id	sid	tid	token	lemma	pos
ejpam-5394	1	1	european	european	PROPN
ejpam-5394	1	2	journal	journal	PROPN
ejpam-5394	1	3	of	of	ADP
ejpam-5394	1	4	pure	pure	ADJ
ejpam-5394	1	5	and	and	CCONJ
ejpam-5394	1	6	applied	applied	ADJ
ejpam-5394	1	7	mathematics	mathematic	NOUN
ejpam-5394	1	8	2025	2025	NUM
ejpam-5394	1	9	,	,	PUNCT
ejpam-5394	1	10	vol	vol	NOUN
ejpam-5394	1	11	.	.	PROPN
ejpam-5394	1	12	18	18	NUM
ejpam-5394	1	13	,	,	PUNCT
ejpam-5394	1	14	issue	issue	NOUN
ejpam-5394	1	15	2	2	NUM
ejpam-5394	1	16	,	,	PUNCT
ejpam-5394	1	17	article	article	NOUN
ejpam-5394	1	18	number	number	NOUN
ejpam-5394	1	19	5394	5394	NUM
ejpam-5394	1	20	issn	issn	PROPN
ejpam-5394	1	21	1307	1307	NUM
ejpam-5394	1	22	-	-	SYM
ejpam-5394	1	23	5543	5543	NUM
ejpam-5394	1	24	–	–	PUNCT
ejpam-5394	1	25	ejpam.com	ejpam.com	X
ejpam-5394	1	26	published	publish	VERB
ejpam-5394	1	27	by	by	ADP
ejpam-5394	1	28	new	new	PROPN
ejpam-5394	1	29	york	york	PROPN
ejpam-5394	1	30	business	business	PROPN
ejpam-5394	1	31	global	global	ADJ
ejpam-5394	1	32	topologies	topology	NOUN
ejpam-5394	1	33	on	on	ADP
ejpam-5394	1	34	hyper	hyper	ADJ
ejpam-5394	1	35	bck	bck	NOUN
ejpam-5394	1	36	-	-	PUNCT
ejpam-5394	1	37	algebra	algebra	NOUN
ejpam-5394	1	38	[	[	X
ejpam-5394	1	39	0	0	NUM
ejpam-5394	1	40	,	,	PUNCT
ejpam-5394	1	41	1	1	NUM
ejpam-5394	1	42	]	]	PUNCT
ejpam-5394	1	43	erneta	erneta	PROPN
ejpam-5394	1	44	payla1,∗	payla1,∗	NOUN
ejpam-5394	1	45	,	,	PUNCT
ejpam-5394	1	46	luzviminda	luzviminda	NOUN
ejpam-5394	1	47	ranara2	ranara2	PROPN
ejpam-5394	1	48	1	1	NUM
ejpam-5394	1	49	general	general	ADJ
ejpam-5394	1	50	education	education	NOUN
ejpam-5394	1	51	,	,	PUNCT
ejpam-5394	1	52	caraga	caraga	PROPN
ejpam-5394	1	53	state	state	PROPN
ejpam-5394	1	54	university	university	PROPN
ejpam-5394	1	55	,	,	PUNCT
ejpam-5394	1	56	8605	8605	NUM
ejpam-5394	1	57	cabadbaran	cabadbaran	VERB
ejpam-5394	1	58	city	city	NOUN
ejpam-5394	1	59	,	,	PUNCT
ejpam-5394	1	60	philippines	philippines	PROPN
ejpam-5394	1	61	2	2	NUM
ejpam-5394	1	62	department	department	NOUN
ejpam-5394	1	63	of	of	ADP
ejpam-5394	1	64	mathematics	mathematic	NOUN
ejpam-5394	1	65	,	,	PUNCT
ejpam-5394	1	66	mindanao	mindanao	PROPN
ejpam-5394	1	67	state	state	PROPN
ejpam-5394	1	68	university	university	PROPN
ejpam-5394	1	69	,	,	PUNCT
ejpam-5394	1	70	9700	9700	NUM
ejpam-5394	1	71	marawi	marawi	PROPN
ejpam-5394	1	72	city	city	PROPN
ejpam-5394	1	73	,	,	PUNCT
ejpam-5394	1	74	philippines	philippine	NOUN
ejpam-5394	1	75	abstract	abstract	ADJ
ejpam-5394	1	76	.	.	PUNCT
ejpam-5394	2	1	in	in	ADP
ejpam-5394	2	2	this	this	DET
ejpam-5394	2	3	paper	paper	NOUN
ejpam-5394	2	4	,	,	PUNCT
ejpam-5394	2	5	we	we	PRON
ejpam-5394	2	6	introduce	introduce	VERB
ejpam-5394	2	7	the	the	DET
ejpam-5394	2	8	definition	definition	NOUN
ejpam-5394	2	9	of	of	ADP
ejpam-5394	2	10	a	a	DET
ejpam-5394	2	11	hyper	hyper	ADJ
ejpam-5394	2	12	operation	operation	NOUN
ejpam-5394	2	13	∗	∗	NOUN
ejpam-5394	2	14	on	on	ADP
ejpam-5394	2	15	the	the	DET
ejpam-5394	2	16	set	set	NOUN
ejpam-5394	2	17	[	[	X
ejpam-5394	2	18	0,1	0,1	NUM
ejpam-5394	2	19	]	]	PUNCT
ejpam-5394	2	20	,	,	PUNCT
ejpam-5394	2	21	and	and	CCONJ
ejpam-5394	2	22	with	with	ADP
ejpam-5394	2	23	this	this	DET
ejpam-5394	2	24	hyper	hyper	ADJ
ejpam-5394	2	25	operation	operation	NOUN
ejpam-5394	2	26	,	,	PUNCT
ejpam-5394	2	27	we	we	PRON
ejpam-5394	2	28	will	will	AUX
ejpam-5394	2	29	show	show	VERB
ejpam-5394	2	30	that	that	SCONJ
ejpam-5394	2	31	[	[	X
ejpam-5394	2	32	0,1	0,1	NOUN
ejpam-5394	2	33	]	]	PUNCT
ejpam-5394	2	34	is	be	AUX
ejpam-5394	2	35	a	a	DET
ejpam-5394	2	36	hyper	hyper	ADJ
ejpam-5394	2	37	bck	bck	NOUN
ejpam-5394	2	38	-	-	PUNCT
ejpam-5394	2	39	algebra	algebra	NOUN
ejpam-5394	2	40	.	.	PUNCT
ejpam-5394	3	1	we	we	PRON
ejpam-5394	3	2	also	also	ADV
ejpam-5394	3	3	investigate	investigate	VERB
ejpam-5394	3	4	the	the	DET
ejpam-5394	3	5	topologies	topology	NOUN
ejpam-5394	3	6	that	that	PRON
ejpam-5394	3	7	will	will	AUX
ejpam-5394	3	8	be	be	AUX
ejpam-5394	3	9	formulated	formulate	VERB
ejpam-5394	3	10	with	with	ADP
ejpam-5394	3	11	br([0	br([0	NOUN
ejpam-5394	3	12	,	,	PUNCT
ejpam-5394	3	13	1	1	NUM
ejpam-5394	3	14	]	]	PUNCT
ejpam-5394	3	15	)	)	PUNCT
ejpam-5394	3	16	and	and	CCONJ
ejpam-5394	3	17	bl([0	bl([0	NOUN
ejpam-5394	3	18	,	,	PUNCT
ejpam-5394	3	19	1	1	NUM
ejpam-5394	3	20	]	]	PUNCT
ejpam-5394	3	21	)	)	PUNCT
ejpam-5394	3	22	and	and	CCONJ
ejpam-5394	3	23	show	show	VERB
ejpam-5394	3	24	some	some	DET
ejpam-5394	3	25	topology	topology	NOUN
ejpam-5394	3	26	of	of	ADP
ejpam-5394	3	27	r[0	r[0	PROPN
ejpam-5394	3	28	,	,	PUNCT
ejpam-5394	3	29	1](a	1](a	NUM
ejpam-5394	3	30	)	)	PUNCT
ejpam-5394	3	31	and	and	CCONJ
ejpam-5394	3	32	l[0	l[0	PROPN
ejpam-5394	3	33	,	,	PUNCT
ejpam-5394	3	34	1](a	1](a	NUM
ejpam-5394	3	35	)	)	PUNCT
ejpam-5394	3	36	.	.	PUNCT
ejpam-5394	4	1	furthermore	furthermore	ADV
ejpam-5394	4	2	,	,	PUNCT
ejpam-5394	4	3	we	we	PRON
ejpam-5394	4	4	investigate	investigate	VERB
ejpam-5394	4	5	a	a	DET
ejpam-5394	4	6	basis	basis	NOUN
ejpam-5394	4	7	for	for	ADP
ejpam-5394	4	8	the	the	DET
ejpam-5394	4	9	intersection	intersection	NOUN
ejpam-5394	4	10	of	of	ADP
ejpam-5394	4	11	topologies	topology	NOUN
ejpam-5394	4	12	τr(h	τr(h	PUNCT
ejpam-5394	4	13	)	)	PUNCT
ejpam-5394	4	14	and	and	CCONJ
ejpam-5394	4	15	τl(h	τl(h	NUM
ejpam-5394	4	16	)	)	PUNCT
ejpam-5394	4	17	.	.	PUNCT
ejpam-5394	5	1	2020	2020	NUM
ejpam-5394	5	2	mathematics	mathematic	NOUN
ejpam-5394	5	3	subject	subject	NOUN
ejpam-5394	5	4	classifications	classification	NOUN
ejpam-5394	5	5	:	:	PUNCT
ejpam-5394	5	6	06f35	06f35	NUM
ejpam-5394	5	7	,	,	PUNCT
ejpam-5394	5	8	54a10	54a10	NUM
ejpam-5394	5	9	,	,	PUNCT
ejpam-5394	5	10	08a72	08a72	NUM
ejpam-5394	5	11	,	,	PUNCT
ejpam-5394	5	12	03g25	03g25	NOUN
ejpam-5394	5	13	key	key	ADJ
ejpam-5394	5	14	words	word	NOUN
ejpam-5394	5	15	and	and	CCONJ
ejpam-5394	5	16	phrases	phrase	NOUN
ejpam-5394	5	17	:	:	PUNCT
ejpam-5394	5	18	hyper	hyper	ADJ
ejpam-5394	5	19	bck	bck	NOUN
ejpam-5394	5	20	-	-	PUNCT
ejpam-5394	5	21	algebra	algebra	NOUN
ejpam-5394	5	22	,	,	PUNCT
ejpam-5394	5	23	hyper	hyper	ADJ
ejpam-5394	5	24	order	order	NOUN
ejpam-5394	5	25	,	,	PUNCT
ejpam-5394	5	26	bases	basis	NOUN
ejpam-5394	5	27	,	,	PUNCT
ejpam-5394	5	28	hyperoperation	hyperoperation	NOUN
ejpam-5394	5	29	,	,	PUNCT
ejpam-5394	5	30	topology	topology	NOUN
ejpam-5394	5	31	1	1	NUM
ejpam-5394	5	32	.	.	PUNCT
ejpam-5394	5	33	introduction	introduction	NOUN
ejpam-5394	5	34	in	in	ADP
ejpam-5394	5	35	1966	1966	NUM
ejpam-5394	5	36	,	,	PUNCT
ejpam-5394	5	37	imai	imai	PROPN
ejpam-5394	5	38	and	and	CCONJ
ejpam-5394	5	39	isèki	isèki	PROPN
ejpam-5394	6	1	[	[	X
ejpam-5394	6	2	1	1	NUM
ejpam-5394	6	3	]	]	PUNCT
ejpam-5394	6	4	introduced	introduce	VERB
ejpam-5394	6	5	the	the	DET
ejpam-5394	6	6	concept	concept	NOUN
ejpam-5394	6	7	of	of	ADP
ejpam-5394	6	8	bck	bck	NOUN
ejpam-5394	6	9	-	-	PUNCT
ejpam-5394	6	10	algebra	algebra	NOUN
ejpam-5394	6	11	as	as	ADP
ejpam-5394	6	12	a	a	DET
ejpam-5394	6	13	generalization	generalization	NOUN
ejpam-5394	6	14	of	of	ADP
ejpam-5394	6	15	the	the	DET
ejpam-5394	6	16	concept	concept	NOUN
ejpam-5394	6	17	of	of	ADP
ejpam-5394	6	18	set	set	NOUN
ejpam-5394	6	19	-	-	PUNCT
ejpam-5394	6	20	theoretic	theoretic	NOUN
ejpam-5394	6	21	difference	difference	NOUN
ejpam-5394	6	22	and	and	CCONJ
ejpam-5394	6	23	propositional	propositional	ADJ
ejpam-5394	6	24	calculi	calculi	NOUN
ejpam-5394	6	25	.	.	PUNCT
ejpam-5394	7	1	the	the	DET
ejpam-5394	7	2	study	study	NOUN
ejpam-5394	7	3	of	of	ADP
ejpam-5394	7	4	algebraic	algebraic	PROPN
ejpam-5394	7	5	hyperstructure	hyperstructure	PROPN
ejpam-5394	7	6	theory	theory	NOUN
ejpam-5394	7	7	(	(	PUNCT
ejpam-5394	7	8	or	or	CCONJ
ejpam-5394	7	9	multialgebras	multialgebra	NOUN
ejpam-5394	7	10	)	)	PUNCT
ejpam-5394	7	11	was	be	AUX
ejpam-5394	7	12	introduced	introduce	VERB
ejpam-5394	7	13	in	in	ADP
ejpam-5394	7	14	1934	1934	NUM
ejpam-5394	7	15	by	by	ADP
ejpam-5394	7	16	f.	f.	PROPN
ejpam-5394	7	17	marty	marty	PROPN
ejpam-5394	8	1	[	[	X
ejpam-5394	8	2	2	2	X
ejpam-5394	8	3	]	]	PUNCT
ejpam-5394	8	4	at	at	ADP
ejpam-5394	8	5	the	the	DET
ejpam-5394	8	6	8th	8th	ADJ
ejpam-5394	8	7	congress	congress	PROPN
ejpam-5394	8	8	of	of	ADP
ejpam-5394	8	9	scandinavian	scandinavian	ADJ
ejpam-5394	8	10	mathematics	mathematic	NOUN
ejpam-5394	8	11	.	.	PUNCT
ejpam-5394	9	1	since	since	SCONJ
ejpam-5394	9	2	then	then	ADV
ejpam-5394	9	3	it	it	PRON
ejpam-5394	9	4	becomes	become	VERB
ejpam-5394	9	5	the	the	DET
ejpam-5394	9	6	interest	interest	NOUN
ejpam-5394	9	7	of	of	ADP
ejpam-5394	9	8	many	many	ADJ
ejpam-5394	9	9	researchers	researcher	NOUN
ejpam-5394	9	10	.	.	PUNCT
ejpam-5394	10	1	recently	recently	ADV
ejpam-5394	10	2	,	,	PUNCT
ejpam-5394	10	3	jun	jun	PROPN
ejpam-5394	10	4	,	,	PUNCT
ejpam-5394	10	5	et	et	PROPN
ejpam-5394	10	6	al	al	PROPN
ejpam-5394	10	7	.	.	PROPN
ejpam-5394	10	8	,[4	,[4	PROPN
ejpam-5394	10	9	]	]	PUNCT
ejpam-5394	10	10	proposed	propose	VERB
ejpam-5394	10	11	hyperstructure	hyperstructure	NOUN
ejpam-5394	10	12	theory	theory	NOUN
ejpam-5394	10	13	on	on	ADP
ejpam-5394	10	14	bck	bck	NOUN
ejpam-5394	10	15	-	-	PUNCT
ejpam-5394	10	16	algebras	algebras	PROPN
ejpam-5394	10	17	and	and	CCONJ
ejpam-5394	10	18	they	they	PRON
ejpam-5394	10	19	were	be	AUX
ejpam-5394	10	20	able	able	ADJ
ejpam-5394	10	21	to	to	PART
ejpam-5394	10	22	prove	prove	VERB
ejpam-5394	10	23	that	that	SCONJ
ejpam-5394	10	24	a	a	DET
ejpam-5394	10	25	hyper	hyper	ADJ
ejpam-5394	10	26	bck	bck	NOUN
ejpam-5394	10	27	-	-	PUNCT
ejpam-5394	10	28	algebra	algebra	NOUN
ejpam-5394	10	29	is	be	AUX
ejpam-5394	10	30	a	a	DET
ejpam-5394	10	31	generalization	generalization	NOUN
ejpam-5394	10	32	of	of	ADP
ejpam-5394	10	33	a	a	DET
ejpam-5394	10	34	bck	bck	NOUN
ejpam-5394	10	35	-	-	PUNCT
ejpam-5394	10	36	algebra	algebra	NOUN
ejpam-5394	10	37	.	.	PUNCT
ejpam-5394	11	1	in	in	ADP
ejpam-5394	11	2	the	the	DET
ejpam-5394	11	3	paper	paper	NOUN
ejpam-5394	11	4	of	of	ADP
ejpam-5394	11	5	patangan	patangan	NOUN
ejpam-5394	11	6	and	and	CCONJ
ejpam-5394	11	7	canoy	canoy	ADJ
ejpam-5394	11	8	[	[	X
ejpam-5394	11	9	3	3	NUM
ejpam-5394	11	10	,	,	PUNCT
ejpam-5394	11	11	4	4	NUM
ejpam-5394	11	12	]	]	PUNCT
ejpam-5394	11	13	,	,	PUNCT
ejpam-5394	11	14	they	they	PRON
ejpam-5394	11	15	defined	define	VERB
ejpam-5394	11	16	the	the	DET
ejpam-5394	11	17	sets	set	NOUN
ejpam-5394	11	18	rh(a	rh(a	NOUN
ejpam-5394	11	19	)	)	PUNCT
ejpam-5394	11	20	=	=	PRON
ejpam-5394	12	1	{	{	PUNCT
ejpam-5394	12	2	x	x	PUNCT
ejpam-5394	12	3	∈	∈	PROPN
ejpam-5394	12	4	h	h	NOUN
ejpam-5394	12	5	:	:	PUNCT
ejpam-5394	12	6	a	a	DET
ejpam-5394	12	7	≪	≪	ADJ
ejpam-5394	12	8	x,∀a	x,∀a	PROPN
ejpam-5394	12	9	∈	∈	PROPN
ejpam-5394	12	10	a	a	DET
ejpam-5394	12	11	}	}	PUNCT
ejpam-5394	12	12	=	=	SYM
ejpam-5394	12	13	{	{	PUNCT
ejpam-5394	12	14	x	x	PUNCT
ejpam-5394	12	15	∈	∈	PROPN
ejpam-5394	12	16	h	h	NOUN
ejpam-5394	12	17	:	:	PUNCT
ejpam-5394	12	18	0	0	NUM
ejpam-5394	12	19	∈	∈	PROPN
ejpam-5394	12	20	a	a	DET
ejpam-5394	12	21	∗	∗	NOUN
ejpam-5394	12	22	x,∀a	x,∀a	PUNCT
ejpam-5394	12	23	∈	∈	PROPN
ejpam-5394	12	24	a	a	PRON
ejpam-5394	12	25	}	}	PUNCT
ejpam-5394	12	26	and	and	CCONJ
ejpam-5394	12	27	lh(a	lh(a	NUM
ejpam-5394	12	28	)	)	PUNCT
ejpam-5394	12	29	=	=	PRON
ejpam-5394	13	1	{	{	PUNCT
ejpam-5394	13	2	x	x	PUNCT
ejpam-5394	13	3	∈	∈	PROPN
ejpam-5394	13	4	h	h	NOUN
ejpam-5394	13	5	:	:	PUNCT
ejpam-5394	13	6	x	x	SYM
ejpam-5394	13	7	≪	≪	PUNCT
ejpam-5394	13	8	a,∀a	a,∀a	PRON
ejpam-5394	13	9	∈	∈	PROPN
ejpam-5394	13	10	a	a	DET
ejpam-5394	13	11	}	}	PUNCT
ejpam-5394	13	12	=	=	SYM
ejpam-5394	13	13	{	{	PUNCT
ejpam-5394	13	14	x	x	PUNCT
ejpam-5394	13	15	∈	∈	PROPN
ejpam-5394	13	16	h	h	NOUN
ejpam-5394	13	17	:	:	PUNCT
ejpam-5394	13	18	0	0	NUM
ejpam-5394	13	19	∈	∈	NOUN
ejpam-5394	13	20	x	x	X
ejpam-5394	13	21	∗	∗	NOUN
ejpam-5394	13	22	a,∀a	a,∀a	X
ejpam-5394	13	23	∈	∈	PROPN
ejpam-5394	13	24	a	a	PRON
ejpam-5394	13	25	}	}	PUNCT
ejpam-5394	13	26	by	by	ADP
ejpam-5394	13	27	the	the	DET
ejpam-5394	13	28	right	right	ADJ
ejpam-5394	13	29	applications	application	NOUN
ejpam-5394	13	30	of	of	ADP
ejpam-5394	13	31	hyperorder	hyperorder	NOUN
ejpam-5394	13	32	on	on	ADP
ejpam-5394	13	33	h	h	NOUN
ejpam-5394	13	34	,	,	PUNCT
ejpam-5394	13	35	respectively	respectively	ADV
ejpam-5394	13	36	.	.	PUNCT
ejpam-5394	14	1	they	they	PRON
ejpam-5394	14	2	showed	show	VERB
ejpam-5394	14	3	that	that	SCONJ
ejpam-5394	14	4	br(h	br(h	NOUN
ejpam-5394	14	5	)	)	PUNCT
ejpam-5394	14	6	consisting	consist	VERB
ejpam-5394	14	7	of	of	ADP
ejpam-5394	14	8	the	the	DET
ejpam-5394	14	9	sets	set	NOUN
ejpam-5394	14	10	rh(a	rh(a	NUM
ejpam-5394	14	11	)	)	PUNCT
ejpam-5394	14	12	,	,	PUNCT
ejpam-5394	14	13	is	be	AUX
ejpam-5394	14	14	a	a	DET
ejpam-5394	14	15	basis	basis	NOUN
ejpam-5394	14	16	for	for	ADP
ejpam-5394	14	17	some	some	DET
ejpam-5394	14	18	topology	topology	NOUN
ejpam-5394	14	19	τr(h	τr(h	PUNCT
ejpam-5394	14	20	)	)	PUNCT
ejpam-5394	14	21	on	on	ADP
ejpam-5394	14	22	a	a	DET
ejpam-5394	14	23	hyper	hyper	ADJ
ejpam-5394	14	24	bck	bck	NOUN
ejpam-5394	14	25	-	-	PUNCT
ejpam-5394	14	26	algebra	algebra	NOUN
ejpam-5394	14	27	via	via	ADP
ejpam-5394	14	28	right	right	ADJ
ejpam-5394	14	29	application	application	NOUN
ejpam-5394	14	30	of	of	ADP
ejpam-5394	14	31	hyperorder	hyperorder	NOUN
ejpam-5394	14	32	.	.	PUNCT
ejpam-5394	15	1	also	also	ADV
ejpam-5394	15	2	,	,	PUNCT
ejpam-5394	15	3	bl(h	bl(h	PUNCT
ejpam-5394	15	4	)	)	PUNCT
ejpam-5394	15	5	consisting	consist	VERB
ejpam-5394	15	6	of	of	ADP
ejpam-5394	15	7	the	the	DET
ejpam-5394	15	8	sets	set	NOUN
ejpam-5394	15	9	lh(a	lh(a	NUM
ejpam-5394	15	10	)	)	PUNCT
ejpam-5394	15	11	,	,	PUNCT
ejpam-5394	15	12	is	be	AUX
ejpam-5394	15	13	a	a	DET
ejpam-5394	15	14	basis	basis	NOUN
ejpam-5394	15	15	for	for	ADP
ejpam-5394	15	16	some	some	DET
ejpam-5394	15	17	topology	topology	NOUN
ejpam-5394	15	18	τl(h	τl(h	PUNCT
ejpam-5394	15	19	)	)	PUNCT
ejpam-5394	15	20	on	on	ADP
ejpam-5394	15	21	a	a	DET
ejpam-5394	15	22	hyper	hyper	ADJ
ejpam-5394	15	23	bck	bck	NOUN
ejpam-5394	15	24	-	-	PUNCT
ejpam-5394	15	25	algebra	algebra	NOUN
ejpam-5394	15	26	via	via	ADP
ejpam-5394	15	27	left	left	ADJ
ejpam-5394	15	28	application	application	NOUN
ejpam-5394	15	29	of	of	ADP
ejpam-5394	15	30	hyperorder	hyperorder	NOUN
ejpam-5394	15	31	.	.	PUNCT
ejpam-5394	16	1	this	this	DET
ejpam-5394	16	2	paper	paper	NOUN
ejpam-5394	16	3	is	be	AUX
ejpam-5394	16	4	motivated	motivate	VERB
ejpam-5394	16	5	by	by	ADP
ejpam-5394	16	6	the	the	DET
ejpam-5394	16	7	work	work	NOUN
ejpam-5394	16	8	of	of	ADP
ejpam-5394	16	9	patangan	patangan	NOUN
ejpam-5394	16	10	and	and	CCONJ
ejpam-5394	16	11	canoy	canoy	ADJ
ejpam-5394	17	1	[	[	X
ejpam-5394	17	2	3	3	X
ejpam-5394	17	3	]	]	PUNCT
ejpam-5394	17	4	on	on	ADP
ejpam-5394	17	5	a	a	DET
ejpam-5394	17	6	topology	topology	NOUN
ejpam-5394	17	7	on	on	ADP
ejpam-5394	17	8	a	a	DET
ejpam-5394	17	9	hyper	hyper	ADJ
ejpam-5394	17	10	bck	bck	NOUN
ejpam-5394	17	11	-	-	PUNCT
ejpam-5394	17	12	algebra	algebra	NOUN
ejpam-5394	17	13	,	,	PUNCT
ejpam-5394	17	14	as	as	SCONJ
ejpam-5394	17	15	published	publish	VERB
ejpam-5394	17	16	in	in	ADP
ejpam-5394	17	17	jp	jp	NOUN
ejpam-5394	17	18	journal	journal	PROPN
ejpam-5394	17	19	of	of	ADP
ejpam-5394	17	20	algebra	algebra	PROPN
ejpam-5394	17	21	,	,	PUNCT
ejpam-5394	17	22	number	number	NOUN
ejpam-5394	17	23	theory	theory	NOUN
ejpam-5394	17	24	and	and	CCONJ
ejpam-5394	17	25	applications	application	NOUN
ejpam-5394	17	26	.	.	PUNCT
ejpam-5394	18	1	in	in	ADP
ejpam-5394	18	2	this	this	DET
ejpam-5394	18	3	paper	paper	NOUN
ejpam-5394	18	4	,	,	PUNCT
ejpam-5394	18	5	we	we	PRON
ejpam-5394	18	6	define	define	VERB
ejpam-5394	18	7	a	a	DET
ejpam-5394	18	8	hyperoperation	hyperoperation	NOUN
ejpam-5394	18	9	∗	∗	NOUN
ejpam-5394	18	10	on	on	ADP
ejpam-5394	18	11	the	the	DET
ejpam-5394	18	12	set	set	NOUN
ejpam-5394	18	13	[	[	X
ejpam-5394	18	14	0	0	NUM
ejpam-5394	18	15	,	,	PUNCT
ejpam-5394	18	16	1	1	NUM
ejpam-5394	18	17	]	]	PUNCT
ejpam-5394	18	18	,	,	PUNCT
ejpam-5394	18	19	and	and	CCONJ
ejpam-5394	18	20	with	with	ADP
ejpam-5394	18	21	this	this	DET
ejpam-5394	18	22	operation	operation	NOUN
ejpam-5394	18	23	,	,	PUNCT
ejpam-5394	18	24	we	we	PRON
ejpam-5394	18	25	will	will	AUX
ejpam-5394	18	26	show	show	VERB
ejpam-5394	18	27	that	that	SCONJ
ejpam-5394	18	28	[	[	X
ejpam-5394	18	29	0	0	NUM
ejpam-5394	18	30	,	,	PUNCT
ejpam-5394	18	31	1	1	NUM
ejpam-5394	18	32	]	]	PUNCT
ejpam-5394	18	33	is	be	AUX
ejpam-5394	18	34	a	a	DET
ejpam-5394	18	35	hyper	hyper	ADJ
ejpam-5394	18	36	bck	bck	NOUN
ejpam-5394	18	37	-	-	PUNCT
ejpam-5394	18	38	algebra	algebra	NOUN
ejpam-5394	18	39	.	.	PUNCT
ejpam-5394	19	1	we	we	PRON
ejpam-5394	19	2	investigate	investigate	VERB
ejpam-5394	19	3	the	the	DET
ejpam-5394	19	4	basis	basis	NOUN
ejpam-5394	19	5	for	for	ADP
ejpam-5394	19	6	intersection	intersection	NOUN
ejpam-5394	19	7	of	of	ADP
ejpam-5394	19	8	topologies	topology	NOUN
ejpam-5394	19	9	τr(h	τr(h	PUNCT
ejpam-5394	19	10	)	)	PUNCT
ejpam-5394	19	11	and	and	CCONJ
ejpam-5394	19	12	τl(h	τl(h	NUM
ejpam-5394	19	13	)	)	PUNCT
ejpam-5394	19	14	.	.	PUNCT
ejpam-5394	20	1	we	we	PRON
ejpam-5394	20	2	also	also	ADV
ejpam-5394	20	3	investigate	investigate	VERB
ejpam-5394	20	4	the	the	DET
ejpam-5394	20	5	topologies	topology	NOUN
ejpam-5394	20	6	that	that	PRON
ejpam-5394	20	7	will	will	AUX
ejpam-5394	20	8	be	be	AUX
ejpam-5394	20	9	formulated	formulate	VERB
ejpam-5394	20	10	or	or	CCONJ
ejpam-5394	20	11	generated	generate	VERB
ejpam-5394	20	12	with	with	ADP
ejpam-5394	20	13	bases	basis	NOUN
ejpam-5394	20	14	br([0	br([0	NOUN
ejpam-5394	20	15	,	,	PUNCT
ejpam-5394	20	16	1	1	NUM
ejpam-5394	20	17	]	]	PUNCT
ejpam-5394	20	18	)	)	PUNCT
ejpam-5394	20	19	and	and	CCONJ
ejpam-5394	20	20	bl([0	bl([0	NOUN
ejpam-5394	20	21	,	,	PUNCT
ejpam-5394	20	22	1	1	NUM
ejpam-5394	20	23	]	]	PUNCT
ejpam-5394	20	24	)	)	PUNCT
ejpam-5394	20	25	and	and	CCONJ
ejpam-5394	20	26	their	their	PRON
ejpam-5394	20	27	intersection	intersection	NOUN
ejpam-5394	20	28	.	.	PUNCT
ejpam-5394	21	1	∗corresponding	∗corresponde	VERB
ejpam-5394	21	2	author	author	NOUN
ejpam-5394	21	3	.	.	PUNCT
ejpam-5394	22	1	doi	doi	NOUN
ejpam-5394	22	2	:	:	PUNCT
ejpam-5394	22	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5394	https://doi.org/10.29020/nybg.ejpam.v18i2.5394	NOUN
ejpam-5394	22	4	email	email	NOUN
ejpam-5394	22	5	addresses	address	NOUN
ejpam-5394	22	6	:	:	PUNCT
ejpam-5394	22	7	eipayla@csucc.edu.ph	eipayla@csucc.edu.ph	PROPN
ejpam-5394	22	8	(	(	PUNCT
ejpam-5394	22	9	e.	e.	PROPN
ejpam-5394	22	10	payla	payla	PROPN
ejpam-5394	22	11	)	)	PUNCT
ejpam-5394	22	12	,	,	PUNCT
ejpam-5394	22	13	luzviminda.ranara@msumain.edu.ph	luzviminda.ranara@msumain.edu.ph	PROPN
ejpam-5394	22	14	(	(	PUNCT
ejpam-5394	22	15	l.	l.	PROPN
ejpam-5394	22	16	ranara	ranara	PROPN
ejpam-5394	22	17	)	)	PUNCT
ejpam-5394	22	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5394	23	1	1	1	NUM
ejpam-5394	23	2	copyright	copyright	NOUN
ejpam-5394	23	3	:	:	PUNCT
ejpam-5394	23	4	©	©	PROPN
ejpam-5394	23	5	2025	2025	NUM
ejpam-5394	23	6	the	the	DET
ejpam-5394	23	7	author(s	author(s	NOUN
ejpam-5394	23	8	)	)	PUNCT
ejpam-5394	23	9	.	.	PUNCT
ejpam-5394	24	1	(	(	PUNCT
ejpam-5394	24	2	cc	cc	NOUN
ejpam-5394	24	3	by	by	ADP
ejpam-5394	24	4	-	-	PUNCT
ejpam-5394	24	5	nc	nc	PROPN
ejpam-5394	24	6	4.0	4.0	NUM
ejpam-5394	24	7	)	)	PUNCT
ejpam-5394	24	8	e.	e.	PROPN
ejpam-5394	24	9	payla	payla	PROPN
ejpam-5394	24	10	,	,	PUNCT
ejpam-5394	24	11	l.	l.	PROPN
ejpam-5394	24	12	ranara	ranara	PROPN
ejpam-5394	24	13	/	/	SYM
ejpam-5394	24	14	eur	eur	PROPN
ejpam-5394	24	15	.	.	PUNCT
ejpam-5394	25	1	j.	j.	PROPN
ejpam-5394	25	2	pure	pure	PROPN
ejpam-5394	25	3	appl	appl	PROPN
ejpam-5394	25	4	.	.	PROPN
ejpam-5394	25	5	math	math	PROPN
ejpam-5394	25	6	,	,	PUNCT
ejpam-5394	25	7	18	18	NUM
ejpam-5394	25	8	(	(	PUNCT
ejpam-5394	25	9	2	2	NUM
ejpam-5394	25	10	)	)	PUNCT
ejpam-5394	25	11	(	(	PUNCT
ejpam-5394	25	12	2025	2025	NUM
ejpam-5394	25	13	)	)	PUNCT
ejpam-5394	25	14	,	,	PUNCT
ejpam-5394	25	15	5394	5394	NUM
ejpam-5394	25	16	2	2	NUM
ejpam-5394	25	17	of	of	ADP
ejpam-5394	25	18	10	10	NUM
ejpam-5394	25	19	2	2	NUM
ejpam-5394	25	20	.	.	PUNCT
ejpam-5394	26	1	known	know	VERB
ejpam-5394	26	2	results	result	NOUN
ejpam-5394	26	3	definition	definition	NOUN
ejpam-5394	26	4	1	1	NUM
ejpam-5394	26	5	.	.	PUNCT
ejpam-5394	27	1	[	[	X
ejpam-5394	27	2	5	5	NUM
ejpam-5394	27	3	]	]	PUNCT
