id	sid	tid	token	lemma	pos
ejpam-4382	1	1	european	european	PROPN
ejpam-4382	1	2	journal	journal	PROPN
ejpam-4382	1	3	of	of	ADP
ejpam-4382	1	4	pure	pure	ADJ
ejpam-4382	1	5	and	and	CCONJ
ejpam-4382	1	6	applied	apply	VERB
ejpam-4382	1	7	mathematics	mathematic	NOUN
ejpam-4382	1	8	vol	vol	NOUN
ejpam-4382	1	9	.	.	PROPN
ejpam-4382	2	1	15	15	NUM
ejpam-4382	2	2	,	,	PUNCT
ejpam-4382	2	3	no	no	INTJ
ejpam-4382	2	4	.	.	NOUN
ejpam-4382	2	5	3	3	NUM
ejpam-4382	2	6	,	,	PUNCT
ejpam-4382	2	7	2022	2022	NUM
ejpam-4382	2	8	,	,	PUNCT
ejpam-4382	2	9	938	938	NUM
ejpam-4382	2	10	-	-	SYM
ejpam-4382	2	11	947	947	NUM
ejpam-4382	2	12	issn	issn	PROPN
ejpam-4382	2	13	1307	1307	NUM
ejpam-4382	2	14	-	-	SYM
ejpam-4382	2	15	5543	5543	NUM
ejpam-4382	2	16	–	–	PUNCT
ejpam-4382	2	17	ejpam.com	ejpam.com	X
ejpam-4382	2	18	published	publish	VERB
ejpam-4382	2	19	by	by	ADP
ejpam-4382	2	20	new	new	PROPN
ejpam-4382	2	21	york	york	PROPN
ejpam-4382	2	22	business	business	PROPN
ejpam-4382	2	23	global	global	ADJ
ejpam-4382	2	24	semi	semi	NOUN
ejpam-4382	2	25	-	-	ADJ
ejpam-4382	2	26	i	i	PRON
ejpam-4382	2	27	-submaximality	-submaximality	NOUN
ejpam-4382	2	28	chawalit	chawalit	VERB
ejpam-4382	2	29	boonpok	boonpok	NOUN
ejpam-4382	2	30	1	1	NUM
ejpam-4382	2	31	mathematics	mathematic	NOUN
ejpam-4382	2	32	and	and	CCONJ
ejpam-4382	2	33	applied	apply	VERB
ejpam-4382	2	34	mathematics	mathematics	PROPN
ejpam-4382	2	35	research	research	NOUN
ejpam-4382	2	36	unit	unit	NOUN
ejpam-4382	2	37	,	,	PUNCT
ejpam-4382	2	38	department	department	NOUN
ejpam-4382	2	39	of	of	ADP
ejpam-4382	2	40	mathematics	mathematic	NOUN
ejpam-4382	2	41	,	,	PUNCT
ejpam-4382	2	42	faculty	faculty	NOUN
ejpam-4382	2	43	of	of	ADP
ejpam-4382	2	44	science	science	NOUN
ejpam-4382	2	45	,	,	PUNCT
ejpam-4382	2	46	mahasarakham	mahasarakham	PROPN
ejpam-4382	2	47	university	university	PROPN
ejpam-4382	2	48	,	,	PUNCT
ejpam-4382	2	49	maha	maha	PROPN
ejpam-4382	2	50	sarakham	sarakham	PROPN
ejpam-4382	2	51	,	,	PUNCT
ejpam-4382	2	52	44150	44150	NUM
ejpam-4382	2	53	,	,	PUNCT
ejpam-4382	2	54	thailand	thailand	PROPN
ejpam-4382	2	55	abstract	abstract	PROPN
ejpam-4382	2	56	.	.	PUNCT
ejpam-4382	3	1	this	this	DET
ejpam-4382	3	2	paper	paper	NOUN
ejpam-4382	3	3	presents	present	VERB
ejpam-4382	3	4	the	the	DET
ejpam-4382	3	5	concept	concept	NOUN
ejpam-4382	3	6	of	of	ADP
ejpam-4382	3	7	semi	semi	ADJ
ejpam-4382	3	8	-	-	ADJ
ejpam-4382	3	9	i	i	PRON
ejpam-4382	3	10	-submaximal	-submaximal	ADJ
ejpam-4382	3	11	ideal	ideal	ADJ
ejpam-4382	3	12	topological	topological	ADJ
ejpam-4382	3	13	spaces	space	NOUN
ejpam-4382	3	14	.	.	PUNCT
ejpam-4382	4	1	in	in	ADP
ejpam-4382	4	2	particular	particular	ADJ
ejpam-4382	4	3	,	,	PUNCT
ejpam-4382	4	4	some	some	DET
ejpam-4382	4	5	characterizations	characterization	NOUN
ejpam-4382	4	6	of	of	ADP
ejpam-4382	4	7	semi	semi	ADJ
ejpam-4382	4	8	-	-	ADJ
ejpam-4382	4	9	i	i	PRON
ejpam-4382	4	10	-submaximal	-submaximal	ADJ
ejpam-4382	4	11	ideal	ideal	ADJ
ejpam-4382	4	12	topological	topological	ADJ
ejpam-4382	4	13	spaces	space	NOUN
ejpam-4382	4	14	are	be	AUX
ejpam-4382	4	15	investigated	investigate	VERB
ejpam-4382	4	16	.	.	PUNCT
ejpam-4382	5	1	2020	2020	NUM
ejpam-4382	5	2	mathematics	mathematic	NOUN
ejpam-4382	5	3	subject	subject	NOUN
ejpam-4382	5	4	classifications	classification	NOUN
ejpam-4382	5	5	:	:	PUNCT
ejpam-4382	5	6	54a05	54a05	NUM
ejpam-4382	5	7	,	,	PUNCT
ejpam-4382	5	8	54a10	54a10	NUM
ejpam-4382	5	9	key	key	ADJ
ejpam-4382	5	10	words	word	NOUN
ejpam-4382	5	11	and	and	CCONJ
ejpam-4382	5	12	phrases	phrase	NOUN
ejpam-4382	5	13	:	:	PUNCT
ejpam-4382	5	14	semi	semi	ADJ
ejpam-4382	5	15	-	-	ADJ
ejpam-4382	5	16	i	i	PRON
ejpam-4382	5	17	-open	-open	NOUN
ejpam-4382	5	18	set	set	NOUN
ejpam-4382	5	19	,	,	PUNCT
ejpam-4382	5	20	semi	semi	ADJ
ejpam-4382	5	21	-	-	ADJ
ejpam-4382	5	22	i	i	ADJ
ejpam-4382	5	23	-dense	-dense	PROPN
ejpam-4382	5	24	set	set	NOUN
ejpam-4382	5	25	,	,	PUNCT
ejpam-4382	5	26	semi	semi	ADJ
ejpam-4382	5	27	-	-	ADJ
ejpam-4382	5	28	i	i	PRON
ejpam-4382	5	29	-submaximal	-submaximal	ADJ
ejpam-4382	5	30	space	space	NOUN
ejpam-4382	5	31	1	1	NUM
ejpam-4382	5	32	.	.	PUNCT
ejpam-4382	6	1	introduction	introduction	NOUN
ejpam-4382	6	2	general	general	ADJ
ejpam-4382	6	3	topology	topology	NOUN
ejpam-4382	6	4	has	have	AUX
ejpam-4382	6	5	shown	show	VERB
ejpam-4382	6	6	its	its	PRON
ejpam-4382	6	7	fruitfulness	fruitfulness	NOUN
ejpam-4382	6	8	in	in	ADP
ejpam-4382	6	9	both	both	CCONJ
ejpam-4382	6	10	pure	pure	ADJ
ejpam-4382	6	11	and	and	CCONJ
ejpam-4382	6	12	applied	applied	ADJ
ejpam-4382	6	13	directions	direction	NOUN
ejpam-4382	6	14	.	.	PUNCT
ejpam-4382	7	1	the	the	DET
ejpam-4382	7	2	importance	importance	NOUN
ejpam-4382	7	3	of	of	ADP
ejpam-4382	7	4	general	general	ADJ
ejpam-4382	7	5	topology	topology	NOUN
ejpam-4382	7	6	has	have	AUX
ejpam-4382	7	7	appeared	appear	VERB
ejpam-4382	7	8	in	in	ADP
ejpam-4382	7	9	many	many	ADJ
ejpam-4382	7	10	fields	field	NOUN
ejpam-4382	7	11	of	of	ADP
ejpam-4382	7	12	applications	application	NOUN
ejpam-4382	7	13	such	such	ADJ
ejpam-4382	7	14	as	as	ADP
ejpam-4382	7	15	computational	computational	ADJ
ejpam-4382	7	16	topology	topology	NOUN
ejpam-4382	7	17	for	for	ADP
ejpam-4382	7	18	geometric	geometric	ADJ
ejpam-4382	7	19	design	design	NOUN
ejpam-4382	7	20	,	,	PUNCT
ejpam-4382	7	21	computer	computer	NOUN
ejpam-4382	7	22	-	-	PUNCT
ejpam-4382	7	23	aided	aid	VERB
ejpam-4382	7	24	geometric	geometric	ADJ
ejpam-4382	7	25	design	design	NOUN
ejpam-4382	7	26	and	and	CCONJ
ejpam-4382	7	27	engineering	engineering	NOUN
ejpam-4382	7	28	design	design	NOUN
ejpam-4382	7	29	.	.	PUNCT
ejpam-4382	8	1	hermann	hermann	PROPN
ejpam-4382	9	1	[	[	X
ejpam-4382	9	2	11	11	NUM
ejpam-4382	9	3	]	]	PUNCT
ejpam-4382	9	4	,	,	PUNCT
ejpam-4382	9	5	khalimsky	khalimsky	PROPN
ejpam-4382	10	1	[	[	X
ejpam-4382	10	2	14	14	NUM
ejpam-4382	10	3	]	]	PUNCT
ejpam-4382	10	4	et	et	PROPN
ejpam-4382	10	5	al	al	PROPN
ejpam-4382	10	6	.	.	PROPN
ejpam-4382	10	7	,	,	PUNCT
ejpam-4382	10	8	kong	kong	PROPN
ejpam-4382	10	9	and	and	CCONJ
ejpam-4382	10	10	koppermann	koppermann	PROPN
ejpam-4382	10	11	[	[	X
ejpam-4382	10	12	15	15	NUM
ejpam-4382	10	13	]	]	PUNCT
ejpam-4382	10	14	applied	apply	VERB
ejpam-4382	10	15	topology	topology	NOUN
ejpam-4382	10	16	in	in	ADP
ejpam-4382	10	17	computer	computer	NOUN
ejpam-4382	10	18	science	science	NOUN
ejpam-4382	10	19	and	and	CCONJ
ejpam-4382	10	20	digital	digital	ADJ
ejpam-4382	10	21	topology	topology	NOUN
ejpam-4382	10	22	.	.	PUNCT
ejpam-4382	11	1	moore	moore	PROPN
ejpam-4382	11	2	and	and	CCONJ
ejpam-4382	11	3	peters	peters	PROPN
ejpam-4382	11	4	[	[	X
ejpam-4382	11	5	17	17	NUM
ejpam-4382	11	6	]	]	PUNCT
ejpam-4382	11	7	investigated	investigate	VERB
ejpam-4382	11	8	computational	computational	ADJ
ejpam-4382	11	9	topology	topology	NOUN
ejpam-4382	11	10	for	for	ADP
ejpam-4382	11	11	geometric	geometric	ADJ
ejpam-4382	11	12	design	design	NOUN
ejpam-4382	11	13	.	.	PUNCT
ejpam-4382	12	1	rosen	rosen	PROPN
ejpam-4382	12	2	and	and	CCONJ
ejpam-4382	12	3	peters	peters	PROPN
ejpam-4382	13	1	[	[	X
ejpam-4382	13	2	18	18	NUM
ejpam-4382	13	3	]	]	PUNCT
ejpam-4382	13	4	used	use	VERB
ejpam-4382	13	5	topology	topology	NOUN
ejpam-4382	13	6	in	in	ADP
ejpam-4382	13	7	computer	computer	NOUN
ejpam-4382	13	8	-	-	PUNCT
ejpam-4382	13	9	aided	aid	VERB
ejpam-4382	13	10	geometric	geometric	ADJ
ejpam-4382	13	11	design	design	NOUN
ejpam-4382	13	12	and	and	CCONJ
ejpam-4382	13	13	engineering	engineering	NOUN
ejpam-4382	13	14	design	design	NOUN
ejpam-4382	13	15	.	.	PUNCT
ejpam-4382	14	1	the	the	DET
ejpam-4382	14	2	concepts	concept	NOUN
ejpam-4382	14	3	of	of	ADP
ejpam-4382	14	4	maximality	maximality	NOUN
ejpam-4382	14	5	and	and	CCONJ
ejpam-4382	14	6	submaximality	submaximality	NOUN
ejpam-4382	14	7	of	of	ADP
ejpam-4382	14	8	general	general	ADJ
ejpam-4382	14	9	topological	topological	ADJ
ejpam-4382	14	10	spaces	space	NOUN
ejpam-4382	14	11	were	be	AUX
ejpam-4382	14	12	introduced	introduce	VERB
ejpam-4382	14	13	by	by	ADP
ejpam-4382	14	14	hewitt	hewitt	PROPN
ejpam-4382	15	1	[	[	X
ejpam-4382	15	2	12	12	NUM
ejpam-4382	15	3	]	]	PUNCT
ejpam-4382	15	4	.	.	PUNCT
ejpam-4382	16	1	he	he	PRON
ejpam-4382	16	2	discovered	discover	VERB
ejpam-4382	16	3	a	a	DET
ejpam-4382	16	4	general	general	ADJ
ejpam-4382	16	5	way	way	NOUN
ejpam-4382	16	6	of	of	ADP
ejpam-4382	16	7	constructing	construct	VERB
ejpam-4382	16	8	maximal	maximal	ADJ
ejpam-4382	16	9	topologies	topology	NOUN
ejpam-4382	16	10	.	.	PUNCT
ejpam-4382	17	1	the	the	DET
ejpam-4382	17	2	existence	existence	NOUN
ejpam-4382	17	3	of	of	ADP
ejpam-4382	17	4	a	a	DET
ejpam-4382	17	5	maximal	maximal	ADJ
ejpam-4382	17	6	space	space	NOUN
ejpam-4382	17	7	that	that	PRON
ejpam-4382	17	8	is	be	AUX
ejpam-4382	17	9	tychonoff	tychonoff	NOUN
ejpam-4382	17	10	is	be	AUX
ejpam-4382	17	11	nontrivial	nontrivial	ADJ
ejpam-4382	17	12	and	and	CCONJ
ejpam-4382	17	13	due	due	ADP
ejpam-4382	17	14	to	to	ADP
ejpam-4382	17	15	van	van	PROPN
ejpam-4382	17	16	douwen	douwen	NOUN
ejpam-4382	17	17	[	[	X
ejpam-4382	17	18	21	21	NUM
ejpam-4382	17	19	]	]	PUNCT
ejpam-4382	17	20	.	.	PUNCT
ejpam-4382	18	1	the	the	DET
ejpam-4382	18	2	first	first	ADJ
ejpam-4382	18	3	systematic	systematic	ADJ
ejpam-4382	18	4	study	study	NOUN
ejpam-4382	18	5	of	of	ADP
ejpam-4382	18	6	submaximal	submaximal	ADJ
ejpam-4382	18	7	spaces	space	NOUN
ejpam-4382	18	8	was	be	AUX
ejpam-4382	18	9	undertaken	undertake	VERB
ejpam-4382	18	10	in	in	ADP
ejpam-4382	18	11	the	the	DET
ejpam-4382	18	12	paper	paper	NOUN
ejpam-4382	18	13	of	of	ADP
ejpam-4382	18	14	arhangel’skĭi	arhangel’skĭi	PROPN
ejpam-4382	18	15	and	and	CCONJ
ejpam-4382	18	16	collins	collin	VERB
ejpam-4382	18	17	[	[	X
ejpam-4382	18	18	2	2	NUM
ejpam-4382	18	19	]	]	PUNCT
ejpam-4382	18	20	.	.	PUNCT
ejpam-4382	19	1	they	they	PRON
ejpam-4382	19	2	gave	give	VERB
ejpam-4382	19	3	various	various	ADJ
ejpam-4382	19	4	necessary	necessary	ADJ
ejpam-4382	19	5	and	and	CCONJ
ejpam-4382	19	6	sufficient	sufficient	ADJ
ejpam-4382	19	7	conditions	condition	NOUN
ejpam-4382	19	8	for	for	ADP
ejpam-4382	19	9	a	a	DET
ejpam-4382	19	10	space	space	NOUN
ejpam-4382	19	11	to	to	PART
ejpam-4382	19	12	be	be	AUX
ejpam-4382	19	13	submaximal	submaximal	ADJ
ejpam-4382	19	14	and	and	CCONJ
ejpam-4382	19	15	showed	show	VERB
ejpam-4382	19	16	that	that	SCONJ
ejpam-4382	19	17	every	every	DET
ejpam-4382	19	18	submaximal	submaximal	ADJ
ejpam-4382	19	19	space	space	NOUN
ejpam-4382	19	20	is	be	AUX
ejpam-4382	19	21	left	leave	VERB
ejpam-4382	19	22	-	-	PUNCT
ejpam-4382	19	23	separated	separate	VERB
ejpam-4382	19	24	.	.	PUNCT
ejpam-4382	20	1	this	this	PRON
ejpam-4382	20	2	led	lead	VERB
ejpam-4382	20	3	to	to	ADP
ejpam-4382	20	4	the	the	DET
ejpam-4382	20	5	question	question	NOUN
ejpam-4382	20	6	whether	whether	SCONJ
ejpam-4382	20	7	every	every	DET
ejpam-4382	20	8	submaximal	submaximal	ADJ
ejpam-4382	20	9	space	space	NOUN
ejpam-4382	20	10	is	be	AUX
ejpam-4382	20	11	σ	σ	NOUN
ejpam-4382	20	12	-	-	NOUN
ejpam-4382	20	13	discrete	discrete	NOUN
ejpam-4382	20	14	[	[	X
ejpam-4382	20	15	2	2	NUM
ejpam-4382	20	16	]	]	PUNCT
ejpam-4382	20	17	.	.	PUNCT
ejpam-4382	21	1	every	every	DET
ejpam-4382	21	2	connected	connect	VERB
ejpam-4382	21	3	hausdorff	hausdorff	NOUN
ejpam-4382	21	4	space	space	NOUN
ejpam-4382	21	5	which	which	PRON
ejpam-4382	21	6	does	do	AUX
ejpam-4382	21	7	not	not	PART
ejpam-4382	21	8	admit	admit	VERB
ejpam-4382	21	9	a	a	DET
ejpam-4382	21	10	larger	large	ADJ
ejpam-4382	21	11	connected	connect	VERB
ejpam-4382	21	12	topology	topology	NOUN
ejpam-4382	21	13	is	be	AUX
ejpam-4382	21	14	submaximal	submaximal	ADJ
ejpam-4382	21	15	[	[	X
ejpam-4382	21	16	7	7	NUM
ejpam-4382	21	17	]	]	PUNCT
ejpam-4382	21	18	.	.	PUNCT
ejpam-4382	22	1	the	the	DET
ejpam-4382	22	2	concept	concept	NOUN
ejpam-4382	22	3	of	of	ADP
ejpam-4382	22	4	ideals	ideal	NOUN
ejpam-4382	22	5	in	in	ADP
ejpam-4382	22	6	topological	topological	ADJ
ejpam-4382	22	7	spaces	space	NOUN
ejpam-4382	22	8	has	have	AUX
ejpam-4382	22	9	been	be	AUX
ejpam-4382	22	10	introduced	introduce	VERB
ejpam-4382	22	11	and	and	CCONJ
ejpam-4382	22	12	studied	study	VERB
ejpam-4382	22	13	by	by	ADP
ejpam-4382	22	14	kuratowski	kuratowski	PROPN
ejpam-4382	22	15	[	[	X
ejpam-4382	22	16	16	16	NUM
ejpam-4382	22	17	]	]	PUNCT
ejpam-4382	22	18	and	and	CCONJ
ejpam-4382	22	19	vaidyanathaswamy	vaidyanathaswamy	NOUN
ejpam-4382	23	1	[	[	X
ejpam-4382	23	2	20	20	NUM
ejpam-4382	23	3	]	]	PUNCT
ejpam-4382	23	4	.	.	PUNCT
ejpam-4382	24	1	the	the	DET
ejpam-4382	24	2	topology	topology	NOUN
ejpam-4382	24	3	τ	τ	PROPN
ejpam-4382	24	4	of	of	ADP
ejpam-4382	24	5	a	a	DET
ejpam-4382	24	6	space	space	NOUN
ejpam-4382	24	7	is	be	AUX
ejpam-4382	24	8	enlarged	enlarge	VERB
ejpam-4382	24	9	to	to	ADP
ejpam-4382	24	10	a	a	DET
ejpam-4382	24	11	topology	topology	NOUN
ejpam-4382	24	12	τ⋆	τ⋆	NOUN
ejpam-4382	24	13	using	use	VERB
ejpam-4382	24	14	an	an	DET
ejpam-4382	24	15	ideal	ideal	NOUN
ejpam-4382	24	16	i	i	PRON
ejpam-4382	24	17	whose	whose	DET
ejpam-4382	24	18	members	member	NOUN
ejpam-4382	24	19	are	be	AUX
ejpam-4382	24	20	disjoint	disjoint	ADJ
ejpam-4382	24	21	with	with	ADP
ejpam-4382	24	22	the	the	DET
ejpam-4382	24	23	members	member	NOUN
ejpam-4382	24	24	of	of	ADP
ejpam-4382	24	25	τ	τ	PROPN
ejpam-4382	24	26	.	.	PUNCT
ejpam-4382	25	1	every	every	DET
ejpam-4382	25	2	topological	topological	ADJ
ejpam-4382	25	3	space	space	NOUN
ejpam-4382	25	4	is	be	AUX
ejpam-4382	25	5	an	an	DET
ejpam-4382	25	6	ideal	ideal	ADJ
ejpam-4382	25	7	topological	topological	ADJ
ejpam-4382	25	8	space	space	NOUN
ejpam-4382	25	9	and	and	CCONJ
ejpam-4382	25	10	all	all	DET
ejpam-4382	25	11	the	the	DET
ejpam-4382	25	12	results	result	NOUN
ejpam-4382	25	13	of	of	ADP
ejpam-4382	25	14	ideal	ideal	ADJ
ejpam-4382	25	15	topological	topological	ADJ
ejpam-4382	25	16	spaces	space	NOUN
ejpam-4382	25	17	are	be	AUX
ejpam-4382	25	18	generalizations	generalization	NOUN
ejpam-4382	25	19	of	of	ADP
ejpam-4382	25	20	the	the	DET
ejpam-4382	25	21	results	result	NOUN
ejpam-4382	25	22	established	establish	VERB
ejpam-4382	25	23	in	in	ADP
ejpam-4382	25	24	topological	topological	ADJ
ejpam-4382	25	25	spaces	space	NOUN
ejpam-4382	25	26	.	.	PUNCT
ejpam-4382	26	1	some	some	DET
ejpam-4382	26	2	early	early	ADJ
ejpam-4382	26	3	applications	application	NOUN
ejpam-4382	26	4	doi	doi	NOUN
ejpam-4382	26	5	:	:	PUNCT
ejpam-4382	26	6	https://doi.org/10.29020/nybg.ejpam.v15i3.4382	https://doi.org/10.29020/nybg.ejpam.v15i3.4382	VERB
ejpam-4382	26	7	email	email	NOUN
ejpam-4382	26	8	address	address	NOUN
ejpam-4382	26	9	:	:	PUNCT
ejpam-4382	27	1	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	INTJ
ejpam-4382	27	2	(	(	PUNCT
ejpam-4382	27	3	c.	c.	PROPN
ejpam-4382	27	4	boonpok	boonpok	PROPN
ejpam-4382	27	5	)	)	PUNCT
ejpam-4382	27	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4382	28	1	938	938	NUM
ejpam-4382	29	1	©	©	ADP
ejpam-4382	29	2	2022	2022	NUM
ejpam-4382	29	3	ejpam	ejpam	VERB
ejpam-4382	29	4	all	all	DET
ejpam-4382	29	5	rights	right	NOUN
ejpam-4382	29	6	reserved	reserve	VERB
ejpam-4382	29	7	.	.	PUNCT
ejpam-4382	30	1	c.	c.	PROPN
ejpam-4382	30	2	boonpok	boonpok	PROPN
ejpam-4382	30	3	/	/	SYM
ejpam-4382	30	4	eur	eur	PROPN
ejpam-4382	30	5	.	.	PUNCT
ejpam-4382	31	1	j.	j.	PROPN
ejpam-4382	31	2	pure	pure	PROPN
ejpam-4382	31	3	appl	appl	PROPN
ejpam-4382	31	4	.	.	PROPN
ejpam-4382	31	5	math	math	PROPN
ejpam-4382	31	6	,	,	PUNCT
ejpam-4382	31	7	15	15	NUM
ejpam-4382	31	8	(	(	PUNCT
ejpam-4382	31	9	3	3	NUM
ejpam-4382	31	10	)	)	PUNCT
ejpam-4382	31	11	(	(	PUNCT
ejpam-4382	31	12	2022	2022	NUM
ejpam-4382	31	13	)	)	PUNCT
ejpam-4382	31	14	,	,	PUNCT
ejpam-4382	31	15	938	938	NUM
ejpam-4382	31	16	-	-	SYM
ejpam-4382	31	17	947	947	NUM
ejpam-4382	31	18	939	939	NUM
ejpam-4382	31	19	of	of	ADP
ejpam-4382	31	20	ideal	ideal	ADJ
ejpam-4382	31	21	topological	topological	ADJ
ejpam-4382	31	22	spaces	space	NOUN
ejpam-4382	31	23	can	can	AUX
ejpam-4382	31	24	be	be	AUX
ejpam-4382	31	25	found	find	VERB
ejpam-4382	31	26	in	in	ADP
ejpam-4382	31	27	various	various	ADJ
ejpam-4382	31	28	branches	branch	NOUN
ejpam-4382	31	29	of	of	ADP
ejpam-4382	31	30	mathematics	mathematic	NOUN
ejpam-4382	31	31	,	,	PUNCT
ejpam-4382	31	32	like	like	ADP
ejpam-4382	31	33	a	a	DET
ejpam-4382	31	34	generalization	generalization	NOUN
ejpam-4382	31	35	of	of	ADP
ejpam-4382	31	36	cantor	cantor	PROPN
ejpam-4382	31	37	-	-	PUNCT
ejpam-4382	31	38	bendixson	bendixson	NOUN
ejpam-4382	31	39	theorem	theorem	NOUN
ejpam-4382	31	40	by	by	ADP
ejpam-4382	31	41	freud	freud	PROPN
ejpam-4382	31	42	[	[	X
ejpam-4382	31	43	6	6	NUM
ejpam-4382	31	44	]	]	PUNCT
ejpam-4382	31	45	,	,	PUNCT
ejpam-4382	31	46	or	or	CCONJ
ejpam-4382	31	47	in	in	ADP
ejpam-4382	31	48	measure	measure	NOUN
ejpam-4382	31	49	theory	theory	NOUN
ejpam-4382	31	50	by	by	ADP
ejpam-4382	31	51	scheinberg	scheinberg	PROPN
ejpam-4382	31	52	[	[	X
ejpam-4382	31	53	19	19	NUM
ejpam-4382	31	54	]	]	PUNCT
ejpam-4382	31	55	.	.	PUNCT
ejpam-4382	32	1	in	in	ADP
ejpam-4382	32	2	[	[	X
ejpam-4382	32	3	13	13	NUM
ejpam-4382	32	4	]	]	PUNCT
ejpam-4382	32	5	,	,	PUNCT
ejpam-4382	32	6	the	the	DET
ejpam-4382	32	7	present	present	ADJ
ejpam-4382	32	8	authors	author	NOUN
ejpam-4382	32	9	investigated	investigate	VERB
ejpam-4382	32	10	some	some	DET
ejpam-4382	32	11	properties	property	NOUN
ejpam-4382	32	12	of	of	ADP
ejpam-4382	32	13	ideal	ideal	ADJ
ejpam-4382	32	14	topological	topological	ADJ
ejpam-4382	32	15	spaces	space	NOUN
ejpam-4382	32	16	.	.	PUNCT
ejpam-4382	33	1	in	in	ADP
ejpam-4382	33	2	2002	2002	NUM
ejpam-4382	33	3	,	,	PUNCT
ejpam-4382	33	4	hatir	hatir	PROPN
ejpam-4382	33	5	and	and	CCONJ
ejpam-4382	33	6	noiri	noiri	ADV
ejpam-4382	33	7	[	[	X
ejpam-4382	33	8	9	9	NUM
ejpam-4382	33	9	]	]	PUNCT
ejpam-4382	33	10	introduced	introduce	VERB
ejpam-4382	33	11	the	the	DET
ejpam-4382	33	12	concepts	concept	NOUN
ejpam-4382	33	13	of	of	ADP
ejpam-4382	33	14	semi	semi	ADJ
ejpam-4382	33	15	-	-	ADJ
ejpam-4382	33	16	i	i	ADJ
ejpam-4382	33	17	-open	-open	NOUN
ejpam-4382	33	18	sets	set	NOUN
ejpam-4382	33	19	,	,	PUNCT
ejpam-4382	33	20	α	α	X
ejpam-4382	33	21	-	-	PUNCT
ejpam-4382	33	22	i	i	PRON
ejpam-4382	33	23	-open	-open	NOUN
ejpam-4382	33	24	sets	set	NOUN
ejpam-4382	33	25	and	and	CCONJ
ejpam-4382	33	26	β	β	X
ejpam-4382	33	27	-	-	ADJ
ejpam-4382	33	28	i	i	PRON
ejpam-4382	33	29	-open	-open	NOUN
ejpam-4382	33	30	sets	set	NOUN
ejpam-4382	33	31	in	in	ADP
ejpam-4382	33	32	topological	topological	ADJ
ejpam-4382	33	33	spaces	space	NOUN
ejpam-4382	33	34	via	via	ADP
ejpam-4382	33	35	ideals	ideal	NOUN
ejpam-4382	33	36	and	and	CCONJ
ejpam-4382	33	37	used	use	VERB
ejpam-4382	33	38	these	these	DET
ejpam-4382	33	39	sets	set	NOUN
ejpam-4382	33	40	to	to	PART
ejpam-4382	33	41	obtain	obtain	VERB
ejpam-4382	33	42	certain	certain	ADJ
ejpam-4382	33	43	decompositions	decomposition	NOUN
ejpam-4382	33	44	of	of	ADP
ejpam-4382	33	45	continuity	continuity	NOUN
ejpam-4382	33	46	.	.	PUNCT
ejpam-4382	34	1	hatir	hatir	PROPN
ejpam-4382	34	2	and	and	CCONJ
ejpam-4382	34	3	noiri	noiri	ADV
ejpam-4382	35	1	[	[	X
ejpam-4382	35	2	10	10	NUM
ejpam-4382	35	3	]	]	PUNCT
ejpam-4382	35	4	investigated	investigate	VERB
ejpam-4382	35	5	the	the	DET
ejpam-4382	35	6	further	further	ADJ
ejpam-4382	35	7	properties	property	NOUN
ejpam-4382	35	8	of	of	ADP
ejpam-4382	35	9	semi	semi	ADJ
ejpam-4382	35	10	-	-	ADJ
ejpam-4382	35	11	i	i	PRON
ejpam-4382	35	12	-open	-open	NOUN
ejpam-4382	35	13	sets	set	NOUN
ejpam-4382	35	14	and	and	CCONJ
ejpam-4382	35	15	semi	semi	ADJ
ejpam-4382	35	16	-	-	ADJ
ejpam-4382	35	17	i	i	ADV
ejpam-4382	35	18	-continuous	-continuous	ADJ
ejpam-4382	35	19	functions	function	NOUN
ejpam-4382	35	20	.	.	PUNCT
ejpam-4382	36	1	in	in	ADP
ejpam-4382	36	2	2005	2005	NUM
ejpam-4382	36	3	,	,	PUNCT
ejpam-4382	36	4	açikgöz	açikgöz	PROPN
ejpam-4382	36	5	et	et	NOUN
ejpam-4382	36	6	al	al	PROPN
ejpam-4382	36	7	.	.	PUNCT
ejpam-4382	37	1	[	[	X
ejpam-4382	37	2	1	1	X
ejpam-4382	37	3	]	]	PUNCT
ejpam-4382	37	4	introduced	introduce	VERB
ejpam-4382	37	5	and	and	CCONJ
ejpam-4382	37	6	studied	study	VERB
ejpam-4382	37	7	the	the	DET
ejpam-4382	37	8	notion	notion	NOUN
ejpam-4382	37	9	of	of	ADP
ejpam-4382	37	10	i	i	PRON
ejpam-4382	37	11	-submaximal	-submaximal	ADJ
ejpam-4382	37	12	ideal	ideal	ADJ
ejpam-4382	37	13	topological	topological	ADJ
ejpam-4382	37	14	spaces	space	NOUN
ejpam-4382	37	15	.	.	PUNCT
ejpam-4382	38	1	in	in	ADP
ejpam-4382	38	2	2010	2010	NUM
ejpam-4382	38	3	,	,	PUNCT
ejpam-4382	38	4	ekici	ekici	NOUN
ejpam-4382	38	5	and	and	CCONJ
ejpam-4382	38	6	noiri	noiri	ADV
ejpam-4382	38	7	[	[	X
ejpam-4382	38	8	4	4	X
ejpam-4382	38	9	]	]	PUNCT
ejpam-4382	38	10	investigated	investigate	VERB
ejpam-4382	38	11	several	several	ADJ
ejpam-4382	38	12	characterizations	characterization	NOUN
ejpam-4382	38	13	of	of	ADP
ejpam-4382	38	14	i	i	PRON
ejpam-4382	38	15	-submaximal	-submaximal	ADJ
ejpam-4382	38	16	ideal	ideal	ADJ
ejpam-4382	38	17	topological	topological	ADJ
ejpam-4382	38	18	spaces	space	NOUN
ejpam-4382	38	19	.	.	PUNCT
ejpam-4382	39	1	the	the	DET
ejpam-4382	39	2	purpose	purpose	NOUN
ejpam-4382	39	3	of	of	ADP
ejpam-4382	39	4	the	the	DET
ejpam-4382	39	5	present	present	ADJ
ejpam-4382	39	6	paper	paper	NOUN
ejpam-4382	39	7	is	be	AUX
ejpam-4382	39	8	to	to	PART
ejpam-4382	39	9	introduce	introduce	VERB
ejpam-4382	39	10	the	the	DET
ejpam-4382	39	11	notion	notion	NOUN
ejpam-4382	39	12	semi	semi	ADJ
ejpam-4382	39	13	-	-	ADJ
ejpam-4382	39	14	i	i	PRON
ejpam-4382	39	15	-submaximal	-submaximal	ADJ
ejpam-4382	39	16	ideal	ideal	ADJ
ejpam-4382	39	17	topological	topological	ADJ
ejpam-4382	39	18	spaces	space	NOUN
ejpam-4382	39	19	.	.	PUNCT
ejpam-4382	40	1	moreover	moreover	ADV
ejpam-4382	40	2	,	,	PUNCT
ejpam-4382	40	3	several	several	ADJ
ejpam-4382	40	4	characterizations	characterization	NOUN
ejpam-4382	40	5	of	of	ADP
ejpam-4382	40	6	semi	semi	ADJ
ejpam-4382	40	7	-	-	ADJ
ejpam-4382	40	8	i	i	PRON
ejpam-4382	40	9	-submaximal	-submaximal	ADJ
ejpam-4382	40	10	ideal	ideal	ADJ
ejpam-4382	40	11	topological	topological	ADJ
ejpam-4382	40	12	spaces	space	NOUN
ejpam-4382	40	13	are	be	AUX
ejpam-4382	40	14	investigated	investigate	VERB
ejpam-4382	40	15	.	.	PUNCT
ejpam-4382	41	1	2	2	X
ejpam-4382	41	2	.	.	X
ejpam-4382	41	3	preliminaries	preliminary	NOUN
ejpam-4382	41	4	throughout	throughout	ADP
ejpam-4382	41	5	the	the	DET
ejpam-4382	41	6	present	present	ADJ
ejpam-4382	41	7	paper	paper	NOUN
ejpam-4382	41	8	,	,	PUNCT
ejpam-4382	41	9	spaces	space	NOUN
ejpam-4382	41	10	(	(	PUNCT
ejpam-4382	41	11	x	x	X
ejpam-4382	41	12	,	,	PUNCT
ejpam-4382	41	13	τ	τ	X
ejpam-4382	41	14	)	)	PUNCT
ejpam-4382	41	15	and	and	CCONJ
ejpam-4382	41	16	(	(	PUNCT
ejpam-4382	41	17	y	y	PROPN
ejpam-4382	41	18	,	,	PUNCT
ejpam-4382	41	19	σ	σ	PROPN
ejpam-4382	41	20	)	)	PUNCT
ejpam-4382	41	21	(	(	PUNCT
ejpam-4382	41	22	or	or	CCONJ
ejpam-4382	41	23	simply	simply	ADV
ejpam-4382	41	24	x	x	X
ejpam-4382	41	25	and	and	CCONJ
ejpam-4382	41	26	y	y	PROPN
ejpam-4382	41	27	)	)	PUNCT
ejpam-4382	41	28	always	always	ADV
ejpam-4382	41	29	mean	mean	VERB
ejpam-4382	41	30	topological	topological	ADJ
ejpam-4382	41	31	spaces	space	NOUN
ejpam-4382	41	32	on	on	ADP
ejpam-4382	41	33	which	which	PRON
ejpam-4382	41	34	no	no	DET
ejpam-4382	41	35	separation	separation	NOUN
ejpam-4382	41	36	axioms	axiom	NOUN
ejpam-4382	41	37	are	be	AUX
ejpam-4382	41	38	assumed	assume	VERB
ejpam-4382	41	39	unless	unless	SCONJ
ejpam-4382	41	40	explicitly	explicitly	ADV
ejpam-4382	41	41	stated	state	VERB
ejpam-4382	41	42	.	.	PUNCT
ejpam-4382	42	1	let	let	VERB
ejpam-4382	42	2	a	a	DET
ejpam-4382	42	3	be	be	AUX
ejpam-4382	42	4	a	a	DET
ejpam-4382	42	5	subset	subset	NOUN
ejpam-4382	42	6	of	of	ADP
ejpam-4382	42	7	a	a	DET
ejpam-4382	42	8	topological	topological	ADJ
ejpam-4382	42	9	space	space	NOUN
ejpam-4382	42	10	(	(	PUNCT
ejpam-4382	42	11	x	x	X
ejpam-4382	42	12	,	,	PUNCT
ejpam-4382	42	13	τ	τ	PROPN
ejpam-4382	42	14	)	)	PUNCT
ejpam-4382	42	15	.	.	PUNCT
ejpam-4382	43	1	the	the	DET
ejpam-4382	43	2	closure	closure	NOUN
ejpam-4382	43	3	of	of	ADP
ejpam-4382	43	4	a	a	PRON
