id	sid	tid	token	lemma	pos
ejpam-4021	1	1	european	european	PROPN
ejpam-4021	1	2	journal	journal	PROPN
ejpam-4021	1	3	of	of	ADP
ejpam-4021	1	4	pure	pure	ADJ
ejpam-4021	1	5	and	and	CCONJ
ejpam-4021	1	6	applied	apply	VERB
ejpam-4021	1	7	mathematics	mathematic	NOUN
ejpam-4021	1	8	vol	vol	NOUN
ejpam-4021	1	9	.	.	PUNCT
ejpam-4021	2	1	14	14	NUM
ejpam-4021	2	2	,	,	PUNCT
ejpam-4021	2	3	no	no	INTJ
ejpam-4021	2	4	.	.	NOUN
ejpam-4021	2	5	3	3	NUM
ejpam-4021	2	6	,	,	PUNCT
ejpam-4021	2	7	2021	2021	NUM
ejpam-4021	2	8	,	,	PUNCT
ejpam-4021	2	9	949	949	NUM
ejpam-4021	2	10	-	-	SYM
ejpam-4021	2	11	968	968	NUM
ejpam-4021	2	12	issn	issn	PROPN
ejpam-4021	2	13	1307	1307	NUM
ejpam-4021	2	14	-	-	SYM
ejpam-4021	2	15	5543	5543	NUM
ejpam-4021	2	16	–	–	PUNCT
ejpam-4021	3	1	ejpam.com	ejpam.com	X
ejpam-4021	3	2	published	publish	VERB
ejpam-4021	3	3	by	by	ADP
ejpam-4021	3	4	new	new	PROPN
ejpam-4021	3	5	york	york	PROPN
ejpam-4021	3	6	business	business	PROPN
ejpam-4021	3	7	global	global	PROPN
ejpam-4021	3	8	on	on	ADP
ejpam-4021	3	9	the	the	DET
ejpam-4021	3	10	aspects	aspect	NOUN
ejpam-4021	3	11	of	of	ADP
ejpam-4021	3	12	enriched	enriched	ADJ
ejpam-4021	3	13	lattice	lattice	NOUN
ejpam-4021	3	14	-	-	PUNCT
ejpam-4021	3	15	valued	value	VERB
ejpam-4021	3	16	topological	topological	ADJ
ejpam-4021	3	17	groups	group	NOUN
ejpam-4021	3	18	and	and	CCONJ
ejpam-4021	3	19	closure	closure	NOUN
ejpam-4021	3	20	of	of	ADP
ejpam-4021	3	21	lattice	lattice	NOUN
ejpam-4021	3	22	-	-	PUNCT
ejpam-4021	3	23	valued	value	VERB
ejpam-4021	3	24	subgroups	subgroup	NOUN
ejpam-4021	3	25	t	t	PROPN
ejpam-4021	3	26	m	m	PROPN
ejpam-4021	3	27	g	g	PROPN
ejpam-4021	3	28	ahsanullah1,∗	ahsanullah1,∗	NOUN
ejpam-4021	3	29	,	,	PUNCT
ejpam-4021	3	30	fawzi	fawzi	PROPN
ejpam-4021	3	31	al	al	PROPN
ejpam-4021	3	32	-	-	PUNCT
ejpam-4021	3	33	thukair1	thukair1	PROPN
ejpam-4021	3	34	1	1	NUM
ejpam-4021	3	35	department	department	NOUN
ejpam-4021	3	36	of	of	ADP
ejpam-4021	3	37	mathematics	mathematic	NOUN
ejpam-4021	3	38	,	,	PUNCT
ejpam-4021	3	39	king	king	PROPN
ejpam-4021	3	40	saud	saud	PROPN
ejpam-4021	3	41	university	university	PROPN
ejpam-4021	3	42	,	,	PUNCT
ejpam-4021	3	43	riyadh	riyadh	PROPN
ejpam-4021	3	44	,	,	PUNCT
ejpam-4021	3	45	saudi	saudi	PROPN
ejpam-4021	3	46	arabia	arabia	PROPN
ejpam-4021	3	47	.	.	PUNCT
ejpam-4021	4	1	dedicated	dedicate	VERB
ejpam-4021	4	2	to	to	ADP
ejpam-4021	4	3	professor	professor	PROPN
ejpam-4021	4	4	john	john	PROPN
ejpam-4021	4	5	n.	n.	PROPN
ejpam-4021	4	6	mordeson	mordeson	PROPN
ejpam-4021	4	7	on	on	ADP
ejpam-4021	4	8	the	the	DET
ejpam-4021	4	9	occasion	occasion	NOUN
ejpam-4021	4	10	of	of	ADP
ejpam-4021	4	11	his	his	PRON
ejpam-4021	4	12	87th	87th	ADJ
ejpam-4021	4	13	birthday	birthday	NOUN
ejpam-4021	4	14	abstract	abstract	NOUN
ejpam-4021	4	15	.	.	PUNCT
ejpam-4021	5	1	starting	start	VERB
ejpam-4021	5	2	with	with	ADP
ejpam-4021	5	3	l	l	NOUN
ejpam-4021	5	4	as	as	ADP
ejpam-4021	5	5	an	an	DET
ejpam-4021	5	6	enriched	enriched	ADJ
ejpam-4021	5	7	cl	cl	NOUN
ejpam-4021	5	8	-	-	ADJ
ejpam-4021	5	9	premonoid	premonoid	ADJ
ejpam-4021	5	10	,	,	PUNCT
ejpam-4021	5	11	in	in	ADP
ejpam-4021	5	12	this	this	DET
ejpam-4021	5	13	paper	paper	NOUN
ejpam-4021	5	14	,	,	PUNCT
ejpam-4021	5	15	we	we	PRON
ejpam-4021	5	16	explore	explore	VERB
ejpam-4021	5	17	some	some	DET
ejpam-4021	5	18	categorical	categorical	ADJ
ejpam-4021	5	19	connections	connection	NOUN
ejpam-4021	5	20	between	between	ADP
ejpam-4021	5	21	l	l	NOUN
ejpam-4021	5	22	-	-	PUNCT
ejpam-4021	5	23	valued	value	VERB
ejpam-4021	5	24	topological	topological	ADJ
ejpam-4021	5	25	groups	group	NOUN
ejpam-4021	5	26	and	and	CCONJ
ejpam-4021	5	27	kent	kent	PROPN
ejpam-4021	5	28	convergence	convergence	NOUN
ejpam-4021	5	29	groups	group	NOUN
ejpam-4021	5	30	,	,	PUNCT
ejpam-4021	5	31	where	where	SCONJ
ejpam-4021	5	32	it	it	PRON
ejpam-4021	5	33	is	be	AUX
ejpam-4021	5	34	shown	show	VERB
ejpam-4021	5	35	that	that	SCONJ
ejpam-4021	5	36	every	every	DET
ejpam-4021	5	37	l	l	NOUN
ejpam-4021	5	38	-	-	PUNCT
ejpam-4021	5	39	valued	value	VERB
ejpam-4021	5	40	topological	topological	ADJ
ejpam-4021	5	41	group	group	NOUN
ejpam-4021	5	42	determines	determine	VERB
ejpam-4021	5	43	a	a	DET
ejpam-4021	5	44	well	well	ADV
ejpam-4021	5	45	-	-	PUNCT
ejpam-4021	5	46	known	know	VERB
ejpam-4021	5	47	kent	kent	PROPN
ejpam-4021	5	48	convergence	convergence	NOUN
ejpam-4021	5	49	group	group	NOUN
ejpam-4021	5	50	,	,	PUNCT
ejpam-4021	5	51	and	and	CCONJ
ejpam-4021	5	52	conversely	conversely	ADV
ejpam-4021	5	53	,	,	PUNCT
ejpam-4021	5	54	every	every	DET
ejpam-4021	5	55	kent	kent	PROPN
ejpam-4021	5	56	convergence	convergence	NOUN
ejpam-4021	5	57	group	group	NOUN
ejpam-4021	5	58	induces	induce	VERB
ejpam-4021	5	59	an	an	DET
ejpam-4021	5	60	l	l	NOUN
ejpam-4021	5	61	-	-	PUNCT
ejpam-4021	5	62	valued	value	VERB
ejpam-4021	5	63	topological	topological	ADJ
ejpam-4021	5	64	group	group	NOUN
ejpam-4021	5	65	.	.	PUNCT
ejpam-4021	6	1	considering	consider	VERB
ejpam-4021	6	2	an	an	DET
ejpam-4021	6	3	l	l	NOUN
ejpam-4021	6	4	-	-	PUNCT
ejpam-4021	6	5	valued	value	VERB
ejpam-4021	6	6	subgroup	subgroup	NOUN
ejpam-4021	6	7	of	of	ADP
ejpam-4021	6	8	a	a	DET
ejpam-4021	6	9	group	group	NOUN
ejpam-4021	6	10	,	,	PUNCT
ejpam-4021	6	11	we	we	PRON
ejpam-4021	6	12	show	show	VERB
ejpam-4021	6	13	that	that	SCONJ
ejpam-4021	6	14	the	the	DET
ejpam-4021	6	15	category	category	NOUN
ejpam-4021	6	16	of	of	ADP
ejpam-4021	6	17	l	l	NOUN
ejpam-4021	6	18	-	-	PUNCT
ejpam-4021	6	19	valued	value	VERB
ejpam-4021	6	20	groups	group	NOUN
ejpam-4021	6	21	,	,	PUNCT
ejpam-4021	6	22	l	l	NOUN
ejpam-4021	6	23	-	-	PUNCT
ejpam-4021	6	24	grp	grp	PROPN
ejpam-4021	6	25	has	have	VERB
ejpam-4021	6	26	initial	initial	ADJ
ejpam-4021	6	27	structure	structure	NOUN
ejpam-4021	6	28	.	.	PUNCT
ejpam-4021	7	1	furthermore	furthermore	ADV
ejpam-4021	7	2	,	,	PUNCT
ejpam-4021	7	3	we	we	PRON
ejpam-4021	7	4	consider	consider	VERB
ejpam-4021	7	5	a	a	DET
ejpam-4021	7	6	category	category	NOUN
ejpam-4021	7	7	l	l	NOUN
ejpam-4021	7	8	-	-	NOUN
ejpam-4021	7	9	cls	cls	NOUN
ejpam-4021	7	10	of	of	ADP
ejpam-4021	7	11	l	l	NOUN
ejpam-4021	7	12	-	-	PUNCT
ejpam-4021	7	13	valued	value	VERB
ejpam-4021	7	14	closure	closure	NOUN
ejpam-4021	7	15	spaces	space	NOUN
ejpam-4021	7	16	,	,	PUNCT
ejpam-4021	7	17	obtaining	obtain	VERB
ejpam-4021	7	18	its	its	PRON
ejpam-4021	7	19	relation	relation	NOUN
ejpam-4021	7	20	with	with	ADP
ejpam-4021	7	21	l	l	NOUN
ejpam-4021	7	22	-	-	PUNCT
ejpam-4021	7	23	valued	value	VERB
ejpam-4021	7	24	moore	moore	NOUN
ejpam-4021	7	25	closure	closure	NOUN
ejpam-4021	7	26	,	,	PUNCT
ejpam-4021	7	27	and	and	CCONJ
ejpam-4021	7	28	provide	provide	VERB
ejpam-4021	7	29	examples	example	NOUN
ejpam-4021	7	30	in	in	ADP
ejpam-4021	7	31	relation	relation	NOUN
ejpam-4021	7	32	to	to	ADP
ejpam-4021	7	33	l	l	NOUN
ejpam-4021	7	34	-	-	PUNCT
ejpam-4021	7	35	valued	value	VERB
ejpam-4021	7	36	subgroups	subgroup	NOUN
ejpam-4021	7	37	that	that	PRON
ejpam-4021	7	38	produce	produce	VERB
ejpam-4021	7	39	moore	moore	PROPN
ejpam-4021	7	40	collection	collection	PROPN
ejpam-4021	7	41	.	.	PUNCT
ejpam-4021	8	1	here	here	ADV
ejpam-4021	8	2	we	we	PRON
ejpam-4021	8	3	look	look	VERB
ejpam-4021	8	4	at	at	ADP
ejpam-4021	8	5	a	a	DET
ejpam-4021	8	6	category	category	NOUN
ejpam-4021	8	7	of	of	ADP
ejpam-4021	8	8	l	l	NOUN
ejpam-4021	8	9	-	-	PUNCT
ejpam-4021	8	10	valued	value	VERB
ejpam-4021	8	11	closure	closure	NOUN
ejpam-4021	8	12	groups	group	NOUN
ejpam-4021	8	13	,	,	PUNCT
ejpam-4021	8	14	l	l	NOUN
ejpam-4021	8	15	-	-	NOUN
ejpam-4021	8	16	clgrp	clgrp	NOUN
ejpam-4021	8	17	proving	prove	VERB
ejpam-4021	8	18	that	that	SCONJ
ejpam-4021	8	19	it	it	PRON
ejpam-4021	8	20	is	be	AUX
ejpam-4021	8	21	a	a	DET
ejpam-4021	8	22	topological	topological	ADJ
ejpam-4021	8	23	category	category	NOUN
ejpam-4021	8	24	.	.	PUNCT
ejpam-4021	9	1	finally	finally	ADV
ejpam-4021	9	2	,	,	PUNCT
ejpam-4021	9	3	we	we	PRON
ejpam-4021	9	4	obtain	obtain	VERB
ejpam-4021	9	5	a	a	DET
ejpam-4021	9	6	relationship	relationship	NOUN
ejpam-4021	9	7	between	between	ADP
ejpam-4021	9	8	l	l	NOUN
ejpam-4021	9	9	-	-	PUNCT
ejpam-4021	9	10	grp	grp	PROPN
ejpam-4021	9	11	and	and	CCONJ
ejpam-4021	9	12	l	l	NOUN
ejpam-4021	9	13	-	-	NOUN
ejpam-4021	9	14	transtolgrp	transtolgrp	NOUN
ejpam-4021	9	15	,	,	PUNCT
ejpam-4021	9	16	the	the	DET
ejpam-4021	9	17	category	category	NOUN
ejpam-4021	9	18	of	of	ADP
ejpam-4021	9	19	l	l	NOUN
ejpam-4021	9	20	-	-	ADJ
ejpam-4021	9	21	transitive	transitive	ADJ
ejpam-4021	9	22	tolerance	tolerance	NOUN
ejpam-4021	9	23	groups	group	NOUN
ejpam-4021	9	24	besides	besides	SCONJ
ejpam-4021	9	25	adding	add	VERB
ejpam-4021	9	26	some	some	DET
ejpam-4021	9	27	properties	property	NOUN
ejpam-4021	9	28	of	of	ADP
ejpam-4021	9	29	l	l	NOUN
ejpam-4021	9	30	-	-	PUNCT
ejpam-4021	9	31	valued	value	VERB
ejpam-4021	9	32	closures	closure	NOUN
ejpam-4021	9	33	of	of	ADP
ejpam-4021	9	34	l	l	NOUN
ejpam-4021	9	35	-	-	PUNCT
ejpam-4021	9	36	valued	value	VERB
ejpam-4021	9	37	subgroups	subgroup	NOUN
ejpam-4021	9	38	on	on	ADP
ejpam-4021	9	39	l	l	ADV
ejpam-4021	9	40	-	-	PUNCT
ejpam-4021	9	41	valued	value	VERB
ejpam-4021	9	42	topological	topological	ADJ
ejpam-4021	9	43	groups	group	NOUN
ejpam-4021	9	44	.	.	PUNCT
ejpam-4021	10	1	2020	2020	NUM
ejpam-4021	10	2	mathematics	mathematic	NOUN
ejpam-4021	10	3	subject	subject	NOUN
ejpam-4021	10	4	classifications	classification	NOUN
ejpam-4021	10	5	:	:	PUNCT
ejpam-4021	10	6	03e72	03e72	NUM
ejpam-4021	10	7	,	,	PUNCT
ejpam-4021	10	8	20n25	20n25	NUM
ejpam-4021	10	9	,	,	PUNCT
ejpam-4021	10	10	18b05	18b05	NUM
ejpam-4021	10	11	,	,	PUNCT
ejpam-4021	10	12	54a05	54a05	NUM
ejpam-4021	10	13	,	,	PUNCT
ejpam-4021	10	14	54a20	54a20	NUM
ejpam-4021	10	15	key	key	ADJ
ejpam-4021	10	16	words	word	NOUN
ejpam-4021	10	17	and	and	CCONJ
ejpam-4021	10	18	phrases	phrase	NOUN
ejpam-4021	10	19	:	:	PUNCT
ejpam-4021	10	20	enriched	enriched	ADJ
ejpam-4021	10	21	lattice	lattice	NOUN
ejpam-4021	10	22	,	,	PUNCT
ejpam-4021	10	23	l	l	NOUN
ejpam-4021	10	24	-	-	PUNCT
ejpam-4021	10	25	valued	value	VERB
ejpam-4021	10	26	topology	topology	NOUN
ejpam-4021	10	27	,	,	PUNCT
ejpam-4021	10	28	l	l	NOUN
ejpam-4021	10	29	-	-	PUNCT
ejpam-4021	10	30	valued	value	VERB
ejpam-4021	10	31	subgroup	subgroup	NOUN
ejpam-4021	10	32	,	,	PUNCT
ejpam-4021	10	33	l	l	NOUN
ejpam-4021	10	34	-	-	PUNCT
ejpam-4021	10	35	valued	value	VERB
ejpam-4021	10	36	topological	topological	ADJ
ejpam-4021	10	37	group	group	NOUN
ejpam-4021	10	38	,	,	PUNCT
ejpam-4021	10	39	moore	moore	PROPN
ejpam-4021	10	40	collection	collection	PROPN
ejpam-4021	10	41	,	,	PUNCT
ejpam-4021	10	42	moore	moore	PROPN
ejpam-4021	10	43	closure	closure	PROPN
ejpam-4021	10	44	,	,	PUNCT
ejpam-4021	10	45	l	l	NOUN
ejpam-4021	10	46	-	-	PUNCT
ejpam-4021	10	47	valued	value	VERB
ejpam-4021	10	48	closure	closure	NOUN
ejpam-4021	10	49	group	group	NOUN
ejpam-4021	10	50	,	,	PUNCT
ejpam-4021	10	51	kent	kent	PROPN
ejpam-4021	10	52	convergence	convergence	PROPN
ejpam-4021	10	53	group	group	NOUN
ejpam-4021	10	54	,	,	PUNCT
ejpam-4021	10	55	category	category	NOUN
ejpam-4021	10	56	theory	theory	NOUN
ejpam-4021	10	57	1	1	NUM
ejpam-4021	10	58	.	.	PUNCT
ejpam-4021	11	1	introduction	introduction	NOUN
ejpam-4021	11	2	we	we	PRON
ejpam-4021	11	3	have	have	AUX
ejpam-4021	11	4	investigated	investigate	VERB
ejpam-4021	11	5	a	a	DET
ejpam-4021	11	6	notion	notion	NOUN
ejpam-4021	11	7	of	of	ADP
ejpam-4021	11	8	l	l	NOUN
ejpam-4021	11	9	-	-	PUNCT
ejpam-4021	11	10	valued	value	VERB
ejpam-4021	11	11	topological	topological	ADJ
ejpam-4021	11	12	groups	group	NOUN
ejpam-4021	11	13	in	in	ADP
ejpam-4021	11	14	[	[	X
ejpam-4021	11	15	3	3	NUM
ejpam-4021	11	16	]	]	PUNCT
ejpam-4021	11	17	,	,	PUNCT
ejpam-4021	11	18	where	where	SCONJ
ejpam-4021	11	19	we	we	PRON
ejpam-4021	11	20	considered	consider	VERB
ejpam-4021	11	21	l	l	ADV
ejpam-4021	11	22	-	-	PUNCT
ejpam-4021	11	23	valued	value	VERB
ejpam-4021	11	24	subgroup	subgroup	NOUN
ejpam-4021	11	25	of	of	ADP
ejpam-4021	11	26	a	a	DET
ejpam-4021	11	27	group	group	NOUN
ejpam-4021	11	28	.	.	PUNCT
ejpam-4021	12	1	various	various	ADJ
ejpam-4021	12	2	aspects	aspect	NOUN
ejpam-4021	12	3	of	of	ADP
ejpam-4021	12	4	l	l	NOUN
ejpam-4021	12	5	-	-	PUNCT
ejpam-4021	12	6	valued	value	VERB
ejpam-4021	12	7	subgroups	subgroup	NOUN
ejpam-4021	12	8	of	of	ADP
ejpam-4021	12	9	groups	group	NOUN
ejpam-4021	12	10	are	be	AUX
ejpam-4021	12	11	studied	study	VERB
ejpam-4021	12	12	over	over	ADP
ejpam-4021	12	13	the	the	DET
ejpam-4021	12	14	years	year	NOUN
ejpam-4021	12	15	by	by	ADP
ejpam-4021	12	16	various	various	ADJ
ejpam-4021	12	17	authors	author	NOUN
ejpam-4021	12	18	,	,	PUNCT
ejpam-4021	12	19	cf	cf	NOUN
ejpam-4021	12	20	.	.	PUNCT
ejpam-4021	13	1	[	[	X
ejpam-4021	13	2	11	11	NUM
ejpam-4021	13	3	,	,	PUNCT
ejpam-4021	13	4	23	23	NUM
ejpam-4021	13	5	,	,	PUNCT
ejpam-4021	13	6	25	25	NUM
ejpam-4021	13	7	,	,	PUNCT
ejpam-4021	13	8	26	26	NUM
ejpam-4021	13	9	,	,	PUNCT
ejpam-4021	13	10	29	29	NUM
ejpam-4021	13	11	]	]	PUNCT
ejpam-4021	13	12	but	but	CCONJ
ejpam-4021	13	13	its	its	PRON
ejpam-4021	13	14	categorical	categorical	ADJ
ejpam-4021	13	15	behaviors	behavior	NOUN
ejpam-4021	13	16	are	be	AUX
ejpam-4021	13	17	explored	explore	VERB
ejpam-4021	13	18	in	in	ADP
ejpam-4021	13	19	a	a	DET
ejpam-4021	13	20	certain	certain	ADJ
ejpam-4021	13	21	extent	extent	NOUN
ejpam-4021	13	22	in	in	ADP
ejpam-4021	13	23	recent	recent	ADJ
ejpam-4021	13	24	times	time	NOUN
ejpam-4021	14	1	[	[	X
ejpam-4021	14	2	26	26	NUM
ejpam-4021	14	3	]	]	PUNCT
ejpam-4021	14	4	,	,	PUNCT
ejpam-4021	14	5	although	although	SCONJ
ejpam-4021	14	6	the	the	DET
ejpam-4021	14	7	category	category	NOUN
ejpam-4021	14	8	of	of	ADP
ejpam-4021	14	9	fuzzy	fuzzy	ADJ
ejpam-4021	14	10	sets	set	NOUN
ejpam-4021	14	11	being	be	AUX
ejpam-4021	14	12	studied	study	VERB
ejpam-4021	14	13	for	for	ADP
ejpam-4021	14	14	quite	quite	DET
ejpam-4021	14	15	a	a	DET
ejpam-4021	14	16	long	long	ADJ
ejpam-4021	14	17	time	time	NOUN
ejpam-4021	14	18	,	,	PUNCT
ejpam-4021	14	19	cf	cf	NOUN
ejpam-4021	14	20	.	.	PUNCT
ejpam-4021	15	1	[	[	X
ejpam-4021	15	2	14	14	NUM
ejpam-4021	15	3	,	,	PUNCT
ejpam-4021	15	4	33	33	NUM
ejpam-4021	15	5	]	]	PUNCT
ejpam-4021	15	6	.	.	PUNCT
ejpam-4021	16	1	in	in	ADP
ejpam-4021	16	2	[	[	X
ejpam-4021	16	3	3	3	NUM
ejpam-4021	16	4	]	]	PUNCT
ejpam-4021	16	5	,	,	PUNCT
ejpam-4021	16	6	we	we	PRON
ejpam-4021	16	7	also	also	ADV
ejpam-4021	16	8	considered	consider	VERB
ejpam-4021	16	9	l	l	NOUN
ejpam-4021	16	10	-	-	PUNCT
ejpam-4021	16	11	valued	value	VERB
ejpam-4021	16	12	closure	closure	NOUN
ejpam-4021	16	13	of	of	ADP
ejpam-4021	16	14	an	an	DET
ejpam-4021	16	15	l	l	NOUN
ejpam-4021	16	16	-	-	PUNCT
ejpam-4021	16	17	valued	value	VERB
ejpam-4021	16	18	subgroup	subgroup	NOUN
ejpam-4021	16	19	of	of	ADP
ejpam-4021	16	20	a	a	DET
ejpam-4021	16	21	group	group	NOUN
ejpam-4021	16	22	in	in	ADP
ejpam-4021	16	23	the	the	DET
ejpam-4021	16	24	context	context	NOUN
ejpam-4021	16	25	of	of	ADP
ejpam-4021	16	26	l	l	NOUN
ejpam-4021	16	27	-	-	PUNCT
ejpam-4021	16	28	valued	value	VERB
ejpam-4021	16	29	neighborhood	neighborhood	NOUN
ejpam-4021	16	30	groups	group	NOUN
ejpam-4021	16	31	,	,	PUNCT
ejpam-4021	16	32	where	where	SCONJ
ejpam-4021	16	33	the	the	DET
ejpam-4021	16	34	lattice	lattice	NOUN
ejpam-4021	16	35	under	under	ADP
ejpam-4021	16	36	consideration	consideration	NOUN
ejpam-4021	16	37	was	be	AUX
ejpam-4021	16	38	a	a	DET
ejpam-4021	16	39	complete	complete	ADJ
ejpam-4021	16	40	mv	mv	NOUN
ejpam-4021	16	41	-	-	NOUN
ejpam-4021	16	42	algebra	algebra	NOUN
ejpam-4021	16	43	with	with	ADP
ejpam-4021	16	44	square	square	ADJ
ejpam-4021	16	45	roots	root	NOUN
ejpam-4021	16	46	.	.	PUNCT
ejpam-4021	17	1	although	although	SCONJ
ejpam-4021	17	2	our	our	PRON
ejpam-4021	17	3	main	main	ADJ
ejpam-4021	17	4	objective	objective	NOUN
ejpam-4021	17	5	of	of	ADP
ejpam-4021	17	6	this	this	DET
ejpam-4021	17	7	paper	paper	NOUN
ejpam-4021	17	8	is	be	AUX
ejpam-4021	17	9	to	to	PART
ejpam-4021	17	10	explore	explore	VERB
ejpam-4021	17	11	further	further	ADJ
ejpam-4021	17	12	l	l	NOUN
ejpam-4021	17	13	-	-	PUNCT
ejpam-4021	17	14	valued	value	VERB
ejpam-4021	17	15	subgroups	subgroup	NOUN
ejpam-4021	17	16	from	from	ADP
ejpam-4021	17	17	categorical	categorical	ADJ
ejpam-4021	17	18	view	view	NOUN
ejpam-4021	17	19	point	point	NOUN
ejpam-4021	17	20	and	and	CCONJ
ejpam-4021	17	21	study	study	NOUN
ejpam-4021	17	22	category	category	NOUN
ejpam-4021	17	23	of	of	ADP
ejpam-4021	17	24	l	l	NOUN
ejpam-4021	17	25	-	-	PUNCT
ejpam-4021	17	26	valued	value	VERB
ejpam-4021	17	27	closure	closure	NOUN
ejpam-4021	17	28	spaces	space	NOUN
ejpam-4021	17	29	vis	vis	X
ejpam-4021	17	30	-	-	PUNCT
ejpam-4021	17	31	à-vis	à-vis	ADJ
ejpam-4021	17	32	category	category	NOUN
ejpam-4021	17	33	of	of	ADP
ejpam-4021	17	34	∗corresponding	∗corresponde	VERB
ejpam-4021	17	35	author	author	NOUN
ejpam-4021	17	36	.	.	PUNCT
ejpam-4021	18	1	doi	doi	NOUN
ejpam-4021	18	2	:	:	PUNCT
ejpam-4021	18	3	https://doi.org/10.29020/nybg.ejpam.v14i3.4021	https://doi.org/10.29020/nybg.ejpam.v14i3.4021	NOUN
ejpam-4021	18	4	email	email	NOUN
ejpam-4021	18	5	addresses	address	NOUN
ejpam-4021	18	6	:	:	PUNCT
ejpam-4021	18	7	tmga1@ksu.edu.sa	tmga1@ksu.edu.sa	PROPN
ejpam-4021	18	8	(	(	PUNCT
ejpam-4021	18	9	t.m.g	t.m.g	X
ejpam-4021	18	10	.	.	PUNCT
ejpam-4021	19	1	ahsanullah	ahsanullah	NOUN
ejpam-4021	19	2	)	)	PUNCT
ejpam-4021	20	1	,	,	PUNCT
ejpam-4021	20	2	thukair@ksu.edu.sa	thukair@ksu.edu.sa	PROPN
ejpam-4021	20	3	(	(	PUNCT
ejpam-4021	20	4	fawzi	fawzi	PROPN
ejpam-4021	20	5	al	al	PROPN
ejpam-4021	20	6	-	-	PUNCT
ejpam-4021	20	7	thukair	thukair	NOUN
ejpam-4021	20	8	)	)	PUNCT
ejpam-4021	20	9	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4021	21	1	949	949	NUM
ejpam-4021	22	1	c	c	X
ejpam-4021	22	2	©	©	PROPN
ejpam-4021	22	3	2021	2021	NUM
ejpam-4021	22	4	ejpam	ejpam	VERB
ejpam-4021	22	5	all	all	DET
ejpam-4021	22	6	rights	right	NOUN
ejpam-4021	22	7	reserved	reserve	VERB
ejpam-4021	22	8	.	.	PUNCT
ejpam-4021	23	1	t	t	PROPN
ejpam-4021	23	2	m	m	PROPN
ejpam-4021	23	3	g	g	NOUN
ejpam-4021	23	4	ahsanullah	ahsanullah	NOUN
ejpam-4021	23	5	,	,	PUNCT
ejpam-4021	23	6	fawzi	fawzi	PROPN
ejpam-4021	23	7	al	al	PROPN
ejpam-4021	23	8	-	-	PUNCT
ejpam-4021	23	9	thukair	thukair	NOUN
ejpam-4021	23	10	/	/	SYM
ejpam-4021	23	11	eur	eur	NOUN
ejpam-4021	23	12	.	.	PUNCT
ejpam-4021	24	1	j.	j.	PROPN
ejpam-4021	24	2	pure	pure	PROPN
ejpam-4021	24	3	appl	appl	PROPN
ejpam-4021	24	4	.	.	PROPN
ejpam-4021	24	5	math	math	PROPN
ejpam-4021	24	6	,	,	PUNCT
ejpam-4021	24	7	14	14	NUM
ejpam-4021	24	8	(	(	PUNCT
ejpam-4021	24	9	3	3	NUM
ejpam-4021	24	10	)	)	PUNCT
ejpam-4021	24	11	(	(	PUNCT
ejpam-4021	24	12	2021	2021	NUM
ejpam-4021	24	13	)	)	PUNCT
ejpam-4021	24	14	,	,	PUNCT
ejpam-4021	24	15	949	949	NUM
ejpam-4021	24	16	-	-	SYM
ejpam-4021	24	17	968	968	NUM
ejpam-4021	24	18	950	950	NUM
ejpam-4021	24	19	l	l	NOUN
ejpam-4021	24	20	-	-	PUNCT
ejpam-4021	24	21	valued	value	VERB
ejpam-4021	24	22	closures	closure	NOUN
ejpam-4021	24	23	groups	group	NOUN
ejpam-4021	24	24	in	in	ADP
ejpam-4021	24	25	conjunction	conjunction	NOUN
ejpam-4021	24	26	with	with	ADP
ejpam-4021	24	27	l	l	ADV
ejpam-4021	24	28	-	-	PUNCT
ejpam-4021	24	29	valued	value	VERB
ejpam-4021	24	30	topological	topological	ADJ
ejpam-4021	24	31	groups	group	NOUN
ejpam-4021	25	1	,	,	PUNCT
ejpam-4021	25	2	we	we	PRON
ejpam-4021	25	3	add	add	VERB
ejpam-4021	25	4	some	some	DET
ejpam-4021	25	5	results	result	NOUN
ejpam-4021	25	6	on	on	ADP
ejpam-4021	25	7	the	the	DET
ejpam-4021	25	8	connection	connection	NOUN
ejpam-4021	25	9	of	of	ADP
ejpam-4021	25	10	l	l	PROPN
ejpam-4021	25	11	-	-	PUNCT
ejpam-4021	25	12	valued	value	VERB
ejpam-4021	25	13	topological	topological	ADJ
ejpam-4021	25	14	groups	group	NOUN
ejpam-4021	25	15	and	and	CCONJ
ejpam-4021	25	16	classical	classical	ADJ
ejpam-4021	25	17	kent	kent	NOUN
ejpam-4021	25	18	convergence	convergence	NOUN
ejpam-4021	25	19	groups	group	NOUN
ejpam-4021	25	20	.	.	PUNCT
ejpam-4021	26	1	however	however	ADV
ejpam-4021	26	2	,	,	PUNCT
ejpam-4021	26	3	we	we	PRON
ejpam-4021	26	4	mainly	mainly	ADV
ejpam-4021	26	5	focused	focus	VERB
ejpam-4021	26	6	on	on	ADP
ejpam-4021	26	7	the	the	DET
ejpam-4021	26	8	impact	impact	NOUN
ejpam-4021	26	9	of	of	ADP
ejpam-4021	26	10	l	l	NOUN
ejpam-4021	26	11	-	-	PUNCT
ejpam-4021	26	12	valued	value	VERB
ejpam-4021	26	13	closure	closure	NOUN
ejpam-4021	26	14	structures	structure	NOUN
ejpam-4021	26	15	on	on	ADP
ejpam-4021	26	16	lvalued	lvalue	VERB
ejpam-4021	26	17	topological	topological	ADJ
ejpam-4021	26	18	groups	group	NOUN
ejpam-4021	26	19	instead	instead	ADV
ejpam-4021	26	20	of	of	ADP
ejpam-4021	26	21	convergence	convergence	NOUN
ejpam-4021	26	22	groups	group	NOUN
ejpam-4021	26	23	.	.	PUNCT
ejpam-4021	27	1	we	we	PRON
ejpam-4021	27	2	arrange	arrange	VERB
ejpam-4021	27	3	our	our	PRON
ejpam-4021	27	4	work	work	NOUN
ejpam-4021	27	5	as	as	SCONJ
ejpam-4021	27	6	follows	follow	VERB
ejpam-4021	27	7	.	.	PUNCT
ejpam-4021	28	1	in	in	ADP
ejpam-4021	28	2	section	section	NOUN
ejpam-4021	28	3	2	2	NUM
ejpam-4021	28	4	,	,	PUNCT
ejpam-4021	28	5	we	we	PRON
ejpam-4021	28	6	give	give	VERB
ejpam-4021	28	7	a	a	DET
ejpam-4021	28	8	short	short	ADJ
ejpam-4021	28	9	survey	survey	NOUN
ejpam-4021	28	10	on	on	ADP
ejpam-4021	28	11	l	l	ADV
ejpam-4021	28	12	-	-	PUNCT
ejpam-4021	28	13	valued	value	VERB
ejpam-4021	28	14	structures	structure	NOUN
ejpam-4021	28	15	that	that	PRON
ejpam-4021	28	16	we	we	PRON
ejpam-4021	28	17	used	use	VERB
ejpam-4021	28	18	in	in	ADP
ejpam-4021	28	19	the	the	DET
ejpam-4021	28	20	text	text	NOUN
ejpam-4021	28	21	.	.	PUNCT
ejpam-4021	29	1	the	the	DET
ejpam-4021	29	2	idea	idea	NOUN
ejpam-4021	29	3	of	of	ADP
ejpam-4021	29	4	convergence	convergence	NOUN
ejpam-4021	29	5	spaces	space	NOUN
ejpam-4021	29	6	and	and	CCONJ
ejpam-4021	29	7	their	their	PRON
ejpam-4021	29	8	connection	connection	NOUN
ejpam-4021	29	9	to	to	ADP
ejpam-4021	29	10	topological	topological	ADJ
ejpam-4021	29	11	spaces	space	NOUN
ejpam-4021	29	12	is	be	AUX
ejpam-4021	29	13	quite	quite	ADV
ejpam-4021	29	14	old	old	ADJ
ejpam-4021	29	15	,	,	PUNCT
ejpam-4021	29	16	cf	cf	NOUN
ejpam-4021	29	17	.	.	PUNCT
ejpam-4021	30	1	[	[	X
ejpam-4021	30	2	4–7	4–7	NOUN
ejpam-4021	30	3	,	,	PUNCT
ejpam-4021	30	4	10	10	NUM
ejpam-4021	30	5	,	,	PUNCT
ejpam-4021	30	6	13	13	NUM
ejpam-4021	30	7	,	,	PUNCT
ejpam-4021	30	8	20	20	NUM
ejpam-4021	30	9	,	,	PUNCT
ejpam-4021	30	10	21	21	NUM
ejpam-4021	30	11	,	,	PUNCT
ejpam-4021	30	12	27	27	NUM
ejpam-4021	30	13	,	,	PUNCT
ejpam-4021	30	14	28	28	NUM
ejpam-4021	30	15	]	]	PUNCT
ejpam-4021	30	16	;	;	PUNCT
ejpam-4021	30	17	following	follow	VERB
ejpam-4021	30	18	the	the	DET
ejpam-4021	30	19	concept	concept	NOUN
ejpam-4021	30	20	of	of	ADP
ejpam-4021	30	21	the	the	DET
ejpam-4021	30	22	compatibility	compatibility	NOUN
ejpam-4021	30	23	of	of	ADP
ejpam-4021	30	24	convergence	convergence	NOUN
ejpam-4021	30	25	structures	structure	NOUN
ejpam-4021	30	26	with	with	ADP
ejpam-4021	30	27	groups	group	NOUN
ejpam-4021	30	28	structures	structure	NOUN
ejpam-4021	30	29	as	as	SCONJ
ejpam-4021	30	30	proposed	propose	VERB
ejpam-4021	30	31	by	by	ADP
ejpam-4021	30	32	d.	d.	PROPN
ejpam-4021	30	33	c.	c.	PROPN
ejpam-4021	30	34	kent	kent	PROPN
ejpam-4021	31	1	[	[	X
ejpam-4021	31	2	20	20	NUM
ejpam-4021	31	3	]	]	PUNCT
ejpam-4021	31	4	,	,	PUNCT
ejpam-4021	31	5	for	for	ADP
ejpam-4021	31	6	the	the	DET
ejpam-4021	31	7	first	first	ADJ
ejpam-4021	31	8	time	time	NOUN
ejpam-4021	31	9	,	,	PUNCT
ejpam-4021	31	10	we	we	PRON
ejpam-4021	31	11	explore	explore	VERB
ejpam-4021	31	12	a	a	DET
ejpam-4021	31	13	connection	connection	NOUN
ejpam-4021	31	14	between	between	ADP
ejpam-4021	31	15	the	the	DET
ejpam-4021	31	16	categories	category	NOUN
ejpam-4021	31	17	of	of	ADP
ejpam-4021	31	18	l	l	NOUN
ejpam-4021	31	19	-	-	PUNCT
ejpam-4021	31	20	valued	value	VERB
ejpam-4021	31	21	topological	topological	ADJ
ejpam-4021	31	22	groups	group	NOUN
ejpam-4021	31	23	and	and	CCONJ
ejpam-4021	31	24	kent	kent	PROPN
ejpam-4021	31	25	convergence	convergence	NOUN
ejpam-4021	31	26	groups	group	NOUN
ejpam-4021	31	27	,	,	PUNCT
ejpam-4021	31	28	this	this	PRON
ejpam-4021	31	29	is	be	AUX
ejpam-4021	31	30	done	do	VERB
ejpam-4021	31	31	in	in	ADP
ejpam-4021	31	32	section	section	NOUN
ejpam-4021	31	33	3	3	NUM
ejpam-4021	31	34	.	.	PUNCT
ejpam-4021	32	1	we	we	PRON
ejpam-4021	32	2	introduce	introduce	VERB
ejpam-4021	32	3	the	the	DET
ejpam-4021	32	4	concept	concept	NOUN
ejpam-4021	32	5	of	of	ADP
ejpam-4021	32	6	l	l	NOUN
ejpam-4021	32	7	-	-	PUNCT
ejpam-4021	32	8	valued	value	VERB
ejpam-4021	32	9	closure	closure	NOUN
ejpam-4021	32	10	space	space	NOUN
ejpam-4021	32	11	,	,	PUNCT
ejpam-4021	32	12	and	and	CCONJ
ejpam-4021	32	13	l	l	NOUN
ejpam-4021	32	14	-	-	NOUN
ejpam-4021	32	15	closure	closure	NOUN
ejpam-4021	32	16	of	of	ADP
ejpam-4021	32	17	l	l	NOUN
ejpam-4021	32	18	-	-	PUNCT
ejpam-4021	32	19	valued	value	VERB
ejpam-4021	32	20	subgroup	subgroup	NOUN
ejpam-4021	32	21	of	of	ADP
ejpam-4021	32	22	a	a	DET
ejpam-4021	32	23	group	group	NOUN
ejpam-4021	32	24	in	in	ADP
ejpam-4021	32	25	section	section	NOUN
ejpam-4021	32	26	4	4	NUM
ejpam-4021	32	27	;	;	PUNCT
ejpam-4021	32	28	we	we	PRON
ejpam-4021	32	29	also	also	ADV
ejpam-4021	32	30	introduce	introduce	VERB
ejpam-4021	32	31	here	here	ADV
ejpam-4021	32	32	a	a	DET
ejpam-4021	32	33	category	category	NOUN
ejpam-4021	32	34	of	of	ADP
ejpam-4021	32	35	l	l	NOUN
ejpam-4021	32	36	-	-	PUNCT
ejpam-4021	32	37	valued	value	VERB
ejpam-4021	32	38	closure	closure	NOUN
ejpam-4021	32	39	groups	group	NOUN
ejpam-4021	32	40	a	a	DET
ejpam-4021	32	41	topological	topological	ADJ
ejpam-4021	32	42	category	category	NOUN
ejpam-4021	32	43	.	.	PUNCT
ejpam-4021	33	1	with	with	ADP
ejpam-4021	33	2	the	the	DET
ejpam-4021	33	3	help	help	NOUN
ejpam-4021	33	4	of	of	ADP
ejpam-4021	33	5	connections	connection	NOUN
ejpam-4021	33	6	,	,	PUNCT
ejpam-4021	33	7	as	as	SCONJ
ejpam-4021	33	8	presented	present	VERB
ejpam-4021	33	9	by	by	ADP
ejpam-4021	33	10	l.	l.	PROPN
ejpam-4021	33	11	n.	n.	PROPN
ejpam-4021	33	12	stout	stout	PROPN
ejpam-4021	33	13	in	in	ADP
ejpam-4021	33	14	[	[	X
ejpam-4021	33	15	32	32	NUM
ejpam-4021	33	16	]	]	PUNCT
ejpam-4021	33	17	and	and	CCONJ
ejpam-4021	33	18	c.	c.	PROPN
ejpam-4021	33	19	l.	l.	PROPN
ejpam-4021	33	20	waker	waker	PROPN
ejpam-4021	33	21	in	in	ADP
ejpam-4021	33	22	[	[	X
ejpam-4021	33	23	33	33	NUM
ejpam-4021	33	24	]	]	PUNCT
ejpam-4021	33	25	between	between	ADP
ejpam-4021	33	26	the	the	DET
ejpam-4021	33	27	categories	category	NOUN
ejpam-4021	33	28	of	of	ADP
ejpam-4021	33	29	l	l	NOUN
ejpam-4021	33	30	-	-	ADJ
ejpam-4021	33	31	set	set	VERB
ejpam-4021	33	32	and	and	CCONJ
ejpam-4021	33	33	l	l	NOUN
ejpam-4021	33	34	-	-	NOUN
ejpam-4021	33	35	tol	tol	NOUN
ejpam-4021	33	36	,	,	PUNCT
ejpam-4021	33	37	the	the	DET
ejpam-4021	33	38	category	category	NOUN
ejpam-4021	33	39	of	of	ADP
ejpam-4021	33	40	l	l	NOUN
ejpam-4021	33	41	-	-	PUNCT
ejpam-4021	33	42	valued	value	VERB
ejpam-4021	33	43	tolerance	tolerance	NOUN
ejpam-4021	33	44	spaces	space	VERB
ejpam-4021	33	45	[	[	X
ejpam-4021	33	46	32	32	NUM
ejpam-4021	33	47	]	]	PUNCT
ejpam-4021	33	48	,	,	PUNCT
ejpam-4021	33	49	we	we	PRON
ejpam-4021	33	50	prove	prove	VERB
ejpam-4021	33	51	a	a	DET
ejpam-4021	33	52	connection	connection	NOUN
ejpam-4021	33	53	between	between	ADP
ejpam-4021	33	54	l	l	NOUN
ejpam-4021	33	55	-	-	NOUN
ejpam-4021	33	56	grp	grp	NOUN
ejpam-4021	33	57	,	,	PUNCT
ejpam-4021	33	58	category	category	NOUN
ejpam-4021	33	59	of	of	ADP
ejpam-4021	33	60	l	l	NOUN
ejpam-4021	33	61	-	-	PUNCT
ejpam-4021	33	62	valued	value	VERB
ejpam-4021	33	63	subgroups	subgroup	NOUN
ejpam-4021	33	64	,	,	PUNCT
ejpam-4021	33	65	and	and	CCONJ
ejpam-4021	33	66	l	l	X
ejpam-4021	33	67	-	-	PUNCT
ejpam-4021	33	68	valued	value	VERB
ejpam-4021	33	69	transitive	transitive	ADJ
ejpam-4021	33	70	tolerance	tolerance	NOUN
ejpam-4021	33	71	spaces	space	NOUN
ejpam-4021	33	72	,	,	PUNCT
ejpam-4021	33	73	l	l	NOUN
ejpam-4021	33	74	-	-	NOUN
ejpam-4021	33	75	trantol	trantol	NOUN
ejpam-4021	33	76	.	.	PUNCT
ejpam-4021	34	1	section	section	NOUN
ejpam-4021	34	2	5	5	NUM
ejpam-4021	34	3	is	be	AUX
ejpam-4021	34	4	devoted	devote	VERB
ejpam-4021	34	5	to	to	PART
ejpam-4021	34	6	study	study	VERB
ejpam-4021	34	7	properties	property	NOUN
ejpam-4021	34	8	of	of	ADP
ejpam-4021	34	9	l	l	NOUN
ejpam-4021	34	10	-	-	PUNCT
ejpam-4021	34	11	valued	value	VERB
ejpam-4021	34	12	closure	closure	NOUN
ejpam-4021	34	13	of	of	ADP
ejpam-4021	34	14	l	l	NOUN
ejpam-4021	34	15	-	-	PUNCT
ejpam-4021	34	16	valued	value	VERB
ejpam-4021	34	17	subgroups	subgroup	NOUN
ejpam-4021	34	18	in	in	ADP
ejpam-4021	34	19	the	the	DET
ejpam-4021	34	20	context	context	NOUN
ejpam-4021	34	21	of	of	ADP
ejpam-4021	34	22	l	l	NOUN
ejpam-4021	34	23	-	-	PUNCT
ejpam-4021	34	24	valued	value	VERB
ejpam-4021	34	25	topological	topological	ADJ
ejpam-4021	34	26	groups	group	NOUN
ejpam-4021	34	27	,	,	PUNCT
ejpam-4021	34	28	where	where	SCONJ
ejpam-4021	34	29	some	some	DET
ejpam-4021	34	30	properties	property	NOUN
ejpam-4021	34	31	from	from	ADP
ejpam-4021	34	32	groups	group	NOUN
ejpam-4021	34	33	are	be	AUX
ejpam-4021	34	34	taken	take	VERB
ejpam-4021	34	35	into	into	ADP
ejpam-4021	34	36	consideration	consideration	NOUN
ejpam-4021	34	37	.	.	PUNCT
ejpam-4021	35	1	2	2	X
ejpam-4021	35	2	.	.	X
ejpam-4021	35	3	preliminaries	preliminary	NOUN
ejpam-4021	35	4	throughout	throughout	ADP
ejpam-4021	35	5	the	the	DET
ejpam-4021	35	6	text	text	NOUN
ejpam-4021	35	7	we	we	PRON
ejpam-4021	35	8	consider	consider	VERB
ejpam-4021	35	9	l	l	NOUN
ejpam-4021	35	10	=	=	SYM
ejpam-4021	35	11	(	(	PUNCT
ejpam-4021	35	12	l,≤	l,≤	PROPN
ejpam-4021	35	13	)	)	PUNCT
ejpam-4021	35	14	a	a	DET
ejpam-4021	35	15	complete	complete	ADJ
ejpam-4021	35	16	lattice	lattice	NOUN
ejpam-4021	35	17	with	with	ADP
ejpam-4021	35	18	>	>	X
ejpam-4021	35	19	,	,	PUNCT
ejpam-4021	35	20	the	the	DET
ejpam-4021	35	21	top	top	ADJ
ejpam-4021	35	22	element	element	NOUN
ejpam-4021	35	23	and	and	CCONJ
ejpam-4021	35	24	⊥	⊥	NOUN
ejpam-4021	35	25	,	,	PUNCT
ejpam-4021	35	26	the	the	DET
ejpam-4021	35	27	bottom	bottom	ADJ
ejpam-4021	35	28	element	element	NOUN
ejpam-4021	35	29	of	of	ADP
ejpam-4021	35	30	l.	l.	PROPN
ejpam-4021	35	31	definition	definition	NOUN
ejpam-4021	35	32	1	1	NUM
ejpam-4021	35	33	.	.	PUNCT
ejpam-4021	36	1	[	[	X
ejpam-4021	36	2	16	16	NUM
ejpam-4021	36	3	,	,	PUNCT
ejpam-4021	36	4	17	17	NUM
ejpam-4021	36	5	]	]	PUNCT
ejpam-4021	36	6	a	a	DET
ejpam-4021	36	7	triple	triple	ADJ
ejpam-4021	36	8	(	(	PUNCT
ejpam-4021	36	9	l,≤	l,≤	PROPN
ejpam-4021	36	10	,	,	PUNCT
ejpam-4021	36	11	∗	∗	NOUN
ejpam-4021	36	12	)	)	PUNCT
ejpam-4021	36	13	,	,	PUNCT
ejpam-4021	36	14	where	where	SCONJ
ejpam-4021	36	15	∗	∗	NOUN
ejpam-4021	36	16	:	:	PUNCT
ejpam-4021	36	17	l×	l×	PROPN
ejpam-4021	36	18	l	l	NOUN
ejpam-4021	36	19	−→	−→	NOUN
ejpam-4021	36	20	l	l	NOUN
ejpam-4021	36	21	is	be	AUX
ejpam-4021	36	22	a	a	DET
ejpam-4021	36	23	binary	binary	ADJ
ejpam-4021	36	24	operation	operation	NOUN
ejpam-4021	36	25	on	on	ADP
ejpam-4021	36	26	l	l	NOUN
ejpam-4021	36	27	,	,	PUNCT
ejpam-4021	36	28	is	be	AUX
ejpam-4021	36	29	called	call	VERB
ejpam-4021	36	30	a	a	DET
ejpam-4021	36	31	gl	gl	NOUN
ejpam-4021	36	32	-	-	NOUN
ejpam-4021	36	33	monoid	monoid	NOUN
ejpam-4021	36	34	if	if	SCONJ
ejpam-4021	36	35	and	and	CCONJ
ejpam-4021	36	36	only	only	ADV
ejpam-4021	36	37	if	if	SCONJ
ejpam-4021	36	38	the	the	DET
ejpam-4021	36	39	following	follow	VERB
ejpam-4021	36	40	holds	hold	VERB
ejpam-4021	36	41	:	:	PUNCT
ejpam-4021	36	42	(	(	PUNCT
ejpam-4021	36	43	glm1	glm1	PROPN
ejpam-4021	36	44	)	)	PUNCT
ejpam-4021	36	45	(	(	PUNCT
ejpam-4021	36	46	l	l	NOUN
ejpam-4021	36	47	,	,	PUNCT
ejpam-4021	36	48	∗	∗	NOUN
ejpam-4021	36	49	)	)	PUNCT
ejpam-4021	36	50	is	be	AUX
ejpam-4021	36	51	a	a	DET
ejpam-4021	36	52	commutative	commutative	ADJ
ejpam-4021	36	53	semigroup	semigroup	NOUN
ejpam-4021	36	54	;	;	PUNCT
ejpam-4021	36	55	(	(	PUNCT
ejpam-4021	36	56	glm2	glm2	NOUN
ejpam-4021	36	57	)	)	PUNCT
ejpam-4021	36	58	∀α	∀α	VERB
ejpam-4021	36	59	∈	∈	PROPN
ejpam-4021	36	60	l	l	NOUN
ejpam-4021	36	61	:	:	PUNCT
ejpam-4021	36	62	α	α	X
ejpam-4021	36	63	∗	∗	NOUN
ejpam-4021	36	64	>	>	X
ejpam-4021	37	1	=	=	PUNCT
ejpam-4021	37	2	α	α	PROPN
ejpam-4021	37	3	,	,	PUNCT
ejpam-4021	37	4	(	(	PUNCT
ejpam-4021	37	5	glm3	glm3	NOUN
ejpam-4021	37	6	)	)	PUNCT
ejpam-4021	37	7	∗	∗	NOUN
ejpam-4021	37	8	is	be	AUX
ejpam-4021	37	9	distributive	distributive	ADJ
ejpam-4021	37	10	over	over	ADP
ejpam-4021	37	11	arbitrary	arbitrary	ADJ
ejpam-4021	37	12	joins	join	NOUN
ejpam-4021	37	13	:	:	PUNCT
ejpam-4021	37	14	γ	γ	PROPN
ejpam-4021	37	15	∗	∗	X
ejpam-4021	37	16	(	(	PUNCT
ejpam-4021	37	17	∨	∨	NOUN
ejpam-4021	37	18	k∈k	k∈k	NOUN
ejpam-4021	37	19	αk	αk	NOUN
ejpam-4021	37	20	)	)	PUNCT
ejpam-4021	37	21	=	=	SYM
ejpam-4021	38	1	∨	∨	PROPN
ejpam-4021	38	2	k∈k(γ	k∈k(γ	PROPN
ejpam-4021	38	3	∗	∗	NOUN
ejpam-4021	38	4	αk	αk	NOUN
ejpam-4021	38	5	)	)	PUNCT
ejpam-4021	38	6	,	,	PUNCT
ejpam-4021	38	7	for	for	ADP
ejpam-4021	38	8	k	k	PROPN
ejpam-4021	38	9	∈	∈	PROPN
ejpam-4021	38	10	k	k	PROPN
ejpam-4021	38	11	,	,	PUNCT
ejpam-4021	38	12	αk	αk	INTJ
ejpam-4021	38	13	,	,	PUNCT
ejpam-4021	38	14	γ	γ	X
ejpam-4021	38	15	∈	∈	PROPN
ejpam-4021	38	16	l	l	NOUN
ejpam-4021	38	17	;	;	PUNCT
ejpam-4021	38	18	(	(	PUNCT
ejpam-4021	38	19	glm4	glm4	NOUN
ejpam-4021	38	20	)	)	PUNCT
ejpam-4021	38	21	for	for	ADP
ejpam-4021	38	22	every	every	DET
ejpam-4021	38	23	γ	γ	PROPN
ejpam-4021	38	24	≤	≤	PROPN
ejpam-4021	38	25	α	α	NOUN
ejpam-4021	38	26	there	there	PRON
ejpam-4021	38	27	exists	exist	VERB
ejpam-4021	38	28	β	β	X
ejpam-4021	38	29	∈	∈	NOUN
ejpam-4021	38	30	l	l	NOUN
ejpam-4021	38	31	such	such	ADJ
ejpam-4021	38	32	that	that	SCONJ
ejpam-4021	38	33	γ	γ	PROPN
ejpam-4021	38	34	=	=	SYM
ejpam-4021	38	35	α	α	PROPN
ejpam-4021	38	36	∗	∗	X
ejpam-4021	38	37	β	β	X
ejpam-4021	38	38	(	(	PUNCT
ejpam-4021	38	39	divisibility	divisibility	NOUN
ejpam-4021	38	40	)	)	PUNCT
ejpam-4021	38	41	.	.	PUNCT
ejpam-4021	39	1	the	the	DET
ejpam-4021	39	2	triple	triple	ADJ
ejpam-4021	39	3	(	(	PUNCT
ejpam-4021	39	4	l,≤	l,≤	PROPN
ejpam-4021	39	5	,	,	PUNCT
ejpam-4021	39	6	∗	∗	NOUN
ejpam-4021	39	7	)	)	PUNCT
ejpam-4021	39	8	is	be	AUX
ejpam-4021	39	9	called	call	VERB
ejpam-4021	39	10	a	a	DET
ejpam-4021	39	11	commutative	commutative	ADJ
ejpam-4021	39	12	quantale	quantale	NOUN
ejpam-4021	39	13	if	if	SCONJ
ejpam-4021	39	14	(	(	PUNCT
ejpam-4021	39	15	glm1)-(glm3	glm1)-(glm3	NOUN
ejpam-4021	39	16	)	)	PUNCT
ejpam-4021	39	17	are	be	AUX
ejpam-4021	39	18	fulfilled	fulfil	VERB
ejpam-4021	39	19	.	.	PUNCT
ejpam-4021	40	1	if	if	SCONJ
ejpam-4021	40	2	∗	∗	NOUN
ejpam-4021	40	3	=	=	SYM
ejpam-4021	40	4	∧	∧	PROPN
ejpam-4021	40	5	,	,	PUNCT
ejpam-4021	40	6	then	then	ADV
ejpam-4021	40	7	the	the	DET
ejpam-4021	40	8	triple	triple	ADJ
ejpam-4021	40	9	(	(	PUNCT
ejpam-4021	40	10	l,≤,∧	l,≤,∧	PROPN
ejpam-4021	40	11	)	)	PUNCT
ejpam-4021	40	12	is	be	AUX
ejpam-4021	40	13	called	call	VERB
ejpam-4021	40	14	a	a	DET
ejpam-4021	40	15	frame	frame	NOUN
ejpam-4021	40	16	or	or	CCONJ
ejpam-4021	40	17	a	a	DET
ejpam-4021	40	18	complete	complete	ADJ
ejpam-4021	40	19	heyting	heyting	NOUN
ejpam-4021	40	20	algebra	algebra	NOUN
ejpam-4021	40	21	.	.	PUNCT
ejpam-4021	41	1	for	for	ADP
ejpam-4021	41	2	a	a	DET
ejpam-4021	41	3	commutative	commutative	ADJ
ejpam-4021	41	4	quantale	quantale	NOUN
ejpam-4021	41	5	,	,	PUNCT
ejpam-4021	41	6	the	the	DET
ejpam-4021	41	7	implication	implication	NOUN
ejpam-4021	41	8	operator→	operator→	X
ejpam-4021	41	9	,	,	PUNCT
ejpam-4021	41	10	also	also	ADV
ejpam-4021	41	11	known	know	VERB
ejpam-4021	41	12	as	as	ADP
ejpam-4021	41	13	residuum	residuum	NOUN
ejpam-4021	41	14	,	,	PUNCT
ejpam-4021	41	15	is	be	AUX
ejpam-4021	41	16	given	give	VERB
ejpam-4021	41	17	by	by	ADP
ejpam-4021	41	18	→	→	PUNCT
ejpam-4021	41	19	:	:	PUNCT
ejpam-4021	41	20	l×	l×	PROPN
ejpam-4021	41	21	l	l	NOUN
ejpam-4021	41	22	−→	−→	PROPN
ejpam-4021	41	23	l	l	NOUN
ejpam-4021	41	24	,	,	PUNCT
ejpam-4021	41	25	α→	α→	PROPN
ejpam-4021	41	26	β	β	X
ejpam-4021	41	27	=	=	SYM
ejpam-4021	41	28	∨	∨	X
ejpam-4021	41	29	{	{	PUNCT
ejpam-4021	41	30	γ	γ	PROPN
ejpam-4021	41	31	∈	∈	PROPN
ejpam-4021	41	32	l|α	l|α	NOUN
ejpam-4021	41	33	∗	∗	NOUN
ejpam-4021	41	34	γ	γ	X
ejpam-4021	41	35	≤	≤	NOUN
ejpam-4021	41	36	β	β	X
ejpam-4021	41	37	}	}	PUNCT
ejpam-4021	41	38	.	.	PUNCT
ejpam-4021	42	1	a	a	DET
ejpam-4021	42	2	gl	gl	NOUN
ejpam-4021	42	3	-	-	NOUN
ejpam-4021	42	4	monoid	monoid	NOUN
ejpam-4021	42	5	(	(	PUNCT
ejpam-4021	42	6	l,≤	l,≤	PROPN
ejpam-4021	42	7	,	,	PUNCT
ejpam-4021	42	8	∗	∗	NOUN
ejpam-4021	42	9	)	)	PUNCT
ejpam-4021	42	10	is	be	AUX
ejpam-4021	42	11	called	call	VERB
ejpam-4021	42	12	a	a	DET
ejpam-4021	42	13	complete	complete	ADJ
ejpam-4021	42	14	mv	mv	NOUN
ejpam-4021	42	15	-	-	NOUN
ejpam-4021	42	16	algebra	algebra	NOUN
ejpam-4021	42	17	if	if	SCONJ
ejpam-4021	42	18	∀α	∀α	NOUN
ejpam-4021	42	19	∈	∈	PROPN
ejpam-4021	42	20	l	l	NOUN
ejpam-4021	42	21	,	,	PUNCT
ejpam-4021	42	22	(	(	PUNCT
ejpam-4021	42	23	α→	α→	PROPN
ejpam-4021	42	24	⊥)→	⊥)→	PROPN
ejpam-4021	42	25	⊥	⊥	NOUN
ejpam-4021	42	26	=	=	SYM
ejpam-4021	42	27	α	α	PROPN
ejpam-4021	42	28	(	(	PUNCT
ejpam-4021	42	29	double	double	ADJ
ejpam-4021	42	30	negation	negation	NOUN
ejpam-4021	42	31	)	)	PUNCT
ejpam-4021	42	32	.	.	PUNCT
ejpam-4021	43	1	this	this	PRON
ejpam-4021	43	2	means	mean	VERB
ejpam-4021	43	3	,	,	PUNCT
ejpam-4021	43	4	in	in	ADP
ejpam-4021	43	5	particular	particular	ADJ
ejpam-4021	43	6	,	,	PUNCT
ejpam-4021	43	7	that	that	SCONJ
ejpam-4021	43	8	the	the	DET
ejpam-4021	43	9	unary	unary	ADJ
ejpam-4021	43	10	operation	operation	NOUN
ejpam-4021	43	11	¬	¬	PROPN
ejpam-4021	43	12	:	:	PUNCT
ejpam-4021	44	1	l	l	X
ejpam-4021	44	2	−→	−→	NOUN
ejpam-4021	44	3	l	l	NOUN
ejpam-4021	44	4	,	,	PUNCT
ejpam-4021	44	5	α	α	NOUN
ejpam-4021	44	6	7→	7→	NUM
ejpam-4021	44	7	¬α	¬α	NOUN
ejpam-4021	44	8	=	=	SYM
ejpam-4021	44	9	α	α	NOUN
ejpam-4021	44	10	→	→	SYM
ejpam-4021	44	11	⊥	⊥	PROPN
ejpam-4021	44	12	is	be	AUX
ejpam-4021	44	13	an	an	DET
ejpam-4021	44	14	order	order	NOUN
ejpam-4021	44	15	-	-	PUNCT
ejpam-4021	44	16	reversing	reverse	VERB
ejpam-4021	44	17	involution	involution	NOUN
ejpam-4021	44	18	.	.	PUNCT
ejpam-4021	45	1	t	t	PROPN
ejpam-4021	45	2	m	m	PROPN
ejpam-4021	45	3	g	g	NOUN
ejpam-4021	45	4	ahsanullah	ahsanullah	NOUN
ejpam-4021	45	5	,	,	PUNCT
ejpam-4021	45	6	fawzi	fawzi	PROPN
ejpam-4021	45	7	al	al	PROPN
ejpam-4021	45	8	-	-	PUNCT
ejpam-4021	45	9	thukair	thukair	NOUN
ejpam-4021	45	10	/	/	SYM
ejpam-4021	45	11	eur	eur	NOUN
ejpam-4021	45	12	.	.	PUNCT
ejpam-4021	46	1	j.	j.	PROPN
ejpam-4021	46	2	pure	pure	PROPN
ejpam-4021	46	3	appl	appl	PROPN
ejpam-4021	46	4	.	.	PROPN
ejpam-4021	46	5	math	math	PROPN
ejpam-4021	46	6	,	,	PUNCT
ejpam-4021	46	7	14	14	NUM
ejpam-4021	46	8	(	(	PUNCT
ejpam-4021	46	9	3	3	NUM
ejpam-4021	46	10	)	)	PUNCT
ejpam-4021	46	11	(	(	PUNCT
ejpam-4021	46	12	2021	2021	NUM
ejpam-4021	46	13	)	)	PUNCT
ejpam-4021	46	14	,	,	PUNCT
ejpam-4021	46	15	949	949	NUM
ejpam-4021	46	16	-	-	SYM
ejpam-4021	46	17	968	968	NUM
ejpam-4021	46	18	951	951	NUM
ejpam-4021	46	19	definition	definition	NOUN
ejpam-4021	46	20	2	2	NUM
ejpam-4021	46	21	.	.	PUNCT
ejpam-4021	47	1	[	[	X
ejpam-4021	47	2	16	16	NUM
ejpam-4021	47	3	,	,	PUNCT
ejpam-4021	47	4	17	17	NUM
ejpam-4021	47	5	]	]	PUNCT
ejpam-4021	47	6	a	a	DET
ejpam-4021	47	7	triple	triple	ADJ
ejpam-4021	47	8	(	(	PUNCT
ejpam-4021	47	9	l,≤,⊗	l,≤,⊗	NOUN
ejpam-4021	47	10	)	)	PUNCT
ejpam-4021	47	11	,	,	PUNCT
ejpam-4021	47	12	where	where	SCONJ
ejpam-4021	47	13	⊗	⊗	ADV
ejpam-4021	47	14	:	:	PUNCT
ejpam-4021	47	15	l×l	l×l	X
ejpam-4021	47	16	−→	−→	ADJ
ejpam-4021	47	17	l	l	NOUN
ejpam-4021	47	18	is	be	AUX
ejpam-4021	47	19	a	a	DET
ejpam-4021	47	20	binary	binary	ADJ
ejpam-4021	47	21	operation	operation	NOUN
ejpam-4021	47	22	on	on	ADP
ejpam-4021	47	23	l	l	NOUN
ejpam-4021	47	24	,	,	PUNCT
ejpam-4021	47	25	is	be	AUX
ejpam-4021	47	26	called	call	VERB
ejpam-4021	47	27	a	a	DET
ejpam-4021	47	28	co	co	NOUN
ejpam-4021	47	29	-	-	ADJ
ejpam-4021	47	30	premonoid	premonoid	ADJ
ejpam-4021	47	31	if	if	SCONJ
ejpam-4021	47	32	and	and	CCONJ
ejpam-4021	47	33	only	only	ADV
ejpam-4021	47	34	if	if	SCONJ
ejpam-4021	47	35	the	the	DET
ejpam-4021	47	36	following	follow	VERB
ejpam-4021	47	37	conditions	condition	NOUN
ejpam-4021	47	38	are	be	AUX
ejpam-4021	47	39	fulfilled	fulfil	VERB
ejpam-4021	47	40	:	:	PUNCT
ejpam-4021	47	41	(	(	PUNCT
ejpam-4021	47	42	cp1	cp1	NOUN
ejpam-4021	47	43	)	)	PUNCT
ejpam-4021	47	44	∀α1	∀α1	PROPN
ejpam-4021	47	45	,	,	PUNCT
ejpam-4021	47	46	α2	α2	ADJ
ejpam-4021	47	47	,	,	PUNCT
ejpam-4021	47	48	β1	β1	PROPN
ejpam-4021	47	49	,	,	PUNCT
ejpam-4021	47	50	β2	β2	NOUN
ejpam-4021	47	51	∈	∈	PROPN
ejpam-4021	47	52	l	l	NOUN
ejpam-4021	47	53	:	:	PUNCT
ejpam-4021	47	54	α1	α1	PROPN
ejpam-4021	47	55	≤	≤	ADJ
ejpam-4021	47	56	β1	β1	PROPN
ejpam-4021	47	57	and	and	CCONJ
ejpam-4021	47	58	α2	α2	PROPN
ejpam-4021	47	59	≤	≤	PROPN
ejpam-4021	47	60	β2	β2	PROPN
ejpam-4021	47	61	implies	imply	VERB
ejpam-4021	47	62	α1	α1	PROPN
ejpam-4021	47	63	⊗	⊗	PROPN
ejpam-4021	47	64	α2	α2	PROPN
ejpam-4021	47	65	≤	≤	PROPN
ejpam-4021	47	66	β1	β1	PROPN
ejpam-4021	47	67	⊗	⊗	PROPN
ejpam-4021	47	68	β2	β2	PROPN
ejpam-4021	47	69	;	;	PUNCT
ejpam-4021	47	70	(	(	PUNCT
ejpam-4021	47	71	cp2	cp2	NOUN
ejpam-4021	47	72	)	)	PUNCT
ejpam-4021	47	73	∀α	∀α	VERB
ejpam-4021	47	74	∈	∈	PROPN
ejpam-4021	47	75	l	l	NOUN
ejpam-4021	47	76	:	:	PUNCT
ejpam-4021	47	77	α	α	PROPN
ejpam-4021	47	78	≤	≤	PROPN
ejpam-4021	47	79	α⊗	α⊗	NOUN
ejpam-4021	47	80	>	>	X
ejpam-4021	47	81	and	and	CCONJ
ejpam-4021	47	82	α	α	NOUN
ejpam-4021	47	83	≤	≤	NOUN
ejpam-4021	47	84	>	>	PUNCT
ejpam-4021	47	85	⊗	⊗	PROPN
ejpam-4021	47	86	α	α	PROPN
ejpam-4021	47	87	.	.	PUNCT
ejpam-4021	48	1	the	the	DET
ejpam-4021	48	2	category	category	NOUN
ejpam-4021	48	3	copml	copml	PROPN
ejpam-4021	48	4	consists	consist	VERB
ejpam-4021	48	5	of	of	ADP
ejpam-4021	48	6	all	all	DET
ejpam-4021	48	7	co	co	NOUN
ejpam-4021	48	8	-	-	NOUN
ejpam-4021	48	9	premonoids	premonoid	NOUN
ejpam-4021	48	10	as	as	ADP
ejpam-4021	48	11	objects	object	NOUN
ejpam-4021	48	12	and	and	CCONJ
ejpam-4021	48	13	morphisms	morphism	NOUN
ejpam-4021	48	14	as	as	ADP
ejpam-4021	48	15	the	the	DET
ejpam-4021	48	16	mappings	mapping	NOUN
ejpam-4021	48	17	ι	ι	X
ejpam-4021	48	18	:	:	PUNCT
ejpam-4021	48	19	(	(	PUNCT
ejpam-4021	48	20	l1,≤1,⊗1	l1,≤1,⊗1	NOUN
ejpam-4021	48	21	)	)	PUNCT
ejpam-4021	48	22	−→	−→	NOUN
ejpam-4021	48	23	(	(	PUNCT
ejpam-4021	48	24	l2,≤2,⊗2	l2,≤2,⊗2	ADJ
ejpam-4021	48	25	)	)	PUNCT
ejpam-4021	48	26	satisfying	satisfy	VERB
ejpam-4021	48	27	the	the	DET
ejpam-4021	48	28	following	follow	VERB
ejpam-4021	48	29	conditions	condition	NOUN
ejpam-4021	48	30	:	:	PUNCT
ejpam-4021	48	31	(	(	PUNCT
ejpam-4021	48	32	cpm1	cpm1	NOUN
ejpam-4021	48	33	)	)	PUNCT
ejpam-4021	48	34	ι	ι	PROPN
ejpam-4021	48	35	preserves	preserve	VERB
ejpam-4021	48	36	arbitrary	arbitrary	ADJ
ejpam-4021	48	37	joins	join	NOUN
ejpam-4021	48	38	;	;	PUNCT
ejpam-4021	48	39	(	(	PUNCT
ejpam-4021	48	40	cpm2	cpm2	PROPN
ejpam-4021	48	41	)	)	PUNCT
ejpam-4021	49	1	ι	ι	PROPN
ejpam-4021	49	2	(	(	PUNCT
ejpam-4021	49	3	α⊗1	α⊗1	NOUN
ejpam-4021	49	4	α	α	NOUN
ejpam-4021	49	5	′	′	NOUN
ejpam-4021	49	6	)	)	PUNCT
ejpam-4021	50	1	=	=	SYM
ejpam-4021	50	2	ι(α)⊗2	ι(α)⊗2	NOUN
ejpam-4021	50	3	ι(α	ι(α	NOUN
ejpam-4021	50	4	′	′	NUM
ejpam-4021	50	5	)	)	PUNCT
ejpam-4021	50	6	,	,	PUNCT
ejpam-4021	50	7	∀α	∀α	NOUN
ejpam-4021	50	8	,	,	PUNCT
ejpam-4021	50	9	α′	α′	NUM
ejpam-4021	50	10	∈	∈	PROPN
ejpam-4021	50	11	l1	l1	PROPN
ejpam-4021	50	12	;	;	PUNCT
ejpam-4021	50	13	(	(	PUNCT
ejpam-4021	50	14	cpm3	cpm3	PROPN
ejpam-4021	50	15	)	)	PUNCT
ejpam-4021	51	1	ι	ι	PROPN
ejpam-4021	51	2	preserves	preserve	VERB
ejpam-4021	51	3	universal	universal	ADJ
ejpam-4021	51	4	upper	upper	ADJ
ejpam-4021	51	5	bounds	bound	NOUN
ejpam-4021	51	6	;	;	PUNCT
ejpam-4021	51	7	i.e.	i.e.	X
ejpam-4021	51	8	,	,	PUNCT
ejpam-4021	51	9	ι	ι	X
ejpam-4021	51	10	(	(	PUNCT
ejpam-4021	51	11	>	>	PUNCT
ejpam-4021	51	12	)	)	PUNCT
ejpam-4021	52	1	=	=	PUNCT
ejpam-4021	52	2	>	>	PUNCT
ejpam-4021	52	3	.	.	PUNCT
ejpam-4021	53	1	definition	definition	NOUN
ejpam-4021	53	2	3	3	NUM
ejpam-4021	53	3	.	.	PUNCT
ejpam-4021	54	1	[	[	X
ejpam-4021	54	2	16	16	NUM
ejpam-4021	54	3	,	,	PUNCT
ejpam-4021	54	4	17	17	NUM
ejpam-4021	54	5	]	]	PUNCT
ejpam-4021	54	6	a	a	DET
ejpam-4021	54	7	co	co	NOUN
ejpam-4021	54	8	-	-	ADJ
ejpam-4021	54	9	premonoid	premonoid	ADJ
ejpam-4021	54	10	(	(	PUNCT
ejpam-4021	54	11	l,≤,⊗	l,≤,⊗	NOUN
ejpam-4021	54	12	)	)	PUNCT
ejpam-4021	54	13	is	be	AUX
ejpam-4021	54	14	called	call	VERB
ejpam-4021	54	15	a	a	DET
ejpam-4021	54	16	cl	cl	NOUN
ejpam-4021	54	17	-	-	ADJ
ejpam-4021	54	18	premonoid	premonoid	ADJ
ejpam-4021	54	19	if	if	SCONJ
ejpam-4021	54	20	and	and	CCONJ
ejpam-4021	54	21	only	only	ADV
ejpam-4021	54	22	if	if	SCONJ
ejpam-4021	54	23	(	(	PUNCT
ejpam-4021	54	24	cp3	cp3	NOUN
ejpam-4021	54	25	)	)	PUNCT
ejpam-4021	54	26	γ	γ	PROPN
ejpam-4021	54	27	⊗	⊗	PROPN
ejpam-4021	54	28	(	(	PUNCT
ejpam-4021	54	29	∨	∨	NOUN
ejpam-4021	54	30	k∈k	k∈k	NOUN
ejpam-4021	54	31	αk	αk	NOUN
ejpam-4021	54	32	)	)	PUNCT
ejpam-4021	54	33	=	=	SYM
ejpam-4021	55	1	∨	∨	PROPN
ejpam-4021	55	2	k∈k(γ	k∈k(γ	PROPN
ejpam-4021	55	3	⊗	⊗	PROPN
ejpam-4021	55	4	αk	αk	NOUN
ejpam-4021	55	5	)	)	PUNCT
ejpam-4021	55	6	,	,	PUNCT
ejpam-4021	55	7	and	and	CCONJ
ejpam-4021	55	8	(	(	PUNCT
ejpam-4021	55	9	∨	∨	NOUN
ejpam-4021	55	10	k∈k	k∈k	NOUN
ejpam-4021	55	11	αk	αk	NOUN
ejpam-4021	55	12	)	)	PUNCT
ejpam-4021	55	13	⊗	⊗	PROPN
ejpam-4021	55	14	γ	γ	X
ejpam-4021	55	15	=	=	SYM
ejpam-4021	55	16	∨	∨	NUM
ejpam-4021	55	17	k∈k	k∈k	NOUN
ejpam-4021	55	18	(	(	PUNCT
ejpam-4021	55	19	αk	αk	ADP
ejpam-4021	55	20	⊗	⊗	PROPN
ejpam-4021	55	21	γ	γ	PROPN
ejpam-4021	55	22	)	)	PUNCT
ejpam-4021	55	23	for	for	ADP
ejpam-4021	55	24	k	k	PROPN
ejpam-4021	55	25	6=	6=	PROPN
ejpam-4021	55	26	∅	∅	NOUN
ejpam-4021	55	27	,	,	PUNCT
ejpam-4021	55	28	k	k	PROPN
ejpam-4021	55	29	∈	∈	PROPN
ejpam-4021	55	30	k	k	PROPN
ejpam-4021	55	31	,	,	PUNCT
ejpam-4021	55	32	αk	αk	INTJ
ejpam-4021	55	33	,	,	PUNCT
ejpam-4021	55	34	γ	γ	PROPN
ejpam-4021	55	35	∈	∈	PROPN
ejpam-4021	55	36	l	l	NOUN
ejpam-4021	55	37	,	,	PUNCT
ejpam-4021	55	38	is	be	AUX
ejpam-4021	55	39	satisfied	satisfied	ADJ
ejpam-4021	55	40	.	.	PUNCT
ejpam-4021	56	1	definition	definition	NOUN
ejpam-4021	56	2	4	4	NUM
ejpam-4021	56	3	.	.	PUNCT
ejpam-4021	57	1	[	[	X
ejpam-4021	57	2	16	16	NUM
ejpam-4021	57	3	,	,	PUNCT
ejpam-4021	57	4	17	17	NUM
ejpam-4021	57	5	]	]	PUNCT
ejpam-4021	57	6	the	the	DET
ejpam-4021	57	7	quadruple	quadruple	NOUN
ejpam-4021	57	8	(	(	PUNCT
ejpam-4021	57	9	l,≤	l,≤	PROPN
ejpam-4021	57	10	,	,	PUNCT
ejpam-4021	57	11	∗,⊗	∗,⊗	PROPN
ejpam-4021	57	12	)	)	PUNCT
ejpam-4021	57	13	is	be	AUX
ejpam-4021	57	14	called	call	VERB
ejpam-4021	57	15	an	an	DET
ejpam-4021	57	16	enriched	enriched	ADJ
ejpam-4021	57	17	cl	cl	NOUN
ejpam-4021	57	18	-	-	ADJ
ejpam-4021	57	19	premonoid	premonoid	ADJ
ejpam-4021	57	20	if	if	SCONJ
ejpam-4021	57	21	and	and	CCONJ
ejpam-4021	57	22	only	only	ADV
ejpam-4021	57	23	if	if	SCONJ
ejpam-4021	57	24	the	the	DET
ejpam-4021	57	25	following	follow	VERB
ejpam-4021	57	26	are	be	AUX
ejpam-4021	57	27	fulfilled	fulfil	VERB
ejpam-4021	57	28	:	:	PUNCT
ejpam-4021	57	29	(	(	PUNCT
ejpam-4021	57	30	clp1	clp1	PROPN
ejpam-4021	57	31	)	)	PUNCT
ejpam-4021	57	32	(	(	PUNCT
ejpam-4021	57	33	l,≤	l,≤	PROPN
ejpam-4021	57	34	,	,	PUNCT
ejpam-4021	57	35	∗	∗	NOUN
ejpam-4021	57	36	)	)	PUNCT
ejpam-4021	57	37	is	be	AUX
ejpam-4021	57	38	a	a	DET
ejpam-4021	57	39	gl	gl	NOUN
ejpam-4021	57	40	-	-	NOUN
ejpam-4021	57	41	monoid	monoid	NOUN
ejpam-4021	57	42	;	;	PUNCT
ejpam-4021	57	43	(	(	PUNCT
ejpam-4021	57	44	clp2	clp2	NOUN
ejpam-4021	57	45	)	)	PUNCT
ejpam-4021	57	46	(	(	PUNCT
ejpam-4021	57	47	l,≤,⊗	l,≤,⊗	NOUN
ejpam-4021	57	48	)	)	PUNCT
ejpam-4021	57	49	is	be	AUX
ejpam-4021	57	50	a	a	DET
ejpam-4021	57	51	cl	cl	NOUN
ejpam-4021	57	52	-	-	ADJ
ejpam-4021	57	53	premonoid	premonoid	ADJ
ejpam-4021	57	54	;	;	PUNCT
ejpam-4021	57	55	(	(	PUNCT
ejpam-4021	57	56	clp3	clp3	NOUN
ejpam-4021	57	57	)	)	PUNCT
ejpam-4021	57	58	∗	∗	NOUN
ejpam-4021	57	59	is	be	AUX
ejpam-4021	57	60	dominated	dominate	VERB
ejpam-4021	57	61	by	by	ADP
ejpam-4021	57	62	⊗	⊗	PROPN
ejpam-4021	57	63	:	:	PUNCT
ejpam-4021	57	64	∀α	∀α	NOUN
ejpam-4021	57	65	,	,	PUNCT
ejpam-4021	57	66	β	β	X
ejpam-4021	57	67	,	,	PUNCT
ejpam-4021	57	68	γ	γ	PROPN
ejpam-4021	57	69	,	,	PUNCT
ejpam-4021	57	70	δ	δ	PROPN
ejpam-4021	57	71	∈	∈	PROPN
ejpam-4021	57	72	l	l	NOUN
ejpam-4021	57	73	,	,	PUNCT
ejpam-4021	57	74	(	(	PUNCT
ejpam-4021	57	75	α⊗	α⊗	NOUN
ejpam-4021	57	76	β	β	NOUN
ejpam-4021	57	77	)	)	PUNCT
ejpam-4021	57	78	∗	∗	NOUN
ejpam-4021	57	79	(	(	PUNCT
ejpam-4021	57	80	γ	γ	PROPN
ejpam-4021	57	81	⊗	⊗	PROPN
ejpam-4021	57	82	δ	δ	PROPN
ejpam-4021	57	83	)	)	PUNCT
ejpam-4021	57	84	≤	≤	NOUN
ejpam-4021	57	85	(	(	PUNCT
ejpam-4021	57	86	α	α	X
ejpam-4021	57	87	∗	∗	NOUN
ejpam-4021	57	88	γ)⊗	γ)⊗	PROPN
ejpam-4021	57	89	(	(	PUNCT
ejpam-4021	57	90	β	β	X
ejpam-4021	57	91	∗	∗	X
ejpam-4021	57	92	δ	δ	PROPN
ejpam-4021	57	93	)	)	PUNCT
ejpam-4021	57	94	.	.	PUNCT
ejpam-4021	58	1	definition	definition	NOUN
ejpam-4021	58	2	5	5	NUM
ejpam-4021	58	3	.	.	PUNCT
ejpam-4021	59	1	[	[	X
ejpam-4021	59	2	16	16	NUM
ejpam-4021	59	3	,	,	PUNCT
ejpam-4021	59	4	17	17	NUM
ejpam-4021	59	5	]	]	PUNCT
ejpam-4021	59	6	a	a	DET
ejpam-4021	59	7	gl	gl	NOUN
ejpam-4021	59	8	-	-	NOUN
ejpam-4021	59	9	monoid	monoid	NOUN
ejpam-4021	59	10	(	(	PUNCT
ejpam-4021	59	11	l,≤	l,≤	PROPN
ejpam-4021	59	12	,	,	PUNCT
ejpam-4021	59	13	∗	∗	NOUN
ejpam-4021	59	14	)	)	PUNCT
ejpam-4021	59	15	is	be	AUX
ejpam-4021	59	16	said	say	VERB
ejpam-4021	59	17	to	to	PART
ejpam-4021	59	18	have	have	VERB
ejpam-4021	59	19	square	square	ADJ
ejpam-4021	59	20	roots	root	NOUN
ejpam-4021	59	21	if	if	SCONJ
ejpam-4021	59	22	and	and	CCONJ
ejpam-4021	59	23	only	only	ADV
ejpam-4021	59	24	if	if	SCONJ
ejpam-4021	59	25	there	there	PRON
ejpam-4021	59	26	exists	exist	VERB
ejpam-4021	59	27	a	a	DET
ejpam-4021	59	28	unary	unary	ADJ
ejpam-4021	59	29	operator	operator	NOUN
ejpam-4021	59	30	s	s	PART
ejpam-4021	59	31	:	:	PUNCT
ejpam-4021	59	32	l	l	NOUN
ejpam-4021	59	33	−→	−→	NOUN
ejpam-4021	59	34	l	l	NOUN
ejpam-4021	59	35	such	such	ADJ
ejpam-4021	59	36	that	that	SCONJ
ejpam-4021	59	37	the	the	DET
ejpam-4021	59	38	conditions	condition	NOUN
ejpam-4021	59	39	below	below	ADV
ejpam-4021	59	40	are	be	AUX
ejpam-4021	59	41	satisfied	satisfied	ADJ
ejpam-4021	59	42	:	:	PUNCT
ejpam-4021	59	43	(	(	PUNCT
ejpam-4021	59	44	s1	s1	NOUN
ejpam-4021	59	45	)	)	PUNCT
ejpam-4021	59	46	s(α	s(α	NOUN
ejpam-4021	59	47	)	)	PUNCT
ejpam-4021	59	48	∗	∗	NOUN
ejpam-4021	59	49	s(α	s(α	NOUN
ejpam-4021	59	50	)	)	PUNCT
ejpam-4021	60	1	=	=	SYM
ejpam-4021	60	2	α	α	X
ejpam-4021	60	3	,	,	PUNCT
ejpam-4021	60	4	∀α	∀α	X
ejpam-4021	60	5	∈	∈	PROPN
ejpam-4021	60	6	l	l	NOUN
ejpam-4021	60	7	;	;	PUNCT
ejpam-4021	60	8	(	(	PUNCT
ejpam-4021	60	9	s2	s2	PROPN
ejpam-4021	60	10	)	)	PUNCT
ejpam-4021	60	11	β	β	PROPN
ejpam-4021	60	12	∗	∗	X
ejpam-4021	60	13	β	β	X
ejpam-4021	60	14	≤	≤	ADJ
ejpam-4021	60	15	α	α	PROPN
ejpam-4021	60	16	implies	imply	VERB
ejpam-4021	60	17	β	β	X
ejpam-4021	60	18	≤	≤	X
ejpam-4021	60	19	s(α	s(α	NOUN
ejpam-4021	60	20	)	)	PUNCT
ejpam-4021	60	21	.	.	PUNCT
ejpam-4021	61	1	since	since	SCONJ
ejpam-4021	61	2	the	the	DET
ejpam-4021	61	3	formation	formation	NOUN
ejpam-4021	61	4	of	of	ADP
ejpam-4021	61	5	square	square	ADJ
ejpam-4021	61	6	roots	root	NOUN
ejpam-4021	61	7	is	be	AUX
ejpam-4021	61	8	uniquely	uniquely	ADV
ejpam-4021	61	9	determined	determine	VERB
ejpam-4021	61	10	by	by	ADP
ejpam-4021	61	11	(	(	PUNCT
ejpam-4021	61	12	s1	s1	NOUN
ejpam-4021	61	13	)	)	PUNCT
ejpam-4021	61	14	and	and	CCONJ
ejpam-4021	61	15	(	(	PUNCT
ejpam-4021	61	16	s2	s2	PROPN
ejpam-4021	61	17	)	)	PUNCT
ejpam-4021	61	18	,	,	PUNCT
ejpam-4021	61	19	s(α	s(α	NOUN
ejpam-4021	61	20	)	)	PUNCT
ejpam-4021	61	21	is	be	AUX
ejpam-4021	61	22	also	also	ADV
ejpam-4021	61	23	written	write	VERB
ejpam-4021	61	24	as	as	ADP
ejpam-4021	61	25	α	α	PROPN
ejpam-4021	61	26	1	1	NUM
ejpam-4021	61	27	2	2	NUM
ejpam-4021	61	28	.	.	PUNCT
ejpam-4021	62	1	a	a	DET
ejpam-4021	62	2	gl	gl	NOUN
ejpam-4021	62	3	-	-	NOUN
ejpam-4021	62	4	monoid	monoid	NOUN
ejpam-4021	62	5	with	with	ADP
ejpam-4021	62	6	square	square	ADJ
ejpam-4021	62	7	roots	root	NOUN
ejpam-4021	62	8	satisfies	satisfie	NOUN
ejpam-4021	62	9	(	(	PUNCT
ejpam-4021	62	10	s3	s3	PROPN
ejpam-4021	62	11	)	)	PUNCT
ejpam-4021	62	12	if	if	SCONJ
ejpam-4021	62	13	it	it	PRON
ejpam-4021	62	14	fulfills	fulfill	VERB
ejpam-4021	62	15	the	the	DET
ejpam-4021	62	16	following	following	ADJ
ejpam-4021	62	17	axiom	axiom	NOUN
ejpam-4021	62	18	:	:	PUNCT
ejpam-4021	62	19	(	(	PUNCT
ejpam-4021	62	20	s3	s3	PROPN
ejpam-4021	62	21	)	)	PUNCT
ejpam-4021	62	22	(	(	PUNCT
ejpam-4021	63	1	α	α	X
ejpam-4021	63	2	∗	∗	NOUN
ejpam-4021	63	3	β	β	NOUN
ejpam-4021	63	4	)	)	PUNCT
ejpam-4021	63	5	1	1	NUM
ejpam-4021	63	6	2	2	NUM
ejpam-4021	63	7	=	=	SYM
ejpam-4021	63	8	(	(	PUNCT
ejpam-4021	63	9	α	α	NOUN
ejpam-4021	63	10	1	1	NUM
ejpam-4021	63	11	2	2	NUM
ejpam-4021	63	12	∗	∗	NOUN
ejpam-4021	63	13	β	β	NOUN
ejpam-4021	63	14	1	1	NUM
ejpam-4021	63	15	2	2	NUM
ejpam-4021	63	16	)	)	PUNCT
ejpam-4021	63	17	∨	∨	NOUN
ejpam-4021	63	18	⊥	⊥	NUM
ejpam-4021	63	19	1	1	NUM
ejpam-4021	63	20	2	2	NUM
ejpam-4021	63	21	,	,	PUNCT
ejpam-4021	63	22	∀α	∀α	NOUN
ejpam-4021	63	23	,	,	PUNCT
ejpam-4021	63	24	β	β	X
