id	sid	tid	token	lemma	pos
ejpam-3632	1	1	european	european	PROPN
ejpam-3632	1	2	journal	journal	PROPN
ejpam-3632	1	3	of	of	ADP
ejpam-3632	1	4	pure	pure	ADJ
ejpam-3632	1	5	and	and	CCONJ
ejpam-3632	1	6	applied	apply	VERB
ejpam-3632	1	7	mathematics	mathematic	NOUN
ejpam-3632	1	8	vol	vol	NOUN
ejpam-3632	1	9	.	.	PROPN
ejpam-3632	2	1	13	13	NUM
ejpam-3632	2	2	,	,	PUNCT
ejpam-3632	2	3	no	no	INTJ
ejpam-3632	2	4	.	.	NOUN
ejpam-3632	2	5	1	1	NUM
ejpam-3632	2	6	,	,	PUNCT
ejpam-3632	2	7	2020	2020	NUM
ejpam-3632	2	8	,	,	PUNCT
ejpam-3632	2	9	1	1	NUM
ejpam-3632	2	10	-	-	SYM
ejpam-3632	2	11	8	8	NUM
ejpam-3632	2	12	issn	issn	PROPN
ejpam-3632	2	13	1307	1307	NUM
ejpam-3632	2	14	-	-	SYM
ejpam-3632	2	15	5543	5543	NUM
ejpam-3632	2	16	–	–	PUNCT
ejpam-3632	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3632	2	18	published	publish	VERB
ejpam-3632	2	19	by	by	ADP
ejpam-3632	2	20	new	new	PROPN
ejpam-3632	2	21	york	york	PROPN
ejpam-3632	2	22	business	business	NOUN
ejpam-3632	2	23	global	global	PROPN
ejpam-3632	2	24	some	some	DET
ejpam-3632	2	25	closure	closure	NOUN
ejpam-3632	2	26	operators	operator	NOUN
ejpam-3632	2	27	and	and	CCONJ
ejpam-3632	2	28	topologies	topology	NOUN
ejpam-3632	2	29	on	on	ADP
ejpam-3632	2	30	a	a	DET
ejpam-3632	2	31	hyper	hyper	ADJ
ejpam-3632	2	32	bck	bck	NOUN
ejpam-3632	2	33	-	-	PUNCT
ejpam-3632	2	34	algebra	algebra	PROPN
ejpam-3632	2	35	rachel	rachel	PROPN
ejpam-3632	2	36	m.	m.	PROPN
ejpam-3632	2	37	patangan1	patangan1	PROPN
ejpam-3632	2	38	,	,	PUNCT
ejpam-3632	2	39	sergio	sergio	PROPN
ejpam-3632	2	40	r.	r.	PROPN
ejpam-3632	2	41	canoy	canoy	PROPN
ejpam-3632	2	42	,	,	PUNCT
ejpam-3632	2	43	jr.2,∗	jr.2,∗	PROPN
ejpam-3632	2	44	1	1	NUM
ejpam-3632	2	45	department	department	NOUN
ejpam-3632	2	46	of	of	ADP
ejpam-3632	2	47	applied	apply	VERB
ejpam-3632	2	48	mathematics	mathematic	NOUN
ejpam-3632	2	49	,	,	PUNCT
ejpam-3632	2	50	college	college	NOUN
ejpam-3632	2	51	of	of	ADP
ejpam-3632	2	52	arts	art	NOUN
ejpam-3632	2	53	and	and	CCONJ
ejpam-3632	2	54	sciences	science	NOUN
ejpam-3632	2	55	,	,	PUNCT
ejpam-3632	2	56	agusan	agusan	ADJ
ejpam-3632	2	57	del	del	PROPN
ejpam-3632	2	58	sur	sur	PROPN
ejpam-3632	2	59	state	state	PROPN
ejpam-3632	2	60	college	college	PROPN
ejpam-3632	2	61	of	of	ADP
ejpam-3632	2	62	agriculture	agriculture	NOUN
ejpam-3632	2	63	and	and	CCONJ
ejpam-3632	2	64	technology	technology	NOUN
ejpam-3632	2	65	,	,	PUNCT
ejpam-3632	2	66	bunawan	bunawan	PROPN
ejpam-3632	2	67	,	,	PUNCT
ejpam-3632	2	68	agusan	agusan	PROPN
ejpam-3632	2	69	del	del	PROPN
ejpam-3632	2	70	sur	sur	PROPN
ejpam-3632	2	71	,	,	PUNCT
ejpam-3632	2	72	philippines	philippines	PROPN
ejpam-3632	2	73	2	2	NUM
ejpam-3632	2	74	department	department	NOUN
ejpam-3632	2	75	of	of	ADP
ejpam-3632	2	76	mathematics	mathematic	NOUN
ejpam-3632	2	77	and	and	CCONJ
ejpam-3632	2	78	statistics	statistic	NOUN
ejpam-3632	2	79	,	,	PUNCT
ejpam-3632	2	80	college	college	NOUN
ejpam-3632	2	81	of	of	ADP
ejpam-3632	2	82	science	science	NOUN
ejpam-3632	2	83	and	and	CCONJ
ejpam-3632	2	84	mathematics	mathematic	NOUN
ejpam-3632	2	85	,	,	PUNCT
ejpam-3632	2	86	center	center	NOUN
ejpam-3632	2	87	for	for	ADP
ejpam-3632	2	88	graph	graph	NOUN
ejpam-3632	2	89	theory	theory	NOUN
ejpam-3632	2	90	,	,	PUNCT
ejpam-3632	2	91	algebra	algebra	NOUN
ejpam-3632	2	92	,	,	PUNCT
ejpam-3632	2	93	and	and	CCONJ
ejpam-3632	2	94	analysis	analysis	NOUN
ejpam-3632	2	95	-	-	PUNCT
ejpam-3632	2	96	prism	prism	NOUN
ejpam-3632	2	97	,	,	PUNCT
ejpam-3632	2	98	mindanao	mindanao	PROPN
ejpam-3632	2	99	state	state	PROPN
ejpam-3632	2	100	university	university	PROPN
ejpam-3632	2	101	iligan	iligan	PROPN
ejpam-3632	2	102	institute	institute	PROPN
ejpam-3632	2	103	of	of	ADP
ejpam-3632	2	104	technology	technology	PROPN
ejpam-3632	2	105	,	,	PUNCT
ejpam-3632	2	106	9200	9200	NUM
ejpam-3632	2	107	,	,	PUNCT
ejpam-3632	2	108	iligan	iligan	ADJ
ejpam-3632	2	109	city	city	NOUN
ejpam-3632	2	110	,	,	PUNCT
ejpam-3632	2	111	philippines	philippine	NOUN
ejpam-3632	2	112	abstract	abstract	ADJ
ejpam-3632	2	113	.	.	PUNCT
ejpam-3632	3	1	given	give	VERB
ejpam-3632	3	2	a	a	DET
ejpam-3632	3	3	hyper	hyper	ADJ
ejpam-3632	3	4	bck	bck	NOUN
ejpam-3632	3	5	-	-	PUNCT
ejpam-3632	3	6	algebra	algebra	NOUN
ejpam-3632	3	7	(	(	PUNCT
ejpam-3632	3	8	h	h	NOUN
ejpam-3632	3	9	,	,	PUNCT
ejpam-3632	3	10	∗	∗	NOUN
ejpam-3632	3	11	,	,	PUNCT
ejpam-3632	3	12	0	0	NUM
ejpam-3632	3	13	)	)	PUNCT
ejpam-3632	3	14	,	,	PUNCT
ejpam-3632	3	15	we	we	PRON
ejpam-3632	3	16	introduce	introduce	VERB
ejpam-3632	3	17	some	some	DET
ejpam-3632	3	18	subsets	subset	NOUN
ejpam-3632	3	19	of	of	ADP
ejpam-3632	3	20	h	h	NOUN
ejpam-3632	3	21	and	and	CCONJ
ejpam-3632	3	22	use	use	VERB
ejpam-3632	3	23	them	they	PRON
ejpam-3632	3	24	to	to	PART
ejpam-3632	3	25	generate	generate	VERB
ejpam-3632	3	26	two	two	NUM
ejpam-3632	3	27	closure	closure	NOUN
ejpam-3632	3	28	operators	operator	NOUN
ejpam-3632	3	29	on	on	ADP
ejpam-3632	3	30	h.	h.	PROPN
ejpam-3632	3	31	in	in	ADP
ejpam-3632	3	32	this	this	DET
ejpam-3632	3	33	paper	paper	NOUN
ejpam-3632	3	34	,	,	PUNCT
ejpam-3632	3	35	we	we	PRON
ejpam-3632	3	36	show	show	VERB
ejpam-3632	3	37	that	that	SCONJ
ejpam-3632	3	38	each	each	PRON
ejpam-3632	3	39	of	of	ADP
ejpam-3632	3	40	the	the	DET
ejpam-3632	3	41	two	two	NUM
ejpam-3632	3	42	closure	closure	NOUN
ejpam-3632	3	43	operators	operator	NOUN
ejpam-3632	3	44	on	on	ADP
ejpam-3632	3	45	h	h	NOUN
ejpam-3632	3	46	can	can	AUX
ejpam-3632	3	47	be	be	AUX
ejpam-3632	3	48	utilized	utilize	VERB
ejpam-3632	3	49	to	to	PART
ejpam-3632	3	50	form	form	VERB
ejpam-3632	3	51	a	a	DET
ejpam-3632	3	52	base	base	NOUN
ejpam-3632	3	53	for	for	ADP
ejpam-3632	3	54	some	some	DET
ejpam-3632	3	55	topology	topology	NOUN
ejpam-3632	3	56	on	on	ADP
ejpam-3632	3	57	h.	h.	PROPN
ejpam-3632	3	58	moreover	moreover	ADV
ejpam-3632	3	59	,	,	PUNCT
ejpam-3632	3	60	we	we	PRON
ejpam-3632	3	61	show	show	VERB
ejpam-3632	3	62	that	that	SCONJ
ejpam-3632	3	63	each	each	PRON
ejpam-3632	3	64	of	of	ADP
ejpam-3632	3	65	the	the	DET
ejpam-3632	3	66	induced	induced	ADJ
ejpam-3632	3	67	topologies	topology	NOUN
ejpam-3632	3	68	coincides	coincide	VERB
ejpam-3632	3	69	with	with	ADP
ejpam-3632	3	70	a	a	DET
ejpam-3632	3	71	previously	previously	ADV
ejpam-3632	3	72	known	know	VERB
ejpam-3632	3	73	topology	topology	NOUN
ejpam-3632	3	74	on	on	ADP
ejpam-3632	3	75	a	a	DET
ejpam-3632	3	76	hyper	hyper	ADJ
ejpam-3632	3	77	bck	bck	NOUN
ejpam-3632	3	78	-	-	PUNCT
ejpam-3632	3	79	algebra	algebra	NOUN
ejpam-3632	3	80	.	.	PUNCT
ejpam-3632	4	1	2020	2020	NUM
ejpam-3632	4	2	mathematics	mathematic	NOUN
ejpam-3632	4	3	subject	subject	NOUN
ejpam-3632	4	4	classifications	classification	NOUN
ejpam-3632	4	5	:	:	PUNCT
ejpam-3632	4	6	06f35	06f35	NUM
ejpam-3632	4	7	,	,	PUNCT
ejpam-3632	4	8	03g25	03g25	NOUN
ejpam-3632	4	9	key	key	ADJ
ejpam-3632	4	10	words	word	NOUN
ejpam-3632	4	11	and	and	CCONJ
ejpam-3632	4	12	phrases	phrase	NOUN
ejpam-3632	4	13	:	:	PUNCT
ejpam-3632	4	14	hyper	hyper	ADJ
ejpam-3632	4	15	bck	bck	NOUN
ejpam-3632	4	16	-	-	PUNCT
ejpam-3632	4	17	algebra	algebra	NOUN
ejpam-3632	4	18	,	,	PUNCT
ejpam-3632	4	19	hyper	hyper	ADJ
ejpam-3632	4	20	order	order	NOUN
ejpam-3632	4	21	,	,	PUNCT
ejpam-3632	4	22	closure	closure	NOUN
ejpam-3632	4	23	operator	operator	NOUN
ejpam-3632	4	24	1	1	NUM
ejpam-3632	4	25	.	.	PUNCT
ejpam-3632	5	1	introduction	introduction	NOUN
ejpam-3632	5	2	the	the	DET
ejpam-3632	5	3	study	study	NOUN
ejpam-3632	5	4	of	of	ADP
ejpam-3632	5	5	bck	bck	PROPN
ejpam-3632	5	6	-	-	PUNCT
ejpam-3632	5	7	algebras	algebras	PROPN
ejpam-3632	5	8	was	be	AUX
ejpam-3632	5	9	initiated	initiate	VERB
ejpam-3632	5	10	by	by	ADP
ejpam-3632	5	11	y.	y.	PROPN
ejpam-3632	5	12	imai	imai	PROPN
ejpam-3632	5	13	and	and	CCONJ
ejpam-3632	5	14	k.	k.	PROPN
ejpam-3632	5	15	iséki	iséki	PROPN
ejpam-3632	6	1	[	[	X
ejpam-3632	6	2	4	4	X
ejpam-3632	6	3	]	]	PUNCT
ejpam-3632	6	4	in	in	ADP
ejpam-3632	6	5	1966	1966	NUM
ejpam-3632	6	6	as	as	ADP
ejpam-3632	6	7	a	a	DET
ejpam-3632	6	8	generalization	generalization	NOUN
ejpam-3632	6	9	of	of	ADP
ejpam-3632	6	10	the	the	DET
ejpam-3632	6	11	concept	concept	NOUN
ejpam-3632	6	12	of	of	ADP
ejpam-3632	6	13	set	set	VERB
ejpam-3632	6	14	theoretic	theoretic	ADJ
ejpam-3632	6	15	difference	difference	NOUN
ejpam-3632	6	16	and	and	CCONJ
ejpam-3632	6	17	propositional	propositional	ADJ
ejpam-3632	6	18	calculi	calculi	NOUN
ejpam-3632	6	19	.	.	PUNCT
ejpam-3632	7	1	the	the	DET
ejpam-3632	7	2	hyperstructure	hyperstructure	PROPN
ejpam-3632	7	3	theory	theory	NOUN
ejpam-3632	7	4	(	(	PUNCT
ejpam-3632	7	5	or	or	CCONJ
ejpam-3632	7	6	multialgebras	multialgebra	NOUN
ejpam-3632	7	7	)	)	PUNCT
ejpam-3632	7	8	was	be	AUX
ejpam-3632	7	9	introduced	introduce	VERB
ejpam-3632	7	10	in	in	ADP
ejpam-3632	7	11	1934	1934	NUM
ejpam-3632	7	12	by	by	ADP
ejpam-3632	7	13	f.	f.	PROPN
ejpam-3632	7	14	marty	marty	PROPN
ejpam-3632	8	1	[	[	X
ejpam-3632	8	2	6	6	NUM
ejpam-3632	8	3	]	]	PUNCT
ejpam-3632	8	4	at	at	ADP
ejpam-3632	8	5	the	the	DET
ejpam-3632	8	6	8th	8th	ADJ
ejpam-3632	8	7	congress	congress	PROPN
ejpam-3632	8	8	of	of	ADP
ejpam-3632	8	9	scandinavian	scandinavian	ADJ
ejpam-3632	8	10	mathematicians	mathematician	NOUN
ejpam-3632	8	11	in	in	ADP
ejpam-3632	8	12	1934	1934	NUM
ejpam-3632	8	13	.	.	PUNCT
ejpam-3632	9	1	in	in	ADP
ejpam-3632	9	2	[	[	X
ejpam-3632	9	3	5	5	NUM
ejpam-3632	9	4	]	]	PUNCT
ejpam-3632	9	5	,	,	PUNCT
ejpam-3632	9	6	y.b	y.b	PROPN
ejpam-3632	9	7	.	.	PROPN
ejpam-3632	9	8	jun	jun	PROPN
ejpam-3632	9	9	et	et	PROPN
ejpam-3632	9	10	al	al	PROPN
ejpam-3632	9	11	.	.	PROPN
ejpam-3632	9	12	applied	apply	VERB
ejpam-3632	9	13	the	the	DET
ejpam-3632	9	14	hyperstructures	hyperstructure	NOUN
ejpam-3632	9	15	to	to	PART
ejpam-3632	9	16	bck	bck	VERB
ejpam-3632	9	17	-	-	PUNCT
ejpam-3632	9	18	algebras	algebras	PROPN
ejpam-3632	9	19	and	and	CCONJ
ejpam-3632	9	20	introduced	introduce	VERB
ejpam-3632	9	21	the	the	DET
ejpam-3632	9	22	notion	notion	NOUN
ejpam-3632	9	23	of	of	ADP
ejpam-3632	9	24	a	a	DET
ejpam-3632	9	25	hyper	hyper	ADJ
ejpam-3632	9	26	bck	bck	NOUN
ejpam-3632	9	27	-	-	PUNCT
ejpam-3632	9	28	algebra	algebra	NOUN
ejpam-3632	9	29	which	which	PRON
ejpam-3632	9	30	is	be	AUX
ejpam-3632	9	31	a	a	DET
ejpam-3632	9	32	generalization	generalization	NOUN
ejpam-3632	9	33	of	of	ADP
ejpam-3632	9	34	a	a	DET
ejpam-3632	9	35	bck	bck	NOUN
ejpam-3632	9	36	-	-	PUNCT
ejpam-3632	9	37	algebra	algebra	NOUN
ejpam-3632	9	38	.	.	PUNCT
ejpam-3632	10	1	by	by	ADP
ejpam-3632	10	2	using	use	VERB
ejpam-3632	10	3	the	the	DET
ejpam-3632	10	4	sets	set	NOUN
ejpam-3632	10	5	lh(a	lh(a	NUM
ejpam-3632	10	6	)	)	PUNCT
ejpam-3632	10	7	and	and	CCONJ
ejpam-3632	10	8	rh(a	rh(a	NUM
ejpam-3632	10	9	)	)	PUNCT
ejpam-3632	10	10	,	,	PUNCT
ejpam-3632	10	11	we	we	PRON
ejpam-3632	10	12	introduce	introduce	VERB
ejpam-3632	10	13	the	the	DET
ejpam-3632	10	14	bases	basis	NOUN
ejpam-3632	10	15	bl(h	bl(h	PUNCT
ejpam-3632	10	16	)	)	PUNCT
ejpam-3632	10	17	and	and	CCONJ
ejpam-3632	10	18	br(h	br(h	NUM
ejpam-3632	10	19	)	)	PUNCT
ejpam-3632	10	20	and	and	CCONJ
ejpam-3632	10	21	the	the	DET
ejpam-3632	10	22	induced	induced	ADJ
ejpam-3632	10	23	topologies	topology	NOUN
ejpam-3632	10	24	τl(h	τl(h	NUM
ejpam-3632	10	25	)	)	PUNCT
ejpam-3632	10	26	and	and	CCONJ
ejpam-3632	10	27	τr(h	τr(h	PUNCT
ejpam-3632	10	28	)	)	PUNCT
ejpam-3632	10	29	by	by	ADP
ejpam-3632	10	30	these	these	DET
ejpam-3632	10	31	sets	set	NOUN
ejpam-3632	10	32	,	,	PUNCT
ejpam-3632	10	33	respectively	respectively	ADV
ejpam-3632	10	34	,	,	PUNCT
ejpam-3632	10	35	and	and	CCONJ
ejpam-3632	10	36	investigate	investigate	VERB
ejpam-3632	10	37	their	their	PRON
ejpam-3632	10	38	related	related	ADJ
ejpam-3632	10	39	properties	property	NOUN
ejpam-3632	10	40	[	[	X
ejpam-3632	10	41	7	7	NUM
ejpam-3632	10	42	,	,	PUNCT
ejpam-3632	10	43	8	8	NUM
ejpam-3632	10	44	]	]	PUNCT
ejpam-3632	10	45	.	.	PUNCT
ejpam-3632	11	1	in	in	ADP
ejpam-3632	11	2	this	this	DET
ejpam-3632	11	3	paper	paper	NOUN
ejpam-3632	11	4	,	,	PUNCT
ejpam-3632	11	5	we	we	PRON
ejpam-3632	11	6	present	present	VERB
ejpam-3632	11	7	two	two	NUM
ejpam-3632	11	8	closure	closure	NOUN
ejpam-3632	11	9	operators	operator	NOUN
ejpam-3632	11	10	on	on	ADP
ejpam-3632	11	11	a	a	DET
ejpam-3632	11	12	hyper	hyper	ADJ
ejpam-3632	11	13	bck	bck	NOUN
ejpam-3632	11	14	-	-	PUNCT
ejpam-3632	11	15	algebra	algebra	NOUN
ejpam-3632	11	16	and	and	CCONJ
ejpam-3632	11	17	consider	consider	VERB
ejpam-3632	11	18	the	the	DET
ejpam-3632	11	19	respective	respective	ADJ
ejpam-3632	11	20	topologies	topology	NOUN
ejpam-3632	11	21	they	they	PRON
ejpam-3632	11	22	generate	generate	VERB
ejpam-3632	11	23	.	.	PUNCT
ejpam-3632	12	1	it	it	PRON
ejpam-3632	12	2	is	be	AUX
ejpam-3632	12	3	shown	show	VERB
ejpam-3632	12	4	that	that	SCONJ
ejpam-3632	12	5	these	these	DET
ejpam-3632	12	6	topologies	topology	NOUN
ejpam-3632	12	7	coincide	coincide	NOUN
ejpam-3632	12	8	,	,	PUNCT
ejpam-3632	12	9	respectively	respectively	ADV
ejpam-3632	12	10	,	,	PUNCT
ejpam-3632	12	11	with	with	ADP
ejpam-3632	12	12	the	the	DET
ejpam-3632	12	13	topologies	topology	NOUN
ejpam-3632	12	14	generated	generate	VERB
ejpam-3632	12	15	by	by	ADP
ejpam-3632	12	16	bl(h	bl(h	PRON
ejpam-3632	12	17	)	)	PUNCT
ejpam-3632	12	18	and	and	CCONJ
ejpam-3632	12	19	br(h	br(h	NUM
ejpam-3632	12	20	)	)	PUNCT
ejpam-3632	12	21	.	.	PUNCT
ejpam-3632	13	1	2	2	X
ejpam-3632	13	2	.	.	X
ejpam-3632	13	3	preliminaries	preliminary	NOUN
ejpam-3632	13	4	a	a	DET
ejpam-3632	13	5	hyper	hyper	ADJ
ejpam-3632	13	6	bck	bck	NOUN
ejpam-3632	13	7	-	-	PUNCT
ejpam-3632	13	8	algebra	algebra	NOUN
ejpam-3632	13	9	is	be	AUX
ejpam-3632	13	10	a	a	DET
ejpam-3632	13	11	nonempty	nonempty	ADV
ejpam-3632	13	12	set	set	VERB
ejpam-3632	13	13	h	h	NOUN
ejpam-3632	13	14	endowed	endow	VERB
ejpam-3632	13	15	with	with	ADP
ejpam-3632	13	16	a	a	DET
ejpam-3632	13	17	hyperoperation	hyperoperation	NOUN
ejpam-3632	13	18	“	"	PUNCT
ejpam-3632	13	19	∗	∗	NOUN
ejpam-3632	13	20	”	"	PUNCT
ejpam-3632	13	21	and	and	CCONJ
ejpam-3632	13	22	a	a	DET
ejpam-3632	13	23	constant	constant	ADJ
ejpam-3632	13	24	0	0	NUM
ejpam-3632	13	25	satisfying	satisfy	VERB
ejpam-3632	13	26	the	the	DET
ejpam-3632	13	27	following	follow	VERB
ejpam-3632	13	28	axioms	axiom	NOUN
ejpam-3632	13	29	:	:	PUNCT
ejpam-3632	13	30	for	for	ADP
ejpam-3632	13	31	all	all	DET
ejpam-3632	13	32	x	x	NOUN
ejpam-3632	13	33	,	,	PUNCT
ejpam-3632	13	34	y	y	PROPN
ejpam-3632	13	35	,	,	PUNCT
ejpam-3632	13	36	z	z	PROPN
ejpam-3632	13	37	∈	∈	PROPN
ejpam-3632	13	38	h	h	NOUN
ejpam-3632	13	39	,	,	PUNCT
ejpam-3632	13	40	∗corresponding	∗corresponde	VERB
ejpam-3632	13	41	author	author	NOUN
ejpam-3632	13	42	.	.	PUNCT
ejpam-3632	14	1	doi	doi	NOUN
ejpam-3632	14	2	:	:	PUNCT
ejpam-3632	14	3	https://doi.org/10.29020/nybg.ejpam.v13i1.3632	https://doi.org/10.29020/nybg.ejpam.v13i1.3632	NOUN
ejpam-3632	14	4	email	email	NOUN
ejpam-3632	14	5	addresses	address	NOUN
ejpam-3632	14	6	:	:	PUNCT
ejpam-3632	14	7	rhapsodistchelar@gmail.com	rhapsodistchelar@gmail.com	X
ejpam-3632	14	8	(	(	PUNCT
ejpam-3632	14	9	r.	r.	NOUN
ejpam-3632	14	10	patangan	patangan	PROPN
ejpam-3632	14	11	)	)	PUNCT
ejpam-3632	14	12	,	,	PUNCT
ejpam-3632	14	13	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-3632	14	14	(	(	PUNCT
ejpam-3632	14	15	s.	s.	PROPN
ejpam-3632	14	16	canoy	canoy	PROPN
ejpam-3632	14	17	,	,	PUNCT
ejpam-3632	14	18	jr	jr	PROPN
ejpam-3632	14	19	.	.	PUNCT
ejpam-3632	14	20	)	)	PUNCT
ejpam-3632	14	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3632	15	1	1	1	NUM
ejpam-3632	15	2	c	c	X
ejpam-3632	15	3	©	©	NOUN
ejpam-3632	15	4	2020	2020	NUM
ejpam-3632	15	5	ejpam	ejpam	VERB
ejpam-3632	15	6	all	all	DET
ejpam-3632	15	7	rights	right	NOUN
ejpam-3632	15	8	reserved	reserve	VERB
ejpam-3632	15	9	.	.	PUNCT
ejpam-3632	16	1	r.	r.	PROPN
ejpam-3632	16	2	patangan	patangan	PROPN
ejpam-3632	16	3	,	,	PUNCT
ejpam-3632	16	4	s.	s.	PROPN
ejpam-3632	16	5	canoy	canoy	PROPN
ejpam-3632	16	6	,	,	PUNCT
ejpam-3632	16	7	jr	jr	PROPN
ejpam-3632	16	8	.	.	PROPN
ejpam-3632	16	9	/	/	SYM
ejpam-3632	16	10	eur	eur	PROPN
ejpam-3632	16	11	.	.	PUNCT
ejpam-3632	17	1	j.	j.	PROPN
ejpam-3632	17	2	pure	pure	PROPN
ejpam-3632	17	3	appl	appl	PROPN
ejpam-3632	17	4	.	.	PROPN
ejpam-3632	17	5	math	math	PROPN
ejpam-3632	17	6	,	,	PUNCT
ejpam-3632	17	7	13	13	NUM
ejpam-3632	17	8	(	(	PUNCT
ejpam-3632	17	9	1	1	NUM
ejpam-3632	17	10	)	)	PUNCT
ejpam-3632	17	11	(	(	PUNCT
ejpam-3632	17	12	2020	2020	NUM
ejpam-3632	17	13	)	)	PUNCT
ejpam-3632	17	14	,	,	PUNCT
ejpam-3632	17	15	1	1	NUM
ejpam-3632	17	16	-	-	SYM
ejpam-3632	17	17	8	8	NUM
ejpam-3632	17	18	2	2	NUM
ejpam-3632	17	19	(	(	PUNCT
ejpam-3632	17	20	h1	h1	PROPN
ejpam-3632	17	21	)	)	PUNCT
ejpam-3632	17	22	(	(	PUNCT
ejpam-3632	17	23	x	x	SYM
ejpam-3632	17	24	∗	∗	PROPN
ejpam-3632	17	25	z	z	NOUN
ejpam-3632	17	26	)	)	PUNCT
ejpam-3632	17	27	∗	∗	NOUN
ejpam-3632	17	28	(	(	PUNCT
ejpam-3632	17	29	y	y	PROPN
ejpam-3632	17	30	∗	∗	PROPN
ejpam-3632	17	31	z	z	PROPN
ejpam-3632	17	32	)	)	PUNCT
ejpam-3632	17	33	�	�	PROPN
ejpam-3632	17	34	x	x	PROPN
ejpam-3632	17	35	∗	∗	PROPN
ejpam-3632	17	36	y	y	PROPN
ejpam-3632	17	37	,	,	PUNCT
ejpam-3632	17	38	(	(	PUNCT
ejpam-3632	17	39	h2	h2	NOUN
ejpam-3632	17	40	)	)	PUNCT
ejpam-3632	17	41	(	(	PUNCT
ejpam-3632	17	42	x	x	SYM
ejpam-3632	17	43	∗	∗	PROPN
ejpam-3632	17	44	y	y	NOUN
ejpam-3632	17	45	)	)	PUNCT
ejpam-3632	17	46	∗	∗	NOUN
ejpam-3632	17	47	z	z	NOUN
ejpam-3632	17	48	=	=	SYM
ejpam-3632	17	49	(	(	PUNCT
ejpam-3632	17	50	x	x	X
ejpam-3632	17	51	∗	∗	PROPN
ejpam-3632	17	52	z	z	NOUN
ejpam-3632	17	53	)	)	PUNCT
ejpam-3632	17	54	∗	∗	PROPN
ejpam-3632	17	55	y	y	PROPN
ejpam-3632	17	56	,	,	PUNCT
ejpam-3632	17	57	(	(	PUNCT
ejpam-3632	17	58	h3	h3	NOUN
ejpam-3632	17	59	)	)	PUNCT
ejpam-3632	17	60	x	x	PUNCT
ejpam-3632	17	61	∗h	∗h	NOUN
ejpam-3632	17	62	�	�	PROPN
ejpam-3632	17	63	x	x	SYM
ejpam-3632	17	64	,	,	PUNCT
ejpam-3632	17	65	(	(	PUNCT
ejpam-3632	17	66	h4	h4	PROPN
ejpam-3632	17	67	)	)	PUNCT
ejpam-3632	17	68	x	x	NOUN
ejpam-3632	17	69	�	�	PROPN
ejpam-3632	17	70	y	y	PROPN
ejpam-3632	17	71	and	and	CCONJ
ejpam-3632	17	72	y	y	PROPN
ejpam-3632	17	73	�	�	PROPN
ejpam-3632	17	74	x	x	PUNCT
ejpam-3632	17	75	imply	imply	VERB
ejpam-3632	17	76	x	x	X
ejpam-3632	17	77	=	=	SYM
ejpam-3632	17	78	y	y	PROPN
ejpam-3632	17	79	,	,	PUNCT
ejpam-3632	17	80	where	where	SCONJ
ejpam-3632	17	81	for	for	ADP
ejpam-3632	17	82	every	every	DET
ejpam-3632	17	83	a	a	PROPN
ejpam-3632	17	84	,	,	PUNCT
ejpam-3632	17	85	b	b	PROPN
ejpam-3632	17	86	⊆	⊆	NUM
ejpam-3632	17	87	h	h	NOUN
ejpam-3632	17	88	,	,	PUNCT
ejpam-3632	17	89	a	a	DET
ejpam-3632	17	90	�	�	PROPN
ejpam-3632	17	91	b	b	PROPN
ejpam-3632	17	92	if	if	SCONJ
ejpam-3632	18	1	and	and	CCONJ
ejpam-3632	18	2	only	only	ADV
ejpam-3632	18	3	if	if	SCONJ
ejpam-3632	18	4	for	for	ADP
ejpam-3632	18	5	each	each	DET
ejpam-3632	18	6	a	a	DET
ejpam-3632	18	7	∈	∈	PROPN
ejpam-3632	18	8	a	a	PRON
ejpam-3632	18	9	,	,	PUNCT
ejpam-3632	18	10	there	there	PRON
ejpam-3632	18	11	exists	exist	VERB
ejpam-3632	18	12	b	b	PROPN
ejpam-3632	18	13	∈	∈	PROPN
ejpam-3632	18	14	b	b	NOUN
ejpam-3632	18	15	such	such	ADJ
ejpam-3632	18	16	that	that	DET
ejpam-3632	18	17	0	0	NUM
ejpam-3632	18	18	∈	∈	PROPN
ejpam-3632	18	19	a	a	DET
ejpam-3632	18	20	∗	∗	X
ejpam-3632	18	21	b.	b.	PROPN
ejpam-3632	18	22	in	in	ADP
ejpam-3632	18	23	particular	particular	ADJ
ejpam-3632	18	24	,	,	PUNCT
ejpam-3632	18	25	for	for	ADP
ejpam-3632	18	26	every	every	DET
ejpam-3632	18	27	x	x	NOUN
ejpam-3632	18	28	,	,	PUNCT
ejpam-3632	18	29	y	y	PROPN
ejpam-3632	18	30	∈	∈	PROPN
ejpam-3632	18	31	h	h	NOUN
ejpam-3632	18	32	,	,	PUNCT
ejpam-3632	18	33	x	x	PROPN
ejpam-3632	18	34	�	�	PROPN
ejpam-3632	18	35	y	y	PROPN
ejpam-3632	18	36	if	if	SCONJ
ejpam-3632	18	37	and	and	CCONJ
ejpam-3632	18	38	only	only	ADV
ejpam-3632	18	39	if	if	SCONJ
