id	sid	tid	token	lemma	pos
ejpam-4283	1	1	european	european	PROPN
ejpam-4283	1	2	journal	journal	PROPN
ejpam-4283	1	3	of	of	ADP
ejpam-4283	1	4	pure	pure	ADJ
ejpam-4283	1	5	and	and	CCONJ
ejpam-4283	1	6	applied	apply	VERB
ejpam-4283	1	7	mathematics	mathematic	NOUN
ejpam-4283	1	8	vol	vol	NOUN
ejpam-4283	1	9	.	.	PROPN
ejpam-4283	2	1	15	15	NUM
ejpam-4283	2	2	,	,	PUNCT
ejpam-4283	2	3	no	no	INTJ
ejpam-4283	2	4	.	.	NOUN
ejpam-4283	2	5	2	2	NUM
ejpam-4283	2	6	,	,	PUNCT
ejpam-4283	2	7	2022	2022	NUM
ejpam-4283	2	8	,	,	PUNCT
ejpam-4283	2	9	403	403	NUM
ejpam-4283	2	10	-	-	SYM
ejpam-4283	2	11	414	414	NUM
ejpam-4283	2	12	issn	issn	PROPN
ejpam-4283	2	13	1307	1307	NUM
ejpam-4283	2	14	-	-	SYM
ejpam-4283	2	15	5543	5543	NUM
ejpam-4283	2	16	–	–	PUNCT
ejpam-4283	3	1	ejpam.com	ejpam.com	X
ejpam-4283	3	2	published	publish	VERB
ejpam-4283	3	3	by	by	ADP
ejpam-4283	3	4	new	new	PROPN
ejpam-4283	3	5	york	york	PROPN
ejpam-4283	3	6	business	business	PROPN
ejpam-4283	3	7	global	global	PROPN
ejpam-4283	3	8	on	on	ADP
ejpam-4283	3	9	nowhere	nowhere	DET
ejpam-4283	3	10	dense	dense	ADJ
ejpam-4283	3	11	sets	set	NOUN
ejpam-4283	3	12	preecha	preecha	PROPN
ejpam-4283	3	13	yupapin1,2	yupapin1,2	PROPN
ejpam-4283	3	14	,	,	PUNCT
ejpam-4283	3	15	vadakasi	vadakasi	PROPN
ejpam-4283	3	16	subramanian3	subramanian3	PROPN
ejpam-4283	3	17	,	,	PUNCT
ejpam-4283	3	18	yasser	yasser	PROPN
ejpam-4283	3	19	farhat4,∗	farhat4,∗	ADJ
ejpam-4283	3	20	1	1	NUM
ejpam-4283	3	21	computational	computational	ADJ
ejpam-4283	3	22	optics	optic	NOUN
ejpam-4283	3	23	research	research	NOUN
ejpam-4283	3	24	group	group	NOUN
ejpam-4283	3	25	,	,	PUNCT
ejpam-4283	3	26	science	science	NOUN
ejpam-4283	3	27	and	and	CCONJ
ejpam-4283	3	28	technology	technology	NOUN
ejpam-4283	3	29	advanced	advanced	ADJ
ejpam-4283	3	30	institue	institue	NOUN
ejpam-4283	3	31	,	,	PUNCT
ejpam-4283	3	32	van	van	PROPN
ejpam-4283	3	33	lang	lang	PROPN
ejpam-4283	3	34	university	university	PROPN
ejpam-4283	3	35	,	,	PUNCT
ejpam-4283	3	36	ho	ho	PROPN
ejpam-4283	3	37	chi	chi	PROPN
ejpam-4283	3	38	minh	minh	PROPN
ejpam-4283	3	39	city	city	PROPN
ejpam-4283	3	40	,	,	PUNCT
ejpam-4283	3	41	vietnam	vietnam	PROPN
ejpam-4283	3	42	2	2	NUM
ejpam-4283	3	43	faculty	faculty	NOUN
ejpam-4283	3	44	of	of	ADP
ejpam-4283	3	45	technology	technology	NOUN
ejpam-4283	3	46	,	,	PUNCT
ejpam-4283	3	47	van	van	PROPN
ejpam-4283	3	48	lang	lang	PROPN
ejpam-4283	3	49	university	university	PROPN
ejpam-4283	3	50	,	,	PUNCT
ejpam-4283	3	51	ho	ho	PROPN
ejpam-4283	3	52	chi	chi	PROPN
ejpam-4283	3	53	minh	minh	PROPN
ejpam-4283	3	54	city	city	PROPN
ejpam-4283	3	55	,	,	PUNCT
ejpam-4283	3	56	vietnam	vietnam	PROPN
ejpam-4283	3	57	3	3	NUM
ejpam-4283	3	58	department	department	NOUN
ejpam-4283	3	59	of	of	ADP
ejpam-4283	3	60	mathematics	mathematic	NOUN
ejpam-4283	3	61	,	,	PUNCT
ejpam-4283	3	62	a.k.d.dharma	a.k.d.dharma	PROPN
ejpam-4283	3	63	raja	raja	PROPN
ejpam-4283	3	64	women	woman	NOUN
ejpam-4283	3	65	’s	’s	PART
ejpam-4283	3	66	college	college	PROPN
ejpam-4283	3	67	,	,	PUNCT
ejpam-4283	3	68	rajapalayam	rajapalayam	PROPN
ejpam-4283	3	69	4	4	NUM
ejpam-4283	3	70	academic	academic	ADJ
ejpam-4283	3	71	support	support	NOUN
ejpam-4283	3	72	department	department	NOUN
ejpam-4283	3	73	,	,	PUNCT
ejpam-4283	3	74	abu	abu	PROPN
ejpam-4283	3	75	dhabi	dhabi	PROPN
ejpam-4283	3	76	polytechnic	polytechnic	PROPN
ejpam-4283	3	77	,	,	PUNCT
ejpam-4283	3	78	p.	p.	PROPN
ejpam-4283	3	79	o.	o.	PROPN
ejpam-4283	3	80	box	box	PROPN
ejpam-4283	3	81	111499	111499	NUM
ejpam-4283	3	82	,	,	PUNCT
ejpam-4283	3	83	abu	abu	PROPN
ejpam-4283	3	84	dhabi	dhabi	PROPN
ejpam-4283	3	85	,	,	PUNCT
ejpam-4283	3	86	uae	uae	PROPN
ejpam-4283	3	87	abstract	abstract	NOUN
ejpam-4283	3	88	.	.	PUNCT
ejpam-4283	4	1	we	we	PRON
ejpam-4283	4	2	introduce	introduce	VERB
ejpam-4283	4	3	two	two	NUM
ejpam-4283	4	4	types	type	NOUN
ejpam-4283	4	5	of	of	ADP
ejpam-4283	4	6	strongly	strongly	ADV
ejpam-4283	4	7	nowhere	nowhere	ADV
ejpam-4283	4	8	dense	dense	ADJ
ejpam-4283	4	9	sets	set	NOUN
ejpam-4283	4	10	,	,	PUNCT
ejpam-4283	4	11	namely	namely	ADV
ejpam-4283	4	12	(	(	PUNCT
ejpam-4283	4	13	s	s	X
ejpam-4283	4	14	,	,	PUNCT
ejpam-4283	4	15	v)-strongly	v)-strongly	ADV
ejpam-4283	4	16	nowhere	nowhere	ADV
ejpam-4283	4	17	dense	dense	ADJ
ejpam-4283	4	18	set	set	NOUN
ejpam-4283	4	19	,	,	PUNCT
ejpam-4283	4	20	(	(	PUNCT
ejpam-4283	4	21	s	s	X
ejpam-4283	4	22	,	,	PUNCT
ejpam-4283	4	23	v)?-strongly	v)?-strongly	ADV
ejpam-4283	4	24	nowhere	nowhere	ADV
ejpam-4283	4	25	dense	dense	ADJ
ejpam-4283	4	26	set	set	NOUN
ejpam-4283	4	27	and	and	CCONJ
ejpam-4283	4	28	analyze	analyze	VERB
ejpam-4283	4	29	their	their	PRON
ejpam-4283	4	30	characteristics	characteristic	NOUN
ejpam-4283	4	31	in	in	ADP
ejpam-4283	4	32	a	a	DET
ejpam-4283	4	33	bigeneralized	bigeneralize	VERB
ejpam-4283	4	34	topological	topological	ADJ
ejpam-4283	4	35	space	space	NOUN
ejpam-4283	4	36	(	(	PUNCT
ejpam-4283	4	37	bgts	bgts	PROPN
ejpam-4283	4	38	)	)	PUNCT
ejpam-4283	4	39	.	.	PUNCT
ejpam-4283	5	1	further	far	ADV
ejpam-4283	5	2	,	,	PUNCT
ejpam-4283	5	3	it	it	PRON
ejpam-4283	5	4	is	be	AUX
ejpam-4283	5	5	also	also	ADV
ejpam-4283	5	6	given	give	VERB
ejpam-4283	5	7	some	some	DET
ejpam-4283	5	8	relations	relation	NOUN
ejpam-4283	5	9	between	between	ADP
ejpam-4283	5	10	these	these	DET
ejpam-4283	5	11	two	two	NUM
ejpam-4283	5	12	types	type	NOUN
ejpam-4283	5	13	of	of	ADP
ejpam-4283	5	14	strongly	strongly	ADV
ejpam-4283	5	15	nowhere	nowhere	ADV
ejpam-4283	5	16	dense	dense	ADJ
ejpam-4283	5	17	sets	set	NOUN
ejpam-4283	5	18	along	along	ADP
ejpam-4283	5	19	with	with	ADP
ejpam-4283	5	20	its	its	PRON
ejpam-4283	5	21	various	various	ADJ
ejpam-4283	5	22	properties	property	NOUN
ejpam-4283	5	23	for	for	ADP
ejpam-4283	5	24	(	(	PUNCT
ejpam-4283	5	25	s	s	X
ejpam-4283	5	26	,	,	PUNCT
ejpam-4283	5	27	v)?-strongly	v)?-strongly	ADV
ejpam-4283	5	28	nowhere	nowhere	ADV
ejpam-4283	5	29	dense	dense	ADJ
ejpam-4283	5	30	set	set	NOUN
ejpam-4283	5	31	.	.	PUNCT
ejpam-4283	6	1	finally	finally	ADV
ejpam-4283	6	2	,	,	PUNCT
ejpam-4283	6	3	the	the	DET
ejpam-4283	6	4	necessary	necessary	ADJ
ejpam-4283	6	5	and	and	CCONJ
ejpam-4283	6	6	sufficient	sufficient	ADJ
ejpam-4283	6	7	condition	condition	NOUN
ejpam-4283	6	8	is	be	AUX
ejpam-4283	6	9	found	find	VERB
ejpam-4283	6	10	between	between	ADP
ejpam-4283	6	11	µ-strongly	µ-strongly	ADV
ejpam-4283	6	12	nowhere	nowhere	ADV
ejpam-4283	6	13	dense	dense	ADJ
ejpam-4283	6	14	set	set	NOUN
ejpam-4283	6	15	and	and	CCONJ
ejpam-4283	6	16	(	(	PUNCT
ejpam-4283	6	17	s	s	X
ejpam-4283	6	18	,	,	PUNCT
ejpam-4283	6	19	v)?-strongly	v)?-strongly	ADV
ejpam-4283	6	20	nowhere	nowhere	ADV
ejpam-4283	6	21	dense	dense	ADJ
ejpam-4283	6	22	set	set	NOUN
ejpam-4283	6	23	in	in	ADP
ejpam-4283	6	24	a	a	DET
ejpam-4283	6	25	bgts	bgts	NOUN
ejpam-4283	6	26	.	.	PUNCT
ejpam-4283	7	1	2020	2020	NUM
ejpam-4283	7	2	mathematics	mathematics	PROPN
ejpam-4283	7	3	subject	subject	NOUN
ejpam-4283	7	4	classifications	classification	NOUN
ejpam-4283	7	5	:	:	PUNCT
ejpam-4283	7	6	54a05	54a05	NUM
ejpam-4283	7	7	,	,	PUNCT
ejpam-4283	7	8	54a10	54a10	NUM
ejpam-4283	7	9	key	key	ADJ
ejpam-4283	7	10	words	word	NOUN
ejpam-4283	7	11	and	and	CCONJ
ejpam-4283	7	12	phrases	phrase	NOUN
ejpam-4283	7	13	:	:	PUNCT
ejpam-4283	7	14	bigeneralized	bigeneralize	VERB
ejpam-4283	7	15	topological	topological	ADJ
ejpam-4283	7	16	spaces	space	NOUN
ejpam-4283	7	17	,	,	PUNCT
ejpam-4283	7	18	µ(s	µ(	NOUN
ejpam-4283	7	19	,	,	PUNCT
ejpam-4283	7	20	v)-open	v)-open	NOUN
ejpam-4283	7	21	,	,	PUNCT
ejpam-4283	7	22	(	(	PUNCT
ejpam-4283	7	23	s	s	X
ejpam-4283	7	24	,	,	PUNCT
ejpam-4283	7	25	v)-open	v)-open	ADJ
ejpam-4283	7	26	,	,	PUNCT
ejpam-4283	7	27	(	(	PUNCT
ejpam-4283	7	28	s	s	X
ejpam-4283	7	29	,	,	PUNCT
ejpam-4283	7	30	v)nowhere	v)nowhere	X
ejpam-4283	7	31	dense	dense	ADJ
ejpam-4283	7	32	1	1	NUM
ejpam-4283	7	33	.	.	X
ejpam-4283	7	34	introduction	introduction	NOUN
ejpam-4283	7	35	the	the	DET
ejpam-4283	7	36	concept	concept	NOUN
ejpam-4283	7	37	of	of	ADP
ejpam-4283	7	38	a	a	DET
ejpam-4283	7	39	generalized	generalized	ADJ
ejpam-4283	7	40	topological	topological	ADJ
ejpam-4283	7	41	space	space	NOUN
ejpam-4283	7	42	was	be	AUX
ejpam-4283	7	43	introduced	introduce	VERB
ejpam-4283	7	44	by	by	ADP
ejpam-4283	7	45	császár	császár	NOUN
ejpam-4283	7	46	in	in	ADP
ejpam-4283	7	47	[	[	X
ejpam-4283	7	48	4	4	NUM
ejpam-4283	7	49	]	]	PUNCT
ejpam-4283	7	50	.	.	PUNCT
ejpam-4283	8	1	let	let	VERB
ejpam-4283	8	2	x	x	PRON
ejpam-4283	8	3	be	be	AUX
ejpam-4283	8	4	any	any	DET
ejpam-4283	8	5	non	non	ADJ
ejpam-4283	8	6	-	-	ADJ
ejpam-4283	8	7	null	null	ADJ
ejpam-4283	8	8	set	set	NOUN
ejpam-4283	8	9	.	.	PUNCT
ejpam-4283	9	1	a	a	DET
ejpam-4283	9	2	collection	collection	NOUN
ejpam-4283	9	3	µ	µ	X
ejpam-4283	9	4	of	of	ADP
ejpam-4283	9	5	subsets	subset	NOUN
ejpam-4283	9	6	of	of	ADP
ejpam-4283	9	7	x	x	X
ejpam-4283	9	8	is	be	AUX
ejpam-4283	9	9	a	a	DET
ejpam-4283	9	10	generalized	generalized	ADJ
ejpam-4283	9	11	topology	topology	NOUN
ejpam-4283	9	12	[	[	X
ejpam-4283	9	13	8	8	NUM
ejpam-4283	9	14	]	]	PUNCT
ejpam-4283	9	15	in	in	ADP
ejpam-4283	9	16	x	x	SYM
ejpam-4283	9	17	if	if	SCONJ
ejpam-4283	9	18	it	it	PRON
ejpam-4283	9	19	contains	contain	VERB
ejpam-4283	9	20	the	the	DET
ejpam-4283	9	21	empty	empty	ADJ
ejpam-4283	9	22	set	set	NOUN
ejpam-4283	9	23	and	and	CCONJ
ejpam-4283	9	24	it	it	PRON
ejpam-4283	9	25	closed	close	VERB
ejpam-4283	9	26	under	under	ADP
ejpam-4283	9	27	arbitrary	arbitrary	ADJ
ejpam-4283	9	28	union	union	NOUN
ejpam-4283	9	29	.	.	PUNCT
ejpam-4283	10	1	then	then	ADV
ejpam-4283	10	2	the	the	DET
ejpam-4283	10	3	pair	pair	NOUN
ejpam-4283	10	4	(	(	PUNCT
ejpam-4283	10	5	x,µ	x,µ	NOUN
ejpam-4283	10	6	)	)	PUNCT
ejpam-4283	10	7	is	be	AUX
ejpam-4283	10	8	called	call	VERB
ejpam-4283	10	9	as	as	ADP
ejpam-4283	10	10	a	a	DET
ejpam-4283	10	11	generalized	generalized	ADJ
ejpam-4283	10	12	topological	topological	ADJ
ejpam-4283	10	13	space	space	NOUN
ejpam-4283	10	14	(	(	PUNCT
ejpam-4283	10	15	gts	gts	NOUN
ejpam-4283	10	16	)	)	PUNCT
ejpam-4283	11	1	[	[	X
ejpam-4283	11	2	8	8	NUM
ejpam-4283	11	3	]	]	PUNCT
ejpam-4283	11	4	.	.	PUNCT
ejpam-4283	12	1	the	the	DET
ejpam-4283	12	2	pair	pair	NOUN
ejpam-4283	12	3	(	(	PUNCT
ejpam-4283	12	4	x,µ	x,µ	NOUN
ejpam-4283	12	5	)	)	PUNCT
ejpam-4283	12	6	is	be	AUX
ejpam-4283	12	7	called	call	VERB
ejpam-4283	12	8	a	a	DET
ejpam-4283	12	9	strong	strong	ADJ
ejpam-4283	12	10	generalized	generalized	ADJ
ejpam-4283	12	11	topological	topological	ADJ
ejpam-4283	12	12	space	space	NOUN
ejpam-4283	12	13	(	(	PUNCT
ejpam-4283	12	14	sgts	sgts	NOUN
ejpam-4283	12	15	)	)	PUNCT
ejpam-4283	13	1	[	[	X
ejpam-4283	13	2	8	8	NUM
ejpam-4283	13	3	]	]	X
ejpam-4283	13	4	if	if	SCONJ
ejpam-4283	13	5	x	x	PROPN
ejpam-4283	13	6	∈	∈	PROPN
ejpam-4283	13	7	µ.	µ.	NOUN
ejpam-4283	13	8	if	if	SCONJ
ejpam-4283	13	9	q	q	PROPN
ejpam-4283	13	10	∈	∈	PROPN
ejpam-4283	13	11	µ	µ	NOUN
ejpam-4283	13	12	,	,	PUNCT
ejpam-4283	13	13	then	then	ADV
ejpam-4283	13	14	q	q	X
ejpam-4283	13	15	is	be	AUX
ejpam-4283	13	16	called	call	VERB
ejpam-4283	13	17	a	a	DET
ejpam-4283	13	18	µ-open	µ-open	NOUN
ejpam-4283	13	19	set	set	VERB
ejpam-4283	13	20	and	and	CCONJ
ejpam-4283	13	21	if	if	SCONJ
ejpam-4283	13	22	x	x	PRON
ejpam-4283	13	23	−	−	X
ejpam-4283	13	24	q	q	PROPN
ejpam-4283	13	25	∈	∈	PROPN
ejpam-4283	13	26	µ	µ	NOUN
ejpam-4283	13	27	,	,	PUNCT
ejpam-4283	13	28	then	then	ADV
ejpam-4283	13	29	q	q	X
ejpam-4283	13	30	is	be	AUX
ejpam-4283	13	31	said	say	VERB
ejpam-4283	13	32	to	to	PART
ejpam-4283	13	33	be	be	AUX
ejpam-4283	13	34	a	a	DET
ejpam-4283	13	35	µ-closed	µ-close	VERB
ejpam-4283	13	36	set	set	NOUN
ejpam-4283	13	37	.	.	PUNCT
ejpam-4283	14	1	let	let	VERB
ejpam-4283	14	2	d	d	PRON
ejpam-4283	14	3	be	be	AUX
ejpam-4283	14	4	a	a	DET
ejpam-4283	14	5	subset	subset	NOUN
ejpam-4283	14	6	of	of	ADP
ejpam-4283	14	7	a	a	DET
ejpam-4283	14	8	gts	gts	NOUN
ejpam-4283	14	9	(	(	PUNCT
ejpam-4283	14	10	x,µ	x,µ	NOUN
ejpam-4283	14	11	)	)	PUNCT
ejpam-4283	14	12	.	.	PUNCT
ejpam-4283	15	1	the	the	DET
ejpam-4283	15	2	interior	interior	NOUN
ejpam-4283	15	3	of	of	ADP
ejpam-4283	15	4	d	d	PROPN
ejpam-4283	15	5	[	[	X
ejpam-4283	15	6	8	8	NUM
ejpam-4283	15	7	]	]	PUNCT
ejpam-4283	15	8	denoted	denote	VERB
ejpam-4283	15	9	by	by	ADP
ejpam-4283	15	10	i	i	PROPN
ejpam-4283	15	11	d	d	PROPN
ejpam-4283	15	12	,	,	PUNCT
ejpam-4283	15	13	is	be	AUX
ejpam-4283	15	14	the	the	DET
ejpam-4283	15	15	union	union	NOUN
ejpam-4283	15	16	of	of	ADP
ejpam-4283	15	17	all	all	DET
ejpam-4283	15	18	µ-open	µ-open	NOUN
ejpam-4283	15	19	sets	set	NOUN
ejpam-4283	15	20	contained	contain	VERB
ejpam-4283	15	21	in	in	ADP
ejpam-4283	15	22	d	d	PROPN
ejpam-4283	15	23	and	and	CCONJ
ejpam-4283	15	24	the	the	DET
ejpam-4283	15	25	closure	closure	NOUN
ejpam-4283	15	26	of	of	ADP
ejpam-4283	15	27	d	d	PROPN
ejpam-4283	15	28	[	[	X
ejpam-4283	15	29	8	8	NUM
ejpam-4283	15	30	]	]	PUNCT
ejpam-4283	15	31	denoted	denote	VERB
ejpam-4283	15	32	by	by	ADP
ejpam-4283	15	33	cd	cd	PROPN
ejpam-4283	15	34	,	,	PUNCT
ejpam-4283	15	35	is	be	AUX
ejpam-4283	15	36	the	the	DET
ejpam-4283	15	37	intersection	intersection	NOUN
ejpam-4283	15	38	of	of	ADP
ejpam-4283	15	39	all	all	DET
ejpam-4283	15	40	µ-closed	µ-close	VERB
ejpam-4283	15	41	sets	set	NOUN
ejpam-4283	15	42	containing	contain	VERB
ejpam-4283	15	43	d	d	PROPN
ejpam-4283	15	44	when	when	SCONJ
ejpam-4283	15	45	no	no	DET
ejpam-4283	15	46	confusion	confusion	NOUN
ejpam-4283	15	47	can	can	AUX
ejpam-4283	15	48	arise	arise	VERB
ejpam-4283	15	49	.	.	PUNCT
ejpam-4283	16	1	denote	denote	VERB
ejpam-4283	16	2	{	{	PUNCT
ejpam-4283	16	3	d	d	X
ejpam-4283	16	4	∈	∈	PROPN
ejpam-4283	16	5	µ	µ	PRON
ejpam-4283	16	6	|	|	NOUN
ejpam-4283	16	7	d	d	X
ejpam-4283	16	8	6=	6=	ADP
ejpam-4283	16	9	∅	∅	NOUN
ejpam-4283	16	10	}	}	PUNCT
ejpam-4283	16	11	by	by	ADP
ejpam-4283	16	12	µ̃	µ̃	PROPN
ejpam-4283	16	13	[	[	X
ejpam-4283	16	14	7	7	NUM
ejpam-4283	16	15	]	]	PUNCT
ejpam-4283	16	16	and	and	CCONJ
ejpam-4283	16	17	denote	denote	VERB
ejpam-4283	16	18	{	{	PUNCT
ejpam-4283	16	19	d	d	X
ejpam-4283	16	20	∈	∈	PROPN
ejpam-4283	16	21	µ	µ	NOUN
ejpam-4283	16	22	|	|	NOUN
ejpam-4283	16	23	x	x	SYM
ejpam-4283	16	24	∈	∈	PROPN
ejpam-4283	17	1	d	d	X
ejpam-4283	17	2	}	}	PUNCT
ejpam-4283	17	3	by	by	ADP
ejpam-4283	17	4	µ(x	µ(x	NOUN
ejpam-4283	17	5	)	)	PUNCT
ejpam-4283	18	1	[	[	X
ejpam-4283	18	2	7	7	NUM
ejpam-4283	18	3	]	]	PUNCT
ejpam-4283	18	4	.	.	PUNCT
ejpam-4283	19	1	define	define	VERB
ejpam-4283	19	2	a	a	DET
ejpam-4283	19	3	generalized	generalized	ADJ
ejpam-4283	19	4	topology	topology	NOUN
ejpam-4283	19	5	µ	µ	NOUN
ejpam-4283	19	6	?	?	PUNCT
ejpam-4283	19	7	as	as	SCONJ
ejpam-4283	19	8	follows	follow	VERB
ejpam-4283	19	9	;	;	PUNCT
ejpam-4283	19	10	µ	µ	X
ejpam-4283	19	11	?	?	PUNCT
ejpam-4283	20	1	=	=	PRON
ejpam-4283	20	2	{	{	PUNCT
ejpam-4283	20	3	⋃	⋃	NOUN
ejpam-4283	20	4	t(u	t(u	NOUN
ejpam-4283	20	5	t	t	PROPN
ejpam-4283	20	6	1	1	NUM
ejpam-4283	20	7	∩	∩	NOUN
ejpam-4283	20	8	u	u	NOUN
ejpam-4283	20	9	t	t	PROPN
ejpam-4283	20	10	2	2	NUM
ejpam-4283	20	11	∩	∩	X
ejpam-4283	20	12	u	u	NOUN
ejpam-4283	20	13	t	t	PROPN
ejpam-4283	20	14	3	3	NUM
ejpam-4283	20	15	∩	∩	X
ejpam-4283	20	16	...	...	PUNCT
ejpam-4283	20	17	∩	∩	X
ejpam-4283	20	18	u	u	PROPN
ejpam-4283	20	19	t	t	PROPN
ejpam-4283	20	20	nt	not	PART
ejpam-4283	20	21	)	)	PUNCT
ejpam-4283	21	1	|	|	ADV
ejpam-4283	21	2	u	u	X
ejpam-4283	21	3	t	t	PROPN
ejpam-4283	21	4	1	1	NUM
ejpam-4283	21	5	,	,	PUNCT
ejpam-4283	21	6	u	u	NOUN
ejpam-4283	21	7	t	t	NOUN
ejpam-4283	21	8	2	2	NUM
ejpam-4283	21	9	,	,	PUNCT
ejpam-4283	21	10	...	...	PUNCT
ejpam-4283	21	11	,	,	PUNCT
ejpam-4283	21	12	u	u	PROPN
ejpam-4283	21	13	t	t	PROPN
ejpam-4283	21	14	nt	not	PART
ejpam-4283	21	15	∈	∈	PROPN
ejpam-4283	21	16	µ	µ	X
ejpam-4283	21	17	}	}	PUNCT
ejpam-4283	21	18	[	[	X
ejpam-4283	21	19	7	7	NUM
ejpam-4283	21	20	]	]	PUNCT
ejpam-4283	21	21	.	.	PUNCT
ejpam-4283	22	1	then	then	ADV
ejpam-4283	22	2	µ	µ	X
ejpam-4283	22	3	⊂	⊂	PROPN
ejpam-4283	22	4	µ	µ	NUM
ejpam-4283	22	5	?	?	PROPN
ejpam-4283	22	6	and	and	CCONJ
ejpam-4283	22	7	µ	µ	X
ejpam-4283	22	8	?	?	NOUN
ejpam-4283	22	9	is	be	AUX
ejpam-4283	22	10	closed	close	VERB
ejpam-4283	22	11	under	under	ADP
ejpam-4283	22	12	finite	finite	ADJ
ejpam-4283	22	13	intersection	intersection	NOUN
ejpam-4283	22	14	[	[	X
ejpam-4283	22	15	7	7	NUM
ejpam-4283	22	16	]	]	PUNCT
ejpam-4283	22	17	.	.	PUNCT
ejpam-4283	23	1	∗corresponding	∗corresponde	VERB
ejpam-4283	23	2	author	author	NOUN
ejpam-4283	23	3	.	.	PUNCT
ejpam-4283	24	1	doi	doi	NOUN
ejpam-4283	24	2	:	:	PUNCT
ejpam-4283	24	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4283	https://doi.org/10.29020/nybg.ejpam.v15i2.4283	NUM
ejpam-4283	24	4	email	email	NOUN
ejpam-4283	24	5	addresses	address	NOUN
ejpam-4283	24	6	:	:	PUNCT
ejpam-4283	24	7	preecha.yupapin@vlu.edu.vn	preecha.yupapin@vlu.edu.vn	PROPN
ejpam-4283	24	8	(	(	PUNCT
ejpam-4283	24	9	p.	p.	NOUN
ejpam-4283	24	10	yupapin	yupapin	NOUN
ejpam-4283	24	11	)	)	PUNCT
ejpam-4283	24	12	,	,	PUNCT
ejpam-4283	24	13	farhat.yasser.1@gmail.com	farhat.yasser.1@gmail.com	X
ejpam-4283	24	14	(	(	PUNCT
ejpam-4283	24	15	y.	y.	PROPN
ejpam-4283	24	16	farhat	farhat	PROPN
ejpam-4283	24	17	)	)	PUNCT
ejpam-4283	24	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4283	25	1	403	403	NUM
ejpam-4283	26	1	©	©	PROPN
ejpam-4283	26	2	2022	2022	NUM
ejpam-4283	26	3	ejpam	ejpam	VERB
ejpam-4283	26	4	all	all	DET
ejpam-4283	26	5	rights	right	NOUN
ejpam-4283	26	6	reserved	reserve	VERB
ejpam-4283	26	7	.	.	PUNCT
ejpam-4283	27	1	p.	p.	NOUN
ejpam-4283	27	2	yupapin	yupapin	NOUN
ejpam-4283	27	3	,	,	PUNCT
ejpam-4283	27	4	v.	v.	CCONJ
ejpam-4283	27	5	subramanian	subramanian	PROPN
ejpam-4283	27	6	,	,	PUNCT
ejpam-4283	27	7	y.	y.	PROPN
ejpam-4283	27	8	farhat	farhat	PROPN
ejpam-4283	27	9	/	/	SYM
ejpam-4283	27	10	eur	eur	PROPN
ejpam-4283	27	11	.	.	PUNCT
ejpam-4283	28	1	j.	j.	PROPN
ejpam-4283	28	2	pure	pure	PROPN
ejpam-4283	28	3	appl	appl	PROPN
ejpam-4283	28	4	.	.	PROPN
ejpam-4283	28	5	math	math	PROPN
ejpam-4283	28	6	,	,	PUNCT
ejpam-4283	28	7	15	15	NUM
ejpam-4283	28	8	(	(	PUNCT
ejpam-4283	28	9	2	2	NUM
ejpam-4283	28	10	)	)	PUNCT
ejpam-4283	28	11	(	(	PUNCT
ejpam-4283	28	12	2022	2022	NUM
ejpam-4283	28	13	)	)	PUNCT
ejpam-4283	28	14	,	,	PUNCT
ejpam-4283	28	15	403	403	NUM
ejpam-4283	28	16	-	-	SYM
ejpam-4283	28	17	414	414	NUM
ejpam-4283	28	18	404	404	NUM
ejpam-4283	28	19	2	2	NUM
ejpam-4283	28	20	.	.	PUNCT
ejpam-4283	29	1	preliminaries	preliminary	NOUN
ejpam-4283	29	2	let	let	VERB
ejpam-4283	29	3	(	(	PUNCT
ejpam-4283	29	4	x,µ	x,µ	NOUN
ejpam-4283	29	5	)	)	PUNCT
ejpam-4283	29	6	be	be	VERB
ejpam-4283	29	7	a	a	DET
ejpam-4283	29	8	gts	gts	NOUN
ejpam-4283	29	9	and	and	CCONJ
ejpam-4283	29	10	q	q	NOUN
ejpam-4283	29	11	⊂	⊂	PROPN
ejpam-4283	29	12	x.	x.	NOUN
ejpam-4283	30	1	then	then	ADV
ejpam-4283	30	2	q	q	X
ejpam-4283	30	3	is	be	AUX
ejpam-4283	30	4	called	call	VERB
ejpam-4283	30	5	a	a	DET
ejpam-4283	30	6	µ-nowhere	µ-nowhere	ADV
ejpam-4283	30	7	dense	dense	ADJ
ejpam-4283	30	8	[	[	X
ejpam-4283	30	9	6	6	NUM
ejpam-4283	30	10	]	]	PUNCT
ejpam-4283	30	11	(	(	PUNCT
ejpam-4283	30	12	resp	resp	NOUN
ejpam-4283	30	13	.	.	PUNCT
ejpam-4283	31	1	µ-dense	µ-dense	NOUN
ejpam-4283	32	1	[	[	X
ejpam-4283	32	2	6	6	NUM
ejpam-4283	32	3	,	,	PUNCT
ejpam-4283	32	4	7	7	NUM
ejpam-4283	32	5	]	]	PUNCT
ejpam-4283	32	6	,	,	PUNCT
ejpam-4283	32	7	µ-codense	µ-codense	PROPN
ejpam-4283	32	8	[	[	X
ejpam-4283	32	9	7	7	NUM
ejpam-4283	32	10	]	]	PUNCT
ejpam-4283	32	11	)	)	PUNCT
ejpam-4283	32	12	set	set	VERB
ejpam-4283	32	13	if	if	SCONJ
ejpam-4283	32	14	icq	icq	NOUN
ejpam-4283	32	15	=	=	SYM
ejpam-4283	32	16	∅	∅	NOUN
ejpam-4283	32	17	(	(	PUNCT
ejpam-4283	32	18	resp	resp	NOUN
ejpam-4283	32	19	.	.	PUNCT
ejpam-4283	33	1	cq	cq	NOUN
ejpam-4283	34	1	=	=	NOUN
ejpam-4283	34	2	x	x	PROPN
ejpam-4283	34	3	;	;	PUNCT
ejpam-4283	34	4	c(x	c(x	NOUN
ejpam-4283	34	5	−q	−q	NOUN
ejpam-4283	34	6	)	)	PUNCT
ejpam-4283	34	7	=	=	SYM
ejpam-4283	34	8	x	x	X
ejpam-4283	34	9	)	)	PUNCT
ejpam-4283	34	10	.	.	PUNCT
ejpam-4283	35	1	let	let	VERB
ejpam-4283	35	2	µ1	µ1	VERB
ejpam-4283	35	3	and	and	CCONJ
ejpam-4283	35	4	µ2	µ2	PROPN
ejpam-4283	35	5	be	be	AUX
ejpam-4283	35	6	two	two	NUM
ejpam-4283	35	7	generalized	generalized	ADJ
ejpam-4283	35	8	topologies	topology	NOUN
ejpam-4283	35	9	on	on	ADP
ejpam-4283	35	10	a	a	DET
ejpam-4283	35	11	non	non	ADJ
ejpam-4283	35	12	-	-	ADJ
ejpam-4283	35	13	null	null	ADJ
ejpam-4283	35	14	set	set	NOUN
ejpam-4283	35	15	x.	x.	NOUN
ejpam-4283	35	16	then	then	ADV
ejpam-4283	35	17	(	(	PUNCT
ejpam-4283	35	18	x,µ1	x,µ1	PROPN
ejpam-4283	35	19	,	,	PUNCT
ejpam-4283	35	20	µ2	µ2	PROPN
ejpam-4283	35	21	)	)	PUNCT
ejpam-4283	35	22	is	be	AUX
ejpam-4283	35	23	called	call	VERB
ejpam-4283	35	24	as	as	ADP
ejpam-4283	35	25	a	a	DET
ejpam-4283	35	26	bigeneralized	bigeneralized	ADJ
ejpam-4283	35	27	topological	topological	ADJ
ejpam-4283	35	28	space	space	NOUN
ejpam-4283	35	29	(	(	PUNCT
ejpam-4283	35	30	briefly	briefly	ADV
ejpam-4283	35	31	,	,	PUNCT
ejpam-4283	35	32	bgts	bgts	PROPN
ejpam-4283	35	33	)	)	PUNCT
ejpam-4283	36	1	[	[	X
ejpam-4283	36	2	2	2	NUM
ejpam-4283	36	3	]	]	PUNCT
ejpam-4283	36	4	.	.	PUNCT
ejpam-4283	37	1	let	let	AUX
ejpam-4283	37	2	(	(	PUNCT
ejpam-4283	37	3	x,µ1	x,µ1	NOUN
ejpam-4283	37	4	,	,	PUNCT
ejpam-4283	37	5	µ2	µ2	PROPN
ejpam-4283	37	6	)	)	PUNCT
ejpam-4283	37	7	be	be	VERB
ejpam-4283	37	8	a	a	DET
ejpam-4283	37	9	bgts	bgts	NOUN
ejpam-4283	37	10	and	and	CCONJ
ejpam-4283	37	11	d	d	PROPN
ejpam-4283	37	12	⊂	⊂	PROPN
ejpam-4283	37	13	x.	x.	PROPN
ejpam-4283	37	14	then	then	ADV
ejpam-4283	37	15	cs(d	cs(d	PUNCT
ejpam-4283	37	16	)	)	PUNCT
ejpam-4283	38	1	denote	denote	VERB
ejpam-4283	38	2	the	the	DET
ejpam-4283	38	3	closure	closure	NOUN
ejpam-4283	38	4	of	of	ADP
ejpam-4283	38	5	d	d	PROPN
ejpam-4283	38	6	and	and	CCONJ
ejpam-4283	38	7	is(d	is(d	NUM
ejpam-4283	38	8	)	)	PUNCT
ejpam-4283	38	9	denote	denote	VERB
ejpam-4283	38	10	the	the	DET
ejpam-4283	38	11	interior	interior	NOUN
ejpam-4283	38	12	of	of	ADP
ejpam-4283	38	13	d	d	PROPN
ejpam-4283	38	14	with	with	ADP
ejpam-4283	38	15	respect	respect	NOUN
ejpam-4283	38	16	to	to	ADP
ejpam-4283	38	17	µs	µs	PRON
ejpam-4283	38	18	,	,	PUNCT
ejpam-4283	38	19	respectively	respectively	ADV
ejpam-4283	38	20	,	,	PUNCT
ejpam-4283	38	21	for	for	ADP
ejpam-4283	38	22	s	s	NOUN
ejpam-4283	38	23	=	=	SYM
ejpam-4283	38	24	1	1	NUM
ejpam-4283	38	25	,	,	PUNCT
ejpam-4283	38	26	2	2	NUM
ejpam-4283	38	27	[	[	X
ejpam-4283	38	28	2	2	NUM
ejpam-4283	38	29	]	]	PUNCT
ejpam-4283	38	30	.	.	PUNCT
ejpam-4283	39	1	a	a	DET
ejpam-4283	39	2	subset	subset	NOUN
ejpam-4283	39	3	q	q	NOUN
ejpam-4283	39	4	of	of	ADP
ejpam-4283	39	5	a	a	DET
ejpam-4283	39	6	bgts	bgts	NOUN
ejpam-4283	39	7	(	(	PUNCT
ejpam-4283	39	8	x,µ1	x,µ1	PROPN
ejpam-4283	39	9	,	,	PUNCT
ejpam-4283	39	10	µ2	µ2	PROPN
ejpam-4283	39	11	)	)	PUNCT
ejpam-4283	39	12	is	be	AUX
ejpam-4283	39	13	called	call	VERB
ejpam-4283	39	14	(	(	PUNCT
ejpam-4283	39	15	s	s	PROPN
ejpam-4283	39	16	,	,	PUNCT
ejpam-4283	39	17	v)-closed	v)-close	VERB
ejpam-4283	39	18	if	if	SCONJ
ejpam-4283	39	19	cs(cv(q	cs(cv(q	NOUN
ejpam-4283	39	20	)	)	PUNCT
ejpam-4283	39	21	)	)	PUNCT
ejpam-4283	40	1	=	=	PUNCT
ejpam-4283	41	1	q	q	X
ejpam-4283	41	2	,	,	PUNCT
ejpam-4283	41	3	where	where	SCONJ
ejpam-4283	41	4	s	s	X
ejpam-4283	41	5	,	,	PUNCT
ejpam-4283	41	6	v	v	NOUN
ejpam-4283	41	7	=	=	SYM
ejpam-4283	41	8	1	1	NUM
ejpam-4283	41	9	or	or	CCONJ
ejpam-4283	41	10	2	2	NUM
ejpam-4283	41	11	;	;	PUNCT
ejpam-4283	41	12	s	s	PROPN
ejpam-4283	41	13	6=	6=	PROPN
ejpam-4283	41	14	v.	v.	ADP
ejpam-4283	41	15	if	if	SCONJ
ejpam-4283	41	16	x	x	PRON
ejpam-4283	41	17	−q	−q	NOUN
ejpam-4283	41	18	is	be	AUX
ejpam-4283	41	19	(	(	PUNCT
ejpam-4283	41	20	s	s	X
ejpam-4283	41	21	,	,	PUNCT
ejpam-4283	41	22	v)-closed	v)-close	VERB
ejpam-4283	41	23	,	,	PUNCT
ejpam-4283	41	24	then	then	ADV
ejpam-4283	41	25	q	q	X
ejpam-4283	41	26	is	be	AUX
ejpam-4283	41	27	called	call	VERB
ejpam-4283	41	28	as	as	ADP
ejpam-4283	41	29	(	(	PUNCT
ejpam-4283	41	30	s	s	X
ejpam-4283	41	31	,	,	PUNCT
ejpam-4283	41	32	v)-open	v)-open	VERB
ejpam-4283	41	33	[	[	X
ejpam-4283	41	34	2	2	NUM
ejpam-4283	41	35	]	]	PUNCT
ejpam-4283	41	36	set	set	NOUN
ejpam-4283	41	37	.	.	PUNCT
ejpam-4283	42	1	in	in	ADP
ejpam-4283	42	2	[	[	X
ejpam-4283	42	3	2	2	NUM
ejpam-4283	42	4	]	]	PUNCT
ejpam-4283	42	5	,	,	PUNCT
ejpam-4283	42	6	let	let	VERB
ejpam-4283	42	7	q	q	PRON
ejpam-4283	42	8	be	be	AUX
ejpam-4283	42	9	a	a	DET
ejpam-4283	42	10	subset	subset	NOUN
ejpam-4283	42	11	of	of	ADP
ejpam-4283	42	12	a	a	DET
ejpam-4283	42	13	bgts	bgts	NOUN
ejpam-4283	42	14	(	(	PUNCT
ejpam-4283	42	15	x,µ1	x,µ1	PROPN
ejpam-4283	42	16	,	,	PUNCT
ejpam-4283	42	17	µ2	µ2	PROPN
ejpam-4283	42	18	)	)	PUNCT
ejpam-4283	42	19	is	be	AUX
ejpam-4283	42	20	called	call	VERB
ejpam-4283	42	21	(	(	PUNCT
ejpam-4283	42	22	1	1	NUM
ejpam-4283	42	23	)	)	PUNCT
ejpam-4283	42	24	(	(	PUNCT
ejpam-4283	42	25	s	s	X
ejpam-4283	42	26	,	,	PUNCT
ejpam-4283	42	27	v)-g	v)-g	NOUN
ejpam-4283	42	28	-	-	PUNCT
ejpam-4283	42	29	preopen	preopen	ADJ
ejpam-4283	42	30	if	if	SCONJ
ejpam-4283	42	31	q	q	NOUN
ejpam-4283	42	32	⊆	⊆	NUM
ejpam-4283	42	33	is(cv(q	is(cv(q	NOUN
ejpam-4283	42	34	)	)	PUNCT
ejpam-4283	42	35	)	)	PUNCT
ejpam-4283	43	1	where	where	SCONJ
ejpam-4283	43	2	s	s	X
ejpam-4283	43	3	,	,	PUNCT
ejpam-4283	43	4	v	v	NOUN
ejpam-4283	43	5	=	=	SYM
ejpam-4283	43	6	1	1	NUM
ejpam-4283	43	7	or	or	CCONJ
ejpam-4283	43	8	2	2	NUM
ejpam-4283	43	9	;	;	PUNCT
ejpam-4283	43	10	s	s	PROPN
ejpam-4283	43	11	6=	6=	PROPN
ejpam-4283	43	12	v.	v.	PROPN
ejpam-4283	43	13	(	(	PUNCT
ejpam-4283	43	14	2	2	NUM
ejpam-4283	43	15	)	)	PUNCT
ejpam-4283	43	16	(	(	PUNCT
ejpam-4283	43	17	s	s	X
ejpam-4283	43	18	,	,	PUNCT
ejpam-4283	43	19	v)-g	v)-g	NOUN
ejpam-4283	43	20	-	-	PUNCT
ejpam-4283	43	21	α	α	NOUN
ejpam-4283	43	22	-	-	NOUN
ejpam-4283	43	23	open	open	ADJ
ejpam-4283	43	24	if	if	SCONJ
ejpam-4283	43	25	q	q	PROPN
ejpam-4283	43	26	⊆	⊆	NUM
ejpam-4283	43	27	is(cv(is(q	is(cv(is(q	NOUN
ejpam-4283	43	28	)	)	PUNCT
ejpam-4283	43	29	)	)	PUNCT
ejpam-4283	43	30	)	)	PUNCT
ejpam-4283	43	31	where	where	SCONJ
ejpam-4283	43	32	s	s	X
ejpam-4283	43	33	,	,	PUNCT
ejpam-4283	43	34	v	v	NOUN
ejpam-4283	43	35	=	=	SYM
ejpam-4283	43	36	1	1	NUM
ejpam-4283	43	37	or	or	CCONJ
ejpam-4283	43	38	2	2	NUM
ejpam-4283	43	39	;	;	PUNCT
ejpam-4283	43	40	s	s	PROPN
ejpam-4283	43	41	6=	6=	PROPN
ejpam-4283	43	42	v.	v.	ADP
ejpam-4283	43	43	lemma	lemma	PROPN
ejpam-4283	43	44	1	1	NUM
ejpam-4283	43	45	.	.	PUNCT
ejpam-4283	44	1	[	[	X
ejpam-4283	44	2	3	3	X
ejpam-4283	44	3	]	]	PUNCT
ejpam-4283	44	4	let	let	VERB
ejpam-4283	44	5	q	q	PART
ejpam-4283	44	6	be	be	AUX
ejpam-4283	44	7	a	a	DET
ejpam-4283	44	8	subset	subset	NOUN
ejpam-4283	44	9	of	of	ADP
ejpam-4283	44	10	a	a	DET
ejpam-4283	44	11	generalized	generalized	ADJ
ejpam-4283	44	12	topological	topological	ADJ
ejpam-4283	44	13	space	space	NOUN
ejpam-4283	44	14	(	(	PUNCT
ejpam-4283	44	15	x,µ	x,µ	NOUN
ejpam-4283	44	16	)	)	PUNCT
ejpam-4283	44	17	.	.	PUNCT
ejpam-4283	45	1	then	then	ADV
ejpam-4283	45	2	y	y	PROPN
ejpam-4283	45	3	∈	∈	PROPN
ejpam-4283	45	4	c(q	c(q	PROPN
ejpam-4283	45	5	)	)	PUNCT
ejpam-4283	46	1	if	if	SCONJ
ejpam-4283	46	2	and	and	CCONJ
ejpam-4283	46	3	only	only	ADV
ejpam-4283	46	4	if	if	SCONJ
ejpam-4283	46	5	m	m	VERB
ejpam-4283	46	6	∩q	∩q	PROPN
ejpam-4283	46	7	6=	6=	ADP
ejpam-4283	46	8	∅	∅	NOUN
ejpam-4283	46	9	for	for	ADP
ejpam-4283	46	10	any	any	DET
ejpam-4283	46	11	m	m	NOUN
ejpam-4283	46	12	∈	∈	NOUN
ejpam-4283	46	13	µ(y	µ(y	PROPN
ejpam-4283	46	14	)	)	PUNCT
ejpam-4283	46	15	.	.	PUNCT
ejpam-4283	47	1	lemma	lemma	PROPN
ejpam-4283	47	2	2	2	NUM
ejpam-4283	47	3	.	.	PUNCT
ejpam-4283	48	1	[	[	X
ejpam-4283	48	2	8	8	NUM
ejpam-4283	48	3	,	,	PUNCT
ejpam-4283	48	4	lemma	lemma	PROPN
ejpam-4283	48	5	3.2	3.2	NUM
ejpam-4283	48	6	]	]	PUNCT
ejpam-4283	48	7	let	let	VERB
ejpam-4283	48	8	(	(	PUNCT
ejpam-4283	48	9	x,µ	x,µ	NOUN
ejpam-4283	48	10	)	)	PUNCT
ejpam-4283	48	11	be	be	VERB
ejpam-4283	48	12	a	a	DET
ejpam-4283	48	13	generalized	generalized	ADJ
ejpam-4283	48	14	topological	topological	ADJ
ejpam-4283	48	15	space	space	NOUN
ejpam-4283	48	16	and	and	CCONJ
ejpam-4283	48	17	d	d	NOUN
ejpam-4283	48	18	,	,	PUNCT
ejpam-4283	48	19	b	b	X
ejpam-4283	48	20	⊂	⊂	PROPN
ejpam-4283	48	21	x.	x.	NOUN
ejpam-4283	49	1	if	if	SCONJ
ejpam-4283	49	2	b	b	PROPN
ejpam-4283	49	3	∈	∈	PROPN
ejpam-4283	49	4	µ̃;b	µ̃;b	NOUN
ejpam-4283	49	5	∩d	∩d	NOUN
ejpam-4283	49	6	=	=	NOUN
ejpam-4283	49	7	∅	∅	NOUN
ejpam-4283	49	8	,	,	PUNCT
ejpam-4283	49	9	then	then	ADV
ejpam-4283	49	10	b	b	PROPN
ejpam-4283	49	11	∩	∩	ADJ
ejpam-4283	49	12	cd	cd	NOUN
ejpam-4283	49	13	=	=	PUNCT
ejpam-4283	49	14	∅.	∅.	PRON
ejpam-4283	49	15	3	3	NUM
ejpam-4283	49	16	.	.	PUNCT
ejpam-4283	50	1	nowhere	nowhere	ADV
ejpam-4283	50	2	dense	dense	ADJ
ejpam-4283	50	3	sets	set	NOUN
ejpam-4283	50	4	in	in	ADP
ejpam-4283	50	5	this	this	DET
ejpam-4283	50	6	section	section	NOUN
ejpam-4283	50	7	,	,	PUNCT
ejpam-4283	50	8	we	we	PRON
ejpam-4283	50	9	define	define	VERB
ejpam-4283	50	10	a	a	DET
ejpam-4283	50	11	set	set	NOUN
ejpam-4283	50	12	namely	namely	ADV
ejpam-4283	50	13	,	,	PUNCT
ejpam-4283	50	14	(	(	PUNCT
ejpam-4283	50	15	s	s	X
ejpam-4283	50	16	,	,	PUNCT
ejpam-4283	50	17	v)?-nowhere	v)?-nowhere	VERB
ejpam-4283	50	18	dense	dense	ADJ
ejpam-4283	50	19	and	and	CCONJ
ejpam-4283	50	20	give	give	VERB
ejpam-4283	50	21	some	some	PRON
ejpam-4283	50	22	of	of	ADP
ejpam-4283	50	23	their	their	PRON
ejpam-4283	50	24	properties	property	NOUN
ejpam-4283	50	25	in	in	ADP
ejpam-4283	50	26	a	a	DET
ejpam-4283	50	27	bgts	bgts	NOUN
ejpam-4283	50	28	.	.	PUNCT
ejpam-4283	51	1	let	let	VERB
ejpam-4283	51	2	q	q	PART
ejpam-4283	51	3	be	be	AUX
ejpam-4283	51	4	a	a	DET
ejpam-4283	51	5	subset	subset	NOUN
ejpam-4283	51	6	of	of	ADP
ejpam-4283	51	7	a	a	DET
ejpam-4283	51	8	generalized	generalized	ADJ
ejpam-4283	51	9	topological	topological	ADJ
ejpam-4283	51	10	space	space	NOUN
ejpam-4283	51	11	(	(	PUNCT
ejpam-4283	51	12	x,µ	x,µ	NOUN
ejpam-4283	51	13	)	)	PUNCT
ejpam-4283	51	14	.	.	PUNCT
ejpam-4283	52	1	then	then	ADV
ejpam-4283	52	2	q	q	X
ejpam-4283	52	3	is	be	AUX
ejpam-4283	52	4	called	call	VERB
ejpam-4283	52	5	µ-semiopen	µ-semiopen	ADJ
ejpam-4283	52	6	if	if	SCONJ
ejpam-4283	52	7	q	q	PROPN
ejpam-4283	52	8	⊂	⊂	PROPN
ejpam-4283	52	9	cµ(iµ(q	cµ(iµ(q	PROPN
ejpam-4283	52	10	)	)	PUNCT
ejpam-4283	52	11	)	)	PUNCT
ejpam-4283	53	1	[	[	X
ejpam-4283	53	2	5	5	NUM
ejpam-4283	53	3	]	]	PUNCT
ejpam-4283	53	4	.	.	PUNCT
ejpam-4283	54	1	if	if	SCONJ
ejpam-4283	54	2	x	x	PRON
ejpam-4283	54	3	−	−	PROPN
ejpam-4283	54	4	q	q	X
ejpam-4283	54	5	is	be	AUX
ejpam-4283	54	6	a	a	DET
ejpam-4283	54	7	µ-semi	µ-semi	ADJ
ejpam-4283	54	8	-	-	ADJ
ejpam-4283	54	9	open	open	ADJ
ejpam-4283	54	10	set	set	NOUN
ejpam-4283	54	11	,	,	PUNCT
ejpam-4283	54	12	then	then	ADV
ejpam-4283	54	13	q	q	X
ejpam-4283	54	14	is	be	AUX
ejpam-4283	54	15	called	call	VERB
ejpam-4283	54	16	µ-semi	µ-semi	NOUN
ejpam-4283	54	17	-	-	ADJ
ejpam-4283	54	18	closed	closed	ADJ
ejpam-4283	54	19	[	[	X
ejpam-4283	54	20	5	5	NUM
ejpam-4283	54	21	]	]	PUNCT
ejpam-4283	54	22	.	.	PUNCT
ejpam-4283	55	1	moreover	moreover	ADV
ejpam-4283	55	2	,	,	PUNCT
ejpam-4283	55	3	σ(µ	σ(µ	PROPN
ejpam-4283	55	4	)	)	PUNCT
ejpam-4283	55	5	or	or	CCONJ
ejpam-4283	55	6	σ(µ(x	σ(µ(x	PROPN
ejpam-4283	55	7	)	)	PUNCT
ejpam-4283	55	8	)	)	PUNCT
ejpam-4283	56	1	=	=	PRON
ejpam-4283	56	2	{	{	PUNCT
ejpam-4283	56	3	q	q	X
ejpam-4283	56	4	⊂	⊂	X
ejpam-4283	56	5	x	x	PUNCT
ejpam-4283	57	1	|	|	ADV
ejpam-4283	57	2	q	q	NOUN
ejpam-4283	57	3	is	be	AUX
ejpam-4283	57	4	µ-semi	µ-semi	NOUN
ejpam-4283	57	5	-	-	ADJ
ejpam-4283	57	6	open	open	ADJ
ejpam-4283	57	7	set	set	NOUN
ejpam-4283	57	8	in	in	ADP
ejpam-4283	57	9	x	x	X
ejpam-4283	57	10	}	}	PUNCT
ejpam-4283	57	11	[	[	X
ejpam-4283	57	12	8	8	NUM
ejpam-4283	57	13	]	]	PUNCT
ejpam-4283	57	14	.	.	PUNCT
ejpam-4283	58	1	also	also	ADV
ejpam-4283	58	2	,	,	PUNCT
ejpam-4283	58	3	iσ(q	iσ(q	NUM
ejpam-4283	58	4	)	)	PUNCT
ejpam-4283	58	5	denote	denote	VERB
ejpam-4283	58	6	the	the	DET
ejpam-4283	58	7	µ-semi	µ-semi	NOUN
ejpam-4283	58	8	-	-	ADJ
ejpam-4283	58	9	interior	interior	ADJ
ejpam-4283	58	10	of	of	ADP
ejpam-4283	58	11	q	q	PROPN
ejpam-4283	58	12	⊂	⊂	PROPN
ejpam-4283	58	13	x	x	PUNCT
ejpam-4283	58	14	is	be	AUX
ejpam-4283	58	15	defined	define	VERB
ejpam-4283	58	16	by	by	ADP
ejpam-4283	58	17	the	the	DET
ejpam-4283	58	18	union	union	NOUN
ejpam-4283	58	19	of	of	ADP
ejpam-4283	58	20	all	all	DET
ejpam-4283	58	21	µ-semi	µ-semi	NOUN
ejpam-4283	58	22	-	-	ADJ
ejpam-4283	58	23	open	open	ADJ
ejpam-4283	58	24	subsets	subset	NOUN
ejpam-4283	58	25	of	of	ADP
ejpam-4283	58	26	(	(	PUNCT
ejpam-4283	58	27	x,µ	x,µ	NOUN
ejpam-4283	58	28	)	)	PUNCT
ejpam-4283	58	29	contained	contain	VERB
ejpam-4283	58	30	in	in	ADP
ejpam-4283	58	31	q	q	NOUN
ejpam-4283	58	32	[	[	X
ejpam-4283	58	33	8	8	NUM
ejpam-4283	58	34	]	]	PUNCT
ejpam-4283	58	35	.	.	PUNCT
ejpam-4283	59	1	let	let	VERB
ejpam-4283	59	2	q	q	PART
ejpam-4283	59	3	be	be	AUX
ejpam-4283	59	4	a	a	DET
ejpam-4283	59	5	subset	subset	NOUN
ejpam-4283	59	6	of	of	ADP
ejpam-4283	59	7	a	a	DET
ejpam-4283	59	8	bgts	bgts	NOUN
ejpam-4283	59	9	(	(	PUNCT
ejpam-4283	59	10	x,µ1	x,µ1	PROPN
ejpam-4283	59	11	,	,	PUNCT
ejpam-4283	59	12	µ2	µ2	PROPN
ejpam-4283	59	13	)	)	PUNCT
ejpam-4283	59	14	is	be	AUX
ejpam-4283	59	15	called	call	VERB
ejpam-4283	59	16	(	(	PUNCT
ejpam-4283	59	17	s	s	PROPN
ejpam-4283	59	18	,	,	PUNCT
ejpam-4283	59	19	v)-nowhere	v)-nowhere	SCONJ
ejpam-4283	59	20	dense	dense	ADJ
ejpam-4283	59	21	[	[	X
ejpam-4283	59	22	1	1	NUM
ejpam-4283	59	23	]	]	X
ejpam-4283	59	24	set	set	VERB
ejpam-4283	59	25	in	in	ADP
ejpam-4283	59	26	x	x	PUNCT
ejpam-4283	59	27	if	if	SCONJ
ejpam-4283	59	28	is(cv(q	is(cv(q	NOUN
ejpam-4283	59	29	)	)	PUNCT
ejpam-4283	59	30	)	)	PUNCT
ejpam-4283	60	1	=	=	NOUN
ejpam-4283	60	2	∅	∅	NOUN
ejpam-4283	60	3	where	where	SCONJ
ejpam-4283	60	4	s	s	X
ejpam-4283	60	5	,	,	PUNCT
ejpam-4283	60	6	v	v	NOUN
ejpam-4283	60	7	=	=	SYM
ejpam-4283	60	8	1	1	NUM
ejpam-4283	60	9	,	,	PUNCT
ejpam-4283	60	10	2	2	NUM
ejpam-4283	60	11	;	;	PUNCT
ejpam-4283	60	12	s	s	PROPN
ejpam-4283	60	13	6=	6=	PROPN
ejpam-4283	60	14	v.	v.	ADP
ejpam-4283	60	15	definition	definition	NOUN
ejpam-4283	60	16	1	1	NUM
ejpam-4283	60	17	.	.	PUNCT
ejpam-4283	61	1	let	let	AUX
ejpam-4283	61	2	(	(	PUNCT
ejpam-4283	61	3	x,µ1	x,µ1	NOUN
ejpam-4283	61	4	,	,	PUNCT
ejpam-4283	61	5	µ2	µ2	PROPN
ejpam-4283	61	6	)	)	PUNCT
ejpam-4283	61	7	be	be	VERB
ejpam-4283	61	8	a	a	DET
ejpam-4283	61	9	bigeneralized	bigeneralized	ADJ
ejpam-4283	61	10	topological	topological	ADJ
ejpam-4283	61	11	space	space	NOUN
ejpam-4283	61	12	and	and	CCONJ
ejpam-4283	61	13	k	k	PROPN
ejpam-4283	61	14	be	be	AUX
ejpam-4283	61	15	a	a	DET
ejpam-4283	61	16	non	non	ADJ
ejpam-4283	61	17	-	-	ADJ
ejpam-4283	61	18	null	null	ADJ
ejpam-4283	61	19	subset	subset	NOUN
ejpam-4283	61	20	of	of	ADP
ejpam-4283	61	21	x.	x.	PROPN
ejpam-4283	61	22	then	then	ADV
ejpam-4283	61	23	k	k	PROPN
ejpam-4283	61	24	is	be	AUX
ejpam-4283	61	25	called	call	VERB
ejpam-4283	61	26	to	to	PART
ejpam-4283	61	27	be	be	AUX
ejpam-4283	61	28	a	a	DET
ejpam-4283	61	29	(	(	PUNCT
ejpam-4283	61	30	s	s	X
ejpam-4283	61	31	,	,	PUNCT
ejpam-4283	61	32	v)?-nowhere	v)?-nowhere	X
ejpam-4283	61	33	dense	dense	ADJ
ejpam-4283	61	34	set	set	NOUN
ejpam-4283	61	35	if	if	SCONJ
ejpam-4283	61	36	iσv(cs(k	iσv(cs(k	X
ejpam-4283	61	37	)	)	PUNCT
ejpam-4283	61	38	)	)	PUNCT
ejpam-4283	62	1	=	=	NOUN
ejpam-4283	62	2	∅	∅	NOUN
ejpam-4283	62	3	where	where	SCONJ
ejpam-4283	62	4	s	s	X
ejpam-4283	62	5	,	,	PUNCT
ejpam-4283	62	6	v	v	NOUN
ejpam-4283	62	7	=	=	SYM
ejpam-4283	62	8	1	1	NUM
ejpam-4283	62	9	,	,	PUNCT
ejpam-4283	62	10	2	2	NUM
ejpam-4283	62	11	;	;	PUNCT
ejpam-4283	62	12	s	s	PROPN
ejpam-4283	62	13	6=	6=	NUM
ejpam-4283	62	14	v;σv	v;σv	NOUN
ejpam-4283	62	15	=	=	SYM
ejpam-4283	62	16	σµv	σµv	NOUN
ejpam-4283	62	17	.	.	PUNCT
ejpam-4283	63	1	moreover	moreover	ADV
ejpam-4283	63	2	,	,	PUNCT
ejpam-4283	63	3	(	(	PUNCT
ejpam-4283	63	4	s	s	X
ejpam-4283	63	5	,	,	PUNCT
ejpam-4283	63	6	v	v	NOUN
ejpam-4283	63	7	)	)	PUNCT
ejpam-4283	63	8	?	?	PUNCT
ejpam-4283	64	1	−	−	PROPN
ejpam-4283	65	1	n	n	CCONJ
ejpam-4283	65	2	(	(	PUNCT
ejpam-4283	65	3	x	x	X
ejpam-4283	65	4	)	)	PUNCT
ejpam-4283	65	5	=	=	PRON
ejpam-4283	65	6	{	{	PUNCT
ejpam-4283	65	7	q	q	X
ejpam-4283	65	8	⊂	⊂	X
ejpam-4283	65	9	x	x	PUNCT
ejpam-4283	66	1	|	|	ADV
ejpam-4283	66	2	q	q	X
ejpam-4283	66	3	is	be	AUX
ejpam-4283	66	4	(	(	PUNCT
ejpam-4283	66	5	s	s	X
ejpam-4283	66	6	,	,	PUNCT
ejpam-4283	66	7	v)?-nowhere	v)?-nowhere	X
ejpam-4283	66	8	dense	dense	ADJ
ejpam-4283	66	9	set	set	NOUN
ejpam-4283	66	10	in	in	ADP
ejpam-4283	66	11	x	x	NOUN
ejpam-4283	66	12	}	}	PUNCT
ejpam-4283	66	13	where	where	SCONJ
ejpam-4283	66	14	s	s	X
ejpam-4283	66	15	,	,	PUNCT
ejpam-4283	66	16	v	v	NOUN
ejpam-4283	66	17	=	=	SYM
ejpam-4283	66	18	1	1	NUM
ejpam-4283	66	19	,	,	PUNCT
ejpam-4283	66	20	2	2	NUM
ejpam-4283	66	21	;	;	PUNCT
ejpam-4283	66	22	s	s	PROPN
ejpam-4283	66	23	6=	6=	PROPN
ejpam-4283	66	24	v.	v.	ADP
ejpam-4283	66	25	example	example	NOUN
ejpam-4283	67	1	2	2	X
ejpam-4283	67	2	.	.	X
ejpam-4283	67	3	consider	consider	VERB
ejpam-4283	67	4	the	the	DET
ejpam-4283	67	5	bigeneralized	bigeneralized	ADJ
ejpam-4283	67	6	topological	topological	ADJ
ejpam-4283	67	7	space	space	NOUN
ejpam-4283	67	8	(	(	PUNCT
ejpam-4283	67	9	x,µ1	x,µ1	PROPN
ejpam-4283	67	10	,	,	PUNCT
ejpam-4283	67	11	µ2	µ2	PROPN
ejpam-4283	67	12	)	)	PUNCT
ejpam-4283	67	13	where	where	SCONJ
ejpam-4283	67	14	x	x	X
ejpam-4283	67	15	=	=	PRON
ejpam-4283	67	16	{	{	PUNCT
ejpam-4283	67	17	p	p	X
ejpam-4283	67	18	,	,	PUNCT
ejpam-4283	67	19	q	q	ADJ
ejpam-4283	67	20	,	,	PUNCT
ejpam-4283	67	21	r	r	NOUN
ejpam-4283	67	22	,	,	PUNCT
ejpam-4283	67	23	s	s	PART
ejpam-4283	67	24	}	}	PUNCT
ejpam-4283	67	25	;	;	PUNCT
ejpam-4283	67	26	µ1	µ1	PROPN
ejpam-4283	67	27	=	=	SYM
ejpam-4283	67	28	{	{	PUNCT
ejpam-4283	67	29	∅	∅	NOUN
ejpam-4283	67	30	,	,	PUNCT
ejpam-4283	67	31	{	{	PUNCT
ejpam-4283	67	32	p	p	X
ejpam-4283	67	33	,	,	PUNCT
ejpam-4283	67	34	q	q	NOUN
ejpam-4283	67	35	}	}	PUNCT
ejpam-4283	67	36	,	,	PUNCT
ejpam-4283	67	37	{	{	PUNCT
ejpam-4283	67	38	q	q	X
ejpam-4283	67	39	,	,	PUNCT
ejpam-4283	67	40	r	r	NOUN
ejpam-4283	67	41	}	}	PUNCT
ejpam-4283	67	42	,	,	PUNCT
ejpam-4283	67	43	{	{	PUNCT
ejpam-4283	67	44	p	p	X
ejpam-4283	67	45	,	,	PUNCT
ejpam-4283	67	46	q	q	ADJ
ejpam-4283	67	47	,	,	PUNCT
ejpam-4283	67	48	r	r	NOUN
ejpam-4283	67	49	}	}	PUNCT
ejpam-4283	67	50	}	}	PUNCT
ejpam-4283	67	51	and	and	CCONJ
ejpam-4283	67	52	µ2	µ2	PROPN
ejpam-4283	67	53	=	=	PUNCT
ejpam-4283	67	54	{	{	PUNCT
ejpam-4283	67	55	∅	∅	NOUN
ejpam-4283	67	56	,	,	PUNCT
ejpam-4283	67	57	{	{	PUNCT
ejpam-4283	67	58	p	p	X
ejpam-4283	67	59	,	,	PUNCT
ejpam-4283	67	60	s	s	PART
ejpam-4283	67	61	}	}	PUNCT
ejpam-4283	67	62	,	,	PUNCT
ejpam-4283	67	63	{	{	PUNCT
ejpam-4283	67	64	q	q	X
ejpam-4283	67	65	,	,	PUNCT
ejpam-4283	67	66	s	s	PART
ejpam-4283	67	67	}	}	PUNCT
ejpam-4283	67	68	,	,	PUNCT
ejpam-4283	67	69	{	{	PUNCT
ejpam-4283	67	70	p	p	X
ejpam-4283	67	71	,	,	PUNCT
ejpam-4283	67	72	q	q	ADJ
ejpam-4283	67	73	,	,	PUNCT
ejpam-4283	67	74	s	s	PART
ejpam-4283	67	75	}	}	PUNCT
ejpam-4283	67	76	}	}	PUNCT
ejpam-4283	67	77	.	.	PUNCT
ejpam-4283	68	1	then	then	ADV
ejpam-4283	68	2	σ1	σ1	PROPN
ejpam-4283	68	3	=	=	PUNCT
ejpam-4283	68	4	{	{	PUNCT
ejpam-4283	68	5	∅	∅	NOUN
ejpam-4283	68	6	,	,	PUNCT
ejpam-4283	68	7	{	{	PUNCT
ejpam-4283	68	8	s	s	X
ejpam-4283	68	9	}	}	PUNCT
ejpam-4283	68	10	,	,	PUNCT
ejpam-4283	68	11	{	{	PUNCT
ejpam-4283	68	12	p	p	X
ejpam-4283	68	13	,	,	PUNCT
ejpam-4283	68	14	q	q	NOUN
ejpam-4283	68	15	}	}	PUNCT
ejpam-4283	68	16	,	,	PUNCT
ejpam-4283	68	17	{	{	PUNCT
ejpam-4283	68	18	q	q	X
ejpam-4283	68	19	,	,	PUNCT
ejpam-4283	68	20	r	r	NOUN
ejpam-4283	68	21	}	}	PUNCT
ejpam-4283	68	22	,	,	PUNCT
ejpam-4283	68	23	{	{	PUNCT
ejpam-4283	68	24	p	p	X
ejpam-4283	68	25	,	,	PUNCT
ejpam-4283	68	26	q	q	ADJ
ejpam-4283	68	27	,	,	PUNCT
ejpam-4283	68	28	r	r	NOUN
ejpam-4283	68	29	}	}	PUNCT
ejpam-4283	68	30	,	,	PUNCT
ejpam-4283	68	31	{	{	PUNCT
ejpam-4283	68	32	p	p	X
ejpam-4283	68	33	,	,	PUNCT
ejpam-4283	68	34	q	q	X
ejpam-4283	68	35	,	,	PUNCT
ejpam-4283	68	36	s	s	PART
ejpam-4283	68	37	}	}	PUNCT
ejpam-4283	68	38	,	,	PUNCT
ejpam-4283	68	39	{	{	PUNCT
ejpam-4283	68	40	q	q	X
ejpam-4283	68	41	,	,	PUNCT
ejpam-4283	68	42	r	r	NOUN
ejpam-4283	68	43	,	,	PUNCT
ejpam-4283	68	44	s	s	PART
ejpam-4283	68	45	}	}	PUNCT
