-5135	65	14	to	to	ADP
ejpam-5135	65	15	τb(g	τb(g	NUM
ejpam-5135	65	16	)	)	PUNCT
ejpam-5135	65	17	and	and	CCONJ
ejpam-5135	65	18	if	if	SCONJ
ejpam-5135	65	19	ac	ac	PROPN
ejpam-5135	65	20	belongs	belong	VERB
ejpam-5135	65	21	to	to	ADP
ejpam-5135	65	22	τb(g	τb(g	NUM
ejpam-5135	65	23	)	)	PUNCT
ejpam-5135	65	24	,	,	PUNCT
ejpam-5135	65	25	then	then	ADV
ejpam-5135	65	26	a	a	PRON
ejpam-5135	65	27	is	be	AUX
ejpam-5135	65	28	τb(g)-closed	τb(g)-close	VERB
ejpam-5135	65	29	.	.	PUNCT
ejpam-5135	65	30	example	example	NOUN
ejpam-5135	66	1	1	1	NUM
ejpam-5135	66	2	.	.	X
ejpam-5135	66	3	consider	consider	VERB
ejpam-5135	66	4	the	the	DET
ejpam-5135	66	5	graph	graph	NOUN
ejpam-5135	66	6	g	g	NOUN
ejpam-5135	66	7	in	in	ADP
ejpam-5135	66	8	figure	figure	NOUN
ejpam-5135	66	9	7	7	NUM
ejpam-5135	66	10	.	.	PUNCT
ejpam-5135	66	11	observe	observe	VERB
ejpam-5135	66	12	that	that	SCONJ
ejpam-5135	66	13	the	the	DET
ejpam-5135	66	14	blocks	block	NOUN
ejpam-5135	66	15	of	of	ADP
ejpam-5135	66	16	g	g	NOUN
ejpam-5135	66	17	are	be	AUX
ejpam-5135	66	18	given	give	VERB
ejpam-5135	66	19	by	by	ADP
ejpam-5135	66	20	b1	b1	NOUN
ejpam-5135	66	21	,	,	PUNCT
ejpam-5135	66	22	b2	b2	NOUN
ejpam-5135	66	23	,	,	PUNCT
ejpam-5135	66	24	and	and	CCONJ
ejpam-5135	66	25	b3	b3	PROPN
ejpam-5135	66	26	implying	imply	VERB
ejpam-5135	66	27	that	that	PRON
ejpam-5135	66	28	σb(g	σb(g	NOUN
ejpam-5135	66	29	)	)	PUNCT
ejpam-5135	66	30	=	=	SYM
ejpam-5135	66	31	{	{	PUNCT
ejpam-5135	66	32	{	{	PUNCT
ejpam-5135	66	33	v1	v1	NOUN
ejpam-5135	66	34	,	,	PUNCT
ejpam-5135	66	35	v2	v2	PROPN
ejpam-5135	66	36	,	,	PUNCT
ejpam-5135	66	37	v3	v3	PROPN
ejpam-5135	66	38	,	,	PUNCT
ejpam-5135	66	39	v4	v4	PROPN
ejpam-5135	66	40	}	}	PUNCT
ejpam-5135	66	41	,	,	PUNCT
ejpam-5135	66	42	{	{	PUNCT
ejpam-5135	66	43	v4	v4	NOUN
ejpam-5135	66	44	,	,	PUNCT
ejpam-5135	66	45	v5	v5	PROPN
ejpam-5135	66	46	}	}	PUNCT
ejpam-5135	66	47	,	,	PUNCT
ejpam-5135	66	48	{	{	PUNCT
ejpam-5135	66	49	v4	v4	NOUN
ejpam-5135	66	50	,	,	PUNCT
ejpam-5135	66	51	v6	v6	NOUN
ejpam-5135	66	52	}	}	PUNCT
ejpam-5135	66	53	}	}	PUNCT
ejpam-5135	66	54	.	.	PUNCT
ejpam-5135	67	1	by	by	ADP
ejpam-5135	67	2	the	the	DET
ejpam-5135	67	3	definition	definition	NOUN
ejpam-5135	67	4	1	1	NUM
ejpam-5135	67	5	,	,	PUNCT
ejpam-5135	67	6	taking	take	VERB
ejpam-5135	67	7	the	the	DET
ejpam-5135	67	8	finite	finite	ADJ
ejpam-5135	67	9	intersections	intersection	NOUN
ejpam-5135	67	10	of	of	ADP
ejpam-5135	67	11	sets	set	NOUN
ejpam-5135	67	12	in	in	ADP
ejpam-5135	67	13	σb(g	σb(g	NOUN
ejpam-5135	67	14	)	)	PUNCT
ejpam-5135	67	15	we	we	PRON
ejpam-5135	67	16	obtain	obtain	VERB
ejpam-5135	67	17	the	the	DET
ejpam-5135	67	18	family	family	NOUN
ejpam-5135	67	19	γb(g	γb(g	PUNCT
ejpam-5135	67	20	)	)	PUNCT
ejpam-5135	67	21	=	=	SYM
ejpam-5135	67	22	justine	justine	PROPN
ejpam-5135	67	23	bryle	bryle	PROPN
ejpam-5135	67	24	c.	c.	PROPN
ejpam-5135	67	25	macaso	macaso	PROPN
ejpam-5135	67	26	,	,	PUNCT
ejpam-5135	67	27	cherry	cherry	PROPN
ejpam-5135	67	28	mae	mae	PROPN
ejpam-5135	67	29	r.	r.	PROPN
ejpam-5135	67	30	balingit	balingit	PROPN
ejpam-5135	67	31	/	/	SYM
ejpam-5135	67	32	eur	eur	PROPN
ejpam-5135	67	33	.	.	PUNCT
ejpam-5135	68	1	j.	j.	PROPN
ejpam-5135	68	2	pure	pure	PROPN
ejpam-5135	68	3	appl	appl	PROPN
ejpam-5135	68	4	.	.	PROPN
ejpam-5135	68	5	math	math	PROPN
ejpam-5135	68	6	,	,	PUNCT
ejpam-5135	68	7	17	17	NUM
ejpam-5135	68	8	(	(	PUNCT
ejpam-5135	68	9	2	2	NUM
ejpam-5135	68	10	)	)	PUNCT
ejpam-5135	68	11	(	(	PUNCT
ejpam-5135	68	12	2024	2024	NUM
ejpam-5135	68	13	)	)	PUNCT
ejpam-5135	68	14	,	,	PUNCT
ejpam-5135	68	15	663	663	NUM
ejpam-5135	68	16	-	-	SYM
ejpam-5135	68	17	675	675	NUM
ejpam-5135	68	18	668	668	NUM
ejpam-5135	68	19	{	{	PUNCT
ejpam-5135	68	20	{	{	PUNCT
ejpam-5135	68	21	v1	v1	NOUN
ejpam-5135	68	22	,	,	PUNCT
ejpam-5135	68	23	v2	v2	PROPN
ejpam-5135	68	24	,	,	PUNCT
ejpam-5135	68	25	v3	v3	PROPN
ejpam-5135	68	26	,	,	PUNCT
ejpam-5135	68	27	v4	v4	PROPN
ejpam-5135	68	28	}	}	PUNCT
ejpam-5135	68	29	,	,	PUNCT
ejpam-5135	68	30	{	{	PUNCT
ejpam-5135	68	31	v4	v4	NOUN
ejpam-5135	68	32	,	,	PUNCT
ejpam-5135	68	33	v5	v5	PROPN
ejpam-5135	68	34	}	}	PUNCT
ejpam-5135	68	35	,	,	PUNCT
ejpam-5135	68	36	{	{	PUNCT
ejpam-5135	68	37	v4	v4	NOUN
ejpam-5135	68	38	,	,	PUNCT
ejpam-5135	68	39	v6	v6	PROPN
ejpam-5135	68	40	}	}	PUNCT
ejpam-5135	68	41	,	,	PUNCT
ejpam-5135	68	42	{	{	PUNCT
ejpam-5135	68	43	v4	v4	NOUN
ejpam-5135	68	44	}	}	PUNCT
ejpam-5135	68	45	}	}	PUNCT
ejpam-5135	68	46	.	.	PUNCT
ejpam-5135	69	1	finally	finally	ADV
ejpam-5135	69	2	,	,	PUNCT
ejpam-5135	69	3	by	by	ADP
ejpam-5135	69	4	taking	take	VERB
ejpam-5135	69	5	the	the	DET
ejpam-5135	69	6	arbitrary	arbitrary	ADJ
ejpam-5135	69	7	union	union	NOUN
ejpam-5135	69	8	of	of	ADP
ejpam-5135	69	9	sets	set	NOUN
ejpam-5135	69	10	in	in	ADP
ejpam-5135	69	11	γb(g	γb(g	NOUN
ejpam-5135	69	12	)	)	PUNCT
ejpam-5135	69	13	we	we	PRON
ejpam-5135	69	14	obtain	obtain	VERB
ejpam-5135	69	15	the	the	DET
ejpam-5135	69	16	block	block	NOUN
ejpam-5135	69	17	topology	topology	NOUN
ejpam-5135	69	18	τb(g	τb(g	PUNCT
ejpam-5135	69	19	)	)	PUNCT
ejpam-5135	70	1	=	=	PRON
ejpam-5135	70	2	{	{	PUNCT
ejpam-5135	70	3	∅	∅	NOUN
ejpam-5135	70	4	,	,	PUNCT
ejpam-5135	70	5	v	v	NOUN
ejpam-5135	70	6	(	(	PUNCT
ejpam-5135	70	7	g	g	NOUN
ejpam-5135	70	8	)	)	PUNCT
ejpam-5135	70	9	,	,	PUNCT
ejpam-5135	70	10	{	{	PUNCT
ejpam-5135	70	11	v4	v4	NOUN
ejpam-5135	70	12	}	}	PUNCT
ejpam-5135	70	13	,	,	PUNCT
ejpam-5135	70	14	{	{	PUNCT
ejpam-5135	70	15	v4	v4	NOUN
ejpam-5135	70	16	,	,	PUNCT
ejpam-5135	70	17	v5	v5	PROPN
ejpam-5135	70	18	}	}	PUNCT
ejpam-5135	70	19	,	,	PUNCT
ejpam-5135	70	20	{	{	PUNCT
ejpam-5135	70	21	v4	v4	NOUN
ejpam-5135	70	22	,	,	PUNCT
ejpam-5135	70	23	v6	v6	PROPN
ejpam-5135	70	24	}	}	PUNCT
ejpam-5135	70	25	,	,	PUNCT
ejpam-5135	70	26	{	{	PUNCT
ejpam-5135	70	27	v4	v4	NOUN
ejpam-5135	70	28	,	,	PUNCT
ejpam-5135	70	29	v5	v5	PROPN
ejpam-5135	70	30	,	,	PUNCT
ejpam-5135	70	31	v6	v6	NOUN
ejpam-5135	70	32	}	}	PUNCT
ejpam-5135	70	33	,	,	PUNCT
ejpam-5135	70	34	{	{	PUNCT
ejpam-5135	70	35	v1	v1	NOUN
ejpam-5135	70	36	,	,	PUNCT
ejpam-5135	70	37	v2	v2	PROPN
ejpam-5135	70	38	,	,	PUNCT
ejpam-5135	70	39	v3	v3	PROPN
ejpam-5135	70	40	,	,	PUNCT
ejpam-5135	70	41	v4	v4	PROPN
ejpam-5135	70	42	}	}	PUNCT
ejpam-5135	70	43	,	,	PUNCT
ejpam-5135	70	44	{	{	PUNCT
ejpam-5135	70	45	v1	v1	NOUN
ejpam-5135	70	46	,	,	PUNCT
ejpam-5135	70	47	v2	v2	PROPN
ejpam-5135	70	48	,	,	PUNCT
ejpam-5135	70	49	v3	v3	PROPN
ejpam-5135	70	50	,	,	PUNCT
ejpam-5135	70	51	v4	v4	PROPN
ejpam-5135	70	52	,	,	PUNCT
ejpam-5135	70	53	v5	v5	PROPN
ejpam-5135	70	54	}	}	PUNCT
ejpam-5135	70	55	,	,	PUNCT
ejpam-5135	70	56	{	{	PUNCT
ejpam-5135	70	57	v1	v1	NOUN
ejpam-5135	70	58	,	,	PUNCT
ejpam-5135	70	59	v2	v2	PROPN
ejpam-5135	70	60	,	,	PUNCT
ejpam-5135	70	61	v3	v3	PROPN
ejpam-5135	70	62	,	,	PUNCT
ejpam-5135	70	63	v4	v4	PROPN
ejpam-5135	70	64	,	,	PUNCT
ejpam-5135	70	65	v6	v6	NOUN
ejpam-5135	70	66	}	}	PUNCT
ejpam-5135	70	67	}	}	PUNCT
ejpam-5135	70	68	.	.	PUNCT
ejpam-5135	71	1	v1	v1	PROPN
ejpam-5135	71	2	v2	v2	PROPN
ejpam-5135	71	3	v3	v3	PROPN
ejpam-5135	71	4	v4	v4	PROPN
ejpam-5135	71	5	v1	v1	PROPN
ejpam-5135	71	6	v2	v2	PROPN
ejpam-5135	71	7	v3	v3	PROPN
ejpam-5135	71	8	v4	v4	PROPN
ejpam-5135	71	9	v5	v5	PROPN
ejpam-5135	71	10	v6	v6	PROPN
ejpam-5135	71	11	v5	v5	PROPN
ejpam-5135	71	12	v6	v6	PROPN
ejpam-5135	71	13	v4	v4	PROPN
ejpam-5135	71	14	v4	v4	PROPN
ejpam-5135	71	15	g	g	PROPN
ejpam-5135	71	16	:	:	PUNCT
ejpam-5135	71	17	b2	b2	NOUN
ejpam-5135	71	18	:	:	PUNCT
ejpam-5135	71	19	b3	b3	PROPN
ejpam-5135	71	20	:	:	PUNCT
ejpam-5135	71	21	b1	b1	NOUN
ejpam-5135	71	22	:	:	PUNCT
ejpam-5135	71	23	figure	figure	VERB
ejpam-5135	71	24	7	7	NUM
ejpam-5135	71	25	:	:	PUNCT
ejpam-5135	71	26	the	the	DET
ejpam-5135	71	27	blocks	block	NOUN
ejpam-5135	71	28	of	of	ADP
ejpam-5135	71	29	g	g	NOUN
ejpam-5135	71	30	by	by	ADP
ejpam-5135	71	31	observation	observation	NOUN
ejpam-5135	71	32	,	,	PUNCT
ejpam-5135	71	33	two	two	NUM
ejpam-5135	71	34	distinct	distinct	ADJ
ejpam-5135	71	35	blocks	block	NOUN
ejpam-5135	71	36	have	have	VERB
ejpam-5135	71	37	at	at	ADP
ejpam-5135	71	38	most	most	ADV
ejpam-5135	71	39	one	one	NUM
ejpam-5135	71	40	vertex	vertex	NOUN
ejpam-5135	71	41	in	in	ADP
ejpam-5135	71	42	common	common	ADJ
ejpam-5135	71	43	and	and	CCONJ
ejpam-5135	71	44	if	if	SCONJ
ejpam-5135	71	45	they	they	PRON
ejpam-5135	71	46	share	share	VERB
ejpam-5135	71	47	a	a	DET
ejpam-5135	71	48	vertex	vertex	NOUN
ejpam-5135	71	49	,	,	PUNCT
ejpam-5135	71	50	then	then	ADV
ejpam-5135	71	51	this	this	DET
ejpam-5135	71	52	vertex	vertex	NOUN
ejpam-5135	71	53	is	be	AUX
ejpam-5135	71	54	a	a	DET
ejpam-5135	71	55	cut	cut	NOUN
ejpam-5135	71	56	-	-	PUNCT
ejpam-5135	71	57	vertex	vertex	NOUN
ejpam-5135	71	58	.	.	PUNCT
ejpam-5135	72	1	this	this	PRON
ejpam-5135	72	2	means	mean	VERB
ejpam-5135	72	3	that	that	SCONJ
ejpam-5135	72	4	the	the	PRON
ejpam-5135	72	5	greater	great	ADJ
ejpam-5135	72	6	the	the	DET
ejpam-5135	72	7	number	number	NOUN
ejpam-5135	72	8	of	of	ADP
ejpam-5135	72	9	cut	cut	NOUN
ejpam-5135	72	10	-	-	PUNCT
ejpam-5135	72	11	vertices	vertex	NOUN
ejpam-5135	72	12	in	in	ADP
ejpam-5135	72	13	a	a	DET
ejpam-5135	72	14	graph	graph	NOUN
ejpam-5135	72	15	the	the	PRON
ejpam-5135	72	16	larger	large	ADJ
ejpam-5135	72	17	the	the	DET
ejpam-5135	72	18	number	number	NOUN
ejpam-5135	72	19	of	of	ADP
ejpam-5135	72	20	blocks	block	NOUN
ejpam-5135	72	21	in	in	ADP
ejpam-5135	72	22	a	a	DET
ejpam-5135	72	23	graph	graph	NOUN
ejpam-5135	72	24	.	.	PUNCT
ejpam-5135	73	1	however	however	ADV
ejpam-5135	73	2	,	,	PUNCT
ejpam-5135	73	3	increasing	increase	VERB
ejpam-5135	73	4	the	the	DET
ejpam-5135	73	5	number	number	NOUN
ejpam-5135	73	6	of	of	ADP
ejpam-5135	73	7	blocks	block	NOUN
ejpam-5135	73	8	does	do	AUX
ejpam-5135	73	9	not	not	PART
ejpam-5135	73	10	imply	imply	VERB
ejpam-5135	73	11	an	an	DET
ejpam-5135	73	12	increased	increase	VERB
ejpam-5135	73	13	number	number	NOUN
ejpam-5135	73	14	of	of	ADP
ejpam-5135	73	15	cut	cut	NOUN
ejpam-5135	73	16	-	-	PUNCT
ejpam-5135	73	17	vertices	vertex	NOUN
ejpam-5135	73	18	(	(	PUNCT
ejpam-5135	73	19	e.g.	e.g.	ADV
ejpam-5135	73	20	the	the	DET
ejpam-5135	73	21	case	case	NOUN
ejpam-5135	73	22	where	where	SCONJ
ejpam-5135	73	23	we	we	PRON
ejpam-5135	73	24	add	add	VERB
ejpam-5135	73	25	an	an	DET
ejpam-5135	73	26	isolated	isolated	ADJ
ejpam-5135	73	27	vertex	vertex	NOUN
ejpam-5135	73	28	to	to	ADP
ejpam-5135	73	29	the	the	DET
ejpam-5135	73	30	graph	graph	NOUN
ejpam-5135	73	31	)	)	PUNCT
ejpam-5135	73	32	.	.	PUNCT
ejpam-5135	74	1	theorem	theorem	NOUN
ejpam-5135	74	2	1	1	X
ejpam-5135	74	3	.	.	PUNCT
ejpam-5135	75	1	let	let	VERB
ejpam-5135	75	2	g	g	PRON
ejpam-5135	75	3	be	be	AUX
ejpam-5135	75	4	a	a	DET
ejpam-5135	75	5	graph	graph	NOUN
ejpam-5135	75	6	.	.	PUNCT
ejpam-5135	76	1	for	for	ADP
ejpam-5135	76	2	a	a	DET
ejpam-5135	76	3	vertex	vertex	NOUN
ejpam-5135	76	4	v	v	NOUN
ejpam-5135	76	5	of	of	ADP
ejpam-5135	76	6	g	g	NOUN
ejpam-5135	76	7	,	,	PUNCT
ejpam-5135	76	8	{	{	PUNCT
ejpam-5135	76	9	v	v	NOUN
ejpam-5135	76	10	}	}	PUNCT
ejpam-5135	76	11	is	be	AUX
ejpam-5135	76	12	τb(g)-open	τb(g)-open	ADJ
ejpam-5135	76	13	if	if	SCONJ
ejpam-5135	76	14	and	and	CCONJ
ejpam-5135	76	15	only	only	ADV
ejpam-5135	76	16	if	if	SCONJ
ejpam-5135	76	17	v	v	NOUN
ejpam-5135	76	18	is	be	AUX
ejpam-5135	76	19	a	a	DET
ejpam-5135	76	20	cut	cut	NOUN
ejpam-5135	76	21	-	-	PUNCT
ejpam-5135	76	22	vertex	vertex	NOUN
ejpam-5135	76	23	of	of	ADP
ejpam-5135	76	24	g	g	NOUN
ejpam-5135	76	25	or	or	CCONJ
ejpam-5135	76	26	v	v	NOUN
ejpam-5135	76	27	is	be	AUX
ejpam-5135	76	28	an	an	DET
ejpam-5135	76	29	isolated	isolated	ADJ
ejpam-5135	76	30	vertex	vertex	NOUN
ejpam-5135	76	31	of	of	ADP
ejpam-5135	76	32	g.	g.	PROPN
ejpam-5135	76	33	proof	proof	NOUN
ejpam-5135	76	34	.	.	PUNCT
ejpam-5135	77	1	(	(	PUNCT
ejpam-5135	77	2	⇒	⇒	PROPN
ejpam-5135	77	3	)	)	PUNCT
ejpam-5135	77	4	let	let	VERB
ejpam-5135	77	5	g	g	NOUN
ejpam-5135	77	6	be	be	AUX
ejpam-5135	77	7	a	a	DET
ejpam-5135	77	8	graph	graph	NOUN
ejpam-5135	77	9	with	with	ADP
ejpam-5135	77	10	blocks	block	NOUN
ejpam-5135	77	11	b1	b1	NOUN
ejpam-5135	77	12	,	,	PUNCT
ejpam-5135	77	13	b2	b2	NOUN
ejpam-5135	77	14	,	,	PUNCT
ejpam-5135	77	15	·	·	PUNCT
ejpam-5135	77	16	·	·	PUNCT
ejpam-5135	77	17	·	·	PUNCT
ejpam-5135	77	18	,	,	PUNCT
ejpam-5135	77	19	bk	bk	AUX
ejpam-5135	77	20	.	.	PUNCT
ejpam-5135	77	21	suppose	suppose	VERB
ejpam-5135	77	22	that	that	SCONJ
ejpam-5135	77	23	{	{	PUNCT
ejpam-5135	77	24	v	v	NOUN
ejpam-5135	77	25	}	}	PUNCT
ejpam-5135	77	26	∈	∈	PROPN
ejpam-5135	77	27	τb(g	τb(g	NUM
ejpam-5135	77	28	)	)	PUNCT
ejpam-5135	77	29	.	.	PUNCT
ejpam-5135	78	1	then	then	ADV
ejpam-5135	78	2	{	{	PUNCT
ejpam-5135	78	3	v	v	NOUN
ejpam-5135	78	4	}	}	PUNCT
ejpam-5135	78	5	∈	∈	PROPN
ejpam-5135	78	6	γb(g	γb(g	NOUN
ejpam-5135	78	7	)	)	PUNCT
ejpam-5135	78	8	.	.	PUNCT
ejpam-5135	79	1	this	this	PRON
ejpam-5135	79	2	means	mean	VERB
ejpam-5135	79	3	that	that	SCONJ
ejpam-5135	79	4	for	for	ADP
ejpam-5135	79	5	some	some	DET
ejpam-5135	79	6	nonempty	nonempty	NOUN
ejpam-5135	79	7	a	a	DET
ejpam-5135	79	8	⊆	⊆	NUM
ejpam-5135	79	9	{	{	SYM
ejpam-5135	79	10	1	1	NUM
ejpam-5135	79	11	,	,	PUNCT
ejpam-5135	79	12	2	2	NUM
ejpam-5135	79	13	,	,	PUNCT
ejpam-5135	79	14	·	·	PUNCT
ejpam-5135	79	15	·	·	PUNCT
ejpam-5135	79	16	·	·	PUNCT
ejpam-5135	79	17	,	,	PUNCT
ejpam-5135	79	18	k	k	X
ejpam-5135	79	19	}	}	PUNCT
ejpam-5135	79	20	,	,	PUNCT
ejpam-5135	79	21	{	{	PUNCT
ejpam-5135	79	22	v	v	NOUN
ejpam-5135	79	23	}	}	PUNCT
ejpam-5135	79	24	=	=	ADJ
ejpam-5135	79	25	⋂	⋂	PROPN
ejpam-5135	79	26	i∈a	i∈a	ADJ
ejpam-5135	79	27	v	v	X
ejpam-5135	79	28	(	(	PUNCT
ejpam-5135	79	29	bi	bi	NOUN
ejpam-5135	79	30	)	)	PUNCT
ejpam-5135	79	31	.	.	PUNCT
ejpam-5135	80	1	if	if	SCONJ
ejpam-5135	80	2	|a	|a	VERB
ejpam-5135	80	3	|	|	NOUN
ejpam-5135	80	4	=	=	SYM
ejpam-5135	80	5	1	1	NUM
ejpam-5135	80	6	,	,	PUNCT
ejpam-5135	80	7	then	then	ADV
ejpam-5135	80	8	{	{	PUNCT
ejpam-5135	80	9	v	v	NOUN
ejpam-5135	80	10	}	}	PUNCT
ejpam-5135	80	11	∈	∈	PROPN
ejpam-5135	80	12	σb(g	σb(g	NOUN
ejpam-5135	80	13	)	)	PUNCT
ejpam-5135	80	14	,	,	PUNCT
ejpam-5135	80	15	which	which	PRON
ejpam-5135	80	16	means	mean	VERB
ejpam-5135	80	17	that	that	SCONJ
ejpam-5135	80	18	g[{v	g[{v	NOUN
ejpam-5135	80	19	}	}	PUNCT
ejpam-5135	80	20	]	]	PUNCT
ejpam-5135	80	21	is	be	AUX
ejpam-5135	80	22	a	a	DET
ejpam-5135	80	23	block	block	NOUN
ejpam-5135	80	24	of	of	ADP
ejpam-5135	80	25	g	g	NOUN
ejpam-5135	80	26	implying	imply	VERB
ejpam-5135	80	27	further	far	ADV
ejpam-5135	80	28	that	that	SCONJ
ejpam-5135	80	29	v	v	NOUN
ejpam-5135	80	30	is	be	AUX
ejpam-5135	80	31	an	an	DET
ejpam-5135	80	32	isolated	isolated	ADJ
ejpam-5135	80	33	vertex	vertex	NOUN
ejpam-5135	80	34	.	.	PUNCT
ejpam-5135	81	1	on	on	ADP
ejpam-5135	81	2	the	the	DET
ejpam-5135	81	3	other	other	ADJ
ejpam-5135	81	4	hand	hand	NOUN
ejpam-5135	81	5	,	,	PUNCT
ejpam-5135	81	6	if	if	SCONJ
ejpam-5135	81	7	|a|	|a|	PROPN
ejpam-5135	81	8	>	>	X
ejpam-5135	81	9	1	1	NUM
ejpam-5135	81	10	,	,	PUNCT
ejpam-5135	81	11	then	then	ADV
ejpam-5135	81	12	{	{	PUNCT
ejpam-5135	81	13	v	v	NOUN
ejpam-5135	81	14	}	}	PUNCT
ejpam-5135	81	15	is	be	AUX
ejpam-5135	81	16	the	the	DET
ejpam-5135	81	17	intersection	intersection	NOUN
ejpam-5135	81	18	of	of	ADP
ejpam-5135	81	19	two	two	NUM
ejpam-5135	81	20	or	or	CCONJ
ejpam-5135	81	21	more	more	ADV
ejpam-5135	81	22	distinct	distinct	ADJ
ejpam-5135	81	23	blocks	block	NOUN
ejpam-5135	81	24	which	which	PRON
ejpam-5135	81	25	further	far	ADV
ejpam-5135	81	26	implies	imply	VERB
ejpam-5135	81	27	that	that	SCONJ
ejpam-5135	81	28	v	v	NOUN
ejpam-5135	81	29	is	be	AUX
ejpam-5135	81	30	a	a	DET
ejpam-5135	81	31	cut	cut	NOUN
ejpam-5135	81	32	-	-	PUNCT
ejpam-5135	81	33	vertex	vertex	NOUN
ejpam-5135	81	34	.	.	PUNCT
ejpam-5135	82	1	(	(	PUNCT
ejpam-5135	82	2	⇐	⇐	NOUN
ejpam-5135	82	3	)	)	PUNCT
ejpam-5135	82	4	if	if	SCONJ
ejpam-5135	82	5	v	v	NOUN
ejpam-5135	82	6	is	be	AUX
ejpam-5135	82	7	an	an	DET
ejpam-5135	82	8	isolated	isolated	ADJ
ejpam-5135	82	9	vertex	vertex	NOUN
ejpam-5135	82	10	,	,	PUNCT
ejpam-5135	82	11	then	then	ADV
ejpam-5135	82	12	g[{v	g[{v	PROPN
ejpam-5135	82	13	}	}	PUNCT
ejpam-5135	82	14	]	]	PUNCT
ejpam-5135	82	15	is	be	AUX
ejpam-5135	82	16	a	a	DET
ejpam-5135	82	17	block	block	NOUN
ejpam-5135	82	18	of	of	ADP
ejpam-5135	82	19	g	g	NOUN
ejpam-5135	82	20	and	and	CCONJ
ejpam-5135	82	21	by	by	ADP
ejpam-5135	82	22	definition	definition	NOUN
ejpam-5135	82	23	1	1	NUM
ejpam-5135	82	24	,	,	PUNCT
ejpam-5135	82	25	{	{	PUNCT
ejpam-5135	82	26	v	v	NOUN
ejpam-5135	82	27	}	}	PUNCT
ejpam-5135	82	28	is	be	AUX
ejpam-5135	82	29	a	a	DET
ejpam-5135	82	30	τb(g)-open	τb(g)-open	NOUN
ejpam-5135	82	31	.	.	PUNCT
ejpam-5135	83	1	suppose	suppose	VERB
ejpam-5135	83	2	that	that	SCONJ
ejpam-5135	83	3	v	v	NOUN
ejpam-5135	83	4	is	be	AUX
ejpam-5135	83	5	a	a	DET
ejpam-5135	83	6	cut	cut	NOUN
ejpam-5135	83	7	-	-	PUNCT
ejpam-5135	83	8	vertex	vertex	NOUN
ejpam-5135	83	9	and	and	CCONJ
ejpam-5135	83	10	let	let	VERB
ejpam-5135	83	11	cj	cj	PRON
ejpam-5135	83	12	be	be	AUX
ejpam-5135	83	13	a	a	DET
ejpam-5135	83	14	component	component	NOUN
ejpam-5135	83	15	of	of	ADP
ejpam-5135	83	16	g	g	NOUN
ejpam-5135	83	17	containing	contain	VERB
ejpam-5135	83	18	v.	v.	ADV
ejpam-5135	83	19	let	let	VERB
ejpam-5135	83	20	bri	bri	NOUN
ejpam-5135	83	21	,	,	PUNCT
ejpam-5135	83	22	i	i	NOUN
ejpam-5135	83	23	=	=	NOUN
ejpam-5135	83	24	1	1	NUM
ejpam-5135	83	25	,	,	PUNCT
ejpam-5135	83	26	2	2	NUM
ejpam-5135	83	27	,	,	PUNCT
ejpam-5135	83	28	·	·	PUNCT
ejpam-5135	83	29	·	·	PUNCT
ejpam-5135	83	30	·	·	PUNCT
ejpam-5135	83	31	,	,	PUNCT
ejpam-5135	83	32	s	s	AUX
ejpam-5135	83	33	,	,	PUNCT
ejpam-5135	83	34	be	be	AUX
ejpam-5135	83	35	the	the	DET
ejpam-5135	83	36	branches	branch	NOUN
ejpam-5135	83	37	of	of	ADP
ejpam-5135	83	38	cj	cj	NOUN
ejpam-5135	83	39	at	at	ADP
ejpam-5135	83	40	v.	v.	ADP
ejpam-5135	83	41	note	note	VERB
ejpam-5135	83	42	that	that	SCONJ
ejpam-5135	83	43	for	for	ADP
ejpam-5135	83	44	each	each	DET
ejpam-5135	83	45	i	i	NOUN
ejpam-5135	83	46	=	=	NOUN
ejpam-5135	83	47	1	1	NUM
ejpam-5135	83	48	,	,	PUNCT
ejpam-5135	83	49	2	2	NUM
ejpam-5135	83	50	,	,	PUNCT
ejpam-5135	83	51	·	·	PUNCT
ejpam-5135	83	52	·	·	PUNCT
ejpam-5135	83	53	·	·	PUNCT
ejpam-5135	83	54	,	,	PUNCT
ejpam-5135	83	55	s	s	AUX
ejpam-5135	83	56	,	,	PUNCT
ejpam-5135	83	57	bri	bri	PROPN
ejpam-5135	83	58	is	be	AUX
ejpam-5135	83	59	composed	compose	VERB
ejpam-5135	83	60	of	of	ADP
ejpam-5135	83	61	blocks	block	NOUN
ejpam-5135	83	62	of	of	ADP
ejpam-5135	83	63	g	g	NOUN
ejpam-5135	83	64	which	which	PRON
ejpam-5135	83	65	further	far	ADV
ejpam-5135	83	66	means	mean	VERB
ejpam-5135	83	67	that	that	SCONJ
ejpam-5135	83	68	each	each	PRON
ejpam-5135	83	69	of	of	ADP
ejpam-5135	83	70	the	the	DET
ejpam-5135	83	71	branch	branch	NOUN
ejpam-5135	83	72	of	of	ADP
ejpam-5135	83	73	cj	cj	NOUN
ejpam-5135	83	74	at	at	ADP
ejpam-5135	83	75	v	v	NOUN
ejpam-5135	83	76	is	be	AUX
ejpam-5135	83	77	τb(g)-open	τb(g)-open	PROPN
ejpam-5135	83	78	.	.	PUNCT
ejpam-5135	84	1	hence	hence	ADV
ejpam-5135	84	2	,	,	PUNCT
ejpam-5135	84	3	by	by	ADP
ejpam-5135	84	4	defintion	defintion	NOUN
ejpam-5135	84	5	1	1	NUM
ejpam-5135	84	6	,	,	PUNCT
ejpam-5135	84	7	⋂s	⋂	VERB
ejpam-5135	84	8	i=1bri	i=1bri	NOUN
ejpam-5135	84	9	=	=	SYM
ejpam-5135	84	10	{	{	PUNCT
ejpam-5135	84	11	v	v	NOUN
ejpam-5135	84	12	}	}	PUNCT
ejpam-5135	84	13	is	be	AUX
ejpam-5135	84	14	τb(g)-open	τb(g)-open	PROPN
ejpam-5135	84	15	.	.	PUNCT
ejpam-5135	85	1	theorem	theorem	NOUN