ejpam-5394	27	4	let	let	VERB
ejpam-5394	27	5	p(h	p(h	NOUN
ejpam-5394	27	6	)	)	PUNCT
ejpam-5394	27	7	be	be	VERB
ejpam-5394	27	8	the	the	DET
ejpam-5394	27	9	power	power	NOUN
ejpam-5394	27	10	set	set	NOUN
ejpam-5394	27	11	of	of	ADP
ejpam-5394	27	12	a	a	DET
ejpam-5394	27	13	nonempty	nonempty	ADV
ejpam-5394	27	14	set	set	VERB
ejpam-5394	27	15	h.	h.	NOUN
ejpam-5394	27	16	consider	consider	VERB
ejpam-5394	27	17	p(h)∗	p(h)∗	NOUN
ejpam-5394	27	18	=	=	SYM
ejpam-5394	27	19	p(h	p(h	PROPN
ejpam-5394	27	20	)	)	PUNCT
ejpam-5394	27	21	\	\	NOUN
ejpam-5394	27	22	{	{	PUNCT
ejpam-5394	27	23	∅	∅	NOUN
ejpam-5394	27	24	}	}	PUNCT
ejpam-5394	27	25	.	.	PUNCT
ejpam-5394	28	1	a	a	DET
ejpam-5394	28	2	hyperoperation	hyperoperation	NOUN
ejpam-5394	28	3	on	on	ADP
ejpam-5394	28	4	a	a	DET
ejpam-5394	28	5	nonempty	nonempty	ADV
ejpam-5394	28	6	set	set	VERB
ejpam-5394	28	7	h	h	NOUN
ejpam-5394	28	8	is	be	AUX
ejpam-5394	28	9	a	a	DET
ejpam-5394	28	10	function	function	NOUN
ejpam-5394	28	11	∗	∗	NOUN
ejpam-5394	28	12	:	:	PUNCT
ejpam-5394	28	13	h	h	NOUN
ejpam-5394	28	14	×h	×h	PROPN
ejpam-5394	28	15	→	→	PUNCT
ejpam-5394	28	16	p(h)∗.	p(h)∗.	VERB
ejpam-5394	28	17	the	the	DET
ejpam-5394	28	18	image	image	NOUN
ejpam-5394	28	19	of	of	ADP
ejpam-5394	28	20	(	(	PUNCT
ejpam-5394	28	21	x	x	NOUN
ejpam-5394	28	22	,	,	PUNCT
ejpam-5394	28	23	y	y	NOUN
ejpam-5394	28	24	)	)	PUNCT
ejpam-5394	28	25	∈	∈	PROPN
ejpam-5394	28	26	h×h	h×h	PROPN
ejpam-5394	28	27	under	under	ADP
ejpam-5394	28	28	∗	∗	NOUN
ejpam-5394	28	29	is	be	AUX
ejpam-5394	28	30	denoted	denote	VERB
ejpam-5394	28	31	by	by	ADP
ejpam-5394	28	32	x∗y	x∗y	PROPN
ejpam-5394	28	33	.	.	PUNCT
ejpam-5394	29	1	if	if	SCONJ
ejpam-5394	29	2	x	x	SYM
ejpam-5394	29	3	∈	∈	PROPN
ejpam-5394	29	4	h	h	NOUN
ejpam-5394	29	5	and	and	CCONJ
ejpam-5394	29	6	a	a	DET
ejpam-5394	29	7	,	,	PUNCT
ejpam-5394	29	8	b	b	NOUN
ejpam-5394	29	9	are	be	AUX
ejpam-5394	29	10	nonempty	nonempty	ADJ
ejpam-5394	29	11	subsets	subset	NOUN
ejpam-5394	29	12	of	of	ADP
ejpam-5394	29	13	h	h	NOUN
ejpam-5394	29	14	,	,	PUNCT
ejpam-5394	29	15	then	then	ADV
ejpam-5394	29	16	we	we	PRON
ejpam-5394	29	17	define	define	VERB
ejpam-5394	29	18	(	(	PUNCT
ejpam-5394	29	19	i	i	NOUN
ejpam-5394	29	20	)	)	PUNCT
ejpam-5394	29	21	a	a	DET
ejpam-5394	29	22	∗b	∗b	NOUN
ejpam-5394	30	1	=	=	PUNCT
ejpam-5394	30	2	⋃	⋃	NOUN
ejpam-5394	30	3	a∈a	a∈a	ADJ
ejpam-5394	30	4	,	,	PUNCT
ejpam-5394	30	5	b∈b	b∈b	VERB
ejpam-5394	30	6	a	a	DET
ejpam-5394	30	7	∗	∗	NOUN
ejpam-5394	30	8	b	b	NOUN
ejpam-5394	30	9	;	;	PUNCT
ejpam-5394	30	10	(	(	PUNCT
ejpam-5394	30	11	ii	ii	NOUN
ejpam-5394	30	12	)	)	PUNCT
ejpam-5394	30	13	a	a	DET
ejpam-5394	30	14	∗	∗	NOUN
ejpam-5394	30	15	x	x	X
ejpam-5394	30	16	=	=	PUNCT
ejpam-5394	30	17	a	a	DET
ejpam-5394	30	18	∗	∗	NOUN
ejpam-5394	30	19	{	{	PUNCT
ejpam-5394	30	20	x	x	NOUN
ejpam-5394	30	21	}	}	PUNCT
ejpam-5394	30	22	;	;	PUNCT
ejpam-5394	30	23	and	and	CCONJ
ejpam-5394	30	24	,	,	PUNCT
ejpam-5394	30	25	(	(	PUNCT
ejpam-5394	30	26	iii	iii	X
ejpam-5394	30	27	)	)	PUNCT
ejpam-5394	30	28	x	x	X
ejpam-5394	31	1	∗b	∗b	NOUN
ejpam-5394	31	2	=	=	PUNCT
ejpam-5394	31	3	{	{	PUNCT
ejpam-5394	31	4	x	x	NOUN
ejpam-5394	31	5	}	}	PUNCT
ejpam-5394	31	6	∗b	∗b	PROPN
ejpam-5394	31	7	.	.	PUNCT
ejpam-5394	32	1	definition	definition	NOUN
ejpam-5394	32	2	2	2	NUM
ejpam-5394	32	3	.	.	PUNCT
ejpam-5394	33	1	[	[	X
ejpam-5394	33	2	5	5	NUM
ejpam-5394	33	3	]	]	PUNCT
ejpam-5394	33	4	let	let	VERB
ejpam-5394	33	5	x	x	PRON
ejpam-5394	33	6	,	,	PUNCT
ejpam-5394	33	7	y	y	PROPN
ejpam-5394	33	8	∈	∈	PROPN
ejpam-5394	33	9	h	h	NOUN
ejpam-5394	33	10	and	and	CCONJ
ejpam-5394	33	11	a	a	PRON
ejpam-5394	33	12	,	,	PUNCT
ejpam-5394	33	13	b	b	PROPN
ejpam-5394	33	14	⊆	⊆	NUM
ejpam-5394	33	15	h.	h.	NOUN
ejpam-5394	33	16	then	then	ADV
ejpam-5394	33	17	(	(	PUNCT
ejpam-5394	33	18	i	i	NOUN
ejpam-5394	33	19	)	)	PUNCT
ejpam-5394	33	20	x	x	PUNCT
ejpam-5394	33	21	≪	≪	VERB
ejpam-5394	33	22	y	y	PROPN
ejpam-5394	33	23	if	if	SCONJ
ejpam-5394	33	24	and	and	CCONJ
ejpam-5394	33	25	only	only	ADV
ejpam-5394	33	26	if	if	SCONJ
ejpam-5394	33	27	0	0	NUM
ejpam-5394	33	28	∈	∈	NOUN
ejpam-5394	33	29	x	x	X
ejpam-5394	33	30	∗	∗	NOUN
ejpam-5394	33	31	y	y	PROPN
ejpam-5394	33	32	;	;	PUNCT
ejpam-5394	33	33	and	and	CCONJ
ejpam-5394	33	34	(	(	PUNCT
ejpam-5394	33	35	ii	ii	NOUN
ejpam-5394	33	36	)	)	PUNCT
ejpam-5394	33	37	a	a	DET
ejpam-5394	33	38	≪	≪	ADJ
ejpam-5394	33	39	b	b	NOUN
ejpam-5394	33	40	if	if	SCONJ
ejpam-5394	33	41	and	and	CCONJ
ejpam-5394	33	42	only	only	ADV
ejpam-5394	33	43	if	if	SCONJ
ejpam-5394	33	44	for	for	ADP
ejpam-5394	33	45	any	any	DET
ejpam-5394	33	46	a	a	DET
ejpam-5394	33	47	∈	∈	PROPN
ejpam-5394	33	48	a	a	PRON
ejpam-5394	33	49	,	,	PUNCT
ejpam-5394	33	50	there	there	PRON
ejpam-5394	33	51	exist	exist	VERB
ejpam-5394	33	52	b	b	PROPN
ejpam-5394	33	53	∈	∈	PROPN
ejpam-5394	33	54	b	b	NOUN
ejpam-5394	33	55	such	such	ADJ
ejpam-5394	33	56	that	that	SCONJ
ejpam-5394	33	57	a	a	DET
ejpam-5394	33	58	≪	≪	ADJ
ejpam-5394	33	59	b.	b.	NOUN
ejpam-5394	33	60	we	we	PRON
ejpam-5394	33	61	call	call	VERB
ejpam-5394	33	62	“	"	PUNCT
ejpam-5394	33	63	≪	≪	PROPN
ejpam-5394	33	64	”	"	PUNCT
ejpam-5394	33	65	a	a	DET
ejpam-5394	33	66	hyperorder	hyperorder	NOUN
ejpam-5394	33	67	on	on	ADP
ejpam-5394	33	68	h.	h.	PROPN
ejpam-5394	33	69	definition	definition	NOUN
ejpam-5394	33	70	3	3	NUM
ejpam-5394	33	71	.	.	PUNCT
ejpam-5394	34	1	[	[	X
ejpam-5394	34	2	6	6	NUM
ejpam-5394	34	3	]	]	PUNCT
ejpam-5394	34	4	a	a	DET
ejpam-5394	34	5	hyper	hyper	ADJ
ejpam-5394	34	6	bck	bck	NOUN
ejpam-5394	34	7	-	-	PUNCT
ejpam-5394	34	8	algebra	algebra	NOUN
ejpam-5394	34	9	is	be	AUX
ejpam-5394	34	10	a	a	DET
ejpam-5394	34	11	nonempty	nonempty	ADV
ejpam-5394	34	12	set	set	VERB
ejpam-5394	34	13	h	h	NOUN
ejpam-5394	34	14	endowed	endow	VERB
ejpam-5394	34	15	with	with	ADP
ejpam-5394	34	16	a	a	DET
ejpam-5394	34	17	hyperoperation	hyperoperation	NOUN
ejpam-5394	34	18	“	"	PUNCT
ejpam-5394	34	19	∗	∗	NOUN
ejpam-5394	34	20	”	"	PUNCT
ejpam-5394	34	21	and	and	CCONJ
ejpam-5394	34	22	a	a	DET
ejpam-5394	34	23	constant	constant	ADJ
ejpam-5394	34	24	0	0	NUM
ejpam-5394	34	25	satisfying	satisfy	VERB
ejpam-5394	34	26	the	the	DET
ejpam-5394	34	27	following	follow	VERB
ejpam-5394	34	28	axioms	axiom	NOUN
ejpam-5394	34	29	:	:	PUNCT
ejpam-5394	34	30	for	for	ADP
ejpam-5394	34	31	all	all	PRON
ejpam-5394	34	32	x	x	NOUN
ejpam-5394	34	33	,	,	PUNCT
ejpam-5394	34	34	y	y	PROPN
ejpam-5394	34	35	,	,	PUNCT
ejpam-5394	34	36	z	z	PROPN
ejpam-5394	34	37	∈	∈	PROPN
ejpam-5394	34	38	h	h	NOUN
ejpam-5394	34	39	,	,	PUNCT
ejpam-5394	34	40	(	(	PUNCT
ejpam-5394	34	41	i	i	NOUN
ejpam-5394	34	42	)	)	PUNCT
ejpam-5394	34	43	(	(	PUNCT
ejpam-5394	34	44	x	x	X
ejpam-5394	34	45	∗	∗	PROPN
ejpam-5394	34	46	z	z	NOUN
ejpam-5394	34	47	)	)	PUNCT
ejpam-5394	34	48	∗	∗	NOUN
ejpam-5394	34	49	(	(	PUNCT
ejpam-5394	34	50	y	y	PROPN
ejpam-5394	34	51	∗	∗	PROPN
ejpam-5394	34	52	z	z	NOUN
ejpam-5394	34	53	)	)	PUNCT
ejpam-5394	34	54	≪	≪	PUNCT
ejpam-5394	35	1	x	x	PUNCT
ejpam-5394	35	2	∗	∗	NOUN
ejpam-5394	35	3	y	y	PROPN
ejpam-5394	35	4	,	,	PUNCT
ejpam-5394	35	5	(	(	PUNCT
ejpam-5394	35	6	ii	ii	NOUN
ejpam-5394	35	7	)	)	PUNCT
ejpam-5394	35	8	(	(	PUNCT
ejpam-5394	35	9	x	x	SYM
ejpam-5394	35	10	∗	∗	PROPN
ejpam-5394	35	11	y	y	NOUN
ejpam-5394	35	12	)	)	PUNCT
ejpam-5394	35	13	∗	∗	NOUN
ejpam-5394	35	14	z	z	NOUN
ejpam-5394	35	15	=	=	SYM
ejpam-5394	35	16	(	(	PUNCT
ejpam-5394	35	17	x	x	X
ejpam-5394	35	18	∗	∗	PROPN
ejpam-5394	35	19	z	z	NOUN
ejpam-5394	35	20	)	)	PUNCT
ejpam-5394	35	21	∗	∗	PROPN
ejpam-5394	35	22	y	y	PROPN
ejpam-5394	35	23	,	,	PUNCT
ejpam-5394	35	24	(	(	PUNCT
ejpam-5394	35	25	iii	iii	NOUN
ejpam-5394	35	26	)	)	PUNCT
ejpam-5394	35	27	x	x	PUNCT
ejpam-5394	35	28	∗h	∗h	NOUN
ejpam-5394	35	29	≪	≪	VERB
ejpam-5394	35	30	x	x	SYM
ejpam-5394	35	31	,	,	PUNCT
ejpam-5394	35	32	(	(	PUNCT
ejpam-5394	35	33	iv	iv	X
ejpam-5394	35	34	)	)	PUNCT
ejpam-5394	35	35	x	x	SYM
ejpam-5394	35	36	≪	≪	PUNCT
ejpam-5394	35	37	y	y	PROPN
ejpam-5394	35	38	and	and	CCONJ
ejpam-5394	35	39	y	y	PROPN
ejpam-5394	35	40	≪	≪	NOUN
ejpam-5394	35	41	x	x	X
ejpam-5394	35	42	imply	imply	ADV
ejpam-5394	35	43	x	x	INTJ
ejpam-5394	35	44	=	=	SYM
ejpam-5394	35	45	y.	y.	NOUN
ejpam-5394	35	46	proposition	proposition	NOUN
ejpam-5394	35	47	1	1	NUM
ejpam-5394	35	48	.	.	PUNCT
ejpam-5394	36	1	[	[	X
ejpam-5394	36	2	6	6	NUM
ejpam-5394	36	3	]	]	PUNCT
ejpam-5394	36	4	in	in	ADP
ejpam-5394	36	5	a	a	DET
ejpam-5394	36	6	hyper	hyper	ADJ
ejpam-5394	36	7	bck	bck	NOUN
ejpam-5394	36	8	-	-	PUNCT
ejpam-5394	36	9	algebra	algebra	NOUN
ejpam-5394	36	10	(	(	PUNCT
ejpam-5394	36	11	h	h	NOUN
ejpam-5394	36	12	,	,	PUNCT
ejpam-5394	36	13	∗	∗	NOUN
ejpam-5394	36	14	,	,	PUNCT
ejpam-5394	36	15	0	0	NUM
ejpam-5394	36	16	)	)	PUNCT
ejpam-5394	36	17	,	,	PUNCT
ejpam-5394	36	18	the	the	DET
ejpam-5394	36	19	condition	condition	NOUN
ejpam-5394	36	20	(	(	PUNCT
ejpam-5394	36	21	iii	iii	NOUN
ejpam-5394	36	22	)	)	PUNCT
ejpam-5394	36	23	of	of	ADP
ejpam-5394	36	24	definition	definition	NOUN
ejpam-5394	36	25	3	3	NUM
ejpam-5394	36	26	is	be	AUX
ejpam-5394	36	27	equivalent	equivalent	ADJ
ejpam-5394	36	28	to	to	ADP
ejpam-5394	36	29	the	the	DET
ejpam-5394	36	30	condition	condition	NOUN
ejpam-5394	36	31	x	x	PUNCT
ejpam-5394	36	32	∗	∗	NOUN
ejpam-5394	36	33	y	y	PROPN
ejpam-5394	36	34	≪	≪	PUNCT
ejpam-5394	36	35	{	{	PUNCT
ejpam-5394	36	36	x	x	X
ejpam-5394	36	37	}	}	PUNCT
ejpam-5394	36	38	for	for	ADP
ejpam-5394	36	39	all	all	DET
ejpam-5394	36	40	x	x	NOUN
ejpam-5394	36	41	,	,	PUNCT
ejpam-5394	36	42	y	y	PROPN
ejpam-5394	36	43	∈	∈	PROPN
ejpam-5394	36	44	h.	h.	PROPN
ejpam-5394	36	45	theorem	theorem	VERB
ejpam-5394	36	46	1	1	NUM
ejpam-5394	36	47	.	.	PUNCT
ejpam-5394	37	1	[	[	X
ejpam-5394	37	2	7	7	X
ejpam-5394	37	3	]	]	X
ejpam-5394	37	4	let	let	VERB
ejpam-5394	37	5	b	b	NOUN
ejpam-5394	37	6	⊆	⊆	NUM
ejpam-5394	37	7	τ	τ	X
ejpam-5394	37	8	.	.	PUNCT
ejpam-5394	38	1	the	the	DET
ejpam-5394	38	2	following	follow	VERB
ejpam-5394	38	3	two	two	NUM
ejpam-5394	38	4	properties	property	NOUN
ejpam-5394	38	5	of	of	ADP
ejpam-5394	38	6	b	b	NOUN
ejpam-5394	38	7	are	be	AUX
ejpam-5394	38	8	equivalent	equivalent	ADJ
ejpam-5394	38	9	:	:	PUNCT
ejpam-5394	38	10	(	(	PUNCT
ejpam-5394	38	11	1	1	X
ejpam-5394	38	12	)	)	PUNCT
ejpam-5394	38	13	b	b	NOUN
ejpam-5394	38	14	is	be	AUX
ejpam-5394	38	15	a	a	DET
ejpam-5394	38	16	basis	basis	NOUN
ejpam-5394	38	17	for	for	ADP
ejpam-5394	38	18	τ	τ	PROPN
ejpam-5394	38	19	.	.	PUNCT
ejpam-5394	39	1	(	(	PUNCT
ejpam-5394	39	2	2	2	X
ejpam-5394	39	3	)	)	PUNCT
ejpam-5394	39	4	for	for	ADP
ejpam-5394	39	5	each	each	DET
ejpam-5394	39	6	g	g	PROPN
ejpam-5394	39	7	∈	∈	PROPN
ejpam-5394	39	8	τ	τ	X
ejpam-5394	39	9	and	and	CCONJ
ejpam-5394	40	1	each	each	DET
ejpam-5394	40	2	x	x	SYM
ejpam-5394	40	3	∈	∈	PROPN
ejpam-5394	40	4	g	g	NOUN
ejpam-5394	40	5	there	there	PRON
ejpam-5394	40	6	is	be	VERB
ejpam-5394	40	7	a	a	DET
ejpam-5394	40	8	u	u	NOUN
ejpam-5394	40	9	∈	∈	PROPN
ejpam-5394	40	10	b	b	NOUN
ejpam-5394	40	11	with	with	ADP
ejpam-5394	40	12	x	x	PROPN
ejpam-5394	40	13	∈	∈	PROPN
ejpam-5394	40	14	u	u	NOUN
ejpam-5394	40	15	⊆	⊆	PROPN
ejpam-5394	40	16	g.	g.	NOUN
ejpam-5394	40	17	theorem	theorem	NOUN
ejpam-5394	40	18	2	2	NUM
ejpam-5394	40	19	.	.	PUNCT
ejpam-5394	41	1	[	[	X
ejpam-5394	41	2	7	7	X
ejpam-5394	41	3	]	]	X
ejpam-5394	41	4	let	let	VERB
ejpam-5394	41	5	x	x	PUNCT
ejpam-5394	41	6	̸=	̸=	PROPN
ejpam-5394	41	7	∅.	∅.	ADP
ejpam-5394	41	8	a	a	DET
ejpam-5394	41	9	class	class	NOUN
ejpam-5394	41	10	of	of	ADP
ejpam-5394	41	11	subsets	subsets	PROPN
ejpam-5394	41	12	b	b	PROPN
ejpam-5394	41	13	of	of	ADP
ejpam-5394	41	14	x	x	PUNCT
ejpam-5394	41	15	is	be	AUX
ejpam-5394	41	16	a	a	DET
ejpam-5394	41	17	basis	basis	NOUN
ejpam-5394	41	18	for	for	ADP
ejpam-5394	41	19	some	some	DET
ejpam-5394	41	20	topology	topology	NOUN
ejpam-5394	41	21	τ	τ	X
ejpam-5394	41	22	on	on	ADP
ejpam-5394	41	23	x	x	SYM
ejpam-5394	41	24	if	if	SCONJ
ejpam-5394	41	25	it	it	PRON
ejpam-5394	41	26	satisfies	satisfy	VERB
ejpam-5394	41	27	the	the	DET
ejpam-5394	41	28	following	following	NOUN
ejpam-5394	41	29	:	:	PUNCT
ejpam-5394	41	30	(	(	PUNCT
ejpam-5394	41	31	i	i	NOUN
ejpam-5394	41	32	)	)	PUNCT
ejpam-5394	41	33	b	b	PROPN
ejpam-5394	41	34	covers	cover	VERB
ejpam-5394	41	35	x	x	PRON
ejpam-5394	41	36	,	,	PUNCT
ejpam-5394	41	37	and	and	CCONJ
ejpam-5394	41	38	(	(	PUNCT
ejpam-5394	41	39	ii	ii	NOUN
ejpam-5394	41	40	)	)	PUNCT
ejpam-5394	41	41	for	for	ADP
ejpam-5394	41	42	each	each	DET
ejpam-5394	41	43	x	x	SYM
ejpam-5394	41	44	∈	∈	PROPN
ejpam-5394	41	45	uα∩uβ	uα∩uβ	PROPN
ejpam-5394	41	46	,	,	PUNCT
ejpam-5394	41	47	there	there	PRON
ejpam-5394	41	48	exists	exist	VERB
ejpam-5394	41	49	u	u	PROPN
ejpam-5394	41	50	∈	∈	PROPN
ejpam-5394	41	51	b	b	PROPN
ejpam-5394	41	52	such	such	ADJ
ejpam-5394	41	53	that	that	SCONJ
ejpam-5394	41	54	x	x	SYM
ejpam-5394	41	55	∈	∈	NOUN
ejpam-5394	41	56	u	u	NOUN
ejpam-5394	41	57	⊆	⊆	NUM
ejpam-5394	41	58	uα∩uβ	uα∩uβ	NOUN
ejpam-5394	41	59	where	where	SCONJ
ejpam-5394	41	60	uα	uα	PROPN
ejpam-5394	41	61	,	,	PUNCT
ejpam-5394	41	62	uβ	uβ	PROPN
ejpam-5394	41	63	∈	∈	PROPN
ejpam-5394	41	64	b.	b.	PROPN
ejpam-5394	41	65	definition	definition	NOUN
ejpam-5394	41	66	4	4	NUM
ejpam-5394	41	67	.	.	PUNCT
ejpam-5394	42	1	[	[	X
ejpam-5394	42	2	7	7	X
ejpam-5394	42	3	]	]	X
ejpam-5394	42	4	a	a	DET
ejpam-5394	42	5	space	space	NOUN
ejpam-5394	42	6	x	x	PUNCT
ejpam-5394	42	7	is	be	AUX
ejpam-5394	42	8	said	say	VERB
ejpam-5394	42	9	to	to	PART
ejpam-5394	42	10	be	be	AUX
ejpam-5394	42	11	connected	connect	VERB
ejpam-5394	42	12	if	if	SCONJ
ejpam-5394	42	13	x	x	PRON
ejpam-5394	42	14	is	be	AUX
ejpam-5394	42	15	not	not	PART
ejpam-5394	42	16	the	the	DET
ejpam-5394	42	17	union	union	NOUN
ejpam-5394	42	18	of	of	ADP
ejpam-5394	42	19	two	two	NUM
ejpam-5394	42	20	disjoint	disjoint	ADJ
ejpam-5394	42	21	open	open	ADJ
ejpam-5394	42	22	sets	set	NOUN
ejpam-5394	42	23	.	.	PUNCT
ejpam-5394	43	1	otherwise	otherwise	ADV
ejpam-5394	43	2	,	,	PUNCT
ejpam-5394	43	3	it	it	PRON
ejpam-5394	43	4	is	be	AUX
ejpam-5394	43	5	said	say	VERB
ejpam-5394	43	6	to	to	PART
ejpam-5394	43	7	be	be	AUX
ejpam-5394	43	8	disconnected	disconnect	VERB
ejpam-5394	43	9	.	.	PUNCT
ejpam-5394	44	1	e.	e.	PROPN
ejpam-5394	44	2	payla	payla	PROPN
ejpam-5394	44	3	,	,	PUNCT
ejpam-5394	44	4	l.	l.	PROPN
ejpam-5394	44	5	ranara	ranara	PROPN
ejpam-5394	44	6	/	/	SYM
ejpam-5394	44	7	eur	eur	PROPN
ejpam-5394	44	8	.	.	PUNCT
ejpam-5394	45	1	j.	j.	PROPN
ejpam-5394	45	2	pure	pure	PROPN
ejpam-5394	45	3	appl	appl	PROPN
ejpam-5394	45	4	.	.	PROPN
ejpam-5394	45	5	math	math	PROPN
ejpam-5394	45	6	,	,	PUNCT
ejpam-5394	45	7	18	18	NUM
ejpam-5394	45	8	(	(	PUNCT
ejpam-5394	45	9	2	2	NUM
ejpam-5394	45	10	)	)	PUNCT
ejpam-5394	45	11	(	(	PUNCT
ejpam-5394	45	12	2025	2025	NUM
ejpam-5394	45	13	)	)	PUNCT
ejpam-5394	45	14	,	,	PUNCT
ejpam-5394	45	15	5394	5394	NUM
ejpam-5394	45	16	3	3	NUM
ejpam-5394	45	17	of	of	ADP
ejpam-5394	45	18	10	10	NUM
ejpam-5394	45	19	definition	definition	NOUN
ejpam-5394	45	20	5	5	NUM
ejpam-5394	45	21	.	.	PUNCT
ejpam-5394	46	1	[	[	X
ejpam-5394	46	2	3	3	X
ejpam-5394	46	3	]	]	PUNCT
ejpam-5394	46	4	let	let	VERB
ejpam-5394	46	5	h	h	PRON
ejpam-5394	46	6	be	be	AUX
ejpam-5394	46	7	a	a	DET
ejpam-5394	46	8	hyper	hyper	ADJ
ejpam-5394	46	9	bck	bck	NOUN
ejpam-5394	46	10	-	-	PUNCT
ejpam-5394	46	11	algebra	algebra	NOUN
ejpam-5394	46	12	and	and	CCONJ
ejpam-5394	46	13	a	a	DET
ejpam-5394	46	14	⊆	⊆	NUM
ejpam-5394	46	15	h.	h.	NOUN
ejpam-5394	46	16	then	then	ADV
ejpam-5394	46	17	the	the	DET
ejpam-5394	46	18	set	set	NOUN
ejpam-5394	46	19	rh(a	rh(a	NOUN
ejpam-5394	46	20	)	)	PUNCT
ejpam-5394	46	21	is	be	AUX
ejpam-5394	46	22	defined	define	VERB
ejpam-5394	46	23	as	as	ADP
ejpam-5394	46	24	rh(a	rh(a	NUM
ejpam-5394	46	25	)	)	PUNCT
ejpam-5394	46	26	=	=	PRON
ejpam-5394	46	27	{	{	PUNCT
ejpam-5394	46	28	x	x	PUNCT
ejpam-5394	46	29	∈	∈	PROPN
ejpam-5394	46	30	h	h	NOUN
ejpam-5394	46	31	:	:	PUNCT
ejpam-5394	46	32	a	a	DET
ejpam-5394	46	33	≪	≪	ADJ
ejpam-5394	46	34	x	x	PUNCT
ejpam-5394	46	35	for	for	ADP
ejpam-5394	46	36	all	all	DET
ejpam-5394	46	37	a	a	DET
ejpam-5394	46	38	∈	∈	PROPN
ejpam-5394	46	39	a	a	DET
ejpam-5394	46	40	}	}	PUNCT
ejpam-5394	46	41	=	=	SYM
ejpam-5394	46	42	{	{	PUNCT
ejpam-5394	46	43	x	x	PUNCT
ejpam-5394	46	44	∈	∈	PROPN
ejpam-5394	46	45	h	h	NOUN
ejpam-5394	46	46	:	:	PUNCT
ejpam-5394	46	47	0	0	NUM
ejpam-5394	46	48	∈	∈	PROPN
ejpam-5394	46	49	a	a	DET
ejpam-5394	46	50	∗	∗	NOUN
ejpam-5394	46	51	x	x	PUNCT
ejpam-5394	46	52	for	for	ADP
ejpam-5394	46	53	all	all	DET
ejpam-5394	46	54	a	a	DET
ejpam-5394	46	55	∈	∈	PROPN
ejpam-5394	46	56	a	a	PRON
ejpam-5394	46	57	}	}	PUNCT
ejpam-5394	46	58	.	.	PUNCT
ejpam-5394	47	1	if	if	SCONJ
ejpam-5394	47	2	a	a	PRON
ejpam-5394	47	3	=	=	X
ejpam-5394	47	4	{	{	PUNCT
ejpam-5394	47	5	a	a	NOUN
ejpam-5394	47	6	}	}	PUNCT
ejpam-5394	47	7	,	,	PUNCT
ejpam-5394	47	8	then	then	ADV
ejpam-5394	47	9	we	we	PRON
ejpam-5394	47	10	write	write	VERB
ejpam-5394	47	11	rh({a	rh({a	NOUN
ejpam-5394	47	12	}	}	PUNCT
ejpam-5394	47	13	)	)	PUNCT
ejpam-5394	47	14	=	=	SYM
ejpam-5394	48	1	rh(a	rh(a	NUM
ejpam-5394	48	2	)	)	PUNCT
ejpam-5394	48	3	.	.	PUNCT
ejpam-5394	49	1	definition	definition	NOUN
ejpam-5394	49	2	6	6	NUM
ejpam-5394	49	3	.	.	PUNCT
ejpam-5394	50	1	[	[	X
ejpam-5394	50	2	3	3	X
ejpam-5394	50	3	]	]	X
ejpam-5394	50	4	an	an	DET
ejpam-5394	50	5	element	element	NOUN
ejpam-5394	50	6	a	a	PRON
ejpam-5394	50	7	of	of	ADP
ejpam-5394	50	8	h	h	NOUN
ejpam-5394	50	9	of	of	ADP
ejpam-5394	50	10	a	a	DET
ejpam-5394	50	11	hyper	hyper	ADJ
ejpam-5394	50	12	bck	bck	NOUN
ejpam-5394	50	13	-	-	PUNCT
ejpam-5394	50	14	algebra	algebra	NOUN
ejpam-5394	50	15	h	h	NOUN
ejpam-5394	50	16	is	be	AUX
ejpam-5394	50	17	called	call	VERB
ejpam-5394	50	18	a	a	DET
ejpam-5394	50	19	hyperatom	hyperatom	NOUN
ejpam-5394	50	20	if	if	SCONJ
ejpam-5394	50	21	x	x	PRON
ejpam-5394	50	22	≪	≪	VERB
ejpam-5394	50	23	a	a	DET
ejpam-5394	50	24	implies	implie	NOUN
ejpam-5394	50	25	x	x	X
ejpam-5394	50	26	=	=	SYM
ejpam-5394	50	27	0	0	NUM
ejpam-5394	50	28	or	or	CCONJ
ejpam-5394	50	29	x	x	X
ejpam-5394	50	30	=	=	PUNCT
ejpam-5394	50	31	a	a	PRON
ejpam-5394	50	32	for	for	ADP
ejpam-5394	50	33	all	all	DET
ejpam-5394	50	34	x	x	SYM
ejpam-5394	50	35	∈	∈	PROPN
ejpam-5394	50	36	h.	h.	PROPN
ejpam-5394	50	37	denote	denote	NOUN
ejpam-5394	50	38	a(h	a(h	PROPN
ejpam-5394	50	39	)	)	PUNCT
ejpam-5394	50	40	the	the	DET
ejpam-5394	50	41	set	set	NOUN
ejpam-5394	50	42	of	of	ADP
ejpam-5394	50	43	all	all	DET
ejpam-5394	50	44	hyperatoms	hyperatom	NOUN
ejpam-5394	50	45	of	of	ADP
ejpam-5394	50	46	h	h	NOUN
ejpam-5394	50	47	and	and	CCONJ
ejpam-5394	50	48	a∗(h	a∗(h	PROPN
ejpam-5394	50	49	)	)	PUNCT
ejpam-5394	50	50	=	=	SYM
ejpam-5394	50	51	a(h	a(h	PROPN
ejpam-5394	50	52	)	)	PUNCT
ejpam-5394	50	53	\	\	NOUN
ejpam-5394	50	54	{	{	PUNCT
ejpam-5394	50	55	0	0	NUM
ejpam-5394	50	56	}	}	PUNCT
ejpam-5394	50	57	.	.	PUNCT
ejpam-5394	51	1	obviously	obviously	ADV
ejpam-5394	51	2	,	,	PUNCT
ejpam-5394	51	3	0	0	NUM
ejpam-5394	51	4	∈	∈	PROPN
ejpam-5394	51	5	a(h	a(h	PROPN
ejpam-5394	51	6	)	)	PUNCT
ejpam-5394	51	7	.	.	PUNCT
ejpam-5394	52	1	if	if	SCONJ
ejpam-5394	52	2	each	each	DET
ejpam-5394	52	3	element	element	NOUN
ejpam-5394	52	4	of	of	ADP
ejpam-5394	52	5	h	h	NOUN
ejpam-5394	52	6	is	be	AUX
ejpam-5394	52	7	a	a	DET
ejpam-5394	52	8	hyperatom	hyperatom	NOUN
ejpam-5394	52	9	,	,	PUNCT
ejpam-5394	52	10	then	then	ADV
ejpam-5394	52	11	h	h	NOUN
ejpam-5394	52	12	is	be	AUX
ejpam-5394	52	13	said	say	VERB
ejpam-5394	52	14	to	to	PART
ejpam-5394	52	15	be	be	AUX
ejpam-5394	52	16	hyperatomic	hyperatomic	ADJ
ejpam-5394	52	17	,	,	PUNCT
ejpam-5394	52	18	that	that	ADV
ejpam-5394	52	19	is	is	ADV
ejpam-5394	52	20	,	,	PUNCT
ejpam-5394	52	21	a∗(h	a∗(h	PROPN
ejpam-5394	52	22	)	)	PUNCT
ejpam-5394	53	1	=	=	PUNCT
ejpam-5394	53	2	h	h	NOUN
ejpam-5394	53	3	\	\	PUNCT
ejpam-5394	53	4	{	{	PUNCT
ejpam-5394	53	5	0	0	NUM
ejpam-5394	53	6	}	}	PUNCT
ejpam-5394	53	7	.	.	PUNCT
ejpam-5394	54	1	a	a	DET
ejpam-5394	54	2	hyper	hyper	ADJ
ejpam-5394	54	3	bck	bck	NOUN
ejpam-5394	54	4	-	-	PUNCT
ejpam-5394	54	5	algebra	algebra	NOUN
ejpam-5394	54	6	h	h	NOUN
ejpam-5394	54	7	is	be	AUX
ejpam-5394	54	8	called	call	VERB
ejpam-5394	54	9	ordered	order	VERB
ejpam-5394	54	10	if	if	SCONJ
ejpam-5394	54	11	the	the	DET
ejpam-5394	54	12	hyperorder	hyperorder	NOUN
ejpam-5394	54	13	“	"	PUNCT
ejpam-5394	54	14	≪	≪	PROPN
ejpam-5394	54	15	”	"	PUNCT