ejpam-4283	68	46	,	,	PUNCT
ejpam-4283	68	47	x	x	NOUN
ejpam-4283	68	48	}	}	PUNCT
ejpam-4283	68	49	and	and	CCONJ
ejpam-4283	68	50	σ2	σ2	PROPN
ejpam-4283	68	51	=	=	SYM
ejpam-4283	68	52	{	{	PUNCT
ejpam-4283	68	53	∅	∅	NOUN
ejpam-4283	68	54	,	,	PUNCT
ejpam-4283	68	55	{	{	PUNCT
ejpam-4283	68	56	r	r	NOUN
ejpam-4283	68	57	}	}	PUNCT
ejpam-4283	68	58	,	,	PUNCT
ejpam-4283	68	59	{	{	PUNCT
ejpam-4283	68	60	p	p	X
ejpam-4283	68	61	,	,	PUNCT
ejpam-4283	68	62	s	s	PART
ejpam-4283	68	63	}	}	PUNCT
ejpam-4283	68	64	,	,	PUNCT
ejpam-4283	68	65	{	{	PUNCT
ejpam-4283	68	66	q	q	X
ejpam-4283	68	67	,	,	PUNCT
ejpam-4283	68	68	s	s	PART
ejpam-4283	68	69	}	}	PUNCT
ejpam-4283	68	70	,	,	PUNCT
ejpam-4283	68	71	{	{	PUNCT
ejpam-4283	68	72	p	p	X
ejpam-4283	68	73	,	,	PUNCT
ejpam-4283	68	74	q	q	X
ejpam-4283	68	75	,	,	PUNCT
ejpam-4283	68	76	s	s	PART
ejpam-4283	68	77	}	}	PUNCT
ejpam-4283	68	78	,	,	PUNCT
ejpam-4283	68	79	{	{	PUNCT
ejpam-4283	68	80	p	p	X
ejpam-4283	68	81	,	,	PUNCT
ejpam-4283	68	82	r	r	NOUN
ejpam-4283	68	83	,	,	PUNCT
ejpam-4283	68	84	s	s	PART
ejpam-4283	68	85	}	}	PUNCT
ejpam-4283	68	86	,	,	PUNCT
ejpam-4283	68	87	{	{	PUNCT
ejpam-4283	68	88	q	q	X
ejpam-4283	68	89	,	,	PUNCT
ejpam-4283	68	90	r	r	NOUN
ejpam-4283	68	91	,	,	PUNCT
ejpam-4283	68	92	s	s	PART
ejpam-4283	68	93	}	}	PUNCT
ejpam-4283	68	94	,	,	PUNCT
ejpam-4283	68	95	x	x	NOUN
ejpam-4283	68	96	}	}	PUNCT
ejpam-4283	68	97	.	.	PUNCT
ejpam-4283	69	1	1	1	X
ejpam-4283	69	2	.	.	X
ejpam-4283	69	3	take	take	VERB
ejpam-4283	69	4	e	e	NOUN
ejpam-4283	69	5	=	=	PUNCT
ejpam-4283	69	6	{	{	PUNCT
ejpam-4283	69	7	s	s	NOUN
ejpam-4283	69	8	}	}	PUNCT
ejpam-4283	69	9	.	.	PUNCT
ejpam-4283	70	1	then	then	ADV
ejpam-4283	70	2	iσ2(c1(e	iσ2(c1(e	NOUN
ejpam-4283	70	3	)	)	PUNCT
ejpam-4283	70	4	)	)	PUNCT
ejpam-4283	71	1	=	=	PUNCT
ejpam-4283	71	2	iσ2(e	iσ2(e	ADV
ejpam-4283	71	3	)	)	PUNCT
ejpam-4283	71	4	=	=	NOUN
ejpam-4283	71	5	∅.	∅.	ADP
ejpam-4283	71	6	thus	thus	ADV
ejpam-4283	71	7	,	,	PUNCT
ejpam-4283	71	8	e	e	X
ejpam-4283	71	9	is	be	AUX
ejpam-4283	71	10	a	a	DET
ejpam-4283	71	11	(	(	PUNCT
ejpam-4283	71	12	1	1	NUM
ejpam-4283	71	13	,	,	PUNCT
ejpam-4283	71	14	2)?-nowhere	2)?-nowhere	NUM
ejpam-4283	71	15	dense	dense	ADJ
ejpam-4283	71	16	set	set	NOUN
ejpam-4283	71	17	in	in	ADP
ejpam-4283	71	18	x.	x.	PROPN
ejpam-4283	71	19	p.	p.	PROPN
ejpam-4283	71	20	yupapin	yupapin	NOUN
ejpam-4283	71	21	,	,	PUNCT
ejpam-4283	71	22	v.	v.	CCONJ
ejpam-4283	71	23	subramanian	subramanian	PROPN
ejpam-4283	71	24	,	,	PUNCT
ejpam-4283	71	25	y.	y.	PROPN
ejpam-4283	71	26	farhat	farhat	PROPN
ejpam-4283	71	27	/	/	SYM
ejpam-4283	71	28	eur	eur	PROPN
ejpam-4283	71	29	.	.	PUNCT
ejpam-4283	72	1	j.	j.	PROPN
ejpam-4283	72	2	pure	pure	PROPN
ejpam-4283	72	3	appl	appl	PROPN
ejpam-4283	72	4	.	.	PROPN
ejpam-4283	72	5	math	math	PROPN
ejpam-4283	72	6	,	,	PUNCT
ejpam-4283	72	7	15	15	NUM
ejpam-4283	72	8	(	(	PUNCT
ejpam-4283	72	9	2	2	NUM
ejpam-4283	72	10	)	)	PUNCT
ejpam-4283	72	11	(	(	PUNCT
ejpam-4283	72	12	2022	2022	NUM
ejpam-4283	72	13	)	)	PUNCT
ejpam-4283	72	14	,	,	PUNCT
ejpam-4283	72	15	403	403	NUM
ejpam-4283	72	16	-	-	SYM
ejpam-4283	72	17	414	414	NUM
ejpam-4283	72	18	405	405	NUM
ejpam-4283	72	19	2	2	NUM
ejpam-4283	72	20	.	.	PUNCT
ejpam-4283	73	1	choose	choose	VERB
ejpam-4283	73	2	f	f	X
ejpam-4283	73	3	=	=	PRON
ejpam-4283	73	4	{	{	PUNCT
ejpam-4283	73	5	p	p	X
ejpam-4283	73	6	,	,	PUNCT
ejpam-4283	73	7	r	r	NOUN
ejpam-4283	73	8	}	}	PUNCT
ejpam-4283	73	9	.	.	PUNCT
ejpam-4283	74	1	then	then	ADV
ejpam-4283	74	2	iσ1(c2(f	iσ1(c2(f	NOUN
ejpam-4283	74	3	)	)	PUNCT
ejpam-4283	74	4	)	)	PUNCT
ejpam-4283	75	1	=	=	PUNCT
ejpam-4283	75	2	iσ1({p	iσ1({p	PROPN
ejpam-4283	75	3	,	,	PUNCT
ejpam-4283	75	4	r	r	NOUN
ejpam-4283	75	5	}	}	PUNCT
ejpam-4283	75	6	)	)	PUNCT
ejpam-4283	76	1	=	=	PUNCT
ejpam-4283	76	2	∅.	∅.	PROPN
ejpam-4283	76	3	then	then	ADV
ejpam-4283	76	4	f	f	PROPN
ejpam-4283	76	5	is	be	AUX
ejpam-4283	76	6	a	a	DET
ejpam-4283	76	7	(	(	PUNCT
ejpam-4283	76	8	2	2	NUM
ejpam-4283	76	9	,	,	PUNCT
ejpam-4283	76	10	1)?-nowhere	1)?-nowhere	NUM
ejpam-4283	76	11	dense	dense	ADJ
ejpam-4283	76	12	in	in	ADP
ejpam-4283	76	13	x.	x.	NOUN
ejpam-4283	76	14	in	in	ADP
ejpam-4283	76	15	a	a	DET
ejpam-4283	76	16	bigeneralized	bigeneralize	VERB
ejpam-4283	76	17	topological	topological	ADJ
ejpam-4283	76	18	space	space	NOUN
ejpam-4283	76	19	,	,	PUNCT
ejpam-4283	76	20	if	if	SCONJ
ejpam-4283	76	21	k	k	PROPN
ejpam-4283	76	22	∈	∈	PROPN
ejpam-4283	76	23	(	(	PUNCT
ejpam-4283	76	24	s	s	PROPN
ejpam-4283	76	25	,	,	PUNCT
ejpam-4283	76	26	v	v	NOUN
ejpam-4283	76	27	)	)	PUNCT
ejpam-4283	76	28	?	?	PUNCT
ejpam-4283	77	1	−	−	PROPN
ejpam-4283	78	1	n	n	CCONJ
ejpam-4283	78	2	(	(	PUNCT
ejpam-4283	78	3	x	x	NOUN
ejpam-4283	78	4	)	)	PUNCT
ejpam-4283	78	5	and	and	CCONJ
ejpam-4283	78	6	l	l	PROPN
ejpam-4283	79	1	⊂	⊂	PROPN
ejpam-4283	79	2	k	k	NOUN
ejpam-4283	79	3	,	,	PUNCT
ejpam-4283	79	4	then	then	ADV
ejpam-4283	79	5	l	l	PROPN
ejpam-4283	79	6	∈	∈	PROPN
ejpam-4283	79	7	(	(	PUNCT
ejpam-4283	79	8	s	s	PROPN
ejpam-4283	79	9	,	,	PUNCT
ejpam-4283	79	10	v	v	NOUN
ejpam-4283	79	11	)	)	PUNCT
ejpam-4283	79	12	?	?	PUNCT
ejpam-4283	80	1	−	−	PROPN
ejpam-4283	81	1	n	n	CCONJ
ejpam-4283	81	2	(	(	PUNCT
ejpam-4283	81	3	x	x	NOUN
ejpam-4283	81	4	)	)	PUNCT
ejpam-4283	81	5	where	where	SCONJ
ejpam-4283	81	6	s	s	X
ejpam-4283	81	7	,	,	PUNCT
ejpam-4283	81	8	v	v	NOUN
ejpam-4283	81	9	=	=	SYM
ejpam-4283	81	10	1	1	NUM
ejpam-4283	81	11	,	,	PUNCT
ejpam-4283	81	12	2	2	NUM
ejpam-4283	81	13	and	and	CCONJ
ejpam-4283	81	14	s	s	X
ejpam-4283	81	15	6=	6=	PROPN
ejpam-4283	81	16	v.	v.	CCONJ
ejpam-4283	81	17	also	also	ADV
ejpam-4283	81	18	,	,	PUNCT
ejpam-4283	81	19	every	every	DET
ejpam-4283	81	20	(	(	PUNCT
ejpam-4283	81	21	s	s	X
ejpam-4283	81	22	,	,	PUNCT
ejpam-4283	81	23	v)?-nowhere	v)?-nowhere	X
ejpam-4283	81	24	dense	dense	ADJ
ejpam-4283	81	25	set	set	NOUN
ejpam-4283	81	26	where	where	SCONJ
ejpam-4283	81	27	s	s	X
ejpam-4283	81	28	,	,	PUNCT
ejpam-4283	81	29	v	v	NOUN
ejpam-4283	81	30	=	=	SYM
ejpam-4283	81	31	1	1	NUM
ejpam-4283	81	32	,	,	PUNCT
ejpam-4283	81	33	2	2	NUM
ejpam-4283	81	34	and	and	CCONJ
ejpam-4283	81	35	s	s	PROPN
ejpam-4283	81	36	6=	6=	PROPN
ejpam-4283	81	37	v	v	NOUN
ejpam-4283	81	38	,	,	PUNCT
ejpam-4283	81	39	is	be	AUX
ejpam-4283	81	40	a	a	DET
ejpam-4283	81	41	µv	µv	NOUN
ejpam-4283	81	42	-	-	PUNCT
ejpam-4283	81	43	codense	codense	NOUN
ejpam-4283	81	44	set	set	NOUN
ejpam-4283	81	45	for	for	ADP
ejpam-4283	81	46	v	v	NOUN
ejpam-4283	81	47	=	=	SYM
ejpam-4283	81	48	1	1	NUM
ejpam-4283	81	49	,	,	PUNCT
ejpam-4283	81	50	2	2	NUM
ejpam-4283	81	51	in	in	ADP
ejpam-4283	81	52	x.	x.	NOUN
ejpam-4283	81	53	moreover	moreover	ADV
ejpam-4283	81	54	,	,	PUNCT
ejpam-4283	81	55	any	any	DET
ejpam-4283	81	56	(	(	PUNCT
ejpam-4283	81	57	s	s	X
ejpam-4283	81	58	,	,	PUNCT
ejpam-4283	81	59	v)?-nowhere	v)?-nowhere	X
ejpam-4283	81	60	dense	dense	ADJ
ejpam-4283	81	61	set	set	NOUN
ejpam-4283	81	62	is	be	AUX
ejpam-4283	81	63	a	a	DET
ejpam-4283	81	64	(	(	PUNCT
ejpam-4283	81	65	v	v	NOUN
ejpam-4283	81	66	,	,	PUNCT
ejpam-4283	81	67	s)-nowhere	s)-nowhere	X
ejpam-4283	81	68	dense	dense	ADJ
ejpam-4283	81	69	set	set	NOUN
ejpam-4283	81	70	in	in	ADP
ejpam-4283	81	71	a	a	DET
ejpam-4283	81	72	bigeneralized	bigeneralize	VERB
ejpam-4283	81	73	topological	topological	ADJ
ejpam-4283	81	74	space	space	NOUN
ejpam-4283	81	75	(	(	PUNCT
ejpam-4283	81	76	x,µ1	x,µ1	PROPN
ejpam-4283	81	77	,	,	PUNCT
ejpam-4283	81	78	µ2	µ2	PROPN
ejpam-4283	81	79	)	)	PUNCT
ejpam-4283	81	80	where	where	SCONJ
ejpam-4283	81	81	s	s	X
ejpam-4283	81	82	,	,	PUNCT
ejpam-4283	81	83	v	v	NOUN
ejpam-4283	81	84	=	=	SYM
ejpam-4283	81	85	1	1	NUM
ejpam-4283	81	86	,	,	PUNCT
ejpam-4283	81	87	2	2	NUM
ejpam-4283	81	88	and	and	CCONJ
ejpam-4283	81	89	s	s	PROPN
ejpam-4283	81	90	6=	6=	PROPN
ejpam-4283	81	91	v	v	NOUN
ejpam-4283	81	92	,	,	PUNCT
ejpam-4283	81	93	since	since	SCONJ
ejpam-4283	81	94	µ	µ	PROPN
ejpam-4283	81	95	⊂	⊂	PROPN
ejpam-4283	81	96	σ	σ	NOUN
ejpam-4283	82	1	[	[	X
ejpam-4283	82	2	3	3	NUM
ejpam-4283	82	3	]	]	PUNCT
ejpam-4283	82	4	.	.	PUNCT
ejpam-4283	82	5	example	example	NOUN
ejpam-4283	82	6	3	3	X
ejpam-4283	82	7	.	.	X
ejpam-4283	82	8	consider	consider	VERB
ejpam-4283	82	9	the	the	DET
ejpam-4283	82	10	bgts	bgts	NOUN
ejpam-4283	82	11	(	(	PUNCT
ejpam-4283	82	12	x,µ1	x,µ1	PROPN
ejpam-4283	82	13	,	,	PUNCT
ejpam-4283	82	14	µ2	µ2	PROPN
ejpam-4283	82	15	)	)	PUNCT
ejpam-4283	82	16	where	where	SCONJ
ejpam-4283	82	17	x	x	X
ejpam-4283	82	18	=	=	PRON
ejpam-4283	82	19	{	{	PUNCT
ejpam-4283	82	20	p	p	X
ejpam-4283	82	21	,	,	PUNCT
ejpam-4283	82	22	q	q	ADJ
ejpam-4283	82	23	,	,	PUNCT
ejpam-4283	82	24	r	r	NOUN
ejpam-4283	82	25	,	,	PUNCT
ejpam-4283	82	26	s	s	PART
ejpam-4283	82	27	}	}	PUNCT
ejpam-4283	82	28	and	and	CCONJ
ejpam-4283	82	29	µ1	µ1	PROPN
ejpam-4283	82	30	,	,	PUNCT
ejpam-4283	82	31	µ2	µ2	PROPN
ejpam-4283	82	32	are	be	AUX
ejpam-4283	82	33	defined	define	VERB
ejpam-4283	82	34	in	in	ADP
ejpam-4283	82	35	example	example	NOUN
ejpam-4283	83	1	2	2	NUM
ejpam-4283	83	2	.	.	X
ejpam-4283	83	3	take	take	VERB
ejpam-4283	83	4	p	p	NOUN
ejpam-4283	83	5	=	=	X
ejpam-4283	83	6	{	{	PUNCT
ejpam-4283	83	7	s	s	NOUN
ejpam-4283	83	8	}	}	PUNCT
ejpam-4283	83	9	.	.	PUNCT
ejpam-4283	84	1	then	then	ADV
ejpam-4283	84	2	p	p	X
ejpam-4283	84	3	is	be	AUX
ejpam-4283	84	4	(	(	PUNCT
ejpam-4283	84	5	1	1	NUM
ejpam-4283	84	6	,	,	PUNCT
ejpam-4283	84	7	2)?-nowhere	2)?-nowhere	NUM
ejpam-4283	84	8	dense	dense	ADJ
ejpam-4283	84	9	set	set	NOUN
ejpam-4283	84	10	,	,	PUNCT
ejpam-4283	84	11	by	by	ADP
ejpam-4283	84	12	example	example	NOUN
ejpam-4283	84	13	2	2	NUM
ejpam-4283	84	14	.	.	PUNCT
ejpam-4283	84	15	now	now	ADV
ejpam-4283	84	16	i2(c1(p	i2(c1(p	NOUN
ejpam-4283	84	17	)	)	PUNCT
ejpam-4283	84	18	)	)	PUNCT
ejpam-4283	85	1	=	=	PUNCT
ejpam-4283	85	2	i2(p	i2(p	PROPN
ejpam-4283	85	3	)	)	PUNCT
ejpam-4283	85	4	=	=	PUNCT
ejpam-4283	85	5	∅.	∅.	VERB
ejpam-4283	85	6	therefore	therefore	ADV
ejpam-4283	85	7	,	,	PUNCT
ejpam-4283	85	8	p	p	NOUN
ejpam-4283	85	9	is	be	AUX
ejpam-4283	85	10	(	(	PUNCT
ejpam-4283	85	11	2	2	NUM
ejpam-4283	85	12	,	,	PUNCT
ejpam-4283	85	13	1)-nowhere	1)-nowhere	NUM
ejpam-4283	85	14	dense	dense	ADJ
ejpam-4283	85	15	set	set	NOUN
ejpam-4283	85	16	in	in	ADP
ejpam-4283	85	17	x.	x.	NOUN
ejpam-4283	85	18	choose	choose	VERB
ejpam-4283	85	19	d	d	PROPN
ejpam-4283	85	20	=	=	PUNCT
ejpam-4283	85	21	{	{	PUNCT
ejpam-4283	85	22	p	p	X
ejpam-4283	85	23	,	,	PUNCT
ejpam-4283	85	24	r	r	NOUN
ejpam-4283	85	25	}	}	PUNCT
ejpam-4283	85	26	.	.	PUNCT
ejpam-4283	86	1	in	in	ADP
ejpam-4283	86	2	example	example	NOUN
ejpam-4283	86	3	2	2	NUM
ejpam-4283	86	4	,	,	PUNCT
ejpam-4283	86	5	d	d	X
ejpam-4283	86	6	is	be	AUX
ejpam-4283	86	7	(	(	PUNCT
ejpam-4283	86	8	2	2	NUM
ejpam-4283	86	9	,	,	PUNCT
ejpam-4283	86	10	1)?-nowhere	1)?-nowhere	NUM
ejpam-4283	86	11	dense	dense	ADJ
ejpam-4283	86	12	set	set	NOUN
ejpam-4283	86	13	in	in	ADP
ejpam-4283	86	14	x.	x.	NOUN
ejpam-4283	86	15	here	here	ADV
ejpam-4283	86	16	i1(c2(d	i1(c2(d	ADV
ejpam-4283	86	17	)	)	PUNCT
ejpam-4283	86	18	)	)	PUNCT
ejpam-4283	87	1	=	=	PUNCT
ejpam-4283	87	2	i1(d	i1(d	X
ejpam-4283	87	3	)	)	PUNCT
ejpam-4283	87	4	=	=	NOUN
ejpam-4283	87	5	∅.	∅.	ADP
ejpam-4283	87	6	thus	thus	ADV
ejpam-4283	87	7	,	,	PUNCT
ejpam-4283	87	8	d	d	X
ejpam-4283	87	9	is	be	AUX
ejpam-4283	87	10	(	(	PUNCT
ejpam-4283	87	11	1	1	NUM
ejpam-4283	87	12	,	,	PUNCT
ejpam-4283	87	13	2)-nowhere	2)-nowhere	NUM
ejpam-4283	87	14	dense	dense	ADJ
ejpam-4283	87	15	set	set	NOUN
ejpam-4283	87	16	in	in	ADP
ejpam-4283	87	17	x.	x.	NOUN
ejpam-4283	87	18	theorem	theorem	VERB
ejpam-4283	87	19	4	4	NUM
ejpam-4283	87	20	.	.	PUNCT
ejpam-4283	88	1	let	let	AUX
ejpam-4283	88	2	(	(	PUNCT
ejpam-4283	88	3	x,µ1	x,µ1	NOUN
ejpam-4283	88	4	,	,	PUNCT
ejpam-4283	88	5	µ2	µ2	PROPN
ejpam-4283	88	6	)	)	PUNCT
ejpam-4283	88	7	be	be	VERB
ejpam-4283	88	8	a	a	DET
ejpam-4283	88	9	bigeneralized	bigeneralized	ADJ
ejpam-4283	88	10	topological	topological	ADJ
ejpam-4283	88	11	space	space	NOUN
ejpam-4283	88	12	.	.	PUNCT
ejpam-4283	89	1	then	then	ADV
ejpam-4283	89	2	the	the	DET
ejpam-4283	89	3	followings	following	NOUN
ejpam-4283	89	4	are	be	AUX
ejpam-4283	89	5	true	true	ADJ
ejpam-4283	89	6	.	.	PUNCT
ejpam-4283	90	1	(	(	PUNCT
ejpam-4283	90	2	a	a	X
ejpam-4283	90	3	)	)	PUNCT
ejpam-4283	90	4	if	if	SCONJ
ejpam-4283	90	5	(	(	PUNCT
ejpam-4283	90	6	x,µ1	x,µ1	NOUN
ejpam-4283	90	7	)	)	PUNCT
ejpam-4283	90	8	is	be	AUX
ejpam-4283	90	9	a	a	DET
ejpam-4283	90	10	sgts	sgts	NOUN
ejpam-4283	90	11	and	and	CCONJ
ejpam-4283	90	12	q	q	NOUN
ejpam-4283	90	13	⊂	⊂	PROPN
ejpam-4283	90	14	x	x	X
ejpam-4283	90	15	is	be	AUX
ejpam-4283	90	16	a	a	DET
ejpam-4283	90	17	(	(	PUNCT
ejpam-4283	90	18	1	1	NUM
ejpam-4283	90	19	,	,	PUNCT
ejpam-4283	90	20	2)-nowhere	2)-nowhere	NUM
ejpam-4283	90	21	dense	dense	ADJ
ejpam-4283	90	22	set	set	NOUN
ejpam-4283	90	23	,	,	PUNCT
ejpam-4283	90	24	then	then	ADV
ejpam-4283	90	25	q	q	PROPN
ejpam-4283	90	26	∈	∈	PROPN
ejpam-4283	90	27	(	(	PUNCT
ejpam-4283	90	28	2	2	NUM
ejpam-4283	90	29	,	,	PUNCT
ejpam-4283	90	30	1)?−n	1)?−n	PROPN
ejpam-4283	90	31	(	(	PUNCT
ejpam-4283	90	32	x	x	NOUN
ejpam-4283	90	33	)	)	PUNCT
ejpam-4283	90	34	.	.	PUNCT
ejpam-4283	91	1	(	(	PUNCT
ejpam-4283	91	2	b	b	X
ejpam-4283	91	3	)	)	PUNCT
ejpam-4283	91	4	if	if	SCONJ
ejpam-4283	91	5	(	(	PUNCT
ejpam-4283	91	6	x,µ2	x,µ2	PROPN
ejpam-4283	91	7	)	)	PUNCT
ejpam-4283	91	8	is	be	AUX
ejpam-4283	91	9	a	a	DET
ejpam-4283	91	10	sgts	sgts	NOUN
ejpam-4283	91	11	and	and	CCONJ
ejpam-4283	91	12	j	j	PROPN
ejpam-4283	91	13	⊂	⊂	PROPN
ejpam-4283	91	14	x	x	X
ejpam-4283	91	15	is	be	AUX
ejpam-4283	91	16	a	a	DET
ejpam-4283	91	17	(	(	PUNCT
ejpam-4283	91	18	2	2	NUM
ejpam-4283	91	19	,	,	PUNCT
ejpam-4283	91	20	1)-nowhere	1)-nowhere	NUM
ejpam-4283	91	21	dense	dense	ADJ
ejpam-4283	91	22	set	set	NOUN
ejpam-4283	91	23	,	,	PUNCT
ejpam-4283	91	24	then	then	ADV
ejpam-4283	91	25	j	j	PROPN
ejpam-4283	91	26	∈	∈	PROPN
ejpam-4283	91	27	(	(	PUNCT
ejpam-4283	91	28	1	1	NUM
ejpam-4283	91	29	,	,	PUNCT
ejpam-4283	91	30	2)?−n	2)?−n	NUM
ejpam-4283	91	31	(	(	PUNCT
ejpam-4283	91	32	x	x	NOUN
ejpam-4283	91	33	)	)	PUNCT
ejpam-4283	91	34	.	.	PUNCT
ejpam-4283	92	1	proof	proof	NOUN
ejpam-4283	92	2	.	.	PUNCT
ejpam-4283	93	1	(	(	PUNCT
ejpam-4283	93	2	a	a	X
ejpam-4283	93	3	)	)	PUNCT
ejpam-4283	93	4	.	.	PUNCT
ejpam-4283	94	1	assume	assume	VERB
ejpam-4283	94	2	that	that	SCONJ
ejpam-4283	94	3	,	,	PUNCT
ejpam-4283	94	4	(	(	PUNCT
ejpam-4283	94	5	x,µ1	x,µ1	NOUN
ejpam-4283	94	6	)	)	PUNCT
ejpam-4283	94	7	is	be	AUX
ejpam-4283	94	8	a	a	DET
ejpam-4283	94	9	sgts	sgts	NOUN
ejpam-4283	94	10	and	and	CCONJ
ejpam-4283	94	11	q	q	NOUN
ejpam-4283	94	12	is	be	AUX
ejpam-4283	94	13	a	a	DET
ejpam-4283	94	14	(	(	PUNCT
ejpam-4283	94	15	1	1	NUM
ejpam-4283	94	16	,	,	PUNCT
ejpam-4283	94	17	2)-nowhere	2)-nowhere	NUM
ejpam-4283	94	18	dense	dense	ADJ
ejpam-4283	94	19	set	set	NOUN
ejpam-4283	94	20	.	.	PUNCT
ejpam-4283	95	1	then	then	ADV
ejpam-4283	95	2	i1(c2(q	i1(c2(q	NUM
ejpam-4283	95	3	)	)	PUNCT
ejpam-4283	95	4	)	)	PUNCT
ejpam-4283	96	1	=	=	VERB
ejpam-4283	96	2	∅.	∅.	AUX
ejpam-4283	96	3	suppose	suppose	VERB
ejpam-4283	96	4	iσ1(c2(q	iσ1(c2(q	NOUN
ejpam-4283	96	5	)	)	PUNCT
ejpam-4283	96	6	)	)	PUNCT
ejpam-4283	96	7	6=	6=	ADP
ejpam-4283	96	8	∅.	∅.	VERB
ejpam-4283	96	9	then	then	ADV
ejpam-4283	96	10	there	there	PRON
ejpam-4283	96	11	exist	exist	VERB
ejpam-4283	96	12	g	g	PROPN
ejpam-4283	96	13	∈	∈	PROPN
ejpam-4283	96	14	σ̃1	σ̃1	PROPN
ejpam-4283	96	15	such	such	ADJ
ejpam-4283	96	16	that	that	SCONJ
ejpam-4283	96	17	g	g	PROPN
ejpam-4283	96	18	⊂	⊂	PROPN
ejpam-4283	96	19	c2(q	c2(q	PROPN
ejpam-4283	96	20	)	)	PUNCT
ejpam-4283	96	21	.	.	PUNCT
ejpam-4283	97	1	since	since	SCONJ
ejpam-4283	97	2	g	g	PROPN
ejpam-4283	97	3	∈	∈	PROPN
ejpam-4283	97	4	σ̃1	σ̃1	PROPN
ejpam-4283	97	5	we	we	PRON
ejpam-4283	97	6	have	have	VERB
ejpam-4283	97	7	g	g	PROPN
ejpam-4283	97	8	⊂	⊂	PROPN
ejpam-4283	97	9	c1(i1(g	c1(i1(g	PROPN
ejpam-4283	97	10	)	)	PUNCT
ejpam-4283	97	11	)	)	PUNCT
ejpam-4283	97	12	which	which	PRON
ejpam-4283	97	13	implies	imply	VERB
ejpam-4283	97	14	c1(i1(g	c1(i1(g	PROPN
ejpam-4283	97	15	)	)	PUNCT
ejpam-4283	97	16	)	)	PUNCT
ejpam-4283	98	1	6=	6=	ADP
ejpam-4283	98	2	∅	∅	NOUN
ejpam-4283	98	3	which	which	PRON
ejpam-4283	98	4	turn	turn	VERB
ejpam-4283	98	5	implies	imply	VERB
ejpam-4283	98	6	that	that	SCONJ
ejpam-4283	98	7	i1(g	i1(g	PROPN
ejpam-4283	98	8	)	)	PUNCT
ejpam-4283	98	9	6=	6=	ADP
ejpam-4283	98	10	∅	∅	NOUN
ejpam-4283	98	11	,	,	PUNCT
ejpam-4283	98	12	by	by	ADP
ejpam-4283	98	13	assumption	assumption	NOUN
ejpam-4283	98	14	.	.	PUNCT
ejpam-4283	99	1	thus	thus	ADV
ejpam-4283	99	2	,	,	PUNCT
ejpam-4283	99	3	i1(g	i1(g	PROPN
ejpam-4283	99	4	)	)	PUNCT
ejpam-4283	99	5	∈	∈	PROPN
ejpam-4283	99	6	µ̃1	µ̃1	NOUN
ejpam-4283	99	7	and	and	CCONJ
ejpam-4283	99	8	i1(g	i1(g	PROPN
ejpam-4283	99	9	)	)	PUNCT
ejpam-4283	99	10	⊂	⊂	PROPN
ejpam-4283	99	11	c2(q	c2(q	PROPN
ejpam-4283	99	12	)	)	PUNCT
ejpam-4283	99	13	.	.	PUNCT
ejpam-4283	100	1	then	then	ADV
ejpam-4283	100	2	i1(c2(q	i1(c2(q	NUM
ejpam-4283	100	3	)	)	PUNCT
ejpam-4283	100	4	)	)	PUNCT
ejpam-4283	101	1	6=	6=	ADP
ejpam-4283	101	2	∅	∅	NOUN
ejpam-4283	101	3	which	which	PRON
ejpam-4283	101	4	is	be	AUX
ejpam-4283	101	5	not	not	PART
ejpam-4283	101	6	possible	possible	ADJ
ejpam-4283	101	7	.	.	PUNCT
ejpam-4283	102	1	therefore	therefore	ADV
ejpam-4283	102	2	,	,	PUNCT
ejpam-4283	102	3	iσ1(c2(q	iσ1(c2(q	PROPN
ejpam-4283	102	4	)	)	PUNCT
ejpam-4283	102	5	)	)	PUNCT
ejpam-4283	103	1	=	=	PUNCT
ejpam-4283	103	2	∅.	∅.	X
ejpam-4283	103	3	(	(	PUNCT
ejpam-4283	103	4	b	b	NOUN
ejpam-4283	103	5	)	)	PUNCT
ejpam-4283	103	6	.	.	PUNCT
ejpam-4283	104	1	follows	follow	VERB
ejpam-4283	104	2	from	from	ADP
ejpam-4283	104	3	the	the	DET
ejpam-4283	104	4	similar	similar	ADJ
ejpam-4283	104	5	arguments	argument	NOUN
ejpam-4283	104	6	in	in	ADP
ejpam-4283	104	7	(	(	PUNCT
ejpam-4283	104	8	a	a	NOUN
ejpam-4283	104	9	)	)	PUNCT
ejpam-4283	104	10	.	.	PUNCT
ejpam-4283	105	1	in	in	ADP
ejpam-4283	105	2	theorem	theorem	NOUN
ejpam-4283	105	3	4	4	NUM
ejpam-4283	105	4	,	,	PUNCT
ejpam-4283	105	5	the	the	DET
ejpam-4283	105	6	condition	condition	NOUN
ejpam-4283	105	7	“	"	PUNCT
ejpam-4283	105	8	µ1	µ1	PROPN
ejpam-4283	105	9	is	be	AUX
ejpam-4283	105	10	a	a	DET
ejpam-4283	105	11	sgt	sgt	PROPN
ejpam-4283	105	12	”	"	PUNCT
ejpam-4283	105	13	is	be	AUX
ejpam-4283	105	14	necessary	necessary	ADJ
ejpam-4283	105	15	as	as	SCONJ
ejpam-4283	105	16	shown	show	VERB
ejpam-4283	105	17	by	by	ADP
ejpam-4283	105	18	the	the	DET
ejpam-4283	105	19	below	below	ADJ
ejpam-4283	105	20	example	example	NOUN
ejpam-4283	105	21	5	5	NUM
ejpam-4283	105	22	.	.	PUNCT
ejpam-4283	106	1	the	the	DET
ejpam-4283	106	2	condition	condition	NOUN
ejpam-4283	106	3	“	"	PUNCT
ejpam-4283	106	4	µ2	µ2	PROPN
ejpam-4283	106	5	is	be	AUX
ejpam-4283	106	6	a	a	DET
ejpam-4283	106	7	sgt	sgt	NOUN
ejpam-4283	106	8	”	"	PUNCT
ejpam-4283	106	9	in	in	ADP
ejpam-4283	106	10	theorem	theorem	NOUN
ejpam-4283	106	11	4	4	NUM
ejpam-4283	106	12	is	be	AUX
ejpam-4283	106	13	necessary	necessary	ADJ
ejpam-4283	106	14	as	as	SCONJ
ejpam-4283	106	15	shown	show	VERB
ejpam-4283	106	16	by	by	ADP
ejpam-4283	106	17	example	example	NOUN
ejpam-4283	106	18	6	6	NUM
ejpam-4283	106	19	.	.	PUNCT
ejpam-4283	106	20	example	example	NOUN
ejpam-4283	107	1	5	5	NUM
ejpam-4283	107	2	.	.	PUNCT
ejpam-4283	107	3	consider	consider	VERB
ejpam-4283	107	4	the	the	DET
ejpam-4283	107	5	bigeneralized	bigeneralized	ADJ
ejpam-4283	107	6	topological	topological	ADJ
ejpam-4283	107	7	space	space	NOUN
ejpam-4283	107	8	(	(	PUNCT
ejpam-4283	107	9	x,µ1	x,µ1	PROPN
ejpam-4283	107	10	,	,	PUNCT
ejpam-4283	107	11	µ2	µ2	PROPN
ejpam-4283	107	12	)	)	PUNCT
ejpam-4283	108	1	where	where	SCONJ
ejpam-4283	108	2	x	x	X
ejpam-4283	108	3	=	=	PRON
ejpam-4283	108	4	{	{	PUNCT
ejpam-4283	108	5	p	p	X
ejpam-4283	108	6	,	,	PUNCT
ejpam-4283	108	7	q	q	ADJ
ejpam-4283	108	8	,	,	PUNCT
ejpam-4283	108	9	r	r	NOUN
ejpam-4283	108	10	,	,	PUNCT
ejpam-4283	108	11	s	s	NOUN
ejpam-4283	108	12	,	,	PUNCT
ejpam-4283	108	13	t};µ1	t};µ1	PROPN
ejpam-4283	108	14	=	=	SYM
ejpam-4283	108	15	{	{	PUNCT
ejpam-4283	108	16	∅	∅	NOUN
ejpam-4283	108	17	,	,	PUNCT
ejpam-4283	108	18	{	{	PUNCT
ejpam-4283	108	19	p	p	X
ejpam-4283	108	20	,	,	PUNCT
ejpam-4283	108	21	q	q	NOUN
ejpam-4283	108	22	}	}	PUNCT
ejpam-4283	108	23	,	,	PUNCT
ejpam-4283	108	24	{	{	PUNCT
ejpam-4283	108	25	p	p	X
ejpam-4283	108	26	,	,	PUNCT
ejpam-4283	108	27	s	s	PART
ejpam-4283	108	28	}	}	PUNCT
ejpam-4283	108	29	,	,	PUNCT
ejpam-4283	108	30	{	{	PUNCT
ejpam-4283	108	31	p	p	X
ejpam-4283	108	32	,	,	PUNCT
ejpam-4283	108	33	q	q	NOUN
ejpam-4283	108	34	,	,	PUNCT
ejpam-4283	108	35	s}};µ2	s}};µ2	VERB
ejpam-4283	108	36	=	=	SYM
ejpam-4283	108	37	{	{	PUNCT
ejpam-4283	108	38	∅	∅	NOUN
ejpam-4283	108	39	,	,	PUNCT
ejpam-4283	108	40	{	{	PUNCT
ejpam-4283	108	41	p	p	X
ejpam-4283	108	42	,	,	PUNCT
ejpam-4283	108	43	q	q	NOUN
ejpam-4283	108	44	}	}	PUNCT
ejpam-4283	108	45	,	,	PUNCT
ejpam-4283	108	46	{	{	PUNCT
ejpam-4283	108	47	q	q	X
ejpam-4283	108	48	,	,	PUNCT
ejpam-4283	108	49	r	r	NOUN
ejpam-4283	108	50	}	}	PUNCT
ejpam-4283	108	51	,	,	PUNCT
ejpam-4283	108	52	{	{	PUNCT
ejpam-4283	108	53	p	p	X
ejpam-4283	108	54	,	,	PUNCT
ejpam-4283	108	55	q	q	ADJ
ejpam-4283	108	56	,	,	PUNCT
ejpam-4283	108	57	r	r	NOUN
ejpam-4283	108	58	}	}	PUNCT
ejpam-4283	108	59	}	}	PUNCT
ejpam-4283	108	60	.	.	PUNCT
ejpam-4283	109	1	here	here	ADV
ejpam-4283	109	2	µ1	µ1	PROPN
ejpam-4283	109	3	is	be	AUX
ejpam-4283	109	4	not	not	PART
ejpam-4283	109	5	a	a	DET
ejpam-4283	109	6	sgt	sgt	PROPN
ejpam-4283	109	7	.	.	PUNCT
ejpam-4283	110	1	then	then	ADV
ejpam-4283	110	2	σ1	σ1	PROPN
ejpam-4283	110	3	=	=	PUNCT
ejpam-4283	110	4	{	{	PUNCT
ejpam-4283	110	5	∅	∅	NOUN
ejpam-4283	110	6	,	,	PUNCT
ejpam-4283	110	7	{	{	PUNCT
ejpam-4283	110	8	r	r	NOUN
ejpam-4283	110	9	}	}	PUNCT
ejpam-4283	110	10	,	,	PUNCT
ejpam-4283	110	11	{	{	PUNCT
ejpam-4283	110	12	t	t	NOUN
ejpam-4283	110	13	}	}	PUNCT
ejpam-4283	110	14	,	,	PUNCT
ejpam-4283	110	15	{	{	PUNCT
ejpam-4283	110	16	r	r	NOUN
ejpam-4283	110	17	,	,	PUNCT
ejpam-4283	110	18	t	t	PROPN
ejpam-4283	110	19	}	}	PUNCT
ejpam-4283	110	20	,	,	PUNCT
ejpam-4283	110	21	{	{	PUNCT
ejpam-4283	110	22	p	p	X
ejpam-4283	110	23	,	,	PUNCT
ejpam-4283	110	24	q	q	NOUN
ejpam-4283	110	25	}	}	PUNCT
ejpam-4283	110	26	,	,	PUNCT
ejpam-4283	110	27	{	{	PUNCT
ejpam-4283	110	28	p	p	X
ejpam-4283	110	29	,	,	PUNCT
ejpam-4283	110	30	s	s	PART
ejpam-4283	110	31	}	}	PUNCT
ejpam-4283	110	32	,	,	PUNCT
ejpam-4283	110	33	{	{	PUNCT
ejpam-4283	110	34	p	p	X
ejpam-4283	110	35	,	,	PUNCT
ejpam-4283	110	36	q	q	ADJ
ejpam-4283	110	37	,	,	PUNCT
ejpam-4283	110	38	r	r	NOUN
ejpam-4283	110	39	}	}	PUNCT
ejpam-4283	110	40	,	,	PUNCT
ejpam-4283	110	41	{	{	PUNCT
ejpam-4283	110	42	p	p	X
ejpam-4283	110	43	,	,	PUNCT
ejpam-4283	110	44	q	q	X
ejpam-4283	110	45	,	,	PUNCT
ejpam-4283	110	46	s	s	PART
ejpam-4283	110	47	}	}	PUNCT
ejpam-4283	110	48	,	,	PUNCT
ejpam-4283	110	49	{	{	PUNCT
ejpam-4283	110	50	p	p	X
ejpam-4283	110	51	,	,	PUNCT
ejpam-4283	110	52	q	q	X
ejpam-4283	110	53	,	,	PUNCT
ejpam-4283	110	54	t	t	PROPN
ejpam-4283	110	55	}	}	PUNCT
ejpam-4283	110	56	,	,	PUNCT
ejpam-4283	110	57	{	{	PUNCT
ejpam-4283	110	58	p	p	X
ejpam-4283	110	59	,	,	PUNCT
ejpam-4283	110	60	r	r	NOUN
ejpam-4283	110	61	,	,	PUNCT
ejpam-4283	110	62	s	s	PART
ejpam-4283	110	63	}	}	PUNCT
ejpam-4283	110	64	,	,	PUNCT
ejpam-4283	110	65	{	{	PUNCT
ejpam-4283	110	66	p	p	X
ejpam-4283	110	67	,	,	PUNCT
ejpam-4283	110	68	s	s	PROPN
ejpam-4283	110	69	,	,	PUNCT
ejpam-4283	110	70	t	t	PROPN
ejpam-4283	110	71	}	}	PUNCT
ejpam-4283	110	72	,	,	PUNCT
ejpam-4283	110	73	{	{	PUNCT
ejpam-4283	110	74	p	p	X
ejpam-4283	110	75	,	,	PUNCT
ejpam-4283	110	76	q	q	ADJ
ejpam-4283	110	77	,	,	PUNCT
ejpam-4283	110	78	r	r	NOUN
ejpam-4283	110	79	,	,	PUNCT
ejpam-4283	110	80	s	s	PART
ejpam-4283	110	81	}	}	PUNCT
ejpam-4283	110	82	,	,	PUNCT
ejpam-4283	110	83	{	{	PUNCT
ejpam-4283	110	84	p	p	X
ejpam-4283	110	85	,	,	PUNCT
ejpam-4283	110	86	q	q	ADJ
ejpam-4283	110	87	,	,	PUNCT
ejpam-4283	110	88	r	r	NOUN
ejpam-4283	110	89	,	,	PUNCT
ejpam-4283	110	90	t	t	PROPN
ejpam-4283	110	91	}	}	PUNCT
ejpam-4283	110	92	,	,	PUNCT
ejpam-4283	110	93	{	{	PUNCT
ejpam-4283	110	94	p	p	X
ejpam-4283	110	95	,	,	PUNCT
ejpam-4283	110	96	q	q	ADJ
ejpam-4283	110	97	,	,	PUNCT
ejpam-4283	110	98	s	s	PROPN
ejpam-4283	110	99	,	,	PUNCT
ejpam-4283	110	100	t	t	PROPN
ejpam-4283	110	101	}	}	PUNCT
ejpam-4283	110	102	,	,	PUNCT
ejpam-4283	110	103	{	{	PUNCT
ejpam-4283	110	104	p	p	X
ejpam-4283	110	105	,	,	PUNCT
ejpam-4283	110	106	r	r	NOUN
ejpam-4283	110	107	,	,	PUNCT
ejpam-4283	110	108	s	s	PROPN
ejpam-4283	110	109	,	,	PUNCT
ejpam-4283	110	110	t	t	PROPN
ejpam-4283	110	111	}	}	PUNCT
ejpam-4283	110	112	,	,	PUNCT
ejpam-4283	110	113	x	x	NOUN
ejpam-4283	110	114	}	}	PUNCT
ejpam-4283	110	115	.	.	PUNCT
ejpam-4283	111	1	take	take	VERB
ejpam-4283	111	2	d	d	NOUN
ejpam-4283	111	3	=	=	PUNCT
ejpam-4283	111	4	{	{	PUNCT
ejpam-4283	111	5	r	r	NOUN
ejpam-4283	111	6	}	}	PUNCT
ejpam-4283	111	7	.	.	PUNCT
ejpam-4283	112	1	then	then	ADV
ejpam-4283	112	2	i1(c2(d	i1(c2(d	VERB
ejpam-4283	112	3	)	)	PUNCT
ejpam-4283	112	4	)	)	PUNCT
ejpam-4283	113	1	=	=	SYM
ejpam-4283	113	2	i1({r	i1({r	NOUN
ejpam-4283	113	3	,	,	PUNCT
ejpam-4283	113	4	s	s	PROPN
ejpam-4283	113	5	,	,	PUNCT
ejpam-4283	113	6	t	t	NOUN
ejpam-4283	113	7	}	}	PUNCT
ejpam-4283	113	8	)	)	PUNCT
ejpam-4283	113	9	=	=	PUNCT
ejpam-4283	113	10	∅.	∅.	ADP
ejpam-4283	113	11	thus	thus	ADV
ejpam-4283	113	12	,	,	PUNCT
ejpam-4283	113	13	d	d	PRON
ejpam-4283	113	14	is	be	AUX
ejpam-4283	113	15	a	a	DET
ejpam-4283	113	16	(	(	PUNCT
ejpam-4283	113	17	1	1	NUM
ejpam-4283	113	18	,	,	PUNCT
ejpam-4283	113	19	2)-nowhere	2)-nowhere	NUM
ejpam-4283	113	20	dense	dense	ADJ
ejpam-4283	113	21	set	set	NOUN
ejpam-4283	113	22	in	in	ADP
ejpam-4283	113	23	x.	x.	NOUN
ejpam-4283	113	24	but	but	CCONJ
ejpam-4283	113	25	iσ1(c2(d	iσ1(c2(d	PROPN
ejpam-4283	113	26	)	)	PUNCT
ejpam-4283	113	27	)	)	PUNCT
ejpam-4283	114	1	=	=	SYM
ejpam-4283	114	2	iσ1({r	iσ1({r	NOUN
ejpam-4283	114	3	,	,	PUNCT
ejpam-4283	114	4	s	s	PROPN
ejpam-4283	114	5	,	,	PUNCT
ejpam-4283	114	6	t	t	NOUN
ejpam-4283	114	7	}	}	PUNCT
ejpam-4283	114	8	)	)	PUNCT
ejpam-4283	114	9	=	=	PRON
ejpam-4283	114	10	{	{	PUNCT
ejpam-4283	114	11	r	r	NOUN
ejpam-4283	114	12	,	,	PUNCT
ejpam-4283	114	13	t	t	PROPN
ejpam-4283	114	14	}	}	PUNCT
ejpam-4283	114	15	6=	6=	ADP
ejpam-4283	114	16	∅.	∅.	ADP
ejpam-4283	114	17	thus	thus	ADV
ejpam-4283	114	18	,	,	PUNCT
ejpam-4283	114	19	d	d	X
ejpam-4283	114	20	/∈	/∈	PUNCT
ejpam-4283	114	21	(	(	PUNCT
ejpam-4283	114	22	2	2	NUM
ejpam-4283	114	23	,	,	PUNCT
ejpam-4283	114	24	1	1	NUM
ejpam-4283	114	25	)	)	PUNCT
ejpam-4283	114	26	?	?	PUNCT
ejpam-4283	115	1	−n	−n	INTJ
ejpam-4283	115	2	(	(	PUNCT
ejpam-4283	115	3	x	x	NOUN
ejpam-4283	115	4	)	)	PUNCT
ejpam-4283	115	5	.	.	PUNCT
ejpam-4283	116	1	example	example	NOUN
ejpam-4283	117	1	6	6	NUM
ejpam-4283	117	2	.	.	PUNCT
ejpam-4283	117	3	consider	consider	VERB
ejpam-4283	117	4	the	the	DET
ejpam-4283	117	5	bigeneralized	bigeneralized	ADJ
ejpam-4283	117	6	topological	topological	ADJ
ejpam-4283	117	7	space	space	NOUN
ejpam-4283	117	8	(	(	PUNCT
ejpam-4283	117	9	x,µ1	x,µ1	PROPN
ejpam-4283	117	10	,	,	PUNCT
ejpam-4283	117	11	µ2	µ2	PROPN
ejpam-4283	117	12	)	)	PUNCT
ejpam-4283	118	1	where	where	SCONJ
ejpam-4283	118	2	x	x	X
ejpam-4283	118	3	=	=	PRON
ejpam-4283	118	4	{	{	PUNCT
ejpam-4283	118	5	p	p	X
ejpam-4283	118	6	,	,	PUNCT
ejpam-4283	118	7	q	q	ADJ
ejpam-4283	118	8	,	,	PUNCT
ejpam-4283	118	9	r	r	NOUN
ejpam-4283	118	10	,	,	PUNCT
ejpam-4283	118	11	s	s	NOUN
ejpam-4283	118	12	,	,	PUNCT
ejpam-4283	118	13	t};µ1	t};µ1	PROPN
ejpam-4283	118	14	=	=	SYM
ejpam-4283	118	15	{	{	PUNCT
ejpam-4283	118	16	∅	∅	NOUN
ejpam-4283	118	17	,	,	PUNCT
ejpam-4283	118	18	{	{	PUNCT
ejpam-4283	118	19	p	p	X
ejpam-4283	118	20	,	,	PUNCT
ejpam-4283	118	21	q	q	ADJ
ejpam-4283	118	22	,	,	PUNCT
ejpam-4283	118	23	r	r	NOUN
ejpam-4283	118	24	}	}	PUNCT
ejpam-4283	118	25	,	,	PUNCT
ejpam-4283	118	26	{	{	PUNCT
ejpam-4283	118	27	p	p	X
ejpam-4283	118	28	,	,	PUNCT
ejpam-4283	118	29	q	q	X
ejpam-4283	118	30	,	,	PUNCT
ejpam-4283	118	31	s	s	PART
ejpam-4283	118	32	}	}	PUNCT
ejpam-4283	118	33	,	,	PUNCT
ejpam-4283	118	34	{	{	PUNCT
ejpam-4283	118	35	q	q	X
ejpam-4283	118	36	,	,	PUNCT
ejpam-4283	118	37	r	r	NOUN
ejpam-4283	118	38	,	,	PUNCT
ejpam-4283	118	39	s	s	PART
ejpam-4283	118	40	}	}	PUNCT
ejpam-4283	118	41	,	,	PUNCT
ejpam-4283	118	42	{	{	PUNCT
ejpam-4283	118	43	p	p	X
ejpam-4283	118	44	,	,	PUNCT
ejpam-4283	118	45	q	q	ADJ
ejpam-4283	118	46	,	,	PUNCT
ejpam-4283	118	47	r	r	NOUN
ejpam-4283	118	48	,	,	PUNCT
ejpam-4283	118	49	s	s	PART
ejpam-4283	118	50	}	}	PUNCT
ejpam-4283	118	51	}	}	PUNCT
ejpam-4283	118	52	and	and	CCONJ
ejpam-4283	118	53	µ2	µ2	PROPN
ejpam-4283	118	54	=	=	PUNCT
ejpam-4283	118	55	{	{	PUNCT
ejpam-4283	118	56	∅	∅	NOUN
ejpam-4283	118	57	,	,	PUNCT
ejpam-4283	118	58	{	{	PUNCT
ejpam-4283	118	59	p	p	X
ejpam-4283	118	60	,	,	PUNCT
ejpam-4283	118	61	q	q	NOUN
ejpam-4283	118	62	}	}	PUNCT
ejpam-4283	118	63	,	,	PUNCT
ejpam-4283	118	64	{	{	PUNCT
ejpam-4283	118	65	q	q	X
ejpam-4283	118	66	,	,	PUNCT
ejpam-4283	118	67	r	r	NOUN
ejpam-4283	118	68	}	}	PUNCT
ejpam-4283	118	69	,	,	PUNCT
ejpam-4283	118	70	{	{	PUNCT
ejpam-4283	118	71	p	p	X
ejpam-4283	118	72	,	,	PUNCT
ejpam-4283	118	73	q	q	ADJ
ejpam-4283	118	74	,	,	PUNCT
ejpam-4283	118	75	r	r	NOUN
ejpam-4283	118	76	}	}	PUNCT
ejpam-4283	118	77	}	}	PUNCT
ejpam-4283	118	78	.	.	PUNCT
ejpam-4283	119	1	here	here	ADV
ejpam-4283	119	2	µ2	µ2	PROPN
ejpam-4283	119	3	is	be	AUX
ejpam-4283	119	4	not	not	PART
ejpam-4283	119	5	a	a	DET
ejpam-4283	119	6	sgt	sgt	PROPN
ejpam-4283	119	7	.	.	PUNCT
ejpam-4283	120	1	then	then	ADV
ejpam-4283	120	2	σ2	σ2	PROPN
ejpam-4283	120	3	=	=	SYM
ejpam-4283	120	4	{	{	PUNCT
ejpam-4283	120	5	∅	∅	NOUN
ejpam-4283	120	6	,	,	PUNCT
ejpam-4283	120	7	{	{	PUNCT
ejpam-4283	120	8	s	s	X
ejpam-4283	120	9	}	}	PUNCT
ejpam-4283	120	10	,	,	PUNCT
ejpam-4283	120	11	{	{	PUNCT
ejpam-4283	120	12	t	t	NOUN
ejpam-4283	120	13	}	}	PUNCT
ejpam-4283	120	14	,	,	PUNCT
ejpam-4283	120	15	{	{	PUNCT
ejpam-4283	120	16	s	s	X
ejpam-4283	120	17	,	,	PUNCT
ejpam-4283	120	18	t	t	PROPN
ejpam-4283	120	19	}	}	PUNCT
ejpam-4283	120	20	,	,	PUNCT
ejpam-4283	120	21	{	{	PUNCT
ejpam-4283	120	22	p	p	X
ejpam-4283	120	23	,	,	PUNCT
ejpam-4283	120	24	q	q	NOUN
ejpam-4283	120	25	}	}	PUNCT
ejpam-4283	120	26	,	,	PUNCT
ejpam-4283	120	27	{	{	PUNCT
ejpam-4283	120	28	q	q	X
ejpam-4283	120	29	,	,	PUNCT
ejpam-4283	120	30	r	r	NOUN
ejpam-4283	120	31	}	}	PUNCT
ejpam-4283	120	32	,	,	PUNCT
ejpam-4283	120	33	{	{	PUNCT
ejpam-4283	120	34	p	p	X
ejpam-4283	120	35	,	,	PUNCT
ejpam-4283	120	36	q	q	ADJ
ejpam-4283	120	37	,	,	PUNCT
ejpam-4283	120	38	r	r	NOUN
ejpam-4283	120	39	}	}	PUNCT
ejpam-4283	120	40	,	,	PUNCT
ejpam-4283	120	41	{	{	PUNCT
ejpam-4283	120	42	p	p	X
ejpam-4283	120	43	,	,	PUNCT
ejpam-4283	120	44	q	q	X
ejpam-4283	120	45	,	,	PUNCT
ejpam-4283	120	46	s	s	PART
ejpam-4283	120	47	}	}	PUNCT
ejpam-4283	120	48	,	,	PUNCT
ejpam-4283	120	49	{	{	PUNCT
ejpam-4283	120	50	p	p	X
ejpam-4283	120	51	,	,	PUNCT
ejpam-4283	120	52	q	q	X
ejpam-4283	120	53	,	,	PUNCT
ejpam-4283	120	54	t	t	PROPN
ejpam-4283	120	55	}	}	PUNCT
ejpam-4283	120	56	,	,	PUNCT
ejpam-4283	120	57	{	{	PUNCT
ejpam-4283	120	58	q	q	X
ejpam-4283	120	59	,	,	PUNCT
ejpam-4283	120	60	r	r	NOUN
ejpam-4283	120	61	,	,	PUNCT
ejpam-4283	120	62	s	s	PART
ejpam-4283	120	63	}	}	PUNCT
ejpam-4283	120	64	,	,	PUNCT
ejpam-4283	120	65	{	{	PUNCT
ejpam-4283	120	66	q	q	X
ejpam-4283	120	67	,	,	PUNCT
ejpam-4283	120	68	r	r	NOUN
ejpam-4283	120	69	,	,	PUNCT
ejpam-4283	120	70	t	t	PROPN
ejpam-4283	120	71	}	}	PUNCT
ejpam-4283	120	72	,	,	PUNCT
ejpam-4283	120	73	{	{	PUNCT
ejpam-4283	120	74	p	p	X
ejpam-4283	120	75	,	,	PUNCT
ejpam-4283	120	76	q	q	ADJ
ejpam-4283	120	77	,	,	PUNCT
ejpam-4283	120	78	r	r	NOUN
ejpam-4283	120	79	,	,	PUNCT
ejpam-4283	120	80	s	s	PART
ejpam-4283	120	81	}	}	PUNCT
ejpam-4283	120	82	,	,	PUNCT
ejpam-4283	120	83	{	{	PUNCT
ejpam-4283	120	84	p	p	X
ejpam-4283	120	85	,	,	PUNCT
ejpam-4283	120	86	q	q	ADJ
ejpam-4283	120	87	,	,	PUNCT
ejpam-4283	120	88	r	r	NOUN
ejpam-4283	120	89	,	,	PUNCT
ejpam-4283	120	90	t	t	PROPN
ejpam-4283	120	91	}	}	PUNCT
ejpam-4283	120	92	,	,	PUNCT
ejpam-4283	120	93	{	{	PUNCT
ejpam-4283	120	94	p	p	X
ejpam-4283	120	95	,	,	PUNCT
ejpam-4283	120	96	q	q	ADJ
ejpam-4283	120	97	,	,	PUNCT
ejpam-4283	120	98	s	s	PROPN
ejpam-4283	120	99	,	,	PUNCT
ejpam-4283	120	100	t	t	PROPN
ejpam-4283	120	101	}	}	PUNCT
ejpam-4283	120	102	,	,	PUNCT
ejpam-4283	120	103	{	{	PUNCT
ejpam-4283	120	104	q	q	X
ejpam-4283	120	105	,	,	PUNCT
ejpam-4283	120	106	r	r	NOUN
ejpam-4283	120	107	,	,	PUNCT
ejpam-4283	120	108	s	s	PROPN
ejpam-4283	120	109	,	,	PUNCT
ejpam-4283	120	110	t	t	PROPN
ejpam-4283	120	111	}	}	PUNCT
ejpam-4283	120	112	,	,	PUNCT
ejpam-4283	120	113	x	x	NOUN
ejpam-4283	120	114	}	}	PUNCT
ejpam-4283	120	115	.	.	PUNCT
ejpam-4283	121	1	choose	choose	VERB
ejpam-4283	121	2	d	d	NOUN
ejpam-4283	121	3	=	=	PUNCT
ejpam-4283	121	4	{	{	PUNCT
ejpam-4283	121	5	s	s	NOUN
ejpam-4283	121	6	}	}	PUNCT
ejpam-4283	121	7	.	.	PUNCT
ejpam-4283	122	1	then	then	ADV
ejpam-4283	122	2	i2(c1(d	i2(c1(d	NUM
ejpam-4283	122	3	)	)	PUNCT
ejpam-4283	122	4	)	)	PUNCT
ejpam-4283	123	1	=	=	SYM
ejpam-4283	123	2	i2({s	i2({s	PROPN
ejpam-4283	123	3	,	,	PUNCT
ejpam-4283	123	4	t	t	PROPN
ejpam-4283	123	5	}	}	PUNCT
ejpam-4283	123	6	)	)	PUNCT
ejpam-4283	124	1	=	=	PUNCT
ejpam-4283	124	2	∅.	∅.	ADP
ejpam-4283	124	3	thus	thus	ADV
ejpam-4283	124	4	,	,	PUNCT
ejpam-4283	124	5	d	d	PRON
ejpam-4283	124	6	is	be	AUX
ejpam-4283	124	7	a	a	DET
ejpam-4283	124	8	(	(	PUNCT
ejpam-4283	124	9	2	2	NUM
ejpam-4283	124	10	,	,	PUNCT
ejpam-4283	124	11	1)-nowhere	1)-nowhere	NUM
ejpam-4283	124	12	dense	dense	ADJ
ejpam-4283	124	13	set	set	NOUN
ejpam-4283	124	14	in	in	ADP
ejpam-4283	124	15	x.	x.	NOUN
ejpam-4283	124	16	but	but	CCONJ
ejpam-4283	124	17	iσ2(c1(d	iσ2(c1(d	NOUN
ejpam-4283	124	18	)	)	PUNCT
ejpam-4283	124	19	)	)	PUNCT
ejpam-4283	125	1	=	=	SYM
ejpam-4283	125	2	iσ2({s	iσ2({s	PROPN
ejpam-4283	125	3	,	,	PUNCT
ejpam-4283	125	4	t	t	NOUN
ejpam-4283	125	5	}	}	PUNCT
ejpam-4283	125	6	)	)	PUNCT
ejpam-4283	125	7	=	=	PRON
ejpam-4283	125	8	{	{	PUNCT
ejpam-4283	125	9	s	s	NOUN
ejpam-4283	125	10	}	}	PUNCT
ejpam-4283	125	11	6=	6=	X
ejpam-4283	125	12	∅.	∅.	ADP
ejpam-4283	125	13	thus	thus	ADV
ejpam-4283	125	14	,	,	PUNCT
ejpam-4283	125	15	d	d	X
ejpam-4283	125	16	/∈	/∈	PUNCT
ejpam-4283	125	17	(	(	PUNCT
ejpam-4283	125	18	1	1	NUM
ejpam-4283	125	19	,	,	PUNCT
ejpam-4283	125	20	2	2	NUM
ejpam-4283	125	21	)	)	PUNCT
ejpam-4283	125	22	?	?	PUNCT
ejpam-4283	126	1	−n	−n	INTJ
ejpam-4283	126	2	(	(	PUNCT
ejpam-4283	126	3	x	x	NOUN
ejpam-4283	126	4	)	)	PUNCT
ejpam-4283	126	5	.	.	PUNCT
ejpam-4283	127	1	theorem	theorem	ADJ
ejpam-4283	127	2	7	7	NUM
ejpam-4283	127	3	.	.	PUNCT
ejpam-4283	128	1	let	let	AUX
ejpam-4283	128	2	(	(	PUNCT
ejpam-4283	128	3	x,µ1	x,µ1	NOUN
ejpam-4283	128	4	,	,	PUNCT
ejpam-4283	128	5	µ2	µ2	PROPN
ejpam-4283	128	6	)	)	PUNCT
ejpam-4283	128	7	be	be	VERB
ejpam-4283	128	8	a	a	DET
ejpam-4283	128	9	bgts	bgts	NOUN
ejpam-4283	128	10	and	and	CCONJ
ejpam-4283	128	11	e	e	NOUN
ejpam-4283	128	12	⊂	⊂	PROPN
ejpam-4283	128	13	x.	x.	PROPN
ejpam-4283	129	1	then	then	ADV
ejpam-4283	129	2	the	the	DET
ejpam-4283	129	3	followings	following	NOUN
ejpam-4283	129	4	are	be	AUX
ejpam-4283	129	5	true	true	ADJ
ejpam-4283	129	6	.	.	PUNCT
ejpam-4283	130	1	(	(	PUNCT
ejpam-4283	130	2	a	a	X
ejpam-4283	130	3	)	)	PUNCT
ejpam-4283	130	4	if	if	SCONJ
ejpam-4283	130	5	(	(	PUNCT
ejpam-4283	130	6	x,µ2	x,µ2	PROPN
ejpam-4283	130	7	)	)	PUNCT
ejpam-4283	130	8	is	be	AUX
ejpam-4283	130	9	a	a	DET
ejpam-4283	130	10	sgts	sgts	NOUN
ejpam-4283	130	11	and	and	CCONJ
ejpam-4283	130	12	if	if	SCONJ
ejpam-4283	130	13	c1(e	c1(e	PROPN
ejpam-4283	130	14	)	)	PUNCT
ejpam-4283	130	15	does	do	AUX
ejpam-4283	130	16	not	not	PART
ejpam-4283	130	17	contain	contain	VERB
ejpam-4283	130	18	a	a	DET
ejpam-4283	130	19	non	non	ADJ
ejpam-4283	130	20	-	-	ADJ
ejpam-4283	130	21	null	null	ADJ
ejpam-4283	130	22	µ2	µ2	ADJ
ejpam-4283	130	23	-	-	PUNCT
ejpam-4283	130	24	open	open	NOUN
ejpam-4283	130	25	set	set	NOUN
ejpam-4283	130	26	,	,	PUNCT
ejpam-4283	130	27	then	then	ADV
ejpam-4283	130	28	e	e	PROPN
ejpam-4283	130	29	∈	∈	PROPN
ejpam-4283	130	30	p.	p.	NOUN
ejpam-4283	130	31	yupapin	yupapin	NOUN
ejpam-4283	130	32	,	,	PUNCT
ejpam-4283	131	1	v.	v.	CCONJ
ejpam-4283	131	2	subramanian	subramanian	PROPN
ejpam-4283	131	3	,	,	PUNCT
ejpam-4283	131	4	y.	y.	PROPN
ejpam-4283	131	5	farhat	farhat	PROPN
ejpam-4283	131	6	/	/	SYM
ejpam-4283	131	7	eur	eur	PROPN
ejpam-4283	131	8	.	.	PUNCT
ejpam-4283	132	1	j.	j.	PROPN
ejpam-4283	132	2	pure	pure	PROPN
ejpam-4283	132	3	appl	appl	PROPN
ejpam-4283	132	4	.	.	PROPN
ejpam-4283	132	5	math	math	PROPN
ejpam-4283	132	6	,	,	PUNCT
ejpam-4283	132	7	15	15	NUM
ejpam-4283	132	8	(	(	PUNCT
ejpam-4283	132	9	2	2	NUM
ejpam-4283	132	10	)	)	PUNCT
ejpam-4283	132	11	(	(	PUNCT
ejpam-4283	132	12	2022	2022	NUM
ejpam-4283	132	13	)	)	PUNCT
ejpam-4283	132	14	,	,	PUNCT
ejpam-4283	132	15	403	403	NUM
ejpam-4283	132	16	-	-	SYM
ejpam-4283	132	17	414	414	NUM
ejpam-4283	132	18	406	406	NUM
ejpam-4283	132	19	(	(	PUNCT
ejpam-4283	132	20	1	1	NUM
ejpam-4283	132	21	,	,	PUNCT
ejpam-4283	132	22	2	2	NUM
ejpam-4283	132	23	)	)	PUNCT
ejpam-4283	132	24	?	?	PUNCT
ejpam-4283	133	1	−n	−n	INTJ
ejpam-4283	133	2	(	(	PUNCT
ejpam-4283	133	3	x	x	NOUN
ejpam-4283	133	4	)	)	PUNCT
ejpam-4283	133	5	.	.	PUNCT
ejpam-4283	134	1	(	(	PUNCT
ejpam-4283	134	2	b	b	X
ejpam-4283	134	3	)	)	PUNCT
ejpam-4283	134	4	if	if	SCONJ
ejpam-4283	134	5	(	(	PUNCT
ejpam-4283	134	6	x,µ1	x,µ1	NOUN
ejpam-4283	134	7	)	)	PUNCT
ejpam-4283	134	8	is	be	AUX
ejpam-4283	134	9	a	a	DET
ejpam-4283	134	10	sgts	sgts	NOUN
ejpam-4283	134	11	and	and	CCONJ
ejpam-4283	134	12	if	if	SCONJ
ejpam-4283	134	13	c2(e	c2(e	NOUN
ejpam-4283	134	14	)	)	PUNCT
ejpam-4283	134	15	does	do	AUX
ejpam-4283	134	16	not	not	PART
ejpam-4283	134	17	contain	contain	VERB
ejpam-4283	134	18	a	a	DET
ejpam-4283	134	19	non	non	ADJ
ejpam-4283	134	20	-	-	ADJ
ejpam-4283	134	21	null	null	ADJ
ejpam-4283	134	22	µ1	µ1	NOUN
ejpam-4283	134	23	-	-	PUNCT
ejpam-4283	134	24	open	open	NOUN
ejpam-4283	134	25	set	set	NOUN
ejpam-4283	134	26	,	,	PUNCT
ejpam-4283	134	27	then	then	ADV
ejpam-4283	134	28	e	e	PROPN
ejpam-4283	134	29	∈	∈	PROPN
ejpam-4283	134	30	(	(	PUNCT
ejpam-4283	134	31	2	2	NUM
ejpam-4283	134	32	,	,	PUNCT
ejpam-4283	134	33	1	1	NUM
ejpam-4283	134	34	)	)	PUNCT
ejpam-4283	134	35	?	?	PUNCT
ejpam-4283	135	1	−n	−n	INTJ
ejpam-4283	135	2	(	(	PUNCT
ejpam-4283	135	3	x	x	NOUN
ejpam-4283	135	4	)	)	PUNCT
ejpam-4283	135	5	.	.	PUNCT
ejpam-4283	136	1	proof	proof	NOUN
ejpam-4283	136	2	.	.	PUNCT
ejpam-4283	137	1	(	(	PUNCT
ejpam-4283	137	2	a	a	X
ejpam-4283	137	3	)	)	PUNCT
ejpam-4283	137	4	.	.	PUNCT
ejpam-4283	138	1	assume	assume	VERB
ejpam-4283	138	2	that	that	SCONJ
ejpam-4283	138	3	,	,	PUNCT
ejpam-4283	138	4	(	(	PUNCT
ejpam-4283	138	5	x,µ2	x,µ2	PROPN
ejpam-4283	138	6	)	)	PUNCT
ejpam-4283	138	7	is	be	AUX
ejpam-4283	138	8	a	a	DET
ejpam-4283	138	9	sgts	sgts	NOUN
ejpam-4283	138	10	.	.	PUNCT
ejpam-4283	139	1	suppose	suppose	VERB
ejpam-4283	139	2	iσ2(c1(e	iσ2(c1(e	NOUN
ejpam-4283	139	3	)	)	PUNCT
ejpam-4283	139	4	)	)	PUNCT
ejpam-4283	140	1	6=	6=	ADP
ejpam-4283	140	2	∅.	∅.	VERB
ejpam-4283	140	3	then	then	ADV
ejpam-4283	140	4	there	there	PRON
ejpam-4283	140	5	is	be	VERB
ejpam-4283	140	6	a	a	DET
ejpam-4283	140	7	non	non	ADJ
ejpam-4283	140	8	-	-	ADJ
ejpam-4283	140	9	null	null	ADJ
ejpam-4283	140	10	σ2	σ2	NOUN
ejpam-4283	140	11	-	-	PUNCT
ejpam-4283	140	12	open	open	NOUN
ejpam-4283	140	13	set	set	NOUN
ejpam-4283	140	14	m	m	VERB
ejpam-4283	140	15	such	such	ADJ
ejpam-4283	140	16	that	that	SCONJ
ejpam-4283	140	17	m	m	VERB
ejpam-4283	140	18	⊂	⊂	X
ejpam-4283	140	19	c1(e	c1(e	PROPN
ejpam-4283	140	20	)	)	PUNCT
ejpam-4283	140	21	.	.	PUNCT
ejpam-4283	141	1	since	since	SCONJ
ejpam-4283	141	2	m	m	PROPN
ejpam-4283	141	3	is	be	AUX
ejpam-4283	141	4	a	a	DET
ejpam-4283	141	5	non	non	ADJ
ejpam-4283	141	6	-	-	ADJ
ejpam-4283	141	7	null	null	ADJ
ejpam-4283	141	8	σ2	σ2	NOUN
ejpam-4283	141	9	-	-	PUNCT
ejpam-4283	141	10	open	open	NOUN
ejpam-4283	141	11	set	set	NOUN
ejpam-4283	141	12	we	we	PRON
ejpam-4283	141	13	have	have	VERB
ejpam-4283	141	14	m	m	PROPN
ejpam-4283	141	15	⊂	⊂	NOUN
ejpam-4283	141	16	c2(i2(m	c2(i2(m	NOUN
ejpam-4283	141	17	)	)	PUNCT
ejpam-4283	141	18	)	)	PUNCT