ejpam-3632	18	40	0	0	NUM
ejpam-3632	18	41	∈	∈	NOUN
ejpam-3632	18	42	x	x	X
ejpam-3632	18	43	∗	∗	NOUN
ejpam-3632	18	44	y.	y.	NOUN
ejpam-3632	18	45	in	in	ADP
ejpam-3632	18	46	such	such	ADJ
ejpam-3632	18	47	case	case	NOUN
ejpam-3632	18	48	,	,	PUNCT
ejpam-3632	18	49	we	we	PRON
ejpam-3632	18	50	call	call	VERB
ejpam-3632	18	51	“	"	PUNCT
ejpam-3632	18	52	�	�	PROPN
ejpam-3632	18	53	”	"	PUNCT
ejpam-3632	18	54	the	the	DET
ejpam-3632	18	55	hyper	hyper	ADJ
ejpam-3632	18	56	order	order	NOUN
ejpam-3632	18	57	in	in	ADP
ejpam-3632	18	58	h.	h.	PROPN
ejpam-3632	18	59	throughout	throughout	ADP
ejpam-3632	18	60	this	this	DET
ejpam-3632	18	61	study	study	NOUN
ejpam-3632	18	62	,	,	PUNCT
ejpam-3632	18	63	(	(	PUNCT
ejpam-3632	18	64	h1	h1	PROPN
ejpam-3632	18	65	,	,	PUNCT
ejpam-3632	18	66	∗1	∗1	PROPN
ejpam-3632	18	67	,	,	PUNCT
ejpam-3632	18	68	01	01	NUM
ejpam-3632	18	69	)	)	PUNCT
ejpam-3632	18	70	(	(	PUNCT
ejpam-3632	18	71	or	or	CCONJ
ejpam-3632	18	72	simply	simply	ADV
ejpam-3632	18	73	h1	h1	ADJ
ejpam-3632	18	74	)	)	PUNCT
ejpam-3632	18	75	and	and	CCONJ
ejpam-3632	18	76	(	(	PUNCT
ejpam-3632	18	77	h2	h2	NOUN
ejpam-3632	18	78	,	,	PUNCT
ejpam-3632	18	79	∗2	∗2	PROPN
ejpam-3632	18	80	,	,	PUNCT
ejpam-3632	18	81	02	02	NUM
ejpam-3632	18	82	)	)	PUNCT
ejpam-3632	18	83	(	(	PUNCT
ejpam-3632	18	84	or	or	CCONJ
ejpam-3632	18	85	simply	simply	ADV
ejpam-3632	18	86	h2	h2	NOUN
ejpam-3632	18	87	)	)	PUNCT
ejpam-3632	18	88	are	be	AUX
ejpam-3632	18	89	hyper	hyper	ADJ
ejpam-3632	18	90	bck	bck	NOUN
ejpam-3632	18	91	-	-	PUNCT
ejpam-3632	18	92	algebras	algebras	X
ejpam-3632	18	93	.	.	PUNCT
ejpam-3632	19	1	let	let	VERB
ejpam-3632	19	2	h	h	PRON
ejpam-3632	19	3	be	be	AUX
ejpam-3632	19	4	a	a	DET
ejpam-3632	19	5	hyper	hyper	ADJ
ejpam-3632	19	6	bck	bck	NOUN
ejpam-3632	19	7	-	-	PUNCT
ejpam-3632	19	8	algebra	algebra	NOUN
ejpam-3632	19	9	and	and	CCONJ
ejpam-3632	19	10	a	a	DET
ejpam-3632	19	11	⊆	⊆	NUM
ejpam-3632	19	12	h.	h.	NOUN
ejpam-3632	19	13	the	the	DET
ejpam-3632	19	14	sets	set	NOUN
ejpam-3632	19	15	lh(a	lh(a	NUM
ejpam-3632	19	16	)	)	PUNCT
ejpam-3632	19	17	and	and	CCONJ
ejpam-3632	20	1	rh(a	rh(a	NUM
ejpam-3632	20	2	)	)	PUNCT
ejpam-3632	20	3	are	be	AUX
ejpam-3632	20	4	given	give	VERB
ejpam-3632	20	5	as	as	SCONJ
ejpam-3632	20	6	follows	follow	VERB
ejpam-3632	20	7	:	:	PUNCT
ejpam-3632	20	8	lh(a	lh(a	NUM
ejpam-3632	20	9	)	)	PUNCT
ejpam-3632	20	10	:	:	PUNCT
ejpam-3632	21	1	=	=	SYM
ejpam-3632	21	2	{	{	PUNCT
ejpam-3632	21	3	x	x	SYM
ejpam-3632	21	4	∈	∈	NOUN
ejpam-3632	21	5	h	h	NOUN
ejpam-3632	22	1	|	|	ADV
ejpam-3632	22	2	x	x	X
ejpam-3632	22	3	�	�	PROPN
ejpam-3632	22	4	a	a	DET
ejpam-3632	22	5	∀a	∀a	X
ejpam-3632	22	6	∈	∈	NOUN
ejpam-3632	22	7	a	a	DET
ejpam-3632	22	8	}	}	PUNCT
ejpam-3632	22	9	=	=	SYM
ejpam-3632	22	10	{	{	PUNCT
ejpam-3632	22	11	x	x	PUNCT
ejpam-3632	22	12	∈	∈	NOUN
ejpam-3632	22	13	h	h	NOUN
ejpam-3632	23	1	|	|	ADV
ejpam-3632	23	2	0	0	NUM
ejpam-3632	23	3	∈	∈	NOUN
ejpam-3632	23	4	x	x	PUNCT
ejpam-3632	23	5	∗	∗	VERB
ejpam-3632	23	6	a	a	DET
ejpam-3632	23	7	∀a	∀a	NOUN
ejpam-3632	23	8	∈	∈	NOUN
ejpam-3632	23	9	a	a	NOUN
ejpam-3632	23	10	}	}	PUNCT
ejpam-3632	23	11	and	and	CCONJ
ejpam-3632	23	12	rh(a	rh(a	NUM
ejpam-3632	23	13	)	)	PUNCT
ejpam-3632	23	14	:	:	PUNCT
ejpam-3632	24	1	=	=	SYM
ejpam-3632	24	2	{	{	PUNCT
ejpam-3632	24	3	x	x	SYM
ejpam-3632	24	4	∈	∈	NOUN
ejpam-3632	24	5	h	h	NOUN
ejpam-3632	24	6	|	|	ADV
ejpam-3632	24	7	a	a	DET
ejpam-3632	24	8	�	�	PROPN
ejpam-3632	24	9	x	x	SYM
ejpam-3632	24	10	∀a	∀a	X
ejpam-3632	24	11	∈	∈	NOUN
ejpam-3632	24	12	a	a	DET
ejpam-3632	24	13	}	}	PUNCT
ejpam-3632	24	14	=	=	SYM
ejpam-3632	24	15	{	{	PUNCT
ejpam-3632	24	16	x	x	PUNCT
ejpam-3632	24	17	∈	∈	NOUN
ejpam-3632	24	18	h	h	NOUN
ejpam-3632	25	1	|	|	ADV
ejpam-3632	25	2	0	0	NUM
ejpam-3632	25	3	∈	∈	PROPN
ejpam-3632	25	4	a	a	DET
ejpam-3632	25	5	∗	∗	NOUN
ejpam-3632	25	6	x	x	SYM
ejpam-3632	25	7	∀a	∀a	X
ejpam-3632	25	8	∈	∈	NOUN
ejpam-3632	25	9	a	a	PRON
ejpam-3632	25	10	}	}	PUNCT
ejpam-3632	25	11	.	.	PUNCT
ejpam-3632	26	1	if	if	SCONJ
ejpam-3632	26	2	a	a	PRON
ejpam-3632	26	3	=	=	X
ejpam-3632	26	4	{	{	PUNCT
ejpam-3632	26	5	a	a	NOUN
ejpam-3632	26	6	}	}	PUNCT
ejpam-3632	26	7	,	,	PUNCT
ejpam-3632	26	8	we	we	PRON
ejpam-3632	26	9	write	write	VERB
ejpam-3632	26	10	lh({a	lh({a	PROPN
ejpam-3632	26	11	}	}	PUNCT
ejpam-3632	26	12	)	)	PUNCT
ejpam-3632	27	1	=	=	SYM
ejpam-3632	27	2	lh(a	lh(a	NOUN
ejpam-3632	27	3	)	)	PUNCT
ejpam-3632	27	4	and	and	CCONJ
ejpam-3632	27	5	rh({a	rh({a	NOUN
ejpam-3632	27	6	}	}	PUNCT
ejpam-3632	27	7	)	)	PUNCT
ejpam-3632	27	8	=	=	SYM
ejpam-3632	28	1	rh(a	rh(a	NUM
ejpam-3632	28	2	)	)	PUNCT
ejpam-3632	28	3	.	.	PUNCT
ejpam-3632	29	1	let	let	VERB
ejpam-3632	29	2	x	x	PRON
ejpam-3632	29	3	be	be	AUX
ejpam-3632	29	4	a	a	DET
ejpam-3632	29	5	nonempty	nonempty	ADV
ejpam-3632	29	6	set	set	VERB
ejpam-3632	29	7	and	and	CCONJ
ejpam-3632	29	8	let	let	VERB
ejpam-3632	29	9	p(x	p(x	NOUN
ejpam-3632	29	10	)	)	PUNCT
ejpam-3632	29	11	denote	denote	VERB
ejpam-3632	29	12	the	the	DET
ejpam-3632	29	13	power	power	NOUN
ejpam-3632	29	14	set	set	NOUN
ejpam-3632	29	15	of	of	ADP
ejpam-3632	29	16	x.	x.	NOUN
ejpam-3632	29	17	a	a	DET
ejpam-3632	29	18	mapping	mapping	NOUN
ejpam-3632	29	19	φ	φ	NOUN
ejpam-3632	29	20	:	:	PUNCT
ejpam-3632	29	21	p(x	p(x	PROPN
ejpam-3632	29	22	)	)	PUNCT
ejpam-3632	29	23	→	→	SYM
ejpam-3632	29	24	p(x	p(x	PROPN
ejpam-3632	29	25	)	)	PUNCT
ejpam-3632	29	26	is	be	AUX
ejpam-3632	29	27	called	call	VERB
ejpam-3632	29	28	a	a	DET
ejpam-3632	29	29	closure	closure	NOUN
ejpam-3632	29	30	operator	operator	NOUN
ejpam-3632	29	31	on	on	ADP
ejpam-3632	29	32	x	x	SYM
ejpam-3632	29	33	,	,	PUNCT
ejpam-3632	29	34	if	if	SCONJ
ejpam-3632	29	35	for	for	ADP
ejpam-3632	29	36	all	all	DET
ejpam-3632	29	37	a	a	DET
ejpam-3632	29	38	,	,	PUNCT
ejpam-3632	29	39	b	b	PROPN
ejpam-3632	29	40	∈	∈	PROPN
ejpam-3632	29	41	p(x	p(x	PROPN
ejpam-3632	29	42	)	)	PUNCT
ejpam-3632	29	43	,	,	PUNCT
ejpam-3632	29	44	the	the	DET
ejpam-3632	29	45	following	follow	VERB
ejpam-3632	29	46	properties	property	NOUN
ejpam-3632	29	47	hold	hold	VERB
ejpam-3632	29	48	[	[	X
ejpam-3632	29	49	2	2	NUM
ejpam-3632	29	50	]	]	NUM
ejpam-3632	29	51	:	:	PUNCT
ejpam-3632	29	52	(	(	PUNCT
ejpam-3632	29	53	i	i	NOUN
ejpam-3632	29	54	)	)	PUNCT
ejpam-3632	30	1	a	a	DET
ejpam-3632	30	2	⊆	⊆	NUM
ejpam-3632	30	3	φ(a	φ(a	ADJ
ejpam-3632	30	4	)	)	PUNCT
ejpam-3632	30	5	(	(	PUNCT
ejpam-3632	30	6	ii	ii	NOUN
ejpam-3632	30	7	)	)	PUNCT
ejpam-3632	30	8	φ2(a	φ2(a	NOUN
ejpam-3632	30	9	)	)	PUNCT
ejpam-3632	31	1	=	=	SYM
ejpam-3632	31	2	φ(a	φ(a	ADJ
ejpam-3632	31	3	)	)	PUNCT
ejpam-3632	31	4	(	(	PUNCT
ejpam-3632	31	5	iii	iii	X
ejpam-3632	31	6	)	)	PUNCT
ejpam-3632	31	7	a	a	DET
ejpam-3632	31	8	⊆	⊆	NUM
ejpam-3632	31	9	b	b	NOUN
ejpam-3632	31	10	⇒	⇒	NOUN
ejpam-3632	31	11	φ(a	φ(a	PROPN
ejpam-3632	31	12	)	)	PUNCT
ejpam-3632	31	13	⊆	⊆	NUM
ejpam-3632	31	14	φ(b	φ(b	NOUN
ejpam-3632	31	15	)	)	PUNCT
ejpam-3632	31	16	.	.	PUNCT
ejpam-3632	32	1	3	3	X
ejpam-3632	32	2	.	.	X
ejpam-3632	32	3	known	know	VERB
ejpam-3632	32	4	results	result	NOUN
ejpam-3632	32	5	proposition	proposition	NOUN
ejpam-3632	32	6	1	1	NUM
ejpam-3632	32	7	.	.	PUNCT
ejpam-3632	33	1	[	[	X
ejpam-3632	33	2	7	7	X
ejpam-3632	33	3	]	]	PUNCT
ejpam-3632	33	4	let	let	VERB
ejpam-3632	33	5	h	h	PRON
ejpam-3632	33	6	be	be	AUX
ejpam-3632	33	7	a	a	DET
ejpam-3632	33	8	hyper	hyper	ADJ
ejpam-3632	33	9	bck	bck	NOUN
ejpam-3632	33	10	-	-	PUNCT
ejpam-3632	33	11	algebra	algebra	NOUN
ejpam-3632	33	12	and	and	CCONJ
ejpam-3632	33	13	a	a	DET
ejpam-3632	33	14	,	,	PUNCT
ejpam-3632	33	15	b	b	PROPN
ejpam-3632	33	16	⊆	⊆	NUM
ejpam-3632	33	17	h.	h.	NOUN
ejpam-3632	33	18	then	then	ADV
ejpam-3632	33	19	the	the	DET
ejpam-3632	33	20	following	follow	VERB
ejpam-3632	33	21	hold	hold	NOUN
ejpam-3632	33	22	:	:	PUNCT
ejpam-3632	33	23	(	(	PUNCT
ejpam-3632	33	24	i	i	NOUN
ejpam-3632	33	25	)	)	PUNCT
ejpam-3632	33	26	rh(∅	rh(∅	PROPN
ejpam-3632	33	27	)	)	PUNCT
ejpam-3632	34	1	=	=	SYM
ejpam-3632	34	2	h.	h.	PROPN
ejpam-3632	34	3	(	(	PUNCT
ejpam-3632	34	4	ii	ii	NOUN
ejpam-3632	34	5	)	)	PUNCT
ejpam-3632	34	6	rh(a	rh(a	NUM
ejpam-3632	34	7	)	)	PUNCT
ejpam-3632	34	8	=	=	SYM
ejpam-3632	35	1	⋂	⋂	PROPN
ejpam-3632	35	2	a∈a	a∈a	ADJ
ejpam-3632	35	3	rh(a	rh(a	NUM
ejpam-3632	35	4	)	)	PUNCT
ejpam-3632	35	5	.	.	PUNCT
ejpam-3632	36	1	(	(	PUNCT
ejpam-3632	36	2	iii	iii	X
ejpam-3632	36	3	)	)	PUNCT
ejpam-3632	36	4	for	for	ADP
ejpam-3632	36	5	any	any	DET
ejpam-3632	36	6	∅	∅	NOUN
ejpam-3632	36	7	6=	6=	ADP
ejpam-3632	36	8	a	a	DET
ejpam-3632	36	9	⊆	⊆	NUM
ejpam-3632	36	10	h	h	NOUN
ejpam-3632	36	11	such	such	ADJ
ejpam-3632	36	12	that	that	SCONJ
ejpam-3632	36	13	a	a	DET
ejpam-3632	36	14	6=	6=	NUM
ejpam-3632	36	15	{	{	PUNCT
ejpam-3632	36	16	0	0	NUM
ejpam-3632	36	17	}	}	PUNCT
ejpam-3632	36	18	,	,	PUNCT
ejpam-3632	36	19	0	0	NUM
ejpam-3632	36	20	/∈	/∈	PUNCT
ejpam-3632	37	1	rh(a	rh(a	NUM
ejpam-3632	37	2	)	)	PUNCT
ejpam-3632	37	3	.	.	PUNCT
ejpam-3632	38	1	(	(	PUNCT
ejpam-3632	38	2	iv	iv	X
ejpam-3632	38	3	)	)	PUNCT
ejpam-3632	38	4	if	if	SCONJ
ejpam-3632	38	5	a	a	DET
ejpam-3632	38	6	⊆	⊆	NUM
ejpam-3632	38	7	b	b	NOUN
ejpam-3632	38	8	,	,	PUNCT
ejpam-3632	38	9	then	then	ADV
ejpam-3632	38	10	rh(b	rh(b	PUNCT
ejpam-3632	38	11	)	)	PUNCT
ejpam-3632	38	12	⊆	⊆	NUM
ejpam-3632	38	13	rh(a	rh(a	NUM
ejpam-3632	38	14	)	)	PUNCT
ejpam-3632	38	15	.	.	PUNCT
ejpam-3632	39	1	the	the	DET
ejpam-3632	39	2	next	next	ADJ
ejpam-3632	39	3	result	result	NOUN
ejpam-3632	39	4	is	be	AUX
ejpam-3632	39	5	generated	generate	VERB
ejpam-3632	39	6	by	by	ADP
ejpam-3632	39	7	albaracin	albaracin	NOUN
ejpam-3632	39	8	and	and	CCONJ
ejpam-3632	39	9	vilela	vilela	NOUN
ejpam-3632	39	10	.	.	PUNCT
ejpam-3632	40	1	proposition	proposition	NOUN
ejpam-3632	40	2	2	2	NUM
ejpam-3632	40	3	.	.	PUNCT
ejpam-3632	41	1	[	[	X
ejpam-3632	41	2	1	1	X
ejpam-3632	41	3	]	]	PUNCT
ejpam-3632	41	4	let	let	VERB
ejpam-3632	41	5	a	a	PRON
ejpam-3632	41	6	and	and	CCONJ
ejpam-3632	41	7	b	b	NOUN
ejpam-3632	41	8	be	be	AUX
ejpam-3632	41	9	subsets	subset	NOUN
ejpam-3632	41	10	of	of	ADP
ejpam-3632	41	11	a	a	DET
ejpam-3632	41	12	hyper	hyper	ADJ
ejpam-3632	41	13	bck	bck	NOUN
ejpam-3632	41	14	-	-	PUNCT
ejpam-3632	41	15	algebra	algebra	NOUN
ejpam-3632	41	16	h.	h.	NOUN
ejpam-3632	41	17	then	then	ADV
ejpam-3632	41	18	the	the	DET
ejpam-3632	41	19	following	follow	VERB
ejpam-3632	41	20	hold	hold	NOUN
ejpam-3632	41	21	:	:	PUNCT
ejpam-3632	41	22	(	(	PUNCT
ejpam-3632	41	23	i	i	NOUN
ejpam-3632	41	24	)	)	PUNCT
ejpam-3632	41	25	lh(∅	lh(∅	PROPN
ejpam-3632	41	26	)	)	PUNCT
ejpam-3632	42	1	=	=	SYM
ejpam-3632	42	2	h.	h.	PROPN
ejpam-3632	42	3	(	(	PUNCT
ejpam-3632	42	4	ii	ii	PROPN
ejpam-3632	42	5	)	)	PUNCT
ejpam-3632	42	6	if	if	SCONJ
ejpam-3632	42	7	a	a	DET
ejpam-3632	42	8	⊆	⊆	NUM
ejpam-3632	42	9	b	b	NOUN
ejpam-3632	42	10	,	,	PUNCT
ejpam-3632	42	11	then	then	ADV
ejpam-3632	42	12	lh(b	lh(b	NOUN
ejpam-3632	42	13	)	)	PUNCT
ejpam-3632	42	14	⊆	⊆	NUM
ejpam-3632	42	15	lh(a	lh(a	NUM
ejpam-3632	42	16	)	)	PUNCT
ejpam-3632	42	17	.	.	PUNCT
ejpam-3632	43	1	r.	r.	PROPN
ejpam-3632	43	2	patangan	patangan	PROPN
ejpam-3632	43	3	,	,	PUNCT
ejpam-3632	43	4	s.	s.	PROPN
ejpam-3632	43	5	canoy	canoy	PROPN
ejpam-3632	43	6	,	,	PUNCT
ejpam-3632	43	7	jr	jr	PROPN
ejpam-3632	43	8	.	.	PROPN
ejpam-3632	43	9	/	/	SYM
ejpam-3632	43	10	eur	eur	PROPN
ejpam-3632	43	11	.	.	PUNCT
ejpam-3632	44	1	j.	j.	PROPN
ejpam-3632	44	2	pure	pure	PROPN
ejpam-3632	44	3	appl	appl	PROPN
ejpam-3632	44	4	.	.	PROPN
ejpam-3632	44	5	math	math	PROPN
ejpam-3632	44	6	,	,	PUNCT
ejpam-3632	44	7	13	13	NUM
ejpam-3632	44	8	(	(	PUNCT
ejpam-3632	44	9	1	1	NUM
ejpam-3632	44	10	)	)	PUNCT
ejpam-3632	44	11	(	(	PUNCT
ejpam-3632	44	12	2020	2020	NUM
ejpam-3632	44	13	)	)	PUNCT
ejpam-3632	44	14	,	,	PUNCT
ejpam-3632	44	15	1	1	NUM
ejpam-3632	44	16	-	-	SYM
ejpam-3632	44	17	8	8	NUM
ejpam-3632	44	18	3	3	NUM
ejpam-3632	44	19	(	(	PUNCT
ejpam-3632	44	20	iii	iii	NOUN
ejpam-3632	44	21	)	)	PUNCT
ejpam-3632	44	22	lh(a	lh(a	NOUN
ejpam-3632	44	23	)	)	PUNCT
ejpam-3632	44	24	=	=	PUNCT
ejpam-3632	45	1	⋂	⋂	PROPN
ejpam-3632	45	2	a∈a	a∈a	ADJ
ejpam-3632	45	3	lh(a	lh(a	NOUN
ejpam-3632	45	4	)	)	PUNCT
ejpam-3632	45	5	.	.	PUNCT
ejpam-3632	46	1	(	(	PUNCT
ejpam-3632	46	2	iv	iv	X
ejpam-3632	46	3	)	)	PUNCT
ejpam-3632	46	4	for	for	ADP
ejpam-3632	46	5	any	any	DET
ejpam-3632	46	6	a	a	DET
ejpam-3632	46	7	⊆	⊆	NUM
ejpam-3632	46	8	h	h	NOUN
ejpam-3632	46	9	,	,	PUNCT
ejpam-3632	46	10	0	0	NUM
ejpam-3632	46	11	∈	∈	PROPN
ejpam-3632	46	12	lh(a	lh(a	NOUN
ejpam-3632	46	13	)	)	PUNCT
ejpam-3632	46	14	.	.	PUNCT
ejpam-3632	47	1	if	if	SCONJ
ejpam-3632	47	2	0	0	NUM
ejpam-3632	47	3	∈	∈	PROPN
ejpam-3632	47	4	a	a	PRON
ejpam-3632	47	5	,	,	PUNCT
ejpam-3632	47	6	then	then	ADV
ejpam-3632	47	7	lh(a	lh(a	NUM
ejpam-3632	47	8	)	)	PUNCT
ejpam-3632	47	9	=	=	PUNCT
ejpam-3632	47	10	{	{	PUNCT
ejpam-3632	47	11	0	0	NUM
ejpam-3632	47	12	}	}	PUNCT
ejpam-3632	47	13	.	.	PUNCT
ejpam-3632	48	1	theorem	theorem	NOUN
ejpam-3632	48	2	1	1	NUM
ejpam-3632	48	3	.	.	PUNCT
ejpam-3632	49	1	[	[	X
ejpam-3632	49	2	8	8	NUM
ejpam-3632	49	3	]	]	PUNCT
ejpam-3632	49	4	let	let	VERB
ejpam-3632	49	5	h	h	PRON
ejpam-3632	49	6	be	be	AUX
ejpam-3632	49	7	a	a	DET
ejpam-3632	49	8	hyper	hyper	ADJ
ejpam-3632	49	9	bck	bck	NOUN
ejpam-3632	49	10	-	-	PUNCT
ejpam-3632	49	11	algebra	algebra	NOUN
ejpam-3632	49	12	.	.	PUNCT
ejpam-3632	50	1	then	then	ADV
ejpam-3632	50	2	bl(h	bl(h	PUNCT
ejpam-3632	50	3	)	)	PUNCT
ejpam-3632	50	4	=	=	PRON
ejpam-3632	50	5	{	{	PUNCT
ejpam-3632	50	6	lh(a	lh(a	NOUN
ejpam-3632	50	7	)	)	PUNCT
ejpam-3632	50	8	:	:	PUNCT
ejpam-3632	50	9	a	a	DET
ejpam-3632	50	10	⊆	⊆	NUM
ejpam-3632	50	11	h	h	NOUN
ejpam-3632	50	12	}	}	PUNCT
ejpam-3632	50	13	is	be	AUX
ejpam-3632	50	14	a	a	DET
ejpam-3632	50	15	basis	basis	NOUN
ejpam-3632	50	16	for	for	ADP
ejpam-3632	50	17	some	some	DET
ejpam-3632	50	18	topology	topology	NOUN
ejpam-3632	50	19	on	on	ADP
ejpam-3632	50	20	h.	h.	PROPN
ejpam-3632	50	21	denote	denote	VERB
ejpam-3632	50	22	by	by	ADP
ejpam-3632	50	23	τl(h	τl(h	NOUN
ejpam-3632	50	24	)	)	PUNCT
ejpam-3632	50	25	the	the	DET
ejpam-3632	50	26	topology	topology	NOUN
ejpam-3632	50	27	generated	generate	VERB
ejpam-3632	50	28	by	by	ADP
ejpam-3632	50	29	bl(h	bl(h	NOUN
ejpam-3632	50	30	)	)	PUNCT
ejpam-3632	50	31	.	.	PUNCT
ejpam-3632	51	1	theorem	theorem	NOUN
ejpam-3632	51	2	2	2	NUM
ejpam-3632	51	3	.	.	PUNCT
ejpam-3632	52	1	[	[	X
ejpam-3632	52	2	7	7	X
ejpam-3632	52	3	]	]	PUNCT
ejpam-3632	52	4	let	let	VERB
ejpam-3632	52	5	h	h	PRON
ejpam-3632	52	6	be	be	AUX
ejpam-3632	52	7	a	a	DET
ejpam-3632	52	8	hyper	hyper	ADJ
ejpam-3632	52	9	bck	bck	NOUN
ejpam-3632	52	10	-	-	PUNCT
ejpam-3632	52	11	algebra	algebra	NOUN
ejpam-3632	52	12	.	.	PUNCT
ejpam-3632	53	1	then	then	ADV
ejpam-3632	53	2	br(h	br(h	NUM
ejpam-3632	53	3	)	)	PUNCT
ejpam-3632	53	4	=	=	PRON
ejpam-3632	53	5	{	{	PUNCT
ejpam-3632	53	6	rh(a	rh(a	NOUN
ejpam-3632	53	7	)	)	PUNCT
ejpam-3632	53	8	:	:	PUNCT
ejpam-3632	53	9	∅	∅	NOUN
ejpam-3632	53	10	6=	6=	ADP
ejpam-3632	53	11	a	a	DET
ejpam-3632	53	12	⊆	⊆	NUM
ejpam-3632	53	13	h	h	NOUN
ejpam-3632	53	14	}	}	PUNCT
ejpam-3632	53	15	is	be	AUX
ejpam-3632	53	16	a	a	DET
ejpam-3632	53	17	basis	basis	NOUN
ejpam-3632	53	18	for	for	ADP
ejpam-3632	53	19	some	some	DET
ejpam-3632	53	20	topology	topology	NOUN
ejpam-3632	53	21	on	on	ADP
ejpam-3632	53	22	h.	h.	PROPN
ejpam-3632	53	23	denote	denote	VERB
ejpam-3632	53	24	by	by	ADP
ejpam-3632	53	25	τr(h	τr(h	NOUN
ejpam-3632	53	26	)	)	PUNCT
ejpam-3632	53	27	the	the	DET
ejpam-3632	53	28	topology	topology	NOUN
ejpam-3632	53	29	generated	generate	VERB
ejpam-3632	53	30	by	by	ADP
ejpam-3632	53	31	br(h	br(h	NOUN
ejpam-3632	53	32	)	)	PUNCT
ejpam-3632	53	33	.	.	PUNCT
ejpam-3632	54	1	4	4	X
ejpam-3632	54	2	.	.	X
ejpam-3632	54	3	topology	topology	NOUN
ejpam-3632	54	4	induced	induce	VERB
ejpam-3632	54	5	by	by	ADP
ejpam-3632	54	6	rhlh	rhlh	NOUN
ejpam-3632	54	7	let	let	VERB
ejpam-3632	54	8	h	h	NOUN
ejpam-3632	54	9	be	be	AUX
ejpam-3632	54	10	any	any	DET
ejpam-3632	54	11	hyper	hyper	ADJ
ejpam-3632	54	12	bck	bck	NOUN
ejpam-3632	54	13	-	-	PUNCT
ejpam-3632	54	14	algebra	algebra	NOUN
ejpam-3632	54	15	with	with	ADP
ejpam-3632	54	16	h	h	PROPN
ejpam-3632	54	17	6=	6=	X
ejpam-3632	54	18	{	{	PUNCT
ejpam-3632	54	19	0	0	NUM
ejpam-3632	54	20	}	}	PUNCT
ejpam-3632	54	21	.	.	PUNCT
ejpam-3632	55	1	by	by	ADP
ejpam-3632	55	2	proposition	proposition	NOUN
ejpam-3632	55	3	1(iii	1(iii	NUM
ejpam-3632	55	4	)	)	PUNCT
ejpam-3632	55	5	,	,	PUNCT
ejpam-3632	55	6	0	0	NUM
ejpam-3632	55	7	/∈	/∈	PUNCT
ejpam-3632	55	8	rh(h	rh(h	PROPN
ejpam-3632	55	9	)	)	PUNCT
ejpam-3632	55	10	.	.	PUNCT
ejpam-3632	56	1	by	by	ADP
ejpam-3632	56	2	definition	definition	NOUN
ejpam-3632	56	3	of	of	ADP
ejpam-3632	56	4	a	a	DET
ejpam-3632	56	5	closure	closure	NOUN
ejpam-3632	56	6	operator	operator	NOUN
ejpam-3632	56	7	,	,	PUNCT
ejpam-3632	56	8	we	we	PRON
ejpam-3632	56	9	have	have	VERB
ejpam-3632	56	10	the	the	DET
ejpam-3632	56	11	following	follow	VERB
ejpam-3632	56	12	remark	remark	NOUN
ejpam-3632	56	13	.	.	PUNCT
ejpam-3632	57	1	remark	remark	PROPN
ejpam-3632	57	2	1	1	NUM
ejpam-3632	57	3	.	.	PUNCT
ejpam-3632	58	1	rh	rh	NOUN
ejpam-3632	58	2	:	:	PUNCT
ejpam-3632	58	3	p(h)→p(h	p(h)→p(h	PROPN
ejpam-3632	58	4	)	)	PUNCT
ejpam-3632	58	5	is	be	AUX
ejpam-3632	58	6	not	not	PART
ejpam-3632	58	7	a	a	DET
ejpam-3632	58	8	closure	closure	NOUN
ejpam-3632	58	9	operator	operator	NOUN
ejpam-3632	58	10	for	for	ADP
ejpam-3632	58	11	every	every	DET
ejpam-3632	58	12	hyper	hyper	ADJ
ejpam-3632	58	13	bck	bck	NOUN
ejpam-3632	58	14	-	-	PUNCT
ejpam-3632	58	15	algebra	algebra	NOUN
ejpam-3632	58	16	h	h	NOUN
ejpam-3632	58	17	6=	6=	X
ejpam-3632	58	18	{	{	PUNCT
ejpam-3632	58	19	0	0	NUM
ejpam-3632	58	20	}	}	PUNCT
ejpam-3632	58	21	.	.	PUNCT
ejpam-3632	59	1	theorem	theorem	NOUN
ejpam-3632	59	2	3	3	X
ejpam-3632	59	3	.	.	PUNCT
ejpam-3632	60	1	let	let	VERB
ejpam-3632	60	2	h	h	PRON
ejpam-3632	60	3	be	be	AUX
ejpam-3632	60	4	a	a	DET
ejpam-3632	60	5	hyper	hyper	ADJ
ejpam-3632	60	6	bck	bck	NOUN
ejpam-3632	60	7	-	-	PUNCT
ejpam-3632	60	8	algebra	algebra	NOUN
ejpam-3632	60	9	and	and	CCONJ
ejpam-3632	60	10	a	a	DET
ejpam-3632	60	11	,	,	PUNCT
ejpam-3632	60	12	b	b	PROPN
ejpam-3632	60	13	⊆	⊆	NUM
ejpam-3632	60	14	h.	h.	NOUN
ejpam-3632	60	15	then	then	ADV
ejpam-3632	60	16	the	the	DET
ejpam-3632	60	17	following	follow	VERB
ejpam-3632	60	18	properties	property	NOUN
ejpam-3632	60	19	hold	hold	VERB
ejpam-3632	60	20	:	:	PUNCT
ejpam-3632	60	21	(	(	PUNCT
ejpam-3632	60	22	i	i	NOUN
ejpam-3632	60	23	)	)	PUNCT
ejpam-3632	60	24	a	a	DET
ejpam-3632	60	25	⊆	⊆	NUM
ejpam-3632	60	26	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	60	27	)	)	PUNCT
ejpam-3632	60	28	)	)	PUNCT
ejpam-3632	60	29	.	.	PUNCT
ejpam-3632	61	1	(	(	PUNCT
ejpam-3632	61	2	ii	ii	NOUN
ejpam-3632	61	3	)	)	PUNCT
ejpam-3632	61	4	if	if	SCONJ
ejpam-3632	61	5	a	a	DET
ejpam-3632	61	6	⊆	⊆	NUM
ejpam-3632	61	7	b	b	NOUN
ejpam-3632	61	8	,	,	PUNCT
ejpam-3632	61	9	then	then	ADV
ejpam-3632	61	10	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	61	11	)	)	PUNCT
ejpam-3632	61	12	)	)	PUNCT
ejpam-3632	62	1	⊆	⊆	NUM
ejpam-3632	62	2	rh(lh(b	rh(lh(b	NOUN
ejpam-3632	62	3	)	)	PUNCT
ejpam-3632	62	4	)	)	PUNCT
ejpam-3632	62	5	.	.	PUNCT
ejpam-3632	63	1	(	(	PUNCT
ejpam-3632	63	2	iii	iii	X
ejpam-3632	63	3	)	)	PUNCT
ejpam-3632	63	4	[	[	X
ejpam-3632	63	5	rhlh	rhlh	NOUN
ejpam-3632	63	6	]	]	SYM
ejpam-3632	63	7	2(a	2(a	NUM
ejpam-3632	63	8	)	)	PUNCT
ejpam-3632	63	9	=	=	X
ejpam-3632	63	10	rhlh	rhlh	VERB
ejpam-3632	63	11	[	[	X
ejpam-3632	63	12	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	63	13	)	)	PUNCT
ejpam-3632	63	14	)	)	PUNCT
ejpam-3632	63	15	]	]	PUNCT
ejpam-3632	64	1	=	=	PUNCT
ejpam-3632	64	2	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	64	3	)	)	PUNCT
ejpam-3632	64	4	)	)	PUNCT
ejpam-3632	64	5	.	.	PUNCT