ejpam-4382	43	5	and	and	CCONJ
ejpam-4382	43	6	the	the	DET
ejpam-4382	43	7	interior	interior	NOUN
ejpam-4382	43	8	of	of	ADP
ejpam-4382	43	9	a	a	PRON
ejpam-4382	43	10	are	be	AUX
ejpam-4382	43	11	denoted	denote	VERB
ejpam-4382	43	12	by	by	ADP
ejpam-4382	43	13	cl(a	cl(a	NOUN
ejpam-4382	43	14	)	)	PUNCT
ejpam-4382	43	15	and	and	CCONJ
ejpam-4382	43	16	int(a	int(a	PROPN
ejpam-4382	43	17	)	)	PUNCT
ejpam-4382	43	18	,	,	PUNCT
ejpam-4382	43	19	respectively	respectively	ADV
ejpam-4382	43	20	.	.	PUNCT
ejpam-4382	44	1	a	a	DET
ejpam-4382	44	2	nonempty	nonempty	ADJ
ejpam-4382	44	3	collection	collection	NOUN
ejpam-4382	44	4	i	i	PRON
ejpam-4382	44	5	of	of	ADP
ejpam-4382	44	6	subsets	subset	NOUN
ejpam-4382	44	7	of	of	ADP
ejpam-4382	44	8	a	a	DET
ejpam-4382	44	9	set	set	NOUN
ejpam-4382	44	10	x	x	PUNCT
ejpam-4382	44	11	is	be	AUX
ejpam-4382	44	12	called	call	VERB
ejpam-4382	44	13	an	an	DET
ejpam-4382	44	14	ideal	ideal	NOUN
ejpam-4382	44	15	on	on	ADP
ejpam-4382	44	16	x	x	SYM
ejpam-4382	44	17	if	if	SCONJ
ejpam-4382	44	18	i	i	PRON
ejpam-4382	44	19	satisfies	satisfy	VERB
ejpam-4382	44	20	the	the	DET
ejpam-4382	44	21	following	follow	VERB
ejpam-4382	44	22	two	two	NUM
ejpam-4382	44	23	properties	property	NOUN
ejpam-4382	44	24	:	:	PUNCT
ejpam-4382	44	25	(	(	PUNCT
ejpam-4382	44	26	i	i	NOUN
ejpam-4382	44	27	)	)	PUNCT
ejpam-4382	45	1	a	a	PRON
ejpam-4382	45	2	∈	∈	NOUN
ejpam-4382	46	1	i	i	PRON
ejpam-4382	46	2	and	and	CCONJ
ejpam-4382	46	3	b	b	X
ejpam-4382	46	4	⊆	⊆	NUM
ejpam-4382	46	5	a	a	DET
ejpam-4382	46	6	⇒	⇒	NOUN
ejpam-4382	46	7	b	b	X
ejpam-4382	46	8	∈	∈	PROPN
ejpam-4382	47	1	i	i	PRON
ejpam-4382	47	2	;	;	PUNCT
ejpam-4382	47	3	(	(	PUNCT
ejpam-4382	47	4	ii	ii	NOUN
ejpam-4382	47	5	)	)	PUNCT
ejpam-4382	47	6	a	a	PRON
ejpam-4382	47	7	∈	∈	PROPN
ejpam-4382	48	1	i	i	PRON
ejpam-4382	48	2	and	and	CCONJ
ejpam-4382	48	3	b	b	X
ejpam-4382	48	4	∈	∈	PROPN
ejpam-4382	48	5	i	i	PRON
ejpam-4382	48	6	⇒	⇒	VERB
ejpam-4382	48	7	a	a	DET
ejpam-4382	48	8	∪	∪	X
ejpam-4382	48	9	b	b	NOUN
ejpam-4382	48	10	∈	∈	NOUN
ejpam-4382	48	11	i	i	PRON
ejpam-4382	48	12	.	.	PUNCT
ejpam-4382	49	1	for	for	ADP
ejpam-4382	49	2	a	a	DET
ejpam-4382	49	3	topological	topological	ADJ
ejpam-4382	49	4	space	space	NOUN
ejpam-4382	49	5	(	(	PUNCT
ejpam-4382	49	6	x	x	X
ejpam-4382	49	7	,	,	PUNCT
ejpam-4382	49	8	τ	τ	X
ejpam-4382	49	9	)	)	PUNCT
ejpam-4382	49	10	with	with	ADP
ejpam-4382	49	11	an	an	DET
ejpam-4382	49	12	ideal	ideal	ADJ
ejpam-4382	49	13	i	i	PRON
ejpam-4382	49	14	on	on	ADP
ejpam-4382	49	15	x	x	NOUN
ejpam-4382	49	16	,	,	PUNCT
ejpam-4382	49	17	a	a	DET
ejpam-4382	49	18	set	set	NOUN
ejpam-4382	49	19	operator	operator	NOUN
ejpam-4382	49	20	(	(	PUNCT
ejpam-4382	49	21	.)⋆	.)⋆	NOUN
ejpam-4382	49	22	:	:	PUNCT
ejpam-4382	49	23	p(x	p(x	PROPN
ejpam-4382	49	24	)	)	PUNCT
ejpam-4382	49	25	→	→	SYM
ejpam-4382	49	26	p(x	p(x	PROPN
ejpam-4382	49	27	)	)	PUNCT
ejpam-4382	49	28	where	where	SCONJ
ejpam-4382	49	29	p(x	p(x	NOUN
ejpam-4382	49	30	)	)	PUNCT
ejpam-4382	49	31	is	be	AUX
ejpam-4382	49	32	the	the	DET
ejpam-4382	49	33	set	set	NOUN
ejpam-4382	49	34	of	of	ADP
ejpam-4382	49	35	all	all	DET
ejpam-4382	49	36	subsets	subset	NOUN
ejpam-4382	49	37	of	of	ADP
ejpam-4382	49	38	x	x	PRON
ejpam-4382	49	39	,	,	PUNCT
ejpam-4382	49	40	called	call	VERB
ejpam-4382	49	41	a	a	DET
ejpam-4382	49	42	local	local	ADJ
ejpam-4382	49	43	function	function	NOUN
ejpam-4382	49	44	[	[	X
ejpam-4382	49	45	16	16	NUM
ejpam-4382	49	46	]	]	PUNCT
ejpam-4382	49	47	of	of	ADP
ejpam-4382	49	48	a	a	PRON
ejpam-4382	49	49	with	with	ADP
ejpam-4382	49	50	respect	respect	NOUN
ejpam-4382	49	51	to	to	ADP
ejpam-4382	49	52	i	i	PRON
ejpam-4382	49	53	and	and	CCONJ
ejpam-4382	49	54	τ	τ	PROPN
ejpam-4382	49	55	is	be	AUX
ejpam-4382	49	56	defined	define	VERB
ejpam-4382	49	57	as	as	SCONJ
ejpam-4382	49	58	follows	follow	VERB
ejpam-4382	49	59	:	:	PUNCT
ejpam-4382	49	60	for	for	ADP
ejpam-4382	49	61	a	a	DET
ejpam-4382	49	62	⊆	⊆	NUM
ejpam-4382	49	63	x	x	SYM
ejpam-4382	49	64	,	,	PUNCT
ejpam-4382	49	65	a⋆(i	a⋆(i	NOUN
ejpam-4382	49	66	,	,	PUNCT
ejpam-4382	49	67	τ	τ	X
ejpam-4382	49	68	)	)	PUNCT
ejpam-4382	49	69	=	=	PRON
ejpam-4382	49	70	{	{	PUNCT
ejpam-4382	49	71	x	x	PUNCT
ejpam-4382	49	72	∈	∈	NOUN
ejpam-4382	49	73	x	x	INTJ
ejpam-4382	49	74	|	|	ADV
ejpam-4382	49	75	g	g	PROPN
ejpam-4382	49	76	∩	∩	VERB
ejpam-4382	49	77	a	a	DET
ejpam-4382	49	78	̸∈	̸∈	PROPN
ejpam-4382	49	79	i	i	PROPN
ejpam-4382	49	80	for	for	ADP
ejpam-4382	49	81	every	every	DET
ejpam-4382	49	82	g	g	PROPN
ejpam-4382	49	83	∈	∈	PROPN
ejpam-4382	49	84	τ(x	τ(x	NOUN
ejpam-4382	49	85	)	)	PUNCT
ejpam-4382	49	86	}	}	PUNCT
ejpam-4382	49	87	where	where	SCONJ
ejpam-4382	49	88	τ(x	τ(x	NOUN
ejpam-4382	49	89	)	)	PUNCT
ejpam-4382	49	90	=	=	PRON
ejpam-4382	49	91	{	{	PUNCT
ejpam-4382	49	92	g	g	PROPN
ejpam-4382	49	93	∈	∈	PROPN
ejpam-4382	49	94	τ	τ	X
ejpam-4382	49	95	|	|	ADV
ejpam-4382	49	96	x	x	X
ejpam-4382	49	97	∈	∈	PROPN
ejpam-4382	49	98	g	g	NOUN
ejpam-4382	49	99	}	}	PUNCT
ejpam-4382	49	100	.	.	PUNCT
ejpam-4382	50	1	a	a	DET
ejpam-4382	50	2	kuratowski	kuratowski	ADJ
ejpam-4382	50	3	closure	closure	NOUN
ejpam-4382	50	4	operator	operator	NOUN
ejpam-4382	50	5	cl⋆	cl⋆	PROPN
ejpam-4382	50	6	(	(	PUNCT
ejpam-4382	50	7	.	.	PUNCT
ejpam-4382	50	8	)	)	PUNCT
ejpam-4382	50	9	for	for	ADP
ejpam-4382	50	10	a	a	DET
ejpam-4382	50	11	topology	topology	NOUN
ejpam-4382	50	12	τ⋆(i	τ⋆(i	NOUN
ejpam-4382	50	13	,	,	PUNCT
ejpam-4382	50	14	τ	τ	PROPN
ejpam-4382	50	15	)	)	PUNCT
ejpam-4382	50	16	,	,	PUNCT
ejpam-4382	50	17	called	call	VERB
ejpam-4382	50	18	the	the	DET
ejpam-4382	50	19	⋆-topology	⋆-topology	NOUN
ejpam-4382	50	20	and	and	CCONJ
ejpam-4382	50	21	finer	fine	ADJ
ejpam-4382	50	22	than	than	ADP
ejpam-4382	50	23	τ	τ	PROPN
ejpam-4382	50	24	,	,	PUNCT
ejpam-4382	50	25	is	be	AUX
ejpam-4382	50	26	defined	define	VERB
ejpam-4382	50	27	by	by	ADP
ejpam-4382	50	28	cl⋆(a	cl⋆(a	NOUN
ejpam-4382	50	29	)	)	PUNCT
ejpam-4382	50	30	=	=	NOUN
ejpam-4382	50	31	a	a	DET
ejpam-4382	50	32	∪	∪	NOUN
ejpam-4382	50	33	a⋆	a⋆	NOUN
ejpam-4382	51	1	[	[	X
ejpam-4382	51	2	13	13	NUM
ejpam-4382	51	3	]	]	PUNCT
ejpam-4382	51	4	.	.	PUNCT
ejpam-4382	52	1	we	we	PRON
ejpam-4382	52	2	shall	shall	AUX
ejpam-4382	52	3	simply	simply	ADV
ejpam-4382	52	4	write	write	VERB
ejpam-4382	52	5	a⋆	a⋆	ADV
ejpam-4382	52	6	for	for	ADP
ejpam-4382	52	7	a⋆(i	a⋆(i	PROPN
ejpam-4382	52	8	,	,	PUNCT
ejpam-4382	52	9	τ	τ	PROPN
ejpam-4382	52	10	)	)	PUNCT
ejpam-4382	52	11	and	and	CCONJ
ejpam-4382	52	12	τ⋆	τ⋆	X
ejpam-4382	52	13	for	for	ADP
ejpam-4382	52	14	τ⋆(i	τ⋆(i	NOUN
ejpam-4382	52	15	,	,	PUNCT
ejpam-4382	52	16	τ	τ	PROPN
ejpam-4382	52	17	)	)	PUNCT
ejpam-4382	52	18	.	.	PUNCT
ejpam-4382	53	1	a	a	DET
ejpam-4382	53	2	basis	basis	NOUN
ejpam-4382	53	3	b(i	b(i	ADJ
ejpam-4382	53	4	,	,	PUNCT
ejpam-4382	53	5	τ	τ	X
ejpam-4382	53	6	)	)	PUNCT
ejpam-4382	53	7	for	for	ADP
ejpam-4382	53	8	τ⋆	τ⋆	PRON
ejpam-4382	53	9	can	can	AUX
ejpam-4382	53	10	be	be	AUX
ejpam-4382	53	11	described	describe	VERB
ejpam-4382	53	12	as	as	ADP
ejpam-4382	53	13	follows	follow	VERB
ejpam-4382	53	14	:	:	PUNCT
ejpam-4382	53	15	b(i	b(i	NUM
ejpam-4382	53	16	,	,	PUNCT
ejpam-4382	53	17	τ	τ	X
ejpam-4382	53	18	)	)	PUNCT
ejpam-4382	53	19	=	=	PRON
ejpam-4382	54	1	{	{	PUNCT
ejpam-4382	54	2	v	v	NOUN
ejpam-4382	54	3	−	−	NOUN
ejpam-4382	55	1	i	i	PRON
ejpam-4382	55	2	′	′	VERB
ejpam-4382	56	1	|	|	ADV
ejpam-4382	56	2	v	v	X
ejpam-4382	56	3	∈	∈	NOUN
ejpam-4382	56	4	τ	τ	X
ejpam-4382	57	1	and	and	CCONJ
ejpam-4382	57	2	i	i	PRON
ejpam-4382	57	3	′	′	VERB
ejpam-4382	58	1	∈	∈	INTJ
ejpam-4382	59	1	i	i	PRON
ejpam-4382	59	2	}	}	PUNCT
ejpam-4382	59	3	.	.	PUNCT
ejpam-4382	60	1	however	however	ADV
ejpam-4382	60	2	,	,	PUNCT
ejpam-4382	60	3	b(i	b(i	PROPN
ejpam-4382	60	4	,	,	PUNCT
ejpam-4382	60	5	τ	τ	X
ejpam-4382	60	6	)	)	PUNCT
ejpam-4382	60	7	is	be	AUX
ejpam-4382	60	8	not	not	PART
ejpam-4382	60	9	always	always	ADV
ejpam-4382	60	10	a	a	DET
ejpam-4382	60	11	topology	topology	NOUN
ejpam-4382	60	12	[	[	X
ejpam-4382	60	13	13	13	NUM
ejpam-4382	60	14	]	]	PUNCT
ejpam-4382	60	15	.	.	PUNCT
ejpam-4382	61	1	a	a	DET
ejpam-4382	61	2	subset	subset	NOUN
ejpam-4382	61	3	a	a	PRON
ejpam-4382	61	4	of	of	ADP
ejpam-4382	61	5	an	an	DET
ejpam-4382	61	6	ideal	ideal	ADJ
ejpam-4382	61	7	topological	topological	ADJ
ejpam-4382	61	8	space	space	NOUN
ejpam-4382	61	9	(	(	PUNCT
ejpam-4382	61	10	x	x	X
ejpam-4382	61	11	,	,	PUNCT
ejpam-4382	61	12	τ	τ	PROPN
ejpam-4382	61	13	,	,	PUNCT
ejpam-4382	61	14	i	i	PROPN
ejpam-4382	61	15	)	)	PUNCT
ejpam-4382	61	16	is	be	AUX
ejpam-4382	61	17	called	call	VERB
ejpam-4382	61	18	⋆-closed	⋆-closed	ADJ
ejpam-4382	61	19	(	(	PUNCT
ejpam-4382	61	20	τ⋆-closed	τ⋆-closed	ADJ
ejpam-4382	61	21	)	)	PUNCT
ejpam-4382	62	1	[	[	X
ejpam-4382	62	2	13	13	NUM
ejpam-4382	62	3	]	]	X
ejpam-4382	62	4	if	if	SCONJ
ejpam-4382	62	5	a⋆	a⋆	ADJ
ejpam-4382	62	6	⊆	⊆	NUM
ejpam-4382	62	7	a.	a.	NOUN
ejpam-4382	62	8	the	the	DET
ejpam-4382	62	9	interior	interior	NOUN
ejpam-4382	62	10	of	of	ADP
ejpam-4382	62	11	a	a	DET
ejpam-4382	62	12	subset	subset	NOUN
ejpam-4382	62	13	a	a	DET
ejpam-4382	62	14	in	in	ADP
ejpam-4382	62	15	(	(	PUNCT
ejpam-4382	62	16	x	x	X
ejpam-4382	62	17	,	,	PUNCT
ejpam-4382	62	18	τ⋆(i	τ⋆(i	NOUN
ejpam-4382	62	19	,	,	PUNCT
ejpam-4382	62	20	τ	τ	PROPN
ejpam-4382	62	21	)	)	PUNCT
ejpam-4382	62	22	)	)	PUNCT
ejpam-4382	62	23	is	be	AUX
ejpam-4382	62	24	denoted	denote	VERB
ejpam-4382	62	25	by	by	ADP
ejpam-4382	62	26	int⋆(a	int⋆(a	NOUN
ejpam-4382	62	27	)	)	PUNCT
ejpam-4382	62	28	.	.	PUNCT
ejpam-4382	63	1	a	a	DET
ejpam-4382	63	2	subset	subset	NOUN
ejpam-4382	63	3	a	a	PRON
ejpam-4382	63	4	of	of	ADP
ejpam-4382	63	5	an	an	DET
ejpam-4382	63	6	ideal	ideal	ADJ
ejpam-4382	63	7	topological	topological	ADJ
ejpam-4382	63	8	space	space	NOUN
ejpam-4382	63	9	(	(	PUNCT
ejpam-4382	63	10	x	x	X
ejpam-4382	63	11	,	,	PUNCT
ejpam-4382	63	12	τ	τ	PROPN
ejpam-4382	63	13	,	,	PUNCT
ejpam-4382	63	14	i	i	PROPN
ejpam-4382	63	15	)	)	PUNCT
ejpam-4382	63	16	is	be	AUX
ejpam-4382	63	17	said	say	VERB
ejpam-4382	63	18	to	to	PART
ejpam-4382	63	19	be	be	AUX
ejpam-4382	63	20	semi	semi	ADJ
ejpam-4382	63	21	-	-	ADJ
ejpam-4382	63	22	i	i	PRON
ejpam-4382	63	23	-open	-open	NOUN
ejpam-4382	64	1	[	[	X
ejpam-4382	64	2	9	9	NUM
ejpam-4382	64	3	]	]	X
ejpam-4382	64	4	if	if	SCONJ
ejpam-4382	64	5	a	a	DET
ejpam-4382	64	6	⊆	⊆	NUM
ejpam-4382	64	7	cl⋆(int(a	cl⋆(int(a	PROPN
ejpam-4382	64	8	)	)	PUNCT
ejpam-4382	64	9	)	)	PUNCT
ejpam-4382	64	10	.	.	PUNCT
ejpam-4382	65	1	the	the	DET
ejpam-4382	65	2	complement	complement	NOUN
ejpam-4382	65	3	of	of	ADP
ejpam-4382	65	4	a	a	DET
ejpam-4382	65	5	semi	semi	ADJ
ejpam-4382	65	6	-	-	ADJ
ejpam-4382	65	7	i	i	PRON
ejpam-4382	65	8	-open	-open	ADJ
ejpam-4382	65	9	set	set	VERB
ejpam-4382	65	10	is	be	AUX
ejpam-4382	65	11	called	call	VERB
ejpam-4382	65	12	semi	semi	ADJ
ejpam-4382	65	13	-	-	ADJ
ejpam-4382	65	14	i	i	ADV
ejpam-4382	65	15	-closed	-closed	ADJ
ejpam-4382	65	16	.	.	PUNCT
ejpam-4382	66	1	by	by	ADP
ejpam-4382	66	2	sio(x	sio(x	PROPN
ejpam-4382	66	3	,	,	PUNCT
ejpam-4382	66	4	τ	τ	PROPN
ejpam-4382	66	5	)	)	PUNCT
ejpam-4382	66	6	,	,	PUNCT
ejpam-4382	66	7	we	we	PRON
ejpam-4382	66	8	denote	denote	VERB
ejpam-4382	66	9	the	the	DET
ejpam-4382	66	10	family	family	NOUN
ejpam-4382	66	11	of	of	ADP
ejpam-4382	66	12	all	all	DET
ejpam-4382	66	13	semi	semi	ADJ
ejpam-4382	66	14	-	-	ADJ
ejpam-4382	66	15	i	i	PRON
ejpam-4382	66	16	-open	-open	ADJ
ejpam-4382	66	17	sets	set	NOUN
ejpam-4382	66	18	of	of	ADP
ejpam-4382	66	19	an	an	DET
ejpam-4382	66	20	ideal	ideal	ADJ
ejpam-4382	66	21	topological	topological	ADJ
ejpam-4382	66	22	space	space	NOUN
ejpam-4382	66	23	(	(	PUNCT
ejpam-4382	66	24	x	x	X
ejpam-4382	66	25	,	,	PUNCT
ejpam-4382	66	26	τ	τ	PROPN
ejpam-4382	66	27	,	,	PUNCT
ejpam-4382	66	28	i	i	NOUN
ejpam-4382	66	29	)	)	PUNCT
ejpam-4382	66	30	.	.	PUNCT
ejpam-4382	67	1	for	for	ADP
ejpam-4382	67	2	a	a	DET
ejpam-4382	67	3	subset	subset	NOUN
ejpam-4382	67	4	a	a	PRON
ejpam-4382	67	5	of	of	ADP
ejpam-4382	67	6	an	an	DET
ejpam-4382	67	7	ideal	ideal	ADJ
ejpam-4382	67	8	topological	topological	ADJ
ejpam-4382	67	9	space	space	NOUN
ejpam-4382	67	10	(	(	PUNCT
ejpam-4382	67	11	x	x	X
ejpam-4382	67	12	,	,	PUNCT
ejpam-4382	67	13	τ	τ	PROPN
ejpam-4382	67	14	,	,	PUNCT
ejpam-4382	67	15	i	i	NOUN
ejpam-4382	67	16	)	)	PUNCT
ejpam-4382	67	17	,	,	PUNCT
ejpam-4382	67	18	the	the	DET
ejpam-4382	67	19	intersection	intersection	NOUN
ejpam-4382	67	20	of	of	ADP
ejpam-4382	67	21	all	all	DET
ejpam-4382	67	22	semi	semi	ADJ
ejpam-4382	67	23	-	-	ADJ
ejpam-4382	67	24	i	i	PRON
ejpam-4382	67	25	-open	-open	NOUN
ejpam-4382	67	26	sets	set	NOUN
ejpam-4382	67	27	containing	contain	VERB
ejpam-4382	67	28	a	a	PRON
ejpam-4382	67	29	is	be	AUX
ejpam-4382	67	30	called	call	VERB
ejpam-4382	67	31	the	the	DET
ejpam-4382	67	32	semi	semi	ADJ
ejpam-4382	67	33	-	-	ADJ
ejpam-4382	67	34	i	i	ADJ
ejpam-4382	67	35	-closure	-closure	NOUN
ejpam-4382	67	36	[	[	X
ejpam-4382	67	37	5	5	NUM
ejpam-4382	67	38	]	]	PUNCT
ejpam-4382	67	39	of	of	ADP
ejpam-4382	67	40	a	a	PRON
ejpam-4382	67	41	and	and	CCONJ
ejpam-4382	67	42	denoted	denote	VERB
ejpam-4382	67	43	by	by	ADP
ejpam-4382	67	44	scli	scli	NOUN
ejpam-4382	67	45	(	(	PUNCT
ejpam-4382	67	46	a	a	NOUN
ejpam-4382	67	47	)	)	PUNCT
ejpam-4382	67	48	.	.	PUNCT
ejpam-4382	68	1	the	the	DET
ejpam-4382	68	2	semi	semi	ADJ
ejpam-4382	68	3	-	-	ADJ
ejpam-4382	68	4	i	i	PRON
ejpam-4382	68	5	-interior	-interior	NOUN
ejpam-4382	69	1	[	[	X
ejpam-4382	69	2	5	5	NUM
ejpam-4382	69	3	]	]	PUNCT
ejpam-4382	69	4	,	,	PUNCT
ejpam-4382	69	5	denoted	denote	VERB
ejpam-4382	69	6	by	by	ADP
ejpam-4382	69	7	sinti	sinti	PROPN
ejpam-4382	69	8	(	(	PUNCT
ejpam-4382	69	9	a	a	NOUN
ejpam-4382	69	10	)	)	PUNCT
ejpam-4382	69	11	,	,	PUNCT
ejpam-4382	69	12	is	be	AUX
ejpam-4382	69	13	defined	define	VERB
ejpam-4382	69	14	by	by	ADP
ejpam-4382	69	15	the	the	DET
ejpam-4382	69	16	union	union	NOUN
ejpam-4382	69	17	of	of	ADP
ejpam-4382	69	18	all	all	DET
ejpam-4382	69	19	semi	semi	ADJ
ejpam-4382	69	20	-	-	ADJ
ejpam-4382	69	21	i	i	PRON
ejpam-4382	69	22	-open	-open	ADJ
ejpam-4382	69	23	sets	set	NOUN
ejpam-4382	69	24	of	of	ADP
ejpam-4382	69	25	x	x	PUNCT
ejpam-4382	69	26	contained	contain	VERB
ejpam-4382	69	27	in	in	ADP
ejpam-4382	69	28	a.	a.	PROPN
ejpam-4382	69	29	lemma	lemma	PROPN
ejpam-4382	69	30	1	1	NUM
ejpam-4382	69	31	.	.	PUNCT
ejpam-4382	70	1	for	for	ADP
ejpam-4382	70	2	a	a	DET
ejpam-4382	70	3	subset	subset	NOUN
ejpam-4382	70	4	a	a	PRON
ejpam-4382	70	5	of	of	ADP
ejpam-4382	70	6	an	an	DET
ejpam-4382	70	7	ideal	ideal	ADJ
ejpam-4382	70	8	topological	topological	ADJ
ejpam-4382	70	9	space	space	NOUN
ejpam-4382	70	10	(	(	PUNCT
ejpam-4382	70	11	x	x	X
ejpam-4382	70	12	,	,	PUNCT
ejpam-4382	70	13	τ	τ	PROPN
ejpam-4382	70	14	,	,	PUNCT
ejpam-4382	70	15	i	i	NOUN
ejpam-4382	70	16	)	)	PUNCT
ejpam-4382	70	17	,	,	PUNCT
ejpam-4382	70	18	the	the	DET
ejpam-4382	70	19	following	follow	VERB
ejpam-4382	70	20	properties	property	NOUN
ejpam-4382	70	21	hold	hold	VERB
ejpam-4382	70	22	:	:	PUNCT
ejpam-4382	70	23	(	(	PUNCT
ejpam-4382	70	24	1	1	X
ejpam-4382	70	25	)	)	PUNCT
ejpam-4382	70	26	sinti	sinti	NOUN
ejpam-4382	70	27	(	(	PUNCT
ejpam-4382	70	28	a	a	NOUN
ejpam-4382	70	29	)	)	PUNCT
ejpam-4382	70	30	is	be	AUX
ejpam-4382	70	31	semi	semi	ADJ
ejpam-4382	70	32	-	-	ADJ
ejpam-4382	70	33	i	i	PRON
ejpam-4382	70	34	-open	-open	ADJ
ejpam-4382	70	35	;	;	PUNCT
ejpam-4382	70	36	(	(	PUNCT
ejpam-4382	70	37	2	2	X
ejpam-4382	70	38	)	)	PUNCT
ejpam-4382	70	39	scli	scli	NOUN
ejpam-4382	70	40	(	(	PUNCT
ejpam-4382	70	41	a	a	NOUN
ejpam-4382	70	42	)	)	PUNCT
ejpam-4382	70	43	is	be	AUX
ejpam-4382	70	44	semi	semi	ADJ
ejpam-4382	70	45	-	-	ADJ
ejpam-4382	70	46	i	i	PRON
ejpam-4382	70	47	-closed	-close	VERB
ejpam-4382	70	48	;	;	PUNCT
ejpam-4382	70	49	c.	c.	PROPN
ejpam-4382	70	50	boonpok	boonpok	PROPN
ejpam-4382	70	51	/	/	SYM
ejpam-4382	70	52	eur	eur	PROPN
ejpam-4382	70	53	.	.	PUNCT
ejpam-4382	71	1	j.	j.	PROPN
ejpam-4382	71	2	pure	pure	PROPN
ejpam-4382	71	3	appl	appl	PROPN
ejpam-4382	71	4	.	.	PROPN
ejpam-4382	71	5	math	math	PROPN
ejpam-4382	71	6	,	,	PUNCT
ejpam-4382	71	7	15	15	NUM
ejpam-4382	71	8	(	(	PUNCT
ejpam-4382	71	9	3	3	NUM
ejpam-4382	71	10	)	)	PUNCT
ejpam-4382	71	11	(	(	PUNCT
ejpam-4382	71	12	2022	2022	NUM
ejpam-4382	71	13	)	)	PUNCT
ejpam-4382	71	14	,	,	PUNCT
ejpam-4382	71	15	938	938	NUM
ejpam-4382	71	16	-	-	SYM
ejpam-4382	71	17	947	947	NUM
ejpam-4382	71	18	940	940	NUM
ejpam-4382	71	19	(	(	PUNCT
ejpam-4382	71	20	3	3	NUM
ejpam-4382	71	21	)	)	PUNCT
ejpam-4382	71	22	a	a	PRON
ejpam-4382	71	23	is	be	AUX
ejpam-4382	71	24	semi	semi	ADJ
ejpam-4382	71	25	-	-	ADJ
ejpam-4382	71	26	i	i	PRON
ejpam-4382	71	27	-open	-open	ADJ
ejpam-4382	71	28	if	if	SCONJ
ejpam-4382	72	1	and	and	CCONJ
ejpam-4382	72	2	only	only	ADV
ejpam-4382	72	3	if	if	SCONJ
ejpam-4382	72	4	a	a	DET
ejpam-4382	72	5	=	=	PUNCT
ejpam-4382	72	6	sinti	sinti	X
ejpam-4382	72	7	(	(	PUNCT
ejpam-4382	72	8	a	a	NOUN
ejpam-4382	72	9	)	)	PUNCT
ejpam-4382	72	10	;	;	PUNCT
ejpam-4382	72	11	(	(	PUNCT
ejpam-4382	72	12	4	4	X
ejpam-4382	72	13	)	)	PUNCT
ejpam-4382	72	14	a	a	PRON
ejpam-4382	72	15	is	be	AUX
ejpam-4382	72	16	semi	semi	ADJ
ejpam-4382	72	17	-	-	ADJ
ejpam-4382	72	18	i	i	PRON
ejpam-4382	72	19	-closed	-close	VERB
ejpam-4382	73	1	if	if	SCONJ
ejpam-4382	73	2	and	and	CCONJ
ejpam-4382	73	3	only	only	ADV
ejpam-4382	73	4	if	if	SCONJ
ejpam-4382	73	5	a	a	DET
ejpam-4382	73	6	=	=	X
ejpam-4382	73	7	scli	scli	NOUN
ejpam-4382	73	8	(	(	PUNCT
ejpam-4382	73	9	a	a	NOUN
ejpam-4382	73	10	)	)	PUNCT
ejpam-4382	73	11	;	;	PUNCT
ejpam-4382	73	12	(	(	PUNCT
ejpam-4382	73	13	5	5	X
ejpam-4382	73	14	)	)	PUNCT
ejpam-4382	73	15	x	x	SYM
ejpam-4382	73	16	∈	∈	PROPN
ejpam-4382	73	17	scli	scli	NOUN
ejpam-4382	73	18	(	(	PUNCT
ejpam-4382	73	19	a	a	X
ejpam-4382	73	20	)	)	PUNCT
ejpam-4382	73	21	if	if	SCONJ
ejpam-4382	74	1	and	and	CCONJ
ejpam-4382	74	2	only	only	ADV
ejpam-4382	74	3	if	if	SCONJ
ejpam-4382	74	4	u	u	PROPN
ejpam-4382	74	5	∩a	∩a	PROPN
ejpam-4382	74	6	̸=	̸=	PROPN
ejpam-4382	74	7	∅	∅	NOUN
ejpam-4382	74	8	for	for	ADP
ejpam-4382	74	9	every	every	DET
ejpam-4382	74	10	semi	semi	ADJ
ejpam-4382	74	11	-	-	ADJ
ejpam-4382	74	12	i	i	PRON
ejpam-4382	74	13	-open	-open	NOUN
ejpam-4382	74	14	set	set	VERB
ejpam-4382	74	15	u	u	NOUN
ejpam-4382	74	16	containing	contain	VERB
ejpam-4382	74	17	x	x	PRON
ejpam-4382	74	18	;	;	PUNCT
ejpam-4382	74	19	(	(	PUNCT
ejpam-4382	74	20	6	6	NUM
ejpam-4382	74	21	)	)	PUNCT
ejpam-4382	74	22	x	x	PUNCT
ejpam-4382	75	1	−	−	PROPN
ejpam-4382	75	2	scli	scli	NOUN
ejpam-4382	75	3	(	(	PUNCT
ejpam-4382	75	4	a	a	X
ejpam-4382	75	5	)	)	PUNCT
ejpam-4382	75	6	=	=	SYM
ejpam-4382	75	7	sinti	sinti	NOUN
ejpam-4382	75	8	(	(	PUNCT
ejpam-4382	75	9	x	x	NOUN
ejpam-4382	75	10	−a	−a	NOUN
ejpam-4382	75	11	)	)	PUNCT
ejpam-4382	75	12	;	;	PUNCT
ejpam-4382	75	13	(	(	PUNCT
ejpam-4382	75	14	7	7	X
ejpam-4382	75	15	)	)	PUNCT
ejpam-4382	75	16	x	x	PUNCT
ejpam-4382	75	17	−	−	PROPN
ejpam-4382	75	18	sinti	sinti	X
ejpam-4382	75	19	(	(	PUNCT
ejpam-4382	75	20	a	a	NOUN
ejpam-4382	75	21	)	)	PUNCT
ejpam-4382	75	22	=	=	SYM
ejpam-4382	75	23	scli	scli	NOUN
ejpam-4382	75	24	(	(	PUNCT
ejpam-4382	75	25	x	x	NOUN
ejpam-4382	75	26	−a	−a	NOUN
ejpam-4382	75	27	)	)	PUNCT
ejpam-4382	75	28	.	.	PUNCT
ejpam-4382	76	1	proof	proof	NOUN
ejpam-4382	76	2	.	.	PUNCT
ejpam-4382	77	1	(	(	PUNCT
ejpam-4382	77	2	1	1	X
ejpam-4382	77	3	)	)	PUNCT
ejpam-4382	77	4	and	and	CCONJ
ejpam-4382	77	5	(	(	PUNCT
ejpam-4382	77	6	2	2	X
ejpam-4382	77	7	)	)	PUNCT
ejpam-4382	77	8	follows	follow	VERB
ejpam-4382	77	9	from	from	ADP
ejpam-4382	77	10	theorem	theorem	ADJ
ejpam-4382	77	11	3.4	3.4	NUM
ejpam-4382	77	12	of	of	ADP
ejpam-4382	77	13	[	[	X
ejpam-4382	77	14	10	10	NUM
ejpam-4382	77	15	]	]	PUNCT
ejpam-4382	77	16	.	.	PUNCT
ejpam-4382	78	1	(	(	PUNCT
ejpam-4382	78	2	3	3	X
ejpam-4382	78	3	)	)	PUNCT
ejpam-4382	78	4	and	and	CCONJ
ejpam-4382	78	5	(	(	PUNCT
ejpam-4382	78	6	4	4	X
ejpam-4382	78	7	)	)	PUNCT
ejpam-4382	78	8	follows	follow	VERB
ejpam-4382	78	9	from	from	ADP
ejpam-4382	78	10	(	(	PUNCT
ejpam-4382	78	11	1	1	NUM
ejpam-4382	78	12	)	)	PUNCT
ejpam-4382	78	13	and	and	CCONJ
ejpam-4382	78	14	(	(	PUNCT
ejpam-4382	78	15	2	2	NUM
ejpam-4382	78	16	)	)	PUNCT
ejpam-4382	78	17	.	.	PUNCT
ejpam-4382	79	1	(	(	PUNCT
ejpam-4382	79	2	5	5	X
ejpam-4382	79	3	)	)	PUNCT
ejpam-4382	79	4	let	let	VERB
ejpam-4382	79	5	x	x	PUNCT
ejpam-4382	79	6	∈	∈	PROPN
ejpam-4382	79	7	scli	scli	NOUN
ejpam-4382	79	8	(	(	PUNCT
ejpam-4382	79	9	a	a	NOUN
ejpam-4382	79	10	)	)	PUNCT
ejpam-4382	79	11	.	.	PUNCT
ejpam-4382	80	1	suppose	suppose	VERB
ejpam-4382	80	2	that	that	SCONJ
ejpam-4382	80	3	u	u	PRON
ejpam-4382	80	4	∩a	∩a	NOUN
ejpam-4382	80	5	=	=	NOUN
ejpam-4382	80	6	∅	∅	NOUN
ejpam-4382	80	7	for	for	ADP
ejpam-4382	80	8	some	some	DET
ejpam-4382	80	9	semi	semi	ADJ
ejpam-4382	80	10	-	-	ADJ
ejpam-4382	80	11	i	i	PRON
ejpam-4382	80	12	-open	-open	NOUN
ejpam-4382	80	13	set	set	VERB
ejpam-4382	80	14	u	u	NOUN
ejpam-4382	80	15	containing	contain	VERB
ejpam-4382	80	16	x.	x.	NOUN
ejpam-4382	80	17	then	then	ADV
ejpam-4382	80	18	,	,	PUNCT
ejpam-4382	80	19	a	a	DET
ejpam-4382	80	20	⊆	⊆	NUM
ejpam-4382	80	21	x−u	x−u	X
ejpam-4382	80	22	and	and	CCONJ
ejpam-4382	80	23	x−u	x−u	PROPN
ejpam-4382	80	24	is	be	AUX
ejpam-4382	80	25	semi	semi	ADJ
ejpam-4382	80	26	-	-	ADJ
ejpam-4382	80	27	i	i	PRON
ejpam-4382	80	28	-closed	-closed	ADJ
ejpam-4382	80	29	.	.	PUNCT
ejpam-4382	81	1	since	since	SCONJ
ejpam-4382	81	2	x	x	PROPN
ejpam-4382	81	3	∈	∈	PROPN
ejpam-4382	81	4	scli	scli	NOUN
ejpam-4382	81	5	(	(	PUNCT
ejpam-4382	81	6	a	a	NOUN
ejpam-4382	81	7	)	)	PUNCT
ejpam-4382	81	8	,	,	PUNCT
ejpam-4382	81	9	x	x	PUNCT
ejpam-4382	81	10	∈	∈	PROPN
ejpam-4382	81	11	scli	scli	NOUN
ejpam-4382	81	12	(	(	PUNCT
ejpam-4382	81	13	x−u	x−u	NOUN
ejpam-4382	81	14	)	)	PUNCT
ejpam-4382	81	15	=	=	PUNCT
ejpam-4382	82	1	x	x	X
ejpam-4382	82	2	−u	−u	NOUN
ejpam-4382	82	3	;	;	PUNCT
ejpam-4382	82	4	hence	hence	ADV
ejpam-4382	82	5	x	x	X
ejpam-4382	82	6	̸∈	̸∈	PROPN
ejpam-4382	82	7	u	u	PROPN
ejpam-4382	82	8	,	,	PUNCT
ejpam-4382	82	9	which	which	PRON
ejpam-4382	82	10	is	be	AUX
ejpam-4382	82	11	a	a	DET
ejpam-4382	82	12	contradiction	contradiction	NOUN
ejpam-4382	82	13	that	that	SCONJ
ejpam-4382	82	14	x	x	PUNCT
ejpam-4382	82	15	∈	∈	PROPN
ejpam-4382	82	16	u	u	NOUN
ejpam-4382	82	17	.	.	PUNCT
ejpam-4382	83	1	therefore	therefore	ADV
ejpam-4382	83	2	,	,	PUNCT
ejpam-4382	83	3	u	u	NOUN
ejpam-4382	83	4	∩a	∩a	PROPN
ejpam-4382	83	5	̸=	̸=	PROPN
ejpam-4382	83	6	∅	∅	NOUN
ejpam-4382	83	7	for	for	ADP
ejpam-4382	83	8	every	every	DET
ejpam-4382	83	9	semi	semi	ADJ
ejpam-4382	83	10	-	-	ADJ
ejpam-4382	83	11	i	i	PRON
ejpam-4382	83	12	-open	-open	NOUN
ejpam-4382	83	13	set	set	VERB
ejpam-4382	83	14	u	u	NOUN
ejpam-4382	83	15	containing	contain	VERB
ejpam-4382	83	16	x.	x.	NOUN
ejpam-4382	83	17	conversely	conversely	ADV
ejpam-4382	83	18	,	,	PUNCT
ejpam-4382	83	19	assume	assume	VERB
ejpam-4382	83	20	that	that	SCONJ
ejpam-4382	83	21	u∩a	u∩a	PROPN
ejpam-4382	83	22	̸=	̸=	PROPN
ejpam-4382	83	23	∅	∅	NOUN
ejpam-4382	83	24	for	for	ADP
ejpam-4382	83	25	every	every	DET
ejpam-4382	83	26	semi	semi	ADJ
ejpam-4382	83	27	-	-	ADJ
ejpam-4382	83	28	i	i	PRON
ejpam-4382	83	29	-open	-open	NOUN
ejpam-4382	83	30	set	set	VERB
ejpam-4382	83	31	u	u	NOUN
ejpam-4382	83	32	containing	contain	VERB
ejpam-4382	83	33	x.	x.	NOUN
ejpam-4382	83	34	we	we	PRON
ejpam-4382	83	35	shall	shall	AUX
ejpam-4382	83	36	show	show	VERB
ejpam-4382	83	37	that	that	SCONJ
ejpam-4382	83	38	x	x	SYM
ejpam-4382	83	39	∈	∈	PROPN
ejpam-4382	83	40	scli	scli	NOUN
ejpam-4382	83	41	(	(	PUNCT
ejpam-4382	83	42	a	a	NOUN
ejpam-4382	83	43	)	)	PUNCT
ejpam-4382	83	44	.	.	PUNCT
ejpam-4382	84	1	suppose	suppose	VERB
ejpam-4382	84	2	that	that	SCONJ
ejpam-4382	84	3	x	x	PROPN
ejpam-4382	84	4	̸∈	̸∈	PROPN
ejpam-4382	84	5	scli	scli	PROPN
ejpam-4382	84	6	(	(	PUNCT
ejpam-4382	84	7	a	a	NOUN
ejpam-4382	84	8	)	)	PUNCT
ejpam-4382	84	9	.	.	PUNCT
ejpam-4382	85	1	then	then	ADV
ejpam-4382	85	2	,	,	PUNCT
ejpam-4382	85	3	there	there	PRON
ejpam-4382	85	4	exists	exist	VERB
ejpam-4382	85	5	a	a	DET
ejpam-4382	85	6	semi	semi	NOUN