ejpam-4283	141	19	.	.	PUNCT
ejpam-4283	142	1	this	this	PRON
ejpam-4283	142	2	implies	imply	VERB
ejpam-4283	142	3	that	that	PRON
ejpam-4283	142	4	c2(i2(m	c2(i2(m	NOUN
ejpam-4283	142	5	)	)	PUNCT
ejpam-4283	142	6	)	)	PUNCT
ejpam-4283	143	1	6=	6=	ADP
ejpam-4283	143	2	∅	∅	NOUN
ejpam-4283	143	3	which	which	PRON
ejpam-4283	143	4	implies	imply	VERB
ejpam-4283	143	5	i2(m	i2(m	PRON
ejpam-4283	143	6	)	)	PUNCT
ejpam-4283	143	7	6=	6=	ADP
ejpam-4283	143	8	∅	∅	NOUN
ejpam-4283	143	9	,	,	PUNCT
ejpam-4283	143	10	by	by	ADP
ejpam-4283	143	11	assumption	assumption	NOUN
ejpam-4283	143	12	.	.	PUNCT
ejpam-4283	144	1	thus	thus	ADV
ejpam-4283	144	2	,	,	PUNCT
ejpam-4283	144	3	c1(e	c1(e	ADJ
ejpam-4283	144	4	)	)	PUNCT
ejpam-4283	144	5	contain	contain	VERB
ejpam-4283	144	6	a	a	DET
ejpam-4283	144	7	non	non	ADJ
ejpam-4283	144	8	-	-	ADJ
ejpam-4283	144	9	null	null	ADJ
ejpam-4283	144	10	µ2	µ2	ADJ
ejpam-4283	144	11	-	-	PUNCT
ejpam-4283	144	12	open	open	NOUN
ejpam-4283	144	13	set	set	NOUN
ejpam-4283	144	14	which	which	PRON
ejpam-4283	144	15	is	be	AUX
ejpam-4283	144	16	not	not	PART
ejpam-4283	144	17	possible	possible	ADJ
ejpam-4283	144	18	.	.	PUNCT
ejpam-4283	145	1	therefore	therefore	ADV
ejpam-4283	145	2	,	,	PUNCT
ejpam-4283	145	3	e	e	PROPN
ejpam-4283	145	4	∈	∈	PROPN
ejpam-4283	145	5	(	(	PUNCT
ejpam-4283	145	6	1	1	NUM
ejpam-4283	145	7	,	,	PUNCT
ejpam-4283	145	8	2	2	NUM
ejpam-4283	145	9	)	)	PUNCT
ejpam-4283	145	10	?	?	PUNCT
ejpam-4283	146	1	−n	−n	INTJ
ejpam-4283	146	2	(	(	PUNCT
ejpam-4283	146	3	x	x	NOUN
ejpam-4283	146	4	)	)	PUNCT
ejpam-4283	146	5	.	.	PUNCT
ejpam-4283	147	1	(	(	PUNCT
ejpam-4283	147	2	b	b	NOUN
ejpam-4283	147	3	)	)	PUNCT
ejpam-4283	147	4	.	.	PUNCT
ejpam-4283	148	1	by	by	ADP
ejpam-4283	148	2	similar	similar	ADJ
ejpam-4283	148	3	arguments	argument	NOUN
ejpam-4283	148	4	in	in	ADP
ejpam-4283	148	5	(	(	PUNCT
ejpam-4283	148	6	a	a	X
ejpam-4283	148	7	)	)	PUNCT
ejpam-4283	148	8	,	,	PUNCT
ejpam-4283	148	9	we	we	PRON
ejpam-4283	148	10	get	get	VERB
ejpam-4283	148	11	the	the	DET
ejpam-4283	148	12	proof	proof	NOUN
ejpam-4283	148	13	.	.	PUNCT
ejpam-4283	149	1	theorem	theorem	ADJ
ejpam-4283	149	2	8	8	NUM
ejpam-4283	149	3	.	.	PUNCT
ejpam-4283	150	1	let	let	AUX
ejpam-4283	150	2	(	(	PUNCT
ejpam-4283	150	3	x,µ1	x,µ1	NOUN
ejpam-4283	150	4	,	,	PUNCT
ejpam-4283	150	5	µ2	µ2	PROPN
ejpam-4283	150	6	)	)	PUNCT
ejpam-4283	150	7	be	be	VERB
ejpam-4283	150	8	a	a	DET
ejpam-4283	150	9	bigeneralized	bigeneralized	ADJ
ejpam-4283	150	10	topological	topological	ADJ
ejpam-4283	150	11	space	space	NOUN
ejpam-4283	150	12	.	.	PUNCT
ejpam-4283	151	1	if	if	SCONJ
ejpam-4283	151	2	µs	µs	X
ejpam-4283	151	3	⊂	⊂	PROPN
ejpam-4283	151	4	µv	µv	PROPN
ejpam-4283	151	5	and	and	CCONJ
ejpam-4283	151	6	q	q	ADJ
ejpam-4283	151	7	∈	∈	PROPN
ejpam-4283	151	8	(	(	PUNCT
ejpam-4283	151	9	s	s	PROPN
ejpam-4283	151	10	,	,	PUNCT
ejpam-4283	151	11	v	v	NOUN
ejpam-4283	151	12	)	)	PUNCT
ejpam-4283	151	13	?	?	PUNCT
ejpam-4283	152	1	−n	−n	INTJ
ejpam-4283	152	2	(	(	PUNCT
ejpam-4283	152	3	x	x	X
ejpam-4283	152	4	)	)	PUNCT
ejpam-4283	152	5	,	,	PUNCT
ejpam-4283	152	6	then	then	ADV
ejpam-4283	152	7	q	q	X
ejpam-4283	152	8	is	be	AUX
ejpam-4283	152	9	a	a	DET
ejpam-4283	152	10	µv	µv	NOUN
ejpam-4283	152	11	-	-	PUNCT
ejpam-4283	152	12	nowhere	nowhere	ADV
ejpam-4283	152	13	dense	dense	ADJ
ejpam-4283	152	14	set	set	NOUN
ejpam-4283	152	15	in	in	ADP
ejpam-4283	152	16	x	x	PUNCT
ejpam-4283	152	17	where	where	SCONJ
ejpam-4283	152	18	s	s	X
ejpam-4283	152	19	,	,	PUNCT
ejpam-4283	152	20	v	v	NOUN
ejpam-4283	152	21	=	=	SYM
ejpam-4283	152	22	1	1	NUM
ejpam-4283	152	23	,	,	PUNCT
ejpam-4283	152	24	2	2	NUM
ejpam-4283	152	25	;	;	PUNCT
ejpam-4283	152	26	s	s	X
ejpam-4283	152	27	6=	6=	PROPN
ejpam-4283	152	28	v.	v.	ADP
ejpam-4283	152	29	proof	proof	NOUN
ejpam-4283	152	30	.	.	PUNCT
ejpam-4283	153	1	take	take	VERB
ejpam-4283	153	2	s	s	NOUN
ejpam-4283	153	3	=	=	SYM
ejpam-4283	153	4	1	1	NUM
ejpam-4283	153	5	and	and	CCONJ
ejpam-4283	153	6	v	v	NOUN
ejpam-4283	153	7	=	=	SYM
ejpam-4283	153	8	2	2	X
ejpam-4283	153	9	.	.	PUNCT
ejpam-4283	153	10	suppose	suppose	VERB
ejpam-4283	153	11	µ1	µ1	PROPN
ejpam-4283	153	12	⊂	⊂	PROPN
ejpam-4283	153	13	µ2	µ2	PROPN
ejpam-4283	153	14	and	and	CCONJ
ejpam-4283	153	15	q	q	ADJ
ejpam-4283	153	16	∈	∈	PROPN
ejpam-4283	153	17	(	(	PUNCT
ejpam-4283	153	18	1	1	NUM
ejpam-4283	153	19	,	,	PUNCT
ejpam-4283	153	20	2	2	NUM
ejpam-4283	153	21	)	)	PUNCT
ejpam-4283	153	22	?	?	PUNCT
ejpam-4283	154	1	−	−	PROPN
ejpam-4283	155	1	n	n	CCONJ
ejpam-4283	155	2	(	(	PUNCT
ejpam-4283	155	3	x	x	NOUN
ejpam-4283	155	4	)	)	PUNCT
ejpam-4283	155	5	.	.	PUNCT
ejpam-4283	156	1	then	then	ADV
ejpam-4283	156	2	iσ2(c1(q	iσ2(c1(q	NUM
ejpam-4283	156	3	)	)	PUNCT
ejpam-4283	156	4	)	)	PUNCT
ejpam-4283	157	1	=	=	PUNCT
ejpam-4283	157	2	∅.	∅.	PRON
ejpam-4283	157	3	this	this	PRON
ejpam-4283	157	4	implies	imply	VERB
ejpam-4283	157	5	that	that	SCONJ
ejpam-4283	157	6	iµ2(cµ1(q	iµ2(cµ1(q	NOUN
ejpam-4283	157	7	)	)	PUNCT
ejpam-4283	157	8	)	)	PUNCT
ejpam-4283	158	1	=	=	PUNCT
ejpam-4283	158	2	∅	∅	NOUN
ejpam-4283	158	3	which	which	PRON
ejpam-4283	158	4	implies	imply	VERB
ejpam-4283	158	5	iµ2(cµ2(q	iµ2(cµ2(q	NOUN
ejpam-4283	158	6	)	)	PUNCT
ejpam-4283	158	7	)	)	PUNCT
ejpam-4283	159	1	=	=	NOUN
ejpam-4283	159	2	∅	∅	NOUN
ejpam-4283	159	3	,	,	PUNCT
ejpam-4283	159	4	by	by	ADP
ejpam-4283	159	5	hypothesis	hypothesis	NOUN
ejpam-4283	159	6	.	.	PUNCT
ejpam-4283	160	1	hence	hence	ADV
ejpam-4283	160	2	q	q	X
ejpam-4283	160	3	is	be	AUX
ejpam-4283	160	4	a	a	DET
ejpam-4283	160	5	µ2	µ2	PROPN
ejpam-4283	160	6	-	-	PUNCT
ejpam-4283	160	7	nowhere	nowhere	ADV
ejpam-4283	160	8	dense	dense	ADJ
ejpam-4283	160	9	set	set	NOUN
ejpam-4283	160	10	in	in	ADP
ejpam-4283	160	11	x.	x.	NOUN
ejpam-4283	160	12	similarly	similarly	ADV
ejpam-4283	160	13	,	,	PUNCT
ejpam-4283	160	14	we	we	PRON
ejpam-4283	160	15	can	can	AUX
ejpam-4283	160	16	prove	prove	VERB
ejpam-4283	160	17	the	the	DET
ejpam-4283	160	18	result	result	NOUN
ejpam-4283	160	19	for	for	ADP
ejpam-4283	160	20	s	s	NOUN
ejpam-4283	160	21	=	=	SYM
ejpam-4283	160	22	2	2	NUM
ejpam-4283	160	23	and	and	CCONJ
ejpam-4283	160	24	v	v	NOUN
ejpam-4283	160	25	=	=	SYM
ejpam-4283	160	26	1	1	X
ejpam-4283	160	27	.	.	PUNCT
ejpam-4283	160	28	in	in	ADP
ejpam-4283	160	29	theorem	theorem	NOUN
ejpam-4283	160	30	8	8	NUM
ejpam-4283	160	31	,	,	PUNCT
ejpam-4283	160	32	the	the	DET
ejpam-4283	160	33	conditions	condition	NOUN
ejpam-4283	160	34	“	"	PUNCT
ejpam-4283	160	35	µ1	µ1	PROPN
ejpam-4283	160	36	⊂	⊂	PROPN
ejpam-4283	160	37	µ2	µ2	PROPN
ejpam-4283	160	38	”	"	PUNCT
ejpam-4283	160	39	and	and	CCONJ
ejpam-4283	160	40	“	"	PUNCT
ejpam-4283	160	41	µ2	µ2	PROPN
ejpam-4283	160	42	⊂	⊂	PROPN
ejpam-4283	160	43	µ1	µ1	PROPN
ejpam-4283	160	44	”	"	PUNCT
ejpam-4283	160	45	are	be	AUX
ejpam-4283	160	46	can	can	AUX
ejpam-4283	160	47	not	not	PART
ejpam-4283	160	48	be	be	AUX
ejpam-4283	160	49	dropped	drop	VERB
ejpam-4283	160	50	as	as	SCONJ
ejpam-4283	160	51	shown	show	VERB
ejpam-4283	160	52	by	by	ADP
ejpam-4283	160	53	the	the	DET
ejpam-4283	160	54	below	below	ADJ
ejpam-4283	160	55	example	example	NOUN
ejpam-4283	160	56	9	9	NUM
ejpam-4283	160	57	.	.	PUNCT
ejpam-4283	160	58	example	example	NOUN
ejpam-4283	160	59	9	9	NUM
ejpam-4283	160	60	.	.	X
ejpam-4283	160	61	consider	consider	VERB
ejpam-4283	160	62	the	the	DET
ejpam-4283	160	63	bigeneralized	bigeneralized	ADJ
ejpam-4283	160	64	topological	topological	ADJ
ejpam-4283	160	65	space	space	NOUN
ejpam-4283	160	66	(	(	PUNCT
ejpam-4283	160	67	x,µ1	x,µ1	PROPN
ejpam-4283	160	68	,	,	PUNCT
ejpam-4283	160	69	µ2	µ2	PROPN
ejpam-4283	160	70	)	)	PUNCT
ejpam-4283	160	71	where	where	SCONJ
ejpam-4283	160	72	x	x	X
ejpam-4283	160	73	=	=	PRON
ejpam-4283	160	74	{	{	PUNCT
ejpam-4283	160	75	p	p	X
ejpam-4283	160	76	,	,	PUNCT
ejpam-4283	160	77	q	q	ADJ
ejpam-4283	160	78	,	,	PUNCT
ejpam-4283	160	79	r	r	NOUN
ejpam-4283	160	80	,	,	PUNCT
ejpam-4283	160	81	s	s	PART
ejpam-4283	160	82	}	}	PUNCT
ejpam-4283	160	83	;	;	PUNCT
ejpam-4283	160	84	µ1	µ1	PROPN
ejpam-4283	160	85	=	=	SYM
ejpam-4283	160	86	{	{	PUNCT
ejpam-4283	160	87	∅	∅	NOUN
ejpam-4283	160	88	,	,	PUNCT
ejpam-4283	160	89	{	{	PUNCT
ejpam-4283	160	90	p	p	X
ejpam-4283	160	91	,	,	PUNCT
ejpam-4283	160	92	q	q	NOUN
ejpam-4283	160	93	}	}	PUNCT
ejpam-4283	160	94	,	,	PUNCT
ejpam-4283	160	95	{	{	PUNCT
ejpam-4283	160	96	q	q	X
ejpam-4283	160	97	,	,	PUNCT
ejpam-4283	160	98	r	r	NOUN
ejpam-4283	160	99	}	}	PUNCT
ejpam-4283	160	100	,	,	PUNCT
ejpam-4283	160	101	{	{	PUNCT
ejpam-4283	160	102	r	r	NOUN
ejpam-4283	160	103	,	,	PUNCT
ejpam-4283	160	104	s	s	PART
ejpam-4283	160	105	}	}	PUNCT
ejpam-4283	160	106	,	,	PUNCT
ejpam-4283	160	107	{	{	PUNCT
ejpam-4283	160	108	p	p	X
ejpam-4283	160	109	,	,	PUNCT
ejpam-4283	160	110	q	q	ADJ
ejpam-4283	160	111	,	,	PUNCT
ejpam-4283	160	112	r	r	NOUN
ejpam-4283	160	113	}	}	PUNCT
ejpam-4283	160	114	,	,	PUNCT
ejpam-4283	160	115	{	{	PUNCT
ejpam-4283	160	116	p	p	X
ejpam-4283	160	117	,	,	PUNCT
ejpam-4283	160	118	q	q	X
ejpam-4283	160	119	,	,	PUNCT
ejpam-4283	160	120	s	s	PART
ejpam-4283	160	121	}	}	PUNCT
ejpam-4283	160	122	,	,	PUNCT
ejpam-4283	160	123	{	{	PUNCT
ejpam-4283	160	124	q	q	X
ejpam-4283	160	125	,	,	PUNCT
ejpam-4283	160	126	r	r	NOUN
ejpam-4283	160	127	,	,	PUNCT
ejpam-4283	160	128	s	s	PART
ejpam-4283	160	129	}	}	PUNCT
ejpam-4283	160	130	,	,	PUNCT
ejpam-4283	160	131	x	x	NOUN
ejpam-4283	160	132	}	}	PUNCT
ejpam-4283	160	133	and	and	CCONJ
ejpam-4283	160	134	µ2	µ2	PROPN
ejpam-4283	160	135	=	=	PUNCT
ejpam-4283	160	136	{	{	PUNCT
ejpam-4283	160	137	∅	∅	NOUN
ejpam-4283	160	138	,	,	PUNCT
ejpam-4283	160	139	{	{	PUNCT
ejpam-4283	160	140	p	p	X
ejpam-4283	160	141	,	,	PUNCT
ejpam-4283	160	142	s	s	PART
ejpam-4283	160	143	}	}	PUNCT
ejpam-4283	160	144	,	,	PUNCT
ejpam-4283	160	145	{	{	PUNCT
ejpam-4283	160	146	q	q	X
ejpam-4283	160	147	,	,	PUNCT
ejpam-4283	160	148	s	s	PART
ejpam-4283	160	149	}	}	PUNCT
ejpam-4283	160	150	,	,	PUNCT
ejpam-4283	160	151	{	{	PUNCT
ejpam-4283	160	152	p	p	X
ejpam-4283	160	153	,	,	PUNCT
ejpam-4283	160	154	q	q	ADJ
ejpam-4283	160	155	,	,	PUNCT
ejpam-4283	160	156	s	s	PART
ejpam-4283	160	157	}	}	PUNCT
ejpam-4283	160	158	}	}	PUNCT
ejpam-4283	160	159	.	.	PUNCT
ejpam-4283	161	1	here	here	ADV
ejpam-4283	161	2	µ1	µ1	PROPN
ejpam-4283	161	3	*	*	PROPN
ejpam-4283	161	4	µ2	µ2	PROPN
ejpam-4283	161	5	.	.	PUNCT
ejpam-4283	162	1	now	now	ADV
ejpam-4283	162	2	σ2	σ2	PROPN
ejpam-4283	162	3	=	=	SYM
ejpam-4283	162	4	{	{	PUNCT
ejpam-4283	162	5	∅	∅	NOUN
ejpam-4283	162	6	,	,	PUNCT
ejpam-4283	162	7	{	{	PUNCT
ejpam-4283	162	8	r	r	NOUN
ejpam-4283	162	9	}	}	PUNCT
ejpam-4283	162	10	,	,	PUNCT
ejpam-4283	162	11	{	{	PUNCT
ejpam-4283	162	12	p	p	X
ejpam-4283	162	13	,	,	PUNCT
ejpam-4283	162	14	s	s	PART
ejpam-4283	162	15	}	}	PUNCT
ejpam-4283	162	16	,	,	PUNCT
ejpam-4283	162	17	{	{	PUNCT
ejpam-4283	162	18	q	q	X
ejpam-4283	162	19	,	,	PUNCT
ejpam-4283	162	20	s	s	PART
ejpam-4283	162	21	}	}	PUNCT
ejpam-4283	162	22	,	,	PUNCT
ejpam-4283	162	23	{	{	PUNCT
ejpam-4283	162	24	p	p	X
ejpam-4283	162	25	,	,	PUNCT
ejpam-4283	162	26	q	q	X
ejpam-4283	162	27	,	,	PUNCT
ejpam-4283	162	28	s	s	PART
ejpam-4283	162	29	}	}	PUNCT
ejpam-4283	162	30	,	,	PUNCT
ejpam-4283	162	31	{	{	PUNCT
ejpam-4283	162	32	p	p	X
ejpam-4283	162	33	,	,	PUNCT
ejpam-4283	162	34	r	r	NOUN
ejpam-4283	162	35	,	,	PUNCT
ejpam-4283	162	36	s	s	PART
ejpam-4283	162	37	}	}	PUNCT
ejpam-4283	162	38	,	,	PUNCT
ejpam-4283	162	39	{	{	PUNCT
ejpam-4283	162	40	q	q	X
ejpam-4283	162	41	,	,	PUNCT
ejpam-4283	162	42	r	r	NOUN
ejpam-4283	162	43	,	,	PUNCT
ejpam-4283	162	44	s	s	PART
ejpam-4283	162	45	}	}	PUNCT
ejpam-4283	162	46	,	,	PUNCT
ejpam-4283	162	47	x	x	NOUN
ejpam-4283	162	48	}	}	PUNCT
ejpam-4283	162	49	.	.	PUNCT
ejpam-4283	163	1	take	take	VERB
ejpam-4283	163	2	q	q	NOUN
ejpam-4283	163	3	=	=	PUNCT
ejpam-4283	163	4	{	{	PUNCT
ejpam-4283	163	5	p	p	X
ejpam-4283	163	6	,	,	PUNCT
ejpam-4283	163	7	q	q	NOUN
ejpam-4283	163	8	}	}	PUNCT
ejpam-4283	163	9	.	.	PUNCT
ejpam-4283	164	1	then	then	ADV
ejpam-4283	164	2	iσ2(c1(q	iσ2(c1(q	NUM
ejpam-4283	164	3	)	)	PUNCT
ejpam-4283	164	4	)	)	PUNCT
ejpam-4283	165	1	=	=	SYM
ejpam-4283	165	2	iσ2({p	iσ2({p	PROPN
ejpam-4283	165	3	,	,	PUNCT
ejpam-4283	165	4	q	q	NOUN
ejpam-4283	165	5	}	}	PUNCT
ejpam-4283	165	6	)	)	PUNCT
ejpam-4283	165	7	=	=	NOUN
ejpam-4283	165	8	∅.	∅.	ADP
ejpam-4283	165	9	thus	thus	ADV
ejpam-4283	165	10	,	,	PUNCT
ejpam-4283	165	11	q	q	PROPN
ejpam-4283	165	12	is	be	AUX
ejpam-4283	165	13	a	a	DET
ejpam-4283	165	14	(	(	PUNCT
ejpam-4283	165	15	1	1	NUM
ejpam-4283	165	16	,	,	PUNCT
ejpam-4283	165	17	2)?-nowhere	2)?-nowhere	NUM
ejpam-4283	165	18	dense	dense	ADJ
ejpam-4283	165	19	set	set	NOUN
ejpam-4283	165	20	in	in	ADP
ejpam-4283	165	21	x.	x.	NOUN
ejpam-4283	165	22	here	here	ADV
ejpam-4283	165	23	i2(c2(q	i2(c2(q	NUM
ejpam-4283	165	24	)	)	PUNCT
ejpam-4283	165	25	)	)	PUNCT
ejpam-4283	166	1	=	=	PUNCT
ejpam-4283	166	2	i2(x	i2(x	PROPN
ejpam-4283	166	3	)	)	PUNCT
ejpam-4283	166	4	=	=	PRON
ejpam-4283	166	5	{	{	PUNCT
ejpam-4283	166	6	p	p	X
ejpam-4283	166	7	,	,	PUNCT
ejpam-4283	166	8	q	q	ADJ
ejpam-4283	166	9	,	,	PUNCT
ejpam-4283	166	10	s	s	PART
ejpam-4283	166	11	}	}	PUNCT
ejpam-4283	166	12	6=	6=	ADP
ejpam-4283	166	13	∅.	∅.	ADP
ejpam-4283	166	14	thus	thus	ADV
ejpam-4283	166	15	,	,	PUNCT
ejpam-4283	166	16	q	q	X
ejpam-4283	166	17	is	be	AUX
ejpam-4283	166	18	not	not	PART
ejpam-4283	166	19	a	a	DET
ejpam-4283	166	20	µ2	µ2	PROPN
ejpam-4283	166	21	-	-	PUNCT
ejpam-4283	166	22	nowhere	nowhere	ADV
ejpam-4283	166	23	dense	dense	ADJ
ejpam-4283	166	24	set	set	NOUN
ejpam-4283	166	25	in	in	ADP
ejpam-4283	166	26	x.	x.	NOUN
ejpam-4283	166	27	(	(	PUNCT
ejpam-4283	166	28	b	b	X
ejpam-4283	166	29	)	)	PUNCT
ejpam-4283	166	30	consider	consider	VERB
ejpam-4283	166	31	the	the	DET
ejpam-4283	166	32	bigeneralized	bigeneralized	ADJ
ejpam-4283	166	33	topological	topological	ADJ
ejpam-4283	166	34	space	space	NOUN
ejpam-4283	166	35	(	(	PUNCT
ejpam-4283	166	36	x,µ1	x,µ1	PROPN
ejpam-4283	166	37	,	,	PUNCT
ejpam-4283	166	38	µ2	µ2	PROPN
ejpam-4283	166	39	)	)	PUNCT
ejpam-4283	167	1	where	where	SCONJ
ejpam-4283	167	2	x	x	X
ejpam-4283	167	3	=	=	PRON
ejpam-4283	167	4	{	{	PUNCT
ejpam-4283	167	5	p	p	X
ejpam-4283	167	6	,	,	PUNCT
ejpam-4283	167	7	q	q	ADJ
ejpam-4283	167	8	,	,	PUNCT
ejpam-4283	167	9	r	r	NOUN
ejpam-4283	167	10	,	,	PUNCT
ejpam-4283	167	11	s};µ1	s};µ1	PROPN
ejpam-4283	167	12	=	=	SYM
ejpam-4283	167	13	{	{	PUNCT
ejpam-4283	167	14	∅	∅	NOUN
ejpam-4283	167	15	,	,	PUNCT
ejpam-4283	167	16	{	{	PUNCT
ejpam-4283	167	17	p	p	X
ejpam-4283	167	18	,	,	PUNCT
ejpam-4283	167	19	r	r	NOUN
ejpam-4283	167	20	}	}	PUNCT
ejpam-4283	167	21	,	,	PUNCT
ejpam-4283	167	22	{	{	PUNCT
ejpam-4283	167	23	q	q	X
ejpam-4283	167	24	,	,	PUNCT
ejpam-4283	167	25	r	r	NOUN
ejpam-4283	167	26	}	}	PUNCT
ejpam-4283	167	27	,	,	PUNCT
ejpam-4283	167	28	{	{	PUNCT
ejpam-4283	167	29	p	p	X
ejpam-4283	167	30	,	,	PUNCT
ejpam-4283	167	31	q	q	ADJ
ejpam-4283	167	32	,	,	PUNCT
ejpam-4283	167	33	r	r	NOUN
ejpam-4283	167	34	}	}	PUNCT
ejpam-4283	167	35	}	}	PUNCT
ejpam-4283	167	36	and	and	CCONJ
ejpam-4283	167	37	µ2	µ2	PROPN
ejpam-4283	167	38	=	=	PUNCT
ejpam-4283	167	39	{	{	PUNCT
ejpam-4283	167	40	∅	∅	NOUN
ejpam-4283	167	41	,	,	PUNCT
ejpam-4283	167	42	{	{	PUNCT
ejpam-4283	167	43	p	p	X
ejpam-4283	167	44	,	,	PUNCT
ejpam-4283	167	45	q	q	NOUN
ejpam-4283	167	46	}	}	PUNCT
ejpam-4283	167	47	,	,	PUNCT
ejpam-4283	167	48	{	{	PUNCT
ejpam-4283	167	49	q	q	X
ejpam-4283	167	50	,	,	PUNCT
ejpam-4283	167	51	s	s	PART
ejpam-4283	167	52	}	}	PUNCT
ejpam-4283	167	53	,	,	PUNCT
ejpam-4283	167	54	{	{	PUNCT
ejpam-4283	167	55	p	p	X
ejpam-4283	167	56	,	,	PUNCT
ejpam-4283	167	57	q	q	ADJ
ejpam-4283	167	58	,	,	PUNCT
ejpam-4283	167	59	s	s	PART
ejpam-4283	167	60	}	}	PUNCT
ejpam-4283	167	61	}	}	PUNCT
ejpam-4283	167	62	.	.	PUNCT
ejpam-4283	168	1	here	here	ADV
ejpam-4283	168	2	µ2	µ2	PROPN
ejpam-4283	168	3	*	*	PUNCT
ejpam-4283	168	4	µ1	µ1	PROPN
ejpam-4283	168	5	.	.	PUNCT
ejpam-4283	169	1	now	now	ADV
ejpam-4283	169	2	σ1	σ1	PROPN
ejpam-4283	170	1	=	=	SYM
ejpam-4283	170	2	{	{	PUNCT
ejpam-4283	170	3	∅	∅	NOUN
ejpam-4283	170	4	,	,	PUNCT
ejpam-4283	170	5	{	{	PUNCT
ejpam-4283	170	6	s	s	X
ejpam-4283	170	7	}	}	PUNCT
ejpam-4283	170	8	,	,	PUNCT
ejpam-4283	170	9	{	{	PUNCT
ejpam-4283	170	10	p	p	X
ejpam-4283	170	11	,	,	PUNCT
ejpam-4283	170	12	r	r	NOUN
ejpam-4283	170	13	}	}	PUNCT
ejpam-4283	170	14	,	,	PUNCT
ejpam-4283	170	15	{	{	PUNCT
ejpam-4283	170	16	q	q	X
ejpam-4283	170	17	,	,	PUNCT
ejpam-4283	170	18	r	r	NOUN
ejpam-4283	170	19	}	}	PUNCT
ejpam-4283	170	20	,	,	PUNCT
ejpam-4283	170	21	{	{	PUNCT
ejpam-4283	170	22	p	p	X
ejpam-4283	170	23	,	,	PUNCT
ejpam-4283	170	24	q	q	ADJ
ejpam-4283	170	25	,	,	PUNCT
ejpam-4283	170	26	r	r	NOUN
ejpam-4283	170	27	}	}	PUNCT
ejpam-4283	170	28	,	,	PUNCT
ejpam-4283	170	29	{	{	PUNCT
ejpam-4283	170	30	p	p	X
ejpam-4283	170	31	,	,	PUNCT
ejpam-4283	170	32	r	r	NOUN
ejpam-4283	170	33	,	,	PUNCT
ejpam-4283	170	34	s	s	PART
ejpam-4283	170	35	}	}	PUNCT
ejpam-4283	170	36	,	,	PUNCT
ejpam-4283	170	37	{	{	PUNCT
ejpam-4283	170	38	q	q	X
ejpam-4283	170	39	,	,	PUNCT
ejpam-4283	170	40	r	r	NOUN
ejpam-4283	170	41	,	,	PUNCT
ejpam-4283	170	42	s	s	PART
ejpam-4283	170	43	}	}	PUNCT
ejpam-4283	170	44	,	,	PUNCT
ejpam-4283	170	45	x	x	NOUN
ejpam-4283	170	46	}	}	PUNCT
ejpam-4283	170	47	.	.	PUNCT
ejpam-4283	171	1	choose	choose	VERB
ejpam-4283	171	2	h	h	NOUN
ejpam-4283	171	3	=	=	SYM
ejpam-4283	171	4	{	{	PUNCT
ejpam-4283	171	5	r	r	NOUN
ejpam-4283	171	6	}	}	PUNCT
ejpam-4283	171	7	.	.	PUNCT
ejpam-4283	172	1	then	then	ADV
ejpam-4283	172	2	iσ1(c2(h	iσ1(c2(h	NUM
ejpam-4283	172	3	)	)	PUNCT
ejpam-4283	172	4	)	)	PUNCT
ejpam-4283	173	1	=	=	SYM
ejpam-4283	173	2	iσ1({r	iσ1({r	NOUN
ejpam-4283	173	3	}	}	PUNCT
ejpam-4283	173	4	)	)	PUNCT
ejpam-4283	174	1	=	=	PUNCT
ejpam-4283	174	2	∅.	∅.	ADP
ejpam-4283	174	3	thus	thus	ADV
ejpam-4283	174	4	,	,	PUNCT
ejpam-4283	174	5	h	h	NOUN
ejpam-4283	174	6	is	be	AUX
ejpam-4283	174	7	a	a	DET
ejpam-4283	174	8	(	(	PUNCT
ejpam-4283	174	9	2	2	NUM
ejpam-4283	174	10	,	,	PUNCT
ejpam-4283	174	11	1)?-nowhere	1)?-nowhere	NUM
ejpam-4283	174	12	dense	dense	ADJ
ejpam-4283	174	13	set	set	NOUN
ejpam-4283	174	14	in	in	ADP
ejpam-4283	174	15	x.	x.	PROPN
ejpam-4283	174	16	but	but	CCONJ
ejpam-4283	174	17	i1(c1(h	i1(c1(h	NOUN
ejpam-4283	174	18	)	)	PUNCT
ejpam-4283	174	19	)	)	PUNCT
ejpam-4283	175	1	=	=	PUNCT
ejpam-4283	175	2	i1(x	i1(x	X
ejpam-4283	175	3	)	)	PUNCT
ejpam-4283	175	4	=	=	PRON
ejpam-4283	175	5	{	{	PUNCT
ejpam-4283	175	6	p	p	X
ejpam-4283	175	7	,	,	PUNCT
ejpam-4283	175	8	q	q	ADJ
ejpam-4283	175	9	,	,	PUNCT
ejpam-4283	175	10	r	r	NOUN
ejpam-4283	175	11	}	}	PUNCT
ejpam-4283	175	12	6=	6=	ADP
ejpam-4283	175	13	∅.	∅.	ADP
ejpam-4283	175	14	thus	thus	ADV
ejpam-4283	175	15	,	,	PUNCT
ejpam-4283	175	16	h	h	NOUN
ejpam-4283	175	17	is	be	AUX
ejpam-4283	175	18	not	not	PART
ejpam-4283	175	19	a	a	DET
ejpam-4283	175	20	µ1	µ1	NOUN
ejpam-4283	175	21	-	-	PUNCT
ejpam-4283	175	22	nowhere	nowhere	ADV
ejpam-4283	175	23	dense	dense	ADJ
ejpam-4283	175	24	set	set	NOUN
ejpam-4283	175	25	in	in	ADP
ejpam-4283	175	26	x.	x.	NOUN
ejpam-4283	175	27	theorem	theorem	VERB
ejpam-4283	175	28	10	10	NUM
ejpam-4283	175	29	.	.	PUNCT
ejpam-4283	176	1	let	let	AUX
ejpam-4283	176	2	(	(	PUNCT
ejpam-4283	176	3	x,µ1	x,µ1	NOUN
ejpam-4283	176	4	,	,	PUNCT
ejpam-4283	176	5	µ2	µ2	PROPN
ejpam-4283	176	6	)	)	PUNCT
ejpam-4283	176	7	be	be	VERB
ejpam-4283	176	8	a	a	DET
ejpam-4283	176	9	bigeneralized	bigeneralized	ADJ
ejpam-4283	176	10	topological	topological	ADJ
ejpam-4283	176	11	space	space	NOUN
ejpam-4283	176	12	.	.	PUNCT
ejpam-4283	177	1	if	if	SCONJ
ejpam-4283	177	2	µv	µv	PRON
ejpam-4283	177	3	⊂	⊂	PART
ejpam-4283	177	4	µs	µs	X
ejpam-4283	177	5	and	and	CCONJ
ejpam-4283	177	6	if	if	SCONJ
ejpam-4283	177	7	µv	µv	PRON
ejpam-4283	177	8	is	be	AUX
ejpam-4283	177	9	a	a	DET
ejpam-4283	177	10	strong	strong	ADJ
ejpam-4283	177	11	generalized	generalized	ADJ
ejpam-4283	177	12	topology	topology	NOUN
ejpam-4283	177	13	,	,	PUNCT
ejpam-4283	177	14	then	then	ADV
ejpam-4283	177	15	any	any	DET
ejpam-4283	177	16	µv	µv	NOUN
ejpam-4283	177	17	-	-	PUNCT
ejpam-4283	177	18	nowhere	nowhere	ADV
ejpam-4283	177	19	dense	dense	ADJ
ejpam-4283	177	20	set	set	NOUN
ejpam-4283	177	21	in	in	ADP
ejpam-4283	177	22	x	x	PRON
ejpam-4283	177	23	is	be	AUX
ejpam-4283	177	24	a	a	DET
ejpam-4283	177	25	(	(	PUNCT
ejpam-4283	177	26	s	s	X
ejpam-4283	177	27	,	,	PUNCT
ejpam-4283	177	28	v)?-nowhere	v)?-nowhere	X
ejpam-4283	177	29	dense	dense	ADJ
ejpam-4283	177	30	set	set	NOUN
ejpam-4283	177	31	in	in	ADP
ejpam-4283	177	32	x	x	PUNCT
ejpam-4283	177	33	where	where	SCONJ
ejpam-4283	177	34	s	s	X
ejpam-4283	177	35	,	,	PUNCT
ejpam-4283	177	36	v	v	NOUN
ejpam-4283	177	37	=	=	SYM
ejpam-4283	177	38	1	1	NUM
ejpam-4283	177	39	,	,	PUNCT
ejpam-4283	177	40	2	2	NUM
ejpam-4283	177	41	and	and	CCONJ
ejpam-4283	177	42	s	s	X
ejpam-4283	177	43	6=	6=	PROPN
ejpam-4283	177	44	v.	v.	ADP
ejpam-4283	177	45	proof	proof	NOUN
ejpam-4283	177	46	.	.	PUNCT
ejpam-4283	178	1	take	take	VERB
ejpam-4283	178	2	s	s	NOUN
ejpam-4283	178	3	=	=	SYM
ejpam-4283	178	4	1	1	NUM
ejpam-4283	178	5	and	and	CCONJ
ejpam-4283	178	6	v	v	NOUN
ejpam-4283	178	7	=	=	SYM
ejpam-4283	178	8	2	2	X
ejpam-4283	178	9	.	.	X
ejpam-4283	178	10	assume	assume	VERB
ejpam-4283	178	11	that	that	SCONJ
ejpam-4283	178	12	,	,	PUNCT
ejpam-4283	178	13	µ2	µ2	PROPN
ejpam-4283	178	14	⊂	⊂	PROPN
ejpam-4283	178	15	µ1	µ1	PROPN
ejpam-4283	178	16	and	and	CCONJ
ejpam-4283	178	17	q	q	NOUN
ejpam-4283	178	18	is	be	AUX
ejpam-4283	178	19	a	a	DET
ejpam-4283	178	20	µ2	µ2	PROPN
ejpam-4283	178	21	-	-	PUNCT
ejpam-4283	178	22	nowhere	nowhere	ADV
ejpam-4283	178	23	dense	dense	ADJ
ejpam-4283	178	24	set	set	NOUN
ejpam-4283	178	25	in	in	ADP
ejpam-4283	178	26	x.	x.	NOUN
ejpam-4283	178	27	then	then	ADV
ejpam-4283	178	28	iµ2(cµ2(q	iµ2(cµ2(q	NUM
ejpam-4283	178	29	)	)	PUNCT
ejpam-4283	178	30	)	)	PUNCT
ejpam-4283	179	1	=	=	VERB
ejpam-4283	179	2	∅.	∅.	AUX
ejpam-4283	179	3	suppose	suppose	VERB
ejpam-4283	179	4	iσ2(c1(q	iσ2(c1(q	NUM
ejpam-4283	179	5	)	)	PUNCT
ejpam-4283	179	6	)	)	PUNCT
ejpam-4283	179	7	6=	6=	ADP
ejpam-4283	179	8	∅.	∅.	VERB
ejpam-4283	179	9	then	then	ADV
ejpam-4283	179	10	there	there	PRON
ejpam-4283	179	11	exists	exist	VERB
ejpam-4283	179	12	m	m	VERB
ejpam-4283	179	13	∈	∈	NOUN
ejpam-4283	179	14	µ̃σ2	µ̃σ2	NOUN
ejpam-4283	179	15	such	such	ADJ
ejpam-4283	179	16	that	that	SCONJ
ejpam-4283	179	17	m	m	VERB
ejpam-4283	179	18	⊂	⊂	PROPN
ejpam-4283	179	19	c1(q	c1(q	ADJ
ejpam-4283	179	20	)	)	PUNCT
ejpam-4283	179	21	.	.	PUNCT
ejpam-4283	180	1	since	since	SCONJ
ejpam-4283	180	2	m	m	PROPN
ejpam-4283	180	3	∈	∈	PROPN
ejpam-4283	180	4	µ̃σ2	µ̃σ2	NOUN
ejpam-4283	180	5	we	we	PRON
ejpam-4283	180	6	have	have	VERB
ejpam-4283	180	7	c2(i2(m	c2(i2(m	NOUN
ejpam-4283	180	8	)	)	PUNCT
ejpam-4283	180	9	)	)	PUNCT
ejpam-4283	180	10	6=	6=	ADP
ejpam-4283	180	11	∅.	∅.	VERB
ejpam-4283	180	12	then	then	ADV
ejpam-4283	180	13	by	by	ADP
ejpam-4283	180	14	hypothesis	hypothesis	NOUN
ejpam-4283	180	15	,	,	PUNCT
ejpam-4283	180	16	i2(m	i2(m	NOUN
ejpam-4283	180	17	)	)	PUNCT
ejpam-4283	180	18	6=	6=	ADP
ejpam-4283	180	19	∅	∅	NOUN
ejpam-4283	180	20	and	and	CCONJ
ejpam-4283	180	21	so	so	ADV
ejpam-4283	180	22	i2(c1(q	i2(c1(q	ADJ
ejpam-4283	180	23	)	)	PUNCT
ejpam-4283	180	24	)	)	PUNCT
ejpam-4283	180	25	6=	6=	ADP
ejpam-4283	180	26	∅.	∅.	ADP
ejpam-4283	180	27	by	by	ADP
ejpam-4283	180	28	hypothesis	hypothesis	NOUN
ejpam-4283	180	29	,	,	PUNCT
ejpam-4283	180	30	i2(c2(q	i2(c2(q	NUM
ejpam-4283	180	31	)	)	PUNCT
ejpam-4283	180	32	)	)	PUNCT
ejpam-4283	180	33	6=	6=	ADP
ejpam-4283	180	34	∅	∅	NOUN
ejpam-4283	180	35	,	,	PUNCT
ejpam-4283	180	36	which	which	PRON
ejpam-4283	180	37	is	be	AUX
ejpam-4283	180	38	not	not	PART
ejpam-4283	180	39	possible	possible	ADJ
ejpam-4283	180	40	.	.	PUNCT
ejpam-4283	181	1	therefore	therefore	ADV
ejpam-4283	181	2	,	,	PUNCT
ejpam-4283	181	3	iσ2(c1(q	iσ2(c1(q	NUM
ejpam-4283	181	4	)	)	PUNCT
ejpam-4283	181	5	)	)	PUNCT
ejpam-4283	182	1	=	=	PUNCT
ejpam-4283	182	2	∅.	∅.	VERB
ejpam-4283	182	3	hence	hence	ADV
ejpam-4283	182	4	q	q	X
ejpam-4283	182	5	∈	∈	PROPN
ejpam-4283	182	6	(	(	PUNCT
ejpam-4283	182	7	1	1	NUM
ejpam-4283	182	8	,	,	PUNCT
ejpam-4283	182	9	2	2	NUM
ejpam-4283	182	10	)	)	PUNCT
ejpam-4283	182	11	?	?	PUNCT
ejpam-4283	183	1	−n	−n	INTJ
ejpam-4283	183	2	(	(	PUNCT
ejpam-4283	183	3	x	x	NOUN
ejpam-4283	183	4	)	)	PUNCT
ejpam-4283	183	5	.	.	PUNCT
ejpam-4283	184	1	similarly	similarly	ADV
ejpam-4283	184	2	,	,	PUNCT
ejpam-4283	184	3	we	we	PRON
ejpam-4283	184	4	can	can	AUX
ejpam-4283	184	5	prove	prove	VERB
ejpam-4283	184	6	the	the	DET
ejpam-4283	184	7	result	result	NOUN
ejpam-4283	184	8	for	for	ADP
ejpam-4283	184	9	s	s	NOUN
ejpam-4283	184	10	=	=	SYM
ejpam-4283	184	11	2	2	NUM
ejpam-4283	184	12	and	and	CCONJ
ejpam-4283	184	13	v	v	NOUN
ejpam-4283	184	14	=	=	SYM
ejpam-4283	184	15	1	1	NUM
ejpam-4283	184	16	.	.	PUNCT
ejpam-4283	185	1	the	the	DET
ejpam-4283	185	2	following	follow	VERB
ejpam-4283	185	3	example	example	NOUN
ejpam-4283	185	4	11	11	NUM
ejpam-4283	185	5	shows	show	VERB
ejpam-4283	185	6	that	that	SCONJ
ejpam-4283	185	7	the	the	DET
ejpam-4283	185	8	hypothesis	hypothesis	NOUN
ejpam-4283	185	9	of	of	ADP
ejpam-4283	185	10	theorem	theorem	NOUN
ejpam-4283	185	11	10	10	NUM
ejpam-4283	185	12	can	can	AUX
ejpam-4283	185	13	not	not	PART
ejpam-4283	185	14	be	be	AUX
ejpam-4283	185	15	dropped	drop	VERB
ejpam-4283	185	16	.	.	PUNCT
ejpam-4283	186	1	p.	p.	NOUN
ejpam-4283	186	2	yupapin	yupapin	NOUN
ejpam-4283	186	3	,	,	PUNCT
ejpam-4283	186	4	v.	v.	CCONJ
ejpam-4283	186	5	subramanian	subramanian	PROPN
ejpam-4283	186	6	,	,	PUNCT
ejpam-4283	186	7	y.	y.	PROPN
ejpam-4283	186	8	farhat	farhat	PROPN
ejpam-4283	186	9	/	/	SYM
ejpam-4283	186	10	eur	eur	PROPN
ejpam-4283	186	11	.	.	PUNCT
ejpam-4283	187	1	j.	j.	PROPN
ejpam-4283	187	2	pure	pure	PROPN
ejpam-4283	187	3	appl	appl	PROPN
ejpam-4283	187	4	.	.	PROPN
ejpam-4283	187	5	math	math	PROPN
ejpam-4283	187	6	,	,	PUNCT
ejpam-4283	187	7	15	15	NUM
ejpam-4283	187	8	(	(	PUNCT
ejpam-4283	187	9	2	2	NUM
ejpam-4283	187	10	)	)	PUNCT
ejpam-4283	187	11	(	(	PUNCT
ejpam-4283	187	12	2022	2022	NUM
ejpam-4283	187	13	)	)	PUNCT
ejpam-4283	187	14	,	,	PUNCT
ejpam-4283	187	15	403	403	NUM
ejpam-4283	187	16	-	-	SYM
ejpam-4283	187	17	414	414	NUM
ejpam-4283	187	18	407	407	NUM
ejpam-4283	187	19	example	example	NOUN
ejpam-4283	187	20	11	11	NUM
ejpam-4283	187	21	.	.	PUNCT
ejpam-4283	188	1	(	(	PUNCT
ejpam-4283	188	2	a	a	X
ejpam-4283	188	3	)	)	PUNCT
ejpam-4283	188	4	.	.	PUNCT
ejpam-4283	189	1	consider	consider	VERB
ejpam-4283	189	2	the	the	DET
ejpam-4283	189	3	bigeneralized	bigeneralized	ADJ
ejpam-4283	189	4	topological	topological	ADJ
ejpam-4283	189	5	space	space	NOUN
ejpam-4283	189	6	(	(	PUNCT
ejpam-4283	189	7	x,µ1	x,µ1	PROPN
ejpam-4283	189	8	,	,	PUNCT
ejpam-4283	189	9	µ2	µ2	PROPN
ejpam-4283	189	10	)	)	PUNCT
ejpam-4283	190	1	where	where	SCONJ
ejpam-4283	190	2	x	x	X
ejpam-4283	190	3	=	=	PRON
ejpam-4283	190	4	{	{	PUNCT
ejpam-4283	190	5	p	p	X
ejpam-4283	190	6	,	,	PUNCT
ejpam-4283	190	7	q	q	ADJ
ejpam-4283	190	8	,	,	PUNCT
ejpam-4283	190	9	r	r	NOUN
ejpam-4283	190	10	,	,	PUNCT
ejpam-4283	190	11	s};µ1	s};µ1	PROPN
ejpam-4283	190	12	=	=	SYM
ejpam-4283	190	13	{	{	PUNCT
ejpam-4283	190	14	∅	∅	NOUN
ejpam-4283	190	15	,	,	PUNCT
ejpam-4283	190	16	{	{	PUNCT
ejpam-4283	190	17	p	p	X
ejpam-4283	190	18	,	,	PUNCT
ejpam-4283	190	19	s	s	PART
ejpam-4283	190	20	}	}	PUNCT
ejpam-4283	190	21	,	,	PUNCT
ejpam-4283	190	22	{	{	PUNCT
ejpam-4283	190	23	q	q	X
ejpam-4283	190	24	,	,	PUNCT
ejpam-4283	190	25	s	s	PART
ejpam-4283	190	26	}	}	PUNCT
ejpam-4283	190	27	,	,	PUNCT
ejpam-4283	190	28	{	{	PUNCT
ejpam-4283	190	29	p	p	X
ejpam-4283	190	30	,	,	PUNCT
ejpam-4283	190	31	q	q	ADJ
ejpam-4283	190	32	,	,	PUNCT
ejpam-4283	190	33	s	s	PART
ejpam-4283	190	34	}	}	PUNCT
ejpam-4283	190	35	}	}	PUNCT
ejpam-4283	190	36	and	and	CCONJ
ejpam-4283	190	37	µ2	µ2	PROPN
ejpam-4283	190	38	=	=	PUNCT
ejpam-4283	190	39	{	{	PUNCT
ejpam-4283	190	40	∅	∅	NOUN
ejpam-4283	190	41	,	,	PUNCT
ejpam-4283	190	42	{	{	PUNCT
ejpam-4283	190	43	p	p	X
ejpam-4283	190	44	,	,	PUNCT
ejpam-4283	190	45	r	r	NOUN
ejpam-4283	190	46	}	}	PUNCT
ejpam-4283	190	47	,	,	PUNCT
ejpam-4283	190	48	{	{	PUNCT
ejpam-4283	190	49	p	p	X
ejpam-4283	190	50	,	,	PUNCT
ejpam-4283	190	51	s	s	PART
ejpam-4283	190	52	}	}	PUNCT
ejpam-4283	190	53	,	,	PUNCT
ejpam-4283	190	54	{	{	PUNCT
ejpam-4283	190	55	q	q	X
ejpam-4283	190	56	,	,	PUNCT
ejpam-4283	190	57	r	r	NOUN
ejpam-4283	190	58	}	}	PUNCT
ejpam-4283	190	59	,	,	PUNCT
ejpam-4283	190	60	{	{	PUNCT
ejpam-4283	190	61	p	p	X
ejpam-4283	190	62	,	,	PUNCT
ejpam-4283	190	63	r	r	NOUN
ejpam-4283	190	64	,	,	PUNCT
ejpam-4283	190	65	s	s	PART
ejpam-4283	190	66	}	}	PUNCT
ejpam-4283	190	67	,	,	PUNCT
ejpam-4283	190	68	{	{	PUNCT
ejpam-4283	190	69	p	p	X
ejpam-4283	190	70	,	,	PUNCT
ejpam-4283	190	71	q	q	ADJ
ejpam-4283	190	72	,	,	PUNCT
ejpam-4283	190	73	r	r	NOUN
ejpam-4283	190	74	}	}	PUNCT
ejpam-4283	190	75	,	,	PUNCT
ejpam-4283	190	76	x	x	NOUN
ejpam-4283	190	77	}	}	PUNCT
ejpam-4283	190	78	.	.	PUNCT
ejpam-4283	191	1	here	here	ADV
ejpam-4283	191	2	µ2	µ2	PROPN
ejpam-4283	191	3	*	*	PUNCT
ejpam-4283	191	4	µ1	µ1	PROPN
ejpam-4283	191	5	but	but	CCONJ
ejpam-4283	191	6	µ2	µ2	PROPN
ejpam-4283	191	7	is	be	AUX
ejpam-4283	191	8	a	a	DET
ejpam-4283	191	9	sgt	sgt	PROPN
ejpam-4283	191	10	.	.	PUNCT
ejpam-4283	192	1	now	now	ADV
ejpam-4283	192	2	σ2	σ2	PROPN
ejpam-4283	192	3	=	=	SYM
ejpam-4283	192	4	{	{	PUNCT
ejpam-4283	192	5	∅	∅	NOUN
ejpam-4283	192	6	,	,	PUNCT
ejpam-4283	192	7	{	{	PUNCT
ejpam-4283	192	8	p	p	X
ejpam-4283	192	9	,	,	PUNCT
ejpam-4283	192	10	r	r	NOUN
ejpam-4283	192	11	}	}	PUNCT
ejpam-4283	192	12	,	,	PUNCT
ejpam-4283	192	13	{	{	PUNCT
ejpam-4283	192	14	p	p	X
ejpam-4283	192	15	,	,	PUNCT
ejpam-4283	192	16	s	s	PART
ejpam-4283	192	17	}	}	PUNCT
ejpam-4283	192	18	,	,	PUNCT
ejpam-4283	192	19	{	{	PUNCT
ejpam-4283	192	20	q	q	X
ejpam-4283	192	21	,	,	PUNCT
ejpam-4283	192	22	r	r	NOUN
ejpam-4283	192	23	}	}	PUNCT
ejpam-4283	192	24	,	,	PUNCT
ejpam-4283	192	25	{	{	PUNCT
ejpam-4283	192	26	p	p	X
ejpam-4283	192	27	,	,	PUNCT
ejpam-4283	192	28	r	r	NOUN
ejpam-4283	192	29	,	,	PUNCT
ejpam-4283	192	30	s	s	PART
ejpam-4283	192	31	}	}	PUNCT
ejpam-4283	192	32	,	,	PUNCT
ejpam-4283	192	33	{	{	PUNCT
ejpam-4283	192	34	p	p	X
ejpam-4283	192	35	,	,	PUNCT
ejpam-4283	192	36	q	q	ADJ
ejpam-4283	192	37	,	,	PUNCT
ejpam-4283	192	38	r	r	NOUN
ejpam-4283	192	39	}	}	PUNCT
ejpam-4283	192	40	,	,	PUNCT
ejpam-4283	192	41	x	x	NOUN
ejpam-4283	192	42	}	}	PUNCT
ejpam-4283	192	43	.	.	PUNCT
ejpam-4283	193	1	take	take	VERB
ejpam-4283	193	2	h	h	NOUN
ejpam-4283	193	3	=	=	PUNCT
ejpam-4283	193	4	{	{	PUNCT
ejpam-4283	193	5	s	s	NOUN
ejpam-4283	193	6	}	}	PUNCT
ejpam-4283	193	7	.	.	PUNCT
ejpam-4283	194	1	then	then	ADV
ejpam-4283	194	2	i2(c2(h	i2(c2(h	NOUN
ejpam-4283	194	3	)	)	PUNCT
ejpam-4283	194	4	)	)	PUNCT
ejpam-4283	195	1	=	=	PUNCT
ejpam-4283	195	2	i2(h	i2(h	X
ejpam-4283	195	3	)	)	PUNCT
ejpam-4283	195	4	=	=	NOUN
ejpam-4283	195	5	∅	∅	NOUN
ejpam-4283	195	6	and	and	CCONJ
ejpam-4283	195	7	so	so	ADV
ejpam-4283	195	8	h	h	NOUN
ejpam-4283	195	9	is	be	AUX
ejpam-4283	195	10	µ2	µ2	ADJ
ejpam-4283	195	11	-	-	PUNCT
ejpam-4283	195	12	nowhere	nowhere	ADV
ejpam-4283	195	13	dense	dense	ADJ
ejpam-4283	195	14	set	set	NOUN
ejpam-4283	195	15	in	in	ADP
ejpam-4283	195	16	x.	x.	NOUN
ejpam-4283	195	17	but	but	CCONJ
ejpam-4283	195	18	iσ2(c1(h	iσ2(c1(h	NOUN
ejpam-4283	195	19	)	)	PUNCT
ejpam-4283	195	20	)	)	PUNCT
ejpam-4283	196	1	=	=	SYM
ejpam-4283	196	2	iσ2(x	iσ2(x	NOUN
ejpam-4283	196	3	)	)	PUNCT
ejpam-4283	196	4	=	=	SYM
ejpam-4283	196	5	x	x	PUNCT
ejpam-4283	196	6	6=	6=	ADP
ejpam-4283	196	7	∅.	∅.	ADP
ejpam-4283	196	8	thus	thus	ADV
ejpam-4283	196	9	,	,	PUNCT
ejpam-4283	196	10	h	h	NOUN
ejpam-4283	196	11	is	be	AUX
ejpam-4283	196	12	not	not	PART
ejpam-4283	196	13	a	a	DET
ejpam-4283	196	14	(	(	PUNCT
ejpam-4283	196	15	1	1	NUM
ejpam-4283	196	16	,	,	PUNCT
ejpam-4283	196	17	2)?-nowhere	2)?-nowhere	NUM
ejpam-4283	196	18	dense	dense	ADJ
ejpam-4283	196	19	set	set	NOUN
ejpam-4283	196	20	in	in	ADP
ejpam-4283	196	21	x.	x.	NOUN
ejpam-4283	196	22	(	(	PUNCT
ejpam-4283	196	23	b	b	NOUN
ejpam-4283	196	24	)	)	PUNCT
ejpam-4283	196	25	.	.	PUNCT
ejpam-4283	197	1	consider	consider	VERB
ejpam-4283	197	2	the	the	DET
ejpam-4283	197	3	bigeneralized	bigeneralized	ADJ
ejpam-4283	197	4	topological	topological	ADJ
ejpam-4283	197	5	space	space	NOUN
ejpam-4283	197	6	(	(	PUNCT
ejpam-4283	197	7	x,µ1	x,µ1	PROPN
ejpam-4283	197	8	,	,	PUNCT
ejpam-4283	197	9	µ2	µ2	PROPN
ejpam-4283	197	10	)	)	PUNCT
ejpam-4283	198	1	where	where	SCONJ
ejpam-4283	198	2	x	x	X
ejpam-4283	198	3	=	=	PRON
ejpam-4283	198	4	{	{	PUNCT
ejpam-4283	198	5	p	p	X
ejpam-4283	198	6	,	,	PUNCT
ejpam-4283	198	7	q	q	ADJ
ejpam-4283	198	8	,	,	PUNCT
ejpam-4283	198	9	r	r	NOUN
ejpam-4283	198	10	,	,	PUNCT
ejpam-4283	198	11	s};µ1	s};µ1	PROPN
ejpam-4283	198	12	=	=	SYM
ejpam-4283	198	13	{	{	PUNCT
ejpam-4283	198	14	∅	∅	NOUN
ejpam-4283	198	15	,	,	PUNCT
ejpam-4283	198	16	{	{	PUNCT
ejpam-4283	198	17	p	p	X
ejpam-4283	198	18	,	,	PUNCT
ejpam-4283	198	19	q	q	NOUN
ejpam-4283	198	20	}	}	PUNCT
ejpam-4283	198	21	,	,	PUNCT
ejpam-4283	198	22	{	{	PUNCT
ejpam-4283	198	23	p	p	X
ejpam-4283	198	24	,	,	PUNCT
ejpam-4283	198	25	s	s	PART
ejpam-4283	198	26	}	}	PUNCT
ejpam-4283	198	27	,	,	PUNCT
ejpam-4283	198	28	{	{	PUNCT
ejpam-4283	198	29	q	q	X
ejpam-4283	198	30	,	,	PUNCT
ejpam-4283	198	31	s	s	PART
ejpam-4283	198	32	}	}	PUNCT
ejpam-4283	198	33	,	,	PUNCT
ejpam-4283	198	34	{	{	PUNCT
ejpam-4283	198	35	p	p	X
ejpam-4283	198	36	,	,	PUNCT
ejpam-4283	198	37	q	q	ADJ
ejpam-4283	198	38	,	,	PUNCT
ejpam-4283	198	39	s	s	PART
ejpam-4283	198	40	}	}	PUNCT
ejpam-4283	198	41	}	}	PUNCT
ejpam-4283	198	42	and	and	CCONJ
ejpam-4283	198	43	µ2	µ2	PROPN
ejpam-4283	198	44	=	=	PUNCT
ejpam-4283	198	45	{	{	PUNCT
ejpam-4283	198	46	∅	∅	NOUN
ejpam-4283	198	47	,	,	PUNCT
ejpam-4283	198	48	{	{	PUNCT
ejpam-4283	198	49	p	p	X
ejpam-4283	198	50	,	,	PUNCT
ejpam-4283	198	51	s	s	PART
ejpam-4283	198	52	}	}	PUNCT
ejpam-4283	198	53	,	,	PUNCT
ejpam-4283	198	54	{	{	PUNCT
ejpam-4283	198	55	q	q	X
ejpam-4283	198	56	,	,	PUNCT
ejpam-4283	198	57	s	s	PART
ejpam-4283	198	58	}	}	PUNCT
ejpam-4283	198	59	,	,	PUNCT
ejpam-4283	198	60	{	{	PUNCT
ejpam-4283	198	61	p	p	X
ejpam-4283	198	62	,	,	PUNCT
ejpam-4283	198	63	q	q	ADJ
ejpam-4283	198	64	,	,	PUNCT
ejpam-4283	198	65	s	s	PART
ejpam-4283	198	66	}	}	PUNCT
ejpam-4283	198	67	}	}	PUNCT
ejpam-4283	198	68	.	.	PUNCT
ejpam-4283	199	1	here	here	ADV
ejpam-4283	199	2	µ2	µ2	PROPN
ejpam-4283	199	3	⊂	⊂	PROPN
ejpam-4283	199	4	µ1	µ1	PROPN
ejpam-4283	200	1	but	but	CCONJ
ejpam-4283	200	2	µ2	µ2	PROPN
ejpam-4283	200	3	is	be	AUX
ejpam-4283	200	4	not	not	PART
ejpam-4283	200	5	a	a	DET
ejpam-4283	200	6	sgt	sgt	PROPN
ejpam-4283	200	7	.	.	PUNCT
ejpam-4283	201	1	now	now	ADV
ejpam-4283	201	2	σ2	σ2	PROPN
ejpam-4283	201	3	=	=	SYM
ejpam-4283	201	4	{	{	PUNCT
ejpam-4283	201	5	∅	∅	NOUN
ejpam-4283	201	6	,	,	PUNCT
ejpam-4283	201	7	{	{	PUNCT
ejpam-4283	201	8	r	r	NOUN
ejpam-4283	201	9	}	}	PUNCT
ejpam-4283	201	10	,	,	PUNCT
ejpam-4283	201	11	{	{	PUNCT
ejpam-4283	201	12	p	p	X
ejpam-4283	201	13	,	,	PUNCT
ejpam-4283	201	14	s	s	PART
ejpam-4283	201	15	}	}	PUNCT
ejpam-4283	201	16	,	,	PUNCT
ejpam-4283	201	17	{	{	PUNCT
ejpam-4283	201	18	q	q	X
ejpam-4283	201	19	,	,	PUNCT
ejpam-4283	201	20	s	s	PART
ejpam-4283	201	21	}	}	PUNCT
ejpam-4283	201	22	,	,	PUNCT
ejpam-4283	201	23	{	{	PUNCT
ejpam-4283	201	24	p	p	X
ejpam-4283	201	25	,	,	PUNCT
ejpam-4283	201	26	q	q	X
ejpam-4283	201	27	,	,	PUNCT
ejpam-4283	201	28	s	s	PART
ejpam-4283	201	29	}	}	PUNCT
ejpam-4283	201	30	,	,	PUNCT
ejpam-4283	201	31	{	{	PUNCT
ejpam-4283	201	32	p	p	X
ejpam-4283	201	33	,	,	PUNCT
ejpam-4283	201	34	r	r	NOUN
ejpam-4283	201	35	,	,	PUNCT
ejpam-4283	201	36	s	s	PART
ejpam-4283	201	37	}	}	PUNCT
ejpam-4283	201	38	,	,	PUNCT
ejpam-4283	201	39	{	{	PUNCT
ejpam-4283	201	40	q	q	X
ejpam-4283	201	41	,	,	PUNCT
ejpam-4283	201	42	r	r	NOUN
ejpam-4283	201	43	,	,	PUNCT
ejpam-4283	201	44	s	s	PART
ejpam-4283	201	45	}	}	PUNCT
ejpam-4283	201	46	,	,	PUNCT
ejpam-4283	201	47	x	x	NOUN
ejpam-4283	201	48	}	}	PUNCT
ejpam-4283	201	49	.	.	PUNCT
ejpam-4283	202	1	choose	choose	VERB
ejpam-4283	202	2	p	p	NOUN
ejpam-4283	202	3	=	=	X
ejpam-4283	202	4	{	{	PUNCT
ejpam-4283	202	5	r	r	NOUN
ejpam-4283	202	6	}	}	PUNCT
ejpam-4283	202	7	.	.	PUNCT
ejpam-4283	203	1	then	then	ADV
ejpam-4283	203	2	i2(c2(p	i2(c2(p	NUM
ejpam-4283	203	3	)	)	PUNCT
ejpam-4283	203	4	)	)	PUNCT
ejpam-4283	204	1	=	=	PUNCT
ejpam-4283	204	2	i2(p	i2(p	X
ejpam-4283	204	3	)	)	PUNCT
ejpam-4283	204	4	=	=	NOUN
ejpam-4283	204	5	∅	∅	NOUN
ejpam-4283	204	6	so	so	SCONJ
ejpam-4283	204	7	that	that	SCONJ
ejpam-4283	204	8	p	p	NOUN
ejpam-4283	204	9	is	be	AUX
ejpam-4283	204	10	a	a	DET
ejpam-4283	204	11	µ2	µ2	PROPN
ejpam-4283	204	12	-	-	PUNCT
ejpam-4283	204	13	nowhere	nowhere	ADV
ejpam-4283	204	14	dense	dense	ADJ
ejpam-4283	204	15	set	set	NOUN
ejpam-4283	204	16	in	in	ADP
ejpam-4283	204	17	x.	x.	NOUN
ejpam-4283	204	18	but	but	CCONJ
ejpam-4283	204	19	iσ2(c1(p	iσ2(c1(p	ADJ
ejpam-4283	204	20	)	)	PUNCT
ejpam-4283	204	21	)	)	PUNCT
ejpam-4283	205	1	=	=	SYM
ejpam-4283	205	2	iσ2(p	iσ2(p	X
ejpam-4283	205	3	)	)	PUNCT
ejpam-4283	206	1	=	=	PUNCT
ejpam-4283	207	1	p	p	PROPN
ejpam-4283	207	2	6=	6=	ADP
ejpam-4283	207	3	∅.	∅.	ADP
ejpam-4283	207	4	thus	thus	ADV
ejpam-4283	207	5	,	,	PUNCT
ejpam-4283	207	6	p	p	PRON
ejpam-4283	207	7	is	be	AUX
ejpam-4283	207	8	not	not	PART
ejpam-4283	207	9	a	a	DET
ejpam-4283	207	10	(	(	PUNCT
ejpam-4283	207	11	1	1	NUM
ejpam-4283	207	12	,	,	PUNCT
ejpam-4283	207	13	2)?-nowhere	2)?-nowhere	NUM
ejpam-4283	207	14	dense	dense	ADJ
ejpam-4283	207	15	set	set	NOUN
ejpam-4283	207	16	in	in	ADP
ejpam-4283	207	17	x.	x.	NOUN
ejpam-4283	207	18	(	(	PUNCT
ejpam-4283	207	19	c	c	NOUN
ejpam-4283	207	20	)	)	PUNCT
ejpam-4283	207	21	.	.	PUNCT
ejpam-4283	208	1	consider	consider	VERB
ejpam-4283	208	2	the	the	DET
ejpam-4283	208	3	bigeneralized	bigeneralized	ADJ
ejpam-4283	208	4	topological	topological	ADJ
ejpam-4283	208	5	space	space	NOUN
ejpam-4283	208	6	(	(	PUNCT
ejpam-4283	208	7	x,µ1	x,µ1	PROPN
ejpam-4283	208	8	,	,	PUNCT
ejpam-4283	208	9	µ2	µ2	PROPN
ejpam-4283	208	10	)	)	PUNCT
ejpam-4283	209	1	where	where	SCONJ
ejpam-4283	209	2	x	x	X
ejpam-4283	209	3	=	=	PRON
ejpam-4283	209	4	{	{	PUNCT
ejpam-4283	209	5	p	p	X
ejpam-4283	209	6	,	,	PUNCT
ejpam-4283	209	7	q	q	ADJ
ejpam-4283	209	8	,	,	PUNCT
ejpam-4283	209	9	r	r	NOUN
ejpam-4283	209	10	,	,	PUNCT
ejpam-4283	209	11	s};µ1	s};µ1	PROPN
ejpam-4283	209	12	=	=	SYM
ejpam-4283	209	13	{	{	PUNCT
ejpam-4283	209	14	∅	∅	NOUN
ejpam-4283	209	15	,	,	PUNCT
ejpam-4283	209	16	{	{	PUNCT
ejpam-4283	209	17	p	p	X
ejpam-4283	209	18	,	,	PUNCT
ejpam-4283	209	19	q	q	NOUN
ejpam-4283	209	20	}	}	PUNCT
ejpam-4283	209	21	,	,	PUNCT
ejpam-4283	209	22	{	{	PUNCT
ejpam-4283	209	23	q	q	X
ejpam-4283	209	24	,	,	PUNCT
ejpam-4283	209	25	r	r	NOUN
ejpam-4283	209	26	}	}	PUNCT
ejpam-4283	209	27	,	,	PUNCT
ejpam-4283	209	28	{	{	PUNCT
ejpam-4283	209	29	p	p	X
ejpam-4283	209	30	,	,	PUNCT
ejpam-4283	209	31	q	q	ADJ
ejpam-4283	209	32	,	,	PUNCT
ejpam-4283	209	33	r	r	NOUN
ejpam-4283	209	34	}	}	PUNCT
ejpam-4283	209	35	,	,	PUNCT
ejpam-4283	209	36	x	x	NOUN
ejpam-4283	209	37	}	}	PUNCT
ejpam-4283	209	38	and	and	CCONJ
ejpam-4283	209	39	µ2	µ2	PROPN
ejpam-4283	209	40	=	=	PUNCT
ejpam-4283	209	41	{	{	PUNCT
ejpam-4283	209	42	∅	∅	NOUN
ejpam-4283	209	43	,	,	PUNCT
ejpam-4283	209	44	{	{	PUNCT
ejpam-4283	209	45	p	p	X
ejpam-4283	209	46	,	,	PUNCT
ejpam-4283	209	47	r	r	NOUN
ejpam-4283	209	48	}	}	PUNCT
ejpam-4283	209	49	,	,	PUNCT
ejpam-4283	209	50	{	{	PUNCT
ejpam-4283	209	51	q	q	X
ejpam-4283	209	52	,	,	PUNCT
ejpam-4283	209	53	r	r	NOUN
ejpam-4283	209	54	}	}	PUNCT
ejpam-4283	209	55	,	,	PUNCT
ejpam-4283	209	56	{	{	PUNCT
ejpam-4283	209	57	p	p	X
ejpam-4283	209	58	,	,	PUNCT
ejpam-4283	209	59	q	q	ADJ
ejpam-4283	209	60	,	,	PUNCT
ejpam-4283	209	61	r	r	NOUN
ejpam-4283	209	62	}	}	PUNCT
ejpam-4283	209	63	}	}	PUNCT
ejpam-4283	209	64	.	.	PUNCT
ejpam-4283	209	65	clearly	clearly	ADV
ejpam-4283	209	66	,	,	PUNCT
ejpam-4283	209	67	µ1	µ1	PROPN
ejpam-4283	209	68	*	*	PROPN
ejpam-4283	209	69	µ2	µ2	PROPN
ejpam-4283	209	70	but	but	CCONJ
ejpam-4283	209	71	µ1	µ1	PROPN
ejpam-4283	209	72	is	be	AUX
ejpam-4283	209	73	a	a	DET
ejpam-4283	209	74	sgt	sgt	PROPN
ejpam-4283	209	75	.	.	PUNCT
ejpam-4283	210	1	here	here	ADV
ejpam-4283	210	2	σ1	σ1	PROPN
ejpam-4283	211	1	=	=	SYM