ejpam-3632	65	1	proof	proof	NOUN
ejpam-3632	65	2	.	.	PUNCT
ejpam-3632	66	1	(	(	PUNCT
ejpam-3632	66	2	i	i	NOUN
ejpam-3632	66	3	)	)	PUNCT
ejpam-3632	66	4	let	let	VERB
ejpam-3632	66	5	a	a	DET
ejpam-3632	66	6	⊆	⊆	NUM
ejpam-3632	66	7	h	h	NOUN
ejpam-3632	66	8	and	and	CCONJ
ejpam-3632	66	9	y	y	PROPN
ejpam-3632	66	10	∈	∈	PROPN
ejpam-3632	66	11	lh(a	lh(a	PROPN
ejpam-3632	66	12	)	)	PUNCT
ejpam-3632	66	13	.	.	PUNCT
ejpam-3632	67	1	then	then	ADV
ejpam-3632	67	2	y	y	PROPN
ejpam-3632	67	3	�	�	PROPN
ejpam-3632	67	4	a	a	PROPN
ejpam-3632	67	5	for	for	ADP
ejpam-3632	67	6	all	all	DET
ejpam-3632	67	7	a	a	DET
ejpam-3632	67	8	∈	∈	PROPN
ejpam-3632	67	9	a.	a.	NOUN
ejpam-3632	67	10	pick	pick	NOUN
ejpam-3632	67	11	x	x	SYM
ejpam-3632	67	12	∈	∈	NOUN
ejpam-3632	67	13	a.	a.	NOUN
ejpam-3632	67	14	then	then	ADV
ejpam-3632	67	15	y	y	PROPN
ejpam-3632	67	16	�	�	PROPN
ejpam-3632	67	17	x	x	PUNCT
ejpam-3632	67	18	for	for	ADP
ejpam-3632	67	19	every	every	DET
ejpam-3632	67	20	y	y	PROPN
ejpam-3632	67	21	∈	∈	PROPN
ejpam-3632	67	22	lh(a	lh(a	PROPN
ejpam-3632	67	23	)	)	PUNCT
ejpam-3632	67	24	.	.	PUNCT
ejpam-3632	68	1	this	this	PRON
ejpam-3632	68	2	means	mean	VERB
ejpam-3632	68	3	that	that	SCONJ
ejpam-3632	68	4	x	x	SYM
ejpam-3632	68	5	∈	∈	NOUN
ejpam-3632	68	6	rh(y	rh(y	NOUN
ejpam-3632	68	7	)	)	PUNCT
ejpam-3632	68	8	for	for	ADP
ejpam-3632	68	9	every	every	DET
ejpam-3632	68	10	y	y	PROPN
ejpam-3632	68	11	∈	∈	PROPN
ejpam-3632	68	12	lh(a	lh(a	PROPN
ejpam-3632	68	13	)	)	PUNCT
ejpam-3632	68	14	.	.	PUNCT
ejpam-3632	69	1	thus	thus	ADV
ejpam-3632	69	2	,	,	PUNCT
ejpam-3632	69	3	by	by	ADP
ejpam-3632	69	4	proposition	proposition	NOUN
ejpam-3632	69	5	1(ii	1(ii	NUM
ejpam-3632	69	6	)	)	PUNCT
ejpam-3632	69	7	,	,	PUNCT
ejpam-3632	69	8	x	x	PUNCT
ejpam-3632	69	9	∈	∈	PROPN
ejpam-3632	69	10	⋂	⋂	PROPN
ejpam-3632	69	11	y∈lh(a	y∈lh(a	PROPN
ejpam-3632	69	12	)	)	PUNCT
ejpam-3632	69	13	rh(y	rh(y	NUM
ejpam-3632	69	14	)	)	PUNCT
ejpam-3632	69	15	=	=	SYM
ejpam-3632	69	16	rhlh(a	rhlh(a	NOUN
ejpam-3632	69	17	)	)	PUNCT
ejpam-3632	69	18	.	.	PUNCT
ejpam-3632	70	1	therefore	therefore	ADV
ejpam-3632	70	2	,	,	PUNCT
ejpam-3632	70	3	a	a	DET
ejpam-3632	70	4	⊆	⊆	NUM
ejpam-3632	70	5	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	70	6	)	)	PUNCT
ejpam-3632	70	7	)	)	PUNCT
ejpam-3632	70	8	.	.	PUNCT
ejpam-3632	71	1	(	(	PUNCT
ejpam-3632	71	2	ii	ii	NOUN
ejpam-3632	71	3	)	)	PUNCT
ejpam-3632	71	4	let	let	VERB
ejpam-3632	71	5	a	a	DET
ejpam-3632	71	6	,	,	PUNCT
ejpam-3632	71	7	b	b	NOUN
ejpam-3632	71	8	be	be	AUX
ejpam-3632	71	9	subsets	subset	NOUN
ejpam-3632	71	10	of	of	ADP
ejpam-3632	71	11	h.	h.	PROPN
ejpam-3632	71	12	suppose	suppose	VERB
ejpam-3632	71	13	a	a	DET
ejpam-3632	71	14	⊆	⊆	NUM
ejpam-3632	71	15	b.	b.	NOUN
ejpam-3632	71	16	by	by	ADP
ejpam-3632	71	17	proposition	proposition	NOUN
ejpam-3632	71	18	2(ii	2(ii	NUM
ejpam-3632	71	19	)	)	PUNCT
ejpam-3632	71	20	,	,	PUNCT
ejpam-3632	71	21	lh(b	lh(b	NOUN
ejpam-3632	71	22	)	)	PUNCT
ejpam-3632	71	23	⊆	⊆	NUM
ejpam-3632	71	24	lh(a	lh(a	NUM
ejpam-3632	71	25	)	)	PUNCT
ejpam-3632	71	26	.	.	PUNCT
ejpam-3632	72	1	thus	thus	ADV
ejpam-3632	72	2	,	,	PUNCT
ejpam-3632	72	3	by	by	ADP
ejpam-3632	72	4	proposition	proposition	NOUN
ejpam-3632	72	5	1(iv	1(iv	NUM
ejpam-3632	72	6	)	)	PUNCT
ejpam-3632	72	7	,	,	PUNCT
ejpam-3632	72	8	rhlh(a	rhlh(a	NOUN
ejpam-3632	72	9	)	)	PUNCT
ejpam-3632	72	10	⊆	⊆	NUM
ejpam-3632	72	11	rhlh(b	rhlh(b	NOUN
ejpam-3632	72	12	)	)	PUNCT
ejpam-3632	72	13	.	.	PUNCT
ejpam-3632	73	1	(	(	PUNCT
ejpam-3632	73	2	iii	iii	X
ejpam-3632	73	3	)	)	PUNCT
ejpam-3632	73	4	by	by	ADP
ejpam-3632	73	5	(	(	PUNCT
ejpam-3632	73	6	i	i	NOUN
ejpam-3632	73	7	)	)	PUNCT
ejpam-3632	73	8	and	and	CCONJ
ejpam-3632	73	9	(	(	PUNCT
ejpam-3632	73	10	ii	ii	NOUN
ejpam-3632	73	11	)	)	PUNCT
ejpam-3632	73	12	,	,	PUNCT
ejpam-3632	73	13	rhlh(a	rhlh(a	NOUN
ejpam-3632	73	14	)	)	PUNCT
ejpam-3632	73	15	⊆	⊆	NUM
ejpam-3632	74	1	[	[	X
ejpam-3632	74	2	rhlh	rhlh	NOUN
ejpam-3632	74	3	]	]	X
ejpam-3632	74	4	2(a	2(a	NUM
ejpam-3632	74	5	)	)	PUNCT
ejpam-3632	74	6	.	.	PUNCT
ejpam-3632	75	1	we	we	PRON
ejpam-3632	75	2	are	be	AUX
ejpam-3632	75	3	left	leave	VERB
ejpam-3632	75	4	to	to	PART
ejpam-3632	75	5	prove	prove	VERB
ejpam-3632	75	6	that	that	SCONJ
ejpam-3632	76	1	[	[	X
ejpam-3632	76	2	rhlh	rhlh	NOUN
ejpam-3632	76	3	]	]	SYM
ejpam-3632	76	4	2(a	2(a	NUM
ejpam-3632	76	5	)	)	PUNCT
ejpam-3632	76	6	⊆	⊆	NUM
ejpam-3632	76	7	(	(	PUNCT
ejpam-3632	76	8	rhlh)(a	rhlh)(a	PROPN
ejpam-3632	76	9	)	)	PUNCT
ejpam-3632	76	10	.	.	PUNCT
ejpam-3632	77	1	first	first	ADV
ejpam-3632	77	2	,	,	PUNCT
ejpam-3632	77	3	we	we	PRON
ejpam-3632	77	4	need	need	VERB
ejpam-3632	77	5	to	to	PART
ejpam-3632	77	6	show	show	VERB
ejpam-3632	77	7	that	that	DET
ejpam-3632	77	8	lh(a	lh(a	NOUN
ejpam-3632	77	9	)	)	PUNCT
ejpam-3632	78	1	⊆	⊆	NUM
ejpam-3632	78	2	lh	lh	PROPN
ejpam-3632	79	1	[	[	X
ejpam-3632	80	1	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	80	2	)	)	PUNCT
ejpam-3632	80	3	)	)	PUNCT
ejpam-3632	81	1	]	]	PUNCT
ejpam-3632	81	2	.	.	PUNCT
ejpam-3632	82	1	let	let	VERB
ejpam-3632	82	2	x	x	X
ejpam-3632	82	3	∈	∈	PROPN
ejpam-3632	82	4	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	82	5	)	)	PUNCT
ejpam-3632	82	6	)	)	PUNCT
ejpam-3632	82	7	.	.	PUNCT
ejpam-3632	83	1	then	then	ADV
ejpam-3632	83	2	y	y	PROPN
ejpam-3632	83	3	�	�	PROPN
ejpam-3632	83	4	x	x	PUNCT
ejpam-3632	83	5	for	for	ADP
ejpam-3632	83	6	all	all	DET
ejpam-3632	83	7	y	y	PROPN
ejpam-3632	83	8	∈	∈	PROPN
ejpam-3632	83	9	lh(a	lh(a	NOUN
ejpam-3632	83	10	)	)	PUNCT
ejpam-3632	83	11	.	.	PUNCT
ejpam-3632	84	1	choose	choose	VERB
ejpam-3632	84	2	z	z	PROPN
ejpam-3632	84	3	∈	∈	PROPN
ejpam-3632	84	4	lh(a	lh(a	PROPN
ejpam-3632	84	5	)	)	PUNCT
ejpam-3632	84	6	.	.	PUNCT
ejpam-3632	85	1	then	then	ADV
ejpam-3632	85	2	z	z	PROPN
ejpam-3632	85	3	�	�	PROPN
ejpam-3632	85	4	x	x	PUNCT
ejpam-3632	85	5	for	for	ADP
ejpam-3632	85	6	every	every	DET
ejpam-3632	85	7	x	x	PROPN
ejpam-3632	85	8	∈	∈	PROPN
ejpam-3632	85	9	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	85	10	)	)	PUNCT
ejpam-3632	85	11	)	)	PUNCT
ejpam-3632	85	12	.	.	PUNCT
ejpam-3632	86	1	this	this	PRON
ejpam-3632	86	2	implies	imply	VERB
ejpam-3632	86	3	that	that	SCONJ
ejpam-3632	86	4	z	z	PROPN
ejpam-3632	86	5	∈	∈	PROPN
ejpam-3632	86	6	lh(x	lh(x	PUNCT
ejpam-3632	86	7	)	)	PUNCT
ejpam-3632	86	8	for	for	ADP
ejpam-3632	86	9	every	every	DET
ejpam-3632	86	10	x	x	PROPN
ejpam-3632	86	11	∈	∈	PROPN
ejpam-3632	86	12	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	86	13	)	)	PUNCT
ejpam-3632	86	14	)	)	PUNCT
ejpam-3632	86	15	.	.	PUNCT
ejpam-3632	87	1	hence	hence	ADV
ejpam-3632	87	2	,	,	PUNCT
ejpam-3632	87	3	by	by	ADP
ejpam-3632	87	4	proposition	proposition	NOUN
ejpam-3632	87	5	2(iii	2(iii	NUM
ejpam-3632	87	6	)	)	PUNCT
ejpam-3632	87	7	,	,	PUNCT
ejpam-3632	87	8	z	z	PROPN
ejpam-3632	87	9	∈	∈	PROPN
ejpam-3632	87	10	⋂	⋂	PROPN
ejpam-3632	87	11	x∈rh(lh(a	x∈rh(lh(a	NUM
ejpam-3632	87	12	)	)	PUNCT
ejpam-3632	87	13	)	)	PUNCT
ejpam-3632	87	14	lh(x	lh(x	PUNCT
ejpam-3632	87	15	)	)	PUNCT
ejpam-3632	88	1	=	=	PRON
ejpam-3632	88	2	lh	lh	PROPN
ejpam-3632	89	1	[	[	X
ejpam-3632	89	2	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	89	3	)	)	PUNCT
ejpam-3632	89	4	)	)	PUNCT
ejpam-3632	89	5	]	]	PUNCT
ejpam-3632	89	6	.	.	PUNCT
ejpam-3632	90	1	consequently	consequently	ADV
ejpam-3632	90	2	,	,	PUNCT
ejpam-3632	90	3	lh(a	lh(a	NUM
ejpam-3632	90	4	)	)	PUNCT
ejpam-3632	91	1	⊆	⊆	NUM
ejpam-3632	91	2	lh	lh	PROPN
ejpam-3632	92	1	[	[	X
ejpam-3632	93	1	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	93	2	)	)	PUNCT
ejpam-3632	93	3	)	)	PUNCT
ejpam-3632	94	1	]	]	PUNCT
ejpam-3632	94	2	.	.	PUNCT
ejpam-3632	95	1	therefore	therefore	ADV
ejpam-3632	95	2	,	,	PUNCT
ejpam-3632	95	3	by	by	ADP
ejpam-3632	95	4	proposition	proposition	NOUN
ejpam-3632	95	5	1(iv	1(iv	NUM
ejpam-3632	95	6	)	)	PUNCT
ejpam-3632	95	7	,	,	PUNCT
ejpam-3632	95	8	rhlh	rhlh	VERB
ejpam-3632	95	9	[	[	X
ejpam-3632	95	10	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	95	11	)	)	PUNCT
ejpam-3632	95	12	)	)	PUNCT
ejpam-3632	95	13	]	]	PUNCT
ejpam-3632	96	1	⊆	⊆	NUM
ejpam-3632	96	2	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	96	3	)	)	PUNCT
ejpam-3632	96	4	)	)	PUNCT
ejpam-3632	96	5	.	.	PUNCT
ejpam-3632	97	1	r.	r.	PROPN
ejpam-3632	97	2	patangan	patangan	PROPN
ejpam-3632	97	3	,	,	PUNCT
ejpam-3632	97	4	s.	s.	PROPN
ejpam-3632	97	5	canoy	canoy	PROPN
ejpam-3632	97	6	,	,	PUNCT
ejpam-3632	97	7	jr	jr	PROPN
ejpam-3632	97	8	.	.	PROPN
ejpam-3632	97	9	/	/	SYM
ejpam-3632	97	10	eur	eur	PROPN
ejpam-3632	97	11	.	.	PUNCT
ejpam-3632	98	1	j.	j.	PROPN
ejpam-3632	98	2	pure	pure	PROPN
ejpam-3632	98	3	appl	appl	PROPN
ejpam-3632	98	4	.	.	PROPN
ejpam-3632	98	5	math	math	PROPN
ejpam-3632	98	6	,	,	PUNCT
ejpam-3632	98	7	13	13	NUM
ejpam-3632	98	8	(	(	PUNCT
ejpam-3632	98	9	1	1	NUM
ejpam-3632	98	10	)	)	PUNCT
ejpam-3632	98	11	(	(	PUNCT
ejpam-3632	98	12	2020	2020	NUM
ejpam-3632	98	13	)	)	PUNCT
ejpam-3632	98	14	,	,	PUNCT
ejpam-3632	98	15	1	1	NUM
ejpam-3632	98	16	-	-	SYM
ejpam-3632	98	17	8	8	NUM
ejpam-3632	98	18	4	4	NUM
ejpam-3632	98	19	theorem	theorem	NOUN
ejpam-3632	98	20	4	4	NUM
ejpam-3632	98	21	.	.	PUNCT
ejpam-3632	99	1	let	let	VERB
ejpam-3632	99	2	h	h	PRON
ejpam-3632	99	3	be	be	AUX
ejpam-3632	99	4	a	a	DET
ejpam-3632	99	5	hyper	hyper	ADJ
ejpam-3632	99	6	bck	bck	NOUN
ejpam-3632	99	7	-	-	PUNCT
ejpam-3632	99	8	algebra	algebra	NOUN
ejpam-3632	99	9	.	.	PUNCT
ejpam-3632	100	1	the	the	DET
ejpam-3632	100	2	function	function	NOUN
ejpam-3632	100	3	rhlh	rhlh	NOUN
ejpam-3632	100	4	:	:	PUNCT
ejpam-3632	100	5	p(h)→p(h	p(h)→p(h	X
ejpam-3632	100	6	)	)	PUNCT
ejpam-3632	100	7	is	be	AUX
ejpam-3632	100	8	a	a	DET
ejpam-3632	100	9	closure	closure	NOUN
ejpam-3632	100	10	operator	operator	NOUN
ejpam-3632	100	11	on	on	ADP
ejpam-3632	100	12	h.	h.	PROPN
ejpam-3632	100	13	proof	proof	NOUN
ejpam-3632	100	14	.	.	PUNCT
ejpam-3632	101	1	since	since	SCONJ
ejpam-3632	101	2	h	h	NOUN
ejpam-3632	101	3	is	be	AUX
ejpam-3632	101	4	a	a	DET
ejpam-3632	101	5	hyper	hyper	ADJ
ejpam-3632	101	6	bck	bck	NOUN
ejpam-3632	101	7	-	-	PUNCT
ejpam-3632	101	8	algebra	algebra	NOUN
ejpam-3632	101	9	,	,	PUNCT
ejpam-3632	101	10	h	h	NOUN
ejpam-3632	101	11	6=	6=	NOUN
ejpam-3632	101	12	∅.	∅.	ADP
ejpam-3632	101	13	hence	hence	ADV
ejpam-3632	101	14	,	,	PUNCT
ejpam-3632	101	15	by	by	ADP
ejpam-3632	101	16	the	the	DET
ejpam-3632	101	17	definition	definition	NOUN
ejpam-3632	101	18	of	of	ADP
ejpam-3632	101	19	a	a	DET
ejpam-3632	101	20	closure	closure	NOUN
ejpam-3632	101	21	operator	operator	NOUN
ejpam-3632	101	22	and	and	CCONJ
ejpam-3632	101	23	theorem	theorem	VERB
ejpam-3632	101	24	3	3	NUM
ejpam-3632	101	25	,	,	PUNCT
ejpam-3632	101	26	rhlh	rhlh	NOUN
ejpam-3632	101	27	is	be	AUX
ejpam-3632	101	28	a	a	DET
ejpam-3632	101	29	closure	closure	NOUN
ejpam-3632	101	30	operator	operator	NOUN
ejpam-3632	101	31	.	.	PUNCT
ejpam-3632	102	1	theorem	theorem	VERB
ejpam-3632	102	2	5	5	NUM
ejpam-3632	102	3	.	.	PUNCT
ejpam-3632	103	1	the	the	DET
ejpam-3632	103	2	family	family	NOUN
ejpam-3632	103	3	brl(h	brl(h	PROPN
ejpam-3632	103	4	)	)	PUNCT
ejpam-3632	103	5	=	=	NOUN
ejpam-3632	103	6	{	{	PUNCT
ejpam-3632	103	7	a	a	DET
ejpam-3632	103	8	:	:	PUNCT
ejpam-3632	103	9	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	103	10	)	)	PUNCT
ejpam-3632	103	11	)	)	PUNCT
ejpam-3632	104	1	=	=	PUNCT
ejpam-3632	104	2	a	a	X
ejpam-3632	104	3	,	,	PUNCT
ejpam-3632	104	4	a	a	DET
ejpam-3632	104	5	⊆	⊆	NUM
ejpam-3632	104	6	h	h	NOUN
ejpam-3632	104	7	}	}	PUNCT
ejpam-3632	104	8	is	be	AUX
ejpam-3632	104	9	a	a	DET
ejpam-3632	104	10	basis	basis	NOUN
ejpam-3632	104	11	for	for	ADP
ejpam-3632	104	12	some	some	DET
ejpam-3632	104	13	topology	topology	NOUN
ejpam-3632	104	14	on	on	ADP
ejpam-3632	104	15	h.	h.	PROPN
ejpam-3632	104	16	proof	proof	NOUN
ejpam-3632	104	17	.	.	PUNCT
ejpam-3632	105	1	since	since	SCONJ
ejpam-3632	105	2	rh(lh(h	rh(lh(h	NOUN
ejpam-3632	105	3	)	)	PUNCT
ejpam-3632	105	4	)	)	PUNCT
ejpam-3632	106	1	⊆	⊆	NUM
ejpam-3632	106	2	h	h	NOUN
ejpam-3632	106	3	and	and	CCONJ
ejpam-3632	106	4	by	by	ADP
ejpam-3632	106	5	theorem	theorem	NOUN
ejpam-3632	106	6	3(i	3(i	NUM
ejpam-3632	106	7	)	)	PUNCT
ejpam-3632	106	8	,	,	PUNCT
ejpam-3632	106	9	rhlh(h	rhlh(h	NOUN
ejpam-3632	106	10	)	)	PUNCT
ejpam-3632	106	11	=	=	SYM
ejpam-3632	106	12	h	h	NOUN
ejpam-3632	106	13	,	,	PUNCT
ejpam-3632	106	14	it	it	PRON
ejpam-3632	106	15	follows	follow	VERB
ejpam-3632	106	16	that	that	SCONJ
ejpam-3632	106	17	h	h	NOUN
ejpam-3632	106	18	∈	∈	PROPN
ejpam-3632	106	19	brl(h	brl(h	PROPN
ejpam-3632	106	20	)	)	PUNCT
ejpam-3632	106	21	.	.	PUNCT
ejpam-3632	107	1	thus	thus	ADV
ejpam-3632	107	2	,	,	PUNCT
ejpam-3632	107	3	brl(h	brl(h	PROPN
ejpam-3632	107	4	)	)	PUNCT
ejpam-3632	107	5	6=	6=	ADP
ejpam-3632	107	6	∅.	∅.	NOUN
ejpam-3632	107	7	let	let	VERB
ejpam-3632	107	8	a	a	DET
ejpam-3632	107	9	,	,	PUNCT
ejpam-3632	107	10	b	b	NOUN
ejpam-3632	107	11	∈	∈	PROPN
ejpam-3632	107	12	brl(h	brl(h	NOUN
ejpam-3632	107	13	)	)	PUNCT
ejpam-3632	107	14	and	and	CCONJ
ejpam-3632	107	15	x	x	PUNCT
ejpam-3632	107	16	∈	∈	PROPN
ejpam-3632	107	17	a	a	DET
ejpam-3632	107	18	∩	∩	ADJ
ejpam-3632	107	19	b.	b.	NOUN
ejpam-3632	107	20	then	then	ADV
ejpam-3632	107	21	by	by	ADP
ejpam-3632	107	22	theorem	theorem	NOUN
ejpam-3632	107	23	3(i	3(i	NUM
ejpam-3632	107	24	)	)	PUNCT
ejpam-3632	107	25	,	,	PUNCT
ejpam-3632	107	26	we	we	PRON
ejpam-3632	107	27	have	have	VERB
ejpam-3632	107	28	a	a	DET
ejpam-3632	107	29	∩b	∩b	NOUN
ejpam-3632	107	30	⊆	⊆	NUM
ejpam-3632	107	31	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	107	32	∩b	∩b	NOUN
ejpam-3632	107	33	)	)	PUNCT
ejpam-3632	107	34	)	)	PUNCT
ejpam-3632	107	35	.	.	PUNCT
ejpam-3632	108	1	also	also	ADV
ejpam-3632	108	2	,	,	PUNCT
ejpam-3632	108	3	since	since	SCONJ
ejpam-3632	108	4	a	a	DET
ejpam-3632	108	5	∩b	∩b	NOUN
ejpam-3632	108	6	⊆	⊆	NUM
ejpam-3632	108	7	a	a	PRON
ejpam-3632	108	8	and	and	CCONJ
ejpam-3632	108	9	a	a	DET
ejpam-3632	108	10	∩b	∩b	NOUN
ejpam-3632	108	11	⊆	⊆	NUM
ejpam-3632	108	12	b	b	NOUN
ejpam-3632	108	13	,	,	PUNCT
ejpam-3632	108	14	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	108	15	∩	∩	ADJ
ejpam-3632	108	16	b	b	NOUN
ejpam-3632	108	17	)	)	PUNCT
ejpam-3632	108	18	)	)	PUNCT
ejpam-3632	108	19	⊆	⊆	NUM
ejpam-3632	108	20	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	108	21	)	)	PUNCT
ejpam-3632	108	22	)	)	PUNCT
ejpam-3632	108	23	and	and	CCONJ
ejpam-3632	108	24	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	108	25	∩	∩	ADJ
ejpam-3632	108	26	b	b	NOUN
ejpam-3632	108	27	)	)	PUNCT
ejpam-3632	108	28	)	)	PUNCT
ejpam-3632	108	29	⊆	⊆	NUM
ejpam-3632	108	30	rh(lh(b	rh(lh(b	NOUN
ejpam-3632	108	31	)	)	PUNCT
ejpam-3632	108	32	)	)	PUNCT
ejpam-3632	108	33	,	,	PUNCT
ejpam-3632	108	34	by	by	ADP
ejpam-3632	108	35	theorem	theorem	NOUN
ejpam-3632	108	36	3(ii	3(ii	NUM
ejpam-3632	108	37	)	)	PUNCT
ejpam-3632	108	38	.	.	PUNCT
ejpam-3632	109	1	since	since	SCONJ
ejpam-3632	109	2	a	a	PRON
ejpam-3632	109	3	and	and	CCONJ
ejpam-3632	109	4	b	b	NOUN
ejpam-3632	109	5	are	be	AUX
ejpam-3632	109	6	elements	element	NOUN
ejpam-3632	109	7	of	of	ADP
ejpam-3632	109	8	brl(h	brl(h	PROPN
ejpam-3632	109	9	)	)	PUNCT
ejpam-3632	109	10	,	,	PUNCT
ejpam-3632	109	11	we	we	PRON
ejpam-3632	109	12	have	have	VERB
ejpam-3632	109	13	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	109	14	)	)	PUNCT
ejpam-3632	109	15	)	)	PUNCT
ejpam-3632	110	1	=	=	PUNCT
ejpam-3632	110	2	a	a	PRON
ejpam-3632	110	3	and	and	CCONJ
ejpam-3632	110	4	rh(lh(b	rh(lh(b	NOUN
ejpam-3632	110	5	)	)	PUNCT
ejpam-3632	110	6	)	)	PUNCT
ejpam-3632	111	1	=	=	SYM
ejpam-3632	111	2	b.	b.	PROPN
ejpam-3632	111	3	consequently	consequently	ADV
ejpam-3632	111	4	,	,	PUNCT
ejpam-3632	111	5	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	111	6	∩	∩	ADJ
ejpam-3632	111	7	b	b	NOUN
ejpam-3632	111	8	)	)	PUNCT
ejpam-3632	111	9	)	)	PUNCT
ejpam-3632	112	1	⊆	⊆	NUM
ejpam-3632	112	2	a	a	DET
ejpam-3632	112	3	∩	∩	ADJ
ejpam-3632	112	4	b.	b.	NOUN
ejpam-3632	112	5	combining	combine	VERB
ejpam-3632	112	6	the	the	DET
ejpam-3632	112	7	two	two	NUM
ejpam-3632	112	8	set	set	ADJ
ejpam-3632	112	9	inclusions	inclusion	NOUN
ejpam-3632	112	10	,	,	PUNCT
ejpam-3632	112	11	we	we	PRON
ejpam-3632	112	12	have	have	VERB
ejpam-3632	112	13	rh(lh(a∩b	rh(lh(a∩b	VERB
ejpam-3632	112	14	)	)	PUNCT
ejpam-3632	112	15	)	)	PUNCT
ejpam-3632	113	1	=	=	SYM
ejpam-3632	113	2	a∩b	a∩b	PROPN
ejpam-3632	113	3	,	,	PUNCT
ejpam-3632	113	4	that	that	PRON
ejpam-3632	113	5	is	is	ADV
ejpam-3632	113	6	,	,	PUNCT
ejpam-3632	113	7	x	x	SYM
ejpam-3632	113	8	∈	∈	PROPN
ejpam-3632	113	9	a∩b	a∩b	NOUN
ejpam-3632	113	10	∈	∈	PROPN
ejpam-3632	113	11	brl(h	brl(h	PROPN
ejpam-3632	113	12	)	)	PUNCT
ejpam-3632	113	13	.	.	PUNCT
ejpam-3632	114	1	therefore	therefore	ADV
ejpam-3632	114	2	,	,	PUNCT
ejpam-3632	114	3	brl(h	brl(h	PROPN
ejpam-3632	114	4	)	)	PUNCT
ejpam-3632	114	5	is	be	AUX
ejpam-3632	114	6	a	a	DET
ejpam-3632	114	7	basis	basis	NOUN
ejpam-3632	114	8	for	for	ADP
ejpam-3632	114	9	some	some	DET
ejpam-3632	114	10	topology	topology	NOUN
ejpam-3632	114	11	on	on	ADP
ejpam-3632	114	12	h.	h.	PROPN
ejpam-3632	114	13	denote	denote	VERB
ejpam-3632	114	14	by	by	ADP
ejpam-3632	114	15	τrl(h	τrl(h	PROPN
ejpam-3632	114	16	)	)	PUNCT
ejpam-3632	114	17	the	the	DET
ejpam-3632	114	18	topology	topology	NOUN
ejpam-3632	114	19	generated	generate	VERB
ejpam-3632	114	20	by	by	ADP
ejpam-3632	114	21	brl(h	brl(h	PROPN
ejpam-3632	114	22	)	)	PUNCT
ejpam-3632	114	23	.	.	PUNCT
ejpam-3632	115	1	example	example	NOUN
ejpam-3632	116	1	1	1	X
ejpam-3632	116	2	.	.	X
ejpam-3632	116	3	consider	consider	VERB
ejpam-3632	116	4	the	the	DET
ejpam-3632	116	5	infinite	infinite	ADJ
ejpam-3632	116	6	hyper	hyper	ADJ
ejpam-3632	116	7	bck	bck	NOUN
ejpam-3632	116	8	-	-	PUNCT
ejpam-3632	116	9	algebra	algebra	NOUN
ejpam-3632	116	10	(	(	PUNCT
ejpam-3632	116	11	h	h	NOUN
ejpam-3632	116	12	,	,	PUNCT
ejpam-3632	116	13	∗	∗	NOUN
ejpam-3632	116	14	,	,	PUNCT
ejpam-3632	116	15	0	0	NUM
ejpam-3632	116	16	)	)	PUNCT
ejpam-3632	116	17	given	give	VERB
ejpam-3632	116	18	by	by	ADP
ejpam-3632	116	19	harizavi	harizavi	NOUN
ejpam-3632	116	20	in	in	ADP
ejpam-3632	116	21	[	[	X
ejpam-3632	116	22	3	3	NUM
ejpam-3632	116	23	]	]	PUNCT
ejpam-3632	116	24	,	,	PUNCT
ejpam-3632	116	25	where	where	SCONJ
ejpam-3632	116	26	h	h	NOUN
ejpam-3632	116	27	=	=	PRON
ejpam-3632	116	28	{	{	PUNCT
ejpam-3632	116	29	0	0	NUM
ejpam-3632	116	30	,	,	PUNCT
ejpam-3632	116	31	1	1	NUM
ejpam-3632	116	32	,	,	PUNCT
ejpam-3632	116	33	2	2	NUM
ejpam-3632	116	34	,	,	PUNCT
ejpam-3632	116	35	.	.	PUNCT
ejpam-3632	116	36	.	.	PUNCT
ejpam-3632	117	1	.	.	PUNCT
ejpam-3632	117	2	}	}	PUNCT
ejpam-3632	118	1	and	and	CCONJ
ejpam-3632	118	2	“	"	PUNCT
ejpam-3632	118	3	∗	∗	NOUN
ejpam-3632	118	4	”	"	PUNCT
ejpam-3632	118	5	is	be	AUX
ejpam-3632	118	6	defined	define	VERB
ejpam-3632	118	7	as	as	SCONJ
ejpam-3632	118	8	follows	follow	VERB
ejpam-3632	118	9	:	:	PUNCT
ejpam-3632	118	10	x	x	SYM
ejpam-3632	118	11	∗	∗	NOUN
ejpam-3632	118	12	y	y	NOUN
ejpam-3632	118	13	=	=	PRON
ejpam-3632	118	14	{	{	PUNCT
ejpam-3632	118	15	{	{	PUNCT
ejpam-3632	118	16	0	0	NUM
ejpam-3632	118	17	,	,	PUNCT
ejpam-3632	118	18	x	x	NOUN
ejpam-3632	118	19	}	}	PUNCT
ejpam-3632	118	20	if	if	SCONJ
ejpam-3632	118	21	x	x	PROPN
ejpam-3632	118	22	≤	≤	PROPN
ejpam-3632	118	23	y	y	PROPN
ejpam-3632	118	24	{	{	PUNCT
ejpam-3632	118	25	x	x	X
ejpam-3632	118	26	}	}	PUNCT
ejpam-3632	118	27	if	if	SCONJ
ejpam-3632	118	28	x	x	PROPN
ejpam-3632	118	29	>	>	X
ejpam-3632	118	30	y	y	PROPN
ejpam-3632	118	31	for	for	ADP
ejpam-3632	118	32	all	all	DET
ejpam-3632	118	33	x	x	NOUN
ejpam-3632	118	34	,	,	PUNCT
ejpam-3632	118	35	y	y	PROPN
ejpam-3632	118	36	∈	∈	PROPN
ejpam-3632	118	37	h.	h.	PROPN
ejpam-3632	118	38	now	now	ADV
ejpam-3632	118	39	,	,	PUNCT
