id	sid	tid	token	lemma	pos
ejpam-4003	1	1	european	european	PROPN
ejpam-4003	1	2	journal	journal	PROPN
ejpam-4003	1	3	of	of	ADP
ejpam-4003	1	4	pure	pure	ADJ
ejpam-4003	1	5	and	and	CCONJ
ejpam-4003	1	6	applied	apply	VERB
ejpam-4003	1	7	mathematics	mathematic	NOUN
ejpam-4003	1	8	vol	vol	NOUN
ejpam-4003	1	9	.	.	PUNCT
ejpam-4003	2	1	14	14	NUM
ejpam-4003	2	2	,	,	PUNCT
ejpam-4003	2	3	no	no	INTJ
ejpam-4003	2	4	.	.	NOUN
ejpam-4003	2	5	3	3	NUM
ejpam-4003	2	6	,	,	PUNCT
ejpam-4003	2	7	2021	2021	NUM
ejpam-4003	2	8	,	,	PUNCT
ejpam-4003	2	9	915	915	NUM
ejpam-4003	2	10	-	-	SYM
ejpam-4003	2	11	922	922	NUM
ejpam-4003	2	12	issn	issn	PROPN
ejpam-4003	2	13	1307	1307	NUM
ejpam-4003	2	14	-	-	SYM
ejpam-4003	2	15	5543	5543	NUM
ejpam-4003	2	16	–	–	PUNCT
ejpam-4003	3	1	ejpam.com	ejpam.com	X
ejpam-4003	3	2	published	publish	VERB
ejpam-4003	3	3	by	by	ADP
ejpam-4003	3	4	new	new	PROPN
ejpam-4003	3	5	york	york	PROPN
ejpam-4003	3	6	business	business	PROPN
ejpam-4003	3	7	global	global	ADJ
ejpam-4003	3	8	note	note	NOUN
ejpam-4003	3	9	on	on	ADP
ejpam-4003	3	10	(	(	PUNCT
ejpam-4003	3	11	i	i	NOUN
ejpam-4003	3	12	,	,	PUNCT
ejpam-4003	3	13	j)−mx	j)−mx	PROPN
ejpam-4003	3	14	−	−	PROPN
ejpam-4003	3	15	β−exterior	β−exterior	PUNCT
ejpam-4003	3	16	sets	set	NOUN
ejpam-4003	3	17	in	in	ADP
ejpam-4003	3	18	biminimal	biminimal	NOUN
ejpam-4003	3	19	structure	structure	NOUN
ejpam-4003	3	20	spaces	space	NOUN
ejpam-4003	3	21	torsak	torsak	ADJ
ejpam-4003	3	22	prasertsang1	prasertsang1	PROPN
ejpam-4003	3	23	,	,	PUNCT
ejpam-4003	3	24	patarawadee	patarawadee	PROPN
ejpam-4003	3	25	prasertsang1,∗	prasertsang1,∗	NOUN
ejpam-4003	3	26	1	1	NUM
ejpam-4003	3	27	faculty	faculty	NOUN
ejpam-4003	3	28	of	of	ADP
ejpam-4003	3	29	science	science	NOUN
ejpam-4003	3	30	and	and	CCONJ
ejpam-4003	3	31	engineering	engineering	NOUN
ejpam-4003	3	32	,	,	PUNCT
ejpam-4003	3	33	kasetsart	kasetsart	PROPN
ejpam-4003	3	34	university	university	PROPN
ejpam-4003	3	35	,	,	PUNCT
ejpam-4003	3	36	chalermprakiat	chalermprakiat	PROPN
ejpam-4003	3	37	sakon	sakon	PROPN
ejpam-4003	3	38	nakhon	nakhon	PROPN
ejpam-4003	3	39	province	province	PROPN
ejpam-4003	3	40	campus	campus	PROPN
ejpam-4003	3	41	,	,	PUNCT
ejpam-4003	3	42	sakon	sakon	PROPN
ejpam-4003	3	43	nakhon	nakhon	PROPN
ejpam-4003	3	44	47000	47000	NUM
ejpam-4003	3	45	,	,	PUNCT
ejpam-4003	3	46	thailand	thailand	PROPN
ejpam-4003	3	47	abstract	abstract	NOUN
ejpam-4003	3	48	.	.	PUNCT
ejpam-4003	4	1	in	in	ADP
ejpam-4003	4	2	that	that	DET
ejpam-4003	4	3	paper	paper	NOUN
ejpam-4003	4	4	,	,	PUNCT
ejpam-4003	4	5	the	the	DET
ejpam-4003	4	6	concept	concept	NOUN
ejpam-4003	4	7	of	of	ADP
ejpam-4003	4	8	(	(	PUNCT
ejpam-4003	4	9	i	i	PROPN
ejpam-4003	4	10	,	,	PUNCT
ejpam-4003	4	11	j	j	PROPN
ejpam-4003	4	12	)	)	PUNCT
ejpam-4003	4	13	−mx	−mx	NOUN
ejpam-4003	4	14	−	−	NOUN
ejpam-4003	4	15	β−exterior	β−exterior	NOUN
ejpam-4003	4	16	sets	set	NOUN
ejpam-4003	4	17	in	in	ADP
ejpam-4003	4	18	a	a	DET
ejpam-4003	4	19	biminimal	biminimal	NOUN
ejpam-4003	4	20	structure	structure	NOUN
ejpam-4003	4	21	space	space	NOUN
ejpam-4003	4	22	(	(	PUNCT
ejpam-4003	4	23	bss	bss	NOUN
ejpam-4003	4	24	)	)	PUNCT
ejpam-4003	4	25	and	and	CCONJ
ejpam-4003	4	26	a	a	DET
ejpam-4003	4	27	biminimal	biminimal	NOUN
ejpam-4003	4	28	structure	structure	NOUN
ejpam-4003	4	29	subspace	subspace	NOUN
ejpam-4003	4	30	(	(	PUNCT
ejpam-4003	4	31	bss	bss	PROPN
ejpam-4003	4	32	)	)	PUNCT
ejpam-4003	4	33	were	be	AUX
ejpam-4003	4	34	introduced	introduce	VERB
ejpam-4003	4	35	.	.	PUNCT
ejpam-4003	5	1	based	base	VERB
ejpam-4003	5	2	on	on	ADP
ejpam-4003	5	3	properties	property	NOUN
ejpam-4003	5	4	of	of	ADP
ejpam-4003	5	5	bss	bss	NOUN
ejpam-4003	5	6	and	and	CCONJ
ejpam-4003	5	7	bss	bss	PROPN
ejpam-4003	5	8	,	,	PUNCT
ejpam-4003	5	9	some	some	DET
ejpam-4003	5	10	new	new	ADJ
ejpam-4003	5	11	notions	notion	NOUN
ejpam-4003	5	12	and	and	CCONJ
ejpam-4003	5	13	several	several	ADJ
ejpam-4003	5	14	properties	property	NOUN
ejpam-4003	5	15	of	of	ADP
ejpam-4003	5	16	those	those	DET
ejpam-4003	5	17	sets	set	NOUN
ejpam-4003	5	18	dealing	deal	VERB
ejpam-4003	5	19	with	with	ADP
ejpam-4003	5	20	this	this	DET
ejpam-4003	5	21	space	space	NOUN
ejpam-4003	5	22	were	be	AUX
ejpam-4003	5	23	obtained	obtain	VERB
ejpam-4003	5	24	in	in	ADP
ejpam-4003	5	25	both	both	PRON
ejpam-4003	5	26	of	of	ADP
ejpam-4003	5	27	bss	bss	PROPN
ejpam-4003	5	28	and	and	CCONJ
ejpam-4003	5	29	bss	bss	PROPN
ejpam-4003	5	30	.	.	PUNCT
ejpam-4003	6	1	some	some	DET
ejpam-4003	6	2	examples	example	NOUN
ejpam-4003	6	3	were	be	AUX
ejpam-4003	6	4	given	give	VERB
ejpam-4003	6	5	to	to	PART
ejpam-4003	6	6	illustrate	illustrate	VERB
ejpam-4003	6	7	the	the	DET
ejpam-4003	6	8	effectiveness	effectiveness	NOUN
ejpam-4003	6	9	of	of	ADP
ejpam-4003	6	10	these	these	DET
ejpam-4003	6	11	results	result	NOUN
ejpam-4003	6	12	.	.	PUNCT
ejpam-4003	7	1	2020	2020	NUM
ejpam-4003	7	2	mathematics	mathematic	NOUN
ejpam-4003	7	3	subject	subject	NOUN
ejpam-4003	7	4	classifications	classification	NOUN
ejpam-4003	7	5	:	:	PUNCT
ejpam-4003	7	6	22a05	22a05	NUM
ejpam-4003	7	7	,	,	PUNCT
ejpam-4003	7	8	22a15	22a15	ADJ
ejpam-4003	7	9	key	key	ADJ
ejpam-4003	7	10	words	word	NOUN
ejpam-4003	7	11	and	and	CCONJ
ejpam-4003	7	12	phrases	phrase	NOUN
ejpam-4003	7	13	:	:	PUNCT
ejpam-4003	7	14	exterior	exterior	ADJ
ejpam-4003	7	15	sets	set	NOUN
ejpam-4003	7	16	,	,	PUNCT
ejpam-4003	7	17	biminimal	biminimal	NOUN
ejpam-4003	7	18	structure	structure	NOUN
ejpam-4003	7	19	spaces	space	VERB
ejpam-4003	7	20	,	,	PUNCT
ejpam-4003	7	21	(	(	PUNCT
ejpam-4003	7	22	i	i	PROPN
ejpam-4003	7	23	,	,	PUNCT
ejpam-4003	7	24	j	j	PROPN
ejpam-4003	7	25	)	)	PUNCT
ejpam-4003	7	26	−mx	−mx	NOUN
ejpam-4003	7	27	−	−	PROPN
ejpam-4003	7	28	β−exterior	β−exterior	SYM
ejpam-4003	7	29	sets,(i	sets,(i	NOUN
ejpam-4003	7	30	,	,	PUNCT
ejpam-4003	7	31	j)−mx	j)−mx	PROPN
ejpam-4003	7	32	−	−	PROPN
ejpam-4003	7	33	β−closed	β−closed	PROPN
ejpam-4003	7	34	sets,(i	sets,(i	PROPN
ejpam-4003	7	35	,	,	PUNCT
ejpam-4003	7	36	j)−mx	j)−mx	PROPN
ejpam-4003	7	37	−	−	NOUN
ejpam-4003	7	38	β−open	β−open	PUNCT
ejpam-4003	7	39	sets	set	VERB
ejpam-4003	7	40	1	1	NUM
ejpam-4003	7	41	.	.	X
ejpam-4003	7	42	introduction	introduction	NOUN
ejpam-4003	7	43	a	a	DET
ejpam-4003	7	44	general	general	ADJ
ejpam-4003	7	45	space	space	NOUN
ejpam-4003	7	46	in	in	ADP
ejpam-4003	7	47	mathematics	mathematic	NOUN
ejpam-4003	7	48	,	,	PUNCT
ejpam-4003	7	49	topology	topology	NOUN
ejpam-4003	7	50	space	space	NOUN
ejpam-4003	7	51	has	have	AUX
ejpam-4003	7	52	been	be	AUX
ejpam-4003	7	53	widely	widely	ADV
ejpam-4003	7	54	studied	study	VERB
ejpam-4003	7	55	in	in	ADP
ejpam-4003	7	56	every	every	DET
ejpam-4003	7	57	field	field	NOUN
ejpam-4003	7	58	of	of	ADP
ejpam-4003	7	59	mathematics	mathematic	NOUN
ejpam-4003	7	60	as	as	ADP
ejpam-4003	7	61	a	a	DET
ejpam-4003	7	62	fundamental	fundamental	ADJ
ejpam-4003	7	63	concept	concept	NOUN
ejpam-4003	7	64	including	include	VERB
ejpam-4003	7	65	the	the	DET
ejpam-4003	7	66	definition	definition	NOUN
ejpam-4003	7	67	of	of	ADP
ejpam-4003	7	68	limits	limit	NOUN
ejpam-4003	7	69	,	,	PUNCT
ejpam-4003	7	70	continuity	continuity	NOUN
ejpam-4003	7	71	,	,	PUNCT
ejpam-4003	7	72	neighborhoods	neighborhood	NOUN
ejpam-4003	7	73	,	,	PUNCT
ejpam-4003	7	74	closed	closed	ADJ
ejpam-4003	7	75	sets	set	NOUN
ejpam-4003	7	76	,	,	PUNCT
ejpam-4003	7	77	open	open	ADJ
ejpam-4003	7	78	set	set	NOUN
ejpam-4003	7	79	and	and	CCONJ
ejpam-4003	7	80	connnectedness	connnectedness	NOUN
ejpam-4003	7	81	among	among	ADP
ejpam-4003	7	82	others	other	NOUN
ejpam-4003	7	83	.	.	PUNCT
ejpam-4003	8	1	in	in	ADP
ejpam-4003	8	2	2020	2020	NUM
ejpam-4003	8	3	,	,	PUNCT
ejpam-4003	8	4	t.	t.	PROPN
ejpam-4003	8	5	m.	m.	PROPN
ejpam-4003	8	6	al	al	PROPN
ejpam-4003	8	7	-	-	PUNCT
ejpam-4003	8	8	shami	shami	PROPN
ejpam-4003	8	9	et	et	PROPN
ejpam-4003	8	10	.	.	PUNCT
ejpam-4003	9	1	al	al	PROPN
ejpam-4003	9	2	.	.	PUNCT
ejpam-4003	10	1	[	[	X
ejpam-4003	10	2	1	1	NUM
ejpam-4003	10	3	]	]	X
ejpam-4003	10	4	focused	focus	VERB
ejpam-4003	10	5	their	their	PRON
ejpam-4003	10	6	attention	attention	NOUN
ejpam-4003	10	7	on	on	ADP
ejpam-4003	10	8	topology	topology	NOUN
ejpam-4003	10	9	space	space	NOUN
ejpam-4003	10	10	.	.	PUNCT
ejpam-4003	11	1	the	the	DET
ejpam-4003	11	2	concept	concept	NOUN
ejpam-4003	11	3	of	of	ADP
ejpam-4003	11	4	supra	supra	PROPN
ejpam-4003	11	5	semi	semi	NOUN
ejpam-4003	11	6	limit	limit	NOUN
ejpam-4003	11	7	points	point	NOUN
ejpam-4003	11	8	of	of	ADP
ejpam-4003	11	9	a	a	DET
ejpam-4003	11	10	set	set	ADJ
ejpam-4003	11	11	and	and	CCONJ
ejpam-4003	11	12	new	new	ADJ
ejpam-4003	11	13	types	type	NOUN
ejpam-4003	11	14	of	of	ADP
ejpam-4003	11	15	separation	separation	NOUN
ejpam-4003	11	16	axioms	axiom	NOUN
ejpam-4003	11	17	using	use	VERB
ejpam-4003	11	18	supra	supra	PROPN
ejpam-4003	11	19	semi	semi	ADJ
ejpam-4003	11	20	-	-	ADJ
ejpam-4003	11	21	open	open	ADJ
ejpam-4003	11	22	sets	set	NOUN
ejpam-4003	11	23	were	be	AUX
ejpam-4003	11	24	introduced	introduce	VERB
ejpam-4003	11	25	to	to	PART
ejpam-4003	11	26	minimize	minimize	VERB
ejpam-4003	11	27	the	the	DET
ejpam-4003	11	28	conditions	condition	NOUN
ejpam-4003	11	29	of	of	ADP
ejpam-4003	11	30	topology	topology	NOUN
ejpam-4003	11	31	for	for	ADP
ejpam-4003	11	32	other	other	ADJ
ejpam-4003	11	33	reasons	reason	NOUN
ejpam-4003	11	34	.	.	PUNCT
ejpam-4003	12	1	some	some	DET
ejpam-4003	12	2	applications	application	NOUN
ejpam-4003	12	3	of	of	ADP
ejpam-4003	12	4	supra	supra	ADJ
ejpam-4003	12	5	preopen	preopen	ADJ
ejpam-4003	12	6	sets	set	NOUN
ejpam-4003	12	7	on	on	ADP
ejpam-4003	12	8	supra	supra	PROPN
ejpam-4003	12	9	topological	topological	ADJ
ejpam-4003	12	10	spaces	space	NOUN
ejpam-4003	12	11	was	be	AUX
ejpam-4003	12	12	studied	study	VERB
ejpam-4003	12	13	by	by	ADP
ejpam-4003	12	14	m.	m.	PROPN
ejpam-4003	12	15	e.	e.	PROPN
ejpam-4003	12	16	el	el	PROPN
ejpam-4003	12	17	-	-	PROPN
ejpam-4003	12	18	shafei	shafei	PROPN
ejpam-4003	12	19	and	and	CCONJ
ejpam-4003	12	20	et	et	NOUN
ejpam-4003	12	21	.	.	PUNCT
ejpam-4003	13	1	al	al	PROPN
ejpam-4003	14	1	[	[	X
ejpam-4003	14	2	5	5	NUM
ejpam-4003	14	3	]	]	PUNCT
ejpam-4003	14	4	.	.	PUNCT
ejpam-4003	15	1	the	the	DET
ejpam-4003	15	2	concept	concept	NOUN
ejpam-4003	15	3	of	of	ADP
ejpam-4003	15	4	supra	supra	PROPN
ejpam-4003	15	5	prehomeomorphism	prehomeomorphism	NOUN
ejpam-4003	15	6	maps	map	NOUN
ejpam-4003	15	7	and	and	CCONJ
ejpam-4003	15	8	the	the	DET
ejpam-4003	15	9	concepts	concept	NOUN
ejpam-4003	15	10	of	of	ADP
ejpam-4003	15	11	supra	supra	PROPN
ejpam-4003	15	12	limit	limit	NOUN
ejpam-4003	15	13	and	and	CCONJ
ejpam-4003	15	14	supra	supra	ADJ
ejpam-4003	15	15	boundary	boundary	ADJ
ejpam-4003	15	16	points	point	NOUN
ejpam-4003	15	17	of	of	ADP
ejpam-4003	15	18	a	a	DET
ejpam-4003	15	19	set	set	NOUN
ejpam-4003	15	20	with	with	ADP
ejpam-4003	15	21	respect	respect	NOUN
ejpam-4003	15	22	to	to	ADP
ejpam-4003	15	23	supra	supra	ADJ
ejpam-4003	15	24	preopen	preopen	ADJ
ejpam-4003	15	25	sets	set	NOUN
ejpam-4003	15	26	and	and	CCONJ
ejpam-4003	15	27	their	their	PRON
ejpam-4003	15	28	properties	property	NOUN
ejpam-4003	15	29	were	be	AUX
ejpam-4003	15	30	introduced	introduce	VERB
ejpam-4003	15	31	.	.	PUNCT
ejpam-4003	16	1	more	more	ADV
ejpam-4003	16	2	recently	recently	ADV
ejpam-4003	16	3	,	,	PUNCT
ejpam-4003	16	4	a.	a.	NOUN
ejpam-4003	16	5	mhemdi	mhemdi	PROPN
ejpam-4003	16	6	and	and	CCONJ
ejpam-4003	16	7	t.	t.	PROPN
ejpam-4003	16	8	m.	m.	PROPN
ejpam-4003	16	9	al	al	PROPN
ejpam-4003	16	10	-	-	PUNCT
ejpam-4003	16	11	shami	shami	PROPN
ejpam-4003	17	1	[	[	X
ejpam-4003	17	2	6	6	NUM
ejpam-4003	17	3	]	]	PUNCT
ejpam-4003	17	4	defined	define	VERB
ejpam-4003	17	5	the	the	DET
ejpam-4003	17	6	functional	functional	ADJ
ejpam-4003	17	7	separation	separation	NOUN
ejpam-4003	17	8	axioms	axiom	NOUN
ejpam-4003	17	9	on	on	ADP
ejpam-4003	17	10	general	general	ADJ
ejpam-4003	17	11	topology	topology	NOUN
ejpam-4003	17	12	and	and	CCONJ
ejpam-4003	17	13	provided	provide	VERB
ejpam-4003	17	14	some	some	DET
ejpam-4003	17	15	notions	notion	NOUN
ejpam-4003	17	16	of	of	ADP
ejpam-4003	17	17	them	they	PRON
ejpam-4003	17	18	.	.	PUNCT
ejpam-4003	18	1	the	the	DET
ejpam-4003	18	2	notions	notion	NOUN
ejpam-4003	18	3	of	of	ADP
ejpam-4003	18	4	almost	almost	ADV
ejpam-4003	18	5	sd	sd	NOUN
ejpam-4003	18	6	-	-	PUNCT
ejpam-4003	18	7	compact	compact	ADJ
ejpam-4003	18	8	and	and	CCONJ
ejpam-4003	18	9	almost	almost	ADV
ejpam-4003	18	10	sd	sd	NOUN
ejpam-4003	18	11	-	-	PUNCT
ejpam-4003	18	12	lindelöf	lindelöf	NOUN
ejpam-4003	18	13	spaces	space	NOUN
ejpam-4003	18	14	,	,	PUNCT
ejpam-4003	18	15	nearly	nearly	ADV
ejpam-4003	18	16	sd	sd	NOUN
ejpam-4003	18	17	-	-	PUNCT
ejpam-4003	18	18	compact	compact	ADJ
ejpam-4003	18	19	and	and	CCONJ
ejpam-4003	18	20	nearly	nearly	ADV
ejpam-4003	18	21	sdlindelöf	sdlindelöf	NOUN
ejpam-4003	18	22	spaces	space	NOUN
ejpam-4003	18	23	,	,	PUNCT
ejpam-4003	18	24	and	and	CCONJ
ejpam-4003	18	25	mildly	mildly	ADV
ejpam-4003	18	26	sd	sd	NOUN
ejpam-4003	18	27	-	-	PUNCT
ejpam-4003	18	28	compact	compact	ADJ
ejpam-4003	18	29	and	and	CCONJ
ejpam-4003	18	30	mildly	mildly	ADV
ejpam-4003	18	31	sd	sd	NOUN
ejpam-4003	18	32	-	-	PUNCT
ejpam-4003	18	33	lindelöf	lindelöf	NOUN
ejpam-4003	18	34	spaces	space	NOUN
ejpam-4003	18	35	were	be	AUX
ejpam-4003	18	36	investigated	investigate	VERB
ejpam-4003	18	37	by	by	ADP
ejpam-4003	18	38	t.	t.	PROPN
ejpam-4003	18	39	m.	m.	PROPN
ejpam-4003	18	40	al	al	PROPN
ejpam-4003	18	41	-	-	PUNCT
ejpam-4003	18	42	shami	shami	PROPN
ejpam-4003	18	43	and	and	CCONJ
ejpam-4003	18	44	t.	t.	PROPN
ejpam-4003	18	45	noiri	noiri	PROPN
ejpam-4003	18	46	[	[	X
ejpam-4003	18	47	13	13	NUM
ejpam-4003	18	48	]	]	PUNCT
ejpam-4003	18	49	.	.	PUNCT
ejpam-4003	19	1	the	the	DET
ejpam-4003	19	2	above	above	ADJ
ejpam-4003	19	3	discussion	discussion	NOUN
ejpam-4003	19	4	motivated	motivate	VERB
ejpam-4003	19	5	the	the	DET
ejpam-4003	19	6	current	current	ADJ
ejpam-4003	19	7	study	study	NOUN
ejpam-4003	19	8	,	,	PUNCT
ejpam-4003	19	9	of	of	ADP
ejpam-4003	19	10	some	some	DET
ejpam-4003	19	11	branches	branch	NOUN
ejpam-4003	19	12	of	of	ADP
ejpam-4003	19	13	topology	topology	NOUN
ejpam-4003	19	14	.	.	PUNCT
ejpam-4003	20	1	the	the	DET
ejpam-4003	20	2	∗corresponding	∗corresponde	VERB
ejpam-4003	20	3	author	author	NOUN
ejpam-4003	20	4	.	.	PUNCT
ejpam-4003	21	1	doi	doi	NOUN
ejpam-4003	21	2	:	:	PUNCT
ejpam-4003	21	3	https://doi.org/10.29020/nybg.ejpam.v14i3.4003	https://doi.org/10.29020/nybg.ejpam.v14i3.4003	NOUN
ejpam-4003	21	4	email	email	NOUN
ejpam-4003	21	5	addresses	address	NOUN
ejpam-4003	21	6	:	:	PUNCT
ejpam-4003	21	7	torsak.p@ku.th	torsak.p@ku.th	NUM
ejpam-4003	21	8	(	(	PUNCT
ejpam-4003	21	9	t.	t.	PROPN
ejpam-4003	21	10	prasertsang	prasertsang	PROPN
ejpam-4003	21	11	)	)	PUNCT
ejpam-4003	21	12	,	,	PUNCT
ejpam-4003	21	13	patarawadee.s@ku.th	patarawadee.s@ku.th	PROPN
ejpam-4003	21	14	(	(	PUNCT
ejpam-4003	21	15	p.	p.	PROPN
ejpam-4003	21	16	prasertsang	prasertsang	PROPN
ejpam-4003	21	17	)	)	PUNCT
ejpam-4003	21	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4003	22	1	915	915	NUM
ejpam-4003	23	1	©	©	NOUN
ejpam-4003	23	2	2021	2021	NUM
ejpam-4003	23	3	ejpam	ejpam	VERB
ejpam-4003	23	4	all	all	DET
ejpam-4003	23	5	rights	right	NOUN
ejpam-4003	23	6	reserved	reserve	VERB
ejpam-4003	23	7	.	.	PUNCT
ejpam-4003	24	1	t.	t.	PROPN
ejpam-4003	24	2	prasertsang	prasertsang	PROPN
ejpam-4003	24	3	,	,	PUNCT
ejpam-4003	24	4	p.	p.	PROPN
ejpam-4003	24	5	prasertsang	prasertsang	PROPN
ejpam-4003	24	6	/	/	SYM
ejpam-4003	24	7	eur	eur	PROPN
ejpam-4003	24	8	.	.	PUNCT
ejpam-4003	25	1	j.	j.	PROPN
ejpam-4003	25	2	pure	pure	PROPN
ejpam-4003	25	3	appl	appl	PROPN
ejpam-4003	25	4	.	.	PROPN
ejpam-4003	25	5	math	math	PROPN
ejpam-4003	25	6	,	,	PUNCT
ejpam-4003	25	7	14	14	NUM
ejpam-4003	25	8	(	(	PUNCT
ejpam-4003	25	9	3	3	NUM
ejpam-4003	25	10	)	)	PUNCT
ejpam-4003	25	11	(	(	PUNCT
ejpam-4003	25	12	2021	2021	NUM
ejpam-4003	25	13	)	)	PUNCT
ejpam-4003	25	14	,	,	PUNCT
ejpam-4003	25	15	915	915	NUM
ejpam-4003	25	16	-	-	SYM
ejpam-4003	25	17	922	922	NUM
ejpam-4003	25	18	916	916	NUM
ejpam-4003	25	19	concept	concept	NOUN
ejpam-4003	25	20	of	of	ADP
ejpam-4003	25	21	a	a	DET
ejpam-4003	25	22	biminimal	biminimal	NOUN
ejpam-4003	25	23	structure	structure	NOUN
ejpam-4003	25	24	space	space	NOUN
ejpam-4003	25	25	(	(	PUNCT
ejpam-4003	25	26	bss	bss	NOUN
ejpam-4003	25	27	)	)	PUNCT
ejpam-4003	25	28	and	and	CCONJ
ejpam-4003	25	29	some	some	DET
ejpam-4003	25	30	properties	property	NOUN
ejpam-4003	25	31	of	of	ADP
ejpam-4003	25	32	m1	m1	PROPN
ejpam-4003	25	33	xm	xm	PROPN
ejpam-4003	25	34	2	2	NUM
ejpam-4003	25	35	x−closed	x−closed	NUM
ejpam-4003	25	36	sets	set	NOUN
ejpam-4003	25	37	and	and	CCONJ
ejpam-4003	25	38	m1	m1	PROPN
ejpam-4003	25	39	xm	xm	PROPN
ejpam-4003	25	40	2	2	NUM
ejpam-4003	25	41	x−open	x−open	VERB
ejpam-4003	25	42	sets	set	NOUN
ejpam-4003	25	43	in	in	ADP
ejpam-4003	25	44	bsss	bsss	NOUN
ejpam-4003	25	45	were	be	AUX
ejpam-4003	25	46	introduced	introduce	VERB
ejpam-4003	25	47	by	by	ADP
ejpam-4003	25	48	boonpok	boonpok	NOUN
ejpam-4003	26	1	[	[	X
ejpam-4003	26	2	2	2	NUM
ejpam-4003	26	3	]	]	PUNCT
ejpam-4003	26	4	in	in	ADP
ejpam-4003	26	5	2010	2010	NUM
ejpam-4003	26	6	.	.	PUNCT
ejpam-4003	27	1	that	that	PRON
ejpam-4003	27	2	is	be	AUX
ejpam-4003	27	3	,	,	PUNCT
ejpam-4003	27	4	(	(	PUNCT
ejpam-4003	27	5	x	x	NOUN
ejpam-4003	27	6	,	,	PUNCT
ejpam-4003	27	7	m1	m1	PROPN
ejpam-4003	27	8	x	x	SYM
ejpam-4003	27	9	,	,	PUNCT
ejpam-4003	27	10	m	m	PROPN
ejpam-4003	27	11	2	2	NUM
ejpam-4003	27	12	x	x	NOUN
ejpam-4003	27	13	)	)	PUNCT
ejpam-4003	27	14	is	be	AUX
ejpam-4003	27	15	called	call	VERB
ejpam-4003	27	16	a	a	DET
ejpam-4003	27	17	biminimal	biminimal	NOUN
ejpam-4003	27	18	structure	structure	NOUN
ejpam-4003	27	19	space	space	NOUN
ejpam-4003	27	20	,	,	PUNCT