ejpam-5135	85	2	2	2	NUM
ejpam-5135	85	3	.	.	PUNCT
ejpam-5135	86	1	a	a	DET
ejpam-5135	86	2	graph	graph	NOUN
ejpam-5135	86	3	g	g	NOUN
ejpam-5135	86	4	is	be	AUX
ejpam-5135	86	5	an	an	DET
ejpam-5135	86	6	empty	empty	ADJ
ejpam-5135	86	7	graph	graph	NOUN
ejpam-5135	86	8	if	if	SCONJ
ejpam-5135	86	9	and	and	CCONJ
ejpam-5135	86	10	only	only	ADV
ejpam-5135	86	11	if	if	SCONJ
ejpam-5135	86	12	τb(g	τb(g	NUM
ejpam-5135	86	13	)	)	PUNCT
ejpam-5135	86	14	is	be	AUX
ejpam-5135	86	15	the	the	DET
ejpam-5135	86	16	discrete	discrete	ADJ
ejpam-5135	86	17	topology	topology	NOUN
ejpam-5135	86	18	on	on	ADP
ejpam-5135	86	19	v	v	ADP
ejpam-5135	86	20	(	(	PUNCT
ejpam-5135	86	21	g	g	NOUN
ejpam-5135	86	22	)	)	PUNCT
ejpam-5135	86	23	.	.	PUNCT
ejpam-5135	87	1	proof	proof	NOUN
ejpam-5135	87	2	.	.	PUNCT
ejpam-5135	88	1	(	(	PUNCT
ejpam-5135	88	2	⇒	⇒	PROPN
ejpam-5135	88	3	)	)	PUNCT
ejpam-5135	88	4	let	let	VERB
ejpam-5135	88	5	g	g	NOUN
ejpam-5135	88	6	be	be	AUX
ejpam-5135	88	7	an	an	DET
ejpam-5135	88	8	empty	empty	ADJ
ejpam-5135	88	9	graph	graph	NOUN
ejpam-5135	88	10	.	.	PUNCT
ejpam-5135	89	1	then	then	ADV
ejpam-5135	89	2	g[{v	g[{v	PROPN
ejpam-5135	89	3	}	}	PUNCT
ejpam-5135	89	4	]	]	PUNCT
ejpam-5135	89	5	is	be	AUX
ejpam-5135	89	6	a	a	DET
ejpam-5135	89	7	block	block	NOUN
ejpam-5135	89	8	of	of	ADP
ejpam-5135	89	9	g	g	NOUN
ejpam-5135	89	10	and	and	CCONJ
ejpam-5135	89	11	by	by	ADP
ejpam-5135	89	12	definition	definition	NOUN
ejpam-5135	89	13	1	1	NUM
ejpam-5135	89	14	,	,	PUNCT
ejpam-5135	89	15	any	any	DET
ejpam-5135	89	16	subset	subset	NOUN
ejpam-5135	89	17	of	of	ADP
ejpam-5135	89	18	v	v	NOUN
ejpam-5135	89	19	(	(	PUNCT
ejpam-5135	89	20	g	g	NOUN
ejpam-5135	89	21	)	)	PUNCT
ejpam-5135	89	22	is	be	AUX
ejpam-5135	89	23	τb(g)-open	τb(g)-open	PROPN
ejpam-5135	89	24	.	.	PUNCT
ejpam-5135	90	1	hence	hence	ADV
ejpam-5135	90	2	,	,	PUNCT
ejpam-5135	90	3	τb(g	τb(g	PUNCT
ejpam-5135	90	4	)	)	PUNCT
ejpam-5135	90	5	is	be	AUX
ejpam-5135	90	6	discrete	discrete	ADJ
ejpam-5135	90	7	.	.	PUNCT
ejpam-5135	91	1	(	(	PUNCT
ejpam-5135	91	2	⇐	⇐	NOUN
ejpam-5135	91	3	)	)	PUNCT
ejpam-5135	91	4	suppose	suppose	VERB
ejpam-5135	91	5	that	that	SCONJ
ejpam-5135	91	6	τb(g	τb(g	PRON
ejpam-5135	91	7	)	)	PUNCT
ejpam-5135	91	8	is	be	AUX
ejpam-5135	91	9	discrete	discrete	ADJ
ejpam-5135	91	10	.	.	PUNCT
ejpam-5135	92	1	then	then	ADV
ejpam-5135	92	2	for	for	ADP
ejpam-5135	92	3	all	all	PRON
ejpam-5135	92	4	v	v	ADP
ejpam-5135	92	5	∈	∈	NUM
ejpam-5135	92	6	v	v	NOUN
ejpam-5135	92	7	(	(	PUNCT
ejpam-5135	92	8	g	g	NOUN
ejpam-5135	92	9	)	)	PUNCT
ejpam-5135	92	10	,	,	PUNCT
ejpam-5135	92	11	{	{	PUNCT
ejpam-5135	92	12	v	v	NOUN
ejpam-5135	92	13	}	}	PUNCT
ejpam-5135	92	14	is	be	AUX
ejpam-5135	92	15	τb(g)-open	τb(g)-open	PROPN
ejpam-5135	92	16	.	.	PUNCT
ejpam-5135	93	1	suppose	suppose	VERB
ejpam-5135	93	2	on	on	ADP
ejpam-5135	93	3	the	the	DET
ejpam-5135	93	4	contrary	contrary	NOUN
ejpam-5135	93	5	that	that	SCONJ
ejpam-5135	93	6	g	g	PROPN
ejpam-5135	93	7	is	be	AUX
ejpam-5135	93	8	not	not	PART
ejpam-5135	93	9	an	an	DET
ejpam-5135	93	10	empty	empty	ADJ
ejpam-5135	93	11	graph	graph	NOUN
ejpam-5135	93	12	.	.	PUNCT
ejpam-5135	94	1	then	then	ADV
ejpam-5135	94	2	|e(g)|	|e(g)|	ADJ
ejpam-5135	94	3	≥	≥	NUM
ejpam-5135	94	4	1	1	NUM
ejpam-5135	94	5	and	and	CCONJ
ejpam-5135	94	6	so	so	ADV
ejpam-5135	94	7	let	let	VERB
ejpam-5135	94	8	cj	cj	PRON
ejpam-5135	94	9	be	be	AUX
ejpam-5135	94	10	a	a	DET
ejpam-5135	94	11	component	component	NOUN
ejpam-5135	94	12	of	of	ADP
ejpam-5135	94	13	g	g	NOUN
ejpam-5135	94	14	for	for	ADP
ejpam-5135	94	15	some	some	DET
ejpam-5135	94	16	j	j	PROPN
ejpam-5135	94	17	∈	∈	PROPN
ejpam-5135	94	18	z+	z+	NUM
ejpam-5135	94	19	such	such	ADJ
ejpam-5135	94	20	that	that	SCONJ
ejpam-5135	94	21	|v	|v	PROPN
ejpam-5135	94	22	(	(	PUNCT
ejpam-5135	94	23	cj)|	cj)|	NOUN
ejpam-5135	94	24	≥	≥	NOUN
ejpam-5135	94	25	2	2	NUM
ejpam-5135	94	26	.	.	PUNCT
ejpam-5135	95	1	in	in	ADP
ejpam-5135	95	2	this	this	DET
ejpam-5135	95	3	case	case	NOUN
ejpam-5135	95	4	,	,	PUNCT
ejpam-5135	95	5	cj	cj	PROPN
ejpam-5135	95	6	has	have	VERB
ejpam-5135	95	7	at	at	ADV
ejpam-5135	95	8	least	least	ADV
ejpam-5135	95	9	two	two	NUM
ejpam-5135	95	10	vertices	vertex	NOUN
ejpam-5135	95	11	that	that	PRON
ejpam-5135	95	12	are	be	AUX
ejpam-5135	95	13	not	not	PART
ejpam-5135	95	14	cut	cut	VERB
ejpam-5135	95	15	-	-	PUNCT
ejpam-5135	95	16	vertices	vertex	NOUN
ejpam-5135	95	17	nor	nor	CCONJ
ejpam-5135	95	18	isolated	isolated	ADJ
ejpam-5135	95	19	vertices	vertex	NOUN
ejpam-5135	95	20	,	,	PUNCT
ejpam-5135	95	21	say	say	VERB
ejpam-5135	95	22	v	v	NOUN
ejpam-5135	95	23	and	and	CCONJ
ejpam-5135	95	24	w.	w.	PROPN
ejpam-5135	95	25	by	by	ADP
ejpam-5135	95	26	theorem	theorem	PROPN
ejpam-5135	95	27	justine	justine	PROPN
ejpam-5135	95	28	bryle	bryle	PROPN
ejpam-5135	95	29	c.	c.	PROPN
ejpam-5135	95	30	macaso	macaso	PROPN
ejpam-5135	95	31	,	,	PUNCT
ejpam-5135	95	32	cherry	cherry	PROPN
ejpam-5135	95	33	mae	mae	PROPN
ejpam-5135	95	34	r.	r.	PROPN
ejpam-5135	95	35	balingit	balingit	PROPN
ejpam-5135	95	36	/	/	SYM
ejpam-5135	95	37	eur	eur	PROPN
ejpam-5135	95	38	.	.	PUNCT
ejpam-5135	96	1	j.	j.	PROPN
ejpam-5135	96	2	pure	pure	PROPN
ejpam-5135	96	3	appl	appl	PROPN
ejpam-5135	96	4	.	.	PROPN
ejpam-5135	96	5	math	math	PROPN
ejpam-5135	96	6	,	,	PUNCT
ejpam-5135	96	7	17	17	NUM
ejpam-5135	96	8	(	(	PUNCT
ejpam-5135	96	9	2	2	NUM
ejpam-5135	96	10	)	)	PUNCT
ejpam-5135	96	11	(	(	PUNCT
ejpam-5135	96	12	2024	2024	NUM
ejpam-5135	96	13	)	)	PUNCT
ejpam-5135	96	14	,	,	PUNCT
ejpam-5135	96	15	663	663	NUM
ejpam-5135	96	16	-	-	SYM
ejpam-5135	96	17	675	675	NUM
ejpam-5135	96	18	669	669	NUM
ejpam-5135	96	19	1	1	NUM
ejpam-5135	96	20	,	,	PUNCT
ejpam-5135	96	21	{	{	PUNCT
ejpam-5135	96	22	v	v	NOUN
ejpam-5135	96	23	}	}	PUNCT
ejpam-5135	96	24	,	,	PUNCT
ejpam-5135	96	25	{	{	PUNCT
ejpam-5135	96	26	w	w	NOUN
ejpam-5135	96	27	}	}	PUNCT
ejpam-5135	96	28	/∈	/∈	PUNCT
ejpam-5135	96	29	τb(g	τb(g	NUM
ejpam-5135	96	30	)	)	PUNCT
ejpam-5135	96	31	.	.	PUNCT
ejpam-5135	97	1	a	a	DET
ejpam-5135	97	2	contradiction	contradiction	NOUN
ejpam-5135	97	3	since	since	SCONJ
ejpam-5135	97	4	τb(g	τb(g	NUM
ejpam-5135	97	5	)	)	PUNCT
ejpam-5135	97	6	is	be	AUX
ejpam-5135	97	7	discrete	discrete	ADJ
ejpam-5135	97	8	.	.	PUNCT
ejpam-5135	98	1	hence	hence	ADV
ejpam-5135	98	2	,	,	PUNCT
ejpam-5135	98	3	g	g	PROPN
ejpam-5135	98	4	is	be	AUX
ejpam-5135	98	5	an	an	DET
ejpam-5135	98	6	empty	empty	ADJ
ejpam-5135	98	7	graph	graph	NOUN
ejpam-5135	98	8	.	.	PUNCT
ejpam-5135	99	1	corollary	corollary	ADJ
ejpam-5135	99	2	1	1	NUM
ejpam-5135	99	3	.	.	PUNCT
ejpam-5135	100	1	let	let	VERB
ejpam-5135	100	2	g	g	PRON
ejpam-5135	100	3	be	be	AUX
ejpam-5135	100	4	a	a	DET
ejpam-5135	100	5	graph	graph	NOUN
ejpam-5135	100	6	.	.	PUNCT
ejpam-5135	101	1	if	if	SCONJ
ejpam-5135	101	2	a	a	PRON
ejpam-5135	101	3	is	be	AUX
ejpam-5135	101	4	the	the	DET
ejpam-5135	101	5	collection	collection	NOUN
ejpam-5135	101	6	of	of	ADP
ejpam-5135	101	7	cut	cut	NOUN
ejpam-5135	101	8	-	-	PUNCT
ejpam-5135	101	9	vertices	vertex	NOUN
ejpam-5135	101	10	of	of	ADP
ejpam-5135	101	11	g	g	NOUN
ejpam-5135	101	12	,	,	PUNCT
ejpam-5135	101	13	then	then	ADV
ejpam-5135	101	14	any	any	DET
ejpam-5135	101	15	subset	subset	NOUN
ejpam-5135	101	16	of	of	ADP
ejpam-5135	101	17	a	a	PRON
ejpam-5135	101	18	is	be	AUX
ejpam-5135	101	19	τb(g)-open	τb(g)-open	PROPN
ejpam-5135	101	20	.	.	PUNCT
ejpam-5135	102	1	theorem	theorem	NOUN
ejpam-5135	102	2	3	3	NUM
ejpam-5135	102	3	.	.	PUNCT
ejpam-5135	103	1	a	a	DET
ejpam-5135	103	2	graph	graph	NOUN
ejpam-5135	103	3	g	g	NOUN
ejpam-5135	103	4	is	be	AUX
ejpam-5135	103	5	connected	connect	VERB
ejpam-5135	103	6	and	and	CCONJ
ejpam-5135	103	7	contains	contain	VERB
ejpam-5135	103	8	no	no	DET
ejpam-5135	103	9	cut	cut	NOUN
ejpam-5135	103	10	-	-	PUNCT
ejpam-5135	103	11	vertices	vertex	NOUN
ejpam-5135	103	12	if	if	SCONJ
ejpam-5135	103	13	and	and	CCONJ
ejpam-5135	103	14	only	only	ADV
ejpam-5135	103	15	if	if	SCONJ
ejpam-5135	103	16	τb(g	τb(g	NUM
ejpam-5135	103	17	)	)	PUNCT
ejpam-5135	103	18	is	be	AUX
ejpam-5135	103	19	the	the	DET
ejpam-5135	103	20	indiscrete	indiscrete	ADJ
ejpam-5135	103	21	topology	topology	NOUN
ejpam-5135	103	22	on	on	ADP
ejpam-5135	103	23	v	v	ADP
ejpam-5135	103	24	(	(	PUNCT
ejpam-5135	103	25	g	g	NOUN
ejpam-5135	103	26	)	)	PUNCT
ejpam-5135	103	27	.	.	PUNCT
ejpam-5135	104	1	proof	proof	NOUN
ejpam-5135	104	2	.	.	PUNCT
ejpam-5135	105	1	(	(	PUNCT
ejpam-5135	105	2	⇒	⇒	PROPN
ejpam-5135	105	3	)	)	PUNCT
ejpam-5135	105	4	let	let	VERB
ejpam-5135	105	5	g	g	NOUN
ejpam-5135	105	6	be	be	AUX
ejpam-5135	105	7	a	a	DET
ejpam-5135	105	8	connected	connected	ADJ
ejpam-5135	105	9	graph	graph	NOUN
ejpam-5135	105	10	without	without	ADP
ejpam-5135	105	11	cut	cut	NOUN
ejpam-5135	105	12	-	-	PUNCT
ejpam-5135	105	13	vertices	vertex	NOUN
ejpam-5135	105	14	.	.	PUNCT
ejpam-5135	106	1	then	then	ADV
ejpam-5135	106	2	v	v	X
ejpam-5135	106	3	(	(	PUNCT
ejpam-5135	106	4	g	g	NOUN
ejpam-5135	106	5	)	)	PUNCT
ejpam-5135	106	6	is	be	AUX
ejpam-5135	106	7	the	the	DET
ejpam-5135	106	8	only	only	ADJ
ejpam-5135	106	9	block	block	NOUN
ejpam-5135	106	10	of	of	ADP
ejpam-5135	106	11	g	g	NOUN
ejpam-5135	106	12	and	and	CCONJ
ejpam-5135	106	13	so	so	ADV
ejpam-5135	106	14	σb(g	σb(g	PUNCT
ejpam-5135	106	15	)	)	PUNCT
ejpam-5135	106	16	=	=	SYM
ejpam-5135	106	17	{	{	PUNCT
ejpam-5135	106	18	v	v	NOUN
ejpam-5135	106	19	(	(	PUNCT
ejpam-5135	106	20	g	g	NOUN
ejpam-5135	106	21	)	)	PUNCT
ejpam-5135	106	22	}	}	PUNCT
ejpam-5135	106	23	which	which	PRON
ejpam-5135	106	24	further	far	ADV
ejpam-5135	106	25	implies	imply	VERB
ejpam-5135	106	26	that	that	SCONJ
ejpam-5135	106	27	s	s	ADP
ejpam-5135	106	28	τb(g	τb(g	PRON
ejpam-5135	106	29	)	)	PUNCT
ejpam-5135	106	30	=	=	PRON
ejpam-5135	106	31	{	{	PUNCT
ejpam-5135	106	32	∅	∅	NOUN
ejpam-5135	106	33	,	,	PUNCT
ejpam-5135	106	34	v	v	NOUN
ejpam-5135	106	35	(	(	PUNCT
ejpam-5135	106	36	g	g	NOUN
ejpam-5135	106	37	)	)	PUNCT
ejpam-5135	106	38	}	}	PUNCT
ejpam-5135	106	39	.	.	PUNCT
ejpam-5135	107	1	(	(	PUNCT
ejpam-5135	107	2	⇐	⇐	NOUN
ejpam-5135	107	3	)	)	PUNCT
ejpam-5135	107	4	suppose	suppose	VERB
ejpam-5135	107	5	that	that	SCONJ
ejpam-5135	107	6	τb(g	τb(g	PRON
ejpam-5135	107	7	)	)	PUNCT
ejpam-5135	107	8	is	be	AUX
ejpam-5135	107	9	indiscrete	indiscrete	ADJ
ejpam-5135	107	10	.	.	PUNCT
ejpam-5135	108	1	then	then	ADV
ejpam-5135	108	2	any	any	DET
ejpam-5135	108	3	nonempty	nonempty	ADJ
ejpam-5135	108	4	proper	proper	ADJ
ejpam-5135	108	5	subset	subset	NOUN
ejpam-5135	108	6	of	of	ADP
ejpam-5135	108	7	v	v	NOUN
ejpam-5135	108	8	(	(	PUNCT
ejpam-5135	108	9	g	g	NOUN
ejpam-5135	108	10	)	)	PUNCT
ejpam-5135	108	11	is	be	AUX
ejpam-5135	108	12	not	not	PART
ejpam-5135	108	13	τb(g)-open	τb(g)-open	PROPN
ejpam-5135	108	14	.	.	PUNCT
ejpam-5135	109	1	suppose	suppose	VERB
ejpam-5135	109	2	on	on	ADP
ejpam-5135	109	3	the	the	DET
ejpam-5135	109	4	contrary	contrary	NOUN
ejpam-5135	109	5	that	that	SCONJ
ejpam-5135	109	6	either	either	CCONJ
ejpam-5135	109	7	g	g	PROPN
ejpam-5135	109	8	disconnected	disconnect	VERB
ejpam-5135	109	9	or	or	CCONJ
ejpam-5135	109	10	has	have	AUX
ejpam-5135	109	11	cut	cut	VERB
ejpam-5135	109	12	-	-	PUNCT
ejpam-5135	109	13	vertices	vertex	NOUN
ejpam-5135	109	14	.	.	PUNCT
ejpam-5135	110	1	if	if	SCONJ
ejpam-5135	110	2	g	g	PROPN
ejpam-5135	110	3	is	be	AUX
ejpam-5135	110	4	disconnected	disconnect	VERB
ejpam-5135	110	5	,	,	PUNCT
ejpam-5135	110	6	then	then	ADV
ejpam-5135	110	7	g	g	PROPN
ejpam-5135	110	8	has	have	VERB
ejpam-5135	110	9	two	two	NUM
ejpam-5135	110	10	or	or	CCONJ
ejpam-5135	110	11	more	more	ADJ
ejpam-5135	110	12	components	component	NOUN
ejpam-5135	110	13	.	.	PUNCT
ejpam-5135	111	1	let	let	VERB
ejpam-5135	111	2	cj	cj	PRON
ejpam-5135	111	3	be	be	AUX
ejpam-5135	111	4	a	a	DET
ejpam-5135	111	5	component	component	NOUN
ejpam-5135	111	6	of	of	ADP
ejpam-5135	111	7	g	g	NOUN
ejpam-5135	111	8	for	for	ADP
ejpam-5135	111	9	some	some	DET
ejpam-5135	111	10	j	j	PROPN
ejpam-5135	111	11	∈	∈	PROPN
ejpam-5135	111	12	z+	z+	PROPN
ejpam-5135	111	13	.	.	PUNCT
ejpam-5135	112	1	then	then	ADV
ejpam-5135	112	2	cj	cj	NOUN
ejpam-5135	112	3	are	be	AUX
ejpam-5135	112	4	composed	compose	VERB
ejpam-5135	112	5	of	of	ADP
ejpam-5135	112	6	blocks	block	NOUN
ejpam-5135	112	7	of	of	ADP
ejpam-5135	112	8	g	g	NOUN
ejpam-5135	112	9	and	and	CCONJ
ejpam-5135	112	10	so	so	ADV
ejpam-5135	112	11	v	v	PROPN
ejpam-5135	112	12	(	(	PUNCT
ejpam-5135	112	13	cj	cj	NOUN
ejpam-5135	112	14	)	)	PUNCT
ejpam-5135	112	15	is	be	AUX
ejpam-5135	112	16	the	the	DET
ejpam-5135	112	17	union	union	NOUN
ejpam-5135	112	18	of	of	ADP
ejpam-5135	112	19	the	the	DET
ejpam-5135	112	20	vertex	vertex	NOUN
ejpam-5135	112	21	sets	set	NOUN
ejpam-5135	112	22	of	of	ADP
ejpam-5135	112	23	these	these	DET
ejpam-5135	112	24	blocks	block	NOUN
ejpam-5135	112	25	implying	imply	VERB
ejpam-5135	112	26	that	that	SCONJ
ejpam-5135	112	27	v	v	NOUN
ejpam-5135	112	28	(	(	PUNCT
ejpam-5135	112	29	cj	cj	NOUN
ejpam-5135	112	30	)	)	PUNCT
ejpam-5135	112	31	is	be	AUX
ejpam-5135	112	32	τb(g)-open	τb(g)-open	PROPN
ejpam-5135	112	33	.	.	PUNCT
ejpam-5135	113	1	but	but	CCONJ
ejpam-5135	113	2	v	v	X
ejpam-5135	113	3	(	(	PUNCT
ejpam-5135	113	4	cj	cj	NOUN
ejpam-5135	113	5	)	)	PUNCT
ejpam-5135	113	6	⊊	⊊	VERB
ejpam-5135	113	7	v	v	NOUN
ejpam-5135	113	8	(	(	PUNCT
ejpam-5135	113	9	g	g	NOUN
ejpam-5135	113	10	)	)	PUNCT
ejpam-5135	113	11	,	,	PUNCT
ejpam-5135	113	12	a	a	DET
ejpam-5135	113	13	contradiction	contradiction	NOUN
ejpam-5135	113	14	since	since	SCONJ
ejpam-5135	113	15	τb(g	τb(g	NUM
ejpam-5135	113	16	)	)	PUNCT
ejpam-5135	113	17	is	be	AUX
ejpam-5135	113	18	indiscrete	indiscrete	ADJ
ejpam-5135	113	19	.	.	PUNCT
ejpam-5135	114	1	therefore	therefore	ADV
ejpam-5135	114	2	,	,	PUNCT
ejpam-5135	114	3	g	g	PROPN
ejpam-5135	114	4	must	must	AUX
ejpam-5135	114	5	be	be	AUX
ejpam-5135	114	6	connected	connect	VERB
ejpam-5135	114	7	.	.	PUNCT
ejpam-5135	115	1	on	on	ADP
ejpam-5135	115	2	the	the	DET
ejpam-5135	115	3	other	other	ADJ
ejpam-5135	115	4	hand	hand	NOUN
ejpam-5135	115	5	,	,	PUNCT
ejpam-5135	115	6	if	if	SCONJ
ejpam-5135	115	7	g	g	PROPN
ejpam-5135	115	8	has	have	VERB
ejpam-5135	115	9	a	a	DET
ejpam-5135	115	10	cut	cut	NOUN
ejpam-5135	115	11	-	-	PUNCT
ejpam-5135	115	12	vertices	vertex	NOUN
ejpam-5135	115	13	,	,	PUNCT
ejpam-5135	115	14	then	then	ADV
ejpam-5135	115	15	let	let	VERB
ejpam-5135	115	16	v	v	PART
ejpam-5135	115	17	be	be	AUX
ejpam-5135	115	18	a	a	DET
ejpam-5135	115	19	cut	cut	NOUN
ejpam-5135	115	20	-	-	PUNCT
ejpam-5135	115	21	vertex	vertex	NOUN
ejpam-5135	115	22	of	of	ADP
ejpam-5135	115	23	g.	g.	PROPN
ejpam-5135	115	24	by	by	ADP
ejpam-5135	115	25	theorem	theorem	NOUN
ejpam-5135	115	26	1	1	NUM
ejpam-5135	115	27	,	,	PUNCT
ejpam-5135	115	28	{	{	PUNCT
ejpam-5135	115	29	v	v	NOUN
ejpam-5135	115	30	}	}	PUNCT
ejpam-5135	115	31	∈	∈	PROPN
ejpam-5135	115	32	τb(g	τb(g	NUM
ejpam-5135	115	33	)	)	PUNCT
ejpam-5135	115	34	,	,	PUNCT
ejpam-5135	115	35	a	a	DET
ejpam-5135	115	36	contradiction	contradiction	NOUN
ejpam-5135	115	37	.	.	PUNCT
ejpam-5135	116	1	hence	hence	ADV
ejpam-5135	116	2	g	g	PROPN
ejpam-5135	116	3	is	be	AUX
ejpam-5135	116	4	connected	connect	VERB
ejpam-5135	116	5	and	and	CCONJ
ejpam-5135	116	6	contains	contain	VERB
ejpam-5135	116	7	no	no	DET
ejpam-5135	116	8	cut	cut	NOUN
ejpam-5135	116	9	-	-	PUNCT
ejpam-5135	116	10	vertices	vertex	NOUN
ejpam-5135	116	11	.	.	PUNCT
ejpam-5135	117	1	suppose	suppose	VERB
ejpam-5135	117	2	that	that	SCONJ
ejpam-5135	117	3	g	g	PROPN
ejpam-5135	117	4	is	be	AUX
ejpam-5135	117	5	a	a	DET
ejpam-5135	117	6	graph	graph	NOUN
ejpam-5135	117	7	and	and	CCONJ
ejpam-5135	117	8	let	let	VERB
ejpam-5135	117	9	b1	b1	NOUN
ejpam-5135	117	10	,	,	PUNCT
ejpam-5135	117	11	b2	b2	NOUN
ejpam-5135	117	12	,	,	PUNCT
ejpam-5135	117	13	·	·	PUNCT
ejpam-5135	117	14	·	·	PUNCT
ejpam-5135	117	15	·	·	PUNCT
ejpam-5135	117	16	,	,	PUNCT
ejpam-5135	117	17	bk	bk	NOUN
ejpam-5135	117	18	be	be	AUX
ejpam-5135	117	19	the	the	DET
ejpam-5135	117	20	blocks	block	NOUN
ejpam-5135	117	21	of	of	ADP
ejpam-5135	117	22	g.	g.	PROPN
ejpam-5135	117	23	denote	denote	PROPN
ejpam-5135	117	24	c	c	PROPN
ejpam-5135	117	25	(	(	PUNCT
ejpam-5135	117	26	g	g	NOUN
ejpam-5135	117	27	)	)	PUNCT
ejpam-5135	117	28	to	to	PART
ejpam-5135	117	29	be	be	AUX
ejpam-5135	117	30	the	the	DET
ejpam-5135	117	31	family	family	NOUN
ejpam-5135	117	32	of	of	ADP
ejpam-5135	117	33	all	all	DET
ejpam-5135	117	34	the	the	DET
ejpam-5135	117	35	cut	cut	NOUN
ejpam-5135	117	36	-	-	PUNCT
ejpam-5135	117	37	vertices	vertex	NOUN
ejpam-5135	117	38	of	of	ADP
ejpam-5135	117	39	g.	g.	PROPN
ejpam-5135	117	40	recall	recall	VERB
ejpam-5135	117	41	that	that	SCONJ
ejpam-5135	117	42	two	two	NUM
ejpam-5135	117	43	distinct	distinct	ADJ
ejpam-5135	117	44	blocks	block	NOUN
ejpam-5135	117	45	have	have	VERB
ejpam-5135	117	46	at	at	ADP
ejpam-5135	117	47	most	most	ADV
ejpam-5135	117	48	one	one	NUM
ejpam-5135	117	49	vertex	vertex	NOUN
ejpam-5135	117	50	in	in	ADP
ejpam-5135	117	51	common	common	ADJ
ejpam-5135	117	52	and	and	CCONJ
ejpam-5135	117	53	this	this	DET
ejpam-5135	117	54	vertex	vertex	NOUN
ejpam-5135	117	55	is	be	AUX
ejpam-5135	117	56	a	a	DET
ejpam-5135	117	57	cut	cut	NOUN
ejpam-5135	117	58	-	-	PUNCT
ejpam-5135	117	59	vertex	vertex	NOUN
ejpam-5135	117	60	[	[	X
ejpam-5135	117	61	4	4	NUM
ejpam-5135	117	62	]	]	PUNCT
ejpam-5135	117	63	.	.	PUNCT
ejpam-5135	118	1	by	by	ADP
ejpam-5135	118	2	definition	definition	NOUN
ejpam-5135	118	3	1	1	NUM
ejpam-5135	118	4	,	,	PUNCT
ejpam-5135	118	5	the	the	DET
ejpam-5135	118	6	collection	collection	NOUN
ejpam-5135	118	7	of	of	ADP
ejpam-5135	118	8	the	the	DET
ejpam-5135	118	9	vertex	vertex	NOUN
ejpam-5135	118	10	set	set	NOUN
ejpam-5135	118	11	of	of	ADP
ejpam-5135	118	12	each	each	PRON
ejpam-5135	118	13	of	of	ADP
ejpam-5135	118	14	the	the	DET
ejpam-5135	118	15	blocks	block	NOUN
ejpam-5135	118	16	of	of	ADP
ejpam-5135	118	17	g	g	PROPN
ejpam-5135	118	18	together	together	ADV
ejpam-5135	118	19	with	with	ADP
ejpam-5135	118	20	all	all	DET
ejpam-5135	118	21	singletons	singleton	NOUN
ejpam-5135	118	22	containing	contain	VERB
ejpam-5135	118	23	the	the	DET
ejpam-5135	118	24	cut	cut	NOUN
ejpam-5135	118	25	-	-	PUNCT
ejpam-5135	118	26	vertices	vertex	NOUN
ejpam-5135	118	27	of	of	ADP
ejpam-5135	118	28	g	g	PROPN
ejpam-5135	118	29	is	be	AUX
ejpam-5135	118	30	a	a	DET
ejpam-5135	118	31	base	base	NOUN
ejpam-5135	118	32	for	for	ADP
ejpam-5135	118	33	the	the	DET
ejpam-5135	118	34	block	block	NOUN
ejpam-5135	118	35	topological	topological	ADJ
ejpam-5135	118	36	space	space	NOUN
ejpam-5135	118	37	of	of	ADP
ejpam-5135	118	38	g.	g.	PROPN
ejpam-5135	118	39	by	by	ADP
ejpam-5135	118	40	this	this	DET
ejpam-5135	118	41	observation	observation	NOUN
ejpam-5135	118	42	,	,	PUNCT
ejpam-5135	118	43	the	the	DET
ejpam-5135	118	44	following	follow	VERB
ejpam-5135	118	45	theorem	theorem	NOUN
ejpam-5135	118	46	characterizes	characterize	VERB
ejpam-5135	118	47	the	the	DET
ejpam-5135	118	48	τb(g)-open	τb(g)-open	NOUN
ejpam-5135	118	49	sets	set	NOUN
ejpam-5135	118	50	.	.	PUNCT
ejpam-5135	119	1	theorem	theorem	NOUN
ejpam-5135	119	2	4	4	NUM
ejpam-5135	119	3	.	.	PUNCT
ejpam-5135	120	1	let	let	VERB
ejpam-5135	120	2	g	g	PRON
ejpam-5135	120	3	be	be	AUX
ejpam-5135	120	4	a	a	DET
ejpam-5135	120	5	graph	graph	NOUN
ejpam-5135	120	6	and	and	CCONJ
ejpam-5135	120	7	let	let	VERB
ejpam-5135	120	8	b1	b1	NOUN
ejpam-5135	120	9	,	,	PUNCT
ejpam-5135	120	10	b2	b2	NOUN
ejpam-5135	120	11	,	,	PUNCT