ejpam-4021	63	25	∈	∈	PROPN
ejpam-4021	63	26	l.	l.	NOUN
ejpam-4021	63	27	if	if	SCONJ
ejpam-4021	63	28	l	l	NOUN
ejpam-4021	63	29	=	=	SYM
ejpam-4021	63	30	(	(	PUNCT
ejpam-4021	63	31	l,≤	l,≤	PROPN
ejpam-4021	63	32	,	,	PUNCT
ejpam-4021	63	33	∗	∗	NOUN
ejpam-4021	63	34	)	)	PUNCT
ejpam-4021	63	35	is	be	AUX
ejpam-4021	63	36	a	a	DET
ejpam-4021	63	37	gl	gl	NOUN
ejpam-4021	63	38	-	-	NOUN
ejpam-4021	63	39	monoid	monoid	NOUN
ejpam-4021	63	40	with	with	ADP
ejpam-4021	63	41	square	square	ADJ
ejpam-4021	63	42	roots	root	NOUN
ejpam-4021	63	43	,	,	PUNCT
ejpam-4021	63	44	then	then	ADV
ejpam-4021	63	45	the	the	DET
ejpam-4021	63	46	monoidal	monoidal	ADJ
ejpam-4021	63	47	mean	mean	NOUN
ejpam-4021	63	48	operator	operator	NOUN
ejpam-4021	63	49	~	~	PUNCT
ejpam-4021	63	50	:	:	PUNCT
ejpam-4021	63	51	l×	l×	PROPN
ejpam-4021	63	52	l	l	NOUN
ejpam-4021	63	53	−→	−→	NOUN
ejpam-4021	63	54	l	l	NOUN
ejpam-4021	63	55	is	be	AUX
ejpam-4021	63	56	given	give	VERB
ejpam-4021	63	57	by	by	ADP
ejpam-4021	63	58	α	α	X
ejpam-4021	63	59	~	~	PUNCT
ejpam-4021	63	60	β	β	X
ejpam-4021	63	61	=	=	PUNCT
ejpam-4021	63	62	α	α	PROPN
ejpam-4021	63	63	1	1	NUM
ejpam-4021	63	64	2	2	NUM
ejpam-4021	63	65	∗	∗	NOUN
ejpam-4021	63	66	β	β	NOUN
ejpam-4021	63	67	1	1	NUM
ejpam-4021	63	68	2	2	NUM
ejpam-4021	63	69	,	,	PUNCT
ejpam-4021	63	70	∀α	∀α	NOUN
ejpam-4021	63	71	,	,	PUNCT
ejpam-4021	63	72	β	β	X
ejpam-4021	63	73	∈	∈	PROPN
ejpam-4021	63	74	l.	l.	NOUN
ejpam-4021	63	75	an	an	DET
ejpam-4021	63	76	enriched	enriched	ADJ
ejpam-4021	63	77	cl	cl	NOUN
ejpam-4021	63	78	-	-	ADJ
ejpam-4021	63	79	premonoid	premonoid	ADJ
ejpam-4021	63	80	l	l	NOUN
ejpam-4021	63	81	=	=	SYM
ejpam-4021	63	82	(	(	PUNCT
ejpam-4021	63	83	l,≤	l,≤	PROPN
ejpam-4021	63	84	,	,	PUNCT
ejpam-4021	63	85	∗,⊗	∗,⊗	PROPN
ejpam-4021	63	86	)	)	PUNCT
ejpam-4021	63	87	is	be	AUX
ejpam-4021	63	88	said	say	VERB
ejpam-4021	63	89	to	to	PART
ejpam-4021	63	90	be	be	AUX
ejpam-4021	63	91	pseudo	pseudo	NOUN
ejpam-4021	63	92	-	-	ADJ
ejpam-4021	63	93	bisymmetric	bisymmetric	ADJ
ejpam-4021	63	94	if	if	SCONJ
ejpam-4021	63	95	it	it	PRON
ejpam-4021	63	96	satisfies	satisfy	VERB
ejpam-4021	63	97	the	the	DET
ejpam-4021	63	98	following	following	ADJ
ejpam-4021	63	99	axiom	axiom	NOUN
ejpam-4021	63	100	:	:	PUNCT
ejpam-4021	63	101	(	(	PUNCT
ejpam-4021	63	102	α	α	X
ejpam-4021	63	103	∗	∗	NOUN
ejpam-4021	63	104	β	β	NOUN
ejpam-4021	63	105	)	)	PUNCT
ejpam-4021	64	1	⊗	⊗	PROPN
ejpam-4021	64	2	(	(	PUNCT
ejpam-4021	64	3	γ	γ	PROPN
ejpam-4021	64	4	∗	∗	X
ejpam-4021	64	5	δ	δ	PROPN
ejpam-4021	64	6	)	)	PUNCT
ejpam-4021	64	7	=	=	SYM
ejpam-4021	65	1	(	(	PUNCT
ejpam-4021	65	2	(	(	PUNCT
ejpam-4021	65	3	α⊗	α⊗	PROPN
ejpam-4021	65	4	γ	γ	PROPN
ejpam-4021	65	5	)	)	PUNCT
ejpam-4021	65	6	∗	∗	NOUN
ejpam-4021	65	7	(	(	PUNCT
ejpam-4021	65	8	β	β	PROPN
ejpam-4021	65	9	⊗	⊗	PROPN
ejpam-4021	65	10	δ	δ	PROPN
ejpam-4021	65	11	)	)	PUNCT
ejpam-4021	65	12	)	)	PUNCT
ejpam-4021	65	13	∨	∨	NUM
ejpam-4021	65	14	(	(	PUNCT
ejpam-4021	65	15	(	(	PUNCT
ejpam-4021	65	16	α⊗⊥	α⊗⊥	NOUN
ejpam-4021	65	17	)	)	PUNCT
ejpam-4021	65	18	∗	∗	NOUN
ejpam-4021	65	19	(	(	PUNCT
ejpam-4021	65	20	β	β	PROPN
ejpam-4021	65	21	⊗	⊗	PROPN
ejpam-4021	65	22	>	>	PROPN
ejpam-4021	65	23	)	)	PUNCT
ejpam-4021	65	24	)	)	PUNCT
ejpam-4021	66	1	∨	∨	NUM
ejpam-4021	66	2	(	(	PUNCT
ejpam-4021	66	3	(	(	PUNCT
ejpam-4021	66	4	⊥⊗	⊥⊗	X
ejpam-4021	66	5	γ	γ	NOUN
ejpam-4021	66	6	)	)	PUNCT
ejpam-4021	66	7	∗	∗	NOUN
ejpam-4021	66	8	(	(	PUNCT
ejpam-4021	66	9	>	>	PROPN
ejpam-4021	66	10	⊗	⊗	PROPN
ejpam-4021	66	11	δ	δ	PROPN
ejpam-4021	66	12	)	)	PUNCT
ejpam-4021	66	13	)	)	PUNCT
ejpam-4021	66	14	,	,	PUNCT
ejpam-4021	66	15	∀α	∀α	NOUN
ejpam-4021	66	16	,	,	PUNCT
ejpam-4021	66	17	β	β	X
ejpam-4021	66	18	,	,	PUNCT
ejpam-4021	66	19	γ	γ	PROPN
ejpam-4021	66	20	,	,	PUNCT
ejpam-4021	66	21	δ	δ	PROPN
ejpam-4021	66	22	∈	∈	PROPN
ejpam-4021	66	23	l.	l.	NOUN
ejpam-4021	66	24	remark	remark	PROPN
ejpam-4021	66	25	1	1	NUM
ejpam-4021	66	26	.	.	PUNCT
ejpam-4021	67	1	[	[	X
ejpam-4021	67	2	16	16	NUM
ejpam-4021	67	3	,	,	PUNCT
ejpam-4021	67	4	17	17	NUM
ejpam-4021	67	5	]	]	PUNCT
ejpam-4021	67	6	(	(	PUNCT
ejpam-4021	67	7	1	1	X
ejpam-4021	67	8	)	)	PUNCT
ejpam-4021	67	9	if	if	SCONJ
ejpam-4021	67	10	(	(	PUNCT
ejpam-4021	67	11	l,≤	l,≤	PROPN
ejpam-4021	67	12	,	,	PUNCT
ejpam-4021	67	13	∗	∗	NOUN
ejpam-4021	67	14	)	)	PUNCT
ejpam-4021	67	15	is	be	AUX
ejpam-4021	67	16	a	a	DET
ejpam-4021	67	17	gl	gl	NOUN
ejpam-4021	67	18	-	-	NOUN
ejpam-4021	67	19	monoid	monoid	NOUN
ejpam-4021	67	20	with	with	ADP
ejpam-4021	67	21	square	square	ADJ
ejpam-4021	67	22	roots	root	NOUN
ejpam-4021	67	23	,	,	PUNCT
ejpam-4021	67	24	satisfying	satisfy	VERB
ejpam-4021	67	25	(	(	PUNCT
ejpam-4021	67	26	s3	s3	PROPN
ejpam-4021	67	27	)	)	PUNCT
ejpam-4021	67	28	,	,	PUNCT
ejpam-4021	67	29	and	and	CCONJ
ejpam-4021	67	30	⊗	⊗	PROPN
ejpam-4021	67	31	is	be	AUX
ejpam-4021	67	32	the	the	DET
ejpam-4021	67	33	monoidal	monoidal	ADJ
ejpam-4021	67	34	mean	mean	NOUN
ejpam-4021	67	35	operator	operator	NOUN
ejpam-4021	67	36	~	~	PUNCT
ejpam-4021	67	37	,	,	PUNCT
ejpam-4021	67	38	then	then	ADV
ejpam-4021	67	39	the	the	DET
ejpam-4021	67	40	quadruple	quadruple	NOUN
ejpam-4021	67	41	(	(	PUNCT
ejpam-4021	67	42	l,≤	l,≤	PROPN
ejpam-4021	67	43	,	,	PUNCT
ejpam-4021	67	44	∗,⊗	∗,⊗	PROPN
ejpam-4021	67	45	)	)	PUNCT
ejpam-4021	67	46	is	be	AUX
ejpam-4021	67	47	pseudo	pseudo	NOUN
ejpam-4021	67	48	-	-	NOUN
ejpam-4021	67	49	bisymmetric	bisymmetric	ADJ
ejpam-4021	67	50	.	.	PUNCT
ejpam-4021	68	1	(	(	PUNCT
ejpam-4021	68	2	2	2	X
ejpam-4021	68	3	)	)	PUNCT
ejpam-4021	68	4	if	if	SCONJ
ejpam-4021	68	5	the	the	DET
ejpam-4021	68	6	cl	cl	NOUN
ejpam-4021	68	7	-	-	ADJ
ejpam-4021	68	8	premonoid	premonoid	ADJ
ejpam-4021	68	9	operation	operation	NOUN
ejpam-4021	68	10	⊗	⊗	PROPN
ejpam-4021	68	11	is	be	AUX
ejpam-4021	68	12	identical	identical	ADJ
ejpam-4021	68	13	to	to	ADP
ejpam-4021	68	14	the	the	DET
ejpam-4021	68	15	quantal	quantal	ADJ
ejpam-4021	68	16	operation	operation	NOUN
ejpam-4021	68	17	∗	∗	NOUN
ejpam-4021	68	18	,	,	PUNCT
ejpam-4021	68	19	that	that	ADV
ejpam-4021	68	20	is	is	ADV
ejpam-4021	68	21	,	,	PUNCT
ejpam-4021	68	22	⊗	⊗	PROPN
ejpam-4021	68	23	=	=	SYM
ejpam-4021	68	24	∗	∗	NOUN
ejpam-4021	68	25	,	,	PUNCT
ejpam-4021	68	26	then	then	ADV
ejpam-4021	68	27	the	the	DET
ejpam-4021	68	28	triple	triple	ADJ
ejpam-4021	68	29	(	(	PUNCT
ejpam-4021	68	30	l,≤	l,≤	PROPN
ejpam-4021	68	31	,	,	PUNCT
ejpam-4021	68	32	∗,⊗	∗,⊗	PROPN
ejpam-4021	68	33	)	)	PUNCT
ejpam-4021	68	34	is	be	AUX
ejpam-4021	68	35	pseudo	pseudo	NOUN
ejpam-4021	68	36	-	-	NOUN
ejpam-4021	68	37	bisymmetric	bisymmetric	ADJ
ejpam-4021	68	38	.	.	PUNCT
ejpam-4021	69	1	t	t	PROPN
ejpam-4021	69	2	m	m	PROPN
ejpam-4021	69	3	g	g	NOUN
ejpam-4021	69	4	ahsanullah	ahsanullah	NOUN
ejpam-4021	69	5	,	,	PUNCT
ejpam-4021	69	6	fawzi	fawzi	PROPN
ejpam-4021	69	7	al	al	PROPN
ejpam-4021	69	8	-	-	PUNCT
ejpam-4021	69	9	thukair	thukair	NOUN
ejpam-4021	69	10	/	/	SYM
ejpam-4021	69	11	eur	eur	NOUN
ejpam-4021	69	12	.	.	PUNCT
ejpam-4021	70	1	j.	j.	PROPN
ejpam-4021	70	2	pure	pure	PROPN
ejpam-4021	70	3	appl	appl	PROPN
ejpam-4021	70	4	.	.	PROPN
ejpam-4021	70	5	math	math	PROPN
ejpam-4021	70	6	,	,	PUNCT
ejpam-4021	70	7	14	14	NUM
ejpam-4021	70	8	(	(	PUNCT
ejpam-4021	70	9	3	3	NUM
ejpam-4021	70	10	)	)	PUNCT
ejpam-4021	70	11	(	(	PUNCT
ejpam-4021	70	12	2021	2021	NUM
ejpam-4021	70	13	)	)	PUNCT
ejpam-4021	70	14	,	,	PUNCT
ejpam-4021	70	15	949	949	NUM
ejpam-4021	70	16	-	-	SYM
ejpam-4021	70	17	968	968	NUM
ejpam-4021	70	18	952	952	NUM
ejpam-4021	70	19	proposition	proposition	NOUN
ejpam-4021	70	20	1	1	NUM
ejpam-4021	70	21	.	.	PUNCT
ejpam-4021	71	1	[	[	X
ejpam-4021	71	2	18	18	NUM
ejpam-4021	71	3	]	]	X
ejpam-4021	71	4	let	let	VERB
ejpam-4021	71	5	(	(	PUNCT
ejpam-4021	71	6	l,≤	l,≤	PROPN
ejpam-4021	71	7	,	,	PUNCT
ejpam-4021	71	8	∗	∗	NOUN
ejpam-4021	71	9	)	)	PUNCT
ejpam-4021	71	10	be	be	VERB
ejpam-4021	71	11	a	a	DET
ejpam-4021	71	12	gl	gl	NOUN
ejpam-4021	71	13	-	-	NOUN
ejpam-4021	71	14	monoid	monoid	NOUN
ejpam-4021	71	15	.	.	PUNCT
ejpam-4021	72	1	then	then	ADV
ejpam-4021	72	2	the	the	DET
ejpam-4021	72	3	following	follow	VERB
ejpam-4021	72	4	are	be	AUX
ejpam-4021	72	5	fulfilled	fulfil	VERB
ejpam-4021	72	6	∀α	∀α	NOUN
ejpam-4021	72	7	,	,	PUNCT
ejpam-4021	72	8	β	β	X
ejpam-4021	72	9	,	,	PUNCT
ejpam-4021	72	10	γ	γ	PROPN
ejpam-4021	72	11	,	,	PUNCT
ejpam-4021	72	12	δ	δ	PROPN
ejpam-4021	72	13	,	,	PUNCT
ejpam-4021	72	14	αj	αj	X
ejpam-4021	72	15	,	,	PUNCT
ejpam-4021	72	16	βj	βj	X
ejpam-4021	72	17	,	,	PUNCT
ejpam-4021	72	18	γj	γj	ADP
ejpam-4021	72	19	∈	∈	PROPN
ejpam-4021	72	20	l	l	NOUN
ejpam-4021	72	21	:	:	PUNCT
ejpam-4021	72	22	(	(	PUNCT
ejpam-4021	72	23	1	1	X
ejpam-4021	72	24	)	)	PUNCT
ejpam-4021	72	25	α	α	NOUN
ejpam-4021	72	26	≤	≤	NOUN
ejpam-4021	72	27	β	β	X
ejpam-4021	72	28	→	→	SYM
ejpam-4021	72	29	γ	γ	X
ejpam-4021	72	30	⇔	⇔	PROPN
ejpam-4021	72	31	α	α	PROPN
ejpam-4021	72	32	∗	∗	NOUN
ejpam-4021	72	33	β	β	X
ejpam-4021	72	34	≤	≤	ADJ
ejpam-4021	72	35	γ	γ	X
ejpam-4021	72	36	;	;	PUNCT
ejpam-4021	72	37	(	(	PUNCT
ejpam-4021	72	38	2	2	X
ejpam-4021	72	39	)	)	PUNCT
ejpam-4021	72	40	α	α	NOUN
ejpam-4021	72	41	∗	∗	NOUN
ejpam-4021	72	42	(	(	PUNCT
ejpam-4021	72	43	α→	α→	PROPN
ejpam-4021	72	44	β	β	NOUN
ejpam-4021	72	45	)	)	PUNCT
ejpam-4021	72	46	≤	≤	NOUN
ejpam-4021	72	47	β	β	NOUN
ejpam-4021	72	48	;	;	PUNCT
ejpam-4021	72	49	(	(	PUNCT
ejpam-4021	72	50	3	3	X
ejpam-4021	72	51	)	)	PUNCT
ejpam-4021	72	52	α	α	NOUN
ejpam-4021	72	53	≤	≤	NOUN
ejpam-4021	72	54	β	β	X
ejpam-4021	72	55	⇒	⇒	NOUN
ejpam-4021	72	56	α→	α→	PROPN
ejpam-4021	72	57	γ	γ	X
ejpam-4021	72	58	≤	≤	X
ejpam-4021	72	59	β	β	X
ejpam-4021	72	60	→	→	SYM
ejpam-4021	72	61	γ	γ	X
ejpam-4021	72	62	;	;	PUNCT
ejpam-4021	72	63	(	(	PUNCT
ejpam-4021	72	64	4	4	X
ejpam-4021	72	65	)	)	PUNCT
ejpam-4021	72	66	α	α	NOUN
ejpam-4021	72	67	≤	≤	NOUN
ejpam-4021	72	68	β	β	AUX
ejpam-4021	72	69	⇒	⇒	PROPN
ejpam-4021	72	70	γ	γ	PROPN
ejpam-4021	72	71	→	→	SYM
ejpam-4021	72	72	α	α	PROPN
ejpam-4021	72	73	≥	≥	NOUN
ejpam-4021	72	74	γ	γ	X
ejpam-4021	72	75	→	→	SYM
ejpam-4021	72	76	β	β	PROPN
ejpam-4021	72	77	;	;	PUNCT
ejpam-4021	72	78	(	(	PUNCT
ejpam-4021	72	79	5	5	NUM
ejpam-4021	72	80	)	)	PUNCT
ejpam-4021	72	81	(	(	PUNCT
ejpam-4021	72	82	α→	α→	PROPN
ejpam-4021	72	83	β)→	β)→	ADV
ejpam-4021	72	84	β	β	NOUN
ejpam-4021	72	85	≥	≥	NUM
ejpam-4021	72	86	α	α	NOUN
ejpam-4021	72	87	;	;	PUNCT
ejpam-4021	72	88	(	(	PUNCT
ejpam-4021	72	89	6	6	X
ejpam-4021	72	90	)	)	PUNCT
ejpam-4021	72	91	α	α	NOUN
ejpam-4021	72	92	∗	∗	NOUN
ejpam-4021	72	93	(	(	PUNCT
ejpam-4021	72	94	β	β	X
ejpam-4021	72	95	→	→	SYM
ejpam-4021	72	96	γ	γ	NOUN
ejpam-4021	72	97	)	)	PUNCT
ejpam-4021	72	98	≤	≤	NOUN
ejpam-4021	72	99	β	β	X
ejpam-4021	72	100	→	→	SYM
ejpam-4021	72	101	(	(	PUNCT
ejpam-4021	72	102	α	α	PROPN
ejpam-4021	72	103	∗	∗	NOUN
ejpam-4021	72	104	γ	γ	PROPN
ejpam-4021	72	105	)	)	PUNCT
ejpam-4021	72	106	;	;	PUNCT
ejpam-4021	72	107	(	(	PUNCT
ejpam-4021	72	108	7	7	X
ejpam-4021	72	109	)	)	PUNCT
ejpam-4021	72	110	α→	α→	NOUN
ejpam-4021	72	111	(	(	PUNCT
ejpam-4021	72	112	∧	∧	PROPN
ejpam-4021	72	113	j∈j	j∈j	NOUN
ejpam-4021	72	114	βj	βj	NOUN
ejpam-4021	72	115	)	)	PUNCT
ejpam-4021	73	1	=	=	PUNCT
ejpam-4021	73	2	∧	∧	NOUN
ejpam-4021	73	3	j∈j(α→	j∈j(α→	PROPN
ejpam-4021	73	4	βj	βj	NOUN
ejpam-4021	73	5	)	)	PUNCT
ejpam-4021	73	6	;	;	PUNCT
ejpam-4021	73	7	(	(	PUNCT
ejpam-4021	73	8	8)	8)	NUM
ejpam-4021	73	9	(	(	PUNCT
ejpam-4021	73	10	∨	∨	NUM
ejpam-4021	73	11	j∈j	j∈j	NOUN
ejpam-4021	73	12	αj)→	αj)→	PROPN
ejpam-4021	73	13	β	β	X
ejpam-4021	73	14	=	=	SYM
ejpam-4021	73	15	∧	∧	PROPN
ejpam-4021	73	16	j∈j(αj	j∈j(αj	PROPN
ejpam-4021	73	17	→	→	SYM
ejpam-4021	73	18	β	β	NOUN
ejpam-4021	73	19	)	)	PUNCT
ejpam-4021	73	20	;	;	PUNCT
ejpam-4021	73	21	(	(	PUNCT
ejpam-4021	73	22	9	9	X
ejpam-4021	73	23	)	)	PUNCT
ejpam-4021	73	24	if	if	SCONJ
ejpam-4021	73	25	α	α	X
ejpam-4021	73	26	,	,	PUNCT
ejpam-4021	73	27	β	β	X
ejpam-4021	73	28	∈	∈	X
ejpam-4021	73	29	l	l	NOUN
ejpam-4021	73	30	with	with	ADP
ejpam-4021	73	31	α	α	NOUN
ejpam-4021	73	32	≤	≤	NUM
ejpam-4021	74	1	β	β	NOUN
ejpam-4021	74	2	,	,	PUNCT
ejpam-4021	74	3	then	then	ADV
ejpam-4021	74	4	for	for	ADP
ejpam-4021	74	5	any	any	DET
ejpam-4021	74	6	γ	γ	X
ejpam-4021	74	7	∈	∈	PROPN
ejpam-4021	74	8	l	l	NOUN
ejpam-4021	74	9	,	,	PUNCT
ejpam-4021	74	10	γ	γ	PROPN
ejpam-4021	74	11	∗	∗	NOUN
ejpam-4021	74	12	α	α	NOUN
ejpam-4021	74	13	≤	≤	X
ejpam-4021	74	14	γ	γ	PROPN
ejpam-4021	74	15	∗	∗	X
ejpam-4021	74	16	β	β	NOUN
ejpam-4021	74	17	;	;	PUNCT
ejpam-4021	74	18	(	(	PUNCT
ejpam-4021	74	19	10	10	X
ejpam-4021	74	20	)	)	PUNCT
ejpam-4021	74	21	∧	∧	NOUN
ejpam-4021	74	22	j∈j	j∈j	NOUN
ejpam-4021	74	23	(	(	PUNCT
ejpam-4021	74	24	αj	αj	NOUN
ejpam-4021	74	25	∗	∗	NOUN
ejpam-4021	74	26	γj	γj	PROPN
ejpam-4021	74	27	)	)	PUNCT
ejpam-4021	74	28	≥	≥	NOUN
ejpam-4021	74	29	(	(	PUNCT
ejpam-4021	74	30	∧	∧	PROPN
ejpam-4021	74	31	j∈j	j∈j	NOUN
ejpam-4021	74	32	αj	αj	NOUN
ejpam-4021	74	33	)	)	PUNCT
ejpam-4021	74	34	∗	∗	NOUN
ejpam-4021	74	35	(	(	PUNCT
ejpam-4021	74	36	∧	∧	PROPN
ejpam-4021	74	37	j∈j	j∈j	NOUN
ejpam-4021	74	38	γj	γj	PROPN
ejpam-4021	74	39	)	)	PUNCT
ejpam-4021	74	40	;	;	PUNCT
ejpam-4021	74	41	(	(	PUNCT
ejpam-4021	74	42	11	11	NUM
ejpam-4021	74	43	)	)	PUNCT
ejpam-4021	74	44	(	(	PUNCT
ejpam-4021	74	45	α→	α→	PROPN
ejpam-4021	74	46	γ	γ	PROPN
ejpam-4021	74	47	)	)	PUNCT
ejpam-4021	74	48	∗	∗	NOUN
ejpam-4021	74	49	(	(	PUNCT
ejpam-4021	74	50	β	β	X
ejpam-4021	74	51	→	→	SYM
ejpam-4021	74	52	δ	δ	PROPN
ejpam-4021	74	53	)	)	PUNCT
ejpam-4021	74	54	≤	≤	NOUN
ejpam-4021	74	55	α	α	PROPN
ejpam-4021	74	56	∗	∗	NOUN
ejpam-4021	74	57	β	β	X
ejpam-4021	74	58	→	→	SYM
ejpam-4021	74	59	γ	γ	X
ejpam-4021	74	60	∗	∗	X
ejpam-4021	74	61	δ	δ	PROPN
ejpam-4021	74	62	;	;	PUNCT
ejpam-4021	74	63	(	(	PUNCT
ejpam-4021	74	64	12	12	X
ejpam-4021	74	65	)	)	PUNCT
ejpam-4021	74	66	α	α	NOUN
ejpam-4021	74	67	≤	≤	NOUN
ejpam-4021	74	68	β	β	X
ejpam-4021	74	69	⇔	⇔	X
ejpam-4021	74	70	α→	α→	PROPN
ejpam-4021	74	71	β	β	X
ejpam-4021	74	72	=	=	PUNCT
ejpam-4021	74	73	>	>	X
ejpam-4021	74	74	;	;	PUNCT
ejpam-4021	74	75	(	(	PUNCT
ejpam-4021	74	76	13	13	NUM
ejpam-4021	74	77	)	)	PUNCT
ejpam-4021	74	78	α→	α→	NOUN
ejpam-4021	74	79	>	>	PUNCT
ejpam-4021	75	1	=	=	PUNCT
ejpam-4021	75	2	>	>	PUNCT
ejpam-4021	75	3	,	,	PUNCT
ejpam-4021	75	4	>	>	X
ejpam-4021	75	5	→	→	SYM
ejpam-4021	75	6	α	α	X
ejpam-4021	75	7	=	=	SYM
ejpam-4021	75	8	α	α	PROPN
ejpam-4021	75	9	,	,	PUNCT
ejpam-4021	75	10	and	and	CCONJ
ejpam-4021	75	11	⊥	⊥	PROPN
ejpam-4021	75	12	→	→	SYM
ejpam-4021	75	13	α	α	X
ejpam-4021	75	14	=	=	PUNCT
ejpam-4021	75	15	>	>	X
ejpam-4021	75	16	.	.	PUNCT
ejpam-4021	76	1	in	in	ADP
ejpam-4021	76	2	what	what	PRON
ejpam-4021	76	3	follows	follow	VERB
ejpam-4021	76	4	,	,	PUNCT
ejpam-4021	76	5	the	the	DET
ejpam-4021	76	6	quadruple	quadruple	NOUN
ejpam-4021	76	7	l	l	NOUN
ejpam-4021	77	1	=	=	SYM
ejpam-4021	77	2	(	(	PUNCT
ejpam-4021	77	3	l,≤	l,≤	PROPN
ejpam-4021	77	4	,	,	PUNCT
ejpam-4021	77	5	∗,⊗	∗,⊗	PROPN
ejpam-4021	77	6	)	)	PUNCT
ejpam-4021	77	7	(	(	PUNCT
ejpam-4021	77	8	or	or	CCONJ
ejpam-4021	77	9	simply	simply	ADV
ejpam-4021	77	10	l	l	NOUN
ejpam-4021	77	11	)	)	PUNCT
ejpam-4021	77	12	is	be	AUX
ejpam-4021	77	13	assumed	assume	VERB
ejpam-4021	77	14	to	to	PART
ejpam-4021	77	15	be	be	AUX
ejpam-4021	77	16	an	an	DET
ejpam-4021	77	17	enriched	enriched	ADJ
ejpam-4021	77	18	cl	cl	NOUN
ejpam-4021	77	19	-	-	ADJ
ejpam-4021	77	20	premonoid	premonoid	ADJ
ejpam-4021	77	21	,	,	PUNCT
ejpam-4021	77	22	where	where	SCONJ
ejpam-4021	77	23	∗	∗	NOUN
ejpam-4021	77	24	is	be	AUX
ejpam-4021	77	25	reserved	reserve	VERB
ejpam-4021	77	26	for	for	ADP
ejpam-4021	77	27	the	the	DET
ejpam-4021	77	28	gl	gl	PROPN
ejpam-4021	77	29	-	-	PROPN
ejpam-4021	77	30	monoid	monoid	NOUN
ejpam-4021	77	31	operation	operation	NOUN
ejpam-4021	77	32	,	,	PUNCT
ejpam-4021	77	33	⊗	⊗	PROPN
ejpam-4021	77	34	is	be	AUX
ejpam-4021	77	35	for	for	ADP
ejpam-4021	77	36	cl	cl	NOUN
ejpam-4021	77	37	-	-	ADJ
ejpam-4021	77	38	premonoid	premonoid	ADJ
ejpam-4021	77	39	,	,	PUNCT
ejpam-4021	77	40	unless	unless	SCONJ
ejpam-4021	77	41	otherwise	otherwise	ADV
ejpam-4021	77	42	specified	specify	VERB
ejpam-4021	77	43	.	.	PUNCT
ejpam-4021	78	1	the	the	DET
ejpam-4021	78	2	set	set	NOUN
ejpam-4021	78	3	of	of	ADP
ejpam-4021	78	4	all	all	DET
ejpam-4021	78	5	l	l	NOUN
ejpam-4021	78	6	-	-	NOUN
ejpam-4021	78	7	sets	set	NOUN
ejpam-4021	78	8	or	or	CCONJ
ejpam-4021	78	9	l	l	NOUN
ejpam-4021	78	10	-	-	PUNCT
ejpam-4021	78	11	valued	value	VERB
ejpam-4021	78	12	sets	set	NOUN
ejpam-4021	78	13	and	and	CCONJ
ejpam-4021	78	14	is	be	AUX
ejpam-4021	78	15	denoted	denote	VERB
ejpam-4021	78	16	by	by	ADP
ejpam-4021	78	17	lx(=	lx(=	NOUN
ejpam-4021	78	18	{	{	PUNCT
ejpam-4021	78	19	ν	ν	NOUN
ejpam-4021	78	20	:	:	PUNCT
ejpam-4021	78	21	x	x	PUNCT
ejpam-4021	78	22	−→	−→	NOUN
ejpam-4021	78	23	l	l	NOUN
ejpam-4021	78	24	}	}	PUNCT
ejpam-4021	78	25	)	)	PUNCT
ejpam-4021	78	26	.	.	PUNCT
ejpam-4021	79	1	if	if	SCONJ
ejpam-4021	79	2	f	f	PROPN
ejpam-4021	79	3	:	:	PUNCT
ejpam-4021	79	4	x	x	X
ejpam-4021	79	5	→	→	SYM
ejpam-4021	79	6	y	y	PROPN
ejpam-4021	79	7	is	be	AUX
ejpam-4021	79	8	a	a	DET
ejpam-4021	79	9	function	function	NOUN
ejpam-4021	79	10	,	,	PUNCT
ejpam-4021	79	11	then	then	ADV
ejpam-4021	79	12	f←	f←	X
ejpam-4021	79	13	:	:	PUNCT
ejpam-4021	79	14	ly	ly	AUX
ejpam-4021	79	15	−→	−→	NOUN
ejpam-4021	79	16	lx	lx	NOUN
ejpam-4021	79	17	is	be	AUX
ejpam-4021	79	18	defined	define	VERB
ejpam-4021	79	19	for	for	ADP
ejpam-4021	79	20	any	any	DET
ejpam-4021	79	21	µ	µ	PRON
ejpam-4021	79	22	∈	∈	NOUN
ejpam-4021	79	23	ly	ly	X
ejpam-4021	79	24	by	by	ADP
ejpam-4021	79	25	f←(µ	f←(µ	NOUN
ejpam-4021	79	26	)	)	PUNCT
ejpam-4021	79	27	=	=	SYM
ejpam-4021	79	28	µ	µ	X
ejpam-4021	79	29	◦	◦	NOUN
ejpam-4021	79	30	f	f	X
ejpam-4021	79	31	;	;	PUNCT
ejpam-4021	79	32	and	and	CCONJ
ejpam-4021	79	33	f→	f→	PROPN
ejpam-4021	79	34	:	:	PUNCT
ejpam-4021	79	35	lx	lx	NOUN
ejpam-4021	79	36	−→	−→	NOUN
ejpam-4021	79	37	ly	ly	X
ejpam-4021	79	38	is	be	AUX
ejpam-4021	79	39	defined	define	VERB
ejpam-4021	79	40	by	by	ADP
ejpam-4021	79	41	f→(ν)(y	f→(ν)(y	PROPN
ejpam-4021	79	42	)	)	PUNCT
ejpam-4021	80	1	=	=	PUNCT
ejpam-4021	80	2	∨	∨	X
ejpam-4021	80	3	{	{	PUNCT
ejpam-4021	80	4	ν(x)|f(x	ν(x)|f(x	NOUN
ejpam-4021	80	5	)	)	PUNCT
ejpam-4021	80	6	=	=	SYM
ejpam-4021	81	1	y	y	PROPN
ejpam-4021	81	2	}	}	PUNCT
ejpam-4021	81	3	,	,	PUNCT
ejpam-4021	81	4	for	for	ADP
ejpam-4021	81	5	all	all	PRON
ejpam-4021	81	6	ν	ν	NOUN
ejpam-4021	81	7	∈	∈	NOUN
ejpam-4021	81	8	lx	lx	NOUN
ejpam-4021	81	9	,	,	PUNCT
ejpam-4021	81	10	y	y	PROPN
ejpam-4021	81	11	∈	∈	PROPN
ejpam-4021	81	12	y	y	PROPN
ejpam-4021	81	13	.	.	PUNCT
ejpam-4021	82	1	if	if	SCONJ
ejpam-4021	82	2	·	·	PUNCT
ejpam-4021	82	3	is	be	AUX
ejpam-4021	82	4	a	a	DET
ejpam-4021	82	5	binary	binary	ADJ
ejpam-4021	82	6	operation	operation	NOUN
ejpam-4021	82	7	on	on	ADP
ejpam-4021	82	8	a	a	DET
ejpam-4021	82	9	set	set	NOUN
ejpam-4021	82	10	x	x	NOUN
ejpam-4021	82	11	,	,	PUNCT
ejpam-4021	82	12	then	then	ADV
ejpam-4021	82	13	we	we	PRON
ejpam-4021	82	14	define	define	VERB
ejpam-4021	82	15	the	the	DET
ejpam-4021	82	16	binary	binary	PROPN
ejpam-4021	82	17	operation	operation	NOUN
ejpam-4021	82	18	�	�	PROPN
ejpam-4021	82	19	on	on	ADP
ejpam-4021	82	20	lx	lx	NOUN
ejpam-4021	82	21	as	as	SCONJ
ejpam-4021	82	22	follows	follow	VERB
ejpam-4021	82	23	.	.	PUNCT
ejpam-4021	83	1	for	for	ADP
ejpam-4021	83	2	ν1	ν1	NOUN
ejpam-4021	83	3	,	,	PUNCT
ejpam-4021	83	4	ν2	ν2	NOUN
ejpam-4021	83	5	∈	∈	NOUN
ejpam-4021	83	6	lx	lx	NOUN
ejpam-4021	83	7	and	and	CCONJ
ejpam-4021	83	8	z	z	NOUN
ejpam-4021	83	9	∈	∈	PROPN
ejpam-4021	83	10	x	x	SYM
ejpam-4021	83	11	ν1	ν1	PROPN
ejpam-4021	83	12	�	�	PROPN
ejpam-4021	83	13	ν2(z	ν2(z	NUM
ejpam-4021	83	14	)	)	PUNCT
ejpam-4021	83	15	=	=	SYM
ejpam-4021	83	16	∨	∨	X
ejpam-4021	83	17	{	{	PUNCT
ejpam-4021	83	18	ν1(x	ν1(x	NOUN
ejpam-4021	83	19	)	)	PUNCT
ejpam-4021	83	20	∗	∗	NOUN
ejpam-4021	83	21	ν2(y)|x	ν2(y)|x	NOUN
ejpam-4021	83	22	,	,	PUNCT
ejpam-4021	83	23	y	y	PROPN
ejpam-4021	83	24	∈	∈	PROPN
ejpam-4021	83	25	x	x	X
ejpam-4021	83	26	,	,	PUNCT
ejpam-4021	83	27	x	x	X
ejpam-4021	83	28	·	·	PUNCT
ejpam-4021	83	29	y	y	X
ejpam-4021	83	30	=	=	PUNCT
ejpam-4021	83	31	z	z	PROPN
ejpam-4021	83	32	}	}	PUNCT
ejpam-4021	83	33	;	;	PUNCT
ejpam-4021	83	34	usually	usually	ADV
ejpam-4021	83	35	,	,	PUNCT
ejpam-4021	83	36	we	we	PRON
ejpam-4021	83	37	write	write	VERB
ejpam-4021	83	38	xy	xy	PROPN
ejpam-4021	83	39	instead	instead	ADV
ejpam-4021	83	40	of	of	ADP
ejpam-4021	83	41	x	x	PART
ejpam-4021	83	42	·	·	PUNCT
ejpam-4021	83	43	y.	y.	NOUN
ejpam-4021	83	44	if	if	SCONJ
ejpam-4021	83	45	ν1	ν1	NOUN
ejpam-4021	83	46	,	,	PUNCT
ejpam-4021	83	47	ν2	ν2	NOUN
ejpam-4021	83	48	∈	∈	NOUN
ejpam-4021	83	49	lx	lx	NOUN
ejpam-4021	83	50	,	,	PUNCT
ejpam-4021	83	51	and	and	CCONJ
ejpam-4021	83	52	→	→	ADP
ejpam-4021	83	53	,	,	PUNCT
ejpam-4021	83	54	∗	∗	NOUN
ejpam-4021	83	55	,	,	PUNCT
ejpam-4021	83	56	⊗	⊗	PROPN
ejpam-4021	83	57	are	be	AUX
ejpam-4021	83	58	operations	operation	NOUN
ejpam-4021	83	59	on	on	ADP
ejpam-4021	83	60	l	l	NOUN
ejpam-4021	83	61	as	as	SCONJ
ejpam-4021	83	62	explained	explain	VERB
ejpam-4021	83	63	before	before	ADV
ejpam-4021	83	64	,	,	PUNCT
ejpam-4021	83	65	then	then	ADV
ejpam-4021	83	66	these	these	DET
ejpam-4021	83	67	operations	operation	NOUN
ejpam-4021	83	68	are	be	AUX
ejpam-4021	83	69	carried	carry	VERB
ejpam-4021	83	70	over	over	ADP
ejpam-4021	83	71	to	to	ADP
ejpam-4021	83	72	lx	lx	ADP
ejpam-4021	83	73	point	point	ADV
ejpam-4021	83	74	-	-	PUNCT
ejpam-4021	83	75	wise	wise	ADJ
ejpam-4021	83	76	:	:	PUNCT
ejpam-4021	83	77	(	(	PUNCT
ejpam-4021	83	78	i	i	NOUN
ejpam-4021	83	79	)	)	PUNCT
ejpam-4021	83	80	(	(	PUNCT
ejpam-4021	83	81	ν1	ν1	NOUN
ejpam-4021	83	82	→	→	SYM
ejpam-4021	83	83	ν2)(x	ν2)(x	PROPN
ejpam-4021	83	84	)	)	PUNCT
ejpam-4021	83	85	=	=	PUNCT
ejpam-4021	83	86	ν1(x)→	ν1(x)→	PROPN
ejpam-4021	83	87	ν2(x	ν2(x	PROPN
ejpam-4021	83	88	)	)	PUNCT
ejpam-4021	83	89	;	;	PUNCT
ejpam-4021	83	90	(	(	PUNCT
ejpam-4021	83	91	ii	ii	NOUN
ejpam-4021	83	92	)	)	PUNCT
ejpam-4021	83	93	(	(	PUNCT
ejpam-4021	83	94	ν1	ν1	NOUN
ejpam-4021	83	95	∗	∗	NOUN
ejpam-4021	83	96	ν2)(x	ν2)(x	PROPN
ejpam-4021	83	97	)	)	PUNCT
ejpam-4021	83	98	=	=	SYM
ejpam-4021	83	99	ν1(x	ν1(x	NOUN
ejpam-4021	83	100	)	)	PUNCT
ejpam-4021	83	101	∗	∗	NOUN
ejpam-4021	83	102	ν2(x	ν2(x	PROPN
ejpam-4021	83	103	)	)	PUNCT
ejpam-4021	83	104	;	;	PUNCT
ejpam-4021	83	105	(	(	PUNCT
ejpam-4021	83	106	iii	iii	X
ejpam-4021	83	107	)	)	PUNCT
ejpam-4021	83	108	(	(	PUNCT
ejpam-4021	83	109	ν1	ν1	NOUN
ejpam-4021	83	110	⊗	⊗	PROPN
ejpam-4021	83	111	ν2	ν2	PROPN
ejpam-4021	83	112	)	)	PUNCT
ejpam-4021	83	113	(	(	PUNCT
ejpam-4021	83	114	x	x	X
ejpam-4021	83	115	)	)	PUNCT
ejpam-4021	83	116	=	=	PUNCT
ejpam-4021	83	117	ν1(x)⊗	ν1(x)⊗	ADP
ejpam-4021	83	118	ν2(x	ν2(x	PROPN
ejpam-4021	83	119	)	)	PUNCT
ejpam-4021	83	120	,	,	PUNCT
ejpam-4021	83	121	∀x	∀x	X
ejpam-4021	83	122	∈	∈	PROPN
ejpam-4021	83	123	x.	x.	NOUN
ejpam-4021	83	124	definition	definition	NOUN
ejpam-4021	83	125	6	6	NUM
ejpam-4021	83	126	.	.	PUNCT
ejpam-4021	84	1	[	[	X
ejpam-4021	84	2	17	17	NUM
ejpam-4021	84	3	,	,	PUNCT
ejpam-4021	84	4	18	18	NUM
ejpam-4021	84	5	]	]	PUNCT
ejpam-4021	84	6	a	a	DET
ejpam-4021	84	7	map	map	NOUN
ejpam-4021	84	8	f	f	X
ejpam-4021	84	9	:	:	PUNCT
ejpam-4021	84	10	lx	lx	AUX
ejpam-4021	84	11	−→	−→	ADJ
ejpam-4021	84	12	l	l	NOUN
ejpam-4021	84	13	is	be	AUX
ejpam-4021	84	14	called	call	VERB
ejpam-4021	84	15	an	an	DET
ejpam-4021	84	16	l	l	NOUN
ejpam-4021	84	17	-	-	PUNCT
ejpam-4021	84	18	valued	value	VERB
ejpam-4021	84	19	filter	filter	NOUN
ejpam-4021	84	20	on	on	ADP
ejpam-4021	84	21	x	x	SYM
ejpam-4021	84	22	if	if	SCONJ
ejpam-4021	84	23	and	and	CCONJ
ejpam-4021	84	24	only	only	ADV
ejpam-4021	84	25	if	if	SCONJ
ejpam-4021	84	26	the	the	DET
ejpam-4021	84	27	conditions	condition	NOUN
ejpam-4021	84	28	below	below	ADV
ejpam-4021	84	29	are	be	AUX
ejpam-4021	84	30	satisfied	satisfied	ADJ
ejpam-4021	84	31	:	:	PUNCT
ejpam-4021	84	32	(	(	PUNCT
ejpam-4021	84	33	lf1	lf1	PROPN
ejpam-4021	84	34	)	)	PUNCT
ejpam-4021	84	35	f(>x	f(>x	NOUN
ejpam-4021	84	36	)	)	PUNCT
ejpam-4021	85	1	=	=	PUNCT
ejpam-4021	85	2	>	>	PUNCT
ejpam-4021	85	3	,	,	PUNCT
ejpam-4021	85	4	f(⊥x	f(⊥x	PROPN
ejpam-4021	85	5	)	)	PUNCT
ejpam-4021	85	6	=	=	PUNCT
ejpam-4021	86	1	⊥	⊥	NOUN
ejpam-4021	86	2	;	;	PUNCT
ejpam-4021	86	3	(	(	PUNCT
ejpam-4021	86	4	lf2	lf2	PROPN
ejpam-4021	86	5	)	)	PUNCT
ejpam-4021	86	6	if	if	SCONJ
ejpam-4021	86	7	ν1	ν1	NOUN
ejpam-4021	86	8	,	,	PUNCT
ejpam-4021	86	9	ν2	ν2	NOUN
ejpam-4021	86	10	∈	∈	NOUN
ejpam-4021	86	11	lx	lx	NOUN
ejpam-4021	86	12	with	with	ADP
ejpam-4021	86	13	ν1	ν1	NOUN
ejpam-4021	86	14	≤	≤	NUM
ejpam-4021	86	15	ν2	ν2	NOUN
ejpam-4021	86	16	,	,	PUNCT
ejpam-4021	86	17	then	then	ADV
ejpam-4021	86	18	f(ν1	f(ν1	NOUN
ejpam-4021	86	19	)	)	PUNCT
ejpam-4021	86	20	≤	≤	NUM
ejpam-4021	86	21	f(ν2	f(ν2	NOUN
ejpam-4021	86	22	)	)	PUNCT
ejpam-4021	86	23	;	;	PUNCT
ejpam-4021	86	24	(	(	PUNCT
ejpam-4021	86	25	lf3	lf3	NOUN
ejpam-4021	86	26	)	)	PUNCT
ejpam-4021	86	27	f(ν1)⊗f(ν2	f(ν1)⊗f(ν2	NOUN
ejpam-4021	86	28	)	)	PUNCT
ejpam-4021	86	29	≤	≤	NOUN
ejpam-4021	86	30	f(ν1	f(ν1	VERB
ejpam-4021	86	31	⊗	⊗	PROPN
ejpam-4021	86	32	ν2	ν2	PROPN
ejpam-4021	86	33	)	)	PUNCT
ejpam-4021	86	34	,	,	PUNCT
ejpam-4021	86	35	∀ν1	∀ν1	PROPN
ejpam-4021	86	36	,	,	PUNCT
ejpam-4021	86	37	ν2	ν2	NOUN
ejpam-4021	86	38	∈	∈	NOUN
ejpam-4021	86	39	lx	lx	NOUN
ejpam-4021	86	40	.	.	PUNCT
ejpam-4021	87	1	(	(	PUNCT
ejpam-4021	87	2	sl	sl	INTJ
ejpam-4021	87	3	)	)	PUNCT
ejpam-4021	87	4	an	an	DET
ejpam-4021	87	5	l	l	NOUN
ejpam-4021	87	6	-	-	PUNCT
ejpam-4021	87	7	valued	value	VERB
ejpam-4021	87	8	filter	filter	NOUN
ejpam-4021	87	9	f	f	PROPN
ejpam-4021	87	10	is	be	AUX
ejpam-4021	87	11	called	call	VERB
ejpam-4021	87	12	a	a	DET
ejpam-4021	87	13	stratified	stratified	ADJ
ejpam-4021	87	14	l	l	ADV
ejpam-4021	87	15	-	-	PUNCT
ejpam-4021	87	16	valued	value	VERB
ejpam-4021	87	17	filter	filter	NOUN
ejpam-4021	87	18	if	if	SCONJ
ejpam-4021	87	19	∀α	∀α	NOUN
ejpam-4021	87	20	∈	∈	PROPN
ejpam-4021	87	21	l,∀µ	l,∀µ	VERB
ejpam-4021	87	22	∈	∈	NOUN
ejpam-4021	87	23	lx	lx	NOUN
ejpam-4021	87	24	,	,	PUNCT
ejpam-4021	87	25	α	α	PROPN
ejpam-4021	87	26	∗	∗	NOUN
ejpam-4021	87	27	f(µ	f(µ	PROPN
ejpam-4021	87	28	)	)	PUNCT
ejpam-4021	87	29	≤	≤	NOUN
ejpam-4021	87	30	f(α	f(α	PROPN
ejpam-4021	87	31	∗	∗	NOUN
ejpam-4021	87	32	µ	µ	NOUN
ejpam-4021	87	33	)	)	PUNCT
ejpam-4021	87	34	.	.	PUNCT
ejpam-4021	88	1	the	the	DET
ejpam-4021	88	2	set	set	NOUN
ejpam-4021	88	3	of	of	ADP
ejpam-4021	88	4	all	all	PRON
ejpam-4021	88	5	stratified	stratified	ADJ
ejpam-4021	88	6	l	l	ADV
ejpam-4021	88	7	-	-	PUNCT
ejpam-4021	88	8	valued	value	VERB
ejpam-4021	88	9	filters	filter	NOUN
ejpam-4021	88	10	on	on	ADP
ejpam-4021	88	11	x	x	VERB
ejpam-4021	88	12	is	be	AUX
ejpam-4021	88	13	denoted	denote	VERB
ejpam-4021	88	14	by	by	ADP
ejpam-4021	88	15	fsl(x	fsl(x	PROPN
ejpam-4021	88	16	)	)	PUNCT
ejpam-4021	88	17	.	.	PUNCT
ejpam-4021	89	1	on	on	ADP
ejpam-4021	89	2	fsl(x	fsl(x	PROPN
ejpam-4021	89	3	)	)	PUNCT
ejpam-4021	89	4	,	,	PUNCT
ejpam-4021	89	5	partial	partial	ADJ
ejpam-4021	89	6	ordering	ordering	NOUN
ejpam-4021	89	7	≤	≤	NOUN
ejpam-4021	89	8	is	be	AUX
ejpam-4021	89	9	defined	define	VERB
ejpam-4021	89	10	by	by	ADP
ejpam-4021	89	11	:	:	PUNCT
ejpam-4021	89	12	if	if	SCONJ
ejpam-4021	89	13	f	f	PROPN
ejpam-4021	89	14	,	,	PUNCT
ejpam-4021	89	15	g	g	PROPN
ejpam-4021	89	16	∈	∈	PROPN
ejpam-4021	89	17	fsl(x	fsl(x	PROPN
ejpam-4021	89	18	)	)	PUNCT
ejpam-4021	89	19	,	,	PUNCT
ejpam-4021	89	20	then	then	ADV
ejpam-4021	89	21	f	f	PROPN
ejpam-4021	89	22	≤	≤	PROPN
ejpam-4021	89	23	g	g	PROPN
ejpam-4021	89	24	⇔	⇔	PROPN
ejpam-4021	89	25	f(ν	f(ν	PROPN
ejpam-4021	89	26	)	)	PUNCT
ejpam-4021	89	27	≤	≤	PART
ejpam-4021	89	28	g(ν	g(ν	PROPN
ejpam-4021	89	29	)	)	PUNCT
ejpam-4021	89	30	,	,	PUNCT
ejpam-4021	89	31	∀ν	∀ν	PROPN
ejpam-4021	89	32	∈	∈	PROPN
ejpam-4021	89	33	lx	lx	NOUN
ejpam-4021	89	34	.	.	PUNCT
ejpam-4021	90	1	if	if	SCONJ
ejpam-4021	90	2	t	t	PROPN
ejpam-4021	90	3	m	m	VERB
ejpam-4021	90	4	g	g	NOUN
ejpam-4021	90	5	ahsanullah	ahsanullah	NOUN
ejpam-4021	90	6	,	,	PUNCT
ejpam-4021	90	7	fawzi	fawzi	PROPN
ejpam-4021	90	8	al	al	PROPN
ejpam-4021	90	9	-	-	PUNCT
ejpam-4021	90	10	thukair	thukair	NOUN
ejpam-4021	90	11	/	/	SYM
ejpam-4021	90	12	eur	eur	NOUN
ejpam-4021	90	13	.	.	PUNCT
ejpam-4021	91	1	j.	j.	PROPN
ejpam-4021	91	2	pure	pure	PROPN
ejpam-4021	91	3	appl	appl	PROPN
ejpam-4021	91	4	.	.	PROPN
ejpam-4021	91	5	math	math	PROPN
ejpam-4021	91	6	,	,	PUNCT
ejpam-4021	91	7	14	14	NUM
ejpam-4021	91	8	(	(	PUNCT
ejpam-4021	91	9	3	3	NUM
ejpam-4021	91	10	)	)	PUNCT
ejpam-4021	91	11	(	(	PUNCT
ejpam-4021	91	12	2021	2021	NUM
ejpam-4021	91	13	)	)	PUNCT
ejpam-4021	91	14	,	,	PUNCT
ejpam-4021	91	15	949	949	NUM
ejpam-4021	91	16	-	-	SYM
ejpam-4021	91	17	968	968	NUM
ejpam-4021	91	18	953	953	NUM
ejpam-4021	91	19	x	x	SYM
ejpam-4021	91	20	∈	∈	NOUN
ejpam-4021	91	21	x	x	NOUN
ejpam-4021	91	22	,	,	PUNCT
ejpam-4021	91	23	then	then	ADV
ejpam-4021	91	24	[	[	X
ejpam-4021	91	25	x	x	X
ejpam-4021	91	26	]	]	X
ejpam-4021	91	27	∈	∈	PROPN
ejpam-4021	91	28	fsl(x	fsl(x	PROPN
ejpam-4021	91	29	)	)	PUNCT
ejpam-4021	91	30	,	,	PUNCT
ejpam-4021	91	31	called	call	VERB
ejpam-4021	91	32	point	point	NOUN
ejpam-4021	91	33	stratified	stratify	VERB
ejpam-4021	91	34	l	l	ADV
ejpam-4021	91	35	-	-	PUNCT
ejpam-4021	91	36	valued	value	VERB
ejpam-4021	91	37	filter	filter	NOUN
ejpam-4021	91	38	on	on	ADP
ejpam-4021	91	39	x	x	NOUN
ejpam-4021	91	40	,	,	PUNCT
ejpam-4021	91	41	and	and	CCONJ
ejpam-4021	91	42	is	be	AUX
ejpam-4021	91	43	defined	define	VERB
ejpam-4021	91	44	as	as	ADP
ejpam-4021	91	45	[	[	X
ejpam-4021	91	46	x](ν	x](ν	X
ejpam-4021	91	47	)	)	PUNCT
ejpam-4021	91	48	=	=	SYM
ejpam-4021	92	1	ν(x	ν(x	PROPN
ejpam-4021	92	2	)	)	PUNCT
ejpam-4021	92	3	,	,	PUNCT
ejpam-4021	92	4	for	for	SCONJ
ejpam-4021	92	5	all	all	PRON
ejpam-4021	92	6	ν	ν	NOUN
ejpam-4021	92	7	∈	∈	NOUN
ejpam-4021	92	8	lx	lx	NOUN
ejpam-4021	92	9	.	.	PUNCT
ejpam-4021	93	1	if	if	SCONJ
ejpam-4021	93	2	f	f	PROPN
ejpam-4021	93	3	∈	∈	PROPN
ejpam-4021	93	4	fsl(x	fsl(x	PROPN
ejpam-4021	93	5	)	)	PUNCT
ejpam-4021	93	6	,	,	PUNCT
ejpam-4021	93	7	then	then	ADV
ejpam-4021	93	8	the	the	DET
ejpam-4021	93	9	stratified	stratified	ADJ
ejpam-4021	93	10	l	l	ADV
ejpam-4021	93	11	-	-	PUNCT
ejpam-4021	93	12	valued	value	VERB
ejpam-4021	93	13	filter	filter	NOUN
ejpam-4021	93	14	f⇒(f	f⇒(f	NOUN
ejpam-4021	93	15	)	)	PUNCT
ejpam-4021	93	16	:	:	PUNCT
ejpam-4021	93	17	ly	ly	X
ejpam-4021	93	18	→	→	SYM
ejpam-4021	93	19	l	l	NOUN
ejpam-4021	93	20	on	on	ADP
ejpam-4021	93	21	y	y	PROPN
ejpam-4021	93	22	is	be	AUX
ejpam-4021	93	23	defined	define	VERB
ejpam-4021	93	24	for	for	ADP
ejpam-4021	93	25	any	any	DET
ejpam-4021	93	26	µ	µ	PROPN
ejpam-4021	93	27	∈	∈	NOUN
ejpam-4021	93	28	ly	ly	X
ejpam-4021	93	29	by	by	ADP
ejpam-4021	93	30	[	[	X
ejpam-4021	93	31	f⇒(f)](µ	f⇒(f)](µ	PUNCT
ejpam-4021	93	32	)	)	PUNCT
ejpam-4021	93	33	=	=	SYM
ejpam-4021	93	34	f	f	PROPN
ejpam-4021	93	35	(	(	PUNCT
ejpam-4021	93	36	f←(µ	f←(µ	NOUN
ejpam-4021	93	37	)	)	PUNCT
ejpam-4021	93	38	)	)	PUNCT
ejpam-4021	94	1	=	=	PUNCT
ejpam-4021	94	2	f(µ	f(µ	NOUN
ejpam-4021	94	3	◦	◦	NOUN
ejpam-4021	94	4	f	f	X
ejpam-4021	94	5	)	)	PUNCT
ejpam-4021	94	6	.	.	PUNCT
ejpam-4021	95	1	if	if	SCONJ
ejpam-4021	95	2	f	f	PROPN
ejpam-4021	95	3	∈	∈	PROPN
ejpam-4021	95	4	fsl(y	fsl(y	PROPN
ejpam-4021	95	5	)	)	PUNCT
ejpam-4021	95	6	,	,	PUNCT
ejpam-4021	95	7	then	then	ADV
ejpam-4021	95	8	f	f	X
ejpam-4021	95	9	⇐	⇐	PROPN
ejpam-4021	95	10	(f	(f	PROPN
ejpam-4021	95	11	)	)	PUNCT
ejpam-4021	95	12	:	:	PUNCT
ejpam-4021	95	13	lx	lx	NOUN
ejpam-4021	95	14	→	→	SYM
ejpam-4021	95	15	l	l	NOUN
ejpam-4021	95	16	is	be	AUX
ejpam-4021	95	17	defined	define	VERB
ejpam-4021	95	18	by	by	ADP
ejpam-4021	95	19	[	[	X
ejpam-4021	95	20	f	f	X
ejpam-4021	95	21	⇐	⇐	NOUN
ejpam-4021	95	22	(f)](ν	(f)](ν	X
ejpam-4021	95	23	)	)	PUNCT
ejpam-4021	95	24	=	=	SYM
ejpam-4021	95	25	∨	∨	X
ejpam-4021	95	26	{	{	PUNCT
ejpam-4021	95	27	f(µ)|µ	f(µ)|µ	PROPN
ejpam-4021	95	28	∈	∈	PROPN
ejpam-4021	95	29	ly	ly	X
ejpam-4021	95	30	,	,	PUNCT
ejpam-4021	95	31	f←(µ	f←(µ	NOUN
ejpam-4021	95	32	)	)	PUNCT
ejpam-4021	95	33	≤	≤	NUM
ejpam-4021	95	34	ν	ν	X
ejpam-4021	95	35	}	}	PUNCT
ejpam-4021	95	36	,	,	PUNCT
ejpam-4021	95	37	for	for	ADP
ejpam-4021	95	38	all	all	PRON
ejpam-4021	95	39	ν	ν	NOUN
ejpam-4021	95	40	∈	∈	NOUN
ejpam-4021	95	41	lx	lx	NOUN
ejpam-4021	95	42	,	,	PUNCT
ejpam-4021	95	43	is	be	AUX
ejpam-4021	95	44	a	a	DET
ejpam-4021	95	45	stratified	stratified	ADJ
ejpam-4021	95	46	l	l	NOUN
ejpam-4021	95	47	-	-	NOUN
ejpam-4021	95	48	filter	filter	NOUN
ejpam-4021	95	49	on	on	ADP
ejpam-4021	95	50	x	x	SYM
ejpam-4021	95	51	if	if	SCONJ
ejpam-4021	95	52	and	and	CCONJ
ejpam-4021	95	53	only	only	ADV
ejpam-4021	95	54	if	if	SCONJ
ejpam-4021	95	55	for	for	ADP
ejpam-4021	95	56	all	all	DET
ejpam-4021	95	57	µ	µ	PRON
ejpam-4021	95	58	∈	∈	NOUN
ejpam-4021	95	59	ly	ly	X
ejpam-4021	95	60	,	,	PUNCT
ejpam-4021	95	61	f←(µ	f←(µ	NOUN
ejpam-4021	95	62	)	)	PUNCT
ejpam-4021	95	63	=	=	PUNCT
ejpam-4021	95	64	⊥x	⊥x	X
ejpam-4021	95	65	⇒	⇒	PROPN
ejpam-4021	95	66	f(µ	f(µ	PROPN
ejpam-4021	95	67	)	)	PUNCT
ejpam-4021	95	68	=	=	SYM
ejpam-4021	95	69	⊥.	⊥.	NUM
ejpam-4021	95	70	if	if	SCONJ
ejpam-4021	95	71	ν	ν	NOUN
ejpam-4021	95	72	∈	∈	NOUN
ejpam-4021	95	73	lx	lx	NOUN
ejpam-4021	95	74	and	and	CCONJ
ejpam-4021	95	75	µ	µ	PRON
ejpam-4021	95	76	∈	∈	NOUN
ejpam-4021	95	77	ly	ly	X
ejpam-4021	95	78	,	,	PUNCT
ejpam-4021	95	79	then	then	ADV
ejpam-4021	95	80	the	the	DET
ejpam-4021	95	81	product	product	NOUN
ejpam-4021	95	82	ν	ν	X
ejpam-4021	95	83	×	×	NOUN
ejpam-4021	95	84	µ	µ	X
ejpam-4021	95	85	:	:	PUNCT
ejpam-4021	95	86	x	x	SYM
ejpam-4021	95	87	×	×	NOUN
ejpam-4021	95	88	y	y	PROPN
ejpam-4021	95	89	−→	−→	NOUN
ejpam-4021	95	90	l	l	NOUN
ejpam-4021	95	91	is	be	AUX
ejpam-4021	95	92	defined	define	VERB
ejpam-4021	95	93	by	by	ADP
ejpam-4021	95	94	:	:	PUNCT
ejpam-4021	95	95	ν	ν	X
ejpam-4021	95	96	×	×	NOUN
ejpam-4021	95	97	µ	µ	X
ejpam-4021	95	98	=	=	SYM
ejpam-4021	95	99	ν	ν	NOUN
ejpam-4021	95	100	◦	◦	NOUN
ejpam-4021	95	101	pr1	pr1	NOUN
ejpam-4021	95	102	∗	∗	X
ejpam-4021	95	103	µ	µ	PROPN
ejpam-4021	95	104	◦	◦	NOUN
ejpam-4021	95	105	pr2	pr2	NOUN
ejpam-4021	95	106	,	,	PUNCT
ejpam-4021	95	107	where	where	SCONJ
ejpam-4021	95	108	pr1	pr1	NOUN
ejpam-4021	95	109	:	:	PUNCT
ejpam-4021	95	110	x×y	x×y	PUNCT
ejpam-4021	95	111	→	→	SYM
ejpam-4021	95	112	x	x	X
ejpam-4021	95	113	,	,	PUNCT
ejpam-4021	95	114	(	(	PUNCT
ejpam-4021	95	115	x	x	NOUN
ejpam-4021	95	116	,	,	PUNCT
ejpam-4021	95	117	y	y	NOUN
ejpam-4021	95	118	)	)	PUNCT
ejpam-4021	95	119	7→	7→	NUM
ejpam-4021	95	120	x	x	PUNCT
ejpam-4021	95	121	and	and	CCONJ
ejpam-4021	95	122	pr2	pr2	NOUN
ejpam-4021	95	123	:	:	PUNCT
ejpam-4021	95	124	x×y	x×y	PROPN
ejpam-4021	95	125	→	→	SYM
ejpam-4021	95	126	y	y	PROPN
ejpam-4021	95	127	,	,	PUNCT
ejpam-4021	95	128	(	(	PUNCT
ejpam-4021	95	129	x	x	NOUN
ejpam-4021	95	130	,	,	PUNCT
ejpam-4021	95	131	y	y	NOUN
ejpam-4021	95	132	)	)	PUNCT
ejpam-4021	95	133	7→	7→	NUM
ejpam-4021	95	134	y	y	NOUN
ejpam-4021	95	135	are	be	AUX
ejpam-4021	95	136	usual	usual	ADJ
ejpam-4021	95	137	projections	projection	NOUN
ejpam-4021	95	138	.	.	PUNCT
ejpam-4021	96	1	note	note	VERB
ejpam-4021	96	2	that	that	SCONJ
ejpam-4021	96	3	in	in	ADP
ejpam-4021	96	4	the	the	DET
ejpam-4021	96	5	preceding	precede	VERB
ejpam-4021	96	6	definition	definition	NOUN
ejpam-4021	96	7	of	of	ADP
ejpam-4021	96	8	product	product	NOUN
ejpam-4021	96	9	l	l	NOUN
ejpam-4021	96	10	-	-	NOUN
ejpam-4021	96	11	set	set	VERB
ejpam-4021	96	12	the	the	DET
ejpam-4021	96	13	operation	operation	NOUN
ejpam-4021	96	14	∗	∗	NOUN
ejpam-4021	96	15	holds	hold	VERB
ejpam-4021	96	16	only	only	ADV
ejpam-4021	96	17	for	for	ADP
ejpam-4021	96	18	finite	finite	ADJ
ejpam-4021	96	19	case	case	NOUN
ejpam-4021	96	20	;	;	PUNCT
ejpam-4021	96	21	otherwise	otherwise	ADV
ejpam-4021	96	22	,	,	PUNCT
ejpam-4021	96	23	we	we	PRON
ejpam-4021	96	24	need	need	VERB
ejpam-4021	96	25	to	to	PART
ejpam-4021	96	26	take	take	VERB
ejpam-4021	96	27	∗	∗	NOUN
ejpam-4021	96	28	=	=	PUNCT
ejpam-4021	96	29	∧.	∧.	NOUN
ejpam-4021	96	30	proposition	proposition	NOUN
ejpam-4021	96	31	2	2	NUM
ejpam-4021	96	32	.	.	PUNCT
ejpam-4021	97	1	[	[	X
ejpam-4021	97	2	16	16	NUM
ejpam-4021	97	3	]	]	X
ejpam-4021	97	4	if	if	SCONJ
ejpam-4021	97	5	(	(	PUNCT
ejpam-4021	97	6	l,≤	l,≤	PROPN
ejpam-4021	97	7	,	,	PUNCT
ejpam-4021	97	8	∗	∗	NOUN
ejpam-4021	97	9	)	)	PUNCT
ejpam-4021	97	10	is	be	AUX
ejpam-4021	97	11	a	a	DET
ejpam-4021	97	12	gl	gl	NOUN
ejpam-4021	97	13	-	-	NOUN
ejpam-4021	97	14	monoid	monoid	NOUN
ejpam-4021	97	15	,	,	PUNCT
ejpam-4021	97	16	then	then	ADV
ejpam-4021	97	17	for	for	ADP
ejpam-4021	97	18	stratified	stratified	ADJ
ejpam-4021	97	19	l	l	ADV
ejpam-4021	97	20	-	-	PUNCT
ejpam-4021	97	21	valued	value	VERB
ejpam-4021	97	22	filters	filter	NOUN
ejpam-4021	97	23	f1	f1	PROPN
ejpam-4021	97	24	and	and	CCONJ
ejpam-4021	97	25	f2	f2	PROPN
ejpam-4021	97	26	,	,	PUNCT
ejpam-4021	97	27	the	the	DET
ejpam-4021	97	28	supremum	supremum	ADJ
ejpam-4021	97	29	f1∨f2	f1∨f2	NOUN
ejpam-4021	97	30	exists	exist	VERB
ejpam-4021	97	31	if	if	SCONJ
ejpam-4021	97	32	and	and	CCONJ
ejpam-4021	97	33	only	only	ADV
ejpam-4021	97	34	if	if	SCONJ
ejpam-4021	97	35	f1(ν1)∗f2(ν2	f1(ν1)∗f2(ν2	ADJ
ejpam-4021	97	36	)	)	PUNCT
ejpam-4021	97	37	=	=	SYM
ejpam-4021	98	1	⊥	⊥	PROPN
ejpam-4021	98	2	∀ν1	∀ν1	PROPN
ejpam-4021	98	3	,	,	PUNCT
ejpam-4021	98	4	ν2	ν2	NOUN
ejpam-4021	98	5	∈	∈	NOUN
ejpam-4021	98	6	lx	lx	ADP
ejpam-4021	98	7	such	such	ADJ
ejpam-4021	98	8	that	that	SCONJ
ejpam-4021	98	9	ν1	ν1	NOUN
ejpam-4021	98	10	∗	∗	NOUN
ejpam-4021	98	11	ν2	ν2	NOUN
ejpam-4021	98	12	=	=	SYM
ejpam-4021	98	13	⊥x	⊥x	NOUN
ejpam-4021	98	14	.	.	PUNCT
ejpam-4021	99	1	in	in	ADP
ejpam-4021	99	2	particular	particular	ADJ
ejpam-4021	99	3	,	,	PUNCT
ejpam-4021	99	4	the	the	DET
ejpam-4021	99	5	supremum	supremum	NOUN
ejpam-4021	99	6	is	be	AUX
ejpam-4021	99	7	the	the	DET
ejpam-4021	99	8	stratified	stratified	ADJ
ejpam-4021	99	9	l	l	NOUN
ejpam-4021	99	10	-	-	PUNCT
ejpam-4021	99	11	valued	value	VERB
ejpam-4021	99	12	filter	filter	NOUN
ejpam-4021	99	13	defined	define	VERB
ejpam-4021	99	14	for	for	ADP
ejpam-4021	99	15	all	all	PRON
ejpam-4021	99	16	ν	ν	NOUN
ejpam-4021	99	17	∈	∈	NOUN
ejpam-4021	99	18	lx	lx	NOUN
ejpam-4021	99	19	by	by	ADP
ejpam-4021	99	20	f1	f1	PROPN
ejpam-4021	99	21	∨	∨	NUM
ejpam-4021	99	22	f2(ν	f2(ν	NUM
ejpam-4021	99	23	)	)	PUNCT
ejpam-4021	99	24	=	=	SYM
ejpam-4021	99	25	∨	∨	X
ejpam-4021	99	26	{	{	PUNCT
ejpam-4021	99	27	f1(ν1	f1(ν1	NOUN
ejpam-4021	99	28	)	)	PUNCT
ejpam-4021	99	29	∗	∗	NOUN
ejpam-4021	99	30	f2(ν2)|	f2(ν2)|	PROPN
ejpam-4021	99	31	ν1	ν1	PROPN
ejpam-4021	99	32	,	,	PUNCT
ejpam-4021	99	33	ν2	ν2	NOUN
ejpam-4021	99	34	∈	∈	PROPN
ejpam-4021	99	35	lx	lx	NOUN
ejpam-4021	99	36	,	,	PUNCT
ejpam-4021	99	37	ν1	ν1	NOUN
ejpam-4021	99	38	∗	∗	NOUN
ejpam-4021	99	39	ν2	ν2	NOUN
ejpam-4021	99	40	≤	≤	NUM
ejpam-4021	99	41	ν	ν	NOUN
ejpam-4021	99	42	}	}	PUNCT
ejpam-4021	99	43	.	.	PUNCT
ejpam-4021	100	1	let	let	AUX
ejpam-4021	100	2	(	(	PUNCT
ejpam-4021	100	3	g	g	NOUN
ejpam-4021	100	4	,	,	PUNCT
ejpam-4021	100	5	·	·	PUNCT
ejpam-4021	100	6	)	)	PUNCT
ejpam-4021	100	7	be	be	AUX
ejpam-4021	100	8	a	a	DET
ejpam-4021	100	9	group	group	NOUN
ejpam-4021	100	10	.	.	PUNCT
ejpam-4021	101	1	if	if	SCONJ
ejpam-4021	101	2	f	f	PROPN
ejpam-4021	101	3	∈	∈	PROPN
ejpam-4021	101	4	ls(g	ls(g	X
ejpam-4021	101	5	)	)	PUNCT
ejpam-4021	101	6	,	,	PUNCT
ejpam-4021	101	7	then	then	ADV
ejpam-4021	101	8	f−1	f−1	PROPN
ejpam-4021	101	9	is	be	AUX
ejpam-4021	101	10	defined	define	VERB
ejpam-4021	101	11	by	by	ADP
ejpam-4021	101	12	f−1(ν	f−1(ν	PROPN
ejpam-4021	101	13	)	)	PUNCT
ejpam-4021	102	1	=	=	SYM
ejpam-4021	102	2	f(ν−1	f(ν−1	NOUN
ejpam-4021	102	3	)	)	PUNCT
ejpam-4021	102	4	,	,	PUNCT
ejpam-4021	103	1	where	where	SCONJ
ejpam-4021	103	2	ν−1	ν−1	ADV
ejpam-4021	103	3	:	:	PUNCT
ejpam-4021	103	4	g	g	ADP
ejpam-4021	103	5	−→	−→	PROPN
ejpam-4021	103	6	l	l	NOUN
ejpam-4021	103	7	,	,	PUNCT
ejpam-4021	103	8	x	x	SYM
ejpam-4021	103	9	7−→	7−→	NOUN
ejpam-4021	103	10	ν(x−1	ν(x−1	ADP
ejpam-4021	103	11	)	)	PUNCT
ejpam-4021	103	12	.	.	PUNCT
ejpam-4021	104	1	clearly	clearly	ADV
ejpam-4021	104	2	,	,	PUNCT
ejpam-4021	104	3	f−1	f−1	PROPN
ejpam-4021	104	4	∈	∈	PROPN
ejpam-4021	104	5	fsl(g	fsl(g	PROPN
ejpam-4021	104	6	)	)	PUNCT
ejpam-4021	104	7	,	,	PUNCT
ejpam-4021	104	8	since	since	SCONJ
ejpam-4021	104	9	for	for	ADP
ejpam-4021	104	10	any	any	DET
ejpam-4021	104	11	ν	ν	NOUN
ejpam-4021	104	12	∈	∈	NOUN
ejpam-4021	104	13	lx	lx	NOUN
ejpam-4021	104	14	,	,	PUNCT
ejpam-4021	104	15	⇒(f)(ν	⇒(f)(ν	PROPN
ejpam-4021	104	16	)	)	PUNCT
ejpam-4021	105	1	=	=	SYM
ejpam-4021	105	2	f	f	PROPN
ejpam-4021	105	3	(	(	PUNCT
ejpam-4021	105	4	←(ν	←(ν	NOUN
ejpam-4021	105	5	)	)	PUNCT
ejpam-4021	105	6	)	)	PUNCT
ejpam-4021	106	1	=	=	PUNCT
ejpam-4021	106	2	f(ν−1	f(ν−1	X
ejpam-4021	106	3	)	)	PUNCT
ejpam-4021	106	4	=	=	SYM
ejpam-4021	107	1	f−1(ν	f−1(ν	PROPN
ejpam-4021	107	2	)	)	PUNCT
ejpam-4021	107	3	,	,	PUNCT
ejpam-4021	107	4	where	where	SCONJ
ejpam-4021	107	5			NOUN
ejpam-4021	107	6	:	:	PUNCT
ejpam-4021	107	7	g	g	ADP
ejpam-4021	107	8	−→	−→	NOUN
ejpam-4021	107	9	g	g	PROPN
ejpam-4021	107	10	,	,	PUNCT
ejpam-4021	107	11	x	x	PROPN
ejpam-4021	107	12	7→	7→	NUM
ejpam-4021	107	13	x−1	x−1	NOUN
ejpam-4021	107	14	.	.	PUNCT
ejpam-4021	108	1	also	also	ADV
ejpam-4021	108	2	,	,	PUNCT
ejpam-4021	108	3	if	if	SCONJ
ejpam-4021	108	4	m	m	ADV
ejpam-4021	108	5	:	:	PUNCT
ejpam-4021	108	6	g	g	ADP
ejpam-4021	108	7	×	×	PROPN
ejpam-4021	108	8	g	g	PROPN
ejpam-4021	108	9	→	→	SYM
ejpam-4021	108	10	g	g	PROPN
ejpam-4021	108	11	,	,	PUNCT
ejpam-4021	108	12	(	(	PUNCT
ejpam-4021	108	13	g	g	NOUN
ejpam-4021	108	14	,	,	PUNCT
ejpam-4021	108	15	h	h	NOUN
ejpam-4021	108	16	)	)	PUNCT
ejpam-4021	108	17	7→	7→	NUM
ejpam-4021	109	1	gh	gh	PROPN
ejpam-4021	109	2	,	,	PUNCT
ejpam-4021	109	3	then	then	ADV
ejpam-4021	109	4	for	for	ADP
ejpam-4021	109	5	any	any	DET
ejpam-4021	109	6	ν1	ν1	NOUN
ejpam-4021	109	7	,	,	PUNCT
ejpam-4021	109	8	ν2	ν2	NOUN
ejpam-4021	109	9	∈	∈	PROPN
ejpam-4021	109	10	lg	lg	NOUN
ejpam-4021	109	11	and	and	CCONJ
ejpam-4021	109	12	z	z	PROPN
ejpam-4021	109	13	∈	∈	PROPN
ejpam-4021	109	14	g	g	NOUN
ejpam-4021	109	15	,	,	PUNCT
ejpam-4021	109	16	m→	m→	PROPN
ejpam-4021	109	17	(	(	PUNCT
ejpam-4021	109	18	ν1	ν1	NOUN
ejpam-4021	109	19	×	×	NOUN
ejpam-4021	109	20	ν2	ν2	NOUN
ejpam-4021	109	21	)	)	PUNCT
ejpam-4021	109	22	(	(	PUNCT
ejpam-4021	109	23	z	z	NOUN
ejpam-4021	109	24	)	)	PUNCT
ejpam-4021	109	25	=	=	SYM
ejpam-4021	109	26	∨	∨	NUM
ejpam-4021	109	27	m(g	m(g	PROPN
ejpam-4021	109	28	,	,	PUNCT
ejpam-4021	109	29	h)=z	h)=z	PROPN
ejpam-4021	109	30	(	(	PUNCT
ejpam-4021	109	31	ν1	ν1	NOUN
ejpam-4021	109	32	×	×	NOUN
ejpam-4021	109	33	ν2	ν2	NOUN
ejpam-4021	109	34	)	)	PUNCT
ejpam-4021	109	35	(	(	PUNCT
ejpam-4021	109	36	g	g	NOUN
ejpam-4021	109	37	,	,	PUNCT
ejpam-4021	109	38	h	h	NOUN
ejpam-4021	109	39	)	)	PUNCT
ejpam-4021	109	40	=	=	PUNCT
ejpam-4021	109	41	∨	∨	NUM
ejpam-4021	109	42	gh	gh	PROPN
ejpam-4021	109	43	=	=	PROPN
ejpam-4021	109	44	z	z	PROPN
ejpam-4021	109	45	(	(	PUNCT
ejpam-4021	109	46	ν1	ν1	NOUN
ejpam-4021	109	47	◦	◦	PROPN
ejpam-4021	109	48	pr1	pr1	NOUN
ejpam-4021	109	49	∗	∗	NOUN
ejpam-4021	109	50	ν2	ν2	ADP
ejpam-4021	109	51	◦	◦	PROPN
ejpam-4021	109	52	pr2	pr2	NOUN
ejpam-4021	109	53	)	)	PUNCT
ejpam-4021	109	54	(	(	PUNCT
ejpam-4021	109	55	g	g	NOUN
ejpam-4021	109	56	,	,	PUNCT
ejpam-4021	109	57	h	h	NOUN
ejpam-4021	109	58	)	)	PUNCT
ejpam-4021	109	59	=	=	PUNCT
ejpam-4021	110	1	∨	∨	NUM
ejpam-4021	110	2	gh	gh	PROPN
ejpam-4021	110	3	=	=	PROPN
ejpam-4021	110	4	z	z	PROPN
ejpam-4021	110	5	ν1	ν1	PROPN
ejpam-4021	110	6	◦	◦	PROPN
ejpam-4021	110	7	pr1(g	pr1(g	PROPN
ejpam-4021	110	8	,	,	PUNCT
ejpam-4021	110	9	h	h	NOUN
ejpam-4021	110	10	)	)	PUNCT
ejpam-4021	110	11	∗	∗	NOUN
ejpam-4021	110	12	ν2	ν2	ADP
ejpam-4021	110	13	◦	◦	NOUN
ejpam-4021	110	14	pr2(g	pr2(g	ADJ
ejpam-4021	110	15	,	,	PUNCT
ejpam-4021	110	16	h	h	NOUN
ejpam-4021	110	17	)	)	PUNCT
ejpam-4021	110	18	=	=	PUNCT
ejpam-4021	111	1	∨	∨	NUM
ejpam-4021	111	2	gh	gh	PROPN
ejpam-4021	111	3	=	=	PROPN
ejpam-4021	111	4	z	z	PROPN
ejpam-4021	111	5	ν1(g	ν1(g	PROPN
ejpam-4021	111	6	)	)	PUNCT
ejpam-4021	111	7	∗	∗	NOUN
ejpam-4021	111	8	ν2(h	ν2(h	PROPN
ejpam-4021	111	9	)	)	PUNCT
ejpam-4021	111	10	=	=	NOUN
ejpam-4021	111	11	ν1	ν1	NOUN
ejpam-4021	111	12	�	�	PROPN
ejpam-4021	111	13	ν2(z	ν2(z	PROPN
ejpam-4021	111	14	)	)	PUNCT
ejpam-4021	111	15	.	.	PUNCT
ejpam-4021	112	1	lemma	lemma	PROPN
ejpam-4021	112	2	1	1	NUM
ejpam-4021	112	3	.	.	PUNCT
ejpam-4021	113	1	[	[	X
ejpam-4021	113	2	3	3	X
ejpam-4021	113	3	]	]	X
ejpam-4021	113	4	let	let	VERB
ejpam-4021	113	5	l	l	NOUN
ejpam-4021	113	6	=	=	SYM
ejpam-4021	113	7	(	(	PUNCT
ejpam-4021	113	8	l,≤	l,≤	PROPN
ejpam-4021	113	9	,	,	PUNCT
ejpam-4021	113	10	∗	∗	NOUN
ejpam-4021	113	11	)	)	PUNCT
ejpam-4021	113	12	be	be	VERB
ejpam-4021	113	13	a	a	DET
ejpam-4021	113	14	gl	gl	NOUN
ejpam-4021	113	15	-	-	NOUN
ejpam-4021	113	16	monoid	monoid	NOUN
ejpam-4021	113	17	and	and	CCONJ
ejpam-4021	113	18	(	(	PUNCT
ejpam-4021	113	19	g	g	PROPN
ejpam-4021	113	20	,	,	PUNCT
ejpam-4021	113	21	·	·	PUNCT
ejpam-4021	113	22	)	)	PUNCT
ejpam-4021	114	1	∈	∈	PROPN
ejpam-4021	114	2	|grp|	|grp|	NOUN
ejpam-4021	114	3	.	.	PUNCT
ejpam-4021	115	1	then	then	ADV
ejpam-4021	115	2	for	for	ADP
ejpam-4021	115	3	any	any	DET
ejpam-4021	115	4	f	f	NOUN
ejpam-4021	115	5	,	,	PUNCT
ejpam-4021	115	6	g	g	PROPN
ejpam-4021	115	7	∈	∈	PROPN
ejpam-4021	115	8	fsl(x	fsl(x	PROPN
ejpam-4021	115	9	)	)	PUNCT
ejpam-4021	115	10	,	,	PUNCT
ejpam-4021	115	11	m⇒(f	m⇒(f	PROPN
ejpam-4021	115	12	×	×	VERB
ejpam-4021	115	13	g	g	NOUN
ejpam-4021	115	14	)	)	PUNCT
ejpam-4021	115	15	=	=	SYM
ejpam-4021	115	16	f	f	PROPN
ejpam-4021	115	17	�	�	PROPN
ejpam-4021	115	18	g.	g.	PROPN
ejpam-4021	115	19	definition	definition	NOUN
ejpam-4021	115	20	7	7	NUM
ejpam-4021	115	21	.	.	PUNCT
ejpam-4021	116	1	[	[	X
ejpam-4021	116	2	17	17	NUM
ejpam-4021	116	3	]	]	PUNCT
ejpam-4021	116	4	consider	consider	VERB
ejpam-4021	116	5	a	a	DET
ejpam-4021	116	6	mapping	mapping	NOUN
ejpam-4021	116	7	n	n	NOUN
ejpam-4021	116	8	:	:	PUNCT
ejpam-4021	116	9	x	x	PUNCT
ejpam-4021	116	10	−→	−→	NOUN
ejpam-4021	116	11	llx	llx	PROPN
ejpam-4021	116	12	such	such	ADJ
ejpam-4021	116	13	that	that	SCONJ
ejpam-4021	116	14	the	the	DET
ejpam-4021	116	15	following	follow	VERB
ejpam-4021	116	16	conditions	condition	NOUN
ejpam-4021	116	17	are	be	AUX
ejpam-4021	116	18	fulfilled	fulfil	VERB
ejpam-4021	116	19	:	:	PUNCT
ejpam-4021	116	20	(	(	PUNCT
ejpam-4021	116	21	ln1	ln1	NOUN
ejpam-4021	116	22	)	)	PUNCT
ejpam-4021	116	23	nx(>x	nx(>x	NOUN
ejpam-4021	116	24	)	)	PUNCT
ejpam-4021	117	1	=	=	PUNCT
ejpam-4021	117	2	>	>	X
ejpam-4021	117	3	;	;	PUNCT
ejpam-4021	117	4	(	(	PUNCT
ejpam-4021	117	5	ln2	ln2	ADJ
ejpam-4021	117	6	)	)	PUNCT
ejpam-4021	117	7	nx(ν1	nx(ν1	NOUN
ejpam-4021	117	8	)	)	PUNCT
ejpam-4021	117	9	≤	≤	NOUN
ejpam-4021	117	10	nx(ν2	nx(ν2	PROPN
ejpam-4021	117	11	)	)	PUNCT
ejpam-4021	117	12	for	for	ADP
ejpam-4021	117	13	all	all	DET
ejpam-4021	117	14	ν1	ν1	NOUN
ejpam-4021	117	15	,	,	PUNCT
ejpam-4021	117	16	ν2	ν2	NOUN
ejpam-4021	117	17	∈	∈	NOUN
ejpam-4021	117	18	lx	lx	NOUN
ejpam-4021	117	19	with	with	ADP
ejpam-4021	117	20	ν1	ν1	NOUN
ejpam-4021	117	21	≤	≤	NUM
ejpam-4021	117	22	ν2	ν2	NOUN
ejpam-4021	117	23	;	;	PUNCT
ejpam-4021	117	24	(	(	PUNCT
ejpam-4021	117	25	ln3	ln3	NOUN
ejpam-4021	117	26	)	)	PUNCT
ejpam-4021	117	27	nx(ν1)⊗nx(ν2	nx(ν1)⊗nx(ν2	CCONJ
ejpam-4021	117	28	)	)	PUNCT
ejpam-4021	117	29	≤	≤	NOUN
ejpam-4021	117	30	nx(ν1	nx(ν1	VERB
ejpam-4021	117	31	⊗	⊗	PROPN
ejpam-4021	117	32	ν2	ν2	NOUN
ejpam-4021	117	33	)	)	PUNCT
ejpam-4021	117	34	,	,	PUNCT
ejpam-4021	117	35	for	for	ADP
ejpam-4021	117	36	all	all	DET
ejpam-4021	117	37	ν1	ν1	NOUN
ejpam-4021	117	38	,	,	PUNCT
ejpam-4021	117	39	ν2	ν2	NOUN
ejpam-4021	117	40	∈	∈	NOUN
ejpam-4021	117	41	lx	lx	NOUN
ejpam-4021	117	42	;	;	PUNCT
ejpam-4021	117	43	(	(	PUNCT
ejpam-4021	117	44	ln4	ln4	INTJ
ejpam-4021	117	45	)	)	PUNCT
ejpam-4021	117	46	nx(ν	nx(ν	PROPN
ejpam-4021	117	47	)	)	PUNCT
ejpam-4021	117	48	≤	≤	NUM
ejpam-4021	118	1	ν(x	ν(x	PROPN
ejpam-4021	118	2	)	)	PUNCT
ejpam-4021	118	3	,	,	PUNCT
ejpam-4021	118	4	for	for	ADP
ejpam-4021	118	5	all	all	PRON
ejpam-4021	118	6	ν	ν	NOUN
ejpam-4021	118	7	∈	∈	NOUN
ejpam-4021	118	8	lx	lx	NOUN
ejpam-4021	118	9	;	;	PUNCT
ejpam-4021	118	10	(	(	PUNCT
ejpam-4021	118	11	ln5	ln5	NOUN
ejpam-4021	118	12	)	)	PUNCT
ejpam-4021	118	13	∀x	∀x	VERB
ejpam-4021	118	14	∈	∈	PROPN
ejpam-4021	118	15	x	x	X
ejpam-4021	118	16	and	and	CCONJ
ejpam-4021	118	17	ν	ν	X
ejpam-4021	118	18	∈	∈	PROPN
ejpam-4021	118	19	lx	lx	NOUN
ejpam-4021	118	20	,	,	PUNCT
ejpam-4021	118	21	nx(ν	nx(ν	PUNCT
ejpam-4021	118	22	)	)	PUNCT
ejpam-4021	118	23	≤	≤	NUM
ejpam-4021	118	24	∨	∨	NUM
ejpam-4021	118	25	{	{	PUNCT
ejpam-4021	118	26	nx(µ	nx(µ	NOUN
ejpam-4021	118	27	)	)	PUNCT
ejpam-4021	118	28	:	:	PUNCT
ejpam-4021	118	29	µ	µ	X
ejpam-4021	118	30	∈	∈	NOUN
ejpam-4021	118	31	lx	lx	NOUN
ejpam-4021	118	32	,	,	PUNCT
ejpam-4021	118	33	µ(y	µ(y	PROPN
ejpam-4021	118	34	)	)	PUNCT
ejpam-4021	118	35	≤	≤	NOUN
ejpam-4021	119	1	[	[	X
ejpam-4021	119	2	ny](ν	ny](ν	PROPN
ejpam-4021	119	3	)	)	PUNCT
ejpam-4021	119	4	,	,	PUNCT
ejpam-4021	119	5	∀y	∀y	PROPN
ejpam-4021	119	6	∈	∈	PROPN
ejpam-4021	119	7	x	x	PRON
ejpam-4021	119	8	}	}	PUNCT
ejpam-4021	119	9	(	(	PUNCT
ejpam-4021	119	10	sln	sln	PROPN
ejpam-4021	119	11	)	)	PUNCT
ejpam-4021	119	12	α	α	PROPN
ejpam-4021	119	13	∗nx(ν	∗nx(ν	PROPN
ejpam-4021	119	14	)	)	PUNCT
ejpam-4021	119	15	≤	≤	NOUN
ejpam-4021	119	16	nx(α	nx(α	PUNCT
ejpam-4021	119	17	∗	∗	NOUN
ejpam-4021	119	18	ν	ν	NOUN
ejpam-4021	119	19	)	)	PUNCT
ejpam-4021	119	20	.	.	PUNCT
ejpam-4021	120	1	then	then	ADV
ejpam-4021	120	2	n	n	ADV
ejpam-4021	120	3	=	=	PUNCT
ejpam-4021	120	4	(	(	PUNCT
ejpam-4021	120	5	nx)x∈x	nx)x∈x	PROPN
ejpam-4021	120	6	is	be	AUX
ejpam-4021	120	7	called	call	VERB
ejpam-4021	120	8	a	a	DET
ejpam-4021	120	9	stratified	stratified	ADJ
ejpam-4021	120	10	l	l	ADV
ejpam-4021	120	11	-	-	PUNCT
ejpam-4021	120	12	valued	value	VERB
ejpam-4021	120	13	neighborhood	neighborhood	NOUN
ejpam-4021	120	14	system	system	NOUN
ejpam-4021	120	15	on	on	ADP
ejpam-4021	120	16	x	x	NOUN
ejpam-4021	120	17	,	,	PUNCT
ejpam-4021	120	18	and	and	CCONJ
ejpam-4021	120	19	the	the	DET
ejpam-4021	120	20	t	t	PROPN
ejpam-4021	120	21	m	m	VERB
ejpam-4021	120	22	g	g	NOUN
ejpam-4021	120	23	ahsanullah	ahsanullah	NOUN
ejpam-4021	120	24	,	,	PUNCT
ejpam-4021	120	25	fawzi	fawzi	PROPN
ejpam-4021	120	26	al	al	PROPN
ejpam-4021	120	27	-	-	PUNCT
ejpam-4021	120	28	thukair	thukair	NOUN
ejpam-4021	120	29	/	/	SYM
ejpam-4021	120	30	eur	eur	NOUN
ejpam-4021	120	31	.	.	PUNCT
ejpam-4021	121	1	j.	j.	PROPN
ejpam-4021	121	2	pure	pure	PROPN
ejpam-4021	121	3	appl	appl	PROPN
ejpam-4021	121	4	.	.	PROPN
ejpam-4021	121	5	math	math	PROPN
ejpam-4021	121	6	,	,	PUNCT
ejpam-4021	121	7	14	14	NUM
ejpam-4021	121	8	(	(	PUNCT
ejpam-4021	121	9	3	3	NUM
ejpam-4021	121	10	)	)	PUNCT
ejpam-4021	121	11	(	(	PUNCT
ejpam-4021	121	12	2021	2021	NUM
ejpam-4021	121	13	)	)	PUNCT
ejpam-4021	121	14	,	,	PUNCT
ejpam-4021	121	15	949	949	NUM
ejpam-4021	121	16	-	-	SYM
ejpam-4021	121	17	968	968	NUM
ejpam-4021	121	18	954	954	NUM
ejpam-4021	121	19	pair	pair	NOUN
ejpam-4021	121	20	(	(	PUNCT
ejpam-4021	121	21	x	x	NOUN
ejpam-4021	121	22	,	,	PUNCT
ejpam-4021	121	23	n	n	NOUN
ejpam-4021	121	24	=	=	SYM
ejpam-4021	121	25	(	(	PUNCT
ejpam-4021	121	26	nx)x∈x	nx)x∈x	NUM
ejpam-4021	121	27	)	)	PUNCT
ejpam-4021	121	28	is	be	AUX
ejpam-4021	121	29	called	call	VERB
ejpam-4021	121	30	a	a	DET
ejpam-4021	121	31	stratified	stratified	ADJ
ejpam-4021	121	32	l	l	ADV
ejpam-4021	121	33	-	-	PUNCT
ejpam-4021	121	34	valued	value	VERB
ejpam-4021	121	35	neighborhood	neighborhood	NOUN
ejpam-4021	121	36	space	space	NOUN
ejpam-4021	121	37	.	.	PUNCT
ejpam-4021	122	1	if	if	SCONJ
ejpam-4021	122	2	(	(	PUNCT
ejpam-4021	122	3	x	x	NOUN
ejpam-4021	122	4	,	,	PUNCT
ejpam-4021	122	5	n	n	CCONJ
ejpam-4021	122	6	)	)	PUNCT
ejpam-4021	122	7	and	and	CCONJ
ejpam-4021	122	8	(	(	PUNCT
ejpam-4021	122	9	y	y	PROPN
ejpam-4021	122	10	,	,	PUNCT
ejpam-4021	122	11	m	m	NOUN
ejpam-4021	122	12	)	)	PUNCT
ejpam-4021	122	13	stratified	stratify	VERB
ejpam-4021	122	14	l	l	NOUN
ejpam-4021	122	15	-	-	PUNCT
ejpam-4021	122	16	valued	value	VERB
ejpam-4021	122	17	neighborhood	neighborhood	NOUN
ejpam-4021	122	18	spaces	space	NOUN
ejpam-4021	122	19	,	,	PUNCT
ejpam-4021	122	20	then	then	ADV
ejpam-4021	122	21	a	a	DET
ejpam-4021	122	22	map	map	NOUN
ejpam-4021	123	1	f	f	X
ejpam-4021	123	2	:	:	PUNCT
ejpam-4021	123	3	(	(	PUNCT
ejpam-4021	123	4	x	x	NOUN
ejpam-4021	123	5	,	,	PUNCT
ejpam-4021	123	6	n	n	CCONJ
ejpam-4021	123	7	)	)	PUNCT
ejpam-4021	123	8	→	→	SYM
ejpam-4021	123	9	(	(	PUNCT
ejpam-4021	123	10	y	y	PROPN
ejpam-4021	123	11	,	,	PUNCT
ejpam-4021	123	12	m	m	PROPN
ejpam-4021	123	13	)	)	PUNCT
ejpam-4021	123	14	is	be	AUX
ejpam-4021	123	15	said	say	VERB
ejpam-4021	123	16	to	to	PART
ejpam-4021	123	17	be	be	AUX
ejpam-4021	123	18	continuous	continuous	ADJ
ejpam-4021	123	19	at	at	ADP
ejpam-4021	123	20	a	a	DET
ejpam-4021	123	21	point	point	NOUN
ejpam-4021	123	22	x	x	SYM
ejpam-4021	123	23	∈	∈	NOUN
ejpam-4021	123	24	x	x	INTJ
ejpam-4021	123	25	if	if	SCONJ
ejpam-4021	123	26	and	and	CCONJ
ejpam-4021	123	27	only	only	ADV
ejpam-4021	123	28	if	if	SCONJ
ejpam-4021	123	29	mf(x)(ν	mf(x)(ν	NUM
ejpam-4021	123	30	)	)	PUNCT
ejpam-4021	123	31	≤	≤	NUM
ejpam-4021	123	32	nx	nx	X