ejpam-4382	85	7	-	-	ADJ
ejpam-4382	85	8	i	i	PRON
ejpam-4382	85	9	-closed	-close	VERB
ejpam-4382	85	10	set	set	VERB
ejpam-4382	85	11	f	f	PROPN
ejpam-4382	85	12	such	such	ADJ
ejpam-4382	85	13	that	that	SCONJ
ejpam-4382	85	14	a	a	DET
ejpam-4382	85	15	⊆	⊆	NUM
ejpam-4382	85	16	f	f	PROPN
ejpam-4382	85	17	and	and	CCONJ
ejpam-4382	85	18	x	x	PROPN
ejpam-4382	85	19	̸∈	̸∈	PROPN
ejpam-4382	85	20	f	f	PROPN
ejpam-4382	85	21	.	.	PUNCT
ejpam-4382	86	1	thus	thus	ADV
ejpam-4382	86	2	,	,	PUNCT
ejpam-4382	86	3	x	x	PUNCT
ejpam-4382	86	4	−	−	PROPN
ejpam-4382	86	5	f	f	PROPN
ejpam-4382	86	6	is	be	AUX
ejpam-4382	86	7	a	a	DET
ejpam-4382	86	8	semi	semi	ADJ
ejpam-4382	86	9	-	-	ADJ
ejpam-4382	86	10	i	i	PRON
ejpam-4382	86	11	-open	-open	NOUN
ejpam-4382	86	12	set	set	VERB
ejpam-4382	86	13	containing	contain	VERB
ejpam-4382	86	14	x	x	PUNCT
ejpam-4382	86	15	such	such	ADJ
ejpam-4382	86	16	that	that	SCONJ
ejpam-4382	86	17	(	(	PUNCT
ejpam-4382	86	18	x	x	SYM
ejpam-4382	86	19	−	−	PROPN
ejpam-4382	86	20	f	f	NOUN
ejpam-4382	86	21	)	)	PUNCT
ejpam-4382	87	1	∩a	∩a	PROPN
ejpam-4382	88	1	=	=	PUNCT
ejpam-4382	88	2	∅.	∅.	ADP
ejpam-4382	88	3	this	this	PRON
ejpam-4382	88	4	a	a	DET
ejpam-4382	88	5	contradiction	contradiction	NOUN
ejpam-4382	88	6	to	to	ADP
ejpam-4382	88	7	u	u	NOUN
ejpam-4382	88	8	∩a	∩a	PROPN
ejpam-4382	88	9	̸=	̸=	PROPN
ejpam-4382	88	10	∅	∅	NOUN
ejpam-4382	88	11	;	;	PUNCT
ejpam-4382	88	12	hence	hence	ADV
ejpam-4382	88	13	x	x	PART
ejpam-4382	88	14	∈	∈	PROPN
ejpam-4382	88	15	scli	scli	NOUN
ejpam-4382	88	16	(	(	PUNCT
ejpam-4382	88	17	a	a	NOUN
ejpam-4382	88	18	)	)	PUNCT
ejpam-4382	88	19	.	.	PUNCT
ejpam-4382	89	1	(	(	PUNCT
ejpam-4382	89	2	6	6	X
ejpam-4382	89	3	)	)	PUNCT
ejpam-4382	89	4	let	let	VERB
ejpam-4382	89	5	x	x	SYM
ejpam-4382	89	6	∈	∈	PROPN
ejpam-4382	89	7	x	x	PUNCT
ejpam-4382	89	8	−	−	PROPN
ejpam-4382	89	9	scli	scli	NOUN
ejpam-4382	89	10	(	(	PUNCT
ejpam-4382	89	11	a	a	NOUN
ejpam-4382	89	12	)	)	PUNCT
ejpam-4382	89	13	.	.	PUNCT
ejpam-4382	90	1	then	then	ADV
ejpam-4382	90	2	,	,	PUNCT
ejpam-4382	90	3	x	x	PROPN
ejpam-4382	90	4	̸∈	̸∈	PROPN
ejpam-4382	90	5	scli	scli	PROPN
ejpam-4382	90	6	(	(	PUNCT
ejpam-4382	90	7	a	a	X
ejpam-4382	90	8	)	)	PUNCT
ejpam-4382	90	9	,	,	PUNCT
ejpam-4382	90	10	there	there	PRON
ejpam-4382	90	11	exists	exist	VERB
ejpam-4382	90	12	a	a	DET
ejpam-4382	90	13	semi	semi	ADJ
ejpam-4382	90	14	-	-	ADJ
ejpam-4382	90	15	i	i	PRON
ejpam-4382	90	16	-open	-open	NOUN
ejpam-4382	90	17	set	set	VERB
ejpam-4382	90	18	v	v	NOUN
ejpam-4382	90	19	containing	contain	VERB
ejpam-4382	90	20	x	x	PUNCT
ejpam-4382	90	21	such	such	ADJ
ejpam-4382	90	22	that	that	PRON
ejpam-4382	90	23	v	v	ADP
ejpam-4382	90	24	∩	∩	NOUN
ejpam-4382	90	25	a	a	DET
ejpam-4382	90	26	=	=	PUNCT
ejpam-4382	90	27	∅.	∅.	NOUN
ejpam-4382	90	28	thus	thus	ADV
ejpam-4382	90	29	,	,	PUNCT
ejpam-4382	90	30	v	v	ADP
ejpam-4382	90	31	⊆	⊆	NUM
ejpam-4382	90	32	x	x	SYM
ejpam-4382	90	33	−	−	NOUN
ejpam-4382	90	34	a	a	PRON
ejpam-4382	90	35	and	and	CCONJ
ejpam-4382	90	36	hence	hence	ADV
ejpam-4382	90	37	x	x	PART
ejpam-4382	90	38	∈	∈	PROPN
ejpam-4382	90	39	sinti	sinti	NOUN
ejpam-4382	90	40	(	(	PUNCT
ejpam-4382	90	41	x	x	PROPN
ejpam-4382	90	42	−	−	PROPN
ejpam-4382	90	43	a	a	NOUN
ejpam-4382	90	44	)	)	PUNCT
ejpam-4382	90	45	.	.	PUNCT
ejpam-4382	91	1	consequently	consequently	ADV
ejpam-4382	91	2	,	,	PUNCT
ejpam-4382	91	3	we	we	PRON
ejpam-4382	91	4	obtain	obtain	VERB
ejpam-4382	91	5	x	x	PUNCT
ejpam-4382	91	6	−	−	PROPN
ejpam-4382	91	7	scli	scli	NOUN
ejpam-4382	91	8	(	(	PUNCT
ejpam-4382	91	9	a	a	X
ejpam-4382	91	10	)	)	PUNCT
ejpam-4382	91	11	⊆	⊆	NUM
ejpam-4382	91	12	sinti	sinti	NOUN
ejpam-4382	91	13	(	(	PUNCT
ejpam-4382	91	14	x	x	PROPN
ejpam-4382	91	15	−	−	PROPN
ejpam-4382	91	16	a	a	NOUN
ejpam-4382	91	17	)	)	PUNCT
ejpam-4382	91	18	.	.	PUNCT
ejpam-4382	92	1	on	on	ADP
ejpam-4382	92	2	the	the	DET
ejpam-4382	92	3	other	other	ADJ
ejpam-4382	92	4	hand	hand	NOUN
ejpam-4382	92	5	,	,	PUNCT
ejpam-4382	92	6	suppose	suppose	VERB
ejpam-4382	92	7	that	that	SCONJ
ejpam-4382	92	8	x	x	PROPN
ejpam-4382	92	9	∈	∈	PROPN
ejpam-4382	92	10	sinti	sinti	NOUN
ejpam-4382	92	11	(	(	PUNCT
ejpam-4382	92	12	x	x	PROPN
ejpam-4382	92	13	−	−	PROPN
ejpam-4382	92	14	a	a	NOUN
ejpam-4382	92	15	)	)	PUNCT
ejpam-4382	92	16	.	.	PUNCT
ejpam-4382	93	1	then	then	ADV
ejpam-4382	93	2	,	,	PUNCT
ejpam-4382	93	3	there	there	PRON
ejpam-4382	93	4	exists	exist	VERB
ejpam-4382	93	5	a	a	DET
ejpam-4382	93	6	semi	semi	ADJ
ejpam-4382	93	7	-	-	ADJ
ejpam-4382	93	8	i	i	PRON
ejpam-4382	93	9	-open	-open	NOUN
ejpam-4382	93	10	set	set	VERB
ejpam-4382	93	11	v	v	NOUN
ejpam-4382	93	12	containing	contain	VERB
ejpam-4382	93	13	x	x	PUNCT
ejpam-4382	93	14	such	such	ADJ
ejpam-4382	93	15	that	that	PRON
ejpam-4382	93	16	v	v	ADP
ejpam-4382	93	17	⊆	⊆	NUM
ejpam-4382	93	18	x	x	SYM
ejpam-4382	93	19	−	−	NOUN
ejpam-4382	93	20	a	a	PRON
ejpam-4382	93	21	and	and	CCONJ
ejpam-4382	93	22	so	so	ADV
ejpam-4382	93	23	v	v	ADP
ejpam-4382	93	24	∩	∩	NOUN
ejpam-4382	93	25	a	a	DET
ejpam-4382	93	26	=	=	SYM
ejpam-4382	93	27	∅.	∅.	NOUN
ejpam-4382	93	28	by	by	ADP
ejpam-4382	93	29	(	(	PUNCT
ejpam-4382	93	30	5	5	NUM
ejpam-4382	93	31	)	)	PUNCT
ejpam-4382	93	32	,	,	PUNCT
ejpam-4382	93	33	we	we	PRON
ejpam-4382	93	34	have	have	VERB
ejpam-4382	93	35	x	x	PART
ejpam-4382	93	36	̸∈	̸∈	PROPN
ejpam-4382	93	37	scli	scli	PROPN
ejpam-4382	93	38	(	(	PUNCT
ejpam-4382	93	39	a	a	NOUN
ejpam-4382	93	40	)	)	PUNCT
ejpam-4382	93	41	;	;	PUNCT
ejpam-4382	94	1	hence	hence	ADV
ejpam-4382	94	2	x	x	SYM
ejpam-4382	94	3	∈	∈	NOUN
ejpam-4382	94	4	x	x	PUNCT
ejpam-4382	94	5	−	−	PROPN
ejpam-4382	94	6	scli	scli	NOUN
ejpam-4382	94	7	(	(	PUNCT
ejpam-4382	94	8	a	a	NOUN
ejpam-4382	94	9	)	)	PUNCT
ejpam-4382	94	10	.	.	PUNCT
ejpam-4382	95	1	thus	thus	ADV
ejpam-4382	95	2	,	,	PUNCT
ejpam-4382	95	3	sinti	sinti	PROPN
ejpam-4382	95	4	(	(	PUNCT
ejpam-4382	95	5	x	x	SYM
ejpam-4382	95	6	−a	−a	ADV
ejpam-4382	95	7	)	)	PUNCT
ejpam-4382	95	8	⊆	⊆	NUM
ejpam-4382	95	9	x	x	SYM
ejpam-4382	95	10	−	−	PROPN
ejpam-4382	95	11	scli	scli	NOUN
ejpam-4382	95	12	(	(	PUNCT
ejpam-4382	95	13	a	a	NOUN
ejpam-4382	95	14	)	)	PUNCT
ejpam-4382	95	15	.	.	PUNCT
ejpam-4382	96	1	this	this	PRON
ejpam-4382	96	2	shows	show	VERB
ejpam-4382	96	3	that	that	SCONJ
ejpam-4382	96	4	x	x	PUNCT
ejpam-4382	96	5	−	−	PROPN
ejpam-4382	96	6	scli	scli	NOUN
ejpam-4382	96	7	(	(	PUNCT
ejpam-4382	96	8	a	a	X
ejpam-4382	96	9	)	)	PUNCT
ejpam-4382	96	10	=	=	SYM
ejpam-4382	96	11	sinti	sinti	NOUN
ejpam-4382	96	12	(	(	PUNCT
ejpam-4382	96	13	x	x	NOUN
ejpam-4382	96	14	−a	−a	NOUN
ejpam-4382	96	15	)	)	PUNCT
ejpam-4382	96	16	.	.	PUNCT
ejpam-4382	97	1	(	(	PUNCT
ejpam-4382	97	2	7	7	X
ejpam-4382	97	3	)	)	PUNCT
ejpam-4382	97	4	this	this	PRON
ejpam-4382	97	5	follows	follow	VERB
ejpam-4382	97	6	from	from	ADP
ejpam-4382	97	7	(	(	PUNCT
ejpam-4382	97	8	6	6	NUM
ejpam-4382	97	9	)	)	PUNCT
ejpam-4382	97	10	.	.	PUNCT
ejpam-4382	98	1	3	3	X
ejpam-4382	98	2	.	.	X
ejpam-4382	98	3	semi	semi	ADJ
ejpam-4382	98	4	-	-	ADJ
ejpam-4382	98	5	i	i	PRON
ejpam-4382	98	6	-submaximal	-submaximal	ADJ
ejpam-4382	98	7	ideal	ideal	ADJ
ejpam-4382	98	8	topological	topological	ADJ
ejpam-4382	98	9	spaces	space	NOUN
ejpam-4382	98	10	in	in	ADP
ejpam-4382	98	11	this	this	DET
ejpam-4382	98	12	section	section	NOUN
ejpam-4382	98	13	,	,	PUNCT
ejpam-4382	98	14	we	we	PRON
ejpam-4382	98	15	introduce	introduce	VERB
ejpam-4382	98	16	the	the	DET
ejpam-4382	98	17	notion	notion	NOUN
ejpam-4382	98	18	of	of	ADP
ejpam-4382	98	19	semi	semi	ADJ
ejpam-4382	98	20	-	-	ADJ
ejpam-4382	98	21	i	i	PRON
ejpam-4382	98	22	-submaximal	-submaximal	ADJ
ejpam-4382	98	23	ideal	ideal	ADJ
ejpam-4382	98	24	topological	topological	ADJ
ejpam-4382	98	25	spaces	space	NOUN
ejpam-4382	98	26	.	.	PUNCT
ejpam-4382	99	1	moreover	moreover	ADV
ejpam-4382	99	2	,	,	PUNCT
ejpam-4382	99	3	several	several	ADJ
ejpam-4382	99	4	characterizations	characterization	NOUN
ejpam-4382	99	5	of	of	ADP
ejpam-4382	99	6	semi	semi	ADJ
ejpam-4382	99	7	-	-	ADJ
ejpam-4382	99	8	i	i	PRON
ejpam-4382	99	9	-submaximal	-submaximal	ADJ
ejpam-4382	99	10	ideal	ideal	ADJ
ejpam-4382	99	11	topological	topological	ADJ
ejpam-4382	99	12	spaces	space	NOUN
ejpam-4382	99	13	are	be	AUX
ejpam-4382	99	14	discussed	discuss	VERB
ejpam-4382	99	15	.	.	PUNCT
ejpam-4382	100	1	definition	definition	NOUN
ejpam-4382	100	2	1	1	NUM
ejpam-4382	100	3	.	.	PUNCT
ejpam-4382	101	1	a	a	DET
ejpam-4382	101	2	subset	subset	NOUN
ejpam-4382	101	3	a	a	PRON
ejpam-4382	101	4	of	of	ADP
ejpam-4382	101	5	an	an	DET
ejpam-4382	101	6	ideal	ideal	ADJ
ejpam-4382	101	7	topological	topological	ADJ
ejpam-4382	101	8	space	space	NOUN
ejpam-4382	101	9	(	(	PUNCT
ejpam-4382	101	10	x	x	X
ejpam-4382	101	11	,	,	PUNCT
ejpam-4382	101	12	τ	τ	PROPN
ejpam-4382	101	13	,	,	PUNCT
ejpam-4382	101	14	i	i	PROPN
ejpam-4382	101	15	)	)	PUNCT
ejpam-4382	101	16	is	be	AUX
ejpam-4382	101	17	said	say	VERB
ejpam-4382	101	18	to	to	PART
ejpam-4382	101	19	be	be	AUX
ejpam-4382	101	20	:	:	PUNCT
ejpam-4382	101	21	(	(	PUNCT
ejpam-4382	101	22	i	i	NOUN
ejpam-4382	101	23	)	)	PUNCT
ejpam-4382	101	24	semi	semi	ADJ
ejpam-4382	101	25	-	-	VERB
ejpam-4382	101	26	i	i	PRON
ejpam-4382	101	27	-dense	-dense	NOUN
ejpam-4382	101	28	if	if	SCONJ
ejpam-4382	101	29	scli	scli	PROPN
ejpam-4382	101	30	(	(	PUNCT
ejpam-4382	101	31	a	a	NOUN
ejpam-4382	101	32	)	)	PUNCT
ejpam-4382	101	33	=	=	SYM
ejpam-4382	101	34	x	x	X
ejpam-4382	101	35	;	;	PUNCT
ejpam-4382	101	36	(	(	PUNCT
ejpam-4382	101	37	ii	ii	NOUN
ejpam-4382	101	38	)	)	PUNCT
ejpam-4382	101	39	semi	semi	ADJ
ejpam-4382	101	40	-	-	VERB
ejpam-4382	101	41	i	i	PRON
ejpam-4382	101	42	-codense	-codense	NOUN
ejpam-4382	101	43	if	if	SCONJ
ejpam-4382	101	44	x	x	PRON
ejpam-4382	101	45	−a	−a	NOUN
ejpam-4382	101	46	is	be	AUX
ejpam-4382	101	47	semi	semi	ADJ
ejpam-4382	101	48	-	-	ADJ
ejpam-4382	101	49	i	i	ADJ
ejpam-4382	101	50	-dense	-dense	NOUN
ejpam-4382	101	51	.	.	PUNCT
ejpam-4382	102	1	definition	definition	NOUN
ejpam-4382	102	2	2	2	NUM
ejpam-4382	102	3	.	.	PUNCT
ejpam-4382	103	1	an	an	DET
ejpam-4382	103	2	ideal	ideal	ADJ
ejpam-4382	103	3	topological	topological	ADJ
ejpam-4382	103	4	space	space	NOUN
ejpam-4382	103	5	(	(	PUNCT
ejpam-4382	103	6	x	x	X
ejpam-4382	103	7	,	,	PUNCT
ejpam-4382	103	8	τ	τ	PROPN
ejpam-4382	103	9	,	,	PUNCT
ejpam-4382	103	10	i	i	PROPN
ejpam-4382	103	11	)	)	PUNCT
ejpam-4382	103	12	is	be	AUX
ejpam-4382	103	13	called	call	VERB
ejpam-4382	103	14	semi	semi	ADJ
ejpam-4382	103	15	-	-	ADJ
ejpam-4382	103	16	i	i	PRON
ejpam-4382	103	17	-submaxiaml	-submaxiaml	PROPN
ejpam-4382	103	18	if	if	SCONJ
ejpam-4382	103	19	each	each	DET
ejpam-4382	103	20	semi	semi	ADJ
ejpam-4382	103	21	-	-	ADJ
ejpam-4382	103	22	i	i	ADJ
ejpam-4382	103	23	-dense	-dense	PROPN
ejpam-4382	103	24	subset	subset	NOUN
ejpam-4382	103	25	of	of	ADP
ejpam-4382	103	26	x	x	PUNCT
ejpam-4382	103	27	is	be	AUX
ejpam-4382	103	28	semi	semi	ADJ
ejpam-4382	103	29	-	-	ADJ
ejpam-4382	103	30	i	i	PRON
ejpam-4382	103	31	-open	-open	NOUN
ejpam-4382	103	32	.	.	PUNCT
ejpam-4382	104	1	definition	definition	NOUN
ejpam-4382	104	2	3	3	NUM
ejpam-4382	104	3	.	.	PUNCT
ejpam-4382	105	1	a	a	DET
ejpam-4382	105	2	subset	subset	NOUN
ejpam-4382	105	3	a	a	PRON
ejpam-4382	105	4	of	of	ADP
ejpam-4382	105	5	an	an	DET
ejpam-4382	105	6	ideal	ideal	ADJ
ejpam-4382	105	7	topological	topological	ADJ
ejpam-4382	105	8	space	space	NOUN
ejpam-4382	105	9	(	(	PUNCT
ejpam-4382	105	10	x	x	X
ejpam-4382	105	11	,	,	PUNCT
ejpam-4382	105	12	τ	τ	PROPN
ejpam-4382	105	13	,	,	PUNCT
ejpam-4382	105	14	i	i	PROPN
ejpam-4382	105	15	)	)	PUNCT
ejpam-4382	105	16	is	be	AUX
ejpam-4382	105	17	said	say	VERB
ejpam-4382	105	18	to	to	PART
ejpam-4382	105	19	be	be	AUX
ejpam-4382	105	20	:	:	PUNCT
ejpam-4382	105	21	(	(	PUNCT
ejpam-4382	105	22	i	i	NOUN
ejpam-4382	105	23	)	)	PUNCT
ejpam-4382	105	24	locally	locally	ADV
ejpam-4382	105	25	semi	semi	ADJ
ejpam-4382	105	26	-	-	VERB
ejpam-4382	105	27	i	i	PRON
ejpam-4382	105	28	-closed	-close	VERB
ejpam-4382	105	29	if	if	SCONJ
ejpam-4382	105	30	a	a	PRON
ejpam-4382	105	31	is	be	AUX
ejpam-4382	105	32	the	the	DET
ejpam-4382	105	33	intersection	intersection	NOUN
ejpam-4382	105	34	of	of	ADP
ejpam-4382	105	35	a	a	DET
ejpam-4382	105	36	semi	semi	ADJ
ejpam-4382	105	37	-	-	ADJ
ejpam-4382	105	38	i	i	PRON
ejpam-4382	105	39	-open	-open	NOUN
ejpam-4382	105	40	set	set	VERB
ejpam-4382	105	41	and	and	CCONJ
ejpam-4382	105	42	a	a	DET
ejpam-4382	105	43	semi	semi	ADJ
ejpam-4382	105	44	-	-	ADJ
ejpam-4382	105	45	i	i	PRON
ejpam-4382	105	46	closed	close	VERB
ejpam-4382	105	47	set	set	VERB
ejpam-4382	105	48	;	;	PUNCT
ejpam-4382	105	49	c.	c.	PROPN
ejpam-4382	105	50	boonpok	boonpok	PROPN
ejpam-4382	105	51	/	/	SYM
ejpam-4382	105	52	eur	eur	PROPN
ejpam-4382	105	53	.	.	PUNCT
ejpam-4382	106	1	j.	j.	PROPN
ejpam-4382	106	2	pure	pure	PROPN
ejpam-4382	106	3	appl	appl	PROPN
ejpam-4382	106	4	.	.	PROPN
ejpam-4382	106	5	math	math	PROPN
ejpam-4382	106	6	,	,	PUNCT
ejpam-4382	106	7	15	15	NUM
ejpam-4382	106	8	(	(	PUNCT
ejpam-4382	106	9	3	3	NUM
ejpam-4382	106	10	)	)	PUNCT
ejpam-4382	106	11	(	(	PUNCT
ejpam-4382	106	12	2022	2022	NUM
ejpam-4382	106	13	)	)	PUNCT
ejpam-4382	106	14	,	,	PUNCT
ejpam-4382	106	15	938	938	NUM
ejpam-4382	106	16	-	-	SYM
ejpam-4382	106	17	947	947	NUM
ejpam-4382	106	18	941	941	NUM
ejpam-4382	106	19	(	(	PUNCT
ejpam-4382	106	20	ii	ii	NOUN
ejpam-4382	106	21	)	)	PUNCT
ejpam-4382	106	22	co	co	NOUN
ejpam-4382	106	23	-	-	NOUN
ejpam-4382	106	24	locally	locally	ADV
ejpam-4382	106	25	semi	semi	NOUN
ejpam-4382	106	26	-	-	AUX
ejpam-4382	106	27	i	i	PRON
ejpam-4382	106	28	-closed	-close	VERB
ejpam-4382	106	29	if	if	SCONJ
ejpam-4382	106	30	a	a	PRON
ejpam-4382	106	31	is	be	AUX
ejpam-4382	106	32	the	the	DET
ejpam-4382	106	33	union	union	NOUN
ejpam-4382	106	34	of	of	ADP
ejpam-4382	106	35	a	a	DET
ejpam-4382	106	36	semi	semi	ADJ
ejpam-4382	106	37	-	-	ADJ
ejpam-4382	106	38	i	i	PRON
ejpam-4382	106	39	-open	-open	NOUN
ejpam-4382	106	40	set	set	VERB
ejpam-4382	106	41	and	and	CCONJ
ejpam-4382	106	42	a	a	DET
ejpam-4382	106	43	semi	semi	ADJ
ejpam-4382	106	44	-	-	ADJ
ejpam-4382	106	45	i	i	PRON
ejpam-4382	106	46	-closed	-close	VERB
ejpam-4382	106	47	set	set	NOUN
ejpam-4382	106	48	.	.	PUNCT
ejpam-4382	107	1	theorem	theorem	NOUN
ejpam-4382	107	2	1	1	NUM
ejpam-4382	107	3	.	.	X
ejpam-4382	107	4	for	for	ADP
ejpam-4382	107	5	a	a	DET
ejpam-4382	107	6	subset	subset	NOUN
ejpam-4382	107	7	a	a	PRON
ejpam-4382	107	8	of	of	ADP
ejpam-4382	107	9	an	an	DET
ejpam-4382	107	10	ideal	ideal	ADJ
ejpam-4382	107	11	topological	topological	ADJ
ejpam-4382	107	12	space	space	NOUN
ejpam-4382	107	13	(	(	PUNCT
ejpam-4382	107	14	x	x	X
ejpam-4382	107	15	,	,	PUNCT
ejpam-4382	107	16	τ	τ	PROPN
ejpam-4382	107	17	,	,	PUNCT
ejpam-4382	107	18	i	i	NOUN
ejpam-4382	107	19	)	)	PUNCT
ejpam-4382	107	20	,	,	PUNCT
ejpam-4382	107	21	the	the	DET
ejpam-4382	107	22	following	follow	VERB
ejpam-4382	107	23	properties	property	NOUN
ejpam-4382	107	24	are	be	AUX
ejpam-4382	107	25	equivalent	equivalent	ADJ
ejpam-4382	107	26	:	:	PUNCT
ejpam-4382	107	27	(	(	PUNCT
ejpam-4382	107	28	1	1	X
ejpam-4382	107	29	)	)	PUNCT
ejpam-4382	107	30	a	a	PRON
ejpam-4382	107	31	is	be	AUX
ejpam-4382	107	32	locally	locally	ADV
ejpam-4382	107	33	semi	semi	ADJ
ejpam-4382	107	34	-	-	ADJ
ejpam-4382	107	35	i	i	PRON
ejpam-4382	107	36	-closed	-close	VERB
ejpam-4382	107	37	;	;	PUNCT
ejpam-4382	107	38	(	(	PUNCT
ejpam-4382	107	39	2	2	X
ejpam-4382	107	40	)	)	PUNCT
ejpam-4382	107	41	a	a	DET
ejpam-4382	107	42	=	=	X
ejpam-4382	107	43	u	u	NOUN
ejpam-4382	107	44	∩	∩	NOUN
ejpam-4382	107	45	scli	scli	NOUN
ejpam-4382	107	46	(	(	PUNCT
ejpam-4382	107	47	a	a	NOUN
ejpam-4382	107	48	)	)	PUNCT
ejpam-4382	107	49	for	for	ADP
ejpam-4382	107	50	some	some	DET
ejpam-4382	107	51	u	u	PROPN
ejpam-4382	107	52	∈	∈	PROPN
ejpam-4382	107	53	sio(x	sio(x	PROPN
ejpam-4382	107	54	,	,	PUNCT
ejpam-4382	107	55	τ	τ	PROPN
ejpam-4382	107	56	)	)	PUNCT
ejpam-4382	107	57	;	;	PUNCT
ejpam-4382	107	58	(	(	PUNCT
ejpam-4382	107	59	3	3	X
ejpam-4382	107	60	)	)	PUNCT
ejpam-4382	107	61	scli	scli	NOUN
ejpam-4382	107	62	(	(	PUNCT
ejpam-4382	107	63	a)−a	a)−a	X
ejpam-4382	107	64	is	be	AUX
ejpam-4382	107	65	semi	semi	ADJ
ejpam-4382	107	66	-	-	ADJ
ejpam-4382	107	67	i	i	PRON
ejpam-4382	107	68	-closed	-close	VERB
ejpam-4382	107	69	;	;	PUNCT
ejpam-4382	107	70	(	(	PUNCT
ejpam-4382	107	71	4	4	X
ejpam-4382	107	72	)	)	PUNCT
ejpam-4382	107	73	a	a	DET
ejpam-4382	107	74	∪	∪	NOUN
ejpam-4382	107	75	(	(	PUNCT
ejpam-4382	107	76	x	x	SYM
ejpam-4382	107	77	−	−	PROPN
ejpam-4382	107	78	scli	scli	NOUN
ejpam-4382	107	79	(	(	PUNCT
ejpam-4382	107	80	a	a	NOUN
ejpam-4382	107	81	)	)	PUNCT
ejpam-4382	107	82	)	)	PUNCT
ejpam-4382	107	83	is	be	AUX
ejpam-4382	107	84	semi	semi	ADJ
ejpam-4382	107	85	-	-	ADJ
ejpam-4382	107	86	i	i	PRON
ejpam-4382	107	87	-open	-open	ADJ
ejpam-4382	107	88	;	;	PUNCT
ejpam-4382	107	89	(	(	PUNCT
ejpam-4382	107	90	5	5	X
ejpam-4382	107	91	)	)	PUNCT
ejpam-4382	107	92	a	a	DET
ejpam-4382	107	93	⊆	⊆	NUM
ejpam-4382	107	94	sinti	sinti	X
ejpam-4382	107	95	(	(	PUNCT
ejpam-4382	107	96	a	a	DET
ejpam-4382	107	97	∪	∪	X
ejpam-4382	107	98	(	(	PUNCT
ejpam-4382	107	99	x	x	SYM
ejpam-4382	107	100	−	−	PROPN
ejpam-4382	107	101	scli	scli	NOUN
ejpam-4382	107	102	(	(	PUNCT
ejpam-4382	107	103	a	a	NOUN
ejpam-4382	107	104	)	)	PUNCT
ejpam-4382	107	105	)	)	PUNCT
ejpam-4382	107	106	)	)	PUNCT
ejpam-4382	107	107	.	.	PUNCT
ejpam-4382	108	1	proof	proof	NOUN
ejpam-4382	108	2	.	.	PUNCT
ejpam-4382	109	1	(	(	PUNCT
ejpam-4382	109	2	1	1	X
ejpam-4382	109	3	)	)	PUNCT
ejpam-4382	109	4	⇒	⇒	NOUN
ejpam-4382	109	5	(	(	PUNCT
ejpam-4382	109	6	2	2	NUM
ejpam-4382	109	7	):	):	PUNCT
ejpam-4382	109	8	suppose	suppose	VERB
ejpam-4382	109	9	that	that	SCONJ
ejpam-4382	109	10	a	a	PRON
ejpam-4382	109	11	is	be	AUX
ejpam-4382	109	12	locally	locally	ADV
ejpam-4382	109	13	semi	semi	ADJ
ejpam-4382	109	14	-	-	ADJ
ejpam-4382	109	15	i	i	PRON
ejpam-4382	109	16	-closed	-closed	ADJ
ejpam-4382	109	17	.	.	PUNCT
ejpam-4382	110	1	then	then	ADV
ejpam-4382	110	2	,	,	PUNCT
ejpam-4382	110	3	there	there	PRON
ejpam-4382	110	4	exist	exist	VERB
ejpam-4382	110	5	a	a	DET
ejpam-4382	110	6	semii	semii	NOUN
ejpam-4382	110	7	-open	-open	NOUN
ejpam-4382	110	8	set	set	VERB
ejpam-4382	110	9	u	u	NOUN
ejpam-4382	110	10	and	and	CCONJ
ejpam-4382	110	11	a	a	DET
ejpam-4382	110	12	semi	semi	ADJ
ejpam-4382	110	13	-	-	ADJ
ejpam-4382	110	14	i	i	PRON
ejpam-4382	110	15	-closed	-close	VERB
ejpam-4382	110	16	set	set	VERB
ejpam-4382	110	17	f	f	PROPN
ejpam-4382	110	18	such	such	ADJ
ejpam-4382	110	19	that	that	SCONJ
ejpam-4382	110	20	a	a	DET
ejpam-4382	110	21	=	=	X
ejpam-4382	110	22	u	u	NOUN
ejpam-4382	110	23	∩f	∩f	NOUN
ejpam-4382	110	24	.	.	PUNCT
ejpam-4382	111	1	since	since	SCONJ
ejpam-4382	111	2	f	f	PROPN
ejpam-4382	111	3	is	be	AUX
ejpam-4382	111	4	semi	semi	ADJ
ejpam-4382	111	5	-	-	ADJ
ejpam-4382	111	6	i	i	PRON
ejpam-4382	111	7	-closed	-close	VERB
ejpam-4382	111	8	,	,	PUNCT
ejpam-4382	111	9	scli	scli	NOUN
ejpam-4382	111	10	(	(	PUNCT
ejpam-4382	111	11	a	a	NOUN
ejpam-4382	111	12	)	)	PUNCT
ejpam-4382	111	13	⊆	⊆	NUM
ejpam-4382	111	14	scli	scli	NOUN
ejpam-4382	111	15	(	(	PUNCT
ejpam-4382	111	16	f	f	NOUN
ejpam-4382	111	17	)	)	PUNCT
ejpam-4382	112	1	=	=	SYM
ejpam-4382	112	2	f	f	PROPN
ejpam-4382	112	3	and	and	CCONJ
ejpam-4382	112	4	so	so	ADV
ejpam-4382	112	5	a	a	DET
ejpam-4382	112	6	⊆	⊆	NUM
ejpam-4382	112	7	u	u	NOUN
ejpam-4382	112	8	∩scli	∩scli	PROPN
ejpam-4382	112	9	(	(	PUNCT
ejpam-4382	112	10	a	a	NOUN
ejpam-4382	112	11	)	)	PUNCT
ejpam-4382	112	12	⊆	⊆	NUM
ejpam-4382	112	13	u	u	NOUN
ejpam-4382	112	14	∩f	∩f	NOUN
ejpam-4382	112	15	=	=	PUNCT
ejpam-4382	113	1	a.	a.	NOUN
ejpam-4382	113	2	thus	thus	ADV
ejpam-4382	113	3	,	,	PUNCT
ejpam-4382	113	4	a	a	DET
ejpam-4382	113	5	=	=	X
ejpam-4382	113	6	u	u	X
ejpam-4382	113	7	∩scli	∩scli	PROPN
ejpam-4382	113	8	(	(	PUNCT
ejpam-4382	113	9	a	a	NOUN
ejpam-4382	113	10	)	)	PUNCT
ejpam-4382	113	11	.	.	PUNCT
ejpam-4382	114	1	(	(	PUNCT
ejpam-4382	114	2	2	2	X
ejpam-4382	114	3	)	)	PUNCT
ejpam-4382	114	4	⇒	⇒	NOUN
ejpam-4382	114	5	(	(	PUNCT
ejpam-4382	114	6	3	3	NUM
ejpam-4382	114	7	):	):	PUNCT
ejpam-4382	114	8	suppose	suppose	VERB
ejpam-4382	114	9	that	that	SCONJ
ejpam-4382	114	10	a	a	DET
ejpam-4382	114	11	=	=	SYM
ejpam-4382	114	12	u	u	NOUN
ejpam-4382	114	13	∩	∩	NOUN
ejpam-4382	114	14	scli	scli	NOUN
ejpam-4382	114	15	(	(	PUNCT
ejpam-4382	114	16	a	a	NOUN
ejpam-4382	114	17	)	)	PUNCT
ejpam-4382	114	18	for	for	ADP
ejpam-4382	114	19	some	some	DET
ejpam-4382	114	20	u	u	PROPN
ejpam-4382	114	21	∈	∈	PROPN
ejpam-4382	114	22	sio(x	sio(x	PROPN
ejpam-4382	114	23	,	,	PUNCT
ejpam-4382	114	24	τ	τ	PROPN
ejpam-4382	114	25	)	)	PUNCT
ejpam-4382	114	26	.	.	PUNCT
ejpam-4382	115	1	since	since	SCONJ
ejpam-4382	115	2	scli	scli	PROPN
ejpam-4382	115	3	(	(	PUNCT
ejpam-4382	115	4	a)−a	a)−a	PROPN
ejpam-4382	115	5	=	=	X
ejpam-4382	115	6	(	(	PUNCT
ejpam-4382	115	7	x	x	NOUN
ejpam-4382	115	8	−a	−a	ADJ
ejpam-4382	115	9	)	)	PUNCT
ejpam-4382	115	10	∩	∩	NOUN
ejpam-4382	115	11	scli	scli	NOUN
ejpam-4382	115	12	(	(	PUNCT
ejpam-4382	115	13	a	a	X
ejpam-4382	115	14	)	)	PUNCT
ejpam-4382	115	15	=	=	PUNCT
ejpam-4382	115	16	x	x	X
ejpam-4382	115	17	−	−	PROPN
ejpam-4382	115	18	(	(	PUNCT
ejpam-4382	115	19	u	u	NOUN
ejpam-4382	115	20	∩	∩	NOUN
ejpam-4382	115	21	scli	scli	NOUN
ejpam-4382	115	22	(	(	PUNCT
ejpam-4382	115	23	a	a	NOUN
ejpam-4382	115	24	)	)	PUNCT
ejpam-4382	115	25	)	)	PUNCT
ejpam-4382	115	26	∩	∩	NOUN
ejpam-4382	115	27	scli	scli	NOUN
ejpam-4382	115	28	(	(	PUNCT
ejpam-4382	115	29	a	a	X
ejpam-4382	115	30	)	)	PUNCT
ejpam-4382	115	31	=	=	SYM
ejpam-4382	115	32	(	(	PUNCT
ejpam-4382	115	33	x	x	X
ejpam-4382	115	34	−	−	PROPN
ejpam-4382	115	35	u	u	NOUN
ejpam-4382	115	36	)	)	PUNCT
ejpam-4382	115	37	∩	∩	ADJ
ejpam-4382	115	38	scli	scli	NOUN
ejpam-4382	115	39	(	(	PUNCT
ejpam-4382	115	40	a	a	X
ejpam-4382	115	41	)	)	PUNCT
ejpam-4382	115	42	,	,	PUNCT
ejpam-4382	115	43	we	we	PRON
ejpam-4382	115	44	have	have	VERB
ejpam-4382	115	45	scli	scli	NOUN
ejpam-4382	115	46	(	(	PUNCT
ejpam-4382	115	47	a)−a	a)−a	X
ejpam-4382	115	48	is	be	AUX
ejpam-4382	115	49	semi	semi	ADJ
ejpam-4382	115	50	-	-	ADJ
ejpam-4382	115	51	i	i	PRON
ejpam-4382	115	52	-closed	-closed	ADJ
ejpam-4382	115	53	.	.	PUNCT
ejpam-4382	116	1	(	(	PUNCT
ejpam-4382	116	2	3	3	X
ejpam-4382	116	3	)	)	PUNCT
ejpam-4382	116	4	⇒	⇒	NOUN
ejpam-4382	116	5	(	(	PUNCT
ejpam-4382	116	6	4	4	NUM
ejpam-4382	116	7	):	):	PUNCT
ejpam-4382	116	8	suppose	suppose	VERB
ejpam-4382	116	9	that	that	SCONJ
ejpam-4382	116	10	scli	scli	PROPN
ejpam-4382	116	11	(	(	PUNCT
ejpam-4382	116	12	a)−	a)−	PROPN
ejpam-4382	116	13	a	a	PRON
ejpam-4382	116	14	is	be	AUX
ejpam-4382	116	15	semi	semi	ADJ
ejpam-4382	116	16	-	-	ADJ
ejpam-4382	116	17	i	i	PRON
ejpam-4382	116	18	-closed	-closed	ADJ
ejpam-4382	116	19	.	.	PUNCT
ejpam-4382	117	1	since	since	SCONJ
ejpam-4382	117	2	x	x	PRON
ejpam-4382	117	3	−	−	PROPN
ejpam-4382	117	4	(	(	PUNCT
ejpam-4382	117	5	scli	scli	PROPN
ejpam-4382	117	6	(	(	PUNCT
ejpam-4382	117	7	a)−	a)−	PROPN
ejpam-4382	117	8	a	a	PRON
ejpam-4382	117	9	)	)	PUNCT
ejpam-4382	117	10	=	=	SYM
ejpam-4382	117	11	(	(	PUNCT
ejpam-4382	117	12	x	x	SYM
ejpam-4382	117	13	−	−	PROPN
ejpam-4382	117	14	scli	scli	NOUN
ejpam-4382	117	15	(	(	PUNCT
ejpam-4382	117	16	a	a	NOUN
ejpam-4382	117	17	)	)	PUNCT
ejpam-4382	117	18	)	)	PUNCT
ejpam-4382	117	19	∪a	∪a	NUM
ejpam-4382	117	20	,	,	PUNCT
ejpam-4382	117	21	a	a	DET
ejpam-4382	117	22	∪	∪	ADJ
ejpam-4382	117	23	(	(	PUNCT
ejpam-4382	117	24	x	x	SYM
ejpam-4382	117	25	−	−	PROPN
ejpam-4382	117	26	scli	scli	NOUN
ejpam-4382	117	27	(	(	PUNCT
ejpam-4382	117	28	a	a	NOUN
ejpam-4382	117	29	)	)	PUNCT
ejpam-4382	117	30	)	)	PUNCT
ejpam-4382	117	31	is	be	AUX
ejpam-4382	117	32	semi	semi	ADJ
ejpam-4382	117	33	-	-	ADJ
ejpam-4382	117	34	i	i	PRON
ejpam-4382	117	35	-open	-open	ADJ
ejpam-4382	117	36	.	.	PUNCT
ejpam-4382	118	1	(	(	PUNCT
ejpam-4382	118	2	4	4	X
ejpam-4382	118	3	)	)	PUNCT
ejpam-4382	118	4	⇒	⇒	NOUN
ejpam-4382	118	5	(	(	PUNCT
ejpam-4382	118	6	5	5	NUM
ejpam-4382	118	7	):	):	PUNCT
ejpam-4382	118	8	the	the	DET
ejpam-4382	118	9	proof	proof	NOUN