ejpam-5394	54	16	is	be	AUX
ejpam-5394	54	17	transitive	transitive	ADJ
ejpam-5394	54	18	.	.	PUNCT
ejpam-5394	55	1	proposition	proposition	NOUN
ejpam-5394	55	2	2	2	NUM
ejpam-5394	55	3	.	.	PUNCT
ejpam-5394	56	1	[	[	X
ejpam-5394	56	2	3	3	X
ejpam-5394	56	3	]	]	PUNCT
ejpam-5394	56	4	let	let	VERB
ejpam-5394	56	5	a	a	PRON
ejpam-5394	56	6	and	and	CCONJ
ejpam-5394	56	7	b	b	NOUN
ejpam-5394	56	8	be	be	AUX
ejpam-5394	56	9	subsets	subset	NOUN
ejpam-5394	56	10	of	of	ADP
ejpam-5394	56	11	h.	h.	PROPN
ejpam-5394	56	12	the	the	DET
ejpam-5394	56	13	the	the	DET
ejpam-5394	56	14	following	follow	VERB
ejpam-5394	56	15	hold	hold	NOUN
ejpam-5394	56	16	:	:	PUNCT
ejpam-5394	56	17	(	(	PUNCT
ejpam-5394	56	18	i	i	NOUN
ejpam-5394	56	19	)	)	PUNCT
ejpam-5394	56	20	rh(∅	rh(∅	PROPN
ejpam-5394	56	21	)	)	PUNCT
ejpam-5394	57	1	=	=	SYM
ejpam-5394	57	2	h.	h.	PROPN
ejpam-5394	57	3	(	(	PUNCT
ejpam-5394	57	4	ii	ii	PROPN
ejpam-5394	57	5	)	)	PUNCT
ejpam-5394	57	6	if	if	SCONJ
ejpam-5394	57	7	a	a	DET
ejpam-5394	57	8	⊆	⊆	NUM
ejpam-5394	57	9	b	b	NOUN
ejpam-5394	57	10	,	,	PUNCT
ejpam-5394	57	11	then	then	ADV
ejpam-5394	57	12	rh(b	rh(b	PUNCT
ejpam-5394	57	13	)	)	PUNCT
ejpam-5394	57	14	⊆	⊆	NUM
ejpam-5394	57	15	rh(a	rh(a	NOUN
ejpam-5394	57	16	)	)	PUNCT
ejpam-5394	57	17	.	.	PUNCT
ejpam-5394	58	1	(	(	PUNCT
ejpam-5394	58	2	iii	iii	X
ejpam-5394	58	3	)	)	PUNCT
ejpam-5394	58	4	if	if	SCONJ
ejpam-5394	58	5	h	h	NOUN
ejpam-5394	58	6	is	be	AUX
ejpam-5394	58	7	an	an	DET
ejpam-5394	58	8	ordered	order	VERB
ejpam-5394	58	9	hyper	hyper	ADJ
ejpam-5394	58	10	bck	bck	NOUN
ejpam-5394	58	11	-	-	PUNCT
ejpam-5394	58	12	algebra	algebra	NOUN
ejpam-5394	58	13	,	,	PUNCT
ejpam-5394	58	14	then	then	ADV
ejpam-5394	58	15	rh(rh(a	rh(rh(a	NOUN
ejpam-5394	58	16	)	)	PUNCT
ejpam-5394	58	17	)	)	PUNCT
ejpam-5394	59	1	⊆	⊆	NUM
ejpam-5394	59	2	rh(a	rh(a	NUM
ejpam-5394	59	3	)	)	PUNCT
ejpam-5394	59	4	.	.	PUNCT
ejpam-5394	60	1	theorem	theorem	NOUN
ejpam-5394	60	2	3	3	NUM
ejpam-5394	60	3	.	.	PUNCT
ejpam-5394	61	1	[	[	X
ejpam-5394	61	2	3	3	X
ejpam-5394	61	3	]	]	PUNCT
ejpam-5394	61	4	let	let	VERB
ejpam-5394	61	5	h	h	PRON
ejpam-5394	61	6	be	be	AUX
ejpam-5394	61	7	a	a	DET
ejpam-5394	61	8	hyper	hyper	ADJ
ejpam-5394	61	9	bck	bck	NOUN
ejpam-5394	61	10	-	-	PUNCT
ejpam-5394	61	11	algebra	algebra	NOUN
ejpam-5394	61	12	then	then	ADV
ejpam-5394	61	13	br(h	br(h	NUM
ejpam-5394	61	14	)	)	PUNCT
ejpam-5394	62	1	=	=	PRON
ejpam-5394	62	2	{	{	PUNCT
ejpam-5394	62	3	rh(a	rh(a	NOUN
ejpam-5394	62	4	)	)	PUNCT
ejpam-5394	62	5	:	:	PUNCT
ejpam-5394	62	6	a	a	DET
ejpam-5394	62	7	⊆	⊆	NUM
ejpam-5394	62	8	h	h	NOUN
ejpam-5394	62	9	}	}	PUNCT
ejpam-5394	62	10	is	be	AUX
ejpam-5394	62	11	a	a	DET
ejpam-5394	62	12	basis	basis	NOUN
ejpam-5394	62	13	for	for	ADP
ejpam-5394	62	14	some	some	DET
ejpam-5394	62	15	topology	topology	NOUN
ejpam-5394	62	16	in	in	ADP
ejpam-5394	62	17	h.	h.	PROPN
ejpam-5394	62	18	remark	remark	PROPN
ejpam-5394	62	19	1	1	NUM
ejpam-5394	62	20	.	.	PUNCT
ejpam-5394	63	1	[	[	X
ejpam-5394	63	2	3	3	X
ejpam-5394	63	3	]	]	PUNCT
ejpam-5394	63	4	let	let	VERB
ejpam-5394	63	5	a	a	PRON
ejpam-5394	63	6	and	and	CCONJ
ejpam-5394	63	7	b	b	NOUN
ejpam-5394	63	8	be	be	AUX
ejpam-5394	63	9	nonempty	nonempty	X
ejpam-5394	63	10	subsets	subset	NOUN
ejpam-5394	63	11	of	of	ADP
ejpam-5394	63	12	h.	h.	PROPN
ejpam-5394	63	13	rh(a	rh(a	PROPN
ejpam-5394	63	14	)	)	PUNCT
ejpam-5394	63	15	∩rh(b	∩rh(b	PROPN
ejpam-5394	63	16	)	)	PUNCT
ejpam-5394	63	17	=	=	PRON
ejpam-5394	63	18	rh(a	rh(a	NUM
ejpam-5394	63	19	∪b	∪b	NOUN
ejpam-5394	63	20	)	)	PUNCT
ejpam-5394	63	21	.	.	PUNCT
ejpam-5394	64	1	definition	definition	NOUN
ejpam-5394	64	2	7	7	NUM
ejpam-5394	64	3	.	.	PUNCT
ejpam-5394	65	1	[	[	X
ejpam-5394	65	2	4	4	X
ejpam-5394	65	3	]	]	PUNCT
ejpam-5394	65	4	let	let	VERB
ejpam-5394	65	5	h	h	PRON
ejpam-5394	65	6	be	be	AUX
ejpam-5394	65	7	a	a	DET
ejpam-5394	65	8	hyper	hyper	ADJ
ejpam-5394	65	9	bck	bck	NOUN
ejpam-5394	65	10	-	-	PUNCT
ejpam-5394	65	11	algebra	algebra	NOUN
ejpam-5394	65	12	and	and	CCONJ
ejpam-5394	65	13	a	a	DET
ejpam-5394	65	14	⊆	⊆	NUM
ejpam-5394	65	15	h.	h.	NOUN
ejpam-5394	65	16	then	then	ADV
ejpam-5394	65	17	the	the	DET
ejpam-5394	65	18	set	set	NOUN
ejpam-5394	65	19	lh(a	lh(a	NOUN
ejpam-5394	65	20	)	)	PUNCT
ejpam-5394	65	21	is	be	AUX
ejpam-5394	65	22	defined	define	VERB
ejpam-5394	65	23	as	as	ADP
ejpam-5394	65	24	lh(a	lh(a	NOUN
ejpam-5394	65	25	)	)	PUNCT
ejpam-5394	66	1	=	=	PRON
ejpam-5394	66	2	{	{	PUNCT
ejpam-5394	66	3	x	x	PUNCT
ejpam-5394	66	4	∈	∈	PROPN
ejpam-5394	66	5	h	h	NOUN
ejpam-5394	66	6	:	:	PUNCT
ejpam-5394	66	7	x	x	SYM
ejpam-5394	66	8	≪	≪	NOUN
ejpam-5394	66	9	a	a	X
ejpam-5394	66	10	,	,	PUNCT
ejpam-5394	66	11	for	for	ADP
ejpam-5394	66	12	all	all	DET
ejpam-5394	66	13	a	a	DET
ejpam-5394	66	14	∈	∈	PROPN
ejpam-5394	66	15	a	a	DET
ejpam-5394	66	16	}	}	PUNCT
ejpam-5394	66	17	=	=	SYM
ejpam-5394	66	18	{	{	PUNCT
ejpam-5394	66	19	x	x	PUNCT
ejpam-5394	66	20	∈	∈	PROPN
ejpam-5394	66	21	h	h	NOUN
ejpam-5394	66	22	:	:	PUNCT
ejpam-5394	66	23	0	0	NUM
ejpam-5394	66	24	∈	∈	NOUN
ejpam-5394	66	25	x	x	PUNCT
ejpam-5394	66	26	∗	∗	NOUN
ejpam-5394	66	27	a	a	X
ejpam-5394	66	28	,	,	PUNCT
ejpam-5394	66	29	for	for	ADP
ejpam-5394	66	30	all	all	DET
ejpam-5394	66	31	a	a	DET
ejpam-5394	66	32	∈	∈	PROPN
ejpam-5394	66	33	a	a	PRON
ejpam-5394	66	34	}	}	PUNCT
ejpam-5394	66	35	.	.	PUNCT
ejpam-5394	67	1	if	if	SCONJ
ejpam-5394	67	2	a	a	PRON
ejpam-5394	67	3	=	=	X
ejpam-5394	67	4	{	{	PUNCT
ejpam-5394	67	5	a	a	NOUN
ejpam-5394	67	6	}	}	PUNCT
ejpam-5394	67	7	,	,	PUNCT
ejpam-5394	67	8	the	the	DET
ejpam-5394	67	9	we	we	PRON
ejpam-5394	67	10	write	write	VERB
ejpam-5394	67	11	lh({a	lh({a	PROPN
ejpam-5394	67	12	}	}	PUNCT
ejpam-5394	67	13	)	)	PUNCT
ejpam-5394	67	14	=	=	SYM
ejpam-5394	67	15	lh(a	lh(a	NOUN
ejpam-5394	67	16	)	)	PUNCT
ejpam-5394	67	17	.	.	PUNCT
ejpam-5394	68	1	theorem	theorem	ADJ
ejpam-5394	68	2	4	4	NUM
ejpam-5394	68	3	.	.	PUNCT
ejpam-5394	69	1	[	[	X
ejpam-5394	69	2	8	8	NUM
ejpam-5394	69	3	]	]	PUNCT
ejpam-5394	69	4	the	the	DET
ejpam-5394	69	5	set	set	NOUN
ejpam-5394	69	6	[	[	X
ejpam-5394	69	7	0	0	NUM
ejpam-5394	69	8	,	,	PUNCT
ejpam-5394	69	9	1	1	NUM
ejpam-5394	69	10	]	]	PUNCT
ejpam-5394	69	11	,	,	PUNCT
ejpam-5394	69	12	together	together	ADV
ejpam-5394	69	13	with	with	ADP
ejpam-5394	69	14	the	the	DET
ejpam-5394	69	15	binary	binary	PROPN
ejpam-5394	69	16	operation	operation	NOUN
ejpam-5394	69	17	“	"	PUNCT
ejpam-5394	69	18	∗	∗	NOUN
ejpam-5394	69	19	”	"	PUNCT
ejpam-5394	69	20	,	,	PUNCT
ejpam-5394	69	21	is	be	AUX
ejpam-5394	69	22	a	a	DET
ejpam-5394	69	23	bck	bck	NOUN
ejpam-5394	69	24	-	-	PUNCT
ejpam-5394	69	25	algebra	algebra	NOUN
ejpam-5394	69	26	.	.	PUNCT
ejpam-5394	70	1	3	3	X
ejpam-5394	70	2	.	.	X
ejpam-5394	70	3	a	a	DET
ejpam-5394	70	4	hyperoperation	hyperoperation	NOUN
ejpam-5394	70	5	on	on	ADP
ejpam-5394	70	6	[	[	X
ejpam-5394	70	7	0	0	NUM
ejpam-5394	70	8	,	,	PUNCT
ejpam-5394	70	9	1	1	NUM
ejpam-5394	70	10	]	]	PUNCT
ejpam-5394	70	11	on	on	ADP
ejpam-5394	70	12	the	the	DET
ejpam-5394	70	13	set	set	NOUN
ejpam-5394	70	14	[	[	X
ejpam-5394	70	15	0	0	NUM
ejpam-5394	70	16	,	,	PUNCT
ejpam-5394	70	17	1	1	NUM
ejpam-5394	70	18	]	]	PUNCT
ejpam-5394	70	19	,	,	PUNCT
ejpam-5394	70	20	we	we	PRON
ejpam-5394	70	21	define	define	VERB
ejpam-5394	70	22	”	"	PUNCT
ejpam-5394	70	23	∗	∗	NOUN
ejpam-5394	70	24	”	"	PUNCT
ejpam-5394	70	25	as	as	SCONJ
ejpam-5394	70	26	follows	follow	VERB
ejpam-5394	70	27	:	:	PUNCT
ejpam-5394	70	28	x	x	SYM
ejpam-5394	70	29	∗	∗	NOUN
ejpam-5394	70	30	y	y	NOUN
ejpam-5394	70	31	=	=	SYM
ejpam-5394	70	32	{	{	PUNCT
ejpam-5394	70	33	x−	x−	PROPN
ejpam-5394	70	34	y	y	PROPN
ejpam-5394	70	35	}	}	PUNCT
ejpam-5394	70	36	,	,	PUNCT
ejpam-5394	70	37	if	if	SCONJ
ejpam-5394	70	38	x	x	PROPN
ejpam-5394	70	39	>	>	X
ejpam-5394	70	40	y	y	PROPN
ejpam-5394	70	41	and	and	CCONJ
ejpam-5394	70	42	x	x	PROPN
ejpam-5394	70	43	∗	∗	NOUN
ejpam-5394	70	44	y	y	NOUN
ejpam-5394	70	45	=	=	PUNCT
ejpam-5394	70	46	{	{	PUNCT
ejpam-5394	70	47	0	0	NUM
ejpam-5394	70	48	}	}	PUNCT
ejpam-5394	70	49	if	if	SCONJ
ejpam-5394	70	50	x	x	X
ejpam-5394	70	51	≤	≤	PROPN
ejpam-5394	70	52	y.	y.	PROPN
ejpam-5394	70	53	lemma	lemma	PROPN
ejpam-5394	70	54	1	1	NUM
ejpam-5394	70	55	.	.	PUNCT
ejpam-5394	71	1	for	for	ADP
ejpam-5394	71	2	each	each	DET
ejpam-5394	71	3	x	x	PROPN
ejpam-5394	71	4	,	,	PUNCT
ejpam-5394	71	5	y	y	PROPN
ejpam-5394	71	6	,	,	PUNCT
ejpam-5394	71	7	z	z	NOUN
ejpam-5394	71	8	∈	∈	PROPN
ejpam-5394	72	1	[	[	X
ejpam-5394	72	2	0	0	NUM
ejpam-5394	72	3	,	,	PUNCT
ejpam-5394	72	4	1	1	NUM
ejpam-5394	72	5	]	]	PUNCT
ejpam-5394	72	6	,	,	PUNCT
ejpam-5394	72	7	(	(	PUNCT
ejpam-5394	72	8	x	x	X
ejpam-5394	72	9	∗	∗	PROPN
ejpam-5394	72	10	z	z	NOUN
ejpam-5394	72	11	)	)	PUNCT
ejpam-5394	72	12	∗	∗	NOUN
ejpam-5394	72	13	(	(	PUNCT
ejpam-5394	72	14	y	y	PROPN
ejpam-5394	72	15	∗	∗	PROPN
ejpam-5394	72	16	z	z	NOUN
ejpam-5394	72	17	)	)	PUNCT
ejpam-5394	72	18	≪	≪	PUNCT
ejpam-5394	72	19	x	x	X
ejpam-5394	72	20	∗	∗	NOUN
ejpam-5394	72	21	y.	y.	NOUN
ejpam-5394	72	22	proof	proof	NOUN
ejpam-5394	72	23	.	.	PUNCT
ejpam-5394	73	1	case	case	NOUN
ejpam-5394	73	2	1	1	NUM
ejpam-5394	73	3	:	:	PUNCT
ejpam-5394	73	4	x	x	SYM
ejpam-5394	73	5	≥	≥	NUM
ejpam-5394	73	6	y	y	NOUN
ejpam-5394	73	7	if	if	SCONJ
ejpam-5394	73	8	y	y	PROPN
ejpam-5394	73	9	≤	≤	X
ejpam-5394	73	10	z	z	NOUN
ejpam-5394	73	11	≤	≤	NUM
ejpam-5394	73	12	x	x	PUNCT
ejpam-5394	73	13	then	then	ADV
ejpam-5394	73	14	x−	x−	PROPN
ejpam-5394	73	15	z	z	PROPN
ejpam-5394	73	16	≥	≥	NUM
ejpam-5394	73	17	0	0	PUNCT
ejpam-5394	74	1	so	so	SCONJ
ejpam-5394	74	2	that	that	SCONJ
ejpam-5394	74	3	(	(	PUNCT
ejpam-5394	74	4	x	x	X
ejpam-5394	74	5	∗	∗	PROPN
ejpam-5394	74	6	z	z	NOUN
ejpam-5394	74	7	)	)	PUNCT
ejpam-5394	74	8	∗	∗	NOUN
ejpam-5394	74	9	(	(	PUNCT
ejpam-5394	74	10	y	y	PROPN
ejpam-5394	74	11	∗	∗	PROPN
ejpam-5394	74	12	z	z	NOUN
ejpam-5394	74	13	)	)	PUNCT
ejpam-5394	74	14	=	=	PRON
ejpam-5394	74	15	{	{	PUNCT
ejpam-5394	74	16	x−	x−	PROPN
ejpam-5394	74	17	z	z	PROPN
ejpam-5394	74	18	}	}	PUNCT
ejpam-5394	74	19	∗	∗	NOUN
ejpam-5394	74	20	{	{	PUNCT
ejpam-5394	74	21	0	0	NUM
ejpam-5394	74	22	}	}	PUNCT
ejpam-5394	74	23	=	=	SYM
ejpam-5394	74	24	{	{	PUNCT
ejpam-5394	74	25	x−	x−	PROPN
ejpam-5394	74	26	z	z	PROPN
ejpam-5394	75	1	−	−	PROPN
ejpam-5394	75	2	0	0	NUM
ejpam-5394	75	3	}	}	PUNCT
ejpam-5394	75	4	=	=	SYM
ejpam-5394	75	5	{	{	PUNCT
ejpam-5394	75	6	x−	x−	PROPN
ejpam-5394	75	7	z	z	PROPN
ejpam-5394	75	8	}	}	PUNCT
ejpam-5394	75	9	while	while	SCONJ
ejpam-5394	75	10	x∗y	x∗y	X
ejpam-5394	75	11	=	=	SYM
ejpam-5394	75	12	{	{	PUNCT
ejpam-5394	75	13	x−y	x−y	PROPN
ejpam-5394	75	14	}	}	PUNCT
ejpam-5394	76	1	so	so	SCONJ
ejpam-5394	76	2	that	that	SCONJ
ejpam-5394	76	3	(	(	PUNCT
ejpam-5394	76	4	x∗z)∗(y∗z	x∗z)∗(y∗z	PROPN
ejpam-5394	76	5	)	)	PUNCT
ejpam-5394	76	6	=	=	PRON
ejpam-5394	76	7	{	{	PUNCT
ejpam-5394	76	8	x−z	x−z	PROPN
ejpam-5394	76	9	}	}	PUNCT
ejpam-5394	76	10	≪	≪	VERB
ejpam-5394	76	11	{	{	PUNCT
ejpam-5394	76	12	x−y	x−y	NOUN
ejpam-5394	76	13	}	}	PUNCT
ejpam-5394	76	14	for	for	ADP
ejpam-5394	76	15	0	0	NUM
ejpam-5394	76	16	∈	∈	PROPN
ejpam-5394	76	17	{	{	PUNCT
ejpam-5394	76	18	x−z}∗{x−y	x−z}∗{x−y	NOUN
ejpam-5394	76	19	}	}	PUNCT
ejpam-5394	76	20	=	=	SYM
ejpam-5394	76	21	{	{	PUNCT
ejpam-5394	76	22	0	0	NUM
ejpam-5394	76	23	}	}	PUNCT
ejpam-5394	76	24	,	,	PUNCT
ejpam-5394	77	1	since	since	SCONJ
ejpam-5394	77	2	x−	x−	PROPN
ejpam-5394	77	3	z	z	PROPN
ejpam-5394	77	4	≤	≤	PROPN
ejpam-5394	77	5	x−	x−	PROPN
ejpam-5394	77	6	y.	y.	NOUN
ejpam-5394	77	7	if	if	SCONJ
ejpam-5394	77	8	z	z	NOUN
ejpam-5394	77	9	≤	≤	NOUN
ejpam-5394	77	10	y	y	PROPN
ejpam-5394	77	11	≤	≤	NUM
ejpam-5394	77	12	x	x	PUNCT
ejpam-5394	77	13	then	then	ADV
ejpam-5394	77	14	x−	x−	PROPN
ejpam-5394	77	15	y	y	PROPN
ejpam-5394	77	16	≤	≤	PROPN
ejpam-5394	78	1	x−	x−	PROPN
ejpam-5394	78	2	z	z	PROPN
ejpam-5394	79	1	so	so	SCONJ
ejpam-5394	79	2	that	that	SCONJ
ejpam-5394	79	3	e.	e.	PROPN
ejpam-5394	79	4	payla	payla	PROPN
ejpam-5394	79	5	,	,	PUNCT
ejpam-5394	79	6	l.	l.	PROPN
ejpam-5394	79	7	ranara	ranara	PROPN
ejpam-5394	79	8	/	/	SYM
ejpam-5394	79	9	eur	eur	PROPN
ejpam-5394	79	10	.	.	PUNCT
ejpam-5394	80	1	j.	j.	PROPN
ejpam-5394	80	2	pure	pure	PROPN
ejpam-5394	80	3	appl	appl	PROPN
ejpam-5394	80	4	.	.	PROPN
ejpam-5394	80	5	math	math	PROPN
ejpam-5394	80	6	,	,	PUNCT
ejpam-5394	80	7	18	18	NUM
ejpam-5394	80	8	(	(	PUNCT
ejpam-5394	80	9	2	2	NUM
ejpam-5394	80	10	)	)	PUNCT
ejpam-5394	80	11	(	(	PUNCT
ejpam-5394	80	12	2025	2025	NUM
ejpam-5394	80	13	)	)	PUNCT
ejpam-5394	80	14	,	,	PUNCT
ejpam-5394	80	15	5394	5394	NUM
ejpam-5394	80	16	4	4	NUM
ejpam-5394	80	17	of	of	ADP
ejpam-5394	80	18	10	10	NUM
ejpam-5394	80	19	(	(	PUNCT
ejpam-5394	80	20	x	x	NOUN
ejpam-5394	80	21	∗	∗	PROPN
ejpam-5394	80	22	z	z	NOUN
ejpam-5394	80	23	)	)	PUNCT
ejpam-5394	80	24	∗	∗	NOUN
ejpam-5394	80	25	(	(	PUNCT
ejpam-5394	80	26	y	y	PROPN
ejpam-5394	80	27	∗	∗	PROPN
ejpam-5394	80	28	z	z	NOUN
ejpam-5394	80	29	)	)	PUNCT
ejpam-5394	80	30	=	=	PRON
ejpam-5394	80	31	{	{	PUNCT
ejpam-5394	80	32	x−	x−	PROPN
ejpam-5394	80	33	z	z	PROPN
ejpam-5394	80	34	}	}	PUNCT
ejpam-5394	80	35	∗	∗	NOUN
ejpam-5394	80	36	{	{	PUNCT
ejpam-5394	80	37	y	y	PROPN
ejpam-5394	80	38	−	−	PROPN
ejpam-5394	81	1	z	z	NOUN
ejpam-5394	81	2	}	}	PUNCT
ejpam-5394	81	3	=	=	SYM
ejpam-5394	81	4	{	{	PUNCT
ejpam-5394	81	5	x−	x−	PROPN
ejpam-5394	81	6	z	z	PROPN
ejpam-5394	81	7	−	−	PROPN
ejpam-5394	82	1	(	(	PUNCT
ejpam-5394	82	2	y	y	PROPN
ejpam-5394	82	3	−	−	PROPN
ejpam-5394	82	4	z	z	PROPN
ejpam-5394	82	5	)	)	PUNCT
ejpam-5394	82	6	}	}	PUNCT
ejpam-5394	82	7	for	for	ADP
ejpam-5394	82	8	x−	x−	PROPN
ejpam-5394	82	9	z	z	PROPN
ejpam-5394	82	10	≥	≥	PROPN
ejpam-5394	83	1	y	y	NOUN
ejpam-5394	83	2	−	−	NOUN
ejpam-5394	83	3	z	z	NOUN
ejpam-5394	83	4	=	=	SYM
ejpam-5394	83	5	{	{	PUNCT
ejpam-5394	83	6	x−	x−	PROPN
ejpam-5394	83	7	y	y	PROPN
ejpam-5394	83	8	}	}	PUNCT
ejpam-5394	83	9	=	=	PUNCT
ejpam-5394	83	10	x	x	SYM
ejpam-5394	83	11	∗	∗	NOUN
ejpam-5394	83	12	y	y	PROPN
ejpam-5394	83	13	thus	thus	ADV
ejpam-5394	83	14	,	,	PUNCT
ejpam-5394	83	15	(	(	PUNCT
ejpam-5394	83	16	x	x	X
ejpam-5394	83	17	∗	∗	PROPN
ejpam-5394	83	18	z	z	NOUN
ejpam-5394	83	19	)	)	PUNCT
ejpam-5394	83	20	∗	∗	NOUN
ejpam-5394	83	21	(	(	PUNCT
ejpam-5394	83	22	y	y	PROPN
ejpam-5394	83	23	∗	∗	PROPN
ejpam-5394	83	24	z	z	NOUN
ejpam-5394	83	25	)	)	PUNCT
ejpam-5394	83	26	=	=	PRON
ejpam-5394	83	27	{	{	PUNCT
ejpam-5394	83	28	x−	x−	PROPN
ejpam-5394	83	29	y	y	PROPN
ejpam-5394	83	30	}	}	PUNCT
ejpam-5394	83	31	≪	≪	VERB
ejpam-5394	83	32	x	x	PUNCT
ejpam-5394	83	33	∗	∗	NOUN
ejpam-5394	83	34	y	y	NOUN
ejpam-5394	83	35	for	for	ADP
ejpam-5394	83	36	0	0	NUM
ejpam-5394	83	37	∈	∈	PROPN
ejpam-5394	83	38	{	{	PUNCT
ejpam-5394	83	39	x−	x−	PROPN
ejpam-5394	83	40	y	y	PROPN
ejpam-5394	83	41	}	}	PUNCT
ejpam-5394	83	42	∗	∗	NOUN
ejpam-5394	83	43	{	{	PUNCT
ejpam-5394	83	44	x−	x−	PROPN
ejpam-5394	83	45	y	y	PROPN
ejpam-5394	83	46	}	}	PUNCT
ejpam-5394	83	47	=	=	PUNCT
ejpam-5394	83	48	{	{	PUNCT
ejpam-5394	83	49	0	0	NUM
ejpam-5394	83	50	}	}	PUNCT
ejpam-5394	83	51	.	.	PUNCT
ejpam-5394	84	1	if	if	SCONJ
ejpam-5394	84	2	y	y	PROPN
ejpam-5394	84	3	≤	≤	NUM
ejpam-5394	84	4	x	x	PUNCT
ejpam-5394	84	5	≤	≤	NUM
ejpam-5394	84	6	z	z	NOUN
ejpam-5394	84	7	then	then	ADV
ejpam-5394	84	8	(	(	PUNCT
ejpam-5394	84	9	x∗z)∗(y∗z	x∗z)∗(y∗z	PROPN
ejpam-5394	84	10	)	)	PUNCT
ejpam-5394	84	11	=	=	PRON
ejpam-5394	84	12	{	{	PUNCT
ejpam-5394	84	13	0}∗{0	0}∗{0	NUM
ejpam-5394	84	14	}	}	PUNCT
ejpam-5394	84	15	=	=	SYM
ejpam-5394	84	16	{	{	PUNCT
ejpam-5394	84	17	0	0	NUM
ejpam-5394	84	18	}	}	PUNCT
ejpam-5394	84	19	,	,	PUNCT
ejpam-5394	84	20	x∗y	x∗y	X
ejpam-5394	84	21	=	=	SYM
ejpam-5394	84	22	{	{	PUNCT
ejpam-5394	84	23	x−y	x−y	PROPN
ejpam-5394	84	24	}	}	PUNCT
ejpam-5394	84	25	and	and	CCONJ
ejpam-5394	84	26	0	0	NUM
ejpam-5394	84	27	∈	∈	NOUN
ejpam-5394	84	28	0∗{x−y	0∗{x−y	NOUN
ejpam-5394	84	29	}	}	PUNCT
ejpam-5394	84	30	=	=	PUNCT
ejpam-5394	84	31	{	{	PUNCT
ejpam-5394	84	32	0	0	NUM
ejpam-5394	84	33	}	}	PUNCT
ejpam-5394	84	34	.	.	PUNCT
ejpam-5394	85	1	thus	thus	ADV
ejpam-5394	85	2	,	,	PUNCT
ejpam-5394	85	3	(	(	PUNCT
ejpam-5394	85	4	x	x	X
ejpam-5394	85	5	∗	∗	PROPN
ejpam-5394	85	6	z	z	NOUN
ejpam-5394	85	7	)	)	PUNCT
ejpam-5394	85	8	∗	∗	NOUN
ejpam-5394	85	9	(	(	PUNCT
ejpam-5394	85	10	y	y	PROPN
ejpam-5394	85	11	∗	∗	PROPN
ejpam-5394	85	12	z	z	NOUN
ejpam-5394	85	13	)	)	PUNCT
ejpam-5394	85	14	=	=	PRON
ejpam-5394	85	15	{	{	PUNCT
ejpam-5394	85	16	0	0	NOUN
ejpam-5394	85	17	}	}	PUNCT
ejpam-5394	85	18	≪	≪	X
ejpam-5394	85	19	{	{	PUNCT
ejpam-5394	85	20	x−	x−	PROPN
ejpam-5394	85	21	y	y	PROPN
ejpam-5394	85	22	}	}	PUNCT
ejpam-5394	85	23	=	=	PUNCT
ejpam-5394	85	24	x	x	SYM
ejpam-5394	85	25	∗	∗	NOUN
ejpam-5394	85	26	y.	y.	PROPN
ejpam-5394	85	27	case	case	NOUN
ejpam-5394	85	28	2	2	NUM
ejpam-5394	85	29	:	:	PUNCT
ejpam-5394	85	30	if	if	SCONJ
ejpam-5394	85	31	x	x	PROPN
ejpam-5394	85	32	≤	≤	NOUN
ejpam-5394	85	33	y	y	NOUN
ejpam-5394	85	34	then	then	ADV
ejpam-5394	85	35	x	x	X
ejpam-5394	85	36	∗	∗	NOUN
ejpam-5394	85	37	y	y	NOUN
ejpam-5394	85	38	=	=	PUNCT
ejpam-5394	85	39	{	{	PUNCT
ejpam-5394	85	40	0	0	NUM
ejpam-5394	85	41	}	}	PUNCT
ejpam-5394	85	42	.	.	PUNCT
ejpam-5394	86	1	if	if	SCONJ
ejpam-5394	86	2	x	x	SYM
ejpam-5394	86	3	≤	≤	X
ejpam-5394	86	4	z	z	NOUN
ejpam-5394	86	5	≤	≤	NOUN
ejpam-5394	86	6	y	y	PROPN
ejpam-5394	86	7	then	then	ADV
ejpam-5394	86	8	(	(	PUNCT
ejpam-5394	86	9	x	x	X
ejpam-5394	86	10	∗	∗	PROPN
ejpam-5394	86	11	z	z	NOUN
ejpam-5394	86	12	)	)	PUNCT
ejpam-5394	86	13	∗	∗	NOUN
ejpam-5394	86	14	(	(	PUNCT
ejpam-5394	86	15	y	y	PROPN
ejpam-5394	86	16	∗	∗	PROPN
ejpam-5394	86	17	z	z	NOUN
ejpam-5394	86	18	)	)	PUNCT
ejpam-5394	86	19	=	=	PRON
ejpam-5394	86	20	{	{	PUNCT
ejpam-5394	86	21	0	0	NUM
ejpam-5394	86	22	}	}	PUNCT
ejpam-5394	86	23	∗	∗	NOUN
ejpam-5394	86	24	{	{	PUNCT
ejpam-5394	86	25	y	y	PROPN
ejpam-5394	86	26	−	−	PROPN
ejpam-5394	86	27	z	z	NOUN
ejpam-5394	86	28	}	}	PUNCT
ejpam-5394	86	29	=	=	SYM
ejpam-5394	86	30	{	{	PUNCT
ejpam-5394	86	31	0	0	NOUN
ejpam-5394	86	32	}	}	PUNCT
ejpam-5394	86	33	≪	≪	X
ejpam-5394	86	34	{	{	PUNCT
ejpam-5394	86	35	0	0	NUM
ejpam-5394	86	36	}	}	PUNCT
ejpam-5394	86	37	=	=	SYM
ejpam-5394	86	38	x	x	SYM
ejpam-5394	86	39	∗	∗	X
ejpam-5394	86	40	y	y	NOUN
ejpam-5394	86	41	for	for	ADP
ejpam-5394	86	42	0	0	NUM
ejpam-5394	86	43	∈	∈	NOUN
ejpam-5394	86	44	0	0	NUM
ejpam-5394	86	45	∗	∗	NOUN
ejpam-5394	86	46	0	0	NUM
ejpam-5394	86	47	=	=	SYM
ejpam-5394	86	48	{	{	PUNCT
ejpam-5394	86	49	0	0	NUM
ejpam-5394	86	50	}	}	PUNCT
ejpam-5394	86	51	.	.	PUNCT
ejpam-5394	87	1	if	if	SCONJ
ejpam-5394	87	2	z	z	NOUN
ejpam-5394	87	3	≤	≤	NUM
ejpam-5394	87	4	x	x	PUNCT
ejpam-5394	87	5	≤	≤	NUM
ejpam-5394	87	6	y	y	NOUN
ejpam-5394	87	7	then	then	ADV
ejpam-5394	87	8	(	(	PUNCT
ejpam-5394	87	9	a	a	DET
ejpam-5394	87	10	∗	∗	NOUN
ejpam-5394	87	11	z	z	NOUN
ejpam-5394	87	12	)	)	PUNCT
ejpam-5394	87	13	∗	∗	NOUN
ejpam-5394	87	14	(	(	PUNCT
ejpam-5394	87	15	y	y	PROPN
ejpam-5394	87	16	∗	∗	PROPN
ejpam-5394	87	17	z	z	NOUN
ejpam-5394	87	18	)	)	PUNCT
ejpam-5394	87	19	=	=	PRON
ejpam-5394	87	20	{	{	PUNCT
ejpam-5394	87	21	x	x	X
ejpam-5394	87	22	−	−	PROPN
ejpam-5394	87	23	z	z	NOUN
ejpam-5394	87	24	}	}	PUNCT
ejpam-5394	87	25	∗	∗	NOUN
ejpam-5394	87	26	{	{	PUNCT
ejpam-5394	87	27	y	y	PROPN
ejpam-5394	87	28	−	−	PROPN
ejpam-5394	88	1	z	z	NOUN
ejpam-5394	88	2	}	}	PUNCT
ejpam-5394	88	3	=	=	SYM
ejpam-5394	88	4	{	{	PUNCT
ejpam-5394	88	5	0	0	NUM
ejpam-5394	88	6	}	}	PUNCT
ejpam-5394	88	7	for	for	ADP
ejpam-5394	88	8	x	x	SYM
ejpam-5394	88	9	−	−	PROPN
ejpam-5394	88	10	z	z	NOUN
ejpam-5394	88	11	≤	≤	NOUN
ejpam-5394	88	12	y	y	PROPN
ejpam-5394	88	13	−	−	PROPN
ejpam-5394	89	1	z	z	NOUN
ejpam-5394	90	1	so	so	ADV
ejpam-5394	90	2	that(x	that(x	PROPN
ejpam-5394	90	3	∗	∗	PROPN
ejpam-5394	90	4	z	z	NOUN
ejpam-5394	90	5	)	)	PUNCT
ejpam-5394	90	6	∗	∗	NOUN
ejpam-5394	90	7	(	(	PUNCT
ejpam-5394	90	8	y	y	PROPN
ejpam-5394	90	9	∗	∗	PROPN
ejpam-5394	90	10	z	z	NOUN
ejpam-5394	90	11	)	)	PUNCT
ejpam-5394	90	12	=	=	PRON
ejpam-5394	90	13	{	{	PUNCT
ejpam-5394	90	14	0	0	NOUN
ejpam-5394	90	15	}	}	PUNCT
ejpam-5394	90	16	≪	≪	X
ejpam-5394	90	17	{	{	PUNCT
ejpam-5394	90	18	0	0	NUM
ejpam-5394	90	19	}	}	PUNCT
ejpam-5394	90	20	=	=	SYM
ejpam-5394	90	21	x	x	SYM
ejpam-5394	90	22	∗	∗	X
ejpam-5394	90	23	y	y	NOUN
ejpam-5394	90	24	for	for	ADP
ejpam-5394	90	25	0	0	NUM
ejpam-5394	90	26	∈	∈	NOUN
ejpam-5394	90	27	0	0	NUM
ejpam-5394	90	28	∗	∗	NOUN