ejpam-5135	120	12	·	·	PUNCT
ejpam-5135	120	13	·	·	PUNCT
ejpam-5135	120	14	·	·	PUNCT
ejpam-5135	120	15	,	,	PUNCT
ejpam-5135	120	16	bk	bk	NOUN
ejpam-5135	120	17	be	be	AUX
ejpam-5135	120	18	the	the	DET
ejpam-5135	120	19	blocks	block	NOUN
ejpam-5135	120	20	of	of	ADP
ejpam-5135	120	21	g.	g.	PROPN
ejpam-5135	120	22	a	a	DET
ejpam-5135	120	23	set	set	NOUN
ejpam-5135	120	24	a	a	DET
ejpam-5135	120	25	⊆	⊆	NUM
ejpam-5135	120	26	v	v	NOUN
ejpam-5135	120	27	(	(	PUNCT
ejpam-5135	120	28	g	g	NOUN
ejpam-5135	120	29	)	)	PUNCT
ejpam-5135	120	30	is	be	AUX
ejpam-5135	120	31	τb(g)-open	τb(g)-open	VERB
ejpam-5135	120	32	if	if	SCONJ
ejpam-5135	120	33	and	and	CCONJ
ejpam-5135	120	34	only	only	ADV
ejpam-5135	120	35	if	if	SCONJ
ejpam-5135	120	36	a	a	PRON
ejpam-5135	120	37	is	be	AUX
ejpam-5135	120	38	the	the	DET
ejpam-5135	120	39	union	union	NOUN
ejpam-5135	120	40	of	of	ADP
ejpam-5135	120	41	sets	set	NOUN
ejpam-5135	120	42	in	in	ADP
ejpam-5135	120	43	σb(g	σb(g	NOUN
ejpam-5135	120	44	)	)	PUNCT
ejpam-5135	120	45	∪	∪	X
ejpam-5135	120	46	{	{	PUNCT
ejpam-5135	120	47	t	t	NOUN
ejpam-5135	120	48	:	:	PUNCT
ejpam-5135	120	49	t	t	PROPN
ejpam-5135	120	50	⊆	⊆	NUM
ejpam-5135	120	51	c	c	X
ejpam-5135	120	52	(	(	PUNCT
ejpam-5135	120	53	g	g	NOUN
ejpam-5135	120	54	)	)	PUNCT
ejpam-5135	120	55	}	}	PUNCT
ejpam-5135	120	56	.	.	PUNCT
ejpam-5135	121	1	proof	proof	NOUN
ejpam-5135	121	2	.	.	PUNCT
ejpam-5135	122	1	(	(	PUNCT
ejpam-5135	122	2	⇒	⇒	PROPN
ejpam-5135	122	3	)	)	PUNCT
ejpam-5135	122	4	let	let	VERB
ejpam-5135	122	5	b1	b1	NOUN
ejpam-5135	122	6	,	,	PUNCT
ejpam-5135	122	7	b2	b2	NOUN
ejpam-5135	122	8	,	,	PUNCT
ejpam-5135	122	9	·	·	PUNCT
ejpam-5135	122	10	·	·	PUNCT
ejpam-5135	122	11	·	·	PUNCT
ejpam-5135	122	12	,	,	PUNCT
ejpam-5135	122	13	bk	bk	NOUN
ejpam-5135	122	14	be	be	AUX
ejpam-5135	122	15	the	the	DET
ejpam-5135	122	16	distinct	distinct	ADJ
ejpam-5135	122	17	blocks	block	NOUN
ejpam-5135	122	18	of	of	ADP
ejpam-5135	122	19	a	a	DET
ejpam-5135	122	20	graph	graph	NOUN
ejpam-5135	122	21	g.	g.	NOUN
ejpam-5135	122	22	suppose	suppose	VERB
ejpam-5135	122	23	a	a	PRON
ejpam-5135	122	24	is	be	AUX
ejpam-5135	122	25	a	a	DET
ejpam-5135	122	26	τb(g)-open	τb(g)-open	NOUN
ejpam-5135	122	27	.	.	PUNCT
ejpam-5135	123	1	then	then	ADV
ejpam-5135	123	2	a	a	PRON
ejpam-5135	123	3	is	be	AUX
ejpam-5135	123	4	the	the	DET
ejpam-5135	123	5	union	union	NOUN
ejpam-5135	123	6	of	of	ADP
ejpam-5135	123	7	finite	finite	ADJ
ejpam-5135	123	8	intersections	intersection	NOUN
ejpam-5135	123	9	of	of	ADP
ejpam-5135	123	10	sets	set	NOUN
ejpam-5135	123	11	in	in	ADP
ejpam-5135	123	12	σb(g	σb(g	NOUN
ejpam-5135	123	13	)	)	PUNCT
ejpam-5135	123	14	.	.	PUNCT
ejpam-5135	124	1	we	we	PRON
ejpam-5135	124	2	now	now	ADV
ejpam-5135	124	3	note	note	VERB
ejpam-5135	124	4	that	that	SCONJ
ejpam-5135	124	5	the	the	DET
ejpam-5135	124	6	intersection	intersection	NOUN
ejpam-5135	124	7	of	of	ADP
ejpam-5135	124	8	two	two	NUM
ejpam-5135	124	9	distinct	distinct	ADJ
ejpam-5135	124	10	blocks	block	NOUN
ejpam-5135	124	11	is	be	AUX
ejpam-5135	124	12	at	at	ADP
ejpam-5135	124	13	most	most	ADV
ejpam-5135	124	14	one	one	NUM
ejpam-5135	124	15	vertex	vertex	NOUN
ejpam-5135	124	16	which	which	PRON
ejpam-5135	124	17	is	be	AUX
ejpam-5135	124	18	a	a	DET
ejpam-5135	124	19	cut	cut	NOUN
ejpam-5135	124	20	-	-	PUNCT
ejpam-5135	124	21	vertex	vertex	NOUN
ejpam-5135	124	22	.	.	PUNCT
ejpam-5135	125	1	hence	hence	ADV
ejpam-5135	125	2	,	,	PUNCT
ejpam-5135	125	3	the	the	DET
ejpam-5135	125	4	conclusion	conclusion	NOUN
ejpam-5135	125	5	follows	follow	VERB
ejpam-5135	125	6	.	.	PUNCT
ejpam-5135	126	1	(	(	PUNCT
ejpam-5135	126	2	⇐	⇐	ADJ
ejpam-5135	126	3	)	)	PUNCT
ejpam-5135	126	4	let	let	VERB
ejpam-5135	126	5	a	a	DET
ejpam-5135	126	6	∈	∈	NOUN
ejpam-5135	126	7	σb(g	σb(g	NOUN
ejpam-5135	126	8	)	)	PUNCT
ejpam-5135	126	9	∪	∪	NOUN
ejpam-5135	126	10	{	{	PUNCT
ejpam-5135	126	11	t	t	NOUN
ejpam-5135	126	12	:	:	PUNCT
ejpam-5135	126	13	t	t	PROPN
ejpam-5135	126	14	⊆	⊆	NUM
ejpam-5135	126	15	c	c	X
ejpam-5135	126	16	(	(	PUNCT
ejpam-5135	126	17	g	g	NOUN
ejpam-5135	126	18	)	)	PUNCT
ejpam-5135	126	19	.	.	PUNCT
ejpam-5135	127	1	by	by	ADP
ejpam-5135	127	2	definition	definition	NOUN
ejpam-5135	127	3	1	1	NUM
ejpam-5135	127	4	and	and	CCONJ
ejpam-5135	127	5	theorem	theorem	VERB
ejpam-5135	127	6	1	1	NUM
ejpam-5135	127	7	,	,	PUNCT
ejpam-5135	127	8	a	a	PRON
ejpam-5135	127	9	is	be	AUX
ejpam-5135	127	10	τb(g)open	τb(g)open	ADJ
ejpam-5135	127	11	.	.	PUNCT
ejpam-5135	128	1	remark	remark	PROPN
ejpam-5135	128	2	1	1	NUM
ejpam-5135	128	3	.	.	PUNCT
ejpam-5135	129	1	let	let	VERB
ejpam-5135	129	2	g	g	PRON
ejpam-5135	129	3	be	be	AUX
ejpam-5135	129	4	a	a	DET
ejpam-5135	129	5	graph	graph	NOUN
ejpam-5135	129	6	with	with	ADP
ejpam-5135	129	7	more	more	ADJ
ejpam-5135	129	8	than	than	ADP
ejpam-5135	129	9	one	one	NUM
ejpam-5135	129	10	block	block	NOUN
ejpam-5135	129	11	.	.	PUNCT
ejpam-5135	130	1	then	then	ADV
ejpam-5135	130	2	the	the	DET
ejpam-5135	130	3	union	union	NOUN
ejpam-5135	130	4	of	of	ADP
ejpam-5135	130	5	all	all	DET
ejpam-5135	130	6	the	the	DET
ejpam-5135	130	7	nontrivial	nontrivial	ADJ
ejpam-5135	130	8	τb(g)-open	τb(g)-open	VERB
ejpam-5135	130	9	proper	proper	ADJ
ejpam-5135	130	10	subsets	subset	NOUN
ejpam-5135	130	11	of	of	ADP
ejpam-5135	130	12	v	v	NOUN
ejpam-5135	130	13	(	(	PUNCT
ejpam-5135	130	14	g	g	NOUN
ejpam-5135	130	15	)	)	PUNCT
ejpam-5135	130	16	equals	equal	VERB
ejpam-5135	130	17	to	to	ADP
ejpam-5135	130	18	v	v	NOUN
ejpam-5135	130	19	(	(	PUNCT
ejpam-5135	130	20	g	g	NOUN
ejpam-5135	130	21	)	)	PUNCT
ejpam-5135	130	22	.	.	PUNCT
ejpam-5135	131	1	remark	remark	PROPN
ejpam-5135	131	2	2	2	NUM
ejpam-5135	131	3	.	.	PUNCT
ejpam-5135	132	1	let	let	VERB
ejpam-5135	132	2	(	(	PUNCT
ejpam-5135	132	3	v	v	NOUN
ejpam-5135	132	4	(	(	PUNCT
ejpam-5135	132	5	g	g	NOUN
ejpam-5135	132	6	)	)	PUNCT
ejpam-5135	132	7	,	,	PUNCT
ejpam-5135	132	8	τb(g	τb(g	NUM
ejpam-5135	132	9	)	)	PUNCT
ejpam-5135	132	10	)	)	PUNCT
ejpam-5135	133	1	be	be	AUX
ejpam-5135	133	2	a	a	DET
ejpam-5135	133	3	non	non	X
ejpam-5135	133	4	indiscrete	indiscrete	ADJ
ejpam-5135	133	5	block	block	NOUN
ejpam-5135	133	6	topological	topological	ADJ
ejpam-5135	133	7	space	space	NOUN
ejpam-5135	133	8	.	.	PUNCT
ejpam-5135	134	1	then	then	ADV
ejpam-5135	134	2	the	the	DET
ejpam-5135	134	3	smallest	small	ADJ
ejpam-5135	134	4	possible	possible	ADJ
ejpam-5135	134	5	number	number	NOUN
ejpam-5135	134	6	of	of	ADP
ejpam-5135	134	7	τb(g)-open	τb(g)-open	NOUN
ejpam-5135	134	8	sets	set	NOUN
ejpam-5135	134	9	is	be	AUX
ejpam-5135	134	10	4	4	NUM
ejpam-5135	134	11	.	.	NOUN
ejpam-5135	134	12	example	example	NOUN
ejpam-5135	134	13	2	2	NUM
ejpam-5135	134	14	.	.	X
ejpam-5135	134	15	consider	consider	VERB
ejpam-5135	134	16	the	the	DET
ejpam-5135	134	17	graph	graph	NOUN
ejpam-5135	134	18	g	g	NOUN
ejpam-5135	134	19	in	in	ADP
ejpam-5135	134	20	figure	figure	NOUN
ejpam-5135	134	21	8	8	NUM
ejpam-5135	134	22	.	.	PUNCT
ejpam-5135	135	1	here	here	ADV
ejpam-5135	135	2	,	,	PUNCT
ejpam-5135	135	3	g[{v1	g[{v1	PROPN
ejpam-5135	135	4	,	,	PUNCT
ejpam-5135	135	5	v2	v2	PROPN
ejpam-5135	135	6	}	}	PUNCT
ejpam-5135	135	7	]	]	PUNCT
ejpam-5135	135	8	and	and	CCONJ
ejpam-5135	135	9	g[{v2	g[{v2	PROPN
ejpam-5135	135	10	,	,	PUNCT
ejpam-5135	135	11	v3	v3	PROPN
ejpam-5135	135	12	}	}	PUNCT
ejpam-5135	135	13	]	]	PUNCT
ejpam-5135	135	14	are	be	AUX
ejpam-5135	135	15	the	the	DET
ejpam-5135	135	16	blocks	block	NOUN
ejpam-5135	135	17	of	of	ADP
ejpam-5135	135	18	g	g	NOUN
ejpam-5135	135	19	and	and	CCONJ
ejpam-5135	135	20	τb(g	τb(g	NUM
ejpam-5135	135	21	)	)	PUNCT
ejpam-5135	136	1	=	=	PRON
ejpam-5135	136	2	{	{	PUNCT
ejpam-5135	136	3	∅	∅	NOUN
ejpam-5135	136	4	,	,	PUNCT
ejpam-5135	136	5	v	v	NOUN
ejpam-5135	136	6	(	(	PUNCT
ejpam-5135	136	7	g	g	NOUN
ejpam-5135	136	8	)	)	PUNCT
ejpam-5135	136	9	,	,	PUNCT
ejpam-5135	136	10	{	{	PUNCT
ejpam-5135	136	11	v1	v1	NOUN
ejpam-5135	136	12	,	,	PUNCT
ejpam-5135	136	13	v2	v2	PROPN
ejpam-5135	136	14	}	}	PUNCT
ejpam-5135	136	15	,	,	PUNCT
ejpam-5135	136	16	{	{	PUNCT
ejpam-5135	136	17	v3	v3	PROPN
ejpam-5135	136	18	,	,	PUNCT
ejpam-5135	136	19	v4	v4	PROPN
ejpam-5135	136	20	}	}	PUNCT
ejpam-5135	136	21	}	}	PUNCT
ejpam-5135	136	22	.	.	PUNCT
ejpam-5135	137	1	moreover	moreover	ADV
ejpam-5135	137	2	,	,	PUNCT
ejpam-5135	137	3	{	{	PUNCT
ejpam-5135	137	4	v1	v1	NOUN
ejpam-5135	137	5	,	,	PUNCT
ejpam-5135	137	6	v2	v2	NOUN
ejpam-5135	137	7	}	}	PUNCT
ejpam-5135	137	8	∪	∪	NOUN
ejpam-5135	137	9	{	{	PUNCT
ejpam-5135	137	10	v3	v3	PROPN
ejpam-5135	137	11	,	,	PUNCT
ejpam-5135	137	12	v4	v4	PROPN
ejpam-5135	137	13	}	}	PUNCT
ejpam-5135	137	14	=	=	SYM
ejpam-5135	137	15	v	v	NOUN
ejpam-5135	137	16	(	(	PUNCT
ejpam-5135	137	17	g	g	NOUN
ejpam-5135	137	18	)	)	PUNCT
ejpam-5135	137	19	and	and	CCONJ
ejpam-5135	137	20	|τb(g)|	|τb(g)|	NOUN
ejpam-5135	137	21	=	=	SYM
ejpam-5135	137	22	4	4	X
ejpam-5135	137	23	.	.	PUNCT
ejpam-5135	137	24	justine	justine	PROPN
ejpam-5135	137	25	bryle	bryle	PROPN
ejpam-5135	137	26	c.	c.	PROPN
ejpam-5135	137	27	macaso	macaso	PROPN
ejpam-5135	137	28	,	,	PUNCT
ejpam-5135	137	29	cherry	cherry	PROPN
ejpam-5135	137	30	mae	mae	PROPN
ejpam-5135	137	31	r.	r.	PROPN
ejpam-5135	137	32	balingit	balingit	PROPN
ejpam-5135	137	33	/	/	SYM
ejpam-5135	137	34	eur	eur	PROPN
ejpam-5135	137	35	.	.	PUNCT
ejpam-5135	138	1	j.	j.	PROPN
ejpam-5135	138	2	pure	pure	PROPN
ejpam-5135	138	3	appl	appl	PROPN
ejpam-5135	138	4	.	.	PROPN
ejpam-5135	138	5	math	math	PROPN
ejpam-5135	138	6	,	,	PUNCT
ejpam-5135	138	7	17	17	NUM
ejpam-5135	138	8	(	(	PUNCT
ejpam-5135	138	9	2	2	NUM
ejpam-5135	138	10	)	)	PUNCT
ejpam-5135	138	11	(	(	PUNCT
ejpam-5135	138	12	2024	2024	NUM
ejpam-5135	138	13	)	)	PUNCT
ejpam-5135	138	14	,	,	PUNCT
ejpam-5135	138	15	663	663	NUM
ejpam-5135	138	16	-	-	SYM
ejpam-5135	138	17	675	675	NUM
ejpam-5135	138	18	670	670	NUM
ejpam-5135	138	19	v4	v4	NOUN
ejpam-5135	138	20	v2	v2	NOUN
ejpam-5135	138	21	v1	v1	NOUN
ejpam-5135	138	22	v3	v3	PROPN
ejpam-5135	138	23	g	g	PROPN
ejpam-5135	138	24	:	:	PUNCT
ejpam-5135	138	25	figure	figure	NOUN
ejpam-5135	138	26	8	8	NUM
ejpam-5135	138	27	:	:	PUNCT
ejpam-5135	138	28	graph	graph	NOUN
ejpam-5135	138	29	g	g	NOUN
ejpam-5135	138	30	theorem	theorem	NOUN
ejpam-5135	138	31	5	5	NUM
ejpam-5135	138	32	.	.	PUNCT
ejpam-5135	139	1	let	let	VERB
ejpam-5135	139	2	g	g	PRON
ejpam-5135	139	3	be	be	AUX
ejpam-5135	139	4	a	a	DET
ejpam-5135	139	5	graph	graph	NOUN
ejpam-5135	139	6	such	such	ADJ
ejpam-5135	139	7	that	that	SCONJ
ejpam-5135	139	8	|e(g)|	|e(g)|	ADJ
ejpam-5135	139	9	≥	≥	NOUN
ejpam-5135	139	10	1	1	NUM
ejpam-5135	139	11	.	.	PUNCT
ejpam-5135	140	1	if	if	SCONJ
ejpam-5135	140	2	v	v	NOUN
ejpam-5135	140	3	is	be	AUX
ejpam-5135	140	4	not	not	PART
ejpam-5135	140	5	a	a	DET
ejpam-5135	140	6	cut	cut	VERB
ejpam-5135	140	7	-	-	PUNCT
ejpam-5135	140	8	vertex	vertex	NOUN
ejpam-5135	140	9	adjacent	adjacent	ADJ
ejpam-5135	140	10	to	to	ADP
ejpam-5135	140	11	w	w	PROPN
ejpam-5135	140	12	,	,	PUNCT
ejpam-5135	140	13	then	then	ADV
ejpam-5135	140	14	every	every	DET
ejpam-5135	140	15	τb(g)-open	τb(g)-open	NOUN
ejpam-5135	140	16	set	set	NOUN
ejpam-5135	140	17	containing	contain	VERB
ejpam-5135	140	18	v	v	NOUN
ejpam-5135	140	19	also	also	ADV
ejpam-5135	140	20	contains	contain	VERB
ejpam-5135	140	21	w.	w.	NOUN
ejpam-5135	140	22	proof	proof	NOUN
ejpam-5135	140	23	.	.	PUNCT
ejpam-5135	141	1	let	let	VERB
ejpam-5135	141	2	g	g	PRON
ejpam-5135	141	3	be	be	AUX
ejpam-5135	141	4	a	a	DET
ejpam-5135	141	5	graph	graph	NOUN
ejpam-5135	141	6	such	such	ADJ
ejpam-5135	141	7	that	that	SCONJ
ejpam-5135	141	8	|e(g)|	|e(g)|	ADJ
ejpam-5135	141	9	≥	≥	NUM
ejpam-5135	141	10	1	1	NUM
ejpam-5135	141	11	.	.	PUNCT
ejpam-5135	141	12	suppose	suppose	VERB
ejpam-5135	141	13	that	that	SCONJ
ejpam-5135	141	14	vertex	vertex	NOUN
ejpam-5135	141	15	v	v	NOUN
ejpam-5135	141	16	is	be	AUX
ejpam-5135	141	17	not	not	PART
ejpam-5135	141	18	a	a	DET
ejpam-5135	141	19	cutvertex	cutvertex	NOUN
ejpam-5135	141	20	adjacent	adjacent	ADJ
ejpam-5135	141	21	to	to	ADP
ejpam-5135	141	22	w.	w.	PROPN
ejpam-5135	141	23	let	let	VERB
ejpam-5135	141	24	o	o	NOUN
ejpam-5135	141	25	be	be	AUX
ejpam-5135	141	26	a	a	DET
ejpam-5135	141	27	τb(g)-open	τb(g)-open	NOUN
ejpam-5135	141	28	containing	contain	VERB
ejpam-5135	141	29	v.	v.	ADP
ejpam-5135	141	30	suppose	suppose	VERB
ejpam-5135	141	31	on	on	ADP
ejpam-5135	141	32	the	the	DET
ejpam-5135	141	33	contrary	contrary	NOUN
ejpam-5135	141	34	that	that	PRON
ejpam-5135	141	35	w	w	PROPN
ejpam-5135	141	36	/∈	/∈	PROPN
ejpam-5135	142	1	o.	o.	NOUN
ejpam-5135	143	1	since	since	SCONJ
ejpam-5135	143	2	v	v	NUM
ejpam-5135	143	3	and	and	CCONJ
ejpam-5135	143	4	w	w	NOUN
ejpam-5135	143	5	are	be	AUX
ejpam-5135	143	6	adjacent	adjacent	ADJ
ejpam-5135	143	7	in	in	ADP
ejpam-5135	143	8	g	g	PROPN
ejpam-5135	143	9	and	and	CCONJ
ejpam-5135	143	10	e(g	e(g	PROPN
ejpam-5135	143	11	)	)	PUNCT
ejpam-5135	144	1	is	be	AUX
ejpam-5135	144	2	the	the	DET
ejpam-5135	144	3	disjoint	disjoint	PROPN
ejpam-5135	144	4	union	union	NOUN
ejpam-5135	144	5	of	of	ADP
ejpam-5135	144	6	the	the	DET
ejpam-5135	144	7	edges	edge	NOUN
ejpam-5135	144	8	of	of	ADP
ejpam-5135	144	9	bis	bis	PROPN
ejpam-5135	144	10	,	,	PUNCT
ejpam-5135	144	11	then	then	ADV
ejpam-5135	144	12	there	there	PRON
ejpam-5135	144	13	exists	exist	VERB
ejpam-5135	144	14	a	a	DET
ejpam-5135	144	15	block	block	NOUN
ejpam-5135	144	16	bj	bj	NOUN
ejpam-5135	144	17	of	of	ADP
ejpam-5135	144	18	g	g	NOUN
ejpam-5135	144	19	such	such	ADJ
ejpam-5135	144	20	that	that	DET
ejpam-5135	144	21	v	v	NOUN
ejpam-5135	144	22	,	,	PUNCT
ejpam-5135	144	23	w	w	PROPN
ejpam-5135	144	24	∈	∈	PROPN
ejpam-5135	144	25	v	v	NOUN
ejpam-5135	144	26	(	(	PUNCT
ejpam-5135	144	27	bj	bj	NOUN
ejpam-5135	144	28	)	)	PUNCT
ejpam-5135	144	29	.	.	PUNCT
ejpam-5135	145	1	on	on	ADP
ejpam-5135	145	2	the	the	DET
ejpam-5135	145	3	other	other	ADJ
ejpam-5135	145	4	hand	hand	NOUN
ejpam-5135	145	5	,	,	PUNCT
ejpam-5135	145	6	since	since	SCONJ
ejpam-5135	145	7	v	v	NOUN
ejpam-5135	145	8	is	be	AUX
ejpam-5135	145	9	not	not	PART
ejpam-5135	145	10	a	a	DET
ejpam-5135	145	11	cut	cut	NOUN
ejpam-5135	145	12	-	-	PUNCT
ejpam-5135	145	13	vertex	vertex	NOUN
ejpam-5135	145	14	,	,	PUNCT
ejpam-5135	145	15	choose	choose	VERB
ejpam-5135	145	16	bk	bk	NOUN
ejpam-5135	145	17	as	as	ADP
ejpam-5135	145	18	a	a	DET
ejpam-5135	145	19	block	block	NOUN
ejpam-5135	145	20	such	such	ADJ
ejpam-5135	145	21	that	that	DET
ejpam-5135	145	22	v	v	NUM
ejpam-5135	145	23	∈	∈	PROPN
ejpam-5135	145	24	v	v	NOUN
ejpam-5135	145	25	(	(	PUNCT
ejpam-5135	145	26	bk	bk	NOUN
ejpam-5135	145	27	)	)	PUNCT
ejpam-5135	145	28	⊆	⊆	NUM
ejpam-5135	145	29	o.	o.	NOUN
ejpam-5135	145	30	in	in	ADP
ejpam-5135	145	31	this	this	DET
ejpam-5135	145	32	case	case	NOUN
ejpam-5135	145	33	,	,	PUNCT
ejpam-5135	145	34	bk	bk	NOUN
ejpam-5135	145	35	and	and	CCONJ
ejpam-5135	145	36	bj	bj	VERB
ejpam-5135	145	37	are	be	AUX
ejpam-5135	145	38	distinct	distinct	ADJ
ejpam-5135	145	39	and	and	CCONJ
ejpam-5135	145	40	{	{	PUNCT
ejpam-5135	145	41	v	v	NOUN
ejpam-5135	145	42	}	}	PUNCT
ejpam-5135	145	43	∈	∈	PROPN
ejpam-5135	145	44	v	v	NOUN
ejpam-5135	145	45	(	(	PUNCT
ejpam-5135	145	46	bk	bk	NOUN
ejpam-5135	145	47	)	)	PUNCT
ejpam-5135	145	48	∩	∩	PROPN
ejpam-5135	145	49	v	v	X
ejpam-5135	145	50	(	(	PUNCT
ejpam-5135	145	51	bj	bj	NOUN
ejpam-5135	145	52	)	)	PUNCT
ejpam-5135	145	53	.	.	PUNCT
ejpam-5135	146	1	but	but	CCONJ
ejpam-5135	146	2	,	,	PUNCT
ejpam-5135	146	3	two	two	NUM
ejpam-5135	146	4	distinct	distinct	ADJ
ejpam-5135	146	5	blocks	block	NOUN
ejpam-5135	146	6	intersect	intersect	ADJ
ejpam-5135	146	7	in	in	ADP
ejpam-5135	146	8	at	at	ADP
ejpam-5135	146	9	most	most	ADV
ejpam-5135	146	10	one	one	NUM
ejpam-5135	146	11	vertex	vertex	NOUN
ejpam-5135	146	12	which	which	PRON
ejpam-5135	146	13	is	be	AUX
ejpam-5135	146	14	a	a	DET
ejpam-5135	146	15	cut	cut	NOUN
ejpam-5135	146	16	-	-	PUNCT
ejpam-5135	146	17	vertex	vertex	NOUN
ejpam-5135	146	18	;	;	PUNCT
ejpam-5135	146	19	hence	hence	ADV
ejpam-5135	146	20	v	v	NOUN
ejpam-5135	146	21	is	be	AUX
ejpam-5135	146	22	a	a	DET
ejpam-5135	146	23	cut	cut	NOUN
ejpam-5135	146	24	-	-	PUNCT
ejpam-5135	146	25	vertex	vertex	NOUN
ejpam-5135	146	26	,	,	PUNCT
ejpam-5135	146	27	a	a	DET
ejpam-5135	146	28	contradiction	contradiction	NOUN
ejpam-5135	146	29	to	to	ADP
ejpam-5135	146	30	our	our	PRON
ejpam-5135	146	31	choice	choice	NOUN
ejpam-5135	146	32	of	of	ADP
ejpam-5135	146	33	v.	v.	ADV
ejpam-5135	146	34	therefore	therefore	ADV
ejpam-5135	146	35	,	,	PUNCT
ejpam-5135	147	1	w	w	PROPN
ejpam-5135	147	2	∈	∈	PROPN
ejpam-5135	147	3	o.	o.	NOUN
ejpam-5135	147	4	a	a	DET
ejpam-5135	147	5	topological	topological	ADJ
ejpam-5135	147	6	space	space	NOUN
ejpam-5135	147	7	is	be	AUX
ejpam-5135	147	8	a	a	DET
ejpam-5135	147	9	hausdorff	hausdorff	NOUN
ejpam-5135	147	10	space	space	NOUN
ejpam-5135	147	11	if	if	SCONJ
ejpam-5135	147	12	for	for	ADP
ejpam-5135	147	13	every	every	DET
ejpam-5135	147	14	two	two	NUM
ejpam-5135	147	15	distinct	distinct	ADJ
ejpam-5135	147	16	elements	element	NOUN
ejpam-5135	147	17	in	in	ADP
ejpam-5135	147	18	the	the	DET
ejpam-5135	147	19	mother	mother	NOUN
ejpam-5135	147	20	set	set	NOUN
ejpam-5135	147	21	can	can	AUX
ejpam-5135	147	22	be	be	AUX
ejpam-5135	147	23	separated	separate	VERB
ejpam-5135	147	24	by	by	ADP
ejpam-5135	147	25	two	two	NUM
ejpam-5135	147	26	disjoint	disjoint	ADJ
ejpam-5135	147	27	open	open	ADJ
ejpam-5135	147	28	sets	set	NOUN
ejpam-5135	147	29	[	[	X
ejpam-5135	147	30	9	9	NUM
ejpam-5135	147	31	]	]	PUNCT
ejpam-5135	147	32	.	.	PUNCT
ejpam-5135	148	1	the	the	DET
ejpam-5135	148	2	following	follow	VERB
ejpam-5135	148	3	theorem	theorem	NOUN
ejpam-5135	148	4	characterizes	characterize	VERB
ejpam-5135	148	5	the	the	DET
ejpam-5135	148	6	block	block	NOUN
ejpam-5135	148	7	topological	topological	ADJ
ejpam-5135	148	8	space	space	NOUN
ejpam-5135	148	9	as	as	ADP
ejpam-5135	148	10	being	be	AUX
ejpam-5135	148	11	a	a	DET
ejpam-5135	148	12	hausdorff	hausdorff	NOUN
ejpam-5135	148	13	space	space	NOUN
ejpam-5135	148	14	.	.	PUNCT
ejpam-5135	149	1	theorem	theorem	VERB
ejpam-5135	149	2	6	6	NUM
ejpam-5135	149	3	.	.	PUNCT
ejpam-5135	150	1	a	a	DET
ejpam-5135	150	2	(	(	PUNCT
ejpam-5135	150	3	v	v	NOUN
ejpam-5135	150	4	(	(	PUNCT
ejpam-5135	150	5	g	g	NOUN
ejpam-5135	150	6	)	)	PUNCT
ejpam-5135	150	7	,	,	PUNCT
ejpam-5135	150	8	τb(g	τb(g	NUM
ejpam-5135	150	9	)	)	PUNCT
ejpam-5135	150	10	)	)	PUNCT
ejpam-5135	150	11	is	be	AUX
ejpam-5135	150	12	a	a	DET
ejpam-5135	150	13	hausdorff	hausdorff	NOUN
ejpam-5135	150	14	space	space	NOUN
ejpam-5135	150	15	if	if	SCONJ
ejpam-5135	150	16	and	and	CCONJ
ejpam-5135	150	17	only	only	ADV
ejpam-5135	150	18	if	if	SCONJ
ejpam-5135	150	19	g	g	PROPN
ejpam-5135	150	20	is	be	AUX
ejpam-5135	150	21	an	an	DET
ejpam-5135	150	22	empty	empty	ADJ
ejpam-5135	150	23	graph	graph	NOUN
ejpam-5135	150	24	.	.	PUNCT
ejpam-5135	151	1	proof	proof	NOUN
ejpam-5135	151	2	.	.	PUNCT
ejpam-5135	152	1	(	(	PUNCT
ejpam-5135	152	2	⇒	⇒	NOUN
ejpam-5135	152	3	)	)	PUNCT
ejpam-5135	152	4	let	let	VERB
ejpam-5135	152	5	(	(	PUNCT
ejpam-5135	152	6	v	v	NOUN
ejpam-5135	152	7	(	(	PUNCT
ejpam-5135	152	8	g	g	NOUN
ejpam-5135	152	9	)	)	PUNCT
ejpam-5135	152	10	,	,	PUNCT
ejpam-5135	152	11	τb(g	τb(g	NUM
ejpam-5135	152	12	)	)	PUNCT
ejpam-5135	152	13	)	)	PUNCT
ejpam-5135	152	14	be	be	AUX
ejpam-5135	152	15	a	a	DET
ejpam-5135	152	16	hausdorff	hausdorff	NOUN
ejpam-5135	152	17	space	space	NOUN
ejpam-5135	152	18	.	.	PUNCT
ejpam-5135	153	1	then	then	ADV
