id	sid	tid	token	lemma	pos
ejpam-3970	1	1	european	european	PROPN
ejpam-3970	1	2	journal	journal	PROPN
ejpam-3970	1	3	of	of	ADP
ejpam-3970	1	4	pure	pure	ADJ
ejpam-3970	1	5	and	and	CCONJ
ejpam-3970	1	6	applied	apply	VERB
ejpam-3970	1	7	mathematics	mathematic	NOUN
ejpam-3970	1	8	vol	vol	NOUN
ejpam-3970	1	9	.	.	PUNCT
ejpam-3970	2	1	14	14	NUM
ejpam-3970	2	2	,	,	PUNCT
ejpam-3970	2	3	no	no	INTJ
ejpam-3970	2	4	.	.	NOUN
ejpam-3970	2	5	2	2	NUM
ejpam-3970	2	6	,	,	PUNCT
ejpam-3970	2	7	2021	2021	NUM
ejpam-3970	2	8	,	,	PUNCT
ejpam-3970	2	9	590	590	NUM
ejpam-3970	2	10	-	-	SYM
ejpam-3970	2	11	600	600	NUM
ejpam-3970	2	12	issn	issn	PROPN
ejpam-3970	2	13	1307	1307	NUM
ejpam-3970	2	14	-	-	SYM
ejpam-3970	2	15	5543	5543	NUM
ejpam-3970	2	16	–	–	PUNCT
ejpam-3970	2	17	ejpam.com	ejpam.com	X
ejpam-3970	2	18	published	publish	VERB
ejpam-3970	2	19	by	by	ADP
ejpam-3970	2	20	new	new	PROPN
ejpam-3970	2	21	york	york	PROPN
ejpam-3970	2	22	business	business	PROPN
ejpam-3970	2	23	global	global	PROPN
ejpam-3970	2	24	a	a	DET
ejpam-3970	2	25	topology	topology	NOUN
ejpam-3970	2	26	on	on	ADP
ejpam-3970	2	27	a	a	DET
ejpam-3970	2	28	hyper	hyper	ADJ
ejpam-3970	2	29	bci	bci	NOUN
ejpam-3970	2	30	-	-	NOUN
ejpam-3970	2	31	algebra	algebra	NOUN
ejpam-3970	2	32	generated	generate	VERB
ejpam-3970	2	33	by	by	ADP
ejpam-3970	2	34	a	a	DET
ejpam-3970	2	35	hyper	hyper	ADJ
ejpam-3970	2	36	-	-	NOUN
ejpam-3970	2	37	order	order	NOUN
ejpam-3970	2	38	michelle	michelle	NOUN
ejpam-3970	2	39	t.	t.	PROPN
ejpam-3970	2	40	panganduyon1	panganduyon1	PROPN
ejpam-3970	2	41	,	,	PUNCT
ejpam-3970	2	42	sergio	sergio	PROPN
ejpam-3970	2	43	r.	r.	PROPN
ejpam-3970	2	44	canoy	canoy	PROPN
ejpam-3970	2	45	,	,	PUNCT
ejpam-3970	2	46	jr.2	jr.2	PROPN
ejpam-3970	2	47	,	,	PUNCT
ejpam-3970	2	48	bijan	bijan	NOUN
ejpam-3970	2	49	davvaz3	davvaz3	NOUN
ejpam-3970	2	50	1	1	NUM
ejpam-3970	2	51	college	college	NOUN
ejpam-3970	2	52	of	of	ADP
ejpam-3970	2	53	arts	art	NOUN
ejpam-3970	2	54	and	and	CCONJ
ejpam-3970	2	55	sciences	science	NOUN
ejpam-3970	2	56	,	,	PUNCT
ejpam-3970	2	57	surigao	surigao	NOUN
ejpam-3970	2	58	state	state	NOUN
ejpam-3970	2	59	college	college	PROPN
ejpam-3970	2	60	of	of	ADP
ejpam-3970	2	61	technology	technology	NOUN
ejpam-3970	2	62	,	,	PUNCT
ejpam-3970	2	63	8400	8400	NUM
ejpam-3970	2	64	surigao	surigao	NOUN
ejpam-3970	2	65	city	city	NOUN
ejpam-3970	2	66	,	,	PUNCT
ejpam-3970	2	67	surigao	surigao	NOUN
ejpam-3970	2	68	del	del	PROPN
ejpam-3970	2	69	norte	norte	NOUN
ejpam-3970	2	70	,	,	PUNCT
ejpam-3970	2	71	philippines	philippine	NOUN
ejpam-3970	2	72	2	2	NUM
ejpam-3970	2	73	department	department	NOUN
ejpam-3970	2	74	of	of	ADP
ejpam-3970	2	75	mathematics	mathematic	NOUN
ejpam-3970	2	76	and	and	CCONJ
ejpam-3970	2	77	statistics	statistic	NOUN
ejpam-3970	2	78	,	,	PUNCT
ejpam-3970	2	79	college	college	NOUN
ejpam-3970	2	80	of	of	ADP
ejpam-3970	2	81	science	science	NOUN
ejpam-3970	2	82	and	and	CCONJ
ejpam-3970	2	83	mathematics	mathematic	NOUN
ejpam-3970	2	84	,	,	PUNCT
ejpam-3970	2	85	center	center	NOUN
ejpam-3970	2	86	of	of	ADP
ejpam-3970	2	87	graph	graph	NOUN
ejpam-3970	2	88	theory	theory	NOUN
ejpam-3970	2	89	,	,	PUNCT
ejpam-3970	2	90	algebra	algebra	NOUN
ejpam-3970	2	91	and	and	CCONJ
ejpam-3970	2	92	analysis	analysis	NOUN
ejpam-3970	2	93	-	-	PUNCT
ejpam-3970	2	94	prism	prism	NOUN
ejpam-3970	2	95	,	,	PUNCT
ejpam-3970	2	96	mindanao	mindanao	PROPN
ejpam-3970	2	97	state	state	PROPN
ejpam-3970	2	98	university	university	PROPN
ejpam-3970	2	99	-	-	PUNCT
ejpam-3970	2	100	iligan	iligan	PROPN
ejpam-3970	2	101	institute	institute	PROPN
ejpam-3970	2	102	of	of	ADP
ejpam-3970	2	103	technology	technology	PROPN
ejpam-3970	2	104	,	,	PUNCT
ejpam-3970	2	105	9200	9200	NUM
ejpam-3970	2	106	iligan	iligan	ADJ
ejpam-3970	2	107	city	city	NOUN
ejpam-3970	2	108	,	,	PUNCT
ejpam-3970	2	109	philippines	philippines	PROPN
ejpam-3970	2	110	3	3	NUM
ejpam-3970	2	111	department	department	NOUN
ejpam-3970	2	112	of	of	ADP
ejpam-3970	2	113	mathematics	mathematics	PROPN
ejpam-3970	2	114	,	,	PUNCT
ejpam-3970	2	115	yadz	yadz	ADJ
ejpam-3970	2	116	university	university	NOUN
ejpam-3970	2	117	,	,	PUNCT
ejpam-3970	2	118	yadz	yadz	PROPN
ejpam-3970	2	119	,	,	PUNCT
ejpam-3970	2	120	iran	iran	PROPN
ejpam-3970	2	121	abstract	abstract	NOUN
ejpam-3970	2	122	.	.	PUNCT
ejpam-3970	3	1	in	in	ADP
ejpam-3970	3	2	this	this	DET
ejpam-3970	3	3	paper	paper	NOUN
ejpam-3970	3	4	,	,	PUNCT
ejpam-3970	3	5	we	we	PRON
ejpam-3970	3	6	introduce	introduce	VERB
ejpam-3970	3	7	an	an	DET
ejpam-3970	3	8	operator	operator	NOUN
ejpam-3970	3	9	on	on	ADP
ejpam-3970	3	10	a	a	DET
ejpam-3970	3	11	hyper	hyper	ADJ
ejpam-3970	3	12	bci	bci	NOUN
ejpam-3970	3	13	-	-	NOUN
ejpam-3970	3	14	algebra	algebra	NOUN
ejpam-3970	3	15	via	via	ADP
ejpam-3970	3	16	application	application	NOUN
ejpam-3970	3	17	of	of	ADP
ejpam-3970	3	18	a	a	DET
ejpam-3970	3	19	left	left	ADJ
ejpam-3970	3	20	hyper	hyper	NOUN
ejpam-3970	3	21	-	-	NOUN
ejpam-3970	3	22	order	order	NOUN
ejpam-3970	3	23	.	.	PUNCT
ejpam-3970	4	1	the	the	DET
ejpam-3970	4	2	family	family	NOUN
ejpam-3970	4	3	consisting	consist	VERB
ejpam-3970	4	4	of	of	ADP
ejpam-3970	4	5	the	the	DET
ejpam-3970	4	6	images	image	NOUN
ejpam-3970	4	7	of	of	ADP
ejpam-3970	4	8	subsets	subset	NOUN
ejpam-3970	4	9	under	under	ADP
ejpam-3970	4	10	the	the	DET
ejpam-3970	4	11	operator	operator	NOUN
ejpam-3970	4	12	turns	turn	VERB
ejpam-3970	4	13	out	out	ADP
ejpam-3970	4	14	to	to	PART
ejpam-3970	4	15	be	be	AUX
ejpam-3970	4	16	a	a	DET
ejpam-3970	4	17	base	base	NOUN
ejpam-3970	4	18	for	for	ADP
ejpam-3970	4	19	some	some	DET
ejpam-3970	4	20	topology	topology	NOUN
ejpam-3970	4	21	on	on	ADP
ejpam-3970	4	22	the	the	DET
ejpam-3970	4	23	hyper	hyper	ADJ
ejpam-3970	4	24	bci	bci	NOUN
ejpam-3970	4	25	-	-	NOUN
ejpam-3970	4	26	algebra	algebra	NOUN
ejpam-3970	4	27	.	.	PUNCT
ejpam-3970	5	1	we	we	PRON
ejpam-3970	5	2	investigate	investigate	VERB
ejpam-3970	5	3	some	some	DET
ejpam-3970	5	4	important	important	ADJ
ejpam-3970	5	5	properties	property	NOUN
ejpam-3970	5	6	of	of	ADP
ejpam-3970	5	7	the	the	DET
ejpam-3970	5	8	induced	induced	ADJ
ejpam-3970	5	9	topology	topology	NOUN
ejpam-3970	5	10	on	on	ADP
ejpam-3970	5	11	certain	certain	ADJ
ejpam-3970	5	12	hyper	hyper	ADJ
ejpam-3970	5	13	bci	bci	NOUN
ejpam-3970	5	14	-	-	PUNCT
ejpam-3970	5	15	algebras	algebra	NOUN
ejpam-3970	5	16	.	.	PUNCT
ejpam-3970	6	1	in	in	ADP
ejpam-3970	6	2	particular	particular	ADJ
ejpam-3970	6	3	,	,	PUNCT
ejpam-3970	6	4	we	we	PRON
ejpam-3970	6	5	show	show	VERB
ejpam-3970	6	6	that	that	SCONJ
ejpam-3970	6	7	the	the	DET
ejpam-3970	6	8	generated	generate	VERB
ejpam-3970	6	9	topology	topology	NOUN
ejpam-3970	6	10	on	on	ADP
ejpam-3970	6	11	a	a	DET
ejpam-3970	6	12	non	non	ADJ
ejpam-3970	6	13	-	-	ADJ
ejpam-3970	6	14	trivial	trivial	ADJ
ejpam-3970	6	15	hyper	hyper	ADJ
ejpam-3970	6	16	subalgebra	subalgebra	NOUN
ejpam-3970	6	17	of	of	ADP
ejpam-3970	6	18	an	an	DET
ejpam-3970	6	19	ordered	order	VERB
ejpam-3970	6	20	hyper	hyper	ADJ
ejpam-3970	6	21	bci	bci	NOUN
ejpam-3970	6	22	-	-	PUNCT
ejpam-3970	6	23	algebra	algebra	NOUN
ejpam-3970	6	24	coincides	coincide	VERB
ejpam-3970	6	25	with	with	ADP
ejpam-3970	6	26	the	the	DET
ejpam-3970	6	27	relative	relative	ADJ
ejpam-3970	6	28	topology	topology	NOUN
ejpam-3970	6	29	on	on	ADP
ejpam-3970	6	30	this	this	DET
ejpam-3970	6	31	hyper	hyper	ADJ
ejpam-3970	6	32	subalgebra	subalgebra	NOUN
ejpam-3970	6	33	.	.	PUNCT
ejpam-3970	7	1	2020	2020	NUM
ejpam-3970	7	2	mathematics	mathematic	NOUN
ejpam-3970	7	3	subject	subject	NOUN
ejpam-3970	7	4	classifications	classification	NOUN
ejpam-3970	7	5	:	:	PUNCT
ejpam-3970	7	6	20m14	20m14	NUM
ejpam-3970	7	7	,	,	PUNCT
ejpam-3970	7	8	05c25	05c25	NOUN
ejpam-3970	7	9	key	key	ADJ
ejpam-3970	7	10	words	word	NOUN
ejpam-3970	7	11	and	and	CCONJ
ejpam-3970	7	12	phrases	phrase	NOUN
ejpam-3970	7	13	:	:	PUNCT
ejpam-3970	7	14	hyper	hyper	ADJ
ejpam-3970	7	15	bci	bci	NOUN
ejpam-3970	7	16	-	-	NOUN
ejpam-3970	7	17	algebra	algebra	NOUN
ejpam-3970	7	18	,	,	PUNCT
ejpam-3970	7	19	topology	topology	NOUN
ejpam-3970	7	20	,	,	PUNCT
ejpam-3970	7	21	hyper	hyper	NOUN
ejpam-3970	7	22	-	-	NOUN
ejpam-3970	7	23	order	order	NOUN
ejpam-3970	7	24	,	,	PUNCT
ejpam-3970	7	25	hyperatom	hyperatom	NOUN
ejpam-3970	7	26	1	1	NUM
ejpam-3970	7	27	.	.	PUNCT
ejpam-3970	7	28	introduction	introduction	NOUN
ejpam-3970	7	29	the	the	DET
ejpam-3970	7	30	notion	notion	NOUN
ejpam-3970	7	31	of	of	ADP
ejpam-3970	7	32	bck	bck	PROPN
ejpam-3970	7	33	-	-	PUNCT
ejpam-3970	7	34	algebras	algebras	PROPN
ejpam-3970	7	35	was	be	AUX
ejpam-3970	7	36	proposed	propose	VERB
ejpam-3970	7	37	by	by	ADP
ejpam-3970	7	38	y.	y.	PROPN
ejpam-3970	7	39	imai	imai	PROPN
ejpam-3970	7	40	and	and	CCONJ
ejpam-3970	7	41	k.	k.	PROPN
ejpam-3970	7	42	iséki	iséki	PROPN
ejpam-3970	7	43	in	in	ADP
ejpam-3970	7	44	1966	1966	NUM
ejpam-3970	7	45	.	.	PUNCT
ejpam-3970	8	1	in	in	ADP
ejpam-3970	8	2	the	the	DET
ejpam-3970	8	3	same	same	ADJ
ejpam-3970	8	4	year	year	NOUN
ejpam-3970	8	5	,	,	PUNCT
ejpam-3970	8	6	k.	k.	PROPN
ejpam-3970	8	7	iséki	iséki	PUNCT
ejpam-3970	9	1	[	[	X
ejpam-3970	9	2	3	3	X
ejpam-3970	9	3	]	]	PUNCT
ejpam-3970	9	4	introduced	introduce	VERB
ejpam-3970	9	5	the	the	DET
ejpam-3970	9	6	notion	notion	NOUN
ejpam-3970	9	7	of	of	ADP
ejpam-3970	9	8	a	a	DET
ejpam-3970	9	9	bci	bci	NOUN
ejpam-3970	9	10	-	-	NOUN
ejpam-3970	9	11	algebra	algebra	NOUN
ejpam-3970	9	12	which	which	PRON
ejpam-3970	9	13	is	be	AUX
ejpam-3970	9	14	a	a	DET
ejpam-3970	9	15	generalization	generalization	NOUN
ejpam-3970	9	16	of	of	ADP
ejpam-3970	9	17	bck	bck	NOUN
ejpam-3970	9	18	-	-	PUNCT
ejpam-3970	9	19	algebra	algebra	NOUN
ejpam-3970	9	20	.	.	PUNCT
ejpam-3970	10	1	r.	r.	PROPN
ejpam-3970	10	2	a.	a.	PROPN
ejpam-3970	10	3	alo	alo	PROPN
ejpam-3970	10	4	and	and	CCONJ
ejpam-3970	10	5	e.	e.	PROPN
ejpam-3970	10	6	y.	y.	PROPN
ejpam-3970	10	7	deeba	deeba	PROPN
ejpam-3970	11	1	[	[	X
ejpam-3970	11	2	1	1	X
ejpam-3970	11	3	]	]	PUNCT
ejpam-3970	11	4	attempted	attempt	VERB
ejpam-3970	11	5	to	to	PART
ejpam-3970	11	6	study	study	VERB
ejpam-3970	11	7	the	the	DET
ejpam-3970	11	8	topological	topological	ADJ
ejpam-3970	11	9	aspects	aspect	NOUN
ejpam-3970	11	10	of	of	ADP
ejpam-3970	11	11	the	the	DET
ejpam-3970	11	12	bck	bck	NOUN
ejpam-3970	11	13	-	-	PUNCT
ejpam-3970	11	14	structures	structure	NOUN
ejpam-3970	11	15	.	.	PUNCT
ejpam-3970	12	1	they	they	PRON
ejpam-3970	12	2	studied	study	VERB
ejpam-3970	12	3	and	and	CCONJ
ejpam-3970	12	4	investigated	investigate	VERB
ejpam-3970	12	5	various	various	ADJ
ejpam-3970	12	6	topologies	topology	NOUN
ejpam-3970	12	7	on	on	ADP
ejpam-3970	12	8	bck	bck	NOUN
ejpam-3970	12	9	-	-	PUNCT
ejpam-3970	12	10	algebras	algebras	NOUN
ejpam-3970	12	11	analogous	analogous	ADJ
ejpam-3970	12	12	to	to	ADP
ejpam-3970	12	13	that	that	PRON
ejpam-3970	12	14	which	which	PRON
ejpam-3970	12	15	had	have	AUX
ejpam-3970	12	16	already	already	ADV
ejpam-3970	12	17	been	be	AUX
ejpam-3970	12	18	studied	study	VERB
ejpam-3970	12	19	on	on	ADP
ejpam-3970	12	20	lattices	lattice	NOUN
ejpam-3970	12	21	.	.	PUNCT
ejpam-3970	13	1	in	in	ADP
ejpam-3970	13	2	[	[	X
ejpam-3970	13	3	4	4	NUM
ejpam-3970	13	4	]	]	PUNCT
ejpam-3970	13	5	,	,	PUNCT
ejpam-3970	13	6	y.	y.	PROPN
ejpam-3970	13	7	b.	b.	PROPN
ejpam-3970	13	8	jun	jun	PROPN
ejpam-3970	13	9	et	et	PROPN
ejpam-3970	13	10	al	al	PROPN
ejpam-3970	13	11	.	.	PROPN
ejpam-3970	13	12	initiated	initiate	VERB
ejpam-3970	13	13	the	the	DET
ejpam-3970	13	14	study	study	NOUN
ejpam-3970	13	15	of	of	ADP
ejpam-3970	13	16	topological	topological	ADJ
ejpam-3970	13	17	bci	bci	NOUN
ejpam-3970	13	18	-	-	PUNCT
ejpam-3970	13	19	algebras	algebras	X
ejpam-3970	13	20	(	(	PUNCT
ejpam-3970	13	21	briefly	briefly	ADV
ejpam-3970	13	22	,	,	PUNCT
ejpam-3970	13	23	tbci	tbci	NOUN
ejpam-3970	13	24	-	-	PUNCT
ejpam-3970	13	25	algebras	algebra	NOUN
ejpam-3970	13	26	)	)	PUNCT
ejpam-3970	13	27	.	.	PUNCT
ejpam-3970	14	1	in	in	ADP
ejpam-3970	14	2	their	their	PRON
ejpam-3970	14	3	study	study	NOUN
ejpam-3970	14	4	a	a	DET
ejpam-3970	14	5	bci	bci	NOUN
ejpam-3970	14	6	-	-	NOUN
ejpam-3970	14	7	algebra	algebra	NOUN
ejpam-3970	14	8	(	(	PUNCT
ejpam-3970	14	9	h	h	NOUN
ejpam-3970	14	10	,	,	PUNCT
ejpam-3970	14	11	∗	∗	NOUN
ejpam-3970	14	12	,	,	PUNCT
ejpam-3970	14	13	0	0	NUM
ejpam-3970	14	14	)	)	PUNCT
ejpam-3970	14	15	is	be	AUX
ejpam-3970	14	16	furnished	furnish	VERB
ejpam-3970	14	17	with	with	ADP
ejpam-3970	14	18	a	a	DET
ejpam-3970	14	19	topology	topology	NOUN
ejpam-3970	14	20	in	in	ADP
ejpam-3970	14	21	such	such	DET
ejpam-3970	14	22	a	a	DET
ejpam-3970	14	23	way	way	NOUN
ejpam-3970	14	24	that	that	PRON
ejpam-3970	14	25	the	the	DET
ejpam-3970	14	26	associated	associated	ADJ
ejpam-3970	14	27	operation	operation	NOUN
ejpam-3970	14	28	∗	∗	NOUN
ejpam-3970	14	29	:	:	PUNCT
ejpam-3970	15	1	h	h	NOUN
ejpam-3970	15	2	×h	×h	PROPN
ejpam-3970	16	1	→	→	SYM
ejpam-3970	16	2	h	h	NOUN
ejpam-3970	16	3	of	of	ADP
ejpam-3970	16	4	the	the	DET
ejpam-3970	16	5	bci	bci	NOUN
ejpam-3970	16	6	-	-	NOUN
ejpam-3970	16	7	algebra	algebra	NOUN
ejpam-3970	16	8	is	be	AUX
ejpam-3970	16	9	continuous	continuous	ADJ
ejpam-3970	16	10	,	,	PUNCT
ejpam-3970	16	11	where	where	SCONJ
ejpam-3970	16	12	the	the	DET
ejpam-3970	16	13	cartesian	cartesian	ADJ
ejpam-3970	16	14	product	product	NOUN
ejpam-3970	16	15	h	h	NOUN
ejpam-3970	16	16	×h	×h	PROPN
ejpam-3970	16	17	is	be	AUX
ejpam-3970	16	18	furnished	furnish	VERB
ejpam-3970	16	19	with	with	ADP
ejpam-3970	16	20	the	the	DET
ejpam-3970	16	21	product	product	NOUN
ejpam-3970	16	22	topology	topology	NOUN
ejpam-3970	16	23	.	.	PUNCT
ejpam-3970	17	1	during	during	ADP
ejpam-3970	17	2	the	the	DET
ejpam-3970	17	3	8th	8th	ADJ
ejpam-3970	17	4	congress	congress	NOUN
ejpam-3970	17	5	of	of	ADP
ejpam-3970	17	6	scandinavian	scandinavian	ADJ
ejpam-3970	17	7	mathematicians	mathematician	NOUN
ejpam-3970	17	8	,	,	PUNCT
ejpam-3970	17	9	f.	f.	PROPN
ejpam-3970	17	10	marty	marty	PROPN
ejpam-3970	18	1	[	[	X
ejpam-3970	18	2	6	6	NUM
ejpam-3970	18	3	]	]	PUNCT
ejpam-3970	18	4	introduced	introduce	VERB
ejpam-3970	18	5	the	the	DET
ejpam-3970	18	6	theory	theory	NOUN
ejpam-3970	18	7	of	of	ADP
ejpam-3970	18	8	hyperstructure	hyperstructure	PROPN
ejpam-3970	18	9	(	(	PUNCT
ejpam-3970	18	10	sometimes	sometimes	ADV
ejpam-3970	18	11	called	call	VERB
ejpam-3970	18	12	multialgebras	multialgebra	NOUN
ejpam-3970	18	13	)	)	PUNCT
ejpam-3970	18	14	.	.	PUNCT
ejpam-3970	19	1	following	follow	VERB
ejpam-3970	19	2	its	its	PRON
ejpam-3970	19	3	introduction	introduction	NOUN
ejpam-3970	19	4	,	,	PUNCT
ejpam-3970	19	5	various	various	ADJ
ejpam-3970	19	6	algebraic	algebraic	ADJ
ejpam-3970	19	7	hyperstructures	hyperstructure	NOUN
ejpam-3970	19	8	have	have	AUX
ejpam-3970	19	9	been	be	AUX
ejpam-3970	19	10	defined	define	VERB
ejpam-3970	19	11	and	and	CCONJ
ejpam-3970	19	12	many	many	ADJ
ejpam-3970	19	13	important	important	ADJ
ejpam-3970	19	14	results	result	NOUN
ejpam-3970	19	15	have	have	VERB
ejpam-3970	19	16	doi	doi	NOUN
ejpam-3970	19	17	:	:	PUNCT
ejpam-3970	19	18	https://doi.org/10.29020/nybg.ejpam.v14i2.3970	https://doi.org/10.29020/nybg.ejpam.v14i2.3970	PROPN
ejpam-3970	19	19	email	email	NOUN
ejpam-3970	19	20	addresses	address	NOUN
ejpam-3970	19	21	:	:	PUNCT
ejpam-3970	19	22	mpanganduyon@ssct.edu.ph	mpanganduyon@ssct.edu.ph	PROPN
ejpam-3970	19	23	(	(	PUNCT
ejpam-3970	19	24	m.	m.	NOUN
ejpam-3970	19	25	panganduyon	panganduyon	NOUN
ejpam-3970	19	26	)	)	PUNCT
ejpam-3970	19	27	,	,	PUNCT
ejpam-3970	19	28	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-3970	19	29	(	(	PUNCT
ejpam-3970	19	30	s.	s.	PROPN
ejpam-3970	19	31	canoy	canoy	PROPN
ejpam-3970	19	32	,	,	PUNCT
ejpam-3970	19	33	jr	jr	PROPN
ejpam-3970	19	34	.	.	PROPN
ejpam-3970	19	35	)	)	PUNCT
ejpam-3970	19	36	,	,	PUNCT
ejpam-3970	20	1	bdavvaz@yahoo.com	bdavvaz@yahoo.com	X
ejpam-3970	20	2	(	(	PUNCT
ejpam-3970	20	3	b.	b.	PROPN
ejpam-3970	20	4	davvaz	davvaz	PROPN
ejpam-3970	20	5	)	)	PUNCT
ejpam-3970	20	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3970	21	1	590	590	NUM
ejpam-3970	21	2	c	c	X
ejpam-3970	21	3	©	©	PROPN
ejpam-3970	21	4	2021	2021	NUM
ejpam-3970	21	5	ejpam	ejpam	VERB
ejpam-3970	21	6	all	all	DET
ejpam-3970	21	7	rights	right	NOUN
ejpam-3970	21	8	reserved	reserve	VERB
ejpam-3970	21	9	.	.	PUNCT
ejpam-3970	22	1	m.	m.	NOUN
ejpam-3970	22	2	panganduyon	panganduyon	NOUN
ejpam-3970	22	3	,	,	PUNCT
ejpam-3970	22	4	s.	s.	PROPN
ejpam-3970	22	5	canoy	canoy	PROPN
ejpam-3970	22	6	,	,	PUNCT
ejpam-3970	22	7	jr	jr	PROPN
ejpam-3970	22	8	.	.	PROPN
ejpam-3970	22	9	,	,	PUNCT
ejpam-3970	22	10	b.	b.	PROPN
ejpam-3970	22	11	davvaz	davvaz	PROPN
ejpam-3970	22	12	/	/	SYM
ejpam-3970	22	13	eur	eur	PROPN
ejpam-3970	22	14	.	.	PUNCT
ejpam-3970	23	1	j.	j.	PROPN
ejpam-3970	23	2	pure	pure	PROPN
ejpam-3970	23	3	appl	appl	PROPN
ejpam-3970	23	4	.	.	PROPN
ejpam-3970	23	5	math	math	PROPN
ejpam-3970	23	6	,	,	PUNCT
ejpam-3970	23	7	14	14	NUM
ejpam-3970	23	8	(	(	PUNCT
ejpam-3970	23	9	2	2	NUM
ejpam-3970	23	10	)	)	PUNCT
ejpam-3970	23	11	(	(	PUNCT
ejpam-3970	23	12	2021	2021	NUM
ejpam-3970	23	13	)	)	PUNCT
ejpam-3970	23	14	,	,	PUNCT
ejpam-3970	23	15	590	590	NUM
ejpam-3970	23	16	-	-	SYM
ejpam-3970	23	17	600	600	NUM
ejpam-3970	23	18	591	591	NUM
ejpam-3970	23	19	appeared	appear	VERB
ejpam-3970	23	20	.	.	PUNCT
ejpam-3970	24	1	some	some	DET
ejpam-3970	24	2	recent	recent	ADJ
ejpam-3970	24	3	studies	study	NOUN
ejpam-3970	24	4	on	on	ADP
ejpam-3970	24	5	hyperstructures	hyperstructure	NOUN
ejpam-3970	24	6	are	be	AUX
ejpam-3970	24	7	on	on	ADP
ejpam-3970	24	8	soft	soft	ADJ
ejpam-3970	24	9	hypervector	hypervector	NOUN
ejpam-3970	24	10	spaces	space	NOUN
ejpam-3970	24	11	and	and	CCONJ
ejpam-3970	24	12	hyper	hyper	ADJ
ejpam-3970	24	13	-	-	ADJ
ejpam-3970	24	14	deductive	deductive	ADJ
ejpam-3970	24	15	systems	system	NOUN
ejpam-3970	24	16	done	do	VERB
ejpam-3970	24	17	by	by	ADP
ejpam-3970	24	18	muhiuddin	muhiuddin	PROPN
ejpam-3970	24	19	et	et	PROPN
ejpam-3970	24	20	al	al	PROPN
ejpam-3970	24	21	.	.	PUNCT
ejpam-3970	25	1	in	in	ADP
ejpam-3970	25	2	[	[	X
ejpam-3970	25	3	8	8	NUM
ejpam-3970	25	4	]	]	PUNCT
ejpam-3970	25	5	,	,	PUNCT
ejpam-3970	25	6	[	[	X
ejpam-3970	25	7	9	9	NUM
ejpam-3970	25	8	]	]	PUNCT
ejpam-3970	25	9	,	,	PUNCT
ejpam-3970	25	10	and	and	CCONJ
ejpam-3970	25	11	[	[	X
ejpam-3970	25	12	10	10	NUM
ejpam-3970	25	13	]	]	PUNCT
ejpam-3970	25	14	.	.	PUNCT
ejpam-3970	26	1	as	as	SCONJ
ejpam-3970	26	2	one	one	PRON
ejpam-3970	26	3	may	may	AUX
ejpam-3970	26	4	find	find	VERB
ejpam-3970	26	5	,	,	PUNCT
ejpam-3970	26	6	these	these	DET
ejpam-3970	26	7	hyperstructures	hyperstructure	NOUN
ejpam-3970	26	8	have	have	VERB
ejpam-3970	26	9	many	many	ADJ
ejpam-3970	26	10	applications	application	NOUN
ejpam-3970	26	11	in	in	ADP
ejpam-3970	26	12	both	both	CCONJ
ejpam-3970	26	13	pure	pure	ADJ
ejpam-3970	26	14	and	and	CCONJ
ejpam-3970	26	15	applied	applied	ADJ
ejpam-3970	26	16	sciences	science	NOUN
ejpam-3970	26	17	.	.	PUNCT
ejpam-3970	27	1	in	in	SCONJ
ejpam-3970	27	2	[	[	X
ejpam-3970	27	3	5	5	NUM
ejpam-3970	27	4	]	]	PUNCT
ejpam-3970	27	5	,	,	PUNCT
ejpam-3970	27	6	y.b	y.b	PROPN
ejpam-3970	27	7	.	.	PROPN
ejpam-3970	27	8	jun	jun	PROPN
ejpam-3970	27	9	et	et	PROPN
ejpam-3970	27	10	al	al	PROPN
ejpam-3970	27	11	.	.	PROPN
ejpam-3970	27	12	introduced	introduce	VERB
ejpam-3970	27	13	and	and	CCONJ
ejpam-3970	27	14	studied	study	VERB
ejpam-3970	27	15	the	the	DET
ejpam-3970	27	16	concept	concept	NOUN
ejpam-3970	27	17	of	of	ADP
ejpam-3970	27	18	a	a	DET
ejpam-3970	27	19	hyper	hyper	ADJ
ejpam-3970	27	20	bck	bck	NOUN
ejpam-3970	27	21	-	-	PUNCT
ejpam-3970	27	22	algebra	algebra	NOUN
ejpam-3970	27	23	.	.	PUNCT
ejpam-3970	28	1	in	in	ADP
ejpam-3970	28	2	[	[	X
ejpam-3970	28	3	7	7	NUM
ejpam-3970	28	4	]	]	PUNCT
ejpam-3970	28	5	,	,	PUNCT
ejpam-3970	28	6	muhiuddin	muhiuddin	VERB
ejpam-3970	28	7	et	et	PROPN
ejpam-3970	28	8	al	al	PROPN
ejpam-3970	28	9	.	.	PROPN
ejpam-3970	28	10	studied	study	VERB
ejpam-3970	28	11	fuzzy	fuzzy	ADJ
ejpam-3970	28	12	soft	soft	ADJ
ejpam-3970	28	13	hyper	hyper	ADJ
ejpam-3970	28	14	bck	bck	NOUN
ejpam-3970	28	15	-	-	PUNCT
ejpam-3970	28	16	ideals	ideal	NOUN
ejpam-3970	28	17	in	in	ADP
ejpam-3970	28	18	hyper	hyper	ADJ
ejpam-3970	28	19	bck	bck	NOUN
ejpam-3970	28	20	-	-	PUNCT
ejpam-3970	28	21	algebras	algebras	PROPN
ejpam-3970	28	22	.	.	PUNCT
ejpam-3970	29	1	in	in	ADP
ejpam-3970	29	2	[	[	X
ejpam-3970	29	3	13	13	NUM
ejpam-3970	29	4	]	]	PUNCT
ejpam-3970	29	5	,	,	PUNCT
ejpam-3970	29	6	xin	xin	PROPN
ejpam-3970	29	7	applied	apply	VERB
ejpam-3970	29	8	hyperstructures	hyperstructure	NOUN
ejpam-3970	29	9	to	to	ADP
ejpam-3970	29	10	bci	bci	PROPN
ejpam-3970	29	11	-	-	PUNCT
ejpam-3970	29	12	algebras	algebras	ADV
ejpam-3970	29	13	giving	give	VERB
ejpam-3970	29	14	rise	rise	NOUN
ejpam-3970	29	15	to	to	ADP
ejpam-3970	29	16	the	the	DET
ejpam-3970	29	17	the	the	DET
ejpam-3970	29	18	concept	concept	NOUN
ejpam-3970	29	19	of	of	ADP
ejpam-3970	29	20	a	a	DET
ejpam-3970	29	21	hyper	hyper	ADJ
ejpam-3970	29	22	bci	bci	NOUN
ejpam-3970	29	23	-	-	NOUN
ejpam-3970	29	24	algebra	algebra	NOUN
ejpam-3970	29	25	.	.	PUNCT
ejpam-3970	30	1	a	a	DET
ejpam-3970	30	2	study	study	NOUN
ejpam-3970	30	3	on	on	ADP
ejpam-3970	30	4	a	a	DET
ejpam-3970	30	5	graph	graph	NOUN
ejpam-3970	30	6	induced	induce	VERB
ejpam-3970	30	7	by	by	ADP
ejpam-3970	30	8	a	a	DET
ejpam-3970	30	9	hyper	hyper	ADJ
ejpam-3970	30	10	bci	bci	NOUN
ejpam-3970	30	11	-	-	NOUN
ejpam-3970	30	12	algebra	algebra	NOUN
ejpam-3970	30	13	is	be	AUX
ejpam-3970	30	14	done	do	VERB
ejpam-3970	30	15	in	in	ADP
ejpam-3970	30	16	[	[	X
ejpam-3970	30	17	11	11	NUM
ejpam-3970	30	18	]	]	PUNCT
ejpam-3970	30	19	.	.	PUNCT
ejpam-3970	31	1	previous	previous	ADJ
ejpam-3970	31	2	studies	study	NOUN
ejpam-3970	31	3	on	on	ADP
ejpam-3970	31	4	the	the	DET
ejpam-3970	31	5	topological	topological	ADJ
ejpam-3970	31	6	aspects	aspect	NOUN
ejpam-3970	31	7	of	of	ADP
ejpam-3970	31	8	certain	certain	ADJ
ejpam-3970	31	9	algebraic	algebraic	ADJ
ejpam-3970	31	10	hyperstructures	hyperstructure	NOUN
ejpam-3970	31	11	motivated	motivate	VERB
ejpam-3970	31	12	us	we	PRON
ejpam-3970	31	13	to	to	PART
ejpam-3970	31	14	study	study	VERB
ejpam-3970	31	15	the	the	DET
ejpam-3970	31	16	topological	topological	ADJ
ejpam-3970	31	17	structure	structure	NOUN
ejpam-3970	31	18	of	of	ADP
ejpam-3970	31	19	a	a	DET
ejpam-3970	31	20	hyper	hyper	ADJ
ejpam-3970	31	21	bci	bci	NOUN
ejpam-3970	31	22	-	-	NOUN
ejpam-3970	31	23	algebra	algebra	NOUN
ejpam-3970	31	24	when	when	SCONJ
ejpam-3970	31	25	it	it	PRON
ejpam-3970	31	26	carries	carry	VERB
ejpam-3970	31	27	a	a	DET
ejpam-3970	31	28	topology	topology	NOUN
ejpam-3970	31	29	other	other	ADJ
ejpam-3970	31	30	the	the	DET
ejpam-3970	31	31	one	one	NOUN
ejpam-3970	31	32	considered	consider	VERB
ejpam-3970	31	33	in	in	ADP
ejpam-3970	31	34	earlier	early	ADJ
ejpam-3970	31	35	studies	study	NOUN
ejpam-3970	31	36	.	.	PUNCT
ejpam-3970	32	1	in	in	ADP
ejpam-3970	32	2	this	this	DET
ejpam-3970	32	3	study	study	NOUN
ejpam-3970	32	4	,	,	PUNCT
ejpam-3970	32	5	we	we	PRON
ejpam-3970	32	6	purposely	purposely	ADV
ejpam-3970	32	7	use	use	VERB
ejpam-3970	32	8	the	the	DET
ejpam-3970	32	9	hyper	hyper	NOUN
ejpam-3970	32	10	-	-	NOUN
ejpam-3970	32	11	order	order	NOUN
ejpam-3970	32	12	associated	associate	VERB
ejpam-3970	32	13	with	with	ADP
ejpam-3970	32	14	the	the	DET
ejpam-3970	32	15	hyperstructure	hyperstructure	NOUN
ejpam-3970	32	16	to	to	PART
ejpam-3970	32	17	topologize	topologize	VERB
ejpam-3970	32	18	it	it	PRON
ejpam-3970	32	19	.	.	PUNCT
ejpam-3970	33	1	specifically	specifically	ADV
ejpam-3970	33	2	,	,	PUNCT
ejpam-3970	33	3	we	we	PRON
ejpam-3970	33	4	topologize	topologize	VERB
ejpam-3970	33	5	a	a	DET
ejpam-3970	33	6	given	give	VERB
ejpam-3970	33	7	hyper	hyper	ADJ
ejpam-3970	33	8	bci	bci	NOUN
ejpam-3970	33	9	-	-	NOUN
ejpam-3970	33	10	algebra	algebra	NOUN
ejpam-3970	33	11	by	by	ADP
ejpam-3970	33	12	considering	consider	VERB
ejpam-3970	33	13	a	a	DET
ejpam-3970	33	14	family	family	NOUN
ejpam-3970	33	15	of	of	ADP
ejpam-3970	33	16	subsets	subset	NOUN
ejpam-3970	33	17	which	which	PRON
ejpam-3970	33	18	will	will	AUX
ejpam-3970	33	19	form	form	VERB
ejpam-3970	33	20	a	a	DET
ejpam-3970	33	21	base	base	NOUN
ejpam-3970	33	22	for	for	ADP
ejpam-3970	33	23	some	some	DET
ejpam-3970	33	24	topology	topology	NOUN
ejpam-3970	33	25	on	on	ADP
ejpam-3970	33	26	the	the	DET
ejpam-3970	33	27	hyper	hyper	ADJ
ejpam-3970	33	28	bci	bci	NOUN
ejpam-3970	33	29	-	-	NOUN
ejpam-3970	33	30	algebra	algebra	NOUN
ejpam-3970	33	31	.	.	PUNCT
ejpam-3970	34	1	these	these	DET
ejpam-3970	34	2	subsets	subset	NOUN
ejpam-3970	34	3	are	be	AUX
ejpam-3970	34	4	generated	generate	VERB
ejpam-3970	34	5	via	via	ADP
ejpam-3970	34	6	left	left	ADJ
ejpam-3970	34	7	application	application	NOUN
ejpam-3970	34	8	of	of	ADP
ejpam-3970	34	9	the	the	DET
ejpam-3970	34	10	hyper	hyper	NOUN
ejpam-3970	34	11	-	-	NOUN
ejpam-3970	34	12	order	order	NOUN
ejpam-3970	34	13	associated	associate	VERB
ejpam-3970	34	14	with	with	ADP
ejpam-3970	34	15	the	the	DET
ejpam-3970	34	16	hyper	hyper	ADJ
ejpam-3970	34	17	bci	bci	NOUN
ejpam-3970	34	18	-	-	NOUN
ejpam-3970	34	19	algebra	algebra	NOUN
ejpam-3970	34	20	.	.	PUNCT
ejpam-3970	35	1	topological	topological	ADJ
ejpam-3970	35	2	properties	property	NOUN
ejpam-3970	35	3	of	of	ADP
ejpam-3970	35	4	the	the	DET
ejpam-3970	35	5	resulting	result	VERB
ejpam-3970	35	6	space	space	NOUN
ejpam-3970	35	7	are	be	AUX
ejpam-3970	35	8	investigated	investigate	VERB
ejpam-3970	35	9	in	in	ADP
ejpam-3970	35	10	various	various	ADJ
ejpam-3970	35	11	aspects	aspect	NOUN
ejpam-3970	35	12	.	.	PUNCT
ejpam-3970	36	1	in	in	ADP