ejpam-4382	118	10	is	be	AUX
ejpam-4382	118	11	obvious	obvious	ADJ
ejpam-4382	118	12	.	.	PUNCT
ejpam-4382	119	1	(	(	PUNCT
ejpam-4382	119	2	5	5	X
ejpam-4382	119	3	)	)	PUNCT
ejpam-4382	119	4	⇒	⇒	NOUN
ejpam-4382	119	5	(	(	PUNCT
ejpam-4382	119	6	1	1	NUM
ejpam-4382	119	7	):	):	PUNCT
ejpam-4382	119	8	by	by	ADP
ejpam-4382	119	9	(	(	PUNCT
ejpam-4382	119	10	5	5	NUM
ejpam-4382	119	11	)	)	PUNCT
ejpam-4382	119	12	and	and	CCONJ
ejpam-4382	119	13	lemma	lemma	PROPN
ejpam-4382	119	14	1(6	1(6	NUM
ejpam-4382	119	15	)	)	PUNCT
ejpam-4382	119	16	,	,	PUNCT
ejpam-4382	119	17	x	x	PUNCT
ejpam-4382	119	18	−	−	PROPN
ejpam-4382	119	19	scli	scli	NOUN
ejpam-4382	119	20	(	(	PUNCT
ejpam-4382	119	21	a	a	X
ejpam-4382	119	22	)	)	PUNCT
ejpam-4382	119	23	=	=	SYM
ejpam-4382	119	24	sinti	sinti	NOUN
ejpam-4382	119	25	(	(	PUNCT
ejpam-4382	119	26	x	x	SYM
ejpam-4382	119	27	−	−	PROPN
ejpam-4382	119	28	scli	scli	NOUN
ejpam-4382	119	29	(	(	PUNCT
ejpam-4382	119	30	a	a	NOUN
ejpam-4382	119	31	)	)	PUNCT
ejpam-4382	119	32	)	)	PUNCT
ejpam-4382	119	33	⊆	⊆	NUM
ejpam-4382	119	34	sinti	sinti	NOUN
ejpam-4382	119	35	(	(	PUNCT
ejpam-4382	119	36	a	a	DET
ejpam-4382	119	37	∪	∪	X
ejpam-4382	119	38	(	(	PUNCT
ejpam-4382	119	39	x	x	SYM
ejpam-4382	119	40	−	−	PROPN
ejpam-4382	119	41	scli	scli	NOUN
ejpam-4382	119	42	(	(	PUNCT
ejpam-4382	119	43	a	a	NOUN
ejpam-4382	119	44	)	)	PUNCT
ejpam-4382	119	45	)	)	PUNCT
ejpam-4382	119	46	)	)	PUNCT
ejpam-4382	119	47	and	and	CCONJ
ejpam-4382	119	48	hence	hence	ADV
ejpam-4382	119	49	a∪	a∪	INTJ
ejpam-4382	119	50	(	(	PUNCT
ejpam-4382	119	51	x	x	NOUN
ejpam-4382	119	52	−	−	PROPN
ejpam-4382	119	53	scli	scli	NOUN
ejpam-4382	119	54	(	(	PUNCT
ejpam-4382	119	55	a	a	NOUN
ejpam-4382	119	56	)	)	PUNCT
ejpam-4382	119	57	)	)	PUNCT
ejpam-4382	119	58	⊆	⊆	NUM
ejpam-4382	119	59	sinti	sinti	NOUN
ejpam-4382	119	60	(	(	PUNCT
ejpam-4382	119	61	a∪	a∪	X
ejpam-4382	119	62	(	(	PUNCT
ejpam-4382	119	63	x	x	NOUN
ejpam-4382	119	64	−	−	PROPN
ejpam-4382	119	65	scli	scli	NOUN
ejpam-4382	119	66	(	(	PUNCT
ejpam-4382	119	67	a	a	NOUN
ejpam-4382	119	68	)	)	PUNCT
ejpam-4382	119	69	)	)	PUNCT
ejpam-4382	119	70	)	)	PUNCT
ejpam-4382	119	71	.	.	PUNCT
ejpam-4382	120	1	thus	thus	ADV
ejpam-4382	120	2	,	,	PUNCT
ejpam-4382	120	3	a∪	a∪	INTJ
ejpam-4382	120	4	(	(	PUNCT
ejpam-4382	120	5	x	x	NOUN
ejpam-4382	120	6	−	−	PROPN
ejpam-4382	120	7	scli	scli	NOUN
ejpam-4382	120	8	(	(	PUNCT
ejpam-4382	120	9	a	a	NOUN
ejpam-4382	120	10	)	)	PUNCT
ejpam-4382	120	11	)	)	PUNCT
ejpam-4382	120	12	is	be	AUX
ejpam-4382	120	13	semi	semi	ADJ
ejpam-4382	120	14	-	-	ADJ
ejpam-4382	120	15	i	i	PRON
ejpam-4382	120	16	-open	-open	NOUN
ejpam-4382	120	17	.	.	PUNCT
ejpam-4382	121	1	since	since	SCONJ
ejpam-4382	121	2	a	a	PRON
ejpam-4382	121	3	=	=	X
ejpam-4382	121	4	(	(	PUNCT
ejpam-4382	121	5	a	a	DET
ejpam-4382	121	6	∪	∪	X
ejpam-4382	121	7	(	(	PUNCT
ejpam-4382	121	8	x	x	SYM
ejpam-4382	121	9	−	−	PROPN
ejpam-4382	121	10	scli	scli	NOUN
ejpam-4382	121	11	(	(	PUNCT
ejpam-4382	121	12	a	a	NOUN
ejpam-4382	121	13	)	)	PUNCT
ejpam-4382	121	14	)	)	PUNCT
ejpam-4382	121	15	)	)	PUNCT
ejpam-4382	121	16	∩	∩	NOUN
ejpam-4382	121	17	scli	scli	NOUN
ejpam-4382	121	18	(	(	PUNCT
ejpam-4382	121	19	a	a	X
ejpam-4382	121	20	)	)	PUNCT
ejpam-4382	121	21	,	,	PUNCT
ejpam-4382	121	22	we	we	PRON
ejpam-4382	121	23	have	have	VERB
ejpam-4382	121	24	a	a	PRON
ejpam-4382	121	25	is	be	AUX
ejpam-4382	121	26	locally	locally	ADV
ejpam-4382	121	27	semi	semi	ADJ
ejpam-4382	121	28	-	-	ADJ
ejpam-4382	121	29	i	i	PRON
ejpam-4382	121	30	closed	close	VERB
ejpam-4382	121	31	.	.	PUNCT
ejpam-4382	122	1	definition	definition	NOUN
ejpam-4382	122	2	4	4	NUM
ejpam-4382	122	3	.	.	PUNCT
ejpam-4382	123	1	a	a	DET
ejpam-4382	123	2	subset	subset	NOUN
ejpam-4382	123	3	a	a	PRON
ejpam-4382	123	4	of	of	ADP
ejpam-4382	123	5	an	an	DET
ejpam-4382	123	6	ideal	ideal	ADJ
ejpam-4382	123	7	topological	topological	ADJ
ejpam-4382	123	8	space	space	NOUN
ejpam-4382	123	9	(	(	PUNCT
ejpam-4382	123	10	x	x	X
ejpam-4382	123	11	,	,	PUNCT
ejpam-4382	123	12	τ	τ	PROPN
ejpam-4382	123	13	,	,	PUNCT
ejpam-4382	123	14	i	i	PROPN
ejpam-4382	123	15	)	)	PUNCT
ejpam-4382	123	16	is	be	AUX
ejpam-4382	123	17	said	say	VERB
ejpam-4382	123	18	to	to	PART
ejpam-4382	123	19	be	be	AUX
ejpam-4382	123	20	:	:	PUNCT
ejpam-4382	123	21	(	(	PUNCT
ejpam-4382	123	22	i	i	NOUN
ejpam-4382	123	23	)	)	PUNCT
ejpam-4382	123	24	a	a	DET
ejpam-4382	123	25	t	t	PROPN
ejpam-4382	123	26	-	-	PUNCT
ejpam-4382	123	27	si	si	NOUN
ejpam-4382	123	28	-set	-set	PUNCT
ejpam-4382	123	29	if	if	SCONJ
ejpam-4382	123	30	sinti	sinti	PROPN
ejpam-4382	123	31	(	(	PUNCT
ejpam-4382	123	32	a	a	X
ejpam-4382	123	33	)	)	PUNCT
ejpam-4382	123	34	=	=	SYM
ejpam-4382	123	35	sinti	sinti	NOUN
ejpam-4382	123	36	(	(	PUNCT
ejpam-4382	123	37	scli	scli	PROPN
ejpam-4382	123	38	(	(	PUNCT
ejpam-4382	123	39	a	a	NOUN
ejpam-4382	123	40	)	)	PUNCT
ejpam-4382	123	41	)	)	PUNCT
ejpam-4382	123	42	;	;	PUNCT
ejpam-4382	123	43	(	(	PUNCT
ejpam-4382	123	44	ii	ii	NOUN
ejpam-4382	123	45	)	)	PUNCT
ejpam-4382	123	46	a	a	DET
ejpam-4382	123	47	b	b	X
ejpam-4382	123	48	-	-	PUNCT
ejpam-4382	123	49	si	si	NOUN
ejpam-4382	123	50	-set	-set	NOUN
ejpam-4382	123	51	if	if	SCONJ
ejpam-4382	123	52	a	a	DET
ejpam-4382	123	53	=	=	X
ejpam-4382	123	54	u	u	NOUN
ejpam-4382	123	55	∩	∩	NOUN
ejpam-4382	123	56	v	v	NOUN
ejpam-4382	123	57	,	,	PUNCT
ejpam-4382	123	58	where	where	SCONJ
ejpam-4382	123	59	u	u	NOUN
ejpam-4382	123	60	is	be	AUX
ejpam-4382	123	61	a	a	DET
ejpam-4382	123	62	semi	semi	ADJ
ejpam-4382	123	63	-	-	ADJ
ejpam-4382	123	64	i	i	PRON
ejpam-4382	123	65	-open	-open	NOUN
ejpam-4382	123	66	set	set	VERB
ejpam-4382	123	67	and	and	CCONJ
ejpam-4382	123	68	v	v	NOUN
ejpam-4382	123	69	is	be	AUX
ejpam-4382	123	70	a	a	DET
ejpam-4382	123	71	t	t	PROPN
ejpam-4382	123	72	-	-	PUNCT
ejpam-4382	123	73	si	si	NOUN
ejpam-4382	123	74	-set	-set	ADJ
ejpam-4382	123	75	.	.	PUNCT
ejpam-4382	124	1	the	the	DET
ejpam-4382	124	2	following	follow	VERB
ejpam-4382	124	3	theorem	theorem	NOUN
ejpam-4382	124	4	gives	give	VERB
ejpam-4382	124	5	some	some	DET
ejpam-4382	124	6	characterizations	characterization	NOUN
ejpam-4382	124	7	of	of	ADP
ejpam-4382	124	8	semi	semi	ADJ
ejpam-4382	124	9	-	-	ADJ
ejpam-4382	124	10	i	i	PRON
ejpam-4382	124	11	-submaximal	-submaximal	ADJ
ejpam-4382	124	12	ideal	ideal	ADJ
ejpam-4382	124	13	topological	topological	ADJ
ejpam-4382	124	14	spaces	space	NOUN
ejpam-4382	124	15	.	.	PUNCT
ejpam-4382	125	1	c.	c.	PROPN
ejpam-4382	125	2	boonpok	boonpok	PROPN
ejpam-4382	125	3	/	/	SYM
ejpam-4382	125	4	eur	eur	PROPN
ejpam-4382	125	5	.	.	PUNCT
ejpam-4382	126	1	j.	j.	PROPN
ejpam-4382	126	2	pure	pure	PROPN
ejpam-4382	126	3	appl	appl	PROPN
ejpam-4382	126	4	.	.	PROPN
ejpam-4382	126	5	math	math	PROPN
ejpam-4382	126	6	,	,	PUNCT
ejpam-4382	126	7	15	15	NUM
ejpam-4382	126	8	(	(	PUNCT
ejpam-4382	126	9	3	3	NUM
ejpam-4382	126	10	)	)	PUNCT
ejpam-4382	126	11	(	(	PUNCT
ejpam-4382	126	12	2022	2022	NUM
ejpam-4382	126	13	)	)	PUNCT
ejpam-4382	126	14	,	,	PUNCT
ejpam-4382	126	15	938	938	NUM
ejpam-4382	126	16	-	-	SYM
ejpam-4382	126	17	947	947	NUM
ejpam-4382	126	18	942	942	NUM
ejpam-4382	126	19	theorem	theorem	NOUN
ejpam-4382	126	20	2	2	NUM
ejpam-4382	126	21	.	.	X
ejpam-4382	126	22	for	for	ADP
ejpam-4382	126	23	an	an	DET
ejpam-4382	126	24	ideal	ideal	ADJ
ejpam-4382	126	25	topological	topological	ADJ
ejpam-4382	126	26	space	space	NOUN
ejpam-4382	126	27	(	(	PUNCT
ejpam-4382	126	28	x	x	X
ejpam-4382	126	29	,	,	PUNCT
ejpam-4382	126	30	τ	τ	PROPN
ejpam-4382	126	31	,	,	PUNCT
ejpam-4382	126	32	i	i	NOUN
ejpam-4382	126	33	)	)	PUNCT
ejpam-4382	126	34	,	,	PUNCT
ejpam-4382	126	35	the	the	DET
ejpam-4382	126	36	following	follow	VERB
ejpam-4382	126	37	properties	property	NOUN
ejpam-4382	126	38	are	be	AUX
ejpam-4382	126	39	equivalent	equivalent	ADJ
ejpam-4382	126	40	:	:	PUNCT
ejpam-4382	126	41	(	(	PUNCT
ejpam-4382	126	42	1	1	X
ejpam-4382	126	43	)	)	PUNCT
ejpam-4382	126	44	(	(	PUNCT
ejpam-4382	126	45	x	x	X
ejpam-4382	126	46	,	,	PUNCT
ejpam-4382	126	47	τ	τ	PROPN
ejpam-4382	126	48	,	,	PUNCT
ejpam-4382	126	49	i	i	PROPN
ejpam-4382	126	50	)	)	PUNCT
ejpam-4382	126	51	is	be	AUX
ejpam-4382	126	52	semi	semi	ADJ
ejpam-4382	126	53	-	-	ADJ
ejpam-4382	126	54	i	i	PRON
ejpam-4382	126	55	-submaximal	-submaximal	ADJ
ejpam-4382	126	56	;	;	PUNCT
ejpam-4382	126	57	(	(	PUNCT
ejpam-4382	126	58	2	2	X
ejpam-4382	126	59	)	)	PUNCT
ejpam-4382	126	60	scli	scli	NOUN
ejpam-4382	126	61	(	(	PUNCT
ejpam-4382	126	62	a)−a	a)−a	X
ejpam-4382	126	63	is	be	AUX
ejpam-4382	126	64	semi	semi	ADJ
ejpam-4382	126	65	-	-	ADJ
ejpam-4382	126	66	i	i	PRON
ejpam-4382	126	67	-closed	-close	VERB
ejpam-4382	126	68	for	for	ADP
ejpam-4382	126	69	every	every	DET
ejpam-4382	126	70	subset	subset	NOUN
ejpam-4382	126	71	a	a	PRON
ejpam-4382	126	72	of	of	ADP
ejpam-4382	126	73	x	x	PRON
ejpam-4382	126	74	;	;	PUNCT
ejpam-4382	126	75	(	(	PUNCT
ejpam-4382	126	76	3	3	X
ejpam-4382	126	77	)	)	PUNCT
ejpam-4382	126	78	every	every	DET
ejpam-4382	126	79	subset	subset	NOUN
ejpam-4382	126	80	of	of	ADP
ejpam-4382	126	81	x	x	PUNCT
ejpam-4382	126	82	is	be	AUX
ejpam-4382	126	83	locally	locally	ADV
ejpam-4382	126	84	semi	semi	ADJ
ejpam-4382	126	85	-	-	ADJ
ejpam-4382	126	86	i	i	PRON
ejpam-4382	126	87	-closed	-close	VERB
ejpam-4382	126	88	;	;	PUNCT
ejpam-4382	126	89	(	(	PUNCT
ejpam-4382	126	90	4	4	X
ejpam-4382	126	91	)	)	PUNCT
ejpam-4382	126	92	every	every	DET
ejpam-4382	126	93	subset	subset	NOUN
ejpam-4382	126	94	of	of	ADP
ejpam-4382	126	95	x	x	PUNCT
ejpam-4382	126	96	is	be	AUX
ejpam-4382	126	97	a	a	DET
ejpam-4382	126	98	b	b	PROPN
ejpam-4382	126	99	-	-	PUNCT
ejpam-4382	126	100	si	si	NOUN
ejpam-4382	126	101	-set	-set	ADJ
ejpam-4382	126	102	;	;	PUNCT
ejpam-4382	126	103	(	(	PUNCT
ejpam-4382	126	104	5	5	X
ejpam-4382	126	105	)	)	PUNCT
ejpam-4382	126	106	every	every	DET
ejpam-4382	126	107	semi	semi	ADJ
ejpam-4382	126	108	-	-	ADJ
ejpam-4382	126	109	i	i	ADJ
ejpam-4382	126	110	-dense	-dense	NOUN
ejpam-4382	126	111	subset	subset	NOUN
ejpam-4382	126	112	of	of	ADP
ejpam-4382	126	113	x	x	PUNCT
ejpam-4382	126	114	is	be	AUX
ejpam-4382	126	115	a	a	DET
ejpam-4382	126	116	b	b	PROPN
ejpam-4382	126	117	-	-	PUNCT
ejpam-4382	126	118	si	si	ADJ
ejpam-4382	126	119	-set	-set	ADJ
ejpam-4382	126	120	.	.	PUNCT
ejpam-4382	127	1	proof	proof	NOUN
ejpam-4382	127	2	.	.	PUNCT
ejpam-4382	128	1	(	(	PUNCT
ejpam-4382	128	2	1	1	X
ejpam-4382	128	3	)	)	PUNCT
ejpam-4382	128	4	⇒	⇒	NOUN
ejpam-4382	128	5	(	(	PUNCT
ejpam-4382	128	6	2	2	NUM
ejpam-4382	128	7	):	):	PUNCT
ejpam-4382	128	8	suppose	suppose	VERB
ejpam-4382	128	9	that	that	SCONJ
ejpam-4382	128	10	(	(	PUNCT
ejpam-4382	128	11	x	x	X
ejpam-4382	128	12	,	,	PUNCT
ejpam-4382	128	13	τ	τ	PROPN
ejpam-4382	128	14	,	,	PUNCT
ejpam-4382	128	15	i	i	PROPN
ejpam-4382	128	16	)	)	PUNCT
ejpam-4382	128	17	is	be	AUX
ejpam-4382	128	18	semi	semi	ADJ
ejpam-4382	128	19	-	-	ADJ
ejpam-4382	128	20	i	i	PRON
ejpam-4382	128	21	-submaximal	-submaximal	ADJ
ejpam-4382	128	22	.	.	PUNCT
ejpam-4382	129	1	let	let	VERB
ejpam-4382	129	2	a	a	DET
ejpam-4382	129	3	be	be	AUX
ejpam-4382	129	4	a	a	DET
ejpam-4382	129	5	subset	subset	NOUN
ejpam-4382	129	6	of	of	ADP
ejpam-4382	129	7	x.	x.	NOUN
ejpam-4382	129	8	since	since	SCONJ
ejpam-4382	129	9	x	x	PROPN
ejpam-4382	129	10	=	=	PRON
ejpam-4382	129	11	scli	scli	NOUN
ejpam-4382	129	12	(	(	PUNCT
ejpam-4382	129	13	a	a	NOUN
ejpam-4382	129	14	)	)	PUNCT
ejpam-4382	129	15	∪	∪	NOUN
ejpam-4382	129	16	(	(	PUNCT
ejpam-4382	129	17	x	x	SYM
ejpam-4382	129	18	−	−	PROPN
ejpam-4382	129	19	scli	scli	NOUN
ejpam-4382	129	20	(	(	PUNCT
ejpam-4382	129	21	a	a	NOUN
ejpam-4382	129	22	)	)	PUNCT
ejpam-4382	129	23	)	)	PUNCT
ejpam-4382	129	24	⊆	⊆	NUM
ejpam-4382	129	25	scli	scli	NOUN
ejpam-4382	129	26	(	(	PUNCT
ejpam-4382	129	27	a	a	NOUN
ejpam-4382	129	28	)	)	PUNCT
ejpam-4382	129	29	∪	∪	NOUN
ejpam-4382	129	30	(	(	PUNCT
ejpam-4382	129	31	x	x	SYM
ejpam-4382	129	32	−	−	PROPN
ejpam-4382	129	33	sinti	sinti	PROPN
ejpam-4382	129	34	(	(	PUNCT
ejpam-4382	129	35	scli	scli	PROPN
ejpam-4382	129	36	(	(	PUNCT
ejpam-4382	129	37	a	a	NOUN
ejpam-4382	129	38	)	)	PUNCT
ejpam-4382	129	39	)	)	PUNCT
ejpam-4382	129	40	)	)	PUNCT
ejpam-4382	130	1	=	=	PRON
ejpam-4382	130	2	scli	scli	NOUN
ejpam-4382	130	3	(	(	PUNCT
ejpam-4382	130	4	a	a	NOUN
ejpam-4382	130	5	)	)	PUNCT
ejpam-4382	130	6	∪	∪	ADP
ejpam-4382	130	7	scli	scli	NOUN
ejpam-4382	130	8	(	(	PUNCT
ejpam-4382	130	9	x	x	NOUN
ejpam-4382	130	10	−	−	PROPN
ejpam-4382	130	11	scli	scli	NOUN
ejpam-4382	130	12	(	(	PUNCT
ejpam-4382	130	13	a	a	NOUN
ejpam-4382	130	14	)	)	PUNCT
ejpam-4382	130	15	)	)	PUNCT
ejpam-4382	130	16	⊆	⊆	NUM
ejpam-4382	130	17	scli	scli	NOUN
ejpam-4382	130	18	(	(	PUNCT
ejpam-4382	130	19	a	a	DET
ejpam-4382	130	20	∪	∪	X
ejpam-4382	130	21	(	(	PUNCT
ejpam-4382	130	22	x	x	SYM
ejpam-4382	130	23	−	−	PROPN
ejpam-4382	130	24	scli	scli	NOUN
ejpam-4382	130	25	(	(	PUNCT
ejpam-4382	130	26	a	a	NOUN
ejpam-4382	130	27	)	)	PUNCT
ejpam-4382	130	28	)	)	PUNCT
ejpam-4382	130	29	)	)	PUNCT
ejpam-4382	130	30	=	=	PRON
ejpam-4382	130	31	scli	scli	NOUN
ejpam-4382	130	32	(	(	PUNCT
ejpam-4382	130	33	x	x	SYM
ejpam-4382	130	34	−	−	PROPN
ejpam-4382	130	35	(	(	PUNCT
ejpam-4382	130	36	scli	scli	PROPN
ejpam-4382	130	37	(	(	PUNCT
ejpam-4382	130	38	a)−a	a)−a	NOUN
ejpam-4382	130	39	)	)	PUNCT
ejpam-4382	130	40	)	)	PUNCT
ejpam-4382	130	41	,	,	PUNCT
ejpam-4382	130	42	we	we	PRON
ejpam-4382	130	43	have	have	VERB
ejpam-4382	130	44	scli	scli	NOUN
ejpam-4382	130	45	(	(	PUNCT
ejpam-4382	130	46	x−(scli	x−(scli	NOUN
ejpam-4382	130	47	(	(	PUNCT
ejpam-4382	130	48	a)−a	a)−a	NOUN
ejpam-4382	130	49	)	)	PUNCT
ejpam-4382	130	50	)	)	PUNCT
ejpam-4382	131	1	=	=	PUNCT
ejpam-4382	132	1	x	x	PUNCT
ejpam-4382	132	2	and	and	CCONJ
ejpam-4382	132	3	hence	hence	ADV
ejpam-4382	132	4	x−(scli	x−(scli	NUM
ejpam-4382	132	5	(	(	PUNCT
ejpam-4382	132	6	a)−a	a)−a	NOUN
ejpam-4382	132	7	)	)	PUNCT
ejpam-4382	132	8	is	be	AUX
ejpam-4382	132	9	semi	semi	ADJ
ejpam-4382	132	10	-	-	ADJ
ejpam-4382	132	11	i	i	ADJ
ejpam-4382	132	12	-dense	-dense	NOUN
ejpam-4382	132	13	.	.	PUNCT
ejpam-4382	133	1	by	by	ADP
ejpam-4382	133	2	the	the	DET
ejpam-4382	133	3	hypothesis	hypothesis	NOUN
ejpam-4382	133	4	,	,	PUNCT
ejpam-4382	133	5	x−	x−	PROPN
ejpam-4382	133	6	(	(	PUNCT
ejpam-4382	133	7	scli	scli	PROPN
ejpam-4382	133	8	(	(	PUNCT
ejpam-4382	133	9	a)−a	a)−a	X
ejpam-4382	133	10	)	)	PUNCT
ejpam-4382	133	11	is	be	AUX
ejpam-4382	133	12	semi	semi	ADJ
ejpam-4382	133	13	-	-	ADJ
ejpam-4382	133	14	i	i	PRON
ejpam-4382	133	15	-open	-open	ADJ
ejpam-4382	133	16	and	and	CCONJ
ejpam-4382	133	17	so	so	ADV
ejpam-4382	133	18	scli	scli	PROPN
ejpam-4382	133	19	(	(	PUNCT
ejpam-4382	133	20	a)−a	a)−a	X
ejpam-4382	133	21	is	be	AUX
ejpam-4382	133	22	semi	semi	ADJ
ejpam-4382	133	23	-	-	ADJ
ejpam-4382	133	24	i	i	PRON
ejpam-4382	133	25	-closed	-closed	ADJ
ejpam-4382	133	26	.	.	PUNCT
ejpam-4382	134	1	(	(	PUNCT
ejpam-4382	134	2	2	2	NUM
ejpam-4382	134	3	)	)	PUNCT
ejpam-4382	134	4	and	and	CCONJ
ejpam-4382	134	5	(	(	PUNCT
ejpam-4382	134	6	3	3	X
ejpam-4382	134	7	)	)	PUNCT
ejpam-4382	134	8	are	be	AUX
ejpam-4382	134	9	equivalent	equivalent	ADJ
ejpam-4382	134	10	by	by	ADP
ejpam-4382	134	11	theorem	theorem	NOUN
ejpam-4382	134	12	1	1	NUM
ejpam-4382	134	13	.	.	PUNCT
ejpam-4382	134	14	(	(	PUNCT
ejpam-4382	134	15	3	3	X
ejpam-4382	134	16	)	)	PUNCT
ejpam-4382	134	17	⇒	⇒	NOUN
ejpam-4382	134	18	(	(	PUNCT
ejpam-4382	134	19	4	4	NUM
ejpam-4382	134	20	)	)	PUNCT
ejpam-4382	134	21	and	and	CCONJ
ejpam-4382	134	22	(	(	PUNCT
ejpam-4382	134	23	4	4	X
ejpam-4382	134	24	)	)	PUNCT
ejpam-4382	134	25	⇒	⇒	NOUN
ejpam-4382	134	26	(	(	PUNCT
ejpam-4382	134	27	5	5	X
ejpam-4382	134	28	)	)	PUNCT
ejpam-4382	134	29	are	be	AUX
ejpam-4382	134	30	obvious	obvious	ADJ
ejpam-4382	134	31	.	.	PUNCT
ejpam-4382	135	1	(	(	PUNCT
ejpam-4382	135	2	5	5	X
ejpam-4382	135	3	)	)	PUNCT
ejpam-4382	135	4	⇒	⇒	NOUN
ejpam-4382	135	5	(	(	PUNCT
ejpam-4382	135	6	1	1	NUM
ejpam-4382	135	7	):	):	PUNCT
ejpam-4382	135	8	let	let	VERB
ejpam-4382	135	9	a	a	PRON
ejpam-4382	135	10	be	be	AUX
ejpam-4382	135	11	a	a	DET
ejpam-4382	135	12	semi	semi	ADJ
ejpam-4382	135	13	-	-	ADJ
ejpam-4382	135	14	i	i	ADJ
ejpam-4382	135	15	-dense	-dense	PROPN
ejpam-4382	135	16	subset	subset	NOUN
ejpam-4382	135	17	of	of	ADP
ejpam-4382	135	18	x.	x.	NOUN
ejpam-4382	135	19	by	by	ADP
ejpam-4382	135	20	(	(	PUNCT
ejpam-4382	135	21	5	5	NUM
ejpam-4382	135	22	)	)	PUNCT
ejpam-4382	135	23	,	,	PUNCT
ejpam-4382	135	24	a	a	PRON
ejpam-4382	135	25	is	be	AUX
ejpam-4382	135	26	a	a	DET
ejpam-4382	135	27	b	b	NOUN
ejpam-4382	135	28	-	-	PUNCT
ejpam-4382	135	29	si	si	NOUN
ejpam-4382	135	30	-set	-set	PUNCT
ejpam-4382	135	31	and	and	CCONJ
ejpam-4382	135	32	so	so	ADV
ejpam-4382	135	33	a	a	DET
ejpam-4382	135	34	=	=	X
ejpam-4382	135	35	u	u	NOUN
ejpam-4382	135	36	∩	∩	NOUN
ejpam-4382	135	37	v	v	NOUN
ejpam-4382	135	38	,	,	PUNCT
ejpam-4382	135	39	where	where	SCONJ
ejpam-4382	135	40	u	u	NOUN
ejpam-4382	135	41	is	be	AUX
ejpam-4382	135	42	semi	semi	ADJ
ejpam-4382	135	43	-	-	ADJ
ejpam-4382	135	44	i	i	PRON
ejpam-4382	135	45	-open	-open	ADJ
ejpam-4382	135	46	and	and	CCONJ
ejpam-4382	135	47	sinti	sinti	PROPN
ejpam-4382	135	48	(	(	PUNCT
ejpam-4382	135	49	v	v	NOUN
ejpam-4382	135	50	)	)	PUNCT
ejpam-4382	135	51	=	=	SYM
ejpam-4382	135	52	sinti	sinti	NOUN
ejpam-4382	135	53	(	(	PUNCT
ejpam-4382	135	54	scli	scli	PROPN
ejpam-4382	135	55	(	(	PUNCT
ejpam-4382	135	56	v	v	NOUN
ejpam-4382	135	57	)	)	PUNCT
ejpam-4382	135	58	)	)	PUNCT
ejpam-4382	135	59	.	.	PUNCT
ejpam-4382	136	1	since	since	SCONJ
ejpam-4382	136	2	a	a	DET
ejpam-4382	136	3	⊆	⊆	NUM
ejpam-4382	136	4	v	v	NOUN
ejpam-4382	136	5	,	,	PUNCT
ejpam-4382	136	6	scli	scli	PROPN
ejpam-4382	136	7	(	(	PUNCT
ejpam-4382	136	8	a	a	NOUN
ejpam-4382	136	9	)	)	PUNCT
ejpam-4382	136	10	⊆	⊆	NUM
ejpam-4382	136	11	scli	scli	NOUN
ejpam-4382	136	12	(	(	PUNCT
ejpam-4382	136	13	v	v	NOUN
ejpam-4382	136	14	)	)	PUNCT
ejpam-4382	136	15	and	and	CCONJ
ejpam-4382	136	16	hence	hence	ADV
ejpam-4382	136	17	x	x	X
ejpam-4382	136	18	=	=	PRON
ejpam-4382	136	19	scli	scli	NOUN
ejpam-4382	136	20	(	(	PUNCT
ejpam-4382	136	21	v	v	NOUN
ejpam-4382	136	22	)	)	PUNCT
ejpam-4382	136	23	.	.	PUNCT
ejpam-4382	137	1	thus	thus	ADV
ejpam-4382	137	2	,	,	PUNCT
ejpam-4382	137	3	x	x	SYM
ejpam-4382	137	4	=	=	SYM
ejpam-4382	137	5	sinti	sinti	X
ejpam-4382	137	6	(	(	PUNCT
ejpam-4382	137	7	scli	scli	PROPN
ejpam-4382	137	8	(	(	PUNCT
ejpam-4382	137	9	v	v	NOUN
ejpam-4382	137	10	)	)	PUNCT
ejpam-4382	137	11	)	)	PUNCT
ejpam-4382	138	1	=	=	SYM
ejpam-4382	138	2	sinti	sinti	X
ejpam-4382	138	3	(	(	PUNCT
ejpam-4382	138	4	v	v	NOUN
ejpam-4382	138	5	)	)	PUNCT
ejpam-4382	138	6	.	.	PUNCT
ejpam-4382	139	1	this	this	PRON
ejpam-4382	139	2	implies	imply	VERB
ejpam-4382	139	3	that	that	SCONJ
ejpam-4382	139	4	v	v	X
ejpam-4382	139	5	=	=	SYM
ejpam-4382	139	6	x.	x.	NOUN
ejpam-4382	139	7	therefore	therefore	ADV
ejpam-4382	139	8	,	,	PUNCT
ejpam-4382	139	9	a	a	DET
ejpam-4382	139	10	=	=	NOUN
ejpam-4382	139	11	u∩v	u∩v	NOUN
ejpam-4382	139	12	=	=	NOUN
ejpam-4382	139	13	u∩x	u∩x	NUM
ejpam-4382	139	14	=	=	PUNCT
ejpam-4382	139	15	u	u	NOUN
ejpam-4382	139	16	and	and	CCONJ
ejpam-4382	139	17	hence	hence	ADV
ejpam-4382	139	18	a	a	PRON
ejpam-4382	139	19	is	be	AUX
ejpam-4382	139	20	semi	semi	ADJ
ejpam-4382	139	21	-	-	ADJ
ejpam-4382	139	22	i	i	PRON
ejpam-4382	139	23	-open	-open	NOUN
ejpam-4382	139	24	.	.	PUNCT
ejpam-4382	140	1	thus	thus	ADV
ejpam-4382	140	2	,	,	PUNCT
ejpam-4382	140	3	(	(	PUNCT
ejpam-4382	140	4	x	x	X
ejpam-4382	140	5	,	,	PUNCT
ejpam-4382	140	6	τ	τ	PROPN
ejpam-4382	140	7	,	,	PUNCT
ejpam-4382	140	8	i	i	PROPN
ejpam-4382	140	9	)	)	PUNCT
ejpam-4382	140	10	is	be	AUX
ejpam-4382	140	11	semi	semi	ADJ
ejpam-4382	140	12	-	-	ADJ
ejpam-4382	140	13	i	i	PRON
ejpam-4382	140	14	-submaximal	-submaximal	ADJ
ejpam-4382	140	15	.	.	PUNCT
ejpam-4382	141	1	definition	definition	NOUN
ejpam-4382	141	2	5	5	NUM
ejpam-4382	141	3	.	.	PUNCT
ejpam-4382	142	1	a	a	DET
ejpam-4382	142	2	point	point	NOUN
ejpam-4382	142	3	x	x	PUNCT
ejpam-4382	142	4	of	of	ADP
ejpam-4382	142	5	an	an	DET
ejpam-4382	142	6	ideal	ideal	ADJ
ejpam-4382	142	7	topological	topological	ADJ
ejpam-4382	142	8	space	space	NOUN
ejpam-4382	142	9	(	(	PUNCT
ejpam-4382	142	10	x	x	X
ejpam-4382	142	11	,	,	PUNCT
ejpam-4382	142	12	τ	τ	PROPN
ejpam-4382	142	13	,	,	PUNCT
ejpam-4382	142	14	i	i	PROPN
ejpam-4382	142	15	)	)	PUNCT
ejpam-4382	142	16	is	be	AUX
ejpam-4382	142	17	called	call	VERB
ejpam-4382	142	18	semi	semi	ADJ
ejpam-4382	142	19	-	-	ADJ
ejpam-4382	142	20	i	i	PRON
ejpam-4382	142	21	-isolated	-isolate	VERB
ejpam-4382	142	22	if	if	SCONJ
ejpam-4382	142	23	{	{	PUNCT
ejpam-4382	142	24	x	x	NOUN
ejpam-4382	142	25	}	}	PUNCT
ejpam-4382	142	26	is	be	AUX
ejpam-4382	142	27	semi	semi	ADJ
ejpam-4382	142	28	-	-	ADJ
ejpam-4382	142	29	i	i	PRON
ejpam-4382	142	30	-open	-open	ADJ
ejpam-4382	142	31	and	and	CCONJ
ejpam-4382	142	32	(	(	PUNCT
ejpam-4382	142	33	x	x	NOUN
ejpam-4382	142	34	,	,	PUNCT
ejpam-4382	142	35	τ	τ	PROPN
ejpam-4382	142	36	,	,	PUNCT
ejpam-4382	142	37	i	i	PROPN
ejpam-4382	142	38	)	)	PUNCT
ejpam-4382	142	39	is	be	AUX
ejpam-4382	142	40	called	call	VERB
ejpam-4382	142	41	semi	semi	ADJ
ejpam-4382	142	42	-	-	ADJ
ejpam-4382	142	43	i	i	PRON
ejpam-4382	142	44	-discrete	-discrete	ADJ
ejpam-4382	142	45	if	if	SCONJ
ejpam-4382	142	46	every	every	DET
ejpam-4382	142	47	point	point	NOUN
ejpam-4382	142	48	of	of	ADP
ejpam-4382	142	49	x	x	NOUN
ejpam-4382	142	50	is	be	AUX
ejpam-4382	142	51	semii	semii	NOUN
ejpam-4382	142	52	-isolated	-isolate	VERB
ejpam-4382	142	53	.	.	PUNCT
ejpam-4382	143	1	lemma	lemma	PROPN
ejpam-4382	143	2	2	2	X
ejpam-4382	143	3	.	.	PUNCT
ejpam-4382	143	4	let	let	VERB
ejpam-4382	143	5	a	a	DET
ejpam-4382	143	6	be	be	AUX
ejpam-4382	143	7	a	a	DET
ejpam-4382	143	8	subset	subset	NOUN
ejpam-4382	143	9	of	of	ADP
ejpam-4382	143	10	an	an	DET
ejpam-4382	143	11	ideal	ideal	ADJ
ejpam-4382	143	12	topological	topological	ADJ
ejpam-4382	143	13	space	space	NOUN
ejpam-4382	143	14	(	(	PUNCT
ejpam-4382	143	15	x	x	X
ejpam-4382	143	16	,	,	PUNCT
ejpam-4382	143	17	τ	τ	PROPN
ejpam-4382	143	18	,	,	PUNCT
ejpam-4382	143	19	i	i	NOUN
ejpam-4382	143	20	)	)	PUNCT
ejpam-4382	143	21	.	.	PUNCT
ejpam-4382	144	1	then	then	ADV
ejpam-4382	144	2	,	,	PUNCT
ejpam-4382	144	3	sinti	sinti	PROPN
ejpam-4382	144	4	(	(	PUNCT
ejpam-4382	144	5	scli	scli	PROPN
ejpam-4382	144	6	(	(	PUNCT
ejpam-4382	144	7	a)−a	a)−a	X
ejpam-4382	144	8	)	)	PUNCT
ejpam-4382	144	9	=	=	PUNCT
ejpam-4382	144	10	∅.	∅.	NOUN
ejpam-4382	144	11	proof	proof	NOUN
ejpam-4382	144	12	.	.	PUNCT
ejpam-4382	145	1	let	let	VERB
ejpam-4382	145	2	a	a	DET
ejpam-4382	145	3	be	be	AUX
ejpam-4382	145	4	a	a	DET
ejpam-4382	145	5	subset	subset	NOUN
ejpam-4382	145	6	of	of	ADP
ejpam-4382	145	7	x.	x.	NOUN
ejpam-4382	145	8	since	since	SCONJ
ejpam-4382	145	9	sinti	sinti	PROPN
ejpam-4382	145	10	(	(	PUNCT
ejpam-4382	145	11	x	x	NOUN
ejpam-4382	145	12	−a	−a	ADV
ejpam-4382	145	13	)	)	PUNCT
ejpam-4382	145	14	=	=	PUNCT
ejpam-4382	146	1	x	x	PUNCT
ejpam-4382	146	2	−	−	PROPN
ejpam-4382	146	3	scli	scli	NOUN
ejpam-4382	146	4	(	(	PUNCT
ejpam-4382	146	5	a	a	X
ejpam-4382	146	6	)	)	PUNCT
ejpam-4382	146	7	,	,	PUNCT
ejpam-4382	146	8	we	we	PRON
ejpam-4382	146	9	have	have	AUX
ejpam-4382	146	10	sinti	sinti	PROPN
ejpam-4382	146	11	(	(	PUNCT
ejpam-4382	146	12	scli	scli	PROPN
ejpam-4382	146	13	(	(	PUNCT
ejpam-4382	146	14	a)−a	a)−a	X
ejpam-4382	146	15	)	)	PUNCT
ejpam-4382	146	16	=	=	SYM
ejpam-4382	146	17	sinti	sinti	NOUN
ejpam-4382	146	18	(	(	PUNCT
ejpam-4382	146	19	scli	scli	PROPN
ejpam-4382	146	20	(	(	PUNCT
ejpam-4382	146	21	a	a	NOUN
ejpam-4382	146	22	)	)	PUNCT
ejpam-4382	146	23	∩	∩	NOUN
ejpam-4382	146	24	(	(	PUNCT
ejpam-4382	146	25	x	x	NOUN
ejpam-4382	146	26	−a	−a	NOUN
ejpam-4382	146	27	)	)	PUNCT
ejpam-4382	146	28	)	)	PUNCT
ejpam-4382	147	1	⊆	⊆	NUM
ejpam-4382	147	2	sinti	sinti	NOUN
ejpam-4382	147	3	(	(	PUNCT
ejpam-4382	147	4	scli	scli	PROPN
ejpam-4382	147	5	(	(	PUNCT
ejpam-4382	147	6	a	a	NOUN
ejpam-4382	147	7	)	)	PUNCT
ejpam-4382	147	8	)	)	PUNCT
ejpam-4382	147	9	∩	∩	PROPN
ejpam-4382	147	10	sinti	sinti	X