ejpam-4021	123	33	(	(	PUNCT
ejpam-4021	123	34	f←(ν	f←(ν	NOUN
ejpam-4021	123	35	)	)	PUNCT
ejpam-4021	123	36	)	)	PUNCT
ejpam-4021	123	37	,	,	PUNCT
ejpam-4021	123	38	for	for	SCONJ
ejpam-4021	123	39	all	all	DET
ejpam-4021	123	40	ν	ν	NOUN
ejpam-4021	123	41	∈	∈	NOUN
ejpam-4021	123	42	ly	ly	X
ejpam-4021	123	43	.	.	PUNCT
ejpam-4021	124	1	sl	sl	NOUN
ejpam-4021	124	2	-	-	PUNCT
ejpam-4021	124	3	ns	ns	PROPN
ejpam-4021	124	4	denotes	denote	NOUN
ejpam-4021	124	5	the	the	DET
ejpam-4021	124	6	category	category	NOUN
ejpam-4021	124	7	of	of	ADP
ejpam-4021	124	8	all	all	PRON
ejpam-4021	124	9	stratified	stratified	ADJ
ejpam-4021	124	10	l	l	ADV
ejpam-4021	124	11	-	-	PUNCT
ejpam-4021	124	12	valued	value	VERB
ejpam-4021	124	13	neighborhood	neighborhood	NOUN
ejpam-4021	124	14	spaces	space	NOUN
ejpam-4021	124	15	as	as	ADP
ejpam-4021	124	16	objects	object	NOUN
ejpam-4021	124	17	and	and	CCONJ
ejpam-4021	124	18	all	all	DET
ejpam-4021	124	19	continuous	continuous	ADJ
ejpam-4021	124	20	maps	map	NOUN
ejpam-4021	124	21	as	as	ADP
ejpam-4021	124	22	morphisms	morphism	NOUN
ejpam-4021	124	23	.	.	PUNCT
ejpam-4021	125	1	definition	definition	NOUN
ejpam-4021	125	2	8	8	NUM
ejpam-4021	125	3	.	.	PUNCT
ejpam-4021	126	1	[	[	X
ejpam-4021	126	2	17	17	NUM
ejpam-4021	126	3	,	,	PUNCT
ejpam-4021	126	4	22	22	NUM
ejpam-4021	126	5	]	]	PUNCT
ejpam-4021	126	6	let	let	VERB
ejpam-4021	126	7	∆	∆	PROPN
ejpam-4021	126	8	⊆	⊆	NUM
ejpam-4021	126	9	lx	lx	ADP
ejpam-4021	126	10	such	such	ADJ
ejpam-4021	126	11	that	that	SCONJ
ejpam-4021	126	12	the	the	DET
ejpam-4021	126	13	following	follow	VERB
ejpam-4021	126	14	are	be	AUX
ejpam-4021	126	15	fulfilled	fulfil	VERB
ejpam-4021	126	16	:	:	PUNCT
ejpam-4021	126	17	(	(	PUNCT
ejpam-4021	126	18	lt1	lt1	NOUN
ejpam-4021	126	19	)	)	PUNCT
ejpam-4021	126	20	>	>	PUNCT
ejpam-4021	127	1	x	x	X
ejpam-4021	127	2	,	,	PUNCT
ejpam-4021	127	3	⊥x	⊥x	NOUN
ejpam-4021	127	4	∈	∈	PROPN
ejpam-4021	127	5	∆	∆	X
ejpam-4021	127	6	;	;	PUNCT
ejpam-4021	127	7	(	(	PUNCT
ejpam-4021	127	8	lt2	lt2	PROPN
ejpam-4021	127	9	)	)	PUNCT
ejpam-4021	127	10	ν1	ν1	PROPN
ejpam-4021	127	11	,	,	PUNCT
ejpam-4021	127	12	ν2	ν2	PROPN
ejpam-4021	127	13	∈	∈	PROPN
ejpam-4021	127	14	∆⇒	∆⇒	NOUN
ejpam-4021	127	15	ν1	ν1	NOUN
ejpam-4021	127	16	⊗	⊗	PROPN
ejpam-4021	127	17	ν2	ν2	PROPN
ejpam-4021	127	18	∈	∈	PROPN
ejpam-4021	127	19	∆	∆	X
ejpam-4021	127	20	;	;	PUNCT
ejpam-4021	127	21	(	(	PUNCT
ejpam-4021	127	22	lt3	lt3	NOUN
ejpam-4021	127	23	)	)	PUNCT
ejpam-4021	127	24	{	{	PUNCT
ejpam-4021	127	25	νj}j∈j	νj}j∈j	ADP
ejpam-4021	127	26	⊆	⊆	NUM
ejpam-4021	127	27	∆⇒	∆⇒	PROPN
ejpam-4021	127	28	∨	∨	NUM
ejpam-4021	127	29	j∈j	j∈j	NOUN
ejpam-4021	127	30	νj	νj	PROPN
ejpam-4021	127	31	∈	∈	PROPN
ejpam-4021	127	32	∆	∆	X
ejpam-4021	127	33	;	;	PUNCT
ejpam-4021	127	34	(	(	PUNCT
ejpam-4021	127	35	slt	slt	X
ejpam-4021	127	36	)	)	PUNCT
ejpam-4021	127	37	ν	ν	PROPN
ejpam-4021	127	38	∈	∈	PROPN
ejpam-4021	127	39	∆	∆	PROPN
ejpam-4021	127	40	,	,	PUNCT
ejpam-4021	127	41	α	α	PROPN
ejpam-4021	127	42	∈	∈	PROPN
ejpam-4021	127	43	l⇒	l⇒	X
ejpam-4021	127	44	αx	αx	ADV
ejpam-4021	127	45	∗	∗	VERB
ejpam-4021	127	46	ν	ν	X
ejpam-4021	127	47	∈	∈	PROPN
ejpam-4021	128	1	∆.	∆.	X
ejpam-4021	128	2	we	we	PRON
ejpam-4021	128	3	call	call	VERB
ejpam-4021	128	4	∆	∆	PROPN
ejpam-4021	128	5	an	an	DET
ejpam-4021	128	6	l	l	ADV
ejpam-4021	128	7	-	-	PUNCT
ejpam-4021	128	8	valued	value	VERB
ejpam-4021	128	9	topology	topology	NOUN
ejpam-4021	128	10	on	on	ADP
ejpam-4021	128	11	x	x	SYM
ejpam-4021	128	12	if	if	SCONJ
ejpam-4021	128	13	it	it	PRON
ejpam-4021	128	14	satisfies	satisfy	VERB
ejpam-4021	128	15	(	(	PUNCT
ejpam-4021	128	16	lt1)-(lt3	lt1)-(lt3	ADV
ejpam-4021	128	17	)	)	PUNCT
ejpam-4021	128	18	,	,	PUNCT
ejpam-4021	128	19	and	and	CCONJ
ejpam-4021	128	20	the	the	DET
ejpam-4021	128	21	pair	pair	NOUN
ejpam-4021	128	22	(	(	PUNCT
ejpam-4021	128	23	x,∆	x,∆	NUM
ejpam-4021	128	24	)	)	PUNCT
ejpam-4021	128	25	is	be	AUX
ejpam-4021	128	26	called	call	VERB
ejpam-4021	128	27	an	an	DET
ejpam-4021	128	28	l	l	NOUN
ejpam-4021	128	29	-	-	PUNCT
ejpam-4021	128	30	valued	value	VERB
ejpam-4021	128	31	topological	topological	ADJ
ejpam-4021	128	32	space	space	NOUN
ejpam-4021	128	33	.	.	PUNCT
ejpam-4021	129	1	if	if	SCONJ
ejpam-4021	129	2	∆	∆	PROPN
ejpam-4021	129	3	satisfies	satisfie	NOUN
ejpam-4021	129	4	(	(	PUNCT
ejpam-4021	129	5	lt1)-(slt	lt1)-(slt	NUM
ejpam-4021	129	6	)	)	PUNCT
ejpam-4021	129	7	then	then	ADV
ejpam-4021	129	8	we	we	PRON
ejpam-4021	129	9	call	call	VERB
ejpam-4021	129	10	it	it	PRON
ejpam-4021	129	11	a	a	DET
ejpam-4021	129	12	stratified	stratified	ADJ
ejpam-4021	129	13	l	l	ADV
ejpam-4021	129	14	-	-	PUNCT
ejpam-4021	129	15	valued	value	VERB
ejpam-4021	129	16	topology	topology	NOUN
ejpam-4021	129	17	on	on	ADP
ejpam-4021	129	18	x	x	PUNCT
ejpam-4021	129	19	and	and	CCONJ
ejpam-4021	129	20	the	the	DET
ejpam-4021	129	21	pair	pair	NOUN
ejpam-4021	129	22	(	(	PUNCT
ejpam-4021	129	23	x,∆	x,∆	NUM
ejpam-4021	129	24	)	)	PUNCT
ejpam-4021	129	25	or	or	CCONJ
ejpam-4021	129	26	x	x	X
ejpam-4021	129	27	in	in	ADP
ejpam-4021	129	28	short	short	ADJ
ejpam-4021	129	29	,	,	PUNCT
ejpam-4021	129	30	if	if	SCONJ
ejpam-4021	129	31	there	there	PRON
ejpam-4021	129	32	is	be	VERB
ejpam-4021	129	33	no	no	DET
ejpam-4021	129	34	confusion	confusion	NOUN
ejpam-4021	129	35	,	,	PUNCT
ejpam-4021	129	36	is	be	AUX
ejpam-4021	129	37	called	call	VERB
ejpam-4021	129	38	a	a	DET
ejpam-4021	129	39	stratified	stratified	ADJ
ejpam-4021	129	40	l	l	NOUN
ejpam-4021	129	41	-	-	PUNCT
ejpam-4021	129	42	valued	value	VERB
ejpam-4021	129	43	topological	topological	ADJ
ejpam-4021	129	44	space	space	NOUN
ejpam-4021	129	45	;	;	PUNCT
ejpam-4021	129	46	members	member	NOUN
ejpam-4021	129	47	of	of	ADP
ejpam-4021	129	48	∆	∆	PROPN
ejpam-4021	129	49	are	be	AUX
ejpam-4021	129	50	called	call	VERB
ejpam-4021	129	51	open	open	ADJ
ejpam-4021	129	52	l	l	NOUN
ejpam-4021	129	53	-	-	PUNCT
ejpam-4021	129	54	valued	value	VERB
ejpam-4021	129	55	sets	set	NOUN
ejpam-4021	129	56	or	or	CCONJ
ejpam-4021	129	57	l	l	NOUN
ejpam-4021	129	58	-	-	PUNCT
ejpam-4021	129	59	valued	value	VERB
ejpam-4021	129	60	subsets	subset	NOUN
ejpam-4021	129	61	;	;	PUNCT
ejpam-4021	129	62	the	the	DET
ejpam-4021	129	63	members	member	NOUN
ejpam-4021	129	64	of	of	ADP
ejpam-4021	129	65	θ(x	θ(x	PROPN
ejpam-4021	129	66	)	)	PUNCT
ejpam-4021	129	67	=	=	PRON
ejpam-4021	129	68	{	{	PUNCT
ejpam-4021	129	69	ξ	ξ	X
ejpam-4021	129	70	∈	∈	NOUN
ejpam-4021	129	71	lx	lx	NOUN
ejpam-4021	129	72	:	:	PUNCT
ejpam-4021	129	73	ξc	ξc	NOUN
ejpam-4021	129	74	is	be	AUX
ejpam-4021	129	75	open	open	ADJ
ejpam-4021	129	76	}	}	PUNCT
ejpam-4021	129	77	are	be	AUX
ejpam-4021	129	78	called	call	VERB
ejpam-4021	129	79	closed	closed	ADJ
ejpam-4021	129	80	lvalued	lvalue	VERB
ejpam-4021	129	81	sets	set	NOUN
ejpam-4021	129	82	or	or	CCONJ
ejpam-4021	129	83	l	l	NOUN
ejpam-4021	129	84	-	-	PUNCT
ejpam-4021	129	85	valued	value	VERB
ejpam-4021	129	86	subsets	subset	NOUN
ejpam-4021	129	87	,	,	PUNCT
ejpam-4021	129	88	where	where	SCONJ
ejpam-4021	129	89	ξc	ξc	PROPN
ejpam-4021	129	90	is	be	AUX
ejpam-4021	129	91	the	the	DET
ejpam-4021	129	92	so	so	ADV
ejpam-4021	129	93	-	-	PUNCT
ejpam-4021	129	94	called	call	VERB
ejpam-4021	129	95	qusi	qusi	ADJ
ejpam-4021	129	96	-	-	PUNCT
ejpam-4021	129	97	complementation	complementation	NOUN
ejpam-4021	129	98	of	of	ADP
ejpam-4021	129	99	ξ	ξ	PROPN
ejpam-4021	129	100	.	.	PUNCT
ejpam-4021	129	101	note	note	VERB
ejpam-4021	129	102	that	that	SCONJ
ejpam-4021	129	103	θ(x	θ(x	PROPN
ejpam-4021	129	104	)	)	PUNCT
ejpam-4021	129	105	is	be	AUX
ejpam-4021	129	106	closed	close	VERB
ejpam-4021	129	107	under	under	ADP
ejpam-4021	129	108	formation	formation	NOUN
ejpam-4021	129	109	of	of	ADP
ejpam-4021	129	110	arbitrary	arbitrary	ADJ
ejpam-4021	129	111	infs	infs	NOUN
ejpam-4021	129	112	and	and	CCONJ
ejpam-4021	129	113	finite	finite	PROPN
ejpam-4021	129	114	sups	sup	NOUN
ejpam-4021	129	115	.	.	PUNCT
ejpam-4021	130	1	furthermore	furthermore	ADV
ejpam-4021	130	2	,	,	PUNCT
ejpam-4021	130	3	recall	recall	VERB
ejpam-4021	130	4	that	that	SCONJ
ejpam-4021	130	5	the	the	DET
ejpam-4021	130	6	closure	closure	NOUN
ejpam-4021	130	7	of	of	ADP
ejpam-4021	130	8	ν	ν	X
ejpam-4021	130	9	∈	∈	PROPN
ejpam-4021	130	10	lx	lx	ADV
ejpam-4021	130	11	,	,	PUNCT
ejpam-4021	130	12	denoted	denote	VERB
ejpam-4021	130	13	by	by	ADP
ejpam-4021	130	14	νx	νx	NOUN
ejpam-4021	130	15	is	be	AUX
ejpam-4021	130	16	defined	define	VERB
ejpam-4021	130	17	as	as	ADP
ejpam-4021	130	18	:	:	PUNCT
ejpam-4021	130	19	νx	νx	PROPN
ejpam-4021	130	20	=	=	PUNCT
ejpam-4021	130	21	∧	∧	PROPN
ejpam-4021	130	22	{	{	PUNCT
ejpam-4021	130	23	θ	θ	PROPN
ejpam-4021	130	24	∈	∈	PROPN
ejpam-4021	130	25	θ(x	θ(x	PROPN
ejpam-4021	130	26	)	)	PUNCT
ejpam-4021	130	27	:	:	PUNCT
ejpam-4021	131	1	ν	ν	X
ejpam-4021	131	2	≤	≤	PROPN
ejpam-4021	131	3	θ	θ	PROPN
ejpam-4021	131	4	}	}	PUNCT
ejpam-4021	131	5	.	.	PUNCT
ejpam-4021	132	1	if	if	SCONJ
ejpam-4021	132	2	(	(	PUNCT
ejpam-4021	132	3	x,∆	x,∆	NUM
ejpam-4021	132	4	)	)	PUNCT
ejpam-4021	132	5	and	and	CCONJ
ejpam-4021	132	6	(	(	PUNCT
ejpam-4021	132	7	y	y	PROPN
ejpam-4021	132	8	,	,	PUNCT
ejpam-4021	132	9	γ	γ	NOUN
ejpam-4021	132	10	)	)	PUNCT
ejpam-4021	132	11	are	be	AUX
ejpam-4021	132	12	stratified	stratify	VERB
ejpam-4021	132	13	l	l	NOUN
ejpam-4021	132	14	-	-	PUNCT
ejpam-4021	132	15	valued	value	VERB
ejpam-4021	132	16	topological	topological	ADJ
ejpam-4021	132	17	spaces	space	NOUN
ejpam-4021	132	18	,	,	PUNCT
ejpam-4021	132	19	then	then	ADV
ejpam-4021	132	20	a	a	DET
ejpam-4021	132	21	function	function	NOUN
ejpam-4021	132	22	f	f	NOUN
ejpam-4021	132	23	:	:	PUNCT
ejpam-4021	132	24	(	(	PUNCT
ejpam-4021	132	25	x,∆)→	x,∆)→	PROPN
ejpam-4021	132	26	(	(	PUNCT
ejpam-4021	132	27	y	y	PROPN
ejpam-4021	132	28	,	,	PUNCT
ejpam-4021	132	29	γ	γ	NOUN
ejpam-4021	132	30	)	)	PUNCT
ejpam-4021	132	31	is	be	AUX
ejpam-4021	132	32	said	say	VERB
ejpam-4021	132	33	to	to	PART
ejpam-4021	132	34	be	be	AUX
ejpam-4021	132	35	continuous	continuous	ADJ
ejpam-4021	132	36	if	if	SCONJ
ejpam-4021	132	37	and	and	CCONJ
ejpam-4021	132	38	only	only	ADV
ejpam-4021	132	39	if	if	SCONJ
ejpam-4021	132	40	for	for	ADP
ejpam-4021	132	41	any	any	DET
ejpam-4021	132	42	σ	σ	PROPN
ejpam-4021	132	43	∈	∈	PROPN
ejpam-4021	132	44	γ	γ	X
ejpam-4021	132	45	,	,	PUNCT
ejpam-4021	132	46	f←(σ	f←(σ	NOUN
ejpam-4021	132	47	)	)	PUNCT
ejpam-4021	132	48	∈	∈	NOUN
ejpam-4021	133	1	∆.	∆.	NOUN
ejpam-4021	133	2	the	the	DET
ejpam-4021	133	3	category	category	NOUN
ejpam-4021	133	4	sl	sl	NOUN
ejpam-4021	133	5	-	-	PUNCT
ejpam-4021	133	6	top	top	NOUN
ejpam-4021	133	7	consists	consist	VERB
ejpam-4021	133	8	of	of	ADP
ejpam-4021	133	9	all	all	DET
ejpam-4021	133	10	stratified	stratified	ADJ
ejpam-4021	133	11	l	l	ADV
ejpam-4021	133	12	-	-	PUNCT
ejpam-4021	133	13	valued	value	VERB
ejpam-4021	133	14	topological	topological	ADJ
ejpam-4021	133	15	spaces	space	NOUN
ejpam-4021	133	16	as	as	ADP
ejpam-4021	133	17	objects	object	NOUN
ejpam-4021	133	18	and	and	CCONJ
ejpam-4021	133	19	all	all	DET
ejpam-4021	133	20	continuous	continuous	ADJ
ejpam-4021	133	21	maps	map	NOUN
ejpam-4021	133	22	between	between	ADP
ejpam-4021	133	23	them	they	PRON
ejpam-4021	133	24	as	as	ADP
ejpam-4021	133	25	morphisms	morphism	NOUN
ejpam-4021	133	26	,	,	PUNCT
ejpam-4021	133	27	while	while	SCONJ
ejpam-4021	133	28	the	the	DET
ejpam-4021	133	29	category	category	NOUN
ejpam-4021	133	30	l	l	NOUN
ejpam-4021	133	31	-	-	NOUN
ejpam-4021	133	32	top	top	ADJ
ejpam-4021	133	33	consisting	consisting	NOUN
ejpam-4021	133	34	of	of	ADP
ejpam-4021	133	35	all	all	DET
ejpam-4021	133	36	l	l	NOUN
ejpam-4021	133	37	-	-	PUNCT
ejpam-4021	133	38	valued	value	VERB
ejpam-4021	133	39	topological	topological	ADJ
ejpam-4021	133	40	spaces	space	NOUN
ejpam-4021	133	41	as	as	ADP
ejpam-4021	133	42	objects	object	NOUN
ejpam-4021	133	43	and	and	CCONJ
ejpam-4021	133	44	all	all	DET
ejpam-4021	133	45	continuous	continuous	ADJ
ejpam-4021	133	46	maps	map	NOUN
ejpam-4021	133	47	between	between	ADP
ejpam-4021	133	48	them	they	PRON
ejpam-4021	133	49	as	as	ADP
ejpam-4021	133	50	morphisms	morphism	NOUN
ejpam-4021	133	51	.	.	PUNCT
ejpam-4021	134	1	every	every	DET
ejpam-4021	134	2	stratified	stratified	ADJ
ejpam-4021	134	3	l	l	NOUN
ejpam-4021	134	4	-	-	PUNCT
ejpam-4021	134	5	valued	value	VERB
ejpam-4021	134	6	topology	topology	NOUN
ejpam-4021	134	7	∆	∆	PROPN
ejpam-4021	134	8	on	on	ADP
ejpam-4021	134	9	x	x	X
ejpam-4021	134	10	induces	induce	VERB
ejpam-4021	134	11	a	a	DET
ejpam-4021	134	12	stratified	stratified	ADJ
ejpam-4021	134	13	l	l	ADV
ejpam-4021	134	14	-	-	PUNCT
ejpam-4021	134	15	valued	value	VERB
ejpam-4021	134	16	neighborhood	neighborhood	NOUN
ejpam-4021	134	17	system	system	NOUN
ejpam-4021	134	18	n∆	n∆	NOUN
ejpam-4021	134	19	=	=	SYM
ejpam-4021	134	20	(	(	PUNCT
ejpam-4021	134	21	nx	nx	X
ejpam-4021	134	22	∆	∆	PROPN
ejpam-4021	134	23	)	)	PUNCT
ejpam-4021	134	24	as	as	SCONJ
ejpam-4021	134	25	follows	follow	VERB
ejpam-4021	134	26	:	:	PUNCT
ejpam-4021	134	27	nx	nx	NUM
ejpam-4021	134	28	∆(µ	∆(µ	NOUN
ejpam-4021	134	29	)	)	PUNCT
ejpam-4021	134	30	=	=	SYM
ejpam-4021	134	31	∨	∨	X
ejpam-4021	134	32	{	{	PUNCT
ejpam-4021	134	33	ν(x	ν(x	PROPN
ejpam-4021	134	34	)	)	PUNCT
ejpam-4021	134	35	:	:	PUNCT
ejpam-4021	134	36	ν	ν	X
ejpam-4021	134	37	∈	∈	PROPN
ejpam-4021	134	38	∆	∆	PROPN
ejpam-4021	134	39	,	,	PUNCT
ejpam-4021	134	40	ν	ν	PROPN
ejpam-4021	134	41	≤	≤	PROPN
ejpam-4021	134	42	µ	µ	NUM
ejpam-4021	134	43	}	}	PUNCT
ejpam-4021	134	44	,	,	PUNCT
ejpam-4021	134	45	for	for	ADP
ejpam-4021	134	46	all	all	DET
ejpam-4021	134	47	µ	µ	PRON
ejpam-4021	134	48	∈	∈	NOUN
ejpam-4021	134	49	lx	lx	NOUN
ejpam-4021	134	50	and	and	CCONJ
ejpam-4021	134	51	x	x	PUNCT
ejpam-4021	134	52	∈	∈	NOUN
ejpam-4021	134	53	x.	x.	NOUN
ejpam-4021	134	54	conversely	conversely	ADV
ejpam-4021	134	55	,	,	PUNCT
ejpam-4021	134	56	every	every	DET
ejpam-4021	134	57	stratified	stratified	ADJ
ejpam-4021	134	58	l	l	NOUN
ejpam-4021	134	59	-	-	PUNCT
ejpam-4021	134	60	valued	value	VERB
ejpam-4021	134	61	neighborhood	neighborhood	NOUN
ejpam-4021	134	62	system	system	NOUN
ejpam-4021	134	63	n	n	NOUN
ejpam-4021	134	64	=	=	PUNCT
ejpam-4021	134	65	(	(	PUNCT
ejpam-4021	134	66	nx)x∈x	nx)x∈x	NUM
ejpam-4021	134	67	on	on	ADP
ejpam-4021	134	68	x	x	AUX
ejpam-4021	134	69	induces	induce	VERB
ejpam-4021	134	70	a	a	DET
ejpam-4021	134	71	stratified	stratified	ADJ
ejpam-4021	134	72	l	l	ADV
ejpam-4021	134	73	-	-	PUNCT
ejpam-4021	134	74	valued	value	VERB
ejpam-4021	134	75	topology	topology	NOUN
ejpam-4021	134	76	∆n	∆n	NOUN
ejpam-4021	134	77	on	on	ADP
ejpam-4021	134	78	x	x	X
ejpam-4021	134	79	:	:	PUNCT
ejpam-4021	134	80	∆n	∆n	PROPN
ejpam-4021	134	81	=	=	PUNCT
ejpam-4021	134	82	{	{	PUNCT
ejpam-4021	134	83	ν	ν	X
ejpam-4021	134	84	∈	∈	NOUN
ejpam-4021	134	85	lx	lx	NOUN
ejpam-4021	134	86	:	:	PUNCT
ejpam-4021	134	87	ν(x	ν(x	PROPN
ejpam-4021	134	88	)	)	PUNCT
ejpam-4021	134	89	≤	≤	NOUN
ejpam-4021	134	90	nx(ν	nx(ν	NUM
ejpam-4021	134	91	)	)	PUNCT
ejpam-4021	134	92	,	,	PUNCT
ejpam-4021	134	93	∀x	∀x	VERB
ejpam-4021	134	94	∈	∈	PROPN
ejpam-4021	134	95	x	x	X
ejpam-4021	134	96	}	}	PUNCT
ejpam-4021	134	97	.	.	PUNCT
ejpam-4021	135	1	it	it	PRON
ejpam-4021	135	2	follows	follow	VERB
ejpam-4021	135	3	that	that	SCONJ
ejpam-4021	135	4	the	the	DET
ejpam-4021	135	5	interrelationship	interrelationship	NOUN
ejpam-4021	135	6	between	between	ADP
ejpam-4021	135	7	l	l	NOUN
ejpam-4021	135	8	-	-	PUNCT
ejpam-4021	135	9	valued	value	VERB
ejpam-4021	135	10	neighborhood	neighborhood	NOUN
ejpam-4021	135	11	system	system	NOUN
ejpam-4021	135	12	and	and	CCONJ
ejpam-4021	135	13	l	l	NOUN
ejpam-4021	135	14	-	-	PUNCT
ejpam-4021	135	15	valued	value	VERB
ejpam-4021	135	16	topologies	topology	NOUN
ejpam-4021	135	17	can	can	AUX
ejpam-4021	135	18	be	be	AUX
ejpam-4021	135	19	viewed	view	VERB
ejpam-4021	135	20	as	as	ADP
ejpam-4021	135	21	:	:	PUNCT
ejpam-4021	135	22	ν	ν	PART
ejpam-4021	135	23	∈	∈	NOUN
ejpam-4021	135	24	∆⇔	∆⇔	NOUN
ejpam-4021	135	25	ν(x	ν(x	X
ejpam-4021	135	26	)	)	PUNCT
ejpam-4021	135	27	≤	≤	NOUN
ejpam-4021	135	28	nx(ν	nx(ν	NUM
ejpam-4021	135	29	)	)	PUNCT
ejpam-4021	135	30	,	,	PUNCT
ejpam-4021	135	31	∀x	∀x	VERB
ejpam-4021	135	32	∈	∈	PROPN
ejpam-4021	135	33	x	x	X
ejpam-4021	135	34	(	(	PUNCT
ejpam-4021	135	35	†	†	NOUN
ejpam-4021	135	36	)	)	PUNCT
ejpam-4021	135	37	.	.	PUNCT
ejpam-4021	136	1	as	as	ADP
ejpam-4021	136	2	a	a	DET
ejpam-4021	136	3	consequence	consequence	NOUN
ejpam-4021	136	4	of	of	ADP
ejpam-4021	136	5	(	(	PUNCT
ejpam-4021	136	6	†	†	X
ejpam-4021	136	7	)	)	PUNCT
ejpam-4021	136	8	it	it	PRON
ejpam-4021	136	9	follows	follow	VERB
ejpam-4021	136	10	that	that	SCONJ
ejpam-4021	136	11	the	the	DET
ejpam-4021	136	12	continuity	continuity	NOUN
ejpam-4021	136	13	between	between	ADP
ejpam-4021	136	14	the	the	DET
ejpam-4021	136	15	objects	object	NOUN
ejpam-4021	136	16	in	in	ADP
ejpam-4021	136	17	sl	sl	NOUN
ejpam-4021	136	18	-	-	PUNCT
ejpam-4021	136	19	top	top	NOUN
ejpam-4021	136	20	,	,	PUNCT
ejpam-4021	136	21	and	and	CCONJ
ejpam-4021	136	22	the	the	DET
ejpam-4021	136	23	continuity	continuity	NOUN
ejpam-4021	136	24	between	between	ADP
ejpam-4021	136	25	objects	object	NOUN
ejpam-4021	136	26	in	in	ADP
ejpam-4021	136	27	sl	sl	NOUN
ejpam-4021	136	28	-	-	PUNCT
ejpam-4021	136	29	ns	ns	NOUN
ejpam-4021	136	30	are	be	AUX
ejpam-4021	136	31	equivalent	equivalent	ADJ
ejpam-4021	136	32	concept	concept	NOUN
ejpam-4021	136	33	,	,	PUNCT
ejpam-4021	136	34	cf	cf	NOUN
ejpam-4021	136	35	.	.	PUNCT
ejpam-4021	137	1	[	[	X
ejpam-4021	137	2	18	18	NUM
ejpam-4021	137	3	]	]	PUNCT
ejpam-4021	137	4	.	.	PUNCT
ejpam-4021	138	1	t	t	PROPN
ejpam-4021	138	2	m	m	PROPN
ejpam-4021	138	3	g	g	NOUN
ejpam-4021	138	4	ahsanullah	ahsanullah	NOUN
ejpam-4021	138	5	,	,	PUNCT
ejpam-4021	138	6	fawzi	fawzi	PROPN
ejpam-4021	138	7	al	al	PROPN
ejpam-4021	138	8	-	-	PUNCT
ejpam-4021	138	9	thukair	thukair	NOUN
ejpam-4021	138	10	/	/	SYM
ejpam-4021	138	11	eur	eur	NOUN
ejpam-4021	138	12	.	.	PUNCT
ejpam-4021	139	1	j.	j.	PROPN
ejpam-4021	139	2	pure	pure	PROPN
ejpam-4021	139	3	appl	appl	PROPN
ejpam-4021	139	4	.	.	PROPN
ejpam-4021	139	5	math	math	PROPN
ejpam-4021	139	6	,	,	PUNCT
ejpam-4021	139	7	14	14	NUM
ejpam-4021	139	8	(	(	PUNCT
ejpam-4021	139	9	3	3	NUM
ejpam-4021	139	10	)	)	PUNCT
ejpam-4021	139	11	(	(	PUNCT
ejpam-4021	139	12	2021	2021	NUM
ejpam-4021	139	13	)	)	PUNCT
ejpam-4021	139	14	,	,	PUNCT
ejpam-4021	139	15	949	949	NUM
ejpam-4021	139	16	-	-	SYM
ejpam-4021	139	17	968	968	NUM
ejpam-4021	139	18	955	955	NUM
ejpam-4021	139	19	3	3	NUM
ejpam-4021	139	20	.	.	PUNCT
ejpam-4021	140	1	l	l	NOUN
ejpam-4021	140	2	-	-	PUNCT
ejpam-4021	140	3	valued	value	VERB
ejpam-4021	140	4	topological	topological	ADJ
ejpam-4021	140	5	groups	group	NOUN
ejpam-4021	140	6	and	and	CCONJ
ejpam-4021	140	7	kent	kent	PROPN
ejpam-4021	140	8	convergence	convergence	NOUN
ejpam-4021	140	9	groups	group	NOUN
ejpam-4021	140	10	we	we	PRON
ejpam-4021	140	11	consider	consider	VERB
ejpam-4021	140	12	l	l	NOUN
ejpam-4021	140	13	=	=	SYM
ejpam-4021	140	14	(	(	PUNCT
ejpam-4021	140	15	l,≤	l,≤	PROPN
ejpam-4021	140	16	,	,	PUNCT
ejpam-4021	140	17	∗,⊗	∗,⊗	X
ejpam-4021	140	18	=	=	SYM
ejpam-4021	140	19	∗	∗	NOUN
ejpam-4021	140	20	)	)	PUNCT
ejpam-4021	140	21	an	an	DET
ejpam-4021	140	22	enriched	enriched	ADJ
ejpam-4021	140	23	cl	cl	NOUN
ejpam-4021	140	24	-	-	ADJ
ejpam-4021	140	25	premonoid	premonoid	ADJ
ejpam-4021	140	26	,	,	PUNCT
ejpam-4021	140	27	where	where	SCONJ
ejpam-4021	140	28	∗	∗	NOUN
ejpam-4021	140	29	is	be	AUX
ejpam-4021	140	30	a	a	DET
ejpam-4021	140	31	gl	gl	NOUN
ejpam-4021	140	32	-	-	PUNCT
ejpam-4021	140	33	monoid	monoid	NOUN
ejpam-4021	140	34	operation	operation	NOUN
ejpam-4021	140	35	.	.	PUNCT
ejpam-4021	141	1	let	let	VERB
ejpam-4021	141	2	the	the	DET
ejpam-4021	141	3	category	category	NOUN
ejpam-4021	141	4	of	of	ADP
ejpam-4021	141	5	groups	group	NOUN
ejpam-4021	141	6	and	and	CCONJ
ejpam-4021	141	7	group	group	NOUN
ejpam-4021	141	8	homomorphisms	homomorphism	NOUN
ejpam-4021	141	9	be	be	AUX
ejpam-4021	141	10	denoted	denote	VERB
ejpam-4021	141	11	by	by	ADP
ejpam-4021	141	12	grp	grp	PROPN
ejpam-4021	141	13	.	.	PROPN
ejpam-4021	141	14	definition	definition	NOUN
ejpam-4021	141	15	9	9	NUM
ejpam-4021	141	16	.	.	PUNCT
ejpam-4021	142	1	let	let	VERB
ejpam-4021	142	2	(	(	PUNCT
ejpam-4021	142	3	x	x	NOUN
ejpam-4021	142	4	,	,	PUNCT
ejpam-4021	142	5	·	·	PUNCT
ejpam-4021	142	6	)	)	PUNCT
ejpam-4021	142	7	∈	∈	PROPN
ejpam-4021	142	8	|grp|	|grp|	NOUN
ejpam-4021	142	9	and	and	CCONJ
ejpam-4021	142	10	(	(	PUNCT
ejpam-4021	142	11	x,∆	x,∆	NUM
ejpam-4021	142	12	)	)	PUNCT
ejpam-4021	142	13	∈	∈	PROPN
ejpam-4021	142	14	|sl	|sl	NOUN
ejpam-4021	142	15	-	-	PUNCT
ejpam-4021	142	16	top|	top|	NOUN
ejpam-4021	142	17	.	.	PUNCT
ejpam-4021	143	1	then	then	ADV
ejpam-4021	143	2	the	the	DET
ejpam-4021	143	3	triple	triple	ADJ
ejpam-4021	143	4	(	(	PUNCT
ejpam-4021	143	5	x	x	NOUN
ejpam-4021	143	6	,	,	PUNCT
ejpam-4021	143	7	·	·	PUNCT
ejpam-4021	143	8	,	,	PUNCT
ejpam-4021	143	9	∆	∆	X
ejpam-4021	143	10	)	)	PUNCT
ejpam-4021	143	11	is	be	AUX
ejpam-4021	143	12	called	call	VERB
ejpam-4021	143	13	a	a	DET
ejpam-4021	143	14	stratified	stratified	ADJ
ejpam-4021	143	15	l	l	NOUN
ejpam-4021	143	16	-	-	PUNCT
ejpam-4021	143	17	valued	value	VERB
ejpam-4021	143	18	topological	topological	ADJ
ejpam-4021	143	19	group	group	NOUN
ejpam-4021	143	20	if	if	SCONJ
ejpam-4021	143	21	and	and	CCONJ
ejpam-4021	143	22	only	only	ADV
ejpam-4021	143	23	if	if	SCONJ
ejpam-4021	143	24	the	the	DET
ejpam-4021	143	25	conditions	condition	NOUN
ejpam-4021	143	26	below	below	ADV
ejpam-4021	143	27	are	be	AUX
ejpam-4021	143	28	fulfilled	fulfil	VERB
ejpam-4021	143	29	:	:	PUNCT
ejpam-4021	143	30	(	(	PUNCT
ejpam-4021	143	31	ltgm	ltgm	PROPN
ejpam-4021	143	32	)	)	PUNCT
ejpam-4021	144	1	the	the	DET
ejpam-4021	144	2	mapping	mapping	NOUN
ejpam-4021	144	3	m	m	VERB
ejpam-4021	144	4	:	:	PUNCT
ejpam-4021	144	5	(	(	PUNCT
ejpam-4021	144	6	x	x	X
ejpam-4021	144	7	×x,∆×∆	×x,∆×∆	NUM
ejpam-4021	144	8	)	)	PUNCT
ejpam-4021	144	9	−→	−→	NOUN
ejpam-4021	144	10	(	(	PUNCT
ejpam-4021	144	11	x,∆	x,∆	NUM
ejpam-4021	144	12	)	)	PUNCT
ejpam-4021	144	13	,	,	PUNCT
ejpam-4021	144	14	(	(	PUNCT
ejpam-4021	144	15	x	x	X
ejpam-4021	144	16	,	,	PUNCT
ejpam-4021	144	17	y	y	NOUN
ejpam-4021	144	18	)	)	PUNCT
ejpam-4021	144	19	7−→	7−→	NOUN
ejpam-4021	144	20	xy	xy	NOUN
ejpam-4021	144	21	is	be	AUX
ejpam-4021	144	22	continuous	continuous	ADJ
ejpam-4021	144	23	;	;	PUNCT
ejpam-4021	144	24	(	(	PUNCT
ejpam-4021	144	25	ltgi	ltgi	NOUN
ejpam-4021	144	26	)	)	PUNCT
ejpam-4021	144	27	the	the	DET
ejpam-4021	144	28	mapping	mapping	NOUN
ejpam-4021	144	29			PROPN
ejpam-4021	144	30	:	:	PUNCT
ejpam-4021	144	31	(	(	PUNCT
ejpam-4021	144	32	x,∆	x,∆	NUM
ejpam-4021	144	33	)	)	PUNCT
ejpam-4021	144	34	−→	−→	NOUN
ejpam-4021	144	35	(	(	PUNCT
ejpam-4021	144	36	x,∆	x,∆	NUM
ejpam-4021	144	37	)	)	PUNCT
ejpam-4021	144	38	,	,	PUNCT
ejpam-4021	144	39	x	x	X
ejpam-4021	144	40	7−→	7−→	NOUN
ejpam-4021	144	41	x−1	x−1	PROPN
ejpam-4021	144	42	is	be	AUX
ejpam-4021	144	43	continuous	continuous	ADJ
ejpam-4021	144	44	.	.	PUNCT
ejpam-4021	145	1	the	the	DET
ejpam-4021	145	2	category	category	NOUN
ejpam-4021	145	3	of	of	ADP
ejpam-4021	145	4	all	all	PRON
ejpam-4021	145	5	stratified	stratified	ADJ
ejpam-4021	145	6	l	l	ADV
ejpam-4021	145	7	-	-	PUNCT
ejpam-4021	145	8	valued	value	VERB
ejpam-4021	145	9	topological	topological	ADJ
ejpam-4021	145	10	groups	group	NOUN
ejpam-4021	145	11	and	and	CCONJ
ejpam-4021	145	12	continuous	continuous	ADJ
ejpam-4021	145	13	group	group	NOUN
ejpam-4021	145	14	homomorphisms	homomorphism	NOUN
ejpam-4021	145	15	is	be	AUX
ejpam-4021	145	16	denoted	denote	VERB
ejpam-4021	145	17	by	by	ADP
ejpam-4021	145	18	sl	sl	NOUN
ejpam-4021	145	19	-	-	PUNCT
ejpam-4021	145	20	topgrp	topgrp	NOUN
ejpam-4021	145	21	.	.	PUNCT
ejpam-4021	146	1	definition	definition	NOUN
ejpam-4021	146	2	10	10	NUM
ejpam-4021	146	3	.	.	PUNCT
ejpam-4021	147	1	[	[	X
ejpam-4021	147	2	3	3	X
ejpam-4021	147	3	]	]	X
ejpam-4021	147	4	let	let	VERB
ejpam-4021	147	5	(	(	PUNCT
ejpam-4021	147	6	x	x	NOUN
ejpam-4021	147	7	,	,	PUNCT
ejpam-4021	147	8	·	·	PUNCT
ejpam-4021	147	9	)	)	PUNCT
ejpam-4021	147	10	∈	∈	PROPN
ejpam-4021	147	11	|grp|	|grp|	NOUN
ejpam-4021	147	12	and	and	CCONJ
ejpam-4021	147	13	(	(	PUNCT
ejpam-4021	147	14	x	x	NOUN
ejpam-4021	147	15	,	,	PUNCT
ejpam-4021	147	16	n	n	NOUN
ejpam-4021	147	17	=	=	SYM
ejpam-4021	147	18	(	(	PUNCT
ejpam-4021	147	19	nx)x∈x	nx)x∈x	NUM
ejpam-4021	147	20	)	)	PUNCT
ejpam-4021	147	21	∈	∈	PROPN
ejpam-4021	147	22	|sl	|sl	NOUN
ejpam-4021	147	23	-	-	PUNCT
ejpam-4021	147	24	ns|	ns|	ADV
ejpam-4021	147	25	.	.	PUNCT
ejpam-4021	148	1	then	then	ADV
ejpam-4021	148	2	the	the	DET
ejpam-4021	148	3	triple	triple	ADJ
ejpam-4021	148	4	(	(	PUNCT
ejpam-4021	148	5	x	x	NOUN
ejpam-4021	148	6	,	,	PUNCT
ejpam-4021	148	7	·	·	PUNCT
ejpam-4021	148	8	,	,	PUNCT
ejpam-4021	148	9	n	n	NOUN
ejpam-4021	148	10	=	=	SYM
ejpam-4021	148	11	(	(	PUNCT
ejpam-4021	148	12	nx)x∈x	nx)x∈x	NUM
ejpam-4021	148	13	)	)	PUNCT
ejpam-4021	148	14	is	be	AUX
ejpam-4021	148	15	called	call	VERB
ejpam-4021	148	16	a	a	DET
ejpam-4021	148	17	stratified	stratified	ADJ
ejpam-4021	148	18	l	l	ADV
ejpam-4021	148	19	-	-	PUNCT
ejpam-4021	148	20	valued	value	VERB
ejpam-4021	148	21	neighborhood	neighborhood	NOUN
ejpam-4021	148	22	group	group	NOUN
ejpam-4021	148	23	if	if	SCONJ
ejpam-4021	148	24	and	and	CCONJ
ejpam-4021	148	25	only	only	ADV
ejpam-4021	148	26	if	if	SCONJ
ejpam-4021	148	27	(	(	PUNCT
ejpam-4021	148	28	lngm	lngm	ADJ
ejpam-4021	148	29	)	)	PUNCT
ejpam-4021	148	30	nxy	nxy	PROPN
ejpam-4021	148	31	≤	≤	PROPN
ejpam-4021	148	32	nx	nx	PROPN
ejpam-4021	148	33	�	�	PROPN
ejpam-4021	148	34	ny	ny	PROPN
ejpam-4021	148	35	,	,	PUNCT
ejpam-4021	148	36	and	and	CCONJ
ejpam-4021	148	37	(	(	PUNCT
ejpam-4021	148	38	lngi	lngi	NOUN
ejpam-4021	148	39	)	)	PUNCT
ejpam-4021	148	40	nx−1	nx−1	PROPN
ejpam-4021	148	41	≤	≤	NOUN
ejpam-4021	148	42	(	(	PUNCT
ejpam-4021	148	43	nx)−1	nx)−1	INTJ
ejpam-4021	148	44	are	be	AUX
ejpam-4021	148	45	satisfied	satisfied	ADJ
ejpam-4021	148	46	,	,	PUNCT
ejpam-4021	148	47	where	where	SCONJ
ejpam-4021	148	48	for	for	ADP
ejpam-4021	148	49	any	any	DET
ejpam-4021	148	50	ξ	ξ	PROPN
ejpam-4021	148	51	∈	∈	PROPN
ejpam-4021	148	52	lg	lg	NOUN
ejpam-4021	148	53	:	:	PUNCT
ejpam-4021	148	54	nx	nx	PROPN
ejpam-4021	148	55	�	�	PROPN
ejpam-4021	148	56	ny(ξ	ny(ξ	NOUN
ejpam-4021	148	57	)	)	PUNCT
ejpam-4021	148	58	=	=	SYM
ejpam-4021	149	1	m⇒	m⇒	X
ejpam-4021	149	2	(	(	PUNCT
ejpam-4021	149	3	nx	nx	PROPN
ejpam-4021	149	4	×ny	×ny	PROPN
ejpam-4021	149	5	)	)	PUNCT
ejpam-4021	149	6	(	(	PUNCT
ejpam-4021	149	7	ξ	ξ	X
ejpam-4021	149	8	)	)	PUNCT
ejpam-4021	149	9	=	=	SYM
ejpam-4021	149	10	∨	∨	X
ejpam-4021	149	11	{	{	PUNCT
ejpam-4021	149	12	nx(ξ1	nx(ξ1	NOUN
ejpam-4021	149	13	)	)	PUNCT
ejpam-4021	149	14	∧ny(ξ2	∧ny(ξ2	PROPN
ejpam-4021	149	15	)	)	PUNCT
ejpam-4021	149	16	:	:	PUNCT
ejpam-4021	150	1	ξ1	ξ1	NOUN
ejpam-4021	150	2	,	,	PUNCT
ejpam-4021	150	3	ξ2	ξ2	NOUN
ejpam-4021	150	4	∈	∈	PROPN
ejpam-4021	150	5	lx	lx	NOUN
ejpam-4021	150	6	,	,	PUNCT
ejpam-4021	150	7	ξ1	ξ1	PROPN
ejpam-4021	150	8	×	×	NOUN
ejpam-4021	150	9	ξ2	ξ2	NOUN
ejpam-4021	150	10	≤	≤	ADJ
ejpam-4021	150	11	m←(ξ	m←(ξ	NOUN
ejpam-4021	150	12	)	)	PUNCT
ejpam-4021	150	13	}	}	PUNCT
ejpam-4021	150	14	.	.	PUNCT
ejpam-4021	151	1	a	a	DET
ejpam-4021	151	2	stratified	stratified	ADJ
ejpam-4021	151	3	l	l	ADV
ejpam-4021	151	4	-	-	PUNCT
ejpam-4021	151	5	valued	value	VERB
ejpam-4021	151	6	neighborhood	neighborhood	NOUN
ejpam-4021	151	7	system	system	NOUN
ejpam-4021	151	8	on	on	ADP
ejpam-4021	151	9	a	a	DET
ejpam-4021	151	10	group	group	NOUN
ejpam-4021	151	11	x	x	PRON
ejpam-4021	151	12	is	be	AUX
ejpam-4021	151	13	said	say	VERB
ejpam-4021	151	14	to	to	PART
ejpam-4021	151	15	be	be	AUX
ejpam-4021	151	16	compatible	compatible	ADJ
ejpam-4021	151	17	with	with	ADP
ejpam-4021	151	18	the	the	DET
ejpam-4021	151	19	group	group	NOUN
ejpam-4021	151	20	structure	structure	NOUN
ejpam-4021	151	21	of	of	ADP
ejpam-4021	151	22	x	x	SYM
ejpam-4021	151	23	if	if	SCONJ
ejpam-4021	151	24	and	and	CCONJ
ejpam-4021	151	25	only	only	ADV
ejpam-4021	151	26	if	if	SCONJ
ejpam-4021	151	27	the	the	DET
ejpam-4021	151	28	group	group	NOUN
ejpam-4021	151	29	operations	operation	NOUN
ejpam-4021	151	30	are	be	AUX
ejpam-4021	151	31	continuous	continuous	ADJ
ejpam-4021	151	32	;	;	PUNCT
ejpam-4021	151	33	i.e.	i.e.	X
ejpam-4021	151	34	,	,	PUNCT
ejpam-4021	151	35	conditions	condition	NOUN
ejpam-4021	151	36	(	(	PUNCT
ejpam-4021	151	37	lngm	lngm	ADJ
ejpam-4021	151	38	)	)	PUNCT
ejpam-4021	151	39	and	and	CCONJ
ejpam-4021	151	40	(	(	PUNCT
ejpam-4021	151	41	lntgi	lntgi	X
ejpam-4021	151	42	)	)	PUNCT
ejpam-4021	151	43	are	be	AUX
ejpam-4021	151	44	fulfilled	fulfil	VERB
ejpam-4021	151	45	.	.	PUNCT
ejpam-4021	152	1	the	the	DET
ejpam-4021	152	2	category	category	NOUN
ejpam-4021	152	3	sl	sl	NOUN
ejpam-4021	152	4	-	-	PUNCT
ejpam-4021	152	5	ns	ns	PROPN
ejpam-4021	152	6	consists	consist	NOUN
ejpam-4021	152	7	of	of	ADP
ejpam-4021	152	8	all	all	DET
ejpam-4021	152	9	stratified	stratified	ADJ
ejpam-4021	152	10	l	l	ADV
ejpam-4021	152	11	-	-	PUNCT
ejpam-4021	152	12	valued	value	VERB
ejpam-4021	152	13	neighborhood	neighborhood	NOUN
ejpam-4021	152	14	groups	group	NOUN
ejpam-4021	152	15	as	as	ADP
ejpam-4021	152	16	objects	object	NOUN
ejpam-4021	152	17	and	and	CCONJ
ejpam-4021	152	18	continuous	continuous	ADJ
ejpam-4021	152	19	group	group	NOUN
ejpam-4021	152	20	homomorphisms	homomorphism	NOUN
ejpam-4021	152	21	as	as	ADP
ejpam-4021	152	22	morphisms	morphism	NOUN
ejpam-4021	152	23	.	.	PUNCT
ejpam-4021	153	1	example	example	NOUN
ejpam-4021	154	1	1	1	NUM
ejpam-4021	154	2	.	.	PUNCT
ejpam-4021	155	1	let	let	VERB
ejpam-4021	155	2	(	(	PUNCT
ejpam-4021	155	3	g	g	NOUN
ejpam-4021	155	4	,	,	PUNCT
ejpam-4021	155	5	·	·	PUNCT
ejpam-4021	155	6	)	)	PUNCT
ejpam-4021	155	7	∈	∈	PROPN
ejpam-4021	155	8	|grp|	|grp|	NOUN
ejpam-4021	155	9	,	,	PUNCT
ejpam-4021	155	10	and	and	CCONJ
ejpam-4021	155	11	ri	ri	INTJ
ejpam-4021	155	12	:	:	PUNCT
ejpam-4021	155	13	lx	lx	ADP
ejpam-4021	155	14	−→	−→	NOUN
ejpam-4021	155	15	l	l	NOUN
ejpam-4021	155	16	defined	define	VERB
ejpam-4021	155	17	by	by	ADP
ejpam-4021	155	18	ni	ni	PROPN
ejpam-4021	155	19	=	=	PROPN
ejpam-4021	155	20	∧	∧	PROPN
ejpam-4021	155	21	x∈g[x	x∈g[x	PROPN
ejpam-4021	155	22	]	]	PUNCT
ejpam-4021	155	23	.	.	PUNCT
ejpam-4021	156	1	then	then	ADV
ejpam-4021	156	2	the	the	DET
ejpam-4021	156	3	triple	triple	ADJ
ejpam-4021	156	4	(	(	PUNCT
ejpam-4021	156	5	g	g	NOUN
ejpam-4021	156	6	,	,	PUNCT
ejpam-4021	156	7	·	·	PUNCT
ejpam-4021	156	8	,	,	PUNCT
ejpam-4021	156	9	ni	ni	PROPN
ejpam-4021	156	10	)	)	PUNCT
ejpam-4021	156	11	is	be	AUX
ejpam-4021	156	12	a	a	DET
ejpam-4021	156	13	stratified	stratified	ADJ
ejpam-4021	156	14	l	l	NOUN
ejpam-4021	156	15	-	-	PUNCT
ejpam-4021	156	16	valued	value	VERB
ejpam-4021	156	17	neighborhood	neighborhood	NOUN
ejpam-4021	156	18	group	group	NOUN
ejpam-4021	156	19	,	,	PUNCT
ejpam-4021	156	20	called	call	VERB
ejpam-4021	156	21	indiscrete	indiscrete	ADJ
ejpam-4021	156	22	stratified	stratified	ADJ
ejpam-4021	156	23	l	l	ADV
ejpam-4021	156	24	-	-	PUNCT
ejpam-4021	156	25	valued	value	VERB
ejpam-4021	156	26	neighborhood	neighborhood	NOUN
ejpam-4021	156	27	group	group	NOUN
ejpam-4021	156	28	.	.	PUNCT
ejpam-4021	156	29	example	example	NOUN
ejpam-4021	157	1	2	2	NUM
ejpam-4021	157	2	.	.	X
ejpam-4021	158	1	let	let	VERB
ejpam-4021	158	2	(	(	PUNCT
ejpam-4021	158	3	g	g	NOUN
ejpam-4021	158	4	,	,	PUNCT
ejpam-4021	158	5	·	·	PUNCT
ejpam-4021	158	6	)	)	PUNCT
ejpam-4021	158	7	∈	∈	PROPN
ejpam-4021	158	8	|grp|	|grp|	NOUN
ejpam-4021	158	9	,	,	PUNCT
ejpam-4021	158	10	and	and	CCONJ
ejpam-4021	158	11	rd	rd	NOUN
ejpam-4021	158	12	:	:	PUNCT
ejpam-4021	159	1	lx	lx	ADP
ejpam-4021	159	2	−→	−→	NOUN
ejpam-4021	159	3	l	l	NOUN
ejpam-4021	159	4	defined	define	VERB
ejpam-4021	159	5	by	by	ADP
ejpam-4021	159	6	nxd(ν	nxd(ν	PROPN
ejpam-4021	159	7	)	)	PUNCT
ejpam-4021	159	8	=	=	PUNCT
ejpam-4021	160	1	ν(x	ν(x	PROPN
ejpam-4021	160	2	)	)	PUNCT
ejpam-4021	160	3	.	.	PUNCT
ejpam-4021	161	1	then	then	ADV
ejpam-4021	161	2	the	the	DET
ejpam-4021	161	3	triple	triple	ADJ
ejpam-4021	161	4	(	(	PUNCT
ejpam-4021	161	5	g	g	NOUN
ejpam-4021	161	6	,	,	PUNCT
ejpam-4021	161	7	·	·	PUNCT
ejpam-4021	161	8	,	,	PUNCT
ejpam-4021	161	9	nd	nd	PRON
ejpam-4021	161	10	)	)	PUNCT
ejpam-4021	161	11	is	be	AUX
ejpam-4021	161	12	a	a	DET
ejpam-4021	161	13	stratified	stratified	ADJ
ejpam-4021	161	14	l	l	NOUN
ejpam-4021	161	15	-	-	PUNCT
ejpam-4021	161	16	valued	value	VERB
ejpam-4021	161	17	neighborhood	neighborhood	NOUN
ejpam-4021	161	18	group	group	NOUN
ejpam-4021	161	19	,	,	PUNCT
ejpam-4021	161	20	called	call	VERB
ejpam-4021	161	21	discrete	discrete	ADV
ejpam-4021	161	22	stratified	stratified	ADJ
ejpam-4021	161	23	l	l	ADV
ejpam-4021	161	24	-	-	PUNCT
ejpam-4021	161	25	valued	value	VERB
ejpam-4021	161	26	neighborhood	neighborhood	NOUN
ejpam-4021	161	27	group	group	NOUN
ejpam-4021	161	28	.	.	PUNCT
ejpam-4021	162	1	lemma	lemma	PROPN
ejpam-4021	162	2	2	2	NUM
ejpam-4021	162	3	.	.	PUNCT
ejpam-4021	163	1	[	[	X
ejpam-4021	163	2	3	3	X
ejpam-4021	163	3	]	]	X
ejpam-4021	163	4	let	let	VERB
ejpam-4021	163	5	(	(	PUNCT
ejpam-4021	163	6	g	g	NOUN
ejpam-4021	163	7	,	,	PUNCT
ejpam-4021	163	8	·	·	PUNCT
ejpam-4021	163	9	,	,	PUNCT
ejpam-4021	163	10	∆	∆	X
ejpam-4021	163	11	)	)	PUNCT
ejpam-4021	163	12	∈	∈	PROPN
ejpam-4021	163	13	|sl	|sl	PROPN
ejpam-4021	163	14	-	-	PUNCT
ejpam-4021	163	15	topgrp|	topgrp|	NOUN
ejpam-4021	163	16	,	,	PUNCT
ejpam-4021	163	17	and	and	CCONJ
ejpam-4021	163	18	a	a	DET
ejpam-4021	163	19	∈	∈	PROPN
ejpam-4021	163	20	g.	g.	NOUN
ejpam-4021	163	21	then	then	ADV
ejpam-4021	163	22	the	the	DET
ejpam-4021	163	23	translations	translation	NOUN
ejpam-4021	163	24	(	(	PUNCT
ejpam-4021	163	25	left	leave	VERB
ejpam-4021	163	26	and	and	CCONJ
ejpam-4021	163	27	right	right	ADJ
ejpam-4021	163	28	)	)	PUNCT
ejpam-4021	163	29	la	la	NOUN
ejpam-4021	163	30	:	:	PUNCT
ejpam-4021	163	31	(	(	PUNCT
ejpam-4021	163	32	g	g	NOUN
ejpam-4021	163	33	,	,	PUNCT
ejpam-4021	163	34	·	·	PUNCT
ejpam-4021	163	35	,	,	PUNCT
ejpam-4021	163	36	∆	∆	X
ejpam-4021	163	37	)	)	PUNCT
ejpam-4021	164	1	−→	−→	NOUN
ejpam-4021	164	2	(	(	PUNCT
ejpam-4021	164	3	g	g	NOUN
ejpam-4021	164	4	,	,	PUNCT
ejpam-4021	164	5	·	·	PUNCT
ejpam-4021	164	6	,	,	PUNCT
ejpam-4021	164	7	∆	∆	X
ejpam-4021	164	8	)	)	PUNCT
ejpam-4021	164	9	,	,	PUNCT
ejpam-4021	164	10	g	g	PROPN
ejpam-4021	164	11	7−→	7−→	PROPN
ejpam-4021	164	12	ag	ag	PROPN
ejpam-4021	164	13	,	,	PUNCT
ejpam-4021	164	14	and	and	CCONJ
ejpam-4021	164	15	lx	lx	ADP
ejpam-4021	164	16	:	:	PUNCT
ejpam-4021	164	17	(	(	PUNCT
ejpam-4021	164	18	g	g	NOUN
ejpam-4021	164	19	,	,	PUNCT
ejpam-4021	164	20	·	·	PUNCT
ejpam-4021	164	21	,	,	PUNCT
ejpam-4021	164	22	∆	∆	X
ejpam-4021	164	23	)	)	PUNCT
ejpam-4021	165	1	−→	−→	NOUN
ejpam-4021	165	2	(	(	PUNCT
ejpam-4021	165	3	g	g	NOUN
ejpam-4021	165	4	,	,	PUNCT
ejpam-4021	165	5	·	·	PUNCT
ejpam-4021	165	6	,	,	PUNCT
ejpam-4021	165	7	∆	∆	X
ejpam-4021	165	8	)	)	PUNCT
ejpam-4021	165	9	,	,	PUNCT
ejpam-4021	165	10	g	g	PROPN
ejpam-4021	165	11	7−→	7−→	PROPN
ejpam-4021	165	12	ga	ga	PROPN
ejpam-4021	165	13	are	be	AUX
ejpam-4021	165	14	homeomorphisms	homeomorphisms	PROPN
ejpam-4021	165	15	.	.	PUNCT
ejpam-4021	166	1	also	also	ADV
ejpam-4021	166	2	the	the	DET
ejpam-4021	166	3	mapping	mapping	NOUN
ejpam-4021	166	4	ca	ca	NOUN
ejpam-4021	166	5	:	:	PUNCT
ejpam-4021	166	6	(	(	PUNCT
ejpam-4021	166	7	g	g	NOUN
ejpam-4021	166	8	,	,	PUNCT
ejpam-4021	166	9	·	·	PUNCT
ejpam-4021	166	10	,	,	PUNCT
ejpam-4021	166	11	∆	∆	X
ejpam-4021	166	12	)	)	PUNCT
ejpam-4021	167	1	−→	−→	NOUN
ejpam-4021	167	2	(	(	PUNCT
ejpam-4021	167	3	g	g	NOUN
ejpam-4021	167	4	,	,	PUNCT
ejpam-4021	167	5	·	·	PUNCT
ejpam-4021	167	6	,	,	PUNCT
ejpam-4021	167	7	∆	∆	X
ejpam-4021	167	8	)	)	PUNCT
ejpam-4021	167	9	,	,	PUNCT
ejpam-4021	167	10	g	g	PROPN
ejpam-4021	167	11	7−→	7−→	PROPN
ejpam-4021	167	12	gag−1	gag−1	PROPN
ejpam-4021	167	13	the	the	DET
ejpam-4021	167	14	inner	inner	ADJ
ejpam-4021	167	15	automorphism	automorphism	NOUN
ejpam-4021	167	16	is	be	AUX
ejpam-4021	167	17	an	an	DET
ejpam-4021	167	18	isomorphism	isomorphism	NOUN
ejpam-4021	167	19	.	.	PUNCT
ejpam-4021	168	1	definition	definition	NOUN
ejpam-4021	168	2	11	11	NUM
ejpam-4021	168	3	.	.	PUNCT
ejpam-4021	169	1	[	[	X
ejpam-4021	169	2	20	20	NUM
ejpam-4021	169	3	,	,	PUNCT
ejpam-4021	169	4	27	27	NUM
ejpam-4021	169	5	]	]	PUNCT
ejpam-4021	169	6	a	a	DET
ejpam-4021	169	7	kent	kent	PROPN
ejpam-4021	169	8	convergence	convergence	NOUN
ejpam-4021	169	9	structure	structure	NOUN
ejpam-4021	169	10	q	q	NOUN
ejpam-4021	169	11	on	on	ADP
ejpam-4021	169	12	x	x	SYM
ejpam-4021	169	13	is	be	AUX
ejpam-4021	169	14	a	a	DET
ejpam-4021	169	15	subset	subset	NOUN
ejpam-4021	169	16	q	q	PUNCT
ejpam-4021	169	17	⊆	⊆	NUM
ejpam-4021	169	18	f(x)×x	f(x)×x	PROPN
ejpam-4021	169	19	such	such	ADJ
ejpam-4021	169	20	that	that	SCONJ
ejpam-4021	169	21	the	the	DET
ejpam-4021	169	22	following	follow	VERB
ejpam-4021	169	23	conditions	condition	NOUN
ejpam-4021	169	24	are	be	AUX
ejpam-4021	169	25	satisfied	satisfied	ADJ
ejpam-4021	169	26	:	:	PUNCT
ejpam-4021	169	27	(	(	PUNCT
ejpam-4021	169	28	c1	c1	NOUN
ejpam-4021	169	29	)	)	PUNCT
ejpam-4021	169	30	x	x	SYM
ejpam-4021	169	31	∈	∈	PROPN
ejpam-4021	169	32	q(ẋ),∀x	q(ẋ),∀x	PROPN
ejpam-4021	169	33	∈	∈	PROPN
ejpam-4021	170	1	x	x	NOUN
ejpam-4021	170	2	,	,	PUNCT
ejpam-4021	170	3	where	where	SCONJ
ejpam-4021	170	4	ẋ	ẋ	PROPN
ejpam-4021	170	5	denotes	denote	VERB
ejpam-4021	170	6	the	the	DET
ejpam-4021	170	7	ordinary	ordinary	ADJ
ejpam-4021	170	8	principal	principal	ADJ
ejpam-4021	170	9	filter	filter	NOUN
ejpam-4021	170	10	on	on	ADP
ejpam-4021	170	11	x	x	PUNCT
ejpam-4021	170	12	generated	generate	VERB
ejpam-4021	170	13	by	by	ADP
ejpam-4021	170	14	the	the	DET
ejpam-4021	170	15	singleton	singleton	PROPN
ejpam-4021	170	16	{	{	PUNCT
ejpam-4021	170	17	x	x	NOUN
ejpam-4021	170	18	}	}	PUNCT
ejpam-4021	170	19	;	;	PUNCT
ejpam-4021	170	20	(	(	PUNCT
ejpam-4021	170	21	c2	c2	PROPN
ejpam-4021	170	22	)	)	PUNCT
ejpam-4021	170	23	f	f	PROPN
ejpam-4021	170	24	,	,	PUNCT
ejpam-4021	170	25	g	g	PROPN
ejpam-4021	170	26	∈	∈	PROPN
ejpam-4021	170	27	f(x	f(x	PROPN
ejpam-4021	170	28	)	)	PUNCT
ejpam-4021	170	29	,	,	PUNCT
ejpam-4021	170	30	f	f	PROPN
ejpam-4021	170	31	⊆	⊆	NUM
ejpam-4021	170	32	g	g	NOUN
ejpam-4021	170	33	,	,	PUNCT
ejpam-4021	170	34	x	x	SYM
ejpam-4021	170	35	∈	∈	PROPN
ejpam-4021	170	36	q(f	q(f	PROPN
ejpam-4021	170	37	)	)	PUNCT
ejpam-4021	170	38	implies	imply	VERB
ejpam-4021	170	39	x	x	X
ejpam-4021	170	40	∈	∈	PROPN
ejpam-4021	170	41	q(g	q(g	PROPN
ejpam-4021	170	42	)	)	PUNCT
ejpam-4021	170	43	;	;	PUNCT
ejpam-4021	170	44	(	(	PUNCT
ejpam-4021	170	45	c3	c3	NOUN
ejpam-4021	170	46	)	)	PUNCT
ejpam-4021	170	47	x	x	SYM
ejpam-4021	170	48	∈	∈	PROPN
ejpam-4021	170	49	q(f	q(f	PROPN
ejpam-4021	170	50	)	)	PUNCT
ejpam-4021	170	51	implies	imply	VERB
ejpam-4021	170	52	x	x	X
ejpam-4021	170	53	∈	∈	PROPN
ejpam-4021	170	54	q(f	q(f	PROPN
ejpam-4021	170	55	∩	∩	PROPN
ejpam-4021	170	56	ẋ	ẋ	PROPN
ejpam-4021	170	57	)	)	PUNCT
ejpam-4021	170	58	.	.	PUNCT
ejpam-4021	171	1	note	note	VERB
ejpam-4021	171	2	that	that	SCONJ
ejpam-4021	171	3	in	in	ADP
ejpam-4021	171	4	[	[	X
ejpam-4021	171	5	4	4	NUM
ejpam-4021	171	6	]	]	PUNCT
ejpam-4021	171	7	,	,	PUNCT
ejpam-4021	171	8	[	[	X
ejpam-4021	171	9	6	6	NUM
ejpam-4021	171	10	]	]	PUNCT
ejpam-4021	171	11	and	and	CCONJ
ejpam-4021	171	12	[	[	X
ejpam-4021	171	13	7	7	X
ejpam-4021	171	14	]	]	X
ejpam-4021	171	15	the	the	DET
ejpam-4021	171	16	above	above	ADJ
ejpam-4021	171	17	notion	notion	NOUN
ejpam-4021	171	18	is	be	AUX
ejpam-4021	171	19	called	call	VERB
ejpam-4021	171	20	a	a	DET
ejpam-4021	171	21	local	local	ADJ
ejpam-4021	171	22	filter	filter	NOUN
ejpam-4021	171	23	convergence	convergence	NOUN
ejpam-4021	171	24	structure	structure	NOUN
ejpam-4021	171	25	q	q	PUNCT
ejpam-4021	171	26	on	on	ADP
ejpam-4021	171	27	x	x	SYM
ejpam-4021	171	28	,	,	PUNCT
ejpam-4021	171	29	however	however	ADV
ejpam-4021	171	30	.	.	PUNCT
ejpam-4021	172	1	a	a	DET
ejpam-4021	172	2	mapping	mapping	NOUN
ejpam-4021	172	3	f	f	NOUN
ejpam-4021	172	4	:	:	PUNCT
ejpam-4021	172	5	(	(	PUNCT
ejpam-4021	172	6	x	x	X
ejpam-4021	172	7	,	,	PUNCT
ejpam-4021	172	8	q	q	ADJ
ejpam-4021	172	9	)	)	PUNCT
ejpam-4021	172	10	−→	−→	NOUN
ejpam-4021	172	11	(	(	PUNCT
ejpam-4021	172	12	x	x	NOUN
ejpam-4021	172	13	′	′	NUM
ejpam-4021	172	14	,	,	PUNCT
ejpam-4021	172	15	q′	q′	NOUN
ejpam-4021	172	16	)	)	PUNCT
ejpam-4021	172	17	is	be	AUX
ejpam-4021	172	18	called	call	VERB
ejpam-4021	172	19	continuous	continuous	ADJ
ejpam-4021	172	20	if	if	SCONJ
ejpam-4021	172	21	for	for	ADP
ejpam-4021	172	22	all	all	DET
ejpam-4021	172	23	f	f	PROPN
ejpam-4021	172	24	∈	∈	PROPN
ejpam-4021	172	25	f(x	f(x	PROPN
ejpam-4021	172	26	)	)	PUNCT
ejpam-4021	172	27	and	and	CCONJ
ejpam-4021	172	28	x	x	PUNCT
ejpam-4021	172	29	∈	∈	NOUN
ejpam-4021	172	30	x	x	X
ejpam-4021	172	31	,	,	PUNCT
ejpam-4021	172	32	x	x	SYM
ejpam-4021	172	33	∈	∈	PROPN
ejpam-4021	172	34	t	t	NOUN
ejpam-4021	172	35	m	m	VERB
ejpam-4021	172	36	g	g	NOUN
ejpam-4021	172	37	ahsanullah	ahsanullah	NOUN
ejpam-4021	172	38	,	,	PUNCT
ejpam-4021	172	39	fawzi	fawzi	PROPN
ejpam-4021	172	40	al	al	PROPN
ejpam-4021	172	41	-	-	PUNCT
ejpam-4021	172	42	thukair	thukair	NOUN
ejpam-4021	172	43	/	/	SYM
ejpam-4021	172	44	eur	eur	NOUN
ejpam-4021	172	45	.	.	PUNCT
ejpam-4021	173	1	j.	j.	PROPN
ejpam-4021	173	2	pure	pure	PROPN
ejpam-4021	173	3	appl	appl	PROPN
ejpam-4021	173	4	.	.	PROPN
ejpam-4021	173	5	math	math	PROPN
ejpam-4021	173	6	,	,	PUNCT
ejpam-4021	173	7	14	14	NUM
ejpam-4021	173	8	(	(	PUNCT
ejpam-4021	173	9	3	3	NUM
ejpam-4021	173	10	)	)	PUNCT
ejpam-4021	173	11	(	(	PUNCT
ejpam-4021	173	12	2021	2021	NUM
ejpam-4021	173	13	)	)	PUNCT
ejpam-4021	173	14	,	,	PUNCT
ejpam-4021	173	15	949	949	NUM
ejpam-4021	173	16	-	-	SYM
ejpam-4021	173	17	968	968	NUM
ejpam-4021	173	18	956	956	NUM
ejpam-4021	173	19	q(f	q(f	NOUN
ejpam-4021	173	20	)	)	PUNCT
ejpam-4021	173	21	implies	imply	VERB
ejpam-4021	173	22	f(x	f(x	PROPN
ejpam-4021	173	23	)	)	PUNCT
ejpam-4021	173	24	∈	∈	PROPN
ejpam-4021	173	25	q(f(f	q(f(f	PROPN
ejpam-4021	173	26	)	)	PUNCT
ejpam-4021	173	27	)	)	PUNCT
ejpam-4021	173	28	.	.	PUNCT
ejpam-4021	174	1	the	the	DET
ejpam-4021	174	2	category	category	NOUN
ejpam-4021	174	3	of	of	ADP
ejpam-4021	174	4	all	all	DET
ejpam-4021	174	5	kent	kent	PROPN
ejpam-4021	174	6	convergence	convergence	NOUN
ejpam-4021	174	7	spaces	space	NOUN
ejpam-4021	174	8	and	and	CCONJ
ejpam-4021	174	9	continuous	continuous	ADJ
ejpam-4021	174	10	mapping	mapping	NOUN
ejpam-4021	174	11	is	be	AUX
ejpam-4021	174	12	denoted	denote	VERB
ejpam-4021	174	13	by	by	ADP
ejpam-4021	174	14	kconv	kconv	PROPN
ejpam-4021	174	15	.	.	PUNCT
ejpam-4021	175	1	the	the	DET
ejpam-4021	175	2	category	category	NOUN
ejpam-4021	175	3	kconv	kconv	NOUN
ejpam-4021	175	4	is	be	AUX
ejpam-4021	175	5	a	a	DET
ejpam-4021	175	6	strong	strong	ADJ
ejpam-4021	175	7	topological	topological	ADJ
ejpam-4021	175	8	universe	universe	NOUN
ejpam-4021	175	9	,	,	PUNCT
ejpam-4021	175	10	cf	cf	NOUN
ejpam-4021	175	11	.	.	PUNCT
ejpam-4021	176	1	[	[	X
ejpam-4021	176	2	10	10	NUM
ejpam-4021	176	3	,	,	PUNCT
ejpam-4021	176	4	28	28	NUM
ejpam-4021	176	5	]	]	PUNCT
ejpam-4021	176	6	.	.	PUNCT
ejpam-4021	177	1	the	the	DET
ejpam-4021	177	2	pair	pair	NOUN
ejpam-4021	177	3	(	(	PUNCT
ejpam-4021	177	4	x	x	NOUN
ejpam-4021	177	5	,	,	PUNCT
ejpam-4021	177	6	q	q	X
ejpam-4021	177	7	)	)	PUNCT
ejpam-4021	177	8	is	be	AUX
ejpam-4021	177	9	called	call	VERB
ejpam-4021	177	10	a	a	DET
ejpam-4021	177	11	limit	limit	NOUN
ejpam-4021	177	12	space	space	NOUN
ejpam-4021	178	1	if	if	SCONJ
ejpam-4021	178	2	conditions	condition	NOUN
ejpam-4021	178	3	(	(	PUNCT
ejpam-4021	178	4	c1	c1	PROPN
ejpam-4021	178	5	)	)	PUNCT
ejpam-4021	178	6	,	,	PUNCT
ejpam-4021	178	7	(	(	PUNCT
ejpam-4021	178	8	c2	c2	PROPN
ejpam-4021	178	9	)	)	PUNCT
ejpam-4021	178	10	and	and	CCONJ
ejpam-4021	178	11	(	(	PUNCT
ejpam-4021	178	12	c4	c4	NOUN
ejpam-4021	178	13	):	):	PUNCT
ejpam-4021	178	14	∀f	∀f	PROPN
ejpam-4021	178	15	,	,	PUNCT
ejpam-4021	178	16	g	g	PROPN
ejpam-4021	178	17	∈	∈	PROPN
ejpam-4021	178	18	f(x	f(x	PROPN
ejpam-4021	178	19	)	)	PUNCT
ejpam-4021	178	20	,	,	PUNCT
ejpam-4021	178	21	x	x	PUNCT
ejpam-4021	178	22	∈	∈	PROPN
ejpam-4021	178	23	q(f	q(f	PROPN
ejpam-4021	178	24	)	)	PUNCT
ejpam-4021	178	25	and	and	CCONJ
ejpam-4021	178	26	x	x	PUNCT
ejpam-4021	178	27	∈	∈	PROPN
ejpam-4021	178	28	q(g	q(g	PROPN
ejpam-4021	178	29	)	)	PUNCT
ejpam-4021	178	30	implies	imply	VERB
ejpam-4021	178	31	x	x	X
ejpam-4021	178	32	∈	∈	PROPN
ejpam-4021	178	33	q(f	q(f	PROPN
ejpam-4021	178	34	∩g	∩g	PROPN
ejpam-4021	178	35	)	)	PUNCT
ejpam-4021	178	36	.	.	PUNCT
ejpam-4021	179	1	the	the	DET
ejpam-4021	179	2	category	category	NOUN
ejpam-4021	179	3	of	of	ADP
ejpam-4021	179	4	limit	limit	NOUN
ejpam-4021	179	5	spaces	space	NOUN
ejpam-4021	179	6	is	be	AUX
ejpam-4021	179	7	denoted	denote	VERB
ejpam-4021	179	8	by	by	ADP
ejpam-4021	179	9	lim	lim	PROPN
ejpam-4021	179	10	.	.	PUNCT
ejpam-4021	180	1	a	a	DET
ejpam-4021	180	2	limit	limit	NOUN
ejpam-4021	180	3	structure	structure	NOUN
ejpam-4021	180	4	q	q	NOUN
ejpam-4021	180	5	on	on	ADP
ejpam-4021	180	6	x	x	SYM
ejpam-4021	180	7	is	be	AUX
ejpam-4021	180	8	called	call	VERB
ejpam-4021	180	9	a	a	DET
ejpam-4021	180	10	principal	principal	ADJ
ejpam-4021	180	11	limit	limit	NOUN
ejpam-4021	180	12	structure	structure	NOUN
ejpam-4021	180	13	on	on	ADP
ejpam-4021	180	14	x	x	SYM
ejpam-4021	180	15	if	if	SCONJ
ejpam-4021	180	16	and	and	CCONJ
ejpam-4021	180	17	only	only	ADV
ejpam-4021	180	18	if	if	SCONJ
ejpam-4021	180	19	for	for	ADP
ejpam-4021	180	20	every	every	DET
ejpam-4021	180	21	x	x	SYM
ejpam-4021	180	22	∈	∈	PROPN
ejpam-4021	180	23	x	x	PUNCT
ejpam-4021	180	24	there	there	PRON
ejpam-4021	180	25	exists	exist	VERB
ejpam-4021	180	26	a	a	DET
ejpam-4021	180	27	unique	unique	ADJ
ejpam-4021	180	28	filter	filter	NOUN
ejpam-4021	180	29	ux	ux	PROPN
ejpam-4021	180	30	∈	∈	PROPN
ejpam-4021	180	31	f(x	f(x	PROPN
ejpam-4021	180	32	)	)	PUNCT
ejpam-4021	180	33	such	such	ADJ
ejpam-4021	180	34	that	that	SCONJ
ejpam-4021	180	35	the	the	DET
ejpam-4021	180	36	following	follow	VERB
ejpam-4021	180	37	relation	relation	NOUN
ejpam-4021	180	38	holds	hold	VERB
ejpam-4021	180	39	:	:	PUNCT
ejpam-4021	180	40	q	q	SYM
ejpam-4021	180	41	=	=	PUNCT
ejpam-4021	180	42	{	{	PUNCT
ejpam-4021	180	43	(	(	PUNCT
ejpam-4021	180	44	f	f	X
ejpam-4021	180	45	,	,	PUNCT
ejpam-4021	180	46	x	x	X
ejpam-4021	180	47	)	)	PUNCT
ejpam-4021	180	48	∈	∈	PROPN
ejpam-4021	180	49	f(x)×x	f(x)×x	PROPN
ejpam-4021	180	50	:	:	PUNCT
ejpam-4021	180	51	ux	ux	PROPN
ejpam-4021	181	1	⊆	⊆	NUM
ejpam-4021	181	2	f	f	X
ejpam-4021	181	3	}	}	PUNCT
ejpam-4021	181	4	.	.	PUNCT
ejpam-4021	182	1	the	the	DET
ejpam-4021	182	2	category	category	NOUN
ejpam-4021	182	3	of	of	ADP
ejpam-4021	182	4	all	all	DET
ejpam-4021	182	5	principal	principal	ADJ
ejpam-4021	182	6	limit	limit	NOUN
ejpam-4021	182	7	spaces	space	NOUN
ejpam-4021	182	8	and	and	CCONJ
ejpam-4021	182	9	continuous	continuous	ADJ
ejpam-4021	182	10	mappings	mapping	NOUN
ejpam-4021	182	11	is	be	AUX
ejpam-4021	182	12	denoted	denote	VERB
ejpam-4021	182	13	by	by	ADP
ejpam-4021	182	14	plim	plim	PROPN
ejpam-4021	182	15	.	.	PUNCT
ejpam-4021	183	1	remark	remark	PROPN
ejpam-4021	183	2	2	2	NUM
ejpam-4021	183	3	.	.	PUNCT
ejpam-4021	184	1	it	it	PRON
ejpam-4021	184	2	is	be	AUX
ejpam-4021	184	3	important	important	ADJ
ejpam-4021	184	4	to	to	PART
ejpam-4021	184	5	mention	mention	VERB
ejpam-4021	184	6	here	here	ADV
ejpam-4021	184	7	that	that	SCONJ
ejpam-4021	184	8	the	the	DET
ejpam-4021	184	9	categories	category	NOUN
ejpam-4021	184	10	of	of	ADP
ejpam-4021	184	11	closure	closure	NOUN
ejpam-4021	184	12	spaces	space	NOUN
ejpam-4021	184	13	,	,	PUNCT
ejpam-4021	184	14	cls	cls	NOUN
ejpam-4021	184	15	,	,	PUNCT
ejpam-4021	184	16	and	and	CCONJ
ejpam-4021	184	17	lim	lim	PROPN
ejpam-4021	184	18	with	with	ADP
ejpam-4021	184	19	principal	principal	ADJ
ejpam-4021	184	20	limit	limit	NOUN
ejpam-4021	184	21	structures	structure	NOUN
ejpam-4021	184	22	are	be	AUX
ejpam-4021	184	23	isomorphic	isomorphic	ADJ
ejpam-4021	184	24	,	,	PUNCT
ejpam-4021	184	25	cf	cf	NOUN
ejpam-4021	184	26	.	.	PUNCT
ejpam-4021	185	1	[	[	X
ejpam-4021	185	2	28	28	NUM
ejpam-4021	185	3	]	]	PUNCT
ejpam-4021	185	4	,	,	PUNCT
ejpam-4021	185	5	we	we	PRON
ejpam-4021	185	6	are	be	AUX
ejpam-4021	185	7	not	not	PART
ejpam-4021	185	8	interested	interested	ADJ
ejpam-4021	185	9	at	at	ADP
ejpam-4021	185	10	this	this	DET
ejpam-4021	185	11	stage	stage	NOUN
ejpam-4021	185	12	to	to	PART
ejpam-4021	185	13	carry	carry	VERB
ejpam-4021	185	14	out	out	ADP
ejpam-4021	185	15	research	research	NOUN
ejpam-4021	185	16	in	in	ADP
ejpam-4021	185	17	this	this	DET
ejpam-4021	185	18	direction	direction	NOUN
ejpam-4021	185	19	,	,	PUNCT
ejpam-4021	185	20	and	and	CCONJ
ejpam-4021	185	21	postpone	postpone	VERB
ejpam-4021	185	22	it	it	PRON
ejpam-4021	185	23	for	for	ADP
ejpam-4021	185	24	further	further	ADJ
ejpam-4021	185	25	investigation	investigation	NOUN
ejpam-4021	185	26	.	.	PUNCT
ejpam-4021	186	1	definition	definition	NOUN
ejpam-4021	186	2	12	12	NUM
ejpam-4021	186	3	.	.	PUNCT
ejpam-4021	187	1	[	[	X
ejpam-4021	187	2	27	27	NUM
ejpam-4021	187	3	]	]	X
ejpam-4021	187	4	let	let	VERB
ejpam-4021	187	5	(	(	PUNCT
ejpam-4021	187	6	g	g	NOUN
ejpam-4021	187	7	,	,	PUNCT
ejpam-4021	187	8	·	·	PUNCT
ejpam-4021	187	9	)	)	PUNCT
ejpam-4021	187	10	∈	∈	PROPN
ejpam-4021	188	1	|grp|	|grp|	NOUN
ejpam-4021	188	2	and	and	CCONJ
ejpam-4021	188	3	(	(	PUNCT
ejpam-4021	188	4	g	g	NOUN
ejpam-4021	188	5	,	,	PUNCT
ejpam-4021	188	6	q	q	NOUN
ejpam-4021	188	7	)	)	PUNCT
ejpam-4021	188	8	∈	∈	PROPN
ejpam-4021	188	9	|kconv|	|kconv|	PROPN
ejpam-4021	188	10	(	(	PUNCT
ejpam-4021	188	11	resp	resp	NOUN
ejpam-4021	188	12	.	.	PUNCT
ejpam-4021	189	1	(	(	PUNCT
ejpam-4021	189	2	g	g	NOUN
ejpam-4021	189	3	,	,	PUNCT
ejpam-4021	189	4	q	q	NOUN
ejpam-4021	189	5	)	)	PUNCT
ejpam-4021	189	6	∈	∈	PROPN
ejpam-4021	189	7	|lim|	|lim|	NOUN
ejpam-4021	189	8	)	)	PUNCT
ejpam-4021	189	9	.	.	PUNCT
ejpam-4021	190	1	then	then	ADV
ejpam-4021	190	2	the	the	DET
ejpam-4021	190	3	triple	triple	ADJ
ejpam-4021	190	4	(	(	PUNCT
ejpam-4021	190	5	g	g	NOUN
ejpam-4021	190	6	,	,	PUNCT
ejpam-4021	190	7	·	·	PUNCT
ejpam-4021	190	8	,	,	PUNCT
ejpam-4021	190	9	q	q	X
ejpam-4021	190	10	)	)	PUNCT
ejpam-4021	190	11	∈	∈	NOUN
ejpam-4021	190	12	|kconvgrp|	|kconvgrp|	NUM
ejpam-4021	190	13	(	(	PUNCT
ejpam-4021	190	14	resp	resp	NOUN
ejpam-4021	190	15	.	.	PUNCT
ejpam-4021	191	1	(	(	PUNCT
ejpam-4021	191	2	g	g	NOUN
ejpam-4021	191	3	,	,	PUNCT
ejpam-4021	191	4	·	·	PUNCT
ejpam-4021	191	5	,	,	PUNCT
ejpam-4021	191	6	q	q	X
ejpam-4021	191	7	)	)	PUNCT
ejpam-4021	191	8	∈	∈	NOUN
ejpam-4021	191	9	|limgrp|	|limgrp|	NOUN
ejpam-4021	191	10	)	)	PUNCT
ejpam-4021	191	11	if	if	SCONJ
ejpam-4021	191	12	the	the	DET
ejpam-4021	191	13	following	follow	VERB
ejpam-4021	191	14	are	be	AUX
ejpam-4021	191	15	fulfilled	fulfil	VERB
ejpam-4021	191	16	:	:	PUNCT
ejpam-4021	191	17	(	(	PUNCT
ejpam-4021	191	18	cgm	cgm	PROPN
ejpam-4021	191	19	)	)	PUNCT
ejpam-4021	191	20	x	x	SYM
ejpam-4021	191	21	∈	∈	PROPN
ejpam-4021	191	22	q(f	q(f	PROPN
ejpam-4021	191	23	)	)	PUNCT
ejpam-4021	191	24	and	and	CCONJ
ejpam-4021	191	25	y	y	PROPN
ejpam-4021	191	26	∈	∈	PROPN
ejpam-4021	191	27	q(g	q(g	PROPN
ejpam-4021	191	28	)	)	PUNCT
ejpam-4021	191	29	implies	imply	VERB
ejpam-4021	191	30	xy	xy	PROPN
ejpam-4021	191	31	∈	∈	PROPN
ejpam-4021	191	32	q	q	X
ejpam-4021	192	1	(	(	PUNCT
ejpam-4021	192	2	f	f	X
ejpam-4021	192	3	�	�	PROPN
ejpam-4021	192	4	g	g	NOUN
ejpam-4021	192	5	)	)	PUNCT
ejpam-4021	192	6	;	;	PUNCT
ejpam-4021	192	7	(	(	PUNCT
ejpam-4021	192	8	cgi	cgi	NOUN
ejpam-4021	192	9	)	)	PUNCT
ejpam-4021	192	10	x	x	SYM
ejpam-4021	192	11	∈	∈	PROPN
ejpam-4021	192	12	q(f	q(f	PROPN
ejpam-4021	192	13	)	)	PUNCT
ejpam-4021	192	14	implies	imply	VERB
ejpam-4021	192	15	x−1	x−1	PROPN
ejpam-4021	192	16	∈	∈	PROPN
ejpam-4021	192	17	q(f−1	q(f−1	PROPN
ejpam-4021	192	18	)	)	PUNCT
ejpam-4021	192	19	.	.	PUNCT
ejpam-4021	193	1	the	the	DET
ejpam-4021	193	2	category	category	NOUN
ejpam-4021	193	3	of	of	ADP
ejpam-4021	193	4	all	all	DET
ejpam-4021	193	5	kent	kent	NOUN
ejpam-4021	193	6	convergence	convergence	NOUN
ejpam-4021	193	7	groups	group	NOUN
ejpam-4021	193	8	and	and	CCONJ
ejpam-4021	193	9	group	group	NOUN
ejpam-4021	193	10	homomorphisms	homomorphism	NOUN
ejpam-4021	193	11	is	be	AUX
ejpam-4021	193	12	denoted	denote	VERB
ejpam-4021	193	13	by	by	ADP
ejpam-4021	193	14	kconvgrp	kconvgrp	PROPN
ejpam-4021	193	15	(	(	PUNCT
ejpam-4021	193	16	resp	resp	NOUN
ejpam-4021	193	17	.	.	PUNCT
ejpam-4021	194	1	the	the	DET
ejpam-4021	194	2	category	category	NOUN
ejpam-4021	194	3	of	of	ADP
ejpam-4021	194	4	all	all	DET
ejpam-4021	194	5	limit	limit	NOUN
ejpam-4021	194	6	groups	group	NOUN
ejpam-4021	194	7	and	and	CCONJ
ejpam-4021	194	8	group	group	NOUN
ejpam-4021	194	9	homomorphisms	homomorphism	NOUN
ejpam-4021	194	10	is	be	AUX
ejpam-4021	194	11	denoted	denote	VERB
ejpam-4021	194	12	by	by	ADP
ejpam-4021	194	13	limgrp	limgrp	NOUN
ejpam-4021	194	14	)	)	PUNCT
ejpam-4021	194	15	.	.	PUNCT
ejpam-4021	195	1	given	give	VERB
ejpam-4021	195	2	a	a	DET
ejpam-4021	195	3	stratified	stratified	ADJ
ejpam-4021	195	4	l	l	ADJ
ejpam-4021	195	5	-	-	ADJ