ejpam-5394	90	29	0	0	NUM
ejpam-5394	90	30	=	=	SYM
ejpam-5394	90	31	{	{	PUNCT
ejpam-5394	90	32	0	0	NUM
ejpam-5394	90	33	}	}	PUNCT
ejpam-5394	90	34	.	.	PUNCT
ejpam-5394	91	1	if	if	SCONJ
ejpam-5394	91	2	x	x	PROPN
ejpam-5394	91	3	≤	≤	NUM
ejpam-5394	91	4	y	y	PROPN
ejpam-5394	91	5	≤	≤	PROPN
ejpam-5394	91	6	z	z	NOUN
ejpam-5394	92	1	then	then	ADV
ejpam-5394	92	2	(	(	PUNCT
ejpam-5394	92	3	x	x	X
ejpam-5394	92	4	∗	∗	PROPN
ejpam-5394	92	5	z	z	NOUN
ejpam-5394	92	6	)	)	PUNCT
ejpam-5394	92	7	∗	∗	NOUN
ejpam-5394	92	8	(	(	PUNCT
ejpam-5394	92	9	y	y	PROPN
ejpam-5394	92	10	∗	∗	PROPN
ejpam-5394	92	11	z	z	NOUN
ejpam-5394	92	12	)	)	PUNCT
ejpam-5394	92	13	=	=	PRON
ejpam-5394	92	14	{	{	PUNCT
ejpam-5394	92	15	0	0	NUM
ejpam-5394	92	16	}	}	PUNCT
ejpam-5394	92	17	∗	∗	NOUN
ejpam-5394	92	18	{	{	PUNCT
ejpam-5394	92	19	0	0	NUM
ejpam-5394	92	20	}	}	PUNCT
ejpam-5394	92	21	=	=	SYM
ejpam-5394	92	22	{	{	PUNCT
ejpam-5394	92	23	0	0	NOUN
ejpam-5394	92	24	}	}	PUNCT
ejpam-5394	92	25	≪	≪	X
ejpam-5394	92	26	{	{	PUNCT
ejpam-5394	92	27	0	0	NUM
ejpam-5394	92	28	}	}	PUNCT
ejpam-5394	92	29	=	=	SYM
ejpam-5394	92	30	x	x	SYM
ejpam-5394	92	31	∗	∗	NOUN
ejpam-5394	92	32	y.	y.	PROPN
ejpam-5394	92	33	■	■	PUNCT
ejpam-5394	92	34	lemma	lemma	PROPN
ejpam-5394	92	35	2	2	NUM
ejpam-5394	92	36	.	.	PUNCT
ejpam-5394	93	1	for	for	ADP
ejpam-5394	93	2	all	all	DET
ejpam-5394	93	3	x	x	NOUN
ejpam-5394	93	4	,	,	PUNCT
ejpam-5394	93	5	y	y	PROPN
ejpam-5394	93	6	,	,	PUNCT
ejpam-5394	93	7	z	z	NOUN
ejpam-5394	93	8	∈	∈	PROPN
ejpam-5394	94	1	[	[	X
ejpam-5394	94	2	0	0	NUM
ejpam-5394	94	3	,	,	PUNCT
ejpam-5394	94	4	1	1	NUM
ejpam-5394	94	5	]	]	PUNCT
ejpam-5394	94	6	,	,	PUNCT
ejpam-5394	94	7	(	(	PUNCT
ejpam-5394	94	8	x	x	X
ejpam-5394	94	9	∗	∗	PROPN
ejpam-5394	94	10	y	y	NOUN
ejpam-5394	94	11	)	)	PUNCT
ejpam-5394	94	12	∗	∗	NOUN
ejpam-5394	94	13	z	z	NOUN
ejpam-5394	95	1	=	=	SYM
ejpam-5394	96	1	(	(	PUNCT
ejpam-5394	96	2	x	x	X
ejpam-5394	96	3	∗	∗	PROPN
ejpam-5394	96	4	z	z	NOUN
ejpam-5394	96	5	)	)	PUNCT
ejpam-5394	96	6	∗	∗	NOUN
ejpam-5394	96	7	y.	y.	PROPN
ejpam-5394	96	8	proof	proof	NOUN
ejpam-5394	96	9	.	.	PUNCT
ejpam-5394	97	1	case	case	NOUN
ejpam-5394	97	2	1	1	NUM
ejpam-5394	97	3	:	:	PUNCT
ejpam-5394	97	4	if	if	SCONJ
ejpam-5394	97	5	x	x	X
ejpam-5394	97	6	≥	≥	VERB
ejpam-5394	97	7	y.	y.	NOUN
ejpam-5394	97	8	if	if	SCONJ
ejpam-5394	97	9	y	y	PROPN
ejpam-5394	97	10	≤	≤	PROPN
ejpam-5394	97	11	z	z	NOUN
ejpam-5394	97	12	≤	≤	NUM
ejpam-5394	97	13	x	x	X
ejpam-5394	97	14	,	,	PUNCT
ejpam-5394	97	15	(	(	PUNCT
ejpam-5394	97	16	x	x	X
ejpam-5394	97	17	∗	∗	PROPN
ejpam-5394	97	18	y	y	NOUN
ejpam-5394	97	19	)	)	PUNCT
ejpam-5394	97	20	∗	∗	NOUN
ejpam-5394	97	21	z	z	NOUN
ejpam-5394	97	22	=	=	SYM
ejpam-5394	97	23	{	{	PUNCT
ejpam-5394	97	24	x−	x−	PROPN
ejpam-5394	97	25	y	y	PROPN
ejpam-5394	97	26	}	}	PUNCT
ejpam-5394	97	27	∗	∗	NOUN
ejpam-5394	97	28	z	z	NOUN
ejpam-5394	97	29	=	=	PRON
ejpam-5394	97	30	{	{	PUNCT
ejpam-5394	97	31	{	{	PUNCT
ejpam-5394	97	32	0	0	NUM
ejpam-5394	97	33	}	}	PUNCT
ejpam-5394	97	34	,	,	PUNCT
ejpam-5394	98	1	if	if	SCONJ
ejpam-5394	98	2	x−	x−	PROPN
ejpam-5394	98	3	y	y	PROPN
ejpam-5394	98	4	≤	≤	PROPN
ejpam-5394	98	5	z	z	X
ejpam-5394	98	6	,	,	PUNCT
ejpam-5394	98	7	{	{	PUNCT
ejpam-5394	98	8	x−	x−	PROPN
ejpam-5394	98	9	y	y	PROPN
ejpam-5394	98	10	−	−	PROPN
ejpam-5394	99	1	z	z	X
ejpam-5394	99	2	}	}	PUNCT
ejpam-5394	99	3	,	,	PUNCT
ejpam-5394	99	4	if	if	SCONJ
ejpam-5394	99	5	x−	x−	PROPN
ejpam-5394	99	6	y	y	PROPN
ejpam-5394	99	7	>	>	X
ejpam-5394	99	8	z	z	PROPN
ejpam-5394	100	1	while	while	SCONJ
ejpam-5394	100	2	(	(	PUNCT
ejpam-5394	100	3	x	x	X
ejpam-5394	100	4	∗	∗	PROPN
ejpam-5394	100	5	z	z	NOUN
ejpam-5394	100	6	)	)	PUNCT
ejpam-5394	100	7	∗	∗	NOUN
ejpam-5394	100	8	y	y	NOUN
ejpam-5394	100	9	=	=	SYM
ejpam-5394	100	10	{	{	PUNCT
ejpam-5394	100	11	x−	x−	PROPN
ejpam-5394	100	12	z	z	PROPN
ejpam-5394	100	13	}	}	PUNCT
ejpam-5394	100	14	∗	∗	NOUN
ejpam-5394	100	15	y	y	NOUN
ejpam-5394	100	16	=	=	PRON
ejpam-5394	100	17	{	{	PUNCT
ejpam-5394	100	18	{	{	PUNCT
ejpam-5394	101	1	x−	x−	PROPN
ejpam-5394	101	2	z	z	PROPN
ejpam-5394	101	3	−	−	PROPN
ejpam-5394	101	4	y	y	PROPN
ejpam-5394	101	5	}	}	PUNCT
ejpam-5394	101	6	,	,	PUNCT
ejpam-5394	101	7	if	if	SCONJ
ejpam-5394	101	8	x−	x−	PROPN
ejpam-5394	101	9	z	z	PROPN
ejpam-5394	101	10	≥	≥	NUM
ejpam-5394	101	11	y	y	PROPN
ejpam-5394	101	12	,	,	PUNCT
ejpam-5394	101	13	{	{	PUNCT
ejpam-5394	101	14	0	0	NUM
ejpam-5394	101	15	}	}	PUNCT
ejpam-5394	101	16	,	,	PUNCT
ejpam-5394	101	17	if	if	SCONJ
ejpam-5394	101	18	x−	x−	PROPN
ejpam-5394	101	19	z	z	PROPN
ejpam-5394	101	20	≤	≤	PROPN
ejpam-5394	101	21	y	y	PROPN
ejpam-5394	101	22	note	note	VERB
ejpam-5394	101	23	that	that	SCONJ
ejpam-5394	101	24	when	when	SCONJ
ejpam-5394	101	25	the	the	DET
ejpam-5394	101	26	result	result	NOUN
ejpam-5394	101	27	of	of	ADP
ejpam-5394	101	28	(	(	PUNCT
ejpam-5394	101	29	x	x	PROPN
ejpam-5394	101	30	∗	∗	PROPN
ejpam-5394	101	31	y	y	NOUN
ejpam-5394	101	32	)	)	PUNCT
ejpam-5394	101	33	∗	∗	NOUN
ejpam-5394	101	34	z	z	NOUN
ejpam-5394	101	35	is	be	AUX
ejpam-5394	101	36	{	{	PUNCT
ejpam-5394	101	37	0	0	NUM
ejpam-5394	101	38	}	}	PUNCT
ejpam-5394	101	39	,	,	PUNCT
ejpam-5394	101	40	it	it	PRON
ejpam-5394	101	41	happens	happen	VERB
ejpam-5394	101	42	when	when	SCONJ
ejpam-5394	101	43	x	x	X
ejpam-5394	101	44	−	−	X
ejpam-5394	101	45	y	y	NOUN
ejpam-5394	101	46	<	<	X
ejpam-5394	101	47	z	z	PROPN
ejpam-5394	102	1	and	and	CCONJ
ejpam-5394	102	2	it	it	PRON
ejpam-5394	102	3	is	be	AUX
ejpam-5394	102	4	just	just	ADV
ejpam-5394	102	5	the	the	DET
ejpam-5394	102	6	same	same	ADJ
ejpam-5394	102	7	as	as	ADP
ejpam-5394	102	8	x−	x−	PROPN
ejpam-5394	102	9	z	z	PROPN
ejpam-5394	102	10	<	<	X
ejpam-5394	102	11	y.	y.	PROPN
ejpam-5394	102	12	also	also	ADV
ejpam-5394	102	13	if	if	SCONJ
ejpam-5394	102	14	the	the	DET
ejpam-5394	102	15	result	result	NOUN
ejpam-5394	102	16	is	be	AUX
ejpam-5394	102	17	{	{	PUNCT
ejpam-5394	102	18	x−	x−	PROPN
ejpam-5394	102	19	y	y	PROPN
ejpam-5394	102	20	−	−	PROPN
ejpam-5394	103	1	z	z	X
ejpam-5394	103	2	}	}	PUNCT
ejpam-5394	103	3	,	,	PUNCT
ejpam-5394	103	4	it	it	PRON
ejpam-5394	103	5	happens	happen	VERB
ejpam-5394	103	6	when	when	SCONJ
ejpam-5394	103	7	x−	x−	PROPN
ejpam-5394	103	8	y	y	PROPN
ejpam-5394	103	9	>	>	PROPN
ejpam-5394	103	10	z	z	PROPN
ejpam-5394	104	1	and	and	CCONJ
ejpam-5394	104	2	it	it	PRON
ejpam-5394	104	3	is	be	AUX
ejpam-5394	104	4	just	just	ADV
ejpam-5394	104	5	the	the	DET
ejpam-5394	104	6	same	same	ADJ
ejpam-5394	104	7	as	as	ADP
ejpam-5394	104	8	x−	x−	PROPN
ejpam-5394	104	9	z	z	PROPN
ejpam-5394	104	10	>	>	X
ejpam-5394	105	1	y.	y.	PROPN
ejpam-5394	106	1	thus	thus	ADV
ejpam-5394	106	2	,	,	PUNCT
ejpam-5394	106	3	(	(	PUNCT
ejpam-5394	106	4	x	x	X
ejpam-5394	106	5	∗	∗	PROPN
ejpam-5394	106	6	y	y	NOUN
ejpam-5394	106	7	)	)	PUNCT
ejpam-5394	106	8	∗	∗	NOUN
ejpam-5394	106	9	z	z	NOUN
ejpam-5394	107	1	=	=	SYM
ejpam-5394	108	1	(	(	PUNCT
ejpam-5394	108	2	x	x	X
ejpam-5394	108	3	∗	∗	PROPN
ejpam-5394	108	4	z	z	NOUN
ejpam-5394	108	5	)	)	PUNCT
ejpam-5394	108	6	∗	∗	NOUN
ejpam-5394	108	7	y.	y.	NOUN
ejpam-5394	108	8	if	if	SCONJ
ejpam-5394	108	9	z	z	NOUN
ejpam-5394	108	10	≤	≤	NUM
ejpam-5394	108	11	y	y	PROPN
ejpam-5394	108	12	≤	≤	NUM
ejpam-5394	109	1	x	x	PUNCT
ejpam-5394	110	1	then	then	ADV
ejpam-5394	110	2	(	(	PUNCT
ejpam-5394	110	3	x	x	X
ejpam-5394	110	4	∗	∗	PROPN
ejpam-5394	110	5	y	y	NOUN
ejpam-5394	110	6	)	)	PUNCT
ejpam-5394	110	7	∗	∗	NOUN
ejpam-5394	110	8	z	z	NOUN
ejpam-5394	110	9	=	=	SYM
ejpam-5394	110	10	{	{	PUNCT
ejpam-5394	110	11	x−	x−	PROPN
ejpam-5394	110	12	y	y	PROPN
ejpam-5394	110	13	}	}	PUNCT
ejpam-5394	110	14	∗	∗	NOUN
ejpam-5394	110	15	z	z	NOUN
ejpam-5394	110	16	=	=	PRON
ejpam-5394	110	17	{	{	PUNCT
ejpam-5394	110	18	{	{	PUNCT
ejpam-5394	110	19	x−	x−	PROPN
ejpam-5394	110	20	y	y	PROPN
ejpam-5394	110	21	−	−	PROPN
ejpam-5394	111	1	z	z	X
ejpam-5394	111	2	}	}	PUNCT
ejpam-5394	111	3	,	,	PUNCT
ejpam-5394	111	4	if	if	SCONJ
ejpam-5394	111	5	x−	x−	PROPN
ejpam-5394	111	6	y	y	PROPN
ejpam-5394	111	7	≥	≥	PROPN
ejpam-5394	111	8	z	z	PROPN
ejpam-5394	111	9	{	{	PUNCT
ejpam-5394	111	10	0	0	NUM
ejpam-5394	111	11	}	}	PUNCT
ejpam-5394	111	12	,	,	PUNCT
ejpam-5394	111	13	if	if	SCONJ
ejpam-5394	111	14	x−	x−	PROPN
ejpam-5394	111	15	y	y	PROPN
ejpam-5394	111	16	<	<	X
ejpam-5394	111	17	z	z	X
ejpam-5394	111	18	(	(	PUNCT
ejpam-5394	111	19	x	x	X
ejpam-5394	111	20	∗	∗	PROPN
ejpam-5394	111	21	z	z	NOUN
ejpam-5394	111	22	)	)	PUNCT
ejpam-5394	111	23	∗	∗	NOUN
ejpam-5394	111	24	y	y	NOUN
ejpam-5394	111	25	=	=	SYM
ejpam-5394	111	26	{	{	PUNCT
ejpam-5394	111	27	x−	x−	PROPN
ejpam-5394	111	28	z	z	PROPN
ejpam-5394	111	29	}	}	PUNCT
ejpam-5394	111	30	∗	∗	NOUN
ejpam-5394	111	31	y	y	NOUN
ejpam-5394	111	32	=	=	PRON
ejpam-5394	111	33	{	{	PUNCT
ejpam-5394	111	34	{	{	PUNCT
ejpam-5394	111	35	x−	x−	PROPN
ejpam-5394	111	36	z	z	PROPN
ejpam-5394	111	37	−	−	PROPN
ejpam-5394	111	38	y	y	PROPN
ejpam-5394	111	39	}	}	PUNCT
ejpam-5394	111	40	,	,	PUNCT
ejpam-5394	111	41	if	if	SCONJ
ejpam-5394	111	42	x−	x−	PROPN
ejpam-5394	111	43	z	z	PROPN
ejpam-5394	111	44	≥	≥	PROPN
ejpam-5394	111	45	y	y	PROPN
ejpam-5394	111	46	{	{	PUNCT
ejpam-5394	111	47	0	0	NUM
ejpam-5394	111	48	}	}	PUNCT
ejpam-5394	111	49	,	,	PUNCT
ejpam-5394	112	1	if	if	SCONJ
ejpam-5394	112	2	x−	x−	PROPN
ejpam-5394	112	3	z	z	PROPN
ejpam-5394	112	4	<	<	X
ejpam-5394	112	5	y	y	PROPN
ejpam-5394	112	6	=	=	X
ejpam-5394	112	7	{	{	PUNCT
ejpam-5394	112	8	{	{	PUNCT
ejpam-5394	112	9	x−	x−	PROPN
ejpam-5394	112	10	y	y	PROPN
ejpam-5394	112	11	−	−	PROPN
ejpam-5394	113	1	z	z	X
ejpam-5394	113	2	}	}	PUNCT
ejpam-5394	113	3	,	,	PUNCT
ejpam-5394	113	4	if	if	SCONJ
ejpam-5394	113	5	x−	x−	PROPN
ejpam-5394	113	6	y	y	PROPN
ejpam-5394	113	7	≥	≥	PROPN
ejpam-5394	113	8	z	z	PROPN
ejpam-5394	113	9	{	{	PUNCT
ejpam-5394	113	10	0	0	NUM
ejpam-5394	113	11	}	}	PUNCT
ejpam-5394	113	12	,	,	PUNCT
ejpam-5394	113	13	if	if	SCONJ
ejpam-5394	113	14	x−	x−	PROPN
ejpam-5394	113	15	y	y	PROPN
ejpam-5394	113	16	<	<	X
ejpam-5394	113	17	z	z	PROPN
ejpam-5394	113	18	=	=	SYM
ejpam-5394	113	19	(	(	PUNCT
ejpam-5394	113	20	x	x	X
ejpam-5394	113	21	∗	∗	PROPN
ejpam-5394	113	22	y	y	NOUN
ejpam-5394	113	23	)	)	PUNCT
ejpam-5394	113	24	∗	∗	NOUN
ejpam-5394	113	25	z	z	NOUN
ejpam-5394	114	1	if	if	SCONJ
ejpam-5394	114	2	y	y	PROPN
ejpam-5394	114	3	≤	≤	NUM
ejpam-5394	114	4	x	x	SYM
ejpam-5394	114	5	≤	≤	NUM
ejpam-5394	114	6	z	z	NOUN
ejpam-5394	114	7	then	then	ADV
ejpam-5394	114	8	(	(	PUNCT
ejpam-5394	114	9	x	x	X
ejpam-5394	114	10	∗	∗	PROPN
ejpam-5394	114	11	y	y	NOUN
ejpam-5394	114	12	)	)	PUNCT
ejpam-5394	114	13	∗	∗	NOUN
ejpam-5394	114	14	z	z	NOUN
ejpam-5394	114	15	=	=	SYM
ejpam-5394	114	16	{	{	PUNCT
ejpam-5394	114	17	x−	x−	PROPN
ejpam-5394	114	18	y	y	PROPN
ejpam-5394	114	19	}	}	PUNCT
ejpam-5394	114	20	∗	∗	NOUN
ejpam-5394	114	21	z	z	NOUN
ejpam-5394	114	22	=	=	SYM
ejpam-5394	114	23	{	{	PUNCT
ejpam-5394	114	24	0	0	NUM
ejpam-5394	114	25	}	}	PUNCT
ejpam-5394	114	26	for	for	ADP
ejpam-5394	114	27	x−	x−	PROPN
ejpam-5394	114	28	y	y	PROPN
ejpam-5394	114	29	<	<	X
ejpam-5394	114	30	z	z	PROPN
ejpam-5394	114	31	and	and	CCONJ
ejpam-5394	114	32	e.	e.	PROPN
ejpam-5394	114	33	payla	payla	PROPN
ejpam-5394	114	34	,	,	PUNCT
ejpam-5394	114	35	l.	l.	PROPN
ejpam-5394	114	36	ranara	ranara	PROPN
ejpam-5394	114	37	/	/	SYM
ejpam-5394	114	38	eur	eur	PROPN
ejpam-5394	114	39	.	.	PUNCT
ejpam-5394	115	1	j.	j.	PROPN
ejpam-5394	115	2	pure	pure	PROPN
ejpam-5394	115	3	appl	appl	PROPN
ejpam-5394	115	4	.	.	PROPN
ejpam-5394	115	5	math	math	PROPN
ejpam-5394	115	6	,	,	PUNCT
ejpam-5394	115	7	18	18	NUM
ejpam-5394	115	8	(	(	PUNCT
ejpam-5394	115	9	2	2	NUM
ejpam-5394	115	10	)	)	PUNCT
ejpam-5394	115	11	(	(	PUNCT
ejpam-5394	115	12	2025	2025	NUM
ejpam-5394	115	13	)	)	PUNCT
ejpam-5394	115	14	,	,	PUNCT
ejpam-5394	115	15	5394	5394	NUM
ejpam-5394	115	16	5	5	NUM
ejpam-5394	115	17	of	of	ADP
ejpam-5394	115	18	10	10	NUM
ejpam-5394	115	19	(	(	PUNCT
ejpam-5394	115	20	x	x	NOUN
ejpam-5394	115	21	∗	∗	PROPN
ejpam-5394	115	22	z	z	NOUN
ejpam-5394	115	23	)	)	PUNCT
ejpam-5394	115	24	∗	∗	NOUN
ejpam-5394	115	25	y	y	NOUN
ejpam-5394	115	26	=	=	PUNCT
ejpam-5394	115	27	{	{	PUNCT
ejpam-5394	115	28	0	0	NUM
ejpam-5394	115	29	}	}	PUNCT
ejpam-5394	115	30	∗	∗	NOUN
ejpam-5394	115	31	y	y	NOUN
ejpam-5394	115	32	=	=	PUNCT
ejpam-5394	115	33	{	{	PUNCT
ejpam-5394	115	34	0	0	NUM
ejpam-5394	115	35	}	}	PUNCT
ejpam-5394	115	36	for	for	ADP
ejpam-5394	115	37	0	0	NUM
ejpam-5394	115	38	≤	≤	NUM
ejpam-5394	115	39	y	y	NOUN
ejpam-5394	116	1	=	=	SYM
ejpam-5394	117	1	(	(	PUNCT
ejpam-5394	117	2	x	x	X
ejpam-5394	117	3	∗	∗	PROPN
ejpam-5394	117	4	y	y	NOUN
ejpam-5394	117	5	)	)	PUNCT
ejpam-5394	117	6	∗	∗	NOUN
ejpam-5394	117	7	z	z	NOUN
ejpam-5394	117	8	case	case	NOUN
ejpam-5394	117	9	2	2	NUM
ejpam-5394	117	10	:	:	PUNCT
ejpam-5394	117	11	if	if	SCONJ
ejpam-5394	117	12	x	x	X
ejpam-5394	117	13	<	<	X
ejpam-5394	117	14	y	y	PROPN
ejpam-5394	117	15	if	if	SCONJ
ejpam-5394	117	16	x	x	PROPN
ejpam-5394	117	17	≤	≤	X
ejpam-5394	117	18	z	z	NOUN
ejpam-5394	117	19	<	<	X
ejpam-5394	117	20	y	y	PROPN
ejpam-5394	117	21	,	,	PUNCT
ejpam-5394	117	22	then	then	ADV
ejpam-5394	117	23	(	(	PUNCT
ejpam-5394	117	24	x	x	PROPN
ejpam-5394	117	25	∗	∗	PROPN
ejpam-5394	117	26	y	y	NOUN
ejpam-5394	117	27	)	)	PUNCT
ejpam-5394	117	28	∗	∗	NOUN
ejpam-5394	117	29	z	z	NOUN
ejpam-5394	117	30	=	=	SYM
ejpam-5394	117	31	{	{	PUNCT
ejpam-5394	117	32	0	0	NUM
ejpam-5394	117	33	}	}	PUNCT
ejpam-5394	117	34	∗	∗	NOUN
ejpam-5394	117	35	z	z	NOUN
ejpam-5394	117	36	=	=	SYM
ejpam-5394	117	37	{	{	PUNCT
ejpam-5394	117	38	0	0	NUM
ejpam-5394	117	39	}	}	PUNCT
ejpam-5394	117	40	and	and	CCONJ
ejpam-5394	117	41	(	(	PUNCT
ejpam-5394	117	42	x	x	PROPN
ejpam-5394	117	43	∗	∗	PROPN
ejpam-5394	117	44	z	z	NOUN
ejpam-5394	117	45	)	)	PUNCT
ejpam-5394	117	46	∗	∗	NOUN
ejpam-5394	117	47	y	y	NOUN
ejpam-5394	117	48	=	=	PUNCT
ejpam-5394	117	49	{	{	PUNCT
ejpam-5394	117	50	0	0	NUM
ejpam-5394	117	51	}	}	PUNCT
ejpam-5394	117	52	∗	∗	NOUN
ejpam-5394	117	53	y	y	NOUN
ejpam-5394	117	54	=	=	PUNCT
ejpam-5394	117	55	{	{	PUNCT
ejpam-5394	117	56	0	0	NUM
ejpam-5394	117	57	}	}	PUNCT
ejpam-5394	117	58	=	=	SYM
ejpam-5394	117	59	(	(	PUNCT
ejpam-5394	117	60	x	x	X
ejpam-5394	117	61	∗	∗	PROPN
ejpam-5394	117	62	y	y	NOUN
ejpam-5394	117	63	)	)	PUNCT
ejpam-5394	117	64	∗	∗	NOUN
ejpam-5394	117	65	z.	z.	PROPN
ejpam-5394	118	1	if	if	SCONJ
ejpam-5394	118	2	z	z	NOUN
ejpam-5394	118	3	≤	≤	NUM
ejpam-5394	118	4	x	x	PUNCT
ejpam-5394	118	5	≤	≤	NUM
ejpam-5394	118	6	y	y	NOUN
ejpam-5394	118	7	,	,	PUNCT
ejpam-5394	118	8	then	then	ADV
ejpam-5394	118	9	(	(	PUNCT
ejpam-5394	118	10	x	x	PROPN
ejpam-5394	118	11	∗	∗	PROPN
ejpam-5394	118	12	y	y	NOUN
ejpam-5394	118	13	)	)	PUNCT
ejpam-5394	118	14	∗	∗	NOUN
ejpam-5394	118	15	z	z	NOUN
ejpam-5394	118	16	=	=	SYM
ejpam-5394	118	17	{	{	PUNCT
ejpam-5394	118	18	0	0	NUM
ejpam-5394	118	19	}	}	PUNCT
ejpam-5394	118	20	∗	∗	NOUN
ejpam-5394	118	21	z	z	NOUN
ejpam-5394	118	22	=	=	SYM
ejpam-5394	118	23	{	{	PUNCT
ejpam-5394	118	24	0	0	NUM
ejpam-5394	118	25	}	}	PUNCT
ejpam-5394	118	26	and	and	CCONJ
ejpam-5394	118	27	(	(	PUNCT
ejpam-5394	118	28	x	x	PROPN
ejpam-5394	118	29	∗	∗	PROPN
ejpam-5394	118	30	z	z	NOUN
ejpam-5394	118	31	)	)	PUNCT
ejpam-5394	118	32	∗	∗	NOUN
ejpam-5394	118	33	y	y	NOUN
ejpam-5394	118	34	=	=	SYM
ejpam-5394	118	35	{	{	PUNCT
ejpam-5394	118	36	x−	x−	PROPN
ejpam-5394	118	37	z	z	PROPN
ejpam-5394	118	38	}	}	PUNCT
ejpam-5394	118	39	∗	∗	NOUN
ejpam-5394	118	40	y	y	NOUN
ejpam-5394	118	41	=	=	PUNCT
ejpam-5394	118	42	{	{	PUNCT
ejpam-5394	118	43	0	0	NUM
ejpam-5394	118	44	}	}	PUNCT
ejpam-5394	118	45	for	for	ADP
ejpam-5394	118	46	x−	x−	PROPN
ejpam-5394	118	47	z	z	PROPN
ejpam-5394	118	48	<	<	X
ejpam-5394	118	49	y	y	PROPN
ejpam-5394	118	50	=	=	SYM
ejpam-5394	118	51	(	(	PUNCT
ejpam-5394	118	52	x	x	X
ejpam-5394	118	53	∗	∗	PROPN
ejpam-5394	118	54	y	y	NOUN
ejpam-5394	118	55	)	)	PUNCT
ejpam-5394	118	56	∗	∗	NOUN
ejpam-5394	118	57	z	z	NOUN
ejpam-5394	119	1	if	if	SCONJ
ejpam-5394	119	2	x	x	PROPN
ejpam-5394	119	3	≤	≤	NUM
ejpam-5394	119	4	y	y	PROPN
ejpam-5394	119	5	≤	≤	PROPN
ejpam-5394	119	6	z	z	NOUN
ejpam-5394	120	1	then	then	ADV
ejpam-5394	120	2	(	(	PUNCT
ejpam-5394	120	3	x	x	X
ejpam-5394	120	4	∗	∗	PROPN
ejpam-5394	120	5	y	y	NOUN
ejpam-5394	120	6	)	)	PUNCT
ejpam-5394	120	7	∗	∗	NOUN
ejpam-5394	120	8	z	z	NOUN
ejpam-5394	120	9	=	=	SYM
ejpam-5394	120	10	{	{	PUNCT
ejpam-5394	120	11	0	0	NUM
ejpam-5394	120	12	}	}	PUNCT
ejpam-5394	120	13	∗	∗	NOUN
ejpam-5394	120	14	z	z	NOUN
ejpam-5394	120	15	=	=	SYM
ejpam-5394	120	16	{	{	PUNCT
ejpam-5394	120	17	0	0	NUM
ejpam-5394	120	18	}	}	PUNCT
ejpam-5394	120	19	and	and	CCONJ
ejpam-5394	120	20	(	(	PUNCT
ejpam-5394	120	21	x	x	PROPN
ejpam-5394	120	22	∗	∗	PROPN
ejpam-5394	120	23	z	z	NOUN
ejpam-5394	120	24	)	)	PUNCT
ejpam-5394	120	25	∗	∗	NOUN
ejpam-5394	120	26	y	y	NOUN
ejpam-5394	120	27	=	=	PUNCT
ejpam-5394	120	28	{	{	PUNCT
ejpam-5394	120	29	0	0	NUM
ejpam-5394	120	30	}	}	PUNCT
ejpam-5394	120	31	∗	∗	NOUN
ejpam-5394	120	32	y	y	NOUN
ejpam-5394	120	33	=	=	PUNCT
ejpam-5394	120	34	{	{	PUNCT
ejpam-5394	120	35	0	0	NUM
ejpam-5394	120	36	}	}	PUNCT
ejpam-5394	120	37	=	=	SYM
ejpam-5394	120	38	(	(	PUNCT
ejpam-5394	120	39	x	x	X
ejpam-5394	120	40	∗	∗	PROPN
ejpam-5394	120	41	y	y	NOUN
ejpam-5394	120	42	)	)	PUNCT
ejpam-5394	120	43	∗	∗	NOUN
ejpam-5394	120	44	z.	z.	PROPN
ejpam-5394	121	1	thus	thus	ADV
ejpam-5394	121	2	(	(	PUNCT
ejpam-5394	121	3	x	x	SYM
ejpam-5394	121	4	∗	∗	PROPN
ejpam-5394	121	5	y	y	NOUN
ejpam-5394	121	6	)	)	PUNCT
ejpam-5394	121	7	∗	∗	NOUN
ejpam-5394	121	8	z	z	NOUN
ejpam-5394	121	9	=	=	SYM
ejpam-5394	121	10	(	(	PUNCT
ejpam-5394	121	11	x	x	X
ejpam-5394	121	12	∗	∗	PROPN
ejpam-5394	121	13	z	z	NOUN
ejpam-5394	121	14	)	)	PUNCT
ejpam-5394	121	15	∗	∗	NOUN
ejpam-5394	121	16	y.	y.	PROPN
ejpam-5394	122	1	■	■	PUNCT
ejpam-5394	122	2	lemma	lemma	PROPN
ejpam-5394	122	3	3	3	NUM
ejpam-5394	122	4	.	.	PUNCT
ejpam-5394	122	5	for	for	ADP
ejpam-5394	122	6	each	each	DET
ejpam-5394	122	7	x	x	SYM
ejpam-5394	122	8	∈	∈	PROPN
ejpam-5394	123	1	[	[	X
ejpam-5394	123	2	0	0	NUM
ejpam-5394	123	3	,	,	PUNCT
ejpam-5394	123	4	1	1	NUM
ejpam-5394	123	5	]	]	PUNCT
ejpam-5394	123	6	,	,	PUNCT
ejpam-5394	123	7	x	x	X
ejpam-5394	123	8	∗	∗	NOUN
ejpam-5394	123	9	[	[	X
ejpam-5394	123	10	0	0	NUM
ejpam-5394	123	11	,	,	PUNCT
ejpam-5394	123	12	1	1	NUM
ejpam-5394	123	13	]	]	PUNCT
ejpam-5394	123	14	≪	≪	X
ejpam-5394	123	15	{	{	PUNCT
ejpam-5394	123	16	x	x	NOUN
ejpam-5394	123	17	}	}	PUNCT
ejpam-5394	123	18	.	.	PUNCT
ejpam-5394	124	1	proof	proof	NOUN
ejpam-5394	124	2	.	.	PUNCT
ejpam-5394	125	1	:	:	PUNCT
ejpam-5394	125	2	case	case	NOUN
ejpam-5394	125	3	1	1	NUM
ejpam-5394	125	4	:	:	PUNCT
ejpam-5394	125	5	if	if	SCONJ
ejpam-5394	125	6	x	x	X
ejpam-5394	125	7	≥	≥	X
ejpam-5394	125	8	y	y	NOUN
ejpam-5394	125	9	,	,	PUNCT
ejpam-5394	125	10	then	then	ADV
ejpam-5394	125	11	x	x	X
ejpam-5394	125	12	∗	∗	NOUN
ejpam-5394	125	13	y	y	NOUN
ejpam-5394	125	14	=	=	SYM
ejpam-5394	125	15	{	{	PUNCT
ejpam-5394	125	16	x−	x−	PROPN
ejpam-5394	125	17	y	y	PROPN
ejpam-5394	125	18	}	}	PUNCT
ejpam-5394	125	19	and	and	CCONJ
ejpam-5394	125	20	that	that	SCONJ
ejpam-5394	125	21	x−	x−	PROPN
ejpam-5394	125	22	y	y	PROPN
ejpam-5394	125	23	<	<	X
ejpam-5394	125	24	x	x	X
ejpam-5394	125	25	so	so	SCONJ
ejpam-5394	125	26	that	that	SCONJ
ejpam-5394	125	27	x−	x−	PROPN
ejpam-5394	125	28	y	y	PROPN
ejpam-5394	125	29	≪	≪	PROPN
ejpam-5394	125	30	x	x	PUNCT
ejpam-5394	125	31	for	for	ADP
ejpam-5394	125	32	0	0	NUM
ejpam-5394	125	33	∈	∈	PROPN
ejpam-5394	125	34	x−	x−	PROPN
ejpam-5394	125	35	y	y	PROPN
ejpam-5394	125	36	∗	∗	NOUN
ejpam-5394	125	37	x	x	PUNCT
ejpam-5394	126	1	=	=	PUNCT
ejpam-5394	126	2	{	{	PUNCT
ejpam-5394	126	3	0	0	NUM
ejpam-5394	126	4	}	}	PUNCT
ejpam-5394	126	5	.	.	PUNCT
ejpam-5394	127	1	case	case	NOUN
ejpam-5394	127	2	2	2	NUM
ejpam-5394	127	3	:	:	PUNCT
ejpam-5394	127	4	if	if	SCONJ
ejpam-5394	127	5	x	x	X
ejpam-5394	127	6	<	<	X
ejpam-5394	127	7	y	y	PROPN
ejpam-5394	127	8	,	,	PUNCT
ejpam-5394	127	9	then	then	ADV
ejpam-5394	127	10	x	x	X
ejpam-5394	127	11	∗	∗	NOUN
ejpam-5394	127	12	y	y	NOUN
ejpam-5394	127	13	=	=	PUNCT
ejpam-5394	127	14	{	{	PUNCT
ejpam-5394	127	15	0	0	NOUN
ejpam-5394	127	16	}	}	PUNCT
ejpam-5394	127	17	≪	≪	PUNCT
ejpam-5394	127	18	{	{	PUNCT
ejpam-5394	127	19	x	x	X
ejpam-5394	127	20	}	}	PUNCT
ejpam-5394	127	21	for	for	ADP
ejpam-5394	127	22	0	0	NUM
ejpam-5394	127	23	∈	∈	NOUN