ejpam-4382	147	11	(	(	PUNCT
ejpam-4382	147	12	x	x	NOUN
ejpam-4382	147	13	−a	−a	NOUN
ejpam-4382	147	14	)	)	PUNCT
ejpam-4382	147	15	=	=	SYM
ejpam-4382	147	16	sinti	sinti	NOUN
ejpam-4382	147	17	(	(	PUNCT
ejpam-4382	147	18	scli	scli	PROPN
ejpam-4382	147	19	(	(	PUNCT
ejpam-4382	147	20	a	a	NOUN
ejpam-4382	147	21	)	)	PUNCT
ejpam-4382	147	22	)	)	PUNCT
ejpam-4382	147	23	∩	∩	NOUN
ejpam-4382	147	24	(	(	PUNCT
ejpam-4382	147	25	x	x	SYM
ejpam-4382	147	26	−	−	PROPN
ejpam-4382	147	27	scli	scli	NOUN
ejpam-4382	147	28	(	(	PUNCT
ejpam-4382	147	29	a	a	NOUN
ejpam-4382	147	30	)	)	PUNCT
ejpam-4382	147	31	)	)	PUNCT
ejpam-4382	147	32	⊆	⊆	NUM
ejpam-4382	147	33	scli	scli	NOUN
ejpam-4382	147	34	(	(	PUNCT
ejpam-4382	147	35	a	a	NOUN
ejpam-4382	147	36	)	)	PUNCT
ejpam-4382	147	37	∩	∩	NOUN
ejpam-4382	147	38	(	(	PUNCT
ejpam-4382	147	39	x	x	SYM
ejpam-4382	147	40	−	−	PROPN
ejpam-4382	147	41	scli	scli	NOUN
ejpam-4382	147	42	(	(	PUNCT
ejpam-4382	147	43	a	a	NOUN
ejpam-4382	147	44	)	)	PUNCT
ejpam-4382	147	45	)	)	PUNCT
ejpam-4382	147	46	=	=	PUNCT
ejpam-4382	147	47	∅.	∅.	PROPN
ejpam-4382	147	48	c.	c.	PROPN
ejpam-4382	147	49	boonpok	boonpok	PROPN
ejpam-4382	147	50	/	/	SYM
ejpam-4382	147	51	eur	eur	PROPN
ejpam-4382	147	52	.	.	PUNCT
ejpam-4382	148	1	j.	j.	PROPN
ejpam-4382	148	2	pure	pure	PROPN
ejpam-4382	148	3	appl	appl	PROPN
ejpam-4382	148	4	.	.	PROPN
ejpam-4382	148	5	math	math	PROPN
ejpam-4382	148	6	,	,	PUNCT
ejpam-4382	148	7	15	15	NUM
ejpam-4382	148	8	(	(	PUNCT
ejpam-4382	148	9	3	3	NUM
ejpam-4382	148	10	)	)	PUNCT
ejpam-4382	148	11	(	(	PUNCT
ejpam-4382	148	12	2022	2022	NUM
ejpam-4382	148	13	)	)	PUNCT
ejpam-4382	148	14	,	,	PUNCT
ejpam-4382	148	15	938	938	NUM
ejpam-4382	148	16	-	-	SYM
ejpam-4382	148	17	947	947	NUM
ejpam-4382	148	18	943	943	NUM
ejpam-4382	148	19	theorem	theorem	NOUN
ejpam-4382	148	20	3	3	NUM
ejpam-4382	148	21	.	.	X
ejpam-4382	149	1	for	for	ADP
ejpam-4382	149	2	an	an	DET
ejpam-4382	149	3	ideal	ideal	ADJ
ejpam-4382	149	4	topological	topological	ADJ
ejpam-4382	149	5	space	space	NOUN
ejpam-4382	149	6	(	(	PUNCT
ejpam-4382	149	7	x	x	X
ejpam-4382	149	8	,	,	PUNCT
ejpam-4382	149	9	τ	τ	PROPN
ejpam-4382	149	10	,	,	PUNCT
ejpam-4382	149	11	i	i	NOUN
ejpam-4382	149	12	)	)	PUNCT
ejpam-4382	149	13	,	,	PUNCT
ejpam-4382	149	14	the	the	DET
ejpam-4382	149	15	following	follow	VERB
ejpam-4382	149	16	properties	property	NOUN
ejpam-4382	149	17	are	be	AUX
ejpam-4382	149	18	equivalent	equivalent	ADJ
ejpam-4382	149	19	:	:	PUNCT
ejpam-4382	149	20	(	(	PUNCT
ejpam-4382	149	21	1	1	X
ejpam-4382	149	22	)	)	PUNCT
ejpam-4382	149	23	(	(	PUNCT
ejpam-4382	149	24	x	x	X
ejpam-4382	149	25	,	,	PUNCT
ejpam-4382	149	26	τ	τ	PROPN
ejpam-4382	149	27	,	,	PUNCT
ejpam-4382	149	28	i	i	PROPN
ejpam-4382	149	29	)	)	PUNCT
ejpam-4382	149	30	is	be	AUX
ejpam-4382	149	31	semi	semi	ADJ
ejpam-4382	149	32	-	-	ADJ
ejpam-4382	149	33	i	i	PRON
ejpam-4382	149	34	-submaximal	-submaximal	ADJ
ejpam-4382	149	35	;	;	PUNCT
ejpam-4382	149	36	(	(	PUNCT
ejpam-4382	149	37	2	2	X
ejpam-4382	149	38	)	)	PUNCT
ejpam-4382	149	39	every	every	DET
ejpam-4382	149	40	subset	subset	NOUN
ejpam-4382	149	41	of	of	ADP
ejpam-4382	149	42	x	x	PUNCT
ejpam-4382	149	43	is	be	AUX
ejpam-4382	149	44	co	co	ADJ
ejpam-4382	149	45	-	-	ADJ
ejpam-4382	149	46	locally	locally	ADV
ejpam-4382	149	47	semi	semi	NOUN
ejpam-4382	149	48	-	-	ADJ
ejpam-4382	149	49	i	i	PRON
ejpam-4382	149	50	-closed	-close	VERB
ejpam-4382	149	51	;	;	PUNCT
ejpam-4382	149	52	(	(	PUNCT
ejpam-4382	149	53	3	3	X
ejpam-4382	149	54	)	)	PUNCT
ejpam-4382	149	55	every	every	PRON
ejpam-4382	149	56	subset	subset	VERB
ejpam-4382	149	57	a	a	PRON
ejpam-4382	149	58	of	of	ADP
ejpam-4382	149	59	x	x	PRON
ejpam-4382	149	60	,	,	PUNCT
ejpam-4382	149	61	for	for	ADP
ejpam-4382	149	62	which	which	PRON
ejpam-4382	149	63	sinti	sinti	PROPN
ejpam-4382	149	64	(	(	PUNCT
ejpam-4382	149	65	a	a	X
ejpam-4382	149	66	)	)	PUNCT
ejpam-4382	149	67	=	=	NOUN
ejpam-4382	149	68	∅	∅	NOUN
ejpam-4382	149	69	,	,	PUNCT
ejpam-4382	149	70	is	be	AUX
ejpam-4382	149	71	semi	semi	ADJ
ejpam-4382	149	72	-	-	ADJ
ejpam-4382	149	73	i	i	PRON
ejpam-4382	149	74	-closed	-close	VERB
ejpam-4382	149	75	;	;	PUNCT
ejpam-4382	149	76	(	(	PUNCT
ejpam-4382	149	77	4	4	X
ejpam-4382	149	78	)	)	PUNCT
ejpam-4382	149	79	for	for	ADP
ejpam-4382	149	80	every	every	DET
ejpam-4382	149	81	subset	subset	NOUN
ejpam-4382	149	82	a	a	PRON
ejpam-4382	149	83	of	of	ADP
ejpam-4382	149	84	x	x	PRON
ejpam-4382	149	85	,	,	PUNCT
ejpam-4382	149	86	scli	scli	PROPN
ejpam-4382	149	87	(	(	PUNCT
ejpam-4382	149	88	a)−a	a)−a	X
ejpam-4382	149	89	is	be	AUX
ejpam-4382	149	90	semi	semi	ADJ
ejpam-4382	149	91	-	-	ADJ
ejpam-4382	149	92	i	i	PRON
ejpam-4382	149	93	-closed	-close	VERB
ejpam-4382	149	94	;	;	PUNCT
ejpam-4382	149	95	(	(	PUNCT
ejpam-4382	149	96	5	5	X
ejpam-4382	149	97	)	)	PUNCT
ejpam-4382	149	98	every	every	DET
ejpam-4382	149	99	subset	subset	NOUN
ejpam-4382	149	100	of	of	ADP
ejpam-4382	149	101	x	x	PUNCT
ejpam-4382	149	102	is	be	AUX
ejpam-4382	149	103	locally	locally	ADV
ejpam-4382	149	104	semi	semi	ADJ
ejpam-4382	149	105	-	-	ADJ
ejpam-4382	149	106	i	i	PRON
ejpam-4382	149	107	-closed	-close	VERB
ejpam-4382	149	108	;	;	PUNCT
ejpam-4382	149	109	(	(	PUNCT
ejpam-4382	149	110	6	6	X
ejpam-4382	149	111	)	)	PUNCT
ejpam-4382	149	112	each	each	DET
ejpam-4382	149	113	semi	semi	ADJ
ejpam-4382	149	114	-	-	ADJ
ejpam-4382	149	115	i	i	PRON
ejpam-4382	149	116	-codense	-codense	NOUN
ejpam-4382	149	117	subset	subset	NOUN
ejpam-4382	149	118	of	of	ADP
ejpam-4382	149	119	x	x	PUNCT
ejpam-4382	149	120	is	be	AUX
ejpam-4382	149	121	semi	semi	ADJ
ejpam-4382	149	122	-	-	ADJ
ejpam-4382	149	123	i	i	PRON
ejpam-4382	149	124	-closed	-closed	ADJ
ejpam-4382	149	125	.	.	PUNCT
ejpam-4382	150	1	proof	proof	NOUN
ejpam-4382	150	2	.	.	PUNCT
ejpam-4382	151	1	(	(	PUNCT
ejpam-4382	151	2	1	1	X
ejpam-4382	151	3	)	)	PUNCT
ejpam-4382	151	4	⇒	⇒	NOUN
ejpam-4382	151	5	(	(	PUNCT
ejpam-4382	151	6	2	2	NUM
ejpam-4382	151	7	):	):	PUNCT
ejpam-4382	151	8	let	let	VERB
ejpam-4382	151	9	a	a	PRON
ejpam-4382	151	10	be	be	AUX
ejpam-4382	151	11	a	a	DET
ejpam-4382	151	12	subset	subset	NOUN
ejpam-4382	151	13	of	of	ADP
ejpam-4382	151	14	x.	x.	NOUN
ejpam-4382	151	15	since	since	SCONJ
ejpam-4382	151	16	(	(	PUNCT
ejpam-4382	151	17	x	x	X
ejpam-4382	151	18	,	,	PUNCT
ejpam-4382	151	19	τ	τ	PROPN
ejpam-4382	151	20	,	,	PUNCT
ejpam-4382	151	21	i	i	PROPN
ejpam-4382	151	22	)	)	PUNCT
ejpam-4382	151	23	is	be	AUX
ejpam-4382	151	24	semi	semi	ADJ
ejpam-4382	151	25	-	-	ADJ
ejpam-4382	151	26	i	i	PRON
ejpam-4382	151	27	-submaximal	-submaximal	ADJ
ejpam-4382	151	28	,	,	PUNCT
ejpam-4382	151	29	by	by	ADP
ejpam-4382	151	30	theorem	theorem	NOUN
ejpam-4382	151	31	2	2	NUM
ejpam-4382	151	32	,	,	PUNCT
ejpam-4382	151	33	there	there	PRON
ejpam-4382	151	34	exist	exist	VERB
ejpam-4382	151	35	a	a	DET
ejpam-4382	151	36	semi	semi	ADJ
ejpam-4382	151	37	-	-	ADJ
ejpam-4382	151	38	i	i	PRON
ejpam-4382	151	39	-open	-open	NOUN
ejpam-4382	151	40	set	set	VERB
ejpam-4382	151	41	u	u	NOUN
ejpam-4382	151	42	and	and	CCONJ
ejpam-4382	151	43	a	a	DET
ejpam-4382	151	44	semi	semi	ADJ
ejpam-4382	151	45	-	-	ADJ
ejpam-4382	151	46	i	i	PRON
ejpam-4382	151	47	-closed	-close	VERB
ejpam-4382	151	48	set	set	VERB
ejpam-4382	151	49	v	v	ADP
ejpam-4382	151	50	such	such	ADJ
ejpam-4382	151	51	that	that	SCONJ
ejpam-4382	151	52	x	x	SYM
ejpam-4382	151	53	−a	−a	NOUN
ejpam-4382	151	54	=	=	PUNCT
ejpam-4382	151	55	u	u	NOUN
ejpam-4382	151	56	∩v	∩v	NOUN
ejpam-4382	151	57	.	.	PUNCT
ejpam-4382	152	1	then	then	ADV
ejpam-4382	152	2	,	,	PUNCT
ejpam-4382	152	3	we	we	PRON
ejpam-4382	152	4	have	have	VERB
ejpam-4382	152	5	a	a	DET
ejpam-4382	152	6	=	=	X
ejpam-4382	152	7	(	(	PUNCT
ejpam-4382	152	8	x	x	SYM
ejpam-4382	152	9	−u)∪	−u)∪	NOUN
ejpam-4382	152	10	(	(	PUNCT
ejpam-4382	152	11	x	x	X
ejpam-4382	152	12	−v	−v	NOUN
ejpam-4382	152	13	)	)	PUNCT
ejpam-4382	152	14	,	,	PUNCT
ejpam-4382	152	15	where	where	SCONJ
ejpam-4382	152	16	x	x	PRON
ejpam-4382	152	17	−u	−u	PROPN
ejpam-4382	152	18	is	be	AUX
ejpam-4382	152	19	a	a	DET
ejpam-4382	152	20	semi	semi	ADJ
ejpam-4382	152	21	-	-	ADJ
ejpam-4382	152	22	i	i	PRON
ejpam-4382	152	23	-closed	-close	VERB
ejpam-4382	152	24	set	set	NOUN
ejpam-4382	152	25	and	and	CCONJ
ejpam-4382	152	26	x	x	SYM
ejpam-4382	152	27	−	−	PROPN
ejpam-4382	152	28	v	v	NOUN
ejpam-4382	152	29	is	be	AUX
ejpam-4382	152	30	a	a	DET
ejpam-4382	152	31	semi	semi	ADJ
ejpam-4382	152	32	-	-	ADJ
ejpam-4382	152	33	i	i	PRON
ejpam-4382	152	34	-open	-open	NOUN
ejpam-4382	152	35	set	set	NOUN
ejpam-4382	152	36	.	.	PUNCT
ejpam-4382	153	1	thus	thus	ADV
ejpam-4382	153	2	,	,	PUNCT
ejpam-4382	153	3	a	a	PRON
ejpam-4382	153	4	is	be	AUX
ejpam-4382	153	5	co	co	ADJ
ejpam-4382	153	6	-	-	ADJ
ejpam-4382	153	7	locally	locally	ADV
ejpam-4382	153	8	semi	semi	NOUN
ejpam-4382	153	9	-	-	ADJ
ejpam-4382	153	10	i	i	ADV
ejpam-4382	153	11	-closed	-closed	ADJ
ejpam-4382	153	12	.	.	PUNCT
ejpam-4382	154	1	(	(	PUNCT
ejpam-4382	154	2	2	2	X
ejpam-4382	154	3	)	)	PUNCT
ejpam-4382	154	4	⇒	⇒	NOUN
ejpam-4382	154	5	(	(	PUNCT
ejpam-4382	154	6	3	3	NUM
ejpam-4382	154	7	):	):	PUNCT
ejpam-4382	154	8	let	let	VERB
ejpam-4382	154	9	a	a	PRON
ejpam-4382	154	10	be	be	AUX
ejpam-4382	154	11	a	a	DET
ejpam-4382	154	12	subset	subset	NOUN
ejpam-4382	154	13	of	of	ADP
ejpam-4382	154	14	x	x	PUNCT
ejpam-4382	154	15	and	and	CCONJ
ejpam-4382	154	16	sinti	sinti	PROPN
ejpam-4382	154	17	(	(	PUNCT
ejpam-4382	154	18	a	a	NOUN
ejpam-4382	154	19	)	)	PUNCT
ejpam-4382	154	20	=	=	PUNCT
ejpam-4382	154	21	∅.	∅.	X
ejpam-4382	154	22	by	by	ADP
ejpam-4382	154	23	(	(	PUNCT
ejpam-4382	154	24	2	2	NUM
ejpam-4382	154	25	)	)	PUNCT
ejpam-4382	154	26	,	,	PUNCT
ejpam-4382	154	27	there	there	PRON
ejpam-4382	154	28	exist	exist	VERB
ejpam-4382	154	29	a	a	DET
ejpam-4382	154	30	semi	semi	NOUN
ejpam-4382	154	31	-	-	ADJ
ejpam-4382	154	32	i	i	PRON
ejpam-4382	154	33	open	open	ADJ
ejpam-4382	154	34	set	set	VERB
ejpam-4382	154	35	u	u	NOUN
ejpam-4382	154	36	and	and	CCONJ
ejpam-4382	154	37	a	a	DET
ejpam-4382	154	38	semi	semi	ADJ
ejpam-4382	154	39	-	-	ADJ
ejpam-4382	154	40	i	i	PRON
ejpam-4382	154	41	-closed	-close	VERB
ejpam-4382	154	42	set	set	VERB
ejpam-4382	154	43	v	v	ADP
ejpam-4382	154	44	such	such	DET
ejpam-4382	154	45	that	that	SCONJ
ejpam-4382	154	46	a	a	DET
ejpam-4382	154	47	=	=	X
ejpam-4382	154	48	u	u	NOUN
ejpam-4382	154	49	∪	∪	NOUN
ejpam-4382	154	50	v	v	NOUN
ejpam-4382	154	51	.	.	PUNCT
ejpam-4382	155	1	then	then	ADV
ejpam-4382	155	2	,	,	PUNCT
ejpam-4382	155	3	we	we	PRON
ejpam-4382	155	4	have	have	VERB
ejpam-4382	155	5	u	u	NOUN
ejpam-4382	155	6	=	=	PROPN
ejpam-4382	155	7	sinti	sinti	X
ejpam-4382	155	8	(	(	PUNCT
ejpam-4382	155	9	u	u	NOUN
ejpam-4382	155	10	)	)	PUNCT
ejpam-4382	155	11	⊆	⊆	NUM
ejpam-4382	155	12	sinti	sinti	NOUN
ejpam-4382	155	13	(	(	PUNCT
ejpam-4382	155	14	a	a	X
ejpam-4382	155	15	)	)	PUNCT
ejpam-4382	155	16	=	=	NOUN
ejpam-4382	155	17	∅	∅	NOUN
ejpam-4382	155	18	which	which	PRON
ejpam-4382	155	19	yields	yield	VERB
ejpam-4382	155	20	u	u	NOUN
ejpam-4382	155	21	=	=	PROPN
ejpam-4382	155	22	∅.	∅.	VERB
ejpam-4382	155	23	thus	thus	ADV
ejpam-4382	155	24	,	,	PUNCT
ejpam-4382	155	25	a	a	DET
ejpam-4382	155	26	=	=	NOUN
ejpam-4382	155	27	v	v	NOUN
ejpam-4382	155	28	is	be	AUX
ejpam-4382	155	29	semi	semi	ADJ
ejpam-4382	155	30	-	-	ADJ
ejpam-4382	155	31	i	i	PRON
ejpam-4382	155	32	-closed	-closed	ADJ
ejpam-4382	155	33	.	.	PUNCT
ejpam-4382	156	1	(	(	PUNCT
ejpam-4382	156	2	3	3	X
ejpam-4382	156	3	)	)	PUNCT
ejpam-4382	156	4	⇒	⇒	NOUN
ejpam-4382	156	5	(	(	PUNCT
ejpam-4382	156	6	4	4	NUM
ejpam-4382	156	7	):	):	PUNCT
ejpam-4382	156	8	let	let	VERB
ejpam-4382	156	9	a	a	PRON
ejpam-4382	156	10	be	be	AUX
ejpam-4382	156	11	a	a	DET
ejpam-4382	156	12	subset	subset	NOUN
ejpam-4382	156	13	of	of	ADP
ejpam-4382	156	14	x.	x.	NOUN
ejpam-4382	156	15	by	by	ADP
ejpam-4382	156	16	lemma	lemma	PROPN
ejpam-4382	156	17	2	2	NUM
ejpam-4382	156	18	,	,	PUNCT
ejpam-4382	156	19	sinti	sinti	PROPN
ejpam-4382	156	20	(	(	PUNCT
ejpam-4382	156	21	scli	scli	PROPN
ejpam-4382	156	22	(	(	PUNCT
ejpam-4382	156	23	a	a	NOUN
ejpam-4382	156	24	)	)	PUNCT
ejpam-4382	156	25	−	−	NOUN
ejpam-4382	156	26	a	a	X
ejpam-4382	156	27	)	)	PUNCT
ejpam-4382	156	28	=	=	NOUN
ejpam-4382	156	29	∅	∅	NOUN
ejpam-4382	156	30	and	and	CCONJ
ejpam-4382	156	31	by	by	ADP
ejpam-4382	156	32	(	(	PUNCT
ejpam-4382	156	33	3	3	NUM
ejpam-4382	156	34	)	)	PUNCT
ejpam-4382	156	35	,	,	PUNCT
ejpam-4382	156	36	we	we	PRON
ejpam-4382	156	37	have	have	VERB
ejpam-4382	156	38	scli	scli	NOUN
ejpam-4382	156	39	(	(	PUNCT
ejpam-4382	156	40	a)−a	a)−a	X
ejpam-4382	156	41	is	be	AUX
ejpam-4382	156	42	semi	semi	ADJ
ejpam-4382	156	43	-	-	ADJ
ejpam-4382	156	44	i	i	PRON
ejpam-4382	156	45	-closed	-closed	ADJ
ejpam-4382	156	46	.	.	PUNCT
ejpam-4382	157	1	(	(	PUNCT
ejpam-4382	157	2	4	4	X
ejpam-4382	157	3	)	)	PUNCT
ejpam-4382	157	4	⇒	⇒	NOUN
ejpam-4382	157	5	(	(	PUNCT
ejpam-4382	157	6	5	5	NUM
ejpam-4382	157	7	):	):	PUNCT
ejpam-4382	157	8	it	it	PRON
ejpam-4382	157	9	follows	follow	VERB
ejpam-4382	157	10	from	from	ADP
ejpam-4382	157	11	theorem	theorem	ADJ
ejpam-4382	157	12	2	2	NUM
ejpam-4382	157	13	.	.	PUNCT
ejpam-4382	157	14	(	(	PUNCT
ejpam-4382	157	15	5	5	X
ejpam-4382	157	16	)	)	PUNCT
ejpam-4382	157	17	⇒	⇒	NOUN
ejpam-4382	157	18	(	(	PUNCT
ejpam-4382	157	19	1	1	NUM
ejpam-4382	157	20	):	):	PUNCT
ejpam-4382	157	21	let	let	VERB
ejpam-4382	157	22	a	a	PRON
ejpam-4382	157	23	be	be	AUX
ejpam-4382	157	24	a	a	DET
ejpam-4382	157	25	semi	semi	ADJ
ejpam-4382	157	26	-	-	ADJ
ejpam-4382	157	27	i	i	ADJ
ejpam-4382	157	28	-dense	-dense	PROPN
ejpam-4382	157	29	subset	subset	NOUN
ejpam-4382	157	30	of	of	ADP
ejpam-4382	157	31	x.	x.	NOUN
ejpam-4382	157	32	by	by	ADP
ejpam-4382	157	33	(	(	PUNCT
ejpam-4382	157	34	5	5	NUM
ejpam-4382	157	35	)	)	PUNCT
ejpam-4382	157	36	,	,	PUNCT
ejpam-4382	157	37	there	there	PRON
ejpam-4382	157	38	exist	exist	VERB
ejpam-4382	157	39	a	a	DET
ejpam-4382	157	40	semi	semi	ADJ
ejpam-4382	157	41	-	-	ADJ
ejpam-4382	157	42	i	i	PRON
ejpam-4382	157	43	-open	-open	NOUN
ejpam-4382	157	44	set	set	VERB
ejpam-4382	157	45	u	u	NOUN
ejpam-4382	157	46	and	and	CCONJ
ejpam-4382	157	47	a	a	DET
ejpam-4382	157	48	semi	semi	ADJ
ejpam-4382	157	49	-	-	ADJ
ejpam-4382	157	50	i	i	PRON
ejpam-4382	157	51	-closed	-close	VERB
ejpam-4382	157	52	set	set	VERB
ejpam-4382	157	53	v	v	ADP
ejpam-4382	157	54	such	such	DET
ejpam-4382	157	55	that	that	SCONJ
ejpam-4382	157	56	a	a	DET
ejpam-4382	157	57	=	=	X
ejpam-4382	157	58	u	u	NOUN
ejpam-4382	157	59	∩v	∩v	NOUN
ejpam-4382	157	60	.	.	PUNCT
ejpam-4382	158	1	since	since	SCONJ
ejpam-4382	158	2	a	a	DET
ejpam-4382	158	3	⊆	⊆	NUM
ejpam-4382	158	4	v	v	NOUN
ejpam-4382	158	5	,	,	PUNCT
ejpam-4382	158	6	scli	scli	PROPN
ejpam-4382	158	7	(	(	PUNCT
ejpam-4382	158	8	a	a	NOUN
ejpam-4382	158	9	)	)	PUNCT
ejpam-4382	158	10	⊆	⊆	NUM
ejpam-4382	158	11	scli	scli	NOUN
ejpam-4382	158	12	(	(	PUNCT
ejpam-4382	158	13	v	v	NOUN
ejpam-4382	158	14	)	)	PUNCT
ejpam-4382	158	15	and	and	CCONJ
ejpam-4382	158	16	so	so	ADV
ejpam-4382	158	17	x	x	X
ejpam-4382	158	18	=	=	PRON
ejpam-4382	158	19	scli	scli	NOUN
ejpam-4382	158	20	(	(	PUNCT
ejpam-4382	158	21	v	v	NOUN
ejpam-4382	158	22	)	)	PUNCT
ejpam-4382	158	23	.	.	PUNCT
ejpam-4382	159	1	thus	thus	ADV
ejpam-4382	159	2	,	,	PUNCT
ejpam-4382	159	3	x	x	SYM
ejpam-4382	159	4	=	=	SYM
ejpam-4382	159	5	sinti	sinti	X
ejpam-4382	159	6	(	(	PUNCT
ejpam-4382	159	7	scli	scli	PROPN
ejpam-4382	159	8	(	(	PUNCT
ejpam-4382	159	9	v	v	NOUN
ejpam-4382	159	10	)	)	PUNCT
ejpam-4382	159	11	)	)	PUNCT
ejpam-4382	160	1	=	=	SYM
ejpam-4382	160	2	sinti	sinti	X
ejpam-4382	160	3	(	(	PUNCT
ejpam-4382	160	4	v	v	NOUN
ejpam-4382	160	5	)	)	PUNCT
ejpam-4382	160	6	which	which	PRON
ejpam-4382	160	7	yields	yield	VERB
ejpam-4382	160	8	v	v	NOUN
ejpam-4382	160	9	=	=	SYM
ejpam-4382	160	10	x.	x.	NOUN
ejpam-4382	160	11	therefore	therefore	ADV
ejpam-4382	160	12	,	,	PUNCT
ejpam-4382	160	13	a	a	DET
ejpam-4382	160	14	=	=	X
ejpam-4382	160	15	u	u	NOUN
ejpam-4382	160	16	∩	∩	NOUN
ejpam-4382	160	17	v	v	NOUN
ejpam-4382	160	18	=	=	SYM
ejpam-4382	160	19	u	u	NOUN
ejpam-4382	160	20	∩	∩	NOUN
ejpam-4382	160	21	x	x	X
ejpam-4382	160	22	=	=	SYM
ejpam-4382	160	23	u	u	NOUN
ejpam-4382	160	24	and	and	CCONJ
ejpam-4382	160	25	hence	hence	ADV
ejpam-4382	160	26	a	a	PRON
ejpam-4382	160	27	is	be	AUX
ejpam-4382	160	28	semi	semi	ADJ
ejpam-4382	160	29	-	-	ADJ
ejpam-4382	160	30	i	i	PRON
ejpam-4382	160	31	-open	-open	ADJ
ejpam-4382	160	32	.	.	PUNCT
ejpam-4382	161	1	this	this	PRON
ejpam-4382	161	2	shows	show	VERB
ejpam-4382	161	3	that	that	SCONJ
ejpam-4382	161	4	(	(	PUNCT
ejpam-4382	161	5	x	x	X
ejpam-4382	161	6	,	,	PUNCT
ejpam-4382	161	7	τ	τ	PROPN
ejpam-4382	161	8	,	,	PUNCT
ejpam-4382	161	9	i	i	PROPN
ejpam-4382	161	10	)	)	PUNCT
ejpam-4382	161	11	is	be	AUX
ejpam-4382	161	12	semi	semi	ADJ
ejpam-4382	161	13	-	-	ADJ
ejpam-4382	161	14	i	i	PRON
ejpam-4382	161	15	-submaximal	-submaximal	ADJ
ejpam-4382	161	16	.	.	PUNCT
ejpam-4382	162	1	(	(	PUNCT
ejpam-4382	162	2	1	1	X
ejpam-4382	162	3	)	)	PUNCT
ejpam-4382	162	4	⇒	⇒	NOUN
ejpam-4382	162	5	(	(	PUNCT
ejpam-4382	162	6	6	6	NUM
ejpam-4382	162	7	):	):	PUNCT
ejpam-4382	162	8	let	let	VERB
ejpam-4382	162	9	a	a	PRON
ejpam-4382	162	10	be	be	AUX
ejpam-4382	162	11	a	a	DET
ejpam-4382	162	12	semi	semi	ADJ
ejpam-4382	162	13	-	-	ADJ
ejpam-4382	162	14	i	i	PRON
ejpam-4382	162	15	-codense	-codense	NOUN
ejpam-4382	162	16	set	set	NOUN
ejpam-4382	162	17	.	.	PUNCT
ejpam-4382	163	1	then	then	ADV
ejpam-4382	163	2	,	,	PUNCT
ejpam-4382	163	3	x	x	PUNCT
ejpam-4382	163	4	−	−	NOUN
ejpam-4382	163	5	a	a	PRON
ejpam-4382	163	6	is	be	AUX
ejpam-4382	163	7	semi	semi	ADJ
ejpam-4382	163	8	-	-	ADJ
ejpam-4382	163	9	i	i	ADJ
ejpam-4382	163	10	-dense	-dense	NOUN
ejpam-4382	163	11	.	.	PUNCT
ejpam-4382	164	1	since	since	SCONJ
ejpam-4382	164	2	(	(	PUNCT
ejpam-4382	164	3	x	x	X
ejpam-4382	164	4	,	,	PUNCT
ejpam-4382	164	5	τ	τ	PROPN
ejpam-4382	164	6	,	,	PUNCT
ejpam-4382	164	7	i	i	PROPN
ejpam-4382	164	8	)	)	PUNCT
ejpam-4382	164	9	is	be	AUX
ejpam-4382	164	10	semi	semi	ADJ
ejpam-4382	164	11	-	-	ADJ
ejpam-4382	164	12	i	i	PRON
ejpam-4382	164	13	-submaximal	-submaximal	ADJ
ejpam-4382	164	14	,	,	PUNCT
ejpam-4382	164	15	we	we	PRON
ejpam-4382	164	16	have	have	VERB
ejpam-4382	164	17	x	x	PART
ejpam-4382	164	18	−a	−a	VERB
ejpam-4382	164	19	is	be	AUX
ejpam-4382	164	20	semi	semi	ADJ
ejpam-4382	164	21	-	-	ADJ
ejpam-4382	164	22	i	i	PRON
ejpam-4382	164	23	-open	-open	ADJ
ejpam-4382	164	24	and	and	CCONJ
ejpam-4382	164	25	hence	hence	ADV
ejpam-4382	164	26	a	a	PRON
ejpam-4382	164	27	is	be	AUX
ejpam-4382	164	28	semi	semi	ADJ
ejpam-4382	164	29	-	-	ADJ
ejpam-4382	164	30	i	i	PRON
ejpam-4382	164	31	closed	close	VERB
ejpam-4382	164	32	.	.	PUNCT
ejpam-4382	165	1	(	(	PUNCT
ejpam-4382	165	2	6	6	NUM
ejpam-4382	165	3	)	)	PUNCT
ejpam-4382	165	4	⇒	⇒	NOUN
ejpam-4382	165	5	(	(	PUNCT
ejpam-4382	165	6	1	1	NUM
ejpam-4382	165	7	):	):	PUNCT
ejpam-4382	165	8	let	let	VERB
ejpam-4382	165	9	a	a	PRON
ejpam-4382	165	10	be	be	AUX
ejpam-4382	165	11	a	a	DET
ejpam-4382	165	12	semi	semi	ADJ
ejpam-4382	165	13	-	-	ADJ
ejpam-4382	165	14	i	i	ADJ
ejpam-4382	165	15	-dense	-dense	PROPN
ejpam-4382	165	16	subset	subset	NOUN
ejpam-4382	165	17	of	of	ADP
ejpam-4382	165	18	x.	x.	NOUN
ejpam-4382	165	19	then	then	ADV
ejpam-4382	165	20	,	,	PUNCT
ejpam-4382	165	21	x	x	PUNCT
ejpam-4382	165	22	−	−	NOUN
ejpam-4382	165	23	a	a	PRON
ejpam-4382	165	24	is	be	AUX
ejpam-4382	165	25	semi	semi	ADJ
ejpam-4382	165	26	-	-	ADJ
ejpam-4382	165	27	i	i	ADJ
ejpam-4382	165	28	-codense	-codense	NOUN
ejpam-4382	165	29	.	.	PUNCT
ejpam-4382	166	1	by	by	ADP
ejpam-4382	166	2	(	(	PUNCT
ejpam-4382	166	3	6	6	NUM
ejpam-4382	166	4	)	)	PUNCT
ejpam-4382	166	5	,	,	PUNCT
ejpam-4382	166	6	x	x	PUNCT
ejpam-4382	166	7	−	−	NOUN
ejpam-4382	166	8	a	a	PRON
ejpam-4382	166	9	is	be	AUX
ejpam-4382	166	10	semi	semi	ADJ
ejpam-4382	166	11	-	-	ADJ
ejpam-4382	166	12	i	i	PRON
ejpam-4382	166	13	-closed	-close	VERB
ejpam-4382	166	14	and	and	CCONJ
ejpam-4382	166	15	so	so	ADV
ejpam-4382	166	16	a	a	PRON
ejpam-4382	166	17	is	be	AUX
ejpam-4382	166	18	semi	semi	ADJ
ejpam-4382	166	19	-	-	ADJ
ejpam-4382	166	20	i	i	PRON
ejpam-4382	166	21	-open	-open	NOUN
ejpam-4382	166	22	.	.	PUNCT
ejpam-4382	167	1	thus	thus	ADV
ejpam-4382	167	2	,	,	PUNCT
ejpam-4382	167	3	(	(	PUNCT
ejpam-4382	167	4	x	x	X
ejpam-4382	167	5	,	,	PUNCT
ejpam-4382	167	6	τ	τ	PROPN
ejpam-4382	167	7	,	,	PUNCT
ejpam-4382	167	8	i	i	PROPN
ejpam-4382	167	9	)	)	PUNCT
ejpam-4382	167	10	is	be	AUX
ejpam-4382	167	11	semi	semi	ADJ
ejpam-4382	167	12	-	-	ADJ
ejpam-4382	167	13	i	i	PRON
ejpam-4382	167	14	submaximal	submaximal	ADJ
ejpam-4382	167	15	.	.	PUNCT
ejpam-4382	168	1	theorem	theorem	VERB
ejpam-4382	168	2	4	4	NUM
ejpam-4382	168	3	.	.	X
ejpam-4382	168	4	for	for	ADP
ejpam-4382	168	5	an	an	DET
ejpam-4382	168	6	ideal	ideal	ADJ
ejpam-4382	168	7	topological	topological	ADJ
ejpam-4382	168	8	space	space	NOUN
ejpam-4382	168	9	(	(	PUNCT
ejpam-4382	168	10	x	x	X
ejpam-4382	168	11	,	,	PUNCT
ejpam-4382	168	12	τ	τ	PROPN
ejpam-4382	168	13	,	,	PUNCT
ejpam-4382	168	14	i	i	NOUN
ejpam-4382	168	15	)	)	PUNCT
ejpam-4382	168	16	,	,	PUNCT
ejpam-4382	168	17	the	the	DET
ejpam-4382	168	18	following	follow	VERB
ejpam-4382	168	19	properties	property	NOUN
ejpam-4382	168	20	are	be	AUX
ejpam-4382	168	21	equivalent	equivalent	ADJ
ejpam-4382	168	22	:	:	PUNCT
ejpam-4382	168	23	(	(	PUNCT
ejpam-4382	168	24	1	1	X
ejpam-4382	168	25	)	)	PUNCT
ejpam-4382	168	26	(	(	PUNCT
ejpam-4382	168	27	x	x	X
ejpam-4382	168	28	,	,	PUNCT
ejpam-4382	168	29	τ	τ	PROPN
ejpam-4382	168	30	,	,	PUNCT
ejpam-4382	168	31	i	i	PROPN
ejpam-4382	168	32	)	)	PUNCT
ejpam-4382	168	33	is	be	AUX
ejpam-4382	168	34	semi	semi	ADJ
ejpam-4382	168	35	-	-	ADJ
ejpam-4382	168	36	i	i	PRON
ejpam-4382	168	37	-submaximal	-submaximal	ADJ
ejpam-4382	168	38	;	;	PUNCT
ejpam-4382	168	39	(	(	PUNCT
ejpam-4382	168	40	2	2	X
ejpam-4382	168	41	)	)	PUNCT
ejpam-4382	168	42	every	every	PRON
ejpam-4382	168	43	subset	subset	VERB
ejpam-4382	168	44	a	a	PRON
ejpam-4382	168	45	of	of	ADP
ejpam-4382	168	46	x	x	PRON
ejpam-4382	168	47	,	,	PUNCT
ejpam-4382	168	48	for	for	ADP
ejpam-4382	168	49	which	which	PRON
ejpam-4382	168	50	sinti	sinti	PROPN
ejpam-4382	168	51	(	(	PUNCT
ejpam-4382	168	52	a	a	X
ejpam-4382	168	53	)	)	PUNCT
ejpam-4382	168	54	=	=	NOUN
ejpam-4382	168	55	∅	∅	NOUN
ejpam-4382	168	56	,	,	PUNCT
ejpam-4382	168	57	is	be	AUX
ejpam-4382	168	58	semi	semi	ADJ
ejpam-4382	168	59	-	-	ADJ
ejpam-4382	168	60	i	i	PRON
ejpam-4382	168	61	-closed	-close	VERB
ejpam-4382	168	62	;	;	PUNCT
ejpam-4382	168	63	c.	c.	PROPN
ejpam-4382	168	64	boonpok	boonpok	PROPN
ejpam-4382	168	65	/	/	SYM
ejpam-4382	168	66	eur	eur	PROPN
ejpam-4382	168	67	.	.	PUNCT
ejpam-4382	169	1	j.	j.	PROPN
ejpam-4382	169	2	pure	pure	PROPN
ejpam-4382	169	3	appl	appl	PROPN
ejpam-4382	169	4	.	.	PROPN
ejpam-4382	169	5	math	math	PROPN
ejpam-4382	169	6	,	,	PUNCT
ejpam-4382	169	7	15	15	NUM
ejpam-4382	169	8	(	(	PUNCT
ejpam-4382	169	9	3	3	NUM
ejpam-4382	169	10	)	)	PUNCT
ejpam-4382	169	11	(	(	PUNCT
ejpam-4382	169	12	2022	2022	NUM
ejpam-4382	169	13	)	)	PUNCT
ejpam-4382	169	14	,	,	PUNCT
ejpam-4382	169	15	938	938	NUM
ejpam-4382	169	16	-	-	SYM
ejpam-4382	169	17	947	947	NUM
ejpam-4382	169	18	944	944	NUM
ejpam-4382	169	19	(	(	PUNCT
ejpam-4382	169	20	3	3	NUM
ejpam-4382	169	21	)	)	PUNCT
ejpam-4382	169	22	every	every	PRON
ejpam-4382	169	23	subset	subset	VERB
ejpam-4382	169	24	a	a	PRON
ejpam-4382	169	25	of	of	ADP
ejpam-4382	169	26	x	x	PRON
ejpam-4382	169	27	,	,	PUNCT
ejpam-4382	169	28	for	for	ADP
ejpam-4382	169	29	which	which	PRON
ejpam-4382	169	30	sinti	sinti	PROPN
ejpam-4382	169	31	(	(	PUNCT
ejpam-4382	169	32	a	a	X
ejpam-4382	169	33	)	)	PUNCT
ejpam-4382	169	34	=	=	NOUN
ejpam-4382	169	35	∅	∅	NOUN
ejpam-4382	169	36	,	,	PUNCT
ejpam-4382	169	37	is	be	AUX
ejpam-4382	169	38	semi	semi	ADJ
ejpam-4382	169	39	-	-	ADJ
ejpam-4382	169	40	i	i	PRON
ejpam-4382	169	41	-closed	-closed	ADJ
ejpam-4382	169	42	and	and	CCONJ
ejpam-4382	169	43	semi	semi	ADJ
ejpam-4382	169	44	-	-	ADJ
ejpam-4382	169	45	i	i	PRON
ejpam-4382	169	46	-discrete	-discrete	ADJ