ejpam-5135	153	2	every	every	DET
ejpam-5135	153	3	two	two	NUM
ejpam-5135	153	4	distinct	distinct	ADJ
ejpam-5135	153	5	vertices	vertex	NOUN
ejpam-5135	153	6	in	in	ADP
ejpam-5135	153	7	g	g	PROPN
ejpam-5135	153	8	can	can	AUX
ejpam-5135	153	9	be	be	AUX
ejpam-5135	153	10	separated	separate	VERB
ejpam-5135	153	11	by	by	ADP
ejpam-5135	153	12	two	two	NUM
ejpam-5135	153	13	disjoint	disjoint	ADJ
ejpam-5135	153	14	τb(g)-open	τb(g)-open	NOUN
ejpam-5135	153	15	sets	set	NOUN
ejpam-5135	153	16	.	.	PUNCT
ejpam-5135	154	1	if	if	SCONJ
ejpam-5135	154	2	g	g	PROPN
ejpam-5135	154	3	is	be	AUX
ejpam-5135	154	4	not	not	PART
ejpam-5135	154	5	an	an	DET
ejpam-5135	154	6	empty	empty	ADJ
ejpam-5135	154	7	graph	graph	NOUN
ejpam-5135	154	8	,	,	PUNCT
ejpam-5135	154	9	then	then	ADV
ejpam-5135	154	10	|e(g)|	|e(g)|	ADJ
ejpam-5135	154	11	≥	≥	NUM
ejpam-5135	154	12	1	1	NUM
ejpam-5135	154	13	.	.	PUNCT
ejpam-5135	155	1	in	in	ADP
ejpam-5135	155	2	this	this	DET
ejpam-5135	155	3	case	case	NOUN
ejpam-5135	155	4	,	,	PUNCT
ejpam-5135	155	5	choose	choose	VERB
ejpam-5135	155	6	a	a	DET
ejpam-5135	155	7	component	component	NOUN
ejpam-5135	155	8	cj	cj	NOUN
ejpam-5135	155	9	of	of	ADP
ejpam-5135	155	10	g	g	PROPN
ejpam-5135	155	11	having	have	VERB
ejpam-5135	155	12	more	more	ADJ
ejpam-5135	155	13	than	than	ADP
ejpam-5135	155	14	one	one	NUM
ejpam-5135	155	15	vertices	vertex	NOUN
ejpam-5135	155	16	.	.	PUNCT
ejpam-5135	156	1	here	here	ADV
ejpam-5135	156	2	,	,	PUNCT
ejpam-5135	156	3	cj	cj	PROPN
ejpam-5135	156	4	has	have	VERB
ejpam-5135	156	5	a	a	DET
ejpam-5135	156	6	vertex	vertex	NOUN
ejpam-5135	156	7	v	v	NOUN
ejpam-5135	156	8	that	that	PRON
ejpam-5135	156	9	is	be	AUX
ejpam-5135	156	10	not	not	PART
ejpam-5135	156	11	a	a	DET
ejpam-5135	156	12	cut	cut	NOUN
ejpam-5135	156	13	-	-	PUNCT
ejpam-5135	156	14	vertex	vertex	NOUN
ejpam-5135	156	15	of	of	ADP
ejpam-5135	156	16	g	g	PROPN
ejpam-5135	156	17	and	and	CCONJ
ejpam-5135	156	18	v	v	NOUN
ejpam-5135	156	19	is	be	AUX
ejpam-5135	156	20	adjacent	adjacent	ADJ
ejpam-5135	156	21	to	to	ADP
ejpam-5135	156	22	some	some	DET
ejpam-5135	156	23	vertex	vertex	NOUN
ejpam-5135	156	24	,	,	PUNCT
ejpam-5135	156	25	say	say	VERB
ejpam-5135	156	26	w.	w.	PROPN
ejpam-5135	156	27	by	by	ADP
ejpam-5135	156	28	theorem	theorem	NOUN
ejpam-5135	156	29	5	5	NUM
ejpam-5135	156	30	,	,	PUNCT
ejpam-5135	156	31	every	every	DET
ejpam-5135	156	32	τb(g)-open	τb(g)-open	NOUN
ejpam-5135	156	33	set	set	NOUN
ejpam-5135	156	34	containing	contain	VERB
ejpam-5135	156	35	v	v	NOUN
ejpam-5135	156	36	also	also	ADV
ejpam-5135	156	37	contains	contain	VERB
ejpam-5135	156	38	w.	w.	NOUN
ejpam-5135	156	39	this	this	PRON
ejpam-5135	156	40	is	be	AUX
ejpam-5135	156	41	a	a	DET
ejpam-5135	156	42	contradiction	contradiction	NOUN
ejpam-5135	156	43	since	since	SCONJ
ejpam-5135	156	44	by	by	ADP
ejpam-5135	156	45	assumption	assumption	NOUN
ejpam-5135	156	46	that	that	SCONJ
ejpam-5135	156	47	(	(	PUNCT
ejpam-5135	156	48	v	v	NOUN
ejpam-5135	156	49	(	(	PUNCT
ejpam-5135	156	50	g	g	NOUN
ejpam-5135	156	51	)	)	PUNCT
ejpam-5135	156	52	,	,	PUNCT
ejpam-5135	156	53	τb(g	τb(g	NUM
ejpam-5135	156	54	)	)	PUNCT
ejpam-5135	156	55	)	)	PUNCT
ejpam-5135	156	56	is	be	AUX
ejpam-5135	156	57	a	a	DET
ejpam-5135	156	58	hausdorff	hausdorff	NOUN
ejpam-5135	156	59	space	space	NOUN
ejpam-5135	156	60	.	.	PUNCT
ejpam-5135	157	1	hence	hence	ADV
ejpam-5135	157	2	,	,	PUNCT
ejpam-5135	157	3	g	g	PROPN
ejpam-5135	157	4	is	be	AUX
ejpam-5135	157	5	an	an	DET
ejpam-5135	157	6	empty	empty	ADJ
ejpam-5135	157	7	graph	graph	NOUN
ejpam-5135	157	8	.	.	PUNCT
ejpam-5135	158	1	(	(	PUNCT
ejpam-5135	158	2	⇐	⇐	NOUN
ejpam-5135	158	3	)	)	PUNCT
ejpam-5135	158	4	let	let	VERB
ejpam-5135	158	5	g	g	NOUN
ejpam-5135	158	6	be	be	AUX
ejpam-5135	158	7	an	an	DET
ejpam-5135	158	8	empty	empty	ADJ
ejpam-5135	158	9	graph	graph	NOUN
ejpam-5135	158	10	.	.	PUNCT
ejpam-5135	159	1	by	by	ADP
ejpam-5135	159	2	theorem	theorem	NOUN
ejpam-5135	159	3	2	2	NUM
ejpam-5135	159	4	,	,	PUNCT
ejpam-5135	159	5	the	the	DET
ejpam-5135	159	6	generated	generate	VERB
ejpam-5135	159	7	block	block	NOUN
ejpam-5135	159	8	topology	topology	NOUN
ejpam-5135	159	9	is	be	AUX
ejpam-5135	159	10	discrete	discrete	ADJ
ejpam-5135	159	11	and	and	CCONJ
ejpam-5135	159	12	thus	thus	ADV
ejpam-5135	159	13	the	the	DET
ejpam-5135	159	14	conclusion	conclusion	NOUN
ejpam-5135	159	15	follows	follow	VERB
ejpam-5135	159	16	.	.	PUNCT
ejpam-5135	160	1	example	example	NOUN
ejpam-5135	161	1	3	3	X
ejpam-5135	161	2	.	.	X
ejpam-5135	161	3	consider	consider	VERB
ejpam-5135	161	4	the	the	DET
ejpam-5135	161	5	graphs	graph	NOUN
ejpam-5135	161	6	in	in	ADP
ejpam-5135	161	7	figure	figure	NOUN
ejpam-5135	161	8	9	9	NUM
ejpam-5135	161	9	.	.	PUNCT
ejpam-5135	161	10	observe	observe	VERB
ejpam-5135	161	11	that	that	SCONJ
ejpam-5135	161	12	vertex	vertex	NOUN
ejpam-5135	161	13	v	v	NOUN
ejpam-5135	161	14	is	be	AUX
ejpam-5135	161	15	not	not	PART
ejpam-5135	161	16	a	a	DET
ejpam-5135	161	17	cut	cut	NOUN
ejpam-5135	161	18	-	-	PUNCT
ejpam-5135	161	19	vertex	vertex	NOUN
ejpam-5135	161	20	of	of	ADP
ejpam-5135	161	21	g	g	NOUN
ejpam-5135	161	22	that	that	PRON
ejpam-5135	161	23	is	be	AUX
ejpam-5135	161	24	adjacent	adjacent	ADJ
ejpam-5135	161	25	to	to	ADP
ejpam-5135	161	26	w.	w.	PROPN
ejpam-5135	161	27	by	by	ADP
ejpam-5135	161	28	theorem	theorem	NOUN
ejpam-5135	161	29	5	5	NUM
ejpam-5135	161	30	,	,	PUNCT
ejpam-5135	161	31	any	any	DET
ejpam-5135	161	32	τb(g)-open	τb(g)-open	NOUN
ejpam-5135	161	33	containing	contain	VERB
ejpam-5135	161	34	v	v	NOUN
ejpam-5135	161	35	also	also	ADV
ejpam-5135	161	36	contains	contain	VERB
ejpam-5135	161	37	w.	w.	PROPN
ejpam-5135	161	38	hence	hence	PROPN
ejpam-5135	161	39	,	,	PUNCT
ejpam-5135	161	40	the	the	DET
ejpam-5135	161	41	block	block	NOUN
ejpam-5135	161	42	topological	topological	ADJ
ejpam-5135	161	43	space	space	NOUN
ejpam-5135	161	44	of	of	ADP
ejpam-5135	161	45	g	g	PROPN
ejpam-5135	161	46	is	be	AUX
ejpam-5135	161	47	not	not	PART
ejpam-5135	161	48	a	a	DET
ejpam-5135	161	49	hausdorff	hausdorff	NOUN
ejpam-5135	161	50	space	space	NOUN
ejpam-5135	161	51	.	.	PUNCT
ejpam-5135	162	1	on	on	ADP
ejpam-5135	162	2	the	the	DET
ejpam-5135	162	3	other	other	ADJ
ejpam-5135	162	4	hand	hand	NOUN
ejpam-5135	162	5	,	,	PUNCT
ejpam-5135	162	6	h	h	NOUN
ejpam-5135	162	7	is	be	AUX
ejpam-5135	162	8	an	an	DET
ejpam-5135	162	9	empty	empty	ADJ
ejpam-5135	162	10	graph	graph	NOUN
ejpam-5135	162	11	and	and	CCONJ
ejpam-5135	162	12	by	by	ADP
ejpam-5135	162	13	theorem	theorem	NOUN
ejpam-5135	162	14	2	2	NUM
ejpam-5135	162	15	,	,	PUNCT
ejpam-5135	162	16	τb(h	τb(h	NUM
ejpam-5135	162	17	)	)	PUNCT
ejpam-5135	162	18	is	be	AUX
ejpam-5135	162	19	the	the	DET
ejpam-5135	162	20	discrete	discrete	ADJ
ejpam-5135	162	21	topology	topology	NOUN
ejpam-5135	162	22	of	of	ADP
ejpam-5135	162	23	v	v	NOUN
ejpam-5135	162	24	(	(	PUNCT
ejpam-5135	162	25	h	h	NOUN
ejpam-5135	162	26	)	)	PUNCT
ejpam-5135	162	27	.	.	PUNCT
ejpam-5135	163	1	hence	hence	ADV
ejpam-5135	163	2	,	,	PUNCT
ejpam-5135	163	3	every	every	DET
ejpam-5135	163	4	singleton	singleton	NOUN
ejpam-5135	163	5	of	of	ADP
ejpam-5135	163	6	v	v	PROPN
ejpam-5135	163	7	(	(	PUNCT
ejpam-5135	163	8	h	h	NOUN
ejpam-5135	163	9	)	)	PUNCT
ejpam-5135	163	10	is	be	AUX
ejpam-5135	163	11	τb(h)-open	τb(h)-open	NOUN
ejpam-5135	163	12	implying	imply	VERB
ejpam-5135	163	13	further	far	ADV
ejpam-5135	163	14	that	that	SCONJ
ejpam-5135	163	15	the	the	DET
ejpam-5135	163	16	block	block	NOUN
ejpam-5135	163	17	topological	topological	ADJ
ejpam-5135	163	18	space	space	NOUN
ejpam-5135	163	19	of	of	ADP
ejpam-5135	163	20	h	h	NOUN
ejpam-5135	163	21	is	be	AUX
ejpam-5135	163	22	a	a	DET
ejpam-5135	163	23	hausdorff	hausdorff	NOUN
ejpam-5135	163	24	space	space	NOUN
ejpam-5135	163	25	.	.	PUNCT
ejpam-5135	164	1	justine	justine	PROPN
ejpam-5135	164	2	bryle	bryle	PROPN
ejpam-5135	164	3	c.	c.	PROPN
ejpam-5135	164	4	macaso	macaso	PROPN
ejpam-5135	164	5	,	,	PUNCT
ejpam-5135	164	6	cherry	cherry	PROPN
ejpam-5135	164	7	mae	mae	PROPN
ejpam-5135	164	8	r.	r.	PROPN
ejpam-5135	164	9	balingit	balingit	PROPN
ejpam-5135	164	10	/	/	SYM
ejpam-5135	164	11	eur	eur	PROPN
ejpam-5135	164	12	.	.	PUNCT
ejpam-5135	165	1	j.	j.	PROPN
ejpam-5135	165	2	pure	pure	PROPN
ejpam-5135	165	3	appl	appl	PROPN
ejpam-5135	165	4	.	.	PROPN
ejpam-5135	165	5	math	math	PROPN
ejpam-5135	165	6	,	,	PUNCT
ejpam-5135	165	7	17	17	NUM
ejpam-5135	165	8	(	(	PUNCT
ejpam-5135	165	9	2	2	NUM
ejpam-5135	165	10	)	)	PUNCT
ejpam-5135	165	11	(	(	PUNCT
ejpam-5135	165	12	2024	2024	NUM
ejpam-5135	165	13	)	)	PUNCT
ejpam-5135	165	14	,	,	PUNCT
ejpam-5135	165	15	663	663	NUM
ejpam-5135	165	16	-	-	SYM
ejpam-5135	165	17	675	675	NUM
ejpam-5135	165	18	671	671	NUM
ejpam-5135	165	19	v	v	NOUN
ejpam-5135	165	20	w	w	NOUN
ejpam-5135	165	21	g	g	NOUN
ejpam-5135	165	22	:	:	PUNCT
ejpam-5135	165	23	h	h	NOUN
ejpam-5135	165	24	:	:	PUNCT
ejpam-5135	165	25	figure	figure	VERB
ejpam-5135	165	26	9	9	NUM
ejpam-5135	165	27	:	:	PUNCT
ejpam-5135	165	28	graph	graph	NOUN
ejpam-5135	165	29	of	of	ADP
ejpam-5135	165	30	a	a	DET
ejpam-5135	165	31	non	non	ADJ
ejpam-5135	165	32	-	-	ADJ
ejpam-5135	165	33	hausdorff	hausdorff	ADJ
ejpam-5135	165	34	space	space	NOUN
ejpam-5135	165	35	and	and	CCONJ
ejpam-5135	165	36	hausdorff	hausdorff	NOUN
ejpam-5135	165	37	space	space	NOUN
ejpam-5135	165	38	,	,	PUNCT
ejpam-5135	165	39	respectively	respectively	ADV
ejpam-5135	165	40	theorem	theorem	VERB
ejpam-5135	165	41	7	7	NUM
ejpam-5135	165	42	.	.	PUNCT
ejpam-5135	166	1	let	let	VERB
ejpam-5135	166	2	g	g	PRON
ejpam-5135	166	3	be	be	AUX
ejpam-5135	166	4	a	a	DET
ejpam-5135	166	5	graph	graph	NOUN
ejpam-5135	166	6	of	of	ADP
ejpam-5135	166	7	order	order	NOUN
ejpam-5135	166	8	n	n	CCONJ
ejpam-5135	166	9	<	<	X
ejpam-5135	166	10	4	4	NUM
ejpam-5135	166	11	.	.	PUNCT
ejpam-5135	167	1	then	then	ADV
ejpam-5135	167	2	g	g	PROPN
ejpam-5135	167	3	has	have	VERB
ejpam-5135	167	4	no	no	DET
ejpam-5135	167	5	isolated	isolate	VERB
ejpam-5135	167	6	vertices	vertex	NOUN
ejpam-5135	167	7	if	if	SCONJ
ejpam-5135	167	8	and	and	CCONJ
ejpam-5135	167	9	only	only	ADV
ejpam-5135	167	10	if	if	SCONJ
ejpam-5135	167	11	there	there	PRON
ejpam-5135	167	12	exists	exist	VERB
ejpam-5135	167	13	a	a	DET
ejpam-5135	167	14	one	one	NUM
ejpam-5135	167	15	-	-	PUNCT
ejpam-5135	167	16	to	to	ADP
ejpam-5135	167	17	-	-	PUNCT
ejpam-5135	167	18	one	one	NUM
ejpam-5135	167	19	correspondence	correspondence	NOUN
ejpam-5135	167	20	from	from	ADP
ejpam-5135	167	21	(	(	PUNCT
ejpam-5135	167	22	v	v	NOUN
ejpam-5135	167	23	(	(	PUNCT
ejpam-5135	167	24	pn	pn	NOUN
ejpam-5135	167	25	)	)	PUNCT
ejpam-5135	167	26	,	,	PUNCT
ejpam-5135	167	27	τb(pn	τb(pn	ADJ
ejpam-5135	167	28	)	)	PUNCT
ejpam-5135	167	29	)	)	PUNCT
ejpam-5135	167	30	to	to	ADP
ejpam-5135	167	31	(	(	PUNCT
ejpam-5135	167	32	v	v	NOUN
ejpam-5135	167	33	(	(	PUNCT
ejpam-5135	167	34	g	g	NOUN
ejpam-5135	167	35	)	)	PUNCT
ejpam-5135	167	36	,	,	PUNCT
ejpam-5135	167	37	τb(g	τb(g	NUM
ejpam-5135	167	38	)	)	PUNCT
ejpam-5135	167	39	)	)	PUNCT
ejpam-5135	167	40	that	that	PRON
ejpam-5135	167	41	is	be	AUX
ejpam-5135	167	42	continuous	continuous	ADJ
ejpam-5135	167	43	.	.	PUNCT
ejpam-5135	168	1	proof	proof	NOUN
ejpam-5135	168	2	.	.	PUNCT
ejpam-5135	169	1	(	(	PUNCT
ejpam-5135	169	2	⇒	⇒	PROPN
ejpam-5135	169	3	)	)	PUNCT
ejpam-5135	169	4	if	if	SCONJ
ejpam-5135	169	5	g	g	PROPN
ejpam-5135	169	6	is	be	AUX
ejpam-5135	169	7	a	a	DET
ejpam-5135	169	8	graph	graph	NOUN
ejpam-5135	169	9	of	of	ADP
ejpam-5135	169	10	order	order	NOUN
ejpam-5135	169	11	n	n	CCONJ
ejpam-5135	169	12	<	<	X
ejpam-5135	169	13	4	4	NUM
ejpam-5135	169	14	without	without	ADP
ejpam-5135	169	15	isolated	isolated	ADJ
ejpam-5135	169	16	vertices	vertex	NOUN
ejpam-5135	169	17	,	,	PUNCT
ejpam-5135	169	18	then	then	ADV
ejpam-5135	169	19	g	g	PROPN
ejpam-5135	169	20	is	be	AUX
ejpam-5135	169	21	one	one	NUM
ejpam-5135	169	22	of	of	ADP
ejpam-5135	169	23	p2	p2	NOUN
ejpam-5135	169	24	,	,	PUNCT
ejpam-5135	169	25	p3	p3	NOUN
ejpam-5135	169	26	,	,	PUNCT
ejpam-5135	169	27	and	and	CCONJ
ejpam-5135	169	28	k3	k3	PROPN
ejpam-5135	169	29	.	.	PUNCT
ejpam-5135	170	1	for	for	ADP
ejpam-5135	170	2	p2	p2	PROPN
ejpam-5135	170	3	and	and	CCONJ
ejpam-5135	170	4	p3	p3	NOUN
ejpam-5135	170	5	,	,	PUNCT
ejpam-5135	170	6	use	use	VERB
ejpam-5135	170	7	the	the	DET
ejpam-5135	170	8	identity	identity	NOUN
ejpam-5135	170	9	mapping	mapping	NOUN
ejpam-5135	170	10	so	so	SCONJ
ejpam-5135	170	11	that	that	SCONJ
ejpam-5135	170	12	we	we	PRON
ejpam-5135	170	13	arrive	arrive	VERB
ejpam-5135	170	14	the	the	DET
ejpam-5135	170	15	desired	desire	VERB
ejpam-5135	170	16	conclusion	conclusion	NOUN
ejpam-5135	170	17	.	.	PUNCT
ejpam-5135	171	1	for	for	ADP
ejpam-5135	171	2	k3	k3	NOUN
ejpam-5135	171	3	,	,	PUNCT
ejpam-5135	171	4	since	since	SCONJ
ejpam-5135	171	5	|v	|v	PROPN
ejpam-5135	171	6	(	(	PUNCT
ejpam-5135	171	7	k3)|	k3)|	PROPN
ejpam-5135	171	8	=	=	SYM
ejpam-5135	171	9	|v	|v	PROPN
ejpam-5135	171	10	(	(	PUNCT
ejpam-5135	171	11	p3)|	p3)|	NOUN
ejpam-5135	171	12	,	,	PUNCT
ejpam-5135	171	13	put	put	VERB
ejpam-5135	171	14	f	f	PROPN
ejpam-5135	171	15	to	to	PART
ejpam-5135	171	16	be	be	AUX
ejpam-5135	171	17	a	a	DET
ejpam-5135	171	18	one	one	NUM
ejpam-5135	171	19	-	-	PUNCT
ejpam-5135	171	20	to	to	ADP
ejpam-5135	171	21	-	-	PUNCT
ejpam-5135	171	22	one	one	NUM
ejpam-5135	171	23	correspondence	correspondence	NOUN
ejpam-5135	171	24	from	from	ADP
ejpam-5135	171	25	(	(	PUNCT
ejpam-5135	171	26	v	v	NOUN
ejpam-5135	171	27	(	(	PUNCT
ejpam-5135	171	28	p3	p3	PROPN
ejpam-5135	171	29	)	)	PUNCT
ejpam-5135	171	30	,	,	PUNCT
ejpam-5135	171	31	τb(p3	τb(p3	PROPN
ejpam-5135	171	32	)	)	PUNCT
ejpam-5135	171	33	)	)	PUNCT
ejpam-5135	171	34	to	to	ADP
ejpam-5135	171	35	(	(	PUNCT
ejpam-5135	171	36	v	v	X
ejpam-5135	171	37	(	(	PUNCT
ejpam-5135	171	38	k3	k3	PROPN
ejpam-5135	171	39	)	)	PUNCT
ejpam-5135	171	40	,	,	PUNCT
ejpam-5135	171	41	τb(k3	τb(k3	NUM
ejpam-5135	171	42	)	)	PUNCT
ejpam-5135	171	43	)	)	PUNCT
ejpam-5135	171	44	.	.	PUNCT
ejpam-5135	172	1	since	since	SCONJ
ejpam-5135	172	2	,	,	PUNCT
ejpam-5135	172	3	τb(k3	τb(k3	NUM
ejpam-5135	172	4	)	)	PUNCT
ejpam-5135	172	5	=	=	PRON
ejpam-5135	172	6	{	{	PUNCT
ejpam-5135	172	7	∅	∅	NOUN
ejpam-5135	172	8	,	,	PUNCT
ejpam-5135	172	9	v	v	PROPN
ejpam-5135	172	10	(	(	PUNCT
ejpam-5135	172	11	k3	k3	PROPN
ejpam-5135	172	12	)	)	PUNCT
ejpam-5135	172	13	}	}	PUNCT
ejpam-5135	172	14	and	and	CCONJ
ejpam-5135	172	15	f−1(∅	f−1(∅	ADJ
ejpam-5135	172	16	)	)	PUNCT
ejpam-5135	172	17	=	=	SYM
ejpam-5135	172	18	∅	∅	NOUN
ejpam-5135	172	19	and	and	CCONJ
ejpam-5135	172	20	f−1(v	f−1(v	PROPN
ejpam-5135	172	21	(	(	PUNCT
ejpam-5135	172	22	k3	k3	PROPN
ejpam-5135	172	23	)	)	PUNCT
ejpam-5135	172	24	)	)	PUNCT
ejpam-5135	173	1	=	=	SYM
ejpam-5135	173	2	v	v	X
ejpam-5135	173	3	(	(	PUNCT
ejpam-5135	173	4	p3	p3	PROPN
ejpam-5135	173	5	)	)	PUNCT
ejpam-5135	173	6	,	,	PUNCT
ejpam-5135	173	7	f	f	PROPN
ejpam-5135	173	8	is	be	AUX
ejpam-5135	173	9	continuous	continuous	ADJ
ejpam-5135	173	10	.	.	PUNCT
ejpam-5135	174	1	(	(	PUNCT
ejpam-5135	174	2	⇐	⇐	NOUN
ejpam-5135	174	3	)	)	PUNCT
ejpam-5135	174	4	let	let	VERB
ejpam-5135	174	5	f	f	PRON
ejpam-5135	174	6	be	be	AUX
ejpam-5135	174	7	a	a	DET
ejpam-5135	174	8	continuous	continuous	ADJ
ejpam-5135	174	9	one	one	NUM
ejpam-5135	174	10	-	-	PUNCT
ejpam-5135	174	11	to	to	ADP
ejpam-5135	174	12	-	-	PUNCT
ejpam-5135	174	13	one	one	NUM
ejpam-5135	174	14	correspondence	correspondence	NOUN
ejpam-5135	174	15	from	from	ADP
ejpam-5135	174	16	(	(	PUNCT
ejpam-5135	174	17	v	v	NOUN
ejpam-5135	174	18	(	(	PUNCT
ejpam-5135	174	19	pn	pn	NOUN
ejpam-5135	174	20	)	)	PUNCT
ejpam-5135	174	21	,	,	PUNCT
ejpam-5135	174	22	τb(pn	τb(pn	ADJ
ejpam-5135	174	23	)	)	PUNCT
ejpam-5135	174	24	)	)	PUNCT
ejpam-5135	174	25	to	to	ADP
ejpam-5135	174	26	(	(	PUNCT
ejpam-5135	174	27	v	v	NOUN
ejpam-5135	174	28	(	(	PUNCT
ejpam-5135	174	29	g	g	NOUN
ejpam-5135	174	30	)	)	PUNCT
ejpam-5135	174	31	,	,	PUNCT
ejpam-5135	174	32	τb(g	τb(g	NUM
ejpam-5135	174	33	)	)	PUNCT
ejpam-5135	174	34	)	)	PUNCT
ejpam-5135	174	35	.	.	PUNCT
ejpam-5135	175	1	suppose	suppose	VERB
ejpam-5135	175	2	that	that	SCONJ
ejpam-5135	175	3	g	g	PROPN
ejpam-5135	175	4	has	have	VERB
ejpam-5135	175	5	an	an	DET
ejpam-5135	175	6	isolated	isolated	ADJ
ejpam-5135	175	7	vertices	vertex	NOUN
ejpam-5135	175	8	.	.	PUNCT
ejpam-5135	176	1	case	case	NOUN
ejpam-5135	176	2	1	1	NUM
ejpam-5135	176	3	:	:	PUNCT
ejpam-5135	176	4	if	if	SCONJ
ejpam-5135	176	5	n	n	PROPN
ejpam-5135	176	6	=	=	SYM
ejpam-5135	176	7	2	2	NUM
ejpam-5135	176	8	,	,	PUNCT
ejpam-5135	176	9	then	then	ADV
ejpam-5135	176	10	τb(g	τb(g	PUNCT
ejpam-5135	176	11	)	)	PUNCT
ejpam-5135	176	12	is	be	AUX
ejpam-5135	176	13	discrete	discrete	ADJ
ejpam-5135	176	14	.	.	PUNCT
ejpam-5135	177	1	let	let	VERB
ejpam-5135	177	2	w	w	NOUN
ejpam-5135	177	3	be	be	AUX
ejpam-5135	177	4	an	an	DET
ejpam-5135	177	5	isolated	isolated	ADJ
ejpam-5135	177	6	vertex	vertex	NOUN
ejpam-5135	177	7	of	of	ADP
ejpam-5135	177	8	g.	g.	PROPN
ejpam-5135	177	9	then	then	ADV
ejpam-5135	177	10	f−1({w	f−1({w	NOUN
ejpam-5135	177	11	}	}	PUNCT
ejpam-5135	177	12	)	)	PUNCT
ejpam-5135	177	13	is	be	AUX
ejpam-5135	177	14	a	a	DET
ejpam-5135	177	15	singleton	singleton	NOUN
ejpam-5135	177	16	subset	subset	NOUN
ejpam-5135	177	17	of	of	ADP
ejpam-5135	177	18	v	v	NOUN
ejpam-5135	177	19	(	(	PUNCT
ejpam-5135	177	20	p2	p2	PROPN
ejpam-5135	177	21	)	)	PUNCT
ejpam-5135	177	22	.	.	PUNCT
ejpam-5135	178	1	since	since	SCONJ
ejpam-5135	178	2	by	by	ADP
ejpam-5135	178	3	theorem	theorem	NOUN
ejpam-5135	178	4	3	3	NUM
ejpam-5135	178	5	,	,	PUNCT
ejpam-5135	178	6	τb(p2	τb(p2	NUM
ejpam-5135	178	7	)	)	PUNCT
ejpam-5135	178	8	is	be	AUX
ejpam-5135	178	9	indiscrete	indiscrete	ADJ
ejpam-5135	178	10	,	,	PUNCT
ejpam-5135	178	11	f	f	PROPN
ejpam-5135	178	12	−1({w	−1({w	PROPN
ejpam-5135	178	13	}	}	PUNCT
ejpam-5135	178	14	)	)	PUNCT
ejpam-5135	179	1	is	be	AUX
ejpam-5135	179	2	not	not	PART
ejpam-5135	179	3	τb(p2)-open	τb(p2)-open	ADJ
ejpam-5135	179	4	.	.	PUNCT
ejpam-5135	180	1	this	this	PRON
ejpam-5135	180	2	is	be	AUX
ejpam-5135	180	3	a	a	DET
ejpam-5135	180	4	contradiction	contradiction	NOUN
ejpam-5135	180	5	since	since	SCONJ
ejpam-5135	180	6	f	f	PROPN
ejpam-5135	180	7	is	be	AUX
ejpam-5135	180	8	continuous	continuous	ADJ
ejpam-5135	180	9	.	.	PUNCT
ejpam-5135	181	1	hence	hence	ADV
ejpam-5135	181	2	,	,	PUNCT
ejpam-5135	181	3	g	g	PROPN
ejpam-5135	181	4	must	must	AUX
ejpam-5135	181	5	not	not	PART
ejpam-5135	181	6	have	have	VERB
ejpam-5135	181	7	an	an	DET
ejpam-5135	181	8	isolated	isolated	ADJ
ejpam-5135	181	9	vertex	vertex	NOUN
ejpam-5135	181	10	.	.	PUNCT
ejpam-5135	182	1	case	case	NOUN
ejpam-5135	182	2	2	2	NUM
ejpam-5135	182	3	:	:	PUNCT
ejpam-5135	182	4	let	let	VERB
ejpam-5135	182	5	w	w	PART
ejpam-5135	182	6	be	be	AUX
ejpam-5135	182	7	an	an	DET
ejpam-5135	182	8	isolated	isolated	ADJ
ejpam-5135	182	9	vertex	vertex	NOUN
ejpam-5135	182	10	of	of	ADP
ejpam-5135	182	11	g.	g.	PROPN
ejpam-5135	182	12	then	then	ADV
ejpam-5135	182	13	for	for	ADP
ejpam-5135	182	14	all	all	PRON
ejpam-5135	182	15	v	v	ADP
ejpam-5135	182	16	∈	∈	NUM
ejpam-5135	182	17	v	v	NOUN
ejpam-5135	182	18	(	(	PUNCT
ejpam-5135	182	19	g	g	NOUN
ejpam-5135	182	20	)	)	PUNCT
ejpam-5135	182	21	∖	∖	NOUN
ejpam-5135	182	22	{	{	PUNCT
ejpam-5135	182	23	w	w	PROPN
ejpam-5135	182	24	}	}	PUNCT
ejpam-5135	182	25	,	,	PUNCT
ejpam-5135	182	26	wv	wv	PROPN
ejpam-5135	182	27	/∈	/∈	PUNCT
ejpam-5135	182	28	e(g	e(g	PROPN
ejpam-5135	182	29	)	)	PUNCT
ejpam-5135	182	30	.	.	PUNCT