ejpam-4283	211	2	{	{	PUNCT
ejpam-4283	211	3	∅	∅	NOUN
ejpam-4283	211	4	,	,	PUNCT
ejpam-4283	211	5	{	{	PUNCT
ejpam-4283	211	6	p	p	X
ejpam-4283	211	7	,	,	PUNCT
ejpam-4283	211	8	q	q	NOUN
ejpam-4283	211	9	}	}	PUNCT
ejpam-4283	211	10	,	,	PUNCT
ejpam-4283	211	11	{	{	PUNCT
ejpam-4283	211	12	q	q	X
ejpam-4283	211	13	,	,	PUNCT
ejpam-4283	211	14	r	r	NOUN
ejpam-4283	211	15	}	}	PUNCT
ejpam-4283	211	16	,	,	PUNCT
ejpam-4283	211	17	{	{	PUNCT
ejpam-4283	211	18	p	p	X
ejpam-4283	211	19	,	,	PUNCT
ejpam-4283	211	20	q	q	ADJ
ejpam-4283	211	21	,	,	PUNCT
ejpam-4283	211	22	r	r	NOUN
ejpam-4283	211	23	}	}	PUNCT
ejpam-4283	211	24	,	,	PUNCT
ejpam-4283	211	25	{	{	PUNCT
ejpam-4283	211	26	p	p	X
ejpam-4283	211	27	,	,	PUNCT
ejpam-4283	211	28	q	q	X
ejpam-4283	211	29	,	,	PUNCT
ejpam-4283	211	30	s	s	PART
ejpam-4283	211	31	}	}	PUNCT
ejpam-4283	211	32	,	,	PUNCT
ejpam-4283	211	33	{	{	PUNCT
ejpam-4283	211	34	q	q	X
ejpam-4283	211	35	,	,	PUNCT
ejpam-4283	211	36	r	r	NOUN
ejpam-4283	211	37	,	,	PUNCT
ejpam-4283	211	38	s	s	PART
ejpam-4283	211	39	}	}	PUNCT
ejpam-4283	211	40	,	,	PUNCT
ejpam-4283	211	41	x	x	NOUN
ejpam-4283	211	42	}	}	PUNCT
ejpam-4283	211	43	.	.	PUNCT
ejpam-4283	212	1	take	take	VERB
ejpam-4283	212	2	q	q	NOUN
ejpam-4283	212	3	=	=	PUNCT
ejpam-4283	212	4	{	{	PUNCT
ejpam-4283	212	5	r	r	NOUN
ejpam-4283	212	6	,	,	PUNCT
ejpam-4283	212	7	s	s	PART
ejpam-4283	212	8	}	}	PUNCT
ejpam-4283	212	9	.	.	PUNCT
ejpam-4283	213	1	then	then	ADV
ejpam-4283	213	2	i1(c1(q	i1(c1(q	PUNCT
ejpam-4283	213	3	)	)	PUNCT
ejpam-4283	213	4	)	)	PUNCT
ejpam-4283	214	1	=	=	PUNCT
ejpam-4283	214	2	i1(q	i1(q	X
ejpam-4283	214	3	)	)	PUNCT
ejpam-4283	214	4	=	=	NOUN
ejpam-4283	214	5	∅	∅	NOUN
ejpam-4283	214	6	so	so	SCONJ
ejpam-4283	214	7	that	that	PRON
ejpam-4283	214	8	q	q	NOUN
ejpam-4283	214	9	is	be	AUX
ejpam-4283	214	10	a	a	DET
ejpam-4283	214	11	µ1	µ1	NOUN
ejpam-4283	214	12	-	-	PUNCT
ejpam-4283	214	13	nowhere	nowhere	ADV
ejpam-4283	214	14	dense	dense	ADJ
ejpam-4283	214	15	set	set	NOUN
ejpam-4283	214	16	in	in	ADP
ejpam-4283	214	17	x.	x.	NOUN
ejpam-4283	214	18	but	but	CCONJ
ejpam-4283	214	19	iσ1(c2(q	iσ1(c2(q	PROPN
ejpam-4283	214	20	)	)	PUNCT
ejpam-4283	214	21	)	)	PUNCT
ejpam-4283	215	1	=	=	PUNCT
ejpam-4283	215	2	iσ1(x	iσ1(x	ADV
ejpam-4283	215	3	)	)	PUNCT
ejpam-4283	215	4	=	=	SYM
ejpam-4283	215	5	x	x	PUNCT
ejpam-4283	216	1	6=	6=	ADP
ejpam-4283	216	2	∅.	∅.	VERB
ejpam-4283	216	3	hence	hence	ADV
ejpam-4283	216	4	q	q	X
ejpam-4283	216	5	is	be	AUX
ejpam-4283	216	6	not	not	PART
ejpam-4283	216	7	a	a	DET
ejpam-4283	216	8	(	(	PUNCT
ejpam-4283	216	9	2	2	NUM
ejpam-4283	216	10	,	,	PUNCT
ejpam-4283	216	11	1)?-nowhere	1)?-nowhere	NUM
ejpam-4283	216	12	dense	dense	ADJ
ejpam-4283	216	13	set	set	NOUN
ejpam-4283	216	14	in	in	ADP
ejpam-4283	216	15	x.	x.	NOUN
ejpam-4283	216	16	(	(	PUNCT
ejpam-4283	216	17	d	d	NOUN
ejpam-4283	216	18	)	)	PUNCT
ejpam-4283	216	19	.	.	PUNCT
ejpam-4283	217	1	consider	consider	VERB
ejpam-4283	217	2	the	the	DET
ejpam-4283	217	3	bigeneralized	bigeneralized	ADJ
ejpam-4283	217	4	topological	topological	ADJ
ejpam-4283	217	5	space	space	NOUN
ejpam-4283	217	6	(	(	PUNCT
ejpam-4283	217	7	x,µ1	x,µ1	PROPN
ejpam-4283	217	8	,	,	PUNCT
ejpam-4283	217	9	µ2	µ2	PROPN
ejpam-4283	217	10	)	)	PUNCT
ejpam-4283	218	1	where	where	SCONJ
ejpam-4283	218	2	x	x	X
ejpam-4283	218	3	=	=	PRON
ejpam-4283	218	4	{	{	PUNCT
ejpam-4283	218	5	p	p	X
ejpam-4283	218	6	,	,	PUNCT
ejpam-4283	218	7	q	q	ADJ
ejpam-4283	218	8	,	,	PUNCT
ejpam-4283	218	9	r	r	NOUN
ejpam-4283	218	10	,	,	PUNCT
ejpam-4283	218	11	s};µ1	s};µ1	PROPN
ejpam-4283	218	12	=	=	SYM
ejpam-4283	218	13	{	{	PUNCT
ejpam-4283	218	14	∅	∅	NOUN
ejpam-4283	218	15	,	,	PUNCT
ejpam-4283	218	16	{	{	PUNCT
ejpam-4283	218	17	q	q	NOUN
ejpam-4283	218	18	,	,	PUNCT
ejpam-4283	218	19	r	r	NOUN
ejpam-4283	218	20	}	}	PUNCT
ejpam-4283	218	21	,	,	PUNCT
ejpam-4283	218	22	{	{	PUNCT
ejpam-4283	218	23	q	q	X
ejpam-4283	218	24	,	,	PUNCT
ejpam-4283	218	25	s	s	PART
ejpam-4283	218	26	}	}	PUNCT
ejpam-4283	218	27	,	,	PUNCT
ejpam-4283	218	28	{	{	PUNCT
ejpam-4283	218	29	q	q	X
ejpam-4283	218	30	,	,	PUNCT
ejpam-4283	218	31	r	r	NOUN
ejpam-4283	218	32	,	,	PUNCT
ejpam-4283	218	33	s	s	PART
ejpam-4283	218	34	}	}	PUNCT
ejpam-4283	218	35	}	}	PUNCT
ejpam-4283	218	36	and	and	CCONJ
ejpam-4283	218	37	µ2	µ2	PROPN
ejpam-4283	218	38	=	=	PUNCT
ejpam-4283	218	39	{	{	PUNCT
ejpam-4283	218	40	∅	∅	NOUN
ejpam-4283	218	41	,	,	PUNCT
ejpam-4283	218	42	{	{	PUNCT
ejpam-4283	218	43	p	p	X
ejpam-4283	218	44	,	,	PUNCT
ejpam-4283	218	45	q	q	NOUN
ejpam-4283	218	46	}	}	PUNCT
ejpam-4283	218	47	,	,	PUNCT
ejpam-4283	218	48	{	{	PUNCT
ejpam-4283	218	49	q	q	X
ejpam-4283	218	50	,	,	PUNCT
ejpam-4283	218	51	r	r	NOUN
ejpam-4283	218	52	}	}	PUNCT
ejpam-4283	218	53	,	,	PUNCT
ejpam-4283	218	54	{	{	PUNCT
ejpam-4283	218	55	q	q	X
ejpam-4283	218	56	,	,	PUNCT
ejpam-4283	218	57	s	s	PART
ejpam-4283	218	58	}	}	PUNCT
ejpam-4283	218	59	,	,	PUNCT
ejpam-4283	218	60	{	{	PUNCT
ejpam-4283	218	61	p	p	X
ejpam-4283	218	62	,	,	PUNCT
ejpam-4283	218	63	q	q	ADJ
ejpam-4283	218	64	,	,	PUNCT
ejpam-4283	218	65	r	r	NOUN
ejpam-4283	218	66	}	}	PUNCT
ejpam-4283	218	67	,	,	PUNCT
ejpam-4283	218	68	{	{	PUNCT
ejpam-4283	218	69	p	p	X
ejpam-4283	218	70	,	,	PUNCT
ejpam-4283	218	71	q	q	X
ejpam-4283	218	72	,	,	PUNCT
ejpam-4283	218	73	s	s	PART
ejpam-4283	218	74	}	}	PUNCT
ejpam-4283	218	75	,	,	PUNCT
ejpam-4283	218	76	{	{	PUNCT
ejpam-4283	218	77	q	q	X
ejpam-4283	218	78	,	,	PUNCT
ejpam-4283	218	79	r	r	NOUN
ejpam-4283	218	80	,	,	PUNCT
ejpam-4283	218	81	s	s	PART
ejpam-4283	218	82	}	}	PUNCT
ejpam-4283	218	83	,	,	PUNCT
ejpam-4283	218	84	x	x	NOUN
ejpam-4283	218	85	}	}	PUNCT
ejpam-4283	218	86	.	.	PUNCT
ejpam-4283	219	1	here	here	ADV
ejpam-4283	219	2	µ1	µ1	PROPN
ejpam-4283	219	3	⊂	⊂	PROPN
ejpam-4283	219	4	µ2	µ2	PROPN
ejpam-4283	219	5	but	but	CCONJ
ejpam-4283	219	6	µ1	µ1	PROPN
ejpam-4283	219	7	is	be	AUX
ejpam-4283	219	8	not	not	PART
ejpam-4283	219	9	a	a	DET
ejpam-4283	219	10	sgt	sgt	PROPN
ejpam-4283	219	11	.	.	PUNCT
ejpam-4283	220	1	now	now	ADV
ejpam-4283	220	2	σ1	σ1	PROPN
ejpam-4283	221	1	=	=	SYM
ejpam-4283	221	2	{	{	PUNCT
ejpam-4283	221	3	∅	∅	NOUN
ejpam-4283	221	4	,	,	PUNCT
ejpam-4283	221	5	{	{	PUNCT
ejpam-4283	221	6	p	p	X
ejpam-4283	221	7	}	}	PUNCT
ejpam-4283	221	8	,	,	PUNCT
ejpam-4283	221	9	{	{	PUNCT
ejpam-4283	221	10	q	q	X
ejpam-4283	221	11	,	,	PUNCT
ejpam-4283	221	12	r	r	NOUN
ejpam-4283	221	13	}	}	PUNCT
ejpam-4283	221	14	,	,	PUNCT
ejpam-4283	221	15	{	{	PUNCT
ejpam-4283	221	16	q	q	X
ejpam-4283	221	17	,	,	PUNCT
ejpam-4283	221	18	s	s	PART
ejpam-4283	221	19	}	}	PUNCT
ejpam-4283	221	20	,	,	PUNCT
ejpam-4283	221	21	{	{	PUNCT
ejpam-4283	221	22	q	q	X
ejpam-4283	221	23	,	,	PUNCT
ejpam-4283	221	24	r	r	NOUN
ejpam-4283	221	25	,	,	PUNCT
ejpam-4283	221	26	s	s	PART
ejpam-4283	221	27	}	}	PUNCT
ejpam-4283	221	28	,	,	PUNCT
ejpam-4283	221	29	{	{	PUNCT
ejpam-4283	221	30	p	p	X
ejpam-4283	221	31	,	,	PUNCT
ejpam-4283	221	32	q	q	ADJ
ejpam-4283	221	33	,	,	PUNCT
ejpam-4283	221	34	r	r	NOUN
ejpam-4283	221	35	}	}	PUNCT
ejpam-4283	221	36	,	,	PUNCT
ejpam-4283	221	37	{	{	PUNCT
ejpam-4283	221	38	p	p	X
ejpam-4283	221	39	,	,	PUNCT
ejpam-4283	221	40	q	q	X
ejpam-4283	221	41	,	,	PUNCT
ejpam-4283	221	42	s	s	PART
ejpam-4283	221	43	}	}	PUNCT
ejpam-4283	221	44	,	,	PUNCT
ejpam-4283	221	45	x	x	NOUN
ejpam-4283	221	46	}	}	PUNCT
ejpam-4283	221	47	.	.	PUNCT
ejpam-4283	222	1	let	let	VERB
ejpam-4283	222	2	k	k	NOUN
ejpam-4283	222	3	=	=	PUNCT
ejpam-4283	222	4	{	{	PUNCT
ejpam-4283	222	5	p	p	X
ejpam-4283	222	6	,	,	PUNCT
ejpam-4283	222	7	r	r	NOUN
ejpam-4283	222	8	}	}	PUNCT
ejpam-4283	222	9	.	.	PUNCT
ejpam-4283	223	1	then	then	ADV
ejpam-4283	223	2	i1(c1(k	i1(c1(k	NOUN
ejpam-4283	223	3	)	)	PUNCT
ejpam-4283	223	4	)	)	PUNCT
ejpam-4283	224	1	=	=	PUNCT
ejpam-4283	224	2	i1(k	i1(k	NOUN
ejpam-4283	224	3	)	)	PUNCT
ejpam-4283	224	4	=	=	NOUN
ejpam-4283	224	5	∅	∅	NOUN
ejpam-4283	224	6	so	so	SCONJ
ejpam-4283	224	7	that	that	SCONJ
ejpam-4283	224	8	k	k	PROPN
ejpam-4283	224	9	is	be	AUX
ejpam-4283	224	10	a	a	DET
ejpam-4283	224	11	µ1	µ1	NOUN
ejpam-4283	224	12	-	-	PUNCT
ejpam-4283	224	13	nowhere	nowhere	ADV
ejpam-4283	224	14	dense	dense	ADJ
ejpam-4283	224	15	set	set	NOUN
ejpam-4283	224	16	in	in	ADP
ejpam-4283	224	17	x.	x.	NOUN
ejpam-4283	224	18	but	but	CCONJ
ejpam-4283	224	19	iσ1(c2(k	iσ1(c2(k	PROPN
ejpam-4283	224	20	)	)	PUNCT
ejpam-4283	224	21	)	)	PUNCT
ejpam-4283	225	1	=	=	SYM
ejpam-4283	225	2	iσ1(k	iσ1(k	PROPN
ejpam-4283	225	3	)	)	PUNCT
ejpam-4283	225	4	=	=	PRON
ejpam-4283	225	5	{	{	PUNCT
ejpam-4283	225	6	p	p	X
ejpam-4283	225	7	}	}	PUNCT
ejpam-4283	225	8	6=	6=	ADP
ejpam-4283	225	9	∅.	∅.	VERB
ejpam-4283	225	10	hence	hence	ADV
ejpam-4283	225	11	k	k	PROPN
ejpam-4283	225	12	is	be	AUX
ejpam-4283	225	13	not	not	PART
ejpam-4283	225	14	a	a	DET
ejpam-4283	225	15	(	(	PUNCT
ejpam-4283	225	16	2	2	NUM
ejpam-4283	225	17	,	,	PUNCT
ejpam-4283	225	18	1)?-nowhere	1)?-nowhere	NUM
ejpam-4283	225	19	dense	dense	ADJ
ejpam-4283	225	20	set	set	NOUN
ejpam-4283	225	21	in	in	ADP
ejpam-4283	225	22	x.	x.	NOUN
ejpam-4283	225	23	4	4	NUM
ejpam-4283	225	24	.	.	PUNCT
ejpam-4283	226	1	(	(	PUNCT
ejpam-4283	226	2	s	s	NOUN
ejpam-4283	226	3	,	,	PUNCT
ejpam-4283	226	4	v)-strongly	v)-strongly	ADV
ejpam-4283	226	5	nowhere	nowhere	ADV
ejpam-4283	226	6	dense	dense	ADJ
ejpam-4283	226	7	sets	set	NOUN
ejpam-4283	226	8	in	in	ADP
ejpam-4283	226	9	this	this	DET
ejpam-4283	226	10	section	section	NOUN
ejpam-4283	226	11	,	,	PUNCT
ejpam-4283	226	12	we	we	PRON
ejpam-4283	226	13	define	define	VERB
ejpam-4283	226	14	a	a	DET
ejpam-4283	226	15	set	set	NOUN
ejpam-4283	226	16	namely	namely	ADV
ejpam-4283	226	17	,	,	PUNCT
ejpam-4283	226	18	(	(	PUNCT
ejpam-4283	226	19	s	s	X
ejpam-4283	226	20	,	,	PUNCT
ejpam-4283	226	21	v)-strongly	v)-strongly	ADV
ejpam-4283	226	22	nowhere	nowhere	ADV
ejpam-4283	226	23	dense	dense	ADJ
ejpam-4283	226	24	set	set	NOUN
ejpam-4283	226	25	and	and	CCONJ
ejpam-4283	226	26	give	give	VERB
ejpam-4283	226	27	some	some	PRON
ejpam-4283	226	28	of	of	ADP
ejpam-4283	226	29	its	its	PRON
ejpam-4283	226	30	properties	property	NOUN
ejpam-4283	226	31	in	in	ADP
ejpam-4283	226	32	a	a	DET
ejpam-4283	226	33	bgts	bgts	NOUN
ejpam-4283	226	34	(	(	PUNCT
ejpam-4283	226	35	x,µ1	x,µ1	PROPN
ejpam-4283	226	36	,	,	PUNCT
ejpam-4283	226	37	µ2	µ2	PROPN
ejpam-4283	226	38	)	)	PUNCT
ejpam-4283	226	39	.	.	PUNCT
ejpam-4283	227	1	let	let	VERB
ejpam-4283	227	2	q	q	PRON
ejpam-4283	227	3	be	be	AUX
ejpam-4283	227	4	a	a	DET
ejpam-4283	227	5	subset	subset	NOUN
ejpam-4283	227	6	of	of	ADP
ejpam-4283	227	7	a	a	DET
ejpam-4283	227	8	gts	gts	NOUN
ejpam-4283	227	9	(	(	PUNCT
ejpam-4283	227	10	x,µ	x,µ	NOUN
ejpam-4283	227	11	)	)	PUNCT
ejpam-4283	227	12	.	.	PUNCT
ejpam-4283	228	1	then	then	ADV
ejpam-4283	228	2	q	q	X
ejpam-4283	228	3	is	be	AUX
ejpam-4283	228	4	called	call	VERB
ejpam-4283	228	5	µ-strongly	µ-strongly	ADV
ejpam-4283	228	6	nowhere	nowhere	ADV
ejpam-4283	228	7	dense	dense	ADJ
ejpam-4283	228	8	[	[	X
ejpam-4283	228	9	7	7	NUM
ejpam-4283	228	10	]	]	PUNCT
ejpam-4283	228	11	set	set	VERB
ejpam-4283	228	12	if	if	SCONJ
ejpam-4283	228	13	for	for	ADP
ejpam-4283	228	14	every	every	DET
ejpam-4283	228	15	k	k	PROPN
ejpam-4283	228	16	∈	∈	PROPN
ejpam-4283	228	17	µ̃	µ̃	PROPN
ejpam-4283	228	18	,	,	PUNCT
ejpam-4283	228	19	there	there	PRON
ejpam-4283	228	20	is	be	VERB
ejpam-4283	228	21	p	p	PROPN
ejpam-4283	228	22	∈	∈	PROPN
ejpam-4283	228	23	µ̃	µ̃	PROPN
ejpam-4283	228	24	such	such	ADJ
ejpam-4283	228	25	that	that	SCONJ
ejpam-4283	228	26	p	p	PROPN
ejpam-4283	228	27	⊂	⊂	PROPN
ejpam-4283	228	28	k	k	PROPN
ejpam-4283	228	29	and	and	CCONJ
ejpam-4283	228	30	p	p	PRON
ejpam-4283	228	31	∩q	∩q	PROPN
ejpam-4283	228	32	=	=	PUNCT
ejpam-4283	228	33	∅.	∅.	VERB
ejpam-4283	228	34	a	a	DET
ejpam-4283	228	35	generalized	generalized	ADJ
ejpam-4283	228	36	topology	topology	NOUN
ejpam-4283	228	37	µ	µ	X
ejpam-4283	228	38	on	on	ADV
ejpam-4283	228	39	x	x	AUX
ejpam-4283	228	40	is	be	AUX
ejpam-4283	228	41	said	say	VERB
ejpam-4283	228	42	to	to	PART
ejpam-4283	228	43	satisfy	satisfy	VERB
ejpam-4283	228	44	the	the	DET
ejpam-4283	228	45	i	i	NOUN
ejpam-4283	228	46	-	-	PUNCT
ejpam-4283	228	47	property	property	NOUN
ejpam-4283	229	1	[	[	X
ejpam-4283	229	2	9	9	NUM
ejpam-4283	229	3	]	]	X
ejpam-4283	229	4	whenever	whenever	SCONJ
ejpam-4283	229	5	w1,w2	w1,w2	PROPN
ejpam-4283	229	6	,	,	PUNCT
ejpam-4283	229	7	.	.	PUNCT
ejpam-4283	229	8	.	.	PUNCT
ejpam-4283	229	9	.	.	PUNCT
ejpam-4283	230	1	,	,	PUNCT
ejpam-4283	230	2	wn	wn	PROPN
ejpam-4283	230	3	∈	∈	PROPN
ejpam-4283	230	4	µ	µ	X
ejpam-4283	230	5	with	with	ADP
ejpam-4283	230	6	w1	w1	NOUN
ejpam-4283	230	7	∩w2	∩w2	PROPN
ejpam-4283	230	8	∩	∩	X
ejpam-4283	230	9	·	·	PUNCT
ejpam-4283	230	10	·	·	PUNCT
ejpam-4283	230	11	·	·	PUNCT
ejpam-4283	231	1	∩wn	∩wn	NOUN
ejpam-4283	231	2	6=	6=	NOUN
ejpam-4283	231	3	∅	∅	NOUN
ejpam-4283	231	4	,	,	PUNCT
ejpam-4283	231	5	iµ(w1	iµ(w1	NOUN
ejpam-4283	231	6	∩w2	∩w2	X
ejpam-4283	231	7	∩	∩	X
ejpam-4283	231	8	·	·	PUNCT
ejpam-4283	231	9	·	·	PUNCT
ejpam-4283	231	10	·	·	PUNCT
ejpam-4283	231	11	∩wn	∩wn	NOUN
ejpam-4283	231	12	)	)	PUNCT
ejpam-4283	231	13	6=	6=	ADP
ejpam-4283	231	14	∅.	∅.	ADP
ejpam-4283	231	15	a	a	DET
ejpam-4283	231	16	gts	gts	NOUN
ejpam-4283	231	17	(	(	PUNCT
ejpam-4283	231	18	x,µ	x,µ	NOUN
ejpam-4283	231	19	)	)	PUNCT
ejpam-4283	231	20	is	be	AUX
ejpam-4283	231	21	called	call	VERB
ejpam-4283	231	22	as	as	ADP
ejpam-4283	231	23	a	a	DET
ejpam-4283	231	24	hyperconnected	hyperconnecte	VERB
ejpam-4283	231	25	space	space	NOUN
ejpam-4283	232	1	[	[	X
ejpam-4283	232	2	6	6	NUM
ejpam-4283	232	3	]	]	X
ejpam-4283	232	4	if	if	SCONJ
ejpam-4283	232	5	cµ(q	cµ(q	NOUN
ejpam-4283	232	6	)	)	PUNCT
ejpam-4283	232	7	=	=	SYM
ejpam-4283	233	1	x	x	PUNCT
ejpam-4283	233	2	for	for	ADP
ejpam-4283	233	3	each	each	DET
ejpam-4283	233	4	q	q	PROPN
ejpam-4283	233	5	∈	∈	PROPN
ejpam-4283	233	6	µ̃.	µ̃.	ADJ
ejpam-4283	233	7	definition	definition	NOUN
ejpam-4283	233	8	12	12	NUM
ejpam-4283	233	9	.	.	PUNCT
ejpam-4283	234	1	let	let	VERB
ejpam-4283	234	2	b	b	X
ejpam-4283	234	3	be	be	AUX
ejpam-4283	234	4	a	a	DET
ejpam-4283	234	5	non	non	ADJ
ejpam-4283	234	6	-	-	ADJ
ejpam-4283	234	7	null	null	ADJ
ejpam-4283	234	8	subset	subset	NOUN
ejpam-4283	234	9	of	of	ADP
ejpam-4283	234	10	a	a	DET
ejpam-4283	234	11	bigeneralized	bigeneralize	VERB
ejpam-4283	234	12	topological	topological	ADJ
ejpam-4283	234	13	space	space	NOUN
ejpam-4283	234	14	(	(	PUNCT
ejpam-4283	234	15	x,µ1	x,µ1	PROPN
ejpam-4283	234	16	,	,	PUNCT
ejpam-4283	234	17	µ2	µ2	PROPN
ejpam-4283	234	18	)	)	PUNCT
ejpam-4283	234	19	.	.	PUNCT
ejpam-4283	235	1	then	then	ADV
ejpam-4283	235	2	b	b	PROPN
ejpam-4283	235	3	is	be	AUX
ejpam-4283	235	4	said	say	VERB
ejpam-4283	235	5	to	to	PART
ejpam-4283	235	6	be	be	AUX
ejpam-4283	235	7	(	(	PUNCT
ejpam-4283	235	8	s	s	X
ejpam-4283	235	9	,	,	PUNCT
ejpam-4283	235	10	v)-strongly	v)-strongly	ADV
ejpam-4283	235	11	nowhere	nowhere	ADV
ejpam-4283	235	12	dense	dense	ADJ
ejpam-4283	235	13	if	if	SCONJ
ejpam-4283	235	14	for	for	SCONJ
ejpam-4283	235	15	every	every	DET
ejpam-4283	235	16	p	p	PROPN
ejpam-4283	235	17	∈	∈	PROPN
ejpam-4283	235	18	µ̃v	µ̃v	VERB
ejpam-4283	235	19	there	there	PRON
ejpam-4283	235	20	is	be	VERB
ejpam-4283	235	21	q	q	PROPN
ejpam-4283	235	22	∈	∈	PROPN
ejpam-4283	235	23	µ̃s	µ̃s	NOUN
ejpam-4283	235	24	such	such	ADJ
ejpam-4283	235	25	that	that	SCONJ
ejpam-4283	235	26	q	q	PROPN
ejpam-4283	235	27	⊂	⊂	X
ejpam-4283	235	28	p	p	NOUN
ejpam-4283	235	29	and	and	CCONJ
ejpam-4283	235	30	q	q	ADJ
ejpam-4283	235	31	∩b	∩b	NOUN
ejpam-4283	235	32	=	=	NOUN
ejpam-4283	235	33	∅	∅	NOUN
ejpam-4283	235	34	where	where	SCONJ
ejpam-4283	235	35	s	s	X
ejpam-4283	235	36	,	,	PUNCT
ejpam-4283	235	37	v	v	NOUN
ejpam-4283	235	38	=	=	SYM
ejpam-4283	235	39	1	1	NUM
ejpam-4283	235	40	,	,	PUNCT
ejpam-4283	235	41	2	2	NUM
ejpam-4283	235	42	;	;	PUNCT
ejpam-4283	235	43	s	s	PROPN
ejpam-4283	235	44	6=	6=	PROPN
ejpam-4283	235	45	v.	v.	ADP
ejpam-4283	235	46	moreover	moreover	ADV
ejpam-4283	235	47	,	,	PUNCT
ejpam-4283	235	48	(	(	PUNCT
ejpam-4283	235	49	s	s	X
ejpam-4283	235	50	,	,	PUNCT
ejpam-4283	235	51	v	v	NOUN
ejpam-4283	235	52	)	)	PUNCT
ejpam-4283	235	53	−	−	PROPN
ejpam-4283	235	54	s(x	s(x	PROPN
ejpam-4283	235	55	)	)	PUNCT
ejpam-4283	235	56	=	=	PRON
ejpam-4283	236	1	{	{	PUNCT
ejpam-4283	236	2	q	q	X
ejpam-4283	236	3	⊂	⊂	X
ejpam-4283	236	4	x	x	PUNCT
ejpam-4283	236	5	|	|	ADV
ejpam-4283	236	6	q	q	NOUN
ejpam-4283	236	7	is	be	AUX
ejpam-4283	236	8	a	a	DET
ejpam-4283	236	9	(	(	PUNCT
ejpam-4283	236	10	s	s	NOUN
ejpam-4283	236	11	,	,	PUNCT
ejpam-4283	236	12	v)-strongly	v)-strongly	ADV
ejpam-4283	236	13	nowhere	nowhere	ADV
ejpam-4283	236	14	dense	dense	ADJ
ejpam-4283	236	15	set	set	NOUN
ejpam-4283	236	16	in	in	ADP
ejpam-4283	236	17	x	x	NOUN
ejpam-4283	236	18	}	}	PUNCT
ejpam-4283	236	19	where	where	SCONJ
ejpam-4283	236	20	s	s	X
ejpam-4283	236	21	,	,	PUNCT
ejpam-4283	236	22	v	v	NOUN
ejpam-4283	236	23	=	=	SYM
ejpam-4283	236	24	1	1	NUM
ejpam-4283	236	25	,	,	PUNCT
ejpam-4283	236	26	2	2	NUM
ejpam-4283	236	27	;	;	PUNCT
ejpam-4283	236	28	s	s	PROPN
ejpam-4283	236	29	6=	6=	PROPN
ejpam-4283	236	30	v.	v.	ADP
ejpam-4283	236	31	in	in	ADP
ejpam-4283	236	32	a	a	DET
ejpam-4283	236	33	bigeneralized	bigeneralize	VERB
ejpam-4283	236	34	topological	topological	ADJ
ejpam-4283	236	35	space	space	NOUN
ejpam-4283	236	36	,	,	PUNCT
ejpam-4283	236	37	if	if	SCONJ
ejpam-4283	236	38	p	p	X
ejpam-4283	236	39	∈	∈	PROPN
ejpam-4283	236	40	(	(	PUNCT
ejpam-4283	236	41	s	s	PROPN
ejpam-4283	236	42	,	,	PUNCT
ejpam-4283	236	43	v	v	NOUN
ejpam-4283	236	44	)	)	PUNCT
ejpam-4283	236	45	−	−	PROPN
ejpam-4283	236	46	s(x	s(x	PROPN
ejpam-4283	236	47	)	)	PUNCT
ejpam-4283	236	48	and	and	CCONJ
ejpam-4283	236	49	q	q	PROPN
ejpam-4283	236	50	⊂	⊂	PROPN
ejpam-4283	236	51	p	p	X
ejpam-4283	236	52	,	,	PUNCT
ejpam-4283	236	53	then	then	ADV
ejpam-4283	236	54	q	q	PROPN
ejpam-4283	236	55	∈	∈	PROPN
ejpam-4283	236	56	(	(	PUNCT
ejpam-4283	236	57	s	s	PROPN
ejpam-4283	236	58	,	,	PUNCT
ejpam-4283	236	59	v	v	NOUN
ejpam-4283	236	60	)	)	PUNCT
ejpam-4283	236	61	−	−	PROPN
ejpam-4283	236	62	s(x	s(x	PROPN
ejpam-4283	236	63	)	)	PUNCT
ejpam-4283	236	64	where	where	SCONJ
ejpam-4283	236	65	s	s	X
ejpam-4283	236	66	,	,	PUNCT
ejpam-4283	236	67	v	v	NOUN
ejpam-4283	236	68	=	=	SYM
ejpam-4283	236	69	1	1	NUM
ejpam-4283	236	70	,	,	PUNCT
ejpam-4283	236	71	2	2	NUM
ejpam-4283	236	72	and	and	CCONJ
ejpam-4283	236	73	s	s	X
ejpam-4283	236	74	6=	6=	PROPN
ejpam-4283	236	75	v.	v.	ADP
ejpam-4283	236	76	moreover	moreover	ADV
ejpam-4283	236	77	,	,	PUNCT
ejpam-4283	236	78	every	every	DET
ejpam-4283	236	79	non	non	ADJ
ejpam-4283	236	80	-	-	ADJ
ejpam-4283	236	81	null	null	ADJ
ejpam-4283	236	82	µv	µv	NOUN
ejpam-4283	236	83	-	-	PUNCT
ejpam-4283	236	84	open	open	ADJ
ejpam-4283	236	85	set	set	NOUN
ejpam-4283	236	86	is	be	AUX
ejpam-4283	236	87	need	need	AUX
ejpam-4283	236	88	not	not	PART
ejpam-4283	236	89	be	be	AUX
ejpam-4283	236	90	a	a	DET
ejpam-4283	236	91	(	(	PUNCT
ejpam-4283	236	92	s	s	NOUN
ejpam-4283	236	93	,	,	PUNCT
ejpam-4283	236	94	v)-strongly	v)-strongly	ADV
ejpam-4283	236	95	nowhere	nowhere	ADV
ejpam-4283	236	96	dense	dense	ADJ
ejpam-4283	236	97	set	set	NOUN
ejpam-4283	236	98	in	in	ADP
ejpam-4283	236	99	x	x	PUNCT
ejpam-4283	236	100	where	where	SCONJ
ejpam-4283	236	101	s	s	X
ejpam-4283	236	102	,	,	PUNCT
ejpam-4283	236	103	v	v	NOUN
ejpam-4283	236	104	=	=	SYM
ejpam-4283	236	105	1	1	NUM
ejpam-4283	236	106	,	,	PUNCT
ejpam-4283	236	107	2	2	NUM
ejpam-4283	236	108	;	;	PUNCT
ejpam-4283	236	109	s	s	PROPN
ejpam-4283	236	110	6=	6=	PROPN
ejpam-4283	236	111	v.	v.	ADP
ejpam-4283	236	112	example	example	NOUN
ejpam-4283	236	113	13	13	NUM
ejpam-4283	236	114	.	.	PUNCT
ejpam-4283	237	1	(	(	PUNCT
ejpam-4283	237	2	a	a	X
ejpam-4283	237	3	)	)	PUNCT
ejpam-4283	237	4	.	.	PUNCT
ejpam-4283	238	1	consider	consider	VERB
ejpam-4283	238	2	the	the	DET
ejpam-4283	238	3	bigeneralized	bigeneralized	ADJ
ejpam-4283	238	4	topological	topological	ADJ
ejpam-4283	238	5	space	space	NOUN
ejpam-4283	238	6	(	(	PUNCT
ejpam-4283	238	7	x,µ1	x,µ1	PROPN
ejpam-4283	238	8	,	,	PUNCT
ejpam-4283	238	9	µ2	µ2	PROPN
ejpam-4283	238	10	)	)	PUNCT
ejpam-4283	239	1	where	where	SCONJ
ejpam-4283	239	2	x	x	X
ejpam-4283	239	3	=	=	PRON
ejpam-4283	239	4	{	{	PUNCT
ejpam-4283	239	5	p	p	X
ejpam-4283	239	6	,	,	PUNCT
ejpam-4283	239	7	q	q	ADJ
ejpam-4283	239	8	,	,	PUNCT
ejpam-4283	239	9	r	r	NOUN
ejpam-4283	239	10	,	,	PUNCT
ejpam-4283	239	11	s};µ1	s};µ1	PROPN
ejpam-4283	239	12	=	=	SYM
ejpam-4283	239	13	{	{	PUNCT
ejpam-4283	239	14	∅	∅	NOUN
ejpam-4283	239	15	,	,	PUNCT
ejpam-4283	239	16	{	{	PUNCT
ejpam-4283	239	17	p	p	X
ejpam-4283	239	18	,	,	PUNCT
ejpam-4283	239	19	q	q	NOUN
ejpam-4283	239	20	}	}	PUNCT
ejpam-4283	239	21	,	,	PUNCT
ejpam-4283	239	22	{	{	PUNCT
ejpam-4283	239	23	q	q	X
ejpam-4283	239	24	,	,	PUNCT
ejpam-4283	239	25	r	r	NOUN
ejpam-4283	239	26	}	}	PUNCT
ejpam-4283	239	27	,	,	PUNCT
ejpam-4283	239	28	{	{	PUNCT
ejpam-4283	239	29	p	p	X
ejpam-4283	239	30	,	,	PUNCT
ejpam-4283	239	31	q	q	ADJ
ejpam-4283	239	32	,	,	PUNCT
ejpam-4283	239	33	r	r	NOUN
ejpam-4283	239	34	}	}	PUNCT
ejpam-4283	239	35	}	}	PUNCT
ejpam-4283	239	36	and	and	CCONJ
ejpam-4283	239	37	µ2	µ2	PROPN
ejpam-4283	239	38	=	=	PUNCT
ejpam-4283	239	39	{	{	PUNCT
ejpam-4283	239	40	∅	∅	NOUN
ejpam-4283	239	41	,	,	PUNCT
ejpam-4283	239	42	{	{	PUNCT
ejpam-4283	239	43	p	p	X
ejpam-4283	239	44	,	,	PUNCT
ejpam-4283	239	45	q	q	ADJ
ejpam-4283	239	46	,	,	PUNCT
ejpam-4283	239	47	r	r	NOUN
ejpam-4283	239	48	}	}	PUNCT
ejpam-4283	239	49	,	,	PUNCT
ejpam-4283	239	50	{	{	PUNCT
ejpam-4283	239	51	p	p	X
ejpam-4283	239	52	,	,	PUNCT
ejpam-4283	239	53	q	q	X
ejpam-4283	239	54	,	,	PUNCT
ejpam-4283	239	55	s	s	PART
ejpam-4283	239	56	}	}	PUNCT
ejpam-4283	239	57	,	,	PUNCT
ejpam-4283	239	58	{	{	PUNCT
ejpam-4283	239	59	q	q	X
ejpam-4283	239	60	,	,	PUNCT
ejpam-4283	239	61	r	r	NOUN
ejpam-4283	239	62	,	,	PUNCT
ejpam-4283	239	63	s	s	PART
ejpam-4283	239	64	}	}	PUNCT
ejpam-4283	239	65	,	,	PUNCT
ejpam-4283	239	66	x	x	NOUN
ejpam-4283	239	67	}	}	PUNCT
ejpam-4283	239	68	.	.	PUNCT
ejpam-4283	240	1	let	let	VERB
ejpam-4283	240	2	p	p	NOUN
ejpam-4283	240	3	=	=	X
ejpam-4283	240	4	{	{	PUNCT
ejpam-4283	240	5	s	s	NOUN
ejpam-4283	240	6	}	}	PUNCT
ejpam-4283	240	7	.	.	PUNCT
ejpam-4283	241	1	then	then	ADV
ejpam-4283	241	2	p	p	PROPN
ejpam-4283	241	3	∈	∈	PROPN
ejpam-4283	241	4	(	(	PUNCT
ejpam-4283	241	5	1	1	NUM
ejpam-4283	241	6	,	,	PUNCT
ejpam-4283	241	7	2)−s(x	2)−s(x	NUM
ejpam-4283	241	8	)	)	PUNCT
ejpam-4283	241	9	.	.	PUNCT
ejpam-4283	242	1	p.	p.	NOUN
ejpam-4283	242	2	yupapin	yupapin	NOUN
ejpam-4283	242	3	,	,	PUNCT
ejpam-4283	242	4	v.	v.	CCONJ
ejpam-4283	242	5	subramanian	subramanian	PROPN
ejpam-4283	242	6	,	,	PUNCT
ejpam-4283	242	7	y.	y.	PROPN
ejpam-4283	242	8	farhat	farhat	PROPN
ejpam-4283	242	9	/	/	SYM
ejpam-4283	242	10	eur	eur	PROPN
ejpam-4283	242	11	.	.	PUNCT
ejpam-4283	243	1	j.	j.	PROPN
ejpam-4283	243	2	pure	pure	PROPN
ejpam-4283	243	3	appl	appl	PROPN
ejpam-4283	243	4	.	.	PROPN
ejpam-4283	243	5	math	math	PROPN
ejpam-4283	243	6	,	,	PUNCT
ejpam-4283	243	7	15	15	NUM
ejpam-4283	243	8	(	(	PUNCT
ejpam-4283	243	9	2	2	NUM
ejpam-4283	243	10	)	)	PUNCT
ejpam-4283	243	11	(	(	PUNCT
ejpam-4283	243	12	2022	2022	NUM
ejpam-4283	243	13	)	)	PUNCT
ejpam-4283	243	14	,	,	PUNCT
ejpam-4283	243	15	403	403	NUM
ejpam-4283	243	16	-	-	SYM
ejpam-4283	243	17	414	414	NUM
ejpam-4283	243	18	408	408	NUM
ejpam-4283	243	19	(	(	PUNCT
ejpam-4283	243	20	b	b	NOUN
ejpam-4283	243	21	)	)	PUNCT
ejpam-4283	243	22	.	.	PUNCT
ejpam-4283	244	1	consider	consider	VERB
ejpam-4283	244	2	the	the	DET
ejpam-4283	244	3	bigeneralized	bigeneralized	ADJ
ejpam-4283	244	4	topological	topological	ADJ
ejpam-4283	244	5	space	space	NOUN
ejpam-4283	244	6	(	(	PUNCT
ejpam-4283	244	7	x,µ1	x,µ1	PROPN
ejpam-4283	244	8	,	,	PUNCT
ejpam-4283	244	9	µ2	µ2	PROPN
ejpam-4283	244	10	)	)	PUNCT
ejpam-4283	244	11	where	where	SCONJ
ejpam-4283	244	12	x	x	X
ejpam-4283	244	13	=	=	PRON
ejpam-4283	244	14	{	{	PUNCT
ejpam-4283	244	15	p	p	X
ejpam-4283	244	16	,	,	PUNCT
ejpam-4283	244	17	q	q	ADJ
ejpam-4283	244	18	,	,	PUNCT
ejpam-4283	244	19	r	r	NOUN
ejpam-4283	244	20	,	,	PUNCT
ejpam-4283	244	21	s	s	PART
ejpam-4283	244	22	}	}	PUNCT
ejpam-4283	244	23	;	;	PUNCT
ejpam-4283	244	24	µ1	µ1	PROPN
ejpam-4283	244	25	=	=	SYM
ejpam-4283	244	26	{	{	PUNCT
ejpam-4283	244	27	∅	∅	NOUN
ejpam-4283	244	28	,	,	PUNCT
ejpam-4283	244	29	{	{	PUNCT
ejpam-4283	244	30	p	p	X
ejpam-4283	244	31	,	,	PUNCT
ejpam-4283	244	32	q	q	NOUN
ejpam-4283	244	33	}	}	PUNCT
ejpam-4283	244	34	,	,	PUNCT
ejpam-4283	244	35	{	{	PUNCT
ejpam-4283	244	36	p	p	X
ejpam-4283	244	37	,	,	PUNCT
ejpam-4283	244	38	r	r	NOUN
ejpam-4283	244	39	}	}	PUNCT
ejpam-4283	244	40	,	,	PUNCT
ejpam-4283	244	41	{	{	PUNCT
ejpam-4283	244	42	p	p	X
ejpam-4283	244	43	,	,	PUNCT
ejpam-4283	244	44	q	q	ADJ
ejpam-4283	244	45	,	,	PUNCT
ejpam-4283	244	46	r	r	NOUN
ejpam-4283	244	47	}	}	PUNCT
ejpam-4283	244	48	}	}	PUNCT
ejpam-4283	244	49	and	and	CCONJ
ejpam-4283	244	50	µ2	µ2	PROPN
ejpam-4283	244	51	=	=	PUNCT
ejpam-4283	244	52	{	{	PUNCT
ejpam-4283	244	53	∅	∅	NOUN
ejpam-4283	244	54	,	,	PUNCT
ejpam-4283	244	55	{	{	PUNCT
ejpam-4283	244	56	p	p	X
ejpam-4283	244	57	}	}	PUNCT
ejpam-4283	244	58	,	,	PUNCT
ejpam-4283	244	59	{	{	PUNCT
ejpam-4283	244	60	q	q	X
ejpam-4283	244	61	,	,	PUNCT
ejpam-4283	244	62	r	r	NOUN
ejpam-4283	244	63	}	}	PUNCT
ejpam-4283	244	64	,	,	PUNCT
ejpam-4283	244	65	{	{	PUNCT
ejpam-4283	244	66	q	q	X
ejpam-4283	244	67	,	,	PUNCT
ejpam-4283	244	68	s	s	PART
ejpam-4283	244	69	}	}	PUNCT
ejpam-4283	244	70	,	,	PUNCT
ejpam-4283	244	71	{	{	PUNCT
ejpam-4283	244	72	p	p	X
ejpam-4283	244	73	,	,	PUNCT
ejpam-4283	244	74	q	q	ADJ
ejpam-4283	244	75	,	,	PUNCT
ejpam-4283	244	76	r	r	NOUN
ejpam-4283	244	77	}	}	PUNCT
ejpam-4283	244	78	,	,	PUNCT
ejpam-4283	244	79	{	{	PUNCT
ejpam-4283	244	80	p	p	X
ejpam-4283	244	81	,	,	PUNCT
ejpam-4283	244	82	q	q	X
ejpam-4283	244	83	,	,	PUNCT
ejpam-4283	244	84	s	s	PART
ejpam-4283	244	85	}	}	PUNCT
ejpam-4283	244	86	,	,	PUNCT
ejpam-4283	244	87	{	{	PUNCT
ejpam-4283	244	88	q	q	X
ejpam-4283	244	89	,	,	PUNCT
ejpam-4283	244	90	r	r	NOUN
ejpam-4283	244	91	,	,	PUNCT
ejpam-4283	244	92	s	s	PART
ejpam-4283	244	93	}	}	PUNCT
ejpam-4283	244	94	,	,	PUNCT
ejpam-4283	244	95	x	x	NOUN
ejpam-4283	244	96	}	}	PUNCT
ejpam-4283	244	97	.	.	PUNCT
ejpam-4283	245	1	let	let	VERB
ejpam-4283	245	2	j	j	PROPN
ejpam-4283	245	3	=	=	PUNCT
ejpam-4283	245	4	{	{	PUNCT
ejpam-4283	245	5	q	q	NOUN
ejpam-4283	245	6	,	,	PUNCT
ejpam-4283	245	7	r	r	NOUN
ejpam-4283	245	8	}	}	PUNCT
ejpam-4283	245	9	.	.	PUNCT
ejpam-4283	246	1	then	then	ADV
ejpam-4283	246	2	j	j	PROPN
ejpam-4283	246	3	∈	∈	PROPN
ejpam-4283	246	4	(	(	PUNCT
ejpam-4283	246	5	2	2	NUM
ejpam-4283	246	6	,	,	PUNCT
ejpam-4283	246	7	1)−s(x	1)−s(x	NUM
ejpam-4283	246	8	)	)	PUNCT
ejpam-4283	246	9	.	.	PUNCT
ejpam-4283	247	1	proposition	proposition	NOUN
ejpam-4283	247	2	14	14	NUM
ejpam-4283	247	3	.	.	PUNCT
ejpam-4283	248	1	let	let	AUX
ejpam-4283	248	2	(	(	PUNCT
ejpam-4283	248	3	x,µ1	x,µ1	NOUN
ejpam-4283	248	4	,	,	PUNCT
ejpam-4283	248	5	µ2	µ2	PROPN
ejpam-4283	248	6	)	)	PUNCT
ejpam-4283	248	7	be	be	VERB
ejpam-4283	248	8	a	a	DET
ejpam-4283	248	9	bigeneralized	bigeneralized	ADJ
ejpam-4283	248	10	topological	topological	ADJ
ejpam-4283	248	11	space	space	NOUN
ejpam-4283	248	12	and	and	CCONJ
ejpam-4283	248	13	d	d	PROPN
ejpam-4283	248	14	⊂	⊂	PROPN
ejpam-4283	248	15	x.	x.	NOUN
ejpam-4283	249	1	then	then	ADV
ejpam-4283	249	2	d	d	PROPN
ejpam-4283	249	3	∈	∈	PROPN
ejpam-4283	249	4	(	(	PUNCT
ejpam-4283	249	5	s	s	NOUN
ejpam-4283	249	6	,	,	PUNCT
ejpam-4283	249	7	v)−s(x	v)−s(x	NUM
ejpam-4283	249	8	)	)	PUNCT
ejpam-4283	250	1	if	if	SCONJ
ejpam-4283	250	2	and	and	CCONJ
ejpam-4283	250	3	only	only	ADV
ejpam-4283	250	4	if	if	SCONJ
ejpam-4283	250	5	cs(d	cs(d	PUNCT
ejpam-4283	250	6	)	)	PUNCT
ejpam-4283	250	7	∈	∈	PROPN
ejpam-4283	250	8	(	(	PUNCT
ejpam-4283	250	9	s	s	NOUN
ejpam-4283	250	10	,	,	PUNCT
ejpam-4283	250	11	v)−s(x	v)−s(x	NUM
ejpam-4283	250	12	)	)	PUNCT
ejpam-4283	251	1	where	where	SCONJ
ejpam-4283	251	2	s	s	X
ejpam-4283	251	3	,	,	PUNCT
ejpam-4283	251	4	v	v	NOUN
ejpam-4283	251	5	=	=	SYM
ejpam-4283	251	6	1	1	NUM
ejpam-4283	251	7	,	,	PUNCT
ejpam-4283	251	8	2	2	NUM
ejpam-4283	251	9	;	;	PUNCT
ejpam-4283	251	10	s	s	PROPN
ejpam-4283	251	11	6=	6=	PROPN
ejpam-4283	251	12	v.	v.	ADP
ejpam-4283	251	13	example	example	NOUN
ejpam-4283	251	14	15	15	NUM
ejpam-4283	251	15	shows	show	VERB
ejpam-4283	251	16	that	that	SCONJ
ejpam-4283	251	17	the	the	DET
ejpam-4283	251	18	collection	collection	NOUN
ejpam-4283	251	19	(	(	PUNCT
ejpam-4283	251	20	s	s	NOUN
ejpam-4283	251	21	,	,	PUNCT
ejpam-4283	251	22	v)−s(x	v)−s(x	NUM
ejpam-4283	251	23	)	)	PUNCT
ejpam-4283	251	24	is	be	AUX
ejpam-4283	251	25	need	need	AUX
ejpam-4283	251	26	not	not	PART
ejpam-4283	251	27	be	be	AUX
ejpam-4283	251	28	closed	close	VERB
ejpam-4283	251	29	under	under	ADP
ejpam-4283	251	30	finite	finite	ADJ
ejpam-4283	251	31	union	union	NOUN
ejpam-4283	251	32	in	in	ADP
ejpam-4283	251	33	a	a	DET
ejpam-4283	251	34	bgts	bgts	NOUN
ejpam-4283	251	35	(	(	PUNCT
ejpam-4283	251	36	x,µ1	x,µ1	PROPN
ejpam-4283	251	37	,	,	PUNCT
ejpam-4283	251	38	µ2	µ2	PROPN
ejpam-4283	251	39	)	)	PUNCT
ejpam-4283	251	40	where	where	SCONJ
ejpam-4283	251	41	s	s	X
ejpam-4283	251	42	,	,	PUNCT
ejpam-4283	251	43	v	v	NOUN
ejpam-4283	251	44	=	=	SYM
ejpam-4283	251	45	1	1	NUM
ejpam-4283	251	46	,	,	PUNCT
ejpam-4283	251	47	2	2	NUM
ejpam-4283	251	48	and	and	CCONJ
ejpam-4283	251	49	s	s	X
ejpam-4283	251	50	6=	6=	PROPN
ejpam-4283	251	51	v.	v.	ADP
ejpam-4283	251	52	example	example	NOUN
ejpam-4283	251	53	15	15	NUM
ejpam-4283	251	54	.	.	PUNCT
ejpam-4283	252	1	(	(	PUNCT
ejpam-4283	252	2	a	a	X
ejpam-4283	252	3	)	)	PUNCT
ejpam-4283	252	4	.	.	PUNCT
ejpam-4283	253	1	consider	consider	VERB
ejpam-4283	253	2	the	the	DET
ejpam-4283	253	3	bigeneralized	bigeneralized	ADJ
ejpam-4283	253	4	topological	topological	ADJ
ejpam-4283	253	5	space	space	NOUN
ejpam-4283	253	6	(	(	PUNCT
ejpam-4283	253	7	x,µ1	x,µ1	PROPN
ejpam-4283	253	8	,	,	PUNCT
ejpam-4283	253	9	µ2	µ2	PROPN
ejpam-4283	253	10	)	)	PUNCT
ejpam-4283	254	1	where	where	SCONJ
ejpam-4283	254	2	x	x	X
ejpam-4283	254	3	=	=	PRON
ejpam-4283	254	4	{	{	PUNCT
ejpam-4283	254	5	p	p	X
ejpam-4283	254	6	,	,	PUNCT
ejpam-4283	254	7	q	q	ADJ
ejpam-4283	254	8	,	,	PUNCT
ejpam-4283	254	9	r	r	NOUN
ejpam-4283	254	10	,	,	PUNCT
ejpam-4283	254	11	s	s	NOUN
ejpam-4283	254	12	,	,	PUNCT
ejpam-4283	254	13	t};µ1	t};µ1	PROPN
ejpam-4283	254	14	=	=	SYM
ejpam-4283	254	15	{	{	PUNCT
ejpam-4283	254	16	∅	∅	NOUN
ejpam-4283	254	17	,	,	PUNCT
ejpam-4283	254	18	{	{	PUNCT
ejpam-4283	254	19	s	s	X
ejpam-4283	254	20	}	}	PUNCT
ejpam-4283	254	21	,	,	PUNCT
ejpam-4283	254	22	{	{	PUNCT
ejpam-4283	254	23	p	p	X
ejpam-4283	254	24	,	,	PUNCT
ejpam-4283	254	25	q	q	NOUN
ejpam-4283	254	26	}	}	PUNCT
ejpam-4283	254	27	,	,	PUNCT
ejpam-4283	254	28	{	{	PUNCT
ejpam-4283	254	29	p	p	X
ejpam-4283	254	30	,	,	PUNCT
ejpam-4283	254	31	r	r	NOUN
ejpam-4283	254	32	}	}	PUNCT
ejpam-4283	254	33	,	,	PUNCT
ejpam-4283	254	34	{	{	PUNCT
ejpam-4283	254	35	p	p	X
ejpam-4283	254	36	,	,	PUNCT
ejpam-4283	254	37	q	q	ADJ
ejpam-4283	254	38	,	,	PUNCT
ejpam-4283	254	39	r	r	NOUN
ejpam-4283	254	40	}	}	PUNCT
ejpam-4283	254	41	,	,	PUNCT
ejpam-4283	254	42	{	{	PUNCT
ejpam-4283	254	43	p	p	X
ejpam-4283	254	44	,	,	PUNCT
ejpam-4283	254	45	q	q	X
ejpam-4283	254	46	,	,	PUNCT
ejpam-4283	254	47	s	s	PART
ejpam-4283	254	48	}	}	PUNCT
ejpam-4283	254	49	,	,	PUNCT
ejpam-4283	254	50	{	{	PUNCT
ejpam-4283	254	51	p	p	X
ejpam-4283	254	52	,	,	PUNCT
ejpam-4283	254	53	r	r	NOUN
ejpam-4283	254	54	,	,	PUNCT
ejpam-4283	254	55	s	s	PART
ejpam-4283	254	56	}	}	PUNCT
ejpam-4283	254	57	,	,	PUNCT
ejpam-4283	254	58	{	{	PUNCT
ejpam-4283	254	59	p	p	X
ejpam-4283	254	60	,	,	PUNCT
ejpam-4283	254	61	q	q	ADJ
ejpam-4283	254	62	,	,	PUNCT
ejpam-4283	254	63	r	r	NOUN
ejpam-4283	254	64	,	,	PUNCT
ejpam-4283	254	65	s	s	PART
ejpam-4283	254	66	}	}	PUNCT
ejpam-4283	254	67	}	}	PUNCT
ejpam-4283	254	68	and	and	CCONJ
ejpam-4283	254	69	µ2	µ2	PROPN
ejpam-4283	254	70	=	=	PUNCT
ejpam-4283	254	71	{	{	PUNCT
ejpam-4283	254	72	∅	∅	NOUN
ejpam-4283	254	73	,	,	PUNCT
ejpam-4283	254	74	{	{	PUNCT
ejpam-4283	254	75	p	p	X
ejpam-4283	254	76	,	,	PUNCT
ejpam-4283	254	77	q	q	ADJ
ejpam-4283	254	78	,	,	PUNCT
ejpam-4283	254	79	r	r	NOUN
ejpam-4283	254	80	}	}	PUNCT
ejpam-4283	254	81	,	,	PUNCT
ejpam-4283	254	82	{	{	PUNCT
ejpam-4283	254	83	p	p	X
ejpam-4283	254	84	,	,	PUNCT
ejpam-4283	254	85	r	r	NOUN
ejpam-4283	254	86	,	,	PUNCT
ejpam-4283	254	87	s	s	PART
ejpam-4283	254	88	}	}	PUNCT
ejpam-4283	254	89	,	,	PUNCT
ejpam-4283	254	90	{	{	PUNCT
ejpam-4283	254	91	p	p	X
ejpam-4283	254	92	,	,	PUNCT
ejpam-4283	254	93	q	q	ADJ
ejpam-4283	254	94	,	,	PUNCT
ejpam-4283	254	95	r	r	NOUN
ejpam-4283	254	96	,	,	PUNCT
ejpam-4283	254	97	s	s	PART
ejpam-4283	254	98	}	}	PUNCT
ejpam-4283	254	99	}	}	PUNCT
ejpam-4283	254	100	.	.	PUNCT
ejpam-4283	255	1	take	take	VERB
ejpam-4283	255	2	k	k	NOUN
ejpam-4283	255	3	=	=	PRON
ejpam-4283	255	4	{	{	PUNCT
ejpam-4283	255	5	q	q	PROPN
ejpam-4283	255	6	,	,	PUNCT
ejpam-4283	255	7	s	s	PART
ejpam-4283	255	8	}	}	PUNCT
ejpam-4283	255	9	,	,	PUNCT
ejpam-4283	255	10	l	l	NOUN
ejpam-4283	255	11	=	=	SYM
ejpam-4283	255	12	{	{	PUNCT
ejpam-4283	255	13	r	r	NOUN
ejpam-4283	255	14	,	,	PUNCT
ejpam-4283	255	15	t	t	PROPN
ejpam-4283	255	16	}	}	PUNCT
ejpam-4283	255	17	.	.	PUNCT
ejpam-4283	256	1	then	then	ADV
ejpam-4283	256	2	k	k	X
ejpam-4283	256	3	,	,	PUNCT
ejpam-4283	256	4	l	l	PROPN
ejpam-4283	256	5	∈	∈	PROPN
ejpam-4283	256	6	(	(	PUNCT
ejpam-4283	256	7	1	1	NUM
ejpam-4283	256	8	,	,	PUNCT
ejpam-4283	256	9	2)−s(x	2)−s(x	NUM
ejpam-4283	256	10	)	)	PUNCT
ejpam-4283	256	11	.	.	PUNCT
ejpam-4283	257	1	now	now	ADV
ejpam-4283	257	2	k	k	X
ejpam-4283	257	3	∪	∪	PROPN
ejpam-4283	257	4	l	l	NOUN
ejpam-4283	257	5	=	=	SYM
ejpam-4283	257	6	{	{	PUNCT
ejpam-4283	257	7	q	q	NOUN
ejpam-4283	257	8	,	,	PUNCT
ejpam-4283	257	9	r	r	NOUN
ejpam-4283	257	10	,	,	PUNCT
ejpam-4283	257	11	s	s	PROPN
ejpam-4283	257	12	,	,	PUNCT
ejpam-4283	257	13	t	t	PROPN
ejpam-4283	257	14	}	}	PUNCT
ejpam-4283	257	15	.	.	PUNCT
ejpam-4283	258	1	but	but	CCONJ
ejpam-4283	258	2	k	k	PROPN
ejpam-4283	258	3	∪	∪	PROPN
ejpam-4283	258	4	l	l	PROPN
ejpam-4283	258	5	/∈	/∈	PUNCT
ejpam-4283	258	6	(	(	PUNCT
ejpam-4283	258	7	1	1	NUM
ejpam-4283	258	8	,	,	PUNCT
ejpam-4283	258	9	2)−s(x	2)−s(x	NUM
ejpam-4283	258	10	)	)	PUNCT
ejpam-4283	258	11	.	.	PUNCT
ejpam-4283	259	1	because	because	SCONJ
ejpam-4283	259	2	,	,	PUNCT
ejpam-4283	259	3	here	here	ADV
ejpam-4283	259	4	,	,	PUNCT
ejpam-4283	259	5	for	for	ADP
ejpam-4283	259	6	every	every	DET
ejpam-4283	259	7	g	g	PROPN
ejpam-4283	259	8	∈	∈	PROPN
ejpam-4283	259	9	µ̃2	µ̃2	PROPN
ejpam-4283	259	10	there	there	PRON
ejpam-4283	259	11	is	be	VERB
ejpam-4283	259	12	no	no	DET
ejpam-4283	259	13	j	j	PROPN
ejpam-4283	259	14	∈	∈	PROPN
ejpam-4283	259	15	µ̃1	µ̃1	NOUN
ejpam-4283	259	16	such	such	ADJ
ejpam-4283	259	17	that	that	SCONJ
ejpam-4283	259	18	j	j	PROPN
ejpam-4283	259	19	⊂	⊂	PROPN
ejpam-4283	259	20	g	g	PROPN
ejpam-4283	259	21	and	and	CCONJ
ejpam-4283	259	22	j	j	PROPN
ejpam-4283	259	23	∩	∩	NOUN
ejpam-4283	259	24	(	(	PUNCT
ejpam-4283	259	25	k	k	PROPN
ejpam-4283	259	26	∪	∪	PROPN
ejpam-4283	259	27	l	l	NOUN
ejpam-4283	259	28	)	)	PUNCT
ejpam-4283	259	29	=	=	SYM
ejpam-4283	259	30	∅.	∅.	X
ejpam-4283	259	31	(	(	PUNCT
ejpam-4283	259	32	b	b	NOUN
ejpam-4283	259	33	)	)	PUNCT
ejpam-4283	259	34	.	.	PUNCT
ejpam-4283	260	1	consider	consider	VERB
ejpam-4283	260	2	the	the	DET
ejpam-4283	260	3	bigeneralized	bigeneralized	ADJ
ejpam-4283	260	4	topological	topological	ADJ
ejpam-4283	260	5	space	space	NOUN
ejpam-4283	260	6	(	(	PUNCT
ejpam-4283	260	7	x,µ1	x,µ1	PROPN
ejpam-4283	260	8	,	,	PUNCT
ejpam-4283	260	9	µ2	µ2	PROPN
ejpam-4283	260	10	)	)	PUNCT
ejpam-4283	261	1	where	where	SCONJ
ejpam-4283	261	2	x	x	X
ejpam-4283	261	3	=	=	PRON
ejpam-4283	261	4	{	{	PUNCT
ejpam-4283	261	5	p	p	X
ejpam-4283	261	6	,	,	PUNCT
ejpam-4283	261	7	q	q	ADJ
ejpam-4283	261	8	,	,	PUNCT
ejpam-4283	261	9	r	r	NOUN
ejpam-4283	261	10	,	,	PUNCT
ejpam-4283	261	11	s	s	NOUN
ejpam-4283	261	12	,	,	PUNCT
ejpam-4283	261	13	t};µ1	t};µ1	PROPN
ejpam-4283	261	14	=	=	SYM
ejpam-4283	261	15	{	{	PUNCT
ejpam-4283	261	16	∅	∅	NOUN
ejpam-4283	261	17	,	,	PUNCT
ejpam-4283	261	18	{	{	PUNCT
ejpam-4283	261	19	p	p	X
ejpam-4283	261	20	,	,	PUNCT
ejpam-4283	261	21	q	q	X
ejpam-4283	261	22	,	,	PUNCT
ejpam-4283	261	23	s	s	PART
ejpam-4283	261	24	}	}	PUNCT
ejpam-4283	261	25	,	,	PUNCT
ejpam-4283	261	26	{	{	PUNCT
ejpam-4283	261	27	p	p	X
ejpam-4283	261	28	,	,	PUNCT
ejpam-4283	261	29	r	r	NOUN
ejpam-4283	261	30	,	,	PUNCT
ejpam-4283	261	31	s	s	PART
ejpam-4283	261	32	}	}	PUNCT
ejpam-4283	261	33	,	,	PUNCT
ejpam-4283	261	34	{	{	PUNCT
ejpam-4283	261	35	p	p	X
ejpam-4283	261	36	,	,	PUNCT
ejpam-4283	261	37	q	q	ADJ
ejpam-4283	261	38	,	,	PUNCT
ejpam-4283	261	39	r	r	NOUN
ejpam-4283	261	40	,	,	PUNCT
ejpam-4283	261	41	s	s	PART
ejpam-4283	261	42	}	}	PUNCT
ejpam-4283	261	43	}	}	PUNCT
ejpam-4283	261	44	and	and	CCONJ
ejpam-4283	261	45	µ2	µ2	PROPN
ejpam-4283	261	46	=	=	PUNCT
ejpam-4283	261	47	{	{	PUNCT
ejpam-4283	261	48	∅	∅	NOUN
ejpam-4283	261	49	,	,	PUNCT
ejpam-4283	261	50	{	{	PUNCT
ejpam-4283	261	51	r	r	NOUN
ejpam-4283	261	52	}	}	PUNCT
ejpam-4283	261	53	,	,	PUNCT
ejpam-4283	261	54	{	{	PUNCT
ejpam-4283	261	55	p	p	X
ejpam-4283	261	56	,	,	PUNCT
ejpam-4283	261	57	q	q	NOUN
ejpam-4283	261	58	}	}	PUNCT
ejpam-4283	261	59	,	,	PUNCT
ejpam-4283	261	60	{	{	PUNCT
ejpam-4283	261	61	p	p	X
ejpam-4283	261	62	,	,	PUNCT
ejpam-4283	261	63	s	s	PART
ejpam-4283	261	64	}	}	PUNCT
ejpam-4283	261	65	,	,	PUNCT
ejpam-4283	261	66	{	{	PUNCT
ejpam-4283	261	67	p	p	X
ejpam-4283	261	68	,	,	PUNCT
ejpam-4283	261	69	q	q	ADJ
ejpam-4283	261	70	,	,	PUNCT
ejpam-4283	261	71	r	r	NOUN
ejpam-4283	261	72	}	}	PUNCT
ejpam-4283	261	73	,	,	PUNCT
ejpam-4283	261	74	{	{	PUNCT
ejpam-4283	261	75	p	p	X
ejpam-4283	261	76	,	,	PUNCT
ejpam-4283	261	77	q	q	X
ejpam-4283	261	78	,	,	PUNCT
ejpam-4283	261	79	s	s	PART
ejpam-4283	261	80	}	}	PUNCT
ejpam-4283	261	81	,	,	PUNCT
ejpam-4283	261	82	{	{	PUNCT
ejpam-4283	261	83	p	p	X
ejpam-4283	261	84	,	,	PUNCT
ejpam-4283	261	85	r	r	NOUN
ejpam-4283	261	86	,	,	PUNCT
ejpam-4283	261	87	s	s	PART
ejpam-4283	261	88	}	}	PUNCT
ejpam-4283	261	89	,	,	PUNCT
ejpam-4283	261	90	{	{	PUNCT
ejpam-4283	261	91	p	p	X
ejpam-4283	261	92	,	,	PUNCT
ejpam-4283	261	93	q	q	ADJ
ejpam-4283	261	94	,	,	PUNCT
ejpam-4283	261	95	r	r	NOUN
ejpam-4283	261	96	,	,	PUNCT
ejpam-4283	261	97	s	s	PART
ejpam-4283	261	98	}	}	PUNCT
ejpam-4283	261	99	}	}	PUNCT
ejpam-4283	261	100	.	.	PUNCT
ejpam-4283	262	1	take	take	VERB
ejpam-4283	262	2	l	l	NOUN
ejpam-4283	262	3	=	=	PRON
ejpam-4283	262	4	{	{	PUNCT
ejpam-4283	262	5	q	q	ADJ
ejpam-4283	262	6	,	,	PUNCT
ejpam-4283	262	7	r},m	r},m	NOUN
ejpam-4283	262	8	=	=	SYM
ejpam-4283	262	9	{	{	PUNCT
ejpam-4283	262	10	s	s	PROPN
ejpam-4283	262	11	,	,	PUNCT
ejpam-4283	262	12	t	t	PROPN
ejpam-4283	262	13	}	}	PUNCT
ejpam-4283	262	14	.	.	PUNCT
ejpam-4283	263	1	then	then	ADV
ejpam-4283	263	2	l	l	NOUN
ejpam-4283	263	3	,	,	PUNCT
ejpam-4283	263	4	m	m	VERB
ejpam-4283	263	5	∈	∈	NOUN
ejpam-4283	263	6	(	(	PUNCT
ejpam-4283	263	7	2	2	NUM
ejpam-4283	263	8	,	,	PUNCT
ejpam-4283	263	9	1	1	NUM
ejpam-4283	263	10	)	)	PUNCT
ejpam-4283	263	11	−	−	PROPN
ejpam-4283	263	12	s(x	s(x	NOUN
ejpam-4283	263	13	)	)	PUNCT
ejpam-4283	263	14	.	.	PUNCT
ejpam-4283	264	1	now	now	ADV
ejpam-4283	264	2	l	l	NOUN
ejpam-4283	264	3	∪	∪	X
ejpam-4283	264	4	m	m	VERB
ejpam-4283	264	5	=	=	SYM
ejpam-4283	264	6	{	{	PUNCT
ejpam-4283	264	7	q	q	NOUN
ejpam-4283	264	8	,	,	PUNCT
ejpam-4283	264	9	r	r	NOUN
ejpam-4283	264	10	,	,	PUNCT
ejpam-4283	264	11	s	s	PROPN
ejpam-4283	264	12	,	,	PUNCT
ejpam-4283	264	13	t	t	PROPN
ejpam-4283	264	14	}	}	PUNCT
ejpam-4283	264	15	.	.	PUNCT
ejpam-4283	265	1	but	but	CCONJ
ejpam-4283	265	2	l	l	PROPN
ejpam-4283	265	3	∪m	∪m	NUM
ejpam-4283	265	4	/∈	/∈	PUNCT
ejpam-4283	265	5	(	(	PUNCT
ejpam-4283	265	6	2	2	NUM
ejpam-4283	265	7	,	,	PUNCT
ejpam-4283	265	8	1	1	NUM
ejpam-4283	265	9	)	)	PUNCT
ejpam-4283	265	10	−	−	PROPN
ejpam-4283	265	11	s(x	s(x	NOUN
ejpam-4283	265	12	)	)	PUNCT
ejpam-4283	265	13	.	.	PUNCT
ejpam-4283	266	1	here	here	ADV
ejpam-4283	266	2	,	,	PUNCT
ejpam-4283	266	3	for	for	ADP
ejpam-4283	266	4	every	every	DET
ejpam-4283	266	5	h	h	NOUN
ejpam-4283	266	6	∈	∈	NOUN
ejpam-4283	266	7	µ̃1	µ̃1	NOUN
ejpam-4283	266	8	there	there	PRON