ejpam-4382	169	47	;	;	PUNCT
ejpam-4382	169	48	(	(	PUNCT
ejpam-4382	169	49	4	4	X
ejpam-4382	169	50	)	)	PUNCT
ejpam-4382	169	51	for	for	ADP
ejpam-4382	169	52	every	every	DET
ejpam-4382	169	53	subset	subset	NOUN
ejpam-4382	169	54	a	a	PRON
ejpam-4382	169	55	of	of	ADP
ejpam-4382	169	56	x	x	PRON
ejpam-4382	169	57	,	,	PUNCT
ejpam-4382	169	58	scli	scli	PROPN
ejpam-4382	169	59	(	(	PUNCT
ejpam-4382	169	60	a)−a	a)−a	X
ejpam-4382	169	61	is	be	AUX
ejpam-4382	169	62	semi	semi	ADJ
ejpam-4382	169	63	-	-	ADJ
ejpam-4382	169	64	i	i	PRON
ejpam-4382	169	65	-closed	-closed	ADJ
ejpam-4382	169	66	and	and	CCONJ
ejpam-4382	169	67	semi	semi	ADJ
ejpam-4382	169	68	-	-	ADJ
ejpam-4382	169	69	i	i	PRON
ejpam-4382	169	70	-discrete	-discrete	ADJ
ejpam-4382	169	71	;	;	PUNCT
ejpam-4382	169	72	(	(	PUNCT
ejpam-4382	169	73	5	5	X
ejpam-4382	169	74	)	)	PUNCT
ejpam-4382	169	75	each	each	DET
ejpam-4382	169	76	semi	semi	ADJ
ejpam-4382	169	77	-	-	ADJ
ejpam-4382	169	78	i	i	PRON
ejpam-4382	169	79	-codense	-codense	NOUN
ejpam-4382	169	80	subset	subset	NOUN
ejpam-4382	169	81	of	of	ADP
ejpam-4382	169	82	x	x	PUNCT
ejpam-4382	169	83	is	be	AUX
ejpam-4382	169	84	semi	semi	ADJ
ejpam-4382	169	85	-	-	ADJ
ejpam-4382	169	86	i	i	PRON
ejpam-4382	169	87	-closed	-closed	ADJ
ejpam-4382	169	88	and	and	CCONJ
ejpam-4382	169	89	semi	semi	ADJ
ejpam-4382	169	90	-	-	ADJ
ejpam-4382	169	91	i	i	PRON
ejpam-4382	169	92	-discrete	-discrete	ADJ
ejpam-4382	169	93	;	;	PUNCT
ejpam-4382	169	94	(	(	PUNCT
ejpam-4382	169	95	6	6	X
ejpam-4382	169	96	)	)	PUNCT
ejpam-4382	169	97	each	each	DET
ejpam-4382	169	98	semi	semi	ADJ
ejpam-4382	169	99	-	-	ADJ
ejpam-4382	169	100	i	i	PRON
ejpam-4382	169	101	-codense	-codense	NOUN
ejpam-4382	169	102	subset	subset	NOUN
ejpam-4382	169	103	of	of	ADP
ejpam-4382	169	104	x	x	PUNCT
ejpam-4382	169	105	is	be	AUX
ejpam-4382	169	106	semi	semi	ADJ
ejpam-4382	169	107	-	-	ADJ
ejpam-4382	169	108	i	i	PRON
ejpam-4382	169	109	-closed	-closed	ADJ
ejpam-4382	169	110	.	.	PUNCT
ejpam-4382	170	1	proof	proof	NOUN
ejpam-4382	170	2	.	.	PUNCT
ejpam-4382	171	1	(	(	PUNCT
ejpam-4382	171	2	1	1	X
ejpam-4382	171	3	)	)	PUNCT
ejpam-4382	171	4	⇒	⇒	NOUN
ejpam-4382	171	5	(	(	PUNCT
ejpam-4382	171	6	2	2	NUM
ejpam-4382	171	7	):	):	PUNCT
ejpam-4382	171	8	let	let	VERB
ejpam-4382	171	9	a	a	PRON
ejpam-4382	171	10	be	be	AUX
ejpam-4382	171	11	a	a	DET
ejpam-4382	171	12	subset	subset	NOUN
ejpam-4382	171	13	of	of	ADP
ejpam-4382	171	14	x	x	PUNCT
ejpam-4382	171	15	and	and	CCONJ
ejpam-4382	171	16	sinti	sinti	PROPN
ejpam-4382	171	17	(	(	PUNCT
ejpam-4382	171	18	a	a	X
ejpam-4382	171	19	)	)	PUNCT
ejpam-4382	171	20	=	=	PUNCT
ejpam-4382	171	21	∅.	∅.	NOUN
ejpam-4382	171	22	then	then	ADV
ejpam-4382	171	23	,	,	PUNCT
ejpam-4382	171	24	we	we	PRON
ejpam-4382	171	25	have	have	VERB
ejpam-4382	171	26	scli	scli	NOUN
ejpam-4382	171	27	(	(	PUNCT
ejpam-4382	171	28	x	x	NOUN
ejpam-4382	171	29	−a	−a	ADV
ejpam-4382	171	30	)	)	PUNCT
ejpam-4382	171	31	=	=	PUNCT
ejpam-4382	172	1	x	x	PUNCT
ejpam-4382	172	2	−	−	PROPN
ejpam-4382	172	3	sinti	sinti	PROPN
ejpam-4382	172	4	(	(	PUNCT
ejpam-4382	172	5	a	a	NOUN
ejpam-4382	172	6	)	)	PUNCT
ejpam-4382	172	7	=	=	SYM
ejpam-4382	172	8	x	x	NOUN
ejpam-4382	172	9	and	and	CCONJ
ejpam-4382	172	10	hence	hence	ADV
ejpam-4382	172	11	x	x	PART
ejpam-4382	172	12	−a	−a	NOUN
ejpam-4382	172	13	is	be	AUX
ejpam-4382	172	14	semi	semi	ADJ
ejpam-4382	172	15	-	-	ADJ
ejpam-4382	172	16	i	i	ADJ
ejpam-4382	172	17	-dense	-dense	NOUN
ejpam-4382	172	18	.	.	PUNCT
ejpam-4382	173	1	since	since	SCONJ
ejpam-4382	173	2	(	(	PUNCT
ejpam-4382	173	3	x	x	X
ejpam-4382	173	4	,	,	PUNCT
ejpam-4382	173	5	τ	τ	PROPN
ejpam-4382	173	6	,	,	PUNCT
ejpam-4382	173	7	i	i	PROPN
ejpam-4382	173	8	)	)	PUNCT
ejpam-4382	173	9	is	be	AUX
ejpam-4382	173	10	semi	semi	ADJ
ejpam-4382	173	11	-	-	ADJ
ejpam-4382	173	12	i	i	PRON
ejpam-4382	173	13	-submaximal	-submaximal	ADJ
ejpam-4382	173	14	,	,	PUNCT
ejpam-4382	173	15	x	x	PRON
ejpam-4382	173	16	−a	−a	NOUN
ejpam-4382	173	17	is	be	AUX
ejpam-4382	173	18	semi	semi	ADJ
ejpam-4382	173	19	-	-	ADJ
ejpam-4382	173	20	i	i	PRON
ejpam-4382	173	21	-open	-open	NOUN
ejpam-4382	173	22	.	.	PUNCT
ejpam-4382	174	1	thus	thus	ADV
ejpam-4382	174	2	,	,	PUNCT
ejpam-4382	174	3	a	a	PRON
ejpam-4382	174	4	is	be	AUX
ejpam-4382	174	5	semi	semi	ADJ
ejpam-4382	174	6	-	-	ADJ
ejpam-4382	174	7	i	i	PRON
ejpam-4382	174	8	-closed	-closed	ADJ
ejpam-4382	174	9	.	.	PUNCT
ejpam-4382	175	1	(	(	PUNCT
ejpam-4382	175	2	2	2	X
ejpam-4382	175	3	)	)	PUNCT
ejpam-4382	175	4	⇒	⇒	NOUN
ejpam-4382	175	5	(	(	PUNCT
ejpam-4382	175	6	3	3	NUM
ejpam-4382	175	7	):	):	PUNCT
ejpam-4382	175	8	let	let	VERB
ejpam-4382	175	9	a	a	PRON
ejpam-4382	175	10	be	be	AUX
ejpam-4382	175	11	a	a	DET
ejpam-4382	175	12	subset	subset	NOUN
ejpam-4382	175	13	of	of	ADP
ejpam-4382	175	14	x	x	PUNCT
ejpam-4382	175	15	and	and	CCONJ
ejpam-4382	175	16	sinti	sinti	PROPN
ejpam-4382	175	17	(	(	PUNCT
ejpam-4382	175	18	a	a	NOUN
ejpam-4382	175	19	)	)	PUNCT
ejpam-4382	175	20	=	=	PUNCT
ejpam-4382	175	21	∅.	∅.	VERB
ejpam-4382	175	22	if	if	SCONJ
ejpam-4382	175	23	b	b	PROPN
ejpam-4382	175	24	⊆	⊆	SYM
ejpam-4382	175	25	a	a	PRON
ejpam-4382	175	26	,	,	PUNCT
ejpam-4382	175	27	then	then	ADV
ejpam-4382	175	28	sinti	sinti	PROPN
ejpam-4382	175	29	(	(	PUNCT
ejpam-4382	175	30	b	b	NOUN
ejpam-4382	175	31	)	)	PUNCT
ejpam-4382	175	32	⊆	⊆	NUM
ejpam-4382	175	33	sinti	sinti	NOUN
ejpam-4382	175	34	(	(	PUNCT
ejpam-4382	175	35	a	a	X
ejpam-4382	175	36	)	)	PUNCT
ejpam-4382	175	37	=	=	NOUN
ejpam-4382	175	38	∅	∅	NOUN
ejpam-4382	175	39	which	which	PRON
ejpam-4382	175	40	yields	yield	VERB
ejpam-4382	175	41	sinti	sinti	PROPN
ejpam-4382	175	42	(	(	PUNCT
ejpam-4382	175	43	b	b	X
ejpam-4382	175	44	)	)	PUNCT
ejpam-4382	175	45	=	=	PUNCT
ejpam-4382	175	46	∅.	∅.	VERB
ejpam-4382	175	47	thus	thus	ADV
ejpam-4382	175	48	,	,	PUNCT
ejpam-4382	175	49	by	by	ADP
ejpam-4382	175	50	(	(	PUNCT
ejpam-4382	175	51	2	2	NUM
ejpam-4382	175	52	)	)	PUNCT
ejpam-4382	175	53	,	,	PUNCT
ejpam-4382	175	54	b	b	PROPN
ejpam-4382	175	55	is	be	AUX
ejpam-4382	175	56	semi	semi	ADJ
ejpam-4382	175	57	-	-	ADJ
ejpam-4382	175	58	i	i	PRON
ejpam-4382	175	59	-closed	-closed	ADJ
ejpam-4382	175	60	.	.	PUNCT
ejpam-4382	176	1	so	so	ADV
ejpam-4382	176	2	every	every	DET
ejpam-4382	176	3	subset	subset	NOUN
ejpam-4382	176	4	of	of	ADP
ejpam-4382	176	5	a	a	PRON
ejpam-4382	176	6	is	be	AUX
ejpam-4382	176	7	semi	semi	ADJ
ejpam-4382	176	8	-	-	ADJ
ejpam-4382	176	9	i	i	PRON
ejpam-4382	176	10	-closed	-closed	ADJ
ejpam-4382	176	11	.	.	PUNCT
ejpam-4382	177	1	consequently	consequently	ADV
ejpam-4382	177	2	,	,	PUNCT
ejpam-4382	177	3	we	we	PRON
ejpam-4382	177	4	obtain	obtain	VERB
ejpam-4382	177	5	a	a	PRON
ejpam-4382	177	6	is	be	AUX
ejpam-4382	177	7	semi	semi	ADJ
ejpam-4382	177	8	-	-	ADJ
ejpam-4382	177	9	i	i	PRON
ejpam-4382	177	10	-discrete	-discrete	ADJ
ejpam-4382	177	11	.	.	PUNCT
ejpam-4382	178	1	(	(	PUNCT
ejpam-4382	178	2	3	3	X
ejpam-4382	178	3	)	)	PUNCT
ejpam-4382	178	4	⇒	⇒	NOUN
ejpam-4382	178	5	(	(	PUNCT
ejpam-4382	178	6	5	5	NUM
ejpam-4382	178	7	):	):	PUNCT
ejpam-4382	178	8	let	let	VERB
ejpam-4382	178	9	a	a	PRON
ejpam-4382	178	10	be	be	AUX
ejpam-4382	178	11	semi	semi	ADJ
ejpam-4382	178	12	-	-	ADJ
ejpam-4382	178	13	i	i	ADJ
ejpam-4382	178	14	-codense	-codense	NOUN
ejpam-4382	178	15	.	.	PUNCT
ejpam-4382	179	1	then	then	ADV
ejpam-4382	179	2	,	,	PUNCT
ejpam-4382	179	3	we	we	PRON
ejpam-4382	179	4	have	have	VERB
ejpam-4382	179	5	x	x	INTJ
ejpam-4382	179	6	−	−	PROPN
ejpam-4382	179	7	a	a	PRON
ejpam-4382	179	8	is	be	AUX
ejpam-4382	179	9	semi	semi	ADJ
ejpam-4382	179	10	-	-	ADJ
ejpam-4382	179	11	i	i	PRON
ejpam-4382	179	12	-dense	-dense	ADJ
ejpam-4382	179	13	and	and	CCONJ
ejpam-4382	179	14	so	so	ADV
ejpam-4382	179	15	scli	scli	PROPN
ejpam-4382	179	16	(	(	PUNCT
ejpam-4382	179	17	x	x	X
ejpam-4382	179	18	−	−	NOUN
ejpam-4382	179	19	a	a	X
ejpam-4382	179	20	)	)	PUNCT
ejpam-4382	180	1	=	=	SYM
ejpam-4382	180	2	x.	x.	NOUN
ejpam-4382	180	3	therefore	therefore	ADV
ejpam-4382	180	4	,	,	PUNCT
ejpam-4382	180	5	sinti	sinti	PROPN
ejpam-4382	180	6	(	(	PUNCT
ejpam-4382	180	7	a	a	NOUN
ejpam-4382	180	8	)	)	PUNCT
ejpam-4382	180	9	=	=	NOUN
ejpam-4382	180	10	∅	∅	NOUN
ejpam-4382	180	11	,	,	PUNCT
ejpam-4382	180	12	by	by	ADP
ejpam-4382	180	13	(	(	PUNCT
ejpam-4382	180	14	3	3	NUM
ejpam-4382	180	15	)	)	PUNCT
ejpam-4382	180	16	,	,	PUNCT
ejpam-4382	180	17	a	a	PRON
ejpam-4382	180	18	is	be	AUX
ejpam-4382	180	19	semi	semi	ADJ
ejpam-4382	180	20	-	-	ADJ
ejpam-4382	180	21	i	i	PRON
ejpam-4382	180	22	-closed	-closed	ADJ
ejpam-4382	180	23	and	and	CCONJ
ejpam-4382	180	24	semi	semi	ADJ
ejpam-4382	180	25	-	-	NOUN
ejpam-4382	180	26	i	i	PRON
ejpam-4382	180	27	discrete	discrete	ADJ
ejpam-4382	180	28	.	.	PUNCT
ejpam-4382	181	1	(	(	PUNCT
ejpam-4382	181	2	5	5	X
ejpam-4382	181	3	)	)	PUNCT
ejpam-4382	181	4	⇒	⇒	NOUN
ejpam-4382	181	5	(	(	PUNCT
ejpam-4382	181	6	3	3	NUM
ejpam-4382	181	7	):	):	PUNCT
ejpam-4382	181	8	let	let	VERB
ejpam-4382	181	9	a	a	PRON
ejpam-4382	181	10	be	be	AUX
ejpam-4382	181	11	a	a	DET
ejpam-4382	181	12	subset	subset	NOUN
ejpam-4382	181	13	of	of	ADP
ejpam-4382	181	14	x	x	PUNCT
ejpam-4382	181	15	and	and	CCONJ
ejpam-4382	181	16	sinti	sinti	PROPN
ejpam-4382	181	17	(	(	PUNCT
ejpam-4382	181	18	a	a	X
ejpam-4382	181	19	)	)	PUNCT
ejpam-4382	181	20	=	=	PUNCT
ejpam-4382	181	21	∅.	∅.	ADP
ejpam-4382	181	22	then	then	ADV
ejpam-4382	181	23	,	,	PUNCT
ejpam-4382	181	24	scli	scli	PROPN
ejpam-4382	181	25	(	(	PUNCT
ejpam-4382	181	26	x	x	X
ejpam-4382	181	27	−	−	NOUN
ejpam-4382	181	28	a	a	X
ejpam-4382	181	29	)	)	PUNCT
ejpam-4382	181	30	=	=	PUNCT
ejpam-4382	181	31	x	x	PUNCT
ejpam-4382	181	32	−	−	PROPN
ejpam-4382	181	33	sinti	sinti	PROPN
ejpam-4382	181	34	(	(	PUNCT
ejpam-4382	181	35	a	a	NOUN
ejpam-4382	181	36	)	)	PUNCT
ejpam-4382	181	37	=	=	SYM
ejpam-4382	181	38	x	x	NOUN
ejpam-4382	181	39	and	and	CCONJ
ejpam-4382	181	40	hence	hence	ADV
ejpam-4382	181	41	x	x	PUNCT
ejpam-4382	181	42	−	−	NOUN
ejpam-4382	181	43	a	a	PRON
ejpam-4382	181	44	is	be	AUX
ejpam-4382	181	45	semi	semi	ADJ
ejpam-4382	181	46	-	-	ADJ
ejpam-4382	181	47	i	i	ADJ
ejpam-4382	181	48	-dense	-dense	NOUN
ejpam-4382	181	49	.	.	PUNCT
ejpam-4382	182	1	thus	thus	ADV
ejpam-4382	182	2	,	,	PUNCT
ejpam-4382	182	3	a	a	PRON
ejpam-4382	182	4	is	be	AUX
ejpam-4382	182	5	semi	semi	ADJ
ejpam-4382	182	6	-	-	ADJ
ejpam-4382	182	7	i	i	PRON
ejpam-4382	182	8	-codense	-codense	NOUN
ejpam-4382	182	9	,	,	PUNCT
ejpam-4382	182	10	by	by	ADP
ejpam-4382	182	11	(	(	PUNCT
ejpam-4382	182	12	5	5	NUM
ejpam-4382	182	13	)	)	PUNCT
ejpam-4382	182	14	,	,	PUNCT
ejpam-4382	182	15	a	a	PRON
ejpam-4382	182	16	is	be	AUX
ejpam-4382	182	17	semi	semi	ADJ
ejpam-4382	182	18	-	-	ADJ
ejpam-4382	182	19	i	i	PRON
ejpam-4382	182	20	-closed	-closed	ADJ
ejpam-4382	182	21	and	and	CCONJ
ejpam-4382	182	22	semi	semi	ADJ
ejpam-4382	182	23	-	-	ADJ
ejpam-4382	182	24	i	i	PRON
ejpam-4382	182	25	-discrete	-discrete	ADJ
ejpam-4382	182	26	.	.	PUNCT
ejpam-4382	183	1	(	(	PUNCT
ejpam-4382	183	2	3	3	X
ejpam-4382	183	3	)	)	PUNCT
ejpam-4382	183	4	⇒	⇒	NOUN
ejpam-4382	183	5	(	(	PUNCT
ejpam-4382	183	6	4	4	NUM
ejpam-4382	183	7	):	):	PUNCT
ejpam-4382	183	8	let	let	VERB
ejpam-4382	183	9	a	a	PRON
ejpam-4382	183	10	be	be	AUX
ejpam-4382	183	11	a	a	DET
ejpam-4382	183	12	subset	subset	NOUN
ejpam-4382	183	13	of	of	ADP
ejpam-4382	183	14	x.	x.	NOUN
ejpam-4382	183	15	by	by	ADP
ejpam-4382	183	16	lemma	lemma	PROPN
ejpam-4382	183	17	2	2	NUM
ejpam-4382	183	18	,	,	PUNCT
ejpam-4382	183	19	sinti	sinti	PROPN
ejpam-4382	183	20	(	(	PUNCT
ejpam-4382	183	21	scli	scli	PROPN
ejpam-4382	183	22	(	(	PUNCT
ejpam-4382	183	23	a	a	NOUN
ejpam-4382	183	24	)	)	PUNCT
ejpam-4382	183	25	−	−	NOUN
ejpam-4382	183	26	a	a	X
ejpam-4382	183	27	)	)	PUNCT
ejpam-4382	183	28	=	=	NOUN
ejpam-4382	183	29	∅	∅	NOUN
ejpam-4382	183	30	and	and	CCONJ
ejpam-4382	183	31	by	by	ADP
ejpam-4382	183	32	(	(	PUNCT
ejpam-4382	183	33	3	3	NUM
ejpam-4382	183	34	)	)	PUNCT
ejpam-4382	183	35	,	,	PUNCT
ejpam-4382	183	36	we	we	PRON
ejpam-4382	183	37	have	have	VERB
ejpam-4382	183	38	scli	scli	NOUN
ejpam-4382	183	39	(	(	PUNCT
ejpam-4382	183	40	a)−a	a)−a	X
ejpam-4382	183	41	is	be	AUX
ejpam-4382	183	42	semi	semi	ADJ
ejpam-4382	183	43	-	-	ADJ
ejpam-4382	183	44	i	i	PRON
ejpam-4382	183	45	-closed	-closed	ADJ
ejpam-4382	183	46	and	and	CCONJ
ejpam-4382	183	47	semi	semi	ADJ
ejpam-4382	183	48	-	-	ADJ
ejpam-4382	183	49	i	i	PRON
ejpam-4382	183	50	-discrete	-discrete	ADJ
ejpam-4382	183	51	.	.	PUNCT
ejpam-4382	184	1	(	(	PUNCT
ejpam-4382	184	2	4	4	X
ejpam-4382	184	3	)	)	PUNCT
ejpam-4382	184	4	⇒	⇒	NOUN
ejpam-4382	184	5	(	(	PUNCT
ejpam-4382	184	6	3	3	NUM
ejpam-4382	184	7	):	):	PUNCT
ejpam-4382	184	8	let	let	VERB
ejpam-4382	184	9	a	a	PRON
ejpam-4382	184	10	be	be	AUX
ejpam-4382	184	11	a	a	DET
ejpam-4382	184	12	subset	subset	NOUN
ejpam-4382	184	13	of	of	ADP
ejpam-4382	184	14	x	x	PUNCT
ejpam-4382	184	15	and	and	CCONJ
ejpam-4382	184	16	sinti	sinti	PROPN
ejpam-4382	184	17	(	(	PUNCT
ejpam-4382	184	18	a	a	X
ejpam-4382	184	19	)	)	PUNCT
ejpam-4382	184	20	=	=	PUNCT
ejpam-4382	184	21	∅.	∅.	ADP
ejpam-4382	184	22	then	then	ADV
ejpam-4382	184	23	,	,	PUNCT
ejpam-4382	184	24	scli	scli	PROPN
ejpam-4382	184	25	(	(	PUNCT
ejpam-4382	184	26	x	x	X
ejpam-4382	184	27	−	−	NOUN
ejpam-4382	184	28	a	a	X
ejpam-4382	184	29	)	)	PUNCT
ejpam-4382	184	30	=	=	PUNCT
ejpam-4382	184	31	x	x	PUNCT
ejpam-4382	184	32	−	−	PROPN
ejpam-4382	184	33	sinti	sinti	PROPN
ejpam-4382	184	34	(	(	PUNCT
ejpam-4382	184	35	a	a	NOUN
ejpam-4382	184	36	)	)	PUNCT
ejpam-4382	184	37	=	=	SYM
ejpam-4382	184	38	x	x	PUNCT
ejpam-4382	184	39	and	and	CCONJ
ejpam-4382	184	40	hence	hence	ADV
ejpam-4382	184	41	a	a	DET
ejpam-4382	184	42	=	=	X
ejpam-4382	184	43	scli	scli	NOUN
ejpam-4382	184	44	(	(	PUNCT
ejpam-4382	184	45	x	x	X
ejpam-4382	184	46	−	−	PROPN
ejpam-4382	184	47	a	a	NOUN
ejpam-4382	184	48	)	)	PUNCT
ejpam-4382	184	49	−	−	PROPN
ejpam-4382	185	1	(	(	PUNCT
ejpam-4382	185	2	x	x	X
ejpam-4382	185	3	−	−	NOUN
ejpam-4382	185	4	a	a	NOUN
ejpam-4382	185	5	)	)	PUNCT
ejpam-4382	185	6	.	.	PUNCT
ejpam-4382	186	1	by	by	ADP
ejpam-4382	186	2	(	(	PUNCT
ejpam-4382	186	3	4	4	NUM
ejpam-4382	186	4	)	)	PUNCT
ejpam-4382	186	5	,	,	PUNCT
ejpam-4382	186	6	we	we	PRON
ejpam-4382	186	7	have	have	VERB
ejpam-4382	186	8	a	a	PRON
ejpam-4382	186	9	is	be	AUX
ejpam-4382	186	10	semi	semi	ADJ
ejpam-4382	186	11	-	-	ADJ
ejpam-4382	186	12	i	i	PRON
ejpam-4382	186	13	-closed	-closed	ADJ
ejpam-4382	186	14	and	and	CCONJ
ejpam-4382	186	15	semi	semi	ADJ
ejpam-4382	186	16	-	-	ADJ
ejpam-4382	186	17	i	i	PRON
ejpam-4382	186	18	-discrete	-discrete	ADJ
ejpam-4382	186	19	.	.	PUNCT
ejpam-4382	187	1	(	(	PUNCT
ejpam-4382	187	2	5	5	X
ejpam-4382	187	3	)	)	PUNCT
ejpam-4382	187	4	⇒	⇒	NOUN
ejpam-4382	187	5	(	(	PUNCT
ejpam-4382	187	6	6	6	NUM
ejpam-4382	187	7	):	):	PUNCT
ejpam-4382	187	8	this	this	PRON
ejpam-4382	187	9	is	be	AUX
ejpam-4382	187	10	obvious	obvious	ADJ
ejpam-4382	187	11	.	.	PUNCT
ejpam-4382	188	1	(	(	PUNCT
ejpam-4382	188	2	6	6	NUM
ejpam-4382	188	3	)	)	PUNCT
ejpam-4382	188	4	⇒	⇒	NOUN
ejpam-4382	188	5	(	(	PUNCT
ejpam-4382	188	6	1	1	NUM
ejpam-4382	188	7	):	):	PUNCT
ejpam-4382	188	8	let	let	VERB
ejpam-4382	188	9	a	a	PRON
ejpam-4382	188	10	be	be	AUX
ejpam-4382	188	11	a	a	DET
ejpam-4382	188	12	semi	semi	ADJ
ejpam-4382	188	13	-	-	ADJ
ejpam-4382	188	14	i	i	ADJ
ejpam-4382	188	15	-dense	-dense	PROPN
ejpam-4382	188	16	subset	subset	NOUN
ejpam-4382	188	17	of	of	ADP
ejpam-4382	188	18	x.	x.	NOUN
ejpam-4382	188	19	then	then	ADV
ejpam-4382	188	20	,	,	PUNCT
ejpam-4382	188	21	we	we	PRON
ejpam-4382	188	22	have	have	VERB
ejpam-4382	188	23	x	x	INTJ
ejpam-4382	188	24	−	−	PROPN
ejpam-4382	188	25	a	a	PRON
ejpam-4382	188	26	is	be	AUX
ejpam-4382	188	27	semi	semi	ADJ
ejpam-4382	188	28	-	-	ADJ
ejpam-4382	188	29	i	i	PRON
ejpam-4382	188	30	codense	codense	NOUN
ejpam-4382	188	31	.	.	PUNCT
ejpam-4382	189	1	by	by	ADP
ejpam-4382	189	2	(	(	PUNCT
ejpam-4382	189	3	6	6	NUM
ejpam-4382	189	4	)	)	PUNCT
ejpam-4382	189	5	,	,	PUNCT
ejpam-4382	189	6	x	x	PUNCT
ejpam-4382	189	7	−	−	NOUN
ejpam-4382	189	8	a	a	PRON
ejpam-4382	189	9	is	be	AUX
ejpam-4382	189	10	semi	semi	ADJ
ejpam-4382	189	11	-	-	ADJ
ejpam-4382	189	12	i	i	PRON
ejpam-4382	189	13	-closed	-close	VERB
ejpam-4382	189	14	and	and	CCONJ
ejpam-4382	189	15	so	so	ADV
ejpam-4382	189	16	a	a	PRON
ejpam-4382	189	17	is	be	AUX
ejpam-4382	189	18	semi	semi	ADJ
ejpam-4382	189	19	-	-	ADJ
ejpam-4382	189	20	i	i	PRON
ejpam-4382	189	21	-open	-open	NOUN
ejpam-4382	189	22	.	.	PUNCT
ejpam-4382	190	1	thus	thus	ADV
ejpam-4382	190	2	,	,	PUNCT
ejpam-4382	190	3	(	(	PUNCT
ejpam-4382	190	4	x	x	X
ejpam-4382	190	5	,	,	PUNCT
ejpam-4382	190	6	τ	τ	PROPN
ejpam-4382	190	7	,	,	PUNCT
ejpam-4382	190	8	i	i	PROPN
ejpam-4382	190	9	)	)	PUNCT
ejpam-4382	190	10	is	be	AUX
ejpam-4382	190	11	semi	semi	ADJ
ejpam-4382	190	12	-	-	ADJ
ejpam-4382	190	13	i	i	PRON
ejpam-4382	190	14	-submaximal	-submaximal	ADJ
ejpam-4382	190	15	.	.	PUNCT
ejpam-4382	191	1	theorem	theorem	VERB
ejpam-4382	191	2	5	5	NUM
ejpam-4382	191	3	.	.	X
ejpam-4382	191	4	for	for	ADP
ejpam-4382	191	5	an	an	DET
ejpam-4382	191	6	ideal	ideal	ADJ
ejpam-4382	191	7	topological	topological	ADJ
ejpam-4382	191	8	space	space	NOUN
ejpam-4382	191	9	(	(	PUNCT
ejpam-4382	191	10	x	x	X
ejpam-4382	191	11	,	,	PUNCT
ejpam-4382	191	12	τ	τ	PROPN
ejpam-4382	191	13	,	,	PUNCT
ejpam-4382	191	14	i	i	NOUN
ejpam-4382	191	15	)	)	PUNCT
ejpam-4382	191	16	,	,	PUNCT
ejpam-4382	191	17	the	the	DET
ejpam-4382	191	18	following	follow	VERB
ejpam-4382	191	19	properties	property	NOUN
ejpam-4382	191	20	are	be	AUX
ejpam-4382	191	21	equivalent	equivalent	ADJ
ejpam-4382	191	22	:	:	PUNCT
ejpam-4382	191	23	(	(	PUNCT
ejpam-4382	191	24	1	1	X
ejpam-4382	191	25	)	)	PUNCT
ejpam-4382	191	26	(	(	PUNCT
ejpam-4382	191	27	x	x	X
ejpam-4382	191	28	,	,	PUNCT
ejpam-4382	191	29	τ	τ	PROPN
ejpam-4382	191	30	,	,	PUNCT
ejpam-4382	191	31	i	i	PROPN
ejpam-4382	191	32	)	)	PUNCT
ejpam-4382	191	33	is	be	AUX
ejpam-4382	191	34	semi	semi	ADJ
ejpam-4382	191	35	-	-	ADJ
ejpam-4382	191	36	i	i	PRON
ejpam-4382	191	37	-submaximal	-submaximal	ADJ
ejpam-4382	191	38	;	;	PUNCT
ejpam-4382	191	39	(	(	PUNCT
ejpam-4382	191	40	2	2	X
ejpam-4382	191	41	)	)	PUNCT
ejpam-4382	191	42	for	for	ADP
ejpam-4382	191	43	every	every	DET
ejpam-4382	191	44	subset	subset	NOUN
ejpam-4382	191	45	a	a	PRON
ejpam-4382	191	46	of	of	ADP
ejpam-4382	191	47	x	x	PRON
ejpam-4382	191	48	,	,	PUNCT
ejpam-4382	191	49	scli	scli	PROPN
ejpam-4382	191	50	(	(	PUNCT
ejpam-4382	191	51	a)−a	a)−a	X
ejpam-4382	191	52	is	be	AUX
ejpam-4382	191	53	semi	semi	ADJ
ejpam-4382	191	54	-	-	ADJ
ejpam-4382	191	55	i	i	PRON
ejpam-4382	191	56	-closed	-close	VERB
ejpam-4382	191	57	;	;	PUNCT
ejpam-4382	191	58	(	(	PUNCT
ejpam-4382	191	59	3	3	X
ejpam-4382	191	60	)	)	PUNCT
ejpam-4382	191	61	every	every	DET
ejpam-4382	191	62	subset	subset	NOUN
ejpam-4382	191	63	of	of	ADP
ejpam-4382	191	64	x	x	PUNCT
ejpam-4382	191	65	is	be	AUX
ejpam-4382	191	66	locally	locally	ADV
ejpam-4382	191	67	semi	semi	ADJ
ejpam-4382	191	68	-	-	ADJ
ejpam-4382	191	69	i	i	PRON
ejpam-4382	191	70	-closed	-close	VERB
ejpam-4382	191	71	;	;	PUNCT
ejpam-4382	191	72	(	(	PUNCT
ejpam-4382	191	73	4	4	X
ejpam-4382	191	74	)	)	PUNCT
ejpam-4382	191	75	each	each	DET
ejpam-4382	191	76	semi	semi	ADJ
ejpam-4382	191	77	-	-	ADJ
ejpam-4382	191	78	i	i	ADJ
ejpam-4382	191	79	-dense	-dense	PROPN
ejpam-4382	191	80	subset	subset	NOUN
ejpam-4382	191	81	of	of	ADP
ejpam-4382	191	82	x	x	PUNCT
ejpam-4382	191	83	is	be	AUX
ejpam-4382	191	84	locally	locally	ADV
ejpam-4382	191	85	semi	semi	ADJ
ejpam-4382	191	86	-	-	ADJ
ejpam-4382	191	87	i	i	PRON
ejpam-4382	191	88	-closed	-closed	ADJ
ejpam-4382	191	89	.	.	PUNCT
ejpam-4382	192	1	proof	proof	NOUN
ejpam-4382	192	2	.	.	PUNCT
ejpam-4382	193	1	(	(	PUNCT
ejpam-4382	193	2	1	1	X
ejpam-4382	193	3	)	)	PUNCT
ejpam-4382	193	4	⇒	⇒	NOUN
ejpam-4382	193	5	(	(	PUNCT
ejpam-4382	193	6	2	2	NUM
ejpam-4382	193	7	)	)	PUNCT
ejpam-4382	193	8	and	and	CCONJ
ejpam-4382	193	9	(	(	PUNCT
ejpam-4382	193	10	2	2	X
ejpam-4382	193	11	)	)	PUNCT
ejpam-4382	193	12	⇒	⇒	NOUN
ejpam-4382	193	13	(	(	PUNCT
ejpam-4382	193	14	3	3	X
ejpam-4382	193	15	)	)	PUNCT
ejpam-4382	193	16	follows	follow	VERB
ejpam-4382	193	17	from	from	ADP
ejpam-4382	193	18	theorem	theorem	ADJ
ejpam-4382	193	19	2	2	NUM
ejpam-4382	193	20	.	.	PUNCT
ejpam-4382	193	21	(	(	PUNCT
ejpam-4382	193	22	3	3	X
ejpam-4382	193	23	)	)	PUNCT
ejpam-4382	193	24	⇒	⇒	NOUN
ejpam-4382	193	25	(	(	PUNCT
ejpam-4382	193	26	4	4	NUM
ejpam-4382	193	27	):	):	PUNCT
ejpam-4382	193	28	the	the	DET
ejpam-4382	193	29	proof	proof	NOUN
ejpam-4382	193	30	is	be	AUX
ejpam-4382	193	31	obvious	obvious	ADJ
ejpam-4382	193	32	.	.	PUNCT
ejpam-4382	194	1	(	(	PUNCT
ejpam-4382	194	2	4	4	X
ejpam-4382	194	3	)	)	PUNCT
ejpam-4382	194	4	⇒	⇒	NOUN
ejpam-4382	194	5	(	(	PUNCT
ejpam-4382	194	6	1	1	NUM
ejpam-4382	194	7	):	):	PUNCT
ejpam-4382	194	8	let	let	VERB
ejpam-4382	194	9	a	a	PRON
ejpam-4382	194	10	be	be	AUX
ejpam-4382	194	11	a	a	DET
ejpam-4382	194	12	semi	semi	ADJ
ejpam-4382	194	13	-	-	ADJ
ejpam-4382	194	14	i	i	ADJ
ejpam-4382	194	15	-dense	-dense	PROPN
ejpam-4382	194	16	subset	subset	NOUN
ejpam-4382	194	17	of	of	ADP
ejpam-4382	194	18	x.	x.	NOUN
ejpam-4382	194	19	by	by	ADP
ejpam-4382	194	20	(	(	PUNCT
ejpam-4382	194	21	4	4	NUM
ejpam-4382	194	22	)	)	PUNCT
ejpam-4382	194	23	,	,	PUNCT
ejpam-4382	194	24	there	there	PRON
ejpam-4382	194	25	exist	exist	VERB
ejpam-4382	194	26	a	a	DET
ejpam-4382	194	27	semi	semi	ADJ
ejpam-4382	194	28	-	-	ADJ
ejpam-4382	194	29	i	i	PRON
ejpam-4382	194	30	-open	-open	NOUN
ejpam-4382	194	31	set	set	VERB
ejpam-4382	194	32	u	u	NOUN
ejpam-4382	194	33	and	and	CCONJ
ejpam-4382	194	34	a	a	DET
ejpam-4382	194	35	semi	semi	ADJ
ejpam-4382	194	36	-	-	ADJ
ejpam-4382	194	37	i	i	PRON
ejpam-4382	194	38	-closed	-close	VERB
ejpam-4382	194	39	set	set	VERB
ejpam-4382	194	40	v	v	ADP
ejpam-4382	194	41	such	such	DET
ejpam-4382	194	42	that	that	SCONJ
ejpam-4382	194	43	a	a	DET
ejpam-4382	194	44	=	=	X
ejpam-4382	194	45	u	u	NOUN
ejpam-4382	194	46	∩	∩	NOUN
ejpam-4382	194	47	v	v	NOUN
ejpam-4382	194	48	.	.	PUNCT
ejpam-4382	195	1	since	since	SCONJ
ejpam-4382	195	2	a	a	DET
ejpam-4382	195	3	⊆	⊆	NUM
ejpam-4382	195	4	v	v	NOUN
ejpam-4382	195	5	,	,	PUNCT
ejpam-4382	195	6	x	x	PUNCT
ejpam-4382	195	7	=	=	PRON
ejpam-4382	195	8	scli	scli	NOUN
ejpam-4382	195	9	(	(	PUNCT
ejpam-4382	195	10	a	a	NOUN
ejpam-4382	195	11	)	)	PUNCT
ejpam-4382	195	12	⊆	⊆	NUM
ejpam-4382	195	13	scli	scli	NOUN
ejpam-4382	195	14	(	(	PUNCT
ejpam-4382	195	15	v	v	NOUN
ejpam-4382	195	16	)	)	PUNCT
ejpam-4382	195	17	=	=	SYM
ejpam-4382	195	18	v	v	ADP
ejpam-4382	195	19	c.	c.	PROPN
ejpam-4382	195	20	boonpok	boonpok	PROPN
ejpam-4382	195	21	/	/	SYM
ejpam-4382	195	22	eur	eur	PROPN
ejpam-4382	195	23	.	.	PUNCT
ejpam-4382	196	1	j.	j.	PROPN
ejpam-4382	196	2	pure	pure	PROPN
ejpam-4382	196	3	appl	appl	PROPN
ejpam-4382	196	4	.	.	PROPN
ejpam-4382	196	5	math	math	PROPN
ejpam-4382	196	6	,	,	PUNCT
ejpam-4382	196	7	15	15	NUM
ejpam-4382	196	8	(	(	PUNCT
ejpam-4382	196	9	3	3	NUM
ejpam-4382	196	10	)	)	PUNCT
ejpam-4382	196	11	(	(	PUNCT
ejpam-4382	196	12	2022	2022	NUM
ejpam-4382	196	13	)	)	PUNCT
ejpam-4382	196	14	,	,	PUNCT
ejpam-4382	196	15	938	938	NUM
ejpam-4382	196	16	-	-	SYM
ejpam-4382	196	17	947	947	NUM
ejpam-4382	196	18	945	945	NUM
ejpam-4382	196	19	which	which	PRON
ejpam-4382	196	20	yields	yield	VERB
ejpam-4382	196	21	v	v	NOUN
ejpam-4382	196	22	=	=	SYM
ejpam-4382	196	23	x.	x.	NOUN
ejpam-4382	197	1	thus	thus	ADV
ejpam-4382	197	2	,	,	PUNCT
ejpam-4382	197	3	a	a	DET
ejpam-4382	197	4	=	=	X
ejpam-4382	197	5	u	u	NOUN
ejpam-4382	197	6	∩	∩	NOUN
ejpam-4382	197	7	v	v	NOUN
ejpam-4382	197	8	=	=	SYM
ejpam-4382	197	9	u	u	NOUN
ejpam-4382	197	10	∩x	∩x	NOUN
ejpam-4382	197	11	=	=	SYM
ejpam-4382	197	12	u	u	NOUN
ejpam-4382	197	13	and	and	CCONJ
ejpam-4382	197	14	hence	hence	ADV
ejpam-4382	197	15	a	a	PRON
ejpam-4382	197	16	is	be	AUX
ejpam-4382	197	17	semi	semi	ADJ
ejpam-4382	197	18	-	-	ADJ
ejpam-4382	197	19	i	i	PRON
ejpam-4382	197	20	-open	-open	ADJ
ejpam-4382	197	21	.	.	PUNCT