ejpam-5394	127	24	0	0	NUM
ejpam-5394	127	25	∗	∗	NOUN
ejpam-5394	127	26	x	x	X
ejpam-5394	127	27	=	=	PUNCT
ejpam-5394	127	28	{	{	PUNCT
ejpam-5394	127	29	0	0	NUM
ejpam-5394	127	30	}	}	PUNCT
ejpam-5394	127	31	.	.	PUNCT
ejpam-5394	128	1	in	in	ADP
ejpam-5394	128	2	any	any	DET
ejpam-5394	128	3	case	case	NOUN
ejpam-5394	128	4	,	,	PUNCT
ejpam-5394	128	5	for	for	ADP
ejpam-5394	128	6	all	all	DET
ejpam-5394	128	7	y	y	PROPN
ejpam-5394	128	8	∈	∈	PROPN
ejpam-5394	128	9	h	h	NOUN
ejpam-5394	128	10	,	,	PUNCT
ejpam-5394	128	11	x	x	PROPN
ejpam-5394	128	12	∗	∗	NOUN
ejpam-5394	128	13	y	y	PROPN
ejpam-5394	128	14	≪	≪	PUNCT
ejpam-5394	128	15	{	{	PUNCT
ejpam-5394	128	16	x	x	NOUN
ejpam-5394	128	17	}	}	PUNCT
ejpam-5394	128	18	.	.	PUNCT
ejpam-5394	129	1	thus	thus	ADV
ejpam-5394	129	2	x	x	X
ejpam-5394	129	3	∗	∗	NOUN
ejpam-5394	129	4	[	[	X
ejpam-5394	129	5	0	0	NUM
ejpam-5394	129	6	,	,	PUNCT
ejpam-5394	129	7	1	1	NUM
ejpam-5394	129	8	]	]	PUNCT
ejpam-5394	129	9	≪	≪	X
ejpam-5394	129	10	{	{	PUNCT
ejpam-5394	129	11	x	x	NOUN
ejpam-5394	129	12	}	}	PUNCT
ejpam-5394	129	13	.	.	PUNCT
ejpam-5394	130	1	■	■	PUNCT
ejpam-5394	130	2	lemma	lemma	PROPN
ejpam-5394	130	3	4	4	NUM
ejpam-5394	130	4	.	.	PUNCT
ejpam-5394	130	5	for	for	ADP
ejpam-5394	130	6	all	all	DET
ejpam-5394	130	7	x	x	NOUN
ejpam-5394	130	8	,	,	PUNCT
ejpam-5394	130	9	y	y	PROPN
ejpam-5394	130	10	∈	∈	PROPN
ejpam-5394	131	1	[	[	X
ejpam-5394	131	2	0	0	NUM
ejpam-5394	131	3	,	,	PUNCT
ejpam-5394	131	4	1	1	NUM
ejpam-5394	131	5	]	]	PUNCT
ejpam-5394	131	6	x	x	SYM
ejpam-5394	131	7	≪	≪	PUNCT
ejpam-5394	131	8	y	y	PROPN
ejpam-5394	131	9	and	and	CCONJ
ejpam-5394	131	10	y	y	PROPN
ejpam-5394	131	11	≪	≪	NOUN
ejpam-5394	131	12	x	x	PUNCT
ejpam-5394	131	13	implies	imply	VERB
ejpam-5394	131	14	x	x	PUNCT
ejpam-5394	131	15	=	=	SYM
ejpam-5394	131	16	y.	y.	NOUN
ejpam-5394	131	17	proof	proof	NOUN
ejpam-5394	131	18	.	.	PUNCT
ejpam-5394	132	1	:	:	PUNCT
ejpam-5394	132	2	suppose	suppose	VERB
ejpam-5394	132	3	x	x	SYM
ejpam-5394	132	4	≪	≪	VERB
ejpam-5394	132	5	y	y	PROPN
ejpam-5394	132	6	and	and	CCONJ
ejpam-5394	132	7	y	y	PROPN
ejpam-5394	132	8	≪	≪	PROPN
ejpam-5394	132	9	x.	x.	NOUN
ejpam-5394	132	10	then	then	ADV
ejpam-5394	132	11	0	0	NUM
ejpam-5394	132	12	∈	∈	NOUN
ejpam-5394	132	13	x	x	X
ejpam-5394	132	14	∗	∗	NOUN
ejpam-5394	132	15	y	y	NOUN
ejpam-5394	132	16	=	=	PRON
ejpam-5394	132	17	{	{	PUNCT
ejpam-5394	132	18	{	{	PUNCT
ejpam-5394	132	19	x−	x−	PROPN
ejpam-5394	132	20	y	y	PROPN
ejpam-5394	132	21	}	}	PUNCT
ejpam-5394	132	22	,	,	PUNCT
ejpam-5394	132	23	if	if	SCONJ
ejpam-5394	132	24	x	x	PROPN
ejpam-5394	132	25	>	>	X
ejpam-5394	132	26	y	y	PROPN
ejpam-5394	132	27	{	{	PUNCT
ejpam-5394	132	28	0	0	NUM
ejpam-5394	132	29	}	}	PUNCT
ejpam-5394	132	30	,	,	PUNCT
ejpam-5394	132	31	if	if	SCONJ
ejpam-5394	132	32	x	x	ADP
ejpam-5394	132	33	≤	≤	ADJ
ejpam-5394	132	34	y	y	NOUN
ejpam-5394	132	35	and	and	CCONJ
ejpam-5394	132	36	0	0	NUM
ejpam-5394	132	37	∈	∈	PROPN
ejpam-5394	132	38	y	y	NOUN
ejpam-5394	132	39	∗	∗	NOUN
ejpam-5394	132	40	x	x	X
ejpam-5394	133	1	=	=	PRON
ejpam-5394	133	2	{	{	PUNCT
ejpam-5394	133	3	{	{	PUNCT
ejpam-5394	133	4	y	y	NOUN
ejpam-5394	133	5	−	−	NOUN
ejpam-5394	133	6	x	x	X
ejpam-5394	133	7	}	}	PUNCT
ejpam-5394	133	8	,	,	PUNCT
ejpam-5394	133	9	if	if	SCONJ
ejpam-5394	133	10	y	y	PROPN
ejpam-5394	133	11	>	>	X
ejpam-5394	133	12	x	x	X
ejpam-5394	133	13	{	{	PUNCT
ejpam-5394	133	14	0	0	NUM
ejpam-5394	133	15	}	}	PUNCT
ejpam-5394	133	16	,	,	PUNCT
ejpam-5394	133	17	if	if	SCONJ
ejpam-5394	133	18	y	y	PROPN
ejpam-5394	133	19	≤	≤	X
ejpam-5394	133	20	x	x	PUNCT
ejpam-5394	133	21	this	this	PRON
ejpam-5394	133	22	implies	imply	VERB
ejpam-5394	133	23	that	that	SCONJ
ejpam-5394	133	24	x	x	SYM
ejpam-5394	133	25	∗	∗	NOUN
ejpam-5394	133	26	y	y	NOUN
ejpam-5394	133	27	=	=	PUNCT
ejpam-5394	133	28	{	{	PUNCT
ejpam-5394	133	29	0	0	NUM
ejpam-5394	133	30	}	}	PUNCT
ejpam-5394	133	31	=	=	SYM
ejpam-5394	133	32	y	y	PROPN
ejpam-5394	133	33	∗	∗	NOUN
ejpam-5394	133	34	x.	x.	NOUN
ejpam-5394	133	35	hence	hence	ADV
ejpam-5394	133	36	,	,	PUNCT
ejpam-5394	133	37	x	x	PUNCT
ejpam-5394	133	38	≤	≤	ADJ
ejpam-5394	133	39	y	y	PROPN
ejpam-5394	133	40	and	and	CCONJ
ejpam-5394	133	41	y	y	PROPN
ejpam-5394	133	42	≤	≤	PROPN
ejpam-5394	133	43	x	x	PUNCT
ejpam-5394	133	44	implies	imply	VERB
ejpam-5394	133	45	x	x	PUNCT
ejpam-5394	133	46	=	=	PUNCT
ejpam-5394	133	47	y.	y.	NOUN
ejpam-5394	133	48	■	■	PUNCT
ejpam-5394	133	49	theorem	theorem	ADJ
ejpam-5394	133	50	5	5	NUM
ejpam-5394	133	51	.	.	PUNCT
ejpam-5394	134	1	(	(	PUNCT
ejpam-5394	134	2	[	[	X
ejpam-5394	134	3	0	0	NUM
ejpam-5394	134	4	,	,	PUNCT
ejpam-5394	134	5	1	1	NUM
ejpam-5394	134	6	]	]	PUNCT
ejpam-5394	134	7	,	,	PUNCT
ejpam-5394	134	8	∗	∗	NOUN
ejpam-5394	134	9	,	,	PUNCT
ejpam-5394	134	10	0	0	NUM
ejpam-5394	134	11	)	)	PUNCT
ejpam-5394	134	12	is	be	AUX
ejpam-5394	134	13	a	a	DET
ejpam-5394	134	14	hyper	hyper	ADJ
ejpam-5394	134	15	bck	bck	NOUN
ejpam-5394	134	16	-	-	PUNCT
ejpam-5394	134	17	algebra	algebra	NOUN
ejpam-5394	134	18	.	.	PUNCT
ejpam-5394	135	1	proof	proof	NOUN
ejpam-5394	135	2	.	.	PUNCT
ejpam-5394	136	1	:	:	PUNCT
ejpam-5394	136	2	it	it	PRON
ejpam-5394	136	3	follows	follow	VERB
ejpam-5394	136	4	immediately	immediately	ADV
ejpam-5394	136	5	from	from	ADP
ejpam-5394	136	6	lemmas	lemmas	PROPN
ejpam-5394	136	7	1	1	NUM
ejpam-5394	136	8	,	,	PUNCT
ejpam-5394	136	9	2	2	NUM
ejpam-5394	136	10	,	,	PUNCT
ejpam-5394	136	11	3	3	NUM
ejpam-5394	136	12	and	and	CCONJ
ejpam-5394	136	13	4	4	NUM
ejpam-5394	136	14	.	.	X
ejpam-5394	137	1	■	■	PUNCT
ejpam-5394	137	2	e.	e.	PROPN
ejpam-5394	137	3	payla	payla	PROPN
ejpam-5394	137	4	,	,	PUNCT
ejpam-5394	137	5	l.	l.	PROPN
ejpam-5394	137	6	ranara	ranara	PROPN
ejpam-5394	137	7	/	/	SYM
ejpam-5394	137	8	eur	eur	PROPN
ejpam-5394	137	9	.	.	PUNCT
ejpam-5394	138	1	j.	j.	PROPN
ejpam-5394	138	2	pure	pure	PROPN
ejpam-5394	138	3	appl	appl	PROPN
ejpam-5394	138	4	.	.	PROPN
ejpam-5394	138	5	math	math	PROPN
ejpam-5394	138	6	,	,	PUNCT
ejpam-5394	138	7	18	18	NUM
ejpam-5394	138	8	(	(	PUNCT
ejpam-5394	138	9	2	2	NUM
ejpam-5394	138	10	)	)	PUNCT
ejpam-5394	138	11	(	(	PUNCT
ejpam-5394	138	12	2025	2025	NUM
ejpam-5394	138	13	)	)	PUNCT
ejpam-5394	138	14	,	,	PUNCT
ejpam-5394	138	15	5394	5394	NUM
ejpam-5394	138	16	6	6	NUM
ejpam-5394	138	17	of	of	ADP
ejpam-5394	138	18	10	10	NUM
ejpam-5394	138	19	4	4	NUM
ejpam-5394	138	20	.	.	PUNCT
ejpam-5394	139	1	the	the	DET
ejpam-5394	139	2	topology	topology	NOUN
ejpam-5394	139	3	τr[0	τr[0	PROPN
ejpam-5394	139	4	,	,	PUNCT
ejpam-5394	139	5	1	1	NUM
ejpam-5394	139	6	]	]	PUNCT
ejpam-5394	139	7	by	by	ADP
ejpam-5394	139	8	definition	definition	NOUN
ejpam-5394	139	9	5	5	NUM
ejpam-5394	139	10	,	,	PUNCT
ejpam-5394	139	11	rh(a	rh(a	NUM
ejpam-5394	139	12	)	)	PUNCT
ejpam-5394	139	13	=	=	PRON
ejpam-5394	139	14	{	{	PUNCT
ejpam-5394	139	15	x	x	PUNCT
ejpam-5394	139	16	∈	∈	PROPN
ejpam-5394	139	17	h	h	NOUN
ejpam-5394	139	18	:	:	PUNCT
ejpam-5394	139	19	a	a	DET
ejpam-5394	139	20	≪	≪	ADJ
ejpam-5394	139	21	x	x	NOUN
ejpam-5394	139	22	,	,	PUNCT
ejpam-5394	139	23	∀	∀	X
ejpam-5394	139	24	a	a	DET
ejpam-5394	139	25	∈	∈	PROPN
ejpam-5394	139	26	a	a	DET
ejpam-5394	139	27	}	}	PUNCT
ejpam-5394	139	28	=	=	SYM
ejpam-5394	139	29	{	{	PUNCT
ejpam-5394	139	30	x	x	PUNCT
ejpam-5394	139	31	∈	∈	PROPN
ejpam-5394	139	32	h	h	NOUN
ejpam-5394	139	33	:	:	PUNCT
ejpam-5394	139	34	0	0	NUM
ejpam-5394	139	35	∈	∈	PROPN
ejpam-5394	139	36	a	a	DET
ejpam-5394	139	37	∗	∗	NOUN
ejpam-5394	139	38	x	x	X
ejpam-5394	139	39	,	,	PUNCT
ejpam-5394	139	40	∀	∀	VERB
ejpam-5394	139	41	a	a	DET
ejpam-5394	139	42	∈	∈	PROPN
ejpam-5394	139	43	a	a	X
ejpam-5394	139	44	}	}	PUNCT
ejpam-5394	139	45	and	and	CCONJ
ejpam-5394	139	46	considering	consider	VERB
ejpam-5394	139	47	the	the	DET
ejpam-5394	139	48	hyper	hyper	ADJ
ejpam-5394	139	49	bck	bck	NOUN
ejpam-5394	139	50	-	-	PUNCT
ejpam-5394	139	51	algebra	algebra	NOUN
ejpam-5394	139	52	[	[	X
ejpam-5394	139	53	0	0	NUM
ejpam-5394	139	54	,	,	PUNCT
ejpam-5394	139	55	1	1	NUM
ejpam-5394	139	56	]	]	PUNCT
ejpam-5394	139	57	.	.	PUNCT
ejpam-5394	140	1	note	note	VERB
ejpam-5394	140	2	that	that	SCONJ
ejpam-5394	140	3	from	from	ADP
ejpam-5394	140	4	now	now	ADV
ejpam-5394	140	5	on	on	ADP
ejpam-5394	140	6	h	h	NOUN
ejpam-5394	140	7	=	=	PUNCT
ejpam-5394	141	1	[	[	X
ejpam-5394	141	2	0	0	NUM
ejpam-5394	141	3	,	,	PUNCT
ejpam-5394	141	4	1	1	NUM
ejpam-5394	141	5	]	]	PUNCT
ejpam-5394	141	6	,	,	PUNCT
ejpam-5394	141	7	we	we	PRON
ejpam-5394	141	8	have	have	VERB
ejpam-5394	141	9	the	the	DET
ejpam-5394	141	10	following	follow	VERB
ejpam-5394	141	11	example	example	NOUN
ejpam-5394	141	12	.	.	PUNCT
ejpam-5394	142	1	example	example	NOUN
ejpam-5394	143	1	1	1	NUM
ejpam-5394	143	2	.	.	X
ejpam-5394	143	3	consider	consider	VERB
ejpam-5394	143	4	a	a	DET
ejpam-5394	143	5	=	=	X
ejpam-5394	143	6	{	{	PUNCT
ejpam-5394	143	7	1	1	NUM
ejpam-5394	143	8	2	2	NUM
ejpam-5394	143	9	,	,	PUNCT
ejpam-5394	143	10	1	1	NUM
ejpam-5394	143	11	3	3	NUM
ejpam-5394	143	12	}	}	PUNCT
ejpam-5394	143	13	.	.	PUNCT
ejpam-5394	144	1	then	then	ADV
ejpam-5394	144	2	rh(a	rh(a	X
ejpam-5394	144	3	)	)	PUNCT
ejpam-5394	144	4	=	=	PRON
ejpam-5394	145	1	{	{	PUNCT
ejpam-5394	145	2	x	x	PUNCT
ejpam-5394	145	3	∈	∈	PROPN
ejpam-5394	146	1	[	[	X
ejpam-5394	146	2	0	0	NUM
ejpam-5394	146	3	,	,	PUNCT
ejpam-5394	146	4	1	1	NUM
ejpam-5394	146	5	]	]	PUNCT
ejpam-5394	146	6	:	:	PUNCT
ejpam-5394	146	7	0	0	NUM
ejpam-5394	146	8	∈	∈	PROPN
ejpam-5394	146	9	a	a	DET
ejpam-5394	146	10	∗	∗	NOUN
ejpam-5394	146	11	x	x	X
ejpam-5394	146	12	,	,	PUNCT
ejpam-5394	146	13	∀	∀	VERB
ejpam-5394	146	14	a	a	DET
ejpam-5394	146	15	∈	∈	PROPN
ejpam-5394	146	16	a	a	DET
ejpam-5394	146	17	}	}	PUNCT
ejpam-5394	146	18	=	=	SYM
ejpam-5394	146	19	{	{	PUNCT
ejpam-5394	146	20	x	x	PUNCT
ejpam-5394	146	21	∈	∈	PROPN
ejpam-5394	147	1	[	[	X
ejpam-5394	147	2	0	0	NUM
ejpam-5394	147	3	,	,	PUNCT
ejpam-5394	147	4	1	1	NUM
ejpam-5394	147	5	]	]	PUNCT
ejpam-5394	147	6	:	:	PUNCT
ejpam-5394	147	7	0	0	NUM
ejpam-5394	147	8	∈	∈	PROPN
ejpam-5394	147	9	a	a	DET
ejpam-5394	147	10	∗	∗	NOUN
ejpam-5394	147	11	x	x	X
ejpam-5394	147	12	,	,	PUNCT
ejpam-5394	147	13	∀	∀	X
ejpam-5394	147	14	a	a	DET
ejpam-5394	147	15	∈	∈	NOUN
ejpam-5394	147	16	{	{	PUNCT
ejpam-5394	147	17	1	1	NUM
ejpam-5394	147	18	2	2	NUM
ejpam-5394	147	19	,	,	PUNCT
ejpam-5394	147	20	1	1	NUM
ejpam-5394	147	21	3	3	NUM
ejpam-5394	147	22	}	}	PUNCT
ejpam-5394	147	23	}	}	PUNCT
ejpam-5394	147	24	=	=	SYM
ejpam-5394	147	25	{	{	PUNCT
ejpam-5394	147	26	x	x	PUNCT
ejpam-5394	147	27	∈	∈	PROPN
ejpam-5394	148	1	[	[	X
ejpam-5394	148	2	0	0	NUM
ejpam-5394	148	3	,	,	PUNCT
ejpam-5394	148	4	1	1	NUM
ejpam-5394	148	5	]	]	PUNCT
ejpam-5394	148	6	:	:	PUNCT
ejpam-5394	148	7	0	0	NUM
ejpam-5394	148	8	∈	∈	NOUN
ejpam-5394	148	9	1	1	NUM
ejpam-5394	148	10	2	2	NUM
ejpam-5394	148	11	∗	∗	NOUN
ejpam-5394	148	12	x	x	PUNCT
ejpam-5394	148	13	and	and	CCONJ
ejpam-5394	148	14	0	0	NUM
ejpam-5394	148	15	∈	∈	NOUN
ejpam-5394	148	16	1	1	NUM
ejpam-5394	148	17	3	3	NUM
ejpam-5394	148	18	∗	∗	NOUN
ejpam-5394	148	19	x	x	PUNCT
ejpam-5394	148	20	}	}	PUNCT
ejpam-5394	148	21	note	note	VERB
ejpam-5394	148	22	that	that	SCONJ
ejpam-5394	148	23	for	for	SCONJ
ejpam-5394	148	24	0	0	NUM
ejpam-5394	148	25	to	to	PART
ejpam-5394	148	26	be	be	AUX
ejpam-5394	148	27	in	in	ADP
ejpam-5394	148	28	1	1	NUM
ejpam-5394	148	29	2	2	NUM
ejpam-5394	148	30	∗	∗	NOUN
ejpam-5394	148	31	x	x	SYM
ejpam-5394	148	32	,	,	PUNCT
ejpam-5394	148	33	1	1	NUM
ejpam-5394	148	34	2	2	NUM
ejpam-5394	148	35	∗	∗	NOUN
ejpam-5394	148	36	x	x	X
ejpam-5394	148	37	=	=	PUNCT
ejpam-5394	148	38	{	{	PUNCT
ejpam-5394	148	39	0	0	NUM
ejpam-5394	148	40	}	}	PUNCT
ejpam-5394	148	41	this	this	PRON
ejpam-5394	148	42	implies	imply	VERB
ejpam-5394	148	43	x	x	X
ejpam-5394	148	44	≥	≥	NUM
ejpam-5394	148	45	1	1	NUM
ejpam-5394	148	46	2	2	NUM
ejpam-5394	148	47	or	or	CCONJ
ejpam-5394	148	48	[	[	PUNCT
ejpam-5394	148	49	1	1	NUM
ejpam-5394	148	50	2	2	NUM
ejpam-5394	148	51	,	,	PUNCT
ejpam-5394	148	52	1	1	NUM
ejpam-5394	148	53	]	]	PUNCT
ejpam-5394	148	54	.	.	PUNCT
ejpam-5394	149	1	also	also	ADV
ejpam-5394	149	2	for	for	ADP
ejpam-5394	149	3	0	0	NUM
ejpam-5394	149	4	∈	∈	PROPN
ejpam-5394	149	5	1	1	NUM
ejpam-5394	149	6	3	3	NUM
ejpam-5394	149	7	∗	∗	NOUN
ejpam-5394	149	8	x	x	X
ejpam-5394	149	9	,	,	PUNCT
ejpam-5394	149	10	x	x	X
ejpam-5394	149	11	≥	≥	NUM
ejpam-5394	149	12	1	1	NUM
ejpam-5394	149	13	3	3	NUM
ejpam-5394	149	14	or	or	CCONJ
ejpam-5394	149	15	[	[	PUNCT
ejpam-5394	149	16	1	1	NUM
ejpam-5394	149	17	3	3	NUM
ejpam-5394	149	18	,	,	PUNCT
ejpam-5394	149	19	1	1	NUM
ejpam-5394	149	20	]	]	PUNCT
ejpam-5394	149	21	.	.	PUNCT
ejpam-5394	150	1	since	since	SCONJ
ejpam-5394	150	2	rh(a	rh(a	NUM
ejpam-5394	150	3	)	)	PUNCT
ejpam-5394	150	4	=	=	SYM
ejpam-5394	150	5	⋂	⋂	PROPN
ejpam-5394	150	6	a∈arh(a	a∈arh(a	PROPN
ejpam-5394	150	7	)	)	PUNCT
ejpam-5394	150	8	this	this	PRON
ejpam-5394	150	9	implies	imply	VERB
ejpam-5394	150	10	that	that	SCONJ
ejpam-5394	150	11	rh({1	rh({1	NOUN
ejpam-5394	150	12	2	2	NUM
ejpam-5394	150	13	,	,	PUNCT
ejpam-5394	150	14	1	1	NUM
ejpam-5394	150	15	3	3	NUM
ejpam-5394	150	16	}	}	PUNCT
ejpam-5394	150	17	)	)	PUNCT
ejpam-5394	150	18	=	=	PUNCT
ejpam-5394	151	1	[	[	X
ejpam-5394	151	2	12	12	NUM
ejpam-5394	151	3	,	,	PUNCT
ejpam-5394	151	4	1	1	NUM
ejpam-5394	151	5	]	]	PUNCT
ejpam-5394	151	6	∩	∩	NOUN
ejpam-5394	151	7	[	[	X
ejpam-5394	151	8	13	13	NUM
ejpam-5394	151	9	,	,	PUNCT
ejpam-5394	151	10	1	1	NUM
ejpam-5394	151	11	]	]	PUNCT
ejpam-5394	151	12	=	=	PUNCT
ejpam-5394	152	1	[	[	X
ejpam-5394	152	2	12	12	NUM
ejpam-5394	152	3	,	,	PUNCT
ejpam-5394	152	4	1	1	NUM
ejpam-5394	152	5	]	]	PUNCT
ejpam-5394	152	6	.	.	PUNCT
ejpam-5394	153	1	therefore	therefore	ADV
ejpam-5394	153	2	,	,	PUNCT
ejpam-5394	153	3	rh	rh	PROPN
ejpam-5394	153	4	(	(	PUNCT
ejpam-5394	153	5	{	{	PUNCT
ejpam-5394	153	6	1	1	NUM
ejpam-5394	153	7	2	2	NUM
ejpam-5394	153	8	,	,	PUNCT
ejpam-5394	153	9	1	1	NUM
ejpam-5394	153	10	3	3	NUM
ejpam-5394	153	11	}	}	PUNCT
ejpam-5394	153	12	)	)	PUNCT
ejpam-5394	153	13	=	=	PUNCT
ejpam-5394	153	14	[	[	PUNCT
ejpam-5394	153	15	1	1	NUM
ejpam-5394	153	16	2	2	NUM
ejpam-5394	153	17	,	,	PUNCT
ejpam-5394	153	18	1	1	NUM
ejpam-5394	153	19	]	]	PUNCT
ejpam-5394	153	20	.	.	PUNCT
ejpam-5394	154	1	theorem	theorem	ADJ
ejpam-5394	154	2	6	6	NUM
ejpam-5394	154	3	.	.	PUNCT
ejpam-5394	155	1	let	let	VERB
ejpam-5394	155	2	a	a	DET
ejpam-5394	155	3	⊆	⊆	NUM
ejpam-5394	155	4	h	h	NOUN
ejpam-5394	155	5	,	,	PUNCT
ejpam-5394	155	6	rh(a	rh(a	NOUN
ejpam-5394	155	7	)	)	PUNCT
ejpam-5394	155	8	=	=	NOUN
ejpam-5394	156	1	[	[	X
ejpam-5394	156	2	sup	sup	NOUN
ejpam-5394	156	3	a	a	PRON
ejpam-5394	156	4	,	,	PUNCT
ejpam-5394	156	5	1	1	NUM
ejpam-5394	156	6	]	]	PUNCT
ejpam-5394	156	7	∩h	∩h	NOUN
ejpam-5394	156	8	.	.	PUNCT
ejpam-5394	157	1	in	in	ADP
ejpam-5394	157	2	particular	particular	ADJ
ejpam-5394	157	3	,	,	PUNCT
ejpam-5394	157	4	rh(a	rh(a	NOUN
ejpam-5394	157	5	)	)	PUNCT
ejpam-5394	157	6	=	=	PRON
ejpam-5394	157	7	{	{	PUNCT
ejpam-5394	157	8	h	h	NOUN
ejpam-5394	157	9	if	if	SCONJ
ejpam-5394	157	10	a	a	PRON
ejpam-5394	157	11	=	=	NOUN
ejpam-5394	157	12	∅	∅	NOUN
ejpam-5394	158	1	[	[	X
ejpam-5394	158	2	sup	sup	NOUN
ejpam-5394	158	3	a	a	PRON
ejpam-5394	158	4	,	,	PUNCT
ejpam-5394	158	5	1	1	X
ejpam-5394	158	6	]	]	PUNCT
ejpam-5394	158	7	if	if	SCONJ
ejpam-5394	158	8	a	a	DET
ejpam-5394	158	9	̸=	̸=	PROPN
ejpam-5394	158	10	∅.	∅.	X
ejpam-5394	158	11	.	.	PUNCT
ejpam-5394	159	1	proof	proof	NOUN
ejpam-5394	159	2	.	.	PUNCT
ejpam-5394	160	1	:	:	PUNCT
ejpam-5394	160	2	note	note	VERB
ejpam-5394	160	3	that	that	SCONJ
ejpam-5394	160	4	x	x	SYM
ejpam-5394	160	5	∈	∈	NOUN
ejpam-5394	160	6	rh(a	rh(a	NOUN
ejpam-5394	160	7	)	)	PUNCT
ejpam-5394	160	8	if	if	SCONJ
ejpam-5394	160	9	and	and	CCONJ
ejpam-5394	160	10	only	only	ADV
ejpam-5394	160	11	if	if	SCONJ
ejpam-5394	160	12	0	0	NUM
ejpam-5394	160	13	∈	∈	PROPN
ejpam-5394	160	14	a	a	DET
ejpam-5394	160	15	∗x	∗x	NOUN
ejpam-5394	160	16	for	for	ADP
ejpam-5394	160	17	all	all	DET
ejpam-5394	160	18	a	a	DET
ejpam-5394	160	19	∈	∈	NOUN
ejpam-5394	160	20	a.	a.	NOUN
ejpam-5394	160	21	now	now	ADV
ejpam-5394	160	22	,	,	PUNCT
ejpam-5394	160	23	0	0	NUM
ejpam-5394	160	24	∈	∈	PROPN
ejpam-5394	160	25	a	a	DET
ejpam-5394	160	26	∗x	∗x	NOUN
ejpam-5394	160	27	for	for	ADP
ejpam-5394	160	28	all	all	DET
ejpam-5394	160	29	a	a	DET
ejpam-5394	160	30	∈	∈	NOUN
ejpam-5394	160	31	a	a	DET
ejpam-5394	160	32	if	if	NOUN
ejpam-5394	161	1	and	and	CCONJ
ejpam-5394	161	2	only	only	ADV
ejpam-5394	161	3	if	if	SCONJ
ejpam-5394	161	4	a	a	DET
ejpam-5394	161	5	≤	≤	NOUN
ejpam-5394	161	6	x	x	PUNCT
ejpam-5394	161	7	for	for	ADP
ejpam-5394	161	8	all	all	DET
ejpam-5394	161	9	a	a	DET
ejpam-5394	161	10	∈	∈	PROPN
ejpam-5394	161	11	a	a	PRON
ejpam-5394	161	12	,	,	PUNCT
ejpam-5394	161	13	that	that	ADV
ejpam-5394	161	14	is	is	ADV
ejpam-5394	161	15	,	,	PUNCT
ejpam-5394	161	16	x	x	SYM
ejpam-5394	161	17	∈	∈	NOUN
ejpam-5394	161	18	h	h	NOUN
ejpam-5394	161	19	is	be	AUX
ejpam-5394	161	20	an	an	DET
ejpam-5394	161	21	upperbound	upperbound	NOUN
ejpam-5394	161	22	of	of	ADP
ejpam-5394	161	23	a.	a.	NOUN
ejpam-5394	161	24	hence	hence	ADV
ejpam-5394	161	25	,	,	PUNCT
ejpam-5394	161	26	x	x	PUNCT
ejpam-5394	161	27	∈	∈	NOUN
ejpam-5394	161	28	rh(a	rh(a	NOUN
ejpam-5394	161	29	)	)	PUNCT
ejpam-5394	162	1	if	if	SCONJ
ejpam-5394	162	2	and	and	CCONJ
ejpam-5394	162	3	only	only	ADV
ejpam-5394	162	4	if	if	SCONJ
ejpam-5394	162	5	x	x	PUNCT
ejpam-5394	162	6	∈	∈	PROPN
ejpam-5394	163	1	[	[	X
ejpam-5394	163	2	sup	sup	NOUN
ejpam-5394	163	3	a	a	PRON
ejpam-5394	163	4	,	,	PUNCT
ejpam-5394	163	5	1	1	X
ejpam-5394	163	6	]	]	PUNCT
ejpam-5394	163	7	∩	∩	PROPN
ejpam-5394	163	8	h.	h.	PROPN
ejpam-5394	164	1	this	this	PRON
ejpam-5394	164	2	shows	show	VERB
ejpam-5394	164	3	that	that	PRON
ejpam-5394	164	4	rh(a	rh(a	NOUN
ejpam-5394	164	5	)	)	PUNCT
ejpam-5394	164	6	=	=	NOUN
ejpam-5394	165	1	[	[	X
ejpam-5394	165	2	sup	sup	NOUN
ejpam-5394	165	3	a	a	PRON
ejpam-5394	165	4	,	,	PUNCT
ejpam-5394	165	5	1	1	X
ejpam-5394	165	6	]	]	PUNCT
ejpam-5394	165	7	∩	∩	ADJ
ejpam-5394	165	8	h.	h.	NOUN
ejpam-5394	165	9	if	if	SCONJ
ejpam-5394	165	10	a	a	DET
ejpam-5394	165	11	=	=	NOUN
ejpam-5394	165	12	∅	∅	NOUN
ejpam-5394	165	13	,	,	PUNCT
ejpam-5394	165	14	then	then	ADV
ejpam-5394	165	15	sup	sup	VERB
ejpam-5394	165	16	a	a	DET
ejpam-5394	165	17	=	=	X
ejpam-5394	165	18	−∞	−∞	NOUN
ejpam-5394	165	19	and	and	CCONJ
ejpam-5394	165	20	so	so	ADV
ejpam-5394	165	21	rh(a	rh(a	NUM
ejpam-5394	165	22	)	)	PUNCT
ejpam-5394	166	1	=	=	SYM
ejpam-5394	166	2	h.	h.	PROPN
ejpam-5394	166	3	otherwise	otherwise	ADV
ejpam-5394	166	4	,	,	PUNCT
ejpam-5394	166	5	sup	sup	VERB
ejpam-5394	166	6	a	a	DET
ejpam-5394	166	7	∈	∈	NOUN
ejpam-5394	166	8	h	h	NOUN
ejpam-5394	166	9	implying	imply	VERB
ejpam-5394	166	10	that	that	DET
ejpam-5394	166	11	rh(a	rh(a	NOUN
ejpam-5394	166	12	)	)	PUNCT
ejpam-5394	166	13	=	=	NOUN
ejpam-5394	167	1	[	[	X
ejpam-5394	167	2	sup	sup	NOUN
ejpam-5394	167	3	a	a	PRON
ejpam-5394	167	4	,	,	PUNCT
ejpam-5394	167	5	1	1	NUM
ejpam-5394	167	6	]	]	PUNCT
ejpam-5394	167	7	.	.	PUNCT
ejpam-5394	168	1	■	■	PUNCT
ejpam-5394	168	2	example	example	NOUN
ejpam-5394	168	3	2	2	X
ejpam-5394	168	4	.	.	X
ejpam-5394	168	5	consider	consider	VERB
ejpam-5394	168	6	a	a	DET
ejpam-5394	168	7	=	=	X
ejpam-5394	168	8	(	(	PUNCT
ejpam-5394	168	9	18	18	NUM
ejpam-5394	168	10	,	,	PUNCT
ejpam-5394	168	11	1	1	NUM
ejpam-5394	168	12	2	2	NUM
ejpam-5394	168	13	)	)	PUNCT
ejpam-5394	168	14	.	.	PUNCT
ejpam-5394	169	1	then	then	ADV
ejpam-5394	169	2	the	the	DET
ejpam-5394	169	3	sup	sup	NOUN
ejpam-5394	169	4	a	a	DET
ejpam-5394	169	5	=	=	NOUN
ejpam-5394	169	6	1	1	NUM
ejpam-5394	169	7	2	2	NUM
ejpam-5394	169	8	.	.	PUNCT
ejpam-5394	170	1	thus	thus	ADV
ejpam-5394	170	2	,	,	PUNCT
ejpam-5394	170	3	rh(a	rh(a	PUNCT
ejpam-5394	170	4	)	)	PUNCT
ejpam-5394	170	5	=	=	PUNCT
ejpam-5394	171	1	[	[	X
ejpam-5394	171	2	12	12	NUM
ejpam-5394	171	3	,	,	PUNCT
ejpam-5394	171	4	1	1	NUM
ejpam-5394	171	5	]	]	PUNCT
ejpam-5394	171	6	.	.	PUNCT
ejpam-5394	172	1	the	the	DET
ejpam-5394	172	2	next	next	ADJ
ejpam-5394	172	3	result	result	NOUN
ejpam-5394	172	4	follows	follow	VERB
ejpam-5394	172	5	from	from	ADP
ejpam-5394	172	6	theorem	theorem	ADJ
ejpam-5394	172	7	6	6	NUM
ejpam-5394	172	8	.	.	PUNCT
ejpam-5394	172	9	corollary	corollary	ADJ
ejpam-5394	172	10	1	1	NUM
ejpam-5394	172	11	.	.	PUNCT
ejpam-5394	173	1	let	let	VERB