ejpam-5135	183	1	also	also	ADV
ejpam-5135	183	2	,	,	PUNCT
ejpam-5135	183	3	f−1(w	f−1(w	PROPN
ejpam-5135	183	4	)	)	PUNCT
ejpam-5135	183	5	must	must	AUX
ejpam-5135	183	6	be	be	AUX
ejpam-5135	183	7	a	a	DET
ejpam-5135	183	8	cut	cut	NOUN
ejpam-5135	183	9	-	-	PUNCT
ejpam-5135	183	10	vertex	vertex	NOUN
ejpam-5135	183	11	of	of	ADP
ejpam-5135	183	12	p3	p3	PROPN
ejpam-5135	183	13	since	since	SCONJ
ejpam-5135	183	14	by	by	ADP
ejpam-5135	183	15	assumption	assumption	NOUN
ejpam-5135	183	16	f	f	PROPN
ejpam-5135	183	17	is	be	AUX
ejpam-5135	183	18	continuous	continuous	ADJ
ejpam-5135	183	19	.	.	PUNCT
ejpam-5135	184	1	subcase	subcase	PROPN
ejpam-5135	184	2	1	1	NUM
ejpam-5135	184	3	:	:	PUNCT
ejpam-5135	184	4	if	if	SCONJ
ejpam-5135	184	5	v	v	NOUN
ejpam-5135	184	6	is	be	AUX
ejpam-5135	184	7	an	an	DET
ejpam-5135	184	8	isolated	isolated	ADJ
ejpam-5135	184	9	vertex	vertex	NOUN
ejpam-5135	184	10	of	of	ADP
ejpam-5135	184	11	g	g	NOUN
ejpam-5135	184	12	,	,	PUNCT
ejpam-5135	184	13	then	then	ADV
ejpam-5135	184	14	g	g	PROPN
ejpam-5135	184	15	must	must	AUX
ejpam-5135	184	16	be	be	AUX
ejpam-5135	184	17	an	an	DET
ejpam-5135	184	18	empty	empty	ADJ
ejpam-5135	184	19	graph	graph	NOUN
ejpam-5135	184	20	.	.	PUNCT
ejpam-5135	185	1	this	this	PRON
ejpam-5135	185	2	means	mean	VERB
ejpam-5135	185	3	that	that	SCONJ
ejpam-5135	185	4	τb(g	τb(g	PUNCT
ejpam-5135	185	5	)	)	PUNCT
ejpam-5135	185	6	is	be	AUX
ejpam-5135	185	7	the	the	DET
ejpam-5135	185	8	discrete	discrete	ADJ
ejpam-5135	185	9	topology	topology	NOUN
ejpam-5135	185	10	.	.	PUNCT
ejpam-5135	186	1	let	let	VERB
ejpam-5135	186	2	u	u	PRON
ejpam-5135	186	3	be	be	AUX
ejpam-5135	186	4	a	a	DET
ejpam-5135	186	5	vertex	vertex	NOUN
ejpam-5135	186	6	in	in	ADP
ejpam-5135	186	7	g	g	PROPN
ejpam-5135	186	8	such	such	ADJ
ejpam-5135	186	9	that	that	DET
ejpam-5135	186	10	f−1(u	f−1(u	PROPN
ejpam-5135	186	11	)	)	PUNCT
ejpam-5135	186	12	is	be	AUX
ejpam-5135	186	13	an	an	DET
ejpam-5135	186	14	end	end	NOUN
ejpam-5135	186	15	-	-	PUNCT
ejpam-5135	186	16	vertex	vertex	NOUN
ejpam-5135	186	17	of	of	ADP
ejpam-5135	186	18	p3	p3	PROPN
ejpam-5135	186	19	.	.	PUNCT
ejpam-5135	187	1	here	here	ADV
ejpam-5135	187	2	,	,	PUNCT
ejpam-5135	187	3	{	{	PUNCT
ejpam-5135	187	4	u	u	NOUN
ejpam-5135	187	5	}	}	PUNCT
ejpam-5135	187	6	is	be	AUX
ejpam-5135	187	7	τb(g)-open	τb(g)-open	ADJ
ejpam-5135	187	8	and	and	CCONJ
ejpam-5135	187	9	f−1({u	f−1({u	PROPN
ejpam-5135	187	10	}	}	PUNCT
ejpam-5135	187	11	)	)	PUNCT
ejpam-5135	187	12	is	be	AUX
ejpam-5135	187	13	not	not	PART
ejpam-5135	187	14	a	a	DET
ejpam-5135	187	15	τb(p3)-open	τb(p3)-open	ADJ
ejpam-5135	187	16	set	set	NOUN
ejpam-5135	187	17	.	.	PUNCT
ejpam-5135	188	1	this	this	PRON
ejpam-5135	188	2	is	be	AUX
ejpam-5135	188	3	a	a	DET
ejpam-5135	188	4	contradiction	contradiction	NOUN
ejpam-5135	188	5	since	since	SCONJ
ejpam-5135	188	6	f	f	PROPN
ejpam-5135	188	7	is	be	AUX
ejpam-5135	188	8	continuous	continuous	ADJ
ejpam-5135	188	9	.	.	PUNCT
ejpam-5135	189	1	subcase2	subcase2	PROPN
ejpam-5135	189	2	:	:	PUNCT
ejpam-5135	190	1	if	if	SCONJ
ejpam-5135	190	2	v	v	NOUN
ejpam-5135	190	3	is	be	AUX
ejpam-5135	190	4	not	not	PART
ejpam-5135	190	5	an	an	DET
ejpam-5135	190	6	isolated	isolated	ADJ
ejpam-5135	190	7	vertex	vertex	NOUN
ejpam-5135	190	8	,	,	PUNCT
ejpam-5135	190	9	then	then	ADV
ejpam-5135	190	10	v	v	NOUN
ejpam-5135	190	11	must	must	AUX
ejpam-5135	190	12	be	be	AUX
ejpam-5135	190	13	adjacent	adjacent	ADJ
ejpam-5135	190	14	to	to	ADP
ejpam-5135	190	15	some	some	DET
ejpam-5135	190	16	vertex	vertex	NOUN
ejpam-5135	190	17	,	,	PUNCT
ejpam-5135	190	18	say	say	VERB
ejpam-5135	190	19	u.	u.	NOUN
ejpam-5135	190	20	in	in	ADP
ejpam-5135	190	21	this	this	DET
ejpam-5135	190	22	case	case	NOUN
ejpam-5135	190	23	,	,	PUNCT
ejpam-5135	190	24	g[{v	g[{v	PROPN
ejpam-5135	190	25	,	,	PUNCT
ejpam-5135	190	26	u	u	NOUN
ejpam-5135	190	27	}	}	PUNCT
ejpam-5135	190	28	]	]	PUNCT
ejpam-5135	190	29	is	be	AUX
ejpam-5135	190	30	a	a	DET
ejpam-5135	190	31	block	block	NOUN
ejpam-5135	190	32	of	of	ADP
ejpam-5135	190	33	g	g	NOUN
ejpam-5135	190	34	implying	imply	VERB
ejpam-5135	190	35	further	far	ADV
ejpam-5135	190	36	that	that	SCONJ
ejpam-5135	190	37	{	{	PUNCT
ejpam-5135	190	38	v	v	NOUN
ejpam-5135	190	39	,	,	PUNCT
ejpam-5135	190	40	u	u	NOUN
ejpam-5135	190	41	}	}	PUNCT
ejpam-5135	190	42	is	be	AUX
ejpam-5135	190	43	τb(g)-open	τb(g)-open	PROPN
ejpam-5135	190	44	.	.	PUNCT
ejpam-5135	191	1	since	since	SCONJ
ejpam-5135	191	2	f	f	PROPN
ejpam-5135	191	3	is	be	AUX
ejpam-5135	191	4	bijective	bijective	ADJ
ejpam-5135	191	5	,	,	PUNCT
ejpam-5135	191	6	f−1({v	f−1({v	NOUN
ejpam-5135	191	7	,	,	PUNCT
ejpam-5135	191	8	u	u	NOUN
ejpam-5135	191	9	}	}	PUNCT
ejpam-5135	191	10	)	)	PUNCT
ejpam-5135	191	11	=	=	SYM
ejpam-5135	191	12	f−1({v	f−1({v	PROPN
ejpam-5135	191	13	}	}	PUNCT
ejpam-5135	191	14	)	)	PUNCT
ejpam-5135	191	15	∪	∪	ADP
ejpam-5135	191	16	f−1({u	f−1({u	NOUN
ejpam-5135	191	17	}	}	PUNCT
ejpam-5135	191	18	)	)	PUNCT
ejpam-5135	191	19	.	.	PUNCT
ejpam-5135	192	1	note	note	VERB
ejpam-5135	192	2	that	that	SCONJ
ejpam-5135	192	3	f−1(w	f−1(w	PROPN
ejpam-5135	192	4	)	)	PUNCT
ejpam-5135	192	5	is	be	AUX
ejpam-5135	192	6	a	a	DET
ejpam-5135	192	7	cut	cut	NOUN
ejpam-5135	192	8	-	-	PUNCT
ejpam-5135	192	9	vertex	vertex	NOUN
ejpam-5135	192	10	of	of	ADP
ejpam-5135	192	11	p3	p3	PROPN
ejpam-5135	192	12	,	,	PUNCT
ejpam-5135	192	13	and	and	CCONJ
ejpam-5135	192	14	so	so	ADV
ejpam-5135	192	15	f−1(v	f−1(v	PROPN
ejpam-5135	192	16	)	)	PUNCT
ejpam-5135	192	17	and	and	CCONJ
ejpam-5135	192	18	f−1(u	f−1(u	NOUN
ejpam-5135	192	19	)	)	PUNCT
ejpam-5135	192	20	are	be	AUX
ejpam-5135	192	21	end	end	NOUN
ejpam-5135	192	22	-	-	PUNCT
ejpam-5135	192	23	vertices	vertex	NOUN
ejpam-5135	192	24	of	of	ADP
ejpam-5135	192	25	p3	p3	PROPN
ejpam-5135	192	26	.	.	PUNCT
ejpam-5135	193	1	by	by	ADP
ejpam-5135	193	2	theorem	theorem	NOUN
ejpam-5135	193	3	1	1	NUM
ejpam-5135	193	4	,	,	PUNCT
ejpam-5135	193	5	f−1({v	f−1({v	NOUN
ejpam-5135	193	6	,	,	PUNCT
ejpam-5135	193	7	u	u	NOUN
ejpam-5135	193	8	}	}	PUNCT
ejpam-5135	193	9	)	)	PUNCT
ejpam-5135	193	10	is	be	AUX
ejpam-5135	193	11	not	not	PART
ejpam-5135	193	12	τb(p3)-open	τb(p3)-open	ADJ
ejpam-5135	193	13	,	,	PUNCT
ejpam-5135	193	14	a	a	DET
ejpam-5135	193	15	contradiction	contradiction	NOUN
ejpam-5135	193	16	.	.	PUNCT
ejpam-5135	194	1	remark	remark	NOUN
ejpam-5135	194	2	3	3	NUM
ejpam-5135	194	3	.	.	PUNCT
ejpam-5135	195	1	if	if	SCONJ
ejpam-5135	195	2	g	g	PROPN
ejpam-5135	195	3	=	=	SYM
ejpam-5135	195	4	p1	p1	PROPN
ejpam-5135	195	5	,	,	PUNCT
ejpam-5135	195	6	then	then	ADV
ejpam-5135	195	7	the	the	DET
ejpam-5135	195	8	identity	identity	NOUN
ejpam-5135	195	9	map	map	NOUN
ejpam-5135	195	10	satisfies	satisfy	VERB
ejpam-5135	195	11	the	the	DET
ejpam-5135	195	12	above	above	ADJ
ejpam-5135	195	13	theorem	theorem	PROPN
ejpam-5135	195	14	.	.	PUNCT
ejpam-5135	196	1	justine	justine	PROPN
ejpam-5135	196	2	bryle	bryle	PROPN
ejpam-5135	196	3	c.	c.	PROPN
ejpam-5135	196	4	macaso	macaso	PROPN
ejpam-5135	196	5	,	,	PUNCT
ejpam-5135	196	6	cherry	cherry	PROPN
ejpam-5135	196	7	mae	mae	PROPN
ejpam-5135	196	8	r.	r.	PROPN
ejpam-5135	196	9	balingit	balingit	PROPN
ejpam-5135	196	10	/	/	SYM
ejpam-5135	196	11	eur	eur	PROPN
ejpam-5135	196	12	.	.	PUNCT
ejpam-5135	197	1	j.	j.	PROPN
ejpam-5135	197	2	pure	pure	PROPN
ejpam-5135	197	3	appl	appl	PROPN
ejpam-5135	197	4	.	.	PROPN
ejpam-5135	197	5	math	math	PROPN
ejpam-5135	197	6	,	,	PUNCT
ejpam-5135	197	7	17	17	NUM
ejpam-5135	197	8	(	(	PUNCT
ejpam-5135	197	9	2	2	NUM
ejpam-5135	197	10	)	)	PUNCT
ejpam-5135	197	11	(	(	PUNCT
ejpam-5135	197	12	2024	2024	NUM
ejpam-5135	197	13	)	)	PUNCT
ejpam-5135	197	14	,	,	PUNCT
ejpam-5135	197	15	663	663	NUM
ejpam-5135	197	16	-	-	SYM
ejpam-5135	197	17	675	675	NUM
ejpam-5135	197	18	672	672	NUM
ejpam-5135	197	19	theorem	theorem	NOUN
ejpam-5135	197	20	8	8	NUM
ejpam-5135	197	21	.	.	PUNCT
ejpam-5135	198	1	let	let	VERB
ejpam-5135	198	2	g	g	PRON
ejpam-5135	198	3	be	be	AUX
ejpam-5135	198	4	a	a	DET
ejpam-5135	198	5	graph	graph	NOUN
ejpam-5135	198	6	of	of	ADP
ejpam-5135	198	7	order	order	NOUN
ejpam-5135	198	8	n	n	PRON
ejpam-5135	198	9	≥	≥	NOUN
ejpam-5135	198	10	4	4	NUM
ejpam-5135	198	11	.	.	PUNCT
ejpam-5135	199	1	then	then	ADV
ejpam-5135	199	2	g	g	PROPN
ejpam-5135	199	3	has	have	AUX
ejpam-5135	199	4	at	at	ADV
ejpam-5135	199	5	least	least	ADV
ejpam-5135	199	6	two	two	NUM
ejpam-5135	199	7	nonadjacent	nonadjacent	ADJ
ejpam-5135	199	8	edges	edge	NOUN
ejpam-5135	199	9	if	if	SCONJ
ejpam-5135	199	10	and	and	CCONJ
ejpam-5135	199	11	only	only	ADV
ejpam-5135	199	12	if	if	SCONJ
ejpam-5135	199	13	there	there	PRON
ejpam-5135	199	14	is	be	VERB
ejpam-5135	199	15	a	a	DET
ejpam-5135	199	16	one	one	NUM
ejpam-5135	199	17	-	-	PUNCT
ejpam-5135	199	18	to	to	ADP
ejpam-5135	199	19	-	-	PUNCT
ejpam-5135	199	20	one	one	NUM
ejpam-5135	199	21	correspondence	correspondence	NOUN
ejpam-5135	199	22	from	from	ADP
ejpam-5135	199	23	(	(	PUNCT
ejpam-5135	199	24	v	v	NOUN
ejpam-5135	199	25	(	(	PUNCT
ejpam-5135	199	26	pn	pn	NOUN
ejpam-5135	199	27	)	)	PUNCT
ejpam-5135	199	28	,	,	PUNCT
ejpam-5135	199	29	τb(pn	τb(pn	ADJ
ejpam-5135	199	30	)	)	PUNCT
ejpam-5135	199	31	)	)	PUNCT
ejpam-5135	199	32	to	to	ADP
ejpam-5135	199	33	(	(	PUNCT
ejpam-5135	199	34	v	v	NOUN
ejpam-5135	199	35	(	(	PUNCT
ejpam-5135	199	36	g	g	NOUN
ejpam-5135	199	37	)	)	PUNCT
ejpam-5135	199	38	,	,	PUNCT
ejpam-5135	199	39	τb(g	τb(g	NUM
ejpam-5135	199	40	)	)	PUNCT
ejpam-5135	199	41	)	)	PUNCT
ejpam-5135	199	42	that	that	PRON
ejpam-5135	199	43	is	be	AUX
ejpam-5135	199	44	continuous	continuous	ADJ
ejpam-5135	199	45	.	.	PUNCT
ejpam-5135	200	1	proof	proof	NOUN
ejpam-5135	200	2	.	.	PUNCT
ejpam-5135	201	1	(	(	PUNCT
ejpam-5135	201	2	⇒	⇒	PROPN
ejpam-5135	201	3	)	)	PUNCT
ejpam-5135	201	4	let	let	VERB
ejpam-5135	201	5	g	g	NOUN
ejpam-5135	201	6	be	be	AUX
ejpam-5135	201	7	a	a	DET
ejpam-5135	201	8	graph	graph	NOUN
ejpam-5135	201	9	of	of	ADP
ejpam-5135	201	10	order	order	NOUN
ejpam-5135	201	11	n	n	PRON
ejpam-5135	201	12	≥	≥	NOUN
ejpam-5135	201	13	4	4	NUM
ejpam-5135	201	14	such	such	ADJ
ejpam-5135	201	15	that	that	SCONJ
ejpam-5135	201	16	g	g	PROPN
ejpam-5135	201	17	has	have	VERB
ejpam-5135	201	18	at	at	ADV
ejpam-5135	201	19	least	least	ADV
ejpam-5135	201	20	two	two	NUM
ejpam-5135	201	21	non	non	ADJ
ejpam-5135	201	22	-	-	ADJ
ejpam-5135	201	23	adjacent	adjacent	ADJ
ejpam-5135	201	24	edges	edge	NOUN
ejpam-5135	201	25	.	.	PUNCT
ejpam-5135	202	1	since	since	SCONJ
ejpam-5135	202	2	g	g	PROPN
ejpam-5135	202	3	has	have	VERB
ejpam-5135	202	4	at	at	ADV
ejpam-5135	202	5	least	least	ADJ
ejpam-5135	202	6	1	1	NUM
ejpam-5135	202	7	nontrivial	nontrivial	ADJ
ejpam-5135	202	8	component	component	NOUN
ejpam-5135	202	9	,	,	PUNCT
ejpam-5135	202	10	there	there	PRON
ejpam-5135	202	11	exists	exist	VERB
ejpam-5135	202	12	at	at	ADP
ejpam-5135	202	13	least	least	ADV
ejpam-5135	202	14	two	two	NUM
ejpam-5135	202	15	vertices	vertex	NOUN
ejpam-5135	202	16	that	that	PRON
ejpam-5135	202	17	are	be	AUX
ejpam-5135	202	18	not	not	PART
ejpam-5135	202	19	cut	cut	VERB
ejpam-5135	202	20	-	-	PUNCT
ejpam-5135	202	21	vertices	vertex	NOUN
ejpam-5135	202	22	and	and	CCONJ
ejpam-5135	202	23	non	non	ADJ
ejpam-5135	202	24	-	-	ADJ
ejpam-5135	202	25	isolated	isolated	ADJ
ejpam-5135	202	26	vertices	vertex	NOUN
ejpam-5135	202	27	in	in	ADP
ejpam-5135	202	28	that	that	DET
ejpam-5135	202	29	component	component	NOUN
ejpam-5135	202	30	.	.	PUNCT
ejpam-5135	203	1	denote	denote	VERB
ejpam-5135	203	2	the	the	DET
ejpam-5135	203	3	vertices	vertex	NOUN
ejpam-5135	203	4	of	of	ADP
ejpam-5135	203	5	g	g	NOUN
ejpam-5135	203	6	by	by	ADP
ejpam-5135	203	7	{	{	PUNCT
ejpam-5135	203	8	v1	v1	NOUN
ejpam-5135	203	9	,	,	PUNCT
ejpam-5135	203	10	v2	v2	PROPN
ejpam-5135	203	11	,	,	PUNCT
ejpam-5135	203	12	·	·	PUNCT
ejpam-5135	203	13	·	·	PUNCT
ejpam-5135	203	14	·	·	PUNCT
ejpam-5135	203	15	,	,	PUNCT
ejpam-5135	203	16	vn	vn	INTJ
ejpam-5135	203	17	}	}	PUNCT
ejpam-5135	203	18	such	such	ADJ
ejpam-5135	203	19	that	that	DET
ejpam-5135	203	20	v1	v1	NOUN
ejpam-5135	203	21	and	and	CCONJ
ejpam-5135	203	22	vn	vn	PROPN
ejpam-5135	203	23	are	be	AUX
ejpam-5135	203	24	not	not	PART
ejpam-5135	203	25	cut	cut	VERB
ejpam-5135	203	26	-	-	PUNCT
ejpam-5135	203	27	vertices	vertex	NOUN
ejpam-5135	203	28	nor	nor	CCONJ
ejpam-5135	203	29	isolated	isolated	ADJ
ejpam-5135	203	30	vertices	vertex	NOUN
ejpam-5135	203	31	of	of	ADP
ejpam-5135	203	32	g	g	PROPN
ejpam-5135	203	33	and	and	CCONJ
ejpam-5135	203	34	v1v2	v1v2	PROPN
ejpam-5135	203	35	,	,	PUNCT
ejpam-5135	203	36	vn−1vn	vn−1vn	NUM
ejpam-5135	203	37	∈	∈	PROPN
ejpam-5135	203	38	e(g	e(g	PROPN
ejpam-5135	203	39	)	)	PUNCT
ejpam-5135	203	40	.	.	PUNCT
ejpam-5135	204	1	let	let	VERB
ejpam-5135	204	2	pn	pn	PART
ejpam-5135	204	3	be	be	AUX
ejpam-5135	204	4	a	a	DET
ejpam-5135	204	5	path	path	NOUN
ejpam-5135	204	6	such	such	ADJ
ejpam-5135	204	7	that	that	DET
ejpam-5135	204	8	v	v	NOUN
ejpam-5135	204	9	(	(	PUNCT
ejpam-5135	204	10	pn	pn	NOUN
ejpam-5135	204	11	)	)	PUNCT
ejpam-5135	204	12	=	=	SYM
ejpam-5135	204	13	{	{	PUNCT
ejpam-5135	204	14	a1	a1	PROPN
ejpam-5135	204	15	,	,	PUNCT
ejpam-5135	204	16	a2	a2	PROPN
ejpam-5135	204	17	,	,	PUNCT
ejpam-5135	204	18	·	·	PUNCT
ejpam-5135	204	19	·	·	PUNCT
ejpam-5135	204	20	·	·	PUNCT
ejpam-5135	204	21	,	,	PUNCT
ejpam-5135	204	22	an	an	PRON
ejpam-5135	204	23	}	}	PUNCT
ejpam-5135	204	24	and	and	CCONJ
ejpam-5135	204	25	e(pn	e(pn	NUM
ejpam-5135	204	26	)	)	PUNCT
ejpam-5135	204	27	=	=	PRON
ejpam-5135	204	28	{	{	PUNCT
ejpam-5135	204	29	aiai+1	aiai+1	NOUN
ejpam-5135	204	30	:	:	PUNCT
ejpam-5135	205	1	i	i	NOUN
ejpam-5135	205	2	=	=	NOUN
ejpam-5135	205	3	1	1	NUM
ejpam-5135	205	4	,	,	PUNCT
ejpam-5135	205	5	2	2	NUM
ejpam-5135	205	6	,	,	PUNCT
ejpam-5135	205	7	·	·	PUNCT
ejpam-5135	205	8	·	·	PUNCT
ejpam-5135	205	9	·	·	PUNCT
ejpam-5135	205	10	,	,	PUNCT
ejpam-5135	205	11	n−	n−	NOUN
ejpam-5135	205	12	1	1	NUM
ejpam-5135	205	13	}	}	PUNCT
ejpam-5135	205	14	.	.	PUNCT
ejpam-5135	206	1	now	now	ADV
ejpam-5135	206	2	,	,	PUNCT
ejpam-5135	206	3	define	define	VERB
ejpam-5135	206	4	f	f	X
ejpam-5135	206	5	:	:	PUNCT
ejpam-5135	206	6	(	(	PUNCT
ejpam-5135	206	7	v	v	X
ejpam-5135	206	8	(	(	PUNCT
ejpam-5135	206	9	pn	pn	NOUN
ejpam-5135	206	10	)	)	PUNCT
ejpam-5135	206	11	,	,	PUNCT
ejpam-5135	206	12	τb(pn	τb(pn	ADJ
ejpam-5135	206	13	)	)	PUNCT
ejpam-5135	206	14	)	)	PUNCT
ejpam-5135	207	1	→	→	PUNCT
ejpam-5135	207	2	(	(	PUNCT
ejpam-5135	207	3	v	v	NOUN
ejpam-5135	207	4	(	(	PUNCT
ejpam-5135	207	5	g	g	NOUN
ejpam-5135	207	6	)	)	PUNCT
ejpam-5135	207	7	,	,	PUNCT
ejpam-5135	207	8	τb(g	τb(g	NUM
ejpam-5135	207	9	)	)	PUNCT
ejpam-5135	207	10	)	)	PUNCT
ejpam-5135	207	11	by	by	ADP
ejpam-5135	207	12	f(ai	f(ai	PROPN
ejpam-5135	207	13	)	)	PUNCT
ejpam-5135	207	14	=	=	SYM
ejpam-5135	207	15	vi	vi	PROPN
ejpam-5135	207	16	.	.	PUNCT
ejpam-5135	207	17	obviously	obviously	ADV
ejpam-5135	207	18	,	,	PUNCT
ejpam-5135	207	19	f	f	PROPN
ejpam-5135	207	20	is	be	AUX
ejpam-5135	207	21	a	a	DET
ejpam-5135	207	22	one	one	NUM
ejpam-5135	207	23	-	-	PUNCT
ejpam-5135	207	24	to	to	ADP
ejpam-5135	207	25	-	-	PUNCT
ejpam-5135	207	26	one	one	NUM
ejpam-5135	207	27	correspondence	correspondence	NOUN
ejpam-5135	207	28	from	from	ADP
ejpam-5135	207	29	(	(	PUNCT
ejpam-5135	207	30	v	v	NOUN
ejpam-5135	207	31	(	(	PUNCT
ejpam-5135	207	32	pn	pn	NOUN
ejpam-5135	207	33	)	)	PUNCT
ejpam-5135	207	34	,	,	PUNCT
ejpam-5135	207	35	τb(pn	τb(pn	ADJ
ejpam-5135	207	36	)	)	PUNCT
ejpam-5135	207	37	)	)	PUNCT
ejpam-5135	207	38	to	to	ADP
ejpam-5135	207	39	(	(	PUNCT
ejpam-5135	207	40	v	v	NOUN
ejpam-5135	207	41	(	(	PUNCT
ejpam-5135	207	42	g	g	NOUN
ejpam-5135	207	43	)	)	PUNCT
ejpam-5135	207	44	,	,	PUNCT
ejpam-5135	207	45	τb(g	τb(g	NUM
ejpam-5135	207	46	)	)	PUNCT
ejpam-5135	207	47	)	)	PUNCT
ejpam-5135	207	48	.	.	PUNCT
ejpam-5135	208	1	it	it	PRON
ejpam-5135	208	2	remains	remain	VERB
ejpam-5135	208	3	to	to	PART
ejpam-5135	208	4	show	show	VERB
ejpam-5135	208	5	that	that	SCONJ
ejpam-5135	208	6	f	f	PROPN
ejpam-5135	208	7	is	be	AUX
ejpam-5135	208	8	continuous	continuous	ADJ
ejpam-5135	208	9	.	.	PUNCT
ejpam-5135	209	1	let	let	VERB
ejpam-5135	209	2	a	a	PRON
ejpam-5135	209	3	be	be	AUX
ejpam-5135	209	4	τb(g)-open	τb(g)-open	NOUN
ejpam-5135	209	5	.	.	PUNCT
ejpam-5135	210	1	if	if	SCONJ
ejpam-5135	210	2	a	a	PRON
ejpam-5135	210	3	is	be	AUX
ejpam-5135	210	4	empty	empty	ADJ
ejpam-5135	210	5	,	,	PUNCT
ejpam-5135	210	6	then	then	ADV
ejpam-5135	210	7	f−1(a	f−1(a	NOUN
ejpam-5135	210	8	)	)	PUNCT
ejpam-5135	211	1	=	=	PUNCT
ejpam-5135	211	2	∅	∅	NOUN
ejpam-5135	211	3	∈	∈	PROPN
ejpam-5135	211	4	τb(pn	τb(pn	VERB
ejpam-5135	211	5	)	)	PUNCT
ejpam-5135	211	6	.	.	PUNCT
ejpam-5135	212	1	suppose	suppose	VERB
ejpam-5135	212	2	that	that	SCONJ
ejpam-5135	212	3	a	a	PRON
ejpam-5135	212	4	is	be	AUX
ejpam-5135	212	5	not	not	PART
ejpam-5135	212	6	empty	empty	ADJ
ejpam-5135	212	7	.	.	PUNCT
ejpam-5135	213	1	case	case	NOUN
ejpam-5135	213	2	1	1	NUM
ejpam-5135	213	3	:	:	PUNCT
ejpam-5135	213	4	if	if	SCONJ
ejpam-5135	213	5	v1	v1	VERB
ejpam-5135	213	6	∈	∈	PROPN
ejpam-5135	213	7	a	a	NOUN
ejpam-5135	213	8	and	and	CCONJ
ejpam-5135	213	9	vn	vn	PROPN
ejpam-5135	213	10	/∈	/∈	PROPN
ejpam-5135	214	1	a	a	PRON
ejpam-5135	214	2	,	,	PUNCT
ejpam-5135	214	3	then	then	ADV
ejpam-5135	214	4	by	by	ADP
ejpam-5135	214	5	theorem	theorem	NOUN
ejpam-5135	214	6	5	5	NUM
ejpam-5135	214	7	,	,	PUNCT
ejpam-5135	214	8	v2	v2	PROPN
ejpam-5135	214	9	∈	∈	PROPN
ejpam-5135	214	10	a.	a.	NOUN
ejpam-5135	214	11	observe	observe	VERB
ejpam-5135	214	12	that	that	SCONJ
ejpam-5135	214	13	,	,	PUNCT
ejpam-5135	214	14	if	if	SCONJ
ejpam-5135	214	15	a	a	PRON
ejpam-5135	214	16	=	=	X
ejpam-5135	214	17	{	{	PUNCT
ejpam-5135	214	18	v1	v1	NOUN
ejpam-5135	214	19	,	,	PUNCT
ejpam-5135	214	20	v2	v2	PROPN
ejpam-5135	214	21	}	}	PUNCT
ejpam-5135	214	22	,	,	PUNCT
ejpam-5135	214	23	then	then	ADV
ejpam-5135	214	24	f−1(a	f−1(a	PROPN
ejpam-5135	214	25	)	)	PUNCT
ejpam-5135	214	26	=	=	SYM
ejpam-5135	215	1	f−1({v1	f−1({v1	NOUN
ejpam-5135	215	2	,	,	PUNCT
ejpam-5135	215	3	v2	v2	PROPN
ejpam-5135	215	4	}	}	PUNCT
ejpam-5135	215	5	)	)	PUNCT
ejpam-5135	215	6	=	=	PRON
ejpam-5135	215	7	{	{	PUNCT
ejpam-5135	215	8	a1	a1	PROPN
ejpam-5135	215	9	,	,	PUNCT
ejpam-5135	215	10	a2	a2	PROPN
ejpam-5135	215	11	}	}	PUNCT
ejpam-5135	215	12	∈	∈	PROPN
ejpam-5135	215	13	τb(pn	τb(pn	VERB
ejpam-5135	215	14	)	)	PUNCT
ejpam-5135	215	15	.	.	PUNCT
ejpam-5135	216	1	suppose	suppose	VERB
ejpam-5135	216	2	that	that	SCONJ
ejpam-5135	216	3	a	a	DET
ejpam-5135	216	4	∖	∖	PROPN
ejpam-5135	216	5	{	{	PUNCT
ejpam-5135	216	6	v1	v1	PROPN
ejpam-5135	216	7	,	,	PUNCT
ejpam-5135	216	8	v2	v2	NOUN
ejpam-5135	216	9	}	}	PUNCT
ejpam-5135	216	10	=	=	NOUN
ejpam-5135	216	11	̸	̸	X
ejpam-5135	216	12	∅.	∅.	ADV
ejpam-5135	216	13	then	then	ADV
ejpam-5135	216	14	for	for	ADP
ejpam-5135	216	15	all	all	DET
ejpam-5135	216	16	vj	vj	PRON
ejpam-5135	216	17	∈	∈	PROPN
ejpam-5135	216	18	a∖	a∖	PROPN
ejpam-5135	216	19	{	{	PUNCT
ejpam-5135	216	20	v1	v1	PROPN
ejpam-5135	216	21	,	,	PUNCT
ejpam-5135	216	22	v2	v2	PROPN
ejpam-5135	216	23	}	}	PUNCT
ejpam-5135	216	24	,	,	PUNCT
ejpam-5135	216	25	f−1(vj	f−1(vj	PROPN
ejpam-5135	216	26	)	)	PUNCT
ejpam-5135	216	27	is	be	AUX
ejpam-5135	216	28	a	a	DET
ejpam-5135	216	29	cut	cut	NOUN
ejpam-5135	216	30	-	-	PUNCT
ejpam-5135	216	31	vertex	vertex	NOUN
ejpam-5135	216	32	of	of	ADP
ejpam-5135	216	33	pn	pn	NOUN
ejpam-5135	216	34	implying	imply	VERB
ejpam-5135	216	35	further	far	ADV