ejpam-4382	198	1	this	this	PRON
ejpam-4382	198	2	shows	show	VERB
ejpam-4382	198	3	that	that	SCONJ
ejpam-4382	198	4	(	(	PUNCT
ejpam-4382	198	5	x	x	X
ejpam-4382	198	6	,	,	PUNCT
ejpam-4382	198	7	τ	τ	PROPN
ejpam-4382	198	8	,	,	PUNCT
ejpam-4382	198	9	i	i	PROPN
ejpam-4382	198	10	)	)	PUNCT
ejpam-4382	198	11	is	be	AUX
ejpam-4382	198	12	semi	semi	ADJ
ejpam-4382	198	13	-	-	ADJ
ejpam-4382	198	14	i	i	PRON
ejpam-4382	198	15	-submaximal	-submaximal	ADJ
ejpam-4382	198	16	.	.	PUNCT
ejpam-4382	199	1	for	for	ADP
ejpam-4382	199	2	a	a	DET
ejpam-4382	199	3	subset	subset	NOUN
ejpam-4382	199	4	a	a	PRON
ejpam-4382	199	5	of	of	ADP
ejpam-4382	199	6	an	an	DET
ejpam-4382	199	7	ideal	ideal	ADJ
ejpam-4382	199	8	topological	topological	ADJ
ejpam-4382	199	9	space	space	NOUN
ejpam-4382	199	10	(	(	PUNCT
ejpam-4382	199	11	x	x	X
ejpam-4382	199	12	,	,	PUNCT
ejpam-4382	199	13	τ	τ	PROPN
ejpam-4382	199	14	,	,	PUNCT
ejpam-4382	199	15	i	i	NOUN
ejpam-4382	199	16	)	)	PUNCT
ejpam-4382	199	17	,	,	PUNCT
ejpam-4382	199	18	we	we	PRON
ejpam-4382	199	19	denote	denote	VERB
ejpam-4382	199	20	by	by	ADP
ejpam-4382	199	21	τ|a	τ|a	PUNCT
ejpam-4382	200	1	the	the	DET
ejpam-4382	200	2	relative	relative	ADJ
ejpam-4382	200	3	topology	topology	NOUN
ejpam-4382	200	4	on	on	ADP
ejpam-4382	200	5	a	a	PRON
ejpam-4382	200	6	and	and	CCONJ
ejpam-4382	200	7	i|a	i|a	ADP
ejpam-4382	200	8	=	=	X
ejpam-4382	200	9	{	{	PUNCT
ejpam-4382	200	10	a	a	DET
ejpam-4382	200	11	∩	∩	NOUN
ejpam-4382	200	12	i0	i0	PROPN
ejpam-4382	200	13	|	|	ADV
ejpam-4382	200	14	i0	i0	PROPN
ejpam-4382	200	15	∈	∈	PROPN
ejpam-4382	201	1	i	i	PRON
ejpam-4382	201	2	}	}	PUNCT
ejpam-4382	201	3	is	be	AUX
ejpam-4382	201	4	an	an	DET
ejpam-4382	201	5	ideal	ideal	NOUN
ejpam-4382	201	6	on	on	ADP
ejpam-4382	201	7	a.	a.	PROPN
ejpam-4382	201	8	lemma	lemma	PROPN
ejpam-4382	201	9	3	3	X
ejpam-4382	201	10	.	.	PUNCT
ejpam-4382	202	1	[	[	X
ejpam-4382	202	2	3	3	X
ejpam-4382	202	3	]	]	X
ejpam-4382	202	4	let	let	VERB
ejpam-4382	202	5	(	(	PUNCT
ejpam-4382	202	6	x	x	NOUN
ejpam-4382	202	7	,	,	PUNCT
ejpam-4382	202	8	τ	τ	PROPN
ejpam-4382	202	9	,	,	PUNCT
ejpam-4382	202	10	i	i	PRON
ejpam-4382	202	11	)	)	PUNCT
ejpam-4382	202	12	be	be	AUX
ejpam-4382	202	13	an	an	DET
ejpam-4382	202	14	ideal	ideal	ADJ
ejpam-4382	202	15	topological	topological	ADJ
ejpam-4382	202	16	space	space	NOUN
ejpam-4382	202	17	and	and	CCONJ
ejpam-4382	202	18	b	b	NOUN
ejpam-4382	202	19	⊆	⊆	NUM
ejpam-4382	202	20	a	a	DET
ejpam-4382	202	21	⊆	⊆	NUM
ejpam-4382	202	22	x.	x.	NOUN
ejpam-4382	202	23	then	then	ADV
ejpam-4382	202	24	,	,	PUNCT
ejpam-4382	202	25	b⋆(τ|a	b⋆(τ|a	PROPN
ejpam-4382	202	26	,	,	PUNCT
ejpam-4382	202	27	i|a	i|a	ADP
ejpam-4382	202	28	)	)	PUNCT
ejpam-4382	202	29	=	=	SYM
ejpam-4382	202	30	b⋆(τ	b⋆(τ	NOUN
ejpam-4382	202	31	,	,	PUNCT
ejpam-4382	202	32	i	i	PRON
ejpam-4382	202	33	)	)	PUNCT
ejpam-4382	203	1	∩a	∩a	PROPN
ejpam-4382	203	2	.	.	PUNCT
ejpam-4382	204	1	lemma	lemma	PROPN
ejpam-4382	204	2	4	4	NUM
ejpam-4382	204	3	.	.	PUNCT
ejpam-4382	205	1	[	[	X
ejpam-4382	205	2	8	8	NUM
ejpam-4382	205	3	]	]	X
ejpam-4382	205	4	let	let	VERB
ejpam-4382	205	5	(	(	PUNCT
ejpam-4382	205	6	x	x	NOUN
ejpam-4382	205	7	,	,	PUNCT
ejpam-4382	205	8	τ	τ	PROPN
ejpam-4382	205	9	,	,	PUNCT
ejpam-4382	205	10	i	i	PRON
ejpam-4382	205	11	)	)	PUNCT
ejpam-4382	205	12	be	be	AUX
ejpam-4382	205	13	an	an	DET
ejpam-4382	205	14	ideal	ideal	ADJ
ejpam-4382	205	15	topological	topological	ADJ
ejpam-4382	205	16	space	space	NOUN
ejpam-4382	205	17	and	and	CCONJ
ejpam-4382	205	18	b	b	NOUN
ejpam-4382	205	19	⊆	⊆	NUM
ejpam-4382	205	20	a	a	DET
ejpam-4382	205	21	⊆	⊆	NUM
ejpam-4382	205	22	x.	x.	NOUN
ejpam-4382	205	23	then	then	ADV
ejpam-4382	205	24	,	,	PUNCT
ejpam-4382	205	25	cl⋆a(b	cl⋆a(b	ADJ
ejpam-4382	205	26	)	)	PUNCT
ejpam-4382	205	27	=	=	SYM
ejpam-4382	205	28	cl⋆(b	cl⋆(b	NOUN
ejpam-4382	205	29	)	)	PUNCT
ejpam-4382	205	30	∩a	∩a	PROPN
ejpam-4382	205	31	.	.	PUNCT
ejpam-4382	206	1	lemma	lemma	PROPN
ejpam-4382	206	2	5	5	X
ejpam-4382	206	3	.	.	PUNCT
ejpam-4382	207	1	let	let	AUX
ejpam-4382	207	2	(	(	PUNCT
ejpam-4382	207	3	x	x	X
ejpam-4382	207	4	,	,	PUNCT
ejpam-4382	207	5	τ	τ	PROPN
ejpam-4382	207	6	,	,	PUNCT
ejpam-4382	207	7	i	i	PRON
ejpam-4382	207	8	)	)	PUNCT
ejpam-4382	207	9	be	be	AUX
ejpam-4382	207	10	an	an	DET
ejpam-4382	207	11	ideal	ideal	ADJ
ejpam-4382	207	12	topological	topological	ADJ
ejpam-4382	207	13	space	space	NOUN
ejpam-4382	207	14	and	and	CCONJ
ejpam-4382	207	15	a	a	DET
ejpam-4382	207	16	⊆	⊆	NUM
ejpam-4382	207	17	b	b	NOUN
ejpam-4382	207	18	⊆	⊆	NUM
ejpam-4382	207	19	x.	x.	NOUN
ejpam-4382	208	1	if	if	SCONJ
ejpam-4382	208	2	(	(	PUNCT
ejpam-4382	208	3	b	b	NOUN
ejpam-4382	208	4	,	,	PUNCT
ejpam-4382	208	5	τ|b	τ|b	NOUN
ejpam-4382	208	6	,	,	PUNCT
ejpam-4382	208	7	i|b	i|b	X
ejpam-4382	208	8	)	)	PUNCT
ejpam-4382	208	9	is	be	AUX
ejpam-4382	208	10	an	an	DET
ejpam-4382	208	11	open	open	ADJ
ejpam-4382	208	12	subspace	subspace	NOUN
ejpam-4382	208	13	of	of	ADP
ejpam-4382	208	14	(	(	PUNCT
ejpam-4382	208	15	x	x	X
ejpam-4382	208	16	,	,	PUNCT
ejpam-4382	208	17	τ	τ	PROPN
ejpam-4382	208	18	,	,	PUNCT
ejpam-4382	208	19	i	i	NOUN
ejpam-4382	208	20	)	)	PUNCT
ejpam-4382	208	21	,	,	PUNCT
ejpam-4382	208	22	then	then	ADV
ejpam-4382	208	23	scli|b	scli|b	ADJ
ejpam-4382	208	24	(	(	PUNCT
ejpam-4382	208	25	a	a	X
ejpam-4382	208	26	)	)	PUNCT
ejpam-4382	208	27	=	=	SYM
ejpam-4382	208	28	scli	scli	NOUN
ejpam-4382	208	29	(	(	PUNCT
ejpam-4382	208	30	a	a	NOUN
ejpam-4382	208	31	)	)	PUNCT
ejpam-4382	208	32	∩b	∩b	NOUN
ejpam-4382	208	33	.	.	PUNCT
ejpam-4382	208	34	proof	proof	NOUN
ejpam-4382	208	35	.	.	PUNCT
ejpam-4382	209	1	suppose	suppose	VERB
ejpam-4382	209	2	that	that	SCONJ
ejpam-4382	209	3	(	(	PUNCT
ejpam-4382	209	4	b	b	NOUN
ejpam-4382	209	5	,	,	PUNCT
ejpam-4382	209	6	τ|b	τ|b	NOUN
ejpam-4382	209	7	,	,	PUNCT
ejpam-4382	209	8	i|b	i|b	X
ejpam-4382	209	9	)	)	PUNCT
ejpam-4382	209	10	is	be	AUX
ejpam-4382	209	11	an	an	DET
ejpam-4382	209	12	open	open	ADJ
ejpam-4382	209	13	subspace	subspace	NOUN
ejpam-4382	209	14	of	of	ADP
ejpam-4382	209	15	(	(	PUNCT
ejpam-4382	209	16	x	x	X
ejpam-4382	209	17	,	,	PUNCT
ejpam-4382	209	18	τ	τ	PROPN
ejpam-4382	209	19	,	,	PUNCT
ejpam-4382	209	20	i	i	PROPN
ejpam-4382	209	21	)	)	PUNCT
ejpam-4382	209	22	and	and	CCONJ
ejpam-4382	209	23	a	a	PRON
ejpam-4382	209	24	⊆	⊆	NUM
ejpam-4382	209	25	b	b	NOUN
ejpam-4382	209	26	⊆	⊆	NUM
ejpam-4382	209	27	x.	x.	NOUN
ejpam-4382	209	28	by	by	ADP
ejpam-4382	209	29	lemma	lemma	PROPN
ejpam-4382	209	30	13(2	13(2	PROPN
ejpam-4382	209	31	)	)	PUNCT
ejpam-4382	209	32	of	of	ADP
ejpam-4382	209	33	[	[	X
ejpam-4382	209	34	5	5	NUM
ejpam-4382	209	35	]	]	PUNCT
ejpam-4382	209	36	and	and	CCONJ
ejpam-4382	209	37	lemma	lemma	PROPN
ejpam-4382	209	38	4	4	NUM
ejpam-4382	209	39	,	,	PUNCT
ejpam-4382	209	40	we	we	PRON
ejpam-4382	209	41	have	have	VERB
ejpam-4382	209	42	scli	scli	NOUN
ejpam-4382	209	43	(	(	PUNCT
ejpam-4382	209	44	a	a	NOUN
ejpam-4382	209	45	)	)	PUNCT
ejpam-4382	209	46	∩b	∩b	NOUN
ejpam-4382	209	47	=	=	PUNCT
ejpam-4382	209	48	(	(	PUNCT
ejpam-4382	209	49	a	a	DET
ejpam-4382	209	50	∪	∪	ADJ
ejpam-4382	209	51	cl⋆(int(a	cl⋆(int(a	NOUN
ejpam-4382	209	52	)	)	PUNCT
ejpam-4382	209	53	)	)	PUNCT
ejpam-4382	209	54	)	)	PUNCT
ejpam-4382	210	1	∩b	∩b	NOUN
ejpam-4382	210	2	=	=	PUNCT
ejpam-4382	210	3	(	(	PUNCT
ejpam-4382	210	4	a	a	DET
ejpam-4382	210	5	∩b	∩b	NOUN
ejpam-4382	210	6	)	)	PUNCT
ejpam-4382	210	7	∪	∪	NOUN
ejpam-4382	210	8	(	(	PUNCT
ejpam-4382	210	9	cl⋆(int(a	cl⋆(int(a	PROPN
ejpam-4382	210	10	)	)	PUNCT
ejpam-4382	210	11	)	)	PUNCT
ejpam-4382	211	1	∩b	∩b	NOUN
ejpam-4382	211	2	)	)	PUNCT
ejpam-4382	211	3	=	=	PUNCT
ejpam-4382	211	4	a	a	DET
ejpam-4382	211	5	∪	∪	ADJ
ejpam-4382	211	6	cl⋆b(int(a	cl⋆b(int(a	NOUN
ejpam-4382	211	7	)	)	PUNCT
ejpam-4382	211	8	)	)	PUNCT
ejpam-4382	212	1	=	=	PUNCT
ejpam-4382	212	2	a	a	DET
ejpam-4382	212	3	∪	∪	ADJ
ejpam-4382	212	4	cl⋆b(int(a	cl⋆b(int(a	NOUN
ejpam-4382	212	5	∩b	∩b	NOUN
ejpam-4382	212	6	)	)	PUNCT
ejpam-4382	212	7	)	)	PUNCT
ejpam-4382	213	1	=	=	PUNCT
ejpam-4382	213	2	a	a	DET
ejpam-4382	213	3	∪	∪	ADJ
ejpam-4382	213	4	cl⋆b(int(a	cl⋆b(int(a	NOUN
ejpam-4382	213	5	)	)	PUNCT
ejpam-4382	213	6	∩b	∩b	NOUN
ejpam-4382	213	7	)	)	PUNCT
ejpam-4382	213	8	=	=	NOUN
ejpam-4382	213	9	a	a	DET
ejpam-4382	213	10	∪	∪	ADJ
ejpam-4382	213	11	cl⋆b(intb(a	cl⋆b(intb(a	NOUN
ejpam-4382	213	12	)	)	PUNCT
ejpam-4382	213	13	)	)	PUNCT
ejpam-4382	214	1	=	=	SYM
ejpam-4382	214	2	scli|b	scli|b	ADJ
ejpam-4382	214	3	(	(	PUNCT
ejpam-4382	214	4	a	a	NOUN
ejpam-4382	214	5	)	)	PUNCT
ejpam-4382	214	6	.	.	PUNCT
ejpam-4382	215	1	lemma	lemma	PROPN
ejpam-4382	215	2	6	6	NUM
ejpam-4382	215	3	.	.	PUNCT
ejpam-4382	216	1	[	[	X
ejpam-4382	216	2	10	10	NUM
ejpam-4382	216	3	]	]	X
ejpam-4382	216	4	let	let	VERB
ejpam-4382	216	5	(	(	PUNCT
ejpam-4382	216	6	x	x	NOUN
ejpam-4382	216	7	,	,	PUNCT
ejpam-4382	216	8	τ	τ	PROPN
ejpam-4382	216	9	,	,	PUNCT
ejpam-4382	216	10	i	i	PRON
ejpam-4382	216	11	)	)	PUNCT
ejpam-4382	216	12	be	be	AUX
ejpam-4382	216	13	an	an	DET
ejpam-4382	216	14	ideal	ideal	ADJ
ejpam-4382	216	15	topological	topological	ADJ
ejpam-4382	216	16	space	space	NOUN
ejpam-4382	216	17	.	.	PUNCT
ejpam-4382	217	1	if	if	SCONJ
ejpam-4382	217	2	u	u	PROPN
ejpam-4382	217	3	∈	∈	PROPN
ejpam-4382	217	4	τ	τ	X
ejpam-4382	217	5	and	and	CCONJ
ejpam-4382	217	6	w	w	PROPN
ejpam-4382	217	7	∈	∈	PROPN
ejpam-4382	217	8	sio(x	sio(x	PROPN
ejpam-4382	217	9	,	,	PUNCT
ejpam-4382	217	10	τ	τ	PROPN
ejpam-4382	217	11	)	)	PUNCT
ejpam-4382	217	12	,	,	PUNCT
ejpam-4382	217	13	then	then	ADV
ejpam-4382	217	14	u	u	X
ejpam-4382	217	15	∩w	∩w	PROPN
ejpam-4382	217	16	∈	∈	PROPN
ejpam-4382	217	17	sio(u	sio(u	PROPN
ejpam-4382	217	18	,	,	PUNCT
ejpam-4382	217	19	τ|u	τ|u	NOUN
ejpam-4382	217	20	,	,	PUNCT
ejpam-4382	217	21	i|u	i|u	NOUN
ejpam-4382	217	22	)	)	PUNCT
ejpam-4382	217	23	.	.	PUNCT
ejpam-4382	218	1	theorem	theorem	NOUN
ejpam-4382	218	2	6	6	NUM
ejpam-4382	218	3	.	.	PUNCT
ejpam-4382	219	1	let	let	VERB
ejpam-4382	219	2	a	a	DET
ejpam-4382	219	3	be	be	AUX
ejpam-4382	219	4	an	an	DET
ejpam-4382	219	5	open	open	ADJ
ejpam-4382	219	6	set	set	NOUN
ejpam-4382	219	7	of	of	ADP
ejpam-4382	219	8	an	an	DET
ejpam-4382	219	9	ideal	ideal	ADJ
ejpam-4382	219	10	topological	topological	ADJ
ejpam-4382	219	11	space	space	NOUN
ejpam-4382	219	12	(	(	PUNCT
ejpam-4382	219	13	x	x	X
ejpam-4382	219	14	,	,	PUNCT
ejpam-4382	219	15	τ	τ	PROPN
ejpam-4382	219	16	,	,	PUNCT
ejpam-4382	219	17	i	i	NOUN
ejpam-4382	219	18	)	)	PUNCT
ejpam-4382	219	19	.	.	PUNCT
ejpam-4382	220	1	if	if	SCONJ
ejpam-4382	220	2	(	(	PUNCT
ejpam-4382	220	3	x	x	X
ejpam-4382	220	4	,	,	PUNCT
ejpam-4382	220	5	τ	τ	PROPN
ejpam-4382	220	6	,	,	PUNCT
ejpam-4382	220	7	i	i	PROPN
ejpam-4382	220	8	)	)	PUNCT
ejpam-4382	220	9	is	be	AUX
ejpam-4382	220	10	semi	semi	ADJ
ejpam-4382	220	11	-	-	ADJ
ejpam-4382	220	12	i	i	PRON
ejpam-4382	220	13	-submaximal	-submaximal	ADJ
ejpam-4382	220	14	,	,	PUNCT
ejpam-4382	220	15	then	then	ADV
ejpam-4382	220	16	(	(	PUNCT
ejpam-4382	220	17	a	a	PRON
ejpam-4382	220	18	,	,	PUNCT
ejpam-4382	220	19	τ|a	τ|a	NUM
ejpam-4382	220	20	,	,	PUNCT
ejpam-4382	220	21	i|a	i|a	PROPN
ejpam-4382	220	22	)	)	PUNCT
ejpam-4382	220	23	is	be	AUX
ejpam-4382	220	24	semi	semi	ADJ
ejpam-4382	220	25	-	-	ADJ
ejpam-4382	220	26	i|a	i|a	ADJ
ejpam-4382	220	27	-	-	PUNCT
ejpam-4382	220	28	submaximal	submaximal	ADJ
ejpam-4382	220	29	.	.	PUNCT
ejpam-4382	221	1	proof	proof	NOUN
ejpam-4382	221	2	.	.	PUNCT
ejpam-4382	222	1	suppose	suppose	VERB
ejpam-4382	222	2	that	that	SCONJ
ejpam-4382	222	3	(	(	PUNCT
ejpam-4382	222	4	x	x	X
ejpam-4382	222	5	,	,	PUNCT
ejpam-4382	222	6	τ	τ	PROPN
ejpam-4382	222	7	,	,	PUNCT
ejpam-4382	222	8	i	i	PROPN
ejpam-4382	222	9	)	)	PUNCT
ejpam-4382	222	10	is	be	AUX
ejpam-4382	222	11	semi	semi	ADJ
ejpam-4382	222	12	-	-	ADJ
ejpam-4382	222	13	i	i	PRON
ejpam-4382	222	14	-submaximal	-submaximal	ADJ
ejpam-4382	222	15	.	.	PUNCT
ejpam-4382	223	1	let	let	VERB
ejpam-4382	223	2	d	d	PRON
ejpam-4382	223	3	be	be	AUX
ejpam-4382	223	4	a	a	DET
ejpam-4382	223	5	semi	semi	ADJ
ejpam-4382	223	6	-	-	ADJ
ejpam-4382	223	7	i|a	i|a	ADJ
ejpam-4382	223	8	-	-	ADJ
ejpam-4382	223	9	dense	dense	ADJ
ejpam-4382	223	10	subset	subset	NOUN
ejpam-4382	223	11	of	of	ADP
ejpam-4382	223	12	(	(	PUNCT
ejpam-4382	223	13	a	a	PRON
ejpam-4382	223	14	,	,	PUNCT
ejpam-4382	223	15	τ|a	τ|a	X
ejpam-4382	223	16	,	,	PUNCT
ejpam-4382	223	17	ia	ia	PROPN
ejpam-4382	223	18	)	)	PUNCT
ejpam-4382	223	19	.	.	PUNCT
ejpam-4382	224	1	let	let	VERB
ejpam-4382	224	2	u	u	NOUN
ejpam-4382	224	3	=	=	NOUN
ejpam-4382	224	4	d	d	X
ejpam-4382	224	5	∪	∪	X
ejpam-4382	224	6	(	(	PUNCT
ejpam-4382	224	7	x	x	NOUN
ejpam-4382	224	8	−a	−a	NOUN
ejpam-4382	224	9	)	)	PUNCT
ejpam-4382	224	10	.	.	PUNCT
ejpam-4382	225	1	by	by	ADP
ejpam-4382	225	2	lemma	lemma	PROPN
ejpam-4382	225	3	5	5	NUM
ejpam-4382	225	4	,	,	PUNCT
ejpam-4382	225	5	we	we	PRON
ejpam-4382	225	6	have	have	VERB
ejpam-4382	225	7	scli	scli	NOUN
ejpam-4382	225	8	(	(	PUNCT
ejpam-4382	225	9	u	u	NOUN
ejpam-4382	225	10	)	)	PUNCT
ejpam-4382	225	11	=	=	SYM
ejpam-4382	225	12	scli	scli	NOUN
ejpam-4382	225	13	(	(	PUNCT
ejpam-4382	225	14	d	d	X
ejpam-4382	225	15	∪	∪	X
ejpam-4382	225	16	(	(	PUNCT
ejpam-4382	225	17	x	x	NOUN
ejpam-4382	225	18	−a	−a	NOUN
ejpam-4382	225	19	)	)	PUNCT
ejpam-4382	225	20	)	)	PUNCT
ejpam-4382	225	21	⊇	⊇	PROPN
ejpam-4382	225	22	scli	scli	NOUN
ejpam-4382	225	23	(	(	PUNCT
ejpam-4382	225	24	d	d	NOUN
ejpam-4382	225	25	)	)	PUNCT
ejpam-4382	225	26	∪	∪	ADP
ejpam-4382	225	27	scli	scli	PROPN
ejpam-4382	225	28	(	(	PUNCT
ejpam-4382	225	29	x	x	NOUN
ejpam-4382	225	30	−a	−a	ADJ
ejpam-4382	225	31	)	)	PUNCT
ejpam-4382	225	32	⊇	⊇	NOUN
ejpam-4382	225	33	(	(	PUNCT
ejpam-4382	225	34	scli	scli	PROPN
ejpam-4382	225	35	(	(	PUNCT
ejpam-4382	225	36	d	d	NOUN
ejpam-4382	225	37	)	)	PUNCT
ejpam-4382	225	38	∩a	∩a	NOUN
ejpam-4382	225	39	)	)	PUNCT
ejpam-4382	225	40	∪	∪	ADP
ejpam-4382	225	41	scli	scli	PROPN
ejpam-4382	225	42	(	(	PUNCT
ejpam-4382	225	43	x	x	NOUN
ejpam-4382	225	44	−a	−a	NOUN
ejpam-4382	225	45	)	)	PUNCT
ejpam-4382	225	46	=	=	PUNCT
ejpam-4382	225	47	scli|a	scli|a	NOUN
ejpam-4382	225	48	(	(	PUNCT
ejpam-4382	225	49	d	d	NOUN
ejpam-4382	225	50	)	)	PUNCT
ejpam-4382	225	51	∪	∪	ADP
ejpam-4382	225	52	scli	scli	PROPN
ejpam-4382	225	53	(	(	PUNCT
ejpam-4382	225	54	x	x	NOUN
ejpam-4382	225	55	−a	−a	ADV
ejpam-4382	225	56	)	)	PUNCT
ejpam-4382	225	57	=	=	PUNCT
ejpam-4382	225	58	a	a	DET
ejpam-4382	225	59	∪	∪	ADJ
ejpam-4382	225	60	scli	scli	NOUN
ejpam-4382	225	61	(	(	PUNCT
ejpam-4382	225	62	x	x	NOUN
ejpam-4382	225	63	−a	−a	ADV
ejpam-4382	225	64	)	)	PUNCT
ejpam-4382	225	65	=	=	PUNCT
ejpam-4382	225	66	a	a	DET
ejpam-4382	225	67	∪	∪	X
ejpam-4382	225	68	(	(	PUNCT
ejpam-4382	225	69	x	x	SYM
ejpam-4382	225	70	−	−	PROPN
ejpam-4382	225	71	sinti	sinti	PROPN
ejpam-4382	225	72	(	(	PUNCT
ejpam-4382	225	73	a	a	NOUN
ejpam-4382	225	74	)	)	PUNCT
ejpam-4382	225	75	)	)	PUNCT
ejpam-4382	225	76	⊇	⊇	NOUN
ejpam-4382	225	77	a	a	DET
ejpam-4382	225	78	∪	∪	X
ejpam-4382	225	79	(	(	PUNCT
ejpam-4382	225	80	x	x	NOUN
ejpam-4382	225	81	−a	−a	NOUN
ejpam-4382	225	82	)	)	PUNCT
ejpam-4382	225	83	=	=	PUNCT
ejpam-4382	225	84	x	x	SYM
ejpam-4382	225	85	references	reference	NOUN
ejpam-4382	225	86	946	946	NUM
ejpam-4382	225	87	and	and	CCONJ
ejpam-4382	225	88	hence	hence	ADV
ejpam-4382	225	89	scli	scli	NOUN
ejpam-4382	225	90	(	(	PUNCT
ejpam-4382	225	91	u	u	NOUN
ejpam-4382	225	92	)	)	PUNCT
ejpam-4382	225	93	=	=	PUNCT
ejpam-4382	226	1	x.	x.	NOUN
ejpam-4382	226	2	since	since	SCONJ
ejpam-4382	226	3	(	(	PUNCT
ejpam-4382	226	4	x	x	X
ejpam-4382	226	5	,	,	PUNCT
ejpam-4382	226	6	τ	τ	PROPN
ejpam-4382	226	7	,	,	PUNCT
ejpam-4382	226	8	i	i	PROPN
ejpam-4382	226	9	)	)	PUNCT
ejpam-4382	226	10	is	be	AUX
ejpam-4382	226	11	semi	semi	ADJ
ejpam-4382	226	12	-	-	ADJ
ejpam-4382	226	13	i	i	PRON
ejpam-4382	226	14	-submaximal	-submaximal	ADJ
ejpam-4382	226	15	,	,	PUNCT
ejpam-4382	226	16	u	u	NOUN
ejpam-4382	226	17	is	be	AUX
ejpam-4382	226	18	semi	semi	ADJ
ejpam-4382	226	19	-	-	ADJ
ejpam-4382	226	20	i	i	PRON
ejpam-4382	226	21	-open	-open	ADJ
ejpam-4382	226	22	.	.	PUNCT
ejpam-4382	227	1	by	by	ADP
ejpam-4382	227	2	lemma	lemma	PROPN
ejpam-4382	227	3	6	6	NUM
ejpam-4382	227	4	,	,	PUNCT
ejpam-4382	227	5	d	d	PROPN
ejpam-4382	227	6	=	=	PUNCT
ejpam-4382	227	7	a	a	DET
ejpam-4382	227	8	∩	∩	ADJ
ejpam-4382	227	9	u	u	NOUN
ejpam-4382	227	10	is	be	AUX
ejpam-4382	227	11	semi	semi	ADJ
ejpam-4382	227	12	-	-	ADJ
ejpam-4382	227	13	i|a	i|a	ADJ
ejpam-4382	227	14	-	-	ADJ
ejpam-4382	227	15	open	open	ADJ
ejpam-4382	227	16	in	in	ADP
ejpam-4382	227	17	(	(	PUNCT
ejpam-4382	227	18	a	a	PRON
ejpam-4382	227	19	,	,	PUNCT
ejpam-4382	227	20	τ|a	τ|a	NUM
ejpam-4382	227	21	,	,	PUNCT
ejpam-4382	227	22	i|a	i|a	PROPN
ejpam-4382	227	23	)	)	PUNCT
ejpam-4382	227	24	.	.	PUNCT
ejpam-4382	228	1	this	this	PRON
ejpam-4382	228	2	shows	show	VERB
ejpam-4382	228	3	that	that	SCONJ
ejpam-4382	228	4	(	(	PUNCT
ejpam-4382	228	5	a	a	PRON
ejpam-4382	228	6	,	,	PUNCT
ejpam-4382	228	7	τ|a	τ|a	NUM
ejpam-4382	228	8	,	,	PUNCT
ejpam-4382	228	9	i|a	i|a	PROPN
ejpam-4382	228	10	)	)	PUNCT
ejpam-4382	228	11	is	be	AUX
ejpam-4382	228	12	semi	semi	ADJ
ejpam-4382	228	13	-	-	ADJ
ejpam-4382	228	14	i|a	i|a	ADJ
ejpam-4382	228	15	-	-	PUNCT
ejpam-4382	228	16	submaximal	submaximal	ADJ
ejpam-4382	228	17	.	.	PUNCT
ejpam-4382	229	1	next	next	ADV
ejpam-4382	229	2	,	,	PUNCT
ejpam-4382	229	3	we	we	PRON
ejpam-4382	229	4	shall	shall	AUX
ejpam-4382	229	5	show	show	VERB
ejpam-4382	229	6	that	that	SCONJ
ejpam-4382	229	7	semi	semi	ADJ
ejpam-4382	229	8	-	-	ADJ
ejpam-4382	229	9	i	i	PRON
ejpam-4382	229	10	-submaximal	-submaximal	ADJ
ejpam-4382	229	11	ideal	ideal	ADJ
ejpam-4382	229	12	topological	topological	ADJ
ejpam-4382	229	13	spaces	space	NOUN
ejpam-4382	229	14	are	be	AUX
ejpam-4382	229	15	invariant	invariant	ADJ
ejpam-4382	229	16	under	under	ADP
ejpam-4382	229	17	semi-(i	semi-(i	PROPN
ejpam-4382	229	18	,	,	PUNCT
ejpam-4382	229	19	j	j	NOUN
ejpam-4382	229	20	)	)	PUNCT
ejpam-4382	229	21	-open	-open	NOUN
ejpam-4382	229	22	surjections	surjection	NOUN
ejpam-4382	229	23	.	.	PUNCT
ejpam-4382	230	1	definition	definition	NOUN
ejpam-4382	230	2	6	6	NUM
ejpam-4382	230	3	.	.	PUNCT
ejpam-4382	231	1	a	a	DET
ejpam-4382	231	2	function	function	NOUN
ejpam-4382	231	3	f	f	NOUN
ejpam-4382	231	4	:	:	PUNCT
ejpam-4382	231	5	(	(	PUNCT
ejpam-4382	231	6	x	x	X
ejpam-4382	231	7	,	,	PUNCT
ejpam-4382	231	8	τ	τ	PROPN
ejpam-4382	231	9	,	,	PUNCT
ejpam-4382	231	10	i	i	NOUN
ejpam-4382	231	11	)	)	PUNCT
ejpam-4382	231	12	→	→	PUNCT
ejpam-4382	231	13	(	(	PUNCT
ejpam-4382	231	14	y	y	PROPN
ejpam-4382	231	15	,	,	PUNCT
ejpam-4382	231	16	σ	σ	PROPN
ejpam-4382	231	17	,	,	PUNCT
ejpam-4382	231	18	j	j	PROPN
ejpam-4382	231	19	)	)	PUNCT
ejpam-4382	231	20	is	be	AUX
ejpam-4382	231	21	said	say	VERB
ejpam-4382	231	22	to	to	PART
ejpam-4382	231	23	be	be	AUX
ejpam-4382	231	24	semi-(i	semi-(i	PROPN
ejpam-4382	231	25	,	,	PUNCT
ejpam-4382	231	26	j	j	NOUN
ejpam-4382	231	27	)	)	PUNCT
ejpam-4382	231	28	-open	-open	NOUN
ejpam-4382	231	29	if	if	SCONJ
ejpam-4382	231	30	f(v	f(v	PROPN
ejpam-4382	231	31	)	)	PUNCT
ejpam-4382	231	32	is	be	AUX
ejpam-4382	231	33	semi	semi	ADJ
ejpam-4382	231	34	-	-	ADJ
ejpam-4382	231	35	j	j	ADJ
ejpam-4382	231	36	-open	-open	NOUN
ejpam-4382	231	37	in	in	ADP
ejpam-4382	231	38	y	y	PROPN
ejpam-4382	231	39	for	for	SCONJ
ejpam-4382	231	40	each	each	DET
ejpam-4382	231	41	semi	semi	ADJ
ejpam-4382	231	42	-	-	ADJ
ejpam-4382	231	43	i	i	PRON
ejpam-4382	231	44	-open	-open	NOUN
ejpam-4382	231	45	set	set	VERB
ejpam-4382	231	46	v	v	NOUN
ejpam-4382	231	47	of	of	ADP
ejpam-4382	231	48	x.	x.	NOUN
ejpam-4382	231	49	theorem	theorem	VERB
ejpam-4382	231	50	7	7	NUM
ejpam-4382	231	51	.	.	PUNCT
ejpam-4382	232	1	let	let	VERB
ejpam-4382	232	2	f	f	NOUN
ejpam-4382	232	3	:	:	PUNCT
ejpam-4382	232	4	(	(	PUNCT
ejpam-4382	232	5	x	x	X
ejpam-4382	232	6	,	,	PUNCT
ejpam-4382	232	7	τ	τ	PROPN
ejpam-4382	232	8	,	,	PUNCT
ejpam-4382	232	9	i	i	NOUN
ejpam-4382	232	10	)	)	PUNCT
ejpam-4382	232	11	→	→	PUNCT
ejpam-4382	232	12	(	(	PUNCT
ejpam-4382	232	13	y	y	PROPN
ejpam-4382	232	14	,	,	PUNCT
ejpam-4382	232	15	σ	σ	PROPN
ejpam-4382	232	16	,	,	PUNCT
ejpam-4382	232	17	j	j	PROPN
ejpam-4382	232	18	)	)	PUNCT
ejpam-4382	232	19	be	be	AUX
ejpam-4382	232	20	a	a	DET
ejpam-4382	232	21	semi-(i	semi-(i	PROPN
ejpam-4382	232	22	,	,	PUNCT
ejpam-4382	232	23	j	j	NOUN
ejpam-4382	232	24	)	)	PUNCT
ejpam-4382	232	25	-open	-open	PROPN
ejpam-4382	232	26	surjection	surjection	NOUN
ejpam-4382	232	27	.	.	PUNCT
ejpam-4382	233	1	if	if	SCONJ
ejpam-4382	233	2	(	(	PUNCT
ejpam-4382	233	3	x	x	X
ejpam-4382	233	4	,	,	PUNCT
ejpam-4382	233	5	τ	τ	PROPN
ejpam-4382	233	6	,	,	PUNCT
ejpam-4382	233	7	i	i	PROPN
ejpam-4382	233	8	)	)	PUNCT
ejpam-4382	233	9	is	be	AUX
ejpam-4382	233	10	semi	semi	ADJ
ejpam-4382	233	11	-	-	ADJ
ejpam-4382	233	12	i	i	PRON
ejpam-4382	233	13	-submaximal	-submaximal	ADJ
ejpam-4382	233	14	,	,	PUNCT
ejpam-4382	233	15	then	then	ADV
ejpam-4382	233	16	(	(	PUNCT
ejpam-4382	233	17	y	y	PROPN
ejpam-4382	233	18	,	,	PUNCT
ejpam-4382	233	19	σ	σ	PROPN
ejpam-4382	233	20	,	,	PUNCT
ejpam-4382	233	21	j	j	PROPN
ejpam-4382	233	22	)	)	PUNCT
ejpam-4382	233	23	is	be	AUX
ejpam-4382	233	24	semi	semi	ADJ
ejpam-4382	233	25	-	-	ADJ
ejpam-4382	233	26	j	j	ADJ
ejpam-4382	233	27	-submaximal	-submaximal	PROPN
ejpam-4382	233	28	.	.	PUNCT
ejpam-4382	234	1	proof	proof	NOUN
ejpam-4382	234	2	.	.	PUNCT
ejpam-4382	235	1	suppose	suppose	VERB
ejpam-4382	235	2	that	that	SCONJ
ejpam-4382	235	3	(	(	PUNCT
ejpam-4382	235	4	x	x	X
ejpam-4382	235	5	,	,	PUNCT
ejpam-4382	235	6	τ	τ	PROPN
ejpam-4382	235	7	,	,	PUNCT
ejpam-4382	235	8	i	i	PROPN
ejpam-4382	235	9	)	)	PUNCT
ejpam-4382	235	10	is	be	AUX
ejpam-4382	235	11	semi	semi	ADJ
ejpam-4382	235	12	-	-	ADJ
ejpam-4382	235	13	i	i	PRON
ejpam-4382	235	14	-submaximal	-submaximal	ADJ
ejpam-4382	235	15	.	.	PUNCT
ejpam-4382	236	1	let	let	VERB
ejpam-4382	236	2	a	a	PRON
ejpam-4382	236	3	be	be	AUX
ejpam-4382	236	4	a	a	DET
ejpam-4382	236	5	semi	semi	ADJ
ejpam-4382	236	6	-	-	ADJ
ejpam-4382	236	7	j	j	ADJ
ejpam-4382	236	8	-dense	-dense	NOUN
ejpam-4382	236	9	subset	subset	NOUN
ejpam-4382	236	10	of	of	ADP
ejpam-4382	236	11	y	y	PROPN
ejpam-4382	236	12	.	.	PUNCT
ejpam-4382	237	1	since	since	SCONJ
ejpam-4382	237	2	sinti	sinti	PROPN
ejpam-4382	237	3	(	(	PUNCT
ejpam-4382	237	4	f−1(y	f−1(y	PROPN
ejpam-4382	237	5	−	−	PROPN
ejpam-4382	237	6	a	a	NOUN
ejpam-4382	237	7	)	)	PUNCT
ejpam-4382	237	8	)	)	PUNCT
ejpam-4382	237	9	⊆	⊆	NUM
ejpam-4382	237	10	f−1(y	f−1(y	NOUN
ejpam-4382	237	11	−	−	PROPN
ejpam-4382	237	12	a	a	X
ejpam-4382	237	13	)	)	PUNCT
ejpam-4382	237	14	,	,	PUNCT
ejpam-4382	237	15	we	we	PRON
ejpam-4382	237	16	have	have	VERB
ejpam-4382	237	17	f(sinti	f(sinti	NOUN
ejpam-4382	237	18	(	(	PUNCT
ejpam-4382	237	19	f−1(y	f−1(y	PROPN
ejpam-4382	237	20	−	−	PROPN
ejpam-4382	237	21	a	a	NOUN
ejpam-4382	237	22	)	)	PUNCT
ejpam-4382	237	23	)	)	PUNCT
ejpam-4382	237	24	)	)	PUNCT
ejpam-4382	238	1	⊆	⊆	NUM
ejpam-4382	238	2	f(f−1(y	f(f−1(y	PROPN
ejpam-4382	238	3	−a	−a	NOUN
ejpam-4382	238	4	)	)	PUNCT
ejpam-4382	238	5	)	)	PUNCT
ejpam-4382	239	1	⊆	⊆	NUM
ejpam-4382	239	2	y	y	PROPN
ejpam-4382	239	3	−a	−a	NOUN
ejpam-4382	239	4	and	and	CCONJ
ejpam-4382	239	5	hence	hence	ADV
ejpam-4382	239	6	sintj	sintj	NOUN
ejpam-4382	239	7	(	(	PUNCT
ejpam-4382	239	8	f(sinti	f(sinti	NOUN
ejpam-4382	239	9	(	(	PUNCT
ejpam-4382	239	10	f−1(y	f−1(y	PROPN
ejpam-4382	239	11	−a	−a	NOUN
ejpam-4382	239	12	)	)	PUNCT
ejpam-4382	239	13	)	)	PUNCT
ejpam-4382	239	14	)	)	PUNCT
ejpam-4382	239	15	)	)	PUNCT
ejpam-4382	240	1	⊆	⊆	NUM
ejpam-4382	240	2	sintj	sintj	NOUN
ejpam-4382	240	3	(	(	PUNCT
ejpam-4382	240	4	y	y	PROPN
ejpam-4382	240	5	−a	−a	PROPN
ejpam-4382	240	6	)	)	PUNCT
ejpam-4382	240	7	.	.	PUNCT
ejpam-4382	241	1	since	since	SCONJ
ejpam-4382	241	2	f	f	PROPN
ejpam-4382	241	3	is	be	AUX
ejpam-4382	241	4	semi-(i	semi-(i	PROPN
ejpam-4382	241	5	,	,	PUNCT
ejpam-4382	241	6	j	j	NOUN
ejpam-4382	241	7	)	)	PUNCT
ejpam-4382	241	8	-open	-open	PROPN
ejpam-4382	241	9	,	,	PUNCT
ejpam-4382	241	10	f(sinti	f(sinti	NOUN
ejpam-4382	241	11	(	(	PUNCT