ejpam-3632	118	40	let	let	VERB
ejpam-3632	118	41	r	r	PRON
ejpam-3632	118	42	∈	∈	PROPN
ejpam-3632	118	43	h.	h.	NOUN
ejpam-3632	118	44	then	then	ADV
ejpam-3632	118	45	rh(lh(r	rh(lh(r	ADV
ejpam-3632	118	46	)	)	PUNCT
ejpam-3632	118	47	)	)	PUNCT
ejpam-3632	119	1	=	=	PUNCT
ejpam-3632	119	2	rh({0	rh({0	X
ejpam-3632	119	3	,	,	PUNCT
ejpam-3632	119	4	1	1	NUM
ejpam-3632	119	5	,	,	PUNCT
ejpam-3632	119	6	2	2	NUM
ejpam-3632	119	7	,	,	PUNCT
ejpam-3632	119	8	.	.	PUNCT
ejpam-3632	119	9	.	.	PUNCT
ejpam-3632	120	1	.	.	PUNCT
ejpam-3632	121	1	,	,	PUNCT
ejpam-3632	121	2	r	r	NOUN
ejpam-3632	121	3	}	}	PUNCT
ejpam-3632	121	4	)	)	PUNCT
ejpam-3632	122	1	=	=	PRON
ejpam-3632	122	2	{	{	PUNCT
ejpam-3632	122	3	r	r	NOUN
ejpam-3632	122	4	,	,	PUNCT
ejpam-3632	122	5	r	r	NOUN
ejpam-3632	122	6	+	+	NOUN
ejpam-3632	122	7	1	1	NUM
ejpam-3632	122	8	,	,	PUNCT
ejpam-3632	122	9	r	r	NOUN
ejpam-3632	122	10	+	+	PROPN
ejpam-3632	122	11	2	2	NUM
ejpam-3632	122	12	,	,	PUNCT
ejpam-3632	122	13	.	.	PUNCT
ejpam-3632	122	14	.	.	PUNCT
ejpam-3632	122	15	.	.	PUNCT
ejpam-3632	122	16	}	}	PUNCT
ejpam-3632	122	17	6=	6=	ADP
ejpam-3632	122	18	{	{	PUNCT
ejpam-3632	122	19	r	r	NOUN
ejpam-3632	122	20	}	}	PUNCT
ejpam-3632	122	21	.	.	PUNCT
ejpam-3632	123	1	hence	hence	ADV
ejpam-3632	123	2	,	,	PUNCT
ejpam-3632	123	3	for	for	ADP
ejpam-3632	123	4	any	any	DET
ejpam-3632	123	5	s	s	X
ejpam-3632	123	6	∈	∈	PROPN
ejpam-3632	123	7	h	h	NOUN
ejpam-3632	123	8	,	,	PUNCT
ejpam-3632	123	9	{	{	PUNCT
ejpam-3632	123	10	s	s	NOUN
ejpam-3632	123	11	}	}	PUNCT
ejpam-3632	123	12	/∈	/∈	PUNCT
ejpam-3632	123	13	brl(h	brl(h	NOUN
ejpam-3632	123	14	)	)	PUNCT
ejpam-3632	123	15	.	.	PUNCT
ejpam-3632	124	1	let	let	VERB
ejpam-3632	124	2	∅	∅	NOUN
ejpam-3632	124	3	6=	6=	ADP
ejpam-3632	124	4	a	a	DET
ejpam-3632	124	5	⊆	⊆	NUM
ejpam-3632	124	6	h	h	NOUN
ejpam-3632	124	7	be	be	AUX
ejpam-3632	124	8	a	a	DET
ejpam-3632	124	9	finite	finite	NOUN
ejpam-3632	124	10	set	set	NOUN
ejpam-3632	124	11	and	and	CCONJ
ejpam-3632	124	12	let	let	VERB
ejpam-3632	124	13	u	u	PRON
ejpam-3632	124	14	=	=	X
ejpam-3632	124	15	mina	mina	PROPN
ejpam-3632	124	16	.	.	PUNCT
ejpam-3632	125	1	since	since	SCONJ
ejpam-3632	125	2	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	125	3	)	)	PUNCT
ejpam-3632	125	4	)	)	PUNCT
ejpam-3632	126	1	=	=	PUNCT
ejpam-3632	126	2	rhlh(u	rhlh(u	X
ejpam-3632	126	3	)	)	PUNCT
ejpam-3632	126	4	=	=	PUNCT
ejpam-3632	127	1	rh({0	rh({0	X
ejpam-3632	127	2	,	,	PUNCT
ejpam-3632	127	3	1	1	NUM
ejpam-3632	127	4	,	,	PUNCT
ejpam-3632	127	5	2	2	NUM
ejpam-3632	127	6	,	,	PUNCT
ejpam-3632	127	7	.	.	PUNCT
ejpam-3632	127	8	.	.	PUNCT
ejpam-3632	127	9	.	.	PUNCT
ejpam-3632	128	1	,	,	PUNCT
ejpam-3632	128	2	u	u	NOUN
ejpam-3632	128	3	}	}	PUNCT
ejpam-3632	128	4	)	)	PUNCT
ejpam-3632	129	1	=	=	PRON
ejpam-3632	129	2	{	{	PUNCT
ejpam-3632	129	3	u	u	NOUN
ejpam-3632	129	4	,	,	PUNCT
ejpam-3632	129	5	u+	u+	NUM
ejpam-3632	129	6	1	1	NUM
ejpam-3632	129	7	,	,	PUNCT
ejpam-3632	129	8	u+	u+	NOUN
ejpam-3632	129	9	2	2	NUM
ejpam-3632	129	10	,	,	PUNCT
ejpam-3632	129	11	.	.	PUNCT
ejpam-3632	129	12	.	.	PUNCT
ejpam-3632	130	1	.	.	PUNCT
ejpam-3632	130	2	}	}	PUNCT
ejpam-3632	131	1	=	=	SYM
ejpam-3632	131	2	rh(u	rh(u	X
ejpam-3632	131	3	)	)	PUNCT
ejpam-3632	132	1	6=	6=	ADP
ejpam-3632	132	2	a	a	X
ejpam-3632	132	3	,	,	PUNCT
ejpam-3632	132	4	it	it	PRON
ejpam-3632	132	5	follows	follow	VERB
ejpam-3632	132	6	that	that	SCONJ
ejpam-3632	132	7	for	for	ADP
ejpam-3632	132	8	any	any	DET
ejpam-3632	132	9	finite	finite	NOUN
ejpam-3632	132	10	set	set	VERB
ejpam-3632	132	11	a	a	DET
ejpam-3632	132	12	⊆	⊆	NUM
ejpam-3632	132	13	h	h	NOUN
ejpam-3632	132	14	,	,	PUNCT
ejpam-3632	132	15	a	a	PRON
ejpam-3632	132	16	/∈	/∈	PUNCT
ejpam-3632	132	17	brl(h	brl(h	NOUN
ejpam-3632	132	18	)	)	PUNCT
ejpam-3632	132	19	.	.	PUNCT
ejpam-3632	133	1	next	next	ADV
ejpam-3632	133	2	,	,	PUNCT
ejpam-3632	133	3	suppose	suppose	VERB
ejpam-3632	133	4	that	that	SCONJ
ejpam-3632	133	5	a	a	DET
ejpam-3632	133	6	⊆	⊆	NUM
ejpam-3632	133	7	h	h	NOUN
ejpam-3632	133	8	is	be	AUX
ejpam-3632	133	9	an	an	DET
ejpam-3632	133	10	infinite	infinite	NOUN
ejpam-3632	133	11	set	set	NOUN
ejpam-3632	133	12	and	and	CCONJ
ejpam-3632	133	13	let	let	VERB
ejpam-3632	133	14	p	p	NOUN
ejpam-3632	133	15	=	=	SYM
ejpam-3632	133	16	mina	mina	PROPN
ejpam-3632	133	17	.	.	PUNCT
ejpam-3632	134	1	then	then	ADV
ejpam-3632	134	2	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	134	3	)	)	PUNCT
ejpam-3632	134	4	)	)	PUNCT
ejpam-3632	135	1	=	=	SYM
ejpam-3632	135	2	rh(p	rh(p	NOUN
ejpam-3632	135	3	)	)	PUNCT
ejpam-3632	136	1	=	=	PRON
ejpam-3632	136	2	{	{	PUNCT
ejpam-3632	136	3	p	p	X
ejpam-3632	136	4	,	,	PUNCT
ejpam-3632	136	5	p+	p+	NOUN
ejpam-3632	136	6	1	1	NUM
ejpam-3632	136	7	,	,	PUNCT
ejpam-3632	136	8	p+	p+	NOUN
ejpam-3632	136	9	2	2	NUM
ejpam-3632	136	10	,	,	PUNCT
ejpam-3632	136	11	.	.	PUNCT
ejpam-3632	136	12	.	.	PUNCT
ejpam-3632	137	1	.	.	PUNCT
ejpam-3632	137	2	}	}	PUNCT
ejpam-3632	137	3	.	.	PUNCT
ejpam-3632	138	1	thus	thus	ADV
ejpam-3632	138	2	,	,	PUNCT
ejpam-3632	138	3	a	a	DET
ejpam-3632	138	4	∈	∈	PROPN
ejpam-3632	138	5	brl(h	brl(h	NOUN
ejpam-3632	138	6	)	)	PUNCT
ejpam-3632	138	7	if	if	SCONJ
ejpam-3632	138	8	and	and	CCONJ
ejpam-3632	138	9	only	only	ADV
ejpam-3632	138	10	if	if	SCONJ
ejpam-3632	138	11	a	a	PRON
ejpam-3632	138	12	=	=	X
ejpam-3632	138	13	{	{	PUNCT
ejpam-3632	138	14	p	p	X
ejpam-3632	138	15	,	,	PUNCT
ejpam-3632	138	16	p+	p+	NOUN
ejpam-3632	138	17	1	1	NUM
ejpam-3632	138	18	,	,	PUNCT
ejpam-3632	138	19	p+	p+	NOUN
ejpam-3632	138	20	2	2	NUM
ejpam-3632	138	21	,	,	PUNCT
ejpam-3632	138	22	.	.	PUNCT
ejpam-3632	138	23	.	.	PUNCT
ejpam-3632	139	1	.	.	PUNCT
ejpam-3632	139	2	}	}	PUNCT
ejpam-3632	139	3	.	.	PUNCT
ejpam-3632	140	1	therefore	therefore	ADV
ejpam-3632	140	2	,	,	PUNCT
ejpam-3632	140	3	τrl(h	τrl(h	PROPN
ejpam-3632	140	4	)	)	PUNCT
ejpam-3632	140	5	=	=	SYM
ejpam-3632	140	6	{	{	PUNCT
ejpam-3632	140	7	∅	∅	NOUN
ejpam-3632	140	8	,	,	PUNCT
ejpam-3632	140	9	h	h	NOUN
ejpam-3632	140	10	}	}	PUNCT
ejpam-3632	140	11	∪	∪	X
ejpam-3632	140	12	{	{	PUNCT
ejpam-3632	140	13	{	{	PUNCT
ejpam-3632	140	14	p	p	X
ejpam-3632	140	15	,	,	PUNCT
ejpam-3632	140	16	p+	p+	NOUN
ejpam-3632	140	17	1	1	NUM
ejpam-3632	140	18	,	,	PUNCT
ejpam-3632	140	19	p+	p+	NOUN
ejpam-3632	140	20	2	2	NUM
ejpam-3632	140	21	,	,	PUNCT
ejpam-3632	140	22	.	.	PUNCT
ejpam-3632	140	23	.	.	PUNCT
ejpam-3632	141	1	.	.	PUNCT
ejpam-3632	141	2	}	}	PUNCT
ejpam-3632	142	1	:	:	PUNCT
ejpam-3632	142	2	p	p	X
ejpam-3632	142	3	∈	∈	PROPN
ejpam-3632	142	4	h	h	NOUN
ejpam-3632	142	5	}	}	PUNCT
ejpam-3632	142	6	.	.	PUNCT
ejpam-3632	143	1	in	in	ADP
ejpam-3632	143	2	the	the	DET
ejpam-3632	143	3	next	next	ADJ
ejpam-3632	143	4	example	example	NOUN
ejpam-3632	143	5	,	,	PUNCT
ejpam-3632	143	6	we	we	PRON
ejpam-3632	143	7	extend	extend	VERB
ejpam-3632	143	8	the	the	DET
ejpam-3632	143	9	set	set	ADJ
ejpam-3632	143	10	h	h	NOUN
ejpam-3632	143	11	in	in	ADP
ejpam-3632	143	12	example	example	NOUN
ejpam-3632	143	13	1	1	NUM
ejpam-3632	143	14	by	by	ADP
ejpam-3632	143	15	adjoining	adjoin	VERB
ejpam-3632	143	16	to	to	ADP
ejpam-3632	143	17	it	it	PRON
ejpam-3632	143	18	the	the	DET
ejpam-3632	143	19	set	set	NOUN
ejpam-3632	143	20	{	{	PUNCT
ejpam-3632	143	21	1n	1n	NUM
ejpam-3632	143	22	:	:	PUNCT
ejpam-3632	143	23	n	n	NOUN
ejpam-3632	143	24	=	=	SYM
ejpam-3632	143	25	2	2	NUM
ejpam-3632	143	26	,	,	PUNCT
ejpam-3632	143	27	3	3	NUM
ejpam-3632	143	28	,	,	PUNCT
ejpam-3632	143	29	...	...	PUNCT
ejpam-3632	143	30	}	}	PUNCT
ejpam-3632	143	31	.	.	PUNCT
ejpam-3632	144	1	example	example	NOUN
ejpam-3632	145	1	2	2	NUM
ejpam-3632	145	2	.	.	X
ejpam-3632	145	3	consider	consider	VERB
ejpam-3632	145	4	now	now	ADV
ejpam-3632	145	5	the	the	DET
ejpam-3632	145	6	infinite	infinite	ADJ
ejpam-3632	145	7	hyper	hyper	ADJ
ejpam-3632	145	8	bck	bck	NOUN
ejpam-3632	145	9	-	-	PUNCT
ejpam-3632	145	10	algebra	algebra	NOUN
ejpam-3632	145	11	(	(	PUNCT
ejpam-3632	145	12	h	h	NOUN
ejpam-3632	145	13	,	,	PUNCT
ejpam-3632	145	14	◦	◦	NOUN
ejpam-3632	145	15	,	,	PUNCT
ejpam-3632	145	16	0	0	NUM
ejpam-3632	145	17	)	)	PUNCT
ejpam-3632	145	18	given	give	VERB
ejpam-3632	145	19	also	also	ADV
ejpam-3632	145	20	by	by	ADP
ejpam-3632	145	21	harizavi	harizavi	NOUN
ejpam-3632	145	22	in	in	ADP
ejpam-3632	145	23	[	[	X
ejpam-3632	145	24	3	3	NUM
ejpam-3632	145	25	]	]	PUNCT
ejpam-3632	145	26	,	,	PUNCT
ejpam-3632	145	27	where	where	SCONJ
ejpam-3632	145	28	h	h	NOUN
ejpam-3632	145	29	=	=	PRON
ejpam-3632	145	30	{	{	PUNCT
ejpam-3632	145	31	0	0	NUM
ejpam-3632	145	32	,	,	PUNCT
ejpam-3632	145	33	1	1	NUM
ejpam-3632	145	34	,	,	PUNCT
ejpam-3632	145	35	2	2	NUM
ejpam-3632	145	36	,	,	PUNCT
ejpam-3632	145	37	.	.	PUNCT
ejpam-3632	145	38	.	.	PUNCT
ejpam-3632	146	1	.	.	PUNCT
ejpam-3632	146	2	}	}	PUNCT
ejpam-3632	147	1	∪	∪	ADP
ejpam-3632	147	2	{	{	PUNCT
ejpam-3632	147	3	1n	1n	NUM
ejpam-3632	147	4	:	:	PUNCT
ejpam-3632	147	5	n	n	NOUN
ejpam-3632	147	6	=	=	SYM
ejpam-3632	147	7	2	2	NUM
ejpam-3632	147	8	,	,	PUNCT
ejpam-3632	147	9	3	3	NUM
ejpam-3632	147	10	,	,	PUNCT
ejpam-3632	147	11	...	...	PUNCT
ejpam-3632	147	12	}	}	PUNCT
ejpam-3632	147	13	and	and	CCONJ
ejpam-3632	147	14	“	"	PUNCT
ejpam-3632	147	15	◦	◦	NOUN
ejpam-3632	147	16	”	"	PUNCT
ejpam-3632	147	17	is	be	AUX
ejpam-3632	147	18	defined	define	VERB
ejpam-3632	147	19	as	as	SCONJ
ejpam-3632	147	20	follows	follow	VERB
ejpam-3632	147	21	:	:	PUNCT
ejpam-3632	147	22	x	x	PUNCT
ejpam-3632	147	23	◦	◦	VERB
ejpam-3632	147	24	y	y	NOUN
ejpam-3632	148	1	=	=	PRON
ejpam-3632	148	2	{	{	PUNCT
ejpam-3632	148	3	{	{	PUNCT
ejpam-3632	148	4	0	0	NUM
ejpam-3632	148	5	,	,	PUNCT
ejpam-3632	148	6	x	x	NOUN
ejpam-3632	148	7	}	}	PUNCT
ejpam-3632	148	8	if	if	SCONJ
ejpam-3632	148	9	x	x	PROPN
ejpam-3632	148	10	≤	≤	PROPN
ejpam-3632	148	11	y	y	PROPN
ejpam-3632	148	12	{	{	PUNCT
ejpam-3632	148	13	x	x	X
ejpam-3632	148	14	}	}	PUNCT
ejpam-3632	148	15	if	if	SCONJ
ejpam-3632	148	16	x	x	PROPN
ejpam-3632	148	17	>	>	X
ejpam-3632	148	18	y	y	PROPN
ejpam-3632	148	19	for	for	ADP
ejpam-3632	148	20	all	all	DET
ejpam-3632	148	21	x	x	NOUN
ejpam-3632	148	22	,	,	PUNCT
ejpam-3632	148	23	y	y	PROPN
ejpam-3632	148	24	∈	∈	PROPN
ejpam-3632	148	25	h.	h.	PROPN
ejpam-3632	148	26	for	for	ADP
ejpam-3632	148	27	convenience	convenience	NOUN
ejpam-3632	148	28	,	,	PUNCT
ejpam-3632	148	29	let	let	VERB
ejpam-3632	148	30	n	n	X
ejpam-3632	148	31	=	=	PRON
ejpam-3632	148	32	{	{	PUNCT
ejpam-3632	148	33	1	1	NUM
ejpam-3632	148	34	,	,	PUNCT
ejpam-3632	148	35	2	2	NUM
ejpam-3632	148	36	,	,	PUNCT
ejpam-3632	148	37	...	...	PUNCT
ejpam-3632	148	38	}	}	PUNCT
ejpam-3632	148	39	,	,	PUNCT
ejpam-3632	148	40	n0	n0	X
ejpam-3632	148	41	=	=	SYM
ejpam-3632	148	42	n	n	PRON
ejpam-3632	148	43	∪	∪	X
ejpam-3632	148	44	{	{	PUNCT
ejpam-3632	148	45	0	0	NUM
ejpam-3632	148	46	}	}	PUNCT
ejpam-3632	148	47	,	,	PUNCT
ejpam-3632	148	48	and	and	CCONJ
ejpam-3632	148	49	let	let	VERB
ejpam-3632	148	50	jk	jk	PROPN
ejpam-3632	148	51	=	=	PRON
ejpam-3632	148	52	{	{	PUNCT
ejpam-3632	148	53	1	1	NUM
ejpam-3632	148	54	m	m	NOUN
ejpam-3632	148	55	:	:	PUNCT
ejpam-3632	148	56	m	m	VERB
ejpam-3632	148	57	is	be	AUX
ejpam-3632	148	58	a	a	DET
ejpam-3632	148	59	positive	positive	ADJ
ejpam-3632	148	60	integer	integer	NOUN
ejpam-3632	148	61	and	and	CCONJ
ejpam-3632	148	62	m	m	PRON
ejpam-3632	148	63	≥	≥	NOUN
ejpam-3632	148	64	k	k	NOUN
ejpam-3632	148	65	}	}	PUNCT
ejpam-3632	148	66	.	.	PUNCT
ejpam-3632	149	1	let	let	VERB
ejpam-3632	149	2	p	p	PROPN
ejpam-3632	149	3	∈	∈	PROPN
ejpam-3632	149	4	h.	h.	NOUN
ejpam-3632	150	1	if	if	SCONJ
ejpam-3632	150	2	p	p	PROPN
ejpam-3632	150	3	=	=	NOUN
ejpam-3632	150	4	0	0	NUM
ejpam-3632	150	5	,	,	PUNCT
ejpam-3632	150	6	then	then	ADV
ejpam-3632	150	7	lh(p	lh(p	X
ejpam-3632	150	8	)	)	PUNCT
ejpam-3632	150	9	=	=	PRON
ejpam-3632	150	10	{	{	PUNCT
ejpam-3632	150	11	0	0	NUM
ejpam-3632	150	12	}	}	PUNCT
ejpam-3632	150	13	and	and	CCONJ
ejpam-3632	150	14	rh(lh(p	rh(lh(p	NOUN
ejpam-3632	150	15	)	)	PUNCT
ejpam-3632	150	16	)	)	PUNCT
ejpam-3632	151	1	=	=	PUNCT
ejpam-3632	152	1	h.	h.	NOUN
ejpam-3632	153	1	if	if	SCONJ
ejpam-3632	153	2	p	p	PROPN
ejpam-3632	153	3	∈	∈	PROPN
ejpam-3632	153	4	n	n	CCONJ
ejpam-3632	153	5	,	,	PUNCT
ejpam-3632	153	6	then	then	ADV
ejpam-3632	153	7	lh(p	lh(p	NOUN
ejpam-3632	153	8	)	)	PUNCT
ejpam-3632	153	9	=	=	SYM
ejpam-3632	153	10	j2	j2	PROPN
ejpam-3632	153	11	∪	∪	X
ejpam-3632	153	12	{	{	PUNCT
ejpam-3632	153	13	0	0	NUM
ejpam-3632	153	14	,	,	PUNCT
ejpam-3632	153	15	1	1	NUM
ejpam-3632	153	16	,	,	PUNCT
ejpam-3632	153	17	2	2	NUM
ejpam-3632	153	18	,	,	PUNCT
ejpam-3632	153	19	...	...	PUNCT
ejpam-3632	153	20	,	,	PUNCT
ejpam-3632	153	21	p	p	X
ejpam-3632	153	22	}	}	PUNCT
ejpam-3632	153	23	.	.	PUNCT
ejpam-3632	154	1	hence	hence	ADV
ejpam-3632	154	2	,	,	PUNCT
ejpam-3632	154	3	rh(lh(p	rh(lh(p	NOUN
ejpam-3632	154	4	)	)	PUNCT
ejpam-3632	154	5	)	)	PUNCT
ejpam-3632	155	1	=	=	VERB
ejpam-3632	155	2	rh(j2	rh(j2	NOUN
ejpam-3632	155	3	∪	∪	X
ejpam-3632	155	4	{	{	PUNCT
ejpam-3632	155	5	0	0	NUM
ejpam-3632	155	6	,	,	PUNCT
ejpam-3632	155	7	1	1	NUM
ejpam-3632	155	8	,	,	PUNCT
ejpam-3632	155	9	2	2	NUM
ejpam-3632	155	10	,	,	PUNCT
ejpam-3632	155	11	.	.	PUNCT
ejpam-3632	155	12	.	.	PUNCT
ejpam-3632	155	13	.	.	PUNCT
ejpam-3632	156	1	,	,	PUNCT
ejpam-3632	156	2	p	p	X
ejpam-3632	156	3	}	}	PUNCT
ejpam-3632	156	4	)	)	PUNCT
ejpam-3632	156	5	=	=	PRON
ejpam-3632	157	1	{	{	PUNCT
ejpam-3632	157	2	p	p	X
ejpam-3632	157	3	,	,	PUNCT
ejpam-3632	157	4	p	p	X
ejpam-3632	157	5	+	+	NOUN
ejpam-3632	157	6	1	1	NUM
ejpam-3632	157	7	,	,	PUNCT
ejpam-3632	157	8	p	p	NOUN
ejpam-3632	157	9	+	+	NOUN
ejpam-3632	157	10	2	2	NUM
ejpam-3632	157	11	,	,	PUNCT
ejpam-3632	157	12	.	.	PUNCT
ejpam-3632	157	13	.	.	PUNCT
ejpam-3632	157	14	.	.	PUNCT
ejpam-3632	157	15	}	}	PUNCT
ejpam-3632	157	16	.	.	PUNCT
ejpam-3632	158	1	if	if	SCONJ
ejpam-3632	158	2	p	p	NOUN
ejpam-3632	158	3	=	=	SYM
ejpam-3632	158	4	1	1	NUM
ejpam-3632	158	5	n	n	NOUN
ejpam-3632	158	6	for	for	ADP
ejpam-3632	158	7	some	some	DET
ejpam-3632	158	8	n	n	PRON
ejpam-3632	158	9	∈	∈	NOUN
ejpam-3632	158	10	{	{	PUNCT
ejpam-3632	158	11	2	2	NUM
ejpam-3632	158	12	,	,	PUNCT
ejpam-3632	158	13	3	3	NUM
ejpam-3632	158	14	,	,	PUNCT
ejpam-3632	158	15	...	...	PUNCT
ejpam-3632	158	16	}	}	PUNCT
ejpam-3632	158	17	,	,	PUNCT
ejpam-3632	158	18	then	then	ADV
ejpam-3632	158	19	r.	r.	PROPN
ejpam-3632	158	20	patangan	patangan	PROPN
ejpam-3632	158	21	,	,	PUNCT
ejpam-3632	158	22	s.	s.	PROPN
ejpam-3632	158	23	canoy	canoy	PROPN
ejpam-3632	158	24	,	,	PUNCT
ejpam-3632	158	25	jr	jr	PROPN
ejpam-3632	158	26	.	.	PROPN
ejpam-3632	158	27	/	/	SYM
ejpam-3632	158	28	eur	eur	PROPN
ejpam-3632	158	29	.	.	PUNCT
ejpam-3632	159	1	j.	j.	PROPN
ejpam-3632	159	2	pure	pure	PROPN
ejpam-3632	159	3	appl	appl	PROPN
ejpam-3632	159	4	.	.	PROPN
ejpam-3632	159	5	math	math	PROPN
ejpam-3632	159	6	,	,	PUNCT
ejpam-3632	159	7	13	13	NUM
ejpam-3632	159	8	(	(	PUNCT
ejpam-3632	159	9	1	1	NUM
ejpam-3632	159	10	)	)	PUNCT
ejpam-3632	159	11	(	(	PUNCT
ejpam-3632	159	12	2020	2020	NUM
ejpam-3632	159	13	)	)	PUNCT
ejpam-3632	159	14	,	,	PUNCT
ejpam-3632	159	15	1	1	NUM
ejpam-3632	159	16	-	-	SYM
ejpam-3632	159	17	8	8	NUM
ejpam-3632	159	18	5	5	NUM
ejpam-3632	159	19	lh(p	lh(p	NOUN
ejpam-3632	159	20	)	)	PUNCT
ejpam-3632	160	1	=	=	SYM
ejpam-3632	160	2	jn	jn	PROPN
ejpam-3632	160	3	∪	∪	X
ejpam-3632	160	4	{	{	PUNCT
ejpam-3632	160	5	0	0	NUM
ejpam-3632	160	6	}	}	PUNCT
ejpam-3632	160	7	=	=	SYM
ejpam-3632	160	8	{	{	PUNCT
ejpam-3632	160	9	0	0	NUM
ejpam-3632	160	10	,	,	PUNCT
ejpam-3632	160	11	1n	1n	NUM
ejpam-3632	160	12	,	,	PUNCT
ejpam-3632	160	13	1	1	NUM
ejpam-3632	160	14	n+1	n+1	NUM
ejpam-3632	160	15	,	,	PUNCT
ejpam-3632	160	16	1	1	NUM
ejpam-3632	160	17	n+2	n+2	PRON
ejpam-3632	160	18	,	,	PUNCT
ejpam-3632	160	19	...	...	PUNCT
ejpam-3632	160	20	}	}	PUNCT
ejpam-3632	160	21	.	.	PUNCT
ejpam-3632	161	1	it	it	PRON
ejpam-3632	161	2	follows	follow	VERB
ejpam-3632	161	3	that	that	SCONJ
ejpam-3632	161	4	rh(lh(p	rh(lh(p	NOUN
ejpam-3632	161	5	)	)	PUNCT
ejpam-3632	161	6	)	)	PUNCT
ejpam-3632	162	1	=	=	PUNCT
ejpam-3632	162	2	rh(jn	rh(jn	NOUN
ejpam-3632	162	3	∪	∪	ADP
ejpam-3632	162	4	{	{	PUNCT
ejpam-3632	162	5	0	0	NUM
ejpam-3632	162	6	}	}	PUNCT
ejpam-3632	162	7	)	)	PUNCT
ejpam-3632	162	8	=	=	PRON
ejpam-3632	162	9	{	{	PUNCT
ejpam-3632	162	10	x	x	PUNCT
ejpam-3632	162	11	∈	∈	PROPN
ejpam-3632	162	12	h	h	NOUN
ejpam-3632	162	13	:	:	PUNCT
ejpam-3632	162	14	a	a	DET
ejpam-3632	162	15	≤	≤	NOUN
ejpam-3632	162	16	x	x	PUNCT
ejpam-3632	162	17	for	for	ADP
ejpam-3632	162	18	all	all	DET
ejpam-3632	162	19	a	a	DET
ejpam-3632	162	20	∈	∈	NOUN
ejpam-3632	162	21	(	(	PUNCT
ejpam-3632	162	22	jn	jn	PROPN
ejpam-3632	162	23	∪	∪	PROPN
ejpam-3632	162	24	{	{	PUNCT
ejpam-3632	162	25	0	0	NUM
ejpam-3632	162	26	}	}	PUNCT
ejpam-3632	162	27	)	)	PUNCT
ejpam-3632	162	28	}	}	PUNCT
ejpam-3632	162	29	=	=	SYM
ejpam-3632	162	30	n	n	PRON
ejpam-3632	162	31	∪	∪	X
ejpam-3632	162	32	{	{	PUNCT
ejpam-3632	162	33	12	12	NUM
ejpam-3632	162	34	,	,	PUNCT
ejpam-3632	162	35	1	1	NUM
ejpam-3632	162	36	3	3	NUM
ejpam-3632	162	37	,	,	PUNCT
ejpam-3632	162	38	...	...	PUNCT
ejpam-3632	162	39	,	,	PUNCT
ejpam-3632	162	40	1	1	NUM
ejpam-3632	162	41	n	n	CCONJ
ejpam-3632	162	42	}	}	PUNCT
ejpam-3632	162	43	.	.	PUNCT
ejpam-3632	163	1	now	now	ADV
ejpam-3632	163	2	let	let	VERB
ejpam-3632	163	3	∅	∅	NOUN
ejpam-3632	163	4	6=	6=	ADP
ejpam-3632	163	5	a	a	DET
ejpam-3632	163	6	⊆	⊆	NUM
ejpam-3632	163	7	h.	h.	NOUN
ejpam-3632	163	8	if	if	SCONJ
ejpam-3632	163	9	0	0	NUM
ejpam-3632	163	10	∈	∈	PROPN
ejpam-3632	163	11	a	a	PRON
ejpam-3632	163	12	,	,	PUNCT
ejpam-3632	163	13	then	then	ADV
ejpam-3632	163	14	lh(a	lh(a	NUM
ejpam-3632	163	15	)	)	PUNCT
ejpam-3632	163	16	=	=	PUNCT
ejpam-3632	164	1	{	{	PUNCT
ejpam-3632	164	2	0	0	NUM
ejpam-3632	164	3	}	}	PUNCT
ejpam-3632	164	4	and	and	CCONJ
ejpam-3632	164	5	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	164	6	)	)	PUNCT
ejpam-3632	164	7	)	)	PUNCT
ejpam-3632	165	1	=	=	SYM
ejpam-3632	166	1	h.	h.	PROPN
ejpam-3632	167	1	thus	thus	ADV
ejpam-3632	167	2	,	,	PUNCT
ejpam-3632	167	3	a	a	DET
ejpam-3632	167	4	∈	∈	PROPN
ejpam-3632	167	5	brl(h	brl(h	NOUN
ejpam-3632	167	6	)	)	PUNCT
ejpam-3632	168	1	if	if	SCONJ
ejpam-3632	168	2	and	and	CCONJ
ejpam-3632	168	3	only	only	ADV
ejpam-3632	168	4	if	if	SCONJ
ejpam-3632	168	5	a	a	DET
ejpam-3632	168	6	=	=	X
ejpam-3632	168	7	h.	h.	PROPN
ejpam-3632	168	8	next	next	ADV
ejpam-3632	168	9	,	,	PUNCT
ejpam-3632	168	10	suppose	suppose	VERB
ejpam-3632	168	11	that	that	SCONJ
ejpam-3632	168	12	0	0	NUM
ejpam-3632	168	13	/∈	/∈	PUNCT
ejpam-3632	168	14	a.	a.	NOUN
ejpam-3632	168	15	suppose	suppose	VERB
ejpam-3632	168	16	first	first	ADV
ejpam-3632	168	17	that	that	SCONJ
ejpam-3632	168	18	a	a	DET
ejpam-3632	168	19	∩	∩	ADJ
ejpam-3632	168	20	j2	j2	NOUN
ejpam-3632	168	21	6=	6=	ADP
ejpam-3632	168	22	∅.	∅.	PROPN
ejpam-3632	168	23	suppose	suppose	VERB
ejpam-3632	168	24	that	that	SCONJ
ejpam-3632	168	25	a∩j2	a∩j2	PROPN
ejpam-3632	168	26	is	be	AUX
ejpam-3632	168	27	infinite	infinite	ADJ
ejpam-3632	168	28	and	and	CCONJ
ejpam-3632	168	29	suppose	suppose	VERB
ejpam-3632	168	30	further	far	ADV
ejpam-3632	168	31	that	that	SCONJ
ejpam-3632	168	32	there	there	PRON
ejpam-3632	168	33	exists	exist	VERB
ejpam-3632	168	34	z	z	PROPN
ejpam-3632	168	35	∈	∈	PROPN
ejpam-3632	168	36	lh(a	lh(a	PROPN
ejpam-3632	168	37	)	)	PUNCT
ejpam-3632	168	38	.	.	PUNCT
ejpam-3632	169	1	then	then	ADV
ejpam-3632	169	2	z	z	NOUN
ejpam-3632	169	3	≤	≤	NOUN
ejpam-3632	169	4	a	a	PRON
ejpam-3632	169	5	for	for	ADP
ejpam-3632	169	6	all	all	DET
ejpam-3632	169	7	a	a	DET
ejpam-3632	169	8	∈	∈	NOUN
ejpam-3632	169	9	a.	a.	NOUN
ejpam-3632	169	10	it	it	PRON
ejpam-3632	169	11	follows	follow	VERB
ejpam-3632	169	12	that	that	SCONJ
ejpam-3632	169	13	z	z	NOUN
ejpam-3632	169	14	≤	≤	NUM
ejpam-3632	169	15	b	b	X