ejpam-5394	173	2	a	a	DET
ejpam-5394	173	3	∈	∈	NOUN
ejpam-5394	174	1	[	[	X
ejpam-5394	174	2	0	0	NUM
ejpam-5394	174	3	,	,	PUNCT
ejpam-5394	174	4	1	1	NUM
ejpam-5394	174	5	]	]	PUNCT
ejpam-5394	174	6	.	.	PUNCT
ejpam-5394	175	1	then	then	ADV
ejpam-5394	175	2	r[0,1](a	r[0,1](a	PROPN
ejpam-5394	175	3	)	)	PUNCT
ejpam-5394	175	4	=	=	PUNCT
ejpam-5394	176	1	[	[	X
ejpam-5394	176	2	a	a	X
ejpam-5394	176	3	,	,	PUNCT
ejpam-5394	176	4	1	1	NUM
ejpam-5394	176	5	]	]	PUNCT
ejpam-5394	176	6	.	.	PUNCT
ejpam-5394	177	1	proposition	proposition	NOUN
ejpam-5394	177	2	3	3	NUM
ejpam-5394	177	3	.	.	PUNCT
ejpam-5394	178	1	(	(	PUNCT
ejpam-5394	178	2	h	h	NOUN
ejpam-5394	178	3	,	,	PUNCT
ejpam-5394	178	4	∗	∗	NOUN
ejpam-5394	178	5	,	,	PUNCT
ejpam-5394	178	6	0	0	NUM
ejpam-5394	178	7	)	)	PUNCT
ejpam-5394	178	8	is	be	AUX
ejpam-5394	178	9	not	not	PART
ejpam-5394	178	10	hyperatomic	hyperatomic	ADJ
ejpam-5394	178	11	.	.	PUNCT
ejpam-5394	179	1	in	in	ADP
ejpam-5394	179	2	particular	particular	ADJ
ejpam-5394	179	3	,	,	PUNCT
ejpam-5394	179	4	a(h	a(h	PROPN
ejpam-5394	179	5	)	)	PUNCT
ejpam-5394	179	6	=	=	SYM
ejpam-5394	179	7	0	0	X
ejpam-5394	179	8	.	.	PUNCT
ejpam-5394	180	1	proof	proof	NOUN
ejpam-5394	180	2	.	.	PUNCT
ejpam-5394	181	1	clearly	clearly	ADV
ejpam-5394	181	2	,	,	PUNCT
ejpam-5394	181	3	0	0	NUM
ejpam-5394	181	4	∈	∈	PROPN
ejpam-5394	181	5	h.	h.	NOUN
ejpam-5394	181	6	let	let	VERB
ejpam-5394	181	7	a	a	DET
ejpam-5394	181	8	∈	∈	PROPN
ejpam-5394	181	9	h	h	NOUN
ejpam-5394	181	10	\{0	\{0	NOUN
ejpam-5394	181	11	}	}	PUNCT
ejpam-5394	181	12	,	,	PUNCT
ejpam-5394	181	13	i.e.	i.e.	X
ejpam-5394	181	14	,	,	PUNCT
ejpam-5394	181	15	a	a	DET
ejpam-5394	181	16	∈	∈	PROPN
ejpam-5394	181	17	(	(	PUNCT
ejpam-5394	181	18	0	0	NUM
ejpam-5394	181	19	,	,	PUNCT
ejpam-5394	181	20	1	1	NUM
ejpam-5394	181	21	]	]	PUNCT
ejpam-5394	181	22	.	.	PUNCT
ejpam-5394	182	1	since	since	SCONJ
ejpam-5394	182	2	a	a	DET
ejpam-5394	182	3	2	2	NUM
ejpam-5394	182	4	<	<	X
ejpam-5394	182	5	a	a	NOUN
ejpam-5394	182	6	,	,	PUNCT
ejpam-5394	182	7	a	a	DET
ejpam-5394	182	8	2	2	NUM
ejpam-5394	182	9	∗a	∗a	NOUN
ejpam-5394	182	10	=	=	SYM
ejpam-5394	182	11	{	{	PUNCT
ejpam-5394	182	12	0	0	NUM
ejpam-5394	182	13	}	}	PUNCT
ejpam-5394	182	14	.	.	PUNCT
ejpam-5394	183	1	here	here	ADV
ejpam-5394	183	2	,	,	PUNCT
ejpam-5394	183	3	we	we	PRON
ejpam-5394	183	4	find	find	VERB
ejpam-5394	183	5	that	that	SCONJ
ejpam-5394	183	6	0	0	NUM
ejpam-5394	183	7	∈	∈	PROPN
ejpam-5394	183	8	a	a	DET
ejpam-5394	183	9	2	2	NUM
ejpam-5394	183	10	but	but	CCONJ
ejpam-5394	183	11	a	a	DET
ejpam-5394	183	12	2	2	NUM
ejpam-5394	183	13	/∈	/∈	PUNCT
ejpam-5394	183	14	{	{	PUNCT
ejpam-5394	183	15	0	0	NUM
ejpam-5394	183	16	,	,	PUNCT
ejpam-5394	183	17	a	a	PRON
ejpam-5394	183	18	}	}	PUNCT
ejpam-5394	183	19	.	.	PUNCT
ejpam-5394	184	1	thus	thus	ADV
ejpam-5394	184	2	a	a	DET
ejpam-5394	184	3	/∈	/∈	PUNCT
ejpam-5394	184	4	a(h	a(h	PROPN
ejpam-5394	184	5	)	)	PUNCT
ejpam-5394	184	6	,	,	PUNCT
ejpam-5394	184	7	showing	show	VERB
ejpam-5394	184	8	that	that	SCONJ
ejpam-5394	184	9	a(h	a(h	PROPN
ejpam-5394	184	10	)	)	PUNCT
ejpam-5394	184	11	=	=	PRON
ejpam-5394	184	12	{	{	PUNCT
ejpam-5394	184	13	0	0	NUM
ejpam-5394	184	14	}	}	PUNCT
ejpam-5394	184	15	.	.	PUNCT
ejpam-5394	185	1	therefore	therefore	ADV
ejpam-5394	185	2	,	,	PUNCT
ejpam-5394	185	3	(	(	PUNCT
ejpam-5394	185	4	h	h	NOUN
ejpam-5394	185	5	,	,	PUNCT
ejpam-5394	185	6	∗	∗	NOUN
ejpam-5394	185	7	,	,	PUNCT
ejpam-5394	185	8	0	0	NUM
ejpam-5394	185	9	)	)	PUNCT
ejpam-5394	185	10	is	be	AUX
ejpam-5394	185	11	not	not	PART
ejpam-5394	185	12	hyperatomic	hyperatomic	ADJ
ejpam-5394	185	13	.	.	PUNCT
ejpam-5394	186	1	■	■	PUNCT
ejpam-5394	186	2	e.	e.	PROPN
ejpam-5394	186	3	payla	payla	PROPN
ejpam-5394	186	4	,	,	PUNCT
ejpam-5394	186	5	l.	l.	PROPN
ejpam-5394	186	6	ranara	ranara	PROPN
ejpam-5394	186	7	/	/	SYM
ejpam-5394	186	8	eur	eur	PROPN
ejpam-5394	186	9	.	.	PUNCT
ejpam-5394	187	1	j.	j.	PROPN
ejpam-5394	187	2	pure	pure	PROPN
ejpam-5394	187	3	appl	appl	PROPN
ejpam-5394	187	4	.	.	PROPN
ejpam-5394	187	5	math	math	PROPN
ejpam-5394	187	6	,	,	PUNCT
ejpam-5394	187	7	18	18	NUM
ejpam-5394	187	8	(	(	PUNCT
ejpam-5394	187	9	2	2	NUM
ejpam-5394	187	10	)	)	PUNCT
ejpam-5394	187	11	(	(	PUNCT
ejpam-5394	187	12	2025	2025	NUM
ejpam-5394	187	13	)	)	PUNCT
ejpam-5394	187	14	,	,	PUNCT
ejpam-5394	187	15	5394	5394	NUM
ejpam-5394	187	16	7	7	NUM
ejpam-5394	187	17	of	of	ADP
ejpam-5394	187	18	10	10	NUM
ejpam-5394	187	19	corollary	corollary	ADJ
ejpam-5394	187	20	2	2	NUM
ejpam-5394	187	21	.	.	PUNCT
ejpam-5394	187	22	br([0	br([0	NOUN
ejpam-5394	187	23	,	,	PUNCT
ejpam-5394	187	24	1	1	NUM
ejpam-5394	187	25	]	]	PUNCT
ejpam-5394	187	26	)	)	PUNCT
ejpam-5394	187	27	=	=	SYM
ejpam-5394	188	1	{	{	PUNCT
ejpam-5394	188	2	[	[	X
ejpam-5394	188	3	r	r	X
ejpam-5394	188	4	,	,	PUNCT
ejpam-5394	188	5	1	1	NUM
ejpam-5394	188	6	]	]	PUNCT
ejpam-5394	188	7	:	:	PUNCT
ejpam-5394	188	8	r	r	X
ejpam-5394	188	9	∈	∈	PROPN
ejpam-5394	189	1	[	[	X
ejpam-5394	189	2	0	0	NUM
ejpam-5394	189	3	,	,	PUNCT
ejpam-5394	189	4	1	1	NUM
ejpam-5394	189	5	]	]	PUNCT
ejpam-5394	189	6	}	}	PUNCT
ejpam-5394	189	7	.	.	PUNCT
ejpam-5394	190	1	let	let	AUX
ejpam-5394	190	2	τr(h	τr(h	VERB
ejpam-5394	190	3	)	)	PUNCT
ejpam-5394	190	4	be	be	VERB
ejpam-5394	190	5	the	the	DET
ejpam-5394	190	6	topology	topology	NOUN
ejpam-5394	190	7	generated	generate	VERB
ejpam-5394	190	8	by	by	ADP
ejpam-5394	190	9	br(h	br(h	NOUN
ejpam-5394	190	10	)	)	PUNCT
ejpam-5394	190	11	.	.	PUNCT
ejpam-5394	191	1	that	that	PRON
ejpam-5394	191	2	is	be	AUX
ejpam-5394	191	3	,	,	PUNCT
ejpam-5394	191	4	for	for	ADP
ejpam-5394	191	5	each	each	DET
ejpam-5394	191	6	g	g	PROPN
ejpam-5394	191	7	∈	∈	PROPN
ejpam-5394	191	8	τr(h	τr(h	PUNCT
ejpam-5394	191	9	)	)	PUNCT
ejpam-5394	191	10	,	,	PUNCT
ejpam-5394	191	11	g	g	PROPN
ejpam-5394	191	12	=	=	NOUN
ejpam-5394	191	13	⋃	⋃	PROPN
ejpam-5394	191	14	bi	bi	NOUN
ejpam-5394	191	15	,	,	PUNCT
ejpam-5394	192	1	i	i	PROPN
ejpam-5394	192	2	∈	∈	VERB
ejpam-5394	192	3	k	k	PROPN
ejpam-5394	192	4	⊆	⊆	NUM
ejpam-5394	192	5	br(h	br(h	NUM
ejpam-5394	192	6	)	)	PUNCT
ejpam-5394	192	7	.	.	PUNCT
ejpam-5394	193	1	note	note	VERB
ejpam-5394	193	2	that	that	SCONJ
ejpam-5394	193	3	for	for	ADP
ejpam-5394	193	4	any	any	DET
ejpam-5394	193	5	a	a	DET
ejpam-5394	193	6	∈	∈	NOUN
ejpam-5394	194	1	[	[	X
ejpam-5394	194	2	0	0	NUM
ejpam-5394	194	3	,	,	PUNCT
ejpam-5394	194	4	1	1	NUM
ejpam-5394	194	5	]	]	PUNCT
ejpam-5394	194	6	,	,	PUNCT
ejpam-5394	194	7	the	the	DET
ejpam-5394	194	8	set	set	NOUN
ejpam-5394	194	9	(	(	PUNCT
ejpam-5394	194	10	a	a	PRON
ejpam-5394	194	11	,	,	PUNCT
ejpam-5394	194	12	1	1	NUM
ejpam-5394	194	13	]	]	PUNCT
ejpam-5394	194	14	is	be	AUX
ejpam-5394	194	15	open	open	ADJ
ejpam-5394	194	16	for	for	ADP
ejpam-5394	194	17	(	(	PUNCT
ejpam-5394	194	18	a	a	DET
ejpam-5394	194	19	,	,	PUNCT
ejpam-5394	194	20	1	1	X
ejpam-5394	194	21	]	]	PUNCT
ejpam-5394	194	22	=	=	SYM
ejpam-5394	194	23	∞⋃	∞⋃	NOUN
ejpam-5394	194	24	n=1	n=1	PROPN
ejpam-5394	194	25	[	[	PUNCT
ejpam-5394	194	26	a+	a+	PUNCT
ejpam-5394	194	27	1	1	NUM
ejpam-5394	194	28	n	n	NOUN
ejpam-5394	194	29	,	,	PUNCT
ejpam-5394	194	30	1	1	NUM
ejpam-5394	194	31	]	]	PUNCT
ejpam-5394	194	32	.	.	PUNCT
ejpam-5394	195	1	example	example	NOUN
ejpam-5394	196	1	3	3	NUM
ejpam-5394	196	2	.	.	PUNCT
ejpam-5394	197	1	the	the	DET
ejpam-5394	197	2	following	follow	VERB
ejpam-5394	197	3	are	be	AUX
ejpam-5394	197	4	open	open	ADJ
ejpam-5394	197	5	set	set	VERB
ejpam-5394	197	6	in	in	ADP
ejpam-5394	197	7	[	[	X
ejpam-5394	197	8	0	0	NUM
ejpam-5394	197	9	,	,	PUNCT
ejpam-5394	197	10	1	1	NUM
ejpam-5394	197	11	]	]	NUM
ejpam-5394	197	12	:	:	PUNCT
ejpam-5394	197	13	•	•	NUM
ejpam-5394	197	14	sets	set	NOUN
ejpam-5394	197	15	of	of	ADP
ejpam-5394	197	16	the	the	DET
ejpam-5394	197	17	form	form	NOUN
ejpam-5394	197	18	(	(	PUNCT
ejpam-5394	197	19	r	r	NOUN
ejpam-5394	197	20	,	,	PUNCT
ejpam-5394	197	21	1	1	NUM
ejpam-5394	197	22	]	]	PUNCT
ejpam-5394	197	23	for	for	ADP
ejpam-5394	197	24	(	(	PUNCT
ejpam-5394	197	25	r	r	NOUN
ejpam-5394	197	26	,	,	PUNCT
ejpam-5394	197	27	1	1	NUM
ejpam-5394	197	28	]	]	PUNCT
ejpam-5394	197	29	=	=	SYM
ejpam-5394	197	30	∞⋃	∞⋃	NOUN
ejpam-5394	197	31	n=1	n=1	PROPN
ejpam-5394	198	1	[	[	PUNCT
ejpam-5394	198	2	r	r	NOUN
ejpam-5394	198	3	+	+	NOUN
ejpam-5394	198	4	1	1	NUM
ejpam-5394	198	5	n	n	NOUN
ejpam-5394	198	6	,	,	PUNCT
ejpam-5394	198	7	1	1	NUM
ejpam-5394	198	8	]	]	PUNCT
ejpam-5394	198	9	•	•	NUM
ejpam-5394	198	10	{	{	PUNCT
ejpam-5394	198	11	1	1	NUM
ejpam-5394	198	12	}	}	PUNCT
ejpam-5394	198	13	is	be	AUX
ejpam-5394	198	14	open	open	ADJ
ejpam-5394	198	15	for	for	ADP
ejpam-5394	198	16	{	{	PUNCT
ejpam-5394	198	17	1	1	NUM
ejpam-5394	198	18	}	}	PUNCT
ejpam-5394	198	19	=	=	PUNCT
ejpam-5394	199	1	[	[	X
ejpam-5394	199	2	1	1	NUM
ejpam-5394	199	3	,	,	PUNCT
ejpam-5394	199	4	1	1	NUM
ejpam-5394	199	5	]	]	PUNCT
ejpam-5394	199	6	example	example	NOUN
ejpam-5394	199	7	4	4	NUM
ejpam-5394	199	8	.	.	PUNCT
ejpam-5394	200	1	the	the	DET
ejpam-5394	200	2	following	follow	VERB
ejpam-5394	200	3	are	be	AUX
ejpam-5394	200	4	closed	close	VERB
ejpam-5394	200	5	sets	set	NOUN
ejpam-5394	200	6	in	in	ADP
ejpam-5394	200	7	[	[	X
ejpam-5394	200	8	0	0	NUM
ejpam-5394	200	9	,	,	PUNCT
ejpam-5394	200	10	1	1	NUM
ejpam-5394	200	11	]	]	PUNCT
ejpam-5394	200	12	:	:	PUNCT
ejpam-5394	200	13	•	•	PRON
ejpam-5394	200	14	[	[	X
ejpam-5394	200	15	0	0	NUM
ejpam-5394	200	16	,	,	PUNCT
ejpam-5394	200	17	r	r	NOUN
ejpam-5394	200	18	)	)	PUNCT
ejpam-5394	200	19	for	for	ADP
ejpam-5394	200	20	[	[	X
ejpam-5394	200	21	0	0	NUM
ejpam-5394	200	22	,	,	PUNCT
ejpam-5394	200	23	r	r	NOUN
ejpam-5394	200	24	)	)	PUNCT
ejpam-5394	200	25	=	=	NOUN
ejpam-5394	201	1	[	[	X
ejpam-5394	201	2	r	r	X
ejpam-5394	201	3	,	,	PUNCT
ejpam-5394	201	4	1]c	1]c	NUM
ejpam-5394	201	5	•	•	NOUN
ejpam-5394	202	1	[	[	X
ejpam-5394	202	2	0	0	NUM
ejpam-5394	202	3	,	,	PUNCT
ejpam-5394	202	4	r	r	NOUN
ejpam-5394	202	5	]	]	PUNCT
ejpam-5394	202	6	for	for	ADP
ejpam-5394	202	7	[	[	X
ejpam-5394	202	8	0	0	NUM
ejpam-5394	202	9	,	,	PUNCT
ejpam-5394	202	10	r	r	NOUN
ejpam-5394	202	11	]	]	X
ejpam-5394	202	12	=	=	SYM
ejpam-5394	202	13	(	(	PUNCT
ejpam-5394	202	14	r	r	NOUN
ejpam-5394	202	15	,	,	PUNCT
ejpam-5394	202	16	1]c	1]c	NUM
ejpam-5394	202	17	,	,	PUNCT
ejpam-5394	202	18	r	r	NOUN
ejpam-5394	202	19	∈	∈	PROPN
ejpam-5394	203	1	[	[	X
ejpam-5394	203	2	0	0	NUM
ejpam-5394	203	3	,	,	PUNCT
ejpam-5394	203	4	1	1	NUM
ejpam-5394	203	5	]	]	PUNCT
ejpam-5394	203	6	thus	thus	ADV
ejpam-5394	203	7	,	,	PUNCT
ejpam-5394	203	8	the	the	DET
ejpam-5394	203	9	next	next	ADJ
ejpam-5394	203	10	theorem	theorem	NOUN
ejpam-5394	203	11	follows	follow	VERB
ejpam-5394	203	12	:	:	PUNCT
ejpam-5394	203	13	theorem	theorem	NOUN
ejpam-5394	203	14	7	7	NUM
ejpam-5394	203	15	.	.	PUNCT
ejpam-5394	203	16	in	in	ADP
ejpam-5394	203	17	a	a	DET
ejpam-5394	203	18	hyper	hyper	ADJ
ejpam-5394	203	19	bck	bck	NOUN
ejpam-5394	203	20	-	-	PUNCT
ejpam-5394	203	21	algebra	algebra	NOUN
ejpam-5394	203	22	[	[	X
ejpam-5394	203	23	0	0	NUM
ejpam-5394	203	24	,	,	PUNCT
ejpam-5394	203	25	1	1	NUM
ejpam-5394	203	26	]	]	PUNCT
ejpam-5394	203	27	,	,	PUNCT
ejpam-5394	203	28	τr	τr	PUNCT
ejpam-5394	203	29	(	(	PUNCT
ejpam-5394	203	30	[	[	X
ejpam-5394	203	31	0	0	NUM
ejpam-5394	203	32	,	,	PUNCT
ejpam-5394	203	33	1	1	NUM
ejpam-5394	203	34	]	]	PUNCT
ejpam-5394	203	35	)	)	PUNCT
ejpam-5394	204	1	=	=	SYM
ejpam-5394	204	2	{	{	PUNCT
ejpam-5394	204	3	∅	∅	NOUN
ejpam-5394	204	4	,	,	PUNCT
ejpam-5394	204	5	[	[	X
ejpam-5394	204	6	0	0	NUM
ejpam-5394	204	7	,	,	PUNCT
ejpam-5394	204	8	1	1	NUM
ejpam-5394	204	9	]	]	PUNCT
ejpam-5394	204	10	,	,	PUNCT
ejpam-5394	204	11	(	(	PUNCT
ejpam-5394	204	12	r	r	NOUN
ejpam-5394	204	13	,	,	PUNCT
ejpam-5394	204	14	1	1	NUM
ejpam-5394	204	15	]	]	PUNCT
ejpam-5394	204	16	,	,	PUNCT
ejpam-5394	204	17	[	[	X
ejpam-5394	204	18	r	r	X
ejpam-5394	204	19	,	,	PUNCT
ejpam-5394	204	20	1	1	NUM
ejpam-5394	204	21	]	]	PUNCT
ejpam-5394	204	22	:	:	PUNCT
ejpam-5394	204	23	r	r	X
ejpam-5394	204	24	∈	∈	PROPN
ejpam-5394	205	1	[	[	X
ejpam-5394	205	2	0	0	NUM
ejpam-5394	205	3	,	,	PUNCT
ejpam-5394	205	4	1	1	NUM
ejpam-5394	205	5	]	]	PUNCT
ejpam-5394	205	6	}	}	PUNCT
ejpam-5394	205	7	.	.	PUNCT
ejpam-5394	206	1	proof	proof	NOUN
ejpam-5394	206	2	.	.	PUNCT
ejpam-5394	207	1	let	let	VERB
ejpam-5394	207	2	g	g	PROPN
ejpam-5394	207	3	∈	∈	PROPN
ejpam-5394	207	4	τr	τr	PUNCT
ejpam-5394	207	5	(	(	PUNCT
ejpam-5394	207	6	[	[	X
ejpam-5394	207	7	0	0	NUM
ejpam-5394	207	8	,	,	PUNCT
ejpam-5394	207	9	1	1	NUM
ejpam-5394	207	10	]	]	NUM
ejpam-5394	207	11	)	)	PUNCT
ejpam-5394	207	12	,	,	PUNCT
ejpam-5394	207	13	and	and	CCONJ
ejpam-5394	207	14	g	g	PROPN
ejpam-5394	207	15	̸=	̸=	PROPN
ejpam-5394	207	16	∅.	∅.	VERB
ejpam-5394	207	17	then	then	ADV
ejpam-5394	207	18	g	g	PROPN
ejpam-5394	207	19	=	=	SYM
ejpam-5394	207	20	⋃	⋃	PROPN
ejpam-5394	207	21	i∈k⊆br([0,1	i∈k⊆br([0,1	NOUN
ejpam-5394	207	22	]	]	PUNCT
ejpam-5394	207	23	)	)	PUNCT
ejpam-5394	207	24	bi	bi	NOUN
ejpam-5394	207	25	.	.	PUNCT
ejpam-5394	208	1	thus	thus	ADV
ejpam-5394	208	2	,	,	PUNCT
ejpam-5394	208	3	bi	bi	NOUN
ejpam-5394	208	4	are	be	AUX
ejpam-5394	208	5	of	of	ADP
ejpam-5394	208	6	the	the	DET
ejpam-5394	208	7	form	form	NOUN
ejpam-5394	208	8	[	[	X
ejpam-5394	208	9	ri	ri	NOUN
ejpam-5394	208	10	,	,	PUNCT
ejpam-5394	208	11	1	1	NUM
ejpam-5394	208	12	]	]	PUNCT
ejpam-5394	208	13	,	,	PUNCT
ejpam-5394	208	14	g	g	NOUN
ejpam-5394	208	15	=	=	PUNCT
ejpam-5394	208	16	⋃	⋃	PROPN
ejpam-5394	208	17	[	[	X
ejpam-5394	208	18	ri	ri	NOUN
ejpam-5394	208	19	,	,	PUNCT
ejpam-5394	208	20	1	1	NUM
ejpam-5394	208	21	]	]	PUNCT
ejpam-5394	208	22	=	=	PUNCT
ejpam-5394	209	1	[	[	X
ejpam-5394	209	2	r	r	X
ejpam-5394	209	3	,	,	PUNCT
ejpam-5394	209	4	1	1	NUM
ejpam-5394	209	5	]	]	PUNCT
ejpam-5394	209	6	,	,	PUNCT
ejpam-5394	209	7	r0	r0	NOUN
ejpam-5394	209	8	=	=	SYM
ejpam-5394	209	9	inf{ri	inf{ri	NOUN
ejpam-5394	209	10	}	}	PUNCT
ejpam-5394	209	11	and	and	CCONJ
ejpam-5394	209	12	(	(	PUNCT
ejpam-5394	209	13	r	r	NOUN
ejpam-5394	209	14	,	,	PUNCT
ejpam-5394	209	15	1	1	NUM
ejpam-5394	209	16	]	]	PUNCT
ejpam-5394	209	17	=	=	SYM
ejpam-5394	209	18	∞⋃	∞⋃	NOUN
ejpam-5394	209	19	n=1	n=1	PROPN
ejpam-5394	209	20	[	[	PUNCT
ejpam-5394	209	21	r	r	NOUN
ejpam-5394	209	22	+	+	NOUN
ejpam-5394	209	23	1	1	NUM
ejpam-5394	209	24	n	n	NOUN
ejpam-5394	209	25	,	,	PUNCT
ejpam-5394	209	26	1	1	NUM
ejpam-5394	209	27	]	]	PUNCT
ejpam-5394	209	28	.	.	PUNCT
ejpam-5394	210	1	thus	thus	ADV
ejpam-5394	210	2	,	,	PUNCT
ejpam-5394	210	3	τr	τr	PUNCT
ejpam-5394	210	4	(	(	PUNCT
ejpam-5394	210	5	[	[	X
ejpam-5394	210	6	0	0	NUM
ejpam-5394	210	7	,	,	PUNCT
ejpam-5394	210	8	1	1	NUM
ejpam-5394	210	9	]	]	PUNCT
ejpam-5394	210	10	)	)	PUNCT
ejpam-5394	211	1	=	=	SYM
ejpam-5394	211	2	{	{	PUNCT
ejpam-5394	211	3	∅	∅	NOUN
ejpam-5394	211	4	,	,	PUNCT
ejpam-5394	211	5	[	[	X
ejpam-5394	211	6	0	0	NUM
ejpam-5394	211	7	,	,	PUNCT
ejpam-5394	211	8	1	1	NUM
ejpam-5394	211	9	]	]	PUNCT
ejpam-5394	211	10	,	,	PUNCT
ejpam-5394	211	11	(	(	PUNCT
ejpam-5394	211	12	r	r	NOUN
ejpam-5394	211	13	,	,	PUNCT
ejpam-5394	211	14	1	1	NUM
ejpam-5394	211	15	]	]	PUNCT
ejpam-5394	211	16	,	,	PUNCT
ejpam-5394	211	17	[	[	X
ejpam-5394	211	18	r	r	X
ejpam-5394	211	19	,	,	PUNCT
ejpam-5394	211	20	1	1	NUM
ejpam-5394	211	21	]	]	PUNCT
ejpam-5394	211	22	:	:	PUNCT
ejpam-5394	211	23	r	r	X
ejpam-5394	211	24	∈	∈	PROPN
ejpam-5394	212	1	[	[	X
ejpam-5394	212	2	0	0	NUM
ejpam-5394	212	3	,	,	PUNCT
ejpam-5394	212	4	1	1	NUM
ejpam-5394	212	5	]	]	PUNCT
ejpam-5394	212	6	}	}	PUNCT
ejpam-5394	212	7	.	.	PUNCT
ejpam-5394	213	1	■	■	PUNCT
ejpam-5394	213	2	theorem	theorem	ADJ
ejpam-5394	213	3	8	8	NUM
ejpam-5394	213	4	.	.	PUNCT
ejpam-5394	214	1	[	[	X
ejpam-5394	214	2	0	0	NUM
ejpam-5394	214	3	,	,	PUNCT
ejpam-5394	214	4	1	1	NUM
ejpam-5394	214	5	]	]	PUNCT
ejpam-5394	214	6	with	with	ADP
ejpam-5394	214	7	topology	topology	NOUN
ejpam-5394	214	8	τr([0	τr([0	NOUN
ejpam-5394	214	9	,	,	PUNCT
ejpam-5394	214	10	1	1	NUM
ejpam-5394	214	11	]	]	PUNCT
ejpam-5394	214	12	)	)	PUNCT
ejpam-5394	214	13	is	be	AUX
ejpam-5394	214	14	connected	connect	VERB
ejpam-5394	214	15	.	.	PUNCT
ejpam-5394	215	1	proof	proof	NOUN
ejpam-5394	215	2	.	.	PUNCT
ejpam-5394	216	1	suppose	suppose	VERB
ejpam-5394	216	2	[	[	X
ejpam-5394	216	3	0	0	NUM
ejpam-5394	216	4	,	,	PUNCT
ejpam-5394	216	5	1	1	NUM
ejpam-5394	216	6	]	]	PUNCT
ejpam-5394	216	7	is	be	AUX
ejpam-5394	216	8	disconnected	disconnect	VERB
ejpam-5394	216	9	.	.	PUNCT
ejpam-5394	217	1	then	then	ADV
ejpam-5394	217	2	,	,	PUNCT
ejpam-5394	217	3	there	there	PRON
ejpam-5394	217	4	exist	exist	VERB
ejpam-5394	217	5	disjoint	disjoint	ADJ
ejpam-5394	217	6	open	open	ADJ
ejpam-5394	217	7	sets	set	NOUN
ejpam-5394	217	8	a	a	DET
ejpam-5394	217	9	,	,	PUNCT
ejpam-5394	217	10	b	b	NOUN
ejpam-5394	217	11	such	such	ADJ
ejpam-5394	217	12	that	that	SCONJ
ejpam-5394	218	1	[	[	X
ejpam-5394	218	2	0	0	NUM
ejpam-5394	218	3	,	,	PUNCT
ejpam-5394	218	4	1	1	NUM
ejpam-5394	218	5	]	]	PUNCT
ejpam-5394	218	6	=	=	PUNCT
ejpam-5394	218	7	a	a	DET
ejpam-5394	218	8	∪	∪	X
ejpam-5394	218	9	b.	b.	NOUN
ejpam-5394	218	10	since	since	SCONJ
ejpam-5394	218	11	a	a	PRON
ejpam-5394	218	12	is	be	AUX
ejpam-5394	218	13	open	open	ADJ
ejpam-5394	218	14	,	,	PUNCT
ejpam-5394	218	15	a	a	PRON
ejpam-5394	218	16	=	=	X
ejpam-5394	219	1	[	[	X
ejpam-5394	219	2	r	r	X
ejpam-5394	219	3	,	,	PUNCT
ejpam-5394	219	4	1	1	NUM
ejpam-5394	219	5	]	]	PUNCT
ejpam-5394	219	6	or	or	CCONJ
ejpam-5394	219	7	(	(	PUNCT
ejpam-5394	219	8	r	r	NOUN
ejpam-5394	219	9	,	,	PUNCT
ejpam-5394	219	10	1	1	NUM
ejpam-5394	219	11	]	]	PUNCT
ejpam-5394	219	12	.	.	PUNCT
ejpam-5394	220	1	if	if	SCONJ
ejpam-5394	220	2	a	a	PRON
ejpam-5394	220	3	=	=	X
ejpam-5394	221	1	[	[	X
ejpam-5394	221	2	r	r	X
ejpam-5394	221	3	,	,	PUNCT
ejpam-5394	221	4	1	1	NUM
ejpam-5394	221	5	]	]	PUNCT
ejpam-5394	221	6	then	then	ADV
ejpam-5394	221	7	b	b	X
ejpam-5394	221	8	=	=	PUNCT
ejpam-5394	222	1	[	[	X
ejpam-5394	222	2	0	0	NUM
ejpam-5394	222	3	,	,	PUNCT
ejpam-5394	222	4	r	r	NOUN
ejpam-5394	222	5	)	)	PUNCT
ejpam-5394	222	6	.	.	PUNCT
ejpam-5394	223	1	if	if	SCONJ
ejpam-5394	223	2	a	a	PRON
ejpam-5394	223	3	=	=	X
ejpam-5394	223	4	(	(	PUNCT
ejpam-5394	223	5	r	r	NOUN
ejpam-5394	223	6	,	,	PUNCT
ejpam-5394	223	7	1	1	NUM
ejpam-5394	223	8	]	]	PUNCT
ejpam-5394	223	9	then	then	ADV
ejpam-5394	223	10	b	b	X
ejpam-5394	223	11	=	=	PUNCT
ejpam-5394	224	1	[	[	X
ejpam-5394	224	2	0	0	NUM
ejpam-5394	224	3	,	,	PUNCT
ejpam-5394	224	4	r	r	NOUN
ejpam-5394	224	5	]	]	PUNCT
ejpam-5394	224	6	.	.	PUNCT
ejpam-5394	225	1	whether	whether	SCONJ
ejpam-5394	225	2	b	b	X
ejpam-5394	225	3	=	=	PUNCT
ejpam-5394	226	1	[	[	X
ejpam-5394	226	2	0	0	NUM
ejpam-5394	226	3	,	,	PUNCT
ejpam-5394	226	4	r	r	NOUN
ejpam-5394	226	5	)	)	PUNCT
ejpam-5394	226	6	or	or	CCONJ
ejpam-5394	226	7	[	[	X
ejpam-5394	226	8	0	0	NUM
ejpam-5394	226	9	,	,	PUNCT
ejpam-5394	226	10	r	r	NOUN
ejpam-5394	226	11	]	]	X
ejpam-5394	226	12	,	,	PUNCT
ejpam-5394	226	13	b	b	PROPN
ejpam-5394	226	14	is	be	AUX
ejpam-5394	226	15	not	not	PART
ejpam-5394	226	16	open	open	ADJ
ejpam-5394	226	17	.	.	PUNCT
ejpam-5394	227	1	this	this	PRON
ejpam-5394	227	2	contradicts	contradict	VERB
ejpam-5394	227	3	the	the	DET
ejpam-5394	227	4	statement	statement	NOUN
ejpam-5394	227	5	that	that	SCONJ
ejpam-5394	227	6	a	a	PRON
ejpam-5394	227	7	and	and	CCONJ
ejpam-5394	227	8	b	b	NOUN
ejpam-5394	227	9	are	be	AUX
ejpam-5394	227	10	open	open	ADJ
ejpam-5394	227	11	sets	set	NOUN
ejpam-5394	227	12	.	.	PUNCT
ejpam-5394	228	1	therefore	therefore	ADV
ejpam-5394	228	2	,	,	PUNCT
ejpam-5394	228	3	by	by	ADP
ejpam-5394	228	4	definition	definition	NOUN
ejpam-5394	228	5	4	4	NUM
ejpam-5394	228	6	,	,	PUNCT
ejpam-5394	228	7	[	[	X
ejpam-5394	228	8	0	0	NUM
ejpam-5394	228	9	,	,	PUNCT
ejpam-5394	228	10	1	1	NUM
ejpam-5394	228	11	]	]	PUNCT
ejpam-5394	228	12	is	be	AUX
ejpam-5394	228	13	connected	connect	VERB
ejpam-5394	228	14	.	.	PUNCT
ejpam-5394	229	1	■	■	PUNCT
ejpam-5394	229	2	5	5	X
ejpam-5394	229	3	.	.	X
ejpam-5394	229	4	the	the	DET
ejpam-5394	229	5	topology	topology	NOUN
ejpam-5394	229	6	τl[0	τl[0	NOUN
ejpam-5394	229	7	,	,	PUNCT
ejpam-5394	229	8	1	1	NUM
ejpam-5394	229	9	]	]	PUNCT
ejpam-5394	229	10	example	example	NOUN
ejpam-5394	229	11	5	5	NUM
ejpam-5394	229	12	.	.	X
ejpam-5394	229	13	consider	consider	VERB
ejpam-5394	229	14	the	the	DET
ejpam-5394	229	15	hyper	hyper	ADJ
ejpam-5394	229	16	bck	bck	NOUN
ejpam-5394	229	17	-	-	PUNCT