ejpam-4382	241	12	f−1(y	f−1(y	PROPN
ejpam-4382	241	13	−a	−a	NOUN
ejpam-4382	241	14	)	)	PUNCT
ejpam-4382	241	15	)	)	PUNCT
ejpam-4382	241	16	)	)	PUNCT
ejpam-4382	242	1	⊆	⊆	NUM
ejpam-4382	242	2	sintj	sintj	NOUN
ejpam-4382	242	3	(	(	PUNCT
ejpam-4382	242	4	y	y	PROPN
ejpam-4382	242	5	−a	−a	PROPN
ejpam-4382	242	6	)	)	PUNCT
ejpam-4382	242	7	.	.	PUNCT
ejpam-4382	243	1	thus	thus	ADV
ejpam-4382	243	2	,	,	PUNCT
ejpam-4382	243	3	sinti	sinti	PROPN
ejpam-4382	243	4	(	(	PUNCT
ejpam-4382	243	5	f−1(y	f−1(y	PROPN
ejpam-4382	243	6	−a	−a	NOUN
ejpam-4382	243	7	)	)	PUNCT
ejpam-4382	243	8	)	)	PUNCT
ejpam-4382	243	9	⊆	⊆	X
ejpam-4382	243	10	f−1(sintj	f−1(sintj	PROPN
ejpam-4382	243	11	(	(	PUNCT
ejpam-4382	243	12	y	y	NOUN
ejpam-4382	243	13	−a	−a	PROPN
ejpam-4382	243	14	)	)	PUNCT
ejpam-4382	243	15	)	)	PUNCT
ejpam-4382	243	16	.	.	PUNCT
ejpam-4382	244	1	it	it	PRON
ejpam-4382	244	2	follows	follow	VERB
ejpam-4382	244	3	that	that	SCONJ
ejpam-4382	244	4	x	x	PUNCT
ejpam-4382	244	5	−	−	PROPN
ejpam-4382	244	6	scli	scli	NOUN
ejpam-4382	244	7	(	(	PUNCT
ejpam-4382	244	8	f−1(a	f−1(a	NOUN
ejpam-4382	244	9	)	)	PUNCT
ejpam-4382	244	10	)	)	PUNCT
ejpam-4382	245	1	⊆	⊆	NUM
ejpam-4382	245	2	x	x	SYM
ejpam-4382	245	3	−	−	NOUN
ejpam-4382	245	4	f−1(sclj	f−1(sclj	X
ejpam-4382	245	5	(	(	PUNCT
ejpam-4382	245	6	a	a	NOUN
ejpam-4382	245	7	)	)	PUNCT
ejpam-4382	245	8	)	)	PUNCT
ejpam-4382	245	9	and	and	CCONJ
ejpam-4382	245	10	hence	hence	ADV
ejpam-4382	245	11	x	x	X
ejpam-4382	245	12	=	=	PUNCT
ejpam-4382	245	13	f−1(sclj	f−1(sclj	X
ejpam-4382	245	14	(	(	PUNCT
ejpam-4382	245	15	a	a	NOUN
ejpam-4382	245	16	)	)	PUNCT
ejpam-4382	245	17	)	)	PUNCT
ejpam-4382	245	18	⊆	⊆	NUM
ejpam-4382	245	19	scli	scli	NOUN
ejpam-4382	245	20	(	(	PUNCT
ejpam-4382	245	21	f−1(a	f−1(a	NOUN
ejpam-4382	245	22	)	)	PUNCT
ejpam-4382	245	23	)	)	PUNCT
ejpam-4382	245	24	.	.	PUNCT
ejpam-4382	246	1	this	this	PRON
ejpam-4382	246	2	implies	imply	VERB
ejpam-4382	246	3	that	that	DET
ejpam-4382	246	4	scli	scli	PROPN
ejpam-4382	246	5	(	(	PUNCT
ejpam-4382	246	6	f−1(a	f−1(a	NOUN
ejpam-4382	246	7	)	)	PUNCT
ejpam-4382	246	8	)	)	PUNCT
ejpam-4382	247	1	=	=	PUNCT
ejpam-4382	247	2	x.	x.	NOUN
ejpam-4382	247	3	therefore	therefore	ADV
ejpam-4382	247	4	,	,	PUNCT
ejpam-4382	247	5	f−1(a	f−1(a	PROPN
ejpam-4382	247	6	)	)	PUNCT
ejpam-4382	247	7	is	be	AUX
ejpam-4382	247	8	semi	semi	ADJ
ejpam-4382	247	9	-	-	ADJ
ejpam-4382	247	10	i	i	PRON
ejpam-4382	247	11	-dense	-dense	ADJ
ejpam-4382	247	12	and	and	CCONJ
ejpam-4382	247	13	so	so	ADV
ejpam-4382	247	14	f−1(a	f−1(a	PROPN
ejpam-4382	247	15	)	)	PUNCT
ejpam-4382	248	1	is	be	AUX
ejpam-4382	248	2	semi	semi	ADJ
ejpam-4382	248	3	-	-	ADJ
ejpam-4382	248	4	i	i	PRON
ejpam-4382	248	5	-open	-open	NOUN
ejpam-4382	248	6	.	.	PUNCT
ejpam-4382	249	1	since	since	SCONJ
ejpam-4382	249	2	f	f	PROPN
ejpam-4382	249	3	is	be	AUX
ejpam-4382	249	4	a	a	DET
ejpam-4382	249	5	semi-(i	semi-(i	PROPN
ejpam-4382	249	6	,	,	PUNCT
ejpam-4382	249	7	j	j	NOUN
ejpam-4382	249	8	)	)	PUNCT
ejpam-4382	249	9	-open	-open	PROPN
ejpam-4382	249	10	surjection	surjection	NOUN
ejpam-4382	249	11	,	,	PUNCT
ejpam-4382	249	12	a	a	DET
ejpam-4382	249	13	=	=	SYM
ejpam-4382	249	14	f(f−1(a	f(f−1(a	PROPN
ejpam-4382	249	15	)	)	PUNCT
ejpam-4382	249	16	)	)	PUNCT
ejpam-4382	249	17	is	be	AUX
ejpam-4382	249	18	semi	semi	ADJ
ejpam-4382	249	19	-	-	ADJ
ejpam-4382	249	20	j	j	ADJ
ejpam-4382	249	21	-open	-open	NOUN
ejpam-4382	249	22	.	.	PUNCT
ejpam-4382	250	1	thus	thus	ADV
ejpam-4382	250	2	,	,	PUNCT
ejpam-4382	250	3	(	(	PUNCT
ejpam-4382	250	4	y	y	PROPN
ejpam-4382	250	5	,	,	PUNCT
ejpam-4382	250	6	σ	σ	PROPN
ejpam-4382	250	7	,	,	PUNCT
ejpam-4382	250	8	j	j	PROPN
ejpam-4382	250	9	)	)	PUNCT
ejpam-4382	250	10	is	be	AUX
ejpam-4382	250	11	semi	semi	ADJ
ejpam-4382	250	12	-	-	ADJ
ejpam-4382	250	13	j	j	ADJ
ejpam-4382	250	14	-submaximal	-submaximal	PROPN
ejpam-4382	250	15	.	.	PUNCT
ejpam-4382	251	1	acknowledgements	acknowledgement	NOUN
ejpam-4382	251	2	this	this	DET
ejpam-4382	251	3	research	research	NOUN
ejpam-4382	251	4	project	project	NOUN
ejpam-4382	251	5	was	be	AUX
ejpam-4382	251	6	financially	financially	ADV
ejpam-4382	251	7	supported	support	VERB
ejpam-4382	251	8	by	by	ADP
ejpam-4382	251	9	mahasarakham	mahasarakham	PROPN
ejpam-4382	251	10	university	university	PROPN
ejpam-4382	251	11	.	.	PUNCT
ejpam-4382	252	1	references	reference	NOUN
ejpam-4382	252	2	[	[	X
ejpam-4382	252	3	1	1	NUM
ejpam-4382	252	4	]	]	PUNCT
ejpam-4382	252	5	a.	a.	NOUN
ejpam-4382	252	6	açikgöz	açikgöz	PROPN
ejpam-4382	252	7	,	,	PUNCT
ejpam-4382	252	8	ş.	ş.	PROPN
ejpam-4382	252	9	yüksel	yüksel	PROPN
ejpam-4382	252	10	,	,	PUNCT
ejpam-4382	252	11	and	and	CCONJ
ejpam-4382	252	12	t.	t.	PROPN
ejpam-4382	252	13	noiri	noiri	PROPN
ejpam-4382	252	14	.	.	PUNCT
ejpam-4382	253	1	α	α	X
ejpam-4382	253	2	-	-	PUNCT
ejpam-4382	253	3	i	i	NOUN
ejpam-4382	253	4	-preirresolute	-preirresolute	NOUN
ejpam-4382	253	5	functions	function	NOUN
ejpam-4382	253	6	and	and	CCONJ
ejpam-4382	253	7	β	β	X
ejpam-4382	253	8	-	-	ADJ
ejpam-4382	253	9	i	i	PRON
ejpam-4382	253	10	preirresolute	preirresolute	PROPN
ejpam-4382	253	11	functions	function	NOUN
ejpam-4382	253	12	.	.	PUNCT
ejpam-4382	254	1	bulletin	bulletin	NOUN
ejpam-4382	254	2	of	of	ADP
ejpam-4382	254	3	the	the	DET
ejpam-4382	254	4	malaysian	malaysian	PROPN
ejpam-4382	254	5	mathematical	mathematical	PROPN
ejpam-4382	254	6	science	science	NOUN
ejpam-4382	254	7	society	society	NOUN
ejpam-4382	254	8	(	(	PUNCT
ejpam-4382	254	9	2	2	NUM
ejpam-4382	254	10	)	)	PUNCT
ejpam-4382	254	11	,	,	PUNCT
ejpam-4382	254	12	28:1–8	28:1–8	NUM
ejpam-4382	254	13	,	,	PUNCT
ejpam-4382	254	14	2005	2005	NUM
ejpam-4382	254	15	.	.	PUNCT
ejpam-4382	255	1	[	[	X
ejpam-4382	255	2	2	2	NUM
ejpam-4382	255	3	]	]	PUNCT
ejpam-4382	255	4	a.	a.	NOUN
ejpam-4382	255	5	v.	v.	ADP
ejpam-4382	255	6	arhangel’skĭi	arhangel’skĭi	PROPN
ejpam-4382	255	7	and	and	CCONJ
ejpam-4382	255	8	p.	p.	PROPN
ejpam-4382	255	9	j.	j.	PROPN
ejpam-4382	255	10	collins	collins	PROPN
ejpam-4382	255	11	.	.	PUNCT
ejpam-4382	256	1	on	on	ADP
ejpam-4382	256	2	submaximal	submaximal	ADJ
ejpam-4382	256	3	spaces	space	NOUN
ejpam-4382	256	4	.	.	PUNCT
ejpam-4382	257	1	topology	topology	NOUN
ejpam-4382	257	2	and	and	CCONJ
ejpam-4382	257	3	its	its	PRON
ejpam-4382	257	4	applications	application	NOUN
ejpam-4382	257	5	,	,	PUNCT
ejpam-4382	257	6	64:219–241	64:219–241	NUM
ejpam-4382	257	7	,	,	PUNCT
ejpam-4382	257	8	1995	1995	NUM
ejpam-4382	257	9	.	.	PUNCT
ejpam-4382	258	1	[	[	X
ejpam-4382	258	2	3	3	X
ejpam-4382	258	3	]	]	PUNCT
ejpam-4382	258	4	j.	j.	PROPN
ejpam-4382	258	5	dontchev	dontchev	PROPN
ejpam-4382	258	6	,	,	PUNCT
ejpam-4382	258	7	m.	m.	NOUN
ejpam-4382	258	8	ganster	ganster	NOUN
ejpam-4382	258	9	,	,	PUNCT
ejpam-4382	258	10	and	and	CCONJ
ejpam-4382	258	11	t.	t.	PROPN
ejpam-4382	258	12	noiri	noiri	PROPN
ejpam-4382	258	13	.	.	PUNCT
ejpam-4382	259	1	unified	unified	ADJ
ejpam-4382	259	2	operation	operation	NOUN
ejpam-4382	259	3	approach	approach	NOUN
ejpam-4382	259	4	of	of	ADP
ejpam-4382	259	5	generalized	generalized	ADJ
ejpam-4382	259	6	closed	close	VERB
ejpam-4382	259	7	sets	set	NOUN
ejpam-4382	259	8	via	via	ADP
ejpam-4382	259	9	topological	topological	ADJ
ejpam-4382	259	10	ideals	ideal	NOUN
ejpam-4382	259	11	.	.	PUNCT
ejpam-4382	260	1	mathematica	mathematica	PROPN
ejpam-4382	260	2	japonica	japonica	PROPN
ejpam-4382	260	3	,	,	PUNCT
ejpam-4382	260	4	49:395–401	49:395–401	PROPN
ejpam-4382	260	5	,	,	PUNCT
ejpam-4382	260	6	1999	1999	NUM
ejpam-4382	260	7	.	.	PUNCT
ejpam-4382	261	1	[	[	X
ejpam-4382	261	2	4	4	X
ejpam-4382	261	3	]	]	PUNCT
ejpam-4382	261	4	e.	e.	PROPN
ejpam-4382	261	5	ekici	ekici	PROPN
ejpam-4382	261	6	and	and	CCONJ
ejpam-4382	261	7	t.	t.	PROPN
ejpam-4382	261	8	noiri	noiri	PROPN
ejpam-4382	261	9	.	.	PUNCT
ejpam-4382	262	1	properties	property	NOUN
ejpam-4382	262	2	of	of	ADP
ejpam-4382	262	3	i	i	PRON
ejpam-4382	262	4	-submaximal	-submaximal	ADJ
ejpam-4382	262	5	ideal	ideal	ADJ
ejpam-4382	262	6	topological	topological	ADJ
ejpam-4382	262	7	spaces	space	NOUN
ejpam-4382	262	8	.	.	PUNCT
ejpam-4382	263	1	filomat	filomat	PROPN
ejpam-4382	263	2	,	,	PUNCT
ejpam-4382	263	3	24:87–94	24:87–94	PROPN
ejpam-4382	263	4	,	,	PUNCT
ejpam-4382	263	5	2010	2010	NUM
ejpam-4382	263	6	.	.	PUNCT
ejpam-4382	264	1	[	[	X
ejpam-4382	264	2	5	5	X
ejpam-4382	264	3	]	]	PUNCT
ejpam-4382	264	4	e.	e.	PROPN
ejpam-4382	264	5	ekici	ekici	PROPN
ejpam-4382	264	6	and	and	CCONJ
ejpam-4382	264	7	t.	t.	PROPN
ejpam-4382	264	8	noiri	noiri	PROPN
ejpam-4382	264	9	.	.	PUNCT
ejpam-4382	265	1	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-4382	265	2	ideal	ideal	ADJ
ejpam-4382	265	3	topological	topological	ADJ
ejpam-4382	265	4	spaces	space	NOUN
ejpam-4382	265	5	.	.	PUNCT
ejpam-4382	266	1	analele	analele	ADP
ejpam-4382	266	2	ştiinţifice	ştiinţifice	NOUN
ejpam-4382	266	3	ale	ale	NOUN
ejpam-4382	266	4	universităţii	universităţii	X
ejpam-4382	266	5	”	"	PUNCT
ejpam-4382	266	6	alexandru	alexandru	PROPN
ejpam-4382	266	7	loan	loan	PROPN
ejpam-4382	266	8	cuza	cuza	PROPN
ejpam-4382	266	9	”	"	PUNCT
ejpam-4382	266	10	din	din	NOUN
ejpam-4382	266	11	laşi	laşi	PRON
ejpam-4382	266	12	(	(	PUNCT
ejpam-4382	266	13	serie	serie	PROPN
ejpam-4382	266	14	nouă	nouă	PROPN
ejpam-4382	266	15	)	)	PUNCT
ejpam-4382	266	16	.	.	PUNCT
ejpam-4382	267	1	matematică	matematică	NOUN
ejpam-4382	267	2	,	,	PUNCT
ejpam-4382	267	3	58:120	58:120	NUM
ejpam-4382	267	4	–	–	PUNCT
ejpam-4382	267	5	129	129	NUM
ejpam-4382	267	6	,	,	PUNCT
ejpam-4382	267	7	2012	2012	NUM
ejpam-4382	267	8	.	.	PUNCT
ejpam-4382	268	1	references	reference	NOUN
ejpam-4382	268	2	947	947	NUM
ejpam-4382	269	1	[	[	X
ejpam-4382	269	2	6	6	NUM
ejpam-4382	269	3	]	]	PUNCT
ejpam-4382	269	4	g.	g.	PROPN
ejpam-4382	269	5	freud	freud	PROPN
ejpam-4382	269	6	.	.	PUNCT
ejpam-4382	270	1	ein	ein	PROPN
ejpam-4382	270	2	beitrag	beitrag	PROPN
ejpam-4382	270	3	zu	zu	PROPN
ejpam-4382	270	4	dem	dem	PROPN
ejpam-4382	270	5	satze	satze	PROPN
ejpam-4382	270	6	von	von	PROPN
ejpam-4382	270	7	cantor	cantor	PROPN
ejpam-4382	270	8	und	und	PROPN
ejpam-4382	270	9	bendixson	bendixson	PROPN
ejpam-4382	270	10	.	.	PUNCT
ejpam-4382	271	1	acta	acta	PROPN
ejpam-4382	271	2	mathematica	mathematica	PROPN
ejpam-4382	271	3	academiae	academiae	PROPN
ejpam-4382	271	4	scientiarum	scientiarum	PROPN
ejpam-4382	271	5	hungaricae	hungaricae	PROPN
ejpam-4382	271	6	,	,	PUNCT
ejpam-4382	271	7	9:333–336	9:333–336	NOUN
ejpam-4382	271	8	,	,	PUNCT
ejpam-4382	271	9	1958	1958	NUM
ejpam-4382	271	10	.	.	PUNCT
ejpam-4382	272	1	[	[	X
ejpam-4382	272	2	7	7	X
ejpam-4382	272	3	]	]	PUNCT
ejpam-4382	272	4	j.	j.	PROPN
ejpam-4382	272	5	a.	a.	PROPN
ejpam-4382	272	6	guthrie	guthrie	PROPN
ejpam-4382	272	7	,	,	PUNCT
ejpam-4382	272	8	h.	h.	PROPN
ejpam-4382	272	9	e.	e.	PROPN
ejpam-4382	272	10	stone	stone	PROPN
ejpam-4382	272	11	,	,	PUNCT
ejpam-4382	272	12	and	and	CCONJ
ejpam-4382	272	13	m.	m.	PROPN
ejpam-4382	272	14	l.	l.	PROPN
ejpam-4382	272	15	wage	wage	PROPN
ejpam-4382	272	16	.	.	PUNCT
ejpam-4382	273	1	maximal	maximal	ADJ
ejpam-4382	273	2	connected	connected	ADJ
ejpam-4382	273	3	hausdorff	hausdorff	NOUN
ejpam-4382	273	4	topologies	topology	NOUN
ejpam-4382	273	5	.	.	PUNCT
ejpam-4382	274	1	topology	topology	NOUN
ejpam-4382	274	2	proceedings	proceeding	NOUN
ejpam-4382	274	3	,	,	PUNCT
ejpam-4382	274	4	2:349–353	2:349–353	NUM
ejpam-4382	274	5	,	,	PUNCT
ejpam-4382	274	6	1977	1977	NUM
ejpam-4382	274	7	.	.	PUNCT
ejpam-4382	275	1	[	[	X
ejpam-4382	275	2	8	8	X
ejpam-4382	275	3	]	]	X
ejpam-4382	275	4	e.	e.	PROPN
ejpam-4382	275	5	hatir	hatir	PROPN
ejpam-4382	275	6	,	,	PUNCT
ejpam-4382	275	7	a.	a.	PROPN
ejpam-4382	275	8	keskin	keskin	PROPN
ejpam-4382	275	9	,	,	PUNCT
ejpam-4382	275	10	and	and	CCONJ
ejpam-4382	275	11	t.	t.	PROPN
ejpam-4382	275	12	noiri	noiri	PROPN
ejpam-4382	275	13	.	.	PUNCT
ejpam-4382	276	1	a	a	DET
ejpam-4382	276	2	note	note	NOUN
ejpam-4382	276	3	on	on	ADP
ejpam-4382	276	4	strong	strong	ADJ
ejpam-4382	276	5	β	β	NOUN
ejpam-4382	276	6	-	-	PUNCT
ejpam-4382	276	7	i	i	PRON
ejpam-4382	276	8	-sets	-set	NOUN
ejpam-4382	276	9	and	and	CCONJ
ejpam-4382	276	10	strongly	strongly	ADV
ejpam-4382	276	11	β	β	X
ejpam-4382	276	12	-	-	ADJ
ejpam-4382	276	13	i	i	VERB
ejpam-4382	276	14	continuous	continuous	ADJ
ejpam-4382	276	15	functions	function	NOUN
ejpam-4382	276	16	.	.	PUNCT
ejpam-4382	277	1	acta	acta	PROPN
ejpam-4382	277	2	mathematica	mathematica	PROPN
ejpam-4382	277	3	hungarica	hungarica	PROPN
ejpam-4382	277	4	,	,	PUNCT
ejpam-4382	277	5	108:87–94	108:87–94	NUM
ejpam-4382	277	6	,	,	PUNCT
ejpam-4382	277	7	2005	2005	NUM
ejpam-4382	277	8	.	.	PUNCT
ejpam-4382	278	1	[	[	X
ejpam-4382	278	2	9	9	X
ejpam-4382	278	3	]	]	X
ejpam-4382	278	4	e.	e.	PROPN
ejpam-4382	278	5	hatir	hatir	PROPN
ejpam-4382	278	6	and	and	CCONJ
ejpam-4382	278	7	t.	t.	PROPN
ejpam-4382	278	8	noiri	noiri	PROPN
ejpam-4382	278	9	.	.	PUNCT
ejpam-4382	279	1	on	on	ADP
ejpam-4382	279	2	decompositions	decomposition	NOUN
ejpam-4382	279	3	of	of	ADP
ejpam-4382	279	4	continuity	continuity	NOUN
ejpam-4382	279	5	via	via	ADP
ejpam-4382	279	6	idealization	idealization	NOUN
ejpam-4382	279	7	.	.	PUNCT
ejpam-4382	280	1	acta	acta	PROPN
ejpam-4382	280	2	mathematica	mathematica	PROPN
ejpam-4382	280	3	hungarica	hungarica	PROPN
ejpam-4382	280	4	,	,	PUNCT
ejpam-4382	280	5	96:341–349	96:341–349	PROPN
ejpam-4382	280	6	,	,	PUNCT
ejpam-4382	280	7	2002	2002	NUM
ejpam-4382	280	8	.	.	PUNCT
ejpam-4382	281	1	[	[	X
ejpam-4382	281	2	10	10	NUM
ejpam-4382	281	3	]	]	X
ejpam-4382	281	4	e.	e.	PROPN
ejpam-4382	281	5	hatir	hatir	PROPN
ejpam-4382	281	6	and	and	CCONJ
ejpam-4382	281	7	t.	t.	PROPN
ejpam-4382	281	8	noiri	noiri	PROPN
ejpam-4382	281	9	.	.	PUNCT
ejpam-4382	282	1	on	on	ADP
ejpam-4382	282	2	semi	semi	ADJ
ejpam-4382	282	3	-	-	ADJ
ejpam-4382	282	4	i	i	PRON
ejpam-4382	282	5	-open	-open	NOUN
ejpam-4382	282	6	sets	set	NOUN
ejpam-4382	282	7	and	and	CCONJ
ejpam-4382	282	8	semi	semi	ADJ
ejpam-4382	282	9	-	-	ADJ
ejpam-4382	282	10	i	i	ADV
ejpam-4382	282	11	-continuous	-continuous	ADJ
ejpam-4382	282	12	functions	function	NOUN
ejpam-4382	282	13	.	.	PUNCT
ejpam-4382	283	1	acta	acta	PROPN
ejpam-4382	283	2	mathematica	mathematica	PROPN
ejpam-4382	283	3	hungarica	hungarica	PROPN
ejpam-4382	283	4	,	,	PUNCT
ejpam-4382	283	5	107:345–353	107:345–353	NUM
ejpam-4382	283	6	,	,	PUNCT
ejpam-4382	283	7	2005	2005	NUM
ejpam-4382	283	8	.	.	PUNCT
ejpam-4382	284	1	[	[	X
ejpam-4382	284	2	11	11	NUM
ejpam-4382	284	3	]	]	X
ejpam-4382	284	4	g.	g.	PROPN
ejpam-4382	284	5	t.	t.	PROPN
ejpam-4382	284	6	hermann	hermann	PROPN
ejpam-4382	284	7	.	.	PROPN
ejpam-4382	285	1	on	on	ADP
ejpam-4382	285	2	topology	topology	NOUN
ejpam-4382	285	3	as	as	ADP
ejpam-4382	285	4	applied	apply	VERB
ejpam-4382	285	5	image	image	NOUN
ejpam-4382	285	6	analysis	analysis	NOUN
ejpam-4382	285	7	.	.	PUNCT
ejpam-4382	286	1	computer	computer	NOUN
ejpam-4382	286	2	vision	vision	NOUN
ejpam-4382	286	3	,	,	PUNCT
ejpam-4382	286	4	graphics	graphic	NOUN
ejpam-4382	286	5	image	image	NOUN
ejpam-4382	286	6	processing	processing	NOUN
ejpam-4382	286	7	,	,	PUNCT
ejpam-4382	286	8	52:409–415	52:409–415	NUM
ejpam-4382	286	9	,	,	PUNCT
ejpam-4382	286	10	1990	1990	NUM
ejpam-4382	286	11	.	.	PUNCT
ejpam-4382	287	1	[	[	X
ejpam-4382	287	2	12	12	NUM
ejpam-4382	287	3	]	]	PUNCT
ejpam-4382	287	4	e.	e.	PROPN
ejpam-4382	287	5	hewitt	hewitt	PROPN
ejpam-4382	287	6	.	.	PUNCT
ejpam-4382	288	1	a	a	DET
ejpam-4382	288	2	problem	problem	NOUN
ejpam-4382	288	3	of	of	ADP
ejpam-4382	288	4	set	set	NOUN
ejpam-4382	288	5	-	-	PUNCT
ejpam-4382	288	6	theoretic	theoretic	NOUN
ejpam-4382	288	7	topology	topology	NOUN
ejpam-4382	288	8	.	.	PUNCT
ejpam-4382	289	1	duke	duke	PROPN
ejpam-4382	289	2	mathematical	mathematical	PROPN
ejpam-4382	289	3	journal	journal	PROPN
ejpam-4382	289	4	,	,	PUNCT
ejpam-4382	289	5	10:309	10:309	NUM
ejpam-4382	289	6	–	–	PUNCT
ejpam-4382	289	7	333	333	NUM
ejpam-4382	289	8	,	,	PUNCT
ejpam-4382	289	9	1943	1943	NUM
ejpam-4382	289	10	.	.	PUNCT
ejpam-4382	290	1	[	[	X
ejpam-4382	290	2	13	13	NUM
ejpam-4382	290	3	]	]	X
ejpam-4382	290	4	d.	d.	PROPN
ejpam-4382	290	5	janković	janković	PROPN
ejpam-4382	290	6	and	and	CCONJ
ejpam-4382	290	7	t.	t.	PROPN
ejpam-4382	290	8	r.	r.	PROPN
ejpam-4382	290	9	hamlett	hamlett	PROPN
ejpam-4382	290	10	.	.	PUNCT
ejpam-4382	291	1	new	new	ADJ
ejpam-4382	291	2	topologies	topology	NOUN
ejpam-4382	291	3	from	from	ADP
ejpam-4382	291	4	old	old	ADJ
ejpam-4382	291	5	via	via	ADP
ejpam-4382	291	6	ideals	ideal	NOUN
ejpam-4382	291	7	.	.	PUNCT
ejpam-4382	292	1	the	the	DET
ejpam-4382	292	2	american	american	PROPN
ejpam-4382	292	3	mathematical	mathematical	PROPN
ejpam-4382	292	4	monthly	monthly	ADV
ejpam-4382	292	5	,	,	PUNCT
ejpam-4382	292	6	97:295–310	97:295–310	PROPN
ejpam-4382	292	7	,	,	PUNCT
ejpam-4382	292	8	1990	1990	NUM
ejpam-4382	292	9	.	.	PUNCT
ejpam-4382	293	1	[	[	X
ejpam-4382	293	2	14	14	NUM
ejpam-4382	293	3	]	]	X
ejpam-4382	293	4	e.	e.	PROPN
ejpam-4382	293	5	d.	d.	PROPN
ejpam-4382	293	6	khalimsky	khalimsky	PROPN
ejpam-4382	293	7	,	,	PUNCT
ejpam-4382	293	8	r.	r.	PROPN
ejpam-4382	293	9	kopperman	kopperman	PROPN
ejpam-4382	293	10	,	,	PUNCT
ejpam-4382	293	11	and	and	CCONJ
ejpam-4382	294	1	p.	p.	PROPN
ejpam-4382	294	2	r.	r.	PROPN
ejpam-4382	294	3	meyer	meyer	PROPN
ejpam-4382	294	4	.	.	PUNCT
ejpam-4382	294	5	computer	computer	NOUN
ejpam-4382	294	6	graphics	graphic	NOUN
ejpam-4382	294	7	and	and	CCONJ
ejpam-4382	294	8	connected	connected	ADJ
ejpam-4382	294	9	topologies	topology	NOUN
ejpam-4382	294	10	an	an	DET
ejpam-4382	294	11	finite	finite	NOUN
ejpam-4382	294	12	ordered	order	VERB
ejpam-4382	294	13	sets	set	NOUN
ejpam-4382	294	14	.	.	PUNCT
ejpam-4382	295	1	topology	topology	NOUN
ejpam-4382	295	2	and	and	CCONJ
ejpam-4382	295	3	its	its	PRON
ejpam-4382	295	4	applications	application	NOUN
ejpam-4382	295	5	,	,	PUNCT
ejpam-4382	295	6	36:1–17	36:1–17	NUM
ejpam-4382	295	7	,	,	PUNCT
ejpam-4382	295	8	1990	1990	NUM
ejpam-4382	295	9	.	.	PUNCT
ejpam-4382	296	1	[	[	X
ejpam-4382	296	2	15	15	NUM
ejpam-4382	296	3	]	]	PUNCT
ejpam-4382	296	4	t.	t.	PROPN
ejpam-4382	296	5	y.	y.	PROPN
ejpam-4382	296	6	kong	kong	PROPN
ejpam-4382	296	7	,	,	PUNCT
ejpam-4382	296	8	r.	r.	PROPN
ejpam-4382	296	9	kopperman	kopperman	PROPN
ejpam-4382	296	10	,	,	PUNCT
ejpam-4382	296	11	and	and	CCONJ
ejpam-4382	296	12	p.	p.	PROPN
ejpam-4382	296	13	r.	r.	PROPN
ejpam-4382	296	14	meyer	meyer	PROPN
ejpam-4382	296	15	.	.	PUNCT
ejpam-4382	297	1	a	a	DET
ejpam-4382	297	2	topological	topological	ADJ
ejpam-4382	297	3	approach	approach	NOUN
ejpam-4382	297	4	to	to	ADP
ejpam-4382	297	5	digital	digital	ADJ
ejpam-4382	297	6	topology	topology	NOUN
ejpam-4382	297	7	.	.	PUNCT
ejpam-4382	298	1	the	the	DET
ejpam-4382	298	2	american	american	PROPN
ejpam-4382	298	3	mathematical	mathematical	PROPN
ejpam-4382	298	4	monthly	monthly	ADV
ejpam-4382	298	5	,	,	PUNCT
ejpam-4382	298	6	98:901–917	98:901–917	NUM
ejpam-4382	298	7	,	,	PUNCT
ejpam-4382	298	8	1991	1991	NUM
ejpam-4382	298	9	.	.	PUNCT
ejpam-4382	299	1	[	[	X
ejpam-4382	299	2	16	16	NUM
ejpam-4382	299	3	]	]	PUNCT
ejpam-4382	299	4	k.	k.	PROPN
ejpam-4382	299	5	kuratowski	kuratowski	PROPN
ejpam-4382	299	6	.	.	PUNCT
ejpam-4382	300	1	topology	topology	PROPN
ejpam-4382	300	2	,	,	PUNCT
ejpam-4382	300	3	vol	vol	NOUN
ejpam-4382	300	4	.	.	PUNCT
ejpam-4382	300	5	i.	i.	PROPN
ejpam-4382	300	6	academic	academic	PROPN
ejpam-4382	300	7	press	press	PROPN
ejpam-4382	300	8	,	,	PUNCT
ejpam-4382	300	9	new	new	PROPN
ejpam-4382	300	10	york	york	PROPN
ejpam-4382	300	11	,	,	PUNCT
ejpam-4382	300	12	1966	1966	NUM
ejpam-4382	300	13	.	.	PUNCT
ejpam-4382	301	1	[	[	X
ejpam-4382	301	2	17	17	NUM
ejpam-4382	301	3	]	]	X
ejpam-4382	301	4	e.	e.	PROPN
ejpam-4382	301	5	l.	l.	PROPN
ejpam-4382	301	6	f.	f.	PROPN
ejpam-4382	301	7	moore	moore	PROPN
ejpam-4382	301	8	and	and	CCONJ
ejpam-4382	301	9	t.	t.	PROPN
ejpam-4382	301	10	j.	j.	PROPN
ejpam-4382	301	11	peters	peters	PROPN
ejpam-4382	301	12	.	.	PUNCT
ejpam-4382	302	1	computational	computational	ADJ
ejpam-4382	302	2	topology	topology	NOUN
ejpam-4382	302	3	for	for	ADP
ejpam-4382	302	4	geometric	geometric	ADJ
ejpam-4382	302	5	design	design	NOUN
ejpam-4382	302	6	and	and	CCONJ
ejpam-4382	302	7	molecular	molecular	ADJ
ejpam-4382	302	8	design	design	NOUN
ejpam-4382	302	9	.	.	PUNCT
ejpam-4382	303	1	mathematics	mathematic	NOUN
ejpam-4382	303	2	for	for	ADP
ejpam-4382	303	3	industry	industry	NOUN
ejpam-4382	303	4	:	:	PUNCT
ejpam-4382	303	5	challenges	challenge	NOUN
ejpam-4382	303	6	and	and	CCONJ
ejpam-4382	303	7	frontiers	frontier	NOUN
ejpam-4382	303	8	,	,	PUNCT
ejpam-4382	303	9	siam	siam	NOUN
ejpam-4382	303	10	,	,	PUNCT
ejpam-4382	303	11	pages	page	NOUN
ejpam-4382	303	12	125–139	125–139	NUM
ejpam-4382	303	13	,	,	PUNCT
ejpam-4382	303	14	2005	2005	NUM
ejpam-4382	303	15	.	.	PUNCT
ejpam-4382	304	1	[	[	X
ejpam-4382	304	2	18	18	NUM
ejpam-4382	304	3	]	]	X
ejpam-4382	304	4	d.	d.	PROPN
ejpam-4382	304	5	w.	w.	PROPN
ejpam-4382	304	6	rosen	rosen	PROPN
ejpam-4382	304	7	and	and	CCONJ
ejpam-4382	304	8	t.	t.	PROPN
ejpam-4382	304	9	peters	peters	PROPN
ejpam-4382	304	10	.	.	PUNCT
ejpam-4382	305	1	the	the	DET
ejpam-4382	305	2	role	role	NOUN
ejpam-4382	305	3	of	of	ADP
ejpam-4382	305	4	topology	topology	NOUN
ejpam-4382	305	5	in	in	ADP
ejpam-4382	305	6	engineering	engineering	NOUN
ejpam-4382	305	7	design	design	NOUN
ejpam-4382	305	8	research	research	NOUN
ejpam-4382	305	9	.	.	PUNCT
ejpam-4382	306	1	research	research	NOUN
ejpam-4382	306	2	in	in	ADP
ejpam-4382	306	3	engineering	engineering	NOUN
ejpam-4382	306	4	design	design	NOUN
ejpam-4382	306	5	,	,	PUNCT
ejpam-4382	306	6	2:81–98	2:81–98	NUM
ejpam-4382	306	7	,	,	PUNCT
ejpam-4382	306	8	1996	1996	NUM
ejpam-4382	306	9	.	.	PUNCT
ejpam-4382	307	1	[	[	X
ejpam-4382	307	2	19	19	NUM
ejpam-4382	307	3	]	]	X
ejpam-4382	307	4	s.	s.	PROPN
ejpam-4382	307	5	scheinberg	scheinberg	PROPN
ejpam-4382	307	6	.	.	PUNCT
ejpam-4382	308	1	topologies	topology	NOUN
ejpam-4382	308	2	which	which	PRON
ejpam-4382	308	3	generate	generate	VERB
ejpam-4382	308	4	a	a	DET
ejpam-4382	308	5	complete	complete	ADJ
ejpam-4382	308	6	measure	measure	NOUN
ejpam-4382	308	7	algebra	algebra	NOUN
ejpam-4382	308	8	.	.	PUNCT
ejpam-4382	309	1	advances	advance	NOUN
ejpam-4382	309	2	in	in	ADP
ejpam-4382	309	3	mathematics	mathematic	NOUN
ejpam-4382	309	4	,	,	PUNCT
ejpam-4382	309	5	7:231–239	7:231–239	NUM
ejpam-4382	309	6	,	,	PUNCT
ejpam-4382	309	7	1971	1971	NUM
ejpam-4382	309	8	.	.	PUNCT
ejpam-4382	310	1	[	[	X
ejpam-4382	310	2	20	20	NUM
ejpam-4382	310	3	]	]	X
ejpam-4382	310	4	r.	r.	PROPN
ejpam-4382	310	5	vaidyanathaswamy	vaidyanathaswamy	PROPN
ejpam-4382	310	6	.	.	PUNCT
ejpam-4382	311	1	the	the	DET
ejpam-4382	311	2	localisation	localisation	NOUN
ejpam-4382	311	3	theory	theory	NOUN
ejpam-4382	311	4	in	in	ADP
ejpam-4382	311	5	set	set	NOUN
ejpam-4382	311	6	-	-	PUNCT
ejpam-4382	311	7	topology	topology	NOUN
ejpam-4382	311	8	.	.	PUNCT
ejpam-4382	312	1	proceedings	proceeding	NOUN
ejpam-4382	312	2	of	of	ADP
ejpam-4382	312	3	the	the	DET
ejpam-4382	312	4	indian	indian	PROPN
ejpam-4382	312	5	academy	academy	PROPN
ejpam-4382	312	6	of	of	ADP
ejpam-4382	312	7	sciences	sciences	PROPN
ejpam-4382	312	8	,	,	PUNCT
ejpam-4382	312	9	20:51–61	20:51–61	NUM
ejpam-4382	312	10	,	,	PUNCT
ejpam-4382	312	11	1945	1945	NUM
ejpam-4382	312	12	.	.	PUNCT
ejpam-4382	313	1	[	[	X
ejpam-4382	313	2	21	21	NUM
ejpam-4382	313	3	]	]	X
ejpam-4382	313	4	e.	e.	PROPN
ejpam-4382	313	5	k.	k.	PROPN
ejpam-4382	313	6	van	van	PROPN
ejpam-4382	313	7	douwen	douwen	PROPN
ejpam-4382	313	8	.	.	PUNCT
ejpam-4382	314	1	applications	application	NOUN
ejpam-4382	314	2	of	of	ADP
ejpam-4382	314	3	maximal	maximal	ADJ
ejpam-4382	314	4	topologies	topology	NOUN
ejpam-4382	314	5	.	.	PUNCT
ejpam-4382	315	1	topology	topology	NOUN
ejpam-4382	315	2	and	and	CCONJ
ejpam-4382	315	3	its	its	PRON
ejpam-4382	315	4	applications	application	NOUN
ejpam-4382	315	5	,	,	PUNCT
ejpam-4382	315	6	51:125–139	51:125–139	PROPN
ejpam-4382	315	7	,	,	PUNCT
ejpam-4382	315	8	1993	1993	NUM
ejpam-4382	315	9	.	.	PUNCT