ejpam-4283	266	9	is	be	VERB
ejpam-4283	266	10	no	no	DET
ejpam-4283	266	11	k	k	PROPN
ejpam-4283	266	12	∈	∈	PROPN
ejpam-4283	266	13	µ̃2	µ̃2	PROPN
ejpam-4283	266	14	such	such	ADJ
ejpam-4283	266	15	that	that	SCONJ
ejpam-4283	266	16	k	k	PROPN
ejpam-4283	266	17	⊂	⊂	PROPN
ejpam-4283	266	18	h	h	PROPN
ejpam-4283	266	19	and	and	CCONJ
ejpam-4283	266	20	k	k	PROPN
ejpam-4283	266	21	∩	∩	NOUN
ejpam-4283	266	22	(	(	PUNCT
ejpam-4283	266	23	l	l	NOUN
ejpam-4283	266	24	∪m	∪m	NUM
ejpam-4283	266	25	)	)	PUNCT
ejpam-4283	266	26	=	=	PUNCT
ejpam-4283	266	27	∅.	∅.	NOUN
ejpam-4283	266	28	theorem	theorem	VERB
ejpam-4283	266	29	16	16	NUM
ejpam-4283	266	30	.	.	PUNCT
ejpam-4283	267	1	let	let	AUX
ejpam-4283	267	2	(	(	PUNCT
ejpam-4283	267	3	x,µ1	x,µ1	NOUN
ejpam-4283	267	4	,	,	PUNCT
ejpam-4283	267	5	µ2	µ2	PROPN
ejpam-4283	267	6	)	)	PUNCT
ejpam-4283	267	7	be	be	VERB
ejpam-4283	267	8	a	a	DET
ejpam-4283	267	9	bgts	bgts	NOUN
ejpam-4283	267	10	where	where	SCONJ
ejpam-4283	267	11	µ2	µ2	PROPN
ejpam-4283	267	12	=	=	PROPN
ejpam-4283	267	13	µ	µ	PROPN
ejpam-4283	267	14	?	?	NOUN
ejpam-4283	267	15	1	1	NUM
ejpam-4283	267	16	.	.	PUNCT
ejpam-4283	268	1	then	then	ADV
ejpam-4283	268	2	the	the	DET
ejpam-4283	268	3	family	family	NOUN
ejpam-4283	268	4	(	(	PUNCT
ejpam-4283	268	5	s	s	PROPN
ejpam-4283	268	6	,	,	PUNCT
ejpam-4283	268	7	v)−s(x	v)−s(x	NUM
ejpam-4283	268	8	)	)	PUNCT
ejpam-4283	268	9	is	be	AUX
ejpam-4283	268	10	closed	close	VERB
ejpam-4283	268	11	under	under	ADP
ejpam-4283	268	12	finite	finite	ADJ
ejpam-4283	268	13	union	union	NOUN
ejpam-4283	268	14	where	where	SCONJ
ejpam-4283	268	15	s	s	X
ejpam-4283	268	16	,	,	PUNCT
ejpam-4283	268	17	v	v	NOUN
ejpam-4283	268	18	=	=	SYM
ejpam-4283	268	19	1	1	NUM
ejpam-4283	268	20	,	,	PUNCT
ejpam-4283	268	21	2	2	NUM
ejpam-4283	268	22	;	;	PUNCT
ejpam-4283	268	23	s	s	PROPN
ejpam-4283	268	24	6=	6=	PROPN
ejpam-4283	268	25	v.	v.	CCONJ
ejpam-4283	268	26	theorem	theorem	NOUN
ejpam-4283	268	27	17	17	NUM
ejpam-4283	268	28	.	.	PUNCT
ejpam-4283	269	1	let	let	AUX
ejpam-4283	269	2	(	(	PUNCT
ejpam-4283	269	3	x,µ1	x,µ1	NOUN
ejpam-4283	269	4	,	,	PUNCT
ejpam-4283	269	5	µ2	µ2	PROPN
ejpam-4283	269	6	)	)	PUNCT
ejpam-4283	269	7	be	be	VERB
ejpam-4283	269	8	a	a	DET
ejpam-4283	269	9	bigeneralized	bigeneralized	ADJ
ejpam-4283	269	10	topological	topological	ADJ
ejpam-4283	269	11	space	space	NOUN
ejpam-4283	269	12	.	.	PUNCT
ejpam-4283	270	1	if	if	SCONJ
ejpam-4283	270	2	(	(	PUNCT
ejpam-4283	270	3	x,µs	x,µs	NUM
ejpam-4283	270	4	)	)	PUNCT
ejpam-4283	270	5	is	be	AUX
ejpam-4283	270	6	hyperconnected	hyperconnecte	VERB
ejpam-4283	270	7	and	and	CCONJ
ejpam-4283	270	8	µs	µs	AUX
ejpam-4283	270	9	satisfy	satisfy	VERB
ejpam-4283	270	10	the	the	DET
ejpam-4283	270	11	i	i	NOUN
ejpam-4283	270	12	-	-	PUNCT
ejpam-4283	270	13	property	property	NOUN
ejpam-4283	270	14	,	,	PUNCT
ejpam-4283	270	15	then	then	ADV
ejpam-4283	270	16	a1	a1	NOUN
ejpam-4283	270	17	∪	∪	PROPN
ejpam-4283	270	18	a2	a2	PROPN
ejpam-4283	270	19	∈	∈	PROPN
ejpam-4283	270	20	(	(	PUNCT
ejpam-4283	270	21	s	s	PROPN
ejpam-4283	270	22	,	,	PUNCT
ejpam-4283	270	23	v	v	NOUN
ejpam-4283	270	24	)	)	PUNCT
ejpam-4283	270	25	−	−	PROPN
ejpam-4283	270	26	s(x	s(x	NOUN
ejpam-4283	270	27	)	)	PUNCT
ejpam-4283	270	28	whenever	whenever	SCONJ
ejpam-4283	270	29	a1	a1	PROPN
ejpam-4283	270	30	,	,	PUNCT
ejpam-4283	270	31	a2	a2	PROPN
ejpam-4283	270	32	∈	∈	PROPN
ejpam-4283	270	33	(	(	PUNCT
ejpam-4283	270	34	s	s	NOUN
ejpam-4283	270	35	,	,	PUNCT
ejpam-4283	270	36	v)−s(x	v)−s(x	NUM
ejpam-4283	270	37	)	)	PUNCT
ejpam-4283	271	1	where	where	SCONJ
ejpam-4283	271	2	s	s	X
ejpam-4283	271	3	,	,	PUNCT
ejpam-4283	271	4	v	v	NOUN
ejpam-4283	271	5	=	=	SYM
ejpam-4283	271	6	1	1	NUM
ejpam-4283	271	7	,	,	PUNCT
ejpam-4283	271	8	2	2	NUM
ejpam-4283	271	9	;	;	PUNCT
ejpam-4283	271	10	s	s	X
ejpam-4283	271	11	6=	6=	PROPN
ejpam-4283	271	12	v.	v.	ADP
ejpam-4283	271	13	proof	proof	NOUN
ejpam-4283	271	14	.	.	PUNCT
ejpam-4283	272	1	take	take	VERB
ejpam-4283	272	2	s	s	NOUN
ejpam-4283	272	3	=	=	SYM
ejpam-4283	272	4	1	1	NUM
ejpam-4283	272	5	and	and	CCONJ
ejpam-4283	272	6	v	v	NOUN
ejpam-4283	272	7	=	=	SYM
ejpam-4283	272	8	2	2	X
ejpam-4283	272	9	.	.	X
ejpam-4283	272	10	assume	assume	VERB
ejpam-4283	272	11	that	that	SCONJ
ejpam-4283	272	12	,	,	PUNCT
ejpam-4283	272	13	(	(	PUNCT
ejpam-4283	272	14	x,µ1	x,µ1	NOUN
ejpam-4283	272	15	)	)	PUNCT
ejpam-4283	272	16	is	be	AUX
ejpam-4283	272	17	hyperconnected	hyperconnecte	VERB
ejpam-4283	272	18	and	and	CCONJ
ejpam-4283	272	19	µ1	µ1	VERB
ejpam-4283	272	20	satisfy	satisfy	VERB
ejpam-4283	272	21	the	the	DET
ejpam-4283	272	22	i	i	NOUN
ejpam-4283	272	23	-	-	PUNCT
ejpam-4283	272	24	property	property	NOUN
ejpam-4283	272	25	.	.	PUNCT
ejpam-4283	273	1	suppose	suppose	VERB
ejpam-4283	273	2	that	that	SCONJ
ejpam-4283	273	3	,	,	PUNCT
ejpam-4283	273	4	a1	a1	NOUN
ejpam-4283	273	5	and	and	CCONJ
ejpam-4283	273	6	a2	a2	NOUN
ejpam-4283	273	7	are	be	AUX
ejpam-4283	273	8	(	(	PUNCT
ejpam-4283	273	9	1	1	NUM
ejpam-4283	273	10	,	,	PUNCT
ejpam-4283	273	11	2)-strongly	2)-strongly	ADV
ejpam-4283	273	12	nowhere	nowhere	ADV
ejpam-4283	273	13	dense	dense	ADJ
ejpam-4283	273	14	sets	set	NOUN
ejpam-4283	273	15	in	in	ADP
ejpam-4283	273	16	x.	x.	NOUN
ejpam-4283	273	17	take	take	VERB
ejpam-4283	273	18	d	d	NOUN
ejpam-4283	273	19	=	=	NOUN
ejpam-4283	273	20	a1	a1	NOUN
ejpam-4283	273	21	∪	∪	NOUN
ejpam-4283	273	22	a2	a2	PROPN
ejpam-4283	273	23	.	.	PUNCT
ejpam-4283	274	1	let	let	VERB
ejpam-4283	274	2	g	g	PROPN
ejpam-4283	274	3	∈	∈	PROPN
ejpam-4283	274	4	µ̃2	µ̃2	PROPN
ejpam-4283	274	5	.	.	PUNCT
ejpam-4283	275	1	then	then	ADV
ejpam-4283	275	2	there	there	PRON
ejpam-4283	275	3	exists	exist	VERB
ejpam-4283	275	4	hi	hi	INTJ
ejpam-4283	275	5	∈	∈	PROPN
ejpam-4283	275	6	µ̃1	µ̃1	NOUN
ejpam-4283	275	7	such	such	ADJ
ejpam-4283	275	8	that	that	SCONJ
ejpam-4283	275	9	hi	hi	PROPN
ejpam-4283	275	10	⊂	⊂	PROPN
ejpam-4283	275	11	g	g	PROPN
ejpam-4283	275	12	and	and	CCONJ
ejpam-4283	275	13	hi	hi	PROPN
ejpam-4283	275	14	∩	∩	NOUN
ejpam-4283	275	15	ai	ai	VERB
ejpam-4283	275	16	=	=	NOUN
ejpam-4283	275	17	∅	∅	NOUN
ejpam-4283	275	18	for	for	ADP
ejpam-4283	275	19	i	i	PRON
ejpam-4283	275	20	=	=	NOUN
ejpam-4283	275	21	1	1	NUM
ejpam-4283	275	22	,	,	PUNCT
ejpam-4283	275	23	2	2	NUM
ejpam-4283	275	24	.	.	PUNCT
ejpam-4283	275	25	by	by	ADP
ejpam-4283	275	26	our	our	PRON
ejpam-4283	275	27	assumption	assumption	NOUN
ejpam-4283	275	28	,	,	PUNCT
ejpam-4283	275	29	iµ1(h1	iµ1(h1	PROPN
ejpam-4283	275	30	∩h2	∩h2	PROPN
ejpam-4283	275	31	)	)	PUNCT
ejpam-4283	275	32	6=	6=	ADP
ejpam-4283	275	33	∅.	∅.	AUX
ejpam-4283	275	34	take	take	VERB
ejpam-4283	275	35	j	j	NOUN
ejpam-4283	275	36	=	=	NOUN
ejpam-4283	275	37	iµ1(h1	iµ1(h1	PROPN
ejpam-4283	275	38	∩h2	∩h2	PROPN
ejpam-4283	275	39	)	)	PUNCT
ejpam-4283	275	40	.	.	PUNCT
ejpam-4283	276	1	then	then	ADV
ejpam-4283	276	2	j	j	PROPN
ejpam-4283	276	3	∈	∈	PROPN
ejpam-4283	276	4	µ̃1	µ̃1	PROPN
ejpam-4283	276	5	.	.	PUNCT
ejpam-4283	277	1	thus	thus	ADV
ejpam-4283	277	2	,	,	PUNCT
ejpam-4283	277	3	there	there	PRON
ejpam-4283	277	4	is	be	VERB
ejpam-4283	277	5	j	j	PROPN
ejpam-4283	277	6	∈	∈	PROPN
ejpam-4283	277	7	µ̃1	µ̃1	NOUN
ejpam-4283	277	8	such	such	ADJ
ejpam-4283	277	9	that	that	SCONJ
ejpam-4283	277	10	j	j	PROPN
ejpam-4283	277	11	⊂	⊂	PROPN
ejpam-4283	277	12	g	g	PROPN
ejpam-4283	277	13	and	and	CCONJ
ejpam-4283	277	14	j	j	PROPN
ejpam-4283	277	15	∩d	∩d	NOUN
ejpam-4283	277	16	=	=	PUNCT
ejpam-4283	277	17	∅.	∅.	VERB
ejpam-4283	277	18	hence	hence	ADV
ejpam-4283	277	19	d	d	X
ejpam-4283	277	20	∈	∈	PROPN
ejpam-4283	277	21	(	(	PUNCT
ejpam-4283	277	22	1	1	NUM
ejpam-4283	277	23	,	,	PUNCT
ejpam-4283	277	24	2)−s(x	2)−s(x	NUM
ejpam-4283	277	25	)	)	PUNCT
ejpam-4283	277	26	.	.	PUNCT
ejpam-4283	278	1	similarly	similarly	ADV
ejpam-4283	278	2	,	,	PUNCT
ejpam-4283	278	3	we	we	PRON
ejpam-4283	278	4	can	can	AUX
ejpam-4283	278	5	prove	prove	VERB
ejpam-4283	278	6	the	the	DET
ejpam-4283	278	7	result	result	NOUN
ejpam-4283	278	8	for	for	ADP
ejpam-4283	278	9	s	s	NOUN
ejpam-4283	278	10	=	=	SYM
ejpam-4283	278	11	2	2	NUM
ejpam-4283	278	12	and	and	CCONJ
ejpam-4283	278	13	v	v	NOUN
ejpam-4283	278	14	=	=	SYM
ejpam-4283	278	15	1	1	NUM
ejpam-4283	278	16	.	.	PUNCT
ejpam-4283	278	17	corollary	corollary	ADJ
ejpam-4283	278	18	18	18	NUM
ejpam-4283	278	19	.	.	PUNCT
ejpam-4283	279	1	let	let	AUX
ejpam-4283	279	2	(	(	PUNCT
ejpam-4283	279	3	x,µ1	x,µ1	NOUN
ejpam-4283	279	4	,	,	PUNCT
ejpam-4283	279	5	µ2	µ2	PROPN
ejpam-4283	279	6	)	)	PUNCT
ejpam-4283	279	7	be	be	VERB
ejpam-4283	279	8	a	a	DET
ejpam-4283	279	9	bigeneralized	bigeneralized	ADJ
ejpam-4283	279	10	topological	topological	ADJ
ejpam-4283	279	11	space	space	NOUN
ejpam-4283	279	12	.	.	PUNCT
ejpam-4283	280	1	if	if	SCONJ
ejpam-4283	280	2	(	(	PUNCT
ejpam-4283	280	3	x,µs	x,µs	NUM
ejpam-4283	280	4	)	)	PUNCT
ejpam-4283	280	5	is	be	AUX
ejpam-4283	280	6	a	a	DET
ejpam-4283	280	7	hyperconnected	hyperconnecte	VERB
ejpam-4283	280	8	space	space	NOUN
ejpam-4283	280	9	and	and	CCONJ
ejpam-4283	280	10	µs	µs	AUX
ejpam-4283	280	11	satisfy	satisfy	VERB
ejpam-4283	280	12	the	the	DET
ejpam-4283	280	13	i	i	NOUN
ejpam-4283	280	14	-	-	PUNCT
ejpam-4283	280	15	property	property	NOUN
ejpam-4283	280	16	,	,	PUNCT
ejpam-4283	280	17	then	then	ADV
ejpam-4283	280	18	the	the	DET
ejpam-4283	280	19	family	family	NOUN
ejpam-4283	280	20	(	(	PUNCT
ejpam-4283	280	21	s	s	PROPN
ejpam-4283	280	22	,	,	PUNCT
ejpam-4283	280	23	v)−s(x	v)−s(x	NUM
ejpam-4283	280	24	)	)	PUNCT
ejpam-4283	280	25	is	be	AUX
ejpam-4283	280	26	closed	close	VERB
ejpam-4283	280	27	under	under	ADP
ejpam-4283	280	28	finite	finite	ADJ
ejpam-4283	280	29	union	union	NOUN
ejpam-4283	280	30	where	where	SCONJ
ejpam-4283	280	31	s	s	X
ejpam-4283	280	32	,	,	PUNCT
ejpam-4283	280	33	v	v	NOUN
ejpam-4283	280	34	=	=	SYM
ejpam-4283	280	35	1	1	NUM
ejpam-4283	280	36	,	,	PUNCT
ejpam-4283	280	37	2	2	NUM
ejpam-4283	280	38	;	;	PUNCT
ejpam-4283	280	39	s	s	PROPN
ejpam-4283	280	40	6=	6=	PROPN
ejpam-4283	280	41	v.	v.	ADP
ejpam-4283	280	42	the	the	DET
ejpam-4283	280	43	following	follow	VERB
ejpam-4283	280	44	example	example	NOUN
ejpam-4283	280	45	19	19	NUM
ejpam-4283	280	46	shows	show	VERB
ejpam-4283	280	47	that	that	SCONJ
ejpam-4283	280	48	(	(	PUNCT
ejpam-4283	280	49	s	s	X
ejpam-4283	280	50	,	,	PUNCT
ejpam-4283	280	51	v)-strongly	v)-strongly	ADV
ejpam-4283	280	52	nowhere	nowhere	ADV
ejpam-4283	280	53	dense	dense	ADJ
ejpam-4283	280	54	and	and	CCONJ
ejpam-4283	280	55	(	(	PUNCT
ejpam-4283	280	56	s	s	X
ejpam-4283	280	57	,	,	PUNCT
ejpam-4283	280	58	v)-nowhere	v)-nowhere	PUNCT
ejpam-4283	280	59	dense	dense	ADJ
ejpam-4283	280	60	sets	set	NOUN
ejpam-4283	280	61	are	be	AUX
ejpam-4283	280	62	not	not	PART
ejpam-4283	280	63	comparable	comparable	ADJ
ejpam-4283	280	64	in	in	ADP
ejpam-4283	280	65	a	a	DET
ejpam-4283	280	66	bgts	bgts	NOUN
ejpam-4283	280	67	.	.	PUNCT
ejpam-4283	281	1	example	example	NOUN
ejpam-4283	282	1	19	19	NUM
ejpam-4283	282	2	.	.	PUNCT
ejpam-4283	283	1	(	(	PUNCT
ejpam-4283	283	2	a	a	X
ejpam-4283	283	3	)	)	PUNCT
ejpam-4283	283	4	.	.	PUNCT
ejpam-4283	284	1	consider	consider	VERB
ejpam-4283	284	2	the	the	DET
ejpam-4283	284	3	bigeneralized	bigeneralized	ADJ
ejpam-4283	284	4	topological	topological	ADJ
ejpam-4283	284	5	space	space	NOUN
ejpam-4283	284	6	(	(	PUNCT
ejpam-4283	284	7	x,µ1	x,µ1	PROPN
ejpam-4283	284	8	,	,	PUNCT
ejpam-4283	284	9	µ2	µ2	PROPN
ejpam-4283	284	10	)	)	PUNCT
ejpam-4283	285	1	where	where	SCONJ
ejpam-4283	285	2	x	x	X
ejpam-4283	285	3	=	=	PUNCT
ejpam-4283	286	1	[	[	X
ejpam-4283	286	2	0	0	NUM
ejpam-4283	286	3	,	,	PUNCT
ejpam-4283	286	4	3];µ1	3];µ1	PROPN
ejpam-4283	286	5	=	=	SYM
ejpam-4283	286	6	{	{	PUNCT
ejpam-4283	286	7	∅	∅	NOUN
ejpam-4283	286	8	,	,	PUNCT
ejpam-4283	286	9	[	[	X
ejpam-4283	286	10	0	0	NUM
ejpam-4283	286	11	,	,	PUNCT
ejpam-4283	286	12	1	1	NUM
ejpam-4283	286	13	)	)	PUNCT
ejpam-4283	286	14	,	,	PUNCT
ejpam-4283	286	15	{	{	PUNCT
ejpam-4283	286	16	3	3	NUM
ejpam-4283	286	17	2	2	NUM
ejpam-4283	286	18	}	}	PUNCT
ejpam-4283	286	19	,	,	PUNCT
ejpam-4283	286	20	[	[	X
ejpam-4283	286	21	1	1	NUM
ejpam-4283	286	22	,	,	PUNCT
ejpam-4283	286	23	2	2	NUM
ejpam-4283	286	24	]	]	PUNCT
ejpam-4283	286	25	,	,	PUNCT
ejpam-4283	286	26	[	[	X
ejpam-4283	286	27	0	0	NUM
ejpam-4283	286	28	,	,	PUNCT
ejpam-4283	286	29	1	1	NUM
ejpam-4283	286	30	)	)	PUNCT
ejpam-4283	286	31	∪	∪	NOUN
ejpam-4283	286	32	{	{	PUNCT
ejpam-4283	286	33	3	3	NUM
ejpam-4283	286	34	2	2	NUM
ejpam-4283	286	35	}	}	PUNCT
ejpam-4283	286	36	,	,	PUNCT
ejpam-4283	286	37	[	[	X
ejpam-4283	286	38	0	0	NUM
ejpam-4283	286	39	,	,	PUNCT
ejpam-4283	286	40	2	2	NUM
ejpam-4283	286	41	]	]	PUNCT
ejpam-4283	286	42	}	}	PUNCT
ejpam-4283	286	43	and	and	CCONJ
ejpam-4283	286	44	µ2	µ2	PROPN
ejpam-4283	286	45	=	=	PUNCT
ejpam-4283	286	46	{	{	PUNCT
ejpam-4283	286	47	∅	∅	NOUN
ejpam-4283	286	48	,	,	PUNCT
ejpam-4283	286	49	[	[	X
ejpam-4283	286	50	0	0	NUM
ejpam-4283	286	51	,	,	PUNCT
ejpam-4283	286	52	32	32	NUM
ejpam-4283	286	53	)	)	PUNCT
ejpam-4283	286	54	,	,	PUNCT
ejpam-4283	287	1	[	[	X
ejpam-4283	287	2	1	1	NUM
ejpam-4283	287	3	,	,	PUNCT
ejpam-4283	287	4	3	3	NUM
ejpam-4283	287	5	]	]	PUNCT
ejpam-4283	287	6	,	,	PUNCT
ejpam-4283	288	1	[	[	X
ejpam-4283	288	2	0	0	NUM
ejpam-4283	288	3	,	,	PUNCT
ejpam-4283	288	4	3	3	NUM
ejpam-4283	288	5	]	]	PUNCT
ejpam-4283	288	6	}	}	PUNCT
ejpam-4283	288	7	.	.	PUNCT
ejpam-4283	289	1	let	let	VERB
ejpam-4283	289	2	g	g	PROPN
ejpam-4283	289	3	=	=	SYM
ejpam-4283	289	4	(	(	PUNCT
ejpam-4283	289	5	2	2	NUM
ejpam-4283	289	6	,	,	PUNCT
ejpam-4283	289	7	3	3	NUM
ejpam-4283	289	8	]	]	PUNCT
ejpam-4283	289	9	.	.	PUNCT
ejpam-4283	290	1	then	then	ADV
ejpam-4283	290	2	g	g	PROPN
ejpam-4283	290	3	∈	∈	PROPN
ejpam-4283	290	4	(	(	PUNCT
ejpam-4283	290	5	1	1	NUM
ejpam-4283	290	6	,	,	PUNCT
ejpam-4283	290	7	2)−s(x	2)−s(x	NUM
ejpam-4283	290	8	)	)	PUNCT
ejpam-4283	290	9	.	.	PUNCT
ejpam-4283	291	1	but	but	CCONJ
ejpam-4283	291	2	g	g	NOUN
ejpam-4283	291	3	is	be	AUX
ejpam-4283	291	4	not	not	PART
ejpam-4283	291	5	a	a	DET
ejpam-4283	291	6	(	(	PUNCT
ejpam-4283	291	7	1	1	NUM
ejpam-4283	291	8	,	,	PUNCT
ejpam-4283	291	9	2)-nowhere	2)-nowhere	NUM
ejpam-4283	291	10	dense	dense	ADJ
ejpam-4283	291	11	set	set	NOUN
ejpam-4283	291	12	in	in	ADP
ejpam-4283	291	13	x.	x.	NOUN
ejpam-4283	291	14	(	(	PUNCT
ejpam-4283	291	15	b	b	NOUN
ejpam-4283	291	16	)	)	PUNCT
ejpam-4283	291	17	.	.	PUNCT
ejpam-4283	292	1	consider	consider	VERB
ejpam-4283	292	2	the	the	DET
ejpam-4283	292	3	bigeneralized	bigeneralized	ADJ
ejpam-4283	292	4	topological	topological	ADJ
ejpam-4283	292	5	space	space	NOUN
ejpam-4283	292	6	(	(	PUNCT
ejpam-4283	292	7	x,µ1	x,µ1	PROPN
ejpam-4283	292	8	,	,	PUNCT
ejpam-4283	292	9	µ2	µ2	PROPN
ejpam-4283	292	10	)	)	PUNCT
ejpam-4283	293	1	where	where	SCONJ
ejpam-4283	293	2	x	x	X
ejpam-4283	293	3	=	=	PUNCT
ejpam-4283	294	1	[	[	X
ejpam-4283	294	2	0	0	NUM
ejpam-4283	294	3	,	,	PUNCT
ejpam-4283	294	4	3	3	NUM
ejpam-4283	294	5	]	]	PUNCT
ejpam-4283	294	6	;	;	PUNCT
ejpam-4283	294	7	µ1	µ1	PROPN
ejpam-4283	294	8	=	=	SYM
ejpam-4283	294	9	{	{	PUNCT
ejpam-4283	294	10	∅	∅	NOUN
ejpam-4283	294	11	,	,	PUNCT
ejpam-4283	294	12	[	[	X
ejpam-4283	294	13	0	0	NUM
ejpam-4283	294	14	,	,	PUNCT
ejpam-4283	294	15	2	2	NUM
ejpam-4283	294	16	)	)	PUNCT
ejpam-4283	294	17	,	,	PUNCT
ejpam-4283	294	18	(	(	PUNCT
ejpam-4283	294	19	1	1	NUM
ejpam-4283	294	20	,	,	PUNCT
ejpam-4283	294	21	3	3	NUM
ejpam-4283	294	22	]	]	PUNCT
ejpam-4283	294	23	,	,	PUNCT
ejpam-4283	294	24	[	[	X
ejpam-4283	294	25	0	0	NUM
ejpam-4283	294	26	,	,	PUNCT
ejpam-4283	294	27	3	3	NUM
ejpam-4283	294	28	]	]	PUNCT
ejpam-4283	294	29	}	}	PUNCT
ejpam-4283	294	30	and	and	CCONJ
ejpam-4283	294	31	µ2	µ2	PROPN
ejpam-4283	294	32	=	=	PUNCT
ejpam-4283	294	33	{	{	PUNCT
ejpam-4283	294	34	∅	∅	NOUN
ejpam-4283	294	35	,	,	PUNCT
ejpam-4283	294	36	[	[	X
ejpam-4283	294	37	0	0	NUM
ejpam-4283	294	38	,	,	PUNCT
ejpam-4283	294	39	1	1	NUM
ejpam-4283	294	40	)	)	PUNCT
ejpam-4283	294	41	,	,	PUNCT
ejpam-4283	294	42	(	(	PUNCT
ejpam-4283	294	43	1	1	NUM
ejpam-4283	294	44	,	,	PUNCT
ejpam-4283	294	45	2	2	NUM
ejpam-4283	294	46	)	)	PUNCT
ejpam-4283	294	47	,	,	PUNCT
ejpam-4283	294	48	{	{	PUNCT
ejpam-4283	294	49	2	2	NUM
ejpam-4283	294	50	}	}	PUNCT
ejpam-4283	294	51	,	,	PUNCT
ejpam-4283	294	52	[	[	X
ejpam-4283	294	53	0	0	NUM
ejpam-4283	294	54	,	,	PUNCT
ejpam-4283	294	55	1	1	NUM
ejpam-4283	294	56	)	)	PUNCT
ejpam-4283	294	57	∪	∪	X
ejpam-4283	294	58	{	{	PUNCT
ejpam-4283	294	59	2	2	NUM
ejpam-4283	294	60	}	}	PUNCT
ejpam-4283	294	61	,	,	PUNCT
ejpam-4283	294	62	(	(	PUNCT
ejpam-4283	294	63	1	1	NUM
ejpam-4283	294	64	,	,	PUNCT
ejpam-4283	294	65	2	2	NUM
ejpam-4283	294	66	]	]	PUNCT
ejpam-4283	294	67	,	,	PUNCT
ejpam-4283	294	68	[	[	X
ejpam-4283	294	69	0	0	NUM
ejpam-4283	294	70	,	,	PUNCT
ejpam-4283	294	71	1	1	NUM
ejpam-4283	294	72	)	)	PUNCT
ejpam-4283	294	73	∪(1	∪(1	NOUN
ejpam-4283	294	74	,	,	PUNCT
ejpam-4283	294	75	2	2	NUM
ejpam-4283	294	76	)	)	PUNCT
ejpam-4283	294	77	,	,	PUNCT
ejpam-4283	294	78	[	[	X
ejpam-4283	294	79	0	0	NUM
ejpam-4283	294	80	,	,	PUNCT
ejpam-4283	294	81	1	1	NUM
ejpam-4283	294	82	)	)	PUNCT
ejpam-4283	294	83	∪	∪	ADP
ejpam-4283	294	84	p.	p.	PROPN
ejpam-4283	294	85	yupapin	yupapin	NOUN
ejpam-4283	294	86	,	,	PUNCT
ejpam-4283	294	87	v.	v.	CCONJ
ejpam-4283	294	88	subramanian	subramanian	PROPN
ejpam-4283	294	89	,	,	PUNCT
ejpam-4283	294	90	y.	y.	PROPN
ejpam-4283	294	91	farhat	farhat	PROPN
ejpam-4283	294	92	/	/	SYM
ejpam-4283	294	93	eur	eur	PROPN
ejpam-4283	294	94	.	.	PUNCT
ejpam-4283	295	1	j.	j.	PROPN
ejpam-4283	295	2	pure	pure	PROPN
ejpam-4283	295	3	appl	appl	PROPN
ejpam-4283	295	4	.	.	PROPN
ejpam-4283	295	5	math	math	PROPN
ejpam-4283	295	6	,	,	PUNCT
ejpam-4283	295	7	15	15	NUM
ejpam-4283	295	8	(	(	PUNCT
ejpam-4283	295	9	2	2	NUM
ejpam-4283	295	10	)	)	PUNCT
ejpam-4283	295	11	(	(	PUNCT
ejpam-4283	295	12	2022	2022	NUM
ejpam-4283	295	13	)	)	PUNCT
ejpam-4283	295	14	,	,	PUNCT
ejpam-4283	295	15	403	403	NUM
ejpam-4283	295	16	-	-	SYM
ejpam-4283	295	17	414	414	NUM
ejpam-4283	295	18	409	409	NUM
ejpam-4283	295	19	(	(	PUNCT
ejpam-4283	295	20	1	1	NUM
ejpam-4283	295	21	,	,	PUNCT
ejpam-4283	295	22	2	2	NUM
ejpam-4283	295	23	]	]	PUNCT
ejpam-4283	295	24	}	}	PUNCT
ejpam-4283	295	25	.	.	PUNCT
ejpam-4283	296	1	let	let	VERB
ejpam-4283	296	2	h	h	NOUN
ejpam-4283	296	3	=	=	PUNCT
ejpam-4283	296	4	(	(	PUNCT
ejpam-4283	296	5	2	2	NUM
ejpam-4283	296	6	,	,	PUNCT
ejpam-4283	296	7	3	3	NUM
ejpam-4283	296	8	]	]	PUNCT
ejpam-4283	296	9	.	.	PUNCT
ejpam-4283	297	1	then	then	ADV
ejpam-4283	297	2	h	h	PROPN
ejpam-4283	297	3	∈	∈	PROPN
ejpam-4283	297	4	(	(	PUNCT
ejpam-4283	297	5	2	2	NUM
ejpam-4283	297	6	,	,	PUNCT
ejpam-4283	297	7	1	1	NUM
ejpam-4283	297	8	)	)	PUNCT
ejpam-4283	297	9	−s(x	−s(x	NOUN
ejpam-4283	297	10	)	)	PUNCT
ejpam-4283	297	11	.	.	PUNCT
ejpam-4283	298	1	but	but	CCONJ
ejpam-4283	298	2	h	h	NOUN
ejpam-4283	298	3	is	be	AUX
ejpam-4283	298	4	not	not	PART
ejpam-4283	298	5	a	a	DET
ejpam-4283	298	6	(	(	PUNCT
ejpam-4283	298	7	2	2	NUM
ejpam-4283	298	8	,	,	PUNCT
ejpam-4283	298	9	1)-nowhere	1)-nowhere	NUM
ejpam-4283	298	10	dense	dense	ADJ
ejpam-4283	298	11	set	set	NOUN
ejpam-4283	298	12	in	in	ADP
ejpam-4283	298	13	x.	x.	NOUN
ejpam-4283	298	14	(	(	PUNCT
ejpam-4283	298	15	c	c	NOUN
ejpam-4283	298	16	)	)	PUNCT
ejpam-4283	298	17	.	.	PUNCT
ejpam-4283	299	1	consider	consider	VERB
ejpam-4283	299	2	the	the	DET
ejpam-4283	299	3	bigeneralized	bigeneralized	ADJ
ejpam-4283	299	4	topological	topological	ADJ
ejpam-4283	299	5	space	space	NOUN
ejpam-4283	299	6	(	(	PUNCT
ejpam-4283	299	7	x,µ1	x,µ1	PROPN
ejpam-4283	299	8	,	,	PUNCT
ejpam-4283	299	9	µ2	µ2	PROPN
ejpam-4283	299	10	)	)	PUNCT
ejpam-4283	300	1	where	where	SCONJ
ejpam-4283	300	2	x	x	X
ejpam-4283	300	3	=	=	PUNCT
ejpam-4283	301	1	[	[	X
ejpam-4283	301	2	0	0	NUM
ejpam-4283	301	3	,	,	PUNCT
ejpam-4283	301	4	3	3	NUM
ejpam-4283	301	5	]	]	PUNCT
ejpam-4283	301	6	;	;	PUNCT
ejpam-4283	301	7	µ1	µ1	PROPN
ejpam-4283	301	8	=	=	SYM
ejpam-4283	301	9	{	{	PUNCT
ejpam-4283	301	10	∅	∅	NOUN
ejpam-4283	301	11	,	,	PUNCT
ejpam-4283	301	12	[	[	X
ejpam-4283	301	13	0	0	NUM
ejpam-4283	301	14	,	,	PUNCT
ejpam-4283	301	15	2	2	NUM
ejpam-4283	301	16	)	)	PUNCT
ejpam-4283	301	17	,	,	PUNCT
ejpam-4283	301	18	(	(	PUNCT
ejpam-4283	301	19	1	1	NUM
ejpam-4283	301	20	,	,	PUNCT
ejpam-4283	301	21	3	3	NUM
ejpam-4283	301	22	]	]	PUNCT
ejpam-4283	301	23	,	,	PUNCT
ejpam-4283	301	24	[	[	X
ejpam-4283	301	25	0	0	NUM
ejpam-4283	301	26	,	,	PUNCT
ejpam-4283	301	27	3	3	NUM
ejpam-4283	301	28	]	]	PUNCT
ejpam-4283	301	29	}	}	PUNCT
ejpam-4283	301	30	and	and	CCONJ
ejpam-4283	301	31	µ2	µ2	PROPN
ejpam-4283	301	32	=	=	PUNCT
ejpam-4283	301	33	{	{	PUNCT
ejpam-4283	301	34	∅	∅	NOUN
ejpam-4283	301	35	,	,	PUNCT
ejpam-4283	301	36	[	[	X
ejpam-4283	301	37	0	0	NUM
ejpam-4283	301	38	,	,	PUNCT
ejpam-4283	301	39	1	1	NUM
ejpam-4283	301	40	)	)	PUNCT
ejpam-4283	301	41	,	,	PUNCT
ejpam-4283	302	1	[	[	X
ejpam-4283	302	2	1	1	NUM
ejpam-4283	302	3	,	,	PUNCT
ejpam-4283	302	4	2	2	NUM
ejpam-4283	302	5	)	)	PUNCT
ejpam-4283	302	6	,	,	PUNCT
ejpam-4283	303	1	[	[	X
ejpam-4283	303	2	0	0	NUM
ejpam-4283	303	3	,	,	PUNCT
ejpam-4283	303	4	2	2	NUM
ejpam-4283	303	5	)	)	PUNCT
ejpam-4283	303	6	}	}	PUNCT
ejpam-4283	303	7	.	.	PUNCT
ejpam-4283	304	1	let	let	VERB
ejpam-4283	304	2	k	k	NOUN
ejpam-4283	305	1	=	=	PUNCT
ejpam-4283	306	1	[	[	X
ejpam-4283	306	2	2	2	NUM
ejpam-4283	306	3	,	,	PUNCT
ejpam-4283	306	4	3	3	NUM
ejpam-4283	306	5	]	]	PUNCT
ejpam-4283	306	6	.	.	PUNCT
ejpam-4283	307	1	then	then	ADV
ejpam-4283	307	2	k	k	PROPN
ejpam-4283	307	3	is	be	AUX
ejpam-4283	307	4	a	a	DET
ejpam-4283	307	5	(	(	PUNCT
ejpam-4283	307	6	s	s	NOUN
ejpam-4283	307	7	,	,	PUNCT
ejpam-4283	307	8	v)nowhere	v)nowhere	X
ejpam-4283	307	9	dense	dense	ADJ
ejpam-4283	307	10	set	set	NOUN
ejpam-4283	307	11	in	in	ADP
ejpam-4283	307	12	x	x	PUNCT
ejpam-4283	307	13	where	where	SCONJ
ejpam-4283	307	14	s	s	X
ejpam-4283	307	15	,	,	PUNCT
ejpam-4283	307	16	v	v	NOUN
ejpam-4283	307	17	=	=	SYM
ejpam-4283	307	18	1	1	NUM
ejpam-4283	307	19	,	,	PUNCT
ejpam-4283	307	20	2	2	NUM
ejpam-4283	307	21	and	and	CCONJ
ejpam-4283	307	22	s	s	X
ejpam-4283	307	23	6=	6=	PROPN
ejpam-4283	308	1	v.	v.	CCONJ
ejpam-4283	309	1	but	but	CCONJ
ejpam-4283	309	2	k	k	PROPN
ejpam-4283	309	3	/∈	/∈	PUNCT
ejpam-4283	309	4	(	(	PUNCT
ejpam-4283	309	5	s	s	NOUN
ejpam-4283	309	6	,	,	PUNCT
ejpam-4283	309	7	v)−s(x	v)−s(x	NUM
ejpam-4283	309	8	)	)	PUNCT
ejpam-4283	309	9	where	where	SCONJ
ejpam-4283	309	10	s	s	X
ejpam-4283	309	11	,	,	PUNCT
ejpam-4283	309	12	v	v	NOUN
ejpam-4283	309	13	=	=	SYM
ejpam-4283	309	14	1	1	NUM
ejpam-4283	309	15	,	,	PUNCT
ejpam-4283	309	16	2	2	NUM
ejpam-4283	309	17	and	and	CCONJ
ejpam-4283	309	18	s	s	X
ejpam-4283	309	19	6=	6=	PROPN
ejpam-4283	309	20	v.	v.	CCONJ
ejpam-4283	309	21	theorem	theorem	NOUN
ejpam-4283	309	22	20	20	NUM
ejpam-4283	309	23	.	.	PUNCT
ejpam-4283	310	1	let	let	AUX
ejpam-4283	310	2	(	(	PUNCT
ejpam-4283	310	3	x,µ1	x,µ1	NOUN
ejpam-4283	310	4	,	,	PUNCT
ejpam-4283	310	5	µ2	µ2	PROPN
ejpam-4283	310	6	)	)	PUNCT
ejpam-4283	310	7	be	be	VERB
ejpam-4283	310	8	a	a	DET
ejpam-4283	310	9	bgts	bgts	NOUN
ejpam-4283	310	10	and	and	CCONJ
ejpam-4283	310	11	q	q	NOUN
ejpam-4283	310	12	⊂	⊂	PROPN
ejpam-4283	310	13	x.	x.	NOUN
ejpam-4283	311	1	if	if	SCONJ
ejpam-4283	311	2	q	q	PROPN
ejpam-4283	311	3	∈	∈	PROPN
ejpam-4283	311	4	(	(	PUNCT
ejpam-4283	311	5	s	s	NOUN
ejpam-4283	311	6	,	,	PUNCT
ejpam-4283	311	7	v)−s(x	v)−s(x	NUM
ejpam-4283	311	8	)	)	PUNCT
ejpam-4283	311	9	,	,	PUNCT
ejpam-4283	311	10	then	then	ADV
ejpam-4283	311	11	q	q	X
ejpam-4283	311	12	is	be	AUX
ejpam-4283	311	13	a	a	DET
ejpam-4283	311	14	(	(	PUNCT
ejpam-4283	311	15	v	v	NOUN
ejpam-4283	311	16	,	,	PUNCT
ejpam-4283	311	17	s)-nowhere	s)-nowhere	X
ejpam-4283	311	18	dense	dense	ADJ
ejpam-4283	311	19	set	set	NOUN
ejpam-4283	311	20	in	in	ADP
ejpam-4283	311	21	x	x	PUNCT
ejpam-4283	311	22	where	where	SCONJ
ejpam-4283	311	23	s	s	X
ejpam-4283	311	24	,	,	PUNCT
ejpam-4283	311	25	v	v	NOUN
ejpam-4283	311	26	=	=	SYM
ejpam-4283	311	27	1	1	NUM
ejpam-4283	311	28	,	,	PUNCT
ejpam-4283	311	29	2	2	NUM
ejpam-4283	311	30	;	;	PUNCT
ejpam-4283	311	31	s	s	X
ejpam-4283	311	32	6=	6=	PROPN
ejpam-4283	311	33	v.	v.	ADP
ejpam-4283	311	34	proof	proof	NOUN
ejpam-4283	311	35	.	.	PUNCT
ejpam-4283	312	1	suppose	suppose	VERB
ejpam-4283	312	2	q	q	X
ejpam-4283	312	3	∈	∈	PROPN
ejpam-4283	312	4	(	(	PUNCT
ejpam-4283	312	5	s	s	NOUN
ejpam-4283	312	6	,	,	PUNCT
ejpam-4283	312	7	v)−s(x	v)−s(x	NUM
ejpam-4283	312	8	)	)	PUNCT
ejpam-4283	312	9	where	where	SCONJ
ejpam-4283	312	10	s	s	X
ejpam-4283	312	11	,	,	PUNCT
ejpam-4283	312	12	v	v	NOUN
ejpam-4283	312	13	=	=	SYM
ejpam-4283	312	14	1	1	NUM
ejpam-4283	312	15	,	,	PUNCT
ejpam-4283	312	16	2	2	NUM
ejpam-4283	312	17	;	;	PUNCT
ejpam-4283	312	18	s	s	PROPN
ejpam-4283	312	19	6=	6=	PROPN
ejpam-4283	312	20	v.	v.	ADP
ejpam-4283	312	21	assume	assume	VERB
ejpam-4283	312	22	that	that	SCONJ
ejpam-4283	312	23	,	,	PUNCT
ejpam-4283	312	24	iv(cs(q	iv(cs(q	NOUN
ejpam-4283	312	25	)	)	PUNCT
ejpam-4283	312	26	)	)	PUNCT
ejpam-4283	312	27	6=	6=	ADP
ejpam-4283	312	28	∅	∅	NOUN
ejpam-4283	312	29	where	where	SCONJ
ejpam-4283	312	30	s	s	X
ejpam-4283	312	31	,	,	PUNCT
ejpam-4283	312	32	v	v	NOUN
ejpam-4283	312	33	=	=	SYM
ejpam-4283	312	34	1	1	NUM
ejpam-4283	312	35	,	,	PUNCT
ejpam-4283	312	36	2	2	NUM
ejpam-4283	312	37	;	;	PUNCT
ejpam-4283	312	38	s	s	PROPN
ejpam-4283	312	39	6=	6=	PROPN
ejpam-4283	312	40	v.	v.	CCONJ
ejpam-4283	312	41	then	then	ADV
ejpam-4283	312	42	there	there	PRON
ejpam-4283	312	43	is	be	VERB
ejpam-4283	312	44	a	a	DET
ejpam-4283	312	45	set	set	NOUN
ejpam-4283	312	46	j	j	PROPN
ejpam-4283	312	47	∈	∈	PROPN
ejpam-4283	312	48	µ̃v	µ̃v	VERB
ejpam-4283	312	49	such	such	ADJ
ejpam-4283	312	50	that	that	SCONJ
ejpam-4283	312	51	j	j	PROPN
ejpam-4283	312	52	⊂	⊂	PROPN
ejpam-4283	312	53	cs(q	cs(q	NOUN
ejpam-4283	312	54	)	)	PUNCT
ejpam-4283	312	55	where	where	SCONJ
ejpam-4283	312	56	s	s	X
ejpam-4283	312	57	,	,	PUNCT
ejpam-4283	312	58	v	v	NOUN
ejpam-4283	312	59	=	=	SYM
ejpam-4283	312	60	1	1	NUM
ejpam-4283	312	61	,	,	PUNCT
ejpam-4283	312	62	2	2	NUM
ejpam-4283	312	63	and	and	CCONJ
ejpam-4283	312	64	s	s	X
ejpam-4283	312	65	6=	6=	PROPN
ejpam-4283	312	66	v	v	NUM
ejpam-4283	312	67	which	which	PRON
ejpam-4283	312	68	implies	imply	VERB
ejpam-4283	312	69	that	that	PRON
ejpam-4283	312	70	q	q	NOUN
ejpam-4283	312	71	/∈	/∈	PUNCT
ejpam-4283	312	72	(	(	PUNCT
ejpam-4283	312	73	s	s	PROPN
ejpam-4283	312	74	,	,	PUNCT
ejpam-4283	312	75	v	v	NOUN
ejpam-4283	312	76	)	)	PUNCT
ejpam-4283	313	1	−	−	PROPN
ejpam-4283	313	2	s(x	s(x	PROPN
ejpam-4283	313	3	)	)	PUNCT
ejpam-4283	313	4	where	where	SCONJ
ejpam-4283	313	5	s	s	X
ejpam-4283	313	6	,	,	PUNCT
ejpam-4283	313	7	v	v	NOUN
ejpam-4283	313	8	=	=	SYM
ejpam-4283	313	9	1	1	NUM
ejpam-4283	313	10	,	,	PUNCT
ejpam-4283	313	11	2	2	NUM
ejpam-4283	313	12	;	;	PUNCT
ejpam-4283	313	13	s	s	PROPN
ejpam-4283	313	14	6=	6=	PROPN
ejpam-4283	313	15	v	v	NUM
ejpam-4283	313	16	which	which	PRON
ejpam-4283	313	17	is	be	AUX
ejpam-4283	313	18	not	not	PART
ejpam-4283	313	19	possible	possible	ADJ
ejpam-4283	313	20	.	.	PUNCT
ejpam-4283	314	1	therefore	therefore	ADV
ejpam-4283	314	2	,	,	PUNCT
ejpam-4283	314	3	q	q	X
ejpam-4283	314	4	is	be	AUX
ejpam-4283	314	5	a	a	DET
ejpam-4283	314	6	(	(	PUNCT
ejpam-4283	314	7	v	v	NOUN
ejpam-4283	314	8	,	,	PUNCT
ejpam-4283	314	9	s)-nowhere	s)-nowhere	X
ejpam-4283	314	10	dense	dense	ADJ
ejpam-4283	314	11	set	set	NOUN
ejpam-4283	314	12	in	in	ADP
ejpam-4283	314	13	x	x	PUNCT
ejpam-4283	314	14	where	where	SCONJ
ejpam-4283	314	15	s	s	X
ejpam-4283	314	16	,	,	PUNCT
ejpam-4283	314	17	v	v	NOUN
ejpam-4283	314	18	=	=	SYM
ejpam-4283	314	19	1	1	NUM
ejpam-4283	314	20	,	,	PUNCT
ejpam-4283	314	21	2	2	NUM
ejpam-4283	314	22	;	;	PUNCT
ejpam-4283	314	23	s	s	PROPN
ejpam-4283	314	24	6=	6=	PROPN
ejpam-4283	314	25	v.	v.	ADP
ejpam-4283	314	26	definition	definition	NOUN
ejpam-4283	314	27	21	21	NUM
ejpam-4283	314	28	.	.	PUNCT
ejpam-4283	315	1	let	let	VERB
ejpam-4283	315	2	q	q	PART
ejpam-4283	315	3	be	be	AUX
ejpam-4283	315	4	a	a	DET
ejpam-4283	315	5	non	non	ADJ
ejpam-4283	315	6	-	-	ADJ
ejpam-4283	315	7	null	null	ADJ
ejpam-4283	315	8	subset	subset	NOUN
ejpam-4283	315	9	of	of	ADP
ejpam-4283	315	10	a	a	DET
ejpam-4283	315	11	bgts	bgts	NOUN
ejpam-4283	315	12	(	(	PUNCT
ejpam-4283	315	13	x,µ1	x,µ1	PROPN
ejpam-4283	315	14	,	,	PUNCT
ejpam-4283	315	15	µ2	µ2	PROPN
ejpam-4283	315	16	)	)	PUNCT
ejpam-4283	315	17	.	.	PUNCT
ejpam-4283	316	1	then	then	ADV
ejpam-4283	316	2	for	for	ADP
ejpam-4283	316	3	s	s	PROPN
ejpam-4283	316	4	,	,	PUNCT
ejpam-4283	316	5	v	v	NOUN
ejpam-4283	316	6	=	=	SYM
ejpam-4283	316	7	1	1	NUM
ejpam-4283	316	8	,	,	PUNCT
ejpam-4283	316	9	2	2	NUM
ejpam-4283	316	10	and	and	CCONJ
ejpam-4283	316	11	s	s	PROPN
ejpam-4283	316	12	6=	6=	PROPN
ejpam-4283	316	13	v	v	NOUN
ejpam-4283	316	14	,	,	PUNCT
ejpam-4283	316	15	(	(	PUNCT
ejpam-4283	316	16	a	a	X
ejpam-4283	316	17	)	)	PUNCT
ejpam-4283	316	18	q	q	NOUN
ejpam-4283	316	19	is	be	AUX
ejpam-4283	316	20	called	call	VERB
ejpam-4283	316	21	(	(	PUNCT
ejpam-4283	316	22	s	s	PROPN
ejpam-4283	316	23	,	,	PUNCT
ejpam-4283	316	24	v)-meager	v)-meager	NOUN
ejpam-4283	316	25	if	if	SCONJ
ejpam-4283	316	26	q	q	PROPN
ejpam-4283	316	27	=	=	PUNCT
ejpam-4283	316	28	⋃	⋃	PROPN
ejpam-4283	316	29	m∈ndm	m∈ndm	PROPN
ejpam-4283	316	30	where	where	SCONJ
ejpam-4283	316	31	each	each	DET
ejpam-4283	316	32	dm	dm	NOUN
ejpam-4283	316	33	is	be	AUX
ejpam-4283	316	34	a	a	DET
ejpam-4283	316	35	(	(	PUNCT
ejpam-4283	316	36	s	s	X
ejpam-4283	316	37	,	,	PUNCT
ejpam-4283	316	38	v)-nowhere	v)-nowhere	PUNCT
ejpam-4283	316	39	dense	dense	ADJ
ejpam-4283	316	40	set	set	NOUN
ejpam-4283	316	41	in	in	ADP
ejpam-4283	316	42	x.	x.	NOUN
ejpam-4283	316	43	(	(	PUNCT
ejpam-4283	316	44	b	b	X
ejpam-4283	316	45	)	)	PUNCT
ejpam-4283	316	46	q	q	PUNCT
ejpam-4283	316	47	is	be	AUX
ejpam-4283	316	48	called	call	VERB
ejpam-4283	316	49	(	(	PUNCT
ejpam-4283	316	50	s	s	PROPN
ejpam-4283	316	51	,	,	PUNCT
ejpam-4283	316	52	v)-residual	v)-residual	ADJ
ejpam-4283	316	53	if	if	SCONJ
ejpam-4283	316	54	x	x	PRON
ejpam-4283	316	55	−q	−q	NOUN
ejpam-4283	316	56	is	be	AUX
ejpam-4283	316	57	a	a	DET
ejpam-4283	316	58	(	(	PUNCT
ejpam-4283	316	59	s	s	X
ejpam-4283	316	60	,	,	PUNCT
ejpam-4283	316	61	v)-meager	v)-meager	NOUN
ejpam-4283	316	62	set	set	VERB
ejpam-4283	316	63	in	in	ADP
ejpam-4283	316	64	x.	x.	PROPN
ejpam-4283	316	65	(	(	PUNCT
ejpam-4283	316	66	c	c	X
ejpam-4283	316	67	)	)	PUNCT
ejpam-4283	316	68	q	q	PUNCT
ejpam-4283	316	69	is	be	AUX
ejpam-4283	316	70	of	of	ADP
ejpam-4283	316	71	(	(	PUNCT
ejpam-4283	316	72	s	s	X
ejpam-4283	316	73	,	,	PUNCT
ejpam-4283	316	74	v)-second	v)-second	PUNCT
ejpam-4283	316	75	category	category	NOUN
ejpam-4283	316	76	set	set	VERB
ejpam-4283	316	77	if	if	SCONJ
ejpam-4283	316	78	q	q	NOUN
ejpam-4283	316	79	is	be	AUX
ejpam-4283	316	80	not	not	PART
ejpam-4283	316	81	a	a	DET
ejpam-4283	316	82	(	(	PUNCT
ejpam-4283	316	83	s	s	X
ejpam-4283	316	84	,	,	PUNCT
ejpam-4283	316	85	v)-meager	v)-meager	NOUN
ejpam-4283	316	86	set	set	VERB
ejpam-4283	316	87	in	in	ADP
ejpam-4283	316	88	x.	x.	NOUN
ejpam-4283	316	89	definition	definition	NOUN
ejpam-4283	316	90	22	22	NUM
ejpam-4283	316	91	.	.	PUNCT
ejpam-4283	317	1	let	let	VERB
ejpam-4283	317	2	b	b	X
ejpam-4283	317	3	be	be	AUX
ejpam-4283	317	4	a	a	DET
ejpam-4283	317	5	non	non	ADJ
ejpam-4283	317	6	-	-	ADJ
ejpam-4283	317	7	null	null	ADJ
ejpam-4283	317	8	subset	subset	NOUN
ejpam-4283	317	9	of	of	ADP
ejpam-4283	317	10	a	a	DET
ejpam-4283	317	11	bgts	bgts	NOUN
ejpam-4283	317	12	(	(	PUNCT
ejpam-4283	317	13	x,µ1	x,µ1	PROPN
ejpam-4283	317	14	,	,	PUNCT
ejpam-4283	317	15	µ2	µ2	PROPN
ejpam-4283	317	16	)	)	PUNCT
ejpam-4283	317	17	.	.	PUNCT
ejpam-4283	318	1	then	then	ADV
ejpam-4283	318	2	for	for	ADP
ejpam-4283	318	3	s	s	PROPN
ejpam-4283	318	4	,	,	PUNCT
ejpam-4283	318	5	v	v	NOUN
ejpam-4283	318	6	=	=	SYM
ejpam-4283	318	7	1	1	NUM
ejpam-4283	318	8	,	,	PUNCT
ejpam-4283	318	9	2	2	NUM
ejpam-4283	318	10	and	and	CCONJ
ejpam-4283	318	11	s	s	PROPN
ejpam-4283	318	12	6=	6=	PROPN
ejpam-4283	318	13	v	v	NOUN
ejpam-4283	318	14	,	,	PUNCT
ejpam-4283	318	15	(	(	PUNCT
ejpam-4283	318	16	a	a	X
ejpam-4283	318	17	)	)	PUNCT
ejpam-4283	318	18	b	b	NOUN
ejpam-4283	318	19	is	be	AUX
ejpam-4283	318	20	said	say	VERB
ejpam-4283	318	21	to	to	PART
ejpam-4283	318	22	be	be	AUX
ejpam-4283	318	23	a	a	DET
ejpam-4283	318	24	(	(	PUNCT
ejpam-4283	318	25	s	s	PROPN
ejpam-4283	318	26	,	,	PUNCT
ejpam-4283	318	27	v)-s	v)-	NOUN
ejpam-4283	318	28	-	-	PUNCT
ejpam-4283	318	29	meager	meager	ADJ
ejpam-4283	318	30	set	set	NOUN
ejpam-4283	318	31	if	if	SCONJ
ejpam-4283	318	32	b	b	PROPN
ejpam-4283	318	33	=	=	SYM
ejpam-4283	318	34	⋃	⋃	VERB
ejpam-4283	318	35	m∈nbm	m∈nbm	PROPN
ejpam-4283	318	36	for	for	ADP
ejpam-4283	318	37	each	each	DET
ejpam-4283	318	38	bm	bm	PROPN
ejpam-4283	318	39	∈	∈	PROPN
ejpam-4283	318	40	(	(	PUNCT
ejpam-4283	318	41	s	s	NOUN
ejpam-4283	318	42	,	,	PUNCT
ejpam-4283	318	43	v)−s(x	v)−s(x	NUM
ejpam-4283	318	44	)	)	PUNCT
ejpam-4283	318	45	.	.	PUNCT
ejpam-4283	319	1	(	(	PUNCT
ejpam-4283	319	2	b	b	X
ejpam-4283	319	3	)	)	PUNCT
ejpam-4283	319	4	b	b	NOUN
ejpam-4283	319	5	is	be	AUX
ejpam-4283	319	6	called	call	VERB
ejpam-4283	319	7	as	as	ADP
ejpam-4283	319	8	a	a	DET
ejpam-4283	319	9	(	(	PUNCT
ejpam-4283	319	10	s	s	PROPN
ejpam-4283	319	11	,	,	PUNCT
ejpam-4283	319	12	v)-s	v)-	NOUN
ejpam-4283	319	13	-	-	ADJ
ejpam-4283	319	14	residual	residual	ADJ
ejpam-4283	319	15	set	set	NOUN
ejpam-4283	319	16	if	if	SCONJ
ejpam-4283	319	17	x	x	PRON
ejpam-4283	319	18	−b	−b	NOUN
ejpam-4283	319	19	is	be	AUX
ejpam-4283	319	20	a	a	DET
ejpam-4283	319	21	(	(	PUNCT
ejpam-4283	319	22	s	s	PROPN
ejpam-4283	319	23	,	,	PUNCT
ejpam-4283	319	24	v)-s	v)-	NOUN
ejpam-4283	319	25	-	-	ADJ
ejpam-4283	319	26	meager	meager	ADJ
ejpam-4283	319	27	set	set	NOUN
ejpam-4283	319	28	in	in	ADP
ejpam-4283	319	29	x.	x.	PROPN
ejpam-4283	319	30	(	(	PUNCT
ejpam-4283	319	31	c	c	X
ejpam-4283	319	32	)	)	PUNCT
ejpam-4283	319	33	b	b	NOUN
ejpam-4283	319	34	is	be	AUX
ejpam-4283	319	35	of	of	ADP
ejpam-4283	319	36	(	(	PUNCT
ejpam-4283	319	37	s	s	X
ejpam-4283	319	38	,	,	PUNCT
ejpam-4283	319	39	v)-s	v)-s	PROPN
ejpam-4283	319	40	-	-	PUNCT
ejpam-4283	319	41	second	second	ADJ
ejpam-4283	319	42	category	category	NOUN
ejpam-4283	319	43	set	set	VERB
ejpam-4283	319	44	if	if	SCONJ
ejpam-4283	319	45	b	b	PROPN
ejpam-4283	319	46	is	be	AUX
ejpam-4283	319	47	not	not	PART
ejpam-4283	319	48	a	a	DET
ejpam-4283	319	49	(	(	PUNCT
ejpam-4283	319	50	s	s	PROPN
ejpam-4283	319	51	,	,	PUNCT
ejpam-4283	319	52	v)-s	v)-	NOUN
ejpam-4283	319	53	-	-	ADJ
ejpam-4283	319	54	meager	meager	ADJ
ejpam-4283	319	55	set	set	NOUN
ejpam-4283	319	56	in	in	ADP
ejpam-4283	319	57	x.	x.	NOUN
ejpam-4283	319	58	corollary	corollary	PROPN
ejpam-4283	319	59	23	23	NUM
ejpam-4283	319	60	.	.	PUNCT
ejpam-4283	320	1	let	let	AUX
ejpam-4283	320	2	(	(	PUNCT
ejpam-4283	320	3	x,µ1	x,µ1	NOUN
ejpam-4283	320	4	,	,	PUNCT
ejpam-4283	320	5	µ2	µ2	PROPN
ejpam-4283	320	6	)	)	PUNCT
ejpam-4283	320	7	be	be	VERB
ejpam-4283	320	8	a	a	DET
ejpam-4283	320	9	bgts	bgts	NOUN
ejpam-4283	320	10	and	and	CCONJ
ejpam-4283	320	11	d	d	X
ejpam-4283	320	12	⊂	⊂	PROPN
ejpam-4283	320	13	x.	x.	NOUN
ejpam-4283	320	14	for	for	ADP
ejpam-4283	320	15	s	s	PROPN
ejpam-4283	320	16	,	,	PUNCT
ejpam-4283	320	17	v	v	NOUN
ejpam-4283	320	18	=	=	SYM
ejpam-4283	320	19	1	1	NUM
ejpam-4283	320	20	,	,	PUNCT
ejpam-4283	320	21	2	2	NUM
ejpam-4283	320	22	and	and	CCONJ
ejpam-4283	320	23	s	s	PROPN
ejpam-4283	320	24	6=	6=	PROPN
ejpam-4283	320	25	v	v	NOUN
ejpam-4283	320	26	,	,	PUNCT
ejpam-4283	320	27	the	the	DET
ejpam-4283	320	28	followings	following	NOUN
ejpam-4283	320	29	are	be	AUX
ejpam-4283	320	30	true	true	ADJ
ejpam-4283	320	31	.	.	PUNCT
ejpam-4283	321	1	(	(	PUNCT
ejpam-4283	321	2	a	a	X
ejpam-4283	321	3	)	)	PUNCT
ejpam-4283	321	4	if	if	SCONJ
ejpam-4283	321	5	d	d	PROPN
ejpam-4283	321	6	is	be	AUX
ejpam-4283	321	7	(	(	PUNCT
ejpam-4283	321	8	s	s	X
ejpam-4283	321	9	,	,	PUNCT
ejpam-4283	321	10	v)-s	v)-	NOUN
ejpam-4283	321	11	-	-	PUNCT
ejpam-4283	321	12	meager	meager	ADJ
ejpam-4283	321	13	,	,	PUNCT
ejpam-4283	321	14	then	then	ADV
ejpam-4283	321	15	it	it	PRON
ejpam-4283	321	16	is	be	AUX
ejpam-4283	321	17	a	a	DET
ejpam-4283	321	18	(	(	PUNCT
ejpam-4283	321	19	v	v	NOUN
ejpam-4283	321	20	,	,	PUNCT
ejpam-4283	321	21	s)-meager	s)-meager	PUNCT
ejpam-4283	321	22	set	set	NOUN
ejpam-4283	321	23	.	.	PUNCT
ejpam-4283	322	1	(	(	PUNCT
ejpam-4283	322	2	b	b	X
ejpam-4283	322	3	)	)	PUNCT
ejpam-4283	322	4	if	if	SCONJ
ejpam-4283	322	5	d	d	PROPN
ejpam-4283	322	6	is	be	AUX
ejpam-4283	322	7	(	(	PUNCT
ejpam-4283	322	8	s	s	X
ejpam-4283	322	9	,	,	PUNCT
ejpam-4283	322	10	v)-s	v)-	NOUN
ejpam-4283	322	11	-	-	NOUN
ejpam-4283	322	12	residual	residual	ADJ
ejpam-4283	322	13	,	,	PUNCT
ejpam-4283	322	14	then	then	ADV
ejpam-4283	322	15	it	it	PRON
ejpam-4283	322	16	is	be	AUX
ejpam-4283	322	17	a	a	DET
ejpam-4283	322	18	(	(	PUNCT
ejpam-4283	322	19	v	v	NOUN
ejpam-4283	322	20	,	,	PUNCT
ejpam-4283	322	21	s)-residual	s)-residual	ADJ
ejpam-4283	322	22	set	set	NOUN
ejpam-4283	322	23	.	.	PUNCT
ejpam-4283	323	1	(	(	PUNCT
ejpam-4283	323	2	c	c	X
ejpam-4283	323	3	)	)	PUNCT
ejpam-4283	323	4	if	if	SCONJ
ejpam-4283	323	5	d	d	PROPN
ejpam-4283	323	6	is	be	AUX
ejpam-4283	323	7	of	of	ADP
ejpam-4283	323	8	(	(	PUNCT
ejpam-4283	323	9	s	s	X
ejpam-4283	323	10	,	,	PUNCT
ejpam-4283	323	11	v)-second	v)-second	PUNCT
ejpam-4283	323	12	category	category	NOUN
ejpam-4283	323	13	set	set	NOUN
ejpam-4283	323	14	,	,	PUNCT
ejpam-4283	323	15	then	then	ADV
ejpam-4283	323	16	it	it	PRON
ejpam-4283	323	17	is	be	AUX
ejpam-4283	323	18	of	of	ADP
ejpam-4283	323	19	(	(	PUNCT
ejpam-4283	323	20	v	v	NOUN
ejpam-4283	323	21	,	,	PUNCT
ejpam-4283	323	22	s)-s	s)-	NOUN
ejpam-4283	323	23	-	-	PUNCT
ejpam-4283	323	24	second	second	ADJ
ejpam-4283	323	25	category	category	NOUN
ejpam-4283	323	26	set	set	VERB
ejpam-4283	323	27	.	.	PUNCT
ejpam-4283	324	1	corollary	corollary	ADJ
ejpam-4283	324	2	24	24	NUM
ejpam-4283	324	3	.	.	PUNCT
ejpam-4283	325	1	let	let	AUX
ejpam-4283	325	2	(	(	PUNCT
ejpam-4283	325	3	x,µ1	x,µ1	NOUN
ejpam-4283	325	4	,	,	PUNCT
ejpam-4283	325	5	µ2	µ2	PROPN
ejpam-4283	325	6	)	)	PUNCT
ejpam-4283	325	7	be	be	AUX
ejpam-4283	325	8	a	a	DET
ejpam-4283	325	9	bgts	bgts	NOUN
ejpam-4283	325	10	.	.	PUNCT
ejpam-4283	326	1	then	then	ADV
ejpam-4283	326	2	the	the	DET
ejpam-4283	326	3	followings	following	NOUN
ejpam-4283	326	4	are	be	AUX
ejpam-4283	326	5	true	true	ADJ
ejpam-4283	326	6	.	.	PUNCT
ejpam-4283	327	1	(	(	PUNCT
ejpam-4283	327	2	a	a	X
ejpam-4283	327	3	)	)	PUNCT
ejpam-4283	327	4	if	if	SCONJ
ejpam-4283	327	5	µ2	µ2	PROPN
ejpam-4283	327	6	is	be	AUX
ejpam-4283	327	7	a	a	DET
ejpam-4283	327	8	strong	strong	ADJ
ejpam-4283	327	9	generalized	generalized	ADJ
ejpam-4283	327	10	topology	topology	NOUN
ejpam-4283	327	11	,	,	PUNCT
ejpam-4283	327	12	then	then	ADV
ejpam-4283	327	13	(	(	PUNCT
ejpam-4283	327	14	1	1	NUM
ejpam-4283	327	15	,	,	PUNCT
ejpam-4283	327	16	2)−s(x	2)−s(x	NUM
ejpam-4283	327	17	)	)	PUNCT
ejpam-4283	327	18	⊂	⊂	PROPN
ejpam-4283	327	19	(	(	PUNCT
ejpam-4283	327	20	1	1	NUM
ejpam-4283	327	21	,	,	PUNCT
ejpam-4283	327	22	2	2	NUM
ejpam-4283	327	23	)	)	PUNCT
ejpam-4283	327	24	?	?	PUNCT
ejpam-4283	328	1	−n	−n	INTJ
ejpam-4283	328	2	(	(	PUNCT
ejpam-4283	328	3	x	x	NOUN
ejpam-4283	328	4	)	)	PUNCT
ejpam-4283	328	5	.	.	PUNCT
ejpam-4283	329	1	(	(	PUNCT
ejpam-4283	329	2	b	b	X
ejpam-4283	329	3	)	)	PUNCT
ejpam-4283	329	4	if	if	SCONJ
ejpam-4283	329	5	µ1	µ1	PROPN
ejpam-4283	329	6	is	be	AUX
ejpam-4283	329	7	a	a	DET
ejpam-4283	329	8	strong	strong	ADJ
ejpam-4283	329	9	generalized	generalized	ADJ
ejpam-4283	329	10	topology	topology	NOUN
ejpam-4283	329	11	,	,	PUNCT
ejpam-4283	329	12	then	then	ADV
ejpam-4283	329	13	(	(	PUNCT
ejpam-4283	329	14	2	2	NUM
ejpam-4283	329	15	,	,	PUNCT
ejpam-4283	329	16	1)−s(x	1)−s(x	NUM
ejpam-4283	329	17	)	)	PUNCT
ejpam-4283	329	18	⊂	⊂	PROPN
ejpam-4283	329	19	(	(	PUNCT
ejpam-4283	329	20	2	2	NUM
ejpam-4283	329	21	,	,	PUNCT
ejpam-4283	329	22	1	1	NUM
ejpam-4283	329	23	)	)	PUNCT
ejpam-4283	329	24	?	?	PUNCT
ejpam-4283	330	1	−n	−n	INTJ
ejpam-4283	330	2	(	(	PUNCT
ejpam-4283	330	3	x	x	NOUN
ejpam-4283	330	4	)	)	PUNCT
ejpam-4283	330	5	.	.	PUNCT
ejpam-4283	331	1	proof	proof	NOUN
ejpam-4283	331	2	.	.	PUNCT
ejpam-4283	332	1	(	(	PUNCT
ejpam-4283	332	2	a	a	X
ejpam-4283	332	3	)	)	PUNCT
ejpam-4283	332	4	.	.	PUNCT
ejpam-4283	333	1	assume	assume	VERB