ejpam-5394	229	18	algebra	algebra	NOUN
ejpam-5394	229	19	[	[	X
ejpam-5394	229	20	0	0	NUM
ejpam-5394	229	21	,	,	PUNCT
ejpam-5394	229	22	1	1	NUM
ejpam-5394	229	23	]	]	PUNCT
ejpam-5394	229	24	and	and	CCONJ
ejpam-5394	229	25	a	a	DET
ejpam-5394	229	26	=	=	X
ejpam-5394	229	27	{	{	PUNCT
ejpam-5394	229	28	1	1	NUM
ejpam-5394	229	29	2	2	NUM
ejpam-5394	229	30	,	,	PUNCT
ejpam-5394	229	31	1	1	NUM
ejpam-5394	229	32	3	3	NUM
ejpam-5394	229	33	}	}	PUNCT
ejpam-5394	229	34	.	.	PUNCT
ejpam-5394	230	1	lh(a	lh(a	NOUN
ejpam-5394	230	2	)	)	PUNCT
ejpam-5394	231	1	=	=	PRON
ejpam-5394	231	2	{	{	PUNCT
ejpam-5394	231	3	x	x	PUNCT
ejpam-5394	231	4	∈	∈	PROPN
ejpam-5394	232	1	[	[	X
ejpam-5394	232	2	0	0	NUM
ejpam-5394	232	3	,	,	PUNCT
ejpam-5394	232	4	1	1	NUM
ejpam-5394	232	5	]	]	PUNCT
ejpam-5394	232	6	:	:	PUNCT
ejpam-5394	232	7	0	0	NUM
ejpam-5394	232	8	∈	∈	NOUN
ejpam-5394	232	9	x	x	PUNCT
ejpam-5394	232	10	∗	∗	NOUN
ejpam-5394	232	11	a	a	NOUN
ejpam-5394	232	12	,	,	PUNCT
ejpam-5394	232	13	∀	∀	PUNCT
ejpam-5394	232	14	a	a	PRON
ejpam-5394	232	15	∈	∈	PROPN
ejpam-5394	232	16	a	a	DET
ejpam-5394	232	17	}	}	PUNCT
ejpam-5394	232	18	e.	e.	PROPN
ejpam-5394	232	19	payla	payla	PROPN
ejpam-5394	232	20	,	,	PUNCT
ejpam-5394	232	21	l.	l.	PROPN
ejpam-5394	232	22	ranara	ranara	PROPN
ejpam-5394	232	23	/	/	SYM
ejpam-5394	232	24	eur	eur	PROPN
ejpam-5394	232	25	.	.	PUNCT
ejpam-5394	233	1	j.	j.	PROPN
ejpam-5394	233	2	pure	pure	PROPN
ejpam-5394	233	3	appl	appl	PROPN
ejpam-5394	233	4	.	.	PROPN
ejpam-5394	233	5	math	math	PROPN
ejpam-5394	233	6	,	,	PUNCT
ejpam-5394	233	7	18	18	NUM
ejpam-5394	233	8	(	(	PUNCT
ejpam-5394	233	9	2	2	NUM
ejpam-5394	233	10	)	)	PUNCT
ejpam-5394	233	11	(	(	PUNCT
ejpam-5394	233	12	2025	2025	NUM
ejpam-5394	233	13	)	)	PUNCT
ejpam-5394	233	14	,	,	PUNCT
ejpam-5394	233	15	5394	5394	NUM
ejpam-5394	233	16	8	8	NUM
ejpam-5394	233	17	of	of	ADP
ejpam-5394	233	18	10	10	NUM
ejpam-5394	233	19	=	=	NOUN
ejpam-5394	233	20	{	{	PUNCT
ejpam-5394	233	21	x	x	PUNCT
ejpam-5394	233	22	∈	∈	PROPN
ejpam-5394	234	1	[	[	X
ejpam-5394	234	2	0	0	NUM
ejpam-5394	234	3	,	,	PUNCT
ejpam-5394	234	4	1	1	NUM
ejpam-5394	234	5	]	]	PUNCT
ejpam-5394	234	6	:	:	PUNCT
ejpam-5394	234	7	0	0	NUM
ejpam-5394	234	8	∈	∈	NOUN
ejpam-5394	234	9	x	x	PUNCT
ejpam-5394	234	10	∗	∗	NOUN
ejpam-5394	234	11	a	a	NOUN
ejpam-5394	234	12	,	,	PUNCT
ejpam-5394	234	13	∀	∀	PUNCT
ejpam-5394	234	14	a	a	DET
ejpam-5394	234	15	∈	∈	PROPN
ejpam-5394	234	16	{	{	PUNCT
ejpam-5394	234	17	1	1	NUM
ejpam-5394	234	18	2	2	NUM
ejpam-5394	234	19	,	,	PUNCT
ejpam-5394	234	20	1	1	NUM
ejpam-5394	234	21	3	3	NUM
ejpam-5394	234	22	}	}	PUNCT
ejpam-5394	234	23	}	}	PUNCT
ejpam-5394	234	24	=	=	SYM
ejpam-5394	234	25	{	{	PUNCT
ejpam-5394	234	26	x	x	PUNCT
ejpam-5394	234	27	∈	∈	PROPN
ejpam-5394	235	1	[	[	X
ejpam-5394	235	2	0	0	NUM
ejpam-5394	235	3	,	,	PUNCT
ejpam-5394	235	4	1	1	NUM
ejpam-5394	235	5	]	]	PUNCT
ejpam-5394	235	6	:	:	PUNCT
ejpam-5394	235	7	0	0	NUM
ejpam-5394	235	8	∈	∈	NOUN
ejpam-5394	235	9	x	x	SYM
ejpam-5394	235	10	∗	∗	NOUN
ejpam-5394	235	11	1	1	NUM
ejpam-5394	235	12	2	2	NUM
ejpam-5394	235	13	and	and	CCONJ
ejpam-5394	235	14	0	0	NUM
ejpam-5394	235	15	∈	∈	NOUN
ejpam-5394	235	16	x	x	SYM
ejpam-5394	235	17	∗	∗	NOUN
ejpam-5394	235	18	1	1	NUM
ejpam-5394	235	19	3	3	NUM
ejpam-5394	235	20	}	}	PUNCT
ejpam-5394	235	21	note	note	VERB
ejpam-5394	235	22	that	that	SCONJ
ejpam-5394	235	23	for	for	SCONJ
ejpam-5394	235	24	0	0	NUM
ejpam-5394	235	25	to	to	PART
ejpam-5394	235	26	be	be	AUX
ejpam-5394	235	27	in	in	ADP
ejpam-5394	235	28	x	x	PROPN
ejpam-5394	235	29	∗	∗	NOUN
ejpam-5394	235	30	1	1	NUM
ejpam-5394	235	31	2	2	NUM
ejpam-5394	235	32	,	,	PUNCT
ejpam-5394	235	33	x	x	PROPN
ejpam-5394	235	34	∗	∗	NOUN
ejpam-5394	235	35	1	1	NUM
ejpam-5394	235	36	2	2	NUM
ejpam-5394	235	37	=	=	SYM
ejpam-5394	235	38	{	{	PUNCT
ejpam-5394	235	39	0	0	NUM
ejpam-5394	235	40	}	}	PUNCT
ejpam-5394	235	41	implies	imply	VERB
ejpam-5394	235	42	x	x	PUNCT
ejpam-5394	235	43	≤	≤	NUM
ejpam-5394	235	44	1	1	NUM
ejpam-5394	235	45	2	2	NUM
ejpam-5394	235	46	or	or	CCONJ
ejpam-5394	235	47	[	[	PUNCT
ejpam-5394	235	48	0	0	NUM
ejpam-5394	235	49	,	,	PUNCT
ejpam-5394	235	50	12	12	NUM
ejpam-5394	235	51	]	]	PUNCT
ejpam-5394	235	52	.	.	PUNCT
ejpam-5394	236	1	also	also	ADV
ejpam-5394	236	2	for	for	ADP
ejpam-5394	236	3	0	0	NUM
ejpam-5394	236	4	∈	∈	PROPN
ejpam-5394	236	5	x	x	SYM
ejpam-5394	236	6	∗	∗	NOUN
ejpam-5394	236	7	1	1	NUM
ejpam-5394	236	8	3	3	NUM
ejpam-5394	236	9	,	,	PUNCT
ejpam-5394	236	10	x	x	PROPN
ejpam-5394	236	11	∗	∗	NOUN
ejpam-5394	236	12	1	1	NUM
ejpam-5394	236	13	3	3	NUM
ejpam-5394	236	14	=	=	SYM
ejpam-5394	236	15	{	{	PUNCT
ejpam-5394	236	16	0	0	NUM
ejpam-5394	236	17	}	}	PUNCT
ejpam-5394	236	18	which	which	PRON
ejpam-5394	236	19	implies	imply	VERB
ejpam-5394	236	20	x	x	PUNCT
ejpam-5394	236	21	≤	≤	NUM
ejpam-5394	236	22	1	1	NUM
ejpam-5394	236	23	3	3	NUM
ejpam-5394	236	24	or	or	CCONJ
ejpam-5394	236	25	[	[	PUNCT
ejpam-5394	236	26	0	0	NUM
ejpam-5394	236	27	,	,	PUNCT
ejpam-5394	236	28	13	13	NUM
ejpam-5394	236	29	]	]	PUNCT
ejpam-5394	236	30	.	.	PUNCT
ejpam-5394	237	1	for	for	SCONJ
ejpam-5394	237	2	these	these	DET
ejpam-5394	237	3	two	two	NUM
ejpam-5394	237	4	to	to	PART
ejpam-5394	237	5	hold	hold	VERB
ejpam-5394	237	6	,	,	PUNCT
ejpam-5394	237	7	therefore	therefore	ADV
ejpam-5394	237	8	lh({1	lh({1	PRON
ejpam-5394	237	9	2	2	NUM
ejpam-5394	237	10	,	,	PUNCT
ejpam-5394	237	11	1	1	NUM
ejpam-5394	237	12	3	3	NUM
ejpam-5394	237	13	}	}	PUNCT
ejpam-5394	237	14	)	)	PUNCT
ejpam-5394	237	15	=[	=[	NOUN
ejpam-5394	237	16	0	0	NUM
ejpam-5394	237	17	,	,	PUNCT
ejpam-5394	237	18	13	13	NUM
ejpam-5394	237	19	]	]	PUNCT
ejpam-5394	237	20	.	.	PUNCT
ejpam-5394	238	1	the	the	DET
ejpam-5394	238	2	proof	proof	NOUN
ejpam-5394	238	3	of	of	ADP
ejpam-5394	238	4	the	the	DET
ejpam-5394	238	5	following	follow	VERB
ejpam-5394	238	6	theorems	theorem	NOUN
ejpam-5394	238	7	are	be	AUX
ejpam-5394	238	8	analogous	analogous	ADJ
ejpam-5394	238	9	to	to	ADP
ejpam-5394	238	10	that	that	DET
ejpam-5394	238	11	topology	topology	NOUN
ejpam-5394	238	12	τr[0	τr[0	PROPN
ejpam-5394	238	13	,	,	PUNCT
ejpam-5394	238	14	1	1	NUM
ejpam-5394	238	15	]	]	PUNCT
ejpam-5394	238	16	.	.	PUNCT
ejpam-5394	239	1	theorem	theorem	VERB
ejpam-5394	239	2	9	9	NUM
ejpam-5394	239	3	.	.	PUNCT
ejpam-5394	240	1	in	in	ADP
ejpam-5394	240	2	the	the	DET
ejpam-5394	240	3	hyper	hyper	ADJ
ejpam-5394	240	4	bck	bck	NOUN
ejpam-5394	240	5	-	-	PUNCT
ejpam-5394	240	6	algebra	algebra	NOUN
ejpam-5394	240	7	[	[	X
ejpam-5394	240	8	0	0	NUM
ejpam-5394	240	9	,	,	PUNCT
ejpam-5394	240	10	1	1	NUM
ejpam-5394	240	11	]	]	PUNCT
ejpam-5394	240	12	,	,	PUNCT
ejpam-5394	240	13	lh(a	lh(a	NOUN
ejpam-5394	240	14	)	)	PUNCT
ejpam-5394	240	15	=	=	PUNCT
ejpam-5394	241	1	[	[	X
ejpam-5394	241	2	0	0	NUM
ejpam-5394	241	3	,	,	PUNCT
ejpam-5394	241	4	a	a	PRON
ejpam-5394	241	5	]	]	X
ejpam-5394	241	6	.	.	PUNCT
ejpam-5394	242	1	theorem	theorem	ADJ
ejpam-5394	242	2	10	10	NUM
ejpam-5394	242	3	.	.	PUNCT
ejpam-5394	243	1	let	let	VERB
ejpam-5394	243	2	a	a	DET
ejpam-5394	243	3	⊆	⊆	NUM
ejpam-5394	243	4	[	[	X
ejpam-5394	243	5	0	0	NUM
ejpam-5394	243	6	,	,	PUNCT
ejpam-5394	243	7	1	1	NUM
ejpam-5394	243	8	]	]	PUNCT
ejpam-5394	243	9	.	.	PUNCT
ejpam-5394	244	1	l[0,1](a	l[0,1](a	NOUN
ejpam-5394	244	2	)	)	PUNCT
ejpam-5394	244	3	=	=	PUNCT
ejpam-5394	245	1	[	[	X
ejpam-5394	245	2	0	0	NUM
ejpam-5394	245	3	,	,	PUNCT
ejpam-5394	245	4	r	r	NOUN
ejpam-5394	245	5	]	]	X
ejpam-5394	245	6	where	where	SCONJ
ejpam-5394	245	7	r	r	NOUN
ejpam-5394	245	8	=	=	SYM
ejpam-5394	245	9	infa	infa	NOUN
ejpam-5394	245	10	.	.	PUNCT
ejpam-5394	246	1	theorem	theorem	VERB
ejpam-5394	246	2	11	11	NUM
ejpam-5394	246	3	.	.	PUNCT
ejpam-5394	247	1	in	in	ADP
ejpam-5394	247	2	the	the	DET
ejpam-5394	247	3	hyper	hyper	ADJ
ejpam-5394	247	4	bck	bck	NOUN
ejpam-5394	247	5	-	-	PUNCT
ejpam-5394	247	6	algebra	algebra	NOUN
ejpam-5394	247	7	[	[	X
ejpam-5394	247	8	0	0	NUM
ejpam-5394	247	9	,	,	PUNCT
ejpam-5394	247	10	1	1	NUM
ejpam-5394	247	11	]	]	PUNCT
ejpam-5394	247	12	,	,	PUNCT
ejpam-5394	247	13	bl([0	bl([0	NOUN
ejpam-5394	247	14	,	,	PUNCT
ejpam-5394	247	15	1	1	NUM
ejpam-5394	247	16	]	]	PUNCT
ejpam-5394	247	17	)	)	PUNCT
ejpam-5394	247	18	=	=	SYM
ejpam-5394	247	19	{	{	PUNCT
ejpam-5394	247	20	[	[	X
ejpam-5394	247	21	0	0	NUM
ejpam-5394	247	22	,	,	PUNCT
ejpam-5394	247	23	r	r	NOUN
ejpam-5394	247	24	]	]	X
ejpam-5394	247	25	:	:	PUNCT
ejpam-5394	247	26	r	r	X
ejpam-5394	247	27	∈	∈	PROPN
ejpam-5394	248	1	[	[	X
ejpam-5394	248	2	0	0	NUM
ejpam-5394	248	3	,	,	PUNCT
ejpam-5394	248	4	1	1	NUM
ejpam-5394	248	5	]	]	PUNCT
ejpam-5394	248	6	}	}	PUNCT
ejpam-5394	248	7	.	.	PUNCT
ejpam-5394	249	1	the	the	DET
ejpam-5394	249	2	following	follow	VERB
ejpam-5394	249	3	examples	example	NOUN
ejpam-5394	249	4	are	be	AUX
ejpam-5394	249	5	open	open	ADJ
ejpam-5394	249	6	and	and	CCONJ
ejpam-5394	249	7	closed	closed	ADJ
ejpam-5394	249	8	sets	set	NOUN
ejpam-5394	249	9	in	in	ADP
ejpam-5394	249	10	[	[	X
ejpam-5394	249	11	0	0	NUM
ejpam-5394	249	12	,	,	PUNCT
ejpam-5394	249	13	1	1	NUM
ejpam-5394	249	14	]	]	PUNCT
ejpam-5394	249	15	.	.	PUNCT
ejpam-5394	250	1	example	example	NOUN
ejpam-5394	250	2	6	6	NUM
ejpam-5394	250	3	.	.	PUNCT
ejpam-5394	251	1	the	the	DET
ejpam-5394	251	2	following	follow	VERB
ejpam-5394	251	3	are	be	AUX
ejpam-5394	251	4	open	open	ADJ
ejpam-5394	251	5	set	set	VERB
ejpam-5394	251	6	in	in	ADP
ejpam-5394	251	7	[	[	X
ejpam-5394	251	8	0	0	NUM
ejpam-5394	251	9	,	,	PUNCT
ejpam-5394	251	10	1	1	NUM
ejpam-5394	251	11	]	]	PUNCT
ejpam-5394	251	12	:	:	PUNCT
ejpam-5394	251	13	•	•	PRON
ejpam-5394	251	14	[	[	X
ejpam-5394	251	15	0	0	NUM
ejpam-5394	251	16	,	,	PUNCT
ejpam-5394	251	17	a	a	PRON
ejpam-5394	251	18	)	)	PUNCT
ejpam-5394	251	19	for	for	ADP
ejpam-5394	251	20	[	[	X
ejpam-5394	251	21	0	0	NUM
ejpam-5394	251	22	,	,	PUNCT
ejpam-5394	251	23	a	a	PRON
ejpam-5394	251	24	)	)	PUNCT
ejpam-5394	251	25	=	=	SYM
ejpam-5394	251	26	∞⋃	∞⋃	NOUN
ejpam-5394	251	27	n=1	n=1	PROPN
ejpam-5394	251	28	[	[	PUNCT
ejpam-5394	251	29	0	0	NUM
ejpam-5394	251	30	,	,	PUNCT
ejpam-5394	251	31	a−	a−	PROPN
ejpam-5394	251	32	1	1	NUM
ejpam-5394	251	33	n	n	NOUN
ejpam-5394	251	34	]	]	PUNCT
ejpam-5394	251	35	•	•	X
ejpam-5394	251	36	{	{	PUNCT
ejpam-5394	251	37	0	0	NUM
ejpam-5394	251	38	}	}	PUNCT
ejpam-5394	251	39	for	for	ADP
ejpam-5394	251	40	{	{	PUNCT
ejpam-5394	251	41	0	0	NUM
ejpam-5394	251	42	}	}	PUNCT
ejpam-5394	251	43	=	=	PUNCT
ejpam-5394	252	1	[	[	X
ejpam-5394	252	2	0	0	NUM
ejpam-5394	252	3	,	,	PUNCT
ejpam-5394	252	4	0	0	NUM
ejpam-5394	252	5	]	]	PUNCT
ejpam-5394	252	6	example	example	NOUN
ejpam-5394	252	7	7	7	NUM
ejpam-5394	252	8	.	.	PUNCT
ejpam-5394	253	1	the	the	DET
ejpam-5394	253	2	following	follow	VERB
ejpam-5394	253	3	are	be	AUX
ejpam-5394	253	4	closed	close	VERB
ejpam-5394	253	5	set	set	VERB
ejpam-5394	253	6	in	in	ADP
ejpam-5394	253	7	[	[	X
ejpam-5394	253	8	0	0	NUM
ejpam-5394	253	9	,	,	PUNCT
ejpam-5394	253	10	1	1	NUM
ejpam-5394	253	11	]	]	PUNCT
ejpam-5394	253	12	:	:	PUNCT
ejpam-5394	253	13	•	•	PRON
ejpam-5394	253	14	(	(	PUNCT
ejpam-5394	253	15	a	a	PRON
ejpam-5394	253	16	,	,	PUNCT
ejpam-5394	253	17	1	1	NUM
ejpam-5394	253	18	]	]	PUNCT
ejpam-5394	253	19	for	for	ADP
ejpam-5394	253	20	(	(	PUNCT
ejpam-5394	253	21	a	a	PRON
ejpam-5394	253	22	,	,	PUNCT
ejpam-5394	253	23	1]c	1]c	NOUN
ejpam-5394	253	24	=	=	PUNCT
ejpam-5394	254	1	[	[	X
ejpam-5394	254	2	0	0	NUM
ejpam-5394	254	3	,	,	PUNCT
ejpam-5394	254	4	a	a	PRON
ejpam-5394	254	5	]	]	X
ejpam-5394	254	6	is	be	AUX
ejpam-5394	254	7	open	open	ADJ
ejpam-5394	254	8	•	•	NOUN
ejpam-5394	255	1	[	[	X
ejpam-5394	255	2	a	a	X
ejpam-5394	255	3	,	,	PUNCT
ejpam-5394	255	4	1	1	NUM
ejpam-5394	255	5	]	]	PUNCT
ejpam-5394	255	6	for	for	ADP
ejpam-5394	255	7	[	[	X
ejpam-5394	255	8	a	a	X
ejpam-5394	255	9	,	,	PUNCT
ejpam-5394	255	10	1]c	1]c	NOUN
ejpam-5394	255	11	=	=	PUNCT
ejpam-5394	256	1	[	[	X
ejpam-5394	256	2	0	0	NUM
ejpam-5394	256	3	,	,	PUNCT
ejpam-5394	256	4	a	a	PRON
ejpam-5394	256	5	)	)	PUNCT
ejpam-5394	256	6	is	be	AUX
ejpam-5394	256	7	open	open	ADJ
ejpam-5394	256	8	•	•	ADP
ejpam-5394	256	9	(	(	PUNCT
ejpam-5394	256	10	0	0	NUM
ejpam-5394	256	11	,	,	PUNCT
ejpam-5394	256	12	1	1	NUM
ejpam-5394	256	13	]	]	PUNCT
ejpam-5394	256	14	for	for	ADP
ejpam-5394	256	15	(	(	PUNCT
ejpam-5394	256	16	0	0	NUM
ejpam-5394	256	17	,	,	PUNCT
ejpam-5394	256	18	1	1	NUM
ejpam-5394	256	19	]	]	PUNCT
ejpam-5394	256	20	=	=	PUNCT
ejpam-5394	256	21	{	{	PUNCT
ejpam-5394	256	22	0}c	0}c	NOUN
ejpam-5394	256	23	thus	thus	ADV
ejpam-5394	256	24	we	we	PRON
ejpam-5394	256	25	have	have	VERB
ejpam-5394	256	26	the	the	DET
ejpam-5394	256	27	following	follow	VERB
ejpam-5394	256	28	result	result	NOUN
ejpam-5394	256	29	.	.	PUNCT
ejpam-5394	257	1	theorem	theorem	NOUN
ejpam-5394	257	2	12	12	NUM
ejpam-5394	257	3	.	.	PUNCT
ejpam-5394	258	1	in	in	ADP
ejpam-5394	258	2	a	a	DET
ejpam-5394	258	3	hyper	hyper	ADJ
ejpam-5394	258	4	bck	bck	NOUN
ejpam-5394	258	5	-	-	PUNCT
ejpam-5394	258	6	algebra	algebra	NOUN
ejpam-5394	258	7	[	[	X
ejpam-5394	258	8	0	0	NUM
ejpam-5394	258	9	,	,	PUNCT
ejpam-5394	258	10	1	1	NUM
ejpam-5394	258	11	]	]	PUNCT
ejpam-5394	258	12	,	,	PUNCT
ejpam-5394	258	13	τl([0	τl([0	PROPN
ejpam-5394	258	14	,	,	PUNCT
ejpam-5394	258	15	1	1	NUM
ejpam-5394	258	16	]	]	PUNCT
ejpam-5394	258	17	)	)	PUNCT
ejpam-5394	258	18	=	=	SYM
ejpam-5394	258	19	{	{	PUNCT
ejpam-5394	258	20	∅	∅	NOUN
ejpam-5394	258	21	,	,	PUNCT
ejpam-5394	258	22	[	[	X
ejpam-5394	258	23	0	0	NUM
ejpam-5394	258	24	,	,	PUNCT
ejpam-5394	258	25	1	1	NUM
ejpam-5394	258	26	]	]	PUNCT
ejpam-5394	258	27	,	,	PUNCT
ejpam-5394	258	28	[	[	X
ejpam-5394	258	29	0	0	NUM
ejpam-5394	258	30	,	,	PUNCT
ejpam-5394	258	31	r	r	NOUN
ejpam-5394	258	32	]	]	PUNCT
ejpam-5394	258	33	,	,	PUNCT
ejpam-5394	258	34	[	[	X
ejpam-5394	258	35	0	0	NUM
ejpam-5394	258	36	,	,	PUNCT
ejpam-5394	258	37	r	r	NOUN
ejpam-5394	258	38	)	)	PUNCT
ejpam-5394	258	39	:	:	PUNCT
ejpam-5394	258	40	r	r	X
ejpam-5394	258	41	∈	∈	PROPN
ejpam-5394	259	1	[	[	X
ejpam-5394	259	2	0	0	NUM
ejpam-5394	259	3	,	,	PUNCT
ejpam-5394	259	4	1	1	NUM
ejpam-5394	259	5	]	]	PUNCT
ejpam-5394	259	6	}	}	PUNCT
ejpam-5394	259	7	.	.	PUNCT
ejpam-5394	260	1	proof	proof	NOUN
ejpam-5394	260	2	.	.	PUNCT
ejpam-5394	261	1	let	let	VERB
ejpam-5394	261	2	g	g	PROPN
ejpam-5394	261	3	∈	∈	PROPN
ejpam-5394	261	4	τl	τl	VERB
ejpam-5394	261	5	(	(	PUNCT
ejpam-5394	261	6	[	[	X
ejpam-5394	261	7	0	0	NUM
ejpam-5394	261	8	,	,	PUNCT
ejpam-5394	261	9	1	1	NUM
ejpam-5394	261	10	]	]	NUM
ejpam-5394	261	11	)	)	PUNCT
ejpam-5394	261	12	,	,	PUNCT
ejpam-5394	261	13	and	and	CCONJ
ejpam-5394	261	14	g	g	PROPN
ejpam-5394	261	15	̸=	̸=	PROPN
ejpam-5394	261	16	∅.	∅.	VERB
ejpam-5394	261	17	then	then	ADV
ejpam-5394	261	18	g	g	PROPN
ejpam-5394	261	19	=	=	SYM
ejpam-5394	261	20	⋃	⋃	PROPN
ejpam-5394	261	21	i∈k⊆bl([0,1	i∈k⊆bl([0,1	NOUN
ejpam-5394	261	22	]	]	SYM
ejpam-5394	261	23	)	)	PUNCT
ejpam-5394	261	24	bi	bi	NOUN
ejpam-5394	261	25	.	.	PUNCT
ejpam-5394	262	1	thus	thus	ADV
ejpam-5394	262	2	,	,	PUNCT
ejpam-5394	262	3	bi	bi	NOUN
ejpam-5394	262	4	are	be	AUX
ejpam-5394	262	5	of	of	ADP
ejpam-5394	262	6	the	the	DET
ejpam-5394	262	7	form	form	NOUN
ejpam-5394	262	8	[	[	X
ejpam-5394	262	9	0	0	NUM
ejpam-5394	262	10	,	,	PUNCT
ejpam-5394	262	11	r	r	NOUN
ejpam-5394	262	12	]	]	X
ejpam-5394	262	13	,	,	PUNCT
ejpam-5394	262	14	g	g	NOUN
ejpam-5394	262	15	=	=	PUNCT
ejpam-5394	262	16	⋃	⋃	PROPN
ejpam-5394	263	1	[	[	X
ejpam-5394	263	2	0	0	NUM
ejpam-5394	263	3	,	,	PUNCT
ejpam-5394	263	4	ri	ri	X
ejpam-5394	263	5	]	]	PUNCT
ejpam-5394	263	6	=	=	PUNCT
ejpam-5394	264	1	[	[	X
ejpam-5394	264	2	0	0	NUM
ejpam-5394	264	3	,	,	PUNCT
ejpam-5394	264	4	r	r	NOUN
ejpam-5394	264	5	]	]	PUNCT
ejpam-5394	264	6	,	,	PUNCT
ejpam-5394	264	7	r0	r0	NOUN
ejpam-5394	264	8	=	=	PUNCT
ejpam-5394	264	9	inf{ri	inf{ri	NOUN
ejpam-5394	264	10	}	}	PUNCT
ejpam-5394	264	11	.	.	PUNCT
ejpam-5394	265	1	thus	thus	ADV
ejpam-5394	265	2	,	,	PUNCT
ejpam-5394	265	3	τl([0	τl([0	PROPN
ejpam-5394	265	4	,	,	PUNCT
ejpam-5394	265	5	1	1	NUM
ejpam-5394	265	6	]	]	PUNCT
ejpam-5394	265	7	)	)	PUNCT
ejpam-5394	266	1	=	=	SYM
ejpam-5394	266	2	{	{	PUNCT
ejpam-5394	266	3	∅	∅	NOUN
ejpam-5394	266	4	,	,	PUNCT
ejpam-5394	266	5	[	[	X
ejpam-5394	266	6	0	0	NUM
ejpam-5394	266	7	,	,	PUNCT
ejpam-5394	266	8	1	1	NUM
ejpam-5394	266	9	]	]	PUNCT
ejpam-5394	266	10	,	,	PUNCT
ejpam-5394	267	1	[	[	X
ejpam-5394	267	2	0	0	NUM
ejpam-5394	267	3	,	,	PUNCT
ejpam-5394	267	4	r	r	NOUN
ejpam-5394	267	5	]	]	PUNCT
ejpam-5394	267	6	,	,	PUNCT
ejpam-5394	267	7	[	[	X
ejpam-5394	267	8	0	0	NUM
ejpam-5394	267	9	,	,	PUNCT
ejpam-5394	267	10	r	r	NOUN
ejpam-5394	267	11	)	)	PUNCT
ejpam-5394	267	12	:	:	PUNCT
ejpam-5394	268	1	r	r	X
ejpam-5394	268	2	∈	∈	PROPN
ejpam-5394	269	1	[	[	X
ejpam-5394	269	2	0	0	NUM
ejpam-5394	269	3	,	,	PUNCT
ejpam-5394	269	4	1	1	NUM
ejpam-5394	269	5	]	]	PUNCT
ejpam-5394	269	6	}	}	PUNCT
ejpam-5394	269	7	.	.	PUNCT
ejpam-5394	270	1	■	■	PUNCT
ejpam-5394	270	2	corollary	corollary	ADJ
ejpam-5394	270	3	3	3	NUM
ejpam-5394	270	4	.	.	PUNCT
ejpam-5394	270	5	τl([0	τl([0	PROPN
ejpam-5394	270	6	,	,	PUNCT
ejpam-5394	270	7	1	1	NUM
ejpam-5394	270	8	]	]	PUNCT
ejpam-5394	270	9	)	)	PUNCT
ejpam-5394	270	10	is	be	AUX
ejpam-5394	270	11	not	not	PART
ejpam-5394	270	12	a	a	DET
ejpam-5394	270	13	subspace	subspace	NOUN
ejpam-5394	270	14	of	of	ADP
ejpam-5394	270	15	r	r	NOUN
ejpam-5394	270	16	with	with	ADP
ejpam-5394	270	17	the	the	DET
ejpam-5394	270	18	usual	usual	ADJ
ejpam-5394	270	19	topology	topology	NOUN
ejpam-5394	270	20	.	.	PUNCT
ejpam-5394	271	1	theorem	theorem	VERB
ejpam-5394	271	2	13	13	NUM
ejpam-5394	271	3	.	.	PUNCT
ejpam-5394	272	1	[	[	X
ejpam-5394	272	2	0	0	NUM
ejpam-5394	272	3	,	,	PUNCT
ejpam-5394	272	4	1	1	NUM
ejpam-5394	272	5	]	]	PUNCT
ejpam-5394	272	6	with	with	ADP
ejpam-5394	272	7	topology	topology	NOUN
ejpam-5394	272	8	τl([0	τl([0	NOUN
ejpam-5394	272	9	,	,	PUNCT
ejpam-5394	272	10	1	1	NUM
ejpam-5394	272	11	]	]	PUNCT
ejpam-5394	272	12	)	)	PUNCT
ejpam-5394	272	13	is	be	AUX
ejpam-5394	272	14	connected	connect	VERB
ejpam-5394	272	15	.	.	PUNCT
ejpam-5394	273	1	e.	e.	PROPN
ejpam-5394	273	2	payla	payla	PROPN
ejpam-5394	273	3	,	,	PUNCT
ejpam-5394	273	4	l.	l.	PROPN
ejpam-5394	273	5	ranara	ranara	PROPN
ejpam-5394	273	6	/	/	SYM
ejpam-5394	273	7	eur	eur	PROPN
ejpam-5394	273	8	.	.	PUNCT
ejpam-5394	274	1	j.	j.	PROPN
ejpam-5394	274	2	pure	pure	PROPN
ejpam-5394	274	3	appl	appl	PROPN
ejpam-5394	274	4	.	.	PROPN
ejpam-5394	274	5	math	math	PROPN
ejpam-5394	274	6	,	,	PUNCT
ejpam-5394	274	7	18	18	NUM
ejpam-5394	274	8	(	(	PUNCT
ejpam-5394	274	9	2	2	NUM
ejpam-5394	274	10	)	)	PUNCT
ejpam-5394	274	11	(	(	PUNCT
ejpam-5394	274	12	2025	2025	NUM
ejpam-5394	274	13	)	)	PUNCT
ejpam-5394	274	14	,	,	PUNCT
ejpam-5394	274	15	5394	5394	NUM
ejpam-5394	274	16	9	9	NUM
ejpam-5394	274	17	of	of	ADP
ejpam-5394	274	18	10	10	NUM
ejpam-5394	274	19	proof	proof	NOUN
ejpam-5394	274	20	.	.	PUNCT
ejpam-5394	274	21	suppose	suppose	VERB
ejpam-5394	274	22	[	[	X
ejpam-5394	274	23	0	0	NUM
ejpam-5394	274	24	,	,	PUNCT
ejpam-5394	274	25	1	1	NUM
ejpam-5394	274	26	]	]	PUNCT
ejpam-5394	274	27	is	be	AUX
ejpam-5394	274	28	disconnected	disconnect	VERB
ejpam-5394	274	29	.	.	PUNCT
ejpam-5394	275	1	then	then	ADV
ejpam-5394	275	2	,	,	PUNCT
ejpam-5394	275	3	there	there	PRON
ejpam-5394	275	4	exist	exist	VERB
ejpam-5394	275	5	disjoint	disjoint	ADJ
ejpam-5394	275	6	open	open	ADJ
ejpam-5394	275	7	sets	set	NOUN
ejpam-5394	275	8	a	a	DET
ejpam-5394	275	9	,	,	PUNCT
ejpam-5394	275	10	b	b	NOUN
ejpam-5394	275	11	such	such	ADJ
ejpam-5394	275	12	that	that	SCONJ
ejpam-5394	276	1	[	[	X
ejpam-5394	276	2	0	0	NUM
ejpam-5394	276	3	,	,	PUNCT
ejpam-5394	276	4	1	1	NUM
ejpam-5394	276	5	]	]	PUNCT
ejpam-5394	276	6	=	=	PUNCT
ejpam-5394	276	7	a	a	DET
ejpam-5394	276	8	∪	∪	X
ejpam-5394	276	9	b.	b.	NOUN
ejpam-5394	276	10	since	since	SCONJ
ejpam-5394	276	11	a	a	PRON
ejpam-5394	276	12	is	be	AUX
ejpam-5394	276	13	open	open	ADJ
ejpam-5394	276	14	,	,	PUNCT
ejpam-5394	276	15	a	a	PRON
ejpam-5394	276	16	=	=	X
ejpam-5394	277	1	[	[	X
ejpam-5394	277	2	0	0	NUM
ejpam-5394	277	3	,	,	PUNCT
ejpam-5394	277	4	r	r	NOUN
ejpam-5394	277	5	]	]	PUNCT
ejpam-5394	277	6	or	or	CCONJ
ejpam-5394	277	7	[	[	X
ejpam-5394	277	8	0	0	NUM
ejpam-5394	277	9	,	,	PUNCT
ejpam-5394	277	10	r	r	NOUN
ejpam-5394	277	11	)	)	PUNCT
ejpam-5394	277	12	.	.	PUNCT
ejpam-5394	278	1	if	if	SCONJ
ejpam-5394	278	2	a	a	PRON