ejpam-3970	36	2	particular	particular	ADJ
ejpam-3970	36	3	,	,	PUNCT
ejpam-3970	36	4	we	we	PRON
ejpam-3970	36	5	show	show	VERB
ejpam-3970	36	6	that	that	SCONJ
ejpam-3970	36	7	the	the	DET
ejpam-3970	36	8	topology	topology	NOUN
ejpam-3970	36	9	generated	generate	VERB
ejpam-3970	36	10	on	on	ADP
ejpam-3970	36	11	a	a	DET
ejpam-3970	36	12	non	non	ADJ
ejpam-3970	36	13	-	-	ADJ
ejpam-3970	36	14	trivial	trivial	ADJ
ejpam-3970	36	15	hyper	hyper	ADJ
ejpam-3970	36	16	subalgebra	subalgebra	NOUN
ejpam-3970	36	17	of	of	ADP
ejpam-3970	36	18	an	an	DET
ejpam-3970	36	19	ordered	order	VERB
ejpam-3970	36	20	hyper	hyper	ADJ
ejpam-3970	36	21	bci	bci	NOUN
ejpam-3970	36	22	-	-	PUNCT
ejpam-3970	36	23	algebra	algebra	NOUN
ejpam-3970	36	24	coincides	coincide	VERB
ejpam-3970	36	25	with	with	ADP
ejpam-3970	36	26	the	the	DET
ejpam-3970	36	27	relative	relative	ADJ
ejpam-3970	36	28	(	(	PUNCT
ejpam-3970	36	29	subspace	subspace	NOUN
ejpam-3970	36	30	)	)	PUNCT
ejpam-3970	36	31	topology	topology	NOUN
ejpam-3970	36	32	.	.	PUNCT
ejpam-3970	37	1	2	2	X
ejpam-3970	37	2	.	.	NUM
ejpam-3970	37	3	preliminaries	preliminary	NOUN
ejpam-3970	37	4	a	a	DET
ejpam-3970	37	5	hyperoperation	hyperoperation	NOUN
ejpam-3970	37	6	on	on	ADP
ejpam-3970	37	7	a	a	DET
ejpam-3970	37	8	nonempty	nonempty	ADV
ejpam-3970	37	9	set	set	VERB
ejpam-3970	37	10	h	h	NOUN
ejpam-3970	37	11	is	be	AUX
ejpam-3970	37	12	a	a	DET
ejpam-3970	37	13	map	map	NOUN
ejpam-3970	37	14	from	from	ADP
ejpam-3970	37	15	h×h	h×h	PROPN
ejpam-3970	37	16	into	into	ADP
ejpam-3970	37	17	the	the	DET
ejpam-3970	37	18	nonempty	nonempty	ADJ
ejpam-3970	37	19	subsets	subset	NOUN
ejpam-3970	37	20	of	of	ADP
ejpam-3970	37	21	h	h	NOUN
ejpam-3970	37	22	,	,	PUNCT
ejpam-3970	37	23	p	p	PROPN
ejpam-3970	37	24	∗(h	∗(h	PROPN
ejpam-3970	37	25	)	)	PUNCT
ejpam-3970	38	1	=	=	SYM
ejpam-3970	38	2	p	p	X
ejpam-3970	38	3	(	(	PUNCT
ejpam-3970	38	4	h	h	NOUN
ejpam-3970	38	5	)	)	PUNCT
ejpam-3970	38	6	\	\	NOUN
ejpam-3970	38	7	{	{	PUNCT
ejpam-3970	38	8	∅	∅	NOUN
ejpam-3970	38	9	}	}	PUNCT
ejpam-3970	38	10	.	.	PUNCT
ejpam-3970	39	1	let	let	VERB
ejpam-3970	39	2	~	~	PUNCT
ejpam-3970	39	3	be	be	AUX
ejpam-3970	39	4	a	a	DET
ejpam-3970	39	5	hyperoperation	hyperoperation	NOUN
ejpam-3970	39	6	on	on	ADP
ejpam-3970	39	7	h	h	NOUN
ejpam-3970	39	8	and	and	CCONJ
ejpam-3970	39	9	(	(	PUNCT
ejpam-3970	39	10	x	x	NOUN
ejpam-3970	39	11	,	,	PUNCT
ejpam-3970	39	12	y	y	NOUN
ejpam-3970	39	13	)	)	PUNCT
ejpam-3970	39	14	∈	∈	PROPN
ejpam-3970	39	15	h	h	NOUN
ejpam-3970	39	16	×h	×h	PROPN
ejpam-3970	39	17	.	.	PUNCT
ejpam-3970	40	1	then	then	ADV
ejpam-3970	40	2	its	its	PRON
ejpam-3970	40	3	image	image	NOUN
ejpam-3970	40	4	under	under	ADP
ejpam-3970	40	5	~	~	PROPN
ejpam-3970	40	6	,	,	PUNCT
ejpam-3970	40	7	denoted	denote	VERB
ejpam-3970	40	8	by	by	ADP
ejpam-3970	40	9	x	x	PROPN
ejpam-3970	40	10	~	~	SYM
ejpam-3970	40	11	y	y	PROPN
ejpam-3970	40	12	,	,	PUNCT
ejpam-3970	40	13	is	be	AUX
ejpam-3970	40	14	called	call	VERB
ejpam-3970	40	15	the	the	DET
ejpam-3970	40	16	hyperproduct	hyperproduct	NOUN
ejpam-3970	40	17	of	of	ADP
ejpam-3970	40	18	x	x	PUNCT
ejpam-3970	40	19	and	and	CCONJ
ejpam-3970	40	20	y.	y.	NOUN
ejpam-3970	40	21	if	if	SCONJ
ejpam-3970	40	22	a	a	PRON
ejpam-3970	40	23	and	and	CCONJ
ejpam-3970	40	24	b	b	NOUN
ejpam-3970	40	25	are	be	AUX
ejpam-3970	40	26	nonempty	nonempty	ADJ
ejpam-3970	40	27	subsets	subset	NOUN
ejpam-3970	40	28	of	of	ADP
ejpam-3970	40	29	h	h	NOUN
ejpam-3970	40	30	,	,	PUNCT
ejpam-3970	40	31	then	then	ADV
ejpam-3970	40	32	a	a	DET
ejpam-3970	40	33	∗b	∗b	PROPN
ejpam-3970	40	34	is	be	AUX
ejpam-3970	40	35	given	give	VERB
ejpam-3970	40	36	by	by	ADP
ejpam-3970	40	37	a	a	DET
ejpam-3970	40	38	~	~	PROPN
ejpam-3970	40	39	b	b	NOUN
ejpam-3970	40	40	=	=	PUNCT
ejpam-3970	40	41	⋃	⋃	NOUN
ejpam-3970	40	42	a∈a	a∈a	ADJ
ejpam-3970	40	43	,	,	PUNCT
ejpam-3970	40	44	b∈b	b∈b	NOUN
ejpam-3970	40	45	a~	a~	PROPN
ejpam-3970	40	46	b.	b.	PROPN
ejpam-3970	40	47	we	we	PRON
ejpam-3970	40	48	shall	shall	AUX
ejpam-3970	40	49	use	use	VERB
ejpam-3970	40	50	x~	x~	PROPN
ejpam-3970	40	51	y	y	PROPN
ejpam-3970	40	52	instead	instead	ADV
ejpam-3970	40	53	of	of	ADP
ejpam-3970	40	54	x~{y	x~{y	PROPN
ejpam-3970	40	55	}	}	PUNCT
ejpam-3970	40	56	,	,	PUNCT
ejpam-3970	40	57	{	{	PUNCT
ejpam-3970	40	58	x}~y	x}~y	NOUN
ejpam-3970	40	59	,	,	PUNCT
ejpam-3970	40	60	or	or	CCONJ
ejpam-3970	40	61	{	{	PUNCT
ejpam-3970	40	62	x}~{y	x}~{y	NOUN
ejpam-3970	40	63	}	}	PUNCT
ejpam-3970	40	64	.	.	PUNCT
ejpam-3970	41	1	when	when	SCONJ
ejpam-3970	41	2	a	a	DET
ejpam-3970	41	3	⊆	⊆	NUM
ejpam-3970	41	4	h	h	NOUN
ejpam-3970	41	5	and	and	CCONJ
ejpam-3970	41	6	x	x	PUNCT
ejpam-3970	41	7	∈	∈	PROPN
ejpam-3970	41	8	h	h	NOUN
ejpam-3970	41	9	,	,	PUNCT
ejpam-3970	41	10	we	we	PRON
ejpam-3970	41	11	agree	agree	VERB
ejpam-3970	41	12	to	to	PART
ejpam-3970	41	13	write	write	VERB
ejpam-3970	41	14	a	a	DET
ejpam-3970	41	15	~	~	NOUN
ejpam-3970	41	16	x	x	PROPN
ejpam-3970	41	17	instead	instead	ADV
ejpam-3970	41	18	of	of	ADP
ejpam-3970	41	19	a~	a~	PROPN
ejpam-3970	41	20	{	{	PUNCT
ejpam-3970	41	21	x	x	NOUN
ejpam-3970	41	22	}	}	PUNCT
ejpam-3970	41	23	.	.	PUNCT
ejpam-3970	42	1	similarly	similarly	ADV
ejpam-3970	42	2	,	,	PUNCT
ejpam-3970	42	3	we	we	PRON
ejpam-3970	42	4	write	write	VERB
ejpam-3970	42	5	x	x	PUNCT
ejpam-3970	42	6	~	~	NOUN
ejpam-3970	42	7	a	a	PRON
ejpam-3970	42	8	for	for	ADP
ejpam-3970	42	9	{	{	PUNCT
ejpam-3970	42	10	x}~a	x}~a	NOUN
ejpam-3970	42	11	.	.	PUNCT
ejpam-3970	43	1	in	in	ADP
ejpam-3970	43	2	effect	effect	NOUN
ejpam-3970	43	3	,	,	PUNCT
ejpam-3970	43	4	a	a	PRON
ejpam-3970	43	5	~	~	NOUN
ejpam-3970	43	6	x	x	SYM
ejpam-3970	43	7	=	=	SYM
ejpam-3970	43	8	⋃	⋃	VERB
ejpam-3970	43	9	a∈a	a∈a	ADJ
ejpam-3970	43	10	a	a	DET
ejpam-3970	43	11	~	~	NOUN
ejpam-3970	43	12	x	x	X
ejpam-3970	43	13	and	and	CCONJ
ejpam-3970	43	14	x	x	X
ejpam-3970	43	15	~	~	PUNCT
ejpam-3970	43	16	a	a	DET
ejpam-3970	43	17	=	=	X
ejpam-3970	43	18	⋃	⋃	NOUN
ejpam-3970	43	19	a∈a	a∈a	ADJ
ejpam-3970	43	20	x~	x~	PROPN
ejpam-3970	43	21	a.	a.	NOUN
ejpam-3970	43	22	a	a	DET
ejpam-3970	43	23	hyper	hyper	ADJ
ejpam-3970	43	24	bci	bci	NOUN
ejpam-3970	43	25	-	-	NOUN
ejpam-3970	43	26	algebra	algebra	NOUN
ejpam-3970	43	27	(	(	PUNCT
ejpam-3970	43	28	h,~	h,~	NOUN
ejpam-3970	43	29	,	,	PUNCT
ejpam-3970	43	30	0	0	NUM
ejpam-3970	43	31	)	)	PUNCT
ejpam-3970	43	32	(	(	PUNCT
ejpam-3970	43	33	see	see	VERB
ejpam-3970	43	34	[	[	X
ejpam-3970	43	35	5	5	NUM
ejpam-3970	43	36	]	]	PUNCT
ejpam-3970	43	37	)	)	PUNCT
ejpam-3970	43	38	is	be	AUX
ejpam-3970	43	39	a	a	DET
ejpam-3970	43	40	nonempty	nonempty	ADV
ejpam-3970	43	41	set	set	VERB
ejpam-3970	43	42	h	h	NOUN
ejpam-3970	43	43	endowed	endow	VERB
ejpam-3970	43	44	with	with	ADP
ejpam-3970	43	45	a	a	DET
ejpam-3970	43	46	hyperoperation	hyperoperation	NOUN
ejpam-3970	43	47	“	"	PUNCT
ejpam-3970	43	48	~	~	PUNCT
ejpam-3970	43	49	”	"	PUNCT
ejpam-3970	43	50	and	and	CCONJ
ejpam-3970	43	51	a	a	DET
ejpam-3970	43	52	constant	constant	ADJ
ejpam-3970	43	53	0	0	NUM
ejpam-3970	43	54	such	such	ADJ
ejpam-3970	43	55	that	that	PRON
ejpam-3970	43	56	:	:	PUNCT
ejpam-3970	43	57	for	for	ADP
ejpam-3970	43	58	all	all	DET
ejpam-3970	43	59	x	x	NOUN
ejpam-3970	43	60	,	,	PUNCT
ejpam-3970	43	61	y	y	PROPN
ejpam-3970	43	62	,	,	PUNCT
ejpam-3970	43	63	z	z	PROPN
ejpam-3970	43	64	∈	∈	PROPN
ejpam-3970	43	65	h	h	NOUN
ejpam-3970	43	66	,	,	PUNCT
ejpam-3970	43	67	(	(	PUNCT
ejpam-3970	43	68	b1	b1	NOUN
ejpam-3970	43	69	)	)	PUNCT
ejpam-3970	43	70	(	(	PUNCT
ejpam-3970	43	71	(	(	PUNCT
ejpam-3970	43	72	x~	x~	PROPN
ejpam-3970	43	73	z	z	PROPN
ejpam-3970	43	74	)	)	PUNCT
ejpam-3970	43	75	~	~	PUNCT
ejpam-3970	43	76	(	(	PUNCT
ejpam-3970	43	77	y	y	X
ejpam-3970	43	78	~	~	PUNCT
ejpam-3970	43	79	z	z	NOUN
ejpam-3970	43	80	)	)	PUNCT
ejpam-3970	43	81	)	)	PUNCT
ejpam-3970	43	82	�	�	PROPN
ejpam-3970	43	83	x~	x~	NUM
ejpam-3970	43	84	y	y	PROPN
ejpam-3970	43	85	,	,	PUNCT
ejpam-3970	43	86	(	(	PUNCT
ejpam-3970	43	87	b2	b2	NOUN
ejpam-3970	43	88	)	)	PUNCT
ejpam-3970	43	89	(	(	PUNCT
ejpam-3970	43	90	x~	x~	PROPN
ejpam-3970	43	91	y	y	NUM
ejpam-3970	43	92	)	)	PUNCT
ejpam-3970	43	93	~	~	PUNCT
ejpam-3970	43	94	z	z	X
ejpam-3970	43	95	=	=	SYM
ejpam-3970	43	96	(	(	PUNCT
ejpam-3970	43	97	x~	x~	PROPN
ejpam-3970	43	98	z	z	PROPN
ejpam-3970	43	99	)	)	PUNCT
ejpam-3970	43	100	~	~	PUNCT
ejpam-3970	43	101	y	y	X
ejpam-3970	43	102	,	,	PUNCT
ejpam-3970	43	103	(	(	PUNCT
ejpam-3970	43	104	b3	b3	PROPN
ejpam-3970	43	105	)	)	PUNCT
ejpam-3970	43	106	x	x	NOUN
ejpam-3970	43	107	�	�	PROPN
ejpam-3970	43	108	x	x	SYM
ejpam-3970	43	109	,	,	PUNCT
ejpam-3970	43	110	(	(	PUNCT
ejpam-3970	43	111	b4	b4	NOUN
ejpam-3970	43	112	)	)	PUNCT
ejpam-3970	43	113	x	x	NOUN
ejpam-3970	43	114	�	�	PROPN
ejpam-3970	43	115	y	y	PROPN
ejpam-3970	43	116	and	and	CCONJ
ejpam-3970	43	117	y	y	PROPN
ejpam-3970	43	118	�	�	PROPN
ejpam-3970	43	119	x	x	PUNCT
ejpam-3970	43	120	imply	imply	VERB
ejpam-3970	43	121	x	x	X
ejpam-3970	43	122	=	=	SYM
ejpam-3970	43	123	y	y	PROPN
ejpam-3970	43	124	,	,	PUNCT
ejpam-3970	43	125	(	(	PUNCT
ejpam-3970	43	126	b5	b5	PROPN
ejpam-3970	43	127	)	)	PUNCT
ejpam-3970	43	128	0	0	PUNCT
ejpam-3970	44	1	~	~	PUNCT
ejpam-3970	44	2	(	(	PUNCT
ejpam-3970	44	3	0	0	NUM
ejpam-3970	44	4	~	~	SYM
ejpam-3970	44	5	x	x	X
ejpam-3970	44	6	)	)	PUNCT
ejpam-3970	44	7	�	�	PROPN
ejpam-3970	44	8	x	x	SYM
ejpam-3970	44	9	,	,	PUNCT
ejpam-3970	44	10	x	x	PROPN
ejpam-3970	44	11	6=	6=	ADP
ejpam-3970	44	12	0	0	NUM
ejpam-3970	44	13	,	,	PUNCT
ejpam-3970	44	14	where	where	SCONJ
ejpam-3970	44	15	for	for	ADP
ejpam-3970	44	16	every	every	DET
ejpam-3970	44	17	a	a	PROPN
ejpam-3970	44	18	,	,	PUNCT
ejpam-3970	44	19	b	b	PROPN
ejpam-3970	44	20	⊆	⊆	NUM
ejpam-3970	44	21	h	h	NOUN
ejpam-3970	44	22	,	,	PUNCT
ejpam-3970	44	23	a	a	DET
ejpam-3970	44	24	�	�	PROPN
ejpam-3970	44	25	b	b	PROPN
ejpam-3970	44	26	if	if	SCONJ
ejpam-3970	45	1	and	and	CCONJ
ejpam-3970	45	2	only	only	ADV
ejpam-3970	45	3	if	if	SCONJ
ejpam-3970	45	4	for	for	ADP
ejpam-3970	45	5	each	each	DET
ejpam-3970	45	6	a	a	DET
ejpam-3970	45	7	∈	∈	PROPN
ejpam-3970	45	8	a	a	PRON
ejpam-3970	45	9	,	,	PUNCT
ejpam-3970	45	10	there	there	PRON
ejpam-3970	45	11	exists	exist	VERB
ejpam-3970	45	12	b	b	PROPN
ejpam-3970	45	13	∈	∈	PROPN
ejpam-3970	45	14	b	b	NOUN
ejpam-3970	45	15	such	such	ADJ
ejpam-3970	45	16	that	that	DET
ejpam-3970	45	17	0	0	NUM
ejpam-3970	45	18	∈	∈	PROPN
ejpam-3970	45	19	a	a	DET
ejpam-3970	45	20	~	~	PUNCT
ejpam-3970	45	21	b.	b.	PROPN
ejpam-3970	45	22	in	in	ADP
ejpam-3970	45	23	particular	particular	ADJ
ejpam-3970	45	24	,	,	PUNCT
ejpam-3970	45	25	for	for	ADP
ejpam-3970	45	26	every	every	DET
ejpam-3970	45	27	x	x	NOUN
ejpam-3970	45	28	,	,	PUNCT
ejpam-3970	45	29	y	y	PROPN
ejpam-3970	45	30	∈	∈	PROPN
ejpam-3970	45	31	h	h	NOUN
ejpam-3970	45	32	,	,	PUNCT
ejpam-3970	45	33	x	x	PROPN
ejpam-3970	45	34	�	�	PROPN
ejpam-3970	45	35	y	y	PROPN
ejpam-3970	45	36	if	if	SCONJ
ejpam-3970	45	37	and	and	CCONJ
ejpam-3970	45	38	only	only	ADV
ejpam-3970	45	39	if	if	SCONJ
ejpam-3970	45	40	0	0	NUM
ejpam-3970	45	41	∈	∈	NOUN
ejpam-3970	45	42	x	x	X
ejpam-3970	45	43	~	~	PUNCT
ejpam-3970	45	44	y.	y.	NOUN
ejpam-3970	45	45	in	in	ADP
ejpam-3970	45	46	such	such	ADJ
ejpam-3970	45	47	case	case	NOUN
ejpam-3970	45	48	,	,	PUNCT
ejpam-3970	45	49	we	we	PRON
ejpam-3970	45	50	call	call	VERB
ejpam-3970	45	51	“	"	PUNCT
ejpam-3970	45	52	�	�	PROPN
ejpam-3970	45	53	”	"	PUNCT
ejpam-3970	45	54	the	the	DET
ejpam-3970	45	55	hyper	hyper	NOUN
ejpam-3970	45	56	-	-	NOUN
ejpam-3970	45	57	order	order	NOUN
ejpam-3970	45	58	in	in	ADP
ejpam-3970	45	59	h.	h.	PROPN
ejpam-3970	45	60	a	a	DET
ejpam-3970	45	61	hyper	hyper	ADJ
ejpam-3970	45	62	bci	bci	NOUN
ejpam-3970	45	63	-	-	NOUN
ejpam-3970	45	64	algebra	algebra	NOUN
ejpam-3970	45	65	(	(	PUNCT
ejpam-3970	45	66	h,~	h,~	NOUN
ejpam-3970	45	67	,	,	PUNCT
ejpam-3970	45	68	0	0	NUM
ejpam-3970	45	69	)	)	PUNCT
ejpam-3970	45	70	is	be	AUX
ejpam-3970	45	71	said	say	VERB
ejpam-3970	45	72	to	to	PART
ejpam-3970	45	73	be	be	AUX
ejpam-3970	45	74	ordered	order	VERB
ejpam-3970	45	75	if	if	SCONJ
ejpam-3970	45	76	for	for	ADP
ejpam-3970	45	77	x	x	PROPN
ejpam-3970	45	78	,	,	PUNCT
ejpam-3970	45	79	y	y	PROPN
ejpam-3970	45	80	,	,	PUNCT
ejpam-3970	45	81	z	z	PROPN
ejpam-3970	45	82	∈	∈	PROPN
ejpam-3970	45	83	h	h	NOUN
ejpam-3970	45	84	,	,	PUNCT
ejpam-3970	45	85	x	x	NOUN
ejpam-3970	45	86	�	�	PROPN
ejpam-3970	45	87	y	y	PROPN
ejpam-3970	45	88	and	and	CCONJ
ejpam-3970	45	89	y	y	PROPN
ejpam-3970	45	90	�	�	PROPN
ejpam-3970	45	91	z	z	PROPN
ejpam-3970	45	92	implies	imply	VERB
ejpam-3970	45	93	x	x	X
ejpam-3970	45	94	�	�	PROPN
ejpam-3970	45	95	z.	z.	PROPN
ejpam-3970	45	96	all	all	PRON
ejpam-3970	45	97	throughout	throughout	ADV
ejpam-3970	45	98	,	,	PUNCT
ejpam-3970	45	99	we	we	PRON
ejpam-3970	45	100	denote	denote	VERB
ejpam-3970	45	101	a	a	DET
ejpam-3970	45	102	hyper	hyper	ADJ
ejpam-3970	45	103	bci	bci	NOUN
ejpam-3970	45	104	-	-	NOUN
ejpam-3970	45	105	algebra	algebra	NOUN
ejpam-3970	45	106	(	(	PUNCT
ejpam-3970	45	107	h,~	h,~	NOUN
ejpam-3970	45	108	,	,	PUNCT
ejpam-3970	45	109	0	0	NUM
ejpam-3970	45	110	)	)	PUNCT
ejpam-3970	45	111	by	by	ADP
ejpam-3970	45	112	h	h	NOUN
ejpam-3970	45	113	,	,	PUNCT
ejpam-3970	45	114	unless	unless	SCONJ
ejpam-3970	45	115	otherwise	otherwise	ADV
ejpam-3970	45	116	specified	specify	VERB
ejpam-3970	45	117	.	.	PUNCT
ejpam-3970	46	1	m.	m.	NOUN
ejpam-3970	46	2	panganduyon	panganduyon	NOUN
ejpam-3970	46	3	,	,	PUNCT
ejpam-3970	46	4	s.	s.	PROPN
ejpam-3970	46	5	canoy	canoy	PROPN
ejpam-3970	46	6	,	,	PUNCT
ejpam-3970	46	7	jr	jr	PROPN
ejpam-3970	46	8	.	.	PROPN
ejpam-3970	46	9	,	,	PUNCT
ejpam-3970	46	10	b.	b.	PROPN
ejpam-3970	46	11	davvaz	davvaz	PROPN
ejpam-3970	46	12	/	/	SYM
ejpam-3970	46	13	eur	eur	PROPN
ejpam-3970	46	14	.	.	PUNCT
ejpam-3970	47	1	j.	j.	PROPN
ejpam-3970	47	2	pure	pure	PROPN
ejpam-3970	47	3	appl	appl	PROPN
ejpam-3970	47	4	.	.	PROPN
ejpam-3970	47	5	math	math	PROPN
ejpam-3970	47	6	,	,	PUNCT
ejpam-3970	47	7	14	14	NUM
ejpam-3970	47	8	(	(	PUNCT
ejpam-3970	47	9	2	2	NUM
ejpam-3970	47	10	)	)	PUNCT
ejpam-3970	47	11	(	(	PUNCT
ejpam-3970	47	12	2021	2021	NUM
ejpam-3970	47	13	)	)	PUNCT
ejpam-3970	47	14	,	,	PUNCT
ejpam-3970	47	15	590	590	NUM
ejpam-3970	47	16	-	-	SYM
ejpam-3970	47	17	600	600	NUM
ejpam-3970	47	18	592	592	NUM
ejpam-3970	47	19	let	let	VERB
ejpam-3970	47	20	h	h	NOUN
ejpam-3970	47	21	be	be	AUX
ejpam-3970	47	22	a	a	DET
ejpam-3970	47	23	hyper	hyper	ADJ
ejpam-3970	47	24	bci	bci	NOUN
ejpam-3970	47	25	-	-	NOUN
ejpam-3970	47	26	algebra	algebra	NOUN
ejpam-3970	47	27	and	and	CCONJ
ejpam-3970	47	28	a	a	DET
ejpam-3970	47	29	⊆	⊆	NUM
ejpam-3970	47	30	h.	h.	NOUN
ejpam-3970	47	31	in	in	ADP
ejpam-3970	47	32	[	[	X
ejpam-3970	47	33	11	11	NUM
ejpam-3970	47	34	]	]	PUNCT
ejpam-3970	47	35	,	,	PUNCT
ejpam-3970	47	36	the	the	DET
ejpam-3970	47	37	set	set	NOUN
ejpam-3970	47	38	lh(a	lh(a	NOUN
ejpam-3970	47	39	)	)	PUNCT
ejpam-3970	47	40	is	be	AUX
ejpam-3970	47	41	given	give	VERB
ejpam-3970	47	42	by	by	ADP
ejpam-3970	47	43	lh(a	lh(a	NOUN
ejpam-3970	47	44	)	)	PUNCT
ejpam-3970	47	45	=	=	PRON
ejpam-3970	48	1	{	{	PUNCT
ejpam-3970	48	2	x	x	PUNCT
ejpam-3970	48	3	∈	∈	NOUN
ejpam-3970	48	4	h	h	NOUN
ejpam-3970	49	1	|	|	ADV
ejpam-3970	49	2	x	x	X
ejpam-3970	49	3	�	�	PROPN
ejpam-3970	49	4	a,∀	a,∀	PROPN
ejpam-3970	49	5	a	a	DET
ejpam-3970	49	6	∈	∈	PROPN
ejpam-3970	49	7	a	a	PRON
ejpam-3970	49	8	}	}	PUNCT
ejpam-3970	49	9	=	=	SYM
ejpam-3970	49	10	{	{	PUNCT
ejpam-3970	49	11	x	x	PUNCT
ejpam-3970	49	12	∈	∈	NOUN
ejpam-3970	49	13	h	h	NOUN
ejpam-3970	50	1	|	|	ADV
ejpam-3970	50	2	0	0	NUM
ejpam-3970	50	3	∈	∈	NOUN
ejpam-3970	50	4	x	x	X
ejpam-3970	50	5	~	~	PUNCT
ejpam-3970	50	6	a,∀	a,∀	PUNCT
ejpam-3970	50	7	a	a	DET
ejpam-3970	50	8	∈	∈	PROPN
ejpam-3970	50	9	a	a	PRON
ejpam-3970	50	10	}	}	PUNCT
ejpam-3970	50	11	.	.	PUNCT
ejpam-3970	51	1	if	if	SCONJ
ejpam-3970	51	2	a	a	PRON
ejpam-3970	51	3	=	=	X
ejpam-3970	51	4	{	{	PUNCT
ejpam-3970	51	5	a	a	NOUN
ejpam-3970	51	6	}	}	PUNCT
ejpam-3970	51	7	,	,	PUNCT
ejpam-3970	51	8	we	we	PRON
ejpam-3970	51	9	write	write	VERB
ejpam-3970	51	10	lh({a	lh({a	PROPN
ejpam-3970	51	11	}	}	PUNCT
ejpam-3970	51	12	)	)	PUNCT
ejpam-3970	52	1	=	=	SYM
ejpam-3970	52	2	lh(a	lh(a	NOUN
ejpam-3970	52	3	)	)	PUNCT
ejpam-3970	52	4	.	.	PUNCT
ejpam-3970	53	1	an	an	DET
ejpam-3970	53	2	element	element	NOUN
ejpam-3970	53	3	a	a	PRON
ejpam-3970	53	4	of	of	ADP
ejpam-3970	53	5	h	h	NOUN
ejpam-3970	53	6	is	be	AUX
ejpam-3970	53	7	called	call	VERB
ejpam-3970	53	8	a	a	DET
ejpam-3970	53	9	hyperatom	hyperatom	NOUN
ejpam-3970	53	10	if	if	SCONJ
ejpam-3970	53	11	for	for	SCONJ
ejpam-3970	53	12	each	each	DET
ejpam-3970	53	13	x	x	SYM
ejpam-3970	53	14	∈	∈	PROPN
ejpam-3970	53	15	h	h	NOUN
ejpam-3970	53	16	,	,	PUNCT
ejpam-3970	53	17	x	x	PROPN
ejpam-3970	53	18	�	�	PROPN
ejpam-3970	53	19	a	a	DET
ejpam-3970	53	20	implies	imply	VERB
ejpam-3970	53	21	x	x	PUNCT
ejpam-3970	53	22	=	=	SYM
ejpam-3970	53	23	0	0	NUM
ejpam-3970	53	24	or	or	CCONJ
ejpam-3970	53	25	x	x	X
ejpam-3970	53	26	=	=	NOUN
ejpam-3970	53	27	a.	a.	NOUN
ejpam-3970	53	28	denote	denote	NOUN
ejpam-3970	53	29	by	by	ADP
ejpam-3970	53	30	a(h	a(h	PROPN
ejpam-3970	53	31	)	)	PUNCT
ejpam-3970	53	32	the	the	DET
ejpam-3970	53	33	set	set	NOUN
ejpam-3970	53	34	of	of	ADP
ejpam-3970	53	35	all	all	DET
ejpam-3970	53	36	hyperatoms	hyperatom	NOUN
ejpam-3970	53	37	of	of	ADP
ejpam-3970	53	38	h	h	NOUN
ejpam-3970	53	39	,	,	PUNCT
ejpam-3970	53	40	and	and	CCONJ
ejpam-3970	53	41	by	by	ADP
ejpam-3970	53	42	a∗(h	a∗(h	PROPN
ejpam-3970	53	43	)	)	PUNCT
ejpam-3970	53	44	the	the	DET
ejpam-3970	53	45	set	set	NOUN
ejpam-3970	53	46	of	of	ADP
ejpam-3970	53	47	all	all	DET
ejpam-3970	53	48	nonzero	nonzero	PROPN
ejpam-3970	53	49	hyperatoms	hyperatom	NOUN
ejpam-3970	53	50	of	of	ADP
ejpam-3970	53	51	h	h	NOUN
ejpam-3970	53	52	;	;	PUNCT
ejpam-3970	53	53	that	that	PRON
ejpam-3970	53	54	is	is	ADV
ejpam-3970	53	55	,	,	PUNCT
ejpam-3970	53	56	a∗(h	a∗(h	PROPN
ejpam-3970	53	57	)	)	PUNCT
ejpam-3970	53	58	=	=	SYM
ejpam-3970	53	59	a(h	a(h	PROPN
ejpam-3970	53	60	)	)	PUNCT
ejpam-3970	53	61	\	\	NOUN
ejpam-3970	53	62	{	{	PUNCT
ejpam-3970	53	63	0	0	NUM
ejpam-3970	53	64	}	}	PUNCT
ejpam-3970	53	65	.	.	PUNCT
ejpam-3970	54	1	h	h	PROPN
ejpam-3970	54	2	is	be	AUX
ejpam-3970	54	3	said	say	VERB
ejpam-3970	54	4	to	to	PART
ejpam-3970	54	5	be	be	AUX
ejpam-3970	54	6	hyperatomic	hyperatomic	ADJ
ejpam-3970	54	7	if	if	SCONJ
ejpam-3970	54	8	each	each	DET
ejpam-3970	54	9	element	element	NOUN
ejpam-3970	54	10	of	of	ADP
ejpam-3970	54	11	h	h	NOUN
ejpam-3970	54	12	is	be	AUX
ejpam-3970	54	13	a	a	DET
ejpam-3970	54	14	hyperatom	hyperatom	NOUN
ejpam-3970	54	15	,	,	PUNCT
ejpam-3970	54	16	that	that	ADV
ejpam-3970	54	17	is	is	ADV
ejpam-3970	54	18	,	,	PUNCT
ejpam-3970	54	19	a(h	a(h	PROPN
ejpam-3970	54	20	)	)	PUNCT
ejpam-3970	55	1	=	=	SYM
ejpam-3970	56	1	h.	h.	NOUN
ejpam-3970	57	1	it	it	PRON
ejpam-3970	57	2	is	be	AUX
ejpam-3970	57	3	shown	show	VERB
ejpam-3970	57	4	in	in	ADP
ejpam-3970	57	5	[	[	X
ejpam-3970	57	6	11	11	NUM
ejpam-3970	57	7	]	]	PUNCT
ejpam-3970	57	8	that	that	SCONJ
ejpam-3970	57	9	h	h	NOUN
ejpam-3970	57	10	is	be	AUX
ejpam-3970	57	11	hyperatomic	hyperatomic	ADJ
ejpam-3970	57	12	if	if	SCONJ
ejpam-3970	57	13	and	and	CCONJ
ejpam-3970	57	14	only	only	ADV
ejpam-3970	57	15	if	if	SCONJ
ejpam-3970	57	16	lh(x	lh(x	PUNCT
ejpam-3970	57	17	)	)	PUNCT
ejpam-3970	57	18	=	=	SYM
ejpam-3970	58	1	{	{	PUNCT
ejpam-3970	58	2	x	x	NOUN
ejpam-3970	58	3	}	}	PUNCT
ejpam-3970	58	4	or	or	CCONJ
ejpam-3970	58	5	lh(x	lh(x	PUNCT
ejpam-3970	58	6	)	)	PUNCT
ejpam-3970	59	1	=	=	SYM
ejpam-3970	59	2	{	{	PUNCT
ejpam-3970	59	3	0	0	NUM
ejpam-3970	59	4	,	,	PUNCT
ejpam-3970	59	5	x	x	NOUN
ejpam-3970	59	6	}	}	PUNCT
ejpam-3970	59	7	for	for	ADP
ejpam-3970	59	8	each	each	DET
ejpam-3970	59	9	x	x	SYM
ejpam-3970	59	10	∈	∈	PROPN
ejpam-3970	59	11	h.	h.	NOUN
ejpam-3970	59	12	3	3	X
ejpam-3970	59	13	.	.	PUNCT
ejpam-3970	59	14	results	result	VERB
ejpam-3970	59	15	the	the	DET
ejpam-3970	59	16	following	following	ADJ
ejpam-3970	59	17	result	result	NOUN
ejpam-3970	59	18	gives	give	VERB
ejpam-3970	59	19	some	some	DET
ejpam-3970	59	20	properties	property	NOUN
ejpam-3970	59	21	of	of	ADP
ejpam-3970	59	22	the	the	DET
ejpam-3970	59	23	operator	operator	NOUN
ejpam-3970	59	24	lh	lh	PROPN
ejpam-3970	59	25	.	.	PUNCT
ejpam-3970	60	1	proposition	proposition	NOUN
ejpam-3970	60	2	1	1	NUM
ejpam-3970	60	3	.	.	PUNCT
ejpam-3970	61	1	[	[	X
ejpam-3970	61	2	11	11	NUM
ejpam-3970	61	3	]	]	PUNCT
ejpam-3970	61	4	let	let	VERB
ejpam-3970	61	5	a	a	PRON
ejpam-3970	61	6	and	and	CCONJ
ejpam-3970	61	7	b	b	NOUN
ejpam-3970	61	8	be	be	AUX
ejpam-3970	61	9	subsets	subset	NOUN
ejpam-3970	61	10	of	of	ADP
ejpam-3970	61	11	h.	h.	PROPN
ejpam-3970	61	12	then	then	ADV
ejpam-3970	61	13	the	the	DET
ejpam-3970	61	14	following	follow	VERB
ejpam-3970	61	15	hold	hold	NOUN
ejpam-3970	61	16	:	:	PUNCT
ejpam-3970	61	17	(	(	PUNCT
ejpam-3970	61	18	i	i	NOUN
ejpam-3970	61	19	)	)	PUNCT
ejpam-3970	61	20	lh(∅	lh(∅	PROPN
ejpam-3970	61	21	)	)	PUNCT
ejpam-3970	62	1	=	=	SYM
ejpam-3970	62	2	h	h	PROPN
ejpam-3970	62	3	(	(	PUNCT
ejpam-3970	62	4	ii	ii	PROPN
ejpam-3970	62	5	)	)	PUNCT
ejpam-3970	62	6	lh({0	lh({0	NOUN
ejpam-3970	62	7	}	}	PUNCT
ejpam-3970	62	8	)	)	PUNCT
ejpam-3970	63	1	=	=	PUNCT
ejpam-3970	63	2	{	{	PUNCT
ejpam-3970	63	3	0	0	NUM
ejpam-3970	63	4	}	}	PUNCT
ejpam-3970	63	5	(	(	PUNCT
ejpam-3970	63	6	iii	iii	X
ejpam-3970	63	7	)	)	PUNCT
ejpam-3970	63	8	if	if	SCONJ
ejpam-3970	63	9	a	a	DET
ejpam-3970	63	10	⊆	⊆	NUM
ejpam-3970	63	11	b	b	NOUN
ejpam-3970	63	12	,	,	PUNCT
ejpam-3970	63	13	then	then	ADV
ejpam-3970	63	14	lh(b	lh(b	NOUN
ejpam-3970	63	15	)	)	PUNCT
ejpam-3970	63	16	⊆	⊆	NUM
ejpam-3970	63	17	lh(a	lh(a	NUM
ejpam-3970	63	18	)	)	PUNCT
ejpam-3970	63	19	.	.	PUNCT
ejpam-3970	64	1	(	(	PUNCT
ejpam-3970	64	2	iv	iv	X
ejpam-3970	64	3	)	)	PUNCT
ejpam-3970	64	4	lh(a	lh(a	NOUN
ejpam-3970	64	5	)	)	PUNCT
ejpam-3970	65	1	=	=	SYM
ejpam-3970	66	1	⋂	⋂	PROPN
ejpam-3970	66	2	a∈a	a∈a	ADJ
ejpam-3970	66	3	lh({a	lh({a	NOUN
ejpam-3970	66	4	}	}	PUNCT
ejpam-3970	66	5	)	)	PUNCT
ejpam-3970	66	6	(	(	PUNCT
ejpam-3970	66	7	v	v	NOUN
ejpam-3970	66	8	)	)	PUNCT
ejpam-3970	66	9	if	if	SCONJ
ejpam-3970	66	10	x	x	SYM
ejpam-3970	66	11	∈	∈	PROPN
ejpam-3970	66	12	h	h	NOUN
ejpam-3970	66	13	,	,	PUNCT
ejpam-3970	66	14	then	then	ADV
ejpam-3970	66	15	x	x	X
ejpam-3970	66	16	∈	∈	PROPN
ejpam-3970	66	17	lh({x	lh({x	NOUN
ejpam-3970	66	18	}	}	PUNCT
ejpam-3970	66	19	)	)	PUNCT
ejpam-3970	66	20	.	.	PUNCT
ejpam-3970	67	1	furthermore	furthermore	ADV
ejpam-3970	67	2	,	,	PUNCT
ejpam-3970	67	3	lh({x	lh({x	NOUN
ejpam-3970	67	4	}	}	PUNCT
ejpam-3970	67	5	)	)	PUNCT
ejpam-3970	68	1	=	=	PUNCT
ejpam-3970	68	2	{	{	PUNCT
ejpam-3970	68	3	0	0	NUM
ejpam-3970	68	4	}	}	PUNCT
ejpam-3970	68	5	if	if	SCONJ
ejpam-3970	68	6	and	and	CCONJ
ejpam-3970	68	7	only	only	ADV
ejpam-3970	68	8	if	if	SCONJ
ejpam-3970	68	9	x	x	SYM
ejpam-3970	68	10	=	=	SYM
ejpam-3970	68	11	0	0	X
ejpam-3970	68	12	.	.	PUNCT
ejpam-3970	68	13	theorem	theorem	NOUN
ejpam-3970	68	14	1	1	NUM
ejpam-3970	68	15	.	.	PUNCT
ejpam-3970	69	1	[	[	X
ejpam-3970	69	2	2	2	NUM
ejpam-3970	69	3	]	]	X
ejpam-3970	69	4	let	let	VERB
ejpam-3970	69	5	(	(	PUNCT
ejpam-3970	69	6	x	x	NOUN
ejpam-3970	69	7	,	,	PUNCT
ejpam-3970	69	8	τ	τ	X
ejpam-3970	69	9	)	)	PUNCT
ejpam-3970	69	10	be	be	VERB
ejpam-3970	69	11	a	a	DET
ejpam-3970	69	12	topological	topological	ADJ
ejpam-3970	69	13	space	space	NOUN
ejpam-3970	69	14	and	and	CCONJ
ejpam-3970	69	15	(	(	PUNCT
ejpam-3970	69	16	y	y	PROPN
ejpam-3970	69	17	,	,	PUNCT
ejpam-3970	69	18	τy	τy	PART
ejpam-3970	69	19	)	)	PUNCT
ejpam-3970	69	20	be	be	AUX
ejpam-3970	69	21	a	a	DET
ejpam-3970	69	22	subspace	subspace	NOUN
ejpam-3970	69	23	.	.	PUNCT
ejpam-3970	70	1	if	if	SCONJ
ejpam-3970	70	2	{	{	PUNCT
ejpam-3970	70	3	uα	uα	PROPN
ejpam-3970	70	4	|α	|α	NOUN
ejpam-3970	70	5	∈	∈	PROPN
ejpam-3970	70	6	a	a	PRON
ejpam-3970	70	7	}	}	PUNCT
ejpam-3970	70	8	is	be	AUX
ejpam-3970	70	9	a	a	DET
ejpam-3970	70	10	basis	basis	NOUN
ejpam-3970	70	11	(	(	PUNCT
ejpam-3970	70	12	subbasis	subbasis	NOUN
ejpam-3970	70	13	)	)	PUNCT
ejpam-3970	70	14	for	for	ADP
ejpam-3970	70	15	τ	τ	PROPN
ejpam-3970	70	16	,	,	PUNCT
ejpam-3970	70	17	{	{	PUNCT
ejpam-3970	70	18	y	y	PROPN
ejpam-3970	70	19	∩	∩	PROPN
ejpam-3970	70	20	uα	uα	PROPN
ejpam-3970	70	21	|α	|α	NOUN
ejpam-3970	70	22	∈	∈	PROPN
ejpam-3970	70	23	a	a	DET
ejpam-3970	70	24	}	}	PUNCT
ejpam-3970	70	25	is	be	AUX
ejpam-3970	70	26	a	a	DET
ejpam-3970	70	27	basis	basis	NOUN
ejpam-3970	70	28	(	(	PUNCT
ejpam-3970	70	29	subbasis	subbasis	NOUN
ejpam-3970	70	30	)	)	PUNCT
ejpam-3970	70	31	for	for	ADP
ejpam-3970	70	32	τy	τy	PUNCT
ejpam-3970	70	33	.	.	PUNCT
ejpam-3970	71	1	lemma	lemma	PROPN
ejpam-3970	71	2	1	1	X
ejpam-3970	71	3	.	.	PUNCT
ejpam-3970	72	1	let	let	VERB
ejpam-3970	72	2	{	{	PUNCT
ejpam-3970	72	3	aα	aα	NOUN
ejpam-3970	72	4	:	:	PUNCT
ejpam-3970	72	5	α	α	PROPN
ejpam-3970	72	6	∈	∈	PROPN
ejpam-3970	73	1	i	i	PRON
ejpam-3970	73	2	}	}	PUNCT
ejpam-3970	73	3	be	be	VERB
ejpam-3970	73	4	a	a	DET
ejpam-3970	73	5	collection	collection	NOUN
ejpam-3970	73	6	of	of	ADP
ejpam-3970	73	7	subsets	subset	NOUN
ejpam-3970	73	8	of	of	ADP
ejpam-3970	73	9	a	a	DET
ejpam-3970	73	10	hyper	hyper	ADJ
ejpam-3970	73	11	bci	bci	NOUN
ejpam-3970	73	12	-	-	PUNCT
ejpam-3970	73	13	algebra	algebra	NOUN
ejpam-3970	73	14	h.	h.	NOUN
ejpam-3970	73	15	then	then	ADV
ejpam-3970	73	16	⋂	⋂	PROPN
ejpam-3970	73	17	α∈i	α∈i	X
ejpam-3970	73	18	lh(aα	lh(aα	PROPN
ejpam-3970	73	19	)	)	PUNCT
ejpam-3970	73	20	=	=	SYM
ejpam-3970	73	21	lh	lh	NOUN
ejpam-3970	73	22	(	(	PUNCT
ejpam-3970	73	23	⋃	⋃	PROPN
ejpam-3970	73	24	α∈i	α∈i	NUM
ejpam-3970	73	25	aα	aα	NOUN
ejpam-3970	73	26	)	)	PUNCT
ejpam-3970	73	27	.	.	PUNCT