ejpam-4283	333	2	that	that	SCONJ
ejpam-4283	333	3	,	,	PUNCT
ejpam-4283	333	4	µ2	µ2	PROPN
ejpam-4283	333	5	is	be	AUX
ejpam-4283	333	6	a	a	DET
ejpam-4283	333	7	strong	strong	ADJ
ejpam-4283	333	8	generalized	generalized	ADJ
ejpam-4283	333	9	topology	topology	NOUN
ejpam-4283	333	10	.	.	PUNCT
ejpam-4283	334	1	let	let	VERB
ejpam-4283	334	2	q	q	PROPN
ejpam-4283	334	3	∈	∈	PROPN
ejpam-4283	334	4	(	(	PUNCT
ejpam-4283	334	5	1	1	NUM
ejpam-4283	334	6	,	,	PUNCT
ejpam-4283	334	7	2)−s(x	2)−s(x	NUM
ejpam-4283	334	8	)	)	PUNCT
ejpam-4283	334	9	.	.	PUNCT
ejpam-4283	335	1	by	by	ADP
ejpam-4283	335	2	theorem	theorem	NOUN
ejpam-4283	335	3	20	20	NUM
ejpam-4283	335	4	,	,	PUNCT
ejpam-4283	335	5	q	q	PUNCT
ejpam-4283	335	6	is	be	AUX
ejpam-4283	335	7	a	a	DET
ejpam-4283	335	8	(	(	PUNCT
ejpam-4283	335	9	2	2	NUM
ejpam-4283	335	10	,	,	PUNCT
ejpam-4283	335	11	1)-nowhere	1)-nowhere	NUM
ejpam-4283	335	12	dense	dense	ADJ
ejpam-4283	335	13	set	set	NOUN
ejpam-4283	335	14	in	in	ADP
ejpam-4283	335	15	x.	x.	NOUN
ejpam-4283	335	16	by	by	ADP
ejpam-4283	335	17	our	our	PRON
ejpam-4283	335	18	assumption	assumption	NOUN
ejpam-4283	335	19	and	and	CCONJ
ejpam-4283	335	20	theorem	theorem	VERB
ejpam-4283	335	21	4	4	NUM
ejpam-4283	335	22	(	(	PUNCT
ejpam-4283	335	23	b	b	NOUN
ejpam-4283	335	24	)	)	PUNCT
ejpam-4283	335	25	,	,	PUNCT
ejpam-4283	335	26	q	q	PROPN
ejpam-4283	335	27	is	be	AUX
ejpam-4283	335	28	a	a	DET
ejpam-4283	335	29	(	(	PUNCT
ejpam-4283	335	30	1	1	NUM
ejpam-4283	335	31	,	,	PUNCT
ejpam-4283	335	32	2)?-nowhere	2)?-nowhere	NUM
ejpam-4283	335	33	dense	dense	ADJ
ejpam-4283	335	34	set	set	NOUN
ejpam-4283	335	35	in	in	ADP
ejpam-4283	335	36	x.	x.	NOUN
ejpam-4283	335	37	(	(	PUNCT
ejpam-4283	335	38	b	b	NOUN
ejpam-4283	335	39	)	)	PUNCT
ejpam-4283	335	40	.	.	PUNCT
ejpam-4283	336	1	suppose	suppose	VERB
ejpam-4283	336	2	that	that	SCONJ
ejpam-4283	336	3	,	,	PUNCT
ejpam-4283	336	4	µ1	µ1	PROPN
ejpam-4283	336	5	is	be	AUX
ejpam-4283	336	6	a	a	DET
ejpam-4283	336	7	strong	strong	ADJ
ejpam-4283	336	8	generalized	generalized	ADJ
ejpam-4283	336	9	topology	topology	NOUN
ejpam-4283	336	10	.	.	PUNCT
ejpam-4283	337	1	let	let	VERB
ejpam-4283	337	2	d	d	X
ejpam-4283	337	3	∈	∈	PROPN
ejpam-4283	337	4	(	(	PUNCT
ejpam-4283	337	5	2	2	NUM
ejpam-4283	337	6	,	,	PUNCT
ejpam-4283	337	7	1)−s(x	1)−s(x	NUM
ejpam-4283	337	8	)	)	PUNCT
ejpam-4283	337	9	.	.	PUNCT
ejpam-4283	338	1	by	by	ADP
ejpam-4283	338	2	theorem	theorem	ADJ
ejpam-4283	338	3	20	20	NUM
ejpam-4283	338	4	and	and	CCONJ
ejpam-4283	338	5	theorem	theorem	VERB
ejpam-4283	338	6	4	4	NUM
ejpam-4283	338	7	(	(	PUNCT
ejpam-4283	338	8	a	a	NOUN
ejpam-4283	338	9	)	)	PUNCT
ejpam-4283	338	10	,	,	PUNCT
ejpam-4283	338	11	d	d	PROPN
ejpam-4283	338	12	∈	∈	PROPN
ejpam-4283	338	13	(	(	PUNCT
ejpam-4283	338	14	2	2	NUM
ejpam-4283	338	15	,	,	PUNCT
ejpam-4283	338	16	1	1	NUM
ejpam-4283	338	17	)	)	PUNCT
ejpam-4283	338	18	?	?	PUNCT
ejpam-4283	339	1	−n	−n	INTJ
ejpam-4283	339	2	(	(	PUNCT
ejpam-4283	339	3	x	x	NOUN
ejpam-4283	339	4	)	)	PUNCT
ejpam-4283	339	5	.	.	PUNCT
ejpam-4283	340	1	definition	definition	NOUN
ejpam-4283	340	2	25	25	NUM
ejpam-4283	340	3	.	.	PUNCT
ejpam-4283	341	1	let	let	AUX
ejpam-4283	341	2	(	(	PUNCT
ejpam-4283	341	3	x,µ1	x,µ1	NOUN
ejpam-4283	341	4	,	,	PUNCT
ejpam-4283	341	5	µ2	µ2	PROPN
ejpam-4283	341	6	)	)	PUNCT
ejpam-4283	341	7	satisfy	satisfy	VERB
ejpam-4283	341	8	the	the	DET
ejpam-4283	341	9	condition	condition	NOUN
ejpam-4283	341	10	;	;	PUNCT
ejpam-4283	341	11	if	if	SCONJ
ejpam-4283	341	12	b1	b1	PROPN
ejpam-4283	341	13	∈	∈	PROPN
ejpam-4283	341	14	µ̃s	µ̃s	NOUN
ejpam-4283	341	15	,	,	PUNCT
ejpam-4283	341	16	b2	b2	NOUN
ejpam-4283	341	17	∈	∈	PROPN
ejpam-4283	341	18	µ̃v	µ̃v	PART
ejpam-4283	341	19	and	and	CCONJ
ejpam-4283	341	20	b1	b1	PROPN
ejpam-4283	341	21	∩b2	∩b2	PROPN
ejpam-4283	341	22	6=	6=	PROPN
ejpam-4283	341	23	∅	∅	NOUN
ejpam-4283	341	24	,	,	PUNCT
ejpam-4283	341	25	then	then	ADV
ejpam-4283	341	26	is(b1	is(b1	VERB
ejpam-4283	341	27	∩b2	∩b2	PROPN
ejpam-4283	341	28	)	)	PUNCT
ejpam-4283	341	29	6=	6=	ADP
ejpam-4283	341	30	∅	∅	NOUN
ejpam-4283	341	31	p.	p.	NOUN
ejpam-4283	341	32	yupapin	yupapin	PROPN
ejpam-4283	341	33	,	,	PUNCT
ejpam-4283	341	34	v.	v.	CCONJ
ejpam-4283	341	35	subramanian	subramanian	PROPN
ejpam-4283	341	36	,	,	PUNCT
ejpam-4283	341	37	y.	y.	PROPN
ejpam-4283	341	38	farhat	farhat	PROPN
ejpam-4283	341	39	/	/	SYM
ejpam-4283	341	40	eur	eur	PROPN
ejpam-4283	341	41	.	.	PUNCT
ejpam-4283	342	1	j.	j.	PROPN
ejpam-4283	342	2	pure	pure	PROPN
ejpam-4283	342	3	appl	appl	PROPN
ejpam-4283	342	4	.	.	PROPN
ejpam-4283	342	5	math	math	PROPN
ejpam-4283	342	6	,	,	PUNCT
ejpam-4283	342	7	15	15	NUM
ejpam-4283	342	8	(	(	PUNCT
ejpam-4283	342	9	2	2	NUM
ejpam-4283	342	10	)	)	PUNCT
ejpam-4283	342	11	(	(	PUNCT
ejpam-4283	342	12	2022	2022	NUM
ejpam-4283	342	13	)	)	PUNCT
ejpam-4283	342	14	,	,	PUNCT
ejpam-4283	342	15	403	403	NUM
ejpam-4283	342	16	-	-	SYM
ejpam-4283	342	17	414	414	NUM
ejpam-4283	342	18	410	410	NUM
ejpam-4283	342	19	where	where	SCONJ
ejpam-4283	342	20	s	s	X
ejpam-4283	342	21	,	,	PUNCT
ejpam-4283	342	22	v	v	NOUN
ejpam-4283	342	23	=	=	SYM
ejpam-4283	342	24	1	1	NUM
ejpam-4283	342	25	,	,	PUNCT
ejpam-4283	342	26	2	2	NUM
ejpam-4283	342	27	and	and	CCONJ
ejpam-4283	342	28	s	s	X
ejpam-4283	342	29	6=	6=	PROPN
ejpam-4283	342	30	v.	v.	ADP
ejpam-4283	342	31	then	then	ADV
ejpam-4283	342	32	the	the	DET
ejpam-4283	342	33	bgts	bgts	NOUN
ejpam-4283	342	34	(	(	PUNCT
ejpam-4283	342	35	x,µ1	x,µ1	PROPN
ejpam-4283	342	36	,	,	PUNCT
ejpam-4283	342	37	µ2	µ2	PROPN
ejpam-4283	342	38	)	)	PUNCT
ejpam-4283	342	39	is	be	AUX
ejpam-4283	342	40	said	say	VERB
ejpam-4283	342	41	to	to	PART
ejpam-4283	342	42	satisfy	satisfy	VERB
ejpam-4283	342	43	the	the	DET
ejpam-4283	342	44	is	is	NOUN
ejpam-4283	342	45	-	-	PUNCT
ejpam-4283	342	46	property	property	NOUN
ejpam-4283	342	47	.	.	PUNCT
ejpam-4283	343	1	theorem	theorem	NOUN
ejpam-4283	343	2	26	26	NUM
ejpam-4283	343	3	.	.	PUNCT
ejpam-4283	344	1	let	let	AUX
ejpam-4283	344	2	(	(	PUNCT
ejpam-4283	344	3	x,µ1	x,µ1	NOUN
ejpam-4283	344	4	,	,	PUNCT
ejpam-4283	344	5	µ2	µ2	PROPN
ejpam-4283	344	6	)	)	PUNCT
ejpam-4283	344	7	be	be	VERB
ejpam-4283	344	8	a	a	DET
ejpam-4283	344	9	bgts	bgts	NOUN
ejpam-4283	344	10	which	which	PRON
ejpam-4283	344	11	has	have	VERB
ejpam-4283	344	12	the	the	DET
ejpam-4283	344	13	is	is	NOUN
ejpam-4283	344	14	-	-	PUNCT
ejpam-4283	344	15	property	property	NOUN
ejpam-4283	344	16	and	and	CCONJ
ejpam-4283	344	17	k	k	NOUN
ejpam-4283	344	18	,	,	PUNCT
ejpam-4283	344	19	l	l	NOUN
ejpam-4283	344	20	,	,	PUNCT
ejpam-4283	344	21	q	q	X
ejpam-4283	344	22	⊂	⊂	PROPN
ejpam-4283	344	23	x.	x.	NOUN
ejpam-4283	344	24	then	then	ADV
ejpam-4283	344	25	(	(	PUNCT
ejpam-4283	344	26	a	a	X
ejpam-4283	344	27	)	)	PUNCT
ejpam-4283	344	28	if	if	SCONJ
ejpam-4283	344	29	k	k	PROPN
ejpam-4283	344	30	∈	∈	PROPN
ejpam-4283	344	31	(	(	PUNCT
ejpam-4283	344	32	s	s	PROPN
ejpam-4283	344	33	,	,	PUNCT
ejpam-4283	344	34	v	v	NOUN
ejpam-4283	344	35	)	)	PUNCT
ejpam-4283	344	36	−	−	PROPN
ejpam-4283	344	37	s(x	s(x	PROPN
ejpam-4283	344	38	)	)	PUNCT
ejpam-4283	344	39	and	and	CCONJ
ejpam-4283	344	40	l	l	NOUN
ejpam-4283	344	41	∈	∈	PROPN
ejpam-4283	344	42	(	(	PUNCT
ejpam-4283	344	43	v	v	NOUN
ejpam-4283	344	44	,	,	PUNCT
ejpam-4283	344	45	s	s	NOUN
ejpam-4283	344	46	)	)	PUNCT
ejpam-4283	344	47	−	−	PROPN
ejpam-4283	344	48	s(x	s(x	PROPN
ejpam-4283	344	49	)	)	PUNCT
ejpam-4283	344	50	,	,	PUNCT
ejpam-4283	344	51	then	then	ADV
ejpam-4283	344	52	k	k	PROPN
ejpam-4283	344	53	∪	∪	VERB
ejpam-4283	344	54	l	l	PROPN
ejpam-4283	344	55	∈	∈	PROPN
ejpam-4283	344	56	(	(	PUNCT
ejpam-4283	344	57	s	s	PROPN
ejpam-4283	344	58	,	,	PUNCT
ejpam-4283	344	59	v	v	NOUN
ejpam-4283	344	60	)	)	PUNCT
ejpam-4283	344	61	−	−	PROPN
ejpam-4283	344	62	s(x	s(x	PROPN
ejpam-4283	344	63	)	)	PUNCT
ejpam-4283	344	64	where	where	SCONJ
ejpam-4283	344	65	s	s	X
ejpam-4283	344	66	,	,	PUNCT
ejpam-4283	344	67	v	v	NOUN
ejpam-4283	344	68	=	=	SYM
ejpam-4283	344	69	1	1	NUM
ejpam-4283	344	70	,	,	PUNCT
ejpam-4283	344	71	2	2	NUM
ejpam-4283	344	72	;	;	PUNCT
ejpam-4283	344	73	s	s	PROPN
ejpam-4283	344	74	6=	6=	PROPN
ejpam-4283	344	75	v.	v.	PROPN
ejpam-4283	344	76	(	(	PUNCT
ejpam-4283	344	77	b	b	NOUN
ejpam-4283	344	78	)	)	PUNCT
ejpam-4283	344	79	if	if	SCONJ
ejpam-4283	344	80	l	l	NOUN
ejpam-4283	344	81	is	be	AUX
ejpam-4283	344	82	a	a	DET
ejpam-4283	344	83	(	(	PUNCT
ejpam-4283	344	84	v	v	NOUN
ejpam-4283	344	85	,	,	PUNCT
ejpam-4283	344	86	s)-nowhere	s)-nowhere	PUNCT
ejpam-4283	344	87	dense	dense	ADJ
ejpam-4283	344	88	set	set	NOUN
ejpam-4283	344	89	,	,	PUNCT
ejpam-4283	344	90	then	then	ADV
ejpam-4283	344	91	l	l	PROPN
ejpam-4283	344	92	∈	∈	PROPN
ejpam-4283	344	93	(	(	PUNCT
ejpam-4283	344	94	s	s	NOUN
ejpam-4283	344	95	,	,	PUNCT
ejpam-4283	344	96	v)−s(x	v)−s(x	NUM
ejpam-4283	344	97	)	)	PUNCT
ejpam-4283	344	98	where	where	SCONJ
ejpam-4283	344	99	s	s	X
ejpam-4283	344	100	,	,	PUNCT
ejpam-4283	344	101	v	v	NOUN
ejpam-4283	344	102	=	=	SYM
ejpam-4283	344	103	1	1	NUM
ejpam-4283	344	104	,	,	PUNCT
ejpam-4283	344	105	2	2	NUM
ejpam-4283	344	106	;	;	PUNCT
ejpam-4283	344	107	s	s	PROPN
ejpam-4283	344	108	6=	6=	PROPN
ejpam-4283	344	109	v.	v.	PROPN
ejpam-4283	344	110	(	(	PUNCT
ejpam-4283	344	111	c	c	X
ejpam-4283	344	112	)	)	PUNCT
ejpam-4283	344	113	if	if	SCONJ
ejpam-4283	344	114	q	q	X
ejpam-4283	344	115	∈	∈	PROPN
ejpam-4283	344	116	(	(	PUNCT
ejpam-4283	344	117	s	s	PROPN
ejpam-4283	344	118	,	,	PUNCT
ejpam-4283	344	119	v	v	NOUN
ejpam-4283	344	120	)	)	PUNCT
ejpam-4283	344	121	?	?	PUNCT
ejpam-4283	345	1	−n	−n	INTJ
ejpam-4283	345	2	(	(	PUNCT
ejpam-4283	345	3	x	x	X
ejpam-4283	345	4	)	)	PUNCT
ejpam-4283	345	5	,	,	PUNCT
ejpam-4283	345	6	then	then	ADV
ejpam-4283	345	7	q	q	PROPN
ejpam-4283	345	8	∈	∈	PROPN
ejpam-4283	345	9	(	(	PUNCT
ejpam-4283	345	10	s	s	NOUN
ejpam-4283	345	11	,	,	PUNCT
ejpam-4283	345	12	v)−s(x	v)−s(x	NUM
ejpam-4283	345	13	)	)	PUNCT
ejpam-4283	345	14	where	where	SCONJ
ejpam-4283	345	15	s	s	X
ejpam-4283	345	16	,	,	PUNCT
ejpam-4283	345	17	v	v	NOUN
ejpam-4283	345	18	=	=	SYM
ejpam-4283	345	19	1	1	NUM
ejpam-4283	345	20	,	,	PUNCT
ejpam-4283	345	21	2	2	NUM
ejpam-4283	345	22	;	;	PUNCT
ejpam-4283	345	23	s	s	X
ejpam-4283	345	24	6=	6=	PROPN
ejpam-4283	345	25	v.	v.	ADP
ejpam-4283	345	26	proof	proof	NOUN
ejpam-4283	345	27	.	.	PUNCT
ejpam-4283	346	1	(	(	PUNCT
ejpam-4283	346	2	a	a	X
ejpam-4283	346	3	)	)	PUNCT
ejpam-4283	346	4	.	.	PUNCT
ejpam-4283	347	1	let	let	VERB
ejpam-4283	347	2	g	g	PROPN
ejpam-4283	347	3	∈	∈	PROPN
ejpam-4283	347	4	µ̃v	µ̃v	VERB
ejpam-4283	347	5	for	for	ADP
ejpam-4283	347	6	v	v	NOUN
ejpam-4283	347	7	=	=	SYM
ejpam-4283	347	8	1	1	NUM
ejpam-4283	347	9	,	,	PUNCT
ejpam-4283	347	10	2	2	NUM
ejpam-4283	347	11	.	.	PUNCT
ejpam-4283	348	1	then	then	ADV
ejpam-4283	348	2	there	there	PRON
ejpam-4283	348	3	is	be	VERB
ejpam-4283	348	4	a	a	DET
ejpam-4283	348	5	set	set	NOUN
ejpam-4283	348	6	j	j	PROPN
ejpam-4283	348	7	∈	∈	PROPN
ejpam-4283	348	8	µ̃s	µ̃s	NOUN
ejpam-4283	349	1	such	such	ADJ
ejpam-4283	349	2	that	that	SCONJ
ejpam-4283	349	3	j	j	PROPN
ejpam-4283	349	4	⊂	⊂	PROPN
ejpam-4283	349	5	g	g	PROPN
ejpam-4283	349	6	and	and	CCONJ
ejpam-4283	349	7	j	j	PROPN
ejpam-4283	349	8	∩	∩	NOUN
ejpam-4283	349	9	k	k	PROPN
ejpam-4283	349	10	=	=	NOUN
ejpam-4283	349	11	∅	∅	NOUN
ejpam-4283	349	12	for	for	ADP
ejpam-4283	349	13	s	s	NOUN
ejpam-4283	349	14	=	=	SYM
ejpam-4283	349	15	1	1	NUM
ejpam-4283	349	16	,	,	PUNCT
ejpam-4283	349	17	2	2	NUM
ejpam-4283	349	18	.	.	PUNCT
ejpam-4283	350	1	by	by	ADP
ejpam-4283	350	2	hypothesis	hypothesis	NOUN
ejpam-4283	350	3	,	,	PUNCT
ejpam-4283	350	4	there	there	PRON
ejpam-4283	350	5	is	be	VERB
ejpam-4283	350	6	a	a	DET
ejpam-4283	350	7	set	set	ADJ
ejpam-4283	350	8	m1	m1	PROPN
ejpam-4283	350	9	∈	∈	PROPN
ejpam-4283	350	10	µ̃v	µ̃v	VERB
ejpam-4283	350	11	such	such	ADJ
ejpam-4283	350	12	that	that	SCONJ
ejpam-4283	350	13	m1	m1	PROPN
ejpam-4283	350	14	⊂	⊂	PROPN
ejpam-4283	350	15	j	j	PROPN
ejpam-4283	350	16	and	and	CCONJ
ejpam-4283	350	17	m1	m1	PROPN
ejpam-4283	350	18	∩l	∩l	NOUN
ejpam-4283	350	19	=	=	SYM
ejpam-4283	350	20	∅	∅	NOUN
ejpam-4283	350	21	for	for	ADP
ejpam-4283	350	22	v	v	NOUN
ejpam-4283	350	23	=	=	SYM
ejpam-4283	350	24	1	1	NUM
ejpam-4283	350	25	,	,	PUNCT
ejpam-4283	350	26	2	2	NUM
ejpam-4283	350	27	.	.	X
ejpam-4283	350	28	take	take	VERB
ejpam-4283	350	29	p	p	NOUN
ejpam-4283	351	1	=	=	X
ejpam-4283	351	2	j	j	PROPN
ejpam-4283	351	3	∩m1	∩m1	PROPN
ejpam-4283	351	4	.	.	PROPN
ejpam-4283	352	1	then	then	ADV
ejpam-4283	352	2	p	p	PROPN
ejpam-4283	352	3	⊂	⊂	PROPN
ejpam-4283	352	4	g	g	NOUN
ejpam-4283	352	5	and	and	CCONJ
ejpam-4283	352	6	is(p	is(p	NUM
ejpam-4283	352	7	)	)	PUNCT
ejpam-4283	352	8	6=	6=	ADP
ejpam-4283	352	9	∅	∅	NOUN
ejpam-4283	352	10	,	,	PUNCT
ejpam-4283	352	11	by	by	ADP
ejpam-4283	352	12	hypothesis	hypothesis	NOUN
ejpam-4283	352	13	for	for	ADP
ejpam-4283	352	14	s	s	NOUN
ejpam-4283	352	15	=	=	SYM
ejpam-4283	352	16	1	1	NUM
ejpam-4283	352	17	,	,	PUNCT
ejpam-4283	352	18	2	2	NUM
ejpam-4283	352	19	.	.	PUNCT
ejpam-4283	352	20	also	also	ADV
ejpam-4283	352	21	,	,	PUNCT
ejpam-4283	352	22	is(p	is(p	X
ejpam-4283	352	23	)	)	PUNCT
ejpam-4283	352	24	∩(k∪l	∩(k∪l	NOUN
ejpam-4283	352	25	)	)	PUNCT
ejpam-4283	352	26	=	=	NOUN
ejpam-4283	352	27	∅	∅	NOUN
ejpam-4283	352	28	for	for	ADP
ejpam-4283	352	29	s	s	NOUN
ejpam-4283	352	30	=	=	SYM
ejpam-4283	352	31	1	1	NUM
ejpam-4283	352	32	,	,	PUNCT
ejpam-4283	352	33	2	2	NUM
ejpam-4283	352	34	.	.	PUNCT
ejpam-4283	353	1	thus	thus	ADV
ejpam-4283	353	2	,	,	PUNCT
ejpam-4283	353	3	there	there	PRON
ejpam-4283	353	4	is	be	VERB
ejpam-4283	353	5	is(p	is(p	X
ejpam-4283	353	6	)	)	PUNCT
ejpam-4283	353	7	∈	∈	PROPN
ejpam-4283	353	8	µ̃s	µ̃s	NOUN
ejpam-4283	353	9	such	such	ADJ
ejpam-4283	353	10	that	that	PRON
ejpam-4283	353	11	is(p	is(p	PRON
ejpam-4283	353	12	)	)	PUNCT
ejpam-4283	354	1	⊂	⊂	PROPN
ejpam-4283	354	2	g	g	NOUN
ejpam-4283	354	3	and	and	CCONJ
ejpam-4283	354	4	is(p	is(p	NUM
ejpam-4283	354	5	)	)	PUNCT
ejpam-4283	354	6	∩	∩	NOUN
ejpam-4283	354	7	(	(	PUNCT
ejpam-4283	354	8	k	k	X
ejpam-4283	354	9	∪l	∪l	X
ejpam-4283	354	10	)	)	PUNCT
ejpam-4283	354	11	=	=	NOUN
ejpam-4283	354	12	∅	∅	NOUN
ejpam-4283	354	13	where	where	SCONJ
ejpam-4283	354	14	s	s	X
ejpam-4283	354	15	,	,	PUNCT
ejpam-4283	354	16	v	v	NOUN
ejpam-4283	354	17	=	=	SYM
ejpam-4283	354	18	1	1	NUM
ejpam-4283	354	19	,	,	PUNCT
ejpam-4283	354	20	2	2	NUM
ejpam-4283	354	21	;	;	PUNCT
ejpam-4283	354	22	s	s	PROPN
ejpam-4283	354	23	6=	6=	PROPN
ejpam-4283	354	24	v.	v.	ADP
ejpam-4283	354	25	therefore	therefore	ADV
ejpam-4283	354	26	,	,	PUNCT
ejpam-4283	354	27	k	k	PROPN
ejpam-4283	354	28	∪l	∪l	PROPN
ejpam-4283	354	29	∈	∈	PROPN
ejpam-4283	354	30	(	(	PUNCT
ejpam-4283	354	31	s	s	NOUN
ejpam-4283	354	32	,	,	PUNCT
ejpam-4283	354	33	v)−s(x	v)−s(x	NUM
ejpam-4283	354	34	)	)	PUNCT
ejpam-4283	354	35	where	where	SCONJ
ejpam-4283	354	36	s	s	X
ejpam-4283	354	37	,	,	PUNCT
ejpam-4283	354	38	v	v	NOUN
ejpam-4283	354	39	=	=	SYM
ejpam-4283	354	40	1	1	NUM
ejpam-4283	354	41	,	,	PUNCT
ejpam-4283	354	42	2	2	NUM
ejpam-4283	354	43	and	and	CCONJ
ejpam-4283	354	44	s	s	PROPN
ejpam-4283	354	45	6=	6=	PROPN
ejpam-4283	354	46	v.	v.	PROPN
ejpam-4283	354	47	(	(	PUNCT
ejpam-4283	354	48	b	b	NOUN
ejpam-4283	354	49	)	)	PUNCT
ejpam-4283	354	50	.	.	PUNCT
ejpam-4283	355	1	suppose	suppose	VERB
ejpam-4283	355	2	l	l	NOUN
ejpam-4283	355	3	is	be	AUX
ejpam-4283	355	4	a	a	DET
ejpam-4283	355	5	(	(	PUNCT
ejpam-4283	355	6	v	v	NOUN
ejpam-4283	355	7	,	,	PUNCT
ejpam-4283	355	8	s)-nowhere	s)-nowhere	PUNCT
ejpam-4283	355	9	dense	dense	ADJ
ejpam-4283	355	10	set	set	NOUN
ejpam-4283	355	11	where	where	SCONJ
ejpam-4283	355	12	s	s	X
ejpam-4283	355	13	,	,	PUNCT
ejpam-4283	355	14	v	v	NOUN
ejpam-4283	355	15	=	=	SYM
ejpam-4283	355	16	1	1	NUM
ejpam-4283	355	17	,	,	PUNCT
ejpam-4283	355	18	2	2	NUM
ejpam-4283	355	19	and	and	CCONJ
ejpam-4283	355	20	s	s	X
ejpam-4283	355	21	6=	6=	PROPN
ejpam-4283	355	22	v.	v.	ADP
ejpam-4283	355	23	then	then	ADV
ejpam-4283	355	24	x	x	X
ejpam-4283	355	25	−	−	PROPN
ejpam-4283	355	26	cs(l	cs(l	NOUN
ejpam-4283	355	27	)	)	PUNCT
ejpam-4283	355	28	is	be	AUX
ejpam-4283	355	29	µv	µv	NOUN
ejpam-4283	355	30	-	-	PUNCT
ejpam-4283	355	31	dense	dense	ADJ
ejpam-4283	355	32	and	and	CCONJ
ejpam-4283	355	33	also	also	ADV
ejpam-4283	355	34	µs	µs	ADP
ejpam-4283	355	35	-	-	ADJ
ejpam-4283	355	36	open	open	ADJ
ejpam-4283	355	37	set	set	NOUN
ejpam-4283	355	38	where	where	SCONJ
ejpam-4283	355	39	s	s	X
ejpam-4283	355	40	,	,	PUNCT
ejpam-4283	355	41	v	v	NOUN
ejpam-4283	355	42	=	=	SYM
ejpam-4283	355	43	1	1	NUM
ejpam-4283	355	44	,	,	PUNCT
ejpam-4283	355	45	2	2	NUM
ejpam-4283	355	46	and	and	CCONJ
ejpam-4283	355	47	s	s	X
ejpam-4283	355	48	6=	6=	PROPN
ejpam-4283	355	49	v.	v.	CCONJ
ejpam-4283	355	50	let	let	VERB
ejpam-4283	355	51	v	v	NUM
ejpam-4283	355	52	∈	∈	PROPN
ejpam-4283	355	53	µ̃v	µ̃v	VERB
ejpam-4283	355	54	for	for	ADP
ejpam-4283	355	55	v	v	NOUN
ejpam-4283	355	56	=	=	SYM
ejpam-4283	355	57	1	1	NUM
ejpam-4283	355	58	,	,	PUNCT
ejpam-4283	355	59	2	2	NUM
ejpam-4283	355	60	.	.	X
ejpam-4283	355	61	then	then	ADV
ejpam-4283	355	62	v	v	ADP
ejpam-4283	355	63	∩	∩	NOUN
ejpam-4283	355	64	(	(	PUNCT
ejpam-4283	355	65	x	x	SYM
ejpam-4283	355	66	−	−	NOUN
ejpam-4283	355	67	cs(l	cs(l	NUM
ejpam-4283	355	68	)	)	PUNCT
ejpam-4283	355	69	)	)	PUNCT
ejpam-4283	356	1	6=	6=	ADP
ejpam-4283	356	2	∅	∅	NOUN
ejpam-4283	356	3	for	for	ADP
ejpam-4283	356	4	s	s	NOUN
ejpam-4283	356	5	=	=	SYM
ejpam-4283	356	6	1	1	NUM
ejpam-4283	356	7	,	,	PUNCT
ejpam-4283	356	8	2	2	NUM
ejpam-4283	356	9	.	.	PUNCT
ejpam-4283	356	10	by	by	ADP
ejpam-4283	356	11	hypothesis	hypothesis	NOUN
ejpam-4283	356	12	,	,	PUNCT
ejpam-4283	356	13	is(v	is(v	X
ejpam-4283	356	14	∩	∩	NOUN
ejpam-4283	356	15	(	(	PUNCT
ejpam-4283	356	16	x	x	X
ejpam-4283	356	17	−	−	NOUN
ejpam-4283	356	18	cs(l	cs(l	NUM
ejpam-4283	356	19	)	)	PUNCT
ejpam-4283	356	20	)	)	PUNCT
ejpam-4283	356	21	6=	6=	ADP
ejpam-4283	356	22	∅	∅	NOUN
ejpam-4283	356	23	for	for	ADP
ejpam-4283	356	24	s	s	NOUN
ejpam-4283	356	25	=	=	SYM
ejpam-4283	356	26	1	1	NUM
ejpam-4283	356	27	,	,	PUNCT
ejpam-4283	356	28	2	2	NUM
ejpam-4283	356	29	.	.	X
ejpam-4283	356	30	take	take	VERB
ejpam-4283	356	31	p	p	NOUN
ejpam-4283	356	32	=	=	NOUN
ejpam-4283	356	33	is(v	is(v	NOUN
ejpam-4283	356	34	∩	∩	NOUN
ejpam-4283	356	35	(	(	PUNCT
ejpam-4283	356	36	x	x	X
ejpam-4283	356	37	−	−	NOUN
ejpam-4283	356	38	cs(l	cs(l	NUM
ejpam-4283	356	39	)	)	PUNCT
ejpam-4283	356	40	)	)	PUNCT
ejpam-4283	356	41	for	for	ADP
ejpam-4283	356	42	s	s	NOUN
ejpam-4283	356	43	=	=	SYM
ejpam-4283	356	44	1	1	NUM
ejpam-4283	356	45	,	,	PUNCT
ejpam-4283	356	46	2	2	NUM
ejpam-4283	356	47	.	.	PUNCT
ejpam-4283	357	1	then	then	ADV
ejpam-4283	357	2	p	p	PROPN
ejpam-4283	357	3	⊂	⊂	PROPN
ejpam-4283	357	4	v	v	NOUN
ejpam-4283	357	5	and	and	CCONJ
ejpam-4283	357	6	p	p	NOUN
ejpam-4283	357	7	∩	∩	ADJ
ejpam-4283	357	8	l	l	NOUN
ejpam-4283	357	9	=	=	PUNCT
ejpam-4283	357	10	∅.	∅.	VERB
ejpam-4283	357	11	therefore	therefore	ADV
ejpam-4283	357	12	,	,	PUNCT
ejpam-4283	357	13	l	l	NOUN
ejpam-4283	357	14	is	be	AUX
ejpam-4283	357	15	a	a	DET
ejpam-4283	357	16	(	(	PUNCT
ejpam-4283	357	17	s	s	NOUN
ejpam-4283	357	18	,	,	PUNCT
ejpam-4283	357	19	v)-strongly	v)-strongly	ADV
ejpam-4283	357	20	nowhere	nowhere	ADV
ejpam-4283	357	21	dense	dense	ADJ
ejpam-4283	357	22	set	set	NOUN
ejpam-4283	357	23	in	in	ADP
ejpam-4283	357	24	x	x	PUNCT
ejpam-4283	357	25	where	where	SCONJ
ejpam-4283	357	26	s	s	X
ejpam-4283	357	27	,	,	PUNCT
ejpam-4283	357	28	v	v	NOUN
ejpam-4283	357	29	=	=	SYM
ejpam-4283	357	30	1	1	NUM
ejpam-4283	357	31	,	,	PUNCT
ejpam-4283	357	32	2	2	NUM
ejpam-4283	357	33	;	;	PUNCT
ejpam-4283	357	34	s	s	PROPN
ejpam-4283	357	35	6=	6=	PROPN
ejpam-4283	357	36	v.	v.	PROPN
ejpam-4283	357	37	(	(	PUNCT
ejpam-4283	357	38	c	c	NOUN
ejpam-4283	357	39	)	)	PUNCT
ejpam-4283	357	40	.	.	PUNCT
ejpam-4283	358	1	it	it	PRON
ejpam-4283	358	2	follows	follow	VERB
ejpam-4283	358	3	from	from	ADP
ejpam-4283	358	4	(	(	PUNCT
ejpam-4283	358	5	b	b	NOUN
ejpam-4283	358	6	)	)	PUNCT
ejpam-4283	358	7	and	and	CCONJ
ejpam-4283	358	8	the	the	DET
ejpam-4283	358	9	fact	fact	NOUN
ejpam-4283	358	10	that	that	SCONJ
ejpam-4283	358	11	every	every	DET
ejpam-4283	358	12	(	(	PUNCT
ejpam-4283	358	13	s	s	X
ejpam-4283	358	14	,	,	PUNCT
ejpam-4283	358	15	v)?-nowhere	v)?-nowhere	X
ejpam-4283	358	16	dense	dense	ADJ
ejpam-4283	358	17	set	set	NOUN
ejpam-4283	358	18	is	be	AUX
ejpam-4283	358	19	a	a	DET
ejpam-4283	358	20	(	(	PUNCT
ejpam-4283	358	21	v	v	NOUN
ejpam-4283	358	22	,	,	PUNCT
ejpam-4283	358	23	s)-nowhere	s)-nowhere	PUNCT
ejpam-4283	358	24	dense	dense	ADJ
ejpam-4283	358	25	set	set	NOUN
ejpam-4283	358	26	where	where	SCONJ
ejpam-4283	358	27	s	s	X
ejpam-4283	358	28	,	,	PUNCT
ejpam-4283	358	29	v	v	NOUN
ejpam-4283	358	30	=	=	SYM
ejpam-4283	358	31	1	1	NUM
ejpam-4283	358	32	,	,	PUNCT
ejpam-4283	358	33	2	2	NUM
ejpam-4283	358	34	;	;	PUNCT
ejpam-4283	358	35	s	s	PROPN
ejpam-4283	358	36	6=	6=	PROPN
ejpam-4283	358	37	v.	v.	ADP
ejpam-4283	358	38	theorem	theorem	ADJ
ejpam-4283	358	39	27	27	NUM
ejpam-4283	358	40	.	.	PUNCT
ejpam-4283	359	1	let	let	AUX
ejpam-4283	359	2	(	(	PUNCT
ejpam-4283	359	3	x,µ1	x,µ1	NOUN
ejpam-4283	359	4	,	,	PUNCT
ejpam-4283	359	5	µ2	µ2	PROPN
ejpam-4283	359	6	)	)	PUNCT
ejpam-4283	359	7	be	be	AUX
ejpam-4283	359	8	a	a	DET
ejpam-4283	359	9	bgts	bgts	NOUN
ejpam-4283	359	10	.	.	PUNCT
ejpam-4283	360	1	if	if	SCONJ
ejpam-4283	360	2	µs	µs	X
ejpam-4283	360	3	⊂	⊂	X
ejpam-4283	360	4	µv	µv	PROPN
ejpam-4283	360	5	and	and	CCONJ
ejpam-4283	360	6	q	q	ADJ
ejpam-4283	360	7	∈	∈	PROPN
ejpam-4283	360	8	(	(	PUNCT
ejpam-4283	360	9	s	s	NOUN
ejpam-4283	360	10	,	,	PUNCT
ejpam-4283	360	11	v)−s(x	v)−s(x	NUM
ejpam-4283	360	12	)	)	PUNCT
ejpam-4283	360	13	,	,	PUNCT
ejpam-4283	360	14	then	then	ADV
ejpam-4283	360	15	q	q	X
ejpam-4283	360	16	is	be	AUX
ejpam-4283	360	17	a	a	DET
ejpam-4283	360	18	µs	µs	NOUN
ejpam-4283	360	19	-	-	PUNCT
ejpam-4283	360	20	strongly	strongly	ADV
ejpam-4283	360	21	nowhere	nowhere	ADV
ejpam-4283	360	22	dense	dense	ADJ
ejpam-4283	360	23	set	set	NOUN
ejpam-4283	360	24	in	in	ADP
ejpam-4283	360	25	x	x	PUNCT
ejpam-4283	360	26	where	where	SCONJ
ejpam-4283	360	27	s	s	X
ejpam-4283	360	28	,	,	PUNCT
ejpam-4283	360	29	v	v	NOUN
ejpam-4283	360	30	=	=	SYM
ejpam-4283	360	31	1	1	NUM
ejpam-4283	360	32	,	,	PUNCT
ejpam-4283	360	33	2	2	NUM
ejpam-4283	360	34	and	and	CCONJ
ejpam-4283	360	35	s	s	X
ejpam-4283	360	36	6=	6=	PROPN
ejpam-4283	360	37	v.	v.	ADP
ejpam-4283	360	38	definition	definition	NOUN
ejpam-4283	360	39	28	28	NUM
ejpam-4283	360	40	.	.	PUNCT
ejpam-4283	361	1	let	let	AUX
ejpam-4283	361	2	(	(	PUNCT
ejpam-4283	361	3	x,µ1	x,µ1	NOUN
ejpam-4283	361	4	,	,	PUNCT
ejpam-4283	361	5	µ2	µ2	PROPN
ejpam-4283	361	6	)	)	PUNCT
ejpam-4283	361	7	satisfy	satisfy	VERB
ejpam-4283	361	8	the	the	DET
ejpam-4283	361	9	condition	condition	NOUN
ejpam-4283	361	10	;	;	PUNCT
ejpam-4283	361	11	if	if	SCONJ
ejpam-4283	361	12	b1	b1	PROPN
ejpam-4283	361	13	∈	∈	PROPN
ejpam-4283	361	14	µ̃s	µ̃s	NOUN
ejpam-4283	361	15	,	,	PUNCT
ejpam-4283	361	16	b2	b2	NOUN
ejpam-4283	361	17	∈	∈	PROPN
ejpam-4283	361	18	µ̃v	µ̃v	PART
ejpam-4283	361	19	and	and	CCONJ
ejpam-4283	361	20	b1	b1	PROPN
ejpam-4283	361	21	∩b2	∩b2	PROPN
ejpam-4283	361	22	6=	6=	PROPN
ejpam-4283	361	23	∅	∅	NOUN
ejpam-4283	361	24	,	,	PUNCT
ejpam-4283	361	25	then	then	ADV
ejpam-4283	361	26	iv(b1	iv(b1	VERB
ejpam-4283	361	27	∩b2	∩b2	NOUN
ejpam-4283	361	28	)	)	PUNCT
ejpam-4283	361	29	6=	6=	ADP
ejpam-4283	361	30	∅	∅	NOUN
ejpam-4283	361	31	where	where	SCONJ
ejpam-4283	361	32	s	s	X
ejpam-4283	361	33	,	,	PUNCT
ejpam-4283	361	34	v	v	NOUN
ejpam-4283	361	35	=	=	SYM
ejpam-4283	361	36	1	1	NUM
ejpam-4283	361	37	,	,	PUNCT
ejpam-4283	361	38	2	2	NUM
ejpam-4283	361	39	and	and	CCONJ
ejpam-4283	361	40	s	s	X
ejpam-4283	361	41	6=	6=	PROPN
ejpam-4283	361	42	v.	v.	ADP
ejpam-4283	361	43	then	then	ADV
ejpam-4283	361	44	the	the	DET
ejpam-4283	361	45	bgts	bgts	NOUN
ejpam-4283	361	46	(	(	PUNCT
ejpam-4283	361	47	x,µ1	x,µ1	PROPN
ejpam-4283	361	48	,	,	PUNCT
ejpam-4283	361	49	µ2	µ2	PROPN
ejpam-4283	361	50	)	)	PUNCT
ejpam-4283	361	51	is	be	AUX
ejpam-4283	361	52	said	say	VERB
ejpam-4283	361	53	to	to	PART
ejpam-4283	361	54	satisfy	satisfy	VERB
ejpam-4283	361	55	the	the	DET
ejpam-4283	361	56	iv	iv	NUM
ejpam-4283	361	57	-property	-property	NOUN
ejpam-4283	361	58	.	.	PUNCT
ejpam-4283	362	1	theorem	theorem	NOUN
ejpam-4283	362	2	29	29	NUM
ejpam-4283	362	3	.	.	PUNCT
ejpam-4283	363	1	let	let	AUX
ejpam-4283	363	2	(	(	PUNCT
ejpam-4283	363	3	x,µ1	x,µ1	NOUN
ejpam-4283	363	4	,	,	PUNCT
ejpam-4283	363	5	µ2	µ2	PROPN
ejpam-4283	363	6	)	)	PUNCT
ejpam-4283	363	7	be	be	VERB
ejpam-4283	363	8	a	a	DET
ejpam-4283	363	9	bgts	bgts	NOUN
ejpam-4283	363	10	which	which	PRON
ejpam-4283	363	11	has	have	VERB
ejpam-4283	363	12	the	the	DET
ejpam-4283	363	13	iv	iv	NUM
ejpam-4283	363	14	-property	-property	NOUN
ejpam-4283	363	15	.	.	PUNCT
ejpam-4283	364	1	if	if	SCONJ
ejpam-4283	364	2	d	d	PROPN
ejpam-4283	364	3	∈	∈	PROPN
ejpam-4283	364	4	(	(	PUNCT
ejpam-4283	364	5	s	s	NOUN
ejpam-4283	364	6	,	,	PUNCT
ejpam-4283	364	7	v)−s(x	v)−s(x	NUM
ejpam-4283	364	8	)	)	PUNCT
ejpam-4283	364	9	,	,	PUNCT
ejpam-4283	364	10	then	then	ADV
ejpam-4283	364	11	d	d	PROPN
ejpam-4283	364	12	is	be	AUX
ejpam-4283	364	13	a	a	DET
ejpam-4283	364	14	µv	µv	NOUN
ejpam-4283	364	15	-	-	PUNCT
ejpam-4283	364	16	strongly	strongly	ADV
ejpam-4283	364	17	nowhere	nowhere	ADV
ejpam-4283	364	18	dense	dense	ADJ
ejpam-4283	364	19	set	set	NOUN
ejpam-4283	364	20	in	in	ADP
ejpam-4283	364	21	x	x	PUNCT
ejpam-4283	364	22	where	where	SCONJ
ejpam-4283	364	23	s	s	X
ejpam-4283	364	24	,	,	PUNCT
ejpam-4283	364	25	v	v	NOUN
ejpam-4283	364	26	=	=	SYM
ejpam-4283	364	27	1	1	NUM
ejpam-4283	364	28	,	,	PUNCT
ejpam-4283	364	29	2	2	NUM
ejpam-4283	364	30	and	and	CCONJ
ejpam-4283	364	31	s	s	X
ejpam-4283	364	32	6=	6=	PROPN
ejpam-4283	364	33	v.	v.	ADP
ejpam-4283	364	34	proof	proof	NOUN
ejpam-4283	364	35	.	.	PUNCT
ejpam-4283	365	1	take	take	VERB
ejpam-4283	365	2	s	s	NOUN
ejpam-4283	365	3	=	=	SYM
ejpam-4283	365	4	1	1	NUM
ejpam-4283	365	5	and	and	CCONJ
ejpam-4283	365	6	v	v	NOUN
ejpam-4283	365	7	=	=	SYM
ejpam-4283	365	8	2	2	X
ejpam-4283	365	9	.	.	X
ejpam-4283	365	10	assume	assume	VERB
ejpam-4283	365	11	that	that	SCONJ
ejpam-4283	365	12	,	,	PUNCT
ejpam-4283	365	13	the	the	DET
ejpam-4283	365	14	bigeneralized	bigeneralize	VERB
ejpam-4283	365	15	topological	topological	ADJ
ejpam-4283	365	16	space	space	NOUN
ejpam-4283	365	17	(	(	PUNCT
ejpam-4283	365	18	x,µ1	x,µ1	PROPN
ejpam-4283	365	19	,	,	PUNCT
ejpam-4283	365	20	µ2	µ2	PROPN
ejpam-4283	365	21	)	)	PUNCT
ejpam-4283	365	22	satisfy	satisfy	VERB
ejpam-4283	365	23	the	the	DET
ejpam-4283	365	24	iv	iv	NUM
ejpam-4283	365	25	-property	-property	NOUN
ejpam-4283	365	26	.	.	PUNCT
ejpam-4283	366	1	let	let	VERB
ejpam-4283	366	2	d	d	X
ejpam-4283	366	3	∈	∈	PROPN
ejpam-4283	366	4	(	(	PUNCT
ejpam-4283	366	5	1	1	NUM
ejpam-4283	366	6	,	,	PUNCT
ejpam-4283	366	7	2	2	NUM
ejpam-4283	366	8	)	)	PUNCT
ejpam-4283	366	9	−	−	PROPN
ejpam-4283	366	10	s(x	s(x	PROPN
ejpam-4283	366	11	)	)	PUNCT
ejpam-4283	366	12	and	and	CCONJ
ejpam-4283	367	1	g	g	PROPN
ejpam-4283	367	2	∈	∈	PROPN
ejpam-4283	367	3	µ̃2	µ̃2	PROPN
ejpam-4283	367	4	.	.	PUNCT
ejpam-4283	368	1	then	then	ADV
ejpam-4283	368	2	there	there	PRON
ejpam-4283	368	3	is	be	VERB
ejpam-4283	368	4	a	a	DET
ejpam-4283	368	5	set	set	NOUN
ejpam-4283	368	6	j	j	PROPN
ejpam-4283	368	7	∈	∈	PROPN
ejpam-4283	368	8	µ̃1	µ̃1	PROPN
ejpam-4283	368	9	such	such	ADJ
ejpam-4283	368	10	that	that	SCONJ
ejpam-4283	368	11	j	j	PROPN
ejpam-4283	368	12	⊂	⊂	PROPN
ejpam-4283	368	13	g	g	PROPN
ejpam-4283	368	14	and	and	CCONJ
ejpam-4283	368	15	j	j	PROPN
ejpam-4283	368	16	∩d	∩d	NOUN
ejpam-4283	368	17	=	=	PUNCT
ejpam-4283	369	1	∅.	∅.	NOUN
ejpam-4283	369	2	here	here	ADV
ejpam-4283	369	3	g	g	PROPN
ejpam-4283	369	4	∈	∈	PROPN
ejpam-4283	369	5	µ̃2	µ̃2	PROPN
ejpam-4283	369	6	,	,	PUNCT
ejpam-4283	369	7	j	j	PROPN
ejpam-4283	369	8	∈	∈	PROPN
ejpam-4283	369	9	µ̃1	µ̃1	PROPN
ejpam-4283	369	10	and	and	CCONJ
ejpam-4283	369	11	j	j	PROPN
ejpam-4283	369	12	∩g	∩g	PROPN
ejpam-4283	369	13	6=	6=	ADP
ejpam-4283	369	14	∅.	∅.	ADP
ejpam-4283	369	15	by	by	ADP
ejpam-4283	369	16	our	our	PRON
ejpam-4283	369	17	assumption	assumption	NOUN
ejpam-4283	369	18	,	,	PUNCT
ejpam-4283	369	19	iµ2(g	iµ2(g	ADJ
ejpam-4283	369	20	∩	∩	ADJ
ejpam-4283	369	21	j	j	PROPN
ejpam-4283	369	22	)	)	PUNCT
ejpam-4283	369	23	6=	6=	ADP
ejpam-4283	369	24	∅.	∅.	AUX
ejpam-4283	369	25	take	take	VERB
ejpam-4283	369	26	k	k	NOUN
ejpam-4283	369	27	=	=	SYM
ejpam-4283	369	28	iµ2(g	iµ2(g	X
ejpam-4283	369	29	∩	∩	ADJ
ejpam-4283	369	30	j	j	PROPN
ejpam-4283	369	31	)	)	PUNCT
ejpam-4283	369	32	.	.	PUNCT
ejpam-4283	370	1	then	then	ADV
ejpam-4283	370	2	k	k	PROPN
ejpam-4283	370	3	∈	∈	PROPN
ejpam-4283	370	4	µ̃2	µ̃2	PROPN
ejpam-4283	370	5	.	.	PUNCT
ejpam-4283	371	1	thus	thus	ADV
ejpam-4283	371	2	,	,	PUNCT
ejpam-4283	371	3	there	there	PRON
ejpam-4283	371	4	is	be	VERB
ejpam-4283	371	5	k	k	PROPN
ejpam-4283	371	6	∈	∈	PROPN
ejpam-4283	371	7	µ̃2	µ̃2	PROPN
ejpam-4283	371	8	such	such	ADJ
ejpam-4283	371	9	that	that	SCONJ
ejpam-4283	371	10	k	k	PROPN
ejpam-4283	371	11	⊂	⊂	PROPN
ejpam-4283	371	12	g	g	PROPN
ejpam-4283	372	1	and	and	CCONJ
ejpam-4283	372	2	k	k	PROPN
ejpam-4283	372	3	∩d	∩d	NOUN
ejpam-4283	372	4	=	=	PUNCT
ejpam-4283	372	5	∅.	∅.	VERB
ejpam-4283	372	6	therefore	therefore	ADV
ejpam-4283	372	7	,	,	PUNCT
ejpam-4283	372	8	d	d	X
ejpam-4283	372	9	is	be	AUX
ejpam-4283	372	10	a	a	DET
ejpam-4283	372	11	µ2	µ2	NOUN
ejpam-4283	372	12	-	-	PUNCT
ejpam-4283	372	13	strongly	strongly	ADV
ejpam-4283	372	14	nowhere	nowhere	ADV
ejpam-4283	372	15	dense	dense	ADJ
ejpam-4283	372	16	set	set	NOUN
ejpam-4283	372	17	in	in	ADP
ejpam-4283	372	18	x.	x.	NOUN
ejpam-4283	372	19	similarly	similarly	ADV
ejpam-4283	372	20	,	,	PUNCT
ejpam-4283	372	21	we	we	PRON
ejpam-4283	372	22	can	can	AUX
ejpam-4283	372	23	prove	prove	VERB
ejpam-4283	372	24	that	that	SCONJ
ejpam-4283	372	25	the	the	DET
ejpam-4283	372	26	result	result	NOUN
ejpam-4283	372	27	is	be	AUX
ejpam-4283	372	28	true	true	ADJ
ejpam-4283	372	29	for	for	ADP
ejpam-4283	372	30	the	the	DET
ejpam-4283	372	31	case	case	NOUN
ejpam-4283	372	32	s	s	PART
ejpam-4283	372	33	=	=	SYM
ejpam-4283	372	34	2	2	NUM
ejpam-4283	372	35	and	and	CCONJ
ejpam-4283	372	36	v	v	NOUN
ejpam-4283	372	37	=	=	SYM
ejpam-4283	372	38	1	1	X
ejpam-4283	372	39	.	.	PUNCT
ejpam-4283	372	40	theorem	theorem	NOUN
ejpam-4283	372	41	30	30	NUM
ejpam-4283	372	42	.	.	PUNCT
ejpam-4283	373	1	let	let	AUX
ejpam-4283	373	2	(	(	PUNCT
ejpam-4283	373	3	x,µ1	x,µ1	NOUN
ejpam-4283	373	4	,	,	PUNCT
ejpam-4283	373	5	µ2	µ2	PROPN
ejpam-4283	373	6	)	)	PUNCT
ejpam-4283	373	7	be	be	VERB
ejpam-4283	373	8	a	a	DET
ejpam-4283	373	9	bigeneralized	bigeneralized	ADJ
ejpam-4283	373	10	topological	topological	ADJ
ejpam-4283	373	11	space	space	NOUN
ejpam-4283	373	12	.	.	PUNCT
ejpam-4283	374	1	if	if	SCONJ
ejpam-4283	374	2	µv	µv	PRON
ejpam-4283	374	3	⊂	⊂	PUNCT
ejpam-4283	374	4	µs	µs	X
ejpam-4283	374	5	where	where	SCONJ
ejpam-4283	374	6	s	s	X
ejpam-4283	374	7	,	,	PUNCT
ejpam-4283	374	8	v	v	NOUN
ejpam-4283	374	9	=	=	SYM
ejpam-4283	374	10	1	1	NUM
ejpam-4283	374	11	,	,	PUNCT
ejpam-4283	374	12	2	2	NUM
ejpam-4283	374	13	and	and	CCONJ
ejpam-4283	374	14	s	s	PROPN
ejpam-4283	374	15	6=	6=	PROPN
ejpam-4283	374	16	v	v	NOUN
ejpam-4283	374	17	,	,	PUNCT
ejpam-4283	374	18	then	then	ADV
ejpam-4283	374	19	the	the	DET
ejpam-4283	374	20	following	follow	VERB
ejpam-4283	374	21	hold	hold	NOUN
ejpam-4283	374	22	.	.	PUNCT
ejpam-4283	375	1	(	(	PUNCT
ejpam-4283	375	2	a	a	X
ejpam-4283	375	3	)	)	PUNCT
ejpam-4283	375	4	if	if	SCONJ
ejpam-4283	375	5	q	q	NOUN
ejpam-4283	375	6	is	be	AUX
ejpam-4283	375	7	a	a	DET
ejpam-4283	375	8	µv	µv	NOUN
ejpam-4283	375	9	-	-	PUNCT
ejpam-4283	375	10	strongly	strongly	ADV
ejpam-4283	375	11	nowhere	nowhere	ADV
ejpam-4283	375	12	dense	dense	ADJ
ejpam-4283	375	13	set	set	NOUN
ejpam-4283	375	14	,	,	PUNCT
ejpam-4283	375	15	then	then	ADV
ejpam-4283	375	16	q	q	PROPN
ejpam-4283	375	17	∈	∈	PROPN
ejpam-4283	375	18	(	(	PUNCT
ejpam-4283	375	19	s	s	NOUN
ejpam-4283	375	20	,	,	PUNCT
ejpam-4283	375	21	v)−s(x	v)−s(x	NUM
ejpam-4283	375	22	)	)	PUNCT
ejpam-4283	375	23	where	where	SCONJ
ejpam-4283	375	24	s	s	X
ejpam-4283	375	25	,	,	PUNCT
ejpam-4283	375	26	v	v	NOUN
ejpam-4283	375	27	=	=	SYM
ejpam-4283	375	28	1	1	NUM
ejpam-4283	375	29	,	,	PUNCT
ejpam-4283	375	30	2	2	NUM
ejpam-4283	375	31	and	and	CCONJ
ejpam-4283	375	32	s	s	X
ejpam-4283	375	33	6=	6=	PROPN
ejpam-4283	375	34	v.	v.	ADP
ejpam-4283	375	35	p.	p.	PROPN
ejpam-4283	375	36	yupapin	yupapin	NOUN
ejpam-4283	375	37	,	,	PUNCT
ejpam-4283	375	38	v.	v.	CCONJ
ejpam-4283	375	39	subramanian	subramanian	PROPN
ejpam-4283	375	40	,	,	PUNCT
ejpam-4283	375	41	y.	y.	PROPN
ejpam-4283	375	42	farhat	farhat	PROPN
ejpam-4283	375	43	/	/	SYM
ejpam-4283	375	44	eur	eur	PROPN
ejpam-4283	375	45	.	.	PUNCT
ejpam-4283	376	1	j.	j.	PROPN
ejpam-4283	376	2	pure	pure	PROPN
ejpam-4283	376	3	appl	appl	PROPN
ejpam-4283	376	4	.	.	PROPN
ejpam-4283	376	5	math	math	PROPN
ejpam-4283	376	6	,	,	PUNCT
ejpam-4283	376	7	15	15	NUM
ejpam-4283	376	8	(	(	PUNCT
ejpam-4283	376	9	2	2	NUM
ejpam-4283	376	10	)	)	PUNCT
ejpam-4283	376	11	(	(	PUNCT
ejpam-4283	376	12	2022	2022	NUM
ejpam-4283	376	13	)	)	PUNCT
ejpam-4283	376	14	,	,	PUNCT
ejpam-4283	376	15	403	403	NUM
ejpam-4283	376	16	-	-	SYM
ejpam-4283	376	17	414	414	NUM
ejpam-4283	376	18	411	411	NUM
ejpam-4283	376	19	(	(	PUNCT
ejpam-4283	376	20	b	b	NOUN
ejpam-4283	376	21	)	)	PUNCT
ejpam-4283	376	22	if	if	SCONJ
ejpam-4283	376	23	j	j	PROPN
ejpam-4283	376	24	is	be	AUX
ejpam-4283	376	25	a	a	DET
ejpam-4283	376	26	µs	µs	NOUN
ejpam-4283	376	27	-	-	PUNCT
ejpam-4283	376	28	strongly	strongly	ADV
ejpam-4283	376	29	nowhere	nowhere	ADV
ejpam-4283	376	30	dense	dense	ADJ
ejpam-4283	376	31	set	set	NOUN
ejpam-4283	376	32	,	,	PUNCT
ejpam-4283	376	33	then	then	ADV
ejpam-4283	376	34	j	j	PROPN
ejpam-4283	376	35	∈	∈	PROPN
ejpam-4283	376	36	(	(	PUNCT
ejpam-4283	376	37	s	s	NOUN
ejpam-4283	376	38	,	,	PUNCT
ejpam-4283	376	39	v)−s(x	v)−s(x	NUM
ejpam-4283	376	40	)	)	PUNCT
ejpam-4283	376	41	where	where	SCONJ
ejpam-4283	376	42	s	s	X
ejpam-4283	376	43	,	,	PUNCT
ejpam-4283	376	44	v	v	NOUN
ejpam-4283	376	45	=	=	SYM
ejpam-4283	376	46	1	1	NUM
ejpam-4283	376	47	,	,	PUNCT
ejpam-4283	376	48	2	2	NUM
ejpam-4283	376	49	and	and	CCONJ
ejpam-4283	376	50	s	s	X
ejpam-4283	376	51	6=	6=	NOUN
ejpam-4283	376	52	v.	v.	ADP
ejpam-4283	376	53	proof	proof	NOUN
ejpam-4283	376	54	.	.	PUNCT
ejpam-4283	377	1	assume	assume	VERB
ejpam-4283	377	2	that	that	SCONJ
ejpam-4283	377	3	,	,	PUNCT
ejpam-4283	377	4	µv	µv	PRON
ejpam-4283	377	5	⊂	⊂	X
ejpam-4283	377	6	µs	µs	X
ejpam-4283	377	7	where	where	SCONJ
ejpam-4283	377	8	s	s	X
ejpam-4283	377	9	,	,	PUNCT
ejpam-4283	377	10	v	v	NOUN
ejpam-4283	377	11	=	=	SYM
ejpam-4283	377	12	1	1	NUM
ejpam-4283	377	13	,	,	PUNCT
ejpam-4283	377	14	2	2	NUM
ejpam-4283	377	15	and	and	CCONJ
ejpam-4283	377	16	s	s	PROPN
ejpam-4283	377	17	6=	6=	PROPN
ejpam-4283	377	18	v.	v.	PROPN
ejpam-4283	377	19	(	(	PUNCT
ejpam-4283	377	20	a	a	NOUN
ejpam-4283	377	21	)	)	PUNCT
ejpam-4283	377	22	.	.	PUNCT
ejpam-4283	378	1	suppose	suppose	VERB
ejpam-4283	378	2	that	that	SCONJ
ejpam-4283	378	3	,	,	PUNCT
ejpam-4283	378	4	q	q	X
ejpam-4283	378	5	is	be	AUX
ejpam-4283	378	6	a	a	DET
ejpam-4283	378	7	µv	µv	NOUN
ejpam-4283	378	8	-	-	PUNCT
ejpam-4283	378	9	strongly	strongly	ADV
ejpam-4283	378	10	nowhere	nowhere	ADV
ejpam-4283	378	11	dense	dense	ADJ
ejpam-4283	378	12	set	set	NOUN
ejpam-4283	378	13	where	where	SCONJ
ejpam-4283	378	14	v	v	NOUN
ejpam-4283	378	15	=	=	SYM
ejpam-4283	378	16	1	1	NUM
ejpam-4283	378	17	,	,	PUNCT
ejpam-4283	378	18	2	2	NUM
ejpam-4283	378	19	.	.	X
ejpam-4283	378	20	take	take	VERB
ejpam-4283	378	21	s	s	NOUN
ejpam-4283	378	22	=	=	SYM
ejpam-4283	378	23	1	1	NUM
ejpam-4283	378	24	and	and	CCONJ
ejpam-4283	378	25	v	v	NOUN
ejpam-4283	378	26	=	=	SYM
ejpam-4283	378	27	2	2	NUM
ejpam-4283	378	28	.	.	PUNCT
ejpam-4283	378	29	then	then	ADV
ejpam-4283	378	30	q	q	X
ejpam-4283	378	31	is	be	AUX
ejpam-4283	378	32	a	a	DET
ejpam-4283	378	33	µ2	µ2	NOUN
ejpam-4283	378	34	-	-	PUNCT
ejpam-4283	378	35	strongly	strongly	ADV
ejpam-4283	378	36	nowhere	nowhere	ADV
ejpam-4283	378	37	dense	dense	ADJ
ejpam-4283	378	38	set	set	NOUN
ejpam-4283	378	39	and	and	CCONJ
ejpam-4283	378	40	µ2	µ2	PROPN
ejpam-4283	378	41	⊂	⊂	PROPN
ejpam-4283	378	42	µ1	µ1	PROPN
ejpam-4283	378	43	.	.	PUNCT
ejpam-4283	379	1	let	let	VERB
ejpam-4283	379	2	g	g	PROPN
ejpam-4283	379	3	∈	∈	PROPN
ejpam-4283	379	4	µ̃2	µ̃2	PROPN
ejpam-4283	379	5	.	.	PUNCT
ejpam-4283	380	1	then	then	ADV
ejpam-4283	380	2	there	there	PRON
ejpam-4283	380	3	is	be	VERB
ejpam-4283	380	4	h	h	PRON
ejpam-4283	380	5	∈	∈	PROPN
ejpam-4283	380	6	µ̃2	µ̃2	PROPN
ejpam-4283	380	7	such	such	ADJ
ejpam-4283	380	8	that	that	SCONJ
ejpam-4283	380	9	h	h	PROPN
ejpam-4283	380	10	⊂	⊂	X
ejpam-4283	380	11	g	g	PROPN
ejpam-4283	380	12	and	and	CCONJ
ejpam-4283	380	13	h	h	NOUN
ejpam-4283	380	14	∩q	∩q	PROPN
ejpam-4283	380	15	=	=	PUNCT
ejpam-4283	381	1	∅.	∅.	VERB
ejpam-4283	381	2	by	by	ADP
ejpam-4283	381	3	hypothesis	hypothesis	NOUN
ejpam-4283	381	4	,	,	PUNCT
ejpam-4283	381	5	h	h	NOUN
ejpam-4283	381	6	∈	∈	PROPN
ejpam-4283	381	7	µ̃1	µ̃1	PROPN
ejpam-4283	381	8	.	.	PUNCT
ejpam-4283	382	1	thus	thus	ADV
ejpam-4283	382	2	,	,	PUNCT
ejpam-4283	382	3	there	there	PRON
ejpam-4283	382	4	is	be	VERB
ejpam-4283	382	5	a	a	DET
ejpam-4283	382	6	set	set	VERB
ejpam-4283	382	7	h	h	NOUN
ejpam-4283	382	8	∈	∈	NOUN
ejpam-4283	382	9	µ̃1	µ̃1	NOUN
ejpam-4283	382	10	such	such	ADJ
ejpam-4283	382	11	that	that	SCONJ
ejpam-4283	382	12	h	h	NOUN
ejpam-4283	382	13	⊂	⊂	X
ejpam-4283	382	14	g	g	PROPN
ejpam-4283	382	15	and	and	CCONJ
ejpam-4283	382	16	h	h	NOUN
ejpam-4283	382	17	∩q	∩q	PROPN
ejpam-4283	383	1	=	=	PUNCT
ejpam-4283	383	2	∅.	∅.	VERB
ejpam-4283	383	3	therefore	therefore	ADV
ejpam-4283	383	4	,	,	PUNCT
ejpam-4283	383	5	q	q	PROPN
ejpam-4283	383	6	∈	∈	PROPN
ejpam-4283	383	7	(	(	PUNCT
ejpam-4283	383	8	1	1	NUM
ejpam-4283	383	9	,	,	PUNCT
ejpam-4283	383	10	2)−s(x	2)−s(x	NUM
ejpam-4283	383	11	)	)	PUNCT
ejpam-4283	383	12	.	.	PUNCT
ejpam-4283	384	1	similarly	similarly	ADV
ejpam-4283	384	2	,	,	PUNCT
ejpam-4283	384	3	we	we	PRON
ejpam-4283	384	4	can	can	AUX
ejpam-4283	384	5	prove	prove	VERB
ejpam-4283	384	6	that	that	SCONJ
ejpam-4283	384	7	the	the	DET
ejpam-4283	384	8	result	result	NOUN
ejpam-4283	384	9	is	be	AUX
ejpam-4283	384	10	true	true	ADJ
ejpam-4283	384	11	for	for	ADP
ejpam-4283	384	12	the	the	DET
ejpam-4283	384	13	case	case	NOUN
ejpam-4283	384	14	s	s	PART
ejpam-4283	384	15	=	=	SYM
ejpam-4283	384	16	2	2	NUM
ejpam-4283	384	17	and	and	CCONJ
ejpam-4283	384	18	v	v	NOUN
ejpam-4283	384	19	=	=	SYM
ejpam-4283	384	20	1	1	NUM
ejpam-4283	384	21	.	.	PUNCT
ejpam-4283	385	1	(	(	PUNCT
ejpam-4283	385	2	b	b	NOUN
ejpam-4283	385	3	)	)	PUNCT
ejpam-4283	385	4	.	.	PUNCT
ejpam-4283	386	1	let	let	VERB
ejpam-4283	386	2	j	j	PROPN
ejpam-4283	386	3	be	be	AUX
ejpam-4283	386	4	a	a	DET
ejpam-4283	386	5	µs	µs	NOUN
ejpam-4283	386	6	-	-	PUNCT
ejpam-4283	386	7	strongly	strongly	ADV
ejpam-4283	386	8	nowhere	nowhere	ADV
ejpam-4283	386	9	dense	dense	ADJ
ejpam-4283	386	10	set	set	NOUN
ejpam-4283	386	11	for	for	ADP
ejpam-4283	386	12	s	s	NOUN
ejpam-4283	386	13	=	=	SYM
ejpam-4283	386	14	1	1	NUM
ejpam-4283	386	15	,	,	PUNCT
ejpam-4283	386	16	2	2	NUM
ejpam-4283	386	17	.	.	X
ejpam-4283	387	1	choose	choose	VERB
ejpam-4283	387	2	s	s	PART
ejpam-4283	387	3	=	=	SYM
ejpam-4283	387	4	1	1	NUM
ejpam-4283	387	5	and	and	CCONJ
ejpam-4283	387	6	v	v	NOUN
ejpam-4283	387	7	=	=	SYM
ejpam-4283	387	8	2	2	NUM
ejpam-4283	387	9	.	.	PUNCT
ejpam-4283	388	1	then	then	ADV
ejpam-4283	388	2	j	j	PROPN
ejpam-4283	388	3	is	be	AUX
ejpam-4283	388	4	a	a	DET
ejpam-4283	388	5	µ1	µ1	NOUN
ejpam-4283	388	6	-	-	PUNCT
ejpam-4283	388	7	strongly	strongly	ADV
ejpam-4283	388	8	nowhere	nowhere	ADV
ejpam-4283	388	9	dense	dense	ADJ
ejpam-4283	388	10	set	set	NOUN
ejpam-4283	388	11	and	and	CCONJ
ejpam-4283	388	12	µ2	µ2	PROPN
ejpam-4283	388	13	⊂	⊂	PROPN
ejpam-4283	388	14	µ1	µ1	PROPN
ejpam-4283	388	15	.	.	PUNCT
ejpam-4283	389	1	let	let	VERB
ejpam-4283	389	2	h	h	NOUN
ejpam-4283	389	3	∈	∈	PROPN
ejpam-4283	389	4	µ̃2	µ̃2	PROPN
ejpam-4283	389	5	.	.	PUNCT
ejpam-4283	390	1	then	then	ADV
ejpam-4283	390	2	h	h	NOUN
ejpam-4283	390	3	∈	∈	PROPN
ejpam-4283	390	4	µ̃1	µ̃1	NOUN