ejpam-4021	195	6	topological	topological	ADJ
ejpam-4021	195	7	space	space	NOUN
ejpam-4021	195	8	(	(	PUNCT
ejpam-4021	195	9	x,∆n	x,∆n	NUM
ejpam-4021	195	10	)	)	PUNCT
ejpam-4021	195	11	with	with	ADP
ejpam-4021	195	12	the	the	DET
ejpam-4021	195	13	corresponding	corresponding	ADJ
ejpam-4021	195	14	l	l	ADJ
ejpam-4021	195	15	-	-	PUNCT
ejpam-4021	195	16	neighborhood	neighborhood	NOUN
ejpam-4021	195	17	system	system	NOUN
ejpam-4021	195	18	n.	n.	NOUN
ejpam-4021	195	19	then	then	ADV
ejpam-4021	195	20	a	a	DET
ejpam-4021	195	21	filter	filter	NOUN
ejpam-4021	195	22	f	f	PROPN
ejpam-4021	195	23	is	be	AUX
ejpam-4021	195	24	said	say	VERB
ejpam-4021	195	25	to	to	PART
ejpam-4021	195	26	be	be	AUX
ejpam-4021	195	27	convergent	convergent	ADJ
ejpam-4021	195	28	to	to	ADP
ejpam-4021	195	29	a	a	DET
ejpam-4021	195	30	point	point	NOUN
ejpam-4021	195	31	x	x	X
ejpam-4021	195	32	∈	∈	NOUN
ejpam-4021	195	33	x	x	X
ejpam-4021	195	34	(	(	PUNCT
ejpam-4021	195	35	we	we	PRON
ejpam-4021	195	36	denoted	denote	VERB
ejpam-4021	195	37	it	it	PRON
ejpam-4021	195	38	as	as	ADP
ejpam-4021	195	39	x	x	PROPN
ejpam-4021	195	40	∈	∈	PROPN
ejpam-4021	195	41	q∆n	q∆n	NOUN
ejpam-4021	195	42	(	(	PUNCT
ejpam-4021	195	43	f	f	X
ejpam-4021	195	44	)	)	PUNCT
ejpam-4021	195	45	)	)	PUNCT
ejpam-4021	195	46	with	with	ADP
ejpam-4021	195	47	respect	respect	NOUN
ejpam-4021	195	48	to	to	ADP
ejpam-4021	195	49	∆n	∆n	PROPN
ejpam-4021	195	50	if	if	SCONJ
ejpam-4021	195	51	and	and	CCONJ
ejpam-4021	195	52	only	only	ADV
ejpam-4021	195	53	if	if	SCONJ
ejpam-4021	195	54	for	for	ADP
ejpam-4021	195	55	all	all	DET
ejpam-4021	195	56	ν	ν	NOUN
ejpam-4021	195	57	∈	∈	NOUN
ejpam-4021	195	58	lx	lx	ADP
ejpam-4021	195	59	the	the	DET
ejpam-4021	195	60	following	follow	VERB
ejpam-4021	195	61	holds	hold	NOUN
ejpam-4021	195	62	:	:	PUNCT
ejpam-4021	195	63	nx(ν	nx(ν	X
ejpam-4021	195	64	)	)	PUNCT
ejpam-4021	195	65	≤	≤	NUM
ejpam-4021	195	66	∨	∨	NUM
ejpam-4021	195	67	f∈f	f∈f	NOUN
ejpam-4021	195	68	(	(	PUNCT
ejpam-4021	195	69	∧	∧	PROPN
ejpam-4021	195	70	y∈f	y∈f	NOUN
ejpam-4021	195	71	ν(y	ν(y	PROPN
ejpam-4021	195	72	)	)	PUNCT
ejpam-4021	195	73	)	)	PUNCT
ejpam-4021	195	74	.	.	PUNCT
ejpam-4021	196	1	lemma	lemma	PROPN
ejpam-4021	196	2	3	3	X
ejpam-4021	196	3	.	.	PUNCT
ejpam-4021	197	1	let	let	VERB
ejpam-4021	197	2	(	(	PUNCT
ejpam-4021	197	3	g	g	NOUN
ejpam-4021	197	4	,	,	PUNCT
ejpam-4021	197	5	·	·	PUNCT
ejpam-4021	197	6	,	,	PUNCT
ejpam-4021	197	7	∆n	∆n	PROPN
ejpam-4021	197	8	)	)	PUNCT
ejpam-4021	197	9	∈	∈	PROPN
ejpam-4021	197	10	|sl	|sl	PROPN
ejpam-4021	197	11	-	-	SYM
ejpam-4021	197	12	topgrp|	topgrp|	NOUN
ejpam-4021	197	13	,	,	PUNCT
ejpam-4021	197	14	where	where	SCONJ
ejpam-4021	197	15	∆	∆	PROPN
ejpam-4021	197	16	is	be	AUX
ejpam-4021	197	17	a	a	DET
ejpam-4021	197	18	stratified	stratified	ADJ
ejpam-4021	197	19	l	l	NOUN
ejpam-4021	197	20	-	-	PUNCT
ejpam-4021	197	21	valued	value	VERB
ejpam-4021	197	22	topology	topology	NOUN
ejpam-4021	197	23	on	on	ADP
ejpam-4021	197	24	g	g	PROPN
ejpam-4021	197	25	and	and	CCONJ
ejpam-4021	197	26	n	n	PROPN
ejpam-4021	197	27	is	be	AUX
ejpam-4021	197	28	a	a	DET
ejpam-4021	197	29	corresponding	corresponding	ADJ
ejpam-4021	197	30	l	l	ADV
ejpam-4021	197	31	-	-	PUNCT
ejpam-4021	197	32	valued	value	VERB
ejpam-4021	197	33	neighborhood	neighborhood	NOUN
ejpam-4021	197	34	system	system	NOUN
ejpam-4021	197	35	.	.	PUNCT
ejpam-4021	198	1	then	then	ADV
ejpam-4021	198	2	(	(	PUNCT
ejpam-4021	198	3	g	g	NOUN
ejpam-4021	198	4	,	,	PUNCT
ejpam-4021	198	5	·	·	PUNCT
ejpam-4021	198	6	,	,	PUNCT
ejpam-4021	198	7	q∆n	q∆n	ADV
ejpam-4021	198	8	)	)	PUNCT
ejpam-4021	198	9	∈	∈	PROPN
ejpam-4021	198	10	|kconvgrp|	|kconvgrp|	NUM
ejpam-4021	198	11	.	.	PUNCT
ejpam-4021	199	1	proof	proof	NOUN
ejpam-4021	199	2	.	.	PUNCT
ejpam-4021	200	1	let	let	VERB
ejpam-4021	200	2	(	(	PUNCT
ejpam-4021	200	3	g	g	NOUN
ejpam-4021	200	4	,	,	PUNCT
ejpam-4021	200	5	·	·	PUNCT
ejpam-4021	200	6	,	,	PUNCT
ejpam-4021	200	7	∆n	∆n	PROPN
ejpam-4021	200	8	)	)	PUNCT
ejpam-4021	200	9	∈	∈	PROPN
ejpam-4021	200	10	|sl	|sl	PROPN
ejpam-4021	200	11	-	-	PUNCT
ejpam-4021	200	12	topgrp|	topgrp|	PROPN
ejpam-4021	200	13	.	.	PUNCT
ejpam-4021	201	1	then	then	ADV
ejpam-4021	201	2	in	in	ADP
ejpam-4021	201	3	view	view	NOUN
ejpam-4021	201	4	of	of	ADP
ejpam-4021	201	5	the	the	DET
ejpam-4021	201	6	lemma	lemma	PROPN
ejpam-4021	201	7	5.4.1[18	5.4.1[18	NUM
ejpam-4021	201	8	]	]	PUNCT
ejpam-4021	201	9	,	,	PUNCT
ejpam-4021	201	10	we	we	PRON
ejpam-4021	201	11	only	only	ADV
ejpam-4021	201	12	need	need	VERB
ejpam-4021	201	13	to	to	PART
ejpam-4021	201	14	check	check	VERB
ejpam-4021	201	15	the	the	DET
ejpam-4021	201	16	conditions	condition	NOUN
ejpam-4021	201	17	(	(	PUNCT
ejpam-4021	201	18	cgm	cgm	NOUN
ejpam-4021	201	19	)	)	PUNCT
ejpam-4021	201	20	and	and	CCONJ
ejpam-4021	201	21	(	(	PUNCT
ejpam-4021	201	22	cgi	cgi	NOUN
ejpam-4021	201	23	)	)	PUNCT
ejpam-4021	201	24	.	.	PUNCT
ejpam-4021	202	1	(	(	PUNCT
ejpam-4021	202	2	cgm	cgm	NOUN
ejpam-4021	202	3	)	)	PUNCT
ejpam-4021	202	4	let	let	VERB
ejpam-4021	202	5	for	for	ADP
ejpam-4021	202	6	f	f	PROPN
ejpam-4021	202	7	,	,	PUNCT
ejpam-4021	202	8	g	g	PROPN
ejpam-4021	202	9	∈	∈	PROPN
ejpam-4021	202	10	f(g	f(g	NOUN
ejpam-4021	202	11	)	)	PUNCT
ejpam-4021	202	12	and	and	CCONJ
ejpam-4021	202	13	x	x	X
ejpam-4021	202	14	,	,	PUNCT
ejpam-4021	202	15	y	y	PROPN
ejpam-4021	202	16	∈	∈	PROPN
ejpam-4021	202	17	g	g	PROPN
ejpam-4021	202	18	,	,	PUNCT
ejpam-4021	202	19	x	x	PROPN
ejpam-4021	202	20	∈	∈	PROPN
ejpam-4021	202	21	q∆n	q∆n	NOUN
ejpam-4021	203	1	(	(	PUNCT
ejpam-4021	203	2	f	f	X
ejpam-4021	203	3	)	)	PUNCT
ejpam-4021	203	4	and	and	CCONJ
ejpam-4021	203	5	y	y	PROPN
ejpam-4021	203	6	∈	∈	PROPN
ejpam-4021	203	7	q∆n	q∆n	NOUN
ejpam-4021	203	8	(	(	PUNCT
ejpam-4021	203	9	g	g	NOUN
ejpam-4021	203	10	)	)	PUNCT
ejpam-4021	203	11	.	.	PUNCT
ejpam-4021	204	1	then	then	ADV
ejpam-4021	204	2	for	for	ADP
ejpam-4021	204	3	any	any	DET
ejpam-4021	204	4	ν	ν	NOUN
ejpam-4021	204	5	,	,	PUNCT
ejpam-4021	204	6	µ	µ	PROPN
ejpam-4021	204	7	∈	∈	PROPN
ejpam-4021	204	8	lg	lg	NOUN
ejpam-4021	204	9	:	:	PUNCT
ejpam-4021	204	10	nx(ν	nx(ν	ADJ
ejpam-4021	204	11	)	)	PUNCT
ejpam-4021	204	12	≤	≤	NUM
ejpam-4021	204	13	∨	∨	NUM
ejpam-4021	204	14	f∈f	f∈f	NOUN
ejpam-4021	204	15	∧	∧	PROPN
ejpam-4021	204	16	y1∈f	y1∈f	NOUN
ejpam-4021	204	17	ν(y1	ν(y1	NOUN
ejpam-4021	204	18	)	)	PUNCT
ejpam-4021	204	19	,	,	PUNCT
ejpam-4021	204	20	and	and	CCONJ
ejpam-4021	204	21	ny(µ	ny(µ	NOUN
ejpam-4021	204	22	)	)	PUNCT
ejpam-4021	204	23	≤	≤	NUM
ejpam-4021	204	24	∨	∨	NUM
ejpam-4021	204	25	g∈g	g∈g	PROPN
ejpam-4021	204	26	∧	∧	PROPN
ejpam-4021	204	27	y2∈g	y2∈g	PROPN
ejpam-4021	204	28	µ(y2	µ(y2	NOUN
ejpam-4021	204	29	)	)	PUNCT
ejpam-4021	204	30	.	.	PUNCT
ejpam-4021	205	1	thus	thus	ADV
ejpam-4021	205	2	,	,	PUNCT
ejpam-4021	205	3	for	for	ADP
ejpam-4021	205	4	any	any	DET
ejpam-4021	205	5	σ	σ	PROPN
ejpam-4021	205	6	∈	∈	PROPN
ejpam-4021	205	7	lg	lg	NOUN
ejpam-4021	205	8	,	,	PUNCT
ejpam-4021	205	9	nxy(σ	nxy(σ	PROPN
ejpam-4021	205	10	)	)	PUNCT
ejpam-4021	205	11	≤	≤	NOUN
ejpam-4021	205	12	∨	∨	NUM
ejpam-4021	205	13	{	{	PUNCT
ejpam-4021	205	14	nx(ν	nx(ν	NOUN
ejpam-4021	205	15	)	)	PUNCT
ejpam-4021	205	16	∗ny(µ	∗ny(µ	NOUN
ejpam-4021	205	17	)	)	PUNCT
ejpam-4021	205	18	:	:	PUNCT
ejpam-4021	205	19	ν(x	ν(x	PROPN
ejpam-4021	205	20	)	)	PUNCT
ejpam-4021	205	21	∗	∗	NOUN
ejpam-4021	205	22	µ(y	µ(y	PROPN
ejpam-4021	205	23	)	)	PUNCT
ejpam-4021	205	24	≤	≤	NOUN
ejpam-4021	205	25	σ(xy	σ(xy	NOUN
ejpam-4021	205	26	)	)	PUNCT
ejpam-4021	205	27	}	}	PUNCT
ejpam-4021	205	28	≤∨	≤∨	X
ejpam-4021	205	29	ν(x)∗µ(y)≤σ(xy	ν(x)∗µ(y)≤σ(xy	NUM
ejpam-4021	205	30	)	)	PUNCT
ejpam-4021	205	31	∨	∨	PROPN
ejpam-4021	205	32	f	f	PROPN
ejpam-4021	205	33	·	·	SYM
ejpam-4021	205	34	g∈f	g∈f	PROPN
ejpam-4021	205	35	�	�	PROPN
ejpam-4021	205	36	g	g	PROPN
ejpam-4021	205	37	∧	∧	PROPN
ejpam-4021	205	38	y1∈f	y1∈f	NUM
ejpam-4021	205	39	,	,	PUNCT
ejpam-4021	205	40	y2∈g	y2∈g	PROPN
ejpam-4021	205	41	ν(x	ν(x	PROPN
ejpam-4021	205	42	)	)	PUNCT
ejpam-4021	205	43	∗	∗	NOUN
ejpam-4021	205	44	µ(y	µ(y	PROPN
ejpam-4021	205	45	)	)	PUNCT
ejpam-4021	205	46	≤	≤	NOUN
ejpam-4021	205	47	∨	∨	NUM
ejpam-4021	205	48	f	f	PROPN
ejpam-4021	205	49	·	·	SYM
ejpam-4021	205	50	g∈f	g∈f	PROPN
ejpam-4021	205	51	�	�	PROPN
ejpam-4021	205	52	g	g	PROPN
ejpam-4021	205	53	∧	∧	PROPN
ejpam-4021	205	54	xy∈f	xy∈f	X
ejpam-4021	205	55	·	·	PUNCT
ejpam-4021	205	56	g	g	PROPN
ejpam-4021	205	57	σ(xy	σ(xy	PROPN
ejpam-4021	205	58	)	)	PUNCT
ejpam-4021	205	59	t	t	PROPN
ejpam-4021	205	60	m	m	PROPN
ejpam-4021	205	61	g	g	NOUN
ejpam-4021	205	62	ahsanullah	ahsanullah	NOUN
ejpam-4021	205	63	,	,	PUNCT
ejpam-4021	205	64	fawzi	fawzi	PROPN
ejpam-4021	205	65	al	al	PROPN
ejpam-4021	205	66	-	-	PUNCT
ejpam-4021	205	67	thukair	thukair	NOUN
ejpam-4021	205	68	/	/	SYM
ejpam-4021	205	69	eur	eur	NOUN
ejpam-4021	205	70	.	.	PUNCT
ejpam-4021	206	1	j.	j.	PROPN
ejpam-4021	206	2	pure	pure	PROPN
ejpam-4021	206	3	appl	appl	PROPN
ejpam-4021	206	4	.	.	PROPN
ejpam-4021	206	5	math	math	PROPN
ejpam-4021	206	6	,	,	PUNCT
ejpam-4021	206	7	14	14	NUM
ejpam-4021	206	8	(	(	PUNCT
ejpam-4021	206	9	3	3	NUM
ejpam-4021	206	10	)	)	PUNCT
ejpam-4021	206	11	(	(	PUNCT
ejpam-4021	206	12	2021	2021	NUM
ejpam-4021	206	13	)	)	PUNCT
ejpam-4021	206	14	,	,	PUNCT
ejpam-4021	206	15	949	949	NUM
ejpam-4021	206	16	-	-	SYM
ejpam-4021	206	17	968	968	NUM
ejpam-4021	206	18	957	957	NUM
ejpam-4021	206	19	this	this	PRON
ejpam-4021	206	20	implies	imply	VERB
ejpam-4021	206	21	that	that	SCONJ
ejpam-4021	206	22	nxy(σ	nxy(σ	PROPN
ejpam-4021	206	23	)	)	PUNCT
ejpam-4021	206	24	≤	≤	NOUN
ejpam-4021	206	25	∨	∨	NUM
ejpam-4021	206	26	f	f	PROPN
ejpam-4021	206	27	·	·	SYM
ejpam-4021	206	28	g∈f	g∈f	PROPN
ejpam-4021	206	29	�	�	PROPN
ejpam-4021	206	30	g	g	PROPN
ejpam-4021	206	31	∧	∧	PROPN
ejpam-4021	206	32	z∈f	z∈f	INTJ
ejpam-4021	206	33	·	·	PUNCT
ejpam-4021	206	34	g	g	NOUN
ejpam-4021	206	35	σ(xy	σ(xy	PROPN
ejpam-4021	206	36	)	)	PUNCT
ejpam-4021	206	37	,	,	PUNCT
ejpam-4021	206	38	i.e.	i.e.	X
ejpam-4021	206	39	,	,	PUNCT
ejpam-4021	206	40	xy	xy	PROPN
ejpam-4021	206	41	∈	∈	PROPN
ejpam-4021	206	42	q∆n	q∆n	NOUN
ejpam-4021	207	1	(	(	PUNCT
ejpam-4021	207	2	f	f	PROPN
ejpam-4021	207	3	�	�	PROPN
ejpam-4021	207	4	g	g	NOUN
ejpam-4021	207	5	)	)	PUNCT
ejpam-4021	207	6	.	.	PUNCT
ejpam-4021	208	1	(	(	PUNCT
ejpam-4021	208	2	cgi	cgi	NOUN
ejpam-4021	208	3	)	)	PUNCT
ejpam-4021	208	4	let	let	VERB
ejpam-4021	208	5	f	f	PROPN
ejpam-4021	208	6	∈	∈	PROPN
ejpam-4021	208	7	f(g	f(g	PROPN
ejpam-4021	208	8	)	)	PUNCT
ejpam-4021	208	9	,	,	PUNCT
ejpam-4021	208	10	and	and	CCONJ
ejpam-4021	208	11	x	x	PUNCT
ejpam-4021	208	12	∈	∈	PROPN
ejpam-4021	208	13	x.	x.	NOUN
ejpam-4021	208	14	then	then	ADV
ejpam-4021	208	15	by	by	ADP
ejpam-4021	208	16	invoking	invoke	VERB
ejpam-4021	208	17	(	(	PUNCT
ejpam-4021	208	18	†	†	NOUN
ejpam-4021	208	19	)	)	PUNCT
ejpam-4021	208	20	in	in	ADP
ejpam-4021	208	21	conjunction	conjunction	NOUN
ejpam-4021	208	22	with	with	ADP
ejpam-4021	208	23	the	the	DET
ejpam-4021	208	24	lemma	lemma	PROPN
ejpam-4021	208	25	5.4.1[18	5.4.1[18	NUM
ejpam-4021	208	26	]	]	X
ejpam-4021	208	27	,	,	PUNCT
ejpam-4021	208	28	if	if	SCONJ
ejpam-4021	208	29	we	we	PRON
ejpam-4021	208	30	consider	consider	VERB
ejpam-4021	208	31	x	x	X
ejpam-4021	208	32	∈	∈	PROPN
ejpam-4021	208	33	q∆n	q∆n	NOUN
ejpam-4021	208	34	(	(	PUNCT
ejpam-4021	208	35	f	f	X
ejpam-4021	208	36	)	)	PUNCT
ejpam-4021	208	37	,	,	PUNCT
ejpam-4021	208	38	then	then	ADV
ejpam-4021	208	39	for	for	ADP
ejpam-4021	208	40	any	any	DET
ejpam-4021	208	41	ν	ν	NOUN
ejpam-4021	208	42	∈	∈	PROPN
ejpam-4021	208	43	lg	lg	NOUN
ejpam-4021	208	44	,	,	PUNCT
ejpam-4021	208	45	we	we	PRON
ejpam-4021	208	46	have	have	VERB
ejpam-4021	208	47	nx(ν	nx(ν	NOUN
ejpam-4021	208	48	)	)	PUNCT
ejpam-4021	208	49	≤	≤	NUM
ejpam-4021	208	50	∨	∨	NUM
ejpam-4021	208	51	f∈f	f∈f	NOUN
ejpam-4021	208	52	(	(	PUNCT
ejpam-4021	208	53	∧	∧	PROPN
ejpam-4021	208	54	y∈f	y∈f	NOUN
ejpam-4021	208	55	ν(y	ν(y	PROPN
ejpam-4021	208	56	)	)	PUNCT
ejpam-4021	208	57	)	)	PUNCT
ejpam-4021	208	58	.	.	PUNCT
ejpam-4021	209	1	now	now	ADV
ejpam-4021	209	2	due	due	ADP
ejpam-4021	209	3	to	to	ADP
ejpam-4021	209	4	the	the	DET
ejpam-4021	209	5	continuity	continuity	NOUN
ejpam-4021	209	6	of	of	ADP
ejpam-4021	209	7			PROPN
ejpam-4021	209	8	,	,	PUNCT
ejpam-4021	209	9	we	we	PRON
ejpam-4021	209	10	have	have	VERB
ejpam-4021	209	11	nx−1(ν	nx−1(ν	ADJ
ejpam-4021	209	12	)	)	PUNCT
ejpam-4021	209	13	≤	≤	NUM
ejpam-4021	209	14	nx(ν−1	nx(ν−1	ADJ
ejpam-4021	209	15	)	)	PUNCT
ejpam-4021	209	16	≤	≤	NOUN
ejpam-4021	209	17	∨	∨	NUM
ejpam-4021	209	18	f∈f	f∈f	NOUN
ejpam-4021	209	19	(	(	PUNCT
ejpam-4021	209	20	∧	∧	PROPN
ejpam-4021	209	21	y∈f	y∈f	NOUN
ejpam-4021	209	22	ν	ν	X
ejpam-4021	209	23	−1(y	−1(y	PROPN
ejpam-4021	209	24	)	)	PUNCT
ejpam-4021	209	25	)	)	PUNCT
ejpam-4021	210	1	=	=	PUNCT
ejpam-4021	210	2	∨	∨	NUM
ejpam-4021	210	3	f−1∈f−1	f−1∈f−1	PROPN
ejpam-4021	210	4	(	(	PUNCT
ejpam-4021	210	5	∧	∧	NOUN
ejpam-4021	210	6	y−1∈f−1	y−1∈f−1	PROPN
ejpam-4021	210	7	ν(y−1	ν(y−1	ADJ
ejpam-4021	210	8	)	)	PUNCT
ejpam-4021	210	9	)	)	PUNCT
ejpam-4021	210	10	.	.	PUNCT
ejpam-4021	211	1	that	that	PRON
ejpam-4021	211	2	is	be	AUX
ejpam-4021	211	3	,	,	PUNCT
ejpam-4021	211	4	nx−1(ν	nx−1(ν	ADJ
ejpam-4021	211	5	)	)	PUNCT
ejpam-4021	211	6	≤	≤	NOUN
ejpam-4021	211	7	∨	∨	NUM
ejpam-4021	211	8	f−1∈f−1	f−1∈f−1	PROPN
ejpam-4021	211	9	(	(	PUNCT
ejpam-4021	211	10	∧	∧	NOUN
ejpam-4021	211	11	y−1∈f−1	y−1∈f−1	PROPN
ejpam-4021	211	12	ν(y−1	ν(y−1	ADJ
ejpam-4021	211	13	)	)	PUNCT
ejpam-4021	211	14	)	)	PUNCT
ejpam-4021	212	1	implying	imply	VERB
ejpam-4021	212	2	x−1	x−1	PROPN
ejpam-4021	212	3	∈	∈	PROPN
ejpam-4021	212	4	q∆n	q∆n	NOUN
ejpam-4021	212	5	(	(	PUNCT
ejpam-4021	212	6	f−1	f−1	PROPN
ejpam-4021	212	7	)	)	PUNCT
ejpam-4021	212	8	.	.	PUNCT
ejpam-4021	213	1	remark	remark	PROPN
ejpam-4021	213	2	3	3	NUM
ejpam-4021	213	3	.	.	PUNCT
ejpam-4021	214	1	referring	refer	VERB
ejpam-4021	214	2	to	to	ADP
ejpam-4021	214	3	the	the	DET
ejpam-4021	214	4	pp	pp	NOUN
ejpam-4021	214	5	.	.	PUNCT
ejpam-4021	215	1	175	175	NUM
ejpam-4021	216	1	[	[	X
ejpam-4021	216	2	18	18	NUM
ejpam-4021	216	3	]	]	PUNCT
ejpam-4021	216	4	,	,	PUNCT
ejpam-4021	216	5	one	one	PRON
ejpam-4021	216	6	can	can	AUX
ejpam-4021	216	7	observe	observe	VERB
ejpam-4021	216	8	that	that	SCONJ
ejpam-4021	216	9	given	give	VERB
ejpam-4021	216	10	a	a	DET
ejpam-4021	216	11	kent	kent	PROPN
ejpam-4021	216	12	convergence	convergence	NOUN
ejpam-4021	216	13	structure	structure	NOUN
ejpam-4021	216	14	q	q	PUNCT
ejpam-4021	216	15	on	on	ADP
ejpam-4021	216	16	x	x	SYM
ejpam-4021	216	17	,	,	PUNCT
ejpam-4021	216	18	then	then	ADV
ejpam-4021	216	19	q	q	X
ejpam-4021	216	20	induces	induce	VERB
ejpam-4021	216	21	a	a	DET
ejpam-4021	216	22	stratified	stratified	ADJ
ejpam-4021	216	23	l	l	ADV
ejpam-4021	216	24	-	-	PUNCT
ejpam-4021	216	25	valued	value	VERB
ejpam-4021	216	26	topology	topology	NOUN
ejpam-4021	216	27	∆̂q	∆̂q	PROPN
ejpam-4021	216	28	in	in	ADP
ejpam-4021	216	29	the	the	DET
ejpam-4021	216	30	following	following	ADJ
ejpam-4021	216	31	way	way	NOUN
ejpam-4021	216	32	:	:	PUNCT
ejpam-4021	216	33	∆̂q	∆̂q	PROPN
ejpam-4021	216	34	=	=	PRON
ejpam-4021	216	35	{	{	PUNCT
ejpam-4021	216	36	σ	σ	NOUN
ejpam-4021	216	37	∈	∈	PROPN
ejpam-4021	216	38	lx	lx	NOUN
ejpam-4021	216	39	:	:	PUNCT
ejpam-4021	216	40	σ(x	σ(x	X
ejpam-4021	216	41	)	)	PUNCT
ejpam-4021	216	42	≤	≤	NOUN
ejpam-4021	216	43	∨	∨	NUM
ejpam-4021	216	44	a∈f	a∈f	NOUN
ejpam-4021	216	45	(	(	PUNCT
ejpam-4021	216	46	∧	∧	PROPN
ejpam-4021	216	47	z∈a	z∈a	PROPN
ejpam-4021	216	48	σ(z	σ(z	PROPN
ejpam-4021	216	49	)	)	PUNCT
ejpam-4021	216	50	)	)	PUNCT
ejpam-4021	216	51	,	,	PUNCT
ejpam-4021	216	52	∀f	∀f	PROPN
ejpam-4021	216	53	∈	∈	PROPN
ejpam-4021	216	54	f(x	f(x	PROPN
ejpam-4021	216	55	)	)	PUNCT
ejpam-4021	216	56	,	,	PUNCT
ejpam-4021	216	57	x	x	PUNCT
ejpam-4021	216	58	∈	∈	PROPN
ejpam-4021	216	59	q(f	q(f	PROPN
ejpam-4021	216	60	)	)	PUNCT
ejpam-4021	216	61	}	}	PUNCT
ejpam-4021	216	62	from	from	ADP
ejpam-4021	216	63	lemma	lemma	PROPN
ejpam-4021	216	64	5.4.2[18	5.4.2[18	NUM
ejpam-4021	216	65	]	]	PUNCT
ejpam-4021	216	66	,	,	PUNCT
ejpam-4021	216	67	it	it	PRON
ejpam-4021	216	68	follows	follow	VERB
ejpam-4021	216	69	that	that	SCONJ
ejpam-4021	216	70	there	there	PRON
ejpam-4021	216	71	is	be	VERB
ejpam-4021	216	72	a	a	DET
ejpam-4021	216	73	functor	functor	PROPN
ejpam-4021	216	74	g	g	NOUN
ejpam-4021	216	75	:	:	PUNCT
ejpam-4021	216	76	kconv	kconv	VERB
ejpam-4021	216	77	−→	−→	ADJ
ejpam-4021	216	78	sl	sl	NOUN
ejpam-4021	216	79	-	-	PUNCT
ejpam-4021	216	80	top	top	NOUN
ejpam-4021	216	81	,	,	PUNCT
ejpam-4021	216	82	where	where	SCONJ
ejpam-4021	216	83	g(x	g(x	NOUN
ejpam-4021	216	84	,	,	PUNCT
ejpam-4021	216	85	q	q	NOUN
ejpam-4021	216	86	)	)	PUNCT
ejpam-4021	216	87	=	=	SYM
ejpam-4021	216	88	(	(	PUNCT
ejpam-4021	216	89	x	x	X
ejpam-4021	216	90	,	,	PUNCT
ejpam-4021	216	91	∆̂q	∆̂q	PROPN
ejpam-4021	216	92	)	)	PUNCT
ejpam-4021	216	93	and	and	CCONJ
ejpam-4021	216	94	g(f	g(f	PROPN
ejpam-4021	216	95	)	)	PUNCT
ejpam-4021	217	1	=	=	SYM
ejpam-4021	217	2	f	f	X
ejpam-4021	217	3	.	.	PUNCT
ejpam-4021	218	1	lemma	lemma	PROPN
ejpam-4021	218	2	4	4	X
ejpam-4021	218	3	.	.	PUNCT
ejpam-4021	219	1	let	let	VERB
ejpam-4021	219	2	(	(	PUNCT
ejpam-4021	219	3	g	g	NOUN
ejpam-4021	219	4	,	,	PUNCT
ejpam-4021	219	5	·	·	PUNCT
ejpam-4021	219	6	,	,	PUNCT
ejpam-4021	219	7	q	q	X
ejpam-4021	219	8	)	)	PUNCT
ejpam-4021	219	9	∈	∈	PROPN
ejpam-4021	219	10	|kconvgrp|	|kconvgrp|	NUM
ejpam-4021	219	11	.	.	PUNCT
ejpam-4021	220	1	then	then	ADV
ejpam-4021	220	2	(	(	PUNCT
ejpam-4021	220	3	g	g	NOUN
ejpam-4021	220	4	,	,	PUNCT
ejpam-4021	220	5	·	·	PUNCT
ejpam-4021	220	6	,	,	PUNCT
ejpam-4021	220	7	∆̂q	∆̂q	PROPN
ejpam-4021	220	8	)	)	PUNCT
ejpam-4021	220	9	∈	∈	PROPN
ejpam-4021	220	10	|sl	|sl	PROPN
ejpam-4021	220	11	-	-	PUNCT
ejpam-4021	220	12	topgrp|	topgrp|	NOUN
ejpam-4021	220	13	.	.	PUNCT
ejpam-4021	221	1	proof	proof	NOUN
ejpam-4021	221	2	.	.	PUNCT
ejpam-4021	222	1	let	let	VERB
ejpam-4021	222	2	(	(	PUNCT
ejpam-4021	222	3	g	g	NOUN
ejpam-4021	222	4	,	,	PUNCT
ejpam-4021	222	5	·	·	PUNCT
ejpam-4021	222	6	,	,	PUNCT
ejpam-4021	222	7	q	q	X
ejpam-4021	222	8	)	)	PUNCT
ejpam-4021	222	9	∈	∈	PROPN
ejpam-4021	222	10	|kconvgrp|	|kconvgrp|	NUM
ejpam-4021	222	11	.	.	PUNCT
ejpam-4021	223	1	note	note	VERB
ejpam-4021	223	2	that	that	SCONJ
ejpam-4021	223	3	the	the	DET
ejpam-4021	223	4	product	product	NOUN
ejpam-4021	223	5	l	l	NOUN
ejpam-4021	223	6	-	-	PUNCT
ejpam-4021	223	7	valued	value	VERB
ejpam-4021	223	8	topology	topology	NOUN
ejpam-4021	223	9	on	on	ADP
ejpam-4021	223	10	∆̂q	∆̂q	PROPN
ejpam-4021	223	11	×	×	NOUN
ejpam-4021	223	12	∆̂q	∆̂q	PROPN
ejpam-4021	223	13	is	be	AUX
ejpam-4021	223	14	the	the	DET
ejpam-4021	223	15	initial	initial	ADJ
ejpam-4021	223	16	l	l	ADV
ejpam-4021	223	17	-	-	PUNCT
ejpam-4021	223	18	valued	value	VERB
ejpam-4021	223	19	topology	topology	NOUN
ejpam-4021	223	20	with	with	ADP
ejpam-4021	223	21	respect	respect	NOUN
ejpam-4021	223	22	to	to	ADP
ejpam-4021	223	23	the	the	DET
ejpam-4021	223	24	projects	project	NOUN
ejpam-4021	223	25	pr1	pr1	NOUN
ejpam-4021	223	26	:	:	PUNCT
ejpam-4021	223	27	x	x	PUNCT
ejpam-4021	223	28	×	×	NOUN
ejpam-4021	223	29	x	x	PUNCT
ejpam-4021	223	30	−→	−→	NOUN
ejpam-4021	223	31	x,(x	x,(x	PROPN
ejpam-4021	223	32	,	,	PUNCT
ejpam-4021	223	33	y	y	NOUN
ejpam-4021	223	34	)	)	PUNCT
ejpam-4021	223	35	7−→	7−→	NOUN
ejpam-4021	223	36	x	x	NOUN
ejpam-4021	223	37	,	,	PUNCT
ejpam-4021	223	38	and	and	CCONJ
ejpam-4021	223	39	pr2	pr2	NOUN
ejpam-4021	223	40	:	:	PUNCT
ejpam-4021	223	41	x	x	PUNCT
ejpam-4021	223	42	×	×	NOUN
ejpam-4021	223	43	x	x	PUNCT
ejpam-4021	223	44	−→	−→	NOUN
ejpam-4021	223	45	x,(x	x,(x	PROPN
ejpam-4021	223	46	,	,	PUNCT
ejpam-4021	223	47	y	y	NOUN
ejpam-4021	223	48	)	)	PUNCT
ejpam-4021	223	49	7−→	7−→	NOUN
ejpam-4021	223	50	y.	y.	NOUN
ejpam-4021	223	51	further	far	ADV
ejpam-4021	223	52	note	note	VERB
ejpam-4021	223	53	that	that	SCONJ
ejpam-4021	223	54	∆̂q	∆̂q	PROPN
ejpam-4021	223	55	×	×	NOUN
ejpam-4021	223	56	∆̂q	∆̂q	PROPN
ejpam-4021	223	57	=	=	PRON
ejpam-4021	223	58	{	{	PUNCT
ejpam-4021	223	59	(	(	PUNCT
ejpam-4021	223	60	ν1	ν1	NOUN
ejpam-4021	223	61	·	·	PUNCT
ejpam-4021	223	62	pr1	pr1	NOUN
ejpam-4021	223	63	)	)	PUNCT
ejpam-4021	223	64	∗	∗	NOUN
ejpam-4021	223	65	(	(	PUNCT
ejpam-4021	223	66	ν2	ν2	PROPN
ejpam-4021	223	67	·	·	SYM
ejpam-4021	223	68	pr2	pr2	NOUN
ejpam-4021	223	69	)	)	PUNCT
ejpam-4021	223	70	:	:	PUNCT
ejpam-4021	223	71	ν1	ν1	NOUN
ejpam-4021	223	72	,	,	PUNCT
ejpam-4021	223	73	ν2	ν2	NOUN
ejpam-4021	223	74	∈	∈	PROPN
ejpam-4021	223	75	∆̂q	∆̂q	PROPN
ejpam-4021	223	76	}	}	PUNCT
ejpam-4021	223	77	is	be	AUX
ejpam-4021	223	78	a	a	DET
ejpam-4021	223	79	base	base	NOUN
ejpam-4021	223	80	for	for	ADP
ejpam-4021	223	81	the	the	DET
ejpam-4021	223	82	product	product	NOUN
ejpam-4021	223	83	l	l	NOUN
ejpam-4021	223	84	-	-	NOUN
ejpam-4021	223	85	topology	topology	NOUN
ejpam-4021	223	86	on	on	ADP
ejpam-4021	223	87	x	x	PROPN
ejpam-4021	223	88	×x	×x	PROPN
ejpam-4021	223	89	,	,	PUNCT
ejpam-4021	223	90	where	where	SCONJ
ejpam-4021	223	91	the	the	DET
ejpam-4021	223	92	l	l	NOUN
ejpam-4021	223	93	-	-	ADJ
ejpam-4021	223	94	set	set	NOUN
ejpam-4021	223	95	can	can	AUX
ejpam-4021	223	96	be	be	AUX
ejpam-4021	223	97	given	give	VERB
ejpam-4021	223	98	by	by	ADP
ejpam-4021	223	99	:	:	PUNCT
ejpam-4021	223	100	µ0	µ0	NOUN
ejpam-4021	223	101	:	:	PUNCT
ejpam-4021	224	1	=	=	SYM
ejpam-4021	224	2	∨	∨	NUM
ejpam-4021	224	3	i∈i	i∈i	ADJ
ejpam-4021	224	4	(	(	PUNCT
ejpam-4021	224	5	ν1	ν1	NOUN
ejpam-4021	224	6	i	i	PRON
ejpam-4021	224	7	·	·	PUNCT
ejpam-4021	224	8	pr1	pr1	NOUN
ejpam-4021	224	9	)	)	PUNCT
ejpam-4021	224	10	∗	∗	NOUN
ejpam-4021	224	11	(	(	PUNCT
ejpam-4021	224	12	µ2	µ2	PROPN
ejpam-4021	224	13	i	i	PRON
ejpam-4021	224	14	·	·	PUNCT
ejpam-4021	224	15	pr2	pr2	NOUN
ejpam-4021	224	16	)	)	PUNCT
ejpam-4021	224	17	)	)	PUNCT
ejpam-4021	224	18	,	,	PUNCT
ejpam-4021	224	19	and	and	CCONJ
ejpam-4021	224	20	ν1	ν1	NOUN
ejpam-4021	224	21	i	i	PRON
ejpam-4021	224	22	,	,	PUNCT
ejpam-4021	224	23	µ	µ	PROPN
ejpam-4021	224	24	2	2	NUM
ejpam-4021	225	1	i	i	NOUN
ejpam-4021	225	2	∈	∈	PROPN
ejpam-4021	225	3	∆̂q	∆̂q	PROPN
ejpam-4021	225	4	.	.	PUNCT
ejpam-4021	226	1	thus	thus	ADV
ejpam-4021	226	2	,	,	PUNCT
ejpam-4021	226	3	we	we	PRON
ejpam-4021	226	4	have	have	VERB
ejpam-4021	226	5	for	for	ADP
ejpam-4021	226	6	any	any	DET
ejpam-4021	226	7	ν	ν	NOUN
ejpam-4021	226	8	∈	∈	PROPN
ejpam-4021	226	9	∆̂q	∆̂q	PROPN
ejpam-4021	226	10	and	and	CCONJ
ejpam-4021	226	11	(	(	PUNCT
ejpam-4021	226	12	x	x	NOUN
ejpam-4021	226	13	,	,	PUNCT
ejpam-4021	226	14	y	y	NOUN
ejpam-4021	226	15	)	)	PUNCT
ejpam-4021	226	16	∈	∈	PROPN
ejpam-4021	226	17	x	x	X
ejpam-4021	226	18	×x	×x	X
ejpam-4021	226	19	,	,	PUNCT
ejpam-4021	226	20	and	and	CCONJ
ejpam-4021	226	21	due	due	ADP
ejpam-4021	226	22	to	to	ADP
ejpam-4021	226	23	the	the	DET
ejpam-4021	226	24	property	property	NOUN
ejpam-4021	226	25	of	of	ADP
ejpam-4021	226	26	∗	∗	NOUN
ejpam-4021	226	27	in	in	ADP
ejpam-4021	226	28	l	l	NOUN
ejpam-4021	226	29	:	:	PUNCT
ejpam-4021	226	30	ν(xy	ν(xy	NUM
ejpam-4021	226	31	)	)	PUNCT
ejpam-4021	226	32	=	=	SYM
ejpam-4021	226	33	m←(ν)(x	m←(ν)(x	PROPN
ejpam-4021	226	34	,	,	PUNCT
ejpam-4021	226	35	y	y	NOUN
ejpam-4021	226	36	)	)	PUNCT
ejpam-4021	226	37	=	=	PUNCT
ejpam-4021	227	1	∨	∨	NUM
ejpam-4021	227	2	i∈i	i∈i	ADJ
ejpam-4021	227	3	[	[	X
ejpam-4021	227	4	(	(	PUNCT
ejpam-4021	227	5	pr←1	pr←1	NOUN
ejpam-4021	227	6	(	(	PUNCT
ejpam-4021	227	7	ν1	ν1	NOUN
ejpam-4021	227	8	i	i	PRON
ejpam-4021	227	9	)	)	PUNCT
ejpam-4021	227	10	(	(	PUNCT
ejpam-4021	227	11	x	x	X
ejpam-4021	227	12	,	,	PUNCT
ejpam-4021	227	13	y	y	NOUN
ejpam-4021	227	14	)	)	PUNCT
ejpam-4021	227	15	)	)	PUNCT
ejpam-4021	227	16	∗	∗	NOUN
ejpam-4021	227	17	(	(	PUNCT
ejpam-4021	227	18	pr←2	pr←2	NOUN
ejpam-4021	227	19	(	(	PUNCT
ejpam-4021	227	20	µ2	µ2	PROPN
ejpam-4021	227	21	i	i	PRON
ejpam-4021	227	22	)	)	PUNCT
ejpam-4021	227	23	(	(	PUNCT
ejpam-4021	227	24	x	x	X
ejpam-4021	227	25	,	,	PUNCT
ejpam-4021	227	26	y	y	NOUN
ejpam-4021	227	27	)	)	PUNCT
ejpam-4021	227	28	)	)	PUNCT
ejpam-4021	227	29	)	)	PUNCT
ejpam-4021	227	30	]	]	PUNCT
ejpam-4021	228	1	(	(	PUNCT
ejpam-4021	228	2	ν1	ν1	NOUN
ejpam-4021	228	3	i	i	PRON
ejpam-4021	228	4	,	,	PUNCT
ejpam-4021	228	5	µ	µ	PROPN
ejpam-4021	228	6	2	2	NUM
ejpam-4021	228	7	i	i	NOUN
ejpam-4021	228	8	∈	∈	PROPN
ejpam-4021	228	9	∆̂q	∆̂q	PROPN
ejpam-4021	228	10	)	)	PUNCT
ejpam-4021	228	11	.	.	PUNCT
ejpam-4021	229	1	=	=	PUNCT
ejpam-4021	230	1	∨	∨	NUM
ejpam-4021	230	2	i∈i	i∈i	ADJ
ejpam-4021	230	3	[	[	PUNCT
ejpam-4021	230	4	ν1	ν1	NOUN
ejpam-4021	230	5	i	i	PRON
ejpam-4021	230	6	(	(	PUNCT
ejpam-4021	230	7	x	x	X
ejpam-4021	230	8	)	)	PUNCT
ejpam-4021	230	9	∗	∗	NOUN
ejpam-4021	230	10	µ2	µ2	PROPN
ejpam-4021	230	11	i	i	PRON
ejpam-4021	230	12	(	(	PUNCT
ejpam-4021	230	13	y	y	PROPN
ejpam-4021	230	14	)	)	PUNCT
ejpam-4021	230	15	]	]	PUNCT
ejpam-4021	230	16	,	,	PUNCT
ejpam-4021	230	17	(	(	PUNCT
ejpam-4021	230	18	ν1	ν1	NOUN
ejpam-4021	230	19	i	i	PRON
ejpam-4021	230	20	,	,	PUNCT
ejpam-4021	230	21	µ	µ	PROPN
ejpam-4021	230	22	2	2	NUM
ejpam-4021	230	23	i	i	NOUN
ejpam-4021	230	24	∈	∈	PROPN
ejpam-4021	230	25	∆̂q	∆̂q	PROPN
ejpam-4021	230	26	)	)	PUNCT
ejpam-4021	230	27	.	.	PUNCT
ejpam-4021	231	1	≤	≤	NOUN
ejpam-4021	231	2	∨	∨	NUM
ejpam-4021	231	3	i∈i	i∈i	ADJ
ejpam-4021	231	4	[	[	X
ejpam-4021	231	5	∨	∨	NUM
ejpam-4021	231	6	a∈f	a∈f	NOUN
ejpam-4021	231	7	(	(	PUNCT
ejpam-4021	231	8	∧	∧	NOUN
ejpam-4021	231	9	z1∈a	z1∈a	NOUN
ejpam-4021	231	10	ν	ν	NOUN
ejpam-4021	231	11	1	1	NUM
ejpam-4021	231	12	i	i	PROPN
ejpam-4021	231	13	(	(	PUNCT
ejpam-4021	231	14	z1	z1	PROPN
ejpam-4021	231	15	)	)	PUNCT
ejpam-4021	231	16	)	)	PUNCT
ejpam-4021	231	17	∗	∗	NOUN
ejpam-4021	231	18	∨	∨	NUM
ejpam-4021	231	19	b∈g	b∈g	NOUN
ejpam-4021	231	20	(	(	PUNCT
ejpam-4021	231	21	∧	∧	NOUN
ejpam-4021	231	22	z2∈b	z2∈b	X
ejpam-4021	231	23	ν	ν	X
ejpam-4021	231	24	2	2	NUM
ejpam-4021	231	25	i	i	NOUN
ejpam-4021	231	26	(	(	PUNCT
ejpam-4021	231	27	z2	z2	PROPN
ejpam-4021	231	28	)	)	PUNCT
ejpam-4021	231	29	)	)	PUNCT
ejpam-4021	231	30	]	]	PUNCT
ejpam-4021	231	31	≤	≤	NUM
ejpam-4021	231	32	∨	∨	NUM
ejpam-4021	231	33	i∈i	i∈i	ADJ
ejpam-4021	232	1	[	[	X
ejpam-4021	232	2	∨	∨	NUM
ejpam-4021	232	3	a.·b∈f	a.·b∈f	PROPN
ejpam-4021	232	4	�	�	PROPN
ejpam-4021	232	5	g	g	PROPN
ejpam-4021	232	6	∧	∧	PROPN
ejpam-4021	232	7	z1z2∈a·b	z1z2∈a·b	PROPN
ejpam-4021	232	8	(	(	PUNCT
ejpam-4021	232	9	ν1	ν1	NOUN
ejpam-4021	232	10	i	i	PRON
ejpam-4021	232	11	(	(	PUNCT
ejpam-4021	232	12	z1	z1	PROPN
ejpam-4021	232	13	)	)	PUNCT
ejpam-4021	232	14	∗	∗	NOUN
ejpam-4021	232	15	ν2	ν2	NOUN
ejpam-4021	232	16	i	i	PRON
ejpam-4021	232	17	(	(	PUNCT
ejpam-4021	232	18	z2	z2	PROPN
ejpam-4021	232	19	)	)	PUNCT
ejpam-4021	232	20	)	)	PUNCT
ejpam-4021	232	21	]	]	PUNCT
ejpam-4021	233	1	=	=	PUNCT
ejpam-4021	234	1	[	[	X
ejpam-4021	234	2	∨	∨	NUM
ejpam-4021	234	3	a·b∈f	a·b∈f	PROPN
ejpam-4021	234	4	�	�	PROPN
ejpam-4021	234	5	g	g	PROPN
ejpam-4021	234	6	∧	∧	PROPN
ejpam-4021	234	7	z1z2∈a·b	z1z2∈a·b	PROPN
ejpam-4021	234	8	ν(z1z2	ν(z1z2	PROPN
ejpam-4021	234	9	)	)	PUNCT
ejpam-4021	234	10	]	]	PUNCT
ejpam-4021	234	11	that	that	ADV
ejpam-4021	234	12	is	be	AUX
ejpam-4021	234	13	,	,	PUNCT
ejpam-4021	234	14	ν(xy	ν(xy	NOUN
ejpam-4021	234	15	)	)	PUNCT
ejpam-4021	234	16	≤	≤	NOUN
ejpam-4021	235	1	[	[	X
ejpam-4021	235	2	∨	∨	NUM
ejpam-4021	235	3	h∈f	h∈f	PROPN
ejpam-4021	235	4	�	�	PROPN
ejpam-4021	235	5	g	g	PROPN
ejpam-4021	235	6	∧	∧	PROPN
ejpam-4021	235	7	z1z2∈h	z1z2∈h	NOUN
ejpam-4021	235	8	ν(z1z2	ν(z1z2	PROPN
ejpam-4021	235	9	)	)	PUNCT
ejpam-4021	235	10	]	]	PUNCT
ejpam-4021	235	11	and	and	CCONJ
ejpam-4021	235	12	xy	xy	PROPN
ejpam-4021	235	13	∈	∈	PROPN
ejpam-4021	235	14	q	q	X
ejpam-4021	235	15	(	(	PUNCT
ejpam-4021	235	16	f	f	PROPN
ejpam-4021	235	17	�	�	PROPN
ejpam-4021	235	18	g	g	NOUN
ejpam-4021	235	19	)	)	PUNCT
ejpam-4021	235	20	due	due	ADP
ejpam-4021	235	21	to	to	ADP
ejpam-4021	235	22	the	the	DET
ejpam-4021	235	23	condition	condition	NOUN
ejpam-4021	235	24	(	(	PUNCT
ejpam-4021	235	25	cgm	cgm	NOUN
ejpam-4021	235	26	)	)	PUNCT
ejpam-4021	235	27	implying	imply	VERB
ejpam-4021	235	28	m←(ν	m←(ν	NOUN
ejpam-4021	235	29	)	)	PUNCT
ejpam-4021	235	30	∈	∈	PROPN
ejpam-4021	235	31	∆̂q	∆̂q	PROPN
ejpam-4021	235	32	×	×	NOUN
ejpam-4021	235	33	∆̂q	∆̂q	PROPN
ejpam-4021	235	34	.	.	PUNCT
ejpam-4021	236	1	this	this	PRON
ejpam-4021	236	2	proves	prove	VERB
ejpam-4021	236	3	condition	condition	NOUN
ejpam-4021	236	4	(	(	PUNCT
ejpam-4021	236	5	ltgm	ltgm	NOUN
ejpam-4021	236	6	)	)	PUNCT
ejpam-4021	236	7	.	.	PUNCT
ejpam-4021	237	1	now	now	ADV
ejpam-4021	237	2	let	let	VERB
ejpam-4021	237	3	x	x	X
ejpam-4021	237	4	∈	∈	PROPN
ejpam-4021	237	5	q(f	q(f	PROPN
ejpam-4021	237	6	)	)	PUNCT
ejpam-4021	237	7	for	for	ADP
ejpam-4021	237	8	any	any	DET
ejpam-4021	237	9	f	f	PROPN
ejpam-4021	237	10	∈	∈	PROPN
ejpam-4021	237	11	f(g	f(g	NOUN
ejpam-4021	237	12	)	)	PUNCT
ejpam-4021	237	13	and	and	CCONJ
ejpam-4021	237	14	let	let	VERB
ejpam-4021	237	15	ν	ν	X
ejpam-4021	237	16	∈	∈	PROPN
ejpam-4021	237	17	∆̂q	∆̂q	PROPN
ejpam-4021	237	18	.	.	PUNCT
ejpam-4021	238	1	then	then	ADV
ejpam-4021	238	2	we	we	PRON
ejpam-4021	238	3	have	have	VERB
ejpam-4021	238	4	←(ν)(x	←(ν)(x	NOUN
ejpam-4021	238	5	)	)	PUNCT
ejpam-4021	238	6	=	=	SYM
ejpam-4021	238	7	ν((x	ν((x	PROPN
ejpam-4021	238	8	)	)	PUNCT
ejpam-4021	238	9	)	)	PUNCT
ejpam-4021	238	10	≤	≤	NUM
ejpam-4021	238	11	∨	∨	NUM
ejpam-4021	238	12	a∈f	a∈f	NOUN
ejpam-4021	238	13	(	(	PUNCT
ejpam-4021	238	14	∧	∧	PROPN
ejpam-4021	238	15	z2∈(a	z2∈(a	PROPN
ejpam-4021	238	16	)	)	PUNCT
ejpam-4021	238	17	ν(z2	ν(z2	NOUN
ejpam-4021	238	18	)	)	PUNCT
ejpam-4021	238	19	)	)	PUNCT
ejpam-4021	239	1	=	=	PUNCT
ejpam-4021	239	2	∨	∨	NUM
ejpam-4021	239	3	a−1∈f−1	a−1∈f−1	PROPN
ejpam-4021	239	4	(	(	PUNCT
ejpam-4021	239	5	∧	∧	PROPN
ejpam-4021	239	6	z1∈a−1	z1∈a−1	NOUN
ejpam-4021	239	7	←(ν)(z1	←(ν)(z1	NOUN
ejpam-4021	239	8	)	)	PUNCT
ejpam-4021	239	9	)	)	PUNCT
ejpam-4021	239	10	,	,	PUNCT
ejpam-4021	239	11	that	that	ADV
ejpam-4021	239	12	is	is	ADV
ejpam-4021	239	13	,	,	PUNCT
ejpam-4021	239	14	←(ν)(x	←(ν)(x	PROPN
ejpam-4021	239	15	)	)	PUNCT
ejpam-4021	239	16	≤	≤	NOUN
ejpam-4021	239	17	∨	∨	NUM
ejpam-4021	239	18	a−1∈f−1	a−1∈f−1	PROPN
ejpam-4021	239	19	(	(	PUNCT
ejpam-4021	239	20	∧	∧	PROPN
ejpam-4021	239	21	z1∈a−1	z1∈a−1	NOUN
ejpam-4021	239	22	←(ν)(z1	←(ν)(z1	NOUN
ejpam-4021	239	23	)	)	PUNCT
ejpam-4021	239	24	)	)	PUNCT
ejpam-4021	239	25	;	;	PUNCT
ejpam-4021	239	26	and	and	CCONJ
ejpam-4021	239	27	x−1	x−1	PROPN
ejpam-4021	239	28	∈	∈	PROPN
ejpam-4021	239	29	q(f−1	q(f−1	PROPN
ejpam-4021	239	30	)	)	PUNCT
ejpam-4021	239	31	because	because	SCONJ
ejpam-4021	239	32	of	of	ADP
ejpam-4021	239	33	the	the	DET
ejpam-4021	239	34	condition	condition	NOUN
ejpam-4021	239	35	(	(	PUNCT
ejpam-4021	239	36	cgi	cgi	NOUN
ejpam-4021	239	37	)	)	PUNCT
ejpam-4021	239	38	.	.	PUNCT
ejpam-4021	240	1	these	these	DET
ejpam-4021	240	2	together	together	ADV
ejpam-4021	240	3	imply	imply	VERB
ejpam-4021	240	4	that	that	DET
ejpam-4021	240	5	←(ν	←(ν	NOUN
ejpam-4021	240	6	)	)	PUNCT
ejpam-4021	240	7	∈	∈	PROPN
ejpam-4021	241	1	∆̂q	∆̂q	PROPN
ejpam-4021	241	2	,	,	PUNCT
ejpam-4021	241	3	this	this	PRON
ejpam-4021	241	4	proves	prove	VERB
ejpam-4021	241	5	(	(	PUNCT
ejpam-4021	241	6	ltgi	ltgi	NOUN
ejpam-4021	241	7	)	)	PUNCT
ejpam-4021	241	8	.	.	PUNCT
ejpam-4021	242	1	theorem	theorem	NOUN
ejpam-4021	242	2	1	1	NUM
ejpam-4021	242	3	.	.	PUNCT
ejpam-4021	243	1	the	the	DET
ejpam-4021	243	2	functor	functor	PROPN
ejpam-4021	243	3	f	f	PROPN
ejpam-4021	243	4	:	:	PUNCT
ejpam-4021	243	5	sl	sl	NUM
ejpam-4021	243	6	-	-	PUNCT
ejpam-4021	243	7	topgrp−→	topgrp−→	NOUN
ejpam-4021	243	8	kconvgrp	kconvgrp	NOUN
ejpam-4021	243	9	as	as	SCONJ
ejpam-4021	243	10	defined	define	VERB
ejpam-4021	243	11	below	below	ADP
ejpam-4021	243	12	f	f	PROPN
ejpam-4021	243	13	:	:	PUNCT
ejpam-4021	243	14			PUNCT
ejpam-4021	243	15	sl	sl	NUM
ejpam-4021	243	16	-	-	PUNCT
ejpam-4021	243	17	topgrp	topgrp	NOUN
ejpam-4021	243	18	−→	−→	NOUN
ejpam-4021	243	19	kconvgrp	kconvgrp	NOUN
ejpam-4021	243	20	(	(	PUNCT
ejpam-4021	243	21	g	g	NOUN
ejpam-4021	243	22	,	,	PUNCT
ejpam-4021	243	23	·	·	PUNCT
ejpam-4021	243	24	,	,	PUNCT
ejpam-4021	243	25	∆n	∆n	PROPN
ejpam-4021	243	26	)	)	PUNCT
ejpam-4021	243	27	7−→	7−→	NOUN
ejpam-4021	243	28	(	(	PUNCT
ejpam-4021	243	29	g	g	NOUN
ejpam-4021	243	30	,	,	PUNCT
ejpam-4021	243	31	·	·	PUNCT
ejpam-4021	243	32	,	,	PUNCT
ejpam-4021	243	33	q∆n	q∆n	NOUN
ejpam-4021	243	34	)	)	PUNCT
ejpam-4021	244	1	f	f	PROPN
ejpam-4021	245	1	7−→	7−→	NOUN
ejpam-4021	245	2	f	f	PROPN
ejpam-4021	245	3	has	have	VERB
ejpam-4021	245	4	a	a	DET
ejpam-4021	245	5	left	left	ADJ
ejpam-4021	245	6	adjoint	adjoint	NOUN
ejpam-4021	245	7	.	.	PUNCT
ejpam-4021	246	1	t	t	PROPN
ejpam-4021	246	2	m	m	PROPN
ejpam-4021	246	3	g	g	NOUN
ejpam-4021	246	4	ahsanullah	ahsanullah	NOUN
ejpam-4021	246	5	,	,	PUNCT
ejpam-4021	246	6	fawzi	fawzi	PROPN
ejpam-4021	246	7	al	al	PROPN
ejpam-4021	246	8	-	-	PUNCT
ejpam-4021	246	9	thukair	thukair	NOUN
ejpam-4021	246	10	/	/	SYM
ejpam-4021	246	11	eur	eur	NOUN
ejpam-4021	246	12	.	.	PUNCT
ejpam-4021	247	1	j.	j.	PROPN
ejpam-4021	247	2	pure	pure	PROPN
ejpam-4021	247	3	appl	appl	PROPN
ejpam-4021	247	4	.	.	PROPN
ejpam-4021	247	5	math	math	PROPN
ejpam-4021	247	6	,	,	PUNCT
ejpam-4021	247	7	14	14	NUM
ejpam-4021	247	8	(	(	PUNCT
ejpam-4021	247	9	3	3	NUM
ejpam-4021	247	10	)	)	PUNCT
ejpam-4021	247	11	(	(	PUNCT
ejpam-4021	247	12	2021	2021	NUM
ejpam-4021	247	13	)	)	PUNCT
ejpam-4021	247	14	,	,	PUNCT
ejpam-4021	247	15	949	949	NUM
ejpam-4021	247	16	-	-	SYM
ejpam-4021	247	17	968	968	NUM
ejpam-4021	247	18	958	958	NUM
ejpam-4021	247	19	proof	proof	NOUN
ejpam-4021	247	20	.	.	PUNCT
ejpam-4021	248	1	in	in	ADP
ejpam-4021	248	2	view	view	NOUN
ejpam-4021	248	3	of	of	ADP
ejpam-4021	248	4	lemma	lemma	PROPN
ejpam-4021	248	5	3	3	NUM
ejpam-4021	248	6	in	in	ADP
ejpam-4021	248	7	conjunction	conjunction	NOUN
ejpam-4021	248	8	with	with	ADP
ejpam-4021	248	9	lemma	lemma	PROPN
ejpam-4021	248	10	5.4.1	5.4.1	PROPN
ejpam-4021	248	11	[	[	X
ejpam-4021	248	12	18	18	NUM
ejpam-4021	248	13	]	]	PUNCT
ejpam-4021	248	14	,	,	PUNCT
ejpam-4021	248	15	f	f	X
ejpam-4021	248	16	:	:	PUNCT
ejpam-4021	248	17	sl	sl	NUM
ejpam-4021	248	18	-	-	PUNCT
ejpam-4021	248	19	topgrp−→	topgrp−→	NOUN
ejpam-4021	248	20	kconvgrp	kconvgrp	NOUN
ejpam-4021	248	21	is	be	AUX
ejpam-4021	248	22	a	a	DET
ejpam-4021	248	23	functor	functor	PROPN
ejpam-4021	248	24	.	.	PUNCT
ejpam-4021	248	25	define	define	VERB
ejpam-4021	248	26	g	g	NOUN
ejpam-4021	248	27	:	:	PUNCT
ejpam-4021	248	28	kconvgrp	kconvgrp	VERB
ejpam-4021	248	29	−→	−→	ADJ
ejpam-4021	248	30	sl	sl	NOUN
ejpam-4021	248	31	-	-	PUNCT
ejpam-4021	248	32	topgrp	topgrp	NOUN
ejpam-4021	248	33	by	by	ADP
ejpam-4021	248	34	g	g	NOUN
ejpam-4021	248	35	:	:	PUNCT
ejpam-4021	248	36			PRON
ejpam-4021	248	37	kconvgrp	kconvgrp	VERB
ejpam-4021	248	38	−→	−→	ADJ
ejpam-4021	248	39	sl	sl	NOUN
ejpam-4021	248	40	-	-	PUNCT
ejpam-4021	248	41	topgrp	topgrp	NOUN
ejpam-4021	248	42	(	(	PUNCT
ejpam-4021	248	43	g	g	NOUN
ejpam-4021	248	44	,	,	PUNCT
ejpam-4021	248	45	·	·	PUNCT
ejpam-4021	248	46	,	,	PUNCT
ejpam-4021	248	47	q	q	X
ejpam-4021	248	48	)	)	PUNCT
ejpam-4021	248	49	7−→	7−→	NOUN
ejpam-4021	248	50	(	(	PUNCT
ejpam-4021	248	51	g	g	NOUN
ejpam-4021	248	52	,	,	PUNCT
ejpam-4021	248	53	·	·	PUNCT
ejpam-4021	248	54	,	,	PUNCT
ejpam-4021	248	55	∆̂q	∆̂q	PROPN
ejpam-4021	248	56	)	)	PUNCT
ejpam-4021	249	1	f	f	X
ejpam-4021	250	1	7−→	7−→	NOUN
ejpam-4021	250	2	f	f	X
ejpam-4021	250	3	then	then	ADV
ejpam-4021	250	4	from	from	ADP
ejpam-4021	250	5	lemma	lemma	PROPN
ejpam-4021	250	6	4	4	NUM
ejpam-4021	250	7	in	in	ADP
ejpam-4021	250	8	conjunction	conjunction	NOUN
ejpam-4021	250	9	with	with	ADP
ejpam-4021	250	10	lemma	lemma	PROPN
ejpam-4021	250	11	5.4.2	5.4.2	NUM
ejpam-4021	250	12	[	[	X
ejpam-4021	250	13	18	18	NUM
ejpam-4021	250	14	]	]	PUNCT
ejpam-4021	250	15	that	that	SCONJ
ejpam-4021	250	16	g	g	PROPN
ejpam-4021	250	17	is	be	AUX
ejpam-4021	250	18	a	a	DET
ejpam-4021	250	19	functor	functor	NOUN
ejpam-4021	250	20	since	since	SCONJ
ejpam-4021	250	21	in	in	ADP
ejpam-4021	250	22	both	both	CCONJ
ejpam-4021	250	23	the	the	DET
ejpam-4021	250	24	cases	case	NOUN
ejpam-4021	250	25	the	the	DET
ejpam-4021	250	26	group	group	NOUN
ejpam-4021	250	27	homomorphism	homomorphism	NOUN
ejpam-4021	250	28	structures	structure	NOUN
ejpam-4021	250	29	remain	remain	VERB
ejpam-4021	250	30	unchanged	unchanged	ADJ
ejpam-4021	250	31	.	.	PUNCT
ejpam-4021	251	1	that	that	SCONJ
ejpam-4021	251	2	the	the	DET
ejpam-4021	251	3	functor	functor	PROPN
ejpam-4021	251	4	g	g	PROPN
ejpam-4021	251	5	is	be	AUX
ejpam-4021	251	6	a	a	DET
ejpam-4021	251	7	left	left	ADJ
ejpam-4021	251	8	adjoint	adjoint	NOUN
ejpam-4021	251	9	since	since	SCONJ
ejpam-4021	251	10	in	in	ADP
ejpam-4021	251	11	both	both	CCONJ
ejpam-4021	251	12	the	the	DET
ejpam-4021	251	13	cases	case	NOUN
ejpam-4021	251	14	group	group	NOUN
ejpam-4021	251	15	homomorphism	homomorphism	NOUN
ejpam-4021	251	16	structures	structure	NOUN
ejpam-4021	251	17	remain	remain	VERB
ejpam-4021	251	18	unchanged	unchanged	ADJ
ejpam-4021	251	19	.	.	PUNCT
ejpam-4021	252	1	that	that	SCONJ
ejpam-4021	252	2	the	the	DET
ejpam-4021	252	3	functor	functor	PROPN
ejpam-4021	252	4	g	g	PROPN
ejpam-4021	252	5	is	be	AUX
ejpam-4021	252	6	a	a	DET
ejpam-4021	252	7	left	left	ADJ
ejpam-4021	252	8	adjoint	adjoint	NOUN
ejpam-4021	252	9	to	to	ADP
ejpam-4021	252	10	f	f	PROPN
ejpam-4021	252	11	is	be	AUX
ejpam-4021	252	12	an	an	DET
ejpam-4021	252	13	immediate	immediate	ADJ
ejpam-4021	252	14	consequence	consequence	NOUN
ejpam-4021	252	15	of	of	ADP
ejpam-4021	252	16	the	the	DET
ejpam-4021	252	17	proposition	proposition	NOUN
ejpam-4021	252	18	5.4.3	5.4.3	NUM
ejpam-4021	252	19	[	[	X
ejpam-4021	252	20	18	18	NUM
ejpam-4021	252	21	]	]	PUNCT
ejpam-4021	252	22	.	.	PUNCT
ejpam-4021	253	1	4	4	X
ejpam-4021	253	2	.	.	NUM
ejpam-4021	253	3	enriched	enrich	VERB
ejpam-4021	253	4	lattice	lattice	NOUN
ejpam-4021	253	5	-	-	PUNCT
ejpam-4021	253	6	valued	value	VERB
ejpam-4021	253	7	subgroup	subgroup	NOUN
ejpam-4021	253	8	of	of	ADP
ejpam-4021	253	9	a	a	DET
ejpam-4021	253	10	group	group	NOUN
ejpam-4021	253	11	and	and	CCONJ
ejpam-4021	253	12	enriched	enriched	ADJ
ejpam-4021	253	13	lattice	lattice	NOUN
ejpam-4021	253	14	-	-	PUNCT
ejpam-4021	253	15	valued	value	VERB
ejpam-4021	253	16	neighborhood	neighborhood	NOUN
ejpam-4021	253	17	groups	group	NOUN
ejpam-4021	253	18	definition	definition	NOUN
ejpam-4021	253	19	13	13	NUM
ejpam-4021	253	20	.	.	PUNCT
ejpam-4021	254	1	let	let	VERB
ejpam-4021	254	2	l	l	NOUN
ejpam-4021	255	1	=	=	SYM
ejpam-4021	255	2	(	(	PUNCT
ejpam-4021	255	3	l,≤,∧	l,≤,∧	PROPN
ejpam-4021	255	4	,	,	PUNCT
ejpam-4021	255	5	∗	∗	NOUN
ejpam-4021	255	6	)	)	PUNCT
ejpam-4021	255	7	be	be	VERB
ejpam-4021	255	8	an	an	DET
ejpam-4021	255	9	enriched	enriched	ADJ
ejpam-4021	255	10	cl	cl	NOUN
ejpam-4021	255	11	-	-	ADJ
ejpam-4021	255	12	premonoid	premonoid	ADJ
ejpam-4021	255	13	,	,	PUNCT
ejpam-4021	255	14	(	(	PUNCT
ejpam-4021	255	15	g	g	NOUN
ejpam-4021	255	16	,	,	PUNCT
ejpam-4021	255	17	·	·	PUNCT
ejpam-4021	255	18	)	)	PUNCT
ejpam-4021	256	1	∈	∈	PROPN
ejpam-4021	256	2	|grp|	|grp|	NOUN
ejpam-4021	256	3	.	.	PUNCT
ejpam-4021	257	1	then	then	ADV
ejpam-4021	257	2	an	an	DET
ejpam-4021	257	3	l	l	NOUN
ejpam-4021	257	4	-	-	ADJ
ejpam-4021	257	5	set	set	VERB
ejpam-4021	257	6	µ	µ	NOUN
ejpam-4021	257	7	:	:	PUNCT
ejpam-4021	257	8	g	g	PROPN
ejpam-4021	257	9	−→	−→	NOUN
ejpam-4021	257	10	l	l	NOUN
ejpam-4021	257	11	is	be	AUX
ejpam-4021	257	12	called	call	VERB
ejpam-4021	257	13	an	an	DET
ejpam-4021	257	14	l	l	NOUN
ejpam-4021	257	15	-	-	PUNCT
ejpam-4021	257	16	valued	value	VERB
ejpam-4021	257	17	subgroup	subgroup	NOUN
ejpam-4021	257	18	of	of	ADP
ejpam-4021	257	19	a	a	DET
ejpam-4021	257	20	group	group	NOUN
ejpam-4021	257	21	g	g	NOUN
ejpam-4021	257	22	if	if	SCONJ
ejpam-4021	257	23	and	and	CCONJ
ejpam-4021	257	24	only	only	ADV
ejpam-4021	257	25	if	if	SCONJ
ejpam-4021	257	26	the	the	DET
ejpam-4021	257	27	following	follow	VERB
ejpam-4021	257	28	conditions	condition	NOUN
ejpam-4021	257	29	are	be	AUX
ejpam-4021	257	30	fulfilled	fulfil	VERB
ejpam-4021	257	31	:	:	PUNCT
ejpam-4021	257	32	(	(	PUNCT
ejpam-4021	257	33	lg1	lg1	PROPN
ejpam-4021	257	34	)	)	PUNCT
ejpam-4021	257	35	µ(e	µ(e	PROPN
ejpam-4021	257	36	)	)	PUNCT
ejpam-4021	258	1	=	=	PUNCT
ejpam-4021	259	1	>	>	X
ejpam-4021	259	2	;	;	PUNCT
ejpam-4021	259	3	(	(	PUNCT
ejpam-4021	259	4	lg2	lg2	X
ejpam-4021	259	5	)	)	PUNCT
ejpam-4021	259	6	µ(g	µ(g	NOUN
ejpam-4021	259	7	)	)	PUNCT
ejpam-4021	259	8	∗	∗	NOUN
ejpam-4021	259	9	µ(h	µ(h	NOUN
ejpam-4021	259	10	)	)	PUNCT
ejpam-4021	259	11	≤	≤	NUM
ejpam-4021	259	12	µ(gh	µ(gh	PROPN
ejpam-4021	259	13	)	)	PUNCT
ejpam-4021	259	14	,	,	PUNCT
ejpam-4021	259	15	∀g	∀g	NOUN
ejpam-4021	259	16	,	,	PUNCT
ejpam-4021	259	17	h	h	NOUN
ejpam-4021	259	18	∈	∈	PROPN
ejpam-4021	259	19	g	g	NOUN
ejpam-4021	259	20	;	;	PUNCT
ejpam-4021	259	21	(	(	PUNCT
ejpam-4021	259	22	lg3	lg3	NOUN
ejpam-4021	259	23	)	)	PUNCT
ejpam-4021	259	24	µ(g	µ(g	NOUN
ejpam-4021	259	25	)	)	PUNCT
ejpam-4021	259	26	≤	≤	NOUN
ejpam-4021	259	27	µ(g−1	µ(g−1	PUNCT
ejpam-4021	259	28	)	)	PUNCT
ejpam-4021	259	29	.	.	PUNCT
ejpam-4021	260	1	then	then	ADV
ejpam-4021	260	2	the	the	DET
ejpam-4021	260	3	pair	pair	NOUN
ejpam-4021	260	4	(	(	PUNCT
ejpam-4021	260	5	g	g	NOUN
ejpam-4021	260	6	,	,	PUNCT
ejpam-4021	260	7	·	·	PUNCT
ejpam-4021	260	8	,	,	PUNCT
ejpam-4021	260	9	µ	µ	X
ejpam-4021	260	10	)	)	PUNCT
ejpam-4021	260	11	is	be	AUX
ejpam-4021	260	12	called	call	VERB
ejpam-4021	260	13	an	an	DET
ejpam-4021	260	14	l	l	NOUN
ejpam-4021	260	15	-	-	PUNCT
ejpam-4021	260	16	valued	value	VERB
ejpam-4021	260	17	subgroup	subgroup	NOUN
ejpam-4021	260	18	space	space	NOUN
ejpam-4021	260	19	.	.	PUNCT
ejpam-4021	261	1	let	let	VERB
ejpam-4021	261	2	(	(	PUNCT
ejpam-4021	261	3	h	h	NOUN
ejpam-4021	261	4	,	,	PUNCT
ejpam-4021	261	5	·	·	PUNCT
ejpam-4021	261	6	,	,	PUNCT
ejpam-4021	261	7	ξ	ξ	X
ejpam-4021	261	8	)	)	PUNCT
ejpam-4021	261	9	be	be	VERB
ejpam-4021	261	10	another	another	DET
ejpam-4021	261	11	l	l	NOUN
ejpam-4021	261	12	-	-	PUNCT
ejpam-4021	261	13	valued	value	VERB
ejpam-4021	261	14	subgroup	subgroup	NOUN
ejpam-4021	261	15	of	of	ADP
ejpam-4021	261	16	a	a	DET
ejpam-4021	261	17	group	group	NOUN
ejpam-4021	261	18	h.	h.	NOUN
ejpam-4021	261	19	define	define	VERB
ejpam-4021	261	20	a	a	DET
ejpam-4021	261	21	mapping	mapping	NOUN
ejpam-4021	261	22	between	between	ADP
ejpam-4021	261	23	l	l	NOUN
ejpam-4021	261	24	-	-	PUNCT
ejpam-4021	261	25	valued	value	VERB
ejpam-4021	261	26	subgroup	subgroup	NOUN
ejpam-4021	261	27	spaces	space	NOUN
ejpam-4021	261	28	,	,	PUNCT
ejpam-4021	261	29	f	f	X
ejpam-4021	261	30	:	:	PUNCT
ejpam-4021	261	31	(	(	PUNCT
ejpam-4021	261	32	g	g	NOUN
ejpam-4021	261	33	,	,	PUNCT
ejpam-4021	261	34	·	·	PUNCT
ejpam-4021	261	35	,	,	PUNCT
ejpam-4021	261	36	µ	µ	X
ejpam-4021	261	37	)	)	PUNCT
ejpam-4021	261	38	−→	−→	NOUN
ejpam-4021	261	39	(	(	PUNCT
ejpam-4021	261	40	h	h	NOUN
ejpam-4021	261	41	,	,	PUNCT
ejpam-4021	261	42	·	·	PUNCT
ejpam-4021	261	43	,	,	PUNCT
ejpam-4021	261	44	ξ	ξ	X
ejpam-4021	261	45	)	)	PUNCT
ejpam-4021	261	46	such	such	ADJ
ejpam-4021	261	47	that	that	SCONJ
ejpam-4021	261	48	µ(g	µ(g	PROPN
ejpam-4021	261	49	)	)	PUNCT
ejpam-4021	261	50	≤	≤	NUM
ejpam-4021	261	51	ξ(f(g	ξ(f(g	NOUN
ejpam-4021	261	52	)	)	PUNCT
ejpam-4021	261	53	)	)	PUNCT
ejpam-4021	261	54	,	,	PUNCT
ejpam-4021	261	55	∀g	∀g	X
ejpam-4021	261	56	∈	∈	PROPN
ejpam-4021	261	57	g	g	PROPN
ejpam-4021	261	58	(	(	PUNCT
ejpam-4021	261	59	‡	‡	NOUN
ejpam-4021	261	60	)	)	PUNCT
ejpam-4021	261	61	the	the	DET
ejpam-4021	261	62	category	category	NOUN
ejpam-4021	261	63	of	of	ADP
ejpam-4021	261	64	all	all	DET
ejpam-4021	261	65	l	l	NOUN
ejpam-4021	261	66	-	-	PUNCT
ejpam-4021	261	67	valued	value	VERB
ejpam-4021	261	68	subgroup	subgroup	NOUN
ejpam-4021	261	69	spaces	space	NOUN
ejpam-4021	261	70	and	and	CCONJ
ejpam-4021	261	71	all	all	DET
ejpam-4021	261	72	group	group	NOUN
ejpam-4021	261	73	homomorphisms	homomorphism	NOUN
ejpam-4021	261	74	satisfying	satisfy	VERB
ejpam-4021	261	75	(	(	PUNCT
ejpam-4021	261	76	‡	‡	X
ejpam-4021	261	77	)	)	PUNCT
ejpam-4021	261	78	is	be	AUX
ejpam-4021	261	79	denoted	denote	VERB
ejpam-4021	261	80	by	by	ADP
ejpam-4021	261	81	l	l	NOUN
ejpam-4021	261	82	-	-	NOUN
ejpam-4021	261	83	grp	grp	PROPN
ejpam-4021	261	84	.	.	PUNCT
ejpam-4021	262	1	sometime	sometime	ADV
ejpam-4021	262	2	we	we	PRON
ejpam-4021	262	3	denote	denote	VERB
ejpam-4021	262	4	the	the	DET
ejpam-4021	262	5	set	set	NOUN
ejpam-4021	262	6	of	of	ADP
ejpam-4021	262	7	l	l	NOUN
ejpam-4021	262	8	-	-	PUNCT
ejpam-4021	262	9	valued	value	VERB
ejpam-4021	262	10	subgroups	subgroup	NOUN
ejpam-4021	262	11	of	of	ADP
ejpam-4021	262	12	a	a	DET
ejpam-4021	262	13	group	group	NOUN
ejpam-4021	262	14	g	g	NOUN
ejpam-4021	262	15	by	by	ADP
ejpam-4021	262	16	l(g	l(g	NOUN
ejpam-4021	262	17	)	)	PUNCT
ejpam-4021	262	18	.	.	PUNCT
ejpam-4021	263	1	example	example	NOUN
ejpam-4021	264	1	3	3	NUM
ejpam-4021	264	2	.	.	PUNCT
ejpam-4021	265	1	[	[	X
ejpam-4021	265	2	3	3	X
ejpam-4021	265	3	]	]	X
ejpam-4021	265	4	let	let	VERB
ejpam-4021	265	5	l	l	NOUN
ejpam-4021	265	6	=	=	PUNCT
ejpam-4021	265	7	(	(	PUNCT
ejpam-4021	265	8	[	[	X
ejpam-4021	265	9	0	0	NUM
ejpam-4021	265	10	,	,	PUNCT
ejpam-4021	265	11	1],≤,∧	1],≤,∧	NUM
ejpam-4021	265	12	,	,	PUNCT
ejpam-4021	265	13	∗	∗	NOUN
ejpam-4021	265	14	)	)	PUNCT
ejpam-4021	265	15	be	be	VERB
ejpam-4021	265	16	an	an	DET
ejpam-4021	265	17	enriched	enriched	ADJ
ejpam-4021	265	18	cl	cl	NOUN
ejpam-4021	265	19	-	-	ADJ
ejpam-4021	265	20	premonoid	premonoid	ADJ
ejpam-4021	265	21	,	,	PUNCT
ejpam-4021	265	22	where	where	SCONJ
ejpam-4021	265	23	∗	∗	NOUN
ejpam-4021	265	24	is	be	AUX
ejpam-4021	265	25	a	a	DET
ejpam-4021	265	26	tnorm	tnorm	NOUN
ejpam-4021	265	27	on	on	ADP
ejpam-4021	265	28	[	[	X
ejpam-4021	265	29	0	0	NUM
ejpam-4021	265	30	,	,	PUNCT
ejpam-4021	265	31	1	1	NUM
ejpam-4021	265	32	]	]	PUNCT
ejpam-4021	265	33	.	.	PUNCT
ejpam-4021	266	1	let	let	VERB
ejpam-4021	266	2	g	g	PRON
ejpam-4021	266	3	be	be	AUX
ejpam-4021	266	4	the	the	DET
ejpam-4021	266	5	cyclic	cyclic	ADJ
ejpam-4021	266	6	group	group	NOUN
ejpam-4021	266	7	cn	cn	PROPN
ejpam-4021	266	8	of	of	ADP
ejpam-4021	266	9	order	order	NOUN
ejpam-4021	266	10	n	n	PRON
ejpam-4021	266	11	(	(	PUNCT
ejpam-4021	266	12	n	n	CCONJ
ejpam-4021	266	13	≥	≥	NOUN
ejpam-4021	266	14	1	1	NUM
ejpam-4021	266	15	)	)	PUNCT
ejpam-4021	266	16	with	with	ADP
ejpam-4021	266	17	a	a	PRON
ejpam-4021	266	18	as	as	ADP
ejpam-4021	266	19	the	the	DET
ejpam-4021	266	20	generator	generator	NOUN
ejpam-4021	266	21	;	;	PUNCT
ejpam-4021	266	22	specifically	specifically	ADV
ejpam-4021	266	23	,	,	PUNCT
ejpam-4021	266	24	cn	cn	X
ejpam-4021	266	25	=	=	PUNCT
ejpam-4021	266	26	{	{	PUNCT
ejpam-4021	266	27	e	e	NOUN
ejpam-4021	266	28	,	,	PUNCT
ejpam-4021	266	29	a	a	PRON
ejpam-4021	266	30	,	,	PUNCT
ejpam-4021	266	31	a2	a2	PROPN
ejpam-4021	266	32	,	,	PUNCT
ejpam-4021	266	33	...	...	PUNCT
ejpam-4021	266	34	,	,	PUNCT
ejpam-4021	266	35	an−1	an−1	ADJ
ejpam-4021	266	36	;	;	PUNCT
ejpam-4021	266	37	an	an	DET
ejpam-4021	266	38	=	=	SYM
ejpam-4021	266	39	e	e	NOUN
ejpam-4021	266	40	}	}	PUNCT
ejpam-4021	266	41	with	with	ADP
ejpam-4021	266	42	respect	respect	NOUN
ejpam-4021	266	43	to	to	ADP
ejpam-4021	266	44	multiplication	multiplication	NOUN
ejpam-4021	266	45	·	·	PUNCT
ejpam-4021	266	46	.	.	PUNCT
ejpam-4021	267	1	define	define	VERB
ejpam-4021	267	2	µ	µ	X
ejpam-4021	267	3	:	:	PUNCT
ejpam-4021	267	4	g→	g→	NOUN
ejpam-4021	267	5	[	[	NOUN
ejpam-4021	267	6	0	0	NUM
ejpam-4021	267	7	,	,	PUNCT
ejpam-4021	267	8	1	1	NUM
ejpam-4021	267	9	]	]	PUNCT
ejpam-4021	267	10	by	by	ADP
ejpam-4021	267	11	µ(x	µ(x	NOUN
ejpam-4021	267	12	)	)	PUNCT
ejpam-4021	267	13	=	=	NOUN
ejpam-4021	267	14	{	{	PUNCT
ejpam-4021	267	15	1	1	NUM
ejpam-4021	267	16	,	,	PUNCT
ejpam-4021	267	17	if	if	SCONJ
ejpam-4021	267	18	x	x	ADP
ejpam-4021	267	19	=	=	SYM
ejpam-4021	267	20	e	e	NOUN
ejpam-4021	267	21	;	;	PUNCT
ejpam-4021	267	22	1	1	NUM
ejpam-4021	267	23	n	n	NOUN
ejpam-4021	267	24	,	,	PUNCT
ejpam-4021	267	25	otherwise	otherwise	ADV
ejpam-4021	267	26	.	.	PUNCT
ejpam-4021	268	1	then	then	ADV
ejpam-4021	268	2	(	(	PUNCT
ejpam-4021	268	3	g	g	NOUN
ejpam-4021	268	4	,	,	PUNCT
ejpam-4021	268	5	·	·	PUNCT
ejpam-4021	268	6	,	,	PUNCT
ejpam-4021	268	7	µ	µ	X
ejpam-4021	268	8	)	)	PUNCT
ejpam-4021	268	9	is	be	AUX
ejpam-4021	268	10	an	an	DET
ejpam-4021	268	11	enriched	enriched	ADJ
ejpam-4021	268	12	lattice	lattice	NOUN
ejpam-4021	268	13	-	-	PUNCT
ejpam-4021	268	14	valued	value	VERB
ejpam-4021	268	15	subgroup	subgroup	NOUN
ejpam-4021	268	16	space	space	NOUN
ejpam-4021	268	17	.	.	PUNCT
ejpam-4021	269	1	in	in	ADP
ejpam-4021	269	2	fact	fact	NOUN
ejpam-4021	269	3	,	,	PUNCT
ejpam-4021	269	4	for	for	ADP
ejpam-4021	269	5	(	(	PUNCT
ejpam-4021	269	6	lg1	lg1	PROPN
ejpam-4021	269	7	)	)	PUNCT
ejpam-4021	269	8	µ(e	µ(e	PROPN
ejpam-4021	269	9	)	)	PUNCT
ejpam-4021	269	10	=	=	SYM
ejpam-4021	269	11	1	1	NUM
ejpam-4021	269	12	while	while	SCONJ
ejpam-4021	269	13	(	(	PUNCT
ejpam-4021	269	14	lg3	lg3	NOUN
ejpam-4021	269	15	)	)	PUNCT
ejpam-4021	269	16	follows	follow	VERB
ejpam-4021	269	17	from	from	ADP
ejpam-4021	269	18	the	the	DET
ejpam-4021	269	19	definition	definition	NOUN
ejpam-4021	269	20	.	.	PUNCT
ejpam-4021	270	1	for	for	ADP
ejpam-4021	270	2	(	(	PUNCT
ejpam-4021	270	3	lg2	lg2	X
ejpam-4021	270	4	)	)	PUNCT
ejpam-4021	270	5	,	,	PUNCT
ejpam-4021	270	6	consider	consider	VERB
ejpam-4021	270	7	x	x	PRON
ejpam-4021	270	8	,	,	PUNCT
ejpam-4021	270	9	y	y	PROPN
ejpam-4021	270	10	∈	∈	PROPN
ejpam-4021	270	11	g	g	NOUN
ejpam-4021	270	12	with	with	ADP
ejpam-4021	270	13	x	x	SYM
ejpam-4021	270	14	6=	6=	ADP
ejpam-4021	270	15	e	e	NOUN
ejpam-4021	270	16	and	and	CCONJ
ejpam-4021	270	17	y	y	PROPN
ejpam-4021	270	18	6=	6=	PROPN
ejpam-4021	270	19	e	e	PROPN
ejpam-4021	270	20	,	,	PUNCT
ejpam-4021	270	21	then	then	ADV
ejpam-4021	270	22	µ(x	µ(x	NOUN
ejpam-4021	270	23	)	)	PUNCT
ejpam-4021	270	24	∗	∗	NOUN
ejpam-4021	270	25	µ(y	µ(y	PROPN
ejpam-4021	270	26	)	)	PUNCT
ejpam-4021	270	27	=	=	SYM
ejpam-4021	271	1	1	1	NUM
ejpam-4021	271	2	n	n	NUM
ejpam-4021	271	3	∗	∗	NOUN
ejpam-4021	271	4	1	1	NUM
ejpam-4021	271	5	n	n	CCONJ
ejpam-4021	271	6	≤	≤	NUM
ejpam-4021	271	7	1	1	NUM
ejpam-4021	271	8	n	n	NOUN
ejpam-4021	271	9	∗	∗	X
ejpam-4021	271	10	1	1	NUM
ejpam-4021	271	11	=	=	SYM
ejpam-4021	271	12	1	1	NUM
ejpam-4021	271	13	n	n	PRON
ejpam-4021	271	14	implying	imply	VERB
ejpam-4021	271	15	µ(x	µ(x	NOUN
ejpam-4021	271	16	)	)	PUNCT
ejpam-4021	271	17	∗	∗	NOUN
ejpam-4021	271	18	µ(y	µ(y	PROPN
ejpam-4021	271	19	)	)	PUNCT
ejpam-4021	271	20	≤	≤	NOUN
ejpam-4021	271	21	µ(xy	µ(xy	PROPN
ejpam-4021	271	22	)	)	PUNCT
ejpam-4021	271	23	;	;	PUNCT
ejpam-4021	271	24	other	other	ADJ
ejpam-4021	271	25	choices	choice	NOUN
ejpam-4021	271	26	follow	follow	VERB
ejpam-4021	271	27	similarly	similarly	ADV
ejpam-4021	271	28	.	.	PUNCT
ejpam-4021	272	1	hence	hence	ADV
ejpam-4021	272	2	µ	µ	X
ejpam-4021	272	3	is	be	AUX
ejpam-4021	272	4	an	an	DET
ejpam-4021	272	5	enriched	enriched	ADJ
ejpam-4021	272	6	lattice	lattice	NOUN
ejpam-4021	272	7	-	-	PUNCT
ejpam-4021	272	8	valued	value	VERB
ejpam-4021	272	9	subgroup	subgroup	NOUN
ejpam-4021	272	10	of	of	ADP
ejpam-4021	272	11	the	the	DET
ejpam-4021	272	12	group	group	NOUN
ejpam-4021	272	13	g.	g.	PROPN
ejpam-4021	272	14	t	t	PROPN
ejpam-4021	272	15	m	m	PROPN
ejpam-4021	272	16	g	g	NOUN
ejpam-4021	272	17	ahsanullah	ahsanullah	NOUN
ejpam-4021	272	18	,	,	PUNCT
ejpam-4021	272	19	fawzi	fawzi	PROPN
ejpam-4021	272	20	al	al	PROPN
ejpam-4021	272	21	-	-	PUNCT
ejpam-4021	272	22	thukair	thukair	NOUN
ejpam-4021	272	23	/	/	SYM
ejpam-4021	272	24	eur	eur	NOUN
ejpam-4021	272	25	.	.	PUNCT
ejpam-4021	273	1	j.	j.	PROPN
ejpam-4021	273	2	pure	pure	PROPN
ejpam-4021	273	3	appl	appl	PROPN
ejpam-4021	273	4	.	.	PROPN
ejpam-4021	273	5	math	math	PROPN
ejpam-4021	273	6	,	,	PUNCT
ejpam-4021	273	7	14	14	NUM
ejpam-4021	273	8	(	(	PUNCT
ejpam-4021	273	9	3	3	NUM
ejpam-4021	273	10	)	)	PUNCT
ejpam-4021	273	11	(	(	PUNCT
ejpam-4021	273	12	2021	2021	NUM
ejpam-4021	273	13	)	)	PUNCT
ejpam-4021	273	14	,	,	PUNCT
ejpam-4021	273	15	949	949	NUM
ejpam-4021	273	16	-	-	SYM
ejpam-4021	273	17	968	968	NUM
ejpam-4021	273	18	959	959	NUM
ejpam-4021	273	19	remark	remark	NOUN
ejpam-4021	273	20	4	4	NUM
ejpam-4021	273	21	.	.	PUNCT
ejpam-4021	274	1	in	in	ADP
ejpam-4021	274	2	[	[	X
ejpam-4021	274	3	33	33	NUM
ejpam-4021	274	4	]	]	PUNCT
ejpam-4021	274	5	,	,	PUNCT
ejpam-4021	274	6	c.	c.	PROPN
ejpam-4021	274	7	l.	l.	PROPN
ejpam-4021	274	8	walker	walker	PROPN
ejpam-4021	274	9	pointed	point	VERB
ejpam-4021	274	10	out	out	ADP
ejpam-4021	274	11	that	that	SCONJ
ejpam-4021	274	12	for	for	ADP
ejpam-4021	274	13	a	a	DET
ejpam-4021	274	14	category	category	NOUN
ejpam-4021	274	15	of	of	ADP
ejpam-4021	274	16	fuzzy	fuzzy	ADJ
ejpam-4021	274	17	subsets	subset	NOUN
ejpam-4021	274	18	f	f	NOUN
ejpam-4021	274	19	=	=	SYM
ejpam-4021	274	20	set(i	set(i	PROPN
ejpam-4021	274	21	)	)	PUNCT
ejpam-4021	274	22	where	where	SCONJ
ejpam-4021	274	23	all	all	DET
ejpam-4021	274	24	objects	object	NOUN
ejpam-4021	274	25	are	be	AUX
ejpam-4021	274	26	(	(	PUNCT
ejpam-4021	274	27	x	x	NOUN
ejpam-4021	274	28	,	,	PUNCT
ejpam-4021	274	29	ν	ν	NOUN
ejpam-4021	274	30	)	)	PUNCT
ejpam-4021	274	31	,	,	PUNCT
ejpam-4021	274	32	x	x	PUNCT
ejpam-4021	274	33	∈	∈	NOUN
ejpam-4021	274	34	|set|	|set|	NOUN