ejpam-5394	278	3	=	=	X
ejpam-5394	279	1	[	[	X
ejpam-5394	279	2	0	0	NUM
ejpam-5394	279	3	,	,	PUNCT
ejpam-5394	279	4	r	r	NOUN
ejpam-5394	279	5	]	]	X
ejpam-5394	279	6	then	then	ADV
ejpam-5394	279	7	b	b	X
ejpam-5394	279	8	=	=	PUNCT
ejpam-5394	280	1	[	[	X
ejpam-5394	280	2	r	r	X
ejpam-5394	280	3	,	,	PUNCT
ejpam-5394	280	4	1	1	NUM
ejpam-5394	280	5	]	]	PUNCT
ejpam-5394	280	6	.	.	PUNCT
ejpam-5394	281	1	if	if	SCONJ
ejpam-5394	281	2	a	a	PRON
ejpam-5394	281	3	=	=	X
ejpam-5394	282	1	[	[	X
ejpam-5394	282	2	0	0	NUM
ejpam-5394	282	3	,	,	PUNCT
ejpam-5394	282	4	r	r	NOUN
ejpam-5394	282	5	)	)	PUNCT
ejpam-5394	283	1	then	then	ADV
ejpam-5394	283	2	b	b	X
ejpam-5394	283	3	=	=	PUNCT
ejpam-5394	284	1	[	[	X
ejpam-5394	284	2	r	r	X
ejpam-5394	284	3	,	,	PUNCT
ejpam-5394	284	4	1	1	NUM
ejpam-5394	284	5	]	]	PUNCT
ejpam-5394	284	6	.	.	PUNCT
ejpam-5394	285	1	whether	whether	SCONJ
ejpam-5394	285	2	b	b	X
ejpam-5394	285	3	=	=	PUNCT
ejpam-5394	286	1	[	[	X
ejpam-5394	286	2	r	r	X
ejpam-5394	286	3	,	,	PUNCT
ejpam-5394	286	4	1	1	NUM
ejpam-5394	286	5	]	]	PUNCT
ejpam-5394	286	6	or	or	CCONJ
ejpam-5394	286	7	[	[	X
ejpam-5394	286	8	r	r	X
ejpam-5394	286	9	,	,	PUNCT
ejpam-5394	286	10	1	1	NUM
ejpam-5394	286	11	]	]	PUNCT
ejpam-5394	286	12	,	,	PUNCT
ejpam-5394	286	13	b	b	NOUN
ejpam-5394	286	14	is	be	AUX
ejpam-5394	286	15	not	not	PART
ejpam-5394	286	16	open	open	ADJ
ejpam-5394	286	17	.	.	PUNCT
ejpam-5394	287	1	this	this	PRON
ejpam-5394	287	2	contradicts	contradict	VERB
ejpam-5394	287	3	the	the	DET
ejpam-5394	287	4	statement	statement	NOUN
ejpam-5394	287	5	that	that	SCONJ
ejpam-5394	287	6	a	a	PRON
ejpam-5394	287	7	and	and	CCONJ
ejpam-5394	287	8	b	b	NOUN
ejpam-5394	287	9	are	be	AUX
ejpam-5394	287	10	open	open	ADJ
ejpam-5394	287	11	sets	set	NOUN
ejpam-5394	287	12	.	.	PUNCT
ejpam-5394	288	1	therefore	therefore	ADV
ejpam-5394	288	2	,	,	PUNCT
ejpam-5394	288	3	by	by	ADP
ejpam-5394	288	4	definition	definition	NOUN
ejpam-5394	288	5	4	4	NUM
ejpam-5394	288	6	,	,	PUNCT
ejpam-5394	288	7	[	[	X
ejpam-5394	288	8	0	0	NUM
ejpam-5394	288	9	,	,	PUNCT
ejpam-5394	288	10	1	1	NUM
ejpam-5394	288	11	]	]	PUNCT
ejpam-5394	288	12	is	be	AUX
ejpam-5394	288	13	connected	connect	VERB
ejpam-5394	288	14	.	.	PUNCT
ejpam-5394	289	1	■	■	PUNCT
ejpam-5394	289	2	theorem	theorem	ADJ
ejpam-5394	289	3	14	14	NUM
ejpam-5394	289	4	.	.	PUNCT
ejpam-5394	290	1	in	in	ADP
ejpam-5394	290	2	a	a	DET
ejpam-5394	290	3	hyper	hyper	ADJ
ejpam-5394	290	4	bck	bck	NOUN
ejpam-5394	290	5	-	-	PUNCT
ejpam-5394	290	6	algebra	algebra	NOUN
ejpam-5394	290	7	[	[	X
ejpam-5394	290	8	0	0	NUM
ejpam-5394	290	9	,	,	PUNCT
ejpam-5394	290	10	1	1	NUM
ejpam-5394	290	11	]	]	PUNCT
ejpam-5394	290	12	,	,	PUNCT
ejpam-5394	290	13	τr([0	τr([0	NOUN
ejpam-5394	290	14	,	,	PUNCT
ejpam-5394	290	15	1])∩τl([0	1])∩τl([0	NUM
ejpam-5394	290	16	,	,	PUNCT
ejpam-5394	290	17	1	1	NUM
ejpam-5394	290	18	]	]	PUNCT
ejpam-5394	290	19	)	)	PUNCT
ejpam-5394	290	20	is	be	AUX
ejpam-5394	290	21	the	the	DET
ejpam-5394	290	22	indiscrete	indiscrete	ADJ
ejpam-5394	290	23	topology	topology	NOUN
ejpam-5394	290	24	on	on	ADP
ejpam-5394	290	25	[	[	X
ejpam-5394	290	26	0	0	NUM
ejpam-5394	290	27	,	,	PUNCT
ejpam-5394	290	28	1	1	NUM
ejpam-5394	290	29	]	]	PUNCT
ejpam-5394	290	30	.	.	PUNCT
ejpam-5394	291	1	proof	proof	NOUN
ejpam-5394	291	2	.	.	PUNCT
ejpam-5394	292	1	in	in	ADP
ejpam-5394	292	2	[	[	X
ejpam-5394	292	3	0	0	NUM
ejpam-5394	292	4	,	,	PUNCT
ejpam-5394	292	5	1	1	NUM
ejpam-5394	292	6	]	]	PUNCT
ejpam-5394	292	7	,	,	PUNCT
ejpam-5394	292	8	br(h	br(h	NUM
ejpam-5394	292	9	)	)	PUNCT
ejpam-5394	292	10	=	=	PRON
ejpam-5394	293	1	{	{	PUNCT
ejpam-5394	293	2	[	[	X
ejpam-5394	293	3	r	r	X
ejpam-5394	293	4	,	,	PUNCT
ejpam-5394	293	5	1	1	NUM
ejpam-5394	293	6	]	]	PUNCT
ejpam-5394	293	7	:	:	PUNCT
ejpam-5394	293	8	r	r	X
ejpam-5394	293	9	∈	∈	PROPN
ejpam-5394	294	1	[	[	X
ejpam-5394	294	2	0	0	NUM
ejpam-5394	294	3	,	,	PUNCT
ejpam-5394	294	4	1	1	NUM
ejpam-5394	294	5	]	]	PUNCT
ejpam-5394	294	6	}	}	PUNCT
ejpam-5394	294	7	and	and	CCONJ
ejpam-5394	294	8	bl(h	bl(h	NUM
ejpam-5394	294	9	)	)	PUNCT
ejpam-5394	294	10	=	=	PRON
ejpam-5394	294	11	{	{	PUNCT
ejpam-5394	294	12	[	[	X
ejpam-5394	294	13	0	0	NUM
ejpam-5394	294	14	,	,	PUNCT
ejpam-5394	294	15	p	p	X
ejpam-5394	294	16	]	]	X
ejpam-5394	294	17	:	:	PUNCT
ejpam-5394	294	18	p	p	X
ejpam-5394	294	19	∈	∈	PROPN
ejpam-5394	295	1	[	[	X
ejpam-5394	295	2	0	0	NUM
ejpam-5394	295	3	,	,	PUNCT
ejpam-5394	295	4	1	1	NUM
ejpam-5394	295	5	]	]	PUNCT
ejpam-5394	295	6	}	}	PUNCT
ejpam-5394	295	7	.	.	PUNCT
ejpam-5394	296	1	suppose	suppose	VERB
ejpam-5394	296	2	there	there	PRON
ejpam-5394	296	3	exixts	exixts	NOUN
ejpam-5394	296	4	g	g	PROPN
ejpam-5394	296	5	∈	∈	PROPN
ejpam-5394	297	1	[	[	X
ejpam-5394	297	2	τr(h	τr(h	NOUN
ejpam-5394	297	3	)	)	PUNCT
ejpam-5394	297	4	∩	∩	NOUN
ejpam-5394	297	5	τl(h	τl(h	NUM
ejpam-5394	297	6	)	)	PUNCT
ejpam-5394	297	7	]	]	PUNCT
ejpam-5394	297	8	\	\	NOUN
ejpam-5394	297	9	{	{	PUNCT
ejpam-5394	297	10	∅	∅	NOUN
ejpam-5394	297	11	,	,	PUNCT
ejpam-5394	297	12	h	h	NOUN
ejpam-5394	297	13	}	}	PUNCT
ejpam-5394	297	14	.	.	PUNCT
ejpam-5394	298	1	let	let	VERB
ejpam-5394	298	2	x	x	SYM
ejpam-5394	298	3	∈	∈	PROPN
ejpam-5394	298	4	g.	g.	NOUN
ejpam-5394	298	5	then	then	ADV
ejpam-5394	298	6	there	there	PRON
ejpam-5394	298	7	exist	exist	VERB
ejpam-5394	298	8	a	a	DET
ejpam-5394	298	9	∈	∈	NOUN
ejpam-5394	298	10	(	(	PUNCT
ejpam-5394	298	11	0	0	NUM
ejpam-5394	298	12	,	,	PUNCT
ejpam-5394	298	13	1	1	NUM
ejpam-5394	298	14	]	]	PUNCT
ejpam-5394	298	15	and	and	CCONJ
ejpam-5394	298	16	b	b	X
ejpam-5394	298	17	∈	∈	PROPN
ejpam-5394	299	1	[	[	X
ejpam-5394	299	2	0	0	NUM
ejpam-5394	299	3	,	,	PUNCT
ejpam-5394	299	4	1	1	NUM
ejpam-5394	299	5	)	)	PUNCT
ejpam-5394	300	1	such	such	ADJ
ejpam-5394	300	2	that	that	SCONJ
ejpam-5394	300	3	x	x	SYM
ejpam-5394	300	4	∈	∈	PROPN
ejpam-5394	300	5	[	[	X
ejpam-5394	300	6	a	a	X
ejpam-5394	300	7	,	,	PUNCT
ejpam-5394	300	8	1	1	NUM
ejpam-5394	300	9	]	]	SYM
ejpam-5394	300	10	⊆	⊆	NUM
ejpam-5394	300	11	g	g	NOUN
ejpam-5394	300	12	and	and	CCONJ
ejpam-5394	300	13	x	x	PUNCT
ejpam-5394	300	14	∈	∈	PROPN
ejpam-5394	300	15	[	[	X
ejpam-5394	300	16	0	0	NUM
ejpam-5394	300	17	,	,	PUNCT
ejpam-5394	300	18	b	b	NOUN
ejpam-5394	300	19	]	]	PUNCT
ejpam-5394	300	20	⊆	⊆	NUM
ejpam-5394	300	21	g.	g.	NOUN
ejpam-5394	300	22	this	this	PRON
ejpam-5394	300	23	implies	imply	VERB
ejpam-5394	300	24	that	that	SCONJ
ejpam-5394	300	25	a	a	DET
ejpam-5394	300	26	≤	≤	PROPN
ejpam-5394	300	27	b	b	NOUN
ejpam-5394	300	28	;	;	PUNCT
ejpam-5394	300	29	hence	hence	ADV
ejpam-5394	300	30	,	,	PUNCT
ejpam-5394	300	31	[	[	X
ejpam-5394	300	32	a	a	X
ejpam-5394	300	33	,	,	PUNCT
ejpam-5394	300	34	1	1	NUM
ejpam-5394	300	35	]	]	PUNCT
ejpam-5394	300	36	∪	∪	ADP
ejpam-5394	300	37	[	[	X
ejpam-5394	300	38	0	0	NUM
ejpam-5394	300	39	,	,	PUNCT
ejpam-5394	300	40	b	b	NOUN
ejpam-5394	300	41	]	]	X
ejpam-5394	300	42	=	=	PUNCT
ejpam-5394	301	1	[	[	X
ejpam-5394	301	2	0	0	NUM
ejpam-5394	301	3	,	,	PUNCT
ejpam-5394	301	4	1	1	NUM
ejpam-5394	301	5	]	]	SYM
ejpam-5394	301	6	⊆	⊆	NUM
ejpam-5394	301	7	g.	g.	NOUN
ejpam-5394	301	8	this	this	PRON
ejpam-5394	301	9	is	be	AUX
ejpam-5394	301	10	a	a	DET
ejpam-5394	301	11	contradiction	contradiction	NOUN
ejpam-5394	301	12	to	to	ADP
ejpam-5394	301	13	our	our	PRON
ejpam-5394	301	14	assumption	assumption	NOUN
ejpam-5394	301	15	of	of	ADP
ejpam-5394	301	16	set	set	PROPN
ejpam-5394	301	17	g.	g.	PROPN
ejpam-5394	301	18	therefore	therefore	ADV
ejpam-5394	301	19	,	,	PUNCT
ejpam-5394	301	20	τr(h	τr(h	NOUN
ejpam-5394	301	21	)	)	PUNCT
ejpam-5394	301	22	∩	∩	NOUN
ejpam-5394	301	23	τl(h	τl(h	NUM
ejpam-5394	301	24	)	)	PUNCT
ejpam-5394	301	25	is	be	AUX
ejpam-5394	301	26	the	the	DET
ejpam-5394	301	27	indiscrete	indiscrete	ADJ
ejpam-5394	301	28	topology	topology	NOUN
ejpam-5394	301	29	on	on	ADP
ejpam-5394	301	30	h.	h.	PROPN
ejpam-5394	301	31	■	■	PUNCT
ejpam-5394	301	32	6	6	X
ejpam-5394	301	33	.	.	X
ejpam-5394	301	34	conclusion	conclusion	NOUN
ejpam-5394	301	35	the	the	DET
ejpam-5394	301	36	paper	paper	NOUN
ejpam-5394	301	37	explores	explore	VERB
ejpam-5394	301	38	the	the	DET
ejpam-5394	301	39	structure	structure	NOUN
ejpam-5394	301	40	and	and	CCONJ
ejpam-5394	301	41	topology	topology	NOUN
ejpam-5394	301	42	of	of	ADP
ejpam-5394	301	43	a	a	DET
ejpam-5394	301	44	hyper	hyper	ADJ
ejpam-5394	301	45	bck	bck	NOUN
ejpam-5394	301	46	-	-	PUNCT
ejpam-5394	301	47	algebra	algebra	NOUN
ejpam-5394	301	48	[	[	X
ejpam-5394	301	49	0	0	NUM
ejpam-5394	301	50	,	,	PUNCT
ejpam-5394	301	51	1	1	NUM
ejpam-5394	301	52	]	]	PUNCT
ejpam-5394	301	53	.	.	PUNCT
ejpam-5394	302	1	two	two	NUM
ejpam-5394	302	2	topologies	topology	NOUN
ejpam-5394	302	3	,	,	PUNCT
ejpam-5394	302	4	τr([0	τr([0	NOUN
ejpam-5394	302	5	,	,	PUNCT
ejpam-5394	302	6	1	1	NUM
ejpam-5394	302	7	]	]	PUNCT
ejpam-5394	302	8	)	)	PUNCT
ejpam-5394	302	9	and	and	CCONJ
ejpam-5394	302	10	τl([0	τl([0	NOUN
ejpam-5394	302	11	,	,	PUNCT
ejpam-5394	302	12	1	1	NUM
ejpam-5394	302	13	]	]	NUM
ejpam-5394	302	14	)	)	PUNCT
ejpam-5394	302	15	,	,	PUNCT
ejpam-5394	302	16	are	be	AUX
ejpam-5394	302	17	constructed	construct	VERB
ejpam-5394	302	18	based	base	VERB
ejpam-5394	302	19	on	on	ADP
ejpam-5394	302	20	right	right	ADJ
ejpam-5394	302	21	and	and	CCONJ
ejpam-5394	302	22	left	leave	VERB
ejpam-5394	302	23	applications	application	NOUN
ejpam-5394	302	24	of	of	ADP
ejpam-5394	302	25	hyperorder	hyperorder	NOUN
ejpam-5394	302	26	,	,	PUNCT
ejpam-5394	302	27	respectively	respectively	ADV
ejpam-5394	302	28	.	.	PUNCT
ejpam-5394	303	1	the	the	DET
ejpam-5394	303	2	paper	paper	NOUN
ejpam-5394	303	3	demonstrates	demonstrate	VERB
ejpam-5394	303	4	the	the	DET
ejpam-5394	303	5	properties	property	NOUN
ejpam-5394	303	6	of	of	ADP
ejpam-5394	303	7	these	these	DET
ejpam-5394	303	8	topologies	topology	NOUN
ejpam-5394	303	9	,	,	PUNCT
ejpam-5394	303	10	including	include	VERB
ejpam-5394	303	11	the	the	DET
ejpam-5394	303	12	formation	formation	NOUN
ejpam-5394	303	13	of	of	ADP
ejpam-5394	303	14	bases	basis	NOUN
ejpam-5394	303	15	,	,	PUNCT
ejpam-5394	303	16	open	open	ADJ
ejpam-5394	303	17	and	and	CCONJ
ejpam-5394	303	18	closed	closed	ADJ
ejpam-5394	303	19	sets	set	NOUN
ejpam-5394	303	20	,	,	PUNCT
ejpam-5394	303	21	and	and	CCONJ
ejpam-5394	303	22	connectedness	connectedness	NOUN
ejpam-5394	303	23	.	.	PUNCT
ejpam-5394	304	1	the	the	DET
ejpam-5394	304	2	intersection	intersection	NOUN
ejpam-5394	304	3	of	of	ADP
ejpam-5394	304	4	these	these	DET
ejpam-5394	304	5	topologies	topology	NOUN
ejpam-5394	304	6	results	result	VERB
ejpam-5394	304	7	in	in	ADP
ejpam-5394	304	8	the	the	DET
ejpam-5394	304	9	indiscrete	indiscrete	ADJ
ejpam-5394	304	10	topology	topology	NOUN
ejpam-5394	304	11	on	on	ADP
ejpam-5394	304	12	[	[	X
ejpam-5394	304	13	0	0	NUM
ejpam-5394	304	14	,	,	PUNCT
ejpam-5394	304	15	1	1	NUM
ejpam-5394	304	16	]	]	PUNCT
ejpam-5394	304	17	,	,	PUNCT
ejpam-5394	304	18	highlighting	highlight	VERB
ejpam-5394	304	19	a	a	DET
ejpam-5394	304	20	unique	unique	ADJ
ejpam-5394	304	21	convergence	convergence	NOUN
ejpam-5394	304	22	of	of	ADP
ejpam-5394	304	23	the	the	DET
ejpam-5394	304	24	two	two	NUM
ejpam-5394	304	25	structures	structure	NOUN
ejpam-5394	304	26	.	.	PUNCT
ejpam-5394	305	1	this	this	DET
ejpam-5394	305	2	study	study	NOUN
ejpam-5394	305	3	builds	build	VERB
ejpam-5394	305	4	on	on	ADP
ejpam-5394	305	5	previous	previous	ADJ
ejpam-5394	305	6	work	work	NOUN
ejpam-5394	305	7	in	in	ADP
ejpam-5394	305	8	algebraic	algebraic	ADJ
ejpam-5394	305	9	hyperstructures	hyperstructure	NOUN
ejpam-5394	305	10	and	and	CCONJ
ejpam-5394	305	11	provides	provide	VERB
ejpam-5394	305	12	a	a	DET
ejpam-5394	305	13	foundational	foundational	ADJ
ejpam-5394	305	14	exploration	exploration	NOUN
ejpam-5394	305	15	of	of	ADP
ejpam-5394	305	16	topologies	topology	NOUN
ejpam-5394	305	17	within	within	ADP
ejpam-5394	305	18	hyper	hyper	ADJ
ejpam-5394	305	19	bck	bck	NOUN
ejpam-5394	305	20	-	-	PUNCT
ejpam-5394	305	21	algebras	algebra	NOUN
ejpam-5394	305	22	.	.	PUNCT
ejpam-5394	306	1	references	reference	NOUN
ejpam-5394	306	2	[	[	X
ejpam-5394	306	3	1	1	NUM
ejpam-5394	306	4	]	]	X
ejpam-5394	306	5	y	y	PROPN
ejpam-5394	306	6	imai	imai	PROPN
ejpam-5394	306	7	and	and	CCONJ
ejpam-5394	306	8	k	k	PROPN
ejpam-5394	306	9	isèki	isèki	PROPN
ejpam-5394	306	10	.	.	PUNCT
ejpam-5394	307	1	on	on	ADP
ejpam-5394	307	2	axiom	axiom	NOUN
ejpam-5394	307	3	systems	system	NOUN
ejpam-5394	307	4	of	of	ADP
ejpam-5394	307	5	propositional	propositional	ADJ
ejpam-5394	307	6	calculi	calculi	PROPN
ejpam-5394	307	7	xiv	xiv	PROPN
ejpam-5394	307	8	.	.	PUNCT
ejpam-5394	308	1	proc	proc	PROPN
ejpam-5394	308	2	.	.	PUNCT
ejpam-5394	309	1	japan	japan	PROPN
ejpam-5394	309	2	academy	academy	PROPN
ejpam-5394	309	3	,	,	PUNCT
ejpam-5394	309	4	42:19–22	42:19–22	NUM
ejpam-5394	309	5	,	,	PUNCT
ejpam-5394	309	6	1966	1966	NUM
ejpam-5394	309	7	.	.	PUNCT
ejpam-5394	310	1	[	[	X
ejpam-5394	310	2	2	2	NUM
ejpam-5394	310	3	]	]	X
ejpam-5394	310	4	f	f	PROPN
ejpam-5394	310	5	marty	marty	PROPN
ejpam-5394	310	6	.	.	PUNCT
ejpam-5394	311	1	sur	sur	PROPN
ejpam-5394	311	2	une	une	PROPN
ejpam-5394	311	3	generalisation	generalisation	PROPN
ejpam-5394	311	4	de	de	X
ejpam-5394	311	5	la	la	PROPN
ejpam-5394	311	6	notion	notion	PROPN
ejpam-5394	311	7	de	de	X
ejpam-5394	311	8	groupe	groupe	PROPN
ejpam-5394	311	9	.	.	PUNCT
ejpam-5394	312	1	pages	page	NOUN
ejpam-5394	312	2	45–49	45–49	PROPN
ejpam-5394	312	3	,	,	PUNCT
ejpam-5394	312	4	stockholm	stockholm	PROPN
ejpam-5394	312	5	,	,	PUNCT
ejpam-5394	312	6	sweden	sweden	PROPN
ejpam-5394	312	7	,	,	PUNCT
ejpam-5394	312	8	1934	1934	NUM
ejpam-5394	312	9	.	.	PUNCT
ejpam-5394	313	1	math.scandinaves	math.scandinave	NOUN
ejpam-5394	313	2	.	.	PUNCT
ejpam-5394	314	1	[	[	X
ejpam-5394	314	2	3	3	NUM
ejpam-5394	314	3	]	]	X
ejpam-5394	314	4	r	r	NOUN
ejpam-5394	314	5	patangan	patangan	NOUN
ejpam-5394	314	6	and	and	CCONJ
ejpam-5394	314	7	s	s	VERB
ejpam-5394	314	8	canoy	canoy	NOUN
ejpam-5394	314	9	.	.	PUNCT
ejpam-5394	315	1	a	a	DET
ejpam-5394	315	2	topology	topology	NOUN
ejpam-5394	315	3	on	on	ADP
ejpam-5394	315	4	a	a	DET
ejpam-5394	315	5	hyper	hyper	ADJ
ejpam-5394	315	6	bck	bck	NOUN
ejpam-5394	315	7	-	-	PUNCT
ejpam-5394	315	8	algebra	algebra	NOUN
ejpam-5394	315	9	.	.	PUNCT
ejpam-5394	316	1	jp	jp	PROPN
ejpam-5394	316	2	journal	journal	PROPN
ejpam-5394	316	3	of	of	ADP
ejpam-5394	316	4	algebra	algebra	PROPN
ejpam-5394	316	5	,	,	PUNCT
ejpam-5394	316	6	number	number	NOUN
ejpam-5394	316	7	theory	theory	NOUN
ejpam-5394	316	8	and	and	CCONJ
ejpam-5394	316	9	applications	application	NOUN
ejpam-5394	316	10	,	,	PUNCT
ejpam-5394	316	11	40(5):787–797	40(5):787–797	NOUN
ejpam-5394	316	12	,	,	PUNCT
ejpam-5394	316	13	2018	2018	NUM
ejpam-5394	316	14	.	.	PUNCT
ejpam-5394	317	1	[	[	X
ejpam-5394	317	2	4	4	NUM
ejpam-5394	317	3	]	]	X
ejpam-5394	317	4	r	r	NOUN
ejpam-5394	317	5	patangan	patangan	NOUN
ejpam-5394	317	6	and	and	CCONJ
ejpam-5394	317	7	s	s	VERB
ejpam-5394	317	8	canoy	canoy	NOUN
ejpam-5394	317	9	.	.	PUNCT
ejpam-5394	318	1	a	a	DET
ejpam-5394	318	2	topology	topology	NOUN
ejpam-5394	318	3	on	on	ADP
ejpam-5394	318	4	a	a	DET
ejpam-5394	318	5	hyper	hyper	ADJ
ejpam-5394	318	6	bck	bck	NOUN
ejpam-5394	318	7	-	-	PUNCT
ejpam-5394	318	8	algebra	algebra	NOUN
ejpam-5394	318	9	via	via	ADP
ejpam-5394	318	10	left	left	ADJ
ejpam-5394	318	11	application	application	NOUN
ejpam-5394	318	12	of	of	ADP
ejpam-5394	318	13	a	a	DET
ejpam-5394	318	14	hyper	hyper	ADJ
ejpam-5394	318	15	order	order	NOUN
ejpam-5394	318	16	.	.	PUNCT
ejpam-5394	319	1	jp	jp	PROPN
ejpam-5394	319	2	journal	journal	PROPN
ejpam-5394	319	3	of	of	ADP
ejpam-5394	319	4	algebra	algebra	PROPN
ejpam-5394	319	5	,	,	PUNCT
ejpam-5394	319	6	number	number	NOUN
ejpam-5394	319	7	theory	theory	NOUN
ejpam-5394	319	8	and	and	CCONJ
ejpam-5394	319	9	applications	application	NOUN
ejpam-5394	319	10	,	,	PUNCT
ejpam-5394	319	11	40(3):321–332	40(3):321–332	PROPN
ejpam-5394	319	12	,	,	PUNCT
ejpam-5394	319	13	2018	2018	NUM
ejpam-5394	319	14	.	.	PUNCT
ejpam-5394	320	1	[	[	X
ejpam-5394	320	2	5	5	X
ejpam-5394	320	3	]	]	PUNCT
ejpam-5394	320	4	j	j	PROPN
ejpam-5394	320	5	albaracin	albaracin	PROPN
ejpam-5394	320	6	and	and	CCONJ
ejpam-5394	320	7	j	j	PROPN
ejpam-5394	320	8	vilela	vilela	NOUN
ejpam-5394	320	9	.	.	PUNCT
ejpam-5394	321	1	zero	zero	NUM
ejpam-5394	321	2	divisor	divisor	NOUN
ejpam-5394	321	3	graph	graph	NOUN
ejpam-5394	321	4	of	of	ADP
ejpam-5394	321	5	finite	finite	ADJ
ejpam-5394	321	6	hyper	hyper	ADJ
ejpam-5394	321	7	bck	bck	NOUN
ejpam-5394	321	8	-	-	PUNCT
ejpam-5394	321	9	algebra	algebra	NOUN
ejpam-5394	321	10	involving	involve	VERB
ejpam-5394	321	11	hyperatoms	hyperatom	NOUN
ejpam-5394	321	12	.	.	PUNCT
ejpam-5394	322	1	far	far	PROPN
ejpam-5394	322	2	east	east	PROPN
ejpam-5394	322	3	journal	journal	PROPN
ejpam-5394	322	4	of	of	ADP
ejpam-5394	322	5	mathematics	mathematics	PROPN
ejpam-5394	322	6	sciences	science	NOUN
ejpam-5394	322	7	,	,	PUNCT
ejpam-5394	322	8	103:743–755	103:743–755	NUM
ejpam-5394	322	9	,	,	PUNCT
ejpam-5394	322	10	2018	2018	NUM
ejpam-5394	322	11	.	.	PUNCT
ejpam-5394	323	1	[	[	X
ejpam-5394	323	2	6	6	NUM
ejpam-5394	323	3	]	]	X
ejpam-5394	323	4	y	y	PROPN
ejpam-5394	323	5	jun	jun	PROPN
ejpam-5394	323	6	and	and	CCONJ
ejpam-5394	323	7	et.al	et.al	PROPN
ejpam-5394	323	8	.	.	PUNCT
ejpam-5394	324	1	on	on	ADP
ejpam-5394	324	2	hyper	hyper	ADJ
ejpam-5394	324	3	bck	bck	NOUN
ejpam-5394	324	4	-	-	PUNCT
ejpam-5394	324	5	algebra	algebra	NOUN
ejpam-5394	324	6	.	.	PUNCT
ejpam-5394	325	1	italian	italian	ADJ
ejpam-5394	325	2	j.	j.	PROPN
ejpam-5394	325	3	pure	pure	PROPN
ejpam-5394	325	4	and	and	CCONJ
ejpam-5394	325	5	appl	appl	PROPN
ejpam-5394	325	6	.	.	PROPN
ejpam-5394	325	7	math	math	PROPN
ejpam-5394	325	8	.	.	PUNCT
ejpam-5394	325	9	,	,	PUNCT
ejpam-5394	325	10	soc	soc	PROPN
ejpam-5394	325	11	,	,	PUNCT
ejpam-5394	325	12	8:493	8:493	NUM
ejpam-5394	325	13	–	–	PUNCT
ejpam-5394	325	14	497	497	NUM
ejpam-5394	325	15	,	,	PUNCT
ejpam-5394	325	16	2000	2000	NUM
ejpam-5394	325	17	.	.	PUNCT
ejpam-5394	326	1	[	[	X
ejpam-5394	326	2	7	7	X
ejpam-5394	326	3	]	]	X
ejpam-5394	326	4	j	j	PROPN
ejpam-5394	326	5	dugundji	dugundji	PROPN
ejpam-5394	326	6	.	.	PUNCT
ejpam-5394	327	1	topology	topology	PROPN
ejpam-5394	327	2	.	.	PUNCT
ejpam-5394	328	1	allyn	allyn	PROPN
ejpam-5394	328	2	and	and	CCONJ
ejpam-5394	328	3	bacon	bacon	PROPN
ejpam-5394	328	4	,	,	PUNCT
ejpam-5394	328	5	boston	boston	PROPN
ejpam-5394	328	6	,	,	PUNCT
ejpam-5394	328	7	1966	1966	NUM
ejpam-5394	328	8	.	.	PUNCT
ejpam-5394	329	1	e.	e.	PROPN
ejpam-5394	329	2	payla	payla	PROPN
ejpam-5394	329	3	,	,	PUNCT
ejpam-5394	329	4	l.	l.	PROPN
ejpam-5394	329	5	ranara	ranara	PROPN
ejpam-5394	329	6	/	/	SYM
ejpam-5394	329	7	eur	eur	PROPN
ejpam-5394	329	8	.	.	PUNCT
ejpam-5394	330	1	j.	j.	PROPN
ejpam-5394	330	2	pure	pure	PROPN
ejpam-5394	330	3	appl	appl	PROPN
ejpam-5394	330	4	.	.	PROPN
ejpam-5394	330	5	math	math	PROPN
ejpam-5394	330	6	,	,	PUNCT
ejpam-5394	330	7	18	18	NUM
ejpam-5394	330	8	(	(	PUNCT
ejpam-5394	330	9	2	2	NUM
ejpam-5394	330	10	)	)	PUNCT
ejpam-5394	330	11	(	(	PUNCT
ejpam-5394	330	12	2025	2025	NUM
ejpam-5394	330	13	)	)	PUNCT
ejpam-5394	330	14	,	,	PUNCT
ejpam-5394	330	15	5394	5394	NUM
ejpam-5394	330	16	10	10	NUM
ejpam-5394	330	17	of	of	ADP
ejpam-5394	330	18	10	10	NUM
ejpam-5394	330	19	[	[	SYM
ejpam-5394	330	20	8	8	NUM
ejpam-5394	330	21	]	]	SYM
ejpam-5394	330	22	l	l	NOUN
ejpam-5394	330	23	ranara	ranara	PROPN
ejpam-5394	330	24	and	and	CCONJ
ejpam-5394	330	25	j	j	PROPN
ejpam-5394	330	26	vilela	vilela	NOUN
ejpam-5394	330	27	.	.	PUNCT
ejpam-5394	331	1	on	on	ADP
ejpam-5394	331	2	ks	k	NOUN
ejpam-5394	331	3	-	-	PUNCT
ejpam-5394	331	4	semigroups	semigroups	X
ejpam-5394	331	5	[	[	X
ejpam-5394	331	6	0	0	NUM
ejpam-5394	331	7	,	,	PUNCT
ejpam-5394	331	8	1	1	NUM
ejpam-5394	331	9	]	]	PUNCT
ejpam-5394	331	10	and	and	CCONJ
ejpam-5394	331	11	fx	fx	PROPN
ejpam-5394	331	12	.	.	PUNCT
ejpam-5394	332	1	in	in	ADP
ejpam-5394	332	2	international	international	PROPN
ejpam-5394	332	3	mathematical	mathematical	ADJ
ejpam-5394	332	4	forum	forum	PROPN
ejpam-5394	332	5	,	,	PUNCT
ejpam-5394	332	6	volume	volume	NOUN
ejpam-5394	332	7	15	15	NUM
ejpam-5394	332	8	,	,	PUNCT
ejpam-5394	332	9	pages	page	NOUN
ejpam-5394	332	10	223–233	223–233	NUM
ejpam-5394	332	11	,	,	PUNCT
ejpam-5394	332	12	2020	2020	NUM
ejpam-5394	332	13	.	.	PUNCT