ejpam-3970	74	1	proof	proof	NOUN
ejpam-3970	74	2	.	.	PUNCT
ejpam-3970	75	1	if	if	SCONJ
ejpam-3970	75	2	⋂	⋂	PROPN
ejpam-3970	75	3	α∈i	α∈i	X
ejpam-3970	75	4	lh(aα	lh(aα	PROPN
ejpam-3970	75	5	)	)	PUNCT
ejpam-3970	75	6	=	=	SYM
ejpam-3970	75	7	∅	∅	NOUN
ejpam-3970	75	8	,	,	PUNCT
ejpam-3970	75	9	then	then	ADV
ejpam-3970	75	10	by	by	ADP
ejpam-3970	75	11	proposition	proposition	NOUN
ejpam-3970	75	12	1(iii	1(iii	NUM
ejpam-3970	75	13	)	)	PUNCT
ejpam-3970	75	14	,	,	PUNCT
ejpam-3970	75	15	lh	lh	PROPN
ejpam-3970	75	16	(	(	PUNCT
ejpam-3970	75	17	⋃	⋃	PROPN
ejpam-3970	75	18	α∈i	α∈i	NUM
ejpam-3970	75	19	aα	aα	NOUN
ejpam-3970	75	20	)	)	PUNCT
ejpam-3970	76	1	⊆	⊆	NUM
ejpam-3970	76	2	⋂	⋂	PROPN
ejpam-3970	76	3	α∈i	α∈i	NUM
ejpam-3970	76	4	lh(aα	lh(aα	PROPN
ejpam-3970	76	5	)	)	PUNCT
ejpam-3970	76	6	=	=	NOUN
ejpam-3970	76	7	∅.	∅.	ADP
ejpam-3970	76	8	thus	thus	ADV
ejpam-3970	76	9	,	,	PUNCT
ejpam-3970	76	10	lh	lh	PROPN
ejpam-3970	76	11	(	(	PUNCT
ejpam-3970	76	12	⋃	⋃	PROPN
ejpam-3970	76	13	α∈i	α∈i	NUM
ejpam-3970	76	14	aα	aα	NOUN
ejpam-3970	76	15	)	)	PUNCT
ejpam-3970	77	1	=	=	PUNCT
ejpam-3970	77	2	∅.	∅.	VERB
ejpam-3970	77	3	if	if	SCONJ
ejpam-3970	77	4	⋂	⋂	PROPN
ejpam-3970	77	5	α∈i	α∈i	X
ejpam-3970	77	6	lh(aα	lh(aα	PROPN
ejpam-3970	77	7	)	)	PUNCT
ejpam-3970	77	8	6=	6=	NOUN
ejpam-3970	77	9	∅	∅	NOUN
ejpam-3970	77	10	,	,	PUNCT
ejpam-3970	77	11	then	then	ADV
ejpam-3970	77	12	x	x	PART
ejpam-3970	77	13	∈	∈	PROPN
ejpam-3970	77	14	⋂	⋂	PROPN
ejpam-3970	77	15	α∈i	α∈i	X
ejpam-3970	77	16	lh(aα	lh(aα	PROPN
ejpam-3970	77	17	)	)	PUNCT
ejpam-3970	77	18	⇔	⇔	NOUN
ejpam-3970	77	19	x	x	SYM
ejpam-3970	77	20	∈	∈	PROPN
ejpam-3970	77	21	lh(aα	lh(aα	PROPN
ejpam-3970	77	22	)	)	PUNCT
ejpam-3970	77	23	for	for	ADP
ejpam-3970	77	24	all	all	DET
ejpam-3970	77	25	α	α	PRON
ejpam-3970	77	26	∈	∈	NOUN
ejpam-3970	77	27	i	i	PRON
ejpam-3970	77	28	⇔	⇔	PROPN
ejpam-3970	77	29	x	x	SYM
ejpam-3970	77	30	�	�	PROPN
ejpam-3970	77	31	a	a	PRON
ejpam-3970	77	32	for	for	ADP
ejpam-3970	77	33	all	all	DET
ejpam-3970	77	34	a	a	DET
ejpam-3970	77	35	∈	∈	ADJ
ejpam-3970	77	36	aα	aα	NOUN
ejpam-3970	77	37	and	and	CCONJ
ejpam-3970	77	38	for	for	ADP
ejpam-3970	77	39	all	all	DET
ejpam-3970	77	40	α	α	PRON
ejpam-3970	77	41	∈	∈	NOUN
ejpam-3970	77	42	i	i	PRON
ejpam-3970	77	43	⇔	⇔	PROPN
ejpam-3970	77	44	x	x	SYM
ejpam-3970	77	45	�	�	PROPN
ejpam-3970	77	46	a	a	PRON
ejpam-3970	77	47	for	for	ADP
ejpam-3970	77	48	all	all	DET
ejpam-3970	77	49	a	a	DET
ejpam-3970	77	50	∈	∈	NOUN
ejpam-3970	77	51	⋃	⋃	NOUN
ejpam-3970	77	52	α∈i	α∈i	NUM
ejpam-3970	77	53	aα	aα	NOUN
ejpam-3970	77	54	⇔	⇔	NOUN
ejpam-3970	77	55	x	x	SYM
ejpam-3970	77	56	∈	∈	PROPN
ejpam-3970	77	57	lh	lh	PROPN
ejpam-3970	77	58	(	(	PUNCT
ejpam-3970	77	59	⋃	⋃	PROPN
ejpam-3970	77	60	α∈i	α∈i	NUM
ejpam-3970	77	61	aα	aα	NOUN
ejpam-3970	77	62	)	)	PUNCT
ejpam-3970	77	63	.	.	PUNCT
ejpam-3970	78	1	this	this	PRON
ejpam-3970	78	2	proves	prove	VERB
ejpam-3970	78	3	the	the	DET
ejpam-3970	78	4	assertion	assertion	NOUN
ejpam-3970	78	5	.	.	PUNCT
ejpam-3970	79	1	m.	m.	NOUN
ejpam-3970	79	2	panganduyon	panganduyon	NOUN
ejpam-3970	79	3	,	,	PUNCT
ejpam-3970	79	4	s.	s.	PROPN
ejpam-3970	79	5	canoy	canoy	PROPN
ejpam-3970	79	6	,	,	PUNCT
ejpam-3970	79	7	jr	jr	PROPN
ejpam-3970	79	8	.	.	PROPN
ejpam-3970	79	9	,	,	PUNCT
ejpam-3970	79	10	b.	b.	PROPN
ejpam-3970	79	11	davvaz	davvaz	PROPN
ejpam-3970	79	12	/	/	SYM
ejpam-3970	79	13	eur	eur	PROPN
ejpam-3970	79	14	.	.	PUNCT
ejpam-3970	80	1	j.	j.	PROPN
ejpam-3970	80	2	pure	pure	PROPN
ejpam-3970	80	3	appl	appl	PROPN
ejpam-3970	80	4	.	.	PROPN
ejpam-3970	80	5	math	math	PROPN
ejpam-3970	80	6	,	,	PUNCT
ejpam-3970	80	7	14	14	NUM
ejpam-3970	80	8	(	(	PUNCT
ejpam-3970	80	9	2	2	NUM
ejpam-3970	80	10	)	)	PUNCT
ejpam-3970	80	11	(	(	PUNCT
ejpam-3970	80	12	2021	2021	NUM
ejpam-3970	80	13	)	)	PUNCT
ejpam-3970	80	14	,	,	PUNCT
ejpam-3970	80	15	590	590	NUM
ejpam-3970	80	16	-	-	SYM
ejpam-3970	80	17	600	600	NUM
ejpam-3970	80	18	593	593	NUM
ejpam-3970	80	19	theorem	theorem	NOUN
ejpam-3970	80	20	2	2	NUM
ejpam-3970	80	21	.	.	PUNCT
ejpam-3970	81	1	let	let	VERB
ejpam-3970	81	2	h	h	PRON
ejpam-3970	81	3	be	be	AUX
ejpam-3970	81	4	a	a	DET
ejpam-3970	81	5	hyper	hyper	ADJ
ejpam-3970	81	6	bci	bci	NOUN
ejpam-3970	81	7	-	-	NOUN
ejpam-3970	81	8	algebra	algebra	NOUN
ejpam-3970	81	9	.	.	PUNCT
ejpam-3970	82	1	then	then	ADV
ejpam-3970	82	2	the	the	DET
ejpam-3970	82	3	family	family	NOUN
ejpam-3970	82	4	bl(h	bl(h	PUNCT
ejpam-3970	82	5	)	)	PUNCT
ejpam-3970	82	6	=	=	PRON
ejpam-3970	82	7	{	{	PUNCT
ejpam-3970	82	8	lh(a	lh(a	NOUN
ejpam-3970	82	9	)	)	PUNCT
ejpam-3970	82	10	:	:	PUNCT
ejpam-3970	82	11	∅	∅	NOUN
ejpam-3970	82	12	6=	6=	ADP
ejpam-3970	82	13	a	a	DET
ejpam-3970	82	14	⊆	⊆	NUM
ejpam-3970	82	15	h	h	NOUN
ejpam-3970	82	16	}	}	PUNCT
ejpam-3970	82	17	is	be	AUX
ejpam-3970	82	18	a	a	DET
ejpam-3970	82	19	basis	basis	NOUN
ejpam-3970	82	20	for	for	ADP
ejpam-3970	82	21	some	some	DET
ejpam-3970	82	22	topology	topology	NOUN
ejpam-3970	82	23	on	on	ADP
ejpam-3970	82	24	h.	h.	PROPN
ejpam-3970	82	25	proof	proof	NOUN
ejpam-3970	82	26	.	.	PUNCT
ejpam-3970	83	1	clearly	clearly	ADV
ejpam-3970	83	2	,	,	PUNCT
ejpam-3970	83	3	h	h	NOUN
ejpam-3970	83	4	=	=	PUNCT
ejpam-3970	84	1	⋃	⋃	PROPN
ejpam-3970	84	2	a∈h	a∈h	NOUN
ejpam-3970	84	3	lh(a	lh(a	NOUN
ejpam-3970	84	4	)	)	PUNCT
ejpam-3970	84	5	.	.	PUNCT
ejpam-3970	85	1	let	let	VERB
ejpam-3970	85	2	a	a	PRON
ejpam-3970	85	3	and	and	CCONJ
ejpam-3970	85	4	b	b	NOUN
ejpam-3970	85	5	be	be	AUX
ejpam-3970	85	6	nonempty	nonempty	X
ejpam-3970	85	7	subsets	subset	NOUN
ejpam-3970	85	8	of	of	ADP
ejpam-3970	85	9	h.	h.	PROPN
ejpam-3970	85	10	then	then	ADV
ejpam-3970	85	11	by	by	ADP
ejpam-3970	85	12	lemma	lemma	PROPN
ejpam-3970	85	13	1	1	NUM
ejpam-3970	85	14	,	,	PUNCT
ejpam-3970	85	15	lh(a	lh(a	NUM
ejpam-3970	85	16	)	)	PUNCT
ejpam-3970	85	17	∩	∩	NOUN
ejpam-3970	85	18	lh(b	lh(b	NOUN
ejpam-3970	85	19	)	)	PUNCT
ejpam-3970	86	1	=	=	SYM
ejpam-3970	86	2	lh(a	lh(a	NOUN
ejpam-3970	86	3	∪b	∪b	NOUN
ejpam-3970	86	4	)	)	PUNCT
ejpam-3970	86	5	∈	∈	PROPN
ejpam-3970	86	6	bl(h	bl(h	PRON
ejpam-3970	86	7	)	)	PUNCT
ejpam-3970	86	8	.	.	PUNCT
ejpam-3970	87	1	therefore	therefore	ADV
ejpam-3970	87	2	,	,	PUNCT
ejpam-3970	87	3	bl(h	bl(h	PUNCT
ejpam-3970	87	4	)	)	PUNCT
ejpam-3970	87	5	is	be	AUX
ejpam-3970	87	6	a	a	DET
ejpam-3970	87	7	basis	basis	NOUN
ejpam-3970	87	8	for	for	ADP
ejpam-3970	87	9	some	some	DET
ejpam-3970	87	10	topology	topology	NOUN
ejpam-3970	87	11	on	on	ADP
ejpam-3970	87	12	h.	h.	PROPN
ejpam-3970	87	13	denote	denote	VERB
ejpam-3970	87	14	by	by	ADP
ejpam-3970	87	15	τl(h	τl(h	NOUN
ejpam-3970	87	16	)	)	PUNCT
ejpam-3970	87	17	the	the	DET
ejpam-3970	87	18	topology	topology	NOUN
ejpam-3970	87	19	generated	generate	VERB
ejpam-3970	87	20	by	by	ADP
ejpam-3970	87	21	bl(h	bl(h	NOUN
ejpam-3970	87	22	)	)	PUNCT
ejpam-3970	87	23	.	.	PUNCT
ejpam-3970	88	1	example	example	NOUN
ejpam-3970	89	1	1	1	X
ejpam-3970	89	2	.	.	X
ejpam-3970	89	3	consider	consider	VERB
ejpam-3970	89	4	h	h	NOUN
ejpam-3970	89	5	:	:	PUNCT
ejpam-3970	89	6	=	=	SYM
ejpam-3970	90	1	[	[	X
ejpam-3970	90	2	0,∞	0,∞	NUM
ejpam-3970	90	3	)	)	PUNCT
ejpam-3970	90	4	with	with	ADP
ejpam-3970	90	5	the	the	DET
ejpam-3970	90	6	hyperoperation	hyperoperation	NOUN
ejpam-3970	90	7	“	"	PUNCT
ejpam-3970	90	8	~	~	PUNCT
ejpam-3970	90	9	”	"	PUNCT
ejpam-3970	90	10	,	,	PUNCT
ejpam-3970	90	11	defined	define	VERB
ejpam-3970	90	12	in	in	ADP
ejpam-3970	90	13	[	[	X
ejpam-3970	90	14	13	13	NUM
ejpam-3970	90	15	]	]	PUNCT
ejpam-3970	90	16	:	:	PUNCT
ejpam-3970	91	1	x~	x~	NUM
ejpam-3970	91	2	y	y	X
ejpam-3970	91	3	:	:	PUNCT
ejpam-3970	91	4	=	=	SYM
ejpam-3970	91	5			PRON
ejpam-3970	92	1	[	[	X
ejpam-3970	92	2	0	0	NUM
ejpam-3970	92	3	,	,	PUNCT
ejpam-3970	92	4	x	x	X
ejpam-3970	92	5	]	]	X
ejpam-3970	92	6	,	,	PUNCT
ejpam-3970	92	7	if	if	SCONJ
ejpam-3970	92	8	x	x	ADP
ejpam-3970	92	9	≤	≤	NOUN
ejpam-3970	92	10	y	y	NOUN
ejpam-3970	92	11	,	,	PUNCT
ejpam-3970	92	12	(	(	PUNCT
ejpam-3970	92	13	0	0	NUM
ejpam-3970	92	14	,	,	PUNCT
ejpam-3970	92	15	y	y	PROPN
ejpam-3970	92	16	]	]	X
ejpam-3970	92	17	,	,	PUNCT
ejpam-3970	92	18	if	if	SCONJ
ejpam-3970	92	19	x	x	PROPN
ejpam-3970	92	20	>	>	X
ejpam-3970	92	21	y	y	PROPN
ejpam-3970	92	22	6=	6=	PROPN
ejpam-3970	92	23	0	0	NUM
ejpam-3970	92	24	,	,	PUNCT
ejpam-3970	92	25	{	{	PUNCT
ejpam-3970	92	26	x	x	X
ejpam-3970	92	27	}	}	PUNCT
ejpam-3970	92	28	,	,	PUNCT
ejpam-3970	92	29	if	if	SCONJ
ejpam-3970	92	30	y	y	PROPN
ejpam-3970	92	31	=	=	NOUN
ejpam-3970	92	32	0	0	NUM
ejpam-3970	92	33	for	for	ADP
ejpam-3970	92	34	all	all	DET
ejpam-3970	92	35	x	x	NOUN
ejpam-3970	92	36	,	,	PUNCT
ejpam-3970	92	37	y	y	PROPN
ejpam-3970	92	38	∈	∈	PROPN
ejpam-3970	92	39	h.	h.	PROPN
ejpam-3970	92	40	then	then	ADV
ejpam-3970	92	41	(	(	PUNCT
ejpam-3970	92	42	h,~	h,~	NOUN
ejpam-3970	92	43	,	,	PUNCT
ejpam-3970	92	44	0	0	NUM
ejpam-3970	92	45	)	)	PUNCT
ejpam-3970	92	46	is	be	AUX
ejpam-3970	92	47	a	a	DET
ejpam-3970	92	48	hyper	hyper	ADJ
ejpam-3970	92	49	bci	bci	NOUN
ejpam-3970	92	50	-	-	NOUN
ejpam-3970	92	51	algebra	algebra	NOUN
ejpam-3970	92	52	.	.	PUNCT
ejpam-3970	93	1	now	now	ADV
ejpam-3970	93	2	,	,	PUNCT
ejpam-3970	93	3	let	let	VERB
ejpam-3970	93	4	k	k	PROPN
ejpam-3970	93	5	∈	∈	PROPN
ejpam-3970	93	6	h.	h.	PROPN
ejpam-3970	93	7	then	then	ADV
ejpam-3970	93	8	lh(k	lh(k	NOUN
ejpam-3970	93	9	)	)	PUNCT
ejpam-3970	93	10	=	=	PUNCT
ejpam-3970	94	1	[	[	X
ejpam-3970	94	2	0	0	NUM
ejpam-3970	94	3	,	,	PUNCT
ejpam-3970	94	4	k	k	NOUN
ejpam-3970	94	5	]	]	X
ejpam-3970	94	6	.	.	PUNCT
ejpam-3970	95	1	let	let	VERB
ejpam-3970	95	2	∅	∅	NOUN
ejpam-3970	95	3	6=	6=	ADP
ejpam-3970	95	4	a	a	DET
ejpam-3970	95	5	⊆	⊆	NUM
ejpam-3970	95	6	h	h	NOUN
ejpam-3970	95	7	and	and	CCONJ
ejpam-3970	95	8	let	let	VERB
ejpam-3970	95	9	p	p	NOUN
ejpam-3970	95	10	=	=	X
ejpam-3970	95	11	inf	inf	PROPN
ejpam-3970	95	12	a.	a.	NOUN
ejpam-3970	95	13	since	since	SCONJ
ejpam-3970	95	14	lh(a	lh(a	NUM
ejpam-3970	95	15	)	)	PUNCT
ejpam-3970	95	16	=	=	PUNCT
ejpam-3970	96	1	⋂	⋂	PROPN
ejpam-3970	96	2	a∈a	a∈a	ADJ
ejpam-3970	96	3	lh(a	lh(a	NUM
ejpam-3970	96	4	)	)	PUNCT
ejpam-3970	96	5	=	=	SYM
ejpam-3970	96	6	lh(p	lh(p	NOUN
ejpam-3970	96	7	)	)	PUNCT
ejpam-3970	97	1	,	,	PUNCT
ejpam-3970	97	2	it	it	PRON
ejpam-3970	97	3	follows	follow	VERB
ejpam-3970	97	4	that	that	DET
ejpam-3970	97	5	lh(a	lh(a	NOUN
ejpam-3970	97	6	)	)	PUNCT
ejpam-3970	97	7	=	=	PUNCT
ejpam-3970	98	1	[	[	X
ejpam-3970	98	2	0	0	NUM
ejpam-3970	98	3	,	,	PUNCT
ejpam-3970	98	4	p	p	X
ejpam-3970	98	5	]	]	X
ejpam-3970	98	6	=	=	X
ejpam-3970	98	7	lh(p	lh(p	NOUN
ejpam-3970	98	8	)	)	PUNCT
ejpam-3970	98	9	.	.	PUNCT
ejpam-3970	99	1	let	let	VERB
ejpam-3970	99	2	∅	∅	NOUN
ejpam-3970	99	3	6=	6=	ADP
ejpam-3970	99	4	g	g	PROPN
ejpam-3970	99	5	∈	∈	PROPN
ejpam-3970	99	6	τl(h	τl(h	NUM
ejpam-3970	99	7	)	)	PUNCT
ejpam-3970	99	8	.	.	PUNCT
ejpam-3970	100	1	then	then	ADV
ejpam-3970	100	2	g	g	PROPN
ejpam-3970	100	3	=	=	SYM
ejpam-3970	100	4	⋃	⋃	NOUN
ejpam-3970	100	5	p∈k	p∈k	ADJ
ejpam-3970	100	6	lh(p	lh(p	NOUN
ejpam-3970	100	7	)	)	PUNCT
ejpam-3970	100	8	,	,	PUNCT
ejpam-3970	100	9	where	where	SCONJ
ejpam-3970	100	10	k	k	PROPN
ejpam-3970	100	11	⊆	⊆	PROPN
ejpam-3970	100	12	h.	h.	PROPN
ejpam-3970	100	13	suppose	suppose	VERB
ejpam-3970	100	14	first	first	ADV
ejpam-3970	100	15	that	that	SCONJ
ejpam-3970	100	16	|g|	|g|	PROPN
ejpam-3970	100	17	<	<	X
ejpam-3970	100	18	∞	∞	PROPN
ejpam-3970	100	19	and	and	CCONJ
ejpam-3970	100	20	let	let	VERB
ejpam-3970	100	21	q	q	NOUN
ejpam-3970	100	22	=	=	NOUN
ejpam-3970	100	23	supg	supg	NOUN
ejpam-3970	100	24	.	.	PUNCT
ejpam-3970	101	1	then	then	ADV
ejpam-3970	101	2	g	g	PROPN
ejpam-3970	101	3	=	=	PUNCT
ejpam-3970	101	4	lh(q	lh(q	NUM
ejpam-3970	101	5	)	)	PUNCT
ejpam-3970	101	6	.	.	PUNCT
ejpam-3970	101	7	suppose	suppose	VERB
ejpam-3970	101	8	q	q	X
ejpam-3970	101	9	>	>	X
ejpam-3970	101	10	0	0	X
ejpam-3970	101	11	.	.	PUNCT
ejpam-3970	102	1	then	then	ADV
ejpam-3970	102	2	g	g	PROPN
ejpam-3970	102	3	=	=	PUNCT
ejpam-3970	102	4	lh(q	lh(q	NUM
ejpam-3970	102	5	)	)	PUNCT
ejpam-3970	103	1	=	=	PUNCT
ejpam-3970	104	1	[	[	X
ejpam-3970	104	2	0	0	NUM
ejpam-3970	104	3	,	,	PUNCT
ejpam-3970	104	4	q	q	NOUN
ejpam-3970	104	5	]	]	X
ejpam-3970	104	6	,	,	PUNCT
ejpam-3970	104	7	a	a	DET
ejpam-3970	104	8	contradiction	contradiction	NOUN
ejpam-3970	104	9	.	.	PUNCT
ejpam-3970	105	1	thus	thus	ADV
ejpam-3970	105	2	,	,	PUNCT
ejpam-3970	105	3	q	q	X
ejpam-3970	105	4	=	=	SYM
ejpam-3970	105	5	0	0	NUM
ejpam-3970	105	6	,	,	PUNCT
ejpam-3970	105	7	that	that	ADV
ejpam-3970	105	8	is	is	ADV
ejpam-3970	105	9	,	,	PUNCT
ejpam-3970	105	10	g	g	PROPN
ejpam-3970	105	11	=	=	PUNCT
ejpam-3970	105	12	lh(0	lh(0	NOUN
ejpam-3970	105	13	)	)	PUNCT
ejpam-3970	106	1	=	=	PUNCT
ejpam-3970	106	2	{	{	PUNCT
ejpam-3970	106	3	0	0	NUM
ejpam-3970	106	4	}	}	PUNCT
ejpam-3970	106	5	.	.	PUNCT
ejpam-3970	107	1	next	next	ADV
ejpam-3970	107	2	,	,	PUNCT
ejpam-3970	107	3	suppose	suppose	VERB
ejpam-3970	107	4	that	that	SCONJ
ejpam-3970	107	5	g	g	PROPN
ejpam-3970	107	6	is	be	AUX
ejpam-3970	107	7	an	an	DET
ejpam-3970	107	8	infinite	infinite	ADJ
ejpam-3970	107	9	set	set	NOUN
ejpam-3970	107	10	.	.	PUNCT
ejpam-3970	108	1	if	if	SCONJ
ejpam-3970	108	2	k	k	PROPN
ejpam-3970	108	3	is	be	AUX
ejpam-3970	108	4	infinite	infinite	ADJ
ejpam-3970	108	5	,	,	PUNCT
ejpam-3970	108	6	then	then	ADV
ejpam-3970	108	7	g	g	PROPN
ejpam-3970	108	8	=	=	SYM
ejpam-3970	108	9	⋃	⋃	PROPN
ejpam-3970	108	10	p∈k	p∈k	VERB
ejpam-3970	108	11	[	[	X
ejpam-3970	108	12	0	0	NUM
ejpam-3970	108	13	,	,	PUNCT
ejpam-3970	108	14	p	p	X
ejpam-3970	108	15	]	]	X
ejpam-3970	108	16	=	=	SYM
ejpam-3970	108	17	h.	h.	PROPN
ejpam-3970	108	18	suppose	suppose	VERB
ejpam-3970	108	19	k	k	PROPN
ejpam-3970	108	20	is	be	AUX
ejpam-3970	108	21	finite	finite	ADJ
ejpam-3970	108	22	.	.	PUNCT
ejpam-3970	109	1	since	since	SCONJ
ejpam-3970	109	2	g	g	PROPN
ejpam-3970	109	3	is	be	AUX
ejpam-3970	109	4	infinite	infinite	ADJ
ejpam-3970	109	5	,	,	PUNCT
ejpam-3970	109	6	0	0	PUNCT
ejpam-3970	109	7	<	<	X
ejpam-3970	109	8	m	m	PROPN
ejpam-3970	109	9	=	=	ADJ
ejpam-3970	109	10	maxk	maxk	NOUN
ejpam-3970	109	11	.	.	PUNCT
ejpam-3970	110	1	hence	hence	ADV
ejpam-3970	110	2	,	,	PUNCT
ejpam-3970	110	3	g	g	PROPN
ejpam-3970	110	4	=	=	PUNCT
ejpam-3970	111	1	[	[	X
ejpam-3970	111	2	0,m	0,m	X
ejpam-3970	111	3	]	]	X
ejpam-3970	111	4	.	.	PUNCT
ejpam-3970	112	1	consequently	consequently	ADV
ejpam-3970	112	2	,	,	PUNCT
ejpam-3970	112	3	τl(h	τl(h	PUNCT
ejpam-3970	112	4	)	)	PUNCT
ejpam-3970	112	5	=	=	SYM
ejpam-3970	112	6	{	{	PUNCT
ejpam-3970	112	7	∅	∅	NOUN
ejpam-3970	112	8	,	,	PUNCT
ejpam-3970	112	9	h	h	NOUN
ejpam-3970	112	10	}	}	PUNCT
ejpam-3970	112	11	∪	∪	X
ejpam-3970	112	12	{	{	PUNCT
ejpam-3970	112	13	[	[	X
ejpam-3970	112	14	0	0	NUM
ejpam-3970	112	15	,	,	PUNCT
ejpam-3970	112	16	p	p	X
ejpam-3970	112	17	]	]	X
ejpam-3970	112	18	:	:	PUNCT
ejpam-3970	112	19	p	p	X
ejpam-3970	112	20	∈	∈	PROPN
ejpam-3970	112	21	h	h	NOUN
ejpam-3970	112	22	}	}	PUNCT
ejpam-3970	112	23	.	.	PUNCT
ejpam-3970	113	1	example	example	NOUN
ejpam-3970	114	1	2	2	NUM
ejpam-3970	114	2	.	.	X
ejpam-3970	114	3	consider	consider	VERB
ejpam-3970	114	4	h	h	NOUN
ejpam-3970	114	5	=	=	PRON
ejpam-3970	114	6	{	{	PUNCT
ejpam-3970	114	7	0	0	NUM
ejpam-3970	114	8	,	,	PUNCT
ejpam-3970	114	9	a	a	DET
ejpam-3970	114	10	,	,	PUNCT
ejpam-3970	114	11	b	b	NOUN
ejpam-3970	114	12	}	}	PUNCT
ejpam-3970	114	13	with	with	ADP
ejpam-3970	114	14	the	the	DET
ejpam-3970	114	15	hyperoperation	hyperoperation	NOUN
ejpam-3970	114	16	“	"	PUNCT
ejpam-3970	114	17	~	~	PUNCT
ejpam-3970	114	18	”	"	PUNCT
ejpam-3970	114	19	defined	define	VERB
ejpam-3970	114	20	as	as	SCONJ
ejpam-3970	114	21	follows	follow	VERB
ejpam-3970	114	22	:	:	PUNCT
ejpam-3970	114	23	~	~	PUNCT
ejpam-3970	114	24	0	0	PUNCT
ejpam-3970	114	25	a	a	DET
ejpam-3970	114	26	b	b	PROPN
ejpam-3970	114	27	0	0	NUM
ejpam-3970	114	28	{	{	PUNCT
ejpam-3970	114	29	0	0	NUM
ejpam-3970	114	30	,	,	PUNCT
ejpam-3970	114	31	a	a	PRON
ejpam-3970	114	32	}	}	PUNCT
ejpam-3970	114	33	{	{	PUNCT
ejpam-3970	114	34	0	0	NUM
ejpam-3970	114	35	,	,	PUNCT
ejpam-3970	114	36	a	a	PRON
ejpam-3970	114	37	}	}	PUNCT
ejpam-3970	114	38	{	{	PUNCT
ejpam-3970	114	39	b	b	NOUN
ejpam-3970	114	40	}	}	PUNCT
ejpam-3970	114	41	a	a	DET
ejpam-3970	114	42	{	{	PUNCT
ejpam-3970	114	43	a	a	NOUN
ejpam-3970	114	44	}	}	PUNCT
ejpam-3970	114	45	{	{	PUNCT
ejpam-3970	114	46	0	0	NUM
ejpam-3970	114	47	,	,	PUNCT
ejpam-3970	114	48	a	a	PRON
ejpam-3970	114	49	}	}	PUNCT
ejpam-3970	114	50	{	{	PUNCT
ejpam-3970	114	51	b	b	NOUN
ejpam-3970	114	52	}	}	PUNCT
ejpam-3970	114	53	b	b	PROPN
ejpam-3970	114	54	{	{	PUNCT
ejpam-3970	114	55	b	b	NOUN
ejpam-3970	114	56	}	}	PUNCT
ejpam-3970	114	57	{	{	PUNCT
ejpam-3970	114	58	b	b	NOUN
ejpam-3970	114	59	}	}	PUNCT
ejpam-3970	114	60	{	{	PUNCT
ejpam-3970	114	61	0	0	NUM
ejpam-3970	114	62	,	,	PUNCT
ejpam-3970	114	63	a	a	PRON
ejpam-3970	114	64	}	}	PUNCT
ejpam-3970	114	65	then	then	ADV
ejpam-3970	114	66	h	h	PROPN
ejpam-3970	114	67	is	be	AUX
ejpam-3970	114	68	a	a	DET
ejpam-3970	114	69	hyper	hyper	ADJ
ejpam-3970	114	70	bci	bci	NOUN
ejpam-3970	114	71	-	-	NOUN
ejpam-3970	114	72	algebra	algebra	NOUN
ejpam-3970	114	73	.	.	PUNCT
ejpam-3970	115	1	by	by	ADP
ejpam-3970	115	2	theorem	theorem	NOUN
ejpam-3970	115	3	2	2	NUM
ejpam-3970	115	4	,	,	PUNCT
ejpam-3970	115	5	bl(h	bl(h	NUM
ejpam-3970	115	6	)	)	PUNCT
ejpam-3970	115	7	=	=	PRON
ejpam-3970	115	8	{	{	PUNCT
ejpam-3970	115	9	lh(a	lh(a	NOUN
ejpam-3970	115	10	)	)	PUNCT
ejpam-3970	115	11	:	:	PUNCT
ejpam-3970	115	12	∅	∅	NOUN
ejpam-3970	115	13	6=	6=	ADP
ejpam-3970	115	14	a	a	DET
ejpam-3970	115	15	⊆	⊆	NUM
ejpam-3970	115	16	h	h	NOUN
ejpam-3970	115	17	}	}	PUNCT
ejpam-3970	115	18	=	=	PRON
ejpam-3970	115	19	{	{	PUNCT
ejpam-3970	115	20	{	{	PUNCT
ejpam-3970	115	21	0	0	NUM
ejpam-3970	115	22	}	}	PUNCT
ejpam-3970	115	23	,	,	PUNCT
ejpam-3970	115	24	{	{	PUNCT
ejpam-3970	115	25	0	0	NUM
ejpam-3970	115	26	,	,	PUNCT
ejpam-3970	115	27	a	a	PRON
ejpam-3970	115	28	}	}	PUNCT
ejpam-3970	115	29	,	,	PUNCT
ejpam-3970	115	30	{	{	PUNCT
ejpam-3970	115	31	b},∅	b},∅	NOUN
ejpam-3970	115	32	}	}	PUNCT
ejpam-3970	115	33	.	.	PUNCT
ejpam-3970	116	1	thus	thus	ADV
ejpam-3970	116	2	,	,	PUNCT
ejpam-3970	116	3	τl(h	τl(h	PUNCT
ejpam-3970	116	4	)	)	PUNCT
ejpam-3970	117	1	=	=	PRON
ejpam-3970	117	2	{	{	PUNCT
ejpam-3970	117	3	{	{	PUNCT
ejpam-3970	117	4	0	0	NUM
ejpam-3970	117	5	}	}	PUNCT
ejpam-3970	117	6	,	,	PUNCT
ejpam-3970	117	7	{	{	PUNCT
ejpam-3970	117	8	0	0	NUM
ejpam-3970	117	9	,	,	PUNCT
ejpam-3970	117	10	a	a	DET
ejpam-3970	117	11	}	}	PUNCT
ejpam-3970	117	12	,	,	PUNCT
ejpam-3970	117	13	{	{	PUNCT
ejpam-3970	117	14	b	b	NOUN
ejpam-3970	117	15	}	}	PUNCT
ejpam-3970	117	16	,	,	PUNCT
ejpam-3970	117	17	{	{	PUNCT
ejpam-3970	117	18	0	0	NUM
ejpam-3970	117	19	,	,	PUNCT
ejpam-3970	117	20	b},∅	b},∅	PROPN
ejpam-3970	117	21	,	,	PUNCT
ejpam-3970	117	22	h	h	NOUN
ejpam-3970	117	23	}	}	PUNCT
ejpam-3970	117	24	.	.	PUNCT
ejpam-3970	118	1	observe	observe	VERB
ejpam-3970	118	2	that	that	SCONJ
ejpam-3970	118	3	in	in	ADP
ejpam-3970	118	4	example	example	NOUN
ejpam-3970	118	5	1	1	NUM
ejpam-3970	118	6	,	,	PUNCT
ejpam-3970	118	7	(	(	PUNCT
ejpam-3970	118	8	h	h	NOUN
ejpam-3970	118	9	,	,	PUNCT
ejpam-3970	118	10	τl(h	τl(h	NUM
ejpam-3970	118	11	)	)	PUNCT
ejpam-3970	118	12	)	)	PUNCT
ejpam-3970	118	13	is	be	AUX
ejpam-3970	118	14	connected	connect	VERB
ejpam-3970	118	15	,	,	PUNCT
ejpam-3970	118	16	however	however	ADV
ejpam-3970	118	17	,	,	PUNCT
ejpam-3970	118	18	in	in	ADP
ejpam-3970	118	19	example	example	NOUN
ejpam-3970	118	20	2	2	NUM
ejpam-3970	118	21	,	,	PUNCT
ejpam-3970	118	22	h	h	NOUN
ejpam-3970	118	23	=	=	SYM
ejpam-3970	118	24	{	{	PUNCT
ejpam-3970	118	25	0	0	NUM
ejpam-3970	118	26	,	,	PUNCT
ejpam-3970	118	27	a	a	PRON
ejpam-3970	118	28	}	}	PUNCT
ejpam-3970	118	29	∪	∪	NOUN
ejpam-3970	118	30	{	{	PUNCT
ejpam-3970	118	31	b	b	NOUN
ejpam-3970	118	32	}	}	PUNCT
ejpam-3970	118	33	.	.	PUNCT
ejpam-3970	119	1	hence	hence	ADV
ejpam-3970	119	2	,	,	PUNCT
ejpam-3970	119	3	(	(	PUNCT
ejpam-3970	119	4	h	h	NOUN
ejpam-3970	119	5	,	,	PUNCT
ejpam-3970	119	6	τl(h	τl(h	NUM
ejpam-3970	119	7	)	)	PUNCT
ejpam-3970	119	8	)	)	PUNCT
ejpam-3970	119	9	is	be	AUX
ejpam-3970	119	10	disconnected	disconnect	VERB
ejpam-3970	119	11	.	.	PUNCT
ejpam-3970	120	1	lemma	lemma	PROPN
ejpam-3970	120	2	2	2	X
ejpam-3970	120	3	.	.	PUNCT
ejpam-3970	121	1	let	let	VERB
ejpam-3970	121	2	h	h	PRON
ejpam-3970	121	3	be	be	AUX
ejpam-3970	121	4	an	an	DET
ejpam-3970	121	5	ordered	order	VERB
ejpam-3970	121	6	hyper	hyper	ADJ
ejpam-3970	121	7	bci	bci	NOUN
ejpam-3970	121	8	-	-	NOUN
ejpam-3970	121	9	algebra	algebra	NOUN
ejpam-3970	121	10	and	and	CCONJ
ejpam-3970	121	11	let	let	VERB
ejpam-3970	121	12	x	x	X
ejpam-3970	121	13	∈	∈	PROPN
ejpam-3970	121	14	h.	h.	NOUN
ejpam-3970	122	1	if	if	SCONJ
ejpam-3970	122	2	z	z	PROPN
ejpam-3970	122	3	∈	∈	PROPN
ejpam-3970	122	4	lh(x	lh(x	PROPN
ejpam-3970	122	5	)	)	PUNCT
ejpam-3970	122	6	,	,	PUNCT
ejpam-3970	122	7	then	then	ADV
ejpam-3970	122	8	lh(z	lh(z	NOUN
ejpam-3970	122	9	)	)	PUNCT
ejpam-3970	122	10	⊆	⊆	NUM
ejpam-3970	122	11	lh(x	lh(x	NOUN
ejpam-3970	122	12	)	)	PUNCT
ejpam-3970	122	13	.	.	PUNCT
ejpam-3970	123	1	proof	proof	NOUN
ejpam-3970	123	2	.	.	PUNCT
ejpam-3970	124	1	suppose	suppose	VERB
ejpam-3970	124	2	that	that	SCONJ
ejpam-3970	124	3	z	z	PROPN
ejpam-3970	124	4	∈	∈	PROPN
ejpam-3970	124	5	lh(x	lh(x	PRON
ejpam-3970	124	6	)	)	PUNCT
ejpam-3970	124	7	and	and	CCONJ
ejpam-3970	124	8	let	let	VERB
ejpam-3970	124	9	w	w	PROPN
ejpam-3970	124	10	∈	∈	PROPN
ejpam-3970	124	11	lh(z	lh(z	NOUN
ejpam-3970	124	12	)	)	PUNCT
ejpam-3970	124	13	.	.	PUNCT
ejpam-3970	125	1	then	then	ADV
ejpam-3970	125	2	w	w	PROPN
ejpam-3970	125	3	�	�	PROPN
ejpam-3970	125	4	z.	z.	PROPN
ejpam-3970	125	5	since	since	SCONJ
ejpam-3970	125	6	z	z	PROPN
ejpam-3970	125	7	�	�	PROPN
ejpam-3970	125	8	x	x	PUNCT
ejpam-3970	125	9	and	and	CCONJ
ejpam-3970	125	10	h	h	NOUN
ejpam-3970	125	11	is	be	AUX
ejpam-3970	125	12	ordered	order	VERB
ejpam-3970	125	13	,	,	PUNCT
ejpam-3970	125	14	w	w	PROPN
ejpam-3970	125	15	�	�	PROPN
ejpam-3970	125	16	x	x	SYM
ejpam-3970	125	17	;	;	PUNCT
ejpam-3970	125	18	that	that	PRON
ejpam-3970	125	19	is	is	ADV
ejpam-3970	125	20	,	,	PUNCT
ejpam-3970	125	21	w	w	PROPN
ejpam-3970	125	22	∈	∈	PROPN
ejpam-3970	125	23	lh(x	lh(x	PUNCT
ejpam-3970	125	24	)	)	PUNCT
ejpam-3970	125	25	.	.	PUNCT
ejpam-3970	126	1	therefore	therefore	ADV
ejpam-3970	126	2	,	,	PUNCT
ejpam-3970	126	3	lh(z	lh(z	PUNCT
ejpam-3970	126	4	)	)	PUNCT
ejpam-3970	126	5	⊆	⊆	NUM
ejpam-3970	126	6	lh(x	lh(x	NOUN
ejpam-3970	126	7	)	)	PUNCT
ejpam-3970	126	8	.	.	PUNCT
ejpam-3970	127	1	an	an	DET
ejpam-3970	127	2	ordered	order	VERB
ejpam-3970	127	3	hyper	hyper	ADJ
ejpam-3970	127	4	bci	bci	NOUN
ejpam-3970	127	5	-	-	ADJ
ejpam-3970	127	6	algebra	algebra	NOUN
ejpam-3970	127	7	h	h	NOUN
ejpam-3970	127	8	is	be	AUX
ejpam-3970	127	9	said	say	VERB
ejpam-3970	127	10	to	to	PART
ejpam-3970	127	11	be	be	AUX
ejpam-3970	127	12	lh	lh	PROPN
ejpam-3970	127	13	-0	-0	PUNCT
ejpam-3970	127	14	hereditary	hereditary	ADJ
ejpam-3970	127	15	if	if	SCONJ
ejpam-3970	127	16	0	0	NUM
ejpam-3970	127	17	∈	∈	PROPN
ejpam-3970	127	18	lh(z	lh(z	NOUN
ejpam-3970	127	19	)	)	PUNCT
ejpam-3970	127	20	for	for	ADP
ejpam-3970	127	21	all	all	DET
ejpam-3970	127	22	z	z	NOUN
ejpam-3970	127	23	∈	∈	NOUN
ejpam-3970	127	24	lh(x	lh(x	PUNCT
ejpam-3970	127	25	)	)	PUNCT
ejpam-3970	127	26	whenever	whenever	SCONJ
ejpam-3970	127	27	x	x	SYM
ejpam-3970	127	28	∈	∈	PROPN
ejpam-3970	127	29	h	h	NOUN
ejpam-3970	127	30	with	with	ADP
ejpam-3970	127	31	0	0	NUM
ejpam-3970	127	32	∈	∈	PROPN
ejpam-3970	127	33	lh(x	lh(x	NOUN
ejpam-3970	127	34	)	)	PUNCT
ejpam-3970	127	35	.	.	PUNCT
ejpam-3970	128	1	m.	m.	NOUN
ejpam-3970	128	2	panganduyon	panganduyon	NOUN
ejpam-3970	128	3	,	,	PUNCT
ejpam-3970	128	4	s.	s.	PROPN
ejpam-3970	128	5	canoy	canoy	PROPN
ejpam-3970	128	6	,	,	PUNCT
ejpam-3970	128	7	jr	jr	PROPN
ejpam-3970	128	8	.	.	PROPN
ejpam-3970	128	9	,	,	PUNCT
ejpam-3970	128	10	b.	b.	PROPN
ejpam-3970	128	11	davvaz	davvaz	PROPN
ejpam-3970	128	12	/	/	SYM
ejpam-3970	128	13	eur	eur	PROPN
ejpam-3970	128	14	.	.	PUNCT
ejpam-3970	129	1	j.	j.	PROPN
ejpam-3970	129	2	pure	pure	PROPN
ejpam-3970	129	3	appl	appl	PROPN
ejpam-3970	129	4	.	.	PROPN
ejpam-3970	129	5	math	math	PROPN
ejpam-3970	129	6	,	,	PUNCT
ejpam-3970	129	7	14	14	NUM
ejpam-3970	129	8	(	(	PUNCT
ejpam-3970	129	9	2	2	NUM
ejpam-3970	129	10	)	)	PUNCT
ejpam-3970	129	11	(	(	PUNCT
ejpam-3970	129	12	2021	2021	NUM
ejpam-3970	129	13	)	)	PUNCT
ejpam-3970	129	14	,	,	PUNCT
ejpam-3970	129	15	590	590	NUM
ejpam-3970	129	16	-	-	SYM
ejpam-3970	129	17	600	600	NUM
ejpam-3970	129	18	594	594	NUM
ejpam-3970	129	19	example	example	NOUN
ejpam-3970	129	20	3	3	NUM
ejpam-3970	129	21	.	.	PUNCT
ejpam-3970	130	1	the	the	DET
ejpam-3970	130	2	hyper	hyper	ADJ
ejpam-3970	130	3	bci	bci	NOUN
ejpam-3970	130	4	-	-	ADJ
ejpam-3970	130	5	algebra	algebra	ADJ
ejpam-3970	130	6	h	h	NOUN
ejpam-3970	130	7	in	in	ADP
ejpam-3970	130	8	example	example	NOUN
ejpam-3970	130	9	2	2	NUM
ejpam-3970	130	10	is	be	AUX
ejpam-3970	130	11	lh	lh	PROPN
ejpam-3970	130	12	-0	-0	PUNCT
ejpam-3970	130	13	hereditary	hereditary	ADJ
ejpam-3970	130	14	.	.	PUNCT
ejpam-3970	131	1	theorem	theorem	NOUN
ejpam-3970	131	2	3	3	X
ejpam-3970	131	3	.	.	PUNCT
ejpam-3970	132	1	let	let	VERB
ejpam-3970	132	2	h	h	PRON
ejpam-3970	132	3	be	be	AUX
ejpam-3970	132	4	an	an	DET
ejpam-3970	132	5	lh-0	lh-0	NUM
ejpam-3970	132	6	hereditary	hereditary	ADJ
ejpam-3970	132	7	hyper	hyper	ADJ
ejpam-3970	132	8	bci	bci	NOUN
ejpam-3970	132	9	-	-	NOUN
ejpam-3970	132	10	algebra	algebra	NOUN
ejpam-3970	132	11	.	.	PUNCT
ejpam-3970	133	1	then	then	ADV
ejpam-3970	133	2	(	(	PUNCT
ejpam-3970	133	3	h	h	NOUN