ejpam-4021	274	35	,	,	PUNCT
ejpam-4021	274	36	with	with	ADP
ejpam-4021	274	37	ν	ν	NOUN
ejpam-4021	274	38	:	:	PUNCT
ejpam-4021	274	39	x	x	PUNCT
ejpam-4021	274	40	−→	−→	NOUN
ejpam-4021	274	41	i	i	PRON
ejpam-4021	274	42	a	a	DET
ejpam-4021	274	43	mapping	mapping	NOUN
ejpam-4021	274	44	from	from	ADP
ejpam-4021	274	45	x	x	X
ejpam-4021	274	46	to	to	ADP
ejpam-4021	274	47	the	the	DET
ejpam-4021	274	48	unit	unit	NOUN
ejpam-4021	274	49	interval	interval	NOUN
ejpam-4021	274	50	.	.	PUNCT
ejpam-4021	275	1	the	the	DET
ejpam-4021	275	2	morphisms	morphism	NOUN
ejpam-4021	275	3	f	f	PROPN
ejpam-4021	275	4	are	be	AUX
ejpam-4021	275	5	all	all	PRON
ejpam-4021	275	6	mappings	mapping	NOUN
ejpam-4021	275	7	f	f	NOUN
ejpam-4021	275	8	:	:	PUNCT
ejpam-4021	275	9	(	(	PUNCT
ejpam-4021	275	10	x	x	NOUN
ejpam-4021	275	11	,	,	PUNCT
ejpam-4021	275	12	ν	ν	NOUN
ejpam-4021	275	13	)	)	PUNCT
ejpam-4021	275	14	−→	−→	NOUN
ejpam-4021	275	15	(	(	PUNCT
ejpam-4021	275	16	y	y	PROPN
ejpam-4021	275	17	,	,	PUNCT
ejpam-4021	275	18	µ	µ	NOUN
ejpam-4021	275	19	)	)	PUNCT
ejpam-4021	275	20	satisfying	satisfy	VERB
ejpam-4021	275	21	ν(x	ν(x	PROPN
ejpam-4021	275	22	)	)	PUNCT
ejpam-4021	275	23	≤	≤	NUM
ejpam-4021	275	24	µ(f(x	µ(f(x	PROPN
ejpam-4021	275	25	)	)	PUNCT
ejpam-4021	275	26	)	)	PUNCT
ejpam-4021	275	27	.	.	PUNCT
ejpam-4021	276	1	furthermore	furthermore	ADV
ejpam-4021	276	2	,	,	PUNCT
ejpam-4021	276	3	note	note	VERB
ejpam-4021	276	4	that	that	SCONJ
ejpam-4021	276	5	in	in	ADP
ejpam-4021	276	6	[	[	X
ejpam-4021	276	7	14	14	NUM
ejpam-4021	276	8	]	]	PUNCT
ejpam-4021	276	9	,	,	PUNCT
ejpam-4021	276	10	j.	j.	PROPN
ejpam-4021	276	11	goguen	goguen	PROPN
ejpam-4021	276	12	,	,	PUNCT
ejpam-4021	276	13	defined	define	VERB
ejpam-4021	276	14	the	the	DET
ejpam-4021	276	15	category	category	NOUN
ejpam-4021	276	16	set(l	set(l	NOUN
ejpam-4021	276	17	)	)	PUNCT
ejpam-4021	276	18	having	have	VERB
ejpam-4021	276	19	objects	object	VERB
ejpam-4021	276	20	the	the	DET
ejpam-4021	276	21	pair	pair	NOUN
ejpam-4021	276	22	(	(	PUNCT
ejpam-4021	276	23	x	x	NOUN
ejpam-4021	276	24	,	,	PUNCT
ejpam-4021	276	25	ν	ν	NOUN
ejpam-4021	276	26	)	)	PUNCT
ejpam-4021	276	27	,	,	PUNCT
ejpam-4021	276	28	where	where	SCONJ
ejpam-4021	276	29	ν	ν	X
ejpam-4021	276	30	:	:	PUNCT
ejpam-4021	276	31	x	x	PUNCT
ejpam-4021	276	32	−→	−→	NOUN
ejpam-4021	276	33	l	l	NOUN
ejpam-4021	276	34	,	,	PUNCT
ejpam-4021	276	35	and	and	CCONJ
ejpam-4021	276	36	morphisms	morphism	NOUN
ejpam-4021	276	37	f	f	NOUN
ejpam-4021	276	38	:	:	PUNCT
ejpam-4021	276	39	(	(	PUNCT
ejpam-4021	276	40	x	x	NOUN
ejpam-4021	276	41	,	,	PUNCT
ejpam-4021	276	42	ν	ν	NOUN
ejpam-4021	276	43	)	)	PUNCT
ejpam-4021	276	44	−→	−→	NOUN
ejpam-4021	276	45	(	(	PUNCT
ejpam-4021	276	46	y	y	PROPN
ejpam-4021	276	47	,	,	PUNCT
ejpam-4021	276	48	µ	µ	NOUN
ejpam-4021	276	49	)	)	PUNCT
ejpam-4021	276	50	such	such	ADJ
ejpam-4021	276	51	that	that	SCONJ
ejpam-4021	276	52	ν(x	ν(x	PROPN
ejpam-4021	276	53	)	)	PUNCT
ejpam-4021	276	54	≤	≤	NUM
ejpam-4021	276	55	µ(f(x	µ(f(x	PROPN
ejpam-4021	276	56	)	)	PUNCT
ejpam-4021	276	57	)	)	PUNCT
ejpam-4021	276	58	holds	hold	VERB
ejpam-4021	276	59	.	.	PUNCT
ejpam-4021	277	1	l.	l.	PROPN
ejpam-4021	277	2	stout	stout	PROPN
ejpam-4021	278	1	[	[	X
ejpam-4021	278	2	32	32	NUM
ejpam-4021	278	3	]	]	PUNCT
ejpam-4021	278	4	argued	argue	VERB
ejpam-4021	278	5	that	that	SCONJ
ejpam-4021	278	6	this	this	DET
ejpam-4021	278	7	category	category	NOUN
ejpam-4021	278	8	set(l	set(l	NOUN
ejpam-4021	278	9	)	)	PUNCT
ejpam-4021	278	10	has	have	VERB
ejpam-4021	278	11	initial	initial	ADJ
ejpam-4021	278	12	structure	structure	NOUN
ejpam-4021	278	13	and	and	CCONJ
ejpam-4021	278	14	is	be	AUX
ejpam-4021	278	15	cartesian	cartesian	ADJ
ejpam-4021	278	16	closed	closed	ADJ
ejpam-4021	278	17	.	.	PUNCT
ejpam-4021	279	1	the	the	DET
ejpam-4021	279	2	initial	initial	ADJ
ejpam-4021	279	3	structure	structure	NOUN
ejpam-4021	279	4	is	be	AUX
ejpam-4021	279	5	given	give	VERB
ejpam-4021	279	6	as	as	ADP
ejpam-4021	279	7	:	:	PUNCT
ejpam-4021	279	8	for	for	ADP
ejpam-4021	279	9	a	a	DET
ejpam-4021	279	10	family	family	NOUN
ejpam-4021	279	11	of	of	ADP
ejpam-4021	279	12	mappings	mapping	NOUN
ejpam-4021	279	13	(	(	PUNCT
ejpam-4021	279	14	fj	fj	INTJ
ejpam-4021	279	15	:	:	PUNCT
ejpam-4021	279	16	x	x	PUNCT
ejpam-4021	279	17	−→	−→	NOUN
ejpam-4021	279	18	(	(	PUNCT
ejpam-4021	279	19	yj	yj	PROPN
ejpam-4021	279	20	,	,	PUNCT
ejpam-4021	279	21	µj))j	µj))j	PROPN
ejpam-4021	279	22	,	,	PUNCT
ejpam-4021	279	23	ν(x	ν(x	PROPN
ejpam-4021	279	24	)	)	PUNCT
ejpam-4021	279	25	=	=	SYM
ejpam-4021	279	26	∧	∧	PROPN
ejpam-4021	279	27	j	j	PROPN
ejpam-4021	279	28	µj(fj(x	µj(fj(x	PROPN
ejpam-4021	279	29	)	)	PUNCT
ejpam-4021	279	30	)	)	PUNCT
ejpam-4021	279	31	gives	give	VERB
ejpam-4021	279	32	the	the	DET
ejpam-4021	279	33	initial	initial	ADJ
ejpam-4021	279	34	structure	structure	NOUN
ejpam-4021	279	35	on	on	ADP
ejpam-4021	279	36	x.	x.	NOUN
ejpam-4021	279	37	the	the	DET
ejpam-4021	279	38	cartesian	cartesian	ADJ
ejpam-4021	279	39	closed	closed	ADJ
ejpam-4021	279	40	structure	structure	NOUN
ejpam-4021	279	41	is	be	AUX
ejpam-4021	279	42	obtained	obtain	VERB
ejpam-4021	279	43	as	as	ADP
ejpam-4021	279	44	:	:	PUNCT
ejpam-4021	279	45	(	(	PUNCT
ejpam-4021	279	46	c(x	c(x	NOUN
ejpam-4021	279	47	,	,	PUNCT
ejpam-4021	279	48	y	y	PROPN
ejpam-4021	279	49	)	)	PUNCT
ejpam-4021	279	50	,	,	PUNCT
ejpam-4021	279	51	∇	∇	PROPN
ejpam-4021	279	52	)	)	PUNCT
ejpam-4021	279	53	,	,	PUNCT
ejpam-4021	279	54	where	where	SCONJ
ejpam-4021	279	55	∇(f	∇(f	NOUN
ejpam-4021	279	56	)	)	PUNCT
ejpam-4021	279	57	=	=	PUNCT
ejpam-4021	280	1	∧	∧	NOUN
ejpam-4021	280	2	x∈x	x∈x	PUNCT
ejpam-4021	281	1	[	[	X
ejpam-4021	281	2	ν(x	ν(x	X
ejpam-4021	281	3	)	)	PUNCT
ejpam-4021	281	4	−→	−→	PROPN
ejpam-4021	281	5	µ(f(x	µ(f(x	PROPN
ejpam-4021	281	6	)	)	PUNCT
ejpam-4021	281	7	)	)	PUNCT
ejpam-4021	282	1	]	]	PUNCT
ejpam-4021	282	2	,	,	PUNCT
ejpam-4021	282	3	where	where	SCONJ
ejpam-4021	282	4	for	for	ADP
ejpam-4021	282	5	all	all	PRON
ejpam-4021	282	6	(	(	PUNCT
ejpam-4021	282	7	f	f	NOUN
ejpam-4021	282	8	:	:	PUNCT
ejpam-4021	282	9	(	(	PUNCT
ejpam-4021	282	10	x	x	NOUN
ejpam-4021	282	11	,	,	PUNCT
ejpam-4021	282	12	ν	ν	NOUN
ejpam-4021	282	13	)	)	PUNCT
ejpam-4021	282	14	−→	−→	NOUN
ejpam-4021	282	15	(	(	PUNCT
ejpam-4021	282	16	y	y	PROPN
ejpam-4021	282	17	,	,	PUNCT
ejpam-4021	282	18	µ	µ	NOUN
ejpam-4021	282	19	)	)	PUNCT
ejpam-4021	282	20	)	)	PUNCT
ejpam-4021	282	21	∈	∈	PROPN
ejpam-4021	282	22	c(x	c(x	PROPN
ejpam-4021	282	23	,	,	PUNCT
ejpam-4021	282	24	y	y	PROPN
ejpam-4021	282	25	)	)	PUNCT
ejpam-4021	282	26	,	,	PUNCT
ejpam-4021	282	27	and	and	CCONJ
ejpam-4021	282	28	the	the	DET
ejpam-4021	282	29	implication	implication	NOUN
ejpam-4021	282	30	→	→	ADP
ejpam-4021	282	31	is	be	AUX
ejpam-4021	282	32	given	give	VERB
ejpam-4021	282	33	by	by	ADP
ejpam-4021	282	34	:	:	PUNCT
ejpam-4021	282	35	ν(x	ν(x	PROPN
ejpam-4021	282	36	)	)	PUNCT
ejpam-4021	282	37	−→	−→	PROPN
ejpam-4021	282	38	µ(f(x	µ(f(x	PROPN
ejpam-4021	282	39	)	)	PUNCT
ejpam-4021	282	40	)	)	PUNCT
ejpam-4021	283	1	=	=	PUNCT
ejpam-4021	283	2	∨	∨	X
ejpam-4021	283	3	{	{	PUNCT
ejpam-4021	283	4	λ	λ	X
ejpam-4021	283	5	:	:	PUNCT
ejpam-4021	283	6	λ	λ	X
ejpam-4021	283	7	∧	∧	PROPN
ejpam-4021	283	8	ν(x	ν(x	PROPN
ejpam-4021	283	9	)	)	PUNCT
ejpam-4021	283	10	≤	≤	NUM
ejpam-4021	283	11	µ(f(x	µ(f(x	PROPN
ejpam-4021	283	12	)	)	PUNCT
ejpam-4021	283	13	)	)	PUNCT
ejpam-4021	283	14	}	}	PUNCT
ejpam-4021	283	15	.	.	PUNCT
ejpam-4021	284	1	lemma	lemma	PROPN
ejpam-4021	284	2	5	5	NUM
ejpam-4021	284	3	.	.	PUNCT
ejpam-4021	285	1	l	l	NOUN
ejpam-4021	285	2	-	-	PUNCT
ejpam-4021	285	3	grp	grp	PROPN
ejpam-4021	285	4	has	have	VERB
ejpam-4021	285	5	initial	initial	ADJ
ejpam-4021	285	6	structure	structure	NOUN
ejpam-4021	285	7	where	where	SCONJ
ejpam-4021	285	8	the	the	DET
ejpam-4021	285	9	underlying	underlie	VERB
ejpam-4021	285	10	forgetful	forgetful	ADJ
ejpam-4021	285	11	functor	functor	NOUN
ejpam-4021	285	12	is	be	AUX
ejpam-4021	285	13	given	give	VERB
ejpam-4021	285	14	by	by	ADP
ejpam-4021	285	15	t	t	NOUN
ejpam-4021	285	16	:	:	PUNCT
ejpam-4021	286	1	l	l	X
ejpam-4021	286	2	-	-	PUNCT
ejpam-4021	286	3	grp−→	grp−→	ADJ
ejpam-4021	286	4	grp	grp	NOUN
ejpam-4021	286	5	.	.	PUNCT
ejpam-4021	286	6	proof	proof	NOUN
ejpam-4021	286	7	.	.	PUNCT
ejpam-4021	287	1	consider	consider	VERB
ejpam-4021	287	2	a	a	DET
ejpam-4021	287	3	group	group	NOUN
ejpam-4021	287	4	(	(	PUNCT
ejpam-4021	287	5	g	g	NOUN
ejpam-4021	287	6	,	,	PUNCT
ejpam-4021	287	7	·	·	PUNCT
ejpam-4021	287	8	)	)	PUNCT
ejpam-4021	287	9	and	and	CCONJ
ejpam-4021	287	10	a	a	DET
ejpam-4021	287	11	family	family	NOUN
ejpam-4021	287	12	of	of	ADP
ejpam-4021	287	13	mappings	mapping	NOUN
ejpam-4021	287	14	(	(	PUNCT
ejpam-4021	287	15	fj	fj	INTJ
ejpam-4021	287	16	:	:	PUNCT
ejpam-4021	287	17	g	g	PROPN
ejpam-4021	287	18	−→	−→	NOUN
ejpam-4021	287	19	(	(	PUNCT
ejpam-4021	287	20	hj	hj	PROPN
ejpam-4021	287	21	,	,	PUNCT
ejpam-4021	287	22	µj))j∈j	µj))j∈j	PROPN
ejpam-4021	287	23	,	,	PUNCT
ejpam-4021	287	24	where	where	SCONJ
ejpam-4021	287	25	each	each	DET
ejpam-4021	287	26	fj	fj	X
ejpam-4021	287	27	:	:	PUNCT
ejpam-4021	287	28	g	g	PROPN
ejpam-4021	287	29	−→	−→	NOUN
ejpam-4021	287	30	hj	hj	PROPN
ejpam-4021	287	31	is	be	AUX
ejpam-4021	287	32	a	a	DET
ejpam-4021	287	33	group	group	NOUN
ejpam-4021	287	34	homomorphism	homomorphism	NOUN
ejpam-4021	287	35	,	,	PUNCT
ejpam-4021	287	36	µj	µj	PROPN
ejpam-4021	287	37	is	be	AUX
ejpam-4021	287	38	a	a	DET
ejpam-4021	287	39	subgroup	subgroup	NOUN
ejpam-4021	287	40	of	of	ADP
ejpam-4021	287	41	hj	hj	PROPN
ejpam-4021	287	42	,	,	PUNCT
ejpam-4021	287	43	for	for	ADP
ejpam-4021	287	44	each	each	DET
ejpam-4021	287	45	j	j	PROPN
ejpam-4021	287	46	∈	∈	PROPN
ejpam-4021	287	47	j	j	PROPN
ejpam-4021	287	48	.	.	PUNCT
ejpam-4021	288	1	then	then	ADV
ejpam-4021	288	2	the	the	DET
ejpam-4021	288	3	structure	structure	NOUN
ejpam-4021	288	4	on	on	ADP
ejpam-4021	288	5	µ	µ	NOUN
ejpam-4021	288	6	on	on	ADP
ejpam-4021	288	7	g	g	PROPN
ejpam-4021	288	8	is	be	AUX
ejpam-4021	288	9	given	give	VERB
ejpam-4021	288	10	by	by	ADP
ejpam-4021	288	11	ν(g	ν(g	NOUN
ejpam-4021	288	12	)	)	PUNCT
ejpam-4021	289	1	=	=	PUNCT
ejpam-4021	289	2	∧	∧	PROPN
ejpam-4021	289	3	j	j	PROPN
ejpam-4021	289	4	µj(fj(g))(=	µj(fj(g))(=	ADP
ejpam-4021	289	5	∧	∧	PROPN
ejpam-4021	289	6	j	j	PROPN
ejpam-4021	289	7	f	f	PROPN
ejpam-4021	289	8	←	←	PROPN
ejpam-4021	289	9	j	j	PROPN
ejpam-4021	289	10	(	(	PUNCT
ejpam-4021	289	11	µj)(g	µj)(g	PROPN
ejpam-4021	289	12	)	)	PUNCT
ejpam-4021	289	13	)	)	PUNCT
ejpam-4021	289	14	,	,	PUNCT
ejpam-4021	289	15	for	for	ADP
ejpam-4021	289	16	all	all	PRON
ejpam-4021	289	17	g	g	PROPN
ejpam-4021	289	18	∈	∈	PROPN
ejpam-4021	289	19	g	g	NOUN
ejpam-4021	289	20	,	,	PUNCT
ejpam-4021	289	21	note	note	VERB
ejpam-4021	289	22	that	that	SCONJ
ejpam-4021	289	23	for	for	SCONJ
ejpam-4021	289	24	each	each	DET
ejpam-4021	289	25	j	j	PROPN
ejpam-4021	289	26	∈	∈	PROPN
ejpam-4021	289	27	j	j	PROPN
ejpam-4021	289	28	,	,	PUNCT
ejpam-4021	289	29	f←j	f←j	PUNCT
ejpam-4021	289	30	(	(	PUNCT
ejpam-4021	289	31	µj	µj	PROPN
ejpam-4021	289	32	)	)	PUNCT
ejpam-4021	289	33	is	be	AUX
ejpam-4021	289	34	also	also	ADV
ejpam-4021	289	35	an	an	DET
ejpam-4021	289	36	l	l	NOUN
ejpam-4021	289	37	-	-	NOUN
ejpam-4021	289	38	subgroup	subgroup	NOUN
ejpam-4021	289	39	of	of	ADP
ejpam-4021	289	40	g	g	PROPN
ejpam-4021	289	41	,	,	PUNCT
ejpam-4021	289	42	and	and	CCONJ
ejpam-4021	289	43	the	the	DET
ejpam-4021	289	44	arbitrary	arbitrary	ADJ
ejpam-4021	289	45	intersection	intersection	NOUN
ejpam-4021	289	46	ν	ν	NOUN
ejpam-4021	289	47	is	be	AUX
ejpam-4021	289	48	also	also	ADV
ejpam-4021	289	49	an	an	DET
ejpam-4021	289	50	l	l	NOUN
ejpam-4021	289	51	-	-	NOUN
ejpam-4021	289	52	subgroup	subgroup	NOUN
ejpam-4021	289	53	of	of	ADP
ejpam-4021	289	54	g	g	PROPN
ejpam-4021	289	55	,	,	PUNCT
ejpam-4021	289	56	and	and	CCONJ
ejpam-4021	289	57	hence	hence	ADV
ejpam-4021	289	58	(	(	PUNCT
ejpam-4021	289	59	g	g	NOUN
ejpam-4021	289	60	,	,	PUNCT
ejpam-4021	289	61	·	·	PUNCT
ejpam-4021	289	62	,	,	PUNCT
ejpam-4021	289	63	ν	ν	NOUN
ejpam-4021	289	64	)	)	PUNCT
ejpam-4021	289	65	∈	∈	PROPN
ejpam-4021	289	66	|l	|l	PROPN
ejpam-4021	289	67	-	-	PUNCT
ejpam-4021	289	68	grp|	grp|	PROPN
ejpam-4021	289	69	.	.	PUNCT
ejpam-4021	290	1	let	let	VERB
ejpam-4021	290	2	(	(	PUNCT
ejpam-4021	290	3	z	z	NOUN
ejpam-4021	290	4	,	,	PUNCT
ejpam-4021	290	5	·	·	PUNCT
ejpam-4021	290	6	,	,	PUNCT
ejpam-4021	290	7	%	%	INTJ
ejpam-4021	290	8	)	)	PUNCT
ejpam-4021	290	9	∈	∈	PROPN
ejpam-4021	290	10	|l	|l	PROPN
ejpam-4021	290	11	-	-	PUNCT
ejpam-4021	290	12	grp|	grp|	PROPN
ejpam-4021	290	13	,	,	PUNCT
ejpam-4021	290	14	we	we	PRON
ejpam-4021	290	15	prove	prove	VERB
ejpam-4021	290	16	that	that	SCONJ
ejpam-4021	290	17	the	the	DET
ejpam-4021	290	18	mapping	mapping	NOUN
ejpam-4021	290	19	ϕ	ϕ	NOUN
ejpam-4021	290	20	:	:	PUNCT
ejpam-4021	290	21	(	(	PUNCT
ejpam-4021	290	22	z	z	NOUN
ejpam-4021	290	23	,	,	PUNCT
ejpam-4021	290	24	·	·	PUNCT
ejpam-4021	290	25	,	,	PUNCT
ejpam-4021	290	26	%	%	INTJ
ejpam-4021	290	27	)	)	PUNCT
ejpam-4021	290	28	−→	−→	NOUN
ejpam-4021	290	29	(	(	PUNCT
ejpam-4021	290	30	g	g	NOUN
ejpam-4021	290	31	,	,	PUNCT
ejpam-4021	290	32	·	·	PUNCT
ejpam-4021	290	33	,	,	PUNCT
ejpam-4021	290	34	ν	ν	NOUN
ejpam-4021	290	35	)	)	PUNCT
ejpam-4021	290	36	a	a	DET
ejpam-4021	290	37	group	group	NOUN
ejpam-4021	290	38	homomorphism	homomorphism	NOUN
ejpam-4021	290	39	is	be	AUX
ejpam-4021	290	40	an	an	DET
ejpam-4021	290	41	l	l	NOUN
ejpam-4021	290	42	-	-	NOUN
ejpam-4021	290	43	grpmorphism	grpmorphism	NOUN
ejpam-4021	290	44	if	if	SCONJ
ejpam-4021	290	45	and	and	CCONJ
ejpam-4021	290	46	only	only	ADV
ejpam-4021	290	47	if	if	SCONJ
ejpam-4021	290	48	fj	fj	PROPN
ejpam-4021	290	49	◦	◦	NOUN
ejpam-4021	290	50	ϕ	ϕ	X
ejpam-4021	290	51	:	:	PUNCT
ejpam-4021	290	52	(	(	PUNCT
ejpam-4021	290	53	z	z	NOUN
ejpam-4021	290	54	,	,	PUNCT
ejpam-4021	290	55	·	·	PUNCT
ejpam-4021	290	56	,	,	PUNCT
ejpam-4021	290	57	%	%	INTJ
ejpam-4021	290	58	)	)	PUNCT
ejpam-4021	290	59	−→	−→	NOUN
ejpam-4021	290	60	(	(	PUNCT
ejpam-4021	290	61	hj	hj	PROPN
ejpam-4021	290	62	,	,	PUNCT
ejpam-4021	290	63	·	·	PUNCT
ejpam-4021	290	64	,	,	PUNCT
ejpam-4021	290	65	µj	µj	PROPN
ejpam-4021	290	66	)	)	PUNCT
ejpam-4021	290	67	is	be	AUX
ejpam-4021	290	68	an	an	DET
ejpam-4021	290	69	l	l	NOUN
ejpam-4021	290	70	-	-	PUNCT
ejpam-4021	290	71	grp	grp	NOUN
ejpam-4021	290	72	-	-	NOUN
ejpam-4021	290	73	morphism	morphism	NOUN
ejpam-4021	290	74	.	.	PUNCT
ejpam-4021	291	1	we	we	PRON
ejpam-4021	291	2	only	only	ADV
ejpam-4021	291	3	show	show	VERB
ejpam-4021	291	4	g	g	NOUN
ejpam-4021	291	5	:	:	PUNCT
ejpam-4021	291	6	(	(	PUNCT
ejpam-4021	291	7	z	z	NOUN
ejpam-4021	291	8	,	,	PUNCT
ejpam-4021	291	9	·	·	PUNCT
ejpam-4021	291	10	,	,	PUNCT
ejpam-4021	291	11	%	%	INTJ
ejpam-4021	291	12	)	)	PUNCT
ejpam-4021	292	1	−→	−→	NOUN
ejpam-4021	292	2	(	(	PUNCT
ejpam-4021	292	3	g	g	NOUN
ejpam-4021	292	4	,	,	PUNCT
ejpam-4021	292	5	·	·	PUNCT
ejpam-4021	292	6	,	,	PUNCT
ejpam-4021	292	7	ν	ν	X
ejpam-4021	292	8	)	)	PUNCT
ejpam-4021	292	9	is	be	AUX
ejpam-4021	292	10	an	an	DET
ejpam-4021	292	11	l	l	NOUN
ejpam-4021	292	12	-	-	PUNCT
ejpam-4021	292	13	grp	grp	NOUN
ejpam-4021	292	14	-	-	NOUN
ejpam-4021	292	15	morphism	morphism	NOUN
ejpam-4021	292	16	.	.	PUNCT
ejpam-4021	293	1	so	so	ADV
ejpam-4021	293	2	,	,	PUNCT
ejpam-4021	293	3	for	for	ADP
ejpam-4021	293	4	any	any	DET
ejpam-4021	293	5	z	z	PROPN
ejpam-4021	293	6	∈	∈	PROPN
ejpam-4021	293	7	z	z	NOUN
ejpam-4021	293	8	,	,	PUNCT
ejpam-4021	293	9	%	%	INTJ
ejpam-4021	293	10	(	(	PUNCT
ejpam-4021	293	11	z	z	NOUN
ejpam-4021	293	12	)	)	PUNCT
ejpam-4021	293	13	≤	≤	NOUN
ejpam-4021	293	14	µj(fj(ϕ(z	µj(fj(ϕ(z	NOUN
ejpam-4021	293	15	)	)	PUNCT
ejpam-4021	293	16	)	)	PUNCT
ejpam-4021	294	1	=	=	PUNCT
ejpam-4021	294	2	∧	∧	PROPN
ejpam-4021	294	3	j∈j	j∈j	NOUN
ejpam-4021	294	4	f	f	PROPN
ejpam-4021	294	5	←	←	PROPN
ejpam-4021	294	6	j	j	PROPN
ejpam-4021	294	7	(	(	PUNCT
ejpam-4021	294	8	µj)(ϕ(z	µj)(ϕ(z	PROPN
ejpam-4021	294	9	)	)	PUNCT
ejpam-4021	294	10	)	)	PUNCT
ejpam-4021	295	1	=	=	SYM
ejpam-4021	295	2	ν(ϕ(z	ν(ϕ(z	PROPN
ejpam-4021	295	3	)	)	PUNCT
ejpam-4021	295	4	)	)	PUNCT
ejpam-4021	295	5	,	,	PUNCT
ejpam-4021	295	6	i.e.	i.e.	X
ejpam-4021	295	7	,	,	PUNCT
ejpam-4021	295	8	%	%	INTJ
ejpam-4021	295	9	(	(	PUNCT
ejpam-4021	295	10	z	z	NOUN
ejpam-4021	295	11	)	)	PUNCT
ejpam-4021	295	12	≤	≤	NOUN
ejpam-4021	295	13	ν(ϕ(z	ν(ϕ(z	NOUN
ejpam-4021	295	14	)	)	PUNCT
ejpam-4021	295	15	)	)	PUNCT
ejpam-4021	295	16	.	.	PUNCT
ejpam-4021	296	1	theorem	theorem	NOUN
ejpam-4021	296	2	2	2	NUM
ejpam-4021	296	3	.	.	PUNCT
ejpam-4021	297	1	let	let	VERB
ejpam-4021	297	2	l	l	NOUN
ejpam-4021	297	3	=	=	SYM
ejpam-4021	297	4	(	(	PUNCT
ejpam-4021	297	5	l,≤	l,≤	PROPN
ejpam-4021	297	6	,	,	PUNCT
ejpam-4021	297	7	∗	∗	NOUN
ejpam-4021	297	8	=	=	SYM
ejpam-4021	297	9	∧	∧	NOUN
ejpam-4021	297	10	)	)	PUNCT
ejpam-4021	297	11	be	be	VERB
ejpam-4021	297	12	a	a	DET
ejpam-4021	297	13	complete	complete	ADJ
ejpam-4021	297	14	heyting	heyting	NOUN
ejpam-4021	297	15	algebra	algebra	NOUN
ejpam-4021	297	16	,	,	PUNCT
ejpam-4021	297	17	and	and	CCONJ
ejpam-4021	297	18	(	(	PUNCT
ejpam-4021	297	19	g	g	NOUN
ejpam-4021	297	20	,	,	PUNCT
ejpam-4021	297	21	·	·	PUNCT
ejpam-4021	297	22	,	,	PUNCT
ejpam-4021	297	23	ν	ν	X
ejpam-4021	297	24	)	)	PUNCT
ejpam-4021	297	25	be	be	AUX
ejpam-4021	297	26	an	an	DET
ejpam-4021	297	27	l	l	NOUN
ejpam-4021	297	28	-	-	PUNCT
ejpam-4021	297	29	valued	value	VERB
ejpam-4021	297	30	subgroup	subgroup	NOUN
ejpam-4021	297	31	space	space	NOUN
ejpam-4021	297	32	and	and	CCONJ
ejpam-4021	297	33	t	t	PROPN
ejpam-4021	297	34	(	(	PUNCT
ejpam-4021	297	35	g	g	NOUN
ejpam-4021	297	36	)	)	PUNCT
ejpam-4021	297	37	=	=	PRON
ejpam-4021	298	1	{	{	PUNCT
ejpam-4021	298	2	f	f	NOUN
ejpam-4021	298	3	:	:	PUNCT
ejpam-4021	298	4	(	(	PUNCT
ejpam-4021	298	5	g	g	NOUN
ejpam-4021	298	6	,	,	PUNCT
ejpam-4021	298	7	ν	ν	NOUN
ejpam-4021	298	8	)	)	PUNCT
ejpam-4021	298	9	−→	−→	NOUN
ejpam-4021	298	10	(	(	PUNCT
ejpam-4021	298	11	g	g	NOUN
ejpam-4021	298	12	,	,	PUNCT
ejpam-4021	298	13	ν	ν	NOUN
ejpam-4021	298	14	)	)	PUNCT
ejpam-4021	298	15	;	;	PUNCT
ejpam-4021	298	16	f	f	PROPN
ejpam-4021	298	17	is	be	AUX
ejpam-4021	298	18	bijective	bijective	ADJ
ejpam-4021	298	19	and	and	CCONJ
ejpam-4021	298	20	both	both	DET
ejpam-4021	298	21	f	f	PROPN
ejpam-4021	298	22	and	and	CCONJ
ejpam-4021	298	23	f−1	f−1	PROPN
ejpam-4021	298	24	satisfy	satisfy	VERB
ejpam-4021	298	25	(	(	PUNCT
ejpam-4021	298	26	‡	‡	X
ejpam-4021	298	27	)	)	PUNCT
ejpam-4021	298	28	}	}	PUNCT
ejpam-4021	298	29	.	.	PUNCT
ejpam-4021	299	1	then	then	ADV
ejpam-4021	299	2	(	(	PUNCT
ejpam-4021	299	3	t	t	PROPN
ejpam-4021	299	4	(	(	PUNCT
ejpam-4021	299	5	g	g	NOUN
ejpam-4021	299	6	)	)	PUNCT
ejpam-4021	299	7	,	,	PUNCT
ejpam-4021	299	8	·	·	PUNCT
ejpam-4021	299	9	,	,	PUNCT
ejpam-4021	299	10	∇	∇	X
ejpam-4021	299	11	)	)	PUNCT
ejpam-4021	299	12	is	be	AUX
ejpam-4021	299	13	an	an	DET
ejpam-4021	299	14	l	l	NOUN
ejpam-4021	299	15	-	-	ADJ
ejpam-4021	299	16	subgroup	subgroup	NOUN
ejpam-4021	299	17	space	space	NOUN
ejpam-4021	299	18	,	,	PUNCT
ejpam-4021	299	19	where	where	SCONJ
ejpam-4021	299	20	(	(	PUNCT
ejpam-4021	299	21	fg)(x	fg)(x	NOUN
ejpam-4021	299	22	)	)	PUNCT
ejpam-4021	299	23	=	=	PUNCT
ejpam-4021	299	24	f(x)g(x	f(x)g(x	X
ejpam-4021	299	25	)	)	PUNCT
ejpam-4021	299	26	and	and	CCONJ
ejpam-4021	299	27	f−1(x	f−1(x	NOUN
ejpam-4021	299	28	)	)	PUNCT
ejpam-4021	300	1	=	=	PRON
ejpam-4021	300	2	(	(	PUNCT
ejpam-4021	300	3	f(x))−1	f(x))−1	NOUN
ejpam-4021	300	4	.	.	PUNCT
ejpam-4021	301	1	proof	proof	NOUN
ejpam-4021	301	2	.	.	PUNCT
ejpam-4021	302	1	clearly	clearly	ADV
ejpam-4021	302	2	(	(	PUNCT
ejpam-4021	302	3	t	t	PROPN
ejpam-4021	302	4	(	(	PUNCT
ejpam-4021	302	5	g	g	NOUN
ejpam-4021	302	6	)	)	PUNCT
ejpam-4021	302	7	,	,	PUNCT
ejpam-4021	302	8	·	·	PUNCT
ejpam-4021	302	9	)	)	PUNCT
ejpam-4021	302	10	is	be	AUX
ejpam-4021	302	11	a	a	DET
ejpam-4021	302	12	group	group	NOUN
ejpam-4021	302	13	under	under	ADP
ejpam-4021	302	14	composition	composition	NOUN
ejpam-4021	302	15	.	.	PUNCT
ejpam-4021	303	1	define	define	VERB
ejpam-4021	303	2	∇(f	∇(f	NOUN
ejpam-4021	303	3	)	)	PUNCT
ejpam-4021	304	1	=	=	PUNCT
ejpam-4021	304	2	∧	∧	PROPN
ejpam-4021	304	3	x∈g[ν(x)→	x∈g[ν(x)→	PROPN
ejpam-4021	304	4	ν(f(x	ν(f(x	PROPN
ejpam-4021	304	5	)	)	PUNCT
ejpam-4021	304	6	)	)	PUNCT
ejpam-4021	305	1	]	]	PUNCT
ejpam-4021	305	2	,	,	PUNCT
ejpam-4021	305	3	∀f	∀f	PROPN
ejpam-4021	305	4	∈	∈	PROPN
ejpam-4021	305	5	t	t	NOUN
ejpam-4021	305	6	(	(	PUNCT
ejpam-4021	305	7	g	g	NOUN
ejpam-4021	305	8	)	)	PUNCT
ejpam-4021	305	9	(	(	PUNCT
ejpam-4021	305	10	a	a	NOUN
ejpam-4021	305	11	)	)	PUNCT
ejpam-4021	305	12	and	and	CCONJ
ejpam-4021	305	13	∇(−1)(f	∇(−1)(f	NUM
ejpam-4021	305	14	)	)	PUNCT
ejpam-4021	306	1	=	=	PUNCT
ejpam-4021	306	2	∧	∧	PROPN
ejpam-4021	306	3	x∈g[ν(x)→	x∈g[ν(x)→	PROPN
ejpam-4021	306	4	ν(f−1(x	ν(f−1(x	PROPN
ejpam-4021	306	5	)	)	PUNCT
ejpam-4021	306	6	)	)	PUNCT
ejpam-4021	306	7	]	]	PUNCT
ejpam-4021	306	8	,	,	PUNCT
ejpam-4021	306	9	∀f	∀f	PROPN
ejpam-4021	306	10	∈	∈	PROPN
ejpam-4021	306	11	t	t	NOUN
ejpam-4021	306	12	(	(	PUNCT
ejpam-4021	306	13	g	g	NOUN
ejpam-4021	306	14	)	)	PUNCT
ejpam-4021	306	15	(	(	PUNCT
ejpam-4021	306	16	b	b	X
ejpam-4021	306	17	)	)	PUNCT
ejpam-4021	306	18	combining	combine	VERB
ejpam-4021	306	19	(	(	PUNCT
ejpam-4021	306	20	a	a	NOUN
ejpam-4021	306	21	)	)	PUNCT
ejpam-4021	306	22	and	and	CCONJ
ejpam-4021	306	23	(	(	PUNCT
ejpam-4021	306	24	b	b	X
ejpam-4021	306	25	)	)	PUNCT
ejpam-4021	306	26	it	it	PRON
ejpam-4021	306	27	follows	follow	VERB
ejpam-4021	306	28	upon	upon	SCONJ
ejpam-4021	306	29	using	use	VERB
ejpam-4021	306	30	proposition	proposition	NOUN
ejpam-4021	306	31	1(7	1(7	NUM
ejpam-4021	306	32	)	)	PUNCT
ejpam-4021	306	33	that	that	PRON
ejpam-4021	306	34	∇(f	∇(f	NOUN
ejpam-4021	306	35	)	)	PUNCT
ejpam-4021	306	36	=	=	PUNCT
ejpam-4021	307	1	∧	∧	PROPN
ejpam-4021	307	2	x∈g[ν(x)→	x∈g[ν(x)→	PROPN
ejpam-4021	307	3	ν(f(x))∧	ν(f(x))∧	PROPN
ejpam-4021	307	4	ν(f−1(x	ν(f−1(x	PROPN
ejpam-4021	307	5	)	)	PUNCT
ejpam-4021	307	6	)	)	PUNCT
ejpam-4021	307	7	]	]	PUNCT
ejpam-4021	307	8	.	.	PUNCT
ejpam-4021	308	1	then	then	ADV
ejpam-4021	308	2	clearly	clearly	ADV
ejpam-4021	308	3	(	(	PUNCT
ejpam-4021	308	4	lg1	lg1	PROPN
ejpam-4021	308	5	)	)	PUNCT
ejpam-4021	308	6	and	and	CCONJ
ejpam-4021	308	7	(	(	PUNCT
ejpam-4021	308	8	lg3	lg3	NOUN
ejpam-4021	308	9	)	)	PUNCT
ejpam-4021	308	10	are	be	AUX
ejpam-4021	308	11	true	true	ADJ
ejpam-4021	308	12	upon	upon	SCONJ
ejpam-4021	308	13	using	use	VERB
ejpam-4021	308	14	proposition	proposition	NOUN
ejpam-4021	308	15	1(7	1(7	NUM
ejpam-4021	308	16	)	)	PUNCT
ejpam-4021	308	17	and	and	CCONJ
ejpam-4021	308	18	(	(	PUNCT
ejpam-4021	308	19	lg2	lg2	X
ejpam-4021	308	20	)	)	PUNCT
ejpam-4021	308	21	,	,	PUNCT
ejpam-4021	308	22	i.e.	i.e.	X
ejpam-4021	308	23	,	,	PUNCT
ejpam-4021	308	24	∇(idg	∇(idg	PROPN
ejpam-4021	308	25	)	)	PUNCT
ejpam-4021	309	1	=	=	PUNCT
ejpam-4021	309	2	>	>	PUNCT
ejpam-4021	309	3	,	,	PUNCT
ejpam-4021	309	4	and	and	CCONJ
ejpam-4021	309	5	∇(f	∇(f	NOUN
ejpam-4021	309	6	)	)	PUNCT
ejpam-4021	309	7	≤	≤	NOUN
ejpam-4021	309	8	∇(f−1	∇(f−1	NOUN
ejpam-4021	309	9	)	)	PUNCT
ejpam-4021	309	10	;	;	PUNCT
ejpam-4021	309	11	we	we	PRON
ejpam-4021	309	12	only	only	ADV
ejpam-4021	309	13	look	look	VERB
ejpam-4021	309	14	at	at	ADP
ejpam-4021	309	15	(	(	PUNCT
ejpam-4021	309	16	lg2	lg2	X
ejpam-4021	309	17	)	)	PUNCT
ejpam-4021	309	18	.	.	PUNCT
ejpam-4021	310	1	for	for	ADP
ejpam-4021	310	2	,	,	PUNCT
ejpam-4021	310	3	let	let	VERB
ejpam-4021	310	4	f	f	X
ejpam-4021	310	5	,	,	PUNCT
ejpam-4021	310	6	g	g	PROPN
ejpam-4021	310	7	∈	∈	PROPN
ejpam-4021	310	8	t	t	PROPN
ejpam-4021	310	9	(	(	PUNCT
ejpam-4021	310	10	x	x	NOUN
ejpam-4021	310	11	)	)	PUNCT
ejpam-4021	310	12	,	,	PUNCT
ejpam-4021	310	13	then	then	ADV
ejpam-4021	310	14	we	we	PRON
ejpam-4021	310	15	have	have	VERB
ejpam-4021	310	16	∇(f	∇(f	NOUN
ejpam-4021	310	17	)	)	PUNCT
ejpam-4021	310	18	∧∇(g	∧∇(g	NUM
ejpam-4021	310	19	)	)	PUNCT
ejpam-4021	310	20	=	=	PUNCT
ejpam-4021	310	21	∧	∧	PROPN
ejpam-4021	310	22	x∈g[ν(x)→	x∈g[ν(x)→	PROPN
ejpam-4021	310	23	ν(f(x	ν(f(x	PROPN
ejpam-4021	310	24	)	)	PUNCT
ejpam-4021	310	25	)	)	PUNCT
ejpam-4021	311	1	∧	∧	PROPN
ejpam-4021	311	2	ν(f−1(x	ν(f−1(x	PROPN
ejpam-4021	311	3	)	)	PUNCT
ejpam-4021	311	4	)	)	PUNCT
ejpam-4021	311	5	]	]	PUNCT
ejpam-4021	312	1	∧	∧	PROPN
ejpam-4021	312	2	∧	∧	PROPN
ejpam-4021	312	3	x∈g[ν(x)→	x∈g[ν(x)→	PROPN
ejpam-4021	312	4	ν(g(x	ν(g(x	NOUN
ejpam-4021	312	5	)	)	PUNCT
ejpam-4021	312	6	)	)	PUNCT
ejpam-4021	313	1	∧	∧	PROPN
ejpam-4021	313	2	ν(g−1(x	ν(g−1(x	PROPN
ejpam-4021	313	3	)	)	PUNCT
ejpam-4021	313	4	)	)	PUNCT
ejpam-4021	313	5	]	]	PUNCT
ejpam-4021	314	1	≤	≤	NUM
ejpam-4021	314	2	∧	∧	PROPN
ejpam-4021	314	3	x∈g[ν(x)→	x∈g[ν(x)→	PROPN
ejpam-4021	314	4	ν(f(x))∧	ν(f(x))∧	PRON
ejpam-4021	314	5	ν(g(x))∧	ν(g(x))∧	VERB
ejpam-4021	314	6	ν(g−1(x))∧	ν(g−1(x))∧	PROPN
ejpam-4021	314	7	ν(f−1(x	ν(f−1(x	PROPN
ejpam-4021	314	8	)	)	PUNCT
ejpam-4021	314	9	)	)	PUNCT
ejpam-4021	314	10	]	]	PUNCT
ejpam-4021	315	1	≤	≤	NUM
ejpam-4021	315	2	∧	∧	PROPN
ejpam-4021	315	3	x∈g[ν(x)→	x∈g[ν(x)→	PROPN
ejpam-4021	315	4	ν(f(x)g(x))∧	ν(f(x)g(x))∧	X
ejpam-4021	315	5	ν(g−1(x)f−1(x	ν(g−1(x)f−1(x	VERB
ejpam-4021	315	6	)	)	PUNCT
ejpam-4021	315	7	)	)	PUNCT
ejpam-4021	315	8	]	]	PUNCT
ejpam-4021	316	1	=	=	PUNCT
ejpam-4021	316	2	∧	∧	NOUN
ejpam-4021	316	3	x∈g[ν(x)→	x∈g[ν(x)→	PROPN
ejpam-4021	316	4	ν(fg(x	ν(fg(x	NOUN
ejpam-4021	316	5	)	)	PUNCT
ejpam-4021	316	6	)	)	PUNCT
ejpam-4021	317	1	∧	∧	NOUN
ejpam-4021	317	2	ν((fg)−1(x	ν((fg)−1(x	NOUN
ejpam-4021	317	3	)	)	PUNCT
ejpam-4021	317	4	)	)	PUNCT
ejpam-4021	317	5	]	]	PUNCT
ejpam-4021	318	1	=	=	PUNCT
ejpam-4021	318	2	∇(fg	∇(fg	NOUN
ejpam-4021	318	3	)	)	PUNCT
ejpam-4021	318	4	.	.	PUNCT
ejpam-4021	319	1	t	t	PROPN
ejpam-4021	319	2	m	m	PROPN
ejpam-4021	319	3	g	g	NOUN
ejpam-4021	319	4	ahsanullah	ahsanullah	NOUN
ejpam-4021	319	5	,	,	PUNCT
ejpam-4021	319	6	fawzi	fawzi	PROPN
ejpam-4021	319	7	al	al	PROPN
ejpam-4021	319	8	-	-	PUNCT
ejpam-4021	319	9	thukair	thukair	NOUN
ejpam-4021	319	10	/	/	SYM
ejpam-4021	319	11	eur	eur	NOUN
ejpam-4021	319	12	.	.	PUNCT
ejpam-4021	320	1	j.	j.	PROPN
ejpam-4021	320	2	pure	pure	PROPN
ejpam-4021	320	3	appl	appl	PROPN
ejpam-4021	320	4	.	.	PROPN
ejpam-4021	320	5	math	math	PROPN
ejpam-4021	320	6	,	,	PUNCT
ejpam-4021	320	7	14	14	NUM
ejpam-4021	320	8	(	(	PUNCT
ejpam-4021	320	9	3	3	NUM
ejpam-4021	320	10	)	)	PUNCT
ejpam-4021	320	11	(	(	PUNCT
ejpam-4021	320	12	2021	2021	NUM
ejpam-4021	320	13	)	)	PUNCT
ejpam-4021	320	14	,	,	PUNCT
ejpam-4021	320	15	949	949	NUM
ejpam-4021	320	16	-	-	SYM
ejpam-4021	320	17	968	968	NUM
ejpam-4021	320	18	960	960	NUM
ejpam-4021	320	19	definition	definition	NOUN
ejpam-4021	320	20	14	14	NUM
ejpam-4021	320	21	.	.	PUNCT
ejpam-4021	321	1	[	[	X
ejpam-4021	321	2	23	23	NUM
ejpam-4021	321	3	,	,	PUNCT
ejpam-4021	321	4	25	25	NUM
ejpam-4021	321	5	]	]	PUNCT
ejpam-4021	321	6	an	an	DET
ejpam-4021	321	7	l	l	NOUN
ejpam-4021	321	8	-	-	PUNCT
ejpam-4021	321	9	valued	value	VERB
ejpam-4021	321	10	subgroup	subgroup	NOUN
ejpam-4021	321	11	is	be	AUX
ejpam-4021	321	12	called	call	VERB
ejpam-4021	321	13	l	l	ADV
ejpam-4021	321	14	-	-	PUNCT
ejpam-4021	321	15	valued	value	VERB
ejpam-4021	321	16	normal	normal	ADJ
ejpam-4021	321	17	subgroup	subgroup	NOUN
ejpam-4021	321	18	if	if	SCONJ
ejpam-4021	321	19	for	for	ADP
ejpam-4021	321	20	all	all	DET
ejpam-4021	321	21	x	x	NOUN
ejpam-4021	321	22	,	,	PUNCT
ejpam-4021	321	23	y	y	PROPN
ejpam-4021	321	24	∈	∈	PROPN
ejpam-4021	321	25	g	g	PROPN
ejpam-4021	321	26	if	if	SCONJ
ejpam-4021	321	27	it	it	PRON
ejpam-4021	321	28	satisfies	satisfy	VERB
ejpam-4021	321	29	one	one	NUM
ejpam-4021	321	30	of	of	ADP
ejpam-4021	321	31	the	the	DET
ejpam-4021	321	32	following	follow	VERB
ejpam-4021	321	33	equivalent	equivalent	ADJ
ejpam-4021	321	34	conditions	condition	NOUN
ejpam-4021	321	35	:	:	PUNCT
ejpam-4021	321	36	(	(	PUNCT
ejpam-4021	321	37	1	1	X
ejpam-4021	321	38	)	)	PUNCT
ejpam-4021	321	39	ν(xy	ν(xy	NUM
ejpam-4021	321	40	)	)	PUNCT
ejpam-4021	321	41	=	=	SYM
ejpam-4021	321	42	ν(yx	ν(yx	PROPN
ejpam-4021	321	43	)	)	PUNCT
ejpam-4021	321	44	;	;	PUNCT
ejpam-4021	321	45	(	(	PUNCT
ejpam-4021	321	46	2	2	X
ejpam-4021	321	47	)	)	PUNCT
ejpam-4021	321	48	ν(xyx−1	ν(xyx−1	NOUN
ejpam-4021	321	49	)	)	PUNCT
ejpam-4021	321	50	≥	≥	NOUN
ejpam-4021	321	51	ν(y	ν(y	PROPN
ejpam-4021	321	52	)	)	PUNCT
ejpam-4021	321	53	;	;	PUNCT
ejpam-4021	321	54	(	(	PUNCT
ejpam-4021	321	55	3	3	X
ejpam-4021	321	56	)	)	PUNCT
ejpam-4021	321	57	ν(xyx−1	ν(xyx−1	NOUN
ejpam-4021	321	58	)	)	PUNCT
ejpam-4021	321	59	=	=	SYM
ejpam-4021	321	60	ν(y	ν(y	PROPN
ejpam-4021	321	61	)	)	PUNCT
ejpam-4021	321	62	.	.	PUNCT
ejpam-4021	322	1	definition	definition	NOUN
ejpam-4021	322	2	15	15	NUM
ejpam-4021	322	3	.	.	PUNCT
ejpam-4021	323	1	a	a	DET
ejpam-4021	323	2	mapping	mapping	NOUN
ejpam-4021	323	3	`	`	PUNCT
ejpam-4021	323	4	:	:	PUNCT
ejpam-4021	323	5	lx	lx	ADP
ejpam-4021	323	6	−→	−→	NOUN
ejpam-4021	323	7	lx	lx	NOUN
ejpam-4021	323	8	is	be	AUX
ejpam-4021	323	9	said	say	VERB
ejpam-4021	323	10	to	to	PART
ejpam-4021	323	11	be	be	AUX
ejpam-4021	323	12	an	an	DET
ejpam-4021	323	13	l	l	NOUN
ejpam-4021	323	14	-	-	PUNCT
ejpam-4021	323	15	valuedclosure	valuedclosure	NOUN
ejpam-4021	323	16	operation	operation	NOUN
ejpam-4021	323	17	on	on	ADP
ejpam-4021	323	18	x	x	SYM
ejpam-4021	323	19	if	if	SCONJ
ejpam-4021	323	20	the	the	DET
ejpam-4021	323	21	following	follow	VERB
ejpam-4021	323	22	conditions	condition	NOUN
ejpam-4021	323	23	hold	hold	VERB
ejpam-4021	323	24	for	for	ADP
ejpam-4021	323	25	every	every	DET
ejpam-4021	323	26	ν	ν	NOUN
ejpam-4021	323	27	,	,	PUNCT
ejpam-4021	323	28	µ	µ	X
ejpam-4021	323	29	∈	∈	NOUN
ejpam-4021	323	30	lx	lx	NOUN
ejpam-4021	323	31	:	:	PUNCT
ejpam-4021	323	32	(	(	PUNCT
ejpam-4021	323	33	1	1	X
ejpam-4021	323	34	)	)	PUNCT
ejpam-4021	323	35	ν	ν	NOUN
ejpam-4021	323	36	≤	≤	NUM
ejpam-4021	323	37	`	`	PUNCT
ejpam-4021	323	38	(	(	PUNCT
ejpam-4021	323	39	ν	ν	NOUN
ejpam-4021	323	40	)	)	PUNCT
ejpam-4021	323	41	;	;	PUNCT
ejpam-4021	323	42	(	(	PUNCT
ejpam-4021	323	43	2	2	X
ejpam-4021	323	44	)	)	PUNCT
ejpam-4021	323	45	ν	ν	NOUN
ejpam-4021	323	46	≤	≤	NOUN
ejpam-4021	323	47	µ	µ	X
ejpam-4021	323	48	implies	imply	VERB
ejpam-4021	323	49	`	`	PUNCT
ejpam-4021	323	50	(	(	PUNCT
ejpam-4021	323	51	ν	ν	NOUN
ejpam-4021	323	52	)	)	PUNCT
ejpam-4021	323	53	≤	≤	NUM
ejpam-4021	323	54	`	`	PUNCT
ejpam-4021	323	55	(	(	PUNCT
ejpam-4021	323	56	µ	µ	NOUN
ejpam-4021	323	57	)	)	PUNCT
ejpam-4021	323	58	;	;	PUNCT
ejpam-4021	323	59	(	(	PUNCT
ejpam-4021	323	60	3	3	X
ejpam-4021	323	61	)	)	PUNCT
ejpam-4021	323	62	`	`	PUNCT
ejpam-4021	323	63	(	(	PUNCT
ejpam-4021	323	64	`	`	PUNCT
ejpam-4021	323	65	(	(	PUNCT
ejpam-4021	323	66	ν	ν	NOUN
ejpam-4021	323	67	)	)	PUNCT
ejpam-4021	323	68	)	)	PUNCT
ejpam-4021	324	1	=	=	PUNCT
ejpam-4021	324	2	`	`	PUNCT
ejpam-4021	324	3	(	(	PUNCT
ejpam-4021	324	4	ν	ν	NOUN
ejpam-4021	324	5	)	)	PUNCT
ejpam-4021	324	6	;	;	PUNCT
ejpam-4021	324	7	(	(	PUNCT
ejpam-4021	324	8	4	4	X
ejpam-4021	324	9	)	)	PUNCT
ejpam-4021	324	10	`	`	PUNCT
ejpam-4021	324	11	(	(	PUNCT
ejpam-4021	324	12	>	>	X
ejpam-4021	324	13	∅	∅	NOUN
ejpam-4021	324	14	)	)	PUNCT
ejpam-4021	324	15	=	=	SYM
ejpam-4021	324	16	⊥.	⊥.	NUM
ejpam-4021	324	17	the	the	DET
ejpam-4021	324	18	pair	pair	NOUN
ejpam-4021	324	19	(	(	PUNCT
ejpam-4021	324	20	x	x	X
ejpam-4021	324	21	,	,	PUNCT
ejpam-4021	324	22	`	`	PUNCT
ejpam-4021	324	23	)	)	PUNCT
ejpam-4021	324	24	is	be	AUX
ejpam-4021	324	25	called	call	VERB
ejpam-4021	324	26	is	be	AUX
ejpam-4021	324	27	called	call	VERB
ejpam-4021	324	28	an	an	DET
ejpam-4021	324	29	l	l	NOUN
ejpam-4021	324	30	-	-	PUNCT
ejpam-4021	324	31	valued	value	VERB
ejpam-4021	324	32	closure	closure	NOUN
ejpam-4021	324	33	space	space	NOUN
ejpam-4021	324	34	and	and	CCONJ
ejpam-4021	324	35	ν	ν	NOUN
ejpam-4021	324	36	∈	∈	NOUN
ejpam-4021	324	37	lx	lx	NOUN
ejpam-4021	324	38	is	be	AUX
ejpam-4021	324	39	called	call	VERB
ejpam-4021	324	40	closed	closed	ADJ
ejpam-4021	324	41	if	if	SCONJ
ejpam-4021	324	42	ν	ν	NOUN
ejpam-4021	324	43	=	=	SYM
ejpam-4021	324	44	`	`	PUNCT
ejpam-4021	324	45	(	(	PUNCT
ejpam-4021	324	46	ν	ν	NOUN
ejpam-4021	324	47	)	)	PUNCT
ejpam-4021	324	48	.	.	PUNCT
ejpam-4021	325	1	note	note	VERB
ejpam-4021	325	2	that	that	SCONJ
ejpam-4021	325	3	(	(	PUNCT
ejpam-4021	325	4	2	2	X
ejpam-4021	325	5	)	)	PUNCT
ejpam-4021	325	6	implies	imply	VERB
ejpam-4021	325	7	`	`	PUNCT
ejpam-4021	325	8	(	(	PUNCT
ejpam-4021	325	9	ν	ν	NOUN
ejpam-4021	325	10	)	)	PUNCT
ejpam-4021	325	11	∨	∨	NUM
ejpam-4021	325	12	`	`	PUNCT
ejpam-4021	325	13	(	(	PUNCT
ejpam-4021	325	14	µ	µ	NOUN
ejpam-4021	325	15	)	)	PUNCT
ejpam-4021	325	16	≤	≤	NOUN
ejpam-4021	325	17	`	`	PUNCT
ejpam-4021	325	18	(	(	PUNCT
ejpam-4021	325	19	ν	ν	PROPN
ejpam-4021	325	20	∨	∨	NUM
ejpam-4021	325	21	µ	µ	NUM
ejpam-4021	325	22	)	)	PUNCT
ejpam-4021	325	23	,	,	PUNCT
ejpam-4021	325	24	for	for	ADP
ejpam-4021	325	25	any	any	DET
ejpam-4021	325	26	ν	ν	NOUN
ejpam-4021	325	27	,	,	PUNCT
ejpam-4021	325	28	µ	µ	X
ejpam-4021	325	29	∈	∈	NOUN
ejpam-4021	325	30	lx	lx	NOUN
ejpam-4021	325	31	.	.	PUNCT
ejpam-4021	326	1	the	the	DET
ejpam-4021	326	2	category	category	NOUN
ejpam-4021	326	3	of	of	ADP
ejpam-4021	326	4	all	all	DET
ejpam-4021	326	5	l	l	NOUN
ejpam-4021	326	6	-	-	PUNCT
ejpam-4021	326	7	valued	value	VERB
ejpam-4021	326	8	closure	closure	NOUN
ejpam-4021	326	9	spaces	space	NOUN
ejpam-4021	326	10	and	and	CCONJ
ejpam-4021	326	11	all	all	DET
ejpam-4021	326	12	closure	closure	NOUN
ejpam-4021	326	13	preserving	preserve	VERB
ejpam-4021	326	14	mappings	mapping	NOUN
ejpam-4021	326	15	,	,	PUNCT
ejpam-4021	326	16	i.e.	i.e.	X
ejpam-4021	326	17	,	,	PUNCT
ejpam-4021	326	18	mappings	mapping	NOUN
ejpam-4021	326	19	f	f	NOUN
ejpam-4021	326	20	:	:	PUNCT
ejpam-4021	326	21	(	(	PUNCT
ejpam-4021	326	22	x	x	X
ejpam-4021	326	23	,	,	PUNCT
ejpam-4021	326	24	`	`	PUNCT
ejpam-4021	326	25	)	)	PUNCT
ejpam-4021	326	26	−→	−→	NOUN
ejpam-4021	326	27	(	(	PUNCT
ejpam-4021	326	28	y	y	NOUN
ejpam-4021	326	29	,	,	PUNCT
ejpam-4021	326	30	`	`	PUNCT
ejpam-4021	326	31	)	)	PUNCT
ejpam-4021	326	32	that	that	PRON
ejpam-4021	326	33	satisfy	satisfy	VERB
ejpam-4021	326	34	f→(`(ν	f→(`(ν	NOUN
ejpam-4021	326	35	)	)	PUNCT
ejpam-4021	326	36	)	)	PUNCT
ejpam-4021	326	37	≤	≤	NUM
ejpam-4021	326	38	`	`	PUNCT
ejpam-4021	326	39	(	(	PUNCT
ejpam-4021	326	40	f→(ν	f→(ν	PROPN
ejpam-4021	326	41	)	)	PUNCT
ejpam-4021	326	42	)	)	PUNCT
ejpam-4021	326	43	for	for	ADP
ejpam-4021	326	44	all	all	PRON
ejpam-4021	326	45	ν	ν	NOUN
ejpam-4021	326	46	∈	∈	NOUN
ejpam-4021	326	47	lx	lx	NOUN
ejpam-4021	326	48	,	,	PUNCT
ejpam-4021	326	49	is	be	AUX
ejpam-4021	326	50	denoted	denote	VERB
ejpam-4021	326	51	by	by	ADP
ejpam-4021	326	52	l	l	NOUN
ejpam-4021	326	53	-	-	NOUN
ejpam-4021	326	54	cls	cls	NOUN
ejpam-4021	326	55	.	.	PUNCT
ejpam-4021	327	1	lemma	lemma	PROPN
ejpam-4021	327	2	6	6	NUM
ejpam-4021	327	3	.	.	PUNCT
ejpam-4021	328	1	we	we	PRON
ejpam-4021	328	2	have	have	VERB
ejpam-4021	328	3	the	the	DET
ejpam-4021	328	4	following	follow	VERB
ejpam-4021	328	5	forgetful	forgetful	ADJ
ejpam-4021	328	6	functor	functor	NOUN
ejpam-4021	328	7	forgetting	forget	VERB
ejpam-4021	328	8	l	l	ADV
ejpam-4021	328	9	-	-	PUNCT
ejpam-4021	328	10	valued	value	VERB
ejpam-4021	328	11	closure	closure	NOUN
ejpam-4021	328	12	structure	structure	NOUN
ejpam-4021	328	13	:	:	PUNCT
ejpam-4021	328	14	u	u	NOUN
ejpam-4021	328	15	:	:	PUNCT
ejpam-4021	328	16			PUNCT
ejpam-4021	328	17	l	l	NOUN
ejpam-4021	328	18	-	-	NOUN
ejpam-4021	328	19	cls	cls	NOUN
ejpam-4021	328	20	−→	−→	NOUN
ejpam-4021	328	21	set(l	set(l	PROPN
ejpam-4021	328	22	)	)	PUNCT
ejpam-4021	328	23	(	(	PUNCT
ejpam-4021	328	24	x	x	X
ejpam-4021	328	25	,	,	PUNCT
ejpam-4021	328	26	`	`	PUNCT
ejpam-4021	328	27	)	)	PUNCT
ejpam-4021	328	28	7−→	7−→	NOUN
ejpam-4021	328	29	(	(	PUNCT
ejpam-4021	328	30	x	x	X
ejpam-4021	328	31	,	,	PUNCT
ejpam-4021	328	32	ν	ν	NOUN
ejpam-4021	328	33	)	)	PUNCT
ejpam-4021	329	1	f	f	PROPN
ejpam-4021	329	2	7−→	7−→	NOUN
ejpam-4021	329	3	f	f	PROPN
ejpam-4021	329	4	where	where	SCONJ
ejpam-4021	329	5	u((x	u((x	VERB
ejpam-4021	329	6	,	,	PUNCT
ejpam-4021	329	7	`	`	PUNCT
ejpam-4021	329	8	)	)	PUNCT
ejpam-4021	329	9	)	)	PUNCT
ejpam-4021	330	1	=	=	PRON
ejpam-4021	330	2	(	(	PUNCT
ejpam-4021	330	3	x	x	X
ejpam-4021	330	4	,	,	PUNCT
ejpam-4021	330	5	ν	ν	NOUN
ejpam-4021	330	6	)	)	PUNCT
ejpam-4021	330	7	and	and	CCONJ
ejpam-4021	330	8	for	for	ADP
ejpam-4021	330	9	f	f	PROPN
ejpam-4021	330	10	:	:	PUNCT
ejpam-4021	330	11	x	x	PUNCT
ejpam-4021	330	12	−→	−→	NOUN
ejpam-4021	330	13	y	y	PROPN
ejpam-4021	330	14	,	,	PUNCT
ejpam-4021	330	15	u(f	u(f	PROPN
ejpam-4021	330	16	)	)	PUNCT
ejpam-4021	330	17	=	=	SYM
ejpam-4021	330	18	f	f	PROPN
ejpam-4021	330	19	,	,	PUNCT
ejpam-4021	330	20	f→	f→	PROPN
ejpam-4021	330	21	:	:	PUNCT
ejpam-4021	330	22	lx	lx	NOUN
ejpam-4021	330	23	−→	−→	NOUN
ejpam-4021	330	24	ly	ly	X
ejpam-4021	330	25	,	,	PUNCT
ejpam-4021	330	26	and	and	CCONJ
ejpam-4021	330	27	u(f	u(f	NOUN
ejpam-4021	330	28	)	)	PUNCT
ejpam-4021	330	29	yields	yield	VERB
ejpam-4021	330	30	an	an	DET
ejpam-4021	330	31	set(l)-morphism	set(l)-morphism	NOUN
ejpam-4021	330	32	.	.	PUNCT
ejpam-4021	331	1	let	let	VERB
ejpam-4021	331	2	x	x	PUNCT
ejpam-4021	331	3	∈	∈	PROPN
ejpam-4021	331	4	|set|	|set|	NOUN
ejpam-4021	331	5	and	and	CCONJ
ejpam-4021	331	6	let	let	VERB
ejpam-4021	331	7	ω	ω	PROPN
ejpam-4021	331	8	⊂	⊂	PROPN
ejpam-4021	331	9	lx	lx	AUX
ejpam-4021	331	10	be	be	AUX
ejpam-4021	331	11	a	a	DET
ejpam-4021	331	12	collection	collection	NOUN
ejpam-4021	331	13	of	of	ADP
ejpam-4021	331	14	l	l	NOUN
ejpam-4021	331	15	-	-	NOUN
ejpam-4021	331	16	subsets	subset	NOUN
ejpam-4021	331	17	of	of	ADP
ejpam-4021	331	18	x.	x.	NOUN
ejpam-4021	331	19	then	then	ADV
ejpam-4021	331	20	we	we	PRON
ejpam-4021	331	21	call	call	VERB
ejpam-4021	331	22	ω	ω	ADP
ejpam-4021	331	23	a	a	DET
ejpam-4021	331	24	latticevalued	latticevalue	VERB
ejpam-4021	331	25	moore	moore	NOUN
ejpam-4021	331	26	collection	collection	NOUN
ejpam-4021	331	27	if	if	SCONJ
ejpam-4021	331	28	every	every	DET
ejpam-4021	331	29	intersection	intersection	NOUN
ejpam-4021	331	30	of	of	ADP
ejpam-4021	331	31	members	member	NOUN
ejpam-4021	331	32	of	of	ADP
ejpam-4021	331	33	ω	ω	PROPN
ejpam-4021	331	34	belongs	belong	VERB
ejpam-4021	331	35	to	to	ADP
ejpam-4021	331	36	ω	ω	NUM
ejpam-4021	331	37	,	,	PUNCT
ejpam-4021	331	38	i.e.	i.e.	ADV
ejpam-4021	331	39	,	,	PUNCT
ejpam-4021	331	40	given	give	VERB
ejpam-4021	331	41	a	a	DET
ejpam-4021	331	42	family	family	NOUN
ejpam-4021	331	43	(	(	PUNCT
ejpam-4021	331	44	νj)j∈j	νj)j∈j	NUM
ejpam-4021	331	45	of	of	ADP
ejpam-4021	331	46	l	l	NOUN
ejpam-4021	331	47	-	-	NOUN
ejpam-4021	331	48	subsets	subset	NOUN
ejpam-4021	331	49	:	:	PUNCT
ejpam-4021	331	50	∀j	∀j	PROPN
ejpam-4021	331	51	∈	∈	PROPN
ejpam-4021	331	52	j	j	PROPN
ejpam-4021	331	53	,	,	PUNCT
ejpam-4021	331	54	νj	νj	PROPN
ejpam-4021	331	55	∈	∈	PROPN
ejpam-4021	331	56	ω	ω	NOUN
ejpam-4021	332	1	=	=	NOUN
ejpam-4021	332	2	⇒	⇒	NOUN
ejpam-4021	332	3	∧	∧	PROPN
ejpam-4021	332	4	j∈j	j∈j	NOUN
ejpam-4021	332	5	νj	νj	PROPN
ejpam-4021	332	6	∈	∈	PROPN
ejpam-4021	332	7	ω	ω	NOUN
ejpam-4021	332	8	.	.	PUNCT
ejpam-4021	333	1	if	if	SCONJ
ejpam-4021	333	2	ω	ω	PROPN
ejpam-4021	333	3	is	be	AUX
ejpam-4021	333	4	a	a	DET
ejpam-4021	333	5	lattice	lattice	NOUN
ejpam-4021	333	6	-	-	PUNCT
ejpam-4021	333	7	valued	value	VERB
ejpam-4021	333	8	moore	moore	NOUN
ejpam-4021	333	9	collection	collection	NOUN
ejpam-4021	333	10	containing	contain	VERB
ejpam-4021	333	11	>	>	SYM
ejpam-4021	333	12	∅	∅	NOUN
ejpam-4021	333	13	,	,	PUNCT
ejpam-4021	333	14	then	then	ADV
ejpam-4021	333	15	if	if	SCONJ
ejpam-4021	333	16	`	`	PUNCT
ejpam-4021	333	17	(	(	PUNCT
ejpam-4021	333	18	µ)ω	µ)ω	X
ejpam-4021	333	19	=	=	PUNCT
ejpam-4021	333	20	∧	∧	NOUN
ejpam-4021	333	21	{	{	PUNCT
ejpam-4021	333	22	ν	ν	PROPN
ejpam-4021	333	23	∈	∈	PROPN
ejpam-4021	333	24	ω	ω	PROPN
ejpam-4021	333	25	:	:	PUNCT
ejpam-4021	333	26	µ	µ	NOUN
ejpam-4021	333	27	≤	≤	NUM
ejpam-4021	333	28	ν	ν	NOUN
ejpam-4021	333	29	,	,	PUNCT
ejpam-4021	333	30	ν	ν	PROPN
ejpam-4021	333	31	is	be	AUX
ejpam-4021	333	32	l	l	ADV
ejpam-4021	333	33	-	-	PUNCT
ejpam-4021	333	34	valued	value	VERB
ejpam-4021	333	35	closed	close	VERB
ejpam-4021	333	36	set	set	NOUN
ejpam-4021	333	37	}	}	PUNCT
ejpam-4021	333	38	,	,	PUNCT
ejpam-4021	333	39	i.e.	i.e.	X
ejpam-4021	333	40	if	if	SCONJ
ejpam-4021	333	41	`	`	PUNCT
ejpam-4021	333	42	(	(	PUNCT
ejpam-4021	333	43	µ	µ	NOUN
ejpam-4021	333	44	)	)	PUNCT
ejpam-4021	333	45	is	be	AUX
ejpam-4021	333	46	the	the	DET
ejpam-4021	333	47	intersection	intersection	NOUN
ejpam-4021	333	48	of	of	ADP
ejpam-4021	333	49	all	all	DET
ejpam-4021	333	50	l	l	ADV
ejpam-4021	333	51	-	-	PUNCT
ejpam-4021	333	52	valued	value	VERB
ejpam-4021	333	53	closed	closed	ADJ
ejpam-4021	333	54	sets	set	NOUN
ejpam-4021	333	55	that	that	PRON
ejpam-4021	333	56	contain	contain	VERB
ejpam-4021	333	57	µ	µ	NUM
ejpam-4021	333	58	,	,	PUNCT
ejpam-4021	333	59	then	then	ADV
ejpam-4021	333	60	`	`	PUNCT
ejpam-4021	333	61	is	be	AUX
ejpam-4021	333	62	an	an	DET
ejpam-4021	333	63	l	l	NOUN
ejpam-4021	333	64	-	-	PUNCT
ejpam-4021	333	65	valued	value	VERB
ejpam-4021	333	66	closure	closure	NOUN
ejpam-4021	333	67	operator	operator	NOUN
ejpam-4021	333	68	.	.	PUNCT
ejpam-4021	334	1	we	we	PRON
ejpam-4021	334	2	refer	refer	VERB
ejpam-4021	334	3	to	to	ADP
ejpam-4021	334	4	birkhoff	birkhoff	NOUN
ejpam-4021	334	5	[	[	X
ejpam-4021	334	6	9	9	NUM
ejpam-4021	334	7	]	]	PUNCT
ejpam-4021	334	8	,	,	PUNCT
ejpam-4021	334	9	and	and	CCONJ
ejpam-4021	334	10	schechter	schechter	NOUN
ejpam-4021	335	1	[	[	X
ejpam-4021	335	2	31	31	NUM
ejpam-4021	335	3	]	]	PUNCT
ejpam-4021	335	4	,	,	PUNCT
ejpam-4021	335	5	for	for	ADP
ejpam-4021	335	6	the	the	DET
ejpam-4021	335	7	classical	classical	ADJ
ejpam-4021	335	8	notion	notion	NOUN
ejpam-4021	335	9	of	of	ADP
ejpam-4021	335	10	moore	moore	PROPN
ejpam-4021	335	11	collection	collection	PROPN
ejpam-4021	335	12	.	.	PUNCT
ejpam-4021	336	1	example	example	NOUN
ejpam-4021	337	1	4	4	NUM
ejpam-4021	337	2	.	.	PUNCT
ejpam-4021	337	3	l	l	NOUN
ejpam-4021	337	4	-	-	PUNCT
ejpam-4021	337	5	valued	value	VERB
ejpam-4021	337	6	subgroups	subgroup	NOUN
ejpam-4021	337	7	of	of	ADP
ejpam-4021	337	8	a	a	DET
ejpam-4021	337	9	group	group	NOUN
ejpam-4021	337	10	(	(	PUNCT
ejpam-4021	337	11	g	g	NOUN
ejpam-4021	337	12	,	,	PUNCT
ejpam-4021	337	13	·	·	PUNCT
ejpam-4021	337	14	)	)	PUNCT
ejpam-4021	337	15	form	form	VERB
ejpam-4021	337	16	a	a	DET
ejpam-4021	337	17	lattice	lattice	NOUN
ejpam-4021	337	18	-	-	PUNCT
ejpam-4021	337	19	valued	value	VERB
ejpam-4021	337	20	moore	moore	PROPN
ejpam-4021	337	21	collection	collection	NOUN
ejpam-4021	337	22	;	;	PUNCT
ejpam-4021	337	23	this	this	PRON
ejpam-4021	337	24	is	be	AUX
ejpam-4021	337	25	so	so	ADV
ejpam-4021	337	26	,	,	PUNCT
ejpam-4021	337	27	since	since	SCONJ
ejpam-4021	337	28	arbitrary	arbitrary	ADJ
ejpam-4021	337	29	intersection	intersection	NOUN
ejpam-4021	337	30	of	of	ADP
ejpam-4021	337	31	l	l	NOUN
ejpam-4021	337	32	-	-	PUNCT
ejpam-4021	337	33	valued	value	VERB
ejpam-4021	337	34	subgroups	subgroup	NOUN
ejpam-4021	337	35	is	be	AUX
ejpam-4021	337	36	again	again	ADV
ejpam-4021	337	37	an	an	DET
ejpam-4021	337	38	l	l	NOUN
ejpam-4021	337	39	-	-	PUNCT
ejpam-4021	337	40	valued	value	VERB
ejpam-4021	337	41	subgroup	subgroup	NOUN
ejpam-4021	337	42	,	,	PUNCT
ejpam-4021	337	43	cf	cf	NOUN
ejpam-4021	337	44	.	.	PUNCT
ejpam-4021	338	1	[	[	X
ejpam-4021	338	2	11	11	NUM
ejpam-4021	338	3	]	]	PUNCT
ejpam-4021	338	4	,	,	PUNCT
ejpam-4021	338	5	pp	pp	ADJ
ejpam-4021	338	6	.	.	PUNCT
ejpam-4021	338	7	115	115	NUM
ejpam-4021	338	8	.	.	PUNCT
ejpam-4021	339	1	in	in	ADP
ejpam-4021	339	2	fact	fact	NOUN
ejpam-4021	339	3	,	,	PUNCT
ejpam-4021	339	4	if	if	SCONJ
ejpam-4021	339	5	we	we	PRON
ejpam-4021	339	6	let	let	VERB
ejpam-4021	339	7	µ	µ	X
ejpam-4021	339	8	=	=	SYM
ejpam-4021	339	9	∧	∧	PROPN
ejpam-4021	339	10	j∈j	j∈j	NOUN
ejpam-4021	339	11	νj	νj	NOUN
ejpam-4021	339	12	,	,	PUNCT
ejpam-4021	339	13	then	then	ADV
ejpam-4021	339	14	we	we	PRON
ejpam-4021	339	15	can	can	AUX
ejpam-4021	339	16	easily	easily	ADV
ejpam-4021	339	17	verify	verify	VERB
ejpam-4021	339	18	the	the	DET
ejpam-4021	339	19	definition	definition	NOUN
ejpam-4021	339	20	13	13	NUM
ejpam-4021	339	21	.	.	PUNCT
ejpam-4021	340	1	in	in	ADP
ejpam-4021	340	2	fact	fact	NOUN
ejpam-4021	340	3	,	,	PUNCT
ejpam-4021	340	4	(	(	PUNCT
ejpam-4021	340	5	lg1	lg1	PROPN
ejpam-4021	340	6	)	)	PUNCT
ejpam-4021	340	7	µ(e	µ(e	PROPN
ejpam-4021	340	8	)	)	PUNCT
ejpam-4021	341	1	=	=	SYM
ejpam-4021	341	2	∧	∧	NOUN
ejpam-4021	341	3	νj(e	νj(e	PUNCT
ejpam-4021	341	4	)	)	PUNCT
ejpam-4021	342	1	=	=	SYM
ejpam-4021	342	2	>	>	X
ejpam-4021	342	3	for	for	ADP
ejpam-4021	342	4	all	all	DET
ejpam-4021	342	5	j	j	PROPN
ejpam-4021	342	6	∈	∈	PROPN
ejpam-4021	342	7	j	j	PROPN
ejpam-4021	342	8	;	;	PUNCT
ejpam-4021	342	9	(	(	PUNCT
ejpam-4021	342	10	lg2	lg2	X
ejpam-4021	342	11	)	)	PUNCT
ejpam-4021	342	12	upon	upon	SCONJ
ejpam-4021	342	13	using	use	VERB
ejpam-4021	342	14	proposition	proposition	NOUN
ejpam-4021	342	15	1(10	1(10	NUM
ejpam-4021	342	16	)	)	PUNCT
ejpam-4021	342	17	,	,	PUNCT
ejpam-4021	342	18	we	we	PRON
ejpam-4021	342	19	have	have	VERB
ejpam-4021	342	20	:	:	PUNCT
ejpam-4021	342	21	µ(x)∗µ(y	µ(x)∗µ(y	NOUN
ejpam-4021	342	22	)	)	PUNCT
ejpam-4021	342	23	=	=	SYM
ejpam-4021	342	24	(	(	PUNCT
ejpam-4021	342	25	∧	∧	PROPN
ejpam-4021	342	26	j∈j	j∈j	NOUN
ejpam-4021	342	27	νj(x))∗	νj(x))∗	PROPN
ejpam-4021	342	28	(	(	PUNCT
ejpam-4021	342	29	∧	∧	PROPN
ejpam-4021	342	30	j∈j	j∈j	NOUN
ejpam-4021	342	31	νj(y	νj(y	PUNCT
ejpam-4021	342	32	)	)	PUNCT
ejpam-4021	342	33	)	)	PUNCT
ejpam-4021	343	1	≤	≤	NUM
ejpam-4021	343	2	∧	∧	PROPN
ejpam-4021	343	3	j∈j	j∈j	NOUN
ejpam-4021	343	4	(	(	PUNCT
ejpam-4021	343	5	νj(x	νj(x	NOUN
ejpam-4021	343	6	)	)	PUNCT
ejpam-4021	343	7	∗	∗	NOUN
ejpam-4021	343	8	νj(y	νj(y	NUM
ejpam-4021	343	9	)	)	PUNCT
ejpam-4021	343	10	)	)	PUNCT
ejpam-4021	344	1	≤	≤	NUM
ejpam-4021	344	2	∧	∧	PROPN
ejpam-4021	344	3	j∈j	j∈j	NOUN
ejpam-4021	344	4	νj(xy	νj(xy	PROPN
ejpam-4021	344	5	)	)	PUNCT
ejpam-4021	344	6	=	=	PUNCT
ejpam-4021	345	1	µ(xy	µ(xy	PROPN
ejpam-4021	345	2	)	)	PUNCT
ejpam-4021	345	3	,	,	PUNCT
ejpam-4021	345	4	so	so	ADV
ejpam-4021	345	5	,	,	PUNCT
ejpam-4021	345	6	µ(x	µ(x	ADJ
ejpam-4021	345	7	)	)	PUNCT
ejpam-4021	345	8	∗µ(y	∗µ(y	PROPN
ejpam-4021	345	9	)	)	PUNCT
ejpam-4021	345	10	≤	≤	PROPN
ejpam-4021	345	11	µ(xy	µ(xy	PROPN
ejpam-4021	345	12	)	)	PUNCT
ejpam-4021	345	13	;	;	PUNCT
ejpam-4021	345	14	(	(	PUNCT
ejpam-4021	345	15	lg3	lg3	NOUN
ejpam-4021	345	16	)	)	PUNCT
ejpam-4021	345	17	µ	µ	X
ejpam-4021	345	18	=	=	SYM
ejpam-4021	345	19	∧	∧	PROPN
ejpam-4021	345	20	j∈j(νj(x	j∈j(νj(x	PROPN
ejpam-4021	345	21	)	)	PUNCT
ejpam-4021	345	22	)	)	PUNCT
ejpam-4021	346	1	≤	≤	NUM
ejpam-4021	346	2	∧	∧	PROPN
ejpam-4021	346	3	j∈j(νj(x	j∈j(νj(x	X
ejpam-4021	346	4	−1	−1	NOUN
ejpam-4021	346	5	)	)	PUNCT
ejpam-4021	346	6	)	)	PUNCT
ejpam-4021	347	1	=	=	PUNCT
ejpam-4021	347	2	µ(x−1	µ(x−1	NOUN
ejpam-4021	347	3	)	)	PUNCT
ejpam-4021	347	4	.	.	PUNCT
ejpam-4021	348	1	also	also	ADV
ejpam-4021	348	2	,	,	PUNCT
ejpam-4021	348	3	if	if	SCONJ
ejpam-4021	348	4	µ	µ	PROPN
ejpam-4021	348	5	∈	∈	PROPN
ejpam-4021	348	6	lg	lg	NOUN
ejpam-4021	348	7	,	,	PUNCT
ejpam-4021	348	8	then	then	ADV
ejpam-4021	348	9	l	l	NOUN
ejpam-4021	348	10	-	-	PUNCT
ejpam-4021	348	11	valued	value	VERB
ejpam-4021	348	12	closure	closure	NOUN
ejpam-4021	348	13	of	of	ADP
ejpam-4021	348	14	µ	µ	NOUN
ejpam-4021	348	15	is	be	AUX
ejpam-4021	348	16	the	the	DET
ejpam-4021	348	17	subgroup	subgroup	NOUN
ejpam-4021	348	18	generated	generate	VERB
ejpam-4021	348	19	by	by	ADP
ejpam-4021	348	20	µ.	µ.	NOUN
ejpam-4021	348	21	this	this	PRON
ejpam-4021	348	22	can	can	AUX
ejpam-4021	348	23	be	be	AUX
ejpam-4021	348	24	given	give	VERB
ejpam-4021	348	25	as	as	ADP
ejpam-4021	348	26	:	:	PUNCT
ejpam-4021	348	27	〈	〈	PROPN
ejpam-4021	348	28	`	`	PUNCT
ejpam-4021	348	29	(	(	PUNCT
ejpam-4021	348	30	µ	µ	NOUN
ejpam-4021	348	31	)	)	PUNCT
ejpam-4021	348	32	〉	〉	NOUN
ejpam-4021	348	33	=	=	SYM
ejpam-4021	348	34	∧	∧	PROPN
ejpam-4021	348	35	{	{	PUNCT
ejpam-4021	348	36	ν	ν	X
ejpam-4021	348	37	:	:	PUNCT
ejpam-4021	348	38	µ	µ	ADJ
ejpam-4021	348	39	≤	≤	NUM
ejpam-4021	348	40	ν	ν	NOUN
ejpam-4021	348	41	,	,	PUNCT
ejpam-4021	348	42	ν	ν	NOUN
ejpam-4021	348	43	is	be	AUX
ejpam-4021	348	44	closed	closed	ADJ
ejpam-4021	348	45	lg	lg	ADJ
ejpam-4021	348	46	-	-	PUNCT
ejpam-4021	348	47	valued	value	VERB
ejpam-4021	348	48	subgroup	subgroup	NOUN
ejpam-4021	348	49	of	of	ADP
ejpam-4021	348	50	g	g	PROPN
ejpam-4021	348	51	}	}	PUNCT
ejpam-4021	348	52	,	,	PUNCT
ejpam-4021	348	53	t	t	PROPN
ejpam-4021	348	54	m	m	PROPN
ejpam-4021	348	55	g	g	NOUN
ejpam-4021	348	56	ahsanullah	ahsanullah	NOUN
ejpam-4021	348	57	,	,	PUNCT
ejpam-4021	348	58	fawzi	fawzi	PROPN
ejpam-4021	348	59	al	al	PROPN
ejpam-4021	348	60	-	-	PUNCT
ejpam-4021	348	61	thukair	thukair	NOUN
ejpam-4021	348	62	/	/	SYM
ejpam-4021	348	63	eur	eur	NOUN
ejpam-4021	348	64	.	.	PUNCT
ejpam-4021	349	1	j.	j.	PROPN
ejpam-4021	349	2	pure	pure	PROPN
ejpam-4021	349	3	appl	appl	PROPN
ejpam-4021	349	4	.	.	PROPN
ejpam-4021	349	5	math	math	PROPN
ejpam-4021	349	6	,	,	PUNCT
ejpam-4021	349	7	14	14	NUM
ejpam-4021	349	8	(	(	PUNCT
ejpam-4021	349	9	3	3	NUM
ejpam-4021	349	10	)	)	PUNCT
ejpam-4021	349	11	(	(	PUNCT
ejpam-4021	349	12	2021	2021	NUM
ejpam-4021	349	13	)	)	PUNCT
ejpam-4021	349	14	,	,	PUNCT
ejpam-4021	349	15	949	949	NUM
ejpam-4021	349	16	-	-	SYM
ejpam-4021	349	17	968	968	NUM
ejpam-4021	349	18	961	961	NUM
ejpam-4021	349	19	the	the	DET
ejpam-4021	349	20	l	l	NOUN
ejpam-4021	349	21	-	-	PUNCT
ejpam-4021	349	22	valued	value	VERB
ejpam-4021	349	23	subgroup	subgroup	NOUN
ejpam-4021	349	24	that	that	PRON
ejpam-4021	349	25	contains	contain	VERB
ejpam-4021	349	26	µ.	µ.	NOUN
ejpam-4021	349	27	in	in	ADP
ejpam-4021	349	28	view	view	NOUN
ejpam-4021	349	29	of	of	ADP
ejpam-4021	349	30	the	the	DET
ejpam-4021	349	31	theorem	theorem	NOUN
ejpam-4021	349	32	5.2.6[11	5.2.6[11	NUM
ejpam-4021	349	33	]	]	PUNCT
ejpam-4021	349	34	,	,	PUNCT
ejpam-4021	349	35	normal	normal	ADJ
ejpam-4021	349	36	l	l	NOUN
ejpam-4021	349	37	-	-	PUNCT
ejpam-4021	349	38	valued	value	VERB
ejpam-4021	349	39	subgroup	subgroup	NOUN
ejpam-4021	349	40	of	of	ADP
ejpam-4021	349	41	the	the	DET
ejpam-4021	349	42	group	group	NOUN
ejpam-4021	349	43	g	g	PROPN
ejpam-4021	349	44	form	form	VERB
ejpam-4021	349	45	a	a	DET
ejpam-4021	349	46	latticevalued	latticevalue	VERB
ejpam-4021	349	47	moore	moore	PROPN
ejpam-4021	349	48	collection	collection	PROPN
ejpam-4021	349	49	,	,	PUNCT
ejpam-4021	349	50	and	and	CCONJ
ejpam-4021	349	51	in	in	ADP
ejpam-4021	349	52	particular	particular	ADJ
ejpam-4021	349	53	,	,	PUNCT
ejpam-4021	349	54	`	`	PUNCT
ejpam-4021	349	55	(	(	PUNCT
ejpam-4021	349	56	µ	µ	NOUN
ejpam-4021	349	57	)	)	PUNCT
ejpam-4021	349	58	,	,	PUNCT
ejpam-4021	349	59	µ	µ	PROPN
ejpam-4021	349	60	∈	∈	NOUN
ejpam-4021	349	61	lg	lg	NOUN
ejpam-4021	349	62	is	be	AUX
ejpam-4021	349	63	the	the	DET
ejpam-4021	349	64	normal	normal	ADJ
ejpam-4021	349	65	l	l	NOUN
ejpam-4021	349	66	-	-	PUNCT
ejpam-4021	349	67	valued	value	VERB
ejpam-4021	349	68	subgroup	subgroup	NOUN
ejpam-4021	349	69	generated	generate	VERB
ejpam-4021	349	70	by	by	ADP
ejpam-4021	349	71	µ.	µ.	PROPN
ejpam-4021	349	72	more	more	ADV
ejpam-4021	349	73	precisely	precisely	ADV
ejpam-4021	349	74	,	,	PUNCT
ejpam-4021	349	75	〈	〈	PROPN
ejpam-4021	349	76	`	`	PUNCT
ejpam-4021	349	77	(	(	PUNCT
ejpam-4021	349	78	µ	µ	NOUN
ejpam-4021	349	79	)	)	PUNCT
ejpam-4021	349	80	〉	〉	NOUN
ejpam-4021	349	81	=	=	SYM
ejpam-4021	349	82	∧	∧	PROPN
ejpam-4021	349	83	{	{	PUNCT
ejpam-4021	349	84	ν	ν	X
ejpam-4021	349	85	:	:	PUNCT
ejpam-4021	349	86	µ	µ	ADJ
ejpam-4021	349	87	≤	≤	NUM
ejpam-4021	349	88	ν	ν	NOUN
ejpam-4021	349	89	,	,	PUNCT
ejpam-4021	349	90	ν	ν	NOUN
ejpam-4021	349	91	is	be	AUX
ejpam-4021	349	92	closed	close	VERB
ejpam-4021	349	93	normal	normal	ADJ
ejpam-4021	349	94	lg	lg	NOUN
ejpam-4021	349	95	-	-	PUNCT
ejpam-4021	349	96	valued	value	VERB
ejpam-4021	349	97	subgroup	subgroup	NOUN
ejpam-4021	349	98	of	of	ADP
ejpam-4021	349	99	g	g	PROPN
ejpam-4021	349	100	}	}	PUNCT
ejpam-4021	349	101	,	,	PUNCT
ejpam-4021	349	102	theorem	theorem	VERB
ejpam-4021	349	103	3	3	NUM
ejpam-4021	349	104	.	.	PUNCT
ejpam-4021	350	1	l	l	NOUN
ejpam-4021	350	2	-	-	NOUN
ejpam-4021	350	3	cls	cls	NOUN
ejpam-4021	350	4	is	be	AUX
ejpam-4021	350	5	a	a	DET
ejpam-4021	350	6	topological	topological	ADJ
ejpam-4021	350	7	category	category	NOUN
ejpam-4021	350	8	.	.	PUNCT
ejpam-4021	351	1	proof	proof	NOUN
ejpam-4021	351	2	.	.	PUNCT
ejpam-4021	352	1	note	note	VERB
ejpam-4021	352	2	that	that	SCONJ
ejpam-4021	352	3	the	the	DET
ejpam-4021	352	4	objects	object	NOUN
ejpam-4021	352	5	of	of	ADP
ejpam-4021	352	6	l	l	NOUN
ejpam-4021	352	7	-	-	NOUN
ejpam-4021	352	8	cls	cls	NOUN
ejpam-4021	352	9	are	be	AUX
ejpam-4021	352	10	structured	structure	VERB
ejpam-4021	352	11	sets	set	NOUN
ejpam-4021	352	12	and	and	CCONJ
ejpam-4021	352	13	the	the	DET
ejpam-4021	352	14	composition	composition	NOUN
ejpam-4021	352	15	of	of	ADP
ejpam-4021	352	16	closure	closure	NOUN
ejpam-4021	352	17	preserving	preserve	VERB
ejpam-4021	352	18	mappings	mapping	NOUN
ejpam-4021	352	19	is	be	AUX
ejpam-4021	352	20	closure	closure	NOUN
ejpam-4021	352	21	preserving	preserve	VERB
ejpam-4021	352	22	.	.	PUNCT
ejpam-4021	353	1	consider	consider	VERB