ejpam-4003	27	21	where	where	SCONJ
ejpam-4003	27	22	x	x	PRON
ejpam-4003	27	23	is	be	AUX
ejpam-4003	27	24	a	a	DET
ejpam-4003	27	25	nonempty	nonempty	ADV
ejpam-4003	27	26	set	set	VERB
ejpam-4003	27	27	and	and	CCONJ
ejpam-4003	27	28	m1	m1	PROPN
ejpam-4003	27	29	x	x	SYM
ejpam-4003	27	30	,	,	PUNCT
ejpam-4003	27	31	m	m	VERB
ejpam-4003	27	32	2	2	NUM
ejpam-4003	27	33	x	x	VERB
ejpam-4003	27	34	are	be	AUX
ejpam-4003	27	35	minimal	minimal	ADJ
ejpam-4003	27	36	structures	structure	NOUN
ejpam-4003	27	37	on	on	ADP
ejpam-4003	27	38	x	x	SYM
ejpam-4003	27	39	where	where	SCONJ
ejpam-4003	27	40	minimal	minimal	ADJ
ejpam-4003	27	41	structures	structure	NOUN
ejpam-4003	27	42	are	be	AUX
ejpam-4003	27	43	defined	define	VERB
ejpam-4003	27	44	by	by	ADP
ejpam-4003	27	45	giving	give	VERB
ejpam-4003	27	46	p	p	PROPN
ejpam-4003	27	47	(	(	PUNCT
ejpam-4003	27	48	x	x	NOUN
ejpam-4003	27	49	)	)	PUNCT
ejpam-4003	27	50	as	as	SCONJ
ejpam-4003	27	51	the	the	DET
ejpam-4003	27	52	power	power	NOUN
ejpam-4003	27	53	set	set	NOUN
ejpam-4003	27	54	of	of	ADP
ejpam-4003	27	55	a	a	DET
ejpam-4003	27	56	nonempty	nonempty	ADV
ejpam-4003	27	57	set	set	VERB
ejpam-4003	27	58	x.	x.	NOUN
ejpam-4003	27	59	a	a	DET
ejpam-4003	27	60	subfamily	subfamily	ADV
ejpam-4003	27	61	mx	mx	NOUN
ejpam-4003	27	62	of	of	ADP
ejpam-4003	27	63	p	p	PROPN
ejpam-4003	27	64	(	(	PUNCT
ejpam-4003	27	65	x	x	X
ejpam-4003	27	66	)	)	PUNCT
ejpam-4003	27	67	is	be	AUX
ejpam-4003	27	68	called	call	VERB
ejpam-4003	27	69	a	a	DET
ejpam-4003	27	70	minimal	minimal	ADJ
ejpam-4003	27	71	structure	structure	NOUN
ejpam-4003	27	72	on	on	ADP
ejpam-4003	27	73	x	x	SYM
ejpam-4003	27	74	if	if	SCONJ
ejpam-4003	27	75	∅	∅	NOUN
ejpam-4003	27	76	∈	∈	PROPN
ejpam-4003	27	77	mx	mx	PROPN
ejpam-4003	27	78	and	and	CCONJ
ejpam-4003	27	79	x	x	PROPN
ejpam-4003	27	80	∈	∈	PROPN
ejpam-4003	27	81	mx	mx	PROPN
ejpam-4003	27	82	.	.	PUNCT
ejpam-4003	28	1	biminimal	biminimal	NOUN
ejpam-4003	28	2	structure	structure	NOUN
ejpam-4003	28	3	space	space	NOUN
ejpam-4003	28	4	has	have	AUX
ejpam-4003	28	5	been	be	AUX
ejpam-4003	28	6	of	of	ADP
ejpam-4003	28	7	wide	wide	ADJ
ejpam-4003	28	8	interest	interest	NOUN
ejpam-4003	28	9	in	in	ADP
ejpam-4003	28	10	studying	study	VERB
ejpam-4003	28	11	in	in	ADP
ejpam-4003	28	12	topology	topology	NOUN
ejpam-4003	28	13	.	.	PUNCT
ejpam-4003	29	1	furthermore	furthermore	ADV
ejpam-4003	29	2	,	,	PUNCT
ejpam-4003	29	3	boonpok	boonpok	PROPN
ejpam-4003	29	4	et	et	PROPN
ejpam-4003	29	5	al	al	PROPN
ejpam-4003	29	6	.	.	PUNCT
ejpam-4003	30	1	[	[	X
ejpam-4003	30	2	2–4	2–4	X
ejpam-4003	30	3	]	]	PUNCT
ejpam-4003	30	4	provided	provide	VERB
ejpam-4003	30	5	some	some	DET
ejpam-4003	30	6	properties	property	NOUN
ejpam-4003	30	7	of	of	ADP
ejpam-4003	30	8	them	they	PRON
ejpam-4003	30	9	to	to	ADP
ejpam-4003	30	10	as	as	ADP
ejpam-4003	30	11	a	a	DET
ejpam-4003	30	12	preliminary	preliminary	NOUN
ejpam-4003	30	13	for	for	ADP
ejpam-4003	30	14	the	the	DET
ejpam-4003	30	15	current	current	ADJ
ejpam-4003	30	16	study	study	NOUN
ejpam-4003	30	17	,	,	PUNCT
ejpam-4003	30	18	such	such	ADJ
ejpam-4003	30	19	as	as	ADP
ejpam-4003	30	20	(	(	PUNCT
ejpam-4003	30	21	i	i	PROPN
ejpam-4003	30	22	,	,	PUNCT
ejpam-4003	30	23	j)−mx−α−closed	j)−mx−α−close	VERB
ejpam-4003	30	24	,	,	PUNCT
ejpam-4003	30	25	(	(	PUNCT
ejpam-4003	30	26	i	i	PROPN
ejpam-4003	30	27	,	,	PUNCT
ejpam-4003	30	28	j)−mx−α−open	j)−mx−α−open	PROPN
ejpam-4003	30	29	,	,	PUNCT
ejpam-4003	30	30	(	(	PUNCT
ejpam-4003	30	31	i	i	PROPN
ejpam-4003	30	32	,	,	PUNCT
ejpam-4003	30	33	j)−mx−β−closed	j)−mx−β−close	VERB
ejpam-4003	30	34	and	and	CCONJ
ejpam-4003	30	35	(	(	PUNCT
ejpam-4003	30	36	i	i	PROPN
ejpam-4003	30	37	,	,	PUNCT
ejpam-4003	30	38	j)−mx	j)−mx	PROPN
ejpam-4003	30	39	−	−	PROPN
ejpam-4003	30	40	β−open	β−open	PROPN
ejpam-4003	30	41	,	,	PUNCT
ejpam-4003	30	42	which	which	PRON
ejpam-4003	30	43	are	be	AUX
ejpam-4003	30	44	advantageous	advantageous	ADJ
ejpam-4003	30	45	for	for	ADP
ejpam-4003	30	46	studying	study	VERB
ejpam-4003	30	47	bss	bss	NOUN
ejpam-4003	30	48	.	.	PUNCT
ejpam-4003	31	1	later	later	ADV
ejpam-4003	31	2	,	,	PUNCT
ejpam-4003	31	3	s.	s.	PROPN
ejpam-4003	31	4	sompong	sompong	PROPN
ejpam-4003	31	5	and	and	CCONJ
ejpam-4003	31	6	s.	s.	PROPN
ejpam-4003	31	7	muangchan	muangchan	PROPN
ejpam-4003	32	1	[	[	X
ejpam-4003	32	2	10	10	NUM
ejpam-4003	32	3	,	,	PUNCT
ejpam-4003	32	4	11	11	NUM
ejpam-4003	32	5	]	]	PUNCT
ejpam-4003	32	6	studied	study	VERB
ejpam-4003	32	7	the	the	DET
ejpam-4003	32	8	notion	notion	NOUN
ejpam-4003	32	9	of	of	ADP
ejpam-4003	32	10	exterior	exterior	ADJ
ejpam-4003	32	11	sets	set	NOUN
ejpam-4003	32	12	in	in	ADP
ejpam-4003	32	13	this	this	DET
ejpam-4003	32	14	space	space	NOUN
ejpam-4003	32	15	and	and	CCONJ
ejpam-4003	32	16	obtained	obtain	VERB
ejpam-4003	32	17	some	some	DET
ejpam-4003	32	18	characterizations	characterization	NOUN
ejpam-4003	32	19	and	and	CCONJ
ejpam-4003	32	20	fundamental	fundamental	ADJ
ejpam-4003	32	21	properties	property	NOUN
ejpam-4003	32	22	of	of	ADP
ejpam-4003	32	23	those	those	DET
ejpam-4003	32	24	sets	set	NOUN
ejpam-4003	32	25	.	.	PUNCT
ejpam-4003	33	1	e.	e.	PROPN
ejpam-4003	33	2	subha	subha	PROPN
ejpam-4003	33	3	and	and	CCONJ
ejpam-4003	33	4	n.	n.	PROPN
ejpam-4003	33	5	nagaveni	nagaveni	PROPN
ejpam-4003	34	1	[	[	X
ejpam-4003	34	2	12	12	NUM
ejpam-4003	34	3	]	]	PUNCT
ejpam-4003	34	4	studied	study	VERB
ejpam-4003	34	5	strongly	strongly	ADV
ejpam-4003	34	6	minimal	minimal	ADJ
ejpam-4003	34	7	generalized	generalize	VERB
ejpam-4003	34	8	closed	close	VERB
ejpam-4003	34	9	set	set	VERB
ejpam-4003	34	10	in	in	ADP
ejpam-4003	34	11	bsss	bsss	NOUN
ejpam-4003	34	12	and	and	CCONJ
ejpam-4003	34	13	obtained	obtain	VERB
ejpam-4003	34	14	some	some	DET
ejpam-4003	34	15	properties	property	NOUN
ejpam-4003	34	16	for	for	ADP
ejpam-4003	34	17	the	the	DET
ejpam-4003	34	18	set	set	NOUN
ejpam-4003	34	19	.	.	PUNCT
ejpam-4003	35	1	later	later	ADV
ejpam-4003	35	2	,	,	PUNCT
ejpam-4003	35	3	p.	p.	PROPN
ejpam-4003	35	4	prasertsang	prasertsang	PROPN
ejpam-4003	35	5	and	and	CCONJ
ejpam-4003	35	6	s.	s.	PROPN
ejpam-4003	35	7	sompong	sompong	PROPN
ejpam-4003	36	1	[	[	X
ejpam-4003	36	2	8	8	NUM
ejpam-4003	36	3	,	,	PUNCT
ejpam-4003	36	4	9	9	NUM
ejpam-4003	36	5	]	]	PUNCT
ejpam-4003	36	6	studied	study	VERB
ejpam-4003	36	7	the	the	DET
ejpam-4003	36	8	concept	concept	NOUN
ejpam-4003	36	9	of	of	ADP
ejpam-4003	36	10	(	(	PUNCT
ejpam-4003	36	11	i	i	PROPN
ejpam-4003	36	12	,	,	PUNCT
ejpam-4003	36	13	j	j	PROPN
ejpam-4003	36	14	)	)	PUNCT
ejpam-4003	36	15	−mx	−mx	NOUN
ejpam-4003	36	16	−	−	PROPN
ejpam-4003	36	17	α−boundary	α−boundary	NOUN
ejpam-4003	36	18	and	and	CCONJ
ejpam-4003	36	19	exterior	exterior	ADJ
ejpam-4003	36	20	sets	set	NOUN
ejpam-4003	36	21	and	and	CCONJ
ejpam-4003	36	22	(	(	PUNCT
ejpam-4003	36	23	i	i	PROPN
ejpam-4003	36	24	,	,	PUNCT
ejpam-4003	36	25	j	j	PROPN
ejpam-4003	36	26	)	)	PUNCT
ejpam-4003	36	27	−mx	−mx	NOUN
ejpam-4003	36	28	−	−	NOUN
ejpam-4003	36	29	β−boundary	β−boundary	NOUN
ejpam-4003	36	30	sets	set	NOUN
ejpam-4003	36	31	and	and	CCONJ
ejpam-4003	36	32	provided	provide	VERB
ejpam-4003	36	33	some	some	DET
ejpam-4003	36	34	fundamental	fundamental	ADJ
ejpam-4003	36	35	properties	property	NOUN
ejpam-4003	36	36	of	of	ADP
ejpam-4003	36	37	such	such	ADJ
ejpam-4003	36	38	sets	set	NOUN
ejpam-4003	36	39	dealing	deal	VERB
ejpam-4003	36	40	with	with	ADP
ejpam-4003	36	41	those	those	DET
ejpam-4003	36	42	spaces	space	NOUN
ejpam-4003	36	43	as	as	ADV
ejpam-4003	36	44	well	well	ADV
ejpam-4003	36	45	,	,	PUNCT
ejpam-4003	36	46	which	which	PRON
ejpam-4003	36	47	was	be	AUX
ejpam-4003	36	48	relevant	relevant	ADJ
ejpam-4003	36	49	to	to	ADP
ejpam-4003	36	50	the	the	DET
ejpam-4003	36	51	current	current	ADJ
ejpam-4003	36	52	research	research	NOUN
ejpam-4003	36	53	.	.	PUNCT
ejpam-4003	37	1	in	in	ADP
ejpam-4003	37	2	this	this	DET
ejpam-4003	37	3	paper	paper	NOUN
ejpam-4003	37	4	,	,	PUNCT
ejpam-4003	37	5	the	the	DET
ejpam-4003	37	6	concepts	concept	NOUN
ejpam-4003	37	7	of	of	ADP
ejpam-4003	37	8	(	(	PUNCT
ejpam-4003	37	9	i	i	PROPN
ejpam-4003	37	10	,	,	PUNCT
ejpam-4003	37	11	j)−mx−β−exterior	j)−mx−β−exterior	ADJ
ejpam-4003	37	12	sets	set	NOUN
ejpam-4003	37	13	are	be	AUX
ejpam-4003	37	14	introduced	introduce	VERB
ejpam-4003	37	15	and	and	CCONJ
ejpam-4003	37	16	some	some	DET
ejpam-4003	37	17	fundamental	fundamental	ADJ
ejpam-4003	37	18	properties	property	NOUN
ejpam-4003	37	19	of	of	ADP
ejpam-4003	37	20	those	those	DET
ejpam-4003	37	21	sets	set	NOUN
ejpam-4003	37	22	are	be	AUX
ejpam-4003	37	23	obtained	obtain	VERB
ejpam-4003	37	24	and	and	CCONJ
ejpam-4003	37	25	some	some	DET
ejpam-4003	37	26	examples	example	NOUN
ejpam-4003	37	27	are	be	AUX
ejpam-4003	37	28	given	give	VERB
ejpam-4003	37	29	for	for	ADP
ejpam-4003	37	30	completing	complete	VERB
ejpam-4003	37	31	some	some	DET
ejpam-4003	37	32	properties	property	NOUN
ejpam-4003	37	33	.	.	PUNCT
ejpam-4003	38	1	lastly	lastly	ADV
ejpam-4003	38	2	,	,	PUNCT
ejpam-4003	38	3	the	the	DET
ejpam-4003	38	4	special	special	ADJ
ejpam-4003	38	5	properties	property	NOUN
ejpam-4003	38	6	of	of	ADP
ejpam-4003	38	7	a	a	DET
ejpam-4003	38	8	biminimal	biminimal	NOUN
ejpam-4003	38	9	structure	structure	NOUN
ejpam-4003	38	10	subspace	subspace	NOUN
ejpam-4003	38	11	and	and	CCONJ
ejpam-4003	38	12	the	the	DET
ejpam-4003	38	13	product	product	NOUN
ejpam-4003	38	14	of	of	ADP
ejpam-4003	38	15	those	those	DET
ejpam-4003	38	16	sets	set	NOUN
ejpam-4003	38	17	are	be	AUX
ejpam-4003	38	18	defined	define	VERB
ejpam-4003	38	19	and	and	CCONJ
ejpam-4003	38	20	then	then	ADV
ejpam-4003	38	21	some	some	DET
ejpam-4003	38	22	fundamental	fundamental	ADJ
ejpam-4003	38	23	properties	property	NOUN
ejpam-4003	38	24	are	be	AUX
ejpam-4003	38	25	provided	provide	VERB
ejpam-4003	38	26	.	.	PUNCT
ejpam-4003	39	1	2	2	X
ejpam-4003	39	2	.	.	NUM
ejpam-4003	39	3	preliminaries	preliminary	NOUN
ejpam-4003	39	4	in	in	ADP
ejpam-4003	39	5	this	this	DET
ejpam-4003	39	6	section	section	NOUN
ejpam-4003	39	7	we	we	PRON
ejpam-4003	39	8	recall	recall	VERB
ejpam-4003	39	9	some	some	DET
ejpam-4003	39	10	notions	notion	NOUN
ejpam-4003	39	11	,	,	PUNCT
ejpam-4003	39	12	notations	notation	NOUN
ejpam-4003	39	13	and	and	CCONJ
ejpam-4003	39	14	previous	previous	ADJ
ejpam-4003	39	15	results	result	NOUN
ejpam-4003	39	16	.	.	PUNCT
ejpam-4003	40	1	definition	definition	NOUN
ejpam-4003	40	2	1	1	NUM
ejpam-4003	40	3	.	.	PUNCT
ejpam-4003	41	1	[	[	X
ejpam-4003	41	2	11	11	NUM
ejpam-4003	41	3	]	]	PUNCT
ejpam-4003	41	4	let	let	VERB
ejpam-4003	41	5	p	p	NOUN
ejpam-4003	41	6	(	(	PUNCT
ejpam-4003	41	7	x	x	NOUN
ejpam-4003	41	8	)	)	PUNCT
ejpam-4003	41	9	be	be	VERB
ejpam-4003	41	10	the	the	DET
ejpam-4003	41	11	power	power	NOUN
ejpam-4003	41	12	of	of	ADP
ejpam-4003	41	13	nonempty	nonempty	ADV
ejpam-4003	41	14	set	set	VERB
ejpam-4003	41	15	x.	x.	NOUN
ejpam-4003	41	16	a	a	DET
ejpam-4003	41	17	subfamily	subfamily	ADV
ejpam-4003	41	18	mx	mx	NOUN
ejpam-4003	41	19	of	of	ADP
ejpam-4003	41	20	p	p	PROPN
ejpam-4003	41	21	(	(	PUNCT
ejpam-4003	41	22	x	x	X
ejpam-4003	41	23	)	)	PUNCT
ejpam-4003	41	24	is	be	AUX
ejpam-4003	41	25	called	call	VERB
ejpam-4003	41	26	a	a	DET
ejpam-4003	41	27	minimal	minimal	ADJ
ejpam-4003	41	28	structure	structure	NOUN
ejpam-4003	41	29	(	(	PUNCT
ejpam-4003	41	30	briefly	briefly	NOUN
ejpam-4003	41	31	m−	m−	PROPN
ejpam-4003	41	32	structure	structure	NOUN
ejpam-4003	41	33	)	)	PUNCT
ejpam-4003	41	34	on	on	ADP
ejpam-4003	41	35	x	x	SYM
ejpam-4003	41	36	if	if	SCONJ
ejpam-4003	41	37	∅	∅	NOUN
ejpam-4003	41	38	∈	∈	PROPN
ejpam-4003	41	39	mx	mx	PROPN
ejpam-4003	41	40	and	and	CCONJ
ejpam-4003	41	41	x	x	PROPN
ejpam-4003	41	42	∈	∈	PROPN
ejpam-4003	41	43	mx	mx	PROPN
ejpam-4003	41	44	.	.	PUNCT
ejpam-4003	42	1	definition	definition	NOUN
ejpam-4003	42	2	2	2	NUM
ejpam-4003	42	3	.	.	PUNCT
ejpam-4003	43	1	[	[	X
ejpam-4003	43	2	2	2	X
ejpam-4003	43	3	]	]	PUNCT
ejpam-4003	43	4	let	let	VERB
ejpam-4003	43	5	x	x	PRON
ejpam-4003	43	6	be	be	AUX
ejpam-4003	43	7	a	a	DET
ejpam-4003	43	8	nonempty	nonempty	ADV
ejpam-4003	43	9	set	set	VERB
ejpam-4003	43	10	and	and	CCONJ
ejpam-4003	43	11	m1	m1	PROPN
ejpam-4003	43	12	x	x	SYM
ejpam-4003	43	13	,	,	PUNCT
ejpam-4003	43	14	m	m	VERB
ejpam-4003	43	15	2	2	NUM
ejpam-4003	43	16	x	x	AUX
ejpam-4003	43	17	be	be	AUX
ejpam-4003	43	18	minimal	minimal	ADJ
ejpam-4003	43	19	structures	structure	NOUN
ejpam-4003	43	20	on	on	ADP
ejpam-4003	43	21	x.	x.	NOUN
ejpam-4003	43	22	the	the	DET
ejpam-4003	43	23	triple	triple	ADJ
ejpam-4003	43	24	(	(	PUNCT
ejpam-4003	43	25	x	x	NOUN
ejpam-4003	43	26	,	,	PUNCT
ejpam-4003	43	27	m1	m1	PROPN
ejpam-4003	43	28	x	x	SYM
ejpam-4003	43	29	,	,	PUNCT
ejpam-4003	43	30	m	m	PROPN
ejpam-4003	43	31	2	2	NUM
ejpam-4003	43	32	x	x	NOUN
ejpam-4003	43	33	)	)	PUNCT
ejpam-4003	43	34	is	be	AUX
ejpam-4003	43	35	called	call	VERB
ejpam-4003	43	36	a	a	DET
ejpam-4003	43	37	biminimal	biminimal	NOUN
ejpam-4003	43	38	structure	structure	NOUN
ejpam-4003	43	39	space	space	NOUN
ejpam-4003	43	40	(	(	PUNCT
ejpam-4003	43	41	briefly	briefly	NOUN
ejpam-4003	43	42	bss	bss	PROPN
ejpam-4003	43	43	)	)	PUNCT
ejpam-4003	43	44	or	or	CCONJ
ejpam-4003	43	45	a	a	DET
ejpam-4003	43	46	bispace	bispace	NOUN
ejpam-4003	43	47	(	(	PUNCT
ejpam-4003	43	48	briefly	briefly	NOUN
ejpam-4003	43	49	bi	bi	ADJ
ejpam-4003	44	1	m−space	m−space	PROPN
ejpam-4003	45	1	[	[	X
ejpam-4003	45	2	7	7	NUM
ejpam-4003	45	3	]	]	SYM
ejpam-4003	45	4	)	)	PUNCT
ejpam-4003	45	5	lemma	lemma	PROPN
ejpam-4003	45	6	1	1	NUM
ejpam-4003	45	7	.	.	PUNCT
ejpam-4003	46	1	[	[	X
ejpam-4003	46	2	3	3	X
ejpam-4003	46	3	]	]	X
ejpam-4003	46	4	let	let	VERB
ejpam-4003	46	5	(	(	PUNCT
ejpam-4003	46	6	x	x	NOUN
ejpam-4003	46	7	,	,	PUNCT
ejpam-4003	46	8	m1	m1	PROPN
ejpam-4003	46	9	x	x	SYM
ejpam-4003	46	10	,	,	PUNCT
ejpam-4003	46	11	m	m	PROPN
ejpam-4003	46	12	2	2	NUM
ejpam-4003	46	13	x	x	NOUN
ejpam-4003	46	14	)	)	PUNCT
ejpam-4003	46	15	be	be	VERB
ejpam-4003	46	16	a	a	DET
ejpam-4003	46	17	biminimal	biminimal	NOUN
ejpam-4003	46	18	structure	structure	NOUN
ejpam-4003	46	19	space	space	NOUN
ejpam-4003	46	20	and	and	CCONJ
ejpam-4003	46	21	a	a	DET
ejpam-4003	46	22	be	be	AUX
ejpam-4003	46	23	a	a	DET
ejpam-4003	46	24	subset	subset	NOUN
ejpam-4003	46	25	of	of	ADP
ejpam-4003	46	26	x.	x.	NOUN
ejpam-4003	46	27	it	it	PRON
ejpam-4003	46	28	follows	follow	VERB
ejpam-4003	46	29	that	that	SCONJ
ejpam-4003	46	30	:	:	PUNCT
ejpam-4003	46	31	1	1	X
ejpam-4003	46	32	.	.	X
ejpam-4003	46	33	a	a	PRON
ejpam-4003	46	34	is	be	AUX
ejpam-4003	46	35	(	(	PUNCT
ejpam-4003	46	36	i	i	NOUN
ejpam-4003	46	37	,	,	PUNCT
ejpam-4003	46	38	j)−mx−regular	j)−mx−regular	PROPN
ejpam-4003	46	39	−closed	−close	VERB
ejpam-4003	46	40	if	if	SCONJ
ejpam-4003	46	41	and	and	CCONJ
ejpam-4003	46	42	only	only	ADV
ejpam-4003	46	43	if	if	SCONJ
ejpam-4003	46	44	a	a	DET
ejpam-4003	46	45	=	=	SYM
ejpam-4003	46	46	mi	mi	X
ejpam-4003	46	47	xcl(m	xcl(m	PROPN
ejpam-4003	46	48	j	j	PROPN
ejpam-4003	46	49	xint(a	xint(a	PROPN
ejpam-4003	46	50	)	)	PUNCT
ejpam-4003	46	51	)	)	PUNCT
ejpam-4003	46	52	,	,	PUNCT
ejpam-4003	47	1	2	2	X
ejpam-4003	47	2	.	.	X
ejpam-4003	47	3	a	a	PRON
ejpam-4003	47	4	is	be	AUX
ejpam-4003	47	5	(	(	PUNCT
ejpam-4003	47	6	i	i	PROPN
ejpam-4003	47	7	,	,	PUNCT
ejpam-4003	47	8	j)−mx−semi−closed	j)−mx−semi−close	VERB
ejpam-4003	47	9	if	if	SCONJ
ejpam-4003	47	10	and	and	CCONJ
ejpam-4003	47	11	only	only	ADV
ejpam-4003	47	12	if	if	SCONJ
ejpam-4003	47	13	mi	mi	PROPN
ejpam-4003	48	1	xint(m	xint(m	PROPN
ejpam-4003	48	2	j	j	PROPN
ejpam-4003	48	3	xcl(a	xcl(a	PROPN
ejpam-4003	48	4	)	)	PUNCT
ejpam-4003	48	5	)	)	PUNCT
ejpam-4003	49	1	⊆	⊆	NUM
ejpam-4003	49	2	a	a	DET
ejpam-4003	49	3	,	,	PUNCT
ejpam-4003	49	4	3	3	X
ejpam-4003	49	5	.	.	X
ejpam-4003	50	1	a	a	PRON
ejpam-4003	50	2	is	be	AUX
ejpam-4003	50	3	(	(	PUNCT
ejpam-4003	50	4	i	i	NOUN
ejpam-4003	50	5	,	,	PUNCT
ejpam-4003	50	6	j)−mx−preclosed	j)−mx−preclose	VERB
ejpam-4003	50	7	if	if	SCONJ
ejpam-4003	50	8	and	and	CCONJ
ejpam-4003	50	9	only	only	ADV
ejpam-4003	50	10	if	if	SCONJ
ejpam-4003	50	11	mi	mi	PROPN
ejpam-4003	50	12	xcl(m	xcl(m	PROPN
ejpam-4003	50	13	j	j	PROPN
ejpam-4003	50	14	xint(a	xint(a	PROPN
ejpam-4003	50	15	)	)	PUNCT
ejpam-4003	50	16	)	)	PUNCT
ejpam-4003	51	1	⊆	⊆	NUM
ejpam-4003	51	2	a	a	DET
ejpam-4003	51	3	,	,	PUNCT
ejpam-4003	51	4	4	4	X
ejpam-4003	51	5	.	.	X
ejpam-4003	52	1	a	a	PRON
ejpam-4003	52	2	is	be	AUX
ejpam-4003	52	3	(	(	PUNCT
ejpam-4003	52	4	i	i	PROPN
ejpam-4003	52	5	,	,	PUNCT
ejpam-4003	52	6	j)−mx	j)−mx	PROPN
ejpam-4003	52	7	−	−	PROPN
ejpam-4003	53	1	α−closed	α−close	VERB
ejpam-4003	53	2	if	if	SCONJ
ejpam-4003	53	3	and	and	CCONJ
ejpam-4003	53	4	only	only	ADV
ejpam-4003	53	5	if	if	SCONJ
ejpam-4003	53	6	mi	mi	PROPN
ejpam-4003	53	7	xcl(m	xcl(m	PROPN
ejpam-4003	53	8	j	j	PROPN
ejpam-4003	54	1	xint(m	xint(m	INTJ
ejpam-4003	54	2	i	i	PROPN
ejpam-4003	54	3	xcl(a	xcl(a	PROPN
ejpam-4003	54	4	)	)	PUNCT
ejpam-4003	54	5	)	)	PUNCT
ejpam-4003	54	6	)	)	PUNCT
ejpam-4003	55	1	⊆	⊆	NUM
ejpam-4003	55	2	a	a	DET
ejpam-4003	55	3	,	,	PUNCT
ejpam-4003	55	4	5	5	NUM
ejpam-4003	55	5	.	.	X
ejpam-4003	55	6	a	a	PRON
ejpam-4003	55	7	is	be	AUX
ejpam-4003	55	8	(	(	PUNCT
ejpam-4003	55	9	i	i	PROPN
ejpam-4003	55	10	,	,	PUNCT
ejpam-4003	55	11	j)−mx	j)−mx	PROPN
ejpam-4003	55	12	−	−	PROPN
ejpam-4003	55	13	β−closed	β−close	VERB
ejpam-4003	55	14	if	if	SCONJ
ejpam-4003	55	15	and	and	CCONJ
ejpam-4003	55	16	only	only	ADV
ejpam-4003	55	17	if	if	SCONJ
ejpam-4003	55	18	mi	mi	PROPN
ejpam-4003	56	1	xint(m	xint(m	INTJ
ejpam-4003	56	2	j	j	PROPN
ejpam-4003	56	3	xcl(m	xcl(m	PROPN
ejpam-4003	56	4	i	i	PROPN
ejpam-4003	56	5	xint(a	xint(a	PROPN
ejpam-4003	56	6	)	)	PUNCT
ejpam-4003	56	7	)	)	PUNCT
ejpam-4003	56	8	)	)	PUNCT
ejpam-4003	57	1	⊆	⊆	NUM
ejpam-4003	57	2	a.	a.	NOUN
ejpam-4003	57	3	definition	definition	NOUN
ejpam-4003	57	4	3	3	NUM
ejpam-4003	57	5	.	.	PUNCT