ejpam-3970	133	4	,	,	PUNCT
ejpam-3970	133	5	τl(h	τl(h	NUM
ejpam-3970	133	6	)	)	PUNCT
ejpam-3970	133	7	)	)	PUNCT
ejpam-3970	133	8	is	be	AUX
ejpam-3970	133	9	connected	connect	VERB
ejpam-3970	133	10	if	if	SCONJ
ejpam-3970	133	11	and	and	CCONJ
ejpam-3970	133	12	only	only	ADV
ejpam-3970	133	13	if	if	SCONJ
ejpam-3970	133	14	0	0	NUM
ejpam-3970	133	15	∈	∈	PROPN
ejpam-3970	133	16	lh(x	lh(x	NOUN
ejpam-3970	133	17	)	)	PUNCT
ejpam-3970	133	18	for	for	ADP
ejpam-3970	133	19	all	all	DET
ejpam-3970	133	20	x	x	SYM
ejpam-3970	133	21	∈	∈	PROPN
ejpam-3970	133	22	h.	h.	NOUN
ejpam-3970	133	23	proof	proof	NOUN
ejpam-3970	133	24	.	.	PUNCT
ejpam-3970	134	1	suppose	suppose	VERB
ejpam-3970	134	2	that	that	SCONJ
ejpam-3970	134	3	(	(	PUNCT
ejpam-3970	134	4	h	h	NOUN
ejpam-3970	134	5	,	,	PUNCT
ejpam-3970	134	6	τl(h	τl(h	NUM
ejpam-3970	134	7	)	)	PUNCT
ejpam-3970	134	8	)	)	PUNCT
ejpam-3970	134	9	is	be	AUX
ejpam-3970	134	10	connected	connect	VERB
ejpam-3970	134	11	and	and	CCONJ
ejpam-3970	134	12	suppose	suppose	VERB
ejpam-3970	134	13	that	that	SCONJ
ejpam-3970	134	14	there	there	PRON
ejpam-3970	134	15	exists	exist	VERB
ejpam-3970	134	16	x	x	X
ejpam-3970	134	17	∈	∈	PROPN
ejpam-3970	134	18	h	h	NOUN
ejpam-3970	134	19	\{0	\{0	NOUN
ejpam-3970	134	20	}	}	PUNCT
ejpam-3970	134	21	such	such	ADJ
ejpam-3970	134	22	that	that	DET
ejpam-3970	134	23	0	0	NUM
ejpam-3970	134	24	/∈	/∈	NUM
ejpam-3970	134	25	lh(x	lh(x	NOUN
ejpam-3970	134	26	)	)	PUNCT
ejpam-3970	134	27	.	.	PUNCT
ejpam-3970	135	1	set	set	VERB
ejpam-3970	135	2	d1	d1	PROPN
ejpam-3970	135	3	=	=	PUNCT
ejpam-3970	135	4	{	{	PUNCT
ejpam-3970	135	5	z	z	NOUN
ejpam-3970	135	6	∈	∈	PROPN
ejpam-3970	135	7	h	h	NOUN
ejpam-3970	135	8	:	:	PUNCT
ejpam-3970	135	9	0	0	NUM
ejpam-3970	135	10	/∈	/∈	INTJ
ejpam-3970	135	11	lh(z	lh(z	NOUN
ejpam-3970	135	12	)	)	PUNCT
ejpam-3970	135	13	}	}	PUNCT
ejpam-3970	135	14	and	and	CCONJ
ejpam-3970	135	15	d2	d2	PROPN
ejpam-3970	135	16	=	=	SYM
ejpam-3970	135	17	h	h	NOUN
ejpam-3970	135	18	\	\	NOUN
ejpam-3970	135	19	d1	d1	PROPN
ejpam-3970	135	20	.	.	PUNCT
ejpam-3970	136	1	since	since	SCONJ
ejpam-3970	136	2	0	0	NUM
ejpam-3970	136	3	/∈	/∈	INTJ
ejpam-3970	136	4	lh(x	lh(x	NOUN
ejpam-3970	136	5	)	)	PUNCT
ejpam-3970	136	6	and	and	CCONJ
ejpam-3970	136	7	0	0	NUM
ejpam-3970	136	8	∈	∈	PROPN
ejpam-3970	136	9	lh(0	lh(0	NOUN
ejpam-3970	136	10	)	)	PUNCT
ejpam-3970	136	11	,	,	PUNCT
ejpam-3970	136	12	d1	d1	PROPN
ejpam-3970	136	13	6=	6=	SYM
ejpam-3970	136	14	∅	∅	NOUN
ejpam-3970	136	15	and	and	CCONJ
ejpam-3970	136	16	d2	d2	PROPN
ejpam-3970	136	17	6=	6=	PUNCT
ejpam-3970	136	18	∅.	∅.	ADV
ejpam-3970	136	19	let	let	VERB
ejpam-3970	136	20	z	z	NOUN
ejpam-3970	136	21	∈	∈	NOUN
ejpam-3970	136	22	d1	d1	PROPN
ejpam-3970	136	23	and	and	CCONJ
ejpam-3970	136	24	let	let	VERB
ejpam-3970	136	25	w	w	PROPN
ejpam-3970	136	26	∈	∈	PROPN
ejpam-3970	136	27	lh(z	lh(z	NOUN
ejpam-3970	136	28	)	)	PUNCT
ejpam-3970	136	29	.	.	PUNCT
ejpam-3970	137	1	then	then	ADV
ejpam-3970	137	2	lh(w	lh(w	NOUN
ejpam-3970	137	3	)	)	PUNCT
ejpam-3970	137	4	⊆	⊆	NUM
ejpam-3970	137	5	lh(z	lh(z	NOUN
ejpam-3970	137	6	)	)	PUNCT
ejpam-3970	137	7	by	by	ADP
ejpam-3970	137	8	lemma	lemma	PROPN
ejpam-3970	137	9	2	2	NUM
ejpam-3970	137	10	.	.	PUNCT
ejpam-3970	138	1	since	since	SCONJ
ejpam-3970	138	2	0	0	NUM
ejpam-3970	138	3	/∈	/∈	NUM
ejpam-3970	138	4	lh(z	lh(z	NOUN
ejpam-3970	138	5	)	)	PUNCT
ejpam-3970	138	6	,	,	PUNCT
ejpam-3970	138	7	0	0	NUM
ejpam-3970	138	8	/∈	/∈	SYM
ejpam-3970	138	9	lh(w	lh(w	PROPN
ejpam-3970	138	10	)	)	PUNCT
ejpam-3970	138	11	;	;	PUNCT
ejpam-3970	138	12	that	that	PRON
ejpam-3970	138	13	is	be	AUX
ejpam-3970	138	14	,	,	PUNCT
ejpam-3970	138	15	w	w	PROPN
ejpam-3970	138	16	∈	∈	PROPN
ejpam-3970	138	17	d1	d1	NOUN
ejpam-3970	138	18	.	.	PUNCT
ejpam-3970	139	1	thus	thus	ADV
ejpam-3970	139	2	,	,	PUNCT
ejpam-3970	139	3	z	z	PROPN
ejpam-3970	139	4	∈	∈	PROPN
ejpam-3970	139	5	lh(z	lh(z	NOUN
ejpam-3970	139	6	)	)	PUNCT
ejpam-3970	139	7	⊆	⊆	NUM
ejpam-3970	139	8	d1	d1	NOUN
ejpam-3970	139	9	and	and	CCONJ
ejpam-3970	139	10	so	so	ADV
ejpam-3970	139	11	,	,	PUNCT
ejpam-3970	139	12	d1	d1	PROPN
ejpam-3970	139	13	is	be	AUX
ejpam-3970	139	14	τl(h)-open	τl(h)-open	VERB
ejpam-3970	139	15	.	.	PUNCT
ejpam-3970	140	1	next	next	ADV
ejpam-3970	140	2	,	,	PUNCT
ejpam-3970	140	3	let	let	VERB
ejpam-3970	140	4	y	y	PROPN
ejpam-3970	140	5	∈	∈	PROPN
ejpam-3970	140	6	d2	d2	PROPN
ejpam-3970	140	7	and	and	CCONJ
ejpam-3970	140	8	let	let	VERB
ejpam-3970	140	9	v	v	ADP
ejpam-3970	140	10	∈	∈	PRON
ejpam-3970	140	11	lh(y	lh(y	PUNCT
ejpam-3970	140	12	)	)	PUNCT
ejpam-3970	140	13	.	.	PUNCT
ejpam-3970	141	1	since	since	SCONJ
ejpam-3970	141	2	0	0	NUM
ejpam-3970	141	3	∈	∈	NOUN
ejpam-3970	141	4	lh(y	lh(y	PUNCT
ejpam-3970	141	5	)	)	PUNCT
ejpam-3970	141	6	and	and	CCONJ
ejpam-3970	141	7	h	h	NOUN
ejpam-3970	141	8	is	be	AUX
ejpam-3970	141	9	lh	lh	PROPN
ejpam-3970	141	10	-0	-0	PUNCT
ejpam-3970	141	11	hereditary	hereditary	ADJ
ejpam-3970	141	12	,	,	PUNCT
ejpam-3970	141	13	it	it	PRON
ejpam-3970	141	14	follows	follow	VERB
ejpam-3970	141	15	that	that	SCONJ
ejpam-3970	141	16	0	0	NUM
ejpam-3970	141	17	∈	∈	PROPN
ejpam-3970	141	18	lh(x	lh(x	PROPN
ejpam-3970	141	19	)	)	PUNCT
ejpam-3970	141	20	;	;	PUNCT
ejpam-3970	141	21	that	that	PRON
ejpam-3970	141	22	is	is	ADV
ejpam-3970	141	23	,	,	PUNCT
ejpam-3970	141	24	v	v	PROPN
ejpam-3970	141	25	∈	∈	PROPN
ejpam-3970	141	26	d2	d2	NOUN
ejpam-3970	141	27	.	.	PUNCT
ejpam-3970	142	1	hence	hence	ADV
ejpam-3970	142	2	,	,	PUNCT
ejpam-3970	142	3	y	y	PROPN
ejpam-3970	142	4	∈	∈	PROPN
ejpam-3970	142	5	lh(y	lh(y	PUNCT
ejpam-3970	142	6	)	)	PUNCT
ejpam-3970	142	7	⊆	⊆	NUM
ejpam-3970	142	8	d2	d2	PROPN
ejpam-3970	142	9	and	and	CCONJ
ejpam-3970	142	10	so	so	ADV
ejpam-3970	142	11	,	,	PUNCT
ejpam-3970	142	12	d2	d2	PROPN
ejpam-3970	142	13	is	be	AUX
ejpam-3970	142	14	τl(h)-open	τl(h)-open	VERB
ejpam-3970	142	15	.	.	PUNCT
ejpam-3970	143	1	since	since	SCONJ
ejpam-3970	143	2	d1	d1	PROPN
ejpam-3970	143	3	∩	∩	ADJ
ejpam-3970	143	4	d2	d2	NOUN
ejpam-3970	143	5	=	=	PUNCT
ejpam-3970	143	6	∅	∅	NOUN
ejpam-3970	143	7	and	and	CCONJ
ejpam-3970	143	8	d1	d1	PROPN
ejpam-3970	143	9	∪	∪	VERB
ejpam-3970	143	10	d2	d2	PROPN
ejpam-3970	143	11	=	=	SYM
ejpam-3970	143	12	h	h	NOUN
ejpam-3970	143	13	,	,	PUNCT
ejpam-3970	143	14	the	the	DET
ejpam-3970	143	15	space	space	NOUN
ejpam-3970	143	16	is	be	AUX
ejpam-3970	143	17	disconnected	disconnect	VERB
ejpam-3970	143	18	,	,	PUNCT
ejpam-3970	143	19	contrary	contrary	ADV
ejpam-3970	143	20	to	to	ADP
ejpam-3970	143	21	our	our	PRON
ejpam-3970	143	22	assumption	assumption	NOUN
ejpam-3970	143	23	.	.	PUNCT
ejpam-3970	144	1	for	for	ADP
ejpam-3970	144	2	the	the	DET
ejpam-3970	144	3	converse	converse	NOUN
ejpam-3970	144	4	,	,	PUNCT
ejpam-3970	144	5	let	let	VERB
ejpam-3970	144	6	g	g	PRON
ejpam-3970	144	7	be	be	AUX
ejpam-3970	144	8	a	a	DET
ejpam-3970	144	9	non	non	ADJ
ejpam-3970	144	10	-	-	ADJ
ejpam-3970	144	11	empty	empty	ADJ
ejpam-3970	144	12	open	open	ADJ
ejpam-3970	144	13	subset	subset	NOUN
ejpam-3970	144	14	of	of	ADP
ejpam-3970	144	15	h.	h.	PROPN
ejpam-3970	144	16	then	then	ADV
ejpam-3970	144	17	there	there	PRON
ejpam-3970	144	18	exists	exist	VERB
ejpam-3970	144	19	a	a	DET
ejpam-3970	144	20	⊆	⊆	NUM
ejpam-3970	144	21	h	h	NOUN
ejpam-3970	144	22	such	such	ADJ
ejpam-3970	144	23	that	that	DET
ejpam-3970	144	24	lh(a	lh(a	NOUN
ejpam-3970	144	25	)	)	PUNCT
ejpam-3970	144	26	⊆	⊆	NUM
ejpam-3970	144	27	g.	g.	NOUN
ejpam-3970	144	28	since	since	SCONJ
ejpam-3970	144	29	0	0	NUM
ejpam-3970	144	30	∈	∈	PROPN
ejpam-3970	144	31	lh(x	lh(x	NOUN
ejpam-3970	144	32	)	)	PUNCT
ejpam-3970	144	33	for	for	ADP
ejpam-3970	144	34	all	all	DET
ejpam-3970	144	35	x	x	SYM
ejpam-3970	144	36	∈	∈	PROPN
ejpam-3970	144	37	h	h	NOUN
ejpam-3970	144	38	,	,	PUNCT
ejpam-3970	144	39	0	0	NUM
ejpam-3970	144	40	∈	∈	PROPN
ejpam-3970	144	41	lh(a	lh(a	NOUN
ejpam-3970	144	42	)	)	PUNCT
ejpam-3970	144	43	.	.	PUNCT
ejpam-3970	145	1	thus	thus	ADV
ejpam-3970	145	2	,	,	PUNCT
ejpam-3970	145	3	0	0	NUM
ejpam-3970	145	4	∈	∈	PROPN
ejpam-3970	145	5	g.	g.	NOUN
ejpam-3970	145	6	it	it	PRON
ejpam-3970	145	7	follows	follow	VERB
ejpam-3970	145	8	that	that	SCONJ
ejpam-3970	145	9	(	(	PUNCT
ejpam-3970	145	10	h	h	NOUN
ejpam-3970	145	11	,	,	PUNCT
ejpam-3970	145	12	τl(h	τl(h	NUM
ejpam-3970	145	13	)	)	PUNCT
ejpam-3970	145	14	)	)	PUNCT
ejpam-3970	145	15	is	be	AUX
ejpam-3970	145	16	connected	connect	VERB
ejpam-3970	145	17	.	.	PUNCT
ejpam-3970	146	1	the	the	DET
ejpam-3970	146	2	next	next	ADJ
ejpam-3970	146	3	result	result	NOUN
ejpam-3970	146	4	follows	follow	VERB
ejpam-3970	146	5	from	from	ADP
ejpam-3970	146	6	theorem	theorem	ADJ
ejpam-3970	146	7	2	2	NUM
ejpam-3970	146	8	and	and	CCONJ
ejpam-3970	146	9	the	the	DET
ejpam-3970	146	10	definition	definition	NOUN
ejpam-3970	146	11	of	of	ADP
ejpam-3970	146	12	discrete	discrete	ADJ
ejpam-3970	146	13	topology	topology	NOUN
ejpam-3970	146	14	.	.	PUNCT
ejpam-3970	147	1	proposition	proposition	NOUN
ejpam-3970	147	2	2	2	NUM
ejpam-3970	147	3	.	.	PUNCT
ejpam-3970	148	1	let	let	VERB
ejpam-3970	148	2	h	h	PRON
ejpam-3970	148	3	be	be	AUX
ejpam-3970	148	4	a	a	DET
ejpam-3970	148	5	hyper	hyper	ADJ
ejpam-3970	148	6	bci	bci	NOUN
ejpam-3970	148	7	-	-	NOUN
ejpam-3970	148	8	algebra	algebra	NOUN
ejpam-3970	148	9	.	.	PUNCT
ejpam-3970	149	1	then	then	ADV
ejpam-3970	149	2	τl(h	τl(h	PUNCT
ejpam-3970	149	3	)	)	PUNCT
ejpam-3970	149	4	is	be	AUX
ejpam-3970	149	5	the	the	DET
ejpam-3970	149	6	discrete	discrete	ADJ
ejpam-3970	149	7	topology	topology	NOUN
ejpam-3970	149	8	d	d	NOUN
ejpam-3970	149	9	on	on	ADP
ejpam-3970	149	10	h	h	NOUN
ejpam-3970	149	11	if	if	SCONJ
ejpam-3970	150	1	and	and	CCONJ
ejpam-3970	150	2	only	only	ADV
ejpam-3970	150	3	if	if	SCONJ
ejpam-3970	150	4	for	for	ADP
ejpam-3970	150	5	each	each	DET
ejpam-3970	150	6	x	x	SYM
ejpam-3970	150	7	∈	∈	PROPN
ejpam-3970	150	8	h	h	NOUN
ejpam-3970	150	9	,	,	PUNCT
ejpam-3970	150	10	there	there	PRON
ejpam-3970	150	11	exists	exist	VERB
ejpam-3970	150	12	ax	ax	NOUN
ejpam-3970	150	13	⊆	⊆	NUM
ejpam-3970	150	14	h	h	NOUN
ejpam-3970	150	15	such	such	ADJ
ejpam-3970	150	16	that	that	DET
ejpam-3970	150	17	lh(ax	lh(ax	NOUN
ejpam-3970	150	18	)	)	PUNCT
ejpam-3970	150	19	=	=	PRON
ejpam-3970	150	20	{	{	PUNCT
ejpam-3970	150	21	x	x	NOUN
ejpam-3970	150	22	}	}	PUNCT
ejpam-3970	150	23	.	.	PUNCT
ejpam-3970	151	1	corollary	corollary	ADJ
ejpam-3970	151	2	1	1	NUM
ejpam-3970	151	3	.	.	PUNCT
ejpam-3970	152	1	let	let	VERB
ejpam-3970	152	2	h	h	PRON
ejpam-3970	152	3	be	be	AUX
ejpam-3970	152	4	a	a	DET
ejpam-3970	152	5	hyper	hyper	ADJ
ejpam-3970	152	6	bci	bci	NOUN
ejpam-3970	152	7	-	-	NOUN
ejpam-3970	152	8	algebra	algebra	NOUN
ejpam-3970	152	9	.	.	PUNCT
ejpam-3970	153	1	if	if	SCONJ
ejpam-3970	153	2	lh(x	lh(x	PUNCT
ejpam-3970	153	3	)	)	PUNCT
ejpam-3970	154	1	=	=	SYM
ejpam-3970	154	2	{	{	PUNCT
ejpam-3970	154	3	x	x	NOUN
ejpam-3970	154	4	}	}	PUNCT
ejpam-3970	154	5	for	for	ADP
ejpam-3970	154	6	each	each	DET
ejpam-3970	154	7	x	x	SYM
ejpam-3970	154	8	∈	∈	PROPN
ejpam-3970	154	9	h	h	NOUN
ejpam-3970	154	10	,	,	PUNCT
ejpam-3970	154	11	then	then	ADV
ejpam-3970	154	12	τl(h	τl(h	PUNCT
ejpam-3970	154	13	)	)	PUNCT
ejpam-3970	154	14	is	be	AUX
ejpam-3970	154	15	the	the	DET
ejpam-3970	154	16	discrete	discrete	ADJ
ejpam-3970	154	17	topology	topology	NOUN
ejpam-3970	154	18	d	d	NOUN
ejpam-3970	154	19	on	on	ADP
ejpam-3970	154	20	h.	h.	PROPN
ejpam-3970	154	21	in	in	ADP
ejpam-3970	154	22	particular	particular	ADJ
ejpam-3970	154	23	,	,	PUNCT
ejpam-3970	154	24	bl(h	bl(h	PUNCT
ejpam-3970	154	25	)	)	PUNCT
ejpam-3970	154	26	=	=	PRON
ejpam-3970	154	27	{	{	PUNCT
ejpam-3970	154	28	{	{	PUNCT
ejpam-3970	154	29	a	a	NOUN
ejpam-3970	154	30	}	}	PUNCT
ejpam-3970	154	31	:	:	PUNCT
ejpam-3970	154	32	a	a	DET
ejpam-3970	154	33	∈	∈	PROPN
ejpam-3970	154	34	h	h	NOUN
ejpam-3970	154	35	}	}	PUNCT
ejpam-3970	154	36	.	.	PUNCT
ejpam-3970	155	1	proof	proof	NOUN
ejpam-3970	155	2	.	.	PUNCT
ejpam-3970	156	1	suppose	suppose	VERB
ejpam-3970	156	2	that	that	SCONJ
ejpam-3970	156	3	for	for	ADP
ejpam-3970	156	4	each	each	DET
ejpam-3970	156	5	x	x	SYM
ejpam-3970	156	6	∈	∈	PROPN
ejpam-3970	156	7	h	h	NOUN
ejpam-3970	156	8	,	,	PUNCT
ejpam-3970	156	9	lh(x	lh(x	PUNCT
ejpam-3970	156	10	)	)	PUNCT
ejpam-3970	156	11	=	=	SYM
ejpam-3970	156	12	{	{	PUNCT
ejpam-3970	156	13	x	x	NOUN
ejpam-3970	156	14	}	}	PUNCT
ejpam-3970	156	15	.	.	PUNCT
ejpam-3970	157	1	then	then	ADV
ejpam-3970	157	2	by	by	ADP
ejpam-3970	157	3	proposition	proposition	NOUN
ejpam-3970	157	4	2	2	NUM
ejpam-3970	157	5	,	,	PUNCT
ejpam-3970	157	6	τl(h	τl(h	NUM
ejpam-3970	157	7	)	)	PUNCT
ejpam-3970	157	8	is	be	AUX
ejpam-3970	157	9	the	the	DET
ejpam-3970	157	10	discrete	discrete	ADJ
ejpam-3970	157	11	topology	topology	NOUN
ejpam-3970	157	12	d	d	NOUN
ejpam-3970	157	13	on	on	ADP
ejpam-3970	157	14	h.	h.	PROPN
ejpam-3970	157	15	furthermore	furthermore	ADV
ejpam-3970	157	16	,	,	PUNCT
ejpam-3970	157	17	for	for	ADP
ejpam-3970	157	18	any	any	DET
ejpam-3970	157	19	a	a	DET
ejpam-3970	157	20	⊆	⊆	NUM
ejpam-3970	157	21	h	h	NOUN
ejpam-3970	157	22	with	with	ADP
ejpam-3970	157	23	|a|	|a|	PROPN
ejpam-3970	157	24	≥	≥	NOUN
ejpam-3970	157	25	2	2	NUM
ejpam-3970	157	26	,	,	PUNCT
ejpam-3970	157	27	lh(a	lh(a	NUM
ejpam-3970	157	28	)	)	PUNCT
ejpam-3970	157	29	=	=	PUNCT
ejpam-3970	157	30	∅.	∅.	VERB
ejpam-3970	157	31	therefore	therefore	ADV
ejpam-3970	157	32	,	,	PUNCT
ejpam-3970	157	33	bl(h	bl(h	PUNCT
ejpam-3970	157	34	)	)	PUNCT
ejpam-3970	157	35	=	=	PRON
ejpam-3970	157	36	{	{	PUNCT
ejpam-3970	157	37	{	{	PUNCT
ejpam-3970	157	38	a	a	NOUN
ejpam-3970	157	39	}	}	PUNCT
ejpam-3970	157	40	:	:	PUNCT
ejpam-3970	157	41	a	a	DET
ejpam-3970	157	42	∈	∈	PROPN
ejpam-3970	157	43	h	h	NOUN
ejpam-3970	157	44	}	}	PUNCT
ejpam-3970	157	45	.	.	PUNCT
ejpam-3970	158	1	example	example	NOUN
ejpam-3970	159	1	4	4	X
ejpam-3970	159	2	.	.	X
ejpam-3970	159	3	consider	consider	VERB
ejpam-3970	159	4	h	h	NOUN
ejpam-3970	159	5	=	=	PRON
ejpam-3970	159	6	{	{	PUNCT
ejpam-3970	159	7	0	0	NUM
ejpam-3970	159	8	,	,	PUNCT
ejpam-3970	159	9	a	a	DET
ejpam-3970	159	10	,	,	PUNCT
ejpam-3970	159	11	b	b	NOUN
ejpam-3970	159	12	}	}	PUNCT
ejpam-3970	159	13	with	with	ADP
ejpam-3970	159	14	the	the	DET
ejpam-3970	159	15	hyperoperation	hyperoperation	NOUN
ejpam-3970	159	16	“	"	PUNCT
ejpam-3970	159	17	~	~	PUNCT
ejpam-3970	159	18	”	"	PUNCT
ejpam-3970	159	19	defined	define	VERB
ejpam-3970	159	20	as	as	SCONJ
ejpam-3970	159	21	follows	follow	VERB
ejpam-3970	159	22	:	:	PUNCT
ejpam-3970	159	23	~	~	PUNCT
ejpam-3970	159	24	0	0	PUNCT
ejpam-3970	159	25	a	a	DET
ejpam-3970	159	26	b	b	PROPN
ejpam-3970	159	27	0	0	NUM
ejpam-3970	159	28	{	{	PUNCT
ejpam-3970	159	29	0	0	NUM
ejpam-3970	159	30	}	}	PUNCT
ejpam-3970	159	31	{	{	PUNCT
ejpam-3970	159	32	b	b	NOUN
ejpam-3970	159	33	}	}	PUNCT
ejpam-3970	159	34	{	{	PUNCT
ejpam-3970	159	35	a	a	PROPN
ejpam-3970	159	36	}	}	PUNCT
ejpam-3970	159	37	a	a	DET
ejpam-3970	159	38	{	{	PUNCT
ejpam-3970	159	39	a	a	NOUN
ejpam-3970	159	40	}	}	PUNCT
ejpam-3970	159	41	{	{	PUNCT
ejpam-3970	159	42	0	0	NUM
ejpam-3970	159	43	}	}	PUNCT
ejpam-3970	159	44	{	{	PUNCT
ejpam-3970	159	45	b	b	NOUN
ejpam-3970	159	46	}	}	PUNCT
ejpam-3970	159	47	b	b	PROPN
ejpam-3970	159	48	{	{	PUNCT
ejpam-3970	159	49	b	b	NOUN
ejpam-3970	159	50	}	}	PUNCT
ejpam-3970	159	51	{	{	PUNCT
ejpam-3970	159	52	a	a	NOUN
ejpam-3970	159	53	}	}	PUNCT
ejpam-3970	159	54	{	{	PUNCT
ejpam-3970	159	55	0	0	NUM
ejpam-3970	159	56	}	}	PUNCT
ejpam-3970	159	57	then	then	ADV
ejpam-3970	159	58	h	h	NOUN
ejpam-3970	159	59	is	be	AUX
ejpam-3970	159	60	a	a	DET
ejpam-3970	159	61	hyper	hyper	ADJ
ejpam-3970	159	62	bci	bci	NOUN
ejpam-3970	159	63	-	-	NOUN
ejpam-3970	159	64	algebra	algebra	NOUN
ejpam-3970	159	65	.	.	PUNCT
ejpam-3970	160	1	by	by	ADP
ejpam-3970	160	2	theorem	theorem	NOUN
ejpam-3970	160	3	2	2	NUM
ejpam-3970	160	4	,	,	PUNCT
ejpam-3970	160	5	bl(h	bl(h	NUM
ejpam-3970	160	6	)	)	PUNCT
ejpam-3970	160	7	=	=	PRON
ejpam-3970	160	8	{	{	PUNCT
ejpam-3970	160	9	lh(a	lh(a	NOUN
ejpam-3970	160	10	)	)	PUNCT
ejpam-3970	160	11	:	:	PUNCT
ejpam-3970	160	12	∅	∅	NOUN
ejpam-3970	160	13	6=	6=	ADP
ejpam-3970	160	14	a	a	DET
ejpam-3970	160	15	⊆	⊆	NUM
ejpam-3970	160	16	h	h	NOUN
ejpam-3970	160	17	}	}	PUNCT
ejpam-3970	160	18	=	=	PRON
ejpam-3970	160	19	{	{	PUNCT
ejpam-3970	160	20	{	{	PUNCT
ejpam-3970	160	21	0	0	NUM
ejpam-3970	160	22	}	}	PUNCT
ejpam-3970	160	23	,	,	PUNCT
ejpam-3970	160	24	{	{	PUNCT
ejpam-3970	160	25	a	a	X
ejpam-3970	160	26	}	}	PUNCT
ejpam-3970	160	27	,	,	PUNCT
ejpam-3970	160	28	{	{	PUNCT
ejpam-3970	160	29	b},∅	b},∅	NOUN
ejpam-3970	160	30	}	}	PUNCT
ejpam-3970	160	31	.	.	PUNCT
ejpam-3970	161	1	thus	thus	ADV
ejpam-3970	161	2	,	,	PUNCT
ejpam-3970	161	3	τl(h	τl(h	PUNCT
ejpam-3970	161	4	)	)	PUNCT
ejpam-3970	162	1	=	=	PRON
ejpam-3970	162	2	{	{	PUNCT
ejpam-3970	162	3	{	{	PUNCT
ejpam-3970	162	4	0	0	NUM
ejpam-3970	162	5	}	}	PUNCT
ejpam-3970	162	6	,	,	PUNCT
ejpam-3970	162	7	{	{	PUNCT
ejpam-3970	162	8	a	a	X
ejpam-3970	162	9	}	}	PUNCT
ejpam-3970	162	10	,	,	PUNCT
ejpam-3970	162	11	{	{	PUNCT
ejpam-3970	162	12	b	b	NOUN
ejpam-3970	162	13	}	}	PUNCT
ejpam-3970	162	14	,	,	PUNCT
ejpam-3970	162	15	{	{	PUNCT
ejpam-3970	162	16	0	0	NUM
ejpam-3970	162	17	,	,	PUNCT
ejpam-3970	162	18	a	a	DET
ejpam-3970	162	19	}	}	PUNCT
ejpam-3970	162	20	,	,	PUNCT
ejpam-3970	162	21	{	{	PUNCT
ejpam-3970	162	22	0	0	NUM
ejpam-3970	162	23	,	,	PUNCT
ejpam-3970	162	24	b	b	NOUN
ejpam-3970	162	25	}	}	PUNCT
ejpam-3970	162	26	,	,	PUNCT
ejpam-3970	162	27	{	{	PUNCT
ejpam-3970	162	28	a	a	PRON
ejpam-3970	162	29	,	,	PUNCT
ejpam-3970	162	30	b},∅	b},∅	PROPN
ejpam-3970	162	31	,	,	PUNCT
ejpam-3970	162	32	h	h	NOUN
ejpam-3970	162	33	}	}	PUNCT
ejpam-3970	162	34	=	=	SYM
ejpam-3970	162	35	d	d	PROPN
ejpam-3970	162	36	.	.	PUNCT
ejpam-3970	162	37	theorem	theorem	NOUN
ejpam-3970	162	38	4	4	NUM
ejpam-3970	162	39	.	.	PUNCT
ejpam-3970	163	1	if	if	SCONJ
ejpam-3970	163	2	h	h	NOUN
ejpam-3970	163	3	is	be	AUX
ejpam-3970	163	4	a	a	DET
ejpam-3970	163	5	finite	finite	ADJ
ejpam-3970	163	6	hyper	hyper	ADJ
ejpam-3970	163	7	bci	bci	NOUN
ejpam-3970	163	8	-	-	NOUN
ejpam-3970	163	9	algebra	algebra	NOUN
ejpam-3970	163	10	,	,	PUNCT
ejpam-3970	163	11	then	then	ADV
ejpam-3970	163	12	the	the	DET
ejpam-3970	163	13	family	family	NOUN
ejpam-3970	163	14	sl(h	sl(h	PUNCT
ejpam-3970	163	15	)	)	PUNCT
ejpam-3970	163	16	=	=	PRON
ejpam-3970	163	17	{	{	PUNCT
ejpam-3970	163	18	lh(a	lh(a	NOUN
ejpam-3970	163	19	)	)	PUNCT
ejpam-3970	163	20	:	:	PUNCT
ejpam-3970	163	21	a	a	DET
ejpam-3970	163	22	∈	∈	PROPN
ejpam-3970	163	23	h	h	NOUN
ejpam-3970	163	24	}	}	PUNCT
ejpam-3970	163	25	is	be	AUX
ejpam-3970	163	26	a	a	DET
ejpam-3970	163	27	subbase	subbase	NOUN
ejpam-3970	163	28	of	of	ADP
ejpam-3970	163	29	τl(h	τl(h	NUM
ejpam-3970	163	30	)	)	PUNCT
ejpam-3970	163	31	.	.	PUNCT
ejpam-3970	164	1	proof	proof	NOUN
ejpam-3970	164	2	.	.	PUNCT
ejpam-3970	165	1	that	that	PRON
ejpam-3970	165	2	sl(h	sl(h	PROPN
ejpam-3970	165	3	)	)	PUNCT
ejpam-3970	165	4	⊆	⊆	NUM
ejpam-3970	165	5	τl(h	τl(h	NUM
ejpam-3970	165	6	)	)	PUNCT
ejpam-3970	165	7	is	be	AUX
ejpam-3970	165	8	evident	evident	ADJ
ejpam-3970	165	9	.	.	PUNCT
ejpam-3970	166	1	since	since	SCONJ
ejpam-3970	166	2	lh(a	lh(a	NUM
ejpam-3970	166	3	)	)	PUNCT
ejpam-3970	166	4	=	=	PUNCT
ejpam-3970	167	1	⋂	⋂	PROPN
ejpam-3970	167	2	a∈a	a∈a	ADJ
ejpam-3970	167	3	lh({a	lh({a	NOUN
ejpam-3970	167	4	}	}	PUNCT
ejpam-3970	167	5	)	)	PUNCT
ejpam-3970	167	6	for	for	ADP
ejpam-3970	167	7	each	each	DET
ejpam-3970	167	8	nonempty	nonempty	NOUN
ejpam-3970	167	9	a	a	DET
ejpam-3970	167	10	⊆	⊆	NUM
ejpam-3970	167	11	h	h	NOUN
ejpam-3970	167	12	,	,	PUNCT
ejpam-3970	167	13	it	it	PRON
ejpam-3970	167	14	follows	follow	VERB
ejpam-3970	167	15	that	that	SCONJ
ejpam-3970	167	16	every	every	DET
ejpam-3970	167	17	element	element	NOUN
ejpam-3970	167	18	of	of	ADP
ejpam-3970	167	19	bl(h	bl(h	PROPN
ejpam-3970	167	20	)	)	PUNCT
ejpam-3970	167	21	is	be	AUX
ejpam-3970	167	22	a	a	DET
ejpam-3970	167	23	finite	finite	ADJ
ejpam-3970	167	24	intersection	intersection	NOUN
ejpam-3970	167	25	of	of	ADP
ejpam-3970	167	26	members	member	NOUN
ejpam-3970	167	27	of	of	ADP
ejpam-3970	167	28	sl(h	sl(h	PROPN
ejpam-3970	167	29	)	)	PUNCT
ejpam-3970	167	30	.	.	PUNCT
ejpam-3970	168	1	hence	hence	ADV
ejpam-3970	168	2	,	,	PUNCT
ejpam-3970	168	3	sl(h	sl(h	PROPN
ejpam-3970	168	4	)	)	PUNCT
ejpam-3970	168	5	is	be	AUX
ejpam-3970	168	6	a	a	DET
ejpam-3970	168	7	subbase	subbase	NOUN
ejpam-3970	168	8	of	of	ADP
ejpam-3970	168	9	τl(h	τl(h	NUM
ejpam-3970	168	10	)	)	PUNCT
ejpam-3970	168	11	.	.	PUNCT
ejpam-3970	169	1	m.	m.	NOUN
ejpam-3970	169	2	panganduyon	panganduyon	NOUN
ejpam-3970	169	3	,	,	PUNCT
ejpam-3970	169	4	s.	s.	PROPN
ejpam-3970	169	5	canoy	canoy	PROPN
ejpam-3970	169	6	,	,	PUNCT
ejpam-3970	169	7	jr	jr	PROPN
ejpam-3970	169	8	.	.	PROPN
ejpam-3970	169	9	,	,	PUNCT
ejpam-3970	169	10	b.	b.	PROPN
ejpam-3970	169	11	davvaz	davvaz	PROPN
ejpam-3970	169	12	/	/	SYM
ejpam-3970	169	13	eur	eur	PROPN
ejpam-3970	169	14	.	.	PUNCT
ejpam-3970	170	1	j.	j.	PROPN
ejpam-3970	170	2	pure	pure	PROPN
ejpam-3970	170	3	appl	appl	PROPN
ejpam-3970	170	4	.	.	PROPN
ejpam-3970	170	5	math	math	PROPN
ejpam-3970	170	6	,	,	PUNCT
ejpam-3970	170	7	14	14	NUM
ejpam-3970	170	8	(	(	PUNCT
ejpam-3970	170	9	2	2	NUM
ejpam-3970	170	10	)	)	PUNCT
ejpam-3970	170	11	(	(	PUNCT
ejpam-3970	170	12	2021	2021	NUM
ejpam-3970	170	13	)	)	PUNCT
ejpam-3970	170	14	,	,	PUNCT
ejpam-3970	170	15	590	590	NUM
ejpam-3970	170	16	-	-	SYM
ejpam-3970	170	17	600	600	NUM
ejpam-3970	170	18	595	595	NUM
ejpam-3970	170	19	proposition	proposition	NOUN
ejpam-3970	170	20	3	3	NUM
ejpam-3970	170	21	.	.	PUNCT
ejpam-3970	171	1	let	let	VERB
ejpam-3970	171	2	h	h	PRON
ejpam-3970	171	3	be	be	AUX
ejpam-3970	171	4	a	a	DET
ejpam-3970	171	5	hyper	hyper	ADJ
ejpam-3970	171	6	bci	bci	NOUN
ejpam-3970	171	7	-	-	NOUN
ejpam-3970	171	8	algebra	algebra	NOUN
ejpam-3970	171	9	with	with	ADP
ejpam-3970	171	10	|h|	|h|	PROPN
ejpam-3970	171	11	≥	≥	NUM
ejpam-3970	171	12	2	2	NUM
ejpam-3970	171	13	.	.	PUNCT
ejpam-3970	171	14	then	then	ADV
ejpam-3970	171	15	bl(h	bl(h	NOUN
ejpam-3970	171	16	)	)	PUNCT
ejpam-3970	172	1	=	=	NOUN
ejpam-3970	172	2	{	{	PUNCT
ejpam-3970	172	3	{	{	PUNCT
ejpam-3970	172	4	a	a	NOUN
ejpam-3970	172	5	}	}	PUNCT
ejpam-3970	172	6	:	:	PUNCT
ejpam-3970	172	7	a	a	DET
ejpam-3970	172	8	∈	∈	PROPN
ejpam-3970	172	9	a∗(h	a∗(h	PROPN
ejpam-3970	172	10	)	)	PUNCT
ejpam-3970	172	11	,	,	PUNCT
ejpam-3970	172	12	0	0	NUM
ejpam-3970	172	13	/∈	/∈	SYM
ejpam-3970	172	14	lh(a	lh(a	NOUN
ejpam-3970	172	15	)	)	PUNCT
ejpam-3970	172	16	}	}	PUNCT
ejpam-3970	172	17	∪	∪	VERB
ejpam-3970	172	18	{	{	PUNCT
ejpam-3970	172	19	{	{	PUNCT
ejpam-3970	172	20	0	0	NUM
ejpam-3970	172	21	,	,	PUNCT
ejpam-3970	172	22	a	a	PRON
ejpam-3970	172	23	}	}	PUNCT
ejpam-3970	172	24	:	:	PUNCT
ejpam-3970	172	25	a	a	DET
ejpam-3970	172	26	∈	∈	PROPN
ejpam-3970	172	27	a∗(h	a∗(h	PROPN
ejpam-3970	172	28	)	)	PUNCT
ejpam-3970	172	29	,	,	PUNCT
ejpam-3970	172	30	0	0	NUM
ejpam-3970	172	31	∈	∈	PROPN
ejpam-3970	172	32	lh(a	lh(a	NOUN
ejpam-3970	172	33	)	)	PUNCT
ejpam-3970	172	34	}	}	PUNCT
ejpam-3970	172	35	∪	∪	ADP
ejpam-3970	172	36	{	{	PUNCT
ejpam-3970	172	37	lh(a	lh(a	NOUN
ejpam-3970	172	38	)	)	PUNCT
ejpam-3970	172	39	:	:	PUNCT
ejpam-3970	172	40	a	a	X
ejpam-3970	172	41	∩a∗(h	∩a∗(h	NOUN
ejpam-3970	172	42	)	)	PUNCT
ejpam-3970	172	43	=	=	NOUN
ejpam-3970	172	44	∅	∅	NOUN
ejpam-3970	172	45	}	}	PUNCT
ejpam-3970	172	46	.	.	PUNCT
ejpam-3970	173	1	proof	proof	NOUN
ejpam-3970	173	2	.	.	PUNCT
ejpam-3970	174	1	for	for	ADP
ejpam-3970	174	2	each	each	DET
ejpam-3970	174	3	a	a	DET
ejpam-3970	174	4	∈	∈	PROPN
ejpam-3970	174	5	a∗(h	a∗(h	PROPN
ejpam-3970	174	6	)	)	PUNCT
ejpam-3970	174	7	,	,	PUNCT
ejpam-3970	174	8	either	either	CCONJ
ejpam-3970	174	9	lh(a	lh(a	NOUN
ejpam-3970	174	10	)	)	PUNCT
ejpam-3970	174	11	=	=	PRON
ejpam-3970	174	12	{	{	PUNCT
ejpam-3970	174	13	a	a	NOUN
ejpam-3970	174	14	}	}	PUNCT
ejpam-3970	174	15	or	or	CCONJ
ejpam-3970	174	16	lh(a	lh(a	NOUN
ejpam-3970	174	17	)	)	PUNCT
ejpam-3970	174	18	=	=	PRON
ejpam-3970	174	19	{	{	PUNCT
ejpam-3970	174	20	0	0	NUM
ejpam-3970	174	21	,	,	PUNCT
ejpam-3970	174	22	a	a	PRON
ejpam-3970	174	23	}	}	PUNCT
ejpam-3970	174	24	.	.	PUNCT
ejpam-3970	175	1	let	let	VERB
ejpam-3970	175	2	a	a	PRON
ejpam-3970	175	3	be	be	AUX
ejpam-3970	175	4	a	a	DET
ejpam-3970	175	5	nonempty	nonempty	ADJ
ejpam-3970	175	6	subset	subset	NOUN
ejpam-3970	175	7	of	of	ADP
ejpam-3970	175	8	h	h	NOUN
ejpam-3970	175	9	such	such	ADJ
ejpam-3970	175	10	that	that	ADV
ejpam-3970	175	11	a∩a∗(h	a∩a∗(h	ADJ
ejpam-3970	175	12	)	)	PUNCT
ejpam-3970	176	1	6=	6=	ADP
ejpam-3970	176	2	∅	∅	NOUN
ejpam-3970	176	3	,	,	PUNCT
ejpam-3970	176	4	say	say	VERB
ejpam-3970	176	5	q	q	PROPN
ejpam-3970	176	6	∈	∈	PROPN
ejpam-3970	176	7	a∩a∗(h	a∩a∗(h	ADJ
ejpam-3970	176	8	)	)	PUNCT
ejpam-3970	176	9	.	.	PUNCT
ejpam-3970	177	1	since	since	SCONJ
ejpam-3970	177	2	lh(a	lh(a	NUM
ejpam-3970	177	3	)	)	PUNCT
ejpam-3970	177	4	⊆	⊆	NUM
ejpam-3970	177	5	lh(q	lh(q	NUM
ejpam-3970	177	6	)	)	PUNCT
ejpam-3970	177	7	(	(	PUNCT
ejpam-3970	177	8	by	by	ADP
ejpam-3970	177	9	proposition	proposition	NOUN
ejpam-3970	177	10	1(iii	1(iii	NUM
ejpam-3970	177	11	)	)	PUNCT
ejpam-3970	177	12	)	)	PUNCT
ejpam-3970	177	13	and	and	CCONJ
ejpam-3970	177	14	lh(q	lh(q	NUM
ejpam-3970	177	15	)	)	PUNCT
ejpam-3970	177	16	∈	∈	NOUN
ejpam-3970	177	17	{	{	PUNCT
ejpam-3970	177	18	{	{	PUNCT
ejpam-3970	177	19	q	q	NOUN
ejpam-3970	177	20	}	}	PUNCT
ejpam-3970	177	21	,	,	PUNCT
ejpam-3970	177	22	{	{	PUNCT
ejpam-3970	177	23	0	0	NUM
ejpam-3970	177	24	,	,	PUNCT
ejpam-3970	177	25	q	q	NOUN
ejpam-3970	177	26	}	}	PUNCT
ejpam-3970	177	27	}	}	PUNCT
ejpam-3970	177	28	,	,	PUNCT