ejpam-3632	169	16	for	for	ADP
ejpam-3632	169	17	all	all	DET
ejpam-3632	169	18	b	b	PROPN
ejpam-3632	169	19	∈	∈	PROPN
ejpam-3632	169	20	a∩j2	a∩j2	PROPN
ejpam-3632	169	21	,	,	PUNCT
ejpam-3632	169	22	contrary	contrary	ADJ
ejpam-3632	169	23	to	to	ADP
ejpam-3632	169	24	the	the	DET
ejpam-3632	169	25	assumption	assumption	NOUN
ejpam-3632	169	26	that	that	SCONJ
ejpam-3632	169	27	a∩j2	a∩j2	PROPN
ejpam-3632	169	28	is	be	AUX
ejpam-3632	169	29	infinite	infinite	ADJ
ejpam-3632	169	30	.	.	PUNCT
ejpam-3632	170	1	thus	thus	ADV
ejpam-3632	170	2	,	,	PUNCT
ejpam-3632	170	3	lh(a	lh(a	NUM
ejpam-3632	170	4	)	)	PUNCT
ejpam-3632	171	1	=	=	PUNCT
ejpam-3632	171	2	∅.	∅.	ADP
ejpam-3632	171	3	next	next	ADV
ejpam-3632	171	4	,	,	PUNCT
ejpam-3632	171	5	suppose	suppose	VERB
ejpam-3632	171	6	that	that	SCONJ
ejpam-3632	171	7	a∩j2	a∩j2	PROPN
ejpam-3632	171	8	is	be	AUX
ejpam-3632	171	9	finite	finite	ADJ
ejpam-3632	171	10	and	and	CCONJ
ejpam-3632	171	11	let	let	VERB
ejpam-3632	171	12	1	1	NUM
ejpam-3632	171	13	q	q	NOUN
ejpam-3632	171	14	=	=	SYM
ejpam-3632	171	15	min(a∩j2	min(a∩j2	NOUN
ejpam-3632	171	16	)	)	PUNCT
ejpam-3632	171	17	.	.	PUNCT
ejpam-3632	172	1	then	then	ADV
ejpam-3632	172	2	lh(a	lh(a	NUM
ejpam-3632	172	3	)	)	PUNCT
ejpam-3632	172	4	=	=	SYM
ejpam-3632	172	5	jq	jq	PROPN
ejpam-3632	172	6	∪	∪	ADP
ejpam-3632	172	7	{	{	PUNCT
ejpam-3632	172	8	0	0	NUM
ejpam-3632	172	9	}	}	PUNCT
ejpam-3632	172	10	.	.	PUNCT
ejpam-3632	173	1	hence	hence	ADV
ejpam-3632	173	2	,	,	PUNCT
ejpam-3632	173	3	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	173	4	)	)	PUNCT
ejpam-3632	173	5	)	)	PUNCT
ejpam-3632	174	1	=	=	SYM
ejpam-3632	174	2	n	n	NOUN
ejpam-3632	174	3	∪	∪	X
ejpam-3632	174	4	{	{	PUNCT
ejpam-3632	174	5	12	12	NUM
ejpam-3632	174	6	,	,	PUNCT
ejpam-3632	174	7	1	1	NUM
ejpam-3632	174	8	3	3	NUM
ejpam-3632	174	9	,	,	PUNCT
ejpam-3632	174	10	...	...	PUNCT
ejpam-3632	174	11	,	,	PUNCT
ejpam-3632	174	12	1	1	NUM
ejpam-3632	174	13	q	q	NOUN
ejpam-3632	174	14	}	}	PUNCT
ejpam-3632	174	15	.	.	PUNCT
ejpam-3632	175	1	therefore	therefore	ADV
ejpam-3632	175	2	,	,	PUNCT
ejpam-3632	175	3	a	a	DET
ejpam-3632	175	4	∈	∈	PROPN
ejpam-3632	175	5	brl(h	brl(h	NOUN
ejpam-3632	175	6	)	)	PUNCT
ejpam-3632	176	1	if	if	SCONJ
ejpam-3632	176	2	and	and	CCONJ
ejpam-3632	176	3	only	only	ADV
ejpam-3632	176	4	if	if	SCONJ
ejpam-3632	176	5	a	a	DET
ejpam-3632	176	6	=	=	NOUN
ejpam-3632	176	7	n	n	NOUN
ejpam-3632	176	8	∪	∪	NOUN
ejpam-3632	176	9	{	{	PUNCT
ejpam-3632	176	10	12	12	NUM
ejpam-3632	176	11	,	,	PUNCT
ejpam-3632	176	12	1	1	NUM
ejpam-3632	176	13	3	3	NUM
ejpam-3632	176	14	,	,	PUNCT
ejpam-3632	176	15	...	...	PUNCT
ejpam-3632	176	16	,	,	PUNCT
ejpam-3632	176	17	1	1	NUM
ejpam-3632	176	18	q	q	NOUN
ejpam-3632	176	19	}	}	PUNCT
ejpam-3632	176	20	.	.	PUNCT
ejpam-3632	177	1	suppose	suppose	VERB
ejpam-3632	177	2	now	now	ADV
ejpam-3632	177	3	that	that	SCONJ
ejpam-3632	177	4	a	a	DET
ejpam-3632	177	5	∩	∩	ADJ
ejpam-3632	177	6	j2	j2	NOUN
ejpam-3632	177	7	=	=	PUNCT
ejpam-3632	177	8	∅.	∅.	PROPN
ejpam-3632	177	9	then	then	ADV
ejpam-3632	177	10	lh(a	lh(a	NUM
ejpam-3632	177	11	)	)	PUNCT
ejpam-3632	177	12	=	=	SYM
ejpam-3632	177	13	j2	j2	PROPN
ejpam-3632	177	14	∪	∪	X
ejpam-3632	177	15	{	{	PUNCT
ejpam-3632	177	16	0	0	NUM
ejpam-3632	177	17	,	,	PUNCT
ejpam-3632	177	18	1	1	NUM
ejpam-3632	177	19	,	,	PUNCT
ejpam-3632	177	20	2	2	NUM
ejpam-3632	177	21	,	,	PUNCT
ejpam-3632	177	22	...	...	PUNCT
ejpam-3632	177	23	,	,	PUNCT
ejpam-3632	177	24	r	r	NOUN
ejpam-3632	177	25	}	}	PUNCT
ejpam-3632	177	26	,	,	PUNCT
ejpam-3632	177	27	where	where	SCONJ
ejpam-3632	177	28	r	r	NOUN
ejpam-3632	177	29	=	=	SYM
ejpam-3632	177	30	mina	mina	ADJ
ejpam-3632	177	31	.	.	PUNCT
ejpam-3632	178	1	thus	thus	ADV
ejpam-3632	178	2	,	,	PUNCT
ejpam-3632	178	3	rh(lh(a	rh(lh(a	NOUN
ejpam-3632	178	4	)	)	PUNCT
ejpam-3632	178	5	)	)	PUNCT
ejpam-3632	179	1	=	=	VERB
ejpam-3632	179	2	rh(j2	rh(j2	NOUN
ejpam-3632	179	3	∪	∪	X
ejpam-3632	179	4	{	{	PUNCT
ejpam-3632	179	5	0	0	NUM
ejpam-3632	179	6	,	,	PUNCT
ejpam-3632	179	7	1	1	NUM
ejpam-3632	179	8	,	,	PUNCT
ejpam-3632	179	9	2	2	NUM
ejpam-3632	179	10	,	,	PUNCT
ejpam-3632	179	11	.	.	PUNCT
ejpam-3632	179	12	.	.	PUNCT
ejpam-3632	179	13	.	.	PUNCT
ejpam-3632	180	1	,	,	PUNCT
ejpam-3632	180	2	r	r	NOUN
ejpam-3632	180	3	}	}	PUNCT
ejpam-3632	180	4	)	)	PUNCT
ejpam-3632	181	1	=	=	PRON
ejpam-3632	181	2	{	{	PUNCT
ejpam-3632	181	3	r	r	NOUN
ejpam-3632	181	4	,	,	PUNCT
ejpam-3632	181	5	r+	r+	NOUN
ejpam-3632	181	6	1	1	NUM
ejpam-3632	181	7	,	,	PUNCT
ejpam-3632	181	8	r+	r+	VERB
ejpam-3632	181	9	2	2	NUM
ejpam-3632	181	10	,	,	PUNCT
ejpam-3632	181	11	.	.	PUNCT
ejpam-3632	181	12	.	.	PUNCT
ejpam-3632	181	13	.	.	PUNCT
ejpam-3632	181	14	}	}	PUNCT
ejpam-3632	181	15	.	.	PUNCT
ejpam-3632	182	1	thus	thus	ADV
ejpam-3632	182	2	,	,	PUNCT
ejpam-3632	182	3	a	a	DET
ejpam-3632	182	4	∈	∈	PROPN
ejpam-3632	182	5	brl(h	brl(h	NOUN
ejpam-3632	182	6	)	)	PUNCT
ejpam-3632	182	7	if	if	SCONJ
ejpam-3632	182	8	and	and	CCONJ
ejpam-3632	182	9	only	only	ADV
ejpam-3632	182	10	if	if	SCONJ
ejpam-3632	182	11	a	a	PRON
ejpam-3632	182	12	=	=	X
ejpam-3632	182	13	{	{	PUNCT
ejpam-3632	182	14	r	r	NOUN
ejpam-3632	182	15	,	,	PUNCT
ejpam-3632	182	16	r+	r+	NOUN
ejpam-3632	182	17	1	1	NUM
ejpam-3632	182	18	,	,	PUNCT
ejpam-3632	182	19	r+	r+	VERB
ejpam-3632	182	20	2	2	NUM
ejpam-3632	182	21	,	,	PUNCT
ejpam-3632	182	22	.	.	PUNCT
ejpam-3632	182	23	.	.	PUNCT
ejpam-3632	183	1	.	.	PUNCT
ejpam-3632	183	2	}	}	PUNCT
ejpam-3632	183	3	.	.	PUNCT
ejpam-3632	184	1	therefore	therefore	ADV
ejpam-3632	184	2	,	,	PUNCT
ejpam-3632	184	3	τrl(h	τrl(h	PROPN
ejpam-3632	184	4	)	)	PUNCT
ejpam-3632	184	5	=	=	SYM
ejpam-3632	184	6	{	{	PUNCT
ejpam-3632	184	7	∅	∅	NOUN
ejpam-3632	184	8	,	,	PUNCT
ejpam-3632	184	9	h	h	NOUN
ejpam-3632	184	10	}	}	PUNCT
ejpam-3632	184	11	∪	∪	X
ejpam-3632	184	12	{	{	PUNCT
ejpam-3632	184	13	{	{	PUNCT
ejpam-3632	184	14	p	p	X
ejpam-3632	184	15	,	,	PUNCT
ejpam-3632	184	16	p+	p+	NOUN
ejpam-3632	184	17	1	1	NUM
ejpam-3632	184	18	,	,	PUNCT
ejpam-3632	184	19	p+	p+	NOUN
ejpam-3632	184	20	2	2	NUM
ejpam-3632	184	21	,	,	PUNCT
ejpam-3632	184	22	.	.	PUNCT
ejpam-3632	184	23	.	.	PUNCT
ejpam-3632	185	1	.	.	PUNCT
ejpam-3632	185	2	}	}	PUNCT
ejpam-3632	186	1	:	:	PUNCT
ejpam-3632	186	2	p	p	X
ejpam-3632	186	3	∈	∈	PROPN
ejpam-3632	186	4	n	n	CCONJ
ejpam-3632	186	5	}	}	PUNCT
ejpam-3632	186	6	∪	∪	X
ejpam-3632	186	7	{	{	PUNCT
ejpam-3632	186	8	n	n	CCONJ
ejpam-3632	186	9	∪	∪	NOUN
ejpam-3632	186	10	{	{	PUNCT
ejpam-3632	186	11	12	12	NUM
ejpam-3632	186	12	,	,	PUNCT
ejpam-3632	186	13	1	1	NUM
ejpam-3632	186	14	3	3	NUM
ejpam-3632	186	15	,	,	PUNCT
ejpam-3632	186	16	...	...	PUNCT
ejpam-3632	186	17	,	,	PUNCT
ejpam-3632	186	18	1	1	NUM
ejpam-3632	186	19	k	k	NOUN
ejpam-3632	186	20	}	}	PUNCT
ejpam-3632	186	21	:	:	PUNCT
ejpam-3632	186	22	k	k	X
ejpam-3632	186	23	=	=	SYM
ejpam-3632	186	24	2	2	NUM
ejpam-3632	186	25	,	,	PUNCT
ejpam-3632	186	26	3	3	NUM
ejpam-3632	186	27	,	,	PUNCT
ejpam-3632	186	28	...	...	PUNCT
ejpam-3632	186	29	}	}	PUNCT
ejpam-3632	186	30	.	.	PUNCT
ejpam-3632	187	1	it	it	PRON
ejpam-3632	187	2	can	can	AUX
ejpam-3632	187	3	be	be	AUX
ejpam-3632	187	4	observed	observe	VERB
ejpam-3632	187	5	that	that	SCONJ
ejpam-3632	187	6	the	the	DET
ejpam-3632	187	7	topology	topology	NOUN
ejpam-3632	187	8	τrl(h	τrl(h	PROPN
ejpam-3632	187	9	)	)	PUNCT
ejpam-3632	187	10	in	in	ADP
ejpam-3632	187	11	example	example	NOUN
ejpam-3632	187	12	1	1	NUM
ejpam-3632	187	13	coincides	coincide	VERB
ejpam-3632	187	14	with	with	ADP
ejpam-3632	187	15	the	the	DET
ejpam-3632	187	16	topology	topology	NOUN
ejpam-3632	187	17	τr(h	τr(h	PUNCT
ejpam-3632	187	18	)	)	PUNCT
ejpam-3632	187	19	in	in	ADP
ejpam-3632	187	20	example	example	NOUN
ejpam-3632	187	21	2.5	2.5	NUM
ejpam-3632	188	1	[	[	X
ejpam-3632	188	2	7	7	NUM
ejpam-3632	188	3	]	]	PUNCT
ejpam-3632	188	4	.	.	PUNCT
ejpam-3632	189	1	in	in	ADP
ejpam-3632	189	2	fact	fact	NOUN
ejpam-3632	189	3	,	,	PUNCT
ejpam-3632	189	4	the	the	DET
ejpam-3632	189	5	next	next	ADJ
ejpam-3632	189	6	result	result	NOUN
ejpam-3632	189	7	shows	show	VERB
ejpam-3632	189	8	that	that	SCONJ
ejpam-3632	189	9	this	this	DET
ejpam-3632	189	10	equality	equality	NOUN
ejpam-3632	189	11	is	be	AUX
ejpam-3632	189	12	true	true	ADJ
ejpam-3632	189	13	for	for	SCONJ
ejpam-3632	189	14	any	any	DET
ejpam-3632	189	15	hyper	hyper	ADJ
ejpam-3632	189	16	bck	bck	NOUN
ejpam-3632	189	17	-	-	PUNCT
ejpam-3632	189	18	algebra	algebra	NOUN
ejpam-3632	189	19	h.	h.	NOUN
ejpam-3632	189	20	theorem	theorem	VERB
ejpam-3632	189	21	6	6	NUM
ejpam-3632	189	22	.	.	PUNCT
ejpam-3632	190	1	let	let	VERB
ejpam-3632	190	2	h	h	PRON
ejpam-3632	190	3	be	be	AUX
ejpam-3632	190	4	a	a	DET
ejpam-3632	190	5	hyper	hyper	ADJ
ejpam-3632	190	6	bck	bck	NOUN
ejpam-3632	190	7	-	-	PUNCT
ejpam-3632	190	8	algebra	algebra	NOUN
ejpam-3632	190	9	.	.	PUNCT
ejpam-3632	191	1	then	then	ADV
ejpam-3632	191	2	the	the	DET
ejpam-3632	191	3	topology	topology	NOUN
ejpam-3632	191	4	τrl(h	τrl(h	PROPN
ejpam-3632	191	5	)	)	PUNCT
ejpam-3632	191	6	coincides	coincide	VERB
ejpam-3632	191	7	with	with	ADP
ejpam-3632	191	8	the	the	DET
ejpam-3632	191	9	topology	topology	NOUN
ejpam-3632	191	10	τr(h	τr(h	PUNCT
ejpam-3632	191	11	)	)	PUNCT
ejpam-3632	191	12	.	.	PUNCT
ejpam-3632	192	1	proof	proof	NOUN
ejpam-3632	192	2	.	.	PUNCT
ejpam-3632	193	1	by	by	ADP
ejpam-3632	193	2	theorem	theorem	NOUN
ejpam-3632	193	3	5	5	NUM
ejpam-3632	193	4	,	,	PUNCT
ejpam-3632	193	5	a	a	DET
ejpam-3632	193	6	basis	basis	NOUN
ejpam-3632	193	7	for	for	ADP
ejpam-3632	193	8	τrl(h	τrl(h	PROPN
ejpam-3632	193	9	)	)	PUNCT
ejpam-3632	193	10	is	be	AUX
ejpam-3632	193	11	the	the	DET
ejpam-3632	193	12	family	family	NOUN
ejpam-3632	193	13	brl(h	brl(h	NOUN
ejpam-3632	193	14	)	)	PUNCT
ejpam-3632	193	15	=	=	NOUN
ejpam-3632	193	16	{	{	PUNCT
ejpam-3632	193	17	a	a	DET
ejpam-3632	193	18	:	:	PUNCT
ejpam-3632	193	19	rhlh(a	rhlh(a	NOUN
ejpam-3632	193	20	)	)	PUNCT
ejpam-3632	193	21	=	=	SYM
ejpam-3632	194	1	a	a	PROPN
ejpam-3632	194	2	,	,	PUNCT
ejpam-3632	194	3	a	a	DET
ejpam-3632	194	4	⊆	⊆	NUM
ejpam-3632	194	5	h	h	NOUN
ejpam-3632	194	6	}	}	PUNCT
ejpam-3632	194	7	while	while	SCONJ
ejpam-3632	194	8	a	a	DET
ejpam-3632	194	9	basis	basis	NOUN
ejpam-3632	194	10	for	for	ADP
ejpam-3632	194	11	τr(h	τr(h	NOUN
ejpam-3632	194	12	)	)	PUNCT
ejpam-3632	194	13	is	be	AUX
ejpam-3632	194	14	the	the	DET
ejpam-3632	194	15	family	family	NOUN
ejpam-3632	194	16	br(h	br(h	NOUN
ejpam-3632	194	17	)	)	PUNCT
ejpam-3632	194	18	=	=	PRON
ejpam-3632	194	19	{	{	PUNCT
ejpam-3632	194	20	rh(a	rh(a	NOUN
ejpam-3632	194	21	)	)	PUNCT
ejpam-3632	194	22	:	:	PUNCT
ejpam-3632	194	23	∅	∅	NOUN
ejpam-3632	194	24	6=	6=	ADP
ejpam-3632	194	25	a	a	DET
ejpam-3632	194	26	⊆	⊆	NUM
ejpam-3632	194	27	h	h	NOUN
ejpam-3632	194	28	}	}	PUNCT
ejpam-3632	194	29	.	.	PUNCT
ejpam-3632	195	1	let	let	VERB
ejpam-3632	195	2	a	a	DET
ejpam-3632	195	3	∈	∈	NOUN
ejpam-3632	195	4	brl(h	brl(h	NOUN
ejpam-3632	195	5	)	)	PUNCT
ejpam-3632	195	6	.	.	PUNCT
ejpam-3632	196	1	then	then	ADV
ejpam-3632	196	2	rhlh(a	rhlh(a	NOUN
ejpam-3632	196	3	)	)	PUNCT
ejpam-3632	196	4	=	=	SYM
ejpam-3632	196	5	a.	a.	NOUN
ejpam-3632	196	6	set	set	NOUN
ejpam-3632	197	1	d	d	PROPN
ejpam-3632	197	2	=	=	SYM
ejpam-3632	197	3	lh(a	lh(a	PROPN
ejpam-3632	197	4	)	)	PUNCT
ejpam-3632	197	5	.	.	PUNCT
ejpam-3632	198	1	then	then	ADV
ejpam-3632	198	2	rh(d	rh(d	NOUN
ejpam-3632	198	3	)	)	PUNCT
ejpam-3632	199	1	=	=	PUNCT
ejpam-3632	199	2	a	a	DET
ejpam-3632	199	3	∈	∈	PROPN
ejpam-3632	199	4	br(h	br(h	NOUN
ejpam-3632	199	5	)	)	PUNCT
ejpam-3632	199	6	,	,	PUNCT
ejpam-3632	199	7	showing	show	VERB
ejpam-3632	199	8	that	that	SCONJ
ejpam-3632	199	9	brl(h	brl(h	NOUN
ejpam-3632	199	10	)	)	PUNCT
ejpam-3632	199	11	⊆	⊆	NUM
ejpam-3632	199	12	br(h	br(h	NUM
ejpam-3632	199	13	)	)	PUNCT
ejpam-3632	199	14	.	.	PUNCT
ejpam-3632	200	1	next	next	ADV
ejpam-3632	200	2	,	,	PUNCT
ejpam-3632	200	3	let	let	VERB
ejpam-3632	200	4	u	u	PRON
ejpam-3632	200	5	∈	∈	PROPN
ejpam-3632	200	6	br(h	br(h	NOUN
ejpam-3632	200	7	)	)	PUNCT
ejpam-3632	200	8	.	.	PUNCT
ejpam-3632	201	1	then	then	ADV
ejpam-3632	201	2	there	there	PRON
ejpam-3632	201	3	exists	exist	VERB
ejpam-3632	201	4	b	b	PROPN
ejpam-3632	201	5	⊆	⊆	NUM
ejpam-3632	201	6	h	h	NOUN
ejpam-3632	201	7	such	such	ADJ
ejpam-3632	201	8	that	that	DET
ejpam-3632	201	9	rh(b	rh(b	PUNCT
ejpam-3632	201	10	)	)	PUNCT
ejpam-3632	202	1	=	=	SYM
ejpam-3632	202	2	u	u	NOUN
ejpam-3632	202	3	.	.	PUNCT
ejpam-3632	203	1	this	this	PRON
ejpam-3632	203	2	implies	imply	VERB
ejpam-3632	203	3	that	that	SCONJ
ejpam-3632	203	4	for	for	ADP
ejpam-3632	203	5	every	every	DET
ejpam-3632	203	6	u	u	PROPN
ejpam-3632	203	7	∈	∈	PROPN
ejpam-3632	203	8	u	u	PROPN
ejpam-3632	203	9	,	,	PUNCT
ejpam-3632	203	10	b	b	PROPN
ejpam-3632	203	11	�	�	PROPN
ejpam-3632	203	12	u	u	PROPN
ejpam-3632	203	13	for	for	ADP
ejpam-3632	203	14	all	all	DET
ejpam-3632	203	15	b	b	PROPN
ejpam-3632	203	16	∈	∈	PROPN
ejpam-3632	203	17	b.	b.	PROPN
ejpam-3632	203	18	hence	hence	ADV
ejpam-3632	203	19	,	,	PUNCT
ejpam-3632	203	20	b	b	PROPN
ejpam-3632	203	21	⊆	⊆	NUM
ejpam-3632	203	22	lh(u	lh(u	NOUN
ejpam-3632	203	23	)	)	PUNCT
ejpam-3632	203	24	.	.	PUNCT
ejpam-3632	204	1	by	by	ADP
ejpam-3632	204	2	proposition	proposition	NOUN
ejpam-3632	204	3	1(iv	1(iv	NUM
ejpam-3632	204	4	)	)	PUNCT
ejpam-3632	204	5	,	,	PUNCT
ejpam-3632	204	6	rhlh(u	rhlh(u	NOUN
ejpam-3632	204	7	)	)	PUNCT
ejpam-3632	204	8	⊆	⊆	NUM
ejpam-3632	204	9	rh(b	rh(b	NUM
ejpam-3632	204	10	)	)	PUNCT
ejpam-3632	205	1	=	=	SYM
ejpam-3632	205	2	u	u	NOUN
ejpam-3632	205	3	.	.	PUNCT
ejpam-3632	206	1	also	also	ADV
ejpam-3632	206	2	,	,	PUNCT
ejpam-3632	206	3	by	by	ADP
ejpam-3632	206	4	theorem	theorem	NOUN
ejpam-3632	206	5	3(i	3(i	NUM
ejpam-3632	206	6	)	)	PUNCT
ejpam-3632	206	7	,	,	PUNCT
ejpam-3632	206	8	we	we	PRON
ejpam-3632	206	9	have	have	VERB
ejpam-3632	206	10	u	u	NOUN
ejpam-3632	206	11	⊆	⊆	NUM
ejpam-3632	206	12	rhlh(u	rhlh(u	NOUN
ejpam-3632	206	13	)	)	PUNCT
ejpam-3632	206	14	.	.	PUNCT
ejpam-3632	207	1	thus	thus	ADV
ejpam-3632	207	2	,	,	PUNCT
ejpam-3632	207	3	u	u	NOUN
ejpam-3632	207	4	=	=	SYM
ejpam-3632	207	5	rhlh(u	rhlh(u	VERB
ejpam-3632	207	6	)	)	PUNCT
ejpam-3632	207	7	∈	∈	PROPN
ejpam-3632	207	8	brl(h	brl(h	PROPN
ejpam-3632	207	9	)	)	PUNCT
ejpam-3632	207	10	,	,	PUNCT
ejpam-3632	207	11	it	it	PRON
ejpam-3632	207	12	shows	show	VERB
ejpam-3632	207	13	that	that	SCONJ
ejpam-3632	207	14	br(h	br(h	NOUN
ejpam-3632	207	15	)	)	PUNCT
ejpam-3632	207	16	⊆	⊆	NUM
ejpam-3632	207	17	brl(h	brl(h	NOUN
ejpam-3632	207	18	)	)	PUNCT
ejpam-3632	207	19	.	.	PUNCT
ejpam-3632	208	1	therefore	therefore	ADV
ejpam-3632	208	2	,	,	PUNCT
ejpam-3632	208	3	brl(h	brl(h	PROPN
ejpam-3632	208	4	)	)	PUNCT
ejpam-3632	208	5	=	=	SYM
ejpam-3632	208	6	br(h	br(h	NOUN
ejpam-3632	208	7	)	)	PUNCT
ejpam-3632	208	8	.	.	PUNCT
ejpam-3632	209	1	accordingly	accordingly	ADV
ejpam-3632	209	2	,	,	PUNCT
ejpam-3632	209	3	τrl(h	τrl(h	PROPN
ejpam-3632	209	4	)	)	PUNCT
ejpam-3632	209	5	=	=	PUNCT
ejpam-3632	209	6	τr(h	τr(h	NOUN
ejpam-3632	209	7	)	)	PUNCT
ejpam-3632	209	8	.	.	PUNCT
ejpam-3632	210	1	5	5	X
ejpam-3632	210	2	.	.	X
ejpam-3632	210	3	topology	topology	NOUN
ejpam-3632	210	4	induced	induce	VERB
ejpam-3632	210	5	by	by	ADP
ejpam-3632	210	6	lhrh	lhrh	NOUN
ejpam-3632	210	7	let	let	VERB
ejpam-3632	210	8	h	h	NOUN
ejpam-3632	210	9	be	be	AUX
ejpam-3632	210	10	any	any	DET
ejpam-3632	210	11	hyper	hyper	ADJ
ejpam-3632	210	12	bck	bck	NOUN
ejpam-3632	210	13	-	-	PUNCT
ejpam-3632	210	14	algebra	algebra	NOUN
ejpam-3632	210	15	with	with	ADP
ejpam-3632	210	16	h	h	PROPN
ejpam-3632	210	17	6=	6=	X
ejpam-3632	210	18	{	{	PUNCT
ejpam-3632	210	19	0	0	NUM
ejpam-3632	210	20	}	}	PUNCT
ejpam-3632	210	21	.	.	PUNCT
ejpam-3632	211	1	by	by	ADP
ejpam-3632	211	2	proposition	proposition	NOUN
ejpam-3632	211	3	2(iv	2(iv	NUM
ejpam-3632	211	4	)	)	PUNCT
ejpam-3632	211	5	,	,	PUNCT
ejpam-3632	211	6	lh(h	lh(h	X
ejpam-3632	211	7	)	)	PUNCT
ejpam-3632	211	8	=	=	PRON
ejpam-3632	211	9	{	{	PUNCT
ejpam-3632	211	10	0	0	NUM
ejpam-3632	211	11	}	}	PUNCT
ejpam-3632	211	12	.	.	PUNCT
ejpam-3632	212	1	by	by	ADP
ejpam-3632	212	2	definition	definition	NOUN
ejpam-3632	212	3	of	of	ADP
ejpam-3632	212	4	a	a	DET
ejpam-3632	212	5	closure	closure	NOUN
ejpam-3632	212	6	operator	operator	NOUN
ejpam-3632	212	7	,	,	PUNCT
ejpam-3632	212	8	we	we	PRON
ejpam-3632	212	9	obtain	obtain	VERB
ejpam-3632	212	10	the	the	DET
ejpam-3632	212	11	following	follow	VERB
ejpam-3632	212	12	remark	remark	NOUN
ejpam-3632	212	13	.	.	PUNCT
ejpam-3632	213	1	remark	remark	PROPN
ejpam-3632	213	2	2	2	NUM
ejpam-3632	213	3	.	.	PUNCT
ejpam-3632	214	1	lh	lh	PROPN
ejpam-3632	214	2	:	:	PUNCT
ejpam-3632	214	3	p(h)→p(h	p(h)→p(h	X
ejpam-3632	214	4	)	)	PUNCT
ejpam-3632	214	5	is	be	AUX
ejpam-3632	214	6	not	not	PART
ejpam-3632	214	7	a	a	DET
ejpam-3632	214	8	closure	closure	NOUN
ejpam-3632	214	9	operator	operator	NOUN
ejpam-3632	214	10	for	for	ADP
ejpam-3632	214	11	every	every	DET
ejpam-3632	214	12	hyper	hyper	ADJ
ejpam-3632	214	13	bck	bck	NOUN
ejpam-3632	214	14	-	-	PUNCT
ejpam-3632	214	15	algebra	algebra	NOUN
ejpam-3632	214	16	h	h	NOUN
ejpam-3632	214	17	6=	6=	X
ejpam-3632	214	18	{	{	PUNCT
ejpam-3632	214	19	0	0	NUM
ejpam-3632	214	20	}	}	PUNCT
ejpam-3632	214	21	.	.	PUNCT
ejpam-3632	215	1	theorem	theorem	VERB
ejpam-3632	215	2	7	7	NUM
ejpam-3632	215	3	.	.	PUNCT
ejpam-3632	216	1	let	let	VERB
ejpam-3632	216	2	a	a	DET
ejpam-3632	216	3	,	,	PUNCT
ejpam-3632	216	4	b	b	NOUN
ejpam-3632	216	5	be	be	AUX
ejpam-3632	216	6	subsets	subset	NOUN
ejpam-3632	216	7	of	of	ADP
ejpam-3632	216	8	a	a	DET
ejpam-3632	216	9	hyper	hyper	ADJ
ejpam-3632	216	10	bck	bck	NOUN
ejpam-3632	216	11	-	-	PUNCT
ejpam-3632	216	12	algebra	algebra	NOUN
ejpam-3632	216	13	h.	h.	NOUN
ejpam-3632	216	14	then	then	ADV
ejpam-3632	216	15	the	the	DET
ejpam-3632	216	16	following	follow	VERB
ejpam-3632	216	17	properties	property	NOUN
ejpam-3632	216	18	hold	hold	VERB
ejpam-3632	216	19	:	:	PUNCT
ejpam-3632	216	20	(	(	PUNCT
ejpam-3632	216	21	i	i	NOUN
ejpam-3632	216	22	)	)	PUNCT
ejpam-3632	216	23	a	a	DET
ejpam-3632	216	24	⊆	⊆	NUM
ejpam-3632	216	25	lhrh(a	lhrh(a	NOUN
ejpam-3632	216	26	)	)	PUNCT
ejpam-3632	216	27	.	.	PUNCT
ejpam-3632	217	1	(	(	PUNCT
ejpam-3632	217	2	ii	ii	NOUN
ejpam-3632	217	3	)	)	PUNCT
ejpam-3632	217	4	if	if	SCONJ
ejpam-3632	217	5	a	a	DET
ejpam-3632	217	6	⊆	⊆	NUM
ejpam-3632	217	7	b	b	NOUN
ejpam-3632	217	8	,	,	PUNCT
ejpam-3632	217	9	then	then	ADV
ejpam-3632	217	10	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	217	11	)	)	PUNCT
ejpam-3632	217	12	)	)	PUNCT
ejpam-3632	217	13	⊆	⊆	NUM
ejpam-3632	217	14	lh(rh(b	lh(rh(b	NOUN
ejpam-3632	217	15	)	)	PUNCT
ejpam-3632	217	16	)	)	PUNCT
ejpam-3632	217	17	.	.	PUNCT
ejpam-3632	218	1	(	(	PUNCT
ejpam-3632	218	2	iii	iii	X
ejpam-3632	218	3	)	)	PUNCT
ejpam-3632	219	1	[	[	X
ejpam-3632	219	2	lhrh	lhrh	X
ejpam-3632	219	3	]	]	X
ejpam-3632	219	4	2(a	2(a	NUM
ejpam-3632	219	5	)	)	PUNCT
ejpam-3632	219	6	=	=	NOUN
ejpam-3632	219	7	lhrh	lhrh	VERB
ejpam-3632	219	8	[	[	X
ejpam-3632	219	9	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	219	10	)	)	PUNCT
ejpam-3632	219	11	)	)	PUNCT
ejpam-3632	219	12	]	]	PUNCT
ejpam-3632	219	13	=	=	PUNCT
ejpam-3632	219	14	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	219	15	)	)	PUNCT
ejpam-3632	219	16	)	)	PUNCT
ejpam-3632	219	17	.	.	PUNCT
ejpam-3632	220	1	r.	r.	PROPN
ejpam-3632	220	2	patangan	patangan	PROPN
ejpam-3632	220	3	,	,	PUNCT
ejpam-3632	220	4	s.	s.	PROPN
ejpam-3632	220	5	canoy	canoy	PROPN
ejpam-3632	220	6	,	,	PUNCT
ejpam-3632	220	7	jr	jr	PROPN
ejpam-3632	220	8	.	.	PROPN
ejpam-3632	220	9	/	/	SYM
ejpam-3632	220	10	eur	eur	PROPN
ejpam-3632	220	11	.	.	PUNCT
ejpam-3632	221	1	j.	j.	PROPN
ejpam-3632	221	2	pure	pure	PROPN
ejpam-3632	221	3	appl	appl	PROPN
ejpam-3632	221	4	.	.	PROPN