ejpam-4003	58	1	[	[	X
ejpam-4003	58	2	9	9	NUM
ejpam-4003	58	3	]	]	X
ejpam-4003	58	4	let	let	VERB
ejpam-4003	58	5	(	(	PUNCT
ejpam-4003	58	6	x	x	NOUN
ejpam-4003	58	7	,	,	PUNCT
ejpam-4003	58	8	m1	m1	PROPN
ejpam-4003	58	9	x	x	SYM
ejpam-4003	58	10	,	,	PUNCT
ejpam-4003	58	11	m	m	PROPN
ejpam-4003	58	12	2	2	NUM
ejpam-4003	58	13	x	x	NOUN
ejpam-4003	58	14	)	)	PUNCT
ejpam-4003	58	15	be	be	VERB
ejpam-4003	58	16	a	a	DET
ejpam-4003	58	17	biminimal	biminimal	NOUN
ejpam-4003	58	18	structure	structure	NOUN
ejpam-4003	58	19	space	space	NOUN
ejpam-4003	58	20	and	and	CCONJ
ejpam-4003	58	21	a	a	DET
ejpam-4003	58	22	be	be	AUX
ejpam-4003	58	23	a	a	DET
ejpam-4003	58	24	subset	subset	NOUN
ejpam-4003	58	25	of	of	ADP
ejpam-4003	58	26	x.	x.	NOUN
ejpam-4003	58	27	then	then	ADV
ejpam-4003	58	28	,	,	PUNCT
ejpam-4003	58	29	mij	mij	NOUN
ejpam-4003	58	30	x	x	PUNCT
ejpam-4003	58	31	−β−closure	−β−closure	NOUN
ejpam-4003	58	32	of	of	ADP
ejpam-4003	58	33	a	a	PRON
ejpam-4003	58	34	and	and	CCONJ
ejpam-4003	58	35	the	the	DET
ejpam-4003	58	36	mij	mij	NOUN
ejpam-4003	58	37	x	x	NOUN
ejpam-4003	58	38	−β−interior	−β−interior	NOUN
ejpam-4003	58	39	of	of	ADP
ejpam-4003	58	40	a	a	PRON
ejpam-4003	58	41	where	where	SCONJ
ejpam-4003	58	42	i	i	PRON
ejpam-4003	58	43	,	,	PUNCT
ejpam-4003	58	44	j	j	PROPN
ejpam-4003	58	45	=	=	SYM
ejpam-4003	58	46	1	1	NUM
ejpam-4003	58	47	,	,	PUNCT
ejpam-4003	58	48	2	2	NUM
ejpam-4003	58	49	and	and	CCONJ
ejpam-4003	58	50	i	i	PRON
ejpam-4003	58	51	6=	6=	PROPN
ejpam-4003	58	52	j.	j.	PROPN
ejpam-4003	58	53	are	be	AUX
ejpam-4003	58	54	defined	define	VERB
ejpam-4003	58	55	as	as	SCONJ
ejpam-4003	58	56	follows	follow	VERB
ejpam-4003	58	57	:	:	PUNCT
ejpam-4003	58	58	t.	t.	PROPN
ejpam-4003	58	59	prasertsang	prasertsang	PROPN
ejpam-4003	58	60	,	,	PUNCT
ejpam-4003	58	61	p.	p.	PROPN
ejpam-4003	58	62	prasertsang	prasertsang	PROPN
ejpam-4003	58	63	/	/	SYM
ejpam-4003	58	64	eur	eur	PROPN
ejpam-4003	58	65	.	.	PUNCT
ejpam-4003	59	1	j.	j.	PROPN
ejpam-4003	59	2	pure	pure	PROPN
ejpam-4003	59	3	appl	appl	PROPN
ejpam-4003	59	4	.	.	PROPN
ejpam-4003	59	5	math	math	PROPN
ejpam-4003	59	6	,	,	PUNCT
ejpam-4003	59	7	14	14	NUM
ejpam-4003	59	8	(	(	PUNCT
ejpam-4003	59	9	3	3	NUM
ejpam-4003	59	10	)	)	PUNCT
ejpam-4003	59	11	(	(	PUNCT
ejpam-4003	59	12	2021	2021	NUM
ejpam-4003	59	13	)	)	PUNCT
ejpam-4003	59	14	,	,	PUNCT
ejpam-4003	59	15	915	915	NUM
ejpam-4003	59	16	-	-	SYM
ejpam-4003	59	17	922	922	NUM
ejpam-4003	59	18	917	917	NUM
ejpam-4003	59	19	1	1	NUM
ejpam-4003	59	20	.	.	PUNCT
ejpam-4003	60	1	mij	mij	PROPN
ejpam-4003	60	2	xclb(a	xclb(a	PROPN
ejpam-4003	60	3	)	)	PUNCT
ejpam-4003	61	1	=	=	SYM
ejpam-4003	61	2	⋂	⋂	PROPN
ejpam-4003	61	3	{	{	PUNCT
ejpam-4003	61	4	f	f	NOUN
ejpam-4003	61	5	:	:	PUNCT
ejpam-4003	61	6	a	a	DET
ejpam-4003	61	7	⊆	⊆	NUM
ejpam-4003	61	8	f	f	NUM
ejpam-4003	61	9	,	,	PUNCT
ejpam-4003	61	10	f	f	PROPN
ejpam-4003	61	11	is	be	AUX
ejpam-4003	61	12	(	(	PUNCT
ejpam-4003	61	13	i	i	NOUN
ejpam-4003	61	14	,	,	PUNCT
ejpam-4003	61	15	j)−mx	j)−mx	PROPN
ejpam-4003	61	16	−	−	PROPN
ejpam-4003	61	17	β−closed	β−closed	PROPN
ejpam-4003	61	18	}	}	PUNCT
ejpam-4003	61	19	,	,	PUNCT
ejpam-4003	61	20	2	2	X
ejpam-4003	61	21	.	.	PUNCT
ejpam-4003	61	22	mij	mij	NOUN
ejpam-4003	61	23	xintb(a	xintb(a	PROPN
ejpam-4003	61	24	)	)	PUNCT
ejpam-4003	61	25	=	=	SYM
ejpam-4003	61	26	⋃	⋃	NOUN
ejpam-4003	61	27	{	{	PUNCT
ejpam-4003	61	28	u	u	NOUN
ejpam-4003	61	29	:	:	PUNCT
ejpam-4003	61	30	u	u	NOUN
ejpam-4003	61	31	⊆	⊆	PROPN
ejpam-4003	61	32	a	a	PRON
ejpam-4003	61	33	,	,	PUNCT
ejpam-4003	61	34	u	u	NOUN
ejpam-4003	61	35	is	be	AUX
ejpam-4003	61	36	(	(	PUNCT
ejpam-4003	61	37	i	i	NOUN
ejpam-4003	61	38	,	,	PUNCT
ejpam-4003	61	39	j)−mx	j)−mx	PROPN
ejpam-4003	62	1	−	−	NOUN
ejpam-4003	62	2	β−	β−	NOUN
ejpam-4003	62	3	open	open	ADJ
ejpam-4003	62	4	}	}	PUNCT
ejpam-4003	62	5	.	.	PUNCT
ejpam-4003	63	1	lemma	lemma	PROPN
ejpam-4003	63	2	2	2	NUM
ejpam-4003	63	3	.	.	PUNCT
ejpam-4003	64	1	[	[	X
ejpam-4003	64	2	9	9	NUM
ejpam-4003	64	3	]	]	X
ejpam-4003	64	4	let	let	VERB
ejpam-4003	64	5	(	(	PUNCT
ejpam-4003	64	6	x	x	NOUN
ejpam-4003	64	7	,	,	PUNCT
ejpam-4003	64	8	m1	m1	PROPN
ejpam-4003	64	9	x	x	SYM
ejpam-4003	64	10	,	,	PUNCT
ejpam-4003	64	11	m	m	PROPN
ejpam-4003	64	12	2	2	NUM
ejpam-4003	64	13	x	x	NOUN
ejpam-4003	64	14	)	)	PUNCT
ejpam-4003	64	15	be	be	VERB
ejpam-4003	64	16	a	a	DET
ejpam-4003	64	17	biminimal	biminimal	NOUN
ejpam-4003	64	18	structure	structure	NOUN
ejpam-4003	64	19	space	space	NOUN
ejpam-4003	64	20	and	and	CCONJ
ejpam-4003	64	21	a	a	DET
ejpam-4003	64	22	,	,	PUNCT
ejpam-4003	64	23	b	b	PROPN
ejpam-4003	64	24	be	be	AUX
ejpam-4003	64	25	subsets	subset	NOUN
ejpam-4003	64	26	of	of	ADP
ejpam-4003	64	27	x	x	PRON
ejpam-4003	64	28	,	,	PUNCT
ejpam-4003	64	29	the	the	DET
ejpam-4003	64	30	following	follow	VERB
ejpam-4003	64	31	hold	hold	NOUN
ejpam-4003	64	32	:	:	PUNCT
ejpam-4003	64	33	1	1	X
ejpam-4003	64	34	.	.	X
ejpam-4003	64	35	mij	mij	PROPN
ejpam-4003	64	36	xclb(∅	xclb(∅	X
ejpam-4003	64	37	)	)	PUNCT
ejpam-4003	65	1	=	=	SYM
ejpam-4003	65	2	∅	∅	NOUN
ejpam-4003	65	3	,	,	PUNCT
ejpam-4003	65	4	mij	mij	NOUN
ejpam-4003	65	5	xclb(x	xclb(x	PROPN
ejpam-4003	65	6	)	)	PUNCT
ejpam-4003	65	7	=	=	SYM
ejpam-4003	65	8	x	x	X
ejpam-4003	65	9	,	,	PUNCT
ejpam-4003	65	10	mij	mij	PROPN
ejpam-4003	65	11	xintb(∅	xintb(∅	PROPN
ejpam-4003	65	12	)	)	PUNCT
ejpam-4003	65	13	=	=	NOUN
ejpam-4003	65	14	∅	∅	NOUN
ejpam-4003	65	15	and	and	CCONJ
ejpam-4003	65	16	mij	mij	PROPN
ejpam-4003	65	17	xintb(x	xintb(x	PROPN
ejpam-4003	65	18	)	)	PUNCT
ejpam-4003	65	19	=	=	SYM
ejpam-4003	65	20	x	x	X
ejpam-4003	65	21	,	,	PUNCT
ejpam-4003	65	22	2	2	NUM
ejpam-4003	65	23	.	.	PUNCT
ejpam-4003	65	24	a	a	DET
ejpam-4003	65	25	⊆	⊆	NUM
ejpam-4003	65	26	mij	mij	X
ejpam-4003	65	27	xclb(a	xclb(a	PROPN
ejpam-4003	65	28	)	)	PUNCT
ejpam-4003	65	29	and	and	CCONJ
ejpam-4003	65	30	mij	mij	X
ejpam-4003	65	31	xintb(a	xintb(a	PROPN
ejpam-4003	65	32	)	)	PUNCT
ejpam-4003	65	33	⊆	⊆	NUM
ejpam-4003	65	34	a	a	PRON
ejpam-4003	65	35	,	,	PUNCT
ejpam-4003	65	36	3	3	X
ejpam-4003	65	37	.	.	PUNCT
ejpam-4003	66	1	if	if	SCONJ
ejpam-4003	66	2	a	a	DET
ejpam-4003	66	3	⊆	⊆	NUM
ejpam-4003	66	4	b	b	NOUN
ejpam-4003	66	5	then	then	ADV
ejpam-4003	66	6	mij	mij	VERB
ejpam-4003	66	7	xclb(a	xclb(a	PROPN
ejpam-4003	66	8	)	)	PUNCT
ejpam-4003	66	9	⊆	⊆	NUM
ejpam-4003	66	10	mij	mij	PROPN
ejpam-4003	66	11	xclb(b	xclb(b	PROPN
ejpam-4003	66	12	)	)	PUNCT
ejpam-4003	66	13	and	and	CCONJ
ejpam-4003	66	14	mij	mij	X
ejpam-4003	66	15	xintb(a	xintb(a	PROPN
ejpam-4003	66	16	)	)	PUNCT
ejpam-4003	66	17	⊆	⊆	NUM
ejpam-4003	66	18	mij	mij	X
ejpam-4003	66	19	xintb(b	xintb(b	PROPN
ejpam-4003	66	20	)	)	PUNCT
ejpam-4003	66	21	.	.	PUNCT
ejpam-4003	67	1	lemma	lemma	PROPN
ejpam-4003	67	2	3	3	X
ejpam-4003	67	3	.	.	PUNCT
ejpam-4003	68	1	[	[	X
ejpam-4003	68	2	9	9	NUM
ejpam-4003	68	3	]	]	X
ejpam-4003	68	4	let	let	VERB
ejpam-4003	68	5	(	(	PUNCT
ejpam-4003	68	6	x	x	NOUN
ejpam-4003	68	7	,	,	PUNCT
ejpam-4003	68	8	m1	m1	PROPN
ejpam-4003	68	9	x	x	SYM
ejpam-4003	68	10	,	,	PUNCT
ejpam-4003	68	11	m	m	PROPN
ejpam-4003	68	12	2	2	NUM
ejpam-4003	68	13	x	x	NOUN
ejpam-4003	68	14	)	)	PUNCT
ejpam-4003	68	15	be	be	VERB
ejpam-4003	68	16	a	a	DET
ejpam-4003	68	17	biminimal	biminimal	NOUN
ejpam-4003	68	18	structure	structure	NOUN
ejpam-4003	68	19	space	space	NOUN
ejpam-4003	68	20	and	and	CCONJ
ejpam-4003	68	21	a	a	DET
ejpam-4003	68	22	be	be	AUX
ejpam-4003	68	23	a	a	DET
ejpam-4003	68	24	subset	subset	NOUN
ejpam-4003	68	25	of	of	ADP
ejpam-4003	68	26	x.	x.	NOUN
ejpam-4003	68	27	the	the	DET
ejpam-4003	68	28	following	follow	VERB
ejpam-4003	68	29	properties	property	NOUN
ejpam-4003	68	30	hold	hold	VERB
ejpam-4003	68	31	:	:	PUNCT
ejpam-4003	68	32	1	1	X
ejpam-4003	68	33	.	.	X
ejpam-4003	68	34	mij	mij	PROPN
ejpam-4003	68	35	xclb(a	xclb(a	PROPN
ejpam-4003	68	36	)	)	PUNCT
ejpam-4003	68	37	is	be	AUX
ejpam-4003	68	38	(	(	PUNCT
ejpam-4003	68	39	i	i	NOUN
ejpam-4003	68	40	,	,	PUNCT
ejpam-4003	68	41	j)−mx	j)−mx	PROPN
ejpam-4003	68	42	−	−	PROPN
ejpam-4003	68	43	β−closed	β−closed	PROPN
ejpam-4003	68	44	,	,	PUNCT
ejpam-4003	68	45	2	2	NUM
ejpam-4003	68	46	.	.	PUNCT
ejpam-4003	68	47	mij	mij	PROPN
ejpam-4003	68	48	xintb(a	xintb(a	PROPN
ejpam-4003	68	49	)	)	PUNCT
ejpam-4003	69	1	is	be	AUX
ejpam-4003	69	2	(	(	PUNCT
ejpam-4003	69	3	i	i	NOUN
ejpam-4003	69	4	,	,	PUNCT
ejpam-4003	69	5	j)−mx	j)−mx	PROPN
ejpam-4003	69	6	−	−	PROPN
ejpam-4003	70	1	β−open	β−open	PROPN
ejpam-4003	70	2	,	,	PUNCT
ejpam-4003	70	3	3	3	X
ejpam-4003	70	4	.	.	X
ejpam-4003	71	1	a	a	PRON
ejpam-4003	71	2	is	be	AUX
ejpam-4003	71	3	(	(	PUNCT
ejpam-4003	71	4	i	i	PROPN
ejpam-4003	71	5	,	,	PUNCT
ejpam-4003	71	6	j)−mx	j)−mx	PROPN
ejpam-4003	71	7	−	−	PROPN
ejpam-4003	71	8	β−closed	β−close	VERB
ejpam-4003	71	9	if	if	SCONJ
ejpam-4003	71	10	and	and	CCONJ
ejpam-4003	71	11	only	only	ADV
ejpam-4003	71	12	if	if	SCONJ
ejpam-4003	71	13	mij	mij	X
ejpam-4003	71	14	xclb(a	xclb(a	PROPN
ejpam-4003	71	15	)	)	PUNCT
ejpam-4003	71	16	=	=	SYM
ejpam-4003	72	1	a	a	PRON
ejpam-4003	72	2	,	,	PUNCT
ejpam-4003	72	3	4	4	X
ejpam-4003	72	4	.	.	X
ejpam-4003	73	1	a	a	PRON
ejpam-4003	73	2	is	be	AUX
ejpam-4003	73	3	(	(	PUNCT
ejpam-4003	73	4	i	i	NOUN
ejpam-4003	73	5	,	,	PUNCT
ejpam-4003	73	6	j)−mx	j)−mx	PROPN
ejpam-4003	74	1	−	−	PROPN
ejpam-4003	75	1	β−open	β−open	PUNCT
ejpam-4003	75	2	if	if	SCONJ
ejpam-4003	75	3	and	and	CCONJ
ejpam-4003	75	4	only	only	ADV
ejpam-4003	75	5	if	if	SCONJ
ejpam-4003	75	6	mij	mij	X
ejpam-4003	75	7	xintb(a	xintb(a	NOUN
ejpam-4003	75	8	)	)	PUNCT
ejpam-4003	75	9	=	=	PUNCT
ejpam-4003	75	10	a.	a.	NOUN
ejpam-4003	75	11	lemma	lemma	PROPN
ejpam-4003	75	12	4	4	X
ejpam-4003	75	13	.	.	PUNCT
ejpam-4003	76	1	[	[	X
ejpam-4003	76	2	9	9	NUM
ejpam-4003	76	3	]	]	X
ejpam-4003	76	4	let	let	VERB
ejpam-4003	76	5	(	(	PUNCT
ejpam-4003	76	6	x	x	NOUN
ejpam-4003	76	7	,	,	PUNCT
ejpam-4003	76	8	m1	m1	PROPN
ejpam-4003	76	9	x	x	SYM
ejpam-4003	76	10	,	,	PUNCT
ejpam-4003	76	11	m	m	PROPN
ejpam-4003	76	12	2	2	NUM
ejpam-4003	76	13	x	x	NOUN
ejpam-4003	76	14	)	)	PUNCT
ejpam-4003	76	15	be	be	VERB
ejpam-4003	76	16	a	a	DET
ejpam-4003	76	17	biminimal	biminimal	NOUN
ejpam-4003	76	18	structure	structure	NOUN
ejpam-4003	76	19	space	space	NOUN
ejpam-4003	76	20	and	and	CCONJ
ejpam-4003	76	21	a	a	DET
ejpam-4003	76	22	,	,	PUNCT
ejpam-4003	76	23	b	b	PROPN
ejpam-4003	76	24	be	be	AUX
ejpam-4003	76	25	subsets	subset	NOUN
ejpam-4003	76	26	of	of	ADP
ejpam-4003	76	27	x	x	PRON
ejpam-4003	76	28	,	,	PUNCT
ejpam-4003	76	29	the	the	DET
ejpam-4003	76	30	following	follow	VERB
ejpam-4003	76	31	hold	hold	NOUN
ejpam-4003	76	32	:	:	PUNCT
ejpam-4003	76	33	1	1	X
ejpam-4003	76	34	.	.	X
ejpam-4003	76	35	if	if	SCONJ
ejpam-4003	76	36	a	a	PRON
ejpam-4003	76	37	and	and	CCONJ
ejpam-4003	76	38	b	b	NOUN
ejpam-4003	76	39	are	be	AUX
ejpam-4003	76	40	(	(	PUNCT
ejpam-4003	76	41	i	i	NOUN
ejpam-4003	76	42	,	,	PUNCT
ejpam-4003	76	43	j)−mx	j)−mx	PROPN
ejpam-4003	76	44	−	−	PROPN
ejpam-4003	76	45	β−closed	β−close	VERB
ejpam-4003	76	46	then	then	ADV
ejpam-4003	76	47	a	a	DET
ejpam-4003	76	48	∩b	∩b	NOUN
ejpam-4003	76	49	is	be	AUX
ejpam-4003	76	50	(	(	PUNCT
ejpam-4003	76	51	i	i	NOUN
ejpam-4003	76	52	,	,	PUNCT
ejpam-4003	76	53	j)−mx	j)−mx	PROPN
ejpam-4003	76	54	−	−	PROPN
ejpam-4003	76	55	β−closed	β−closed	PROPN
ejpam-4003	76	56	,	,	PUNCT
ejpam-4003	76	57	2	2	NUM
ejpam-4003	76	58	.	.	PUNCT
ejpam-4003	77	1	if	if	SCONJ
ejpam-4003	77	2	a	a	PRON
ejpam-4003	77	3	and	and	CCONJ
ejpam-4003	77	4	b	b	NOUN
ejpam-4003	77	5	are	be	AUX
ejpam-4003	77	6	(	(	PUNCT
ejpam-4003	77	7	i	i	NOUN
ejpam-4003	77	8	,	,	PUNCT
ejpam-4003	77	9	j)−mx	j)−mx	PROPN
ejpam-4003	78	1	−	−	PROPN
ejpam-4003	79	1	β−open	β−open	PUNCT
ejpam-4003	79	2	then	then	ADV
ejpam-4003	79	3	a	a	DET
ejpam-4003	79	4	∪b	∪b	X
ejpam-4003	79	5	is	be	AUX
ejpam-4003	79	6	(	(	PUNCT
ejpam-4003	79	7	i	i	NOUN
ejpam-4003	79	8	,	,	PUNCT
ejpam-4003	79	9	j)−mx	j)−mx	PROPN
ejpam-4003	79	10	−	−	PROPN
ejpam-4003	79	11	β−open	β−open	PROPN
ejpam-4003	79	12	.	.	PUNCT
ejpam-4003	80	1	lemma	lemma	PROPN
ejpam-4003	80	2	5	5	NUM
ejpam-4003	80	3	.	.	PUNCT
ejpam-4003	81	1	[	[	X
ejpam-4003	81	2	9	9	NUM
ejpam-4003	81	3	]	]	X
ejpam-4003	81	4	let	let	VERB
ejpam-4003	81	5	(	(	PUNCT
ejpam-4003	81	6	x	x	NOUN
ejpam-4003	81	7	,	,	PUNCT
ejpam-4003	81	8	m1	m1	PROPN
ejpam-4003	81	9	x	x	SYM
ejpam-4003	81	10	,	,	PUNCT
ejpam-4003	81	11	m	m	PROPN
ejpam-4003	81	12	2	2	NUM
ejpam-4003	81	13	x	x	NOUN
ejpam-4003	81	14	)	)	PUNCT
ejpam-4003	81	15	be	be	VERB
ejpam-4003	81	16	a	a	DET
ejpam-4003	81	17	biminimal	biminimal	NOUN
ejpam-4003	81	18	structure	structure	NOUN
ejpam-4003	81	19	space	space	NOUN
ejpam-4003	81	20	and	and	CCONJ
ejpam-4003	81	21	a	a	DET
ejpam-4003	81	22	a	a	DET
ejpam-4003	81	23	subset	subset	NOUN
ejpam-4003	81	24	of	of	ADP
ejpam-4003	81	25	x	x	NOUN
ejpam-4003	81	26	:	:	PUNCT
ejpam-4003	81	27	1	1	X
ejpam-4003	81	28	.	.	PUNCT
ejpam-4003	81	29	mij	mij	NOUN
ejpam-4003	81	30	xintb(x\a	xintb(x\a	NOUN
ejpam-4003	81	31	)	)	PUNCT
ejpam-4003	82	1	=	=	PUNCT
ejpam-4003	83	1	x\mij	x\mij	PROPN
ejpam-4003	83	2	xclb(a	xclb(a	PROPN
ejpam-4003	83	3	)	)	PUNCT
ejpam-4003	83	4	,	,	PUNCT
ejpam-4003	83	5	2	2	X
ejpam-4003	83	6	.	.	PUNCT
ejpam-4003	83	7	mij	mij	NOUN
ejpam-4003	83	8	xclb(x\a	xclb(x\a	PROPN
ejpam-4003	83	9	)	)	PUNCT
ejpam-4003	83	10	=	=	PUNCT
ejpam-4003	84	1	x\mij	x\mij	NUM
ejpam-4003	84	2	xintb(a	xintb(a	NOUN
ejpam-4003	84	3	)	)	PUNCT
ejpam-4003	84	4	.	.	PUNCT
ejpam-4003	85	1	lemma	lemma	PROPN
ejpam-4003	85	2	6	6	NUM
ejpam-4003	85	3	.	.	PUNCT
ejpam-4003	86	1	[	[	X
ejpam-4003	86	2	9	9	NUM
ejpam-4003	86	3	]	]	X
ejpam-4003	86	4	let	let	VERB
ejpam-4003	86	5	(	(	PUNCT
ejpam-4003	86	6	x	x	NOUN
ejpam-4003	86	7	,	,	PUNCT
ejpam-4003	86	8	m1	m1	PROPN
ejpam-4003	86	9	x	x	SYM
ejpam-4003	86	10	,	,	PUNCT
ejpam-4003	86	11	m	m	PROPN
ejpam-4003	86	12	2	2	NUM
ejpam-4003	86	13	x	x	NOUN
ejpam-4003	86	14	)	)	PUNCT
ejpam-4003	86	15	be	be	VERB
ejpam-4003	86	16	a	a	DET
ejpam-4003	86	17	biminimal	biminimal	NOUN
ejpam-4003	86	18	structure	structure	NOUN
ejpam-4003	86	19	space	space	NOUN
ejpam-4003	86	20	and	and	CCONJ
ejpam-4003	86	21	a	a	DET
ejpam-4003	86	22	a	a	DET
ejpam-4003	86	23	subset	subset	NOUN
ejpam-4003	86	24	of	of	ADP
ejpam-4003	86	25	x	x	PRON
ejpam-4003	86	26	,	,	PUNCT
ejpam-4003	86	27	for	for	ADP
ejpam-4003	86	28	any	any	DET
ejpam-4003	86	29	i	i	PROPN
ejpam-4003	86	30	,	,	PUNCT
ejpam-4003	86	31	j	j	PROPN
ejpam-4003	86	32	=	=	SYM
ejpam-4003	86	33	1	1	NUM
ejpam-4003	86	34	,	,	PUNCT
ejpam-4003	86	35	2	2	NUM
ejpam-4003	86	36	and	and	CCONJ
ejpam-4003	86	37	i	i	PRON
ejpam-4003	86	38	6=	6=	PROPN
ejpam-4003	86	39	j	j	PROPN
ejpam-4003	86	40	,	,	PUNCT
ejpam-4003	86	41	1	1	NUM
ejpam-4003	86	42	.	.	PUNCT
ejpam-4003	86	43	mij	mij	X
ejpam-4003	86	44	xbdrb(a	xbdrb(a	NOUN
ejpam-4003	86	45	)	)	PUNCT
ejpam-4003	86	46	∩mij	∩mij	ADJ
ejpam-4003	86	47	xintb(x\a	xintb(x\a	NOUN
ejpam-4003	86	48	)	)	PUNCT
ejpam-4003	87	1	=	=	NOUN
ejpam-4003	87	2	∅	∅	NOUN
ejpam-4003	87	3	,	,	PUNCT
ejpam-4003	87	4	2	2	NUM
ejpam-4003	87	5	.	.	PUNCT
ejpam-4003	87	6	mij	mij	NOUN
ejpam-4003	87	7	xclb(x\a	xclb(x\a	PROPN
ejpam-4003	87	8	)	)	PUNCT
ejpam-4003	87	9	=	=	SYM
ejpam-4003	87	10	mij	mij	X
ejpam-4003	87	11	xbdrb(a	xbdrb(a	NOUN
ejpam-4003	87	12	)	)	PUNCT
ejpam-4003	87	13	∪mij	∪mij	NOUN
ejpam-4003	87	14	xintb(a	xintb(a	NOUN
ejpam-4003	87	15	)	)	PUNCT
ejpam-4003	87	16	,	,	PUNCT
ejpam-4003	87	17	3	3	X
ejpam-4003	87	18	.	.	PUNCT
ejpam-4003	87	19	x	x	X
ejpam-4003	88	1	=	=	PUNCT
ejpam-4003	88	2	mij	mij	X
ejpam-4003	88	3	xintb(a	xintb(a	PROPN
ejpam-4003	88	4	)	)	PUNCT
ejpam-4003	88	5	∪mij	∪mij	NOUN
ejpam-4003	88	6	xbdrb(a	xbdrb(a	NOUN
ejpam-4003	88	7	)	)	PUNCT
ejpam-4003	88	8	∪mij	∪mij	NOUN
ejpam-4003	88	9	xintb(x\a	xintb(x\a	NOUN
ejpam-4003	88	10	)	)	PUNCT
ejpam-4003	88	11	is	be	AUX
ejpam-4003	88	12	a	a	DET
ejpam-4003	88	13	pairwise	pairwise	NOUN
ejpam-4003	88	14	disjoint	disjoint	PROPN
ejpam-4003	88	15	union	union	PROPN
ejpam-4003	88	16	.	.	PUNCT
ejpam-4003	89	1	definition	definition	NOUN
ejpam-4003	89	2	4	4	NUM
ejpam-4003	89	3	.	.	PUNCT
ejpam-4003	90	1	[	[	X
ejpam-4003	90	2	9	9	NUM
ejpam-4003	90	3	]	]	X
ejpam-4003	90	4	let	let	VERB
ejpam-4003	90	5	(	(	PUNCT
ejpam-4003	90	6	x	x	NOUN
ejpam-4003	90	7	,	,	PUNCT
ejpam-4003	90	8	m1	m1	PROPN
ejpam-4003	90	9	x	x	SYM
ejpam-4003	90	10	,	,	PUNCT
ejpam-4003	90	11	m	m	PROPN
ejpam-4003	90	12	2	2	NUM
ejpam-4003	90	13	x	x	NOUN
ejpam-4003	90	14	)	)	PUNCT
ejpam-4003	90	15	be	be	VERB
ejpam-4003	90	16	a	a	DET
ejpam-4003	90	17	biminimal	biminimal	NOUN
ejpam-4003	90	18	structure	structure	NOUN
ejpam-4003	90	19	spaces	space	NOUN
ejpam-4003	90	20	and	and	CCONJ
ejpam-4003	90	21	w	w	AUX
ejpam-4003	90	22	be	be	AUX
ejpam-4003	90	23	a	a	DET
ejpam-4003	90	24	subset	subset	NOUN
ejpam-4003	90	25	of	of	ADP
ejpam-4003	90	26	x.	x.	NOUN
ejpam-4003	90	27	define	define	VERB
ejpam-4003	90	28	m1	m1	PROPN
ejpam-4003	90	29	w	w	PROPN
ejpam-4003	90	30	and	and	CCONJ
ejpam-4003	90	31	m2	m2	PROPN
ejpam-4003	90	32	w	w	PROPN
ejpam-4003	90	33	as	as	SCONJ
ejpam-4003	90	34	follows	follow	VERB
ejpam-4003	90	35	:	:	PUNCT
ejpam-4003	90	36	m1	m1	PROPN
ejpam-4003	90	37	w	w	NOUN
ejpam-4003	90	38	=	=	PUNCT
ejpam-4003	90	39	a	a	DET
ejpam-4003	90	40	∩w	∩w	NOUN
ejpam-4003	90	41	:	:	PUNCT
ejpam-4003	90	42	a	a	DET
ejpam-4003	90	43	∈	∈	PROPN
ejpam-4003	90	44	m1	m1	NOUN
ejpam-4003	90	45	x	x	X
ejpam-4003	90	46	and	and	CCONJ
ejpam-4003	90	47	m2	m2	PROPN
ejpam-4003	90	48	y	y	PROPN
ejpam-4003	90	49	=	=	SYM
ejpam-4003	90	50	b	b	PROPN
ejpam-4003	91	1	∩w	∩w	NOUN
ejpam-4003	91	2	:	:	PUNCT
ejpam-4003	91	3	b	b	X
ejpam-4003	91	4	∈	∈	NOUN
ejpam-4003	91	5	m2	m2	PROPN
ejpam-4003	91	6	x	x	X
ejpam-4003	91	7	.	.	PUNCT
ejpam-4003	92	1	a	a	PRON
ejpam-4003	92	2	triple	triple	ADJ
ejpam-4003	92	3	(	(	PUNCT
ejpam-4003	92	4	w	w	PROPN
ejpam-4003	92	5	,	,	PUNCT