ejpam-4021	353	2	x	x	PRON
ejpam-4021	353	3	is	be	AUX
ejpam-4021	353	4	a	a	DET
ejpam-4021	353	5	set	set	NOUN
ejpam-4021	353	6	,	,	PUNCT
ejpam-4021	353	7	(	(	PUNCT
ejpam-4021	353	8	yj	yj	PROPN
ejpam-4021	353	9	,	,	PUNCT
ejpam-4021	353	10	`	`	PUNCT
ejpam-4021	353	11	j	j	PROPN
ejpam-4021	353	12	)	)	PUNCT
ejpam-4021	353	13	j∈j	j∈j	NOUN
ejpam-4021	353	14	a	a	DET
ejpam-4021	353	15	family	family	NOUN
ejpam-4021	353	16	of	of	ADP
ejpam-4021	353	17	l	l	PROPN
ejpam-4021	353	18	-	-	PUNCT
ejpam-4021	353	19	valued	value	VERB
ejpam-4021	353	20	closure	closure	NOUN
ejpam-4021	353	21	spaces	space	NOUN
ejpam-4021	353	22	and	and	CCONJ
ejpam-4021	353	23	a	a	DET
ejpam-4021	353	24	source	source	NOUN
ejpam-4021	353	25	s	s	PART
ejpam-4021	353	26	=(	=(	NOUN
ejpam-4021	354	1	fj	fj	X
ejpam-4021	354	2	:	:	PUNCT
ejpam-4021	354	3	x	x	PUNCT
ejpam-4021	354	4	−→	−→	NOUN
ejpam-4021	354	5	(	(	PUNCT
ejpam-4021	354	6	yj	yj	PROPN
ejpam-4021	354	7	,	,	PUNCT
ejpam-4021	354	8	`	`	PUNCT
ejpam-4021	354	9	j	j	NOUN
ejpam-4021	354	10	)	)	PUNCT
ejpam-4021	354	11	)	)	PUNCT
ejpam-4021	354	12	j∈j	j∈j	NOUN
ejpam-4021	354	13	of	of	ADP
ejpam-4021	354	14	family	family	NOUN
ejpam-4021	354	15	of	of	ADP
ejpam-4021	354	16	functions	function	NOUN
ejpam-4021	354	17	,	,	PUNCT
ejpam-4021	354	18	then	then	ADV
ejpam-4021	354	19	ω	ω	X
ejpam-4021	354	20	=	=	SYM
ejpam-4021	354	21	{	{	PUNCT
ejpam-4021	354	22	ω	ω	NUM
ejpam-4021	354	23	∈	∈	PROPN
ejpam-4021	354	24	lx	lx	NOUN
ejpam-4021	354	25	:	:	PUNCT
ejpam-4021	354	26	ω	ω	X
ejpam-4021	354	27	=	=	SYM
ejpam-4021	354	28	∧	∧	PROPN
ejpam-4021	354	29	j∈j	j∈j	NOUN
ejpam-4021	354	30	f	f	PROPN
ejpam-4021	354	31	←	←	PROPN
ejpam-4021	354	32	j	j	PROPN
ejpam-4021	354	33	(	(	PUNCT
ejpam-4021	354	34	ωj	ωj	NOUN
ejpam-4021	354	35	)	)	PUNCT
ejpam-4021	354	36	,	,	PUNCT
ejpam-4021	354	37	∀ωj	∀ωj	NOUN
ejpam-4021	354	38	=	=	PUNCT
ejpam-4021	354	39	`	`	PUNCT
ejpam-4021	354	40	j(ωj	j(ωj	PROPN
ejpam-4021	354	41	)	)	PUNCT
ejpam-4021	354	42	,	,	PUNCT
ejpam-4021	354	43	j	j	PROPN
ejpam-4021	354	44	∈	∈	PROPN
ejpam-4021	354	45	j	j	PROPN
ejpam-4021	354	46	}	}	PUNCT
ejpam-4021	354	47	is	be	AUX
ejpam-4021	354	48	a	a	DET
ejpam-4021	354	49	lattice	lattice	NOUN
ejpam-4021	354	50	-	-	PUNCT
ejpam-4021	354	51	valued	value	VERB
ejpam-4021	354	52	moore	moore	PROPN
ejpam-4021	354	53	family	family	NOUN
ejpam-4021	354	54	which	which	PRON
ejpam-4021	354	55	contains	contain	VERB
ejpam-4021	354	56	>	>	X
ejpam-4021	354	57	∅.	∅.	PROPN
ejpam-4021	354	58	then	then	ADV
ejpam-4021	354	59	ω	ω	PROPN
ejpam-4021	354	60	induces	induce	VERB
ejpam-4021	354	61	an	an	DET
ejpam-4021	354	62	l	l	NOUN
ejpam-4021	354	63	-	-	PUNCT
ejpam-4021	354	64	valued	value	VERB
ejpam-4021	354	65	closure	closure	NOUN
ejpam-4021	354	66	operation	operation	NOUN
ejpam-4021	354	67	on	on	ADP
ejpam-4021	354	68	x	x	PUNCT
ejpam-4021	354	69	given	give	VERB
ejpam-4021	354	70	by	by	ADP
ejpam-4021	354	71	:	:	PUNCT
ejpam-4021	354	72	`	`	PUNCT
ejpam-4021	354	73	(	(	PUNCT
ejpam-4021	354	74	µ)ω	µ)ω	X
ejpam-4021	354	75	=	=	PUNCT
ejpam-4021	354	76	∧	∧	NOUN
ejpam-4021	354	77	{	{	PUNCT
ejpam-4021	354	78	ω	ω	PROPN
ejpam-4021	354	79	∈	∈	PROPN
ejpam-4021	354	80	ω	ω	NOUN
ejpam-4021	354	81	:	:	PUNCT
ejpam-4021	354	82	µ	µ	PROPN
ejpam-4021	354	83	≤	≤	NUM
ejpam-4021	354	84	ω	ω	NUM
ejpam-4021	354	85	}	}	PUNCT
ejpam-4021	354	86	,	,	PUNCT
ejpam-4021	354	87	for	for	ADP
ejpam-4021	354	88	all	all	DET
ejpam-4021	354	89	µ	µ	PRON
ejpam-4021	354	90	∈	∈	NOUN
ejpam-4021	354	91	lx	lx	NOUN
ejpam-4021	354	92	.	.	PUNCT
ejpam-4021	355	1	now	now	ADV
ejpam-4021	355	2	let	let	VERB
ejpam-4021	355	3	(	(	PUNCT
ejpam-4021	355	4	z	z	NOUN
ejpam-4021	355	5	,	,	PUNCT
ejpam-4021	355	6	`	`	PUNCT
ejpam-4021	355	7	)	)	PUNCT
ejpam-4021	355	8	∈	∈	PROPN
ejpam-4021	355	9	|l	|l	PROPN
ejpam-4021	355	10	-	-	PUNCT
ejpam-4021	355	11	cls|	cls|	NOUN
ejpam-4021	355	12	,	,	PUNCT
ejpam-4021	355	13	and	and	CCONJ
ejpam-4021	355	14	g	g	NOUN
ejpam-4021	355	15	:	:	PUNCT
ejpam-4021	356	1	z	z	NOUN
ejpam-4021	356	2	−→	−→	NOUN
ejpam-4021	356	3	x	x	PUNCT
ejpam-4021	356	4	be	be	AUX
ejpam-4021	356	5	a	a	DET
ejpam-4021	356	6	function	function	NOUN
ejpam-4021	356	7	such	such	ADJ
ejpam-4021	356	8	that	that	SCONJ
ejpam-4021	356	9	fj	fj	PROPN
ejpam-4021	356	10	◦	◦	NOUN
ejpam-4021	356	11	g	g	NOUN
ejpam-4021	356	12	:	:	PUNCT
ejpam-4021	356	13	(	(	PUNCT
ejpam-4021	356	14	z	z	NOUN
ejpam-4021	356	15	,	,	PUNCT
ejpam-4021	356	16	`	`	PUNCT
ejpam-4021	356	17	)	)	PUNCT
ejpam-4021	356	18	−→	−→	NOUN
ejpam-4021	356	19	(	(	PUNCT
ejpam-4021	356	20	y	y	PROPN
ejpam-4021	356	21	,	,	PUNCT
ejpam-4021	356	22	`	`	PUNCT
ejpam-4021	356	23	j	j	NOUN
ejpam-4021	356	24	)	)	PUNCT
ejpam-4021	356	25	is	be	AUX
ejpam-4021	356	26	closure	closure	NOUN
ejpam-4021	356	27	preserving	preserve	VERB
ejpam-4021	356	28	mapping	mapping	NOUN
ejpam-4021	356	29	for	for	ADP
ejpam-4021	356	30	all	all	DET
ejpam-4021	356	31	j	j	PROPN
ejpam-4021	356	32	∈	∈	PROPN
ejpam-4021	356	33	j	j	PROPN
ejpam-4021	356	34	.	.	PUNCT
ejpam-4021	357	1	if	if	SCONJ
ejpam-4021	357	2	µ	µ	PRON
ejpam-4021	357	3	∈	∈	NOUN
ejpam-4021	357	4	lx	lx	NOUN
ejpam-4021	357	5	is	be	AUX
ejpam-4021	357	6	a	a	DET
ejpam-4021	357	7	−	−	PROPN
ejpam-4021	357	8	ω	ω	NUM
ejpam-4021	357	9	closed	closed	ADJ
ejpam-4021	357	10	,	,	PUNCT
ejpam-4021	357	11	then	then	ADV
ejpam-4021	357	12	µ	µ	PROPN
ejpam-4021	357	13	∈	∈	PROPN
ejpam-4021	357	14	ω	ω	NOUN
ejpam-4021	357	15	and	and	CCONJ
ejpam-4021	357	16	thus	thus	ADV
ejpam-4021	357	17	µ	µ	ADJ
ejpam-4021	357	18	=	=	SYM
ejpam-4021	357	19	∧	∧	PROPN
ejpam-4021	357	20	j∈j	j∈j	NOUN
ejpam-4021	357	21	f	f	PROPN
ejpam-4021	357	22	←	←	PROPN
ejpam-4021	357	23	j	j	PROPN
ejpam-4021	357	24	(	(	PUNCT
ejpam-4021	357	25	ωj	ωj	ADP
ejpam-4021	357	26	)	)	PUNCT
ejpam-4021	357	27	where	where	SCONJ
ejpam-4021	357	28	ωj	ωj	ADP
ejpam-4021	357	29	=	=	SYM
ejpam-4021	357	30	`	`	PUNCT
ejpam-4021	357	31	j(ωj	j(ωj	PROPN
ejpam-4021	357	32	)	)	PUNCT
ejpam-4021	357	33	in	in	ADP
ejpam-4021	357	34	(	(	PUNCT
ejpam-4021	357	35	yj	yj	PROPN
ejpam-4021	357	36	,	,	PUNCT
ejpam-4021	357	37	`	`	PUNCT
ejpam-4021	357	38	j	j	NOUN
ejpam-4021	357	39	)	)	PUNCT
ejpam-4021	357	40	.	.	PUNCT
ejpam-4021	358	1	in	in	ADP
ejpam-4021	358	2	view	view	NOUN
ejpam-4021	358	3	of	of	ADP
ejpam-4021	358	4	proposition	proposition	NOUN
ejpam-4021	358	5	1.2(5	1.2(5	NUM
ejpam-4021	358	6	)	)	PUNCT
ejpam-4021	358	7	[	[	X
ejpam-4021	358	8	22	22	NUM
ejpam-4021	358	9	]	]	PUNCT
ejpam-4021	358	10	,	,	PUNCT
ejpam-4021	358	11	we	we	PRON
ejpam-4021	358	12	have	have	VERB
ejpam-4021	358	13	:	:	PUNCT
ejpam-4021	358	14	g←(µ	g←(µ	X
ejpam-4021	358	15	)	)	PUNCT
ejpam-4021	359	1	=	=	PRON
ejpam-4021	359	2	g←	g←	PROPN
ejpam-4021	359	3	∧	∧	PROPN
ejpam-4021	359	4	j	j	PROPN
ejpam-4021	359	5	f←j	f←j	X
ejpam-4021	359	6	(	(	PUNCT
ejpam-4021	359	7	ωj	ωj	NOUN
ejpam-4021	359	8	)	)	PUNCT
ejpam-4021	359	9			PROPN
ejpam-4021	359	10	=	=	SYM
ejpam-4021	359	11	∧	∧	PROPN
ejpam-4021	359	12	j	j	PROPN
ejpam-4021	359	13	g←	g←	PROPN
ejpam-4021	359	14	(	(	PUNCT
ejpam-4021	359	15	f←j	f←j	ADJ
ejpam-4021	359	16	(	(	PUNCT
ejpam-4021	359	17	ωj	ωj	NOUN
ejpam-4021	359	18	)	)	PUNCT
ejpam-4021	359	19	)	)	PUNCT
ejpam-4021	360	1	=	=	PUNCT
ejpam-4021	360	2	∧	∧	PROPN
ejpam-4021	360	3	j	j	PROPN
ejpam-4021	360	4	(	(	PUNCT
ejpam-4021	360	5	fj	fj	INTJ
ejpam-4021	360	6	◦	◦	VERB
ejpam-4021	360	7	g)←(ωj	g)←(ωj	X
ejpam-4021	360	8	)	)	PUNCT
ejpam-4021	360	9	this	this	PRON
ejpam-4021	360	10	implies	imply	VERB
ejpam-4021	360	11	(	(	PUNCT
ejpam-4021	360	12	fj	fj	INTJ
ejpam-4021	360	13	◦	◦	NOUN
ejpam-4021	360	14	g)←(ωj	g)←(ωj	VERB
ejpam-4021	360	15	)	)	PUNCT
ejpam-4021	360	16	is	be	AUX
ejpam-4021	360	17	closed	close	VERB
ejpam-4021	360	18	in	in	ADP
ejpam-4021	360	19	(	(	PUNCT
ejpam-4021	360	20	z	z	NOUN
ejpam-4021	360	21	,	,	PUNCT
ejpam-4021	360	22	`	`	PUNCT
ejpam-4021	360	23	)	)	PUNCT
ejpam-4021	360	24	implying	imply	VERB
ejpam-4021	360	25	g←(µ	g←(µ	NOUN
ejpam-4021	360	26	)	)	PUNCT
ejpam-4021	360	27	is	be	AUX
ejpam-4021	360	28	closed	close	VERB
ejpam-4021	360	29	in	in	ADP
ejpam-4021	360	30	(	(	PUNCT
ejpam-4021	360	31	z	z	NOUN
ejpam-4021	360	32	,	,	PUNCT
ejpam-4021	360	33	`	`	PUNCT
ejpam-4021	360	34	)	)	PUNCT
ejpam-4021	360	35	.	.	PUNCT
ejpam-4021	361	1	remark	remark	PROPN
ejpam-4021	361	2	5	5	NUM
ejpam-4021	361	3	.	.	PUNCT
ejpam-4021	362	1	every	every	DET
ejpam-4021	362	2	l	l	NOUN
ejpam-4021	362	3	-	-	PUNCT
ejpam-4021	362	4	valued	value	VERB
ejpam-4021	362	5	topological	topological	ADJ
ejpam-4021	362	6	space	space	NOUN
ejpam-4021	362	7	(	(	PUNCT
ejpam-4021	362	8	x,∆	x,∆	NUM
ejpam-4021	362	9	)	)	PUNCT
ejpam-4021	362	10	is	be	AUX
ejpam-4021	362	11	an	an	DET
ejpam-4021	362	12	l	l	NOUN
ejpam-4021	362	13	-	-	PUNCT
ejpam-4021	362	14	valued	value	VERB
ejpam-4021	362	15	closure	closure	NOUN
ejpam-4021	362	16	space	space	NOUN
ejpam-4021	362	17	with	with	ADP
ejpam-4021	362	18	the	the	DET
ejpam-4021	362	19	closure	closure	NOUN
ejpam-4021	362	20	operation	operation	NOUN
ejpam-4021	362	21	defined	define	VERB
ejpam-4021	362	22	by	by	ADP
ejpam-4021	362	23	:	:	PUNCT
ejpam-4021	362	24	`	`	PUNCT
ejpam-4021	362	25	(	(	PUNCT
ejpam-4021	362	26	ν	ν	NOUN
ejpam-4021	362	27	)	)	PUNCT
ejpam-4021	362	28	=	=	SYM
ejpam-4021	362	29	ν(x,∆	ν(x,∆	X
ejpam-4021	362	30	)	)	PUNCT
ejpam-4021	362	31	=	=	VERB
ejpam-4021	362	32	νx	νx	NOUN
ejpam-4021	362	33	for	for	ADP
ejpam-4021	362	34	every	every	DET
ejpam-4021	362	35	ν	ν	NOUN
ejpam-4021	362	36	∈	∈	NOUN
ejpam-4021	362	37	lx	lx	NOUN
ejpam-4021	362	38	.	.	PUNCT
ejpam-4021	363	1	also	also	ADV
ejpam-4021	363	2	,	,	PUNCT
ejpam-4021	363	3	every	every	DET
ejpam-4021	363	4	mapping	mapping	NOUN
ejpam-4021	363	5	f	f	X
ejpam-4021	363	6	:	:	PUNCT
ejpam-4021	363	7	(	(	PUNCT
ejpam-4021	363	8	x,∆	x,∆	NUM
ejpam-4021	363	9	)	)	PUNCT
ejpam-4021	363	10	−→	−→	NOUN
ejpam-4021	363	11	(	(	PUNCT
ejpam-4021	363	12	y	y	PROPN
ejpam-4021	363	13	,	,	PUNCT
ejpam-4021	363	14	γ	γ	NOUN
ejpam-4021	363	15	)	)	PUNCT
ejpam-4021	363	16	continuous	continuous	ADJ
ejpam-4021	363	17	if	if	SCONJ
ejpam-4021	363	18	and	and	CCONJ
ejpam-4021	363	19	only	only	ADV
ejpam-4021	363	20	if	if	SCONJ
ejpam-4021	363	21	it	it	PRON
ejpam-4021	363	22	is	be	AUX
ejpam-4021	363	23	closure	closure	NOUN
ejpam-4021	363	24	preserving	preserve	VERB
ejpam-4021	363	25	with	with	ADP
ejpam-4021	363	26	respect	respect	NOUN
ejpam-4021	363	27	to	to	ADP
ejpam-4021	363	28	the	the	DET
ejpam-4021	363	29	induced	induced	ADJ
ejpam-4021	363	30	l	l	NOUN
ejpam-4021	363	31	-	-	PUNCT
ejpam-4021	363	32	valued	value	VERB
ejpam-4021	363	33	closure	closure	NOUN
ejpam-4021	363	34	operations	operation	NOUN
ejpam-4021	363	35	.	.	PUNCT
ejpam-4021	364	1	in	in	ADP
ejpam-4021	364	2	fact	fact	NOUN
ejpam-4021	364	3	,	,	PUNCT
ejpam-4021	364	4	if	if	SCONJ
ejpam-4021	364	5	ν	ν	NOUN
ejpam-4021	364	6	∈	∈	PROPN
ejpam-4021	364	7	lx	lx	NOUN
ejpam-4021	364	8	,	,	PUNCT
ejpam-4021	364	9	then	then	ADV
ejpam-4021	364	10	in	in	ADP
ejpam-4021	364	11	view	view	NOUN
ejpam-4021	364	12	of	of	ADP
ejpam-4021	364	13	the	the	DET
ejpam-4021	364	14	proposition	proposition	NOUN
ejpam-4021	364	15	1.4	1.4	NUM
ejpam-4021	365	1	[	[	X
ejpam-4021	365	2	22	22	NUM
ejpam-4021	365	3	]	]	PUNCT
ejpam-4021	365	4	,	,	PUNCT
ejpam-4021	365	5	f→(`(ν	f→(`(ν	NOUN
ejpam-4021	365	6	)	)	PUNCT
ejpam-4021	365	7	)	)	PUNCT
ejpam-4021	366	1	=	=	SYM
ejpam-4021	366	2	f→(νx	f→(νx	PROPN
ejpam-4021	366	3	)	)	PUNCT
ejpam-4021	366	4	≤	≤	NOUN
ejpam-4021	367	1	f→(ν	f→(ν	PROPN
ejpam-4021	367	2	)	)	PUNCT
ejpam-4021	367	3	y	y	NOUN
ejpam-4021	367	4	=	=	PUNCT
ejpam-4021	367	5	`	`	PUNCT
ejpam-4021	367	6	(	(	PUNCT
ejpam-4021	367	7	f→(ν	f→(ν	PROPN
ejpam-4021	367	8	)	)	PUNCT
ejpam-4021	367	9	)	)	PUNCT
ejpam-4021	367	10	,	,	PUNCT
ejpam-4021	367	11	i.e.	i.e.	X
ejpam-4021	367	12	,	,	PUNCT
ejpam-4021	367	13	f→(`(ν	f→(`(ν	NOUN
ejpam-4021	367	14	)	)	PUNCT
ejpam-4021	367	15	)	)	PUNCT
ejpam-4021	367	16	≤	≤	NUM
ejpam-4021	368	1	`	`	PUNCT
ejpam-4021	368	2	(	(	PUNCT
ejpam-4021	368	3	f→(ν	f→(ν	PROPN
ejpam-4021	368	4	)	)	PUNCT
ejpam-4021	368	5	)	)	PUNCT
ejpam-4021	368	6	,	,	PUNCT
ejpam-4021	368	7	meaning	mean	VERB
ejpam-4021	368	8	f	f	PROPN
ejpam-4021	368	9	is	be	AUX
ejpam-4021	368	10	closure	closure	NOUN
ejpam-4021	368	11	preserving	preserving	NOUN
ejpam-4021	368	12	.	.	PUNCT
ejpam-4021	369	1	conversely	conversely	ADV
ejpam-4021	369	2	,	,	PUNCT
ejpam-4021	369	3	let	let	VERB
ejpam-4021	369	4	ν	ν	X
ejpam-4021	369	5	∈	∈	VERB
ejpam-4021	369	6	lx	lx	NOUN
ejpam-4021	369	7	and	and	CCONJ
ejpam-4021	369	8	f	f	PROPN
ejpam-4021	369	9	be	be	VERB
ejpam-4021	369	10	closure	closure	NOUN
ejpam-4021	369	11	preserving	preserve	VERB
ejpam-4021	369	12	,	,	PUNCT
ejpam-4021	369	13	then	then	ADV
ejpam-4021	369	14	f→(νx	f→(νx	PROPN
ejpam-4021	369	15	)	)	PUNCT
ejpam-4021	370	1	=	=	SYM
ejpam-4021	370	2	f→(`(ν	f→(`(ν	NOUN
ejpam-4021	370	3	)	)	PUNCT
ejpam-4021	370	4	)	)	PUNCT
ejpam-4021	371	1	≤	≤	NUM
ejpam-4021	372	1	`	`	PUNCT
ejpam-4021	372	2	(	(	PUNCT
ejpam-4021	372	3	f→(ν	f→(ν	PROPN
ejpam-4021	372	4	)	)	PUNCT
ejpam-4021	372	5	)	)	PUNCT
ejpam-4021	372	6	=	=	SYM
ejpam-4021	372	7	f→(ν	f→(ν	PROPN
ejpam-4021	372	8	)	)	PUNCT
ejpam-4021	372	9	y	y	PROPN
ejpam-4021	372	10	,	,	PUNCT
ejpam-4021	372	11	i.e.	i.e.	X
ejpam-4021	372	12	,	,	PUNCT
ejpam-4021	372	13	f→(νx	f→(νx	PROPN
ejpam-4021	372	14	)	)	PUNCT
ejpam-4021	372	15	≤	≤	NOUN
ejpam-4021	372	16	f→(ν	f→(ν	PROPN
ejpam-4021	372	17	)	)	PUNCT
ejpam-4021	372	18	y	y	PROPN
ejpam-4021	372	19	meaning	mean	VERB
ejpam-4021	372	20	the	the	DET
ejpam-4021	372	21	mapping	mapping	NOUN
ejpam-4021	372	22	f	f	NOUN
ejpam-4021	372	23	:	:	PUNCT
ejpam-4021	372	24	(	(	PUNCT
ejpam-4021	372	25	x,∆	x,∆	NUM
ejpam-4021	372	26	)	)	PUNCT
ejpam-4021	372	27	−→	−→	NOUN
ejpam-4021	372	28	(	(	PUNCT
ejpam-4021	372	29	y	y	PROPN
ejpam-4021	372	30	,	,	PUNCT
ejpam-4021	372	31	γ	γ	NOUN
ejpam-4021	372	32	)	)	PUNCT
ejpam-4021	372	33	is	be	AUX
ejpam-4021	372	34	continuous	continuous	ADJ
ejpam-4021	372	35	by	by	ADP
ejpam-4021	372	36	the	the	DET
ejpam-4021	372	37	proposition	proposition	NOUN
ejpam-4021	372	38	1.4	1.4	NUM
ejpam-4021	373	1	[	[	X
ejpam-4021	373	2	22	22	NUM
ejpam-4021	373	3	]	]	PUNCT
ejpam-4021	373	4	.	.	PUNCT
ejpam-4021	374	1	thus	thus	ADV
ejpam-4021	374	2	we	we	PRON
ejpam-4021	374	3	have	have	VERB
ejpam-4021	374	4	the	the	DET
ejpam-4021	374	5	following	following	NOUN
ejpam-4021	374	6	.	.	PUNCT
ejpam-4021	375	1	corollary	corollary	ADJ
ejpam-4021	375	2	1	1	NUM
ejpam-4021	375	3	.	.	PUNCT
ejpam-4021	376	1	l	l	NOUN
ejpam-4021	376	2	-	-	NOUN
ejpam-4021	376	3	top	top	NOUN
ejpam-4021	376	4	,	,	PUNCT
ejpam-4021	376	5	the	the	DET
ejpam-4021	376	6	category	category	NOUN
ejpam-4021	376	7	of	of	ADP
ejpam-4021	376	8	l	l	NOUN
ejpam-4021	376	9	-	-	PUNCT
ejpam-4021	376	10	valued	value	VERB
ejpam-4021	376	11	topological	topological	ADJ
ejpam-4021	376	12	spaces	space	NOUN
ejpam-4021	376	13	and	and	CCONJ
ejpam-4021	376	14	continuous	continuous	ADJ
ejpam-4021	376	15	mappings	mapping	NOUN
ejpam-4021	376	16	is	be	AUX
ejpam-4021	376	17	a	a	DET
ejpam-4021	376	18	full	full	ADJ
ejpam-4021	376	19	subcategory	subcategory	NOUN
ejpam-4021	376	20	of	of	ADP
ejpam-4021	376	21	the	the	DET
ejpam-4021	376	22	category	category	NOUN
ejpam-4021	376	23	l	l	NOUN
ejpam-4021	376	24	-	-	NOUN
ejpam-4021	376	25	cls	cls	NOUN
ejpam-4021	376	26	definition	definition	NOUN
ejpam-4021	376	27	16	16	NUM
ejpam-4021	376	28	.	.	PUNCT
ejpam-4021	377	1	a	a	DET
ejpam-4021	377	2	triple	triple	ADJ
ejpam-4021	377	3	(	(	PUNCT
ejpam-4021	377	4	g	g	NOUN
ejpam-4021	377	5	,	,	PUNCT
ejpam-4021	377	6	·	·	PUNCT
ejpam-4021	377	7	,	,	PUNCT
ejpam-4021	377	8	`	`	PUNCT
ejpam-4021	377	9	)	)	PUNCT
ejpam-4021	377	10	is	be	AUX
ejpam-4021	377	11	called	call	VERB
ejpam-4021	377	12	an	an	DET
ejpam-4021	377	13	l	l	NOUN
ejpam-4021	377	14	-	-	PUNCT
ejpam-4021	377	15	closure	closure	NOUN
ejpam-4021	377	16	group	group	NOUN
ejpam-4021	377	17	if	if	SCONJ
ejpam-4021	377	18	(	(	PUNCT
ejpam-4021	377	19	g	g	NOUN
ejpam-4021	377	20	,	,	PUNCT
ejpam-4021	377	21	·	·	PUNCT
ejpam-4021	377	22	)	)	PUNCT
ejpam-4021	377	23	∈	∈	PROPN
ejpam-4021	377	24	|grp|	|grp|	NOUN
ejpam-4021	377	25	and	and	CCONJ
ejpam-4021	377	26	(	(	PUNCT
ejpam-4021	377	27	g	g	NOUN
ejpam-4021	377	28	,	,	PUNCT
ejpam-4021	377	29	`	`	PUNCT
ejpam-4021	377	30	)	)	PUNCT
ejpam-4021	377	31	∈	∈	PROPN
ejpam-4021	377	32	|l	|l	PROPN
ejpam-4021	377	33	-	-	PUNCT
ejpam-4021	377	34	cls|	cls|	NOUN
ejpam-4021	377	35	such	such	DET
ejpam-4021	377	36	the	the	DET
ejpam-4021	377	37	following	following	NOUN
ejpam-4021	377	38	are	be	AUX
ejpam-4021	377	39	fulfilled	fulfil	VERB
ejpam-4021	377	40	:	:	PUNCT
ejpam-4021	377	41	(	(	PUNCT
ejpam-4021	377	42	clgm	clgm	ADJ
ejpam-4021	377	43	)	)	PUNCT
ejpam-4021	377	44	`	`	PUNCT
ejpam-4021	377	45	(	(	PUNCT
ejpam-4021	377	46	ν)(x	ν)(x	NOUN
ejpam-4021	377	47	)	)	PUNCT
ejpam-4021	377	48	∗	∗	NOUN
ejpam-4021	377	49	`	`	PUNCT
ejpam-4021	377	50	(	(	PUNCT
ejpam-4021	377	51	ν)(y	ν)(y	PROPN
ejpam-4021	377	52	)	)	PUNCT
ejpam-4021	377	53	≤	≤	NUM
ejpam-4021	378	1	`	`	PUNCT
ejpam-4021	378	2	(	(	PUNCT
ejpam-4021	378	3	ν	ν	X
ejpam-4021	378	4	·	·	PUNCT
ejpam-4021	378	5	ν)(xy	ν)(xy	NUM
ejpam-4021	378	6	)	)	PUNCT
ejpam-4021	379	1	,	,	PUNCT
ejpam-4021	379	2	∀ν	∀ν	PROPN
ejpam-4021	379	3	∈	∈	PROPN
ejpam-4021	379	4	lg	lg	NOUN
ejpam-4021	379	5	and	and	CCONJ
ejpam-4021	379	6	∀x	∀x	NUM
ejpam-4021	379	7	,	,	PUNCT
ejpam-4021	379	8	y	y	PROPN
ejpam-4021	379	9	∈	∈	PROPN
ejpam-4021	379	10	g	g	NOUN
ejpam-4021	379	11	;	;	PUNCT
ejpam-4021	379	12	(	(	PUNCT
ejpam-4021	379	13	clgi	clgi	NOUN
ejpam-4021	379	14	)	)	PUNCT
ejpam-4021	379	15	`	`	PUNCT
ejpam-4021	379	16	(	(	PUNCT
ejpam-4021	379	17	ν)(x	ν)(x	NOUN
ejpam-4021	379	18	)	)	PUNCT
ejpam-4021	379	19	≤	≤	NUM
ejpam-4021	380	1	`	`	PUNCT
ejpam-4021	380	2	(	(	PUNCT
ejpam-4021	380	3	ν−1)(x−1	ν−1)(x−1	NOUN
ejpam-4021	380	4	)	)	PUNCT
ejpam-4021	380	5	,	,	PUNCT
ejpam-4021	380	6	∀ν	∀ν	PROPN
ejpam-4021	380	7	∈	∈	PROPN
ejpam-4021	380	8	lg	lg	NOUN
ejpam-4021	380	9	and	and	CCONJ
ejpam-4021	380	10	x	x	SYM
ejpam-4021	380	11	∈	∈	PROPN
ejpam-4021	380	12	g.	g.	NOUN
ejpam-4021	380	13	the	the	DET
ejpam-4021	380	14	category	category	NOUN
ejpam-4021	380	15	of	of	ADP
ejpam-4021	380	16	all	all	DET
ejpam-4021	380	17	l	l	NOUN
ejpam-4021	380	18	-	-	PUNCT
ejpam-4021	380	19	valued	value	VERB
ejpam-4021	380	20	closure	closure	NOUN
ejpam-4021	380	21	groups	group	NOUN
ejpam-4021	380	22	and	and	CCONJ
ejpam-4021	380	23	closure	closure	NOUN
ejpam-4021	380	24	-	-	PUNCT
ejpam-4021	380	25	preserving	preserve	VERB
ejpam-4021	380	26	group	group	NOUN
ejpam-4021	380	27	homomorphisms	homomorphism	NOUN
ejpam-4021	380	28	is	be	AUX
ejpam-4021	380	29	denoted	denote	VERB
ejpam-4021	380	30	by	by	ADP
ejpam-4021	380	31	l	l	NOUN
ejpam-4021	380	32	-	-	NOUN
ejpam-4021	380	33	clgrp	clgrp	NOUN
ejpam-4021	380	34	.	.	PUNCT
ejpam-4021	381	1	t	t	PROPN
ejpam-4021	381	2	m	m	PROPN
ejpam-4021	381	3	g	g	NOUN
ejpam-4021	381	4	ahsanullah	ahsanullah	NOUN
ejpam-4021	381	5	,	,	PUNCT
ejpam-4021	381	6	fawzi	fawzi	PROPN
ejpam-4021	381	7	al	al	PROPN
ejpam-4021	381	8	-	-	PUNCT
ejpam-4021	381	9	thukair	thukair	NOUN
ejpam-4021	381	10	/	/	SYM
ejpam-4021	381	11	eur	eur	NOUN
ejpam-4021	381	12	.	.	PUNCT
ejpam-4021	382	1	j.	j.	PROPN
ejpam-4021	382	2	pure	pure	PROPN
ejpam-4021	382	3	appl	appl	PROPN
ejpam-4021	382	4	.	.	PROPN
ejpam-4021	382	5	math	math	PROPN
ejpam-4021	382	6	,	,	PUNCT
ejpam-4021	382	7	14	14	NUM
ejpam-4021	382	8	(	(	PUNCT
ejpam-4021	382	9	3	3	NUM
ejpam-4021	382	10	)	)	PUNCT
ejpam-4021	382	11	(	(	PUNCT
ejpam-4021	382	12	2021	2021	NUM
ejpam-4021	382	13	)	)	PUNCT
ejpam-4021	382	14	,	,	PUNCT
ejpam-4021	382	15	949	949	NUM
ejpam-4021	382	16	-	-	SYM
ejpam-4021	382	17	968	968	NUM
ejpam-4021	382	18	962	962	NUM
ejpam-4021	382	19	remark	remark	NOUN
ejpam-4021	382	20	6	6	NUM
ejpam-4021	382	21	.	.	PUNCT
ejpam-4021	383	1	if	if	SCONJ
ejpam-4021	383	2	we	we	PRON
ejpam-4021	383	3	consider	consider	VERB
ejpam-4021	383	4	each	each	DET
ejpam-4021	383	5	ν	ν	NOUN
ejpam-4021	383	6	∈	∈	PROPN
ejpam-4021	383	7	l(g	l(g	NOUN
ejpam-4021	383	8	)	)	PUNCT
ejpam-4021	383	9	,	,	PUNCT
ejpam-4021	383	10	i.e.	i.e.	X
ejpam-4021	383	11	,	,	PUNCT
ejpam-4021	383	12	each	each	PRON
ejpam-4021	383	13	ν	ν	X
ejpam-4021	383	14	∈	∈	PROPN
ejpam-4021	383	15	lg	lg	NOUN
ejpam-4021	383	16	is	be	AUX
ejpam-4021	383	17	an	an	DET
ejpam-4021	383	18	l	l	NOUN
ejpam-4021	383	19	-	-	PUNCT
ejpam-4021	383	20	valued	value	VERB
ejpam-4021	383	21	subgroup	subgroup	NOUN
ejpam-4021	383	22	of	of	ADP
ejpam-4021	383	23	the	the	DET
ejpam-4021	383	24	group	group	NOUN
ejpam-4021	383	25	g	g	PROPN
ejpam-4021	383	26	,	,	PUNCT
ejpam-4021	383	27	then	then	ADV
ejpam-4021	383	28	we	we	PRON
ejpam-4021	383	29	obtain	obtain	VERB
ejpam-4021	383	30	a	a	DET
ejpam-4021	383	31	category	category	NOUN
ejpam-4021	383	32	l	l	NOUN
ejpam-4021	383	33	-	-	NOUN
ejpam-4021	383	34	clgrp∗	clgrp∗	NOUN
ejpam-4021	383	35	of	of	ADP
ejpam-4021	383	36	all	all	DET
ejpam-4021	383	37	l	l	NOUN
ejpam-4021	383	38	-	-	PUNCT
ejpam-4021	383	39	valued	value	VERB
ejpam-4021	383	40	closure	closure	NOUN
ejpam-4021	383	41	of	of	ADP
ejpam-4021	383	42	l	l	NOUN
ejpam-4021	383	43	-	-	PUNCT
ejpam-4021	383	44	valued	value	VERB
ejpam-4021	383	45	subgroups	subgroup	NOUN
ejpam-4021	383	46	of	of	ADP
ejpam-4021	383	47	g	g	NOUN
ejpam-4021	383	48	,	,	PUNCT
ejpam-4021	383	49	and	and	CCONJ
ejpam-4021	383	50	closure	closure	NOUN
ejpam-4021	383	51	-	-	PUNCT
ejpam-4021	383	52	preserving	preserve	VERB
ejpam-4021	383	53	mappings	mapping	NOUN
ejpam-4021	383	54	.	.	PUNCT
ejpam-4021	384	1	then	then	ADV
ejpam-4021	384	2	l	l	NOUN
ejpam-4021	384	3	-	-	NOUN
ejpam-4021	384	4	clgrp∗	clgrp∗	NOUN
ejpam-4021	384	5	is	be	AUX
ejpam-4021	384	6	a	a	DET
ejpam-4021	384	7	subcategory	subcategory	NOUN
ejpam-4021	384	8	of	of	ADP
ejpam-4021	384	9	l	l	NOUN
ejpam-4021	384	10	-	-	PUNCT
ejpam-4021	384	11	clgrp	clgrp	NOUN
ejpam-4021	384	12	.	.	PUNCT
ejpam-4021	385	1	theorem	theorem	NOUN
ejpam-4021	385	2	4	4	NUM
ejpam-4021	385	3	.	.	PUNCT
ejpam-4021	386	1	l	l	NOUN
ejpam-4021	386	2	-	-	PUNCT
ejpam-4021	386	3	clgrp	clgrp	NOUN
ejpam-4021	386	4	is	be	AUX
ejpam-4021	386	5	a	a	DET
ejpam-4021	386	6	topological	topological	ADJ
ejpam-4021	386	7	category	category	NOUN
ejpam-4021	386	8	.	.	PUNCT
ejpam-4021	387	1	proof	proof	NOUN
ejpam-4021	387	2	.	.	PUNCT
ejpam-4021	388	1	consider	consider	VERB
ejpam-4021	388	2	(	(	PUNCT
ejpam-4021	388	3	g	g	NOUN
ejpam-4021	388	4	,	,	PUNCT
ejpam-4021	388	5	·	·	PUNCT
ejpam-4021	388	6	)	)	PUNCT
ejpam-4021	388	7	a	a	DET
ejpam-4021	388	8	group	group	NOUN
ejpam-4021	388	9	,	,	PUNCT
ejpam-4021	388	10	and	and	CCONJ
ejpam-4021	388	11	a	a	DET
ejpam-4021	388	12	source	source	NOUN
ejpam-4021	388	13	s	s	PART
ejpam-4021	388	14	=	=	X
ejpam-4021	388	15	(	(	PUNCT
ejpam-4021	388	16	fj	fj	INTJ
ejpam-4021	388	17	:	:	PUNCT
ejpam-4021	388	18	(	(	PUNCT
ejpam-4021	388	19	g	g	NOUN
ejpam-4021	388	20	,	,	PUNCT
ejpam-4021	388	21	·	·	PUNCT
ejpam-4021	388	22	)	)	PUNCT
ejpam-4021	389	1	−→	−→	NOUN
ejpam-4021	389	2	(	(	PUNCT
ejpam-4021	389	3	gj	gj	NOUN
ejpam-4021	389	4	,	,	PUNCT
ejpam-4021	389	5	·	·	PUNCT
ejpam-4021	389	6	,	,	PUNCT
ejpam-4021	389	7	`	`	PUNCT
ejpam-4021	389	8	j))j∈j	j))j∈j	NOUN
ejpam-4021	389	9	of	of	ADP
ejpam-4021	389	10	family	family	NOUN
ejpam-4021	389	11	of	of	ADP
ejpam-4021	389	12	functions	function	NOUN
ejpam-4021	389	13	,	,	PUNCT
ejpam-4021	389	14	where	where	SCONJ
ejpam-4021	389	15	for	for	ADP
ejpam-4021	389	16	each	each	DET
ejpam-4021	389	17	j	j	PROPN
ejpam-4021	389	18	∈	∈	PROPN
ejpam-4021	389	19	j	j	PROPN
ejpam-4021	389	20	,	,	PUNCT
ejpam-4021	389	21	fj	fj	INTJ
ejpam-4021	389	22	:	:	PUNCT
ejpam-4021	389	23	g	g	PROPN
ejpam-4021	389	24	−→	−→	NOUN
ejpam-4021	389	25	gj	gj	NOUN
ejpam-4021	389	26	is	be	AUX
ejpam-4021	389	27	a	a	DET
ejpam-4021	389	28	group	group	NOUN
ejpam-4021	389	29	homomorphism	homomorphism	NOUN
ejpam-4021	389	30	,	,	PUNCT
ejpam-4021	389	31	then	then	ADV
ejpam-4021	389	32	ω	ω	X
ejpam-4021	389	33	=	=	SYM
ejpam-4021	389	34	{	{	PUNCT
ejpam-4021	389	35	ω	ω	NUM
ejpam-4021	389	36	∈	∈	PROPN
ejpam-4021	389	37	lg	lg	NOUN
ejpam-4021	389	38	:	:	PUNCT
ejpam-4021	389	39	ω	ω	NUM
ejpam-4021	389	40	=	=	SYM
ejpam-4021	389	41	∧	∧	PROPN
ejpam-4021	389	42	j∈j	j∈j	NOUN
ejpam-4021	389	43	f	f	PROPN
ejpam-4021	389	44	←	←	PROPN
ejpam-4021	389	45	j	j	PROPN
ejpam-4021	389	46	(	(	PUNCT
ejpam-4021	389	47	ωj	ωj	NOUN
ejpam-4021	389	48	)	)	PUNCT
ejpam-4021	389	49	,	,	PUNCT
ejpam-4021	389	50	∀ωj	∀ωj	NOUN
ejpam-4021	389	51	=	=	PUNCT
ejpam-4021	389	52	`	`	PUNCT
ejpam-4021	389	53	j(ωj	j(ωj	PROPN
ejpam-4021	389	54	)	)	PUNCT
ejpam-4021	389	55	,	,	PUNCT
ejpam-4021	389	56	j	j	PROPN
ejpam-4021	389	57	∈	∈	PROPN
ejpam-4021	389	58	j	j	PROPN
ejpam-4021	389	59	}	}	PUNCT
ejpam-4021	389	60	in	in	ADP
ejpam-4021	389	61	view	view	NOUN
ejpam-4021	389	62	of	of	ADP
ejpam-4021	389	63	theorem	theorem	NOUN
ejpam-4021	389	64	3	3	NUM
ejpam-4021	389	65	,	,	PUNCT
ejpam-4021	389	66	we	we	PRON
ejpam-4021	389	67	have	have	AUX
ejpam-4021	389	68	(	(	PUNCT
ejpam-4021	389	69	g	g	NOUN
ejpam-4021	389	70	,	,	PUNCT
ejpam-4021	389	71	·	·	PUNCT
ejpam-4021	389	72	,	,	PUNCT
ejpam-4021	389	73	`	`	PUNCT
ejpam-4021	389	74	)	)	PUNCT
ejpam-4021	389	75	is	be	AUX
ejpam-4021	389	76	an	an	DET
ejpam-4021	389	77	l	l	NOUN
ejpam-4021	389	78	-	-	PUNCT
ejpam-4021	389	79	valued	value	VERB
ejpam-4021	389	80	closure	closure	NOUN
ejpam-4021	389	81	space	space	NOUN
ejpam-4021	389	82	.	.	PUNCT
ejpam-4021	390	1	we	we	PRON
ejpam-4021	390	2	only	only	ADV
ejpam-4021	390	3	verify	verify	VERB
ejpam-4021	390	4	(	(	PUNCT
ejpam-4021	390	5	clgm	clgm	NOUN
ejpam-4021	390	6	)	)	PUNCT
ejpam-4021	390	7	.	.	PUNCT
ejpam-4021	391	1	so	so	ADV
ejpam-4021	391	2	we	we	PRON
ejpam-4021	391	3	have	have	VERB
ejpam-4021	391	4	:	:	PUNCT
ejpam-4021	391	5	`	`	PUNCT
ejpam-4021	391	6	(	(	PUNCT
ejpam-4021	391	7	ω)(x	ω)(x	NOUN
ejpam-4021	391	8	)	)	PUNCT
ejpam-4021	391	9	∗	∗	NOUN
ejpam-4021	391	10	`	`	PUNCT
ejpam-4021	391	11	(	(	PUNCT
ejpam-4021	391	12	ω)(y	ω)(y	NUM
ejpam-4021	391	13	)	)	PUNCT
ejpam-4021	391	14	=	=	SYM
ejpam-4021	392	1	∧	∧	PROPN
ejpam-4021	392	2	j∈j	j∈j	NOUN
ejpam-4021	392	3	f	f	PROPN
ejpam-4021	392	4	←	←	PROPN
ejpam-4021	392	5	j	j	PROPN
ejpam-4021	392	6	(	(	PUNCT
ejpam-4021	392	7	ωj)(x	ωj)(x	PROPN
ejpam-4021	392	8	)	)	PUNCT
ejpam-4021	392	9	∗	∗	NOUN
ejpam-4021	392	10	∧	∧	PROPN
ejpam-4021	392	11	j∈j	j∈j	NOUN
ejpam-4021	392	12	f	f	PROPN
ejpam-4021	392	13	←	←	PROPN
ejpam-4021	392	14	j	j	PROPN
ejpam-4021	392	15	(	(	PUNCT
ejpam-4021	392	16	ωj)(y	ωj)(y	PROPN
ejpam-4021	392	17	)	)	PUNCT
ejpam-4021	392	18	≤	≤	NUM
ejpam-4021	393	1	∧	∧	PROPN
ejpam-4021	393	2	j∈j	j∈j	NOUN
ejpam-4021	393	3	f	f	PROPN
ejpam-4021	393	4	←	←	PROPN
ejpam-4021	393	5	j	j	PROPN
ejpam-4021	393	6	(	(	PUNCT
ejpam-4021	393	7	ωj	ωj	NOUN
ejpam-4021	393	8	)	)	PUNCT
ejpam-4021	393	9	�	�	PROPN
ejpam-4021	393	10	f←j	f←j	PUNCT
ejpam-4021	393	11	(	(	PUNCT
ejpam-4021	393	12	ωj)(xy	ωj)(xy	PROPN
ejpam-4021	393	13	)	)	PUNCT
ejpam-4021	393	14	=	=	SYM
ejpam-4021	394	1	∧	∧	PROPN
ejpam-4021	394	2	j∈j	j∈j	NOUN
ejpam-4021	394	3	f	f	PROPN
ejpam-4021	394	4	←	←	PROPN
ejpam-4021	394	5	j	j	PROPN
ejpam-4021	394	6	(	(	PUNCT
ejpam-4021	394	7	ωj	ωj	ADP
ejpam-4021	394	8	�	�	PROPN
ejpam-4021	394	9	ωj)(xy	ωj)(xy	NUM
ejpam-4021	394	10	)	)	PUNCT
ejpam-4021	394	11	≤	≤	NUM
ejpam-4021	394	12	`	`	PUNCT
ejpam-4021	394	13	(	(	PUNCT
ejpam-4021	394	14	ω	ω	PROPN
ejpam-4021	394	15	·	·	PUNCT
ejpam-4021	394	16	ω)(xy	ω)(xy	NUM
ejpam-4021	394	17	)	)	PUNCT
ejpam-4021	394	18	.	.	PUNCT
ejpam-4021	395	1	definition	definition	NOUN
ejpam-4021	395	2	17	17	NUM
ejpam-4021	395	3	.	.	PUNCT
ejpam-4021	396	1	[	[	X
ejpam-4021	396	2	8	8	NUM
ejpam-4021	396	3	,	,	PUNCT
ejpam-4021	396	4	19	19	NUM
ejpam-4021	396	5	,	,	PUNCT
ejpam-4021	396	6	32	32	NUM
ejpam-4021	396	7	]	]	PUNCT
ejpam-4021	396	8	an	an	DET
ejpam-4021	396	9	l	l	NOUN
ejpam-4021	396	10	-	-	NOUN
ejpam-4021	396	11	tolerance	tolerance	NOUN
ejpam-4021	396	12	space	space	NOUN
ejpam-4021	396	13	is	be	AUX
ejpam-4021	396	14	a	a	DET
ejpam-4021	396	15	pair	pair	NOUN
ejpam-4021	396	16	(	(	PUNCT
ejpam-4021	396	17	x	x	X
ejpam-4021	396	18	,	,	PUNCT
ejpam-4021	396	19	τ	τ	PROPN
ejpam-4021	396	20	)	)	PUNCT
ejpam-4021	396	21	,	,	PUNCT
ejpam-4021	396	22	where	where	SCONJ
ejpam-4021	396	23	τ	τ	PROPN
ejpam-4021	396	24	:	:	PUNCT
ejpam-4021	396	25	x	x	SYM
ejpam-4021	396	26	×x	×x	VERB
ejpam-4021	396	27	−→	−→	NOUN
ejpam-4021	396	28	l	l	NOUN
ejpam-4021	396	29	such	such	ADJ
ejpam-4021	396	30	that	that	SCONJ
ejpam-4021	396	31	(	(	PUNCT
ejpam-4021	396	32	t1	t1	NOUN
ejpam-4021	396	33	)	)	PUNCT
ejpam-4021	396	34	τ(x	τ(x	NOUN
ejpam-4021	396	35	,	,	PUNCT
ejpam-4021	396	36	x	x	X
ejpam-4021	396	37	)	)	PUNCT
ejpam-4021	397	1	=	=	SYM
ejpam-4021	397	2	>	>	PUNCT
ejpam-4021	397	3	,	,	PUNCT
ejpam-4021	397	4	∀x	∀x	VERB
ejpam-4021	397	5	∈	∈	NOUN
ejpam-4021	397	6	x	x	INTJ
ejpam-4021	397	7	(	(	PUNCT
ejpam-4021	397	8	reflexivity	reflexivity	NOUN
ejpam-4021	397	9	)	)	PUNCT
ejpam-4021	397	10	;	;	PUNCT
ejpam-4021	397	11	(	(	PUNCT
ejpam-4021	397	12	t2	t2	NOUN
ejpam-4021	397	13	)	)	PUNCT
ejpam-4021	397	14	τ(x	τ(x	NOUN
ejpam-4021	397	15	,	,	PUNCT
ejpam-4021	397	16	y	y	NOUN
ejpam-4021	397	17	)	)	PUNCT
ejpam-4021	397	18	=	=	PUNCT
ejpam-4021	398	1	τ(y	τ(y	PROPN
ejpam-4021	398	2	,	,	PUNCT
ejpam-4021	398	3	x	x	NOUN
ejpam-4021	398	4	)	)	PUNCT
ejpam-4021	398	5	(	(	PUNCT
ejpam-4021	398	6	symmetry	symmetry	NOUN
ejpam-4021	398	7	)	)	PUNCT
ejpam-4021	398	8	.	.	PUNCT
ejpam-4021	399	1	if	if	SCONJ
ejpam-4021	399	2	,	,	PUNCT
ejpam-4021	399	3	in	in	ADP
ejpam-4021	399	4	addition	addition	NOUN
ejpam-4021	399	5	τ	τ	PROPN
ejpam-4021	399	6	satisfies	satisfie	NOUN
ejpam-4021	399	7	(	(	PUNCT
ejpam-4021	399	8	t3	t3	NOUN
ejpam-4021	399	9	)	)	PUNCT
ejpam-4021	399	10	τ(x	τ(x	PROPN
ejpam-4021	399	11	,	,	PUNCT
ejpam-4021	399	12	y	y	NOUN
ejpam-4021	399	13	)	)	PUNCT
ejpam-4021	399	14	∗	∗	NOUN
ejpam-4021	399	15	τ(y	τ(y	PROPN
ejpam-4021	399	16	,	,	PUNCT
ejpam-4021	399	17	z	z	NOUN
ejpam-4021	399	18	)	)	PUNCT
ejpam-4021	399	19	≤	≤	NOUN
ejpam-4021	400	1	τ(x	τ(x	PUNCT
ejpam-4021	400	2	,	,	PUNCT
ejpam-4021	400	3	z	z	NOUN
ejpam-4021	400	4	)	)	PUNCT
ejpam-4021	400	5	,	,	PUNCT
ejpam-4021	400	6	for	for	ADP
ejpam-4021	400	7	any	any	DET
ejpam-4021	400	8	x	x	NOUN
ejpam-4021	400	9	,	,	PUNCT
ejpam-4021	400	10	y	y	PROPN
ejpam-4021	400	11	,	,	PUNCT
ejpam-4021	400	12	z	z	PROPN
ejpam-4021	400	13	∈	∈	PROPN
ejpam-4021	401	1	x	x	X
ejpam-4021	401	2	,	,	PUNCT
ejpam-4021	401	3	then	then	ADV
ejpam-4021	401	4	we	we	PRON
ejpam-4021	401	5	speak	speak	VERB
ejpam-4021	401	6	of	of	ADP
ejpam-4021	401	7	transitive	transitive	ADJ
ejpam-4021	401	8	tolerance	tolerance	NOUN
ejpam-4021	401	9	relation	relation	NOUN
ejpam-4021	401	10	which	which	PRON
ejpam-4021	401	11	is	be	AUX
ejpam-4021	401	12	essentially	essentially	ADV
ejpam-4021	401	13	gives	give	VERB
ejpam-4021	401	14	an	an	DET
ejpam-4021	401	15	l	l	NOUN
ejpam-4021	401	16	-	-	PUNCT
ejpam-4021	401	17	equivalence	equivalence	NOUN
ejpam-4021	401	18	relation	relation	NOUN
ejpam-4021	401	19	.	.	PUNCT
ejpam-4021	402	1	a	a	DET
ejpam-4021	402	2	mapping	mapping	NOUN
ejpam-4021	402	3	between	between	ADP
ejpam-4021	402	4	l	l	NOUN
ejpam-4021	402	5	-	-	PUNCT
ejpam-4021	402	6	valued	value	VERB
ejpam-4021	402	7	tolerance	tolerance	NOUN
ejpam-4021	402	8	spaces	space	NOUN
ejpam-4021	402	9	(	(	PUNCT
ejpam-4021	402	10	resp	resp	NOUN
ejpam-4021	402	11	.	.	PUNCT
ejpam-4021	403	1	transitive	transitive	PROPN
ejpam-4021	403	2	l	l	ADV
ejpam-4021	403	3	-	-	PUNCT
ejpam-4021	403	4	valued	value	VERB
ejpam-4021	403	5	tolerance	tolerance	NOUN
ejpam-4021	403	6	spaces	space	VERB
ejpam-4021	403	7	):	):	PUNCT
ejpam-4021	403	8	f	f	X
ejpam-4021	403	9	:	:	PUNCT
ejpam-4021	403	10	(	(	PUNCT
ejpam-4021	403	11	x	x	X
ejpam-4021	403	12	,	,	PUNCT
ejpam-4021	403	13	τ	τ	NOUN
ejpam-4021	403	14	)	)	PUNCT
ejpam-4021	403	15	−→	−→	NOUN
ejpam-4021	403	16	(	(	PUNCT
ejpam-4021	403	17	y	y	PROPN
ejpam-4021	403	18	,	,	PUNCT
ejpam-4021	403	19	τ	τ	PROPN
ejpam-4021	403	20	′	′	NUM
ejpam-4021	403	21	)	)	PUNCT
ejpam-4021	403	22	is	be	AUX
ejpam-4021	403	23	called	call	VERB
ejpam-4021	403	24	l	l	ADV
ejpam-4021	403	25	-	-	PUNCT
ejpam-4021	403	26	valued	value	VERB
ejpam-4021	403	27	tolerance	tolerance	NOUN
ejpam-4021	403	28	preserving	preserve	VERB
ejpam-4021	403	29	if	if	SCONJ
ejpam-4021	403	30	τ(x	τ(x	NOUN
ejpam-4021	403	31	,	,	PUNCT
ejpam-4021	403	32	y	y	NOUN
ejpam-4021	403	33	)	)	PUNCT
ejpam-4021	403	34	≤	≤	NOUN
ejpam-4021	403	35	τ	τ	X
ejpam-4021	403	36	′(f(x	′(f(x	NOUN
ejpam-4021	403	37	)	)	PUNCT
ejpam-4021	403	38	,	,	PUNCT
ejpam-4021	403	39	f(y	f(y	NOUN
ejpam-4021	403	40	)	)	PUNCT
ejpam-4021	403	41	)	)	PUNCT
ejpam-4021	403	42	.	.	PUNCT
ejpam-4021	404	1	the	the	DET
ejpam-4021	404	2	category	category	NOUN
ejpam-4021	404	3	of	of	ADP
ejpam-4021	404	4	all	all	DET
ejpam-4021	404	5	l	l	NOUN
ejpam-4021	404	6	-	-	PUNCT
ejpam-4021	404	7	valued	value	VERB
ejpam-4021	404	8	tolerance	tolerance	NOUN
ejpam-4021	404	9	spaces	space	NOUN
ejpam-4021	404	10	and	and	CCONJ
ejpam-4021	404	11	l	l	NOUN
ejpam-4021	404	12	-	-	NOUN
ejpam-4021	404	13	tolerance	tolerance	NOUN
ejpam-4021	404	14	preserving	preserve	VERB
ejpam-4021	404	15	mappings	mapping	NOUN
ejpam-4021	404	16	is	be	AUX
ejpam-4021	404	17	denoted	denote	VERB
ejpam-4021	404	18	by	by	ADP
ejpam-4021	404	19	l	l	NOUN
ejpam-4021	404	20	-	-	NOUN
ejpam-4021	404	21	tol	tol	NOUN
ejpam-4021	404	22	while	while	SCONJ
ejpam-4021	404	23	l	l	NOUN
ejpam-4021	404	24	-	-	ADJ
ejpam-4021	404	25	trantol	trantol	NOUN
ejpam-4021	404	26	denotes	denote	VERB
ejpam-4021	404	27	the	the	DET
ejpam-4021	404	28	category	category	NOUN
ejpam-4021	404	29	of	of	ADP
ejpam-4021	404	30	transitive	transitive	ADJ
ejpam-4021	404	31	l	l	NOUN
ejpam-4021	404	32	-	-	NOUN
ejpam-4021	404	33	tolerance	tolerance	NOUN
ejpam-4021	404	34	spaces	space	NOUN
ejpam-4021	404	35	.	.	PUNCT
ejpam-4021	405	1	for	for	ADP
ejpam-4021	405	2	an	an	DET
ejpam-4021	405	3	mv	mv	PROPN
ejpam-4021	405	4	-	-	PUNCT
ejpam-4021	405	5	valued	value	VERB
ejpam-4021	405	6	algebra	algebra	NOUN
ejpam-4021	405	7	l	l	NOUN
ejpam-4021	405	8	,	,	PUNCT
ejpam-4021	405	9	given	give	VERB
ejpam-4021	405	10	l	l	NOUN
ejpam-4021	405	11	-	-	NOUN
ejpam-4021	405	12	trantol	trantol	VERB
ejpam-4021	405	13	a	a	DET
ejpam-4021	405	14	category	category	NOUN
ejpam-4021	405	15	of	of	ADP
ejpam-4021	405	16	transitive	transitive	ADJ
ejpam-4021	405	17	l	l	ADV
ejpam-4021	405	18	-	-	PUNCT
ejpam-4021	405	19	valued	value	VERB
ejpam-4021	405	20	tolerance	tolerance	NOUN
ejpam-4021	405	21	spaces	space	NOUN
ejpam-4021	405	22	and	and	CCONJ
ejpam-4021	405	23	l	l	NOUN
ejpam-4021	405	24	-	-	PUNCT
ejpam-4021	405	25	valued	value	VERB
ejpam-4021	405	26	tolerance	tolerance	NOUN
ejpam-4021	405	27	preserving	preserve	VERB
ejpam-4021	405	28	mappings	mapping	NOUN
ejpam-4021	405	29	,	,	PUNCT
ejpam-4021	405	30	one	one	PRON
ejpam-4021	405	31	can	can	AUX
ejpam-4021	405	32	obtain	obtain	VERB
ejpam-4021	405	33	a	a	DET
ejpam-4021	405	34	functor	functor	NOUN
ejpam-4021	405	35	a	a	DET
ejpam-4021	405	36	:	:	PUNCT
ejpam-4021	405	37	ltol−→	ltol−→	NOUN
ejpam-4021	405	38	l	l	NOUN
ejpam-4021	405	39	-	-	PUNCT
ejpam-4021	405	40	set	set	VERB
ejpam-4021	405	41	where	where	SCONJ
ejpam-4021	405	42	a(x	a(x	NOUN
ejpam-4021	405	43	,	,	PUNCT
ejpam-4021	405	44	τ	τ	NOUN
ejpam-4021	405	45	)	)	PUNCT
ejpam-4021	405	46	=	=	SYM
ejpam-4021	405	47	(	(	PUNCT
ejpam-4021	405	48	x	x	X
ejpam-4021	405	49	,	,	PUNCT
ejpam-4021	405	50	τd	τd	ADJ
ejpam-4021	405	51	)	)	PUNCT
ejpam-4021	405	52	,	,	PUNCT
ejpam-4021	406	1	d	d	NOUN
ejpam-4021	406	2	:	:	PUNCT
ejpam-4021	406	3	x	x	PUNCT
ejpam-4021	406	4	−→	−→	NOUN
ejpam-4021	406	5	x	x	X
ejpam-4021	406	6	×x	×x	VERB
ejpam-4021	406	7	and	and	CCONJ
ejpam-4021	406	8	a(f	a(f	PROPN
ejpam-4021	406	9	)	)	PUNCT
ejpam-4021	407	1	=	=	SYM
ejpam-4021	407	2	f	f	PROPN
ejpam-4021	407	3	,	,	PUNCT
ejpam-4021	407	4	here	here	ADV
ejpam-4021	407	5	a(f	a(f	PROPN
ejpam-4021	407	6	)	)	PUNCT
ejpam-4021	407	7	sends	send	VERB
ejpam-4021	407	8	f	f	PROPN
ejpam-4021	407	9	to	to	ADP
ejpam-4021	407	10	an	an	DET
ejpam-4021	407	11	l	l	NOUN
ejpam-4021	407	12	-	-	NOUN
ejpam-4021	407	13	tolerance	tolerance	NOUN
ejpam-4021	407	14	preserving	preserve	VERB
ejpam-4021	407	15	mapping	mapping	NOUN
ejpam-4021	407	16	to	to	ADP
ejpam-4021	407	17	f	f	PROPN
ejpam-4021	407	18	:	:	PUNCT
ejpam-4021	407	19	(	(	PUNCT
ejpam-4021	407	20	x	x	X
ejpam-4021	407	21	,	,	PUNCT
ejpam-4021	407	22	τd	τd	ADJ
ejpam-4021	407	23	)	)	PUNCT
ejpam-4021	407	24	−→	−→	NOUN
ejpam-4021	407	25	(	(	PUNCT
ejpam-4021	407	26	y	y	PROPN
ejpam-4021	407	27	,	,	PUNCT
ejpam-4021	407	28	τ	τ	PROPN
ejpam-4021	407	29	′d	′d	NOUN
ejpam-4021	407	30	)	)	PUNCT
ejpam-4021	407	31	,	,	PUNCT
ejpam-4021	407	32	i.e.	i.e.	X
ejpam-4021	407	33	,	,	PUNCT
ejpam-4021	407	34	τd(x	τd(x	PUNCT
ejpam-4021	407	35	)	)	PUNCT
ejpam-4021	407	36	=	=	SYM
ejpam-4021	407	37	τ(x	τ(x	NOUN
ejpam-4021	407	38	,	,	PUNCT
ejpam-4021	407	39	x	x	X
ejpam-4021	407	40	)	)	PUNCT
ejpam-4021	407	41	≤	≤	NUM
ejpam-4021	407	42	τ	τ	X
ejpam-4021	407	43	′(f(x	′(f(x	NOUN
ejpam-4021	407	44	)	)	PUNCT
ejpam-4021	407	45	,	,	PUNCT
ejpam-4021	407	46	f(x	f(x	PROPN
ejpam-4021	407	47	)	)	PUNCT
ejpam-4021	407	48	)	)	PUNCT
ejpam-4021	408	1	=	=	PUNCT
ejpam-4021	408	2	τ	τ	X
ejpam-4021	408	3	′d(f(x	′d(f(x	NUM
ejpam-4021	408	4	)	)	PUNCT
ejpam-4021	408	5	)	)	PUNCT
ejpam-4021	408	6	,	,	PUNCT
ejpam-4021	408	7	i.e.	i.e.	X
ejpam-4021	408	8	,	,	PUNCT
ejpam-4021	408	9	τd(x	τd(x	PUNCT
ejpam-4021	408	10	)	)	PUNCT
ejpam-4021	408	11	≤	≤	NUM
ejpam-4021	408	12	τ	τ	X
ejpam-4021	408	13	′d(f(x	′d(f(x	NUM
ejpam-4021	408	14	)	)	PUNCT
ejpam-4021	408	15	)	)	PUNCT
ejpam-4021	408	16	.	.	PUNCT
ejpam-4021	409	1	conversely	conversely	ADV
ejpam-4021	409	2	,	,	PUNCT
ejpam-4021	409	3	given	give	VERB
ejpam-4021	409	4	l	l	NOUN
ejpam-4021	409	5	-	-	NOUN
ejpam-4021	409	6	set	set	ADJ
ejpam-4021	409	7	,	,	PUNCT
ejpam-4021	409	8	one	one	PRON
ejpam-4021	409	9	obtains	obtain	VERB
ejpam-4021	409	10	a	a	DET
ejpam-4021	409	11	functor	functor	PROPN
ejpam-4021	409	12	b	b	PROPN
ejpam-4021	409	13	:	:	PUNCT
ejpam-4021	409	14	l	l	NOUN
ejpam-4021	409	15	-	-	PUNCT
ejpam-4021	409	16	set−→	set−→	NOUN
ejpam-4021	409	17	l	l	NOUN
ejpam-4021	409	18	-	-	NOUN
ejpam-4021	409	19	trantol	trantol	NOUN
ejpam-4021	409	20	as	as	SCONJ
ejpam-4021	409	21	defined	define	VERB
ejpam-4021	409	22	by	by	ADP
ejpam-4021	409	23	:	:	PUNCT
ejpam-4021	409	24	b(x	b(x	ADJ
ejpam-4021	409	25	,	,	PUNCT
ejpam-4021	409	26	ν	ν	NOUN
ejpam-4021	409	27	)	)	PUNCT
ejpam-4021	409	28	=	=	SYM
ejpam-4021	409	29	(	(	PUNCT
ejpam-4021	409	30	x	x	X
ejpam-4021	409	31	,	,	PUNCT
ejpam-4021	409	32	τ	τ	X
ejpam-4021	409	33	:	:	PUNCT
ejpam-4021	409	34	=	=	PUNCT
ejpam-4021	409	35	ν∧ν	ν∧ν	VERB
ejpam-4021	409	36	)	)	PUNCT
ejpam-4021	409	37	and	and	CCONJ
ejpam-4021	409	38	b(f	b(f	PROPN
ejpam-4021	409	39	)	)	PUNCT
ejpam-4021	410	1	=	=	SYM
ejpam-4021	410	2	f	f	PROPN
ejpam-4021	410	3	,	,	PUNCT
ejpam-4021	410	4	τ(x	τ(x	PROPN
ejpam-4021	410	5	,	,	PUNCT
ejpam-4021	410	6	y	y	NOUN
ejpam-4021	410	7	)	)	PUNCT
ejpam-4021	410	8	=	=	SYM
ejpam-4021	411	1	ν(x	ν(x	PROPN
ejpam-4021	411	2	)	)	PUNCT
ejpam-4021	411	3	∧	∧	PROPN
ejpam-4021	411	4	ν(y	ν(y	PROPN
ejpam-4021	411	5	)	)	PUNCT
ejpam-4021	411	6	≤	≤	NUM
ejpam-4021	411	7	ν(f(x	ν(f(x	PROPN
ejpam-4021	411	8	)	)	PUNCT
ejpam-4021	411	9	)	)	PUNCT
ejpam-4021	412	1	∧	∧	PROPN
ejpam-4021	412	2	ν(f(y	ν(f(y	PROPN
ejpam-4021	412	3	)	)	PUNCT
ejpam-4021	412	4	)	)	PUNCT
ejpam-4021	413	1	=	=	PUNCT
ejpam-4021	413	2	τ(f(x	τ(f(x	PROPN
ejpam-4021	413	3	)	)	PUNCT
ejpam-4021	413	4	,	,	PUNCT
ejpam-4021	413	5	f(y	f(y	NOUN
ejpam-4021	413	6	)	)	PUNCT
ejpam-4021	413	7	)	)	PUNCT
ejpam-4021	413	8	.	.	PUNCT
ejpam-4021	414	1	in	in	ADP
ejpam-4021	414	2	view	view	NOUN
ejpam-4021	414	3	of	of	ADP
ejpam-4021	414	4	[	[	X
ejpam-4021	414	5	11	11	NUM
ejpam-4021	414	6	]	]	PUNCT
ejpam-4021	414	7	,	,	PUNCT
ejpam-4021	414	8	pp	pp	ADP
ejpam-4021	414	9	148	148	NUM
ejpam-4021	414	10	,	,	PUNCT
ejpam-4021	414	11	for	for	ADP
ejpam-4021	414	12	a	a	DET
ejpam-4021	414	13	group	group	NOUN
ejpam-4021	414	14	(	(	PUNCT
ejpam-4021	414	15	g	g	NOUN
ejpam-4021	414	16	,	,	PUNCT
ejpam-4021	414	17	·	·	PUNCT
ejpam-4021	414	18	)	)	PUNCT
ejpam-4021	414	19	,	,	PUNCT
ejpam-4021	414	20	we	we	PRON
ejpam-4021	414	21	consider	consider	VERB
ejpam-4021	414	22	a	a	DET
ejpam-4021	414	23	mapping	mapping	NOUN
ejpam-4021	414	24	%	%	NOUN
ejpam-4021	414	25	l	l	NOUN
ejpam-4021	414	26	:	:	PUNCT
ejpam-4021	414	27	lg	lg	NOUN
ejpam-4021	414	28	−→	−→	ADJ
ejpam-4021	414	29	lg×g	lg×g	PROPN
ejpam-4021	414	30	defined	define	VERB
ejpam-4021	414	31	by	by	ADP
ejpam-4021	414	32	:	:	PUNCT
ejpam-4021	414	33	%	%	NOUN
ejpam-4021	414	34	l(ν)(x	l(ν)(x	PROPN
ejpam-4021	414	35	,	,	PUNCT
ejpam-4021	414	36	y	y	NOUN
ejpam-4021	414	37	)	)	PUNCT
ejpam-4021	414	38	=	=	SYM
ejpam-4021	414	39	ν(x−1y	ν(x−1y	ADJ
ejpam-4021	414	40	)	)	PUNCT
ejpam-4021	414	41	,	,	PUNCT
ejpam-4021	414	42	and	and	CCONJ
ejpam-4021	414	43	analogously	analogously	ADV
ejpam-4021	414	44	,	,	PUNCT
ejpam-4021	414	45	%	%	NOUN
ejpam-4021	414	46	r(ν)(x	r(ν)(x	PROPN
ejpam-4021	414	47	,	,	PUNCT
ejpam-4021	414	48	y	y	NOUN
ejpam-4021	414	49	)	)	PUNCT
ejpam-4021	414	50	=	=	SYM
ejpam-4021	414	51	ν(xy−1	ν(xy−1	NOUN
ejpam-4021	414	52	)	)	PUNCT
ejpam-4021	414	53	.	.	PUNCT
ejpam-4021	415	1	then	then	ADV
ejpam-4021	415	2	we	we	PRON
ejpam-4021	415	3	have	have	VERB
ejpam-4021	415	4	the	the	DET
ejpam-4021	415	5	following	following	NOUN
ejpam-4021	415	6	.	.	PUNCT
ejpam-4021	416	1	lemma	lemma	PROPN
ejpam-4021	416	2	7	7	X
ejpam-4021	416	3	.	.	PUNCT
ejpam-4021	417	1	let	let	VERB
ejpam-4021	417	2	(	(	PUNCT
ejpam-4021	417	3	g	g	NOUN
ejpam-4021	417	4	,	,	PUNCT
ejpam-4021	417	5	·	·	PUNCT
ejpam-4021	417	6	)	)	PUNCT
ejpam-4021	417	7	∈	∈	PROPN
ejpam-4021	417	8	|grp|	|grp|	NOUN
ejpam-4021	417	9	,	,	PUNCT
ejpam-4021	417	10	and	and	CCONJ
ejpam-4021	417	11	the	the	DET
ejpam-4021	417	12	category	category	NOUN
ejpam-4021	417	13	l	l	NOUN
ejpam-4021	417	14	-	-	NOUN
ejpam-4021	417	15	trantol	trantol	NOUN
ejpam-4021	417	16	consists	consist	VERB
ejpam-4021	417	17	of	of	ADP
ejpam-4021	417	18	morphisms	morphism	NOUN
ejpam-4021	417	19	f	f	NOUN
ejpam-4021	417	20	:	:	PUNCT
ejpam-4021	417	21	(	(	PUNCT
ejpam-4021	417	22	g	g	NOUN
ejpam-4021	417	23	,	,	PUNCT
ejpam-4021	417	24	τ	τ	NOUN
ejpam-4021	417	25	)	)	PUNCT
ejpam-4021	417	26	−→	−→	NOUN
ejpam-4021	417	27	(	(	PUNCT
ejpam-4021	417	28	h	h	NOUN
ejpam-4021	417	29	,	,	PUNCT
ejpam-4021	417	30	%	%	NOUN
ejpam-4021	417	31	′	′	NOUN
ejpam-4021	417	32	)	)	PUNCT
ejpam-4021	417	33	which	which	PRON
ejpam-4021	417	34	are	be	AUX
ejpam-4021	417	35	l	l	ADV
ejpam-4021	417	36	-	-	PUNCT
ejpam-4021	417	37	valued	value	VERB
ejpam-4021	417	38	tolerance	tolerance	NOUN
ejpam-4021	417	39	preserving	preserve	VERB
ejpam-4021	417	40	such	such	ADJ
ejpam-4021	417	41	that	that	SCONJ
ejpam-4021	417	42	each	each	DET
ejpam-4021	417	43	morphism	morphism	NOUN
ejpam-4021	417	44	is	be	AUX
ejpam-4021	417	45	a	a	DET
ejpam-4021	417	46	group	group	NOUN
ejpam-4021	417	47	homomorphism	homomorphism	NOUN
ejpam-4021	417	48	.	.	PUNCT
ejpam-4021	418	1	then	then	ADV
ejpam-4021	418	2	a	a	DET
ejpam-4021	418	3	:	:	PUNCT
ejpam-4021	418	4			PUNCT
ejpam-4021	418	5	l	l	NOUN
ejpam-4021	418	6	-	-	PUNCT
ejpam-4021	418	7	grp	grp	NOUN
ejpam-4021	418	8	−→	−→	NOUN
ejpam-4021	418	9	l−trantol	l−trantol	PROPN
ejpam-4021	418	10	(	(	PUNCT
ejpam-4021	418	11	g	g	NOUN
ejpam-4021	418	12	,	,	PUNCT
ejpam-4021	418	13	ν	ν	NOUN
ejpam-4021	418	14	)	)	PUNCT
ejpam-4021	418	15	7−→	7−→	NOUN
ejpam-4021	418	16	(	(	PUNCT
ejpam-4021	418	17	g	g	NOUN
ejpam-4021	418	18	,	,	PUNCT
ejpam-4021	418	19	%	%	X
ejpam-4021	418	20	l(ν	l(ν	PROPN
ejpam-4021	418	21	)	)	PUNCT
ejpam-4021	418	22	)	)	PUNCT
ejpam-4021	419	1	f	f	X
ejpam-4021	420	1	7−→	7−→	NOUN
ejpam-4021	420	2	f	f	PROPN
ejpam-4021	421	1	t	t	PROPN
ejpam-4021	421	2	m	m	PROPN
ejpam-4021	421	3	g	g	NOUN
ejpam-4021	421	4	ahsanullah	ahsanullah	NOUN
ejpam-4021	421	5	,	,	PUNCT
ejpam-4021	421	6	fawzi	fawzi	PROPN
ejpam-4021	421	7	al	al	PROPN
ejpam-4021	421	8	-	-	PUNCT
ejpam-4021	421	9	thukair	thukair	NOUN
ejpam-4021	421	10	/	/	SYM
ejpam-4021	421	11	eur	eur	NOUN
ejpam-4021	421	12	.	.	PUNCT
ejpam-4021	422	1	j.	j.	PROPN
ejpam-4021	422	2	pure	pure	PROPN
ejpam-4021	422	3	appl	appl	PROPN
ejpam-4021	422	4	.	.	PROPN
ejpam-4021	422	5	math	math	PROPN
ejpam-4021	422	6	,	,	PUNCT
ejpam-4021	422	7	14	14	NUM
ejpam-4021	422	8	(	(	PUNCT
ejpam-4021	422	9	3	3	NUM
ejpam-4021	422	10	)	)	PUNCT
ejpam-4021	422	11	(	(	PUNCT
ejpam-4021	422	12	2021	2021	NUM
ejpam-4021	422	13	)	)	PUNCT
ejpam-4021	422	14	,	,	PUNCT
ejpam-4021	422	15	949	949	NUM
ejpam-4021	422	16	-	-	SYM
ejpam-4021	422	17	968	968	NUM
ejpam-4021	422	18	963	963	NUM
ejpam-4021	422	19	proof	proof	NOUN
ejpam-4021	422	20	.	.	PUNCT
ejpam-4021	423	1	let	let	VERB
ejpam-4021	423	2	ν	ν	X
ejpam-4021	423	3	∈	∈	PROPN
ejpam-4021	423	4	l(g	l(g	NOUN
ejpam-4021	423	5	)	)	PUNCT
ejpam-4021	423	6	,	,	PUNCT
ejpam-4021	423	7	then	then	ADV
ejpam-4021	423	8	we	we	PRON
ejpam-4021	423	9	have	have	VERB
ejpam-4021	423	10	ρl(ν)(x	ρl(ν)(x	NOUN
ejpam-4021	423	11	,	,	PUNCT
ejpam-4021	423	12	x	x	NOUN
ejpam-4021	423	13	)	)	PUNCT
ejpam-4021	423	14	=	=	SYM
ejpam-4021	423	15	ν(x−1x	ν(x−1x	PROPN
ejpam-4021	423	16	)	)	PUNCT
ejpam-4021	423	17	=	=	SYM
ejpam-4021	424	1	ν(e	ν(e	PROPN
ejpam-4021	424	2	)	)	PUNCT
ejpam-4021	424	3	=	=	SYM
ejpam-4021	424	4	>	>	X
ejpam-4021	424	5	which	which	PRON
ejpam-4021	424	6	is	be	AUX
ejpam-4021	424	7	(	(	PUNCT
ejpam-4021	424	8	t1	t1	NOUN
ejpam-4021	424	9	)	)	PUNCT
ejpam-4021	424	10	;	;	PUNCT
ejpam-4021	424	11	for	for	ADP
ejpam-4021	424	12	(	(	PUNCT
ejpam-4021	424	13	t2	t2	NOUN
ejpam-4021	424	14	)	)	PUNCT
ejpam-4021	424	15	,	,	PUNCT
ejpam-4021	424	16	we	we	PRON
ejpam-4021	424	17	apply	apply	VERB
ejpam-4021	424	18	theorem	theorem	ADJ
ejpam-4021	424	19	5.1.1(5)[11](see	5.1.1(5)[11](see	PROPN
ejpam-4021	424	20	also	also	ADV
ejpam-4021	424	21	,	,	PUNCT
ejpam-4021	424	22	theorem	theorem	VERB
ejpam-4021	424	23	1.2.2[24	1.2.2[24	NUM
ejpam-4021	424	24	]	]	PUNCT
ejpam-4021	424	25	)	)	PUNCT
ejpam-4021	424	26	to	to	PART
ejpam-4021	424	27	get	get	VERB
ejpam-4021	424	28	ρl(ν)(x	ρl(ν)(x	NOUN
ejpam-4021	424	29	,	,	PUNCT
ejpam-4021	424	30	y	y	NOUN
ejpam-4021	424	31	)	)	PUNCT
ejpam-4021	424	32	=	=	SYM
ejpam-4021	424	33	ν(x−1y	ν(x−1y	ADJ
ejpam-4021	424	34	)	)	PUNCT
ejpam-4021	424	35	=	=	SYM
ejpam-4021	424	36	ν((x−1y)−1	ν((x−1y)−1	NOUN
ejpam-4021	424	37	)	)	PUNCT
ejpam-4021	424	38	=	=	SYM
ejpam-4021	424	39	ν(y−1x	ν(y−1x	NOUN
ejpam-4021	424	40	)	)	PUNCT
ejpam-4021	424	41	=	=	SYM
ejpam-4021	424	42	ρl(y	ρl(y	X
ejpam-4021	424	43	,	,	PUNCT
ejpam-4021	424	44	x	x	NOUN
ejpam-4021	424	45	)	)	PUNCT
ejpam-4021	424	46	.	.	PUNCT
ejpam-4021	425	1	now	now	ADV
ejpam-4021	425	2	for	for	ADP
ejpam-4021	425	3	any	any	DET
ejpam-4021	425	4	x	x	NOUN
ejpam-4021	425	5	,	,	PUNCT
ejpam-4021	425	6	y	y	PROPN
ejpam-4021	425	7	,	,	PUNCT
ejpam-4021	425	8	z	z	PROPN
ejpam-4021	425	9	∈	∈	PROPN
ejpam-4021	425	10	x	x	SYM
ejpam-4021	425	11	,	,	PUNCT
ejpam-4021	425	12	ρl(ν)(x	ρl(ν)(x	PROPN
ejpam-4021	425	13	,	,	PUNCT
ejpam-4021	425	14	y	y	PROPN
ejpam-4021	425	15	)	)	PUNCT
ejpam-4021	425	16	∗	∗	NOUN
ejpam-4021	425	17	ρl(y	ρl(y	NUM
ejpam-4021	425	18	,	,	PUNCT
ejpam-4021	425	19	z	z	NOUN
ejpam-4021	425	20	)	)	PUNCT
ejpam-4021	425	21	=	=	SYM
ejpam-4021	425	22	ν(x−1y	ν(x−1y	ADJ
ejpam-4021	425	23	)	)	PUNCT
ejpam-4021	425	24	∗	∗	NOUN
ejpam-4021	425	25	ν(y−1z	ν(y−1z	PROPN
ejpam-4021	425	26	)	)	PUNCT
ejpam-4021	425	27	≤	≤	NUM
ejpam-4021	425	28	ν(x−1yy−1z	ν(x−1yy−1z	NOUN
ejpam-4021	425	29	)	)	PUNCT
ejpam-4021	425	30	=	=	SYM
ejpam-4021	425	31	ν(x−1z	ν(x−1z	X
ejpam-4021	425	32	)	)	PUNCT
ejpam-4021	425	33	=	=	SYM
ejpam-4021	425	34	ρl(ν)(x	ρl(ν)(x	NOUN
ejpam-4021	425	35	,	,	PUNCT
ejpam-4021	425	36	z	z	NOUN
ejpam-4021	425	37	)	)	PUNCT
ejpam-4021	425	38	,	,	PUNCT
ejpam-4021	425	39	which	which	PRON
ejpam-4021	425	40	is	be	AUX
ejpam-4021	425	41	(	(	PUNCT
ejpam-4021	425	42	t3	t3	PROPN
ejpam-4021	425	43	)	)	PUNCT
ejpam-4021	425	44	.	.	PUNCT
ejpam-4021	426	1	to	to	PART
ejpam-4021	426	2	check	check	VERB
ejpam-4021	426	3	the	the	DET
ejpam-4021	426	4	morphism	morphism	NOUN
ejpam-4021	426	5	part	part	NOUN
ejpam-4021	426	6	,	,	PUNCT
ejpam-4021	426	7	we	we	PRON
ejpam-4021	426	8	have	have	VERB
ejpam-4021	426	9	for	for	ADP
ejpam-4021	426	10	any	any	DET
ejpam-4021	426	11	x	x	NOUN
ejpam-4021	426	12	,	,	PUNCT
ejpam-4021	426	13	y	y	PROPN
ejpam-4021	426	14	∈	∈	PROPN
ejpam-4021	426	15	g	g	NOUN
ejpam-4021	426	16	and	and	CCONJ
ejpam-4021	426	17	ν	ν	X
ejpam-4021	426	18	∈	∈	PROPN
ejpam-4021	426	19	l(g	l(g	PROPN
ejpam-4021	426	20	):	):	PUNCT
ejpam-4021	426	21	τ(x	τ(x	PROPN
ejpam-4021	426	22	,	,	PUNCT
ejpam-4021	426	23	y	y	NOUN
ejpam-4021	426	24	)	)	PUNCT
ejpam-4021	427	1	=	=	SYM
ejpam-4021	427	2	ρl(ν)(x	ρl(ν)(x	NOUN
ejpam-4021	427	3	,	,	PUNCT
ejpam-4021	427	4	y	y	PROPN
ejpam-4021	427	5	)	)	PUNCT
ejpam-4021	427	6	=	=	SYM
ejpam-4021	427	7	ν(x−1y	ν(x−1y	ADJ
ejpam-4021	427	8	)	)	PUNCT
ejpam-4021	427	9	≤	≤	NUM
ejpam-4021	427	10	ν	ν	ADP
ejpam-4021	427	11	′(f(x−1y	′(f(x−1y	NOUN
ejpam-4021	427	12	)	)	PUNCT
ejpam-4021	427	13	)	)	PUNCT
ejpam-4021	428	1	=	=	PUNCT
ejpam-4021	429	1	ν	ν	X
ejpam-4021	429	2	′((f(x))−1f(y	′((f(x))−1f(y	NOUN
ejpam-4021	429	3	)	)	PUNCT
ejpam-4021	429	4	)	)	PUNCT
ejpam-4021	430	1	=	=	SYM
ejpam-4021	430	2	ρl(ν)(f(x	ρl(ν)(f(x	NOUN
ejpam-4021	430	3	)	)	PUNCT
ejpam-4021	430	4	,	,	PUNCT
ejpam-4021	430	5	f(y	f(y	NOUN
ejpam-4021	430	6	)	)	PUNCT
ejpam-4021	430	7	)	)	PUNCT
ejpam-4021	431	1	=	=	PUNCT
ejpam-4021	431	2	τ	τ	PROPN
ejpam-4021	431	3	′(f(x	′(f(x	NOUN
ejpam-4021	431	4	)	)	PUNCT
ejpam-4021	431	5	,	,	PUNCT
ejpam-4021	431	6	f(y	f(y	NOUN
ejpam-4021	431	7	)	)	PUNCT
ejpam-4021	431	8	)	)	PUNCT
ejpam-4021	431	9	,	,	PUNCT
ejpam-4021	431	10	i.e.	i.e.	X
ejpam-4021	431	11	,	,	PUNCT
ejpam-4021	431	12	τ(x	τ(x	PROPN
ejpam-4021	431	13	,	,	PUNCT
ejpam-4021	431	14	y	y	NOUN
ejpam-4021	431	15	)	)	PUNCT
ejpam-4021	431	16	≤	≤	PROPN
ejpam-4021	431	17	τ	τ	PROPN
ejpam-4021	431	18	′(ν	′(ν	PROPN
ejpam-4021	431	19	′)(f(x	′)(f(x	PROPN
ejpam-4021	431	20	)	)	PUNCT
ejpam-4021	431	21	,	,	PUNCT
ejpam-4021	431	22	f(y	f(y	NOUN
ejpam-4021	431	23	)	)	PUNCT
ejpam-4021	431	24	)	)	PUNCT
ejpam-4021	431	25	.	.	PUNCT
ejpam-4021	432	1	lemma	lemma	PROPN
ejpam-4021	432	2	8	8	NUM
ejpam-4021	432	3	.	.	PUNCT
ejpam-4021	433	1	let	let	VERB
ejpam-4021	433	2	(	(	PUNCT
ejpam-4021	433	3	g	g	NOUN
ejpam-4021	433	4	,	,	PUNCT
ejpam-4021	433	5	·	·	PUNCT
ejpam-4021	433	6	)	)	PUNCT
ejpam-4021	433	7	∈	∈	PROPN
ejpam-4021	433	8	|grp|	|grp|	NOUN
ejpam-4021	433	9	,	,	PUNCT
ejpam-4021	433	10	and	and	CCONJ
ejpam-4021	433	11	the	the	DET
ejpam-4021	433	12	category	category	NOUN
ejpam-4021	433	13	l	l	NOUN
ejpam-4021	433	14	-	-	NOUN
ejpam-4021	433	15	trantol	trantol	NOUN
ejpam-4021	433	16	consists	consist	VERB
ejpam-4021	433	17	of	of	ADP
ejpam-4021	433	18	morphisms	morphism	NOUN
ejpam-4021	433	19	f	f	NOUN
ejpam-4021	433	20	:	:	PUNCT
ejpam-4021	433	21	(	(	PUNCT
ejpam-4021	433	22	g	g	NOUN
ejpam-4021	433	23	,	,	PUNCT
ejpam-4021	433	24	ρl(ν	ρl(ν	NUM
ejpam-4021	433	25	)	)	PUNCT
ejpam-4021	433	26	)	)	PUNCT
ejpam-4021	434	1	−→	−→	NOUN
ejpam-4021	434	2	(	(	PUNCT
ejpam-4021	434	3	h	h	NOUN
ejpam-4021	434	4	,	,	PUNCT
ejpam-4021	434	5	ρl(ν	ρl(ν	PRON
ejpam-4021	434	6	′	′	NUM
ejpam-4021	434	7	)	)	PUNCT
ejpam-4021	434	8	)	)	PUNCT
ejpam-4021	434	9	which	which	PRON
ejpam-4021	434	10	are	be	AUX
ejpam-4021	434	11	l	l	ADV
ejpam-4021	434	12	-	-	PUNCT
ejpam-4021	434	13	valued	value	VERB
ejpam-4021	434	14	tolerance	tolerance	NOUN
ejpam-4021	434	15	preserving	preserve	VERB
ejpam-4021	434	16	such	such	ADJ
ejpam-4021	434	17	that	that	SCONJ
ejpam-4021	434	18	each	each	DET
ejpam-4021	434	19	morphism	morphism	NOUN
ejpam-4021	434	20	is	be	AUX
ejpam-4021	434	21	a	a	DET
ejpam-4021	434	22	group	group	NOUN
ejpam-4021	434	23	homomorphism	homomorphism	NOUN
ejpam-4021	434	24	.	.	PUNCT
ejpam-4021	435	1	then	then	ADV
ejpam-4021	435	2	b	b	X
ejpam-4021	435	3	:	:	PUNCT
ejpam-4021	435	4			PUNCT
ejpam-4021	435	5	l−trantol	l−trantol	AUX
ejpam-4021	435	6	−→	−→	ADJ
ejpam-4021	435	7	l	l	NOUN
ejpam-4021	435	8	-	-	NOUN
ejpam-4021	435	9	grp	grp	PROPN
ejpam-4021	435	10	(	(	PUNCT
ejpam-4021	435	11	g	g	NOUN
ejpam-4021	435	12	,	,	PUNCT
ejpam-4021	435	13	%	%	INTJ
ejpam-4021	435	14	l(ν	l(ν	PROPN
ejpam-4021	435	15	)	)	PUNCT
ejpam-4021	435	16	)	)	PUNCT
ejpam-4021	435	17	7−→	7−→	NOUN
ejpam-4021	435	18	(	(	PUNCT
ejpam-4021	435	19	g	g	NOUN
ejpam-4021	435	20	,	,	PUNCT
ejpam-4021	435	21	ν	ν	NOUN
ejpam-4021	435	22	)	)	PUNCT
ejpam-4021	435	23	f	f	PROPN
ejpam-4021	435	24	7−→	7−→	NOUN
ejpam-4021	435	25	f	f	NOUN
ejpam-4021	435	26	proof	proof	NOUN
ejpam-4021	435	27	.	.	PUNCT
ejpam-4021	436	1	let	let	VERB
ejpam-4021	436	2	ν	ν	PROPN
ejpam-4021	436	3	∈	∈	PROPN
ejpam-4021	436	4	lg	lg	NOUN
ejpam-4021	436	5	,	,	PUNCT
ejpam-4021	436	6	and	and	CCONJ
ejpam-4021	436	7	(	(	PUNCT
ejpam-4021	436	8	g	g	NOUN
ejpam-4021	436	9	,	,	PUNCT
ejpam-4021	436	10	ρl(ν	ρl(ν	NUM
ejpam-4021	436	11	)	)	PUNCT
ejpam-4021	436	12	)	)	PUNCT
ejpam-4021	437	1	∈	∈	PROPN
ejpam-4021	437	2	|l	|l	PROPN
ejpam-4021	437	3	-	-	PUNCT
ejpam-4021	437	4	trantol|	trantol|	PROPN
ejpam-4021	437	5	,	,	PUNCT
ejpam-4021	437	6	it	it	PRON
ejpam-4021	437	7	suffices	suffice	VERB
ejpam-4021	437	8	to	to	PART
ejpam-4021	437	9	show	show	VERB