ejpam-5135	216	36	that	that	SCONJ
ejpam-5135	216	37	f−1(a	f−1(a	NOUN
ejpam-5135	216	38	∖	∖	NOUN
ejpam-5135	216	39	{	{	PUNCT
ejpam-5135	216	40	v1	v1	PROPN
ejpam-5135	216	41	,	,	PUNCT
ejpam-5135	216	42	v2	v2	PROPN
ejpam-5135	216	43	}	}	PUNCT
ejpam-5135	216	44	)	)	PUNCT
ejpam-5135	216	45	is	be	AUX
ejpam-5135	216	46	a	a	DET
ejpam-5135	216	47	subset	subset	NOUN
ejpam-5135	216	48	of	of	ADP
ejpam-5135	216	49	c	c	PROPN
ejpam-5135	216	50	(	(	PUNCT
ejpam-5135	216	51	pn	pn	NOUN
ejpam-5135	216	52	)	)	PUNCT
ejpam-5135	216	53	.	.	PUNCT
ejpam-5135	217	1	hence	hence	ADV
ejpam-5135	217	2	,	,	PUNCT
ejpam-5135	217	3	f−1(a	f−1(a	PROPN
ejpam-5135	217	4	)	)	PUNCT
ejpam-5135	217	5	=	=	SYM
ejpam-5135	217	6	f−1({v1	f−1({v1	NOUN
ejpam-5135	217	7	,	,	PUNCT
ejpam-5135	217	8	v2	v2	PROPN
ejpam-5135	217	9	}	}	PUNCT
ejpam-5135	217	10	)	)	PUNCT
ejpam-5135	217	11	∪	∪	ADP
ejpam-5135	217	12	f−1(a∖{v1	f−1(a∖{v1	PROPN
ejpam-5135	217	13	,	,	PUNCT
ejpam-5135	217	14	v2	v2	PROPN
ejpam-5135	217	15	}	}	PUNCT
ejpam-5135	217	16	)	)	PUNCT
ejpam-5135	217	17	is	be	AUX
ejpam-5135	217	18	τb(g)-open	τb(g)-open	PROPN
ejpam-5135	217	19	.	.	PUNCT
ejpam-5135	218	1	the	the	DET
ejpam-5135	218	2	argument	argument	NOUN
ejpam-5135	218	3	follows	follow	VERB
ejpam-5135	218	4	when	when	SCONJ
ejpam-5135	218	5	vn	vn	PROPN
ejpam-5135	218	6	∈	∈	PROPN
ejpam-5135	218	7	a	a	PRON
ejpam-5135	218	8	and	and	CCONJ
ejpam-5135	218	9	v1	v1	ADJ
ejpam-5135	218	10	/∈	/∈	PUNCT
ejpam-5135	218	11	a.	a.	NOUN
ejpam-5135	218	12	case	case	NOUN
ejpam-5135	218	13	2	2	NUM
ejpam-5135	218	14	:	:	PUNCT
ejpam-5135	218	15	if	if	SCONJ
ejpam-5135	218	16	v1	v1	PROPN
ejpam-5135	218	17	,	,	PUNCT
ejpam-5135	218	18	vn	vn	PROPN
ejpam-5135	218	19	∈	∈	PROPN
ejpam-5135	218	20	a	a	DET
ejpam-5135	218	21	,	,	PUNCT
ejpam-5135	218	22	then	then	ADV
ejpam-5135	218	23	v2	v2	PROPN
ejpam-5135	218	24	,	,	PUNCT
ejpam-5135	218	25	vn−1	vn−1	PROPN
ejpam-5135	218	26	∈	∈	PROPN
ejpam-5135	218	27	a.	a.	NOUN
ejpam-5135	218	28	similarly	similarly	ADV
ejpam-5135	218	29	,	,	PUNCT
ejpam-5135	218	30	if	if	SCONJ
ejpam-5135	218	31	a	a	PRON
ejpam-5135	218	32	=	=	X
ejpam-5135	218	33	{	{	PUNCT
ejpam-5135	218	34	v1	v1	PROPN
ejpam-5135	218	35	,	,	PUNCT
ejpam-5135	218	36	v2	v2	PROPN
ejpam-5135	218	37	,	,	PUNCT
ejpam-5135	218	38	vn−1	vn−1	PROPN
ejpam-5135	218	39	,	,	PUNCT
ejpam-5135	218	40	vn	vn	NOUN
ejpam-5135	218	41	}	}	PUNCT
ejpam-5135	218	42	,	,	PUNCT
ejpam-5135	218	43	then	then	ADV
ejpam-5135	218	44	f−1(a	f−1(a	PROPN
ejpam-5135	218	45	)	)	PUNCT
ejpam-5135	218	46	=	=	SYM
ejpam-5135	218	47	f−1({v1	f−1({v1	NOUN
ejpam-5135	218	48	,	,	PUNCT
ejpam-5135	218	49	v2	v2	PROPN
ejpam-5135	218	50	,	,	PUNCT
ejpam-5135	218	51	vn−1	vn−1	PROPN
ejpam-5135	218	52	,	,	PUNCT
ejpam-5135	218	53	vn	vn	NOUN
ejpam-5135	218	54	}	}	PUNCT
ejpam-5135	218	55	)	)	PUNCT
ejpam-5135	219	1	=	=	PRON
ejpam-5135	219	2	{	{	PUNCT
ejpam-5135	219	3	a1	a1	PROPN
ejpam-5135	219	4	,	,	PUNCT
ejpam-5135	219	5	a2	a2	PROPN
ejpam-5135	219	6	,	,	PUNCT
ejpam-5135	219	7	an−1	an−1	ADJ
ejpam-5135	219	8	,	,	PUNCT
ejpam-5135	219	9	an	an	DET
ejpam-5135	219	10	}	}	PUNCT
ejpam-5135	219	11	∈	∈	PROPN
ejpam-5135	219	12	τb(pn	τb(pn	VERB
ejpam-5135	219	13	)	)	PUNCT
ejpam-5135	219	14	.	.	PUNCT
ejpam-5135	220	1	also	also	ADV
ejpam-5135	220	2	,	,	PUNCT
ejpam-5135	220	3	if	if	SCONJ
ejpam-5135	220	4	a	a	DET
ejpam-5135	220	5	∖	∖	NOUN
ejpam-5135	220	6	{	{	PUNCT
ejpam-5135	220	7	v1	v1	PROPN
ejpam-5135	220	8	,	,	PUNCT
ejpam-5135	220	9	v2	v2	PROPN
ejpam-5135	220	10	,	,	PUNCT
ejpam-5135	220	11	vn−1	vn−1	PROPN
ejpam-5135	220	12	,	,	PUNCT
ejpam-5135	220	13	vn	vn	INTJ
ejpam-5135	220	14	}	}	PUNCT
ejpam-5135	220	15	̸=	̸=	PROPN
ejpam-5135	220	16	∅	∅	NOUN
ejpam-5135	220	17	,	,	PUNCT
ejpam-5135	220	18	then	then	ADV
ejpam-5135	220	19	f−1({v1	f−1({v1	PROPN
ejpam-5135	220	20	,	,	PUNCT
ejpam-5135	220	21	v2	v2	PROPN
ejpam-5135	220	22	,	,	PUNCT
ejpam-5135	220	23	vn−1	vn−1	PROPN
ejpam-5135	220	24	,	,	PUNCT
ejpam-5135	220	25	vn	vn	NOUN
ejpam-5135	220	26	}	}	PUNCT
ejpam-5135	220	27	)	)	PUNCT
ejpam-5135	221	1	⊆	⊆	NUM
ejpam-5135	221	2	c	c	X
ejpam-5135	221	3	(	(	PUNCT
ejpam-5135	221	4	pn	pn	NOUN
ejpam-5135	221	5	)	)	PUNCT
ejpam-5135	221	6	.	.	PUNCT
ejpam-5135	222	1	hence	hence	ADV
ejpam-5135	222	2	,	,	PUNCT
ejpam-5135	222	3	f−1(a	f−1(a	PROPN
ejpam-5135	222	4	)	)	PUNCT
ejpam-5135	222	5	=	=	SYM
ejpam-5135	222	6	f−1({v1	f−1({v1	NOUN
ejpam-5135	222	7	,	,	PUNCT
ejpam-5135	222	8	v2	v2	PROPN
ejpam-5135	222	9	,	,	PUNCT
ejpam-5135	222	10	vn−1	vn−1	PROPN
ejpam-5135	222	11	,	,	PUNCT
ejpam-5135	222	12	vn	vn	NOUN
ejpam-5135	222	13	}	}	PUNCT
ejpam-5135	222	14	)	)	PUNCT
ejpam-5135	222	15	∪	∪	ADP
ejpam-5135	222	16	f−1(a∖	f−1(a∖	PUNCT
ejpam-5135	222	17	{	{	PUNCT
ejpam-5135	222	18	v1	v1	NOUN
ejpam-5135	222	19	,	,	PUNCT
ejpam-5135	222	20	v2	v2	PROPN
ejpam-5135	222	21	,	,	PUNCT
ejpam-5135	222	22	vn−1	vn−1	PROPN
ejpam-5135	222	23	,	,	PUNCT
ejpam-5135	222	24	vn	vn	NOUN
ejpam-5135	222	25	}	}	PUNCT
ejpam-5135	222	26	)	)	PUNCT
ejpam-5135	222	27	is	be	AUX
ejpam-5135	222	28	τb(g)-open	τb(g)-open	PROPN
ejpam-5135	222	29	.	.	PUNCT
ejpam-5135	223	1	case	case	NOUN
ejpam-5135	223	2	3	3	NUM
ejpam-5135	223	3	:	:	PUNCT
ejpam-5135	223	4	if	if	SCONJ
ejpam-5135	223	5	v1	v1	PROPN
ejpam-5135	223	6	,	,	PUNCT
ejpam-5135	223	7	vn	vn	PROPN
ejpam-5135	223	8	/∈	/∈	PUNCT
ejpam-5135	224	1	a	a	DET
ejpam-5135	224	2	,	,	PUNCT
ejpam-5135	224	3	then	then	ADV
ejpam-5135	224	4	f−1(a	f−1(a	PROPN
ejpam-5135	224	5	)	)	PUNCT
ejpam-5135	225	1	⊆	⊆	NUM
ejpam-5135	225	2	c	c	NOUN
ejpam-5135	225	3	(	(	PUNCT
ejpam-5135	225	4	pn	pn	NOUN
ejpam-5135	225	5	)	)	PUNCT
ejpam-5135	225	6	so	so	SCONJ
ejpam-5135	225	7	that	that	DET
ejpam-5135	225	8	f−1(a	f−1(a	NOUN
ejpam-5135	225	9	)	)	PUNCT
ejpam-5135	225	10	is	be	AUX
ejpam-5135	225	11	τb(g)-open	τb(g)-open	PROPN
ejpam-5135	225	12	.	.	PUNCT
ejpam-5135	226	1	thus	thus	ADV
ejpam-5135	226	2	,	,	PUNCT
ejpam-5135	226	3	f	f	PROPN
ejpam-5135	226	4	is	be	AUX
ejpam-5135	226	5	continuous	continuous	ADJ
ejpam-5135	226	6	.	.	PUNCT
ejpam-5135	227	1	(	(	PUNCT
ejpam-5135	227	2	⇐	⇐	NOUN
ejpam-5135	227	3	)	)	PUNCT
ejpam-5135	227	4	let	let	VERB
ejpam-5135	227	5	f	f	PRON
ejpam-5135	227	6	be	be	AUX
ejpam-5135	227	7	a	a	DET
ejpam-5135	227	8	one	one	NUM
ejpam-5135	227	9	-	-	PUNCT
ejpam-5135	227	10	to	to	ADP
ejpam-5135	227	11	-	-	PUNCT
ejpam-5135	227	12	one	one	NUM
ejpam-5135	227	13	correspondence	correspondence	NOUN
ejpam-5135	227	14	from	from	ADP
ejpam-5135	227	15	(	(	PUNCT
ejpam-5135	227	16	v	v	NOUN
ejpam-5135	227	17	(	(	PUNCT
ejpam-5135	227	18	pn	pn	NOUN
ejpam-5135	227	19	)	)	PUNCT
ejpam-5135	227	20	,	,	PUNCT
ejpam-5135	227	21	τb(pn	τb(pn	ADJ
ejpam-5135	227	22	)	)	PUNCT
ejpam-5135	227	23	)	)	PUNCT
ejpam-5135	227	24	to	to	ADP
ejpam-5135	227	25	(	(	PUNCT
ejpam-5135	227	26	v	v	NOUN
ejpam-5135	227	27	(	(	PUNCT
ejpam-5135	227	28	g	g	NOUN
ejpam-5135	227	29	)	)	PUNCT
ejpam-5135	227	30	,	,	PUNCT
ejpam-5135	227	31	τb(g	τb(g	NUM
ejpam-5135	227	32	)	)	PUNCT
ejpam-5135	227	33	)	)	PUNCT
ejpam-5135	227	34	that	that	PRON
ejpam-5135	227	35	is	be	AUX
ejpam-5135	227	36	continuous	continuous	ADJ
ejpam-5135	227	37	.	.	PUNCT
ejpam-5135	227	38	suppose	suppose	VERB
ejpam-5135	227	39	that	that	SCONJ
ejpam-5135	227	40	g	g	PROPN
ejpam-5135	227	41	has	have	VERB
ejpam-5135	227	42	no	no	DET
ejpam-5135	227	43	nonadjacent	nonadjacent	ADJ
ejpam-5135	227	44	edges	edge	NOUN
ejpam-5135	227	45	.	.	PUNCT
ejpam-5135	228	1	then	then	ADV
ejpam-5135	228	2	g	g	PROPN
ejpam-5135	228	3	is	be	AUX
ejpam-5135	228	4	one	one	NUM
ejpam-5135	228	5	of	of	ADP
ejpam-5135	228	6	the	the	DET
ejpam-5135	228	7	following	following	NOUN
ejpam-5135	228	8	:	:	PUNCT
ejpam-5135	228	9	(	(	PUNCT
ejpam-5135	228	10	1	1	X
ejpam-5135	228	11	)	)	PUNCT
ejpam-5135	228	12	g	g	PROPN
ejpam-5135	228	13	=	=	SYM
ejpam-5135	228	14	kn	kn	PROPN
ejpam-5135	228	15	;	;	PUNCT
ejpam-5135	228	16	(	(	PUNCT
ejpam-5135	228	17	2	2	X
ejpam-5135	228	18	)	)	PUNCT
ejpam-5135	228	19	|e(g)|	|e(g)|	NOUN
ejpam-5135	228	20	=	=	NOUN
ejpam-5135	228	21	1	1	NUM
ejpam-5135	228	22	;	;	PUNCT
ejpam-5135	228	23	or	or	CCONJ
ejpam-5135	228	24	(	(	PUNCT
ejpam-5135	228	25	3	3	X
ejpam-5135	228	26	)	)	PUNCT
ejpam-5135	228	27	the	the	DET
ejpam-5135	228	28	edges	edge	NOUN
ejpam-5135	228	29	of	of	ADP
ejpam-5135	228	30	g	g	PROPN
ejpam-5135	228	31	share	share	VERB
ejpam-5135	228	32	a	a	DET
ejpam-5135	228	33	common	common	ADJ
ejpam-5135	228	34	vertex	vertex	NOUN
ejpam-5135	228	35	.	.	PUNCT
ejpam-5135	229	1	case	case	NOUN
ejpam-5135	229	2	1	1	NUM
ejpam-5135	229	3	:	:	PUNCT
ejpam-5135	229	4	suppose	suppose	VERB
ejpam-5135	229	5	g	g	PROPN
ejpam-5135	229	6	=	=	PROPN
ejpam-5135	229	7	kn	kn	PROPN
ejpam-5135	229	8	.	.	PUNCT
ejpam-5135	230	1	let	let	VERB
ejpam-5135	230	2	v	v	PART
ejpam-5135	230	3	be	be	AUX
ejpam-5135	230	4	a	a	DET
ejpam-5135	230	5	vertex	vertex	NOUN
ejpam-5135	230	6	in	in	ADP
ejpam-5135	230	7	g	g	PROPN
ejpam-5135	230	8	such	such	ADJ
ejpam-5135	230	9	that	that	DET
ejpam-5135	230	10	f−1(v	f−1(v	PROPN
ejpam-5135	230	11	)	)	PUNCT
ejpam-5135	230	12	is	be	AUX
ejpam-5135	230	13	an	an	DET
ejpam-5135	230	14	end	end	NOUN
ejpam-5135	230	15	vertex	vertex	NOUN
ejpam-5135	230	16	of	of	ADP
ejpam-5135	230	17	pn	pn	PROPN
ejpam-5135	230	18	.	.	PUNCT
ejpam-5135	231	1	here	here	ADV
ejpam-5135	231	2	,	,	PUNCT
ejpam-5135	231	3	{	{	PUNCT
ejpam-5135	231	4	v	v	NOUN
ejpam-5135	231	5	}	}	PUNCT
ejpam-5135	231	6	is	be	AUX
ejpam-5135	231	7	τb	τb	ADJ
ejpam-5135	231	8	-	-	PUNCT
ejpam-5135	231	9	open	open	ADJ
ejpam-5135	231	10	and	and	CCONJ
ejpam-5135	231	11	{	{	PUNCT
ejpam-5135	231	12	f−1(v	f−1(v	PROPN
ejpam-5135	231	13	)	)	PUNCT
ejpam-5135	231	14	}	}	PUNCT
ejpam-5135	231	15	is	be	AUX
ejpam-5135	231	16	not	not	PART
ejpam-5135	231	17	τb(pn)-open	τb(pn)-open	ADJ
ejpam-5135	231	18	;	;	PUNCT
ejpam-5135	231	19	a	a	DET
ejpam-5135	231	20	contradiction	contradiction	NOUN
ejpam-5135	231	21	since	since	SCONJ
ejpam-5135	231	22	f	f	PROPN
ejpam-5135	231	23	is	be	AUX
ejpam-5135	231	24	continuous	continuous	ADJ
ejpam-5135	231	25	.	.	PUNCT
ejpam-5135	232	1	hence	hence	ADV
ejpam-5135	232	2	,	,	PUNCT
ejpam-5135	232	3	g	g	PROPN
ejpam-5135	232	4	is	be	AUX
ejpam-5135	232	5	not	not	PART
ejpam-5135	232	6	an	an	DET
ejpam-5135	232	7	empty	empty	ADJ
ejpam-5135	232	8	graph	graph	NOUN
ejpam-5135	232	9	.	.	PUNCT
ejpam-5135	233	1	case	case	NOUN
ejpam-5135	233	2	2	2	NUM
ejpam-5135	233	3	:	:	PUNCT
ejpam-5135	233	4	suppose	suppose	VERB
ejpam-5135	233	5	|e(g)|	|e(g)|	PROPN
ejpam-5135	233	6	=	=	NOUN
ejpam-5135	233	7	1	1	X
ejpam-5135	233	8	.	.	PUNCT
ejpam-5135	234	1	let	let	VERB
ejpam-5135	234	2	vw	vw	PRON
ejpam-5135	234	3	∈	∈	PROPN
ejpam-5135	234	4	e(g	e(g	PROPN
ejpam-5135	234	5	)	)	PUNCT
ejpam-5135	234	6	.	.	PUNCT
ejpam-5135	235	1	then	then	ADV
ejpam-5135	235	2	{	{	PUNCT
ejpam-5135	235	3	v	v	NOUN
ejpam-5135	235	4	,	,	PUNCT
ejpam-5135	235	5	w	w	NOUN
ejpam-5135	235	6	}	}	PUNCT
ejpam-5135	235	7	is	be	AUX
ejpam-5135	235	8	τb(g)-open	τb(g)-open	ADJ
ejpam-5135	235	9	and	and	CCONJ
ejpam-5135	235	10	so	so	ADV
ejpam-5135	235	11	by	by	ADP
ejpam-5135	235	12	the	the	DET
ejpam-5135	235	13	continuity	continuity	NOUN
ejpam-5135	235	14	of	of	ADP
ejpam-5135	235	15	f	f	PROPN
ejpam-5135	235	16	,	,	PUNCT
ejpam-5135	235	17	f−1({v	f−1({v	PROPN
ejpam-5135	235	18	,	,	PUNCT
ejpam-5135	235	19	w	w	NOUN
ejpam-5135	235	20	}	}	PUNCT
ejpam-5135	235	21	)	)	PUNCT
ejpam-5135	235	22	is	be	AUX
ejpam-5135	235	23	τb(pn)-open	τb(pn)-open	PROPN
ejpam-5135	235	24	.	.	PUNCT
ejpam-5135	236	1	note	note	VERB
ejpam-5135	236	2	that	that	DET
ejpam-5135	236	3	f−1(v	f−1(v	PROPN
ejpam-5135	236	4	)	)	PUNCT
ejpam-5135	236	5	and	and	CCONJ
ejpam-5135	236	6	f−1(w	f−1(w	PROPN
ejpam-5135	236	7	)	)	PUNCT
ejpam-5135	236	8	can	can	AUX
ejpam-5135	236	9	not	not	PART
ejpam-5135	236	10	be	be	AUX
ejpam-5135	236	11	both	both	DET
ejpam-5135	236	12	end	end	NOUN
ejpam-5135	236	13	-	-	PUNCT
ejpam-5135	236	14	vertices	vertex	NOUN
ejpam-5135	236	15	of	of	ADP
ejpam-5135	236	16	pn	pn	NOUN
ejpam-5135	236	17	;	;	PUNCT
ejpam-5135	236	18	otherwise	otherwise	ADV
ejpam-5135	236	19	,	,	PUNCT
ejpam-5135	236	20	f	f	PROPN
ejpam-5135	236	21	−1({v	−1({v	PROPN
ejpam-5135	236	22	,	,	PUNCT
ejpam-5135	236	23	w	w	NOUN
ejpam-5135	236	24	}	}	PUNCT
ejpam-5135	236	25	)	)	PUNCT
ejpam-5135	236	26	is	be	AUX
ejpam-5135	236	27	not	not	PART
ejpam-5135	236	28	τb(pn)-open	τb(pn)-open	ADJ
ejpam-5135	236	29	.	.	PUNCT
ejpam-5135	237	1	now	now	ADV
ejpam-5135	237	2	,	,	PUNCT
ejpam-5135	237	3	choose	choose	VERB
ejpam-5135	237	4	a	a	DET
ejpam-5135	237	5	vertex	vertex	NOUN
ejpam-5135	237	6	u	u	NOUN
ejpam-5135	237	7	in	in	ADP
ejpam-5135	237	8	g	g	PROPN
ejpam-5135	237	9	different	different	ADJ
ejpam-5135	237	10	from	from	ADP
ejpam-5135	237	11	v	v	NOUN
ejpam-5135	237	12	and	and	CCONJ
ejpam-5135	237	13	w	w	ADP
ejpam-5135	237	14	such	such	ADJ
ejpam-5135	237	15	that	that	DET
ejpam-5135	237	16	f−1(u	f−1(u	PROPN
ejpam-5135	237	17	)	)	PUNCT
ejpam-5135	237	18	is	be	AUX
ejpam-5135	237	19	an	an	DET
ejpam-5135	237	20	endvertex	endvertex	NOUN
ejpam-5135	237	21	of	of	ADP
ejpam-5135	237	22	pn	pn	PROPN
ejpam-5135	237	23	.	.	PROPN
ejpam-5135	237	24	note	note	VERB
ejpam-5135	237	25	that	that	SCONJ
ejpam-5135	237	26	{	{	PUNCT
ejpam-5135	237	27	f−1(u	f−1(u	PROPN
ejpam-5135	237	28	)	)	PUNCT
ejpam-5135	237	29	}	}	PUNCT
ejpam-5135	237	30	is	be	AUX
ejpam-5135	237	31	not	not	PART
ejpam-5135	237	32	a	a	DET
ejpam-5135	237	33	τb(pn)-open	τb(pn)-open	NOUN
ejpam-5135	237	34	set	set	NOUN
ejpam-5135	237	35	.	.	PUNCT
ejpam-5135	238	1	in	in	ADP
ejpam-5135	238	2	this	this	DET
ejpam-5135	238	3	case	case	NOUN
ejpam-5135	238	4	,	,	PUNCT
ejpam-5135	238	5	u	u	NOUN
ejpam-5135	238	6	is	be	AUX
ejpam-5135	238	7	an	an	DET
ejpam-5135	238	8	isolated	isolated	ADJ
ejpam-5135	238	9	vertex	vertex	NOUN
ejpam-5135	238	10	and	and	CCONJ
ejpam-5135	238	11	thus	thus	ADV
ejpam-5135	238	12	{	{	PUNCT
ejpam-5135	238	13	u	u	NOUN
ejpam-5135	238	14	}	}	PUNCT
ejpam-5135	238	15	is	be	AUX
ejpam-5135	238	16	τb(g)-open	τb(g)-open	PROPN
ejpam-5135	238	17	.	.	PUNCT
ejpam-5135	239	1	this	this	PRON
ejpam-5135	239	2	is	be	AUX
ejpam-5135	239	3	a	a	DET
ejpam-5135	239	4	contradiction	contradiction	NOUN
ejpam-5135	239	5	since	since	SCONJ
ejpam-5135	239	6	f	f	PROPN
ejpam-5135	239	7	is	be	AUX
ejpam-5135	239	8	continuous	continuous	ADJ
ejpam-5135	239	9	.	.	PUNCT
ejpam-5135	240	1	hence	hence	ADV
ejpam-5135	240	2	,	,	PUNCT
ejpam-5135	240	3	|e(g)|	|e(g)|	ADJ
ejpam-5135	240	4	>	>	ADP
ejpam-5135	240	5	1	1	NUM
ejpam-5135	240	6	.	.	PUNCT
ejpam-5135	240	7	case	case	NOUN
ejpam-5135	240	8	3	3	X
ejpam-5135	240	9	:	:	PUNCT
ejpam-5135	240	10	suppose	suppose	VERB
ejpam-5135	240	11	the	the	DET
ejpam-5135	240	12	edges	edge	NOUN
ejpam-5135	240	13	of	of	ADP
ejpam-5135	240	14	g	g	PROPN
ejpam-5135	240	15	share	share	VERB
ejpam-5135	240	16	a	a	DET
ejpam-5135	240	17	common	common	ADJ
ejpam-5135	240	18	vertex	vertex	NOUN
ejpam-5135	240	19	and	and	CCONJ
ejpam-5135	240	20	let	let	VERB
ejpam-5135	240	21	x	x	PRON
ejpam-5135	240	22	and	and	CCONJ
ejpam-5135	240	23	y	y	PROPN
ejpam-5135	240	24	be	be	AUX
ejpam-5135	240	25	vertices	vertex	NOUN
ejpam-5135	240	26	in	in	ADP
ejpam-5135	240	27	g	g	PROPN
ejpam-5135	240	28	such	such	ADJ
ejpam-5135	240	29	that	that	DET
ejpam-5135	240	30	f−1(x	f−1(x	NOUN
ejpam-5135	240	31	)	)	PUNCT
ejpam-5135	240	32	and	and	CCONJ
ejpam-5135	240	33	f−1(y	f−1(y	PROPN
ejpam-5135	240	34	)	)	PUNCT
ejpam-5135	240	35	are	be	AUX
ejpam-5135	240	36	the	the	DET
ejpam-5135	240	37	end	end	NOUN
ejpam-5135	240	38	-	-	PUNCT
ejpam-5135	240	39	vertices	vertex	NOUN
ejpam-5135	240	40	of	of	ADP
ejpam-5135	240	41	pn	pn	PROPN
ejpam-5135	240	42	.	.	PUNCT
ejpam-5135	241	1	now	now	ADV
ejpam-5135	241	2	,	,	PUNCT
ejpam-5135	241	3	x	x	PUNCT
ejpam-5135	241	4	and	and	CCONJ
ejpam-5135	241	5	y	y	PROPN
ejpam-5135	241	6	are	be	AUX
ejpam-5135	241	7	not	not	PART
ejpam-5135	241	8	justine	justine	PROPN
ejpam-5135	241	9	bryle	bryle	PROPN
ejpam-5135	241	10	c.	c.	PROPN
ejpam-5135	241	11	macaso	macaso	PROPN
ejpam-5135	241	12	,	,	PUNCT
ejpam-5135	241	13	cherry	cherry	PROPN
ejpam-5135	241	14	mae	mae	PROPN
ejpam-5135	241	15	r.	r.	PROPN
ejpam-5135	241	16	balingit	balingit	PROPN
ejpam-5135	241	17	/	/	SYM
ejpam-5135	241	18	eur	eur	PROPN
ejpam-5135	241	19	.	.	PUNCT
ejpam-5135	242	1	j.	j.	PROPN
ejpam-5135	242	2	pure	pure	PROPN
ejpam-5135	242	3	appl	appl	PROPN
ejpam-5135	242	4	.	.	PROPN
ejpam-5135	242	5	math	math	PROPN
ejpam-5135	242	6	,	,	PUNCT
ejpam-5135	242	7	17	17	NUM
ejpam-5135	242	8	(	(	PUNCT
ejpam-5135	242	9	2	2	NUM
ejpam-5135	242	10	)	)	PUNCT
ejpam-5135	242	11	(	(	PUNCT
ejpam-5135	242	12	2024	2024	NUM
ejpam-5135	242	13	)	)	PUNCT
ejpam-5135	242	14	,	,	PUNCT
ejpam-5135	242	15	663	663	NUM
ejpam-5135	242	16	-	-	SYM
ejpam-5135	242	17	675	675	NUM
ejpam-5135	242	18	673	673	NUM
ejpam-5135	242	19	isolated	isolated	ADJ
ejpam-5135	242	20	vertices	vertex	NOUN
ejpam-5135	242	21	of	of	ADP
ejpam-5135	242	22	g	g	NOUN
ejpam-5135	242	23	nor	nor	CCONJ
ejpam-5135	242	24	cut	cut	NOUN
ejpam-5135	242	25	-	-	PUNCT
ejpam-5135	242	26	vertices	vertex	NOUN
ejpam-5135	242	27	of	of	ADP
ejpam-5135	242	28	g	g	NOUN
ejpam-5135	242	29	,	,	PUNCT
ejpam-5135	242	30	otherwise	otherwise	ADV
ejpam-5135	242	31	f	f	X
ejpam-5135	242	32	is	be	AUX
ejpam-5135	242	33	not	not	PART
ejpam-5135	242	34	continuous	continuous	ADJ
ejpam-5135	242	35	since	since	SCONJ
ejpam-5135	242	36	f−1({x	f−1({x	PROPN
ejpam-5135	242	37	,	,	PUNCT
ejpam-5135	242	38	y	y	NOUN
ejpam-5135	242	39	}	}	PUNCT
ejpam-5135	242	40	)	)	PUNCT
ejpam-5135	242	41	is	be	AUX
ejpam-5135	242	42	not	not	PART
ejpam-5135	242	43	τb(pn)-open	τb(pn)-open	PROPN
ejpam-5135	242	44	.	.	PUNCT
ejpam-5135	243	1	subcase	subcase	PROPN
ejpam-5135	243	2	1	1	NUM
ejpam-5135	243	3	:	:	PUNCT
ejpam-5135	243	4	if	if	SCONJ
ejpam-5135	243	5	xy	xy	PROPN
ejpam-5135	243	6	∈	∈	PROPN
ejpam-5135	243	7	e(g	e(g	PROPN
ejpam-5135	243	8	)	)	PUNCT
ejpam-5135	244	1	,	,	PUNCT
ejpam-5135	244	2	then	then	ADV
ejpam-5135	244	3	there	there	PRON
ejpam-5135	244	4	is	be	VERB
ejpam-5135	244	5	another	another	DET
ejpam-5135	244	6	vertex	vertex	NOUN
ejpam-5135	244	7	v	v	NOUN
ejpam-5135	244	8	that	that	PRON
ejpam-5135	244	9	is	be	AUX
ejpam-5135	244	10	adjacent	adjacent	ADJ
ejpam-5135	244	11	to	to	ADP
ejpam-5135	244	12	both	both	PRON
ejpam-5135	244	13	x	x	PROPN
ejpam-5135	244	14	and	and	CCONJ
ejpam-5135	244	15	y	y	PROPN
ejpam-5135	244	16	since	since	SCONJ
ejpam-5135	244	17	x	x	PROPN
ejpam-5135	244	18	and	and	CCONJ
ejpam-5135	244	19	y	y	PROPN
ejpam-5135	244	20	are	be	AUX
ejpam-5135	244	21	not	not	PART
ejpam-5135	244	22	cut	cut	VERB
ejpam-5135	244	23	-	-	PUNCT
ejpam-5135	244	24	vertices	vertex	NOUN
ejpam-5135	244	25	.	.	PUNCT
ejpam-5135	245	1	in	in	ADP
ejpam-5135	245	2	this	this	DET
ejpam-5135	245	3	case	case	NOUN
ejpam-5135	245	4	,	,	PUNCT
ejpam-5135	245	5	g[{x	g[{x	PROPN
ejpam-5135	245	6	,	,	PUNCT
ejpam-5135	245	7	v	v	NOUN
ejpam-5135	245	8	,	,	PUNCT
ejpam-5135	245	9	y	y	PROPN
ejpam-5135	245	10	}	}	PUNCT
ejpam-5135	245	11	]	]	PUNCT
ejpam-5135	245	12	is	be	AUX
ejpam-5135	245	13	a	a	DET
ejpam-5135	245	14	block	block	NOUN
ejpam-5135	245	15	of	of	ADP
ejpam-5135	245	16	g	g	NOUN
ejpam-5135	245	17	which	which	PRON
ejpam-5135	245	18	further	far	ADV
ejpam-5135	245	19	implies	imply	VERB
ejpam-5135	245	20	that	that	SCONJ
ejpam-5135	245	21	{	{	PUNCT
ejpam-5135	245	22	x	x	NOUN
ejpam-5135	245	23	,	,	PUNCT
ejpam-5135	245	24	v	v	NOUN
ejpam-5135	245	25	,	,	PUNCT
ejpam-5135	245	26	y	y	NOUN