ejpam-3970	177	29	it	it	PRON
ejpam-3970	177	30	follows	follow	VERB
ejpam-3970	177	31	that	that	PRON
ejpam-3970	177	32	lh(a	lh(a	NOUN
ejpam-3970	177	33	)	)	PUNCT
ejpam-3970	177	34	∈	∈	PROPN
ejpam-3970	177	35	{	{	PUNCT
ejpam-3970	177	36	{	{	PUNCT
ejpam-3970	177	37	0	0	NUM
ejpam-3970	177	38	}	}	PUNCT
ejpam-3970	177	39	,	,	PUNCT
ejpam-3970	177	40	{	{	PUNCT
ejpam-3970	177	41	q	q	X
ejpam-3970	177	42	}	}	PUNCT
ejpam-3970	177	43	,	,	PUNCT
ejpam-3970	177	44	{	{	PUNCT
ejpam-3970	177	45	0	0	NUM
ejpam-3970	177	46	,	,	PUNCT
ejpam-3970	177	47	q	q	NOUN
ejpam-3970	177	48	}	}	PUNCT
ejpam-3970	177	49	}	}	PUNCT
ejpam-3970	177	50	.	.	PUNCT
ejpam-3970	178	1	corollary	corollary	ADJ
ejpam-3970	178	2	2	2	NUM
ejpam-3970	178	3	.	.	PUNCT
ejpam-3970	179	1	let	let	VERB
ejpam-3970	179	2	h	h	PRON
ejpam-3970	179	3	be	be	AUX
ejpam-3970	179	4	a	a	DET
ejpam-3970	179	5	hyper	hyper	ADJ
ejpam-3970	179	6	bci	bci	NOUN
ejpam-3970	179	7	-	-	NOUN
ejpam-3970	179	8	algebra	algebra	NOUN
ejpam-3970	179	9	such	such	ADJ
ejpam-3970	179	10	that	that	DET
ejpam-3970	179	11	0	0	NUM
ejpam-3970	179	12	∈	∈	PROPN
ejpam-3970	179	13	lh(x	lh(x	NOUN
ejpam-3970	179	14	)	)	PUNCT
ejpam-3970	179	15	for	for	ADP
ejpam-3970	179	16	each	each	DET
ejpam-3970	179	17	x	x	SYM
ejpam-3970	179	18	∈	∈	PROPN
ejpam-3970	179	19	h	h	NOUN
ejpam-3970	179	20	\	\	PUNCT
ejpam-3970	179	21	{	{	PUNCT
ejpam-3970	179	22	0	0	NUM
ejpam-3970	179	23	}	}	PUNCT
ejpam-3970	179	24	with	with	ADP
ejpam-3970	179	25	|h|	|h|	PROPN
ejpam-3970	179	26	≥	≥	NOUN
ejpam-3970	179	27	2	2	NUM
ejpam-3970	179	28	.	.	PUNCT
ejpam-3970	179	29	then	then	ADV
ejpam-3970	179	30	bl(h	bl(h	PUNCT
ejpam-3970	179	31	)	)	PUNCT
ejpam-3970	180	1	=	=	PRON
ejpam-3970	180	2	{	{	PUNCT
ejpam-3970	180	3	{	{	PUNCT
ejpam-3970	180	4	0	0	NUM
ejpam-3970	180	5	,	,	PUNCT
ejpam-3970	180	6	a	a	PRON
ejpam-3970	180	7	}	}	PUNCT
ejpam-3970	180	8	:	:	PUNCT
ejpam-3970	180	9	a	a	DET
ejpam-3970	180	10	∈	∈	PROPN
ejpam-3970	180	11	a∗(h	a∗(h	PROPN
ejpam-3970	180	12	)	)	PUNCT
ejpam-3970	180	13	}	}	PUNCT
ejpam-3970	180	14	∪	∪	ADP
ejpam-3970	180	15	{	{	PUNCT
ejpam-3970	180	16	lh(a	lh(a	NOUN
ejpam-3970	180	17	)	)	PUNCT
ejpam-3970	180	18	:	:	PUNCT
ejpam-3970	180	19	a	a	X
ejpam-3970	180	20	∩a∗(h	∩a∗(h	NOUN
ejpam-3970	180	21	)	)	PUNCT
ejpam-3970	180	22	=	=	NOUN
ejpam-3970	180	23	∅	∅	NOUN
ejpam-3970	180	24	}	}	PUNCT
ejpam-3970	180	25	.	.	PUNCT
ejpam-3970	181	1	corollary	corollary	ADJ
ejpam-3970	181	2	3	3	X
ejpam-3970	181	3	.	.	PUNCT
ejpam-3970	182	1	let	let	VERB
ejpam-3970	182	2	h	h	PRON
ejpam-3970	182	3	be	be	AUX
ejpam-3970	182	4	a	a	DET
ejpam-3970	182	5	hyper	hyper	ADJ
ejpam-3970	182	6	bci	bci	NOUN
ejpam-3970	182	7	-	-	NOUN
ejpam-3970	182	8	algebra	algebra	NOUN
ejpam-3970	182	9	such	such	ADJ
ejpam-3970	182	10	that	that	DET
ejpam-3970	182	11	0	0	NUM
ejpam-3970	182	12	∈	∈	PROPN
ejpam-3970	182	13	lh(x	lh(x	NOUN
ejpam-3970	182	14	)	)	PUNCT
ejpam-3970	182	15	for	for	ADP
ejpam-3970	182	16	each	each	DET
ejpam-3970	182	17	x	x	SYM
ejpam-3970	182	18	∈	∈	PROPN
ejpam-3970	182	19	h	h	NOUN
ejpam-3970	182	20	\	\	PUNCT
ejpam-3970	182	21	{	{	PUNCT
ejpam-3970	182	22	0	0	NUM
ejpam-3970	182	23	}	}	PUNCT
ejpam-3970	182	24	with	with	ADP
ejpam-3970	182	25	|h|	|h|	PROPN
ejpam-3970	182	26	≥	≥	NOUN
ejpam-3970	182	27	2	2	NUM
ejpam-3970	182	28	.	.	PUNCT
ejpam-3970	183	1	if	if	SCONJ
ejpam-3970	183	2	a∗(h	a∗(h	PROPN
ejpam-3970	183	3	)	)	PUNCT
ejpam-3970	184	1	=	=	PRON
ejpam-3970	184	2	{	{	PUNCT
ejpam-3970	184	3	a	a	NOUN
ejpam-3970	184	4	}	}	PUNCT
ejpam-3970	184	5	,	,	PUNCT
ejpam-3970	184	6	then	then	ADV
ejpam-3970	184	7	bl(h	bl(h	PUNCT
ejpam-3970	184	8	)	)	PUNCT
ejpam-3970	184	9	=	=	PRON
ejpam-3970	184	10	{	{	PUNCT
ejpam-3970	184	11	{	{	PUNCT
ejpam-3970	184	12	0	0	NUM
ejpam-3970	184	13	,	,	PUNCT
ejpam-3970	184	14	a	a	DET
ejpam-3970	184	15	}	}	PUNCT
ejpam-3970	184	16	}	}	PUNCT
ejpam-3970	184	17	∪	∪	ADJ
ejpam-3970	184	18	{	{	PUNCT
ejpam-3970	184	19	lh(a	lh(a	NOUN
ejpam-3970	184	20	)	)	PUNCT
ejpam-3970	184	21	:	:	PUNCT
ejpam-3970	185	1	a	a	DET
ejpam-3970	185	2	/∈	/∈	NOUN
ejpam-3970	185	3	a	a	PRON
ejpam-3970	185	4	}	}	PUNCT
ejpam-3970	185	5	.	.	PUNCT
ejpam-3970	186	1	theorem	theorem	NOUN
ejpam-3970	186	2	5	5	NUM
ejpam-3970	186	3	.	.	PUNCT
ejpam-3970	187	1	let	let	VERB
ejpam-3970	187	2	h	h	PRON
ejpam-3970	187	3	be	be	AUX
ejpam-3970	187	4	a	a	DET
ejpam-3970	187	5	hyper	hyper	ADJ
ejpam-3970	187	6	bci	bci	NOUN
ejpam-3970	187	7	-	-	NOUN
ejpam-3970	187	8	algebra	algebra	NOUN
ejpam-3970	187	9	with	with	ADP
ejpam-3970	187	10	|h|	|h|	PROPN
ejpam-3970	187	11	≥	≥	NUM
ejpam-3970	187	12	2	2	NUM
ejpam-3970	187	13	.	.	PUNCT
ejpam-3970	187	14	then	then	ADV
ejpam-3970	187	15	bl(h	bl(h	PUNCT
ejpam-3970	187	16	)	)	PUNCT
ejpam-3970	188	1	=	=	PRON
ejpam-3970	188	2	{	{	PUNCT
ejpam-3970	188	3	{	{	PUNCT
ejpam-3970	188	4	0	0	NUM
ejpam-3970	188	5	}	}	PUNCT
ejpam-3970	188	6	}	}	PUNCT
ejpam-3970	188	7	∪	∪	X
ejpam-3970	188	8	{	{	PUNCT
ejpam-3970	188	9	{	{	PUNCT
ejpam-3970	188	10	a	a	NOUN
ejpam-3970	188	11	}	}	PUNCT
ejpam-3970	188	12	:	:	PUNCT
ejpam-3970	188	13	a	a	DET
ejpam-3970	188	14	∈	∈	PROPN
ejpam-3970	188	15	h	h	NOUN
ejpam-3970	188	16	\{0	\{0	NOUN
ejpam-3970	188	17	}	}	PUNCT
ejpam-3970	188	18	,	,	PUNCT
ejpam-3970	188	19	0	0	NUM
ejpam-3970	188	20	/∈	/∈	PUNCT
ejpam-3970	189	1	lh(a)}∪{{0	lh(a)}∪{{0	NOUN
ejpam-3970	189	2	,	,	PUNCT
ejpam-3970	189	3	a	a	PRON
ejpam-3970	189	4	}	}	PUNCT
ejpam-3970	189	5	:	:	PUNCT
ejpam-3970	189	6	a	a	DET
ejpam-3970	189	7	∈	∈	PROPN
ejpam-3970	189	8	h	h	NOUN
ejpam-3970	189	9	\{0	\{0	NOUN
ejpam-3970	189	10	}	}	PUNCT
ejpam-3970	189	11	,	,	PUNCT
ejpam-3970	189	12	0	0	NUM
ejpam-3970	189	13	∈	∈	PROPN
ejpam-3970	189	14	lh(a	lh(a	NOUN
ejpam-3970	189	15	)	)	PUNCT
ejpam-3970	189	16	}	}	PUNCT
ejpam-3970	189	17	if	if	SCONJ
ejpam-3970	189	18	and	and	CCONJ
ejpam-3970	189	19	only	only	ADV
ejpam-3970	189	20	if	if	SCONJ
ejpam-3970	189	21	h	h	NOUN
ejpam-3970	189	22	is	be	AUX
ejpam-3970	189	23	hyperatomic	hyperatomic	ADJ
ejpam-3970	189	24	.	.	PUNCT
ejpam-3970	190	1	proof	proof	NOUN
ejpam-3970	190	2	.	.	PUNCT
ejpam-3970	191	1	suppose	suppose	VERB
ejpam-3970	191	2	h	h	NOUN
ejpam-3970	191	3	is	be	AUX
ejpam-3970	191	4	hyperatomic	hyperatomic	ADJ
ejpam-3970	191	5	.	.	PUNCT
ejpam-3970	192	1	then	then	ADV
ejpam-3970	192	2	for	for	ADP
ejpam-3970	192	3	any	any	DET
ejpam-3970	192	4	nonempty	nonempty	NOUN
ejpam-3970	192	5	subset	subset	VERB
ejpam-3970	192	6	a	a	PRON
ejpam-3970	192	7	of	of	ADP
ejpam-3970	192	8	h	h	NOUN
ejpam-3970	192	9	such	such	ADJ
ejpam-3970	192	10	that	that	SCONJ
ejpam-3970	192	11	a	a	DET
ejpam-3970	192	12	6=	6=	NUM
ejpam-3970	192	13	{	{	PUNCT
ejpam-3970	192	14	0	0	NUM
ejpam-3970	192	15	}	}	PUNCT
ejpam-3970	192	16	,	,	PUNCT
ejpam-3970	192	17	a	a	DET
ejpam-3970	192	18	∩	∩	ADJ
ejpam-3970	192	19	a∗(h	a∗(h	PROPN
ejpam-3970	192	20	)	)	PUNCT
ejpam-3970	192	21	6=	6=	ADP
ejpam-3970	192	22	∅.	∅.	ADP
ejpam-3970	192	23	thus	thus	ADV
ejpam-3970	192	24	,	,	PUNCT
ejpam-3970	192	25	{	{	PUNCT
ejpam-3970	192	26	lh(a	lh(a	NOUN
ejpam-3970	192	27	)	)	PUNCT
ejpam-3970	192	28	:	:	PUNCT
ejpam-3970	192	29	a	a	DET
ejpam-3970	192	30	6=	6=	NUM
ejpam-3970	192	31	∅	∅	NOUN
ejpam-3970	192	32	and	and	CCONJ
ejpam-3970	192	33	a	a	DET
ejpam-3970	192	34	∩	∩	ADJ
ejpam-3970	192	35	a∗(h	a∗(h	PROPN
ejpam-3970	192	36	)	)	PUNCT
ejpam-3970	192	37	=	=	NOUN
ejpam-3970	192	38	∅	∅	NOUN
ejpam-3970	192	39	}	}	PUNCT
ejpam-3970	192	40	=	=	SYM
ejpam-3970	192	41	{	{	PUNCT
ejpam-3970	192	42	{	{	PUNCT
ejpam-3970	192	43	0	0	NUM
ejpam-3970	192	44	}	}	PUNCT
ejpam-3970	192	45	}	}	PUNCT
ejpam-3970	192	46	.	.	PUNCT
ejpam-3970	193	1	the	the	DET
ejpam-3970	193	2	result	result	NOUN
ejpam-3970	193	3	then	then	ADV
ejpam-3970	193	4	follows	follow	VERB
ejpam-3970	193	5	from	from	ADP
ejpam-3970	193	6	proposition	proposition	NOUN
ejpam-3970	193	7	3	3	NUM
ejpam-3970	193	8	.	.	PUNCT
ejpam-3970	194	1	for	for	ADP
ejpam-3970	194	2	the	the	DET
ejpam-3970	194	3	converse	converse	NOUN
ejpam-3970	194	4	,	,	PUNCT
ejpam-3970	194	5	suppose	suppose	VERB
ejpam-3970	194	6	that	that	SCONJ
ejpam-3970	194	7	bl(h	bl(h	PUNCT
ejpam-3970	194	8	)	)	PUNCT
ejpam-3970	194	9	is	be	AUX
ejpam-3970	194	10	the	the	DET
ejpam-3970	194	11	given	give	VERB
ejpam-3970	194	12	family	family	NOUN
ejpam-3970	194	13	of	of	ADP
ejpam-3970	194	14	subsets	subset	NOUN
ejpam-3970	194	15	of	of	ADP
ejpam-3970	194	16	h.	h.	PROPN
ejpam-3970	194	17	let	let	VERB
ejpam-3970	194	18	a	a	DET
ejpam-3970	194	19	∈	∈	PROPN
ejpam-3970	194	20	h	h	NOUN
ejpam-3970	194	21	\	\	PUNCT
ejpam-3970	194	22	{	{	PUNCT
ejpam-3970	194	23	0	0	NUM
ejpam-3970	194	24	}	}	PUNCT
ejpam-3970	194	25	.	.	PUNCT
ejpam-3970	195	1	then	then	ADV
ejpam-3970	195	2	either	either	DET
ejpam-3970	195	3	lh(a	lh(a	NOUN
ejpam-3970	195	4	)	)	PUNCT
ejpam-3970	195	5	=	=	PRON
ejpam-3970	195	6	{	{	PUNCT
ejpam-3970	195	7	a	a	NOUN
ejpam-3970	195	8	}	}	PUNCT
ejpam-3970	195	9	or	or	CCONJ
ejpam-3970	195	10	lh(a	lh(a	NOUN
ejpam-3970	195	11	)	)	PUNCT
ejpam-3970	195	12	=	=	PRON
ejpam-3970	195	13	{	{	PUNCT
ejpam-3970	195	14	0	0	NUM
ejpam-3970	195	15	,	,	PUNCT
ejpam-3970	195	16	a	a	PRON
ejpam-3970	195	17	}	}	PUNCT
ejpam-3970	195	18	.	.	PUNCT
ejpam-3970	196	1	hence	hence	ADV
ejpam-3970	196	2	,	,	PUNCT
ejpam-3970	196	3	if	if	SCONJ
ejpam-3970	196	4	x	x	SYM
ejpam-3970	196	5	∈	∈	NOUN
ejpam-3970	196	6	h	h	NOUN
ejpam-3970	196	7	and	and	CCONJ
ejpam-3970	196	8	x	x	PROPN
ejpam-3970	196	9	�	�	PROPN
ejpam-3970	196	10	a	a	X
ejpam-3970	196	11	,	,	PUNCT
ejpam-3970	196	12	then	then	ADV
ejpam-3970	196	13	either	either	CCONJ
ejpam-3970	196	14	x	x	X
ejpam-3970	196	15	=	=	PUNCT
ejpam-3970	196	16	a	a	DET
ejpam-3970	196	17	or	or	CCONJ
ejpam-3970	196	18	x	x	SYM
ejpam-3970	196	19	=	=	NOUN
ejpam-3970	196	20	0	0	NUM
ejpam-3970	196	21	.	.	PUNCT
ejpam-3970	197	1	thus	thus	ADV
ejpam-3970	197	2	,	,	PUNCT
ejpam-3970	197	3	a	a	DET
ejpam-3970	197	4	∈	∈	PROPN
ejpam-3970	197	5	a(h	a(h	PROPN
ejpam-3970	197	6	)	)	PUNCT
ejpam-3970	197	7	.	.	PUNCT
ejpam-3970	198	1	therefore	therefore	ADV
ejpam-3970	198	2	,	,	PUNCT
ejpam-3970	198	3	h	h	NOUN
ejpam-3970	198	4	is	be	AUX
ejpam-3970	198	5	hyperatomic	hyperatomic	ADJ
ejpam-3970	198	6	.	.	PUNCT
ejpam-3970	199	1	example	example	NOUN
ejpam-3970	200	1	5	5	NUM
ejpam-3970	200	2	.	.	PUNCT
ejpam-3970	200	3	refer	refer	VERB
ejpam-3970	200	4	to	to	ADP
ejpam-3970	200	5	example	example	NOUN
ejpam-3970	200	6	2	2	X
ejpam-3970	200	7	.	.	PUNCT
ejpam-3970	201	1	it	it	PRON
ejpam-3970	201	2	is	be	AUX
ejpam-3970	201	3	easy	easy	ADJ
ejpam-3970	201	4	to	to	PART
ejpam-3970	201	5	verify	verify	VERB
ejpam-3970	201	6	that	that	SCONJ
ejpam-3970	201	7	h	h	NOUN
ejpam-3970	201	8	is	be	AUX
ejpam-3970	201	9	hyperatomic	hyperatomic	ADJ
ejpam-3970	201	10	.	.	PUNCT
ejpam-3970	202	1	corollary	corollary	ADJ
ejpam-3970	202	2	4	4	NUM
ejpam-3970	202	3	.	.	PUNCT
ejpam-3970	203	1	let	let	VERB
ejpam-3970	203	2	h	h	PRON
ejpam-3970	203	3	be	be	AUX
ejpam-3970	203	4	a	a	DET
ejpam-3970	203	5	hyper	hyper	ADJ
ejpam-3970	203	6	bci	bci	NOUN
ejpam-3970	203	7	-	-	NOUN
ejpam-3970	203	8	algebra	algebra	NOUN
ejpam-3970	203	9	such	such	ADJ
ejpam-3970	203	10	that	that	DET
ejpam-3970	203	11	0	0	NUM
ejpam-3970	203	12	∈	∈	PROPN
ejpam-3970	203	13	lh(x	lh(x	NOUN
ejpam-3970	203	14	)	)	PUNCT
ejpam-3970	203	15	for	for	ADP
ejpam-3970	203	16	each	each	DET
ejpam-3970	203	17	x	x	SYM
ejpam-3970	203	18	∈	∈	PROPN
ejpam-3970	203	19	h	h	NOUN
ejpam-3970	203	20	with	with	ADP
ejpam-3970	203	21	|h|	|h|	PROPN
ejpam-3970	203	22	≥	≥	NOUN
ejpam-3970	203	23	2	2	NUM
ejpam-3970	203	24	.	.	PUNCT
ejpam-3970	203	25	then	then	ADV
ejpam-3970	203	26	bl(h	bl(h	PUNCT
ejpam-3970	203	27	)	)	PUNCT
ejpam-3970	204	1	=	=	PRON
ejpam-3970	204	2	{	{	PUNCT
ejpam-3970	204	3	{	{	PUNCT
ejpam-3970	204	4	0	0	NUM
ejpam-3970	204	5	}	}	PUNCT
ejpam-3970	204	6	}	}	PUNCT
ejpam-3970	204	7	∪	∪	X
ejpam-3970	204	8	{	{	PUNCT
ejpam-3970	204	9	{	{	PUNCT
ejpam-3970	204	10	0	0	NUM
ejpam-3970	204	11	,	,	PUNCT
ejpam-3970	204	12	a	a	PRON
ejpam-3970	204	13	}	}	PUNCT
ejpam-3970	204	14	:	:	PUNCT
ejpam-3970	204	15	a	a	DET
ejpam-3970	204	16	∈	∈	PROPN
ejpam-3970	204	17	h	h	NOUN
ejpam-3970	204	18	\	\	PUNCT
ejpam-3970	204	19	{	{	PUNCT
ejpam-3970	204	20	0	0	NUM
ejpam-3970	204	21	}	}	PUNCT
ejpam-3970	204	22	}	}	PUNCT
ejpam-3970	204	23	if	if	SCONJ
ejpam-3970	204	24	and	and	CCONJ
ejpam-3970	204	25	only	only	ADV
ejpam-3970	204	26	if	if	SCONJ
ejpam-3970	204	27	h	h	NOUN
ejpam-3970	204	28	is	be	AUX
ejpam-3970	204	29	hyperatomic	hyperatomic	ADJ
ejpam-3970	204	30	.	.	PUNCT
ejpam-3970	205	1	theorem	theorem	ADJ
ejpam-3970	205	2	6	6	NUM
ejpam-3970	205	3	.	.	PUNCT
ejpam-3970	206	1	let	let	VERB
ejpam-3970	206	2	h	h	PRON
ejpam-3970	206	3	be	be	AUX
ejpam-3970	206	4	a	a	DET
ejpam-3970	206	5	hyperatomic	hyperatomic	ADJ
ejpam-3970	206	6	hyper	hyper	ADJ
ejpam-3970	206	7	bci	bci	NOUN
ejpam-3970	206	8	-	-	NOUN
ejpam-3970	206	9	algebra	algebra	NOUN
ejpam-3970	206	10	.	.	PUNCT
ejpam-3970	207	1	then	then	ADV
ejpam-3970	207	2	a	a	DET
ejpam-3970	207	3	∈	∈	NOUN
ejpam-3970	207	4	τl(h	τl(h	NUM
ejpam-3970	207	5	)	)	PUNCT
ejpam-3970	207	6	if	if	SCONJ
ejpam-3970	207	7	and	and	CCONJ
ejpam-3970	207	8	only	only	ADV
ejpam-3970	207	9	if	if	SCONJ
ejpam-3970	207	10	a	a	DET
ejpam-3970	207	11	=	=	NOUN
ejpam-3970	207	12	∅	∅	NOUN
ejpam-3970	207	13	or	or	CCONJ
ejpam-3970	207	14	0	0	NUM
ejpam-3970	207	15	∈	∈	PROPN
ejpam-3970	207	16	a	a	PRON
ejpam-3970	207	17	or	or	CCONJ
ejpam-3970	207	18	0	0	NUM
ejpam-3970	207	19	/∈	/∈	SYM
ejpam-3970	207	20	lh(a	lh(a	NOUN
ejpam-3970	207	21	)	)	PUNCT
ejpam-3970	207	22	for	for	ADP
ejpam-3970	207	23	all	all	DET
ejpam-3970	207	24	a	a	DET
ejpam-3970	207	25	∈	∈	NOUN
ejpam-3970	207	26	a.	a.	NOUN
ejpam-3970	207	27	proof	proof	NOUN
ejpam-3970	207	28	.	.	PUNCT
ejpam-3970	208	1	let	let	VERB
ejpam-3970	208	2	a	a	DET
ejpam-3970	208	3	∈	∈	NOUN
ejpam-3970	208	4	τl(h	τl(h	NUM
ejpam-3970	208	5	)	)	PUNCT
ejpam-3970	208	6	\	\	NOUN
ejpam-3970	208	7	{	{	PUNCT
ejpam-3970	208	8	∅	∅	NOUN
ejpam-3970	208	9	}	}	PUNCT
ejpam-3970	208	10	and	and	CCONJ
ejpam-3970	208	11	let	let	VERB
ejpam-3970	208	12	a	a	DET
ejpam-3970	208	13	∈	∈	NOUN
ejpam-3970	208	14	a.	a.	NOUN
ejpam-3970	208	15	since	since	SCONJ
ejpam-3970	208	16	bl(h	bl(h	NUM
ejpam-3970	208	17	)	)	PUNCT
ejpam-3970	208	18	is	be	AUX
ejpam-3970	208	19	a	a	DET
ejpam-3970	208	20	basis	basis	NOUN
ejpam-3970	208	21	for	for	ADP
ejpam-3970	208	22	τl(h	τl(h	NUM
ejpam-3970	208	23	)	)	PUNCT
ejpam-3970	208	24	,	,	PUNCT
ejpam-3970	208	25	there	there	PRON
ejpam-3970	208	26	exists	exist	VERB
ejpam-3970	208	27	ba	ba	PROPN
ejpam-3970	208	28	⊆	⊆	NUM
ejpam-3970	208	29	h	h	NOUN
ejpam-3970	208	30	such	such	ADJ
ejpam-3970	208	31	that	that	SCONJ
ejpam-3970	208	32	a	a	DET
ejpam-3970	208	33	∈	∈	PROPN
ejpam-3970	208	34	lh(ba	lh(ba	NOUN
ejpam-3970	208	35	)	)	PUNCT
ejpam-3970	208	36	⊆	⊆	NUM
ejpam-3970	208	37	a.	a.	NOUN
ejpam-3970	208	38	since	since	SCONJ
ejpam-3970	208	39	h	h	NOUN
ejpam-3970	208	40	is	be	AUX
ejpam-3970	208	41	hyperatomic	hyperatomic	ADJ
ejpam-3970	208	42	,	,	PUNCT
ejpam-3970	208	43	lh(b	lh(b	NOUN
ejpam-3970	208	44	)	)	PUNCT
ejpam-3970	208	45	=	=	PRON
ejpam-3970	208	46	{	{	PUNCT
ejpam-3970	208	47	b	b	NOUN
ejpam-3970	208	48	}	}	PUNCT
ejpam-3970	208	49	or	or	CCONJ
ejpam-3970	208	50	{	{	PUNCT
ejpam-3970	208	51	0	0	NUM
ejpam-3970	208	52	,	,	PUNCT
ejpam-3970	208	53	b	b	NOUN
ejpam-3970	208	54	}	}	PUNCT
ejpam-3970	208	55	for	for	ADP
ejpam-3970	208	56	each	each	DET
ejpam-3970	208	57	b	b	PROPN
ejpam-3970	208	58	∈	∈	PROPN
ejpam-3970	208	59	ba	ba	PROPN
ejpam-3970	208	60	.	.	PUNCT
ejpam-3970	209	1	if	if	SCONJ
ejpam-3970	209	2	a	a	DET
ejpam-3970	209	3	=	=	SYM
ejpam-3970	209	4	0	0	NUM
ejpam-3970	209	5	,	,	PUNCT
ejpam-3970	209	6	then	then	ADV
ejpam-3970	209	7	0	0	NUM
ejpam-3970	209	8	∈	∈	NOUN
ejpam-3970	209	9	a.	a.	NOUN
ejpam-3970	209	10	suppose	suppose	VERB
ejpam-3970	209	11	that	that	SCONJ
ejpam-3970	209	12	a	a	DET
ejpam-3970	209	13	6=	6=	NUM
ejpam-3970	209	14	0	0	NUM
ejpam-3970	209	15	and	and	CCONJ
ejpam-3970	209	16	let	let	VERB
ejpam-3970	209	17	b	b	X
ejpam-3970	209	18	∈	∈	PROPN
ejpam-3970	209	19	ba	ba	PROPN
ejpam-3970	209	20	.	.	PUNCT
ejpam-3970	210	1	then	then	ADV
ejpam-3970	210	2	b	b	X
ejpam-3970	210	3	6=	6=	NUM
ejpam-3970	210	4	0	0	NUM
ejpam-3970	210	5	and	and	CCONJ
ejpam-3970	210	6	a	a	DET
ejpam-3970	210	7	∈	∈	NOUN
ejpam-3970	210	8	lh(b	lh(b	NOUN
ejpam-3970	210	9	)	)	PUNCT
ejpam-3970	210	10	.	.	PUNCT
ejpam-3970	211	1	hence	hence	ADV
ejpam-3970	211	2	,	,	PUNCT
ejpam-3970	211	3	a	a	DET
ejpam-3970	211	4	=	=	SYM
ejpam-3970	211	5	b	b	NOUN
ejpam-3970	211	6	;	;	PUNCT
ejpam-3970	211	7	that	that	PRON
ejpam-3970	211	8	is	is	ADV
ejpam-3970	211	9	,	,	PUNCT
ejpam-3970	211	10	ba	ba	PROPN
ejpam-3970	211	11	=	=	PRON
ejpam-3970	211	12	{	{	PUNCT
ejpam-3970	211	13	a	a	X
ejpam-3970	211	14	}	}	PUNCT
ejpam-3970	211	15	.	.	PUNCT
ejpam-3970	212	1	thus	thus	ADV
ejpam-3970	212	2	,	,	PUNCT
ejpam-3970	212	3	lh(ba	lh(ba	NOUN
ejpam-3970	212	4	)	)	PUNCT
ejpam-3970	212	5	=	=	SYM
ejpam-3970	212	6	lh(a	lh(a	NOUN
ejpam-3970	212	7	)	)	PUNCT
ejpam-3970	212	8	=	=	PRON
ejpam-3970	212	9	{	{	PUNCT
ejpam-3970	212	10	a	a	NOUN
ejpam-3970	212	11	}	}	PUNCT
ejpam-3970	212	12	.	.	PUNCT
ejpam-3970	213	1	therefore	therefore	ADV
ejpam-3970	213	2	,	,	PUNCT
ejpam-3970	213	3	either	either	CCONJ
ejpam-3970	213	4	0	0	NUM
ejpam-3970	213	5	∈	∈	PROPN
ejpam-3970	213	6	a	a	PRON
ejpam-3970	213	7	or	or	CCONJ
ejpam-3970	213	8	0	0	NUM
ejpam-3970	213	9	/∈	/∈	PROPN
ejpam-3970	213	10	a	a	PRON
ejpam-3970	213	11	and	and	CCONJ
ejpam-3970	213	12	lh(a	lh(a	NOUN
ejpam-3970	213	13	)	)	PUNCT
ejpam-3970	214	1	=	=	PRON
ejpam-3970	214	2	{	{	PUNCT
ejpam-3970	214	3	a	a	NOUN
ejpam-3970	214	4	}	}	PUNCT
ejpam-3970	214	5	for	for	ADP
ejpam-3970	214	6	each	each	DET
ejpam-3970	214	7	a	a	DET
ejpam-3970	214	8	∈	∈	PROPN
ejpam-3970	214	9	a.	a.	NOUN
ejpam-3970	214	10	for	for	ADP
ejpam-3970	214	11	the	the	DET
ejpam-3970	214	12	converse	converse	NOUN
ejpam-3970	214	13	,	,	PUNCT
ejpam-3970	214	14	suppose	suppose	VERB
ejpam-3970	214	15	first	first	ADV
ejpam-3970	214	16	that	that	SCONJ
ejpam-3970	214	17	0	0	NUM
ejpam-3970	214	18	/∈	/∈	SYM
ejpam-3970	214	19	lh(a	lh(a	NOUN
ejpam-3970	214	20	)	)	PUNCT
ejpam-3970	214	21	for	for	ADP
ejpam-3970	214	22	each	each	DET
ejpam-3970	214	23	a	a	DET
ejpam-3970	214	24	∈	∈	PROPN
ejpam-3970	214	25	a.	a.	NOUN
ejpam-3970	214	26	then	then	ADV
ejpam-3970	214	27	a	a	DET
ejpam-3970	214	28	=	=	PUNCT
ejpam-3970	214	29	⋃	⋃	ADP
ejpam-3970	214	30	a∈a	a∈a	ADJ
ejpam-3970	214	31	lh(a	lh(a	NOUN
ejpam-3970	214	32	)	)	PUNCT
ejpam-3970	214	33	∈	∈	PROPN
ejpam-3970	214	34	τl(h	τl(h	NUM
ejpam-3970	214	35	)	)	PUNCT
ejpam-3970	214	36	.	.	PUNCT
ejpam-3970	215	1	next	next	ADV
ejpam-3970	215	2	,	,	PUNCT
ejpam-3970	215	3	suppose	suppose	VERB
ejpam-3970	215	4	that	that	SCONJ
ejpam-3970	215	5	0	0	NUM
ejpam-3970	215	6	∈	∈	PROPN
ejpam-3970	215	7	a.	a.	NOUN
ejpam-3970	215	8	since	since	SCONJ
ejpam-3970	215	9	lh(x	lh(x	PROPN
ejpam-3970	215	10	)	)	PUNCT
ejpam-3970	216	1	=	=	SYM
ejpam-3970	216	2	{	{	PUNCT
ejpam-3970	216	3	x	x	NOUN
ejpam-3970	216	4	}	}	PUNCT
ejpam-3970	216	5	or	or	CCONJ
ejpam-3970	216	6	{	{	PUNCT
ejpam-3970	216	7	0	0	NUM
ejpam-3970	216	8	,	,	PUNCT
ejpam-3970	216	9	x	x	NOUN
ejpam-3970	216	10	}	}	PUNCT
ejpam-3970	216	11	for	for	ADP
ejpam-3970	216	12	all	all	DET
ejpam-3970	216	13	x	x	SYM
ejpam-3970	216	14	∈	∈	PROPN
ejpam-3970	216	15	h	h	NOUN
ejpam-3970	216	16	,	,	PUNCT
ejpam-3970	216	17	it	it	PRON
ejpam-3970	216	18	follows	follow	VERB
ejpam-3970	216	19	that	that	DET
ejpam-3970	216	20	lh(a	lh(a	NOUN
ejpam-3970	216	21	)	)	PUNCT
ejpam-3970	216	22	⊆	⊆	NUM
ejpam-3970	216	23	a	a	DET
ejpam-3970	216	24	for	for	ADP
ejpam-3970	216	25	all	all	DET
ejpam-3970	216	26	a	a	DET
ejpam-3970	216	27	∈	∈	PROPN
ejpam-3970	216	28	a.	a.	NOUN
ejpam-3970	216	29	thus	thus	ADV
ejpam-3970	216	30	,	,	PUNCT
ejpam-3970	216	31	a	a	DET
ejpam-3970	216	32	=	=	X
ejpam-3970	216	33			PROPN
ejpam-3970	216	34	⋃	⋃	ADV
ejpam-3970	216	35	a∈a	a∈a	ADJ
ejpam-3970	216	36	0∈lh(a	0∈lh(a	NUM
ejpam-3970	216	37	)	)	PUNCT
ejpam-3970	216	38	lh(a	lh(a	NOUN
ejpam-3970	216	39	)	)	PUNCT
ejpam-3970	216	40	⋃	⋃	NOUN
ejpam-3970	216	41			PROPN
ejpam-3970	216	42	⋃	⋃	VERB
ejpam-3970	216	43	a∈a	a∈a	ADJ
ejpam-3970	216	44	0/∈lh(a	0/∈lh(a	NOUN
ejpam-3970	216	45	)	)	PUNCT
ejpam-3970	216	46	lh(a	lh(a	NOUN
ejpam-3970	216	47	)	)	PUNCT
ejpam-3970	216	48			NOUN
ejpam-3970	216	49	∈	∈	PROPN
ejpam-3970	216	50	τl(h	τl(h	NUM
ejpam-3970	216	51	)	)	PUNCT
ejpam-3970	216	52	.	.	PUNCT
ejpam-3970	217	1	m.	m.	NOUN
ejpam-3970	217	2	panganduyon	panganduyon	NOUN
ejpam-3970	217	3	,	,	PUNCT
ejpam-3970	217	4	s.	s.	PROPN
ejpam-3970	217	5	canoy	canoy	PROPN
ejpam-3970	217	6	,	,	PUNCT
ejpam-3970	217	7	jr	jr	PROPN
ejpam-3970	217	8	.	.	PROPN
ejpam-3970	217	9	,	,	PUNCT
ejpam-3970	217	10	b.	b.	PROPN
ejpam-3970	217	11	davvaz	davvaz	PROPN
ejpam-3970	217	12	/	/	SYM
ejpam-3970	217	13	eur	eur	PROPN
ejpam-3970	217	14	.	.	PUNCT
ejpam-3970	218	1	j.	j.	PROPN
ejpam-3970	218	2	pure	pure	PROPN
ejpam-3970	218	3	appl	appl	PROPN
ejpam-3970	218	4	.	.	PROPN
ejpam-3970	218	5	math	math	PROPN
ejpam-3970	218	6	,	,	PUNCT
ejpam-3970	218	7	14	14	NUM
ejpam-3970	218	8	(	(	PUNCT
ejpam-3970	218	9	2	2	NUM
ejpam-3970	218	10	)	)	PUNCT
ejpam-3970	218	11	(	(	PUNCT
ejpam-3970	218	12	2021	2021	NUM
ejpam-3970	218	13	)	)	PUNCT
ejpam-3970	218	14	,	,	PUNCT
ejpam-3970	218	15	590	590	NUM
ejpam-3970	218	16	-	-	SYM
ejpam-3970	218	17	600	600	NUM
ejpam-3970	218	18	596	596	NUM
ejpam-3970	218	19	this	this	PRON
ejpam-3970	218	20	proves	prove	VERB
ejpam-3970	218	21	the	the	DET
ejpam-3970	218	22	assertion	assertion	NOUN
ejpam-3970	218	23	.	.	PUNCT
ejpam-3970	219	1	recall	recall	VERB
ejpam-3970	219	2	that	that	PRON
ejpam-3970	219	3	for	for	ADP
ejpam-3970	219	4	a	a	DET
ejpam-3970	219	5	nonempty	nonempty	ADV
ejpam-3970	219	6	set	set	VERB
ejpam-3970	219	7	x	x	PUNCT
ejpam-3970	219	8	and	and	CCONJ
ejpam-3970	219	9	a	a	DET
ejpam-3970	219	10	fixed	fix	VERB
ejpam-3970	219	11	p	p	NOUN
ejpam-3970	219	12	∈	∈	PROPN
ejpam-3970	219	13	x	x	NOUN
ejpam-3970	219	14	,	,	PUNCT
ejpam-3970	219	15	the	the	DET
ejpam-3970	219	16	topology	topology	NOUN
ejpam-3970	219	17	τp	τp	NOUN
ejpam-3970	219	18	given	give	VERB
ejpam-3970	219	19	by	by	ADP
ejpam-3970	219	20	τp	τp	PRON
ejpam-3970	219	21	=	=	SYM
ejpam-3970	219	22	{	{	PUNCT
ejpam-3970	219	23	∅	∅	NOUN
ejpam-3970	219	24	}	}	PUNCT
ejpam-3970	219	25	∪	∪	X
ejpam-3970	219	26	{	{	PUNCT
ejpam-3970	219	27	a	a	DET
ejpam-3970	219	28	⊆	⊆	NUM
ejpam-3970	219	29	x	x	SYM
ejpam-3970	219	30	:	:	PUNCT
ejpam-3970	219	31	p	p	X
ejpam-3970	219	32	∈	∈	PROPN
ejpam-3970	219	33	a	a	PRON
ejpam-3970	219	34	}	}	PUNCT
ejpam-3970	219	35	is	be	AUX
ejpam-3970	219	36	called	call	VERB
ejpam-3970	219	37	the	the	DET
ejpam-3970	219	38	particular	particular	ADJ
ejpam-3970	219	39	point	point	NOUN
ejpam-3970	219	40	p	p	PRON
ejpam-3970	219	41	topology	topology	NOUN
ejpam-3970	219	42	on	on	ADP
ejpam-3970	219	43	x	x	PROPN
ejpam-3970	219	44	(	(	PUNCT
ejpam-3970	219	45	see	see	VERB
ejpam-3970	219	46	[	[	X
ejpam-3970	219	47	12	12	NUM
ejpam-3970	219	48	]	]	NUM
ejpam-3970	219	49	)	)	PUNCT
ejpam-3970	219	50	.	.	PUNCT
ejpam-3970	220	1	the	the	DET
ejpam-3970	220	2	next	next	ADJ
ejpam-3970	220	3	result	result	NOUN
ejpam-3970	220	4	gives	give	VERB
ejpam-3970	220	5	a	a	DET
ejpam-3970	220	6	characterization	characterization	NOUN
ejpam-3970	220	7	of	of	ADP
ejpam-3970	220	8	τl(h	τl(h	NUM
ejpam-3970	220	9	)	)	PUNCT
ejpam-3970	220	10	involving	involve	VERB
ejpam-3970	220	11	a	a	DET
ejpam-3970	220	12	particular	particular	ADJ
ejpam-3970	220	13	point	point	NOUN
ejpam-3970	220	14	topology	topology	NOUN
ejpam-3970	220	15	.	.	PUNCT
ejpam-3970	221	1	theorem	theorem	VERB
ejpam-3970	221	2	7	7	NUM
ejpam-3970	221	3	.	.	PUNCT
ejpam-3970	222	1	let	let	VERB
ejpam-3970	222	2	h	h	PRON
ejpam-3970	222	3	be	be	AUX
ejpam-3970	222	4	a	a	DET
ejpam-3970	222	5	hyper	hyper	ADJ
ejpam-3970	222	6	bci	bci	NOUN
ejpam-3970	222	7	-	-	NOUN
ejpam-3970	222	8	algebra	algebra	NOUN
ejpam-3970	222	9	such	such	ADJ
ejpam-3970	222	10	that	that	PRON
ejpam-3970	222	11	lh({x	lh({x	NOUN
ejpam-3970	222	12	,	,	PUNCT
ejpam-3970	222	13	y	y	NOUN
ejpam-3970	222	14	}	}	PUNCT
ejpam-3970	222	15	)	)	PUNCT
ejpam-3970	223	1	=	=	PRON
ejpam-3970	223	2	{	{	PUNCT
ejpam-3970	223	3	0	0	NUM
ejpam-3970	223	4	}	}	PUNCT
ejpam-3970	223	5	for	for	ADP
ejpam-3970	223	6	every	every	DET
ejpam-3970	223	7	pair	pair	NOUN
ejpam-3970	223	8	of	of	ADP
ejpam-3970	223	9	distinct	distinct	ADJ
ejpam-3970	223	10	points	point	NOUN
ejpam-3970	223	11	x	x	PUNCT
ejpam-3970	223	12	and	and	CCONJ
ejpam-3970	223	13	y	y	PROPN
ejpam-3970	223	14	of	of	ADP
ejpam-3970	223	15	h.	h.	PROPN
ejpam-3970	223	16	then	then	ADV
ejpam-3970	223	17	τl(h	τl(h	PUNCT
ejpam-3970	223	18	)	)	PUNCT
ejpam-3970	223	19	is	be	AUX
ejpam-3970	223	20	the	the	DET
ejpam-3970	223	21	particular	particular	ADJ
ejpam-3970	223	22	point	point	NOUN
ejpam-3970	223	23	0	0	NUM
ejpam-3970	223	24	topology	topology	NOUN
ejpam-3970	223	25	τ0	τ0	NOUN
ejpam-3970	223	26	on	on	ADP
ejpam-3970	223	27	h	h	NOUN
ejpam-3970	223	28	if	if	SCONJ
ejpam-3970	224	1	and	and	CCONJ
ejpam-3970	224	2	only	only	ADV
ejpam-3970	224	3	if	if	SCONJ
ejpam-3970	224	4	h	h	NOUN
ejpam-3970	224	5	is	be	AUX
ejpam-3970	224	6	hyperatomic	hyperatomic	ADJ
ejpam-3970	224	7	.	.	PUNCT
ejpam-3970	225	1	proof	proof	NOUN
ejpam-3970	225	2	.	.	PUNCT
ejpam-3970	226	1	suppose	suppose	VERB
ejpam-3970	226	2	that	that	SCONJ
ejpam-3970	226	3	h	h	NOUN
ejpam-3970	226	4	is	be	AUX
ejpam-3970	226	5	hyperatomic	hyperatomic	ADJ
ejpam-3970	226	6	.	.	PUNCT
ejpam-3970	227	1	then	then	ADV