ejpam-4003	92	6	m1	m1	PROPN
ejpam-4003	92	7	w	w	PROPN
ejpam-4003	92	8	,	,	PUNCT
ejpam-4003	92	9	m	m	PROPN
ejpam-4003	92	10	2	2	NUM
ejpam-4003	92	11	w	w	NOUN
ejpam-4003	92	12	)	)	PUNCT
ejpam-4003	92	13	is	be	AUX
ejpam-4003	92	14	called	call	VERB
ejpam-4003	92	15	a	a	DET
ejpam-4003	92	16	biminimal	biminimal	NOUN
ejpam-4003	92	17	structure	structure	NOUN
ejpam-4003	92	18	subspace	subspace	NOUN
ejpam-4003	92	19	of	of	ADP
ejpam-4003	92	20	(	(	PUNCT
ejpam-4003	92	21	x	x	NOUN
ejpam-4003	92	22	,	,	PUNCT
ejpam-4003	92	23	m1	m1	PROPN
ejpam-4003	92	24	x	x	SYM
ejpam-4003	92	25	,	,	PUNCT
ejpam-4003	92	26	m	m	PROPN
ejpam-4003	92	27	2	2	NUM
ejpam-4003	92	28	x	x	NOUN
ejpam-4003	92	29	)	)	PUNCT
ejpam-4003	92	30	.	.	PUNCT
ejpam-4003	93	1	let	let	VERB
ejpam-4003	93	2	(	(	PUNCT
ejpam-4003	93	3	w	w	PROPN
ejpam-4003	93	4	,	,	PUNCT
ejpam-4003	93	5	m1	m1	PROPN
ejpam-4003	93	6	w	w	PROPN
ejpam-4003	93	7	,	,	PUNCT
ejpam-4003	93	8	m	m	PROPN
ejpam-4003	93	9	2	2	NUM
ejpam-4003	93	10	w	w	NOUN
ejpam-4003	93	11	)	)	PUNCT
ejpam-4003	93	12	be	be	AUX
ejpam-4003	93	13	a	a	DET
ejpam-4003	93	14	biminimal	biminimal	NOUN
ejpam-4003	93	15	structure	structure	NOUN
ejpam-4003	93	16	subspace	subspace	NOUN
ejpam-4003	93	17	of	of	ADP
ejpam-4003	93	18	(	(	PUNCT
ejpam-4003	93	19	x	x	NOUN
ejpam-4003	93	20	,	,	PUNCT
ejpam-4003	93	21	m1	m1	PROPN
ejpam-4003	93	22	x	x	SYM
ejpam-4003	93	23	,	,	PUNCT
ejpam-4003	93	24	m	m	PROPN
ejpam-4003	93	25	2	2	NUM
ejpam-4003	93	26	x	x	NOUN
ejpam-4003	93	27	)	)	PUNCT
ejpam-4003	93	28	,	,	PUNCT
ejpam-4003	93	29	and	and	CCONJ
ejpam-4003	93	30	a	a	PRON
ejpam-4003	93	31	be	be	AUX
ejpam-4003	93	32	a	a	DET
ejpam-4003	93	33	subset	subset	NOUN
ejpam-4003	93	34	of	of	ADP
ejpam-4003	93	35	w.	w.	PROPN
ejpam-4003	93	36	the	the	PRON
ejpam-4003	93	37	(	(	PUNCT
ejpam-4003	93	38	i	i	PROPN
ejpam-4003	93	39	,	,	PUNCT
ejpam-4003	93	40	j)−mw	j)−mw	NOUN
ejpam-4003	93	41	−	−	NOUN
ejpam-4003	93	42	β−closure	β−closure	NOUN
ejpam-4003	94	1	and	and	CCONJ
ejpam-4003	94	2	(	(	PUNCT
ejpam-4003	94	3	i	i	NOUN
ejpam-4003	94	4	,	,	PUNCT
ejpam-4003	94	5	j)−mw	j)−mw	PROPN
ejpam-4003	94	6	−	−	NOUN
ejpam-4003	94	7	β−interior	β−interior	PUNCT
ejpam-4003	94	8	of	of	ADP
ejpam-4003	94	9	a	a	PRON
ejpam-4003	94	10	with	with	ADP
ejpam-4003	94	11	respect	respect	NOUN
ejpam-4003	94	12	to	to	ADP
ejpam-4003	94	13	mij	mij	PROPN
ejpam-4003	94	14	w	w	NOUN
ejpam-4003	94	15	are	be	AUX
ejpam-4003	94	16	denoted	denote	VERB
ejpam-4003	94	17	by	by	ADP
ejpam-4003	94	18	mij	mij	PROPN
ejpam-4003	94	19	wclb(a	wclb(a	PROPN
ejpam-4003	94	20	)	)	PUNCT
ejpam-4003	94	21	and	and	CCONJ
ejpam-4003	94	22	mij	mij	X
ejpam-4003	94	23	w	w	PROPN
ejpam-4003	94	24	intb(a	intb(a	PROPN
ejpam-4003	94	25	)	)	PUNCT
ejpam-4003	94	26	,	,	PUNCT
ejpam-4003	94	27	respectively	respectively	ADV
ejpam-4003	94	28	(	(	PUNCT
ejpam-4003	94	29	for	for	ADP
ejpam-4003	94	30	i	i	PRON
ejpam-4003	94	31	=	=	SYM
ejpam-4003	94	32	1	1	NUM
ejpam-4003	94	33	,	,	PUNCT
ejpam-4003	94	34	2	2	NUM
ejpam-4003	94	35	and	and	CCONJ
ejpam-4003	94	36	i	i	PRON
ejpam-4003	94	37	6=	6=	PROPN
ejpam-4003	94	38	j	j	PROPN
ejpam-4003	94	39	)	)	PUNCT
ejpam-4003	94	40	.	.	PUNCT
ejpam-4003	95	1	then	then	ADV
ejpam-4003	95	2	,	,	PUNCT
ejpam-4003	95	3	mij	mij	PROPN
ejpam-4003	95	4	wclb(a	wclb(a	PROPN
ejpam-4003	95	5	)	)	PUNCT
ejpam-4003	95	6	=	=	PUNCT
ejpam-4003	96	1	w	w	ADP
ejpam-4003	96	2	∩mij	∩mij	PROPN
ejpam-4003	96	3	xclb(a	xclb(a	PROPN
ejpam-4003	96	4	)	)	PUNCT
ejpam-4003	96	5	,	,	PUNCT
ejpam-4003	96	6	mij	mij	NOUN
ejpam-4003	96	7	w	w	NOUN
ejpam-4003	96	8	intb(a	intb(a	PROPN
ejpam-4003	96	9	)	)	PUNCT
ejpam-4003	96	10	=	=	PUNCT
ejpam-4003	96	11	w	w	ADP
ejpam-4003	96	12	∩mij	∩mij	ADJ
ejpam-4003	96	13	xintb(a	xintb(a	NOUN
ejpam-4003	96	14	)	)	PUNCT
ejpam-4003	96	15	and	and	CCONJ
ejpam-4003	96	16	mij	mij	NOUN
ejpam-4003	96	17	wbdrb(a	wbdrb(a	PROPN
ejpam-4003	96	18	)	)	PUNCT
ejpam-4003	96	19	=	=	PUNCT
ejpam-4003	97	1	w	w	ADP
ejpam-4003	97	2	∩mij	∩mij	PROPN
ejpam-4003	97	3	xbdrb(a	xbdrb(a	NUM
ejpam-4003	97	4	)	)	PUNCT
ejpam-4003	97	5	consequently	consequently	ADV
ejpam-4003	97	6	,	,	PUNCT
ejpam-4003	97	7	mij	mij	NOUN
ejpam-4003	97	8	wextb(a	wextb(a	PROPN
ejpam-4003	97	9	)	)	PUNCT
ejpam-4003	97	10	=	=	PUNCT
ejpam-4003	98	1	w	w	PROPN
ejpam-4003	98	2	∩mij	∩mij	PROPN
ejpam-4003	98	3	xextb(a	xextb(a	PROPN
ejpam-4003	98	4	)	)	PUNCT
ejpam-4003	98	5	.	.	PUNCT
ejpam-4003	99	1	t.	t.	PROPN
ejpam-4003	99	2	prasertsang	prasertsang	PROPN
ejpam-4003	99	3	,	,	PUNCT
ejpam-4003	99	4	p.	p.	PROPN
ejpam-4003	99	5	prasertsang	prasertsang	PROPN
ejpam-4003	99	6	/	/	SYM
ejpam-4003	99	7	eur	eur	PROPN
ejpam-4003	99	8	.	.	PUNCT
ejpam-4003	100	1	j.	j.	PROPN
ejpam-4003	100	2	pure	pure	PROPN
ejpam-4003	100	3	appl	appl	PROPN
ejpam-4003	100	4	.	.	PROPN
ejpam-4003	100	5	math	math	PROPN
ejpam-4003	100	6	,	,	PUNCT
ejpam-4003	100	7	14	14	NUM
ejpam-4003	100	8	(	(	PUNCT
ejpam-4003	100	9	3	3	NUM
ejpam-4003	100	10	)	)	PUNCT
ejpam-4003	100	11	(	(	PUNCT
ejpam-4003	100	12	2021	2021	NUM
ejpam-4003	100	13	)	)	PUNCT
ejpam-4003	100	14	,	,	PUNCT
ejpam-4003	100	15	915	915	NUM
ejpam-4003	100	16	-	-	SYM
ejpam-4003	100	17	922	922	NUM
ejpam-4003	100	18	918	918	NUM
ejpam-4003	100	19	3	3	NUM
ejpam-4003	100	20	.	.	PUNCT
ejpam-4003	100	21	main	main	ADJ
ejpam-4003	100	22	results	result	NOUN
ejpam-4003	100	23	in	in	ADP
ejpam-4003	100	24	this	this	DET
ejpam-4003	100	25	section	section	NOUN
ejpam-4003	100	26	,	,	PUNCT
ejpam-4003	100	27	we	we	PRON
ejpam-4003	100	28	introduce	introduce	VERB
ejpam-4003	100	29	the	the	DET
ejpam-4003	100	30	concepts	concept	NOUN
ejpam-4003	100	31	of	of	ADP
ejpam-4003	100	32	(	(	PUNCT
ejpam-4003	100	33	i	i	PROPN
ejpam-4003	100	34	,	,	PUNCT
ejpam-4003	100	35	j)−mx−β−exterior	j)−mx−β−exterior	PROPN
ejpam-4003	100	36	sets	set	NOUN
ejpam-4003	100	37	in	in	ADP
ejpam-4003	100	38	biminimal	biminimal	NOUN
ejpam-4003	100	39	structure	structure	NOUN
ejpam-4003	100	40	space	space	NOUN
ejpam-4003	100	41	which	which	PRON
ejpam-4003	100	42	contains	contain	VERB
ejpam-4003	100	43	some	some	DET
ejpam-4003	100	44	characterizations	characterization	NOUN
ejpam-4003	100	45	and	and	CCONJ
ejpam-4003	100	46	several	several	ADJ
ejpam-4003	100	47	fundamental	fundamental	ADJ
ejpam-4003	100	48	properties	property	NOUN
ejpam-4003	100	49	of	of	ADP
ejpam-4003	100	50	those	those	DET
ejpam-4003	100	51	sets	set	NOUN
ejpam-4003	100	52	.	.	PUNCT
ejpam-4003	101	1	definition	definition	NOUN
ejpam-4003	101	2	5	5	NUM
ejpam-4003	101	3	.	.	PUNCT
ejpam-4003	102	1	let	let	VERB
ejpam-4003	102	2	(	(	PUNCT
ejpam-4003	102	3	x	x	X
ejpam-4003	102	4	,	,	PUNCT
ejpam-4003	102	5	m1	m1	PROPN
ejpam-4003	102	6	x	x	SYM
ejpam-4003	102	7	,	,	PUNCT
ejpam-4003	102	8	m	m	PROPN
ejpam-4003	102	9	2	2	NUM
ejpam-4003	102	10	x	x	NOUN
ejpam-4003	102	11	)	)	PUNCT
ejpam-4003	102	12	be	be	AUX
ejpam-4003	102	13	a	a	DET
ejpam-4003	102	14	biminimal	biminimal	NOUN
ejpam-4003	102	15	structure	structure	NOUN
ejpam-4003	102	16	space	space	NOUN
ejpam-4003	102	17	,	,	PUNCT
ejpam-4003	102	18	a	a	PRON
ejpam-4003	102	19	be	be	AUX
ejpam-4003	102	20	a	a	DET
ejpam-4003	102	21	subset	subset	NOUN
ejpam-4003	102	22	of	of	ADP
ejpam-4003	102	23	x	x	PUNCT
ejpam-4003	102	24	and	and	CCONJ
ejpam-4003	102	25	x	x	SYM
ejpam-4003	102	26	∈	∈	PROPN
ejpam-4003	102	27	x.	x.	NOUN
ejpam-4003	102	28	then	then	ADV
ejpam-4003	102	29	,	,	PUNCT
ejpam-4003	102	30	x	x	PRON
ejpam-4003	102	31	is	be	AUX
ejpam-4003	102	32	called	call	VERB
ejpam-4003	102	33	(	(	PUNCT
ejpam-4003	102	34	i	i	PROPN
ejpam-4003	102	35	,	,	PUNCT
ejpam-4003	102	36	j)−mx	j)−mx	PROPN
ejpam-4003	103	1	−	−	PROPN
ejpam-4003	104	1	β−exterior	β−exterior	SYM
ejpam-4003	104	2	point	point	NOUN
ejpam-4003	104	3	of	of	ADP
ejpam-4003	104	4	a	a	DET
ejpam-4003	104	5	if	if	NOUN
ejpam-4003	104	6	x	x	X
ejpam-4003	104	7	∈	∈	NOUN
ejpam-4003	104	8	mij	mij	NOUN
ejpam-4003	104	9	xintb(x\a	xintb(x\a	NOUN
ejpam-4003	104	10	)	)	PUNCT
ejpam-4003	104	11	.	.	PUNCT
ejpam-4003	105	1	the	the	DET
ejpam-4003	105	2	set	set	NOUN
ejpam-4003	105	3	of	of	ADP
ejpam-4003	105	4	all	all	PRON
ejpam-4003	105	5	(	(	PUNCT
ejpam-4003	105	6	i	i	NOUN
ejpam-4003	105	7	,	,	PUNCT
ejpam-4003	105	8	j)−mx−β−exterior	j)−mx−β−exterior	ADJ
ejpam-4003	105	9	point	point	NOUN
ejpam-4003	105	10	of	of	ADP
ejpam-4003	105	11	a	a	PRON
ejpam-4003	105	12	are	be	AUX
ejpam-4003	105	13	denoted	denote	VERB
ejpam-4003	105	14	by	by	ADP
ejpam-4003	105	15	:	:	PUNCT
ejpam-4003	105	16	mij	mij	PROPN
ejpam-4003	105	17	xextb(a	xextb(a	PROPN
ejpam-4003	105	18	)	)	PUNCT
ejpam-4003	106	1	where	where	SCONJ
ejpam-4003	106	2	i	i	PRON
ejpam-4003	106	3	,	,	PUNCT
ejpam-4003	106	4	j	j	PROPN
ejpam-4003	106	5	=	=	SYM
ejpam-4003	106	6	1	1	NUM
ejpam-4003	106	7	,	,	PUNCT
ejpam-4003	106	8	2	2	NUM
ejpam-4003	106	9	and	and	CCONJ
ejpam-4003	106	10	i	i	PRON
ejpam-4003	106	11	6=	6=	PROPN
ejpam-4003	106	12	j.	j.	PROPN
ejpam-4003	106	13	by	by	ADP
ejpam-4003	106	14	the	the	DET
ejpam-4003	106	15	definition	definition	NOUN
ejpam-4003	106	16	5	5	NUM
ejpam-4003	106	17	,	,	PUNCT
ejpam-4003	106	18	mij	mij	X
ejpam-4003	106	19	xextb(a	xextb(a	PROPN
ejpam-4003	106	20	)	)	PUNCT
ejpam-4003	106	21	=	=	SYM
ejpam-4003	106	22	mij	mij	NOUN
ejpam-4003	106	23	xintb(x\a	xintb(x\a	NOUN
ejpam-4003	106	24	)	)	PUNCT
ejpam-4003	107	1	=	=	PUNCT
ejpam-4003	108	1	x\mij	x\mij	PROPN
ejpam-4003	108	2	xclb(a	xclb(a	PROPN
ejpam-4003	108	3	)	)	PUNCT
ejpam-4003	108	4	.	.	PUNCT
ejpam-4003	109	1	example	example	NOUN
ejpam-4003	110	1	1	1	X
ejpam-4003	110	2	.	.	PUNCT
ejpam-4003	110	3	let	let	VERB
ejpam-4003	110	4	x	x	PUNCT
ejpam-4003	110	5	=	=	PRON
ejpam-4003	110	6	{	{	PUNCT
ejpam-4003	110	7	1	1	NUM
ejpam-4003	110	8	,	,	PUNCT
ejpam-4003	110	9	2	2	NUM
ejpam-4003	110	10	,	,	PUNCT
ejpam-4003	110	11	3	3	NUM
ejpam-4003	110	12	}	}	PUNCT
ejpam-4003	110	13	.	.	PUNCT
ejpam-4003	111	1	define	define	VERB
ejpam-4003	111	2	m−structures	m−structure	NOUN
ejpam-4003	111	3	m1	m1	PROPN
ejpam-4003	111	4	x	x	X
ejpam-4003	111	5	and	and	CCONJ
ejpam-4003	111	6	m2	m2	PROPN
ejpam-4003	111	7	x	x	PROPN
ejpam-4003	111	8	on	on	ADP
ejpam-4003	111	9	the	the	DET
ejpam-4003	111	10	biminimal	biminimal	NOUN
ejpam-4003	111	11	structure	structure	NOUN
ejpam-4003	111	12	space	space	NOUN
ejpam-4003	111	13	x	x	PUNCT
ejpam-4003	111	14	as	as	SCONJ
ejpam-4003	111	15	follows	follow	VERB
ejpam-4003	111	16	:	:	PUNCT
ejpam-4003	112	1	m1	m1	NOUN
ejpam-4003	112	2	x	x	PUNCT
ejpam-4003	113	1	=	=	PRON
ejpam-4003	113	2	{	{	PUNCT
ejpam-4003	113	3	∅	∅	NOUN
ejpam-4003	113	4	,	,	PUNCT
ejpam-4003	113	5	{	{	PUNCT
ejpam-4003	113	6	2	2	NUM
ejpam-4003	113	7	}	}	PUNCT
ejpam-4003	113	8	,	,	PUNCT
ejpam-4003	113	9	{	{	PUNCT
ejpam-4003	113	10	1	1	NUM
ejpam-4003	113	11	,	,	PUNCT
ejpam-4003	113	12	3	3	NUM
ejpam-4003	113	13	}	}	PUNCT
ejpam-4003	113	14	,	,	PUNCT
ejpam-4003	113	15	x	x	X
ejpam-4003	113	16	}	}	PUNCT
ejpam-4003	113	17	and	and	CCONJ
ejpam-4003	113	18	m2	m2	PROPN
ejpam-4003	113	19	x	x	SYM
ejpam-4003	113	20	=	=	PRON
ejpam-4003	113	21	{	{	PUNCT
ejpam-4003	113	22	∅	∅	NOUN
ejpam-4003	113	23	,	,	PUNCT
ejpam-4003	113	24	{	{	PUNCT
ejpam-4003	113	25	1	1	NUM
ejpam-4003	113	26	}	}	PUNCT
ejpam-4003	113	27	,	,	PUNCT
ejpam-4003	113	28	{	{	PUNCT
ejpam-4003	113	29	3	3	NUM
ejpam-4003	113	30	}	}	PUNCT
ejpam-4003	113	31	,	,	PUNCT
ejpam-4003	113	32	{	{	PUNCT
ejpam-4003	113	33	1	1	NUM
ejpam-4003	113	34	,	,	PUNCT
ejpam-4003	113	35	2	2	NUM
ejpam-4003	113	36	}	}	PUNCT
ejpam-4003	113	37	,	,	PUNCT
ejpam-4003	113	38	{	{	PUNCT
ejpam-4003	113	39	2	2	NUM
ejpam-4003	113	40	,	,	PUNCT
ejpam-4003	113	41	3	3	NUM
ejpam-4003	113	42	}	}	PUNCT
ejpam-4003	113	43	,	,	PUNCT
ejpam-4003	113	44	x	x	NOUN
ejpam-4003	113	45	}	}	PUNCT
ejpam-4003	113	46	.	.	PUNCT
ejpam-4003	114	1	we	we	PRON
ejpam-4003	114	2	have	have	VERB
ejpam-4003	114	3	that	that	PRON
ejpam-4003	114	4	:	:	PUNCT
ejpam-4003	114	5	m12	m12	PROPN
ejpam-4003	114	6	xextb({1	xextb({1	PROPN
ejpam-4003	114	7	,	,	PUNCT
ejpam-4003	114	8	2	2	NUM
ejpam-4003	114	9	}	}	PUNCT
ejpam-4003	114	10	)	)	PUNCT
ejpam-4003	115	1	=	=	PUNCT
ejpam-4003	115	2	{	{	PUNCT
ejpam-4003	115	3	3	3	NUM
ejpam-4003	115	4	}	}	PUNCT
ejpam-4003	115	5	and	and	CCONJ
ejpam-4003	115	6	m21	m21	PROPN
ejpam-4003	115	7	xextb({1	xextb({1	PROPN
ejpam-4003	115	8	,	,	PUNCT
ejpam-4003	115	9	2	2	NUM
ejpam-4003	115	10	}	}	PUNCT
ejpam-4003	115	11	)	)	PUNCT
ejpam-4003	116	1	=	=	PUNCT
ejpam-4003	116	2	∅.	∅.	PRON
ejpam-4003	116	3	lemma	lemma	PROPN
ejpam-4003	116	4	7	7	NUM
ejpam-4003	116	5	.	.	PUNCT
ejpam-4003	117	1	let	let	VERB
ejpam-4003	117	2	(	(	PUNCT
ejpam-4003	117	3	x	x	X
ejpam-4003	117	4	,	,	PUNCT
ejpam-4003	117	5	m1	m1	PROPN
ejpam-4003	117	6	x	x	SYM
ejpam-4003	117	7	,	,	PUNCT
ejpam-4003	117	8	m	m	PROPN
ejpam-4003	117	9	2	2	NUM
ejpam-4003	117	10	x	x	NOUN
ejpam-4003	117	11	)	)	PUNCT
ejpam-4003	117	12	be	be	AUX
ejpam-4003	117	13	a	a	DET
ejpam-4003	117	14	biminimal	biminimal	NOUN
ejpam-4003	117	15	structure	structure	NOUN
ejpam-4003	117	16	space	space	NOUN
ejpam-4003	117	17	,	,	PUNCT
ejpam-4003	117	18	a	a	PRON
ejpam-4003	117	19	be	be	AUX
ejpam-4003	117	20	a	a	DET
ejpam-4003	117	21	subset	subset	NOUN
ejpam-4003	117	22	of	of	ADP
ejpam-4003	117	23	x.	x.	NOUN
ejpam-4003	117	24	then	then	ADV
ejpam-4003	117	25	,	,	PUNCT
ejpam-4003	117	26	for	for	ADP
ejpam-4003	117	27	any	any	DET
ejpam-4003	117	28	i	i	PROPN
ejpam-4003	117	29	,	,	PUNCT
ejpam-4003	117	30	j	j	PROPN
ejpam-4003	117	31	=	=	SYM
ejpam-4003	117	32	1	1	NUM
ejpam-4003	117	33	,	,	PUNCT
ejpam-4003	117	34	2	2	NUM
ejpam-4003	117	35	and	and	CCONJ
ejpam-4003	117	36	i	i	PRON
ejpam-4003	117	37	6=	6=	PROPN
ejpam-4003	117	38	j	j	PROPN
ejpam-4003	117	39	,	,	PUNCT
ejpam-4003	117	40	the	the	DET
ejpam-4003	117	41	following	following	ADJ
ejpam-4003	117	42	statements	statement	NOUN
ejpam-4003	117	43	hold	hold	VERB
ejpam-4003	117	44	:	:	PUNCT
ejpam-4003	117	45	1	1	X
ejpam-4003	117	46	.	.	X
ejpam-4003	117	47	mij	mij	PROPN
ejpam-4003	117	48	xextb(∅	xextb(∅	PROPN
ejpam-4003	117	49	)	)	PUNCT
ejpam-4003	118	1	=	=	SYM
ejpam-4003	118	2	x	x	PUNCT
ejpam-4003	118	3	and	and	CCONJ
ejpam-4003	118	4	mij	mij	NOUN
ejpam-4003	118	5	xextb(x	xextb(x	NUM
ejpam-4003	118	6	)	)	PUNCT
ejpam-4003	119	1	=	=	NOUN
ejpam-4003	119	2	∅	∅	NOUN
ejpam-4003	119	3	,	,	PUNCT
ejpam-4003	119	4	2	2	NUM
ejpam-4003	119	5	.	.	X
ejpam-4003	119	6	mij	mij	PROPN
ejpam-4003	119	7	xextb(a	xextb(a	PROPN
ejpam-4003	119	8	)	)	PUNCT
ejpam-4003	119	9	∩a	∩a	NOUN
ejpam-4003	119	10	=	=	PUNCT
ejpam-4003	119	11	∅	∅	NOUN
ejpam-4003	119	12	and	and	CCONJ
ejpam-4003	119	13	mij	mij	ADJ
ejpam-4003	119	14	xextb(a	xextb(a	PROPN
ejpam-4003	119	15	)	)	PUNCT
ejpam-4003	119	16	∩mij	∩mij	PROPN
ejpam-4003	119	17	xclb(a	xclb(a	PROPN
ejpam-4003	119	18	)	)	PUNCT
ejpam-4003	119	19	=	=	NOUN
ejpam-4003	119	20	∅	∅	NOUN
ejpam-4003	119	21	,	,	PUNCT
ejpam-4003	119	22	3	3	X
ejpam-4003	119	23	.	.	PUNCT
ejpam-4003	119	24	mij	mij	PROPN
ejpam-4003	119	25	xextb(a	xextb(a	PROPN
ejpam-4003	119	26	)	)	PUNCT
ejpam-4003	119	27	∩mij	∩mij	ADJ
ejpam-4003	119	28	xextb(x\a	xextb(x\a	PUNCT
ejpam-4003	119	29	)	)	PUNCT
ejpam-4003	120	1	=	=	NOUN
ejpam-4003	120	2	∅	∅	NOUN
ejpam-4003	120	3	and	and	CCONJ
ejpam-4003	120	4	mij	mij	ADJ
ejpam-4003	120	5	xextb(a	xextb(a	PROPN
ejpam-4003	120	6	)	)	PUNCT
ejpam-4003	120	7	∩mij	∩mij	PROPN
ejpam-4003	120	8	xbdrb(a	xbdrb(a	PROPN
ejpam-4003	120	9	)	)	PUNCT
ejpam-4003	120	10	=	=	SYM
ejpam-4003	120	11	∅	∅	NOUN
ejpam-4003	120	12	,	,	PUNCT
ejpam-4003	120	13	4	4	NUM
ejpam-4003	120	14	.	.	PUNCT
ejpam-4003	120	15	x	x	X
ejpam-4003	121	1	=	=	PUNCT
ejpam-4003	121	2	mij	mij	X
ejpam-4003	121	3	xintb(a	xintb(a	PROPN
ejpam-4003	121	4	)	)	PUNCT
ejpam-4003	121	5	∪mij	∪mij	NOUN
ejpam-4003	121	6	xbdrb(a	xbdrb(a	NOUN
ejpam-4003	121	7	)	)	PUNCT
ejpam-4003	121	8	∪mij	∪mij	NOUN
ejpam-4003	121	9	xextb(a	xextb(a	PROPN
ejpam-4003	121	10	)	)	PUNCT
ejpam-4003	121	11	is	be	AUX
ejpam-4003	121	12	a	a	DET
ejpam-4003	121	13	pairwise	pairwise	NOUN
ejpam-4003	121	14	disjoint	disjoint	NOUN
ejpam-4003	121	15	union	union	NOUN
ejpam-4003	121	16	.	.	PUNCT
ejpam-4003	122	1	proof	proof	NOUN
ejpam-4003	122	2	.	.	PUNCT
ejpam-4003	123	1	assume	assume	VERB
ejpam-4003	123	2	that	that	SCONJ
ejpam-4003	123	3	(	(	PUNCT
ejpam-4003	123	4	x	x	X
ejpam-4003	123	5	,	,	PUNCT
ejpam-4003	123	6	m1	m1	PROPN
ejpam-4003	123	7	x	x	SYM
ejpam-4003	123	8	,	,	PUNCT
ejpam-4003	123	9	m	m	PROPN
ejpam-4003	123	10	2	2	NUM
ejpam-4003	123	11	x	x	NOUN
ejpam-4003	123	12	)	)	PUNCT
ejpam-4003	123	13	is	be	AUX
ejpam-4003	123	14	a	a	DET
ejpam-4003	123	15	biminimal	biminimal	NOUN
ejpam-4003	123	16	structure	structure	NOUN
ejpam-4003	123	17	space	space	NOUN
ejpam-4003	123	18	and	and	CCONJ
ejpam-4003	123	19	a	a	PRON
ejpam-4003	123	20	is	be	AUX
ejpam-4003	123	21	a	a	DET
ejpam-4003	123	22	subset	subset	NOUN
ejpam-4003	123	23	of	of	ADP
ejpam-4003	123	24	x.	x.	NOUN
ejpam-4003	123	25	1	1	NUM
ejpam-4003	123	26	.	.	PUNCT
ejpam-4003	124	1	since	since	SCONJ
ejpam-4003	124	2	mij	mij	NOUN
ejpam-4003	124	3	xclb(∅	xclb(∅	X
ejpam-4003	124	4	)	)	PUNCT
ejpam-4003	124	5	=	=	NOUN
ejpam-4003	124	6	∅	∅	NOUN
ejpam-4003	124	7	and	and	CCONJ
ejpam-4003	124	8	mij	mij	PROPN
ejpam-4003	124	9	xclb(x	xclb(x	PROPN
ejpam-4003	124	10	)	)	PUNCT
ejpam-4003	125	1	=	=	SYM
ejpam-4003	125	2	x	x	X
ejpam-4003	125	3	,	,	PUNCT
ejpam-4003	125	4	we	we	PRON
ejpam-4003	125	5	obtain	obtain	VERB
ejpam-4003	125	6	:	:	PUNCT
ejpam-4003	125	7	mij	mij	PROPN
ejpam-4003	125	8	xextb(∅	xextb(∅	PROPN
ejpam-4003	125	9	)	)	PUNCT
ejpam-4003	126	1	=	=	PUNCT
ejpam-4003	126	2	x\∅	x\∅	PROPN
ejpam-4003	126	3	=	=	PUNCT
ejpam-4003	126	4	x	x	PROPN
ejpam-4003	126	5	and	and	CCONJ
ejpam-4003	126	6	mij	mij	NOUN
ejpam-4003	126	7	xextb(x	xextb(x	NUM
ejpam-4003	126	8	)	)	PUNCT
ejpam-4003	126	9	=	=	PUNCT
ejpam-4003	126	10	x\x	x\x	X
ejpam-4003	127	1	=	=	PUNCT
ejpam-4003	127	2	∅.	∅.	PRON
ejpam-4003	127	3	2	2	NUM