ejpam-3632	221	5	math	math	PROPN
ejpam-3632	221	6	,	,	PUNCT
ejpam-3632	221	7	13	13	NUM
ejpam-3632	221	8	(	(	PUNCT
ejpam-3632	221	9	1	1	NUM
ejpam-3632	221	10	)	)	PUNCT
ejpam-3632	221	11	(	(	PUNCT
ejpam-3632	221	12	2020	2020	NUM
ejpam-3632	221	13	)	)	PUNCT
ejpam-3632	221	14	,	,	PUNCT
ejpam-3632	221	15	1	1	NUM
ejpam-3632	221	16	-	-	SYM
ejpam-3632	221	17	8	8	NUM
ejpam-3632	221	18	6	6	NUM
ejpam-3632	221	19	proof	proof	NOUN
ejpam-3632	221	20	.	.	PUNCT
ejpam-3632	222	1	(	(	PUNCT
ejpam-3632	222	2	i	i	NOUN
ejpam-3632	222	3	)	)	PUNCT
ejpam-3632	222	4	let	let	VERB
ejpam-3632	222	5	a	a	DET
ejpam-3632	222	6	⊆	⊆	NUM
ejpam-3632	222	7	h	h	NOUN
ejpam-3632	222	8	and	and	CCONJ
ejpam-3632	222	9	x	x	PUNCT
ejpam-3632	222	10	∈	∈	NOUN
ejpam-3632	222	11	rh(a	rh(a	NUM
ejpam-3632	222	12	)	)	PUNCT
ejpam-3632	222	13	.	.	PUNCT
ejpam-3632	223	1	then	then	ADV
ejpam-3632	223	2	a	a	DET
ejpam-3632	223	3	�	�	PROPN
ejpam-3632	223	4	x	x	PUNCT
ejpam-3632	223	5	for	for	ADP
ejpam-3632	223	6	all	all	DET
ejpam-3632	223	7	a	a	DET
ejpam-3632	223	8	∈	∈	PROPN
ejpam-3632	223	9	a.	a.	NOUN
ejpam-3632	223	10	select	select	NOUN
ejpam-3632	223	11	b	b	PROPN
ejpam-3632	223	12	∈	∈	PROPN
ejpam-3632	223	13	a.	a.	NOUN
ejpam-3632	223	14	then	then	ADV
ejpam-3632	223	15	b	b	PROPN
ejpam-3632	223	16	�	�	PROPN
ejpam-3632	223	17	x	x	PUNCT
ejpam-3632	223	18	for	for	ADP
ejpam-3632	223	19	every	every	DET
ejpam-3632	223	20	x	x	SYM
ejpam-3632	223	21	∈	∈	PROPN
ejpam-3632	223	22	rh(a	rh(a	NOUN
ejpam-3632	223	23	)	)	PUNCT
ejpam-3632	223	24	.	.	PUNCT
ejpam-3632	224	1	this	this	PRON
ejpam-3632	224	2	means	mean	VERB
ejpam-3632	224	3	that	that	SCONJ
ejpam-3632	224	4	b	b	PROPN
ejpam-3632	224	5	∈	∈	PROPN
ejpam-3632	224	6	lh(x	lh(x	PUNCT
ejpam-3632	224	7	)	)	PUNCT
ejpam-3632	224	8	for	for	ADP
ejpam-3632	224	9	every	every	DET
ejpam-3632	224	10	x	x	SYM
ejpam-3632	224	11	∈	∈	PROPN
ejpam-3632	224	12	rh(a	rh(a	NOUN
ejpam-3632	224	13	)	)	PUNCT
ejpam-3632	224	14	.	.	PUNCT
ejpam-3632	225	1	hence	hence	ADV
ejpam-3632	225	2	,	,	PUNCT
ejpam-3632	225	3	b	b	PROPN
ejpam-3632	225	4	∈	∈	PROPN
ejpam-3632	225	5	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	225	6	)	)	PUNCT
ejpam-3632	225	7	)	)	PUNCT
ejpam-3632	225	8	.	.	PUNCT
ejpam-3632	226	1	therefore	therefore	ADV
ejpam-3632	226	2	,	,	PUNCT
ejpam-3632	226	3	a	a	DET
ejpam-3632	226	4	⊆	⊆	NUM
ejpam-3632	226	5	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	226	6	)	)	PUNCT
ejpam-3632	226	7	)	)	PUNCT
ejpam-3632	226	8	.	.	PUNCT
ejpam-3632	227	1	(	(	PUNCT
ejpam-3632	227	2	ii	ii	NOUN
ejpam-3632	227	3	)	)	PUNCT
ejpam-3632	227	4	let	let	VERB
ejpam-3632	227	5	a	a	DET
ejpam-3632	227	6	,	,	PUNCT
ejpam-3632	227	7	b	b	NOUN
ejpam-3632	227	8	⊆	⊆	NUM
ejpam-3632	227	9	h	h	NOUN
ejpam-3632	227	10	such	such	ADJ
ejpam-3632	227	11	that	that	SCONJ
ejpam-3632	227	12	a	a	DET
ejpam-3632	227	13	⊆	⊆	NUM
ejpam-3632	227	14	b.	b.	NOUN
ejpam-3632	227	15	by	by	ADP
ejpam-3632	227	16	proposition	proposition	NOUN
ejpam-3632	227	17	1(iv	1(iv	NUM
ejpam-3632	227	18	)	)	PUNCT
ejpam-3632	227	19	,	,	PUNCT
ejpam-3632	227	20	rh(b	rh(b	PUNCT
ejpam-3632	227	21	)	)	PUNCT
ejpam-3632	227	22	⊆	⊆	NUM
ejpam-3632	227	23	rh(a	rh(a	NUM
ejpam-3632	227	24	)	)	PUNCT
ejpam-3632	227	25	.	.	PUNCT
ejpam-3632	228	1	thus	thus	ADV
ejpam-3632	228	2	,	,	PUNCT
ejpam-3632	228	3	by	by	ADP
ejpam-3632	228	4	proposition	proposition	NOUN
ejpam-3632	228	5	2(ii	2(ii	NUM
ejpam-3632	228	6	)	)	PUNCT
ejpam-3632	228	7	,	,	PUNCT
ejpam-3632	228	8	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	228	9	)	)	PUNCT
ejpam-3632	228	10	)	)	PUNCT
ejpam-3632	229	1	⊆	⊆	NUM
ejpam-3632	229	2	lh(rh(b	lh(rh(b	NOUN
ejpam-3632	229	3	)	)	PUNCT
ejpam-3632	229	4	)	)	PUNCT
ejpam-3632	229	5	.	.	PUNCT
ejpam-3632	230	1	(	(	PUNCT
ejpam-3632	230	2	iii	iii	X
ejpam-3632	230	3	)	)	PUNCT
ejpam-3632	230	4	by	by	ADP
ejpam-3632	230	5	(	(	PUNCT
ejpam-3632	230	6	i	i	NOUN
ejpam-3632	230	7	)	)	PUNCT
ejpam-3632	230	8	and	and	CCONJ
ejpam-3632	230	9	(	(	PUNCT
ejpam-3632	230	10	ii	ii	NOUN
ejpam-3632	230	11	)	)	PUNCT
ejpam-3632	230	12	,	,	PUNCT
ejpam-3632	230	13	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	230	14	)	)	PUNCT
ejpam-3632	230	15	)	)	PUNCT
ejpam-3632	231	1	⊆	⊆	NUM
ejpam-3632	231	2	[	[	X
ejpam-3632	231	3	lhrh	lhrh	X
ejpam-3632	231	4	]	]	X
ejpam-3632	231	5	2(a	2(a	NUM
ejpam-3632	231	6	)	)	PUNCT
ejpam-3632	231	7	.	.	PUNCT
ejpam-3632	232	1	we	we	PRON
ejpam-3632	232	2	are	be	AUX
ejpam-3632	232	3	left	leave	VERB
ejpam-3632	232	4	to	to	PART
ejpam-3632	232	5	prove	prove	VERB
ejpam-3632	232	6	that	that	SCONJ
ejpam-3632	232	7	[	[	X
ejpam-3632	232	8	lhrh	lhrh	X
ejpam-3632	232	9	]	]	X
ejpam-3632	232	10	2(a	2(a	NUM
ejpam-3632	232	11	)	)	PUNCT
ejpam-3632	232	12	⊆	⊆	NUM
ejpam-3632	232	13	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	232	14	)	)	PUNCT
ejpam-3632	232	15	)	)	PUNCT
ejpam-3632	232	16	.	.	PUNCT
ejpam-3632	233	1	first	first	ADV
ejpam-3632	233	2	,	,	PUNCT
ejpam-3632	233	3	we	we	PRON
ejpam-3632	233	4	need	need	VERB
ejpam-3632	233	5	to	to	PART
ejpam-3632	233	6	show	show	VERB
ejpam-3632	233	7	that	that	PRON
ejpam-3632	233	8	rh(a	rh(a	NOUN
ejpam-3632	233	9	)	)	PUNCT
ejpam-3632	233	10	⊆	⊆	NUM
ejpam-3632	233	11	rh	rh	PROPN
ejpam-3632	233	12	[	[	X
ejpam-3632	233	13	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	233	14	)	)	PUNCT
ejpam-3632	233	15	)	)	PUNCT
ejpam-3632	233	16	]	]	PUNCT
ejpam-3632	233	17	.	.	PUNCT
ejpam-3632	234	1	let	let	VERB
ejpam-3632	234	2	x	x	PUNCT
ejpam-3632	234	3	∈	∈	PROPN
ejpam-3632	234	4	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	234	5	)	)	PUNCT
ejpam-3632	234	6	)	)	PUNCT
ejpam-3632	234	7	.	.	PUNCT
ejpam-3632	235	1	then	then	ADV
ejpam-3632	235	2	x	x	X
ejpam-3632	235	3	�	�	PROPN
ejpam-3632	235	4	y	y	PROPN
ejpam-3632	235	5	for	for	ADP
ejpam-3632	235	6	all	all	DET
ejpam-3632	235	7	y	y	PROPN
ejpam-3632	235	8	∈	∈	PROPN
ejpam-3632	235	9	rh(a	rh(a	NOUN
ejpam-3632	235	10	)	)	PUNCT
ejpam-3632	235	11	.	.	PUNCT
ejpam-3632	236	1	take	take	VERB
ejpam-3632	236	2	z	z	NOUN
ejpam-3632	236	3	∈	∈	NOUN
ejpam-3632	236	4	rh(a	rh(a	NOUN
ejpam-3632	236	5	)	)	PUNCT
ejpam-3632	236	6	.	.	PUNCT
ejpam-3632	237	1	it	it	PRON
ejpam-3632	237	2	follows	follow	VERB
ejpam-3632	237	3	that	that	SCONJ
ejpam-3632	237	4	x	x	PROPN
ejpam-3632	237	5	�	�	PROPN
ejpam-3632	237	6	z	z	PROPN
ejpam-3632	237	7	for	for	ADP
ejpam-3632	237	8	every	every	DET
ejpam-3632	237	9	x	x	PROPN
ejpam-3632	237	10	∈	∈	PROPN
ejpam-3632	237	11	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	237	12	)	)	PUNCT
ejpam-3632	237	13	)	)	PUNCT
ejpam-3632	237	14	.	.	PUNCT
ejpam-3632	238	1	this	this	PRON
ejpam-3632	238	2	implies	imply	VERB
ejpam-3632	238	3	that	that	SCONJ
ejpam-3632	238	4	z	z	PROPN
ejpam-3632	238	5	∈	∈	PROPN
ejpam-3632	238	6	rh(x	rh(x	NUM
ejpam-3632	238	7	)	)	PUNCT
ejpam-3632	238	8	for	for	ADP
ejpam-3632	238	9	each	each	DET
ejpam-3632	238	10	x	x	SYM
ejpam-3632	238	11	∈	∈	PROPN
ejpam-3632	238	12	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	238	13	)	)	PUNCT
ejpam-3632	238	14	)	)	PUNCT
ejpam-3632	238	15	.	.	PUNCT
ejpam-3632	239	1	hence	hence	ADV
ejpam-3632	239	2	,	,	PUNCT
ejpam-3632	239	3	z	z	PROPN
ejpam-3632	239	4	∈	∈	PROPN
ejpam-3632	239	5	rh	rh	PROPN
ejpam-3632	239	6	[	[	X
ejpam-3632	239	7	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	239	8	)	)	PUNCT
ejpam-3632	239	9	)	)	PUNCT
ejpam-3632	239	10	]	]	PUNCT
ejpam-3632	239	11	.	.	PUNCT
ejpam-3632	240	1	this	this	PRON
ejpam-3632	240	2	shows	show	VERB
ejpam-3632	240	3	that	that	SCONJ
ejpam-3632	240	4	rh(a	rh(a	NOUN
ejpam-3632	240	5	)	)	PUNCT
ejpam-3632	240	6	⊆	⊆	NUM
ejpam-3632	240	7	rh	rh	PROPN
ejpam-3632	240	8	[	[	X
ejpam-3632	240	9	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	240	10	)	)	PUNCT
ejpam-3632	240	11	)	)	PUNCT
ejpam-3632	240	12	]	]	PUNCT
ejpam-3632	240	13	.	.	PUNCT
ejpam-3632	241	1	thus	thus	ADV
ejpam-3632	241	2	,	,	PUNCT
ejpam-3632	241	3	by	by	ADP
ejpam-3632	241	4	proposition	proposition	NOUN
ejpam-3632	241	5	2(ii	2(ii	NUM
ejpam-3632	241	6	)	)	PUNCT
ejpam-3632	241	7	,	,	PUNCT
ejpam-3632	241	8	lhrh	lhrh	VERB
ejpam-3632	241	9	[	[	X
ejpam-3632	241	10	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	241	11	)	)	PUNCT
ejpam-3632	241	12	)	)	PUNCT
ejpam-3632	241	13	]	]	PUNCT
ejpam-3632	242	1	⊆	⊆	NUM
ejpam-3632	242	2	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	242	3	)	)	PUNCT
ejpam-3632	242	4	)	)	PUNCT
ejpam-3632	242	5	.	.	PUNCT
ejpam-3632	243	1	by	by	ADP
ejpam-3632	243	2	combining	combine	VERB
ejpam-3632	243	3	the	the	DET
ejpam-3632	243	4	two	two	NUM
ejpam-3632	243	5	set	set	ADJ
ejpam-3632	243	6	inclusions	inclusion	NOUN
ejpam-3632	243	7	,	,	PUNCT
ejpam-3632	243	8	we	we	PRON
ejpam-3632	243	9	have	have	AUX
ejpam-3632	243	10	lhrh	lhrh	NOUN
ejpam-3632	243	11	[	[	X
ejpam-3632	243	12	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	243	13	)	)	PUNCT
ejpam-3632	243	14	)	)	PUNCT
ejpam-3632	243	15	]	]	PUNCT
ejpam-3632	244	1	=	=	PUNCT
ejpam-3632	244	2	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	244	3	)	)	PUNCT
ejpam-3632	244	4	)	)	PUNCT
ejpam-3632	244	5	.	.	PUNCT
ejpam-3632	245	1	theorem	theorem	ADJ
ejpam-3632	245	2	8	8	NUM
ejpam-3632	245	3	.	.	PUNCT
ejpam-3632	246	1	let	let	VERB
ejpam-3632	246	2	h	h	PRON
ejpam-3632	246	3	be	be	AUX
ejpam-3632	246	4	a	a	DET
ejpam-3632	246	5	hyper	hyper	ADJ
ejpam-3632	246	6	bck	bck	NOUN
ejpam-3632	246	7	-	-	PUNCT
ejpam-3632	246	8	algebra	algebra	NOUN
ejpam-3632	246	9	.	.	PUNCT
ejpam-3632	247	1	the	the	DET
ejpam-3632	247	2	function	function	NOUN
ejpam-3632	247	3	lhrh	lhrh	VERB
ejpam-3632	247	4	:	:	PUNCT
ejpam-3632	248	1	p(h)→p(h	p(h)→p(h	X
ejpam-3632	248	2	)	)	PUNCT
ejpam-3632	248	3	is	be	AUX
ejpam-3632	248	4	a	a	DET
ejpam-3632	248	5	closure	closure	NOUN
ejpam-3632	248	6	operator	operator	NOUN
ejpam-3632	248	7	on	on	ADP
ejpam-3632	248	8	h.	h.	PROPN
ejpam-3632	248	9	proof	proof	NOUN
ejpam-3632	248	10	.	.	PUNCT
ejpam-3632	249	1	since	since	SCONJ
ejpam-3632	249	2	h	h	NOUN
ejpam-3632	249	3	is	be	AUX
ejpam-3632	249	4	a	a	DET
ejpam-3632	249	5	hyper	hyper	ADJ
ejpam-3632	249	6	bck	bck	NOUN
ejpam-3632	249	7	-	-	PUNCT
ejpam-3632	249	8	algebra	algebra	NOUN
ejpam-3632	249	9	,	,	PUNCT
ejpam-3632	249	10	h	h	PROPN
ejpam-3632	249	11	6=	6=	NOUN
ejpam-3632	249	12	∅.	∅.	VERB
ejpam-3632	249	13	then	then	ADV
ejpam-3632	249	14	by	by	ADP
ejpam-3632	249	15	the	the	DET
ejpam-3632	249	16	definition	definition	NOUN
ejpam-3632	249	17	of	of	ADP
ejpam-3632	249	18	a	a	DET
ejpam-3632	249	19	closure	closure	NOUN
ejpam-3632	249	20	operator	operator	NOUN
ejpam-3632	249	21	and	and	CCONJ
ejpam-3632	249	22	theorem	theorem	VERB
ejpam-3632	249	23	7	7	NUM
ejpam-3632	249	24	,	,	PUNCT
ejpam-3632	249	25	lhrh	lhrh	VERB
ejpam-3632	249	26	is	be	AUX
ejpam-3632	249	27	a	a	DET
ejpam-3632	249	28	closure	closure	NOUN
ejpam-3632	249	29	operator	operator	NOUN
ejpam-3632	249	30	.	.	PUNCT
ejpam-3632	250	1	theorem	theorem	VERB
ejpam-3632	250	2	9	9	NUM
ejpam-3632	250	3	.	.	PUNCT
ejpam-3632	251	1	the	the	DET
ejpam-3632	251	2	family	family	NOUN
ejpam-3632	251	3	blr(h	blr(h	PROPN
ejpam-3632	251	4	)	)	PUNCT
ejpam-3632	252	1	=	=	PRON
ejpam-3632	252	2	{	{	PUNCT
ejpam-3632	252	3	a	a	DET
ejpam-3632	252	4	:	:	PUNCT
ejpam-3632	252	5	lhrh(a	lhrh(a	NOUN
ejpam-3632	252	6	)	)	PUNCT
ejpam-3632	252	7	=	=	SYM
ejpam-3632	252	8	a	a	PRON
ejpam-3632	252	9	,	,	PUNCT
ejpam-3632	252	10	∅	∅	NOUN
ejpam-3632	252	11	6=	6=	ADP
ejpam-3632	252	12	a	a	DET
ejpam-3632	252	13	⊆	⊆	NUM
ejpam-3632	252	14	h	h	NOUN
ejpam-3632	252	15	}	}	PUNCT
ejpam-3632	252	16	is	be	AUX
ejpam-3632	252	17	a	a	DET
ejpam-3632	252	18	basis	basis	NOUN
ejpam-3632	252	19	for	for	ADP
ejpam-3632	252	20	some	some	DET
ejpam-3632	252	21	topology	topology	NOUN
ejpam-3632	252	22	on	on	ADP
ejpam-3632	252	23	h.	h.	PROPN
ejpam-3632	252	24	proof	proof	NOUN
ejpam-3632	252	25	.	.	PUNCT
ejpam-3632	253	1	since	since	SCONJ
ejpam-3632	253	2	lhrh(h	lhrh(h	PROPN
ejpam-3632	253	3	)	)	PUNCT
ejpam-3632	253	4	⊆	⊆	NUM
ejpam-3632	253	5	h	h	NOUN
ejpam-3632	253	6	and	and	CCONJ
ejpam-3632	253	7	by	by	ADP
ejpam-3632	253	8	theorem	theorem	NOUN
ejpam-3632	253	9	7(i	7(i	NUM
ejpam-3632	253	10	)	)	PUNCT
ejpam-3632	253	11	,	,	PUNCT
ejpam-3632	253	12	we	we	PRON
ejpam-3632	253	13	have	have	AUX
ejpam-3632	253	14	lhrh(h	lhrh(h	VERB
ejpam-3632	253	15	)	)	PUNCT
ejpam-3632	254	1	=	=	SYM
ejpam-3632	254	2	h	h	NOUN
ejpam-3632	254	3	and	and	CCONJ
ejpam-3632	254	4	so	so	ADV
ejpam-3632	254	5	,	,	PUNCT
ejpam-3632	254	6	h	h	PROPN
ejpam-3632	254	7	∈	∈	PROPN
ejpam-3632	254	8	blr(h	blr(h	PROPN
ejpam-3632	254	9	)	)	PUNCT
ejpam-3632	254	10	.	.	PUNCT
ejpam-3632	255	1	thus	thus	ADV
ejpam-3632	255	2	,	,	PUNCT
ejpam-3632	255	3	blr(h	blr(h	PROPN
ejpam-3632	255	4	)	)	PUNCT
ejpam-3632	255	5	6=	6=	ADP
ejpam-3632	255	6	∅.	∅.	ADP
ejpam-3632	255	7	next	next	ADV
ejpam-3632	255	8	,	,	PUNCT
ejpam-3632	255	9	let	let	VERB
ejpam-3632	255	10	a	a	DET
ejpam-3632	255	11	,	,	PUNCT
ejpam-3632	255	12	b	b	PROPN
ejpam-3632	255	13	∈	∈	PROPN
ejpam-3632	255	14	blr(h	blr(h	PROPN
ejpam-3632	255	15	)	)	PUNCT
ejpam-3632	255	16	and	and	CCONJ
ejpam-3632	255	17	x	x	PUNCT
ejpam-3632	255	18	∈	∈	PROPN
ejpam-3632	255	19	a	a	DET
ejpam-3632	255	20	∩	∩	ADJ
ejpam-3632	255	21	b.	b.	NOUN
ejpam-3632	255	22	then	then	ADV
ejpam-3632	255	23	by	by	ADP
ejpam-3632	255	24	theorem	theorem	NOUN
ejpam-3632	255	25	7(i	7(i	NUM
ejpam-3632	255	26	)	)	PUNCT
ejpam-3632	255	27	,	,	PUNCT
ejpam-3632	255	28	we	we	PRON
ejpam-3632	255	29	have	have	VERB
ejpam-3632	255	30	a	a	DET
ejpam-3632	255	31	∩	∩	ADJ
ejpam-3632	255	32	b	b	NOUN
ejpam-3632	255	33	⊆	⊆	NUM
ejpam-3632	255	34	lhrh(a	lhrh(a	NOUN
ejpam-3632	255	35	∩	∩	ADJ
ejpam-3632	255	36	b	b	NOUN
ejpam-3632	255	37	)	)	PUNCT
ejpam-3632	255	38	.	.	PUNCT
ejpam-3632	256	1	also	also	ADV
ejpam-3632	256	2	,	,	PUNCT
ejpam-3632	256	3	since	since	SCONJ
ejpam-3632	256	4	a	a	DET
ejpam-3632	256	5	∩	∩	NOUN
ejpam-3632	256	6	b	b	ADP
ejpam-3632	256	7	⊆	⊆	NUM
ejpam-3632	256	8	a	a	PRON
ejpam-3632	256	9	and	and	CCONJ
ejpam-3632	256	10	a	a	DET
ejpam-3632	256	11	∩	∩	ADJ
ejpam-3632	256	12	b	b	PROPN
ejpam-3632	256	13	⊆	⊆	NUM
ejpam-3632	256	14	b	b	NOUN
ejpam-3632	256	15	,	,	PUNCT
ejpam-3632	256	16	lhrh(a	lhrh(a	NOUN
ejpam-3632	256	17	∩	∩	ADJ
ejpam-3632	256	18	b	b	NOUN
ejpam-3632	256	19	)	)	PUNCT
ejpam-3632	256	20	⊆	⊆	NUM
ejpam-3632	256	21	lhrh(a	lhrh(a	NOUN
ejpam-3632	256	22	)	)	PUNCT
ejpam-3632	256	23	and	and	CCONJ
ejpam-3632	256	24	lhrh(a	lhrh(a	NOUN
ejpam-3632	256	25	∩	∩	ADJ
ejpam-3632	256	26	b	b	X
ejpam-3632	256	27	)	)	PUNCT
ejpam-3632	256	28	⊆	⊆	NUM
ejpam-3632	256	29	lhrh(b	lhrh(b	NOUN
ejpam-3632	256	30	)	)	PUNCT
ejpam-3632	256	31	by	by	ADP
ejpam-3632	256	32	theorem	theorem	ADJ
ejpam-3632	256	33	7(ii	7(ii	PROPN
ejpam-3632	256	34	)	)	PUNCT
ejpam-3632	256	35	.	.	PUNCT
ejpam-3632	257	1	since	since	SCONJ
ejpam-3632	257	2	a	a	DET
ejpam-3632	257	3	,	,	PUNCT
ejpam-3632	257	4	b	b	PROPN
ejpam-3632	257	5	∈	∈	PROPN
ejpam-3632	257	6	blr(h	blr(h	PROPN
ejpam-3632	257	7	)	)	PUNCT
ejpam-3632	257	8	,	,	PUNCT
ejpam-3632	257	9	we	we	PRON
ejpam-3632	257	10	have	have	VERB
ejpam-3632	257	11	lhrh(a	lhrh(a	NOUN
ejpam-3632	257	12	)	)	PUNCT
ejpam-3632	257	13	=	=	PUNCT
ejpam-3632	258	1	a	a	PRON
ejpam-3632	258	2	and	and	CCONJ
ejpam-3632	258	3	lhrh(b	lhrh(b	NOUN
ejpam-3632	258	4	)	)	PUNCT
ejpam-3632	259	1	=	=	SYM
ejpam-3632	259	2	b.	b.	PROPN
ejpam-3632	259	3	hence	hence	ADV
ejpam-3632	259	4	,	,	PUNCT
ejpam-3632	259	5	lhrh(a∩b	lhrh(a∩b	PROPN
ejpam-3632	259	6	)	)	PUNCT
ejpam-3632	259	7	⊆	⊆	NUM
ejpam-3632	259	8	a∩b	a∩b	PROPN
ejpam-3632	259	9	.	.	PUNCT
ejpam-3632	260	1	accordingly	accordingly	ADV
ejpam-3632	260	2	,	,	PUNCT
ejpam-3632	260	3	lhrh(a∩b	lhrh(a∩b	PROPN
ejpam-3632	260	4	)	)	PUNCT
ejpam-3632	261	1	=	=	PUNCT
ejpam-3632	261	2	a∩b	a∩b	PROPN
ejpam-3632	261	3	∈	∈	PROPN
ejpam-3632	261	4	blr(h	blr(h	PROPN
ejpam-3632	261	5	)	)	PUNCT
ejpam-3632	261	6	.	.	PUNCT
ejpam-3632	262	1	this	this	PRON
ejpam-3632	262	2	shows	show	VERB
ejpam-3632	262	3	that	that	SCONJ
ejpam-3632	262	4	blr(h	blr(h	PROPN
ejpam-3632	262	5	)	)	PUNCT
ejpam-3632	262	6	is	be	AUX
ejpam-3632	262	7	a	a	DET
ejpam-3632	262	8	basis	basis	NOUN
ejpam-3632	262	9	for	for	ADP
ejpam-3632	262	10	some	some	DET
ejpam-3632	262	11	topology	topology	NOUN
ejpam-3632	262	12	on	on	ADP
ejpam-3632	262	13	h.	h.	PROPN
ejpam-3632	262	14	denote	denote	NOUN
ejpam-3632	262	15	by	by	ADP
ejpam-3632	262	16	τlr(h	τlr(h	PROPN
ejpam-3632	262	17	)	)	PUNCT
ejpam-3632	262	18	the	the	DET
ejpam-3632	262	19	topology	topology	NOUN
ejpam-3632	262	20	generated	generate	VERB
ejpam-3632	262	21	by	by	ADP
ejpam-3632	262	22	blr(h	blr(h	PROPN
ejpam-3632	262	23	)	)	PUNCT
ejpam-3632	262	24	.	.	PUNCT
ejpam-3632	263	1	example	example	NOUN
ejpam-3632	264	1	3	3	X
ejpam-3632	264	2	.	.	X
ejpam-3632	264	3	consider	consider	VERB
ejpam-3632	264	4	the	the	DET
ejpam-3632	264	5	hyper	hyper	ADJ
ejpam-3632	264	6	bck	bck	NOUN
ejpam-3632	264	7	-	-	PUNCT
ejpam-3632	264	8	algebra	algebra	NOUN
ejpam-3632	264	9	(	(	PUNCT
ejpam-3632	264	10	h	h	NOUN
ejpam-3632	264	11	,	,	PUNCT
ejpam-3632	264	12	∗	∗	NOUN
ejpam-3632	264	13	,	,	PUNCT
ejpam-3632	264	14	0	0	NUM
ejpam-3632	264	15	)	)	PUNCT
ejpam-3632	264	16	in	in	ADP
ejpam-3632	264	17	example	example	NOUN
ejpam-3632	265	1	1	1	X
ejpam-3632	265	2	.	.	PUNCT
ejpam-3632	266	1	let	let	VERB
ejpam-3632	266	2	n	n	PRON
ejpam-3632	266	3	∈	∈	PROPN
ejpam-3632	266	4	h.	h.	NOUN
ejpam-3632	266	5	then	then	ADV
ejpam-3632	266	6	lhrh(n	lhrh(n	PROPN
ejpam-3632	266	7	)	)	PUNCT
ejpam-3632	267	1	=	=	PUNCT
ejpam-3632	267	2	lh({n	lh({n	X
ejpam-3632	267	3	,	,	PUNCT
ejpam-3632	267	4	n	n	PROPN
ejpam-3632	267	5	+	+	NUM
ejpam-3632	267	6	1	1	NUM
ejpam-3632	267	7	,	,	PUNCT
ejpam-3632	267	8	n	n	PROPN
ejpam-3632	267	9	+	+	NOUN
ejpam-3632	267	10	2	2	NUM
ejpam-3632	267	11	,	,	PUNCT
ejpam-3632	267	12	.	.	PUNCT
ejpam-3632	267	13	.	.	PUNCT
ejpam-3632	267	14	.	.	PUNCT
ejpam-3632	267	15	}	}	PUNCT
ejpam-3632	267	16	)	)	PUNCT
ejpam-3632	268	1	=	=	PRON
ejpam-3632	268	2	{	{	PUNCT
ejpam-3632	268	3	0	0	NUM
ejpam-3632	268	4	,	,	PUNCT
ejpam-3632	268	5	1	1	NUM
ejpam-3632	268	6	,	,	PUNCT
ejpam-3632	268	7	2	2	NUM
ejpam-3632	268	8	,	,	PUNCT
ejpam-3632	268	9	.	.	PUNCT
ejpam-3632	268	10	.	.	PUNCT
ejpam-3632	269	1	.	.	PUNCT
ejpam-3632	269	2	,	,	PUNCT
ejpam-3632	270	1	n	n	CCONJ
ejpam-3632	270	2	}	}	PUNCT
ejpam-3632	270	3	6=	6=	NUM
ejpam-3632	270	4	{	{	PUNCT
ejpam-3632	270	5	n	n	CCONJ
ejpam-3632	270	6	}	}	PUNCT
ejpam-3632	270	7	.	.	PUNCT
ejpam-3632	271	1	hence	hence	ADV
ejpam-3632	271	2	,	,	PUNCT
ejpam-3632	271	3	for	for	ADP
ejpam-3632	271	4	any	any	DET
ejpam-3632	271	5	m	m	PROPN
ejpam-3632	271	6	∈	∈	PROPN
ejpam-3632	271	7	h	h	NOUN
ejpam-3632	271	8	,	,	PUNCT
ejpam-3632	271	9	{	{	PUNCT
ejpam-3632	271	10	m	m	NOUN
ejpam-3632	271	11	}	}	PUNCT
ejpam-3632	271	12	/∈	/∈	PUNCT
ejpam-3632	271	13	blr(h	blr(h	PROPN
ejpam-3632	271	14	)	)	PUNCT
ejpam-3632	271	15	.	.	PUNCT
ejpam-3632	272	1	let	let	VERB
ejpam-3632	272	2	a	a	DET
ejpam-3632	272	3	be	be	AUX
ejpam-3632	272	4	any	any	DET
ejpam-3632	272	5	infinite	infinite	ADJ
ejpam-3632	272	6	subset	subset	NOUN
ejpam-3632	272	7	of	of	ADP
ejpam-3632	272	8	h.	h.	PROPN
ejpam-3632	272	9	then	then	ADV
ejpam-3632	272	10	lhrh(a	lhrh(a	PROPN
ejpam-3632	272	11	)	)	PUNCT
ejpam-3632	272	12	=	=	PUNCT
ejpam-3632	272	13	lh(∅	lh(∅	PROPN
ejpam-3632	272	14	)	)	PUNCT
ejpam-3632	273	1	=	=	SYM
ejpam-3632	273	2	h	h	PROPN
ejpam-3632	273	3	6=	6=	NOUN
ejpam-3632	273	4	a.	a.	NOUN
ejpam-3632	273	5	it	it	PRON
ejpam-3632	273	6	follows	follow	VERB
ejpam-3632	273	7	that	that	SCONJ
ejpam-3632	273	8	a	a	DET
ejpam-3632	273	9	/∈	/∈	SYM
ejpam-3632	273	10	blr(h	blr(h	NOUN
ejpam-3632	273	11	)	)	PUNCT
ejpam-3632	273	12	.	.	PUNCT
ejpam-3632	274	1	now	now	ADV
ejpam-3632	274	2	,	,	PUNCT