ejpam-3970	227	2	by	by	ADP
ejpam-3970	227	3	corollary	corollary	ADJ
ejpam-3970	227	4	4	4	NUM
ejpam-3970	227	5	,	,	PUNCT
ejpam-3970	227	6	bl(h	bl(h	PUNCT
ejpam-3970	227	7	)	)	PUNCT
ejpam-3970	227	8	=	=	PRON
ejpam-3970	227	9	{	{	PUNCT
ejpam-3970	227	10	{	{	PUNCT
ejpam-3970	227	11	0}}∪{{0	0}}∪{{0	PROPN
ejpam-3970	227	12	,	,	PUNCT
ejpam-3970	227	13	a	a	PRON
ejpam-3970	227	14	}	}	PUNCT
ejpam-3970	227	15	:	:	PUNCT
ejpam-3970	227	16	a	a	DET
ejpam-3970	227	17	∈	∈	PROPN
ejpam-3970	227	18	h	h	NOUN
ejpam-3970	227	19	\	\	PUNCT
ejpam-3970	227	20	{	{	PUNCT
ejpam-3970	227	21	0	0	NUM
ejpam-3970	227	22	}	}	PUNCT
ejpam-3970	227	23	}	}	PUNCT
ejpam-3970	227	24	.	.	PUNCT
ejpam-3970	228	1	since	since	SCONJ
ejpam-3970	228	2	bl(h	bl(h	NUM
ejpam-3970	228	3	)	)	PUNCT
ejpam-3970	228	4	is	be	AUX
ejpam-3970	228	5	a	a	DET
ejpam-3970	228	6	basis	basis	NOUN
ejpam-3970	228	7	for	for	ADP
ejpam-3970	228	8	τl(h	τl(h	NUM
ejpam-3970	228	9	)	)	PUNCT
ejpam-3970	228	10	,	,	PUNCT
ejpam-3970	228	11	a	a	DET
ejpam-3970	228	12	∈	∈	NOUN
ejpam-3970	228	13	τl(h	τl(h	NUM
ejpam-3970	228	14	)	)	PUNCT
ejpam-3970	228	15	⇔	⇔	NOUN
ejpam-3970	228	16	a	a	X
ejpam-3970	228	17	=	=	ADJ
ejpam-3970	228	18	∅	∅	NOUN
ejpam-3970	228	19	or	or	CCONJ
ejpam-3970	228	20	a	a	DET
ejpam-3970	228	21	=	=	X
ejpam-3970	228	22	{	{	PUNCT
ejpam-3970	228	23	0	0	NUM
ejpam-3970	228	24	}	}	PUNCT
ejpam-3970	228	25	or	or	CCONJ
ejpam-3970	228	26	a	a	DET
ejpam-3970	228	27	=	=	X
ejpam-3970	228	28	⋃	⋃	NOUN
ejpam-3970	228	29	a∈a	a∈a	ADJ
ejpam-3970	228	30	{	{	PUNCT
ejpam-3970	228	31	0	0	NUM
ejpam-3970	228	32	,	,	PUNCT
ejpam-3970	228	33	a	a	DET
ejpam-3970	228	34	}	}	PUNCT
ejpam-3970	228	35	⇔	⇔	X
ejpam-3970	228	36	a	a	DET
ejpam-3970	228	37	=	=	ADJ
ejpam-3970	228	38	∅	∅	NOUN
ejpam-3970	228	39	or	or	CCONJ
ejpam-3970	228	40	0	0	NUM
ejpam-3970	228	41	∈	∈	PROPN
ejpam-3970	228	42	a	a	DET
ejpam-3970	228	43	⇔	⇔	PROPN
ejpam-3970	228	44	a	a	DET
ejpam-3970	228	45	∈	∈	PROPN
ejpam-3970	228	46	τ0	τ0	NOUN
ejpam-3970	228	47	.	.	PUNCT
ejpam-3970	229	1	thus	thus	ADV
ejpam-3970	229	2	,	,	PUNCT
ejpam-3970	229	3	τl(h	τl(h	NUM
ejpam-3970	229	4	)	)	PUNCT
ejpam-3970	229	5	=	=	SYM
ejpam-3970	229	6	τ0	τ0	NOUN
ejpam-3970	229	7	.	.	PUNCT
ejpam-3970	230	1	for	for	ADP
ejpam-3970	230	2	the	the	DET
ejpam-3970	230	3	converse	converse	NOUN
ejpam-3970	230	4	,	,	PUNCT
ejpam-3970	230	5	suppose	suppose	VERB
ejpam-3970	230	6	that	that	SCONJ
ejpam-3970	230	7	τl(h	τl(h	PUNCT
ejpam-3970	230	8	)	)	PUNCT
ejpam-3970	231	1	=	=	SYM
ejpam-3970	231	2	τ0	τ0	NOUN
ejpam-3970	231	3	and	and	CCONJ
ejpam-3970	231	4	let	let	VERB
ejpam-3970	231	5	x	x	PUNCT
ejpam-3970	231	6	∈	∈	PROPN
ejpam-3970	231	7	h	h	NOUN
ejpam-3970	231	8	\	\	PUNCT
ejpam-3970	231	9	{	{	PUNCT
ejpam-3970	231	10	0	0	NUM
ejpam-3970	231	11	}	}	PUNCT
ejpam-3970	231	12	.	.	PUNCT
ejpam-3970	232	1	then	then	ADV
ejpam-3970	232	2	{	{	PUNCT
ejpam-3970	232	3	0	0	NUM
ejpam-3970	232	4	,	,	PUNCT
ejpam-3970	232	5	x	x	NOUN
ejpam-3970	232	6	}	}	PUNCT
ejpam-3970	232	7	∈	∈	PROPN
ejpam-3970	232	8	τl(h	τl(h	NUM
ejpam-3970	232	9	)	)	PUNCT
ejpam-3970	232	10	.	.	PUNCT
ejpam-3970	233	1	since	since	SCONJ
ejpam-3970	233	2	bl(h	bl(h	NUM
ejpam-3970	233	3	)	)	PUNCT
ejpam-3970	233	4	is	be	AUX
ejpam-3970	233	5	a	a	DET
ejpam-3970	233	6	basis	basis	NOUN
ejpam-3970	233	7	for	for	ADP
ejpam-3970	233	8	τl(h	τl(h	NUM
ejpam-3970	233	9	)	)	PUNCT
ejpam-3970	233	10	,	,	PUNCT
ejpam-3970	233	11	there	there	PRON
ejpam-3970	233	12	exists	exist	VERB
ejpam-3970	233	13	a	a	DET
ejpam-3970	233	14	subset	subset	NOUN
ejpam-3970	233	15	a	a	PRON
ejpam-3970	233	16	of	of	ADP
ejpam-3970	233	17	h	h	NOUN
ejpam-3970	233	18	such	such	ADJ
ejpam-3970	233	19	that	that	SCONJ
ejpam-3970	233	20	x	x	SYM
ejpam-3970	233	21	∈	∈	PROPN
ejpam-3970	233	22	lh(a	lh(a	NOUN
ejpam-3970	233	23	)	)	PUNCT
ejpam-3970	233	24	⊆	⊆	NUM
ejpam-3970	233	25	{	{	PUNCT
ejpam-3970	233	26	0	0	NUM
ejpam-3970	233	27	,	,	PUNCT
ejpam-3970	233	28	x	x	NOUN
ejpam-3970	233	29	}	}	PUNCT
ejpam-3970	233	30	.	.	PUNCT
ejpam-3970	234	1	hence	hence	ADV
ejpam-3970	234	2	,	,	PUNCT
ejpam-3970	234	3	lh(a	lh(a	NUM
ejpam-3970	234	4	)	)	PUNCT
ejpam-3970	234	5	=	=	PRON
ejpam-3970	235	1	{	{	PUNCT
ejpam-3970	235	2	x	x	NOUN
ejpam-3970	235	3	}	}	PUNCT
ejpam-3970	235	4	or	or	CCONJ
ejpam-3970	235	5	lh(a	lh(a	NOUN
ejpam-3970	235	6	)	)	PUNCT
ejpam-3970	236	1	=	=	PUNCT
ejpam-3970	236	2	{	{	PUNCT
ejpam-3970	236	3	0	0	NUM
ejpam-3970	236	4	,	,	PUNCT
ejpam-3970	236	5	x	x	NOUN
ejpam-3970	236	6	}	}	PUNCT
ejpam-3970	236	7	.	.	PUNCT
ejpam-3970	237	1	now	now	ADV
ejpam-3970	237	2	,	,	PUNCT
ejpam-3970	237	3	since	since	SCONJ
ejpam-3970	237	4	0	0	NUM
ejpam-3970	237	5	∈	∈	PROPN
ejpam-3970	237	6	lh(a	lh(a	NOUN
ejpam-3970	237	7	)	)	PUNCT
ejpam-3970	237	8	for	for	ADP
ejpam-3970	237	9	each	each	DET
ejpam-3970	237	10	a	a	DET
ejpam-3970	237	11	∈	∈	PROPN
ejpam-3970	237	12	a	a	PRON
ejpam-3970	237	13	,	,	PUNCT
ejpam-3970	237	14	lh(a	lh(a	NOUN
ejpam-3970	237	15	)	)	PUNCT
ejpam-3970	237	16	=	=	PUNCT
ejpam-3970	237	17	{	{	PUNCT
ejpam-3970	237	18	0	0	NUM
ejpam-3970	237	19	,	,	PUNCT
ejpam-3970	237	20	x	x	NOUN
ejpam-3970	237	21	}	}	PUNCT
ejpam-3970	237	22	.	.	PUNCT
ejpam-3970	238	1	if	if	SCONJ
ejpam-3970	238	2	a	a	DET
ejpam-3970	238	3	=	=	NOUN
ejpam-3970	238	4	∅	∅	NOUN
ejpam-3970	238	5	,	,	PUNCT
ejpam-3970	238	6	then	then	ADV
ejpam-3970	238	7	by	by	ADP
ejpam-3970	238	8	proposition	proposition	NOUN
ejpam-3970	238	9	1(i	1(i	NUM
ejpam-3970	238	10	)	)	PUNCT
ejpam-3970	238	11	,	,	PUNCT
ejpam-3970	238	12	lh(a	lh(a	NOUN
ejpam-3970	238	13	)	)	PUNCT
ejpam-3970	238	14	=	=	SYM
ejpam-3970	238	15	h	h	NOUN
ejpam-3970	238	16	=	=	SYM
ejpam-3970	238	17	{	{	PUNCT
ejpam-3970	238	18	0	0	NUM
ejpam-3970	238	19	,	,	PUNCT
ejpam-3970	238	20	x	x	NOUN
ejpam-3970	238	21	}	}	PUNCT
ejpam-3970	238	22	.	.	PUNCT
ejpam-3970	239	1	hence	hence	ADV
ejpam-3970	239	2	,	,	PUNCT
ejpam-3970	239	3	h	h	NOUN
ejpam-3970	239	4	is	be	AUX
ejpam-3970	239	5	hyperatomic	hyperatomic	ADJ
ejpam-3970	239	6	.	.	PUNCT
ejpam-3970	240	1	if	if	SCONJ
ejpam-3970	240	2	a	a	DET
ejpam-3970	240	3	6=	6=	NUM
ejpam-3970	240	4	∅	∅	NOUN
ejpam-3970	240	5	,	,	PUNCT
ejpam-3970	240	6	then	then	ADV
ejpam-3970	240	7	|a|	|a|	PROPN
ejpam-3970	240	8	=	=	SYM
ejpam-3970	240	9	1	1	NUM
ejpam-3970	240	10	(	(	PUNCT
ejpam-3970	240	11	otherwise	otherwise	ADV
ejpam-3970	240	12	,	,	PUNCT
ejpam-3970	240	13	lh(a	lh(a	NOUN
ejpam-3970	240	14	)	)	PUNCT
ejpam-3970	240	15	=	=	PUNCT
ejpam-3970	240	16	{	{	PUNCT
ejpam-3970	240	17	0	0	NUM
ejpam-3970	240	18	}	}	PUNCT
ejpam-3970	240	19	which	which	PRON
ejpam-3970	240	20	is	be	AUX
ejpam-3970	240	21	a	a	DET
ejpam-3970	240	22	contradiction	contradiction	NOUN
ejpam-3970	240	23	)	)	PUNCT
ejpam-3970	240	24	.	.	PUNCT
ejpam-3970	241	1	therefore	therefore	ADV
ejpam-3970	241	2	,	,	PUNCT
ejpam-3970	241	3	since	since	SCONJ
ejpam-3970	241	4	y	y	PROPN
ejpam-3970	241	5	∈	∈	PROPN
ejpam-3970	241	6	lh(y	lh(y	PUNCT
ejpam-3970	241	7	)	)	PUNCT
ejpam-3970	241	8	for	for	ADP
ejpam-3970	241	9	each	each	DET
ejpam-3970	241	10	y	y	PROPN
ejpam-3970	241	11	∈	∈	PROPN
ejpam-3970	241	12	h	h	NOUN
ejpam-3970	241	13	,	,	PUNCT
ejpam-3970	241	14	a	a	DET
ejpam-3970	241	15	=	=	X
ejpam-3970	241	16	{	{	PUNCT
ejpam-3970	241	17	x	x	NOUN
ejpam-3970	241	18	}	}	PUNCT
ejpam-3970	241	19	,	,	PUNCT
ejpam-3970	241	20	that	that	ADV
ejpam-3970	241	21	is	be	AUX
ejpam-3970	241	22	,	,	PUNCT
ejpam-3970	241	23	lh(a	lh(a	NOUN
ejpam-3970	241	24	)	)	PUNCT
ejpam-3970	241	25	=	=	SYM
ejpam-3970	241	26	lh(x	lh(x	X
ejpam-3970	241	27	)	)	PUNCT
ejpam-3970	241	28	=	=	SYM
ejpam-3970	241	29	{	{	PUNCT
ejpam-3970	241	30	0	0	NUM
ejpam-3970	241	31	,	,	PUNCT
ejpam-3970	241	32	x	x	NOUN
ejpam-3970	241	33	}	}	PUNCT
ejpam-3970	241	34	.	.	PUNCT
ejpam-3970	242	1	this	this	PRON
ejpam-3970	242	2	shows	show	VERB
ejpam-3970	242	3	that	that	SCONJ
ejpam-3970	242	4	h	h	NOUN
ejpam-3970	242	5	is	be	AUX
ejpam-3970	242	6	hyperatomic	hyperatomic	ADJ
ejpam-3970	242	7	.	.	PUNCT
ejpam-3970	243	1	remark	remark	PROPN
ejpam-3970	243	2	1	1	NUM
ejpam-3970	243	3	.	.	PUNCT
ejpam-3970	244	1	the	the	DET
ejpam-3970	244	2	condition	condition	NOUN
ejpam-3970	244	3	lh({x	lh({x	NOUN
ejpam-3970	244	4	,	,	PUNCT
ejpam-3970	244	5	y	y	NOUN
ejpam-3970	244	6	}	}	PUNCT
ejpam-3970	244	7	)	)	PUNCT
ejpam-3970	245	1	=	=	PRON
ejpam-3970	245	2	{	{	PUNCT
ejpam-3970	245	3	0	0	NUM
ejpam-3970	245	4	}	}	PUNCT
ejpam-3970	245	5	for	for	ADP
ejpam-3970	245	6	each	each	DET
ejpam-3970	245	7	pair	pair	NOUN
ejpam-3970	245	8	(	(	PUNCT
ejpam-3970	245	9	x	x	NOUN
ejpam-3970	245	10	,	,	PUNCT
ejpam-3970	245	11	y	y	NOUN
ejpam-3970	245	12	)	)	PUNCT
ejpam-3970	245	13	∈	∈	PROPN
ejpam-3970	245	14	h	h	NOUN
ejpam-3970	245	15	×h	×h	PROPN
ejpam-3970	245	16	,	,	PUNCT
ejpam-3970	245	17	where	where	SCONJ
ejpam-3970	245	18	x	x	PUNCT
ejpam-3970	245	19	6=	6=	PROPN
ejpam-3970	245	20	y	y	PROPN
ejpam-3970	245	21	,	,	PUNCT
ejpam-3970	245	22	can	can	AUX
ejpam-3970	245	23	not	not	PART
ejpam-3970	245	24	be	be	AUX
ejpam-3970	245	25	omitted	omit	VERB
ejpam-3970	245	26	.	.	PUNCT
ejpam-3970	246	1	the	the	DET
ejpam-3970	246	2	hyper	hyper	ADJ
ejpam-3970	246	3	bci	bci	NOUN
ejpam-3970	246	4	-	-	NOUN
ejpam-3970	246	5	algebra	algebra	NOUN
ejpam-3970	246	6	in	in	ADP
ejpam-3970	246	7	example	example	NOUN
ejpam-3970	246	8	2	2	NUM
ejpam-3970	246	9	is	be	AUX
ejpam-3970	246	10	hyperatomic	hyperatomic	ADJ
ejpam-3970	246	11	but	but	CCONJ
ejpam-3970	246	12	does	do	AUX
ejpam-3970	246	13	not	not	PART
ejpam-3970	246	14	satisfy	satisfy	VERB
ejpam-3970	246	15	this	this	DET
ejpam-3970	246	16	condition	condition	NOUN
ejpam-3970	246	17	.	.	PUNCT
ejpam-3970	247	1	hence	hence	ADV
ejpam-3970	247	2	,	,	PUNCT
ejpam-3970	247	3	τl(h	τl(h	PUNCT
ejpam-3970	247	4	)	)	PUNCT
ejpam-3970	247	5	6=	6=	ADP
ejpam-3970	248	1	τ0	τ0	NOUN
ejpam-3970	248	2	.	.	PUNCT
ejpam-3970	249	1	theorem	theorem	ADJ
ejpam-3970	249	2	8	8	NUM
ejpam-3970	249	3	.	.	PUNCT
ejpam-3970	250	1	let	let	VERB
ejpam-3970	250	2	h	h	PRON
ejpam-3970	250	3	be	be	AUX
ejpam-3970	250	4	a	a	DET
ejpam-3970	250	5	hyperatomic	hyperatomic	ADJ
ejpam-3970	250	6	hyper	hyper	ADJ
ejpam-3970	250	7	bci	bci	NOUN
ejpam-3970	250	8	-	-	NOUN
ejpam-3970	250	9	algebra	algebra	NOUN
ejpam-3970	250	10	and	and	CCONJ
ejpam-3970	250	11	let	let	VERB
ejpam-3970	250	12	a	a	PRON
ejpam-3970	250	13	,	,	PUNCT
ejpam-3970	250	14	f	f	PROPN
ejpam-3970	250	15	⊆	⊆	NUM
ejpam-3970	250	16	h.	h.	PROPN
ejpam-3970	250	17	then	then	ADV
ejpam-3970	250	18	with	with	ADP
ejpam-3970	250	19	respect	respect	NOUN
ejpam-3970	250	20	to	to	ADP
ejpam-3970	250	21	τl(h	τl(h	NUM
ejpam-3970	250	22	)	)	PUNCT
ejpam-3970	250	23	,	,	PUNCT
ejpam-3970	251	1	(	(	PUNCT
ejpam-3970	251	2	i	i	NOUN
ejpam-3970	251	3	)	)	PUNCT
ejpam-3970	251	4	int(a	int(a	PROPN
ejpam-3970	251	5	)	)	PUNCT
ejpam-3970	252	1	=	=	PUNCT
ejpam-3970	253	1			PRON
ejpam-3970	253	2	a	a	PRON
ejpam-3970	253	3	if	if	SCONJ
ejpam-3970	253	4	a	a	DET
ejpam-3970	253	5	=	=	NOUN
ejpam-3970	253	6	∅	∅	NOUN
ejpam-3970	253	7	or	or	CCONJ
ejpam-3970	253	8	0	0	NUM
ejpam-3970	253	9	∈	∈	PROPN
ejpam-3970	253	10	a	a	PRON
ejpam-3970	253	11	or	or	CCONJ
ejpam-3970	253	12	0	0	NUM
ejpam-3970	253	13	/∈	/∈	SYM
ejpam-3970	253	14	lh(a	lh(a	NOUN
ejpam-3970	253	15	)	)	PUNCT
ejpam-3970	253	16	∀	∀	X
ejpam-3970	254	1	a	a	DET
ejpam-3970	254	2	∈	∈	PROPN
ejpam-3970	254	3	a	a	PRON
ejpam-3970	254	4	,	,	PUNCT
ejpam-3970	254	5	a	a	DET
ejpam-3970	254	6	\	\	NOUN
ejpam-3970	254	7	{	{	PUNCT
ejpam-3970	254	8	a	a	PRON
ejpam-3970	254	9	∈	∈	PROPN
ejpam-3970	254	10	a	a	DET
ejpam-3970	254	11	:	:	SYM
ejpam-3970	254	12	0	0	NUM
ejpam-3970	254	13	∈	∈	PROPN
ejpam-3970	254	14	lh(a	lh(a	NOUN
ejpam-3970	254	15	)	)	PUNCT
ejpam-3970	254	16	}	}	PUNCT
ejpam-3970	254	17	otherwise	otherwise	ADV
ejpam-3970	254	18	;	;	PUNCT
ejpam-3970	254	19	and	and	CCONJ
ejpam-3970	254	20	(	(	PUNCT
ejpam-3970	254	21	ii	ii	NOUN
ejpam-3970	254	22	)	)	PUNCT
ejpam-3970	254	23	f	f	NOUN
ejpam-3970	255	1	=	=	PUNCT
ejpam-3970	255	2			NOUN
ejpam-3970	255	3	f	f	NOUN
ejpam-3970	256	1	if	if	SCONJ
ejpam-3970	256	2	0	0	NUM
ejpam-3970	256	3	∈	∈	PROPN
ejpam-3970	256	4	f	f	PROPN
ejpam-3970	256	5	and	and	CCONJ
ejpam-3970	256	6	0	0	NUM
ejpam-3970	256	7	/∈	/∈	INTJ
ejpam-3970	256	8	lh(x	lh(x	PUNCT
ejpam-3970	256	9	)	)	PUNCT
ejpam-3970	256	10	∀x	∀x	VERB
ejpam-3970	256	11	∈	∈	PROPN
ejpam-3970	256	12	h	h	NOUN
ejpam-3970	256	13	\	\	NOUN
ejpam-3970	256	14	f	f	PROPN
ejpam-3970	256	15	or	or	CCONJ
ejpam-3970	256	16	0	0	NUM
ejpam-3970	256	17	/∈	/∈	PUNCT
ejpam-3970	257	1	f	f	X
ejpam-3970	257	2	,	,	PUNCT
ejpam-3970	257	3	f	f	PROPN
ejpam-3970	257	4	∪	∪	X
ejpam-3970	257	5	{	{	PUNCT
ejpam-3970	257	6	x	x	SYM
ejpam-3970	257	7	∈	∈	PROPN
ejpam-3970	257	8	h	h	NOUN
ejpam-3970	257	9	\	\	NOUN
ejpam-3970	258	1	f	f	PROPN
ejpam-3970	258	2	:	:	PUNCT
ejpam-3970	258	3	0	0	NUM
ejpam-3970	258	4	∈	∈	NOUN
ejpam-3970	258	5	lh(x	lh(x	NOUN
ejpam-3970	258	6	)	)	PUNCT
ejpam-3970	258	7	}	}	PUNCT
ejpam-3970	258	8	otherwise	otherwise	ADV
ejpam-3970	258	9	.	.	PUNCT
ejpam-3970	259	1	m.	m.	NOUN
ejpam-3970	259	2	panganduyon	panganduyon	NOUN
ejpam-3970	259	3	,	,	PUNCT
ejpam-3970	259	4	s.	s.	PROPN
ejpam-3970	259	5	canoy	canoy	PROPN
ejpam-3970	259	6	,	,	PUNCT
ejpam-3970	259	7	jr	jr	PROPN
ejpam-3970	259	8	.	.	PROPN
ejpam-3970	259	9	,	,	PUNCT
ejpam-3970	259	10	b.	b.	PROPN
ejpam-3970	259	11	davvaz	davvaz	PROPN
ejpam-3970	259	12	/	/	SYM
ejpam-3970	259	13	eur	eur	PROPN
ejpam-3970	259	14	.	.	PUNCT
ejpam-3970	260	1	j.	j.	PROPN
ejpam-3970	260	2	pure	pure	PROPN
ejpam-3970	260	3	appl	appl	PROPN
ejpam-3970	260	4	.	.	PROPN
ejpam-3970	260	5	math	math	PROPN
ejpam-3970	260	6	,	,	PUNCT
ejpam-3970	260	7	14	14	NUM
ejpam-3970	260	8	(	(	PUNCT
ejpam-3970	260	9	2	2	NUM
ejpam-3970	260	10	)	)	PUNCT
ejpam-3970	260	11	(	(	PUNCT
ejpam-3970	260	12	2021	2021	NUM
ejpam-3970	260	13	)	)	PUNCT
ejpam-3970	260	14	,	,	PUNCT
ejpam-3970	260	15	590	590	NUM
ejpam-3970	260	16	-	-	SYM
ejpam-3970	260	17	600	600	NUM
ejpam-3970	260	18	597	597	NUM
ejpam-3970	260	19	proof	proof	NOUN
ejpam-3970	260	20	.	.	PUNCT
ejpam-3970	261	1	(	(	PUNCT
ejpam-3970	261	2	i	i	NOUN
ejpam-3970	261	3	)	)	PUNCT
ejpam-3970	261	4	if	if	SCONJ
ejpam-3970	261	5	a	a	DET
ejpam-3970	261	6	=	=	NOUN
ejpam-3970	261	7	∅	∅	NOUN
ejpam-3970	261	8	or	or	CCONJ
ejpam-3970	261	9	0	0	NUM
ejpam-3970	261	10	∈	∈	PROPN
ejpam-3970	261	11	a	a	PRON
ejpam-3970	261	12	or	or	CCONJ
ejpam-3970	261	13	0	0	NUM
ejpam-3970	261	14	/∈	/∈	SYM
ejpam-3970	261	15	lh(a	lh(a	NOUN
ejpam-3970	261	16	)	)	PUNCT
ejpam-3970	261	17	for	for	ADP
ejpam-3970	261	18	all	all	DET
ejpam-3970	261	19	a	a	DET
ejpam-3970	261	20	∈	∈	PROPN
ejpam-3970	261	21	a	a	PRON
ejpam-3970	261	22	,	,	PUNCT
ejpam-3970	261	23	then	then	ADV
ejpam-3970	261	24	a	a	DET
ejpam-3970	261	25	∈	∈	NOUN
ejpam-3970	261	26	τl(h	τl(h	NUM
ejpam-3970	261	27	)	)	PUNCT
ejpam-3970	261	28	by	by	ADP
ejpam-3970	261	29	theorem	theorem	NOUN
ejpam-3970	261	30	6	6	NUM
ejpam-3970	261	31	.	.	PUNCT
ejpam-3970	261	32	thus	thus	ADV
ejpam-3970	261	33	,	,	PUNCT
ejpam-3970	261	34	inta	inta	PROPN
ejpam-3970	261	35	=	=	SYM
ejpam-3970	261	36	a.	a.	NOUN
ejpam-3970	261	37	now	now	ADV
ejpam-3970	261	38	,	,	PUNCT
ejpam-3970	261	39	suppose	suppose	VERB
ejpam-3970	261	40	a	a	DET
ejpam-3970	261	41	/∈	/∈	NOUN
ejpam-3970	261	42	τl(h	τl(h	NUM
ejpam-3970	261	43	)	)	PUNCT
ejpam-3970	261	44	.	.	PUNCT
ejpam-3970	262	1	then	then	ADV
ejpam-3970	262	2	a	a	DET
ejpam-3970	262	3	6=	6=	NUM
ejpam-3970	262	4	∅	∅	NOUN
ejpam-3970	262	5	,	,	PUNCT
ejpam-3970	262	6	0	0	NUM
ejpam-3970	262	7	/∈	/∈	INTJ
ejpam-3970	262	8	a	a	PRON
ejpam-3970	262	9	,	,	PUNCT
ejpam-3970	262	10	and	and	CCONJ
ejpam-3970	262	11	there	there	PRON
ejpam-3970	262	12	exists	exist	VERB
ejpam-3970	262	13	a	a	DET
ejpam-3970	262	14	∈	∈	NOUN
ejpam-3970	262	15	a	a	DET
ejpam-3970	262	16	such	such	ADJ
ejpam-3970	262	17	that	that	DET
ejpam-3970	262	18	0	0	NUM
ejpam-3970	262	19	∈	∈	PROPN
ejpam-3970	262	20	lh(a	lh(a	NOUN
ejpam-3970	262	21	)	)	PUNCT
ejpam-3970	262	22	by	by	ADP
ejpam-3970	262	23	theorem	theorem	NOUN
ejpam-3970	262	24	6	6	NUM
ejpam-3970	262	25	.	.	PUNCT
ejpam-3970	263	1	let	let	VERB
ejpam-3970	263	2	ba	ba	PROPN
ejpam-3970	263	3	=	=	PUNCT
ejpam-3970	263	4	a	a	PRON
ejpam-3970	263	5	\	\	NOUN
ejpam-3970	263	6	{	{	PUNCT
ejpam-3970	263	7	x	x	PUNCT
ejpam-3970	263	8	∈	∈	PROPN
ejpam-3970	263	9	a	a	DET
ejpam-3970	263	10	:	:	SYM
ejpam-3970	263	11	0	0	NUM
ejpam-3970	263	12	∈	∈	NOUN
ejpam-3970	263	13	lh(x	lh(x	NOUN
ejpam-3970	263	14	)	)	PUNCT
ejpam-3970	263	15	}	}	PUNCT
ejpam-3970	263	16	.	.	PUNCT
ejpam-3970	264	1	clearly	clearly	ADV
ejpam-3970	264	2	,	,	PUNCT
ejpam-3970	264	3	ba	ba	PROPN
ejpam-3970	264	4	(	(	PUNCT
ejpam-3970	264	5	a.	a.	NOUN
ejpam-3970	264	6	let	let	VERB
ejpam-3970	264	7	z	z	PROPN
ejpam-3970	264	8	∈	∈	PROPN
ejpam-3970	264	9	ba	ba	PROPN
ejpam-3970	264	10	.	.	PUNCT
ejpam-3970	265	1	then	then	ADV
ejpam-3970	265	2	0	0	NUM
ejpam-3970	265	3	/∈	/∈	PUNCT
ejpam-3970	265	4	lh(z	lh(z	PROPN
ejpam-3970	265	5	)	)	PUNCT
ejpam-3970	265	6	.	.	PUNCT
ejpam-3970	266	1	by	by	ADP
ejpam-3970	266	2	theorem	theorem	NOUN
ejpam-3970	266	3	6	6	NUM
ejpam-3970	266	4	,	,	PUNCT
ejpam-3970	266	5	ba	ba	PROPN
ejpam-3970	266	6	∈	∈	PROPN
ejpam-3970	266	7	τl(h	τl(h	NUM
ejpam-3970	266	8	)	)	PUNCT
ejpam-3970	266	9	.	.	PUNCT
ejpam-3970	267	1	next	next	ADV
ejpam-3970	267	2	,	,	PUNCT
ejpam-3970	267	3	let	let	VERB
ejpam-3970	267	4	g	g	PROPN
ejpam-3970	267	5	∈	∈	PROPN
ejpam-3970	267	6	τl(h	τl(h	PUNCT
ejpam-3970	267	7	)	)	PUNCT
ejpam-3970	267	8	such	such	ADJ
ejpam-3970	267	9	that	that	SCONJ
ejpam-3970	267	10	g	g	PROPN
ejpam-3970	267	11	⊆	⊆	NUM
ejpam-3970	267	12	a	a	PRON
ejpam-3970	267	13	and	and	CCONJ
ejpam-3970	267	14	let	let	VERB
ejpam-3970	267	15	v	v	NUM
ejpam-3970	267	16	∈	∈	PROPN
ejpam-3970	267	17	g.	g.	NOUN
ejpam-3970	267	18	since	since	SCONJ
ejpam-3970	267	19	0	0	NUM
ejpam-3970	267	20	/∈	/∈	PROPN
ejpam-3970	267	21	a	a	PRON
ejpam-3970	267	22	,	,	PUNCT
ejpam-3970	267	23	0	0	NUM
ejpam-3970	267	24	/∈	/∈	PUNCT
ejpam-3970	268	1	g.	g.	PROPN
ejpam-3970	268	2	hence	hence	ADV
ejpam-3970	268	3	,	,	PUNCT
ejpam-3970	268	4	by	by	ADP
ejpam-3970	268	5	theorem	theorem	NOUN
ejpam-3970	268	6	6	6	NUM
ejpam-3970	268	7	,	,	PUNCT
ejpam-3970	268	8	0	0	NUM
ejpam-3970	268	9	/∈	/∈	PUNCT
ejpam-3970	268	10	lh(v	lh(v	PROPN
ejpam-3970	268	11	)	)	PUNCT
ejpam-3970	268	12	,	,	PUNCT
ejpam-3970	268	13	that	that	ADV
ejpam-3970	268	14	is	is	ADV
ejpam-3970	268	15	,	,	PUNCT
ejpam-3970	268	16	v	v	PROPN
ejpam-3970	268	17	∈	∈	PROPN
ejpam-3970	268	18	ba	ba	PROPN
ejpam-3970	268	19	.	.	PUNCT
ejpam-3970	269	1	therefore	therefore	ADV
ejpam-3970	269	2	,	,	PUNCT
ejpam-3970	269	3	inta	inta	PROPN
ejpam-3970	269	4	=	=	SYM
ejpam-3970	269	5	ba	ba	PROPN
ejpam-3970	269	6	.	.	PUNCT
ejpam-3970	269	7	(	(	PUNCT
ejpam-3970	269	8	ii	ii	NOUN
ejpam-3970	269	9	)	)	PUNCT
ejpam-3970	269	10	suppose	suppose	VERB
ejpam-3970	269	11	first	first	ADV
ejpam-3970	269	12	that	that	SCONJ
ejpam-3970	269	13	0	0	NUM
ejpam-3970	270	1	/∈	/∈	NUM
ejpam-3970	271	1	f	f	PROPN
ejpam-3970	271	2	.	.	PUNCT
ejpam-3970	272	1	then	then	ADV
ejpam-3970	272	2	0	0	NUM
ejpam-3970	272	3	∈	∈	PROPN
ejpam-3970	272	4	h	h	NOUN
ejpam-3970	272	5	\	\	NOUN
ejpam-3970	273	1	f	f	PROPN
ejpam-3970	273	2	=	=	SYM
ejpam-3970	273	3	f	f	PROPN
ejpam-3970	273	4	c	c	NOUN
ejpam-3970	273	5	;	;	PUNCT
ejpam-3970	273	6	hence	hence	ADV
ejpam-3970	273	7	f	f	PROPN
ejpam-3970	273	8	c	c	PROPN
ejpam-3970	273	9	∈	∈	PROPN
ejpam-3970	273	10	τl(h	τl(h	NUM
ejpam-3970	273	11	)	)	PUNCT
ejpam-3970	273	12	by	by	ADP
ejpam-3970	273	13	theorem	theorem	NOUN
ejpam-3970	273	14	6	6	NUM
ejpam-3970	273	15	.	.	PUNCT
ejpam-3970	274	1	if	if	SCONJ
ejpam-3970	274	2	0	0	NUM
ejpam-3970	274	3	∈	∈	PROPN
ejpam-3970	274	4	f	f	PROPN
ejpam-3970	274	5	and	and	CCONJ
ejpam-3970	274	6	0	0	NUM
ejpam-3970	274	7	/∈	/∈	INTJ
ejpam-3970	274	8	lh(x	lh(x	NOUN
ejpam-3970	274	9	)	)	PUNCT
ejpam-3970	274	10	for	for	ADP
ejpam-3970	274	11	all	all	DET
ejpam-3970	274	12	x	x	SYM
ejpam-3970	274	13	∈	∈	PROPN
ejpam-3970	274	14	f	f	NOUN
ejpam-3970	274	15	c	c	NOUN
ejpam-3970	274	16	,	,	PUNCT
ejpam-3970	274	17	then	then	ADV
ejpam-3970	274	18	by	by	ADP
ejpam-3970	274	19	theorem	theorem	NOUN
ejpam-3970	274	20	6	6	NUM
ejpam-3970	274	21	,	,	PUNCT
ejpam-3970	274	22	f	f	PROPN
ejpam-3970	274	23	c	c	NOUN
ejpam-3970	274	24	∈	∈	PROPN
ejpam-3970	274	25	τl(h	τl(h	NUM
ejpam-3970	274	26	)	)	PUNCT
ejpam-3970	274	27	.	.	PUNCT
ejpam-3970	275	1	thus	thus	ADV
ejpam-3970	275	2	,	,	PUNCT
ejpam-3970	275	3	in	in	ADP
ejpam-3970	275	4	both	both	DET
ejpam-3970	275	5	cases	case	NOUN
ejpam-3970	275	6	,	,	PUNCT
ejpam-3970	275	7	f	f	PROPN
ejpam-3970	275	8	is	be	AUX
ejpam-3970	275	9	a	a	DET
ejpam-3970	275	10	τl(h)-closed	τl(h)-close	VERB
ejpam-3970	275	11	set	set	NOUN
ejpam-3970	275	12	.	.	PUNCT
ejpam-3970	276	1	therefore	therefore	ADV
ejpam-3970	276	2	,	,	PUNCT
ejpam-3970	276	3	f	f	PROPN
ejpam-3970	276	4	=	=	SYM
ejpam-3970	276	5	f	f	PROPN
ejpam-3970	276	6	.	.	PUNCT
ejpam-3970	277	1	next	next	ADV
ejpam-3970	277	2	,	,	PUNCT
ejpam-3970	277	3	suppose	suppose	VERB
ejpam-3970	277	4	that	that	SCONJ
ejpam-3970	277	5	0	0	NUM
ejpam-3970	277	6	∈	∈	PROPN
ejpam-3970	277	7	f	f	NOUN
ejpam-3970	277	8	and	and	CCONJ
ejpam-3970	277	9	there	there	PRON
ejpam-3970	277	10	exists	exist	VERB
ejpam-3970	277	11	x	x	X
ejpam-3970	277	12	∈	∈	NOUN
ejpam-3970	277	13	h	h	NOUN
ejpam-3970	277	14	\	\	NOUN
ejpam-3970	277	15	f	f	PROPN
ejpam-3970	277	16	such	such	ADJ
ejpam-3970	277	17	that	that	DET
ejpam-3970	277	18	0	0	NUM
ejpam-3970	277	19	∈	∈	PROPN
ejpam-3970	277	20	lh(x	lh(x	NOUN
ejpam-3970	277	21	)	)	PUNCT
ejpam-3970	277	22	.	.	PUNCT
ejpam-3970	278	1	let	let	VERB
ejpam-3970	278	2	q	q	NOUN
ejpam-3970	279	1	=	=	PUNCT
ejpam-3970	279	2	f	f	X
ejpam-3970	279	3	∪	∪	X
ejpam-3970	279	4	{	{	PUNCT
ejpam-3970	279	5	z	z	PROPN
ejpam-3970	279	6	∈	∈	PROPN
ejpam-3970	279	7	h	h	NOUN
ejpam-3970	279	8	\	\	NOUN
ejpam-3970	279	9	f	f	PROPN
ejpam-3970	279	10	:	:	PUNCT
ejpam-3970	279	11	0	0	NUM
ejpam-3970	279	12	∈	∈	PROPN
ejpam-3970	279	13	lh(z	lh(z	NOUN
ejpam-3970	279	14	)	)	PUNCT
ejpam-3970	279	15	}	}	PUNCT
ejpam-3970	279	16	and	and	CCONJ
ejpam-3970	279	17	let	let	VERB
ejpam-3970	279	18	q	q	PROPN
ejpam-3970	279	19	∈	∈	PROPN
ejpam-3970	279	20	qc	qc	PROPN
ejpam-3970	279	21	.	.	PUNCT
ejpam-3970	280	1	then	then	ADV
ejpam-3970	280	2	0	0	NUM
ejpam-3970	280	3	/∈	/∈	SYM
ejpam-3970	280	4	qc	qc	PROPN
ejpam-3970	280	5	and	and	CCONJ
ejpam-3970	280	6	0	0	NUM
ejpam-3970	280	7	/∈	/∈	INTJ
ejpam-3970	280	8	lh(q	lh(q	NUM
ejpam-3970	280	9	)	)	PUNCT
ejpam-3970	280	10	.	.	PUNCT
ejpam-3970	281	1	by	by	ADP
ejpam-3970	281	2	theorem	theorem	NOUN
ejpam-3970	281	3	6	6	NUM
ejpam-3970	281	4	,	,	PUNCT
ejpam-3970	281	5	qc	qc	PROPN
ejpam-3970	281	6	∈	∈	PROPN
ejpam-3970	281	7	τl(h	τl(h	NUM
ejpam-3970	281	8	)	)	PUNCT
ejpam-3970	281	9	,	,	PUNCT
ejpam-3970	281	10	that	that	ADV
ejpam-3970	281	11	is	is	ADV
ejpam-3970	281	12	,	,	PUNCT
ejpam-3970	281	13	q	q	X
ejpam-3970	281	14	is	be	AUX
ejpam-3970	281	15	τl(h)-closed	τl(h)-close	VERB
ejpam-3970	281	16	.	.	PUNCT
ejpam-3970	282	1	now	now	ADV
ejpam-3970	282	2	,	,	PUNCT
ejpam-3970	282	3	let	let	VERB
ejpam-3970	282	4	w	w	NOUN
ejpam-3970	282	5	∈	∈	PROPN
ejpam-3970	282	6	h	h	NOUN
ejpam-3970	282	7	\	\	NOUN
ejpam-3970	282	8	f	f	PROPN
ejpam-3970	282	9	such	such	ADJ
ejpam-3970	282	10	that	that	DET
ejpam-3970	282	11	0	0	NUM
ejpam-3970	282	12	/∈	/∈	SYM
ejpam-3970	282	13	lh(w	lh(w	PROPN
ejpam-3970	282	14	)	)	PUNCT
ejpam-3970	282	15	.	.	PUNCT
ejpam-3970	283	1	then	then	ADV
ejpam-3970	283	2	lh(w	lh(w	NOUN
ejpam-3970	283	3	)	)	PUNCT
ejpam-3970	283	4	=	=	PRON
ejpam-3970	283	5	{	{	PUNCT
ejpam-3970	283	6	w	w	NOUN
ejpam-3970	283	7	}	}	PUNCT
ejpam-3970	283	8	is	be	AUX
ejpam-3970	283	9	a	a	DET
ejpam-3970	283	10	neighborhood	neighborhood	NOUN
ejpam-3970	283	11	of	of	ADP
ejpam-3970	283	12	w	w	NOUN
ejpam-3970	283	13	with	with	ADP
ejpam-3970	283	14	lh(w)∩f	lh(w)∩f	PROPN
ejpam-3970	283	15	=	=	X
ejpam-3970	283	16	∅.	∅.	NOUN
ejpam-3970	283	17	thus	thus	ADV
ejpam-3970	283	18	,	,	PUNCT
ejpam-3970	283	19	w	w	PROPN
ejpam-3970	283	20	/∈	/∈	PROPN
ejpam-3970	284	1	f	f	PROPN
ejpam-3970	284	2	.	.	PUNCT
ejpam-3970	285	1	therefore	therefore	ADV
ejpam-3970	285	2	,	,	PUNCT
ejpam-3970	285	3	the	the	DET
ejpam-3970	285	4	smallest	small	ADJ
ejpam-3970	285	5	closed	closed	ADJ
ejpam-3970	285	6	set	set	NOUN
ejpam-3970	285	7	containing	contain	VERB
ejpam-3970	285	8	f	f	PROPN
ejpam-3970	285	9	is	be	AUX
ejpam-3970	285	10	q	q	ADJ
ejpam-3970	285	11	,	,	PUNCT
ejpam-3970	285	12	that	that	ADV
ejpam-3970	285	13	is	is	ADV
ejpam-3970	285	14	,	,	PUNCT
ejpam-3970	285	15	f	f	PROPN
ejpam-3970	285	16	=	=	SYM
ejpam-3970	285	17	q.	q.	PROPN
ejpam-3970	285	18	theorem	theorem	VERB
ejpam-3970	285	19	9	9	NUM
ejpam-3970	285	20	.	.	PUNCT
ejpam-3970	286	1	let	let	VERB
ejpam-3970	286	2	h	h	PRON
ejpam-3970	286	3	be	be	AUX
ejpam-3970	286	4	a	a	DET
ejpam-3970	286	5	hyper	hyper	ADJ
ejpam-3970	286	6	bci	bci	NOUN
ejpam-3970	286	7	-	-	NOUN
ejpam-3970	286	8	algebra	algebra	NOUN
ejpam-3970	286	9	and	and	CCONJ
ejpam-3970	286	10	let	let	VERB
ejpam-3970	286	11	d	d	PROPN
ejpam-3970	286	12	(	(	PUNCT
ejpam-3970	286	13	h.	h.	PROPN
ejpam-3970	286	14	(	(	PUNCT
ejpam-3970	286	15	i	i	NOUN
ejpam-3970	286	16	)	)	PUNCT
ejpam-3970	287	1	if	if	SCONJ
ejpam-3970	287	2	0	0	NUM
ejpam-3970	287	3	∈	∈	PROPN
ejpam-3970	287	4	lh(x	lh(x	NOUN
ejpam-3970	287	5	)	)	PUNCT
ejpam-3970	287	6	for	for	ADP
ejpam-3970	287	7	all	all	DET
ejpam-3970	287	8	x	x	SYM
ejpam-3970	287	9	∈	∈	PROPN
ejpam-3970	287	10	h	h	NOUN
ejpam-3970	287	11	,	,	PUNCT
ejpam-3970	287	12	then	then	ADV
ejpam-3970	287	13	d	d	PROPN
ejpam-3970	287	14	is	be	AUX
ejpam-3970	287	15	dense	dense	ADJ