ejpam-4003	127	4	.	.	PUNCT
ejpam-4003	127	5	by	by	ADP
ejpam-4003	127	6	lemma	lemma	PROPN
ejpam-4003	127	7	2	2	NUM
ejpam-4003	127	8	(	(	PUNCT
ejpam-4003	127	9	2	2	NUM
ejpam-4003	127	10	)	)	PUNCT
ejpam-4003	127	11	,	,	PUNCT
ejpam-4003	127	12	x\mij	x\mij	PROPN
ejpam-4003	127	13	xclb(a	xclb(a	X
ejpam-4003	127	14	)	)	PUNCT
ejpam-4003	127	15	⊆	⊆	NUM
ejpam-4003	127	16	x\a	x\a	NOUN
ejpam-4003	127	17	,	,	PUNCT
ejpam-4003	127	18	(	(	PUNCT
ejpam-4003	127	19	x\mij	x\mij	X
ejpam-4003	127	20	xclb(a	xclb(a	PROPN
ejpam-4003	127	21	)	)	PUNCT
ejpam-4003	127	22	)	)	PUNCT
ejpam-4003	127	23	∩	∩	NOUN
ejpam-4003	127	24	a	a	DET
ejpam-4003	127	25	⊆	⊆	NUM
ejpam-4003	127	26	∅.	∅.	NOUN
ejpam-4003	127	27	that	that	PRON
ejpam-4003	127	28	is	be	AUX
ejpam-4003	127	29	:	:	PUNCT
ejpam-4003	127	30	mij	mij	X
ejpam-4003	127	31	xextb(a	xextb(a	PROPN
ejpam-4003	127	32	)	)	PUNCT
ejpam-4003	127	33	∩a	∩a	PROPN
ejpam-4003	128	1	=	=	PUNCT
ejpam-4003	128	2	∅.	∅.	AUX
ejpam-4003	128	3	it	it	PRON
ejpam-4003	128	4	follow	follow	VERB
ejpam-4003	128	5	that	that	SCONJ
ejpam-4003	128	6	:	:	PUNCT
ejpam-4003	128	7	mij	mij	VERB
ejpam-4003	128	8	xextb(a	xextb(a	PROPN
ejpam-4003	128	9	)	)	PUNCT
ejpam-4003	128	10	∩mij	∩mij	PROPN
ejpam-4003	128	11	xclb(a	xclb(a	PROPN
ejpam-4003	128	12	)	)	PUNCT
ejpam-4003	128	13	=	=	PUNCT
ejpam-4003	128	14	∅.	∅.	PRON
ejpam-4003	128	15	3	3	NUM
ejpam-4003	128	16	.	.	PUNCT
ejpam-4003	129	1	it	it	PRON
ejpam-4003	129	2	follows	follow	VERB
ejpam-4003	129	3	by	by	ADP
ejpam-4003	129	4	lemma	lemma	PROPN
ejpam-4003	129	5	6	6	NUM
ejpam-4003	129	6	(	(	PUNCT
ejpam-4003	129	7	1	1	NUM
ejpam-4003	129	8	)	)	PUNCT
ejpam-4003	129	9	.	.	PUNCT
ejpam-4003	130	1	4	4	X
ejpam-4003	130	2	.	.	X
ejpam-4003	130	3	it	it	PRON
ejpam-4003	130	4	is	be	AUX
ejpam-4003	130	5	obvious	obvious	ADJ
ejpam-4003	130	6	by	by	ADP
ejpam-4003	130	7	definition	definition	NOUN
ejpam-4003	130	8	5	5	NUM
ejpam-4003	130	9	and	and	CCONJ
ejpam-4003	130	10	lemma	lemma	PROPN
ejpam-4003	130	11	6	6	NUM
ejpam-4003	130	12	(	(	PUNCT
ejpam-4003	130	13	2	2	NUM
ejpam-4003	130	14	)	)	PUNCT
ejpam-4003	130	15	,	,	PUNCT
ejpam-4003	130	16	(	(	PUNCT
ejpam-4003	130	17	3	3	NUM
ejpam-4003	130	18	)	)	PUNCT
ejpam-4003	130	19	.	.	PUNCT
ejpam-4003	131	1	theorem	theorem	NOUN
ejpam-4003	131	2	1	1	X
ejpam-4003	131	3	.	.	PUNCT
ejpam-4003	132	1	let	let	VERB
ejpam-4003	132	2	(	(	PUNCT
ejpam-4003	132	3	x	x	X
ejpam-4003	132	4	,	,	PUNCT
ejpam-4003	132	5	m1	m1	PROPN
ejpam-4003	132	6	x	x	SYM
ejpam-4003	132	7	,	,	PUNCT
ejpam-4003	132	8	m	m	PROPN
ejpam-4003	132	9	2	2	NUM
ejpam-4003	132	10	x	x	NOUN
ejpam-4003	132	11	)	)	PUNCT
ejpam-4003	132	12	be	be	AUX
ejpam-4003	132	13	a	a	DET
ejpam-4003	132	14	biminimal	biminimal	NOUN
ejpam-4003	132	15	structure	structure	NOUN
ejpam-4003	132	16	space	space	NOUN
ejpam-4003	132	17	and	and	CCONJ
ejpam-4003	132	18	a	a	DET
ejpam-4003	132	19	,	,	PUNCT
ejpam-4003	132	20	b	b	PROPN
ejpam-4003	132	21	be	be	AUX
ejpam-4003	132	22	subsets	subset	NOUN
ejpam-4003	132	23	of	of	ADP
ejpam-4003	132	24	x	x	PUNCT
ejpam-4003	132	25	with	with	ADP
ejpam-4003	132	26	a	a	DET
ejpam-4003	132	27	⊆	⊆	NUM
ejpam-4003	132	28	b.	b.	NOUN
ejpam-4003	132	29	then	then	ADV
ejpam-4003	132	30	,	,	PUNCT
ejpam-4003	132	31	for	for	ADP
ejpam-4003	132	32	i	i	PRON
ejpam-4003	132	33	,	,	PUNCT
ejpam-4003	132	34	j	j	PROPN
ejpam-4003	132	35	=	=	SYM
ejpam-4003	132	36	1	1	NUM
ejpam-4003	132	37	,	,	PUNCT
ejpam-4003	132	38	2	2	NUM
ejpam-4003	132	39	and	and	CCONJ
ejpam-4003	132	40	i	i	PRON
ejpam-4003	132	41	6=	6=	PROPN
ejpam-4003	133	1	j	j	PROPN
ejpam-4003	133	2	,	,	PUNCT
ejpam-4003	133	3	1	1	NUM
ejpam-4003	133	4	.	.	PUNCT
ejpam-4003	133	5	mij	mij	PROPN
ejpam-4003	133	6	xextb(b	xextb(b	PROPN
ejpam-4003	133	7	)	)	PUNCT
ejpam-4003	133	8	⊆	⊆	NUM
ejpam-4003	133	9	mij	mij	X
ejpam-4003	133	10	xextb(a	xextb(a	PROPN
ejpam-4003	133	11	)	)	PUNCT
ejpam-4003	133	12	,	,	PUNCT
ejpam-4003	133	13	2	2	X
ejpam-4003	133	14	.	.	PUNCT
ejpam-4003	133	15	mij	mij	PROPN
ejpam-4003	133	16	xextb(b	xextb(b	PROPN
ejpam-4003	133	17	)	)	PUNCT
ejpam-4003	133	18	⊆	⊆	NUM
ejpam-4003	133	19	x\mij	x\mij	PUNCT
ejpam-4003	133	20	xbdrb(a	xbdrb(a	PROPN
ejpam-4003	133	21	)	)	PUNCT
ejpam-4003	133	22	.	.	PUNCT
ejpam-4003	134	1	proof	proof	NOUN
ejpam-4003	134	2	.	.	PUNCT
ejpam-4003	135	1	assume	assume	VERB
ejpam-4003	135	2	that	that	SCONJ
ejpam-4003	135	3	(	(	PUNCT
ejpam-4003	135	4	x	x	X
ejpam-4003	135	5	,	,	PUNCT
ejpam-4003	135	6	m1	m1	PROPN
ejpam-4003	135	7	x	x	SYM
ejpam-4003	135	8	,	,	PUNCT
ejpam-4003	135	9	m	m	PROPN
ejpam-4003	135	10	2	2	NUM
ejpam-4003	135	11	x	x	NOUN
ejpam-4003	135	12	)	)	PUNCT
ejpam-4003	135	13	is	be	AUX
ejpam-4003	135	14	a	a	DET
ejpam-4003	135	15	biminimal	biminimal	NOUN
ejpam-4003	135	16	structure	structure	NOUN
ejpam-4003	135	17	space	space	NOUN
ejpam-4003	135	18	and	and	CCONJ
ejpam-4003	135	19	a	a	DET
ejpam-4003	135	20	,	,	PUNCT
ejpam-4003	135	21	b	b	NOUN
ejpam-4003	135	22	are	be	AUX
ejpam-4003	135	23	subsets	subset	NOUN
ejpam-4003	135	24	of	of	ADP
ejpam-4003	135	25	x	x	PUNCT
ejpam-4003	135	26	with	with	ADP
ejpam-4003	135	27	a	a	DET
ejpam-4003	135	28	⊆	⊆	NUM
ejpam-4003	135	29	b.	b.	NOUN
ejpam-4003	135	30	for	for	ADP
ejpam-4003	135	31	any	any	DET
ejpam-4003	135	32	i	i	PROPN
ejpam-4003	135	33	,	,	PUNCT
ejpam-4003	135	34	j	j	PROPN
ejpam-4003	135	35	=	=	SYM
ejpam-4003	135	36	1	1	NUM
ejpam-4003	135	37	,	,	PUNCT
ejpam-4003	135	38	2	2	NUM
ejpam-4003	135	39	and	and	CCONJ
ejpam-4003	135	40	i	i	PRON
ejpam-4003	135	41	6=	6=	PROPN
ejpam-4003	136	1	j	j	PROPN
ejpam-4003	136	2	,	,	PUNCT
ejpam-4003	136	3	1	1	NUM
ejpam-4003	136	4	.	.	X
ejpam-4003	136	5	from	from	ADP
ejpam-4003	136	6	lemma	lemma	PROPN
ejpam-4003	136	7	2	2	NUM
ejpam-4003	136	8	(	(	PUNCT
ejpam-4003	136	9	3	3	NUM
ejpam-4003	136	10	)	)	PUNCT
ejpam-4003	136	11	,	,	PUNCT
ejpam-4003	136	12	mij	mij	X
ejpam-4003	136	13	xclb(a	xclb(a	PROPN
ejpam-4003	136	14	)	)	PUNCT
ejpam-4003	136	15	⊆	⊆	NUM
ejpam-4003	136	16	mij	mij	PROPN
ejpam-4003	136	17	xclb(b	xclb(b	PROPN
ejpam-4003	136	18	)	)	PUNCT
ejpam-4003	136	19	yields	yield	VERB
ejpam-4003	136	20	x\mij	x\mij	PUNCT
ejpam-4003	137	1	xclb(b	xclb(b	PROPN
ejpam-4003	137	2	)	)	PUNCT
ejpam-4003	137	3	⊆	⊆	NUM
ejpam-4003	137	4	x\mij	x\mij	PUNCT
ejpam-4003	137	5	xclb(a	xclb(a	PROPN
ejpam-4003	137	6	)	)	PUNCT
ejpam-4003	137	7	,	,	PUNCT
ejpam-4003	137	8	mij	mij	NOUN
ejpam-4003	137	9	xextb(b	xextb(b	PROPN
ejpam-4003	137	10	)	)	PUNCT
ejpam-4003	137	11	⊆	⊆	NUM
ejpam-4003	137	12	mij	mij	X
ejpam-4003	137	13	xextb(a	xextb(a	PROPN
ejpam-4003	137	14	)	)	PUNCT
ejpam-4003	137	15	.	.	PUNCT
ejpam-4003	138	1	t.	t.	PROPN
ejpam-4003	138	2	prasertsang	prasertsang	PROPN
ejpam-4003	138	3	,	,	PUNCT
ejpam-4003	138	4	p.	p.	PROPN
ejpam-4003	138	5	prasertsang	prasertsang	PROPN
ejpam-4003	138	6	/	/	SYM
ejpam-4003	138	7	eur	eur	PROPN
ejpam-4003	138	8	.	.	PUNCT
ejpam-4003	139	1	j.	j.	PROPN
ejpam-4003	139	2	pure	pure	PROPN
ejpam-4003	139	3	appl	appl	PROPN
ejpam-4003	139	4	.	.	PROPN
ejpam-4003	139	5	math	math	PROPN
ejpam-4003	139	6	,	,	PUNCT
ejpam-4003	139	7	14	14	NUM
ejpam-4003	139	8	(	(	PUNCT
ejpam-4003	139	9	3	3	NUM
ejpam-4003	139	10	)	)	PUNCT
ejpam-4003	139	11	(	(	PUNCT
ejpam-4003	139	12	2021	2021	NUM
ejpam-4003	139	13	)	)	PUNCT
ejpam-4003	139	14	,	,	PUNCT
ejpam-4003	139	15	915	915	NUM
ejpam-4003	139	16	-	-	SYM
ejpam-4003	139	17	922	922	NUM
ejpam-4003	139	18	919	919	NUM
ejpam-4003	139	19	2	2	NUM
ejpam-4003	139	20	.	.	PUNCT
ejpam-4003	140	1	by	by	ADP
ejpam-4003	140	2	lemma	lemma	PROPN
ejpam-4003	140	3	7	7	NUM
ejpam-4003	140	4	(	(	PUNCT
ejpam-4003	140	5	3	3	NUM
ejpam-4003	140	6	)	)	PUNCT
ejpam-4003	140	7	,	,	PUNCT
ejpam-4003	140	8	mij	mij	X
ejpam-4003	140	9	xextb(a	xextb(a	PROPN
ejpam-4003	140	10	)	)	PUNCT
ejpam-4003	140	11	⊆	⊆	NUM
ejpam-4003	140	12	x\mij	x\mij	PUNCT
ejpam-4003	140	13	xbdrb(a	xbdrb(a	PROPN
ejpam-4003	140	14	)	)	PUNCT
ejpam-4003	140	15	and	and	CCONJ
ejpam-4003	140	16	by	by	ADP
ejpam-4003	140	17	(	(	PUNCT
ejpam-4003	140	18	1	1	NUM
ejpam-4003	140	19	)	)	PUNCT
ejpam-4003	140	20	,	,	PUNCT
ejpam-4003	140	21	we	we	PRON
ejpam-4003	140	22	have	have	VERB
ejpam-4003	140	23	mij	mij	NOUN
ejpam-4003	140	24	xextb(b	xextb(b	PROPN
ejpam-4003	140	25	)	)	PUNCT
ejpam-4003	140	26	⊆	⊆	NUM
ejpam-4003	140	27	x\mij	x\mij	PUNCT
ejpam-4003	140	28	xbdrb(a	xbdrb(a	PROPN
ejpam-4003	140	29	)	)	PUNCT
ejpam-4003	140	30	.	.	PUNCT
ejpam-4003	141	1	corollary	corollary	ADJ
ejpam-4003	141	2	1	1	NUM
ejpam-4003	141	3	.	.	PUNCT
ejpam-4003	142	1	let	let	VERB
ejpam-4003	142	2	(	(	PUNCT
ejpam-4003	142	3	x	x	X
ejpam-4003	142	4	,	,	PUNCT
ejpam-4003	142	5	m1	m1	PROPN
ejpam-4003	142	6	x	x	SYM
ejpam-4003	142	7	,	,	PUNCT
ejpam-4003	142	8	m	m	PROPN
ejpam-4003	142	9	2	2	NUM
ejpam-4003	142	10	x	x	NOUN
ejpam-4003	142	11	)	)	PUNCT
ejpam-4003	142	12	be	be	AUX
ejpam-4003	142	13	a	a	DET
ejpam-4003	142	14	biminimal	biminimal	NOUN
ejpam-4003	142	15	structure	structure	NOUN
ejpam-4003	142	16	space	space	NOUN
ejpam-4003	142	17	and	and	CCONJ
ejpam-4003	142	18	a	a	DET
ejpam-4003	142	19	be	be	NOUN
ejpam-4003	142	20	subsets	subset	NOUN
ejpam-4003	142	21	of	of	ADP
ejpam-4003	142	22	x.	x.	NOUN
ejpam-4003	142	23	then	then	ADV
ejpam-4003	142	24	,	,	PUNCT
ejpam-4003	142	25	for	for	ADP
ejpam-4003	142	26	i	i	PRON
ejpam-4003	142	27	,	,	PUNCT
ejpam-4003	142	28	j	j	PROPN
ejpam-4003	142	29	=	=	SYM
ejpam-4003	142	30	1	1	NUM
ejpam-4003	142	31	,	,	PUNCT
ejpam-4003	142	32	2	2	NUM
ejpam-4003	142	33	and	and	CCONJ
ejpam-4003	142	34	i	i	PRON
ejpam-4003	142	35	6=	6=	PROPN
ejpam-4003	142	36	j	j	PROPN
ejpam-4003	142	37	,	,	PUNCT
ejpam-4003	142	38	1	1	NUM
ejpam-4003	142	39	.	.	PUNCT
ejpam-4003	142	40	mij	mij	PROPN
ejpam-4003	142	41	xextb(a	xextb(a	PROPN
ejpam-4003	142	42	)	)	PUNCT
ejpam-4003	142	43	⊆	⊆	NUM
ejpam-4003	142	44	mij	mij	X
ejpam-4003	142	45	xextb(mij	xextb(mij	PROPN
ejpam-4003	142	46	xintb(a	xintb(a	NOUN
ejpam-4003	142	47	)	)	PUNCT
ejpam-4003	142	48	)	)	PUNCT
ejpam-4003	142	49	,	,	PUNCT
ejpam-4003	142	50	2	2	X
ejpam-4003	142	51	.	.	X
ejpam-4003	142	52	mij	mij	PROPN
ejpam-4003	142	53	xextb(mij	xextb(mij	PROPN
ejpam-4003	142	54	xclb(a	xclb(a	PROPN
ejpam-4003	142	55	)	)	PUNCT
ejpam-4003	142	56	)	)	PUNCT
ejpam-4003	143	1	⊆	⊆	NUM
ejpam-4003	143	2	mij	mij	X
ejpam-4003	143	3	xextb(a	xextb(a	PROPN
ejpam-4003	143	4	)	)	PUNCT
ejpam-4003	143	5	,	,	PUNCT
ejpam-4003	143	6	3	3	X
ejpam-4003	143	7	.	.	PUNCT
ejpam-4003	143	8	mij	mij	PROPN
ejpam-4003	143	9	xextb(a	xextb(a	PROPN
ejpam-4003	143	10	)	)	PUNCT
ejpam-4003	143	11	⊆	⊆	NUM
ejpam-4003	143	12	x\mij	x\mij	PUNCT
ejpam-4003	143	13	xbdrb(mij	xbdrb(mij	ADJ
ejpam-4003	143	14	xintb(a	xintb(a	PROPN
ejpam-4003	143	15	)	)	PUNCT
ejpam-4003	143	16	)	)	PUNCT
ejpam-4003	143	17	,	,	PUNCT
ejpam-4003	143	18	4	4	X
ejpam-4003	143	19	.	.	X
ejpam-4003	143	20	mij	mij	PROPN
ejpam-4003	143	21	xextb(mij	xextb(mij	PROPN
ejpam-4003	143	22	xclb(a	xclb(a	PROPN
ejpam-4003	143	23	)	)	PUNCT
ejpam-4003	143	24	)	)	PUNCT
ejpam-4003	144	1	⊆	⊆	NUM
ejpam-4003	144	2	x\mij	x\mij	PUNCT
ejpam-4003	144	3	xbdrb(a	xbdrb(a	PROPN
ejpam-4003	144	4	)	)	PUNCT
ejpam-4003	144	5	.	.	PUNCT
ejpam-4003	145	1	proof	proof	NOUN
ejpam-4003	145	2	.	.	PUNCT
ejpam-4003	146	1	it	it	PRON
ejpam-4003	146	2	follows	follow	VERB
ejpam-4003	146	3	by	by	ADP
ejpam-4003	146	4	theorem	theorem	NOUN
ejpam-4003	146	5	1	1	NUM
ejpam-4003	146	6	and	and	CCONJ
ejpam-4003	146	7	lemma	lemma	PROPN
ejpam-4003	146	8	2	2	NUM
ejpam-4003	146	9	(	(	PUNCT
ejpam-4003	146	10	2	2	NUM
ejpam-4003	146	11	)	)	PUNCT
ejpam-4003	146	12	.	.	PUNCT
ejpam-4003	147	1	theorem	theorem	NOUN
ejpam-4003	147	2	2	2	NUM
ejpam-4003	147	3	.	.	X
ejpam-4003	148	1	let	let	VERB
ejpam-4003	148	2	(	(	PUNCT
ejpam-4003	148	3	x	x	X
ejpam-4003	148	4	,	,	PUNCT
ejpam-4003	148	5	m1	m1	PROPN
ejpam-4003	148	6	x	x	SYM
ejpam-4003	148	7	,	,	PUNCT
ejpam-4003	148	8	m	m	PROPN
ejpam-4003	148	9	2	2	NUM
ejpam-4003	148	10	x	x	NOUN
ejpam-4003	148	11	)	)	PUNCT
ejpam-4003	148	12	be	be	AUX
ejpam-4003	148	13	a	a	DET
ejpam-4003	148	14	biminimal	biminimal	NOUN
ejpam-4003	148	15	structure	structure	NOUN
ejpam-4003	148	16	space	space	NOUN
ejpam-4003	148	17	and	and	CCONJ
ejpam-4003	148	18	a	a	DET
ejpam-4003	148	19	be	be	AUX
ejpam-4003	148	20	a	a	DET
ejpam-4003	148	21	subset	subset	NOUN
ejpam-4003	148	22	of	of	ADP
ejpam-4003	148	23	x.	x.	NOUN
ejpam-4003	148	24	then	then	ADV
ejpam-4003	148	25	,	,	PUNCT
ejpam-4003	148	26	for	for	ADP
ejpam-4003	148	27	any	any	DET
ejpam-4003	148	28	i	i	PROPN
ejpam-4003	148	29	,	,	PUNCT
ejpam-4003	148	30	j	j	PROPN
ejpam-4003	148	31	=	=	SYM
ejpam-4003	148	32	1	1	NUM
ejpam-4003	148	33	,	,	PUNCT
ejpam-4003	148	34	2	2	NUM
ejpam-4003	148	35	and	and	CCONJ
ejpam-4003	148	36	i	i	PRON
ejpam-4003	148	37	6=	6=	PROPN
ejpam-4003	149	1	j	j	PROPN
ejpam-4003	149	2	,	,	PUNCT
ejpam-4003	149	3	the	the	DET
ejpam-4003	149	4	following	follow	VERB
ejpam-4003	149	5	statement	statement	NOUN
ejpam-4003	149	6	are	be	AUX
ejpam-4003	149	7	true	true	ADJ
ejpam-4003	149	8	:	:	PUNCT
ejpam-4003	149	9	1	1	X
ejpam-4003	149	10	.	.	X
ejpam-4003	149	11	a	a	PRON
ejpam-4003	149	12	is	be	AUX
ejpam-4003	149	13	(	(	PUNCT
ejpam-4003	149	14	i	i	PROPN
ejpam-4003	149	15	,	,	PUNCT
ejpam-4003	149	16	j)−mx	j)−mx	PROPN
ejpam-4003	149	17	−	−	PROPN
ejpam-4003	149	18	β−closed	β−close	VERB
ejpam-4003	149	19	if	if	SCONJ
ejpam-4003	149	20	and	and	CCONJ
ejpam-4003	149	21	only	only	ADV
ejpam-4003	149	22	if	if	SCONJ
ejpam-4003	149	23	mij	mij	X
ejpam-4003	149	24	xextb(a	xextb(a	PROPN
ejpam-4003	149	25	)	)	PUNCT
ejpam-4003	149	26	=	=	PUNCT
ejpam-4003	150	1	x\	x\	NOUN
ejpam-4003	150	2	,	,	PUNCT
ejpam-4003	150	3	2	2	NUM
ejpam-4003	150	4	.	.	X
ejpam-4003	150	5	a	a	PRON
ejpam-4003	150	6	is	be	AUX
ejpam-4003	150	7	(	(	PUNCT
ejpam-4003	150	8	i	i	NOUN
ejpam-4003	150	9	,	,	PUNCT
ejpam-4003	150	10	j)−mx	j)−mx	PROPN
ejpam-4003	151	1	−	−	PROPN
ejpam-4003	151	2	β−open	β−open	PUNCT
ejpam-4003	151	3	if	if	SCONJ
ejpam-4003	151	4	and	and	CCONJ
ejpam-4003	151	5	only	only	ADV
ejpam-4003	151	6	if	if	SCONJ
ejpam-4003	151	7	mij	mij	NOUN
ejpam-4003	151	8	xextb(x\a	xextb(x\a	X
ejpam-4003	151	9	)	)	PUNCT
ejpam-4003	152	1	=	=	SYM
ejpam-4003	152	2	a.	a.	NOUN
ejpam-4003	152	3	proof	proof	NOUN
ejpam-4003	152	4	.	.	PUNCT
ejpam-4003	153	1	assume	assume	VERB
ejpam-4003	153	2	that	that	SCONJ
ejpam-4003	153	3	(	(	PUNCT
ejpam-4003	153	4	x	x	X
ejpam-4003	153	5	,	,	PUNCT
ejpam-4003	153	6	m1	m1	PROPN
ejpam-4003	153	7	x	x	SYM
ejpam-4003	153	8	,	,	PUNCT
ejpam-4003	153	9	m	m	PROPN
ejpam-4003	153	10	2	2	NUM
ejpam-4003	153	11	x	x	NOUN
ejpam-4003	153	12	)	)	PUNCT
ejpam-4003	153	13	is	be	AUX
ejpam-4003	153	14	a	a	DET
ejpam-4003	153	15	biminimal	biminimal	NOUN
ejpam-4003	153	16	structure	structure	NOUN
ejpam-4003	153	17	space	space	NOUN
ejpam-4003	153	18	and	and	CCONJ
ejpam-4003	153	19	a	a	PRON
ejpam-4003	153	20	is	be	AUX
ejpam-4003	153	21	a	a	DET
ejpam-4003	153	22	subset	subset	NOUN
ejpam-4003	153	23	of	of	ADP
ejpam-4003	153	24	x.	x.	NOUN
ejpam-4003	153	25	1	1	NUM
ejpam-4003	153	26	.	.	PUNCT
ejpam-4003	154	1	(=	(=	AUX
ejpam-4003	154	2	⇒	⇒	NOUN
ejpam-4003	154	3	)	)	PUNCT
ejpam-4003	154	4	suppose	suppose	VERB
ejpam-4003	154	5	thata	thata	PROPN
ejpam-4003	154	6	is	be	AUX
ejpam-4003	154	7	(	(	PUNCT
ejpam-4003	154	8	i	i	PRON
ejpam-4003	154	9	,	,	PUNCT
ejpam-4003	154	10	j)−mx−β−closed	j)−mx−β−closed	PROPN
ejpam-4003	154	11	.	.	PUNCT
ejpam-4003	155	1	then	then	ADV
ejpam-4003	155	2	,	,	PUNCT
ejpam-4003	155	3	mij	mij	X
ejpam-4003	155	4	xextb(a	xextb(a	PROPN
ejpam-4003	155	5	)	)	PUNCT
ejpam-4003	155	6	=	=	SYM
ejpam-4003	156	1	x\mij	x\mij	PROPN
ejpam-4003	156	2	xclb(a	xclb(a	PROPN
ejpam-4003	156	3	)	)	PUNCT
ejpam-4003	156	4	=	=	SYM
ejpam-4003	156	5	x\a	x\a	PROPN
ejpam-4003	156	6	.	.	PUNCT
ejpam-4003	157	1	(	(	PUNCT
ejpam-4003	157	2	⇐	⇐	NOUN
ejpam-4003	157	3	=)	=)	PROPN
ejpam-4003	157	4	suppose	suppose	VERB
ejpam-4003	157	5	that	that	SCONJ
ejpam-4003	157	6	mij	mij	PROPN
ejpam-4003	157	7	xextb(a	xextb(a	PROPN
ejpam-4003	157	8	)	)	PUNCT
ejpam-4003	157	9	=	=	SYM
ejpam-4003	158	1	x\a	x\a	PROPN
ejpam-4003	158	2	.	.	PUNCT
ejpam-4003	159	1	it	it	PRON
ejpam-4003	159	2	means	mean	VERB
ejpam-4003	159	3	that	that	SCONJ
ejpam-4003	159	4	x\mij	x\mij	PROPN
ejpam-4003	159	5	xclb(a	xclb(a	X
ejpam-4003	159	6	)	)	PUNCT
ejpam-4003	159	7	=	=	SYM
ejpam-4003	160	1	x\a	x\a	PROPN
ejpam-4003	160	2	.	.	PUNCT
ejpam-4003	161	1	since	since	SCONJ
ejpam-4003	161	2	a	a	DET
ejpam-4003	161	3	⊆	⊆	NUM
ejpam-4003	161	4	mij	mij	X
ejpam-4003	161	5	xclb(a	xclb(a	PROPN
ejpam-4003	161	6	)	)	PUNCT
ejpam-4003	161	7	,	,	PUNCT
ejpam-4003	161	8	then	then	ADV
ejpam-4003	161	9	mij	mij	VERB
ejpam-4003	161	10	xclb(a	xclb(a	PROPN
ejpam-4003	161	11	)	)	PUNCT
ejpam-4003	161	12	=	=	SYM
ejpam-4003	161	13	a.	a.	NOUN
ejpam-4003	161	14	finally	finally	ADV
ejpam-4003	161	15	,	,	PUNCT
ejpam-4003	161	16	a	a	PRON
ejpam-4003	161	17	is	be	AUX
ejpam-4003	161	18	(	(	PUNCT
ejpam-4003	161	19	i	i	PROPN
ejpam-4003	161	20	,	,	PUNCT
ejpam-4003	161	21	j)−mx	j)−mx	PROPN
ejpam-4003	161	22	−	−	PROPN
ejpam-4003	161	23	β−closed	β−closed	PROPN
ejpam-4003	161	24	.	.	PUNCT
ejpam-4003	162	1	2	2	X
ejpam-4003	162	2	.	.	PUNCT
ejpam-4003	162	3	(=	(=	NOUN
ejpam-4003	162	4	⇒	⇒	NOUN
ejpam-4003	162	5	)	)	PUNCT
ejpam-4003	162	6	suppose	suppose	VERB
ejpam-4003	162	7	that	that	SCONJ
ejpam-4003	162	8	a	a	PRON
ejpam-4003	162	9	is	be	AUX
ejpam-4003	162	10	(	(	PUNCT
ejpam-4003	162	11	i	i	PROPN
ejpam-4003	162	12	,	,	PUNCT
ejpam-4003	162	13	j)−mx−β−open	j)−mx−β−open	PROPN
ejpam-4003	162	14	.	.	PUNCT
ejpam-4003	163	1	then	then	ADV
ejpam-4003	163	2	,	,	PUNCT
ejpam-4003	163	3	x\a	x\a	PROPN
ejpam-4003	163	4	is	be	AUX
ejpam-4003	163	5	(	(	PUNCT
ejpam-4003	163	6	i	i	PRON
ejpam-4003	163	7	,	,	PUNCT
ejpam-4003	163	8	j)−mx−β−closed	j)−mx−β−close	VERB
ejpam-4003	163	9	.	.	PUNCT
ejpam-4003	164	1	using	use	VERB
ejpam-4003	164	2	(	(	PUNCT