ejpam-3632	274	3	suppose	suppose	VERB
ejpam-3632	274	4	that	that	SCONJ
ejpam-3632	274	5	a	a	PRON
ejpam-3632	274	6	is	be	AUX
ejpam-3632	274	7	any	any	DET
ejpam-3632	274	8	finite	finite	ADJ
ejpam-3632	274	9	set	set	NOUN
ejpam-3632	274	10	of	of	ADP
ejpam-3632	274	11	h	h	NOUN
ejpam-3632	274	12	such	such	ADJ
ejpam-3632	274	13	that	that	SCONJ
ejpam-3632	274	14	a	a	PRON
ejpam-3632	274	15	=	=	X
ejpam-3632	274	16	{	{	PUNCT
ejpam-3632	274	17	0	0	NUM
ejpam-3632	274	18	,	,	PUNCT
ejpam-3632	274	19	1	1	NUM
ejpam-3632	274	20	,	,	PUNCT
ejpam-3632	274	21	2	2	NUM
ejpam-3632	274	22	,	,	PUNCT
ejpam-3632	274	23	.	.	PUNCT
ejpam-3632	274	24	.	.	PUNCT
ejpam-3632	274	25	.	.	PUNCT
ejpam-3632	275	1	,	,	PUNCT
ejpam-3632	275	2	r	r	NOUN
ejpam-3632	275	3	}	}	PUNCT
ejpam-3632	275	4	.	.	PUNCT
ejpam-3632	276	1	then	then	ADV
ejpam-3632	276	2	lhrh(a	lhrh(a	NOUN
ejpam-3632	276	3	)	)	PUNCT
ejpam-3632	276	4	=	=	SYM
ejpam-3632	277	1	lh({r	lh({r	NOUN
ejpam-3632	277	2	,	,	PUNCT
ejpam-3632	277	3	r	r	NOUN
ejpam-3632	277	4	+	+	NOUN
ejpam-3632	277	5	1	1	NUM
ejpam-3632	277	6	,	,	PUNCT
ejpam-3632	277	7	r	r	NOUN
ejpam-3632	277	8	+	+	PROPN
ejpam-3632	277	9	2	2	NUM
ejpam-3632	277	10	,	,	PUNCT
ejpam-3632	277	11	.	.	PUNCT
ejpam-3632	277	12	.	.	PUNCT
ejpam-3632	277	13	.	.	PUNCT
ejpam-3632	277	14	}	}	PUNCT
ejpam-3632	277	15	)	)	PUNCT
ejpam-3632	278	1	=	=	PRON
ejpam-3632	278	2	{	{	PUNCT
ejpam-3632	278	3	0	0	NUM
ejpam-3632	278	4	,	,	PUNCT
ejpam-3632	278	5	1	1	NUM
ejpam-3632	278	6	,	,	PUNCT
ejpam-3632	278	7	2	2	NUM
ejpam-3632	278	8	,	,	PUNCT
ejpam-3632	278	9	.	.	PUNCT
ejpam-3632	278	10	.	.	PUNCT
ejpam-3632	279	1	.	.	PUNCT
ejpam-3632	280	1	,	,	PUNCT
ejpam-3632	280	2	r	r	X
ejpam-3632	280	3	}	}	PUNCT
ejpam-3632	280	4	=	=	PUNCT
ejpam-3632	280	5	a.	a.	NOUN
ejpam-3632	280	6	thus	thus	ADV
ejpam-3632	280	7	,	,	PUNCT
ejpam-3632	280	8	{	{	PUNCT
ejpam-3632	280	9	0	0	NUM
ejpam-3632	280	10	,	,	PUNCT
ejpam-3632	280	11	1	1	NUM
ejpam-3632	280	12	,	,	PUNCT
ejpam-3632	280	13	2	2	NUM
ejpam-3632	280	14	,	,	PUNCT
ejpam-3632	280	15	.	.	PUNCT
ejpam-3632	280	16	.	.	PUNCT
ejpam-3632	281	1	.	.	PUNCT
ejpam-3632	282	1	,	,	PUNCT
ejpam-3632	282	2	r	r	X
ejpam-3632	282	3	}	}	PUNCT
ejpam-3632	282	4	∈	∈	PROPN
ejpam-3632	282	5	blr(h	blr(h	PROPN
ejpam-3632	282	6	)	)	PUNCT
ejpam-3632	282	7	.	.	PUNCT
ejpam-3632	283	1	now	now	ADV
ejpam-3632	283	2	,	,	PUNCT
ejpam-3632	283	3	for	for	ADP
ejpam-3632	283	4	any	any	DET
ejpam-3632	283	5	finite	finite	NOUN
ejpam-3632	283	6	set	set	VERB
ejpam-3632	283	7	b	b	PROPN
ejpam-3632	283	8	6=	6=	ADP
ejpam-3632	283	9	a	a	DET
ejpam-3632	283	10	,	,	PUNCT
ejpam-3632	283	11	lhrh(b	lhrh(b	PROPN
ejpam-3632	283	12	)	)	PUNCT
ejpam-3632	283	13	6=	6=	PROPN
ejpam-3632	283	14	b.	b.	PROPN
ejpam-3632	283	15	therefore	therefore	ADV
ejpam-3632	283	16	,	,	PUNCT
ejpam-3632	283	17	τlr(h	τlr(h	PROPN
ejpam-3632	283	18	)	)	PUNCT
ejpam-3632	283	19	=	=	PRON
ejpam-3632	283	20	{	{	PUNCT
ejpam-3632	283	21	∅	∅	NOUN
ejpam-3632	283	22	,	,	PUNCT
ejpam-3632	283	23	h	h	NOUN
ejpam-3632	283	24	}	}	PUNCT
ejpam-3632	283	25	∪	∪	X
ejpam-3632	283	26	{	{	PUNCT
ejpam-3632	283	27	{	{	PUNCT
ejpam-3632	283	28	0	0	NUM
ejpam-3632	283	29	,	,	PUNCT
ejpam-3632	283	30	1	1	NUM
ejpam-3632	283	31	,	,	PUNCT
ejpam-3632	283	32	2	2	NUM
ejpam-3632	283	33	,	,	PUNCT
ejpam-3632	283	34	.	.	PUNCT
ejpam-3632	283	35	.	.	PUNCT
ejpam-3632	283	36	.	.	PUNCT
ejpam-3632	284	1	,	,	PUNCT
ejpam-3632	284	2	r	r	X
ejpam-3632	284	3	}	}	PUNCT
ejpam-3632	284	4	:	:	PUNCT
ejpam-3632	284	5	r	r	NOUN
ejpam-3632	284	6	∈	∈	PROPN
ejpam-3632	284	7	h	h	NOUN
ejpam-3632	284	8	}	}	PUNCT
ejpam-3632	284	9	.	.	PUNCT
ejpam-3632	285	1	example	example	NOUN
ejpam-3632	286	1	4	4	NUM
ejpam-3632	286	2	.	.	PUNCT
ejpam-3632	286	3	consider	consider	VERB
ejpam-3632	286	4	the	the	DET
ejpam-3632	286	5	infinite	infinite	ADJ
ejpam-3632	286	6	hyper	hyper	ADJ
ejpam-3632	286	7	bck	bck	NOUN
ejpam-3632	286	8	-	-	PUNCT
ejpam-3632	286	9	algebra	algebra	NOUN
ejpam-3632	286	10	(	(	PUNCT
ejpam-3632	286	11	h	h	NOUN
ejpam-3632	286	12	,	,	PUNCT
ejpam-3632	286	13	◦	◦	NOUN
ejpam-3632	286	14	,	,	PUNCT
ejpam-3632	286	15	0	0	NUM
ejpam-3632	286	16	)	)	PUNCT
ejpam-3632	286	17	given	give	VERB
ejpam-3632	286	18	in	in	ADP
ejpam-3632	286	19	example	example	NOUN
ejpam-3632	286	20	2	2	NUM
ejpam-3632	286	21	.	.	PUNCT
ejpam-3632	286	22	again	again	ADV
ejpam-3632	286	23	,	,	PUNCT
ejpam-3632	286	24	for	for	ADP
ejpam-3632	286	25	convenience	convenience	NOUN
ejpam-3632	286	26	,	,	PUNCT
ejpam-3632	286	27	let	let	VERB
ejpam-3632	286	28	n	n	X
ejpam-3632	286	29	=	=	PRON
ejpam-3632	286	30	{	{	PUNCT
ejpam-3632	286	31	1	1	NUM
ejpam-3632	286	32	,	,	PUNCT
ejpam-3632	286	33	2	2	NUM
ejpam-3632	286	34	,	,	PUNCT
ejpam-3632	286	35	...	...	PUNCT
ejpam-3632	286	36	}	}	PUNCT
ejpam-3632	286	37	,	,	PUNCT
ejpam-3632	286	38	n0	n0	ADJ
ejpam-3632	286	39	=	=	SYM
ejpam-3632	286	40	n∪{0	n∪{0	NOUN
ejpam-3632	286	41	}	}	PUNCT
ejpam-3632	286	42	,	,	PUNCT
ejpam-3632	286	43	and	and	CCONJ
ejpam-3632	286	44	let	let	VERB
ejpam-3632	286	45	jk	jk	PROPN
ejpam-3632	286	46	=	=	PRON
ejpam-3632	286	47	{	{	PUNCT
ejpam-3632	286	48	1	1	NUM
ejpam-3632	286	49	m	m	NOUN
ejpam-3632	286	50	:	:	PUNCT
ejpam-3632	286	51	m	m	VERB
ejpam-3632	286	52	is	be	AUX
ejpam-3632	286	53	a	a	DET
ejpam-3632	286	54	positive	positive	ADJ
ejpam-3632	286	55	integer	integer	NOUN
ejpam-3632	286	56	r.	r.	PROPN
ejpam-3632	286	57	patangan	patangan	PROPN
ejpam-3632	286	58	,	,	PUNCT
ejpam-3632	286	59	s.	s.	PROPN
ejpam-3632	286	60	canoy	canoy	PROPN
ejpam-3632	286	61	,	,	PUNCT
ejpam-3632	286	62	jr	jr	PROPN
ejpam-3632	286	63	.	.	PROPN
ejpam-3632	286	64	/	/	SYM
ejpam-3632	286	65	eur	eur	PROPN
ejpam-3632	286	66	.	.	PUNCT
ejpam-3632	287	1	j.	j.	PROPN
ejpam-3632	287	2	pure	pure	PROPN
ejpam-3632	287	3	appl	appl	PROPN
ejpam-3632	287	4	.	.	PROPN
ejpam-3632	287	5	math	math	PROPN
ejpam-3632	287	6	,	,	PUNCT
ejpam-3632	287	7	13	13	NUM
ejpam-3632	287	8	(	(	PUNCT
ejpam-3632	287	9	1	1	NUM
ejpam-3632	287	10	)	)	PUNCT
ejpam-3632	287	11	(	(	PUNCT
ejpam-3632	287	12	2020	2020	NUM
ejpam-3632	287	13	)	)	PUNCT
ejpam-3632	287	14	,	,	PUNCT
ejpam-3632	287	15	1	1	NUM
ejpam-3632	287	16	-	-	SYM
ejpam-3632	287	17	8	8	NUM
ejpam-3632	287	18	7	7	NUM
ejpam-3632	287	19	and	and	CCONJ
ejpam-3632	287	20	m	m	PROPN
ejpam-3632	287	21	≥	≥	NOUN
ejpam-3632	287	22	k	k	NOUN
ejpam-3632	287	23	}	}	PUNCT
ejpam-3632	287	24	.	.	PUNCT
ejpam-3632	288	1	let	let	VERB
ejpam-3632	288	2	p	p	PROPN
ejpam-3632	288	3	∈	∈	PROPN
ejpam-3632	288	4	h.	h.	NOUN
ejpam-3632	289	1	if	if	SCONJ
ejpam-3632	289	2	p	p	PROPN
ejpam-3632	289	3	=	=	NOUN
ejpam-3632	289	4	0	0	NUM
ejpam-3632	289	5	,	,	PUNCT
ejpam-3632	289	6	then	then	ADV
ejpam-3632	289	7	rh(0	rh(0	VERB
ejpam-3632	289	8	)	)	PUNCT
ejpam-3632	289	9	=	=	PRON
ejpam-3632	289	10	{	{	PUNCT
ejpam-3632	289	11	x	x	PUNCT
ejpam-3632	289	12	∈	∈	PROPN
ejpam-3632	289	13	h	h	NOUN
ejpam-3632	289	14	:	:	PUNCT
ejpam-3632	289	15	0	0	NUM
ejpam-3632	289	16	≤	≤	NUM
ejpam-3632	289	17	x	x	X
ejpam-3632	289	18	}	}	PUNCT
ejpam-3632	289	19	=	=	SYM
ejpam-3632	289	20	h	h	NOUN
ejpam-3632	289	21	and	and	CCONJ
ejpam-3632	289	22	lh(rh(0	lh(rh(0	NOUN
ejpam-3632	289	23	)	)	PUNCT
ejpam-3632	289	24	)	)	PUNCT
ejpam-3632	290	1	=	=	SYM
ejpam-3632	290	2	lh(h	lh(h	X
ejpam-3632	290	3	)	)	PUNCT
ejpam-3632	290	4	=	=	PRON
ejpam-3632	290	5	{	{	PUNCT
ejpam-3632	290	6	0	0	NUM
ejpam-3632	290	7	}	}	PUNCT
ejpam-3632	290	8	.	.	PUNCT
ejpam-3632	291	1	it	it	PRON
ejpam-3632	291	2	follows	follow	VERB
ejpam-3632	291	3	that	that	SCONJ
ejpam-3632	291	4	{	{	PUNCT
ejpam-3632	291	5	0	0	NUM
ejpam-3632	291	6	}	}	PUNCT
ejpam-3632	291	7	∈	∈	PROPN
ejpam-3632	291	8	blr(h	blr(h	PROPN
ejpam-3632	291	9	)	)	PUNCT
ejpam-3632	291	10	.	.	PUNCT
ejpam-3632	292	1	let	let	VERB
ejpam-3632	292	2	p	p	PROPN
ejpam-3632	292	3	∈	∈	PROPN
ejpam-3632	292	4	n.	n.	NOUN
ejpam-3632	292	5	then	then	ADV
ejpam-3632	292	6	rh(p	rh(p	NOUN
ejpam-3632	292	7	)	)	PUNCT
ejpam-3632	293	1	=	=	PRON
ejpam-3632	293	2	{	{	PUNCT
ejpam-3632	293	3	x	x	PUNCT
ejpam-3632	293	4	∈	∈	NOUN
ejpam-3632	293	5	h	h	NOUN
ejpam-3632	293	6	:	:	PUNCT
ejpam-3632	293	7	p	p	X
ejpam-3632	293	8	≤	≤	NUM
ejpam-3632	293	9	x	x	SYM
ejpam-3632	293	10	}	}	PUNCT
ejpam-3632	293	11	=	=	SYM
ejpam-3632	293	12	{	{	PUNCT
ejpam-3632	293	13	p	p	X
ejpam-3632	293	14	,	,	PUNCT
ejpam-3632	293	15	p	p	X
ejpam-3632	293	16	+	+	NOUN
ejpam-3632	293	17	1	1	NUM
ejpam-3632	293	18	,	,	PUNCT
ejpam-3632	293	19	p	p	NOUN
ejpam-3632	293	20	+	+	NOUN
ejpam-3632	293	21	2	2	NUM
ejpam-3632	293	22	,	,	PUNCT
ejpam-3632	293	23	.	.	PUNCT
ejpam-3632	293	24	.	.	PUNCT
ejpam-3632	293	25	.	.	PUNCT
ejpam-3632	293	26	}	}	PUNCT
ejpam-3632	293	27	.	.	PUNCT
ejpam-3632	294	1	it	it	PRON
ejpam-3632	294	2	follows	follow	VERB
ejpam-3632	294	3	that	that	SCONJ
ejpam-3632	294	4	lh(rh(p	lh(rh(p	NOUN
ejpam-3632	294	5	)	)	PUNCT
ejpam-3632	294	6	)	)	PUNCT
ejpam-3632	295	1	=	=	SYM
ejpam-3632	295	2	lh({p	lh({p	NOUN
ejpam-3632	295	3	,	,	PUNCT
ejpam-3632	295	4	p	p	X
ejpam-3632	295	5	+	+	NOUN
ejpam-3632	295	6	1	1	NUM
ejpam-3632	295	7	,	,	PUNCT
ejpam-3632	295	8	p	p	NOUN
ejpam-3632	295	9	+	+	NOUN
ejpam-3632	295	10	2	2	NUM
ejpam-3632	295	11	,	,	PUNCT
ejpam-3632	295	12	.	.	PUNCT
ejpam-3632	295	13	.	.	PUNCT
ejpam-3632	295	14	.	.	PUNCT
ejpam-3632	295	15	}	}	PUNCT
ejpam-3632	295	16	)	)	PUNCT
ejpam-3632	296	1	=	=	SYM
ejpam-3632	296	2	j2∪{0	j2∪{0	PROPN
ejpam-3632	296	3	,	,	PUNCT
ejpam-3632	296	4	1	1	NUM
ejpam-3632	296	5	,	,	PUNCT
ejpam-3632	296	6	2	2	NUM
ejpam-3632	296	7	,	,	PUNCT
ejpam-3632	296	8	.	.	PUNCT
ejpam-3632	296	9	.	.	PUNCT
ejpam-3632	296	10	.	.	PUNCT
ejpam-3632	297	1	,	,	PUNCT
ejpam-3632	297	2	p	p	X
ejpam-3632	297	3	}	}	PUNCT
ejpam-3632	297	4	.	.	PUNCT
ejpam-3632	298	1	if	if	SCONJ
ejpam-3632	298	2	p	p	NOUN
ejpam-3632	298	3	=	=	SYM
ejpam-3632	298	4	1	1	NUM
ejpam-3632	298	5	n	n	NOUN
ejpam-3632	298	6	for	for	ADP
ejpam-3632	298	7	some	some	DET
ejpam-3632	298	8	n	n	PRON
ejpam-3632	298	9	∈	∈	NOUN
ejpam-3632	298	10	{	{	PUNCT
ejpam-3632	298	11	2	2	NUM
ejpam-3632	298	12	,	,	PUNCT
ejpam-3632	298	13	3	3	NUM
ejpam-3632	298	14	,	,	PUNCT
ejpam-3632	298	15	...	...	PUNCT
ejpam-3632	298	16	}	}	PUNCT
ejpam-3632	298	17	,	,	PUNCT
ejpam-3632	298	18	then	then	ADV
ejpam-3632	298	19	rh(p	rh(p	NOUN
ejpam-3632	298	20	)	)	PUNCT
ejpam-3632	299	1	=	=	PRON
ejpam-3632	299	2	{	{	PUNCT
ejpam-3632	299	3	x	x	PUNCT
ejpam-3632	299	4	∈	∈	PROPN
ejpam-3632	299	5	h	h	NOUN
ejpam-3632	299	6	:	:	PUNCT
ejpam-3632	299	7	1	1	NUM
ejpam-3632	299	8	n	n	DET
ejpam-3632	299	9	≤	≤	NUM
ejpam-3632	299	10	x	x	X
ejpam-3632	299	11	}	}	PUNCT
ejpam-3632	299	12	=	=	SYM
ejpam-3632	299	13	n∪	n∪	X
ejpam-3632	299	14	{	{	PUNCT
ejpam-3632	299	15	12	12	NUM
ejpam-3632	299	16	,	,	PUNCT
ejpam-3632	299	17	1	1	NUM
ejpam-3632	299	18	3	3	NUM
ejpam-3632	299	19	,	,	PUNCT
ejpam-3632	299	20	...	...	PUNCT
ejpam-3632	299	21	,	,	PUNCT
ejpam-3632	299	22	1	1	NUM
ejpam-3632	299	23	n	n	CCONJ
ejpam-3632	299	24	}	}	PUNCT
ejpam-3632	299	25	.	.	PUNCT
ejpam-3632	300	1	hence	hence	ADV
ejpam-3632	300	2	,	,	PUNCT
ejpam-3632	300	3	lh(rh(p	lh(rh(p	PROPN
ejpam-3632	300	4	)	)	PUNCT
ejpam-3632	300	5	)	)	PUNCT
ejpam-3632	301	1	=	=	SYM
ejpam-3632	301	2	lh(n∪{12	lh(n∪{12	ADJ
ejpam-3632	301	3	,	,	PUNCT
ejpam-3632	301	4	1	1	NUM
ejpam-3632	301	5	3	3	NUM
ejpam-3632	301	6	,	,	PUNCT
ejpam-3632	301	7	...	...	PUNCT
ejpam-3632	301	8	,	,	PUNCT
ejpam-3632	301	9	1	1	NUM
ejpam-3632	301	10	n	n	CCONJ
ejpam-3632	301	11	}	}	PUNCT
ejpam-3632	301	12	)	)	PUNCT
ejpam-3632	302	1	=	=	SYM
ejpam-3632	302	2	jn	jn	PROPN
ejpam-3632	302	3	∪{0	∪{0	PROPN
ejpam-3632	302	4	}	}	PUNCT
ejpam-3632	302	5	=	=	PUNCT
ejpam-3632	302	6	{	{	PUNCT
ejpam-3632	302	7	0	0	NUM
ejpam-3632	302	8	,	,	PUNCT
ejpam-3632	302	9	1n	1n	NUM
ejpam-3632	302	10	,	,	PUNCT
ejpam-3632	302	11	1	1	NUM
ejpam-3632	302	12	n+1	n+1	NUM
ejpam-3632	302	13	,	,	PUNCT
ejpam-3632	302	14	1	1	NUM
ejpam-3632	302	15	n+2	n+2	PRON
ejpam-3632	302	16	,	,	PUNCT
ejpam-3632	302	17	...	...	PUNCT
ejpam-3632	302	18	}	}	PUNCT
ejpam-3632	302	19	.	.	PUNCT
ejpam-3632	303	1	next	next	ADV
ejpam-3632	303	2	,	,	PUNCT
ejpam-3632	303	3	let	let	VERB
ejpam-3632	303	4	∅	∅	NOUN
ejpam-3632	303	5	6=	6=	ADP
ejpam-3632	303	6	a	a	DET
ejpam-3632	303	7	⊆	⊆	NUM
ejpam-3632	303	8	h	h	NOUN
ejpam-3632	303	9	with	with	ADP
ejpam-3632	303	10	a	a	DET
ejpam-3632	303	11	6=	6=	NUM
ejpam-3632	303	12	{	{	PUNCT
ejpam-3632	303	13	0	0	NUM
ejpam-3632	303	14	}	}	PUNCT
ejpam-3632	303	15	.	.	PUNCT
ejpam-3632	304	1	suppose	suppose	VERB
ejpam-3632	304	2	first	first	ADV
ejpam-3632	304	3	that	that	SCONJ
ejpam-3632	304	4	a∩n	a∩n	PROPN
ejpam-3632	304	5	6=	6=	ADP
ejpam-3632	304	6	∅.	∅.	VERB
ejpam-3632	304	7	if	if	SCONJ
ejpam-3632	304	8	a∩n0	a∩n0	ADJ
ejpam-3632	304	9	is	be	AUX
ejpam-3632	304	10	infinite	infinite	ADJ
ejpam-3632	304	11	,	,	PUNCT
ejpam-3632	304	12	then	then	ADV
ejpam-3632	304	13	rh(a	rh(a	PUNCT
ejpam-3632	304	14	)	)	PUNCT
ejpam-3632	304	15	=	=	NOUN
ejpam-3632	304	16	∅	∅	NOUN
ejpam-3632	304	17	and	and	CCONJ
ejpam-3632	304	18	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	304	19	)	)	PUNCT
ejpam-3632	304	20	)	)	PUNCT
ejpam-3632	305	1	=	=	SYM
ejpam-3632	305	2	h.	h.	PROPN
ejpam-3632	305	3	suppose	suppose	VERB
ejpam-3632	305	4	a	a	DET
ejpam-3632	305	5	∩	∩	NOUN
ejpam-3632	305	6	n	n	PRON
ejpam-3632	305	7	is	be	AUX
ejpam-3632	305	8	finite	finite	ADJ
ejpam-3632	305	9	and	and	CCONJ
ejpam-3632	305	10	let	let	VERB
ejpam-3632	305	11	s	s	PRON
ejpam-3632	305	12	=	=	NOUN
ejpam-3632	305	13	max(a	max(a	PROPN
ejpam-3632	305	14	∩	∩	NOUN
ejpam-3632	305	15	n	n	CCONJ
ejpam-3632	305	16	)	)	PUNCT
ejpam-3632	305	17	.	.	PUNCT
ejpam-3632	306	1	then	then	ADV
ejpam-3632	306	2	rh(a	rh(a	X
ejpam-3632	306	3	)	)	PUNCT
ejpam-3632	306	4	=	=	SYM
ejpam-3632	307	1	rh(s	rh(s	X
ejpam-3632	307	2	)	)	PUNCT
ejpam-3632	307	3	and	and	CCONJ
ejpam-3632	307	4	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	307	5	)	)	PUNCT
ejpam-3632	307	6	)	)	PUNCT
ejpam-3632	308	1	=	=	SYM
ejpam-3632	308	2	j2	j2	PROPN
ejpam-3632	308	3	∪	∪	X
ejpam-3632	308	4	{	{	PUNCT
ejpam-3632	308	5	0	0	NUM
ejpam-3632	308	6	,	,	PUNCT
ejpam-3632	308	7	1	1	NUM
ejpam-3632	308	8	,	,	PUNCT
ejpam-3632	308	9	2	2	NUM
ejpam-3632	308	10	,	,	PUNCT
ejpam-3632	308	11	.	.	PUNCT
ejpam-3632	308	12	.	.	PUNCT
ejpam-3632	308	13	.	.	PUNCT
ejpam-3632	309	1	,	,	PUNCT
ejpam-3632	309	2	s	s	X
ejpam-3632	309	3	}	}	PUNCT
ejpam-3632	309	4	.	.	PUNCT
ejpam-3632	310	1	hence	hence	ADV
ejpam-3632	310	2	,	,	PUNCT
ejpam-3632	310	3	a	a	DET
ejpam-3632	310	4	∈	∈	PROPN
ejpam-3632	310	5	blr(h	blr(h	NOUN
ejpam-3632	310	6	)	)	PUNCT
ejpam-3632	310	7	if	if	SCONJ
ejpam-3632	310	8	and	and	CCONJ
ejpam-3632	310	9	only	only	ADV
ejpam-3632	310	10	if	if	SCONJ
ejpam-3632	310	11	a	a	DET
ejpam-3632	310	12	=	=	NOUN
ejpam-3632	310	13	h	h	NOUN
ejpam-3632	310	14	or	or	CCONJ
ejpam-3632	310	15	a	a	DET
ejpam-3632	310	16	=	=	X
ejpam-3632	310	17	j2	j2	PROPN
ejpam-3632	310	18	∪	∪	X
ejpam-3632	310	19	{	{	PUNCT
ejpam-3632	310	20	0	0	NUM
ejpam-3632	310	21	,	,	PUNCT
ejpam-3632	310	22	1	1	NUM
ejpam-3632	310	23	,	,	PUNCT
ejpam-3632	310	24	2	2	NUM
ejpam-3632	310	25	,	,	PUNCT
ejpam-3632	310	26	.	.	PUNCT
ejpam-3632	310	27	.	.	PUNCT
ejpam-3632	310	28	.	.	PUNCT
ejpam-3632	311	1	,	,	PUNCT
ejpam-3632	311	2	s	s	X
ejpam-3632	311	3	}	}	PUNCT
ejpam-3632	311	4	.	.	PUNCT
ejpam-3632	312	1	suppose	suppose	VERB
ejpam-3632	312	2	now	now	ADV
ejpam-3632	312	3	that	that	SCONJ
ejpam-3632	312	4	a∩n	a∩n	PRON
ejpam-3632	313	1	=	=	PUNCT
ejpam-3632	313	2	∅.	∅.	NOUN
ejpam-3632	313	3	since	since	SCONJ
ejpam-3632	313	4	a	a	DET
ejpam-3632	313	5	6=	6=	NUM
ejpam-3632	313	6	{	{	PUNCT
ejpam-3632	313	7	0	0	NUM
ejpam-3632	313	8	}	}	PUNCT
ejpam-3632	313	9	,	,	PUNCT
ejpam-3632	313	10	a∩j2	a∩j2	PROPN
ejpam-3632	313	11	6=	6=	ADP
ejpam-3632	313	12	∅.	∅.	AUX
ejpam-3632	313	13	let	let	VERB
ejpam-3632	313	14	d	d	NOUN
ejpam-3632	313	15	=	=	SYM
ejpam-3632	313	16	min{k	min{k	PROPN
ejpam-3632	313	17	∈	∈	PROPN
ejpam-3632	313	18	{	{	PUNCT
ejpam-3632	313	19	2	2	NUM
ejpam-3632	313	20	,	,	PUNCT
ejpam-3632	313	21	3	3	NUM
ejpam-3632	313	22	,	,	PUNCT
ejpam-3632	313	23	...	...	PUNCT
ejpam-3632	313	24	}	}	PUNCT
ejpam-3632	313	25	:	:	PUNCT
ejpam-3632	313	26	1	1	NUM
ejpam-3632	313	27	k	k	X
ejpam-3632	313	28	∈	∈	PROPN
ejpam-3632	313	29	a	a	PRON
ejpam-3632	313	30	}	}	PUNCT
ejpam-3632	313	31	.	.	PUNCT
ejpam-3632	314	1	then	then	ADV
ejpam-3632	314	2	rh(a	rh(a	X
ejpam-3632	314	3	)	)	PUNCT
ejpam-3632	314	4	=	=	SYM
ejpam-3632	314	5	rh(1d	rh(1d	ADJ
ejpam-3632	314	6	)	)	PUNCT
ejpam-3632	314	7	=	=	SYM
ejpam-3632	315	1	n	n	NOUN
ejpam-3632	315	2	∪	∪	X
ejpam-3632	315	3	{	{	PUNCT
ejpam-3632	315	4	12	12	NUM
ejpam-3632	315	5	,	,	PUNCT
ejpam-3632	315	6	1	1	NUM
ejpam-3632	315	7	3	3	NUM
ejpam-3632	315	8	,	,	PUNCT
ejpam-3632	315	9	...	...	PUNCT
ejpam-3632	315	10	,	,	PUNCT
ejpam-3632	315	11	1	1	NUM
ejpam-3632	315	12	d	d	NOUN
ejpam-3632	315	13	}	}	PUNCT
ejpam-3632	315	14	and	and	CCONJ
ejpam-3632	315	15	lh(rh(a	lh(rh(a	NOUN
ejpam-3632	315	16	)	)	PUNCT
ejpam-3632	315	17	)	)	PUNCT
ejpam-3632	316	1	=	=	PUNCT
ejpam-3632	316	2	jd	jd	PROPN
ejpam-3632	316	3	∪	∪	X
ejpam-3632	316	4	{	{	PUNCT
ejpam-3632	316	5	0	0	NUM
ejpam-3632	316	6	}	}	PUNCT
ejpam-3632	316	7	=	=	SYM
ejpam-3632	316	8	{	{	PUNCT
ejpam-3632	316	9	0	0	NUM
ejpam-3632	316	10	,	,	PUNCT
ejpam-3632	316	11	1d	1d	NUM
ejpam-3632	316	12	,	,	PUNCT
ejpam-3632	316	13	1	1	NUM
ejpam-3632	316	14	d+1	d+1	PROPN
ejpam-3632	316	15	,	,	PUNCT
ejpam-3632	316	16	1	1	NUM
ejpam-3632	316	17	d+2	d+2	NOUN
ejpam-3632	316	18	,	,	PUNCT
ejpam-3632	316	19	...	...	PUNCT
ejpam-3632	316	20	}	}	PUNCT
ejpam-3632	316	21	.	.	PUNCT
ejpam-3632	317	1	consequently	consequently	ADV
ejpam-3632	317	2	,	,	PUNCT
ejpam-3632	317	3	a	a	DET
ejpam-3632	317	4	∈	∈	PROPN
ejpam-3632	317	5	blr(h	blr(h	NOUN
ejpam-3632	317	6	)	)	PUNCT
ejpam-3632	317	7	if	if	SCONJ
ejpam-3632	317	8	and	and	CCONJ
ejpam-3632	317	9	only	only	ADV
ejpam-3632	317	10	if	if	SCONJ
ejpam-3632	317	11	a	a	PRON
ejpam-3632	317	12	=	=	X
ejpam-3632	317	13	{	{	PUNCT
ejpam-3632	317	14	0	0	NUM
ejpam-3632	317	15	,	,	PUNCT
ejpam-3632	317	16	1d	1d	NUM
ejpam-3632	317	17	,	,	PUNCT
ejpam-3632	317	18	1	1	NUM
ejpam-3632	317	19	d+1	d+1	PROPN
ejpam-3632	317	20	,	,	PUNCT
ejpam-3632	317	21	1	1	NUM
ejpam-3632	317	22	d+2	d+2	NOUN
ejpam-3632	317	23	,	,	PUNCT
ejpam-3632	317	24	...	...	PUNCT
ejpam-3632	317	25	}	}	PUNCT
ejpam-3632	317	26	.	.	PUNCT
ejpam-3632	318	1	therefore	therefore	ADV
ejpam-3632	318	2	,	,	PUNCT
ejpam-3632	318	3	τlr(h	τlr(h	PROPN
ejpam-3632	318	4	)	)	PUNCT
ejpam-3632	319	1	=	=	PRON
ejpam-3632	319	2	{	{	PUNCT
ejpam-3632	319	3	∅	∅	NOUN
ejpam-3632	319	4	,	,	PUNCT
ejpam-3632	319	5	{	{	PUNCT
ejpam-3632	319	6	0	0	NUM
ejpam-3632	319	7	}	}	PUNCT
ejpam-3632	319	8	,	,	PUNCT
ejpam-3632	319	9	h}∪{j2∪{0	h}∪{j2∪{0	PROPN
ejpam-3632	319	10	,	,	PUNCT
ejpam-3632	319	11	1	1	NUM
ejpam-3632	319	12	,	,	PUNCT
ejpam-3632	319	13	2	2	NUM
ejpam-3632	319	14	,	,	PUNCT
ejpam-3632	319	15	.	.	PUNCT
ejpam-3632	319	16	.	.	PUNCT
ejpam-3632	320	1	.	.	PUNCT
ejpam-3632	321	1	,	,	PUNCT
ejpam-3632	321	2	p	p	X
ejpam-3632	321	3	}	}	PUNCT
ejpam-3632	321	4	:	:	PUNCT
ejpam-3632	321	5	p	p	PROPN
ejpam-3632	321	6	∈	∈	PROPN
ejpam-3632	321	7	h}∪{{0	h}∪{{0	NOUN
ejpam-3632	321	8	,	,	PUNCT
ejpam-3632	321	9	1k	1k	NUM
ejpam-3632	321	10	,	,	PUNCT
ejpam-3632	321	11	1	1	NUM
ejpam-3632	321	12	k+1	k+1	NOUN
ejpam-3632	321	13	,	,	PUNCT
ejpam-3632	321	14	1	1	NUM
ejpam-3632	321	15	k+2	k+2	NUM
ejpam-3632	321	16	,	,	PUNCT
ejpam-3632	321	17	...	...	PUNCT
ejpam-3632	321	18	}	}	PUNCT
ejpam-3632	321	19	:	:	PUNCT
ejpam-3632	322	1	k	k	X
ejpam-3632	322	2	=	=	SYM
ejpam-3632	322	3	2	2	NUM
ejpam-3632	322	4	,	,	PUNCT
ejpam-3632	322	5	3	3	NUM
ejpam-3632	322	6	,	,	PUNCT
ejpam-3632	322	7	...	...	PUNCT
ejpam-3632	322	8	}	}	PUNCT
ejpam-3632	322	9	.	.	PUNCT
ejpam-3632	323	1	it	it	PRON