ejpam-4021	437	10	that	that	SCONJ
ejpam-4021	437	11	ν	ν	PROPN
ejpam-4021	437	12	∈	∈	PROPN
ejpam-4021	437	13	l(g	l(g	PROPN
ejpam-4021	437	14	)	)	PUNCT
ejpam-4021	437	15	.	.	PUNCT
ejpam-4021	438	1	thus	thus	ADV
ejpam-4021	438	2	,	,	PUNCT
ejpam-4021	438	3	for	for	ADP
ejpam-4021	438	4	any	any	DET
ejpam-4021	438	5	x	x	SYM
ejpam-4021	438	6	∈	∈	PROPN
ejpam-4021	438	7	x	x	NOUN
ejpam-4021	438	8	,	,	PUNCT
ejpam-4021	438	9	ν(e	ν(e	PROPN
ejpam-4021	438	10	)	)	PUNCT
ejpam-4021	438	11	=	=	SYM
ejpam-4021	438	12	ν(x−1x	ν(x−1x	PROPN
ejpam-4021	438	13	)	)	PUNCT
ejpam-4021	438	14	=	=	SYM
ejpam-4021	438	15	ρl(ν)(x	ρl(ν)(x	NOUN
ejpam-4021	438	16	,	,	PUNCT
ejpam-4021	438	17	x	x	NOUN
ejpam-4021	438	18	)	)	PUNCT
ejpam-4021	438	19	=	=	SYM
ejpam-4021	438	20	>	>	X
ejpam-4021	438	21	which	which	PRON
ejpam-4021	438	22	is	be	AUX
ejpam-4021	438	23	(	(	PUNCT
ejpam-4021	438	24	lg1	lg1	PROPN
ejpam-4021	438	25	)	)	PUNCT
ejpam-4021	438	26	.	.	PUNCT
ejpam-4021	439	1	for	for	ADP
ejpam-4021	439	2	(	(	PUNCT
ejpam-4021	439	3	lg2	lg2	X
ejpam-4021	439	4	)	)	PUNCT
ejpam-4021	439	5	is	be	AUX
ejpam-4021	439	6	obviously	obviously	ADV
ejpam-4021	439	7	true	true	ADJ
ejpam-4021	439	8	while	while	SCONJ
ejpam-4021	439	9	for	for	ADP
ejpam-4021	439	10	(	(	PUNCT
ejpam-4021	439	11	lg3	lg3	NOUN
ejpam-4021	439	12	)	)	PUNCT
ejpam-4021	439	13	,	,	PUNCT
ejpam-4021	439	14	we	we	PRON
ejpam-4021	439	15	have	have	VERB
ejpam-4021	439	16	for	for	ADP
ejpam-4021	439	17	any	any	DET
ejpam-4021	439	18	x	x	NOUN
ejpam-4021	439	19	,	,	PUNCT
ejpam-4021	439	20	y	y	PROPN
ejpam-4021	439	21	∈	∈	PROPN
ejpam-4021	439	22	g	g	NOUN
ejpam-4021	439	23	:	:	PUNCT
ejpam-4021	439	24	ν(x	ν(x	PROPN
ejpam-4021	439	25	)	)	PUNCT
ejpam-4021	439	26	∗	∗	NOUN
ejpam-4021	439	27	ν(y	ν(y	PROPN
ejpam-4021	439	28	)	)	PUNCT
ejpam-4021	439	29	=	=	SYM
ejpam-4021	439	30	ν(xe	ν(xe	NUM
ejpam-4021	439	31	)	)	PUNCT
ejpam-4021	439	32	∗	∗	PROPN
ejpam-4021	439	33	ν(ey	ν(ey	PROPN
ejpam-4021	439	34	)	)	PUNCT
ejpam-4021	439	35	=	=	SYM
ejpam-4021	439	36	ρl(ν)(x	ρl(ν)(x	NOUN
ejpam-4021	439	37	,	,	PUNCT
ejpam-4021	439	38	e	e	NOUN
ejpam-4021	439	39	)	)	PUNCT
ejpam-4021	439	40	∗	∗	NOUN
ejpam-4021	439	41	ρl(ν)(e	ρl(ν)(e	NOUN
ejpam-4021	439	42	,	,	PUNCT
ejpam-4021	439	43	y	y	NOUN
ejpam-4021	439	44	)	)	PUNCT
ejpam-4021	439	45	≤	≤	NOUN
ejpam-4021	439	46	ρl(ν)(x	ρl(ν)(x	PROPN
ejpam-4021	439	47	,	,	PUNCT
ejpam-4021	439	48	y	y	PROPN
ejpam-4021	439	49	)	)	PUNCT
ejpam-4021	439	50	=	=	SYM
ejpam-4021	439	51	ν(x−1y	ν(x−1y	ADJ
ejpam-4021	439	52	)	)	PUNCT
ejpam-4021	439	53	,	,	PUNCT
ejpam-4021	439	54	i.e.	i.e.	X
ejpam-4021	439	55	,	,	PUNCT
ejpam-4021	439	56	ν(x	ν(x	PROPN
ejpam-4021	439	57	)	)	PUNCT
ejpam-4021	439	58	∗	∗	NOUN
ejpam-4021	439	59	ν(y	ν(y	PROPN
ejpam-4021	439	60	)	)	PUNCT
ejpam-4021	439	61	≤	≤	NUM
ejpam-4021	439	62	ν(x−1y	ν(x−1y	NOUN
ejpam-4021	439	63	)	)	PUNCT
ejpam-4021	439	64	,	,	PUNCT
ejpam-4021	439	65	this	this	PRON
ejpam-4021	439	66	happens	happen	VERB
ejpam-4021	439	67	when	when	SCONJ
ejpam-4021	439	68	we	we	PRON
ejpam-4021	439	69	combine	combine	VERB
ejpam-4021	439	70	(	(	PUNCT
ejpam-4021	439	71	lg2	lg2	X
ejpam-4021	439	72	)	)	PUNCT
ejpam-4021	439	73	and	and	CCONJ
ejpam-4021	439	74	(	(	PUNCT
ejpam-4021	439	75	lg3	lg3	NOUN
ejpam-4021	439	76	)	)	PUNCT
ejpam-4021	439	77	,	,	PUNCT
ejpam-4021	439	78	cf	cf	X
ejpam-4021	439	79	.	.	PUNCT
ejpam-4021	439	80	theorem	theorem	VERB
ejpam-4021	439	81	5.1.3[11	5.1.3[11	NUM
ejpam-4021	439	82	]	]	PUNCT
ejpam-4021	439	83	.	.	PUNCT
ejpam-4021	440	1	this	this	PRON
ejpam-4021	440	2	shows	show	VERB
ejpam-4021	440	3	that	that	SCONJ
ejpam-4021	440	4	ν	ν	PROPN
ejpam-4021	440	5	∈	∈	PROPN
ejpam-4021	440	6	l(g	l(g	PROPN
ejpam-4021	440	7	)	)	PUNCT
ejpam-4021	440	8	.	.	PUNCT
ejpam-4021	441	1	for	for	ADP
ejpam-4021	441	2	the	the	DET
ejpam-4021	441	3	morphism	morphism	NOUN
ejpam-4021	441	4	part	part	NOUN
ejpam-4021	441	5	,	,	PUNCT
ejpam-4021	441	6	let	let	VERB
ejpam-4021	441	7	x	x	PUNCT
ejpam-4021	441	8	∈	∈	PROPN
ejpam-4021	441	9	g	g	NOUN
ejpam-4021	441	10	and	and	CCONJ
ejpam-4021	441	11	ν	ν	NOUN
ejpam-4021	441	12	∈	∈	PROPN
ejpam-4021	441	13	lg	lg	PROPN
ejpam-4021	441	14	.	.	PROPN
ejpam-4021	441	15	then	then	ADV
ejpam-4021	441	16	ν(x	ν(x	PROPN
ejpam-4021	441	17	)	)	PUNCT
ejpam-4021	441	18	=	=	SYM
ejpam-4021	442	1	ν(ex	ν(ex	PROPN
ejpam-4021	442	2	)	)	PUNCT
ejpam-4021	442	3	=	=	SYM
ejpam-4021	443	1	ρl(ν)(e	ρl(ν)(e	NOUN
ejpam-4021	443	2	,	,	PUNCT
ejpam-4021	443	3	x	x	X
ejpam-4021	443	4	)	)	PUNCT
ejpam-4021	443	5	≤	≤	NOUN
ejpam-4021	443	6	ρl(ν	ρl(ν	PRON
ejpam-4021	443	7	′)(f(e	′)(f(e	PROPN
ejpam-4021	443	8	)	)	PUNCT
ejpam-4021	443	9	,	,	PUNCT
ejpam-4021	443	10	f(x	f(x	PROPN
ejpam-4021	443	11	)	)	PUNCT
ejpam-4021	443	12	)	)	PUNCT
ejpam-4021	444	1	=	=	PUNCT
ejpam-4021	445	1	ν	ν	NOUN
ejpam-4021	445	2	′	′	NUM
ejpam-4021	446	1	(	(	PUNCT
ejpam-4021	446	2	(	(	PUNCT
ejpam-4021	446	3	f(e))−1f(x	f(e))−1f(x	PROPN
ejpam-4021	446	4	)	)	PUNCT
ejpam-4021	446	5	)	)	PUNCT
ejpam-4021	447	1	=	=	PUNCT
ejpam-4021	447	2	ν	ν	X
ejpam-4021	447	3	′(f(ex	′(f(ex	NUM
ejpam-4021	447	4	)	)	PUNCT
ejpam-4021	447	5	)	)	PUNCT
ejpam-4021	448	1	=	=	SYM
ejpam-4021	448	2	ν	ν	NOUN
ejpam-4021	448	3	′(f(x	′(f(x	NOUN
ejpam-4021	448	4	)	)	PUNCT
ejpam-4021	448	5	)	)	PUNCT
ejpam-4021	448	6	,	,	PUNCT
ejpam-4021	448	7	i.e.	i.e.	X
ejpam-4021	448	8	,	,	PUNCT
ejpam-4021	448	9	ν(x	ν(x	PROPN
ejpam-4021	448	10	)	)	PUNCT
ejpam-4021	448	11	≤	≤	NUM
ejpam-4021	448	12	ν	ν	NOUN
ejpam-4021	448	13	′(f(x	′(f(x	NOUN
ejpam-4021	448	14	)	)	PUNCT
ejpam-4021	448	15	)	)	PUNCT
ejpam-4021	448	16	.	.	PUNCT
ejpam-4021	449	1	5	5	X
ejpam-4021	449	2	.	.	NUM
ejpam-4021	449	3	enriched	enrich	VERB
ejpam-4021	449	4	latticed	lattice	VERB
ejpam-4021	449	5	-	-	PUNCT
ejpam-4021	449	6	valued	value	VERB
ejpam-4021	449	7	subgroups	subgroup	NOUN
ejpam-4021	449	8	on	on	ADP
ejpam-4021	449	9	lattice	lattice	NOUN
ejpam-4021	449	10	-	-	PUNCT
ejpam-4021	449	11	valued	value	VERB
ejpam-4021	449	12	neighborhood	neighborhood	NOUN
ejpam-4021	449	13	groups	group	NOUN
ejpam-4021	449	14	let	let	VERB
ejpam-4021	449	15	l	l	NOUN
ejpam-4021	449	16	=	=	SYM
ejpam-4021	449	17	(	(	PUNCT
ejpam-4021	449	18	l,≤	l,≤	PROPN
ejpam-4021	449	19	,	,	PUNCT
ejpam-4021	449	20	∗	∗	NOUN
ejpam-4021	449	21	)	)	PUNCT
ejpam-4021	449	22	be	be	VERB
ejpam-4021	449	23	a	a	DET
ejpam-4021	449	24	complete	complete	ADJ
ejpam-4021	449	25	mv	mv	NOUN
ejpam-4021	449	26	-	-	PUNCT
ejpam-4021	449	27	valued	value	VERB
ejpam-4021	449	28	algebra	algebra	NOUN
ejpam-4021	449	29	with	with	ADP
ejpam-4021	449	30	square	square	ADJ
ejpam-4021	449	31	roots	root	NOUN
ejpam-4021	449	32	.	.	PUNCT
ejpam-4021	450	1	if	if	SCONJ
ejpam-4021	450	2	(	(	PUNCT
ejpam-4021	450	3	x	x	X
ejpam-4021	450	4	,	,	PUNCT
ejpam-4021	450	5	n	n	NOUN
ejpam-4021	450	6	=	=	SYM
ejpam-4021	450	7	(	(	PUNCT
ejpam-4021	450	8	nx)x∈x	nx)x∈x	PROPN
ejpam-4021	450	9	)	)	PUNCT
ejpam-4021	450	10	is	be	AUX
ejpam-4021	450	11	a	a	DET
ejpam-4021	450	12	stratified	stratified	ADJ
ejpam-4021	450	13	l	l	ADJ
ejpam-4021	450	14	-	-	PUNCT
ejpam-4021	450	15	neighborhood	neighborhood	NOUN
ejpam-4021	450	16	space	space	NOUN
ejpam-4021	450	17	,	,	PUNCT
ejpam-4021	450	18	then	then	ADV
ejpam-4021	450	19	in	in	ADP
ejpam-4021	450	20	view	view	NOUN
ejpam-4021	450	21	of	of	ADP
ejpam-4021	450	22	[	[	X
ejpam-4021	450	23	12	12	NUM
ejpam-4021	450	24	]	]	X
ejpam-4021	450	25	(	(	PUNCT
ejpam-4021	450	26	page	page	NOUN
ejpam-4021	450	27	13	13	NUM
ejpam-4021	450	28	)	)	PUNCT
ejpam-4021	450	29	,	,	PUNCT
ejpam-4021	450	30	and	and	CCONJ
ejpam-4021	450	31	[	[	X
ejpam-4021	450	32	18	18	NUM
ejpam-4021	450	33	]	]	X
ejpam-4021	450	34	(	(	PUNCT
ejpam-4021	450	35	page	page	NOUN
ejpam-4021	450	36	226	226	NUM
ejpam-4021	450	37	)	)	PUNCT
ejpam-4021	450	38	,	,	PUNCT
ejpam-4021	450	39	one	one	PRON
ejpam-4021	450	40	can	can	AUX
ejpam-4021	450	41	see	see	VERB
ejpam-4021	450	42	that	that	SCONJ
ejpam-4021	450	43	n	n	PUNCT
ejpam-4021	450	44	induces	induce	VERB
ejpam-4021	450	45	a	a	DET
ejpam-4021	450	46	closure	closure	NOUN
ejpam-4021	450	47	operator	operator	NOUN
ejpam-4021	450	48	−	−	NOUN
ejpam-4021	450	49	:	:	PUNCT
ejpam-4021	450	50	lx	lx	ADP
ejpam-4021	450	51	−→	−→	NOUN
ejpam-4021	450	52	lx	lx	ADV
ejpam-4021	450	53	given	give	VERB
ejpam-4021	450	54	for	for	ADP
ejpam-4021	450	55	any	any	DET
ejpam-4021	450	56	x	x	SYM
ejpam-4021	450	57	∈	∈	PROPN
ejpam-4021	450	58	x	x	X
ejpam-4021	450	59	and	and	CCONJ
ejpam-4021	450	60	ν	ν	X
ejpam-4021	450	61	∈	∈	NOUN
ejpam-4021	450	62	lx	lx	NOUN
ejpam-4021	450	63	by	by	ADP
ejpam-4021	450	64	ν(x	ν(x	PROPN
ejpam-4021	450	65	)	)	PUNCT
ejpam-4021	450	66	=	=	PUNCT
ejpam-4021	451	1	(	(	PUNCT
ejpam-4021	451	2	[	[	X
ejpam-4021	451	3	nx](ν	nx](ν	PROPN
ejpam-4021	451	4	→	→	SYM
ejpam-4021	451	5	⊥))→	⊥))→	PROPN
ejpam-4021	451	6	⊥.	⊥.	NUM
ejpam-4021	451	7	theorem	theorem	VERB
ejpam-4021	451	8	5	5	NUM
ejpam-4021	451	9	.	.	PUNCT
ejpam-4021	452	1	[	[	X
ejpam-4021	452	2	3	3	NUM
ejpam-4021	452	3	,	,	PUNCT
ejpam-4021	452	4	12	12	NUM
ejpam-4021	452	5	,	,	PUNCT
ejpam-4021	452	6	18	18	NUM
ejpam-4021	452	7	]	]	PUNCT
ejpam-4021	452	8	(	(	PUNCT
ejpam-4021	452	9	a	a	X
ejpam-4021	452	10	)	)	PUNCT
ejpam-4021	452	11	let	let	VERB
ejpam-4021	452	12	(	(	PUNCT
ejpam-4021	452	13	x	x	X
ejpam-4021	452	14	,	,	PUNCT
ejpam-4021	452	15	n	n	NOUN
ejpam-4021	452	16	=	=	SYM
ejpam-4021	452	17	(	(	PUNCT
ejpam-4021	452	18	nx)x∈x	nx)x∈x	NUM
ejpam-4021	452	19	)	)	PUNCT
ejpam-4021	452	20	∈	∈	PROPN
ejpam-4021	452	21	|sl	|sl	NOUN
ejpam-4021	452	22	-	-	PUNCT
ejpam-4021	452	23	ns|	ns|	NOUN
ejpam-4021	452	24	.	.	PUNCT
ejpam-4021	453	1	then	then	ADV
ejpam-4021	453	2	ν(x	ν(x	PROPN
ejpam-4021	453	3	)	)	PUNCT
ejpam-4021	453	4	=	=	PUNCT
ejpam-4021	453	5	∨	∨	X
ejpam-4021	453	6	{	{	PUNCT
ejpam-4021	453	7	f(ν	f(ν	NOUN
ejpam-4021	453	8	)	)	PUNCT
ejpam-4021	453	9	:	:	PUNCT
ejpam-4021	454	1	f	f	PROPN
ejpam-4021	454	2	∈	∈	PROPN
ejpam-4021	454	3	fsl(x	fsl(x	PROPN
ejpam-4021	454	4	)	)	PUNCT
ejpam-4021	454	5	,	,	PUNCT
ejpam-4021	454	6	f	f	PROPN
ejpam-4021	454	7	≥	≥	NUM
ejpam-4021	454	8	nx	nx	PROPN
ejpam-4021	454	9	}	}	PUNCT
ejpam-4021	454	10	,	,	PUNCT
ejpam-4021	454	11	∀ν	∀ν	PROPN
ejpam-4021	454	12	∈	∈	PROPN
ejpam-4021	454	13	lx	lx	NOUN
ejpam-4021	454	14	,	,	PUNCT
ejpam-4021	454	15	and	and	CCONJ
ejpam-4021	454	16	∀x	∀x	X
ejpam-4021	454	17	∈	∈	PROPN
ejpam-4021	454	18	x.	x.	NOUN
ejpam-4021	454	19	(	(	PUNCT
ejpam-4021	454	20	b	b	X
ejpam-4021	454	21	)	)	PUNCT
ejpam-4021	454	22	let	let	VERB
ejpam-4021	454	23	(	(	PUNCT
ejpam-4021	454	24	g	g	NOUN
ejpam-4021	454	25	,	,	PUNCT
ejpam-4021	454	26	·	·	PUNCT
ejpam-4021	454	27	,	,	PUNCT
ejpam-4021	454	28	n	n	X
ejpam-4021	454	29	=	=	SYM
ejpam-4021	454	30	(	(	PUNCT
ejpam-4021	454	31	nx)x∈g	nx)x∈g	NUM
ejpam-4021	454	32	)	)	PUNCT
ejpam-4021	454	33	∈	∈	PROPN
ejpam-4021	454	34	|sl	|sl	PROPN
ejpam-4021	454	35	-	-	PUNCT
ejpam-4021	454	36	ngrp|	ngrp|	NOUN
ejpam-4021	454	37	and	and	CCONJ
ejpam-4021	454	38	ν	ν	PROPN
ejpam-4021	454	39	∈	∈	PROPN
ejpam-4021	454	40	lg	lg	NOUN
ejpam-4021	454	41	be	be	AUX
ejpam-4021	454	42	an	an	DET
ejpam-4021	454	43	l	l	NOUN
ejpam-4021	454	44	-	-	PUNCT
ejpam-4021	454	45	valued	value	VERB
ejpam-4021	454	46	subgroup	subgroup	NOUN
ejpam-4021	454	47	of	of	ADP
ejpam-4021	454	48	a	a	DET
ejpam-4021	454	49	group	group	NOUN
ejpam-4021	454	50	g.	g.	NOUN
ejpam-4021	454	51	then	then	ADV
ejpam-4021	454	52	the	the	DET
ejpam-4021	454	53	l	l	NOUN
ejpam-4021	454	54	-	-	PUNCT
ejpam-4021	454	55	valued	value	VERB
ejpam-4021	454	56	closure	closure	NOUN
ejpam-4021	454	57	ν	ν	NOUN
ejpam-4021	454	58	of	of	ADP
ejpam-4021	454	59	ν	ν	NOUN
ejpam-4021	454	60	in	in	ADP
ejpam-4021	454	61	(	(	PUNCT
ejpam-4021	454	62	a	a	X
ejpam-4021	454	63	)	)	PUNCT
ejpam-4021	454	64	is	be	AUX
ejpam-4021	454	65	an	an	DET
ejpam-4021	454	66	l	l	NOUN
ejpam-4021	454	67	-	-	PUNCT
ejpam-4021	454	68	valued	value	VERB
ejpam-4021	454	69	subgroup	subgroup	NOUN
ejpam-4021	454	70	of	of	ADP
ejpam-4021	454	71	g.	g.	PROPN
ejpam-4021	455	1	(	(	PUNCT
ejpam-4021	455	2	c	c	X
ejpam-4021	455	3	)	)	PUNCT
ejpam-4021	455	4	let	let	VERB
ejpam-4021	455	5	(	(	PUNCT
ejpam-4021	455	6	g	g	NOUN
ejpam-4021	455	7	,	,	PUNCT
ejpam-4021	455	8	·	·	PUNCT
ejpam-4021	455	9	,	,	PUNCT
ejpam-4021	455	10	n	n	CCONJ
ejpam-4021	455	11	)	)	PUNCT
ejpam-4021	456	1	−→	−→	NOUN
ejpam-4021	456	2	(	(	PUNCT
ejpam-4021	456	3	h	h	NOUN
ejpam-4021	456	4	,	,	PUNCT
ejpam-4021	456	5	·	·	PUNCT
ejpam-4021	456	6	,	,	PUNCT
ejpam-4021	456	7	m	m	VERB
ejpam-4021	456	8	)	)	PUNCT
ejpam-4021	456	9	be	be	AUX
ejpam-4021	456	10	continuous	continuous	ADJ
ejpam-4021	456	11	group	group	NOUN
ejpam-4021	456	12	homomorphism	homomorphism	NOUN
ejpam-4021	456	13	.	.	PUNCT
ejpam-4021	457	1	then	then	ADV
ejpam-4021	457	2	ν(x	ν(x	PROPN
ejpam-4021	457	3	)	)	PUNCT
ejpam-4021	457	4	≤	≤	NUM
ejpam-4021	457	5	f→(ν)(f(x	f→(ν)(f(x	PROPN
ejpam-4021	457	6	)	)	PUNCT
ejpam-4021	457	7	)	)	PUNCT
ejpam-4021	457	8	for	for	ADP
ejpam-4021	457	9	all	all	PRON
ejpam-4021	457	10	ν	ν	X
ejpam-4021	457	11	∈	∈	PROPN
ejpam-4021	457	12	lg	lg	NOUN
ejpam-4021	457	13	and	and	CCONJ
ejpam-4021	457	14	x	x	PROPN
ejpam-4021	457	15	∈	∈	PROPN
ejpam-4021	458	1	g.	g.	NOUN
ejpam-4021	458	2	moreover	moreover	ADV
ejpam-4021	458	3	,	,	PUNCT
ejpam-4021	458	4	if	if	SCONJ
ejpam-4021	458	5	ν	ν	PROPN
ejpam-4021	458	6	∈	∈	PROPN
ejpam-4021	458	7	lg	lg	NOUN
ejpam-4021	458	8	is	be	AUX
ejpam-4021	458	9	an	an	DET
ejpam-4021	458	10	l	l	NOUN
ejpam-4021	458	11	-	-	PUNCT
ejpam-4021	458	12	valued	value	VERB
ejpam-4021	458	13	subgroup	subgroup	NOUN
ejpam-4021	458	14	of	of	ADP
ejpam-4021	458	15	g	g	PROPN
ejpam-4021	458	16	,	,	PUNCT
ejpam-4021	458	17	then	then	ADV
ejpam-4021	458	18	f→(ν	f→(ν	PROPN
ejpam-4021	458	19	)	)	PUNCT
ejpam-4021	458	20	is	be	AUX
ejpam-4021	458	21	an	an	DET
ejpam-4021	458	22	l	l	NOUN
ejpam-4021	458	23	-	-	PUNCT
ejpam-4021	458	24	valued	value	VERB
ejpam-4021	458	25	subgroup	subgroup	NOUN
ejpam-4021	458	26	of	of	ADP
ejpam-4021	458	27	h	h	NOUN
ejpam-4021	458	28	,	,	PUNCT
ejpam-4021	458	29	and	and	CCONJ
ejpam-4021	458	30	if	if	SCONJ
ejpam-4021	458	31	µ	µ	PRON
ejpam-4021	458	32	∈	∈	NOUN
ejpam-4021	458	33	lg	lg	NOUN
ejpam-4021	458	34	is	be	AUX
ejpam-4021	458	35	a	a	DET
ejpam-4021	458	36	l	l	NOUN
ejpam-4021	458	37	-	-	PUNCT
ejpam-4021	458	38	valued	value	VERB
ejpam-4021	458	39	subgroup	subgroup	NOUN
ejpam-4021	458	40	of	of	ADP
ejpam-4021	458	41	h	h	NOUN
ejpam-4021	458	42	,	,	PUNCT
ejpam-4021	458	43	then	then	ADV
ejpam-4021	458	44	f←(µ	f←(µ	NOUN
ejpam-4021	458	45	)	)	PUNCT
ejpam-4021	458	46	is	be	AUX
ejpam-4021	458	47	an	an	DET
ejpam-4021	458	48	l	l	NOUN
ejpam-4021	458	49	-	-	PUNCT
ejpam-4021	458	50	valued	value	VERB
ejpam-4021	458	51	subgroup	subgroup	NOUN
ejpam-4021	458	52	of	of	ADP
ejpam-4021	458	53	g.	g.	PROPN
ejpam-4021	458	54	(	(	PUNCT
ejpam-4021	458	55	d	d	X
ejpam-4021	458	56	)	)	PUNCT
ejpam-4021	458	57	if	if	SCONJ
ejpam-4021	458	58	ν	ν	PROPN
ejpam-4021	458	59	∈	∈	PROPN
ejpam-4021	458	60	lg	lg	NOUN
ejpam-4021	458	61	is	be	AUX
ejpam-4021	458	62	an	an	DET
ejpam-4021	458	63	l	l	NOUN
ejpam-4021	458	64	-	-	PUNCT
ejpam-4021	458	65	valued	value	VERB
ejpam-4021	458	66	normal	normal	ADJ
ejpam-4021	458	67	subgroup	subgroup	NOUN
ejpam-4021	458	68	of	of	ADP
ejpam-4021	458	69	a	a	DET
ejpam-4021	458	70	group	group	NOUN
ejpam-4021	458	71	g	g	NOUN
ejpam-4021	458	72	,	,	PUNCT
ejpam-4021	458	73	then	then	ADV
ejpam-4021	458	74	ν	ν	PROPN
ejpam-4021	458	75	is	be	AUX
ejpam-4021	458	76	also	also	ADV
ejpam-4021	458	77	an	an	DET
ejpam-4021	458	78	l	l	NOUN
ejpam-4021	458	79	-	-	PUNCT
ejpam-4021	458	80	valued	value	VERB
ejpam-4021	458	81	t	t	PROPN
ejpam-4021	458	82	m	m	PROPN
ejpam-4021	458	83	g	g	NOUN
ejpam-4021	458	84	ahsanullah	ahsanullah	NOUN
ejpam-4021	458	85	,	,	PUNCT
ejpam-4021	458	86	fawzi	fawzi	PROPN
ejpam-4021	458	87	al	al	PROPN
ejpam-4021	458	88	-	-	PUNCT
ejpam-4021	458	89	thukair	thukair	NOUN
ejpam-4021	458	90	/	/	SYM
ejpam-4021	458	91	eur	eur	NOUN
ejpam-4021	458	92	.	.	PUNCT
ejpam-4021	459	1	j.	j.	PROPN
ejpam-4021	459	2	pure	pure	PROPN
ejpam-4021	459	3	appl	appl	PROPN
ejpam-4021	459	4	.	.	PROPN
ejpam-4021	459	5	math	math	PROPN
ejpam-4021	459	6	,	,	PUNCT
ejpam-4021	459	7	14	14	NUM
ejpam-4021	459	8	(	(	PUNCT
ejpam-4021	459	9	3	3	NUM
ejpam-4021	459	10	)	)	PUNCT
ejpam-4021	459	11	(	(	PUNCT
ejpam-4021	459	12	2021	2021	NUM
ejpam-4021	459	13	)	)	PUNCT
ejpam-4021	459	14	,	,	PUNCT
ejpam-4021	459	15	949	949	NUM
ejpam-4021	459	16	-	-	SYM
ejpam-4021	459	17	968	968	NUM
ejpam-4021	459	18	964	964	NUM
ejpam-4021	459	19	normal	normal	ADJ
ejpam-4021	459	20	subgroup	subgroup	NOUN
ejpam-4021	459	21	of	of	ADP
ejpam-4021	459	22	g.	g.	PROPN
ejpam-4021	459	23	(	(	PUNCT
ejpam-4021	459	24	e	e	NOUN
ejpam-4021	459	25	)	)	PUNCT
ejpam-4021	459	26	if	if	SCONJ
ejpam-4021	459	27	(	(	PUNCT
ejpam-4021	459	28	g	g	NOUN
ejpam-4021	459	29	,	,	PUNCT
ejpam-4021	459	30	·	·	PUNCT
ejpam-4021	459	31	,	,	PUNCT
ejpam-4021	459	32	n	n	CCONJ
ejpam-4021	459	33	)	)	PUNCT
ejpam-4021	459	34	−→	−→	NOUN
ejpam-4021	459	35	(	(	PUNCT
ejpam-4021	459	36	h	h	NOUN
ejpam-4021	459	37	,	,	PUNCT
ejpam-4021	459	38	·	·	PUNCT
ejpam-4021	459	39	,	,	PUNCT
ejpam-4021	459	40	m	m	VERB
ejpam-4021	459	41	)	)	PUNCT
ejpam-4021	459	42	is	be	AUX
ejpam-4021	459	43	a	a	DET
ejpam-4021	459	44	continuous	continuous	ADJ
ejpam-4021	459	45	group	group	NOUN
ejpam-4021	459	46	homomorphism	homomorphism	NOUN
ejpam-4021	459	47	and	and	CCONJ
ejpam-4021	459	48	µ	µ	PROPN
ejpam-4021	459	49	∈	∈	NOUN
ejpam-4021	459	50	lh	lh	PROPN
ejpam-4021	459	51	is	be	AUX
ejpam-4021	459	52	an	an	DET
ejpam-4021	459	53	l	l	NOUN
ejpam-4021	459	54	-	-	PUNCT
ejpam-4021	459	55	valued	value	VERB
ejpam-4021	459	56	subgroup	subgroup	NOUN
ejpam-4021	459	57	of	of	ADP
ejpam-4021	459	58	h	h	NOUN
ejpam-4021	459	59	,	,	PUNCT
ejpam-4021	459	60	then	then	ADV
ejpam-4021	459	61	f←(µ	f←(µ	NOUN
ejpam-4021	459	62	)	)	PUNCT
ejpam-4021	459	63	is	be	AUX
ejpam-4021	459	64	an	an	DET
ejpam-4021	459	65	l	l	NOUN
ejpam-4021	459	66	-	-	PUNCT
ejpam-4021	459	67	valued	value	VERB
ejpam-4021	459	68	subgroup	subgroup	NOUN
ejpam-4021	459	69	of	of	ADP
ejpam-4021	459	70	g.	g.	PROPN
ejpam-4021	459	71	proof	proof	PROPN
ejpam-4021	459	72	.	.	PUNCT
ejpam-4021	460	1	(	(	PUNCT
ejpam-4021	460	2	b	b	X
ejpam-4021	460	3	)	)	PUNCT
ejpam-4021	460	4	follows	follow	VERB
ejpam-4021	460	5	from	from	ADP
ejpam-4021	460	6	the	the	DET
ejpam-4021	460	7	theorem	theorem	ADJ
ejpam-4021	460	8	5.1[3	5.1[3	NUM
ejpam-4021	460	9	]	]	PUNCT
ejpam-4021	460	10	.	.	PUNCT
ejpam-4021	461	1	(	(	PUNCT
ejpam-4021	461	2	c	c	X
ejpam-4021	461	3	)	)	PUNCT
ejpam-4021	461	4	let	let	VERB
ejpam-4021	461	5	ν	ν	X
ejpam-4021	461	6	∈	∈	PROPN
ejpam-4021	461	7	lg	lg	NOUN
ejpam-4021	461	8	,	,	PUNCT
ejpam-4021	461	9	and	and	CCONJ
ejpam-4021	461	10	x	x	PUNCT
ejpam-4021	461	11	∈	∈	PROPN
ejpam-4021	461	12	g.	g.	NOUN
ejpam-4021	461	13	then	then	ADV
ejpam-4021	461	14	since	since	SCONJ
ejpam-4021	461	15	ν	ν	PROPN
ejpam-4021	461	16	≤	≤	PROPN
ejpam-4021	461	17	f←(f→(ν	f←(f→(ν	NOUN
ejpam-4021	461	18	)	)	PUNCT
ejpam-4021	461	19	)	)	PUNCT
ejpam-4021	461	20	due	due	ADP
ejpam-4021	461	21	to	to	ADP
ejpam-4021	461	22	definition	definition	NOUN
ejpam-4021	461	23	6	6	NUM
ejpam-4021	461	24	(	(	PUNCT
ejpam-4021	461	25	lf2	lf2	PROPN
ejpam-4021	461	26	)	)	PUNCT
ejpam-4021	461	27	,	,	PUNCT
ejpam-4021	461	28	f(ν	f(ν	NOUN
ejpam-4021	461	29	)	)	PUNCT
ejpam-4021	461	30	≤	≤	NUM
ejpam-4021	461	31	f	f	X
ejpam-4021	461	32	(	(	PUNCT
ejpam-4021	461	33	f←(f→(ν	f←(f→(ν	PROPN
ejpam-4021	461	34	)	)	PUNCT
ejpam-4021	461	35	)	)	PUNCT
ejpam-4021	461	36	)	)	PUNCT
ejpam-4021	462	1	=	=	PUNCT
ejpam-4021	462	2	f⇒(f)(f→(ν	f⇒(f)(f→(ν	PROPN
ejpam-4021	462	3	)	)	PUNCT
ejpam-4021	462	4	)	)	PUNCT
ejpam-4021	462	5	,	,	PUNCT
ejpam-4021	462	6	and	and	CCONJ
ejpam-4021	462	7	since	since	SCONJ
ejpam-4021	462	8	mf(x	mf(x	NOUN
ejpam-4021	462	9	)	)	PUNCT
ejpam-4021	462	10	≤	≤	NOUN
ejpam-4021	462	11	f⇒(nx	f⇒(nx	NOUN
ejpam-4021	462	12	)	)	PUNCT
ejpam-4021	462	13	due	due	ADP
ejpam-4021	462	14	to	to	ADP
ejpam-4021	462	15	continuity	continuity	NOUN
ejpam-4021	462	16	of	of	ADP
ejpam-4021	462	17	f	f	PROPN
ejpam-4021	462	18	,	,	PUNCT
ejpam-4021	462	19	we	we	PRON
ejpam-4021	462	20	have	have	VERB
ejpam-4021	462	21	ν(x	ν(x	PROPN
ejpam-4021	462	22	)	)	PUNCT
ejpam-4021	462	23	=	=	PUNCT
ejpam-4021	462	24	∨	∨	X
ejpam-4021	462	25	{	{	PUNCT
ejpam-4021	462	26	f(ν	f(ν	NOUN
ejpam-4021	462	27	)	)	PUNCT
ejpam-4021	462	28	:	:	PUNCT
ejpam-4021	462	29	f	f	PROPN
ejpam-4021	462	30	∈	∈	PROPN
ejpam-4021	462	31	fsl(x),f	fsl(x),f	PROPN
ejpam-4021	462	32	≥	≥	NOUN
ejpam-4021	462	33	nx	nx	PROPN
ejpam-4021	462	34	}	}	PUNCT
ejpam-4021	462	35	≤	≤	NUM
ejpam-4021	462	36	∨	∨	NUM
ejpam-4021	462	37	{	{	PUNCT
ejpam-4021	462	38	f⇒(f)(f→(ν	f⇒(f)(f→(ν	PROPN
ejpam-4021	462	39	)	)	PUNCT
ejpam-4021	462	40	)	)	PUNCT
ejpam-4021	462	41	:	:	PUNCT
ejpam-4021	463	1	f⇒(f	f⇒(f	X
ejpam-4021	463	2	)	)	PUNCT
ejpam-4021	463	3	∈	∈	PROPN
ejpam-4021	463	4	fsl(y	fsl(y	PROPN
ejpam-4021	463	5	)	)	PUNCT
ejpam-4021	463	6	,	,	PUNCT
ejpam-4021	463	7	f⇒(f)(f→(ν	f⇒(f)(f→(ν	PROPN
ejpam-4021	463	8	)	)	PUNCT
ejpam-4021	463	9	)	)	PUNCT
ejpam-4021	463	10	≥	≥	NOUN
ejpam-4021	463	11	f⇒(nx)(f→(ν	f⇒(nx)(f→(ν	NOUN
ejpam-4021	463	12	)	)	PUNCT
ejpam-4021	463	13	)	)	PUNCT
ejpam-4021	463	14	}	}	PUNCT
ejpam-4021	463	15	≤	≤	NUM
ejpam-4021	463	16	∨	∨	NUM
ejpam-4021	463	17	{	{	PUNCT
ejpam-4021	463	18	f⇒(f)(f→(ν	f⇒(f)(f→(ν	PROPN
ejpam-4021	463	19	)	)	PUNCT
ejpam-4021	463	20	)	)	PUNCT
ejpam-4021	463	21	:	:	PUNCT
ejpam-4021	464	1	f⇒(f	f⇒(f	X
ejpam-4021	464	2	)	)	PUNCT
ejpam-4021	464	3	∈	∈	PROPN
ejpam-4021	464	4	fsl(h	fsl(h	PROPN
ejpam-4021	464	5	)	)	PUNCT
ejpam-4021	464	6	,	,	PUNCT
ejpam-4021	464	7	f⇒(f)(f→(ν	f⇒(f)(f→(ν	PROPN
ejpam-4021	464	8	)	)	PUNCT
ejpam-4021	464	9	)	)	PUNCT
ejpam-4021	464	10	≥mf(x)(f	≥mf(x)(f	VERB
ejpam-4021	464	11	→(ν	→(ν	NOUN
ejpam-4021	464	12	)	)	PUNCT
ejpam-4021	464	13	)	)	PUNCT
ejpam-4021	464	14	}	}	PUNCT
ejpam-4021	464	15	=	=	SYM
ejpam-4021	464	16	∨	∨	X
ejpam-4021	464	17	{	{	PUNCT
ejpam-4021	464	18	g(f→(ν	g(f→(ν	PROPN
ejpam-4021	464	19	)	)	PUNCT
ejpam-4021	464	20	)	)	PUNCT
ejpam-4021	464	21	:	:	PUNCT
ejpam-4021	464	22	g	g	PROPN
ejpam-4021	464	23	∈	∈	PROPN
ejpam-4021	464	24	fsl(y	fsl(y	PROPN
ejpam-4021	464	25	)	)	PUNCT
ejpam-4021	464	26	,	,	PUNCT
ejpam-4021	464	27	g	g	PROPN
ejpam-4021	464	28	≥mf(x	≥mf(x	NUM
ejpam-4021	464	29	)	)	PUNCT
ejpam-4021	464	30	}	}	PUNCT
ejpam-4021	464	31	=	=	SYM
ejpam-4021	464	32	f→(ν)(f(x	f→(ν)(f(x	PROPN
ejpam-4021	464	33	)	)	PUNCT
ejpam-4021	464	34	)	)	PUNCT
ejpam-4021	464	35	,	,	PUNCT
ejpam-4021	464	36	i.e.	i.e.	X
ejpam-4021	464	37	,	,	PUNCT
ejpam-4021	464	38	ν(x	ν(x	PROPN
ejpam-4021	464	39	)	)	PUNCT
ejpam-4021	464	40	≤	≤	NUM
ejpam-4021	464	41	f→(ν)(f(x	f→(ν)(f(x	PROPN
ejpam-4021	464	42	)	)	PUNCT
ejpam-4021	464	43	)	)	PUNCT
ejpam-4021	464	44	.	.	PUNCT
ejpam-4021	465	1	(	(	PUNCT
ejpam-4021	465	2	d	d	X
ejpam-4021	465	3	)	)	PUNCT
ejpam-4021	465	4	let	let	VERB
ejpam-4021	465	5	ν	ν	PRON
ejpam-4021	465	6	∈	∈	PROPN
ejpam-4021	465	7	lg	lg	NOUN
ejpam-4021	465	8	be	be	AUX
ejpam-4021	465	9	an	an	DET
ejpam-4021	465	10	l	l	NOUN
ejpam-4021	465	11	-	-	PUNCT
ejpam-4021	465	12	valued	value	VERB
ejpam-4021	465	13	normal	normal	ADJ
ejpam-4021	465	14	subgroup	subgroup	NOUN
ejpam-4021	465	15	of	of	ADP
ejpam-4021	465	16	a	a	DET
ejpam-4021	465	17	group	group	NOUN
ejpam-4021	465	18	g	g	NOUN
ejpam-4021	465	19	,	,	PUNCT
ejpam-4021	465	20	and	and	CCONJ
ejpam-4021	465	21	consider	consider	VERB
ejpam-4021	465	22	the	the	DET
ejpam-4021	465	23	mapping	mapping	NOUN
ejpam-4021	465	24	ca	can	AUX
ejpam-4021	465	25	:	:	PUNCT
ejpam-4021	466	1	g	g	ADP
ejpam-4021	466	2	−→	−→	NOUN
ejpam-4021	466	3	g	g	PROPN
ejpam-4021	466	4	defined	define	VERB
ejpam-4021	466	5	by	by	ADP
ejpam-4021	466	6	ca(g	ca(g	NOUN
ejpam-4021	466	7	)	)	PUNCT
ejpam-4021	466	8	=	=	SYM
ejpam-4021	466	9	a−1ga	a−1ga	NOUN
ejpam-4021	466	10	;	;	PUNCT
ejpam-4021	466	11	need	need	VERB
ejpam-4021	466	12	to	to	ADP
ejpam-4021	466	13	that	that	DET
ejpam-4021	466	14	ν	ν	NOUN
ejpam-4021	466	15	is	be	AUX
ejpam-4021	466	16	also	also	ADV
ejpam-4021	466	17	an	an	DET
ejpam-4021	466	18	l	l	ADJ
ejpam-4021	466	19	-	-	ADJ
ejpam-4021	466	20	normal	normal	ADJ
ejpam-4021	466	21	subgroup	subgroup	NOUN
ejpam-4021	466	22	of	of	ADP
ejpam-4021	466	23	g.	g.	PROPN
ejpam-4021	466	24	note	note	VERB
ejpam-4021	466	25	that	that	SCONJ
ejpam-4021	466	26	ν	ν	NOUN
ejpam-4021	466	27	is	be	AUX
ejpam-4021	466	28	l	l	ADJ
ejpam-4021	466	29	-	-	ADJ
ejpam-4021	466	30	normal	normal	ADJ
ejpam-4021	466	31	subgroup	subgroup	NOUN
ejpam-4021	466	32	of	of	ADP
ejpam-4021	466	33	g	g	PROPN
ejpam-4021	466	34	if	if	SCONJ
ejpam-4021	467	1	and	and	CCONJ
ejpam-4021	467	2	only	only	ADV
ejpam-4021	467	3	if	if	SCONJ
ejpam-4021	467	4	ν(aga−1	ν(aga−1	PROPN
ejpam-4021	467	5	)	)	PUNCT
ejpam-4021	468	1	=	=	PUNCT
ejpam-4021	468	2	ν(g	ν(g	PROPN
ejpam-4021	468	3	)	)	PUNCT
ejpam-4021	468	4	.	.	PUNCT
ejpam-4021	469	1	now	now	ADV
ejpam-4021	469	2	since	since	SCONJ
ejpam-4021	469	3	the	the	DET
ejpam-4021	469	4	mapping	mapping	NOUN
ejpam-4021	469	5	ca	can	AUX
ejpam-4021	469	6	is	be	AUX
ejpam-4021	469	7	continuous	continuous	ADJ
ejpam-4021	469	8	,	,	PUNCT
ejpam-4021	469	9	we	we	PRON
ejpam-4021	469	10	have	have	VERB
ejpam-4021	469	11	ν(g	ν(g	NOUN
ejpam-4021	469	12	)	)	PUNCT
ejpam-4021	469	13	≤	≤	NOUN
ejpam-4021	469	14	ca(ν)(ca(g	ca(ν)(ca(g	NOUN
ejpam-4021	469	15	)	)	PUNCT
ejpam-4021	469	16	)	)	PUNCT
ejpam-4021	470	1	=	=	PUNCT
ejpam-4021	471	1	∨	∨	NUM
ejpam-4021	471	2	x∈c←a	x∈c←a	NUM
ejpam-4021	471	3	(	(	PUNCT
ejpam-4021	471	4	g	g	NOUN
ejpam-4021	471	5	)	)	PUNCT
ejpam-4021	471	6	ν(x	ν(x	PROPN
ejpam-4021	471	7	)	)	PUNCT
ejpam-4021	471	8	=	=	PUNCT
ejpam-4021	472	1	∨	∨	NUM
ejpam-4021	472	2	ca(x)=g	ca(x)=g	PROPN
ejpam-4021	472	3	ν(x	ν(x	PROPN
ejpam-4021	472	4	)	)	PUNCT
ejpam-4021	472	5	=	=	SYM
ejpam-4021	472	6	ν(aga−1	ν(aga−1	PROPN
ejpam-4021	472	7	)	)	PUNCT
ejpam-4021	472	8	,	,	PUNCT
ejpam-4021	472	9	i.e.	i.e.	X
ejpam-4021	472	10	,	,	PUNCT
ejpam-4021	472	11	ν(aga−1	ν(aga−1	PROPN
ejpam-4021	472	12	)	)	PUNCT
ejpam-4021	472	13	≥	≥	NOUN
ejpam-4021	472	14	ν(g	ν(g	PROPN
ejpam-4021	472	15	)	)	PUNCT
ejpam-4021	472	16	,	,	PUNCT
ejpam-4021	472	17	meaning	mean	VERB
ejpam-4021	472	18	that	that	SCONJ
ejpam-4021	472	19	ν	ν	NOUN
ejpam-4021	472	20	is	be	AUX
ejpam-4021	472	21	a	a	DET
ejpam-4021	472	22	normal	normal	ADJ
ejpam-4021	472	23	l	l	NOUN
ejpam-4021	472	24	-	-	PUNCT
ejpam-4021	472	25	valued	value	VERB
ejpam-4021	472	26	subgroup	subgroup	NOUN
ejpam-4021	472	27	of	of	ADP
ejpam-4021	472	28	g.	g.	PROPN
ejpam-4021	472	29	(	(	PUNCT
ejpam-4021	472	30	e	e	X
ejpam-4021	472	31	)	)	PUNCT
ejpam-4021	472	32	let	let	VERB
ejpam-4021	472	33	(	(	PUNCT
ejpam-4021	472	34	g	g	NOUN
ejpam-4021	472	35	,	,	PUNCT
ejpam-4021	472	36	·	·	PUNCT
ejpam-4021	472	37	,	,	PUNCT
ejpam-4021	472	38	n	n	CCONJ
ejpam-4021	472	39	)	)	PUNCT
ejpam-4021	472	40	−→	−→	NOUN
ejpam-4021	472	41	(	(	PUNCT
ejpam-4021	472	42	h	h	NOUN
ejpam-4021	472	43	,	,	PUNCT
ejpam-4021	472	44	·	·	PUNCT
ejpam-4021	472	45	,	,	PUNCT
ejpam-4021	472	46	m	m	VERB
ejpam-4021	472	47	)	)	PUNCT
ejpam-4021	472	48	be	be	VERB
ejpam-4021	472	49	a	a	DET
ejpam-4021	472	50	continuous	continuous	ADJ
ejpam-4021	472	51	group	group	NOUN
ejpam-4021	472	52	homomorphism	homomorphism	NOUN
ejpam-4021	472	53	,	,	PUNCT
ejpam-4021	472	54	and	and	CCONJ
ejpam-4021	472	55	µ	µ	PRON
ejpam-4021	472	56	∈	∈	NOUN
ejpam-4021	472	57	l(h	l(h	PROPN
ejpam-4021	472	58	)	)	PUNCT
ejpam-4021	472	59	.	.	PUNCT
ejpam-4021	473	1	then	then	ADV
ejpam-4021	473	2	f←(µ)(e	f←(µ)(e	NOUN
ejpam-4021	473	3	)	)	PUNCT
ejpam-4021	473	4	=	=	SYM
ejpam-4021	473	5	∨	∨	X
ejpam-4021	473	6	{	{	PUNCT
ejpam-4021	473	7	f(f←(µ	f(f←(µ	NOUN
ejpam-4021	473	8	)	)	PUNCT
ejpam-4021	473	9	)	)	PUNCT
ejpam-4021	473	10	:	:	PUNCT
ejpam-4021	474	1	f	f	PROPN
ejpam-4021	474	2	∈	∈	PROPN
ejpam-4021	474	3	fsl(g),f	fsl(g),f	PROPN
ejpam-4021	474	4	≥	≥	PART
ejpam-4021	474	5	ne	ne	PROPN
ejpam-4021	474	6	}	}	PUNCT
ejpam-4021	474	7	≥	≥	NOUN
ejpam-4021	474	8	∨	∨	NUM
ejpam-4021	474	9	{	{	PUNCT
ejpam-4021	474	10	[	[	X
ejpam-4021	474	11	e](f←(µ	e](f←(µ	NOUN
ejpam-4021	474	12	)	)	PUNCT
ejpam-4021	474	13	:	:	PUNCT
ejpam-4021	475	1	[	[	X
ejpam-4021	475	2	e	e	X
ejpam-4021	475	3	]	]	X
ejpam-4021	475	4	∈	∈	PROPN
ejpam-4021	475	5	fsl(g	fsl(g	PROPN
ejpam-4021	475	6	)	)	PUNCT
ejpam-4021	475	7	,	,	PUNCT
ejpam-4021	476	1	[	[	X
ejpam-4021	476	2	e	e	X
ejpam-4021	476	3	]	]	X
ejpam-4021	476	4	≥	≥	X
ejpam-4021	476	5	ne	ne	PROPN
ejpam-4021	476	6	}	}	PUNCT
ejpam-4021	476	7	≥	≥	PROPN
ejpam-4021	476	8	∨	∨	NUM
ejpam-4021	476	9	{	{	PUNCT
ejpam-4021	476	10	µ(e	µ(e	PROPN
ejpam-4021	476	11	)	)	PUNCT
ejpam-4021	476	12	:	:	PUNCT
ejpam-4021	477	1	[	[	X
ejpam-4021	477	2	e	e	X
ejpam-4021	477	3	]	]	X
ejpam-4021	477	4	∈	∈	PROPN
ejpam-4021	477	5	fsl(g	fsl(g	PROPN
ejpam-4021	477	6	)	)	PUNCT
ejpam-4021	477	7	,	,	PUNCT
ejpam-4021	478	1	[	[	X
ejpam-4021	478	2	e	e	X
ejpam-4021	478	3	]	]	X
ejpam-4021	478	4	≥	≥	X
ejpam-4021	478	5	ne	ne	NOUN
ejpam-4021	478	6	}	}	PUNCT
ejpam-4021	478	7	=	=	SYM
ejpam-4021	478	8	>	>	PUNCT
ejpam-4021	478	9	,	,	PUNCT
ejpam-4021	478	10	whence	whence	PROPN
ejpam-4021	478	11	µ(e	µ(e	PROPN
ejpam-4021	478	12	)	)	PUNCT
ejpam-4021	478	13	=	=	PUNCT
ejpam-4021	479	1	>	>	PUNCT
ejpam-4021	479	2	,	,	PUNCT
ejpam-4021	479	3	since	since	SCONJ
ejpam-4021	479	4	µ	µ	NOUN
ejpam-4021	479	5	∈	∈	PROPN
ejpam-4021	479	6	l(g	l(g	NOUN
ejpam-4021	479	7	)	)	PUNCT
ejpam-4021	479	8	,	,	PUNCT
ejpam-4021	479	9	implying	imply	VERB
ejpam-4021	479	10	f←(µ)(e	f←(µ)(e	NOUN
ejpam-4021	479	11	)	)	PUNCT
ejpam-4021	479	12	=	=	PUNCT
ejpam-4021	480	1	>	>	PUNCT
ejpam-4021	480	2	.	.	PUNCT
ejpam-4021	481	1	now	now	ADV
ejpam-4021	481	2	let	let	VERB
ejpam-4021	481	3	x	x	PRON
ejpam-4021	481	4	,	,	PUNCT
ejpam-4021	481	5	y	y	PROPN
ejpam-4021	481	6	∈	∈	PROPN
ejpam-4021	481	7	g	g	PROPN
ejpam-4021	481	8	and	and	CCONJ
ejpam-4021	481	9	µ	µ	PRON
ejpam-4021	481	10	∈	∈	PROPN
ejpam-4021	481	11	lh	lh	NOUN
ejpam-4021	481	12	.	.	PUNCT
ejpam-4021	482	1	then	then	ADV
ejpam-4021	482	2	in	in	ADP
ejpam-4021	482	3	view	view	NOUN
ejpam-4021	482	4	of	of	ADP
ejpam-4021	482	5	the	the	DET
ejpam-4021	482	6	definition	definition	NOUN
ejpam-4021	482	7	1(glm3	1(glm3	NUM
ejpam-4021	482	8	)	)	PUNCT
ejpam-4021	482	9	,	,	PUNCT
ejpam-4021	482	10	we	we	PRON
ejpam-4021	482	11	have	have	VERB
ejpam-4021	482	12	:	:	PUNCT
ejpam-4021	482	13	f←(µ)(x)∗f←(µ)(y	f←(µ)(x)∗f←(µ)(y	X
ejpam-4021	482	14	)	)	PUNCT
ejpam-4021	483	1	=	=	PUNCT
ejpam-4021	483	2	∨	∨	X
ejpam-4021	483	3	{	{	PUNCT
ejpam-4021	483	4	f(f←(µ	f(f←(µ	NOUN
ejpam-4021	483	5	)	)	PUNCT
ejpam-4021	483	6	)	)	PUNCT
ejpam-4021	483	7	:	:	PUNCT
ejpam-4021	484	1	f	f	PROPN
ejpam-4021	484	2	∈	∈	PROPN
ejpam-4021	484	3	fsl(g),f	fsl(g),f	PROPN
ejpam-4021	484	4	≥	≥	NUM
ejpam-4021	484	5	nx}∗	nx}∗	NOUN
ejpam-4021	484	6	∨	∨	X
ejpam-4021	484	7	{	{	PUNCT
ejpam-4021	484	8	g(f←(µ	g(f←(µ	NOUN
ejpam-4021	484	9	)	)	PUNCT
ejpam-4021	484	10	)	)	PUNCT
ejpam-4021	484	11	:	:	PUNCT
ejpam-4021	484	12	g	g	PROPN
ejpam-4021	484	13	∈	∈	PROPN
ejpam-4021	484	14	fsl(g),g	fsl(g),g	PROPN
ejpam-4021	484	15	≥	≥	NUM
ejpam-4021	484	16	ny	ny	NOUN
ejpam-4021	484	17	}	}	PUNCT
ejpam-4021	484	18	=	=	SYM
ejpam-4021	484	19	∨	∨	X
ejpam-4021	484	20	{	{	PUNCT
ejpam-4021	484	21	f(f←(µ	f(f←(µ	NOUN
ejpam-4021	484	22	)	)	PUNCT
ejpam-4021	484	23	)	)	PUNCT
ejpam-4021	484	24	∗	∗	NOUN
ejpam-4021	484	25	g(f←(µ	g(f←(µ	ADJ
ejpam-4021	484	26	)	)	PUNCT
ejpam-4021	484	27	)	)	PUNCT
ejpam-4021	484	28	:	:	PUNCT
ejpam-4021	485	1	f	f	X
ejpam-4021	485	2	,	,	PUNCT
ejpam-4021	485	3	g	g	PROPN
ejpam-4021	485	4	∈	∈	PROPN
ejpam-4021	485	5	fsl(g),f	fsl(g),f	PROPN
ejpam-4021	485	6	≥	≥	NUM
ejpam-4021	485	7	nx	nx	PROPN
ejpam-4021	485	8	,	,	PUNCT
ejpam-4021	485	9	g	g	PROPN
ejpam-4021	485	10	≥	≥	NUM
ejpam-4021	485	11	ny	ny	NOUN
ejpam-4021	485	12	}	}	PUNCT
ejpam-4021	485	13	≤	≤	NUM
ejpam-4021	485	14	∨	∨	NUM
ejpam-4021	485	15	{	{	PUNCT
ejpam-4021	485	16	f	f	PROPN
ejpam-4021	485	17	�	�	PROPN
ejpam-4021	485	18	g(f←(µ	g(f←(µ	PROPN
ejpam-4021	485	19	)	)	PUNCT
ejpam-4021	485	20	)	)	PUNCT
ejpam-4021	485	21	:	:	PUNCT
ejpam-4021	486	1	f	f	X
ejpam-4021	486	2	�	�	PROPN
ejpam-4021	486	3	g	g	PROPN
ejpam-4021	486	4	∈	∈	PROPN
ejpam-4021	486	5	fsl(g),f	fsl(g),f	PROPN
ejpam-4021	486	6	�	�	PROPN
ejpam-4021	486	7	g	g	PROPN
ejpam-4021	486	8	≥	≥	NUM
ejpam-4021	486	9	nx	nx	PROPN
ejpam-4021	486	10	�	�	PROPN
ejpam-4021	486	11	ny	ny	PROPN
ejpam-4021	486	12	}	}	PUNCT
ejpam-4021	486	13	(	(	PUNCT
ejpam-4021	486	14	by	by	ADP
ejpam-4021	486	15	applying	apply	VERB
ejpam-4021	486	16	theorem	theorem	ADJ
ejpam-4021	486	17	1.2.8	1.2.8	NUM
ejpam-4021	486	18	and	and	CCONJ
ejpam-4021	486	19	theorem	theorem	ADJ
ejpam-4021	486	20	1.2.11[24	1.2.11[24	NUM
ejpam-4021	486	21	]	]	X
ejpam-4021	486	22	,	,	PUNCT
ejpam-4021	486	23	whence	whence	NOUN
ejpam-4021	486	24	f←(µ	f←(µ	NOUN
ejpam-4021	486	25	)	)	PUNCT
ejpam-4021	486	26	∈	∈	PROPN
ejpam-4021	486	27	l(g	l(g	PROPN
ejpam-4021	486	28	)	)	PUNCT
ejpam-4021	486	29	)	)	PUNCT
ejpam-4021	486	30	≤	≤	NUM
ejpam-4021	486	31	∨	∨	NUM
ejpam-4021	486	32	{	{	PUNCT
ejpam-4021	486	33	f	f	PROPN
ejpam-4021	486	34	�	�	PROPN
ejpam-4021	486	35	g(f←(µ	g(f←(µ	PROPN
ejpam-4021	486	36	)	)	PUNCT
ejpam-4021	486	37	)	)	PUNCT
ejpam-4021	486	38	:	:	PUNCT
ejpam-4021	487	1	f	f	X
ejpam-4021	487	2	�	�	PROPN
ejpam-4021	487	3	g	g	PROPN
ejpam-4021	487	4	∈	∈	PROPN
ejpam-4021	487	5	fsl(g),nxy	fsl(g),nxy	ADJ
ejpam-4021	487	6	≤	≤	NUM
ejpam-4021	487	7	f	f	PROPN
ejpam-4021	487	8	�	�	PROPN
ejpam-4021	487	9	g	g	PROPN
ejpam-4021	487	10	}	}	PUNCT
ejpam-4021	487	11	(	(	PUNCT
ejpam-4021	487	12	since	since	SCONJ
ejpam-4021	487	13	(	(	PUNCT
ejpam-4021	487	14	g	g	NOUN
ejpam-4021	487	15	,	,	PUNCT
ejpam-4021	487	16	·	·	PUNCT
ejpam-4021	487	17	,	,	PUNCT
ejpam-4021	487	18	n	n	CCONJ
ejpam-4021	487	19	)	)	PUNCT
ejpam-4021	487	20	∈	∈	PROPN
ejpam-4021	487	21	|sl	|sl	NOUN
ejpam-4021	487	22	-	-	PUNCT
ejpam-4021	487	23	ns|	ns|	ADV
ejpam-4021	487	24	,	,	PUNCT
ejpam-4021	487	25	applying	apply	VERB
ejpam-4021	487	26	the	the	DET
ejpam-4021	487	27	definition	definition	NOUN
ejpam-4021	487	28	10(lngm	10(lngm	NUM
ejpam-4021	487	29	)	)	PUNCT
ejpam-4021	487	30	,	,	PUNCT
ejpam-4021	487	31	and	and	CCONJ
ejpam-4021	487	32	due	due	ADP
ejpam-4021	487	33	to	to	ADP
ejpam-4021	487	34	lemma	lemma	PROPN
ejpam-4021	487	35	1	1	NUM
ejpam-4021	487	36	,	,	PUNCT
ejpam-4021	487	37	f	f	PROPN
ejpam-4021	487	38	�	�	PROPN
ejpam-4021	487	39	g	g	PROPN
ejpam-4021	487	40	∈	∈	PROPN
ejpam-4021	487	41	fsl(g	fsl(g	PROPN
ejpam-4021	487	42	)	)	PUNCT
ejpam-4021	487	43	)	)	PUNCT
ejpam-4021	488	1	=	=	SYM
ejpam-4021	488	2	∨	∨	X
ejpam-4021	488	3	{	{	PUNCT
ejpam-4021	488	4	h(f←(µ	h(f←(µ	PROPN
ejpam-4021	488	5	)	)	PUNCT
ejpam-4021	488	6	)	)	PUNCT
ejpam-4021	488	7	:	:	PUNCT
ejpam-4021	489	1	h	h	PROPN
ejpam-4021	489	2	∈	∈	PROPN
ejpam-4021	489	3	fsl(g),nxy	fsl(g),nxy	ADJ
ejpam-4021	489	4	≤	≤	NUM
ejpam-4021	489	5	h	h	NOUN
ejpam-4021	489	6	}	}	PUNCT
ejpam-4021	489	7	=	=	SYM
ejpam-4021	489	8	f←(µ)(xy	f←(µ)(xy	NUM
ejpam-4021	489	9	)	)	PUNCT
ejpam-4021	489	10	.	.	PUNCT
ejpam-4021	490	1	finally	finally	ADV
ejpam-4021	490	2	,	,	PUNCT
ejpam-4021	490	3	since	since	SCONJ
ejpam-4021	490	4	f←(µ	f←(µ	NOUN
ejpam-4021	490	5	)	)	PUNCT
ejpam-4021	490	6	≥	≥	NOUN
ejpam-4021	490	7	f←(µ	f←(µ	NOUN
ejpam-4021	490	8	)	)	PUNCT
ejpam-4021	490	9	,	,	PUNCT
ejpam-4021	490	10	we	we	PRON
ejpam-4021	490	11	get	get	VERB
ejpam-4021	490	12	f←(µ)(x−1	f←(µ)(x−1	PROPN
ejpam-4021	490	13	)	)	PUNCT
ejpam-4021	490	14	≥	≥	NOUN
ejpam-4021	490	15	f←(µ)(x	f←(µ)(x	PROPN
ejpam-4021	490	16	)	)	PUNCT
ejpam-4021	490	17	,	,	PUNCT
ejpam-4021	490	18	for	for	ADP
ejpam-4021	490	19	any	any	DET
ejpam-4021	490	20	x	x	SYM
ejpam-4021	490	21	∈	∈	PROPN
ejpam-4021	490	22	g.	g.	NOUN
ejpam-4021	490	23	in	in	ADP
ejpam-4021	490	24	fact	fact	NOUN
ejpam-4021	490	25	,	,	PUNCT
ejpam-4021	490	26	for	for	ADP
ejpam-4021	490	27	any	any	DET
ejpam-4021	490	28	µ	µ	PRON
ejpam-4021	490	29	∈	∈	NOUN
ejpam-4021	490	30	l(h	l(h	PROPN
ejpam-4021	490	31	)	)	PUNCT
ejpam-4021	490	32	,	,	PUNCT
ejpam-4021	490	33	f←(µ	f←(µ	NOUN
ejpam-4021	490	34	)	)	PUNCT
ejpam-4021	490	35	∈	∈	PROPN
ejpam-4021	490	36	l(g	l(g	PROPN
ejpam-4021	490	37	)	)	PUNCT
ejpam-4021	490	38	by	by	ADP
ejpam-4021	490	39	theorem	theorem	ADJ
ejpam-4021	490	40	1.2.11[24	1.2.11[24	PROPN
ejpam-4021	490	41	]	]	PUNCT
ejpam-4021	490	42	.	.	PUNCT
ejpam-4021	491	1	so	so	ADV
ejpam-4021	491	2	,	,	PUNCT
ejpam-4021	491	3	we	we	PRON
ejpam-4021	491	4	have	have	VERB
ejpam-4021	491	5	:	:	PUNCT
ejpam-4021	491	6	f←(µ)(x	f←(µ)(x	NUM
ejpam-4021	491	7	)	)	PUNCT
ejpam-4021	491	8	=	=	SYM
ejpam-4021	491	9	∨	∨	X
ejpam-4021	491	10	{	{	PUNCT
ejpam-4021	491	11	f(f←(µ	f(f←(µ	NOUN
ejpam-4021	491	12	)	)	PUNCT
ejpam-4021	491	13	)	)	PUNCT
ejpam-4021	491	14	:	:	PUNCT
ejpam-4021	492	1	f	f	PROPN
ejpam-4021	492	2	∈	∈	PROPN
ejpam-4021	492	3	fsl(g),f	fsl(g),f	PROPN
ejpam-4021	492	4	≥	≥	NOUN
ejpam-4021	492	5	nx	nx	PROPN
ejpam-4021	492	6	}	}	PUNCT
ejpam-4021	492	7	≤	≤	NUM
ejpam-4021	492	8	∨	∨	NUM
ejpam-4021	492	9	{	{	PUNCT
ejpam-4021	492	10	f−1(f←(µ	f−1(f←(µ	ADJ
ejpam-4021	492	11	)	)	PUNCT
ejpam-4021	492	12	)	)	PUNCT
ejpam-4021	492	13	:	:	PUNCT
ejpam-4021	492	14	f−1	f−1	PROPN
ejpam-4021	492	15	∈	∈	PROPN
ejpam-4021	492	16	fsl(g),f−1	fsl(g),f−1	X
ejpam-4021	492	17	≥	≥	X
ejpam-4021	492	18	(	(	PUNCT
ejpam-4021	492	19	nx)−1	nx)−1	NOUN
ejpam-4021	492	20	}	}	PUNCT
ejpam-4021	492	21	≤	≤	ADJ
ejpam-4021	492	22	∨	∨	NUM
ejpam-4021	492	23	{	{	PUNCT
ejpam-4021	492	24	f−1(f←(µ	f−1(f←(µ	ADJ
ejpam-4021	492	25	)	)	PUNCT
ejpam-4021	492	26	)	)	PUNCT
ejpam-4021	492	27	:	:	PUNCT
ejpam-4021	492	28	f−1	f−1	PROPN
ejpam-4021	492	29	∈	∈	PROPN
ejpam-4021	492	30	fsl(g),f−1	fsl(g),f−1	X
ejpam-4021	492	31	≥	≥	X
ejpam-4021	492	32	nx−1	nx−1	PROPN
ejpam-4021	492	33	}	}	PUNCT
ejpam-4021	492	34	(	(	PUNCT
ejpam-4021	492	35	by	by	ADP
ejpam-4021	492	36	definition	definition	NOUN
ejpam-4021	492	37	10(lngi	10(lngi	NUM
ejpam-4021	492	38	)	)	PUNCT
ejpam-4021	492	39	)	)	PUNCT
ejpam-4021	492	40	=	=	PUNCT
ejpam-4021	492	41	∨	∨	X
ejpam-4021	492	42	{	{	PUNCT
ejpam-4021	492	43	g(f←(µ	g(f←(µ	NOUN
ejpam-4021	492	44	)	)	PUNCT
ejpam-4021	492	45	)	)	PUNCT
ejpam-4021	492	46	:	:	PUNCT
ejpam-4021	492	47	g	g	PROPN
ejpam-4021	492	48	∈	∈	PROPN
ejpam-4021	492	49	fsl(g),g	fsl(g),g	PROPN
ejpam-4021	492	50	≥	≥	NOUN
ejpam-4021	492	51	nx−1	nx−1	PROPN
ejpam-4021	492	52	}	}	PUNCT
ejpam-4021	492	53	=	=	SYM
ejpam-4021	492	54	f←(µ)(x−1	f←(µ)(x−1	PROPN
ejpam-4021	492	55	)	)	PUNCT
ejpam-4021	492	56	.	.	PUNCT
ejpam-4021	493	1	lemma	lemma	PROPN
ejpam-4021	493	2	9	9	NUM
ejpam-4021	493	3	.	.	PUNCT
ejpam-4021	494	1	[	[	X
ejpam-4021	494	2	2	2	NUM
ejpam-4021	494	3	]	]	X
ejpam-4021	494	4	let	let	VERB
ejpam-4021	494	5	(	(	PUNCT
ejpam-4021	494	6	g	g	NOUN
ejpam-4021	494	7	,	,	PUNCT
ejpam-4021	494	8	·	·	PUNCT
ejpam-4021	494	9	,	,	PUNCT
ejpam-4021	494	10	∆	∆	X
ejpam-4021	494	11	)	)	PUNCT
ejpam-4021	495	1	∈	∈	PROPN
ejpam-4021	495	2	|sl	|sl	PROPN
ejpam-4021	495	3	-	-	PUNCT
ejpam-4021	495	4	topgrp|	topgrp|	PROPN
ejpam-4021	495	5	,	,	PUNCT
ejpam-4021	495	6	µ	µ	PRON
ejpam-4021	495	7	∈	∈	NOUN
ejpam-4021	495	8	∆	∆	PROPN
ejpam-4021	495	9	and	and	CCONJ
ejpam-4021	495	10	ν	ν	PROPN
ejpam-4021	495	11	∈	∈	PROPN
ejpam-4021	495	12	lg	lg	PROPN
ejpam-4021	495	13	.	.	PROPN
ejpam-4021	495	14	then	then	ADV
ejpam-4021	495	15	µ	µ	X
ejpam-4021	495	16	·	·	PUNCT
ejpam-4021	495	17	ν	ν	X
ejpam-4021	495	18	∈	∈	NOUN
ejpam-4021	495	19	∆.	∆.	ADJ
ejpam-4021	495	20	proof	proof	NOUN
ejpam-4021	495	21	.	.	PUNCT
ejpam-4021	496	1	let	let	VERB
ejpam-4021	496	2	x	x	PUNCT
ejpam-4021	496	3	∈	∈	PROPN
ejpam-4021	496	4	g	g	PROPN
ejpam-4021	496	5	,	,	PUNCT
ejpam-4021	496	6	µ	µ	X
ejpam-4021	496	7	∈	∈	NOUN
ejpam-4021	496	8	∆	∆	PROPN
ejpam-4021	496	9	and	and	CCONJ
ejpam-4021	496	10	ν	ν	PROPN
ejpam-4021	496	11	∈	∈	PROPN
ejpam-4021	496	12	lg	lg	PROPN
ejpam-4021	496	13	.	.	PROPN
ejpam-4021	496	14	then	then	ADV
ejpam-4021	496	15	µ	µ	X
ejpam-4021	496	16	·	·	PUNCT
ejpam-4021	496	17	ν(x	ν(x	PROPN
ejpam-4021	496	18	)	)	PUNCT
ejpam-4021	496	19	=	=	PUNCT
ejpam-4021	496	20	∨	∨	NUM
ejpam-4021	496	21	st	st	NOUN
ejpam-4021	496	22	=	=	NOUN
ejpam-4021	496	23	x	x	NOUN
ejpam-4021	496	24	µ(x	µ(x	ADJ
ejpam-4021	496	25	)	)	PUNCT
ejpam-4021	496	26	∗	∗	NOUN
ejpam-4021	496	27	ν(t	ν(t	NOUN
ejpam-4021	496	28	)	)	PUNCT
ejpam-4021	497	1	=	=	NUM
ejpam-4021	497	2	∨	∨	NUM
ejpam-4021	497	3	t∈g	t∈g	X
ejpam-4021	497	4	µ(xt−1	µ(xt−1	NOUN
ejpam-4021	497	5	)	)	PUNCT
ejpam-4021	497	6	∗	∗	NOUN
ejpam-4021	497	7	ν(t	ν(t	NOUN
ejpam-4021	497	8	)	)	PUNCT
ejpam-4021	497	9	=	=	PUNCT
ejpam-4021	497	10	∨	∨	NUM
ejpam-4021	497	11	t∈grt(µ)(x	t∈grt(µ)(x	NOUN
ejpam-4021	497	12	)	)	PUNCT
ejpam-4021	497	13	∗	∗	NOUN
ejpam-4021	497	14	ν(t	ν(t	NOUN
ejpam-4021	497	15	)	)	PUNCT
ejpam-4021	497	16	.	.	PUNCT
ejpam-4021	498	1	fix	fix	NOUN
ejpam-4021	498	2	t	t	PROPN
ejpam-4021	498	3	∈	∈	PROPN
ejpam-4021	498	4	g	g	NOUN
ejpam-4021	498	5	,	,	PUNCT
ejpam-4021	498	6	then	then	ADV
ejpam-4021	498	7	ν(t	ν(t	NOUN
ejpam-4021	498	8	)	)	PUNCT
ejpam-4021	498	9	is	be	AUX
ejpam-4021	498	10	constant	constant	ADJ
ejpam-4021	498	11	and	and	CCONJ
ejpam-4021	498	12	t	t	PROPN
ejpam-4021	498	13	m	m	PROPN
ejpam-4021	498	14	g	g	NOUN
ejpam-4021	498	15	ahsanullah	ahsanullah	NOUN
ejpam-4021	498	16	,	,	PUNCT
ejpam-4021	498	17	fawzi	fawzi	PROPN
ejpam-4021	498	18	al	al	PROPN
ejpam-4021	498	19	-	-	PUNCT
ejpam-4021	498	20	thukair	thukair	NOUN
ejpam-4021	498	21	/	/	SYM
ejpam-4021	498	22	eur	eur	NOUN
ejpam-4021	498	23	.	.	PUNCT
ejpam-4021	499	1	j.	j.	PROPN
ejpam-4021	499	2	pure	pure	PROPN
ejpam-4021	499	3	appl	appl	PROPN
ejpam-4021	499	4	.	.	PROPN
ejpam-4021	499	5	math	math	PROPN
ejpam-4021	499	6	,	,	PUNCT
ejpam-4021	499	7	14	14	NUM
ejpam-4021	499	8	(	(	PUNCT
ejpam-4021	499	9	3	3	NUM
ejpam-4021	499	10	)	)	PUNCT
ejpam-4021	499	11	(	(	PUNCT
ejpam-4021	499	12	2021	2021	NUM
ejpam-4021	499	13	)	)	PUNCT
ejpam-4021	499	14	,	,	PUNCT
ejpam-4021	499	15	949	949	NUM
ejpam-4021	499	16	-	-	SYM
ejpam-4021	499	17	968	968	NUM
ejpam-4021	499	18	965	965	NUM
ejpam-4021	499	19	ν(t	ν(t	NOUN
ejpam-4021	499	20	)	)	PUNCT
ejpam-4021	499	21	∈	∈	PROPN
ejpam-4021	499	22	l.	l.	NOUN
ejpam-4021	499	23	since	since	ADV
ejpam-4021	499	24	and	and	CCONJ
ejpam-4021	499	25	rt	rt	INTJ
ejpam-4021	499	26	:	:	PUNCT
ejpam-4021	499	27	g	g	PROPN
ejpam-4021	499	28	−→	−→	NOUN
ejpam-4021	499	29	g	g	PROPN
ejpam-4021	499	30	is	be	AUX
ejpam-4021	499	31	a	a	DET
ejpam-4021	499	32	homeomorphism	homeomorphism	NOUN
ejpam-4021	499	33	,	,	PUNCT
ejpam-4021	499	34	and	and	CCONJ
ejpam-4021	499	35	µ	µ	PRON
ejpam-4021	499	36	∈	∈	PROPN
ejpam-4021	499	37	∆	∆	X
ejpam-4021	499	38	,	,	PUNCT
ejpam-4021	499	39	∨	∨	PROPN
ejpam-4021	499	40	t∈grt(µ	t∈grt(µ	NOUN
ejpam-4021	499	41	)	)	PUNCT
ejpam-4021	499	42	∈	∈	PROPN
ejpam-4021	499	43	∆	∆	PROPN
ejpam-4021	499	44	and	and	CCONJ
ejpam-4021	499	45	since	since	SCONJ
ejpam-4021	499	46	∆	∆	PROPN
ejpam-4021	499	47	is	be	AUX
ejpam-4021	499	48	stratified	stratify	VERB
ejpam-4021	499	49	,	,	PUNCT
ejpam-4021	499	50	and	and	CCONJ
ejpam-4021	499	51	(	(	PUNCT
ejpam-4021	499	52	l	l	NOUN
ejpam-4021	499	53	,	,	PUNCT
ejpam-4021	499	54	∗	∗	NOUN
ejpam-4021	499	55	)	)	PUNCT
ejpam-4021	499	56	is	be	AUX
ejpam-4021	499	57	commutative	commutative	ADJ
ejpam-4021	499	58	semigroup	semigroup	NOUN
ejpam-4021	499	59	,	,	PUNCT
ejpam-4021	499	60	we	we	PRON
ejpam-4021	499	61	have	have	VERB
ejpam-4021	499	62	∨	∨	VERB
ejpam-4021	499	63	t∈grt(µ	t∈grt(µ	NUM
ejpam-4021	499	64	)	)	PUNCT
ejpam-4021	499	65	∗	∗	NOUN
ejpam-4021	499	66	ν(t	ν(t	NOUN
ejpam-4021	499	67	)	)	PUNCT
ejpam-4021	499	68	=	=	PUNCT
ejpam-4021	499	69	ν(t	ν(t	NOUN
ejpam-4021	499	70	)	)	PUNCT
ejpam-4021	499	71	∗	∗	NOUN
ejpam-4021	499	72	∨	∨	NUM
ejpam-4021	499	73	t∈g	t∈g	X
ejpam-4021	499	74	lt(µ	lt(µ	PRON
ejpam-4021	499	75	)	)	PUNCT
ejpam-4021	499	76	∈	∈	PROPN
ejpam-4021	499	77	∆	∆	PROPN
ejpam-4021	499	78	,	,	PUNCT
ejpam-4021	499	79	i.e.	i.e.	X
ejpam-4021	499	80	,	,	PUNCT
ejpam-4021	499	81	µ	µ	X
ejpam-4021	499	82	·	·	PUNCT
ejpam-4021	499	83	ν	ν	X
ejpam-4021	499	84	∈	∈	NOUN
ejpam-4021	499	85	∆.	∆.	ADJ
ejpam-4021	499	86	proposition	proposition	NOUN
ejpam-4021	499	87	3	3	X
ejpam-4021	499	88	.	.	PUNCT
ejpam-4021	500	1	[	[	X
ejpam-4021	500	2	18	18	NUM
ejpam-4021	500	3	]	]	X
ejpam-4021	500	4	let	let	VERB
ejpam-4021	500	5	(	(	PUNCT
ejpam-4021	500	6	x,∆n	x,∆n	NUM
ejpam-4021	500	7	)	)	PUNCT
ejpam-4021	500	8	be	be	VERB
ejpam-4021	500	9	a	a	DET
ejpam-4021	500	10	stratified	stratified	ADJ
ejpam-4021	500	11	l	l	NOUN
ejpam-4021	500	12	-	-	PUNCT
ejpam-4021	500	13	valued	value	VERB
ejpam-4021	500	14	topological	topological	ADJ
ejpam-4021	500	15	space	space	NOUN
ejpam-4021	500	16	with	with	ADP
ejpam-4021	500	17	a	a	DET
ejpam-4021	500	18	corresponding	correspond	VERB
ejpam-4021	500	19	stratified	stratified	ADJ
ejpam-4021	500	20	l	l	ADV
ejpam-4021	500	21	-	-	PUNCT
ejpam-4021	500	22	valued	value	VERB
ejpam-4021	500	23	neighborhood	neighborhood	NOUN
ejpam-4021	500	24	system	system	NOUN
ejpam-4021	500	25	n.	n.	NOUN
ejpam-4021	500	26	then	then	ADV
ejpam-4021	500	27	(	(	PUNCT
ejpam-4021	500	28	x,∆n	x,∆n	NUM
ejpam-4021	500	29	)	)	PUNCT
ejpam-4021	500	30	is	be	AUX
ejpam-4021	500	31	hausdorff	hausdorff	NOUN
ejpam-4021	500	32	-	-	PUNCT
ejpam-4021	500	33	separated	separate	VERB
ejpam-4021	500	34	if	if	SCONJ
ejpam-4021	500	35	and	and	CCONJ
ejpam-4021	500	36	only	only	ADV
ejpam-4021	500	37	if	if	SCONJ
ejpam-4021	500	38	for	for	ADP
ejpam-4021	500	39	all	all	DET
ejpam-4021	500	40	x	x	SYM
ejpam-4021	500	41	6=	6=	ADP
ejpam-4021	500	42	y	y	PROPN
ejpam-4021	500	43	∈	∈	PROPN
ejpam-4021	500	44	x	x	PUNCT
ejpam-4021	500	45	there	there	PRON
ejpam-4021	500	46	are	be	VERB
ejpam-4021	500	47	ν1	ν1	NOUN
ejpam-4021	500	48	,	,	PUNCT
ejpam-4021	500	49	ν2	ν2	NOUN
ejpam-4021	500	50	∈	∈	PROPN
ejpam-4021	500	51	∆n	∆n	PROPN
ejpam-4021	500	52	such	such	ADJ
ejpam-4021	500	53	that	that	SCONJ
ejpam-4021	500	54	ν1	ν1	NOUN
ejpam-4021	500	55	∗	∗	NOUN
ejpam-4021	500	56	ν2	ν2	NOUN
ejpam-4021	500	57	=	=	SYM
ejpam-4021	500	58	>	>	NOUN
ejpam-4021	500	59	∅	∅	NOUN
ejpam-4021	500	60	and	and	CCONJ
ejpam-4021	500	61	ν1(x	ν1(x	NOUN
ejpam-4021	500	62	)	)	PUNCT
ejpam-4021	500	63	∗	∗	NOUN
ejpam-4021	500	64	ν2(y	ν2(y	NOUN
ejpam-4021	500	65	)	)	PUNCT
ejpam-4021	500	66	6=	6=	ADP
ejpam-4021	500	67	⊥.	⊥.	NUM
ejpam-4021	500	68	definition	definition	NOUN
ejpam-4021	500	69	18	18	NUM
ejpam-4021	500	70	.	.	PUNCT
ejpam-4021	501	1	[	[	X
ejpam-4021	501	2	18	18	NUM
ejpam-4021	501	3	]	]	X
ejpam-4021	501	4	let	let	VERB
ejpam-4021	501	5	(	(	PUNCT
ejpam-4021	501	6	x,∆	x,∆	NUM
ejpam-4021	501	7	)	)	PUNCT
ejpam-4021	501	8	be	be	VERB
ejpam-4021	501	9	a	a	DET
ejpam-4021	501	10	stratified	stratified	ADJ
ejpam-4021	501	11	l	l	NOUN
ejpam-4021	501	12	-	-	PUNCT
ejpam-4021	501	13	valued	value	VERB
ejpam-4021	501	14	topological	topological	ADJ
ejpam-4021	501	15	space	space	NOUN
ejpam-4021	501	16	,	,	PUNCT
ejpam-4021	501	17	n	n	NOUN
ejpam-4021	501	18	=	=	PUNCT
ejpam-4021	501	19	(	(	PUNCT
ejpam-4021	501	20	nx)x∈x	nx)x∈x	NUM
ejpam-4021	501	21	be	be	AUX
ejpam-4021	501	22	the	the	DET
ejpam-4021	501	23	corresponding	corresponding	ADJ
ejpam-4021	501	24	l	l	ADV
ejpam-4021	501	25	-	-	PUNCT
ejpam-4021	501	26	valued	value	VERB
ejpam-4021	501	27	neighborhood	neighborhood	NOUN
ejpam-4021	501	28	system	system	NOUN
ejpam-4021	501	29	,	,	PUNCT
ejpam-4021	501	30	and	and	CCONJ
ejpam-4021	501	31	a	a	PRON
ejpam-4021	501	32	be	be	AUX
ejpam-4021	501	33	a	a	DET
ejpam-4021	501	34	subset	subset	NOUN
ejpam-4021	501	35	of	of	ADP
ejpam-4021	501	36	x.	x.	NOUN
ejpam-4021	501	37	then	then	ADV
ejpam-4021	501	38	closure	closure	NOUN
ejpam-4021	501	39	of	of	ADP
ejpam-4021	501	40	a	a	PRON
ejpam-4021	501	41	,	,	PUNCT
ejpam-4021	501	42	written	write	VERB
ejpam-4021	501	43	as	as	ADP
ejpam-4021	501	44	a	a	PRON
ejpam-4021	501	45	,	,	PUNCT
ejpam-4021	501	46	is	be	AUX
ejpam-4021	501	47	given	give	VERB
ejpam-4021	501	48	by	by	ADP
ejpam-4021	501	49	a	a	DET
ejpam-4021	501	50	=	=	X
ejpam-4021	501	51	{	{	PUNCT
ejpam-4021	501	52	x	x	SYM
ejpam-4021	501	53	∈	∈	PROPN
ejpam-4021	501	54	x	x	X
ejpam-4021	501	55	:	:	PUNCT
ejpam-4021	501	56	nx(>x∩ac	nx(>x∩ac	PROPN
ejpam-4021	501	57	)	)	PUNCT
ejpam-4021	501	58	=	=	PUNCT
ejpam-4021	502	1	⊥	⊥	X
ejpam-4021	502	2	}	}	PUNCT
ejpam-4021	502	3	a	a	DET
ejpam-4021	502	4	subset	subset	NOUN
ejpam-4021	502	5	of	of	ADP
ejpam-4021	502	6	x	x	PRON
ejpam-4021	502	7	is	be	AUX
ejpam-4021	502	8	said	say	VERB
ejpam-4021	502	9	to	to	PART
ejpam-4021	502	10	be	be	AUX
ejpam-4021	502	11	closed	close	VERB
ejpam-4021	502	12	with	with	ADP
ejpam-4021	502	13	respect	respect	NOUN
ejpam-4021	502	14	to	to	ADP
ejpam-4021	502	15	∆	∆	PROPN
ejpam-4021	502	16	if	if	SCONJ
ejpam-4021	502	17	a	a	DET
ejpam-4021	502	18	=	=	NOUN
ejpam-4021	502	19	a.	a.	NOUN
ejpam-4021	502	20	lemma	lemma	PROPN
ejpam-4021	502	21	10	10	NUM
ejpam-4021	502	22	.	.	PUNCT
ejpam-4021	503	1	a	a	DET
ejpam-4021	503	2	stratified	stratified	ADJ
ejpam-4021	503	3	l	l	NOUN
ejpam-4021	503	4	-	-	PUNCT
ejpam-4021	503	5	valued	value	VERB
ejpam-4021	503	6	topological	topological	ADJ
ejpam-4021	503	7	group	group	NOUN
ejpam-4021	503	8	(	(	PUNCT
ejpam-4021	503	9	g	g	PROPN
ejpam-4021	503	10	,	,	PUNCT
ejpam-4021	503	11	·	·	PUNCT
ejpam-4021	503	12	,	,	PUNCT
ejpam-4021	503	13	∆n	∆n	PROPN
ejpam-4021	503	14	)	)	PUNCT
ejpam-4021	503	15	is	be	AUX
ejpam-4021	503	16	hausdorff	hausdorff	NOUN
ejpam-4021	503	17	-	-	PUNCT
ejpam-4021	503	18	separated	separate	VERB
ejpam-4021	503	19	if	if	SCONJ
ejpam-4021	503	20	and	and	CCONJ
ejpam-4021	503	21	only	only	ADV
ejpam-4021	503	22	if	if	SCONJ
ejpam-4021	503	23	some	some	DET
ejpam-4021	503	24	singleton	singleton	NOUN
ejpam-4021	503	25	{	{	PUNCT
ejpam-4021	503	26	a	a	NOUN
ejpam-4021	503	27	}	}	PUNCT
ejpam-4021	503	28	⊆	⊆	NUM
ejpam-4021	503	29	g	g	NOUN
ejpam-4021	503	30	is	be	AUX
ejpam-4021	503	31	closed	closed	ADJ
ejpam-4021	503	32	.	.	PUNCT
ejpam-4021	504	1	in	in	ADP
ejpam-4021	504	2	particular	particular	ADJ
ejpam-4021	504	3	{	{	PUNCT
ejpam-4021	504	4	e	e	NOUN
ejpam-4021	504	5	}	}	PUNCT
ejpam-4021	504	6	is	be	AUX
ejpam-4021	504	7	a	a	DET
ejpam-4021	504	8	closed	closed	ADJ
ejpam-4021	504	9	subgroup	subgroup	NOUN
ejpam-4021	504	10	of	of	ADP
ejpam-4021	504	11	g.	g.	PROPN
ejpam-4021	504	12	proof	proof	PROPN
ejpam-4021	504	13	.	.	PUNCT
ejpam-4021	505	1	let	let	VERB
ejpam-4021	505	2	{	{	PUNCT
ejpam-4021	505	3	a	a	NOUN
ejpam-4021	505	4	}	}	PUNCT
ejpam-4021	505	5	⊆	⊆	NUM
ejpam-4021	505	6	g	g	NOUN
ejpam-4021	505	7	be	be	AUX
ejpam-4021	505	8	closed	close	VERB
ejpam-4021	505	9	subset	subset	VERB
ejpam-4021	505	10	ofg	ofg	PROPN
ejpam-4021	505	11	.	.	PUNCT
ejpam-4021	506	1	then	then	ADV
ejpam-4021	506	2	since	since	SCONJ
ejpam-4021	506	3	the	the	DET
ejpam-4021	506	4	mapping	mapping	NOUN
ejpam-4021	506	5	ϕ	ϕ	NOUN
ejpam-4021	506	6	:	:	PUNCT
ejpam-4021	506	7	(	(	PUNCT
ejpam-4021	506	8	g×g,∆×∆)→	g×g,∆×∆)→	PROPN
ejpam-4021	506	9	(	(	PUNCT
ejpam-4021	506	10	g,∆	g,∆	PROPN
ejpam-4021	506	11	)	)	PUNCT
ejpam-4021	506	12	,	,	PUNCT
ejpam-4021	506	13	(	(	PUNCT
ejpam-4021	506	14	g	g	NOUN
ejpam-4021	506	15	,	,	PUNCT
ejpam-4021	506	16	h	h	NOUN
ejpam-4021	506	17	)	)	PUNCT
ejpam-4021	506	18	7−→	7−→	NOUN
ejpam-4021	506	19	g−1	g−1	PROPN
ejpam-4021	506	20	ha	ha	X
ejpam-4021	506	21	is	be	AUX
ejpam-4021	506	22	continuous	continuous	ADJ
ejpam-4021	506	23	,	,	PUNCT
ejpam-4021	506	24	we	we	PRON
ejpam-4021	506	25	have	have	VERB
ejpam-4021	506	26	ϕ−1({a	ϕ−1({a	PRON
ejpam-4021	506	27	}	}	PUNCT
ejpam-4021	506	28	)	)	PUNCT
ejpam-4021	507	1	=	=	PRON
ejpam-4021	507	2	{	{	PUNCT
ejpam-4021	507	3	(	(	PUNCT
ejpam-4021	507	4	g	g	NOUN
ejpam-4021	507	5	,	,	PUNCT
ejpam-4021	507	6	g	g	NOUN
ejpam-4021	507	7	)	)	PUNCT
ejpam-4021	507	8	:	:	PUNCT
ejpam-4021	507	9	g	g	PROPN
ejpam-4021	507	10	∈	∈	PROPN
ejpam-4021	507	11	g	g	PROPN
ejpam-4021	507	12	}	}	PUNCT
ejpam-4021	507	13	⊆	⊆	NUM
ejpam-4021	507	14	g×g	g×g	PROPN
ejpam-4021	507	15	,	,	PUNCT
ejpam-4021	507	16	the	the	DET
ejpam-4021	507	17	diagonal	diagonal	ADJ
ejpam-4021	507	18	which	which	PRON
ejpam-4021	507	19	in	in	ADP
ejpam-4021	507	20	view	view	NOUN
ejpam-4021	507	21	of	of	ADP
ejpam-4021	507	22	the	the	DET
ejpam-4021	507	23	corollary	corollary	NOUN
ejpam-4021	507	24	6.2.1.2	6.2.1.2	NUM
ejpam-4021	508	1	[	[	SYM
ejpam-4021	508	2	18	18	NUM
ejpam-4021	508	3	]	]	PUNCT
ejpam-4021	508	4	,	,	PUNCT
ejpam-4021	508	5	is	be	AUX
ejpam-4021	508	6	a	a	DET
ejpam-4021	508	7	closed	closed	ADJ
ejpam-4021	508	8	subset	subset	NOUN
ejpam-4021	508	9	of	of	ADP
ejpam-4021	508	10	g×g	g×g	PROPN
ejpam-4021	508	11	with	with	ADP
ejpam-4021	508	12	respect	respect	NOUN
ejpam-4021	508	13	to	to	ADP
ejpam-4021	508	14	the	the	DET
ejpam-4021	508	15	product	product	NOUN
ejpam-4021	508	16	stratified	stratify	VERB
ejpam-4021	508	17	l	l	NOUN
ejpam-4021	508	18	-	-	NOUN
ejpam-4021	508	19	topology	topology	NOUN
ejpam-4021	508	20	∆×∆	∆×∆	NOUN
ejpam-4021	508	21	implying	imply	VERB
ejpam-4021	508	22	that	that	SCONJ
ejpam-4021	508	23	(	(	PUNCT
ejpam-4021	508	24	g	g	NOUN
ejpam-4021	508	25	,	,	PUNCT
ejpam-4021	508	26	·	·	PUNCT
ejpam-4021	508	27	,	,	PUNCT
ejpam-4021	508	28	∆	∆	X
ejpam-4021	508	29	)	)	PUNCT
ejpam-4021	508	30	is	be	AUX
ejpam-4021	508	31	hausdorff	hausdorff	NOUN
ejpam-4021	508	32	-	-	PUNCT
ejpam-4021	508	33	separated	separate	VERB
ejpam-4021	508	34	.	.	PUNCT
ejpam-4021	509	1	conversely	conversely	ADV