ejpam-5135	245	27	}	}	PUNCT
ejpam-5135	245	28	is	be	AUX
ejpam-5135	245	29	τb(g)-open	τb(g)-open	PROPN
ejpam-5135	245	30	.	.	PUNCT
ejpam-5135	246	1	also	also	ADV
ejpam-5135	246	2	,	,	PUNCT
ejpam-5135	246	3	note	note	VERB
ejpam-5135	246	4	that	that	DET
ejpam-5135	246	5	f−1(v	f−1(v	PROPN
ejpam-5135	246	6	)	)	PUNCT
ejpam-5135	246	7	is	be	AUX
ejpam-5135	246	8	a	a	DET
ejpam-5135	246	9	cut	cut	NOUN
ejpam-5135	246	10	-	-	PUNCT
ejpam-5135	246	11	vertex	vertex	NOUN
ejpam-5135	246	12	of	of	ADP
ejpam-5135	246	13	pn	pn	PROPN
ejpam-5135	246	14	.	.	PUNCT
ejpam-5135	247	1	now	now	ADV
ejpam-5135	247	2	,	,	PUNCT
ejpam-5135	247	3	we	we	PRON
ejpam-5135	247	4	have	have	VERB
ejpam-5135	247	5	f−1({x	f−1({x	PROPN
ejpam-5135	247	6	,	,	PUNCT
ejpam-5135	247	7	v	v	NOUN
ejpam-5135	247	8	,	,	PUNCT
ejpam-5135	247	9	y	y	NOUN
ejpam-5135	247	10	}	}	PUNCT
ejpam-5135	247	11	)	)	PUNCT
ejpam-5135	248	1	=	=	PRON
ejpam-5135	248	2	{	{	PUNCT
ejpam-5135	248	3	f−1(x	f−1(x	NOUN
ejpam-5135	248	4	)	)	PUNCT
ejpam-5135	248	5	}	}	PUNCT
ejpam-5135	248	6	∪	∪	ADP
ejpam-5135	248	7	{	{	PUNCT
ejpam-5135	248	8	f−1(v	f−1(v	NOUN
ejpam-5135	248	9	)	)	PUNCT
ejpam-5135	248	10	}	}	PUNCT
ejpam-5135	248	11	∪	∪	VERB
ejpam-5135	248	12	{	{	PUNCT
ejpam-5135	248	13	f−1(y	f−1(y	PROPN
ejpam-5135	248	14	)	)	PUNCT
ejpam-5135	248	15	}	}	PUNCT
ejpam-5135	248	16	=	=	SYM
ejpam-5135	248	17	f−1({x	f−1({x	PROPN
ejpam-5135	248	18	,	,	PUNCT
ejpam-5135	248	19	v	v	NOUN
ejpam-5135	248	20	}	}	PUNCT
ejpam-5135	248	21	)	)	PUNCT
ejpam-5135	248	22	∪	∪	ADP
ejpam-5135	248	23	{	{	PUNCT
ejpam-5135	248	24	f−1(y	f−1(y	PROPN
ejpam-5135	248	25	)	)	PUNCT
ejpam-5135	248	26	}	}	PUNCT
ejpam-5135	248	27	=	=	SYM
ejpam-5135	248	28	f−1({x	f−1({x	PROPN
ejpam-5135	248	29	,	,	PUNCT
ejpam-5135	248	30	y	y	NOUN
ejpam-5135	248	31	}	}	PUNCT
ejpam-5135	248	32	)	)	PUNCT
ejpam-5135	248	33	∪	∪	ADP
ejpam-5135	248	34	{	{	PUNCT
ejpam-5135	248	35	f−1(v	f−1(v	NOUN
ejpam-5135	248	36	)	)	PUNCT
ejpam-5135	248	37	}	}	PUNCT
ejpam-5135	248	38	=	=	SYM
ejpam-5135	248	39	f−1({v	f−1({v	PROPN
ejpam-5135	248	40	,	,	PUNCT
ejpam-5135	248	41	y	y	NOUN
ejpam-5135	248	42	}	}	PUNCT
ejpam-5135	248	43	)	)	PUNCT
ejpam-5135	248	44	∪	∪	ADP
ejpam-5135	248	45	{	{	PUNCT
ejpam-5135	248	46	f−1(x	f−1(x	NOUN
ejpam-5135	248	47	)	)	PUNCT
ejpam-5135	248	48	}	}	PUNCT
ejpam-5135	248	49	.	.	PUNCT
ejpam-5135	249	1	thus	thus	ADV
ejpam-5135	249	2	,	,	PUNCT
ejpam-5135	249	3	f−1({x	f−1({x	PROPN
ejpam-5135	249	4	,	,	PUNCT
ejpam-5135	249	5	v	v	NOUN
ejpam-5135	249	6	,	,	PUNCT
ejpam-5135	249	7	y	y	NOUN
ejpam-5135	249	8	}	}	PUNCT
ejpam-5135	249	9	)	)	PUNCT
ejpam-5135	249	10	is	be	AUX
ejpam-5135	249	11	not	not	PART
ejpam-5135	249	12	τb(pn)-open	τb(pn)-open	VERB
ejpam-5135	249	13	by	by	ADP
ejpam-5135	249	14	theorem	theorem	NOUN
ejpam-5135	249	15	4	4	NUM
ejpam-5135	249	16	.	.	PUNCT
ejpam-5135	250	1	this	this	PRON
ejpam-5135	250	2	is	be	AUX
ejpam-5135	250	3	a	a	DET
ejpam-5135	250	4	contradiction	contradiction	NOUN
ejpam-5135	250	5	since	since	SCONJ
ejpam-5135	250	6	f	f	PROPN
ejpam-5135	250	7	is	be	AUX
ejpam-5135	250	8	continuous	continuous	ADJ
ejpam-5135	250	9	.	.	PUNCT
ejpam-5135	251	1	subcase	subcase	PROPN
ejpam-5135	251	2	2	2	NUM
ejpam-5135	251	3	:	:	PUNCT
ejpam-5135	251	4	if	if	SCONJ
ejpam-5135	251	5	xy	xy	PROPN
ejpam-5135	251	6	/∈	/∈	PUNCT
ejpam-5135	251	7	e(g	e(g	PROPN
ejpam-5135	251	8	)	)	PUNCT
ejpam-5135	252	1	,	,	PUNCT
ejpam-5135	252	2	then	then	ADV
ejpam-5135	252	3	there	there	PRON
ejpam-5135	252	4	exists	exist	VERB
ejpam-5135	252	5	a	a	DET
ejpam-5135	252	6	vertex	vertex	NOUN
ejpam-5135	252	7	v	v	NOUN
ejpam-5135	252	8	that	that	PRON
ejpam-5135	252	9	is	be	AUX
ejpam-5135	252	10	adjacent	adjacent	ADJ
ejpam-5135	252	11	to	to	ADP
ejpam-5135	252	12	x	x	PUNCT
ejpam-5135	252	13	and	and	CCONJ
ejpam-5135	252	14	y.	y.	NOUN
ejpam-5135	252	15	here	here	ADV
ejpam-5135	252	16	,	,	PUNCT
ejpam-5135	252	17	g[{x	g[{x	PROPN
ejpam-5135	252	18	,	,	PUNCT
ejpam-5135	252	19	v	v	NOUN
ejpam-5135	252	20	}	}	PUNCT
ejpam-5135	252	21	]	]	PUNCT
ejpam-5135	252	22	and	and	CCONJ
ejpam-5135	252	23	g[{v	g[{v	PROPN
ejpam-5135	252	24	,	,	PUNCT
ejpam-5135	252	25	y	y	PROPN
ejpam-5135	252	26	}	}	PUNCT
ejpam-5135	252	27	]	]	PUNCT
ejpam-5135	252	28	are	be	AUX
ejpam-5135	252	29	blocks	block	NOUN
ejpam-5135	252	30	of	of	ADP
ejpam-5135	252	31	g	g	NOUN
ejpam-5135	252	32	and	and	CCONJ
ejpam-5135	252	33	so	so	ADV
ejpam-5135	252	34	{	{	PUNCT
ejpam-5135	252	35	x	x	NOUN
ejpam-5135	252	36	,	,	PUNCT
ejpam-5135	252	37	v	v	NOUN
ejpam-5135	252	38	,	,	PUNCT
ejpam-5135	252	39	y	y	NOUN
ejpam-5135	252	40	}	}	PUNCT
ejpam-5135	252	41	is	be	AUX
ejpam-5135	252	42	τb(g)-open	τb(g)-open	PROPN
ejpam-5135	252	43	.	.	PUNCT
ejpam-5135	253	1	similarly	similarly	ADV
ejpam-5135	253	2	,	,	PUNCT
ejpam-5135	253	3	f−1({x	f−1({x	PROPN
ejpam-5135	253	4	,	,	PUNCT
ejpam-5135	253	5	v	v	NOUN
ejpam-5135	253	6	,	,	PUNCT
ejpam-5135	253	7	y	y	NOUN
ejpam-5135	253	8	}	}	PUNCT
ejpam-5135	253	9	can	can	AUX
ejpam-5135	253	10	not	not	PART
ejpam-5135	253	11	be	be	AUX
ejpam-5135	253	12	expressed	express	VERB
ejpam-5135	253	13	as	as	ADP
ejpam-5135	253	14	a	a	DET
ejpam-5135	253	15	union	union	NOUN
ejpam-5135	253	16	of	of	ADP
ejpam-5135	253	17	vertex	vertex	NOUN
ejpam-5135	253	18	sets	set	NOUN
ejpam-5135	253	19	of	of	ADP
ejpam-5135	253	20	blocks	block	NOUN
ejpam-5135	253	21	in	in	ADP
ejpam-5135	253	22	pn	pn	PROPN
ejpam-5135	253	23	and	and	CCONJ
ejpam-5135	253	24	a	a	DET
ejpam-5135	253	25	subset	subset	NOUN
ejpam-5135	253	26	of	of	ADP
ejpam-5135	253	27	c	c	PROPN
ejpam-5135	253	28	(	(	PUNCT
ejpam-5135	253	29	pn	pn	NOUN
ejpam-5135	253	30	)	)	PUNCT
ejpam-5135	253	31	.	.	PUNCT
ejpam-5135	254	1	this	this	PRON
ejpam-5135	254	2	means	mean	VERB
ejpam-5135	254	3	that	that	SCONJ
ejpam-5135	254	4	f−1({x	f−1({x	PROPN
ejpam-5135	254	5	,	,	PUNCT
ejpam-5135	254	6	v	v	NOUN
ejpam-5135	254	7	,	,	PUNCT
ejpam-5135	254	8	y	y	NOUN
ejpam-5135	254	9	}	}	PUNCT
ejpam-5135	254	10	is	be	AUX
ejpam-5135	254	11	not	not	PART
ejpam-5135	254	12	τb(pn)-open	τb(pn)-open	ADJ
ejpam-5135	254	13	.	.	PUNCT
ejpam-5135	255	1	but	but	CCONJ
ejpam-5135	255	2	f	f	PROPN
ejpam-5135	255	3	is	be	AUX
ejpam-5135	255	4	continuous	continuous	ADJ
ejpam-5135	255	5	;	;	PUNCT
ejpam-5135	255	6	hence	hence	ADV
ejpam-5135	255	7	a	a	DET
ejpam-5135	255	8	contradiction	contradiction	NOUN
ejpam-5135	255	9	.	.	PUNCT
ejpam-5135	256	1	4	4	X
ejpam-5135	256	2	.	.	X
ejpam-5135	256	3	the	the	DET
ejpam-5135	256	4	block	block	NOUN
ejpam-5135	256	5	topological	topological	ADJ
ejpam-5135	256	6	graph	graph	NOUN
ejpam-5135	256	7	definition	definition	NOUN
ejpam-5135	256	8	2	2	NUM
ejpam-5135	256	9	.	.	PUNCT
ejpam-5135	257	1	let	let	VERB
ejpam-5135	257	2	(	(	PUNCT
ejpam-5135	257	3	v	v	NOUN
ejpam-5135	257	4	(	(	PUNCT
ejpam-5135	257	5	g	g	NOUN
ejpam-5135	257	6	)	)	PUNCT
ejpam-5135	257	7	,	,	PUNCT
ejpam-5135	257	8	τb(g	τb(g	NUM
ejpam-5135	257	9	)	)	PUNCT
ejpam-5135	257	10	)	)	PUNCT
ejpam-5135	258	1	be	be	AUX
ejpam-5135	258	2	block	block	NOUN
ejpam-5135	258	3	topological	topological	ADJ
ejpam-5135	258	4	space	space	NOUN
ejpam-5135	258	5	where	where	SCONJ
ejpam-5135	258	6	τb(g	τb(g	PUNCT
ejpam-5135	258	7	)	)	PUNCT
ejpam-5135	258	8	is	be	AUX
ejpam-5135	258	9	not	not	PART
ejpam-5135	258	10	the	the	DET
ejpam-5135	258	11	indiscrete	indiscrete	ADJ
ejpam-5135	258	12	topology	topology	NOUN
ejpam-5135	258	13	on	on	ADP
ejpam-5135	258	14	v	v	ADP
ejpam-5135	258	15	(	(	PUNCT
ejpam-5135	258	16	g	g	NOUN
ejpam-5135	258	17	)	)	PUNCT
ejpam-5135	258	18	.	.	PUNCT
ejpam-5135	259	1	a	a	DET
ejpam-5135	259	2	block	block	NOUN
ejpam-5135	259	3	topological	topological	ADJ
ejpam-5135	259	4	graph	graph	NOUN
ejpam-5135	259	5	of	of	ADP
ejpam-5135	259	6	(	(	PUNCT
ejpam-5135	259	7	v	v	NOUN
ejpam-5135	259	8	(	(	PUNCT
ejpam-5135	259	9	g	g	NOUN
ejpam-5135	259	10	)	)	PUNCT
ejpam-5135	259	11	,	,	PUNCT
ejpam-5135	259	12	τb(g	τb(g	NUM
ejpam-5135	259	13	)	)	PUNCT
ejpam-5135	259	14	)	)	PUNCT
ejpam-5135	259	15	is	be	AUX
ejpam-5135	259	16	a	a	DET
ejpam-5135	259	17	graph	graph	NOUN
ejpam-5135	259	18	gτb(g	gτb(g	PROPN
ejpam-5135	259	19	)	)	PUNCT
ejpam-5135	259	20	with	with	ADP
ejpam-5135	259	21	vertex	vertex	NOUN
ejpam-5135	259	22	set	set	VERB
ejpam-5135	259	23	v	v	NOUN
ejpam-5135	259	24	(	(	PUNCT
ejpam-5135	259	25	gτb(g	gτb(g	PROPN
ejpam-5135	259	26	)	)	PUNCT
ejpam-5135	259	27	)	)	PUNCT
ejpam-5135	260	1	=	=	SYM
ejpam-5135	260	2	τb(g	τb(g	X
ejpam-5135	260	3	)	)	PUNCT
ejpam-5135	260	4	∖	∖	X
ejpam-5135	260	5	{	{	PUNCT
ejpam-5135	260	6	∅	∅	NOUN
ejpam-5135	260	7	,	,	PUNCT
ejpam-5135	260	8	v	v	NOUN
ejpam-5135	260	9	(	(	PUNCT
ejpam-5135	260	10	g	g	NOUN
ejpam-5135	260	11	)	)	PUNCT
ejpam-5135	260	12	}	}	PUNCT
ejpam-5135	260	13	and	and	CCONJ
ejpam-5135	260	14	edge	edge	VERB
ejpam-5135	260	15	set	set	VERB
ejpam-5135	260	16	e(gτb(g	e(gτb(g	NOUN
ejpam-5135	260	17	)	)	PUNCT
ejpam-5135	260	18	)	)	PUNCT
ejpam-5135	261	1	=	=	PRON
ejpam-5135	261	2	{	{	PUNCT
ejpam-5135	261	3	ab	ab	NOUN
ejpam-5135	261	4	:	:	PUNCT
ejpam-5135	261	5	a	a	DET
ejpam-5135	261	6	⊆	⊆	NUM
ejpam-5135	261	7	b	b	NOUN
ejpam-5135	261	8	,	,	PUNCT
ejpam-5135	261	9	a	a	PRON
ejpam-5135	261	10	,	,	PUNCT
ejpam-5135	261	11	b	b	PROPN
ejpam-5135	261	12	∈	∈	PROPN
ejpam-5135	261	13	v	v	NOUN
ejpam-5135	261	14	(	(	PUNCT
ejpam-5135	261	15	gτb(g	gτb(g	PROPN
ejpam-5135	261	16	)	)	PUNCT
ejpam-5135	261	17	)	)	PUNCT
ejpam-5135	261	18	}	}	PUNCT
ejpam-5135	261	19	.	.	PUNCT
ejpam-5135	262	1	example	example	NOUN
ejpam-5135	263	1	4	4	NUM
ejpam-5135	263	2	.	.	PUNCT
ejpam-5135	264	1	the	the	DET
ejpam-5135	264	2	corresponding	corresponding	ADJ
ejpam-5135	264	3	block	block	NOUN
ejpam-5135	264	4	topological	topological	ADJ
ejpam-5135	264	5	graph	graph	NOUN
ejpam-5135	264	6	of	of	ADP
ejpam-5135	264	7	g	g	NOUN
ejpam-5135	264	8	in	in	ADP
ejpam-5135	264	9	figure	figure	NOUN
ejpam-5135	264	10	7	7	NUM
ejpam-5135	264	11	is	be	AUX
ejpam-5135	264	12	shown	show	VERB
ejpam-5135	264	13	in	in	ADP
ejpam-5135	264	14	figure	figure	NOUN
ejpam-5135	264	15	10	10	NUM
ejpam-5135	264	16	.	.	PUNCT
ejpam-5135	265	1	gτb(g	gτb(g	PROPN
ejpam-5135	265	2	)	)	PUNCT
ejpam-5135	265	3	:	:	PUNCT
ejpam-5135	265	4	{	{	PUNCT
ejpam-5135	265	5	v4	v4	NOUN
ejpam-5135	265	6	}	}	PUNCT
ejpam-5135	265	7	{	{	PUNCT
ejpam-5135	265	8	v4	v4	NOUN
ejpam-5135	265	9	,	,	PUNCT
ejpam-5135	265	10	v5	v5	PROPN
ejpam-5135	265	11	,	,	PUNCT
ejpam-5135	265	12	v6	v6	NOUN
ejpam-5135	265	13	}	}	PUNCT
ejpam-5135	265	14	{	{	PUNCT
ejpam-5135	265	15	v4	v4	NOUN
ejpam-5135	265	16	,	,	PUNCT
ejpam-5135	265	17	v5	v5	PROPN
ejpam-5135	265	18	}	}	PUNCT
ejpam-5135	265	19	{	{	PUNCT
ejpam-5135	265	20	v4	v4	NOUN
ejpam-5135	265	21	,	,	PUNCT
ejpam-5135	265	22	v6	v6	NOUN
ejpam-5135	265	23	}	}	PUNCT
ejpam-5135	265	24	{	{	PUNCT
ejpam-5135	265	25	v1	v1	NOUN
ejpam-5135	265	26	,	,	PUNCT
ejpam-5135	265	27	v2	v2	PROPN
ejpam-5135	265	28	,	,	PUNCT
ejpam-5135	265	29	v3	v3	PROPN
ejpam-5135	265	30	,	,	PUNCT
ejpam-5135	265	31	v4	v4	PROPN
ejpam-5135	265	32	,	,	PUNCT
ejpam-5135	265	33	v5}{v1	v5}{v1	NOUN
ejpam-5135	265	34	,	,	PUNCT
ejpam-5135	265	35	v2	v2	PROPN
ejpam-5135	265	36	,	,	PUNCT
ejpam-5135	265	37	v3	v3	PROPN
ejpam-5135	265	38	,	,	PUNCT
ejpam-5135	265	39	v4	v4	PROPN
ejpam-5135	265	40	,	,	PUNCT
ejpam-5135	265	41	v6	v6	PROPN
ejpam-5135	265	42	}	}	PUNCT
ejpam-5135	265	43	{	{	PUNCT
ejpam-5135	265	44	v1	v1	NOUN
ejpam-5135	265	45	,	,	PUNCT
ejpam-5135	265	46	v2	v2	PROPN
ejpam-5135	265	47	,	,	PUNCT
ejpam-5135	265	48	v3	v3	PROPN
ejpam-5135	265	49	,	,	PUNCT
ejpam-5135	265	50	v4	v4	PROPN
ejpam-5135	265	51	}	}	PUNCT
ejpam-5135	265	52	figure	figure	NOUN
ejpam-5135	265	53	10	10	NUM
ejpam-5135	265	54	:	:	PUNCT
ejpam-5135	265	55	block	block	VERB
ejpam-5135	265	56	topological	topological	ADJ
ejpam-5135	265	57	graph	graph	NOUN
ejpam-5135	265	58	of	of	ADP
ejpam-5135	265	59	g	g	PROPN
ejpam-5135	265	60	references	reference	NOUN
ejpam-5135	265	61	674	674	NUM
ejpam-5135	265	62	remark	remark	NOUN
ejpam-5135	265	63	4	4	NUM
ejpam-5135	265	64	.	.	PUNCT
ejpam-5135	266	1	let	let	VERB
ejpam-5135	266	2	gτb(g	gτb(g	PROPN
ejpam-5135	266	3	)	)	PUNCT
ejpam-5135	266	4	be	be	AUX
ejpam-5135	266	5	a	a	DET
ejpam-5135	266	6	block	block	NOUN
ejpam-5135	266	7	topological	topological	ADJ
ejpam-5135	266	8	graph	graph	NOUN
ejpam-5135	266	9	.	.	PUNCT
ejpam-5135	267	1	then	then	ADV
ejpam-5135	267	2	|v	|v	PROPN
ejpam-5135	267	3	(	(	PUNCT
ejpam-5135	267	4	gτb(g))|	gτb(g))|	NOUN
ejpam-5135	267	5	=	=	PUNCT
ejpam-5135	267	6	|τb(g)|	|τb(g)|	NOUN
ejpam-5135	267	7	−	−	NOUN
ejpam-5135	267	8	2	2	X
ejpam-5135	267	9	.	.	PUNCT
ejpam-5135	267	10	a	a	DET
ejpam-5135	267	11	connected	connected	ADJ
ejpam-5135	267	12	graph	graph	NOUN
ejpam-5135	267	13	containing	contain	VERB
ejpam-5135	267	14	no	no	DET
ejpam-5135	267	15	cut	cut	NOUN
ejpam-5135	267	16	-	-	PUNCT
ejpam-5135	267	17	vertices	vertex	NOUN
ejpam-5135	267	18	has	have	VERB
ejpam-5135	267	19	no	no	DET
ejpam-5135	267	20	corresponding	corresponding	ADJ
ejpam-5135	267	21	block	block	NOUN
ejpam-5135	267	22	topological	topological	ADJ
ejpam-5135	267	23	graph	graph	NOUN
ejpam-5135	267	24	.	.	PUNCT
ejpam-5135	268	1	recall	recall	VERB
ejpam-5135	268	2	that	that	SCONJ
ejpam-5135	268	3	a	a	DET
ejpam-5135	268	4	block	block	NOUN
ejpam-5135	268	5	in	in	ADP
ejpam-5135	268	6	a	a	DET
ejpam-5135	268	7	graph	graph	NOUN
ejpam-5135	268	8	is	be	AUX
ejpam-5135	268	9	not	not	PART
ejpam-5135	268	10	a	a	DET
ejpam-5135	268	11	subgraph	subgraph	NOUN
ejpam-5135	268	12	to	to	ADP
ejpam-5135	268	13	any	any	DET
ejpam-5135	268	14	other	other	ADJ
ejpam-5135	268	15	block	block	NOUN
ejpam-5135	268	16	in	in	ADP
ejpam-5135	268	17	a	a	DET
ejpam-5135	268	18	graph	graph	NOUN
ejpam-5135	268	19	.	.	PUNCT
ejpam-5135	269	1	hence	hence	ADV
ejpam-5135	269	2	,	,	PUNCT
ejpam-5135	269	3	a	a	DET
ejpam-5135	269	4	block	block	NOUN
ejpam-5135	269	5	topological	topological	ADJ
ejpam-5135	269	6	graph	graph	NOUN
ejpam-5135	269	7	is	be	AUX
ejpam-5135	269	8	never	never	ADV
ejpam-5135	269	9	trivial	trivial	ADJ
ejpam-5135	269	10	nor	nor	CCONJ
ejpam-5135	269	11	complete	complete	ADJ
ejpam-5135	269	12	.	.	PUNCT
ejpam-5135	270	1	5	5	X
ejpam-5135	270	2	.	.	X
ejpam-5135	270	3	concluding	conclude	VERB
ejpam-5135	270	4	remarks	remark	VERB
ejpam-5135	270	5	the	the	DET
ejpam-5135	270	6	notion	notion	NOUN
ejpam-5135	270	7	of	of	ADP
ejpam-5135	270	8	block	block	NOUN
ejpam-5135	270	9	topological	topological	ADJ
ejpam-5135	270	10	space	space	NOUN
ejpam-5135	270	11	induced	induce	VERB
ejpam-5135	270	12	by	by	ADP
ejpam-5135	270	13	undirected	undirected	ADJ
ejpam-5135	270	14	simple	simple	ADJ
ejpam-5135	270	15	graphs	graph	NOUN
ejpam-5135	270	16	has	have	AUX
ejpam-5135	270	17	been	be	AUX
ejpam-5135	270	18	successfully	successfully	ADV
ejpam-5135	270	19	introduced	introduce	VERB
ejpam-5135	270	20	in	in	ADP
ejpam-5135	270	21	this	this	DET
ejpam-5135	270	22	paper	paper	NOUN
ejpam-5135	270	23	together	together	ADV
ejpam-5135	270	24	with	with	ADP
ejpam-5135	270	25	some	some	DET
ejpam-5135	270	26	important	important	ADJ
ejpam-5135	270	27	characterizations	characterization	NOUN
ejpam-5135	270	28	and	and	CCONJ
ejpam-5135	270	29	special	special	ADJ
ejpam-5135	270	30	attributes	attribute	NOUN
ejpam-5135	270	31	of	of	ADP
ejpam-5135	270	32	the	the	DET
ejpam-5135	270	33	resulting	result	VERB
ejpam-5135	270	34	block	block	NOUN
ejpam-5135	270	35	topological	topological	ADJ
ejpam-5135	270	36	space	space	NOUN
ejpam-5135	270	37	.	.	PUNCT
ejpam-5135	271	1	here	here	ADV
ejpam-5135	271	2	,	,	PUNCT
ejpam-5135	271	3	the	the	DET
ejpam-5135	271	4	authors	author	NOUN
ejpam-5135	271	5	presented	present	VERB
ejpam-5135	271	6	an	an	DET
ejpam-5135	271	7	initial	initial	ADJ
ejpam-5135	271	8	idea	idea	NOUN
ejpam-5135	271	9	of	of	ADP
ejpam-5135	271	10	the	the	DET
ejpam-5135	271	11	corresponding	corresponding	ADJ
ejpam-5135	271	12	block	block	NOUN
ejpam-5135	271	13	topological	topological	ADJ
ejpam-5135	271	14	graph	graph	NOUN
ejpam-5135	271	15	.	.	PUNCT
ejpam-5135	272	1	one	one	NUM
ejpam-5135	272	2	definite	definite	ADJ
ejpam-5135	272	3	extension	extension	NOUN
ejpam-5135	272	4	of	of	ADP
ejpam-5135	272	5	this	this	DET
ejpam-5135	272	6	research	research	NOUN
ejpam-5135	272	7	is	be	AUX
ejpam-5135	272	8	the	the	DET
ejpam-5135	272	9	study	study	NOUN
ejpam-5135	272	10	of	of	ADP
ejpam-5135	272	11	the	the	DET
ejpam-5135	272	12	block	block	NOUN
ejpam-5135	272	13	topological	topological	ADJ
ejpam-5135	272	14	space	space	NOUN
ejpam-5135	272	15	and	and	CCONJ
ejpam-5135	272	16	the	the	DET
ejpam-5135	272	17	block	block	NOUN
ejpam-5135	272	18	topological	topological	ADJ
ejpam-5135	272	19	graph	graph	NOUN
ejpam-5135	272	20	induced	induce	VERB
ejpam-5135	272	21	by	by	ADP
ejpam-5135	272	22	special	special	ADJ
ejpam-5135	272	23	families	family	NOUN
ejpam-5135	272	24	of	of	ADP
ejpam-5135	272	25	graphs	graph	NOUN
ejpam-5135	272	26	and	and	CCONJ
ejpam-5135	272	27	those	those	DET
ejpam-5135	272	28	graphs	graph	NOUN
ejpam-5135	272	29	resulting	result	VERB
ejpam-5135	272	30	from	from	ADP
ejpam-5135	272	31	unary	unary	ADJ
ejpam-5135	272	32	and	and	CCONJ
ejpam-5135	272	33	binary	binary	ADJ
ejpam-5135	272	34	operations	operation	NOUN
ejpam-5135	272	35	that	that	PRON
ejpam-5135	272	36	the	the	DET
ejpam-5135	272	37	authors	author	NOUN
ejpam-5135	272	38	had	have	AUX
ejpam-5135	272	39	already	already	ADV
ejpam-5135	272	40	started	start	VERB
ejpam-5135	272	41	working	work	VERB
ejpam-5135	272	42	on	on	ADP
ejpam-5135	272	43	.	.	PUNCT
ejpam-5135	273	1	meanwhile	meanwhile	ADV
ejpam-5135	273	2	,	,	PUNCT
ejpam-5135	273	3	some	some	DET
ejpam-5135	273	4	possible	possible	ADJ
ejpam-5135	273	5	and	and	CCONJ
ejpam-5135	273	6	interesting	interesting	ADJ
ejpam-5135	273	7	direction	direction	NOUN
ejpam-5135	273	8	for	for	ADP
ejpam-5135	273	9	further	further	ADJ
ejpam-5135	273	10	study	study	NOUN
ejpam-5135	273	11	is	be	AUX
ejpam-5135	273	12	on	on	ADP
ejpam-5135	273	13	extending	extend	VERB
ejpam-5135	273	14	the	the	DET
ejpam-5135	273	15	idea	idea	NOUN
ejpam-5135	273	16	of	of	ADP
ejpam-5135	273	17	the	the	DET
ejpam-5135	273	18	block	block	NOUN
ejpam-5135	273	19	topology	topology	NOUN
ejpam-5135	273	20	of	of	ADP
ejpam-5135	273	21	a	a	DET
ejpam-5135	273	22	graph	graph	NOUN
ejpam-5135	273	23	to	to	ADP
ejpam-5135	273	24	various	various	ADJ
ejpam-5135	273	25	topological	topological	ADJ
ejpam-5135	273	26	structures	structure	NOUN
ejpam-5135	273	27	such	such	ADJ
ejpam-5135	273	28	as	as	ADP
ejpam-5135	273	29	soft	soft	ADJ
ejpam-5135	273	30	bitopological	bitopological	ADJ
ejpam-5135	273	31	spaces	space	NOUN
ejpam-5135	273	32	[	[	X
ejpam-5135	273	33	13	13	NUM
ejpam-5135	273	34	]	]	PUNCT
ejpam-5135	273	35	,	,	PUNCT
ejpam-5135	273	36	soft	soft	ADJ
ejpam-5135	273	37	topological	topological	ADJ
ejpam-5135	273	38	subspaces	subspace	NOUN
ejpam-5135	273	39	[	[	X
ejpam-5135	273	40	12	12	NUM
ejpam-5135	273	41	]	]	PUNCT
ejpam-5135	273	42	and	and	CCONJ
ejpam-5135	273	43	[	[	X
ejpam-5135	273	44	14	14	NUM
ejpam-5135	273	45	]	]	X
ejpam-5135	273	46	,	,	PUNCT
ejpam-5135	273	47	fuzzy	fuzzy	ADJ
ejpam-5135	273	48	topological	topological	ADJ
ejpam-5135	273	49	space	space	NOUN
ejpam-5135	273	50	[	[	X
ejpam-5135	273	51	15	15	NUM
ejpam-5135	273	52	]	]	X
ejpam-5135	273	53	,	,	PUNCT
ejpam-5135	273	54	regular	regular	ADJ
ejpam-5135	273	55	spaces	space	NOUN
ejpam-5135	273	56	,	,	PUNCT
ejpam-5135	273	57	normal	normal	ADJ
ejpam-5135	273	58	spaces	space	NOUN
ejpam-5135	273	59	,	,	PUNCT