ejpam-4283	390	5	and	and	CCONJ
ejpam-4283	390	6	so	so	ADV
ejpam-4283	390	7	there	there	PRON
ejpam-4283	390	8	is	be	VERB
ejpam-4283	390	9	a	a	DET
ejpam-4283	390	10	set	set	NOUN
ejpam-4283	390	11	k	k	PROPN
ejpam-4283	390	12	∈	∈	PROPN
ejpam-4283	390	13	µ̃1	µ̃1	NOUN
ejpam-4283	390	14	such	such	ADJ
ejpam-4283	390	15	that	that	SCONJ
ejpam-4283	390	16	k	k	PROPN
ejpam-4283	390	17	⊂	⊂	PROPN
ejpam-4283	390	18	h	h	PROPN
ejpam-4283	390	19	and	and	CCONJ
ejpam-4283	390	20	k	k	PROPN
ejpam-4283	390	21	∩	∩	PROPN
ejpam-4283	390	22	j	j	PROPN
ejpam-4283	391	1	=	=	PRON
ejpam-4283	391	2	∅.	∅.	PROPN
ejpam-4283	391	3	thus	thus	ADV
ejpam-4283	391	4	,	,	PUNCT
ejpam-4283	391	5	there	there	PRON
ejpam-4283	391	6	is	be	VERB
ejpam-4283	391	7	a	a	DET
ejpam-4283	391	8	set	set	NOUN
ejpam-4283	391	9	k	k	PROPN
ejpam-4283	391	10	∈	∈	PROPN
ejpam-4283	391	11	µ̃1	µ̃1	NOUN
ejpam-4283	391	12	such	such	ADJ
ejpam-4283	391	13	that	that	SCONJ
ejpam-4283	391	14	k	k	PROPN
ejpam-4283	391	15	⊂	⊂	PROPN
ejpam-4283	391	16	h	h	PROPN
ejpam-4283	391	17	and	and	CCONJ
ejpam-4283	391	18	k	k	PROPN
ejpam-4283	391	19	∩	∩	PROPN
ejpam-4283	391	20	j	j	PROPN
ejpam-4283	391	21	=	=	PRON
ejpam-4283	391	22	∅.	∅.	VERB
ejpam-4283	391	23	hence	hence	ADV
ejpam-4283	391	24	j	j	PROPN
ejpam-4283	391	25	∈	∈	PROPN
ejpam-4283	391	26	(	(	PUNCT
ejpam-4283	391	27	1	1	NUM
ejpam-4283	391	28	,	,	PUNCT
ejpam-4283	391	29	2)−s(x	2)−s(x	NUM
ejpam-4283	391	30	)	)	PUNCT
ejpam-4283	391	31	.	.	PUNCT
ejpam-4283	392	1	by	by	ADP
ejpam-4283	392	2	similar	similar	ADJ
ejpam-4283	392	3	arguments	argument	NOUN
ejpam-4283	392	4	,	,	PUNCT
ejpam-4283	392	5	we	we	PRON
ejpam-4283	392	6	can	can	AUX
ejpam-4283	392	7	prove	prove	VERB
ejpam-4283	392	8	that	that	SCONJ
ejpam-4283	392	9	the	the	DET
ejpam-4283	392	10	result	result	NOUN
ejpam-4283	392	11	is	be	AUX
ejpam-4283	392	12	true	true	ADJ
ejpam-4283	392	13	for	for	ADP
ejpam-4283	392	14	the	the	DET
ejpam-4283	392	15	case	case	NOUN
ejpam-4283	392	16	s	s	PART
ejpam-4283	392	17	=	=	SYM
ejpam-4283	392	18	2	2	NUM
ejpam-4283	392	19	and	and	CCONJ
ejpam-4283	392	20	v	v	NOUN
ejpam-4283	392	21	=	=	SYM
ejpam-4283	392	22	1	1	NUM
ejpam-4283	392	23	.	.	NOUN
ejpam-4283	392	24	5	5	NUM
ejpam-4283	392	25	.	.	PUNCT
ejpam-4283	392	26	(	(	PUNCT
ejpam-4283	392	27	s	s	NOUN
ejpam-4283	392	28	,	,	PUNCT
ejpam-4283	392	29	v)?-strongly	v)?-strongly	ADV
ejpam-4283	392	30	nowhere	nowhere	ADV
ejpam-4283	392	31	dense	dense	ADJ
ejpam-4283	392	32	sets	set	NOUN
ejpam-4283	392	33	in	in	ADP
ejpam-4283	392	34	this	this	DET
ejpam-4283	392	35	section	section	NOUN
ejpam-4283	392	36	,	,	PUNCT
ejpam-4283	392	37	we	we	PRON
ejpam-4283	392	38	introduce	introduce	VERB
ejpam-4283	392	39	(	(	PUNCT
ejpam-4283	392	40	s	s	ADJ
ejpam-4283	392	41	,	,	PUNCT
ejpam-4283	392	42	v)?-strongly	v)?-strongly	ADV
ejpam-4283	392	43	nowhere	nowhere	ADV
ejpam-4283	392	44	dense	dense	ADJ
ejpam-4283	392	45	set	set	NOUN
ejpam-4283	392	46	and	and	CCONJ
ejpam-4283	392	47	analzye	analzye	VERB
ejpam-4283	392	48	its	its	PRON
ejpam-4283	392	49	nature	nature	NOUN
ejpam-4283	392	50	in	in	ADP
ejpam-4283	392	51	a	a	DET
ejpam-4283	392	52	bgts	bgts	NOUN
ejpam-4283	392	53	(	(	PUNCT
ejpam-4283	392	54	x,µ1	x,µ1	PROPN
ejpam-4283	392	55	,	,	PUNCT
ejpam-4283	392	56	µ2	µ2	PROPN
ejpam-4283	392	57	)	)	PUNCT
ejpam-4283	392	58	.	.	PUNCT
ejpam-4283	393	1	definition	definition	NOUN
ejpam-4283	393	2	31	31	NUM
ejpam-4283	393	3	.	.	PUNCT
ejpam-4283	394	1	let	let	AUX
ejpam-4283	394	2	(	(	PUNCT
ejpam-4283	394	3	x,µ1	x,µ1	NOUN
ejpam-4283	394	4	,	,	PUNCT
ejpam-4283	394	5	µ2	µ2	PROPN
ejpam-4283	394	6	)	)	PUNCT
ejpam-4283	394	7	be	be	VERB
ejpam-4283	394	8	a	a	DET
ejpam-4283	394	9	bgts	bgts	NOUN
ejpam-4283	394	10	and	and	CCONJ
ejpam-4283	394	11	b	b	NOUN
ejpam-4283	394	12	be	be	AUX
ejpam-4283	394	13	a	a	DET
ejpam-4283	394	14	non	non	ADJ
ejpam-4283	394	15	-	-	ADJ
ejpam-4283	394	16	null	null	ADJ
ejpam-4283	394	17	subset	subset	NOUN
ejpam-4283	394	18	of	of	ADP
ejpam-4283	394	19	x.	x.	PROPN
ejpam-4283	394	20	then	then	ADV
ejpam-4283	394	21	b	b	PROPN
ejpam-4283	394	22	is	be	AUX
ejpam-4283	394	23	called	call	VERB
ejpam-4283	394	24	(	(	PUNCT
ejpam-4283	394	25	s	s	ADJ
ejpam-4283	394	26	,	,	PUNCT
ejpam-4283	394	27	v)?-strongly	v)?-strongly	ADV
ejpam-4283	394	28	nowhere	nowhere	ADV
ejpam-4283	394	29	dense	dense	ADJ
ejpam-4283	394	30	if	if	SCONJ
ejpam-4283	394	31	for	for	ADP
ejpam-4283	394	32	every	every	DET
ejpam-4283	394	33	k	k	PROPN
ejpam-4283	394	34	∈	∈	PROPN
ejpam-4283	394	35	µ̃s	µ̃s	NOUN
ejpam-4283	394	36	there	there	PRON
ejpam-4283	394	37	is	be	VERB
ejpam-4283	394	38	m	m	PROPN
ejpam-4283	394	39	∈	∈	NOUN
ejpam-4283	394	40	σ̃v	σ̃v	ADJ
ejpam-4283	394	41	such	such	ADJ
ejpam-4283	394	42	that	that	SCONJ
ejpam-4283	394	43	m	m	VERB
ejpam-4283	394	44	⊂	⊂	PROPN
ejpam-4283	394	45	k	k	PROPN
ejpam-4283	394	46	and	and	CCONJ
ejpam-4283	394	47	m	m	PROPN
ejpam-4283	394	48	∩b	∩b	NOUN
ejpam-4283	394	49	=	=	NOUN
ejpam-4283	394	50	∅	∅	NOUN
ejpam-4283	394	51	where	where	SCONJ
ejpam-4283	394	52	s	s	X
ejpam-4283	394	53	,	,	PUNCT
ejpam-4283	394	54	v	v	NOUN
ejpam-4283	394	55	=	=	SYM
ejpam-4283	394	56	1	1	NUM
ejpam-4283	394	57	,	,	PUNCT
ejpam-4283	394	58	2	2	NUM
ejpam-4283	394	59	;	;	PUNCT
ejpam-4283	394	60	s	s	PROPN
ejpam-4283	394	61	6=	6=	PROPN
ejpam-4283	394	62	v.	v.	ADP
ejpam-4283	394	63	moreover	moreover	ADV
ejpam-4283	394	64	,	,	PUNCT
ejpam-4283	394	65	(	(	PUNCT
ejpam-4283	394	66	s	s	X
ejpam-4283	394	67	,	,	PUNCT
ejpam-4283	394	68	v	v	NOUN
ejpam-4283	394	69	)	)	PUNCT
ejpam-4283	394	70	?	?	PUNCT
ejpam-4283	395	1	−s(x	−s(x	NOUN
ejpam-4283	395	2	)	)	PUNCT
ejpam-4283	396	1	=	=	PRON
ejpam-4283	396	2	{	{	PUNCT
ejpam-4283	396	3	q	q	X
ejpam-4283	396	4	⊂	⊂	X
ejpam-4283	396	5	x	x	PUNCT
ejpam-4283	397	1	|	|	ADV
ejpam-4283	397	2	q	q	NOUN
ejpam-4283	397	3	is	be	AUX
ejpam-4283	397	4	a	a	DET
ejpam-4283	397	5	(	(	PUNCT
ejpam-4283	397	6	s	s	X
ejpam-4283	397	7	,	,	PUNCT
ejpam-4283	397	8	v)?-strongly	v)?-strongly	ADV
ejpam-4283	397	9	nowhere	nowhere	ADV
ejpam-4283	397	10	dense	dense	ADJ
ejpam-4283	397	11	set	set	NOUN
ejpam-4283	397	12	in	in	ADP
ejpam-4283	397	13	x	x	NOUN
ejpam-4283	397	14	}	}	PUNCT
ejpam-4283	397	15	where	where	SCONJ
ejpam-4283	397	16	s	s	X
ejpam-4283	397	17	,	,	PUNCT
ejpam-4283	397	18	v	v	NOUN
ejpam-4283	397	19	=	=	SYM
ejpam-4283	397	20	1	1	NUM
ejpam-4283	397	21	,	,	PUNCT
ejpam-4283	397	22	2	2	NUM
ejpam-4283	397	23	;	;	PUNCT
ejpam-4283	397	24	s	s	PROPN
ejpam-4283	397	25	6=	6=	PROPN
ejpam-4283	397	26	v.	v.	ADP
ejpam-4283	397	27	moreover	moreover	ADV
ejpam-4283	397	28	,	,	PUNCT
ejpam-4283	397	29	every	every	DET
ejpam-4283	397	30	non	non	ADJ
ejpam-4283	397	31	-	-	ADJ
ejpam-4283	397	32	null	null	ADJ
ejpam-4283	397	33	µs	µs	NOUN
ejpam-4283	397	34	-	-	ADJ
ejpam-4283	397	35	open	open	ADJ
ejpam-4283	397	36	set	set	NOUN
ejpam-4283	397	37	is	be	AUX
ejpam-4283	397	38	need	need	AUX
ejpam-4283	397	39	not	not	PART
ejpam-4283	397	40	be	be	AUX
ejpam-4283	397	41	an	an	DET
ejpam-4283	397	42	element	element	NOUN
ejpam-4283	397	43	of	of	ADP
ejpam-4283	397	44	(	(	PUNCT
ejpam-4283	397	45	s	s	PROPN
ejpam-4283	397	46	,	,	PUNCT
ejpam-4283	397	47	v)?−s(x	v)?−s(x	PROPN
ejpam-4283	397	48	)	)	PUNCT
ejpam-4283	397	49	where	where	SCONJ
ejpam-4283	397	50	s	s	X
ejpam-4283	397	51	,	,	PUNCT
ejpam-4283	397	52	v	v	NOUN
ejpam-4283	397	53	=	=	SYM
ejpam-4283	397	54	1	1	NUM
ejpam-4283	397	55	,	,	PUNCT
ejpam-4283	397	56	2	2	NUM
ejpam-4283	397	57	and	and	CCONJ
ejpam-4283	397	58	s	s	X
ejpam-4283	397	59	6=	6=	PROPN
ejpam-4283	397	60	v.	v.	ADP
ejpam-4283	397	61	definition	definition	NOUN
ejpam-4283	397	62	32	32	NUM
ejpam-4283	397	63	.	.	PUNCT
ejpam-4283	398	1	let	let	VERB
ejpam-4283	398	2	d	d	PRON
ejpam-4283	398	3	be	be	AUX
ejpam-4283	398	4	a	a	DET
ejpam-4283	398	5	non	non	ADJ
ejpam-4283	398	6	-	-	ADJ
ejpam-4283	398	7	null	null	ADJ
ejpam-4283	398	8	subset	subset	NOUN
ejpam-4283	398	9	of	of	ADP
ejpam-4283	398	10	a	a	DET
ejpam-4283	398	11	bgts	bgts	NOUN
ejpam-4283	398	12	(	(	PUNCT
ejpam-4283	398	13	x,µ1	x,µ1	PROPN
ejpam-4283	398	14	,	,	PUNCT
ejpam-4283	398	15	µ2	µ2	PROPN
ejpam-4283	398	16	)	)	PUNCT
ejpam-4283	398	17	.	.	PUNCT
ejpam-4283	399	1	then	then	ADV
ejpam-4283	399	2	for	for	ADP
ejpam-4283	399	3	s	s	PROPN
ejpam-4283	399	4	,	,	PUNCT
ejpam-4283	399	5	v	v	NOUN
ejpam-4283	399	6	=	=	SYM
ejpam-4283	399	7	1	1	NUM
ejpam-4283	399	8	,	,	PUNCT
ejpam-4283	399	9	2	2	NUM
ejpam-4283	399	10	and	and	CCONJ
ejpam-4283	399	11	s	s	PROPN
ejpam-4283	399	12	6=	6=	PROPN
ejpam-4283	399	13	v	v	NOUN
ejpam-4283	399	14	,	,	PUNCT
ejpam-4283	399	15	(	(	PUNCT
ejpam-4283	399	16	a	a	X
ejpam-4283	399	17	)	)	PUNCT
ejpam-4283	399	18	d	d	NOUN
ejpam-4283	399	19	is	be	AUX
ejpam-4283	399	20	said	say	VERB
ejpam-4283	399	21	to	to	PART
ejpam-4283	399	22	be	be	AUX
ejpam-4283	399	23	a	a	DET
ejpam-4283	399	24	(	(	PUNCT
ejpam-4283	399	25	s	s	NOUN
ejpam-4283	399	26	,	,	PUNCT
ejpam-4283	399	27	v)?-s	v)?-	NOUN
ejpam-4283	399	28	-	-	PUNCT
ejpam-4283	399	29	meager	meager	ADJ
ejpam-4283	399	30	set	set	NOUN
ejpam-4283	399	31	if	if	SCONJ
ejpam-4283	399	32	d	d	PROPN
ejpam-4283	399	33	=	=	PUNCT
ejpam-4283	399	34	⋃	⋃	PROPN
ejpam-4283	399	35	m∈ndm	m∈ndm	PROPN
ejpam-4283	399	36	,	,	PUNCT
ejpam-4283	399	37	for	for	ADP
ejpam-4283	399	38	each	each	DET
ejpam-4283	399	39	dm	dm	PROPN
ejpam-4283	399	40	∈	∈	PROPN
ejpam-4283	399	41	(	(	PUNCT
ejpam-4283	399	42	s	s	PROPN
ejpam-4283	399	43	,	,	PUNCT
ejpam-4283	399	44	v	v	NOUN
ejpam-4283	399	45	)	)	PUNCT
ejpam-4283	399	46	?	?	PUNCT
ejpam-4283	400	1	−s(x	−s(x	NOUN
ejpam-4283	400	2	)	)	PUNCT
ejpam-4283	400	3	.	.	PUNCT
ejpam-4283	401	1	(	(	PUNCT
ejpam-4283	401	2	b	b	X
ejpam-4283	401	3	)	)	PUNCT
ejpam-4283	401	4	d	d	NOUN
ejpam-4283	401	5	is	be	AUX
ejpam-4283	401	6	called	call	VERB
ejpam-4283	401	7	(	(	PUNCT
ejpam-4283	401	8	s	s	NOUN
ejpam-4283	401	9	,	,	PUNCT
ejpam-4283	401	10	v)?-s	v)?-	NOUN
ejpam-4283	401	11	-	-	PUNCT
ejpam-4283	401	12	residual	residual	ADJ
ejpam-4283	401	13	if	if	SCONJ
ejpam-4283	401	14	x	x	PROPN
ejpam-4283	401	15	−d	−d	PROPN
ejpam-4283	401	16	is	be	AUX
ejpam-4283	401	17	a	a	DET
ejpam-4283	401	18	(	(	PUNCT
ejpam-4283	401	19	s	s	NOUN
ejpam-4283	401	20	,	,	PUNCT
ejpam-4283	401	21	v)?-s	v)?-	NOUN
ejpam-4283	401	22	-	-	PUNCT
ejpam-4283	401	23	meager	meager	ADJ
ejpam-4283	401	24	set	set	NOUN
ejpam-4283	401	25	in	in	ADP
ejpam-4283	401	26	x.	x.	PROPN
ejpam-4283	401	27	(	(	PUNCT
ejpam-4283	401	28	c	c	X
ejpam-4283	401	29	)	)	PUNCT
ejpam-4283	401	30	d	d	NOUN
ejpam-4283	401	31	is	be	AUX
ejpam-4283	401	32	of	of	ADP
ejpam-4283	401	33	a	a	DET
ejpam-4283	401	34	(	(	PUNCT
ejpam-4283	401	35	s	s	NOUN
ejpam-4283	401	36	,	,	PUNCT
ejpam-4283	401	37	v)?-s	v)?-	NOUN
ejpam-4283	401	38	-	-	PUNCT
ejpam-4283	401	39	second	second	ADJ
ejpam-4283	401	40	category	category	NOUN
ejpam-4283	401	41	set	set	VERB
ejpam-4283	401	42	if	if	SCONJ
ejpam-4283	401	43	d	d	NOUN
ejpam-4283	401	44	is	be	AUX
ejpam-4283	401	45	not	not	PART
ejpam-4283	401	46	a	a	DET
ejpam-4283	401	47	(	(	PUNCT
ejpam-4283	401	48	s	s	NOUN
ejpam-4283	401	49	,	,	PUNCT
ejpam-4283	401	50	v)?-s	v)?-	NOUN
ejpam-4283	401	51	-	-	PUNCT
ejpam-4283	401	52	meager	meager	ADJ
ejpam-4283	401	53	set	set	NOUN
ejpam-4283	401	54	in	in	ADP
ejpam-4283	401	55	x.	x.	NOUN
ejpam-4283	401	56	in	in	ADP
ejpam-4283	401	57	a	a	DET
ejpam-4283	401	58	bigeneralized	bigeneralize	VERB
ejpam-4283	401	59	topological	topological	ADJ
ejpam-4283	401	60	space	space	NOUN
ejpam-4283	401	61	,	,	PUNCT
ejpam-4283	401	62	if	if	SCONJ
ejpam-4283	401	63	p	p	X
ejpam-4283	401	64	∈	∈	PROPN
ejpam-4283	401	65	(	(	PUNCT
ejpam-4283	401	66	s	s	PROPN
ejpam-4283	401	67	,	,	PUNCT
ejpam-4283	401	68	v	v	NOUN
ejpam-4283	401	69	)	)	PUNCT
ejpam-4283	401	70	?	?	PUNCT
ejpam-4283	402	1	−	−	PROPN
ejpam-4283	402	2	s(x	s(x	PROPN
ejpam-4283	402	3	)	)	PUNCT
ejpam-4283	402	4	and	and	CCONJ
ejpam-4283	402	5	q	q	PROPN
ejpam-4283	402	6	⊂	⊂	PROPN
ejpam-4283	402	7	p	p	X
ejpam-4283	402	8	,	,	PUNCT
ejpam-4283	402	9	then	then	ADV
ejpam-4283	402	10	q	q	PROPN
ejpam-4283	402	11	∈	∈	PROPN
ejpam-4283	402	12	(	(	PUNCT
ejpam-4283	402	13	s	s	PROPN
ejpam-4283	402	14	,	,	PUNCT
ejpam-4283	402	15	v	v	NOUN
ejpam-4283	402	16	)	)	PUNCT
ejpam-4283	402	17	?	?	PUNCT
ejpam-4283	403	1	−s(x	−s(x	NOUN
ejpam-4283	403	2	)	)	PUNCT
ejpam-4283	403	3	where	where	SCONJ
ejpam-4283	403	4	s	s	X
ejpam-4283	403	5	,	,	PUNCT
ejpam-4283	403	6	v	v	NOUN
ejpam-4283	403	7	=	=	SYM
ejpam-4283	403	8	1	1	NUM
ejpam-4283	403	9	,	,	PUNCT
ejpam-4283	403	10	2	2	NUM
ejpam-4283	403	11	and	and	CCONJ
ejpam-4283	403	12	s	s	X
ejpam-4283	403	13	6=	6=	PROPN
ejpam-4283	403	14	v.	v.	ADP
ejpam-4283	403	15	moreover	moreover	ADV
ejpam-4283	403	16	,	,	PUNCT
ejpam-4283	403	17	(	(	PUNCT
ejpam-4283	403	18	s	s	X
ejpam-4283	403	19	,	,	PUNCT
ejpam-4283	403	20	v)−s(x	v)−s(x	NUM
ejpam-4283	403	21	)	)	PUNCT
ejpam-4283	404	1	⊂	⊂	PROPN
ejpam-4283	404	2	(	(	PUNCT
ejpam-4283	404	3	v	v	NOUN
ejpam-4283	404	4	,	,	PUNCT
ejpam-4283	404	5	s	s	NOUN
ejpam-4283	404	6	)	)	PUNCT
ejpam-4283	404	7	?	?	PUNCT
ejpam-4283	405	1	−s(x	−s(x	NOUN
ejpam-4283	405	2	)	)	PUNCT
ejpam-4283	405	3	where	where	SCONJ
ejpam-4283	405	4	s	s	X
ejpam-4283	405	5	,	,	PUNCT
ejpam-4283	405	6	v	v	NOUN
ejpam-4283	405	7	=	=	SYM
ejpam-4283	405	8	1	1	NUM
ejpam-4283	405	9	,	,	PUNCT
ejpam-4283	405	10	2	2	NUM
ejpam-4283	405	11	and	and	CCONJ
ejpam-4283	405	12	s	s	PROPN
ejpam-4283	405	13	6=	6=	PROPN
ejpam-4283	405	14	v.	v.	CCONJ
ejpam-4283	405	15	theorem	theorem	NOUN
ejpam-4283	405	16	33	33	NUM
ejpam-4283	405	17	.	.	PUNCT
ejpam-4283	406	1	let	let	AUX
ejpam-4283	406	2	(	(	PUNCT
ejpam-4283	406	3	x,µ1	x,µ1	NOUN
ejpam-4283	406	4	,	,	PUNCT
ejpam-4283	406	5	µ2	µ2	PROPN
ejpam-4283	406	6	)	)	PUNCT
ejpam-4283	406	7	be	be	VERB
ejpam-4283	406	8	a	a	DET
ejpam-4283	406	9	bigeneralized	bigeneralized	ADJ
ejpam-4283	406	10	topological	topological	ADJ
ejpam-4283	406	11	space	space	NOUN
ejpam-4283	406	12	.	.	PUNCT
ejpam-4283	407	1	then	then	ADV
ejpam-4283	407	2	the	the	DET
ejpam-4283	407	3	following	follow	VERB
ejpam-4283	407	4	hold	hold	NOUN
ejpam-4283	407	5	.	.	PUNCT
ejpam-4283	408	1	(	(	PUNCT
ejpam-4283	408	2	a	a	X
ejpam-4283	408	3	)	)	PUNCT
ejpam-4283	408	4	if	if	SCONJ
ejpam-4283	408	5	µ2	µ2	PROPN
ejpam-4283	408	6	is	be	AUX
ejpam-4283	408	7	a	a	DET
ejpam-4283	408	8	strong	strong	ADJ
ejpam-4283	408	9	generalized	generalized	ADJ
ejpam-4283	408	10	topology	topology	NOUN
ejpam-4283	408	11	,	,	PUNCT
ejpam-4283	408	12	then	then	ADV
ejpam-4283	408	13	(	(	PUNCT
ejpam-4283	408	14	1	1	NUM
ejpam-4283	408	15	,	,	PUNCT
ejpam-4283	408	16	2	2	NUM
ejpam-4283	408	17	)	)	PUNCT
ejpam-4283	408	18	?	?	PUNCT
ejpam-4283	409	1	−s(x	−s(x	NOUN
ejpam-4283	409	2	)	)	PUNCT
ejpam-4283	410	1	⊂	⊂	PROPN
ejpam-4283	410	2	(	(	PUNCT
ejpam-4283	410	3	2	2	NUM
ejpam-4283	410	4	,	,	PUNCT
ejpam-4283	410	5	1)−s(x	1)−s(x	NUM
ejpam-4283	410	6	)	)	PUNCT
ejpam-4283	410	7	.	.	PUNCT
ejpam-4283	411	1	(	(	PUNCT
ejpam-4283	411	2	b	b	X
ejpam-4283	411	3	)	)	PUNCT
ejpam-4283	411	4	if	if	SCONJ
ejpam-4283	411	5	µ1	µ1	PROPN
ejpam-4283	411	6	is	be	AUX
ejpam-4283	411	7	a	a	DET
ejpam-4283	411	8	strong	strong	ADJ
ejpam-4283	411	9	generalized	generalized	ADJ
ejpam-4283	411	10	topology	topology	NOUN
ejpam-4283	411	11	,	,	PUNCT
ejpam-4283	411	12	then	then	ADV
ejpam-4283	411	13	(	(	PUNCT
ejpam-4283	411	14	2	2	NUM
ejpam-4283	411	15	,	,	PUNCT
ejpam-4283	411	16	1	1	NUM
ejpam-4283	411	17	)	)	PUNCT
ejpam-4283	411	18	?	?	PUNCT
ejpam-4283	412	1	−s(x	−s(x	NOUN
ejpam-4283	412	2	)	)	PUNCT
ejpam-4283	413	1	⊂	⊂	PROPN
ejpam-4283	413	2	(	(	PUNCT
ejpam-4283	413	3	1	1	NUM
ejpam-4283	413	4	,	,	PUNCT
ejpam-4283	413	5	2)−s(x	2)−s(x	NUM
ejpam-4283	413	6	)	)	PUNCT
ejpam-4283	413	7	.	.	PUNCT
ejpam-4283	414	1	proof	proof	NOUN
ejpam-4283	414	2	.	.	PUNCT
ejpam-4283	415	1	(	(	PUNCT
ejpam-4283	415	2	a	a	X
ejpam-4283	415	3	)	)	PUNCT
ejpam-4283	415	4	.	.	PUNCT
ejpam-4283	416	1	suppose	suppose	VERB
ejpam-4283	416	2	µ2	µ2	PROPN
ejpam-4283	416	3	is	be	AUX
ejpam-4283	416	4	a	a	DET
ejpam-4283	416	5	strong	strong	ADJ
ejpam-4283	416	6	generalized	generalized	ADJ
ejpam-4283	416	7	topology	topology	NOUN
ejpam-4283	416	8	and	and	CCONJ
ejpam-4283	416	9	q	q	NOUN
ejpam-4283	416	10	∈	∈	PROPN
ejpam-4283	416	11	(	(	PUNCT
ejpam-4283	416	12	1	1	NUM
ejpam-4283	416	13	,	,	PUNCT
ejpam-4283	416	14	2	2	NUM
ejpam-4283	416	15	)	)	PUNCT
ejpam-4283	416	16	?	?	PUNCT
ejpam-4283	417	1	−s(x	−s(x	NOUN
ejpam-4283	417	2	)	)	PUNCT
ejpam-4283	417	3	.	.	PUNCT
ejpam-4283	418	1	let	let	VERB
ejpam-4283	418	2	g	g	PROPN
ejpam-4283	418	3	∈	∈	PROPN
ejpam-4283	418	4	µ̃1	µ̃1	PROPN
ejpam-4283	418	5	.	.	PUNCT
ejpam-4283	419	1	then	then	ADV
ejpam-4283	419	2	there	there	PRON
ejpam-4283	419	3	is	be	VERB
ejpam-4283	419	4	a	a	DET
ejpam-4283	419	5	set	set	NOUN
ejpam-4283	419	6	p	p	NOUN
ejpam-4283	419	7	∈	∈	NOUN
ejpam-4283	419	8	σ̃2	σ̃2	PROPN
ejpam-4283	419	9	such	such	ADJ
ejpam-4283	419	10	that	that	SCONJ
ejpam-4283	419	11	p	p	PROPN
ejpam-4283	419	12	⊂	⊂	PROPN
ejpam-4283	419	13	g	g	PROPN
ejpam-4283	419	14	and	and	CCONJ
ejpam-4283	419	15	p	p	PRON
ejpam-4283	419	16	∩q	∩q	PROPN
ejpam-4283	419	17	=	=	PUNCT
ejpam-4283	419	18	∅.	∅.	ADV
ejpam-4283	419	19	since	since	SCONJ
ejpam-4283	419	20	p	p	PROPN
ejpam-4283	419	21	∈	∈	PROPN
ejpam-4283	419	22	σ̃2	σ̃2	PROPN
ejpam-4283	419	23	we	we	PRON
ejpam-4283	419	24	have	have	VERB
ejpam-4283	419	25	i2(p	i2(p	X
ejpam-4283	419	26	)	)	PUNCT
ejpam-4283	419	27	∈	∈	PROPN
ejpam-4283	419	28	µ̃2	µ̃2	PROPN
ejpam-4283	419	29	,	,	PUNCT
ejpam-4283	419	30	by	by	ADP
ejpam-4283	419	31	assumption	assumption	NOUN
ejpam-4283	419	32	.	.	PUNCT
ejpam-4283	420	1	take	take	VERB
ejpam-4283	420	2	j	j	PROPN
ejpam-4283	420	3	=	=	PUNCT
ejpam-4283	420	4	i2(p	i2(p	PROPN
ejpam-4283	420	5	)	)	PUNCT
ejpam-4283	420	6	.	.	PUNCT
ejpam-4283	421	1	then	then	ADV
ejpam-4283	421	2	j	j	PROPN
ejpam-4283	421	3	∈	∈	PROPN
ejpam-4283	421	4	µ̃2	µ̃2	PROPN
ejpam-4283	421	5	and	and	CCONJ
ejpam-4283	421	6	j	j	PROPN
ejpam-4283	421	7	⊂	⊂	PROPN
ejpam-4283	421	8	g.	g.	PROPN
ejpam-4283	422	1	also	also	ADV
ejpam-4283	422	2	,	,	PUNCT
ejpam-4283	422	3	j	j	PROPN
ejpam-4283	422	4	∩	∩	ADJ
ejpam-4283	422	5	q	q	X
ejpam-4283	422	6	=	=	PUNCT
ejpam-4283	422	7	∅.	∅.	PROPN
ejpam-4283	422	8	p.	p.	NOUN
ejpam-4283	422	9	yupapin	yupapin	NOUN
ejpam-4283	422	10	,	,	PUNCT
ejpam-4283	422	11	v.	v.	CCONJ
ejpam-4283	422	12	subramanian	subramanian	PROPN
ejpam-4283	422	13	,	,	PUNCT
ejpam-4283	422	14	y.	y.	PROPN
ejpam-4283	422	15	farhat	farhat	PROPN
ejpam-4283	422	16	/	/	SYM
ejpam-4283	422	17	eur	eur	PROPN
ejpam-4283	422	18	.	.	PUNCT
ejpam-4283	423	1	j.	j.	PROPN
ejpam-4283	423	2	pure	pure	PROPN
ejpam-4283	423	3	appl	appl	PROPN
ejpam-4283	423	4	.	.	PROPN
ejpam-4283	423	5	math	math	PROPN
ejpam-4283	423	6	,	,	PUNCT
ejpam-4283	423	7	15	15	NUM
ejpam-4283	423	8	(	(	PUNCT
ejpam-4283	423	9	2	2	NUM
ejpam-4283	423	10	)	)	PUNCT
ejpam-4283	423	11	(	(	PUNCT
ejpam-4283	423	12	2022	2022	NUM
ejpam-4283	423	13	)	)	PUNCT
ejpam-4283	423	14	,	,	PUNCT
ejpam-4283	423	15	403	403	NUM
ejpam-4283	423	16	-	-	SYM
ejpam-4283	423	17	414	414	NUM
ejpam-4283	423	18	412	412	NUM
ejpam-4283	423	19	thus	thus	ADV
ejpam-4283	423	20	,	,	PUNCT
ejpam-4283	423	21	there	there	PRON
ejpam-4283	423	22	is	be	VERB
ejpam-4283	423	23	a	a	DET
ejpam-4283	423	24	set	set	NOUN
ejpam-4283	423	25	j	j	PROPN
ejpam-4283	423	26	∈	∈	PROPN
ejpam-4283	423	27	µ̃2	µ̃2	PROPN
ejpam-4283	423	28	such	such	ADJ
ejpam-4283	423	29	that	that	SCONJ
ejpam-4283	423	30	j	j	PROPN
ejpam-4283	423	31	⊂	⊂	PROPN
ejpam-4283	423	32	g	g	PROPN
ejpam-4283	423	33	and	and	CCONJ
ejpam-4283	423	34	j	j	PROPN
ejpam-4283	423	35	∩q	∩q	PROPN
ejpam-4283	424	1	=	=	PUNCT
ejpam-4283	425	1	∅.	∅.	VERB
ejpam-4283	425	2	therefore	therefore	ADV
ejpam-4283	425	3	,	,	PUNCT
ejpam-4283	425	4	q	q	PROPN
ejpam-4283	425	5	∈	∈	PROPN
ejpam-4283	425	6	(	(	PUNCT
ejpam-4283	425	7	2	2	NUM
ejpam-4283	425	8	,	,	PUNCT
ejpam-4283	425	9	1)−s(x	1)−s(x	NUM
ejpam-4283	425	10	)	)	PUNCT
ejpam-4283	425	11	.	.	PUNCT
ejpam-4283	426	1	by	by	ADP
ejpam-4283	426	2	similar	similar	ADJ
ejpam-4283	426	3	arguments	argument	NOUN
ejpam-4283	426	4	,	,	PUNCT
ejpam-4283	426	5	we	we	PRON
ejpam-4283	426	6	get	get	VERB
ejpam-4283	426	7	the	the	DET
ejpam-4283	426	8	proof	proof	NOUN
ejpam-4283	426	9	for	for	ADP
ejpam-4283	426	10	(	(	PUNCT
ejpam-4283	426	11	b	b	NOUN
ejpam-4283	426	12	)	)	PUNCT
ejpam-4283	426	13	.	.	PUNCT
ejpam-4283	427	1	moreover	moreover	ADV
ejpam-4283	427	2	,	,	PUNCT
ejpam-4283	427	3	the	the	DET
ejpam-4283	427	4	family	family	NOUN
ejpam-4283	427	5	(	(	PUNCT
ejpam-4283	427	6	s	s	PROPN
ejpam-4283	427	7	,	,	PUNCT
ejpam-4283	427	8	v	v	NOUN
ejpam-4283	427	9	)	)	PUNCT
ejpam-4283	427	10	?	?	PUNCT
ejpam-4283	428	1	−	−	PROPN
ejpam-4283	428	2	s(x	s(x	PROPN
ejpam-4283	428	3	)	)	PUNCT
ejpam-4283	428	4	is	be	AUX
ejpam-4283	428	5	need	need	AUX
ejpam-4283	428	6	not	not	PART
ejpam-4283	428	7	be	be	AUX
ejpam-4283	428	8	closed	close	VERB
ejpam-4283	428	9	under	under	ADP
ejpam-4283	428	10	finite	finite	ADJ
ejpam-4283	428	11	union	union	NOUN
ejpam-4283	428	12	where	where	SCONJ
ejpam-4283	428	13	s	s	X
ejpam-4283	428	14	,	,	PUNCT
ejpam-4283	428	15	v	v	NOUN
ejpam-4283	428	16	=	=	SYM
ejpam-4283	428	17	1	1	NUM
ejpam-4283	428	18	,	,	PUNCT
ejpam-4283	428	19	2	2	NUM
ejpam-4283	428	20	and	and	CCONJ
ejpam-4283	428	21	s	s	X
ejpam-4283	428	22	6=	6=	PROPN
ejpam-4283	428	23	v	v	NOUN
ejpam-4283	428	24	as	as	SCONJ
ejpam-4283	428	25	shown	show	VERB
ejpam-4283	428	26	by	by	ADP
ejpam-4283	428	27	example	example	NOUN
ejpam-4283	428	28	34	34	NUM
ejpam-4283	428	29	.	.	PUNCT
ejpam-4283	428	30	example	example	NOUN
ejpam-4283	429	1	34	34	NUM
ejpam-4283	429	2	.	.	PUNCT
ejpam-4283	430	1	(	(	PUNCT
ejpam-4283	430	2	a	a	X
ejpam-4283	430	3	)	)	PUNCT
ejpam-4283	430	4	.	.	PUNCT
ejpam-4283	431	1	consider	consider	VERB
ejpam-4283	431	2	the	the	DET
ejpam-4283	431	3	bigeneralized	bigeneralized	ADJ
ejpam-4283	431	4	topological	topological	ADJ
ejpam-4283	431	5	space	space	NOUN
ejpam-4283	431	6	(	(	PUNCT
ejpam-4283	431	7	x,µ1	x,µ1	PROPN
ejpam-4283	431	8	,	,	PUNCT
ejpam-4283	431	9	µ2	µ2	PROPN
ejpam-4283	431	10	)	)	PUNCT
ejpam-4283	432	1	where	where	SCONJ
ejpam-4283	432	2	x	x	X
ejpam-4283	432	3	=	=	PRON
ejpam-4283	432	4	{	{	PUNCT
ejpam-4283	432	5	p	p	X
ejpam-4283	432	6	,	,	PUNCT
ejpam-4283	432	7	q	q	ADJ
ejpam-4283	432	8	,	,	PUNCT
ejpam-4283	432	9	r	r	NOUN
ejpam-4283	432	10	,	,	PUNCT
ejpam-4283	432	11	s};µ1	s};µ1	PROPN
ejpam-4283	432	12	=	=	SYM
ejpam-4283	432	13	{	{	PUNCT
ejpam-4283	432	14	∅	∅	NOUN
ejpam-4283	432	15	,	,	PUNCT
ejpam-4283	432	16	{	{	PUNCT
ejpam-4283	432	17	p	p	X
ejpam-4283	432	18	,	,	PUNCT
ejpam-4283	432	19	q	q	NOUN
ejpam-4283	432	20	}	}	PUNCT
ejpam-4283	432	21	,	,	PUNCT
ejpam-4283	432	22	{	{	PUNCT
ejpam-4283	432	23	q	q	X
ejpam-4283	432	24	,	,	PUNCT
ejpam-4283	432	25	r	r	NOUN
ejpam-4283	432	26	}	}	PUNCT
ejpam-4283	432	27	,	,	PUNCT
ejpam-4283	432	28	{	{	PUNCT
ejpam-4283	432	29	p	p	X
ejpam-4283	432	30	,	,	PUNCT
ejpam-4283	432	31	q	q	NOUN
ejpam-4283	432	32	,	,	PUNCT
ejpam-4283	432	33	r}};µ2	r}};µ2	VERB
ejpam-4283	432	34	=	=	SYM
ejpam-4283	432	35	{	{	PUNCT
ejpam-4283	432	36	∅	∅	NOUN
ejpam-4283	432	37	,	,	PUNCT
ejpam-4283	432	38	{	{	PUNCT
ejpam-4283	432	39	p	p	X
ejpam-4283	432	40	}	}	PUNCT
ejpam-4283	432	41	,	,	PUNCT
ejpam-4283	432	42	{	{	PUNCT
ejpam-4283	432	43	q	q	X
ejpam-4283	432	44	}	}	PUNCT
ejpam-4283	432	45	,	,	PUNCT
ejpam-4283	432	46	{	{	PUNCT
ejpam-4283	432	47	p	p	X
ejpam-4283	432	48	,	,	PUNCT
ejpam-4283	432	49	q	q	NOUN
ejpam-4283	432	50	}	}	PUNCT
ejpam-4283	432	51	,	,	PUNCT
ejpam-4283	432	52	{	{	PUNCT
ejpam-4283	432	53	p	p	X
ejpam-4283	432	54	,	,	PUNCT
ejpam-4283	432	55	s	s	PART
ejpam-4283	432	56	}	}	PUNCT
ejpam-4283	432	57	,	,	PUNCT
ejpam-4283	432	58	{	{	PUNCT
ejpam-4283	432	59	q	q	X
ejpam-4283	432	60	,	,	PUNCT
ejpam-4283	432	61	s	s	PART
ejpam-4283	432	62	}	}	PUNCT
ejpam-4283	432	63	,	,	PUNCT
ejpam-4283	432	64	{	{	PUNCT
ejpam-4283	432	65	p	p	X
ejpam-4283	432	66	,	,	PUNCT
ejpam-4283	432	67	q	q	ADJ
ejpam-4283	432	68	,	,	PUNCT
ejpam-4283	432	69	s	s	PART
ejpam-4283	432	70	}	}	PUNCT
ejpam-4283	432	71	}	}	PUNCT
ejpam-4283	432	72	.	.	PUNCT
ejpam-4283	433	1	then	then	ADV
ejpam-4283	433	2	σ2	σ2	PROPN
ejpam-4283	433	3	=	=	SYM
ejpam-4283	433	4	{	{	PUNCT
ejpam-4283	433	5	∅	∅	NOUN
ejpam-4283	433	6	,	,	PUNCT
ejpam-4283	433	7	{	{	PUNCT
ejpam-4283	433	8	p	p	X
ejpam-4283	433	9	}	}	PUNCT
ejpam-4283	433	10	,	,	PUNCT
ejpam-4283	433	11	{	{	PUNCT
ejpam-4283	433	12	q	q	X
ejpam-4283	433	13	}	}	PUNCT
ejpam-4283	433	14	,	,	PUNCT
ejpam-4283	433	15	{	{	PUNCT
ejpam-4283	433	16	r	r	NOUN
ejpam-4283	433	17	}	}	PUNCT
ejpam-4283	433	18	,	,	PUNCT
ejpam-4283	433	19	{	{	PUNCT
ejpam-4283	433	20	p	p	X
ejpam-4283	433	21	,	,	PUNCT
ejpam-4283	433	22	q	q	NOUN
ejpam-4283	433	23	}	}	PUNCT
ejpam-4283	433	24	,	,	PUNCT
ejpam-4283	433	25	{	{	PUNCT
ejpam-4283	433	26	p	p	X
ejpam-4283	433	27	,	,	PUNCT
ejpam-4283	433	28	r	r	NOUN
ejpam-4283	433	29	}	}	PUNCT
ejpam-4283	433	30	,	,	PUNCT
ejpam-4283	433	31	{	{	PUNCT
ejpam-4283	433	32	q	q	X
ejpam-4283	433	33	,	,	PUNCT
ejpam-4283	433	34	r	r	NOUN
ejpam-4283	433	35	}	}	PUNCT
ejpam-4283	433	36	,	,	PUNCT
ejpam-4283	433	37	{	{	PUNCT
ejpam-4283	433	38	p	p	X
ejpam-4283	433	39	,	,	PUNCT
ejpam-4283	433	40	s	s	PART
ejpam-4283	433	41	}	}	PUNCT
ejpam-4283	433	42	,	,	PUNCT
ejpam-4283	433	43	{	{	PUNCT
ejpam-4283	433	44	q	q	X
ejpam-4283	433	45	,	,	PUNCT
ejpam-4283	433	46	s	s	PART
ejpam-4283	433	47	}	}	PUNCT
ejpam-4283	433	48	,	,	PUNCT
ejpam-4283	433	49	{	{	PUNCT
ejpam-4283	433	50	p	p	X
ejpam-4283	433	51	,	,	PUNCT
ejpam-4283	433	52	q	q	ADJ
ejpam-4283	433	53	,	,	PUNCT
ejpam-4283	433	54	r	r	NOUN
ejpam-4283	433	55	}	}	PUNCT
ejpam-4283	433	56	,	,	PUNCT
ejpam-4283	433	57	{	{	PUNCT
ejpam-4283	433	58	p	p	X
ejpam-4283	433	59	,	,	PUNCT
ejpam-4283	433	60	q	q	X
ejpam-4283	433	61	,	,	PUNCT
ejpam-4283	433	62	s	s	PART
ejpam-4283	433	63	}	}	PUNCT
ejpam-4283	433	64	,	,	PUNCT
ejpam-4283	433	65	{	{	PUNCT
ejpam-4283	433	66	p	p	X
ejpam-4283	433	67	,	,	PUNCT
ejpam-4283	433	68	r	r	NOUN
ejpam-4283	433	69	,	,	PUNCT
ejpam-4283	433	70	s	s	PART
ejpam-4283	433	71	}	}	PUNCT
ejpam-4283	433	72	,	,	PUNCT
ejpam-4283	433	73	{	{	PUNCT
ejpam-4283	433	74	q	q	X
ejpam-4283	433	75	,	,	PUNCT
ejpam-4283	433	76	r	r	NOUN
ejpam-4283	433	77	,	,	PUNCT
ejpam-4283	433	78	s	s	PART
ejpam-4283	433	79	}	}	PUNCT
ejpam-4283	433	80	,	,	PUNCT
ejpam-4283	433	81	x	x	NOUN
ejpam-4283	433	82	}	}	PUNCT
ejpam-4283	433	83	.	.	PUNCT
ejpam-4283	434	1	take	take	VERB
ejpam-4283	434	2	p	p	NOUN
ejpam-4283	434	3	=	=	X
ejpam-4283	434	4	{	{	PUNCT
ejpam-4283	434	5	q	q	PROPN
ejpam-4283	434	6	,	,	PUNCT
ejpam-4283	434	7	s	s	PART
ejpam-4283	434	8	}	}	PUNCT
ejpam-4283	434	9	and	and	CCONJ
ejpam-4283	434	10	q	q	NOUN
ejpam-4283	434	11	=	=	SYM
ejpam-4283	434	12	{	{	PUNCT
ejpam-4283	434	13	r	r	NOUN
ejpam-4283	434	14	,	,	PUNCT
ejpam-4283	434	15	s	s	PART
ejpam-4283	434	16	}	}	PUNCT
ejpam-4283	434	17	.	.	PUNCT
ejpam-4283	435	1	then	then	ADV
ejpam-4283	435	2	p	p	PROPN
ejpam-4283	435	3	and	and	CCONJ
ejpam-4283	435	4	q	q	NOUN
ejpam-4283	435	5	are	be	AUX
ejpam-4283	435	6	(	(	PUNCT
ejpam-4283	435	7	1	1	NUM
ejpam-4283	435	8	,	,	PUNCT
ejpam-4283	435	9	2)?-strongly	2)?-strongly	ADV
ejpam-4283	435	10	nowhere	nowhere	ADV
ejpam-4283	435	11	dense	dense	ADJ
ejpam-4283	435	12	sets	set	NOUN
ejpam-4283	435	13	in	in	ADP
ejpam-4283	435	14	x.	x.	NOUN
ejpam-4283	435	15	but	but	CCONJ
ejpam-4283	435	16	p	p	NOUN
ejpam-4283	435	17	∪q	∪q	X
ejpam-4283	435	18	=	=	SYM
ejpam-4283	435	19	{	{	PUNCT
ejpam-4283	435	20	q	q	NOUN
ejpam-4283	435	21	,	,	PUNCT
ejpam-4283	435	22	r	r	NOUN
ejpam-4283	435	23	,	,	PUNCT
ejpam-4283	435	24	s	s	PART
ejpam-4283	435	25	}	}	PUNCT
ejpam-4283	435	26	/∈	/∈	PUNCT
ejpam-4283	436	1	(	(	PUNCT
ejpam-4283	436	2	1	1	NUM
ejpam-4283	436	3	,	,	PUNCT
ejpam-4283	436	4	2	2	NUM
ejpam-4283	436	5	)	)	PUNCT
ejpam-4283	436	6	?	?	PUNCT
ejpam-4283	437	1	−s(x	−s(x	NOUN
ejpam-4283	437	2	)	)	PUNCT
ejpam-4283	437	3	.	.	PUNCT
ejpam-4283	438	1	(	(	PUNCT
ejpam-4283	438	2	b	b	X
ejpam-4283	438	3	)	)	PUNCT
ejpam-4283	438	4	.	.	PUNCT
ejpam-4283	439	1	consider	consider	VERB
ejpam-4283	439	2	the	the	DET
ejpam-4283	439	3	bigeneralized	bigeneralized	ADJ
ejpam-4283	439	4	topological	topological	ADJ
ejpam-4283	439	5	space	space	NOUN
ejpam-4283	439	6	(	(	PUNCT
ejpam-4283	439	7	x,µ1	x,µ1	PROPN
ejpam-4283	439	8	,	,	PUNCT
ejpam-4283	439	9	µ2	µ2	PROPN
ejpam-4283	439	10	)	)	PUNCT
ejpam-4283	440	1	where	where	SCONJ
ejpam-4283	440	2	x	x	X
ejpam-4283	440	3	=	=	PRON
ejpam-4283	440	4	{	{	PUNCT
ejpam-4283	440	5	p	p	X
ejpam-4283	440	6	,	,	PUNCT
ejpam-4283	440	7	q	q	ADJ
ejpam-4283	440	8	,	,	PUNCT
ejpam-4283	440	9	r	r	NOUN
ejpam-4283	440	10	,	,	PUNCT
ejpam-4283	440	11	s};µ1	s};µ1	PROPN
ejpam-4283	440	12	=	=	SYM
ejpam-4283	440	13	{	{	PUNCT
ejpam-4283	440	14	∅	∅	NOUN
ejpam-4283	440	15	,	,	PUNCT
ejpam-4283	440	16	{	{	PUNCT
ejpam-4283	440	17	r	r	NOUN
ejpam-4283	440	18	}	}	PUNCT
ejpam-4283	440	19	,	,	PUNCT
ejpam-4283	440	20	{	{	PUNCT
ejpam-4283	440	21	p	p	X
ejpam-4283	440	22	,	,	PUNCT
ejpam-4283	440	23	s	s	PART
ejpam-4283	440	24	}	}	PUNCT
ejpam-4283	440	25	,	,	PUNCT
ejpam-4283	440	26	{	{	PUNCT
ejpam-4283	440	27	q	q	X
ejpam-4283	440	28	,	,	PUNCT
ejpam-4283	440	29	s	s	PART
ejpam-4283	440	30	}	}	PUNCT
ejpam-4283	440	31	,	,	PUNCT
ejpam-4283	440	32	{	{	PUNCT
ejpam-4283	440	33	p	p	X
ejpam-4283	440	34	,	,	PUNCT
ejpam-4283	440	35	q	q	X
ejpam-4283	440	36	,	,	PUNCT
ejpam-4283	440	37	s	s	PART
ejpam-4283	440	38	}	}	PUNCT
ejpam-4283	440	39	,	,	PUNCT
ejpam-4283	440	40	{	{	PUNCT
ejpam-4283	440	41	p	p	X
ejpam-4283	440	42	,	,	PUNCT
ejpam-4283	440	43	r	r	NOUN
ejpam-4283	440	44	,	,	PUNCT
ejpam-4283	440	45	s	s	PART
ejpam-4283	440	46	}	}	PUNCT
ejpam-4283	440	47	,	,	PUNCT
ejpam-4283	440	48	{	{	PUNCT
ejpam-4283	440	49	q	q	X
ejpam-4283	440	50	,	,	PUNCT
ejpam-4283	440	51	r	r	NOUN
ejpam-4283	440	52	,	,	PUNCT
ejpam-4283	440	53	s	s	PART
ejpam-4283	440	54	}	}	PUNCT
ejpam-4283	440	55	,	,	PUNCT
ejpam-4283	440	56	x};µ2	x};µ2	PROPN
ejpam-4283	440	57	=	=	PRON
ejpam-4283	440	58	{	{	PUNCT
ejpam-4283	440	59	∅	∅	NOUN
ejpam-4283	440	60	,	,	PUNCT
ejpam-4283	440	61	{	{	PUNCT
ejpam-4283	440	62	q	q	NOUN
ejpam-4283	440	63	,	,	PUNCT
ejpam-4283	440	64	r	r	NOUN
ejpam-4283	440	65	}	}	PUNCT
ejpam-4283	440	66	,	,	PUNCT
ejpam-4283	440	67	{	{	PUNCT
ejpam-4283	440	68	r	r	NOUN
ejpam-4283	440	69	,	,	PUNCT
ejpam-4283	440	70	s	s	PART
ejpam-4283	440	71	}	}	PUNCT
ejpam-4283	440	72	,	,	PUNCT
ejpam-4283	440	73	{	{	PUNCT
ejpam-4283	440	74	q	q	X
ejpam-4283	440	75	,	,	PUNCT
ejpam-4283	440	76	r	r	NOUN
ejpam-4283	440	77	,	,	PUNCT
ejpam-4283	440	78	s	s	PART
ejpam-4283	440	79	}	}	PUNCT
ejpam-4283	440	80	,	,	PUNCT
ejpam-4283	440	81	{	{	PUNCT
ejpam-4283	440	82	p	p	X
ejpam-4283	440	83	,	,	PUNCT
ejpam-4283	440	84	q	q	X
ejpam-4283	440	85	,	,	PUNCT
ejpam-4283	440	86	s	s	PART
ejpam-4283	440	87	}	}	PUNCT
ejpam-4283	440	88	,	,	PUNCT
ejpam-4283	440	89	x	x	NOUN
ejpam-4283	440	90	}	}	PUNCT
ejpam-4283	440	91	.	.	PUNCT
ejpam-4283	440	92	then	then	ADV
ejpam-4283	440	93	σ1	σ1	PROPN
ejpam-4283	440	94	=	=	PUNCT
ejpam-4283	440	95	{	{	PUNCT
ejpam-4283	440	96	∅	∅	NOUN
ejpam-4283	440	97	,	,	PUNCT
ejpam-4283	440	98	{	{	PUNCT
ejpam-4283	440	99	r	r	NOUN
ejpam-4283	440	100	}	}	PUNCT
ejpam-4283	440	101	,	,	PUNCT
ejpam-4283	440	102	{	{	PUNCT
ejpam-4283	440	103	p	p	X
ejpam-4283	440	104	,	,	PUNCT
ejpam-4283	440	105	s	s	PART
ejpam-4283	440	106	}	}	PUNCT
ejpam-4283	440	107	,	,	PUNCT
ejpam-4283	440	108	{	{	PUNCT
ejpam-4283	440	109	q	q	X
ejpam-4283	440	110	,	,	PUNCT
ejpam-4283	440	111	s	s	PART
ejpam-4283	440	112	}	}	PUNCT
ejpam-4283	440	113	,	,	PUNCT
ejpam-4283	440	114	{	{	PUNCT
ejpam-4283	440	115	p	p	X
ejpam-4283	440	116	,	,	PUNCT
ejpam-4283	440	117	q	q	X
ejpam-4283	440	118	,	,	PUNCT
ejpam-4283	440	119	s	s	PART
ejpam-4283	440	120	}	}	PUNCT
ejpam-4283	440	121	,	,	PUNCT
ejpam-4283	440	122	{	{	PUNCT
ejpam-4283	440	123	p	p	X
ejpam-4283	440	124	,	,	PUNCT
ejpam-4283	440	125	r	r	NOUN
ejpam-4283	440	126	,	,	PUNCT
ejpam-4283	440	127	s	s	PART
ejpam-4283	440	128	}	}	PUNCT
ejpam-4283	440	129	,	,	PUNCT
ejpam-4283	440	130	{	{	PUNCT
ejpam-4283	440	131	q	q	X
ejpam-4283	440	132	,	,	PUNCT
ejpam-4283	440	133	r	r	NOUN
ejpam-4283	440	134	,	,	PUNCT
ejpam-4283	440	135	s	s	PART
ejpam-4283	440	136	}	}	PUNCT
ejpam-4283	440	137	,	,	PUNCT
ejpam-4283	440	138	x	x	NOUN
ejpam-4283	440	139	}	}	PUNCT
ejpam-4283	440	140	.	.	PUNCT
ejpam-4283	440	141	take	take	VERB
ejpam-4283	440	142	k	k	NOUN
ejpam-4283	440	143	=	=	PRON
ejpam-4283	440	144	{	{	PUNCT
ejpam-4283	440	145	p	p	NOUN
ejpam-4283	440	146	}	}	PUNCT
ejpam-4283	440	147	and	and	CCONJ
ejpam-4283	440	148	l	l	NOUN
ejpam-4283	440	149	=	=	PUNCT
ejpam-4283	440	150	{	{	PUNCT
ejpam-4283	440	151	q	q	NOUN
ejpam-4283	440	152	}	}	PUNCT
ejpam-4283	440	153	.	.	PUNCT
ejpam-4283	441	1	then	then	ADV
ejpam-4283	441	2	k	k	PROPN
ejpam-4283	441	3	and	and	CCONJ
ejpam-4283	441	4	l	l	NOUN
ejpam-4283	441	5	are	be	AUX
ejpam-4283	441	6	(	(	PUNCT
ejpam-4283	441	7	2	2	NUM
ejpam-4283	441	8	,	,	PUNCT
ejpam-4283	441	9	1)?-strongly	1)?-strongly	ADV
ejpam-4283	441	10	nowhere	nowhere	ADV
ejpam-4283	441	11	dense	dense	ADJ
ejpam-4283	441	12	sets	set	NOUN
ejpam-4283	441	13	in	in	ADP
ejpam-4283	441	14	x.	x.	NOUN
ejpam-4283	441	15	but	but	CCONJ
ejpam-4283	441	16	k	k	PROPN
ejpam-4283	441	17	∪	∪	PROPN
ejpam-4283	441	18	l	l	NOUN
ejpam-4283	441	19	=	=	PUNCT
ejpam-4283	441	20	{	{	PUNCT
ejpam-4283	441	21	p	p	X
ejpam-4283	441	22	,	,	PUNCT
ejpam-4283	441	23	q	q	NOUN
ejpam-4283	441	24	}	}	PUNCT
ejpam-4283	441	25	/∈	/∈	PUNCT
ejpam-4283	442	1	(	(	PUNCT
ejpam-4283	442	2	2	2	NUM
ejpam-4283	442	3	,	,	PUNCT
ejpam-4283	442	4	1	1	NUM
ejpam-4283	442	5	)	)	PUNCT
ejpam-4283	442	6	?	?	PUNCT
ejpam-4283	443	1	−s(x	−s(x	NOUN
ejpam-4283	443	2	)	)	PUNCT
ejpam-4283	443	3	.	.	PUNCT
ejpam-4283	444	1	the	the	DET
ejpam-4283	444	2	following	following	ADJ
ejpam-4283	444	3	example	example	NOUN
ejpam-4283	444	4	35	35	NUM
ejpam-4283	444	5	shows	show	VERB
ejpam-4283	444	6	that	that	SCONJ
ejpam-4283	444	7	a.	a.	NOUN
ejpam-4283	444	8	p	p	NOUN
ejpam-4283	444	9	∪	∪	ADJ
ejpam-4283	444	10	q	q	PROPN
ejpam-4283	444	11	/∈	/∈	PUNCT
ejpam-4283	444	12	(	(	PUNCT
ejpam-4283	444	13	s	s	PROPN
ejpam-4283	444	14	,	,	PUNCT
ejpam-4283	444	15	v	v	NOUN
ejpam-4283	444	16	)	)	PUNCT
ejpam-4283	444	17	?	?	PUNCT
ejpam-4283	445	1	−	−	PROPN
ejpam-4283	445	2	s(x	s(x	NOUN
ejpam-4283	445	3	)	)	PUNCT
ejpam-4283	445	4	even	even	ADV
ejpam-4283	445	5	if	if	SCONJ
ejpam-4283	445	6	p	p	X
ejpam-4283	445	7	∈	∈	PROPN
ejpam-4283	445	8	(	(	PUNCT
ejpam-4283	445	9	s	s	PROPN
ejpam-4283	445	10	,	,	PUNCT
ejpam-4283	445	11	v	v	NOUN
ejpam-4283	445	12	)	)	PUNCT
ejpam-4283	445	13	?	?	PUNCT
ejpam-4283	446	1	−	−	PROPN
ejpam-4283	446	2	s(x	s(x	PROPN
ejpam-4283	446	3	)	)	PUNCT
ejpam-4283	446	4	and	and	CCONJ
ejpam-4283	446	5	q	q	ADJ
ejpam-4283	446	6	∈	∈	PROPN
ejpam-4283	446	7	(	(	PUNCT
ejpam-4283	446	8	v	v	NOUN
ejpam-4283	446	9	,	,	PUNCT
ejpam-4283	446	10	s	s	NOUN
ejpam-4283	446	11	)	)	PUNCT
ejpam-4283	446	12	?	?	PUNCT
ejpam-4283	447	1	−	−	PROPN
ejpam-4283	447	2	s(x	s(x	PROPN
ejpam-4283	447	3	)	)	PUNCT
ejpam-4283	447	4	where	where	SCONJ
ejpam-4283	447	5	s	s	X
ejpam-4283	447	6	,	,	PUNCT
ejpam-4283	447	7	v	v	NOUN
ejpam-4283	447	8	=	=	SYM
ejpam-4283	447	9	1	1	NUM
ejpam-4283	447	10	,	,	PUNCT
ejpam-4283	447	11	2	2	NUM
ejpam-4283	447	12	and	and	CCONJ
ejpam-4283	447	13	s	s	X
ejpam-4283	447	14	6=	6=	PROPN
ejpam-4283	447	15	v.	v.	PROPN
ejpam-4283	447	16	b.	b.	PROPN
ejpam-4283	447	17	p	p	PROPN
ejpam-4283	447	18	∪	∪	PROPN
ejpam-4283	447	19	q	q	PROPN
ejpam-4283	447	20	/∈	/∈	PUNCT
ejpam-4283	447	21	(	(	PUNCT
ejpam-4283	447	22	v	v	NOUN
ejpam-4283	447	23	,	,	PUNCT
ejpam-4283	447	24	s	s	NOUN
ejpam-4283	447	25	)	)	PUNCT
ejpam-4283	447	26	?	?	PUNCT
ejpam-4283	448	1	−	−	PROPN
ejpam-4283	448	2	s(x	s(x	NOUN
ejpam-4283	448	3	)	)	PUNCT
ejpam-4283	448	4	even	even	ADV
ejpam-4283	448	5	if	if	SCONJ
ejpam-4283	448	6	p	p	X
ejpam-4283	448	7	∈	∈	PROPN
ejpam-4283	448	8	(	(	PUNCT
ejpam-4283	448	9	s	s	PROPN
ejpam-4283	448	10	,	,	PUNCT
ejpam-4283	448	11	v	v	NOUN
ejpam-4283	448	12	)	)	PUNCT
ejpam-4283	448	13	?	?	PUNCT
ejpam-4283	449	1	−	−	PROPN
ejpam-4283	449	2	s(x	s(x	PROPN
ejpam-4283	449	3	)	)	PUNCT
ejpam-4283	449	4	and	and	CCONJ
ejpam-4283	449	5	q	q	ADJ
ejpam-4283	449	6	∈	∈	PROPN
ejpam-4283	449	7	(	(	PUNCT
ejpam-4283	449	8	v	v	NOUN
ejpam-4283	449	9	,	,	PUNCT
ejpam-4283	449	10	s	s	NOUN
ejpam-4283	449	11	)	)	PUNCT
ejpam-4283	449	12	?	?	PUNCT
ejpam-4283	450	1	−	−	PROPN
ejpam-4283	450	2	s(x	s(x	PROPN
ejpam-4283	450	3	)	)	PUNCT
ejpam-4283	450	4	where	where	SCONJ
ejpam-4283	450	5	s	s	X
ejpam-4283	450	6	,	,	PUNCT
ejpam-4283	450	7	v	v	NOUN
ejpam-4283	450	8	=	=	SYM
ejpam-4283	450	9	1	1	NUM
ejpam-4283	450	10	,	,	PUNCT
ejpam-4283	450	11	2	2	NUM
ejpam-4283	450	12	and	and	CCONJ
ejpam-4283	450	13	s	s	X
ejpam-4283	450	14	6=	6=	PROPN
ejpam-4283	450	15	v.	v.	ADP
ejpam-4283	450	16	example	example	NOUN
ejpam-4283	450	17	35	35	NUM
ejpam-4283	450	18	.	.	PUNCT
ejpam-4283	450	19	consider	consider	VERB
ejpam-4283	450	20	the	the	DET
ejpam-4283	450	21	bigeneralized	bigeneralized	ADJ
ejpam-4283	450	22	topological	topological	ADJ
ejpam-4283	450	23	space	space	NOUN
ejpam-4283	450	24	(	(	PUNCT
ejpam-4283	450	25	x,µ1	x,µ1	PROPN
ejpam-4283	450	26	,	,	PUNCT
ejpam-4283	450	27	µ2	µ2	PROPN
ejpam-4283	450	28	)	)	PUNCT
ejpam-4283	450	29	where	where	SCONJ
ejpam-4283	450	30	x	x	X
ejpam-4283	450	31	=	=	PRON
ejpam-4283	450	32	{	{	PUNCT
ejpam-4283	450	33	p	p	X
ejpam-4283	450	34	,	,	PUNCT
ejpam-4283	450	35	q	q	ADJ
ejpam-4283	450	36	,	,	PUNCT
ejpam-4283	450	37	r	r	NOUN
ejpam-4283	450	38	,	,	PUNCT
ejpam-4283	450	39	s};µ1	s};µ1	PROPN
ejpam-4283	450	40	=	=	SYM
ejpam-4283	450	41	{	{	PUNCT
ejpam-4283	450	42	∅	∅	NOUN
ejpam-4283	450	43	,	,	PUNCT
ejpam-4283	450	44	{	{	PUNCT
ejpam-4283	450	45	p	p	X
ejpam-4283	450	46	}	}	PUNCT
ejpam-4283	450	47	,	,	PUNCT
ejpam-4283	450	48	{	{	PUNCT
ejpam-4283	450	49	r	r	NOUN
ejpam-4283	450	50	}	}	PUNCT
ejpam-4283	450	51	,	,	PUNCT
ejpam-4283	450	52	{	{	PUNCT
ejpam-4283	450	53	p	p	X
ejpam-4283	450	54	,	,	PUNCT
ejpam-4283	450	55	r	r	NOUN
ejpam-4283	450	56	}	}	PUNCT
ejpam-4283	450	57	,	,	PUNCT
ejpam-4283	450	58	{	{	PUNCT
ejpam-4283	450	59	p	p	X
ejpam-4283	450	60	,	,	PUNCT
ejpam-4283	450	61	q	q	NOUN
ejpam-4283	450	62	}	}	PUNCT
ejpam-4283	450	63	,	,	PUNCT
ejpam-4283	450	64	{	{	PUNCT
ejpam-4283	450	65	q	q	X
ejpam-4283	450	66	,	,	PUNCT
ejpam-4283	450	67	r	r	NOUN
ejpam-4283	450	68	}	}	PUNCT
ejpam-4283	450	69	,	,	PUNCT
ejpam-4283	450	70	{	{	PUNCT
ejpam-4283	450	71	p	p	X
ejpam-4283	450	72	,	,	PUNCT
ejpam-4283	450	73	q	q	ADJ
ejpam-4283	450	74	,	,	PUNCT
ejpam-4283	450	75	r	r	NOUN
ejpam-4283	450	76	}	}	PUNCT
ejpam-4283	450	77	}	}	PUNCT
ejpam-4283	450	78	and	and	CCONJ
ejpam-4283	450	79	µ2	µ2	PROPN
ejpam-4283	450	80	=	=	PUNCT
ejpam-4283	450	81	{	{	PUNCT
ejpam-4283	450	82	∅	∅	NOUN
ejpam-4283	450	83	,	,	PUNCT
ejpam-4283	450	84	{	{	PUNCT
ejpam-4283	450	85	p	p	X
ejpam-4283	450	86	}	}	PUNCT
ejpam-4283	450	87	,	,	PUNCT
ejpam-4283	450	88	{	{	PUNCT
ejpam-4283	450	89	p	p	X
ejpam-4283	450	90	,	,	PUNCT
ejpam-4283	450	91	q	q	NOUN
ejpam-4283	450	92	}	}	PUNCT
ejpam-4283	450	93	,	,	PUNCT
ejpam-4283	450	94	{	{	PUNCT
ejpam-4283	450	95	p	p	X
ejpam-4283	450	96	,	,	PUNCT
ejpam-4283	450	97	s	s	PART
ejpam-4283	450	98	}	}	PUNCT
ejpam-4283	450	99	,	,	PUNCT
ejpam-4283	450	100	{	{	PUNCT
ejpam-4283	450	101	q	q	X
ejpam-4283	450	102	,	,	PUNCT
ejpam-4283	450	103	s	s	PART
ejpam-4283	450	104	}	}	PUNCT
ejpam-4283	450	105	,	,	PUNCT
ejpam-4283	450	106	{	{	PUNCT
ejpam-4283	450	107	p	p	X
ejpam-4283	450	108	,	,	PUNCT
ejpam-4283	450	109	q	q	ADJ
ejpam-4283	450	110	,	,	PUNCT
ejpam-4283	450	111	s	s	PART
ejpam-4283	450	112	}	}	PUNCT
ejpam-4283	450	113	}	}	PUNCT
ejpam-4283	450	114	.	.	PUNCT
ejpam-4283	451	1	then	then	ADV
ejpam-4283	451	2	σ1	σ1	PROPN
ejpam-4283	451	3	=	=	PUNCT
ejpam-4283	451	4	{	{	PUNCT
ejpam-4283	451	5	∅	∅	NOUN
ejpam-4283	451	6	,	,	PUNCT
ejpam-4283	451	7	{	{	PUNCT
ejpam-4283	451	8	p	p	X
ejpam-4283	451	9	}	}	PUNCT
ejpam-4283	451	10	,	,	PUNCT
ejpam-4283	451	11	{	{	PUNCT
ejpam-4283	451	12	r	r	NOUN
ejpam-4283	451	13	}	}	PUNCT
ejpam-4283	451	14	,	,	PUNCT
ejpam-4283	451	15	{	{	PUNCT
ejpam-4283	451	16	s	s	X
ejpam-4283	451	17	}	}	PUNCT
ejpam-4283	451	18	,	,	PUNCT
ejpam-4283	451	19	{	{	PUNCT
ejpam-4283	451	20	p	p	X
ejpam-4283	451	21	,	,	PUNCT
ejpam-4283	451	22	r	r	NOUN
ejpam-4283	451	23	}	}	PUNCT