ejpam-3970	287	16	in	in	ADP
ejpam-3970	287	17	h	h	NOUN
ejpam-3970	287	18	if	if	SCONJ
ejpam-3970	288	1	and	and	CCONJ
ejpam-3970	288	2	only	only	ADV
ejpam-3970	288	3	if	if	SCONJ
ejpam-3970	288	4	0	0	NUM
ejpam-3970	288	5	∈	∈	PROPN
ejpam-3970	288	6	d.	d.	PROPN
ejpam-3970	288	7	(	(	PUNCT
ejpam-3970	288	8	ii	ii	PROPN
ejpam-3970	288	9	)	)	PUNCT
ejpam-3970	288	10	if	if	SCONJ
ejpam-3970	288	11	h	h	NOUN
ejpam-3970	288	12	is	be	AUX
ejpam-3970	288	13	hyperatomic	hyperatomic	ADJ
ejpam-3970	288	14	,	,	PUNCT
ejpam-3970	288	15	then	then	ADV
ejpam-3970	288	16	d	d	PROPN
ejpam-3970	288	17	is	be	AUX
ejpam-3970	288	18	dense	dense	ADJ
ejpam-3970	288	19	if	if	SCONJ
ejpam-3970	288	20	and	and	CCONJ
ejpam-3970	288	21	only	only	ADV
ejpam-3970	288	22	if	if	SCONJ
ejpam-3970	288	23	0	0	NUM
ejpam-3970	288	24	∈	∈	PROPN
ejpam-3970	288	25	d	d	NOUN
ejpam-3970	288	26	and	and	CCONJ
ejpam-3970	288	27	0	0	NUM
ejpam-3970	288	28	∈	∈	NOUN
ejpam-3970	288	29	lh(x	lh(x	NOUN
ejpam-3970	288	30	)	)	PUNCT
ejpam-3970	288	31	for	for	ADP
ejpam-3970	288	32	all	all	PRON
ejpam-3970	288	33	x	x	SYM
ejpam-3970	288	34	∈	∈	PROPN
ejpam-3970	288	35	h	h	PROPN
ejpam-3970	288	36	\d	\d	NOUN
ejpam-3970	288	37	.	.	PUNCT
ejpam-3970	289	1	proof	proof	NOUN
ejpam-3970	289	2	.	.	PUNCT
ejpam-3970	290	1	(	(	PUNCT
ejpam-3970	290	2	i	i	NOUN
ejpam-3970	290	3	)	)	PUNCT
ejpam-3970	290	4	if	if	SCONJ
ejpam-3970	290	5	d	d	NOUN
ejpam-3970	290	6	is	be	AUX
ejpam-3970	290	7	dense	dense	ADJ
ejpam-3970	290	8	in	in	ADP
ejpam-3970	290	9	h	h	NOUN
ejpam-3970	290	10	,	,	PUNCT
ejpam-3970	290	11	then	then	ADV
ejpam-3970	290	12	lh(0	lh(0	NOUN
ejpam-3970	290	13	)	)	PUNCT
ejpam-3970	290	14	∩d	∩d	VERB
ejpam-3970	290	15	6=	6=	ADP
ejpam-3970	290	16	∅.	∅.	ADP
ejpam-3970	290	17	hence	hence	ADV
ejpam-3970	290	18	,	,	PUNCT
ejpam-3970	290	19	0	0	NUM
ejpam-3970	290	20	∈	∈	PROPN
ejpam-3970	290	21	d.	d.	NOUN
ejpam-3970	290	22	next	next	ADV
ejpam-3970	290	23	,	,	PUNCT
ejpam-3970	290	24	suppose	suppose	VERB
ejpam-3970	290	25	that	that	SCONJ
ejpam-3970	290	26	0	0	NUM
ejpam-3970	290	27	∈	∈	PROPN
ejpam-3970	290	28	d	d	NOUN
ejpam-3970	290	29	and	and	CCONJ
ejpam-3970	290	30	a	a	DET
ejpam-3970	290	31	⊆	⊆	NUM
ejpam-3970	290	32	h	h	NOUN
ejpam-3970	290	33	with	with	ADP
ejpam-3970	290	34	lh(a	lh(a	NOUN
ejpam-3970	290	35	)	)	PUNCT
ejpam-3970	290	36	6=	6=	ADP
ejpam-3970	290	37	∅.	∅.	ADP
ejpam-3970	290	38	since	since	SCONJ
ejpam-3970	290	39	0	0	NUM
ejpam-3970	290	40	∈	∈	PROPN
ejpam-3970	290	41	lh(a	lh(a	NOUN
ejpam-3970	290	42	)	)	PUNCT
ejpam-3970	290	43	for	for	ADP
ejpam-3970	290	44	all	all	DET
ejpam-3970	290	45	a	a	DET
ejpam-3970	290	46	∈	∈	PROPN
ejpam-3970	290	47	a	a	DET
ejpam-3970	290	48	,	,	PUNCT
ejpam-3970	290	49	0	0	NUM
ejpam-3970	290	50	∈	∈	PROPN
ejpam-3970	290	51	lh(a	lh(a	NOUN
ejpam-3970	290	52	)	)	PUNCT
ejpam-3970	290	53	.	.	PUNCT
ejpam-3970	291	1	thus	thus	ADV
ejpam-3970	291	2	,	,	PUNCT
ejpam-3970	291	3	lh(a	lh(a	NOUN
ejpam-3970	291	4	)	)	PUNCT
ejpam-3970	291	5	∩d	∩d	VERB
ejpam-3970	291	6	6=	6=	ADP
ejpam-3970	291	7	∅.	∅.	VERB
ejpam-3970	291	8	therefore	therefore	ADV
ejpam-3970	291	9	,	,	PUNCT
ejpam-3970	291	10	d	d	PROPN
ejpam-3970	291	11	is	be	AUX
ejpam-3970	291	12	dense	dense	ADJ
ejpam-3970	291	13	in	in	ADP
ejpam-3970	291	14	h.	h.	PROPN
ejpam-3970	291	15	(	(	PUNCT
ejpam-3970	291	16	ii	ii	NOUN
ejpam-3970	291	17	)	)	PUNCT
ejpam-3970	291	18	suppose	suppose	VERB
ejpam-3970	291	19	d	d	NOUN
ejpam-3970	291	20	is	be	AUX
ejpam-3970	291	21	dense	dense	ADJ
ejpam-3970	291	22	in	in	ADP
ejpam-3970	291	23	h.	h.	PROPN
ejpam-3970	291	24	then	then	ADV
ejpam-3970	291	25	0	0	NUM
ejpam-3970	291	26	∈	∈	PROPN
ejpam-3970	291	27	d.	d.	NOUN
ejpam-3970	291	28	since	since	SCONJ
ejpam-3970	291	29	d	d	PROPN
ejpam-3970	291	30	6=	6=	PROPN
ejpam-3970	291	31	h	h	PROPN
ejpam-3970	291	32	,	,	PUNCT
ejpam-3970	291	33	d	d	PRON
ejpam-3970	291	34	is	be	AUX
ejpam-3970	291	35	not	not	PART
ejpam-3970	291	36	τl(h)-closed	τl(h)-close	VERB
ejpam-3970	291	37	(	(	PUNCT
ejpam-3970	292	1	otherwise	otherwise	ADV
ejpam-3970	292	2	,	,	PUNCT
ejpam-3970	292	3	d	d	PROPN
ejpam-3970	292	4	=	=	SYM
ejpam-3970	292	5	d	d	PROPN
ejpam-3970	292	6	6=	6=	PROPN
ejpam-3970	292	7	h	h	PROPN
ejpam-3970	292	8	,	,	PUNCT
ejpam-3970	292	9	a	a	DET
ejpam-3970	292	10	contradiction	contradiction	NOUN
ejpam-3970	292	11	.	.	PUNCT
ejpam-3970	292	12	)	)	PUNCT
ejpam-3970	293	1	thus	thus	ADV
ejpam-3970	293	2	,	,	PUNCT
ejpam-3970	293	3	by	by	ADP
ejpam-3970	293	4	theorem	theorem	NOUN
ejpam-3970	293	5	8	8	NUM
ejpam-3970	293	6	and	and	CCONJ
ejpam-3970	293	7	the	the	DET
ejpam-3970	293	8	assumption	assumption	NOUN
ejpam-3970	293	9	that	that	SCONJ
ejpam-3970	293	10	d	d	NOUN
ejpam-3970	293	11	is	be	AUX
ejpam-3970	293	12	dense	dense	ADJ
ejpam-3970	293	13	,	,	PUNCT
ejpam-3970	293	14	d	d	PROPN
ejpam-3970	293	15	=	=	SYM
ejpam-3970	293	16	d	d	X
ejpam-3970	293	17	∪	∪	X
ejpam-3970	293	18	{	{	PUNCT
ejpam-3970	293	19	x	x	SYM
ejpam-3970	293	20	∈	∈	PROPN
ejpam-3970	293	21	h	h	NOUN
ejpam-3970	293	22	\	\	PUNCT
ejpam-3970	294	1	d	d	X
ejpam-3970	294	2	:	:	PUNCT
ejpam-3970	294	3	0	0	NUM
ejpam-3970	294	4	∈	∈	NOUN
ejpam-3970	294	5	lh(x	lh(x	NOUN
ejpam-3970	294	6	)	)	PUNCT
ejpam-3970	294	7	}	}	PUNCT
ejpam-3970	295	1	=	=	SYM
ejpam-3970	295	2	h.	h.	PROPN
ejpam-3970	295	3	therefore	therefore	ADV
ejpam-3970	295	4	,	,	PUNCT
ejpam-3970	295	5	0	0	NUM
ejpam-3970	295	6	∈	∈	PROPN
ejpam-3970	295	7	lh(x	lh(x	PUNCT
ejpam-3970	295	8	)	)	PUNCT
ejpam-3970	295	9	for	for	ADP
ejpam-3970	295	10	all	all	DET
ejpam-3970	295	11	x	x	SYM
ejpam-3970	295	12	∈	∈	PROPN
ejpam-3970	295	13	h	h	NOUN
ejpam-3970	295	14	\	\	PROPN
ejpam-3970	295	15	d.	d.	PROPN
ejpam-3970	295	16	for	for	ADP
ejpam-3970	295	17	the	the	DET
ejpam-3970	295	18	converse	converse	NOUN
ejpam-3970	295	19	,	,	PUNCT
ejpam-3970	295	20	suppose	suppose	VERB
ejpam-3970	295	21	that	that	SCONJ
ejpam-3970	295	22	the	the	DET
ejpam-3970	295	23	given	give	VERB
ejpam-3970	295	24	conditions	condition	NOUN
ejpam-3970	295	25	hold	hold	VERB
ejpam-3970	295	26	.	.	PUNCT
ejpam-3970	296	1	by	by	ADP
ejpam-3970	296	2	theorem	theorem	NOUN
ejpam-3970	296	3	8	8	NUM
ejpam-3970	296	4	,	,	PUNCT
ejpam-3970	296	5	d	d	PROPN
ejpam-3970	296	6	=	=	PUNCT
ejpam-3970	296	7	h.	h.	PROPN
ejpam-3970	296	8	thus	thus	ADV
ejpam-3970	296	9	,	,	PUNCT
ejpam-3970	296	10	d	d	PROPN
ejpam-3970	296	11	is	be	AUX
ejpam-3970	296	12	dense	dense	ADJ
ejpam-3970	296	13	in	in	ADP
ejpam-3970	296	14	h.	h.	PROPN
ejpam-3970	296	15	lemma	lemma	PROPN
ejpam-3970	297	1	3	3	X
ejpam-3970	297	2	.	.	PUNCT
ejpam-3970	297	3	let	let	VERB
ejpam-3970	297	4	k	k	PRON
ejpam-3970	297	5	be	be	AUX
ejpam-3970	297	6	a	a	DET
ejpam-3970	297	7	hyper	hyper	ADJ
ejpam-3970	297	8	subalgebra	subalgebra	NOUN
ejpam-3970	297	9	of	of	ADP
ejpam-3970	297	10	a	a	DET
ejpam-3970	297	11	hyper	hyper	ADJ
ejpam-3970	297	12	bci	bci	NOUN
ejpam-3970	297	13	-	-	PUNCT
ejpam-3970	297	14	algebra	algebra	NOUN
ejpam-3970	297	15	h.	h.	NOUN
ejpam-3970	297	16	then	then	ADV
ejpam-3970	297	17	(	(	PUNCT
ejpam-3970	297	18	i	i	NOUN
ejpam-3970	297	19	)	)	PUNCT
ejpam-3970	297	20	a∗(h	a∗(h	PROPN
ejpam-3970	297	21	)	)	PUNCT
ejpam-3970	297	22	∩k	∩k	NOUN
ejpam-3970	297	23	⊆	⊆	NUM
ejpam-3970	297	24	a∗(k	a∗(k	NUM
ejpam-3970	297	25	)	)	PUNCT
ejpam-3970	297	26	;	;	PUNCT
ejpam-3970	297	27	and	and	CCONJ
ejpam-3970	297	28	(	(	PUNCT
ejpam-3970	297	29	ii	ii	NOUN
ejpam-3970	297	30	)	)	PUNCT
ejpam-3970	297	31	lk(d	lk(d	NUM
ejpam-3970	297	32	)	)	PUNCT
ejpam-3970	297	33	=	=	SYM
ejpam-3970	297	34	lh(d	lh(d	NOUN
ejpam-3970	297	35	)	)	PUNCT
ejpam-3970	297	36	∩k	∩k	NOUN
ejpam-3970	297	37	for	for	ADP
ejpam-3970	297	38	every	every	DET
ejpam-3970	297	39	d	d	PROPN
ejpam-3970	297	40	⊆	⊆	NUM
ejpam-3970	297	41	k.	k.	PROPN
ejpam-3970	297	42	(	(	PUNCT
ejpam-3970	297	43	iii	iii	NOUN
ejpam-3970	297	44	)	)	PUNCT
ejpam-3970	297	45	lh(a	lh(a	NOUN
ejpam-3970	297	46	)	)	PUNCT
ejpam-3970	297	47	∩k	∩k	NOUN
ejpam-3970	297	48	⊆	⊆	NUM
ejpam-3970	297	49	lh(a	lh(a	NOUN
ejpam-3970	297	50	∩k	∩k	NOUN
ejpam-3970	297	51	)	)	PUNCT
ejpam-3970	297	52	for	for	ADP
ejpam-3970	297	53	any	any	DET
ejpam-3970	297	54	a	a	DET
ejpam-3970	297	55	⊆	⊆	NUM
ejpam-3970	297	56	h.	h.	PROPN
ejpam-3970	297	57	m.	m.	NOUN
ejpam-3970	297	58	panganduyon	panganduyon	NOUN
ejpam-3970	297	59	,	,	PUNCT
ejpam-3970	297	60	s.	s.	PROPN
ejpam-3970	297	61	canoy	canoy	PROPN
ejpam-3970	297	62	,	,	PUNCT
ejpam-3970	297	63	jr	jr	PROPN
ejpam-3970	297	64	.	.	PROPN
ejpam-3970	297	65	,	,	PUNCT
ejpam-3970	297	66	b.	b.	PROPN
ejpam-3970	297	67	davvaz	davvaz	PROPN
ejpam-3970	297	68	/	/	SYM
ejpam-3970	297	69	eur	eur	PROPN
ejpam-3970	297	70	.	.	PUNCT
ejpam-3970	298	1	j.	j.	PROPN
ejpam-3970	298	2	pure	pure	PROPN
ejpam-3970	298	3	appl	appl	PROPN
ejpam-3970	298	4	.	.	PROPN
ejpam-3970	298	5	math	math	PROPN
ejpam-3970	298	6	,	,	PUNCT
ejpam-3970	298	7	14	14	NUM
ejpam-3970	298	8	(	(	PUNCT
ejpam-3970	298	9	2	2	NUM
ejpam-3970	298	10	)	)	PUNCT
ejpam-3970	298	11	(	(	PUNCT
ejpam-3970	298	12	2021	2021	NUM
ejpam-3970	298	13	)	)	PUNCT
ejpam-3970	298	14	,	,	PUNCT
ejpam-3970	298	15	590	590	NUM
ejpam-3970	298	16	-	-	SYM
ejpam-3970	298	17	600	600	NUM
ejpam-3970	298	18	598	598	NUM
ejpam-3970	298	19	proof	proof	NOUN
ejpam-3970	298	20	.	.	PUNCT
ejpam-3970	299	1	(	(	PUNCT
ejpam-3970	299	2	i	i	NOUN
ejpam-3970	299	3	)	)	PUNCT
ejpam-3970	299	4	let	let	VERB
ejpam-3970	299	5	a	a	DET
ejpam-3970	299	6	∈	∈	PROPN
ejpam-3970	299	7	a∗(h	a∗(h	PROPN
ejpam-3970	299	8	)	)	PUNCT
ejpam-3970	299	9	∩k	∩k	NOUN
ejpam-3970	299	10	.	.	PUNCT
ejpam-3970	300	1	then	then	ADV
ejpam-3970	300	2	a	a	DET
ejpam-3970	300	3	∈	∈	PROPN
ejpam-3970	300	4	k	k	NOUN
ejpam-3970	300	5	and	and	CCONJ
ejpam-3970	300	6	for	for	ADP
ejpam-3970	300	7	all	all	DET
ejpam-3970	300	8	x	x	SYM
ejpam-3970	300	9	∈	∈	PROPN
ejpam-3970	300	10	h	h	NOUN
ejpam-3970	300	11	,	,	PUNCT
ejpam-3970	300	12	x	x	PROPN
ejpam-3970	300	13	�	�	PROPN
ejpam-3970	300	14	a	a	PRON
ejpam-3970	300	15	implies	imply	VERB
ejpam-3970	300	16	that	that	SCONJ
ejpam-3970	300	17	x	x	X
ejpam-3970	300	18	=	=	PUNCT
ejpam-3970	300	19	a	a	DET
ejpam-3970	300	20	or	or	CCONJ
ejpam-3970	300	21	x	x	SYM
ejpam-3970	300	22	=	=	NOUN
ejpam-3970	300	23	0	0	X
ejpam-3970	300	24	.	.	PUNCT
ejpam-3970	301	1	in	in	ADP
ejpam-3970	301	2	particular	particular	ADJ
ejpam-3970	301	3	,	,	PUNCT
ejpam-3970	301	4	for	for	ADP
ejpam-3970	301	5	all	all	DET
ejpam-3970	301	6	y	y	PROPN
ejpam-3970	301	7	∈	∈	PROPN
ejpam-3970	301	8	k	k	PROPN
ejpam-3970	301	9	,	,	PUNCT
ejpam-3970	301	10	y	y	PROPN
ejpam-3970	301	11	�	�	PROPN
ejpam-3970	301	12	a	a	PRON
ejpam-3970	301	13	implies	imply	VERB
ejpam-3970	301	14	y	y	PROPN
ejpam-3970	301	15	=	=	SYM
ejpam-3970	301	16	0	0	PROPN
ejpam-3970	301	17	or	or	CCONJ
ejpam-3970	301	18	y	y	NOUN
ejpam-3970	301	19	=	=	PUNCT
ejpam-3970	301	20	a.	a.	NOUN
ejpam-3970	301	21	thus	thus	ADV
ejpam-3970	301	22	,	,	PUNCT
ejpam-3970	301	23	a	a	DET
ejpam-3970	301	24	∈	∈	PROPN
ejpam-3970	301	25	a∗(k	a∗(k	PROPN
ejpam-3970	301	26	)	)	PUNCT
ejpam-3970	301	27	.	.	PUNCT
ejpam-3970	302	1	(	(	PUNCT
ejpam-3970	302	2	ii	ii	X
ejpam-3970	302	3	)	)	PUNCT
ejpam-3970	302	4	let	let	VERB
ejpam-3970	302	5	d	d	PROPN
ejpam-3970	302	6	⊆	⊆	NUM
ejpam-3970	303	1	k.	k.	NOUN
ejpam-3970	304	1	then	then	ADV
ejpam-3970	304	2	z	z	PROPN
ejpam-3970	304	3	∈	∈	PROPN
ejpam-3970	304	4	lk(d	lk(d	NOUN
ejpam-3970	304	5	)	)	PUNCT
ejpam-3970	305	1	if	if	SCONJ
ejpam-3970	305	2	and	and	CCONJ
ejpam-3970	305	3	only	only	ADV
ejpam-3970	305	4	if	if	SCONJ
ejpam-3970	305	5	z	z	PROPN
ejpam-3970	305	6	∈	∈	PROPN
ejpam-3970	305	7	k	k	PROPN
ejpam-3970	305	8	and	and	CCONJ
ejpam-3970	305	9	z	z	PROPN
ejpam-3970	305	10	�	�	PROPN
ejpam-3970	305	11	d	d	PROPN
ejpam-3970	305	12	for	for	ADP
ejpam-3970	305	13	all	all	DET
ejpam-3970	305	14	d	d	PROPN
ejpam-3970	305	15	∈	∈	PROPN
ejpam-3970	305	16	d.	d.	PROPN
ejpam-3970	305	17	thus	thus	ADV
ejpam-3970	305	18	,	,	PUNCT
ejpam-3970	305	19	z	z	PROPN
ejpam-3970	305	20	∈	∈	PROPN
ejpam-3970	305	21	lk(d	lk(d	NOUN
ejpam-3970	305	22	)	)	PUNCT
ejpam-3970	305	23	if	if	SCONJ
ejpam-3970	305	24	and	and	CCONJ
ejpam-3970	305	25	only	only	ADV
ejpam-3970	305	26	if	if	SCONJ
ejpam-3970	305	27	z	z	PROPN
ejpam-3970	305	28	∈	∈	PROPN
ejpam-3970	305	29	k	k	PROPN
ejpam-3970	305	30	∩	∩	NOUN
ejpam-3970	305	31	lh(d	lh(d	X
ejpam-3970	305	32	)	)	PUNCT
ejpam-3970	305	33	for	for	ADP
ejpam-3970	305	34	each	each	DET
ejpam-3970	305	35	d	d	PROPN
ejpam-3970	305	36	∈	∈	PROPN
ejpam-3970	305	37	d	d	PROPN
ejpam-3970	305	38	⊆	⊆	NUM
ejpam-3970	305	39	k	k	PROPN
ejpam-3970	305	40	⊆	⊆	NUM
ejpam-3970	305	41	h.	h.	PROPN
ejpam-3970	305	42	consequently	consequently	ADV
ejpam-3970	305	43	,	,	PUNCT
ejpam-3970	305	44	lk(d	lk(d	NUM
ejpam-3970	305	45	)	)	PUNCT
ejpam-3970	305	46	=	=	SYM
ejpam-3970	305	47	k	k	PROPN
ejpam-3970	305	48	∩	∩	NOUN
ejpam-3970	305	49	lh(d	lh(d	ADJ
ejpam-3970	305	50	)	)	PUNCT
ejpam-3970	305	51	.	.	PUNCT
ejpam-3970	306	1	(	(	PUNCT
ejpam-3970	306	2	iii	iii	X
ejpam-3970	306	3	)	)	PUNCT
ejpam-3970	306	4	let	let	VERB
ejpam-3970	306	5	a	a	DET
ejpam-3970	306	6	⊆	⊆	NUM
ejpam-3970	306	7	h.	h.	NOUN
ejpam-3970	306	8	since	since	SCONJ
ejpam-3970	306	9	a	a	DET
ejpam-3970	306	10	∩k	∩k	NOUN
ejpam-3970	306	11	⊆	⊆	NUM
ejpam-3970	306	12	a	a	PRON
ejpam-3970	306	13	,	,	PUNCT
ejpam-3970	306	14	by	by	ADP
ejpam-3970	306	15	proposition	proposition	NOUN
ejpam-3970	306	16	1(iii	1(iii	NUM
ejpam-3970	306	17	)	)	PUNCT
ejpam-3970	306	18	,	,	PUNCT
ejpam-3970	306	19	lh(a	lh(a	NUM
ejpam-3970	306	20	)	)	PUNCT
ejpam-3970	306	21	⊆	⊆	NUM
ejpam-3970	306	22	lh(a	lh(a	NOUN
ejpam-3970	306	23	∩k	∩k	NOUN
ejpam-3970	306	24	)	)	PUNCT
ejpam-3970	306	25	.	.	PUNCT
ejpam-3970	307	1	thus	thus	ADV
ejpam-3970	307	2	,	,	PUNCT
ejpam-3970	307	3	lh(a	lh(a	NOUN
ejpam-3970	307	4	)	)	PUNCT
ejpam-3970	307	5	∩	∩	NOUN
ejpam-3970	307	6	k	k	PROPN
ejpam-3970	307	7	⊆	⊆	NUM
ejpam-3970	307	8	lh(a	lh(a	NOUN
ejpam-3970	307	9	∩	∩	ADJ
ejpam-3970	307	10	k	k	NOUN
ejpam-3970	307	11	)	)	PUNCT
ejpam-3970	307	12	∩	∩	NOUN
ejpam-3970	307	13	k	k	PROPN
ejpam-3970	307	14	=	=	X
ejpam-3970	307	15	lk(a	lk(a	X
ejpam-3970	307	16	∩	∩	X
ejpam-3970	307	17	k	k	NOUN
ejpam-3970	307	18	)	)	PUNCT
ejpam-3970	307	19	,	,	PUNCT
ejpam-3970	307	20	by	by	ADP
ejpam-3970	307	21	(	(	PUNCT
ejpam-3970	307	22	ii	ii	NOUN
ejpam-3970	307	23	)	)	PUNCT
ejpam-3970	307	24	.	.	PUNCT
ejpam-3970	308	1	hence	hence	ADV
ejpam-3970	308	2	,	,	PUNCT
ejpam-3970	308	3	lh(a	lh(a	NOUN
ejpam-3970	308	4	)	)	PUNCT
ejpam-3970	308	5	∩	∩	NOUN
ejpam-3970	308	6	k	k	PROPN
ejpam-3970	308	7	⊆	⊆	NUM
ejpam-3970	308	8	lk(a	lk(a	X
ejpam-3970	308	9	∩k	∩k	NOUN
ejpam-3970	308	10	)	)	PUNCT
ejpam-3970	308	11	.	.	PUNCT
ejpam-3970	309	1	lemma	lemma	PROPN
ejpam-3970	309	2	4	4	X
ejpam-3970	309	3	.	.	PUNCT
ejpam-3970	310	1	let	let	VERB
ejpam-3970	310	2	k	k	PRON
ejpam-3970	310	3	be	be	AUX
ejpam-3970	310	4	a	a	DET
ejpam-3970	310	5	hyper	hyper	ADJ
ejpam-3970	310	6	subalgebra	subalgebra	NOUN
ejpam-3970	310	7	of	of	ADP
ejpam-3970	310	8	an	an	DET
ejpam-3970	310	9	ordered	order	VERB
ejpam-3970	310	10	hyper	hyper	ADJ
ejpam-3970	310	11	bci	bci	NOUN
ejpam-3970	310	12	-	-	PUNCT
ejpam-3970	310	13	algebra	algebra	NOUN
ejpam-3970	310	14	h.	h.	NOUN
ejpam-3970	310	15	then	then	ADV
ejpam-3970	310	16	for	for	ADP
ejpam-3970	310	17	any	any	DET
ejpam-3970	310	18	∅	∅	NOUN
ejpam-3970	310	19	6=	6=	ADP
ejpam-3970	310	20	a	a	DET
ejpam-3970	310	21	⊆	⊆	NUM
ejpam-3970	310	22	h	h	NOUN
ejpam-3970	310	23	,	,	PUNCT
ejpam-3970	310	24	lh(a	lh(a	NUM
ejpam-3970	310	25	)	)	PUNCT
ejpam-3970	310	26	∩k	∩k	NOUN
ejpam-3970	310	27	=	=	PUNCT
ejpam-3970	311	1	⋃	⋃	PROPN
ejpam-3970	311	2	x∈lh(a)∩k	x∈lh(a)∩k	PROPN
ejpam-3970	311	3	lk(x	lk(x	NOUN
ejpam-3970	311	4	)	)	PUNCT
ejpam-3970	311	5	.	.	PUNCT
ejpam-3970	312	1	proof	proof	NOUN
ejpam-3970	312	2	.	.	PUNCT
ejpam-3970	313	1	let	let	VERB
ejpam-3970	313	2	∅	∅	NOUN
ejpam-3970	313	3	6=	6=	ADP
ejpam-3970	313	4	a	a	DET
ejpam-3970	313	5	⊆	⊆	NUM
ejpam-3970	313	6	h	h	NOUN
ejpam-3970	313	7	and	and	CCONJ
ejpam-3970	313	8	x	x	PROPN
ejpam-3970	313	9	∈	∈	PROPN
ejpam-3970	313	10	lh(a	lh(a	NOUN
ejpam-3970	313	11	)	)	PUNCT
ejpam-3970	314	1	∩	∩	PROPN
ejpam-3970	314	2	k.	k.	PROPN
ejpam-3970	314	3	then	then	ADV
ejpam-3970	314	4	x	x	PROPN
ejpam-3970	314	5	�	�	PROPN
ejpam-3970	314	6	a	a	X
ejpam-3970	314	7	for	for	ADP
ejpam-3970	314	8	all	all	DET
ejpam-3970	314	9	a	a	DET
ejpam-3970	314	10	∈	∈	PROPN
ejpam-3970	314	11	a	a	PRON
ejpam-3970	314	12	and	and	CCONJ
ejpam-3970	314	13	x	x	SYM
ejpam-3970	314	14	∈	∈	PROPN
ejpam-3970	314	15	k.	k.	PROPN
ejpam-3970	314	16	let	let	VERB
ejpam-3970	314	17	y	y	PROPN
ejpam-3970	314	18	∈	∈	PROPN
ejpam-3970	314	19	lh(x	lh(x	PUNCT
ejpam-3970	314	20	)	)	PUNCT
ejpam-3970	314	21	∩k	∩k	PROPN
ejpam-3970	314	22	.	.	PUNCT
ejpam-3970	315	1	then	then	ADV
ejpam-3970	315	2	y	y	PROPN
ejpam-3970	315	3	�	�	PROPN
ejpam-3970	315	4	x	x	PUNCT
ejpam-3970	315	5	and	and	CCONJ
ejpam-3970	315	6	y	y	PROPN
ejpam-3970	315	7	∈	∈	PROPN
ejpam-3970	315	8	k.	k.	PROPN
ejpam-3970	316	1	since	since	SCONJ
ejpam-3970	316	2	h	h	PROPN
ejpam-3970	316	3	is	be	AUX
ejpam-3970	316	4	ordered	order	VERB
ejpam-3970	316	5	,	,	PUNCT
ejpam-3970	316	6	y	y	PROPN
ejpam-3970	316	7	�	�	PROPN
ejpam-3970	316	8	a	a	PROPN
ejpam-3970	316	9	for	for	ADP
ejpam-3970	316	10	all	all	DET
ejpam-3970	316	11	a	a	DET
ejpam-3970	316	12	∈	∈	NOUN
ejpam-3970	316	13	a.	a.	NOUN
ejpam-3970	316	14	hence	hence	ADV
ejpam-3970	316	15	,	,	PUNCT
ejpam-3970	316	16	y	y	PROPN
ejpam-3970	316	17	∈	∈	PROPN
ejpam-3970	316	18	lh(a	lh(a	NOUN
ejpam-3970	316	19	)	)	PUNCT
ejpam-3970	316	20	∩	∩	NOUN
ejpam-3970	317	1	k	k	X
ejpam-3970	317	2	showing	show	VERB
ejpam-3970	317	3	that	that	SCONJ
ejpam-3970	317	4	lh(x	lh(x	PUNCT
ejpam-3970	317	5	)	)	PUNCT
ejpam-3970	317	6	∩	∩	NOUN
ejpam-3970	317	7	k	k	PROPN
ejpam-3970	317	8	⊆	⊆	NUM
ejpam-3970	317	9	lh(a	lh(a	NUM
ejpam-3970	317	10	)	)	PUNCT
ejpam-3970	317	11	∩	∩	PROPN
ejpam-3970	317	12	k.	k.	PROPN
ejpam-3970	317	13	consequently,⋃	consequently,⋃	PROPN
ejpam-3970	317	14	x∈lh(a)∩k	x∈lh(a)∩k	PROPN
ejpam-3970	317	15	(	(	PUNCT
ejpam-3970	317	16	lh(x	lh(x	NOUN
ejpam-3970	317	17	)	)	PUNCT
ejpam-3970	317	18	∩k	∩k	NOUN
ejpam-3970	317	19	)	)	PUNCT
ejpam-3970	317	20	⊆	⊆	NUM
ejpam-3970	317	21	lh(a	lh(a	NUM
ejpam-3970	317	22	)	)	PUNCT
ejpam-3970	317	23	∩k	∩k	PROPN
ejpam-3970	317	24	.	.	PUNCT
ejpam-3970	318	1	next	next	ADV
ejpam-3970	318	2	,	,	PUNCT
ejpam-3970	318	3	let	let	VERB
ejpam-3970	318	4	z	z	NOUN
ejpam-3970	318	5	∈	∈	VERB
ejpam-3970	318	6	lh(a)∩k	lh(a)∩k	PROPN
ejpam-3970	318	7	.	.	PUNCT
ejpam-3970	319	1	by	by	ADP
ejpam-3970	319	2	proposition	proposition	NOUN
ejpam-3970	319	3	1(v	1(v	NUM
ejpam-3970	319	4	)	)	PUNCT
ejpam-3970	319	5	,	,	PUNCT
ejpam-3970	319	6	z	z	NOUN
ejpam-3970	319	7	∈	∈	PROPN
ejpam-3970	319	8	lh(z	lh(z	NOUN
ejpam-3970	319	9	)	)	PUNCT
ejpam-3970	319	10	.	.	PUNCT
ejpam-3970	320	1	it	it	PRON
ejpam-3970	320	2	follows	follow	VERB
ejpam-3970	320	3	that	that	SCONJ
ejpam-3970	320	4	z	z	PROPN
ejpam-3970	320	5	∈	∈	PROPN
ejpam-3970	320	6	lh(z)∩k	lh(z)∩k	PROPN
ejpam-3970	320	7	showing	show	VERB
ejpam-3970	320	8	that	that	DET
ejpam-3970	320	9	lh(a	lh(a	NOUN
ejpam-3970	320	10	)	)	PUNCT
ejpam-3970	320	11	∩	∩	NOUN
ejpam-3970	320	12	k	k	PROPN
ejpam-3970	320	13	⊆	⊆	NUM
ejpam-3970	320	14	lh(z	lh(z	NOUN
ejpam-3970	320	15	)	)	PUNCT
ejpam-3970	320	16	∩	∩	PROPN
ejpam-3970	320	17	k.	k.	PROPN
ejpam-3970	320	18	thus	thus	ADV
ejpam-3970	320	19	,	,	PUNCT
ejpam-3970	320	20	lh(a	lh(a	NOUN
ejpam-3970	320	21	)	)	PUNCT
ejpam-3970	320	22	∩	∩	NOUN
ejpam-3970	320	23	k	k	PROPN
ejpam-3970	320	24	⊆	⊆	NUM
ejpam-3970	320	25	⋃	⋃	PROPN
ejpam-3970	320	26	x∈lh(a)∩k	x∈lh(a)∩k	NOUN
ejpam-3970	320	27	(	(	PUNCT
ejpam-3970	320	28	lh(x	lh(x	NOUN
ejpam-3970	320	29	)	)	PUNCT
ejpam-3970	320	30	∩	∩	PROPN
ejpam-3970	320	31	k	k	NOUN
ejpam-3970	320	32	)	)	PUNCT
ejpam-3970	320	33	.	.	PUNCT
ejpam-3970	321	1	therefore	therefore	ADV
ejpam-3970	321	2	,	,	PUNCT
ejpam-3970	321	3	by	by	ADP
ejpam-3970	321	4	lemma	lemma	PROPN
ejpam-3970	321	5	3(ii	3(ii	NUM
ejpam-3970	321	6	)	)	PUNCT
ejpam-3970	321	7	,	,	PUNCT
ejpam-3970	321	8	lh(a	lh(a	NUM
ejpam-3970	321	9	)	)	PUNCT
ejpam-3970	321	10	∩k	∩k	NOUN
ejpam-3970	322	1	=	=	PUNCT
ejpam-3970	322	2	⋃	⋃	PROPN
ejpam-3970	322	3	x∈lh(a)∩k	x∈lh(a)∩k	PROPN
ejpam-3970	322	4	(	(	PUNCT
ejpam-3970	322	5	lh(x	lh(x	NOUN
ejpam-3970	322	6	)	)	PUNCT
ejpam-3970	322	7	∩k	∩k	NOUN
ejpam-3970	322	8	)	)	PUNCT
ejpam-3970	322	9	=	=	PUNCT
ejpam-3970	323	1	⋃	⋃	PROPN
ejpam-3970	323	2	x∈lh(a)∩k	x∈lh(a)∩k	PROPN
ejpam-3970	323	3	lk(x	lk(x	NOUN
ejpam-3970	323	4	)	)	PUNCT
ejpam-3970	323	5	.	.	PUNCT
ejpam-3970	324	1	this	this	PRON
ejpam-3970	324	2	proves	prove	VERB
ejpam-3970	324	3	the	the	DET
ejpam-3970	324	4	assertion	assertion	NOUN
ejpam-3970	324	5	.	.	PUNCT
ejpam-3970	325	1	theorem	theorem	ADJ
ejpam-3970	325	2	10	10	NUM
ejpam-3970	325	3	.	.	PUNCT
ejpam-3970	326	1	let	let	VERB
ejpam-3970	326	2	k	k	PRON
ejpam-3970	326	3	be	be	AUX
ejpam-3970	326	4	a	a	DET
ejpam-3970	326	5	hyper	hyper	ADJ
ejpam-3970	326	6	subalgebra	subalgebra	NOUN
ejpam-3970	326	7	of	of	ADP
ejpam-3970	326	8	an	an	DET
ejpam-3970	326	9	ordered	order	VERB
ejpam-3970	326	10	hyper	hyper	ADJ
ejpam-3970	326	11	bci	bci	NOUN
ejpam-3970	326	12	-	-	ADJ
ejpam-3970	326	13	algebra	algebra	ADJ
ejpam-3970	326	14	h	h	NOUN
ejpam-3970	326	15	with	with	ADP
ejpam-3970	326	16	|k|	|k|	PRON
ejpam-3970	326	17	≥	≥	NUM
ejpam-3970	326	18	2	2	NUM
ejpam-3970	326	19	.	.	PUNCT
ejpam-3970	327	1	then	then	ADV
ejpam-3970	327	2	τl(k	τl(k	NOUN
ejpam-3970	327	3	)	)	PUNCT
ejpam-3970	327	4	coincides	coincide	VERB
ejpam-3970	327	5	with	with	ADP
ejpam-3970	327	6	the	the	DET
ejpam-3970	327	7	relative	relative	ADJ
ejpam-3970	327	8	topology	topology	NOUN
ejpam-3970	327	9	τk	τk	ADP
ejpam-3970	327	10	on	on	ADP
ejpam-3970	327	11	k.	k.	PROPN
ejpam-3970	327	12	proof	proof	PROPN
ejpam-3970	327	13	.	.	PUNCT
ejpam-3970	328	1	by	by	ADP
ejpam-3970	328	2	theorem	theorem	NOUN
ejpam-3970	328	3	1	1	NUM
ejpam-3970	328	4	and	and	CCONJ
ejpam-3970	328	5	theorem	theorem	VERB
ejpam-3970	328	6	2	2	NUM
ejpam-3970	328	7	,	,	PUNCT
ejpam-3970	328	8	bases	basis	NOUN
ejpam-3970	328	9	for	for	ADP
ejpam-3970	328	10	τk	τk	NOUN
ejpam-3970	328	11	and	and	CCONJ
ejpam-3970	328	12	τl(k	τl(k	NUM
ejpam-3970	328	13	)	)	PUNCT
ejpam-3970	328	14	are	be	AUX
ejpam-3970	328	15	given	give	VERB
ejpam-3970	328	16	by	by	ADP
ejpam-3970	328	17	the	the	DET
ejpam-3970	328	18	families	family	NOUN
ejpam-3970	328	19	bk	bk	ADP
ejpam-3970	328	20	=	=	SYM
ejpam-3970	328	21	{	{	PUNCT
ejpam-3970	328	22	lh(a	lh(a	NOUN
ejpam-3970	328	23	)	)	PUNCT
ejpam-3970	328	24	∩k	∩k	NOUN
ejpam-3970	328	25	:	:	PUNCT
ejpam-3970	328	26	∅	∅	NOUN
ejpam-3970	328	27	6=	6=	ADP
ejpam-3970	328	28	a	a	DET
ejpam-3970	328	29	⊆	⊆	NUM
ejpam-3970	328	30	h	h	NOUN
ejpam-3970	328	31	}	}	PUNCT
ejpam-3970	328	32	and	and	CCONJ
ejpam-3970	328	33	bl(k	bl(k	NOUN
ejpam-3970	328	34	)	)	PUNCT
ejpam-3970	329	1	=	=	SYM
ejpam-3970	329	2	{	{	PUNCT
ejpam-3970	329	3	lk(a	lk(a	NOUN
ejpam-3970	329	4	)	)	PUNCT
ejpam-3970	329	5	:	:	PUNCT
ejpam-3970	329	6	∅	∅	NOUN
ejpam-3970	329	7	6=	6=	ADP
ejpam-3970	329	8	a	a	DET
ejpam-3970	329	9	⊆	⊆	NUM
ejpam-3970	329	10	k	k	NOUN
ejpam-3970	329	11	}	}	PUNCT
ejpam-3970	329	12	,	,	PUNCT
ejpam-3970	329	13	respectively	respectively	ADV
ejpam-3970	329	14	.	.	PUNCT
ejpam-3970	330	1	let	let	VERB
ejpam-3970	330	2	u	u	PRON
ejpam-3970	330	3	=	=	NOUN
ejpam-3970	330	4	lh(a	lh(a	NOUN
ejpam-3970	330	5	)	)	PUNCT
ejpam-3970	330	6	∩	∩	NOUN
ejpam-3970	330	7	k	k	PROPN
ejpam-3970	330	8	∈	∈	PROPN
ejpam-3970	330	9	bk	bk	PROPN
ejpam-3970	330	10	and	and	CCONJ
ejpam-3970	330	11	let	let	VERB
ejpam-3970	330	12	x	x	PUNCT
ejpam-3970	330	13	∈	∈	PROPN
ejpam-3970	330	14	u	u	NOUN
ejpam-3970	330	15	.	.	PUNCT
ejpam-3970	331	1	since	since	SCONJ
ejpam-3970	331	2	x	x	PROPN
ejpam-3970	331	3	∈	∈	PROPN
ejpam-3970	331	4	lh(x	lh(x	PRON
ejpam-3970	331	5	)	)	PUNCT
ejpam-3970	331	6	and	and	CCONJ
ejpam-3970	331	7	x	x	PUNCT
ejpam-3970	331	8	∈	∈	PROPN
ejpam-3970	331	9	k	k	NOUN
ejpam-3970	331	10	,	,	PUNCT
ejpam-3970	331	11	x	x	SYM
ejpam-3970	331	12	∈	∈	PROPN
ejpam-3970	331	13	lh(x)∩k	lh(x)∩k	PROPN
ejpam-3970	331	14	=	=	SYM
ejpam-3970	331	15	lk(x	lk(x	PROPN
ejpam-3970	331	16	)	)	PUNCT
ejpam-3970	331	17	by	by	ADP
ejpam-3970	331	18	lemma	lemma	PROPN
ejpam-3970	331	19	3	3	NUM
ejpam-3970	331	20	.	.	PUNCT
ejpam-3970	331	21	by	by	ADP
ejpam-3970	331	22	lemma	lemma	PROPN
ejpam-3970	331	23	4	4	NUM
ejpam-3970	331	24	,	,	PUNCT
ejpam-3970	331	25	lk(x	lk(x	NOUN
ejpam-3970	331	26	)	)	PUNCT
ejpam-3970	331	27	⊆	⊆	NUM
ejpam-3970	331	28	⋃	⋃	PUNCT
ejpam-3970	331	29	y∈lh(a)∩k	y∈lh(a)∩k	NOUN
ejpam-3970	331	30	lk(y	lk(y	PUNCT
ejpam-3970	331	31	)	)	PUNCT
ejpam-3970	331	32	=	=	SYM
ejpam-3970	332	1	lh(a)∩k	lh(a)∩k	PROPN
ejpam-3970	332	2	.	.	PUNCT
ejpam-3970	333	1	take	take	VERB
ejpam-3970	333	2	u	u	PRON
ejpam-3970	333	3	′	′	NOUN
ejpam-3970	333	4	=	=	PUNCT
ejpam-3970	333	5	lh(x	lh(x	X
ejpam-3970	333	6	)	)	PUNCT
ejpam-3970	333	7	.	.	PUNCT
ejpam-3970	334	1	it	it	PRON
ejpam-3970	334	2	follows	follow	VERB
ejpam-3970	334	3	that	that	SCONJ
ejpam-3970	334	4	τk	τk	ADP
ejpam-3970	334	5	⊆	⊆	NUM
ejpam-3970	334	6	τl(k	τl(k	NUM
ejpam-3970	334	7	)	)	PUNCT
ejpam-3970	334	8	.	.	PUNCT
ejpam-3970	335	1	to	to	PART
ejpam-3970	335	2	show	show	VERB
ejpam-3970	335	3	the	the	DET
ejpam-3970	335	4	other	other	ADJ
ejpam-3970	335	5	inclusion	inclusion	NOUN
ejpam-3970	335	6	,	,	PUNCT
ejpam-3970	335	7	let	let	VERB
ejpam-3970	335	8	u	u	PRON
ejpam-3970	335	9	∈	∈	NOUN
ejpam-3970	335	10	bl(k	bl(k	NOUN
ejpam-3970	335	11	)	)	PUNCT
ejpam-3970	335	12	.	.	PUNCT
ejpam-3970	336	1	then	then	ADV
ejpam-3970	336	2	there	there	PRON