ejpam-3632	323	2	can	can	AUX
ejpam-3632	323	3	be	be	AUX
ejpam-3632	323	4	seen	see	VERB
ejpam-3632	323	5	that	that	SCONJ
ejpam-3632	323	6	the	the	DET
ejpam-3632	323	7	topology	topology	NOUN
ejpam-3632	323	8	τlr(h	τlr(h	PROPN
ejpam-3632	323	9	)	)	PUNCT
ejpam-3632	323	10	generated	generate	VERB
ejpam-3632	323	11	in	in	ADP
ejpam-3632	323	12	example	example	NOUN
ejpam-3632	323	13	3	3	NUM
ejpam-3632	323	14	is	be	AUX
ejpam-3632	323	15	equal	equal	ADJ
ejpam-3632	323	16	to	to	ADP
ejpam-3632	323	17	the	the	DET
ejpam-3632	323	18	topology	topology	NOUN
ejpam-3632	323	19	τl(h	τl(h	PUNCT
ejpam-3632	323	20	)	)	PUNCT
ejpam-3632	323	21	generated	generate	VERB
ejpam-3632	323	22	in	in	ADP
ejpam-3632	323	23	example	example	NOUN
ejpam-3632	323	24	2.5	2.5	NUM
ejpam-3632	324	1	[	[	SYM
ejpam-3632	324	2	8	8	NUM
ejpam-3632	324	3	]	]	PUNCT
ejpam-3632	324	4	.	.	PUNCT
ejpam-3632	325	1	the	the	DET
ejpam-3632	325	2	next	next	ADJ
ejpam-3632	325	3	result	result	NOUN
ejpam-3632	325	4	says	say	VERB
ejpam-3632	325	5	that	that	SCONJ
ejpam-3632	325	6	the	the	DET
ejpam-3632	325	7	equality	equality	NOUN
ejpam-3632	325	8	of	of	ADP
ejpam-3632	325	9	these	these	DET
ejpam-3632	325	10	topologies	topology	NOUN
ejpam-3632	325	11	holds	hold	VERB
ejpam-3632	325	12	for	for	ADP
ejpam-3632	325	13	any	any	DET
ejpam-3632	325	14	hyper	hyper	ADJ
ejpam-3632	325	15	bck	bck	NOUN
ejpam-3632	325	16	-	-	PUNCT
ejpam-3632	325	17	algebra	algebra	NOUN
ejpam-3632	325	18	h.	h.	NOUN
ejpam-3632	325	19	theorem	theorem	VERB
ejpam-3632	325	20	10	10	NUM
ejpam-3632	325	21	.	.	PUNCT
ejpam-3632	326	1	let	let	VERB
ejpam-3632	326	2	h	h	PRON
ejpam-3632	326	3	be	be	AUX
ejpam-3632	326	4	a	a	DET
ejpam-3632	326	5	hyper	hyper	ADJ
ejpam-3632	326	6	bck	bck	NOUN
ejpam-3632	326	7	-	-	PUNCT
ejpam-3632	326	8	algebra	algebra	NOUN
ejpam-3632	326	9	.	.	PUNCT
ejpam-3632	327	1	the	the	DET
ejpam-3632	327	2	the	the	DET
ejpam-3632	327	3	topology	topology	NOUN
ejpam-3632	327	4	τlr(h	τlr(h	PROPN
ejpam-3632	327	5	)	)	PUNCT
ejpam-3632	327	6	coincides	coincide	VERB
ejpam-3632	327	7	with	with	ADP
ejpam-3632	327	8	the	the	DET
ejpam-3632	327	9	topology	topology	NOUN
ejpam-3632	327	10	τl(h	τl(h	PUNCT
ejpam-3632	327	11	)	)	PUNCT
ejpam-3632	327	12	.	.	PUNCT
ejpam-3632	328	1	proof	proof	NOUN
ejpam-3632	328	2	.	.	PUNCT
ejpam-3632	329	1	by	by	ADP
ejpam-3632	329	2	theorem	theorem	NOUN
ejpam-3632	329	3	9	9	NUM
ejpam-3632	329	4	,	,	PUNCT
ejpam-3632	329	5	a	a	DET
ejpam-3632	329	6	basis	basis	NOUN
ejpam-3632	329	7	for	for	ADP
ejpam-3632	329	8	τlr(h	τlr(h	PROPN
ejpam-3632	329	9	)	)	PUNCT
ejpam-3632	329	10	is	be	AUX
ejpam-3632	329	11	given	give	VERB
ejpam-3632	329	12	by	by	ADP
ejpam-3632	329	13	blr(h	blr(h	PROPN
ejpam-3632	329	14	)	)	PUNCT
ejpam-3632	330	1	=	=	PRON
ejpam-3632	330	2	{	{	PUNCT
ejpam-3632	330	3	a	a	DET
ejpam-3632	330	4	:	:	PUNCT
ejpam-3632	330	5	lhrh(a	lhrh(a	NOUN
ejpam-3632	330	6	)	)	PUNCT
ejpam-3632	330	7	=	=	SYM
ejpam-3632	331	1	a	a	PRON
ejpam-3632	331	2	,	,	PUNCT
ejpam-3632	331	3	∅	∅	NOUN
ejpam-3632	331	4	6=	6=	ADP
ejpam-3632	331	5	a	a	DET
ejpam-3632	331	6	⊆	⊆	NUM
ejpam-3632	331	7	h	h	NOUN
ejpam-3632	331	8	}	}	PUNCT
ejpam-3632	331	9	while	while	SCONJ
ejpam-3632	331	10	a	a	DET
ejpam-3632	331	11	basis	basis	NOUN
ejpam-3632	331	12	for	for	ADP
ejpam-3632	331	13	τl(h	τl(h	NUM
ejpam-3632	331	14	)	)	PUNCT
ejpam-3632	331	15	is	be	AUX
ejpam-3632	331	16	the	the	DET
ejpam-3632	331	17	family	family	NOUN
ejpam-3632	331	18	bl(h	bl(h	PUNCT
ejpam-3632	331	19	)	)	PUNCT
ejpam-3632	331	20	=	=	PRON
ejpam-3632	331	21	{	{	PUNCT
ejpam-3632	331	22	lh(a	lh(a	NOUN
ejpam-3632	331	23	)	)	PUNCT
ejpam-3632	331	24	:	:	PUNCT
ejpam-3632	332	1	∅	∅	NOUN
ejpam-3632	332	2	6=	6=	ADP
ejpam-3632	332	3	a	a	DET
ejpam-3632	332	4	⊆	⊆	NUM
ejpam-3632	332	5	h	h	NOUN
ejpam-3632	332	6	}	}	PUNCT
ejpam-3632	332	7	.	.	PUNCT
ejpam-3632	333	1	let	let	VERB
ejpam-3632	333	2	a	a	DET
ejpam-3632	333	3	∈	∈	PROPN
ejpam-3632	333	4	blr(h	blr(h	PROPN
ejpam-3632	333	5	)	)	PUNCT
ejpam-3632	333	6	.	.	PUNCT
ejpam-3632	334	1	then	then	ADV
ejpam-3632	334	2	lhrh(a	lhrh(a	NOUN
ejpam-3632	334	3	)	)	PUNCT
ejpam-3632	334	4	=	=	SYM
ejpam-3632	334	5	a.	a.	NOUN
ejpam-3632	334	6	put	put	VERB
ejpam-3632	334	7	b	b	NOUN
ejpam-3632	334	8	=	=	SYM
ejpam-3632	334	9	rh(a	rh(a	NUM
ejpam-3632	334	10	)	)	PUNCT
ejpam-3632	335	1	⊆	⊆	PROPN
ejpam-3632	335	2	h.	h.	PROPN
ejpam-3632	335	3	then	then	ADV
ejpam-3632	335	4	lh(b	lh(b	PUNCT
ejpam-3632	335	5	)	)	PUNCT
ejpam-3632	335	6	=	=	PUNCT
ejpam-3632	335	7	a	a	DET
ejpam-3632	335	8	∈	∈	PROPN
ejpam-3632	335	9	bl(h	bl(h	PRON
ejpam-3632	335	10	)	)	PUNCT
ejpam-3632	335	11	,	,	PUNCT
ejpam-3632	335	12	showing	show	VERB
ejpam-3632	335	13	that	that	SCONJ
ejpam-3632	335	14	blr(h	blr(h	PROPN
ejpam-3632	335	15	)	)	PUNCT
ejpam-3632	335	16	⊆	⊆	NUM
ejpam-3632	335	17	bl(h	bl(h	NUM
ejpam-3632	335	18	)	)	PUNCT
ejpam-3632	335	19	.	.	PUNCT
ejpam-3632	336	1	next	next	ADV
ejpam-3632	336	2	,	,	PUNCT
ejpam-3632	336	3	let	let	VERB
ejpam-3632	336	4	v	v	ADP
ejpam-3632	336	5	∈	∈	PROPN
ejpam-3632	336	6	bl(h	bl(h	PRON
ejpam-3632	336	7	)	)	PUNCT
ejpam-3632	336	8	.	.	PUNCT
ejpam-3632	337	1	then	then	ADV
ejpam-3632	337	2	there	there	PRON
ejpam-3632	337	3	exists	exist	VERB
ejpam-3632	337	4	d	d	PROPN
ejpam-3632	337	5	⊆	⊆	NUM
ejpam-3632	337	6	h	h	NOUN
ejpam-3632	337	7	such	such	ADJ
ejpam-3632	337	8	that	that	SCONJ
ejpam-3632	337	9	lh(d	lh(d	NOUN
ejpam-3632	337	10	)	)	PUNCT
ejpam-3632	337	11	=	=	SYM
ejpam-3632	337	12	v	v	NOUN
ejpam-3632	337	13	.	.	PUNCT
ejpam-3632	338	1	now	now	ADV
ejpam-3632	338	2	,	,	PUNCT
ejpam-3632	338	3	for	for	ADP
ejpam-3632	338	4	every	every	DET
ejpam-3632	338	5	v	v	NUM
ejpam-3632	338	6	∈	∈	PROPN
ejpam-3632	338	7	v	v	NOUN
ejpam-3632	338	8	,	,	PUNCT
ejpam-3632	338	9	v	v	X
ejpam-3632	338	10	�	�	PROPN
ejpam-3632	338	11	d	d	PROPN
ejpam-3632	338	12	for	for	ADP
ejpam-3632	338	13	all	all	DET
ejpam-3632	338	14	d	d	PROPN
ejpam-3632	338	15	∈	∈	PROPN
ejpam-3632	338	16	d.	d.	PROPN
ejpam-3632	338	17	thus	thus	ADV
ejpam-3632	338	18	,	,	PUNCT
ejpam-3632	338	19	d	d	PROPN
ejpam-3632	338	20	⊆	⊆	NUM
ejpam-3632	338	21	rh(v	rh(v	NUM
ejpam-3632	338	22	)	)	PUNCT
ejpam-3632	338	23	.	.	PUNCT
ejpam-3632	339	1	by	by	ADP
ejpam-3632	339	2	proposition	proposition	NOUN
ejpam-3632	339	3	2(ii	2(ii	NUM
ejpam-3632	339	4	)	)	PUNCT
ejpam-3632	339	5	,	,	PUNCT
ejpam-3632	339	6	lhrh(v	lhrh(v	PROPN
ejpam-3632	339	7	)	)	PUNCT
ejpam-3632	339	8	⊆	⊆	NUM
ejpam-3632	339	9	lh(d	lh(d	X
ejpam-3632	339	10	)	)	PUNCT
ejpam-3632	339	11	=	=	SYM
ejpam-3632	339	12	v	v	X
ejpam-3632	339	13	.	.	PUNCT
ejpam-3632	340	1	by	by	ADP
ejpam-3632	340	2	theorem	theorem	NOUN
ejpam-3632	340	3	7(i	7(i	NUM
ejpam-3632	340	4	)	)	PUNCT
ejpam-3632	340	5	,	,	PUNCT
ejpam-3632	340	6	we	we	PRON
ejpam-3632	340	7	have	have	VERB
ejpam-3632	340	8	v	v	NUM
ejpam-3632	340	9	⊆	⊆	NUM
ejpam-3632	340	10	lhrh(v	lhrh(v	NOUN
ejpam-3632	340	11	)	)	PUNCT
ejpam-3632	340	12	.	.	PUNCT
ejpam-3632	341	1	by	by	ADP
ejpam-3632	341	2	combining	combine	VERB
ejpam-3632	341	3	the	the	DET
ejpam-3632	341	4	two	two	NUM
ejpam-3632	341	5	set	set	ADJ
ejpam-3632	341	6	inclusions	inclusion	NOUN
ejpam-3632	341	7	,	,	PUNCT
ejpam-3632	341	8	we	we	PRON
ejpam-3632	341	9	obtain	obtain	VERB
ejpam-3632	341	10	v	v	NOUN
ejpam-3632	341	11	=	=	SYM
ejpam-3632	341	12	lhrh(v	lhrh(v	NOUN
ejpam-3632	341	13	)	)	PUNCT
ejpam-3632	341	14	∈	∈	PROPN
ejpam-3632	341	15	blr(h	blr(h	PROPN
ejpam-3632	341	16	)	)	PUNCT
ejpam-3632	341	17	.	.	PUNCT
ejpam-3632	342	1	accordingly	accordingly	ADV
ejpam-3632	342	2	,	,	PUNCT
ejpam-3632	342	3	blr(h	blr(h	PROPN
ejpam-3632	342	4	)	)	PUNCT
ejpam-3632	342	5	=	=	SYM
ejpam-3632	343	1	bl(h	bl(h	PRON
ejpam-3632	343	2	)	)	PUNCT
ejpam-3632	343	3	,	,	PUNCT
ejpam-3632	344	1	showing	show	VERB
ejpam-3632	344	2	that	that	SCONJ
ejpam-3632	344	3	τlr(h	τlr(h	PROPN
ejpam-3632	344	4	)	)	PUNCT
ejpam-3632	344	5	=	=	PUNCT
ejpam-3632	344	6	τl(h	τl(h	NUM
ejpam-3632	344	7	)	)	PUNCT
ejpam-3632	344	8	.	.	PUNCT
ejpam-3632	345	1	conclusion	conclusion	NOUN
ejpam-3632	345	2	right	right	ADV
ejpam-3632	345	3	and	and	CCONJ
ejpam-3632	345	4	left	leave	VERB
ejpam-3632	345	5	applications	application	NOUN
ejpam-3632	345	6	of	of	ADP
ejpam-3632	345	7	a	a	DET
ejpam-3632	345	8	hyper	hyper	ADJ
ejpam-3632	345	9	order	order	NOUN
ejpam-3632	345	10	associated	associate	VERB
ejpam-3632	345	11	with	with	ADP
ejpam-3632	345	12	a	a	DET
ejpam-3632	345	13	hyper	hyper	ADJ
ejpam-3632	345	14	bckalgebra	bckalgebra	NOUN
ejpam-3632	345	15	can	can	AUX
ejpam-3632	345	16	give	give	VERB
ejpam-3632	345	17	rise	rise	NOUN
ejpam-3632	345	18	to	to	ADP
ejpam-3632	345	19	two	two	NUM
ejpam-3632	345	20	closure	closure	NOUN
ejpam-3632	345	21	operators	operator	NOUN
ejpam-3632	345	22	which	which	PRON
ejpam-3632	345	23	,	,	PUNCT
ejpam-3632	345	24	in	in	ADP
ejpam-3632	345	25	turn	turn	NOUN
ejpam-3632	345	26	,	,	PUNCT
ejpam-3632	345	27	can	can	AUX
ejpam-3632	345	28	be	be	AUX
ejpam-3632	345	29	used	use	VERB
ejpam-3632	345	30	to	to	PART
ejpam-3632	345	31	generate	generate	VERB
ejpam-3632	345	32	bases	basis	NOUN
ejpam-3632	345	33	for	for	ADP
ejpam-3632	345	34	some	some	DET
ejpam-3632	345	35	topologies	topology	NOUN
ejpam-3632	345	36	on	on	ADP
ejpam-3632	345	37	the	the	DET
ejpam-3632	345	38	given	give	VERB
ejpam-3632	345	39	hyper	hyper	ADJ
ejpam-3632	345	40	structure	structure	NOUN
ejpam-3632	345	41	.	.	PUNCT
ejpam-3632	346	1	the	the	DET
ejpam-3632	346	2	two	two	NUM
ejpam-3632	346	3	induced	induced	ADJ
ejpam-3632	346	4	topologies	topology	NOUN
ejpam-3632	346	5	turn	turn	VERB
ejpam-3632	346	6	out	out	ADP
ejpam-3632	346	7	to	to	PART
ejpam-3632	346	8	coincide	coincide	VERB
ejpam-3632	346	9	,	,	PUNCT
ejpam-3632	346	10	respectively	respectively	ADV
ejpam-3632	346	11	,	,	PUNCT
ejpam-3632	346	12	with	with	ADP
ejpam-3632	346	13	some	some	DET
ejpam-3632	346	14	previously	previously	ADV
ejpam-3632	346	15	known	know	VERB
ejpam-3632	346	16	topologies	topology	NOUN
ejpam-3632	346	17	on	on	ADP
ejpam-3632	346	18	this	this	DET
ejpam-3632	346	19	hyper	hyper	ADJ
ejpam-3632	346	20	bck	bck	NOUN
ejpam-3632	346	21	-	-	PUNCT
ejpam-3632	346	22	algebra	algebra	NOUN
ejpam-3632	346	23	.	.	PUNCT
ejpam-3632	347	1	acknowledgements	acknowledgement	NOUN
ejpam-3632	347	2	the	the	DET
ejpam-3632	347	3	authors	author	NOUN
ejpam-3632	347	4	would	would	AUX
ejpam-3632	347	5	like	like	VERB
ejpam-3632	347	6	to	to	PART
ejpam-3632	347	7	thank	thank	VERB
ejpam-3632	347	8	the	the	DET
ejpam-3632	347	9	referees	referee	NOUN
ejpam-3632	347	10	for	for	ADP
ejpam-3632	347	11	their	their	PRON
ejpam-3632	347	12	invaluable	invaluable	ADJ
ejpam-3632	347	13	comments	comment	NOUN
ejpam-3632	347	14	and	and	CCONJ
ejpam-3632	347	15	corrections	correction	NOUN
ejpam-3632	347	16	which	which	PRON
ejpam-3632	347	17	led	lead	VERB
ejpam-3632	347	18	to	to	ADP
ejpam-3632	347	19	the	the	DET
ejpam-3632	347	20	improvement	improvement	NOUN
ejpam-3632	347	21	of	of	ADP
ejpam-3632	347	22	the	the	DET
ejpam-3632	347	23	manuscript	manuscript	NOUN
ejpam-3632	347	24	.	.	PUNCT
ejpam-3632	348	1	this	this	DET
ejpam-3632	348	2	research	research	NOUN
ejpam-3632	348	3	is	be	AUX
ejpam-3632	348	4	funded	fund	VERB
ejpam-3632	348	5	by	by	ADP
ejpam-3632	348	6	asscat	asscat	NOUN
ejpam-3632	348	7	and	and	CCONJ
ejpam-3632	348	8	msu	msu	PROPN
ejpam-3632	348	9	-	-	PUNCT
ejpam-3632	348	10	iligan	iligan	PROPN
ejpam-3632	348	11	institute	institute	PROPN
ejpam-3632	348	12	of	of	ADP
ejpam-3632	348	13	technology	technology	PROPN
ejpam-3632	348	14	.	.	PUNCT
ejpam-3632	349	1	references	reference	NOUN
ejpam-3632	349	2	8	8	NUM
ejpam-3632	349	3	references	reference	NOUN
ejpam-3632	349	4	[	[	X
ejpam-3632	349	5	1	1	NUM
ejpam-3632	349	6	]	]	PUNCT
ejpam-3632	349	7	j	j	PROPN
ejpam-3632	349	8	albaracin	albaracin	PROPN
ejpam-3632	349	9	and	and	CCONJ
ejpam-3632	349	10	j	j	PROPN
ejpam-3632	349	11	vilela	vilela	NOUN
ejpam-3632	349	12	.	.	PUNCT
ejpam-3632	350	1	zero	zero	NUM
ejpam-3632	350	2	divisor	divisor	NOUN
ejpam-3632	350	3	graph	graph	NOUN
ejpam-3632	350	4	of	of	ADP
ejpam-3632	350	5	finite	finite	ADJ
ejpam-3632	350	6	hyper	hyper	ADJ
ejpam-3632	350	7	bck	bck	NOUN
ejpam-3632	350	8	-	-	PUNCT
ejpam-3632	350	9	algebra	algebra	NOUN
ejpam-3632	350	10	involving	involve	VERB
ejpam-3632	350	11	hyperatoms	hyperatom	NOUN
ejpam-3632	350	12	.	.	PUNCT
ejpam-3632	351	1	far	far	PROPN
ejpam-3632	351	2	east	east	PROPN
ejpam-3632	351	3	journal	journal	PROPN
ejpam-3632	351	4	mathematical	mathematical	PROPN
ejpam-3632	351	5	sciences	sciences	PROPN
ejpam-3632	351	6	,	,	PUNCT
ejpam-3632	351	7	103(4):743–755	103(4):743–755	NUM
ejpam-3632	351	8	,	,	PUNCT
ejpam-3632	351	9	2018	2018	NUM
ejpam-3632	351	10	.	.	PUNCT
ejpam-3632	352	1	[	[	X
ejpam-3632	352	2	2	2	NUM
ejpam-3632	352	3	]	]	X
ejpam-3632	352	4	s	s	PART
ejpam-3632	352	5	burris	burris	PROPN
ejpam-3632	352	6	and	and	CCONJ
ejpam-3632	352	7	h	h	PROPN
ejpam-3632	352	8	sankappanavar	sankappanavar	NOUN
ejpam-3632	352	9	.	.	PUNCT
ejpam-3632	353	1	a	a	DET
ejpam-3632	353	2	course	course	NOUN
ejpam-3632	353	3	in	in	ADP
ejpam-3632	353	4	universal	universal	ADJ
ejpam-3632	353	5	algebra	algebra	NOUN
ejpam-3632	353	6	.	.	PUNCT
ejpam-3632	354	1	springer	springer	NOUN
ejpam-3632	354	2	-	-	PUNCT
ejpam-3632	354	3	verlag	verlag	PROPN
ejpam-3632	354	4	,	,	PUNCT
ejpam-3632	354	5	new	new	PROPN
ejpam-3632	354	6	york	york	PROPN
ejpam-3632	354	7	.	.	PROPN
ejpam-3632	354	8	,	,	PUNCT
ejpam-3632	354	9	heidelbery	heidelbery	PROPN
ejpam-3632	354	10	,	,	PUNCT
ejpam-3632	354	11	berlin	berlin	PROPN
ejpam-3632	354	12	,	,	PUNCT
ejpam-3632	354	13	1981	1981	NUM
ejpam-3632	354	14	.	.	PUNCT
ejpam-3632	355	1	[	[	X
ejpam-3632	355	2	3	3	NUM
ejpam-3632	355	3	]	]	PUNCT
ejpam-3632	355	4	h	h	NOUN
ejpam-3632	355	5	harizavi	harizavi	NOUN
ejpam-3632	355	6	.	.	PUNCT
ejpam-3632	356	1	on	on	ADP
ejpam-3632	356	2	direct	direct	ADJ
ejpam-3632	356	3	sum	sum	NOUN
ejpam-3632	356	4	of	of	ADP
ejpam-3632	356	5	branches	branch	NOUN
ejpam-3632	356	6	in	in	ADP
ejpam-3632	356	7	hyper	hyper	ADJ
ejpam-3632	356	8	bck	bck	NOUN
ejpam-3632	356	9	-	-	PUNCT
ejpam-3632	356	10	algebras	algebras	PROPN
ejpam-3632	356	11	.	.	PUNCT
ejpam-3632	356	12	iranian	iranian	PROPN
ejpam-3632	356	13	journal	journal	PROPN
ejpam-3632	356	14	of	of	ADP
ejpam-3632	356	15	mathematical	mathematical	ADJ
ejpam-3632	356	16	sciences	sciences	PROPN
ejpam-3632	356	17	and	and	CCONJ
ejpam-3632	356	18	informatics	informatic	NOUN
ejpam-3632	356	19	,	,	PUNCT
ejpam-3632	356	20	11(2):43–55	11(2):43–55	NUM
ejpam-3632	356	21	,	,	PUNCT
ejpam-3632	356	22	2016	2016	NUM
ejpam-3632	356	23	.	.	PUNCT
ejpam-3632	357	1	[	[	X
ejpam-3632	357	2	4	4	NUM
ejpam-3632	357	3	]	]	X
ejpam-3632	357	4	y	y	PROPN
ejpam-3632	357	5	imai	imai	PROPN
ejpam-3632	357	6	and	and	CCONJ
ejpam-3632	357	7	k	k	PROPN
ejpam-3632	357	8	iséki	iséki	PROPN
ejpam-3632	357	9	.	.	PROPN
ejpam-3632	357	10	on	on	ADP
ejpam-3632	357	11	axiom	axiom	NOUN
ejpam-3632	357	12	systems	system	NOUN
ejpam-3632	357	13	of	of	ADP
ejpam-3632	357	14	propositional	propositional	ADJ
ejpam-3632	357	15	calculi	calculi	PROPN
ejpam-3632	357	16	xiv	xiv	PROPN
ejpam-3632	357	17	.	.	PUNCT
ejpam-3632	358	1	proc	proc	PROPN
ejpam-3632	358	2	.	.	PUNCT
ejpam-3632	359	1	japan	japan	PROPN
ejpam-3632	359	2	academy	academy	PROPN
ejpam-3632	359	3	,	,	PUNCT
ejpam-3632	359	4	42:19–22	42:19–22	NUM
ejpam-3632	359	5	,	,	PUNCT
ejpam-3632	359	6	1966	1966	NUM
ejpam-3632	359	7	.	.	PUNCT
ejpam-3632	360	1	[	[	X
ejpam-3632	360	2	5	5	NUM
ejpam-3632	360	3	]	]	X
ejpam-3632	360	4	y	y	PROPN
ejpam-3632	360	5	jun	jun	PROPN
ejpam-3632	360	6	m	m	PROPN
ejpam-3632	360	7	zahedi	zahedi	PROPN
ejpam-3632	360	8	,	,	PUNCT
ejpam-3632	360	9	x	x	PROPN
ejpam-3632	360	10	xin	xin	PROPN
ejpam-3632	360	11	and	and	CCONJ
ejpam-3632	360	12	r	r	PROPN
ejpam-3632	360	13	borzooei	borzooei	PROPN
ejpam-3632	360	14	.	.	PUNCT
ejpam-3632	361	1	on	on	ADP
ejpam-3632	361	2	hyper	hyper	ADJ
ejpam-3632	361	3	bck	bck	NOUN
ejpam-3632	361	4	-	-	PUNCT
ejpam-3632	361	5	algebras	algebras	PROPN
ejpam-3632	361	6	.	.	PUNCT
ejpam-3632	362	1	italian	italian	ADJ
ejpam-3632	362	2	journal	journal	NOUN
ejpam-3632	362	3	of	of	ADP
ejpam-3632	362	4	pure	pure	ADJ
ejpam-3632	362	5	and	and	CCONJ
ejpam-3632	362	6	applied	applied	ADJ
ejpam-3632	362	7	mathematics	mathematic	NOUN
ejpam-3632	362	8	,	,	PUNCT
ejpam-3632	362	9	8:127–136	8:127–136	NUM
ejpam-3632	362	10	,	,	PUNCT
ejpam-3632	362	11	2000	2000	NUM
ejpam-3632	362	12	.	.	PUNCT
ejpam-3632	363	1	[	[	X
ejpam-3632	363	2	6	6	NUM
ejpam-3632	363	3	]	]	X
ejpam-3632	363	4	f	f	PROPN
ejpam-3632	363	5	marty	marty	PROPN
ejpam-3632	363	6	.	.	PUNCT
ejpam-3632	364	1	sun	sun	PROPN
ejpam-3632	364	2	une	une	PROPN
ejpam-3632	364	3	generalization	generalization	NOUN
ejpam-3632	364	4	da	da	PROPN
ejpam-3632	364	5	la	la	PROPN
ejpam-3632	364	6	notion	notion	NOUN
ejpam-3632	364	7	de	de	PROPN
ejpam-3632	364	8	group	group	NOUN
ejpam-3632	364	9	.	.	PUNCT
ejpam-3632	365	1	stockholm	stockholm	PROPN
ejpam-3632	365	2	:	:	PUNCT
ejpam-3632	365	3	8th	8th	ADJ
ejpam-3632	365	4	congress	congress	PROPN
ejpam-3632	365	5	math	math	NOUN
ejpam-3632	365	6	.	.	PUNCT
ejpam-3632	366	1	scandinaves	scandinave	NOUN
ejpam-3632	366	2	,	,	PUNCT
ejpam-3632	366	3	pages	page	NOUN
ejpam-3632	366	4	45–49	45–49	NUM
ejpam-3632	366	5	,	,	PUNCT
ejpam-3632	366	6	1934	1934	NUM
ejpam-3632	366	7	.	.	PUNCT
ejpam-3632	367	1	[	[	X
ejpam-3632	367	2	7	7	NUM
ejpam-3632	367	3	]	]	X
ejpam-3632	367	4	r	r	NOUN
ejpam-3632	367	5	patangan	patangan	NOUN
ejpam-3632	367	6	and	and	CCONJ
ejpam-3632	367	7	s	s	X
ejpam-3632	367	8	canoy	canoy	PROPN
ejpam-3632	367	9	jr	jr	PROPN
ejpam-3632	367	10	.	.	PUNCT
ejpam-3632	368	1	a	a	DET
ejpam-3632	368	2	topology	topology	NOUN
ejpam-3632	368	3	on	on	ADP
ejpam-3632	368	4	a	a	DET
ejpam-3632	368	5	hyper	hyper	ADJ
ejpam-3632	368	6	bck	bck	NOUN
ejpam-3632	368	7	-	-	PUNCT
ejpam-3632	368	8	algebra	algebra	NOUN
ejpam-3632	368	9	.	.	PUNCT
ejpam-3632	369	1	jp	jp	PROPN
ejpam-3632	369	2	journal	journal	PROPN
ejpam-3632	369	3	of	of	ADP
ejpam-3632	369	4	algebra	algebra	PROPN
ejpam-3632	369	5	,	,	PUNCT
ejpam-3632	369	6	number	number	NOUN
ejpam-3632	369	7	theory	theory	NOUN
ejpam-3632	369	8	and	and	CCONJ
ejpam-3632	369	9	applications	application	NOUN
ejpam-3632	369	10	,	,	PUNCT
ejpam-3632	369	11	40:787–797	40:787–797	NUM
ejpam-3632	369	12	,	,	PUNCT
ejpam-3632	369	13	2018	2018	NUM
ejpam-3632	369	14	.	.	PUNCT
ejpam-3632	370	1	[	[	X
ejpam-3632	370	2	8	8	NUM
ejpam-3632	370	3	]	]	X
ejpam-3632	370	4	r	r	NOUN
ejpam-3632	370	5	patangan	patangan	NOUN
ejpam-3632	370	6	and	and	CCONJ
ejpam-3632	370	7	s	s	X
ejpam-3632	370	8	canoy	canoy	PROPN
ejpam-3632	370	9	jr	jr	PROPN
ejpam-3632	370	10	.	.	PUNCT
ejpam-3632	371	1	a	a	DET
ejpam-3632	371	2	topology	topology	NOUN
ejpam-3632	371	3	on	on	ADP
ejpam-3632	371	4	a	a	DET
ejpam-3632	371	5	hyper	hyper	ADJ
ejpam-3632	371	6	bck	bck	NOUN
ejpam-3632	371	7	-	-	PUNCT
ejpam-3632	371	8	algebra	algebra	NOUN
ejpam-3632	371	9	via	via	ADP
ejpam-3632	371	10	left	left	ADJ
ejpam-3632	371	11	application	application	NOUN
ejpam-3632	371	12	of	of	ADP
ejpam-3632	371	13	a	a	DET
ejpam-3632	371	14	hyper	hyper	ADJ
ejpam-3632	371	15	order	order	NOUN
ejpam-3632	371	16	.	.	PUNCT
ejpam-3632	372	1	jp	jp	PROPN
ejpam-3632	372	2	journal	journal	PROPN
ejpam-3632	372	3	of	of	ADP
ejpam-3632	372	4	algebra	algebra	PROPN
ejpam-3632	372	5	,	,	PUNCT
ejpam-3632	372	6	number	number	NOUN
ejpam-3632	372	7	theory	theory	NOUN
ejpam-3632	372	8	and	and	CCONJ
ejpam-3632	372	9	applications	application	NOUN
ejpam-3632	372	10	,	,	PUNCT
ejpam-3632	372	11	40:321	40:321	NUM
ejpam-3632	372	12	–	–	PUNCT
ejpam-3632	372	13	332	332	NUM
ejpam-3632	372	14	,	,	PUNCT
ejpam-3632	372	15	2018	2018	NUM
ejpam-3632	372	16	.	.	PUNCT