ejpam-4021	509	2	,	,	PUNCT
ejpam-4021	509	3	let	let	VERB
ejpam-4021	509	4	x	x	PRON
ejpam-4021	509	5	6∈	6∈	PROPN
ejpam-4021	509	6	{	{	PUNCT
ejpam-4021	509	7	a	a	X
ejpam-4021	509	8	}	}	PUNCT
ejpam-4021	509	9	.	.	PUNCT
ejpam-4021	510	1	then	then	ADV
ejpam-4021	510	2	x	x	X
ejpam-4021	510	3	6=	6=	ADP
ejpam-4021	510	4	a	a	DET
ejpam-4021	510	5	∈	∈	NOUN
ejpam-4021	510	6	x	x	PUNCT
ejpam-4021	510	7	yields	yield	NOUN
ejpam-4021	510	8	that	that	SCONJ
ejpam-4021	510	9	there	there	PRON
ejpam-4021	510	10	are	be	VERB
ejpam-4021	510	11	ν1	ν1	NOUN
ejpam-4021	510	12	,	,	PUNCT
ejpam-4021	510	13	ν2	ν2	NOUN
ejpam-4021	510	14	∈	∈	NOUN
ejpam-4021	510	15	∆	∆	X
ejpam-4021	510	16	such	such	ADJ
ejpam-4021	510	17	that	that	SCONJ
ejpam-4021	510	18	ν1	ν1	NOUN
ejpam-4021	510	19	∗	∗	NOUN
ejpam-4021	510	20	ν2	ν2	NOUN
ejpam-4021	510	21	≤	≤	NOUN
ejpam-4021	510	22	>	>	PUNCT
ejpam-4021	510	23	x∩{a}c	x∩{a}c	PROPN
ejpam-4021	510	24	and	and	CCONJ
ejpam-4021	510	25	nx(ν1	nx(ν1	NOUN
ejpam-4021	510	26	)	)	PUNCT
ejpam-4021	510	27	∗na(ν2	∗na(ν2	PROPN
ejpam-4021	510	28	)	)	PUNCT
ejpam-4021	510	29	6=	6=	ADP
ejpam-4021	511	1	⊥	⊥	NOUN
ejpam-4021	511	2	,	,	PUNCT
ejpam-4021	511	3	which	which	PRON
ejpam-4021	511	4	implies	imply	VERB
ejpam-4021	511	5	that	that	SCONJ
ejpam-4021	511	6	x	x	SYM
ejpam-4021	511	7	6∈	6∈	NOUN
ejpam-4021	511	8	{	{	PUNCT
ejpam-4021	511	9	a	a	X
ejpam-4021	511	10	}	}	PUNCT
ejpam-4021	511	11	.	.	PUNCT
ejpam-4021	512	1	lemma	lemma	PROPN
ejpam-4021	512	2	11	11	NUM
ejpam-4021	512	3	.	.	PUNCT
ejpam-4021	513	1	if	if	SCONJ
ejpam-4021	513	2	(	(	PUNCT
ejpam-4021	513	3	g	g	NOUN
ejpam-4021	513	4	,	,	PUNCT
ejpam-4021	513	5	·	·	PUNCT
ejpam-4021	513	6	,	,	PUNCT
ejpam-4021	513	7	∆n	∆n	PROPN
ejpam-4021	513	8	)	)	PUNCT
ejpam-4021	513	9	is	be	AUX
ejpam-4021	513	10	a	a	DET
ejpam-4021	513	11	hausdorff	hausdorff	NOUN
ejpam-4021	513	12	-	-	PUNCT
ejpam-4021	513	13	separated	separate	VERB
ejpam-4021	513	14	stratified	stratified	ADJ
ejpam-4021	513	15	l	l	NOUN
ejpam-4021	513	16	-	-	PUNCT
ejpam-4021	513	17	valued	value	VERB
ejpam-4021	513	18	topological	topological	ADJ
ejpam-4021	513	19	group	group	NOUN
ejpam-4021	513	20	,	,	PUNCT
ejpam-4021	513	21	and	and	CCONJ
ejpam-4021	513	22	a	a	PRON
ejpam-4021	513	23	be	be	AUX
ejpam-4021	513	24	a	a	DET
ejpam-4021	513	25	closed	closed	ADJ
ejpam-4021	513	26	subgroup	subgroup	NOUN
ejpam-4021	513	27	of	of	ADP
ejpam-4021	513	28	g	g	PROPN
ejpam-4021	513	29	,	,	PUNCT
ejpam-4021	513	30	then	then	ADV
ejpam-4021	513	31	the	the	DET
ejpam-4021	513	32	normalizer	normalizer	NOUN
ejpam-4021	513	33	of	of	ADP
ejpam-4021	513	34	a	a	PRON
ejpam-4021	513	35	in	in	ADP
ejpam-4021	513	36	g	g	NOUN
ejpam-4021	513	37	:	:	PUNCT
ejpam-4021	513	38	ng(a	ng(a	X
ejpam-4021	513	39	)	)	PUNCT
ejpam-4021	513	40	=	=	PRON
ejpam-4021	513	41	{	{	PUNCT
ejpam-4021	513	42	g	g	PROPN
ejpam-4021	513	43	∈	∈	PROPN
ejpam-4021	513	44	g	g	PROPN
ejpam-4021	513	45	:	:	PUNCT
ejpam-4021	513	46	γa(a	γa(a	PUNCT
ejpam-4021	513	47	)	)	PUNCT
ejpam-4021	514	1	=	=	SYM
ejpam-4021	514	2	a	a	PRON
ejpam-4021	514	3	}	}	PUNCT
ejpam-4021	514	4	is	be	AUX
ejpam-4021	514	5	a	a	DET
ejpam-4021	514	6	closed	closed	ADJ
ejpam-4021	514	7	subgroup	subgroup	NOUN
ejpam-4021	514	8	of	of	ADP
ejpam-4021	514	9	g	g	PROPN
ejpam-4021	514	10	,	,	PUNCT
ejpam-4021	515	1	where	where	SCONJ
ejpam-4021	515	2	γa	γa	NOUN
ejpam-4021	515	3	:	:	PUNCT
ejpam-4021	515	4	g	g	PROPN
ejpam-4021	515	5	−→	−→	NOUN
ejpam-4021	515	6	g	g	PROPN
ejpam-4021	515	7	defined	define	VERB
ejpam-4021	515	8	by	by	ADP
ejpam-4021	515	9	γa(g	γa(g	NOUN
ejpam-4021	515	10	)	)	PUNCT
ejpam-4021	515	11	=	=	SYM
ejpam-4021	516	1	ag−1a	ag−1a	PROPN
ejpam-4021	516	2	the	the	DET
ejpam-4021	516	3	conjugation	conjugation	NOUN
ejpam-4021	516	4	map	map	NOUN
ejpam-4021	516	5	.	.	PUNCT
ejpam-4021	517	1	proof	proof	NOUN
ejpam-4021	517	2	.	.	PUNCT
ejpam-4021	518	1	if	if	SCONJ
ejpam-4021	518	2	a	a	DET
ejpam-4021	518	3	∈	∈	PROPN
ejpam-4021	518	4	a	a	PRON
ejpam-4021	518	5	,	,	PUNCT
ejpam-4021	518	6	take	take	VERB
ejpam-4021	518	7	ca(g	ca(g	NOUN
ejpam-4021	518	8	)	)	PUNCT
ejpam-4021	518	9	=	=	SYM
ejpam-4021	519	1	gag−1	gag−1	PROPN
ejpam-4021	519	2	.	.	PUNCT
ejpam-4021	520	1	then	then	ADV
ejpam-4021	520	2	the	the	DET
ejpam-4021	520	3	mapping	mapping	NOUN
ejpam-4021	520	4	ca	can	AUX
ejpam-4021	520	5	:	:	PUNCT
ejpam-4021	520	6	g	g	ADP
ejpam-4021	520	7	−→	−→	NOUN
ejpam-4021	520	8	g	g	PROPN
ejpam-4021	520	9	is	be	AUX
ejpam-4021	520	10	continuous	continuous	ADJ
ejpam-4021	520	11	and	and	CCONJ
ejpam-4021	520	12	hence	hence	ADV
ejpam-4021	520	13	the	the	DET
ejpam-4021	520	14	inverse	inverse	ADJ
ejpam-4021	520	15	image	image	NOUN
ejpam-4021	520	16	of	of	ADP
ejpam-4021	520	17	the	the	DET
ejpam-4021	520	18	closed	closed	ADJ
ejpam-4021	520	19	set	set	NOUN
ejpam-4021	520	20	a	a	PRON
ejpam-4021	520	21	:	:	PUNCT
ejpam-4021	520	22	c−1	c−1	PROPN
ejpam-4021	520	23	a	a	DET
ejpam-4021	520	24	(	(	PUNCT
ejpam-4021	520	25	a	a	NOUN
ejpam-4021	520	26	)	)	PUNCT
ejpam-4021	520	27	=	=	SYM
ejpam-4021	520	28	{	{	PUNCT
ejpam-4021	520	29	g	g	PROPN
ejpam-4021	520	30	∈	∈	PROPN
ejpam-4021	520	31	g	g	NOUN
ejpam-4021	520	32	:	:	PUNCT
ejpam-4021	520	33	gag−1	gag−1	PROPN
ejpam-4021	520	34	∈	∈	PROPN
ejpam-4021	520	35	a	a	PRON
ejpam-4021	520	36	}	}	PUNCT
ejpam-4021	520	37	is	be	AUX
ejpam-4021	520	38	closed	closed	ADJ
ejpam-4021	520	39	.	.	PUNCT
ejpam-4021	521	1	thus	thus	ADV
ejpam-4021	521	2	,	,	PUNCT
ejpam-4021	521	3	we	we	PRON
ejpam-4021	521	4	have	have	VERB
ejpam-4021	521	5	b	b	NOUN
ejpam-4021	521	6	:	:	PUNCT
ejpam-4021	521	7	=	=	SYM
ejpam-4021	521	8	∧	∧	NOUN
ejpam-4021	521	9	a∈a	a∈a	ADJ
ejpam-4021	521	10	c	c	NOUN
ejpam-4021	521	11	−1	−1	NOUN
ejpam-4021	521	12	a	a	DET
ejpam-4021	521	13	(	(	PUNCT
ejpam-4021	521	14	a	a	NOUN
ejpam-4021	521	15	)	)	PUNCT
ejpam-4021	521	16	=	=	SYM
ejpam-4021	521	17	{	{	PUNCT
ejpam-4021	521	18	g	g	PROPN
ejpam-4021	521	19	∈	∈	PROPN
ejpam-4021	521	20	g	g	PROPN
ejpam-4021	521	21	:	:	PUNCT
ejpam-4021	521	22	γa(a	γa(a	PUNCT
ejpam-4021	521	23	)	)	PUNCT
ejpam-4021	521	24	⊆	⊆	X
ejpam-4021	521	25	a	a	PRON
ejpam-4021	521	26	}	}	PUNCT
ejpam-4021	521	27	is	be	AUX
ejpam-4021	521	28	a	a	DET
ejpam-4021	521	29	closed	closed	ADJ
ejpam-4021	521	30	subset	subset	NOUN
ejpam-4021	521	31	of	of	ADP
ejpam-4021	521	32	g.	g.	PROPN
ejpam-4021	521	33	since	since	SCONJ
ejpam-4021	521	34	the	the	DET
ejpam-4021	521	35	inversion	inversion	NOUN
ejpam-4021	521	36	mapping	map	VERB
ejpam-4021	521	37			NOUN
ejpam-4021	521	38	:	:	PUNCT
ejpam-4021	521	39	g	g	ADP
ejpam-4021	521	40	−→	−→	NOUN
ejpam-4021	521	41	g	g	NOUN
ejpam-4021	521	42	,	,	PUNCT
ejpam-4021	521	43	g	g	PROPN
ejpam-4021	521	44	7−→	7−→	PROPN
ejpam-4021	521	45	g−1	g−1	PROPN
ejpam-4021	521	46	is	be	AUX
ejpam-4021	521	47	a	a	DET
ejpam-4021	521	48	homeomorphism	homeomorphism	NOUN
ejpam-4021	521	49	,	,	PUNCT
ejpam-4021	521	50	a−1	a−1	PROPN
ejpam-4021	521	51	is	be	AUX
ejpam-4021	521	52	closed	close	VERB
ejpam-4021	521	53	,	,	PUNCT
ejpam-4021	521	54	since	since	SCONJ
ejpam-4021	521	55	a	a	PRON
ejpam-4021	521	56	is	be	AUX
ejpam-4021	521	57	closed	closed	ADJ
ejpam-4021	521	58	,	,	PUNCT
ejpam-4021	521	59	and	and	CCONJ
ejpam-4021	521	60	hence	hence	ADV
ejpam-4021	521	61	ng(a	ng(a	NUM
ejpam-4021	521	62	)	)	PUNCT
ejpam-4021	522	1	=	=	SYM
ejpam-4021	523	1	b	b	X
ejpam-4021	523	2	∩a−1	∩a−1	PROPN
ejpam-4021	523	3	is	be	AUX
ejpam-4021	523	4	closed	closed	ADJ
ejpam-4021	523	5	.	.	PUNCT
ejpam-4021	524	1	lemma	lemma	PROPN
ejpam-4021	524	2	12	12	NUM
ejpam-4021	524	3	.	.	PUNCT
ejpam-4021	525	1	let	let	AUX
ejpam-4021	525	2	(	(	PUNCT
ejpam-4021	525	3	g	g	NOUN
ejpam-4021	525	4	,	,	PUNCT
ejpam-4021	525	5	·	·	PUNCT
ejpam-4021	525	6	,	,	PUNCT
ejpam-4021	525	7	∆	∆	X
ejpam-4021	525	8	)	)	PUNCT
ejpam-4021	525	9	be	be	AUX
ejpam-4021	525	10	a	a	DET
ejpam-4021	525	11	stratified	stratified	ADJ
ejpam-4021	525	12	l	l	NOUN
ejpam-4021	525	13	-	-	PUNCT
ejpam-4021	525	14	valued	value	VERB
ejpam-4021	525	15	topological	topological	ADJ
ejpam-4021	525	16	group	group	NOUN
ejpam-4021	525	17	,	,	PUNCT
ejpam-4021	525	18	n	n	X
ejpam-4021	525	19	be	be	AUX
ejpam-4021	525	20	a	a	DET
ejpam-4021	525	21	corresponding	corresponding	ADJ
ejpam-4021	525	22	stratified	stratified	ADJ
ejpam-4021	525	23	l	l	ADV
ejpam-4021	525	24	-	-	PUNCT
ejpam-4021	525	25	valued	value	VERB
ejpam-4021	525	26	neighborhood	neighborhood	NOUN
ejpam-4021	525	27	system	system	NOUN
ejpam-4021	525	28	on	on	ADP
ejpam-4021	525	29	g	g	PROPN
ejpam-4021	525	30	and	and	CCONJ
ejpam-4021	525	31	a	a	PRON
ejpam-4021	525	32	is	be	AUX
ejpam-4021	525	33	a	a	DET
ejpam-4021	525	34	subset	subset	NOUN
ejpam-4021	525	35	of	of	ADP
ejpam-4021	525	36	g.	g.	PROPN
ejpam-4021	525	37	then	then	ADV
ejpam-4021	525	38	the	the	DET
ejpam-4021	525	39	centralizer	centralizer	NOUN
ejpam-4021	525	40	zg(a	zg(a	PRON
ejpam-4021	525	41	)	)	PUNCT
ejpam-4021	525	42	=	=	PRON
ejpam-4021	525	43	{	{	PUNCT
ejpam-4021	525	44	g	g	PROPN
ejpam-4021	525	45	∈	∈	PROPN
ejpam-4021	525	46	g	g	NOUN
ejpam-4021	526	1	:	:	PUNCT
ejpam-4021	527	1	[	[	X
ejpam-4021	527	2	g	g	X
ejpam-4021	527	3	,	,	PUNCT
ejpam-4021	527	4	a	a	PRON
ejpam-4021	527	5	]	]	X
ejpam-4021	527	6	=	=	SYM
ejpam-4021	527	7	e	e	X
ejpam-4021	527	8	∀a	∀a	X
ejpam-4021	527	9	∈	∈	PROPN
ejpam-4021	527	10	a	a	PRON
ejpam-4021	527	11	}	}	PUNCT
ejpam-4021	527	12	is	be	AUX
ejpam-4021	527	13	closed	close	VERB
ejpam-4021	527	14	with	with	ADP
ejpam-4021	527	15	respect	respect	NOUN
ejpam-4021	527	16	to	to	ADP
ejpam-4021	527	17	∆.	∆.	PROPN
ejpam-4021	527	18	in	in	ADP
ejpam-4021	527	19	particular	particular	ADJ
ejpam-4021	527	20	,	,	PUNCT
ejpam-4021	527	21	the	the	DET
ejpam-4021	527	22	center	center	NOUN
ejpam-4021	527	23	of	of	ADP
ejpam-4021	527	24	g	g	PROPN
ejpam-4021	527	25	is	be	AUX
ejpam-4021	527	26	closed	close	VERB
ejpam-4021	527	27	subgroup	subgroup	NOUN
ejpam-4021	527	28	.	.	PUNCT
ejpam-4021	528	1	references	reference	NOUN
ejpam-4021	528	2	966	966	NUM
ejpam-4021	528	3	proof	proof	NOUN
ejpam-4021	528	4	.	.	PUNCT
ejpam-4021	529	1	if	if	SCONJ
ejpam-4021	529	2	a	a	DET
ejpam-4021	529	3	∈	∈	PROPN
ejpam-4021	529	4	a	a	X
ejpam-4021	529	5	,	,	PUNCT
ejpam-4021	529	6	then	then	ADV
ejpam-4021	529	7	the	the	DET
ejpam-4021	529	8	mapping	mapping	NOUN
ejpam-4021	529	9	ϕ	ϕ	NOUN
ejpam-4021	529	10	:	:	PUNCT
ejpam-4021	529	11	g	g	ADP
ejpam-4021	529	12	−→	−→	NOUN
ejpam-4021	529	13	g	g	NOUN
ejpam-4021	529	14	,	,	PUNCT
ejpam-4021	529	15	g	g	PROPN
ejpam-4021	529	16	7−→	7−→	PROPN
ejpam-4021	530	1	[	[	X
ejpam-4021	530	2	g	g	NOUN
ejpam-4021	530	3	,	,	PUNCT
ejpam-4021	530	4	a	a	PRON
ejpam-4021	530	5	]	]	X
ejpam-4021	530	6	=	=	SYM
ejpam-4021	530	7	gag−1a−1	gag−1a−1	NOUN
ejpam-4021	530	8	is	be	AUX
ejpam-4021	530	9	continuous	continuous	ADJ
ejpam-4021	530	10	,	,	PUNCT
ejpam-4021	530	11	where	where	SCONJ
ejpam-4021	530	12	the	the	DET
ejpam-4021	530	13	element	element	NOUN
ejpam-4021	530	14	of	of	ADP
ejpam-4021	530	15	the	the	DET
ejpam-4021	530	16	type	type	NOUN
ejpam-4021	530	17	gag−1a−1	gag−1a−1	NOUN
ejpam-4021	530	18	is	be	AUX
ejpam-4021	530	19	called	call	VERB
ejpam-4021	530	20	commutator	commutator	NOUN
ejpam-4021	530	21	of	of	ADP
ejpam-4021	530	22	the	the	DET
ejpam-4021	530	23	group	group	NOUN
ejpam-4021	530	24	g.	g.	PROPN
ejpam-4021	530	25	now	now	ADV
ejpam-4021	530	26	since	since	SCONJ
ejpam-4021	530	27	{	{	PUNCT
ejpam-4021	530	28	e	e	NOUN
ejpam-4021	530	29	}	}	PUNCT
ejpam-4021	530	30	is	be	AUX
ejpam-4021	530	31	closed	close	VERB
ejpam-4021	530	32	subset	subset	NOUN
ejpam-4021	530	33	of	of	ADP
ejpam-4021	530	34	g	g	NOUN
ejpam-4021	530	35	,	,	PUNCT
ejpam-4021	530	36	and	and	CCONJ
ejpam-4021	530	37	since	since	SCONJ
ejpam-4021	530	38	the	the	DET
ejpam-4021	530	39	inverse	inverse	NOUN
ejpam-4021	530	40	image	image	NOUN
ejpam-4021	530	41	of	of	ADP
ejpam-4021	530	42	closed	closed	ADJ
ejpam-4021	530	43	subsets	subset	NOUN
ejpam-4021	530	44	under	under	ADP
ejpam-4021	530	45	continuous	continuous	ADJ
ejpam-4021	530	46	mapping	mapping	NOUN
ejpam-4021	530	47	are	be	AUX
ejpam-4021	530	48	again	again	ADV
ejpam-4021	530	49	closed	close	VERB
ejpam-4021	530	50	,	,	PUNCT
ejpam-4021	530	51	in	in	ADP
ejpam-4021	530	52	view	view	NOUN
ejpam-4021	530	53	of	of	ADP
ejpam-4021	530	54	the	the	DET
ejpam-4021	530	55	corollary	corollary	NOUN
ejpam-4021	530	56	6.2.1.2	6.2.1.2	NUM
ejpam-4021	531	1	[	[	X
ejpam-4021	531	2	18	18	NUM
ejpam-4021	531	3	]	]	PUNCT
ejpam-4021	531	4	,	,	PUNCT
ejpam-4021	531	5	zg(a	zg(a	X
ejpam-4021	531	6	)	)	PUNCT
ejpam-4021	531	7	=	=	PRON
ejpam-4021	531	8	{	{	PUNCT
ejpam-4021	531	9	g	g	PROPN
ejpam-4021	531	10	∈	∈	PROPN
ejpam-4021	531	11	g	g	NOUN
ejpam-4021	531	12	:	:	PUNCT
ejpam-4021	532	1	[	[	X
ejpam-4021	532	2	g	g	X
ejpam-4021	532	3	,	,	PUNCT
ejpam-4021	532	4	a	a	PRON
ejpam-4021	532	5	]	]	X
ejpam-4021	532	6	=	=	SYM
ejpam-4021	532	7	e	e	X
ejpam-4021	532	8	}	}	PUNCT
ejpam-4021	532	9	is	be	AUX
ejpam-4021	532	10	closed	close	VERB
ejpam-4021	532	11	,	,	PUNCT
ejpam-4021	532	12	and	and	CCONJ
ejpam-4021	532	13	as	as	ADP
ejpam-4021	532	14	the	the	DET
ejpam-4021	532	15	zg(a	zg(a	NOUN
ejpam-4021	532	16	)	)	PUNCT
ejpam-4021	533	1	=	=	PUNCT
ejpam-4021	533	2	∧	∧	NOUN
ejpam-4021	533	3	a∈a	a∈a	ADJ
ejpam-4021	533	4	zg(a	zg(a	NOUN
ejpam-4021	533	5	)	)	PUNCT
ejpam-4021	533	6	is	be	AUX
ejpam-4021	533	7	closed	close	VERB
ejpam-4021	533	8	,	,	PUNCT
ejpam-4021	533	9	hence	hence	ADV
ejpam-4021	533	10	the	the	DET
ejpam-4021	533	11	result	result	NOUN
ejpam-4021	533	12	follows	follow	VERB
ejpam-4021	533	13	.	.	PUNCT
ejpam-4021	534	1	6	6	X
ejpam-4021	534	2	.	.	X
ejpam-4021	534	3	conclusion	conclusion	NOUN
ejpam-4021	534	4	in	in	ADP
ejpam-4021	534	5	this	this	DET
ejpam-4021	534	6	article	article	NOUN
ejpam-4021	534	7	,	,	PUNCT
ejpam-4021	534	8	as	as	ADP
ejpam-4021	534	9	a	a	DET
ejpam-4021	534	10	continuation	continuation	NOUN
ejpam-4021	534	11	of	of	ADP
ejpam-4021	534	12	our	our	PRON
ejpam-4021	534	13	previous	previous	ADJ
ejpam-4021	534	14	work	work	NOUN
ejpam-4021	534	15	on	on	ADP
ejpam-4021	534	16	l	l	ADV
ejpam-4021	534	17	-	-	PUNCT
ejpam-4021	534	18	valued	value	VERB
ejpam-4021	534	19	topological	topological	ADJ
ejpam-4021	534	20	groups	group	NOUN
ejpam-4021	534	21	,	,	PUNCT
ejpam-4021	534	22	where	where	SCONJ
ejpam-4021	534	23	the	the	DET
ejpam-4021	534	24	underlying	underlie	VERB
ejpam-4021	534	25	lattice	lattice	NOUN
ejpam-4021	534	26	l	l	NOUN
ejpam-4021	534	27	was	be	AUX
ejpam-4021	534	28	an	an	DET
ejpam-4021	534	29	enriched	enriched	ADJ
ejpam-4021	534	30	cl	cl	NOUN
ejpam-4021	534	31	-	-	ADJ
ejpam-4021	534	32	premonoid	premonoid	ADJ
ejpam-4021	534	33	,	,	PUNCT
ejpam-4021	534	34	we	we	PRON
ejpam-4021	534	35	have	have	AUX
ejpam-4021	534	36	presented	present	VERB
ejpam-4021	534	37	two	two	NUM
ejpam-4021	534	38	types	type	NOUN
ejpam-4021	534	39	of	of	ADP
ejpam-4021	534	40	results	result	NOUN
ejpam-4021	534	41	,	,	PUNCT
ejpam-4021	534	42	one	one	PRON
ejpam-4021	534	43	is	be	AUX
ejpam-4021	534	44	about	about	ADP
ejpam-4021	534	45	the	the	DET
ejpam-4021	534	46	relationship	relationship	NOUN
ejpam-4021	534	47	between	between	ADP
ejpam-4021	534	48	l	l	NOUN
ejpam-4021	534	49	-	-	PUNCT
ejpam-4021	534	50	valued	value	VERB
ejpam-4021	534	51	topological	topological	ADJ
ejpam-4021	534	52	groups	group	NOUN
ejpam-4021	534	53	and	and	CCONJ
ejpam-4021	534	54	their	their	PRON
ejpam-4021	534	55	corresponding	correspond	VERB
ejpam-4021	534	56	kent	kent	PROPN
ejpam-4021	534	57	convergence	convergence	NOUN
ejpam-4021	534	58	groups	group	NOUN
ejpam-4021	534	59	and	and	CCONJ
ejpam-4021	534	60	conversely	conversely	ADV
ejpam-4021	534	61	;	;	PUNCT
ejpam-4021	534	62	the	the	DET
ejpam-4021	534	63	other	other	ADJ
ejpam-4021	534	64	is	be	AUX
ejpam-4021	534	65	about	about	ADP
ejpam-4021	534	66	l	l	NOUN
ejpam-4021	534	67	-	-	PUNCT
ejpam-4021	534	68	valued	value	VERB
ejpam-4021	534	69	closure	closure	NOUN
ejpam-4021	534	70	of	of	ADP
ejpam-4021	534	71	l	l	NOUN
ejpam-4021	534	72	-	-	PUNCT
ejpam-4021	534	73	valued	value	VERB
ejpam-4021	534	74	subgroup	subgroup	NOUN
ejpam-4021	534	75	of	of	ADP
ejpam-4021	534	76	a	a	DET
ejpam-4021	534	77	group	group	NOUN
ejpam-4021	534	78	.	.	PUNCT
ejpam-4021	535	1	although	although	SCONJ
ejpam-4021	535	2	,	,	PUNCT
ejpam-4021	535	3	it	it	PRON
ejpam-4021	535	4	is	be	AUX
ejpam-4021	535	5	an	an	DET
ejpam-4021	535	6	well	well	ADV
ejpam-4021	535	7	-	-	PUNCT
ejpam-4021	535	8	known	know	VERB
ejpam-4021	535	9	fact	fact	NOUN
ejpam-4021	535	10	that	that	SCONJ
ejpam-4021	535	11	there	there	PRON
ejpam-4021	535	12	is	be	VERB
ejpam-4021	535	13	a	a	DET
ejpam-4021	535	14	close	close	ADJ
ejpam-4021	535	15	connection	connection	NOUN
ejpam-4021	535	16	between	between	ADP
ejpam-4021	535	17	principal	principal	ADJ
ejpam-4021	535	18	limit	limit	NOUN
ejpam-4021	535	19	convergence	convergence	NOUN
ejpam-4021	535	20	spaces	space	NOUN
ejpam-4021	535	21	and	and	CCONJ
ejpam-4021	535	22	closure	closure	NOUN
ejpam-4021	535	23	spaces	space	NOUN
ejpam-4021	535	24	,	,	PUNCT
ejpam-4021	535	25	but	but	CCONJ
ejpam-4021	535	26	we	we	PRON
ejpam-4021	535	27	did	do	AUX
ejpam-4021	535	28	not	not	PART
ejpam-4021	535	29	touch	touch	VERB
ejpam-4021	535	30	upon	upon	SCONJ
ejpam-4021	535	31	this	this	DET
ejpam-4021	535	32	issue	issue	NOUN
ejpam-4021	535	33	here	here	ADV
ejpam-4021	535	34	even	even	ADV
ejpam-4021	535	35	for	for	ADP
ejpam-4021	535	36	l	l	NOUN
ejpam-4021	535	37	-	-	PUNCT
ejpam-4021	535	38	valued	value	VERB
ejpam-4021	535	39	generalization	generalization	NOUN
ejpam-4021	535	40	of	of	ADP
ejpam-4021	535	41	these	these	DET
ejpam-4021	535	42	structures	structure	NOUN
ejpam-4021	535	43	in	in	ADP
ejpam-4021	535	44	conjunction	conjunction	NOUN
ejpam-4021	535	45	with	with	ADP
ejpam-4021	535	46	group	group	NOUN
ejpam-4021	535	47	structures	structure	NOUN
ejpam-4021	535	48	,	,	PUNCT
ejpam-4021	535	49	that	that	ADV
ejpam-4021	535	50	is	is	ADV
ejpam-4021	535	51	,	,	PUNCT
ejpam-4021	535	52	to	to	PART
ejpam-4021	535	53	study	study	VERB
ejpam-4021	535	54	l	l	ADV
ejpam-4021	535	55	-	-	PUNCT
ejpam-4021	535	56	valued	value	VERB
ejpam-4021	535	57	principal	principal	ADJ
ejpam-4021	535	58	convergence	convergence	NOUN
ejpam-4021	535	59	spaces	space	NOUN
ejpam-4021	535	60	and	and	CCONJ
ejpam-4021	535	61	l	l	NOUN
ejpam-4021	535	62	-	-	PUNCT
ejpam-4021	535	63	valued	value	VERB
ejpam-4021	535	64	closure	closure	NOUN
ejpam-4021	535	65	spaces	space	NOUN
ejpam-4021	535	66	.	.	PUNCT
ejpam-4021	536	1	we	we	PRON
ejpam-4021	536	2	intend	intend	VERB
ejpam-4021	536	3	to	to	PART
ejpam-4021	536	4	look	look	VERB
ejpam-4021	536	5	into	into	ADP
ejpam-4021	536	6	this	this	DET
ejpam-4021	536	7	issue	issue	NOUN
ejpam-4021	536	8	in	in	ADP
ejpam-4021	536	9	a	a	DET
ejpam-4021	536	10	future	future	ADJ
ejpam-4021	536	11	paper	paper	NOUN
ejpam-4021	536	12	.	.	PUNCT
ejpam-4021	537	1	7	7	X
ejpam-4021	537	2	.	.	X
ejpam-4021	537	3	acknowledgements	acknowledgement	NOUN
ejpam-4021	537	4	we	we	PRON
ejpam-4021	537	5	are	be	AUX
ejpam-4021	537	6	sincerely	sincerely	ADV
ejpam-4021	537	7	grateful	grateful	ADJ
ejpam-4021	537	8	to	to	ADP
ejpam-4021	537	9	anonymous	anonymous	ADJ
ejpam-4021	537	10	referees	referee	NOUN
ejpam-4021	537	11	for	for	ADP
ejpam-4021	537	12	generously	generously	ADV
ejpam-4021	537	13	giving	give	VERB
ejpam-4021	537	14	their	their	PRON
ejpam-4021	537	15	time	time	NOUN
ejpam-4021	537	16	to	to	PART
ejpam-4021	537	17	read	read	VERB
ejpam-4021	537	18	our	our	PRON
ejpam-4021	537	19	earlier	early	ADJ
ejpam-4021	537	20	version	version	NOUN
ejpam-4021	537	21	of	of	ADP
ejpam-4021	537	22	this	this	DET
ejpam-4021	537	23	manuscript	manuscript	NOUN
ejpam-4021	537	24	and	and	CCONJ
ejpam-4021	537	25	providing	provide	VERB
ejpam-4021	537	26	various	various	ADJ
ejpam-4021	537	27	useful	useful	ADJ
ejpam-4021	537	28	suggestions	suggestion	NOUN
ejpam-4021	537	29	.	.	PUNCT
ejpam-4021	538	1	references	reference	NOUN
ejpam-4021	538	2	[	[	X
ejpam-4021	538	3	1	1	X
ejpam-4021	538	4	]	]	PUNCT
ejpam-4021	538	5	j.	j.	PROPN
ejpam-4021	538	6	adámek	adámek	PROPN
ejpam-4021	538	7	,	,	PUNCT
ejpam-4021	538	8	h.	h.	PROPN
ejpam-4021	538	9	herrlich	herrlich	PROPN
ejpam-4021	538	10	and	and	CCONJ
ejpam-4021	538	11	g.	g.	PROPN
ejpam-4021	538	12	e.	e.	PROPN
ejpam-4021	538	13	strecker	strecker	PROPN
ejpam-4021	538	14	.	.	PUNCT
ejpam-4021	539	1	abstract	abstract	ADJ
ejpam-4021	539	2	and	and	CCONJ
ejpam-4021	539	3	concrete	concrete	ADJ
ejpam-4021	539	4	categories	category	NOUN
ejpam-4021	539	5	.	.	PUNCT
ejpam-4021	540	1	j.	j.	PROPN
ejpam-4021	540	2	wiley	wiley	PROPN
ejpam-4021	540	3	&	&	CCONJ
ejpam-4021	540	4	sons	son	NOUN
ejpam-4021	540	5	,	,	PUNCT
ejpam-4021	540	6	new	new	PROPN
ejpam-4021	540	7	york	york	PROPN
ejpam-4021	540	8	,	,	PUNCT
ejpam-4021	540	9	1990	1990	NUM
ejpam-4021	540	10	.	.	PUNCT
ejpam-4021	541	1	[	[	X
ejpam-4021	541	2	2	2	X
ejpam-4021	541	3	]	]	PUNCT
ejpam-4021	541	4	t.	t.	NOUN
ejpam-4021	541	5	m.	m.	NOUN
ejpam-4021	541	6	g.	g.	PROPN
ejpam-4021	541	7	ahsanullah	ahsanullah	PROPN
ejpam-4021	541	8	.	.	PUNCT
ejpam-4021	542	1	on	on	ADP
ejpam-4021	542	2	fuzzy	fuzzy	ADJ
ejpam-4021	542	3	neighborhood	neighborhood	NOUN
ejpam-4021	542	4	groups	group	NOUN
ejpam-4021	542	5	.	.	PUNCT
ejpam-4021	543	1	j.	j.	PROPN
ejpam-4021	543	2	math	math	PROPN
ejpam-4021	543	3	.	.	PUNCT
ejpam-4021	544	1	anal	anal	PROPN
ejpam-4021	544	2	.	.	PUNCT
ejpam-4021	545	1	appl	appl	PROPN
ejpam-4021	545	2	.	.	PROPN
ejpam-4021	545	3	,	,	PUNCT
ejpam-4021	545	4	130	130	NUM
ejpam-4021	545	5	:	:	PUNCT
ejpam-4021	545	6	237–251	237–251	NUM
ejpam-4021	545	7	,	,	PUNCT
ejpam-4021	545	8	1988	1988	NUM
ejpam-4021	545	9	.	.	PUNCT
ejpam-4021	546	1	[	[	X
ejpam-4021	546	2	3	3	X
ejpam-4021	546	3	]	]	PUNCT
ejpam-4021	546	4	t.	t.	NOUN
ejpam-4021	546	5	m.	m.	NOUN
ejpam-4021	546	6	g.	g.	PROPN
ejpam-4021	546	7	ahsanullah	ahsanullah	PROPN
ejpam-4021	546	8	,	,	PUNCT
ejpam-4021	546	9	d.	d.	PROPN
ejpam-4021	546	10	gauld	gauld	AUX
ejpam-4021	546	11	,	,	PUNCT
ejpam-4021	546	12	j.	j.	PROPN
ejpam-4021	546	13	al	al	PROPN
ejpam-4021	546	14	-	-	PUNCT
ejpam-4021	546	15	mufarrij	mufarrij	PROPN
ejpam-4021	546	16	and	and	CCONJ
ejpam-4021	546	17	f.	f.	PROPN
ejpam-4021	546	18	al	al	PROPN
ejpam-4021	546	19	-	-	PUNCT
ejpam-4021	546	20	thukair	thukair	NOUN
ejpam-4021	546	21	.	.	PUNCT
ejpam-4021	547	1	enriched	enrich	VERB
ejpam-4021	547	2	latticevalued	latticevalue	VERB
ejpam-4021	547	3	topological	topological	ADJ
ejpam-4021	547	4	groups	group	NOUN
ejpam-4021	547	5	.	.	PUNCT
ejpam-4021	548	1	new	new	ADJ
ejpam-4021	548	2	math	math	NOUN
ejpam-4021	548	3	.	.	PUNCT
ejpam-4021	548	4	&	&	CCONJ
ejpam-4021	548	5	nat	nat	PROPN
ejpam-4021	548	6	.	.	PUNCT
ejpam-4021	549	1	comput	comput	NOUN
ejpam-4021	549	2	.	.	PUNCT
ejpam-4021	549	3	,	,	PUNCT
ejpam-4021	550	1	10(1	10(1	NUM
ejpam-4021	550	2	):	):	PUNCT
ejpam-4021	550	3	27–53	27–53	NUM
ejpam-4021	550	4	,	,	PUNCT
ejpam-4021	550	5	2014	2014	NUM
ejpam-4021	550	6	.	.	PUNCT
ejpam-4021	551	1	[	[	X
ejpam-4021	551	2	4	4	NUM
ejpam-4021	551	3	]	]	PUNCT
ejpam-4021	551	4	m.	m.	NOUN
ejpam-4021	551	5	baran	baran	NOUN
ejpam-4021	551	6	.	.	PUNCT
ejpam-4021	552	1	closure	closure	NOUN
ejpam-4021	552	2	operators	operator	NOUN
ejpam-4021	552	3	in	in	ADP
ejpam-4021	552	4	convergence	convergence	NOUN
ejpam-4021	552	5	spaces	space	NOUN
ejpam-4021	552	6	.	.	PUNCT
ejpam-4021	553	1	acta	acta	PROPN
ejpam-4021	553	2	math	math	PROPN
ejpam-4021	553	3	.	.	PUNCT
ejpam-4021	554	1	hungarica	hungarica	ADJ
ejpam-4021	554	2	,	,	PUNCT
ejpam-4021	554	3	87(1	87(1	PROPN
ejpam-4021	554	4	-	-	SYM
ejpam-4021	554	5	2	2	NUM
ejpam-4021	554	6	):	):	PUNCT
ejpam-4021	554	7	33–45	33–45	NUM
ejpam-4021	554	8	,	,	PUNCT
ejpam-4021	554	9	2000	2000	NUM
ejpam-4021	554	10	.	.	PUNCT
ejpam-4021	555	1	[	[	X
ejpam-4021	555	2	5	5	NUM
ejpam-4021	555	3	]	]	PUNCT
ejpam-4021	555	4	m.	m.	NOUN
ejpam-4021	555	5	baran	baran	NOUN
ejpam-4021	555	6	,	,	PUNCT
ejpam-4021	555	7	s.	s.	PROPN
ejpam-4021	555	8	kula	kula	PROPN
ejpam-4021	555	9	,	,	PUNCT
ejpam-4021	555	10	t.	t.	PROPN
ejpam-4021	555	11	m.	m.	NOUN
ejpam-4021	555	12	baran	baran	PROPN
ejpam-4021	555	13	,	,	PUNCT
ejpam-4021	555	14	m.	m.	NOUN
ejpam-4021	555	15	qasim	qasim	PROPN
ejpam-4021	555	16	.	.	PUNCT
ejpam-4021	556	1	closure	closure	NOUN
ejpam-4021	556	2	operators	operator	NOUN
ejpam-4021	556	3	in	in	ADP
ejpam-4021	556	4	semiuniform	semiuniform	NOUN
ejpam-4021	556	5	convergence	convergence	NOUN
ejpam-4021	556	6	spaces	space	NOUN
ejpam-4021	556	7	.	.	PUNCT
ejpam-4021	557	1	filomat	filomat	NOUN
ejpam-4021	557	2	,	,	PUNCT
ejpam-4021	557	3	30(1	30(1	NUM
ejpam-4021	557	4	):	):	PUNCT
ejpam-4021	557	5	131–140	131–140	NUM
ejpam-4021	557	6	,	,	PUNCT
ejpam-4021	557	7	2016	2016	NUM
ejpam-4021	557	8	.	.	PUNCT
ejpam-4021	558	1	[	[	X
ejpam-4021	558	2	6	6	NUM
ejpam-4021	558	3	]	]	PUNCT
ejpam-4021	558	4	m.	m.	NOUN
ejpam-4021	558	5	baran	baran	NOUN
ejpam-4021	558	6	.	.	PUNCT
ejpam-4021	559	1	compactness	compactness	NOUN
ejpam-4021	559	2	,	,	PUNCT
ejpam-4021	559	3	perfectness	perfectness	NOUN
ejpam-4021	559	4	,	,	PUNCT
ejpam-4021	559	5	separation	separation	NOUN
ejpam-4021	559	6	,	,	PUNCT
ejpam-4021	559	7	minimality	minimality	NOUN
ejpam-4021	559	8	and	and	CCONJ
ejpam-4021	559	9	closedness	closedness	ADJ
ejpam-4021	559	10	with	with	ADP
ejpam-4021	559	11	respect	respect	NOUN
ejpam-4021	559	12	to	to	ADP
ejpam-4021	559	13	closure	closure	NOUN
ejpam-4021	559	14	operators	operator	NOUN
ejpam-4021	559	15	.	.	PUNCT
ejpam-4021	560	1	appl	appl	PROPN
ejpam-4021	560	2	.	.	PROPN
ejpam-4021	560	3	categor	categor	PROPN
ejpam-4021	560	4	.	.	PUNCT
ejpam-4021	561	1	struc	struc	PROPN
ejpam-4021	561	2	.	.	PUNCT
ejpam-4021	561	3	,	,	PUNCT
ejpam-4021	561	4	10	10	NUM
ejpam-4021	561	5	:	:	PUNCT
ejpam-4021	561	6	403–415	403–415	NUM
ejpam-4021	561	7	,	,	PUNCT
ejpam-4021	561	8	2002	2002	NUM
ejpam-4021	561	9	.	.	PUNCT
ejpam-4021	562	1	[	[	X
ejpam-4021	562	2	7	7	X
ejpam-4021	562	3	]	]	PUNCT
ejpam-4021	562	4	m.	m.	NOUN
ejpam-4021	562	5	baran	baran	NOUN
ejpam-4021	562	6	.	.	PUNCT
ejpam-4021	563	1	the	the	DET
ejpam-4021	563	2	notion	notion	NOUN
ejpam-4021	563	3	of	of	ADP
ejpam-4021	563	4	closedness	closedness	NOUN
ejpam-4021	563	5	in	in	ADP
ejpam-4021	563	6	topological	topological	ADJ
ejpam-4021	563	7	categories	category	NOUN
ejpam-4021	563	8	.	.	PUNCT
ejpam-4021	564	1	comment	comment	NOUN
ejpam-4021	564	2	.	.	PUNCT
ejpam-4021	565	1	math	math	NOUN
ejpam-4021	565	2	.	.	PUNCT
ejpam-4021	566	1	univ	univ	PROPN
ejpam-4021	566	2	.	.	PUNCT
ejpam-4021	566	3	carol	carol	PROPN
ejpam-4021	566	4	.	.	PUNCT
ejpam-4021	566	5	,	,	PUNCT
ejpam-4021	567	1	34(2):383–395	34(2):383–395	PROPN
ejpam-4021	567	2	,	,	PUNCT
ejpam-4021	567	3	1993	1993	NUM
ejpam-4021	567	4	.	.	PUNCT
ejpam-4021	568	1	references	reference	NOUN
ejpam-4021	568	2	967	967	NUM
ejpam-4021	569	1	[	[	X
ejpam-4021	569	2	8	8	NUM
ejpam-4021	569	3	]	]	X
ejpam-4021	569	4	r.	r.	PROPN
ejpam-4021	569	5	bělohlávek	bělohlávek	PROPN
ejpam-4021	569	6	.	.	PUNCT
ejpam-4021	570	1	fuzzy	fuzzy	ADJ
ejpam-4021	570	2	relational	relational	ADJ
ejpam-4021	570	3	system	system	NOUN
ejpam-4021	570	4	:	:	PUNCT
ejpam-4021	570	5	foundations	foundation	NOUN
ejpam-4021	570	6	and	and	CCONJ
ejpam-4021	570	7	principles	principle	NOUN
ejpam-4021	570	8	.	.	PUNCT
ejpam-4021	571	1	kluwer	kluwer	NOUN
ejpam-4021	571	2	academic	academic	ADJ
ejpam-4021	571	3	publishers	publisher	NOUN
ejpam-4021	571	4	,	,	PUNCT
ejpam-4021	571	5	dredrecht	dredrecht	PROPN
ejpam-4021	571	6	,	,	PUNCT
ejpam-4021	571	7	2002	2002	NUM
ejpam-4021	571	8	.	.	PUNCT
ejpam-4021	572	1	[	[	X
ejpam-4021	572	2	9	9	NUM
ejpam-4021	572	3	]	]	X
ejpam-4021	572	4	g.	g.	NOUN
ejpam-4021	572	5	birkhoff	birkhoff	PROPN
ejpam-4021	572	6	.	.	PUNCT
ejpam-4021	573	1	lattice	lattice	PROPN
ejpam-4021	573	2	theory	theory	PROPN
ejpam-4021	573	3	.	.	PUNCT
ejpam-4021	574	1	amer	amer	PROPN
ejpam-4021	574	2	.	.	PUNCT
ejpam-4021	574	3	math	math	PROPN
ejpam-4021	574	4	.	.	PUNCT
ejpam-4021	575	1	soc	soc	PROPN
ejpam-4021	575	2	.	.	PUNCT
ejpam-4021	576	1	colloq	colloq	PROPN
ejpam-4021	576	2	.	.	PUNCT
ejpam-4021	577	1	publ	publ	PROPN
ejpam-4021	577	2	.	.	PUNCT
ejpam-4021	578	1	,	,	PUNCT
ejpam-4021	578	2	vol	vol	NOUN
ejpam-4021	578	3	.	.	PROPN
ejpam-4021	578	4	25	25	NUM
ejpam-4021	578	5	,	,	PUNCT
ejpam-4021	578	6	providence	providence	NOUN
ejpam-4021	578	7	,	,	PUNCT
ejpam-4021	578	8	ri	ri	PROPN
ejpam-4021	578	9	,	,	PUNCT
ejpam-4021	578	10	1967	1967	NUM
ejpam-4021	578	11	.	.	PUNCT
ejpam-4021	579	1	[	[	X
ejpam-4021	579	2	10	10	NUM
ejpam-4021	579	3	]	]	X
ejpam-4021	579	4	e.	e.	PROPN
ejpam-4021	579	5	čech	čech	PROPN
ejpam-4021	579	6	.	.	PUNCT
ejpam-4021	580	1	topological	topological	ADJ
ejpam-4021	580	2	spaces	space	NOUN
ejpam-4021	580	3	.	.	PUNCT
ejpam-4021	581	1	revised	revise	VERB
ejpam-4021	581	2	ed	ed	NOUN
ejpam-4021	581	3	.	.	PUNCT
ejpam-4021	582	1	by	by	ADP
ejpam-4021	582	2	z.	z.	PROPN
ejpam-4021	582	3	forĺık	forĺık	PROPN
ejpam-4021	582	4	and	and	CCONJ
ejpam-4021	582	5	m.	m.	PROPN
ejpam-4021	582	6	katětov	katětov	PROPN
ejpam-4021	582	7	,	,	PUNCT
ejpam-4021	582	8	wily	wily	PROPN
ejpam-4021	582	9	&	&	CCONJ
ejpam-4021	582	10	son	son	PROPN
ejpam-4021	582	11	,	,	PUNCT
ejpam-4021	582	12	london	london	PROPN
ejpam-4021	582	13	,	,	PUNCT
ejpam-4021	582	14	1996	1996	NUM
ejpam-4021	582	15	.	.	PUNCT
ejpam-4021	583	1	[	[	X
ejpam-4021	583	2	11	11	NUM
ejpam-4021	583	3	]	]	PUNCT
ejpam-4021	583	4	s.	s.	PROPN
ejpam-4021	583	5	c.	c.	PROPN
ejpam-4021	583	6	cheng	cheng	PROPN
ejpam-4021	583	7	,	,	PUNCT
ejpam-4021	583	8	j.	j.	PROPN
ejpam-4021	583	9	n.	n.	PROPN
ejpam-4021	583	10	mordeson	mordeson	PROPN
ejpam-4021	583	11	,	,	PUNCT
ejpam-4021	583	12	and	and	CCONJ
ejpam-4021	583	13	yu	yu	PROPN
ejpam-4021	583	14	yandong	yandong	PROPN
ejpam-4021	583	15	.	.	PUNCT
ejpam-4021	583	16	lectures	lecture	VERB
ejpam-4021	583	17	notes	note	NOUN
ejpam-4021	583	18	in	in	ADP
ejpam-4021	583	19	fuzzy	fuzzy	ADJ
ejpam-4021	583	20	mathematics	mathematic	NOUN
ejpam-4021	583	21	and	and	CCONJ
ejpam-4021	583	22	computer	computer	NOUN
ejpam-4021	583	23	science	science	NOUN
ejpam-4021	583	24	,	,	PUNCT
ejpam-4021	583	25	center	center	NOUN
ejpam-4021	583	26	for	for	ADP
ejpam-4021	583	27	research	research	NOUN
ejpam-4021	583	28	in	in	ADP
ejpam-4021	583	29	fuzzy	fuzzy	ADJ
ejpam-4021	583	30	mathematics	mathematic	NOUN
ejpam-4021	583	31	and	and	CCONJ
ejpam-4021	583	32	computer	computer	NOUN
ejpam-4021	583	33	science	science	NOUN
ejpam-4021	583	34	.	.	PUNCT
ejpam-4021	584	1	creighton	creighton	PROPN
ejpam-4021	584	2	university	university	PROPN
ejpam-4021	584	3	,	,	PUNCT
ejpam-4021	584	4	omaha	omaha	NOUN
ejpam-4021	584	5	,	,	PUNCT
ejpam-4021	584	6	nebaraska	nebaraska	PROPN
ejpam-4021	584	7	,	,	PUNCT
ejpam-4021	584	8	usa	usa	PROPN
ejpam-4021	584	9	,	,	PUNCT
ejpam-4021	584	10	1994	1994	NUM
ejpam-4021	584	11	.	.	PUNCT
ejpam-4021	585	1	[	[	X
ejpam-4021	585	2	12	12	NUM
ejpam-4021	585	3	]	]	PUNCT
ejpam-4021	585	4	m.	m.	NOUN
ejpam-4021	585	5	demirci	demirci	PROPN
ejpam-4021	585	6	.	.	PUNCT
ejpam-4021	586	1	on	on	ADP
ejpam-4021	586	2	the	the	DET
ejpam-4021	586	3	convergence	convergence	NOUN
ejpam-4021	586	4	structure	structure	NOUN
ejpam-4021	586	5	of	of	ADP
ejpam-4021	586	6	l	l	ADJ
ejpam-4021	586	7	-	-	ADJ
ejpam-4021	586	8	topological	topological	ADJ
ejpam-4021	586	9	spaces	space	NOUN
ejpam-4021	586	10	and	and	CCONJ
ejpam-4021	586	11	the	the	DET
ejpam-4021	586	12	continuity	continuity	NOUN
ejpam-4021	586	13	in	in	ADP
ejpam-4021	586	14	l	l	ADJ
ejpam-4021	586	15	-	-	ADJ
ejpam-4021	586	16	topological	topological	ADJ
ejpam-4021	586	17	spaces	space	NOUN
ejpam-4021	586	18	.	.	PUNCT
ejpam-4021	587	1	new	new	ADJ
ejpam-4021	587	2	math	math	NOUN
ejpam-4021	587	3	.	.	PUNCT
ejpam-4021	587	4	&	&	CCONJ
ejpam-4021	587	5	nat	nat	PROPN
ejpam-4021	587	6	.	.	PUNCT
ejpam-4021	588	1	comput	comput	PROPN
ejpam-4021	588	2	.	.	PUNCT
ejpam-4021	588	3	,	,	PUNCT
ejpam-4021	588	4	3(1	3(1	NUM
ejpam-4021	588	5	):	):	PUNCT
ejpam-4021	588	6	1–25	1–25	PROPN
ejpam-4021	588	7	,	,	PUNCT
ejpam-4021	588	8	2007	2007	NUM
ejpam-4021	588	9	.	.	PUNCT
ejpam-4021	589	1	[	[	X
ejpam-4021	589	2	13	13	NUM
ejpam-4021	589	3	]	]	X
ejpam-4021	589	4	d.	d.	PROPN
ejpam-4021	589	5	dikranjan	dikranjan	PROPN
ejpam-4021	589	6	,	,	PUNCT
ejpam-4021	589	7	e.	e.	PROPN
ejpam-4021	589	8	giuli	giuli	PROPN
ejpam-4021	589	9	and	and	CCONJ
ejpam-4021	589	10	a.	a.	NOUN
ejpam-4021	589	11	tozzi	tozzi	PROPN
ejpam-4021	589	12	.	.	PUNCT
ejpam-4021	590	1	topological	topological	ADJ
ejpam-4021	590	2	categories	category	NOUN
ejpam-4021	590	3	and	and	CCONJ
ejpam-4021	590	4	closure	closure	NOUN
ejpam-4021	590	5	operators	operator	NOUN
ejpam-4021	590	6	.	.	PUNCT
ejpam-4021	591	1	quaest	quaest	VERB
ejpam-4021	591	2	.	.	PUNCT
ejpam-4021	592	1	math	math	NOUN
ejpam-4021	592	2	.	.	PUNCT
ejpam-4021	592	3	,	,	PUNCT
ejpam-4021	593	1	11	11	NUM
ejpam-4021	593	2	:	:	PUNCT
ejpam-4021	593	3	323–337	323–337	NUM
ejpam-4021	593	4	,	,	PUNCT
ejpam-4021	593	5	1988	1988	NUM
ejpam-4021	593	6	.	.	PUNCT
ejpam-4021	594	1	[	[	X
ejpam-4021	594	2	14	14	NUM
ejpam-4021	594	3	]	]	X
ejpam-4021	594	4	j.	j.	PROPN
ejpam-4021	594	5	a.	a.	PROPN
ejpam-4021	594	6	goguen	goguen	PROPN
ejpam-4021	594	7	.	.	PUNCT
ejpam-4021	595	1	l	l	ADJ
ejpam-4021	595	2	-	-	ADJ
ejpam-4021	595	3	fuzzy	fuzzy	ADJ
ejpam-4021	595	4	sets	set	NOUN
ejpam-4021	595	5	.	.	PUNCT
ejpam-4021	596	1	j.	j.	PROPN
ejpam-4021	596	2	math	math	PROPN
ejpam-4021	596	3	.	.	PUNCT
ejpam-4021	597	1	anal	anal	PROPN
ejpam-4021	597	2	.	.	PUNCT
ejpam-4021	597	3	appl	appl	PROPN
ejpam-4021	597	4	.	.	PROPN
ejpam-4021	597	5	,	,	PUNCT
ejpam-4021	597	6	18	18	NUM
ejpam-4021	597	7	:	:	SYM
ejpam-4021	597	8	145–174,1967	145–174,1967	NUM
ejpam-4021	597	9	.	.	PUNCT
ejpam-4021	598	1	[	[	X
ejpam-4021	598	2	15	15	NUM
ejpam-4021	598	3	]	]	X
ejpam-4021	598	4	j.	j.	PROPN
ejpam-4021	598	5	a.	a.	PROPN
ejpam-4021	598	6	goguen	goguen	PROPN
ejpam-4021	598	7	.	.	PUNCT
ejpam-4021	599	1	concept	concept	NOUN
ejpam-4021	599	2	representations	representation	NOUN
ejpam-4021	599	3	in	in	ADP
ejpam-4021	599	4	natural	natural	ADJ
ejpam-4021	599	5	and	and	CCONJ
ejpam-4021	599	6	artificial	artificial	ADJ
ejpam-4021	599	7	languages	language	NOUN
ejpam-4021	599	8	:	:	PUNCT
ejpam-4021	599	9	axioms	axiom	NOUN
ejpam-4021	599	10	,	,	PUNCT
ejpam-4021	599	11	extensions	extension	NOUN
ejpam-4021	599	12	,	,	PUNCT
ejpam-4021	599	13	and	and	CCONJ
ejpam-4021	599	14	applications	application	NOUN
ejpam-4021	599	15	for	for	ADP
ejpam-4021	599	16	fuzzy	fuzzy	ADJ
ejpam-4021	599	17	sets	set	NOUN
ejpam-4021	599	18	.	.	PUNCT
ejpam-4021	600	1	int	int	NOUN
ejpam-4021	600	2	.	.	PUNCT
ejpam-4021	601	1	j.	j.	PROPN
ejpam-4021	601	2	man	man	PROPN
ejpam-4021	601	3	-	-	PUNCT
ejpam-4021	601	4	machine	machine	NOUN
ejpam-4021	601	5	studies	study	NOUN
ejpam-4021	601	6	,	,	PUNCT
ejpam-4021	601	7	6	6	NUM
ejpam-4021	601	8	:	:	SYM
ejpam-4021	601	9	513	513	NUM
ejpam-4021	601	10	–	–	PUNCT
ejpam-4021	601	11	561,1974	561,1974	NUM
ejpam-4021	601	12	.	.	PUNCT
ejpam-4021	602	1	[	[	X
ejpam-4021	602	2	16	16	NUM
ejpam-4021	602	3	]	]	PUNCT
ejpam-4021	602	4	j.	j.	PROPN
ejpam-4021	602	5	gutiérrez	gutiérrez	PROPN
ejpam-4021	602	6	garćıa	garćıa	PROPN
ejpam-4021	602	7	,	,	PUNCT
ejpam-4021	602	8	i.	i.	NOUN
ejpam-4021	602	9	mardones	mardones	PROPN
ejpam-4021	602	10	pérez	pérez	NOUN
ejpam-4021	602	11	,	,	PUNCT
ejpam-4021	602	12	and	and	CCONJ
ejpam-4021	602	13	m.	m.	PROPN
ejpam-4021	602	14	h.	h.	PROPN
ejpam-4021	602	15	barton	barton	PROPN
ejpam-4021	602	16	.	.	PUNCT
ejpam-4021	603	1	the	the	DET
ejpam-4021	603	2	relationship	relationship	NOUN
ejpam-4021	603	3	between	between	ADP
ejpam-4021	603	4	various	various	ADJ
ejpam-4021	603	5	filter	filter	NOUN
ejpam-4021	603	6	notions	notion	NOUN
ejpam-4021	603	7	on	on	ADP
ejpam-4021	603	8	a	a	DET
ejpam-4021	603	9	gl	gl	NOUN
ejpam-4021	603	10	-	-	NOUN
ejpam-4021	603	11	monoid	monoid	NOUN
ejpam-4021	603	12	.	.	PUNCT
ejpam-4021	604	1	j.	j.	PROPN
ejpam-4021	604	2	math	math	PROPN
ejpam-4021	604	3	.	.	PUNCT
ejpam-4021	605	1	anal	anal	PROPN
ejpam-4021	605	2	.	.	PUNCT
ejpam-4021	605	3	appl	appl	PROPN
ejpam-4021	605	4	.	.	PUNCT
ejpam-4021	606	1	230	230	NUM
ejpam-4021	606	2	:	:	PUNCT
ejpam-4021	606	3	291–302	291–302	NUM
ejpam-4021	606	4	,	,	PUNCT
ejpam-4021	606	5	1999	1999	NUM
ejpam-4021	606	6	.	.	PUNCT
ejpam-4021	607	1	[	[	X
ejpam-4021	607	2	17	17	NUM
ejpam-4021	607	3	]	]	X
ejpam-4021	607	4	u.	u.	PROPN
ejpam-4021	607	5	höhle	höhle	PROPN
ejpam-4021	607	6	and	and	CCONJ
ejpam-4021	607	7	a.	a.	NOUN
ejpam-4021	607	8	p.	p.	NOUN
ejpam-4021	607	9	šosta	šosta	PROPN
ejpam-4021	607	10	.	.	PUNCT
ejpam-4021	608	1	axiomatic	axiomatic	ADJ
ejpam-4021	608	2	foundations	foundation	NOUN
ejpam-4021	608	3	of	of	ADP
ejpam-4021	608	4	fixed	fix	VERB
ejpam-4021	608	5	basis	basis	NOUN
ejpam-4021	608	6	fuzzy	fuzzy	ADJ
ejpam-4021	608	7	topology	topology	NOUN
ejpam-4021	608	8	,	,	PUNCT
ejpam-4021	608	9	chap	chap	NOUN
ejpam-4021	608	10	.	.	PUNCT
ejpam-4021	609	1	3	3	NUM
ejpam-4021	609	2	mathematics	mathematic	NOUN
ejpam-4021	609	3	of	of	ADP
ejpam-4021	609	4	fuzzy	fuzzy	ADJ
ejpam-4021	609	5	sets	set	NOUN
ejpam-4021	609	6	:	:	PUNCT
ejpam-4021	609	7	logic	logic	NOUN
ejpam-4021	609	8	,	,	PUNCT
ejpam-4021	609	9	topology	topology	NOUN
ejpam-4021	609	10	,	,	PUNCT
ejpam-4021	609	11	and	and	CCONJ
ejpam-4021	609	12	measure	measure	NOUN
ejpam-4021	609	13	theory	theory	NOUN
ejpam-4021	609	14	,	,	PUNCT
ejpam-4021	609	15	the	the	DET
ejpam-4021	609	16	handbooks	handbook	NOUN
ejpam-4021	609	17	of	of	ADP
ejpam-4021	609	18	fuzzy	fuzzy	ADJ
ejpam-4021	609	19	sets	set	NOUN
ejpam-4021	609	20	series	series	NOUN
ejpam-4021	609	21	,	,	PUNCT
ejpam-4021	609	22	eds	eds	PROPN
ejpam-4021	609	23	.	.	PUNCT
ejpam-4021	610	1	u.	u.	PROPN
ejpam-4021	610	2	höhle	höhle	PROPN
ejpam-4021	610	3	and	and	CCONJ
ejpam-4021	610	4	s.	s.	PROPN
ejpam-4021	610	5	e.	e.	PROPN
ejpam-4021	610	6	rodabaugh	rodabaugh	PROPN
ejpam-4021	610	7	.	.	PUNCT
ejpam-4021	611	1	vol	vol	NOUN
ejpam-4021	611	2	.	.	PROPN
ejpam-4021	611	3	3	3	NUM
ejpam-4021	611	4	,	,	PUNCT
ejpam-4021	612	1	kluwer	kluwer	NOUN
ejpam-4021	612	2	academic	academic	ADJ
ejpam-4021	612	3	publishers	publisher	NOUN
ejpam-4021	612	4	,	,	PUNCT
ejpam-4021	612	5	dordrecht	dordrecht	PROPN
ejpam-4021	612	6	,	,	PUNCT
ejpam-4021	612	7	1999	1999	NUM
ejpam-4021	612	8	,	,	PUNCT
ejpam-4021	612	9	pp	pp	ADJ
ejpam-4021	612	10	.	.	PUNCT
ejpam-4021	613	1	123–272	123–272	NUM
ejpam-4021	613	2	.	.	PUNCT
ejpam-4021	614	1	[	[	X
ejpam-4021	614	2	18	18	NUM
ejpam-4021	614	3	]	]	X
ejpam-4021	614	4	u.	u.	PROPN
ejpam-4021	614	5	höhle	höhle	PROPN
ejpam-4021	614	6	.	.	PUNCT
ejpam-4021	615	1	many	many	ADJ
ejpam-4021	615	2	valued	value	VERB
ejpam-4021	615	3	topology	topology	NOUN
ejpam-4021	615	4	and	and	CCONJ
ejpam-4021	615	5	its	its	PRON
ejpam-4021	615	6	applications	application	NOUN
ejpam-4021	615	7	.	.	PUNCT
ejpam-4021	616	1	kluwer	kluwer	NOUN
ejpam-4021	616	2	academic	academic	ADJ
ejpam-4021	616	3	publishers	publisher	NOUN
ejpam-4021	616	4	,	,	PUNCT
ejpam-4021	616	5	dordrecht	dordrecht	PROPN
ejpam-4021	616	6	,	,	PUNCT
ejpam-4021	616	7	2001	2001	NUM
ejpam-4021	616	8	.	.	PUNCT
ejpam-4021	617	1	[	[	X
ejpam-4021	617	2	19	19	NUM
ejpam-4021	617	3	]	]	PUNCT
ejpam-4021	617	4	g.	g.	PROPN
ejpam-4021	617	5	jäger	jäger	PROPN
ejpam-4021	617	6	and	and	CCONJ
ejpam-4021	617	7	t.	t.	PROPN
ejpam-4021	617	8	m.	m.	NOUN
ejpam-4021	617	9	g.	g.	PROPN
ejpam-4021	617	10	ahsanullah	ahsanullah	PROPN
ejpam-4021	617	11	.	.	PUNCT
ejpam-4021	618	1	characterization	characterization	NOUN
ejpam-4021	618	2	of	of	ADP
ejpam-4021	618	3	transitivity	transitivity	NOUN
ejpam-4021	618	4	in	in	ADP
ejpam-4021	618	5	l	l	NOUN
ejpam-4021	618	6	-	-	NOUN
ejpam-4021	618	7	tolerance	tolerance	NOUN
ejpam-4021	618	8	spaces	space	NOUN
ejpam-4021	618	9	by	by	ADP
ejpam-4021	618	10	convergence	convergence	NOUN
ejpam-4021	618	11	and	and	CCONJ
ejpam-4021	618	12	closure	closure	NOUN
ejpam-4021	618	13	,	,	PUNCT
ejpam-4021	618	14	submitted	submit	VERB
ejpam-4021	618	15	,	,	PUNCT
ejpam-4021	618	16	priprint	priprint	NOUN
ejpam-4021	618	17	,	,	PUNCT
ejpam-4021	618	18	2021	2021	NUM
ejpam-4021	618	19	.	.	PUNCT
ejpam-4021	619	1	[	[	X
ejpam-4021	619	2	20	20	NUM
ejpam-4021	619	3	]	]	X
ejpam-4021	619	4	d.	d.	PROPN
ejpam-4021	619	5	c.	c.	PROPN
ejpam-4021	619	6	kent	kent	PROPN
ejpam-4021	619	7	.	.	PUNCT
ejpam-4021	620	1	convergence	convergence	NOUN
ejpam-4021	620	2	functions	function	NOUN
ejpam-4021	620	3	and	and	CCONJ
ejpam-4021	620	4	their	their	PRON
ejpam-4021	620	5	related	related	ADJ
ejpam-4021	620	6	topologies	topology	NOUN
ejpam-4021	620	7	,	,	PUNCT
ejpam-4021	620	8	fund	fund	NOUN
ejpam-4021	620	9	.	.	PUNCT
ejpam-4021	621	1	math	math	NOUN
ejpam-4021	621	2	.	.	PUNCT
ejpam-4021	622	1	54	54	NUM
ejpam-4021	622	2	:	:	PUNCT
ejpam-4021	622	3	125–133	125–133	NUM
ejpam-4021	622	4	,	,	PUNCT
ejpam-4021	622	5	1964	1964	NUM
ejpam-4021	622	6	.	.	PUNCT
ejpam-4021	623	1	[	[	X
ejpam-4021	623	2	21	21	NUM
ejpam-4021	623	3	]	]	X
ejpam-4021	623	4	y.	y.	PROPN
ejpam-4021	623	5	c.	c.	PROPN
ejpam-4021	623	6	kim	kim	PROPN
ejpam-4021	623	7	.	.	PUNCT
ejpam-4021	624	1	initial	initial	ADJ
ejpam-4021	624	2	l	l	ADJ
ejpam-4021	624	3	-	-	ADJ
ejpam-4021	624	4	fuzzy	fuzzy	ADJ
ejpam-4021	624	5	closure	closure	NOUN
ejpam-4021	624	6	spaces	space	NOUN
ejpam-4021	624	7	,	,	PUNCT
ejpam-4021	624	8	fuzzy	fuzzy	ADJ
ejpam-4021	624	9	sets	set	NOUN
ejpam-4021	624	10	and	and	CCONJ
ejpam-4021	624	11	systems	system	NOUN
ejpam-4021	624	12	,	,	PUNCT
ejpam-4021	624	13	133(3	133(3	NUM
ejpam-4021	624	14	):	):	PUNCT
ejpam-4021	624	15	277	277	NUM
ejpam-4021	624	16	-	-	SYM
ejpam-4021	624	17	297	297	NUM
ejpam-4021	624	18	,	,	PUNCT
ejpam-4021	624	19	2003	2003	NUM
ejpam-4021	624	20	.	.	PUNCT
ejpam-4021	625	1	[	[	X
ejpam-4021	625	2	22	22	NUM
ejpam-4021	625	3	]	]	PUNCT
ejpam-4021	625	4	t.	t.	PROPN
ejpam-4021	625	5	kubiak	kubiak	PROPN
ejpam-4021	625	6	.	.	PUNCT
ejpam-4021	625	7	separation	separation	NOUN
ejpam-4021	625	8	axiom	axiom	NOUN
ejpam-4021	625	9	:	:	PUNCT
ejpam-4021	625	10	extension	extension	NOUN
ejpam-4021	625	11	of	of	ADP
ejpam-4021	625	12	mappings	mapping	NOUN
ejpam-4021	625	13	and	and	CCONJ
ejpam-4021	625	14	embedding	embedding	NOUN
ejpam-4021	625	15	of	of	ADP
ejpam-4021	625	16	spaces	space	NOUN
ejpam-4021	625	17	,	,	PUNCT
ejpam-4021	625	18	chap	chap	NOUN
ejpam-4021	625	19	.	.	PUNCT
ejpam-4021	626	1	6	6	NUM
ejpam-4021	626	2	,	,	PUNCT
ejpam-4021	626	3	mathematics	mathematic	NOUN
ejpam-4021	626	4	of	of	ADP
ejpam-4021	626	5	fuzzy	fuzzy	ADJ
ejpam-4021	626	6	sets	set	NOUN
ejpam-4021	626	7	:	:	PUNCT
ejpam-4021	626	8	logic	logic	NOUN
ejpam-4021	626	9	,	,	PUNCT
ejpam-4021	626	10	topology	topology	NOUN
ejpam-4021	626	11	,	,	PUNCT
ejpam-4021	626	12	and	and	CCONJ
ejpam-4021	626	13	measure	measure	NOUN
ejpam-4021	626	14	theory	theory	NOUN
ejpam-4021	626	15	,	,	PUNCT
ejpam-4021	626	16	the	the	DET
ejpam-4021	626	17	handbooks	handbook	NOUN
ejpam-4021	626	18	of	of	ADP
ejpam-4021	626	19	fuzzy	fuzzy	ADJ
ejpam-4021	626	20	sets	set	NOUN
ejpam-4021	626	21	series	series	NOUN
ejpam-4021	626	22	,	,	PUNCT
ejpam-4021	626	23	eds	eds	PROPN
ejpam-4021	626	24	.	.	PUNCT
ejpam-4021	627	1	u.	u.	PROPN
ejpam-4021	627	2	höhle	höhle	PROPN
ejpam-4021	627	3	and	and	CCONJ
ejpam-4021	627	4	s.	s.	PROPN
ejpam-4021	627	5	e.	e.	PROPN
ejpam-4021	627	6	rodabaugh	rodabaugh	PROPN
ejpam-4021	627	7	,	,	PUNCT
ejpam-4021	627	8	vol	vol	NOUN
ejpam-4021	627	9	.	.	PROPN
ejpam-4021	628	1	3	3	X
ejpam-4021	628	2	.	.	X
ejpam-4021	628	3	kluwer	kluwer	NOUN
ejpam-4021	628	4	academic	academic	ADJ
ejpam-4021	628	5	publishers	publisher	NOUN
ejpam-4021	628	6	,	,	PUNCT
ejpam-4021	628	7	dordrecht	dordrecht	PROPN
ejpam-4021	628	8	,	,	PUNCT
ejpam-4021	628	9	433–479	433–479	NUM
ejpam-4021	628	10	,	,	PUNCT
ejpam-4021	628	11	1999	1999	NUM
ejpam-4021	628	12	.	.	PUNCT
ejpam-4021	629	1	references	reference	NOUN
ejpam-4021	629	2	968	968	NUM
ejpam-4021	630	1	[	[	X
ejpam-4021	630	2	23	23	NUM
ejpam-4021	630	3	]	]	PUNCT
ejpam-4021	630	4	j.	j.	PROPN
ejpam-4021	630	5	n.	n.	PROPN
ejpam-4021	630	6	mordeson	mordeson	PROPN
ejpam-4021	630	7	,	,	PUNCT
ejpam-4021	630	8	k.	k.	PROPN
ejpam-4021	630	9	r.	r.	PROPN
ejpam-4021	630	10	bhutani	bhutani	PROPN
ejpam-4021	630	11	,	,	PUNCT
ejpam-4021	630	12	and	and	CCONJ
ejpam-4021	630	13	a.	a.	NOUN
ejpam-4021	630	14	rosenfeld	rosenfeld	PROPN
ejpam-4021	630	15	.	.	PUNCT
ejpam-4021	631	1	fuzzy	fuzzy	ADJ
ejpam-4021	631	2	group	group	NOUN
ejpam-4021	631	3	theory	theory	NOUN
ejpam-4021	631	4	,	,	PUNCT
ejpam-4021	631	5	in	in	ADP
ejpam-4021	631	6	:	:	PUNCT
ejpam-4021	631	7	fuzziness	fuzziness	NOUN
ejpam-4021	631	8	and	and	CCONJ
ejpam-4021	631	9	soft	soft	ADJ
ejpam-4021	631	10	computing	computing	NOUN
ejpam-4021	631	11	,	,	PUNCT
ejpam-4021	631	12	springer	springer	NOUN
ejpam-4021	631	13	,	,	PUNCT
ejpam-4021	631	14	2005	2005	NUM
ejpam-4021	631	15	.	.	PUNCT
ejpam-4021	632	1	[	[	X
ejpam-4021	632	2	24	24	NUM
ejpam-4021	632	3	]	]	PUNCT
ejpam-4021	632	4	j.	j.	PROPN
ejpam-4021	632	5	n.	n.	PROPN
ejpam-4021	632	6	mordeson	mordeson	PROPN
ejpam-4021	632	7	and	and	CCONJ
ejpam-4021	632	8	d.	d.	PROPN
ejpam-4021	632	9	s.	s.	PROPN
ejpam-4021	632	10	malik	malik	PROPN
ejpam-4021	632	11	.	.	PUNCT
ejpam-4021	633	1	fuzzy	fuzzy	ADJ
ejpam-4021	633	2	commutative	commutative	ADJ
ejpam-4021	633	3	algebra	algebra	NOUN
ejpam-4021	633	4	.	.	PUNCT
ejpam-4021	634	1	world	world	NOUN
ejpam-4021	634	2	scientific	scientific	PROPN
ejpam-4021	634	3	,	,	PUNCT
ejpam-4021	634	4	singapore	singapore	PROPN
ejpam-4021	634	5	.	.	PUNCT
ejpam-4021	635	1	1998	1998	NUM
ejpam-4021	635	2	.	.	PUNCT
ejpam-4021	636	1	[	[	X
ejpam-4021	636	2	25	25	NUM
ejpam-4021	636	3	]	]	PUNCT
ejpam-4021	636	4	j.	j.	PROPN
ejpam-4021	636	5	n.	n.	PROPN
ejpam-4021	636	6	mordeson	mordeson	PROPN
ejpam-4021	636	7	,	,	PUNCT
ejpam-4021	636	8	and	and	CCONJ
ejpam-4021	636	9	p.	p.	PROPN
ejpam-4021	636	10	nair	nair	NOUN
ejpam-4021	636	11	.	.	PUNCT
ejpam-4021	637	1	fuzzy	fuzzy	ADJ
ejpam-4021	637	2	mathematics	mathematic	NOUN
ejpam-4021	637	3	.	.	PUNCT
ejpam-4021	638	1	springer	springer	NOUN
ejpam-4021	638	2	-	-	PUNCT
ejpam-4021	638	3	verlag	verlag	PROPN
ejpam-4021	638	4	,	,	PUNCT
ejpam-4021	638	5	berlin	berlin	PROPN
ejpam-4021	638	6	,	,	PUNCT
ejpam-4021	638	7	2001	2001	NUM
ejpam-4021	638	8	.	.	PUNCT
ejpam-4021	639	1	[	[	X
ejpam-4021	639	2	26	26	NUM
ejpam-4021	639	3	]	]	PUNCT
ejpam-4021	639	4	a.	a.	NOUN
ejpam-4021	639	5	di	di	PROPN
ejpam-4021	639	6	nola	nola	PROPN
ejpam-4021	639	7	and	and	CCONJ
ejpam-4021	639	8	g.	g.	PROPN
ejpam-4021	639	9	gerla	gerla	PROPN
ejpam-4021	639	10	.	.	PUNCT
ejpam-4021	640	1	lattice	lattice	PROPN
ejpam-4021	640	2	-	-	PUNCT
ejpam-4021	640	3	valued	value	VERB
ejpam-4021	640	4	algebras	algebra	NOUN
ejpam-4021	640	5	.	.	PUNCT
ejpam-4021	641	1	stochastica	stochastica	PROPN
ejpam-4021	641	2	xi	xi	PROPN
ejpam-4021	641	3	,	,	PUNCT
ejpam-4021	641	4	2	2	NUM
ejpam-4021	641	5	-	-	SYM
ejpam-4021	641	6	3	3	NUM
ejpam-4021	641	7	:	:	SYM
ejpam-4021	641	8	137–150	137–150	NUM
ejpam-4021	641	9	,	,	PUNCT
ejpam-4021	641	10	1987	1987	NUM
ejpam-4021	641	11	.	.	PUNCT
ejpam-4021	642	1	[	[	X
ejpam-4021	642	2	27	27	NUM
ejpam-4021	642	3	]	]	X
ejpam-4021	642	4	g.	g.	PROPN
ejpam-4021	642	5	preuss	preuss	PROPN
ejpam-4021	642	6	.	.	PUNCT
ejpam-4021	643	1	semiuniform	semiuniform	VERB
ejpam-4021	643	2	convergence	convergence	NOUN
ejpam-4021	643	3	convergence	convergence	NOUN
ejpam-4021	643	4	spaces	space	NOUN
ejpam-4021	643	5	.	.	PUNCT
ejpam-4021	644	1	math	math	NOUN
ejpam-4021	644	2	.	.	PUNCT
ejpam-4021	645	1	japonica	japonica	PROPN
ejpam-4021	645	2	,	,	PUNCT
ejpam-4021	645	3	41	41	NUM
ejpam-4021	645	4	:	:	SYM
ejpam-4021	645	5	465	465	NUM
ejpam-4021	645	6	–	–	PUNCT
ejpam-4021	645	7	491	491	NUM
ejpam-4021	645	8	,	,	PUNCT
ejpam-4021	645	9	1995	1995	NUM
ejpam-4021	645	10	.	.	PUNCT
ejpam-4021	646	1	[	[	X
ejpam-4021	646	2	28	28	NUM
ejpam-4021	646	3	]	]	X
ejpam-4021	646	4	g.	g.	PROPN
ejpam-4021	646	5	preuss	preuss	PROPN
ejpam-4021	646	6	.	.	PUNCT
ejpam-4021	647	1	foundations	foundation	NOUN
ejpam-4021	647	2	of	of	ADP
ejpam-4021	647	3	topology	topology	NOUN
ejpam-4021	647	4	:	:	PUNCT
ejpam-4021	647	5	an	an	DET
ejpam-4021	647	6	approach	approach	NOUN
ejpam-4021	647	7	to	to	ADP
ejpam-4021	647	8	convenient	convenient	ADJ
ejpam-4021	647	9	topology	topology	NOUN
ejpam-4021	647	10	.	.	PUNCT
ejpam-4021	648	1	kluwer	kluwer	NOUN
ejpam-4021	648	2	academic	academic	ADJ
ejpam-4021	648	3	publishers	publisher	NOUN
ejpam-4021	648	4	,	,	PUNCT
ejpam-4021	648	5	dordrecht	dordrecht	PROPN
ejpam-4021	648	6	.	.	PUNCT
ejpam-4021	648	7	2002	2002	NUM
ejpam-4021	648	8	.	.	PUNCT
ejpam-4021	649	1	[	[	X
ejpam-4021	649	2	29	29	NUM
ejpam-4021	649	3	]	]	PUNCT
ejpam-4021	649	4	a.	a.	PROPN
ejpam-4021	649	5	rosenfeld	rosenfeld	PROPN
ejpam-4021	649	6	.	.	PUNCT
ejpam-4021	650	1	fuzzy	fuzzy	ADJ
ejpam-4021	650	2	groups	group	NOUN
ejpam-4021	650	3	.	.	PUNCT
ejpam-4021	651	1	j.	j.	PROPN
ejpam-4021	651	2	math	math	PROPN
ejpam-4021	651	3	.	.	PUNCT
ejpam-4021	652	1	anal	anal	PROPN
ejpam-4021	652	2	.	.	PUNCT
ejpam-4021	653	1	and	and	CCONJ
ejpam-4021	653	2	appl	appl	PROPN
ejpam-4021	653	3	.	.	PUNCT
ejpam-4021	654	1	35(1971	35(1971	NUM
ejpam-4021	654	2	)	)	PUNCT
ejpam-4021	654	3	,	,	PUNCT
ejpam-4021	655	1	512–517	512–517	NUM
ejpam-4021	655	2	.	.	PUNCT
ejpam-4021	656	1	[	[	X
ejpam-4021	656	2	30	30	NUM
ejpam-4021	656	3	]	]	PUNCT
ejpam-4021	656	4	k.	k.	PROPN
ejpam-4021	656	5	i.	i.	PROPN
ejpam-4021	656	6	rosenthal	rosenthal	PROPN
ejpam-4021	656	7	.	.	PUNCT
ejpam-4021	657	1	quantales	quantale	NOUN
ejpam-4021	657	2	and	and	CCONJ
ejpam-4021	657	3	their	their	PRON
ejpam-4021	657	4	applications	application	NOUN
ejpam-4021	657	5	.	.	PUNCT
ejpam-4021	658	1	pitman	pitman	NOUN
ejpam-4021	658	2	research	research	NOUN
ejpam-4021	658	3	notes	note	NOUN
ejpam-4021	658	4	in	in	ADP
ejpam-4021	658	5	mathematics	mathematic	NOUN
ejpam-4021	658	6	.	.	PUNCT
ejpam-4021	659	1	vol	vol	NOUN
ejpam-4021	659	2	.	.	PROPN
ejpam-4021	660	1	234	234	NUM
ejpam-4021	660	2	longman	longman	NOUN
ejpam-4021	660	3	,	,	PUNCT
ejpam-4021	660	4	burnt	burn	VERB
ejpam-4021	660	5	mill	mill	NOUN
ejpam-4021	660	6	,	,	PUNCT
ejpam-4021	660	7	harlow	harlow	NOUN
ejpam-4021	660	8	,	,	PUNCT
ejpam-4021	660	9	1990	1990	NUM
ejpam-4021	660	10	.	.	PUNCT
ejpam-4021	661	1	[	[	X
ejpam-4021	661	2	31	31	NUM
ejpam-4021	661	3	]	]	PUNCT
ejpam-4021	661	4	e.	e.	PROPN
ejpam-4021	661	5	schechter	schechter	PROPN
ejpam-4021	661	6	.	.	PUNCT
ejpam-4021	662	1	handbook	handbook	NOUN
ejpam-4021	662	2	of	of	ADP
ejpam-4021	662	3	analysis	analysis	NOUN
ejpam-4021	662	4	and	and	CCONJ
ejpam-4021	662	5	its	its	PRON
ejpam-4021	662	6	foundations	foundation	NOUN
ejpam-4021	662	7	.	.	PUNCT
ejpam-4021	663	1	academic	academic	ADJ
ejpam-4021	663	2	press	press	NOUN
ejpam-4021	663	3	,	,	PUNCT
ejpam-4021	663	4	first	first	PROPN
ejpam-4021	663	5	edition	edition	NOUN
ejpam-4021	663	6	.	.	PUNCT
ejpam-4021	664	1	october	october	PROPN
ejpam-4021	664	2	30	30	NUM
ejpam-4021	664	3	,	,	PUNCT
ejpam-4021	664	4	1996	1996	NUM
ejpam-4021	664	5	.	.	PUNCT
ejpam-4021	665	1	[	[	X
ejpam-4021	665	2	32	32	NUM
ejpam-4021	665	3	]	]	PUNCT
ejpam-4021	665	4	l.	l.	PROPN
ejpam-4021	665	5	n.	n.	PROPN
ejpam-4021	665	6	stout	stout	PROPN
ejpam-4021	665	7	.	.	PUNCT
ejpam-4021	666	1	the	the	DET
ejpam-4021	666	2	logic	logic	NOUN
ejpam-4021	666	3	of	of	ADP
ejpam-4021	666	4	unbalanced	unbalanced	ADJ
ejpam-4021	666	5	objects	object	NOUN
ejpam-4021	666	6	in	in	ADP
ejpam-4021	666	7	a	a	DET
ejpam-4021	666	8	category	category	NOUN
ejpam-4021	666	9	with	with	ADP
ejpam-4021	666	10	two	two	NUM
ejpam-4021	666	11	closed	closed	ADJ
ejpam-4021	666	12	structures	structure	NOUN
ejpam-4021	666	13	.	.	PUNCT
ejpam-4021	667	1	chapter	chapter	NOUN
ejpam-4021	667	2	3	3	NUM
ejpam-4021	667	3	;	;	PUNCT
ejpam-4021	667	4	s.	s.	PROPN
ejpam-4021	667	5	e.	e.	PROPN
ejpam-4021	667	6	rodabaugh	rodabaugh	PROPN
ejpam-4021	667	7	st	st	PROPN
ejpam-4021	667	8	al	al	PROPN
ejpam-4021	667	9	(	(	PUNCT
ejpam-4021	667	10	eds	eds	PROPN
ejpam-4021	667	11	.	.	PUNCT
ejpam-4021	667	12	)	)	PUNCT
ejpam-4021	667	13	,	,	PUNCT
ejpam-4021	667	14	applications	application	NOUN
ejpam-4021	667	15	of	of	ADP
ejpam-4021	667	16	category	category	NOUN
ejpam-4021	667	17	theory	theory	NOUN
ejpam-4021	667	18	to	to	ADP
ejpam-4021	667	19	fuzzy	fuzzy	ADJ
ejpam-4021	667	20	subsets	subset	NOUN
ejpam-4021	667	21	.	.	PUNCT
ejpam-4021	668	1	kluwer	kluwer	NOUN
ejpam-4021	668	2	academic	academic	ADJ
ejpam-4021	668	3	publishers	publisher	NOUN
ejpam-4021	668	4	,	,	PUNCT
ejpam-4021	668	5	dordrecht	dordrecht	PROPN
ejpam-4021	668	6	.	.	PUNCT
ejpam-4021	669	1	73–105,1992	73–105,1992	X
ejpam-4021	669	2	.	.	PUNCT
ejpam-4021	670	1	[	[	X
ejpam-4021	670	2	33	33	NUM
ejpam-4021	670	3	]	]	PUNCT
ejpam-4021	670	4	c.	c.	PROPN
ejpam-4021	670	5	l.	l.	PROPN
ejpam-4021	670	6	walker	walker	PROPN
ejpam-4021	670	7	.	.	PUNCT
ejpam-4021	671	1	categories	category	NOUN
ejpam-4021	671	2	of	of	ADP
ejpam-4021	671	3	fuzzy	fuzzy	ADJ
ejpam-4021	671	4	sets	set	NOUN
ejpam-4021	671	5	.	.	PUNCT
ejpam-4021	672	1	soft	soft	ADJ
ejpam-4021	672	2	computing	computing	NOUN
ejpam-4021	672	3	,	,	PUNCT
ejpam-4021	672	4	8	8	NUM
ejpam-4021	672	5	:	:	SYM
ejpam-4021	672	6	299–304	299–304	NUM
ejpam-4021	672	7	,	,	PUNCT
ejpam-4021	672	8	2004	2004	NUM
ejpam-4021	672	9	.	.	PUNCT