ejpam-4003	164	3	1	1	NUM
ejpam-4003	164	4	)	)	PUNCT
ejpam-4003	164	5	,	,	PUNCT
ejpam-4003	164	6	mij	mij	NOUN
ejpam-4003	164	7	xextb(x\a	xextb(x\a	X
ejpam-4003	164	8	)	)	PUNCT
ejpam-4003	164	9	=	=	SYM
ejpam-4003	164	10	x\(x\a	x\(x\a	NOUN
ejpam-4003	164	11	)	)	PUNCT
ejpam-4003	164	12	=	=	SYM
ejpam-4003	164	13	a.	a.	NOUN
ejpam-4003	164	14	(	(	PUNCT
ejpam-4003	164	15	⇐	⇐	ADJ
ejpam-4003	164	16	=)	=)	PROPN
ejpam-4003	164	17	suppose	suppose	VERB
ejpam-4003	164	18	that	that	SCONJ
ejpam-4003	164	19	mij	mij	NOUN
ejpam-4003	164	20	xextb(x\a	xextb(x\a	X
ejpam-4003	164	21	)	)	PUNCT
ejpam-4003	165	1	=	=	PUNCT
ejpam-4003	165	2	a.	a.	NOUN
ejpam-4003	165	3	we	we	PRON
ejpam-4003	165	4	have	have	VERB
ejpam-4003	165	5	a	a	DET
ejpam-4003	165	6	=	=	SYM
ejpam-4003	165	7	x\mij	x\mij	X
ejpam-4003	165	8	xclb(x\a	xclb(x\a	PROPN
ejpam-4003	165	9	)	)	PUNCT
ejpam-4003	166	1	=	=	SYM
ejpam-4003	166	2	x\(x\mij	x\(x\mij	PROPN
ejpam-4003	166	3	xintb(a	xintb(a	PROPN
ejpam-4003	166	4	)	)	PUNCT
ejpam-4003	166	5	)	)	PUNCT
ejpam-4003	167	1	=	=	PUNCT
ejpam-4003	167	2	mij	mij	X
ejpam-4003	167	3	xintb(a	xintb(a	PROPN
ejpam-4003	167	4	)	)	PUNCT
ejpam-4003	167	5	)	)	PUNCT
ejpam-4003	167	6	.	.	PUNCT
ejpam-4003	168	1	hence	hence	ADV
ejpam-4003	168	2	,	,	PUNCT
ejpam-4003	168	3	a	a	PRON
ejpam-4003	168	4	is	be	AUX
ejpam-4003	168	5	(	(	PUNCT
ejpam-4003	168	6	i	i	NOUN
ejpam-4003	168	7	,	,	PUNCT
ejpam-4003	168	8	j)−mx	j)−mx	PROPN
ejpam-4003	168	9	−	−	PROPN
ejpam-4003	168	10	β−open	β−open	PROPN
ejpam-4003	168	11	.	.	PUNCT
ejpam-4003	169	1	corollary	corollary	ADJ
ejpam-4003	169	2	2	2	NUM
ejpam-4003	169	3	.	.	PUNCT
ejpam-4003	170	1	let	let	VERB
ejpam-4003	170	2	(	(	PUNCT
ejpam-4003	170	3	x	x	X
ejpam-4003	170	4	,	,	PUNCT
ejpam-4003	170	5	m1	m1	PROPN
ejpam-4003	170	6	x	x	SYM
ejpam-4003	170	7	,	,	PUNCT
ejpam-4003	170	8	m	m	PROPN
ejpam-4003	170	9	2	2	NUM
ejpam-4003	170	10	x	x	NOUN
ejpam-4003	170	11	)	)	PUNCT
ejpam-4003	170	12	be	be	AUX
ejpam-4003	170	13	a	a	DET
ejpam-4003	170	14	biminimal	biminimal	NOUN
ejpam-4003	170	15	structure	structure	NOUN
ejpam-4003	170	16	space	space	NOUN
ejpam-4003	170	17	and	and	CCONJ
ejpam-4003	170	18	a	a	DET
ejpam-4003	170	19	be	be	AUX
ejpam-4003	170	20	a	a	DET
ejpam-4003	170	21	subset	subset	NOUN
ejpam-4003	170	22	of	of	ADP
ejpam-4003	170	23	x.	x.	NOUN
ejpam-4003	170	24	then	then	ADV
ejpam-4003	170	25	,	,	PUNCT
ejpam-4003	170	26	for	for	ADP
ejpam-4003	170	27	i	i	PRON
ejpam-4003	170	28	,	,	PUNCT
ejpam-4003	170	29	j	j	PROPN
ejpam-4003	170	30	=	=	SYM
ejpam-4003	170	31	1	1	NUM
ejpam-4003	170	32	,	,	PUNCT
ejpam-4003	170	33	2	2	NUM
ejpam-4003	170	34	and	and	CCONJ
ejpam-4003	170	35	i	i	PRON
ejpam-4003	170	36	6=	6=	PROPN
ejpam-4003	170	37	j	j	PROPN
ejpam-4003	170	38	,	,	PUNCT
ejpam-4003	170	39	1	1	NUM
ejpam-4003	170	40	.	.	PUNCT
ejpam-4003	171	1	mij	mij	PROPN
ejpam-4003	171	2	xextb(mij	xextb(mij	PROPN
ejpam-4003	171	3	xclb(a	xclb(a	PROPN
ejpam-4003	171	4	)	)	PUNCT
ejpam-4003	171	5	)	)	PUNCT
ejpam-4003	172	1	=	=	PUNCT
ejpam-4003	172	2	mij	mij	X
ejpam-4003	172	3	xextb(a	xextb(a	PROPN
ejpam-4003	172	4	)	)	PUNCT
ejpam-4003	172	5	,	,	PUNCT
ejpam-4003	172	6	2	2	X
ejpam-4003	172	7	.	.	X
ejpam-4003	173	1	mij	mij	PROPN
ejpam-4003	173	2	xextb(x\mij	xextb(x\mij	PROPN
ejpam-4003	173	3	xextb(a	xextb(a	PROPN
ejpam-4003	173	4	)	)	PUNCT
ejpam-4003	173	5	)	)	PUNCT
ejpam-4003	174	1	=	=	PUNCT
ejpam-4003	174	2	mij	mij	X
ejpam-4003	174	3	xextb(a	xextb(a	ADJ
ejpam-4003	174	4	)	)	PUNCT
ejpam-4003	174	5	proof	proof	NOUN
ejpam-4003	174	6	.	.	PUNCT
ejpam-4003	175	1	this	this	PRON
ejpam-4003	175	2	follows	follow	VERB
ejpam-4003	175	3	by	by	ADP
ejpam-4003	175	4	theorem	theorem	NOUN
ejpam-4003	175	5	2	2	NUM
ejpam-4003	175	6	immediately	immediately	ADV
ejpam-4003	175	7	.	.	PUNCT
ejpam-4003	176	1	from	from	ADP
ejpam-4003	176	2	example	example	NOUN
ejpam-4003	176	3	1	1	NUM
ejpam-4003	176	4	,	,	PUNCT
ejpam-4003	176	5	m12	m12	PROPN
ejpam-4003	176	6	xextb({2})∪m12	xextb({2})∪m12	PROPN
ejpam-4003	176	7	xextb({1	xextb({1	PROPN
ejpam-4003	176	8	,	,	PUNCT
ejpam-4003	176	9	3	3	NUM
ejpam-4003	176	10	}	}	PUNCT
ejpam-4003	176	11	)	)	PUNCT
ejpam-4003	176	12	6=	6=	SYM
ejpam-4003	176	13	m12	m12	PROPN
ejpam-4003	176	14	xextb({2}∩{1	xextb({2}∩{1	PROPN
ejpam-4003	176	15	,	,	PUNCT
ejpam-4003	176	16	3	3	NUM
ejpam-4003	176	17	}	}	PUNCT
ejpam-4003	176	18	)	)	PUNCT
ejpam-4003	176	19	,	,	PUNCT
ejpam-4003	176	20	whereas	whereas	SCONJ
ejpam-4003	176	21	m12	m12	PROPN
ejpam-4003	176	22	xextb({2})∪m12	xextb({2})∪m12	PROPN
ejpam-4003	176	23	xextb({1	xextb({1	PROPN
ejpam-4003	176	24	,	,	PUNCT
ejpam-4003	176	25	2	2	NUM
ejpam-4003	176	26	}	}	PUNCT
ejpam-4003	176	27	)	)	PUNCT
ejpam-4003	176	28	=	=	SYM
ejpam-4003	176	29	m12	m12	PROPN
ejpam-4003	176	30	xextb({2	xextb({2	PROPN
ejpam-4003	176	31	}	}	PUNCT
ejpam-4003	176	32	∩	∩	NOUN
ejpam-4003	176	33	{	{	PUNCT
ejpam-4003	176	34	1	1	NUM
ejpam-4003	176	35	,	,	PUNCT
ejpam-4003	176	36	}	}	PUNCT
ejpam-4003	176	37	)	)	PUNCT
ejpam-4003	176	38	.	.	PUNCT
ejpam-4003	177	1	therefore	therefore	ADV
ejpam-4003	177	2	,	,	PUNCT
ejpam-4003	177	3	it	it	PRON
ejpam-4003	177	4	needs	need	VERB
ejpam-4003	177	5	some	some	DET
ejpam-4003	177	6	conditions	condition	NOUN
ejpam-4003	177	7	to	to	PART
ejpam-4003	177	8	show	show	VERB
ejpam-4003	177	9	that	that	SCONJ
ejpam-4003	177	10	mij	mij	PROPN
ejpam-4003	177	11	xextb(a	xextb(a	PROPN
ejpam-4003	177	12	)	)	PUNCT
ejpam-4003	177	13	∪mij	∪mij	NOUN
ejpam-4003	177	14	xextb(b	xextb(b	PROPN
ejpam-4003	177	15	)	)	PUNCT
ejpam-4003	177	16	=	=	SYM
ejpam-4003	177	17	mij	mij	VERB
ejpam-4003	177	18	xextb(a	xextb(a	PROPN
ejpam-4003	177	19	∩b	∩b	NOUN
ejpam-4003	177	20	)	)	PUNCT
ejpam-4003	177	21	,	,	PUNCT
ejpam-4003	177	22	which	which	PRON
ejpam-4003	177	23	found	find	VERB
ejpam-4003	177	24	in	in	ADP
ejpam-4003	177	25	the	the	DET
ejpam-4003	177	26	next	next	ADJ
ejpam-4003	177	27	result	result	NOUN
ejpam-4003	177	28	.	.	PUNCT
ejpam-4003	178	1	similarly	similarly	ADV
ejpam-4003	178	2	,	,	PUNCT
ejpam-4003	178	3	the	the	DET
ejpam-4003	178	4	following	follow	VERB
ejpam-4003	178	5	equation	equation	NOUN
ejpam-4003	178	6	mij	mij	X
ejpam-4003	178	7	xextb(a	xextb(a	PROPN
ejpam-4003	178	8	∪b	∪b	NOUN
ejpam-4003	178	9	)	)	PUNCT
ejpam-4003	178	10	=	=	SYM
ejpam-4003	178	11	mij	mij	X
ejpam-4003	178	12	xextb(a	xextb(a	PROPN
ejpam-4003	178	13	)	)	PUNCT
ejpam-4003	178	14	∩mij	∩mij	PROPN
ejpam-4003	178	15	xextb(b	xextb(b	PROPN
ejpam-4003	178	16	)	)	PUNCT
ejpam-4003	178	17	is	be	AUX
ejpam-4003	178	18	true	true	ADJ
ejpam-4003	178	19	if	if	SCONJ
ejpam-4003	178	20	it	it	PRON
ejpam-4003	178	21	has	have	VERB
ejpam-4003	178	22	some	some	DET
ejpam-4003	178	23	appropriate	appropriate	ADJ
ejpam-4003	178	24	conditions	condition	NOUN
ejpam-4003	178	25	.	.	PUNCT
ejpam-4003	179	1	t.	t.	PROPN
ejpam-4003	179	2	prasertsang	prasertsang	PROPN
ejpam-4003	179	3	,	,	PUNCT
ejpam-4003	179	4	p.	p.	PROPN
ejpam-4003	179	5	prasertsang	prasertsang	PROPN
ejpam-4003	179	6	/	/	SYM
ejpam-4003	179	7	eur	eur	PROPN
ejpam-4003	179	8	.	.	PUNCT
ejpam-4003	180	1	j.	j.	PROPN
ejpam-4003	180	2	pure	pure	PROPN
ejpam-4003	180	3	appl	appl	PROPN
ejpam-4003	180	4	.	.	PROPN
ejpam-4003	180	5	math	math	PROPN
ejpam-4003	180	6	,	,	PUNCT
ejpam-4003	180	7	14	14	NUM
ejpam-4003	180	8	(	(	PUNCT
ejpam-4003	180	9	3	3	NUM
ejpam-4003	180	10	)	)	PUNCT
ejpam-4003	180	11	(	(	PUNCT
ejpam-4003	180	12	2021	2021	NUM
ejpam-4003	180	13	)	)	PUNCT
ejpam-4003	180	14	,	,	PUNCT
ejpam-4003	180	15	915	915	NUM
ejpam-4003	180	16	-	-	SYM
ejpam-4003	180	17	922	922	NUM
ejpam-4003	180	18	920	920	NUM
ejpam-4003	180	19	theorem	theorem	NOUN
ejpam-4003	180	20	3	3	X
ejpam-4003	180	21	.	.	PUNCT
ejpam-4003	181	1	let	let	VERB
ejpam-4003	181	2	(	(	PUNCT
ejpam-4003	181	3	x	x	X
ejpam-4003	181	4	,	,	PUNCT
ejpam-4003	181	5	m1	m1	PROPN
ejpam-4003	181	6	x	x	SYM
ejpam-4003	181	7	,	,	PUNCT
ejpam-4003	181	8	m	m	PROPN
ejpam-4003	181	9	2	2	NUM
ejpam-4003	181	10	x	x	NOUN
ejpam-4003	181	11	)	)	PUNCT
ejpam-4003	181	12	be	be	AUX
ejpam-4003	181	13	a	a	DET
ejpam-4003	181	14	biminimal	biminimal	NOUN
ejpam-4003	181	15	structure	structure	NOUN
ejpam-4003	181	16	space	space	NOUN
ejpam-4003	181	17	,	,	PUNCT
ejpam-4003	181	18	a	a	PRON
ejpam-4003	181	19	,	,	PUNCT
ejpam-4003	181	20	b	b	NOUN
ejpam-4003	181	21	be	be	AUX
ejpam-4003	181	22	subsets	subset	NOUN
ejpam-4003	181	23	of	of	ADP
ejpam-4003	181	24	x.	x.	NOUN
ejpam-4003	181	25	then	then	ADV
ejpam-4003	181	26	,	,	PUNCT
ejpam-4003	181	27	for	for	ADP
ejpam-4003	181	28	any	any	DET
ejpam-4003	181	29	i	i	PROPN
ejpam-4003	181	30	,	,	PUNCT
ejpam-4003	181	31	j	j	PROPN
ejpam-4003	181	32	=	=	SYM
ejpam-4003	181	33	1	1	NUM
ejpam-4003	181	34	,	,	PUNCT
ejpam-4003	181	35	2	2	NUM
ejpam-4003	181	36	and	and	CCONJ
ejpam-4003	181	37	i	i	PRON
ejpam-4003	181	38	6=	6=	PROPN
ejpam-4003	182	1	j	j	PROPN
ejpam-4003	182	2	,	,	PUNCT
ejpam-4003	182	3	we	we	PRON
ejpam-4003	182	4	have	have	VERB
ejpam-4003	182	5	:	:	PUNCT
ejpam-4003	183	1	1	1	X
ejpam-4003	183	2	.	.	X
ejpam-4003	184	1	if	if	SCONJ
ejpam-4003	184	2	a	a	PRON
ejpam-4003	184	3	and	and	CCONJ
ejpam-4003	184	4	b	b	NOUN
ejpam-4003	184	5	are	be	AUX
ejpam-4003	184	6	(	(	PUNCT
ejpam-4003	184	7	i	i	NOUN
ejpam-4003	184	8	,	,	PUNCT
ejpam-4003	184	9	j)−mx	j)−mx	PROPN
ejpam-4003	184	10	−	−	PROPN
ejpam-4003	185	1	β−closed	β−closed	PROPN
ejpam-4003	185	2	,	,	PUNCT
ejpam-4003	185	3	then	then	ADV
ejpam-4003	185	4	mij	mij	VERB
ejpam-4003	185	5	xextb(a	xextb(a	PROPN
ejpam-4003	185	6	)	)	PUNCT
ejpam-4003	185	7	∪mij	∪mij	NOUN
ejpam-4003	185	8	xextb(b	xextb(b	PROPN
ejpam-4003	185	9	)	)	PUNCT
ejpam-4003	185	10	=	=	SYM
ejpam-4003	185	11	mij	mij	VERB
ejpam-4003	185	12	xextb(a	xextb(a	PROPN
ejpam-4003	185	13	∩b	∩b	NOUN
ejpam-4003	185	14	)	)	PUNCT
ejpam-4003	185	15	.	.	PUNCT
ejpam-4003	186	1	2	2	X
ejpam-4003	186	2	.	.	X
ejpam-4003	186	3	if	if	SCONJ
ejpam-4003	186	4	a	a	DET
ejpam-4003	186	5	,	,	PUNCT
ejpam-4003	186	6	b	b	NOUN
ejpam-4003	186	7	and	and	CCONJ
ejpam-4003	186	8	a	a	DET
ejpam-4003	186	9	∪b	∪b	X
ejpam-4003	186	10	are	be	AUX
ejpam-4003	186	11	(	(	PUNCT
ejpam-4003	186	12	i	i	NOUN
ejpam-4003	186	13	,	,	PUNCT
ejpam-4003	186	14	j)−mx	j)−mx	PROPN
ejpam-4003	186	15	−	−	PROPN
ejpam-4003	187	1	β−closed	β−closed	PROPN
ejpam-4003	187	2	,	,	PUNCT
ejpam-4003	187	3	then	then	ADV
ejpam-4003	187	4	mij	mij	VERB
ejpam-4003	187	5	xextb(a	xextb(a	PROPN
ejpam-4003	187	6	∪b	∪b	NOUN
ejpam-4003	187	7	)	)	PUNCT
ejpam-4003	187	8	=	=	SYM
ejpam-4003	187	9	mij	mij	X
ejpam-4003	187	10	xextb(a	xextb(a	PROPN
ejpam-4003	187	11	)	)	PUNCT
ejpam-4003	187	12	∩mij	∩mij	ADJ
ejpam-4003	187	13	xextb(b	xextb(b	PROPN
ejpam-4003	187	14	)	)	PUNCT
ejpam-4003	187	15	.	.	PUNCT
ejpam-4003	188	1	proof	proof	NOUN
ejpam-4003	188	2	.	.	PUNCT
ejpam-4003	189	1	assume	assume	VERB
ejpam-4003	189	2	that	that	SCONJ
ejpam-4003	189	3	(	(	PUNCT
ejpam-4003	189	4	x	x	X
ejpam-4003	189	5	,	,	PUNCT
ejpam-4003	189	6	m1	m1	PROPN
ejpam-4003	189	7	x	x	SYM
ejpam-4003	189	8	,	,	PUNCT
ejpam-4003	189	9	m	m	PROPN
ejpam-4003	189	10	2	2	NUM
ejpam-4003	189	11	x	x	NOUN
ejpam-4003	189	12	)	)	PUNCT
ejpam-4003	189	13	is	be	AUX
ejpam-4003	189	14	a	a	DET
ejpam-4003	189	15	biminimal	biminimal	NOUN
ejpam-4003	189	16	structure	structure	NOUN
ejpam-4003	189	17	space	space	NOUN
ejpam-4003	189	18	and	and	CCONJ
ejpam-4003	189	19	a	a	DET
ejpam-4003	189	20	,	,	PUNCT
ejpam-4003	189	21	b	b	NOUN
ejpam-4003	189	22	are	be	AUX
ejpam-4003	189	23	subsets	subset	NOUN
ejpam-4003	189	24	of	of	ADP
ejpam-4003	189	25	x.	x.	NOUN
ejpam-4003	189	26	1	1	NUM
ejpam-4003	189	27	.	.	PUNCT
ejpam-4003	189	28	assume	assume	VERB
ejpam-4003	189	29	that	that	SCONJ
ejpam-4003	189	30	a	a	PRON
ejpam-4003	189	31	and	and	CCONJ
ejpam-4003	189	32	b	b	NOUN
ejpam-4003	189	33	are	be	AUX
ejpam-4003	189	34	(	(	PUNCT
ejpam-4003	189	35	i	i	PROPN
ejpam-4003	189	36	,	,	PUNCT
ejpam-4003	189	37	j	j	PROPN
ejpam-4003	189	38	)	)	PUNCT
ejpam-4003	189	39	−	−	PROPN
ejpam-4003	189	40	mx	mx	PROPN
ejpam-4003	189	41	−	−	PROPN
ejpam-4003	189	42	β−closed	β−closed	PROPN
ejpam-4003	189	43	.	.	PUNCT
ejpam-4003	190	1	therefore	therefore	ADV
ejpam-4003	190	2	,	,	PUNCT
ejpam-4003	190	3	a	a	DET
ejpam-4003	190	4	∩	∩	ADJ
ejpam-4003	190	5	b	b	NOUN
ejpam-4003	190	6	is	be	AUX
ejpam-4003	190	7	also	also	ADV
ejpam-4003	190	8	(	(	PUNCT
ejpam-4003	190	9	i	i	NOUN
ejpam-4003	190	10	,	,	PUNCT
ejpam-4003	190	11	j)−mx	j)−mx	PROPN
ejpam-4003	190	12	−	−	PROPN
ejpam-4003	190	13	β−closed	β−closed	PROPN
ejpam-4003	190	14	.	.	PUNCT
ejpam-4003	191	1	by	by	ADP
ejpam-4003	191	2	theorem	theorem	NOUN
ejpam-4003	191	3	2	2	NUM
ejpam-4003	191	4	(	(	PUNCT
ejpam-4003	191	5	1	1	NUM
ejpam-4003	191	6	)	)	PUNCT
ejpam-4003	191	7	,	,	PUNCT
ejpam-4003	191	8	mij	mij	VERB
ejpam-4003	191	9	xextb(a	xextb(a	PRON
ejpam-4003	191	10	∩b	∩b	NOUN
ejpam-4003	191	11	)	)	PUNCT
ejpam-4003	191	12	=	=	SYM
ejpam-4003	192	1	x\a	x\a	PUNCT
ejpam-4003	192	2	∩b	∩b	NOUN
ejpam-4003	192	3	=	=	SYM
ejpam-4003	192	4	(	(	PUNCT
ejpam-4003	192	5	x\a	x\a	PROPN
ejpam-4003	192	6	)	)	PUNCT
ejpam-4003	192	7	∪	∪	NOUN
ejpam-4003	192	8	(	(	PUNCT
ejpam-4003	192	9	x\b	x\b	NOUN
ejpam-4003	192	10	)	)	PUNCT
ejpam-4003	192	11	=	=	PUNCT
ejpam-4003	192	12	mij	mij	X
ejpam-4003	192	13	xextb(a	xextb(a	PROPN
ejpam-4003	192	14	)	)	PUNCT
ejpam-4003	192	15	∪mij	∪mij	NOUN
ejpam-4003	192	16	xextb(b	xextb(b	PROPN
ejpam-4003	192	17	)	)	PUNCT
ejpam-4003	192	18	.	.	PUNCT
ejpam-4003	193	1	2	2	X
ejpam-4003	193	2	.	.	X
ejpam-4003	193	3	assume	assume	VERB
ejpam-4003	193	4	thata	thata	PROPN
ejpam-4003	193	5	,	,	PUNCT
ejpam-4003	193	6	b	b	PROPN
ejpam-4003	193	7	anda∪b	anda∪b	NUM
ejpam-4003	193	8	are	be	AUX
ejpam-4003	193	9	(	(	PUNCT
ejpam-4003	193	10	i	i	PRON
ejpam-4003	193	11	,	,	PUNCT
ejpam-4003	193	12	j)−mx−β−closed	j)−mx−β−closed	PROPN
ejpam-4003	193	13	.	.	PUNCT
ejpam-4003	194	1	by	by	ADP
ejpam-4003	194	2	theorem	theorem	NOUN
ejpam-4003	194	3	2	2	NUM
ejpam-4003	194	4	(	(	PUNCT
ejpam-4003	194	5	1),mij	1),mij	NUM
ejpam-4003	194	6	xextb(a	xextb(a	PROPN
ejpam-4003	194	7	)	)	PUNCT
ejpam-4003	194	8	=	=	SYM
ejpam-4003	194	9	x\a	x\a	PROPN
ejpam-4003	194	10	,	,	PUNCT
ejpam-4003	194	11	mij	mij	NOUN
ejpam-4003	194	12	xextb(b	xextb(b	PROPN
ejpam-4003	194	13	)	)	PUNCT
ejpam-4003	194	14	=	=	SYM
ejpam-4003	194	15	x\b	x\b	PROPN
ejpam-4003	194	16	and	and	CCONJ
ejpam-4003	194	17	mij	mij	VERB
ejpam-4003	194	18	xextb(a	xextb(a	PROPN
ejpam-4003	194	19	∪b	∪b	NOUN
ejpam-4003	194	20	)	)	PUNCT
ejpam-4003	194	21	=	=	PUNCT
ejpam-4003	194	22	x\(a	x\(a	PROPN
ejpam-4003	194	23	∪b	∪b	NOUN
ejpam-4003	194	24	)	)	PUNCT
ejpam-4003	194	25	.	.	PUNCT
ejpam-4003	195	1	furthermore	furthermore	ADV
ejpam-4003	195	2	,	,	PUNCT
ejpam-4003	195	3	mij	mij	X
ejpam-4003	195	4	xextb(a	xextb(a	PROPN
ejpam-4003	195	5	∪b	∪b	NOUN
ejpam-4003	195	6	)	)	PUNCT
ejpam-4003	195	7	=	=	PUNCT
ejpam-4003	195	8	x\(a	x\(a	X
ejpam-4003	195	9	∪b	∪b	X
ejpam-4003	195	10	)	)	PUNCT
ejpam-4003	195	11	=	=	SYM
ejpam-4003	195	12	(	(	PUNCT
ejpam-4003	195	13	x\a	x\a	PROPN
ejpam-4003	195	14	)	)	PUNCT
ejpam-4003	195	15	∩	∩	NOUN
ejpam-4003	195	16	(	(	PUNCT
ejpam-4003	195	17	x\b	x\b	PROPN
ejpam-4003	195	18	)	)	PUNCT
ejpam-4003	195	19	=	=	SYM
ejpam-4003	195	20	mij	mij	X
ejpam-4003	195	21	xextb(a	xextb(a	PROPN
ejpam-4003	195	22	)	)	PUNCT
ejpam-4003	195	23	∩mij	∩mij	ADJ
ejpam-4003	195	24	xextb(b	xextb(b	PROPN
ejpam-4003	195	25	)	)	PUNCT
ejpam-4003	195	26	.	.	PUNCT
ejpam-4003	196	1	next	next	ADV
ejpam-4003	196	2	,	,	PUNCT
ejpam-4003	196	3	we	we	PRON
ejpam-4003	196	4	give	give	VERB
ejpam-4003	196	5	some	some	DET
ejpam-4003	196	6	notions	notion	NOUN
ejpam-4003	196	7	for	for	ADP
ejpam-4003	196	8	the	the	DET
ejpam-4003	196	9	product	product	NOUN
ejpam-4003	196	10	of	of	ADP
ejpam-4003	196	11	two	two	NUM
ejpam-4003	196	12	biminimal	biminimal	NOUN
ejpam-4003	196	13	structure	structure	NOUN
ejpam-4003	196	14	space	space	NOUN
ejpam-4003	196	15	as	as	ADP
ejpam-4003	196	16	the	the	DET
ejpam-4003	196	17	following	following	NOUN
ejpam-4003	196	18	:	:	PUNCT
ejpam-4003	196	19	definition	definition	NOUN
ejpam-4003	196	20	6	6	NUM
ejpam-4003	196	21	.	.	PUNCT
ejpam-4003	197	1	let	let	VERB
ejpam-4003	197	2	(	(	PUNCT
ejpam-4003	197	3	x	x	X
ejpam-4003	197	4	,	,	PUNCT
ejpam-4003	197	5	m1	m1	PROPN
ejpam-4003	197	6	x	x	SYM
ejpam-4003	197	7	,	,	PUNCT
ejpam-4003	197	8	m	m	PROPN
ejpam-4003	197	9	2	2	NUM
ejpam-4003	197	10	x	x	NOUN
ejpam-4003	197	11	)	)	PUNCT
ejpam-4003	197	12	and	and	CCONJ
ejpam-4003	197	13	(	(	PUNCT
ejpam-4003	197	14	y	y	PROPN
ejpam-4003	197	15	,	,	PUNCT
ejpam-4003	197	16	m1	m1	PROPN
ejpam-4003	197	17	y	y	PROPN
ejpam-4003	197	18	,	,	PUNCT
ejpam-4003	197	19	m	m	PROPN
ejpam-4003	197	20	2	2	NUM
ejpam-4003	197	21	y	y	NOUN
ejpam-4003	197	22	)	)	PUNCT
ejpam-4003	197	23	be	be	AUX
ejpam-4003	197	24	biminimal	biminimal	ADJ
ejpam-4003	197	25	structure	structure	NOUN
ejpam-4003	197	26	spaces	space	NOUN
ejpam-4003	197	27	,	,	PUNCT
ejpam-4003	197	28	a	a	PRON
ejpam-4003	197	29	,	,	PUNCT
ejpam-4003	197	30	b	b	NOUN
ejpam-4003	197	31	be	be	AUX
ejpam-4003	197	32	subsets	subset	NOUN
ejpam-4003	197	33	of	of	ADP
ejpam-4003	197	34	x	x	X
ejpam-4003	197	35	and	and	CCONJ
ejpam-4003	197	36	y	y	PROPN
ejpam-4003	197	37	,	,	PUNCT
ejpam-4003	197	38	respectively	respectively	ADV
ejpam-4003	197	39	.	.	PUNCT
ejpam-4003	198	1	then	then	ADV
ejpam-4003	198	2	,	,	PUNCT
ejpam-4003	198	3	mij	mij	PROPN
ejpam-4003	198	4	x×y	x×y	PROPN
ejpam-4003	198	5	clb(a×b	clb(a×b	PROPN
ejpam-4003	198	6	)	)	PUNCT
ejpam-4003	198	7	=	=	PUNCT
ejpam-4003	199	1	[	[	X
ejpam-4003	199	2	mij	mij	X
ejpam-4003	199	3	xclb(a)×	xclb(a)×	PROPN
ejpam-4003	199	4	y	y	PROPN
ejpam-4003	199	5	]	]	PUNCT
ejpam-4003	199	6	∩	∩	NOUN
ejpam-4003	199	7	[	[	X
ejpam-4003	199	8	x	x	SYM
ejpam-4003	199	9	×mij	×mij	NUM
ejpam-4003	199	10	y	y	PROPN
ejpam-4003	199	11	clb(b	clb(b	PROPN
ejpam-4003	199	12	)	)	PUNCT