ejpam-5135	273	60	and	and	CCONJ
ejpam-5135	273	61	completely	completely	ADV
ejpam-5135	273	62	regular	regular	ADJ
ejpam-5135	273	63	spaces	space	NOUN
ejpam-5135	273	64	[	[	X
ejpam-5135	273	65	9	9	NUM
ejpam-5135	273	66	]	]	PUNCT
ejpam-5135	273	67	or	or	CCONJ
ejpam-5135	273	68	perhaps	perhaps	ADV
ejpam-5135	273	69	in	in	ADP
ejpam-5135	273	70	looking	look	VERB
ejpam-5135	273	71	into	into	ADP
ejpam-5135	273	72	the	the	DET
ejpam-5135	273	73	block	block	NOUN
ejpam-5135	273	74	topology	topology	NOUN
ejpam-5135	273	75	of	of	ADP
ejpam-5135	273	76	a	a	DET
ejpam-5135	273	77	directed	direct	VERB
ejpam-5135	273	78	graph	graph	NOUN
ejpam-5135	273	79	using	use	VERB
ejpam-5135	273	80	the	the	DET
ejpam-5135	273	81	method	method	NOUN
ejpam-5135	273	82	of	of	ADP
ejpam-5135	273	83	hassan	hassan	PROPN
ejpam-5135	273	84	and	and	CCONJ
ejpam-5135	273	85	abed	abe	VERB
ejpam-5135	273	86	in	in	ADP
ejpam-5135	273	87	[	[	X
ejpam-5135	273	88	7	7	NUM
ejpam-5135	273	89	]	]	PUNCT
ejpam-5135	273	90	.	.	PUNCT
ejpam-5135	274	1	acknowledgements	acknowledgement	NOUN
ejpam-5135	274	2	the	the	DET
ejpam-5135	274	3	authors	author	NOUN
ejpam-5135	274	4	are	be	AUX
ejpam-5135	274	5	beyond	beyond	ADP
ejpam-5135	274	6	grateful	grateful	ADJ
ejpam-5135	274	7	and	and	CCONJ
ejpam-5135	274	8	would	would	AUX
ejpam-5135	274	9	love	love	VERB
ejpam-5135	274	10	to	to	PART
ejpam-5135	274	11	express	express	VERB
ejpam-5135	274	12	their	their	PRON
ejpam-5135	274	13	heartfelt	heartfelt	ADJ
ejpam-5135	274	14	appreciation	appreciation	NOUN
ejpam-5135	274	15	to	to	ADP
ejpam-5135	274	16	the	the	DET
ejpam-5135	274	17	people	people	NOUN
ejpam-5135	274	18	who	who	PRON
ejpam-5135	274	19	were	be	AUX
ejpam-5135	274	20	behind	behind	ADP
ejpam-5135	274	21	the	the	DET
ejpam-5135	274	22	success	success	NOUN
ejpam-5135	274	23	of	of	ADP
ejpam-5135	274	24	this	this	DET
ejpam-5135	274	25	paper	paper	NOUN
ejpam-5135	274	26	.	.	PUNCT
ejpam-5135	275	1	special	special	ADJ
ejpam-5135	275	2	thanks	thank	NOUN
ejpam-5135	275	3	to	to	ADP
ejpam-5135	275	4	prof	prof	PROPN
ejpam-5135	275	5	.	.	PUNCT
ejpam-5135	276	1	rolito	rolito	PROPN
ejpam-5135	276	2	g.	g.	PROPN
ejpam-5135	276	3	eballe	eballe	PROPN
ejpam-5135	276	4	for	for	ADP
ejpam-5135	276	5	the	the	DET
ejpam-5135	276	6	two	two	NUM
ejpam-5135	276	7	questions	question	NOUN
ejpam-5135	276	8	in	in	ADP
ejpam-5135	276	9	his	his	PRON
ejpam-5135	276	10	exam	exam	NOUN
ejpam-5135	276	11	which	which	PRON
ejpam-5135	276	12	were	be	AUX
ejpam-5135	276	13	the	the	DET
ejpam-5135	276	14	motivations	motivation	NOUN
ejpam-5135	276	15	of	of	ADP
ejpam-5135	276	16	this	this	DET
ejpam-5135	276	17	research	research	NOUN
ejpam-5135	276	18	study	study	NOUN
ejpam-5135	276	19	.	.	PUNCT
ejpam-5135	277	1	also	also	ADV
ejpam-5135	277	2	,	,	PUNCT
ejpam-5135	277	3	the	the	DET
ejpam-5135	277	4	authors	author	NOUN
ejpam-5135	277	5	would	would	AUX
ejpam-5135	277	6	like	like	VERB
ejpam-5135	277	7	to	to	PART
ejpam-5135	277	8	express	express	VERB
ejpam-5135	277	9	their	their	PRON
ejpam-5135	277	10	profound	profound	ADJ
ejpam-5135	277	11	gratitude	gratitude	NOUN
ejpam-5135	277	12	to	to	ADP
ejpam-5135	277	13	the	the	DET
ejpam-5135	277	14	department	department	NOUN
ejpam-5135	277	15	of	of	ADP
ejpam-5135	277	16	science	science	NOUN
ejpam-5135	277	17	and	and	CCONJ
ejpam-5135	277	18	technology	technology	NOUN
ejpam-5135	277	19	-	-	PUNCT
ejpam-5135	277	20	science	science	NOUN
ejpam-5135	277	21	education	education	PROPN
ejpam-5135	277	22	institute	institute	PROPN
ejpam-5135	277	23	science	science	PROPN
ejpam-5135	277	24	and	and	CCONJ
ejpam-5135	277	25	technology	technology	NOUN
ejpam-5135	277	26	regional	regional	ADJ
ejpam-5135	277	27	alliance	alliance	NOUN
ejpam-5135	277	28	of	of	ADP
ejpam-5135	277	29	universities	university	NOUN
ejpam-5135	277	30	for	for	ADP
ejpam-5135	277	31	inclusive	inclusive	ADJ
ejpam-5135	277	32	national	national	ADJ
ejpam-5135	277	33	development	development	NOUN
ejpam-5135	277	34	(	(	PUNCT
ejpam-5135	277	35	dost	dost	NOUN
ejpam-5135	277	36	-	-	PUNCT
ejpam-5135	277	37	sei	sei	ADJ
ejpam-5135	277	38	strand	strand	NOUN
ejpam-5135	277	39	)	)	PUNCT
ejpam-5135	277	40	through	through	ADP
ejpam-5135	277	41	the	the	DET
ejpam-5135	277	42	office	office	NOUN
ejpam-5135	277	43	of	of	ADP
ejpam-5135	277	44	admissions	admission	NOUN
ejpam-5135	277	45	,	,	PUNCT
ejpam-5135	277	46	scholarship	scholarship	NOUN
ejpam-5135	277	47	,	,	PUNCT
ejpam-5135	277	48	and	and	CCONJ
ejpam-5135	277	49	placement	placement	NOUN
ejpam-5135	277	50	(	(	PUNCT
ejpam-5135	277	51	oasp	oasp	NOUN
ejpam-5135	277	52	)	)	PUNCT
ejpam-5135	277	53	of	of	ADP
ejpam-5135	277	54	central	central	ADJ
ejpam-5135	277	55	mindanao	mindanao	PROPN
ejpam-5135	277	56	university	university	PROPN
ejpam-5135	277	57	for	for	ADP
ejpam-5135	277	58	the	the	DET
ejpam-5135	277	59	opportunities	opportunity	NOUN
ejpam-5135	277	60	and	and	CCONJ
ejpam-5135	277	61	privileges	privilege	NOUN
ejpam-5135	277	62	given	give	VERB
ejpam-5135	277	63	to	to	ADP
ejpam-5135	277	64	them	they	PRON
ejpam-5135	277	65	which	which	PRON
ejpam-5135	277	66	are	be	AUX
ejpam-5135	277	67	a	a	DET
ejpam-5135	277	68	very	very	ADV
ejpam-5135	277	69	big	big	ADJ
ejpam-5135	277	70	factor	factor	NOUN
ejpam-5135	277	71	in	in	ADP
ejpam-5135	277	72	this	this	DET
ejpam-5135	277	73	research	research	NOUN
ejpam-5135	277	74	journey	journey	NOUN
ejpam-5135	277	75	.	.	PUNCT
ejpam-5135	278	1	references	reference	NOUN
ejpam-5135	278	2	[	[	X
ejpam-5135	278	3	1	1	NUM
ejpam-5135	278	4	]	]	X
ejpam-5135	278	5	k.a	k.a	PROPN
ejpam-5135	278	6	.	.	PROPN
ejpam-5135	278	7	abdu	abdu	PROPN
ejpam-5135	278	8	and	and	CCONJ
ejpam-5135	278	9	a.	a.	NOUN
ejpam-5135	278	10	kilicman	kilicman	PROPN
ejpam-5135	278	11	.	.	PUNCT
ejpam-5135	279	1	topologies	topology	NOUN
ejpam-5135	279	2	on	on	ADP
ejpam-5135	279	3	the	the	DET
ejpam-5135	279	4	edges	edge	NOUN
ejpam-5135	279	5	set	set	VERB
ejpam-5135	279	6	of	of	ADP
ejpam-5135	279	7	directed	direct	VERB
ejpam-5135	279	8	graphs	graph	NOUN
ejpam-5135	279	9	.	.	PUNCT
ejpam-5135	280	1	international	international	ADJ
ejpam-5135	280	2	journal	journal	PROPN
ejpam-5135	280	3	of	of	ADP
ejpam-5135	280	4	mathematical	mathematical	ADJ
ejpam-5135	280	5	analysis	analysis	NOUN
ejpam-5135	280	6	,	,	PUNCT
ejpam-5135	280	7	12(2):71–84	12(2):71–84	NUM
ejpam-5135	280	8	,	,	PUNCT
ejpam-5135	280	9	2018	2018	NUM
ejpam-5135	280	10	.	.	PUNCT
ejpam-5135	281	1	[	[	X
ejpam-5135	281	2	2	2	X
ejpam-5135	281	3	]	]	PUNCT
ejpam-5135	281	4	a	a	DET
ejpam-5135	281	5	alsinaia	alsinaia	NOUN
ejpam-5135	281	6	,	,	PUNCT
ejpam-5135	281	7	b.	b.	PROPN
ejpam-5135	282	1	v.	v.	ADP
ejpam-5135	282	2	dhanaanjayamurthy	dhanaanjayamurthy	PROPN
ejpam-5135	282	3	,	,	PUNCT
ejpam-5135	282	4	a	a	DET
ejpam-5135	282	5	mohammed	mohammed	PROPN
ejpam-5135	282	6	,	,	PUNCT
ejpam-5135	282	7	m	m	VERB
ejpam-5135	282	8	abdlhusein	abdlhusein	NOUN
ejpam-5135	282	9	,	,	PUNCT
ejpam-5135	282	10	and	and	CCONJ
ejpam-5135	282	11	m	m	PROPN
ejpam-5135	282	12	cancan	cancan	ADJ
ejpam-5135	282	13	.	.	PUNCT
ejpam-5135	283	1	topological	topological	ADJ
ejpam-5135	283	2	space	space	NOUN
ejpam-5135	283	3	generated	generate	VERB
ejpam-5135	283	4	by	by	ADP
ejpam-5135	283	5	edges	edge	NOUN
ejpam-5135	283	6	neighborhoods	neighborhood	NOUN
ejpam-5135	283	7	of	of	ADP
ejpam-5135	283	8	discrete	discrete	ADJ
ejpam-5135	283	9	topological	topological	ADJ
ejpam-5135	283	10	graph	graph	NOUN
ejpam-5135	283	11	.	.	PUNCT
ejpam-5135	284	1	[	[	X
ejpam-5135	284	2	3	3	NUM
ejpam-5135	284	3	]	]	X
ejpam-5135	284	4	s	s	VERB
ejpam-5135	284	5	canoy	canoy	NOUN
ejpam-5135	284	6	and	and	CCONJ
ejpam-5135	284	7	r	r	NOUN
ejpam-5135	284	8	lemence	lemence	NOUN
ejpam-5135	284	9	.	.	PUNCT
ejpam-5135	285	1	topologies	topology	NOUN
ejpam-5135	285	2	induced	induce	VERB
ejpam-5135	285	3	by	by	ADP
ejpam-5135	285	4	some	some	DET
ejpam-5135	285	5	special	special	ADJ
ejpam-5135	285	6	graphs	graph	NOUN
ejpam-5135	285	7	.	.	PUNCT
ejpam-5135	286	1	journal	journal	NOUN
ejpam-5135	286	2	of	of	ADP
ejpam-5135	286	3	mathematics	mathematic	NOUN
ejpam-5135	286	4	,	,	PUNCT
ejpam-5135	286	5	2(2):45–50	2(2):45–50	NUM
ejpam-5135	286	6	,	,	PUNCT
ejpam-5135	286	7	1999	1999	NUM
ejpam-5135	286	8	.	.	PUNCT
ejpam-5135	287	1	references	reference	NOUN
ejpam-5135	287	2	675	675	NUM
ejpam-5135	287	3	[	[	X
ejpam-5135	287	4	4	4	NUM
ejpam-5135	287	5	]	]	PUNCT
ejpam-5135	287	6	g	g	PROPN
ejpam-5135	287	7	chartrand	chartrand	NOUN
ejpam-5135	287	8	,	,	PUNCT
ejpam-5135	287	9	l	l	PROPN
ejpam-5135	287	10	lesniak	lesniak	PROPN
ejpam-5135	287	11	,	,	PUNCT
ejpam-5135	287	12	and	and	CCONJ
ejpam-5135	287	13	p	p	PROPN
ejpam-5135	287	14	zhang	zhang	PROPN
ejpam-5135	287	15	.	.	PUNCT
ejpam-5135	287	16	graphs	graph	NOUN
ejpam-5135	287	17	and	and	CCONJ
ejpam-5135	287	18	digraphs	digraph	NOUN
ejpam-5135	287	19	.	.	PUNCT
ejpam-5135	288	1	crc	crc	NOUN
ejpam-5135	288	2	press	press	PROPN
ejpam-5135	288	3	,	,	PUNCT
ejpam-5135	288	4	western	western	PROPN
ejpam-5135	288	5	michigan	michigan	PROPN
ejpam-5135	288	6	university	university	PROPN
ejpam-5135	288	7	,	,	PUNCT
ejpam-5135	288	8	2010	2010	NUM
ejpam-5135	288	9	.	.	PUNCT
ejpam-5135	289	1	[	[	X
ejpam-5135	289	2	5	5	NUM
ejpam-5135	289	3	]	]	X
ejpam-5135	289	4	s	s	VERB
ejpam-5135	289	5	diesto	diesto	ADJ
ejpam-5135	289	6	and	and	CCONJ
ejpam-5135	289	7	s	s	NOUN
ejpam-5135	289	8	gervacio	gervacio	NOUN
ejpam-5135	289	9	.	.	PUNCT
ejpam-5135	290	1	finite	finite	PROPN
ejpam-5135	290	2	topological	topological	ADJ
ejpam-5135	290	3	graphs	graph	NOUN
ejpam-5135	290	4	.	.	PUNCT
ejpam-5135	291	1	journal	journal	NOUN
ejpam-5135	291	2	of	of	ADP
ejpam-5135	291	3	research	research	NOUN
ejpam-5135	291	4	and	and	CCONJ
ejpam-5135	291	5	development	development	NOUN
ejpam-5135	291	6	,	,	PUNCT
ejpam-5135	291	7	1(1):76–81	1(1):76–81	NUM
ejpam-5135	291	8	,	,	PUNCT
ejpam-5135	291	9	1983	1983	NUM
ejpam-5135	291	10	.	.	PUNCT
ejpam-5135	292	1	[	[	X
ejpam-5135	292	2	6	6	NUM
ejpam-5135	292	3	]	]	PUNCT
ejpam-5135	292	4	a.	a.	PROPN
ejpam-5135	292	5	e.	e.	PROPN
ejpam-5135	292	6	gamorez	gamorez	PROPN
ejpam-5135	292	7	,	,	PUNCT
ejpam-5135	292	8	c.	c.	PROPN
ejpam-5135	292	9	g.	g.	PROPN
ejpam-5135	292	10	nianga	nianga	ADV
ejpam-5135	292	11	,	,	PUNCT
ejpam-5135	292	12	and	and	CCONJ
ejpam-5135	292	13	s	s	VERB
ejpam-5135	292	14	canoy	canoy	NOUN
ejpam-5135	292	15	.	.	PUNCT
ejpam-5135	293	1	topologies	topology	NOUN
ejpam-5135	293	2	induced	induce	VERB
ejpam-5135	293	3	by	by	ADP
ejpam-5135	293	4	neighborhoods	neighborhood	NOUN
ejpam-5135	293	5	of	of	ADP
ejpam-5135	293	6	a	a	DET
ejpam-5135	293	7	graph	graph	NOUN
ejpam-5135	293	8	under	under	ADP
ejpam-5135	293	9	some	some	DET
ejpam-5135	293	10	binary	binary	ADJ
ejpam-5135	293	11	operations	operation	NOUN
ejpam-5135	293	12	.	.	PUNCT
ejpam-5135	294	1	european	european	ADJ
ejpam-5135	294	2	journal	journal	PROPN
ejpam-5135	294	3	of	of	ADP
ejpam-5135	294	4	pure	pure	ADJ
ejpam-5135	294	5	and	and	CCONJ
ejpam-5135	294	6	applied	applied	ADJ
ejpam-5135	294	7	mathematics	mathematic	NOUN
ejpam-5135	294	8	,	,	PUNCT
ejpam-5135	294	9	12(3):749–755	12(3):749–755	NUM
ejpam-5135	294	10	,	,	PUNCT
ejpam-5135	294	11	2019	2019	NUM
ejpam-5135	294	12	.	.	PUNCT
ejpam-5135	295	1	[	[	X
ejpam-5135	295	2	7	7	X
ejpam-5135	295	3	]	]	X
ejpam-5135	295	4	a.f	a.f	PROPN
ejpam-5135	295	5	.	.	PROPN
ejpam-5135	295	6	hassan	hassan	PROPN
ejpam-5135	295	7	and	and	CCONJ
ejpam-5135	295	8	z.i	z.i	PROPN
ejpam-5135	295	9	.	.	PROPN
ejpam-5135	295	10	abed	abed	PROPN
ejpam-5135	295	11	.	.	PUNCT
ejpam-5135	296	1	independent	independent	ADJ
ejpam-5135	296	2	(	(	PUNCT
ejpam-5135	296	3	non	non	ADJ
ejpam-5135	296	4	-	-	ADJ
ejpam-5135	296	5	adjacent	adjacent	ADJ
ejpam-5135	296	6	vertices	vertex	NOUN
ejpam-5135	296	7	)	)	PUNCT
ejpam-5135	296	8	topological	topological	ADJ
ejpam-5135	296	9	spaces	space	NOUN
ejpam-5135	296	10	associated	associate	VERB
ejpam-5135	296	11	with	with	ADP
ejpam-5135	296	12	undirected	undirected	ADJ
ejpam-5135	296	13	graphs	graph	NOUN
ejpam-5135	296	14	,	,	PUNCT
ejpam-5135	296	15	with	with	ADP
ejpam-5135	296	16	some	some	DET
ejpam-5135	296	17	applications	application	NOUN
ejpam-5135	296	18	in	in	ADP
ejpam-5135	296	19	biomathematices	biomathematice	NOUN
ejpam-5135	296	20	.	.	PUNCT
ejpam-5135	297	1	in	in	ADP
ejpam-5135	297	2	journal	journal	PROPN
ejpam-5135	297	3	of	of	ADP
ejpam-5135	297	4	physics	physics	PROPN
ejpam-5135	297	5	,	,	PUNCT
ejpam-5135	297	6	1591(1	1591(1	NUM
ejpam-5135	297	7	)	)	PUNCT
ejpam-5135	297	8	,	,	PUNCT
ejpam-5135	297	9	2020	2020	NUM
ejpam-5135	297	10	.	.	PUNCT
ejpam-5135	298	1	[	[	X
ejpam-5135	298	2	8	8	NUM
ejpam-5135	298	3	]	]	X
ejpam-5135	298	4	d.d	d.d	PROPN
ejpam-5135	298	5	.	.	PROPN
ejpam-5135	298	6	laping	laping	PROPN
ejpam-5135	298	7	and	and	CCONJ
ejpam-5135	298	8	c.m	c.m	PROPN
ejpam-5135	298	9	.	.	PROPN
ejpam-5135	298	10	balingit	balingit	PROPN
ejpam-5135	298	11	.	.	PUNCT
ejpam-5135	299	1	a	a	DET
ejpam-5135	299	2	generalized	generalized	ADJ
ejpam-5135	299	3	topology	topology	NOUN
ejpam-5135	299	4	from	from	ADP
ejpam-5135	299	5	the	the	DET
ejpam-5135	299	6	edge	edge	NOUN
ejpam-5135	299	7	set	set	NOUN
ejpam-5135	299	8	of	of	ADP
ejpam-5135	299	9	maximal	maximal	ADJ
ejpam-5135	299	10	paths	path	NOUN
ejpam-5135	299	11	of	of	ADP
ejpam-5135	299	12	directed	direct	VERB
ejpam-5135	299	13	graphs	graph	NOUN
ejpam-5135	299	14	.	.	PUNCT
ejpam-5135	300	1	asian	asian	ADJ
ejpam-5135	300	2	research	research	PROPN
ejpam-5135	300	3	journal	journal	NOUN
ejpam-5135	300	4	of	of	ADP
ejpam-5135	300	5	mathematics	mathematic	NOUN
ejpam-5135	300	6	,	,	PUNCT
ejpam-5135	300	7	18(10):11–21	18(10):11–21	NUM
ejpam-5135	300	8	,	,	PUNCT
ejpam-5135	300	9	2022	2022	NUM
ejpam-5135	300	10	.	.	PUNCT
ejpam-5135	301	1	[	[	X
ejpam-5135	301	2	9	9	NUM
ejpam-5135	301	3	]	]	PUNCT
ejpam-5135	301	4	s	s	VERB
ejpam-5135	301	5	lipschutz	lipschutz	NOUN
ejpam-5135	301	6	.	.	PUNCT
ejpam-5135	302	1	schaum	schaum	PROPN
ejpam-5135	302	2	’s	’s	PART
ejpam-5135	302	3	outline	outline	NOUN
ejpam-5135	302	4	of	of	ADP
ejpam-5135	302	5	theory	theory	NOUN
ejpam-5135	302	6	and	and	CCONJ
ejpam-5135	302	7	problems	problem	NOUN
ejpam-5135	302	8	of	of	ADP
ejpam-5135	302	9	general	general	ADJ
ejpam-5135	302	10	topology	topology	NOUN
ejpam-5135	302	11	.	.	PUNCT
ejpam-5135	303	1	mcgraw	mcgraw	PROPN
ejpam-5135	303	2	hill	hill	PROPN
ejpam-5135	303	3	,	,	PUNCT
ejpam-5135	303	4	temple	temple	PROPN
ejpam-5135	303	5	university	university	PROPN
ejpam-5135	303	6	,	,	PUNCT
ejpam-5135	303	7	1965	1965	NUM
ejpam-5135	303	8	.	.	PUNCT
ejpam-5135	304	1	[	[	X
ejpam-5135	304	2	10	10	NUM
ejpam-5135	304	3	]	]	X
ejpam-5135	304	4	o.y	o.y	PROPN
ejpam-5135	304	5	.	.	PUNCT
ejpam-5135	305	1	viro	viro	PROPN
ejpam-5135	305	2	,	,	PUNCT
ejpam-5135	305	3	o.a	o.a	PROPN
ejpam-5135	305	4	.	.	PROPN
ejpam-5135	305	5	ivanov	ivanov	PROPN
ejpam-5135	305	6	,	,	PUNCT
ejpam-5135	305	7	n.y	n.y	PROPN
ejpam-5135	305	8	.	.	PROPN
ejpam-5135	305	9	netsvetaev	netsvetaev	PROPN
ejpam-5135	305	10	,	,	PUNCT
ejpam-5135	305	11	and	and	CCONJ
ejpam-5135	305	12	v.m	v.m	PROPN
ejpam-5135	305	13	.	.	PROPN
ejpam-5135	305	14	kharlamov	kharlamov	PROPN
ejpam-5135	305	15	.	.	PUNCT
ejpam-5135	306	1	elementary	elementary	ADJ
ejpam-5135	306	2	topology	topology	PROPN
ejpam-5135	306	3	problem	problem	NOUN
ejpam-5135	306	4	textbook	textbook	NOUN
ejpam-5135	306	5	.	.	PUNCT
ejpam-5135	307	1	[	[	X
ejpam-5135	307	2	11	11	NUM
ejpam-5135	307	3	]	]	X
ejpam-5135	307	4	e	e	X
ejpam-5135	307	5	weisstein	weisstein	NOUN
ejpam-5135	307	6	.	.	PUNCT
ejpam-5135	308	1	block	block	NOUN
ejpam-5135	308	2	.	.	PUNCT
ejpam-5135	309	1	from	from	ADP
ejpam-5135	309	2	mathworld	mathworld	NOUN
ejpam-5135	309	3	–	–	PUNCT
ejpam-5135	309	4	a	a	DET
ejpam-5135	309	5	wolfram	wolfram	PROPN
ejpam-5135	309	6	web	web	NOUN
ejpam-5135	309	7	resource	resource	NOUN
ejpam-5135	309	8	.	.	PUNCT
ejpam-5135	309	9	https://mathworld.wolfram.com/block.html	https://mathworld.wolfram.com/block.html	X
ejpam-5135	309	10	.	.	PUNCT
ejpam-5135	310	1	[	[	X
ejpam-5135	310	2	12	12	NUM
ejpam-5135	310	3	]	]	X
ejpam-5135	310	4	g	g	PROPN
ejpam-5135	310	5	şenel	şenel	PROPN
ejpam-5135	310	6	.	.	PUNCT
ejpam-5135	311	1	a	a	DET
ejpam-5135	311	2	new	new	ADJ
ejpam-5135	311	3	approach	approach	NOUN
ejpam-5135	311	4	to	to	ADP
ejpam-5135	311	5	hausdorff	hausdorff	NOUN
ejpam-5135	311	6	space	space	NOUN
ejpam-5135	311	7	theory	theory	NOUN
ejpam-5135	311	8	via	via	ADP
ejpam-5135	311	9	the	the	DET
ejpam-5135	311	10	soft	soft	ADJ
ejpam-5135	311	11	sets	set	NOUN
ejpam-5135	311	12	.	.	PUNCT
ejpam-5135	312	1	mathematical	mathematical	ADJ
ejpam-5135	312	2	problems	problem	NOUN
ejpam-5135	312	3	in	in	ADP
ejpam-5135	312	4	engineerings	engineering	NOUN
ejpam-5135	312	5	,	,	PUNCT
ejpam-5135	312	6	2016	2016	NUM
ejpam-5135	312	7	.	.	PUNCT
ejpam-5135	313	1	[	[	X
ejpam-5135	313	2	13	13	NUM
ejpam-5135	313	3	]	]	SYM
ejpam-5135	313	4	g	g	NOUN
ejpam-5135	313	5	şenel	şenel	PROPN
ejpam-5135	313	6	and	and	CCONJ
ejpam-5135	313	7	n	n	PRON
ejpam-5135	313	8	cagman	cagman	NOUN
ejpam-5135	313	9	.	.	PUNCT
ejpam-5135	314	1	soft	soft	ADJ
ejpam-5135	314	2	closed	closed	ADJ
ejpam-5135	314	3	sets	set	NOUN
ejpam-5135	314	4	on	on	ADP
ejpam-5135	314	5	soft	soft	ADJ
ejpam-5135	314	6	bitopological	bitopological	ADJ
ejpam-5135	314	7	space	space	NOUN
ejpam-5135	314	8	.	.	PUNCT
ejpam-5135	315	1	journal	journal	NOUN
ejpam-5135	315	2	of	of	ADP
ejpam-5135	315	3	new	new	ADJ
ejpam-5135	315	4	results	result	NOUN
ejpam-5135	315	5	in	in	ADP
ejpam-5135	315	6	science	science	NOUN
ejpam-5135	315	7	,	,	PUNCT
ejpam-5135	315	8	3(5):57–66	3(5):57–66	NUM
ejpam-5135	315	9	,	,	PUNCT
ejpam-5135	315	10	2014	2014	NUM
ejpam-5135	315	11	.	.	PUNCT
ejpam-5135	316	1	[	[	X
ejpam-5135	316	2	14	14	NUM
ejpam-5135	316	3	]	]	X
ejpam-5135	316	4	g	g	NOUN
ejpam-5135	316	5	şenel	şenel	PROPN
ejpam-5135	316	6	and	and	CCONJ
ejpam-5135	316	7	n	n	PRON
ejpam-5135	316	8	cagman	cagman	NOUN
ejpam-5135	316	9	.	.	PUNCT
ejpam-5135	317	1	soft	soft	ADJ
ejpam-5135	317	2	topological	topological	ADJ
ejpam-5135	317	3	subspaces	subspace	NOUN
ejpam-5135	317	4	.	.	PUNCT
ejpam-5135	318	1	annals	annal	NOUN
ejpam-5135	318	2	of	of	ADP
ejpam-5135	318	3	fuzzy	fuzzy	ADJ
ejpam-5135	318	4	mathematics	mathematic	NOUN
ejpam-5135	318	5	and	and	CCONJ
ejpam-5135	318	6	informatics	informatic	NOUN
ejpam-5135	318	7	,	,	PUNCT
ejpam-5135	318	8	10(4):525–535	10(4):525–535	NUM
ejpam-5135	318	9	,	,	PUNCT
ejpam-5135	318	10	2015	2015	NUM
ejpam-5135	318	11	.	.	PUNCT
ejpam-5135	319	1	[	[	X
ejpam-5135	319	2	15	15	NUM
ejpam-5135	319	3	]	]	X
ejpam-5135	319	4	a.p	a.p	PROPN
ejpam-5135	319	5	.	.	PROPN
ejpam-5135	319	6	šostak	šostak	NOUN
ejpam-5135	319	7	.	.	PUNCT
ejpam-5135	320	1	on	on	ADP
ejpam-5135	320	2	a	a	DET
ejpam-5135	320	3	fuzzy	fuzzy	ADJ
ejpam-5135	320	4	topological	topological	ADJ
ejpam-5135	320	5	structure	structure	NOUN
ejpam-5135	320	6	.	.	PUNCT
ejpam-5135	321	1	in	in	ADP
ejpam-5135	321	2	proceedings	proceeding	NOUN
ejpam-5135	321	3	of	of	ADP
ejpam-5135	321	4	the	the	DET
ejpam-5135	321	5	13th	13th	NOUN
ejpam-5135	321	6	winter	winter	NOUN
ejpam-5135	321	7	school	school	NOUN
ejpam-5135	321	8	on	on	ADP
ejpam-5135	321	9	abstract	abstract	ADJ
ejpam-5135	321	10	analysis	analysis	NOUN
ejpam-5135	321	11	,	,	PUNCT
ejpam-5135	321	12	page	page	NOUN
ejpam-5135	321	13	89–103	89–103	PROPN
ejpam-5135	321	14	,	,	PUNCT
ejpam-5135	321	15	1985	1985	NUM
ejpam-5135	321	16	.	.	PUNCT