ejpam-3970	336	3	exists	exist	VERB
ejpam-3970	336	4	b	b	PROPN
ejpam-3970	336	5	⊆	⊆	NUM
ejpam-3970	336	6	k	k	PRON
ejpam-3970	336	7	such	such	ADJ
ejpam-3970	336	8	that	that	DET
ejpam-3970	336	9	u	u	NOUN
ejpam-3970	336	10	=	=	PUNCT
ejpam-3970	336	11	lk(b	lk(b	X
ejpam-3970	336	12	)	)	PUNCT
ejpam-3970	336	13	.	.	PUNCT
ejpam-3970	337	1	by	by	ADP
ejpam-3970	337	2	lemma	lemma	PROPN
ejpam-3970	337	3	3	3	NUM
ejpam-3970	337	4	,	,	PUNCT
ejpam-3970	337	5	u	u	NOUN
ejpam-3970	337	6	=	=	NOUN
ejpam-3970	337	7	lk(b	lk(b	X
ejpam-3970	337	8	)	)	PUNCT
ejpam-3970	337	9	=	=	SYM
ejpam-3970	337	10	lh(b	lh(b	X
ejpam-3970	337	11	)	)	PUNCT
ejpam-3970	337	12	∩k	∩k	NOUN
ejpam-3970	337	13	∈	∈	PROPN
ejpam-3970	337	14	bk	bk	NOUN
ejpam-3970	337	15	.	.	PUNCT
ejpam-3970	338	1	hence	hence	ADV
ejpam-3970	338	2	,	,	PUNCT
ejpam-3970	338	3	bl(k	bl(k	NOUN
ejpam-3970	338	4	)	)	PUNCT
ejpam-3970	338	5	⊆	⊆	NUM
ejpam-3970	338	6	bk	bk	NOUN
ejpam-3970	338	7	,	,	PUNCT
ejpam-3970	338	8	that	that	ADV
ejpam-3970	338	9	is	is	ADV
ejpam-3970	338	10	,	,	PUNCT
ejpam-3970	338	11	τl(k	τl(k	X
ejpam-3970	338	12	)	)	PUNCT
ejpam-3970	338	13	⊆	⊆	NUM
ejpam-3970	338	14	τk	τk	ADV
ejpam-3970	338	15	.	.	PUNCT
ejpam-3970	339	1	therefore	therefore	ADV
ejpam-3970	339	2	,	,	PUNCT
ejpam-3970	339	3	τl(k	τl(k	ADV
ejpam-3970	339	4	)	)	PUNCT
ejpam-3970	340	1	=	=	PRON
ejpam-3970	340	2	τk	τk	ADP
ejpam-3970	340	3	.	.	PUNCT
ejpam-3970	341	1	references	reference	NOUN
ejpam-3970	341	2	599	599	NUM
ejpam-3970	341	3	conclusion	conclusion	NOUN
ejpam-3970	341	4	:	:	PUNCT
ejpam-3970	341	5	an	an	DET
ejpam-3970	341	6	operator	operator	NOUN
ejpam-3970	341	7	on	on	ADP
ejpam-3970	341	8	the	the	DET
ejpam-3970	341	9	power	power	NOUN
ejpam-3970	341	10	set	set	NOUN
ejpam-3970	341	11	of	of	ADP
ejpam-3970	341	12	a	a	DET
ejpam-3970	341	13	hyper	hyper	ADJ
ejpam-3970	341	14	bci	bci	NOUN
ejpam-3970	341	15	-	-	NOUN
ejpam-3970	341	16	algebra	algebra	NOUN
ejpam-3970	341	17	into	into	ADP
ejpam-3970	341	18	the	the	DET
ejpam-3970	341	19	family	family	NOUN
ejpam-3970	341	20	of	of	ADP
ejpam-3970	341	21	its	its	PRON
ejpam-3970	341	22	nonempty	nonempty	ADJ
ejpam-3970	341	23	subsets	subset	NOUN
ejpam-3970	341	24	had	have	AUX
ejpam-3970	341	25	been	be	AUX
ejpam-3970	341	26	defined	define	VERB
ejpam-3970	341	27	via	via	ADP
ejpam-3970	341	28	left	left	ADJ
ejpam-3970	341	29	application	application	NOUN
ejpam-3970	341	30	of	of	ADP
ejpam-3970	341	31	the	the	DET
ejpam-3970	341	32	hyper	hyper	NOUN
ejpam-3970	341	33	-	-	NOUN
ejpam-3970	341	34	order	order	NOUN
ejpam-3970	341	35	associated	associate	VERB
ejpam-3970	341	36	with	with	ADP
ejpam-3970	341	37	the	the	DET
ejpam-3970	341	38	hyper	hyper	ADJ
ejpam-3970	341	39	bci	bci	NOUN
ejpam-3970	341	40	-	-	NOUN
ejpam-3970	341	41	algebra	algebra	NOUN
ejpam-3970	341	42	.	.	PUNCT
ejpam-3970	342	1	the	the	DET
ejpam-3970	342	2	collection	collection	NOUN
ejpam-3970	342	3	of	of	ADP
ejpam-3970	342	4	images	image	NOUN
ejpam-3970	342	5	of	of	ADP
ejpam-3970	342	6	subsets	subset	NOUN
ejpam-3970	342	7	under	under	ADP
ejpam-3970	342	8	this	this	DET
ejpam-3970	342	9	operator	operator	NOUN
ejpam-3970	342	10	turned	turn	VERB
ejpam-3970	342	11	out	out	ADP
ejpam-3970	342	12	to	to	PART
ejpam-3970	342	13	be	be	AUX
ejpam-3970	342	14	a	a	DET
ejpam-3970	342	15	basis	basis	NOUN
ejpam-3970	342	16	for	for	ADP
ejpam-3970	342	17	some	some	DET
ejpam-3970	342	18	topology	topology	NOUN
ejpam-3970	342	19	on	on	ADP
ejpam-3970	342	20	the	the	DET
ejpam-3970	342	21	given	give	VERB
ejpam-3970	342	22	hyperstructure	hyperstructure	NOUN
ejpam-3970	342	23	.	.	PUNCT
ejpam-3970	343	1	the	the	DET
ejpam-3970	343	2	topological	topological	ADJ
ejpam-3970	343	3	space	space	NOUN
ejpam-3970	343	4	generated	generate	VERB
ejpam-3970	343	5	in	in	ADP
ejpam-3970	343	6	this	this	DET
ejpam-3970	343	7	way	way	NOUN
ejpam-3970	343	8	enabled	enable	VERB
ejpam-3970	343	9	us	we	PRON
ejpam-3970	343	10	to	to	PART
ejpam-3970	343	11	look	look	VERB
ejpam-3970	343	12	into	into	ADP
ejpam-3970	343	13	the	the	DET
ejpam-3970	343	14	topological	topological	ADJ
ejpam-3970	343	15	structure	structure	NOUN
ejpam-3970	343	16	of	of	ADP
ejpam-3970	343	17	hyper	hyper	ADJ
ejpam-3970	343	18	bci	bci	NOUN
ejpam-3970	343	19	-	-	NOUN
ejpam-3970	343	20	algebra	algebra	NOUN
ejpam-3970	343	21	in	in	ADP
ejpam-3970	343	22	many	many	ADJ
ejpam-3970	343	23	ways	way	NOUN
ejpam-3970	343	24	.	.	PUNCT
ejpam-3970	344	1	in	in	ADP
ejpam-3970	344	2	particular	particular	ADJ
ejpam-3970	344	3	,	,	PUNCT
ejpam-3970	344	4	under	under	ADP
ejpam-3970	344	5	some	some	DET
ejpam-3970	344	6	conditions	condition	NOUN
ejpam-3970	344	7	on	on	ADP
ejpam-3970	344	8	the	the	DET
ejpam-3970	344	9	hyper	hyper	ADJ
ejpam-3970	344	10	bci	bci	NOUN
ejpam-3970	344	11	-	-	NOUN
ejpam-3970	344	12	algebra	algebra	NOUN
ejpam-3970	344	13	,	,	PUNCT
ejpam-3970	344	14	elementary	elementary	ADJ
ejpam-3970	344	15	concepts	concept	NOUN
ejpam-3970	344	16	associated	associate	VERB
ejpam-3970	344	17	with	with	ADP
ejpam-3970	344	18	the	the	DET
ejpam-3970	344	19	space	space	NOUN
ejpam-3970	344	20	such	such	ADJ
ejpam-3970	344	21	as	as	ADP
ejpam-3970	344	22	open	open	ADJ
ejpam-3970	344	23	,	,	PUNCT
ejpam-3970	344	24	closed	closed	ADJ
ejpam-3970	344	25	,	,	PUNCT
ejpam-3970	344	26	density	density	NOUN
ejpam-3970	344	27	,	,	PUNCT
ejpam-3970	344	28	closure	closure	NOUN
ejpam-3970	344	29	,	,	PUNCT
ejpam-3970	344	30	interior	interior	NOUN
ejpam-3970	344	31	,	,	PUNCT
ejpam-3970	344	32	and	and	CCONJ
ejpam-3970	344	33	relative	relative	ADJ
ejpam-3970	344	34	space	space	NOUN
ejpam-3970	344	35	had	have	AUX
ejpam-3970	344	36	been	be	AUX
ejpam-3970	344	37	described	describe	VERB
ejpam-3970	344	38	or	or	CCONJ
ejpam-3970	344	39	characterized	characterize	VERB
ejpam-3970	344	40	.	.	PUNCT
ejpam-3970	345	1	the	the	DET
ejpam-3970	345	2	topological	topological	ADJ
ejpam-3970	345	3	space	space	NOUN
ejpam-3970	345	4	generated	generate	VERB
ejpam-3970	345	5	in	in	ADP
ejpam-3970	345	6	this	this	DET
ejpam-3970	345	7	study	study	NOUN
ejpam-3970	345	8	may	may	AUX
ejpam-3970	345	9	be	be	AUX
ejpam-3970	345	10	studied	study	VERB
ejpam-3970	345	11	further	far	ADV
ejpam-3970	345	12	for	for	ADP
ejpam-3970	345	13	other	other	ADJ
ejpam-3970	345	14	topological	topological	ADJ
ejpam-3970	345	15	aspects	aspect	NOUN
ejpam-3970	345	16	such	such	ADJ
ejpam-3970	345	17	as	as	ADP
ejpam-3970	345	18	connectedness	connectedness	NOUN
ejpam-3970	345	19	and	and	CCONJ
ejpam-3970	345	20	compactness	compactness	NOUN
ejpam-3970	345	21	.	.	PUNCT
ejpam-3970	346	1	also	also	ADV
ejpam-3970	346	2	,	,	PUNCT
ejpam-3970	346	3	if	if	SCONJ
ejpam-3970	346	4	it	it	PRON
ejpam-3970	346	5	were	be	AUX
ejpam-3970	346	6	possibe	possibe	ADJ
ejpam-3970	346	7	to	to	PART
ejpam-3970	346	8	define	define	VERB
ejpam-3970	346	9	hyper	hyper	NOUN
ejpam-3970	346	10	-	-	NOUN
ejpam-3970	346	11	orders	order	NOUN
ejpam-3970	346	12	on	on	ADP
ejpam-3970	346	13	the	the	DET
ejpam-3970	346	14	sum	sum	NOUN
ejpam-3970	346	15	(	(	PUNCT
ejpam-3970	346	16	or	or	CCONJ
ejpam-3970	346	17	join	join	VERB
ejpam-3970	346	18	)	)	PUNCT
ejpam-3970	346	19	and	and	CCONJ
ejpam-3970	346	20	product	product	NOUN
ejpam-3970	346	21	of	of	ADP
ejpam-3970	346	22	two	two	NUM
ejpam-3970	346	23	hyper	hyper	ADJ
ejpam-3970	346	24	bci	bci	NOUN
ejpam-3970	346	25	-	-	PUNCT
ejpam-3970	346	26	algebras	algebra	NOUN
ejpam-3970	346	27	so	so	SCONJ
ejpam-3970	346	28	as	as	SCONJ
ejpam-3970	346	29	to	to	PART
ejpam-3970	346	30	obtain	obtain	VERB
ejpam-3970	346	31	two	two	NUM
ejpam-3970	346	32	hyper	hyper	ADJ
ejpam-3970	346	33	bci	bci	NOUN
ejpam-3970	346	34	-	-	NOUN
ejpam-3970	346	35	algebras	algebra	NOUN
ejpam-3970	346	36	,	,	PUNCT
ejpam-3970	346	37	it	it	PRON
ejpam-3970	346	38	would	would	AUX
ejpam-3970	346	39	be	be	AUX
ejpam-3970	346	40	interesting	interesting	ADJ
ejpam-3970	346	41	to	to	PART
ejpam-3970	346	42	know	know	VERB
ejpam-3970	346	43	what	what	PRON
ejpam-3970	346	44	the	the	DET
ejpam-3970	346	45	respective	respective	ADJ
ejpam-3970	346	46	bases	basis	NOUN
ejpam-3970	346	47	would	would	AUX
ejpam-3970	346	48	be	be	AUX
ejpam-3970	346	49	for	for	ADP
ejpam-3970	346	50	the	the	DET
ejpam-3970	346	51	sum	sum	NOUN
ejpam-3970	346	52	and	and	CCONJ
ejpam-3970	346	53	product	product	NOUN
ejpam-3970	346	54	.	.	PUNCT
ejpam-3970	347	1	further	far	ADV
ejpam-3970	347	2	,	,	PUNCT
ejpam-3970	347	3	it	it	PRON
ejpam-3970	347	4	may	may	AUX
ejpam-3970	347	5	be	be	AUX
ejpam-3970	347	6	worthwhile	worthwhile	ADJ
ejpam-3970	347	7	to	to	PART
ejpam-3970	347	8	investigate	investigate	VERB
ejpam-3970	347	9	whether	whether	SCONJ
ejpam-3970	347	10	or	or	CCONJ
ejpam-3970	347	11	not	not	PART
ejpam-3970	347	12	the	the	DET
ejpam-3970	347	13	right	right	ADJ
ejpam-3970	347	14	application	application	NOUN
ejpam-3970	347	15	of	of	ADP
ejpam-3970	347	16	the	the	DET
ejpam-3970	347	17	hyper	hyper	NOUN
ejpam-3970	347	18	-	-	NOUN
ejpam-3970	347	19	order	order	NOUN
ejpam-3970	347	20	or	or	CCONJ
ejpam-3970	347	21	the	the	DET
ejpam-3970	347	22	combination	combination	NOUN
ejpam-3970	347	23	of	of	ADP
ejpam-3970	347	24	the	the	DET
ejpam-3970	347	25	left	left	ADJ
ejpam-3970	347	26	and	and	CCONJ
ejpam-3970	347	27	right	right	ADJ
ejpam-3970	347	28	applications	application	NOUN
ejpam-3970	347	29	will	will	AUX
ejpam-3970	347	30	also	also	ADV
ejpam-3970	347	31	give	give	VERB
ejpam-3970	347	32	rise	rise	NOUN
ejpam-3970	347	33	to	to	ADP
ejpam-3970	347	34	a	a	DET
ejpam-3970	347	35	topological	topological	ADJ
ejpam-3970	347	36	space	space	NOUN
ejpam-3970	347	37	.	.	PUNCT
ejpam-3970	348	1	if	if	SCONJ
ejpam-3970	348	2	any	any	PRON
ejpam-3970	348	3	of	of	ADP
ejpam-3970	348	4	these	these	PRON
ejpam-3970	348	5	does	do	VERB
ejpam-3970	348	6	,	,	PUNCT
ejpam-3970	348	7	then	then	ADV
ejpam-3970	348	8	one	one	NUM
ejpam-3970	348	9	needs	need	VERB
ejpam-3970	348	10	to	to	PART
ejpam-3970	348	11	know	know	VERB
ejpam-3970	348	12	if	if	SCONJ
ejpam-3970	348	13	the	the	DET
ejpam-3970	348	14	resulting	result	VERB
ejpam-3970	348	15	space	space	NOUN
ejpam-3970	348	16	is	be	AUX
ejpam-3970	348	17	the	the	DET
ejpam-3970	348	18	same	same	ADJ
ejpam-3970	348	19	(	(	PUNCT
ejpam-3970	348	20	or	or	CCONJ
ejpam-3970	348	21	homeomorphic	homeomorphic	ADJ
ejpam-3970	348	22	)	)	PUNCT
ejpam-3970	348	23	to	to	ADP
ejpam-3970	348	24	the	the	DET
ejpam-3970	348	25	one	one	NOUN
ejpam-3970	348	26	generated	generate	VERB
ejpam-3970	348	27	in	in	ADP
ejpam-3970	348	28	this	this	DET
ejpam-3970	348	29	study	study	NOUN
ejpam-3970	348	30	.	.	PUNCT
ejpam-3970	349	1	acknowledgements	acknowledgement	NOUN
ejpam-3970	349	2	the	the	DET
ejpam-3970	349	3	authors	author	NOUN
ejpam-3970	349	4	would	would	AUX
ejpam-3970	349	5	like	like	VERB
ejpam-3970	349	6	to	to	PART
ejpam-3970	349	7	thank	thank	VERB
ejpam-3970	349	8	the	the	DET
ejpam-3970	349	9	referees	referee	NOUN
ejpam-3970	349	10	for	for	ADP
ejpam-3970	349	11	reading	read	VERB
ejpam-3970	349	12	the	the	DET
ejpam-3970	349	13	initial	initial	ADJ
ejpam-3970	349	14	manuscript	manuscript	NOUN
ejpam-3970	349	15	and	and	CCONJ
ejpam-3970	349	16	giving	give	VERB
ejpam-3970	349	17	comments	comment	NOUN
ejpam-3970	349	18	and	and	CCONJ
ejpam-3970	349	19	suggestions	suggestion	NOUN
ejpam-3970	349	20	that	that	PRON
ejpam-3970	349	21	led	lead	VERB
ejpam-3970	349	22	to	to	ADP
ejpam-3970	349	23	this	this	DET
ejpam-3970	349	24	much	much	ADJ
ejpam-3970	349	25	improved	improved	ADJ
ejpam-3970	349	26	paper	paper	NOUN
ejpam-3970	349	27	.	.	PUNCT
ejpam-3970	350	1	we	we	PRON
ejpam-3970	350	2	would	would	AUX
ejpam-3970	350	3	like	like	VERB
ejpam-3970	350	4	to	to	PART
ejpam-3970	350	5	extend	extend	VERB
ejpam-3970	350	6	our	our	PRON
ejpam-3970	350	7	gratitude	gratitude	NOUN
ejpam-3970	350	8	to	to	PART
ejpam-3970	350	9	surigao	surigao	VERB
ejpam-3970	350	10	state	state	NOUN
ejpam-3970	350	11	college	college	NOUN
ejpam-3970	350	12	of	of	ADP
ejpam-3970	350	13	technology	technology	NOUN
ejpam-3970	350	14	-	-	PUNCT
ejpam-3970	350	15	main	main	ADJ
ejpam-3970	350	16	campus	campus	NOUN
ejpam-3970	350	17	,	,	PUNCT
ejpam-3970	350	18	department	department	NOUN
ejpam-3970	350	19	of	of	ADP
ejpam-3970	350	20	science	science	NOUN
ejpam-3970	350	21	and	and	CCONJ
ejpam-3970	350	22	technology	technology	NOUN
ejpam-3970	350	23	accelerated	accelerate	VERB
ejpam-3970	350	24	science	science	NOUN
ejpam-3970	350	25	and	and	CCONJ
ejpam-3970	350	26	technology	technology	NOUN
ejpam-3970	350	27	human	human	ADJ
ejpam-3970	350	28	resource	resource	NOUN
ejpam-3970	350	29	development	development	NOUN
ejpam-3970	350	30	program	program	NOUN
ejpam-3970	350	31	(	(	PUNCT
ejpam-3970	350	32	dost	dost	NOUN
ejpam-3970	350	33	-	-	PUNCT
ejpam-3970	350	34	asthrdp	asthrdp	NOUN
ejpam-3970	350	35	)	)	PUNCT
ejpam-3970	350	36	and	and	CCONJ
ejpam-3970	350	37	msu	msu	PROPN
ejpam-3970	350	38	-	-	PUNCT
ejpam-3970	350	39	iligan	iligan	PROPN
ejpam-3970	350	40	institute	institute	PROPN
ejpam-3970	350	41	of	of	ADP
ejpam-3970	350	42	technology	technology	PROPN
ejpam-3970	350	43	,	,	PUNCT
ejpam-3970	350	44	philippines	philippine	NOUN
ejpam-3970	350	45	for	for	ADP
ejpam-3970	350	46	funding	fund	VERB
ejpam-3970	350	47	this	this	DET
ejpam-3970	350	48	research	research	NOUN
ejpam-3970	350	49	.	.	PUNCT
ejpam-3970	351	1	references	reference	NOUN
ejpam-3970	351	2	[	[	X
ejpam-3970	351	3	1	1	NUM
ejpam-3970	351	4	]	]	X
ejpam-3970	351	5	r.a	r.a	PROPN
ejpam-3970	351	6	.	.	PROPN
ejpam-3970	351	7	alo	alo	PROPN
ejpam-3970	351	8	and	and	CCONJ
ejpam-3970	351	9	e.y	e.y	PROPN
ejpam-3970	351	10	.	.	PROPN
ejpam-3970	351	11	deeba	deeba	PROPN
ejpam-3970	351	12	.	.	PUNCT
ejpam-3970	352	1	topologies	topology	NOUN
ejpam-3970	352	2	of	of	ADP
ejpam-3970	352	3	bck	bck	NOUN
ejpam-3970	352	4	-	-	PUNCT
ejpam-3970	352	5	algebras	algebras	PROPN
ejpam-3970	352	6	.	.	PUNCT
ejpam-3970	353	1	math	math	PROPN
ejpam-3970	353	2	.	.	PUNCT
ejpam-3970	354	1	japon	japon	PROPN
ejpam-3970	354	2	.	.	PROPN
ejpam-3970	354	3	,	,	PUNCT
ejpam-3970	354	4	31(6):841–853	31(6):841–853	NUM
ejpam-3970	354	5	,	,	PUNCT
ejpam-3970	354	6	1986	1986	NUM
ejpam-3970	354	7	.	.	PUNCT
ejpam-3970	355	1	[	[	X
ejpam-3970	355	2	2	2	X
ejpam-3970	355	3	]	]	PUNCT
ejpam-3970	355	4	j.	j.	PROPN
ejpam-3970	355	5	dugundji	dugundji	PROPN
ejpam-3970	355	6	.	.	PUNCT
ejpam-3970	355	7	topology	topology	PROPN
ejpam-3970	355	8	.	.	PUNCT
ejpam-3970	356	1	allyn	allyn	PROPN
ejpam-3970	356	2	and	and	CCONJ
ejpam-3970	356	3	bacon	bacon	PROPN
ejpam-3970	356	4	,	,	PUNCT
ejpam-3970	356	5	inc	inc	PROPN
ejpam-3970	356	6	.	.	PROPN
ejpam-3970	356	7	,	,	PUNCT
ejpam-3970	356	8	boston	boston	PROPN
ejpam-3970	356	9	,	,	PUNCT
ejpam-3970	356	10	1966	1966	NUM
ejpam-3970	356	11	.	.	PUNCT
ejpam-3970	357	1	[	[	X
ejpam-3970	357	2	3	3	X
ejpam-3970	357	3	]	]	X
ejpam-3970	357	4	k.	k.	PROPN
ejpam-3970	357	5	iséki	iséki	PROPN
ejpam-3970	357	6	.	.	PUNCT
ejpam-3970	358	1	an	an	DET
ejpam-3970	358	2	algebra	algebra	NOUN
ejpam-3970	358	3	related	relate	VERB
ejpam-3970	358	4	with	with	ADP
ejpam-3970	358	5	a	a	DET
ejpam-3970	358	6	propositional	propositional	ADJ
ejpam-3970	358	7	calculus	calculus	NOUN
ejpam-3970	358	8	.	.	PUNCT
ejpam-3970	359	1	proc	proc	PROPN
ejpam-3970	359	2	.	.	PUNCT
ejpam-3970	360	1	japan	japan	PROPN
ejpam-3970	360	2	.	.	PUNCT
ejpam-3970	361	1	acad	acad	PROPN
ejpam-3970	361	2	.	.	PROPN
ejpam-3970	361	3	,	,	PUNCT
ejpam-3970	361	4	42:351–366	42:351–366	PROPN
ejpam-3970	361	5	,	,	PUNCT
ejpam-3970	361	6	1966	1966	NUM
ejpam-3970	361	7	.	.	PUNCT
ejpam-3970	362	1	[	[	X
ejpam-3970	362	2	4	4	NUM
ejpam-3970	362	3	]	]	X
ejpam-3970	362	4	y.b	y.b	PROPN
ejpam-3970	362	5	.	.	PROPN
ejpam-3970	362	6	jun	jun	PROPN
ejpam-3970	362	7	,	,	PUNCT
ejpam-3970	362	8	x.l	x.l	PROPN
ejpam-3970	362	9	.	.	PUNCT
ejpam-3970	362	10	xin	xin	PROPN
ejpam-3970	362	11	,	,	PUNCT
ejpam-3970	362	12	and	and	CCONJ
ejpam-3970	362	13	d.s	d.s	PROPN
ejpam-3970	362	14	.	.	PROPN
ejpam-3970	362	15	lee	lee	PROPN
ejpam-3970	362	16	.	.	PROPN
ejpam-3970	363	1	on	on	ADP
ejpam-3970	363	2	topological	topological	ADJ
ejpam-3970	363	3	bci	bci	NOUN
ejpam-3970	363	4	-	-	PUNCT
ejpam-3970	363	5	algebras	algebra	NOUN
ejpam-3970	363	6	.	.	PUNCT
ejpam-3970	364	1	information	information	NOUN
ejpam-3970	364	2	sciences	sciences	PROPN
ejpam-3970	364	3	,	,	PUNCT
ejpam-3970	364	4	116(2	116(2	NUM
ejpam-3970	364	5	-	-	PUNCT
ejpam-3970	364	6	4):253–261	4):253–261	NUM
ejpam-3970	364	7	,	,	PUNCT
ejpam-3970	364	8	1999	1999	NUM
ejpam-3970	364	9	.	.	PUNCT
ejpam-3970	365	1	[	[	X
ejpam-3970	365	2	5	5	NUM
ejpam-3970	365	3	]	]	X
ejpam-3970	365	4	y.b	y.b	PROPN
ejpam-3970	365	5	.	.	PROPN
ejpam-3970	365	6	jun	jun	PROPN
ejpam-3970	365	7	,	,	PUNCT
ejpam-3970	365	8	m.m	m.m	PROPN
ejpam-3970	365	9	.	.	PROPN
ejpam-3970	365	10	zahedi	zahedi	PROPN
ejpam-3970	365	11	,	,	PUNCT
ejpam-3970	365	12	x.l	x.l	PROPN
ejpam-3970	365	13	.	.	PUNCT
ejpam-3970	365	14	xin	xin	PROPN
ejpam-3970	365	15	,	,	PUNCT
ejpam-3970	365	16	and	and	CCONJ
ejpam-3970	365	17	r.a	r.a	PROPN
ejpam-3970	365	18	.	.	PROPN
ejpam-3970	365	19	borzoei	borzoei	PROPN
ejpam-3970	365	20	.	.	PUNCT
ejpam-3970	366	1	on	on	ADP
ejpam-3970	366	2	hyper	hyper	ADJ
ejpam-3970	366	3	bck	bck	NOUN
ejpam-3970	366	4	-	-	PUNCT
ejpam-3970	366	5	algebras	algebras	PROPN
ejpam-3970	366	6	.	.	PUNCT
ejpam-3970	367	1	italian	italian	ADJ
ejpam-3970	367	2	j.	j.	PROPN
ejpam-3970	367	3	pure	pure	PROPN
ejpam-3970	367	4	and	and	CCONJ
ejpam-3970	367	5	appl	appl	PROPN
ejpam-3970	367	6	.	.	PROPN
ejpam-3970	367	7	math	math	PROPN
ejpam-3970	367	8	.	.	PUNCT
ejpam-3970	367	9	,	,	PUNCT
ejpam-3970	367	10	8(4):127–136	8(4):127–136	NUM
ejpam-3970	367	11	,	,	PUNCT
ejpam-3970	367	12	2000	2000	NUM
ejpam-3970	367	13	.	.	PUNCT
ejpam-3970	368	1	[	[	X
ejpam-3970	368	2	6	6	NUM
ejpam-3970	368	3	]	]	PUNCT
ejpam-3970	368	4	f.	f.	PROPN
ejpam-3970	368	5	marty	marty	PROPN
ejpam-3970	368	6	.	.	PUNCT
ejpam-3970	369	1	sur	sur	PROPN
ejpam-3970	369	2	une	une	PROPN
ejpam-3970	369	3	generalization	generalization	PROPN
ejpam-3970	369	4	de	de	X
ejpam-3970	369	5	la	la	PROPN
ejpam-3970	369	6	notion	notion	PROPN
ejpam-3970	369	7	de	de	X
ejpam-3970	369	8	groupe	groupe	PROPN
ejpam-3970	369	9	.	.	PUNCT
ejpam-3970	370	1	8th	8th	ADJ
ejpam-3970	370	2	congress	congress	PROPN
ejpam-3970	370	3	math.scandinaves	math.scandinave	NOUN
ejpam-3970	370	4	,	,	PUNCT
ejpam-3970	370	5	stockholm	stockholm	PROPN
ejpam-3970	370	6	,	,	PUNCT
ejpam-3970	370	7	6:45–49	6:45–49	PROPN
ejpam-3970	370	8	,	,	PUNCT
ejpam-3970	370	9	1934	1934	NUM
ejpam-3970	370	10	.	.	PUNCT
ejpam-3970	371	1	references	reference	NOUN
ejpam-3970	371	2	600	600	NUM
ejpam-3970	371	3	[	[	X
ejpam-3970	371	4	7	7	NUM
ejpam-3970	371	5	]	]	X
ejpam-3970	371	6	g.	g.	PROPN
ejpam-3970	371	7	muhiuddin	muhiuddin	PROPN
ejpam-3970	371	8	.	.	PUNCT
ejpam-3970	372	1	int	int	NOUN
ejpam-3970	372	2	-	-	PUNCT
ejpam-3970	372	3	soft	soft	ADJ
ejpam-3970	372	4	hyper	hyper	ADJ
ejpam-3970	372	5	-	-	ADJ
ejpam-3970	372	6	mv	mv	ADJ
ejpam-3970	372	7	-	-	ADJ
ejpam-3970	372	8	deductive	deductive	ADJ
ejpam-3970	372	9	systems	system	NOUN
ejpam-3970	372	10	in	in	ADP
ejpam-3970	372	11	hyper	hyper	ADJ
ejpam-3970	372	12	-	-	ADJ
ejpam-3970	372	13	mv	mv	ADJ
ejpam-3970	372	14	-algebras	-algebras	PROPN
ejpam-3970	372	15	.	.	PROPN
ejpam-3970	372	16	azerbaijan	azerbaijan	PROPN
ejpam-3970	372	17	journal	journal	PROPN
ejpam-3970	372	18	of	of	ADP
ejpam-3970	372	19	mathematics	mathematic	NOUN
ejpam-3970	372	20	,	,	PUNCT
ejpam-3970	372	21	6:39–51	6:39–51	PROPN
ejpam-3970	372	22	,	,	PUNCT
ejpam-3970	372	23	2016	2016	NUM
ejpam-3970	372	24	.	.	PUNCT
ejpam-3970	373	1	[	[	X
ejpam-3970	373	2	8	8	NUM
ejpam-3970	373	3	]	]	X
ejpam-3970	373	4	g.	g.	PROPN
ejpam-3970	373	5	muhiuddin	muhiuddin	PROPN
ejpam-3970	373	6	.	.	PUNCT
ejpam-3970	374	1	intersectional	intersectional	ADJ
ejpam-3970	374	2	soft	soft	ADJ
ejpam-3970	374	3	sets	set	NOUN
ejpam-3970	374	4	theory	theory	NOUN
ejpam-3970	374	5	applied	apply	VERB
ejpam-3970	374	6	to	to	ADP
ejpam-3970	374	7	generalized	generalized	ADJ
ejpam-3970	374	8	hypervector	hypervector	NOUN
ejpam-3970	374	9	spaces	space	NOUN
ejpam-3970	374	10	.	.	PUNCT
ejpam-3970	375	1	analele	analele	ADP
ejpam-3970	375	2	stiintifice	stiintifice	PROPN
ejpam-3970	375	3	ale	ale	PROPN
ejpam-3970	375	4	universitatii	universitatii	PROPN
ejpam-3970	375	5	ovidus	ovidus	PROPN
ejpam-3970	375	6	constanta	constanta	PROPN
ejpam-3970	375	7	,	,	PUNCT
ejpam-3970	375	8	seria	seria	PROPN
ejpam-3970	375	9	matematica	matematica	PROPN
ejpam-3970	375	10	,	,	PUNCT
ejpam-3970	375	11	28:171–191	28:171–191	NUM
ejpam-3970	375	12	,	,	PUNCT
ejpam-3970	375	13	2020	2020	NUM
ejpam-3970	375	14	.	.	PUNCT
ejpam-3970	376	1	[	[	X
ejpam-3970	376	2	9	9	NUM
ejpam-3970	376	3	]	]	X
ejpam-3970	376	4	g.	g.	PROPN
ejpam-3970	376	5	muhiuddin	muhiuddin	PROPN
ejpam-3970	376	6	and	and	CCONJ
ejpam-3970	376	7	a.m.	a.m.	NOUN
ejpam-3970	376	8	a.m.	a.m.	PROPN
ejpam-3970	377	1	al	al	PROPN
ejpam-3970	377	2	-	-	PUNCT
ejpam-3970	377	3	roqi	roqi	PROPN
ejpam-3970	377	4	.	.	PUNCT
ejpam-3970	378	1	double	double	ADJ
ejpam-3970	378	2	-	-	PUNCT
ejpam-3970	378	3	framed	frame	VERB
ejpam-3970	378	4	soft	soft	ADJ
ejpam-3970	378	5	hypervector	hypervector	NOUN
ejpam-3970	378	6	spaces	space	NOUN
ejpam-3970	378	7	.	.	PUNCT
ejpam-3970	379	1	the	the	DET
ejpam-3970	379	2	scientific	scientific	ADJ
ejpam-3970	379	3	world	world	NOUN
ejpam-3970	379	4	journal	journal	NOUN
ejpam-3970	379	5	,	,	PUNCT
ejpam-3970	379	6	https://doi.org/10.1155/2014/451928	https://doi.org/10.1155/2014/451928	PROPN
ejpam-3970	379	7	,	,	PUNCT
ejpam-3970	379	8	12:2050018	12:2050018	NUM
ejpam-3970	379	9	,	,	PUNCT
ejpam-3970	379	10	2014	2014	NUM
ejpam-3970	379	11	.	.	PUNCT
ejpam-3970	380	1	[	[	X
ejpam-3970	380	2	10	10	NUM
ejpam-3970	380	3	]	]	X
ejpam-3970	380	4	g.	g.	PROPN
ejpam-3970	380	5	muhiuddin	muhiuddin	PROPN
ejpam-3970	380	6	,	,	PUNCT
ejpam-3970	380	7	h.	h.	PROPN
ejpam-3970	380	8	harizavi	harizavi	PROPN
ejpam-3970	380	9	,	,	PUNCT
ejpam-3970	380	10	and	and	CCONJ
ejpam-3970	380	11	y.	y.	PROPN
ejpam-3970	380	12	b.	b.	PROPN
ejpam-3970	380	13	jun	jun	PROPN
ejpam-3970	380	14	.	.	PROPN
ejpam-3970	380	15	bipolar	bipolar	ADJ
ejpam-3970	380	16	-	-	PUNCT
ejpam-3970	380	17	valued	value	VERB
ejpam-3970	380	18	fuzzy	fuzzy	ADJ
ejpam-3970	380	19	soft	soft	ADJ
ejpam-3970	380	20	hyper	hyper	ADJ
ejpam-3970	380	21	bck	bck	NOUN
ejpam-3970	380	22	ideals	ideal	NOUN
ejpam-3970	380	23	in	in	ADP
ejpam-3970	380	24	hyper	hyper	ADJ
ejpam-3970	380	25	bck	bck	PROPN
ejpam-3970	380	26	algebras	algebra	NOUN
ejpam-3970	380	27	.	.	PUNCT
ejpam-3970	381	1	discrete	discrete	ADJ
ejpam-3970	381	2	mathematics	mathematic	NOUN
ejpam-3970	381	3	algorithms	algorithm	NOUN
ejpam-3970	381	4	and	and	CCONJ
ejpam-3970	381	5	applications	application	NOUN
ejpam-3970	381	6	,	,	PUNCT
ejpam-3970	381	7	https://doi.org/10.1142/s1793830920500184	https://doi.org/10.1142/s1793830920500184	X
ejpam-3970	381	8	,	,	PUNCT
ejpam-3970	381	9	12:2050018	12:2050018	NUM
ejpam-3970	381	10	,	,	PUNCT
ejpam-3970	381	11	2020	2020	NUM
ejpam-3970	381	12	.	.	PUNCT
ejpam-3970	382	1	[	[	X
ejpam-3970	382	2	11	11	NUM
ejpam-3970	382	3	]	]	PUNCT
ejpam-3970	382	4	m.	m.	NOUN
ejpam-3970	382	5	panganduyon	panganduyon	NOUN
ejpam-3970	382	6	and	and	CCONJ
ejpam-3970	382	7	jr	jr	PROPN
ejpam-3970	382	8	.	.	PUNCT
ejpam-3970	382	9	s.r	s.r	PROPN
ejpam-3970	382	10	.	.	PROPN
ejpam-3970	382	11	canoy	canoy	PROPN
ejpam-3970	382	12	.	.	PUNCT
ejpam-3970	383	1	on	on	ADP
ejpam-3970	383	2	a	a	DET
ejpam-3970	383	3	graph	graph	NOUN
ejpam-3970	383	4	induced	induce	VERB
ejpam-3970	383	5	by	by	ADP
ejpam-3970	383	6	a	a	DET
ejpam-3970	383	7	hyper	hyper	ADJ
ejpam-3970	383	8	bci	bci	NOUN
ejpam-3970	383	9	-	-	NOUN
ejpam-3970	383	10	algebra	algebra	NOUN
ejpam-3970	383	11	.	.	PUNCT
ejpam-3970	384	1	european	european	ADJ
ejpam-3970	384	2	journal	journal	PROPN
ejpam-3970	384	3	of	of	ADP
ejpam-3970	384	4	pure	pure	ADJ
ejpam-3970	384	5	and	and	CCONJ
ejpam-3970	384	6	applied	applied	ADJ
ejpam-3970	384	7	mathematics	mathematic	NOUN
ejpam-3970	384	8	,	,	PUNCT
ejpam-3970	384	9	12:146–158	12:146–158	NUM
ejpam-3970	384	10	,	,	PUNCT
ejpam-3970	384	11	2019	2019	NUM
ejpam-3970	384	12	.	.	PUNCT
ejpam-3970	385	1	[	[	X
ejpam-3970	385	2	12	12	NUM
ejpam-3970	385	3	]	]	X
ejpam-3970	385	4	l.	l.	PROPN
ejpam-3970	385	5	steen	steen	PROPN
ejpam-3970	385	6	and	and	CCONJ
ejpam-3970	385	7	j.a	j.a	PROPN
ejpam-3970	385	8	.	.	PROPN
ejpam-3970	385	9	seebach	seebach	PROPN
ejpam-3970	385	10	.	.	PUNCT
ejpam-3970	386	1	counterexamples	counterexample	NOUN
ejpam-3970	386	2	in	in	ADP
ejpam-3970	386	3	topology	topology	NOUN
ejpam-3970	386	4	.	.	PUNCT
ejpam-3970	387	1	new	new	PROPN
ejpam-3970	387	2	york	york	PROPN
ejpam-3970	387	3	:	:	PUNCT
ejpam-3970	387	4	springer	springer	NOUN
ejpam-3970	387	5	-	-	PUNCT
ejpam-3970	387	6	verlag	verlag	PROPN
ejpam-3970	387	7	,	,	PUNCT
ejpam-3970	387	8	berlin	berlin	PROPN
ejpam-3970	387	9	,	,	PUNCT
ejpam-3970	387	10	1978	1978	NUM
ejpam-3970	387	11	.	.	PUNCT
ejpam-3970	388	1	[	[	X
ejpam-3970	388	2	13	13	NUM
ejpam-3970	388	3	]	]	X
ejpam-3970	388	4	x.l	x.l	PROPN
ejpam-3970	388	5	.	.	PUNCT
ejpam-3970	389	1	xin	xin	PROPN
ejpam-3970	389	2	.	.	PUNCT
ejpam-3970	390	1	hyper	hyper	PROPN
ejpam-3970	390	2	bci	bci	NOUN
ejpam-3970	390	3	-	-	PUNCT
ejpam-3970	390	4	algebras	algebra	NOUN
ejpam-3970	390	5	.	.	PUNCT
ejpam-3970	391	1	discussiones	discussione	NOUN
ejpam-3970	391	2	mathematicae	mathematicae	PROPN
ejpam-3970	391	3	,	,	PUNCT
ejpam-3970	391	4	26:5–19	26:5–19	NUM
ejpam-3970	391	5	,	,	PUNCT
ejpam-3970	391	6	2006	2006	NUM
ejpam-3970	391	7	.	.	PUNCT