ejpam-4283	451	24	,	,	PUNCT
ejpam-4283	451	25	{	{	PUNCT
ejpam-4283	451	26	p	p	X
ejpam-4283	451	27	,	,	PUNCT
ejpam-4283	451	28	q	q	NOUN
ejpam-4283	451	29	}	}	PUNCT
ejpam-4283	451	30	,	,	PUNCT
ejpam-4283	451	31	{	{	PUNCT
ejpam-4283	451	32	p	p	X
ejpam-4283	451	33	,	,	PUNCT
ejpam-4283	451	34	s	s	PART
ejpam-4283	451	35	}	}	PUNCT
ejpam-4283	451	36	,	,	PUNCT
ejpam-4283	451	37	{	{	PUNCT
ejpam-4283	451	38	q	q	X
ejpam-4283	451	39	,	,	PUNCT
ejpam-4283	451	40	r	r	NOUN
ejpam-4283	451	41	}	}	PUNCT
ejpam-4283	451	42	,	,	PUNCT
ejpam-4283	451	43	{	{	PUNCT
ejpam-4283	451	44	r	r	NOUN
ejpam-4283	451	45	,	,	PUNCT
ejpam-4283	451	46	s	s	PART
ejpam-4283	451	47	}	}	PUNCT
ejpam-4283	451	48	,	,	PUNCT
ejpam-4283	451	49	{	{	PUNCT
ejpam-4283	451	50	p	p	X
ejpam-4283	451	51	,	,	PUNCT
ejpam-4283	451	52	q	q	ADJ
ejpam-4283	451	53	,	,	PUNCT
ejpam-4283	451	54	r	r	NOUN
ejpam-4283	451	55	}	}	PUNCT
ejpam-4283	451	56	,	,	PUNCT
ejpam-4283	451	57	{	{	PUNCT
ejpam-4283	451	58	p	p	X
ejpam-4283	451	59	,	,	PUNCT
ejpam-4283	451	60	q	q	X
ejpam-4283	451	61	,	,	PUNCT
ejpam-4283	451	62	s	s	PART
ejpam-4283	451	63	}	}	PUNCT
ejpam-4283	451	64	,	,	PUNCT
ejpam-4283	451	65	{	{	PUNCT
ejpam-4283	451	66	p	p	X
ejpam-4283	451	67	,	,	PUNCT
ejpam-4283	451	68	r	r	NOUN
ejpam-4283	451	69	,	,	PUNCT
ejpam-4283	451	70	s	s	PART
ejpam-4283	451	71	}	}	PUNCT
ejpam-4283	451	72	,	,	PUNCT
ejpam-4283	451	73	{	{	PUNCT
ejpam-4283	451	74	q	q	X
ejpam-4283	451	75	,	,	PUNCT
ejpam-4283	451	76	r	r	NOUN
ejpam-4283	451	77	,	,	PUNCT
ejpam-4283	451	78	s	s	PART
ejpam-4283	451	79	}	}	PUNCT
ejpam-4283	451	80	,	,	PUNCT
ejpam-4283	451	81	x	x	NOUN
ejpam-4283	451	82	}	}	PUNCT
ejpam-4283	451	83	and	and	CCONJ
ejpam-4283	451	84	σ2	σ2	PROPN
ejpam-4283	451	85	=	=	SYM
ejpam-4283	451	86	{	{	PUNCT
ejpam-4283	451	87	∅	∅	NOUN
ejpam-4283	451	88	,	,	PUNCT
ejpam-4283	451	89	{	{	PUNCT
ejpam-4283	451	90	p	p	X
ejpam-4283	451	91	}	}	PUNCT
ejpam-4283	451	92	,	,	PUNCT
ejpam-4283	451	93	{	{	PUNCT
ejpam-4283	451	94	r	r	NOUN
ejpam-4283	451	95	}	}	PUNCT
ejpam-4283	451	96	,	,	PUNCT
ejpam-4283	451	97	{	{	PUNCT
ejpam-4283	451	98	p	p	X
ejpam-4283	451	99	,	,	PUNCT
ejpam-4283	451	100	q	q	NOUN
ejpam-4283	451	101	}	}	PUNCT
ejpam-4283	451	102	,	,	PUNCT
ejpam-4283	451	103	{	{	PUNCT
ejpam-4283	451	104	p	p	X
ejpam-4283	451	105	,	,	PUNCT
ejpam-4283	451	106	r	r	NOUN
ejpam-4283	451	107	}	}	PUNCT
ejpam-4283	451	108	,	,	PUNCT
ejpam-4283	451	109	{	{	PUNCT
ejpam-4283	451	110	p	p	X
ejpam-4283	451	111	,	,	PUNCT
ejpam-4283	451	112	s	s	PART
ejpam-4283	451	113	}	}	PUNCT
ejpam-4283	451	114	,	,	PUNCT
ejpam-4283	451	115	{	{	PUNCT
ejpam-4283	451	116	q	q	X
ejpam-4283	451	117	,	,	PUNCT
ejpam-4283	451	118	s	s	PART
ejpam-4283	451	119	}	}	PUNCT
ejpam-4283	451	120	,	,	PUNCT
ejpam-4283	451	121	{	{	PUNCT
ejpam-4283	451	122	p	p	X
ejpam-4283	451	123	,	,	PUNCT
ejpam-4283	451	124	q	q	ADJ
ejpam-4283	451	125	,	,	PUNCT
ejpam-4283	451	126	r	r	NOUN
ejpam-4283	451	127	}	}	PUNCT
ejpam-4283	451	128	,	,	PUNCT
ejpam-4283	451	129	{	{	PUNCT
ejpam-4283	451	130	p	p	X
ejpam-4283	451	131	,	,	PUNCT
ejpam-4283	451	132	q	q	X
ejpam-4283	451	133	,	,	PUNCT
ejpam-4283	451	134	s	s	PART
ejpam-4283	451	135	}	}	PUNCT
ejpam-4283	451	136	,	,	PUNCT
ejpam-4283	451	137	{	{	PUNCT
ejpam-4283	451	138	p	p	X
ejpam-4283	451	139	,	,	PUNCT
ejpam-4283	451	140	r	r	NOUN
ejpam-4283	451	141	,	,	PUNCT
ejpam-4283	451	142	s	s	PART
ejpam-4283	451	143	}	}	PUNCT
ejpam-4283	451	144	,	,	PUNCT
ejpam-4283	451	145	{	{	PUNCT
ejpam-4283	451	146	q	q	X
ejpam-4283	451	147	,	,	PUNCT
ejpam-4283	451	148	r	r	NOUN
ejpam-4283	451	149	,	,	PUNCT
ejpam-4283	451	150	s	s	PART
ejpam-4283	451	151	}	}	PUNCT
ejpam-4283	451	152	,	,	PUNCT
ejpam-4283	451	153	x	x	NOUN
ejpam-4283	451	154	}	}	PUNCT
ejpam-4283	451	155	.	.	PUNCT
ejpam-4283	452	1	take	take	VERB
ejpam-4283	452	2	p	p	NOUN
ejpam-4283	452	3	=	=	X
ejpam-4283	452	4	{	{	PUNCT
ejpam-4283	452	5	q	q	PROPN
ejpam-4283	452	6	,	,	PUNCT
ejpam-4283	452	7	s	s	PART
ejpam-4283	452	8	}	}	PUNCT
ejpam-4283	452	9	and	and	CCONJ
ejpam-4283	452	10	q	q	NOUN
ejpam-4283	452	11	=	=	X
ejpam-4283	452	12	{	{	PUNCT
ejpam-4283	452	13	q	q	NOUN
ejpam-4283	452	14	,	,	PUNCT
ejpam-4283	452	15	r	r	NOUN
ejpam-4283	452	16	}	}	PUNCT
ejpam-4283	452	17	.	.	PUNCT
ejpam-4283	453	1	then	then	ADV
ejpam-4283	453	2	p	p	PROPN
ejpam-4283	453	3	∈	∈	PROPN
ejpam-4283	453	4	(	(	PUNCT
ejpam-4283	453	5	1	1	NUM
ejpam-4283	453	6	,	,	PUNCT
ejpam-4283	453	7	2	2	NUM
ejpam-4283	453	8	)	)	PUNCT
ejpam-4283	453	9	?	?	PUNCT
ejpam-4283	454	1	−s(x	−s(x	NOUN
ejpam-4283	454	2	)	)	PUNCT
ejpam-4283	455	1	and	and	CCONJ
ejpam-4283	455	2	q	q	NOUN
ejpam-4283	455	3	∈	∈	PROPN
ejpam-4283	455	4	(	(	PUNCT
ejpam-4283	455	5	2	2	NUM
ejpam-4283	455	6	,	,	PUNCT
ejpam-4283	455	7	1	1	NUM
ejpam-4283	455	8	)	)	PUNCT
ejpam-4283	455	9	?	?	PUNCT
ejpam-4283	456	1	−s(x	−s(x	NOUN
ejpam-4283	456	2	)	)	PUNCT
ejpam-4283	456	3	.	.	PUNCT
ejpam-4283	457	1	here	here	ADV
ejpam-4283	457	2	p	p	X
ejpam-4283	457	3	∪q	∪q	X
ejpam-4283	457	4	=	=	SYM
ejpam-4283	457	5	{	{	PUNCT
ejpam-4283	457	6	q	q	NOUN
ejpam-4283	457	7	,	,	PUNCT
ejpam-4283	457	8	r	r	NOUN
ejpam-4283	457	9	,	,	PUNCT
ejpam-4283	457	10	s	s	PART
ejpam-4283	457	11	}	}	PUNCT
ejpam-4283	457	12	.	.	PUNCT
ejpam-4283	458	1	but	but	CCONJ
ejpam-4283	458	2	p	p	NOUN
ejpam-4283	458	3	∪q	∪q	X
ejpam-4283	458	4	/∈	/∈	X
ejpam-4283	458	5	(	(	PUNCT
ejpam-4283	458	6	1	1	NUM
ejpam-4283	458	7	,	,	PUNCT
ejpam-4283	458	8	2	2	NUM
ejpam-4283	458	9	)	)	PUNCT
ejpam-4283	458	10	?	?	PUNCT
ejpam-4283	458	11	−s(x	−s(x	NOUN
ejpam-4283	458	12	)	)	PUNCT
ejpam-4283	458	13	.	.	PUNCT
ejpam-4283	459	1	also	also	ADV
ejpam-4283	459	2	,	,	PUNCT
ejpam-4283	459	3	p	p	X
ejpam-4283	459	4	∪q	∪q	X
ejpam-4283	459	5	/∈	/∈	X
ejpam-4283	459	6	(	(	PUNCT
ejpam-4283	459	7	2	2	NUM
ejpam-4283	459	8	,	,	PUNCT
ejpam-4283	459	9	1	1	NUM
ejpam-4283	459	10	)	)	PUNCT
ejpam-4283	459	11	?	?	PUNCT
ejpam-4283	459	12	−s(x	−s(x	NOUN
ejpam-4283	459	13	)	)	PUNCT
ejpam-4283	459	14	.	.	PUNCT
ejpam-4283	460	1	theorem	theorem	NOUN
ejpam-4283	460	2	36	36	NUM
ejpam-4283	460	3	.	.	PUNCT
ejpam-4283	461	1	let	let	AUX
ejpam-4283	461	2	(	(	PUNCT
ejpam-4283	461	3	x,µ1	x,µ1	NOUN
ejpam-4283	461	4	,	,	PUNCT
ejpam-4283	461	5	µ2	µ2	PROPN
ejpam-4283	461	6	)	)	PUNCT
ejpam-4283	461	7	be	be	AUX
ejpam-4283	461	8	a	a	DET
ejpam-4283	461	9	bgts	bgts	NOUN
ejpam-4283	461	10	.	.	PUNCT
ejpam-4283	462	1	if	if	SCONJ
ejpam-4283	462	2	µ1	µ1	PROPN
ejpam-4283	462	3	and	and	CCONJ
ejpam-4283	462	4	µ2	µ2	PROPN
ejpam-4283	462	5	are	be	AUX
ejpam-4283	462	6	strong	strong	ADJ
ejpam-4283	462	7	generalized	generalized	ADJ
ejpam-4283	462	8	topologies	topology	NOUN
ejpam-4283	462	9	,	,	PUNCT
ejpam-4283	462	10	then	then	ADV
ejpam-4283	462	11	the	the	DET
ejpam-4283	462	12	followings	following	NOUN
ejpam-4283	462	13	are	be	AUX
ejpam-4283	462	14	true	true	ADJ
ejpam-4283	462	15	.	.	PUNCT
ejpam-4283	463	1	(	(	PUNCT
ejpam-4283	463	2	a	a	X
ejpam-4283	463	3	)	)	PUNCT
ejpam-4283	463	4	(	(	PUNCT
ejpam-4283	463	5	1	1	NUM
ejpam-4283	463	6	,	,	PUNCT
ejpam-4283	463	7	2	2	NUM
ejpam-4283	463	8	)	)	PUNCT
ejpam-4283	463	9	?	?	PUNCT
ejpam-4283	464	1	−s(x	−s(x	NOUN
ejpam-4283	464	2	)	)	PUNCT
ejpam-4283	465	1	⊂	⊂	PROPN
ejpam-4283	465	2	(	(	PUNCT
ejpam-4283	465	3	2	2	NUM
ejpam-4283	465	4	,	,	PUNCT
ejpam-4283	465	5	1	1	NUM
ejpam-4283	465	6	)	)	PUNCT
ejpam-4283	465	7	?	?	PUNCT
ejpam-4283	466	1	−n	−n	INTJ
ejpam-4283	466	2	(	(	PUNCT
ejpam-4283	466	3	x	x	NOUN
ejpam-4283	466	4	)	)	PUNCT
ejpam-4283	466	5	.	.	PUNCT
ejpam-4283	467	1	(	(	PUNCT
ejpam-4283	467	2	b	b	X
ejpam-4283	467	3	)	)	PUNCT
ejpam-4283	467	4	(	(	PUNCT
ejpam-4283	467	5	2	2	NUM
ejpam-4283	467	6	,	,	PUNCT
ejpam-4283	467	7	1	1	NUM
ejpam-4283	467	8	)	)	PUNCT
ejpam-4283	467	9	?	?	PUNCT
ejpam-4283	468	1	−s(x	−s(x	NOUN
ejpam-4283	468	2	)	)	PUNCT
ejpam-4283	469	1	⊂	⊂	PROPN
ejpam-4283	469	2	(	(	PUNCT
ejpam-4283	469	3	1	1	NUM
ejpam-4283	469	4	,	,	PUNCT
ejpam-4283	469	5	2	2	NUM
ejpam-4283	469	6	)	)	PUNCT
ejpam-4283	469	7	?	?	PUNCT
ejpam-4283	470	1	−n	−n	INTJ
ejpam-4283	470	2	(	(	PUNCT
ejpam-4283	470	3	x	x	NOUN
ejpam-4283	470	4	)	)	PUNCT
ejpam-4283	470	5	.	.	PUNCT
ejpam-4283	471	1	proof	proof	NOUN
ejpam-4283	471	2	.	.	PUNCT
ejpam-4283	472	1	it	it	PRON
ejpam-4283	472	2	is	be	AUX
ejpam-4283	472	3	enough	enough	ADJ
ejpam-4283	472	4	to	to	PART
ejpam-4283	472	5	prove	prove	VERB
ejpam-4283	472	6	(	(	PUNCT
ejpam-4283	472	7	a	a	X
ejpam-4283	472	8	)	)	PUNCT
ejpam-4283	472	9	only	only	ADV
ejpam-4283	472	10	.	.	PUNCT
ejpam-4283	473	1	let	let	VERB
ejpam-4283	473	2	e	e	X
ejpam-4283	473	3	∈	∈	PROPN
ejpam-4283	473	4	(	(	PUNCT
ejpam-4283	473	5	1	1	NUM
ejpam-4283	473	6	,	,	PUNCT
ejpam-4283	473	7	2)?−s(x	2)?−s(x	NUM
ejpam-4283	473	8	)	)	PUNCT
ejpam-4283	473	9	.	.	PUNCT
ejpam-4283	474	1	suppose	suppose	VERB
ejpam-4283	474	2	iσ1(c2(e	iσ1(c2(e	NOUN
ejpam-4283	474	3	)	)	PUNCT
ejpam-4283	474	4	)	)	PUNCT
ejpam-4283	475	1	6=	6=	ADP
ejpam-4283	475	2	∅.	∅.	VERB
ejpam-4283	475	3	then	then	ADV
ejpam-4283	475	4	there	there	PRON
ejpam-4283	475	5	exist	exist	VERB
ejpam-4283	475	6	g	g	PROPN
ejpam-4283	475	7	∈	∈	PROPN
ejpam-4283	475	8	σ̃1	σ̃1	PROPN
ejpam-4283	475	9	such	such	ADJ
ejpam-4283	475	10	that	that	SCONJ
ejpam-4283	475	11	g	g	PROPN
ejpam-4283	475	12	⊂	⊂	PROPN
ejpam-4283	475	13	c2(e	c2(e	NOUN
ejpam-4283	475	14	)	)	PUNCT
ejpam-4283	475	15	.	.	PUNCT
ejpam-4283	476	1	since	since	SCONJ
ejpam-4283	476	2	g	g	PROPN
ejpam-4283	476	3	∈	∈	PROPN
ejpam-4283	476	4	σ̃1	σ̃1	PROPN
ejpam-4283	476	5	we	we	PRON
ejpam-4283	476	6	have	have	VERB
ejpam-4283	476	7	i1(g	i1(g	PROPN
ejpam-4283	476	8	)	)	PUNCT
ejpam-4283	476	9	6=	6=	ADP
ejpam-4283	476	10	∅	∅	NOUN
ejpam-4283	476	11	,	,	PUNCT
ejpam-4283	476	12	by	by	ADP
ejpam-4283	476	13	assumption	assumption	NOUN
ejpam-4283	476	14	.	.	PUNCT
ejpam-4283	477	1	thus	thus	ADV
ejpam-4283	477	2	,	,	PUNCT
ejpam-4283	477	3	i1(g	i1(g	PROPN
ejpam-4283	477	4	)	)	PUNCT
ejpam-4283	477	5	∈	∈	PROPN
ejpam-4283	477	6	µ̃1	µ̃1	PROPN
ejpam-4283	477	7	.	.	PUNCT
ejpam-4283	478	1	since	since	SCONJ
ejpam-4283	478	2	g	g	PROPN
ejpam-4283	478	3	⊂	⊂	PROPN
ejpam-4283	478	4	c2(e	c2(e	NOUN
ejpam-4283	478	5	)	)	PUNCT
ejpam-4283	478	6	we	we	PRON
ejpam-4283	478	7	have	have	VERB
ejpam-4283	478	8	h	h	NOUN
ejpam-4283	478	9	∩	∩	NOUN
ejpam-4283	478	10	e	e	NOUN
ejpam-4283	478	11	6=	6=	NOUN
ejpam-4283	478	12	∅	∅	NOUN
ejpam-4283	478	13	for	for	ADP
ejpam-4283	478	14	every	every	DET
ejpam-4283	478	15	h	h	NOUN
ejpam-4283	478	16	∈	∈	NOUN
ejpam-4283	478	17	σ̃2	σ̃2	PROPN
ejpam-4283	478	18	such	such	ADJ
ejpam-4283	478	19	that	that	SCONJ
ejpam-4283	478	20	h	h	PROPN
ejpam-4283	478	21	⊂	⊂	PROPN
ejpam-4283	478	22	i1(g	i1(g	PROPN
ejpam-4283	478	23	)	)	PUNCT
ejpam-4283	478	24	which	which	PRON
ejpam-4283	478	25	is	be	AUX
ejpam-4283	478	26	a	a	DET
ejpam-4283	478	27	contradiction	contradiction	NOUN
ejpam-4283	478	28	to	to	ADP
ejpam-4283	478	29	hypothesis	hypothesis	NOUN
ejpam-4283	478	30	.	.	PUNCT
ejpam-4283	479	1	for	for	ADP
ejpam-4283	479	2	,	,	PUNCT
ejpam-4283	479	3	h	h	NOUN
ejpam-4283	479	4	∈	∈	PROPN
ejpam-4283	479	5	σ̃2	σ̃2	PROPN
ejpam-4283	479	6	which	which	PRON
ejpam-4283	479	7	implies	imply	VERB
ejpam-4283	479	8	h	h	PROPN
ejpam-4283	479	9	⊂	⊂	PROPN
ejpam-4283	479	10	c2(i2(h	c2(i2(h	PROPN
ejpam-4283	479	11	)	)	PUNCT
ejpam-4283	479	12	)	)	PUNCT
ejpam-4283	479	13	.	.	PUNCT
ejpam-4283	480	1	since	since	SCONJ
ejpam-4283	480	2	µ2	µ2	PROPN
ejpam-4283	480	3	is	be	AUX
ejpam-4283	480	4	a	a	DET
ejpam-4283	480	5	strong	strong	ADJ
ejpam-4283	480	6	generalized	generalized	ADJ
ejpam-4283	480	7	topology	topology	NOUN
ejpam-4283	480	8	,	,	PUNCT
ejpam-4283	480	9	i2(h	i2(h	NOUN
ejpam-4283	480	10	)	)	PUNCT
ejpam-4283	480	11	∈	∈	PROPN
ejpam-4283	480	12	µ̃2	µ̃2	PROPN
ejpam-4283	480	13	.	.	PUNCT
ejpam-4283	481	1	here	here	ADV
ejpam-4283	481	2	i2(h	i2(h	PROPN
ejpam-4283	481	3	)	)	PUNCT
ejpam-4283	481	4	⊂	⊂	PROPN
ejpam-4283	481	5	i1(g	i1(g	PROPN
ejpam-4283	481	6	)	)	PUNCT
ejpam-4283	481	7	⊂	⊂	PROPN
ejpam-4283	481	8	c2(e	c2(e	NOUN
ejpam-4283	481	9	)	)	PUNCT
ejpam-4283	481	10	.	.	PUNCT
ejpam-4283	482	1	this	this	PRON
ejpam-4283	482	2	implies	imply	VERB
ejpam-4283	482	3	i2(h	i2(h	NOUN
ejpam-4283	482	4	)	)	PUNCT
ejpam-4283	482	5	∩	∩	ADJ
ejpam-4283	482	6	c2(e	c2(e	NOUN
ejpam-4283	482	7	)	)	PUNCT
ejpam-4283	482	8	6=	6=	NUM
ejpam-4283	482	9	∅	∅	NOUN
ejpam-4283	482	10	which	which	PRON
ejpam-4283	482	11	implies	imply	VERB
ejpam-4283	482	12	that	that	SCONJ
ejpam-4283	482	13	i2(h	i2(h	NOUN
ejpam-4283	482	14	)	)	PUNCT
ejpam-4283	482	15	∩	∩	ADJ
ejpam-4283	482	16	e	e	X
ejpam-4283	482	17	6=	6=	PROPN
ejpam-4283	482	18	∅	∅	NOUN
ejpam-4283	482	19	,	,	PUNCT
ejpam-4283	482	20	by	by	ADP
ejpam-4283	482	21	lemma	lemma	PROPN
ejpam-4283	482	22	2	2	NUM
ejpam-4283	482	23	.	.	PUNCT
ejpam-4283	483	1	thus	thus	ADV
ejpam-4283	483	2	,	,	PUNCT
ejpam-4283	483	3	h	h	NOUN
ejpam-4283	483	4	∩	∩	NOUN
ejpam-4283	483	5	e	e	PROPN
ejpam-4283	483	6	6=	6=	PROPN
ejpam-4283	483	7	∅.	∅.	ADP
ejpam-4283	483	8	therefore	therefore	ADV
ejpam-4283	483	9	,	,	PUNCT
ejpam-4283	483	10	e	e	PROPN
ejpam-4283	483	11	∈	∈	PROPN
ejpam-4283	483	12	(	(	PUNCT
ejpam-4283	483	13	2	2	NUM
ejpam-4283	483	14	,	,	PUNCT
ejpam-4283	483	15	1	1	NUM
ejpam-4283	483	16	)	)	PUNCT
ejpam-4283	483	17	?	?	PUNCT
ejpam-4283	484	1	−n	−n	INTJ
ejpam-4283	484	2	(	(	PUNCT
ejpam-4283	484	3	x	x	NOUN
ejpam-4283	484	4	)	)	PUNCT
ejpam-4283	484	5	.	.	PUNCT
ejpam-4283	485	1	theorem	theorem	VERB
ejpam-4283	485	2	37	37	NUM
ejpam-4283	485	3	.	.	PUNCT
ejpam-4283	486	1	let	let	AUX
ejpam-4283	486	2	(	(	PUNCT
ejpam-4283	486	3	x,µ1	x,µ1	NOUN
ejpam-4283	486	4	,	,	PUNCT
ejpam-4283	486	5	µ2	µ2	PROPN
ejpam-4283	486	6	)	)	PUNCT
ejpam-4283	486	7	be	be	VERB
ejpam-4283	486	8	a	a	DET
ejpam-4283	486	9	bgts	bgts	NOUN
ejpam-4283	486	10	which	which	PRON
ejpam-4283	486	11	has	have	VERB
ejpam-4283	486	12	the	the	DET
ejpam-4283	486	13	is	is	NOUN
ejpam-4283	486	14	-	-	PUNCT
ejpam-4283	486	15	property	property	NOUN
ejpam-4283	486	16	.	.	PUNCT
ejpam-4283	487	1	then	then	ADV
ejpam-4283	487	2	(	(	PUNCT
ejpam-4283	487	3	s	s	X
ejpam-4283	487	4	,	,	PUNCT
ejpam-4283	487	5	v	v	NOUN
ejpam-4283	487	6	)	)	PUNCT
ejpam-4283	487	7	?	?	PUNCT
ejpam-4283	488	1	−	−	PROPN
ejpam-4283	489	1	n	n	CCONJ
ejpam-4283	489	2	(	(	PUNCT
ejpam-4283	489	3	x	x	X
ejpam-4283	489	4	)	)	PUNCT
ejpam-4283	489	5	⊂	⊂	PROPN
ejpam-4283	489	6	(	(	PUNCT
ejpam-4283	489	7	v	v	NOUN
ejpam-4283	489	8	,	,	PUNCT
ejpam-4283	489	9	s	s	NOUN
ejpam-4283	489	10	)	)	PUNCT
ejpam-4283	489	11	?	?	PUNCT
ejpam-4283	490	1	−s(x	−s(x	NOUN
ejpam-4283	490	2	)	)	PUNCT
ejpam-4283	490	3	where	where	SCONJ
ejpam-4283	490	4	s	s	X
ejpam-4283	490	5	,	,	PUNCT
ejpam-4283	490	6	v	v	NOUN
ejpam-4283	490	7	=	=	SYM
ejpam-4283	490	8	1	1	NUM
ejpam-4283	490	9	,	,	PUNCT
ejpam-4283	490	10	2	2	NUM
ejpam-4283	490	11	and	and	CCONJ
ejpam-4283	490	12	s	s	X
ejpam-4283	490	13	6=	6=	PROPN
ejpam-4283	490	14	v.	v.	ADP
ejpam-4283	490	15	references	reference	NOUN
ejpam-4283	490	16	413	413	NUM
ejpam-4283	490	17	proof	proof	NOUN
ejpam-4283	490	18	.	.	PUNCT
ejpam-4283	491	1	assume	assume	VERB
ejpam-4283	491	2	that	that	SCONJ
ejpam-4283	491	3	,	,	PUNCT
ejpam-4283	491	4	(	(	PUNCT
ejpam-4283	491	5	x,µ1	x,µ1	NOUN
ejpam-4283	491	6	,	,	PUNCT
ejpam-4283	491	7	µ2	µ2	PROPN
ejpam-4283	491	8	)	)	PUNCT
ejpam-4283	491	9	satisfy	satisfy	NOUN
ejpam-4283	491	10	the	the	DET
ejpam-4283	491	11	is	is	NOUN
ejpam-4283	491	12	-	-	PUNCT
ejpam-4283	491	13	property	property	NOUN
ejpam-4283	491	14	.	.	PUNCT
ejpam-4283	492	1	let	let	VERB
ejpam-4283	492	2	q	q	PROPN
ejpam-4283	492	3	∈	∈	PROPN
ejpam-4283	492	4	(	(	PUNCT
ejpam-4283	492	5	s	s	NOUN
ejpam-4283	492	6	,	,	PUNCT
ejpam-4283	492	7	v)?−n	v)?−n	X
ejpam-4283	492	8	(	(	PUNCT
ejpam-4283	492	9	x	x	X
ejpam-4283	492	10	)	)	PUNCT
ejpam-4283	492	11	where	where	SCONJ
ejpam-4283	492	12	s	s	X
ejpam-4283	492	13	,	,	PUNCT
ejpam-4283	492	14	v	v	NOUN
ejpam-4283	492	15	=	=	SYM
ejpam-4283	492	16	1	1	NUM
ejpam-4283	492	17	,	,	PUNCT
ejpam-4283	492	18	2	2	NUM
ejpam-4283	492	19	and	and	CCONJ
ejpam-4283	492	20	s	s	X
ejpam-4283	492	21	6=	6=	PROPN
ejpam-4283	492	22	v.	v.	ADP
ejpam-4283	492	23	by	by	ADP
ejpam-4283	492	24	hypothesis	hypothesis	NOUN
ejpam-4283	492	25	and	and	CCONJ
ejpam-4283	492	26	theorem	theorem	VERB
ejpam-4283	492	27	26	26	NUM
ejpam-4283	492	28	,	,	PUNCT
ejpam-4283	492	29	q	q	NOUN
ejpam-4283	492	30	∈	∈	PROPN
ejpam-4283	492	31	(	(	PUNCT
ejpam-4283	492	32	s	s	NOUN
ejpam-4283	492	33	,	,	PUNCT
ejpam-4283	492	34	v)−s(x	v)−s(x	NUM
ejpam-4283	492	35	)	)	PUNCT
ejpam-4283	492	36	where	where	SCONJ
ejpam-4283	492	37	s	s	X
ejpam-4283	492	38	,	,	PUNCT
ejpam-4283	492	39	v	v	NOUN
ejpam-4283	492	40	=	=	SYM
ejpam-4283	492	41	1	1	NUM
ejpam-4283	492	42	,	,	PUNCT
ejpam-4283	492	43	2	2	NUM
ejpam-4283	492	44	and	and	CCONJ
ejpam-4283	492	45	s	s	X
ejpam-4283	492	46	6=	6=	PROPN
ejpam-4283	492	47	v.	v.	ADP
ejpam-4283	492	48	also	also	ADV
ejpam-4283	492	49	,	,	PUNCT
ejpam-4283	492	50	(	(	PUNCT
ejpam-4283	492	51	s	s	X
ejpam-4283	492	52	,	,	PUNCT
ejpam-4283	492	53	v	v	NOUN
ejpam-4283	492	54	)	)	PUNCT
ejpam-4283	492	55	−s(x	−s(x	NOUN
ejpam-4283	492	56	)	)	PUNCT
ejpam-4283	493	1	⊂	⊂	PROPN
ejpam-4283	493	2	(	(	PUNCT
ejpam-4283	493	3	v	v	NOUN
ejpam-4283	493	4	,	,	PUNCT
ejpam-4283	493	5	s	s	NOUN
ejpam-4283	493	6	)	)	PUNCT
ejpam-4283	493	7	?	?	PUNCT
ejpam-4283	494	1	−s(x	−s(x	NOUN
ejpam-4283	494	2	)	)	PUNCT
ejpam-4283	494	3	where	where	SCONJ
ejpam-4283	494	4	s	s	X
ejpam-4283	494	5	,	,	PUNCT
ejpam-4283	494	6	v	v	NOUN
ejpam-4283	494	7	=	=	SYM
ejpam-4283	494	8	1	1	NUM
ejpam-4283	494	9	,	,	PUNCT
ejpam-4283	494	10	2	2	NUM
ejpam-4283	494	11	and	and	CCONJ
ejpam-4283	494	12	s	s	X
ejpam-4283	494	13	6=	6=	PROPN
ejpam-4283	494	14	v.	v.	ADP
ejpam-4283	494	15	therefore	therefore	ADV
ejpam-4283	494	16	,	,	PUNCT
ejpam-4283	494	17	q	q	PROPN
ejpam-4283	494	18	∈	∈	PROPN
ejpam-4283	494	19	(	(	PUNCT
ejpam-4283	494	20	v	v	NOUN
ejpam-4283	494	21	,	,	PUNCT
ejpam-4283	494	22	s	s	NOUN
ejpam-4283	494	23	)	)	PUNCT
ejpam-4283	494	24	?	?	PUNCT
ejpam-4283	495	1	−s(x	−s(x	NOUN
ejpam-4283	495	2	)	)	PUNCT
ejpam-4283	495	3	where	where	SCONJ
ejpam-4283	495	4	s	s	X
ejpam-4283	495	5	,	,	PUNCT
ejpam-4283	495	6	v	v	NOUN
ejpam-4283	495	7	=	=	SYM
ejpam-4283	495	8	1	1	NUM
ejpam-4283	495	9	,	,	PUNCT
ejpam-4283	495	10	2	2	NUM
ejpam-4283	495	11	and	and	CCONJ
ejpam-4283	495	12	s	s	PROPN
ejpam-4283	495	13	6=	6=	PROPN
ejpam-4283	495	14	v.	v.	CCONJ
ejpam-4283	495	15	theorem	theorem	VERB
ejpam-4283	495	16	38	38	NUM
ejpam-4283	495	17	.	.	PUNCT
ejpam-4283	496	1	let	let	AUX
ejpam-4283	496	2	(	(	PUNCT
ejpam-4283	496	3	x,µ1	x,µ1	NOUN
ejpam-4283	496	4	,	,	PUNCT
ejpam-4283	496	5	µ2	µ2	PROPN
ejpam-4283	496	6	)	)	PUNCT
ejpam-4283	496	7	be	be	AUX
ejpam-4283	496	8	a	a	DET
ejpam-4283	496	9	bgts	bgts	NOUN
ejpam-4283	496	10	.	.	PUNCT
ejpam-4283	497	1	if	if	SCONJ
ejpam-4283	497	2	µv	µv	PRON
ejpam-4283	497	3	⊂	⊂	PUNCT
ejpam-4283	497	4	µs	µs	PART
ejpam-4283	497	5	,	,	PUNCT
ejpam-4283	497	6	µv	µv	PROPN
ejpam-4283	497	7	is	be	AUX
ejpam-4283	497	8	a	a	DET
ejpam-4283	497	9	sgt	sgt	NOUN
ejpam-4283	497	10	and	and	CCONJ
ejpam-4283	497	11	q	q	NOUN
ejpam-4283	497	12	∈	∈	PROPN
ejpam-4283	497	13	(	(	PUNCT
ejpam-4283	497	14	s	s	PROPN
ejpam-4283	497	15	,	,	PUNCT
ejpam-4283	497	16	v)?−s(x	v)?−s(x	PROPN
ejpam-4283	497	17	)	)	PUNCT
ejpam-4283	497	18	,	,	PUNCT
ejpam-4283	497	19	then	then	ADV
ejpam-4283	497	20	q	q	X
ejpam-4283	497	21	is	be	AUX
ejpam-4283	497	22	a	a	DET
ejpam-4283	497	23	µv	µv	NOUN
ejpam-4283	497	24	-	-	PUNCT
ejpam-4283	497	25	strongly	strongly	ADV
ejpam-4283	497	26	nowhere	nowhere	ADV
ejpam-4283	497	27	dense	dense	ADJ
ejpam-4283	497	28	set	set	NOUN
ejpam-4283	497	29	where	where	SCONJ
ejpam-4283	497	30	s	s	X
ejpam-4283	497	31	,	,	PUNCT
ejpam-4283	497	32	v	v	NOUN
ejpam-4283	497	33	=	=	SYM
ejpam-4283	497	34	1	1	NUM
ejpam-4283	497	35	,	,	PUNCT
ejpam-4283	497	36	2	2	NUM
ejpam-4283	497	37	and	and	CCONJ
ejpam-4283	497	38	s	s	X
ejpam-4283	497	39	6=	6=	NOUN
ejpam-4283	497	40	v.	v.	ADP
ejpam-4283	497	41	proof	proof	NOUN
ejpam-4283	497	42	.	.	PUNCT
ejpam-4283	498	1	assume	assume	VERB
ejpam-4283	498	2	that	that	SCONJ
ejpam-4283	498	3	,	,	PUNCT
ejpam-4283	498	4	µv	µv	PRON
ejpam-4283	498	5	⊂	⊂	ADJ
ejpam-4283	498	6	µs	µs	X
ejpam-4283	498	7	,	,	PUNCT
ejpam-4283	498	8	µv	µv	PROPN
ejpam-4283	498	9	is	be	AUX
ejpam-4283	498	10	a	a	DET
ejpam-4283	498	11	sgt	sgt	NOUN
ejpam-4283	498	12	and	and	CCONJ
ejpam-4283	498	13	q	q	NOUN
ejpam-4283	498	14	∈	∈	PROPN
ejpam-4283	498	15	(	(	PUNCT
ejpam-4283	498	16	s	s	PROPN
ejpam-4283	498	17	,	,	PUNCT
ejpam-4283	498	18	v	v	NOUN
ejpam-4283	498	19	)	)	PUNCT
ejpam-4283	498	20	?	?	PUNCT
ejpam-4283	499	1	−	−	PROPN
ejpam-4283	499	2	s(x	s(x	PROPN
ejpam-4283	499	3	)	)	PUNCT
ejpam-4283	499	4	where	where	SCONJ
ejpam-4283	499	5	s	s	X
ejpam-4283	499	6	,	,	PUNCT
ejpam-4283	499	7	v	v	NOUN
ejpam-4283	499	8	=	=	SYM
ejpam-4283	499	9	1	1	NUM
ejpam-4283	499	10	,	,	PUNCT
ejpam-4283	499	11	2	2	NUM
ejpam-4283	499	12	and	and	CCONJ
ejpam-4283	499	13	s	s	X
ejpam-4283	499	14	6=	6=	PROPN
ejpam-4283	499	15	v.	v.	ADP
ejpam-4283	499	16	take	take	NOUN
ejpam-4283	499	17	s	s	PART
ejpam-4283	499	18	=	=	SYM
ejpam-4283	499	19	1	1	NUM
ejpam-4283	499	20	and	and	CCONJ
ejpam-4283	499	21	v	v	NOUN
ejpam-4283	499	22	=	=	SYM
ejpam-4283	499	23	2	2	NUM
ejpam-4283	499	24	.	.	PUNCT
ejpam-4283	499	25	then	then	ADV
ejpam-4283	499	26	q	q	PROPN
ejpam-4283	499	27	∈	∈	PROPN
ejpam-4283	499	28	(	(	PUNCT
ejpam-4283	499	29	1	1	NUM
ejpam-4283	499	30	,	,	PUNCT
ejpam-4283	499	31	2	2	NUM
ejpam-4283	499	32	)	)	PUNCT
ejpam-4283	499	33	?	?	PUNCT
ejpam-4283	500	1	−s(x);µ2	−s(x);µ2	NOUN
ejpam-4283	501	1	⊂	⊂	PROPN
ejpam-4283	501	2	µ1	µ1	PROPN
ejpam-4283	501	3	and	and	CCONJ
ejpam-4283	501	4	µ2	µ2	PROPN
ejpam-4283	501	5	is	be	AUX
ejpam-4283	501	6	a	a	DET
ejpam-4283	501	7	sgt	sgt	PROPN
ejpam-4283	501	8	.	.	PUNCT
ejpam-4283	502	1	let	let	VERB
ejpam-4283	502	2	h	h	NOUN
ejpam-4283	502	3	∈	∈	PROPN
ejpam-4283	502	4	µ̃2	µ̃2	PROPN
ejpam-4283	502	5	.	.	PUNCT
ejpam-4283	503	1	then	then	ADV
ejpam-4283	503	2	h	h	PROPN
ejpam-4283	503	3	∈	∈	PROPN
ejpam-4283	503	4	µ̃1	µ̃1	PROPN
ejpam-4283	503	5	.	.	PUNCT
ejpam-4283	503	6	by	by	ADP
ejpam-4283	503	7	assumption	assumption	NOUN
ejpam-4283	503	8	,	,	PUNCT
ejpam-4283	503	9	there	there	PRON
ejpam-4283	503	10	is	be	VERB
ejpam-4283	503	11	k	k	PROPN
ejpam-4283	503	12	∈	∈	PROPN
ejpam-4283	503	13	σ̃2	σ̃2	PROPN
ejpam-4283	503	14	such	such	ADJ
ejpam-4283	503	15	that	that	SCONJ
ejpam-4283	503	16	k	k	PROPN
ejpam-4283	503	17	⊂	⊂	PROPN
ejpam-4283	503	18	h	h	PROPN
ejpam-4283	504	1	and	and	CCONJ
ejpam-4283	504	2	k	k	X
ejpam-4283	504	3	∩q	∩q	PROPN
ejpam-4283	505	1	=	=	PUNCT
ejpam-4283	505	2	∅.	∅.	ADV
ejpam-4283	505	3	since	since	SCONJ
ejpam-4283	505	4	k	k	PROPN
ejpam-4283	505	5	∈	∈	PROPN
ejpam-4283	505	6	σ̃2	σ̃2	PROPN
ejpam-4283	505	7	we	we	PRON
ejpam-4283	505	8	have	have	VERB
ejpam-4283	505	9	k	k	PROPN
ejpam-4283	505	10	⊂	⊂	X
ejpam-4283	505	11	c2(i2(k	c2(i2(k	PROPN
ejpam-4283	505	12	)	)	PUNCT
ejpam-4283	505	13	)	)	PUNCT
ejpam-4283	505	14	.	.	PUNCT
ejpam-4283	506	1	this	this	PRON
ejpam-4283	506	2	implies	imply	VERB
ejpam-4283	506	3	i2(k	i2(k	PROPN
ejpam-4283	506	4	)	)	PUNCT
ejpam-4283	506	5	6=	6=	ADP
ejpam-4283	506	6	∅	∅	NOUN
ejpam-4283	506	7	,	,	PUNCT
ejpam-4283	506	8	since	since	SCONJ
ejpam-4283	506	9	µ2	µ2	PROPN
ejpam-4283	506	10	is	be	AUX
ejpam-4283	506	11	a	a	DET
ejpam-4283	506	12	sgt	sgt	NOUN
ejpam-4283	506	13	which	which	PRON
ejpam-4283	506	14	implies	imply	VERB
ejpam-4283	506	15	that	that	SCONJ
ejpam-4283	506	16	i2(k	i2(k	NOUN
ejpam-4283	506	17	)	)	PUNCT
ejpam-4283	506	18	∈	∈	PROPN
ejpam-4283	506	19	µ̃2	µ̃2	PROPN
ejpam-4283	506	20	.	.	PUNCT
ejpam-4283	507	1	take	take	VERB
ejpam-4283	507	2	b	b	NOUN
ejpam-4283	507	3	=	=	SYM
ejpam-4283	507	4	i2(k	i2(k	PROPN
ejpam-4283	507	5	)	)	PUNCT
ejpam-4283	507	6	.	.	PUNCT
ejpam-4283	508	1	thus	thus	ADV
ejpam-4283	508	2	,	,	PUNCT
ejpam-4283	508	3	there	there	PRON
ejpam-4283	508	4	is	be	VERB
ejpam-4283	508	5	b	b	PRON
ejpam-4283	508	6	∈	∈	NOUN
ejpam-4283	508	7	µ̃2	µ̃2	PROPN
ejpam-4283	508	8	such	such	ADJ
ejpam-4283	508	9	that	that	SCONJ
ejpam-4283	508	10	b	b	PROPN
ejpam-4283	508	11	⊂	⊂	PROPN
ejpam-4283	508	12	h	h	PROPN
ejpam-4283	508	13	and	and	CCONJ
ejpam-4283	508	14	b	b	NOUN
ejpam-4283	508	15	∩q	∩q	PROPN
ejpam-4283	508	16	=	=	PUNCT
ejpam-4283	508	17	∅.	∅.	VERB
ejpam-4283	508	18	hence	hence	ADV
ejpam-4283	508	19	q	q	X
ejpam-4283	508	20	is	be	AUX
ejpam-4283	508	21	a	a	DET
ejpam-4283	508	22	µ2	µ2	NOUN
ejpam-4283	508	23	-	-	PUNCT
ejpam-4283	508	24	strongly	strongly	ADV
ejpam-4283	508	25	nowhere	nowhere	ADV
ejpam-4283	508	26	dense	dense	ADJ
ejpam-4283	508	27	set	set	NOUN
ejpam-4283	508	28	in	in	ADP
ejpam-4283	508	29	x.	x.	NOUN
ejpam-4283	508	30	by	by	ADP
ejpam-4283	508	31	similar	similar	ADJ
ejpam-4283	508	32	arguments	argument	NOUN
ejpam-4283	508	33	,	,	PUNCT
ejpam-4283	508	34	we	we	PRON
ejpam-4283	508	35	can	can	AUX
ejpam-4283	508	36	prove	prove	VERB
ejpam-4283	508	37	the	the	DET
ejpam-4283	508	38	result	result	NOUN
ejpam-4283	508	39	for	for	ADP
ejpam-4283	508	40	the	the	DET
ejpam-4283	508	41	case	case	NOUN
ejpam-4283	508	42	s	s	PART
ejpam-4283	508	43	=	=	SYM
ejpam-4283	508	44	2	2	NUM
ejpam-4283	508	45	and	and	CCONJ
ejpam-4283	508	46	v	v	NOUN
ejpam-4283	508	47	=	=	SYM
ejpam-4283	508	48	1	1	NUM
ejpam-4283	508	49	.	.	PUNCT
ejpam-4283	508	50	theorem	theorem	VERB
ejpam-4283	508	51	39	39	NUM
ejpam-4283	508	52	.	.	PUNCT
ejpam-4283	509	1	let	let	AUX
ejpam-4283	509	2	(	(	PUNCT
ejpam-4283	509	3	x,µ1	x,µ1	NOUN
ejpam-4283	509	4	,	,	PUNCT
ejpam-4283	509	5	µ2	µ2	PROPN
ejpam-4283	509	6	)	)	PUNCT
ejpam-4283	509	7	be	be	VERB
ejpam-4283	509	8	a	a	DET
ejpam-4283	509	9	bgts	bgts	NOUN
ejpam-4283	509	10	which	which	PRON
ejpam-4283	509	11	has	have	VERB
ejpam-4283	509	12	the	the	DET
ejpam-4283	509	13	is	is	NOUN
ejpam-4283	509	14	-	-	PUNCT
ejpam-4283	509	15	property	property	NOUN
ejpam-4283	509	16	.	.	PUNCT
ejpam-4283	510	1	if	if	SCONJ
ejpam-4283	510	2	µv	µv	NOUN
ejpam-4283	510	3	is	be	AUX
ejpam-4283	510	4	a	a	DET
ejpam-4283	510	5	sgt	sgt	PROPN
ejpam-4283	510	6	and	and	CCONJ
ejpam-4283	510	7	d	d	PROPN
ejpam-4283	510	8	∈	∈	PROPN
ejpam-4283	510	9	(	(	PUNCT
ejpam-4283	510	10	s	s	PROPN
ejpam-4283	510	11	,	,	PUNCT
ejpam-4283	510	12	v	v	NOUN
ejpam-4283	510	13	)	)	PUNCT
ejpam-4283	510	14	?	?	PUNCT
ejpam-4283	511	1	−s(x	−s(x	NOUN
ejpam-4283	511	2	)	)	PUNCT
ejpam-4283	511	3	,	,	PUNCT
ejpam-4283	511	4	then	then	ADV
ejpam-4283	511	5	d	d	PROPN
ejpam-4283	511	6	is	be	AUX
ejpam-4283	511	7	a	a	DET
ejpam-4283	511	8	µs	µs	NOUN
ejpam-4283	511	9	-	-	PUNCT
ejpam-4283	511	10	strongly	strongly	ADV
ejpam-4283	511	11	nowhere	nowhere	ADV
ejpam-4283	511	12	dense	dense	ADJ
ejpam-4283	511	13	set	set	NOUN
ejpam-4283	511	14	where	where	SCONJ
ejpam-4283	511	15	s	s	X
ejpam-4283	511	16	,	,	PUNCT
ejpam-4283	511	17	v	v	NOUN
ejpam-4283	511	18	=	=	SYM
ejpam-4283	511	19	1	1	NUM
ejpam-4283	511	20	,	,	PUNCT
ejpam-4283	511	21	2	2	NUM
ejpam-4283	511	22	;	;	PUNCT
ejpam-4283	511	23	s	s	X
ejpam-4283	511	24	6=	6=	PROPN
ejpam-4283	511	25	v.	v.	ADP
ejpam-4283	511	26	proof	proof	NOUN
ejpam-4283	511	27	.	.	PUNCT
ejpam-4283	512	1	we	we	PRON
ejpam-4283	512	2	give	give	VERB
ejpam-4283	512	3	the	the	DET
ejpam-4283	512	4	detailed	detailed	ADJ
ejpam-4283	512	5	proof	proof	NOUN
ejpam-4283	512	6	only	only	ADV
ejpam-4283	512	7	for	for	ADP
ejpam-4283	512	8	s	s	NOUN
ejpam-4283	512	9	=	=	SYM
ejpam-4283	512	10	2	2	NUM
ejpam-4283	512	11	and	and	CCONJ
ejpam-4283	512	12	v	v	NOUN
ejpam-4283	512	13	=	=	SYM
ejpam-4283	512	14	1	1	X
ejpam-4283	512	15	.	.	PUNCT
ejpam-4283	512	16	assume	assume	VERB
ejpam-4283	512	17	that	that	SCONJ
ejpam-4283	512	18	,	,	PUNCT
ejpam-4283	512	19	the	the	DET
ejpam-4283	512	20	bigeneralized	bigeneralize	VERB
ejpam-4283	512	21	topological	topological	ADJ
ejpam-4283	512	22	space	space	NOUN
ejpam-4283	512	23	(	(	PUNCT
ejpam-4283	512	24	x,µ1	x,µ1	PROPN
ejpam-4283	512	25	,	,	PUNCT
ejpam-4283	512	26	µ2	µ2	PROPN
ejpam-4283	512	27	)	)	PUNCT
ejpam-4283	512	28	satisfy	satisfy	NOUN
ejpam-4283	512	29	the	the	DET
ejpam-4283	512	30	is	is	NOUN
ejpam-4283	512	31	-	-	PUNCT
ejpam-4283	512	32	property	property	NOUN
ejpam-4283	512	33	and	and	CCONJ
ejpam-4283	512	34	µ1	µ1	NOUN
ejpam-4283	512	35	is	be	AUX
ejpam-4283	512	36	a	a	DET
ejpam-4283	512	37	strong	strong	ADJ
ejpam-4283	512	38	generalized	generalized	ADJ
ejpam-4283	512	39	topology	topology	NOUN
ejpam-4283	512	40	.	.	PUNCT
ejpam-4283	513	1	let	let	VERB
ejpam-4283	513	2	d	d	PRON
ejpam-4283	513	3	be	be	AUX
ejpam-4283	513	4	(	(	PUNCT
ejpam-4283	513	5	2	2	NUM
ejpam-4283	513	6	,	,	PUNCT
ejpam-4283	513	7	1)?-strongly	1)?-strongly	ADV
ejpam-4283	513	8	nowhere	nowhere	ADV
ejpam-4283	513	9	dense	dense	ADJ
ejpam-4283	513	10	set	set	NOUN
ejpam-4283	513	11	and	and	CCONJ
ejpam-4283	513	12	g	g	NOUN
ejpam-4283	513	13	∈	∈	PROPN
ejpam-4283	513	14	µ̃2	µ̃2	PROPN
ejpam-4283	513	15	.	.	PUNCT
ejpam-4283	514	1	then	then	ADV
ejpam-4283	514	2	there	there	PRON
ejpam-4283	514	3	is	be	VERB
ejpam-4283	514	4	a	a	DET
ejpam-4283	514	5	set	set	NOUN
ejpam-4283	514	6	p	p	NOUN
ejpam-4283	514	7	∈	∈	PROPN
ejpam-4283	514	8	σ̃1	σ̃1	PROPN
ejpam-4283	514	9	such	such	ADJ
ejpam-4283	514	10	that	that	SCONJ
ejpam-4283	514	11	p	p	PROPN
ejpam-4283	514	12	⊂	⊂	PROPN
ejpam-4283	514	13	g	g	PROPN
ejpam-4283	514	14	and	and	CCONJ
ejpam-4283	514	15	p	p	NOUN
ejpam-4283	514	16	∩	∩	ADJ
ejpam-4283	514	17	d	d	NOUN
ejpam-4283	514	18	=	=	PUNCT
ejpam-4283	514	19	∅.	∅.	NOUN
ejpam-4283	514	20	since	since	SCONJ
ejpam-4283	514	21	p	p	PROPN
ejpam-4283	514	22	∈	∈	PROPN
ejpam-4283	514	23	σ̃1	σ̃1	PROPN
ejpam-4283	514	24	we	we	PRON
ejpam-4283	514	25	have	have	VERB
ejpam-4283	514	26	iµ1(p	iµ1(p	PROPN
ejpam-4283	514	27	)	)	PUNCT
ejpam-4283	514	28	6=	6=	ADP
ejpam-4283	514	29	∅	∅	NOUN
ejpam-4283	514	30	,	,	PUNCT
ejpam-4283	514	31	by	by	ADP
ejpam-4283	514	32	our	our	PRON
ejpam-4283	514	33	assumption	assumption	NOUN
ejpam-4283	514	34	.	.	PUNCT
ejpam-4283	515	1	take	take	VERB
ejpam-4283	515	2	j	j	NOUN
ejpam-4283	515	3	=	=	PUNCT
ejpam-4283	515	4	iµ1(p	iµ1(p	PROPN
ejpam-4283	515	5	)	)	PUNCT
ejpam-4283	515	6	.	.	PUNCT
ejpam-4283	516	1	then	then	ADV
ejpam-4283	516	2	j	j	PROPN
ejpam-4283	516	3	∈	∈	PROPN
ejpam-4283	516	4	µ̃1	µ̃1	PROPN
ejpam-4283	516	5	.	.	PUNCT
ejpam-4283	516	6	here	here	ADV
ejpam-4283	516	7	g	g	PROPN
ejpam-4283	516	8	∈	∈	PROPN
ejpam-4283	516	9	µ̃2	µ̃2	PROPN
ejpam-4283	516	10	,	,	PUNCT
ejpam-4283	516	11	j	j	PROPN
ejpam-4283	516	12	∈	∈	PROPN
ejpam-4283	516	13	µ̃1	µ̃1	PROPN
ejpam-4283	516	14	and	and	CCONJ
ejpam-4283	516	15	j	j	PROPN
ejpam-4283	516	16	∩	∩	PROPN
ejpam-4283	516	17	g	g	PROPN
ejpam-4283	516	18	6=	6=	ADP
ejpam-4283	516	19	∅.	∅.	VERB
ejpam-4283	516	20	by	by	ADP
ejpam-4283	516	21	our	our	PRON
ejpam-4283	516	22	assumption	assumption	NOUN
ejpam-4283	516	23	,	,	PUNCT
ejpam-4283	516	24	iµ2(j	iµ2(j	PROPN
ejpam-4283	516	25	∩	∩	PROPN
ejpam-4283	516	26	g	g	NOUN
ejpam-4283	516	27	)	)	PUNCT
ejpam-4283	516	28	6=	6=	ADP
ejpam-4283	516	29	∅.	∅.	ADP
ejpam-4283	516	30	take	take	NOUN
ejpam-4283	516	31	e	e	NOUN
ejpam-4283	516	32	=	=	NOUN
ejpam-4283	516	33	iµ2(j	iµ2(j	PROPN
ejpam-4283	516	34	∩	∩	PROPN
ejpam-4283	516	35	g	g	NOUN
ejpam-4283	516	36	)	)	PUNCT
ejpam-4283	516	37	.	.	PUNCT
ejpam-4283	517	1	then	then	ADV
ejpam-4283	517	2	e	e	PROPN
ejpam-4283	517	3	∈	∈	PROPN
ejpam-4283	517	4	µ̃2	µ̃2	PROPN
ejpam-4283	517	5	.	.	PUNCT
ejpam-4283	518	1	thus	thus	ADV
ejpam-4283	518	2	,	,	PUNCT
ejpam-4283	518	3	there	there	PRON
ejpam-4283	518	4	exists	exist	VERB
ejpam-4283	518	5	e	e	PROPN
ejpam-4283	518	6	∈	∈	PROPN
ejpam-4283	518	7	µ̃2	µ̃2	PROPN
ejpam-4283	518	8	such	such	ADJ
ejpam-4283	518	9	that	that	SCONJ
ejpam-4283	518	10	e	e	PROPN
ejpam-4283	518	11	⊂	⊂	PROPN
ejpam-4283	518	12	g	g	PROPN
ejpam-4283	518	13	and	and	CCONJ
ejpam-4283	518	14	e	e	NOUN
ejpam-4283	518	15	∩d	∩d	NOUN
ejpam-4283	518	16	=	=	PUNCT
ejpam-4283	518	17	∅.	∅.	VERB
ejpam-4283	518	18	hence	hence	ADV
ejpam-4283	518	19	d	d	PROPN
ejpam-4283	518	20	is	be	AUX
ejpam-4283	518	21	µ2	µ2	ADJ
ejpam-4283	518	22	-	-	PUNCT
ejpam-4283	518	23	strongly	strongly	ADV
ejpam-4283	518	24	nowhere	nowhere	ADV
ejpam-4283	518	25	dense	dense	ADJ
ejpam-4283	518	26	in	in	ADP
ejpam-4283	518	27	x.	x.	NOUN
ejpam-4283	518	28	references	reference	NOUN
ejpam-4283	518	29	[	[	X
ejpam-4283	518	30	1	1	NUM
ejpam-4283	518	31	]	]	PUNCT
ejpam-4283	518	32	santanu	santanu	ADJ
ejpam-4283	518	33	acharjee	acharjee	NOUN
ejpam-4283	518	34	,	,	PUNCT
ejpam-4283	518	35	binod	binod	PROPN
ejpam-4283	518	36	chandra	chandra	PROPN
ejpam-4283	518	37	tripathy	tripathy	PROPN
ejpam-4283	518	38	,	,	PUNCT
ejpam-4283	518	39	and	and	CCONJ
ejpam-4283	518	40	kyriakos	kyriakos	PROPN
ejpam-4283	518	41	papadopoulos	papadopoulos	PROPN
ejpam-4283	518	42	.	.	PUNCT
ejpam-4283	519	1	two	two	NUM
ejpam-4283	519	2	forms	form	NOUN
ejpam-4283	519	3	of	of	ADP
ejpam-4283	519	4	pairwise	pairwise	NOUN
ejpam-4283	519	5	lindelöfness	lindelöfness	NOUN
ejpam-4283	519	6	and	and	CCONJ
ejpam-4283	519	7	some	some	DET
ejpam-4283	519	8	results	result	NOUN
ejpam-4283	519	9	related	relate	VERB
ejpam-4283	519	10	to	to	ADP
ejpam-4283	519	11	hereditary	hereditary	ADJ
ejpam-4283	519	12	class	class	NOUN
ejpam-4283	519	13	in	in	ADP
ejpam-4283	519	14	a	a	DET
ejpam-4283	519	15	bigeneralized	bigeneralize	VERB
ejpam-4283	519	16	topological	topological	ADJ
ejpam-4283	519	17	space	space	NOUN
ejpam-4283	519	18	.	.	PUNCT
ejpam-4283	520	1	new	new	ADJ
ejpam-4283	520	2	mathematics	mathematic	NOUN
ejpam-4283	520	3	and	and	CCONJ
ejpam-4283	520	4	natural	natural	ADJ
ejpam-4283	520	5	computation	computation	NOUN
ejpam-4283	520	6	,	,	PUNCT
ejpam-4283	520	7	13(02):181–193	13(02):181–193	NUM
ejpam-4283	520	8	,	,	PUNCT
ejpam-4283	520	9	2017	2017	NUM
ejpam-4283	520	10	.	.	PUNCT
ejpam-4283	521	1	[	[	X
ejpam-4283	521	2	2	2	X
ejpam-4283	521	3	]	]	PUNCT
ejpam-4283	521	4	chawalit	chawalit	VERB
ejpam-4283	521	5	boonpok	boonpok	NOUN
ejpam-4283	521	6	.	.	PUNCT
ejpam-4283	522	1	weakly	weakly	ADJ
ejpam-4283	522	2	open	open	ADJ
ejpam-4283	522	3	functions	function	NOUN
ejpam-4283	522	4	on	on	ADP
ejpam-4283	522	5	bigeneralized	bigeneralize	VERB
ejpam-4283	522	6	topological	topological	ADJ
ejpam-4283	522	7	spaces	space	NOUN
ejpam-4283	522	8	.	.	PUNCT
ejpam-4283	523	1	int	int	NOUN
ejpam-4283	523	2	.	.	PUNCT
ejpam-4283	524	1	journal	journal	PROPN
ejpam-4283	524	2	of	of	ADP
ejpam-4283	524	3	math	math	NOUN
ejpam-4283	524	4	.	.	PUNCT
ejpam-4283	525	1	analysis	analysis	NOUN
ejpam-4283	525	2	,	,	PUNCT
ejpam-4283	525	3	4(18):891–897	4(18):891–897	NUM
ejpam-4283	525	4	,	,	PUNCT
ejpam-4283	525	5	2010	2010	NUM
ejpam-4283	525	6	.	.	PUNCT
ejpam-4283	526	1	[	[	X
ejpam-4283	526	2	3	3	X
ejpam-4283	526	3	]	]	X
ejpam-4283	526	4	a	a	DET
ejpam-4283	526	5	csaszar	csaszar	NOUN
ejpam-4283	526	6	.	.	PUNCT
ejpam-4283	527	1	extremally	extremally	ADV
ejpam-4283	527	2	disconnected	disconnect	VERB
ejpam-4283	527	3	generalized	generalized	ADJ
ejpam-4283	527	4	topologies	topology	NOUN
ejpam-4283	527	5	.	.	PUNCT
ejpam-4283	528	1	in	in	ADP
ejpam-4283	528	2	annales	annales	PROPN
ejpam-4283	528	3	univ	univ	PROPN
ejpam-4283	528	4	.	.	PUNCT
ejpam-4283	529	1	sci	sci	PROPN
ejpam-4283	529	2	.	.	PUNCT
ejpam-4283	529	3	budapest	budapest	PROPN
ejpam-4283	529	4	,	,	PUNCT
ejpam-4283	529	5	volume	volume	NOUN
ejpam-4283	529	6	47	47	NUM
ejpam-4283	529	7	,	,	PUNCT
ejpam-4283	529	8	pages	page	NOUN
ejpam-4283	529	9	151–161	151–161	NUM
ejpam-4283	529	10	,	,	PUNCT
ejpam-4283	529	11	2004	2004	NUM
ejpam-4283	529	12	.	.	PUNCT
ejpam-4283	530	1	[	[	X
ejpam-4283	530	2	4	4	X
ejpam-4283	530	3	]	]	X
ejpam-4283	530	4	akos	akos	NOUN
ejpam-4283	530	5	császár	császár	PROPN
ejpam-4283	530	6	.	.	PUNCT
ejpam-4283	531	1	generalized	generalize	VERB
ejpam-4283	531	2	open	open	ADJ
ejpam-4283	531	3	sets	set	NOUN
ejpam-4283	531	4	.	.	PUNCT
ejpam-4283	532	1	acta	acta	PROPN
ejpam-4283	532	2	mathematica	mathematica	PROPN
ejpam-4283	532	3	hungarica	hungarica	PROPN
ejpam-4283	532	4	,	,	PUNCT
ejpam-4283	532	5	75	75	NUM
ejpam-4283	532	6	,	,	PUNCT
ejpam-4283	532	7	1997	1997	NUM
ejpam-4283	532	8	.	.	PUNCT
ejpam-4283	533	1	[	[	X
ejpam-4283	533	2	5	5	X
ejpam-4283	533	3	]	]	PUNCT
ejpam-4283	533	4	akos	akos	NOUN
ejpam-4283	533	5	császár	császár	PROPN
ejpam-4283	533	6	.	.	PUNCT
ejpam-4283	534	1	generalized	generalize	VERB
ejpam-4283	534	2	open	open	ADJ
ejpam-4283	534	3	sets	set	NOUN
ejpam-4283	534	4	in	in	ADP
ejpam-4283	534	5	generalized	generalized	ADJ
ejpam-4283	534	6	topologies	topology	NOUN
ejpam-4283	534	7	.	.	PUNCT
ejpam-4283	535	1	acta	acta	PROPN
ejpam-4283	535	2	mathematica	mathematica	PROPN
ejpam-4283	535	3	hungarica	hungarica	PROPN
ejpam-4283	535	4	,	,	PUNCT
ejpam-4283	535	5	106	106	NUM
ejpam-4283	535	6	,	,	PUNCT
ejpam-4283	535	7	2005	2005	NUM
ejpam-4283	535	8	.	.	PUNCT
ejpam-4283	536	1	[	[	X
ejpam-4283	536	2	6	6	NUM
ejpam-4283	536	3	]	]	PUNCT
ejpam-4283	536	4	erdal	erdal	PROPN
ejpam-4283	536	5	ekici	ekici	PROPN
ejpam-4283	536	6	.	.	PUNCT
ejpam-4283	537	1	generalized	generalized	ADJ
ejpam-4283	537	2	hyperconnectedness	hyperconnectedness	NOUN
ejpam-4283	537	3	.	.	PUNCT
ejpam-4283	538	1	acta	acta	PROPN
ejpam-4283	538	2	mathematica	mathematica	PROPN
ejpam-4283	538	3	hungarica	hungarica	PROPN
ejpam-4283	538	4	,	,	PUNCT
ejpam-4283	538	5	133	133	NUM
ejpam-4283	538	6	,	,	PUNCT
ejpam-4283	538	7	2011	2011	NUM
ejpam-4283	538	8	.	.	PUNCT
ejpam-4283	539	1	references	reference	NOUN
ejpam-4283	539	2	414	414	NUM
ejpam-4283	540	1	[	[	X
ejpam-4283	540	2	7	7	NUM
ejpam-4283	540	3	]	]	X
ejpam-4283	540	4	ewa	ewa	PROPN
ejpam-4283	540	5	korczak	korczak	PROPN
ejpam-4283	540	6	-	-	PUNCT
ejpam-4283	540	7	kubiak	kubiak	PROPN
ejpam-4283	540	8	,	,	PUNCT
ejpam-4283	540	9	anna	anna	PROPN
ejpam-4283	540	10	loranty	loranty	PROPN
ejpam-4283	540	11	,	,	PUNCT
ejpam-4283	540	12	and	and	CCONJ
ejpam-4283	540	13	ryszard	ryszard	PROPN
ejpam-4283	540	14	j	j	PROPN
ejpam-4283	540	15	pawlak	pawlak	PROPN
ejpam-4283	540	16	.	.	PUNCT
ejpam-4283	541	1	baire	baire	NOUN
ejpam-4283	541	2	generalized	generalize	VERB
ejpam-4283	541	3	topological	topological	ADJ
ejpam-4283	541	4	spaces	space	NOUN
ejpam-4283	541	5	,	,	PUNCT
ejpam-4283	541	6	generalized	generalize	VERB
ejpam-4283	541	7	metric	metric	ADJ
ejpam-4283	541	8	spaces	space	NOUN
ejpam-4283	541	9	and	and	CCONJ
ejpam-4283	541	10	infinite	infinite	ADJ
ejpam-4283	541	11	games	game	NOUN
ejpam-4283	541	12	.	.	PUNCT
ejpam-4283	542	1	acta	acta	PROPN
ejpam-4283	542	2	mathematica	mathematica	PROPN
ejpam-4283	542	3	hungarica	hungarica	PROPN
ejpam-4283	542	4	,	,	PUNCT
ejpam-4283	542	5	140(3):203–231	140(3):203–231	NUM
ejpam-4283	542	6	,	,	PUNCT
ejpam-4283	542	7	2013	2013	NUM
ejpam-4283	542	8	.	.	PUNCT
ejpam-4283	543	1	[	[	X
ejpam-4283	543	2	8	8	NUM
ejpam-4283	543	3	]	]	PUNCT
ejpam-4283	543	4	zhaowen	zhaowen	PROPN
ejpam-4283	543	5	li	li	PROPN
ejpam-4283	543	6	and	and	CCONJ
ejpam-4283	543	7	funing	fune	VERB
ejpam-4283	543	8	lin	lin	PROPN
ejpam-4283	543	9	.	.	PUNCT
ejpam-4283	544	1	baireness	baireness	PROPN
ejpam-4283	544	2	on	on	ADP
ejpam-4283	544	3	generalized	generalized	ADJ
ejpam-4283	544	4	topological	topological	ADJ
ejpam-4283	544	5	spaces	space	NOUN
ejpam-4283	544	6	.	.	PUNCT
ejpam-4283	545	1	acta	acta	PROPN
ejpam-4283	545	2	mathematica	mathematica	PROPN
ejpam-4283	545	3	hungarica	hungarica	PROPN
ejpam-4283	545	4	,	,	PUNCT
ejpam-4283	545	5	139(4	139(4	NUM
ejpam-4283	545	6	)	)	PUNCT
ejpam-4283	545	7	,	,	PUNCT
ejpam-4283	545	8	2013	2013	NUM
ejpam-4283	545	9	.	.	PUNCT
ejpam-4283	546	1	[	[	X
ejpam-4283	546	2	9	9	NUM
ejpam-4283	546	3	]	]	SYM
ejpam-4283	546	4	v	v	NOUN
ejpam-4283	546	5	renukadevi	renukadevi	NOUN
ejpam-4283	546	6	and	and	CCONJ
ejpam-4283	546	7	s	s	NOUN
ejpam-4283	546	8	vadakasi	vadakasi	NOUN
ejpam-4283	546	9	.	.	PUNCT
ejpam-4283	547	1	on	on	ADP
ejpam-4283	547	2	lower	low	ADJ
ejpam-4283	547	3	and	and	CCONJ
ejpam-4283	547	4	upper	upper	ADJ
ejpam-4283	547	5	semi	semi	ADJ
ejpam-4283	547	6	-	-	ADJ
ejpam-4283	547	7	continuous	continuous	ADJ
ejpam-4283	547	8	functions	function	NOUN
ejpam-4283	547	9	.	.	PUNCT
ejpam-4283	548	1	acta	acta	PROPN
ejpam-4283	548	2	mathematica	mathematica	PROPN
ejpam-4283	548	3	hungarica	hungarica	PROPN
ejpam-4283	548	4	,	,	PUNCT
ejpam-4283	548	5	160(1):1–12	160(1):1–12	NUM
ejpam-4283	548	6	,	,	PUNCT
ejpam-4283	548	7	2020	2020	NUM
ejpam-4283	548	8	.	.	PUNCT