ejpam-4003	199	13	]	]	PUNCT
ejpam-4003	199	14	where	where	SCONJ
ejpam-4003	199	15	i	i	PRON
ejpam-4003	199	16	,	,	PUNCT
ejpam-4003	199	17	j	j	PROPN
ejpam-4003	199	18	=	=	SYM
ejpam-4003	199	19	1	1	NUM
ejpam-4003	199	20	,	,	PUNCT
ejpam-4003	199	21	2	2	NUM
ejpam-4003	199	22	and	and	CCONJ
ejpam-4003	199	23	i	i	PRON
ejpam-4003	199	24	6=	6=	PROPN
ejpam-4003	199	25	j.	j.	PROPN
ejpam-4003	199	26	from	from	ADP
ejpam-4003	199	27	example	example	NOUN
ejpam-4003	199	28	1	1	NUM
ejpam-4003	199	29	,	,	PUNCT
ejpam-4003	199	30	let	let	VERB
ejpam-4003	199	31	y	y	PROPN
ejpam-4003	199	32	=	=	PRON
ejpam-4003	199	33	{	{	PUNCT
ejpam-4003	199	34	a	a	DET
ejpam-4003	199	35	,	,	PUNCT
ejpam-4003	199	36	b	b	NOUN
ejpam-4003	199	37	,	,	PUNCT
ejpam-4003	199	38	c	c	NOUN
ejpam-4003	199	39	}	}	PUNCT
ejpam-4003	199	40	,	,	PUNCT
ejpam-4003	199	41	we	we	PRON
ejpam-4003	199	42	have	have	VERB
ejpam-4003	199	43	m1	m1	PROPN
ejpam-4003	199	44	y	y	PROPN
ejpam-4003	199	45	=	=	PUNCT
ejpam-4003	199	46	{	{	PUNCT
ejpam-4003	199	47	∅	∅	NOUN
ejpam-4003	199	48	,	,	PUNCT
ejpam-4003	199	49	{	{	PUNCT
ejpam-4003	199	50	a	a	X
ejpam-4003	199	51	}	}	PUNCT
ejpam-4003	199	52	,	,	PUNCT
ejpam-4003	199	53	{	{	PUNCT
ejpam-4003	199	54	b	b	NOUN
ejpam-4003	199	55	}	}	PUNCT
ejpam-4003	199	56	,	,	PUNCT
ejpam-4003	199	57	{	{	PUNCT
ejpam-4003	199	58	a	a	X
ejpam-4003	199	59	,	,	PUNCT
ejpam-4003	199	60	c	c	NOUN
ejpam-4003	199	61	}	}	PUNCT
ejpam-4003	199	62	,	,	PUNCT
ejpam-4003	199	63	y	y	PROPN
ejpam-4003	199	64	}	}	PUNCT
ejpam-4003	199	65	and	and	CCONJ
ejpam-4003	200	1	m2	m2	PROPN
ejpam-4003	200	2	y	y	PROPN
ejpam-4003	200	3	=	=	PROPN
ejpam-4003	200	4	{	{	PUNCT
ejpam-4003	200	5	∅	∅	NOUN
ejpam-4003	200	6	,	,	PUNCT
ejpam-4003	200	7	{	{	PUNCT
ejpam-4003	200	8	c	c	NOUN
ejpam-4003	200	9	}	}	PUNCT
ejpam-4003	200	10	,	,	PUNCT
ejpam-4003	200	11	{	{	PUNCT
ejpam-4003	200	12	a	a	PRON
ejpam-4003	200	13	,	,	PUNCT
ejpam-4003	200	14	b}{b	b}{b	PROPN
ejpam-4003	200	15	,	,	PUNCT
ejpam-4003	200	16	c	c	NOUN
ejpam-4003	200	17	}	}	PUNCT
ejpam-4003	200	18	,	,	PUNCT
ejpam-4003	200	19	y	y	PROPN
ejpam-4003	200	20	}	}	PUNCT
ejpam-4003	200	21	.	.	PUNCT
ejpam-4003	201	1	therefore	therefore	ADV
ejpam-4003	201	2	,	,	PUNCT
ejpam-4003	201	3	m12	m12	PROPN
ejpam-4003	201	4	x×y	x×y	PROPN
ejpam-4003	201	5	clb({2	clb({2	PROPN
ejpam-4003	201	6	}	}	PUNCT
ejpam-4003	201	7	×	×	NOUN
ejpam-4003	201	8	{	{	PUNCT
ejpam-4003	201	9	c	c	NOUN
ejpam-4003	201	10	}	}	PUNCT
ejpam-4003	201	11	)	)	PUNCT
ejpam-4003	201	12	=	=	PUNCT
ejpam-4003	202	1	[	[	X
ejpam-4003	202	2	m12	m12	NOUN
ejpam-4003	202	3	xclb({2})×	xclb({2})×	PROPN
ejpam-4003	202	4	y	y	PROPN
ejpam-4003	202	5	]	]	PUNCT
ejpam-4003	202	6	∩	∩	NOUN
ejpam-4003	202	7	[	[	X
ejpam-4003	202	8	x	x	X
ejpam-4003	202	9	×m12	×m12	PROPN
ejpam-4003	202	10	y	y	PROPN
ejpam-4003	202	11	clb({c	clb({c	PROPN
ejpam-4003	202	12	}	}	PUNCT
ejpam-4003	202	13	)	)	PUNCT
ejpam-4003	202	14	]	]	PUNCT
ejpam-4003	203	1	=	=	PUNCT
ejpam-4003	203	2	{	{	PUNCT
ejpam-4003	203	3	2	2	NUM
ejpam-4003	203	4	,	,	PUNCT
ejpam-4003	203	5	c	c	NOUN
ejpam-4003	203	6	}	}	PUNCT
ejpam-4003	203	7	.	.	PUNCT
ejpam-4003	204	1	lemma	lemma	PROPN
ejpam-4003	204	2	8	8	NUM
ejpam-4003	204	3	.	.	PUNCT
ejpam-4003	205	1	let	let	VERB
ejpam-4003	205	2	(	(	PUNCT
ejpam-4003	205	3	x	x	X
ejpam-4003	205	4	,	,	PUNCT
ejpam-4003	205	5	m1	m1	PROPN
ejpam-4003	205	6	x	x	SYM
ejpam-4003	205	7	,	,	PUNCT
ejpam-4003	205	8	m	m	PROPN
ejpam-4003	205	9	2	2	NUM
ejpam-4003	205	10	x	x	NOUN
ejpam-4003	205	11	)	)	PUNCT
ejpam-4003	205	12	and	and	CCONJ
ejpam-4003	205	13	(	(	PUNCT
ejpam-4003	205	14	y	y	PROPN
ejpam-4003	205	15	,	,	PUNCT
ejpam-4003	205	16	m1	m1	PROPN
ejpam-4003	205	17	y	y	PROPN
ejpam-4003	205	18	,	,	PUNCT
ejpam-4003	205	19	m	m	PROPN
ejpam-4003	205	20	2	2	NUM
ejpam-4003	205	21	y	y	NOUN
ejpam-4003	205	22	)	)	PUNCT
ejpam-4003	205	23	be	be	AUX
ejpam-4003	205	24	biminimal	biminimal	ADJ
ejpam-4003	205	25	structure	structure	NOUN
ejpam-4003	205	26	spaces	space	NOUN
ejpam-4003	205	27	,	,	PUNCT
ejpam-4003	205	28	a	a	PRON
ejpam-4003	205	29	,	,	PUNCT
ejpam-4003	205	30	b	b	NOUN
ejpam-4003	205	31	be	be	AUX
ejpam-4003	205	32	subsets	subset	NOUN
ejpam-4003	205	33	of	of	ADP
ejpam-4003	205	34	x	x	X
ejpam-4003	205	35	and	and	CCONJ
ejpam-4003	205	36	y	y	PROPN
ejpam-4003	205	37	,	,	PUNCT
ejpam-4003	205	38	respectively	respectively	ADV
ejpam-4003	205	39	.	.	PUNCT
ejpam-4003	206	1	then	then	ADV
ejpam-4003	206	2	,	,	PUNCT
ejpam-4003	206	3	mij	mij	NOUN
ejpam-4003	206	4	x×yextb(a×b	x×yextb(a×b	PROPN
ejpam-4003	206	5	)	)	PUNCT
ejpam-4003	206	6	=	=	PUNCT
ejpam-4003	207	1	[	[	X
ejpam-4003	207	2	mij	mij	VERB
ejpam-4003	207	3	xextb(a)×	xextb(a)×	PROPN
ejpam-4003	207	4	y	y	PROPN
ejpam-4003	207	5	]	]	PUNCT
ejpam-4003	207	6	∪	∪	ADP
ejpam-4003	207	7	[	[	X
ejpam-4003	207	8	x	x	INTJ
ejpam-4003	207	9	×mij	×mij	NUM
ejpam-4003	207	10	yextb(b	yextb(b	NOUN
ejpam-4003	207	11	)	)	PUNCT
ejpam-4003	207	12	]	]	PUNCT
ejpam-4003	207	13	.	.	PUNCT
ejpam-4003	208	1	proof	proof	NOUN
ejpam-4003	208	2	.	.	PUNCT
ejpam-4003	209	1	let	let	AUX
ejpam-4003	209	2	(	(	PUNCT
ejpam-4003	209	3	y	y	NOUN
ejpam-4003	209	4	,	,	PUNCT
ejpam-4003	209	5	m1	m1	PROPN
ejpam-4003	209	6	y	y	PROPN
ejpam-4003	209	7	,	,	PUNCT
ejpam-4003	209	8	m	m	PROPN
ejpam-4003	209	9	2	2	NUM
ejpam-4003	209	10	y	y	NOUN
ejpam-4003	209	11	)	)	PUNCT
ejpam-4003	209	12	be	be	AUX
ejpam-4003	209	13	a	a	DET
ejpam-4003	209	14	biminimal	biminimal	NOUN
ejpam-4003	209	15	structure	structure	NOUN
ejpam-4003	209	16	subspace	subspace	NOUN
ejpam-4003	209	17	of	of	ADP
ejpam-4003	209	18	(	(	PUNCT
ejpam-4003	209	19	x	x	NOUN
ejpam-4003	209	20	,	,	PUNCT
ejpam-4003	209	21	m1	m1	PROPN
ejpam-4003	209	22	x	x	SYM
ejpam-4003	209	23	,	,	PUNCT
ejpam-4003	209	24	m	m	PROPN
ejpam-4003	209	25	2	2	NUM
ejpam-4003	209	26	x	x	NOUN
ejpam-4003	209	27	)	)	PUNCT
ejpam-4003	209	28	and	and	CCONJ
ejpam-4003	209	29	a	a	DET
ejpam-4003	209	30	a	a	DET
ejpam-4003	209	31	subset	subset	NOUN
ejpam-4003	209	32	of	of	ADP
ejpam-4003	209	33	y	y	PROPN
ejpam-4003	209	34	.	.	PUNCT
ejpam-4003	210	1	let	let	VERB
ejpam-4003	210	2	us	we	PRON
ejpam-4003	210	3	consider	consider	VERB
ejpam-4003	210	4	:	:	PUNCT
ejpam-4003	210	5	mij	mij	NOUN
ejpam-4003	210	6	x×yextb(a×b	x×yextb(a×b	PROPN
ejpam-4003	210	7	)	)	PUNCT
ejpam-4003	210	8	=	=	PRON
ejpam-4003	211	1	(	(	PUNCT
ejpam-4003	211	2	x	x	SYM
ejpam-4003	211	3	×	×	PROPN
ejpam-4003	211	4	y	y	PROPN
ejpam-4003	211	5	)	)	PUNCT
ejpam-4003	211	6	\mij	\mij	PROPN
ejpam-4003	211	7	x×y	x×y	PUNCT
ejpam-4003	211	8	clb(a×b	clb(a×b	PROPN
ejpam-4003	211	9	)	)	PUNCT
ejpam-4003	211	10	=	=	PRON
ejpam-4003	212	1	(	(	PUNCT
ejpam-4003	212	2	x	x	SYM
ejpam-4003	212	3	×	×	PROPN
ejpam-4003	212	4	y	y	PROPN
ejpam-4003	212	5	)	)	PUNCT
ejpam-4003	212	6	\((mij	\((mij	PROPN
ejpam-4003	212	7	xclb(a)×	xclb(a)×	PROPN
ejpam-4003	212	8	y	y	PROPN
ejpam-4003	212	9	)	)	PUNCT
ejpam-4003	212	10	∩	∩	NOUN
ejpam-4003	212	11	(	(	PUNCT
ejpam-4003	212	12	x	x	SYM
ejpam-4003	212	13	×mij	×mij	VERB
ejpam-4003	212	14	y	y	PROPN
ejpam-4003	212	15	clb(b	clb(b	PROPN
ejpam-4003	212	16	)	)	PUNCT
ejpam-4003	212	17	)	)	PUNCT
ejpam-4003	212	18	)	)	PUNCT
ejpam-4003	213	1	=	=	PUNCT
ejpam-4003	213	2	(	(	PUNCT
ejpam-4003	213	3	(	(	PUNCT
ejpam-4003	213	4	x	x	SYM
ejpam-4003	213	5	×	×	PROPN
ejpam-4003	213	6	y	y	PROPN
ejpam-4003	213	7	)	)	PUNCT
ejpam-4003	214	1	\(mij	\(mij	PROPN
ejpam-4003	214	2	xclb(a)×	xclb(a)×	PROPN
ejpam-4003	214	3	y	y	PROPN
ejpam-4003	214	4	)	)	PUNCT
ejpam-4003	214	5	)	)	PUNCT
ejpam-4003	215	1	∪	∪	X
ejpam-4003	215	2	(	(	PUNCT
ejpam-4003	215	3	(	(	PUNCT
ejpam-4003	215	4	x	x	SYM
ejpam-4003	215	5	×	×	PROPN
ejpam-4003	215	6	y	y	PROPN
ejpam-4003	215	7	)	)	PUNCT
ejpam-4003	215	8	\(x	\(x	PROPN
ejpam-4003	215	9	×mij	×mij	NUM
ejpam-4003	215	10	y	y	PROPN
ejpam-4003	215	11	clb(b	clb(b	PROPN
ejpam-4003	215	12	)	)	PUNCT
ejpam-4003	215	13	)	)	PUNCT
ejpam-4003	215	14	)	)	PUNCT
ejpam-4003	216	1	=	=	PUNCT
ejpam-4003	216	2	(	(	PUNCT
ejpam-4003	216	3	(	(	PUNCT
ejpam-4003	216	4	x\mij	x\mij	NOUN
ejpam-4003	216	5	xclb(a))×	xclb(a))×	PROPN
ejpam-4003	216	6	y	y	PROPN
ejpam-4003	216	7	)	)	PUNCT
ejpam-4003	216	8	∪	∪	VERB
ejpam-4003	216	9	(	(	PUNCT
ejpam-4003	216	10	x	x	SYM
ejpam-4003	216	11	×	×	PROPN
ejpam-4003	216	12	(	(	PUNCT
ejpam-4003	216	13	y	y	PROPN
ejpam-4003	216	14	\mij	\mij	PROPN
ejpam-4003	216	15	y	y	PROPN
ejpam-4003	216	16	clb(b	clb(b	PROPN
ejpam-4003	216	17	)	)	PUNCT
ejpam-4003	216	18	)	)	PUNCT
ejpam-4003	216	19	)	)	PUNCT
ejpam-4003	216	20	)	)	PUNCT
ejpam-4003	217	1	=	=	PUNCT
ejpam-4003	217	2	(	(	PUNCT
ejpam-4003	217	3	mij	mij	X
ejpam-4003	217	4	xextb(a)×	xextb(a)×	PROPN
ejpam-4003	217	5	y	y	PROPN
ejpam-4003	217	6	)	)	PUNCT
ejpam-4003	217	7	∪	∪	ADV
ejpam-4003	217	8	(	(	PUNCT
ejpam-4003	217	9	x	x	SYM
ejpam-4003	217	10	×mij	×mij	NUM
ejpam-4003	217	11	yextb(b	yextb(b	NOUN
ejpam-4003	217	12	)	)	PUNCT
ejpam-4003	217	13	)	)	PUNCT
ejpam-4003	217	14	.	.	PUNCT
ejpam-4003	218	1	the	the	DET
ejpam-4003	218	2	next	next	ADJ
ejpam-4003	218	3	results	result	NOUN
ejpam-4003	218	4	study	study	VERB
ejpam-4003	218	5	the	the	DET
ejpam-4003	218	6	biminimal	biminimal	NOUN
ejpam-4003	218	7	structure	structure	NOUN
ejpam-4003	218	8	subspace	subspace	NOUN
ejpam-4003	218	9	and	and	CCONJ
ejpam-4003	218	10	obtain	obtain	VERB
ejpam-4003	218	11	some	some	DET
ejpam-4003	218	12	properties	property	NOUN
ejpam-4003	218	13	of	of	ADP
ejpam-4003	218	14	them	they	PRON
ejpam-4003	218	15	.	.	PUNCT
ejpam-4003	219	1	furthermore	furthermore	ADV
ejpam-4003	219	2	,	,	PUNCT
ejpam-4003	219	3	the	the	DET
ejpam-4003	219	4	product	product	NOUN
ejpam-4003	219	5	of	of	ADP
ejpam-4003	219	6	the	the	DET
ejpam-4003	219	7	(	(	PUNCT
ejpam-4003	219	8	i	i	PROPN
ejpam-4003	219	9	,	,	PUNCT
ejpam-4003	219	10	j)−mx	j)−mx	PROPN
ejpam-4003	219	11	−	−	PROPN
ejpam-4003	219	12	β−exterior	β−exterior	PUNCT
ejpam-4003	219	13	sets	set	NOUN
ejpam-4003	219	14	is	be	AUX
ejpam-4003	219	15	introduced	introduce	VERB
ejpam-4003	219	16	.	.	PUNCT
ejpam-4003	220	1	references	reference	NOUN
ejpam-4003	220	2	921	921	NUM
ejpam-4003	220	3	lemma	lemma	PROPN
ejpam-4003	220	4	9	9	NUM
ejpam-4003	220	5	.	.	PUNCT
ejpam-4003	221	1	let	let	VERB
ejpam-4003	221	2	(	(	PUNCT
ejpam-4003	221	3	w	w	PROPN
ejpam-4003	221	4	,	,	PUNCT
ejpam-4003	221	5	m1	m1	PROPN
ejpam-4003	221	6	w	w	PROPN
ejpam-4003	221	7	,	,	PUNCT
ejpam-4003	221	8	m	m	PROPN
ejpam-4003	221	9	2	2	NUM
ejpam-4003	221	10	w	w	NOUN
ejpam-4003	221	11	)	)	PUNCT
ejpam-4003	221	12	be	be	AUX
ejpam-4003	221	13	a	a	DET
ejpam-4003	221	14	biminimal	biminimal	NOUN
ejpam-4003	221	15	structure	structure	NOUN
ejpam-4003	221	16	subspace	subspace	NOUN
ejpam-4003	221	17	of	of	ADP
ejpam-4003	221	18	(	(	PUNCT
ejpam-4003	221	19	x	x	NOUN
ejpam-4003	221	20	,	,	PUNCT
ejpam-4003	221	21	m1	m1	PROPN
ejpam-4003	221	22	x	x	SYM
ejpam-4003	221	23	,	,	PUNCT
ejpam-4003	221	24	m	m	PROPN
ejpam-4003	221	25	2	2	NUM
ejpam-4003	221	26	x	x	NOUN
ejpam-4003	221	27	)	)	PUNCT
ejpam-4003	221	28	,	,	PUNCT
ejpam-4003	221	29	a	a	PRON
ejpam-4003	221	30	and	and	CCONJ
ejpam-4003	221	31	b	b	NOUN
ejpam-4003	221	32	are	be	AUX
ejpam-4003	221	33	subsets	subset	NOUN
ejpam-4003	221	34	of	of	ADP
ejpam-4003	221	35	x	x	X
ejpam-4003	221	36	and	and	CCONJ
ejpam-4003	221	37	w	w	NOUN
ejpam-4003	221	38	,	,	PUNCT
ejpam-4003	221	39	respectively	respectively	ADV
ejpam-4003	221	40	,	,	PUNCT
ejpam-4003	221	41	and	and	CCONJ
ejpam-4003	221	42	a	a	DET
ejpam-4003	221	43	=	=	SYM
ejpam-4003	221	44	b	b	NOUN
ejpam-4003	221	45	∩w	∩w	NOUN
ejpam-4003	221	46	are	be	AUX
ejpam-4003	221	47	(	(	PUNCT
ejpam-4003	221	48	i	i	PROPN
ejpam-4003	221	49	,	,	PUNCT
ejpam-4003	221	50	j	j	PROPN
ejpam-4003	221	51	)	)	PUNCT
ejpam-4003	221	52	−	−	PROPN
ejpam-4003	221	53	mx	mx	NOUN
ejpam-4003	222	1	−	−	NOUN
ejpam-4003	222	2	β	β	SYM
ejpam-4003	222	3	−	−	NOUN
ejpam-4003	222	4	closed	closed	ADJ
ejpam-4003	222	5	.	.	PUNCT
ejpam-4003	223	1	then	then	ADV
ejpam-4003	223	2	,	,	PUNCT
ejpam-4003	223	3	mij	mij	NOUN
ejpam-4003	223	4	wextb(a	wextb(a	PROPN
ejpam-4003	223	5	)	)	PUNCT
ejpam-4003	224	1	=	=	PUNCT
ejpam-4003	224	2	mij	mij	X
ejpam-4003	224	3	xextb(b	xextb(b	PROPN
ejpam-4003	224	4	)	)	PUNCT
ejpam-4003	224	5	∩w	∩w	ADJ
ejpam-4003	224	6	.	.	PUNCT
ejpam-4003	225	1	proof	proof	NOUN
ejpam-4003	225	2	.	.	PUNCT
ejpam-4003	226	1	let	let	VERB
ejpam-4003	226	2	(	(	PUNCT
ejpam-4003	226	3	w	w	PROPN
ejpam-4003	226	4	,	,	PUNCT
ejpam-4003	226	5	m1	m1	PROPN
ejpam-4003	226	6	w	w	PROPN
ejpam-4003	226	7	,	,	PUNCT
ejpam-4003	226	8	m	m	PROPN
ejpam-4003	226	9	2	2	NUM
ejpam-4003	226	10	w	w	NOUN
ejpam-4003	226	11	)	)	PUNCT
ejpam-4003	226	12	be	be	AUX
ejpam-4003	226	13	a	a	DET
ejpam-4003	226	14	biminimal	biminimal	NOUN
ejpam-4003	226	15	structure	structure	NOUN
ejpam-4003	226	16	subspace	subspace	NOUN
ejpam-4003	226	17	of	of	ADP
ejpam-4003	226	18	(	(	PUNCT
ejpam-4003	226	19	x	x	NOUN
ejpam-4003	226	20	,	,	PUNCT
ejpam-4003	226	21	m1	m1	PROPN
ejpam-4003	226	22	x	x	SYM
ejpam-4003	226	23	,	,	PUNCT
ejpam-4003	226	24	m	m	PROPN
ejpam-4003	226	25	2	2	NUM
ejpam-4003	226	26	x	x	NOUN
ejpam-4003	226	27	)	)	PUNCT
ejpam-4003	226	28	and	and	CCONJ
ejpam-4003	226	29	a	a	DET
ejpam-4003	226	30	be	be	AUX
ejpam-4003	226	31	a	a	DET
ejpam-4003	226	32	subset	subset	NOUN
ejpam-4003	226	33	of	of	ADP
ejpam-4003	226	34	y	y	PROPN
ejpam-4003	226	35	.	.	PUNCT
ejpam-4003	227	1	consider	consider	VERB
ejpam-4003	227	2	,	,	PUNCT
ejpam-4003	227	3	mij	mij	NOUN
ejpam-4003	227	4	yextb(a	yextb(a	NOUN
ejpam-4003	227	5	)	)	PUNCT
ejpam-4003	227	6	=	=	PUNCT
ejpam-4003	227	7	mij	mij	X
ejpam-4003	227	8	wextb(b	wextb(b	NOUN
ejpam-4003	227	9	∩w	∩w	PROPN
ejpam-4003	227	10	)	)	PUNCT
ejpam-4003	228	1	=	=	PUNCT
ejpam-4003	228	2	mij	mij	VERB
ejpam-4003	228	3	xextb(b	xextb(b	X
ejpam-4003	228	4	∩w	∩w	NOUN
ejpam-4003	228	5	)	)	PUNCT
ejpam-4003	228	6	∩	∩	NOUN
ejpam-4003	228	7	y	y	NOUN
ejpam-4003	229	1	=	=	PUNCT
ejpam-4003	230	1	[	[	X
ejpam-4003	230	2	mij	mij	NOUN
ejpam-4003	230	3	xextb(b	xextb(b	PROPN
ejpam-4003	230	4	)	)	PUNCT
ejpam-4003	230	5	∪mij	∪mij	NOUN
ejpam-4003	230	6	xextb(w	xextb(w	PROPN
ejpam-4003	230	7	)	)	PUNCT
ejpam-4003	230	8	]	]	PUNCT
ejpam-4003	231	1	∩	∩	PROPN
ejpam-4003	231	2	y	y	NOUN
ejpam-4003	231	3	=	=	PUNCT
ejpam-4003	232	1	[	[	X
ejpam-4003	232	2	mij	mij	X
ejpam-4003	232	3	xextb(b	xextb(b	PROPN
ejpam-4003	232	4	)	)	PUNCT
ejpam-4003	232	5	∩w	∩w	NOUN
ejpam-4003	232	6	]	]	PUNCT
ejpam-4003	232	7	∪	∪	X
ejpam-4003	232	8	[	[	PUNCT
ejpam-4003	232	9	mij	mij	NOUN
ejpam-4003	232	10	xextb(w	xextb(w	NOUN
ejpam-4003	232	11	)	)	PUNCT
ejpam-4003	232	12	∩w	∩w	PUNCT
ejpam-4003	232	13	]	]	PUNCT
ejpam-4003	233	1	=	=	PUNCT
ejpam-4003	234	1	[	[	X
ejpam-4003	234	2	mij	mij	X
ejpam-4003	234	3	xextb(b	xextb(b	PROPN
ejpam-4003	234	4	)	)	PUNCT
ejpam-4003	234	5	∩w	∩w	NOUN
ejpam-4003	234	6	]	]	X
ejpam-4003	234	7	.	.	PUNCT
ejpam-4003	235	1	4	4	X
ejpam-4003	235	2	.	.	X
ejpam-4003	235	3	conclusion	conclusion	NOUN
ejpam-4003	235	4	this	this	DET
ejpam-4003	235	5	study	study	NOUN
ejpam-4003	235	6	investigated	investigate	VERB
ejpam-4003	235	7	(	(	PUNCT
ejpam-4003	235	8	i	i	PROPN
ejpam-4003	235	9	,	,	PUNCT
ejpam-4003	235	10	j	j	PROPN
ejpam-4003	235	11	)	)	PUNCT
ejpam-4003	235	12	−mx	−mx	NOUN
ejpam-4003	235	13	−	−	NOUN
ejpam-4003	235	14	β−exterior	β−exterior	NOUN
ejpam-4003	235	15	sets	set	NOUN
ejpam-4003	235	16	in	in	ADP
ejpam-4003	235	17	a	a	DET
ejpam-4003	235	18	biminimal	biminimal	NOUN
ejpam-4003	235	19	structure	structure	NOUN
ejpam-4003	235	20	space	space	NOUN
ejpam-4003	235	21	(	(	PUNCT
ejpam-4003	235	22	bss	bss	NOUN
ejpam-4003	235	23	)	)	PUNCT
ejpam-4003	235	24	and	and	CCONJ
ejpam-4003	235	25	a	a	DET
ejpam-4003	235	26	biminimal	biminimal	NOUN
ejpam-4003	235	27	structure	structure	NOUN
ejpam-4003	235	28	subspace	subspace	NOUN
ejpam-4003	235	29	(	(	PUNCT
ejpam-4003	235	30	bss	bss	PROPN
ejpam-4003	235	31	)	)	PUNCT
ejpam-4003	235	32	.	.	PUNCT
ejpam-4003	236	1	first	first	ADV
ejpam-4003	236	2	,	,	PUNCT
ejpam-4003	236	3	(	(	PUNCT
ejpam-4003	236	4	i	i	NOUN
ejpam-4003	236	5	,	,	PUNCT
ejpam-4003	236	6	j)−mx	j)−mx	PROPN
ejpam-4003	236	7	−	−	PROPN
ejpam-4003	236	8	β−exterior	β−exterior	PUNCT
ejpam-4003	236	9	sets	set	NOUN
ejpam-4003	236	10	in	in	ADP
ejpam-4003	236	11	a	a	DET
ejpam-4003	236	12	biminimal	biminimal	NOUN
ejpam-4003	236	13	structure	structure	NOUN
ejpam-4003	236	14	space	space	NOUN
ejpam-4003	236	15	are	be	AUX
ejpam-4003	236	16	defined	define	VERB
ejpam-4003	236	17	in	in	ADP
ejpam-4003	236	18	definition	definition	NOUN
ejpam-4003	236	19	5	5	NUM
ejpam-4003	236	20	.	.	PUNCT
ejpam-4003	236	21	second	second	ADJ
ejpam-4003	236	22	,	,	PUNCT
ejpam-4003	236	23	theorem	theorem	VERB
ejpam-4003	236	24	1	1	NUM
ejpam-4003	236	25	present	present	VERB
ejpam-4003	236	26	the	the	DET
ejpam-4003	236	27	notion	notion	NOUN
ejpam-4003	236	28	for	for	ADP
ejpam-4003	236	29	the	the	DET
ejpam-4003	236	30	subsets	subset	NOUN
ejpam-4003	236	31	of	of	ADP
ejpam-4003	236	32	(	(	PUNCT
ejpam-4003	236	33	i	i	PROPN
ejpam-4003	236	34	,	,	PUNCT
ejpam-4003	236	35	j)−mx	j)−mx	PROPN
ejpam-4003	236	36	−β−exterior	−β−exterior	NOUN
ejpam-4003	236	37	sets	set	NOUN
ejpam-4003	236	38	.	.	PUNCT
ejpam-4003	237	1	third	third	ADJ
ejpam-4003	237	2	,	,	PUNCT
ejpam-4003	237	3	the	the	DET
ejpam-4003	237	4	relation	relation	NOUN
ejpam-4003	237	5	of	of	ADP
ejpam-4003	237	6	(	(	PUNCT
ejpam-4003	237	7	i	i	PROPN
ejpam-4003	237	8	,	,	PUNCT
ejpam-4003	237	9	j)−mx	j)−mx	PROPN
ejpam-4003	237	10	−	−	NUM
ejpam-4003	238	1	β−exterior	β−exterior	PUNCT
ejpam-4003	238	2	sets	set	NOUN
ejpam-4003	238	3	and	and	CCONJ
ejpam-4003	238	4	(	(	PUNCT
ejpam-4003	238	5	i	i	NOUN
ejpam-4003	238	6	,	,	PUNCT
ejpam-4003	238	7	j)−mx	j)−mx	PROPN
ejpam-4003	238	8	−	−	PROPN
ejpam-4003	238	9	β−closed	β−close	VERB
ejpam-4003	238	10	and	and	CCONJ
ejpam-4003	238	11	open	open	ADJ
ejpam-4003	238	12	sets	set	NOUN
ejpam-4003	238	13	are	be	AUX
ejpam-4003	238	14	covered	cover	VERB
ejpam-4003	238	15	in	in	ADP
ejpam-4003	238	16	theorem	theorem	NOUN
ejpam-4003	238	17	2	2	NUM
ejpam-4003	238	18	.	.	PUNCT
ejpam-4003	239	1	the	the	DET
ejpam-4003	239	2	union	union	NOUN
ejpam-4003	239	3	,	,	PUNCT
ejpam-4003	239	4	intersection	intersection	NOUN
ejpam-4003	239	5	and	and	CCONJ
ejpam-4003	239	6	product	product	NOUN
ejpam-4003	239	7	of	of	ADP
ejpam-4003	239	8	(	(	PUNCT
ejpam-4003	239	9	i	i	PROPN
ejpam-4003	239	10	,	,	PUNCT
ejpam-4003	239	11	j	j	PROPN
ejpam-4003	239	12	)	)	PUNCT
ejpam-4003	239	13	−mx	−mx	NOUN
ejpam-4003	239	14	−	−	NOUN
ejpam-4003	239	15	β−exterior	β−exterior	PUNCT
ejpam-4003	239	16	sets	set	NOUN
ejpam-4003	239	17	are	be	AUX
ejpam-4003	239	18	given	give	VERB
ejpam-4003	239	19	in	in	ADP
ejpam-4003	239	20	theorem	theorem	ADJ
ejpam-4003	239	21	3	3	NUM
ejpam-4003	239	22	and	and	CCONJ
ejpam-4003	239	23	lemma	lemma	PROPN
ejpam-4003	239	24	8	8	NUM
ejpam-4003	239	25	.	.	PUNCT
ejpam-4003	240	1	the	the	DET
ejpam-4003	240	2	authors	author	NOUN
ejpam-4003	240	3	describe	describe	VERB
ejpam-4003	240	4	the	the	DET
ejpam-4003	240	5	(	(	PUNCT
ejpam-4003	240	6	i	i	PROPN
ejpam-4003	240	7	,	,	PUNCT
ejpam-4003	240	8	j	j	PROPN
ejpam-4003	240	9	)	)	PUNCT
ejpam-4003	240	10	−	−	PROPN
ejpam-4003	240	11	mx	mx	PROPN
ejpam-4003	240	12	−	−	ADP
ejpam-4003	240	13	β−exterior	β−exterior	NOUN
ejpam-4003	240	14	sets	set	NOUN
ejpam-4003	240	15	of	of	ADP
ejpam-4003	240	16	a	a	DET
ejpam-4003	240	17	biminimal	biminimal	NOUN
ejpam-4003	240	18	structure	structure	NOUN
ejpam-4003	240	19	subspace	subspace	NOUN
ejpam-4003	240	20	(	(	PUNCT
ejpam-4003	240	21	bss	bss	PROPN
ejpam-4003	240	22	)	)	PUNCT
ejpam-4003	240	23	,	,	PUNCT
ejpam-4003	240	24	in	in	ADP
ejpam-4003	240	25	the	the	DET
ejpam-4003	240	26	last	last	ADJ
ejpam-4003	240	27	section	section	NOUN
ejpam-4003	240	28	3	3	NUM
ejpam-4003	240	29	.	.	PUNCT
ejpam-4003	241	1	acknowledgements	acknowledgement	NOUN
ejpam-4003	241	2	the	the	DET
ejpam-4003	241	3	authors	author	NOUN
ejpam-4003	241	4	thank	thank	VERB
ejpam-4003	241	5	the	the	DET
ejpam-4003	241	6	referees	referee	NOUN
ejpam-4003	241	7	for	for	ADP
ejpam-4003	241	8	valuable	valuable	ADJ
ejpam-4003	241	9	comments	comment	NOUN
ejpam-4003	241	10	and	and	CCONJ
ejpam-4003	241	11	suggestions	suggestion	NOUN
ejpam-4003	241	12	on	on	ADP
ejpam-4003	241	13	this	this	DET
ejpam-4003	241	14	manuscript	manuscript	NOUN
ejpam-4003	241	15	.	.	PUNCT
ejpam-4003	242	1	this	this	DET
ejpam-4003	242	2	research	research	NOUN
ejpam-4003	242	3	was	be	AUX
ejpam-4003	242	4	supported	support	VERB
ejpam-4003	242	5	by	by	ADP
ejpam-4003	242	6	the	the	DET
ejpam-4003	242	7	faculty	faculty	NOUN
ejpam-4003	242	8	of	of	ADP
ejpam-4003	242	9	sciences	science	NOUN
ejpam-4003	242	10	and	and	CCONJ
ejpam-4003	242	11	engineering	engineering	NOUN
ejpam-4003	242	12	,	,	PUNCT
ejpam-4003	242	13	kasetsart	kasetsart	PROPN
ejpam-4003	242	14	university	university	PROPN
ejpam-4003	242	15	,	,	PUNCT
ejpam-4003	242	16	chalermprakiat	chalermprakiat	PROPN
ejpam-4003	242	17	sakon	sakon	PROPN
ejpam-4003	242	18	nakhon	nakhon	PROPN
ejpam-4003	242	19	province	province	PROPN
ejpam-4003	242	20	campus	campus	PROPN
ejpam-4003	242	21	,	,	PUNCT
ejpam-4003	242	22	thailand	thailand	PROPN
ejpam-4003	242	23	.	.	PUNCT
ejpam-4003	243	1	references	reference	NOUN
ejpam-4003	243	2	[	[	X
ejpam-4003	243	3	1	1	X
ejpam-4003	243	4	]	]	PUNCT
ejpam-4003	243	5	t.	t.	PROPN
ejpam-4003	243	6	m.	m.	PROPN
ejpam-4003	243	7	al	al	PROPN
ejpam-4003	243	8	-	-	PUNCT
ejpam-4003	243	9	shami	shami	PROPN
ejpam-4003	243	10	,	,	PUNCT
ejpam-4003	243	11	e.	e.	PROPN
ejpam-4003	243	12	a.	a.	PROPN
ejpam-4003	243	13	abo	abo	PROPN
ejpam-4003	243	14	-	-	PUNCT
ejpam-4003	243	15	tabl	tabl	NOUN
ejpam-4003	243	16	,	,	PUNCT
ejpam-4003	243	17	b.	b.	PROPN
ejpam-4003	243	18	a.	a.	PROPN
ejpam-4003	243	19	asaad	asaad	PROPN
ejpam-4003	243	20	and	and	CCONJ
ejpam-4003	243	21	m.	m.	NOUN
ejpam-4003	243	22	a.	a.	PROPN
ejpam-4003	243	23	arahet	arahet	PROPN
ejpam-4003	243	24	,	,	PUNCT
ejpam-4003	243	25	limit	limit	VERB
ejpam-4003	243	26	points	point	NOUN
ejpam-4003	243	27	and	and	CCONJ
ejpam-4003	243	28	separation	separation	NOUN
ejpam-4003	243	29	axioms	axiom	NOUN
ejpam-4003	243	30	with	with	ADP
ejpam-4003	243	31	respect	respect	NOUN
ejpam-4003	243	32	to	to	ADP
ejpam-4003	243	33	supra	supra	PROPN
ejpam-4003	243	34	semi	semi	ADJ
ejpam-4003	243	35	-	-	ADJ
ejpam-4003	243	36	open	open	ADJ
ejpam-4003	243	37	sets	set	NOUN
ejpam-4003	243	38	,	,	PUNCT
ejpam-4003	243	39	eur	eur	PROPN
ejpam-4003	243	40	.	.	PUNCT
ejpam-4003	244	1	j.	j.	PROPN
ejpam-4003	244	2	appl	appl	PROPN
ejpam-4003	244	3	.	.	PROPN
ejpam-4003	244	4	math	math	PROPN
ejpam-4003	244	5	,	,	PUNCT
ejpam-4003	244	6	13(3	13(3	NUM
ejpam-4003	244	7	):	):	PUNCT
ejpam-4003	244	8	427	427	NUM
ejpam-4003	244	9	-	-	SYM
ejpam-4003	244	10	443	443	NUM
ejpam-4003	244	11	,	,	PUNCT
ejpam-4003	244	12	2020	2020	NUM
ejpam-4003	244	13	.	.	PUNCT
ejpam-4003	245	1	[	[	X
ejpam-4003	245	2	2	2	NUM
ejpam-4003	245	3	]	]	PUNCT
ejpam-4003	245	4	c.	c.	PROPN
ejpam-4003	245	5	boonpok	boonpok	PROPN
ejpam-4003	245	6	,	,	PUNCT
ejpam-4003	245	7	biminimal	biminimal	NOUN
ejpam-4003	245	8	structure	structure	NOUN
ejpam-4003	245	9	spaces	space	NOUN
ejpam-4003	245	10	,	,	PUNCT
ejpam-4003	245	11	int	int	PROPN
ejpam-4003	245	12	.	.	PUNCT
ejpam-4003	245	13	math	math	PROPN
ejpam-4003	245	14	.	.	PUNCT
ejpam-4003	246	1	forum	forum	PROPN
ejpam-4003	246	2	.	.	PROPN
ejpam-4003	246	3	,	,	PUNCT
ejpam-4003	246	4	5(15):703	5(15):703	NUM
ejpam-4003	246	5	-	-	SYM
ejpam-4003	246	6	707	707	NUM
ejpam-4003	246	7	,	,	PUNCT
ejpam-4003	246	8	2010	2010	NUM
ejpam-4003	246	9	.	.	PUNCT
ejpam-4003	247	1	[	[	X
ejpam-4003	247	2	3	3	X
ejpam-4003	247	3	]	]	PUNCT
ejpam-4003	247	4	c.	c.	PROPN
ejpam-4003	247	5	boonpok	boonpok	PROPN
ejpam-4003	247	6	,	,	PUNCT
ejpam-4003	247	7	m−continuous	m−continuous	ADJ
ejpam-4003	247	8	functions	function	NOUN
ejpam-4003	247	9	on	on	ADP
ejpam-4003	247	10	biminimal	biminimal	NOUN
ejpam-4003	247	11	structure	structure	NOUN
ejpam-4003	247	12	spaces	space	NOUN
ejpam-4003	247	13	,	,	PUNCT
ejpam-4003	247	14	far	far	ADV
ejpam-4003	247	15	east	east	ADV
ejpam-4003	247	16	of	of	ADP
ejpam-4003	247	17	math	math	NOUN
ejpam-4003	247	18	.	.	PUNCT
ejpam-4003	248	1	sci	sci	PROPN
ejpam-4003	248	2	.	.	PROPN
ejpam-4003	248	3	,	,	PUNCT
ejpam-4003	248	4	43(1):41	43(1):41	PROPN
ejpam-4003	248	5	-	-	PUNCT
ejpam-4003	248	6	58,2010	58,2010	NUM
ejpam-4003	248	7	.	.	PUNCT
ejpam-4003	249	1	[	[	X
ejpam-4003	249	2	4	4	X
ejpam-4003	249	3	]	]	PUNCT
ejpam-4003	249	4	c.	c.	PROPN
ejpam-4003	249	5	boonpok	boonpok	PROPN
ejpam-4003	249	6	,	,	PUNCT
ejpam-4003	249	7	c.	c.	PROPN
ejpam-4003	249	8	chokchai	chokchai	PROPN
ejpam-4003	249	9	,	,	PUNCT
ejpam-4003	249	10	m.	m.	NOUN
ejpam-4003	249	11	thongmoon	thongmoon	NOUN
ejpam-4003	249	12	,	,	PUNCT
ejpam-4003	249	13	n.	n.	PROPN
ejpam-4003	249	14	viriyapong	viriyapong	PROPN
ejpam-4003	249	15	,	,	PUNCT
ejpam-4003	249	16	on	on	ADP
ejpam-4003	249	17	m	m	PROPN
ejpam-4003	249	18	(	(	PUNCT
ejpam-4003	249	19	i	i	PROPN
ejpam-4003	249	20	,	,	PUNCT
ejpam-4003	249	21	j	j	PROPN
ejpam-4003	249	22	)	)	PUNCT
ejpam-4003	249	23	a	a	DET
ejpam-4003	249	24	−	−	PROPN
ejpam-4003	249	25	continuous	continuous	ADJ
ejpam-4003	249	26	functions	function	NOUN
ejpam-4003	249	27	in	in	ADP
ejpam-4003	249	28	biminimal	biminimal	NOUN
ejpam-4003	249	29	space	space	NOUN
ejpam-4003	249	30	structure	structure	NOUN
ejpam-4003	249	31	spaces	space	NOUN
ejpam-4003	249	32	,	,	PUNCT
ejpam-4003	249	33	int	int	NOUN
ejpam-4003	249	34	.	.	PUNCT
ejpam-4003	250	1	j.	j.	PROPN
ejpam-4003	250	2	math	math	PROPN
ejpam-4003	250	3	and	and	CCONJ
ejpam-4003	250	4	math	math	NOUN
ejpam-4003	250	5	.	.	PUNCT
ejpam-4003	251	1	sci	sci	PROPN
ejpam-4003	251	2	.	.	PROPN
ejpam-4003	251	3	,	,	PUNCT
ejpam-4003	251	4	2013:381068	2013:381068	NUM
ejpam-4003	251	5	,	,	PUNCT
ejpam-4003	251	6	2013	2013	NUM
ejpam-4003	251	7	.	.	PUNCT
ejpam-4003	252	1	references	reference	NOUN
ejpam-4003	252	2	922	922	NUM
ejpam-4003	253	1	[	[	SYM
ejpam-4003	253	2	5	5	NUM
ejpam-4003	253	3	]	]	PUNCT
ejpam-4003	253	4	m.	m.	PROPN
ejpam-4003	253	5	e.	e.	PROPN
ejpam-4003	253	6	el	el	PROPN
ejpam-4003	253	7	-	-	PROPN
ejpam-4003	253	8	shafei	shafei	PROPN
ejpam-4003	253	9	,	,	PUNCT
ejpam-4003	253	10	a.	a.	NOUN
ejpam-4003	253	11	h.	h.	PROPN
ejpam-4003	253	12	zakari	zakari	PROPN
ejpam-4003	253	13	and	and	CCONJ
ejpam-4003	253	14	t.	t.	PROPN
ejpam-4003	253	15	m.	m.	PROPN
ejpam-4003	253	16	al	al	PROPN
ejpam-4003	253	17	-	-	PUNCT
ejpam-4003	253	18	shami	shami	PROPN
ejpam-4003	253	19	,	,	PUNCT
ejpam-4003	253	20	some	some	DET
ejpam-4003	253	21	applications	application	NOUN
ejpam-4003	253	22	of	of	ADP
ejpam-4003	253	23	supra	supra	ADJ
ejpam-4003	253	24	preopen	preopen	ADJ
ejpam-4003	253	25	sets	set	NOUN
ejpam-4003	253	26	,	,	PUNCT
ejpam-4003	253	27	j.	j.	PROPN
ejpam-4003	253	28	math	math	PROPN
ejpam-4003	253	29	.	.	PUNCT
ejpam-4003	253	30	,	,	PUNCT
ejpam-4003	253	31	2020	2020	NUM
ejpam-4003	253	32	:	:	PUNCT
ejpam-4003	253	33	9634206	9634206	NUM
ejpam-4003	253	34	,	,	PUNCT
ejpam-4003	253	35	11	11	NUM
ejpam-4003	253	36	pages	page	NOUN
ejpam-4003	253	37	.	.	PUNCT
ejpam-4003	254	1	[	[	X
ejpam-4003	254	2	6	6	NUM
ejpam-4003	254	3	]	]	PUNCT
ejpam-4003	254	4	a.	a.	NOUN
ejpam-4003	254	5	mhemdi	mhemdi	NOUN
ejpam-4003	254	6	and	and	CCONJ
ejpam-4003	254	7	t.	t.	PROPN
ejpam-4003	254	8	m.	m.	PROPN
ejpam-4003	254	9	al	al	PROPN
ejpam-4003	254	10	-	-	PUNCT
ejpam-4003	254	11	shami	shami	PROPN
ejpam-4003	254	12	,	,	PUNCT
ejpam-4003	254	13	functionally	functionally	ADV
ejpam-4003	254	14	separation	separation	NOUN
ejpam-4003	254	15	axioms	axiom	NOUN
ejpam-4003	254	16	on	on	ADP
ejpam-4003	254	17	general	general	ADJ
ejpam-4003	254	18	topology	topology	NOUN
ejpam-4003	254	19	,	,	PUNCT
ejpam-4003	254	20	j.	j.	PROPN
ejpam-4003	254	21	math	math	PROPN
ejpam-4003	254	22	.	.	PUNCT
ejpam-4003	254	23	,	,	PUNCT
ejpam-4003	254	24	2021	2021	NUM
ejpam-4003	254	25	:	:	PUNCT
ejpam-4003	254	26	5590047	5590047	NUM
ejpam-4003	254	27	,	,	PUNCT
ejpam-4003	254	28	5	5	NUM
ejpam-4003	254	29	pages	page	NOUN
ejpam-4003	254	30	.	.	PUNCT
ejpam-4003	255	1	[	[	X
ejpam-4003	255	2	7	7	X
ejpam-4003	255	3	]	]	X
ejpam-4003	255	4	t.	t.	PROPN
ejpam-4003	255	5	noiri	noiri	PROPN
ejpam-4003	255	6	,	,	PUNCT
ejpam-4003	255	7	the	the	DET
ejpam-4003	255	8	further	further	ADJ
ejpam-4003	255	9	unified	unified	ADJ
ejpam-4003	255	10	theory	theory	NOUN
ejpam-4003	255	11	for	for	ADP
ejpam-4003	255	12	modifications	modification	NOUN
ejpam-4003	255	13	of	of	ADP
ejpam-4003	255	14	g	g	NOUN
ejpam-4003	255	15	-	-	PUNCT
ejpam-4003	255	16	closed	close	VERB
ejpam-4003	255	17	sets	set	NOUN
ejpam-4003	255	18	,	,	PUNCT
ejpam-4003	255	19	rendiconti	rendiconti	ADJ
ejpam-4003	255	20	del	del	PROPN
ejpam-4003	255	21	circolo	circolo	PROPN
ejpam-4003	255	22	mathematico	mathematico	NOUN
ejpam-4003	255	23	di	di	X
ejpam-4003	255	24	palermo	palermo	NOUN
ejpam-4003	255	25	,	,	PUNCT
ejpam-4003	255	26	57(3):411	57(3):411	NOUN
ejpam-4003	255	27	-	-	SYM
ejpam-4003	255	28	42	42	NUM
ejpam-4003	255	29	,	,	PUNCT
ejpam-4003	255	30	2008	2008	NUM
ejpam-4003	255	31	.	.	PUNCT
ejpam-4003	256	1	[	[	X
ejpam-4003	256	2	8	8	NUM
ejpam-4003	256	3	]	]	X
ejpam-4003	256	4	p.	p.	NOUN
ejpam-4003	256	5	prasertsang	prasertsang	PROPN
ejpam-4003	256	6	,	,	PUNCT
ejpam-4003	256	7	s.	s.	PROPN
ejpam-4003	256	8	sompong	sompong	PROPN
ejpam-4003	256	9	,	,	PUNCT
ejpam-4003	256	10	(	(	PUNCT
ejpam-4003	256	11	i	i	PROPN
ejpam-4003	256	12	,	,	PUNCT
ejpam-4003	256	13	j)−mx−α−boundary	j)−mx−α−boundary	ADJ
ejpam-4003	256	14	and	and	CCONJ
ejpam-4003	256	15	exterior	exterior	ADJ
ejpam-4003	256	16	sets	set	NOUN
ejpam-4003	256	17	in	in	ADP
ejpam-4003	256	18	biminimal	biminimal	NOUN
ejpam-4003	256	19	structure	structure	NOUN
ejpam-4003	256	20	spaces	space	NOUN
ejpam-4003	256	21	,	,	PUNCT
ejpam-4003	256	22	far	far	ADV
ejpam-4003	256	23	east	east	ADV
ejpam-4003	256	24	of	of	ADP
ejpam-4003	256	25	math	math	NOUN
ejpam-4003	256	26	.	.	PUNCT
ejpam-4003	257	1	sci	sci	PROPN
ejpam-4003	257	2	.	.	PUNCT
ejpam-4003	258	1	96(1):97	96(1):97	NUM
ejpam-4003	258	2	-	-	PUNCT
ejpam-4003	258	3	111	111	NUM
ejpam-4003	258	4	,	,	PUNCT
ejpam-4003	258	5	2015	2015	NUM
ejpam-4003	258	6	.	.	PUNCT
ejpam-4003	259	1	[	[	X
ejpam-4003	259	2	9	9	NUM
ejpam-4003	259	3	]	]	PUNCT
ejpam-4003	259	4	p.	p.	NOUN
ejpam-4003	259	5	prasertsang	prasertsang	PROPN
ejpam-4003	259	6	,	,	PUNCT
ejpam-4003	259	7	s.	s.	PROPN
ejpam-4003	259	8	sompong	sompong	PROPN
ejpam-4003	259	9	,	,	PUNCT
ejpam-4003	259	10	(	(	PUNCT
ejpam-4003	259	11	i	i	NOUN
ejpam-4003	259	12	,	,	PUNCT
ejpam-4003	259	13	j)−mx	j)−mx	PROPN
ejpam-4003	259	14	−	−	PROPN
ejpam-4003	260	1	β−boundary	β−boundary	NUM
ejpam-4003	260	2	sets	set	NOUN
ejpam-4003	260	3	in	in	ADP
ejpam-4003	260	4	biminimal	biminimal	NOUN
ejpam-4003	260	5	structure	structure	NOUN
ejpam-4003	260	6	spaces	space	NOUN
ejpam-4003	260	7	,	,	PUNCT
ejpam-4003	260	8	far	far	ADV
ejpam-4003	260	9	east	east	ADV
ejpam-4003	260	10	of	of	ADP
ejpam-4003	260	11	math	math	NOUN
ejpam-4003	260	12	.	.	PUNCT
ejpam-4003	261	1	sci	sci	PROPN
ejpam-4003	261	2	.	.	PROPN
ejpam-4003	261	3	,	,	PUNCT
ejpam-4003	261	4	99(10):1513	99(10):1513	X
ejpam-4003	261	5	-	-	SYM
ejpam-4003	261	6	1531	1531	NUM
ejpam-4003	261	7	,	,	PUNCT
ejpam-4003	261	8	2016	2016	NUM
ejpam-4003	261	9	.	.	PUNCT
ejpam-4003	262	1	[	[	X
ejpam-4003	262	2	10	10	NUM
ejpam-4003	262	3	]	]	X
ejpam-4003	262	4	s.	s.	PROPN
ejpam-4003	262	5	sompong	sompong	PROPN
ejpam-4003	262	6	,	,	PUNCT
ejpam-4003	262	7	s.	s.	PROPN
ejpam-4003	262	8	muangchan	muangchan	PROPN
ejpam-4003	262	9	,	,	PUNCT
ejpam-4003	262	10	exterior	exterior	ADJ
ejpam-4003	262	11	set	set	VERB
ejpam-4003	262	12	in	in	ADP
ejpam-4003	262	13	biminimal	biminimal	NOUN
ejpam-4003	262	14	structure	structure	NOUN
ejpam-4003	262	15	spaces	space	NOUN
ejpam-4003	262	16	,	,	PUNCT
ejpam-4003	262	17	int	int	NOUN
ejpam-4003	262	18	.	.	PUNCT
ejpam-4003	263	1	j.	j.	PROPN
ejpam-4003	263	2	of	of	ADP
ejpam-4003	263	3	math	math	PROPN
ejpam-4003	263	4	.	.	PUNCT
ejpam-4003	264	1	analysis	analysis	NOUN
ejpam-4003	264	2	.	.	PUNCT
ejpam-4003	264	3	,	,	PUNCT
ejpam-4003	264	4	5(22):1087	5(22):1087	NUM
ejpam-4003	264	5	-	-	SYM
ejpam-4003	264	6	1091	1091	NUM
ejpam-4003	264	7	,	,	PUNCT
ejpam-4003	264	8	2011	2011	NUM
ejpam-4003	264	9	.	.	PUNCT
ejpam-4003	265	1	[	[	X
ejpam-4003	265	2	11	11	NUM
ejpam-4003	265	3	]	]	X
ejpam-4003	265	4	s.	s.	PROPN
ejpam-4003	265	5	sompong	sompong	PROPN
ejpam-4003	265	6	,	,	PUNCT
ejpam-4003	265	7	s.	s.	PROPN
ejpam-4003	265	8	muangchan	muangchan	PROPN
ejpam-4003	265	9	,	,	PUNCT
ejpam-4003	265	10	the	the	DET
ejpam-4003	265	11	relation	relation	NOUN
ejpam-4003	265	12	on	on	ADP
ejpam-4003	265	13	boundary	boundary	ADJ
ejpam-4003	265	14	and	and	CCONJ
ejpam-4003	265	15	exterior	exterior	ADJ
ejpam-4003	265	16	sets	set	NOUN
ejpam-4003	265	17	in	in	ADP
ejpam-4003	265	18	biminimal	biminimal	NOUN
ejpam-4003	265	19	structure	structure	NOUN
ejpam-4003	265	20	spaces	space	NOUN
ejpam-4003	265	21	,	,	PUNCT
ejpam-4003	265	22	int	int	NOUN
ejpam-4003	265	23	.	.	PUNCT
ejpam-4003	266	1	j.	j.	PROPN
ejpam-4003	266	2	of	of	ADP
ejpam-4003	266	3	math	math	PROPN
ejpam-4003	266	4	.	.	PUNCT
ejpam-4003	267	1	analysis	analysis	NOUN
ejpam-4003	267	2	.	.	PUNCT
ejpam-4003	267	3	,	,	PUNCT
ejpam-4003	267	4	6(6):285	6(6):285	NUM
ejpam-4003	267	5	-	-	SYM
ejpam-4003	267	6	289	289	NUM
ejpam-4003	267	7	,	,	PUNCT
ejpam-4003	267	8	2012	2012	NUM
ejpam-4003	267	9	.	.	PUNCT
ejpam-4003	268	1	[	[	X
ejpam-4003	268	2	12	12	NUM
ejpam-4003	268	3	]	]	X
ejpam-4003	268	4	e.	e.	PROPN
ejpam-4003	268	5	subha	subha	PROPN
ejpam-4003	268	6	,	,	PUNCT
ejpam-4003	268	7	n.	n.	PROPN
ejpam-4003	268	8	nagaveni	nagaveni	NOUN
ejpam-4003	268	9	,	,	PUNCT
ejpam-4003	268	10	strongly	strongly	ADV
ejpam-4003	268	11	minimal	minimal	ADJ
ejpam-4003	268	12	generalized	generalize	VERB
ejpam-4003	268	13	closed	close	VERB
ejpam-4003	268	14	set	set	VERB
ejpam-4003	268	15	in	in	ADP
ejpam-4003	268	16	biminimal	biminimal	NOUN
ejpam-4003	268	17	structure	structure	NOUN
ejpam-4003	268	18	space	space	NOUN
ejpam-4003	268	19	,	,	PUNCT
ejpam-4003	268	20	procedia	procedia	NOUN
ejpam-4003	268	21	comput	comput	NOUN
ejpam-4003	268	22	.	.	PUNCT
ejpam-4003	269	1	sci	sci	PROPN
ejpam-4003	269	2	.	.	PROPN
ejpam-4003	269	3	,	,	PUNCT
ejpam-4003	269	4	47:394–399	47:394–399	PROPN
ejpam-4003	269	5	,	,	PUNCT
ejpam-4003	269	6	2015	2015	NUM
ejpam-4003	269	7	.	.	PUNCT
ejpam-4003	270	1	[	[	X
ejpam-4003	270	2	13	13	NUM
ejpam-4003	270	3	]	]	PUNCT
ejpam-4003	270	4	t.	t.	PROPN
ejpam-4003	270	5	m.	m.	PROPN
ejpam-4003	270	6	al	al	PROPN
ejpam-4003	270	7	-	-	PUNCT
ejpam-4003	270	8	shami	shami	PROPN
ejpam-4003	270	9	and	and	CCONJ
ejpam-4003	270	10	t.	t.	PROPN
ejpam-4003	270	11	noiri	noiri	PROPN
ejpam-4003	270	12	,	,	PUNCT
ejpam-4003	270	13	compactness	compactness	NOUN
ejpam-4003	270	14	and	and	CCONJ
ejpam-4003	270	15	lindelöfness	lindelöfness	NOUN
ejpam-4003	270	16	using	use	VERB
ejpam-4003	270	17	somewhere	somewhere	ADV
ejpam-4003	270	18	dense	dense	ADJ
ejpam-4003	270	19	and	and	CCONJ
ejpam-4003	270	20	cs	cs	ADJ
ejpam-4003	270	21	-	-	ADJ
ejpam-4003	270	22	dense	dense	ADJ
ejpam-4003	270	23	sets	set	NOUN
ejpam-4003	270	24	,	,	PUNCT
ejpam-4003	270	25	novi	novi	PROPN
ejpam-4003	270	26	sad	sad	PROPN
ejpam-4003	270	27	j.	j.	PROPN
ejpam-4003	270	28	math	math	PROPN
ejpam-4003	270	29	.	.	PUNCT
ejpam-4003	270	30	,	,	PUNCT
ejpam-4003	270	31	2021	2021	NUM
ejpam-4003	270	32	:	:	PUNCT
ejpam-4003	270	33	12283	12283	NUM
ejpam-4003	270	34	,	,	PUNCT
ejpam-4003	270	35	12	12	NUM
ejpam-4003	270	36	pages	page	NOUN
ejpam-4003	270	37	.	.	PUNCT